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Physics-based bistatic radar scattering model for vegetated terrains in support of soil moisture retrieval from signals of opportunity

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Physics-based bistatic radar scattering model for vegetated terrains in support of soil moisture retrieval from signals of opportunity

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Content PHYSICS-BASED BISTATIC RADAR SCATTERING
MODEL FOR VEGETATED TERRAINS IN SUPPORT OF
SOIL MOISTURE RETRIEV AL FROM SIGNALS OF
OPPORTUNITY
by
AMIR AZEMATI
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)
August 2021
Copyright 2021 AMIR AZEMATI
To my parents and my sister.
ii
Acknowledgements
I would like to express my deepest gratitude to my faculty advisor Prof. Mahta Moghaddam
for her continuous support of my Ph.D. study, for her encouragement, motivation, and valuable
guidance. I have been extremely lucky to have her as my Ph.D. advisor and without her guidance
and persistent support this dissertation would not have been possible. I would also like to thank
my other dissertation committee members, Prof. Kelly T. Sanders, and Prof. Mike Shuo-Wei Chen
for their insightful suggestions and feedback.
I would like to thank my colleague Amer Melebari, who contributed to the implementation of
the soil moisture retrieval algorithm. In addition, I thank Prof. Jeffrey Walker form the Monash
University for providing the soil moisture in-situ sensor measurements of the Soil Moisture Active
Passive (SMAP) Yanco, Australia (AUS) sites. Moreover, I thank the entire Distributed Space-
craft with Heuristic Intelligence to Enable Logistical Decisions (D-SHIELD) and Cyclone Global
Navigation Satellite System (CYGNSS) science team members for their valuable discussions and
feedback. I would like to thank the entire Microwave Systems, Sensors, and Imaging Laboratory
(MiXIL) group for their friendship and support over the course of my Ph.D. journey.
My Ph.D. work was funded through a fellowship from the University of Southern California
(USC) Viterbi School of Engineering and also supported in part by National Aeronautics and Space
Administration (NASA) and National Science Foundation (NSF).
iii
Table of Contents
Dedication ii
Acknowledgements iii
List of Tables vi
List of Figures vii
Abstract xi
Chapter 1: Introduction 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Soil Moisture Remote Sensing from Signals of Opportunity . . . . . . . . . . . . . 3
1.4 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Chapter 2: Review of Related Work 7
2.1 Single-Species Monostatic Radar Model . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Scattering Mechanisms in Backscatter Radar Model . . . . . . . . . . . . . . . . . 10
Chapter 3: Bistatic Radar Scattering Model for Vegetated Land Covers 13
3.1 Bistatic Scattering Forward Model . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.1.1 Bistatic Scattering Geometry . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1.2 Direct Ground Bistatic Scattering (G) . . . . . . . . . . . . . . . . . . . . 16
3.1.3 Vegetation V olume Bistatic Scattering (B) . . . . . . . . . . . . . . . . . . 19
3.1.4 Branch-Ground (BG) and Trunk-Ground (TG) Double-Bounce Bistatic Scat-
tering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1.5 Total Bistatic Scattering Stokes Matrix . . . . . . . . . . . . . . . . . . . 24
3.2 Forward Model Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2.1 Direct Ground Bistatic Scattering(G) . . . . . . . . . . . . . . . . . . . . 24
3.2.2 Vegetation V olume Bistatic Scattering(B) . . . . . . . . . . . . . . . . . . 29
3.2.3 Double Bounce Bistatic Scattering (BG and TG) . . . . . . . . . . . . . . 33
3.2.4 Total Bistatic Scattering Normalized radar cross section (RCS) . . . . . . . 33
3.3 Sensitivity Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3.2 Sensitivity Analysis Simulation Results . . . . . . . . . . . . . . . . . . . 38
iv
3.3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Chapter 4: Forward Model Evaluation 44
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.2 Airborne global navigation satellite system (GNSS) Reflectometry with GNSS Re-
flectometer Instrument for Bistatic Synthetic Aperture Radar (GRIBSAR) . . . . . 44
4.3 Spaceborne global navigation satellite system (GNSS) Reflectometry with CYGNSS 46
4.4 DDM Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.4.2 Estimating the Positions of Scattering Points of a DDM . . . . . . . . . . . 49
4.4.3 Converting NBRCS to DDM . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.5 Bistatic Model Validation Using GNSS Reflectometer Instrument for Bistatic Syn-
thetic Aperture Radar (GRIBSAR) Data . . . . . . . . . . . . . . . . . . . . . . . 57
Chapter 5: Soil Moisture Retrieval from Bistatic Radar Observations 61
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.2 Soil Moisture Retrieval Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.2.1 Validation Site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.3.1 Validation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.3.2 First Scheme of Retrieval Algorithm . . . . . . . . . . . . . . . . . . . . . 68
5.3.3 Second Scheme of Retrieval Algorithm . . . . . . . . . . . . . . . . . . . 70
5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Chapter 6: Noise Sensitivity Analysis 74
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6.2 Sensitivity Analysis With Respect to Noise Standard Deviation . . . . . . . . . . . 75
6.3 Noise sensitivity analysis for D-SHIELD multi-instrument measurements . . . . . 78
6.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Chapter 7: Summary and Future Work 103
List of Acronyms 106
References 110
v
List of Tables
3.1 Vegetation parameters used as inputs to the bistatic scattering forward model . . . . 20
3.2 Forward Model Input Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.3 Forward Model Input Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.4 Forward Model Vegetation Parameters . . . . . . . . . . . . . . . . . . . . . . . . 38
4.1 Tonzi-Ranch Input Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.1 The vegetation parameters of Yanco site (grassland (IGBP: 5)). The parameters
are inputs to the single-species bistatic scattering model (SSBM). . . . . . . . . . . 65
6.1 Forward Model Input Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6.2 D-SHIELD Instrument metrics and specifications (Incidence angle = 35
o
). . . . . . 79
6.3 D-SHIELD Instrument metrics and specifications (Incidence angle = 45
o
). . . . . . 80
6.4 D-SHIELD Instrument metrics and specifications (Incidence angle = 55
o
). . . . . . 80
6.5 D-SHIELD Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
6.6 Walnut Gulch in-situ soil moisture measurements . . . . . . . . . . . . . . . . . . 81
6.7 Tonzi ranch in-situ soil moisture measurements. . . . . . . . . . . . . . . . . . . . 84
6.8 Metolius in-situ soil moisture measurements. . . . . . . . . . . . . . . . . . . . . 87
6.9 Las Cruces in-situ soil moisture measurements . . . . . . . . . . . . . . . . . . . . 90
6.10 Yanco in-situ soil moisture measurements . . . . . . . . . . . . . . . . . . . . . . 93
vi
List of Figures
2.1 Vegetation geometry for single-species bistatic scattering model (SSBM) model,
which consists of three layers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Scattering from large and thin vertical cylinders at L-band (1.26 (GHz)). . . . . . . 9
3.1 Single species bistatic scattering model, single-species bistatic scattering model
(SSBM), with major scattering mechanisms: ground (G), branch (B), branch ground
(BG), and trunk ground (TG). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.2 Bistatic scattering coordinate system based on the forward scattering alignment
(FSA). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.3 Linear and circular polarization. . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.4 Vegetation geometry for mono-species bistatic scattering model, which consists of
three layers and different discrete scattering components. . . . . . . . . . . . . . . 19
3.5 (a-f) Ground bistatic scattering at L-band and P-band . . . . . . . . . . . . . . . . 28
3.6 (a-f) Vegetation volume bistatic scattering (B) at L-band and P-band (vegetation
water content (VWC) = 2.6 kg=m
2
). . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.7 (a-d) Co-polarization (HH) TG and BG double bounce scattering at L-band and
P-band. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.8 (a-d) Bistatic co-polarized scattering cross section at L-band and P-band, incidence
angle is 40
o
, vegetation water content (VWC) is 2.6 kg=m
2
and surface roughness
is 1.00 cm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.9 (a-d) Effect of vegetation water content (VWC) on backscatter and specular sig-
nals at L-band and P-band: horizontal scale max is 5:5kg=m
2
of vegetation water
content (VWC); Trunk and branch densities (1=m
2
) are gradually increased for
vegetation water content (VWC) variation. (e-h) Effect of soil moisture content
on backscatter and specular signals: vegetation water content (VWC) is fixed at
2:6kg=m
2
. The HH and VV normalized bistatic radar cross section (BRCS) for
specular scattering are sensitive and change by 5 dB for soil moisture content
range of approx. 0:1 0:45m
3
=m
3
. . . . . . . . . . . . . . . . . . . . . . . . . . . 42
vii
4.1 global navigation satellite system (GNSS) reflectometry by using GNSS Reflec-
tometer Instrument for Bistatic Synthetic Aperture Radar (GRIBSAR). . . . . . . . 45
4.2 CYGNSS satellites. Image credit: University of Michigan. . . . . . . . . . . . . . 46
4.3 CYGNSS observation of Global Positioning System (GPS) direct signal and Global
Positioning System (GPS) signal scattered in the specular direction . Image credit:
University of Michigan. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.4 Iso delay and Doppler lines in a delay-Doppler map (DDM). Image credit: Uni-
versity of Michigan. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.5 An example of CYGNSS delay-Doppler map (DDM) for SMAP Yanco site. . . . . 48
4.6 specular point (SP) geometry,
¯
R
t
is the transmitter position,
¯
R
r
is the receiver posi-
tion and R
SP
is the specular point (SP) position. . . . . . . . . . . . . . . . . . . . 50
4.7 delay-Doppler map (DDM) of Tonzi-ranch area in northern California measured
by GNSS Reflectometer Instrument for Bistatic Synthetic Aperture Radar (GRIB-
SAR) on July 31, 2018. This delay-Doppler map (DDM) presents high resolution
bistatic radar cross section (BRCS) over an area of 293 [m] × 293 [m] (one chip in
the delay-Doppler map (DDM) corresponds to a distance of 293 [m]). . . . . . . . 57
4.8 GNSS Reflectometer Instrument for Bistatic Synthetic Aperture Radar (GRIB-
SAR) flight path from east to west of the Tonzi ranch. The Tonzi ranch Soil mois-
ture Sensing Controller and oPtimal Estimator (SoilSCAPE) sensors are located
close to GRIBSAR measurement points. These measurements correspond to the
Global Positioning System (GPS) psuedo-random noise code number 12 reflections. 58
4.9 GNSS Reflectometer Instrument for Bistatic Synthetic Aperture Radar (GRIB-
SAR) Twin Otter Aircraft, antenna integration, and rack-mount hardware integra-
tion, which are used for the GRIBSAR measurements over Tonzi ranch. . . . . . . 58
4.10 Figure (13. a) presents delay-Doppler map (DDM) of Tonzi-ranch as measured
by GRIBSAR, and figure (13. b) shows the Tonzi-ranch DDM simulated by the
proposed bistatic scattering forward model with the technique described in [27]. . . 60
5.1 Soil moisture retrieval inversion algorithm, which includes the delay-Doppler map
(DDM) of the single-species bistatic scattering model (SSBM) and the hybrid lo-
cal/global scheme. C
md
= i
md
< N
md
or step step limit and C
N
= i N or
f
cost
< f
stop
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.2 Comparison between delay-Doppler maps (DDMs) generated by the forward model
(Figure 5.2.a) and CYGNSS (Figure 5.2.b). The delay-Doppler maps (DDMs) are
over Yanco site, Australia. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.3 Time series of retrieved soil moisture; cyan dots represent the in-situ soil moisture
close to delay-Doppler maps (DDMs)’s time. . . . . . . . . . . . . . . . . . . . . 69
viii
5.4 Soil moisture retrieval using the first retrieval scheme from delay-Doppler maps
(DDMs) close to Y8, Yanco site in 2019, total number of retrievals: 93. The
RMSE is 0:075 m
3
m
3
, ubRMSE is 0:075 m
3
m
3
, and r is 0:29. . . . . . . . . . . 69
5.5 Time series of retrieved soil moisture; cyan dots represent the in-situ soil moisture
close to delay-Doppler maps (DDMs)’s time. . . . . . . . . . . . . . . . . . . . . 70
5.6 Time series of the root mean square (RMS) surface roughness retrieval. . . . . . . 71
5.7 Soil moisture retrieval using the second retrieval scheme from delay-Doppler maps
(DDMs) close to Y8, Yanco site in 2019, total number of retrievals: 95. The RMSE
is 0:098 m
3
m
3
, ubRMSE is 0:094 m
3
m
3
, and r is 0:37. . . . . . . . . . . . . . . 71
6.1 Soil moisture Sensing Controller and oPtimal Estimator (SoilSCAPE) Walnut Gulch,
Az. Image credit:https://daac.ornl.gov. . . . . . . . . . . . . . . . . . . . . . . . . 76
6.2 Walnut Gulch, Az. Image credit:www.ars.usda.gov. . . . . . . . . . . . . . . . . . 77
6.3 Soil moisture root mean square (RMS) error (RMSE) vs different k
p
values. . . . . 78
6.4 Walnut Gulch Soil Moisture Time Series. . . . . . . . . . . . . . . . . . . . . . . 81
6.5 Walnut Gulch (shrubland) Soil Moisture RMSE. . . . . . . . . . . . . . . . . . . . 82
6.6 Soil moisture Sensing Controller and oPtimal Estimator (SoilSCAPE) Tonzi ranch,
CA site. Image credit: https://daac.ornl.gov. . . . . . . . . . . . . . . . . . . . . . 83
6.7 Tonzi ranch Soil Moisture Time Series. . . . . . . . . . . . . . . . . . . . . . . . 84
6.8 Tonzi ranch (Woody Savannah) Soil Moisture RMSE. . . . . . . . . . . . . . . . . 85
6.9 Airborne Microwave Observatory of Subcanopy and Subsurface (AirMOSS) Metolius,
OR site. Image credit: https://uavsar.jpl.nasa.gov. . . . . . . . . . . . . . . . . . . 86
6.10 Metolius Soil Moisture Time Series. . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.11 Metolius (evergreen forest) Soil Moisture RMSE. . . . . . . . . . . . . . . . . . . 88
6.12 Las Cruces, NM. Image credit: https://www.las-cruces.org. . . . . . . . . . . . . . 89
6.13 Las Cruces Soil Moisture Time Series. . . . . . . . . . . . . . . . . . . . . . . . . 90
6.14 Las Cruces (bare surface) Soil Moisture RMSE. . . . . . . . . . . . . . . . . . . . 91
6.15 Soil Moisture Active Passive (SMAP) Yanco site, Australia. Image credit: http://www.oznet.org. 92
6.16 Yanco Soil Moisture Time Series. . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.17 Yanco (cropland) Soil Moisture RMSE. . . . . . . . . . . . . . . . . . . . . . . . 94
6.18 Walnut Gulch (shrubland) Soil Moisture RMSE. . . . . . . . . . . . . . . . . . . . 96
ix
6.19 Tonzi ranch (Woody Savannah) Soil Moisture RMSE. . . . . . . . . . . . . . . . . 97
6.20 Metolius (evergreen forest) Soil Moisture RMSE. . . . . . . . . . . . . . . . . . . 98
6.21 Las Cruces (bare surface) Soil Moisture RMSE. . . . . . . . . . . . . . . . . . . . 99
6.22 Yanco (cropland) Soil Moisture RMSE. . . . . . . . . . . . . . . . . . . . . . . . 100
x
Abstract
Soil moisture is a key variable in studying the global ecosystems, exerting first-order control on
land-atmosphere interactions. Quantifying soil moisture fields is needed for improving our knowl-
edge of the water, carbon, and energy cycles. Soil moisture measurements on global and local
scales contribute to many areas of human interest such as weather and climate forecasting, flood
prediction, drought analysis, crop productivity evaluation, and human health. Thus, developing
novel and reliable soil moisture observation and retrieval techniques is a subject of great interest.
We begin by presenting the physics-based bistatic radar scattering forward model from signals
of opportunity (SoOp) at L-band and P-band/very high frequency (VHF) for both bare surfaces
and vegetated land covers, including forests, in support of soil moisture retrieval. The interest in
developing bistatic scattering models stems from the observation that existing SoOp, such as those
transmitted by global positioning system (GPS)/global navigation satellite system (GNSS) signals,
can be used in lieu of conventional mono-static radar transmitters, as long as the appropriate re-
ceiver systems and retrieval methods can be developed. Such an approach to a “passive” radar
results in substantially reduced hardware costs, but at the expense of modeling and retrieval com-
plexity. It also enables enhanced sensitivity to soil moisture and reduced sensitivity to vegetation
water content (VWC). The physics-based bistatic scattering forward model has three main scat-
tering mechanisms, including a direct bistatic scattering from vegetation volume, a direct bistatic
scattering from a flat ground surface with small roughness, and a double-bounce bistatic scattering
from the vegetation layer and the ground. All mechanisms are considered simultaneously in the
bistatic scattering geometry and treated using wave-based coherent models. The total bistatic radar
cross section (BRCS) of the forest will be determined by superimposing the BRCS for each of the
specified contributions.
xi
Next, the bistatic scattering model is investigated via a thorough sensitivity analysis with re-
spect to soil moisture and vegetation water content (VWC) for different land covers through a
comprehensive set of numerical simulations, which leads to selection of optimal incidence angle
for best soil moisture retrieval results. Moreover, the bistatic scattering model is validated with the
GNSS Reflectometer Instrument for Bistatic Synthetic Aperture Radar (GRIBSAR) and NASA
Cyclone Global Navigation Satellite System (CYGNSS) delay-Doppler maps (DDMs).
Finally, we present a soil moisture retrieval scheme from CYGNSS over land DDMs. The in-
version algorithm consists of a hybrid global and local optimization method and a physics-based
bistatic scattering forward model, which estimates the circularly polarized BRCS of the land sur-
face, and it is applicable to bare-to-densely vegetated terrains. The proposed inversion method
is utilized for soil moisture retrieval from CYGNSS DDMs over the Soil Moisture Active Passive
(SMAP) Yanco site located in Australia. Ultimately, the retrieved soil moisture values are validated
with the SMAP in-situ soil moisture measurements.
xii
Chapter 1
Introduction
1.1 Introduction
Soil moisture is one of the most important parameters in studying the global ecosystem. Soil
moisture measurements on global and local scales provide essential information for analyzing the
processes of evapotranspiration and groundwater recharge. Thus, quantifying soil moisture values
leads to a better understanding of the water, carbon, and energy cycles [1–4]. As global concern
about the impact of climate change continues to grow, studies on soil moisture variation have be-
come even more important. The United Nations Framework Convention on Climate Change [5]
warned that the agricultural and manufacturing industries have already been negatively affected by
extreme weather events, which have become more common with increased climate change. Conse-
quently, soil moisture observations contribute to many areas of human interest, including flood and
landslide prediction, climate forecasting, drought analysis, wildfire prevention, crop productivity
evaluation, and human health. Thus, the development of reliable soil moisture retrieval schemes is
a subject of great interest.
1.2 Motivation
Over the past decade, many approaches have been made to measure soil moisture on local and
global scales by using monostatic radars as an active mode of microwave remote sensing [1, 6–9].
1
The conventional spaceborne and airborne radars for soil moisture observation include NASA Soil
Moisture Active Passive (SMAP) [1] when the radar was operational, NASA/Jet Propulsion Lab-
oratory (JPL) Uninhabited Aerial Vehicle Synthetic Aperture Radar (UA VSAR) [10], European
Space Agency (ESA) Soil Moisture and Ocean Salinity (SMOS) mission [11] , the Airborne Mi-
crowave Observatory of Subcanopy and Subsurface (AirMOSS) [12], the Environmental Satellite
(EnviSat) [13], RADARSAT-1 [14], and Polarimetric L-band Imaging Synthetic Aperture Radar
(PLIS) [15]. However, these missions are not sufficiently meeting the spatial and temporal resolu-
tion challenges for soil moisture observations [16]. To overcome the barriers of mono-static radars
and backscatter approaches, it is essential to utilize bistatic or multi-static radars, which create a
data space of higher dimensionality. Using them enables retrieving scattered field measurements
via passive receiver systems, which are simpler and less expensive than the monostatic radars and
potentially provide more accurate soil moisture retrievals with higher spatial and temporal resolu-
tion [4, 17, 18].
Studies have recently focused on the use of signals of opportunity (SoOp) for addressing the
soil moisture observation challenges on local and global scales.SoOp includes signals transmitted
from global navigation satellite system (GNSS) and communications satellites. Due to the perva-
sive presence and reliability of L-band Global Positioning System (GPS)/GNSS signals and the
availability of affordable receivers, using SoOp from GPS/GNSS satellites for soil moisture re-
trieval of various land covers has been receiving increasing attention over the recent years [4, 19–
22]. For instance, NASA Cyclone Global Navigation Satellite System (CYGNSS) was originally
designed and used for sensing sea level wind speed in tropical cyclones from GNSS signals [23].
Recently, it has been utilized for observations over land [24]. CYGNSS uses a constellation of eight
satellites in low Earth orbit (LEO) at 35° orbit inclination. Each CYGNSS satellite is equipped with
a four-channel GNSS bistatic radar receiver, which are capable of bistatic radar measurements of
GNSS-reflectometry (GNSS-R) from land and ocean surfaces. Unlike conventional monostatic
radars, the CYGNSS receivers and the GPS transmitters are not collocated. Instead, the CYGNSS
2
satellites measure GPS signals scattered from land and ocean surfaces in the vicinity of the specu-
lar direction (glistening zone) [23]. The CYGNSS level-1a and level-1b data products present the
received power and the bistatic radar cross section (BRCS), respectively, in the form of a delay-
Doppler map (DDM) [23]. Previous approaches for soil moisture retrieval from CYGNSS observa-
tions include empirical- and machine learning (ML)-based methods. An example of the empirical
retrieval techniques is the UCAR/CU retrieval algorithm [25]. Chew et al. [25] presented a method
for soil moisture retrieval (UCAR/CU soil moisture product), which utilizes the CYGNSS data,
calibrated to the SMAP soil moisture data. According to [25], this retrieval algorithm has critical
limitations, including potential errors in SMAP retrieved soil moisture data, using preliminary veg-
etation model, which only addresses the attenuation due to the vegetation layer, and a low spatial
resolution (36 km). Moreover, Senyurek et al. [26] presented a ML-based model for soil moisture
retrieval from CYGNSS data over International Soil Moisture Network (ISMN) sites in continen-
tal United States (CONUS). In this work Senyurek et al. [26] used and compared three different
ML-based approaches, namely, artificial neural network (ANN), random forest (RF), and support
vector machine (SVM) for soil moisture retrieval from CYGNSS data. According to [26], this
ML-based retrieval framework is valid for low-vegetated terrains with low spatial heterogeneity.
Moreover, the incoherent reflections were excluded from this approach, which potentially leads to
inaccurate retrievals for terrains with high surface roughness. Considering the limitations in the
empirical [25] and ML-based [26] approaches, it is essential to develop a reliable and comprehen-
sive polarimetric microwave bistatic scattering model in order to utilize GNSS-R for soil moisture
retrieval.
1.3 Soil Moisture Remote Sensing from Signals of Opportunity
We have developed a physics-based polarimetric single-species bistatic scattering model (SSBM),
which utilizes the approximate solution of Maxwell’s equation [17, 27, 28]. In this model, the scat-
tered wave is formulated based on the distorted Born approximation (DBA). Unlike microwave
3
scattering models based on radiative transfer (RT) theory [29], which solves the incoherent RT
equations in random media, models based on the wave theory (Maxwell’s equation) have been
shown to be more accurate specifically for considering the coherent interaction of waves with a
vegetation layer and a ground layer. For instance, Liang et al. [29] developed a bistatic scatter-
ing model based on Michigan microwave canopy scattering (MIMICS), which uses a first-order
RT theory at three different frequencies, namely L-, C-, and X-bands. The SSBM in comparison
with the bistatic MIMICS (Bi-MIMICS) model estimates the interaction between the vegetation
layer and the rough ground surface (double-bounce scattering between vegetation and ground)
in a more accurate way [17]. Moreover, the previous physics-based models utilized empirical
or regression-based approaches for soil moisture retrieval over bare or low-vegetated surfaces,
whereas the bistatic scattering model is applicable to moderate to densely vegetated (forest) land
covers. For instance, Kurum et al. [30] proposed the signals of opportunity coherent bistatic scat-
tering model for vegetated terrains (SCoBi-Veg). The estimated received complex electromagnetic
(EM) field in the SCoBi-Veg model has three main categories of contributions: 1) direct path;
2) Fresnel reflection (scattering in specular direction); 3) an average diffuse term, which results
from bistatic scattering from the vegetation layer, estimated by an ample number of realizations of
vegetation via Monte Carlo simulations. Based on [30] the SCoBi-Veg uses a simple multilayer
canopy model, in which the scatterers are assumed to be independent, and the mutual interactions
between vegetation scatterers are not included. Unlike the SCoBi-Veg model, which only includes
the direct bistatic scattering from the vegetation layer, the SSBM computes the vegetation contri-
bution by using the DBA method [30].Moreover, it estimates the direct bistatic scattering from the
vegetation layer and vegetation-ground double-bounce bistatic scattering contributions.
The SSBM is applicable to various terrain types and vegetated land covers including forests.
While no specific restriction is placed on the operating frequency, similar to [31] and [32], some
of the model approximations are most valid for lower frequencies such as L-band and P-band. The
advanced bistatic scattering model has three main categories of contribution, which include: 1)
direct bistatic scattering from the rough ground surface with the assumption of flat topography, 2)
4
direct bistatic scattering from the vegetation layer, and 3) double-bounce bistatic scattering from
the vegetation layer and ground. The model is validated with the GNSS Reflectometer Instrument
for Bistatic Synthetic Aperture Radar (GRIBSAR) measurements at Tonzi ranch located in central
valley of California and the CYGNSS DDM data for SMAP-Yanco site located in south east of
Australia.
We used the advanced SSBM in inversion algorithm for soil moisture retrieval from the CYGNSS
over-land observations (DDMs). The proposed inversion technique hinges on the bistatic scattering
forward model for various land covers and the hybrid global and local optimization method [33].
In order to simulate the CYGNSS observations (DDMs), the SSBM is utilized to predict the circu-
larly polarized BRCS of the region of interest observed by CYGNSS satellites [27]. The circularly
polarized BRCS values computed by the forward model are then used to construct the desired
DDM. The hybrid global and local optimization scheme used in the inversion algorithm takes
advantage of the speed of a local optimization method while ensuring convergence to the global
minimum of the inverse problem [33]. Compared to the conventional simulated annealing meth-
ods, this optimization technique has been shown to be faster, and it predicts more accurate soil
moisture values [33]. The proposed inversion method is used for soil moisture retrieval over the
SMAP-Yanco site located in Australia. The retrieved soil moisture values are validated with the
Yanco in-situ soil moisture sensor measurements.
This document is organized as follows. A review of related works is provided in chapter 2. In
chapter 3, the SSBM is presented. Moreover, the numerical simulation results of SSBM for each
of the bistatic scattering mechanisms along with the total scattering normalized bistatic radar cross
section (NBRCS) are included in this chapter. Furthermore, In chapter 3, the sensitivity analysis
of SSBM is performed with respect to soil moisture and vegetation water content (VWC) for
different frequencies and land cover types. In chapter 4, the computational predictions of SSBM
are evaluated against actual measurements of CYGNSS and GRIBSAR missions. Furthermore,
the method for generating DDMs using SSBM is provided in this chapter. In chapter 5 retrieval
algorithm is presented for estimating soil moisture from bistatic radar measurements (DDM). This
5
retrieval algorithm is then used for soil moisture estimation at the SMAP Yanco site from CYGNSS
DDMs, and the retrieved values are compared with the in-situ soil moisture measurements. A
comprehensive noise sensitivity study for multi-instrument observations of soil moisture in support
of Distributed Spacecraft with Heuristic Intelligence to Enable Logistical Decisions (D-SHIELD)
is presented in chapter 6. Finally, chapter 7 provides a summary of this Thesis and outlines.
1.4 Contributions
1. Development of a novel single-species bistatic radar scattering forward model (SSBM) for
soil moisture retrieval from SoOp including GPS/GNSS signals.
2. Validation of the SSBM predictions with the actual Airborne (GRIBSAR) and Spaceborne
(CYGNSS) measured data (DDMs).
3. Improved understanding of the sensitivity of the monostatic and bistatic radar observations
to soil moisture and VWC by using the SSBM.
4. Development of a soil moisture inversion algorithm, which comprises of the proposed SSBM
forward model and a hybrid global and local optimization method, and using the over land
CYGNSS DDMs for soil moisture retrieval.
5. Evaluation of the proposed inversion algorithm soil moisture predictions with the in-situ soil
moisture measurements of the SMAP Yanco site.
6. Enhanced understanding of the sensitivity of the proposed soil moisture inversion algorithm
to noise for single and multi-instrument monostatic radar observations.
6
Chapter 2
Review of Related Work
2.1 Single-Species Monostatic Radar Model
This chapter provides an overview of the conventional single-species backscattering model pro-
posed by Durden et al. [31], based on which the advanced single-species bistatic scattering model
(SSBM) forward model was developed.
Following [31], in the single-species backscattering forward model the the forest floor can be
considered as a dielectrically rough surface, with trunks and the crown layer (branches) placed
on top [32]. As illustrated in Figure 2.1, the general geometry for a vegetated land surface pixel
consists of vertical cylinders (trunk), randomly oriented cylinders (branches). These scattering
elements are used to build vegetation layers using distributions relevant to pertinent land cover
types. The h-pol and v-pols scattered electric fields for a single infinite dielectric cylinder in the
cylindrical coordinate system (r, z andq
i
) are computed as
2
6
4
E
h
E
v
3
7
5
s
= exp

