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Physics-based models and microwave sensors for mapping soil carbon in arctic permafrost using long-wavelength radars
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Physics-based models and microwave sensors for mapping soil carbon in arctic permafrost using long-wavelength radars
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Content
PHYSICS-BASED MODELS AND MICROWAVE SENSORS FOR
MAPPING SOIL CARBON IN ARCTIC PERMAFROST USING
LONG-WAVELENGTH RADARS
by
Kazem Bakian-Dogaheh
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)
December 2024
Doctoral Committee:
Professor Mahta Moghaddam (Chair)
Professor Gianluca Lazzi
Associate Professor Felipe De Barros
Associate Professor Wei Wu
Assistant Professor Constantine Sideris
Defense Date: Dec 3, 2024
Copyright 2024 Kazem Bakian-Dogaheh
Grit—Noun
The power of passion and perseverance.
Courage, bravery, pluck, mettle, backbone, spirit,
strength of character, strength of will, moral fiber, steel,
nerve, fortitude, roughness, hardness, resolve, resolution,
determination, tenacity, perseverance, endurance;
informal: guts, spunk.
ii
To my family,
for their endless love, continuous support, encouragement, and all the sacrifices they
have made.
My mother Kobra Koohi-Lakeh and my father Heshmatallah Bakian-Dogaheh:
for all the love and support throughout my life, and everything they sacrificed in their
life for my life and education.
My sisters Shiva Bakian-Dogaheh and Shahla Bakian-Dogaheh:
for all the love, for being the trailblazers in my life, whom I always looked up to, and
for being my absolute source of inspiration and motivation.
iii
Acknowledgements
While the academic endeavor and life continues, the end of the Ph.D. program is a moment for me
to pause and acknowledge the contribution of many people in my life, who without their support
and encouragement accomplishing this chapter of my life would have been impossible 1
. I would
like to acknowledge and thank:
My Advisor
I would like to start by expressing my deepest gratitude to my advisor, Prof. Mahta Moghaddam for
her exceptional source of inspiration, for encouraging a culture of hard work, her research vision,
her belief in me, her commitment to freedom in research, and the development of independent
researchers. I am grateful for every opportunity she provided to me, and all I learned from her in
the lab and classroom. Beyond the professional setting, I have learned so many things from her,
including her patience, tolerance, and kindness to name a few.
My Defense Committee
I would like to thank my other dissertation committee members: Prof. Gianluca Lazzi, Prof. Felipe
De Barros, Prof. Wei Wu, and Prof. Constantine Sideris for agreeing to be on my dissertation
committee, for constructive evaluation and feedback on my research. I would like to particularly
thank Prof. De Barros for his continuous support, and encouragement of the ideas regarding
harmonizing land surface models and remote sensing models. I also would like to thank Prof.
Sideris, who has always been very kind and supportive and had always time for discussion on many
things, particularly about life in academia.
Microwave Systems, Sensors, and Imaging Lab (MiXIL)
Over the past 7.5 years, I was privileged to be part of MiXIL. I am very grateful for the lab culture
that always encouraged teamwork, which allowed me to work with many of my labmates in various
sub-working groups2
. I have learned so many things from my labmates and I’m very grateful for
their generosity in sharing their knowledge and experience about work and life.
ABoVE Sub-Working Group
I have been part of this sub-working group since Aug 2017, in which part I of my dissertation
was conducted mainly in close collaboration with this subgroup. I would like to thank Dr. Alireza
Tabatabaeenejad, who served as the PI for ABoVE phase I between Aug 2017 to May 2020 . I
would like to thank my former labmate and senior Dr. Richard Chen, who gave me a big picture
1This is a relatively long acknowledgment, as I had to decide either to keep it at a high level or detailed, which I
chose the latter.
2A timeline of my research activities is provided in the appendices.
iv
of radar remote sensing research in the Arctic back in the early days of my Ph.D. I then would
like to thank Yuhuan (Mia) Zhao, with whom I shared many ups and downs in our academic life
and discussed many technical research and life matters together. I am also greaftul for help with
preprocessing AirMOSS and UAVSAR data. I also would like to thank Jane Whitcomb, for her
kindness and helping me with preprocessing SoilGrids data.
Medical Imaging Sub-Working Group
I have been part of this sub-working group since Aug 2019. While the medical imaging research is
not directly part of this dissertation, the experience and knowledge that I acquired as part of this
subgroup were instrumental for part II of my dissertation. I would like to thank Dr. John Stang,
who had significant role in instilling my interest in medical imaging research. I then would like
to thank Dr. Yuan Fang, whom I have enjoyed working with over the past 5.5 years, and I have
learned many things, particularly in the area of inverse problems, computational EM. I then would
like to thank Dr. Mark Haynes, Dr. Guanbo Chen, and Dr. Pratik Shah, who left a rich legacy of
microwave imaging hardware and software related materials.
Soil moisture Sensing Controller and oPtimal Estimator (SoilSCAPE) Sub-Working Group
I have been part of this sub-working group since Aug 2017. While no direct material from
SoilSCAPE was used in this dissertation, the overall significance of the experiences that I acquired
by contributing to SoilSCAPE is undeniable in my professional development. Within this subworking group, I had the privilege to work with Dr. Ruzbeh Akbar (aka Sir), who played a mentor
role for me, he always had time for a quick conversation and always generously shared his insights,
and experiences about life during and after Ph.D.. I then need to thank Dr. Agnelo Silva (aka Gi),
who taught many things about wireless sensor network design, and deployment in the field, and his
exemplary work ethics has been inspiring to me.
SDRadar Sub-Working Group
I was part of this sub-working group between Aug 2021 to May 2023. I would like to thanks Dr.
Sam Prager who left a rich legacy of hardware and softare materials that helped us desiging the
next generation of dual-polarimetric wideband software-defined radars. Also, I would like to thank
Sepehr Eskandari and Piril Nergis for being patient with me while I was learning and fine-tuning
my mentoring skills.
Beyond Sub-Working Groups
Beyond the abovementioned sub-working groups, there are other MiXIL members and alumni, that
I would like to acknowledge with whom I had interactions over the years. I would like to start with
Dr. Mariko Burgin, who was very generous with her time and shared her honest opinion about
life and her experiences in academia. I would like then to thank Dr. James Campbell, particulalry
for his exemplary commitment to the theory of electromagnetic scattering, which has always been
inspiring, Dr. Negar Golestani, as she always had time for me to discuss things and shared her
experiences with me early on, Dr. Jessica Fayne who is a dear friend and she always have been very
kind and generous with her time to discuss various things, Dr. Majid Albahkali for his kindness and
all the interesting conversations we had, Archanna Kannan, for her kindness and also for allowing
me to run multiple retrievals on her HPC accounts, Melebari brothers for bringing Arabic coffee
and sweets to the lab and group meetings, Erik Hodges for bringing cookies and brownies to the
group meetings, Alireza Farhadian, and Parnia Shokri for brining snacks to the lab.
v
NASA ABoVE Science Team
The impact of being a member of the NASA ABoVE science team is undeniable in my professional
development. ABoVE science team meetings gave me an excellent opportunity to witness the
impact of the multidisciplinary area of remote sensing research in terrestrial ecology. I also enjoyed
stimulating conversations at various working groups and learning from so many inspiring role
models. I would like to start by expressing my gratitude to our long-term collaborators, the
Numerical Terradynamic Simulation Group (NTSG) at the University of Montana. Particularly Prof.
John Kimball (NTSG Director), from whom I learned so many things about the climate science
and ecosystem in the Arctic. I then would like to thank Dr. Yonghong Yi, Dr. Jinyang Du, and Dr.
Artuhur Endsley from NTSG, who have been always very kind and supportive of my research. I
also would like to thank Dr. Kevin Schaefer Dr. Roger Michaelides, and Dr. Andy Parsekian for
their support and for helping me collect soil samples from Interior Alaska in 2018. I then would
like to thank ABoVE leadership, particularly Dr. Peter Griffith, Dr. Chip Miller, Dr. Scot Goetz, Dr.
Liz Hoy, and former TE program manager Dr. Hanks Moraglius. I am very grateful for everything
that I have learned through ABoVE, for the unique coordinated Airborne/Ground campaign, and for
all the data that was available through ABoVE.
Field Deployments
Among various field campaigns, the Alaska deployments directly contributed to this dissertation
and my ongoing future research. Conducting fieldwork, particularly in the Arctic is not possible
except with tremendous logistical support, which enables scientific research in that environment. To
that end, I am grateful for the NASA ABoVE Logistics Office at Fairbanks, Sarah Sacket and Dan
Hodgkinson, who always were helpful with preparation, planning, and safety before heading to the
field. I would also need to express my deepest gratitude to the Toolik Field Station (TFS) leadership
and staff for all the logistical help. Particularly Randy Fluweber at the GIS & Remote Sensing for
his significant role in helping us with the planning and permission process for our sites, and I look
forward to continue visiting TFS for my future research!
Funding
This work was funded through three phases of the Arctic Boreal Vulnerability Experiment by the
NASA Terrestrial Ecology Program with the following grant numbers: NNX17AC65A (ABoVE
Phase #1), 80NSSC19M0114 (ABoVE Phase #2), and 80NSSC22K1238 (ABoVE Phase #3).
Additionally, the main part of the work between 2018-2022 was supported through the NASA Earth
and Space Science Fellowship program with grant number: 80NSSC18K1410.
Health Science Campus
While as mentioned above, my medical imaging research is not part of this dissertation, however, I
have learned so many things at HSC, which I am very grateful for and would need acknowledgment.
I would like to thank Prof. Naomi Sta Maria, Prof. Gianluca Lazzi, Prof. Kimberly Gokoffski, Prof.
Krishna Nayak, Sasha Medvidovic, Jin Suh Yu who helped us with various steps of our phantom,
and animal trial experiments.
The IEEE Geoscience and Remote Sensing Society (GRSS)
I would like to start by thanking Dr. Tianlin Wang, from whom I have learned so many things
over the years and I’m very grateful for his kindness and friendship and continuous support and
encouragement. I would like to thank Michelle Rustom for her great work ethic, with whom we
co-founded the USC IEEE GRSS-APS-SSCS joint student branch chapter in the Spring of 2020.
vi
Over the past 5 years, it has been a great pleasure working with Michella and other officers in the
chapter including Archana Kannan and Davit Aslanyan. Additionally, I would like to thank Dr.
Maryam Salim, Dr. Rashmi Shah, Dr. Omkar Pradhan, and Dr. Sid Misra for their positivity, and
their continuous help and support to our student chapter through the Metro LA IEEE GRSS Chapter.
Professors
Over the past 12.5 years, there have been a few Professors, whose commitment to teaching and
mensch had a profound impact on me and I have learned so many things from them in the classroom
settings. At USC and in the ECE department I would like to thank Prof. Hossein Hashemi, Prof.
Aluizio Prata, Prof. Robert A. Scholtz, and Prof. Justin P. Haldar for their excellent teaching, in the
ASTE department I would like to thank Prof. Mike Gruntman for his amazing classes and teaching
style. I also would like to thank Prof. Elizabeth Fife at the Communication Hub for teaching me
many things related to technical writing and communication skills. Earlier during my undergrad I
had the privilege to attend a number of classes with Prof. Mahmoud Shahabadi, and Prof. Ali Olfat
and I am forever grateful for their commitment to high-quality teaching.
Research and Academic Staff at USC
My Ph.D. work during these years at USC was not possible without the significant support that
I received from our lab research administrators and academic staff at USC. I would like thanks
Kim Reid , Jennifer Ramos, Luz Castillo, and Elise Lee for all their help with various aspect of
our research business. I would like then to thank Diane Demteras, who has always been kind and
supportive and always had time to answer my questions regarding the department.
My Friends in Los Angeles
At USC I would like to start with Dr. Samer Idris, Dr. Mahdad Mansouree, Mahsa Torfe, Dr. Ahmad
Fallahpour, Dr. Ali Zarei, Dr. Hanie Hashemi, Dr. Mahdi Jafarnia Jahromi, Dr. Ghasem Pasandi,
Dr. Mehrdad Kiamari, Dr. Mohammadreza Mousavi, Amir Minoofar, Omar Zamzam, Dr. Abotalib
Abotalib, and Farshad Serat Nahai for their kindness, friendship and support. Also, I cannot discuss
my Ph.D. journey in Los Angeles and not acknowledge the support and kindness I received from
the Shia community in Greater Los Angeles, particularly the lovely Iranians, Iraqis, and Afghans at
the Masjid Al-Zahra.
My Dearest Friends
I would like to express my deepest gratitude to Haddad Miladi, Amirali Omidfar, Hossein Sharifazadeh, Aslan Seifi, Amin Bagheri, Abbas Malaki, Mohhamdreza Dolatpour-Lakeh, and Hamed
Eskandari for being my dearest and true friends. They all have one quality in common and that has
been ‘Maram’ in its finest form. They have been there for me in my ups and downs and always
supported me, they made me a better person, kept me accountable, and never hesitated to share their
genuine honest opinions with me whenever I needed them. I am grateful for their friendship and
brotherhood.
My Extended Family in Iran
I would like to thank my extended family, my lovely aunts, uncles, and cousins. They have been
always supportive of my education and have always encouraged me to keep working hard and
pursue my dreams. I am grateful for all the love and support.
vii
My Family
I would like now thank my family, and first my parent, my dad Heshmatallah Bakian-Dogaheh,
and my mom Kobra Koohi-Lakeh. I wanted to thank you, I mean for everything, my whole
life! For believing in me, always encouraging me to go the extra mile, for instilling the value of
hard work, and for sacrificing everything in your life for us and our education. I am grateful for
your unconditional love and support and all the hardship you have gone through to support us in
achieving our dreams. I would like then thank my lovely sisters Shiva and Shahla for your love and
support my whole life, and for being the absolute source of inspiration, perseverance, and grit. As
first-generation college students, you were my trailblazers who enlightened my path. I am grateful
for being there for me, for being the definition of the term “collective success”. I would like to also
thank my lovely brother-in-laws Mohsen and Sebastian for their kindness and support.
In the end
I would like to acknowledge that, I have not taken any moment of the opportunity of studying Ph.D.
as granted. While I felt privileged for the opportunity to do my Ph.D., at the same time I had to keep
reminding myself that this opportunity could have also easily not been possible for many reasons.
For that and many other reasons I did what I could and was possible to make any moment count,
and if I fell short I have always attempted to do better, and I will keep trying in my ongoing and
future endeavors to do better and I will make every moments I will make it all count!
Kazem Bakian-Dogaheh
11/17/2024
viii
Table of Contents
Epigraph ............................................................................................ ii
Dedication........................................................................................... iii
Acknowledgements................................................................................. iv
List of Tables........................................................................................ xiii
List of Figures ...................................................................................... xv
List of Algorithms..................................................................................xxxi
Abbreviations.......................................................................................xxxii
Abstract .............................................................................................xxxiv
Chapter 1: Overview of the Dissertation ........................................................ 1
1.1 Introduction................................................................................ 1
1.2 Motivation ................................................................................. 2
1.2.1 Part I: Physics-Based Computational Radar Mapping of SOC in Arctic
Permafrost ........................................................................ 2
1.2.2 Part II: Microwave Sensors for Dielectric Imaging of Arctic Organic Soil.... 3
1.3 Objectives ................................................................................. 3
1.3.1 Objectives of Part I ............................................................... 3
1.3.2 Objectives of Part II .............................................................. 4
1.4 Contribution ............................................................................... 4
1.4.1 Contributions of Part I............................................................ 4
1.4.2 Contributions of Part II........................................................... 5
Part I: Physics-Based Computational Radar Mapping of SOC in Arctic Permafrost...... 6
Chapter 2: Introduction to Part I ................................................................ 7
2.1 Water and Carbon Cycle in Permafrost Landscape ...................................... 7
2.2 Microwave Remote Sensing Principle ................................................... 9
2.3 Physics-Based Computational Radar Retrieval Cycle ................................... 13
2.3.1 Contiguous US Temperate Sites ................................................. 14
2.3.2 Permafrost Sites .................................................................. 15
2.4 Forward Model ............................................................................ 16
ix
2.4.1 Contiguous US Temperate Sites ................................................. 16
2.4.2 Permafrost Sites .................................................................. 17
2.5 Global Optimization Methods ............................................................ 17
2.6 Physics-Based Computational Radar Mapping of SOC ................................. 18
Chapter 3: Subsurface Profile Model ............................................................ 20
3.1 Introduction................................................................................ 20
3.2 Materials................................................................................... 22
3.2.1 Sites Description.................................................................. 22
3.2.2 Field Experiment Design......................................................... 23
3.2.3 Lab Experiment Design .......................................................... 28
3.3 Methods.................................................................................... 28
3.3.1 Pedotransfer Function ............................................................ 28
3.3.2 Organic Matter Profile Model.................................................... 30
3.3.3 Soil Moisture Profile Model ..................................................... 33
3.4 Results ..................................................................................... 33
3.5 Discussion ................................................................................. 36
3.6 Conclusion................................................................................. 38
Chapter 4: Organic Soil Dielectric Model: Hydrology Prespective .......................... 44
4.1 Introduction................................................................................ 44
4.2 Methods.................................................................................... 46
4.2.1 Study Area ........................................................................ 46
4.2.2 Soil Component Analysis and Volumetric Fractions ........................... 48
4.2.3 Soil-Water Retention Curve Parametrization.................................... 52
4.2.4 Soil-Water Dielectric Prediction ................................................. 61
4.3 Results ..................................................................................... 62
4.3.1 Root Biomass to Predict Permafrost Soil Water Retention Curve Behavior... 62
4.3.2 Eyring equation as a predictor for soil-water dielectric properties............. 63
4.4 Discussion ................................................................................. 66
4.5 Conclusions................................................................................ 66
Chapter 5: Organic Soil Dielectric Model: Electromagnetic Prespective ................... 67
5.1 Introduction................................................................................ 68
5.1.1 Current State of the Problem: Measurement Perspective ...................... 68
5.1.2 Current State of the Problem: Modeling Perspective ........................... 69
5.1.3 Remaining Major Challenges .................................................... 73
5.1.4 New Set of Dielectric and Matric Potential Measurement and Modeling ..... 74
5.2 Methods.................................................................................... 76
5.2.1 Coupled Hydro-EM Approach for Soil Dielectric Modeling................... 76
5.2.2 Soil Dielectric and Soil Matric Potential Measurement ........................ 85
5.2.3 In-situ Soil Physical Properties and Dielectric Profile Measurement .......... 90
5.2.4 Role of Organic Soil Dielectric Model in Physics-Based Radar Remote
Sensing ............................................................................ 92
5.3 Results ..................................................................................... 93
x
5.3.1 Organic Soil Dielectric Model Validation in Lab ............................... 93
5.3.2 Organic Soil Dielectric Model Validation in Field.............................. 97
5.4 Discussion ................................................................................. 98
5.4.1 Empirical Modeling an Inevitable Necessity.................................... 98
5.4.2 Frequency and Temperature Behavior of Soil Dielectric Model ............... 101
5.4.3 Comparison Between the Behavior of Existing Organic Soil Dielectric Model102
5.4.4 Limitation of Organic Soil Dielectric Model.................................... 107
5.4.5 Potential for Retrieving Water and Carbon Characteristics from Radar
Observations ...................................................................... 109
5.5 Conclusions................................................................................ 111
Chapter 6: Physics-Based Radar-Driven SOC Mapping ...................................... 113
6.1 Introduction................................................................................ 113
6.1.1 Importance of Soil Carbon (Stock and Changes) .............................. 113
6.1.2 Discrepancies is C Estimates Driven from Field and Upscaling approaches .. 114
6.1.3 Remote Sensing Techniques and Modeling Approaches for C mapping ...... 115
6.1.4 Physics Based Computational Mapping of C ................................... 115
6.2 Methods.................................................................................... 116
6.2.1 Study Sites ........................................................................ 116
6.2.2 Physics-Based Computational Radar Retrieval Algorithms ................... 119
6.2.3 Subsurface Profile Model ........................................................ 119
6.2.4 Organic Soil Dielectric Model .................................................. 123
6.2.5 Electromagnetic Scattering Model............................................... 124
6.2.6 Freeze/Thaw Detection with P-band ............................................ 125
6.2.7 Time-Series Inversion Scheme .................................................. 127
6.2.8 Probability of Freeze/Thaw ...................................................... 129
6.2.9 Simulated Retrieved Parameters ................................................. 130
6.2.10 Simulated Retrieval Framework Performance Against Noise and Calibration
Accuracy .......................................................................... 132
6.2.11 Validation Pixels Retrieved Parameters.......................................... 156
6.2.12 Validation Data Gap Filling ...................................................... 158
6.2.13 Validation Data Profile Fitting ................................................... 160
6.2.14 Retrieved Soil Organic Carbon Profile .......................................... 160
6.2.15 Profile Depth Averaging ......................................................... 162
6.2.16 SOCC Calculation ................................................................ 163
6.2.17 Scalability of the Approach ...................................................... 164
6.3 Results ..................................................................................... 165
6.3.1 Mapping Soil Organic Carbon .................................................. 165
6.3.2 SOC Validation .................................................................. 165
6.3.3 Impact of Land Cover Type on SOC ............................................ 165
6.3.4 Soil Organic Carbon Stock Content (SOCC) ................................... 167
6.4 Discussion ................................................................................. 168
6.4.1 The Performance of the Retrieval, and Sensitivity Analysis (Synthetic Case). 171
6.4.2 Consistency in Retrieval ......................................................... 171
6.5 Conclusions................................................................................ 172
xi
Chapter 7: Conclusion and Future Work of Part I............................................. 176
7.1 Coining “Radar Ecology”................................................................. 176
7.2 Concluding Remarks on Part I: Arctic Ecosystem ...................................... 178
7.3 Ongoing and Future Work ................................................................ 179
Part II: Microwave Sensors for Dielectric Imaging of Arctic Organic Soil.................. 183
Chapter 8: Introduction to Part II ............................................................... 184
8.1 Microwave Imaging for Medical Application ........................................... 185
8.2 Microwave Sensors for Dielectric Imaging of Arctic Organic Soil..................... 186
Chapter 9: Microwave Sensors for Dielectric Imaging of Arctic Organic Soil.............. 187
9.1 Introduction................................................................................ 188
9.2 Methods.................................................................................... 189
9.2.1 Microwave Imaging System ..................................................... 189
9.2.2 Matching Fluid ................................................................... 192
9.2.3 Sample Holder .................................................................... 192
9.2.4 Antenna and Array System....................................................... 194
9.2.5 Data Acquisition System, System Calibration, and Data Post Processing..... 197
9.2.6 Dielectric Imaging Algorithm ................................................... 199
9.2.7 Reference Materials .............................................................. 203
9.3 Results and Discussion.................................................................... 204
9.3.1 Microwave Signal Analysis ...................................................... 205
9.3.2 Preliminary Imaging Results..................................................... 212
9.4 Conclusions and Future Work ............................................................ 212
Chapter 10:Conclusion and Future Work of Part II........................................... 215
10.1 Ongoing work ............................................................................. 215
10.2 Future Work ............................................................................... 216
References........................................................................................... 216
Appendices.......................................................................................... 237
A Soil Dielectric Measurement ............................................................. 238
B Timeline of Research Activities During Ph.D............................................ 246
xii
List of Tables
2.1 The operation frequency of radar instruments that flew as part of ABoVE Airborne
Campagin (AAC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 List of land surface or subsurface parameters(X¯) . . . . . . . . . . . . . . . . . . . 14
3.1 Sites name and soil pit locations for the field campaign during August 22-26, 2018 22
3.2 List of soil physical properties and corresponding description of each parameter . . 25
3.3 Number of sample and representative sampling depth . . . . . . . . . . . . . . . . 27
3.4 The mean and standard deviation of soil physical properties for all the sites. . . . . 35
3.5 Profile models performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1 Independent basic soil properties measured. The root biomass and soil organic
matter needed to be measured to quantify the total organic matter. Bulk density and
porosity need to be measured to find the specific density of each sample. Finally,
mineral texture, including sand, silt, and clay fraction were also delineated. . . . . 48
4.2 Basic soil properties, being calculated from Table 4.1. The specific density is being
calculated using measured bulk density and porosity. The total organic matter
is calculated based on root biomass and soil organic matter. The mineral mass
fraction for each component is the fraction of solid components to the total sample
mass. To find the volumetric fraction, the specific density of each subcomponent is
being used. As described in main text, the OM= 0, 70, 100 denotes the Min, SOM,
RB soil components. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.3 Median value of SWRC parametrization of 11 types of tundra soil for organic
subcomponents. As for mineral part, the actual value was calculated using the
Fig. 4.7. The value reported for RB and SOM can be used in Equation (4.8) and
(5.1) for calculating the variation of SWRC parameters. . . . . . . . . . . . . . . . 60
5.1 The current state of the problem from a measurement perspective and description of
existing soil dielectric measurement data containing organic matter samples. Point
refers to a pair of soil moisture (θ) and dielectric permittivity (ε) measurements
(ε,θ). Soil moisture and dielectric properties can be obtained from respective soil
gravimetric and probing measurements acquired during a field campaign. Sample
refers to a “soil sample” under test in a controlled environment e.g., laboratory.
Sample measurements are usually conducted over the entire range of soil moisture
conditions, which results in multiple points (ε,θ) from saturation to completely dry. 70
5.2 Summary of soil samples collected from the North Slope and Interior of Alaska [8]. 86
5.3 Model validation against the laboratory measurements for all 66 tundra soil samples.107
xiii
5.4 List of state parameters in the retrieval scheme, assumptions and sets of parameters
that were fixed based on ancillary field data and the literature. For the unknown
parameters and measurements, the range of variation is provided; in data cube
development the unknowns are discretized with corresponding discretization steps. 111
6.1 AirMOSS flights used in this chapter. . . . . . . . . . . . . . . . . . . . . . . . . 119
6.2 List of state parameters, constants, and assumptions regarding state parameters details.122
6.3 Pixel analysis for possible freeze/thaw phenomenon, excluding a prefiltering scheme.126
6.4 Various filters applied to the PolSAR data before retrieval, in the preprocessing stage.127
6.5 List of empirical parameters in simulated Annealing set for this framework. . . . . 128
6.6 Comparison of performance of the simulated retrieval for various case study. . . . 134
6.7 Comparison of performance of the validation pixels retrieval for various case study. 159
6.8 The total estimated carbon in Tg for each flightline, for existing mapping techniques.168
9.1 Overview of soil dielectric characterization with a focus on measurement techniques190
9.2 Operation frequency of the AirMOSS and UAVSAR. . . . . . . . . . . . . . . . . 194
9.3 Antenna Element, Panel, Feed, and Array Dimensions. Unit: mm . . . . . . . . . . 196
9.4 Reference Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
9.5 The statistics of the system resonant frequencies. . . . . . . . . . . . . . . . . . . 206
10.1 Soil Sample Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
xiv
List of Figures
2.1 (a) The layers of permafrost [20]. (b) Soil organic carbon content to a depth of 1 m
adapted from Northern Circumpolar Soil Carbon Database [21] . . . . . . . . . . . 8
2.2 (a) The thaw gradient of active layer [18]. (b) The key variables in studying Arctic
responses to climate change are the soil carbon and soil moisture . . . . . . . . . . 9
2.3 The scaling diagram for environmental monitoring, redrawed and modified from the
original design “Leaf to Orbit” credit: Piers Selters, and Arctic Boreal Vulnearbility
Experiment (ABoVE). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 (a) Electromagnetic wave interaction with a target, including incident and scattering
mechanism. (b) Airborne PolSAR measurement in the Arctic and schematic of
permafrost active layer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.5 ABoVE airborne campaign study area, which consists of a gradient of critical
bioclimatic zones in the Arctic. Flight lines (denoted by orange transects) comprised
of multi-year P-band and L-band PolSAR acquisition from the pre-ABoVE era
(2014, and 2015) to intensive sampling years in 2017 and more recently in 2018,
2019, 2022, and 2024. The P-band acquisition in 2017 within 5 flightlines in the
North Slope of Alaska (A1) is used for SOC mapping in this work. The blue boxes
refers to Alaskan (A1-A4) and Candian (C1-C6) regions [5, 26]. . . . . . . . . . . 13
2.6 Physics-based computational radar retrieval cycle, which relates the field-scale
parameters that govern key processes in the terrestrial ecosystem (e.g., water and
carbon cycle) to corresponding radar measurement. The exit point ultimately links
the radar observation to ecosystem state parameters by satisfying the inverse model
stopping criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.7 AirMOSS mission P-band retrieval cycle schematic for temperate sites, which uses
a single snapshot of P-Band pplsar measurement. . . . . . . . . . . . . . . . . . . 15
2.8 Time-series P-band retrieval cycle schematic for permafrost landscape that uses
August and October snapshots with active layer stagnation assumption. . . . . . . . 16
2.9 AirMOSS forward model developed for roo zone soil moisture retrieval a single
polsar snapshot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.10 Time-series permafrost soil retrieval forward model developed for active layer
thickness retrieval in August and October, with stagnation assumption. . . . . . . . 18
2.11 Forward model for physics-based computational radar retrieval of soil organic
carbon in permafrost, using three snapshots (June, August, and October) across the
thaw season in Alaska. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
xv
3.1 The location of the five in-situ tundra sites located along the Dalton Highway,
on the Alaskan North Slope, USA. The sites locations fall within two of the
ABoVE Airborne Campagin (AAC) flight lines shown on a regional land cover map
National Land Cover Database (NLCD) and geographic projection. The land cover
categories are adapted from the National Land Cover Database (NLCD) classification. 23
3.2 Dielectric permittivity profile characterization and soil sampling protocol, from the
side wall of a soil pit using TEROS 12. Two side-by-side replicate samples were
extracted from each layer. For PTF development, adjacent samples are assumed to
be independent, and for profile modeling, ‘a’ and ‘b’ averaged values are used. . . 24
3.3 Soil pits excavated at the HV and ICC study sites. (a) Happy Valley 1. (b) Ice Cut 1. 26
3.4 Organic matter (OM) histogram for both datasets. . . . . . . . . . . . . . . . . . . 29
3.5 (a) OM Profile Distribution. (b) OM Median profile at each depth suggests a
sigmoid function for representing profile behavior) . . . . . . . . . . . . . . . . . 30
3.6 The differences between sigmoid profile model and exponential profile
OM(z) = OMz0e
−κz
for organic matter. (a)-(h) shows each of soil pits, it appears,
except Franklin Bluffs, in the remaining sites, a sigmoid function shows a better
representation for OM profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.7 Gravel fractions for each soil pits, it is appearing only SGW-1 has a significant GF,
and for the other site this value is 0, therefore for reducing model complexiy we
assume GF is 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.8 Pedo Transfer Functions (PTF)s that find porosity and bulk density from the
mineral texture and OM. Figure (a) shows the model behavior that derives ρb
from soil mineral texture and OM; the FB samples are outliers and excluded from
modeling. (b) Shows the linerar relationship between φ and ρb. (c) Shows the
behavior of φ against OM, herein for mineral texture we considered the mean value
of Savg = 39% and Cavg = 25%. . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.9 Soil active layer profile physical properties from soil pit measurement and model
estimated at tundra sites; including (a) OM at SGW-1 (red circle), SWG-2 (blue
triangle), HV-1 (black square), and HV-2 (magenta diamond), (b) bulk density, (c)
porosity, (d) OM at FB-1 (red circle), IMN-1 (blue triangle), ICC-1 (black square),
and ICC-2 (magenta diamond), (e) bulk density, (f) porosity. At each depth two
replicate samples were harvested. Both measured values are shown. For profile
modeling, the average value was selected. OM profile was found based on sigmoid
function and accordingly porosity and bulk density profiles were found by inserting
OM profile into PTF models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.10 Observed vs estimated SOM and RB profiles for the SGW tundra site (sampling
location SGW-1 in red and sampling location SGW-2 in blue). The model RB and
SOM profiles are derived from equation (3.7) as shown and plotted against the
associated site measurements. Total OM, was found based on RB and SOM profile.
(a) OM at SGW-1 (red circle), SGW-2 (blue triangle), HV-1 (black square), and
HV-2 (magneta diamond), (b) RB, (c) SOM, (d) OM at FB-1 (red circle), IMN-1
(blue triangle), ICC-1 (black square) and ICC-2 (magneta diamond), (e) RB, and (f)
SOM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
xvi
3.11 Active layer measured soil dielectric constant and electrical conductivity profiles
using TEROS 12 probes. Measured and modeled soil moisture and SW fraction
(quadratic model) the tundra site, including, (a) real parts of the dielectric SGW-1
(red circle), SGW-2 (blue triangle), HV-1 (black square), and HV-2 (magneta
diamond) (b) electrical conductivity, (c) volumetric soil moisture, and (d) SW
fraction, (e) real parts of the dielectric FB-1 (red circle), IMN-1 (blue triangle),
ICC-1 (black square), and ICC-2 (magneta diamond) (f) electrical conductivity, (g)
volumetric soil SW fraction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.12 The framework of radar remote sensing forward model in the physics-based
retrieval of active layer properties. Subsurface properties can be categorized
into three groups, (a) OM profile parameters X¯t
OM = [OMz0,OMM,β,m], (b) soil
saturation profile parameters X¯t
SW = [SWz0,zWT ], and (c) active layer parameters
X¯t
ALT = [h,zALT ], which are surface roughness height and ALT respectively. These
parameters, serve as unknowns in a radar retrieval procedure, and through an
iterative method their value estimated at each radar pixel cell. . . . . . . . . . . . . 42
3.13 Profile model parameter ranges. The red bar shows the median and the box
boundaries show the 25%−75% range of value within the distribution. . . . . . . 42
3.14 The distribution of correlation coefficients between adjacent samples, showing the
precision of soil properties measurements as listed in equations (10a) and (10b),
assuming two harvested sample at each layer exhibit similar physical properties. . . 43
4.1 Locations of our nine study sites and associated land cover types across Alaska.
The Alaskan North Slope, and interior Alaska regions are indicated by the
green and yellow shades, respectively, in the inset in (a). The purple and cyan
boxes around (a) and (b) correspond to the same color boxes in the inset map,
respectively. Black dots in (a) and (b) show the site locations where soil samples
were collected and analyzed for determining soil characteristics, and laboratory
analysis. Sampling locations fall within airborne synthetic aperture radar (SAR)
transects from the National Aeronautics and Space Administration (NASA) Arctic
Boreal Vulnearbility Experiment (ABoVE) ABoVE Airborne Campagin (AAC).
(c) An example soil profile from an excavated pit, where active layer (active layer
thickness (ALT)) samples were harvested from the surface to permafrost table. . . 47
4.2 Soil component analysis measurements denoted by points and empirical fitted
curves, including: (a) empirical relationship between root biomass and total OM;
(b) linear variation between SOM and total OM; (c) mass fraction variation of each
soil solid component as a function of total OM; (d) specific density variation used
to estimate volumetric fraction; (e) volumetric fraction of soil solids and pore space
compared with measured porosity; and (f) normalized volumetric fraction fitted
model compared with measurements. . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.3 Sample harvested from permafrost active layer. (a) Surface sample at Creamers
Field. (b) Surface sample at Scottie Creek . . . . . . . . . . . . . . . . . . . . . . 53
xvii
4.4 A total of 66 soil samples were collected from 13 sampling locations at 9 sites. The
samples were divided into half, then TEROS 21 sensors were inserted to measure
soil matric potential properties. Samples were under a constant air circulation
caused by a network of cooling fans to facilitate the moisture evaporation. Sample
weight loss was recorded from saturation to dry regime and the gravimetric
moisture content was translated to volumetric moisture content knowing the sample
volume. (a) North slope samples. (b) Interior Alaska samples. (c) Network of
cooling fans to circulate the air and expedite the evaporation. . . . . . . . . . . . . 53
4.5 Distribution of measured soil water matric potential (pF = log10(ψm [hPa])) as a
function of SW for various soil samples using TEROS 21 sensors. . . . . . . . . . 54
4.6 Measured matric potential for 66 soil samples collected from permafrost active
layer, measurement conducted from saturated to oven dry region. The Van
Genuchten water retention curve is being fitted to the measured data, and estimated
model parameters being used for empirical model parameterization. The Campbell
curve also being fitted, but the figures are not shown to avoid clutter. The dot
with same color denotes one soil sample and measurement covers the full range.
Color bar in each plot shows the variation of total organic matter in each soil
sample and category(a) shows the soil samples with the range of OM between
[0−5]%. (b) shows the OM range between [5−10]%. (c) shows the range between
[10−35]%. (d) shows the range between [35−60]%. (e) to (f) shows the range
from [60 − 100]% with increment of 10%, it appears the beyond 60% the soil
water retention curve behaves fairly similar, while the maximum saturation level
(porosity) is monotonically increasing. . . . . . . . . . . . . . . . . . . . . . . . . 54
4.7 The van Genuchten, and Campbell water retention curve parameter for purely
mineral soil. The data for van Genuchten SWRC parameters are adapted from M.G.
Hodnett et al., (2002), and data for Campbell SWRC parameters are adapted from
B. J. Cosby et al., (1984) [98]. (a) Shows the behavior of residual water content
(θr), which is modeled based on Clay mass fraction. (b) Silt mass fraction was used
to model the (α). (c) Clay mass fraction was used to model the parameter (n) of
van Genuchten SWRC. (d) Sand mass fraction shows a high correlation with (ψs).
The (b) parameter of the Campbell SWRC can be modeled with Clay mass fraction. 56
4.8 The estimated SWRC parameters from measurement. To solve the set of equations
in equation (4.6), simple equations (4.7) were fitted to estimated parameters. The
value of each parameters at OM=0, 70, 100 % are designators for the pure mineral,
soil organic matter and root biomass. These values then use on the right side of
equation (4.6), to find the contribution of each subcomponent of samples. Note
that the pure mineral soil SWRC parameters as described in figure S4 are a function
of mineral texture. Therefore in equation (4.6), those value find based on figure 4.7.
However, the SWRC parameters value for RB and SOM, will be find based on
solving the system of equations. (a)-(c) show the fitted curve as function of OM for
Van Genuchten parameters. (d), and (e) show the Campbell parameters. . . . . . . 57
xviii
4.9 Equation (4.6) and (4.9) was solved for 11 types of mineral soil to find the
distribution of each parameter. The distribution of SWRC parameters for various
(x
i
j
, or log10(y
i
j
)) for i= RB, SOM, Min solved in (4.6) or (4.9) was found each
soil. The box plot shows the median (red strip) and the 25% −75% percentile.
While the mineral parameters can be find from figure 4.7, for the SOM and RB we
associates the median value for SWRC parameterization, the results are reported
in Table 4.3 accordingly. (a)-(c) show the variation of van-Genuchten SWRC
parameters for different type of mineral soil. (d), and (e) show the variation of
Campbell SWRC parameter for different type of mineral soil. . . . . . . . . . . . . 58
4.10 The parameters (x
i
j
, or log10(y
i
j
)) as shown in figure 4.9 for eleven type of mineral
soil were used to find the SWRC parameter behavior for the total OM, where the
contribution of each component is calculated using arithmetic or logarithmic mean
of normalized volumetric fraction. (a)-(c) show the variation of van-Genuchten
SWRC parameters for different type of mineral soil. (d), and (e) show the variation
of Campbell SWRC parameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.11 Full parameterization of SWRC using the input variables OM, sand and clay
fraction, with blue markers showing estimated SWRC parameter values from
observations, and the parameterized model (equation (4.4), (4.8)) in black
curve.(a)-(c) show the variation of van-Genuchten SWRC parameters. (d), and (e)
show the variation of Campbell SWRC parameters. . . . . . . . . . . . . . . . . . 62
4.12 Behavior of the reconstructed SWRC for various OM levels. (a) van-Genuchten.
(b) Campbell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.13 Estimated relaxation time of soil-water for various OM levels. (a) van-Genuchten.
(b) Campbell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.14 Real part of the soil-water dielectric behavior as predicted from a the continuous
phase approach. Imaginary part of soil-water dielectric behavior (dielectric loss).
(a-b) van-Genuchten. (c-d) Campbell. . . . . . . . . . . . . . . . . . . . . . . . . 65
5.1 The current state of the problem from a modeling perspective. A description of
existing organic soil dielectric models, including: (a) empirical models that relate
soil dielectric permittivity to soil moisture through a generic polynomial; (b) the
semiempirical physics-based model developed by Mironov et al. and consisting of
a spectroscopic and single-frequency approach, where organic matter serves as a
model input; (c) the semiempirical physics-based model developed by Park et al.
that relies on wilting point as a proxy measure of bound water. . . . . . . . . . . . 72
5.2 Locations of our nine study sites and associated land cover types across Alaska.
The Alaskan North Slope, and interior Alaska regions are indicated by the green
and yellow shades, respectively, in the inset in (a). The purple and cyan boxes
around (a) and (b) correspond to the same color boxes in the inset map, respectively.
Black dots in (a) and (b) show the site locations where soil samples were collected
and analyzed for determining soil characteristics, and laboratory analysis. Sampling
locations fall within airborne SAR transects from the NASA ABoVE airborne
campaign. (c) An example soil profile from an excavated pit, where active layer
samples were harvested from the surface to permafrost table. . . . . . . . . . . . . 75
xix
5.3 The end-to-end coupled hydrologic-electromagnetic organic soil dielectric
model aims to use basic soil properties (including soil moisture, organic matter,
mineral texture, temperature, and frequency) as input parameters to determine
the effective soil dielectric of the soil sample. The model consists of a hydrology
perspective that parametrizes the soil water retention curve using various inputs.
The electromagnetic perspective relates the estimated soil water retention curve
to the soil water relaxation time using the Eyring equation and arrives at the
water-in-soil dielectric condition using the Debye dielectric model. Finally, the
resulting water-in-soil dielectric is applied to the organic soil dielectric mixing
model along with other subphases to calculate the organic soil dielectric properties. 77
5.4 In all cases, the solid lines are derived from the model simulation for a fraction
of S=36% and C=25% as OM varies between [0−100] [g/g] %, and the shaded
areas are associated with the total range of variation simulated for all classes of
mineral soil. (a) Shows the volumetric fractions of solid soil components (solid
plot), which includes root biomass, soil organic matter, and mineral soil, and the
porosity along with their associated variation (shaded) as the model presented in
Eq. ((5.2)-(5.5)) simulated different classes of mineral soil. (b) Shows the variation
of air entry potential (ψs) of Campbell SWRC model parameters. (c) The behavior
of exponent parameters of the Campbell SWRC and its associated variation. . . . . 80
5.5 The full simulation of the hydrology perspective for the full range of soil moisture
and organic matter content for an average mineral texture with S=36% and C=25%.
(a) Shows variation of soil matric potential pF = log10|ψm|.(b) Relaxation time of
water molecules in soils. (c) Real part of water-in-soil dielectric permittivity. (d)
Imaginary part of water-in-soil dielectric permittivity. . . . . . . . . . . . . . . . 82
5.6 The simulation of freeze/thaw state, and volumetric fraction behavior of water
and ice content as temperature varies from sub-zero to above zero conditions
for a representative soil sample (OM=80%, S=36%, C=25%). While the
OM +S+C summation can exceed 100% based on the equations provided in (5.4),
f
OM
m + f
S
m + f
C
m + f
Si
m = 100% and differentiates the mass fraction of the entire
sample compared to the estimated sand/clay soil fractions. . . . . . . . . . . . . . 84
5.7 The organic matter (OM) content histogram distribution of the Alaska samples used
in the laboratory analysis for characterizing the soil dielectric and matric potential. 85
5.8 (a) The TEROS 12 sensor enables raw ADC, conductivity and temperature
measurements. (b) Schematic of soil dielectric and soil matric potential
measurement set up, where sensors are inserted horizontally within the saturated
soil layer. Measurement was conducted in a dry-down manner with the help of
several fans that accelerated evaporation rates. (c) TEROS 21 sensor enabled soil
matric potential measurement. (d) The batch of 50 samples that were collected
from 8 sampling locations in the North Slope of Alaska. (e) A total of 16 soil
samples from Interior Alaska were also collected. (f) Samples on the bench top in
the vicinity of the fan used for air circulation. . . . . . . . . . . . . . . . . . . . . 87
xx
5.9 The TEROS 12 manufacturer curve (red line) tends to slightly underestimate
the relative permittivity of reference samples compared to the in-lab generated
calibration curve (fitted blue line). The range of raw ADC values was generated by
45 measurements acquired from 9 TEROS 12 probes. The calibration curve was
generated from the measured mean values. . . . . . . . . . . . . . . . . . . . . . . 89
5.10 The profile behaviors of the active layer soil properties that serve as input
parameters for the soil dielectric model. (a) Organic matter content, (b-c) sand and
clay fraction, (d) soil saturation fraction, and (e) temperature profile. . . . . . . . . 91
5.11 (a) A schematic of the subsurface geometry, which consists of a discretized
multi-layered dielectric structure along with surface roughness height behavior. The
SPM accepts the dielectric profile at average depth points. (b-c) The in-situ range
of real and imaginary parts of dielectric permittivity for all 8 sampling locations. . 93
5.12 Mineral soil dielectric behavior. In all cases the x-axis shows the soil saturation
fraction, and the color bar represents the OM content for each soil sample. (a) Real
part of complex permittivity for sandy loam that includes FB-1 and SGW-1 samples.
(b) Imaginary part of the complex permittivity for sandy loam soil. (c-d) Real and
imaginary parts of the complex permittivity for silty clay loam that includes the
SGW-2, HV-1, HV-2, ICC-1, ICC-2, and IMN-1 sites. . . . . . . . . . . . . . . . . 94
5.13 Organic soil dielectric behavior. (a-b) Real and imaginary parts of the complex
permittivity for the organic soil with OM variation between [60−80] %. (c-d)
Real and imaginary parts of the complex permittivity for the organic soil with OM
variation between [80−100] %. . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.14 (a) 1:1 plot of the real part of dielectric permittivity measurements against the
model for all data points (dielectric for various soil moisture levels across all soil
samples). (b) 1:1 plot for the imaginary part of the soil dielectric. (c) RMSE
variation of the real and imaginary parts of soil dielectric properties of all soil
samples, where each point represents a soil sample. (d) The histogram of RMSE
for both real and imaginary parts of all soil dielectric properties. . . . . . . . . . . 96
5.15 Validation of the dielectric model against in-situ dielectric measurements. In all
cases, measurements are shown with blue dots, the profile models are plotted with a
red line, and the shaded red area represents the model as input profile parameters
are perturbed to account for a 15% error. The OM, SW, real, and imaginary part of
dielectric for (a-d) SGW-2, (e-h) HV-1, and (i-l) ICC-1. . . . . . . . . . . . . . . . 98
5.16 Empirical modeling minimized the RMSE of the dielectric model against
measurements over the range of OM conditions. In each plot, the blue dots
represent the values that were found based on simulated annealing to minimize the
RMSE of the soil dielectric model. The red squares show the model predictions
derived from Eq. (24), and the black line plots the model simulations for an average
soil containing 36% Sand and 25% Clay. (a) Soil water electrical conductivity (σw),
behavior and (b) the mixing model term (α). . . . . . . . . . . . . . . . . . . . . . 100
xxi
5.17 The frequency behavior of the developed soil dielectric model under thawed and
frozen conditions. The color legend represents the soil saturation ranges (red
shows the 0.25 saturation fraction, blue for 0.5, black for 0.75, and magenta
shows fully saturated soil behavior). The markers represent the soil organic matter
contents, where the unmarked plot shows 0% OM content (pure mineral soil),
and respectively the circle, square, diamond, and triangle symbols correspond
to [25%,50%,75%,and100%] OM contents. (a-b) The model simulation for
above zero temperatures represents the real and imaginary parts of the dielectric
behavior as frequency, OM content, and saturation fraction vary. (c-d) shows the
model simulation for saturated soil with variable frequency and OM at sub-zero
temperatures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.18 The temperature behavior of the developed soil dielectric model at P-band for
saturated soil. The color legend represents the different OM levels represented
(blue shows 0%, red circle for 25%, black square for 50, magenta diamond for 75%,
and green triangle shows fully organic soil behavior). (a-b) The model simulation
shows the real and imaginary parts of the soil dielectric behavior as temperature
and OM content vary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.19 Comparison of parameterization schemes used in prevailing organic soil dielectric
models. In all figures, the blue lines show model results from Park et al., 2019
and the blue circles show results from Park et al., 2021; the black lines represent
Mironov et al., 2019; Magenta lines correspond to Savin et al., 2022, and red lines
shows our work. (a) Shows the variation of bulk density used in previous work,
where the Park et al. model exhibits non-physical values (negative or large bulk
density) for larger OM. (b) Shows the behavior of the maximum bound water
fraction, which was determined from the wilting point. (c) shows the porosity
behavior of the above models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.20 Bound water argument. (a) Comparison of the real part of soil dielectric for organic
and mineral soils at the same soil moisture level. High sand and clay fractions are
simulated with corresponding red and blue curves. (b) Comparison for the same
soil saturation level. (c) Observations and claims about bound water from this study
and other existing works reported in the literature. . . . . . . . . . . . . . . . . . . 105
5.21 Comparison of the existing organic soil dielectric models at 435 MHz, and 1400
MHz. The color legend denotes the particular model, where the markers show the
OM variation. (a) Model behavior at 435 MHz and (b) model behavior at 1400
MHz are presented. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.22 The limitation of organic soil dielectric model. . . . . . . . . . . . . . . . . . . . . 108
5.23 The feasibility of retrieving permafrost active layer subsurface water and carbon
characteristics using radar (P-band) observation. (a) Shows the CALM sites,
our North Slope sampling locations (filled circles), and two ABoVE Airborne
Campaign flight swaths. (b) shows the variation of the simulated backscattering
coefficient for HH polarization, where the range of input parameters are adapted
from Table 5.4, along with radar observation for each point. (c) Accordingly shows
the variation of simulated backscattering coefficient for VV polarization . . . . . . 110
xxii
6.1 Locations of in-situ soil profiles input in state-of-the-art digital soil mapping. (A)
The global map, and location of all the in-situ soil profile collected across multiple
decades, which serves as the main input layer for digital soil mapping techniques
such as those used in Soil Grids. (B) The higher latitude soil profile locations in
North America, including Alaska, and Canada, which shows significantly lower
density of measurements. (C) The location of soil profiles in North Europe and
Russia. (D) The focus area in this study, including the North Slope of Alaska. . . . 117
6.2 Mapping soil organic carbon. (A) Schematic of the permafrost subsurface, and
radar measurement in the backscattering mode. Notice the presence of a root
layer on top, the distribution of soil organic matter, and the transition to the
organic-mineral layer. The total organic matter consists of a combination of root
biomass and soil organic matter. See Fig. S7 for additional information. (B) The
study sites and AirMOSS P-band PolSAR flight lines were conducted by the NASA
ABoVE Airborne campaign. Five flight lines are measured at three snapshots,
including Deadhorse (blue), Toolik (red), Barrow (Purple), Atqasuk (black), and
Ivotuk (orange). (C) The map of surface organic carbon parameter (SOC[0−5] (cm)
)
of the SOC averaged profile driven from computational physics-based algorithm
retrieval, where SOC unit is (g/g) %. (D) Map of SOC[5−15] (cm)
. (E) Map of
SOC[15−30] (cm)
. The corresponding uncertainties in SOC distribution is shown in
Figure 6.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.3 Uncertainty (standard deviation) of SOC map. (A) The uncertainty of the estimated
SOC[0−5](cm) map driven from standard deviation over converged inverse problem
for each pixel for 20 iterations. (B) The uncertainty for second standard depth
SOC[5−15] (cm)
. (C) The uncertainty for third standard depth SOC[15−30] (cm)
. . . . . 135
6.4 Physic-based computational radar retrieval framework. The physics-based
computational radar retrieval framework aims to relate radar measurement at
each pixel on the ground to the corresponding state parameters that control the
field scale surface and subsurface processes. Such techniques rely on detailed
field observation to parametrize the subsurface into a meaningful first-order set
of parameters and the foundation of electromagnetic to translate them into radar
backscattering coefficients. An iterative inverse model is then applied to find the
optimum set of state parameters that results in the radar observation, through the
forward model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
6.5 Forward Model. The forward model consists of three submodules, where initial
state parameters are used to model critical subsurface processes such as organic
matter (OM), soil saturation (SW), and thaw depth. The equivalent soil profile
model then translates into a soil dielectric profile (ε˜) through an organic soil
dielectric model. Finally, a layered dielectric structure along with the soil rms
roughness height (h) feed into an electromagnetic scattering model that via
solving Maxwell’s equations and calculation of the electromagnetic wave (E¯
i
, E¯
s)
interaction with the structure arrives at the radar backscattering coefficients (σxx). . 137
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6.6 Active layer profile variation across the season. Early in the thaw season soil
columns experience a shallow thaw depth (z
JUNE
T HD ), shallow water table depth
(z
JUNE
WT )and highly saturated surface soil (SWJUNE
z0
). Later in the season, the thaw
depth reaches its maximum thaw depth (zALT ) and maintains this depth throughout
the stagnation period that can last from August until October. The water table
depth in August z
AUG
WT usually hit a maximum and deepens as the evapotranspiration
generally overcomes the precipitation, which results in a dryer surface (SWAUG
z0
).
Later in the season and depending on the temperature drop or pixels geolocation
October might start the accumulate snow, which may result in a surface freeze effect.
Such phenomenon might not be widespread across the flightline, but field and radar
data agree with the possibility of F/T effect in October. Across the season, the
organic matter profile parameters (OMz0, zOLT ) and the soil roughness rms height
(h) are assumed to remain constant due to limited time-series observation across the
season. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
6.7 State parameters snapshot an example of simulated profile behavior. (A) Organic
matter profile. (B) Sand fraction profile. (C) Clay fraction profile. (D) Silt
fraction profile. (E) Soil saturation profile in June. (F) Soil saturation profile in
August. (G) Soil saturation profile in October, for an unfrozen surface. (H) Soil
saturation profile in October for a frozen surface. (I) Temperature profile in June.
(J) Temperature profile in August. (K) Temperature profile in October, for an
unfrozen surface. (L) Temperature profile in October for a frozen surface. . . . . . 139
6.8 Range and distribution of state parameters from in-situ observation. (A) Surface
organic matter. (B) Depth of organic layer thickness, indicating the profile inflection
point. (C) Thaw depth in June 2016. (D) Water table depth in June 2016. (E) Active
layer thickness in August 2016. (F) Water table depth in August 2016. . . . . . . . 140
6.9 Sketch of simulated time-variant behavior of state parameters. (A) Surface soil
saturation. (B) Water table depth. (C) Thaw Depth. (D-E) Top frozen depth
in October, for the case of unfrozen column and frozen column. (F-G) Surface
temperature behavior for both unfrozen and frozen case. . . . . . . . . . . . . . . 141
6.10 Sketch of simulated 2D variation of time-variant parameters across time-depth. (A)
Example of 2D Temperature variation, for the case of unfrozen surface October
(unfrozen/thawed). (B) 2D temperature behavior for a frozen surface in October
(frozen). (C) Soil saturation 2D variation. . . . . . . . . . . . . . . . . . . . . . . 141
6.11 Snapshots of soil dielectric behavior across the season. (A) Organic soil dielectric
profile behavior in early June, where real and imaginary are denoted by red and
blue respectively. The dashed lines show the zOLT , z
JUNE
WT , and z
JUNE
T HD , with the
black, green and magenta respectively. (B) Organic soil dielectric profile behavior
for August. (C) October soil dielectric profile behavior for the case of unfrozen
column. (D) Top frozen case in October and corresponding organic soil dielectric
profile, the sky-blue dashed line shows the top frozen depth (z
OCT,Fr
T FD ). . . . . . . . 142
6.12 Sketch of simulated 2D variation of time-variant active layer soil dielectric
properties across time-depth. (A, B) Real and imaginary part of 2D organic soil
dielectric properties variation across the time and depth, for an unfrozen October.
(C, D) The same 2D organic soil dielectric behavior for a frozen October case. . . . 143
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6.13 The 1D discretization of the subsurface for electromagnetic scattering modeling.
