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A comparative study of ground and satellite evapotranspiration models for southern California

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A comparative study of ground and satellite evapotranspiration models for southern California

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A Comparative Study of Ground and Satellite Evapotranspiration
Models for Southern California

by

Jeffrey K. Snoddy

A Thesis Presented to the
Faculty of the USC Graduate School
University of Southern California
In Partial Fulfillment of the
Requirements for the Degree
Master of Science
(Geographic Information Science and Technology)

December 2018

Copyright © 2018 by Jeffrey K. Snoddy
All rights reserved

Dedicated to the members of my biggest fan club, consisting of “Little One”, Bailey, Noriko, and
Marshmallow. They have supported me the entire way, despite the time I have spent away from
home. Though I stumbled and felt frustrated at times, not once did they think I could fail.

iv

Table of Contents

List of Figures.………………………………………………………………………………....vii
List of Tables......………………………………………………………………………….…...viii
Acknowledgements….……….……………………………………………….…………….…ix
List of abbreviations….……………………………………………………………………......x
Abstract.……………………………………………………………………………….…........ xii
Chapter 1 Introduction.……………………………………………………….…………..…...1
1.1 Motivation...……...…………………………………………………………….……...1
1.2 Evapotranspiration......………………………………………………………………...10
1.2.1 Evaporation Model – Penman-Monteith………………..…………….………....11
1.2.2 Evaporation Model – NDVI Triangle…………………………...……………....11
1.3 Study Area................ ….………………………….………………………….………..11
1.4 Research Objectives................…………………….………………………….……….14
1.5 Thesis Organization.................…………………….………………………….………14
Chapter 2 Related Work.…………………………………………………………….………...15
2.1 Water Conservation Efforts……………………………………………………….......16
2.2 Penman-Monteith Reference Evapotranspiration Model.…….................……….........17
2.3 Triangle Method Model …………………………….…………………………….…...21
2.3.1 Triangle Method Workflow........……………………………………………..…..21
2.4 Penman-Monteith Model vs Triangle Method………………………………………....23
Chapter 3 Methodology……………………………………………………………………......25
3.1 Research Design.……...……………………………………………………………….25
3.2 Penman-Monteith Evapotranspiration Model............…….………………………..25

v

3.2.1 CIMIS Sensor………………………………………………………….………...26
3.2.2 Sensor Data Collection...………….………………………….…………….…....28
3.2.2.1 Total Solar Radiation………………………………………………………28
3.2.2.2 Soil Temperature...…….…………………….………………………….....29
3.2.2.3 Air Temperature/Relative Humidity.….…………………………………...29
3.2.2.4 Wind Direction / Wind Speed…….………………………………………..30
3.2.2.5 Slope of Saturation Vapor Pressure Curve (Δ)…………………………….30
3.2.2.6 Atmospheric Pressure (P)……………………………….…………………30
3.2.2.7 Mean Saturation Vapor Pressure………………………………….….…....30
3.2.2.8 Actual Vapor Pressure (ea.) …...…………………………………………..31
3.3 NDVI Triangle Method...……………………………………………………………...31
3.3.1 Data Collection….……………………………………………………………….33
3.3.2 Workflow……………………………………………………………………...…34
3.4 Statistical Analysis.….…………………………………………………...……………35
Chapter 4 Results………………………………………………………………………………38
4.1 Penman-Monteith Results......………………………………………………….………39
4.2 Triangle Method Results…………………………………….…...……………………40
4.3 Comparison.……...…………………………………………………………………….44
Chapter 5 Conclusions.…………...………………………………………….…………..........45
5.1 Discoveries......................................................................................................................45
5.2 Considerations and Limitations.......................................................................................47
5.3 SWOT Analysis.……...…………………………………………………………….......48
5.3.1 Strength…………………………………………………………………………...48
5.3.2 Weaknesses……………………………………………………………………….49

vi

5.3.3 Opportunities……………………………………………………………………...49
5.3.4 Threats…………………………………………………………………………….50
5.4 Future Work…………………………………………………………………………......51
References………………………………………………………………………………………52
Appendix A Tables……………………………………………………………………………...56

vii

List of Figures

Figure 1. Ten hydrologic regions for the state of California…………………………………....2
Figure 2. The process of evapotranspiration via water loss by evaporation and transpiration …5
Figure 3. Plot showing MNWD’s average solar radiation and precipitation for 2016………….6
Figure 4. California drought conditions year comparison (May 2007 vs May 2017)…..………7
Figure 5. Processed annual maximum temperature & normal yearly precipitation from 1981 to
2010……………………………………………………………………………………………...8
Figure 6. Quantified 2015 urban water flow nodes and water use in California……………….10
Figure 7. (MNWD) study area selected for evapotranspiration comparative study…………....12
Figure 8. CIMIS weather stations in California…………………..…………………………….15
Figure 9. Coto De Caza CIMIS weather sensor #245…………………………………………..27
Figure 10. Calculation of estimated evapotranspiration by NDVI in triangular space………....32
Figure 11. Identification of areas of potential high ET by the use of albedo in the MNWD study
area……………………………………………………………………………....….……..........33
Figure 12. NDVI Data processing workflow for NDVI Triangle method.....……........………..35
Figure 13. Two-dimensional scatter plots of satellite pixel values of NDVI versus the average of
Top of Atmospheric (TOA) spectral radiance from LCDM satellite imagery)………...……….43

viii

List of Tables
Table 1. Summary of data needs for Penman-Monteith…………………………………...........18
Table 2. CIMIS Station# 245 reference data on four days.……………………………………..40
Table 3. Results of four days of NDVI Triangle Method calculations on a cloudless day…......43
Table 4. Penman-Monteith vs Triangle Method......…………………………………..………...44
Table 5. Summary of equipment and software needs for Normalized Difference Vegetation Index
(NDVI) equation………………………………………………………………………………...56
Table 6. Downloaded earth explorer Landsat Data Continuity Mission (LDCM) satellite
imagery...……………………………………………………………………………………..…56
Table 7. Calculation of Reflectance for study area using multispectral
calculations.……………………………………………………………………………………..56
Table 8. Calculation of Albedo from multispectral bands 1,2,3,4 and
5…………………………………………………………………………………………………57
Table 9. Calculation of NDVI from Near Infrared (NIR) and Red multispectral
bands…………………………………………………………………………………………….57
Table 10. Resize data using pixel aggregation resampling methods……………………....……57
Table 11. Calculation of Weighted Difference Vegetation Index (WDVI) from multispectral
bands 3, 4 and the y intercept from the resampled data…………………..…………………….58
Table 12. Calculation of the soil brightness correction L Value from NDVI and WDVI……...58
Table 13. Calculation of Soil-adjusted Vegetation Index (SAVI) from bands 3, 4, and the L value
…………………………………………………………………………………………………..58
Table 14. Calculation of the Leaf Area Index (LAI) from the SAVI values…….……………..58
Table 15. Calculation of surface emissivity from calculated LAI…………..………………….58
Table 16. Calculation of Thermal Infrared (TIR) from LCDM multispectral bands 10 and
11….…………………………………………………………………………………….………59
Table 17. Calculation of the canopy resistance to vapor transit (Rc) from both Thermal Infrared
(TIR) bands…………………………………………………………….………………………..59
Table 18. Calculation of Top of Atmospheric (TOA) spectral radiance from Band 10………...59
Table 19. Calculation of Top of Atmospheric (TOA) spectral radiance from Band 11……......59
Table 20. Conversion of TOA average temperatures from K to °C ……………………………59
Table 21. Conversion to °C from K by adding absolute zero …….………………………….....59

ix

Acknowledgements
I would like to thank my primary advisers consisting of Drs. Darren Ruddell, John Wilson, Andrew
Marx, Elisabeth Sedano, and Vanessa Osborne and the many instructors throughout my time in
this program. They provided proper feedback, established parameters for my study, and tightened
my focus. Special thanks go out to Ken Watson who guided me through the start of my application
process.

x

List of Abbreviations
ASCE American Society of Civil Engineering
AWS Amazon Web Services
°C Celsius
d Solar Declination
dr Relative Distance Earth-Sun
DT Delta Term (auxiliary calculation for Radiation Term)
ea Actual Vapor Pressure
ENVI Environment for Visualizing Images
ESRI Environmental Systems Research Institute
ETₒ Reference Evapotranspiration Value
ETrad Radiation Term
ETwind Wind Term
EWRI Environmental and Water Resource Institute
F Fahrenheit
FAO – 56 Food and Agriculture Organization Irrigation and Drainage Paper 56
GIS Geographic Information Systems
K Kelvin
LAEMD Los Angeles Emergency Management Department
LAI Leaf Area Index
LCDM Landsat Data Continuity Mission
MNWD Moulton Niguel Water District
MODIS Moderate Resolution Imaging Spectroradiometer

xi

NDVI Normalized Difference Vegetation Index
P Atmospheric Pressure
PT Psi Term (auxiliary calculation for wind Term)
Ra Extraterrestrial Radiation
Rc Canopy resistance to vapor transit (sm-1)
Rn Net Radiation
Rnl Net Outgoing Long Wave Solar Radiation
Rns Net Shortwave Radiation
Rs Mean Daily Solar Radiation
Rso Clear Sky Radiation
SAVI Soil-adjusted Vegetation Index
TT Temperature Term (auxiliary calculation for Wind Term)
u2 Wind Speed
WDVI Weighted Difference Vegetation Index
Δ Slope of Saturation Vapor Pressure Curve
γ Psychrometric Constant
φ Latitude
ῳ Sunset Hour Angle

xii

Abstract

This project offers a comparative study between a ground-based weather station and
satellite-based method of calculating evapotranspiration (ET). Using four selected cloudless days
measured between 10:28 am and 11:30 am DST local in Los Angeles in 2016 (08 February, 19
April, 22 June, and 08 July), the aim of this project is to determine if the Normalized Difference
Vegetation Index (NDVI) Triangle method, a satellite-based methodology, could be used as an
acceptable alternative to measure ET for locations without a ground-based weather station.
The Moulton Niguel Water District (MNWD), located in Orange County, California was
selected as the study area for this project. Weather station #245, located on the Coto De Caza
golf course, generated the ground-based weather data for the Penman-Monteith calculation of
evapotranspiration for the MNWD. In contrast, the satellite method used the Landsat Data
Continuity Mission’s (LDCM) multispectral and thermal bands to calculate ET by Land Surface
Temperature (LST) and NDVI values. These two data inputs, by the application of band math,
were combined to create a two-dimensional NDVI Triangle pixel plot evapotranspiration
estimate for each day calculated. The data from the two methodologies were then compared,
with the assumption the Penman-Monteith method was the most accurate measure of ET.
The results were statistically compared and analyzed for accuracy through Root Mean Square
Error (RMSE), Mean Absolute Deviation (MAD), Mean Absolute Percentage Error (MAPE) and
the coefficient of determination calculations. The results, although limited by sample size,
indicate the NDVI Triangle method can be used to estimate ET. The process of creating the
NDVI Triangle 2-D plot from multispectral and thermal bands from the LDCM is presented in
detail, in addition to the process of defining the dry and wet edges of the plotted NDVI Triangle.

