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Active and passive microwave remote sensing of soil moisture

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The Pennsylvania State University
The Graduate School
Department o f Civil and Environmental Engineering
ACTIVE AND PASSIVE MICROWAVE REMOTE SENSING
OF SOIL MOISTURE
A Thesis in
Civil Engineering
by
Rajat Bindlish
© 2000 Rajat Bindlish
Submitted in Partial Fulfillment
o f the Requirements
for the Degree o f
Doctor o f Philosophy
May 2000
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Rajat Bindlish
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h
oZcrerQ
Ana P. Bi
A ssociate P rofessor o f C ivil E ngin eering
T hesis A dvisor
Chair o f C om m ittee
Christopher J>
A ssociate Profess,
'C iv il Enuineerinu
Arthur C. M iller
Professor o f C iv il Enuineeriim
T oby hr Carlspn
(
Professor o f/M eteorolou
7 e 6-
jo CO
‘
nrevv S. RogoW^ki
j
iunct P r o f e s s o r o r S e iiH r y s ic s
A ssociate P rofessor o f Electrical E ngineering
P.
Q w m
aul P. Jovan isc^ /
Professor o f C iv il E ngineering
Head o f the D epartm ent o f C ivil and
E nvironm ental E ngineering
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Abstract
Soil moisture plays a major role in the global hydrologic cycle. Most importantly,
soil moisture controls the partitioning o f available energy at the land surface into latent and
sensible heat fluxes. This study focuses on the development o f a consistent methodology for
soil moisture inversion from Synthetic Aperture Radar (SAR) data using the Integral
Equation Model (Fung et al., 1992) without the need to prescribe time-varying land-surface
attributes as constraining parameters.
Specifically,
the dependence of
backscatter
coefficients obtained from Synthetic Aperture Radar (SAR) on the soil dielectric constant,
surface roughness height and correlation length was investigated. The IEM was used in
conjunction with an inversion model to retrieve soil moisture using multi-frequency and
multi-polarization data (L, C and X-Bands) simultaneously. The results were cross-validated
with gravimetric observations obtained during the Washita ‘94 field experiment in the Little
Washita Watershed, Oklahoma. The average error in the estimated soil moisture was o f the
order of 3.4%, which is comparable to that expected due to noise in the SAR data. The
retrieval algorithm performed very well for low incidence angles and over bare soil fields,
and it deteriorated slightly for vegetated areas, and overall for very dry soil conditions.
The IEM was originally developed for scattering from a bare soil surface, and
therefore the vegetation effects are not explicitly incorporated in the model. We coupled a
semi-empirical vegetation scattering parameterization to our multi-frequency soil moisture
inversion algorithm. This approach allows for the explicit representation o f vegetation
backscattering effects without the need to specify a large number o f parameters. One
important result o f this study was the fact that the retrieval algorithm performed well for
vegetated conditions when a land use based vegetation parameterization was used. The
explicit incorporation o f land-use in the parameterization scheme is equivalent to
incorporating the effect o f vegetation structure in the soil moisture estimates obtained using
the SAR observations.
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iv
ESTAR images o f brightness temperature obtained during the same period were
inverted independently for soil moisture. The results at individual sampling sites were first
compared against gravimetric soil moisture observations for Washita '94, and the RMS errors
for both applications were between 3% and 4%. Subsequently, we investigated the use o f
high resolution SAR-derived soil moisture fields to estimate sub-pixel variability in ESTAR
derived fields. The effect o f sub-pixel variability o f various land surface properties (namely
soil moisture, soil texture, soil temperature, and vegetation). The results demonstrated the
linear scaling behavior o f ESTAR based soil moisture estimates.
We also investigated the problem o f consistency between the two systems. Estimated
and observed brightness temperature fields were compared and analyzed to establish the
aggregation
kernel inherent
to
ESTAR, that
is, how
the
instrument actually
processes/integrates sub-pixel variability. The scaling properties o f both SAR and ESTAR
at all frequencies were investigated and the results indicated that both sensors demonstrated
fractal behavior. The objective was to determine whether scaling arguments can be used to
disaggregate ESTAR data to finer spatial resolutions. The results suggested that the two
systems can be used to complement each other, and there is a potential to downscale ESTAR
observations for high resolution soil moisture estimation, using only one SAR frequency
(e.g. L-band).
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TABLE OF CONTENTS
LIST OF FIG U R ES............................................................................................................ viii
LIST OF TABLES.............................................................................................................. xiii
ACKNOWLEDGEMENTS............................................................................................... xiv
CHAPTER 1 - INTRODUCTION...................................................................................... 1
1.1 Importance o f Soil M oisture..................................................................................1
1.1.1 Weather and Climate Modeling................................................................. 3
1.1.2 Flood Forecasting........................................................................................5
1.2 Use o f Microwave Remote Sensing.................................................................... 6
1.3 Objectives o f this W ork.........................................................................................9
1.4 Thesis Structure.......................................................................................................10
CHAPTER 2 - LITERATURE REVIEW.........................................................................11
2.1 Introduction.............................................................................................................. 11
2.2 Fundamentals o f Microwave Remote Sensing....................................................14
2.2.1 Role o f Dielectric Constant o f Soils and Soil Texture............................14
2.2.2 Penetration D epth........................................................................................21
2.2.3 Choice o f Microwave Frequency..............................................................23
2.3 Types o f Microwave Remote Sensing (Active and Passive)............................ 27
2.3.1 Active Microwave Remote Sensing.................................................. 28
2.3.1.1 Backscattering M odels.............................................................30
2.3.1.2 Effect of Surface Roughness................................................... 31
2.3.1.3 Effect o f Vegetation................................................................. 31
2.3.2 Passive Microwave Remote Sensing.................................................32
2.3.2.1 Brightness Temperature Models..............................................36
2.3.2.2 Effect o f Surface Roughness................................................... 40
2.3.2.3 Effect of Vegetation................................................................. 41
CFLAPTER 3 - MULTIFREQUENCY SOIL MOISTURE INVERSION FROM
SAR MEASUREMENTS WITH THE USE OF IEM .............................................44
3.1 Introduction........................................................................................................... 44
3.2 The Relationship between Backscattering Coefficient and Volumetric
Soil M oisture......................................................................................................... 46
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vi
3.3
3.4
3.5
3.6
3.2.1 Empirical Soil Moisture Estimation M odels............................................47
3.2.2 Integral Equation Model (IEM, Fung et al.,1992)................................. 49
3.2.3 Effect o f Land Surface Parameters on Backscattering Coefficient in
IEM ...................................................................................................................49
Data S ynopsis..........................................................................................................51
3.3.1 Description o f SAR Data.............................................................................51
3.3.2 Little Washita W atershed........................................................................... 57
M ethodology............................................................................................................ 60
Results and D iscussion...........................................................................................64
3.5.1 Soil Moisture Inversion...............................................................................64
3.5.2 Aggregation and Data Compression.......................................................... 80
Final Com m ents...................................................................................................... 92
CHAPTER 4 - PARAMETERIZATION OF VEGETATION BACKSCATTER
EFFECTS IN RADAR BASED SOIL MOISTURE ESTIMATION.....................95
4.1 Introduction.............................................................................................................. 95
4.2 Backscatter from Vegetation Canopies.................................................................96
4.3 Current Approaches to Modeling Backscatter from Vegetation Canopies
98
4.3.1 Empirical M odels........................................................................................ 99
4.3.2 Theoretical M odels.......................................................................................102
4.3.3 Semi-empirical M odels............................................................................... 105
4.4 Vegetation Backscattering Parameterization....................................................... 105
4.5 Empirical Formulation to Parameterize Vegetation Effects..............................107
4.6 Application o f Vegetation Backscattering M o d el.............................................. 112
CHAPTER 5 - SUB-PIXEL VARIABILITY OF REMOTELY SENSED SOIL
MOISTURE: AN INTER-COMPARISON STUDY OF SAR AND ESTA R
117
5.1
5.2
5.3
5.4
5.5
5.6
Introduction...............................................................................................................117
Data Synopsis.......................................................................................................... 119
Soil Moisture Retrieval from SA R ........................................................................119
Soil Moisture Retrieval from ESTA R.................................................................. 120
Compatibility o f SAT and ESTAR Soil Moisture Retrievals............................121
Sub-pixel Variability o f ESTAR Soil Moisture R etrievals............................... 127
5.6.1 Soil M oisture................................................................................................ 127
5.6.2 Soil T exture...................................................................................................130
5.6.3 Soil Tem perature.......................................................................................... 132
5.6.4 Vegetation...................................................................................................... 134
5.7 Error Analysis for ESTAR Estimated Soil M oisture..........................................144
5.8 ESTAR Aggregation Kernel and Land Surface Properties................................ 147
5.9 Scaling Behavior o f SAR and ESTA R................................................................. 149
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vii
CHAPTER 6 - CONTRIBUTIONS AND RESEARCH NEEDS.................................. 155
6.1 Summary and Research Findings......................................................................... 155
6.1.1 Multi-frequency, Multi-polarization Soil Moisture Model from
SAR Measurements....................................................................................... 155
6.1.2 Parameterization o f Vegetation Effects in Radar based Soil
Moisture Estimates.........................................................................................156
6.1.3 Sensitivity and Sub-pixel Variability o f ESTAR Soil Moisture
E stim ates......................................................................................................... 156
6.1.4 Compatibility o f SAR and E S T A R ........................................................... 156
6.1.5 Scaling and Disaggregation o f ESTAR Imagery......................................157
6.2 Research Needs and Recommendations for FutureW ork.................................157
6.2.1 Transportability o f Soil Moisture Estimation Algorithms........................157
6.2.2 Optimal Estimates of Soil Moisture using Hydrologic Models and
its Use in Climate M odels.............................................................................158
6.2.3 Operational Soil Moisture Monitoring from Space.......................................158
APPENDIX - SENSITIVITY OF SAR BASED SOIL MOISTURE
ESTIMATION ALGORITHM TO INITIAL G U ESS............................................. 159
A.l Sensitivity to Soil M oisture.................................................................................. 159
4.2 Sensitivity to Soil Roughness................................................................................ 159
BIBLIOGRAPHY..................................................................................................................163
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LIST OF FIGURES
Figure 2.1
-
Laboratory measurements o f the real and imaginary parts o f
the dielectric constant for three soils as a function o f moisture
content at a wavelength o f 21 cm.....................................................17
Figure 2.2
-
Measured dielectric constant at 4, 10, and 18 GHz for three
different fields....................................................................................22
Figure 2.3
-
Calculated temperature sensing depth for sand as a function
o f frequency for five different moisture profiles........................... 24
Figure 2.4
-
Summary of experimental data o f the vegetation parameter b
as a function o f wavelength for different land uses......................26
Figure 2.5
-
Schematic diagram o f a passive microwave emission model
from land surfaces............................................................................. 34
Figure 2.6
-
Step-wise flow diagram o f soil moisture estimation algorithm
using passive microwave observations.......................................... 39
Figure 3.1
-
Backscattering from randomly rough surface................................ 50
Figure 3.2a
-
Relationship between backscattering coefficient and
dielectric constant............................................................................. 52
Figure 3.2b
-
Relationship between backscattering coefficient and surface
roughness........................................................................................... 53
Figure 3.2c
-
Relationship between backscattering coefficient and surface
correlation length.............................................................................. 54
Figure 3.3
-
Differential increase in backscatter coefficient with respect to
soil moisture as a function o f land surface parameters................ 55
Figure 3.4a
-
Digital Elevation Map (DEM) o f Little Washita watershed........ 58
Figure 3.4b
-
Soil texture map o f Little W ashita w atershed................................59
Figure 3.5
-
Location o f sampling sites during W ash ita’9 4 ............................ 61
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ix
Figure 3.6a
-
Estimated
volumetric soil moisture for Little Washita
watershed on April 11, 1994........................................................... 65
Figure 3.6b
-
Estimated
volumetric soil moisture for Little Washita
watershed on April 12, 1994........................................................... 66
Figure 3.6c
-
Estimated
volumetric soil moisture for Little Washita
watershed on April 13, 1994........................................................... 67
Figure 3.6d
-
Estimated
volumetric soil moisture for Little Washita
watershed on April 15, 1994............................................................68
Figure 3.6e
-
Estimated
volumetric soil moisture for Little Washita
watershed on April 16, 1994............................................................69
Figure 3.6f
-
Estimated
volumetric soil moisture for Little Washita
watershed on April 18, 1994............................................................70
Figure 3.7a
-
Scatter plot o f measured volumetric soil moisture and
estimated volumetric soil moisture for all the sampling sites
for the entire duration o f the Washita ‘94 experiment................. 71
Figure 3.7b
-
Time evolution o f retrieval errors o f soil moisture (estimatedobserved) for different vegetation types........................................72
Figure 3.7c
-
Relationship between retrieval errors o f soil moisture and
vegetation water content at the sites where vegetation
sampling was conducted during Washita’9 4 .................................73
Figure 3.7d
-
Scatter plot o f measured volumetric soil moisture and
estimated volumetric soil moisture for all the sampling sites
for the entire duration o f the Washita ‘94 experiment after the
vegetation correction (Eq. 3.13) was applied................................ 74
Figure 3.7e
-
Time evolution o f retrieval errors o f soil moisture (estimatedobserved) for different vegetation types after the vegetation
correction (Eq. 3.13) was applied...................................................75
Figure 3.8
-
Scatter plot o f measured surface roughness and estimated
surface roughness for all the Washita ‘94 sampling sites............81
Figure 3.9
-
Estimated Volumetric Soil Moisture using different methods
o f aggregation for April 11, 1994...................................................83
Figure 3.10
-
Estimated volumetric soil moisture for site 14 on April 11,
1994....................................................................................................84
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X
Figure 3.11
-
Estimated soil moisture using different aggregation
methodologies at 300 m for site 14 on April 11, 1994................ 85
Figure 3.12a
-
Scatter plot o f measured volumetric soil moisture and
estimated volumetric soil moisture using different methods o f
aggregation for all sampling sites and for the entire duration
o f the Washita ‘94 experiment on April 11, 1994 ........................86
Figure 3.12b
-
Scatter plot o f measured volumetric soil moisture and
estimated volumetric soil moisture using different methods o f
aggregation for all sampling sites and for the entire duration
o f the Washita ‘94 experiment on April 12, 1994........................87
Figure 3.12c
-
Scatter plot o f measured volumetric soil moisture and
estimated volumetric soil moisture using different methods of
aggregation for all sampling sites and for the entire duration
o f the Washita ‘94 experiment on April 13, 1994...................... 88
Figure 3 .12d
-
Scatter plot o f measured volumetric soil moisture and
estimated volumetric soil moisture using different methods o f
aggregation for all sampling sites and for the entire duration
o f the Washita ‘94 experiment on April 15, 1994...................... 89
Figure 3 .12e
-
Scatter plot o f measured volumetric soil moisture and
estimated volumetric soil moisture using different methods o f
aggregation for all sampling sites and for the entire duration
o f the Washita ‘94 experiment on April 16, 1994...................... 90
Figure 3 .12f
-
Scatter plot o f measured volumetric soil moisture and
estimated volumetric soil moisture using different methods o f
aggregation for all sampling sites and for the entire duration
o f the Washita ‘94 experiment on April 18, 1994...................... 91
Figure 4.1a
-
C-band imagery over Little Washita watershed on April 11,
1994...................................................................................................109
Figure 4. lb
-
L-band imagery over Little Washita watershed on April 11,
1994...................................................................................................110
Figure 4.2
-
Scatter plot o f measured volumetric soil moisture and
estimated volumetric soil moisture for all the sampling sites
for the entire duration o f the Washita ‘94 experim ent................ 114
Figure 4.3
-
Scatter plot o f measured volumetric soil moisture and
estimated volumetric soil moisture for all the sampling sites
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xi
for the entire duration o f the Washita ‘94 experiment after
land use based vegetation parameterization................................... 115
Figure 5.1
-
Estimated volumetric soil moisture for April 11 derived from
ESTAR (200 m resolution), and SAR data (30 m resolution)
(only over the SAR shuttle trajectory)............................................ 122
Figure 5.2
-
Comparison between measured and estimated volumetric soil
moisture using SAR and ESTAR at the test sites for April 11,
1994.....................................................................................................124
Figure 5.3
-
Brightness temperature image observed by ESTAR, and that
derived from SAR estimated soil moisture (only over the
SAR shuttle trajectory)..................................................................... 125
Figure 5.4
-
Comparison o f ESTAR brightness temperature observations
with SAR derived brightness temperature estim ates....................126
Figure 5.5
-
Schematic diagram to estimate sensitivity o f ESTAR based
soil moisture estimation model to sub-pixel variability o f soil
m oisture.............................................................................................. 128
Figure 5.6
-
Sensitivity o f ESTAR soil moisture retrieval algorithm to
sub-pixel variability o f soil moisture.............................................. 129
Figure 5.7
-
Sensitivity o f ESTAR retrieval algorithm to sub-pixel
variability o f soil texture...................................................................131
Figure 5.8
-
Sensitivity o f ESTAR soil moisture estimation algorithm to
soil temperature and vegetation water content............................... 133
Figure 5.9a
-
Average value o f Normalized Difference Vegetation Index
(NDVI) at ESTAR resolution (800 m ) ........................................... 135
Figure 5.9b
-
Sub-pixel variability o f NDVI at ESTAR footprint (obtained
by using 30 m Thematic Mapper d ata)........................................... 136
Figure 5.9c
-
Land-use classification map o f SGP ‘97 domain obtained by
using the most commonly occuring land-use classification
Figure 5.10a
-
Sub-pixel variability o f NDVI as a function o f average value
o f NDVI for W inter W heatl39
Figure 5.10b
-
Sub-pixel variability o f NDVI as a function o f average value
o f NDVI for most prevalent land-uses in SGP ‘97 dom ain
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137
140
xii
Figure 5.11a -
Soil moisture imagery over SGP ‘97 domain obtained by
using the average value o f NDVI.....................................................141
Figure 5.11b
-
Soil moisture imagery over SGP ‘97 domain obtained by
using a one-fold increase in vegetation water content................. 142
Figure 5.11c
-
Soil moisture imagery over SGP ‘97 domain obtained by
using a one-fold decrease in vegetation water content................ 143
Figure 5.12
-
Error analysis for ESTAR estimated soil moisture retrieval
algorithm for sand and clay for different levels o f soil
temperature, vegetation water content and brightness
tem perature........................................................................................ 146
Figure 5.13
-
Plot o f spectral density function at different resolutions for
ESTAR and SAR im agery............................................................... 150
Figure 5.14
-
Soil moisture estimate obtained by using downscaled ESTAR
brightness temperature......................................................................152
Figure 5.15
-
Comparison between measured and estimated volumetric soil
moisture using SAR. ESTAR, and downscaled ESTAR data
at the test sites for April 11, 1994....................................................153
Figure AI
-
Sensitivity o f SAR based soil moisture estimates to initial
soil moisture....................................................................................... 152
Figure A2
-
Sensitivity o f SAR based soil moisture estimates to initial
soil surface roughness.......................................................................153
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LIST OF TABLES
Table 3.1
Daily specification o f the SIR-C/X-SAR data during Washita
'94........................................................................................................ 56
Table 3.2
Site characterization for W ashita '94 April m ission.....................77
Table 3.3
Difference in field-averaged backscatter coefficients [I.Band, HH polarization] between bare soil (BS-Site 12) and
winter wheat (WW-Site 53), and between bare soil and
alfalfa (AL-Site 11)........................................................................... 79
Table4.1a-c
-
Regression constant for linear and exponential fit to
NDVI for Washita '94 study area...............................................111-112
Table 4.2
Values o f vegetation constants used in the semi-empirical
vegetation m odel................................................................................113
Table 5.1
Mean sand and clay content present in different soil textures.... 132
Table 5.2
Statistics o f the difference in soil moisture (%) due to
vegetation uncertainty....................................................................... 144
Table 5.3
Ratio o f multi-linear regression aggregation kernel to the
standard error for different land surface properties as a
function o f land-use.......................................................................... 149
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xiv
Acknowledgments
I would like to express my gratitude to my advisor, Dr. Barros, for her guidance,
insight, and support during the course o f this work. I would also like to thank the members
o f my committee, Drs. Chris Ruf, Andy Rogowski, Chris Duffy, Toby Carlson, and Art
Miller for their helpful suggestions. I am thankful to Dr. Tom Jackson for providing the
ESTAR data for the Washita ‘94 experiment. I thank Drs. Ted Engman, A.K. Fung, Ann
Hsu, and Tom Jackson for their input at different stages o f this research.
I would like to acknowledge the contribution o f my parents and my brother. They
have instilled in me the value o f education from my earliest days and have provided
encouragement throughout my studies.
This research was funded by National Aeronautics and Space Administration
(NASA) under contract NAGW-2686 with the Earth System Science Center at The
Pennsylvania State University.
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1
Chapter 1
Introduction
“Hydrology is primarily concerned with water on or near land surface....” (Maidment,
1991).
In an era o f advances in scientific understanding and public awareness o f
environmental issues, National Aeronautics and Space Administration (NASA) launched the
Mission to Planet Earth (MTPE) program. Viewing the Earth from space is essential to
comprehending the cumulative influence o f human activities on its natural resource base.
This thesis focuses on the development o f operational soil moisture retrieval algorithms
using microwave observations from airbome/spacebome sensors.
1.1
Im portance of Soil M oisture
Soil moisture is a key state variable in land surface hydrology; it controls the
proportion o f rainfall that percolates, runs off, or evaporates from the land. Soil moisture
tracks precipitation and evaporation over periods o f days to weeks and provides a historical
record o f atmospheric-land interactions. It integrates much o f the land surface hydrology and
plays a crucial role in the interface between the earth surface and the atmosphere. Recycling
o f water through evapotranspiration and precipitation is the primary factor in the persistence
o f dry or wet anomalies over large continental regions during summer. As a result, soil
moisture is the most significant boundary condition controlling summer precipitation over
the central U.S. and other large mid-latitude continental regions (Beljaars et al., 1996).
Although soil moisture constitutes a small percentage o f global water, it is a key storage o f
water and is responsible for Earth’s physical capacity to sustain life.
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9
The measurement o f soil moisture is important for understanding the global
hydrologic cycle and its effect on weather and climate. Soil moisture is a useful parameter
across all scales. On a global scale, soil moisture is important as a boundary condition for
hydrologic and climate models.
On a regional scale, it is important for agricultural
assessment (crop yield models, drought prediction, etc.) and flood control. A number o f
environmental disasters - including floods, flash floods, droughts, and landslides - are
closely linked to soil moisture that better measurements would help reduce the potential for
damage from such events. Floods are, by a large margin, the most costly of natural hazards
in terms o f both human lives and property damages (NRC, 1996).
As important as it seems to our understanding o f hydrology, soil moisture is a
descriptor that has not had widespread application in the modeling o f these processes
(Engman and Gumey, 1991). There are two important reasons for this omission. First, soil
moisture is a difficult variable to measure on a consistent and spatially comprehensive basis.
The large spatial and temporal variability that soil moisture exhibits in the natural
environment makes it difficult to measure and use in Earth Science applications. Secondly,
the understanding o f the role o f soil moisture in hydrology and ecosystem processes has been
developed from point studies where the emphasis has been on the variability o f soil moisture
with depth. As a result, most models have been designed around the available point data,
and do not describe the influence o f spatial variability.
Precise in situ (point) measurements o f soil moisture are sparse and each value is
representative o f only a small area for the time period o f measurement.