(A) Shows a schematic of the subsurface, including the buffer in surface, subsurface
discretization, and number of layers. (B) Shows an example of active layer soil
profile behavior, where various horizons can be denoted by the colors. . . . . . . . 144
6.14 (A-C) Time-invariant parameters. Variation of σxx as a function of OMz0, zOLT ,
and h, respectively. (D-F) June parameters. (G-I) August parameters. (J) October
parameters. Notice that zALT is assumed to be stagnation period and remains
constant between August and October (Fig. 6.9.C). . . . . . . . . . . . . . . . . . 145
6.15 Example of simulated σxx(t) time-series behavior. The behavior of the
backscattering coefficients, including vertical (dashed blue) and horizon (dashed
red) polarization for the unfrozen column, respectively. The frozen column is
shown by red and blue curves for vv and hh polarization. The vertical lines show
the associated acquisition times of radar measurements, in June, August and
October (magenta, black and green), followed by the zero crossing (cyan). Notice
the behavior is simulated by inserting the time-series behavior as shown in Figure
S11 into Equation 6 and the resulting Figure 6.12 into Equation (6.7). . . . . . . . 146
6.16 The binary behavior of (σhh −σvv) > 0. The binary map that shows the subtractions
of horizontal channel from vertical behavior, where 1 shows the positive values
meaning hh is larger than vv and 0 corresponds to vv being larger than hh. (A) The
June acquisition. (B) August. (C) October. The pattern shows a larger number of
pixels being impacted by ()σhh −σvv) > 0 in October. . . . . . . . . . . . . . . . 147
6.17 Simulated backscattering coefficient forward model framework. From left to
right, simulated inputs are adapted from Table 6.2, completely randomly. Notice
the z
OCT
T FD varies between either 0, which results in an unfrozen October column,
or [0.05−0.25] (m) which results in a frozen October case. At the heart of the
framework, the forward model translates input parameters into profile models,
organic soil dielectric model, and eventually results in simulated outputs which are
the snapshots of multi-channel backscattering coefficients. Notice, that the incident
angle was randomly chosen between [15−60] degrees. . . . . . . . . . . . . . . . 148
6.18 Simulated backscattering coefficient behavior and the indication of freeze/thaw. (A)
Shows the portion of a simulated backscattering from the pool of 2500 parameters
for unfrozen case. The hh channel never exceeds the vv channel under the
variations of all incidence angles and parameters. (B) The portion of the simulated
backscattering with frozen columns assumption, where the z
Oct
T FD ̸= 0. The only
case that hh shows larger values than vv. . . . . . . . . . . . . . . . . . . . . . . 148
6.19 Cost function behavior. (A-C) Time-invariant parameters. Variation of L(X¯) as a
function of OMz0, zOLT , and h, respectively. (D-F) June parameters. (G-I) August
parameters. (J) October parameters. Notice that zALT is assumed to be stagnation
period and remains constant between August and October (Fig. 6.19.C). . . . . . . 149
6.20 First step in inversion. Shows the comparison between hh and vv channels in
October to either directly use the frozen column for retrieval or running both.
Notice, the whole inversion scheme is run 20 times to achieve statistics of retrieval
parameters. The retrieval framework is detailed in Figure 6.20. . . . . . . . . . . . 150
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6.21 Additional details within the physics-based computational radar retrieval framework.
Color codes are consistent with those from Figure 6.21, where the high-level
end-to-end framework was depicted. The output of the framework could be either a
potential converged solution or no convergence within the stopping criteria of the
global optimizer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
6.22 Distribution of the total number of Cost function evaluation. (A) Shows the cost
function distribution and associated values for simulated retrieval (using synthetic
measurement). (B) Distribution of the cost function for validation case using
AirMOSS radar measurements at 2349 pixels after running each pixel up to 40
times, (20 per each column assumptions). . . . . . . . . . . . . . . . . . . . . . . 151
6.23 Total number of converged cost functions for frozen and unfrozen (thawed) cases.
(A) Shows behavior of convergence and number of converged inversions for
simulated (synthetic) measurement. (B) Same behavior for validation dataset
(AirMOSS radar measurement). In both cases, red shows the unfrozen, and blue
shows the frozen cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
6.24 Freeze/Thaw probability for simulated and actual radar data. (A) Simulation results.
(B) Validation (radar data). Legend follows Figure 6.23. . . . . . . . . . . . . . . . 152
6.25 Simulated retrieval of the time-invariant parameters. (A-C) Shows the expected
values of averaged retrieved parameters for the OMz0, zOLT , and h respectively.
(D-E) The standard deviation, of retrieved parameters. (G-I) Shows the RMSE
behavior as described in equation 16. All the plots show the 2D histogram, where
the color bar shows the density of pixels. Plots are generated based on 2349
synthetic pixels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
6.26 Simulated retrieval of the June parameters. (A-C) Shows the expected values of
averaged retrieved parameters for the SWJune
z0
,z
June
WT , and z
June
T HD respectively. (D-E)
The standard deviation, of retrieved parameters. (G-I) Shows the RMSE behavior
as described in equation 16. All the plots show the 2D histogram, where the color
bar shows the density of pixels. Plots are generated based on 2349 synthetic pixels.
The x-axis shows the parameter variations within the range that was shown in Table
6.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
6.27 Simulated retrieval of the August and October parameters. (A-D) Shows the
expected values of averaged retrieved parameters for the SWAug
z0
, z
Aug
WT , zALT , and
z
Oct
T FD respectively. (E-H) The standard deviation, of retrieved parameters. (I-L)
Shows the RMSE behavior as described in equation 16. All the plots show the 2D
histogram, where the color bar shows the density of pixels. Plots are generated
based on 2349 synthetic pixels. Lower point density is represented by cooler colors
and higher density by warmer colors. . . . . . . . . . . . . . . . . . . . . . . . . 155
6.28 Super pixel formation in validation against in-situ data. (A) Shows an example
of in-situ soil organic matter properties at multiple pixels within a 90x90 m super
pixel. (B) Shows compilation of the in-situ data from various adjacent pixels into a
super pixel that represents each pixel independently. . . . . . . . . . . . . . . . . 155
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6.29 Performance of the retrieved organic matter profile’s parameters against in-situ
data for each pixel. (A-B) Shows the performance of expected retrieved parameters
values at each pixel (µ
Exp−i
OMz0
and µ
Exp−i
zOLT , respectively) using AirMOSS data against
in-situ values. (C-D) RMSE distribution. . . . . . . . . . . . . . . . . . . . . . . . 157
6.30 Performance of the retrieved organic matter profile’s parameters against in-situ
data for super pixel (3×3). (A-B) Shows the performance of expected retrieved
parameters values at each pixel (µ
Exp−SP−i
OMz0
and µ
Exp−SP−i
zOLT , respectively) using
AirMOSS data against in-situ values. (C-D) RMSE distribution. . . . . . . . . . . 158
6.31 Map of radar driven OMz0 and zOLT . (A) The expected values of average surface
organic matter (OMz0). (B) The expected values of average organic layer thickness
(zOLT ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
6.32 Distribution of total calculated SOCC based on equation (6.30). . . . . . . . . . . 164
6.33 Validation for physics-based radar retrieval. (A) Over 2349 soil profiles are
compiled from various soil inventories. (B) Validation of SOC (g/g) % is
conducted for three depth intervals, [0−5], [5−15], and [15−30] cm for 1×1
pixels using only 2018 field data. (C) Validation of SOC (g/g) % at three standard
depths for 3×3 pixels. (D) The Super pixel orientation (more details Figure 6.28).
(E) Validation of SOC for all 1×1 pixels. (F) Validation of SOC for all 3×3 pixels. 166
6.34 Validation of soil properties adapted from Soil Grids v1, and v2 against in-situ data.
(A-C) The inter-relationship between SOC and ρb for in-situ, SoilGrids-v1, and
SoilGrids-v2, respectively. (D-F) The validation of SoilGrids-v1 SOC and ρb and
SOCC against in-situ data. (G-I) The validation of SoilGrids-v2 SOC and ρb and
SOCC against in-situ data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
6.35 Impact of land cover type on SOC for all the flight lines. (A) The variation of
standard depth interval, SOC[0−5] (cm)
,SOC[5−15] (cm)
, SOC[15−30] (cm)
for different
types of land cover including Barren, Dwarf Scrub, Shrub, Grassland, Sedges,
Lichens, Moss, Woody Wetlands, and Herbaceous wetlands. The box plot shows,
the median (line), and the 25%, 75% percentile. The blue color shows the
physics-based retrieval, red shows the SoilGrids v1, and yellow shows the SoilGrids
v2. The palette was created for the Toolik line. (B) Deadhorse flightline. (C)
Barrow flightline. (D) Atqasuk flightline. (E) Ivotuk flightline. . . . . . . . . . . . 169
6.36 Comparison of the SOCC estimates for [0 − 30] (cm) between this study and
state-of-the-art estimations. (A) The estimates of the SOCC in our study for all the
lines using time-series P-Band PolSAR data, with a total of 65.56 T g C for all the.
(B) The C-band estimation of SOCC using regression-based approach between
C-Band PolSAR and NCSCD data with a total of 45.02 T g C for all flightlines. (C)
The NCSCD product, with a total of 65.56 T g C. (D) SoilGrids v1, with a total of
125.3 T g C. (E) SoilGrids v2 with a total of 43.14 T g C. . . . . . . . . . . . . . . 170
xxvii
6.37 Simulated sensitivity analysis of the retrieved depth interval SOC for a threshold of
1.00 (dB). (A) The estimates of the µSOC[0−5] (cm)
, which is the average based on
solving the inverse problem for each pixel 20 times followed by averaging over
depth interval of [0−5] (cm), and corresponding standard deviation σSOC[0−5] (cm)
,
which refers to the error bar in retrieval for 20 iterations for each pixel. The pixels
are denoted by blue dots and the shaded area shows the standard deviation. (B)
Synthetic retrieval results for µSOC[5−15] (cm)
and σSOC[5−15] (cm)
. (C) Synthetic retrieval
results for µSOC[15−30] (cm)
and σSOC[15−30] (cm)
. (D) The RMSE for each pixel is based
on the iterated number of converged values for the depth interval of [0−5] (cm).
(E) Corresponding RMSE variation for depth interval of [5−15] (cm). (F) RMSE
variation for depth interval of [15−30] (cm). Additional information in Figure
6.25 to 6.27. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
6.38 Simulated sensitivity analysis of the retrieved depth interval SOC for a threshold of
0.50 (dB). Subfigures follow the 6.37. . . . . . . . . . . . . . . . . . . . . . . . . 173
6.39 Consistency in Retrieval. (A) The estimate of SOCC[0−30] (cm)
for Deadhorse line in
the overlap area. (B) The estimate of SOCC[0−30] (cm)
for Toolik line in the overlap
area. (C) Incidence angle for Deadhorse line. (D) Incidence angle for Toolik line.
(E) Landcover map for the overlap area. (F) The 2D histogram of the retrieved
SOCC[0−30] (cm)
, and comparison between the distribution of the retrieved values
for both flightlines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
7.1 Search results for the term “Radar Ecology”, and the reveiw paper by Erik Kasiscke.177
7.2 Conventional large-scale remote sensing product layers. A major contribution of
this dissertation is bringing a process-based understanding of the ecosystem into
the development and advancement of L−2/3 type products. A contribution that we
refer to as the new field of study “radar ecology”. . . . . . . . . . . . . . . . . . . 178
7.3 Legacy flightlines in the Seward Peninsula that needed to be completed for archival. 180
7.4 The focus of upscaling efforts will be in the Tundra region encompassing, the North
Slope of Alaska, and the Seward Peninsula region [188]. . . . . . . . . . . . . . . 181
7.5 Field sites measured on Aug 2024. . . . . . . . . . . . . . . . . . . . . . . . . . . 182
8.1 Thermal therapy and monitoring system for live animal trials using microwave
imaging. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
9.1 Microwave imaging system for characterizing the microwave dielectric behavior of
organic soil. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
9.2 Complex dielectric permittivity of the matching fluid. The blue curve shows the
real part, and the red color corresponds to the imaginary part as shown. For each
curve, the shaded areas determine the range of dielectric variation, assuming a 10%
error. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
9.3 Sample holder geometry, from a top and cross-section viewpoint. The soil container
is located at the center, with a diameter of 75 mm and a height of 250 mm. The
cavity is filled with coupling fluid. The 6 layer PCB stack up is also depicted in this
figure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
9.4 a) Different Layers of the Antenna Structure. b) Size and geometry of the single
elements with different symbols, along with size symbols for the Array structure. c)
Feeding mechanism and location of the patch within the multi-layer structure. . . . 195
xxviii
9.5 Fabricated imaging system and under test. (a) The 3D simulation setup in CST. (b)
Fabricated imaging system with the sample holder. (c) Antenna panel. (d) Imaging
chamber filled with the matching fluid. . . . . . . . . . . . . . . . . . . . . . . . . 197
9.6 Data acquistion system consist of the switching metwork, which shows the
configuration of the transmit and resecivers, the array schematic, and the TTL Circuit.198
9.7 The validity range of the BA compared with DBA. . . . . . . . . . . . . . . . . . 201
9.8 Reference Material Dielectric Properties. . . . . . . . . . . . . . . . . . . . . . . . 204
9.9 Constrast χ function for (a)BA and (b) DBA. . . . . . . . . . . . . . . . . . . . . 204
9.10 The entire measurement cycle including the reference materials and soil samples. . 205
9.11 The statistics of the system resonant frequencies. . . . . . . . . . . . . . . . . . . 206
9.12 Variation in S
BG
mn signal for all 94 background measurement across all channels,
indicates the time-variation of the background. (a,b) Magnitude and phase for first
resnoant frequency. (c,d) Second resonant frequency. (e,f) Third resonant frequency.207
9.13 Standard deviation σ of the background microwave signal S21. (a,b) Magnitude
and phase for small sample container. (c,d) Large sample container. . . . . . . . . 208
9.14 Total number of channel for small container each frequency that shows a differential
signal exceeding the noise threshold for both magnitude and phase. The noise
threshold here refers to variation of the background signal. (a) Repetition number
1, of reference materials. (b) Measurement of reference materials with 5-6 days
sepration from repition 1. (c) Repetition 3, measurement of reference materials
with 12-13 days seperation from 1. Each color shows different resonant frequencies,
with blue showing the lowest, orange a middle, and yellow has the highest resonant
frequencies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
9.15 Total number of channels for larger containers. Each frequency shows a differential
signal exceeding the noise threshold for both magnitude and phase. Caption follows
Fig. 9.14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
9.16 Conventional differential BA (Approach 1) compared with double differential (D
2BA).212
9.17 Statistics of segmented background variation associated to each batch of sample
measurment based on the timeline as shown in Fig. 9.12. . . . . . . . . . . . . . . 213
9.18 Reconstruction results for resonance frequency at 415 MHz, where 5 samples
including water (W), glycerin (G100), half-half mixture of water and glycerin
(G50W50), isoproyl alcohol (LE), and Oil (O). . . . . . . . . . . . . . . . . . . . 214
10.1 (a) Reference samples scanned 3 times across ∼ 14 days. (b) Soil samples were
measured up to 8 times at different soil moisture levels. . . . . . . . . . . . . . . . 215
10.2 The end-to-end soil dielectric imaging framework. . . . . . . . . . . . . . . . . . 216
A.1 Franklin Bluffs samples with corresponding organic soil dielectric measurement
and models. The behavior of real (red curve) and imaginary (dashed red curve) part
organic soil dielectric model against laboratory measurement for the full range of
soil saturation (SW). The measurement comprised of the real part (blue circle), and
imaginary part (blue diamond). Notice, in reality more measurement points were
conducted, however, the values are averaged with 0.1 interval in soil saturation.
Therefore, an error bar is shown for measurement points. The shaded transparent
red area shows the averaged of the corresponding model for 0.1 interval. . . . . . 238
A.2 Sagwon-1 samples with corresponding organic soil dielectric measurement and
models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
xxix
A.3 Sagwon-2 samples with corresponding organic soil dielectric measurement and
models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
A.4 Happy Valley-1 samples with corresponding organic soil dielectric measurement
and models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
A.5 Happy Valley-2 samples with corresponding organic soil dielectric measurement
and models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
A.6 Ice Cut-1 samples with corresponding organic soil dielectric measurement and
models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
A.7 Ice Cut-2 samples with corresponding organic soil dielectric measurement and
models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
A.8 Imnavait Creek-1 samples with corresponding organic soil dielectric measurement
and models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
A.9 Creamers Field-1 samples with corresponding organic soil dielectric measurement
and models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
A.10 Ballaine Road-1 samples with corresponding organic soil dielectric measurement
and models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
A.11 Scottie Creek-1 samples with corresponding organic soil dielectric measurement
and models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
A.12 8-Mile Lake-1 samples with corresponding organic soil dielectric measurement and
models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
B.1 Timeline of research activities during Ph.D. program. Timeline is shown after
filtering a 1-year moving averaging windowing. The overall time commitment for
this dissertation is around 60% of the total time that was spent on various projects. 246
xxx
List of Algorithms
1 Data acquisition workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
xxxi
Abbreviations
AAC ABoVE Airborne Campagin
ABoVE Arctic Boreal Vulnearbility Experiment
ABR Arctic Boreal Region
AirMOSS Airborne Microwave Observatory of Subcanopy and Subsurface
ALT active layer thickness
BR Ballaine Road
CALM Circumpolar Active Layer Monitoring
CF Creamers Field
DBA Differntial Born Approximation
EM Electromagnetics
EML Eight Mile Lake
FB Franklin Bluffs
GPR Ground Penetrating Radar
GRSS Geoscience and Remote Sensing Society
HV Happy Valley
ICC Ice Cut
IMN Imnavait Creek
LOI Loss on Ignition
MiXIL Microwave Systems, Sensors, and Imaging Lab
NASA National Aeronautics and Space Administration
NEE Net Ecosystem Exchange
NLCD National Land Cover Database
xxxii
NTSG Numerical Terradynamic Simulation Group
OLT Organic Layer Thickness
OM Organic Matter
PolSAR Polarimetric Syntethic Aperture Radar
PTF Pedo Transfer Functions
RB Root Biomass
RMSE Root Mean Square Error
RZSM root zone soil moisture
SA Simulated Annealing
SAR synthetic aperture radar
SC Scottie Creek
SEBCM Stabilized Extended Boundary Condition Method
SGW Sagwon
SM Soil Moisture
SOC Soil Ogranic Carbon
SoilSCAPE Soil moisture Sensing Controller and oPtimal Estimator
SOM Soil Organic Matter
SPM Small Perturbation Method
SSURGO Soil Survey Geographic Database
SW Saturation Water
SWRC Soil Water Retention Curve
TE Terrestrial Ecology
TFS Toolik Field Station
UAF Univeristy of Alaska Fairbanks
UAVSAR Unmanned Aerial Vehicle Synthetic Aperture Radar
USC University of Southern California
USDA United States Departement of Agrictulture
xxxiii
Abstract
This dissertation comprises two parts. In part I, a detailed investigation of physics-based computational radar remote sensing models is conducted for mapping the soil organic carbon in permafrost
landscape using long-wavelength airborne polarimetric synthetic aperture radars. Part II delves
into microwave sensors and imaging techniques, which enable a non-destructive approach for
characterizing the dielectric properties of heterogeneous materials such as highly organic soil.
Chapter 1, provides a high-level introduction to the entire dissertation and discusses the motivations, objectives, and broader contribution of this work.
Part I covers chapter 2 to chapter 7. Initially, in chapter 2, we discuss motivations and details of
the recent status of remote sensing research in the Arctic and permafrost landscape, and particularly
we examine physics-based computational remote sensing for characterizing subsurface. Chapter 3
addresses the first element in forward-centric physics-based remote sensing, where a detailed profile
modeling is provided to establish a process-based understanding of the subsurface drivers of the
ecosystems (e.g., soil organic matter and soil moisture) that control radar signals. Chapters 4 and
5, subsequently address two major elements for developing a coupled hydrologic-electromagnetic
framework for modeling organic soil dielectric behavior in the Arctic. Chapter 6, provides an
end-to-end retrieval framework, with a detailed and comprehensive assessment of the retrieval
performance analysis in simulated and actual radar data. The major outcome of chapter 6 is a map
of soc generated from the ABoVE airborne campaign time-series P-band acquisition across the
thaw season in the North Slope of Alaska. Finally, chapter 7 provides a conclusion where the main
contribution of part I is described through the “radar ecology” a field that attempts to understand
terrestrial ecosystems through physics-based computational modeling and linking of the field scale
processes to the radar response.
Part II covers chapters 8 to 10. Initially, in chapter 8 we discuss the application of microwave
imaging systems in medical imaging and then we broadly discuss the advantages of microwave
imaging and sensor design in non-destructive characterization of the Arctic organic soil. Chapter 9
discusses various details on the design and fabrication of a multi-static multi-frequency imaging
system and its various subsystems for the purpose of soil dielectric imaging. The detailed experiment
was described along with compressing microwave signal analysis and preliminary imaging results.
Finally, chapter 10 discusses ongoing and future work on the microwave imaging of Arctic organic
soil.
xxxiv
Chapter 1
Overview of the Dissertation
1.1 Introduction
Soil and its associated subsurface processes are in the ‘front-line’ of global/regional environmental
changes [1]. Soil moisture and soil organic carbon are the fundamental subsurface properties that
govern water, energy, and carbon cycles and enable a better understanding of the role of land in
the Earth system. Soil moisture and soil organic carbon measurements on local, regional, and
global scales contribute to many areas of human interest such as weather and climate forecasting,
drought analysis, crop productivity evaluation, and human health [2]. A deeper understanding of the
climate-driven dynamics of terrestrial ecosystems, water, and carbon cycles is vital for integration
into policy decisions about the management of water resources and carbon in a warming world.
Tracking bio-/geophyiscal parameters such as soil moisture (SM) and soil organic carbon (SOC)
variabilities and their interaction with the climate system through a combination of computational
models, remote sensing, and field campaigns is key in coming years.
Specifically, satellite and airborne remote sensing allow real-time and large-scale monitoring
and produce a rich variety of data at periodic intervals. Detailed physics-based remote sensing
models that rely on the understanding of electromagnetic (EM) wave interactions with surface/subsurface can be used to extract immense information about bio/geophysical parameters, their spatial
distribution at different scales, and their evolution over time from these observations.
The overarching theme of this dissertation is “physics-based computational” approaches that
help quantify the underlying key processes in soils by linking their observed physical and chemical
properties to the associated electromagnetic, hydrological, and thermal properties. Additionally,
understanding the ecosystem dynamics in an era of rapid climate change requires new “sensor
technologies” that enable novel measurement concepts in service of multi-physics approaches.
The primary focus on new sensor development is bench-top setups that can be used in controlledenvironment experiments for characterizing and understanding soil microwave behavior.
While the physics-based approach and sensor developments for understanding biogeophysical
parameters can be applied to various ecosystem types, the primary focus of the application in this
dissertation concerns northern high latitudes and particularly the Arctic permafrost regions. This
dissertation is therefore comprised of two parts. In part I physics-based computational models are
advanced to seek insights into the characteristics of highly organic soil in Arctic permafrost using
long wavelength radars. In part II, we shift our focus from a macro scale (radar remote sensing) to
a microscale (microwave imaging), where microwave imaging techniques are advanced to better
understand the controlled response of highly organic Arctic soils’ microwave behavior.
1
1.2 Motivation
1.2.1 Part I: Physics-Based Computational Radar Mapping of SOC in
Arctic Permafrost
Soil Ogranic Carbon (SOC) and Soil Moisture (SM) observations are very sparse in the northern
higher latitude, where there is a prevalence of permafrost. Yet these parameters are among the most
needed information to better project the future of the Arctic ecosystem in the era of rapid climate
change [3]. The NASA Terrestrial Ecology (TE) program seeks to “strengthen the theoretical and
scientific basis for measuring Earth sub/surface properties using reflected, emitted and scattered
electromagnetic radiation.” To this end, TE runs a decadal field campaign Arctic Boreal Vulnearbility
Experiment (ABoVE) within the Arctic Boreal Region (ABR) of Alaska and Northwest Canada [4].
Airborne science is the key in this study and through the ABoVE Airborne Campagin (AAC)
an area of 4 million km2 of ABR was surveyed to sample diverse critical ecosystems, gradients,
and bioclimatic zones [5]. AAC provides foundational datasets, particularly radar backscattered
measured by the P- and L-band Polarimetric Syntethic Aperture Radar (PolSAR), which enables
study of the spatiotemporal distribution of permafrost properties at a large regional scale.
Physics-based forward-centric retrieval methods have the potential to study the soil organic
carbon and soil moisture using PolSAR data. Accurate characterization of the organic horizon
(in conjugation with below-ground biomass) is a necessary step for accurately linking the surface
and subsurface processes within the permafrost active layer in the ABR to the corresponding radar
measurement. This characterization can be conducted in two manners, first by understanding the
physics of active layer organic soil and the behavior of soil moisture and organic matter through
the profile. Additionally, an accurate dielectric model is required that represents organic soil at
P- and L-band behavior with various amounts of organic matter and mineral soil. The interest in
developing an organic soil dielectric model stems from the observation that existing models have a
limited validity range as far as organic matter and volumetric soil moisture are concerned.
The main challenge in the modeling is the dielectric properties of water in the soil, which
has been conveniently treated as an optimization variable to fit dielectric models to measurement.
The hydrological properties of water in soil have indicated a promising physics-based framework
that enables characterizing the dielectric behavior of water in soil. However, currently, a lack
of simultaneous measurement of soil hydrological and dielectric properties has limited further
experimental investigation as well as model development. The significance of such an approach,
not only synergizes the modeling activity on the fundamental physics of both disciplines but also
enables a broader area of research in Earth and radar science.
Once the physics of the sensor (PolSAR) response is constructed by understanding subsurface
profile behavior and organic soil dielectric behavior, an electromagnetic scattering model closes
the loop by relating those processes to the corresponding radar backscattering measurement. The
ultimate goal in part I of this dissertation is to develop and advance the physics-based computational
framework that enables mapping SOC from long-wavelength radars. To that end, a detailed analysis
is required to construct a time-series remote sensing framework that combines multiple radar
snapshots across the thaw season in Alaska to arrive at the radar-driven SOC maps.
2
1.2.2 Part II: Microwave Sensors for Dielectric Imaging of Arctic Organic
Soil
The microwave characterization of organic soil has been traditionally conducted with instruments
that were designed for less heterogeneous soil such as mineral type. Microwave imaging provides
an alternative modality, where the dielectric properties of matter can be imaged through a nondestructive method. The significance of such an approach relies on physics-based inverse scattering
methods where through novel differential imaging methods the complex dielectric properties of the
target under test can be characterized.
In part II of this dissertation, we discuss a novel multi-static microwave imaging setup that
achieves multi-frequency observations at P-, and L-bands similar to the operation frequency of
the state-of-the-art radar systems such as Airborne Microwave Observatory of Subcanopy and
Subsurface (AirMOSS), and Unmanned Aerial Vehicle Synthetic Aperture Radar (UAVSAR) that
flew by AAC. Various reference materials are tested to show the performance of the instrument
under a controlled environment and detailed long-term soil dielectric imaging is conducted. In part
II of this dissertation, we suffice to show the experiment setup and preliminary results, while we
leave the final results to our ongoing and future work.
1.3 Objectives
1.3.1 Objectives of Part I
The purpose of the part I of the dissertation is to initially develop a physics-based computational
framework for retrieving the soil organic carbon on a regional scale using the backscattered radar
data acquired from AirMOSS through the AAC. Besides the initial goals defined in this dissertation,
an additional co-product of this work consists of capabilities to map root zone soil moisture (RZSM)
as well as to detect the freeze/thaw effect in the late season.
In part I of this dissertation we maintain the focus on SOC retrieval in permafrost active layer,
therefore we will focus on the following three topics:
I-1 Develop a profile model to characterize the 1-D soil moisture and organic matter behavior in
permafrost active layer using in-situ and field observations
– To simplify the problem, the focus will be North Slope of Alaska, where the vegetation
is dominated by Tundra
I-2 Develop a coupled hydrologic-electromagnetic organic soil dielectric model through simultaneous characterization of hydrological and dielectric properties of organic soil
– Use commercially available sensors, including porous disk probes, and dielectric capacitive probes to conduct measurement and model development
– Detailed soil process parametrization, and introducing the root biomass as a new parameter in modeling
3
I-3 Developing an end-to-end retrieval framework based on time-series P-Band observations acquired from the NASA ABoVE campaign to map soil organic carbon profile in the permafrost
active layer
– Focusing on five foundational flight lines in the North Slope, which has the most ground
truth data
1.3.2 Objectives of Part II
The secondary purpose of this dissertation is to understand the microwave behavior of Arctic soil in
a controlled environment by designing a novel microwave imaging suitable for dielectric mapping
of heterogeneous materials such as highly organic Arctic soil in a non-destructive way.
In part II of this dissertation, we maintain the focus on the system development and preliminary
system test. The ultimate objectives can be listed as follows:
II-1 Design a multi-band multi-static dielectric imaging station that enables the microwave behavior of organic soil
– Use Differntial Born Approximation (DBA), to simplify the imaging problem by leveraging a known geometric shape, and background.
1.4 Contribution
The major contributions of this dissertation and corresponding published products or products in
preparation can be listed as follows:
1.4.1 Contributions of Part I
Objective I-1 represents a new contribution because the detailed characterization of active layer
soil reveals new information to model the soil properties profile behavior. These characteristics
have been traditionally overlooked in the Earth system science community due to the fundamental
difference in stratification approaches that are developed for coupled thermo-hydrological models
compared to electromagnetic scattering methods in radar science. Following are the status of the I-1
products.
I-1-1 Published Article [6]: K. Bakian-Dogaheh et al., ”A Model to Characterize Soil Moisture and
Organic Matter Profiles in the Permafrost Active Layer in Support of Radar Remote Sensing
in Alaskan Arctic Tundra,“ Environmental Research Letter, vol. 17, no. 2, 2022.
I-1-2 Published Dataset [7]: K. Bakian-Dogaheh et al., ”ABoVE: Active Layer Soil Characterization
of Permafrost Sites, Northern Alaska, 2018“ ORNL DAAC, 2020.
Objective I-2 for the first time provides a joint measurement of both hydrological (matric potential)
and electromagnetic (dielectric permittivity) of Arctic organic soil for a large pool of samples.
In-depth physics-based modeling that leverages both hydrological and electromagnetic perspectives
enables detailed organic soil modeling along with a comprehensive physics-based understanding of
water’s dielectric behavior in organic soil. Following is the status of the I-2 products.
4
I-2-1 Prepared Article 1
: K. Bakian-Dogaheh et al., ”Empirical Models for Predicting Soil Water
Dielectric Behavior Using Hydrologic Properties of Permafrost Soils,“
I-2-2 Published Dataset [8]: K. Bakian-Dogaheh et al., ”Soil Matric Potential, Dielectric, and
Physical Properties, Arctic Alaska, 2018“ ORNL DAAC, 2023.
I-2-3 Article in Review 2
: K. Bakian-Dogaheh et al., “Coupled Hydrologic-Electromagnetic
Framework to Model Permafrost Active Layer Organic Soil Dielectric Properties”
Objective I-3 presents the end-to-end physics-based computational framework using time-series
P-band SAR, which is completely novel and has never been studied nor investigated before. The
resulted SOC maps are among the first-ever reported maps of SOC using airborne SAR, and
potentially can be used for mapping and monitoring SOC stock and dynamics in the Arctic using
future satellite missions. While not mentioned here a major sub-product of this work is the
algorithm’s capability to detect the Freeze/Thaw by leveraging the rich time-series P- and L-band
data as well as the in-depth interpretation of the signal using physics of sensors. As part of the
SOC map assessment, the most updated and comprehensive in-situ SOC was also compiled which
encompasses 30 years’ worth of data across the North Slope of Alaska. A partial list of the product
for objective I-3 is listed below:
I-3-1 Submitted Draft 3
: K. Bakian-Dogaheh et al., “Soil Carbon Distribution in Arctic Tundra via
P-Band, Physics-Based Computational Mapping ”
I-3-2 Dataset in Prepration 4
: K. Bakian-Dogaheh et al., ”Soil Organic Carbon, Soil Moisture, and
Freeze/Thaw Properties from AirMOSS P-band SAR in Alaskan Tundra“
1.4.2 Contributions of Part II
Objective II-1 is a novel approach and a new instrument to characterize the dielectric behavior of
materials in a non-destructive way including organic soil. None of the traditional soil dielectric
measurements are based on dielectric imaging techniques. A list of the product for objective II-1 is
listed below
II-2-1 Draft in Preparation: K. Bakian-Dogaheh et al., “Microwave Dielectric Behavior of the Arctic
Organic Soil a Non-Destructive Approach-Part I: Instrument Performance”
II-2-2 Draft in Preparation: K. Bakian-Dogaheh et al., ”“Microwave Dielectric Behavior of the
Arctic Organic Soil a Non-Destructive Approach-Part II: Organic Soil Dielectric Modeling“
1
Initial draft submitted on 08/18/2022, rejected on 01/10/2023. A redraft is in preparation for resubmission as of
12/03/2024.
2
Initial draft was submitted on 01/19/2027, and has been through 3 review rounds as of 10/30/2024.
3
Initial draft ready for submittion as of 11/15/2024
4Additional ongoing processing for non-North Slope flight lines as of 12/03/2024
5
Part I
Physics-Based Computational Radar Mapping
of SOC in Arctic Permafrost
6
Chapter 2
Introduction to Part I
In this chapter, we provide a general background on the physics-based computational framework
for retrieving subsurface geophysical properties of the Arctic using radar remote sensing. In particular, we will elaborate on the characteristics of water and carbon cycle in permafrost landscapes,
microwave remote sensing principles, and physics-based radar retrieval building blocks. We further
review the previously developed forward models for physics-based radar retrieval of subsurface
properties in temperate and permafrost-affected sites. We then briefly review metaheuristic global
optimization methods as the inverse solver. Finally, we discuss the objectives of part I and how we
can relate the subsurface processes that capture soil organic carbon and soil moisture information to
the radar response. The bulk of the remaining chapters will be focused on addressing each element
of a new forward model that plays a critical role at the heart of physics-based computational models
in mapping SOC in the Arctic permafrost region.
2.1 Water and Carbon Cycle in Permafrost Landscape
Permafrost is a widespread subsurface feature that underlain ∼ 25% of the northern hemisphere
exposed land surface [9]. Permafrost refers to the frozen ground that remains at or below ◦C
for at least two consecutive years, which is overlain by the active layer that freezes and thaws
seasonally as shown in Fig. 2.1a. The low temperature and abundance of soil moisture within the
northern circumpolar region led to an accumulation of organic matter due to slow decomposition
rates. Upscaling estimates that, up to half of global soil organic carbon is stored in permafrost
landscapes as illustrated in Fig. 2.1b [10, 11]. In the last 3 decades Arctic has been experiencing an
unfolding increase in temperature about twice the global average [12,13]. This warming trend could
potentially thaw the sequesterd soil organic carbon SOC, which in turn the SOC could be released
as CH4 or CO2 gases into the atmosphere under anaerobic (saturated) or aerobic (unsaturated) soil
respiration [14, 15]. Another dominant feature of the Arctic is the abundance of wetlands, which is
caused by shallow water table depth due to the perennially frozen layer, which blocks vertical water
movement as shown in Fig. 2.2a [16–18]. Thus, in addition to the impact of increasing temperatures,
soil moisture variability also plays a major role in the loss of carbon from the permafrost SOC to
the atmosphere [19]. In a recent study, land surface modelers prioritized soil organic carbon and
soil moisture as key variables (Fig. 2.2b) for studying Arctic ecosystem dynamics in a changing
7
(a) (b)
Figure 2.1: (a) The layers of permafrost [20]. (b) Soil organic carbon content to a depth of 1 m
adapted from Northern Circumpolar Soil Carbon Database [21]
climate [3]. However, the vastness, remoteness, and harsh environment in the Arctic region have led
to sparse sampling and often incomplete and poorly constrained carbon inventory and sporadic soil
moisture information [22, 23].
In short, the challenges for studying the water and carbon cycle dynamics in permafrost encompass the poor constraint, lack of accuracy, and sparsity of the soil moisture and soil organic matter
information from a spatial and temporal resolution standing point as well as the coverage in the
local and regional scales. Different methods have been used that provide monitoring and predicting
capabilities to acquire information on the permafrost changes on various scales as shown in Fig. 2.3.
On a local scale, the soil moisture information can be collected at permanently installed sites with
near-real-time data at several depths within the active layer. Additionally, in-situ measurement
and sampling conducted during a field campaign can provide a snapshot of organic matter and soil
moisture on a local scale [6, 24]. These field observations can often be used to better understand
and characterize the subsurface, which can be applied to radar remote sensing. On a regional scale,
microwave remote sensing can be used, where the subsurface properties such as soil moisture and
organic matter can be inferred from the dielectric properties of the subsurface, roughness height, and
overall interaction of the electromagnetic waves with inhomogeneous subsurface, which impacts
the acquired radar backscattered signal. While field and radar measurements provide direct and
indirect techniques to monitor the permafrost characteristics, respectively, Earth system models can
be used to predict the future response of the permafrost landscape.
The bulk focus of this work is centered around a regional scale study, where we learn from field
observation to develop and use microwave and radar remote sensing models and principles to study
subsurface water and carbon characteristics in permafrost landscapes.
8
(a) (b)
Figure 2.2: (a) The thaw gradient of active layer [18]. (b) The key variables in studying Arctic
responses to climate change are the soil carbon and soil moisture
2.2 Microwave Remote Sensing Principle
The complex (real and imaginary) dielectric permittivity of soil is governed by soil texture including
organic and mineral fractions, and is primarily sensitive to the soil moisture content in the microwave
regime. Microwave sensors encompass passive and active systems and both can capture the surface
and subsurface soil moisture variation. Passive sensors such as radiometers are highly sensitive
receivers that measure microwave thermal emission of soils, which incorporates the contribution
of electromagnetic scattering response of the soil and its surface and subsurface and the soil
temperature. The Electromagnetics (EM) scattering of soils primarily is controlled by the soil
roughness height and dielectric permittivity. The active microwave sensors, and particularly the
PolSAR imager consist of a transmitter and a receiver that measures the scattering response of a
target as shown in Fig. 2.4. Radars illuminate (⃗E
i
) the environment with microwaves (2.1), and the
environment responses (⃗E
s
) through the complex scattering matrix (Spq), which is dependent on the
geometry, dielectric permittivity profile, and the roughness height of the area of interests, and the
polarization of incident wave (h, v) as shown in (2.4).
9
Figure 2.3: The scaling diagram for environmental monitoring, redrawed and modified from the
original design “Leaf to Orbit” credit: Piers Selters, and ABoVE.
(a) (b)
Figure 2.4: (a) Electromagnetic wave interaction with a target, including incident and scattering
mechanism. (b) Airborne PolSAR measurement in the Arctic and schematic of permafrost active
layer.
10
The incident field can be decomposed into horizontal and vertical polarization
⃗E
i
(⃗r) = ⃗E
i
0
e
ik0
ˆki
.rˆ
(2.1)
where k0 represents the wave number in free space, ˆki shows the direction of propagation, and ⃗E
i
0
denotes the fields in the plane prependicular to ˆki and consist of two components:
⃗E
i
0
.
ˆki = 0 (2.2a)
hˆ
i =
ˆki ×zˆ
|
ˆki ×zˆ|
(2.2b)
vˆi = hˆ
i × ˆki (2.2c)
where hˆ
i
is the horizontal unit vector and is defined parallel to x-y, and perpendicular to ˆki
, and vˆi
shows the vertical unit vector perpendicular to both hˆ
i and ˆki
. The unit vectors for the incident field
can be decomposed into the cartesian coordinate as follows:
ˆki = sin(θi)cos(φi)xˆ+sin(θi)sin(φi)yˆ+cos(θi)zˆ (2.3a)
hˆ
i = sin(φi)xˆ−cos(φi)yˆ (2.3b)
vˆi = −cos(θi)cos(φi)xˆ−cos(θi)sin(φi)yˆ+sin(θi)zˆ (2.3c)
where θi and φi determine the angles of the direction of propagation once projected into the x-y-z
coordinates, and accordingly, the incident field can be written as follows:
⃗E
i = E
i
h
hˆ
i +E
i
v
vˆi (2.4)
Similar decomposition can be applied to the scattered field as follows:
ˆks = sin(θs)cos(φs)xˆ+sin(θs)sin(φs)yˆ+cos(θs)zˆ (2.5a)
hˆ
s = sin(φs)xˆ−cos(φs)yˆ (2.5b)
vˆs = −cos(θs)cos(φs)xˆ−cos(θs)sin(φs)yˆ+sin(θs)zˆ (2.5c)
where index s denotes the scattered field.
⃗E
s = E
s
h
hˆ
s +E
s
v
vˆs (2.6)
As mentioned above, the Scattering matrix (S) is a complex matrix that relates the incident field to
the scattered field and contains the geophysical properties of a remotely sensed target.
E
s
h
E
s
v
= (e
ik0r
r
)
Shh Shv
Svh Svv E
i
h
E
i
v
(2.7)
11
Incorporating the physics of the electromagnetic wave interaction with the polarimetric (pq :
hh, vv, hv, vh) radar equation we can show:
P
r
p =
G
2λ
2P
t
q
(4π)
3R4
σpq (2.8)
where the received power for polarization p due to transmitting at q polarization Ppq
r
, is related to
the gain of the transmit and receive antenna G, radar operation wavelength λ, distance R, transmit
power P
t
q
and the backscattering coefficient of the target σpq. The radar backscattering coefficient is
a measure of the unit are [m
2
] and shows how detectable a target is by radar and varies as a function
of frequency, polarization, incident angle, and target dielectric properties and is defined as the ratio
of the scattered power over the incident power:
σpq = limR→∞(4πR
2
|E
s
p
|
2
|Ei
q
|
2
) (2.9a)
σpq = 4π|Spq|
2
[m
2
] (2.9b)
For a distributed target, which extends beyond the radar’s beamwidth, the radar equation must be
integrated over the target area such as:
P
r
p =
Z Z G
2λ
2P
t
q
(4π)
3R4
σ
0
pqdA (2.10)
The average value of a radar backscatter coefficient of a distributed target is shown as the normalized
backscattering coefficient and can be written as follows:
σ
0
pq =
σpq
A
(2.11)
In other words, the normalized backscattered coefficient (σ
0
pq) for each polarization (pq :
hh, vv, hv, vh) in a radar measurement includes information on the surface and subsurface electromagnetic properties, which mainly manifests itself as soil dielectric properties (2.12) [25].
σ
0
pq ∝ |Spq|
2 ∝ target properties (2.12)
In this work, we utilize the radar instruments known as AirMOSS and UAVSAR that operate at Pand L-bands (Table. 2.1)respectively, by National Aeronautics and Space Administration (NASA)
and flew over the Alaskan Arctic and Boreal Region as part of the ABoVE Airborne Campaign
(AAC) as shown in Fig. 2.5.
12
Figure 2.5: ABoVE airborne campaign study area, which consists of a gradient of critical bioclimatic
zones in the Arctic. Flight lines (denoted by orange transects) comprised of multi-year P-band and
L-band PolSAR acquisition from the pre-ABoVE era (2014, and 2015) to intensive sampling years
in 2017 and more recently in 2018, 2019, 2022, and 2024. The P-band acquisition in 2017 within 5
flightlines in the North Slope of Alaska (A1) is used for SOC mapping in this work. The blue boxes
refers to Alaskan (A1-A4) and Candian (C1-C6) regions [5, 26].
Table 2.1: The operation frequency of radar instruments that flew as part of AAC
Band Frequency
(GHz)
Bandwidth
(MHz)
P 0.430 20
L 1.2575 20, 40, 80
2.3 Physics-Based Computational Radar Retrieval Cycle
The measured backscattered signal (σhh, σvv) acquired through AAC then will be applied into
a physics-based computational radar retrieval cycle as shown in 2.6 to retrieve the surface or
subsurface bio/geophysical parameters (Partial list is shown in Table 2.2). The algorithms start with
an initial guess of the state parameters to characterize the subsurface bio/geophysical properties,
these properties then will be used in a Forward Model to arrive at the electromagnetic properties
of the subsurface with the help of ancillary data layers such as soil mineral texture or temperature.
Finally, the estimated backscattering coefficients derived from the forward model will be compared
with the radar observations in iterative inverse solvers, and this cycle will be continued until it
reaches the minimum error in the cost function.
13
Figure 2.6: Physics-based computational radar retrieval cycle, which relates the field-scale parameters that govern key processes in the terrestrial ecosystem (e.g., water and carbon cycle) to
corresponding radar measurement. The exit point ultimately links the radar observation to ecosystem
state parameters by satisfying the inverse model stopping criteria.
Table 2.2: List of land surface or subsurface parameters(X¯)
Parameters Definition Notation Unit
Soil Moisture θ (cm3/cm3
)
Soil Saturation SW (cm3/cm3
)
Organic Matter OM (g/g)
Bulk Density ρb (g/cm3
)
Porosity φ (cm3/cm3
)
Sand Fraction S (g/g)
Clay Fraction C (g/g)
Active Layer Thickness zALT (cm)
Soil Roughness Height h (cm)
Soil Permittivity ε˜ = ε
′
r +iε
′′
r
(−)
2.3.1 Contiguous US Temperate Sites
The forward-model centric retrieval methods have been previously proposed to retrieve the soil
moisture profile model parameters for temperate sites within the contiguous US as part of AirMOSS
mission [27, 28]. The retrieval cycle (Fig.2.7) starts with estimating the quadratic soil moisture
profile model parameters. The mineral soil is the dominant feature of the temperate sites and has
been studied extensively in those sites and is available in various soil texture databases such as
Soil Survey Geographic Database (SSURGO). Consequently, by incorporating the texture map,
which includes the Sand (S), Clay (C), and bulk density (ρb) and the estimated soil moisture
profile (θ(z)) into the Peplinski’s well established mineral soil dielectric model [29] we arrive at
soil dielectric permittivity profile. The calculated soil dielectric profile then will be discretized
into a multi-layered dielectric structure and applied into an EM scattering forward model to find
14
the corresponding backscattering coefficient from estimated subsurface parameters [30]. The soil
roughness information in the AirMOSS mission retrieval was assumed to be known from field
observation for each land cover type, and the incidence angle (θˆ
inc) was also known for each radar
pixel. Finally a cost function was formed and through an iterative global optimizer (simulated
annealing) the soil moisture profile parameters were estimated [31].
Figure 2.7: AirMOSS mission P-band retrieval cycle schematic for temperate sites, which uses a
single snapshot of P-Band pplsar measurement.
2.3.2 Permafrost Sites
The initial AirMOSS mission took advantage of the well-established soil texture maps along with
existing mineral soil dielectric model to construct a fully physics-based radar retrieval framework
to arrive at subsurface soil moisture profile by using P-band backscattered data. A follow-up and
pathfinder project was conducted under the NASA Interdisciplinary Research in Earth Science (IDS)
for regional mapping of soil conditions in northern Alaska permafrost landscapes using AirMOSS
and land model data assimilation. The study aimed to produce the first-ever microwave remote
sensing-based maps of soil profile characteristics in Alaska permafrost landscapes by using a time
series of airborne P-band PolSAR. However, unlike the temperate site, the northern higher latitude
15
is dominated by the high organic matter content, and the lack of a delineated subsurface profile
model, poorly characterized soil databases, and lack of a well-established organic soil dielectric
model prevented a fully physics-based radar retrieval for profile characterization. Thus instead of
subsurface soil physical properties such as soil moisture, the retrieval algorithm aimed to retrieve
the dielectric properties and depth of each layer directly as shown in Fig. 2.8 [32].
Figure 2.8: Time-series P-band retrieval cycle schematic for permafrost landscape that uses August
and October snapshots with active layer stagnation assumption.
The cost function in time-series study of the permafrost combines two snapshots of PolSAR
acquisitions in August and October. With the assumption of negligible variation in the active layer
thickness (z2) between August and October (stagnation period), the only time-variant variables
in each radar pixel will be the water table depth z
Oct
1
, z
Aug
1
, while assuming the saturated and
unsaturated zone maintain similar dielectric constant.
2.4 Forward Model
2.4.1 Contiguous US Temperate Sites
The AirMOSS mission forward model is shown in Fig. 2.9, which as explained above consists
of: 1) a soil moisture profile model, 2) mineral soil dielectric model, and 3) electromagnetic
scattering model. The soil moisture profile model was developed based on detailed field and in-situ
observation of soil moisture [33]. Initially a quadratic function has been suggested to model the
soil moisture behavior, however, a follow-up work has suggested a more realistic model by using
Richard’s equation [34]. The mineral soil dielectric has been studied comprehensively since the
early 80s. Peplinski’s model accepts soil moisture, sand, clay, bulk density, and frequency as input,
and arrive at equivalent complex dielectric permittivity of the soil. EM scattering from random
rough surfaces has been also studied widely in the past few decades and a number of analytical,
16
semi-analytical, and numerical methods were developed to calculate the scattering coefficient in
backward or forward directions. In the initial AirMOSS mission a multi-layer analytical approach
known as Small Perturbation Method (SPM) has been chosen, which relies on assuming relatively
small roughness height [30, 35]. Follow-up methods have suggested more advanced scattering
mechanisms such as Stabilized Extended Boundary Condition Method (SEBCM), which consists
of semi-numerical approaches [36]. However, due to complexity and computation time, and also
validity of SPM for the AirMOSS mission was chosen.
Figure 2.9: AirMOSS forward model developed for roo zone soil moisture retrieval a single polsar
snapshot.
2.4.2 Permafrost Sites
As discussed above, in microwave remote sensing of permafrost active layer soils, neither soil
moisture nor organic matter profiles have been quantified to capture the large variations of these
parameters within the short vertical distance of the active layer, additionally, the existing understanding of organic soil dielectric behavior was very limited. Therefore, instead of soil profile modeling
the subsurface geometry was modeled based on an unsaturated, saturated, and frozen layer. The aim
of this model is mainly to study the variation of water table depth between August and October, as
well as to retrieve the active layer thickness.
2.5 Global Optimization Methods
Once the forward model generates the simulated backscattered coefficients from the initial guess,
the results will be compared with measured radar signals and the optimizer will decide on the next
guess based on stopping criteria. In the previous works, for both the AirMOSS mission, and IDS
project the optimizer was based on the simulated annealing method, and the Corona algorithm [31].
17
Figure 2.10: Time-series permafrost soil retrieval forward model developed for active layer thickness
retrieval in August and October, with stagnation assumption.
Furthermore, various methods such as time-series or spatial constraints could be considered to
relax the ratio of measurement and unknown parameters in the inverse problem. In the initial
AirMOSS mission, the subsurface parameters include the soil moisture profile models, which
results in 2 measurements v.s 3 unknowns (2.13). For the permafrost remote sensing the subsurface
parameters in August and October were the unknowns, which resulted in a total of 7 unknown v.s. 4
measurements (2.14).
AirMOSS Temperate Sites :
Radar Data : [σhh, σvv]
State Parameters : [a,b, c]
Ancillay Data : [S, C, ρb]
(2.13)
AirMOSS Perma f rost Sites :
Radar Data : [σ
Aug
hh , σ
Aug
vv , σ
Oct
hh , σ
Oct
vv ]
State Parameters : [z
Aug
1
,z
Oct
1
,z2, ε
Aug
1
, ε
Oct
1
, ε2,h]
Ancillay Data : [−]
(2.14)
2.6 Physics-Based Computational Radar Mapping of SOC
The comparative literature review provided in the previous sections shows the importance of soil
organic carbon and soil moisture as key subsurface parameters in understanding the water and
carbon cycle in the Arctic ecosystem. The previous studies also identify the major research gaps in
18
physics-based computational models for mapping SOC and SM using long-wavelength radars. In a
broad sense, a process-based understanding of the ecosystem drivers (such as SOC and SM) that
can be captured by time-series radar observation does not exist. More particularly, the main area of
investigation is advancing the forward model as shown in Fig. 2.11, which is comprised of three
elements: 1) Subsurface Profile Model, 2) Organic Soil Dielectric Model, and 3) Electromagnetic
Scattering Models. Once the forward model is established, the end-to-end framework has to be
tested for simulated data and eventually actual time-series radar data acquired from AAC. Therefore
a detailed investigation is needed for construting a time-series P-band observations of SOC.
Figure 2.11: Forward model for physics-based computational radar retrieval of soil organic carbon
in permafrost, using three snapshots (June, August, and October) across the thaw season in Alaska.
Therefore the objectives of Part I can be listed as follows:
I-1 Develop a profile model to characterize the 1-D soil moisture and organic matter behavior in
permafrost active layer using in-situ and field observations
I-2 Develop a coupled hyrdologic-electromgantic organic soil dielectric model through simultaneous characterization of hydrological and dielectric properties of organic soil
I-3 Devleoping and end-to-end retrieval framework based on time-series P-Band observation acquired from the NASA ABoVE campaign to map soil organic carbon profile in the permafrost
active layer
19
Chapter 3
Subsurface Profile Model
Disclaimer: The content of this chapter is adapted in large from the following papers:
I-1-1 Published Article [6]: K. Bakian-Dogaheh et al., ”A model to characterize soil moisture and
organic matter profiles in the permafrost active layer in support of radar remote sensing in
alaska arctic tundra,“ Environmental Research Letter, vol. 17, no. 2, 2022.
I-1-2 Published Dataset [7]: K. Bakian-Dogaheh et al., ”ABoVE: Active Layer Soil Characterization
of Permafrost Sites, Northern Alaska, 2018“ ORNL DAAC, 2020.
Organic Matter (OM) content and a shallow water table are two key variables that govern the
physical properties of the subsurface within the active layer of arctic soils underlain by permafrost,
where the majority of biogeochemical activities take place. A detailed understanding of the soil
moisture and OM profile behavior over short vertical distances through the active layer is needed to
adequately model the subsurface physical processes. To observe and characterize the profiles of
soil properties in the active layer, we conducted detailed soil sampling at five sites along Dalton
Highway on Alaska’s North Slope. These data were used to derive a generalized logistics function to
characterize the total OM and water saturation fraction behavior through the profile. Furthermore, a
new pedotransfer function was developed to estimate the soil bulk density and porosity—information
that is largely missing from existing soil datasets—within each layer, solely from the soil texture
(organic and mineral properties). Given the currently sparse soil database of the Alaskan Arctic,
these profile models can be highly beneficial for radar remote sensing models to study active layer
dynamics.
3.1 Introduction
In northern circumpolar regions, it is estimated that 70% of the total carbon (1000 Pg) is stored in
the top 3 m of ground underlain by permafrost [10, 11]. Due to the current warming trends and
the resulting impact on both anaerobic and aerobic soil respiration, the sequestered soil organic
carbon (SOC) in permafrost could be released into the atmosphere as CH4 and CO2 [12, 14, 15].
In addition to the impact of increasing temperatures, soil moisture variability also plays a major
role in the loss of carbon from the permafrost SOC to the atmosphere [19]. In a recent study, land
surface modelers prioritized SOC and soil moisture as key variables for studying Arctic ecosystem
dynamics in a changing climate [3]. Within US soils alone, observational SOC estimated from soil
20
pedon data indicates that Alaskan soil accounts for up to half of the stored total US soil carbon [37]
. However, the vastness, remoteness, and harsh environment in the Arctic region have led to sparse
sampling and an often incomplete and poorly constrained carbon inventory in Alaska [23].
In permafrost regions, almost all biogeochemical activities occur in the active layer, the layer
above permafrost that freezes and thaws seasonally [38].The permafrost table restricts vertical water
flow and maintains a shallow water table and a highly saturated soil across the active layer in the
Arctic. Furthermore, cold temperatures and shallow water tables lead to a low SOC decomposition
rate and subsequently cause an accumulation of high OM content in active layer soils [6]. Pedon
delineation and sampling process designed for permafrost affected soil often collect samples from
representative horizons [39, 40]. The horizon-based sampling results in just a few samples within
the active layer with coarse sampling depths. Therefore, in part, some of the critical processes
associated with variations of organic matter properties over the short vertical distances through the
active layer soil profile might be overlooked [41, 42]. Consequently, a more detailed study of soil
properties is on interest to model the fine-scale vertical profile, more specifically, the OM profile
through the permafrost active layer [43].
Soil moisture variations in the active layer are a primary driver of Arctic carbon exchanges,
active layer thermal conductivity, and energy transfer affecting permafrost stability [44], yet in-situ
soil moisture data in the ABR of Northern America is quite sporadic. In-situ observations have
been collected either at permanently installed sites with near-real-time soil moisture data at several
depths within the active layer or manually during field campaigns [22, 24]. While permanently
installed sensors provide sufficient temporal resolution, they suffer from lack of sufficient spatial
distribution and a limited number of sensors per profile that do not capture active layer fine-scale
dynamics [45–47]. The second observation method, employed during limited field campaigns, uses
a soil moisture probe, ground penetrating radar, and/or gravimetric sampling of soil water content.
While these samples can be taken with high spatial density; the total spatial coverage remains
rather limited. These field campaign measurements are temporarily sparse and comprise single
(or multiple) point(s) measurements in time and space. Furthermore, even the largest available
soil moisture dataset collected within the Alaskan tundra provides only the average values of soil
moisture from probe inserted vertically into the ground in conjunction with Ground Penetrating
Radar (GPR) measurement [48–50]. The challenge still remains, in that there is a lack of fine-scale
vertical profile characterization of soil moisture throughout the active layer.
A major user of fine-scale vertical profile models characterizing OM and soil moisture behavior
through the active layer is the radar remote sensing community. For example, soil moisture
profile models and detailed soil texture maps available for temperate sites within the contiguous
US have been used for retrieval of subsurface soil moisture from airborne low frequency radar
observations [27, 28, 33]. However, in microwave remote sensing of permafrost active layer soils,
neither soil moisture nor SOM profile models have been quantified [32, 46]. Such models could
also be incorporated into land surface models, replacing current approximate SOC profile models
being used in numerical simulations, such as the exponential form used by Yi et al., [51].