i3p
4

r
2
pkr sinq
i
exp(ik(r sinq
i
zcosq
i
))
2
6
4
A
hh
A
hv
A
vh
A
vv
3
7
5
2
6
4
E
h
E
v
3
7
5
i
(2.1)
where k is the wavenumber, q
i
is the incidence angle with respect to the vertical axis (z axis) and
A(q
i
;f
s
f
i
) are infinite cylinder scattering matrix elements, which are function of the dielectric
7
Figure 2.1: Vegetation geometry for SSBM model, which consists of three layers.
constant, radius, incident and azimuth angles. Assuming that the length of the cylinder is substan-
tially larger than the wavelength, it is feasible to utilize the truncated equivalent-current approach
discussed in [31] to approximate the scattering matrix of a finite cylinder. Consequently, the scat-
tering matrix S for a finite cylinder with a length of l is represented as [31]
s
pq
(q
i
;f
i
;q
s
;f
s
)=
ikl sinq
s
p sinq
i
sin(kl(cosq
i
+ cosq
s
))=2
kl(cosq
i
+ cosq
s
)=2
A
pq
(q
i
;f
s
f
i
): (2.2)
Equation (2.2) presented the scattering matrix for a finite vertical dielectric cylinder. Examples
of two typical cases corresponding to a tree trunk and a crop stalk are illustrated in Figure 2.2,
where the magnitude of the quantity on the right-hand-side of Equation (2.2) at L-band is plotted
against the observation angle in the incidence plane. As seen in Figure 2.2, the magnitude of the
scattering matrix elements varies rapidly with respect to scattering angles in the case of a large
vertical cylinder. In this scenario, the wave is most strongly scattered in the specular (q
s
= 140
o
)
and forward (q
s
=140
o
) directions, whereq
s
=pq
i
. Scattering from a thin short cylinder has
smoother ripples and the absolute value of the scattering matrix element, which is proportional to
amplitude of scattered field, is substantially lower than the previous case.
8
Figure 2.2: Scattering from large and thin vertical cylinders at L-band (1.26 (GHz)).
9
Equation (2.2) is valid for a vertically oriented finite cylinder. In Section 3.1.3 tilt anglesy and
d are defined where y is the tilting angle within the incidence plane and d is the angle of tilting
from the direction normal to the incidence plane. The incident wave can be transformed into the
tilted cylinder coordinate system, and the scattering matrix calculated by using Equation (2.2) in
the cylinder’s coordinate system. The transformation matrix is then used to express the scattering
matrix in the radar geometry. Hence, the new scattering matrix for an arbitrarily oriented cylin-
der s(q
i
;f
i
;q
s
;f
s
;d;y) defined based on incidence, scattering, and tilt angles with respect to the
ground.
2.2 Scattering Mechanisms in Backscatter Radar Model
The main scattering mechanisms considered in [31] are direct ground (G) backscattering, direct
backscattering from branch (B) layer, branch ground (BG), and trunk ground (TG) double bounce
backscattering. In order to add the contributions of various scattering mechanisms the scattering
matrix of each contribution is converted to Muller matrix M (from scattered electric field (E) to
power). The Muller matrix M is consists of elements of the scattering matrix, and it is expressed
as
M=
2
6
6
6
6
6
6
6
4
js
vv
j
2
js
vh
j
2
Re