1

Chapter 1 Introduction
Governor Jerry Brown’s Executive Order B-37-16 stipulated that California’s water retailers must
reduce urban water use by 20% by the year 2020. This project researches how to meet that 20%
reduction of urban water use through a comparison calculation of evapotranspiration models. This
project compares local ET measurement with ground-based weather stations to large-scale ET
measurement through orbiting satellites.
1.1 Motivation
On 17 January 2014, Governor Jerry Brown declared a drought state of emergency to
reflect the status of the reservoirs and lakes, which were below their record low with the snowpack
20 percent below average. In addition, Executive Order B-29-15 imposed restrictions to achieve a
25% reduction in urban water use and replace 50 million square feet of lawns with drought-
resistant landscapes (Marcus et al. 2018). This executive order was executed successfully with an
achievement of near the 25% reduction target for urban water use. Governor Brown then issued
Executive Order B-37-16 to continue to build upon that success. Executive Order B-37-16 created
long-term water conservation measures and set a new urban water use target of 20 percent
reduction by the year 2020 (Marcus et al. 2018). On 07 April 2017, due to heavy precipitation
conditions, lowered temperatures, and heavy snow fall, Governor Brown issued Executive Order
B-40-17, declaring the drought over in but four California Counties: Fresno, Tulare, Kings, and
Tuolumne (Marcus et al. 2018).

2

Figure 1 Ten hydrologic regions for the State of California
(Source https://water.usgs.gov/edu/watercycleevapotranspiration.html)

3

This thesis focuses on hydrological region four, which is where the MNWD is located as
seen in Figure 1. The State of California has continually adjusted to the depreciation of urban water
supplies in the event of a drought. Executive B-37-16 was created to mitigate an overuse of water
by setting new urban water conservation targets for California’s urban water retailers.
Instead of using a percentage from a baseline to measure water savings, the unique climate
demographic and land-use characteristic of each urban service area will be the new standard of the
measure of successful adherence to Executive Order B-37-16 (Marcus et al. 2018). This order
states:
The water use targets shall be customized to the unique conditions of each water agency,
shall generate more statewide water conservation than existing requirements, and shall be
based on strengthened standards for:
A. Indoor residential per capita water use;
B. Outdoor irrigation, in a manner that incorporates landscape area, local climate, and
new satellite imagery data;
C. Commercial, industrial, and institutional water use; and
D. Water lost through leaks (Marcus et al. 2018).
The new urban water reduction methods are individually based on how the different water
districts intend to apply water reduction initiatives. California population trends are creating areas
of heavy irrigation, high population and increasing population density. Gleick (1998) observes
large urban growth has been supported by sourcing water from out-of-state urban water regions,
like the Colorado River via the Colorado River Aqueduct, and snowpack levels for in-state
demands requirements. Approximately 50 percent of the water used throughout Orange County

4

comes from imported supplies (MWDOC 2017). California conservation efforts are critical if we
are to lessen reliance on external water supplies. Evapotranspiration, which dictates how much
water is needed for an irrigable field to remain fertile, is a critical key point for reducing urban
water use per the Executive Directive B-37-16.
Urban water conservation efforts have been very active for the State of California. The
primary user of urban water is outdoor irrigation and irrigated agriculture. The motivation to
conserve water, especially saving from outdoor use, is to create more water available for residential
areas and the environment. Gleick et al. (2003) estimated, in 2003, that a 25-40 percent reduction
in outdoor residential water use, (360,000 – 580,000 acre/feet per year) could be conserved if the
proper conservation efforts were put in place.
Entities with a large space to irrigate, the primary way to determine the amount of water to
ensure their crops stay fertile or golf greens stay playable without the waste of water resources, is
by using and acting upon the value of calculated evapotranspiration. That is obtained through a
variety of methodologies with acquired data specifically for that microclimate.
This project seeks to discover if the NDVI Triangle, a versatile method with the ability to
cover large geographical areas from space, can be utilized as an acceptable method for accurately
calculating ET. This will be determined by comparing ET values obtained from the LDCM to the
California Irrigation Management Information System (CIMIS) weather station #245 (Coto de
Caza) which uses the Penman-Monteith Method for ET calculation. The accuracy and feasibility of
this new method will be decided by statistical analysis. All CIMIS weather stations in California
and, for the most part, the remainder of the world, uses the Penman-Monteith model to measure
and calculate Evapotranspiration (Temesgen et al. 2018).

5

Evapotranspiration is the measure of how quickly, over time, water is evaporated from a
defined vegetated surface (Zotarelli et al. 2009). Evapotranspiration (ET) is therefore a term that
explains surface water loss by two processes: evaporation and transpiration. Evaporation is the
process by which liquid waters is converted to water vapor from land surfaces and lakes, while
transpiration is the process of the vaporization of water within a plant and plant stomata (Zotarelli
et al. 2009). Transpiration and evaporation happen simultaneously and cannot be separated as two
individual actions for evapotranspiration as seen in Figure 2. An accurate reference
evapotranspiration, or better recognized as ET, is vital to reduce over and under use of water for
irrigated surfaces. This may serve as an urban water use indicator to ensure as much water as
possible is being conserved when irrigating.

Figure 2 The process of evapotranspiration via water loss by evaporation and transpiration
(Source https://water.usgs.gov/edu/watercycleevapotranspiration.html)
In line with supply chain resiliency research performed for sectors critical to the City of Los
Angeles by the Los Angeles Emergency Management Department (LA EMD) in collaboration with
a Federal Emergency Management Agency Technical Assistance Team (FEMA-TA), this project
looks for ways to decrease the waste of urban water resources. This is to be done by establishing
and proving the most versatile and acceptably accurate way to measure ET in areas, without a local

6

means to measure, by comparative studies. As water resources are at a premium, we need to
conserve water, fill our reservoirs, and establish a set of guidelines for urban water use in
preparation for our next drought.
California has suffered greatly from extreme drought conditions from 2007-2009 and 2011-
2017, with conditions that have not been seen for over 1,200 years. (Griffin and Anchukaitis 2014).
California’s drought conditions were further exacerbated by the increased temperature and the lack
of precipitation in California as seen in Figure 3 and 4. When there is a lack of rain accompanied
by high temperatures as seen in Figure 5, the combination of low precipitation and increased heat
leads to a greater probability of a higher occurrence of drought conditions (Diffenbaugh, Swain and
Touma 2015). In addition, ET will increase, assuming water is available for transmission into the
atmosphere.

Figure 3 Plot showing MNWD’s average solar radiation and precipitation for 2016
(Source: Temesgen et al. 2018)

7

This study aims to advance Governor Jerry Brown’s Executive Directive B-37-16 which
sets new water efficiency targets for California’s urban water retailers. By calculating the best
reference ET for irrigable areas, which is a large percentage of water usage in California and is a
main target in the urban water reduction plan, irrigation can be turned off when unneeded. The
calculation of ET reduces overwatering and decreases the waste of our water resources by the
largest water users. This study explores the possibility of a reflective reference and a
geographically expansive ET value, for areas without a ground-based weather station, using
satellite imagery. Executive Directive B-37-16 intends to preserve more water resources for urban
users in the event of another drought. In addition, this directive anticipates continued population
growth for the State of California.

Figure 4 California drought conditions year comparison (May 2007 vs May 2017)
(Source: Blunden 2018)

8

Figure 5 Processed annual maximum temperature & normal yearly precipitation from 1981
to 2010
(Source: McCarthy 2017)

California is the most populous State in the United States, with a population of nearly 40
million and grew at 0.7% in 2017 (Crane et al. 2018). Though not directly part of this project,
California’s progressive population growth continues to place a strain upon the State’s water
resources. The increase in residents has also increased the density of population centers within the
city. This, in turn, has created even a greater demand for water. The population of California went
from 10 million residents in 1950 to more than 39 million residents in 2016 and the state’s
population is predicted to reach 50 million residents by the year 2050 (Johnson 2017). There are
extremely heavily populated centers within the state that creates a need for resources sustainment,
preservation, and conservation. This large California population base creates an extreme need for

9

urban water resources in an area that naturally, not sustainable as an independent water supply
node.
Precisely calculating urban water use in California is very challenging. It is an extremely
complex system with diverse supply and demands nodes with multiple owners and complicated
interoperability systems and processes. This adds a great deal of difficulty in achieving California’s
urban water use targets as set by the Governor. For example, potable and non-potable sources for
California is a combination of imported water, local groundwater, reclaimed water, and recycled
water. Water supply flows from water desalination plants, precipitation, ground water, purchased
water, surface water, and water storage supplies as seen in Figure 6 (Allen et al. 2017). California’s
water resources provide not only drinking water but also water for irrigation and wetland
maintenance. The California water supply is broken into many uses throughout the state, with over
40% going to agricultural irrigation and a small percentage going to urban water for personal use as
seen in Figure 6 (Allen et al. 2017). This would seem to indicate irrigated agriculture is the “low
hanging fruit” to research water conservation for the State of California. Previous water saving
initiatives, in response to earlier droughts, had focused on constricting residential water use. This
effort effectively reduced water waste for California residents. However, with most of urban water
utilized for land irrigation, further constrictions in residential water use would not produce the
desired outcome of reducing water use while meeting the Governor’s urban water conservation
targets. This project explores how to meet that 20% reduction of urban water use through a
comparison of evapotranspiration models and methodologies for irrigated lands.