The work reported here directly supports the NASA airborne campaigns within the Arctic Boreal
Vulnerability Experiment (ABoVE) [5,26], by providing a detailed experimentally derived model to
describe soil moisture and OM distribution in the active layer soil profiles. We further developed a
Pedo Transfer Functions (PTF) that related soil mineral texture and OM to bulk density and porosity
and can be used to fill the data gap in existing databases, in which critical information such as
bulk density is often lacking [14, 52]. The dataset used in this chapter was obtained in August
21
2018, through a series of field experiments conducted at five tundra sites located along the Dalton
Highway in northern Alaska [7]. The sites are located within two of the AAC flight lines, commonly
referred to as the ‘Deadhorse’, and ‘Toolik’ lines.
3.2 Materials
3.2.1 Sites Description
The Deadhorse and Toolik flight swaths of the AAC (Fig. 3.1) are among the most widely studied
areas in the North Slope of Alaska. The vicinity of the these lines along the Dalton Highway and
the Toolik Field Stations are densely sampled areas and a benchmark for Arctic ecosystem studies.
During the 2018 field survey, we selected five study sites along the Dalton Highways to acquire field
measurements within the airborne synthetic aperture radar (SAR) footprints of the 2017 AAC. The
sites includes Franklin Bluffs (FB), Sagwon (SGW), Happy Valley (HV), Ice Cut (ICC), which are
located within the Deadhorse flight line, and Imnavait Creek (IMN) within the Toolik flight line. The
sites were chosen after close coordination with the ABoVE field scientist. The SGW site was chosen
based on preliminary results from the ABoVE radar science team suggesting an unexpectedly deep
active layer thickness (ALT) in the radar retrievals. The HV site was chosen because of its proximity
to the Univeristy of Alaska Fairbanks (UAF) borehole temperature monitoring systems [53], the
University of Southern California (USC) Arctic Soil moisture Sensing Controller and oPtimal
Estimator (SoilSCAPE) site [46], and Alaska Circumpolar Active Layer Monitoring (CALM)
sites [54]. Also, there had been multiple soil coring efforts in previous years the area. The presence
of multiple eddy covariance flux towers in the IMN site was another factor in choosing the site.
Further consideration and deciding factors for the site (Fig. 3.1 and Table. 3.1) selections involved
capturing a wide range of land cover types and permafrost soil features specifically related to OM
content. The National Land Cover Database (NLCD) map and in-situ observations show that the
IMN site is dominated by tussock graminoid tundra (tussock sedge, dwarf shrub, and moss tundra).
The HV and ICC sites are covered mostly with erect dwarf shrub tundra (low shrub tundra), while
the SGW site is characterized by non-tussock graminoid (non-tussock sedge and dwarf shrub) or
wetland (wet sedge) tundra [55–59].
Table 3.1: Sites name and soil pit locations for the field campaign during August 22-26, 2018
Sites Name Official Name Soil Pit ID Latitude Longitude
FB Franklin Bluffs 1 69◦48′44.54′′ N 148◦45′59.35′′ W
1 69◦28′46.48′′ N 148◦33′51.99′′ W SGW Sagwon 2 69◦28′35.68′′ N 148◦33′51.96′′ W
1 69◦9
′19.28′′ N 148◦50′19.64′′ W HV Happy Valley 2 69◦9
′19.29′′ N 148◦50′30.48′′ W
1 69◦2
′30.82′′ N 148◦49′37.31′′ W ICC Ice Cut 2 69◦2
′32.94′′ N 148◦49′31.38′′ W
IMN Imnavait Creek 1 69◦36′17.90′′ N 148◦18′22.86′′ W
22
Figure 3.1: The location of the five in-situ tundra sites located along the Dalton Highway, on the
Alaskan North Slope, USA. The sites locations fall within two of the AAC flight lines shown on a
regional land cover map NLCD and geographic projection. The land cover categories are adapted
from the NLCD classification.
3.2.2 Field Experiment Design
3.2.2.1 Soil moisture measurement
The in-situ determination of soil moisture content at the study sites was made using direct and
indirect methods. Most conventional indirect methods for in-situ soil moisture measurement are
electroamgnetric techniques that use either capacitive measurement or time domain reflectrometry [60, 61]. These methods, which exploit the relationship between soil dielectric permittivity, soil
moisture, and other physical properties of soil, always need further calibration (via a soil dielectric
mixing model) to translate the measured capacitance or time delay of the permittvity measurement
to the SM content. On the other hand, the direct methods of soil moisture observation rely on field
sampling of moist soil and finding the soil moisture value via oven drying (this is often referred to
as gravimetric water content and is the gold standard).
In this work, we used both measurement types. However in this section we emphasis on the
the direct soil moisture measurement and leave dielectric probing to future chapter. For the direct
soil moisture measurement, two side-by-side (adjacent) soil samples were extracted from each
layer (Fig. 3.2), and wet soil mass was recorded for each sample in the field to measure the in-situ
soil moisture content (θ). The gravimetric soil moisture content was calculated via oven drying
23
(Table.3.2). For the indirect method (dielectric probing) the values of dielectric constant were not
translated into soil moisture because of the need for an organic soil dielectric model, which will be
reported in future chapters.
For dielectric probing, the previous measurement method [48, 50] did not capture the profile
behavior and only provided average information about near-surface or total active layer soil moisture.
Our dielectric measurements were taken along the soil profiles using METER Group’s TEROS
12 sensors [62] and the ProCheck data logger. These sensors operate at 70 MHz and measure the
dielectric permittivity and electrical conductivity. Measurements were taken at multiple discrete
points along the active layer soil profile. Soil pits were dug, and sensors were inserted horizontally
into the soil to collect the measurements (Fig. 3.2). This horizontal sampling was performed along
the inner wall of the soil pits, with a sampling interval of 2.5 cm from the surface down to the top
of the permafrost table, located at the base of the active layer up to 55 cm below the surface at the
tundra sites. This approach provides the opportunity to capture the vertical variations of dielectric
permittivity at a fine resolution throughout the active layer profile, which is not possible in alternate
methods where probes are inserted vertically or at an angle. Furthermore, while vertical sampling
may be faster in a field survey, it only measures the effective dielectric properties along the length
of the probe from the surface, which cannot capture the subsurface features that are observable by
low-frequency radars such as P-band [49]
Figure 3.2: Dielectric permittivity profile characterization and soil sampling protocol, from the
side wall of a soil pit using TEROS 12. Two side-by-side replicate samples were extracted from
each layer. For PTF development, adjacent samples are assumed to be independent, and for profile
modeling, ‘a’ and ‘b’ averaged values are used.
24
Table 3.2: List of soil physical properties and corresponding description of each parameter
Soil Physical
Parameter Symbol Units Description Equation Note
Soil
Moisture
θ (cm
3/cm
3
) Volumetric water content
θ
=
(Mw−
Md )
V
×1(g/cm
3
)
V: Sample Volume = 251 cm
3
Mw: Wet sample mass (field mass)
Md: Dry sample mass
(Oven dried at 65
◦C for 72 hours)
Porosity
φ (cm
3/cm
3
) Porosity of soil sample
φ
=
Ms
V
Ms: Saturated soil mass
Saturation
Water
Fraction
SW (−) Degree of saturation of moist soil sample SW
=
θ
φ
Bulk
Density
ρb (g/cm
3
) Bulk density of soil sample
ρb =
Md
V
Root
Biomass RB (g/g)
Fraction of sample
with dimension
>
2 mm
over the total dry sample (fine roots)
RB
=
MRB
Md
MRB: Mass of organic sample
>
2 mm excluding gravel
Soil Organic
Matter SOM (g/g)
Soil organic matter content,
loss on ignition
over samples
<
2 mm
SOM
=
MSOM
Md< 2 mm
Md < 2 mm: Mass of soil
<
2 mm
MSOM: Mass of soil organic matter
with dimension
<
2 mm
(LOI at 360
◦C for 2 hours and 15 minutes)
Gravel
Fraction GF (g/g)
Fractions of the samples’ gravel with
dimension
>
2 mm
over the total sample
GF
=
MGF
Md
MGF: Mass of gravel
>
2 mm
Organic
Matter OM (g/g) Total organic matter of the sample OM
= RB
+SOM
×(1−GF
−RB)
Sand
S (g/g) Sand fraction
Silt Si (g/g) Silt fraction
Clay
C (g/g) Clay fraction
Texture analysis of the soil samples with
dimension
<
2 mm
using the hydrometer method.
Type of Soil
− (−) Type of mineral soil according to soil classification
25
3.2.2.2 Soil property measurement
The soil sampling procedure was designed to obtain a full characterization of the subsurface profile.
Conventional field protocols and soil sampling procedure in the Arctic Tundra region often consists
of single coring or opening a soil pit a soil pit and sampling from representative horizons, which
results in coarse characterization of the active layer (2–3 samples) [10, 14, 23, 39, 40, 43, 52, 63–65].
The majority of the previous studies were conducted by researchers focused on Earth system and/or
hydrology models. There is a fundamental difference between the way subsurface is characterized
in Earth system models and physics-based radar remote sensing models. In the latter, as coarse
horizon based soil sampling may not capture the transition and details of the soil property variations
in the active layer, where, despite its relatively shallow depth, its soil moisture and OM vary
substantially. While we mainily follow the sampling protocols suggested by previous methods,
the main difference in our method is fine resolution sampling to acquire more sampling points in
the subsurface to characterize the active layer soil profile model. Otherwise, the transition points
between each horizon will be ignored. Therefore after opening each soil pit, two side-by-side tin
cans of soil samples were harvested from the sidewall. Usually, the samples closer to the surface,
which typically have more organic matter, are done at depths of 7–8 cm, and the deeper layer that
have more minerals content are sampled at intervals of around 5–6 cm (Table. 3.3).
In addition to capture the fine resolution variations of the subsurface, in previous protocols som
piceces of information such as bulk density (ρb), porosity (φ), and Root Biomass (RB) are often
missing in datasets. Sample conatiners with the same volume (V = 251cm3
) were used so that ρb
and φ could be measured in the lab. Wet soil mass was recorded in the field to measure the in-situ
soil moisture content (θ). The root layer, decomposed organic layer, and the mineral layer ware
visually distinguishable in the example soil pit excavated at HV and ICC (Fig. 3.3).
(a) (b)
Figure 3.3: Soil pits excavated at the HV and ICC study sites. (a) Happy Valley 1. (b) Ice Cut 1.
26
Table 3.3: Number of sample and representative sampling depth
Soil Pit Total # Samples Sample ID Coarse Depth Interval
(cm)
Representative Sampling Depth
(cm)
1 [0-7.5] 7.5
2 [7.5-15] 7.5
3 [15-22] 7
4 [22-29] 7
5 [29-35.5] 6.5
6 [35.5-42] 6.5
7 [42-48.5] 6.5
FB 16
8 [48.5-55] 6.5
1 [0-8] 8
2 [8-16] 8
3 [16-23.5] 7.5
4 [23.5-31] 7.5
5 [31-38] 7
SGW-1 12
6 [38-45] 7
1 [0-6] 6
2 [6-12] 6
3 [12-17] 5
4 [17-22] 5
5 [22-27] 5
6 [27-32] 5
7 [32-39] 5
SGW-2 16
8 [39-44] 5
1 [0-7] 7
2 [7-14] 7
3 [14-20] 6
4 [20-26] 6
5 [26-31] 5
6 [31-36] 5
7 [36-41] 5
HV-1 16
8 [41-46] 5
1 [0-7.5] 7.5
2 [7.5-15] 7.5
3 [15-22] 7
4 [22-28] 6
HV-2 10
5 [28-34] 6
1 [0-7] 7
2 [7-14] 7
3 [14-20] 6
4 [20-26] 6
5 [26-31] 5
ICC-1 12
6 [31-36] 5
1 [0-7] 7
2 [7-14] 7
3 [14-20] 6
4 [20-26] 6
ICC-2 10
5 [26-31] 5
1 [0-7.5] 7.5
2 [7.5-15] 7.5
3 [15-22] 7
4 [22-29] 7
IMN-1 10
5 [29-36] 7
27
3.2.3 Lab Experiment Design
A total number of 102 harvested samples were weighed in the field. As needed, they were brought to
saturation for porosity measurement at Toolik Field station. Soil samples collected during the field
campaign were shipped to our lab at USC for further analysis. Upon arrival, a complete oven drying
process was conducted for 72 h at 65◦C to avoid charring the OM content to measure porosity.
Subsurface (herein referred to as ground) samples consisted of soil matter, root systems, and
gravel. Hereafter, we refer to all live and dead OM and roots with diameters (particle size) larger
than 2 mm as RB. All ground samples were wet sieved with a 2 mm mesh. The remaining RB that
did not pass the through 2 mm mesh, was visually excluded from gravel fractions. Once wet organic
matter with dimensions larger than 2 mm (RB) was excluded, we oven-dried them and measured
the weight to calculate RB.
Consequently, we refer to subsurface samples with particle size less than 2mm as soil, based on
the United States Departement of Agrictulture (USDA) definition. If a sample contained a gravel
fraction, it was characterized based on a size greater than 2mm [66]. Soil samples with particles
size less than 2 mm were then sent to a soil lab (The Ward Laboratories in Nebraska) for analysis
for the mineral texture and Soil Organic Matter (SOM) content. SOM was measured using a Loss
on Ignition (LOI) method, which heats the soil samples in a drying oven at 360◦C for 2h and 15
min to combust the SOM. Mineral texture analysis was performed using the hydrometer method.
All parameters, including porosity, bulk density, RB, SOM content, and mineral texture, were
measured for all soil samples. No samples were excluded in a certain analysis, except for mineral
texture measurements, when the mass of the sample that contained more than 35% OM content
was too small to measure the mineral texture. This level of detailed and the classification based on
particle size is important because RB and the surface organic mat are often excluded in the subsurface
parameterization (Table.3.2). In contrast, our experiment revealed more detailed information about
the subsurface and differentiation between RB and SOM, which are collectively known as total
OM.
3.3 Methods
3.3.1 Pedotransfer Function
Numerical coupled thermal-hydrologic processes used in land surface models and electromagnetic
scattering models used in radar remote sensing usually represent the subsurface as a multi-layered
structure. The subsurface thermal, hydraluic, and dielectric properties need to be parameterized for
numerical simulations, and these properties are strongly dependent on soil moisture variation and
texture (mineral, organic, root layer) [30,44,67]. Generalized models for subsurface parametrization
often rely on soil properties, such as mineral texture (sand (S) and clay (C) fractions), OM (which
encompasses SOM and RB), bulk density (ρb), and porosity (φ) (Table. 3.2). These soil properties
serve as inputs for these parametrization models. PTFs leverge the strong correspondence between
different soil properties and provide a means of reducing the number of input data layers. The goal
here was to find a function that estimates ρb and φ from soil texture (OM, sand, and clay fractions)
through simple empirical modeling.
28
Important points that must be made are the definitions for organic and mineral soil. Our field
observations indicate 35% OM (equivalent to 20% carbon content) as distinguisher threshold
between mineral and organic soils [39, 42, 63]. Above this threshold, the properties of soil are
governed only by OM [42]. This is consistent with our measurement observations, that for organic
samples (OM > 35%) even combinations of the two adjacent samples did not have sufficient
mineral constituents and was dominated by organic particles. Therefore, mineral texture of soil with
OM beyond this range had minimal influence on the pedotransfer modeling. Subsequently, in our
modeling of samples OM > 35% we estimated the texture with the mean value of each component
(sand and clay) due to almost-uniform behavior of mineral texture throughout the profile.
Figure 3.4: Organic matter (OM) histogram for both datasets.
Our dataset provided 102 samples from eight soil pits including replicates, which are referred to
as sample ‘a’ and ‘b’ and can be treated as an independent sample for PTF development (Fig. 3.2,
Table. 3.3). We combined our data with another recently published dataset (including 112 samples)
collected within the Toolik flight line [68], which resulted in an expanded set of 214 covering a
wide range of OM distribution ( 3.4), from mineral to organic soil. It is important to note that
O’Conner [68] sampling follows a coarse characterization of the active layer; nevertheless, the data
can be used for PTF model development. Unlike conventional PTFs that are based on data-driven
regressions, herein we focused on correlation-based models. Here, a data-driven regressions PTF
refers to multi-variable models that use machine learning techniques such as Random Forest to find
a PTF model. Correlation-based models are parsimonious models with great explanatory predictive
power. For instance, in the following we estimate different soil properties from soil textures.
Analysis of our data indicates that the bulk density for mineral fraction can be found as follows:
ρ
Min
b = e
0.0056S+0.0081C
(3.1)
29
where ρ
Min
b
is the mineral bulk density associated with mineral texture fraction. Sand and clay
mass fraction [0−100]%, which serve as input variables are denoted by (S) and (C) respectively.
Furthermore, knowing that pure organic soil often shows very small bulk density, to find the total
bulk density we used an exponential function as follows:
ρb = ρ
Min
b
e
−0.0314OM (3.2)
where the OM refers to organic matter mass percentage that varies in the range of [0 − 100]%.
Accordingly, once the value of ρb was found based on OM, S, and C, to find the soil sample porosity
we adopted a linear relationship between φ and ρb [68].
φ = −0.3771ρb +0.9247 (3.3)
The above relationship was confirmed from our site soil measurements, with parameters calculated
from data.
3.3.2 Organic Matter Profile Model
3.3.2.1 OM profile
Both soil moisture and OM vary substantially along the active layer profile. Therefore, and accurate
empirical characterization to describe this profile behavior is necessary. For the purpose of profile
characterization, we used only our fieldwork soil sample; the O’Connor et al., (2020) samples were
not included due to their sporadic sampling points within the profile [39]. The OM distribution for
depth intervals of 5 cm throughout the profile (Fig 3.5a) and the median of OM content at each
corresponding depth (Fig 3.5b) show that the OM profile behavior is effectively represented using a
logistics sigmoid (S-shaped) function.
(a) (b)
Figure 3.5: (a) OM Profile Distribution. (b) OM Median profile at each depth suggests a sigmoid
function for representing profile behavior)
30
OM(z) = OMz0 +
OMM −OMz0
1+e
−β(z−m)
(3.4)
Equation (3.4) explains the behavior of the OM(z) profile, where 0 ≤ OMM ≤ 35% is the OM
fraction in mineral horizon, 0 ≤ OMz0 ≤ 100 is the surface OM, β > 0 is the decay rate, and
m > 0 indicates the depth where the maximum decay rate occurred (herein we refer it az Organic
Layer Thickness (OLT), which we sometimes alternatively describe it by zOLT ). Note that here
we don’t use the 35% OM criterion as indication for OLT. This S-shaped profile is different from
previous observations, in which the OM was expressed as an exponential function [65, 69]. The
difference in profile functional forms reflects the more detailed sampling procedure used in this
study, which provides finer resolution of profile gradients than more conventional bulk sampling
from representative soil horizon 3.6.
(a) (b) (c) (d)
(e) (f) (g) (h)
Figure 3.6: The differences between sigmoid profile model and exponential profile OM(z) =
OMz0e
−κz
for organic matter. (a)-(h) shows each of soil pits, it appears, except Franklin Bluffs, in
the remaining sites, a sigmoid function shows a better representation for OM profile.
3.3.2.2 RB and SOM profile
Aboveground vegetation biomass plays a crucial role in governing subsurface hydraulic, thermal,
and dielectric characteristics [38]. While between 70% and 80% of the vascular plant biomass
in Arctic tundra is located below ground, there is still only limited knowledge about the belowground responses of tundra ecosystems to climate change [70–73]. One conventional approach to
31
quantifying the RB distribution is finding a relationship between roots (underground) biomass and
shoot (aboveground) biomass, namely, the root:shoot ratio. Species dependent root:shoot and other
allometric equations are poorly constrained for tundra [70, 73]. Our detailed soil analysis based on
particle dimensions also provides detailed information on the RB profile, RB(z), and SOM profile,
SOM(z). As described in equation (3.5), the total subsurface OM profile OM(z) at each sample
site is associated with different subsurface constituents, including RB(z), SOM(z), gravel fraction
(GF(z)), and mineral fraction of the soil through mass fraction (Table. 3.2).
OM(z) = RB(z) +SOM(z)(1−
RB(z) +GF(z)
100
) (3.5)
RB(z) and SOM(z) can be derived from the in-situ observations. The best profile model for RB(z)
is an exponential function, as shown in equation (3.6), where 0 ≤ RBz0 ≤ 100% is the surface RB
and κ ≤ 0 is the exponential decay factor. SOM(z) follows an S-shaped behavior similar to OM(z),
where the corresponding parameters are also similar to what was described in equation (3.4).
RB(z) = RBz0e
κz
(3.6)
SOM(z) = SOMz0 +
SOMM −SOMz0
1+e
−β(z−m)
(3.7)
Note the two different expressions for OM(z) in equations (3.4) and (3.5). In reality, we measure
SOM(z), RB(z), GF(z), and find the total OM(z) based on equation (3.5). However, one can also fit
an S-shaped behavior for total OM as described in equation (3.4). Among the 8 soil pits, except
for SGW-1, the rest show negligible gravel fraction (Fig. 3.7). In equation (3.4), which we refer
to as model 1, for convenience we ignore the gravel fraction (GF(z) = 0). A comparison between
these two models is depicted in the results section. For the purpose of the radar retrievals, we use
equation (3.4) as it requires fewer parameters to characterize the total OM profile.
Figure 3.7: Gravel fractions for each soil pits, it is appearing only SGW-1 has a significant GF, and
for the other site this value is 0, therefore for reducing model complexiy we assume GF is 0.
32
3.3.3 Soil Moisture Profile Model
Because the porosity (φ), or maximum saturation level, substantially changes within different active
layer soil horizons, the Saturation Water (SW) fraction is a better representation for soil moisture
(θ), where it can be denoted as a normalized soil moisture level. This also allows for estimating the
water table depth (zWT ), where SW reaches 1. The soil moisture profile θ(z) can be found as the
product of SW fraction and porosity:
θ(z) = SW(z)×φ(z) (3.8)
The porosity profile φ(z) is found by substituting eq. (3.4) into eq. (3.2), and knowing the soil
mineral texture; then the resulting ρb(z) profile is applied to eq. (3.3) to find φ(z). Our field
observations show the best fit to characterize the SW(z) is represented by a quadratic function:
SW(z) =
1−(1−SWz0)( z
zWT
−1)
2
z ≤ zWT
1 z > zWT
(3.9)
where SWz0 indicates the surface SW fraction, which varies between [0−1], and zWT is the water
table depth.
3.4 Results
Soil mineral texture and organic properties serve as inputs of the PTF model (Fig. 3.8). We assumed
and average value for the mineral textures, with Savg = 39%, and Cavg = 25%. The model showed
close agreement with the measurements and was able to estimate ρb with a Root Mean Square Error
(RMSE) of 0.13 (g/cm3
) (Fig. 3.8a). Once the bulk density was found, it was used in eq. (3.2) to
reconstruct soil porosity with RMSE of 0.05 (cm3/cm3
) as shown in Fig. 3.8b and Fig. 3.8c. The
FB samples were outliers in the PTF development, the major feature of the FB soil is a thin RB layer
with a homogeneous mineral texture profile having an average sand fraction around 60% −70%
and OM less than 35%. Therefore, the developed PTF in section 3 and the corresponding results
suggests that the model is overestimating ρb for mineral soil that contains a high sand fraction
(Fig. 3.8 and 3.9).
Next, we show the in-situ measurement results and profile model behavior for all of the soil pits
in tundra sites (Fig. 3.9), which are the OM, ρb, and φ.
At each depth, the measured values for adjacent samples ‘a’ and ’b’ is reported (Fig. 3.2). In
most cases, the two measurement are consistent. However, due to microtopography variation within
a site, profile behavior at each soil pit is distinct from other neighboring pits at the same site. Here,
the OM(z) profile follows the suggested S-shaped (sigmoid function) behavior in both soil pits
(Fig. 3.9a and 3.9d). For the SGW-1 and HV-1 locations the organic layer si shallower, and OM(z)
rapidly decreases from the surface to the mineral layer (compare SGW-1(red) amd HV-1(black) in
Fig. 3.9a). However, the SGW-2 and HV-2 (compare SGW-2(blue) and HV-2(magenta) in Fig. 3.9a)
and IMN-1, ICC-1, and ICC-2 (compare IMN-1 (blue), ICC-1 (black), and ICC-2 (magenta) in
Fig. 3.9d) locations include a thicker organic of about 20−30 cm. FB shows a fairly homogeneous
mineral soil throughout the profile (see FB-1 (red) in Fig. 3.9d). The corresponding ρb and φ
33
(a) ρb v.s OM (b) φ v.s ρb (c) φ v.s OM
Figure 3.8: PTFs that find porosity and bulk density from the mineral texture and OM. Figure (a)
shows the model behavior that derives ρb from soil mineral texture and OM; the FB samples are
outliers and excluded from modeling. (b) Shows the linerar relationship between φ and ρb. (c)
Shows the behavior of φ against OM, herein for mineral texture we considered the mean value of
Savg = 39% and Cavg = 25%.
profiles were acquired by applying the OM(z) profile from eq. (3.4) and inserting it into the PTF
models (Fig. 3.9). In almost all soil pits except FB, which was outlier, the porosity and bulk density
profile behavior also follows the measured values.
The determination of FB measurements as an outlier was in part visually and also based on the
soil type analysis, and not based on any statistical test for outlier detection. For FB, the soil type
is sandy clay loam, and therefore higher bulk density is expected (because it should have larger
but fewer porse spaces). However, this behavior is not observed in our measurement (Table. 3.4).
Compared to SGW-1, which is the same soil type and follows a higher bulk density and lowere
porosity, we considered FB-1 to be an outlier. Although it is also important to note that the relatively
small porosity and higher bulk density in SGW-1 is due to the presence of gravel fraction (Fig. 3.7).
Nevertheless the bulk density in FB-1 is smaller than expected withing the range for sandy clay
loam.
As for ICC, the model also cannot estimate the porosity well; however, the profile behavior still
follows the measurements (Fig. 3.9d- 3.9d). Therefore, to summarizes, we refer to FB site as an
outlier, because no only the model shows error in estimating the absolute values, it also cannot show
the profile behavior.
Comparing R
2
and the RMSE values shows that the total OM, found from equation (3.5), does
not show better performance in comparison to the OM profile that is based solely on equation (3.4),
except at the IMN site (Fig. 3.10a, 3.10d, and Table. 3.5). Furthermore, one must note the difference
between SOM and OM. The conventional LOI methods exclude particles with a dimension greater
than 2 mm prior to the LOI process. Our method distinguishes between RB and SOM based on the
sample particle dimensions as described in section 3.2.3. RB is not considered as soil; therefore,
conventionally, it is being excluded from the LOI, resulting in the underestimation of the total OM
content. However, this layer is in the subsurface and could substantially change subsurface thermal
hydraulic, and electromagnetic properties. The suggested exponential profile in equation (3.4)
effectively captures the RB profile (Fig. 3.10b and Fig. 3.10e), while the S-shaped function shows
similar utility in representing the SOM profile (Fig. 3.10c and Fig. 3.10f). Overall, the OM profile
34
Table 3.4: The mean and standard deviation of soil physical properties for all the sites.
Porosity Bulk Density Organic Matter Site ID # Mineral
Sample
Soil
Type Mean Std Mean Std Mean Std
FB-1 16 Sandy Clay Loam 0.64 0.08 0.73 0.13 6.6 1.2
SGW-1 10 Sandy Clay Loam 0.43 0.11 1.34 0.30 5.5 3.5
SGW-2 6 Clay Loam 0.53 0.03 1.19 0.08 9 0.8
HV-1 14 Silty Clay Loam 0.54 0.08 1.03 0.24 8.7 3.6
HV-2 4 Silt Loam 0.47 0.03 1.10 0.03 6.4 0.5
ICC-1 8 Silt Loam 0.48 0.06 1.16 0.16 10 2.1
ICC-2 4 Loam 0.69 0.07 0.53 0.27 40.6 23
IMN-1 2 Loam 0.69 0.05 0.71 0.20 7.8 0
Total 64 0.55 0.11 1.00 0.13 9.7 9.8
behavior performs well when it is reconstructed from the S-shape function, which is recommended
for polarimetric SAR (PolSAR) and interferometric SAR (InSAR) retrievals. With the way that we
distinguish between RB and SOM one can develop an empirical approach to finding RB from the
total OM content. Such an approach has potential utility in estimating RB and the root layer from
radar remote sensing but requires further research. Following soil texture characterization, the
Table 3.5: Profile models performance.
OM
Model-1
OM
Model-2 SOM RB SW
Site ID R
2 RMSE R
2 RMSE R
2 RMSE R
2 RMSE R
2 RMSE
FB-1 0.62 1.4 0.74 1.2 0.01 1.2 0.95 1.1 1 0
SGW-1 0.99 1.6 0.14 15.9 0.98 1.5 0.99 0.5 0.95 0.04
SGW-2 0.95 7.3 0.93 8 0.92 7.7 0.86 5.5 0.87 0.02
HV-1 0.99 2.3 0.99 2.5 0.99 2.2 0.98 2.2 0.81 0.09
HV-2 0.99 3.2 0.99 4 0.99 2.8 0.85 10.2 0.43 0.05
ICC-1 0.97 5.1 0.97 6.2 0.97 5 0.81 8.4 0.95 0.05
ICC-2 0.81 9.8 0.81 10.2 0.70 10.6 0.87 8.9 0.97 0.04
IMN-1 0.90 9.0 0.87 6.3 0.92 7.7 0.87 8.8 0.19 0.08
behavior of soil dielectric permittivity, electrical conductivity, soil moisture, and the corresponding
SW fraction is of interest (Fig. 3.11). At the surface, due to faster evapotranspiration and lower soil
moisture (figures 7(c) and (g)), and a highly porous RB layer, almost all of the samples exhibit a
low dielectric constant (Fig. 3.11a and Fig. 3.11e). Among these sites, SGW-2, IMN-1, and FB-1
show a higher surface dielectric value because of higher moisture content (compare SGW-2 (blue),
IMN-1 (blue), FB-1 (red) in Fig. 3.11c and Fig. 3.11g). As we go deeper into the active layer, the
dielectric constant in all soil pits (except FB-1) reaches a maximum value (saturated organic layer)
and then decreases as it reaches the deeper mineral layer. The transition depth varies based on the
organic layer thickness (compare SGW-2 (black) and ICC-1 (blue) in Fig. 3.9a, Fig. 3.9e, Fig. 3.11a
and Fig. 3.11e). The dielectric variation for the mineral layer is relatively constant due to saturation.
35
The SGW-1 samples exhibit an unexpected low dielectric constant, and low soil moisture even
though the mineral layer is fully saturated (Fig. 3.11a, Fig. 3.11c, and Fig. 3.11d SGW-1 (red)). The
SGW-1 and SGW2 soil samples are mostly sandy clay loam types (table S6). However, the measured
porosity at the mineral horizon for the SGW-1 location is much lower than the expected porosity
of sandy clay loam soils (compare SGW-1 (red) and SGW-2 (blue) in Fig. 3.9c). Furthermore, the
mineral layers in SGW1 and SGW-2 are fully saturated, but the dielectric constant and the soil
moisture in SGW-1 are almost half of what they are in SGW-2 (Fig. 3.11a and Fig. 3.11c). The
underlying reason for this behavior in SGW-1 is a substantially higher gravel fraction, leading to a
lower porosity (Fig. 3.7)).
The electrical conductivity, which determines the imaginary part of the soil dielectric constant
and accounts for the lossy behavior of soil, is higher for the mineral layer compared to the surface
organic layer. The abundance of cations in the mineral layer explains a higher electric conductivity
(Fig. 3.11b SGW-2 (blue), HV-2 (magenta)) and, in turn, a higher loss for the mineral soil layer,
which is consistent in all soil profiles (Fig. 3.11b and Fig. 3.11f). This is in agreement with the
fact that the radar signal attenuation is greater in deeper soil layers, and radar sensitivity decreases
accordingly [32].
3.5 Discussion
While one can use various data-driven regression based methods to develop a model to study the
inter-relationship among soil physical properties, we focused on deriving a correlation-based PTF
model that would be useful for further parametrization and predication of Arctic soil hydraluic and
dielectric permittvity behavior [6]. The developed PTF suggest that, except for sandy soils, the two
essential soil physical properties ρb and φ can be found solely based on mineral soil texture and
OM. This is of particular interest for developing a soil dielectric model for the permafrost active
layer.
The detailed analysis and results findings suggests fewer independent variables as input parameters for soil dielectric modeling, which can avoid unnecessary modeling complexity and the need for
including too many unknowns in the radarretrievals. We leave the topic of soil dielectric modeling
to chapter 3 and 4 because of the need for extensive dielectric measurement for a wide range of
organic soil and full soil moisture ranges from saturation to oven dry.
We showed that the PTF model was able to accurately find ρb for the relatively high OM
content soils in the near-surface layer. However, the model underestimates ρb for the deeper
mineral soil layers. This underestimation also propagates to the estimation of soil porosity depends
on the mineral texture. However, OM(z) profile model can reconstruct a realistc soil physical
model, in particular, by estimating the porosity profile φ(z); where φ(z) may have additional
utility for estimating surface subsidence from permafrost degradation using InSAR remote sensing
methods [74–77].
As depicted in the results, soil moisture and OM variations can explain the soil dielectric
behavior throughout the active layer profile. These profile models are of particular interest for radar
retrieval algorithms using both PolSAR and InSAR methods (Fig. 3.12). In a physics-based PolSAR
retrieval, the subsurface parameters (X¯t
) serves as unknowns (for each radar pixel). At each retrieval
iteration, an estimation of parameters reconstructs the subsurface properties (soil SW fraction and
OM). Accordingly, these subsurface profiles translate into the dielectric profile by employing an
36
organic soil dielectric model. Subsequently, the subsurface discretized into a multi-layer structure
with N-layer and a depth interval of ∆z =
zALT
N
. This discretized multi-layer dielectric structure
along with the soil roughness height (h) feed into a multi-layer electromagnetic scattering model to
find the simulated backscattering model to find the backscattered response of subsurface, where
eventually these simulated values compared with the measured backscattere signal (Fig. 3.12).
X¯
t = [OMz0,OMM,β,m;SWz0,zWT ;h,zALT ] (3.10)
In summary the physics-based radar retrieval using PolSAR data requires three models: (a) A
realistic subsurface soil properties profile model (SW(z), OM(z)) (b) A well-established organic
soil dielectric model (εˆ(z)), and (c) A multi-layer electromagnetic scattering model (Fig. 3.12).
The subsurface parameters can be categorized into three subgroups: (a) OM profile parameters
X¯t
OM = [OMz0,OMM,β,m], (b) soil saturation profile parameters X¯t
SW = [SWz0,zWT ], and (c) active
layer parameters X¯t
ALT = [h,zALT ], which are surface roughness height and ALT respectively. The
distribution analysis of OM profile model parameters suggest at the deep OM content in the
mineral layer OMM can be assumed to vary conservatively over the range from [5−7] (igonoring
cryturbation). Furthermore, the decay parameter β can also be assumed to be nearly constant, at
around 0.5 as shown in Fig. 3.13. In a PolSAR retrieval algorithm, these profile parameters serve as
unknowns. The above analysis reduces the number of unknowns for OM(z) from four to two, which
is crucial for the PolSAR retrieval algorithm, given very few radar measurements (usually 2) are
available.
There are four primary sources of uncertainty in our measurements: (a) compressing highly
organic porous samples, which results in over-estimating soil moisture and bulk density, (b) oversaturation while adding water to reach saturation, which may lead to overestimating porosity, (c)
crushing/rubbing samples and passing excessive amount of OM through 2 mm sieve, which can
lead to underestimating RB, and (d) the apparent dielectric permittivity measured by TEROS 12
sensors has an accuracy of ±1 for soil in the relative permittivity range of 1−40 and 15% for soil
with a relative permittivity range of 40–80.
Estimating the error and uncertainty of items (1)–(3) above will be qualitative because the error
value is variable for different soil types, and since such an analysis will require a larger data set, we
will leave this analysis to future work and a more comprehensive field campaign.
However, given that we have extracted multiple samples at each sampling depth, an estimation
of the measurement precision (Fig. 3.14) can be calculated. Assuming the two adjacent samples
(Fig. 3.2) should exhibit a similar soil physical property, we can find a distribution of correlation
coefficient based on equation (3.12).
a¯ =[ρ
a
b
,φ
a
,RBa
,OMa
,SOMa
,S
a
,Sia
,C
a
,θ
a
,SWa
] (3.11a)
b¯ =[ρ
b
b
,φ
b
,RBb
,OMb
,SOMb
,S
b
,Sib
,C
b
,θ
b
,SWb
] (3.11b)
ρ(a,b) = ∑(ai −a¯)(bi −b¯)
p
∑(ai −a¯)
2(bi −b¯)
2
(3.12)
37
3.6 Conclusion
In this chapter, we presented a detailed study of soil properties in the active layer profile of Alaskan
tundra. A fine-resolution dielectric (ε
′
r
and σ) profile characterization was provided, along with soil
hysical properties (OM, RB, SOM, ρb, φ, θ, SW) throughout the profile. The interrelationship
between different soil textures (OM, S, and C) and soil physical properties (ρb, φ) was used to
develop a new PTF, which could be used in further modeling, especially to develop a soil organic
model with a minimum number of parameters.
Furthermore, we showed that OM(z) and SW(z) follow independent S-shaped and quadratic
profile distributions within the active layer. The parameters used to characterize these models were
also studied. The resulting profile model can in turn be used to develop more realistic organic
soil dielectric models for tundra, and the resulting dielectric profile can feed into a multilayer
electromagnetic scattering forward model for predicting the radar backscattering coefficients.
Subsequently it improves the assessments and monitoring of permafrost active layer from airborne
and spaceborne SARs.
Also, the study of the cryoturbation effect, in which the surface organic layer relocates to a
deeper layer below the mineral horizon, has not been discussed in this work, although some of
our observations were able to capture this phenomenon. This will be further studied in the future.
The method used in this paper is a baseline study, and more extensive fieldwork and datasets could
provide more insight into the fine resolution profile behavior of active layer soils.
38
(a) (b) (c)
(d) (e) (f)
Figure 3.9: Soil active layer profile physical properties from soil pit measurement and model
estimated at tundra sites; including (a) OM at SGW-1 (red circle), SWG-2 (blue triangle), HV-1
(black square), and HV-2 (magenta diamond), (b) bulk density, (c) porosity, (d) OM at FB-1 (red
circle), IMN-1 (blue triangle), ICC-1 (black square), and ICC-2 (magenta diamond), (e) bulk density,
(f) porosity. At each depth two replicate samples were harvested. Both measured values are shown.
For profile modeling, the average value was selected. OM profile was found based on sigmoid
function and accordingly porosity and bulk density profiles were found by inserting OM profile into
PTF models.
39
(a) (b) (c)
(d) (e) (f)
Figure 3.10: Observed vs estimated SOM and RB profiles for the SGW tundra site (sampling
location SGW-1 in red and sampling location SGW-2 in blue). The model RB and SOM profiles
are derived from equation (3.7) as shown and plotted against the associated site measurements.
Total OM, was found based on RB and SOM profile. (a) OM at SGW-1 (red circle), SGW-2 (blue
triangle), HV-1 (black square), and HV-2 (magneta diamond), (b) RB, (c) SOM, (d) OM at FB-1
(red circle), IMN-1 (blue triangle), ICC-1 (black square) and ICC-2 (magneta diamond), (e) RB,
and (f) SOM.
40
(a) (b) (c) (d)
(e) (f) (g) (h)
Figure 3.11: Active layer measured soil dielectric constant and electrical conductivity profiles using
TEROS 12 probes. Measured and modeled soil moisture and SW fraction (quadratic model) the
tundra site, including, (a) real parts of the dielectric SGW-1 (red circle), SGW-2 (blue triangle),
HV-1 (black square), and HV-2 (magneta diamond) (b) electrical conductivity, (c) volumetric soil
moisture, and (d) SW fraction, (e) real parts of the dielectric FB-1 (red circle), IMN-1 (blue triangle),
ICC-1 (black square), and ICC-2 (magneta diamond) (f) electrical conductivity, (g) volumetric soil
SW fraction.
41
Figure 3.12: The framework of radar remote sensing forward model in the physics-based retrieval of
active layer properties. Subsurface properties can be categorized into three groups, (a) OM profile
parameters X¯t
OM = [OMz0,OMM,β,m], (b) soil saturation profile parameters X¯t
SW = [SWz0,zWT ],
and (c) active layer parameters X¯t
ALT = [h,zALT ], which are surface roughness height and ALT
respectively. These parameters, serve as unknowns in a radar retrieval procedure, and through an
iterative method their value estimated at each radar pixel cell.
Figure 3.13: Profile model parameter ranges. The red bar shows the median and the box boundaries
show the 25%−75% range of value within the distribution.
42
Figure 3.14: The distribution of correlation coefficients between adjacent samples, showing the
precision of soil properties measurements as listed in equations (10a) and (10b), assuming two
harvested sample at each layer exhibit similar physical properties.
43
Chapter 4
Organic Soil Dielectric Model: Hydrology Prespective
Disclaimer: The content of this chapter is adapted in large from the following papers:
I-2-1 Prepared Article 1
: K. Bakian-Dogaheh et al., ”Empirical Models for Predicting Soil Water
Dielectric Behavior Using Hydrologic Properties of Permafrost Soils,“
I-2-2 Published Dataset [8]: K. Bakian-Dogaheh et al., ”Soil Matric Potential, Dielectric, and
Physical Properties, Arctic Alaska, 2018“ ORNL DAAC, 2023.
The behavior of soil dielectric vertical profile within the permafrost active layer can be inferred
from remotely sensed radar observations. Water dielectric behavior inside the soil matrix is key
to understanding subsurface dielectric traits in the active layer. However, predicting this behavior
is a radar modeling challenge due to poor knowledge of soil-water dielectric properties. We
exploited the Debye relaxation model, in which the soil-water relaxation time is predicted from
the soil water retention curve. To that end, we developed an empirical model of active layer soil
hydrologic properties that utilizes basic soil components such as organic matter and mineral texture
to parameterize the soil water retention curve. This approach offers a foundational method to
harmonize ecosystem and radar models by generating realistic soil dielectric models for organic-rich
permafrost soil, which are critical for the success of physics-based radar retrieval algorithms in
mapping water and carbon characteristics in permafrost landscapes.
4.1 Introduction
Permafrost soils are in the ‘front line’ of regional environmental changes in the Arctic. A principal
characteristics of the active layer subsurface is high organic matter (OM) accumulation, due to
relatively low litter decomposition rates induced by cold temperature and shallow water table
depth [1, 21]. Ecosystem modeling and remote sensing are critical components for predicting and
studying how water and carbon in permafrost soils will respond to a changing climate [3, 5]. A
numerical coupled thermal-hydrological framework is commonly used in ecosystem models, and
electromagnetic scattering models in radar remote sensing often characterized the subsurface as a
multi layered structure [30, 78]. The subsurface hydrological, thermal and dielectric characteristics
must be parameterized at each layer for numerical modeling. This is particularly challenging for
1
Initial draft submitted on 08/18/2022, rejected on 01/10/2023. A redraft is in prepration for resubmission as of
12/03/2024.
44
the active layer, as the abundance of OM and shallow water table depth strongly alter these soil
properties throughout the vertical profile [79]. Currently, the above mentioned characteristics and
subsurface processes are either poorly represented or entirely missing in the ecosystem models,
which results in large prediction uncertainties in the amount and timing of further soil carbon
release to the atmosphere [12, 80]. Additionally, the lack of a well established soil dielectric
model incorporating organic soil properties limits the capabilities of physics-based radar retrieval
algorithms for mapping carbon and water characteristics across permafrost landscapes [6].
Over the past three decades, various experiments have been conducted to parameterize hydrological and thermal processes of permafrost active layer soils in ecosystem models [38, 81–83].
More recent investigations, have taken a systematic approach to simultaneously measure basic soil
properties across diverse Arctic land covers [6, 7, 39, 68]. These soil properties include mineral
texture (i.e., sand, silt, and clay fractions), total organic matter (OM), root biomass (RB), soil
organic matter (SOM), bulk density (rhob), porosity (φ), hydraulic conductivity (Kh), and thermal
conductivity (KT ). The results from these studies indicate that empirical models can predict all
of these properties from OM and ρb alone. While advancements have been made for understanding organic soil properties, hydralogic properties in the form of the Soil Water Retention Curve
(SWRC) that explains the relationship between soil moisture (θ) and soil water matric potential (θ),
remains poorly characterized for the active layer. Existing models’ parametrization often rely on
historic measurements that have not been updated [84]. This would consequently, lead to a large
inconsistency between various methods (e.g., Beringer et al., (2001) and Letts et al., (2001)).
Soil dielectric properties are strongly controlled by hydrology and soil organic and mineral
components. Rising concern regarding warming climate trends in higher latitudes, where there is
a prevalence of permafrost, accentuate the need for an organic soil dielectirc model for inclusion
physics-abased radar retrieval algorithm. Soil dielectic mixing models usually uses a multi-phase
approach, in which the overall the overall soil dielectric behavior is dominated by the associated
dielectric behavior of soil water [67, 85–91]. The water dielectric behavior in soil has been an
open question within the soil dielctric modeling community. While dielectric characterization of
soil-water dielectric properties remains an ongoing challenge, few studies have reported a way to
model these properties using the SWRC [92–95]. Transferring the findings from both theoretical
and empirical studies on soil hydrologic properties to soil-water dielectric behavior continues to be
a challenge because of the disciplinary gap between ecosystem and radar remote sensing modeling
and the lack of harmonized model parameterization. Bridging this gap by synergizing the soil
processes from both science perspectives is paramount to developing a realistic physics-based soil
dielectric model that enables mapping of water and carbon in permafrost soils using microwave
radar remote sensing.
This subsection aims to develope a coupled hydrologic-electromagnetic modeling framework
for predicting water dielectric properties in organic soils that are widely applicable for permafrost
active layer across the Arctic tundra region. The term “soil-water” didlectric is used hereafter to
refer to water dielectric behaviors inside the soil matrix. We need simultaneous measurements of
soil physical, hydrological, and dielectric properties along a wide range of OM and soil moisture.
To this end our analysis starts by characterzing the key subsurface active layer soil properties
such as total organic matter and mineral texture. The soil water retention curve parameters were
estimated by fitting the SWRC model to soil water matric potential measurements from a large
tundra soil sample pool. The derived soil characteristics were then used as inputs to a parametrization
scheme to calculate the SWRC model parameters for a given set of organic matter and mineral
45
texture conditions. The estimated SWRC for various soil moisture conditions was then used to
predict the soil-water dielectric properties. A physics-based approach was developed, in which
the Eyring equation is used to relate SWRC to the relaxation time of the water molecules inside
the soil matrix [93]. The predicted relaxation time was then applied in Debye dielectric model to
characterize the soil-water dielectric properties.
4.2 Methods
4.2.1 Study Area
During the 2018 field season, 66 soil samples were collected from nine sites spanning a latitudinal
tundra transect and loacted within synthetic aperture radar (SAR) footprints of the 2017 NASA
Arctic and Boreal Vulnearability Experiment (ABoVE) Airborne Campagin (AAC) [5]. Five sites
were located within the North Slope region of Alaska and include Franklin Bluffs (FB), Sagwon
(SGW), Happy Valley (HV), and Ice Cut (ICC), and Imnavait Creek (IMN). The sites in interior
Alaska include Eight Mile Lake (EML), Creamers Field (CF), Ballaine Road (BR), and Scottie
Creek (SC). The site selections were designed to capture a wide variety of land cover types and
permafrost soil features to establish a representative model across the Arctic tundra landscape
(Fig. 4.1)
46
Figure 4.1: Locations of our nine study sites and associated land cover types across Alaska. The
Alaskan North Slope, and interior Alaska regions are indicated by the green and yellow shades,
respectively, in the inset in (a). The purple and cyan boxes around (a) and (b) correspond to the
same color boxes in the inset map, respectively. Black dots in (a) and (b) show the site locations
where soil samples were collected and analyzed for determining soil characteristics, and laboratory
analysis. Sampling locations fall within airborne SAR transects from the NASA ABoVE AAC. (c)
An example soil profile from an excavated pit, where active layer (ALT) samples were harvested
from the surface to permafrost table.
47
4.2.2 Soil Component Analysis and Volumetric Fractions
This work proposes a parametrization scheme that exploits the soil volumetric fraction classification
of subsurface components including root biomass, soil organic matter, and mineral fraction. Rather
than using a qualtiative visual based subsurface strata description to delineate acrotelm, catotel,
and mineral components [39], a quantitative soil classification was conducted using a wet sieving
method involving 2 mm mesj screening to disnguish roots from soil. In this method, the rootbiomass
(RB, the contribution of dead and live organic matter with particle size > 2mm), soil organic matter
(SOM, organic matter with particle size < 2mm measured by loss on ignition), and mineral soil
(Min, particles with size < 2mm) were identified as shown in Fig. 4.1. The grain-size based soil
classification provides a degree of harmonization between ecosystem and radar remote sensing
models. Subsurface soil descriptions in the form of volumetric fractions are highly beneficial when
using dielectric mixing approaches for combining the effect of each constituent property on the
effective dielectric behavior of moist soil [96]. Soil samples taken from side wall of soil pits through
the profile were used to quantify soil properties such as RB, SOM, mineral texture fractions (sand,
silt, and clay), porosity (φ), and bulk density (ρb) (Table 4.1).
Each samples was saturated, and its bulk density and porosity were measured. We then sieved
(dry) the sample with a 2 mm sieve to exclude the coarse root, and we characterized the root
biomass, which includes all dead and live organic matter with particle size larger than 2mm. The
remaining soil particles were shipped to the Ward laboratories for measuring the soil organic matter
and mineral texture. Accordingly, the total organic matter, mass, and volumetric fractions were
calculated.
Table 4.1: Independent basic soil properties measured. The root biomass and soil organic matter
needed to be measured to quantify the total organic matter. Bulk density and porosity need to be
measured to find the specific density of each sample. Finally, mineral texture, including sand, silt,
and clay fraction were also delineated.
Soil Physical
Properties Symbol Units Equation Notes
Bulk density ρb g/cm3 Md
V
V: Sample volume
Md: Dry sample mass
(Oven dried at 65◦C for 72 hours)
Porosity φ cm3/cm3 Ms−Md
V ×ρ
w
s
Ms
: Saturated sample mass
ρ
w
s = 1(g/cm3
)
Root Biomass RB g/g
MRB
Md
MRB: Mass of organic sample > 2 mm
Excluding gravel
Soil Organic
Matter SOM g/g
MSOM
Md<2mm
Md<2mm: Mass of soil < 2mm
MSOM: Mass of organic matter < 2mm
(LOI at 360◦C for 2 hours and 15 mins)
Sand S g/g
MS
MMin
Silt Si g/g
MSi
MMin
Clay C g/g
MC
MMin
MMin: Mass of mineral soil < 2mm
Hydrometer method.
S+Si+C = 1
48
Based on the set of measured independent soil properties, the volumetric fraction can be
expressed as follows:
f
i
v = f
i
m ×
ρb
ρ
i
s
(4.1)
where i = {RB, SOM, or Min}, f
i
v
is the subcomponent volumetric fraction, f
i
m is the mass
fraction, and ρ
i
s denotes the specific density, which is related to porosity and bulk density. The total
organic matter (OM) of the subsurface calculated from RB and SOM (Table. 4.2). The relationship
between OM and other variables (4.2) are used to assess how these variables change with increasing
OM (Fig. 4.2a and 4.2b). For the rest of this paper and in the parametrization section, we use
OM = {0,70,100} as designators of respective pure mineral, soil organic matter, and root biomass
fractions, respectively. Therefore, to find the specific density of RB we refer to ρs − OM curve
(5.3c), which results in ρ
RB
s = 0.83 (g/cm3
) at OM = 100%. To find the SOM specific density, we
use the relationship between SOM and OM that maximizes the SOM mass fraction (OM = 70%);
consequently, we calculate ρ
SOM
s = 1.2 (g/cm3
), shown in Fig. 4.2c. Finally, the specific density
of the mineral fraction for total organic matter (OM = 0) is derived as ρ
Min
s = 2.36 (g/cm3
) and
is depicted in Fig. 4.2d. We used the empirical model provided in Bakian-Dogaheh et al., (2022)
to determine bulk density from OM and mineral texture. Also, to incorporate the solid phase
components of soil into SWRC parametrization, we used ˜f
i
v
as described in eq. (4.3), which denotes
the normalizrde volumetric fraction (Fig. 4.2f).
49
Table 4.2: Basic soil properties, being calculated from Table 4.1. The specific density is being
calculated using measured bulk density and porosity. The total organic matter is calculated based on
root biomass and soil organic matter. The mineral mass fraction for each component is the fraction
of solid components to the total sample mass. To find the volumetric fraction, the specific density of
each subcomponent is being used. As described in main text, the OM= 0, 70, 100 denotes the Min,
SOM, RB soil components.
Soil Physical
Properties Symbol Equation
Specific Density ρs 1−
ρb
φ
Total Organic
Matter OM MOM
Md
= RB+SOM ×(1−RB
Root
Biomass f
RB
m
MRB
Md
= RB
Md = MRB + Md<2mm
Soil Organic
Matter f
SOM
m
MSOM
Md
= (1−RB)×SOM
Sand f
S
m
MS
Md
= S× f
Min
m
Silt f
Si
m
MSi
Md
= Si× f
Min
m
Mass
Fraction Mineral
Clay
f
Min
m
f
C
m
MMin
Md
= (1−RB)×(1−SOM)
MC
Md
= C × f
Min
m
Root
Biomass f
RB
v
VRB
V = f
RB
m
ρb
ρ
RB
s
Soil Organic
Matter f
SOM
v
VSOM
V = f
SOM
m
ρb
ρ
SOM
s
Sand f
S
v
VS
V = S× f
Min
v
Silt f
Si
v
VSi
V = Si× f
Min Mineral v
Clay
f
Min
v
f
C
v
VMin
V = f
Min
m
ρb
ρMin
s VC
V = C × f
Min
v
Volumetric
Fraction
Pore Space f
Pore
v
VA
V = φ = 1− f
RB
v − f
SOM
v − f
Min
v
50
(a) (b) (c)
(d) (e) (f)
Figure 4.2: Soil component analysis measurements denoted by points and empirical fitted curves,
including: (a) empirical relationship between root biomass and total OM; (b) linear variation between
SOM and total OM; (c) mass fraction variation of each soil solid component as a function of total
OM; (d) specific density variation used to estimate volumetric fraction; (e) volumetric fraction of
soil solids and pore space compared with measured porosity; and (f) normalized volumetric fraction
fitted model compared with measurements.
51
RB = 0.0016×e
6.393×OM (4.2a)
SOM = 0.9164×OM +0.003 (4.2b)
ρs = −1.535×OM +2.3656 (4.2c)
˜f
i
v =
f
i
v
1− f
Pore
v
(4.3)
where the f
Pore
v denotes the pore space and is equal to porosity (φ).
4.2.3 Soil-Water Retention Curve Parametrization
4.2.3.1 Soil Water Matric Potential Measurement
Soil water matric potential was measured for 66 soil samples collected from nine tundra sites
locations at various active layer depths. The measurements were conducted over a full rage of soil
saturation degrees in a dry down manner (Fig. 4.6 and Fig. 4.5). We used TEROS 21 porous disk
probe for characterizing the matric potential. Soil samples were collected back-to-back from the
surface down to the permafrost tables using a knife and a 64 oz plastic container from each soil
pit. The samples were shipped to the University of Southern California for lab measurement. Each
sample length is approximately 11.5 cm and fills the entire container (Fig. 4.3a). Upon arrival at the
lab, samples were divided in half. For each resulting sample, the TEROS 21 porous disk probe was
inserted into the middle of the soil, and the measurement was conducted two times from saturation
to dry regime. For each measurement, we made sure the sensor had good hydraulic contact with
the soil to make accurate measurements. Measurements were started by taking the samples to the
saturation, and 20 measurement points were conducted for each soil moisture point. We report the
mean value here. The samples were under a constant airflow generated by a network of A/C fans
to expedite the evaporation. The gravimetric weight loss of soil samples due to evaporations was
recorded and translated into volumetric soil moisture, knowing the sample volumes (Fig. 4.4).
52
(a) (b)
Figure 4.3: Sample harvested from permafrost active layer. (a) Surface sample at Creamers Field.