s

vh
s
vv

Im

s

vh
s
vv

js
hv
j
2
js
hh
j
2
Re

s

hh
s
hv

Im

s

hh
s
hv

2Re

s
vv
s

hv

2Re

s
vh
s

hh

Re

s
vv
s

hh
+ s

hv
s
vh

Im

s
vv
s

hh
s

hv
s
vh

2Im

s
vv
s

hv

2Im

s
vh
s

hh

Im

s
vv
s

hh
+ s

hv
s
vh

Re

s
vv
s

hh
s

hv
s
vh

3
7
7
7
7
7
7
7
5
: (2.3)
In order to compute the Stokes matrix of the vegetation layer M
B
, the scattering matrix of
a randomly oriented cylinder ( Equation (2.2)) is converted to Muller matrix by using the Equa-
tion (2.3) and the Muller matrix is multiplied by the probability density function (PDF) of randomly
oriented cylinders. According to empirical field observations, the probability density function PDF
10
of branch orientation is proportional to sin
2
a, wherea is the angle with respect to the vertical di-
rection. This PDF is used to calculate transmission and scattering Stokes matrices of the vegetation
layer. It can be easily modified to model other functions as well. Furthermore, the trunks in the
scattering models are assumed to be near-vertical but allowed to have small variations from the
vertical line. This is expressed as a Gaussian PDF with a small-angle, e.g., 5 degrees, standard
deviation with respect to the vertical line.
The forward scattering matrix related to the transmission of the wave through vegetation layer
(branches) with thickness z is expressed as
s
T
=
2
6
4
exp

s
hh
z
cosq
i

0
0 exp

s
vv
z
cosq
i

3
7
5
: (2.4)
The transmission Stokes matrix T(z) is computed from Equation (2.3). Thus, the backscattering
scattering Stokes matrix for a single layer of vegetation with total thickness H is calculated as
M
H
(q
i
;f
i
)=
Z
H
0
T(z)M(q
i
;f
i
)T(z)dz: (2.5)
where T(z)M(q
i
;f
i
)T(z)dz is denoted as the backscattering Stokes matrix of an infinitesimal layer
dz. For the cases of double bounce (trunk ground (TG) and branch ground (BG)) and direct ground
(G) backscattering, the two-way propagation from the vegetation layer to the ground and vice versa
are taken into consideration by cascading direct ground and double bounce Stokes matrices with
the transmission matrices in both directions.
Consequently, the total Stokes matrix for a single species monostatic radar model is determined
by adding four scattering contributions together, which is given by
M
total
(q
i
;f
i
)=M
B
(q
i
;f
i
)+ T
B
T
T
M
BG
(q
i
;f
i
)T
T
T
B
+ T
B
T
T
M
TG
(q
i
;f
i
)T
T
T
B
+ T
B
T
T
M
G
(q
i
;f
i
)T
T
T
B
(2.6)
11
where branch, trunk, and ground are denoted as B, T , and G, respectively. The total Stokes matrix
calculated in Equation (2.6) is then converted to the backscatter radar cross section (RCS) with the
method presented in [34].
The single-species backscattering model presented in Section 2.1 has been further developed
to include terrains with mult-ilayer multi-species vegetation and topography [32, 35]. Burgin et.
al [32] proposed a generalized radar backscattering model for multi-layer multi-species vegetated
terrains. This model generalizes the single-species backscatter model by computing the scatter-
ing and transmission Stokes matrices of multi-species vegetated terrains with different vegetation
layers.
According to [32] the computational predictions of the backscattering model for multi-layer
multi-species vegetation are in good agreement with the actual mono-static radar measurements of
Advanced Observing Satellite (ALOS) and Airborne Synthetic Aperture Radar (AIRSAR). More-
over, [36] showed that the scattering mechanisms discussed in Section 2.2 have different effects
depending on the frequency of transmitted signal and vegetation land cover type. At higher fre-
quencies, e.g., X-band and C-band, the transmitted signal does not penetrate into the vegetation
layer, which results in domination of vegetation volume scattering mechanism. Whereas, at lower
frequencies, e.g., P-band and L-band, the transmitted EM wave can penetrate into the canopy layer;
In this scenario the direct ground scattering and double-bounce scattering contributions are dom-
inant. Furthermore, [36] showed that trunk-ground doubleb-ounce backscattering is dominant
in the regions with high trunk density (number of trunks per square meter) and the direct ground
backscattering is dominant in areas with low trunk density and vegetation. Burgin et. al [35] further
generalize the multi-layer multi-species backscattering model to include regions with topography.
12
Chapter 3
Bistatic Radar Scattering Model for Vegetated Land Covers
3.1 Bistatic Scattering Forward Model
A physics-based fully bistatic scattering model from signals of opportunity (SoOp) (for both lin-
early and circularly polarized incident waves) for various land cover, including vegetated terrains,
has been developed [4, 17]. This model is built on the existing monostatic (backscatter) single-
species model proposed by Durden et al. [4, 31] and described in the previous chapter.
The bistatic scattering model developed here is shown in Figure 3.1, and it has three major
categories of contributions: 1) direct ground bistatic scattering, 2) vegetation volume bistatic scat-
tering, and 3) double-bounce bistatic scattering from vegetation (branches and trunks) and ground.
The contribution of direct bistatic scattering from trunks is not significant in comparison with other
contributions. Thus, it is not considered as one of the scattering mechanisms [31, 32].
Figure 3.1 shows the proposed bistatic scattering model with all the scattering mechanisms,
which are ground (G), branch (B), branch ground (BG), and trunk ground (TG). The details of
each of the scattering contribution are presented in the Sections 3.1.2 to 3.1.4 as well as the total
bistatic scattering Stokes matrix discussed in Section 3.1.5 [4].
13
Figure 3.1: Single species bistatic scattering model, SSBM, with major scattering mechanisms: ground (G), branch (B), branch ground
(BG), and trunk ground (TG).
14
3.1.1 Bistatic Scattering Geometry
The forward scattering alignment (FSA) convention is used for the bistatic scattering coordinate
system of the proposed model, as depicted in Figure 3.2 [4, 17]. Four spherical angles are utilized
to show the incidence and scattering propagation directions and i and s indices represent incidence
and scattering directions, respectively. Thus, q
i
, q
s
, f
i
, and f
s
are denoted as the incidence and
scattering angles in the elevation and azimuth directions, respectively.
Based on this definition, the relation between these angles for two special cases of scattering in
the backscattering direction and specular direction are given by
1. Backscattering direction: q
s
=q
i
;f
s
=f
i
+p
2. Specular direction: q
s
=q
i
;f
s
=f
i
.
Figure 3.3 shows the polarization vectors for linearly polarized (h polarized and v polarized) and
circularly polarized (left-hand and right-hand circularly polarized) wave traveling in the z direction.
Figure 3.2: Bistatic scattering coordinate system based on the FSA.
15
Figure 3.3: Linear and circular polarization.
3.1.2 Direct Ground Bistatic Scattering (G)
Generally, the bistatic scattering contribution from a single rough ground surface (with the as-
sumption of flat topography) has been estimated using analytical or numerical methods [17]. The
analytical methods, which are mostly derived using approximations about the roughness scale of
the ground surface, have the advantage of lower computational time with the cost of complex
analysis and approximated results.
However, unlike the analytical methods, the numerical techniques have the capability of com-
puting the scattering from a rough ground surface with any arbitrary distribution and roughness
scale [37]. For instance, stabilized extended boundary condition (SEBCM) [38] is a numerical
method for computing the bistatic radar cross section (BRCS) from a multi-layer rough ground
surface, which uses periodic boundary conditions and Floquet modes to formulate a plane wave
modal expansion of fields.
Due to the high complexity of numerical approaches, analytical methods have often been uti-
lized for the estimation of ground contribution. The small perturbation method (SPM) is one of
the most well-known analytical methods, which has been used for the analysis of scattering from a
slightly random rough surface. In this method, the random rough surface height is assumed to have
a zero-mean Gaussian random distribution with a small mean-square variance [37]. The major con-
dition under which the SPM can be applied for a slightly random rough surface is kh< 0:3, which
16
for L-band and P-band means approx. h< 1:1cm and h< 3:3cm, respectively, where parameters
k and h are wavenumber and root mean square (RMS) surface height deviation from mean surface,
respectively [39].
In the bistatic scattering forward model, the forest floor is considered as a dielectric random
rough surface, and the method presented by Mironov et al. [40] is used to estimate the dielectric
constant of the soil. Moreover, the SPM is used up to second order for estimating the co-pol, s
hh
ands
vv
, and cross-pol BRCS ,s
hv
ands
vh
[37]. Furthermore, the scattering matrix of the ground
contribution is used to construct the direct ground bistatic scattering (G) Stokes matrix M
G
[31,
32]. The zeroth-order SPM solution calculates the scattered field from a smooth flat surface, and it
is modified by the Kirchhoff approximation (KA) [31] to include the surface roughness. The KA
is valid for rough surfaces whose horizontal roughness scale is large relative to the wavelength.
Furthermore, unlike the SPM, the KA does not require the surface roughness height to have a
small mean-square variance. Thus, the combination of the SPM and KA can be implemented for
the terrains that satisfy the requirements of both methods. Consequently, in the bistatic scattering
model, the incoherent and coherent scattering from the ground surface are estimated by using the
SPM and the KA, respectively. Moreover, the ground layer in Figure 3.1 is assumed to have a
1-D dielectric rough surface with Gaussian height distribution. Thus, the ground layer can be fully
characterized by the rough surface correlation function, as given in Equation (3.7) [41].
Scattering elements of the zeroth-order SPM are equal to Fresnel reflection coefficients, which
are given by
r
0
h
= r
h
exp

2h
2
k
2
cos
2
q
i

(3.1)
r
0
v
= r
v
exp

2h
2
k
2
cos
2
q
i

: (3.2)
The solution to the first-order SPM is presented as
s
0
hh
= 16pk
4

k
r

cos
2
q
s
cosq
i
cos
2
(f
s
f
i
) (3.3)
17
s
0
hv
= 16pk
4
W

k
r

cos
2
q
s
sin
2
(f
s
f
i
) (3.4)
s
0
vh
= 16pk
4
W

k
r

cosq
i
sin
2
(f
s
f
i
) (3.5)
s
0
vv
= 16pk
4
W

k
r

(cos(f
s
f
i
) sinq
i
sinq
s
)
2
(3.6)
where W

k
r

is the spectral density function, which is defined for modeling the random rough
surface with a Gaussian form and correlation length of l [37]. W

k
r

and k
r
are defined
W

k
r

=
h
2
l
2
4p
exp

k
2
r
l
2
4
!
(3.7)
k
2
r
= k
2

sin
2
q
i
+ sin
2
q
s
2sinq
s
sinq
i
cos(f
i
f
s
)

: (3.8)
The co-pol and cross-pol normalized bistatic radar cross section (NBRCS) of the second-order
SPM are presented by Tabatabaeenejad et. al [37]. The NBRCS values computed by the SPM are
converted to the scattering matrix of ground contribution, which is expressed as
s
pq
=
s
s
0
pq
4p
(3.9)
where, pq represents hh, hv, vh, and vv polarization. Consequently, the scattering matrix of ground
contribution, Equation (3.9), is converted to ground Stokes matrix M
G
with the Equation (2.3).
18
Figure 3.4: Vegetation geometry for mono-species bistatic scattering model, which consists of
three layers and different discrete scattering components.
3.1.3 Vegetation Volume Bistatic Scattering (B)
Bistatic scattering from the vegetation layer on top of the ground surface is estimated by extending
the models proposed by [31, 32]. Figure 3.4 presents the vegetation geometry and the three differ-
ent layers (branch layer, trunk layer, and ground layer) used in the bistatic scattering model. In this
model, trunks are considered as finite vertical dielectric cylinders, and the branches are considered
as randomly oriented dielectric cylinders. The vegetation parameters used in the bistatic scattering
forward model are expressed in Table 3.1. Based on the land cover type, the discrete scattering
elements in Table 3.1 are utilized with the pertinent distribution function to construct vegetation
layers.
According to empirical observations, the probability density function (PDF) of the branch ori-
entations is considered to have sin
2
a dependence, wherea is the deviation angle from the vertical
line. For the vegetation volume and double-bounce bistatic scattering contributions, the scattering
matrix for an arbitrary oriented finite dielectric cylinder S(q
i
;f
i
;q
s
;f
s
;d;y) is first determined and
converted to the corresponding Stokes matrix, and then multiplied by the PDF of cylinder orienta-
tion, and at last, averaged over all the cylinder tilts [17, 31]. Tilt angles,y, andd are defined where
19
Table 3.1: Vegetation parameters used as inputs to the bistatic scattering forward model
Parameter
Large branch dielectric constant
Large branch length (m)
Large branch radius (m)
Large branch density (m
2
)
Short branch dielectric constant
Short branch length (m)
Short branch radius (m)
Short branch density (m
2
)
Trunk dielectric constant
Trunk length (m)
Trunk radius (m)
Trunk density (m
2
)
y is the tilting angle within the incidence plane, and d is the angle of tilting from the direction
normal to the incidence plane.
According to [31], the h-pol and v-pol scattered electric fields for a single infinite dielec-
tric cylinder in the cylindrical coordinate system (r, z and q
i
) are computed as Equation (2.1).
Moreover, the scattering matrix S for a finite cylinder with a length of l is represented as Equa-
tion (2.2). This equation is further generalized to include arbitrarily oriented finite cylinders
s
pq
(q
i
;f
i
;q
s
;f
s
;d;y) where the scattering matrix for an arbitrarily oriented cylinder is a func-
tion of incident and scattering elevation and azimuth angles(q
i
;q
s
;f
i
;f
s
) and tilting angles (d,y).
The scattering matrix of an arbitrarily oriented cylinder is given by
s
pq
(q
i
;f
i
;q
s
;f
s
;d;y)=
2
6
4
a
11
a
12
a
21
a
22
3
7
5
2
6
4
s
hh
s
hv
s
vh
s
vv
3
7
5
2
6
4
b
11
b
12
b
21
b
22
3
7
5
(3.10)
where, s
pq
is the scattering matrix from a finite vertical dielectric cylinder, given in Equation (2.2),
and a
22
and b
22
are transformation matrices due to tilting angles. The transformation matrices
a
22
and b
22
are computed as
q
0
i
=q
i
+y (3.11a)
20
q
0
s
=q
s
+y (3.11b)
q
00
i
= arccos

cosd cosq
0
i

(3.11c)
q
00
s
= arccos

cosd cosq
0
s

(3.11d)
x
1
= sinq
0
i
cosf
i
(3.11e)
x
2
= sinq
0
s
cosf
s
(3.11f)
y
1
= sind cosq
0
i
+ cosd sinf
i
sinq
0
i
(3.11g)
y
2
= sind cosq
0
s
+ cosd sinf
s
sinq
0
s
(3.11h)
f
00
i
= arctan

y
1
x
1

(3.11i)
f
00
s
= arctan

y
2
x
2

(3.11j)
a
11
= cosd cosf
00
i
(3.11k)
a
12
=sinq
0
i
sind cosf
00
i
cosq
0
i
sinf
00
i
(3.11l)
21
a
21
= sinq
00
i
sind+ cosq
00
i
cosd sinf
00
i
(3.11m)
a
22
= cosq
0
i
cosq
00
i
cosf
00
i
sinq
0
i
cosq
00
i
sinf
00
i
sind+ sinq
0
i
sinq
00
i
cosd (3.11n)
b
11
= sinf
s
sinf
00
s
+ cosf
00
s
cosf
s
cosd (3.11o)
b
12
=cosq
00
s
cosf
00
s
sinq
s
+ cosq
00
s
sinf
00
s
cosf
s
cosd+ sinq
00
s
cosf
s
sind (3.11p)
b
21
=sinf
00
s
cosq
0
s
cosf
s
+ cosq
0
s
sinf
00
s
sinf
s
cosd sinq
0
s
cosf
00
s
sind (3.11q)
b
22
=cosq
00
s
cosq
0
s
cosf
00
s
cosf
s
+ cosq
00
s
cosq
0
s
sinf
00
s
sinf
s
cosd
+ cosq
0
s
sinq
00
s
sinf
s
sind cosq
00
s
sinq
0
s
cosf
00
s
sind+ sinq
0
s
sinq
00
s
cosd:
(3.11r)
In order to add the contributions of various bistatic scattering mechanisms, the scattering ma-
trix of each contribution (including vegetation volume bistatic scattering) is converted to the Stokes
matrix M presented in Equation (2.3) [4, 17]. Therefore, in order to compute the Stokes matrix
of the vegetation layer M
B
in the bistatic scenario, the scattering matrix of a randomly oriented
cylinder ( Equation (2.2)) is converted to Muller matrix by using the Equation (2.3) and the Muller
matrix is multiplied by the PDF of the vegetation layer and the density of each of elements. Ac-
cording to [31], the scattering matrix related to the transmission of the wave through vegetation
layer (branches) with thickness z is presented in Equation (2.4). Consequently, the bistatic scatter-
ing Stokes matrix for vegetation layer (branches) with thickness H is calculated as:
M
B
(q
s
;f
s
)=
Z
H
0
T
B
(z)M(q
s
;f
s
)T
B
(z)dz: (3.12)
22
3.1.4 Branch-Ground (BG) and Trunk-Ground (TG) Double-Bounce Bistatic
Scattering
The double-bounce bistatic scattering contribution (Figure 3.1) consists of two paths: 1) transmis-
sion through the vegetation layer (branches) from the transmitter and bistatic scattering from the
vegetation layer (trunks or branches) in the specular direction, and 2) bistatic scattering from the
dielectric rough ground surface and transmission through vegetation layer (branches and trunks)
towards the receiver.
According to [35], the scattering pattern of a vertically oriented finite cylinder resembles a skirt.
In other words, the scattering pattern of a finite cylinder presents a strong return in the specular
direction (q
s
=pq
i
) over all the azimuth angles f
s
. Therefore, the interaction of the incident
wave between the vegetation layer and the ground layer is estimated using the scattering matrices of
cylindrical distributions, given in Equation (3.10), and the random rough surface in Section 3.1.2.
The coherent component of the physical optics model, which is based on the KA is utilized for
estimating the bistatic scattering matrix from the ground layer in the second path of the double-
bounce bistatic scattering contribution. Thus, the scattering matrix for the double-bounce bistatic
scattering contribution from vegetation and ground layer is expressed as
s
DB
=
2
6
4
2r
0
h
s
hh