10

Figure 6 Quantified 2015 urban water flow nodes and water use in California
(Source: Allen et al. 2017)

1.2 Evapotranspiration
There are two different measures of evapotranspiration: Potential Evapotranspiration (PE)
and Actual Evaporation (AE). Potential Evapotranspiration (PE) measures how effective the
atmosphere removes water from the surface using evaporation and transpiration with an unlimited
water supply (Pidwirny 2006). PE is an energy-driven process, with the majority (80%) of it
coming from the sun. Wind is the second factor as wind removes water from the ground to the
atmosphere by a process called eddy diffusion (Pidwirny 2006). In addition, the gradient of vapor
pressure plays a major role in accelerating the evapotranspiration rate (Pidwirny 2006). These two
measures are then used to calculate how much water the crops need. Actual Evaporation is the
water that is removed from the effects of evaporation and transpiration (Pidwirny 2006). California
is a semi-arid region which makes it critical every drop of water is being used in the most efficient

11

manner possible. Comprehending how much water is needed, can save hundreds of thousands of
gallons of water if properly calculated. An ET of 25.4 mm or one inch means the farmer needs to
irrigate with 27,154 gallons to replace the water lost to the evapotranspiration.
As an example, say that a farmer mistakenly overestimated and calculated his reference ET,
the water lost from land surfaces, stomata, and vegetation, as 0.5 inch for that day when it was only
0.35 inch. That means the farmer will irrigate the crops with wasted extra gallons of water. Not
only is that urban water waste but, it could mean an overwatering of the field, flooding of new
seedlings, washing away of topsoil, and ruination of the crop.
1.2.1 Evaporation Model – Penman Monteith
This method is a weather-based methodology for calculating reference evaporation. It uses
data from ground-based weather stations as input to calculate the Penman-Monteith equation. The
Penman-Monteith model is the most commonly used method for computing irrigation needs for
crops and other surfaces that require irrigation (Cai et al. 2007). This method will be discussed in
greater detail in chapter 2.
1.2.2 Evaporation Model – NDVI Triangle
The NDVI Triangle method for calculating evapotranspiration is based on multispectral and
thermal imagery bands from the LDCM orbiting satellite. This technique is relatively new and,
according to my research, has not been used in southern California, to calculate evapotranspiration
for a large area. The use of satellites instead of ground-based stations brings flexibility to the
estimation of evapotranspiration. This methodology is discussed in greater detail in chapter 2 as
well.
1.3 Study Area
The Moulton Niguel Water District (MNWD), shown in Figure 7, was selected as

12

the study area for this project as its service area covers my own residence and the residences of
family and friends. The MNWD provides water, recycled water and waste water treatment to
approximately 170,000 southern California customers that live in Aliso Viejo, Laguna Niguel,
Laguna Hills, Mission Viejo, Dana Point, and San Juan Capistrano (Moulton Niguel Water
District, 2017).

Figure 7 MNWD study area selected for evapotranspiration comparative study
(Source: California Data Collaborative / CA-Stormwater-Data-Challenge)

13

Weather station #245, the basis of the ground-based ET measurement, lies four miles to the
east of the (MNWD) service area. This weather station was selected as it was the closest working
weather station with obtainable historical data for this study period and, in addition despite the
distance, the land, soil, and climate, is like that of the MNWD. CIMIS station #245 is situated on
the Coto de Caza Golf & Racquet Club greens, centered in the north most fairways on top of well
irrigated and maintained turf grass at a latitude of 33º37’18N & longitude 117º35’7W. CIMIS
Station # 245 collects data hourly on a minute-by-minute basis. This station uses the Penman-
Monteith equation to calculate reference ET. The assumption for the reference crop, for the
Penman-Monteith equation, is a height is 0.12m with a fixed surface resistant of 70 sm-1 and an
albedo value of 0.23 (Zotarelli et al. 2009).
The water needs of Orange County have increased with the population growth in urban
areas. The population of Orange County, California grew from 3,010,232 residents in 2010 to
3,172,532 in 2016 (TIGERweb 2017). More residents mean more water consumption. As water
supplies are limited, initiatives to conserve urban water across the county may be promoted. In
2016, the Metropolitan Water District (MWD) provided drinking water to nearly 19 million people
in parts of Los Angeles, Orange, San Diego, Riverside, San Bernardino, and Ventura counties, and
delivered an average of 1.7 billion gallons of water per day to a 5,200-square-mile service area
(Lopez 2017). The MWD is the largest distributor of treated drinking water in the United States.
Water provided by MWD is imported from Northern California via the State Water Project and the
Colorado River via the Colorado River Aqueduct. MWD infrastructure also includes 16
hydroelectric facilities, nine reservoirs, 819 miles of large-scale piping, and five water treatment
plants (Allen et al. 2017). The Municipal Water District of Orange County (MWDOC 2017), a
wholesale importer of water from MWD, treats the water at the Diemer Filtration Plant in Yorba

14

Linda and delivers the treated water to its customers through the East Orange County Feeder #2
and the Allen-McColloch Pipeline ("Request for Proposal Water/Recycled Water/Wastewater Cost
of Service and Rate Design Study" 2017). That water is then supplied to the MNWD for
dissemination to the residents of the service area (Allen et al. 2017).
1.4 Research Objectives
This study measured evapotranspiration using two different methods and sought to
investigate the following three research objectives:
• To assess the effectiveness of estimating ET using ground and satellite-based methods;
• To determine the correlations between ground and satellite-based methods of calculating
ET; and
• To determine the practicality of using a satellite-based method of measuring ET with
considerations to the required software availability, necessary GIS operator skill level, and
number of available personnel able to master the techniques needed for this method.
1.5 Thesis Organization
Chapter 2 discusses Evapotranspiration in greater detail and examines past work calculating
Reference evapotranspiration using the traditional method and the Triangle Method which uses
satellite imagery. Chapter 3 provides the many calculations and methods needed to obtain reference
Evapotranspiration for both the Penman-Monteith and NDVI Triangle method. Chapter 4 presents
the results obtained using the two methods and discusses why one model may be more appropriate
than the other. Chapter 5 offers some conclusions and suggestions for future work.

15

Chapter 2 Related Work
Evapotranspiration is the critical value, which tells growers when to water and irrigate, when to
stop, and when to adjust the irrigation flow as the climate changes. There are a variety of ways to
calculate reference evapotranspiration, but none is more globally used than the Penman-Monteith
model (Liang et al. 2012). This model is used by the 145 CIMIS weather stations to calculate
Evapotranspiration using ground-based sensor data as input as seen in Figure 8. This study sought
to determine if the Triangle method can be reliably used as a substitute for the Penman-Monteith
method to measure evapotranspiration.

Figure 8 CIMIS weather stations in California
Source: http://www.cimis.water.ca.gov/.

16

2.1 Water Conservation Efforts in California
Since much of California is an arid to semi-arid state and the necessity to conserve water is
quite high, many different methods have been employed with varying degrees of success. Ward
and Pulido-Velazquez (2008) noted, during their studies of water conservation efforts, the use of
subsidies was unlikely to create any improvement in the overuse of water resources. Dickerson et
al. (1992) used the psychological method of Cognitive Dissonance to Encourage Water
Conservation. This approach tried to shame people from abusing and wasting water resources after
being reminded of past behavior. The heart of the study was the public commitment the
participants took not to waste water as it created a sort of “hypocrisy condition” for the
participants. The method worked, however, only on those that were exposed to the hypocrisy
conditioning. Ferguson (1987) observed that methods to conserve water of irrigate agriculture
fields could not be used and applied to urban residential landscapes, without amendments. Allen et
al. (2005) noted, California and the west coast has a unique hydrogeological structure. By
observing only small amounts of deep percolation, which leaves the project directly for subsurface
flows, it is conducive for very accurate measurements of evapotranspiration. After measuring the
limited benefits of using subsidies to promote urban water savings, Ward and Pulido-Velazquez
(2008) concluded that a more structured and scientific way to measure and conserve water was
needed for California. Monteith (1965) used evapotranspiration to explain the movement of water,
evaporation, from soil and land surfaces. In addition, the transpiration from the surfaces and
stomata of plants were also included in his calculations. He combined the all the factors that caused
transpiration from plants and evaporation from the ground surfaces and formed relationships. He
connected the rates of evaporation with heat exchange and created, along with his partner Howard

17

Penman, a formula to determine a reference evapotranspiration model. This model was called the
Penman-Monteith model.
2.2 Penman-Monteith Reference Evapotranspiration Model
The Penman-Monteith Reference Evapotranspiration Model is the most widely used and
highly regarded standard for measuring reference evapotranspiration (Liang et al. 2012). This
model was developed over 50 years ago and has been continuously refined to estimate
evapotranspiration, accurately, for different climates (Zotarelli et al. 2009; Allen et al. 1998). There
was a need to standardize the measurement to better accommodate the users and their availability
to weather data. After a test of four different evapotranspiration models (the Blaney-Criddle,
radiation, modified Penman, and pan evaporation) to establish which method best met the
guidelines as published in the FAO Irrigation and Drainage Paper No. 24 ‘Crop water requirements
(1998), The Penman – Monteith equation was considered superior with the best results and lowest
error for a living grass crop (Allen et al. 1998).
However, due to the large number and variety of inputs required from CIMIS weather
stations, it is not a practical method for many areas. The California Irrigation Management
Information Systems (CIMIS) weather stations measure air temperature, relative humidity,
precipitation, solar radiation, wind direction, and wind speed amongst other weather data. These
are all utilized to calculate ET, for the Penman-Monteith equation as well as a modified version of
the Penman-Monteith equation. Statistically, however, there is not a difference between the two
Penman-Monteith methods (Temesgen et al. 2018).
The Penman-Monteith equation requires the inputs listed in Table 1. However, many
locations cannot afford to calculate the reference ET values to collect these input data. Other ways
to collect these inputs, such as satellite imagery, must be considered as viable solutions.