Therefore,
hydrologists often estimate this key hydrologic variable as a residual in water balance
calculations.
Remote sensing, if achievable with sufficient accuracy, reliability and
repeatability, would provide truly meaningful wide-area soil wetness or soil moisture data
for hydrological studies across large continental regions (Engman and Gumey, 1991).
Soil physical and hydraulic properties are o f prime interest for water and energy
balance studies and simulations o f land surface atmosphere interaction at various scales.
Although soil properties typically are measured in the field at the point scale, such data are
unavailable over large areas, or have limitations in accounting for regional spatial variability,
or are prohibitively expensive, tedious and time consuming to cover large areas. Methods
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3
based on remote sensing provide alternate tools to obtain quick estimates o f soil properties.
For example, Van de Griend and O ’Neill (1986) used microwave brightness temperature
( TB), thermal infrared data and inversion o f soil hydraulic models to estimate soil hydraulic
parameters at a plot scale. The reliability o f such methods is questionable, due to the
uncertainties involved in the microwave estimation o f soil moisture and soil hydraulic
models. Remotely sensed TB may be inverted to estimate soil hydraulic properties using a
microwave emission model and soil moisture and temperature profiles generated by moisture
and energy balance equations (Camillo, 1987). Application o f such approaches on a regional
scale may generate large-scale soil properties for input into land-atmosphere models.
Regional soil properties may be estimated by inversion o f a dynamic one-dimensional soilwater-vegetation model in conjunction with soil moisture obtained from microwave remote
sensing, and evaporation derived from reflective and thermal infrared remote sensing
(Feddes et al., 1993). These approaches are promising if all input data requirements are
satisfied, which is not the case over areas having limited or no data on hydrologic and
meteorological parameters.
1.1.1
Weather and Climate Modeling
The land surface boundary condition plays a key role in determining the diumal
evolution o f the atmospheric boundary layer together with geographic and synoptic controls.
In turn, the boundary layer largely controls the evolution o f convection and the diumal cycle
o f precipitation (again influenced by regional dynamic features). The key boundary layer
parameters are the equivalent potential temperature and the lifting condensation level. The
seasonal cycle o f soil temperature is closely linked to the seasonal cycle o f equivalent
potential temperature (Betts and Ball, 1995), but superimposed on this is the large impact o f
soil moisture changes. High values o f soil moisture lead, in the mean, to a large evaporation
fraction, a higher afternoon equivalent potential temperature, and a lower cloud-base. These
favor the development o f precipitating convection, which has a positive feedback on soil
moisture (Beljaars et al., 1996). Large-scale studies using both climate and forecast models
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4
show this positive feedback, which can extend periods o f drought or excess precipitation
until the cycle is broken by changes in the planetary-scale wave pattern.
Near surface soil moisture serves a fundamental role in this redistribution through the
energy associated with evaporation. A number o f numerical climate modeling studies have
demonstrated the sensitivity o f climate to soil moisture (W alker and Rowntree, 1977; Rind,
1982; Shukla and Mintz, 1982; Rowntree and Bolton, 1983; Delworth and Manabe, 1988,
1989,1993; Mintz and Walker, 1993). The practical implication o f this sensitivity is that the
predictability of the climate system, whether it is for seasonal prediction or global change
assessment, is dependent on robust characterization o f soil moisture in global climate models
(GCMs). Access to global soil moisture estimates derived from spacebome sensors at scales
resolved by these numerical models of weather and climate (ranging from 30 to hundreds of
kilometers) will provide a powerful means to validate and improve the land component of
these models.
Current GCMs incorporate land surface and soil hydrological processes in rather
simplified forms. Often these models do not recognize the dynamic nature of soil moisture
movement. The major impediment to doing so is the spatial variability o f soil hydrologic
properties within the grid size o f GCMs. The non-linear relationships between soil moisture
content and moisture flux are neglected in the land surface parameterization schemes in the
GCMs.
The potential impact o f surface soil moisture observations in GCMs is related to
providing increased accuracy. Koster and Suarez (1996) provides an illustration o f the
enhanced predictability resulting from the correct knowledge o f soil moisture fields. They
show that with the added foreknowledge o f land surface moisture conditions, precipitation
predictability is enhanced in many continental regions, even in mid-latitudes. The land
mainly contributes to predictability in the transition zones between dry and humid regions
that coincide with areas where large scale variations in soil moisture are strongest.
Furthermore, Mitchell et al. (1996) demonstrated that the increase in skill associated
with including estimates o f soil moisture in Numerical W eather Prediction (NWP) models
used in the U.S. is equivalent to the increase in skill when model resolution was doubled.
Current NWP models have a 30 km resolution; in the future the enhanced models may
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5
achieve 10 km resolution. Remotely sensed soil moisture observations can provide valuable
initialization fields.
Climate variations cause large-scale patterns in soil moisture and they in turn are
influenced by soil moisture at smaller scales (> 30 km) (Grell et al., 1994). In order to
develop useful data sets to understand and predict hydroclimatic processes (such as largescale droughts and changes in continental water cycling), variations in soil moisture fields
resolved down to this scale are required.
Other physical processes such as severe
hydrometeorological events that cause flash floods are influenced by surface moisture
conditions at the scale o f convective storms and small basins (< 10 km). Useful soil moisture
data sets for understanding and predicting hydrometeorological events should resolve
variations that occur at this scale (Sellers, 1992).
The predictability o f a recent severe flooding event in the mid-western United States,
for example, has been shown to be highly sensitive to the characterization and tracking of
soil moisture conditions across the region. Betts et al. (1996), Beljaars et al. (1996), Chen
et al. (1996), and Paegle et al. (1996) consistently show that the skills o f operational highresolution NWP and regional atmospheric model forecasts o f the 1993 Upper Midwest U.S.
flooding event (a disaster that produced $15 billion in damages) is improved with realistic
soil moisture initial conditions. Wetter-than-normal soils preceding July 1993 caused greater
recycling o f local precipitation, leading to enhanced flooding.
1.1.2
Flood Forecasting
Soil moisture data can assist with operational flood forecasting.
Operational
forecasting is currently based on limited measurements o f rainfall and river stage, and in
some cases on some type o f soil moisture description usually in the form o f an antecedent
precipitation index. In many cases, poor forecasts are attributed to lack o f information about
the initial conditions, i.e., about soil moisture.
For watershed hydrologic model applications, there is an urgent need to have access
to distributed soil water fluxes at regular temporal resolutions over large areas. The yearly
integrated land surface and base flow water budgets are generally well predicted by the
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6
recent generation o f hydrologic models. However, estimation o f the ratio between base flow
and surface runoff, as well as the ratio between deep drainage and soil moisture content, is
very imprecise. The soil stratum, and in particular the unsaturated zone between the soil
surface and groundwater table (vadose zone), plays an important role (Bear, 1972). The
estimation o f soil moisture in the vadose zone is an important issue for short- and mediumterm meteorological modeling, hydrologic modeling, and monitoring o f plant C 0 2
assimilation and plant growth. If the vadose zone is inaccurately described, attempts to
monitor water quality and flooding risks often fail. Thus, “new ways” to parameterize
effective soil characteristics are needed.
Plant water supply is the dominant factor that affects plant growth and crop yields.
Monitoring soil moisture is a valuable way to detect water stress period (excess or deficit)
for yield forecasting or biomass monitoring, especially in areas where meteorologic
monitoring stations are sparse.
Soil moisture data also can help with flash flood and flood forecasting hazard
mitigation. The U.S. National Weather Service (NWS) River Forecast Centers (RFCs)
currently produce flash-flood guidance data products that are used by NWS local offices to
issue flash-flood warnings and watches (NRC, 1996). These guidance products are essential
antecedent surface moisture fields at about 30 km scale and higher. Observed precipitation
fields (principally from radar) are imposed on these fields to produce flood warnings and
flood watches. Availability o f observed soil moisture at these scales would substantially
impact the operational practices o f validating and calibrating flash-flood guidance products.
1.2
Use o f M icrowave Rem ote Sensing
Latent and sensible heat fluxes between the land and the atmosphere are critical
elements in the water and energy budgets over continental areas. Locally, the relative
contribution o f latent versus sensible heat fluxes is determined by the availability o f moisture
at the atmosphere-vegetation-soil interface. On average, the top 5-25 cm o f soil is the
principal reservoir o f this moisture supply to plants. Because soil moisture varies greatly
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7
from one location to another and from one time to another, single measurements have limited
meaning. On the other hand, it is difficult to conduct ground-based measurements o f soil
moisture on a consistent and widespread basis. Remote sensing and the prospect o f long­
term monitoring over large areas offer such an opportunity, both for science and for
operational applications ranging from precision farming to land and water resource
management (Engman and Gumey, 1991; Feddes, 1995; Jackson et al., 1995). To derive
physically consistent soil moisture fields from remote-sensing data, the observations must
be processed through adequate transformation models (retrieval algorithms); that is, the
inverse problem must be solved. One challenge that lies ahead o f the establishment o f
operational global soil moisture monitoring from space is the need to establish a framework
to address the inverse problem at the macroscale.
Microwave remote sensing can provide a direct measurement o f the surface soil
moisture for a range o f cover conditions and within reasonable error bounds. Since spatially
distributed and multi-temporal observations o f surface soil moisture are rare, the use of these
data in hydrology and other disciplines has not been fully explored or developed. The ability
to observe soil moisture frequently over large regions could significantly improve our ability
to predict runoff and to partition incoming radiant energy into latent and sensible heat fluxes
at a variety o f scales up to those used in global circulation models. A recent study by Ahuja
et al. (1993) indicates that average surface and profile properties (viz. the saturated hydraulic
conductivity, Ksal) can be estimated using changes in moisture content o f the surface soil, two
days after a thorough wetting. These findings were based on both controlled laboratory
experiments on selected soils and on numerical simulations. Such relations are valuable to
obtain estimates o f average Ksal from remotely sensed soil moisture observations made at two
days temporal resolution. Temporal observations o f surface soil moisture can provide the
information needed to determine key soil parameters such as saturated conductivity (Ahuja
et al., 1993). It should be noted that no satellite systems are in operation that are truly
capable o f reliable soil moisture measurement.
Nonetheless, an extensive amount o f research work has been done over the past few
decades in the form o f experimental and theoretical models. Most o f the work has focused
on (1) sensing soil moisture under bare soil and sparse vegetation conditions, (2) estimation
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8
o f vegetation properties, (3) estimating the depth o f snow pack, and (4) determining the
extent o f ice formation in the oceans and lakes.
The use o f remote sensing to measure soil moisture has been researched over the last
twenty years, using both passive and active microwave instruments (Ulaby et al., 1986).
Passive microwave measurements from low flying aircraft have proven measurement
accuracies on the order o f 3% of volumetric soil moisture at spatial scales o f a few tens o f
meters (Jackson et al., 1995). Unfortunately, the anticipated spatial resolution o f passive
microwave instruments operating in space is o f the order o f 10-30 km (Le Vine et al., 1989).
Given the large spatial variability o f soil moisture and land cover at much smaller spatial
scales, it is difficult to relate the remote sensing measurements to point measurements o f soil
moisture inside such a large pixel area, or over a range o f scales within the pixel.
Satellite-borne microwave radiometers have been providing information about
atmospheric and oceanic parameters in either a fully operational o r a quasi-operational mode
for several years. Nevertheless, with the exception of snow monitoring, this has not been the
case for land parameters. Primarily, this is because (1) the spatial resolution or field o f view
(FOV) o f the satellite is more compatible with the dimensions associated with the spatial
variations o f most atmospheric and oceanic parameters than with those o f most land
parameters; and (2) the mechanisms responsible for microwave emission from land surfaces
and volumes are not well understood, in part because land targets have complicated dielectric
and geometric properties.
Developing an effective soil moisture remote sensing system based on microwave
radiometry requires the deployment o f large antennas (or realization o f a correspondingly
large synthetic aperture) in order to achieve meaningful spatial resolution at the low
microwave frequencies necessary to penetrate moderately dense vegetation.
In the context o f operational remote sensing, a num ber o f specific soil moisture
parameter requirements emerge. The moisture algorithm m ust define whether the soil
moisture level at each point in the region is at saturation, at the onset o f moisture stress, or
in the transition range. Within the transition range, the moisture algorithm must specify a
minimum o f three soil moisture levels (high, medium and low), although five levels would
be desirable. In a region following a large scale precipitation event, daily maps would be
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9
desirable, particularly for regions dominated by well-drained soils and relatively infrequent
rainfall. However, given data processing volumes on a global scale, one observation in two
days might be more practical.
Whether it is hydroclimatic or hydrometeorological analysis, useful soil moisture data
sets are those that resolve variations in surface moisture fields at scales that impact the
phenomenon under consideration. These are scales at which remote sensing becomes
limited, such as in investigating the influence o f soil texture and micro-topography on soil
moisture at the pore to meter scales. Although hydrologists must study soil moisture at these
micro-pore scales, it is not possible to remotely sense soil moisture at these smaller scales.
1.3
Objectives o f this W ork
In the context o f the importance o f spatial and temporal variability o f soil moisture
the objectives of this work are:
1.
To develop independent operational soil moisture retrieval algorithms using active
and passive microwave remote sensing.
2.
To develop two independent methodologies enabling the quantification o f the
microwave radiometer aggregation/disaggregation kernel as a function o f land
surface parameters (soils, vegetation). The active sensors can be used for soil
moisture estimates over pilot sites to study the sub-pixel variability and aggregation
kernel o f passive systems, which can be used for global monitoring.
3.
To develop a semi-empirical vegetation backscattering model, which can be coupled
with the multi-polarization, multi-frequency soil moisture retrieval model to
explicitly account for vegetation backscatter.
4.
To evaluate the accuracy o f the soil moisture retrievals from the two microwave
sensors and to assess their compatibility.
5.
To study the effect o f sub-pixel variability in the context o f passive microwave
radiometers.
This is important because the size o f the anticipated brightness
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temperature foot-print from spacebome radiometers using current technology is o f
the order o f 10-25 km.
1.4
Thesis Structure
Chapter 2 o f this thesis provides a review o f the science behind the use o f remote
sensing (microwave in particular) to estimate soil moisture. The choice o f frequency is an
important criterion in the successful estimation o f soil moisture values. The dependence o f
microwave signal on land surface parameters (soils and vegetation) and the currently
available correction algorithms for the same are described.
In the third chapter, a multi-frequency soil moisture estimation methodology using
the Integral Equation Model (IEM) (Fung et al., 1992) is developed. This methodology does
not use site parameters and thus can be used on an operational basis to estimate soil moisture
from a spacebome sensor. This work has been published in the journal Remote Sensing o f
Environment (Bindlish and Barros, 2000).
In Chapter 4, a semi-empirical vegetation correction algorithm is coupled with the
multi-frequency soil moisture estimation to incorporate vegetation effects. This will lead to
the development o f a generalized soil moisture retrieval algorithm with can be used over a
wider range o f land-use characterizations. A preliminary analysis o f this work has been
submitted to the International Association o f Hydrologic Sciences Journal, and a complete
paper will be submitted to Remote Sensing o f Environment.
A soil moisture estimation algorithm based on passive radiometer observations is
presented in the fifth chapter. The effect o f sub-pixel variability o f soil moisture, soil texture
and vegetation within the radiometer pixel are investigated. The soil moisture estimates from
the two independent microwave sensors (active and passive) are compared and the
compatibility o f the two sensors evaluated. The use o f two independent sensor systems at
different spatial resolutions enables us to quantify the aggregation kernel o f the passive
microwave radiometer. The results in this chapter will be published in IEEE Transaction o f
Geosciences and Remote Sensing.
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11
Chapter 2
Literature Review
2.1
Introduction
Recent advances in remote sensing technology have shown that soil moisture can be
measured by a variety o f techniques using all parts o f the electromagnetic spectrum. Infrared
and microwave wavelengths have been used effectively to m onitor soil moisture from space
for a num ber o f years.
Brightness temperature measurements in the thermal infrared
frequency range have shown good correlation with evapotranspiration rates (Wetzel and
Chang, 1988), as well as with the thermal conductivities o f soils (Carlson et al., 1990).
Indirect retrieval methods based on the use o f soil moisture surrogates such as the
Antecedent Precipitation Index and the Normalized Difference Vegetation Index (API and
NDVI, respectively) have proven to work well both in the microwave and infrared frequency
ranges (Blanchard et al., 1981; Schmugge et al., 1986; Choudhury and Golus, 1988; Kerr and
Njoku, 1990; Choudhury, 1991; Carlson et al., 1994; Schmugge and Jackson, 1994).
Microwave sensing (in the decimeter range) has several advantages which could be
explored for large scale soil moisture mapping using remote sensed data: (1) the atmosphere
is transparent at these wavelengths, providing all weather coverage; (2) vegetation is semi­
transparent; (3) the microwave signal received is strongly dependent on the dielectric
constant o f the target; (4) independence o f solar illumination, provides all time coverage; and
(5) better sensitivity to moisture profile (not just surface skin layer). A general advantage
o f microwave sensors (as opposed to visible and infrared) is that observations can be made
under conditions o f cloud cover.
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12
The microwave region o f the electromagnetic spectrum consists o f wavelengths
between 1 and 100 cm. This region is sub-divided into bands which are often referred to by
a lettering system. Some o f the relevant bands that are used are: K.u (~1 cm), X (-3 cm), C
(-5 cm), S (-10 cm), L (-20 cm), and P (-5 0 cm).
By assuming that the target being observed is a plane surface with surface geometric
variations and volume discontinuities much less than the wavelength, only refraction and
absorption o f the media need to be considered. This permits the use o f the Fresnel reflection
equations. These equations predict the surface reflectivity as a function o f the index of
refraction o f the target and the viewing angle, based on the polarization o f the sensor
(horizontal or vertical). The index o f refraction is related to the dielectric constant o f the
target (Ulaby et al., 1986).
If the sensor provides a measure o f reflectivity, and the viewing angle and
polarization are defined, it should therefore be possible to estimate the index o f refraction.
For a land surface, the target consists o f an interface o f air and soil. Since the dielectric
constant o f air is known, the reflectivity provides a measure o f the dielectric constant o f the
medium (soil) at a given water content.
These measures, however, are wavelength
dependent.
The only existing satellite passive microwave system with any potential in soil
moisture applications is the Special Sensor Microwave/Imager (SSM/I). The limiting feature
o f the SSM/I for soil moisture related studies is that the lowest frequency (Ku-Band) is
marked higher than L-band. This impacts the data in two ways: the depth o f soil over which
the measurement is integrated, and the attenuation o f the signal resulting from vegetation.
The depth o f the soil moisture layer to which the microwave signal responds is a
function o f the frequency o f the sensor and the moisture content. At some amount of
biomass the vegetation will mask the signal from the soil. The use o f longer wavelengths
can minimize this effect. Instruments operating at longer wavelengths (> 5 cm) have fewer
problems with the atmosphere and vegetation, sense a deeper soil layer, and maximize soil
moisture sensitivity.
Wang (1985), Schmugge et al. (1986) and Choudhury et al. (1987) studied the
relationship between Scanning Multichannel Microwave Radiometer (SMMR) observed
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13
brightness temperature (TB) and the Antecedent Precipitation Index (API), which is an
indicator o f soil wetness. For the 6.6 GHz frequency with a spatial resolution o f 150 km,
Wang (1985) correlated TBwith API for two regions in Oklahoma and Texas. Unfortunately,
these spatial resolutions are much coarser than the spatial variability o f observed soil
moisture and that from aircraft-borne radiometers, which presents some difficulties in
interpreting the brightness temperature values. Choudhury et al. (1987) used the AVHRR
observed NDVI to account to vegetation effect and to improve the correlation between
SMMR observed TBand API.
It should be noted that the SSM/I was not designed to retrieve soil moisture
(Heymsfield and Fulton, 1992). However, a number o f studies have attempted to relate the
SSM/I data to soil moisture related parameters. Choudhury (1993) examined the reflectivity
patterns o f three regions (desert, rainforest and grass savanna) over a two year period using
data collected by the SSM/I. Comparisons o f the desert and rainforest sites showed the
expected theoretical results. The differences correlated well with observed rainfall patterns,
indicating the possibility that some moisture signal could be present in the data.
Most of the satellite soil moisture related studies have not actually used soil moisture.
Instead, they have utilized the Antecedent Precipitation Index (API). Teng et al. (1993)
examined four years o f SSM/I 19 and 37 GHz data collected over a four state region o f the
mid-western United States. Using API as the soil moisture surrogate, the authors found that
the relationship between .API and the 19 GHz brightness temperature (Tg) was highly
dependent on the geographical location, which in turn was correlated with the amount of
biomass. The sensitivity o f this relationship (the slope o f the regression) was found to be
well correlated with the polarization difference at 37 GHz. The implied procedure for
predicting API is to use the polarization difference (H H -W ) at 37 GHz to determine the
regression parameter and then to predict API using the 19 GHz TB. The limiting factor in this
approach is the sensitivity to vegetation, making the API estimates unreliable.
Detailed studies o f the retrieval o f soil moisture from remotely sensed measurements
have been conducted over various study areas (Mahantango, PA; FIFE; and Washita, OK)
(Jackson and Schmugge 1985; Jackson et al., 1993; Carlson etal., 1994; Dubois etal., 1995).
These studies have consistently shown that only microwave technology has the ability to
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14
quantitatively measure soil moisture under a variety o f topographic and vegetation cover
conditions.
An additional approach for using soil moisture data derived with microwave
approaches is through change detection. The change detection method minimizes the impact
o f variables such as soil texture, roughness, and vegetation because these tend to change
slowly, if at all, with time. Next, the effects o f soil texture, depth o f measurement, surface
roughness, vegetation effects, and instrument parameters, such as incidence angle and
frequency, are reviewed in detail.
2.2
Fundam entals o f Microwave Rem ote Sensing
2.2.1
Role of Dielectric Constant of Soils and Soil Texture
The theoretical basis for measuring soil moisture by microwave techniques is based
on the large contrast between the dielectric properties o f liquid water and o f dry soil. The
large dielectric constant (e) o f water is the result o f the water molecule’s alignment o f the
electric dipole in response to an applied electromagnetic field. For example, at L-band
(wavelength o f 21 cm) frequency the dielectric constant o f water is approximately 80
compared to that o f dry soils, which is o f the order of 3-5. Thus, as the soil moisture
increases, the dielectric constant can increase to a value o f 20 or greater (Schmugge, 1983).
Four components must be considered in computing the dielectric constant o f soil: air, soil
particles, bound water, and free water. To interpret the data correctly, some knowledge o f
soil texture is necessary. Because the dielectric constant is a volume property, the volumetric
fraction o f each component is involved. The computation o f the mixture dielectric constant
has been the subject o f many studies, and there are different theories as to the exact form o f
the mixing equation. A simple linear weighting function is typically used (Schmugge, 1980;
Dobson et al., 1985). Based on an estimate o f the mixture dielectric constant derived from
the Fresnel equations and soil texture, it is possible to then estimate volumetric soil moisture.
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15
The water contained in the soil usually is divided into two fractions: (1) bound water
and (2) free water. Bound water refers to the water molecules contained in the first few
molecular layers surrounding the soil particles; these are tightly held by the soil particles due
to the influence o f matric and osmotic forces (Jury et al., 1991). Because the matric forces
acting on a water molecule decrease rapidly with distance away from the soil-particle
surface, water molecules located several molecular layers away from soil particles are able
to move within the soil medium with relative ease, and hence are referred to as “free”.