r
0
h
+ r
0
v

s
hv

r
0
h
+ r
0
v

s
vh
2r
0
v
s
vv
3
7
5
(3.13)
where r
0
h
and r
0
v
are the modified Fresnel reflection coefficients, which are presented in Equa-
tion (3.1) and Equation (3.2). Moreover, s
hh
, s
hv
, s
vh
, and s
vv
are the elements of the bistatic
scattering matrix, defined in Equation (3.10), for vertically (trunks) and arbitrarily (branches) ori-
ented cylinders. Ultimately, the bistatic scattering matrices of double-bounce contribution (branch-
ground and trunk-ground), presented in Equation (3.13), are converted to Stokes matrices M
G
and
M
TG
using Equation (2.3), respectively.
23
3.1.5 Total Bistatic Scattering Stokes Matrix
The bistatic scattering Stokes matrices of the three scattering mechanisms computed in Sections 3.1.2
to 3.1.4 are utilized to determine the total bistatic scattering Stokes matrix of the vegetated land
cover M
total
. In other words, M
total
is calculated by adding the effect of all scattering contributions
presented in previous subsections, and it is expressed as
M
total
(q
s
;f
s
)=M
B
(q
s
;f
s
)+ T
B
(q
i
;f
i
)T
T
(q
i
;f
i
)M
BG
(q
s
;f
s
)T
T
(q
s
;f
s
)T
B
(q
s
;f
s
)
+ T
B
(q
i
;f
i
)T
T
(q
i
;f
i
)M
TG
(q
s
;f
s
)T
T
(q
s
;f
s
)T
B
(q
s
;f
s
)
+ T
B
(q
i
;f
i
)T
T
(q
i
;f
i
)M
G
(q
s
;f
s
)T
T
(q
s
;f
s
)T
B
(q
s
;f
s
)
(3.14)
where incident and scattering paths are denoted as i and s, respectively, and ground, branch, and
trunk are expressed as G, B, and T, respectively.
Ultimately, the total bistatic Stokes matrix M
total
presented in Equation (3.14) is converted to
co-pol and cross-pol linearly polarized total NBRCS (s
0
total
) by the method expressed in [34]. The
predicted linearly polarized total NBRCS is then converted to circularly polarized NBRCS with
the technique described in Section 4.4.3.
3.2 Forward Model Simulation Results
This section provides the simulation results for each of the bistatic scattering mechanisms, which
are discussed in Sections 3.1.2 to 3.1.5. Each of the bistatic scattering contributions is simulated in
L-band (1.26 GHz) and P-band (0.430 GHz). The single species bistatic scattering forward model
is developed via Fortran programming language.
3.2.1 Direct Ground Bistatic Scattering(G)
Figure 3.5 illustrates the NBRCS values estimated by the bistatic scattering model at L-band and
P-band for the ground bistatic scattering with the input parameters provided in Table 3.2 in the
24
absence of vegetation. Moreover, the range of scattering and azimuth angles considered for the
forward bistatic model were 0
o
q
s
90
o
and 0
o
f
s
360
o
. As expected, the co-pol NBRCS for
the scattering from a slightly rough surface resembled a cone, holding a maximum in the specular
direction (q
s
= 40
o
,f
s
= 0
o
). In addition, since the geometry of the problem was symmetric over
the plane of incidence, the scattering pattern was symmetric aroundf
s
= 180
o
.
Table 3.2: Forward Model Input Parameters
Parameter Value
Frequency(L-band) 1:26 GHz
Frequency(P-band) 0:430 GHz
Incidence angle 40
o
Soil dielectric constant (27.68, 1.78)
Surface roughness 0:01 m
25
(a)
(b)
26
(c)
(d)
27
(e)
(f)
Figure 3.5: (a-f) Ground bistatic scattering at L-band and P-band
28
3.2.2 Vegetation Volume Bistatic Scattering(B)
Figure 3.6 illustrates an example of the bistatic scattering from the volume of the vegetation layer
for different polarizations (HH, VV , and HV) and given input parameters in Table 3.3. Based
on the forward model simulation results for co-polarization cases (HH and VV), the value of the
NBRCS rises as the observation angle (q
s
) increases toward the forward and specular directions
(q
s
=pq
i
). In addition, for a given vegetation distribution, the scattered signals were weaker at
P-band compared to L-band. Therefore, as shown in Figure 3.6, the bistatic scattering values from
branches were lower at P-band in comparison with the forward model simulation results computed
at L-band.
By comparing the simulation results in Figure 3.5 and Figure 3.6, it is inferred that even for
moderate amounts of vegetation (VWC = 2.6 kg=m
2
), volume scattering (B) can be higher than
ground scattering (G) in the non-specular directions. For more densely vegetated land covers such
as forests it is expected that the vegetation volume scattering contribution is higher than the direct
ground scattering contribution for non-specular directions.
Table 3.3: Forward Model Input Parameters
Parameter Value
Frequency(L-band) 1:26 GHz
Frequency(P-band) 0:430 GHz
Incidence angle 40
o
Soil dielectric constant (27.68, 1.78)
Surface roughness 0:01 m
Large branch dielectric constant 32:0+ j4:0
Large branch length 1:2 m
Large branch radius 0:0066 m
Large branch density 0:3 m
2
Short branch dielectric constant 32:0+ j4:0
Short branch length 0:0046 m
Short branch radius 0:3 m
Short branch density 0:3 m
2
Trunk dielectric constant 36:0+ j2:0
Trunk length 2:00 m
Trunk radius 0:0682 m
Trunk density 0:15 m
2
29
(a)
(b)
30
(c)
(d)
31
(e)
(f)
Figure 3.6: (a-f) Vegetation volume bistatic scattering (B) at L-band and P-band (VWC = 2.6
kg=m
2
).
32
3.2.3 Double Bounce Bistatic Scattering (BG and TG)
An example of the forward model simulation results of double bounce scattering (BG and TG)
contributions are illustrated in Figure 3.7 and for the input parameters given in Table 3.3. As seen
in Figure 3.7, due to the specular scattering from rough ground surface, the double-bounce NBRCS
for the case where q
s
=q
i
= 40
o
is substantially higher than other scattering angles. This strong
scattering “cone” defined by a constant elevation angle is a result of the forward scattering by large
cylinders representing trunks, subsequently specular scattering from the ground.
3.2.4 Total Bistatic Scattering Normalized RCS
Figure 3.8 shows the total NBRCS values for a mono-species forest over a rough surface. As a
result of specular scattering from the ground there is a peak in the forward scattering direction
(q
s
= 40
o
;f
s
= 0
o
). The peak in the backscatter direction (q
s
= 40
o
;f
s
= 180
o
) is largely due
to double bounce scattering between trunks/branches and the ground, resulting from the specular
scattering from the ground in the second bounce of TG and BG contributions. Furthermore, the
bistatic scattered signals around the specular and backscatter directions were several dB higher
than at other scattering angles, enabling higher signal-to-noise ratio (SNR) observations.
33
(a)
(b)
34
(c)
(d)
Figure 3.7: (a-d) Co-polarization (HH) TG and BG double bounce scattering at L-band and P-band.
35
(a)
(b)
36
(c)
(d)
Figure 3.8: (a-d) Bistatic co-polarized scattering cross section at L-band and P-band, incidence
angle is 40
o
, VWC is 2.6 kg=m
2
and surface roughness is 1.00 cm.
37
3.3 Sensitivity Study
3.3.1 Introduction
The proposed bistatic scattering model (SSBM) provides the opportunity to benefit from the mea-
surements of scattered waves in arbitrary directions and enables more accurate retrievals of soil
moisture for a large range of VWC [4, 17]. The bistatic model takes the dielectric constants and
geometric parameters of vegetation and the ground as inputs. In remote sensing applications,
these fundamental parameters are typically converted to their equivalent water-content descriptors,
namely soil moisture and vegetation water content VWC. Here a sensitivity analysis of the bistatic
model was performed with respect to the soil moisture and VWC. The results of this analysis
can be used to choose the most efficient observation direction for bistatic and multi-static radar
measurements, and to better understand the limitations of the approach with respect to VWC.
3.3.2 Sensitivity Analysis Simulation Results
Figure 3.9 shows the sensitivity of the forward model with respect to soil moisture content and
VWC at L-band (1.26 GHz) and P-band (0.43 GHz) for three different land cover types ( Ta-
ble 3.4), which include: 1) bare rough surface, 2) open shrub, and 3) woody savanna. Each of these
three cases were analyzed for backscatter (q
s
= 40
o
;f
s
= 180
o
) and specular (q
s
= 40
o
;f
s
= 0
o
)
observations. The parameters shown in Table 3.4 were derived from ground observations at Wal-
nut Gulch, AZ, and Tonzi-ranch, CA, which are considered as shrub-land and woody savanna,
respectively [4].
Table 3.4: Forward Model Vegetation Parameters
Type Branch length Branch radius Trunk length Trunk radius
Open shrub 0:65 m 0:008 m 1:17 m 0:019 m
Woody savanna 1:44 m 0:015 m 2:95 m 0:096 m
38
(a)
(b)
39
(c)
(d)
40
(e)
(f)
41
(g)
(h)
Figure 3.9: (a-d) Effect of VWC on backscatter and specular signals at L-band and P-band: hori-
zontal scale max is 5:5kg=m
2
of VWC; Trunk and branch densities (1=m
2
) are gradually increased
for VWC variation. (e-h) Effect of soil moisture content on backscatter and specular signals: VWC
is fixed at 2:6kg=m
2
. The HH and VV normalized BRCS for specular scattering are sensitive and
change by 5 dB for soil moisture content range of approx. 0:1 0:45m
3
=m
3
.
42
3.3.3 Discussion
Different types of vegetation have different impacts on total NBRCS. Based on the forward model
simulation results presented in Figure 3.9, these impacts are more significant in the backscatter
direction. As an example, according to Figure 3.9.e, for the cases of bare soil and woody savanna,
L-bands
0
HH
increased with soil moisture from 20 dB to -15 dB, and from 7 dB to -5 dB,
respectively.
Conversely, scattering in the specular direction was less sensitive to the type of vegetation
on the ground and sensitivity mainly remained to the soil moisture content. For bare soil at L-
band (Figure 3.9.f), the dynamic range for s
0
HH
specular scattering cross section was6 dB to
11 dB as a function of soil moisture, and for woody savannah it was4 dB to 8 dB. At P-band
(Figure 3.9.h), the open shrubs
0
HH
changed from 4 dB to 8 dB as a function of soil moisture in the
specular direction (Figure 3.9.h), whereas in backscatter direction (Figure 3.9.g) it changed from
20 dB to -18 dB. Furthermore, P-band open shrubs
0
HH
for the specular direction changed only
slightly (1 dB) as a function of VWC in Figure 3.9.d, whereas it varied10 dB in the backscatter
direction (Figure 3.9.c). Therefore, for both polarizations (s
0
HH
and s
0
VV
), there was a strong
sensitivity to soil moisture in the specular direction and the sensitivity to VWC, or biomass, was
not quite as strong but discernible. This is a major strength of the bistatic (specular) observation
scenario, because it is not as significantly impacted by vegetation cover (especially for P-band), and
therefore the knowledge of vegetation parameters may not be a strong determinant of the accuracy
of scattering cross section predictions. Furthermore, the amplitude of cross section observations
in the specular direction was 10 dB stronger than the backscatter direction, resulting in easier
detection of scattered signal and higher signal-to-noise ratios. In the retrieval mode, this potentially
low sensitivity to VWC is highly desirable, as it enables more accurate soil moisture retrievals
without the need for accurate vegetation parameterization [4].
43
Chapter 4
Forward Model Evaluation
4.1 Introduction
This chapter focuses on evaluation of the single-species bistatic scattering model (SSBM) predic-
tions with the actual measurements of Cyclone Global Navigation Satellite System (CYGNSS)
and GNSS Reflectometer Instrument for Bistatic Synthetic Aperture Radar (GRIBSAR) missions,
which are spaceborne and airborne GNSS reflectometry missions, respectively. Sections 4.2 and 4.3
provide an overview of the GRIBSAR and the CYGNSS missions. Section 4.4.2 provides the
delay-Doppler map (DDM) model, which includes the estimation of the location of scattering posi-
tions of a DDM presented in Section 4.4.2, and the method implemented for converting normalized
bistatic radar cross section (NBRCS) computed by the SSBM, which is presented in Section 4.4.3.
Finally, the numerical results predicted by SSBM are evaluated with the actual GRIBSAR mea-
surements (DDM) in Section 4.5 [27].
4.2 Airborne GNSS Reflectometry with GRIBSAR
As shown in Figure 4.1, GRIBSAR instrumentation is integrated in a Twin Otter DHC-6 Aircraft
and it consists of a Global Positioning System (GPS) recorder hardware and antennas [27, 42, 43].
The minimum altitude requirement for the aircraft is considered to be 300 meters, which is derived
from GPS signal characteristics. GRIBSAR consists of a right-handed circularly polarized (RHCP)
44
zenith antenna and an array of 4 left-handed circularly polarized (LHCP) Nadir pointing antenna
elements. The LHCP Nadir pointing antenna array allows for digital beam-steering capabilities,
and looking at multiple specular points in post-processing of the antenna measurements. Moreover,
the GPS data from all antenna elements are collected synchronously and simultaneously from the
GPS recorder hardware inside the aircraft. The GRIBSAR zenith antenna receives the GPS direct
signal (navigation signal), and the nadir looking antenna receives signals scattered from the ground
in the specular direction [42]. The navigation signal received by the zenith antenna is used to
compute the position and velocity of GRIBSAR and it is also used to adjust the GRIBSAR nadir
looking antenna to receive the reflections from ground surface in the specular direction. Moreover,
as is customary in reflectometry observations, the GRIBSAR measurements of GPS reflections are
illustrated as a DDM [44–49]. In order to use these observations for quantitative soil moisture
retrieval, the DDMs need to be converted to radar cross sections and vice versa, which is discussed
in Section 4.4.3.
Figure 4.1: GNSS reflectometry by using GRIBSAR.
45
4.3 Spaceborne GNSS Reflectometry with CYGNSS
NASA CYGNSS was launched in December, 2016 and it uses a constellation of eight satellites in
low orbit (500 km altitude) at 35
o
orbit inclination, where most tropical cyclones happen [23, 50,
51]. Each of the CYGNSS satellites shown in Figure 4.2 is equipped with a four-channel GNSS
bistatic radar receivers, which are capable of bistatic measurements of GPS signals reflected by
land and ocean surfaces. Over the past years CYGNSS GNSS bistatic receivers have been used to
map the ocean surface scattered signal power in the vicinity of specular direction by utilizing the
DDM [52]. Furthermore, the original objective of CYGNSS mission was focused on sensing sea
level wind speed in tropical cyclones, including in high precipitation conditions [23]. However,
recent studies show that the L-band GPS bistatic radar measurements are sensitive to soil moisture,
and the CYGNSS Level 1B (L1B) over-land data products, which are in the form of DDMs, can
be used for soil moisture retrieval over various regions [45, 49, 53, 54].
Figure 4.2: CYGNSS satellites. Image credit: University of Michigan.
46
Figure 4.3: CYGNSS observation of GPS direct signal and GPS signal scattered in the specular
direction . Image credit: University of Michigan.
The CYGNSS instrument contains a RHCP zenith facing navigation antenna and two LHCP
nadir looking antennas for receiving the ocean and land GPS reflections in the specular direc-
tion [23]. As shown in Figure 4.3 the direct GPS signal (navigation signal) received by the zenith
facing antenna is used for estimation of the position and velocity of the receiving satellite. More-
over, this information is further used to target the specular points, which are related to the coherent
scattering component, on the ocean and land surfaces and adjusting the receivers toward those
points [23]. As shown in Figure 4.3 the region in the vicinity of the specular point (SP) is called
the glistening zone. The area of the glistening zone is a function of geometry and root mean square
(RMS) surface roughness height, and it is related to the incoherent scattering component.
The DDM is the basic measurement in the GNSS remote sensing, and it consists of mapping the
spread in the signal in both time delay and Doppler frequency over land and ocean surfaces [23].
An example of the CYGNSS DDM is presented in Figure 4.5, which is recorded over Soil Moisture
Active Passive (SMAP) Yanco site located in Australia. The center bin in this DDM at zero delay
and Doppler has the strongest bistatic radar cross section (BRCS) value and the region, which
includes 5 delay bins and 3 Doppler bins, is related to the glistening zone. In order to map the DDM
bins into their corresponding locations on the land and ocean surfaces it is crucial to identify the
DDM bins, which have same delay and Doppler [23]. Figure 4.4 presents the iso delay and Doppler
47
lines in a DDM. According to Figure 4.4, for a specific location on ocean or land surfaces, there
are two DDM bins with same delay and Doppler, which are related to that specific location. Thus,
this ambiguity needs to be addressed in the soil moisture retrieval algorithm, which is discussed
in Section 4.4.3.
Figure 4.4: Iso delay and Doppler lines in a DDM. Image credit: University of Michigan.
8 6 4 2 0 2 4 6 8
Delay bin
5
3
1
1
3
5
Doppler bin
90
95
100
105 BRCS [dBsm]
Figure 4.5: An example of CYGNSS DDM for SMAP Yanco site.
48
4.4 DDM Model
4.4.1 Introduction
This section focuses on the DDM model, which is proposed for modeling the DDM of a flat rough
surface in the presence of vegetation. The DDM model maps the delay-Doppler bins in the DDM to
points on the ground surface and estimates the NBRCS of each point. As discussed in Section 3.1.2
the NBRCS is calculated using the KA for the SP and the SPM for non-specular points. Ultimately,
the NBRCS values of the points on the ground surface are converted to a DDM. The DDM model
can be divided into three parts: (1) estimating the position of the scattering point(s) for each bin
of the DDM, (2) calculating the NBRCS for the scattering points, and (3) converting the NBRCS
values of the points on the ground surface to a DDM. The details of the first and the last parts will
be given in Section 4.4.2 and Section 4.4.3. The second part of the DDM model was presented
in Section 3.1.
4.4.2 Estimating the Positions of Scattering Points of a DDM
This section focuses on the method used for estimating the position of scattering points on the
ground. The model assumes that the ground is flat with a small RMS surface roughness and no
topography. Furthermore, it assumes the receiver’s altitude is much lower than the transmitter’s
altitude. This assumption is valid for CYGNSS satellites as their altitude is about 500 km, and
the altitude of the GPS satellites is about 20200 km. The first assumption simplifies the geometry
of the problem, which makes it similar to the geometry of the ocean. Thus, there exists ellipses
on the ground that have constant delays, and parabolas that have constant Doppler frequencies,
which are mentioned in Section 4.3 [16, 55]. The ellipse of the SP’s delay has both semi-major
and semi-minor axes equal to zero. Hence, it is a point. Each delay-Doppler bin of the DDM
corresponds to at most two points on the ground. The derivation of the mapping between a delay-
Doppler bin to the ground points uses the SP as a reference point. The geometry of the problem
is shown in Figure 4.6, where the SP position
¯
R
SP
is the origin,
¯
R
t
is the transmitter position,
¯
R
r
is
49
the receiver position,
¯
V
t
is the velocity of the transmitter, the GPS satellite,
¯
V
r
is the velocity of the
receiver, the CYGNSS satellite, q
SP
i
is the incident angle of the SP. Both
¯
R
t
and
¯
R
r
are parallel to
the y-axis. The defined local coordinate system, with SP position at the origin, is consistent with
both [16, 55]. According to [16], the ellipses of constant delay are defined as
X
Y
Z
¯
R
t
¯
R
r
¯
R
SP
¯
V
t
¯
V
r
q
SP
i
q
SP
i
Figure 4.6: SP geometry,
¯
R
t
is the transmitter position,
¯
R
r
is the receiver position and R
SP
is the SP
position.
x
2
b
2
+
y
2
a
2
= 1 (4.1)
where a and b are the semi-major axis and the semi-minor axis, respectively. They are given as
a
2
= b
2
secq
SP
i
(4.2)
b
2
=
2R
SP
rs
R
SP
st
cdt
R
SP
rs
+ R
SP
st
: (4.3)
In Equation (4.3), R
SP
st
is the distance from the transmitter to the SP, R
SP
rs
is the distance from the
SP to the receiver, c is the speed of light, and dt is the delay relative to the SP. The dt is always
positive as the SP has the minimum delay. The Doppler frequency of the SP is defined as
f
D
=
1
l