18

Table 1 Summary of data needs for Penman-Monteith Method
# Name Source Format Purpose
1
Mean daily
temperature
Station #245
Collected/calculated
value
Used to calculate Tmean which
is a feeder equation for four
calculations for Penman-
Monteith
2
Mean daily
solar data
Station #245
Collected/calculated
value
Measures the strength of solar
radiation
3 Wind Speed Station #245
Collected/calculated
value
Measured for evaporation
effect
4
Slope of
saturation vapor
pressure curve
Calculated
Tmean
Collected/calculated
value
Find relationship of saturation
vapor pressure and temperature
5
Atmospheric
Pressure
Station #245
MSL
Collected/calculated
value
Pressure from Earth’s
atmosphere as it affects ET
6
Psychrometric
constant
Station #245
Collected/calculated
value
Relates partial pressure of
water in the air to the
temperature vapor pressure est.
7
Delta Term
(DT)
Slope of
saturation,
wind speed,
psychrometric
constant
Collected/calculated
value
Used to calculate the radiation
term for the overall reference
ET equation
8 Psi Term (PT)
Slope of
saturation,
wind speed,
psychrometric
constant
Collected/calculated
value
Used to calculate the Wind
Term of the overall reference
ET equation
9
Temperature
Term (TT)
Station #245/
Weather
Underground
Collected/calculated
value
Used to calculate the Wind
Term of the overall reference
ET equation
10
Mean saturation
vapor pressure
Station #245/
Weather
Underground
Collected/calculated
value
Used to calculate saturation
vapor pressure from air
temperature

19

derived from air
temperature(es)
11
Maximum daily
temperature at
2 m height, °C
Station #245
Collected/calculated
value
Used to calculate the mean
saturation vapor pressure
12
Minimum daily
temperature at 2
m height, °C
Station #245
Collected/calculated
value
Used to calculate the mean
saturation vapor pressure
13
Actual vapor
pressure (ea)
derived from
relative
humidity
Station #245/
Weather
Underground
Collected/calculated
value
Used to calculate actual vapor
pressure from relative humidity
14
The inverse
relative distance
Earth-Sun (dr)
and solar
declination (δ)
Julian date
Collected/calculated
value
Used to calculate the sunset
hour angle
15
Conversion of
latitude (φ) in
degrees to
radians
Latitude
conversion of
study area
Collected/calculated
value
Converts the latitude of the
study area to radian for use in
the Penman Monteith equation
16
Extraterrestrial
radiation (Ra)
Solar constant,
solar dec. and
time of year
Collected/calculated
value
Calculates the intensity of solar
radiation based upon the angle
of the sun
17
Clear sky solar
radiation (Rso)
MSL and the
calculated Ra
Collected/calculated
value
Used to calculate net longwave
radiation
18
Net solar or net
shortwave
radiation (Rns)
Mean daily
solar radiation
calculation
albedo
constant
Collected/calculated
value
Used to calculate the
cloudiness of the sky
19
Net outgoing
long wave solar
radiation (Rnl)
Tmin, Tmax, The
Stefan –
Boltzmann
constant,
calculated
actual vapor
Collected/calculated
value
Used to measure the Earth’s
emission of radiation

20

pressure,
calculated
incoming and
clear sky
radiation
20
Net radiation
(Rn)
Shortwave and
longwave
radiation
Collected/calculated
value
Used to calculate the
difference between the long
and short-wave radiation

Cai et al. (2007) says of all the values that are needed to calculate ET using the Penman-
Monteith method, most are not available, and weather stations that could collect these data are very
expensive, and not affordable for most areas. Davis and Dukes (2012) counter that argument as
they used, in a study with the southern California MWD, affordable ET controllers to control
irrigation through ET calculations for three types of landscapes: cool season turf on loam soils with
full sun, shaded annuals on sandy soils, and low water using ground cover on a sunny, 20° slope.
The tests showed there was very little over irrigation. Due to general and broad settings on the
controller, however, there were many water deficits throughout the testing period which resulted in
areas with insufficient irrigation.
The Penman-Monteith method performs well in areas with arid or humid climates. Tegos et
al. (2015) tells us that the detailed measurements that are required for this method are dependent
upon the number of weather stations that are available. Without the density of stations, especially
in sparsely populated places, the evapotranspiration values become unreliable (Tegos et al. 2015).
The Penman-Monteith model, which is a ground-based system, is susceptible to errors. Westerhoff
(2015) points out the uncertainty that comes with the input equations. He discovered the reference
ET as measured by the Penman-Monteith ground source method, is most sensitive to temperature,

21

solar radiation, relative humidity, and the cloudiness ratio, and that errors may range from 10 to 40
percent.
2.3 Triangle Method Model
Satellite imagery that show differences in land cover, harvested crop lands, lands used by
grazing cattle and irrigated crops and waterbodies are indicators of possible patterns for ET
(Schmugge et al. 2002). Lillesand, Kiefer and Chipman (2012) point out, with high-resolution
cameras, vegetation and land cover conditions can be seen, gathered and transmitted from orbiting
instruments for critical analysis of ET. Using their data to determine the wet and dry edge of the
triangle when surface temperature and NDVI are combined in a two-dimensional plot, reference
evapotranspiration can be estimated. The Triangle method requires satellite input, the ability to
calculate multispectral and thermal bands and develop two-dimensional maps to estimate
evapotranspiration between the dry and wet edge (Suzuki et al. 2004).
2.3.1 Triangle Method Workflow
The workflow of data gathering was mapped so that a repeatable process could be used for
a repetitive process. Some of the difficulties included creating band math from equations, creating
a Region of Interest (ROI) within the thermal bands, and matching map future resolutions with
previously created data sets. Each calculation, much like the Penman-Monteith formula, builds
upon each other and becomes the input for the next equation as seen in Figure 8. These steps will
be explained in more detail in Chapter 3.
The Triangle method is a way to calculate, using remotely sensed data, evapotranspiration
values through two-dimensional NDVI pixel plots, regardless of geographic location. Suzuki and
Masuda (2004) noted that NDVI is a reasonable measure of ET in a large- scale area. For this
project, a region of interest was created in ENVI to reflect the MNWD. NDVI can give a value

22

equal to traditionally measured ET (Suzuki et al. 2004). The triangle method is a comparison of
NDVI and Land Surface Temperature (LST), in °C, to determine wet and dry edges of the
measured surface. The top of the triangle is the lowest Evaporation as it represents bare earth as the
bottom of the triangle is representative of maximum ET. These two values are plotted as X/Y
values to create a measure of evapotranspiration. Suzuki and Masuda (2004) observed that NDVI,
obtained via remote sensing, has equivalency to evapotranspiration measured in more traditional
ways while Cai et al. (2007) argues the weather-based Penman-Monteith method has provided
consistent ET values over a variety of regions and climates.
The calculation of the NDVI Triangle starts with the Surface Energy Balance Algorithm for
Land (SEBAL). SEBAL estimates evapotranspiration, spatially, using energy balance, satellite
imagery, and spectral analysis (Bastiaanssen et al. 1998). With this method, Vegetation indexes,
Land Surface Temperatures, and evapotranspiration can be calculated for a region. SEBAL can be
used without knowledge of the ground being measured, independent of ground-based weather
stations. This makes it especially useful in remote areas.
To use the satellite imagery, the normal mathematical computations for the vegetation
indexes and surface temperatures must be put into a format that can be understood and visualized
geographically. The way to accomplish this is to use band math. Band math converts the static
measure of an equation and uses band math to convert the imagery to that equation. For example,
the NDVI equation is Near Infrared (NIR) – Red divided by Near Infrared (NIR) plus Red. Band
math associates that measurement to the sensors on a satellite that measures NIR and Red and
completes that equation and produces a two-dimensional scatter plot based upon the pixels
gathered from the satellite image. The spectral data can be compared to spatial location to gain
insight on a Region of Interest.

23

2.4 Penman-Monteith Model vs Triangle Method
The results of using the NDVI Triangle method were compared with the results obtained
with the Penman-Monteith method using the methods of Suleiman and Hoogenboom (2007) to
analyze statistical error and determine model performance for the MNWD.
Triangle method relies on wet and dry edges to determine the Evapotranspiration when
compared to the calculated surface temperature from the LDCM (Suzuki et al. 2004; Bastiaanssen
et al. 1998).
The Penman-Monteith has proven to be effective measures of reference of
evapotranspiration in the climate that fits the strength of its equation. Beyazgül, Kayam and
Engelsman (2000) states the Penman-Monteith method performed excellently in both humid and
arid climates. However, The Penman-Monteith model tends to overestimate in hotter climates
(Tegus, Alamos and Houstonians 2015; Pandey et al. 2014; Jhajharia, DebBar and Argrawal 2004).
Suleiman and Hoogenboom (2007) used the Penman-Monteith evaporation method for the
humid climate of Georgia, for daily reference evapotranspiration estimation. This study was done
as a comparative study between the Penman-Monteith and Triangle method of calculating
evapotranspiration. They found that in a humid climate the Penman-Monteith equation yielded a
more accurate value for reference evapotranspiration than the Triangle Method. They set up the
study using nine sites with weather stations. These weather stations, part of a larger collection of
70, collected weather data for agriculture, including irrigation and water management. The
Penman-Monteith requires many climatic inputs and, those inputs were gathered from the nine
chosen weather stations for this study. The weather stations provided, air temperature, relative
humidity, precipitation, wind speed, wind direction, solar radiation, soil moisture, soil temperature,
and barometric pressure. These are all the inputs needed to calculate a reference evapotranspiration.

24

From that gathered data, calculations for the Penman-Monteith equation were conducted. Quality
control checks were performed daily, and the research team reported no missing data for this study
from the nine sensors. The Triangle method requires multispectral and thermal sensor inputs and
the proper program to calculate and display two-dimensional plots to visualize the estimated
evapotranspiration between the dry and wet edge (Suzuki et al. 2004).
This project followed Suleiman and Hoogenboom (2007) method of data collection from
Station # 245 (Coto de Caza) and used the collected weather values to calculate reference
evapotranspiration for the Penman-Monteith method. The Triangle model, for this study, used the
Surface Energy Balance Algorithm for Land (SEBAL) to estimate evapotranspiration through the
calculation of essential hydro-metrological parameters (Bastiaanssen et al. 1998).

25

Chapter 3 Methodology
The aims of this thesis were to: 1) assess the effectiveness of estimating ET using ground and
satellite-based methods; 2) determine the correlations between ground and satellite-based methods
of calculating ET; and 3) determine the practicality of using a satellite-based method of measuring
ET with considerations to the required software availability, necessary GIS operator skill level, and
number of available personnel able to master the techniques needed for this method.
The weather-based Penman-Monteith method uses multiple weather data measurements as
primary input to estimate ET. Data can be obtained from CIMIS online data portal. Alternatively,
the NDVI Triangle method uses satellite imagery from the LDCM as the primary data input to
estimate ET. Data need to be manipulated before use in evapotranspiration measurements. The
intent is to discover, using statistical analysis, if the NDVI Triangle method might provide a
suitable alternative to the Penman-Monteith method for locations that lack weather stations.
3.1 Research Design
This project involved the calculation of evapotranspiration on four different days in 2016
using ground-based weather stations and orbiting satellites. The spatial differences between the
CIMIS weather station # 245 located on the Coto De Caza golf course and the area of study, the
MNWD located four miles to the west is negligible because the two locations share similar soil
types, climates, and humidity. ENVI 5.4, ENVI Classic, LDCM at 30 m for multispectral, and 100
m but resampled to 30 m pixels for thermal bands, excel for computations, ArcGIS and ArcMap
were the main tools and data used for this project.
3.2 Penman-Monteith Evapotranspiration Model
The Equation 1 shows the Penman-Monteith formula for calculating ET Reference for
clipped grass reference crop. This formula assumes the hypothetical crop has a height of 0.12 m, a

26

fixed surface resistance of 70 s m
-1
and an albedo value of 0.23. The albedo measure is the portion
of light reflected off the surfaces of leaves (Zotarelli et al. 2009). This equation reads as:
ETo=
0.408∆ (𝑅 𝑛 −𝐺 )+ 𝛾 900
𝑇 +273
𝑢 2(𝑒 𝑠 − 𝑒 𝑎 )
𝛥 + 𝛾 (1+0.34 𝑢 2
(1)
Where:
ETo is the reference evapotranspiration in mm day
-1
;
Rn is the net radiation at the crop surface in MJ m
-2
day
-1
;
G is the soil heat flux density in MJ m
-2
day
-1
;
T is the air temperature at 2 m height in °C;
u2 is the wind speed at 2 m height in m s
-1
;
es is the saturation vapor pressure in kPa;
ea is the actual vapor pressure in kPa;
es - ea is the saturation vapor pressure deficit in kPa;
Δ is the slope vapor pressure curve in kPa °C
-1
;
γ is the psychrometric constant in kPa °C
-1
.