Dividing the water into bound and free fractions describes only approximately the actual
distribution o f water molecules within the soil medium, and this is based on a somewhat
arbitrary criterion for the transition point between bound and free water layers. The amount
o f water contained in the first molecular layer adjoining the soil particles is directly
proportional to the total surface area o f the soil particles contained in a unit volume. The
total surface area o f the particles is a function of the soil particle size distribution and
mineralogy. A soil usually is assigned to a textural class on the basis o f its particle-size
distribution and mineralogy.
The binding o f the water-to-soil particle can be described in terms o f the pressure
potential. At low moisture levels, the pressure (matric) potential is the tension with which
water is held by soil particles. In the intermediate range, the pressure potential is determined
largely by the radii o f curvature o f water films between soil particles. When the soil is
saturated, the matric potential is zero.
The amount o f water in the soil when the surface tension forces are in equilibrium
with the gravitational forces o f flow is called the field capacity (FC) o f the soil (Maidment,
1992), and is estimated at a pressure o f -1/3 bar. Wilting point (W P) is the moisture level
at which plants experience difficulty drawing water from the soil. The wilting point is
estimated at a pressure o f -15 bar.
Thus the field capacity and wilting point give a
quantitative measure o f the water holding capacity of a soil. The clay particles (particle size
~ 0.001 mm) have a greater surface area than sandy soils (particle size ~ 0.3 mm). The
smaller particle sizes also results in smaller porosity values. The higher capillary pressure
in clay results is higher water holding capacity than in sandy soil. Clay also have a higher
cation exchange rate because o f their chemical composition. Due to these reasons clay have
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16
a higher dielectric constant than sandy soils. Soil texture affects the microwave sensing of
soil moisture in the way that the dielectric constant changes with the relative amounts o f
sand, silt and clay in the soil. Figure 2.1 shows the effect with laboratory data and an
empirical model developed by Wang and Schmugge (1980). The difference between the two
is the available water capacity o f the soil. Both field capacity and wilting point depend on
soil texture (Schmugge, 1980).
WP = 0.068 - 0.00064 Sand + 0.0048 Clay
(2.1)
FC = 0.30 - 0.0023 Sand + 0.005 Clay
(2.2)
where sand and clay represent the sand and clay fractions by volume.
The effect o f soil texture on the radiometric response to soil moisture content was
first reported by Schmugge et al. (1974) in their study o f airborne measurements o f bare soil
fields at 19.35 GHz. Subsequent analysis o f the data led to the conclusion that the effect of
soil texture can be accounted for empirically by expressing the measured soil moisture as a
percentage o f field capacity (FC) for the soil (Schmugge, 1980). The percent o f field
capacity is defined as mj=mJFCg, where mg is gravimetric soil moisture content and FCg is
moisture content at field capacity expressed in gravimetric terms.
The use o f this
normalizing procedure was found to lead to a Ts versus mf response that is approximately
independent o f soil type (Schmugge, 1980; Wang et al., 1983).
These results were
corroborated by Dobson and Ulaby (1981) and Dobson et al. (1985) for backscattering
measurements.
The dielectric constant o f water mentioned earlier is that o f free water, in which case
the molecules are free to rotate and align with an electric field. However, not all the water
in soil satisfies this condition. Schmugge (1980) suggested that some water in the soil had
different properties and that the fraction o f free, bound, and transition water could be
calculated for a given soil texture in much the same way that general procedures are used to
estimate 15 bar and 1/3 bar moisture contents. He proposed that the initial water added to
soil below the “transition” moisture had the dielectric properties o f frozen water (~3). If the
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17
1— YUMA SANO. V ^-0.17. , - 0 . 5
— VERNON CLAY. W ,-0 7 8 . , -0 .4 6
1— MILLER CLAY. W, - 0 J3. , - 0 JO
>—
Z
<
h<
/»
z
o
(J
«K
*O
0
0.1
0J
0.8
VOLUMETRIC WATER CONTENT, err^/oir*
Figure 2.1
Laboratory measurements o f the real and imaginary parts o f the dielectric
constant for three soils as a function o f moisture content at a wavelength of
21 cm. (Adapted from Schmugge, 1980)
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18
molecule dipole rotation is prevented, as it is in ice (c=3.5), or hindered by being tightly
bound to a soil particle, the value o f e will be reduced.
The frequency (/) dependence o f the dielectric constant o f pure water is given by the
Debye equation (Ulaby et al., 1986)
g„=e„~+— '— TT
1 +j2 n fr w
(2-3)
where
e w0
= static dielectric constant o f pure water, dimensionless
ew„ = high-frequency (or optical) limit o f e w, dimensionless
rw= relaxation time o f pure water
27trw(7) =1.1109 x 10 10 - 3.824 x 10 12 T
+ 6.938 x 10 14 T2 - 5.096 x 10 16 T3
(2.4)
where T is the temperature in °C.
The variations o f esml with soil type are reflected by the shapes o f the brightness
temperature curves (Fig. 2.1). For oven-dried soil, eS0ll is approximately the same for all soil
types, and depends on the bulk density only. The variation o f eS0ll with increasing soil
moisture (mv) may be divided into two ranges: (1) the range between mv = 0 and the transition
moisture level m, and (2) the range for mv £ m r The transition moisture, which is a constant
for a given type o f soil composition, represents the boundary between the bound condition
o f the water molecules and the free condition ( Schmugge, 1980; Wang and Schmugge,
1980; Hallikainen et al., 1985). Below the transition moisture level, most o f the water
molecules in the soil-water mixture are considered to be bound (at least partially) to the soil
particles by the influence o f both matric and osmotic forces. Hence, the effective dielectric
constant o f these partially bound water molecules is much smaller than that o f free water.
Consequently, the dielectric constant o f the mixture increases only slowly with increasing
mv. Beyond m v = m„ the water molecules are considered to be free particles with a dielectric
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19
constant much larger than that o f soil, thereby exercising a strong influence on the dielectric
constant o f the mixture. The transition moisture m, depends on soil particle surface area per
unit volume and on the geochemical properties o f the soil particle, and therefore it is a
function o f soil type.
To obtain the dielectric properties o f the moist soil a simple mixing formula can be
used in which the components are the soil mineral (or rock), air, and water (er) with ex being
a function o f the water content, m v, in the soil (Schmugge, 1980). At zero water content
£x-E lce, and it increases linearly until the transition moisture m, is reached, when £x=eliqmtj. The
equations are
e - mvex + (P~mv) ea + (1 -P) er,
fo r
mv<mt
(2.5)
with
m„
£x = e, -
— Pi
m.
(2 .6 )
and
e = m tex
(mv~mt) ew+ (P-mJ ea - (1-/0 sr
fo r
m>mt
(2 .7)
with
£/ + (£w“£/) Pi
where P is the porosity o f the dry soil; sa, sw,
(2 .8)
and e, are the dielectric constants o f air,
water, rock, and ice, respectively; exstands for the dielectric constant o f the initially absorbed
water; and p b is the bulk density o f the soil. The values o f m, m d p b were determined for 18
soils by a least squares fit to the data (Wang and Schmugge, 1980).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
20
m t = 0.49 WP + 0.16
(2.9)
pb = -0.57 WP + 0.48
(2 . 10)
Dobson et al. (1985) proposed two mixing models for e. In the first approach, the
fractions o f free water and bound water are computed using a detailed description o f the soil
structure.
For some applications, such as in the case o f satellite data analysis, many
parameters required by this model cannot be determined with sufficient accuracy. Therefore,
Dobson et al. (1985) introduced a simplified formulation that is still able to describe the
frequency and the soil texture dependence ofe. In this approach, bound water is related to
an empirical constant shape factor rj. Another coefficient, /?, takes the soil texture into
account. This model is commonly used over the frequency range 4-18 GHz. The complex
soil permittivity is written as
(2 . 11)
Sw0~g>y- _j Ci
Pj P&
l+j2nfrw 2kfeQ Pjwv
where mv, ps,
( 2 . 12)
er, sfiv are, respectively, the soil volumetric moisture, the dry soil and the
solid rock densities, and the solid rock and free water dielectric permittivities. The dielectric
constant o f free water is frequency and temperature dependent, and is given by the Debye
equation. The parameters /? and c, are empirically related to sand and clay fractions from
laboratory experiments
Pe/=1.275 - 0.519 Sand - 0.152 Clay
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(2.13)
21
for the real part o f z
(e")
pE/=1.338 - 0.603 Sand - 0.166 Clay
(2.14)
for the imaginary part o f e (e ”) and
c , - -1.645 + 1.939 p, - 2.256 Sand + 1.594 Clay
(2.15)
Figure 2.2 (adapted from Hallikainen et al., 1985) illustrates the change between the
real (z ’S0ll) and imaginary (z ”J0(/) parts o f the dielectric constant for soil at several microwave
frequencies. As the frequency increases, the real part decreases and the imaginary part (a
measure o f losses) increases with the increase o f soil moisture.
Both mixing models are based on the soil textural composition o f the underlying soil.
In the context o f operational remote sensing o f soil moisture, it is not possible to know the
soil texture accurately over the entire globe.
Moreover, at the spatial resolution of
spacebome passive radiometers the soil texture would vary within the sensor footprint. The
effect o f soil texture variability in the context o f passive radiometers is investigated in
Chapter five o f this thesis.
2.2.2
Penetration Depth
The reflected microwave emission from the soil is a function o f the incident
frequency o f radiation and o f the amount o f soil moisture present.
Remotely-sensed
estimates o f soil moisture concern areal averages o f soil water content over a certain depth.
Parameters such as the penetration depth-defined as the distance in the soil over which
microwave radiant power is attenuated by a factor o f e (e=2.718)—depend on the dielectric
properties o f water in the soil (Njoku and Kong, 1977).
The depth over which one can associate soil moisture with the signal received by the
sensor is called the sensing depth. The sensing depth varies as a function o f the frequency,
and with the dielectric properties o f the soil. In general, longer wavelengths correspond to
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
F ield 5
5
F ield 5
c
3
«3_i
wt
S
o
u
Cl
o
•/
/•
18 GH;
u
V
IB GHz
a
1 8 GHz
0.0
0.1
0.2
v o liM trlc tolstu re
(a)
Figure 2.2
0 .5
0.5
I o n i a n ' 1)
0 .0
0.1
0 .2
0.3
V o l i M t r l c M o is tu r e m, ( a n J a r J>
Cb)
0.5
o.o
0. 1
0.2
0.5
0.4
V o l t M t r l c M o is tu re mv icm3 a i r , >
(C)
Measured dielectric constant at 4, 10, and 18 GHz for three different fields. Polynomial regression fits are
also shown. (Adapted from Hallikainen et al., 1985)
KJ
NJ
23
higher penetration depths as compared to shorter wavelengths. On the other hand, wet soils
(higher dielectric constant) correspond to lower penetration depths as compared to drier soils
(lower dielectric constant).
The relationship between emissivity and soil moisture depends on the dielectric
constant across the air-soil interface. Consequently, this results in some uncertainty as to
exactly how thick the soil layer is for determining the dielectric constant. According to
Wilheit (1978), the layer of soil would be on the order o f a tenth o f a wavelength or less. Mo
et al. (1982) determined that the radiometric sampling depth is between 0.06 and 0.1 times
the wavelength. The soil depth contributing to L-band measurements is primarily the top 5
cm, while that for the C-band is about 1.0-2.0 cm (Jackson and Schmugge, 1989). In an
experiment comparing dry-down measurements o f soil layers at three frequencies, Newton
et al. (1982) found that for L-band (21 cm wavelength) the sampling depth was about twotenths o f the wavelength. Nevertheless, the measurement depth is in fact not a constant, but
is related to the moisture content, and to the operational frequency o f the sensor. A good
estimate o f the measurement depth can be obtained from penetration depth, Sp inside the soil.
This is given by
Sp = k |/m(Ve) |
(2.16)
where k=2n/X is free space propagation constant, e is dielectric constant o f soil, Im denotes
the imaginary part, and the vertical bars refer to the absolute value. A plot o f penetration
depth versus soil moisture for various frequencies is shown in Figure 2.3 (adapted from
Ulaby et al., 1986).
2.2.3
Choice o f Microwave Frequency
W avelength is the most critical parameter for the design o f a radiometer. As the
wavelength o f emission decreases, the dielectric constant o f soil decreases. The effect o f
wavelength on the sensitivity (d n /d T B) o f the relationship between soil moisture (mv) and
brightness temperature (Tg) was studied by Jackson (1980), who showed that the sensitivity
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24
Depth 6T (cm)
100
•
\
\ \
\
Moisture
P ro file
Temperature
Sensing
\
(2)
(3)
0. 1
1 30
r( i )
( 1)
(5)
Moisture Content ■ g ( X )
0.011
0.1
1
1____________________
1
10
100
Frequency (GHz)
Figure 2.3
Calculated temperature sensing depth for sand as a function o f frequency for
five different moisture profiles. (Adapted from U laby et al., 1986)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
25
is relatively constant up to a wavelength o f 5 cm, and then drops off rapidly for longer
wavelengths. This suggests that instrument error and noise factor (signal to noise ratio) are
significant at shorter wavelengths, and thus hinder our ability to estimate soil moisture.
As the wavelength is decreased, the attenuation o f the signal by vegetation increases.
Vegetation cover behaves like a mask, which can be treated as an attenuating layer, and
defines the local transmissivity (transmissivity o f the region is a function o f the optical depth
[O] of vegetation cover). As a first order approximation, this is a function o f water content
o f the vegetation (vwc), and sensor response function (defined as the signal received by the
sensor from a particular object, which in turn is a function o f frequency and water content)
for a particular plant (Jackson et al., 1982).
Jackson and Schmugge (1991) have examined the effect o f plant shape and
wavelength on the vegetation parameter (b).
Ot = b*vwc
(2.17)
Figure 2.4 (adapted from Jackson and Schmugge, 1991) shows a plot of this
parameter as a function o f wavelength. It illustrates two important points. First, as the
wavelength decreases, the attenuation, b, will increase. This means that sensitivity to
vegetation water content increases. The sensitivity decreases at a slower rate for vegetated
soil than for bare soil, and the optical thickness o f vegetation decreases with increasing
wavelength. The general trend of the data indicates that the rate o f change is rather small
down to 10 cm, and then increases rapidly. Secondly, the scatter within any wavelength
increases as the wavelength decreases.
This is due to the increase in importance o f
vegetation structure (and scattering phenomena) at shorter wavelengths. More ancillary
vegetation information is necessary to estimate soil moisture at shorter wavelengths.
With the increase in wavelength, the sensing depth o f soil also increases. Pampaloni
et al. ( 1990) conducted an experiment in which they varied the thickness o f soil over a metal
plate and recorded the brightness temperatures for different wavelengths. Based on these
observations, they concluded the significant depth for L band to be between 5-10 cm. They
also studied the variation o f brightness temperature for different bands. All o f the climatic
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
LEGEND
2.0
FIT TO LLA8Y AM) W LSONM 985)
•
SOYBEANS
O
broadleaf
□
SMALL GRAINS
SOYBEANS
WFEAT
FIT TO MATZLERf 1990)
OATS
FIT TO ULABY AM)
OC
lu
I—
LU
EL-RAYESf 19871
OATS
1
5
<
A
CO R N
▼
ALFALFA
O
SHO RT G R A SS
♦
TALL G R A SS
oc
<
Q.
5
10
15
20
25
30
WAVELENGTH (CM)
Figure 2.4 Summary o f experimental data o f the vegetation parameter b as a function o f wavelength for different land
uses. (Adapted from Jackson and Schmugge, 1991)
O
n
27
conditions are reflected in the measurements obtained by using larger wavelengths (L band).
Day-to-day changes in soil moisture cannot be observed using small wavelengths, because
these can see only the dry top layer o f soil.
Radio frequency interference (RFI) increases for wavelengths above the L-band (21
cm). Thus, very high wavelengths cannot be used. For horizontal polarization the sensitivity
to soil moisture was higher for all look angles, for both bare and vegetated soil. As the look
angle changes the size o f the footprint changes, which introduces a negative effect for large
look angles.
2.3
Types o f M icrowave Remote Sensing (Active and Passive)
Microwave techniques for measuring soil moisture include both the passive and
active microwave approaches, with each having distinct advantages.
Passive methods
measure the natural thermal emission o f the land surface at microwave wavelengths. Active
methods or radars send and receive a microwave pulse. The power o f the received signal is
compared to that which was sent to determine the backscattering coefficient.
That
coefficient is then related to the characteristics o f the target.
Passive and active microwave remote sensing instruments are capable o f measuring
the surface soil moisture (0-5 cm), and can be implemented on high altitude platforms, e.g.
spacecraft, for repetitive large area observations. Active approaches, especially synthetic
aperture radar, can provide extremely good ground resolution from space (< 100 m). Passive
methods currently provide much coarser resolution data (> 10 km).
The spatial resolution o f passive instruments will limit the range o f applications when
used on a satellite. Sensitivity to other surface features could limit the usefulness o f active
systems for direct soil moisture estimation. Selecting the best system w ill require tradeoffs
and prioritizing applications. It may be that the optimal sensor system would include both
an active and a passive instrument. This would allow a range o f applications and the
synergism o f the two types o f measurements to provide new information.
However,
systematic research and development o f the use o f either technology for remote sensing o f
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28
soil moisture is severely hampered by the limitations o f currently available, and planned,
satellite instruments (NASA, 1998).
2.3.1
Active Microwave Remote Sensing
An active microwave sensor that measures the emitted and received power is called
a scatterometer. The measurement provided is the backscattering coefficient ((f). Through
theory described in Ulaby et al. (1986), the a0 can be related to the surface reflectivity, and
to surface soil moisture. The relationship between backscatter coefficient a° and the soil
moisture is quite involved, and there is no simple model which corrects for surface roughness
effects. The geometric properties o f the soil surface and any vegetation have a greater effect
on these measurements and simple correction procedures are difficult to develop.
Dobson et al. (1992) reported the first set of results which used only a single ERS-l
scene (Michigan, USA) and a few grass fields as ground truth. However, the authors
augmented their analysis by using a sophisticated radar simulation model. The model was
used a priori to predict a relationship between soil moisture and cf. The results supported
application to areas o f low vegetation.
Sabburg (1994) analyzed a single ERS-l scene for an agricultural area in Australia.
The ground truth in this investigation was also very limited. The author utilized an empirical
model to establish the soil moisture vs cf relationship a priori. He determined that, for the
conditions studied, the surface soil moisture (0-5 cm) could be estimated within 10%.
Another extensive ERS-l study was reported by Cognard et al. (1995).
This
investigation involved a total o f 14 ERS-1 scenes collected over a two year period. The data
were collected within the context o f a river basin study (located in northwestern France) with
13 soil moisture sampling sites. The authors tried to correlate the radar signal with the
observed soil moisture using regression analysis, and they found that the ( f - soil moisture
relationship was highly dependent on vegetation and associated tillage conditions.
A
significant improvement in the regression analysis was made when the average <7° for the
basin (12 km 2) on each day was compared to the average soil moisture from the 13 sites.
However, the sensitivity o f <f to soil moisture was very low, about 10% volumetric soil
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29
moisture for 1 dB <ri. This loss in sensitivity was primarily due to averaging o f the radar
signal and soil moisture observations over the entire watershed. Considering the absolute
accuracy o f the <f values, a considerable amount o f uncertainty must be expected in their soil
moisture estimates.
The signals emitted and received by a radar are usually linearly polarized, either
horizontally (H) or vertically (V). Combinations possible are horizontal transmit-horizontal
receive (HH), horizontal transmit-vertical receive (HV), vertical transmit-horizontal receive
(VH), and vertical transmit-vertical receive (VV). More advanced systems can make multipolarization measurements simultaneously. The Spacebome Imaging Radar-C (SIR-C)
mission was the first multi-frequency, multi-polarization imaging radar system flown in
space. The radar was designed and built to make eight different measurements at the same
time: L-band (24 cm wavelength) and C-band (6 cm wavelength) backscatter at four different
polarization combinations, including HH, VV, HV and VH. The SIR-C antenna is an
electronically steered, active phased array antenna which uses different electronic elements
to transmit power all across the array (Freeman et al., 1995).
SIR-C provides high resolution imagery at two different wavelengths—L-band (24
cm) and C-band (6 cm)-- for two incidence angles (30° and 45°) at a horizontal resolution o f
12.1 m. The land surface information received at these wavelengths is received by two
different channels (vertical and horizontal polarizations). Thus, SIR-C provides images o f
backscatter for four polarization combinations for each wavelength: HH, HV, VH and W .
X-SAR operates within the X-band (3 cm) with W polarization only.
The development o f a soil moisture estimation model for multi-frequency, multi­
polarization radar data using the IEM is presented in Chapter three (Bindlish and Barros,
2000). In Chapter four, a semi-empirical model to parameterize vegetation effects was
coupled to the soil moisture estimation model. A detailed discussion on the relationship
between backscattering coefficient and soil moisture is presented in these two chapters.
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30
2.3.1.1 Backscattering Models
For bare soils, all models that relate <f to soil moisture require at least two soil
parameters, the dielectric constant and the surface height standard deviation (RMS). This
means that in order to invert these models, the surface height standard deviation must be
known accurately. Also, because o f the high spatial resolution, surface topography must
often be taken into account. For a given sensor configuration o f wavelength and viewing
angle, different results are obtained at different polarizations, but depend on these same two
variables. Therefore, most approaches to determining soil moisture with active microwave
methods utilize dual polarization measurements. With two independent measurements o f
the two variables, it is possible to solve for both the dielectric constant and the RMS.
Algorithms incorporating this approach are presented in Oh et al. (1992) and Dubois et al.
(1995).
For the active microwave approach over a bare soil, the measured radar backscatter,
cr/, is related directly to soil moisture, and it is written in functional form as
o,
(2.18)
where s is a surface roughness term and L is the correlation length term. Although s and L
are known to vary with wavelength, polarization, and incidence angle, no satisfactory
theoretical model is suitable for estimating these terms independently.
The Integral Equation Model (IEM) is a backscattering model o f microwave
scattering from a rough dielectric surface that is based on an approximate solution o f a pair
o f integral equations for tangential surface fields at a point.
The multiple scattering
contribution is considered negligible for surfaces with small roughness. Based on the results,
two separate sets o f equations were developed for rough and smooth surfaces (Fung et al.,
1992; Fung, 1994). The use o f a multi-frequency remote sensing instrument provides two
independent data sets for soil moisture retrieval. The soil roughness observed at different
frequencies (L- and C-band) (scale dependent) and soil moisture then could be computed
using the IEM. The present equations that describe the relationship between backscatter
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31
coefficient and soil water are highly non-linear and lack analytical solution, or even
numerical solution if no linearization is attempted in the radiative transfer models (IEM).
Due to the complexity in the backscattering algorithms, Bindlish and Barros (2000)
developed a multi-frequency, multi-polarization soil moisture estimation model using the
IEM.
With radar, the effect o f the vegetation canopy adds more complexity to the problem.
To determine soil moisture, one must determine the soil roughness effects and the effects o f
the vegetation canopy.
2.3.1.2 Effect o f Surface Roughness
Although, roughness may not be a serious limitation for passive sensors, at least for
most natural surfaces, it is a major limiting factor for radar. Based on the scattering behavior
in extreme cases and experimental data, Oh et al. (1992) have developed an empirical model
in terms o f the RMS roughness height, the wave number and the relative dielectric constant.