(b) Surface sample at Scottie Creek
(a) (b) (c)
Figure 4.4: A total of 66 soil samples were collected from 13 sampling locations at 9 sites. The
samples were divided into half, then TEROS 21 sensors were inserted to measure soil matric
potential properties. Samples were under a constant air circulation caused by a network of cooling
fans to facilitate the moisture evaporation. Sample weight loss was recorded from saturation to dry
regime and the gravimetric moisture content was translated to volumetric moisture content knowing
the sample volume. (a) North slope samples. (b) Interior Alaska samples. (c) Network of cooling
fans to circulate the air and expedite the evaporation.
53
Figure 4.5: Distribution of measured soil water matric potential (pF = log10(ψm [hPa])) as a
function of SW for various soil samples using TEROS 21 sensors.
(a) (b) (c) (d)
(e) (f) (g) (h)
Figure 4.6: Measured matric potential for 66 soil samples collected from permafrost active layer,
measurement conducted from saturated to oven dry region. The Van Genuchten water retention
curve is being fitted to the measured data, and estimated model parameters being used for empirical
model parameterization. The Campbell curve also being fitted, but the figures are not shown to
avoid clutter. The dot with same color denotes one soil sample and measurement covers the full
range. Color bar in each plot shows the variation of total organic matter in each soil sample and
category(a) shows the soil samples with the range of OM between [0−5]%. (b) shows the OM
range between [5−10]%. (c) shows the range between [10−35]%. (d) shows the range between
[35 − 60]%. (e) to (f) shows the range from [60 − 100]% with increment of 10%, it appears the
beyond 60% the soil water retention curve behaves fairly similar, while the maximum saturation
level (porosity) is monotonically increasing.
54
4.2.3.2 Campbell SWRC Model Parametrization
From these measurements (Fig. 4.5), the Campbell model parameters, including air entry potential
(ψs) and the exponent parameter (b) were estimated to reconstruct the soil water retention curve [97].
To determine the SWRC model parameters, we categorized the soil observation into two groups with
linear (ψs) and logarithmic (b) behavior. The arithmetic mean was used to find each component
(RB, SOM, and Min) contribution to the following soil parameters:
ψs = ˜f
Min
v ψ
Min
s + ˜f
SOM
v ψ
SOM
s + ˜f
RB
v ψ
RB
s
(4.4a)
log10(b) = ˜f
Min
v
log10(b
Min) + ˜f
SOM
v
log10(b
SOM) + ˜f
RB
v
log10(b
RB) (4.4b)
Campbell model parameters for eleven classes of mineral soils were used base on Cosby et al.,
(1984), where mineral b
Min and ψ
Min
s
can be fully characterized using mineral texture as shown in
Fig. 4.7 and Eq. (4.5) [98].
θ
Min
r = ln(0.48× f
C
m +1.0699) (4.5a)
α
Min =
1
5.92×
√
2π
e
−
1
2
(
ln(100×f
C
m)+27.59
10.76 )
2
(4.5b)
n
Min =
1
0.0045×
√
2π
e
−
1
2
(
ln(100×f
Si
m )−2.49
0.96 )
2
(4.5c)
b
Min = 16.1× f
C
m +2.826 (4.5d)
|ψ
Min
s
| = 10−1.31×f
S
m+1.88 (4.5e)
55
(a) (b) (c)
(d) (e)
Figure 4.7: The van Genuchten, and Campbell water retention curve parameter for purely mineral
soil. The data for van Genuchten SWRC parameters are adapted from M.G. Hodnett et al., (2002),
and data for Campbell SWRC parameters are adapted from B. J. Cosby et al., (1984) [98]. (a)
Shows the behavior of residual water content (θr), which is modeled based on Clay mass fraction.
(b) Silt mass fraction was used to model the (α). (c) Clay mass fraction was used to model the
parameter (n) of van Genuchten SWRC. (d) Sand mass fraction shows a high correlation with (ψs).
The (b) parameter of the Campbell SWRC can be modeled with Clay mass fraction.
To find the other subsurface constituent SWRC parameters for RB and SOM, a few simple
functions were fitted to the observed b and ψs values obtained from the soil measurement with
varying OM (Fig. 4.8). Consequently, the following set of equations was used to determine ψs
,
while similar approach was used to derive the other parameters:
˜f
Min
v
(OM = 0)
˜f
SOM
v
(OM = 0)
˜f
RB
v
(OM = 0)
˜f
Min
v
(OM = 70)
˜f
SOM
v
(OM = 70)
˜f
RB
v
(OM = 70)
˜f
Min
v
(OM = 100)
˜f
SOM
v
(OM = 100)
˜f
RB
v
(OM = 100)
ψ
Min
s
ψ
SOM
s
ψ
RB
s
=
ψ
Min
s
ψs(OM = 70)
ψs(OM = 100)
(4.6)
As mentioned above, OM = {0, 70, 100}% refers to respective pure mineral, soil organic matter,
and root biomass fractions. Equation. (4.6) shows the set of calculations for estimating ψ
i
s
, or
interchangeably we use the log10 to find the b
i
, where i=RB, SOM, Min. The distribution of each
parameter was found by solving eq. (4.6) for all eleven tundra soil types (Fig. 4.9). As expected, the
SWRC parameters for mineral soil varies for different soil types, however the distributions for RB
and SOM show very small variations (Fig. 4.9 and 4.10).
56
θ
OM
r =
1
4.4×
√
2π
e
−
1
2
(ln(OM)−1.4)
2
(4.7a)
α
OM = 0.06×OM2 −0.09×OM +0.05 (4.7b)
n
OM = 0.75×OM2 +0.58×OM +1.67 (4.7c)
b
OM = (8.8×OM2 +5.7×OM) +16.8×(cos(π
OM
2
)−0.85) (4.7d)
|ψ
OM
s
| = −90×OM2 +98.3×OM +21.5 (4.7e)
(a) (b) (c)
(d) (e)
Figure 4.8: The estimated SWRC parameters from measurement. To solve the set of equations
in equation (4.6), simple equations (4.7) were fitted to estimated parameters. The value of each
parameters at OM=0, 70, 100 % are designators for the pure mineral, soil organic matter and root
biomass. These values then use on the right side of equation (4.6), to find the contribution of
each subcomponent of samples. Note that the pure mineral soil SWRC parameters as described in
figure S4 are a function of mineral texture. Therefore in equation (4.6), those value find based on
figure 4.7. However, the SWRC parameters value for RB and SOM, will be find based on solving the
system of equations. (a)-(c) show the fitted curve as function of OM for Van Genuchten parameters.
(d), and (e) show the Campbell parameters.
57
(a) (b) (c)
(d) (e)
Figure 4.9: Equation (4.6) and (4.9) was solved for 11 types of mineral soil to find the distribution
of each parameter. The distribution of SWRC parameters for various (x
i
j
, or log10(y
i
j
)) for i= RB,
SOM, Min solved in (4.6) or (4.9) was found each soil. The box plot shows the median (red
strip) and the 25% −75% percentile. While the mineral parameters can be find from figure 4.7,
for the SOM and RB we associates the median value for SWRC parameterization, the results are
reported in Table 4.3 accordingly. (a)-(c) show the variation of van-Genuchten SWRC parameters
for different type of mineral soil. (d), and (e) show the variation of Campbell SWRC parameter for
different type of mineral soil.
58
(a) (b) (c)
(d) (e)
Figure 4.10: The parameters (x
i
j
, or log10(y
i
j
)) as shown in figure 4.9 for eleven type of mineral soil
were used to find the SWRC parameter behavior for the total OM, where the contribution of each
component is calculated using arithmetic or logarithmic mean of normalized volumetric fraction.
(a)-(c) show the variation of van-Genuchten SWRC parameters for different type of mineral soil.
(d), and (e) show the variation of Campbell SWRC parameter.
59
4.2.3.3 van-Genuchten SWRC Model Parametrization
To find a model to predict Van-Genuchten SWRC parameters, we categorized estimated parameters
from observation into two groups with linear (n) or logarithmic (α, θr) parameters. The arithmetic
mean was being used to find each component (RB, SOM, and Min) contribution.
n = ˜f
Min
v n
Min + ˜f
SOM
v n
SOM + ˜f
RB
v n
RB (4.8a)
log10(α) = ˜f
Min
v
log10(α
Min) + ˜f
SOM
v
log10(α
SOM) + ˜f
RB
v
log10(α
RB) (4.8b)
log10(θr) = ˜f
Min
v
log10(θ
Min
r
) + ˜f
SOM
v
log10(θ
SOM
r
) + ˜f
RB
v
log10(θ
RB
r
) (4.8c)
(4.8d)
To find the van Genuchten parameters for eleven class of mineral soils we used the data provided
M.G. Hodnett et al., (2002) [99]. Therefore, n
Min
, α
Min, and θ
Min
r
can be fully characterized using
mineral texture (Fig. 4.7).To find the SWRC parameters for the RB (OM=100) and SOM (OM=70),
a few simple functions fitted to the observed n, α, and θr from measurement to find their behavior as
OM varies (Fig. 4.8). For the brevity here we just show a system of equations to find the parameter
n as follow:
˜f
Min
v
(OM = 0)
˜f
SOM
v
(OM = 0)
˜f
RB
v
(OM = 0)
˜f
Min
v
(OM = 70)
˜f
SOM
v
(OM = 70)
˜f
RB
v
(OM = 70)
˜f
Min
v
(OM = 100)
˜f
SOM
v
(OM = 100)
˜f
RB
v
(OM = 100)
n
Min
n
SOM
n
RB
=
n
Min
n(OM = 70)
n(OM = 100)
(4.9)
where, as mentioned above the OM=0,70, and 100 are designators of pure Mineral, Soil Organic
Matter and Root Biomass fractions. The equation (S-2) shows the set of equations for finding the
n
i
, or interchangeably if we use the log10 to find the (α
i
, and θ
i
r
), where i= RB, SOM, Min. We
solve the equation (4.9) for all eleven types of soil, and we find the distribution of each parameter.
As expected, the SWRC parameter for mineral soil varies for different soil types, however the
distribution for RB and SOM shows very small variation (Fig. 4.9, Fig. 4.10). The median value of
the SWRC parametrization for each subcomponent is reported in Table. 4.3.
Table 4.3: Median value of SWRC parametrization of 11 types of tundra soil for organic subcomponents. As for mineral part, the actual value was calculated using the Fig. 4.7. The value reported
for RB and SOM can be used in Equation (4.8) and (5.1) for calculating the variation of SWRC
parameters.
Soil Texture Campbell SWRC
Parameters
Van Genuchten SWRC
Parameters
Soil Type OM
[g/g]%
S
[g/g]%
C
[g/g]%
|ψs
|
[cm]
b
[−]
θr
[cm3/cm3
]
n
[−]
α
[cm]
RB 100 - - 28.63 0.22 0.03 3.03 0.024
SOM 70 - - 58.52 1.81 0.04 2.61 0.013
Min (Example) 0 36 25 25.5 6.89 0.17 1.46 0.032
60
4.2.4 Soil-Water Dielectric Prediction
Once the SWRC is fully parameterized based on the volumetric fractional contributions of soil
solid subcomponents, we utilize a physics-based approach for the soil-water dielectric prediction, in
which soil-water dielectric behavior is explained by the Debye relaxation model [100]. We then use
the Eyring equation to show that the water dielectric relaxation time can be predicted from the soil
water retention curve [93, 95]. The complex temperature-dependent single-relaxation Debye model
for soil-water can be written as follows:
εsw = εsw∞ +
εsw0 −εsw∞
1−i(2π f)τsw
+i
σsw
(2π f)ε0
(4.10)
where εsw0 [−] is the static dielectric constant (at f = 0), high-frequency dielectric constant (as
f → ∞ ) is denoted by εsw∞ [−] , the relaxation time is described by τsw [ns], and electrical
conductivity due to salinity [psu] is described by σsw [S/m]. For free water (not soil-water εsw)
the Debye model parameters (ε f w∞, ε f w0, τ f w, σf w) are expressed empirically in Ulaby et al.,
(2014) [25]. To find the soil-water Debye parameters, we assume that all of the parameters except
relaxation time (τsw) of the soil-water molecules are similar to free water [93, 95]. The relaxation
time (τsw) of soil-water molecules can be modeled from the Eyring approach [101]:
τsw(T,θ) = h
kBT
e
h
∆G
∗
sw(T,θ)
RT
i
(4.11)
where h and kB are the Planck and Boltzmann constants, respectively, T is the soil temperature in
Kelvin, R is the ideal gas constant, and θ is the soil moisture level. The free enthalpy of activation
of water molecules in the soil is described by ∆G
∗
sw [kJ/mol]. Hilhorts et al., (2001) argue that
the difference between the Gibbs energy of activation of free water molecules (∆G
∗
f w) and water
molecules inside the soil matrix (∆G
∗
sw) is related to the soil matric potential (ψm(θ) [kPa]), where
V [m
3/mol] is the molar volumetric fraction of water.
∆G
∗
sw(T,θ) = ∆G
∗
f w(T,θ) +|ψm(θ)|V (4.12)
Note that in eq. (4.12) free water solely refers to a water molecule at standard condition. Consequently, we incorporate eq. (4.11) and (4.12) into eq. (4.13). The dielectric properties of water
inside soil matrix can be then predicted as follows:
εsw = εsw∞ +
1
θ
Z θ
0
εsw0−εsw∞
1−i2π f
h
kBT
e
∆G∗
f w(T)+|ψm(θ)|V
RT
dθ +i
σsw
2π f ε0
(4.13)
61
4.3 Results
4.3.1 Root Biomass to Predict Permafrost Soil Water Retention Curve
Behavior
Quantitative volumetric descriptions of the subsurface coarse organic ( > 2mm) components as root
biomass, fine soil organic matter ( < 2mm), and mineral fraction help find the contribution of each
subcomponent in governing the behavior of SWRC model parameters. Root biomass is particularly
important, since it is widely missing in previous ecosystem model parametrizations and can be used
instead of fiber content to describe peat and organic permafrost soil physics [63, 102, 103] . Root
biomass exhibits a continuous distribution from purely mineral (where RB=0) to completely organic
soil (RB 100); this framework overcomes the limitation of fiber content as a sole descriptor of peat
properties [83]. For the purpose of model simulation, the average observed mineral texture fractions
can be replaced by more generic soil properties that include sand=36% and clay=25% [7]. Both
the SWRC from Campbell and model van-Genuchten parameters for this soil type under varying
OM levels show good agreement between estimated parameters derived from measurements and
modeling (Fig. 4.11, Fig. 4.12) . However, note that the parameters show larger variation for lower
organic range, and this behavior is expected (Fig. 4.10).
(a) (b) (c)
(d) (e)
Figure 4.11: Full parameterization of SWRC using the input variables OM, sand and clay fraction,
with blue markers showing estimated SWRC parameter values from observations, and the parameterized model (equation (4.4), (4.8)) in black curve.(a)-(c) show the variation of van-Genuchten
SWRC parameters. (d), and (e) show the variation of Campbell SWRC parameters.
62
(a) (b)
Figure 4.12: Behavior of the reconstructed SWRC for various OM levels. (a) van-Genuchten. (b)
Campbell.
4.3.2 Eyring equation as a predictor for soil-water dielectric properties
The relaxation time of water inside the soil matrix can be modeled from the Eyring equation, which
incorporates the water matric potential (Fig. 4.12). For soils approaching saturation, the relaxation
time behavior (Fig. 4.13) is more similar to the free water relaxation time (0.01 ns) predicted from
Ulaby et al. (2014). As the saturation level decreases, the relaxation time for less organic soils
decreases, whereas more organic soils maintain the same free water behavior at lower saturation
levels. We then find the soil-water from the soil water retention curve for various organic soils
and a mineral texture of sand=36%, and clay=25% as the saturation level varies (Fig. 4.14). The
dielectric of soil water is calculated at 70 MHz, which is the TEROS 12 dielectric probe operation
frequency, by which we measured the soil sample dielectric properties (TEROS 12 manual 2020).
The soil-water dielectric permittivity (real part) and loss (imaginary part) for mineral soil are smaller
than those for organic soil. For highly organic soil the associated water dielectric behavior is fairly
similar over a large range of OM variation (see the OM range between 65-95 in Fig. 4.14). This is
due to the small variation of relaxation time as well as the saturation level (porosity) within this
range (Fig. 4.2).
63
(a) (b)
Figure 4.13: Estimated relaxation time of soil-water for various OM levels. (a) van-Genuchten. (b)
Campbell.
64
(a) (b)
(c) (d)
Figure 4.14: Real part of the soil-water dielectric behavior as predicted from a the continuous phase
approach. Imaginary part of soil-water dielectric behavior (dielectric loss). (a-b) van-Genuchten.
(c-d) Campbell.
65
4.4 Discussion
The full soil water retention curve (SWRC) parameterization presented in this study covers a vast
tundra landscape and a wide gradient of soil organic matter content, providing new information
that can be used in ecosystem modeling and potentially leading to model predictions with substantially reduced uncertainty. For example, the new parameterization provided in Table. 4.3 may be
incorporated into ecosystem models such as community land model (CLM) in order to improve its
representation of detailed soil characteristics particularly the root biomass layer and its differences
compared with finer soil organic matter [44, 104, 105] (Huntzinger et al. 2020 ERL; Wieder et al.
2019 GRL; Lawrence et al. 2015 ERL). The work presented here can be combined with the active
layer soil profile model to capture the large variation of these properties throughout the profile [6].
In addition to immediate implications of the proposed SWRC parameterization for land surface
models, in this study, we developed an integrated framework that relates the hydrological properties
of soil to water dielectric properties within the permafrost active layer. Previous studies used similar
approaches for mineral soils, either using a discrete phase or continuous phase approach [92,93,106].
In the discrete phase approach, the water inside the soil matrix is treated as bound and free water,
where the bound water fraction can be associated with the permanent wilting point or specific
surface area [107, 108] . However, soil water dielectric properties still remain unknown [96].
Furthermore, other work indicates the that the overall soil-water dielectric behavior might be
impacted by microstructure and phase and not “bound water” [94, 109].
4.5 Conclusions
Here, we extend the continuous phase approach by providing detailed experimental investigation
that incorporates organic soil into the modeling framework and simultaneously parametrize SWRC
for Arctic organic soil. This is the first study to develop an end-to-end generalized model that starts
with basic soil properties as input (OM, sand, and clay) and characterizes key parameters needed to
reconstruct the water retention curve, which can be used to find soil water dielectric properties. This
approach effectively links hydrology with electromagnetic principles, which can harmonize the
ecosystem and microwave radar and radiometer models. While we demonstrated a physics-based
model to predict soil-water dielectric behavior, an independent validation of soil-water dielectric
was not performed, due to the absence of existing measurements. However, the behavior of water in
highly organic soil, compare to mineral soil represent a realistic case, in which is more similar to
free water. Furthermore, the dielectric behavior of soil-water presented in this work are close to
existing literature for mineral soil-water (bound water) dielectric values that initially were optimized
as curve fitting variable [29, 110].
Exploiting the volumetric fraction approach in SWRC parametrization (i.e., root biomass,
soil organic matter, mineral fraction), would be helpful for inclusion the contribution of each
subcomponent for a realistic representation of soil-water dielectric in a multi-phase organic soil
dielectric mixing model. The resulting organic soil dielectric models can be incorporated into a
new radar retrieval algorithm that are more effective in estimating pertinent active layer carbon and
water characteristics in permafrost landscape.
66
Chapter 5
Organic Soil Dielectric Model: Electromagnetic Prespective
Disclaimer: The content of this chapter is adapted in large from the following papers:
I-2-2 Published Dataset [8]: K. Bakian-Dogaheh et al., ”Soil Matric Potential, Dielectric, and
Physical Properties, Arctic Alaska, 2018“ ORNL DAAC, 2023.
I-2-3 Article in Review 1
: K. Bakian-Dogaheh et al., “Coupled Hydrologic-Electromagnetic
Framework to Model Permafrost Active Layer Organic Soil Dielectric Properties”
Arctic permafrost soils contain a vast reservoir of soil organic carbon (SOC) vulnerable to
increasing mobilization and decomposition from polar warming and permafrost thaw. How these
SOC stocks are responding to global warming is uncertain, partly due to a lack of information on
the distribution and status of SOC over vast Arctic landscapes. Soil moisture and organic matter
vary substantially over the short vertical distance of the permafrost active layer. The hydrological
properties of this seasonally thawed soil layer provide insights for understanding the dielectric
behavior of water inside the soil matrix, which is key for developing more effective physics-based
radar remote sensing retrieval algorithms for large-scale mapping of SOC. This study provides
a coupled hydrologic-electromagnetic framework to model the frequency-dependent dielectric
behavior of active layer organic soil. For the first time, we present joint measurement and modeling
of the water matric potential, dielectric permittivity, and basic physical properties of 66 soil samples
collected across the Alaskan Arctic tundra. The matric potential measurement allows for estimating
the soil water retention curve, which helps determine the relaxation time through the Eyring
equation. The estimated relaxation time of water molecules in soil is then used in the Debye model
to predict the water dielectric behavior in soil. A multi-phase dielectric mixing model is applied
to incorporate the contribution of various soil components. The resulting organic soil dielectric
model accepts saturation water fraction, organic matter content, mineral texture, temperature, and
microwave frequency as inputs to calculate the effective soil dielectric characteristic. The developed
dielectric model was validated against lab-measured dielectric data for all soil samples and exhibited
robust accuracy. We further validated the dielectric model against field-measured dielectric profiles
acquired from five sites on the Alaskan North Slope. Model behavior was also compared against
other existing dielectric models, and an in-depth discussion on their validity and limitations in
permafrost soils is given. The resulting organic soil dielectric model was then integrated with a
multi-layer electromagnetic scattering forward model to simulate radar backscatter under a range
1
Initial draft was submitted on 01/19/2027, and has been through 3 review rounds as of 10/30/2024.
67
of soil profile conditions and model parameters. The results indicate that low frequency (P-, Lband) polarimetric synthetic aperture radars (SARs) have the potential to map water and carbon
characteristics in permafrost active layer soils using physics-based radar retrieval algorithms.
5.1 Introduction
In the past several decades, rising temperatures in the northern high latitudes (NHL) have played
a primary role in altering ecosystem dynamics of the Arctic regions. Permafrost, or perennially
frozen soil, is among the dominant subsurface features in the NHL Arctic tundra biome. As Arctic
warming unfolds at more than three times the mean global warming rate, the vulnerability of soil
organic matter exposed by permafrost thaw and the deepening of the active layer needs to be studied
on a synoptic basis. To that end, the NASA Arctic Boreal Vulnerability Experiment (ABoVE)
was designed and is conducting a decadal campaign to study the Arctic ecosystem state properties
that include integrated field and airborne observations capturing a wide bio-geophysical gradient
[5, 26, 111]. Airborne science, particularly the use of long wavelength P- and L-band (430MHz –
1.26 GHz) radar instruments, plays a key role in the ABoVE campaign because microwave remote
sensing has shown the potential to capture and monitor surface and subsurface properties in the
Arctic relating to permafrost at various spatial and temporal scales [55, 112]. Dielectric mixing
models for soils are the critical component in developing physics-based computational algorithms
for retrieving soil moisture and soil organic matter based on radar or radiometer data obtained from
airborne and spaceborne microwave sensors [96, 113]. The lack of a well-established soil organic
dielectric model limits the capabilities of radar retrieval algorithms for mapping the subsurface water
and carbon characteristics in the permafrost landscape [6]. This work takes a comprehensive look
at the current state of the problem by addressing the challenges of previous organic soil dielectric
models and provides insights from measurement and modeling perspectives. Consequently, a
new organic soil dielectric model is developed via detailed joint measurements and modeling of
hydrological and dielectric properties of the permafrost active layer soils in Alaska.
5.1.1 Current State of the Problem: Measurement Perspective
Characterizing the dielectric behavior of soil is a mature field of study and dates back to the early
1980s [91, 114, 115]. However, those early efforts were mainly focused on mineral soils. Studying
the dielectric characteristics of highly organic soils (histosols), typical of the Arctic permafrost
active layer, has gained increasing attention more recently and especially within the last decade.
Table 1 summarizes, to the best of our knowledge, the existing soil dielectric measurements reported
in the literature that contain organic matter content. The measurements are categorized into insitu (field) observations or lab-driven experiments. The field measurements are usually done by
vertical insertion of a probe or opening a soil pit and horizontal insertion of the probe in each soil
layer. The probes utilized in the field campaigns often operate in two manners: either based on
time domain reflectometry (TDR) generating a wideband pulse, or frequency domain capacitive
probes that operate at a single frequency of around 100 MHz or lower. Soil core samples are
usually extracted for gravimetric soil moisture measurements along with detailed texture analysis
to characterize the organic and mineral fractions [7, 67, 88, 116–118]. In Table 5.1, only the work
that simultaneously includes dielectric constant, soil moisture, and soil texture data was reported.
68
Field measurements provide snapshot-type information and can be limited by other underlying
factors, such as weather-related soil moisture variability. However, lab measurements provide a
controlled environment where soil dielectric properties can be measured with greater precision
over a full range of soil moisture conditions by either systematically drying or wetting a soil
sample. Furthermore, the variety of instruments for lab experiments is more diverse, and reportedly
coaxial probes, waveguides, resonant cavities, or dielectric probes have been used for dielectric
characterization [85, 86, 89, 90, 119–121]. The lab measurement instruments often use a vector
network analyzer that can potentially enable a wide frequency response characterization of soil
dielectric up to 15 GHz, particularly using coaxial probes and coaxial waveguides.
The existing challenges in the reported organic soil dielectric measurement in the literature
could be studied from various aspects. Initially and from a textural analysis standpoint, the majority
of in-lab measurements are conducted over a small number of samples that only contain an extreme
range of organic matter (OM) contents. In other words, the soil samples are either highly organic or
highly mineral with minimal OM content. The limited number of samples and associated limited
OM range leads to large uncertainty in OM models developed and validated based on these samples,
particularly for an area such as the Arctic, which encompasses a wide range of soil texture variability.
Additionally, the measurement methods utilized for in-lab characterization are often destructive.
For example, one study reported that soil samples were ground with a coffee grinder to make
them homogenized for filling the coaxial container [113]. This is primarily due to measurement
techniques that are more suitable for homogenized samples, such as mineral soils, which have
fundamentally different physical properties than organic soils. These destructive measurement
methods are likely to change the physics of more heterogeneous organic soils by disturbing the
pore distribution of soil particles. Consequently, as shown in Table 1, the range of soil saturation
(porosity) is often limited to a range [e.g., 0−0.6 m
3/m
3
], whereas in reality, a much higher range
of saturation is expected for organic soils (in 5.1, compare Bircher et al., 2016a and Mironov et al.,
2019 [67, 119]). Lastly, and from a practical standpoint, state-of-the-art land surface remote sensing
radar instruments often operate at a lower frequency range of the microwave spectrum, particularly
at P- or L-bands [122, 123]. Therefore, a wideband frequency response of soil up to 15 GHz is not
expected to be utilized in remote sensing of soil profiles and adds more complexity when dealing
with highly heterogeneous and porous organic soil.
5.1.2 Current State of the Problem: Modeling Perspective
The early development of soil dielectric models focused on mineral soils. The availability of new
organic soil dielectric datasets in recent years has enabled a few organic soil dielectric modeling
studies, which can be broadly categorized into three main types (Fig. 5.1). Initially, empirical
(calibration) models were used to describe simple relationships between soil moisture and measured
dielectric permittivity [67, 89]. While most of these calibration equations are generic polynomial
functions without including soil physical information, a few models reported multivariable frameworks that, besides soil moisture, include other soil properties such as bulk density as inputs [124].
The significance of finding a relationship between soil dielectric and soil bulk density is inherently
due to the strong correlation of bulk density to soil texture, particularly with OM content [7]. The
second category of organic soil dielectric models was adapted from the original work of Mironov
et al., (2004) for mineral soil dielectric modeling, which treats water in soil as having multiple
phases [126]. Through a semi-empirical physics-based model, the dielectric behavior and fraction of
69
Table 5.1: The current state of the problem from a measurement perspective and description of existing soil dielectric measurement data
containing organic matter samples. Point refers to a pair of soil moisture (
θ) and dielectric permittivity (
ε) measurements (
ε,θ). Soil
moisture and dielectric properties can be obtained from respective soil gravimetric and probing measurements acquired during a field
campaign. Sample refers to a “soil sample” under test in a controlled environment e.g., laboratory. Sample measurements are usually
conducted over the entire range of soil moisture conditions, which results in multiple points (
ε,θ) from saturation to completely dry.
Paper
# of
Sample
OM Range
[g/g]%
θ Range
[m
3/m
3
]
Frequency
[GHz]
Temperature
[
◦C]
ε
[−]
Measurement
Methods Type Notes
Malicki et al.,
1996 [124] 62 [0 – 95]* [0 – 0.8] NA*** NA ε
′
r TDR Lab Sieved with 2-mm mesh and packed
Gnatowski et al.,
2018 [116]
278
Points [81 – 86]** [0.25 –0.85] NA NA ε
′
r TDR Field
7 [31 – 93] 0.07 εa 5TE Probe Bircher et al.,
2016a [89] 5 [5 – 15] [0 – 0.9] 0.1 NA
εa Theta Probe Lab
εa: Apparent
permittivity
9 [51 – 98] [0 – 0.85] Bircher et al.,
2016b [67] 5 [3 – 20] [0-0.5] 1.26 20 ε
′
r +iε′′
r
Resonant
Cavity Lab
1.4 Mironov et al.,
2015b, 2010 [90, 121] 1 [80 – 90] [0 – 0.6] [1– 16]
[−30
−25] ε
′
r +iε′′
r
Mironov et al.,
2015a [120] 1 50 [0 – 0.4] [0.05 – 15] [−30
−25] ε
′
r +iε′′
r
Mironov et al.,
2019 [119] 5 [35 – 80] [0 – 0.5] 1.4 [−30
−25] ε
′
r +iε′′
r
[0.01 – 15] Savin et al.,
2020, 2022 [85, 86] 7 35 – 90 [0 – 0.6] 0.435
[−30
−25] ε
′
r +iε′′
r
Coaxial
waveguide Lab
Sample was dried
and then ground
with a coffee grinder.
Technique applied
for mineral soil.
15 [0 – 3] 0.030
9 25 0.030
8 [5 – 69] 0.1
Park et al.,
2019 [87]
1 0.6
[0 – 0.6]
1
20 ε
′
r +iε′′
r
No new
measurement
Lab Literature Based
Park et al.,
2021 [88]
702
Points [0 – 10] [0 – 0.6] 0.05 NA ε
′
r Hydra Probe Field
Rowlandson et al., 2013
Manns et al., 2014
[117, 118]
Liu et al.,
2013 [125] 12 [0 – 18] [0 – 0.6] [0.05– 40] 23 ε
′
r +iε′′
r Coaxial Probe Lab
Bakian-Dogaheh et al.,
2020, 2022 [6, 7]
144
Points [2 – 100] [0 – 0.9] 0.07 [5−15] ε
′
r +iε′′
r Field
This work 66 [2 –100] 0 – 0.95 0.07 22.5 ε
′
r +iε′′
r
TEROS 12
Probe Lab
* In the paper, the organic carbon (OC) is reported, herein we used OM
= 1.72
×OC
** In the paper, the ash (AC) content is reported, herein we used OM
= 100
−AC
*** Not Available
70
water subphases are found based on fitting the water dielectric behavior parameters to the measured
soil dielectric permittivity [85, 86, 90, 119–121, 125]. Two sub-categories of this model include a
spectroscopic model and a single-frequency approach. The spectroscopic model was based on a
single soil sample, which accepts soil moisture (θ), temperature, and frequency as inputs and arrives
at the bound, free, transient bound water and ice dielectric properties through multi-relaxation
empirical dielectric models (MREDM) along with their associated fractions. The single-frequency
approach, however, accepts OM content along with temperature and soil moisture as input parameters. The last category of organic soil dielectric models is similar to the semi-empirical physics-based
approach but relies on certain hydrological assumptions to arrive at the bound water fraction. In
this method, bound water fraction is associated with the permanent wilting point, and bound water
dielectric properties are treated as a variable to fit the measured soil dielectric properties [87, 88].
71
Figure 5.1: The current state of the problem from a modeling perspective. A description of existing
organic soil dielectric models, including: (a) empirical models that relate soil dielectric permittivity
to soil moisture through a generic polynomial; (b) the semiempirical physics-based model developed
by Mironov et al. and consisting of a spectroscopic and single-frequency approach, where organic
matter serves as a model input; (c) the semiempirical physics-based model developed by Park et al.
that relies on wilting point as a proxy measure of bound water.
72
A physics-based radar retrieval algorithm, particularly for permafrost active layer soil, requires
a physics-based organic soil dielectric model that - in the most general form- accepts soil moisture
(θ), OM, sand (S) and clay (C) fractions, temperature (T), and microwave frequency (freq) as inputs
and arrives at the equivalent complex dielectric permittivity of the soil sample. A main idea in the
physics-based modeling framework is to rely on the fundamental soil properties that govern other
physical properties of soil. For instance, bulk density (ρb) and soil porosity (φ) both can be derived
from OM and mineral texture. Therefore, a generic calibration-based model, in which oftentimes
only the real part of the dielectric (relative permittivity) is found through a polynomial function of
soil moisture, won’t be applicable. While the semi-empirical physics-based models such as Mironov
et al. (2017) have introduced major advances in the area of organic soil dielectric modeling, for
a more complete representation of arctic soils, models are needed that can represent the physical
construct of the soil matrix, the full range of soil moisture values, and the full range of organic
matter content. Lastly, Park et al. (2019) proposed a new avenue of organic soil dielectric modeling
by associating the bound water fraction in soil to the permanent wilting point. However, the initial
parametrization of this model is based on Jin et al., (2017), and Yang et al., (2014) in which the
OM variation is constrained to a lower range that doesn’t capture the wide variety of arctic soil
conditions (a more detailed analysis is provided in the discussion section 5.3-5.4) [127, 128].
5.1.3 Remaining Major Challenges
The above literature review reveals two major challenges for a reliable organic soil dielectric model
development: 1) a more realistic approach to model the dielectric behavior of water inside the
soil matrix is needed, and 2) a detailed set of dielectric measurements for a wide range of organic
matter to achieve a more comprehensive model validation is needed. Characterizing the behavior of
water-in-soil has been a challenging open problem in the field of soil dielectric mixture modeling.
Historically, water in the soil would be treated as a discrete multiphase system composed of bound
and free water fractions. Oftentimes, the amount and dielectric properties of bound water would
conveniently serve as fitting parameters to match with measurements and soil dielectric model
predictions [109]. Bound water generally refers to the first few layers of water molecules adjacent
to soil particles and is correlated with the specific surface area (SSA) of soil particles [29]. Over
the past few decades, a number of approaches have been proposed for determining the amount of
bound water volumetric fraction and estimating its dielectric properties. For example, some models
suggested the relaxation time of bound water molecules, and the associated volumetric fraction can
be found as a function of distance from soil particles, in which the distance is related to the soil
bulk density and SSA [108, 129–131]. While specific surface area has been shown as an essential
parameter that governs the physical and chemical properties of porous media, a well-established
relationship between SSA and general soil physical properties is required for soil dielectric modeling.
Particularly for Arctic organic soil, the basic information of soil physical properties, along with a
comprehensive SSA characterization, are very sparse. Petersen et al., (1996) showed that SSA is
highly correlated to water-in-soil content at -1500 kPa. In the water-in-soil retention curve, this
pressure is known as the permanent wilting point, where plants are no longer able to overcome the
adsorption force between solid soil particles and water molecules [132]. Accordingly, this provided
new promise in soil dielectric modeling, in which the wilting point (θwp) has been assumed as a
proxy for determining the bound water fraction in soil [87, 92].
73
While the importance of determining dielectric properties for different water subphases (bound
and free) is apparent in governing soil dielectric permittivity, some other studies note the additional
importance of other parameters such as structural configuration, bulk density, and porosity [110,
133–135]. Overall, there has been debate on the contribution of “bound” water to govern the
(water content – permittivity) relationship in soil compared to the “microstructure” and “phase
configuration” that is governed by inter/intra aggregate pores [94, 109, 136]. The boundary between
inter/intra aggregate pores could be determined using the hydraulic critical water content (θhc)
calculated from the soil water retention curve (SWRC). Accordingly, at θhc a change in dielectric
response is expected.
Whether the changes in soil dielectric properties at lower soil moisture levels could be associated
with the critical water content (θhc), or permanent wilting points (θwp) a sufficient understanding of
water dielectric properties inside soil still remains unknown, due to the lack of a direct measurement
method. Regardless, the hydrological properties of soil in the form of soil water retention curves
have been shown to be important for determining the soil dielectric permittivity. Additionally,
other studies have suggested another approach in dealing with water dielectric properties in soil.
Hilhorst et al., (2001) suggested that water-in-soil should be treated as a continuous phase, where
the Debye relaxation model can predict its dielectric permittivity. Accordingly, the relaxation time
of water-in-soil molecules can be found from the Gibbs free energy enthalpy through the Eyring
equations, where the Gibbs energy is associated with soil matric potential [95]. While this approach
shows promise toward establishing a universal organic-mineral soil dielectric model, it has not
been widely verified and experimentally investigated, and it has only been studied for very limited
mineral soil conditions [93].
5.1.4 New Set of Dielectric and Matric Potential Measurement and Modeling
The significance of using a soil water retention curve in modeling water-in-soil dielectric permittivity
goes beyond soil dielectric modeling and can potentially synergize the modeling activities of
electromagnetic and hydrology communities. However, a detailed soil measurement is needed
to explore the validity of this model experimentally. To that end, a total of 66 soil samples were
harvested from 9 sites within the North slope and interior Alaska ( 5.2). Five sites were located
within the North slope including Franklin Bluffs (FB), Sagwon (SGW), Happy Valley (HV), Ice
Cut (ICC), and Imnavait Creek (IMN). The sites in interior Alaska include Eight Mile Lake (EML),
Creamers Field (CF), Ballaine Road (BR), and Scottie Creek (SC). Sampling locations fall within
airborne SAR transects from the NASA ABoVE Airborne Campaign (AAC). Samples were carefully
extracted from 12 soil pits and were shipped to the University of Southern California for further
analysis. A comprehensive soil characterization was conducted that included measuring dielectric,
matric potential, and volumetric soil moisture for all soil samples. Furthermore, a detailed soil
texture analysis was performed to fully characterize the physical properties of soil samples, such
as total organic matter, root biomass, soil organic matter, bulk density, porosity, and fiber content.
These measurements form the basis for the model development and validation in this paper. We used
a soil dielectric probe (METER TEROS 12), which measures the dielectric permittivity and electrical
conductivity at 70MHz, and a TEROS 21 porous disk probe for measuring soil matric potential; a
complete description of the measurements is discussed in the following method section [62, 137].
74
Figure 5.2: Locations of our nine study sites and associated land cover types across Alaska. The
Alaskan North Slope, and interior Alaska regions are indicated by the green and yellow shades,
respectively, in the inset in (a). The purple and cyan boxes around (a) and (b) correspond to the
same color boxes in the inset map, respectively. Black dots in (a) and (b) show the site locations
where soil samples were collected and analyzed for determining soil characteristics, and laboratory
analysis. Sampling locations fall within airborne SAR transects from the NASA ABoVE airborne
campaign. (c) An example soil profile from an excavated pit, where active layer samples were
harvested from the surface to permafrost table.
75
The work presented here is comprised of both hydrology and electromagnetic perspectives. The
hydrology part of this work is presented in another study (Bakian Dogaheh, In Prep.), where the
volumetric fraction of soil constituents including root biomass (RB), soil organic matter (SOM), and
mineral (Min) content, are used to derive the model soil water retention curve parameters. This paper
presents the remaining work, where the Method section addresses the complete end-to-end coupled
hydrologic-electromagnetic (Hydro-EM) model; provides a detailed description of soil dielectric,
matric potential, and other soil physical properties derived from laboratory analysis, which serve
as the main validation dataset for the model assessment along with additional in-situ soil profile
characterization as ancillary validation. The methods also include discussion on the implication
of the organic soil dielectric model in physics-based radar remote sensing. The Results section
analyzes the organic soil dielectric model performance in estimating soil dielectric properties against
laboratory and in-situ measurements. Various discussion points are then detailed to clarify the
requirements of empirical modeling, organic soil dielectric model behavior at different frequencies
and temperatures; an intercomparison between the new and existing organic soil dielectric models,
and discussion on the limitations of our proposed model. Finally, the importance of the new soil
dielectric model is demonstrated by integrating it into a physics-based radar retrieval algorithm to
investigate the feasibility of the model for retrieving water and carbon characteristics of the active
layer, which is paramount to determining SOC vulnerability in Arctic permafrost landscapes.
5.2 Methods
5.2.1 Coupled Hydro-EM Approach for Soil Dielectric Modeling
The framework of an end-to-end Hydro-EM approach for modeling the dielectric properties of
organic soil aims to arrive at a model that relates the input parameters including soil moisture,
organic matter, mineral texture, temperature, and frequency to the organic soil dielectric behavior
(Fig. 5.3). The framework consists of a hydrology perspective, from which one can determine the
soil water retention curve of a given soil sample through a detailed model parameterization scheme,
using basic soil physical properties such as root biomass, soil organic matter, and mineral fraction.
The Eyring equation bridges the hydrology and electromagnetic components of the framework by
relating the estimated soil water retention curve to predict the water relaxation time in soil, which
can then be applied to a Debye relaxation model to determine the water-in-soil dielectric properties.
Finally, the resulting water dielectric properties are inserted into a dielectric mixing model, where
the contribution of water and other subphases in soil are taken into account to arrive at the effective
dielectric behavior of the organic soil samples.
76
Figure 5.3: The end-to-end coupled hydrologic-electromagnetic organic soil dielectric model aims
to use basic soil properties (including soil moisture, organic matter, mineral texture, temperature,
and frequency) as input parameters to determine the effective soil dielectric of the soil sample. The
model consists of a hydrology perspective that parametrizes the soil water retention curve using
various inputs. The electromagnetic perspective relates the estimated soil water retention curve to
the soil water relaxation time using the Eyring equation and arrives at the water-in-soil dielectric
condition using the Debye dielectric model. Finally, the resulting water-in-soil dielectric is applied
to the organic soil dielectric mixing model along with other subphases to calculate the organic soil
dielectric properties.
5.2.1.1 Water-in-Soil Dielectric Model
A detailed soil model parameterization scheme was developed from the hydrology perspective,
which aims to model the soil water retention curve (SWRC) parameters. In this work, we present
a summary of the parameterization scheme for the Campbell water retention curve, while a more
detailed parameterization description is provided in previous chapter (Bakian Dogaheh, In Prep.).
77
The Campbell SWRC relates the soil saturation fraction (SW) and soil matric potential (ψm) through
an exponential model for non-saturated zones [97]:
ψm = ψs(SW)
−b
(5.1a)
SW =
θ
φ
(5.1b)
where, the Campbell model parameters include air entry potential (ψs) and the exponent parameter
(b). Soil saturation fraction (SW), can be found as the normalized ratio of soil moisture (θ) with
respect to maximum saturation or porosity (φ). The Campbell model parameterization developed in
our previous work suggests that ψs and b can be derived from the contribution of three main solid
components of the soil: root biomass (RB), soil organic matter (SOM), and mineral fraction (Min).
The total organic matter (OM) as shown in Eq. (5.2) consists of RB, which refers to all organic
matter larger than 2 mm in diameter, and SOM, which refers to organic matter less than 2 mm in
size (Compare ground sample, RB and SOM in Fig. 5.2c). Throughout this paper, the soils refer
to material existing in a ground sample that are less than 2 mm in diameter. Additionally, mineral
fraction refers to the mineral parts of the soil particles that are determined through hydrometer
methods for the samples and include sand (S), silt (Si), and clay (C) fractions.
OM = RB+ (1−RB)×SOM (5.2)
While RB and SOM are the independent variables for characterizing organic properties of soil
samples, based on detailed soil physical properties measurements we developed empirical equations
to determine these properties along with other soil properties such as bulk density (ρb), specific bulk
density (ρs), and porosity (φ) as OM varies between [0−1] [g/g].
RB = 0.0016×e
6.393×OM (5.3a)
SOM = 0.9164×OM +0.003 (5.3b)
ρs = −1.535×OM +2.3656 (5.3c)
ρb = e
0.564S+0.8134C−3.143OM (5.3d)
φ = −0.3733×ρb +0.9282 (5.3e)
In eq. (5.3), bulk density was expressed as a function of total organic matter (OM), and the mass
fraction of sand (S) and clay (C) in soil. Accordingly, the mass fraction for each of the solid
components can be found through the following equations:
f
RB
m = RB (5.4a)
f
SOM
m = (1−RB)×SOM (5.4b)
f
Min
m = (1−RB)×(1−SOM) (5.4c)
f
S
m = S× f
Min
m (5.4d)
f
C
m = C × f
Min
m (5.4e)
f
Si
m = Si× f
Min
m (5.4f)
(5.4g)
78
Note that in determining mass fractions, we assumed the soil samples are gravel (rock, pebble) free.
The volumetric fraction (f
i
v
) of each subcomponent denoted with i=RB, SOM, or Min, and can
be found by incorporating the specific density (ρ
i
s
) of each element into the corresponding mass
fraction (f
i
m) and bulk density (ρb).
f
i
v = f
i
m ×
ρb
ρs
(5.5a)
˜f
i
v =
f
i
v
1−φ
(5.5b)
We use OM=0, 70, 100% as designators of respective pure mineral, soil organic matter, and root
biomass fractions, respectively. Therefore the corresponding specific density of RB, SOM, Min,
can be find as to the ρ
RB
s = 0.8306,ρ
SOM
s = 1.29,ρ
Min
s = 2.36 Accordingly, we use eq. (5.5b) to
normalize the volumetric fraction of each sub component to the total pore space fraction, which
determines the contribution solid sub components of soil samples in deriving the SWRC model
parameters as follows:
ψs = (ψ
Min
s
)
˜f
Min
v + (58.52)
˜f
SOM
v + (28.63)
˜f
RB
v
(5.6a)
b = (ψ
Min
s
)
˜f
Min
v ×(1.82)
˜f
SOM
v + (0.22)
˜f
RB
v (5.6b)
(5.6c)
The coefficients in Eq. (6) are adapted from chapter 5. Additionally, the mineral soil contribution
can be expressed using the following empirical relationship:
ψ
Min
s = 10−1.31×S+1.88 (5.7a)
b
Min = 16.1×C +2.8266 (5.7b)
(5.7c)
where S and C are sand and clay fractions, respectively, and vary between [0–1] [g/g]. Equations
((5.2)-(5.7)) enable the complete reconstruction of the Campbell soil water retention curve. The
SWRC model parameters were simulated for an average soil consisting of 36% sand and 25%
clay as well as for all different classes of mineral soil (all class types) over the full OM range of
[0−100][g/g]%, shown as the shaded area in Fig. 5.4. Once the SWRC is fully characterized, the
water-in-soil dielectric can be predicted by incorporating the SWRC into the Eyring equation to
find the relaxation time of water-in-soil, and finally by applying the relaxation time into Debye
relaxation model.
εw = εw∞ +
1
θ
Z θ
0
εw0−εw∞
1−i2π f τw
dθ +i
σw
2π f ε0
(5.8)
where εw0 [−] is the static dielectric constant (at f = 0), the high-frequency dielectric constant (as
f → ∞ ) is denoted by εw∞ [−], the relaxation time is described by τw [ns], electrical conductivity is
described by σw [S/m], and ε0 is the free space permittivity.
Buchner et al., (1999) proposed that the relaxation time of water-in-soil (τw) is directly connected
to the corresponding average number of hydrogen bonds, which must be broken to achieve ‘mobile’
water molecules, which are able to re-orient with the applied electromagnetic field [101]. Arrhenius
79
(a) (b) (c)
Figure 5.4: In all cases, the solid lines are derived from the model simulation for a fraction of
S=36% and C=25% as OM varies between [0−100] [g/g] %, and the shaded areas are associated
with the total range of variation simulated for all classes of mineral soil. (a) Shows the volumetric
fractions of solid soil components (solid plot), which includes root biomass, soil organic matter, and
mineral soil, and the porosity along with their associated variation (shaded) as the model presented
in Eq. ((5.2)-(5.5)) simulated different classes of mineral soil. (b) Shows the variation of air entry
potential (ψs) of Campbell SWRC model parameters. (c) The behavior of exponent parameters of
the Campbell SWRC and its associated variation.
equations with temperature independent parameters fail to capture the connection of τw to the
kinetics of the hydrogen-bond network. Therefore, the characteristic feature of τw with nonlinear
temperature dependence of its activation energy, suggests that τw (T) should be modeled by an
Eyring approach with a temperature-dependent free energy of activation (∆GW ∗) [93, 101].
In equation (5.8) the water-in-soil relaxation time (τw) can be expressed by Eyring equation as:
τw(T,θ) = h
kBT
e
∆G
∗
0
(T,θ)+|ψm(θ)V|
R(T+273.15)
(5.9)
where h and kB are the Planck and Boltzmann constants, T is the soil temperature in Celsius (
◦C),
R is the ideal gas constant and θ shows the soil moisture level. The difference between the Gibbs
energy of activation of free water molecules (∆G
∗
0
[J] ) and water molecules inside the soil matrix
(∆G
∗
W ) is related to the soil matric potential (ψm(θ) [kPa]), where V = 18.07 × 10−6
[m
3/mol]
is the molar volumetric fraction of water. By incorporating eq. (5.9) into eq. (5.8), we can find
the equivalent soil-water dielectric properties. The remaining Debye relaxation parameters (e.g.,
εw∞, εw0, τ0) are assumed to be equal to that of “free-water” and are adapted from Ulaby et al.,
2014 [25]. Similar assumptions have been made in other studies such as Dyck et al., (2019),
where the lower and upper frequency Debye parameter was substituted by existing “free-water”
80
models [109]. Finally, the water-in-soil electrical conductivity (σw) was modeled empirically as a
function of soil mineral texture (see discussion section).
εw0 = 88.045−0.415×T +6.29×10−4 ×T
2 +1.07×10−5 ×T
3
(5.10a)
εw∞ = 4.9 (5.10b)
τ0 = ( 1
2π
)(1.1109×10−10 −3.824×
−12 ×T +6.938×10−14 ×T
2
) (5.10c)
∆G0∗ = ln(
τ0 ×(T +273.15)×kB
h
)×
R
T +273.15 (5.10d)
The full simulation of the model is shown in Fig. 5. For a typical mineral soil that contains 36% sand
and 25% clay, the soil water retention curve was simulated for the full range of saturation and OM
content (Fig.5.5a). Subsequently, the relaxation time is calculated by incorporating the SWRC into
the Eyring equation. Results reveal that the variation of the relaxation time only exhibits non-free
water behavior at the lower end of soil moisture content compared to the overall free-water type
behavior of water in the soil for the majority of the range at higher soil moisture levels (Fig.5.5b).
Finally, the real and imaginary parts of the water-in-soil dielectric are plotted for the variation of
soil moisture and OM (Fig. Fig.5.5c-5.5d).
81
(a) (b)
(c) (d)
Figure 5.5: The full simulation of the hydrology perspective for the full range of soil moisture
and organic matter content for an average mineral texture with S=36% and C=25%. (a) Shows
variation of soil matric potential pF = log10|ψm|.(b) Relaxation time of water molecules in soils.
(c) Real part of water-in-soil dielectric permittivity. (d) Imaginary part of water-in-soil dielectric
permittivity.
Throughout the manuscript the matric potential (ψm) or air entry potential (ψs) is alternatively
represented with kPa or cm units using the following conversion: 1 [kPa] ≈ 10.19 [cm] of water.
5.2.1.2 Freeze/Thaw State
The temperature varies substantially within the permafrost active layer soil profile, and across the
profile the heat flux determines whether the water-in-soil is frozen or thawed [138]. When the soil
temperature reaches the freezing temperature (Tf), not all water-in-soil will be frozen. In winter, the
active layer can experience soil temperatures below −10◦C with about 8% and 6% of volumetric
soil moisture remaining unfrozen in the mineral and organic soil layers, respectively [38].
82
The amount of unfrozen and frozen water content in the soil matrix should be characterized
before incorporating the water dielectric behavior contribution into the dielectric mixing model.
Over the past decades and for fully saturated soils, many approximations have been proposed to
estimate the unfrozen water content in soil (also known as supercooled liquid soil water), including a
power law function (V
UnFrozen
w = A|T|
(−B)
) described by Romanvosky and Osterkamp (2000) [139].
Other works such as Niu and Yong (2006), which are the basis for freeze/thaw modeling for
Land Surface Models such as the Community Land Model-5 (CLM5), describe super cooled soil
water at subfreezing temperatures according to a depression in freezing point [140, 141]. When ice
forms in the soil matrix, the water matric potential (ψm) and vapor pressure over pure ice reach
equilibrium [142]. Fuchs et al., (1978) expressed ψm as a function of latent heat (Lf) and soil
temperature (T) in degree Celsius :
ψm =
Lf(Tf −T)
g(T +273.15)
(5.11)
where Lf = 333000 [J/kg], and g = 9.82 [m/s
2
] is the gravitational constant. The volumetric frozen
water content (V
Frozen
w ) is calculated based on the difference between total water within the soil and
the maximum liquid water (V
UnFrozen
w ) content below freezing temperature (Tf):
V
total
w =
ρ
Frozen
w
ρ
UnFrozen
w
×V
Frozen
w +V
UnFrozen
w (5.12)
In Eq. (5.12), ρ
Frozen
w = 917 [kg/m
3
] refers to ice density and, ρ
UnFrozen
w = 1000 [kg/m
3
] is the
liquid water content.
By equating equations (5.11) and (5.1) describing the soil water matric potential of liquid water,
we can derive the freezing-point depression equation, which can be used to determine the upper
limit of the unfrozen water content at subfreezing temperature:
V
Un f rozen
w =
φ T ⩾ Tf
φ
h
Lf(Tf −T)
gψs
(T +273.15)
i−
1
b
T < Tf
(5.13)
where the ψs
[cm], and b [−] as described previously are the Campbell SWRC parameters. The
freezing temperature (Tf) in general is governed by soil physical properties and can be estimated
through various methods such as variational data assimilation [24]. In this work and for simplicity
we follow the CLM-5 assumptions and assume Tf = 0
◦C.
While Eq. (5.12) is potentially applicable to the full range of soil saturation, for the sake of
model simplicity and in the case of permafrost active layer soil, to find the V
Frozen
w , we assume that
the soil in the vicinity of frozen water table is saturated:
V
Frozen
w =
ρ
UnFrozen
w
ρ
Frozen
w
×(φ −V
UnFrozen
w ) (5.14)
83
It is important to note that Eqs. (5.13)- (5.14) only work for below freezing temperatures, and for
thawed soil we still use Eq. (5.1). The model simulation for a representative tundra soil sample
(OM=80%, S=36%, C=25%) shows the behavior of frozen and unfrozen water content for different
subzero temperatures, where the model exhibits an increase in total volume of water under subzero
temperatures (Fig. 5.6).
Figure 5.6: The simulation of freeze/thaw state, and volumetric fraction behavior of water and
ice content as temperature varies from sub-zero to above zero conditions for a representative soil
sample (OM=80%, S=36%, C=25%). While the OM +S+C summation can exceed 100% based on
the equations provided in (5.4), f
OM
m + f
S
m + f
C
m + f
Si
m = 100% and differentiates the mass fraction
of the entire sample compared to the estimated sand/clay soil fractions.
Dielectric Mixing Model
Once the water-in-soil dielectric properties are characterized, and the freeze/thaw state is determined, the contribution of soil constituents can be incorporated into the dielectric mixing model.
Historically, various soil dielectric mixing models have been suggested for mineral soil dielectric
models (e.g., Ulaby et al., 2014). In this work, we utilize a simplified version that is based on the
volumetric fraction mixing by suggesting an empirical exponent power term (α). The term α varies
between [0.3 − 1] [−] and was found for each soil sample based on the soil physical properties
(discussion section).
εsoil =
(
(f
Min
v
ε
α
Min + f
OM
v
ε
α
OM + f
W
v
ε
α
w + f
A
v
ε
α
A
)
1
α T ≥ Tf
(f
Min
v
ε
α
Min + f
OM
v
ε
α
OM + f
UnFW
v
ε
α
w + f
I
v
ε
α
I
)
1
α T < Tf
(5.15)
The dielectric constant of solid subcomponents usually shows negligible dispersion (no sensitivity
to frequency) and is determined from the literature. Accordingly, for mineral soil, organic soil,
and frozen water (ice) components we use εMin = 4.7, εOM = 1.7, and εI = 3.17, respectively
[91, 143–145].