¯
V
t

ˆ
R
st

¯
V
r

ˆ
R
rs

(4.4)
50
where l is the wavelength,
¯
V
t
is the transmitter velocity,
¯
V
r
is the receiver velocity,
ˆ
R
st
is a unit
vector from the transmitter pointing toward the SP,
ˆ
R
rs
is a unit vector from the SP pointing toward
the receiver. The Cartesian components of the velocity vectors
¯
V
t
and
¯
V
r
are defined as
¯
V
t
= ˆ xV
t
x
+ ˆ yV
t
y
+ ˆ zV
t
z
(4.5)
¯
V
r
= ˆ xV
r
x
+ ˆ yV
r
y
+ ˆ zV
r
z
: (4.6)
The unit vectors
ˆ
R
st
and
ˆ
R
rs
are expressed as
ˆ
R
st
=
¯
R
SP

¯
R
t
R
SP
st
(4.7)
ˆ
R
rs
=
¯
R
r

¯
R
SP
R
SP
rs
: (4.8)
Using Equations (4.4) to (4.8), the Doppler shift of the SP can be written as
f
D
=
1
l

V
r
y
V
t
y

sinq
i

V
r
z
+V
t
z

cosq
i

: (4.9)
As the transmitter altitude is much higher than the receiver, the Doppler shift relative to the SP can
be approximated [56] as
d f
D
=
cosq
i
l(
¯
R
r
ˆ z)

xV
r
x
+ ycosq
i

V
r
y
cosq
i
+V
r
z
sinq
i

(4.10)
where x and y are the local coordinate relative to the SP. Using Equations (4.1) and (4.10) and
solving the quadratic equation in y, the solution is given as
y=
a
0
b
0

q

b
2
0
+ d
2
0

c
0
(d
0
a
0
)
2
b
2
o
+ d
2
0
(4.11)
51
where a
0
, b
0
, c
0
and d
0
are
a
0
=d f
D
l(
¯
R
r
ˆ z)
cosq
i
(4.12a)
b
0
= cosq
i

V
r
y
cosq
i
+V
r
z
sinq
i

(4.12b)
c
0
=(V
r
x
)
2
2R
SP
rs
R
SP
st
cDt
R
SP
rs
+ R
SP
st
(4.12c)
d
0
= V
r
x
cosq
i
: (4.12d)
The value of x can be found from y using
x=
a
0
yb
0
V
r
x
: (4.13)
The position of the points on the ground for a specific delay and Doppler relative to the SP can
be found in the Cartesian coordinate system. The x and y components are from Equations (4.11)
and (4.13), respectively. The z component is zero. Only real values solutions to Equation (4.11)
are kept, as x and y are positions on the ground. The incident and scattering angles are calculated
using the positions of the scatterers with the transmitter position
¯
R
t
and the receiver position
¯
R
r
,
respectively. The incident angles,q
i
andf
i
are
q
i
= arctan
q
(
¯
R
t
ˆ x x)
2
+(
¯
R
t
ˆ y y)
2
;
¯
R
t
ˆ z

(4.14a)
f
i
= arctan(
¯
R
t
ˆ x x;
¯
R
t
ˆ y y): (4.14b)
The two-argument arctan is used for numerical stability and it is defined asa = arctan(a;b) such
that tan(a)= a=b. This is defined in many programming languages, including MATLAB and C++,
asatan2.
52
The scattering angles,q
s
andf
s
are
q
s
= arctan
q
(
¯
R
r
ˆ x x)
2
+(
¯
R
r
ˆ y y)
2
;
¯
R
r
ˆ z

(4.15a)
f
s
= arctan(
¯
R
r
ˆ x x;
¯
R
r
ˆ y+ y): (4.15b)
The incident and scattering angles are the input to the SSBM forward model, which was previously
discussed in the Section 3.1.
4.4.3 Converting NBRCS to DDM
The conversion from NBRCS to a DDM is performed by first calculating the circularly polarized
NBRCS from the linearly polarized NBRCS, given in Section 3.1. Then using the GPS coarse
acquisition (C/A) Woodward ambiguity function (WAF), the LHCP NBRCS is converted to BRCS
DDM. The coherent and the incoherent components of the DDM BRCS will be calculated individ-
ually. The total BRCS DDM is the summation of the two components.
CYGNSS delay Doppler mapping instrument (DDMI) contains one RHCP zenith facing nav-
igation antenna and two LHCP nadir looking science antennas. The RHCP zenith facing antenna
receives GPS signals in the direct path between GPS and CYGNSS satellites, and it is used for lo-
cating the SP on land and ocean surfaces. Moreover, two LHCP nadir facing antennas are utilized
for GNSS-R. Therefore, in order to use the CYGNSS DDMs for soil moisture retrieval over various
land covers, the co-pol (hh and vv) and cross-pol (hv and vh) linearly polarized NBRCS predicted
by the forward model, SSBM in Section 3.1 are converted to LHCP NBRCSs
0
lr
. According to [16],
the LHCP NBRCS is expressed as
s
0
lr
=p

js
vv
+ s
hh
j
2
+ 2Im

(s
vh
s
hv
)

(s
vv
+ s
hh
)

+js
vh
s
hv
j
2

(4.16)
53
where s
hh
and s
vv
are the co-pol scattering elements of the total scattering matrix, and s
vh
and s
hv
are the cross-pol scattering elements of the total scattering matrix, which are derived from Equa-
tions (2.3) and (3.14). As the difference between the cross-pol components is much smaller than
the co-pol components [32], Equation (4.16) can be approximated as
s
0
lr

1
4

s
0
vv
+s
0
hh
+ 2Re(r)
q
s
0
vv
s
0
hh

(4.17)
wherer is defined as
r =

s
vv
s

hh

r
D
js
hh
j
2
ED
js
vv
j
2
E
: (4.18)
hs
vv
s

hh
i=
M
33
+ M
44
2
(4.19)
r
D
js
hh
j
2
ED
js
vv
j
2
E
=
p
M
22
M
11
(4.20)
where M
11
, M
22
, M
33
and M
44
are the elements of Stokes matrix expressed in Equation (2.3). In
Equation (4.17), s
0
hh
ands
0
vv
are the co-pol NBRCS estimated by the advanced bistatic scattering
forward model. Equation (4.17) is valid for both the coherent and incoherent components. The
subscript lr of s
0
lr
will be dropped in the rest of this section, as the conversion from NBRCS to
BRCS DDM is general for any polarization.
The GPS C/A WAF, with a good approximation, is expressed as
D
jc(dt;d f)j
2
E
=L(dt)
2
S(d f)
2
(4.21)
whereL(dt) and S(d f) are
L(dt)= max(0;1jdtj=t
c
) (4.22)
54
S(d f)= sinc(T
i
d f): (4.23)
In Equations (4.22) and (4.23),t
c
is the chip length, and T
i
is the coherent integration period [55].
The approximation of the GPS C/A WAF is good for a relative accuracy of 10
4
[55], which is
more than enough for this application. The coherent component of the BRCS DDM s
coh
[16] is
given as
s
coh
[i; j]=

R
SP
rs

2

R
SP
st

2

R
SP
rs
+ R
SP
st

2
s
0
coh
D

c

t
i
; f
j

2
E
(4.24)
where i and j are the indices of the delay and Doppler bins, respectively,t
i
is the relative delay of
bin i to the delay of the SP, and f
j
is the relative Doppler frequency of bin j to the Doppler fre-
quency of the SP. The SP bin is located at i= 0 and j= 0 of the DDM. The incoherent components
of the BRCS DDMs
inc
[16] are given as
s
inc
(i; j)=
Z
s
0
inc
D

c

t
i
t; f
j
f
D

2
E
d~ r (4.25)
where
R
d~ r is an integral over the ground surface. t and f
D
are the delay and the Doppler, re-
spectively, of the surface relative to the SP. For a discrete, finite areas
0
inc
, Equation (4.25) can be
written as
s
inc
(i; j)=
å
i
0
å
j
0
s
0
inc

i
0
; j
0

A
0

i
0
; j
0

D

c

t
i
t
i
0; f
j
f
j
0

2
E
(4.26)
where A
0
[i
0
; j
0
] is the surface area ofs
0
inc
[i
0
; j
0
]. Observing the double summation in Equation (4.26)
is a two-dimension discrete linear convolution. Thus, Equation (4.26) can be written as
s
inc
[i; j]=(s
0
inc
A
0
)
D

c

t
i
; f
j

2
E
(4.27)
where denotes two-dimension discrete linear convolution, which can be implemented in the
frequency domain by utilizing the convolution theorem and the fast Fourier transform (FFT). This
implementation required fewer computations compared to the regular convolution implementation.
55
With the assumption of a flat ground surface with small roughness, each delay and Doppler values
correspond to two patches on the ground. We also assume the energy of s
0
inc
[i
0
; j
0
] with delay
and Doppler values outside the CYGNSS DDM is negligible. This assumption is valid as, for
flat surfaces, the coherent scatters are dominant [34] and the GPS C/A WAF decays within few
delay/Doppler bins. Furthermore, we assume the two patches of each delay and Doppler bin have
the same surface area. Thus,s
0
inc
can be written as
s
inc
[i; j]=s
bin
inc