By using this model with multi-polarized radar data the soil moisture content can be
determined. The key to this approach is that the co-polarization ratios (HH/VV) and cross­
polarization ratios (H V /W ) are expressed explicitly in terms o f the surface roughness and
soil dielectric constant. Surface roughness is also a key parameter in the IEM. Through the
use o f multi-polarization data, or with the knowledge o f other land surface parameters, it is
possible to computationally obtain an estimate for surface roughness, as it is a function of
frequency, incidence angle, and polarization. Soil roughness varies for point-to-point within
the area o f interest, and thus it is impossible to obtain a unique value o f soil roughness.
2.3.1.3 Effect o f Vegetation
To compare the modeling results (using dielectric random media technique) with
radar, the model cross-sections from individual scatterers such as leaves and stems are
converted to backscattering cross-section per unit area from a layer o f leaves, stems, etc
(Karam et al., 1992, Ulaby et al., 1983). The distorted Bom method has been used to
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32
compute backscattering per unit area (Chauhan et al., 1994; Karam et al., 1992). Based on
this approach, the radar backscatter from the vegetation layer is composed o f four principle
components: direct, reflected, direct-reflected and surface scattering terms. The soil moisture
information is present in the last three terms. The reflected term is usually very small,
because the wave hits the ground twice. If the surface is very rough (or is vegetated), the
direct-reflected terms become negligible; therefore, the soil moisture information will be
contained only in the surface scattering term.
The L-band single scattering albedo for vegetation canopies is generally less than
0.02 (Ulaby et al., 1983; Kerr and Wigneron, 1994; O ’Neill et al., 1996) so that these
canopies can be modeled as an absorbing layer. The optical thickness o f crop or grassland
canopies is typically much less than 1, and they can be estimated from knowledge of the
equivalent water column in the canopy. This requires ancillary data from an independent
source such as satellite derived vegetation index (Jackson, 1993). Alternatively, dual­
polarized (V and H) measurements at incidence angles o f 40° or greater or other passive and
active channels may be used to estimate the vegetation optical thickness (Njoku and Li,
1999; Njoku et al., 1999).
A detailed description o f the effect o f vegetation on the
backscatter coefficient is presented in Chapter four.
Furthermore, a semi-empirical
vegetation backscattering model is coupled to the soil moisture estimation model to
explicitly account for the presence o f vegetation.
2.3.2
Passive Microwave Remote Sensing
Passive microwave remote sensing utilizes highly sensitive radiometers that measure
the natural thermal radio emission at a particular wavelength. The measurement provided
is the brightness temperature, TB, that includes contributions from the atmosphere, reflected
cosmic radiation, and the land surface.
Atmospheric contributions are negligible at
wavelengths > 10 cm (Jackson, 1980).
The brightness temperature o f a surface is equal to its emissivity multiplied by its
physical temperature. If the physical temperature is estimated independently, emissivity can
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33
be determined. Microwave emissivity varies between 0.6 and 0.95 for most land surfaces.
At these wavelengths the reflectivity is given by
reflectivity=1 -emissivity
(2.19)
This then provides the linkage to Fresnel equations and soil moisture.
The use o f microwave radiometers for the remote sensing o f soil moisture has been
studied extensively from aircraft and field platforms. These radiometers measure the thermal
emission from the soils in the frequency range 1-30 GHz (wavelength region between I and
30 cm). The magnitude of this emission depends on the temperature o f soil, on the surface
features o f roughness and vegetation cover, and on the dielectric or emission properties o f
the soil.
The approach evolved from small-scale studies using tower-mounted radiometers in
the late 1960s and early 1970s, and truck- and aircraft-mounted radiometers during the late
1970s and early 1980s (Wang et al., 1983; Jackson et al., 1984). Upon the development o f
L-band Push Broom Microwave Radiometer (PBMR), it became the standard technique for
soil moisture retrieval in the comprehensive airborne field campaigns between 1986-1992
(Jackson and O ’Neill, 1987; Schmugge et al., 1992).
Passive microwave sensing (radiometry) has shown the greatest potential among
remote sensing methods for satisfying the soil moisture measurement objectives o f regionalto-global scale w eather and climate forecasting. Measurements at 1 to 3 GHz are directly
sensitive to changes in surface soil moisture, are little affected by clouds, and can penetrate
moderate amounts o f vegetation. They can also sense moisture in the surface layer to depths
o f 2 to 5 cm (depending on wavelength and soil wetness). With radiometry, the effect o f soil
moisture on the measured signal dominates over that o f surface roughness. Figure 2.5
(adapted from Jackson, 1993) is a schematic o f the components that comprise the microwave
scene brightness at L-band frequencies.
A number o f experiments have been done to estimate the soil moisture using passive
microwave data. These experiments are limited to small scale and over selected areas. Most
o f the L-band data has been collected from sensors that have been installed over trucks,
towers or aircrafts. Jackson et al. (1984,1995,1999) observed sim ilar trends in the relation
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
PA SSIVE MIC R OW A V E RADIOMETER M EA SU R EM EN T
O F S O I L M O I S T U R E AT NAD IR
T B - B r i g h t n e s s T e m p e r a t u r e (*K)
T .^ -A tm ospheric Transmissivity (-1)
T1 uB - t' a t m (' TB
+TB
)+TB
'
SKY
* w c /
'
ATM
T B sirr- R e f l e c t e d S k y B r i g h t n e s s (~5°K)
TBc- C a n o p y B r i g h t n e s s T e m p e r a t u r e (*K)
TBC- (1 +(1 - e sun) 0 ( 1
-r)(1 -o) V e su„ r T
T B , IM- D i r e c t S k y B r i g h t n e s s (~0*K)
e jun"Emissivi ty at Soil S u r f a c e
a - V e g e t a t i o n Single S c a t t e r i n g Alb ed o (-0 )
r - T r a n s m i s s i v i t y of V e g e t a t i o n
e so»i“ l + ( e s o a ‘ U e x P ( h )
Tv- T e m p e r a t u r e of V e g e t a t i o n (*K)
T S01l- T e m p e r a t u r e of Soil (T10il- T v)
w - H O 'h - W K + i ) ) '
e soll- E m i s s i v i t y of t h e Soil
h-Surface Roughness Parameter
k - D i e l e c t r i c C o n s t a n t of Soil
k= f ( V o lu m e t ri c Soil Moisture (%))
Figure 2.5
Schematic diagram o f a passive microwave emission model from land surfaces. (Adapted from Jackson,
1993)
OJ
4^
35
between soil moisture and emissivity o f soil for different years of L-band data collected from
aircrafts flown at different altitudes.
Real aperture radiometers like the PBMR produced highly useful soil moisture
products, but implementing the technology for large-aperture spacebome systems presented
a substantial engineering challenge.
Synthetic aperture technology was explored as a
potential solution. An aircraft prototype for Earth viewing applications was developed in the
1990s, called the Electronically Scanned Thinned Array Radiometer (ESTAR), its
performance was equivalent to traditional radiometers for sensing soil moisture (Jackson et
al., 1993, 1995, 1999; Le Vine et al., 1994). ESTAlR observations over the Southern Great
Plains and ancillary information about vegetation characteristics (vwc and b) was used to
retrieve soil moisture with a 0.03 m3/m3 precision error. An hydrology experiment known
as the Southern Great Plains Experiment (SGP97) was conducted over an area o f over 11,000
km2 for nearly every day for a one month period (Jackson et al., 1999). The estimated soil
moisture values (sensor footprint o f 800 m) where cross-validated over about 35 points
located in three different areas (Little Washita - 610 km2, El Reno - 20 km2 and Central
Facility - 5 km2) in the mapping domain.
Only one low-frequency (< 3 GHz) spacebome radiometer, the Skylab 1.4 GHz
radiometer (S-194 mission), has ever flown in space. This radiometer operated on a short
duration mission in 1973 and 1974, providing nadir only measurements at a spatial resolution
o f -115 km. At nadir, horizontal and vertical polarization, measurements should be the
same.
As part o f this mission, Eagleman and Lin (1976) collected actual ground
observations of soil moisture. These observations and water balance simulations were used
to study relationships between brightness temperature and soil moisture. The data were
collected over the U.S. Great Plains during the summer. Their results demonstrated the
following key points: (1) observed brightness temperature has a large dynamic range due to
changing surface wetness conditions (55 K), (2) there is a strong relationship between
brightness temperature and soil moisture even at a resolution o f 115 km, and (3) the basic
relationship is consistent with theory (model curve).
Since then, other higher frequency Earth imaging microwave radiometers have
operated in space, including the Scanning Multichannel Microwave Radiometer (SMMR)
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36
(lower frequency 6.6 GHz) launched on the Seasat (1978) and Nimbus-7 (1978-87) satellites,
and the Special Sensor Microwave Imager (SSM/I) (lowest frequency 19.35 GHz) launched
on the Defense Meteorological Satellite Program (DMSP) satellite series. Attempts have
been made to utilize these sensors in soil moisture studies with some limited success (Kerr
and Njoku, 1990; Owe et al., 1992; Wang, 1985; Choudhury and Golus, 1988; Jackson,
1997).
The soil moisture sensing limitations o f these higher frequency radiometers is
particularly pertinent to the SSM/I instrument. Much effort has been devoted to extracting
land information from this sensor since it has been an operational instrument since 1987.
The SSM/I has shown only limited capability to observe soil moisture from space (Jackson,
1997; Lakshmi et al., 1997). At its lowest frequency o f 19.35 GHz, the SSM/I is highly
sensitive to even small amounts o f vegetation which obscures the underlying soil. Large
variations in soil moisture (e.g., flood/no-flood) in sparsely vegetated regions and
quantitative river flooding indices are all that have been shown feasible using the SSM/I.
2.3.2.1 Brightness Temperature Models
For passive microwave remote sensing o f soil moisture from a bare soil, a radiometer
measures the intensity o f emission from the soil surface. This emission is proportional to the
product o f the surface temperature and the surface emissivity, which is commonly referred
to as the microwave brightness temperature ( TB) and can be expressed as follows (Jackson,
1993):
T, -- m
[r
<■ (1 -
r) r j
♦ T„
(2.20)
where t(H) is the atmospheric transmissivity for a radiometer at height H above the soil, r
is the smooth surface reflectivity, Tsoil is the thermometric temperature o f the soil, Tam is the
average thermometric temperature o f the atmosphere, and Tskv is the contribution from the
reflected sky brightness. For typical remote sensing applications using longer microwave
wavelengths (greater than 5 cm, which are better for soil moisture), the atmospheric
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37
transmission will approach 99%. The atmospheric contributions from clouds and water
vapor (at L-band) are considered negligible (~2 K) (Schmugge and Jackson, 1994). Cosmic
background radiation contributes to about 2 K. Therefore the total atmospheric, Tatm, and
sky, Tsk>„ contributions are less than 5 K. The surface reflectivity is on the order o f 0.4,
which yields a reflected sky brightness o f 1-2 K. (Schmugge and Jackson, 1994), as compared
to the dynamic range contribution o f soil brightness temperatures (~ 55 K). Moreover, these
brightness temperature values are comparable to the noise level o f the instrument. Thus,
neglecting these two terms, Eq. (2.20) can be simplified to
Tb = 0
- r) Tsoii = * T,oa
(2.21)
where e=(l-r) is the emissivity and is dependent on dielectric constant o f the soil and the
surface roughness. Over the normal range o f soil moisture, a decrease in the emissivity from
about 0.95 to 0.60 or lower can be expected. This translates to a change in brightness
temperature on the order o f 100°K.
Though the relationship between emissivity and
brightness temperature is linear, the soil moisture has a nonlinear dependence on reflectivity
because the reflection coefficient 3 t o f the ground is related in a nonlinear way to the
dielectric constant o f the ground (e). For horizontal polarization, the reflection coefficient
is given by
a
= 008 9 - C
(2.22)
COS 9 + ^
where
C, = Je - sin20
(2.23)
and 6 is the angle o f incidence. The expression for vertical polarization can be written in a
similar way. The dielectric constant, e, is a complex quantity and the empirical relationships
between dielectric constant and soil moisture derived by Schmugge (1980) and Dobson et
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38
al. (1985) show that the dielectric constant has a nonlinear dependence on soil moisture.
However, even though the brightness temperature-soil moisture relation has a strong
theoretical basis, most algorithms are empirical in that they rely on ground data for the
relationship.
For natural conditions, a wide range o f biomass levels and land-use classes are
encountered which affect the microwave measurements. Vegetation reduces the sensitivity
o f the interpretation algorithm to soil moisture changes. An important reason for using
longer wavelengths is that attenuation increases as wavelength decreases. As proposed by
Jackson and Schmugge ( 1989), it is possible to correct for vegetation at longer wavelengths
using a vegetation water content related parameter.
The soil moisture can be estimated from the calibrated brightness temperature
following a step-wise process (Fig. 2.6). The land-cover information for the area is provided
and the vegetation and land-cover types not suitable for estimation are eliminated. The
surface emissivity then can be computed from the corrected brightness temperature values.
For this process, the surface temperature o f the soil is required.
Vegetation and soil
roughness corrections are calculated next. The vegetation correction is based on the value
o f vegetation water content.
The soil roughness correction depends on the land use
characteristics. The final step is to use the Fresnel’s equation and the dielectric-soil moisture
model relationship for estimating soil moisture.
An algorithm for estimating surface soil moisture from TBbased on the inversion o f
the Fresnel equations was presented by Jackson (1993). This algorithm incorporates soil
texture, surface roughness and temperature. It also includes corrections for vegetation, and
has been applied in a number o f ground and aircraft studies using L-band radiometers (21
cm).
For longer passive microwave wavelengths (> 5 cm) the effects o f surface roughness
are small, and the field experiments conducted so far suggest that the effects o f most types
o f sparse and moderately dense vegetation (with the exception o f forests) can be accounted
for. A problem with passive microwave methods is spatial resolution. For a given antenna
size, the footprint size increases as wavelength and altitude increase. For realistic satellite
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I Calibrated BT j
39
j Soil Temperature
I
Com pute Pixel Emissivity
V egetation Water Content
V egetation Correction
(Jackson and S ch m u gge, 1991)
Soil R ou gh n ess
R o u g h n ess Correction
(Choudhury et al., 1978)
Fresnel Equation
Soil Dielectric C onstant
Soil Texture
Soil Moisture
(W ang and S ch m u gge, 1980)
Figure 2.6
Step-wise flow diagram o f soil moisture estimation algorithm using passive
microwave observations.
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40
designs at L-band, this might result in a footprint as large as 100 km. Recent research has
focused on the use o f synthetic aperture thinned array radiometers which could decrease the
footprint size from satellites to 10-25 km (Le Vine et al., 1994).
2.3.2.2 Effect o f Surface Roughness
The scattering o f passive microwave emission from rough surfaces has been studied
by several investigators (Barrick, 1970; Sung and Eberhardt, 1978). These studies show that
for a detailed quantitative calculation o f the scattering o f a rough surface, knowledge o f the
statistical surface parameters is important.
Microwave signatures from the soil are related to the reflectivity o f the surface, which
if smooth can be calculated by the usual Fresnel equations. Smoothness in microwave terms
is relative, as it is dependent on the wavelength. The effect o f a rough surface is to increase
the surface emissivity and thus to decrease the sensitivity to soil moisture (Newton and
Rouse, 1980).
To study the effects o f surface roughness on the observed dependence o f the
brightness temperature on the soil moisture, a simplistic model has been developed by
Choudhury et al. (1979). The surface roughness effect has been incorporated into the
calculation by modifying the Fresnel reflectivity. This modification is based upon the theory
developed by Ament (1953) for a conducting surface.
Choudhury et al. (1979) have shown that surface roughness (s ) can affect the soil
reflectivity r in the following way:
r '- r exp{ -h cos2©)
(2.24)
where r is the smooth surface reflectivity, h is a roughness parameter (=4 s:/c) proportional
to the root mean square (RMS) height variations o f the soil surface, 6 is the incidence angle,
and k= 2z/L The value o f reflectivity decreases rapidly with a slight increase o f a. Thus, as
the surface roughness increases, the attenuation effects on the bare soil emissivity increase,
and therefore the sensitivity o f the observed signal to soil moisture decreases.
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41
2.3.2.3 Effect o f Vegetation
The effect o f vegetation is to attenuate the microwave emission from the soil. It also
adds to the total radiative flux with its own emission. The degree to which vegetation affects
the determination o f soil moisture depends on the mass o f vegetation and the wavelength.
Barton (1978) used an aircraft-mounted 2.8 cm radiometer to measure soil moisture over
bare soils and uniform grass cover. Although he demonstrated a strong relationship between
brightness temperature and moisture for the bare fields, no relationship for the grass sites
could be determined.
In studies over bare soil and sorghum, Newton and Rouse (1980) found no sensitivity
to soil moisture with the 2.8 cm measurements over the sorghum, but with the 21 cm data
the radiometer was sensitive to soil moisture even under the tallest sorghum.
Basharinov and Shutko (1975) and Kirdiashev et al. (1979) studied a variety o f crops
in the former USSR with wavelengths varying from 3 cm to 30 cm. For wavelengths greater
than 10 cm, their results indicate that one can expect a decrease in sensitivity of about 10 %20% for small grains over what would be expected for bare soil. With broadleaf crops such
as com, the sensitivity decreased by as much as 80% for wavelengths shorter than 10 cm, and
40% for a 30 cm wavelength. Thus, these studies show that a vegetation canopy is more
transparent for longer wavelengths than for shorter wavelengths.
Several other studies have analyzed the relationship between the microwave
brightness temperatures and vegetation characteristics for different canopy types (Kirdyashev
et al., 1979; Jackson et al., 1982; Brunfeldt and Ulaby, 1984; Brunfeldt and Ulaby, 1986,
Pampaloni and Paloscia, 1986; Matzler, 1990; Jackson and Schmugge, 1991; Wegmiilleret
al., 1993). The values o f retrieved single scattering albedo are usually less than 0.15 and the
time variations o f a are weak during the growing cycle o f vegetation. The opacity r is almost
linearly related to the integrated vegetation water content vwc (kg/m2), using a factor b which
is mainly dependent on the frequency and on crop type (Jackson and Schmugge, 1991). The
retrieved r was found to be linearly related to the time variation o f vegetation index (NDVT),
using satellite observations over semiarid areas and ancillary data about soil moisture
(Griend and Owe, 1993; Jackson et al., 1995).
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42
Jackson et al. (1982) developed a parametric approach to correct for vegetation
attenuation based on a theoretical model proposed by Basharinov and Shutko (1975). This
model treats the vegetation as an absorbing layer that can be quantified in terms o f the water
content o f the vegetation by the following relationship:
mv = 78.9-78.4 [1 + (e - 1) exp(0.22 vwc)]
(2.25)
where mv is the volumetric soil moisture (0-0.25 cm), e is the measured emissivity, and vwc
is the water content o f the vegetation (kg/m2).
Theis et al. (1984) demonstrated the use o f visible and infrared data to calculate a
perpendicular vegetation index (PVI), which in turn was used to correct the L-band
emissivity determined with a passive microwave radiometer. They found that as long as the
PVI was less than 4.3, good results could be obtained. Jackson and Schmugge (1991)
studied the relationship between wavelength and vegetation water content, and concatenated
their observations with a large amount o f previously published data to define a vegetation
parameter that is based on the optical depth o f the canopy. This parameter appears to be
inversely related to the wavelength, and can represent four types o f vegetation classes (leafdominated, stem-dominated, grasses, and trees and shrubs). Furthermore, they showed how
this parameter could be obtained operationally using visible and near infrared satellite data.
They correlated the vegetation water content as a function o f Normalized Vegetation Index
(NDVI), which is readily available from currently available remote sensing instruments.
These studies point out the possibility o f a total satellite remote sensing approach for soil
moisture with a minimum amount o f ground sampling.
A fairly simple model for the brightness temperature o f a scene consisting o f a semi­
infinite soil layer o f physical temperature Ts, an air-soil reflectivity ys, and a layer o f
vegetation o f physical temperature Tv, was proposed by Jackson and Schmugge (1991):
^ = [ 1 +r (i -^ > 1 (1 - r x i -a)rv+( < W ^ 0</)
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(2.26)
43
where a is the single-scattering albedo o f the vegetation layer, and /"is the transmissivity o f
the vegetation layer at the reflection angle 6
r ( 0 > e x p ( - 0 , secQ')
For a canopy o f height H and extinction coefficient
(2.27)
K e,
the optical thickness is
0 = K fl. This model is based on the following assumptions: (a) the albedo a is smaller than
about 0 .2 , and diffuse scattering may be ignored; (b) the canopy has no distinct air-vegetation
boundary, which allows the setting o f the air-vegetation reflectivity to zero; and (c) the
average index o f reflection o f the vegetation layer is only slightly larger than that o f air,
which allows the use o f Ms, the air-soil reflectivity, in place o f vegetation-soil reflectivity.
An additional advantage to the correction proposed by Jackson et al. (1982) is that all data
needed in Equation (2.26) can be measured by remote sensing.
As with the roughness case, the effect o f vegetation on the active microwave sensing
of soil moisture is greatly dependent on the instrument incidence angle, frequency, and
polarization.
The sensitivity of vegetation to the soil moisture retrieval algorithm is investigated
in detail in Chapter five. The dependence o f the current soil moisture algorithm on the
correct specification o f vegetation parameters restricts its transportability over regions where
vegetation parameters can be obtained with reasonable reliability. The algorithm is valid
only for moderately vegetated regions. The effect o f sub-pixel variability o f vegetation is
investigated in the context o f the Southern Great Plains (SGP 97) experiment.
Dead vegetation also can have an attenuating effect on the microwave emissions from
the soil as was demonstrated by Schmugge et al. (1988). Aircraft experiments with an Lband push broom microwave radiometer over the Konza prairie grasslands showed that, for
areas that had not been burned, a buildup o f a thatch layer serves as a highly emissive layer
above the soil, thus masking the emission o f the soil itself. Where there was an absence of
this thatch layer because o f burning or grazing, the microwave sensitivity to soil moisture
was as expected for bare soil.
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44
Chapter 3
Multifrequency Soil Moisture Inversion from SAR
Measurements with the Use of IEM
3.1
Introduction
Active microwave technology such as Synthetic Aperture Radar (SAR) has emerged
over the past few years as an alternative way o f measuring soil moisture at finer spatial
resolutions (10's m). Radar response is measured in terms ofbackscatter coefficient - defined
as the ratio o f the power density received by the radar to the transmitted power density. The
backscatter coefficient is defined only when the scattering angle is equal to the incidence
angle (Ulaby et al., 1986). Extracting soil moisture from these data is problematic due to
the difficulty in isolating the effects o f surface roughness and vegetation from the soil
moisture signal.
Generally, a decrease in the value o f soil moisture results in a decrease in the
observed backscatter coefficient (Ulaby and Batlivala, 1976; Ulaby et al., 1986). Several
algorithms have been developed to relate volumetric soil moisture to observed backscatter
coefficients, ranging from empirically-based models to those based on complex
electromagnetic scattering theories (Fung et al., 1992; Oh et al., 1992; Dubois et al., 1995).
However, the relationship between soil moisture and the received backscatter coefficient is
nonlinear, and hence the inverse problem is generally ill-posed (Twomey, 1977). The
nonlinear behavior o f the relationship is even more complex w hen surface roughness and
vegetation cover are also taken into consideration. Multi-frequency, multi-polarization
sensors can provide the necessary data to remedy this condition by providing additional
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45
constraints to the model. Ancillary data, such as terrain, land-use and land-cover data, can
also be used for the same purpose. This was the approach adopted in our work.