84
As stated above, for frozen soil, the volumetric frozen and unfrozen water content are found
based on the assumption that the soil is saturated. Therefore, the pore space is only filled with
unfrozen water and ice. In other words, for above-zero (°C) temperature, Eq. (5.15) works for
the whole range of saturation, whereas the mixing model at subzero temperatures is only valid for
saturated soil as described in Eq. (5.13)- (5.14). The total volumetric fraction behavior of each
subcomponent can be described as:
f
W
v + f
A
v + f
Min
v + f
OM
v = 1 T ≥ Tf
f
UnFW
v + f
I
v + f
Min
v + f
OM
v = 1 T < Tf
(5.16a)
f
I
v = V
Frozen
W
f
UnFW
v = V
UnFrozen
W
(5.16b)
5.2.2 Soil Dielectric and Soil Matric Potential Measurement
The soil samples collected for laboratory measurements exhibit a relatively uniform distribution for
low OM content (below 20%, No. 26), and higher OM (above 60%, No. 32), whereas the mid-range
of organic matter content (between 20-60%) is less represented in our samples (Fig. 5.7). Soil
samples were collected from 12 sampling points at 8 locations in the Alaskan North Slope and
4 locations in Interior Alaska. At each sampling point, samples were collected at various depths
through the active layer profile. A brief summary of soil properties collected is provided in Table 2,
along with a full description of the samples in the associated dataset [8]. Notice, for the top soil,
the measurements of soil mineral texture were not applicable (shown with dash) due to minimal
presence of mineral soil.
Figure 5.7: The organic matter (OM) content histogram distribution of the Alaska samples used in
the laboratory analysis for characterizing the soil dielectric and matric potential.
85
Table 5.2: Summary of soil samples collected from the North Slope and Interior of Alaska [8].
Soil Texture [g/g] % No. Site Name Soil ID Depth
[cm]
Mineral Soil type Location OM Sand Silt Clay
1 FB-1-1 [0 – 7.5] Sandy Loam 12.3 58.5 20.5 21
2 FB-1-2 [7.5 – 15] Sandy Loam 9.8 64 17 19
3 FB-1-3 [15 – 22] Sandy Clay Loam 6.7 62.5 16.5 21
4 FB-1-4 [22 – 29] Sandy Loam 6.6 66.5 16.5 17
5 FB-1-5 [29 – 35.5] Silt Loam 8.5 60 19 21
6 FB-1-6 [35.5 – 42] Loam 7.2 50.5 30.5 19
7 FB-1-7 [42 – 48.5] Sandy Clay Loam 4.7 53.5 24.5 22
8
Franklin Bluffs
FB-1-8 [48.5 – 55] Loam
N 69◦48′44.54′′
W 148◦45′59.35′′
5.8 52.5 29.5 18
9 SGW-1-1 [0 – 8] - 50.2 - - -
10 SGW-1-2 [8 – 8] Sandy Loam 9.1 55 27 18
11 SGW-1-3 [16 – 23.5] Sandy Clay Loam 5.4 52 26 22
12 SGW-1-4 [23.5 – 30] Sandy Clay Loam 2.7 55 21 24
13 SGW-1-5 [30 – 37] Sandy Clay Loam 2.8 52 21 27
14
Sagwon
SGW-1-6 [37 – 44] Sandy Clay Loam
N 69◦28′46.48′′
W 148◦33′51.99′′
2.8 45 26 29
15 SGW-2-1 [0 – 6] - 72.8 - - -
16 SGW-2-2 [6 – 12] - 80 - - -
17 SGW-2-3 [12 – 17] - 82 - - -
18 SGW-2-4 [17 – 22] - 66.6 - - -
19 SGW-2-5 [22 – 27] Clay Loam 48.8 23 46 31
20 SGW-2-6 [27 – 32] Clay Loam 9.7 26 40 34
21 SGW-2-7 [32 – 37] Clay 8.4 31 29 40
22
Sagwon
SGW-2-8 [37 – 42] Clay Loam
N 69◦28′35.68′′
W 148◦33′51.96′′
8.9 26 39 40
23 HV-1-1 [0 – 7] - 87.5 - - -
24 HV-1-2 [7 – 14] Silty Clay Loam 17.6 20.5 59 20.5
25 HV-1-3 [14 – 19] Silt Loam 11.1 17.5 53 29.5
26 HV-1-4 [19 – 24] Silt Loam 9 18.5 53 28.5
27 HV-1-5 [24 – 29] Silty Clay Loam 7.2 14.5 56 29.5
28 HV-1-6 [29 – 34] Silty Clay Loam 5.5 14.5 50 35.5
29 HV-1-7 [34 – 39] Silty Clay Loam 6.1 14.5 50 35.5
30
Happy Valley
HV-1-8 [39 – 44] Silty Clay Loam
N 69◦9
′19.28′′
W 148◦50′19.64′′
8.6 16.5 55.5 28
31 HV-2-1 [0 –7.5] - 93.5 - - -
32 HV-2-2 [7.5 – 15] - 89.5 - - -
33 HV-2-3 [15 – 22] - 71.1 - - -
34 HV-2-4 [22 – 29] Silt Loam 6.2 17 60 35.5
35
Happy Valley
HV-2-5 [29 – 36] Silt Loam
N 69◦9
′19.29′′
W 148◦50′30.48′′
7.1 18 55.5 28
36 ICC-1-1 [0 – 7] - 88.1 - - -
37 ICC-1-2 [7 – 14] - 76.3 - - -
38 ICC-1-3 [14 – 20] Loam 17.7 28 49 23
39 ICC-1-4 [20 – 26] Loam 10.4 28 50 22
40 ICC-1-5 [26 – 32] Silt Loam 8.6 29 55 16
41
Ice Cut
ICC-1-6 [32 – 38] Silt Loam
N 69◦2
′30.82′′
W 148◦49′37.31′′
10.7 33.5 49.5 17
42 ICC-2-1 [0 –7] - 83.3 - - -
43 ICC-2-2 [7 – 14] - 79.2 - - -
44 ICC-2-3 [14 – 20] - 72.9 - - -
45
Ice Cut
ICC-2-4 [20 – 26] Loam
N 69◦2
′32.94′′
W 148◦49′31.38′′
41.2 51.5 32 16.5
46 IMN-1-1 [0 – 7.5] - 93.2 - - -
47 IMN-1-2 [7.5– 15] - 67.4 - - -
48 IMN-1-3 [15 – 22] - 74.3 - - -
49 IMN-1-4 [22 – 29] - 61.4 - - -
North Slope of Alaska
50
Imnavait Creek
IMN-1-5 [29 – 36] Loam
N 68◦36′17.90′′
W 149◦18′22.86′′
7.8 44 31 25
51 CF-1-1 [0 – 5] - 87 - - -
52 CF-1-2 [5 – 10] - 85.8 - - -
53 CF-1-3 [10 – 15] - 84.9 - - -
54
Creamers Field
CF-1-4 [15 – 20] -
N 64 ◦ 52′10.08′′
W 147 ◦ 44′20.54′′
79 - - -
55 BR-1-1 [0 – 5] - 92.8 - - -
56 BR-1-2 [5 – 10] - 90.8 - - -
57 BR-1-3 [10 – 15] - 82.1 - - -
58
Ballaine Road
BR-1-4 [15 – 20] -
N 64 ◦ 54′54.00′′
W 147 ◦ 50′19.10′′
86.5 - - -
59 SC-1-1 [0 – 5] - 74.2 - - -
60 SC-1-2 [5 – 10] - 75.7 - - -
61 SC-1-3 [10 – 15] - 65.2 - - -
62
Scottie Creek
SC-1-4 [15 – 20] -
N 62◦41′50.47′′
W 141◦8
′32.40′′
48.3 - - -
63 EML-1-1 [0 – 5] - 100 - - -
64 EML-1-2 [5 – 10] - 96.2 - - -
65 EML-1-3 [10 – 15] - 89.5 - - -
Interior Alaska
66
8-Mile Lake
EML-1-4 [15 – 20] -
N 63◦52′39.32′′
W 149◦15′20.70′′
81.2 - - -
86
Soil Dielectric Measurement
The soil dielectric measurement was conducted using METER TEROS 12 capacitive dielectric
probes (TEROS 12 manual). The TEROS 12 probe consists of 3 needles, which enable measuring
the raw analog to digital converter (ADC) value as an indicator of real part of the soil complex
permittivity (needles 1-2), the measurement of electrical conductivity (σ) that helps characterize
the imaginary part (ε
′′
r =
σ
2πε0 f0
) of the soil complex dielectric permittivity (needles 2-3), and a
thermistor (needle 2) that measures the soil temperature (Fig. 5.8a). The soil measurements were
conducted in the laboratory at an ambient temperature (22.5
◦C).
Figure 5.8: (a) The TEROS 12 sensor enables raw ADC, conductivity and temperature measurements.
(b) Schematic of soil dielectric and soil matric potential measurement set up, where sensors are
inserted horizontally within the saturated soil layer. Measurement was conducted in a dry-down
manner with the help of several fans that accelerated evaporation rates. (c) TEROS 21 sensor
enabled soil matric potential measurement. (d) The batch of 50 samples that were collected from 8
sampling locations in the North Slope of Alaska. (e) A total of 16 soil samples from Interior Alaska
were also collected. (f) Samples on the bench top in the vicinity of the fan used for air circulation.
The sensors were inserted into the soil layer horizontally, and once the excess water was
evaporated, the measurement started as the sample dried down (Fig. 5.8b, 5.8d- 5.8e). At each
measurement point (soil moisture values), the raw ADC and electrical conductivity were recorded
20 times for redundancy. Furthermore, the saturation-drying process was repeated twice to ensure
repeatability. The mean value for each measurement set (each sample consisting of 2 sets) was used
for validation purposes.
87
The TEROS 12 sensors operate at 70 MHz and needles 1 and 2 measure raw ADC values
derived from an internal algorithm to minimize the electrode polarization effect [62]. To translate
raw ADC to relative permittivity (real part of dielectric), usually one can refer to the manufacturer
curve. However, as mentioned in the TEROS 12 user manual, the curve provided by the company
was meant to map the raw ADC to the apparent permittivity εa, which incorporates both real and
imaginary parts of the permittivity [110, 146].
εa = ε
′
(
1+
q
1+tan2(
ε
′′
ε
′ )
2
) (5.17)
Therefore, to calibrate the TEROS 12 sensors, we created several synthetic samples (a mixture
of isopropyl and water) to capture the entire range of relative permittivity [1−80]. Accordingly,
the Agilent 85070E Dielectric Probe Kit and a Vector Network Analyzer were used to measure
the reference dielectric values for each sample. To study the variation among probes, a total of 9
TEROS 12 probes were used, with a total of 45 measurements for each synthetic sample. Using
a ProCheck datalogger and TEROS 12 probe, five measurement points were recorded for each
sensor. Accordingly, a new calibration curve was constructed that enabled analysis of the accuracy
of the provided calibration curve by METER (Fig. 5.9). While the overall behavior of the new
calibration curve is very similar to the manufacturer, there is a slight underestimation between
manufacturer curve compared with our measurement. Therefore, for the analysis in this paper,
we used the calibration curve developed from the mean values of measurements in Eq. (5.18). It
is important to note that the nominal operating frequency of the Agilent Probe starts from 500
MHz, whereas the TEROS 12 sensor operates at 70 MHz. To calibrate the TEROS 12 sensors, we
established a relationship between raw ADC values measured by the TEROS 12 and a reference
dielectric mixture measured by the Agilent Probe. The frequency response for all of the dielectric
mixtures is relatively flat, exhibiting negligible dispersion. Therefore, we assumed the frequency
response for the dielectric mixture behavior at 70 MHz to be similar to those measured at 500 MHz
using the Agilent Probe.
ε
′ =
2.2×10−9 ×ADC3 −1.58×10−5 ×ADC2 +0.035×ADC −27.252
(5.18)
5.2.2.1 Soil Matric Potential
The details of the soil matric potential measurement have been reported in Bakian-Dogaheh et
al., (2023). Here we present a summary of the measurement procedure [8]. To measure the soil
water matric potential, the TEROS-21 sensor uses a solid matrix equilibration technique, which is
achieved by introducing a ceramic disk with known pore size distribution into soil and allowing the
material to reach hydraulic equilibrium (Fig. 5.8c). At equilibrium, measuring the water potential
of the solid matrix of the porous ceramic disk gives the soil water matric potential. The operation of
the TEROS-21 sensor is agnostic to the soil type as long as the hydraulic equilibrium and sufficient
hydraulic connectivity are satisfied according to Second Law of Thermodynamics [137].
8
Figure 5.9: The TEROS 12 manufacturer curve (red line) tends to slightly underestimate the relative
permittivity of reference samples compared to the in-lab generated calibration curve (fitted blue
line). The range of raw ADC values was generated by 45 measurements acquired from 9 TEROS
12 probes. The calibration curve was generated from the measured mean values.
To determine the water potential of the solid matrix (porous ceramic disk), the TEROS-21
measures the dielectric permittivity of the solid matrix. The dielectric permittivity of the porous
ceramic disk is substantially dependent on the moisture content in the pore spaces. The TEROS-21
measures the permittivity of the porous disk, which in-turn can be translated into moisture level.
Such techniques do not impose any requirements for further calibration and are agnostic to soil-type
since the relationship between the engineered porous ceramic disk water content and permittivity
are well established and are dependent on the pore space permittivity (εCeramic), and the amount of
air (εAir) and water (εWater) in the ceramic pore spaces.
εPorous Ceramic Disk = f unction(εWater, εCeramic, εAir) (5.19)
The water potential is inferred from the water content of the porous disk through the water
characteristics (retention) curve of the engineered porous disk. The total soil water potential
(ψt) of the solid matrix can be written from the various subcomponents including pressure (ψp),
gravitational (ψg), osmotic (ψo), and matric (ψm) potentials as follows:
ψt = ψp +ψg +ψo +ψm (5.20)
For the TEROS-21 probe, the first three terms (ψp,ψg, and ψo) are negligible, and only matric
potential is influenced by the forces and attraction of water molecules to soil particles, which is the
dominant element in the total soil water potential. Therefore, in effect the TEROS-21 measures the
soil water matric potential.
The main shortcoming of the porous disk method is the range of measurement, which is limited
by the distribution and size of the pore spaces in the ceramic disk. Additionally, the measurement at
low moisture levels may be less accurate; although, the manufacturer guarantees accuracy down to
wilting point (1500 kPa). Another challenge with the TEROS-21 is ensuring adequate hydraulic
89
connectivity, particularly for highly organic soil; this was addressed by horizontally inserting
the probe within the soil container and using multiple redundant measurements at various soil
moisture levels. While a more detailed description and discussion of the measurement is left to a
forthcoming paper, we note that the major contribution of the soil matric potential measurement
was to build a parametrization scheme for relatively poorly studied tundra organic soil, which has
a significant influence on soil hydraulic and thermal properties [51]. The 66-soil water retention
curves estimated from the measurement of soil matric potential (not shown here) were essential in
developing Equations (5.16) and (5.1).
5.2.2.2 Soil Moisture Measurement
Each sample was brought to saturation by adding water to an overflow range. The samples were
then left until excess water levels decreased to the soil surface as confirmed from visual inspection.
Accordingly, the volume of the saturated soil was then measured and marked on each container (Fig.
5.8b). The average volume of each sample was around 950 [cm3
], comprising a container with
diameter of 16 [cm], and filled to 5 [cm] height. For each measurement point (soil moisture level),
we recorded the mass of soil samples, including the container and sensor. The samples were under
constant air flow generated by several fans, which were turned off for weight measurement (Fig.
5.8d). At each soil moisture level, the total mass of the container, sensors, and soil were measured
to find the equivalent volumetric water content based on knowing the volume of the soil and the
bulk density of the sample.
5.2.3 In-situ Soil Physical Properties and Dielectric Profile Measurement
In 2018, a comprehensive field survey was conducted on the North Slope of Alaska to characterize
tundra active layer soil physical properties (organic matter, mineral texture, bulk density, and
porosity) along with soil moisture and soil dielectric properties throughout the active layer profile.
These measurements were acquired from eight soil pits at five sites. The set of in-situ soil moisture
and dielectric permittivity measurements serves as an additional validation dataset in this work.
Details regarding the various measurement procedures used in this study are described in BakianDogaheh et al., (2020a), while here the measurements are briefly summarized [7].
5.2.3.1 Soil Physical Properties
The field campaign was initially focused to collect a representative sample pool that helps to develop
models to capture OM, SW, and T variation along the active layer profile (z). At each soil pit, two
replicate samples with the interval of 5 cm were extracted from the side wall of the soil pit. The
weight of the samples was measured in the field and samples were shipped to the laboratory for
further analysis to determine in-situ soil saturation fraction bulk-density, porosity, OM content
(Loss-on-Ignition), and soil mineral texture analysis using hydrometer methods.
90
The collective analysis of soil physical properties across the different soil pits resulted in
developing models that capture the variation of fundamental surface and subsurface geophysical
parameters including OM, SW, and T along the active layer soil profile.
OM(z) = OM(z) = OMz0 +
OMM −OMz0
1+e
−β(z−m)
(5.21a)
SW(z) =
1−(1−SWz0)( z
zWT
−1)
2
z ≤ zWT
1 z > zWT
(5.21b)
T(z) = Tz0(1−(
z
zALT
)
2
) (5.21c)
The organic matter profile model in Eq. (5.21)a consists of four parameters, including surface
organic matter (OMz0), and deep mineral organic matter (OMM) along with an empirical shape
factor (β) and the organic layer thickness (zOLT ). Two main parameters, surface saturation fractions
(SWz0) and water table depth (zOLT ) govern the behavior of soil saturation profile. Finally, we
modeled the temperature profile with a quadratic function, where (Tz0) represents the soil surface
temperature, and (zALT ) denotes the active layer thickness. We further assumed that the mineral
fraction through the profile is constant and equal to the average value of the mineral layer.
S(z) = Savg (5.22a)
C(z) = Cavg (5.22b)
Based on our modeling approach the contribution of mineral fractions for the highly organic
soil model parametrization will be very small, since the mineral fraction is negligible. The range of
measured parameters and associated model behavior for OM, S, C, SW, and T and their associated
variations at each depth interval [5 cm] through the profile is shown in Fig. 5.10 for all sites and
sampling locations.
Figure 5.10: The profile behaviors of the active layer soil properties that serve as input parameters
for the soil dielectric model. (a) Organic matter content, (b-c) sand and clay fraction, (d) soil
saturation fraction, and (e) temperature profile.
91
5.2.3.2 In-situ Dielectric Measurements
The soil dielectric measurements in the field were conducted by inserting the TEROS-12 probes
horizontally at the excavated side wall of each soil pit, where the measurement was conducted
before soil sampling. The in-situ dielectric measurements were more detailed across the active
layer profile with an interval depth of 2.5 cm. Besides the soil dielectric measurement, which was
adopted from the raw ADC measurement as described in section 3.2.1, the TEROS-12 probes also
provided measurements of soil temperature and soil electrical conductivity.
This dielectric measurement was used to assess the estimated soil dielectric profile behavior,
which was reconstructed using the organic soil dielectric model and the soil physical properties as
model inputs.
εsoil(z) = ε
′
soil(z) +iε
′′
soil(z) (5.23a)
εsoil(z) = MODEL(OM(z),SW(z),T(z),S(z),C(z); f req) (5.23b)
where the soil complex permittivity including real part (ε
′
soil) and imaginary parts (ε
′′
soil) can be
expressed through MODEL, which refers to the developed soil dielectric model in this work.
5.2.4 Role of Organic Soil Dielectric Model in Physics-Based Radar Remote
Sensing
The ultimate implication of an organic soil dielectric model is the integration of such model into a
physics-based radar retrieval algorithm to estimate the permafrost active layer subsurface geophysical parameters (e.g., organic matter, soil-saturation, and temperature profiles). In forward-centric
retrieval techniques, understanding the forward model is key [147] . The forward model consists
of three main steps: 1) subsurface profile model, 2) soil dielectric model, and 3) electromagnetic
scattering model. First, the geometry of the subsurface will be reconstructed by inserting the state
parameters (X¯
STAT E) into the profile model. In the case of the permafrost active layer, the state
parameters can be described as follows:
X¯ = {OMz0,zOLT ;SWz0,zWT ;h,zALT } (5.24)
where the OM parameters including shape factor (β), and the deep organic matter (OMM), were
assumed to be constant. Furthermore, the (T0,Savg, and Cavg) are assumed to be known. Once the
profiles are reconstructed, they feed into Eq. (5.23) to arrive at the soil dielectric profile at the radar
operating frequencies (freq). Then a layered dielectric structure is constructed (Fig. 5.11). Finally,
this layered structure along with the surface roughness height (h), and the radar incidence angle
(θinc) is fed into the electromagnetic scattering model that utilizes small perturbation method (SPM)
to arrive at radar backscattering coefficients (σxx) by [30].
92
Figure 5.11: (a) A schematic of the subsurface geometry, which consists of a discretized multilayered dielectric structure along with surface roughness height behavior. The SPM accepts the
dielectric profile at average depth points. (b-c) The in-situ range of real and imaginary parts of
dielectric permittivity for all 8 sampling locations.
5.3 Results
5.3.1 Organic Soil Dielectric Model Validation in Lab
The developed model was validated against both laboratory and in-situ measurements. The laboratory soil samples were initially divided into organic and mineral categories (Fig. 5.7). The
OM distribution of the mineral samples mainly varies between [0−20]% and based on the mineral
texture analysis as shown in Table 2, the mineral soil can be roughly divided into coarse and
fine texture classes. The coarse texture class mainly includes sandy loam (FB-1, SGW-1), while
the fine soil class is silty clay loam (SGW-2, HV-1, HV-2, ICC-1, ICC-2, IMN-1). The overall
model performs better for finer soil textures (silty clay loam) for both real and imaginary parts
of the dielectric. Although the samples with finer textures tend to contain higher OM content,
the overall real part of the dielectric permittivity exhibits smaller values compared with coarser
textured samples at the same soil moisture level. Note that in Fig. 5.12, each color corresponds to a
single soil sample, in which the dielectric permittivity was measured two times for the full range of
saturation.
For validating the organic samples, we divided them into two sub pools covering the respective
OM ranges [60 − 80]% and [80 − 100]%. As stated in Table 2, the mineral texture for organic
soil wasn’t available, mainly due to the lack of sufficient mass to perform texture analysis (see
Bakian-Dogaheh et al., 2022). Therefore, for the model simulation, we used the average mineral
texture of the deeper active layer sampled from each soil pit in the Alaskan North Slope. In the case
of the Interior Alaska soil samples, a fraction of Sand=36% and Clay=25% was used to represent the
typical mineral texture of all samples. The model behavior was consistent with measurements for
93
both ranges of OM content, and the model predicted the real and imaginary parts of the permittivity
very well (Fig. 5.13). It is important to note that, given the small variation in organic soil porosity
between 60-100% OM, overall, the dielectric variation in the organic soils is similar. However,
it appears that for a higher range of OM (> 70%), the dielectric tends to increase at a lower rate,
indicating less sensitivity, compared to the lower range of OM (¡70%). Discussion on model
sensitivity to OM and SW are beyond the scope of this work and will be addressed in a forthcoming
paper.
Figure 5.12: Mineral soil dielectric behavior. In all cases the x-axis shows the soil saturation
fraction, and the color bar represents the OM content for each soil sample. (a) Real part of complex
permittivity for sandy loam that includes FB-1 and SGW-1 samples. (b) Imaginary part of the
complex permittivity for sandy loam soil. (c-d) Real and imaginary parts of the complex permittivity
for silty clay loam that includes the SGW-2, HV-1, HV-2, ICC-1, ICC-2, and IMN-1 sites.
94
Figure 5.13: Organic soil dielectric behavior. (a-b) Real and imaginary parts of the complex
permittivity for the organic soil with OM variation between [60−80] %. (c-d) Real and imaginary
parts of the complex permittivity for the organic soil with OM variation between [80−100] %.
The model was simulated for over 1500 measurement points (in-lab) encompassing a broad
range in soil moisture levels for all 66 soil samples. Accordingly, a 1:1 plot was generated to
compare the model predictions and measurements for both real and imaginary parts of the dielectric
permittivity. These results indicate favorable model performance without any observable bias (Fig.
5.14a-b). The root mean square error (RMSE) was calculated as follows:
RMSE j =
s
∑
Nj
i=1
(εi −ε
MODEL
i
)
2
N j
(5.25)
where Nj
is the number of soil dielectric measurement points for j−th soil samples, which may
vary from [10 - 34] given the experiment situation. The term εi refers to the ground truth dielectric
measurement for the i-th soil moisture manner, and ε
MODEL
i
is the model output as described in
Eq. (5.23)b, once the corresponding soil properties (OM j
, SW j
i
, S
j
, C
j
, T, f req) are inserted. The
RMSE values for the real and imaginary parts of the dielectric were calculated separately and then
95
plotted, as OM varies among the soil samples (Fig. 5.14c). Each point in Fig. 5.14c refers to a
single soil sample; among all samples, the average RMSE for the real part of the dielectric is 4.7,
and 1.1 for the imaginary part (Fig 5.14d).
Figure 5.14: (a) 1:1 plot of the real part of dielectric permittivity measurements against the model
for all data points (dielectric for various soil moisture levels across all soil samples). (b) 1:1 plot
for the imaginary part of the soil dielectric. (c) RMSE variation of the real and imaginary parts
of soil dielectric properties of all soil samples, where each point represents a soil sample. (d) The
histogram of RMSE for both real and imaginary parts of all soil dielectric properties.
In this study, individual samples were not analyzed to compare their corresponding measurement
and organic soil dielectric model behavior. Rather, we arranged the samples into mineral soil with
fine and coarse texture, and organic soil categories with high [80−100] %, and low [60−80] %
concentration. The individual soil measurement and model behavior for both real and imaginary
parts of the dielectric permittivity are shown in the supplement. Each figure (A.1-A.12) is associated
with a sampling location listed in Table 2 and consists of multiple sub-figures corresponding to
the identifiers listed in Table 5.2. As mentioned above, the number of (εi
, SWi) measurement pairs
96
for each sample might be as large as 34, however in plotting the figures (A.1-A.12), we averaged
the measurement points across the soil saturation range at intervals of 0.1 [−]. Therefore, plots are
shown with error bars.
For each subplot, the soil identifier (ID), organic matter content, and corresponding RMSE for
both real and imaginary parts of the dielectric are listed. The legacy mineral soil dielectric behavior
(e.g., such as those reported in Hallikainen et al., (1985)) show a curvature which is in agreement
with our measurements; however, our model curve is slightly concave, which may reflect limitations
of the model since a lower soil moisture simulation model cannot be used due to soil water retention
curve limitations.
5.3.2 Organic Soil Dielectric Model Validation in Field
Besides the laboratory measurement-based validation, the model performance was also assessed
against in-situ soil profile dielectric measurements collected during the 2018 field campaign. For
this purpose, measurements from three soil pits (SGW-2, HV-1, and ICC-1) were selected for the
model validation assessment out of eight total soil pits characterized over the Alaskan North Slope.
The measured organic matter content and soil saturation profile were adapted from our previous
work, and the profile model was fitted to the measurements using the Eq. (5.21). As stated in Eq.
(5.23)b, the model inputs consist of the profiles of organic matter, soil saturation, temperature, and
sand and clay fractions, where the total variation for all North Slope sampling locations is shown in
Fig. 2. Model outputs for a representative selection of sites (SGW-2, HV-1, and ICC-1) are shown
in Figure 5.15 (Fig. 5.15a-b, 5.15e-f, 5.15i-j). Furthermore, a 15% error was introduced to the
model profile parameters to account for possible error contributed from field measurements. Note
that in cases where the error simulation exceeds the physical valid range of OM or SW, the range
was limited to stay below 100% or 1, respectively.
The model and error simulations show acceptable agreement with the measurements for the real
part of the dielectric permittivity through the active layer profile for all sites (Fig. 5.15c, 5.15g, and
5.15k). It appears the model can capture the fine variation of the soil dielectric profile, where a
smaller dielectric near the surface is associated with higher OM content and lower soil saturation
fraction, and much lower variation in the deeper layer corresponds to the saturated homogeneous
mineral layer. However, the model underestimates the imaginary part of the dielectric for all the
sites except SGW-2; further elaboration on the underlying reasoning for this observation is provided
in the discussion section.
97
Figure 5.15: Validation of the dielectric model against in-situ dielectric measurements. In all cases,
measurements are shown with blue dots, the profile models are plotted with a red line, and the
shaded red area represents the model as input profile parameters are perturbed to account for a 15%
error. The OM, SW, real, and imaginary part of dielectric for (a-d) SGW-2, (e-h) HV-1, and (i-l)
ICC-1.
5.4 Discussion
5.4.1 Empirical Modeling an Inevitable Necessity
Existing literature on soil dielectric modeling (organic or mineral) is abundant with empirical
models and over (or hyper) parametrization schemes used to minimize the RMSE and enhance
the fit between model predictions with measurements. Some of the drawbacks of such empirical
approaches are discussed in the introduction, including limited validity (due to limited samples) and
potential unrealistic model behavior. Given the limited understanding of tundra soil processes and
98
sparse availability of Arctic observational data, some empirical modeling is an inevitable necessity,
and can be effective as long as the models are developed from a large representative pool of soil
samples and conditions, and the corresponding model predictions are physically realistic. Further,
the fundamental basis of this work is to produce a physics-based model for tundra that relates a set
of soil physical properties to soil dielectric behavior. Further enhancements in model design and
performance are anticipated as Arctic soil data and other complimentary observations continue to
be collected and analyzed.
Two parameters that include the overall water-in-soil electrical conductivity (σw), and the
dielectric mixing model term (α) require an empirical approach for optimal performance. Given that
a measure of soil salinity wasn’t available, the water-in-soil electrical conductivity was treated as an
optimization variable to fit the imaginary part of the soil dielectric permittivity to the measurements.
A correlation analysis revealed that σw tends to increase with bulk density and sand and clay
fractions, in accordance with the following relationship:
σw = 0.021× ˜f
OM
v +0.093× ˜f
S
v +0.294× ˜f
C
v
(5.26a)
α = 0.357× ˜f
OM
v +1.048× ˜f
S
v +0.987× ˜f
Si
v
(5.26b)
where ˜f
OM
v
is the normalized volumetric fraction of total organic matter ( ˜f
OM
v = ˜f
SOM
v + ˜f
RB
v
),
and ˜f
S
v
,
˜f
C
v
, and ˜f
Si
v
are normalized volumetric fractions for sand, clay, and silt. Subsequently,
further analysis revealed a high correlation between ( ˜f
S
v
,
˜f
C
v
, and ˜f
Si
v
) and the dielectric mixing
model term α as described in Eq. (5.26b).
The optimized values (designated as measurements) along with the models for all soil samples
and the simulation for a specific mineral texture of S=36%, and C=25% for the whole range of
OM was then analyzed and showed general agreement between model and optimized values (Fig.
5.16). The optimized values (σw, α) for each soil sample were initially found based on a Simulated
Annealing (SA) optimization scheme, where SA gave the best fit in minimizing the RMSE between
the measured and estimated dielectric from Eq. (5.25). Accordingly, we refer to (σw, α) driven
from SA as the measurement. The empirical model suggested in Eq. (5.26) was then found based
on the correlation study of σw and α with soil properties.
99
Figure 5.16: Empirical modeling minimized the RMSE of the dielectric model against measurements
over the range of OM conditions. In each plot, the blue dots represent the values that were found
based on simulated annealing to minimize the RMSE of the soil dielectric model. The red squares
show the model predictions derived from Eq. (24), and the black line plots the model simulations
for an average soil containing 36% Sand and 25% Clay. (a) Soil water electrical conductivity (σw),
behavior and (b) the mixing model term (α).
Overall, a higher water-in-soil electrical conductivity is observed for mineral soil compared
to more organic soil, which can be attributed to higher cation exchange capacity for mineral soil
compared to organic soil (Fig. 5.16.a). As shown in the Results section, the model performs well
in predicting the real and imaginary parts of dielectric permittivity for all lab samples (Fig. 5.12,
Fig. 5.13). However, the model validation against the in-situ dielectric profile model failed to
capture the imaginary part, where the main contributor to the discrepancy between the model and
field observations is field measurement error. Particularly, the TEROS 12 probe measurement is
more susceptible to error in field deployments due to improper connections between probe needles
and surrounding soil (TEROS 12 manual). Therefore, in an ideal measurement procedure, such
as the controlled environment in the lab, where the probe is inserted within the soil layer, the
measurement is more reliable. The redundancy of the measurement in the lab also further supports
this observation.
The dielectric mixing model term (α) also monotonically decreases as OM increases, and the
values vary between [1-0.3] for better fitting of the model to measurements. For values equal to 0.5,
the dielectric mixing model turns into a refractive index mixing model, and for pure mineral soil, it
has been shown that a value of around 0.65 provides the best fit (Peplinski et al., 1985). Further,
as mineral texture becomes coarser, the values for α tend to be around 1 (not shown), while the
optimized values of α for the organic soil are in the lower range of around 0.4.
100
5.4.2 Frequency and Temperature Behavior of Soil Dielectric Model
The model validation results were obtained using dielectric measurements from the TEROS 12
dielectric probe, which operates at 70 MHz. However, the radar instruments flown during the
ABoVE Airborne Campaign in Alaska operate at higher frequency ranges (P- and L- bands);
therefore, studying the behavior of the soil dielectric model over these frequencies is of interest (Fig.
). The soil dielectric model was simulated for the frequency range between [70 MHz – 2000 MHz]
for multiple saturation points and a representative class of organic soil. The model simulation was
conducted at sub-zero (T = −5
◦
) and above-zero (T = 15◦
temperatures, as representative values
for freeze and thawed state. The frequency response of the soil dielectric was flat for the real part
with negligible changes, whereas the imaginary parts exhibited more variation within the range,
particularly for more saturated soil (Fig a and b). This observation is consistent with the previous
measurement for the mineral soil counterpart and mainly corresponds to the frequency response of
the water dielectric behavior [25, 91, 114]. Note that the model simulation for subzero temperatures
was only conducted for saturated soil consistent with the model design (Fig. c-d).
Figure 5.17: The frequency behavior of the developed soil dielectric model under thawed and frozen
conditions. The color legend represents the soil saturation ranges (red shows the 0.25 saturation
fraction, blue for 0.5, black for 0.75, and magenta shows fully saturated soil behavior). The markers
represent the soil organic matter contents, where the unmarked plot shows 0% OM content (pure
mineral soil), and respectively the circle, square, diamond, and triangle symbols correspond to
[25%,50%,75%,and100%] OM contents. (a-b) The model simulation for above zero temperatures
represents the real and imaginary parts of the dielectric behavior as frequency, OM content, and
saturation fraction vary. (c-d) shows the model simulation for saturated soil with variable frequency
and OM at sub-zero temperatures.
101
The dielectric measurement provided in this work was conducted at room temperature (≈ 22◦
).
However, given the complex temperature variation in Arctic soil, the model incorporates temperature
as a dynamic input by modeling the freeze/thaw state. Therefore, the dielectric behavior of organic
soil is studied as temperature varies from subzero (frozen) to above zero (thawed) conditions. Given
the limitation in freeze/thaw modeling, the simulation is conducted for saturated soil, and only for
P-band at 435 MHz.
Figure 5.18: The temperature behavior of the developed soil dielectric model at P-band for saturated
soil. The color legend represents the different OM levels represented (blue shows 0%, red circle
for 25%, black square for 50, magenta diamond for 75%, and green triangle shows fully organic
soil behavior). (a-b) The model simulation shows the real and imaginary parts of the soil dielectric
behavior as temperature and OM content vary.
5.4.3 Comparison Between the Behavior of Existing Organic Soil Dielectric
Model
As discussed in the introduction, the major difference between the model developed in this work
and the existing organic soil dielectric models (see Fig. 5.1) is the treatment of water subphases.
Previous works divided water into discrete phases, including bound, transient, and free water.
In contrast, our work considered a continuous phase for water, where the associated dielectric
properties were fully characterized using water matric potential, the Eyring equation, and the Debye
model. A fair comparison between the performance of our model against other prevailing organic
soil dielectric models can be performed from multiple perspectives: 1) parametrization, 2) model
simulated behavior, and 3) validation at 70MHz.
102
Parametrization and Bound Water Argument
We first focused on model parametrization, and particularly addressed how the bound water fraction,
soil bulk density, and wilting point were characterized in previous work. For the comparison, we
implemented the Park et al., (2019, 2021), Mironov et al., (2019), and Savin et al., (2022) methods
using spectroscopic and single frequencies (1400 and 435 MHz), respectively [86–88, 119].
While the work presented here does not address bound water as a sub-component, we use
the assumption that considers the maximum bound water fraction equal to the soil moisture at
wilting point (Bakian-Dogaheh et al., 2022d). Accordingly, Park et al., (2019, 2021) used the
parameterization provided by Jin et al., (2017), Yong et al., (2014), whereas Mironov et al., (2019)
developed the model based on curve fitting and used Hossein et al., (2011) to account for OM
variation. Similarly, Savin et al., (2022) found the bound water fraction based on curve fitting.
For the purpose of model simulation, we assumed that the first transition points suggested in
Mironov, and Savin’s works are virtually identical to the wilting point. In all model simulations the
temperature was assumed to be 20◦C. Therefore, the behavior of the wilting point can be described
as follows:
θ
KBD
wp = θ(ψm = −1500kPa) (5.27a)
θ
Park−2019
wp = 0.02982+0.089×C +0.00789×OM (5.27b)
θ
Park−2021
wp = 0.02982+0.089×C +0.0065×OM (5.27c)
θ
Savin
wp = 63×10−3 +4.23×10−4 ×OM −1.84×10−4 ×T −4.65×10−6 ×T ×OM
(5.27d)
θ
Mironov
wp = (0.118+8.964×
−4 ×OM −10−4 ×T)(0.071+1.32×e
−0.0412×OM) (5.27e)
where in this study wilting point is defined as the soil moisture at a matric potential of (-1500
kPa). Park et al. (2019) accept clay and OM as inputs, and Savin et al. (2020) and Mironov
(2019) require temperature and OM as inputs. We further compared the bulk density and porosity
parametrizations in the existing models. As shown in Fig. 19, the model behavior for Park et
al., (2019) exhibits a non-physical behavior for the range of OM beyond 35%, (Fig. 5.19a, c).
Furthermore, the wilting point in Park et al., (2019) tends to monotonically increase as OM increases,
which is also inconsistent with observations and previous works such as [96, 103]. This finding
further contradicts the argument that a higher OM content tends to contain a higher bound water
fraction if we assume the maximum bound water fraction as a proxy of bound water.
The comparison of bound water between Savin et al. (2022) and Mironov et al. (2019) are not
consistent. Another observation shows the consistency between bound water behavior of our work
and Mironov et al., 2019. This is mainly due to the similar bulk density behavior between the two
models. It is important to note that not all parameters were available for comparison; for instance,
Savin and Mironov avoid using porosity in their parameterization.
103
Figure 5.19: Comparison of parameterization schemes used in prevailing organic soil dielectric
models. In all figures, the blue lines show model results from Park et al., 2019 and the blue circles
show results from Park et al., 2021; the black lines represent Mironov et al., 2019; Magenta lines
correspond to Savin et al., 2022, and red lines shows our work. (a) Shows the variation of bulk
density used in previous work, where the Park et al. model exhibits non-physical values (negative
or large bulk density) for larger OM. (b) Shows the behavior of the maximum bound water fraction,
which was determined from the wilting point. (c) shows the porosity behavior of the above models.
The relationship between the presence of organic matter and bound water fraction (f
BW
v
) in soil
has been discussed in previous studies (Park et al., 2021). A major observation case relevant to
the current study is the contrasting behavior in dielectric permittivity between mineral soil (εM)
and organic soil (εO) at the same soil moisture level (θ), where the εM tends to be larger than
εO (Fig. 5.20, model simulation). Park et al., (2021) indicated that this contrasting behavior is
due to the larger amount of bound water in organic soil compared to mineral soil (Fig. 5.20c).
This claim can be discussed from two perspectives, initially from the comparison of soil moisture
level (θ) and saturation level (SW = θ/φ), because of the porosity (φ) differences between the
two soil types it is important to perform the comparison at the same saturation level rather than at
a consistent soil moisture level. For the same saturation level, the εO tends to be larger than εM,
which can be explained by a smaller bound water fraction in organic soil compared to mineral soil
(θ
O
wp < θ
M
wp → f
BW
v,O < f
BW
v,M ).
Additionally, a general misconception regarding organic soil is that a higher OM level corresponds with more soil particle surface area and therefore a larger bound water component
(θ
O
wp > θ
M
wp → f
BW
v,O > f
BW
v,M ). Such correspondence could lead to a false assumption of similar
hydraulic behavior between organic soil and clay soil, since clay particles also have relatively larger
surface area and in turn larger bound water (wilting point). While the behavior over the lower
range of OM is yet to be determined, for highly organic soil (OM ¿35%) such as peat, the larger
OM fiber content (such as in Fibric or Hemic soils, also referred to as acrotelm) coincides with
larger hydraulic conductivity and a smaller particle surface area, which results in a lower bound
water content (wilting point). Thus, the hydraulic behavior of a highly fibrous peat soil can be
more similar to sand than a clay mineral soil. Smaller OM fiber contents characteristic of Sapric
(catotelm) soils are more decomposed and exhibit relatively lower hydraulic conductivity, larger
surface area, and a larger bound water fraction.
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In this study, we used root biomass (RB) measurements as a proxy for OM fiber content. The
introduction of RB and its soil organic matter (SOM) differentiation in our parameterization had
a major impact on the model organic soil hydrology and dielectric behavior. The resulting model
approach enables the development of soil dielectric curves for diverse Arctic soils with substantial
variability in soil physical properties and across different spatial and vertical extents.
Figure 5.20: Bound water argument. (a) Comparison of the real part of soil dielectric for organic
and mineral soils at the same soil moisture level. High sand and clay fractions are simulated
with corresponding red and blue curves. (b) Comparison for the same soil saturation level. (c)
Observations and claims about bound water from this study and other existing works reported in the
literature.
P- and L-band Model Behavior Comparison
Another approach for comparing our model with other existing organic soil dielectric models is to
compare the real and imaginary behavior of the models at 1400 MHz and 435 MHz for a constant
temperature (T=20 °C) over the full range of OM and soil moisture conditions. The major goal
here is to further study the model performance and validity for potential use in physics-based
radar retrievals. A comparison between our work and Park et al. (2019) shows that the models
perform similarly for lower OM content (0 and 25%). However, the Park et al. (2019) model
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parametrization is not valid at higher OM ranges, and the subsequent discrepancy between the two
models increases drastically. The real part of the permittivity from Savin et al. (2022), which was
developed at 435 MHz, performs similarly to Mironov et al., (2019), which works at 1400 MHz.
However, the imaginary part of the dielectric behavior is not consistent as soil moisture increases.
Furthermore, both models show minimal sensitivity to the organic matter content. This observation
further emphasizes the importance of measurement methods. Both Mironov and Savin’s models are
based on a destructive measurement method that ground the soil samples (Fig. 5.21). Therefore,
the homogenized samples perform very much the same. Similar observations from mineral-only
soils are also applicable. In general, the Mironov models were developed using similar destructive
grinding methods for mineral soil as well. Therefore, the coarser texture that includes a larger sand
fraction after grinding performs similarly to clay (finer) soil [121].
Figure 5.21: Comparison of the existing organic soil dielectric models at 435 MHz, and 1400 MHz.
The color legend denotes the particular model, where the markers show the OM variation. (a) Model
behavior at 435 MHz and (b) model behavior at 1400 MHz are presented.
Validation of All Models
A fair assessment and validation of all existing models against our entire validation pool (complex
dielectric permittivity at 70 MHz), is challenging. Since some of the available models do not accept
frequency as input, and their corresponding spectroscopic models do not accept OM as an input
(Fig. 2). The frequency exerts the largest impact on the imaginary part of soil dielectric, whereas for
the real part, the frequency behavior of soil tends to be less dispersive and flat. To that end, we ran
the Park et al., 2019, Mironov et al., 2019, and Savin et al., 2022 models with the inputs driven from
our validation pool (derived from laboratory measurements). For each model, the corresponding
106
Table 5.3: Model validation against the laboratory measurements for all 66 tundra soil samples.
RMSE with ε
′
r
70 MHz
ε
′
r
70 MHz
ε
′′
r
435 MHz
ε
′′
r
1400 MHz
This work 4.7 1.1 0.4 1.2
Park et al., 2019 5.7 7.1 - -
Savin et al., 2022 5.5 - 2 -
Mironov et al., 2019 5.6 - - 2.7
estimated permittivity is compared with our measurements, and the RMSE was calculated according
to Eq. (5.25). For the imaginary part of the soil dielectric, we translated the measured electrical
conductivity to the corresponding frequency (ε
′′
r =
σ
2πε0 f0
) of each model.
Without considering the existing model validity range (Table 5.1), the RMSE analysis for the
real part of the dielectric permittivity shows that our model performs slightly better than the other
models. The RMSE analysis for the imaginary part of the soil dielectric was performed at multiple
frequencies and shows that the proposed model produces better estimates of the imaginary part of
the soil dielectric at 70 MHz, 435 MHz, and 1400 MHz frequencies than the other models (Table
5.3).
5.4.4 Limitation of Organic Soil Dielectric Model
While the model introduced in this study incorporates a comprehensive measurement and modeling
approach and demonstrates higher accuracy for dielectric mixture modeling of tundra soils than
the other prevailing models evaluated, it still has limitations. This work initially focused on highly
organic soils common in Arctic tundra, which exhibit certain features such as higher surface OM and
lower moisture content than the deeper mineral soil of the active layer. The model parametrization
developed in this work was based on soil matric potential measurement using the TEROS 21 porous
disk probe, where the resulting matric potential measurement at lower soil moisture was more
erroneous. Therefore, the resulting model has limitation in the lower soil moisture regime, and
particularly for mineral soils. Future work needs more extensive measurement of soil water matric
potential at lower soil moisture levels for less organic soil.
The lower range of soil moisture is limited to a water matric potential (ψ
Lim
m ) equivalent to
−100,000 [kPa]. The inverse presence of soil moisture in equation (5.8) does not result in an
unrealistic estimate, but what limits the lower end of the soil moisture (saturation) estimate is the
asymptotic behavior of the soil water retention curve at the lower soil moisture range. Therefore,
the organic soil dielectric model predictions at the lower saturation level (0.1) are not shown in
Fig. 5.22. The empirical modeling and validation assessment in this work was conducted with
this limitation. In a practical case such as physics-based remote sensing of Arctic soil, additional
assumptions have to be made to simulate the lower saturation end for Mineral soil (e.g., for
θ < θ(ψ
Lim
m ),theθ = θ(ψ
Lim
m )), which can impose a small bias for mineral soil relative to the more
accurate model predictions expected for highly organic soil (5.22).
107
Figure 5.22: The limitation of organic soil dielectric model.
In equation (5.20) and for the measurement of soil water potential, the first three terms (ψp,ψg,
and ψo) were assumed negligible. While such assumptions might hold for the pressure potential
(ψp) and gravitational potential (ψg), the osmotic potential (psio) can be impacted by solute
concentration, which in the case of Arctic soil primarily comprises of salt and dissolved organic
matter. For salinity, the TEROS 21 manufacturer reports that an electrical conductivity larger
than 10 dS/m can potentially result in erroneous matric potential readings by confounding the
TEROS-21 capacitance measurement. However, the joint measurement of soil dielectric properties
using TEROS-12 showed relatively small electrical conductivity in the range of ¡1 dS/m for all soil
samples, which results from very low salinity. Therefore, the osmotic potential due to salinity can
be assumed negligible. On the other hand, the presence of dissolved organic matter, particularly
for highly decomposed soil samples (with lower fiber content) can potentially impact the matric
potential, particularly since the equation (5.19) assumes the dielectric constant of the ceramic disk
is not affected by other components and is only controlled by water within the ceramic disk. Other
matric potential techniques, such as evaporation at relatively high soil pressure (e.g., HYPROP) and
dew point for relatively low soil pressure (e.g., WP4C Dew Point PotentiaMeter), could be used
in future work to capture more accurate water matric potential measurements. Nonetheless, the
measurements provided from TEROS-21 do not change the generality of our approach in organic
soil dielectric model development, and in characterizing water-in-soil dielectric properties from
matric potential and estimated soil retention curves.
Additionally, the freeze-thaw modeling and the expansion behavior described in Section 3.1.2 is
potentially much more sophisticated, particularly the freezing point of soil varies with dissolved
solute concentrations, which should produce more gradual slopes near 0
◦C, and asymmetric behavior
between freezing and thawing (e.g., see Devoie et al. 2022) [148]. Nevertheless, this model shows
significant improvement in capturing the full soil moisture range in highly organic soils characteristic
of the tundra permafrost active layer and is suitable for application to other Arctic soils.
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5.4.5 Potential for Retrieving Water and Carbon Characteristics from
Radar Observations
While the major focus of this study was to develop and validate a new organic soil dielectric model,
the ultimate application of the model is integration within a physics-based radar retrieval framework
to study the water and carbon characteristics of permafrost active layer soil using radar observation
(section 3.4). Once the soil dielectric model is developed and validated, it can be used to study
the feasibility of retrieval for a few locations. To this end, five sites from the Circumpolar Active
Layer Network (CALM) were selected within the Deadhorse flight line from the ABoVE airborne
campaign [5, 26, 54]. For each location, the associated backscattered P-band data from flights
in August, 2017 were acquired, and accordingly, the forward solver was simulated to construct
a data cube that consists of state parameter variations (Fig. 5.23a, Table 5.4). Additionally, we
set the sand and clay fractions as 36%, and 25% respectively, OM profile parameters were set
(β = 0.5,OMM = 7%) from soil inventory records, and the surface temperature was assumed to be
Tz0 = 8
◦
. Notice that the temperature profile behavior is controlled by the zALT and Tz0 according to
equation (5.21).
Once the state parameters data cube is constructed, the corresponding soil profile models
(OM(z), SW(z), S(z), C(z), T(z)) for each realization are fed into the soil dielectric model to arrive
at the soil dielectric profile behavior. Consequently, the layered dielectric structure adapted from
MODEL output, roughness height, and incidence angles (θi) from P-band radar measurement was
applied to the backscattering forward model known as SPM (The layered dielectric structure is
depicted in Fig. 5.10, section 2.4). The variation of simulated backscattered coefficients for both
HH and VV polarization is then compared to the 1:1 plot that shows the feasibility of retrieval of
active layer soil subsurface water and carbon characteristics for each tundra subregion as it crosses
the 1:1 line (Fig. 5.23b,c).
109
Figure 5.23: The feasibility of retrieving permafrost active layer subsurface water and carbon
characteristics using radar (P-band) observation. (a) Shows the CALM sites, our North Slope
sampling locations (filled circles), and two ABoVE Airborne Campaign flight swaths. (b) shows the
variation of the simulated backscattering coefficient for HH polarization, where the range of input
parameters are adapted from Table 5.4, along with radar observation for each point. (c) Accordingly
shows the variation of simulated backscattering coefficient for VV polarization
In Arctic tundra, and at a radar pixel level (e.g., ABoVE Airborne Campaign conventional
data product ∼ 30x30 m
2
), the heterogeneity of OM and soil moisture both spatially and along the
vertical profile can be substantial. We collected 66 soil samples at diverse locations and across
different depths, which served as the foundation for validating the presented soil dielectric model.
While a representative pool of samples is important for validation purposes, the soil dielectric
modeling as described in the general form in Eq. 23b is agnostic to radar pixel soil heterogeneity.
Since modeling the 3D soil heterogeneity within a radar pixel is a separate task from modeling
organic soil dielectric behavior.
In the above case study for retrieving active layer subsurface water and carbon characteristics
using radar observations, the organic soil dielectric model effectively links the surface and subsurface
soil parameters (e.g., OM and soil saturation profile) to the equivalent soil dielectric profile, which
can then be applied to a multi-layered electromagnetic scattering model to derive the corresponding
110
Table 5.4: List of state parameters in the retrieval scheme, assumptions and sets of parameters
that were fixed based on ancillary field data and the literature. For the unknown parameters and
measurements, the range of variation is provided; in data cube development the unknowns are
discretized with corresponding discretization steps.
Parameter Definition Symbol Status Unit Range/Value Discretization
Surface Organic Matter OMz0 Unknown [g/g] % [10−100] 10
Organic Layer Thickness zOLT Unknown [cm] [16−44] 4
Surface Saturation SWz0 Unknown [−]% [0.25−1] 0.25
Water Table Depth zWT Unknown [cm] [16−44] 4
Soil Roughness RMS Height h Unknown [cm] [0.5−4] 0.5
Active Layer Thickness zALT Unknown [cm] [28−60] 4
OM Profile Shape Factor β Known (1/cm) 0.5 (−)
Mineral Layer Organic Matter OMM Known [g/g] % 7 (−)
Sand Fraction Savg Known [g/g] % 36 (−)
Clay Fraction Cavg Known [g/g] % 25 (−)
Surface Temperature Tz0 Known [
◦C] +8.0 (−)
Backscattering Coefficients σ
0
HH, σ
0
VV Measurement [dB] [−35−0] (−)
Incident Angle θinc Measurement [degree] [15−60] (−)
radar backscatter coefficients (Fig.5.11). A major assumption for retrieval purposes is to model
the radar pixel as a multi-layered dielectric structure with dielectric properties controlled by soil
OM, soil moisture, and other constituents as described in Eq. (5.23). The other building blocks in a
physics-based retrieval algorithm were described in subsection 2.3.1, where we briefly discussed
the active layer soil profile model, and in section 2.4, which describes how equivalent soil dielectric
profiles play a role in calculating the radar backscattering coefficients (e.g. see Fig. 8 in BakianDogaheh et al., 2022).
The influence of surface and sub-surface heterogeneity on physics-based radar retrievals of
Arctic soil parameters and on estimates of water and carbon characteristics at local and regional
scales requires further research.
5.5 Conclusions
This work provides a comprehensive organic soil dielectric characterization based on the largestknown sampling campaign to-date for Arctic permafrost active layer soils. A physics-based dielectric
model that leverages the hydrological properties of soil was developed to predict the water-in-soil
dielectric behavior. Subsequently, the water-in-soil dielectric properties were incorporated into a
dielectric mixing model to arrive at effective soil dielectric properties. The model was validated
against a large pool of soil samples, which covers the realistic range of organic matter and soil
moisture conditions. The model inputs consist of basic soil physical properties, including soil
saturation, organic and mineral texture, and additionally, accept temperature and frequency.
111
The major goal of the organic soil dielectric model is for integration with a physics-based radar
retrieval algorithm for remote sensing applications to study the dynamics of water and carbon in
organic-rich permafrost active layer soil. To this end, a feasibility study of radar retrieval was
conducted, in which the results exhibit the possibility of retrieving subsurface profile parameters
such as organic matter and soil saturation profile along with the active layer thickness.
Future work may include adding more representative soil samples for the range of OM between
20 to 60%, which were lacking in the current study. A dedicated validation of the soil dielectric at
lower frequencies, particularly P- and L-bands [149] may also be employed to better inform ABoVE
airborne SAR retrievals and planning for next generation P- and L-band satellite SAR missions
such as European Space Agency (ESA) BIOMASS and NASA and ISRO Synthetic Aperture Radar
(NISAR) missions [150, 151]. Additionally, a more controlled thermal measurement experiment
for subzero temperatures is needed to improve dielectric model response to variations in unfrozen
water content during freeze/thaw transitions, which strongly influence soil OM decomposition and
greenhouse gas emissions [152], ALT and permafrost stability [153]. Overall, the results of this
study and the new physics-based soil dielectric model are expected to improve remote sensing
based monitoring and physical process modeling of permafrost active layer soils, leading to better
understanding of the changing Arctic and its role in reinforcing global climate change.
112
Chapter 6
Physics-Based Radar-Driven SOC Mapping
Disclaimer: The content of this chapter is adapted in large from the following papers:
I-3-1 Submitted Draft 1
: K. Bakian-Dogaheh et al., “Soil Carbon Distribution in Arctic Tundra via
P-Band, Physics-Based Computational Mapping ”
I-3-2 Dataset in Prepration 2
: K. Bakian-Dogaheh et al., ”Soil Organic Carbon, Soil Moisture, and
Freeze/Thaw Properties from AirMOSS P-band SAR in Alaskan Tundra“
Estimates indicates that the northern higher latitudes within the permafrost region stores the
largest terrestrial soil carbon pool on earth. Projecting the future of the Arctic ecosystem in a
warming earth has shown large uncertainties due to poor constraints on the extent and dynamics
of the carbon stock in this region. In this paper we show, Physics-based computational methods
that leverage P-Band SAR acquisitions can provide a sensitivity to the soil organic carbon (SOC).
This method for the first time, alleviate the necessity of in-situ measurements, which are extremely
sparse and are the main source of uncertainty in characterizing the SOC maps. Additionally, our
analysis suggests that a time-series radar observation, particularly with a focus on early thaw season
can potentially improve the radar-driven carbon estimates much more than late season acquisitions.
Our results, show the significance of physics-based approach that links the field-scale process to
the radar observation by understanding details terrestrial ecological parameters that control radar
response, and suggest a new avenue of mapping and monitoring soil carbon reservoir in a region
that historically suffered from poor observations. Our results show robust performance and are
validated against the most comprehensive and updated in-situ carbon inventory in North Slope of
Alaska, with a total of 104 Tg C within five foundational flight lines, that encompasses an area of
9000 km2 in North Slope of Alaska.