D

c

t
i
; f
j

2
E
(4.28)
where,s
bin
inc
is defined as
s
bin
inc
[i; j]=
A[i; j]
2
å
n=1;2
s
0
inc
[q
i
(i; j;n);q
s
(i; j;n);f
i
(i; j;n);f
s
(i; j;n)]: (4.29)
In Equation (4.29), q
i
, q
s
, f
i
, and f
s
are estimated using Equations (4.14a), (4.14b), (4.15a)
and (4.15b), respectively. A[i; j] is the effective area of i delay bin and j Doppler bin of the DDM,
and it can be calculated using
A[i; j]=
å
n=1;2
Z
R
i; j;n
D

c

t
i
t; f
j
f
D

2
E
d~ r (4.30)
The effective area of CYGNSS DDM is provided in the CYGNSS L1B data. In our implementa-
tion, we used the value in CYGNSS L1B data.
The total BRCS DDM can be calculated by adding Equation (4.29) and Equation (4.24), which
is mathematically expressed as
s
tot
[i; j]=s
bin
inc
[i; j]+s
coh
[i; j]: (4.31)
The SSBM BRCS DDM is used by the inversion algorithm discussed in chapter 5 for soil moisture
retrieval from DDM.
56
4.5 Bistatic Model Validation Using GRIBSAR Data
In order to validate the forward model with GRIBSAR data, the method described in Section 3.1
has been used to simulate the DDM of Tonzi-ranch GPS reflections by applying the SSBM. In Sec-
tion 3.1 the specular bin of the forward model DDM was considered as the reference point and
each bin around that had scattering contributions from specific scattering (q
s
) and azimuth angles
(f
s
). Here Equation (4.24) was used for estimating the bistatic BRCS of the center bin (coherent
reflection component). The BRCS values of the rest of the DDM bins ( Equation (4.29)) were
estimated by running the forward bistatic scattering model, with specific range, scattering angles,
and azimuth angles.
Table 4.1: Tonzi-Ranch Input Parameters
Parameter Value
Frequency(L-band) 1:57 GHz
Incidence angle 40
o
Soil dielectric constant (14.41,0.18)
Surface roughness 0:01 m
Correlation length 0:1 m
GPS range to SP 21283000 m
GRIBSAR range to SP 2021 m
Figure 4.7: DDM of Tonzi-ranch area in northern California measured by GRIBSAR on July 31,
2018. This DDM presents high resolution BRCS over an area of 293 [m] × 293 [m] (one chip in
the DDM corresponds to a distance of 293 [m]).
57
Figure 4.8: GRIBSAR flight path from east to west of the Tonzi ranch. The Tonzi ranch Soil mois-
ture Sensing Controller and oPtimal Estimator (SoilSCAPE) sensors are located close to GRIB-
SAR measurement points. These measurements correspond to the GPS psuedo-random noise code
number 12 reflections.
Figure 4.9: GRIBSAR Twin Otter Aircraft, antenna integration, and rack-mount hardware integra-
tion, which are used for the GRIBSAR measurements over Tonzi ranch.
58
Figure 4.7 shows the GRIBSAR measurements over the Tonzi-ranch area in California. This
flight site was chosen because of the availability of ground in-situ observations from the Soil mois-
ture Sensing Controller and oPtimal Estimator (SoilSCAPE) soil moisture sensor network at Tonzi
ranch, which are specified in Figure 4.8 [27]. Consequently, the Tonzi-ranch SoilSCAPE in-situ
data along with the extensive existing database of vegetation and ground surface roughness were
used to parameterize the proposed bistatic scattering model expressed in Table 4.1 [1].
As depicted in Figure 4.7, the center of the DDM (Frequency offset = 0 (Hz) and delay off-
set (chips) = 11.6) corresponds to the SP (coherent scattering component), which has the highest
RCS value, namely 71 dBsm, and the intensity of the area around the SP, called the glistening
zone (non-coherent scattering component) [40], ranged from 64 to 70 dBsm. Figure 4.10 shows
the comparison of the measured and simulated Tonzi-ranch DDMs. The DDMs presented in Fig-
ure 4.10 show the RCS (s
LR
) of the scattering over an area of 146 [m] × 146 [m], which includes
the area around the SP. The comparison between the DDMS from the actual GRIBSAR data and
the developed bistatic scattering model shows that there is a good agreement between the peak val-
ues of DDMs, corresponding to the SP. The shapes of the glistening zone are slightly different as
that is simulated based on assumed topographic flatness and a corresponding Woodward ambiguity
function. Based on the results presented in Figure 4.7, it is feasible to utilize the proposed bistatic
model predictions for soil moisture retrieval at Tonzi ranch for future flights over this site.
59
(a)
(b)
Figure 4.10: Figure (13. a) presents DDM of Tonzi-ranch as measured by GRIBSAR, and figure
(13. b) shows the Tonzi-ranch DDM simulated by the proposed bistatic scattering forward model
with the technique described in [27].
60
Chapter 5
Soil Moisture Retrieval from Bistatic Radar Observations
5.1 Introduction
This chapter focuses on the soil moisture retrieval algorithm, which is composed of the physics-
based bistatic scattering forward model discussed in chapter 3 and the local/global hybrid multi-
directional search scheme [33]. In Section 5.3.1 the computational predictions of the retrieval algo-
rithm is evaluated with the Cyclone Global Navigation Satellite System (CYGNSS) measurements
(delay-Doppler maps (DDMs)) over the Soil Moisture Active Passive (SMAP) Yanco site located
in southeast of Australia. Moreover, two different soil moisture retrieval schemes are proposed in
this chapter. In the first retrieval scheme, the surface roughness is known and the soil moisture
value is unknown. Whereas, in the second retrieval scheme, both the surface roughness and soil
moisture values are unknown. The retrieval schemes are then used for soil moisture retrieval over
the SMAP Yanco site from Level-1B (L1B) CYGNSS data. The soil moisture retrieval algorithm
and the computational results are presented in Section 5.2 and Sections 5.3.2 and 5.3.3, respec-
tively. Ultimately, based on the computational results the performance of the two soil moisture
retrieval schemes are analyzed in Section 5.4.
61
5.2 Soil Moisture Retrieval Method
The soil moisture retrieval approach adopted here take advantage of a local/global hybrid multi-
directional search method based on the simulated annealing method, discussed in detail in [33]. In
the inverse-scattering problem, this method proved to be faster than the classic simulated annealing
method in converging to the global minimum. CYGNSS L1B science data version 2:1, along with
ancillary data, were used in the soil moisture retrieval. The single-species bistatic scattering model,
(SSBM) DDM, of Sections 4.4 and 3.1 is used with parameters from CYGNSS data and ancillary
data as inputs to the forward model. The parameters from CYGNSS data are the position and
velocity of both the transmitter and the receiver, the position of the specular point (SP), the relative
delay, the relative Doppler of the DDM bins to the specular point (SP), and the bistatic radar cross
section (BRCS). Moreover, the coherent integration period of the signal T
i
is 1 ms. The ancillary
data are divided into vegetation parameters and ground parameters. The vegetation parameters
discussed in Section 3.1 are the dielectric constant, the length, the radius, and the density of the
three vegetation components: the large branches, the short branches, and the trunk. The ground
parameters are the clay percentage of the soil, the correlation length of the rough surface, and the
root mean square (RMS) surface roughness. The correlation length of the surface was considered
to be ten times the RMS surface roughness [57].
Two retrieval schemes were used in retrieving the soil moisture from the CYGNSS DDMs.
The first scheme assumes that the root mean square (RMS) surface roughness is known and only
retrieves the soil moisture. The second scheme retrieves both the soil moisture and the RMS
surface roughness. The RMS surface roughness has a high effect on the scattering wave. In
general, the RMS surface roughness ancillary data is limited. Consequently, in the second scheme,
the algorithm retrieves both the RMS surface roughness and the soil moisture. In the retrieval
algorithm, the dynamic range of soil moisture is between 0:1 and 1 m
3
m
3
, and the allowed range
of RMS surface roughness is between 0:5 and 2:5 cm. In order to include the specular point
(SP) bin and the DDM bins related to glistening zone, the retrieval algorithm uses a subset of the
DDM, which consists of three delay and five Doppler bins. The subset DDM is used to calculate an
62
averaged normalized bistatic radar cross section (NBRCS). The method of calculating the averaged
NBRCS is similar to the method used by the CYGNSS processor [23], which is expressed as
s
0
=
å
3
i=0
å
2
j=2
s(i; j)
å
3
i=0
å
2
j=2
A(i; j)
(5.1)
where s is the BRCS, and A is the bin area in the unit of m
2
. i and j are the delay and Doppler
bin indices relative to the SP, respectively. The SP is at i= 0 and j= 0, and this bin corresponds
to the bin with the maximum BRCS value. The reason for this is that the CYGNSS on-board
processor was designed for ocean surface and did not take the land elevation into account. Thus
it is recommended for land application to use the peak value as the SP. The forward model DDM,
described in Section 4.4, is used to construct the DDM and then estimate the averaged NBRCS.
The flowchart of the proposed inversion algorithm is shown in Figure 5.1. The retrieval algorithm
starts by initializing the initial solution, calculating the averaged NBRCS of CYGNSS s
0
CYGNSS
,
and setting the input parameters of the DDM of SSBM. After the initialization, the algorithm
generates a random solution around the accepted solution, which is considered the initial solution.
After that, the algorithm performs a multi-directional random search. For the first retrieval scheme,
a single directional random search is performed, as there is only one unknown. Moreover, by using
Metropolis criteria, the new solution is accepted [33]. The multi-directional search is repeated for
N
md
times or until the maximum moving distance is smaller than the step limit, which is one
of the algorithm’s tuning parameters. The process of generating a random solution to this point is
repeated N
s
times. The whole process is repeated N times or until the cost function f
cost
is less than
f
stop
, each time with a decreased temperature. The f
stop
is a tuning parameter for the algorithm.
The cost function is defined as
f
cost
=