Weather sensors contribute greatly to the calculation of evapotranspiration as the Penman-
Monteith formula requires several different climate inputs.
3.2.1 CIMIS Sensor
As indicated in the Penman-Monteith equation and Table 1 in chapter two, there are many
inputs required to calculate evapotranspiration. For this study area, the Moulton Niguel Water
District (MNWD) weather sensors, maintained by CIMIS, gather and collect data needed to
calculate evapotranspiration for the area on a minute-by-minute basis. The weather sensor used for
this project study is located at an elevation of 846ft Mean Sea Level (MSL). Sensor #245 is

27

centered on the northernmost fairway, placed amongst several acres of irrigated and maintained
turf grass as seen in figure 9 (Temesgen et al. 2018).

Figure 9 Coto De Caza CIMIS weather sensor #245
(Source: Temesgen et al. 2018; https://eros.usgs.gov//)

28

A concern for this sensor is that the sand traps and nearby houses, depending on the wind direction,
may compromise the data collected. This is because obstructing buildings can either cut down on
wind exposure to the collecting sensor or redirect the wind. H Jiang (2014) observed sand
traps disturbed the velocity field and the wind-sand coupling effect can greatly change the wind
flow field.
The data needs to calculate the Penman-Monteith formula are listed in Table One. The data
and evapotranspiration values were taken directly from the sensor database itself. The Penman-
Monteith calculations were done via the weather station internal sensors.
3.2.2 Sensor Data Collection
The CIMIS weather station collects a variety of environmental data. As evapotranspiration
is affected by many weather and climate factors, one sensor needs to measure many readings, in
one location, for consistency.
3.2.2.1 Total Solar Radiation
Sensor #245 used a pyranometer, which is a collection of thermocouples that generate
electricity according to how much solar radiation is received. Woodford (2017) better explains this
relationship, the more sun, the hotter the temperature gets, the more electricity the pyranometer
produces. The response varies with the angle of the sun: when the sun is directly overhead, the
maximum electricity is generated. The greater the angle of the sun changes, the less electricity is
produced. When the sun starts to move from its 12:00 noon position, the CIMIS sensor performs a
cosine correction to adjust for the change of electrical changes due to angle difference (Temesgen
et al. 2018). However, the measured radiation was measured in Langley units instead of Mega
joules; Mega joules is needed for the Penman-Monteith Equation.

29

3.2.2.2 Soil Temperature
This sensor uses a negative temperature coefficient thermistor, which is a temperature-
resistant resistor whose resistance decreases as the temperature rises. This sensor measures soil
temperature in °C. This project used negative temperature coefficient thermistors to indicate if
electrical equipment was overheating. For this study, this is an important piece of data as it is a
major part of evaporation. The more sun hits the ground, the more the soil heats up. When the soil
heats up, evaporation starts to increase.
3.2.2.3 Air Temperature / Relative Humidity
This sensor also uses a thermistor to measure air temperature. This is a primary feed in to
the calculation as the temperature maximum and minimum values are used to calculate the average
temperature which is then used to estimate the Temperature Term (TT), which is used to calculate
the Wind Term for the overall Penman-Monteith equation, minimum daily temperature, actual
vapor pressure, and net outgoing long wave solar radiation for the Penman-Monteith formula
(Temesgen et al. 2018).
The same sensor also measures humidity using a combination of wet and dry bulbs. The
humidity of the atmosphere is measured in percent. Anderson (1936) recognized that percent
humidity, by itself, is not strictly a measure of dryness but the vapor pressure deficit. This
measurement requires the input of partial pressure in the air as compared to the air temperature
using paired wet and dry thermometers. The psychrometric stays constant and an average
atmosphere condition was used for this computation. Loescher et al. (2009) however, disagree with
the psychrometric being labeled a constant. They recommend using open- and-closed-path infrared
gas analyzers (IRGAs) because these instruments operate at greater than 10 megahertz, which is
the speed at which latent energy flux is transported (Loescher et al. 2009).

30

3.2.2.4 Wind Direction / Wind Speed
The Penman-Monteith method requires wind direction and speed measured two m above
the ground. The direction was measured with a wind vane and the wind speed was measured with
an anemometer, a device that simply turns as fast as the wind is blowing. The concern for station
#245 is the fact sand traps and houses lie near the weather sensor. These two obstacles can affect
the quality of wind readings (Temesgen et al. 2018).
3.2.2.5 Slope of Saturation Vapor Pressure Curve (Δ)
When an equilibrium is reached between water molecules escaping and returning to the water
reservoir, the air is said to be saturated since it cannot store any extra water molecules. The
associated pressure is called the saturation vapor pressure (Manivanan 2006).
The higher the air temperature, the more water molecules can be stored. Consequently, the higher
the storage capacity, the higher its saturation vapor pressure (Manivanan 2006). I calculated this
value by using the Tmean calculated in section 3.2.1 and the constant for the base of the natural
logarithm (i.e. 2.7183).
3.2.2.6 Atmospheric Pressure (P)
The atmospheric pressure is the pressure exerted by the weight of the Earth's atmosphere.
The higher the altitude, the more evapotranspiration is promoted due to low pressure (Zotarelli et
al. 2009). For this equation this project found and plugged in the Mean Sea Level (MSL) elevation
of the Coto de Caza weather station # 245.
3.2.2.7 Mean Saturation Vapor Pressure
As discussed, the slope of saturation vapor pressure curve, is related to air temperature.
(Manivanan 2006) This project accomplished the calculation of the mean saturation vapor pressure
curve by calculating the mean between the saturation pressure at both the minimum and maximum

31

temperature. From that point, the mean saturation vapor pressure was calculated, from the daily
minimum and maximum temperatures.
3.2.2.8 Actual Vapor Pressure (ea)
Relative humidity was used to calculate actual vapor pressure for this equation. Anderson
(1936) recognized that percent humidity, by itself, is not strictly a measure of dryness but the vapor
pressure deficit.
The calculation of the variables for the Penman-Monteith methodology are all completed
on-site via the collecting weather station: Weather station #245 collects and calculates
evapotranspiration. In addition, the data used to calculate ET is available for review and analysis.
The measured data includes solar radiation, air temperature, soil temperature, relative humidity,
wind speed, wind direction, and precipitation. The calculated values that are available through the
CIMIS station are net radiation, reference evapotranspiration, wind speed and direction, wind run,
vapor pressure, and dew point temperature (Temesgen et al. 2018). The reports available for each
reporting station are hourly, daily, and monthly reports, daily ETo variance reports, and monthly
average ETo reports. This data, accessible through the CIMIS website, is downloadable in four
formats: Web, XML, CSV, and PDF.
3.3 NDVI Triangle Method
The triangle method is a way, using remotely sensed data, to calculate evapotranspiration. Suzuki
and Masuda (2004) noted that NDVI is a reasonable measure of ET in large areas. For this project,
a region of interest was created to reflect the MNWD area. NDVI, when compared to surface
temperature, can give a value equal to traditionally measured ET (Suzuki et al. 2004). The triangle
method is a comparison of NDVI and LST to determine wet and dry edges of the measured surface.
The top of the triangle is the lowest Evaporation as it represents bare earth as the bottom of the

32

triangle is representative of maximum ET. This seen in Figure 10. ENVI permits the manipulation
of data to a point you can select areas of the triangle and associate it with the map as far as
determining the location of the highest and lowest ET as seen in Figure 11. This image visualizes
the Arroyo Trabuco golf course, Casta del Sol golf course, Lake Mission Viejo, and the Sulphur
Creek Reservoir as areas of high ET. Figure 10 also classifies the wet/dry edge.

Figure 10 Calculation of estimated evapotranspiration by NDVI in triangular space
(Source: Han et al. 2004)

The red areas indicate the dry edge or areas of low ET. That is representative of areas that are
residential, roads, or dirt. Water absorbs light, so satellite imagery will read those areas as a dark
color such as blue or black. Those would be areas of high evapotranspiration potential. Inversely
vegetation will appear as green due to its low reflective and high absorptive nature of red and
infrared due to the chlorophyll in plants. Bare earth, dirt and areas with low vegetation coverage

33

will more easily reflect Red and will indicate as such when viewed through the multispectral bands
of a satellite (GISGeography 2018).
3.3.1 Data Collection
Figure 11 Identification of areas of potential high ET by the use of albedo in the MNWD
study area (Source: https://earthexplorer.usgs.gov/)

The NDVI triangle methodology requires the application and manipulation of remotely
sensed data for calculation of the triangle. This method requires the most skill as the data is created
by the user through Region of Interest (ROI) designation, band selection, and spectral analysis of
the GeoTIFF elected, after determining the requirements for the study area as seen in Figure 10.
The triangle method eliminates the need for base-station input as all data is collected from the
orbiting body. ENVI proved to be the program of choice as it was found to be the most applicable
for the project’s satellite imagery processing needs. This program provided the ability to more
accurately determine and visualize NDVI Triangle values.

34

For this project, the LDCM was selected instead of MODIS data. The main advantage of
MODIS is more frequent passes. This would have allowed the use of all 20 days for this project
study. On the other hand, the disadvantage of MODIS, is the coarse resolution. The main
advantage of the LDCM satellite is (a) very good resolution, 30 m at multispectral and 30 m at
thermal. The disadvantage is, the pass is only every 16 days. This caused some difficulty when
attempting to line up specific days to measure. Considering the temporal limitation of LANDSAT,
four days, as recorded by the LDCM for this project were matched out of the 20 days in 2016 (08
February, 19 April, 22 June, and 08 July). To ensure directed and purposeful readings, a Region of
Interest (ROI) was created in ENVI of the Moulton Niguel Water District (MNWD). A mask was
generated for that ROI, so calculations could only read what is inside the ROI and nothing outside
of it. The intercept, slope, and the coefficient of determination was calculated for all four days. The
temperature was then converted from K to °C from the LDCM’s thermal bands.
3.3.2 Workflow
A summary description of the workflow used to calculate the NDVI Triangle for the
MNWD is shown in Figure 12. The data Source for the NDVI Triangle method is the LDCM
OLI/TIRS C1 Level-1 Multispectral (30 m) data/7 BSQ through USGS earth explorer and the
program used to construct the triangle was: Environment for Visualizing Images (ENVI).