6.1 Introduction
6.1.1 Importance of Soil Carbon (Stock and Changes)
The surface soil (0-3 m) in northern higher latitude (NHL) permafrost zones store an estimated
1035 Pg of soil carbon (C) in the form of organic matter [11, 12]. While the NHL regions accounts
for 15% of global soil area, it encompasses at least 30% of the Earth’s surface C [154, 155].
1
Initial draft submitted on 11/15/2024
2Additionl ongoing processing for non-North Slope flightlines as of 12/03/2024
113
Anthropogenic warming trends in the NHL unfolds at a faster rate than elsewhere [13, 156], which
could thaw the permafrost and in turn expose a substantial amount of legacy stabilized frozen
permafrost C to microbial decomposition [157]. The process that describes mobilization of stored
permafrost C and its conversion as greenhouse gases carbon dioxide (CO2) and methane (CH4)
into atmosphere is known as permafrost carbon feedback (PCF) and can potentially increase the
magnitude and rate of future climate change [158, 159]. Earth system models (ESM) projection on
the future trajectory of the Arctic ecosystem remains highly uncertain despite growing attention
toward PCF in past few years [160]. A recent meta-analysis study that inquired modeling needs of
the ESM community focused on NHL indicated soil carbon status, such as stocks (static) and change
(dynamic) trajectories by far as the highest demand [3]. Initially, the importance of permafrost C
stems from model parametrization, where C content is required to improve the representation of
physical and biological processes that control the dynamic of permafrost soil [78,161]. Additionally,
direct measurement of C pool changes reveals the permafrost degradation in response to regional
climate change [162, 163]. As the new generation of ESMs advances by inclusion of various
permafrost thaw processes (gradual and abrupt), the permafrost C status plays a significant role the
as the main driver of PCF [164].
6.1.2 Discrepancies is C Estimates Driven from Field and Upscaling
approaches
The static stance of soil C is represented by C content - alternatively referred to as soil organic carbon
(SOC). The C stocks account for the areal distribution of C that requires additional information,
such as representative soil depth and bulk density, for calculation. Despite growing efforts for
regional and global mapping of C stock [21, 165, 166], currently, there is a large discrepancy among
these existing datasets with respect to stocks size and spatial distributions [167, 168]. Different
factors such as differences in data gap filling for missing information (e.g., bulk density), stock
calculation methods, sampling approaches (e.g. pedon delineation or profile coring), and upscaling
methods collectively contribute to these discrepancies, which their severity particularly arises for
the NHL permafrost zones. Focused on limited study areas, quantification of the dynamic stance
(changes over time) of permafrost soil C, similarly exhibits significant observational discrepancies
among a few permafrost ecosystem warming experiments [155, 164, 169]. Differences in sampling
methods, particularly the fixed-depth inventory, which relies on assuming bulk density and soil
horizons remain time-invariant fails to capture changes in soil C overtime, whereas equivalent ash
method that accounts for ground subsidence and soil compaction reveal detectable changes from the
original C pool [155]. The underlying common theme between ‘first-order’ methods of quantifying
the soil C status relies on direct field measurements. While such methods provide highest point-wise
accuracy, the vastness, environment harshness, and limited access in the permafrost zones along with
labor-intensive and high cost-demands limits the spatiotemporal extent of such field observations
(Fig. 6.1).
114
6.1.3 Remote Sensing Techniques and Modeling Approaches for C mapping
Remote sensing techniques have shown promises as an alternative approach for mapping the static
and dynamic stance of soil C, which can potentially alleviate some of the aforementioned challenges
of field measurements [170]. Such techniques can be largely categorized into short wavelength
that covers optical and hyperspectral imaging and long wavelength that encompasses microwave
radars or radiometers sensing [171, 172]. While each method differs in their respective fundamental
physics of image formation, a significant similarity between majority of existing methods is arguably
the corresponding framework to achieve a digital mapping of soil C, which is relied on regression
(learning) based techniques. To that end, microwave remote sensing (active or passive) methods
have shown generally better performance in mapping soil organic carbon than optical methods [173].
The polarimetric synthetic aperture radars (PolSARs) at different frequencies such as L-, C-, and XBands have shown promises in mapping C particularly for Tundra ecosystem [173–177]. However,
a major drawback in almost all of these techniques, is the reliance of mapping on the existing soil
carbon databases, or sporadic field observations for regressions or model training. Such an approach,
potentially propagate the existing uncertainties in the current soil C map into the remote sensing
technique.
6.1.4 Physics Based Computational Mapping of C
Another class of mapping techniques that exists within the remote sensing community is known
as “Physics-Based Computational” algorithms. A very well-known method that has been used for
passive microwave radiometry is referred to as radiation transfer (RT) models, which has long
been in coupled hydrological-thermal land surface modeling and hydrological data assimilation
techniques [178,179]. Fundamentally, an RT model for bare soil (simple case) relates the variability
of soil moisture and temperature to the brightness temperature (Tb) through Maxwell’s equations
[180, 181]. More recently, RT was use to study the feasibility of mapping surface soil C in Arctic
Tundra using SMAP L-band Tb [96]. In the past decade, and for multi-channel active sensor a
significant effort has gone into developing physics-based computational algorithm, that relates the
physics of subsurface processes within a radar pixel (≈ 30x30 m
2
) to co-polarization backscattering
radar measurement. Such technique was primarily used for mapping root zone soil moisture
in Airborne Microwave Observatory of Subsurface and Subcanopy (AirMOSS) mission for 10
biomes within the contiguous US, which is dominantly underlain by mineral soil [27]. AirMOSS
instrument provides a unique P-band PolSAR system, which enables deeper sensing than any other
existing platform [122], and in recent years was flew as part of NASA Arctic Boreal Vulnerability
Experiment (ABoVE) airborne campaign [26]. The wealth of P-band acquisition across a gradient
of bioclimatic zone in Alaska provided through ABoVE, enables a unique opportunity to advance
physics-based computational algorithms for mapping the soil organic carbon (SOC) within the
Arctic tundra region for the first time from P-band PolSAR imagery.
115
6.2 Methods
6.2.1 Study Sites
The study area in this work focuses on five flight lines within the continuous permafrost zone of
the North Slope of Alaska across a wide range of diverse bioclimatic zones, which spans from the
foothills of Brooks Ranges to the shorelines of Beaufort and the Chukchi Sea (Fig 6.2.B). During
the 2017 foundational airborne campaign ABoVE flew the P-band PolSAR instrument at each site
across the season to capture a variety of surface and subsurface features. The acquisitions were
conducted in Early June (the start of the thaw season), mid-August (maximum thaw season), and
Early October (the start of the frozen season). The swath width is within ∼13 km, whereas the
length varies between ∼66km for Toolik to ∼185.5 for Deadhorse (Table 6.1). Notice, that the first
acquisition for Toolik and Ivoutk was acquired in late May, throughout this paper and for the sake
of simplicity these measurements are also referred to as June data.
116
Figure 6.1: Locations of in-situ soil profiles input in state-of-the-art digital soil mapping. (A) The
global map, and location of all the in-situ soil profile collected across multiple decades, which
serves as the main input layer for digital soil mapping techniques such as those used in Soil Grids.
(B) The higher latitude soil profile locations in North America, including Alaska, and Canada,
which shows significantly lower density of measurements. (C) The location of soil profiles in North
Europe and Russia. (D) The focus area in this study, including the North Slope of Alaska.
117
Figure 6.2: Mapping soil organic carbon. (A) Schematic of the permafrost subsurface, and radar
measurement in the backscattering mode. Notice the presence of a root layer on top, the distribution
of soil organic matter, and the transition to the organic-mineral layer. The total organic matter
consists of a combination of root biomass and soil organic matter. See Fig. S7 for additional
information. (B) The study sites and AirMOSS P-band PolSAR flight lines were conducted by the
NASA ABoVE Airborne campaign. Five flight lines are measured at three snapshots, including
Deadhorse (blue), Toolik (red), Barrow (Purple), Atqasuk (black), and Ivotuk (orange). (C) The
map of surface organic carbon parameter (SOC[0−5] (cm)
) of the SOC averaged profile driven
from computational physics-based algorithm retrieval, where SOC unit is (g/g) %. (D) Map of
SOC[5−15] (cm)
. (E) Map of SOC[15−30] (cm)
. The corresponding uncertainties in SOC distribution is
shown in Figure 6.3.
118
For each flight, only the co-polarized channels (HH and VV) were used due to the limitations
of the physics-based model in capturing cross-polarized channels, as well as unknown calibration
accuracy for the cross-pol channel.
6.2.2 Physics-Based Computational Radar Retrieval Algorithms
The physics-based computational radar retrieval algorithms aim to relate the surface and subsurface
state parameters that capture the field scale process to the PolSAR radar measurements provided
by the instrument at each pixel. For the case of Arctic permafrost and particularly in the tundra
area, the set of state parameters within each radar pixel describe organic matter, soil saturation
fraction, active layer thaw depth, freeze/thaw effect, and soil roughness height, which depending
on the physics of electromagnetic wave interaction with surface and subsurface exhibits various
level of sensitivity to the radar signal. At the heart of the retrieval algorithm a forward model
f(X¯) exists that translate the state parameters X¯ into radar backscattering coefficient, which in turn
being compared with the radar observation (σxx) through an iterative inversion scheme L(X¯), until
a stopping criterion is met (Fig. 6.4).
The forward model consists of three major components, where at each stage the field scale
processes progressively transform into the equivalent organic soil dielectric permittivity, which is
the main subsurface electromagnetic characteristic that radar can capture. Eventually, the equivalent
subsurface dielectric along with soil roughness parameters inserted into a forward electromagnetic
scattering solver that accounts for the interaction of EM waves with inhomogeneous subsurface and
soil roughness and translates those into radar backscattering coefficients (Fig. 6.5).
6.2.3 Subsurface Profile Model
Primarily a detailed understanding of the state parameters in the field is of interest. From a timevariation perspective, the parameters can be categorized into two sets: those that are time-invariant
across the season such as organic matter profile parameters (OMz0, zOLT ) and the soil roughness
rms height (h), and the time-variant parameters such as the soil surface saturation (SWz0) and (zWT )
water table depth in June and August along with the thaw depth (zT HD) and surface frozen depth
(zT FD) in October (Fig. 6.6).
The thaw season in the North Slope starts with a fast snow melt, which results in a highly
saturated surface, and shallow thaw depth early in the season (June). As time progresses, the
thaw depth deepens and around mid-August reaches to its maximum depth known as active layer
thickness (zALT ). From the maximum thaw depth through the late-season active layer goes through
Table 6.1: AirMOSS flights used in this chapter.
Flight Line ID Acquisition Date
(Year: 2017)
Swath Size
(km)
Swath Center Coordinate
Start Stop
Atqasuk AT
06/06 08/13 10/09
14.3×157.1 (69.6805◦
, −156.7960◦
) (71.0411◦
, −157.8875◦
)
Barrow BA 13.5×155.9 (70.1972◦
, −154.6362◦
) (71.4031◦
, −156.7807◦
)
Deadhorse DH 14.3×185.5 (68.7874◦
, −148.9068◦
) (70.4429◦
, −148.4216◦
)
Ivotuk IV 05/29 08/13 10/09 12.5×120.7 (67.9065◦
, −156.5299◦
) (68.8921◦
, −155.0510◦
)
Toolik TL 13.0×65.7 (68.4808◦
, −149.9403◦
) (68.8200◦
, −148.6335◦
)
119
the stagnation period, where the zALT remains relatively constant. Later in the season and in October,
snow accumulation and surface temperature drop will trigger the frozen season, which starts with
surface frost, and gradually the top frozen depths reach the bottom frozen depth and make the
column completely frozen (Fig. 6.6). In warmer years or at different locations across the flight lines
the soil column in October might still be totally unfrozen. While the freeze/thaw effect in October
is an unknown state parameter that is left to the framework to be determined, field observations
and the late-season precipitation gains over the evapotranspiration loss allow us to assume a highly
saturated column for October.
Multiple field observations within Deadhorse and Toolik flight lines were conducted over the
span of 2016 to 2019. While these measurements are a subset of our validation pool (see the
validation). The in-situ data from these two lines was used for a detailed understanding of the
field scale process and underlying parameters that control these processes for the purpose of model
development. The model development particularly aims to characterize the subsurface organic
matter and soil saturation profile behavior, additional observations were made to understand the
temperature behavior across the season. Availability of the time series temperature and soil moisture
data are very limited in the North Slope, and existing dataset are significantly sparse to capture
the depth microheterogeneity of the active layer soil. Additional challenges stem from the spatial
microheterogeneity within a radar pixel (30×30 m
2
). Integrated datasets suffers from inconsistency
of measurement protocols in field observations, such as sampling depth, number of samples at each
location, spatial distribution, and investigation depth. Nonetheless, sufficient sampling accumulated
across different years enabled to the construction of generalized profile models that captures the
static (snapshot) behavior of the three fundamental field-scale processes, including organic matter,
soil saturation, and temperature profiles (Fig. 6.6).
The organic matter profile was modeled with a sigmoid function, requiring two parameters
that control surface organic matter (OMz0) and organic layer thickness (zOLT ). Note that the term
organic layer thickness is being used loosely as it describes the OM curve inflection point rather
than referring to a certain depth with physical attribution that captures a particular OM value.
OM(z) = OM(z) = OMz0 +
OMM −OMz0
1+e
−β(z−m)
(6.1)
Other parameters in the OM profile such as the organic matter for the mineral asymptote (OMM)
and the shape factor (β), are assumed to be constant values given the filed observations.
The active layer mineral soil texture is assumed to be constant through the profile, where the
values are adopted by the typical range of sand (S) and clay (C) fractions from field observations.
S(z) = Savg (6.2a)
C(z) = Cavg (6.2b)
The snapshot behavior of the soil saturation controls with two parameters including the surface
saturation (SWz0) and the depth of the water table depth (zWT ). The quadratic function seemed to
be the best match to describe the instantaneous behavior of Arctic soil. While such a description
overlooks the physics of hydrology particularly the Richard’s equation and moisture diffusion in
120
porous medium, the discrete radar snapshots limit to incorporate a time-series more sophisticated
incorporation of soil saturation vertical profile.
SW(z) =
1−(1−SWz0)( z
zWT
−1)
2
z ≤ zWT
1 z > zWT
(6.3)
A significant assumption in this work is with respect to vertical temperature profile behavior. A
detailed analysis of in-situ temperature behavior resulted in a simplistic approach for modeling the
soil temperature profile, using piecewise linear curves. The temperature in the Arctic is among
the parameters with drastic variation across the season. In reality, the most significant parameters
that temperature controls suffice to the thaw depth and surface Freeze/Thaw effect. Therefore,
two simplistic models that capture an unfrozen column (T
UnFr(z)) and frozen column (T
Fr(z)) is
designed to model the temperature profile behavior. The temperature parameters at the surface and
at the thaw depth (T
UnFr
z0
, T
UnFr
z0
, TzT HD, TzREF ) are considered constant and known, whereas the
depth related parameters (zT HD, zT FD) are among the state parameters.
T
UnFr(z) =
(T
UnFr
z0 −TzT HD)
(0−zT HD)
(z−zT HD) +TzT HD z < zT HD
(TzT HD−TzREF )
(zT HD−zREF )
(z−zREF) +TzT HD zT HD ≤ z < zREF
(6.4a)
T
Fr(z) =
(T
Fr
z0 −TzT FD)
(0−zT FD)
(z−zT FD) +TzT FD z < zT FD
(TzT FD−T
Fr
zc
)
(zT FD−zc)
(z−zT FD) +TzT FD zT FD ≤ z < zc
(TzT HD−T
Fr
zc
)
(zT HD−zc)
(z−zT HD) +TzT HD zc ≤ z < zT HD
(TzT HD−TzREF )
(zT HD−zREF )
(z−zREF) +TzREF zT HD ≤ z < zREF
(6.4b)
zc =
zT HD +zT FD
2
(6.4c)
A detailed description of all the state parametrs, constants, and assumptions are listed in Table
6.2
As described in the method section a major idea in physics-based computational radar retrieval
algorithm is parameterizing the radar pixel with a set of state parameters, which governs the
key field-scale processes (Table 6.2). The profile behavior of various subsurface key elements is
governed by the state parameters (Fig. 6.7).
While ideally the entire set of parameters including organic matter, soil saturation, and temperature should be potentially considered as unknowns within a radar pixel, a few parameters exhibit
higher priority in controlling fundamental processes, while the other can be assumed known. As
such and based on the field observations some parameters are assumed to be constant and removed
from the unknown set. The range of the variation of unknowns is also constrained based on field
observations (Fig. 6.8).
For a radar pixel, and depends on the freeze/thaw effect in October the set of state parameters
can be listed as follow:
X¯ =
OMz0,zOLT ,h,SWJUNE
z0
,z
JUNE
WT ,z
JUNE
T HD ,SWAUG
z0
,z
AUG
WT ,zALT Oct : UnFr
OMz0,zOLT ,h,SWJUNE
z0
,z
JUNE
WT ,z
JUNE
T HD ,SWAUG
z0
,z
AUG
WT ,zALT ,z
Oct
T FD Oct : Fr (6.5)
121
Table 6.2: List of state parameters, constants, and assumptions regarding state parameters details.
Parameter Definition Time Variation Symbol Status Unit Range/Value Discretization
(∆) Notes
Surface Organic Matter OMz0 Unknown (g/g) % [40
−100] 1.0
Organic Layer Thickness zOLT Unknown (m) [
0.05
−
0.30] 0.01
Shape Factor
β Known (1/m) 50 (−)
Mineral Layer Organic Matter OMM Known (g/g) % 7 (−)
Sand Fraction
Savg Known (g/g) % 36 (−)
Clay Fraction
Cavg Known (g/g) % 25 (−)
Known from field observation
or typical field values
Roughness RMS height
Time Invariant
h Unknown (m) [
0.001
−
0.02] 0.001
June zJune T HD Unknown (m) [
0.05
−
0.20] 0.01
August Stagnation Assumption Thaw Depth
Oct
zALT Unknown (m) [
0.25
−
0.75] 0.01
Reference Depth Time Invariant zREF Known (m) 0.80 (−)
Mid-Point Depth Oct zC Known (m) (zALT
+zT FD)/2 (−) Frozen Oct
June SWJUNE
z0 Unknown (−) [
0.5−1.0] 0.01 Highly Saturated
August SWAUG
z0 Unknown (−) [
0.05
−1.0] 0.01 Surface Saturation
Oct SWOCT
z0 Known (−) 1 (−) Saturated Oct
June zJUNE WT Unknown (m) [
0.05
−zJUNE T HD
]
August zAUG WT Unknown (m) [
0.05
−zALT ] 0.01 Water Table Depth
Oct zOCT WT Known (m) 0 (−) Saturated Oct
June zJUNE T FD Known (m) 0 (−)
August zAUG T FD Known (m) 0 (−)
UnFr*: Known (m) 0 (−) Top Frozen Depth Oct zOCT T FD Fr**: Unknown (m) [
0.05
−
0.25] 0.01
Freeze/Thaw in
October
June
TJUNE
z0 Known (
◦C) +1.0 (−)
August
T AUG
z0 Known (
◦C) +8.0 (−)
UnFr: Known (
◦C) +8.0 (−) Surface Temperature Oct
T OCT
z0 Fr: known (
◦C) -1.0 (−)
Reference Depth Temperature
TzREF Known (
◦C) -5.0 (−)
Temperature at Permafrost Table Time Invariant
TzT HD Known (
◦C) -0.1 (−)
Temperature at Mid-Point Oct
TzC Known (
◦C) 1.0 (−)
Temperature Across the
season assumed to be known
*UnFrozen
**Frozen
122
Inspections of the polarimetric data for all the flight lines, and considering the field observations,
allowed us to remove pixels that are susceptible to freeze/thaw effect in June or August, which
prevent introducing unnecessary unknowns to the retrieval algorithm. However, those pixels for
October couldn’t be avoided. Therefore, with the cost of adding a new unknown that captures
the top frozen depth (z
OCT
T FD), our physics-based algorithm enables capturing the freeze/thaw effect.
While the major focus of this paper is to introduce the physic-based computational algorithms as a
powerful tool for mapping permafrost active layer soil organic carbon, the capability and maturity of
our model to detect freeze/thaw phenomena is another testimony to the significance of physics-based
approaches. Besides additional details in following subsections, we will leave further details on the
capabilities of framework for mapping F/T phenomenon to another work.
The 2017 foundational radar acquisition provides three snapshots in June, August, and October,
therefore the set of state parameters as listed in Table 6.2, controls the snapshots’ behavior rather
than the entire season time-series behavior. The time-series behavior of the state parameters across
the season is essentially controlled via atmospheric drivers such as precipitation, evapotranspiration,
and temperature, and their behavior across the profile is governed by a coupled thermal-hydrological
set of Richard’s and heat conduction equations. Nevertheless, a rudimentary approach to view
the time-series behavior of state parameters is by connecting the dots at each snapshot with a
rudimentary linear behavior that captures the parameter trends (Fig. 6.9).
Incorporating the time-series behavior of state parameters into the profile models as described in
Equations 3 and 4, we can arrive at the 2-dimensional variation time-variant soil profile parameters,
particularly for SW(z;t) and T(z;t). While this behavior, represents a simulated and simplistic
behavior of both soil saturation and temperature across the season and depth, it does capture the
realistic trends in the variation of both profiles (Fig. 6.10).
6.2.4 Organic Soil Dielectric Model
The organic soil dielectric model is the key element in translating surface and subsurface parameters
that control the field scale process into complex dielectric permittivity, which manifests its impact
on the radar signal. While the characterization of mineral soil dielectric properties dates back to the
early 80s, organic soil dielectric has not been explored except more recently and in the past 10 years.
The presence of organic matter substantially changes the physics of soils compared to mineral soil.
Organic soils are more porous, exhibit lower bulk density, and potentially can store more water
than mineral soils. In a recent work, we conducted extensive measurement and modeling efforts
to characterize the dielectric behavior of organic soil. The new organic soil dielectric model was
developed and validated against a large pool of Arctic organic soil that encompasses a wide range
of OM and soil moisture variability. The discussion on the details of the model performance and
operations is beyond the scope of our work and is addressed in another paper. However, in a broad
sense, the organic soil dielectric model exhibits a transformer, which can be described as follows:
εsoil(z) = ε
′
soil(z) +iε
′′
soil(z) (6.6a)
εsoil(z) = MODEL(OM(z),SW(z),T(z),S(z),C(z); f req) (6.6b)
Where the soil complex permittivity comprised of a real part (ε
′
soil) and imaginary part (ε
′′
soil), and
controls by soil physical properties such as OM, SW, T, S, C, and Frequency.
123
An example of the simulated organic soil dielectric profile behavior is shown in Figure 6.11,
where the dielectric profile is constructed for June, August, and October (both frozen and unfrozen
cases) by applying the input profiles from Figure. 6.7. Multiple large contrasts are observed
particularly at the interface of the frozen/unfrozen layer for all the snapshots at the permafrost table,
and additionally at the interface of the top frozen layer in the October frozen case (Fig. 6.11). The
surface dielectric layer is largely controlled by the OM and varies due to soil saturation variation
across the season, with a major assumption that suggests high saturation in June due to snow melt,
low saturation in August due to loss of evapotranspiration over perception gain, and finally in
October, as precipitations gains. Notice the large contrast in the frozen October case on the surface,
which is due to the top layer frozen soil (Fig. 6.11D).
By applying the time-series trends of permafrost active layer soil profile properties as shown in
Figure 6.9 into Equation 6.6b, we can show a simulated behavior of the 2-D variation of the soil
dielectric properties across the season. Such behavior is shown for both the case that late season
(October) stays unfrozen and the case for frozen (Figure 6.12). The variation of soil dielectric
properties is the main element in capturing the influence of subsurface state parameters in controlling
radar responses. The last element in capturing the end-to-end framework that related filed-scale
processes to radar measurement is known as electromagnetic scattering forward modeling.
6.2.5 Electromagnetic Scattering Model
As described in Figure S6, the last element of the forward model in the physics-based computational
model deals with the electromagnetic scattering model, which accounts for interactions of the
electromagnetic waves with the inhomogeneous dielectric structure and surface roughness of each
snapshot. This element closes the loop between field scale parameters that control the radar response
(Within a radar pixel) with the instrument measurements, which are the normalized backscattering
coefficients. A key element in the electromagnetic scattering model is the surface parameterization
and subsurface discretization. The permafrost active layer soil in the Arctic often consists of
convoluted and often broken horizons. A first-order assumption in our modeling suggests that such
heterogeneity which is being captured by our 1D profile models as described by equations (3-5),
and a surface roughness parameter (hsur f) it also requires another set of small-scale roughness (hsub)
associated with the convoluted horizons (Fig. 6.13). The number of layers (NL), discretization (∆z),
buffer depth (Bu f f), and the value of hsub have all been determined based on multiple computational
simulations to better understand the accuracy of the forward model, avoid numerical errors, as well
as computational cost (efficiency) and therefore are in-part empirical. The exact range of hsur f was
merely estimated in a range up to 2 mm to stay within the validity range of the electromagnetic
scattering forward solver, which is an analytical approach known as small perturbation method.
Notice, the philosophy of subsurface discretization and the associated structure as shown in Figure
6.13, follows the subsurface discretization that are performed in land surface models (LSMs) to
run coupled hydrological/thermal models . Particularly the isolation of the profile and subsurface
modeling from soil layers parameterization in the LSMs are similar to the steps that explained in
profile and soil dielectric modeling.
Ultimately the electromagnetic scattering model can be simplified as follows:
σxx = SPM(εsoil(z),h,θinc,Freq) (6.7)
124
Where xx : hh, vv denotes the horizontal and vertical co-polarized radar observations, respectively.
The (discretized) layered dielectric structure (εsoil(z)) along with the surface roughness height (h),
the incidence angle (θinc), and the radar operation frequency (Freq) are fed into the electromagnetic
scattering model that utilizes small perturbation method (SPM) to arrive at radar backscattering
coefficients (σxx). Notice, that the model only accounts for the co-polarized channel, and the
cross-polarized channel is not modeled, nor being used in the process of bio-geophysical retrieval.
Analyzing the behavior of backscattering coefficients as all the state parameters (X¯) varies, is
often of interest. However, as described in equation 5, the set of X¯ includes 9 parameters for June,
August, and unfrozen October, and 10 parameters for the case of frozen October. Therefore, a 9x9 or
10x10 datacube is needed to be constructed for such analysis. A first-order principle in such analysis
is to keep 8(9) parameters fixed, and just study the variations of σxx against one parameter (Fig.
6.14). Such study and the behavior of σxx against each parameter will reveal an initial assessment
of radar signal sensitivity to state parameters (X¯). Notice the term “state-parameter” as described in
Figure 6.4, are the sets of parameters within a radar pixel that impact (or are expected to impact) the
radar response.
An example of the time-series behavior of the backscattering coefficients is shown in Figure
6.15. The behavior is analyzed for both an unfrozen and frozen column. Notice, that the airborne
campaign only provides 3 snapshots in (June, August, and October). The simulated results are
driven by inserting the time-series behavior as shown in Figure S11 into Equation 6 and the resulting
Figure 6.12 into Equation (6.7). It is evident that for the case of P-band across the season, hh
polarization is always smaller than vv. However, once there is a freeze/thaw phenomenon, the hh
exceeds the vv. Such behavior will be briefly discussed in the following subsection, while we skip
details analysis to a forthcoming paper.
6.2.6 Freeze/Thaw Detection with P-band
A major significance of the physics-based approach is providing new insights into the interpretation
of the radar measurements. Looking at the radar backscattering coefficient measurements revealed
that across the season there is a pattern in the values of σhh and σvv that do not fit into our baseline
understanding of electromagnetics wave interactions with subsurface (Fig. 6.16). Our extensive
model simulations and observations have shown that for bare soil without vegetation, the vertical
channel always shows a larger value compared to the horizontal channel. However, such behavior
particularly was almost the opposite for the P-band flights in October for the Toolik flights. Our
observations have shown many pixels (up to 25%) in Toolik flightlines and in October experiences
hh being larger than vv (Table 6.3). Such an observation was relatively consistent when comparing
the distribution of σhh −σvv pixels between August and October, whereas it was less severed in
comparison between June and October flights. Interpreting such behavior was initially not possible,
as the case where hh exceeds vv is usually caused by a double bounce scattering due to vegetation,
or surface water. However, such pixels particularly for the vegetation have to be almost consistent
over the different flights with a more significant effect in August due to higher vegetation water
content.
Our electromagnetic analysis along with incorporations of more radar observations on other
flightlines and other frequencies (those collected by ABoVE Airborne Campaign) suggested that
such behavior can be associated with either snow or a freeze/thaw effect. While we skip further
125
Table 6.3: Pixel analysis for possible freeze/thaw phenomenon, excluding a prefiltering scheme.
Flight Line ID June August October June August October ∼ # Pixels×103
× 10 Total 3 ∼ #Pixels
(σHH −σVV ) ≥ 0 (dB)
× 103 ∼ #Pixels
(σHH −σVV ) ≥ 1.0 (dB)
Atqasuk AT 237 68 238 130 6 126 1716
Barrow BA 251 45 105 140 1 59 1096
Deadhorse DH 115 14 135 41 19 18 2283
Ivotuk IV 340 543 539 201 320 164 1687
Toolik TL 73 56 232 22 15 57 909
Total 1016 726 1249 534 361 424 7691
discussion about other airborne measurements and frequencies here to a forthcoming paper, the
electromagnetic analysis shows a surface frozen soil as shown in figure 6.6 creates a small-largesmall dielectric contrast that can cause σhh > σvv (compare Fig. 6.11C and D ).
Therefore, in order to study the end-to-end forward model behavior, a set of ∼ 2500 parameters
(X¯) is randomly chosen from the range that is provided by Table 6.2. The simulated input parameters
are inserted into the forward model to arrive at three snapshots for June, August, and October (Fig.
6.17).
The output of the forward model from a pool of 2500 parameters is divided into a frozen and
unfrozen case, and it is shown in Figure 6.18. It is evident that the only case that allowsσHH > σVV is
for the frozen case. Notice, that a major counterargument in our observations might be the calibration
accuracy, where the reasoning for a larger hh channel might just stem from the calibration error.
The AirMOSS instruments have shown a radiometric calibration accuracy of better than 0.5 dB.
However, a more conservative case still holds and shows that there are a large number of pixels in
October where the difference between hh and vv can surpass 1.0 dB (Table 6.3).
Given these observations and modeling, the freeze/thaw effect is incorporated for October,
however, to prevent further complexity model is not able to capture any hh > vv in June and August.
Therefore those pixels are removed before the retrieval algorithm is used. Table 6.4 lists the filtering
in the data preprocessing stage. For each flight line, different filtering based on pixel information
and masking based on the NLCD landcover map was applied, which in turn resulted in reducing
the initial number of pixels per flight swath. Initially, a filter was used to keep the pixels that their
corresponding incidence angles lie between the range of [15◦ −60◦
], additionally and for the June
and August acquisitions a filter was used to exclude the pixels for which the horizontal components
were larger than the vertical (σHH > σVV ). This filtering was mainly to reduce the complexity of
the subsurface models in early/mid-season. However, such a filter was not used for October, since
the major attributes of (σHH > σVV ) in late season is to detect the freeze/thaw characteristics (More
detailed in the method section). Another filtering was used to ensure the pixels with backscattering
coefficients between [−35 dB−0 dB]. Finally, and based on the NLCD landcover map a mask was
applied to exclude the pixels with open water, perennial ice/snow, developed areas, and possible
forested particularly for Ivotuk, pasture, and cultivated crops.
126
Table 6.4: Various filters applied to the PolSAR data before retrieval, in the preprocessing stage.
Step-1 Step-2 Step-3 Setp-4
Incidence Angle SNR Land Cover (NLCD 2016) Non-Modeled
Remove Remove Remove Remove
15 ≥ θ
ti
inc
Or
thetati
inc ≥ 60
−35 ≥ σ
ti
xx
Or
σ
ti
xx ≥ 0
0. Ocean
σ
June
HH > σ
June
VV
Or
σ
Aug
HH > σ
Aug
VV
11. Open Water
12. Perennial Ice/Snow
21. Developed, Open Space
22. Developed, Low Intensity
23. Developed, Medium Intensity
24. Developed High Intensity
41. Deciduous Forest
42. Evergreen Forest
43. Mixed Forest
81. Pasture/Hay
82. Cultivated Crops
6.2.7 Time-Series Inversion Scheme
The time-series inversion scheme consists of the last elements in the physics-based computational
framework as depicted in Figure 6.4, and accounts for a time-series L−2 norm cost function along
with a global optimization method known as Simulated Annealing . The cost function can be written
as follows:
L(X¯) =
vuut
1
N
ti
:J,A, O
∑
xx:{vv,hh}
σSPM
xx (X¯ ∆
SA)−σ MEAS
xx (X¯
in)
2
(6.8)
Where L(X¯) shows the L − 2 norm cost function, σ
SPM
xx is the SPM model as described in
equation 6.7, where at each iteration of the optimization, Simulated Annealing (SA) find the best
set of state parameters X¯ Delta
SA , and σ
MEAS
xx in this case is the simulated output, which is resulted
by inserting X¯
in into the forward model framework. Given the imbalance between the number of
measurements (N=6), and the number of unknowns (10 in frozen and 9 in unfrozen cases), we run
the SA algorithms 20 times. This allows us to calculate a statistical representation of the solution’s
space. Table 6.5, lists the set of empirical parameters for the global optimizer. These empirical
parameters are in-part optimized based on the computation time, and available resources particularly
when dealing with millions of pixels for an entire flight line. Additionally, the cost function
threshold stopping criteria ( L(X¯) < Error) is designated based on a conservative case, which allows
more pixels to be converged within the limited number of cost-function evaluations (5000) while
compromising a small sensitivity on the parameters by allowing more available solutions within the
measurement calibration accuracy, which is reported to be 0.5 dB.
The actual cost function behavior for a set of input parameters (as the known solution) can be
constructed based on a 9×9 or 10×10 data cube for the frozen and unfrozen case accordingly.
However similar to the backscattering coefficient as shown in Figure S15, here we only show a slice
of the cost function behavior, where for each plot, all the remaining parameters are assumed to be
12
Table 6.5: List of empirical parameters in simulated Annealing set for this framework.
Definition Symbol Value
Maximum number of cost function evaluation MaxEval
CF 5000
Number of Sequential Perturbation Ns 2
Number of Step Length NT 35
Modified Corana step length to avoid local minima Nε 3
Local minima avoidance threshold ε 10−3
Initial temperature T0 106
Reduction temperature scale RT 0.85
Error, cost function threshold stopping criteria Error 1.0 (dB)
Number of unknown for unfrozen case N
UnFr 9
Number of unknown for frozen case N
Fr 10
Number of measurements N
Meas 6
Number of retrieval iteration for achieving statistics N
Iter 20
Parameters upper bound, and lower bound [LB¯ , UB¯ ] Table 6.2
Parameters discretization Delta ¯ Table 6.2
State parameters for unfrozen case or frozen case X¯ Equation 6.5 or Table 6.2
Simulated annealing estimated state parameters X¯
SA
Discretized SA estimate X¯ ∆
SA
fixed, and the cost function only varies as a function of single parameters. The convex behavior
of the cost function in the case of OMz0 and zOLT is promising in retrieving these parameters
for studying the organic matter properties from a radar retrieval (Fig. 6.19A, B). It is evident
that overall the surface parameters show better chance (e.g., SWJune
z0
,SWAug
z0
,h ) for retrieval than
depth parameters (e.g., zALT , z
June
T HD, z
Oct
T FD). Nonetheless except for the zALT it can be shown depth
parameters indeed show sensitivity within a certain range until reaching saturation in sensitivity. It
is also worth noting that the choice of the cost function and its behavior have been decided after
extensive test and experiment scenarios among various other forms including but not limited to
linear, normalized form, and/or other cases. The current format is based on the L−2 norm of the
dB values.
The end-to-end inversion framework (as shown in Figure 6.4), starts by comparing the hh
and vv channels to decide whether directly using the frozen column retrieval framework when
(σ
Oct
HH > σ
Oct
VV ) or otherwise run both frozen and unfrozen frameworks (Figure 6.20). The inversion
(alternatively refers as retrieval framework) runs for 20 iterations to achieve a statistic of retrieved
parameters.
The retrieval framework is part of the (or equivalent) to what we depicted in Figure 6.4 as the
physics-based computational radar retrieval framework. Figure 6.21 shows the additional details,
and how various elements from radar observations (measurements) to cost function, forward model
and global optimizer interact to relate those measurements to the corresponding state parameters.
This algorithm was initially run for two sets of radar observations, the first pool of radar
observations was driven from the simulated (synthetic) framework, which was detailed in Figure
6.17. Additionally, and for our validation pixels (as described in the main text), we compiled over
2349 pixels, which corresponds to 261 super pixels (3×3). Multiple soil profiles are compiled
128
within a 3 × 3 pixels and serve as a validation for a superpixel. However, in the retrieval, we
deal with each single pixel independently, since not all the pixels converge to state-parameter
solutions. After the retrieval for all of the 2349 simulated and validation pixels are completed, we
analyze the convergence behavior. Figure 6.22 shows the total number of cost function evaluations
and the distribution of L(X¯) for both synthetic and validation pixels. It is evident that the radar
measurements acquired by AirMOSS will achieve a smaller number of convergences.
6.2.8 Probability of Freeze/Thaw
For each pixel, we have 6 measurements, which come from 3 snapshots and two polarizations.
Given the October situation, which can be either frozen or unfrozen, we have to run the retrieval
for both cases. Therefore, for a pixel, we might have a case that both frameworks converge to a
set of state parameters. In this situation, we need to find a way to report the retrieval results. Here
we suggest an approach to calculate the probability of the freeze/thaw for a pixel given the number
of total numbers of convergence for a particular pixel. Figure 6.23 shows a stacked bar plot of the
number of time that the retrieval framework converges for each pixel. The length of a bar is the sum
of the frozen and unfrozen number of convergences, which can be up to 40.
Here we define a probability for the freeze/thaw in each pixel, which can be written as follows:
PrUnFr =
N
UnFr
tot
N
UnFr
tot +N
Fr
tot
(6.9a)
PrFr = 1−PrUnFr (6.9b)
Where the N
UnFr
tot accounts for the total number of convergences for the unfrozen framework,
which can reach 20, and N
Fr
tot shows the same value for the frozen framework. The terms PrUnFr
and PrFr show the calculated probability of a pixel to be thawed or frozen in October. Accordingly,
the freeze/thaw probability behavior can be shown in Figure 6.23.
Before, we proceed two major arguments must be discussed. Looking at Figure 6.24 would
show that for cases when (σ
Oct
HH > σ
Oct
VV ) both frozen and unfrozen retrieval algorithms might
converge. This situation could have been avoided if we changed the stopping criteria by reducing
the Error values or for instance increasing the MaxEval
CF to 10000 or larger values. While for a set of
synthetic data this can potentially reduce the algorithm confusion and result in a better distinguishing
between the frozen and unfrozen case (notice that based on Figure S15, there are frozen cases
that satisfy (σ
Oct
HH > σ
Oct
VV ) however such a scenario might not be suitable when dealing with actual
radar data. A primary issue is the computation costs for retrievals of millions of pixels within a
flightline. Therefore, there is a trade-off between (Error, MaxEval
CF ), which directly impacts the
number of pixels that will converge. Another argument that is important to discuss concerns about
the mathematical differences between the frozen and unfrozen framework, where in the case of
frozen framework we add an additional unknown as the depth of top frozen soil in October (z
Oct
T FD),
such addition might be thought of as a degree of freedom in the inverse problem, which causes
the algorithm to converge better for the frozen column particularly when dealing with actual radar
data (see Figure 6.24B). Therefore, the same arguments might apply here: allowing the algorithm
to run for larger number of MaxEval
CF ,perhaps allows the convergence for unfrozen column. While
such an argument mathematically might hold, when dealing with actual radar data might not be
consistent. Authors, in fact, investigated this possibility extensively, and in many cases when we
129
allow the algorithm to run for a longer time the convergence it will no result in the convergence
of unfrozen column. As mentioned above, eventually computation is a main aspect of this work,
while the skeleton of the framework solely relies on physics, relating the state parameters to radar
measurements has to deal with various computational practicality details. Nonetheless, further
details is skipped here and will be discussed in a forthcoming paper with a focus on the retrieval of
freeze/thaw phenomena using computational physics-based algorithms (Table 6.5).
6.2.9 Simulated Retrieved Parameters
Once the freeze/thaw probability is calculated; to find the estimated parameters for each pixel, we
suggest an expected value of each parameter (X¯ Exp).
X¯ Exp = PrUnFr ×X¯UnFr +PrFr ×X¯ Fr (6.10)
This approach accounts for the contribution of probability and the retrieved parameters from each
framework. For each pixel and based on the number of converged parameters, we can report three
first-order statistical values. The following equations show all the retrieved and synthetic real
ground truth values in a pixel for the case of surface organic matter (OMz0).
OM¯
UnFr,Retrieval
z0 = [OMUnFr,Iter−1
z0
,...,OMUnFr,Iter−20
z0
]1×20 (6.11a)
OM¯
Fr,Retrieval
z0 = [OMFr,Iter−1
z0
,...,OMFr,Iter−20
z0
]1×20 (6.11b)
OM¯
GroundTruth
z0 = [OMPixel−1
z0
,...,OMPixel−1
z0
]1×20 (6.11c)
(6.11d)
Where (OM¯
UnFr,Retrieval
z0
) and (OM¯
Fr,Retrieval
z0
) are two vectors containing the 20 possible converged solutions from running the retrieval framework for a single pixel. Notice, the maximum
number of these vectors’ elements might be 20, and usually some of inversion iterations might not
converge. Additionally, the (OM¯
GroundTruth
z0
) is a vector constructed by repeating the ground truth
value of the OMPixel−1
z0
for specific pixel number 1 (or any other).
The first reported value for retrieval is the average value of each retrieval framework (µ
UnFr
OMz0
and
µ
Fr
OMz0
) among the number of converged iterations for the corresponding pixel.
µ
UnFr
OMz0
= mean(OM¯
UnFr,Retrieval
z0
) (6.12a)
µ
Fr
OMz0 = mean(OM¯
Fr,Retrieval
z0
) (6.12b)
Where mean refers to the averaging operator. Accordingly, the expected value of the retrieved
parameter for the pixel can be calculated using equation 6.10.
µ
Exp
OMz0
= PrUnFr × µ
UnFr
OMz0
+PrFr × µ
Fr
OMz0
(6.13)
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Next, we calculate the standard deviation of the retrieved parameters for each retrieval framework, following by the expected value of the standard deviation.
σ
UnFr
OMz0
= sd(OM¯
UnFr,Retrieval
z0
) (6.14a)
σ
Fr
OMz0 = sd(OM¯
Fr,Retrieval
z0
) (6.14b)
Where sd refers to the standard deviation operator. The standard deviation for the pixel that accounts
for the contribution of both retrieval framework can be calculated as follows (if we assume the
definition of sd =
p
(
1
n
(∑
n
i=1
(xi − µx)
2
)) ):
σ
Exp
OMz0
=
q
PrUnFr ×(σ
UnFr
OMz0
)
2 +PrFr ×(σ
Fr
OMz0
)
2 +PrUnFr ×PrFr ×(µ
UnFr
OMz0
− µ
Fr
OMz0
)
2
(6.15)
Finally, the RMSE is calculated for each pixel as a weighted average of RMSE for each retrieval
framework.
RMSEUnFr
OMz0
= RMSE(OM¯
GroundTruth
z0
,OM¯
UnFr,Retrieval
z0
) (6.16a)
RMSEFr
OMz0 = RMSE(OM¯
GroundTruth
z0
,OM¯
Fr,Retrieval
z0
) (6.16b)
RMSEExp
OMz0
=
q
PrUnFr ×(RMSEUnFr
OMz0
)
2 +PrFr ×(RMSEFr
OMz0
)
2
(6.16c)
The first batch of retrieval results, which includes the time-invariant parameters (e.g., OMz0, zOLT ,
and h) is shown in Figure 6.25, where the first row shows the expected average value for all the
pixels in the simulated retrieval case. Followed by the standard deviation resulted from convergence
for a total of 40 iterations (20 frozen, and 20 unfrozen), and finally the RMSE value for each pixel.
The 1:1 and 2D histogram evidently demonstrate that the proposed end-to-end simulated framework
performs very well in retrieving the time-variant parameters for the majority of the pixels with an
RMSE of 15.2 (g/g) %, 6.5 (cm), and 2 (mm) for the OMz0, zOLT , and hrespectively. While the
rest of the parameters and their performance are out of the scope of this work, it is worth showing
their behavior for the simulated framework (Figure 6.26, and 6.27).
The behavior of retrieved parameters for June is shown in Figure 6.26, where a RMSE of
SWJune
z0
,z
June
WT , and z
June
T HD achieve an RMSE of 0.135 (−), 3.4 (cm), and 4.4 (cm), respectively.
Notice, that for the highly saturated pixels in June, the sensitivity degrades (Fig. 6.26A, D, C). In
most cases, the uncertainty (standard deviation) in retrieval lies within the range of RMSE.
Finally, the simulated retrieved parameters for August and October are shown in Figure S28.
The RMSE for SWAug
z0
, z
Aug
WT , zALT , and z
Oct
T FD are 0.143 (−), 10.9 (cm), 13.4 (cm), and 6.2 (cm)
respectively. Notice, among all the parameters, the retrieval framework shows minimum sensitivity
to zALT . Based on these results, one might argue that zALT could be assumed as a constant value,
however, the presence of zALT in our parametrization scheme is important particularly its relationship
with other values such as z
Aug
WT .
Notice, that an important goal in our physics-based computational framework was laying the
groundwork for radar-driven mapping of the soil organic carbon, which is related to OMz0 and zOLT .
The simulated framework performance demonstrates the feasibility of retrieving these parameters
and further proves the sensitivity of the P-Band time-series to these parameters.
131
In our current version of the framework, we are dealing with 6 measurements v.s. 9/10 unknowns.
Our investigations have also shown that the presence of June data is crucial in improving the sensitivity of mapping organic matter parameters. Other than additional radar measurements that could
be available in the future through Airborne or spaceborne missions, the inter-relationship between
the state parameters is very important. The current state of simulated framework performance
analysis as studied in Figures 6.25 to 6.27 is in fact a “stress test” of the end-to-end framework.
Here we assumed all the state parameters are randomly chosen from their respective ranges and fed
into the forward model as synthetic measurements. Such behavior in reality is a very conservative
assumption, and various field studies have shown that there are empirical relationships between
subsurface parameters such as Organic matter, soil saturation, and active layer thickness. Another
area that we have widely skipped (which in parts was due to lack of sufficient radar observations),
was the soil saturation profile behavior within the active layer. It is well known that moisture and
heat follow Richard’s equations and heat diffusion equations, such as those that are used in land
surface models. In reality, the soil saturation profiles that we modeled in this work have to follow
the physics of hydrology and are intertwined with heat diffusion and temperature profile behavior.
6/7 out of 9/10 unknowns in this work deal with soil saturation and temperature profile parameters
(e.g., surface saturations, water table depth, and thaw depth). Authors believe further incorporation
of those physics in the presence of more frequent radar observations can be key in improving the
sensitivity of physics-based computation radar retrieval frameworks to some of these subsurface
parameters.
Another area of investigation concerns the inversion algorithms and various regularization
terms, which can be highly beneficial in improving the retrieval results. In the study conducted
here, we assumed a 1D profile for organic matter and soil saturation for a 30×30 m
2 pixel. Such
an assumption in the lack of any field observations was a first-order assumption in our work.
Incorporating the statistical spatial distribution of soil properties (organic matter, soil saturation) can
be highly beneficial by grouping a number of sub-pixels to increase the number of locally measured
parameters.
Another area of investigation concerns the inversion algorithms and various regularization
terms, which can be highly beneficial in improving the retrieval results. In the study conducted
here, we assumed a 1D profile for organic matter and soil saturation for a 30x30 pixel. Such
an assumption in the lack of any field observations was a first-order assumption in our work.
Incorporating the statistical spatial distribution of soil properties (organic matter, soil saturation) can
be highly beneficial by grouping a number of sub-pixels to increase the number of locally measured
parameters .
6.2.10 Simulated Retrieval Framework Performance Against Noise and
Calibration Accuracy
In this work, we let the stopping criteria for the retrieval framework to be a 1.00 (dB). This condition
was in part to accommodate the reported 0.50 (dB) calibration accuracy of the measured radar
signals, along with practical computational limitations particularly when we deal with millions of
pixels. We refer to the retrieval framework as Noiseless, and the backscattering coefficients that
were used in the simulated retrieval are noiseless. Authors believe the given the high 1.00 (dB)
threshold as the stopping criterion, the additional 0.50 (dB) noise due to calibration accuracy will
132
not have any impact on the simulated parameters retrievals. However, to demonstrate this claim
we studied an additional case, where a 0.50 (dB) Gaussian noise was added to the output of the
forward model (when constructing the synthetic backscattering coefficients).
σ
SPM+N0
xx = SPM(εsoil(z),h,θinc,Freq) +N (0,σ
2
n
) (6.17a)
N (0,σ
2
n
) = 1
σn
√
2π
e
−
x
2
2σ
2
n (6.17b)
Where N (0,σ
2
n
) is an additive zero mean white gaussian noise, x is random variable, and σnis the
standard deviation that captures the calibration accuracy of measurement and is set to be 0.5 (dB).
To assess the retrieval framework performance, we list the achieved RMSE, total computation time,
and number of converged pixels for two cases of noiseless and with noise, and for two sets of
stopping criteria in Table 6.6.
It is evident that, based on 6.6 detailed analysis, the algorithm we run in our framework
(Case ID=1) is robust with almost identical to the presence of noise (Compare ID=1 and ID=2).
Additionally, for smaller cost function thresholds and a larger number of cost function evaluations,
the presence of noise up to 0.5 (dB) does not impact the retrieval much if the threshold is around
0.5 (dB). The RMSE analysis does perform better when we account for a smaller threshold, however,
the number of converged pixels (compare validation pixels) reduces significantly from 2012 to
961 out of 2349. Therefore, the main compromise in our algorithm is to allow a larger threshold
for a greater number of convergences. Comparison between case ID=3 and 4 also indicates that
allowing the retrieval to run longer (From 5000 to 10000) does not necessarily result in extraordinary
convergences (Compare 961 with 1172).
133
Table 6.6: Comparison of performance of the simulated retrieval for various case study.
Case
ID
L(
¯X)
(dB)
σn
(dB) MaxEval CF
Convergence*
2349 Pixels Time (1,1)**
(s)
Simulation Results
Sim Val*** OMz0
(g
/
g) %
zOLT
(cm)
h
(cm)
SWJune
z0
(−)
zJune WT
(cm)
zJune T HD
(cm)
SWAug
z0
(−)
zAug WT
(cm)
zAug T HD
(cm)
zOct T FD
(cm)
1 1 0 5000 2349 2012 30 15.23 6.5 0.2 0.135 3.4 4.4 0.143 10.9 13.4 6.2
2 1 0.5 5000 2341 2017 30 15.33 6.6 0.2 0.135 3.4 4.4 0.149 11.1 13.4 6.2
3 0.5 0 5000 2269 961 30 14.88 6.3 0.2 0.132 3.5 4.4 0.116 10.8 13.8 5.5
4 0.5 0 10000 2317 1172 60 14.54 6.1 0.2 0.129 3.4 4.3 0.113 10.6 13.5 5.4
5 0.5 0.5 10000 2178 1161 60 15.47 6.5 0.2 0.14 3.6 4.5 0.14 11.2 13.7 5.9
* While the table mainly analyses the simulated results, a major trade off is concerns about the number of converged pixels, which in this
case the validation pixels are used as a representation of the entire flight lines. Also, note that the number of convergences is counted
based on overlapping both frozen and unfrozen frameworks.
** (1,1) refers to computation time for 1 pixel in 1 iteration of inversion. Notice, the inversion runs a total number of 20 times to achieve
statistics for retrieval. The latter can be parallelized to reduce the time of computation.
*** Note that, the addition of the noise only impact the simulations, as the validation data is already experiencing
0.5 (dB) calibration
accuracy uncertainties.
134
Figure 6.3: Uncertainty (standard deviation) of SOC map. (A) The uncertainty of the estimated
SOC[0−5](cm) map driven from standard deviation over converged inverse problem for each pixel for
20 iterations. (B) The uncertainty for second standard depth SOC[5−15] (cm)
. (C) The uncertainty for
third standard depth SOC[15−30] (cm)
.
135
Figure 6.4: Physic-based computational radar retrieval framework. The physics-based computational
radar retrieval framework aims to relate radar measurement at each pixel on the ground to the
corresponding state parameters that control the field scale surface and subsurface processes. Such
techniques rely on detailed field observation to parametrize the subsurface into a meaningful
first-order set of parameters and the foundation of electromagnetic to translate them into radar
backscattering coefficients. An iterative inverse model is then applied to find the optimum set of
state parameters that results in the radar observation, through the forward model.
136
Figure 6.5: Forward Model. The forward model consists of three submodules, where initial state
parameters are used to model critical subsurface processes such as organic matter (OM), soil
saturation (SW), and thaw depth. The equivalent soil profile model then translates into a soil
dielectric profile (ε˜) through an organic soil dielectric model. Finally, a layered dielectric structure
along with the soil rms roughness height (h) feed into an electromagnetic scattering model that via
solving Maxwell’s equations and calculation of the electromagnetic wave (E¯
i
, E¯
s) interaction with
the structure arrives at the radar backscattering coefficients (σxx).
137
Figure 6.6: Active layer profile variation across the season. Early in the thaw season soil columns
experience a shallow thaw depth (z
JUNE
T HD ), shallow water table depth (z
JUNE
WT )and highly saturated
surface soil (SWJUNE
z0
). Later in the season, the thaw depth reaches its maximum thaw depth (zALT )
and maintains this depth throughout the stagnation period that can last from August until October.
The water table depth in August z
AUG
WT usually hit a maximum and deepens as the evapotranspiration
generally overcomes the precipitation, which results in a dryer surface (SWAUG
z0
). Later in the season
and depending on the temperature drop or pixels geolocation October might start the accumulate
snow, which may result in a surface freeze effect. Such phenomenon might not be widespread
across the flightline, but field and radar data agree with the possibility of F/T effect in October.
Across the season, the organic matter profile parameters (OMz0, zOLT ) and the soil roughness rms
height (h) are assumed to remain constant due to limited time-series observation across the season.
138
Figure 6.7: State parameters snapshot an example of simulated profile behavior. (A) Organic matter
profile. (B) Sand fraction profile. (C) Clay fraction profile. (D) Silt fraction profile. (E) Soil
saturation profile in June. (F) Soil saturation profile in August. (G) Soil saturation profile in October,
for an unfrozen surface. (H) Soil saturation profile in October for a frozen surface. (I) Temperature
profile in June. (J) Temperature profile in August. (K) Temperature profile in October, for an
unfrozen surface. (L) Temperature profile in October for a frozen surface.
139
Figure 6.8: Range and distribution of state parameters from in-situ observation. (A) Surface organic
matter. (B) Depth of organic layer thickness, indicating the profile inflection point. (C) Thaw depth
in June 2016. (D) Water table depth in June 2016. (E) Active layer thickness in August 2016. (F)
Water table depth in August 2016.
140
Figure 6.9: Sketch of simulated time-variant behavior of state parameters. (A) Surface soil saturation.
(B) Water table depth. (C) Thaw Depth. (D-E) Top frozen depth in October, for the case of unfrozen
column and frozen column. (F-G) Surface temperature behavior for both unfrozen and frozen case.
Figure 6.10: Sketch of simulated 2D variation of time-variant parameters across time-depth. (A)
Example of 2D Temperature variation, for the case of unfrozen surface October (unfrozen/thawed).
(B) 2D temperature behavior for a frozen surface in October (frozen). (C) Soil saturation 2D
variation.
141
Figure 6.11: Snapshots of soil dielectric behavior across the season. (A) Organic soil dielectric
profile behavior in early June, where real and imaginary are denoted by red and blue respectively.
The dashed lines show the zOLT , z
JUNE
WT , and z
JUNE
T HD , with the black, green and magenta respectively.
(B) Organic soil dielectric profile behavior for August. (C) October soil dielectric profile behavior
for the case of unfrozen column. (D) Top frozen case in October and corresponding organic soil
dielectric profile, the sky-blue dashed line shows the top frozen depth (z
OCT,Fr
T FD ).
142
Figure 6.12: Sketch of simulated 2D variation of time-variant active layer soil dielectric properties
across time-depth. (A, B) Real and imaginary part of 2D organic soil dielectric properties variation
across the time and depth, for an unfrozen October. (C, D) The same 2D organic soil dielectric
behavior for a frozen October case.