The objective o f the work described in this chapter was to formulate and constrain
a transformation model to solve the inverse problem for operational retrieval ofsoil moisture.
The strategy consists o f formulating the inverse problem in the context o f multi-frequency
and multi-polarization data. Specifically, we studied the relationship between the radar
response and soil dielectric constant as a function o f soil roughness and correlation length,
which are used as constraining land surface parameters in the Integral Equation Model (IEM)
(Fung et al., 1992). The radar response was then inverted for soil moisture using an
inversion model along with the IEM. The empirical models proposed by Dobson et al.
(1985); (valid in the 1.4-18 GHz range) and Peplinski et al. (1995); (valid in the 0.3-1.3 GHz
range) were used to relate the dielectric values to volumetric soil moisture, and the retrieved
values were compared with the in-situ observations.
Van Oevelen and Hoekman (1999) also have developed an inverse model based on
the IEM. However, their model can be applied only one-frequency at a time, and it requires
the specification o f surface roughness conditions (Van Oevelen and Hoekman, 1999).
Another difference is that their inversion algorithm is based on linear interpolation from
look-up-tables generated in forward application o f the IEM model for expected ranges o f
variability o f soil moisture and surface roughness. In this respect, that model is very similar
to the semi-empirical models o f Dubois et al. (1995) and Shi et al. (1996), which have also
been applied one-frequency at a time (e.g., L-band; Wang et al., 1997). By contrast, the
Inverse IEM model presented here consists o f a full multi-frequency, multi-polarization
application, which does not require land-surface ancillary data except for soil texture; the
IEM equations are solved in inverse mode at all times, for all pixels, simultaneously for three
frequencies (L-, C- and X-Bands) and two polarizations (HH and W ) .
The capability o f SAR to provide massive amounts o f high resolution data ( 30 m)
poses a problem in terms o f data transmittal from space back to the receiving stations. Thus,
data transmittal rate is one o f the constraints in the implementation o f multi-polarization,
multi-frequency high resolution sensors. One possible solution to this problem could be the
aggregation o f the data to coarser resolution prior to transmittal. This issue is addressed in
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46
this thesis by investigating the sensitivity o f soil moisture estimates to the aggregation o f
backscatter coefficients before retrieval.
The relationship between backscatter coefficient and soil moisture is explored in
section 3.2, and a review o f some o f the existing models is provided. The soil moisture
inversion methodology adopted in conjunction with the IEM is explained in section 3.3.
Section 3.4 describes the specifications o f the data and the characteristics o f the Washita ‘94
study area (Little Washita watershed). Finally, the results obtained are presented and
discussed in section 3.5.
3.2
The Relationship Between Backscattering Coefficient and Volumetric Soil
M oisture
Several studies have been conducted over the past few decades to study the
relationship between backscattering coefficient and soil moisture (Ulaby and Batlivala, 1976;
Ulaby etal., 1978; Dobson and Ulaby, 1986a, 1986b; Ulaby etal., 1986; W angetal., 1986;
Engman and Wang, 1987; Fung etal., 1992; Oh etal., 1992; Fung etal., 1994; Dubois etal.,
1995). The basis for the estimation o f soil moisture using microwave instruments relies on
the sensitivity o f the dielectric constant to water content; for instance, the real part o f the
dielectric constant (e) o f a dry soil is about 2.5, whereas it is about 80.1 for a free water
surface. For a moist soil, the dielectric constant can range anywhere from 2.5 for very dry
soil to 25 for very moist soil, as a function o f both the composition o f the soil and the
microwave frequency (Ulaby and Batlivala, 1976; Ulaby et al., 1978).
Dobson and Ulaby (1986) and Wang et al. (1986) used data at 1.28 GHz and HH
polarization to show that the values o f backscattering coefficients could change by as much
as 10 dB due to changes in soil wetness. The effect o f vegetation is similar to that o f soil
moisture, and Dobson and Ulaby (1986) showed that the backscattering coefficients could
vary by as much as 15 dB due to variation in vegetation cover.
Previous studies o f the relationship between backscatter coefficients and soil moisture
have addressed the “forward” problem, and focused on the effect o f land surface parameters,
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47
soil roughness (Choudhury et al., 1979), and vegetation (Lang et al., 1986; Ulaby et al.,
1986; Lin et al., 1994) on the radar response. In the forward mode, measured soil moisture
values and the land surface parameters obtained from the field are used to develop or validate
a microwave scattering model. The computed backscatter coefficients then are compared
with the observed radar response and the performance o f the model is evaluated on the basis
o f these sampled fields. Therefore, this is possible only when and where extensive ground
sampling exists. One o f the assumptions normally involved in these studies is that the
surface parameters (roughness and correlation length), which are measured at only a few
points in the field, are constant over the entire sampling site.
3.2.1
Empirical Soil Moisture Estimation Models
Empirical estimation models developed by Oh et al. (1992) and Dubois et al. (1995)
use ground-based scatterometer measurements over bare soils o f different root mean square
(RMS) roughness heights (j) to develop relationships between volumetric soil moisture (mv)
and backscatter coefficients (rr). The model developed by Oh et al. (1992) relates the ratios
o f the backscattering coefficients in distinct polarizations with volumetric soil moisture and
surface roughness:
P=
(3.1)
(3.2)
where r o is the Fresnel reflectivity o f the surface at nadir given by
(3.3)
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48
k=2izJX is the wavenumber, X is the wavelength, e is the complex permittivity, cf is the
backscattering coefficient in HH (horizontally transmitted, horizontally received), W
(vertically transmitted, vertically received) and HV (horizontally transmitted, vertically
received) polarizations.
Dubois et al. (1995) made use o f the ground-based scatterometer measurements o f
Oh et al. (1992) and W egmuller (1993) and obtained equations for the backscattering
coefficients, which can be solved simultaneously to estimate volumetric soil moisture (m J
and RMS roughness height (5 ), as follows:
/w ~ 10 27S( ~ ~ J ~ ) 1OOO28£tan0(far sinG)1-4) 0'7
aV =10~2'35( ^ ^ ) 1 0 0' ° ^ 0(fa sine)11*.0-7
sin30
( 3 .4 )
(3.5)
where 9 is the beam incidence angle.
Using the results o f sensitivity analysis o f the integral equation model (IEM, Fung
et al., 1992), Shi et al. (1995) derived empirical “best-fitting” functions to relate backscatter
coefficients with surface roughness, dielectric constant and incidence angle for L-Band. The
model is valid for incidence angles between 30° and 60° only. Dawson et al. (1997) explored
the use o f neural networks to study the relationship between backscatter coefficient and soil
moisture, and obtained an RMS error in the estimation o f soil moisture in the order o f 3-4%
using the scatterometer data collected by Oh et al. (1992).
One characteristic o f empirical models is that they include explicitly all the relevant
parameters in the model’s formulation, and hence the inversion can be carried out by simply
solving a simultaneous system o f equations (Wang et al., 1997). Typically, these models
were developed and have been successfully applied over specific sites, and because o f their
reliance on local observations they generally are valid only for these conditions, and cannot
be directly transferred to other locations. In addition, these models assume that the effect o f
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49
correlation length on the backscatter coefficient is minimal, which further restricts their
applicability.
3.2.2
Integral Equation Model (IEM. Fung et al.. 1992)
The IEM is a physically-based radiative transfer backscattering model from a
randomly rough dielectric surface, and thus it is, in principle, transportable to any location.
The use o f such a model results in the formulation o f a generalized soil moisture retrieval
algorithm, with does not make use of any land surface properties. Because the equations in
the model are highly non-linear, an analytical solution for soil moisture is not possible.
The parameters used in the IEM are: (a) the beam incidence angle {&), defined as the
angle that the beam makes with the surface; (b) the surface roughness (s), defined as the
standard deviation o f the surface heights; (c) the surface correlation length (L), a measure o f
the similarity between height z, at point x, and height z: at another point .t_, (Fig. 3.1), which
is defined as the distance at which the auto-correlation function o f the surface height
decreases by one-fold; and (d) the dielectric constant o f the soil media (e). For further details
on the IEM model, the reader is referred to Fung et al. (1992). Fung et al. (1994) showed
that for moderately rough surfaces, an exponential statistical distribution performs better than
the Gaussian or the 1.5 power law distributions. Thus, the statistical distribution o f land
surface was assumed to be exponential for the applications described in this chapter.
3.2.3
Effect o f Land Surface Parameters on Backscattering Coefficient in IEM
The relationship between backscattering coefficient (dB) and dielectric constant is
exponential in nature. For low soil water content, the backscatter coefficient is very sensitive
to changes in soil moisture (the rate o f change o f backscatter coefficient with dielectric
constant is very high), but for wet soil (high dielectric constant) the backscatter coefficient
is almost constant (Fig. 3.2a). The backscatter coefficient is lower for high incidence angles,
due to increase in scattering (effect o f surface roughness) for the dielectric surface.
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50
Medium 1
Medium 2
Figure 3.1
Backscattering from randomly rough surfaces.
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51
The effect o f surface roughness on backscatter is highly dependent on the angle o f
incidence. For low angle o f incidence, the effect o f surface roughness is small, while the
backscatter coefficient becomes almost independent o f angle o f incidence for high values o f
surface roughness (Ulaby et al., 1986).
For the same value o f incidence angle, the
backscatter coefficient also increases with the surface roughness.
The backscatter
coefficients vary over a 20 dB range when surface roughness height changes from -0 .0 to
4.0 cm (W anget al., 1986) as illustrated in Fig. 3.2b. For high incidence angles, the function
has both a local maxima and a local minima.
A sharp discontinuity exists in the relationship between backscatter coefficient and
correlation length, when the correlation length is half o f the wavelength o f the incident
frequency (Fig. 3.2c). This discontinuity is greater for higher incidence angles, therefore
making convergence very difficult. For correlation lengths less than half the incident
wavelength, the dielectric surface profile is considered perfectly random, whereas for higher
values an exponential correlation function is used in the formulation.
Figures 3.3 a-b show the effect o f land surface parameters on the differential increase
of backscatter coefficient with respect to soil moisture. The effect o f surface roughness is
especially significant for lower soil moisture values, but it diminishes for higher values o f
soil moisture (> 30%, Fig. 3.3a).
The correlation length is weakly connected to the
differential increase in backscatter coefficient with respect to soil moisture (Fig. 3.3b).
3.3
Data Synopsis
3.3.1
Description of SAR Data
W ashita ‘94 data for the Little Washita Watershed in Oklahoma were used for this
study. It consisted o f two different shuttle flights in April and October, 1994. Only data
from the April mission is used in this analysis. The data set consisted o f backscatter images
for three different microwave bands: L-Band (23.5 cm), C-Band (5.8 cm), and X-Band (3.1
cm). For the L- and C-Bands, two different polarized images were used: HH (horizontally
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
L = 1 . 5 c m , s = 2 . 0 c m , HH Pol ari zati on, C - B a n d
-5
CD
TJ
-10
S
0=45
-2 0
CD
-2 5
0
20
40
60
BO
Dielectric Constant
Figure 3.2a
Relationship between backscatter coefficient and dielectric constant.
Ui
to
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
£ = 2 . 7 7 , L = 1 . 5 c m , HH Po la ri za ti on, C—Band
o
CD
-1 0
-3 0
CD
-4 0
0
Figure 3.2b
2
3
R o u g h n ess Factor (c m )
Relationship between backscatter coefficient and surface roughness.
4
5
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8 = 2 . 7 7 , s = 2 . 0 c m , HH P ol ari zati on, C —Band
m
-2 0
X)
-4 0
<u
o
u
o
o
u
at
M
U
-6 0
S
-8 0
-100
0
Figure 3.2c
2
4
6
Correlotion Length (cm )
a
Relationship betw een backscatter coefficient and surface correlation length.
10
L/1
4^
55
E
a) L =5.0, Variation with R o u g h n e s s f a c t o r
3 0.81
s=3.4.5
o 0.6
? O 0.4
0
CD
2 0.2
10
20
30
Soil Moisture {%]
4-0
50
b) R a u g h n e s s = 2 . 0 , Variation with L
3 0.8
L>5.0
*
L=2.5
5
o
0.4
J
0.2
13 CD
ro
_o
oc
o.o
a
0
10
20
30
40
50
Soil M oistu re (%)
Figure 3.3 a-b Differential increase in backscatter coefficient with respect to soil moisture
as a function o f land surface parameters.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
56
transmitted, horizontally received), and W (vertically transmitted, vertically received). For
the X-Band, only the W image was available. Table 3.1 provides the daily information
about the SAR data during the Washita ‘94 experiment. The data set comprises spatial
distributions o f backscatter coefficients, at a resolution o f 30 m over the Little Washita
watershed in Oklahoma (Jackson et al., 1996). For very high incidence angles (> 50°), SIR-C
data were collected only for HH and HV polarizations because o f low signal-to-noise ratio.
The noise level for all three bands was o f the order o f ±2 dB during the SIR-C/X-SAR
experiment (Freeman et al., 1995). The SIR-C/X-SAR for the W ashita‘94 experiment was
placed in the cargo-bay o f the shuttle; hence it was north-west looking for ascending track
and south-west for descending track, and the incidence angle increased from east to west in
the image (Ann Hsu, per. comm.).
Table 3.1
Daily specification o f the SIR-C/X-SAR data during Washita ‘94
Date
Flight
Incidence Angle
11 April, 94
A
28.0°
12 April, 94
A
42.3°
hhh’ ^-hv> I'w' ^-hh> ^-hv’ ^w» ^w
hhh> h|jV, Lw, Cjjij, C|,v, Cvv, X^.v
13 April, 94
A
50.1°
^-hh’ ^hv» i-vv’ ^-hh’ ^-hv> ^"w*
14 April, 94
A
56.3°
hhh’ ^hv» ^'hh’ ^"hv>
14 April, 94
D
48.3°
^hh’ 1-hv’
15 April, 94
A
60.2°
^hh’ ^hv> ^w»
15 April, 94
D
42.4°
^hh’ ^hv’ ^w’ ^-hh’ ^-"hv’ ^w*
16 April, 94
D
36.2°
^hh’ ^hv’ I'w'
17 April, 94
D
30.9°
1-hh’ ^hv’
18 April, 94
D
26.5°
Lhh» h(,v, Lvv, Cy,, C|,v, Cvv, Xvv
*A
-
Ascending pass
*D
-
Descending pass
Bands and Polarizations
^-hv>
^hv» ^"w
^hv’ ^"w>
C|,h, C|,v, Cyy
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
57
3.3.2
Little Washita Watershed
The Little Washita watershed is located in southwest Oklahoma and has a drainage
area o f about 610 km2, with a sub-humid climate (average annual rainfall o f about 750 mm)
(Allen and Naney, 1991). Forty-two rain gauges are distributed at 5 km spacing in and
around the watershed (Allen and Naney, 199 1). The c limatic average cumulative rainfall for
April is about 55 mm, and the average daily high temperature is about 25°C. During the
experiment, the land was covered by rangeland, pasture, winter wheat, com and alfalfa
(Starks and Humes, 1996).
The study area experienced rainfall on April 10-11 ,1994, just before the shuttle data
takes were initiated. However, for the entire duration o f the Washita ‘94 experiment no
rainfall was recorded in the watershed (Starks and Humes, 1996). The hydrologic conditions
in the watershed were such that it was possible to follow a drying period starting with a wet
surface (volumetric water content up to 40%) to a dry state (volumetric water content as low
as 10%) over a period o f eight days. This is a valuable data set to study the spatial and
temporal variation o f surface soil moisture, and to establish relationships between changes
in surface soil moisture and soil properties. The topography o f the region is relatively flat.
Figures 3.4a-b show the topography and soils maps, respectively, for the Little Washita study
area. For this work the effect o f local topography was neglected and the sensor look angle
was assumed to represent the local incidence angle. This assumption was used previously
by Wang et al. (1997) for the Little Washita watershed without reported problems.
The soils in the eastern and western regions o f the Little Washita watershed are
mostly silty loams and loams, separated by an area o f fine sandy loam and sand. At the start
of the experiment (April 11), silt loam and loamy soils had a higher moisture content (-30% ;
high backscatter coefficient), whereas areas associated with sandy loam and sand had lower
moisture content (-20% ; lower backscatter coefficient). Generally, sandy soils with higher
hydraulic conductivity drain faster than loamy soils, which drain steadily for the entire
duration o f the experiment independently o f land-use.
The penetration depth o f airborne active microwave sensors in soils is in the range
between 1 and 5 cm, depending on the incident frequency, the organic matter content o f the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 3.4a
Digital Elevation Map (DEM) of Little Washita watershed.
58
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
m
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
u
1
5 Km
Figure 3.4b
Soil Texture Map o f Little Washita watershed
I
Sand
Loamy Fine Sand
Fine Sandy Loam
Loam
Silt Loam
Silty Clay Loam
Gypsum
I Water
60
soil layer (especially in areas that have tall vegetation), or the presence o f a mineral layer
(e.g. gypsum crust is present in some areas in Little Washita). Higher organic matter and the
mineralogical content o f the upper soil layer result in a bias in the estimation o f the
dielectric constant.
For example, soils rich in organic matter normally exhibit higher
moisture content.
Gravimetric soil moisture samples were collected during the entire duration o f the
Washita ‘94 experiment from a number o f selected agricultural fields, rangelands, and
pastures (Fig. 3.5) (Starks and Humes, 1996). The sampling was similar to that conducted
during a previous experiment (Washita ‘92) at the same site (Jackson and Schiebe, 1993).
About 12-18 samples were taken at each site depending on the size o f the field. The standard
deviation o f the gravimetric soil moisture observations was o f the order o f 3-4%.
Measurements o f bulk density values at each o f these sampling sites also were made during
this experiment. The gravimetric soil moisture measurements were converted to volumetric
soil moisture using the bulk density measurements. Soil surface roughness was measured
by photographing the surface profile against a 2 m grid, and then digitizing the profile at a
resolution o f I cm.
3.4
M ethodology
This study adopted a semi-empirical approach, which consisted o f combining the
IEM model to with empirical model that relates the dielectric constant o f soils to the soil
texture and the volumetric soil moisture. By doing this, the soil dielectric constant was
eliminated from the IEM model, and the volumetric soil moisture was introduced as a new
model variable.
The relationship between the dielectric constant o f the soil media and the surface soil
water content adopted was dependent on the microwave frequency used. In particular, the
empirical model (Eq. 3.6) developed by Dobson et al. (1985) (valid for 1.4-18 GHz) and that
shown in Eq. (3.7), proposed by Peplinski et al. (1995) (valid for 0 .3 -1.3 GHz) can be used:
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
<n
Uf
55
£
1
I
*
1
*
i
=
5
1
■
o
et
Figure 3.5
98-15
55
Location of sampling sites during Washita ‘94. (Adapted from Jackson et al., 1996)
61
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
62
Ye#=-1.645+1.939 pA-2.25622 5+1.594 C
(3.6)
7^=0.0467 +0.2204 p6 -0.4111 5+0.6614 C
(3 .7 )
where yeff is the effective conductivity, pb is the bulk density o f the soil, S is the sand content
and C is the clay content. For this application, Eq. 3.6 (Dobson et al., 1985) was used for the
C- and X-Band measurements, while Eq. 3.7 (Peplinski et al., 1995) was used for the L-Band
(1.27 GHz) measurements. The soil textural properties were obtained from the soil sub­
series for the Little Washita watershed (Soil Survey o f Oklahoma, 1965).
The Jacobian method, an iterative scheme similar to the Newton-Raphson method,
is used in the retrieval algorithm to solve the inverse problem.
These methods are
recommended when the inverse problem is over-constrained (Twomey, 1977). Because the
signal-to-noise ratio for the retrieved variable is a function o f noise in the data and the
performance of the forward model, existence o f a good forward model such as the IEM is,
therefore, one o f the primary requirements o f this method. The variables (T) used in the
formulation are volumetric soil moisture (mv), surface roughness (s ), and correlation length
(L). The known (i.e., observed) parameters in the model are the backscatter coefficients at
three different frequencies (L-, C- and X-Band) and two different polarizations (HH and W
for L- and C-Bands, W for X-Band). The algorithm can be summarized as follows:
Step 1 - the backscatter coefficients ((f) are computed using the IEM based on an
initial guess of the variables (mv, s and L);
Step 2 - using the computed and the measured values, an error matrix (z/er) is
computed for backscatter coefficients;
Step 3 - the Jacobian matrix (Eq. 3.8), which is the relation between the backscatter
coefficients and the land surface parameters, is computed subsequently using small
perturbations to each o f the parameters;
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
63
(3.8)
C<J X T y
d t f X IT
d (T x v v
Step 4 - the error in the estimation o f land surface properties (J F) is computed using
the pseudo-inverse o f the Jacobian matrix and the error matrix (Eq. 3.9);
(3.9)
&Y=(JTj ) iJrKa
Step 5 - these errors in the estimation o f land surface parameters are corrected by
(J F ) for the next iteration:
? (/+ l)= ? (0 +A p
(3.10)
Steps 1 through 5 are repeated until convergence is reached, that is A g = ± 2 dB in this case.
One o f the advantages o f this methodology is that the magnitude o f the surface
parameters can be controlled to remain within physically possible ranges. The values of
volumetric soil moisture were constrained between 0.0 and 100.0%.
For the surface
roughness values, an upper bound o f 5.0 cm and a lower bound o f 0.1 cm were prescribed
during the inversion process, which cover the entire range o f values observed in previous
studies. For example, the surface roughness values measured during the Washita ‘94
experiment were between 0.5 cm and 1.2 cm (Starks and Humes, 1996).
The mean o f the typical values o f surface parameters was used as an initial guess in
the inversion algorithm. The initial guesses for surface parameters were: soil moisture -
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
64
20.0%, soil roughness -1.5, and correlation length - 5.0. The sensitivity o f the algorithm to
these initial guesses is discussed in appendix.
3.5
Results and Discussion
3.5.1
Soil Moisture Inversion
The spatial distribution o f retrieved soil moisture obtained by using this methodology
is shown in Figs. 3.6a-f for the six days o f data available from Washita ‘94 (April 11
through April 18). The spatial distribution o f the retrieved soil moisture is similar to the
prevalent soil texture data (Fig. 3.4b). On April 11, the volumetric soil moisture in the
central part o f the watershed is about 20%, whereas in the eastern part it is about 30%, which
is in agreement with the ground-based soil moisture observations. This is also consistent
with the spatial variability of soil texture: the soils in the central part o f the watershed are
mostly fine sandy loam and sand, whereas the eastern part is dominated by silty loam and
loamy soils. The Little Washita river (which flows through the middle o f the watershed),
and Lake Burtschi (located in the north-central part o f the watershed) also can be located in
the image, as well as the drainage patterns prevalent in the watershed.
There is good agreement between the measured soil moisture and that estimated for
each o f the sampling sites (see Fig. 3.5 for location, and Figs. 3.7a and 3.7b for results).
Since no rainfall occurred during the entire duration o f the experiment, the volumetric soil
moisture values obtained using both measured and estimated methods decreased with time,
and the dry-down during the course o f the experiment is clearly evident from the two images.
The spatial distribution o f soil moisture on April 18 is similar to that for April 11, and the
volumetric soil moisture across the entire watershed has decreased by 10-15% (compare
Figs. 3.6a and 3.6f). The noise level for both polarizations in the three bands was on the
order o f ±2-3 dB during the SIR-C/X-SAR experiment (Freeman et al., 1995). Given this
signal-to-noise ratio, we can expect errors on the order o f ±5% in the retrieval process based
on sensitivity analysis (e.g., see Figs. 3.3a and 3.3b).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 3.6a
Estimated volumetric soil moisture for Little Washita watershed on April 11, 1994.