35

Figure 12 NDVI Data processing required for NDVI Triangle method.
Multiple computations were completed to identify NDVI, ALBEDO, SAVI, WDVI, L Value, via
band math as seen in Appendix A. In addition to band math, band layering highlighted
characteristics of the area to identify foliage growth of varying conditions. To that end NDVI and
LST were calculated and combined, using the SEBAL method, to estimate evapotranspiration
values for the Moulton Niguel Water District.
3.4 Statistical Analysis
To measure performance of the Penman-Monteith and the remotely-sensed NDVI Triangle
evapotranspiration model, statistical analysis was needed. Equation 2 shows the Root Mean Square
Error (RMSE) which measured how far from the regression line the data falls. The lower the

36

RMSE value, the better the agreement (Suleiman et al. 2007). Equation 3 shows the index of
agreement (d), which measured the predicted error. This varies between -1.0 and 1.0. A value of
1.0 means a perfect agreement while a value a value of 0 would indicated a poor one (Willmott et
al. 2011). The Root Mean Square Error (RMSE) and the index of agreement (d) was used to
determine the value for agreement between the two models. Willmott, Robeson and Matsuura
(2011) tells us these two calculations are useful in calculating the performance of diverse models.
Equation 4 shows the Mean Absolute Deviation (MAD). This equation was selected because, as a
performance measure, it is not overly sensitive to outliers. Equation 5, the Mean Absolute
Percentage Error (MAPE) formula was used to determine trend analysis and the forecasted error of
measurement.
𝑅𝑀𝑆𝐸 = [𝑁 −1
∑ (𝑃 𝑖 −
𝑂 𝑖 )
2

𝑁 𝑖 −1
]
0.5
(2)
Where:
N is the number of cases
O is the observed
P is the predicted ET
𝑑 = 1 − [
∑ (𝑃 𝑖 −
𝑂 𝑖 )
2

𝑁 𝑖 −1
∑ (|𝑃 𝑖 |
−
|𝑂 𝑖 |)
2

𝑁 𝑖 −1
]
0 ≤ 𝑑 ≤ 1 (3)
Where:
d is the index of agreement
O is the observed
P is the predicted ET
𝑀𝐴𝐷 =
1
𝑛 ∑ | 𝑥 𝑖 −
𝑥 ̅|
𝑛 𝑖 =1
(4)
Where:
n is the number in the data set

37

i is the percentile location

𝑀𝐴𝑃𝐸 =
∑ |( 𝐴 𝑡 −
𝐹 𝑡 /𝐴 𝑡 |
𝑛 𝑡 =1
𝑛 (5)
Where:
A is the actual value
F is the predicted value

38

Chapter 4 Results
The use of satellites and remote sensing to measure evapotranspiration provides viable options to
areas that find the acquisition, maintenance, and repair of more expensive weather monitoring
stations beyond their ability to obtain and sustain. Remote sensing to measure evapotranspiration
provides global versatility to the scientist and removes the geographic limitations one would have
with an earth-bound measuring point. Ground-based weather stations are limited to a single form of
measurement as it is dictated by the installed hardware. In contrast, there are many satellites that
measure an array of readings depending on the need of the user and the mission of the remote
body. The ability to compare remote sensed readings of one satellite against another provides a
better comparative analysis when you can access a multitude of differently obtained data for the
same study area.
The objectives for this study were to assess the effectiveness of estimating ET using ground
and satellite-based methods, determine the correlations between ground and satellite-based
methods of calculating ET and, determine the practicality of using a satellite-based method of
measuring ET with considerations to the required software availability, necessary GIS operator
skill level, and number of available personnel able to master the techniques needed for this method.
For this study the LDCM satellite data was used to calculate estimated evapotranspiration in the
MNWD by NDVI in triangular space. The results of data gathering, and final calculations are
presented in Tables 5 and 6. The visual analysis for the Triangle Method is presented in Figure 13.
The two-dimensional pixel scatter plots for the Triangle method for the days of 08 February, 19
April, 22 June, and 08 July 2016 were formed from the mathematical computation of the LDCM’s
multispectral bands and thermal bands. The Land Surface Temperature (LST) is represented by the

39

Y axis while the X axis shows the NDVI computation. When compared together, they create a two-
dimension pixel scatter plot in triangular space.
4.1 Penman-Monteith Method Results
The evapotranspiration calculation was performed by using the Penman-Monteith method
with data collected with station # 245. This calculation was performed internally by the station
itself and was determined to be suitable for the MNWD due to the similarity of the landscape and
climate of the area. This calculation was used as the base comparison to determine the accuracy of
the NDVI Triangle method. The reference data and evapotranspiration estimates for the 08
February, 19 April, 22 June, and 08 Jul 2016 are summarized in Table 3. These data points were
collected at 12:00 p.m. on cloudless sunny days to estimate maximum evaporation and
transpiration potential for the days of measurement.
All the calculations for evapotranspiration were performed on-site, within the weather
station itself. The findings were uploaded to CIMIS, a minute-by-minute basis, to match the
frequency of data collection. This frequency allows the grower and irrigator to quickly pivot and
adjust water irrigation based on yesterday’s readings. The Triangle method, though versatile in an
area of measurement, cannot meet those operational standards.
The data collected by this weather station is accurate for the surrounding area. Weather
station # 245 data readings can be influenced by external interferences. Wind is the second biggest
factor, after the sun, for evaporation and transpiration processes However, the average wind speed
for the entire year of 2016 at weather station #245 never exceeded 1.7 m/s (Temesgen et al. 2018).
Another factor that may affect ET readings is the fact that the current location, situated on well-
watered and irrigated blue grass, may affect the soil temperature readings which in turn reflect in
the evapotranspiration readings. These readings may not reflect the expanse land of which these

40

readings represent. The soil temperatures predictably waxed and waned with the changing of the
seasons, with a high of 21.3 °C in July 2016 and a low of 11.8 °C in January (Temesgen et al.
2018). Each of the weather station’s sensors must be calibrated as they are exposed to the elements
and inclement weather. As the Penman-Monteith requires many inputs for evapotranspiration
calculation, each data point has the potential to adversely affect the final calculation.
Table 2. CIMIS Station# 245 reference data on four days
Day/Year/Time
08 Feb 2016
Noon/Cloudless
19 April 2016
Noon/Cloudless
22 June 2016
Noon/Cloudless
08 July 2016
Noon/Cloudless
Data Collected
Total Precipitation
(mm)
0 0 0 0
Average Solar Rad
(W/m
2
)
721.5 1018.6 1030.7 1025.9
Average Vapor
Pres (kPa)
4.3 6.9 19.5 20
Average Air Temp
(°F)
83.7 85 80.9 81.1
Average Relative
Humidity (%)
11 17 54 55
Average Dew Point
(°F)
35.5 35.5 60.8 61.2
Average Wind
Speed (m/s)
5.0 3.6 4.1 3.8
Average Soil Temp
(°F)
55.3 63.1 68.5 69.7
PM ET
(mm d
-1
)
0.16 0.25 0.25 0.25

4.2 Triangle Method Results
The Triangle method calculation was performed using the LDCM multispectral and thermal
band calculations for 08 February, 19 April, 22 June, and 08 July 2016. The dates were specifically
picked to fall on cloudless days as, close to noon as possible, measure NDVI when the
evapotranspiration was at its highest potential as seen in Table 3. The actual evapotranspiration, as
calculated by the Penman-Monteith method, was compared to the satellite evapotranspiration

41

method, as calculated by the Triangle method for the four days of measurement. Multispectral
bands were used to calculate the greenness of a pixel relative to its neighbor. The NDVI was used
to determine the satellite-based evapotranspiration for this project. NDVI values rise when more
vegetation covers a pixel. This indicated by a rise in NIR reflectance and a fall in Red reflectance.
The opposite is true when vegetation is sparse on non-existent. NDVI measures and shows the
greenness of a pixel and is known to provide accurate evapotranspiration estimates (Rossato, et al.
2005).
NDVI values range from -1 to +1 with +1 indicating high vegetation cover and -1
indicating low vegetation cover. Thermal bands were manipulated to find the LST and converted
from K to °C. The wet and dry edges of the triangle were annotated to reflect the placement of the
pixel scatterplot. In the triangle method, the top of the opposite side indicates the least amount of
evaporation, based on bare dirt. The point where the hypotenuse and adjacent side converge
indicates where the greatest amount of transpiration occurs. To achieve this, LST and NDVI was
calculated from the bands of the LDCM and placed on a two-dimensional plot as seen in Figure 12.
To ensure the best reading possible, a Region of Interest (ROI) was specified to eliminate outliers.
As a secondary check, classes were used to color code known areas of wet and dry such as golf
courses, scrub land to reduce the error in selecting the triangle coordinates.
The accuracy and correlation between the Penman-Monteith method was greatly limited by
the lack of measurable data for this project. For better accuracy, more data is required for a proper
statistical analysis. Table 4 summarizes the variations between the measured Penman-Monteith
values and the satellite-based evapotranspiration values. On the first day of measure, a large
discrepancy occurred between the satellite and the measured evaporation. As the variables
measured with the LDCM satellite did not capture weather conditions and were focused on the

42

measure of vegetation vigor, some variables that affect evapotranspiration on the ground may not
be factored into the calculations. On the day in question (08 Feb 2016), there were wind gusts of up
to 26 miles per hour. Wind plays a large part in the evaporation over a surface. In addition, the
water restrictions for California, which limited heavy customer potable water use for watering, was
still being enforced for the Coto De Caza Golf course. Because an orbiting body was used to
measure evapotranspiration, which covered an entire region of interest and not two miles in radius
as measured from the weather ground station, the numbers may have been inflated. Due to the
ground station being a fixed point and the NDVI measure covers lakes, rivers, and other locations
that may have irrigated, the readings, assumedly due to these factors, did not correlate. The results
of the measurement are indicated in Table 4. This method has shown to closely track with actual
evapotranspiration as measured by a weather station using the Penman-Monteith for
evapotranspiration computation. This method should be considered as an acceptable method to
develop a snapshot estimate of a measured area. However, when comparing it to a weather ground
station, care must be taken if using only one. As each ground station is a study of the climate and
conditions directly surrounding itself, while the NDVI Triangle method is more used for large-
scale areas but not to that detail, caution must be taken if taken as actual readings against a single
station.