143
Figure 6.13: The 1D discretization of the subsurface for electromagnetic scattering modeling. (A)
Shows a schematic of the subsurface, including the buffer in surface, subsurface discretization,
and number of layers. (B) Shows an example of active layer soil profile behavior, where various
horizons can be denoted by the colors.
144
Figure 6.14: (A-C) Time-invariant parameters. Variation of σxx as a function of OMz0, zOLT , and h,
respectively. (D-F) June parameters. (G-I) August parameters. (J) October parameters. Notice that
zALT is assumed to be stagnation period and remains constant between August and October (Fig.
6.9.C).
145
Figure 6.15: Example of simulated σxx(t) time-series behavior. The behavior of the backscattering
coefficients, including vertical (dashed blue) and horizon (dashed red) polarization for the unfrozen
column, respectively. The frozen column is shown by red and blue curves for vv and hh polarization.
The vertical lines show the associated acquisition times of radar measurements, in June, August
and October (magenta, black and green), followed by the zero crossing (cyan). Notice the behavior
is simulated by inserting the time-series behavior as shown in Figure S11 into Equation 6 and the
resulting Figure 6.12 into Equation (6.7).
146
Figure 6.16: The binary behavior of (σhh −σvv) > 0. The binary map that shows the subtractions
of horizontal channel from vertical behavior, where 1 shows the positive values meaning hh is
larger than vv and 0 corresponds to vv being larger than hh. (A) The June acquisition. (B) August.
(C) October. The pattern shows a larger number of pixels being impacted by ()σhh −σvv) > 0 in
October.
147
Figure 6.17: Simulated backscattering coefficient forward model framework. From left to right,
simulated inputs are adapted from Table 6.2, completely randomly. Notice the z
OCT
T FD varies between
either 0, which results in an unfrozen October column, or [0.05−0.25] (m) which results in a frozen
October case. At the heart of the framework, the forward model translates input parameters into
profile models, organic soil dielectric model, and eventually results in simulated outputs which
are the snapshots of multi-channel backscattering coefficients. Notice, that the incident angle was
randomly chosen between [15−60] degrees.
Figure 6.18: Simulated backscattering coefficient behavior and the indication of freeze/thaw. (A)
Shows the portion of a simulated backscattering from the pool of 2500 parameters for unfrozen
case. The hh channel never exceeds the vv channel under the variations of all incidence angles
and parameters. (B) The portion of the simulated backscattering with frozen columns assumption,
where the z
Oct
T FD ̸= 0. The only case that hh shows larger values than vv.
148
Figure 6.19: Cost function behavior. (A-C) Time-invariant parameters. Variation of L(X¯) as a
function of OMz0, zOLT , and h, respectively. (D-F) June parameters. (G-I) August parameters. (J)
October parameters. Notice that zALT is assumed to be stagnation period and remains constant
between August and October (Fig. 6.19.C).
149
Figure 6.20: First step in inversion. Shows the comparison between hh and vv channels in October
to either directly use the frozen column for retrieval or running both. Notice, the whole inversion
scheme is run 20 times to achieve statistics of retrieval parameters. The retrieval framework is
detailed in Figure 6.20.
150
Figure 6.21: Additional details within the physics-based computational radar retrieval framework.
Color codes are consistent with those from Figure 6.21, where the high-level end-to-end framework
was depicted. The output of the framework could be either a potential converged solution or no
convergence within the stopping criteria of the global optimizer.
Figure 6.22: Distribution of the total number of Cost function evaluation. (A) Shows the cost
function distribution and associated values for simulated retrieval (using synthetic measurement).
(B) Distribution of the cost function for validation case using AirMOSS radar measurements at
2349 pixels after running each pixel up to 40 times, (20 per each column assumptions).
151
Figure 6.23: Total number of converged cost functions for frozen and unfrozen (thawed) cases.
(A) Shows behavior of convergence and number of converged inversions for simulated (synthetic)
measurement. (B) Same behavior for validation dataset (AirMOSS radar measurement). In both
cases, red shows the unfrozen, and blue shows the frozen cases.
Figure 6.24: Freeze/Thaw probability for simulated and actual radar data. (A) Simulation results.
(B) Validation (radar data). Legend follows Figure 6.23.
152
Figure 6.25: Simulated retrieval of the time-invariant parameters. (A-C) Shows the expected values
of averaged retrieved parameters for the OMz0, zOLT , and h respectively. (D-E) The standard
deviation, of retrieved parameters. (G-I) Shows the RMSE behavior as described in equation 16.
All the plots show the 2D histogram, where the color bar shows the density of pixels. Plots are
generated based on 2349 synthetic pixels.
153
Figure 6.26: Simulated retrieval of the June parameters. (A-C) Shows the expected values of
averaged retrieved parameters for the SWJune
z0
,z
June
WT , and z
June
T HD respectively. (D-E) The standard
deviation, of retrieved parameters. (G-I) Shows the RMSE behavior as described in equation 16.
All the plots show the 2D histogram, where the color bar shows the density of pixels. Plots are
generated based on 2349 synthetic pixels. The x-axis shows the parameter variations within the
range that was shown in Table 6.2.
154
Figure 6.27: Simulated retrieval of the August and October parameters. (A-D) Shows the expected
values of averaged retrieved parameters for the SWAug
z0
, z
Aug
WT , zALT , and z
Oct
T FD respectively. (E-H)
The standard deviation, of retrieved parameters. (I-L) Shows the RMSE behavior as described in
equation 16. All the plots show the 2D histogram, where the color bar shows the density of pixels.
Plots are generated based on 2349 synthetic pixels. Lower point density is represented by cooler
colors and higher density by warmer colors.
Figure 6.28: Super pixel formation in validation against in-situ data. (A) Shows an example of
in-situ soil organic matter properties at multiple pixels within a 90x90 m super pixel. (B) Shows
compilation of the in-situ data from various adjacent pixels into a super pixel that represents each
pixel independently.
155
6.2.11 Validation Pixels Retrieved Parameters
Following the detailed performance analysis of the simulated (synthetic) retrieval framework for
various state parameters, we then analyze the performance of the framework in retrieving the organic
matter state parameters (OMz0 and zOLT ) using our validation pools that are the compilation of
various soil organic matter data. The legacy soil profile datasets [7, 64, 68, 182–184] are adapted
from the International Soil Carbon Network (ISCN), and National Cooperative Soil Survey (NCSS),
which mainly serve as the input layer of state-of-the-art digital soil mapping techniques used for
SoilGrids, or the NCSCD. For each soil profile, not all the soil’s physical properties were available.
In many cases either bulk density, organic matter, or soil organic carbon where available. Overall,
there are two main categories, where soil profile data either include ρb only, or ρb, and OM is
present, or lastly the profiles only include SOC. In these cases, we have used gap-filling techniques
to fill the gap for missing soil physical properties (See gap-filling subsection in methods). As
described in Figure 2, we first analyze the retrieval by assuming the soil profile information to
be identical for every 9 pixels within a superpixel (3 × 3). As mentioned before, overall, 261
super pixels, that contain various number of soil profile within an area of 90×90 m
2
is used to
serve as validation. Figure 6.28 depict how a validation pixel is compiled, which is mainly based
on combining various in-situ pixels within a 3x3 ABoVE (P-Band) pixels and assuming the new
compiled super pixel in-situ information act independently for each sub-pixel. Each of the subpixels
radar measurements across June, August and October is acted independently and was fed into the
retrieval framework. The retrieved µ
Exp−i
OMz0
and µ
Exp−i
zOLT , is then compared with the estimated OMSP−i
z0
and z
SP−i
OLT by fitting organic matter profile model (equation 1) to the validation data. Where (SP-i)
refers to ith super pixel number. It also important to note that, a primary motivation for creating a
superpixel in this validation effort stems from the possibility of sufficient algorithm convergence for
single pixels. In other words, in an already sparse validation dataset, some of the corresponding
pixels that contain validation data might not converge in the physics-based retrieval, therefore
compiling the neighboring pixels and grouping them as a superpixel is primarily aimed to create
a more comprehensive validation set. Additionally, it is known that geolocations in the northern
higher latitudes might be erroneous due to limited GPS coverages and since the validation dataset in
this work is a compilation of multiple sets of data, without any information of GPS location, authors
suggested the creation of a super pixel for validation purposes.
Figure 6.29 shows the first attempt to analyze the radar retrievals of organic matter properties
using time-series AirMOSS data is to compare the retrieved µ
Exp−i
OMz0
and µ
Exp−i
zOLT at i-th pixel with the
estimated OMSP−i
z0
and z
SP−i
OLT . It is evident that the retrieval parameters behavior against in-situ soil
information performs worse than the simulated framework. Such behavior initially stems from the
quality of the validation organic matter data. While Figure 6.29 shows the retrieval for sub-pixels
(30×30) m, Figure 6.30 analyses the retrieval performance for the super-pixel by calculating the
spatial average of retrieved values of 9 sub-pixels.
Analyzing and detailed assessments of the radar retrieval framework and its performance against
in retrieving organic matter properties for validation pixels requires a deeper and more focused
study. As author believe a major bottleneck in the validation is lack of consistent in-situ information
on soil organic matter properties and various other uncertainties that arise due to data gap fillings.
Therefore, we leave further analysis to our future work such as those published recently in soil
156
Figure 6.29: Performance of the retrieved organic matter profile’s parameters against in-situ data
for each pixel. (A-B) Shows the performance of expected retrieved parameters values at each
pixel (µ
Exp−i
OMz0
and µ
Exp−i
zOLT , respectively) using AirMOSS data against in-situ values. (C-D) RMSE
distribution.
moisture assessment . Nonetheless, and similar to simulated framework assessments, we study the
effects of cost function threshold and inversion empirical parameters on the convergence and RMSE
of the retrieved radar-driven organic matter properties.
Table 6.7 lists the comparison of the validation pixels retrieval performance for various case
studies. Notice in the assessments, that multiple pixels were excluded, initially based on visual
inspection and extreme discrepancies between in-situ soil properties from multiple sources of data.
Additionally, and based on the RMSE for 1x1 pixels, we removed pixels that resulted in RMSE of
larger than 35% and 15 cm for µ
Exp−i
OMz0
and µ
Exp−i
zOLT , respectively. The analysis of RMSE is provided
for various cost function thresholds including 1.0 (dB), and 0.5 (dB). In almost all the cases the
surface organic matter driven from radar measurements performs within a range that is comparable
with simulated results. On the other hand, the retrieved organic layer thickness results are worse
than the simulations.
The bulk of the method sections was devoted to establishing the physics-based computational
retrieval framework and assessing its performance in a simulation manner and against in-situ data
for validation pixels. The main text in this paper, however, deals with driven information from
the output of radar retrieval framework, particularly the soil organic carbon. The main product
157
Figure 6.30: Performance of the retrieved organic matter profile’s parameters against in-situ data for
super pixel (3×3). (A-B) Shows the performance of expected retrieved parameters values at each
pixel (µ
Exp−SP−i
OMz0
and µ
Exp−SP−i
zOLT , respectively) using AirMOSS data against in-situ values. (C-D)
RMSE distribution.
of this paper as shown in Figure 1 is calculated based on the incorporation of two main retrieved
parameters OMz0 and zOLT (Figure 6.31). The remainder of the method section focuses on the
calculation of SOC, and related products that are presented in the method section. However, before
proceeding with the calculation of SOC profiles, an important part of the validation process, which
deals with validation data gap filling has to be discussed.
6.2.12 Validation Data Gap Filling
As mentioned in the results part and previous parts, the validation data in many cases, misses one
or two data layers. Multiple gap filling was applied to fix this issue. The first step of gap filling
concerns filling the soil properties gaps such as bulk density, organic matter and soil organic carbon.
A meta-analysis over all the soil profiles reveals that overall, there are two main categories that
a pair of soil data layers is available. Cases, in which (ρb, OM) is available, or/and cases where
(ρb, SOC) are available. Since the variation between (ρb, SOC) are very large, for cases which
158
Table 6.7: Comparison of performance of the validation pixels retrieval for various case study.
Case
ID
L(X¯)
(dB)
MaxEval
CF
Pixel
Orientation
Converged
Pixels
# of Pixels
used for
Assessment
Simulation Results RMSE
OMz0
(g/g) %
zOLT
(cm)
1 1.0 5000 1×1 2012/2349 1458/2012 16.96 8.5
3×3 252/261 168/252 16.2 8
2 0.5 10000 1×1 1172/2349 663/1172 17.52 8.1
3×3 213/261 70/213 16.66 7.7
Figure 6.31: Map of radar driven OMz0 and zOLT . (A) The expected values of average surface
organic matter (OMz0). (B) The expected values of average organic layer thickness (zOLT ).
SOC and OM are missing, we use an empirical relationship between OM and ρb, followed by the
empirical relationship between OM and SOM, and SOM with SOC. Equation (6.18) describes the
first approach in gap-filling.
i f OM and SOC missing, but ρb present −→
OM = f(ρb)
SOC = g(OM)
(6.18)
Notice, that we intentionally show the equation 18 in symbolical forms (f and g), since we defer a
more comprehensive validation and analysis of the compiled soil organic pool to another work. In
other cases where only SOC is present, we use SOC to find the missing data layers.
i f SOC is only present −→
OM = g
−1
(SOC)
ρb = f
−1
(OM)
(6.19)
159
Equations (6.18) and (6.19) collectively allow us to fill all the data gaps. It is worth mentioning,
similar to any other empirical modeling, there are cases in equation (6.18) or (6.19) that might result
in non-physical values, particularly for large SOC values, values with OM large 100% might occur,
in those cases we set OM values to 100.
Notice, here there is a fundamental difference between total organic matter, which accounts
for all organic matter in the ground (below and above including the moss layer), with soil organic
matter which only encompasses the organic matter with size less than 2 mm. The estimation of
SOM from OM has been established before in our previous work by a detailed study and profile
characterization . The SOM to SOC conversion rate is used as 0.5.
6.2.13 Validation Data Profile Fitting
While the first stage of gap filling helps with finding all the missing soil physical properties, the
number of soil sample (points) per each profile in some cases might be very few or in case of
enough samples per depth, there might be multiple soil profile in a 3×3 profile (as shown in Figure
6.28). The next step in validation data gap filling, is to fit a profile to the discrete soil points. In this
case, we use the OM profile sigmoid function (equation 6.1) to find the profile parameters (OMSP−i
z0
,
z
SP−i
OLT ) for ith pixel.
z¯validation = [z1,...,zN]
OM¯
validation = [OM(z1),...,OM(zN)] −→ OM(z) −→
SOC(z) = g(OM(z))
ρb(z) = f
−1
(OM(z)) (6.20)
Therefore, with proper optimization, we can fit a profile to the SOC(z), OM(z), and ρb(z).
6.2.14 Retrieved Soil Organic Carbon Profile
The calculation of averaged SOC per depth interval initially requires calculating the SOC profile. There are two approaches in finding the SOC profiles, which both rely on calculating the
organic matter profile (OM(z)) at first. These two approaches can be summarized as 1) using the
expected values of retrieved µ
Exp−i
OMz0
and µ
Exp−i
zOLT for each pixel and inserting them into equation
1 to arrive at the µOM(z)
Exp−i , and 2) use both frozen and unfrozen framework and retrieved pairs
of (OMUnFr,Iter−j,i
z0
,z
UnFr,Iter−j,i
OLT ) and (OMFr,Iter−j,i
z0
, z
Fr,Iter−j,i
OLT ) to arrive at corresponding profiles
(OM (z)
UnFr, Iter−j,i
and OM (z)
Fr, Iter−j,i
) for the jth iteration of inversion at i-th pixel, followed by
calculating the expected values of the µ
Exp−i
OM(z)
of the pixel. In short, we refer to them as expectation
first profile second and profile first expectation second. Our analysis shows the latter might be a
better approach, particularly as it also helps to better assess the uncertainties (outside the scope
160
of this work). The second approach is described in equations (6.21) to (6.23), where retrieved
parameters at each pixel for 20 iterations are listed in equation (6.21).
OM¯
UnFr,Retrieval
z0 =
h
OMUnFr, Iter−1
z0
, ..., OMUnFr,Iter−20
z0
i
1×20
(6.21a)
z¯
UnFr,Retrieval
OLT =
h
z
UnFr, Iter−1
OLT , ..., z
UnFr, Iter−20
OLT i
1×20
(6.21b)
OM¯
Fr,Retrieval
z0 =
h
OMFr, Iter−1
z0
, ....., OMFr,Iter−20
z0
i
1×20
(6.21c)
z¯
Fr,Retrieval
OLT =
h
z
Fr, Iter−1
OLT , ....., z
Fr, Iter−20
OLT i
1×20
(6.21d)
Accordingly, the OM profile is constructed for each iteration of converged inversion as described in
equation (6.23), followed by using symbolic function (g) as described earlier to arrive at the SOC.
OM¯ (z)
UnFr, Retrival =
OM(z)
UnFr, Iter−1
,...,OM(z)
UnFr, Iter−20
1×20 (6.22a)
OM¯ (z)
Fr, Retrival =
OM(z)
Fr, Iter−1
,..., OM(z)
Fr, Iter−20
1×20 (6.22b)
SOC¯ (z)
UnFr, Retrival =
SOC(z)
UnFr, Iter−1
,...,SOC(z)
UnFr, Iter−20
1×20 (6.22c)
SOC¯ (z)
Fr, Retrival =
SOC(z)
Fr, Iter−1
,..., SOC(z)
Fr, Iter−20
1×20 (6.22d)
Once the profile is constructed, we then apply averaging similar to what described previously in the
parameter retrieval framework.
µSOC¯ (z)
UnFr,Retrival = mean(SOC¯ (z)
UnFr, Retrival) (6.23a)
µSOC¯ (z)
Fr,Retrival = mean(SOC¯ (z)
Fr, Retrival) (6.23b)
σSOC¯ (z)
UnFr,Retrival = sd(SOC¯ (z)
UnFr, Retrival) (6.23c)
σSOC¯ (z)
Fr,Retrival = sd(SOC¯ (z)
Fr, Retrival) (6.23d)
Where µ and σ shows the average and standard deviation of retrieved SOC profile at each pixel.
The reported SOC in Figure 6.2C, 6.2D, and 6.2E are the expected valued for each parameter after
depth average. The depth average for interval of [a-b] can be calculated as follows:
µSOCUnFr
a−b
=
1
b−a
Z b
a
µSOC¯ (z)
UnFr, Retrivaldz (6.24a)
µSOCUnFr
a−b
=
1
b−a
Z b
a
µSOC¯ (z)
UnFr, Retrivaldz (6.24b)
µSOCUnFr
a−b
=
1
b−a
Z b
a
µSOC¯ (z)
UnFr, Retrivaldz (6.24c)
σSOCFr
a−b
=
1
b−a
Z b
a
σSOC¯ (z)
Fr, Retrivaldz (6.24d)
161
Finally similar to equation (6.10), the expected value of SOC is calculated as:
µSOCExp
a−b
= PrUnFr × µSOCUnFr
a−b
+ PrFr × µSOCFr
a−b
(6.25a)
σ
Exp
SOCExp
a−b
=
s
PrUnFr ×
σ
UnFr
SOCExp
a−b
2
+PrFr ×
σ
Fr
SOCExp
a−b
2
+PrUnFr ×PrFr ×
µSOCUnFr
a−b
− µSOCFr
a−b
2
(6.25b)
Notice that across the main manuscript the µSOCExp
a−b
, which represents the expected value of the
retrieved soil organic carbon for a pixel that was calculated by contribution of both froze, and
unfrozen framework often and alternatively presents as SOC[a−b] or SOCRet
[a−b]
.
6.2.15 Profile Depth Averaging
The average values per depth can be calculated for each depth interval as follows. It is important
to note that the ∆z in profile averaging is much finer (herein 1 cm) than what was selected in
electromagnetic scattering and subsurface discretization (which was 4 cm). In the calculation, the a
and b represent the lower and upper interval depth.
SOC[a−b] (cm) =
1
b−a
Z b
a
SOC(z)dz =
1
b−a
N−1
∑
k=1
SOC(zk)×∆z (6.26a)
SOC[0−5] =
1
5−0
5
∑
k=1
SOC(zk)×(1) (6.26b)
SOC[5−15] =
1
15−5
15
∑
k=6
SOC(zk)×(1) (6.26c)
SOC[15−30] =
1
30−15
30
∑
k=16
SOC(zk)×(1) (6.26d)
Notice that alternatively we could use trapezoid method for numerical integration, however given
the fine discretization in profile construction, the integral results are not different.
SOC[a−b] =
1
b−a
Z b
a
SOC(z)dz =
1
b−a
N−1
∑
k=1
(SOC(zk) +SOC(zk+1))
2
×∆z (6.27)
It is worth mentioning that, in this work, we used a profile model for organic matter that was
empirically developed for the active layer. Other soil digital mapping such as SoilGrids, use six
GlobalSoilMap standard depth intervals [0−5], [5−15], [15−30], [30−60], [60−100], [100−
200], and a mass preserving spline is used to calculate a particular interval of [a−b].
162
6.2.16 SOCC Calculation
A literature survey among multiple approaches for calculating the soil organic carbon stock content
(SOCC) was conducted, which shows that typically there are two approaches in calculating stocks
for a depth interval of [a−b]. Equation (6.28) are used for the cases where the bulk density (ρb)
accounts for the total sample, without removing coarse fractions. Among the state of arts soil carbon
dataset, NCSCD calculates SOCC following equation (6.28).
SOCC[a−b] = SOC[a−b] ×ρb[a−b] ×(b−a)×(1− fm
>2mm
[a−b]
) (6.28)
Where SOCC is reported in kg/m
2
, SOC is reported in (g/g) with a range between [0 − 1],
ρb[a−b]
(kg/m
3
) and fm
>2mm
[a−b]
is the mass fraction of coarse fragment (> 2 mmsize) in the range of
[0 − 1], which accounts rock or ice fraction, and the depth (b − a) is reported in (m) unit. For
the NCSCD and to calculate the SOCC in the plow depth [0−30] (cm), the SOCC data from all
sampled soil layers in each pedon (or profile) are summed up for the [0−30] cm reference depths.
On the other hands SoilGrids v1 and v2 suggests a different method of SOC stock calculation.
Equation 6.29, was used in SoilGrids calculation of SOCC ,
SOCC[a−b] = SOC[a−b] ×ρ
≤2mm
b[a−b]
×(b−a)×(1− f
v
>2mm
[a−b]
) (6.29)
Where the ρ
≤2mm
b[a−b]
is referred to as bulk density of the fine earth fractions, (particles with size
less than 2 mm), and f
v
>2mm
[a−b]
is the volumetric fraction of coarse fragment (> 2 mm size) in the range
of [0−1], which accounts mostly for gravel fractions, and the depth (b-a) is reported in (m) unit.
Soil Grids version 1 (2017) uses interpolation first calculate later, where the stocks were calculated
from the maps of SOC, ρb, and f
v
>2mm
[a−b]
for standard depth, using mass preserving spline followed by
calculation. In SoilGrids version 2 (2020), the SOCC was calculated first at sampling locations and
then interpolated to the globe. The calculation in version 2 is seemingly similar to version 1, and its
only the difference in upscaling and other inputs layer in upscaling create the changes. Notice, both
version 1 and version 2 are based on random forest.
While between equation (6.28) and 6.29 and among SoilGrids v1 and v2 there are multiple
differences that can cause significant changes. A major consistent problem with both however
is disregarding the correlation between SOC and ρb, which causes significant numerical error in
equation 6.29. Here we ignore, the coarse fraction information as it was evidently very sparse in the
compiled validation dataset. In a detailed analysis conducted in our previous work, we have shown
how the root biomass fraction can change as the coarse organic matter in the surface. But without
163
losing the generality, we assume ignore the coarse fraction and show how much the calculated
SOCC for validation pixels will differ using the following equations:
SOCC[0−30] =
Z 30
0
SOC(z)×ρb (z)dz
(6.30a)
SOCC[0−30] = SOC[0−30] ×ρb[0−30] ×
30
100
(6.30b)
SOCC[0−30] = SOCC[0−5] +SOCC[5−15] +SOCC[15−30]
(6.30c)
SOCC[0−30] =
5×SOCC[0−5] +10×SOCC[5−15] +15×SOCC[15−30]
30
(6.30d)
Applying equation (6.30) on the in-situ data results in significantly different distributions of SOCC
(Fig. 6.32).
Figure 6.32: Distribution of total calculated SOCC based on equation (6.30).
6.2.17 Scalability of the Approach
The significance of the physics-based approach that developed in this work was establishing a
process-based link between biogeochemical (e.g., soil carbon), and biophysical (e.g., soil saturation)
parameters at the filed-scale and within a radar pixel with physics of radar data collection. A main
critical component in this approach was an organic soil dielectric model, which plays a fundamental
role in linking field-scale processes to the radar response. Currently, the multiple bottlenecks prevent
an of upscaling the approach to the entire North Slope region, which initially stems from the limited
P-Band airborne SAR observations in the region (e.g, ABoVE Airborne Campaign, which was only
focused on representative bioclimatic zones). Additionally, even if such data existed, a tremendous
effort is needed to improve the computation costs of our current method. An alternative approach to
circumventing both shortcomings is physics-based data-driven upscaling approaches, that utilize the
radar-driven estimates and available large-scale satellite observations to extend the SOC estimation
to the Arctic, and tundra regions.
Such approaches with adequate considerations of the field-scale processes and coupled with
the upcoming satellite missions such NASA-ISRO NISAR L-band mission, and EAS BIOMASS
P-band mission enable unprecedented PolSAR data in the future will allow for extending the SOC
mapping and monitoring from the Arctic to Pan-Arctic regions.
164
6.3 Results
6.3.1 Mapping Soil Organic Carbon
In this study, we used the P-band PolSAR data collected by the AirMOSS instrument through the
ABoVE airborne campaign (Fig. 1A). The focus of the study area is limited to the North slope
of Alaska, where five flight lines are sampled three times through the thaw season (Fig. 6.2B,
Table 6.1). Physics-based computational map of SOC (with a spatial resolution of 30 × 30 m
2
)
for three standard soil depth averages, [0−5] cm, [5−15] cm, and [15−30] cm is driven from the
time-series radar retrieval algorithm (Fig. 6.2C, 6.2D, 1E, and methods). The spatial pattern across
a gradient of land cover is observable, where larger SOC is more abundant within lower latitudes
between [68.7
◦ −69.5
◦
]. The reported SOC map is an expected value between two scenarios that
allows a probability of a freeze/thaw effect in the October snapshot (Methods, F/T Probability).
The estimated uncertainties for the estimated SOC map at different depth intervals show acceptable
accuracy (Fig. 6.3).
6.3.2 SOC Validation
In order to validate the time-series radar-driven SOC, we compiled and integrated multiple sources
of contemporary and legacy soil inventories [7, 64, 68, 182–184] (Method). To the author’s best
knowledge, the compiled dataset is the most updated and comprehensive soil carbon dataset
integrated for the North Slope of Alaska region (Fig.6.33, Method). Overall, around 2349 soil
profiles were processed, which grouped into 261 super pixels (Fig. S25). The super pixel creation
serves two purposes, 1) in some cases the center pixel, which corresponds to the location of validation
pixel might not converge through the computational retrieval process and 2) the geolocation of the
soil profiles is in some cases erroneous and might be scattered. Therefore, we grouped soil profiles
within 3x3 super pixels (Fig. 6.33C). The validation of the physics-based retrieval and the in-situ
SOC shows a total RMSE of 11.7 (g/g) %, with an RMSE of 10.8 (g/g) % for the [0−5] cm and
[5−15] cm intervals, and 13.2 (g/g) % for deeper layer at [15−30] cm interval. To compare the
validation, the corresponding Soil Grids v1, v2 data for each center pixels was also processed (Fig.
6.34).
6.3.3 Impact of Land Cover Type on SOC
The retrieved SOC at different depth intervals and for each flight line is then classified based on the
landcover type according to the NLCD landcover map (Fig. 3). For Toolik flightline the Barren,
Woody Wetlands, and Herbaceous Wetlands landcover, the physics-based retrieval shows an over
estimation compared to SoilGrids v1, and v2, whereas for Dwarf Scrub and Shrub the range of
retrieved SOC agrees with SoilGrids v2. Notice, the purpose of this comparison, is “not” to show
an agreement between the physics-based retrieval and existing digital soil mapping techniques
products such as SoilGrids v1, and v2 since the same comparison between SoilGrids v1 and v2
itself shows major discrepancies. However, a collective comparison of the SOC range for various
land cover and across different land cover shows an agreement on the trends. For instance, in all
165
Figure 6.33: Validation for physics-based radar retrieval. (A) Over 2349 soil profiles are compiled
from various soil inventories. (B) Validation of SOC (g/g) % is conducted for three depth intervals,
[0 − 5], [5 − 15], and [15 − 30] cm for 1 × 1 pixels using only 2018 field data. (C) Validation of
SOC (g/g) % at three standard depths for 3×3 pixels. (D) The Super pixel orientation (more details
Figure 6.28). (E) Validation of SOC for all 1×1 pixels. (F) Validation of SOC for all 3×3 pixels.
flight lines, the retrieved SOC for Barren lands tends to be lower than all the other landcover types.
Such behavior is also consistent for Herbaceous wetlands, where lower SOC is observed amongst
the physics-based retrieval and prevailing SOC maps from SoilGrids.
A Significant superiority in our approach compared to existing mapping techniques stems from
the fact that except for filtering purposes the landcover information is not included in steps of our
computational retrieval, whereas, for digital soil mapping techniques, the landcover information is
critical in upscaling the in-situ soil data to the entire region (method).
166
Figure 6.34: Validation of soil properties adapted from Soil Grids v1, and v2 against in-situ data.
(A-C) The inter-relationship between SOC and ρb for in-situ, SoilGrids-v1, and SoilGrids-v2,
respectively. (D-F) The validation of SoilGrids-v1 SOC and ρb and SOCC against in-situ data. (G-I)
The validation of SoilGrids-v2 SOC and ρb and SOCC against in-situ data.
6.3.4 Soil Organic Carbon Stock Content (SOCC)
The ultimate goal of mapping SOC, and corresponding ρb is to calculate the soil organic carbon
stock content (SOCC). In this study, we compared the SOCC map for the [0−30] (cm) interval
driven from our physics-based approach, which uses 3 P-band radar acquisition with existing SOCC
map driven from C-Band via regression analysis, NCSDS map driven from in-situ soil pedon
167
Table 6.8: The total estimated carbon in Tg for each flightline, for existing mapping techniques.
Estimation Method Toolik
T g C
Deadhorse
T g C
Barrow
T g C
Atqasuk
T g C
Ivotuk
T g C
Total
T g C
This Work 9.73 22.21 12.41 13.83 7.74 65.56
C-Band 6.6 14.85 8.97 9.8 4.8 45.02
NCSCD 4.88 19.03 14.32 15.42 6.15 59.8
Soil Grids v1 16.05 41.37 22.68 30.56 14.64 125.3
Soil Grids v2 5.71 14.07 7.98 9.44 5.94 43.14
data, Soil Grids v1 and Soil Grids v2 (Fig. 6.36, method section SOCC calculation). The spatial
distribution of SOCC for each flight lines and from each product are quite different. The total
amount of Carbon (C) in Tg for each flight line is calculated. Notice that the original resolution
of the physics-based retrieval in this work is 30×30 m
2
. For the remaining products, including
C-Band estimation, NCSCD, and SoilGrids v1, v2 the products are resampled from their original
data layers into 30×30 m
2
, and finally the C is calculated (Table 6.8). Also note that the same mask
and filtering were applied to all the flightlines to make sure the number of pixels with available
data was consistent. The calculations show, the C-Band estimates around 45.02 T g C for the 5
flightlines, whereas the NCSDC estimates was around 59.8 T g C. Our physics-based retrieval results
in 65.56 T g C, and finally the SoilGrids v1 and v2 estimates are around 125.3, and 43.14 T g C
respectively.
6.4 Discussion
168
Figure 6.35: Impact of land cover type on SOC for all the flight lines. (A) The variation of
standard depth interval, SOC[0−5] (cm)
,SOC[5−15] (cm)
, SOC[15−30] (cm)
for different types of land
cover including Barren, Dwarf Scrub, Shrub, Grassland, Sedges, Lichens, Moss, Woody Wetlands,
and Herbaceous wetlands. The box plot shows, the median (line), and the 25%, 75% percentile.
The blue color shows the physics-based retrieval, red shows the SoilGrids v1, and yellow shows
the SoilGrids v2. The palette was created for the Toolik line. (B) Deadhorse flightline. (C) Barrow
flightline. (D) Atqasuk flightline. (E) Ivotuk flightline.
169
Figure 6.36: Comparison of the SOCC estimates for [0−30] (cm) between this study and state-ofthe-art estimations. (A) The estimates of the SOCC in our study for all the lines using time-series
P-Band PolSAR data, with a total of 65.56 T g C for all the. (B) The C-band estimation of
SOCC using regression-based approach between C-Band PolSAR and NCSCD data with a total of
45.02 T g C for all flightlines. (C) The NCSCD product, with a total of 65.56 T g C. (D) SoilGrids
v1, with a total of 125.3 T g C. (E) SoilGrids v2 with a total of 43.14 T g C.
170
6.4.1 The Performance of the Retrieval, and Sensitivity Analysis (Synthetic
Case).
A large portion of the development of the physics-based approach focuses on developing an end-toend framework, which is used in the retrieval process (method). Assessing the performance of the
retrieval framework, particularly the sensitivity of our approach regarding the subsurface parameters,
and the averaged depth interval of the key products (SOC) is crucial (method). To that end, a set of
∼ 2500 unknown parameters (state parameters as denoted in Table 6.2) was randomly generated
and fed into the forward model to arrive at synthetic time-series backscattering coefficients. The
retrieval was conducted for this set of ∼ 2500 simulated measurements, and retrieved parameters
then were used to arrive at the estimated profiles. The inversion scheme was run for two cases, a
conservative approach with a 1.00 (dB) threshold, which is the threshold that accounts for radar
calibration accuracy and trade-off on the computation costs for flight lines in this work (Fig. 6.37).
Additional test was conducted for 0.50 (dB) threshold. Note that the reported radar calibration
accuracy indeed is reported to be better than 0.50 (dB), therefore it was tested for the test case study
(Fig. 6.38).
The simulated retrieval results were then validated against the synthetic ground truth, and for
the 1.00 (dB) threshold, we achieve an RMSE of 6.9 (g/g) %, 8.6 (g/g) %, and 8.4 (g/g) % for
depth interval of [0−5] (cm), [5−15] (cm), and [15−30] (cm) (Figure 6.37.A-C). Additionally,
an RMSE analysis is conducted based on the converged number of iterations for each pixel (Figure
6.37.D-F). The RMSE and sensitivity analysis for 0.50 (dB) threshold shows relatively similar
values (Figure. 6.38). This analysis shows that retrieval using 1.00 (dB) shows acceptable sensitivity
to the various depth intervals, given the complexity of the radar scene from June to August, and
October. An important observation (not shown here) is the influence of the inclusion of early thaw
season (June) data in the retrieval, which improves the sensitivity significantly. Such observations
and the importance of winter data or snow season was shown in the C-Band regression-based
retrieval.
6.4.2 Consistency in Retrieval
The main premise in physics-based retrieval is to establish a framework that links the field scale
processes, which controls the radar response to the measured radar signal. This framework in
the forward direction (arriving from state parameters to radar measurements), as well as inverse
direction (Arriving from radar measurement to state parameters), may not be unique. Different
incidence angles, various soil saturation or organic matter, roughness height, and other parameters
collectively control the radar response. The sensitivity analysis as shown in Fig. 6.37, proves that
our framework is sensitive to key parameters including SOC. However, a major question, which
remains here is whether two separate sets of radar measurements from the same scene can arrive at
the same parameters.
Among all the flight lines in the North Slope of Alaska, between Toolik and Deadhorse flight
lines, an area of ∼ 60 km2 overlaps, which due to differences in the flight direction provides a
diversity in the incidence angle. Notice the measurements are conducted on the same day (except
the June flights, which are a few days apart). From the physics of the problem, and due to the
variation of incidence angle initially, we expect to observe differences in estimated retrieval results.
171
Figure 6.37: Simulated sensitivity analysis of the retrieved depth interval SOC for a threshold
of 1.00 (dB). (A) The estimates of the µSOC[0−5] (cm)
, which is the average based on solving the
inverse problem for each pixel 20 times followed by averaging over depth interval of [0−5] (cm),
and corresponding standard deviation σSOC[0−5] (cm)
, which refers to the error bar in retrieval for
20 iterations for each pixel. The pixels are denoted by blue dots and the shaded area shows the
standard deviation. (B) Synthetic retrieval results for µSOC[5−15] (cm)
and σSOC[5−15] (cm)
. (C) Synthetic
retrieval results for µSOC[15−30] (cm)
and σSOC[15−30] (cm)
. (D) The RMSE for each pixel is based on the
iterated number of converged values for the depth interval of [0−5] (cm). (E) Corresponding RMSE
variation for depth interval of [5−15] (cm). (F) RMSE variation for depth interval of [15−30] (cm).
Additional information in Figure 6.25 to 6.27.
However, a comparison between the two retrievals in fact shows the total estimated C from each
flight for the area of flight is relatively close with Toolik part accumulating around 0.33 T g C, and
Deadhorse stores 0.32 T g C (Fig. 6.39).
6.5 Conclusions
172
Figure 6.38: Simulated sensitivity analysis of the retrieved depth interval SOC for a threshold of
0.50 (dB). Subfigures follow the 6.37.
173
Figure 6.39: Consistency in Retrieval. (A) The estimate of SOCC[0−30] (cm)
for Deadhorse line
in the overlap area. (B) The estimate of SOCC[0−30] (cm)
for Toolik line in the overlap area. (C)
Incidence angle for Deadhorse line. (D) Incidence angle for Toolik line. (E) Landcover map for the
overlap area. (F) The 2D histogram of the retrieved SOCC[0−30] (cm)
, and comparison between the
distribution of the retrieved values for both flightlines.
174
While traditional approaches in digital soil mapping techniques continue to suffer from limited
soil inventories in the northern higher latitudes, many refer to the coming decades as the “golden age”
of Synthetic Aperture Radar (SAR), which enables tremendous ecosystem science opportunities
[185]. As mentioned above, the scalability of the approach presented in this work enables applying
physics-based computational mapping techniques to upcoming satellite missions such as NASAISRO SAR (NISAR) L-Band missions, as well as ESA BIOMASS P-band. Such satellite missions
not only allow to use of long-term time-series acquisitions, which help to constrain the inverse
problem but also the diurnal data collection allows for monitoring and improving the soil carbon
estimates dynamics in NHL regions. The main product of this study, which is the physics-based
radar-driven map of SOC, SOCC is the first ever reported high-resolution map of such a product.
175
Chapter 7
Conclusion and Future Work of Part I
Part I of this dissertation started in the Fall of 2017 as part of the ABoVE phase I project, and
it branched out through a NESSF fellowship and continued support through phase II, and phase
III of ABoVE. The major consistent goal of this dissertation was to map soil organic carbon by
developing and advancing the physics and computation of microwave remote sensing to capture the
processes that govern terrestrial ecosystems. A reflection on the major contributions of the part I
can be discussed from an objective perspective which concerns high-level achievement, as well as
more subjective achievements. In the following author first discusses and shares thoughts on the
contribution of part I of this dissertation on a broad scale followed by more detailed and subjective
achievements focused on radar remote sensing in permafrost landscapes.
7.1 Coining “Radar Ecology”
The term “Radar Ecology” to the best knowledge of the author, has not been previously used in the
context that was introduced in this dissertation. While we discussed various aspects of radar ecology
in the context of radar remote sensing for the Arctic ecosystem, here is the appropriate place to
define it in a broader sense. We define “Radar Ecology” as a multi-disciplinary effort that advances
process-based understanding of the terrestrial ecosystem by linking the physics and computations
of radar remote sensing to those key processes that govern the terrestrial ecosystem such as energy,
water, and carbon cycle. This goes well beyond the more conventional approach of radar retrievals
of geophysical variables that are used in ecology. A combination of detailed long-term ecological
(in-situ) measurement, remote sensing (such as airborne science), and theoretical and computational
modeling is key in radar ecology.
A major reason to claim “Radar Ecology” as a new field, in fact, can be found through a
literature survey on the term “radar ecology” in Google Scholar, which resulted in 325,000 outcomes.
Interestingly the top-search results direct to a review paper written by Erik Kasischke et al., 1997
entitled “The use of imaging radars for ecological applications–A review” [186] (Fig.7.1). It is
no surprise that a few decades later Erik Kasiscke led the effort and contributed as the co-chair of
the ABoVE Science Definition Team, which led to the ABoVE Concise Experiment Plan [111].
Here we argue that the state of research has progressed from “radars for ecological applications”
and rather what “radar ecology” offers is harmonized efforts, which advnaces the process based
understanding of the terrestrial ecosystem.
176
Figure 7.1: Search results for the term “Radar Ecology”, and the reveiw paper by Erik Kasiscke.
The traditional large-scale remote sensing missions, often provide a concise definition of
different layers of products, which are historically categorized as L-0 for raw observation, L-1 for
calibrated, geolocated data (e.g., backscattering coefficients or brightness temperature), L−2/3
for bio/geophysical retrieval (e.g., half-orbit soil moisture), and finally L-4 for science value-added
products such as daily soil moisture, Net Ecosystem Exchange (NEE), Carbon fluxes (Fig.7.2).
One can argue the main product of part I of this dissertation (the SOC map, F/T map, and other
additional products such as surface saturation, and water table depth, which were produced but not
reported because of the length) lies within the category of L-2/3 type product since much of the
efforts were focused on technique development as opposed to show-case science valued product.
While the author agrees with such a viewpoint, the fundamental aspects that can often be overlooked
are the impact and contribution of the process-based understanding of the ecosystem that was used
in developing the technique. In fact, the main argument here lies in the definition of “radar ecology”
which attempts to understand the key processes in the terrestrial ecosystem by advancing physics
and computation of sensing.
Another argument that might be helpful for the introduction of “radar ecology” can be discussed
from the traditional remote sensing perspective, which concerns the calibration/validation activities.
Often in large-scale remote sensing missions, calibration/validation and in-situ measurement are
used at the end of a remote sensing production cycle, here what we did was start from a processbased understanding of the key parameters that govern ecosystem processes and as such show a
signature on radar signal (within a representative radar pixel). In other word, the cal/val is indeed
replaced by detailed in-situ and field observation in support of remote sensing model development
and coordinated airborne/ground campaign.
177
Figure 7.2: Conventional large-scale remote sensing product layers. A major contribution of this
dissertation is bringing a process-based understanding of the ecosystem into the development and
advancement of L−2/3 type products. A contribution that we refer to as the new field of study
“radar ecology”.
While the “old guard” might react to the term “multi-disciplinary” slightly negatively, and
assume such work will sacrifice details from two disciplines (herein radar remote sensing, and
ecosystem ecology). We believe, the novel and complex sensing problems that are particularly
rising in the era of rapid climate changes, require a fresh look at our traditional way of approaching
both fields. Works such as those presented in part I of this dissertation are among the first efforts that
attempt to provide a framework where process-based understanding of ecosystem directly applies to
physics-based remote sensing a field that the author refers to as “radar ecology”!
Such an area of research will require a deep understanding of applied electromagnetics to
understand the physics of sensing, various computational techniques, and a deep understanding of
the terrestrial ecosystem and its main drivers.
7.2 Concluding Remarks on Part I: Arctic Ecosystem
Beyond the broad aspect of the work in part I of this dissertation, the major focus of part I was
developing an end-to-end framework, which relates the key processes in the Arctic ecosystem and
permafrost region to the radar remote sensing. Our particular main focus was understanding the soil
organic carbon in the permafrost active layer, which is among the most vulnerable processes to the
rapid warming in north higher latitudes and yet among the least understood.
In chapter 3 we showed an initial need to better understand the subsurface soil parameters such
as organic matter and soil moisture and their 1D profile behavior, which are among the first-order
parameters that govern the water and carbon cycle as well as the radar response. The detailed field
observation and simplistic profile model lay the ground as the first step in building a framework
that relates these field processes to the radar responses. While there are still many other processes
such as cryoturbation, ice structure, and time-series behavior of subsurface parameters, which are
among the less understood processes in permafrost active layer, chapter 3 provided an initial step
with enough first-order sophistications.
178
The materials presented as part of chapters 4 and 5, where we conducted a joint measurement
of soil dielectric properties and soil water matric potential are among the largest pool of Arctic
organic soil characterization to date. The detailed coupled hydrologic-electromagnetic organic
soil modeling, for the first time, was experimentally validated, while being widely advanced for
organic soil. The significance of chapters 4 and 5 goes beyond Arctic soil and rather provides a
theoretical foundation toward universal soil dielectric models which play a key role in translating
key subsurface processes that govern the terrestrial ecosystem to electromagnetic counterparts,
which can be sensed and measured via radars.
Finally, chapter 6 provides a baseline time-series retrieval framework, where we demonstrate
the sensitivity to the SOC for an end-to-end framework, and we validated our SOC map with
in-situ measurement based on the most comprehensive and updated in-situ SOC compiled within
5 foundational flightlines across 3 decades (although large inconsistency is still existing in-situ).
We showed the SOC map follows the pattern and trend of the landcover map. We showed multiple
retrievals from the same areas are consistent, and therefore we are not merely dealing with noise.
Finally, we also showed that our SOCC and total retrieved carbon are well within the range of other
techniques such as NCSCD or SoilGrids v2. Based on the author’s knowledge there is no existing
research that has tried to provide an in-depth investigation into mapping SOC using a physics-based
approach nor any of the current SOCC maps such as NCSCD are validated as comprehensively as
we scrutinized our research and framework. Yet, this is just a start to advancing the physics and
computation of sensing to track processes that govern Arctic ecosystems. The length of part I did
not allow us to include additional findings on Freeze/Thaw detection and time-series soil moisture
variation.
7.3 Ongoing and Future Work
The ongoing and future work regarding part I of the dissertation initially focuses on concluding the
first-order process-based understanding of the Arctic ecosystem using time-series radar observation
and physics-based computational models. Following is a list of ongoing tasks: 1. Completing the
additional retrieval for the legacy flightlines in the Seward Peninsula. The remaining lines consist
of Teller, Council, Koyukk, Huslia, and Coldfoot 7.3. Upon completion of the lines, the driven SOC
map will be archived on the ORNL DAAC.
2. An ongoing follow-up effort in collaboration with other members of MiXIL after the
completion of all the legacy flightline retrievals is upscaling the airborne radar-driven SOC to
the entire tundra region. Such efforts will leverage multiple other remote sensing products and
data-driven machine learning methods such as Random Forest to extend the airborne swath to the
entire region (Fig. 7.4). Similar efforts have been made for upscaling radar-driven ALT maps in the
Arctic [187].
3. Another area of ongoing work is to expand the validation dataset that was compiled in chapter
6 to the entire Tundra region and potentially the whole of Alaska. The new synthesized in-situ SOC
data compiles and integrates 30 years of SOC measurement across the entire of Alaska (with a focus
on the Tundra region), and will initially serve as validation for upscaling while paving ways for
research regarding soc disturbances such as fire and/or retrogressive thaw slumps.
179
Figure 7.3: Legacy flightlines in the Seward Peninsula that needed to be completed for archival.
4. Beyond the immediate SOC focus, another area of research is a physics-based analysis of
a decade-long airborne long-wavelength radar observation of the North Slope to understand the
time-series ecosystem dynamics and particularly detecting and characterizing the Freeze/Thaw
effect across the North Slope of Alaska. A preliminary notion of this work was discussed in chapter
6, while we left the remaining work to the future.
As the abovementioned ongoing tasks wrap up within the next year, we will continue or focus on
advancing our process-based understanding of the Arctic ecosystem and applying such processes in
our radar remote sensing models. As such and as part of ABoVE Phase III, we recently conducted a
detailed field campaign in the North Slope of Alaska, in the vicinity of the Imnavait Creek watershed
region. The major goal of this field campaign was characterizing the micro-heterogeneity of the
surface and subsurface characteristics at a local scale 7.5.
The field measurement consisted of detailed grid-based measurement of active layer thickness
(ALT), detailed soil coring using a 3
′′ × 2
′′ AMS soil core sampler, soil roughness height measurement at multiple locations using laser profiler, and RGB and multi-spectral drone imagery,
and finally a double-directional UAVSAR flight was also conducted on August 21. Among the 6
planned plots, we initially focused on plot #2 to plot #6, and dropped plot #1 due to logistical issues.
We followed the super-pixel idea that was proposed in chapter 6, which consists of a 90x90 m
2
180
Figure 7.4: The focus of upscaling efforts will be in the Tundra region encompassing, the North
Slope of Alaska, and the Seward Peninsula region [188].
that contains 9 ABoVE pixels (30x30 m
2
). Within each ABoVE pixel, we did finer resolution
measurements within 10x10 m
2
and 5x5 m
2
scales. ALT measurement was conducted with a 5-m
interval in most of the plot, soil cores were collected at 10-m intervals for topsoil [0-3”], and finally,
roughness height was measured at multiple locations with an interval of 2 cm. The collective
measurements conducted in August 2024 are among the most comprehensive field measurement
that simultaneously characterizes multiple key surface and subsurface processes (parameters) that
directly control the radar response. To that end, our future work consists of:
1. Detailed SOC assessment of the Physics-Based retrieval using time-series P-band, at multiple
scales (10x10 m
2
), (30x30 m
2
), and (90x90 m
2
). This work will address the large inconsistency in
our current validation set and additionally address the multi-scale study of the SOC mapping using
the physics-based computational retrieval.
2. High-resolution regional mapping of the ALT using in-situ measurement and optical imagery
with Machine learning.
3. 3D structural characterization of the top organic matter distribution in permafrost active layer,
which expands on our initial 1D understanding that was established in chapter 3.
4. Multi-scale surface SOC mapping using UAVSAR L-band data.
181
Figure 7.5: Field sites measured on Aug 2024.
182
Part II
Microwave Sensors for Dielectric Imaging of Arctic Organic Soil
183
Chapter 8
Introduction to Part II
In this chapter, we provide a general background on microwave imaging sensors, systems, and
techniques for various applications to characterize the dielectric distribution of heterogeneous
materials. We start by reviewing the microwave imaging systems for medical applications, particularly for thermal therapy monitoring. We then discuss microwave characterization of the soils
and elaborate on the objectives of part II, where we use microwave sensor design and imaging as a
non-destructive approach for characterizing the microwave response of Arctic organic soil. The
bulk of the remaining chapters will be focused on system design and various experiments conducted
with the microwave imaging systems followed by a conclusion and future work remark.
Disclaimer: The content of this chapter is adapted in large from the following papers:
II-2-1 Draft in Preparation: K. Bakian-Dogaheh et al., “Microwave Dielectric Behavior of the Arctic
Organic Soil a Non-Destructive Approach-Part I: Instrument Performance ”
II-2-2 Draft in Preparation: K. Bakian-Dogaheh et al., ”“Microwave Dielectric Behavior of the
Arctic Organic Soil a Non-Destructive Approach-Part II: Organic Soil Dielectric Modeling‘
Additionally, while we suffice to a brief elaboration on medical imaging applications, the content
in this chapter is in part adapted from the following papers:
M-1 Draft in Preparation: K. Bakian-Dogaheh,Y. Fang, et al., “3D Validation of the Temperature
Distribution for Interstitial Thermal Therapy Using Real-Time Microwave Imaging”
M-2 Published [189]: Y. Fang, K. Bakian-Dogaheh, et al., “A Dual-band Microwave Imaging
System Prototype for Quantitative 3D Dielectric Reconstruction,” IEEE Transactions on
Instrumentation and Measurement, 2024.
EqualContributions
M-3 Published [190]: Y. Fang, K. Bakian-Dogaheh, et al., “A multi-frequency inverse algorithm
for 3D microwave imaging,” IEEE Transactions on Antennas and Propagation, 2023.
M-4 Published [191]: K. Bakian-Dogaheh,Y. Fang, et al., “A quad-band near-field antenna array
for a multistatic microwave imaging chamber,” IEEE Antennas and Wireless Propagation
Letters, 2023.
184
M-5 Published [?]: Y. Fang, K. Bakian-Dogaheh, et al., “Real-time 3D microwave medical imaging
with enhanced variational born iterative method,” IEEE Transactions on Medical Imaging,
2022.
M-6 Published [192]: Y. Fang, K. Bakian-Dogaheh, et al., “A versatile and shelf-stable dielectric
coupling medium for microwave imaging,” IEEE Transactions on Biomedical Engineering,
2022.
EqualContributions
8.1 Microwave Imaging for Medical Application
In the past few decades microwave imaging (MWI) techniques have been gaining increasing attention
as a non-destructive imaging method for the reconstruction of complex dielectric distribution (e.g.,
geometry, shape, dielectric permittivity, and electrical conductivity) of various targets [193–202].
MWI system prototypes have demonstrated successful capabilities for diagnosing brain stroke,
breast cancer and bone fracture [?, 193, 199]. Compared to conventional (clinical) medical imaging,
MWI is less expensive than magnetic resonance imaging and ultrasound techniques and does not
impose radiation risk compared to X-ray or CT scans. Although many efforts have gone into
improving MWI resolution quality, there is still a long way for MWI systems to proceed from the
preclinical stage into a clinical setting. Particularly for conventional imaging one might prefer to
choose prevailing techniques such as MRI. That being said, in recent years a particular application
of microwave imaging has emerged and presents novel methods that can potentially facilitate the
treatment of maligned cancerous tissues and tumors by enabling monitoring for minimally invasive
surgical procedures such as interstitial thermal ablation therapy [203–205].
Over the past 10 years, our group first demonstrated the potential of thermal monitoring for
simplistic canonical phantom in a cooling experiment [203]. The legacy imaging system consisted of
a single-frequency resonant antenna and quantitative physics-based microwave imaging techniques,
where a numerical Green’s function kernel was directly relating the total field and incident field
to the measured scattered parameters using differential born approximation [206]. Over the past
5.5 years, we designed and fabricated a new dual-band microwave imaging system that utilizes
an in-house produced matching fluid, VBIM-based imaging techniques while achieving a faster
real-time data acquisition for a combination of 768 transmit-receive pairs. Multiple canonical
phantoms and complex phantoms were tested in heating and cooling experiments, where the results
can be found in our published papers [189–192, 205]. As the next step, we used MRI-assisted
microwave imaging, where we used MRI scans as preconditioning for the phantom shape and
applied imaging for real-time thermal monitoring. More recently, our work has been focused on
conducting thermal ablation therapy and monitoring live animals 8.1
185
Figure 8.1: Thermal therapy and monitoring system for live animal trials using microwave imaging.
8.2 Microwave Sensors for Dielectric Imaging of Arctic
Organic Soil
The main motivation for using microwave imaging techniques for characterizing the organic soil
dielectric properties stems from the non-invasiveness and nondestructive approach that microwave
imaging offers in reconstructing the dielectric distribution of non-homogenous medium. Organic
soil is a highly porous and highly heterogeneous soil, and conventional dielectric measurement
methods in the microwave range often fail to capture the degree of heterogeneity that organic soil
presents.
The idea of using multi-static multi-frequency microwave imaging systems highly relies on the
author’s research in the realm of medical imaging, however in the following chapter we present
various novelty and fundamental differences when dealing with organic soil compared to biological
tissues or canonical phantoms.
Therefore the objective of Part II can be listed as follows:
II-1 Design a multi-band multi-static dielectric imaging station that enables the microwave behavior of organic soil
It is worth mentioning the imaging system is fabricated, and preliminary synthetic, simulated
results and system tests show promising performance for reconstructing the dielectric image of
synthetic material using the imaging system. In the following chapter, we will mainly focus on instrument performance and explain the detailed measurement scheme, while the image reconstruction
results are left to future work.
186
Chapter 9
Microwave Sensors for Dielectric Imaging of Arctic Organic Soil
Disclaimer: The content of this chapter is adapted in large from the following papers:
II-2-1 Draft in Prepration: K. Bakian-Dogaheh et al., “Microwave Dielectric Behavior of the Arctic
Organic Soil a Non-Destructive Approach-Part I: Instrument Performance ”
II-2-2 Draft in Preparation: K. Bakian-Dogaheh et al., ”“Microwave Dielectric Behavior of the
Arctic Organic Soil a Non-Destructive Approach-Part II: Organic Soil Dielectric Modeling“
This is the first chapter in a two-part sequence that introduces a new microwave imaging system
designed for studying the microwave dielectric behavior of the Arctic organic soil with minimal
disturbance. Part I presents the instrument performance analysis using standard reference materials
and shows the feasibility of reconstructing the dielectric properties of an organic soil sample.