Volumetric Soil Moisture tor April 1 1 ,1 9 9 4
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Volum etric Soil Moisture tor April 12, 1994
(30 m resolution)
Figure 3.6b
Estimated volum etric soil moisture for Little W ashita watershed on April 12, 1994.
o\
0\
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Volumetric Soil M oisture tor April 13, 1994
(30 m resolution)
Figure 3.6c
Estimated volum etric soil m oisture for Little Washita watershed on April 13, 1994.
O'
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Volumetric Soil Moisture 1or April 15, 1994
(30 m resolution)
0 .1 0
Figure 3.6d
Estimated volumetric soil moisture for Little W ashita watershed on April 15, 1994.
ON
00
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Volumetric Soil Moisture tor April 1 6 ,1 9 9 4
(30 m resolution)
4A;*-5G
Figure 3.6e
Estimated volum etric soil moisture for Little Washita watershed on April 16, 1994.
On
NO
Figure 3.6f
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tor April 18, 19 94
Estimated volumetric soil moisture for Little Washita watershed on April 18, 1994.
Volumetric Soil Moisture
70
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Comparison of Estim ated Soil Moisture with M easurem ent
0 .4 0
April
April
April
April
April
April
•h- +
*o
s
<8 0.20
■o
□
•E
—
oQ
LU
0.10
0.00
0.00
0 .1 0
0.20
0.30
0 .4 0
M easured Soil Moisture
Figure 3.7a
Scatter plot o f measured volumetric soil moisture and estimated
volumetric soil moisture for all the sampling sites for the entire
duration o f the Washita ‘94 experiment.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0 16
•MbHa
■ Bare Soil
+ P a siu re
-^Ranaaiand
0.12
fcWimar Whaa
0.08 -
^ xj
UJ
►
*
0.04 T
1°
lli
o-oo t 1
( f lS
“ §
I
|J -0 .0 4 <
■
:
T
+
►
►
♦
►
12
13
15
o
‘>
►
*
■
-0 0 8
-012
-0 .1 6
11
16
18
A p ril
Figure 3.7b
Time evolution o f retrieval errors o f soil moisture (estimated-observed) for different vegetation types.
^
N>
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0 16
0.12
0 .0 B
o
0 04
—O.QB
-0 1 2
-0 .1 6
0.0
Figure 3.7c
500 0
1000 0
1500 0
Vegetation W ater Content (g/m2)
200 0 0
Relationship between retrieval errors o f soil moisture and vegetation water content at the sites where
vegetation sampling was conducted during W ashita’94.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Comparison of Estim ated Soil Moisture with M easurement
0 .4 0
0J 0
1 I i i i i i i
+
I 11
+ April II
A
A
April 12
0
A
April 13
a
a April 15
X
X
*
m April 16
April 16
R (veq)= 0.8444R =0.B 275
o
s
w 0.20
x»
V
15
E
0.10
0.00 i i i i i i i i i I i i i i i i i i i I i i i i i i i i i I i i
0 .0 0
Figure 3.7d
0 .1 0
0 .2 0
M easured Soil Moisture
0 .3 0
..............
0 .4 0
Scatter plot o f measured volumetric soil moisture and estimated
volumetric soil moisture for all the sampling sites for the entire
duration o f the Washita ‘94 experiment after the vegetation
correction (Eq. 3.13) was applied.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0 .1 6
OAltall* (w>al
< J > P a £ iu r e ( v e g )
X R a n g e la n d fv e g )
f r W im e t W h m i fv eg j
£ |
o.Q4<
^=-6 0.00
%
^ -0 .0 4 *
-0 .0 B
-
0.12
- 0 16
A p ril
Figure 3.7e
Time evolution o f retrieval errors o f soil moisture (estimated-observed) for different vegetation types
after the vegetation correction (Eq. 3.13) was applied.
Ul
76
Overall, the errors obtained never exceed 10%, and on average the error is 3.4% (Fig.
3.7b). These results are consistent with the results of Wang et al. (1997) for bare soils, and
represent an
improvement for the vegetated sites. The errors in results obtained by
Woodhouse et al. (1996) for agricultural fields, and for L-Band and C-Band separately,
varied between 5 and 13% for L-Band, and between I and 13% for C-Band; best results were
obtained for the low-incidence angle (20°) data with the C-Band error varying between only
1 and 5%, and between 1 and 10% for L-Band.
In this study, the estimation errors were larger for soil moisture values below the 1015% range, at which point it appears that the sensitivity o f the retrieval algorithm to the
magnitude o f the changes in the backscatter coefficients is greatly reduced (Fig. 3.7b). This
contrasts with results presented by Van Oevelen and Hoekman (1999) for a single-frequency
application, which exhibit a consistent dry bias at all soil moisture levels, although it levels
o ff for high soil moisture. The existence o f a lower detection limit for the IEM in practical
applications should be further investigated over a variety o f conditions, and it is out o f the
scope o f this work.
On a site-by-site basis, the largest errors in estimated volumetric soil moisture
occurred for sites 32 and 55 (see Table 3.2 for details), which had moderate vegetation.
However, there is not one consistent pattern that could explain the estimation errors in terms
o f vegetation type or vegetation water content (Fig. 3.7c). Considering that the IEM model
was originally developed to simulate scattering from a bare soil surface, a simple sensitivity
analysis test was conducted to assess the effect o f vegetation variability and differences in
vegetation water content among different sampling sites.
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77
Table 3.2
" Site
Site characterization for Washita ‘94 April mission.
Vegetation Water Content
[g/nr]
Surface Roughness
[cm]
Land Cover
11
1,798
0.81
Alfalfa
12
0
3.43
Bare Soil
13
1,386
0.81
Winter Wheat
14
96
0.73
Rangeland
21
78
0.87
Rangeland
22
107
0.67
Rangeland
23
65
1.31
Rangeland
31
797
0.99
Winter Wheat
32
1,933
0.56
Winter Wheat
33
1,916
0.85
Winter Wheat
34
103
0.49
Pasture
53
797
1.18
Winter Wheat
54
86
0.76
Pasture
55
817
0.73
Winter Wheat
71
0
0.55
Bare Soil
Ulaby et al. (1986) showed that the backscattering coefficient from a vegetation
canopy is the sum o f the vegetation volume scatter, vegetation-soil interaction, and soil
backscatter (attenuated by canopy):
®total~®veg+®v«g-ioil ^ *®sotl
(3-1 1)
where r is the canopy attenuation factor. The first two terms can be combined to obtain:
^total~®v€g■vtg-jotl '^*^tatl
(3.12)
Similarly, we imposed a correction to the backscatter coefficient (<r,oto/) as follows:
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
where the maximum value o f the correction is AoveV vwc is the vegetation water content in
g/m 2, and vwcref is a reference value. Vegetation sampling was done at 15 out o f 25 sites at
which gravimetric soil moisture measurements were conducted in the watershed. The value
o f vwcnJ-was set to 2,000 g/m2, the highest mean value for the vegetation water content at
the Little Washita sampling sites (Table 3.2). The correction imposed is based on the
assumption that the relationship between vegetation water content and vegetation attenuation
is approximately linear ( Wang et al., 1986; Dobson and Ulaby,1986). The value o f Aa veg
was taken equal to 2 dB, which is the maximum observed difference between the average
backscatter between bare soil and winter wheat with the highest vegetation water content
(Table 3.3). This correction corresponds to 20% o f the maximum field-average range o f the
backscatter coefficient. The maximum difference in the estimated volumetric soil moisture
with and without vegetation effects is about 3% (Figs. 3.7d and 3.7e). However, it is
difficult to attribute any type o f bias in the results to vegetation as a function o f water content
alone. In fact, although the results improve slightly for pasture, rangeland and winter wheat
in the first three days o f the experiment, the results for alfalfa deteriorated significantly
(compare Figs. 3.7b and 3.7e). An attempt was made to organize the retrieval errors as a
function o f antecedent precipitation index, soil texture, and topographic indices without
success.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
79
Table 3.3
Difference in field-averaged backscatter coefficients [L-Band, HH
polarization] between bare soil (BS - Site 12) and winter wheat (WW- Site
53), and between bare soil and alfalfa (AL- Site 11).
......... BS-AL [dBJ
Day
BS-WW [dBJ
April 11
1.66
0.36
April 12
0.06
0.95
April 13
2.03
0.70
April 15
1.5
0.89
April 16
no data
0.59
April 18
0.83
1.45
In principle, one could expect that this result would be different if a model of
backscattering interactions between the vegetation and the land-surface, and among the
different layers o f the vegetation canopy, had been incorporated directly into the IEM . Yet,
given that the magnitude o f the errors obtained in our application are w ithin the accepted
level for soil moisture measurements using TDR. or volumetric sampling, it would be
difficult to assess the value added by a complex conceptual backscatter model. The
performance o f the multi-frequency approach model for forested areas, and in general for
vegetated areas at difference stages o f growth must, however, be investigated. For example,
Woodhouse et al. (1996) demonstrated the importance o f incorporating geometric backscatter
effects for the boreal forest, albeit in the context o f single-frequency applications. On the
other hand, because vegetation will affect the backscatter mechanisms at different
frequencies in different ways, one can also hypothesize that those effects are naturally
incorporated in the context o f the multi-frequency, multi-polarization framework of our
algorithm. That is, the parameterization o f vegetation effects is not in the EEM equations per
se, but is implicitly assimilated into the model by the data.
The reliability o f the inversion algorithm can be evaluated based on the performance
o f the iterative Jacobian scheme measured by the convergence ratio (defined as the number
o f pixels within an image for which convergence was not reached over the total number o f
pixels). Generally, the number o f pixels for which no solution was obtained increases as the
soil dries. This is evident by comparing the number o f pixels where no convergence was
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
80
reached for April 11 and 18 (incidence angle were almost the same), 2.6% and 8.4%,
respectively. For drier soils (mv < 10%), the value o f partial derivative o f backscatter with
respect to soil moisture (e.g. cb/cG) is 2-3 times higher than that for wet soils (mv > 40%),
as shown in Fig. 3.3a. The number o f pixels where solution could not be achieved also
increases for high incidence angles. This is expected given the highly non-linear relationship
between the backscatter coefficient and surface roughness (presence o f a local minima, Fig.
3.2). In any case, convergence always was obtained for more than 90% o f the pixels in the
entire image, hence suggesting that the inversion algorithm is robust for applications over
a large area, and for a wide range o f soil moisture and land-cover conditions. Previously,
Wang et al. (1997) reported significantly lower convergence ratios using the Dubois et al.
(1995) and Shi et al. (1996) algorithms, ranging between 27 and 60% for the former, and
between 53 and 60% for the latter.
Figure 3.8 shows the comparison between the estimated and measured surface
roughness for the sites in the Little Washita watershed. Although it exhibits a large scatter,
the estimated values fall within the range o f values observed in the field. The large scatter
can be explained by the fact that the surface roughness height is a function o f the incidence
angle o f the beam as shown by Ulaby et al. (1986). Surface roughness, which varies from
day to day and point to point within the path o f the satellite, was measured at only a few
points within a site at an incidence angle o f 0 °, i.e. the photographs were taken parallel to the
ground (normal to the calibration board), and therefore one would expect that these values
would change from location to location, and from day to day. Our results are also consistent
with the results derived by Wang et al. (1997) using the empirical models o f Dubois et al.
(1995) and Shi et al. (1996).
3.5.2
Aggregation and Data Compression
Aggregation o f “raw” pixel data (i.e., averaging the data using windows of different
sizes (2 to 8 pixels) has been a routine procedure adopted by other researchers in order to
reduce speckle (Woodhouse and Hoekman, 1996; Wang et al. 1997). One limitation o f the
operational use o f a multi-frequency, multi-polarization active microwave sensor is the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1.2
E
u
o* 1.0
a
o
a
vo
o
0.8
o
E
L iJ
0.6
0 .4
0 .4
0.6
1.0
M easured S u rfa c e R oughness (c m )
Figure 3.8
Scatter plot o f measured surface roughness and estimated surface
roughness for all the Washita ‘94 sampling sites.
00
82
volume o f data collected, which needs to be transmitted to the receiving stations. A possible
solution to this problem could be the aggregation o f the data to coarser scales before
transmittal. In this context, a relevant question is whether the aggregation o f remotely sensed
images should (could) be carried out before or after the soil moisture inversion.
To address this question, the backscatter coefficient images were aggregated from
30 m to 300 m and up to 900 m using three different methodologies: (a) arithmetic
aggregation; (b) geometric aggregation; and (c) fractal aggregation, an aggregation scheme
that preserves the fractal behavior o f the data (Bindlish and Barros, 1996). The spatial
distributions of soil moisture estimated using these different methodologies for both
aggregation levels are shown in Fig. 3.9. The spatial distribution o f the estimated soil
moisture at the coarser resolutions is similar to the fine resolution retrieval, although, as
expected, the small scale spatial variability is lost. The effect o f soil texture is present in
both coarse resolution retrievals, while the Little Washita River can be detected only at the
300 m resolution.
The estimated volumetric soil moisture for a sampling site, located in the eastern part
o f the watershed and just south o f the river (site 14, Fig. 3.5), is shown in Fig. 3.10. This
location was selected because o f the significant amount o f spatial variability in soil moisture
within the site: the central part o f the site is significantly wetter than the western part. The
average measured soil moisture was 25.3% with standard deviation 3.3% based on 14
gravimetric samples across the site. Our average result, based on 600 pixels at 30 m
resolution, is 28.4% with standard deviation 7.4%. When arithmetic aggregation is used the
spatial gradients in the resulting soil moisture images are lost, though the overall spatial
distribution is preserved (Fig. 3.11). Based on the definition o f backscatter coefficient
(defined as the log o f the power spectrum density function), geometric aggregation should
perform better than arithmetic aggregation. This is consistent with our results, which show
that geometric and fractal aggregations conserve the spatial variability and gradients o f soil
moisture fields, while the soil moisture estimates at all the sampling sites on different days
compare very well with the measurements.
Figures 3.12 (a-f) serve to compare measured soil moisture and the estimated
(retrieved) soil moisture at all sites based on the aggregated backscatter images using seven
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83
Volumetric Soil Moisture tor April 11, 1994
Arithmetic Aggregation (300 m)
Arithmetic Aggregation (900 m)
Geometric Aggregation (300 m)
G eometric Aggregation (900 m)
Fractal Aggregation (300 m)
Fractal Aggregation (900 m)
Figure 3.9
Estimated Volumetric Soil Moisture for April 11, 1994 using different
methods o f aggregation.
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84
Soil Moisture for site 14 (April 11, 1994)
0.40
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GrtDS: COU/IGES
Figure 3.10
Estimated volumetric soil moisture for site 14 on April 11,1994.
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85
Arithmetic Aggregation
Geometric Aggregation
Fractal Aggregation
GrADS: COLA/ICES
Figure 3.11
Estimated soil moisture using different aggregation methodologies at 300 m
for site 14 on April 11, 1994.
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C o m p a ris o n of E s tim a te d Soil M o istu re with M e a s u r e m e n ts u sin g d iffe re n t m e th o d s of a g g r e g a tio n
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C o m p o ris o n of E s tim o te d Soil M oisture with M e o s u re m e n ts u s in g d iffe re n t m e th o d s of o g g re g o tio n
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Comporison of Estimoted Soil Moisture with Meosurements using different m ethods of oggregation
0.40
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Comporison of Estimoted Soil Moisture with Meosurements using different methods of oggregotion
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e x p erim e n t o n A p ril 18, 1994.
92
different options: (a) original data (30 m); (b) arithmetic aggregation (300 m); (c) geometric
aggregation (300 m); (d) fractal aggregation (300 m); (e) arithmetic aggregation (900 m); (f)
geometric aggregation (900 m); and (g) fractal aggregation (900 m). Although there is a
relative increase in bias with successive aggregation o f the backscatter coefficient fields,
there is no significant difference between the overall performance o f the retrieval algorithm
for any o f the options above, as long as the soil moisture remains above 10-15 %. Below this
value, which as discussed previously could be interpreted as a lower detection limit for the
retrieval algorithm, the degradation o f the performance is substantial for all cases (see for
example, the large scatter in Figs. 3.12d and 3.12e). Therefore, it can be concluded that,
within the range o f sensitivity o f the model, these exploratory sensitivity tests suggest that
moisture retrieval from aggregated backscatter coefficient fields is a viable alternative to
increase the operational real-time utility o f SAR data.
3.6.
Final Com m ents
This work demonstrated the possibility o f using
multi-frequency and multi­
polarization instruments to derive soil moisture fields from the remotely sensed images
without prescribing time-varying land-surface parameters such as roughness height and
correlation length as input, and without conducting site specific calibration. This case-study
provides a proof-of-concept for further research using the inverse problem approach to
evaluate soil-water functional relationships at the scale o f remote-sensing instruments over
large areas, and to facilitate the operational use o f satellite data for hydrologic applications
in data-sparse regions. Although the methodology was demonstrated using the SAR data
from the W ashita ‘94 experiment, it can be applied to any other data. Caution should be
exercised, however, in the case o f vegetated areas, especially when geometric backscatter
effects are dominant. The focus o f ongoing research is on determining to the degree to which
such effects are implicitly parameterized in our multi-frequency, multi-polarization inverse
LEM algorithm.
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93
On the question o f transferability, an important point that must not be overlooked is
the underlying rationale for this type o f work. As hydrologists, our major concern is to
investigate the viability o f operational, real-time soil moisture monitoring from space.
Introducing into IEM a complex backscatter algorithm which would require the specification
of a large number o f surface parameters (see, for example, Karam et al., 1992) is a positive
contribution only if the means to specify such parameters objectively and with adequate
accuracy are available on a global basis. We are currently working on the development o f
a multi-frequency, multi-polarization approach to address this issue.
One major danger in “free” inversion algorithms such as the one used in this exercise
is the risk o f reaching convergence despite the fact that the model parameters are out o f the
range o f physically acceptable values. When the parameters generated by the inversion
algorithm (e.g., surface roughness) were compared with the ground-values obtained at a few
sampling locations during the Washita ‘94 experiment, it was found that they were within
the observed range with a level o f accuracy consistent with the accuracy o f the ground
measurements, and the procedure to generate areal averages. This was possible because the
surface roughness values were constrained in the inversion algorithm between values that are
physically realistic in natural settings. In this particular application, the problem was over­
constrained, thus reducing the effect o f noise in the data. For weakly constrained situations
(i.e., in the lack o f a multi-frequency and multi-polarization sensor), one would have to
include other sources o f ancillary data (e.g., NDVT, topography, etc) to provide additional
constraints.
The soil moisture estimates obtained using different aggregation methodologies
showed that it is possible to map soil moisture distribution with an accuracy adequate for
macroscale climate and hydrologic modeling as long as the soil does not become very dry
(i.e., 10-15% soil moisture content). The aggregation could be implemented in space aboard
the satellite, resulting in a large reduction o f data volume. Nevertheless, high resolution data
is required for pilot study sites and for small-scale hydrological applications.
Surface soil moisture retrieved from remotely sensed brightness temperature has
inherent errors and uncertainties associated with it. Moreover, at best it represents the
integrated soil moisture content over the top 5 cm o f soil, a layer which is mostly governed
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94
by evaporation. Hence, it should be used in conjunction (as a boundary condition and for
validation) with a hydrologic model that explicitly accounts for the presence o f soil moisture
in the root zone (e.g. Capehart and Carlson, 1997). One would expect an optimal estimate
o f the two outputs would yield more accurate estimates o f soil moisture content and related
variables that can be obtained by either approach.
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95
Chapter 4
Parameterization o f Vegetation Backscatter Effects
in Radar Based Soil Moisture Estimation
4.1
Introduction
Remote sensing satellites have a considerable potential for monitoring forests on a
regional or local scale. Estimates o f regional and global forest biomass can be used for
understanding and monitoring ecosystem response to climate change and human activities,
where knowledge o f the distribution o f structure o f above-ground woody biomass is
important for accessing production and decomposition rates in forests. The presence o f
vegetation canopy complicates the retrieval o f moisture in the underlying soil because the
canopy contains moisture of its own. The challenge, therefore, is to separate the contribution
o f vegetation backscatter from that o f soil moisture.
The potential o f remote sensing techniques in the optical domain (visible and
shortwave infrared) to monitor the status and temporal evolution o f vegetation canopies is
well recognized (Asrar et al., 1985; Sellers, 1985; Tucker et al., 1985). Cloud cover,
however, strongly limits the number o f available optical images. Also, these techniques are
limited by the observed saturation o f the signal with increasing biomass.
A number o f studies have evaluated the utility o f radar data for forest ecosystem
analysis. Cimino et al. (1986) demonstrated that SAR data can be used to discriminate
different forest types, and that the intensity in a SAR image at L-band is proportional to the
aboveground biomass o f the forest stands (Wu, 1987).
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96
Radar provides a useful tool for accessing forest biomass since it is unaffected by
cloud cover, or low solar zenith angles (a potentially significant problem at high latitudes).
While the optical reflectance spectra respond mainly to green foliage biomass, microwave
data may be related primarily to standing woody biomass, especially at longer wavelengths
such as L and P bands. Because o f the greater penetration depth o f microwaves in natural
media such as vegetation and the atmosphere (compared to optical waves), radar techniques
have the potential to overcome these limitations. As in the optical domain, the use o f
microwave data for monitoring vegetation canopies requires the development o f suitable
inversion algorithms to estimate variables such as LAI. But the estimation o f vegetation
parameters using microwave radars is neither as developed nor as straightforward as that o f
optical images due to multiple scattering effects within vegetation, and the interaction
between vegetation and the underlying soil layer.
4.2
Backscatter from Vegetation Canopies
The effect o f vegetation on microwave backscattering is very complex to describe,
because it is difficult to separate the effect o f vegetation structure and that o f surface
roughness from one another. Over the last several years, significant efforts in microwave
remote sensing have been devoted to relating forest parameters to radar backscattering
coefficients. These and other studies have shown that, in most cases, the longer wavelength
(i.e. P-band) and cross-polarization (HV) backscattering had greater sensitivity and better
correlation to forest biomass. This probably is due to the fact that the multiple scattering at
L- and P-bands, which contributes to the cross-polarization return, takes place mainly within
the lower part o f the forest canopy, (i.e., large branches and trunks). The backscattering at
C-band corresponds mainly to the upper layer o f the canopy, but saturates when the biomass
reaches higher levels, and this is useful for providing discrimination among biomass
categories (Imhoff, 1995).
Vegetation canopies may be divided into several groups, depending on the
complexity o f the canopy architecture and the sizes o f the scattering elements relative to the
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97
wavelength, L For some scattering elements, such as curved or curled leaves, accurate
measurement is problematic (Karam et al., 1992).
The radar backscatter signal at high frequencies is particularly sensitive to vegetation
(Ulaby et al., 1986; Prevot et al., 1993), whereas at low frequencies it is particularly sensitive
to soil moisture (Ulaby et al., 1986; Fung, 1994). Thus, a combination o f high and low
frequency SAR data has been used to improve the estimation o f soil moisture (Prevot et al.,
1993; Taconet et al., 1994). These studies suggested that the vegetation scattering for low
frequency SAR data was important only when vegetation density was high. In humid and
moist environments, typically the vegetation density is very high and it is very difficult to
account for vegetation effects. Moreover, in such environments the soil moisture is also
high, and so is its contribution to the observed backscatter. In sparsely vegetated areas, the
contribution from vegetation to the scattering process is significantly smaller than that from
soil, and the vegetation scattering can be neglected. However, in arid and semi-arid regions,
soil moisture content rarely exceeds 20 %, indicating that the soil contribution may be small
or approximately the same magnitude as the vegetation contribution.