43

Figure 13 Two-dimensional scatter plots of satellite pixel values of NDVI versus the
average of Top of Atmospheric (TOA) spectral radiance from LCDM satellite imagery
(Source https://earthexplorer.usgs.gov/)

Table 3 Results of four days of NDVI Triangle Method calculations on a cloudless day

Day/Year/Time
Cloudless

08 Feb 2016
10:22 a.m.
19 April 2016
11:28 a.m.
22 June 2016
11:28 a.m.
08 July 2016
11:28 a.m.
NDVI Index
0.4 0.35 0.35 0.37

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4.3 Comparison of Methods
The Triangle method results were compared against the Penman-Monteith method to
answer the question on whether the Triangle method could be used as a substitute for weather
stations, which use the Penman-Monteith method, for evapotranspiration measurement. To find is
the Triangle method was a suitable facsimile, the period, actual ET (Penman-Monteith), forecasted
ET (Triangle Method), the error, the absolute value of error and square of error, and the absolute
values of errors divided by the actual values. These values were then used to compute the Mean
Absolute Deviation (MAD), the Root Mean Square Error (RMSE), R
^2
, and the Mean Absolute
Percentage Error (MAPE) as seen in Table 4.
Table 4 Penman-Monteith vs Triangle Method
Period/2016 Actual
(Penman-
Monteith)
Forecast
(Triangle
Method)
Error Absolute
Value of
Error
Square of
Error
1. 08 Feb 0.16 0.4 -0.24 0.24 0.0576
2. 19 Apr 0.25 0.35 -0.1 0.1 0.01
3. 22 Jun 0.25 0.35 -0.1 0.1 0.01
4. 08 Jul 0.25 0.37 -0.12 0.12 0.0144
Totals 1.47 -0.56 0.56 0.092
N = 4

This project aimed to compare the two methods of calculating evapotranspiration statistically to
determine the feasibility of using the NDVI Triangle method as an acceptable substitute for the
Penman-Monteith model. However, with only four data points analyzed in this study, it is not
feasible make any trusted statement on the NDVI Triangle Method.

45

Chapter 5 Conclusion
This study aimed to assess the effectiveness of estimating ET by comparing a ground-based
method with a satellite-based method to determine the feasibility in using a satellite-based method
for measuring ET. Using the generated study area, the satellite-based Triangle method can be used
to estimate evapotranspiration for every area of the State of California that is not covered by a
weather station. This research showed the geographic versatility of a satellite-based method of
measuring ET when compared to a ground-based method. The main metric used to compare the
data is a value called evapotranspiration which represents the water lost from the surface of the
land (evaporation) and vegetation growth (transpiration). Together, these two values can be
combined to estimate the total water loss from a land surface with vegetation cover. The remotely-
sensed ET values were higher than those predicted by the Penman-Monteith method for the 4 days
used in this study.
The NDVI Triangle method is an advanced-level method to generate evapotranspiration for
a study area. The user must be intimately familiar with GeoTIFFs and the program of choice to
extract the data into individual bands for evaluation. Band math knowledge and proficiency is
critical for the calculation of SEBAL to obtain the values of NDVI and surface temperatures. The
user must have knowledge of GIS as well as other mapping programs, and the ability to fully
comprehend and execute the steps needed to integrate the multispectral and thermal bands for
visualization. This method is not recommended for the medium to novice user and is impractical
for the average GIS shop whose expertise is something other than satellite imagery analysis.
5.1 Discoveries
This study compared the Penman-Monteith method and the Triangle method suitability for
estimating ET for the Moulton Niguel Water District. This project discovered satellite imagery is

46

the most versatile way to predict vegetation indexes as it has the capability of being very efficient
when it comes to collecting and presenting data for diverse calculations of evapotranspiration. This
provided confirmation that, when it is too difficult to obtain all the data sets needed to complete the
Penman-Monteith measurements for evapotranspiration, remotely-sensed imagery can adequately
fill the need. There has been many previous thoughts and methods on uses of remote satellite
imagery to predict evapotranspiration. However, it still needs ground truth to confirm the data
measured. In addition, satellite imagery is subjected to cloud cover and infrequent passes which
make it great for an overall look and study of an area but poor due to the temporal delay from each
pass. There have been only a few studies using remotely sensed data in a triangle form in a large-
scaled area and compare it against the in-place weather station for the evapotranspiration value.
This study found the evapotranspiration values from the remotely-sensed station range
from .35 to .4 inches of ET while the CIMIS weather station #245 measured evapotranspiration at a
lower value range of .16 to .25 inches of ET. The trend matched on the months of April and June
but diverged in February and July. It should be noted that in February, precipitation was at the
lowest while in July, radiation was at its highest level. This may be due to the fact the ground-
based weather station reading is greatly influenced by its direct surroundings while the satellite
data, though measuring a large-scaled area, are not influenced by micro-climate weather and
atmosphere changes. The Penman-Monteith method was directly created to measure
evapotranspiration value shifts. Satellite data, using the Triangle Method, is subjective and requires
the analyst to determine the wet and dry edges before it can be assumed where the value of
evapotranspiration lie. The NDVI Triangle method, which is the measure of greenness in a pixel,
with 30m resolution for the multispectral bands and 60m for the calculation of surface temperature,
creates an estimation of evapotranspiration when the two are placed into a two-dimensional plot.

47

The two values, when placed on a plot, form a triangle consisting of a wet and dry edge for
evapotranspiration measurement.
The difficulty of the SEBAL calculations for remotely-sensed imagery and the temporal
latency of satellite passes, highlights the advantage local ground-based weather sensors have over
orbiting bodies. The spatial inconsistencies are greater, 30m pixel to a point measurement for a
ground-based weather station. However, the fact satellite data can measure large geographic tracts
of land whose locations can be selected to regions of interest, show that advantage of the broadness
of scope of evapotranspiration by orbiting bodies versus the more accurate but limited in area of
measure ground unit.
5.2 Considerations and Limitations
One major limitation of this study is the fact that the wet and dry edge of the region of
interest as measured using the NDVI Triangle Method is subjective and determined by the user.
The surface land temperature must be calculated using the thermal bands of the satellite displayed
against the NDVI, which is calculated through a series of steps. A second limitation was the
number of days that were measured. Due to the study’s focus on a region’s clear cloudless day
rather than a single pixel, accompanied by the LDCM’s low rate of passes (every 16 days) This
caused an inadequate amount of measured and matching cloudless days to the ground-based
weather station, to definitively determine statistical error between the measured values. Other
studies may opt to use a different orbiting body, one whose resolution is not as well as the LDCM
but has more frequent passes. With additional data collected over a longer period and a more
densely populated equation, a deeper assessment on how the Triangle method compares to the
Penman-Monteith method of measuring evapotranspiration can be discovered.

48

Evapotranspiration is a very broad and complex concept, one that should be taken only if
there is a single plan and track in place so that no distractions come in play. Originally this study
did intend to utilize more than one station located within the Region of Interest (ROI) but, that
station was inoperative at the time of measure. The additional station could have provided a more
solid trend for the evapotranspiration values.
This study, with its limited data points, finds that there is no clear indication of agreement
based upon the small number of readings taken. However, understanding the lack of data points,
there is not a significant difference between the selected methods of measurement of
evapotranspiration for the studied ROI. The NDVI Triangle method may provide comparable ET
values when compared to ground-based weather stations. Locations that are remote, inaccessible
or undeveloped may benefit from using free data to reasonably compute evapotranspiration by the
NDVI Triangle method.
5.3 SWOT (Strengths Weaknesses, Opportunities, and Threats) Analysis
5.3.1 Strengths
The Penman- Monteith has many strengths as it is considered a world standard. It has been
used globally to measure evapotranspiration in a variety climate condition for the last 50 years.
With its multiple weather data sensor inputs from ground-based weather stations, it compensates
for the smallest of change, ensuring even the slightest variation in weather is compensated and
considered. It can measure and produce ET values on a minute-by-minute basis leaving no gap of
information for the irrigator.
The NDVI Triangle Method strengths reflect its versatility in the size of land surface it can
measure, and the myriad ways satellite imagery can be interpreted. This method, with its use of
satellites, can provide current and historical ET values from any point of the globe. This data is free

49

to any user and can be accessed from anywhere in the world. The fact that no inventory, by the end
user, is required for world-wide measurements makes this method extremely convenient and
economical. When measuring ET, the NDVI Triangle method can produce an equivalent value
without the need for a ground-based weather station assuming enough data has been collected.
5.3.2 Weaknesses
The Penman-Monteith method main weakness is the multiple sensor inputs for the
equation. To gather that sensor data, a ground-based weather station, capable of taking all required
weather readings must be available for use. These can be expensive and hard to maintain as each
sensor needs to be calibrated regularly. Since these weather stations are so expensive, there are not
enough to provide complete overlap of the areas measured for ET. In addition, this means
locations, that cannot afford a weather station, will not be able to secure as accurate of a reading of
a location that has a fully equipped weather. Weather stations can go dark as they are complicated
instruments. This creates a gap in measurement or a discontinuation of data, altogether.
The NDVI Triangle uses satellites to measure ET. The fact there are so many selections can
make the process more complicated as there are tradeoffs. Some satellites have very good
resolution but a low pass rate while others have a daily pass, but the resolution is compromised in
the process. Weather and cloud cover can prevent the satellite from creating a complete picture for
ET values. While other ET measurements can be automated, the learning curve for SEBAL and the
Triangle Method can be daunting.
5.3.3 Opportunities
The Penman-Monteith method relies on ground-based weather stations. Companies have
taken the concept of a weather station and packaged it into a portable module which is disposable
in tactical situations. These miniaturized versions of the large ground-based weather stations are

50

mobile, with interoperability with other like weather stations, via a cellular network, to increase the
area being measured.
The NDVI Triangle Method can cover all areas of non-coverage without inventory cost,
operating expense, or maintenance requirements. As climate change continues to cause variations
in weather patterns, there will be a need for a wide-ranging method and inexpensive way to
measure ET for all of California. This method may be the preferred option as local government’s
budgets are unaffected using satellite imagery.
5.3.4 Threats
The Penman-Monteith data for its equation comes from ground-based weather stations.
These stations need to be set on irrigated land to provide accurate estimates of reference ET. If
another drought occurs and water restrictions occur, there will be limited locations to place a
weather station to measure ET. Many weather stations in California have been moved because the
land they are situated upon is leased and when it expires, they must relocate. In addition, the
Government’s support of climate change is waning and that may affect the grants provided to fund
these stations. Finally, methods using satellites may undermine the need for expensive and high
maintenance weather stations.
Practitioners of the NDVI Triangle method may not have to directly pay for access to
satellite imagery data but, there is an associated cost in keeping these in orbit. Satellites age, break
in space where they cannot be fixed, lose orbit and are lost forever. Replacing a satellite or putting
a constellation in orbit is prohibitively expensive and may only serve the sponsors of the satellite
directly. Cloud cover and smoke from large fires remain a hindrance to accurately computing ET
with satellite imagery.