s
0
CYGNSS
s
0
forward

l
2
(5.2)
wheres
0
forward
is the averaged NBRCS of the SSBM.
63
Initialize the In-
version Algorithm
Generate a random
solution around the
accepted solution
Perform multi-
directional ran-
dom search
Accept new so-
lution based on
Metropolis criterion
C
md
i
md
++
i
s
< N
s
i
s
++
Step length adjustment
i
t
< N
t
i
t
++
C
N
decrease temperature
i++
STOP
Yes
No
Yes
No
Yes
No
No
Yes
Figure 5.1: Soil moisture retrieval inversion algorithm, which includes the DDM of the SSBM
and the hybrid local/global scheme. C
md
= i
md
< N
md
or step step limit and C
N
= i N or
f
cost
< f
stop
.
64
5.2.1 Validation Site
SMAP-Yanco region was selected for validating the retrieval algorithm. The main reasons for
selecting this region were this site (1) has no topography, (2) has active in-situ soil moisture sensors,
and (3) is located within the CYGNSS coverage area. The Yanco region is located in the southeast
of Australia, and it is a large flat area (2500 km
2
), which includes 13 sites with in-situ soil
measurement sensors [58]. The sensors installed at Yanco sites measure surface soil moisture (0-
5 cm) and soil temperature at three depths (1, 2:5 and 5 cm) [58]. Moreover, according to [58],
the median root zone(0 90cm) moisture content of Yanco region sites (Y1-Y13) from 2004 to
2010 is 0:186-0:33 m
3
m
3
. Consequently, the in-situ measurements over this region show that soil
moisture variation is far below the saturation level (0:6 m
3
m
3
).
Table 5.1: The vegetation parameters of Yanco site (grassland (IGBP: 5)). The parameters are
inputs to the SSBM.
Parameter Grasslands
Large branch dielectric constant 15+ j3
Large branch length 0:491 m
Large branch radius 0:4 cm
Large branch density 7:339 m
2
Short branch dielectric constant 15+ j3
Short branch length 0:246 m
Short branch radius 0:1 cm
Short branch density 29:35 m
2
Trunk dielectric constant 15+ j3
Trunk length 0:05 m
Trunk radius 0:4 cm
Trunk density 0:432 m
2
5.3 Results
In this section, the SSBM forward model predictions are evaluated with the DDMs provided by
CYGNSS measurements. Moreover, we used the retrieval algorithm of Section 5.2 and the SSBM
DDM of Section 4.4 to retrieve soil moisture from simulated DDMs. For validation, CYGNSS
L1B data, which includes BRCS DDMs, was used to retrieve the soil moisture. The retrieved soil
65
moisture values were compared to the in-situ soil moisture at the validation site. The same tuning
parameters of the retrieval algorithm were used with both the simulated DDMs and CYGNSS
DDMs. The metrics for the soil moisture retrievals are RMS error (RMSE), unbiased RMSE
(ubRMSE), and the correlation coefficient r, all were calculated according to Entekhabi et al. [59].
5.3.1 Validation Results
The inversion algorithm, presented in Section 5.2, and the SSBM DDM of Section 4.4 were used
to retrieve the soil moisture from CYGNSS L1B version 2:1 data for 2019 over the validation
site. More details of the validation site were given in Section 5.2.1. 98 DDMs were used for soil
moisture retrieval. The SP locations of the DDMs are within 5 km of the sensor’s location and have
reported signal to noise ration (SNR) over 10 dB. Moreover, in selecting the DDMs, we discarded
any data with quality flags that indicate issues in the CYGNSS measurements. Specifically, data
with attitude errors, abnormality in the hardware, or a reported negative antenna gain at the SP
location. The criteria of selecting the CYGNSS data were similar to the criteria reported in other
soil moisture retrievals methods using CYGNSS data [25, 26]. According to [58], the vegetation
type of the Yanco region is mostly improved pasture with minimal woody vegetation, which falls
under grasslands The International Geosphere–Biosphere Programme (IGBP) land cover types.
The vegetation parameters used in the inversion algorithm are the grasslands vegetation parameters
presented in Table 5.1. Furthermore, the soil clay percentage is 11:7 %, which is the reported clay
percentage of the nearest location to the in-situ sensors [60]. The tuning parameters of the retrieval
algorithm were the same as the values used in the simulations.
Figure 5.2 shows the BRCS DDM of both CYGNSS and the SSBM. The CYGNSS DDM
was collected on 2019-10-00 20:45:01.5 UTC with spacecraft number one and channel two. The
incident angle of SP was 22°, and the reported SP location was34:8054° latitude and 146:3956°
longitude. The forward model was generated with a RMS surface roughness of 2 cm and a soil
moisture value of 0:025 m
3
m
3
, derived from the in-situ soil moisture measurements. For the
retrievals, the SSBM generated a DDM with three delay bins with positive delay and five Doppler
66
bins. However, in Figure 5.2, the full DDM is shown with 17 delay bins and 11 Doppler bins. The
full DDM was generated for comparison with the CYGNSS DDM.
The results of the soil moisture retrievals using the two schemes are given in the following
subsections.
8 6 4 2 0 2 4 6 8
Delay bin
5
3
1
1
3
5
Doppler bin
90
95
100
105
BRCS [dBsm]
(a)
8 6 4 2 0 2 4 6 8
Delay bin
5
3
1
1
3
5
Doppler bin
90
95
100
105 BRCS [dBsm]
(b)
Figure 5.2: Comparison between DDMs generated by the forward model (Figure 5.2.a) and
CYGNSS (Figure 5.2.b). The DDMs are over Yanco site, Australia.
67
5.3.2 First Scheme of Retrieval Algorithm
The first retrieval scheme, as discussed in Section 5.2, considers the RMS surface roughness as a
known parameter and the soil moisture as an unknown. The retrieval scheme was used to retrieve
the soil moisture values from the selected CYGNSS DDMs. The RMS surface roughness was
set to 2 cm. Thus, the surface correlation length is 20 cm. We discarded the retrievals that were
nonphysical or unexpected. The criteria of discarding retrievals are based on the retrieved soil
moisture values and not the in-situ soil moisture values. The discarded retrievals are considered
unreliable retrievals, and the retrieval algorithm failed to retrieve the soil moisture values from
the CYGNSS DDMs. A retrieval is discarded if the retrieved soil moisture value is greater than
0:5 m
3
m
3
or less than 0:0025 m
3
m
3
. The lower limit was selected to be the lower limit of
soil moisture value in the retrieval’s algorithm. The upper limit was set to 0:5 m
3
m
3
as we do
not expect the soil moisture to reach this value in this region. For the first retrieval scheme, five
retrievals were discarded out of 98 retrievals.
Figure 5.3 shows the time series of the retrieved soil moisture values, where the blue lines
represent the in-situ soil moisture values, the cyan dots represent the in-situ soil moisture values
that the algorithm attempted to retrieve, the green dots represent the retrieved soil moisture.
Figure 5.4 shows the in-situ versus the retrieved soil moisture values. The retrieved soil mois-
ture values of the retrievals had RMSE of 0:075 m
3
m
3
, ubRMSE of 0:075 m
3
m
3
, and correla-
tion coefficient r of 0:29.
68
2019-01-01 2019-05-02 2019-08-31 2019-12-30
Time
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Soil moisture [m
3
/m
3
]
In-situ
In-situ
Retrieved
Figure 5.3: Time series of retrieved soil moisture; cyan dots represent the in-situ soil moisture
close to DDMs’s time.
0.0 0.1 0.2 0.3 0.4 0.5
In-situ soil moisture [m
3
/m
3
]
0.0
0.1
0.2
0.3
0.4
0.5
Retrieved soil moisture [m
3
/m
3
]
Figure 5.4: Soil moisture retrieval using the first retrieval scheme from DDMs close to Y8, Yanco
site in 2019, total number of retrievals: 93. The RMSE is 0:075 m
3
m
3
, ubRMSE is 0:075 m
3
m
3
,
and r is 0:29.
69
5.3.3 Second Scheme of Retrieval Algorithm
The second retrieval scheme, discussed in Section 5.2, considers both the RMS surface roughness
and the soil moisture as unknowns. Similar to the first scheme, presented in Section 5.3.2, the
vegetation parameters presented in Table 5.1 and the same soil clay percentage were used in the
retrieval algorithm. The surface correlation length was set to ten times the RMS surface roughness.
Furthermore, similar to the first scheme, the nonphysical or unexpected retrieved soil moisture
values were discarded, and the same criteria were used. Three out of 96 retrievals were discarded.
The time series of the soil moisture and RMS surface roughness retrievals are shown in Figure 5.5
and Figure 5.6, respectively. Similar to the plot of the first scheme results, the blue lines represent
the in-situ Soil Moisture values. The cyan dots represent the in-situ soil moisture that the algorithm
tried to retrieve, and the green dots represent the retrieved soil moisture values. Figure 5.7 shows
the in-situ soil moisture values versus the retrieved soil moisture values. The retrieved soil moisture
values had a RMSE 0:097 m
3
m
3
, ubRMSE of 0:094 m
3
m
3
, and a correlation coefficient r of
0:37.
2019-01-01 2019-05-02 2019-08-31 2019-12-30
Time
0.0
0.1
0.2
0.3
0.4
Soil moisture [m
3
/m
3
]
In-situ
In-situ
Retrieved
Figure 5.5: Time series of retrieved soil moisture; cyan dots represent the in-situ soil moisture
close to DDMs’s time.
70
2019-01-01 2019-07-02 2019-12-31
Time
1.25
1.50
1.75
2.00
2.25
Soil roughness [cm]
Figure 5.6: Time series of the RMS surface roughness retrieval.
0.0 0.1 0.2 0.3 0.4 0.5
In-situ soil moisture [m
3
/m
3
]
0.0
0.1
0.2
0.3
0.4
0.5
Retrieved soil moisture [m
3
/m
3
]
Figure 5.7: Soil moisture retrieval using the second retrieval scheme from DDMs close to Y8,
Yanco site in 2019, total number of retrievals: 95. The RMSE is 0:098 m
3
m
3
, ubRMSE is
0:094 m
3
m
3
, and r is 0:37.
71
5.4 Discussion
The BRCS DDMs predicted by the SSBM and the BRCS DDMs provided by the L1B CYGNSS
data for SMAP-Yanco sites were presented in Section 5.3. Figure 5.2 illustrated the SSBM DDM
constructed with the method expressed in Section 4.4. Furthermore, Figure 5.2 showed that the
structure and shape of the DDM predicted by the forward model were in acceptable accordance
with the CYGNSS DDM, especially around the SP. The SP bin, which is the bin with the maxi-
mum BRCS value, for both DDMs was located at (0 delay, 0 Doppler). The inversion algorithm,
illustrated in Figure 5.1, includes the SSBM, discussed in Section 3.1, and the hybrid local/global
optimization method [33]. In Section 5.3, two soil moisture retrieval schemes were used. In the
first scheme, presented in Section 5.3.2, the surface roughness was known, and the soil moisture
(at 0-5 cm) was unknown. The second scheme of soil moisture retrieval, presented in Section 5.3.3,
considered both surface roughness and soil moisture as unknowns. For each retrieval scheme, soil
moisture values were retrieved from CYGNSS DDMs.
For the retrieval from the CYGNSS DDMs, the first retrieval scheme had a better performance
compared to the second retrieval scheme. This was expected as the first scheme retrieved a sin-
gle geophysical parameter, the soil moisture, while the second scheme retrieved two geophysical
parameters, soil moisture and surface roughness, from a single DDM. Thus, the second retrieval
scheme tries to find the solution to an ill-posed inverse problem.
According to Figures 5.4 and 5.7 the inversion algorithm retrieved soil moisture values from
CYGNSS DDMs, with a ubRMSE of less than 0:1 m
3
m
3
for both retrievals schemes. The
ubRMSE of the first and second retrieval schemes were 0:075 m
3
m
3
and 0:094 m
3
m
3
, respec-
tively. Furthermore, the bias errors were insignificant; it was 0:004 m
3
m
3
and 0:027 m
3
m
3
for
the first scheme and the second scheme, respectively. The error variance was proportional to the
in-situ soil moisture values, as illustrated in Figure 5.4 and Figure 5.7. Both retrievals had a low
correlation coefficient r. Specifically, 0:29 and 0:37 for the first and second schemes, respectively.
The first scheme performed better compared to the second scheme in the RMSE and the ubRMSE
merits. However, the second scheme had a slightly higher correlation coefficient. As we noted
72
earlier in this section, the second scheme suffers from retrieving soil moisture from an ill-posed
inverse problem, as the algorithm retrieves two parameters from a single DDM. Thus, the inverse
problem is under-determined. On the other hand, the first scheme performance depends heavily on
the selected values of RMS surface roughness.
The performance of both schemes is lower than the performances of other soil moisture re-
trievals using CYGNSS DDM/data [25, 26]. Specifically, Chew et al. [25] reported a median
ubRMSE of 0:049 m
3
m
3
, Senyurek et al. [26] reported a minimum ubRMSE of 0:052 m
3
m
3
using all data for training and 0:049 m
3
m
3
using site’s specific training. Although our retrieval
methods achieved a lower performance than the other methods, the usage of a physics-based for-
ward model makes it prone to errors in different environments within the SSBM assumptions. Fur-
thermore, our model is capable of retrieving soil moisture in the presence of moderate-to-densely
vegetated land cover.
The factors that contribute to the errors in the retrievals are listed as follows:
1. The foot-print of CYGNSS DDM is large, but the in-situ soil moisture sensors cover a small
region of the foot-print. Thus, the average soil moisture value, which is observed by the
CYGNSS DDM, could be different from the in-situ soil moisture values.
2. The small variations in vegetation land cover over the year, as the seasonal changes were not
included because of the lack of such information.
3. Errors in the current CYGNSS L1B products, which include the SP location as CYGNSS
was designed for ocean surfaces, errors in the GPS power as the current version, version 2.1,
does not account for the transmitter power changes. Some of the issues will be addressed in
future CYGNSS products [61].
73
Chapter 6
Noise Sensitivity Analysis
6.1 Introduction
This chapter provides the noise sensitivity analysis of the single-species bistatic scattering model
(SSBM) with respect to the soil moisture for single and multi-instrument observations of differ-
ent land covers. The results of this analysis provide better insight to the performance of the soil
moisture retrieval algorithm discussed in chapter 5. This work has been done in support of the
Distributed Spacecraft with Heuristic Intelligence to Enable Logistical Decisions (D-SHIELD)
research project funded by NASA [62]. D-SHIELD is a set of scalable software tools, which
contributes to schedule payload operations of a large constellation. In order to maximize the sci-
ence value for specific use case, e.g., local and global soil moisture monitoring, the D-SHIELD
scheduling system for a large constellation is preformed in such a way that the collection of ob-
servational data and their downlink are constrained by the constellation constraints, resources, and
subsystems [62]. The main part of the satellites’ decision making system is Observing System
Simulation Experiment (OSSE). The OSSE is a data analysis experiment for analysing the ef-
fect of new observing instruments on operational forecast, when the actual measured data are not
available [62]. The SSBM discussed in Section 3.1 is used for developing a physics-based OSSE,
which will be one of the bases of the D-SHIELD decision-making system. The SSBM is capable
of modeling the monostatic and bistatic radar observations, and it can be used in any arbitrary
74
configuration of instruments in support of D-SHIELD. For instance, it is feasible to include mono-
static radars at different frequencies and incidence angles. Furthermore, it is possible to add the
bistatic radar systems such as Cyclone Global Navigation Satellite System (CYGNSS) (L-band)
and SigNals of Opportunity P-band Investigation (SNoOPI) (P-band), which benefit from higher
temporal and spacial resolutions.
Noise sensitivity study for the estimation of error in the retrieved soil moisture values, con-
tribute to the D-SHIELD decision-making system. In order to model the actual radar measurements
, the system and speckle noise contributions are added to the SSBM predictions. The following
sections focuses on the the root mean square error (RMSE) in soil moisture estimation with the
presence of noise for different scenarios.
6.2 Sensitivity Analysis With Respect to Noise Standard Deviation
In this section we assume that the radar measured scattered signal power is contaminated by noise.
The SSBM in the presence of Gaussian noise and the soil moisture retrieval algorithm discussed in
chapter 5 are used for sensitivity analysis with respect to Gaussian noise standard deviation. This
analysis is crucial for finding the upper bound limit for noise standard deviation in order to achieve
the desired soil moisture retrieval error, which is assumed to be 0.04. The noisy data is modeled as
s
0
n
=s
0
+ k
p
N(0;1)s
0
(6.1)
where s
0
n
is the generated noisy normalized bistatic radar cross section (NBRCS), s
0
is the
synthesized clean (noise free) NBRCS estimated by SSBM in the backscatter direction, k
p
is the
additive noise standard deviation, and N(0;1) represents a random number from Gaussian distribu-
tion with a zero mean and unit standard deviation. For the noise standard deviation (k
p
) sensitivity
analysis the Soil moisture Sensing Controller and oPtimal Estimator (SoilSCAPE) Walnut Gulch
site ( Figure 6.2) located in southeastern Arizona, US is chosen.
75
Figure 6.1: SoilSCAPE Walnut Gulch, Az. Image credit:https://daac.ornl.gov.
76
Figure 6.2: Walnut Gulch, Az. Image credit:www.ars.usda.gov.
In our analysis 50 days of soil moisture samples in the year of 2019 are used from SoilSCAPE
Walnut Gulch in-situ soil moisture measurements database. Figure 6.1 presents the Walnut Gulch
site and the different in-situ soil moisture sensors implemented in this site, which include the
SoilSCAPE in-situ sensors. Consequently, for each of the k
p
values the SSBM is used to first
generate the noise free NBRCS and then the noisy NBRCS (s
0
n
) is computed by using the Equa-
tion (6.1). Furthermore for each of the k
p
values the Monte Carlo method is used in order to have
enough samples of the noise Gaussian distribution. Thus, for a particular k
p
and a soil moisture
value the SSBM is run for 100 times and the averaged (s
0
n
) is used as the noisy data point in the
inversion algorithm for soil moisture retrieval. Ultimately, the RMSE between actual measured
soil moisture data and retrieved soil moisture data are computed. Table 6.1 shows the SSBM input
parameters and their values used for the k
p
sensitivity analysis.
Figure 6.3 presents the RMSE between the retrieved soil moisture value and the SoilSCAPE
in-situ soil moisture measurements for different k
p
values. According to Figure 6.3 the maximum
77
Table 6.1: Forward Model Input Parameters
Parameter Value
Frequency(L-band) 1:57 GHz
Incidence angle 55
o
VWC 0:29 kg=m
2
Surface roughness 0:01 m
Figure 6.3: Soil moisture RMSE vs different k
p
values.
additive Gaussian noise standard deviation (k
p
(max)) in order to achieve the RMSE = 0.04 is
(k
p
(max)) = 0.1085.
6.3 Noise sensitivity analysis for D-SHIELD multi-instrument
measurements
As mentioned in Section 6.1 the goal of D-SHIELD research project is to provide scalable soft-
ware tools, which support schedule operations of a large constellation with multiple observation
instruments. Thus, it is important to analyze the impact of multi-instrument observations on the
soil moisture RMSE in the presence of noise. In this section the relative importance of making
multiple measurements, which can be combined (at different times within a short time period) to a
78
single more accurate measurement is investigated. This requires to establish a rule-book on choos-
ing the different times during which multiple measurements can be considered as constant within
certain error bounds. Moreover, we need to establish tables mapping multiple measurements to
analyse the impact of using multi-instrument measurements on the soil moisture RMSE for dif-
ferent vegetation types and input parameters. Similar to the study presented in Section 6.2, in
the multi-instrument observations noise sensitivity analysis, it is assumed that the scattered power
is contaminated by noise. According to [62] the radar measurement error is impacted by radar
measurement precision (K
pc
), which is proportional to speckle noise, and any contributions from
calibration error or radio frequency interference (RFI). The noisy data for the radar measurement
precision contribution is modeled as
s
0
n
=s
0
+ k
pc
N(0;1)s
0
(6.2)
where s
0
n
is the generated noisy NBRCS, s
0
is the synthesized noise free NBRCS estimated
by SSBM in the backscatter direction, K
pc
is the measurement precision, and N(0;1) represents
a random number from Gaussian distribution with a zero mean and unit standard deviation. The
radar measurement precision is estimated as
K
pc
=
1
p
N
a
N
e
(1+
1
SNR
): (6.3)
where (K
pc
) is the normalized backscatter standard deviation of NBRCS, N
a
and N
e
are the
number of azimuth and elevation independent looks, and SNR is the ratio of NBRCS and the noise
equivalent NBRCS (s
0
NESZ
)
Table 6.2: D-SHIELD Instrument metrics and specifications (Incidence angle = 35
o
).
Parameter Instrument 1 Instrument 2 Instrument 3 Instrument 4
Incidence angle 35
o
35
o
35
o
35
o
Frequency 1:28 GHz 1:28 GHz 0:435 GHz 0:435 GHz
s
NESZ
-40.69 dB -40.69 dB -41.45 dB -41.45 dB
Number of looks 411 1=km
2
411 1=km
2
4213 1=km
2
4213 1=km
2
Swath 25 km 25 km 50 km 50 km
79
Table 6.3: D-SHIELD Instrument metrics and specifications (Incidence angle = 45
o
).
Parameter Instrument 1 Instrument 2 Instrument 3 Instrument 4
Incidence angle 45
o
45
o
45
o
45
o
Frequency 1:28 GHz 1:28 GHz 0:435 GHz 0:435 GHz
s
NESZ
-37.29 dB -37.29 dB -38.29 dB -38.29 dB
Number of looks 507 1=km
2
507 1=km
2
5195 1=km
2
5195 1=km
2
Swath 25 km 25 km 50 km 50 km
Table 6.4: D-SHIELD Instrument metrics and specifications (Incidence angle = 55
o
).
Parameter Instrument 1 Instrument 2 Instrument 3 Instrument 4
Incidence angle 55
o
55
o
55
o
55
o
Frequency 1:28 GHz 1:28 GHz 0:435 GHz 0:435 GHz
s
NESZ
-32.87 dB -32.87 dB -35.38 dB -35.38 dB
Number of looks 587 1=km
2
587 1=km
2
6018 1=km
2
6018 1=km
2
Swath 25 km 25 km 50 km 50 km
Table 6.5: D-SHIELD Coding
Code Meaning
0 No operation
1 incident angle = 35
o
, 1 observation
2 incident angle = 45
o
, 1 observation
3 incident angle = 55
o
, 1 observation
4 incident angle = 35
o
, 2 observations
5 incident angle = 45
o
, 2 observations
6 incident angle = 55
o
, 2 observations
Tables 6.2 to 6.4 include the D-SHIELD instrument metrics and specifications for three dif-
ferent operating points at three different incident angles, and the data presented in these tables
are used as inputs to the SSBM for the noise sensitivity analysis. In order to analyze the impact
of multi-instrument measurements on the RMSE between retrieved soil moisture value and actual
in-situ soil moisture measurements, the inversion algorithm is run for after precipitation event soil
moisture values (4 soil moisture values within 3 hours of in-situ measurements). Moreover, 5
regions with different vegetation types ( Figures 6.2, 6.6, 6.9, 6.12 and 6.15) are considered for
the sensitivity study. Table 6.5 presents the mapping codes and their meanings. These mapping
80
codes specify the incident angle and number of observations for each of the instruments expressed
in Tables 6.2 to 6.4.
Table 6.6: Walnut Gulch in-situ soil moisture measurements
Date Time Soil Moisture Value
08/02/2016 19:00 0.40016 m
3
=m
3
08/02/2016 20:00 0.36879 m
3
=m
3
08/02/2016 21:00 0.35471 m
3
=m
3
08/02/2016 22:00 0.3383 m
3
=m
3
Figure 6.4: Walnut Gulch Soil Moisture Time Series.
81
Figure 6.5: Walnut Gulch (shrubland) Soil Moisture RMSE.
82
Figure 6.6: SoilSCAPE Tonzi ranch, CA site. Image credit: https://daac.ornl.gov.
83
Table 6.7: Tonzi ranch in-situ soil moisture measurements.
Date Time Soil Moisture Value
05/15/2015 2:00 0.23378 m
3
=m
3
05/15/2015 3:00 0.22762 m
3
=m
3
05/15/2015 4:00 0.22055 m
3
=m
3
05/15/2015 5:00 0.21640 m
3
=m
3
Figure 6.7: Tonzi ranch Soil Moisture Time Series.
84
Figure 6.8: Tonzi ranch (Woody Savannah) Soil Moisture RMSE.
85
Figure 6.9: Airborne Microwave Observatory of Subcanopy and Subsurface (AirMOSS) Metolius, OR site. Image credit:
https://uavsar.jpl.nasa.gov.
86
Table 6.8: Metolius in-situ soil moisture measurements.
Date Time Soil Moisture Value
06/25/2013 6:00 0.2124 m
3
=m
3
06/25/2013 7:00 0.202 m
3
=m
3
06/25/2013 8:00 0.1981 m
3
=m
3
06/25/2013 9:00 0.1952 m
3
=m
3
Figure 6.10: Metolius Soil Moisture Time Series.
87
Figure 6.11: Metolius (evergreen forest) Soil Moisture RMSE.
88
Figure 6.12: Las Cruces, NM. Image credit: https://www.las-cruces.org.
89
Table 6.9: Las Cruces in-situ soil moisture measurements
Date Time Soil Moisture Value
01/31/2015 2:00 0.171 m
3
=m
3
01/31/2015 3:00 0.168 m
3
=m
3
01/31/2015 4:00 0.167 m
3
=m
3
01/31/2015 5:00 0.163 m
3
=m
3
Figure 6.13: Las Cruces Soil Moisture Time Series.
90
Figure 6.14: Las Cruces (bare surface) Soil Moisture RMSE.
91
Figure 6.15: Soil Moisture Active Passive (SMAP) Yanco site, Australia. Image credit: http://www.oznet.org.
92
Table 6.10: Yanco in-situ soil moisture measurements
Date Time Soil Moisture Value
10/12/2017 23:00 0.3036 m
3
=m
3
10/12/2017 0:00 0.2908 m
3
=m
3
10/12/2017 1:00 0.2789 m
3
=m
3
10/12/2017 2:00 0.2733 m
3
=m
3
Figure 6.16: Yanco Soil Moisture Time Series.
93
Figure 6.17: Yanco (cropland) Soil Moisture RMSE.
94
Figures 6.4, 6.7, 6.10, 6.13 and 6.16 illustrate the time series in-situ soil moisture measure-
ments for Walnut Gulch (located in Arizona, US), Tonzi ranch (located in California, US), Metolius
(located in Oregon, US), Las Cruces (located in New Mexico, US), and Yanco (Located in Aus-
tralia) sites, respectively. Tables 6.6 to 6.10 present the date and time of the in-situ soil moisture
measurements for the selected sites after the precipitation event, during which the soil moisture
values vary significantly.
The D-SHIELD instrument metrics and specifications provided in Tables 6.2 to 6.4 along with
the in-situ soil moisture measurements data given in Figures 6.4, 6.7, 6.10, 6.13 and 6.16 are used
in the inversion algorithm for estimating the RMSE between the retrieved soil moisture and in-situ
measured soil moisture values. Moreover, Equation (6.1) with k
p
= 0:11 is used in the SSBM
forward model in order to model the system noise and generate the noisy NBRCS based on the
Monte Carlo scheme discussed in Section 6.2.
Figures 6.5, 6.8, 6.11, 6.14 and 6.17 present the RMSE of the retrieved soil moisture and in-situ
measured soil moisture values for multi-instrument observations in the presence of system noise.
The horizontal axis of these figures represents different measurement codes, which are provided
in Table 6.5. The system noise sensitivity study presented in Figures 6.5, 6.8, 6.11, 6.14 and 6.17
show that the RMSE in estimation of soil moisture is sensitive to vegetation land cover type and
the number of instruments used for the observations. The upper bound of the RMSE in estimation
of soil moisture is below 0.035 for all the vegetation types.
Furthermore, based on the numerical results presented in presented in Figures 6.5, 6.8, 6.11,
6.14 and 6.17, it can be inferred that the radar observations with single instrument lead to lower
RMSE in soil moisture estimation compare to multi-instrument observations. In order to analyze
the impacts of both system noise (k
p
) and the speckle noise (k
pc
) on the RMSE of estimated soil
moisture for multi-instrument observations, the Equations (6.1) and (6.2) are combined
s
0
n
=s
0
+(k
p
+ k
pc
) N(0;1)s
0
(6.4)
95
Figure 6.18: Walnut Gulch (shrubland) Soil Moisture RMSE.
96
Figure 6.19: Tonzi ranch (Woody Savannah) Soil Moisture RMSE.
97
Figure 6.20: Metolius (evergreen forest) Soil Moisture RMSE.
98
Figure 6.21: Las Cruces (bare surface) Soil Moisture RMSE.
99
Figure 6.22: Yanco (cropland) Soil Moisture RMSE.
100
Figures 6.18 to 6.22 present the numerical results for the RMSE in estimation of soil moisture
in the presence of system noise and speckle noise for multi-instrument observations and different
land cover types. Compare to the previous sensitivity results depicted in Figures 6.5, 6.8, 6.11,
6.14 and 6.17, the numerical results presented in Figures 6.18 to 6.22 show that the RMSE in the
estimation of soil moisture is significantly increased in the cases, where both the system noise and
the speckle noise are considered ( Figures 6.18 to 6.22).
Moreover, for densely vegetated terrains such as Metolius, OR site ( Figure 6.20) the multi-
instrument observations, which include soil moisture observation with more than one P-band in-
strument, lead to lower RMSE in estimation of soil moisture. The EM signals transmitted from
P-band radar instruments can penetrated into terrains with densely vegetation layers, which result
in higher sensitivity to variations in soil moisture and lower RMSE in the estimated soil moisture
value.
On the other hand, the EM signals transmitted from L-band radar instruments show higher
sensitivity to soil moisture in the low-vegetated sites such as Walnut Gulch, Yanco, and Las Cruces.
The sensitivity analysis numerical results presented in Figures 6.18, 6.19, 6.21 and 6.22 show that
the multi-instrument radar observation at L-band results in lower RMSE in soil moisture estimation
for low-vegetated terrains.
6.4 Conclusion
From the noise sensitivity study discussed in this chapter, it can be deduced that the multi-instrument
observations of soil moisture at L-band and P-band result in more accurate soil moisture retrievals
compare to observations with single instrument. Moreover, it was shown that for the purpose of
soil moisture retrieval over densely vegetated terrain, e.g., Metolius, the P-band multi-instrument
measurements have better performance in comparison with the L-band multi-instrument and P-
band single instrument measurements. Furthermore, for the case of soil moisture observations
101
over low-vegetated terrains, e.g., Walnut Gulch site, and bare surfaces, e.g., Las Cruces site, the
multi-instrument L-band measurements lead to more accurate soil moisture retrieval results.
The noise sensitivity analysis so far addressed the single and multi-instrument monostatic radar
observations in different configurations for various types of land cover. This work will be extended
to include the noise sensitivity analysis for the bistaic radar systems, e.g., CYGNSS measurements.
Moreover, the noise sensitivity analysis has been performed by using the SSBM with the assump-
tion of flat topography. However, in future work the SSBM will be enhanced to include the vege-
tated terrains with non-flat topography, and ultimately it will be used for noise sensitivity analysis
of various types of land cover with consideration of topography in support of D-SHIELD.
102
Chapter 7
Summary and Future Work
Advancement of a radar scattering model from monostatic to fully bistatic creates the opportu-
nity to exploit measurements of scattered fields from vegetated landscapes in arbitrary directions,
as might be available from signals of opportunity (SoOp) such as global navigation satellite sys-
tem (GNSS)/global positioning system (GPS) reflected signals. We developed a physics-based
single-species bistatic scattering forward model, the SSBM, for soil moisture retrieval from GNSS
reflected signals over various terrains, including vegetated land covers. Unlike scattering mod-
els based on radiative transfer (RT), the proposed bistatic scattering model formulates the scat-
tered waves based on the distorted Born approximation (DBA). Previous approaches for soil mois-
ture retrieval from Cyclone Global Navigation Satellite System (CYGNSS) delay-Doppler maps
(DDMs) utilized empirical or regression-based methods for soil moisture retrieval over bare or
low-vegetated land cover. Those methods are not applicable to retrieve soil moisture in the pres-
ence of moderate-to-densely vegetated land covers. Whereas, The developed retrieval algorithm
has the capability of retrieving soil moisture even in the presence of densely vegetated land covers.
The three main scattering mechanisms for the SSBM are discussed and the total normalized
bistatic radar cross section (NBRCS) values analyzed via forward model simulation results. The
potential applicability of this bistatic scattering model for soil moisture estimation was demon-
strated through numerical simulations and sensitivity analysis with respect to soil moisture content
and vegetation water content (VWC) for three different land cover types. It was shown that sen-
sitivity to VWC was highly reduced in the specular direction, whereas sensitivity to soil moisture
103
was preserved. This finding has potential for more accurate soil moisture retrievals regardless of
the amount of VWC.
The DDM model was developed to include the circularly polarized incident and scattered wave
cases. Consequently, this model is capable of generating the DDMs of SoOp for various vegetated
terrains. Finally, the proposed forward model was evaluated with the GNSS Reflectometer Instru-
ment for Bistatic Synthetic Aperture Radar (GRIBSAR) measurements at Tonzi ranch located in
the central valley of California. Moreover, the developed retrieval algorithm was evaluated with
measured CYGNSS DDMs (version 2.1). Two retrieval schemes were proposed and analyzed.
In the first scheme, the retrieval was performed with the assumption that root mean square (RMS)
surface roughness is a known parameter, and soil moisture is unknown. In the second scheme, both
soil moisture and RMS surface roughness were considered unknowns. The soil moisture retrievals
from the CYGNSS DDMs had a unbiased root mean square error (ubRMSE) less than 0:1 m
3
=m
3
for both retrievals schemes, with insignificant bias. Thus, The simulation results of the proposed
inversion algorithm showed the capability of soil moisture retrieval from CYGNSS DDMs.
In Future, the retrieval algorithm will be used as a basis for more advanced retrieval algorithms.
One way of advancing the algorithm is to integrate the SSBM presented in chapter 3 with the
DDM model proposed in [63] to extend the model for heterogeneous surfaces and topography.
Furthermore, to solve the under-determined issue in the second scheme, multiple DDMs within a
small spatial and temporal window can be used to retrieve both the soil moisture values and the
RMS surface roughness. However, this will increase the complexity and the computational cost of
the retrieval algorithm.
A comprehensive noise sensitivity analysis for single and multi-observations of soil moisture
was presented. According to numerical simulation results of the noise sensitivity study, the root
mean square error (RMSE) in estimation of soil moisture for multi-instrument observation of soil
moisture at L-band and P-band provide more accurate soil moisture retrievals compare to single
instrument observations.
104
The noise sensitivity study presented in chapter 6 will be extended to include the noise sensi-
tivity analysis for the bistaic radar systems such as CYGNSS and SigNals of Opportunity P-band
Investigation (SNoOPI). Furthermore, the noise sensitivity study discussed in chapter 6 has been
performed with the assumption of flat surface for the ground layer in the SSBM, and it has been
applied over regions with no-topography. However, in the future work the SSBM will be further
developed to include the vegetation diversity with non-flat topography. Ultimately the updated
SSBM will be used for noise sensitivity analysis of single and multi-instrument observations of
soil moisture over various types of land cover with consideration of topography in support of D-
SHIELD.
105
Acronyms
AirMOSS Airborne Microwave Observatory of Subcanopy and Subsurface
AIRSAR Airborne Synthetic Aperture Radar
ALOS Advanced Observing Satellite
ANN artificial neural network
AUS Australia
B branch
BG branch ground
Bi-MIMICS bistatic MIMICS
BRCS bistatic radar cross section
C/A coarse acquisition
CONUS continental United States
CYGNSS Cyclone Global Navigation Satellite System
D-SHIELD Distributed Spacecraft with Heuristic Intelligence to Enable Logistical Decisions
DBA distorted Born approximation
DDM delay-Doppler map
106
DDMI delay Doppler mapping instrument
EM electromagnetic
EnviSat Environmental Satellite
ESA European Space Agency
FFT fast Fourier transform
FSA forward scattering alignment
G ground
GNSS global navigation satellite system
GNSS-R GNSS-reflectometry
GPS Global Positioning System
GRIBSAR GNSS Reflectometer Instrument for Bistatic Synthetic Aperture Radar
IGBP The International Geosphere–Biosphere Programme
ISMN International Soil Moisture Network
JPL Jet Propulsion Laboratory
KA Kirchhoff approximation
L1B Level 1B
LEO low Earth orbit
LHCP left-handed circularly polarized
MIMICS Michigan microwave canopy scattering
MiXIL Microwave Systems, Sensors, and Imaging Laboratory
107
ML machine learning
NASA National Aeronautics and Space Administration
NBRCS normalized bistatic radar cross section
NSF National Science Foundation
OSSE Observing System Simulation Experiment
PDF probability density function
PLIS Polarimetric L-band Imaging Synthetic Aperture Radar
RCS radar cross section
RF random forest
RFI radio frequency interference
RHCP right-handed circularly polarized
RMS root mean square
RMSE RMS error
RT radiative transfer
SCoBi-Veg signals of opportunity coherent bistatic scattering model for vegetated terrains
SEBCM stabilized extended boundary condition
SMAP Soil Moisture Active Passive
SMOS Soil Moisture and Ocean Salinity
SNoOPI SigNals of Opportunity P-band Investigation
SNR signal-to-noise ratio
108
SoilSCAPE Soil moisture Sensing Controller and oPtimal Estimator
SoOp signal of opportunity
SP specular point
SPM small perturbation method
SSBM single-species bistatic scattering model
SVM support vector machine
TG trunk ground
UA VSAR Uninhabited Aerial Vehicle Synthetic Aperture Radar
ubRMSE unbiased RMSE
USC University of Southern California
VHF very high frequency
VWC vegetation water content
WAF Woodward ambiguity function
109
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114