Some of the factors that are known to govern backscattering behavior are:
1.
The dielectric constant o f the vegetation material, which is strongly influenced by
moisture content.
2.
The size distribution o f the scatters in a canopy.
3.
The shape distribution o f the scatters in a canopy.
4.
The orientation distribution o f the scatters in a canopy.
5.
The canopy cover’s geometry (row direction and spacing,cover fraction, etc.)
6.
The roughness and dielectric constant o f the underlying soil surface.
At higher viewing angles, the backscattering contribution o f the canopy increases and
is dominated by the return from the vertically aligned stalks and cobs, whereas the canopy
loss component is apparently dominated by the leaves (Ulaby et al., 1986).
The use o f SAR data to estimate woody biomass is predicated on the fact that
scattering and attenuation by the foliar layer scales with frequency, while large branches,
trunks and the soil surface are strong scatterers at all frequencies. Hence, radar backscatter
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98
at high frequencies (C- and X-bands) will be dominated by scattering processes in the crown
layer o f branches and foliage, and backscatter at lower frequencies (P- and L-bands) will be
dominated by scattering processes involving the major woody biomass components (trunks
and branches) (Ulaby et al., 1990; McDonald et al., 1991).
4.3
Current Approaches to M odeling Backscatter from Vegetation Canopies
To use radar data for modeling backscatter from vegetation canopies, a common
approach is first to develop direct models simulating the backscattering coefficient o f a given
canopy. These models then may be inverted to estimate canopy characteristics. Next, we
present a review o f several direct modeling approaches presented in the literature. We group
them in three general classes of models: empirical, theoretical, and semiempirical.
4.3.1
Empirical Models
Most studies have concentrated on a single tree structural type (i.e., mono-species).
Observed data show that, for a given species (structural type), the radar backscattering
coefficient (cf at frequency band f polarization p and incidence angle 6) increases with
biomass tracing a power-law relationship. Backscatter becomes insensitive to increases with
biomass at a threshold level (saturation level), which scales with wavelength for a each
species. The HV- and HH- polarized backscatter are found to be the most sensitive to
vegetation and hence yield the highest correlations. The W - polarized backscatter tends to
saturate at lower levels o f NDVI.
Some investigators have proposedthat these saturation points define the upper limits
for accurate estimation o f forest biomass (Imhoff, 1995; Dobson et al., 1995). This indeed
is the case when only single frequency and polarization data are available. However, models
and empirical data have shown that polarization ratios and spectral gradients do not saturate
as quickly in the case o f multi-frequency, multi-polarization data, and can therefore be used
to extend the range o f biomass estimation beyond that imposed by the “apparent” saturation
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99
o fasingle frequency/polarization configuration (Dobson etal., 1992; RansonandSun, 1994;
Imhoff, 1995).
Approaches using polarization ratios and empirical relationships do not adequately
account for structural effects o f different species, although they can extend the range o f the
estimates to higher levels of biomass within a given forest structural type. Most empirical
investigations o f mono-species forest stands show that considerable scatter exists about the
power-law relationship between backscatter and net vegetation biomass. However, model
results indicate that much o f this scatter is also a consequence o f structural control, and
therefore it should be expected, and it does not necessarily pose a limitation to accurate
estimation o f forest biomass (Pierce et al., 1993; Dobson et al., 1995).
Dobson et al. (1995) used polarimetric SAR data at L- and C- bands to estimate basal
area, height and dry crown biomass for forested areas. The calculations were based on
empirical relationships specific to each structural class. Within a vegetation class the total
biomass was estimated as the sum o f crown and trunk biomass.
4.3.2
Theoretical Models
Both canopy structure and canopy water content affect the backscatter, thus adding
more complexity to the problem o f soil moisture estimation. A num ber o f theoretical models
have been developed to account separately for these effects.
Although, a tree canopy is an inhomogeneous medium comprised o f scattering
elements with many different shapes, sizes and orientation, most models for radar scattering
from vegetation treat the canopy as a uniform layer o f some specified height containing a
random distribution o f scatterers (Attema and Ulaby, 1978; Fung and Ulaby, 1978; Tsang
and Kong, 1981; Lang and Sidhu, 1983; Eom and Fung, 1984; Karam and Fung, 1988).
Models based on the “field approach” (Fung and Ulaby, 1978; Tsang and Kong, 1981)
account for the inhomogeneity o f the medium through a correlation function between the
dielectric constant o f vegetation and the observed backscatter coefficient representing the
fluctuating component o f the dielectric constant. The models based on the radiative transfer
approach (Eom and Fung, 1984; Tsang et al., 1985; Ulaby et al., 1986; Ulaby et al., 1990)
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100
account for the inhomogeneity by averaging the Stokes matrix (it relates the amplitude,
phase, and polarization state o f the scattered electromagnatic wave with the incident wave)
over the statistical distributions characterizing the sizes, shapes and orientations o f the
canopy.
In general, the field approach is appropriate for weakly scattering media in which the
ratio o f the fluctuating component o f the dielectric constant to the mean value o f the medium
is small (Lee and Kong, 1985; Ulaby et al., 1986). When the vegetation scatters (leaves,
branches etc.) have discrete configurations and have distant dielectric constants, the radiative
transfer approach is more appropriate because it allows the integration o f vegetation effects
over the distribution.
In both approaches, vegetation can be described as a discrete or as a continuous
medium. Because the effect o f time-varying vegetation and soil parameters can be studied,
these models are excellent tools for understanding the mechanism o f volume scattering.
The discrete model approach for a random layer o f vegetation was first used by Du
and Peake (1969) to compute the attenuation through a layer o f leaves. Later, Lang (1981),
Karam and Fung (1983), and Ulaby et al. (1990) have used the approach to develop more
rigorous theoretical models for backscatter from a layer o f vegetation over soil surface. The
advantage o f the discrete approach is that the results are expressed in terms o f quantities
(plant geometry and orientation statistics) that are easily related to the biophysical properties
o f individual plants, which can potentially be measured.
In theoretical models, the canopy is modeled as a two-layered medium above a rough
interface. The upper layer is the crown containing leaves, stems, and branches. The lower
layer is the trunk region modeled as randomly positioned cylinders with a preferred
orientation distribution above an irregular soil surface. Depending on the architecture o f the
canopy, in terms o f both the shapes and the sizes o f the scattering elements relative to A., it
may be reasonable to treat the canopy as a single layer having uniform properties. In some
cases, however, the uniform canopy assumption may not be adequate, thereby leading to
poor agreement between experimental observations and model calculations (Karam and
Fung, 1983).
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101
Most o f the existing scattering models are restricted by assumptions regarding the
shape ofthescatterers (Karam and Fung, 1983; Lang and Sidhu, 1983; Eom and Fung, 1986;
Fung et al., 1987; Karam and Fung, 1988; McDonald et al., 1991), or the applicable
frequency (Karam and Fung, 1983; Le Vine et al., 1985). Some models account only for
leaves but not branches, or vice versa (Karam and Fung, 1983; Lang and Sidhu, 1983; Eom
and Fung, 1986; Fung et al., 1987; Karam and Fung, 1988), while others treat branches and
the soil surface but not the leaves (Karam and Fung, 1988). In all these models the scatterers
were embedded in one layer above the soil surface, or a half space medium.
Ulaby et al. (1990) proposed a two-layer physical model based on the first-order
solution o f the radiative transfer theory. This model was used by McDonald et al. ( 1991) to
model multi-angular and temporal backscatter. Yueh et al. (1992) showed that it is necessary
for theoretical models to take into account the architecture o f vegetation which plays an
important role in determining the observed coherent effects.
In summary, the major shortcomings o f available models can be listed as follows: (1)
the canopy is treated as a continuous layer in the horizontal direction, which is valid only for
closed canopies; ( 2 ) the canopy is treated as having uniform properties in the vertical
direction, thereby treating the crown (foliage) section and the trunk section the same; (3)
usually the scatterers are chosen to be uniform in shape, size and dielectric constant in order
to simplify computations; and (4) large number o f variables and parameters (canopy
properties) involved in the theoretical models makes their use difficult. Because o f these
limitations, available theoretical models are inadequate for relating the radar backscatter
coefficient to the physical properties o f the canopy.
In practice, two types o f problems are encountered when modeling the backscatter
behavior of a vegetation canopy. The first relates to the difficulties in specifying model
parameters that adequately describe the canopy. For example, for a canopy consisting
primarily of leaves, an appropriate scattering phase function may be developed when
information is available on leaf-angle distribution, leaf-size distribution, and the dielectric
properties o f the leaf material. However, measuring these distributions for a given canopy
is a time consuming process, and it is seldom done along with the remote sensing
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102
measurements. In the absence o f this information, a realistic assumption must be made about
the distribution.
The second type o f problem in modeling relates to mathematical complexity. Most
vegetation canopies consist o f three major constituents: leaves, stalks and fruit. Each o f the
constituents o f a canopy has specific orientations, size distributions, and dielectric properties.
Furthermore, each constituent is characterized by a different polarization-dependent
scattering phase function. In terms o f the geometry o f a given scatterer, the scattering phase
function usually is more complicated when the scatterer’s dimensions are comparable to the
wavelength X, which is true o f most vegetation canopies at microwave frequencies. Thus,
taking all these factors into account, the scattering model would become both very
complicated and difficult to use. Fortunately, the scattering process involves a certain
amount o f averaging as a result o f the multiple scattering and the quasi-randomness o f the
locations, sizes, and orientations o f the scatterers. This averaging effect, together with
specific information about the attenuation properties o f a given canopy constituent, makes
it possible to make assumptions that simplify the scattering models in terms o f physical
vegetation parameters. Furthermore, despite a few attempts (Lang and Saleh, 1985), the
large number o f variables and parameters involved makes their inversion difficult.
4.3.3
Semi-empirical Models
In order to circumvent these problems, a simpler approach, based on the so-called
water-cloud models, was developed first by Attena and Ulaby (1978), and subsequently
modified or extended by various authors (Floekman et al., 1982; Ulaby et al., 1984; Paris,
1986). In these models, the power backscattered by the whole canopy is represented as the
incoherent sum o f the contributions o f vegetation and soil. These models are simple, and use
few parameters and variables. The canopy is represented by “bulk” variables such as LAI or
total water content, and it has been shown that they can easily be inverted (Bouman, 1991).
They are, therefore, good candidates for use in inversion algorithms. Because o f their
simplicity, water-cloud models lack generality, and their parameters have to be fitted to
experimental data sets; this is the reason why water-cloud models are also called semi-
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103
empirical models.
In the semi-empirical models, the vegetation layer is modeled by
assuming that its dielectric constant or permittivity is a random process whose moments,
such as the mean and correlation function, are known.
The microwave dielectric constant o f dry vegetative matter is much smaller than the
dielectric constant o f water. Because the vegetation usually constitutes one percent or less
o f the canopy volume, Attema and Ulaby (1978) proposed that the canopy can be modeled
as a water cloud whose droplets are held in place structurally by dry matter. The cloud
model is based on the radiative transfer theory and assumes that:
1.
The vegetation is represented as a homogeneous horizontal cloud o f identical water
spheres, uniformly distributed throughout the space defined by the soil surface and
the vegetation height.
2.
Multiple scattering between canopy and soil can be neglected.
3.
The only significant variables are the height o f the canopy layer and the cloud
density, the latter assumed to be proportional to the volumetric water content o f the
canopy.
Based on these assumptions, radar backscattering from a tree canopy can be
expressed as the sum o f contributions due to ( 1) volume scattering in the canopy itself, (2 )
surface scattering by the underlying ground surface, and (3) multiple interactions involving
both the canopy and the ground surface. The water cloud models represent the power
backscattered by the whole canopy ( f as the incoherent sum o f the contribution o f the
vegetation a°veg and the contribution o f the underlying soil a°so:l. The latter is attenuated by
the vegetation layer. For a given incidence angle 6, the backscatter is represented in water
cloud models by the general form:
®canopy + ®canopy ~soil + ^
®soil
where r is the two-way vegetation transmissivity.
The first and second terms can be combined together to obtain:
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(4 * 1 )
104
(4.2)
where
O
= A mv cos 0 (1 - t 2)
(4.3)
t 2 = ex p (-2 B mv sec 0)
(4.4)
CT,
veg
and mv is the vegetation water content (kg/m2).
A and B are parameters depending on the canopy type. The constant A represents the
maximum allowable attenuation from the vegetation canopy (both cos 9 and I - r are less than
I). Thus, A can be interpreted as the land cover parameter (0 for bare soil and a very high
value for evergreen forests). The formulation corresponds to the first-order solution o f
radiative transfer equation through a weak medium, where multiple scattering effects can be
neglected.
These variations in the canopy descriptors used in the models that describe canopy
backscattering are due to the complexity o f vegetation structure, and to the relative simplicity
o f the models: there is no general theoretical basis to define the best set o f canopy
descriptors, and consequently to derive the values o f the A and B parameters. Furthermore,
for a given canopy, strong functional relationships exist between these canopy descriptors.
As a m atter of fact, the geometrical structure o f the canopy is implicitly accounted for
through these parameters A and B, which are always determined by fitting the models against
experimental data sets.
The maximum backscatter attenuation studied in the literature is about 3 dB
(deciduous forests, Ulaby et al., 1986). One would expect vegetation attenuation from
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105
tropical rain forests and dense evergreen forests to be higher, and thus the water-cloud model
may not be valid.
In order to account for possible nonhomogenity o f canopies due to the existence o f
vertical variations or different types o f scatterers (leaves, stems, ears, etc.), multilayer or
multi-component water cloud models were also developed (Hoekman et al., 1982; Ulaby et
al., 1984; Bernard et al., 1987).
The authors, however, did not find any significant
improvement in the results. Moreover, the use o f such models resulted in the increase o f
empirically derived parameters.
The choice o f two suitable radar configurations in the water-cloud models results in
the use of frequencies which are sensitive to two different parts o f the vegetation canopy.
The use of multi-frequency data in the water-cloud model, provided encouraging results.
Nevertheless, further validation o f this method is needed, as various authors, (Hoekman et
al., 1982; Ulaby et al., 1984; Bouman, 1991) stressed the variability o f the parameters in the
water-cloud models. This could constitute a strong limitation o f this approach, as the
sensitivity o f the parameters to canopy structure will also affect the accuracy o f the inversion
scheme. It is almost certainly impossible to define a universal semi-empirical inversion
algorithm, but in principle it should be possible to develop one for each class o f vegetation
as defined by geometric structure.
This was the motivation for this study, and a
parameterization scheme to account for vegetation backscatter is proposed.
4.4
Vegetation Backscattering Parameterization
The backscattering coefficient o f the canopy is interpreted in the framework o f semiempirical ‘water-cloud’ models. The use o f the water-cloud model results in the adoption
o f its assumptions and limitations, which are recapitulated below:
1.
Both the canopy loss and the vegetation volume scattering coefficient are linked to
the canopy’s biophysical properties, and especially, but not exclusively, to canopy
type, canopy structure, and the water volume fraction within the canopy.
2.
The canopy loss and the volume scattering coefficient increase with frequency.
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106
3.
The vegetation term tends to dominate the net return as either frequency or incidence
angle increases.
4.
The interactive term functions to enhance radar sensitivity to the moisture contained
in the soil beneath a vegetation canopy.
The backscattering in the presence o f vegetation is approximated as a combination
o f the individual backscatter from the vegetation canopy and the underlying soil layer as
given by Eq. (4.4). As mentioned previously, the orientation and geometry o f the vegetation
are also key governing factors for vegetation backscatter. It is possible that two or more tree
canopies overlap, and are caught in the same radar beam. The standard water-cloud model
however, does not account for vegetation overlap. Layover occurs when two tree canopies
o f different heights are located at the same range distance, and the vegetation backscatter
from one is affected by the other and vice versa. Thus, the standard water cloud model will
account for scattering o f the same beam by two different trees, which would lead to over­
estimation o f vegetation backscatter.
Here, it is proposed to model the effect o f ‘radar shadow’ or ‘layover’ using an
exponential vegetation correlation function. The geometric effect o f the tree spacing can be
accounted for by introducing a vegetation correlation length, which is a function o f the
distance between the plant canopies at which the plants function as independent scatterers.
This vegetation correlation length is a function o f plant type or land-use, and the effect o f
vegetation layover is described as follows:
=
t 1 ■ exp ( ~ a )]
(4 -5)
where <f‘veg is the corrected vegetation contribution, and a is the radar shadow coefficient.
The concept o f radar shadow coefficient can be interpreted as a function the vegetation
correlation length (L veg), which is a function o f land-use, and the average distance between
the discrete vegetation canopies within a pixel (xveg).
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107
(4.6)
veg
veg
Thus, x veg is a spatially distributed variable within the area o f study and describes the
shape, size and distribution o f the vegetation at the site.
The concept o f vegetation
correlation length is similar to the correlation length for soils described in chapter 3. After
the threshold value o f xveg = Lveg is reached, there is no radar shadow and the coefficient
becomes zero. A maximum damping o f one-fold is assumed for densely vegetated areas.
The vegetation attenuation generally increases with increasing frequency, whereas
the volume scattering coefficient is proportional to the fourth power o f frequency ( f) (Ulaby
et al., 1984). Ulaby et al. (1984) also showed that the combined effect in the water-cloud
model, as well as the geometric scattering effect, varies approximately a s / . Thus, the effect
of frequency in the multi-frequency inversion algorithm (Bindlish and Barros, 2000) was
incorporated as follows:
(4.7)
One o f the advantages o f this model is that all the vegetation parameters can be
defined using ancillary data. Thus, it is possible to use such models for operational soil
moisture monitoring.
4.5
Em pirical Formulation to Parameterize Vegetation Effects
This study was conducted using the data collected during the W ashita ’94 data for the
Little Washita watershed in southwest Oklahoma. The watershed has a sub-humid climate
with an average rainfall o f 750 mm. During the experiment, the land was covered by
rangeland, pasture, winter wheat, com, and alfalfa. Chapter 3 provided a description o f the
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108
site characteristics and radar data. A complete description o f the watershed is available in
Allen and Naney (1991) or Starks and Humes (1996).
The linear dependence o f ( f on biomass o f forests is found to decrease with frequency
as scattering and attenuation by the crown layer o f foliage and small branches becomes more
significant (Table 4.1). The polarizations most sensitive to specular scattering mechanisms
by the trunk and ground surface (HH and HV) show the highest sensitivity to biomass,
whereas the linear dependence o f <r° on biomass tends to saturate at biomass levels which
scale with wavelength (Dobson et al., 1992). Cross-polarization signatures have shown more
sensitivity to the crown structure than the like-polarization signature (Sun and Ranson,
1995).
Based on observations from SAR data analysis and radar backscattering modeling,
the ratio o f HV backscattering from a longer wavelength (P or L) to that from a shorter
wavelength (C) appears to be a good combination for mapping the forest biomass. As
discussed by Sun and Ranson (1992), this ratio enhances the correlation o f the image
signature to the standing biomass, and compensates for part o f the variations in
backscattering attributed to radar incidence angle.
The L-band imagery depicts the drainage patterns in the watershed (Fig. 4.1a). It
gives an overview o f the watershed characteristics. The C-band imagery shows the local soil
and geomorphological features present in the watershed (Fig. 4.1b).
Based on these
observations, an attempt was made to use a combination o f these two bands to provide a
remotely sensed soil mapping surrogate.
The correlation coefficient increases to 0.5 (maximum value o f 0.6) from around 0.3
(maximum value o f 0.4), when an exponential function is used instead o f a linear
relationship. Table 4 .1 shows the values o f correlation coefficients for different frequencies
and polarizations (both for linear and exponential fit). These results suggest a significant
improvement by using multi-frequency radar data to account for vegetation backscatter.
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Figure 4.1 a
-
C-band imagery over Little Washita watershed on April 11,1994.
109
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Ill
Table 4.1
A.
Regression constant for linear and exponential fit to NDVI for Washita ’94
study area.
Rangeland
Frequency polarization ratio
Linear tit
hxponential tit
c hh
0.23
0.45
Chv
0.26
0.48
Chh
0.21
0.41
U v
0.25
0.56
Lw
0.18
0.38
Q i/L h h
0.30
0.56
C h t/L h v
0.33
0.58
>
.C
_l
'T.
jr
U
0.33
0.59
CJU,
0.29
0.55
Frequency polarization ratio
Linear tit
bxponential ht
C hh
0.26
0.48
Chv
0.28
0.52
C hh
0.22
0.46
C hv
0.25
0.51
LyV
0.20
0.42
Q t/C h h
0.32
0.58
Chh/Lhv
0.36
0.61
Ch/L hv
0.34
0.55
Chv/Lhh
0.36
0.62
B.
Winter Wheat
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112
C.
Pasture
Frequency polarization ratio
Linear ht
Exponential tit
Chh
0.24
0.40
Chv
0.25
0.42
Lhh
0.19
0.32
Lhv
0.22
0.39
Lw
0.23
0.41
Chl/Lhh
Cht/Lhv
0.28
0.53
0.28
0.52
Ch/ L hv
0.31
0.56
Ch/ L hh
0.29
0.50
4.6
A pplication o f Vegetation Backscattering M odel
In Chapter 3, a multi-frequency, multi-polarization inversion model based on the IEM
was used to estimate soil moisture, and an attempt was made to relate the errors obtained in
the soil moisture estimate to the vegetation characteristics without clear results. An ad-hoc
approach to account for vegetation backscatter also was tried with mixed results. In an effort
to make the soil moisture estimation model more dynamic, the proposed vegetation
parameterization was coupled to the soil moisture estimation model.
First, the IEM model was run in the forward mode with the site characteristics to
obtain the contribution from the underlying soil layer, by using the site observed
characteristics. Using this soil contribution, the vegetation contribution at each o f these sites
was determined.
The vegetation parameters were obtained by using a simple multi­
parameter regression. Table 4.2 shows the values o f the vegetation constants obtained based
on this semi-empirical vegetation parameterization formulation. Due to lack o f on-site
calibration data, all the land-uses were initially grouped together, and a single value o f
vegetation parameters was obtained for the entire study area.
The use o f the explicit parameterization o f vegetation backscatter results in a small
increase in the correlation coefficient with respect to the observed backscatter values o f only
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113
4% (0.87 as compared to 0.83 when no vegetation correction was used; and 0.84 obtained
in Chapter 3 when an ah-hoc vegetation correction was used). These vegetation parameters
values were used in the semi-empirical model to obtain the vegetation contribution at each
point. The soil moisture then can be obtained by using the multi-frequency soil moisture
inversion methodology as described in Chapter 3 (Bindlish and Barros, 2000). Figure 4.2
shows values o f estimated soil moisture before and after using the explicit vegetation
parameterization.
The use o f common vegetation parameters for all land-uses limits the ability o f the
model to differentiate between various vegetation canopies. The effect o f different canopy
structure (function o f land-use) was not accounted for in this preliminary approach. To
investigate the effect o f land-use characterization, three different land-use classes (rangeland,
winter wheat and pasture) where multiple sampling sites were available were separated from
the data set, which corresponded to 12 o f the 15 sampling sites. The vegetation backscatter
parameterization in the semi-empirical model was subsequently derived independently for
each o f the three land uses (Table 4.2). The correlation coefficient improved to 0.95, as
compared to 0.87, when the land-use classification was used (Fig. 4.3).