51

5.4 Future Work
The study of using the NDVI Triangle to measure ET may be expanded to areas of
California where CIMIS ground stations are more prevalent in the region. In the future, there
should be an increased frequency of data collection from satellites to better resolve the accuracy of
this method of measuring ET. If the temporal data points were increased and more densely
populated, an accurate value would come from the additional comparative days. Future studies
could also combine a set of weather stations in a region of interest and compare it to the region of
interest. In that way, microclimate influence would be nullified by the integration of values from
other stations outside that realm of weather influence.
A more pointed and directed study of a location, using a pixel as a point of study instead of
and entire region, would include more LDCM’s cloudless day passes required for this
measurement. In turn, a more robust project conclusion and clearer refinement of the results could
be established.
Studying evapotranspiration by continual comparisons of ground and satellite-based
methods can give rise to a broad-based use of satellite imagery for evapotranspiration value
measurements for remote areas that are either inaccessible or are unable to purchase expensive
ground-based stations due to fiscal considerations.

52

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56

Appendix A Tables

Table 5. Summary of equipment and software needs for Normalized Difference Vegetation
Index (NDVI) equation

Equipment/Software Source Application
ENVI ENVI
Visualization/Analysis/
Data Organization
ArcMap ESRI Visualization/Analysis
ArcCatalog ESRI Data Organization
Sankey www.Sankeymatic.com Mode Flow Charts
S3 Amazon Web Services Database Storage
Slack Slack.com Team Posting
USC Library Services MyUSC Research
Google Scholar https://scholar.google.com Research

Table 6 Download earth explorer Landsat Data Continuity Mission (LDCM) satellite
imagery

Step One Goto https://earthexplorer.usgs.gov/ for satellite data.
Step Two Select location: MNWD – Centroid, Lat. 33.158269, Long. -117.268689
Step Three Select date range
Step Four Select data sets i.e. LDCM OLI/TIRS C1 Level-1
Step Five Select additional criteria i.e. cloud cover
Step Six Select results
Step Seven Select area of interest for download
Step Eight Download Level-1 GeoTIFF Data Product (967.1 MB)
Step Nine Open “7 Zip”
Step Ten Select *. Tar file
Step Eleven Select “Open Inside”
Step Twelve Extract data
Step Thirteen Save to folder
Step Fourteen Test data

Table 7 Calculation of Reflectance for study area using multispectral calculations

Step One Open ENVI
Step Two File open
Step Three Select Shapefile
Step Four Select file dropdown
Step Five Open as Optical Sensor
Step Six Select “LANDSAT”
Step Seven Geotiff with Metadata
Step Eight Open MTL File

57

Step Nine Place shapefile over MTL in the Layer Manager
Step Ten Goto tool box
Step Eleven Select “Radiometric Calibration”
Step Twelve Select “Multispectral “Calibration (ensure spectral subset indicates 7
out of 7 bands)
Step Thirteen Select “file selection” in the right pane
Step Fourteen Select the shape file
Step Fifteen Click “OK”
Step Sixteen Select “Reflectance in the Radiometric calibration”
Step Seventeen Save as Reflectance
Step Eighteen Remove MTL from the Layer Manager

Table 8 Calculation of Albedo from multispectral bands 1,2,3,4 and 5

Step One Insert Band Math Expression = [((0.356*B1) + (0.130*B2) +
(0.373*B3) + (0.085*B4) + (0.072*B5) -0.0018) / 1.016]
Step Two Select Band 1 “Blue”
Step Three Select Band 2 “Red”
Step Four Select Band 3 “Infrared”
Step Five Select Band 4 “Shortwave infrared 1”
Step Six Select Band 5 “Shortwave infrared 2”

Table 9 Calculation of NDVI from Near Infrared (NIR) and Red multispectral bands

Step One Insert Band Math Expression = [(b1-b2)/(b1+b2)]
Step Two Select “Toolbox”
Step Three Select “Reflectance” file
Step Four Select Band 1 “NIR”
Step Five Select Band 2 “Red”

Table 10 Resize data using pixel aggregation resampling methods

Step One Select “Toolbox”
Step Two Select “Resize Data”
Step Three Select “Reflectance”
Step Four Select “Spatial Subset” > (select map, 20 samples, 20 lines)
Step Five Select “Red” & “Near Infrared”
Step Six Select Layer Manager
Step Seven Right click on resized data
Step Eight Select “Quick Stats”
Step Nine Copy the DN for band One, open Excel and paste band one data into
new column. Repeat with band two
Step Ten Highlight to select both columns and create chart/scatter plot
Step Eleven Right click data line in chart
Step Twelve Select “Add Trend Line”

58

Step Thirteen Select “display equation on chart” and “display R-squared value on
chart”
Step Fourteen Copy the y intercept number on the chart
Step Fifteen Click on the file name (The header information will appear on the right)
Step Sixteen At the bottom click on "Spatial Subset" to subset all the bands in the
image or "Spectral Subset" to choose one band to subset
Step Seventeen "Spatial Subset" brings up another box for choosing the exact location
of the subset
Step Eighteen "Image" will bring up the image with a subset box that can be re-sized
and moved around the image.

Table 11 Calculation of Weighted Difference Vegetation Index (WDVI) from multispectral
bands 3, 4 and the y intercept from the resampled data

Step One Insert Band Math Expression = B3-1.0157*B4
Step Two Add equation B3-1.2337*B4 (the 1.2337 number comes from the Y
intercept copied from the chart)
Step Three Select Band 3 “Red” from calculated reflectance
Step Four Select Band 4 “NIR” from calculated reflectance

Table 12 Calculation of the soil brightness correction L Value from NDVI and WDVI

Step One Insert Band Math Expression = [(1-2*1.6-b11*b22)]
Step Two Select Band 11 “NDVI”
Step Three Select Band 22 “WDVI”

Table 13 Calculation of Soil-adjusted Vegetation Index (SAVI) from bands 3,4, and the L
value
Step One Insert Band Math Expression = ((B4-B3) *(1+B33))/(B4+B3+B33)
Step Two Select Band 3 “Red”
Step Three Select Band 4 “NIR”
Step Four Select Band 33 “L” value

Table 14 Calculation of the Leaf Area Index (LAI) from the SAVI values

Step One Insert Band Math Expression = [(11*(b44^3))]
Step Two Select Band 44 “SAVI”

Table 15 Calculation of surface emissivity from calculated LAI

Step One Insert Band Math Expression = [.986+0.004*b11]
Step Two Select Band 11 “LAI”

59

Table 16 Calculation of Thermal Infrared (TIR) from LCDM multispectral bands 10 and
11

Step One Select “Toolbox”
Step Two Select “Radiometric Calibration”
Step Three Select “Thermal Bands” (2 of 2 bands)
Step Four Select “Spatial Subset”
Step Five Select shapefile of study area
Step Six In the radiometric Calibration box> keep “Radiance “selected

Table 17 Calculation of the canopy resistance to vapor transit (Rc) from both Thermal
Infrared (TIR) bands

Step One Insert Band Math Expression = [(((B1-0)/1) - ((1-b6) *1))]
Step Two Select Band 1 “TIR” (check that the bands are 2/2)
Step Three Select Band 6 “Emissivity”

Table 18 Calculation of Top of Atmospheric (TOA) spectral radiance from Band 10

Step One Insert Band Math Expression = [((1201.14)/(alog(((b1*480.89)/b2)
+1)))]
Step Two Select Band 1 “Emissivity”
Step Three Select Band 2 “Rc Band 10”

Table 19 Calculation of Top of Atmospheric (TOA) spectral radiance from Band 11

Step One Insert Band Math Expression =
[((1321.08)/(alog(((b1*774.89)/b2)+1)))]
Step Two Select Band 1 “Enb”
Step Three Select Band 6 “Rc Band 11”

Table 20 Conversion of TOA average temperatures from K to °C

Step One Insert Band Math Expression = ((b10+b11)/2)
Step Two Select Band 10 “LST B10”
Step Three Select Band 11 “LST B11”

Table 21 Conversion to °C from K by adding absolute zero

Step One Insert Band Math Expression = [B1-273.15]
Step Two Select Band 1 “Average Temperature”

Abstract (if available)

Abstract This project offers a comparative study between a ground-based weather station and satellite-based method of calculating evapotranspiration (ET). Using four selected cloudless days measured between 10:28 am and 11:30 am DST local in Los Angeles in 2016 (08 February, 19 April, 22 June, and 08 July), the aim of this project is to determine if the Normalized Difference Vegetation Index (NDVI) Triangle method, a satellite-based methodology, could be used as an acceptable alternative to measure ET for locations without a ground-based weather station. ❧ The Moulton Niguel Water District (MNWD), located in Orange County, California was selected as the study area for this project. Weather station #245, located on the Coto De Caza golf course, generated the ground-based weather data for the Penman-Monteith calculation of evapotranspiration for the MNWD. In contrast, the satellite method used the Landsat Data Continuity Mission’s (LDCM) multi-spectral and thermal bands to calculate ET by Land Surface Temperature (LST) and NDVI values. These two data inputs, by the application of band math, were combined to create a two-dimensional NDVI Triangle pixel plot evapotranspiration estimate for each day calculated. The data from the two methodologies were then compared, with the assumption the Penman-Monteith method was the most accurate measure of ET. The results were statistically compared and analyzed for accuracy through Root Mean Square Error (RMSE), Mean Absolute Deviation (MAD), Mean Absolute Percentage Error (MAPE) and the coefficient of determination calculations. The results, although limited by sample size, indicate the NDVI Triangle method can be used to estimate ET. The process of creating the NDVI Triangle 2-D plot from multi-spectral and thermal bands from the LDCM is presented in detail, in addition to the process of defining the dry and wet edges of the plotted NDVI Triangle.

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Asset Metadata

Creator Snoddy, Jeffrey Keith (author)

Core Title A comparative study of ground and satellite evapotranspiration models for southern California

School College of Letters, Arts and Sciences

Degree Master of Science

Degree Program Geographic Information Science and Technology

Publication Date 10/19/2018

Defense Date 10/18/2018

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

Tag 2-D,band math,Drought,ENVI,ET,evapotranspiration,imagery,landsat,LDCM,NDVI,OAI-PMH Harvest,satellite,Triangle

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Wilson, John (committee chair), Marx, Andrew (committee member), Ruddell, Darren (committee member)

Creator Email snoddy@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-85802

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