Abstract (if available)

Abstract Soil moisture is a key variable in studying the global ecosystems, exerting first-order control on land-atmosphere interactions. Quantifying soil moisture fields is needed for improving our knowledge of the water, carbon, and energy cycles. Soil moisture measurements on global and local scales contribute to many areas of human interest such as weather and climate forecasting, flood prediction, drought analysis, crop productivity evaluation, and human health. Thus, developing novel and reliable soil moisture observation and retrieval techniques is a subject of great interest. We begin by presenting the physics based bistatic radar scattering forward model from signals of opportunity (SoOp) at L-band and P-band/very high frequency (VHF) for both bare surfaces and vegetated land covers, including forests, in support of soil moisture retrieval. The interest in developing bistatic scattering models stems from the observation that existing SoOp, such as those transmitted by global positioning system (GPS)/global navigation satellite system (GNSS) signals, can be used in lieu of conventional mono-static radar transmitters, as long as the appropriate receiver systems and retrieval methods can be developed. Such an approach to a “passive” radar results in substantially reduced hardware costs, but at the expense of modeling and retrieval complexity. It also enables enhanced sensitivity to soil moisture and reduced sensitivity to vegetation water content (VWC). The physics-based bistatic scattering forward model has three main scattering mechanisms, including a direct bistatic scattering from vegetation volume, a direct bistatic scattering from a flat ground surface with small roughness, and a double-bounce bistatic scattering from the vegetation layer and the ground. All mechanisms are considered simultaneously in the bistatic scattering geometry and treated using wave-based coherent models. The total bistatic radar cross section (BRCS) of the forest will be determined by superimposing the BRCS for each of the specified contributions. Next, the bistatic scattering model is investigated via a thorough sensitivity analysis with respect to soil moisture and vegetation water content (VWC) for different land covers through a comprehensive set of numerical simulations, which leads to selection of optimal incidence angle for best soil moisture retrieval results. Moreover, the bistatic scattering model is validated with the GNSS Reflectometer Instrument for Bistatic Synthetic Aperture Radar (GRIBSAR) and NASA Cyclone Global Navigation Satellite System (CYGNSS) delay-Doppler maps (DDMs). Finally, we present a soil moisture retrieval scheme from CYGNSS over land DDMs. The inversion algorithm consists of a hybrid global and local optimization method and a physics-based bistatic scattering forward model, which estimates the circularly polarized BRCS of the land surface, and it is applicable to bare-to-densely vegetated terrains. The proposed inversion method is utilized for soil moisture retrieval from CYGNSS DDMs over the Soil Moisture Active Passive (SMAP) Yanco site located in Australia. Ultimately, the retrieved soil moisture values are validated with the SMAP in-situ soil moisture measurements.

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Creator Azemati, Amir (author)

Core Title Physics-based bistatic radar scattering model for vegetated terrains in support of soil moisture retrieval from signals of opportunity

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Degree Conferral Date 2021-08

Publication Date 07/15/2021

Defense Date 05/06/2021

Publisher Los Angeles (original), University of Southern California (original), University of Southern California. Libraries (digital)

Tag Airborne Microwave Observatory of Subcanopy and Subsurface (AirMOSS),bistatic radar,Cyclone Global Navigation Satellite System (CYGNSS),delay-Doppler map (DDM),Distributed Spacecraft with Heuristic Intelligence to Enable Logistical Decisions (D-SHIELD),global navigation satellite system-reflectometry (GNSS-R),Global Positioning System (GPS),GNSS Reflectometer Instrument for Bistatic Synthetic Aperture Radar (GRIBSAR),OAI-PMH Harvest,remote sensing,signals of opportunity-reflectometry (SoOp-R),soil moisture,Soil moisture Sensing Controller and oPtimal Estimator (SoilSCAPE)

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Language English

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Advisor Moghaddam, Mahta (committee chair), Chen, Shuo-wei (committee member), Sanders, Kelly (committee member)

Creator Email aazemati@gmail.com,azemati@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC15491154

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Legacy Identifier etd-AzematiAmi-9743

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Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given.

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA

Repository Email cisadmin@lib.usc.edu