The system consists of a multi-band microwave imaging cavity with 32 antenna elements that
operate at the P- and L-bands for the quantitative dielectric characterization of highly organic
permafrost soil at different saturation levels. The imaging chamber is filled with a matching
fluid to submerge a centered cylindrical tube that is designed as a sample container. The known
geometry and location of the sample were considered to simplify the inverse scattering dielectric
reconstruction algorithm. The multi-band, low-frequency operation and miniaturization were
achieved by sandwiching a slotted microstrip antenna between a substrate and superstrate layer. The
complete antenna design is comprised of a 6-layer PCB layout. A differential Born Approximation
was used to achieve a 3D dielectric image of test samples. This work provides a foundational
instrument for developing and validating the organic soil dielectric model, which is of particular
interest for physics-based radar retrieval of highly organic Arctic permafrost soil that helps unravel
the water and carbon characteristics within northern higher latitudes.
In part II (future work), multiple dielectric measurements of different Arctic organic soil for a
wide range of organic matter and soil moisture variation will be provided. This dataset enables the
extension of the validation range of a new organic soil dielectric model that was developed at a lower
frequency range to the microwave frequency, particularly those coinciding with state-of-the-art
airborne or space-bore radars that operate at P- and L-bands.
187
9.1 Introduction
In the past few decades, several airborne and spaceborne active/passive microwave sensors were
designated to study the dynamic of regional and global water and carbon cycle characteristics as
climate undergoes rapid changes [122, 123, 207, 208]. In coming years, new spaceborne sensors
such as NASA-ISRO SAR Mission (NISAR), the ESA BIOMASS mission that operates conventional SAR systems along with SigNals of Opportunity: P-band Investigation (SNOOPI) that will
demonstrate in-space technology of reflectometry will bring unprecedented new avenues of research
to study the ecosystem dynamics [151, 209, 210]. Soil properties, including physical texture such
as organic or mineral fractions, along with the variability of the moisture content, are the key
underlying elements in the microwave signatures that are measured by these sensors. Whether the
backscattering coefficients, brightness temperature, or the delay Doppler maps, they all manifest
their microwave presence from dielectric properties on a first-order principle [211]. Hence, understanding the microwave dielectric behavior of soil is paramount in microwave remote sensing of
surface and subsurface characteristics.
Controlled measurement scenarios for characterizing the microwave dielectric behavior of soil
dates back to the early 1980s. Table 9.1 lists a substantial portion of the existing soil dielectric
characterization with a focus on measurement techniques. Traditionally, the majority of the legacy
measurements were focused on mineral soil with negligible organic matter content [29, 114, 212].
The past decade, however, has observed increasing attention toward organic soil, particularly in
response to the recent warming trends in northern higher latitude, where highly organic soil is more
dominant [67, 85, 90, 121]. Herein, we refer to organic soil when the gravimetrical organic matter
content of the sample is more than 20%. While the physics of organic soil can be significantly
different from mineral soil samples in terms of heterogeneity, porosity, bulk density, and particle
distribution and size, the measurement methods that have been used for characterizing the dielectric
behavior of organic soil largely remained similar to the mineral ones. With only one exception
of [67], which used a waveguide resonant cavity system that operates based on the weak perturbation
methods, almost all the other reported measurement techniques could be summarized into the
waveguide, free space, or coaxial methods that measure the transmission and reflection of a sample,
or the open-ended coaxial probe measurement.
Conventional dielectric measurement methods (those used for mineral soil), particularly coaxial
methods, usually consist of a very small cell for the soil sample (refer to sample holder sizes
in Table 9.1), and in many occasions it was necessary to use various soil processing techniques
including grinding the soil with a coffee grinder to achieve a finer texture soil samples. These
methods drastically change the physics of soil; as such, the porosity and bulk density can be affected
significantly [67]. Additionally and universally, among almost all measurement methods, small soil
samples are chosen to achieve a uniform moisture distribution; preparing such small size samples
can disturb the heterogeneity and pore size distribution in the soil sample and deviate the realistic
soil characteristic from the field to the lab.
Techniques for dielectric characterization of materials are not solely limited to soil. In fact, soil
dielectric measurement methods are just a subset of a larger number of methods developed for the
measurement of the complex dielectric permittivity of different materials. A comprehensive review
of these methods is provided in [218] and can be listed as parallel plate, split cylinder resonators,
Split port resonators, Open-ended coaxial probe, Free-space, Two-port waveguide, T E01n cylindrical
188
cavity, and Open resonators. The unique physics of organic soil possesses a significant heterogeneity
level compared to mineral soil or other solid materials and, therefore, require a fresh look into
the techniques for dielectric characterization. These requirements can be listed as 1) minimal or
negligible disturbance, 2) focus on P- and L-band behavior (that coincide with state-of-the-art
radar systems), 3) reasonable sample size to achieve uniform soil moisture distribution and avoid
disturbance in soil sampling, 4) dry down experiment to avoid adding water through experiment, 5)
and finally conducting an experiment on a large pool of sample to capture the variability of organic
matter.
Microwave imaging (MWI) techniques offer a non-destructive approach for characterizing the
shape, geometry, and complex dielectric permittivity distribution of objects under test [219, 220].
Microwave imaging techniques largely encompass 1) qualitative approaches, where detection of
a dielectric anomaly within a background is the main objective and is primarily achieved through
wideband signal processing techniques, and 2) where reconstruction of the complex dielectric
permittivity for a region of interest is the goal, which is achieved through iterative inverse scattering
based algorithm applied on single resonant frequencies [221].
The present study is motivated by the challenges previously outlined in the current measurement
techniques for understanding the microwave behavior of organic soils. Its objective is 1) to design
a microwave imaging system that operates at state-of-the-art microwave remote sensing systems
frequencies (P- and L-bands) to characterize the complex dielectric permittivity of organic soil
with a high degree of accuracy, precision, and minimal disturbance for an organic soil sample and
reference standard materials, and 2) to extend the validity range of our previously developed organic
soil dielectric model at lower frequencies to microwave range by providing extensive measurements
for various organic soil with different degree of mineral texture, and organic matter at different soil
moisture levels. The realization of the first objective is the subject of this paper, which reports the
instrument design and performance analysis; the second objective is realized in part II (and as part
of future work).
9.2 Methods
9.2.1 Microwave Imaging System
Figure 9.1 shows the different hardware elements of the microwave imaging system designed
for characterizing the microwave dielectric behavior of organic soil. The instrument consists of
an imaging cavity with a size of 150 mm×150 mm×250 mm, which encompasses 32 antenna
elements. Inside, the cavity is filled with a matching fluid and a centered sample holder. The
imaging cavity is connected to the data acquisition system, which consists of two Mini-Circuits
USB-1SP16T-83H that are controlled with a National Instrument NI-USB6210 to select 16 channels
of receivers and 16 transmitters. Measurements are conducted by Agilent N5230-A Vector Network
Analyzer using Standard Commands for Programmable Instruments (SCPI) script. The following
subsections detail various elements of the systems and their performance.
189
Table 9.1: Overview of soil dielectric characterization with a focus on measurement techniques
Author
#
Sample
Organic Matter
(%)
Soil Moisture
(m
3/m
3
)
Frequencies
(GHz)
Measurement*
Technique
Sample holder
(mm
×mm
×mm)
Soil***
Processing
TGRS 1985
Hallikainen et al. [114] 5 0 [0
−
0.5]
[1.4
−
6]
[4
−18]
Waveguide
Free space
−
(D
= 30,L
≤ 5.0) Yes
TGRS 1995
Peplinski et al. [29] 4 0 0.25 [0.3−1.3] Open-ended probe − − TIM 2001
Curtis [212]
−
0
− [0.05
−26] Coaxial
(0.75
×
0.75
×1.5)
(0.75
×
0.75
×10) No
TGRS 2010
Mironov et al. [121]
1 [80
−90] [
0
−
0.55] [1−16] Coaxial
(D1 =
0.3,D2 =
0.7)∗∗
(L
= 1.7) Yes
TGRS 2011
Wagner et al. [213] 1 0
− [0
−10] Open-ended probe Coaxial
−
(0.7
×1.6
×10.0) No
TGRS 2014
Bobrov et al. [214] 1 0
− [0.01
−8.5] Coaxial (D
= 1.58,L
=
−) No
J-STARS 2015
Mironov et al. [90] 1 50 [0
−
0.55] [
0.05
−15] Coaxial Same as [121] Yes
RS 2016
Bircher et al. [67]
12
5
[50
−100]
[0
−20]
[0
−
0.85]
[0
−
0.65]
1.4 Resonant cavity (D
= 1.0,L
=
4.0) No
TGRS 2018
Liu et al. [215] 5 0 [0
−
0.4]
[1−
6]
[4
−18]
Waveguide
Free space − − TGRS 2019
Mironov et al. [119]
5 [35
−80] [
0
−
0.5] 1.4 Coaxial Same as [121] Yes
TGRS 2019
Lewandoski et al. [216]
6 − − [0.1−3] Coaxial
(D1 = 1.7,D2 = 3.9)
(L
=
6)
- TGRSL 2019
Pantoja et al. [217]
6 [0
−20] 0.40 [0.3−5.5] Coaxial
(D1 = 1.7,D2 = 3.9)
(L
= 3) No
ESSD 2020
Savin et al. [85]
7 [30
−90] [
0
−
0.4] [
0.01
−16] Coaxial
(D1 =
0.3,D2 =
0.7)
(L
= 1.7,L
= 3.7) Yes
2023
This Work 15 [0
−100] [
0
−1]
0.43
0.86
1.26
Non-Destructive
Microwave Imaging
(D
= 68,L
= 50)
(D
= 68,L
= 84) No
* Unless otherwise determined, waveguide, free space, and coaxial methods refer to conventional transmission and reflection measurements.
**
D1 refers to the inner diameter, and
D2 refers to the outer diameter of the coaxial waveguide cross-section.
*** Soil processing mainly refers to grinding of the soil samples with a coffee grinder to achieve a fine-scale soil sample.
190
Channel
Selection
Switching
Network
Imaging Cavity
System
Sample
Holder
Soil
Fluid
Inside
Cavity
to VNA
Matching
Fluid
S L
Fluid
Figure 9.1: Microwave imaging system for characterizing the microwave dielectric behavior of
organic soil.
191
9.2.2 Matching Fluid
In a microwave imaging system, matching fluid is needed to improve the electromagnetic wave
propagation into the object. Additionally, the presence of a matching fluid helps with achieving
miniaturization techniques for the antenna design and achieving lower resonance frequencies,
particularly at the P-band. Finally, a matching fluid can relax the dielectric contrast ratio between
an object (region of interest) and the background, which relaxes the nonlinearity of the inverse
scattering algorithm to reconstruct the complex dielectric permittivity. The matching fluid used in
our design was an in-house built fluid, with versatility in its dielectric properties (given different
ratios of ingredients) and with thermal and temporal stability [192]. Figure 9.2 shows the complex
dielectric permittivity of the matching fluid, with a conservative 20% error that mainly accounts for
the production of the fluid.
0.5 1 1.5 2
Frequency (GHz)
0
5
10
15
20
Dielectric Permittivity (-)
0r
0
0r
00
Figure 9.2: Complex dielectric permittivity of the matching fluid. The blue curve shows the real
part, and the red color corresponds to the imaginary part as shown. For each curve, the shaded areas
determine the range of dielectric variation, assuming a 10% error.
9.2.3 Sample Holder
The idea of using a microwave imaging technique to characterize the complex dielectric permittivity
of organic soil was mainly to minimize the sample disturbance that was induced in the current
measurement procedures. Over the last few years, authors acquired extensive experience in collecting highly organic soil samples -particularly in the Alaskan Arctic Tundra region- to avoid
crushing, squeezing, and disturbing the samples, which can largely change the soil macroscopic
physical properties [6, 7]. Additionally, the sample size, shape, and location (overall geometry) in
an inverse-scattering-based microwave imaging method are significant information and primarily
are among the unknowns (dielectric distribution) [205]. Once known, the geometry and location of
the sample (alternatively, the object under test) can be hugely beneficial as a-priory information for
the dielectric reconstruction.
192
Figure 9.3 shows the geometry of the sample holder. A Plexiglas pipe located at the center of
the cavity with (Din=70 mm, H=250) is used as the sample holder, which isolates the cavity from
the sample. Two additional small containers are used to fill the gap in the bottom and top of the
sample holder, these containers are filled with the fluid. For the experiment conduted on small soil
contaienr, the size of the top-bottom fluid container is (Din=68 mm, H=97 mm), whereas for the
case with large soil container the size of the top-bottom fluid container are (Din=68 mm, H=84 mm) .
The soil sample container in the small case is (Din=68 mm, H=50 mm) and (Din=68 mm, H=84 mm)
for the large case, which both are located in the center. The size of the sample containers is such
way that we can assume a uniform soil moisture distribution. Furthermore, the size of the sample
captures the heterogeneity of the organic soil. Additionally, the samples were directly sampled from
the field, which remove any disturbance in sample preparation. Further details of the experiment
procedure will be provided in later sections. It is worth mentioning that, the main reasoning to use
two sets of soil containers was the observation regarding signal-to-noise ratio, which was better for
a larger container.
Figure 9.3: Sample holder geometry, from a top and cross-section viewpoint. The soil container is
located at the center, with a diameter of 75 mm and a height of 250 mm. The cavity is filled with
coupling fluid. The 6 layer PCB stack up is also depicted in this figure.
193
9.2.4 Antenna and Array System
The main operation frequency of the microwave imaging system was intended to overlap with
state-of-the-art Airborne polarimetric synthetic aperture radar (PolSAR) systems that flew by NASA
as part of the Airborne Survey through Arctic Boreal Vulnerability Experiment (ABoVE) field
campaign [5, 222]. The two main instruments included the Airborne Microwave Observatory of
Subcanopy and Subsurface (AirMOSS), which operates in the P-band, and the Uninhabited Aerial
Vehicle Synthetic Aperture Radar (UAVSAR), which operates in the L-band [122, 123]. Table
9.2 summarizes the operation frequencies of both airborne instruments. Therefore, our initial
Table 9.2: Operation frequency of the AirMOSS and UAVSAR.
UAVSAR AirMOSS
Frequency L-band P-band
Center frequency (MHz) 1260 430
Bandwidth (MHz) 80 20
Frequency range (MHz) 1217.5-1297.5 420-440
efforts are focused on designing an antenna that captures both P- and L-bands. Previously, we
listed several design considerations for the antenna and array system, particularly for quantitative
inverse-scattering-based MWI systems [191]. These design considerations can be summarized as
follows 1) miniturarization and compactness of the antenna and array system for maximum spatial
sampling, and 2) shielded and reverberating chamber for unilateral propagation, and 3) ease of
fabrication. Achieving miniaturization for employing as many antennas as possible in the imaging
chamber, particularly for the P-band, can be extremely cumbersome if we impose multi-band
operation as an additional requirement.
A number of design configurations and techniques were initially considered for the antenna to
achieve multi-band and miniaturization, which includes an exhaustive list such as tapered patch
antennas [191], fractal antennas [223], slotted patch antennas [224–226], folded slot antennas [227],
dielectric loading and distortion of the current path [228, 229], and finally sandwiching effect
between a substrate and superstrate [230]. Our final design effectively benefited several of these
techniques by incorporating slotted patch antennas, superstrate effect, and dielectric loading due to
the matching fluid.
194
Figure 9.4: a) Different Layers of the Antenna Structure. b) Size and geometry of the single elements
with different symbols, along with size symbols for the Array structure. c) Feeding mechanism and
location of the patch within the multi-layer structure.
Figure 9.4 shows different layers of the antenna, geometry details with corresponding symbols
of each parameter’s size, array structure, and feeding mechanism. Antenna elements are located at
layer 3, effectively sandwiched between a substrate consisting of an FR4 core, a 7628 Prepreg, and
a 3313 Prepreg. The superstrate layer consists of a FR4 core and 3313 prepreg. The details of the
6-layer PCB stack-up thicknesses are depicted in Fig. 9.4. The feeding mechanism consists of a via
that connects the SMA feed to the feed cap in layer 1. It is worth noting that layers 3, 4, and 5 also
include a narrow metallic side edge. The inner side edge on Layer 1 and associated square-tooth
195
shapes are intended for building the imaging cavity, while the side edges of Layers 2-5 are just
for layer numbering. Table 9.3 lists the detailed dimensions of the antenna, panel, feed, and array
configuration.
Table 9.3: Antenna Element, Panel, Feed, and Array Dimensions. Unit: mm
Slots Size Slots Vertical Offset
Lsc Lse Lsp1 Lsp2 Ws Yse Ysp1 Ysp2
52 20 10 28 2.5 15 15 25
Patch Size Array Feed
Lpat Wpat Xpd Ypd Yo f f Ht Dt Ds
44 59 67 55 5 10 4.2 1.27
Panel Size Panel Edges Feed Cap Via
Lpan Wpan Ew Et St Dc Dv Hv
250 150 2.5 1.87 5 5 1.524 1.87
Figure 9.5 shows the 3D simulation setup in the CST Microwave Studio software, the fabricated
cavity with the plexiglass sample holder in the center, and the in/outside of the panel. The imaging
cavity consists of a total of 32 antenna elements, where each panel encompasses 8 elements. The
void space in the cavity is filled with the matching fluid for the experiment.
196
Figure 9.5: Fabricated imaging system and under test. (a) The 3D simulation setup in CST. (b)
Fabricated imaging system with the sample holder. (c) Antenna panel. (d) Imaging chamber filled
with the matching fluid.
9.2.5 Data Acquisition System, System Calibration, and Data Post
Processing
At its core, the dielectric imaging station data acquisition system relies on a vector network analyzer
(VNA) to collect accurate and coherent phases and magnitudes of the scattering parameters. The
full scattering parameters are measured using a standard command for programmable instruments
(SCPI) script that controls an N5230A Keysight VNA. Figure 9.6 shows the different elements
of the data acquisition, including the system (VNA), switching network, TTL circuit, and the
receivers (RXs) and transmitters (TXs) configurations. The switching network consists of two
Mini-Circuits USB-1SP16T-83H, which enables sweeping all RX-TX channels. The RF switch
197
network is controlled by a 10-bit TTL digital output, which was provided by a National Instrument
NI USB 6212. The RXs and TXs configuration follows a zig-zag pattern. The total number of
possible channel pairs (tx,rx), reaches 256, where all the 16 transmitter and 16 receivers are sweeped.
Figure 9.6: Data acquistion system consist of the switching metwork, which shows the configuration
of the transmit and resecivers, the array schematic, and the TTL Circuit.
Although more detailed goes into calculating the resonant frequency (as described in following
sections), the system operation frequency bands effectively coincide with the antenna resonant
frequencies. The sandwiched structure and matching fluid protect the large frequency shift when
different soil samples or reference materials are inserted into the sample holder. Nevertheless, the
measurement is conducted for an entire frequency range spanning from [200−1400] MHz. However,
the imaging algorithm and dielectric reconstruction are conducted at three discrete frequencies
(404 MHz, 735 MHz, and 1311 MHz). These frequencies are very close to the radar instruments’
operation frequency bands. Notice that the additional intermediate frequency (735 MHz) was added
to the measurement scheme to provide further frequency-dependent information.
The overall data acquisition workflow is shown in Algorithm 1. The algorithm sequences and
high-level architecture mostly follow our previous works reported in [189]. Nevertheless, for the
sake of completeness and to capture small nuances in the measurement procedure, it is reported and
can be summarized into three sections: 1) Offline error term extraction, 2) Offline Calibration, and
3) Online Measurement.
Once the measurement is completed, sign corrections for measured S-parameters need to be conducted. The unknown Thru calibration method, which was used in calibrating the imaging, requires
this additional step based on the comparison between the simulated results and measurements.
198
Algorithm 1 Data acquisition workflow
Error term extraction
1: for i = 1 : 16 do ▷ Manual
2: One-port calibration using open, short, load (OSL) standards;
3: Save one-port calibration files;
4: end for
5: for j = 1 : 256 do ▷ SCPI script
6: Unknown thru calibration by SCPI script;
7: Saving 12 Error terms;
8: end for
Calibration (Offline)
9: Load error terms in MATLAB;
10: Load uncalibrated measured S-parameters;
11: Run the 2-port error correction (calibration script) [231, 232];
Measurement
12: for i = 1 : 256 do ▷ SCPI script
13: Correction off;
14: Set frequency [200−1400] MHz with 1 MHz resolution;
15: Select channel by NI-USB6212 TTL;
16: Trigger VNA and store full 2-port S-parameters;
17: end for
9.2.6 Dielectric Imaging Algorithm
To achieve a practical dielectric imaging scheme suitable for our soil dielectric imaging station, we
have to address two challenges: 1) How to use measured S-parameters to achieve dielectric images,
and 2) How to circumvent the computation cost of iterative inverse scattering algorithms.
Microwave imaging systems, such as those described in this work, rely on measuring calibrated
S-parameters. In contrast, from a theoretical point of view, microwave imaging relies on volume
internal equations (VIEs), which relate the object dielectric contrast with the total electromagnetic
field and the Green functions of the imaging domain (background) to the electromagnetic scattered
field. To that end, S-parameters VIE (SVIE) was proposed, which directly relates the object
dielectric contrast, total field to the measured S-parameters, through a kernel known as waveport
vector Green’s function (WVGF) [206].
The SVIE can be described as follows:
S
s
n,m = k
2
b
Z
V
Gn,m(r
′
)· χ(r
′
)E
o
m(r
′
)dv′
, r
′ ∈ V (9.1)
where S
s
n,m is the scattered S-parameter measured from the data channel with the combination of nth
Rx and mth Tx (m ∈ [1,M] and n ∈ [1,N]). The kb is the complex background wave number (with
complex permittivity of ε˜b) and is shown in (9.2).
199
kb = ω
p
ε˜bµ0 (9.2a)
ε˜b = ε0ε˜rb (9.2b)
ε˜rb = ε
′
rb +iε
′′
rb (9.2c)
The dielectric contrast χ(r
′
) between target and background within the object location r
′
is
described as:
χ(r
′
) = ε˜ro(r
′
)
ε˜rb
−1, (9.3)
where ε˜rb and ε˜ro(r
′
) are the complex relative permittivities of the background and object. Subsequently, the Gn,m(r
′
) denotes the waveport vector Green’s function (WVGF), where [206] showed
it could be derived from computed incident Electric field of the nth Rx.
Gn,m(r
′
) = i
4ωµ0
E
b
n
(r
′
) (9.4)
Finally, the term E
o
m(r
′
) describes the total electromagnetic field due to mth Tx. The S
s
n,m refers to
the differential S-parameters between the measured S
o
n,m of the object and S
b
n,m of the object.
S
s
n,m = S
o
n,m −S
b
n,m (9.5)
Thus (9.1) can be written as follows:
S
s
n,m =
iωε0
4
Z
V
E
b
n
(r
′
)·(ε˜ro(r
′
)−ε˜rb)E
o
m(r
′
)dv′
, r
′ ∈ V (9.6)
While Microwave imaging provides a unique means to achieve a non-destructive dielectric image of
the object under test, the inverse scattering algorithm used in the imaging algorithm can potentially
possess an expensive computational cost to achieve proper imaging accuracy. General approaches
such as Born Iterative Methods (BIM), which require updating the total Electrical field, or Distorted
BIM (DBIM) and requires additional updates of the Green’s function at every iteration step, demand
high computational cost by rerunning the electromagnetic forward solver [233, 234]. In the case of
multi-static microwave imaging systems such as those presented here, this computation can be very
lengthy even after hardware acceleration techniques such as GPUs since the forward solver needs to
be run for many channels.
The iterative methods were initially proposed for the inverse scattering problems when the
first-order Born approximation (BA) breaks down [235, 236]. For a 3D object that is circumscribed
within a sphere with radius (a), the BA limitation conditions can be expressed mathematically as:
|
p
ε˜ro(r
′)−
p
ε˜rb| ≤ λ0
4a
(9.7)
Where λ0 is the free space wavelength of the incident wave.
If we ignore the imaginary part of the complex permittivity (without losing generality), for
organic soil, the dielectric permittivity can vary within the range of [3−70]. Ignoring the imaginary
part of the background fluid dielectric permittivity, in Figure 9.7 first-order BA approximation has
200
a small range of validity at the highest frequency (L-band around 1311 MHz), while for the lowest
frequency (P-band around 404 MHz), the validity appears to be much larger. Therefore, accurate
imaging to reconstruct the organic soil dielectric distribution may require iterative methods.
Figure 9.7: The validity range of the BA compared with DBA.
Fortunately, the dielectric behavior of soil possesses a unique feature that can be exploited to
relax the computation costs. Both real and imaginary parts of the soil (whether organic or mineral)
complex dielectric permittivity follow a monotonic behavior starting from a dry region to full
saturation. Such behavior enables the use of Differential Born Approximation (DBA), in which the
background for the next (i+1) soil moisture level can be used as the previous soil moisture level (i).
|
q
ε˜
(i+1)
ro (r
′)−
q
ε˜
(i)
ro (r
′)| ≤ λ0
4a
(9.8)
This situation largely relaxes the initial BA validity range, and for the entire range of dielectric and
at multiple frequencies, the DBA stays within the validity range as described in equation (9.8) as
shown in Figure 9.7.
ai =
r
(
di
2
)
2 + (hi
2
)
2
(9.9)
Where i is the denominator for small (1) and large container (2). For small container (d1, h1) are
(6.8, 5) (cm), and for a large container (d2, h2) are (6.8, 8.4) (cm). With proper discretization,
equation (9.6) for all the voxels can be written as:
201
S
s
n,m =
iωε0
4
q=Q
∑
q=1
E
(i)
n (rq
′
)·O˜(rq
′
)E
(i+1)
m (rq
′
)∆Vq (9.10a)
S
s
n,m = S
o,(i+1)
n,m −S
o,(i)
n,m (9.10b)
O˜(rq
′
) = ε˜
(i+1)
ro (rq
′
)−ε˜
(i)
ro (rq
′
) (9.10c)
where subscript q indicates the voxel index number from 1 to the total voxel Q, and rq
′
is the
position of qth voxel. Note that O˜(rq
′
) represents the differential dielectric and differs from the
dielectric contrast as described in equation (9.3). Additionally, the differences between the complex
sign i and the (i), which indicates the soil moisture level should be noted.
For the combination of all Tx-Rx pairs, a system of matrix equations can be written as:
s=Ao (9.11)
where the elements in the measured data vector s, system matrix A, and unknown-voxel differential
dielectric vector o are denoted in the following equation:
S
s
1,1
.
.
.
S
s
N,1
S
s
1,2
.
.
.
S
s
N,2
.
.
.
.
.
.
S
s
1,m
.
.
.
S
s
N,m
.
.
.
.
.
.
S
s
1,M
.
.
.
S
s
N,M
| {z }
Vector s
=
A
(1)
1,1
··· ··· A
(Q)
1,1
.
.
.
.
.
.
.
.
.
.
.
.
A
(1)
N,1
··· ··· A
(Q)
N,1
A
(1)
1,2
··· ··· A
(Q)
1,2
.
.
.
.
.
.
.
.
.
.
.
.
A
(1)
N,2
··· ··· A
(Q)
N,2
.
.
.
.
.
.
A
(1)
1,m
··· ··· A
(Q)
1,m
.
.
.
.
.
.
.
.
.
.
.
.
A
(1)
N,m
··· ··· A
(Q)
N,m
.
.
.
.
.
.
A
(1)
1,M
··· ··· A
(Q)
1,M
.
.
.
.
.
.
.
.
.
.
.
.
A
(1)
N,M ··· ··· A
(Q)
N,M
| {z }
Matrix A
O˜(r
′
1
)
O˜(r
′
2
)
.
.
.
O˜(r
′
q
)
.
.
.
O˜(r
′
Q
)
| {z }
Vector o
(9.12)
202
The elements in matrix A can be written as follows:
A
(q)
n,m =
iωε0
4
E
(i)
n (rq
′
)·E
(i+1)
m (rq
′
)∆Vq (9.13)
Rewriting equation (9.12) in a more organized way by combining all the sub-vectors and submatrices results in:
S
s
1
S
s
2
.
.
.
S
s
p
.
.
.
S
s
P
=
A
(1)
1
··· ··· A
(Q)
1
A
(1)
2
··· ··· A
(Q)
2
.
.
.
.
.
.
.
.
.
.
.
.
A
(1)
p ··· ··· A
(Q)
p
.
.
.
.
.
.
.
.
.
.
.
.
A
(1)
P
··· ··· A
(Q)
P
O˜(r
′
1
)
O˜(r
′
2
)
.
.
.
O˜(r
′
q
)
.
.
.
O˜(r
′
Q
)
(9.14)
where P = M ×N is the total number of the Tx-Rx pairs (herein 256), and the p-th pair can be found
from p = (m−1)×N +n based on the nth Rx and mth Tx.
The cost function of the inversion model, therefore, can be written as follows:
F(o, s) = 1
2
||s−Ao||2 +
1
2
γ
2
||o||2
(9.15)
where γ is the Tikhonov regularization term. The cost function is then minimized through a Least
Square Conjugate Gradient optimization scheme.
9.2.7 Reference Materials
The main point of using DBA is not only to circumvent the BA validity range, but also to prevent
iterative BIM or DBIM-based inverse scattering, which requires running the EM forward solver for
updating the E
i
n or E
i+1
m . To use the imaging station as a standalone dielectric imaging station with a
plug-and-play performance, extensive precomputation of the system matrix (9.13) is required. This
precomputation should be conducted using a range of reference materials that cover the potential
variations of organic soil complex dielectric permittivity as shown in Fig. 9.8. Accordingly the
contrast function behavior of BA and DBA is shown in Fig. 9.9.
The reference materials were produced using different fluids as listed in Table 9.4, which for
lower range of permittivity follows our initial approach as reported in [192], and in higher range
we used a combination of other liquid with addition of salt to compensate for the imagainary part.
Overall 10 reference material R x is produced, where x : [1−10] refers to each references material.
Notice R 3 also represents the background fluid.
203
((a) a) (b) (c)
Figure 9.8: Reference Material Dielectric Properties.
(a)
(b)
Figure 9.9: Constrast χ function for (a)BA and (b) DBA.
9.3 Results and Discussion
In the following subsection, we elaborate on measurement details and analyze the results from two
prespectives, initially we focuse on the microwave signal behavior for various reference materials.
Next we discuss some preliminary imaging results. The full extent of the imaging and dielectric
reconstruntion for both reference materials and soil is left to the future work.
204
Table 9.4: Reference Material Properties
ID Symbol Volume/Mass Note
R 1 O 300 (ml) O: Oil
R 2 E 300 (ml) E: Ethyl Ether
R 3∗
Ri:LE:O
50 (ml) : 50 (ml) : 250 (ml) Ri: Ripple Milk
LE: Lemon Extract
O: Oil
* R 3 = BG
R 4 150 (ml) : 50 (ml) : 250 (ml)
R 5 150 (ml) : 50 (ml) : 150 (ml)
R 6 225 (ml) : 75 (ml) : 150 (ml)
R 7 225 (ml) : 75 (ml) : 75 (ml)
R 8
M:V:S
150 (ml) : 150 (ml) : 400 (mg) M: Methanol
V: Vinegar
S: Salt
R 9 75 (ml) : 225 (ml) : 550 (mg)
R 10 0 (ml) : 300 (ml) : 600 (mg)
9.3.1 Microwave Signal Analysis
9.3.1.1 Experiment Design
The experiment for both reference materials and the soil samples was conducted over two periods.
Fig. 9.10, shows the measurement sequence, where reference materials were measured 3 times for
the reduduncy, and soil samples were scanned at least 7 times for different soil moisture levels.
Between each sample (whether reference material or soil sample) a background measurement was
conducted. This was to analyze two feautres, the shift of resonant frequency over time and also
study the background bulk changes over time a process that makes the microwave imaging complex.
Total of 10 reference samples were measured for small and large container. Also, a total of 8 soil
samples were tested with large a container and additional 8 soil samples with a small container,
which resulted in 16 independent samples.
07/12
07/13
07/14
07/15
07/16
07/17
07/18
07/19
07/20
07/21
07/22
07/23
07/24
07/25
07/26
S-BG
S-Ref
S-Soil
L-BG
L-Ref
L-Soil
Background
Reference
Soil
Figure 9.10: The entire measurement cycle including the reference materials and soil samples.
205
Table 9.5: The statistics of the system resonant frequencies.
Sample
Holder
Experiment
Scenario
f
1
res
(MHz)
f
2
res
(MHz)
f
3
res
(MHz)
Large Measurement 409.9±2.7 735.3±5.5 1274.8±9.2
Small Measurement 409.9±2.6 735.4±5.3 1275.1±8.7
Large Simulation 415.3 743.5 1309.4
Small Simulation 415.2 743.8 1310
9.3.1.2 System Resonant Frequency
The first step in analysing the microwave signal concerns involves characterizing the system resonant
frequency. A histogram analysis of the resonant frequency (herein we refer to as the minimum
of Sxx, where x can be transmitter or receivers) of all background (R 3) measurement across two
weeks of data collection (94 independent measurement) shows that the resonance frequency might
show slight variation overtime, however the maximum resonant frequency shift is smaller than 10
MHz. Table 9.5 list the measurement and simulation resonant frequencies. Notice there is a slight
difference between simulation and measurement, which is often expented due various reasons, such
as numerical errors due to computation costs and fabrication errors.
The distribution analysis of the statistiscs of the system resonant frequencies as shown in
Fig. 9.11 shows the three resonance frequencies achieved in design including: ∼ 410 MHz,
∼ 735.5 MHz, and finally ∼ 1275 MHz. It is worth mentioning, our design achieves signficant degree of minitaturzation by operating three resonant frequnecies at a total size that is far
smaller than reported designs in the litearture.
200 400 600 800 1000 1200 1400
Freq (MHz)
0
500
1000
1500
# of Repetition
Figure 9.11: The statistics of the system resonant frequencies.
206
9.3.1.3 Background Time-Variance
Analysizng the S
BG
mn (herein we refer to m,n pairs as 2,1, which collectively refers to a pair of
receive, transmit channel) for all channels and for all measurement reveals an obvious shift in both
magnitude and phase of the signal. Such variation is evident in figure 9.12, and imposes a challenge
on the imaging and therefore delneating the signal variation due to actual change in the sample from
the time-variant changes of the bulk fluid is important.
(a) (b)
(c) (d)
(e) (f)
Figure 9.12: Variation in S
BG
mn signal for all 94 background measurement across all channels, indicates
the time-variation of the background. (a,b) Magnitude and phase for first resnoant frequency. (c,d)
Second resonant frequency. (e,f) Third resonant frequency.
Initially we can follow the conventional DBA as explained in previous sections. By analyzing
the variation of the background microwave signal, we can define a calibration accuracy terms for
both magintude and phase, where it allows us to to determine which channel has a usable signal. In
otherwords, by anaylyzing the statistics of signal variation and setting a treshold we can decide if a
sample (whether reference or soil) can surpass the a higher differential signal than the calibration
accuracy. This approach is somewhat similar to conventional remote sensing calibration accuracy
assesement.
Figure 9.13 shows the background signal variation for each channel across 94 measurement
over the 2 weeks, and for all the three resonant frequencies. Given the large variation of the signal
for each channel over time, we set a 2.0 (dB) calibration accuracy threshold for magnitude and a
0.15 (Rad) on phase. This value is based on a tradeoff of how many channels can be preserved
when dealing with actual differential signals from two samples. We then construct two forms of
differential signals, the first is the conventional signal compared to the background, which here we
207
refer as BA (S
R i
21 −S
R 3
21 ), and second we focus on DBA (S
R (i+1)
21 −S
R (i)
21 ), which as described above
refere to sequential differential signal based on two reference sample. This analysis is conducted for
both small and large container for all the reference samples. Subsequently, we apply the (2.0 (dB),
0.15 (Rad)) calibration accuracy on the differential signal, and if any magnitude or phase falls
below the thereshold we consider the signal buried in the noise. The total number of the channel
was then calculted for three sets of reference measurement and for each frequency as shown in
Fig. 9.14 and Fig. 9.15.
(a) (b)
(c) (d)
Figure 9.13: Standard deviation σ of the background microwave signal S21. (a,b) Magnitude and
phase for small sample container. (c,d) Large sample container.
The analysis shown in Fig. 9.14 and Fig. 9.15 will result in a very few number of channels that
can be used particularly for the DBA, which has the best validation range and doesn’t require iterative
imaging. Additionally notice in both figures and for R 3 in both small and large containers the BA
is nonzero, which further indicate the extend of issue regarding the background variation. It is also
important to note that, when we assign a calibration accuracy to the background measurment signal
effectively we assume an average background signal among all the 94 independent measurements
to be repersentative of the background. Therefore, eventhough in DBA the differential signal might
not be a few days apart, it still has to exceed the variational noise level calculated for magnitude and
phase. Another aspect of the challenge is when dealing with soil measurement since a dry-down
208
Small-BA-Repetition-1
R_1-BG
R_2-BG
R_3-BG
R_4-BG
R_5-BG
R_6-BG
R_7-BG
R_8-BG
R_9-BG
R_10-BG
0
20
40
60
# of Valid Channel
f
res
1
f
res
2
f
res
3
Small-DBA-Repetition-1
R_2-R_1
R_3-R_2
R_4-R_3
R_5-R_4
R_6-R_5
R_7-R_6
R_8-R_7
R_9-R_8
R_10-R_9
0
20
40
60
# of Valid Channel
Small-BA-Repetition-2
R_1-BG
R_2-BG
R_3-BG
R_4-BG
R_5-BG
R_6-BG
R_7-BG
R_8-BG
R_9-BG
R_10-BG
0
20
40
60
# of Valid Channel
Small-DBA-Repetition-2
R_2-R_1
R_3-R_2
R_4-R_3
R_5-R_4
R_6-R_5
R_7-R_6
R_8-R_7
R_9-R_8
R_10-R_9
0
20
40
60
# of Valid Channel
Small-BA-Repetition-3
R_1-BG
R_2-BG
R_3-BG
R_4-BG
R_5-BG
R_6-BG
R_7-BG
R_8-BG
R_9-BG
R_10-BG
0
20
40
60
# of Valid Channel
Small-DBA-Repetition-3
R_2-R_1
R_3-R_2
R_4-R_3
R_5-R_4
R_6-R_5
R_7-R_6
R_8-R_7
R_9-R_8
R_10-R_9
0
20
40
60
# of Valid Channel
Figure 9.14: Total number of channel for small container each frequency that shows a differential
signal exceeding the noise threshold for both magnitude and phase. The noise threshold here
refers to variation of the background signal. (a) Repetition number 1, of reference materials. (b)
Measurement of reference materials with 5-6 days sepration from repition 1. (c) Repetition 3,
measurement of reference materials with 12-13 days seperation from 1. Each color shows different
resonant frequencies, with blue showing the lowest, orange a middle, and yellow has the highest
resonant frequencies.
experiment has taken over ∼ 14 days therefore delineating between background time-variation
and actual signal change due to variation of soil moisture is signficant for the purpose of dielectric
imaging of the soil.
209
Large-BA-Repetition-1
R_1-BG
R_2-BG
R_3-BG
R_4-BG
R_5-BG
R_6-BG
R_7-BG
R_8-BG
R_9-BG
R_10-BG
0
20
40
60
# of Valid Channel
f
res
1
f
res
2
f
res
3
Large-DBA-Repetition-1
R_2-R_1
R_3-R_2
R_4-R_3
R_5-R_4
R_6-R_5
R_7-R_6
R_8-R_7
R_9-R_8
R_10-R_9
0
20
40
60
# of Valid Channel
Large-BA-Repetition-2
R_1-BG
R_2-BG
R_3-BG
R_4-BG
R_5-BG
R_6-BG
R_7-BG
R_8-BG
R_9-BG
R_10-BG
0
20
40
60
# of Valid Channel
Large-DBA-Repetition-2
R_2-R_1
R_3-R_2
R_4-R_3
R_5-R_4
R_6-R_5
R_7-R_6
R_8-R_7
R_9-R_8
R_10-R_9
0
20
40
60
# of Valid Channel
Large-BA-Repetition-3
R_1-BG
R_2-BG
R_3-BG
R_4-BG
R_5-BG
R_6-BG
R_7-BG
R_8-BG
R_9-BG
R_10-BG
0
20
40
60
# of Valid Channel
Large-DBA-Repetition-3
R_2-R_1
R_3-R_2
R_4-R_3
R_5-R_4
R_6-R_5
R_7-R_6
R_8-R_7
R_9-R_8
R_10-R_9
0
20
40
60
# of Valid Channel
Figure 9.15: Total number of channels for larger containers. Each frequency shows a differential
signal exceeding the noise threshold for both magnitude and phase. Caption follows Fig. 9.14.
The approach described above can be explained via the following equation (9.16) and corresponding Fig. 9.16, where in approach one conventional differential Born Approximation (DBA)
fails in practice, since the bulk background fluid changes overtime surpasses the signal variation
due to changes in two subsequent reference material or two soil-moisture level.
∆SR 2−R 1 = S
t2
R 2 −S
t1
R 1
(9.16a)
∆SR 2−R 1 ≈ (ε
t2
C−R 2 +ε
t2
B−BG)−(ε
t1
C−R 1 +ε
t1
B−BG) (9.16b)
∆SR 2−R 1 ≈ (ε
t2
C−R 2 −ε
t1
C−R 1
) + (ε
t2
B−BG −ε
t1
B−BG)
| {z }
Non-negligible if (t2 −t1) > 1 h
(9.16c)
210
A possible soultion to address this challenge is the pair (background, sample) measurement as
described in the double differential approach depicted in Fig. 9.16. The major assumption here is
that the background fluid R 3 shows signficant variation for the bulk (anything except the sample
volume), whereas for the sample volume these variations are negligible, particulalry within a 1 hour
time-window. Most of the measurement for each bach of reference materials or samples usually
take a few hours, but between each pair (background, sample) the data acqusition time is less than
20 minutes. Hereafter we refer to this method as double differential Born Approximation (D
2BA),
which is a solution to address practical challenges due to the background bulk changes over time.
Equation (9.17) and (9.18) describes the steps to achieve D
2BA, which no longer requires
defining a high-level of variational noise due to background changes as described in approach
1. In fact, calculation of the standard deviation (statistics of background signal) instead of a full
94 independent measurement for specfic bataches of measurement as shown in the timeline of
measurment in Fig. 9.12, (e.g., for 10 measurement in repetition 1 or reference materials or 8
measurement in level-1 soil moisture of small samples), the variation of the background signal is
much smaller than what we showed in Fig. 9.13.
∆SR 1−BG = S
t1+∆t
R 1 −S
t1+∆t
BG (9.17a)
∆SR 2−BG = S
t2+∆t
R 2 −S
t2+∆t
BG (9.17b)
∆SR 1−BG ≈ (ε
t1+∆t
C−R 1 +ε
t1+∆t
B−BG)−(ε
t1
C−BG +ε
t1
B−BG) (9.17c)
∆SR 2−BG ≈ (ε
t2+∆t
C−R 2 +ε
t2+∆t
B−BG)−(ε
t2
C−BG +ε
t2
B−BG) (9.17d)
∆SR 1−BG ≈ (ε
t1+∆t
C−R 1 −ε
t1+∆t
C−BG) + (ε
t1+∆t
B−BG −ε
t1
B−BG)
| {z }
Negligible if (∆t) > 10 min
(9.17e)
∆SR 2−BG ≈ (ε
t2+∆t
C−R 2 −ε
t2+∆t
C−BG) + (ε
t2+∆t
B−BG −ε
t2
B−BG)
| {z }
Negligible if (∆t) > 10 min
(9.17f)
∆SR 2−R 1 = ∆SR 2−BG −∆SR 1−BG (9.18a)
∆SR 2−R 1 ≈ (ε
t2+∆t
C−R 2 −ε
t2+∆t
C−BG)−(ε
t1+∆t
C−R 1 −ε
t1+∆t
C−BG) (9.18b)
∆SR 2−R 1 ≈ (ε
t2+∆t
C−R 2 −ε
t1+∆t
C−R 1
) + (ε
t2+∆t
C−BG −ε
t1+∆t
C−BG)
| {z }
Negligible local variation
(9.18c)
∆SR 2−R 1 ≈ (ε
t2+∆t
C−R 2 −ε
t1+∆t
C−R 1
) (9.18d)
The results of segemented statistcal analsysis of magnitude and phase of background signal
for both large and small container is shown in Fig. 9.17, and it is apparent that for all resonant
frequencies the majority of the channels show a standard deviation σ of smaller than 0.2 (dB) and
0.05 (Rad) for magnitude and phase respectively. Such an approach is essentially and while add
additional background measurment to complement each sample measurement aleivates signficantly
the challneges due to bulk background changes.
211
@ = 1 _
: −
:
(−
1 +−_1
1 ) _1
1
@ = 2 _
(−
2 +−_2
2 ) _2
2
@ = 1 (−
1 +−
1 )
1
@ = 1 + Δ _ (−
1+Δ+−_1
1+Δ ) _1
1+Δ
@ = 2 (−
2 +−
2 )
2
@ = 2 + Δ _ (−
2+Δ+−_2
2+Δ ) _2
2+Δ
Δ_2−_1 = _2
2 − _1
1
Δ_1− = _1
1+Δ −
1
Δ_2− = _1
2+Δ −
2
Δ_2−_1 = Δ_2− − Δ_1−
Figure 9.16: Conventional differential BA (Approach 1) compared with double differential (D
2BA).
9.3.2 Preliminary Imaging Results
While at the time of writing this dissertation, the results from our extensive microwave scans over the
detailed reference materials and soil measurements is still in developement, a preliminary imaging
results conducted over another set of reference materials consists of (oil, water, glycerin-water,
glycerin, and lemon extract) shows the feasibility of the proposed approach and closes the loop from
measurement to actual dielectric perimittivity reconstruction and capability of microwave imaging as
a non-destructive approach and instrumentation for dielectric measurment [149]. Figure 9.18 shows
the first-order Born approximation (BA) method demonstrates promising dielectric reconstruction
for the real part of permittivity. The ground truth dielectric values are illustrated with a pink dot,
and the box plot shows the median (red stripe) and 25-75% percentile of the reconstructed results.
9.4 Conclusions and Future Work
The main focus in this chapter was assessing the microwave imaging system as an insrutment
for characterizing the dielectric properties of the materials with a focus on Arctic soils. A novel
MWI that encompasses a multistatic multifreqency system is designed and fabricted. A detailed
experiment was conducted and comprehensive signal analysis conducted in this chapter shows the
quality of the signal and its usage in microwave imaging. While the taks of microwave imaging are
left as our ongoing work and are not included in the dissertation, a preliminary imaging for another
set of samples that was tested with the system and closes the loop to achieve dielectric images and
demonstrate the capability of the system in imaging dielectric distribution of materials.
212
(a) (b)
(c) (d)
Figure 9.17: Statistics of segmented background variation associated to each batch of sample
measurment based on the timeline as shown in Fig. 9.12.
Various novelties in this chapter include but not are limited to the new design of the multifrequency antenna and array configuration, which achieves a signficant degree of minituariazation.
We addititionally discussed various practical issues and workarounds to circumevent some of the
challenegs that arises when dealing with a microwave imaging for qauntitatve dielectric mapping of
materials, particulalry soil dielectric at various soil moisture levels.
213
Figure 9.18: Reconstruction results for resonance frequency at 415 MHz, where 5 samples including
water (W), glycerin (G100), half-half mixture of water and glycerin (G50W50), isoproyl alcohol
(LE), and Oil (O).
214
Chapter 10
Conclusion and Future Work of Part II
Part II of this dissertation showcases the capability of a microwave imaging system as a standalone
dielectric scanner, which suggests a new approach for the non-destructive characterization of
the material’s dielectric properties. Using the microwave imaging method overcomes historical
challenges in the dielectric measurement of materials, particularly when the degree of heterogeneity
imposes significant errors on conventional techniques.
10.1 Ongoing work
The major focus of ongoing work is to complete the image reconstruction for all the reference
samples and the soil samples Fig. 10.1. Detailed soil measurement as described in the previous
chapter was conducted on two batches of small and large containers. Table 10.1 lists the samples
that were harvested from multiple locations in the North Slope and Interior Alaska. The microwave
scan has been already concluded and the microwave signal was processed and calibrated for all the
soil samples at different soil moisture levels.
Figure 10.1: (a) Reference samples scanned 3 times across ∼ 14 days. (b) Soil samples were
measured up to 8 times at different soil moisture levels.
215
The full imaging framework as described partially in the previous chapter eventually closes the
loop from the imaging sample in the cavity, to the processed data that will be fed into the inverse
scattering which reconstructs the 3D dielectric image of the materials Fig. 10.2.
Figure 10.2: The end-to-end soil dielectric imaging framework.
10.2 Future Work
Future work on the application of microwave imaging for non-destructive characterization of imaging systems encompasses multiple fronts:
1. Initially from a practical perspective, the author would like to investigate the possibility
of removing the matching fluid and investigate a data-driven approach for mapping 3D dielectric
structure. While an initial experiment (not reported here) has shown other challenges due to the
removal of the fluid, an area of interest is to use of the reference materials in the void cavity as a
way to calibrate the system. This approach at its core is inspired by the 3 calibration measurements
(short, open, reference) that are necessary for coaxial probes used in dielectric characterization.
2. Another area of significant interest is the potential of the imaging cavity to be located in
a thermal chamber to studying the near-zero dielectric behavior of the Arctic soil. The existing
techniques that characterize the thermal behavior of the soil (particularly for organic soil) suffer
from the same challenges that were the main motivation to use the imaging technique instead of
conventional methods.
3. Lastly, another potential area of investigation is advancing the imaging technique to be
suitable as a field sensor, replacing the traditional soil-moisture probes.
4. In addition to the imaging techniques the antenna design that was proposed as part of the
cavity design also has significant potential for use in future multi-frequency imaging systems.
216
Table 10.1: Soil Sample Properties
Location Sample
ID Site Name Soil ID Latitude Longitude Depth (cm) ρb (g/cm3) φ (cm3/cm3) RB (g/g)% SOM (g/g)% S (g/g)% C (g/g)%
S-1-1 Scottie Creek SC-2 62.697352 -141.142333 [0−5] 0.15 0.9 17 70.8 - -
S-2-1 Creamers Field CF-1 64.869467 -147.73904 [0−5] 0.08 0.93 37 79.4 - - S-3-1 Imnavait Creek IMN-4 68.604972 -149.30635 [22−29] 0.19 0.88 4 59.9 - -
S-4-1 Happy Valley HV-1-4 69.155356 -148.838789 [19−24] 1.08 0.51 0.5 8.6 18.5 28.5
S-5-1 Ice Cut ICC-1-5 69.041894 -148.827031 [26−32] 1.27 0.47 0 8.6 29 16
S-6-1 Ice Cut ICC-2-3 69.042483 -148.825383 [14−20] 0.2 0.79 5.6 71.2 - - S-7-1 Happy Valley HV-2-3 69.155358 -148.8418 [15−22] 0.18 0.87 8.3 68.5 - -
Small
S-8-1 Happy Valley HV-2-4 69.155358 -148.8418 [22−29] 1.12 0.49 0 6.3 17 22.5
S-2-1 Scottie Creek SC-4 62.697352 -141.142333 [15−20] 0.32 0.75 0 48.3 - -
S-2-2 Imnavait Creek IMN-5 68.604972 -149.30635 [29−36] 0.6 0.69 0 7.8 44 25
S-3-2 Franklin Bluffs FB-3 69.812372 -148.766486 [15−22] 0.71 0.67 1.1 5.65 62.5 21
S-4-2 Creamers Field CF-4 64.869467 -147.73904 [15−20] 0.16 0.86 8 77.2 - - S-5-2 Ice Cut ICC-2-4 69.042483 -148.825383 [20−26] 0.54 0.7 1.25 40.6 51.5 16.5
S-6-2 Ice Cut ICC-2-1 69.042483 -148.825383 [0−7] 0.09 0.91 61 58.9 - - S-7-2 Ice Cut ICC-1-4 69.041894 -148.827031 [20−26] 1.23 0.55 1 9.5 28 22
Large
S-8-2 Ballaine Road BR-1 64.915 -147.838638 [0−5] 0.08 0.89 58 82.9 - -
217
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Appendices
A Soil Dielectric Measurement
Figure A.1: Franklin Bluffs samples with corresponding organic soil dielectric measurement and
models. The behavior of real (red curve) and imaginary (dashed red curve) part organic soil
dielectric model against laboratory measurement for the full range of soil saturation (SW). The
measurement comprised of the real part (blue circle), and imaginary part (blue diamond). Notice, in
reality more measurement points were conducted, however, the values are averaged with 0.1 interval
in soil saturation. Therefore, an error bar is shown for measurement points. The shaded transparent
red area shows the averaged of the corresponding model for 0.1 interval.
238
Figure A.2: Sagwon-1 samples with corresponding organic soil dielectric measurement and models.
239
Figure A.3: Sagwon-2 samples with corresponding organic soil dielectric measurement and models.
240
Figure A.4: Happy Valley-1 samples with corresponding organic soil dielectric measurement and
models.
241
Figure A.5: Happy Valley-2 samples with corresponding organic soil dielectric measurement and
models.
242
Figure A.6: Ice Cut-1 samples with corresponding organic soil dielectric measurement and models.
Figure A.7: Ice Cut-2 samples with corresponding organic soil dielectric measurement and models.
243
Figure A.8: Imnavait Creek-1 samples with corresponding organic soil dielectric measurement and
models.
Figure A.9: Creamers Field-1 samples with corresponding organic soil dielectric measurement and
models.
244
Figure A.10: Ballaine Road-1 samples with corresponding organic soil dielectric measurement and
models.
Figure A.11: Scottie Creek-1 samples with corresponding organic soil dielectric measurement and
models.
Figure A.12: 8-Mile Lake-1 samples with corresponding organic soil dielectric measurement and
models.
245
B Timeline of Research Activities During Ph.D.
The timeline of my research activities during the period of 7.5 years is shown in Fig. B.1. Overall up
to 60% of time was focused on part I and part II of this dissertation, with the overwhelming majority
∼ 55% devoted to the part I (ABoVE) project, and ∼ 5% on the part II (soil imaging). Other time
commitment distribution is shown in the pie-chart, where ∼ 23% of the effort was focused on the
medical imaging project, ∼ 10% on the sdradar project, and finally ∼ 7% on the soilscape project.
2017-2018
2018-2019
2019-2020
2021-2022
2020-2021 2022-2023 2023-2024
Figure B.1: Timeline of research activities during Ph.D. program. Timeline is shown after filtering
a 1-year moving averaging windowing. The overall time commitment for this dissertation is around
60% of the total time that was spent on various projects.
246
Abstract (if available)
Abstract
This dissertation comprises two parts. In part I, a detailed investigation of physics-based computational radar remote sensing models is conducted for mapping the soil organic carbon in permafrost landscape using long-wavelength airborne polarimetric synthetic aperture radars. Part II delves into microwave sensors and imaging techniques, which enable a non-destructive approach for characterizing the dielectric properties of heterogeneous materials such as highly organic soil. Chapter 1, provides a high-level introduction to the entire dissertation and discusses the motivations, objectives, and broader contribution of this work. Part I covers chapter 2 to chapter 7. Initially, in Chapter 2, we discuss motivations and details of the recent status of remote sensing research in the Arctic and permafrost landscape, and particularly we examine physics-based computational remote sensing for characterizing subsurface. Chapter 3 addresses the first element in forward-centric physics-based remote sensing, where a detailed profile modeling is provided to establish a process-based understanding of the subsurface drivers of the ecosystems (e.g., soil organic matter and soil moisture) that control radar signals. Chapters 4 and 5, subsequently address two major elements for developing a coupled hydrologic-electromagnetic framework for modeling organic soil dielectric behavior in the Arctic. Chapter 6, provides an end-to-end retrieval framework, with a detailed and comprehensive assessment of the retrieval performance analysis in simulated and actual radar data. The major outcome of Chapter 6 is a map
of soc generated from the ABoVE airborne campaign time-series P-band acquisition across the thaw season in the North Slope of Alaska. Finally, chapter 7 provides a conclusion where the main contribution of part I is described through the “radar ecology” a field that attempts to understand terrestrial ecosystems through physics-based computational modeling and linking of the field scale processes to the radar response.
Part II covers chapters 8 to 10. Initially, in chapter 8 we discuss the application of microwave imaging systems in medical imaging and then we broadly discuss the advantages of microwave imaging and sensor design in non-destructive characterization of the Arctic organic soil. Chapter 9 discusses various details on the design and fabrication of a multi-static multi-frequency imaging system and its various subsystems for the purpose of soil dielectric imaging. The detailed experiment was described along with compressing microwave signal analysis and preliminary imaging results.
Finally, chapter 10 discusses ongoing and future work on the microwave imaging of Arctic organic soil.
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Bakian-Dogaheh, Kazem
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Physics-based models and microwave sensors for mapping soil carbon in arctic permafrost using long-wavelength radars
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Viterbi School of Engineering
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Electrical Engineering
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