The land-use class based approach requires separate empirical relationships for each
vegetation type, and thus the need to carry out large-scale vegetation characterization studies.
In the case o f a spacebome SAR based soil moisture mission, long-term field measurements
o f vegetation parameters at the pilot sites is needed, since over longer periods o f time these
parameters will change.
Table 4.2.
Values o f vegetation constants used in the semi-empirical vegetation model
All Landuses
Rangeland
W inter Wheat
Pasture
A
0.0012
0.0009
0.0018
0.0014
B
0.091
0.032
0.138
0.084
a
2.12
1.87
10.6
1.29
At any sampling site the maximum vegetation am ount was moderate (less than 2
kg/m2). None o f the sampling sites had dense vegetation, which is true for most o f the
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114
C o m p a r i s o n of E s tim a te d Soil Moisture with M e a s u r e m e n t s
0 .4 0
Apr
Apr
Apr
Apr
0 .3 0
Apr
Estimated
Soil Moisture
Apr
0.20
0.10
R =0.83
R (veg)=0.87
0.00
0.00
Figure 4.2
0.10
0.20
0 .3 0
Measured Soil Moisture (m*3/rrr3)
0.40
Scatter plot o f measured volumetric soil moisture and estimated volumetric
soil m oisture for all the sampling sites for the entire duration o f the Washita
‘94 experiment.
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115
C o m p a r i s o n of E s tim a t e d Soil Moisture with M e a s u r e m e n t s
0 .4 0
Apr
Apr
Apr
Apr
Estimoted
Soil Moisture
(nrv^/m ^)
Apr
Apr
0.20
0 .1 0
R (veg)=0.95
0.00
0.00
Figure 4.3
0.10
0 .3 0
0.20
Measured Soil Moisture (nrr3/m*3)
0 .4 0
Scatter plot o f measured volumetric soil moisture and estimated volumetric
soil moisture for all the sampling sites for the entire duration o f the Washita
‘94 experiment after land use based vegetation parameterization.
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116
watershed. The saturation levels reported by Imhoff (1995) were as follows: C-band = 2
kg/m 2, L-band = 4 kg/m2, and P-band = 10 kg/m2. Thus, none o f the sampling sites were
above the saturation level for C-band, and all sites were well below the L-band saturation
levels. This could be one o f the reasons for the success o f this methodology. The current
models should be tested under more diverse conditions to evaluate their ability to “see
through” dense vegetation.
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117
Chapter 5
Sub-Pixel Variability of Remotely Sensed Soil Moisture:
An Inter-Comparison Study of SAR and ESTAR
5.1
Introduction
Microwave radiometry at long wavelengths can be used to measure and monitor
surface soil moisture. A key issue in implementing this approach has been the coarse spatial
resolution inherent to long wavelength microwave radiometry from a spacecraft. The only
controlling factor that can be changed is the antenna size o f the instrument. However,
increasing the antenna size introduces extremely difficult engineering problems that cannot
be solved using conventional technologies. This has been a major reason for looking at
innovative approaches such as synthetic aperture radiometry (LeVine et al., 1994; Njoku et
al„ 1999).
It should be noted that even if a synthetic aperture antenna, or any o f the other
alternatives underdevelopment, is used for soil moisture measurement, the spatial resolution
will be on the order o f 10-30 km. This resolution is coarse compared with sensors operating
at visible wavelengths, but it is compatible with other spacebome microwave radiometers
used for water vapor as well as current global climate models.
Active microwave remote sensing provides very large quantities o f data at very high
spatial resolution (10's m). Because the volume o f data produced cannot be efficiently (and
timely) transmitted from space, global or even regional coverage o f soil moisture is
prohibitive.
Passive microwave remote sensing, however, can provide greater spatial
coverage, though at coarser resolution (10’s km). In the case o f operational applications, one
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118
scenario would consist o f making use o f both systems to produce high spatial resolution for
selected areas o f interest, while global coverage could be attained at lower resolution. The
higher resolution viewing system (in this case SAR) could be used to quantify sub-pixel
variability, or the aggregation kernel o f the lower resolution sensing system (in this case
ESTAR).
Theis et al. ( 1986) demonstrated the possibility o f using a multi-sensor approach for
improving the estimates o f soil moisture under field conditions. In this case, the effects o f
surface roughness were accounted for with scatterometer measurements. These were then
used in a soil moisture equation that included terms related to the emissivity measured by the
radiometer and to the scatterometer roughness term.
Inclusion o f the roughness term
improved the r ’’ values from 0.22 to 0.65 for C-band and from 0.69 to 0.95 for L-band.
A challenge to the feasibility o f such a dual system is how to assimilate and/or
combine active and passive microwave data in a manner that is consistent with the scaling
behavior o f soil moisture, vegetation and geomorphic variability in the landscape. We begin
to address this problem by conducting an inter-comparison study o f SAR and ESTAR during
Washita '94 (a field experiment in the Little W ashita Watershed, Oklahoma, US). The focus
o f this study is on the SAR and ESTAR data collected on April 11, 1994. This is the only
day on which both active and passive microwave systems were flown. Thus, this study can
be viewed as exploratory. To the best o f our knowledge, however, this is the first study in
which soil moisture estimates from active and passive spacebome/airbome microwave
systems were compared over any region. Earlier studies have compared the soil moisture
estimates over controlled plots using truck-based sensors.
The overall objective o f this part o f the research is to investigate the relationship
between the remotely sensed soil moisture aggregation kernel and land surface properties.
This would enable us to disaggregate coarse resolution passive microwave imagery to spatial
resolutions relevant for hydrologic applications. The specific objectives o f this work were
to investigate the compatibility o f SAR and ESTAR for soil moisture retrievals, and to
investigate the relationship between ESTAR’s aggregation kernel and landscape features:
namely vegetation, soil hydraulic conductivity, and land use.
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119
5.2
Data Synopsis
A description o f the Little W ashita watershed can be found in chapter 3. Allen and
Naney (1991), and Starks and Humes (1995) provide a detailed description o f the watershed.
The SAR data from the Washita ‘94 experiment is also described in chapter 3.
Electronically Scanned Thinned Array Radiometer (ESTAR) is a synthetic aperture,
passive microwave radiometer operating at a center frequency o f 1.413 GHz or 21 cm
wavelength (L-Band) (LeVine et al., 1989). It operates in a horizontally polarized mode.
The ground resolution o f ESTAR for this experiment was 200 m.
To study the effect o f sub-pixel variability land surface parameters, ESTAR data from
Southern Great Plains 1997 (SGP ‘97) experiment was used in this study. The L-band
ESTAR was used for daily mapping o f surface soil moisture over an area greater than 10,000
km2 for a one month period. The ground resolution o f ESTAR for this experiment was 800
m. Coarser resolution data-sets and larger spatial coverage provides us with an opportunity
to investigate the effect o f sub-pixel variability over a larger scale and over a wider range o f
land-use and soil texture classes. Additional information about the watershed and these data­
sets can be found at the following world wide web site: http://hydrolab.arsusda.gov/.
5.3
Soil M oisture Retrieval from SAR
The Integral Equation Model (IEM) (Fung et al., 1992), which is a physically-based
radiative transfer backscattering model from a randomly rough dielectric surface, was
combined with an empirical model that relates the dielectric constant o f soils to the soil
texture and the volumetric soil moisture. In particular, the empirical model developed by
(Dobson et al., 1985) [valid for 1.4-18 GHz: C and X-Bands] and that proposed by (Peplinski
et al., 1995) [valid for 0.3-1.3 GHz: L-Band] were used.
The methodology consists o f formulating the inverse problem in the context o f multi­
frequency and multi-polarization data to derive soil moisture fields from remotely sensed
images without prescribing time-varying land-surface parameters such as roughness height
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120
and correlation length as input, and without conducting site specific calibration. The Jacobian
method, an iterative scheme similar to the Newton-Raphson method, is used in the retrieval
algorithm to solve the inverse problem. One o f the advantages o f this methodology is that
we can constraint the magnitude o f the surface parameters to remain within physically
possible limits. The values of volumetric soil moisture were constrained between 0 and 100
percent. For the surface roughness values an upper bound o f 5.0 cm and a lower bound o f 0.1
cm was prescribed during the inversion process, which cover the entire range o f values
observed in previous studies. For further details, the reader is referred to Bindlish and Barros
(2000) [Chapter 3 in this dissertation].
5.4
Soil Moisture Retrieval from ESTAR
A soil moisture retrieval algorithm, similar to as described by Jackson et al. (1995)
was developed (Fig. 2.6).
Surface emissivity is calculated by dividing the brightness
temperature by the soil surface temperature. The pixel emissivity is corrected for vegetation
using the approach proposed by Jackson and Schmugge (1991).
In this approach the
vegetation is treated as an attenuating layer that is described by its optical depth. The optical
depth o f the canopy is a first-order approximation o f the vegetation parameter (a function o f
land use) and vegetation water content. The correction for surface roughness effects follows
Choudhury et al. (1979). The effective dielectric constant o f the surface layer is computed
by inverting the Fresnel equations.
Finally, the dielectric mixing model (Wang and
Schmugge, 1980), which is based on soil texture, was used to estimate volumetric soil
moisture at each pixel. A complete description along with the equations involved about each
o f the modules is available in Chapter 2. An upper bound o f 51% (maximum porosity) and
a lower bound o f 5% (wilting point) was used in our soil moisture computations.
The input data, calibration parameters (vegetation water content, vegetation
parameter, roughness factor) and soil properties (bulk density and soil texture) were obtained
for each pixel. The surface soil temperature (5 cm) collected by the Little Washita micronet
stations were re-gridded to generate spatial surface soil temperature at 200 m resolution. The
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121
vegetation parameterization was done based on the Thematic M apper (TM) data.
Normalized Difference Vegetation Index (NDVI) values were computed for the entire
imagery, and a relationship to the vegetation water content was established for the test sites.
This relationship was extrapolated for the entire imagery. More information about the
vegetation
data-set
can
be
found
at
the
following
world
wide
web
site:
http://hydrolab.arsusda.gov/. Soil properties were obtained from the high resolution (30 m)
soil sub-series data available for the watershed. The ESTAR retrieval algorithm has an
explicit vegetation correction module, and the algorithm corrects both for soil roughness and
vegetation.
5.5
Com patibility o f SAR and ESTAR Soil Moisture Retrievals
The compatibility o f SAR and ESTAR was investigated in the context of soil
moisture retrieval. In this study we used the SAR and ESTAR data collected during the
Washita '94 experiment. The 200 m ESTAR data was used to estimate soil moisture by
using the retrieval algorithm. The high resolution 30 m SAR data was also used to estimate
soil moisture. These 30 m soil moisture estimates were aggregated to ESTAR resolution.
The soil moisture fields obtained by these two methods can then be compared. The SAR
derived soil moisture shows clearly the drainage patterns inside the watershed (Fig. 5.1). Silt
loam and loamy coils had a higher moisture content (-3 0 percent), whereas areas associated
with sandy loam and sand had lower moisture content (-2 0 percent), which is in agreement
with the ground-based soil moisture observations. This is also consistent with the spatial
distribution o f soil texture: the soils in the central part o f the watershed are mostly fine sandy
loam and sand, whereas the eastern part is dominated by silty loam and loamy soils (Fig.
3.4b). Generally, sandy soils with higher hydraulic conductivity drain faster than loamy
soils, which drain at a slower rate independently o f land-use. The Little Washita river (which
flows through the middle o f the watershed), and Lake Burtschi (located in the north-central
part o f the watershed) can also be located in the image (Fig. 5.1). The spatial distribution o f
the estimated soil moisture from ESTAR imagery (Fig. 5.1) is similar to that obtained from
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122
ESTAR e s tim a t e d Soil Moisture
Soil
Moisture
SAR estimated Soil Moisture
CrAOS: COLA/ICES
Figure 5.1
Estimated volumetric soil moisture for April 11 derived from ESTAR (200
m resolution), and SAR data (30 m resolution) (only over the SAR shuttle
trajectory).
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123
the SAR estimates, although, as expected, the small scale spatial variability is lost. The effect
o f soil texture is present in both retrievals, while the Little Washita river can only be detected
in the SAR retrieval.
There is good agreement between the ground measured soil moisture and that
estimated by using SAR and ESTAR data for each o f the sampling sites (Fig. 5.2). Overall,
the ESTAR retrieved soil moisture exhibits a sm aller error. The absolute RMS error for
ESTAR soil moisture estimates is 3.16%, whereas for SAR is 3.78%. In the case o f the
latter, some uncertainty should be attributed in part to the speckle noise (the random intensity
distribution in the radar image).
Subsequently, the standard deviation o f estimated
volumetric soil moisture for the SAR imagery within each ESTAR pixel was determined.
On an average, this value is about 2%, but the standard deviations are much higher (up to
10%) near the Little W ashita river, where the SAR imagery is able to capture the small scale
variations implicitly integrated/averaged by ESTAR. An attempt was made to correlate the
differences in the soil moisture estimates to the observed NDVI values at each pixel. No
consistent pattern that could explain the differences in the SAR and ESTAR brightness
temperature data in terms o f vegetation index (NDVI) could be found.
Furthermore, to investigate the consistency between the two landscape viewing
systems, the forward problem was solved by deriving the brightness temperature field from
the 200 m resolution SAR estimated soil moisture using the model described in chapter 3.
To facilitate comparison the ESTAR observations are shown over the SIR-C/X-SAR flight
trajectory (Fig. 5.3). The SAR derived brightness temperature estimates show a stronger
effect o f the presence o f the Little Washita river, whereas the results over other regions are
comparable to the ESTAR observations. The SAR brightness temperature estimates exhibit
significantly higher spatial variability than the ESTAR observations. The effect o f soil
texture is not so prominent in the spatial fields o f brightness temperatures. In general, the
SAR estimates of brightness temperature have a higher range than the ESTAR observations
(Fig. 5.4), i.e., the ESTAR viewing system aggregates and smooths the spatial variability
observed in the landscape. This analysis points to the need to understand how ESTAR
integrates brightness temperatures over a mixed pixel in a quantitative manner.
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124
C o m p ariso n of SAR a n d ESTAR E stim a te d Soil M oisture with M e asu rem en ts
0.40
j_+
+
SAR Ooto (30 m)
I
O
ESTAR Ooto (200 m)
o
-H-
0.20 r
Estimoted
Soil M oisture
0.30
0.10
0.00
0.00
0.10
0.20
0.30
0.40
Meosured Soil M oisture
Figure 5.2
Comparison between measured and estim ated volumetric soil
moisture using SAR and ESTAR at the test sites for April 11,1994.
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125
ESTAR observed Brightness Temperature
B rightness
Temp.
(K)
SAR estimated Brightness Temperature
290
200
270
260
250 I
240
230
220
210
200
190
160
5 Itm
CrAOS: C O U /IC E S
Figure 5.3
Brightness temperature image observed by ESTAR, and that derived from
SAR estimated soil moisture (only over the SAR shuttle trajectory).
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126
Com parison between ESTAR e n d SAR Brightness T em peratures
SAR estimated
Brightness Temp, (K)
300
250
200
150
150
200
250
300
ESTAR observed Brightness Temp. (K)
Figure 5.4
Comparison o f ESTAR brightness temperature observations with SAR
derived brightness temperature estimates.
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127
Finally, one feasible application o f the SAR derived brightness temperature can be
to fill up missing areas in ESTAR imagery, which could have been lost to radio frequency
interference (as was in this case for April 11).
5.6
Sub-pixel Variability of ESTAR Soil M oisture Retrievals
5.6.1
Soil Moisture
Next, we investigated the sensitivity o f ESTAR retrieval algorithm to a ‘mixed’ pixel.
For this application a mixed field consisting o f 10 x 10 pixels was used. It was assumed that
the field o f view was o f the size of the sensor footprint (Fig. 5.5). The soil moisture at each
sub-pixel was perturbed randomly with a maximum perturbation level of Smv.
The
perturbations were added such that the overall soil moisture mv remains a constant. The
spatial field o f soil moisture was then used in the ESTAR forward model to estimate the
brightness temperature fields, and the brightness temperature fields were averaged to obtain
a single value o f brightness temperature for the ESTAR viewing field. The value o f this
brightness temperature represents the ESTAR observation. Soil moisture for this viewing
field was then estimated using the ESTAR retrieval model (as described in section 5.4), and
the synthetic ground truth was used to perform the error analysis. The mean of one thousand
realizations for each value of synthetic soil moisture and maximum perturbation level was
used for the error analysis.
Figure 5.6 shows the error in soil moisture retrieval for different perturbation levels
and different base soil moisture. Both the perturbation level and soil moisture were changed
in steps o f 1%. For very high and low soil moisture, the error in soil moisture estimation is
very low. For moderately wet soils (20%-35% volumetric soil moisture) and high levels o f
perturbation the error in retrieved soil moisture is high (1%). For very dry conditions the
algorithm over-predicts soil moisture, whereas for wetter conditions the ESTAR retrieval
algorithm under-predicts soil moisture. The absolute error in the retrieved is below the effect
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128
ESTAR
“Synthetic
Ground Truth"
L
ESTA R torward model
Simulated Brightness Tem peratures
as seen by ESTAR [Tb]
ESTA R Soil Moisture
retrieval model
Estimated Soil Moisture [m
Error Analysis
Amv=>mv-mv
Figure 5.5
Schematic diagram to estimate sensitivity o f ESTAR based soil moisture
estimation model to sub-pixel variability o f soil moisture.
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Sensitivity of ESTAR Retrieval Algorithm
1.0
0.5
c
o
i
0.0
CO
0)
£
3
CO
O -0.5
10
o
CO
c
k-
2
0)
-
1.0
&
3
20
20
25
40
45
Soil M oisture (% )
Figure 5 .6
S en sitiv ity o f E ST A R soil m oistu re retrieval algorithm to su b -p ix el variability o f so il
m oisture.
130
o f noise in the ESTAR instrument (brightness temperature o f 2K, which corresponds to a soil
moisture of about 2%) (Jackson et al., 1995).
The absolute RMS error in soil moisture retrieved from brightness temperature in the
sensor footprint compared to the mean soil moisture present in the individual sub-pixels was
o f the order of 2 % (variability o f ± 20 % soil moisture).
5.6.2
Soil Texture
The soil dielectric model describes the relationship between the dielectric constant
and soil moisture. For lower values o f soil moisture (m < m,) (m, is the transition moisture),
the real part of dielectric constant increases slowly with mc. In the second region (mv > m,)
the relationship between dielectric constant and soil moisture is linear with a steep slope (i.e.,
the dielectric constant increases rapidly with soil moisture) (Fig. 5.7). For low values of
dielectric constant, soil texture does not have any effect on the value o f soil moisture. At
these values all the soil moisture is bound to the soil particles and there is no free water
available. The sensitivity o f soil moisture for changes in dielectric constant is low, which
results is poor estimates o f soil moisture at low values (as observed in chapter 3 and 4). The
over-estimation in the values o f soil moisture below 10% soil moisture (Fig. 3.7 a) can be
attributed to the loss in sensitivity o f the dielectric mixing model to changes in soil moisture.
An average value for each one o f the textural classes was obtained from the United
States Department o f Agriculture (USDA) texture triangle in terms o f percent sand and clay
(Table 5.1). These cover the entire domain o f the textural classification. In operational
remote sensing, it is likely that the soil texture o f the site may be inaccurately specified in
the database. We investigated the effect o f the incorrect classification o f soil texture on soil
moisture estimates.
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131
in
o
CM
in
(0 O
in
o
CM
in
^
o
o
f
ju bjsu o q
o u p e |a ;G
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Volumetric Soil Moisture (%)
CM
Sensitivity of ESTAR retrieval algorithm
in
Figure 5.7
co
to sub-pixel variability of soil texture.
co
132
Table 5.1
Mean sand and clay content present in different soil textures.
Texture
% Sand
% Clay
Sand
95.0
5.0
Clay
20.0
70.0
Silt
7.0
7.0
Silty Loam
20.0
15.0
Silty Clay
5.0
45.0
Silty Clay Loam
10.0
35.0
Clay Loam
30.0
35.0
Loam
40.0
20.0
Sandy Clay
50.0
45.0
Sandy Loam
65.0
15.0
Loamy Sand
80.0
5.0
Sandy Clay Loam
60.0
30.0
For this study, the percentage o f sand and clay was perturbed by ±15% within the
ESTAR footprint for different types o f soil textures (Fig. 5.7). A ±15% change in soil
texture results in a ±3% change in soil moisture estimates. For lower values o f dielectric
constant (or soil moisture) (m < m,) the effect o f soil texture is minimal, and it increases as
the soil moisture content approaches the transition moisture. The error in the estimation of
soil moisture due to uncertainty in soil texture becomes nearly a constant for values o f soil
moisture content after the critical value. Overall, the change in soil texture does not have a
very significant effect on the soil moisture estimates. But care should be taken, when soil
hydrologic properties are derived from remote sensing observations. A small error in the
estimation o f soil moisture can lead to a relatively large error in soil texture classification,
which can in turn affect the soil property estimates.
5.6.3
Soil Temperature
For a particular value o f vegetation water content, the soil moisture estimate is highly
dependent on soil temperature. For example, a 10°C change in soil temperature can lead to
soil moisture changes o f 10%, exhibited by Figure 5.8. This effect is more prominent for
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CD
lission of the copyright owner. Further reproduction prohibited without permission.
45
£3 5
¥
aM
o
Z
125
co
o
*c
Q>
E
3
£15
170
Figure 5.8
190
210
230
250
B rig h tn e s s T e m p e ra tu re (K)
270
290
Sensitivity o f ESTAR soil moisture estimation algorithm to soil temperature and vegetation
water content.
U>
U>
134
higher values o f vegetation water content and higher brightness temperatures (lower soil
moisture). As the vegetation water content increases, the microwave radiometer “sees less
and less” o f the ground. Thus, a small change in soil surface properties has a greater effect
o f the soil moisture estimates.
This sensitivity analysis suggests that an infra-red sensor that could estimate the soil
surface temperature should be paired with the microwave radiometer for operational
applications. Installation o f an infra-red sensor would also provide us valuable information
about the characteristics o f the land surface.
Finally, unlike vegetation, soil surface
temperature changes rapidly, and therefore it is essential that the microwave radiometer data
takes overlap with the infra-red sensor; that is, the two instruments operate in synchronous
mode.
5.6.4
Vegetation
The relationship between vegetation water content and soil moisture is non-linear
(maximum increase and decrease in the soil moisture is unequal), and as shown earlier it is
also a function ofother land surface parameters. Figure 5.8 shows the sensitivity o f ESTAR
retrieval algorithm to different levels o f vegetation water content and soil temperature. The
retrieval algorithm is very sensitive to the vegetation water content. The unit error (1 kg/m2)
in the estimation o f vegetation water content can introduce an error o f 10 % soil moisture in
the retrieval.
This error is greater for higher values o f soil moisture, as it becomes
impossible to distinguish the vegetation from that o f the soil moisture signal.
ESTAR data collected during SGP ‘97 experiment was used to investigate the effect
o f sub-grid scale variability o f vegetation on soil moisture estimation. The values ofN D V I
were aggregated to ESTAR resolution (800 m) (Fig. 5.9a) and spatial map o f sub-grid scale
variability ofNDVI within an ESTAR pixel was determined (Fig. 5.9b). NDVI and land-use
data obtained from Thematic Mapper (30 m) are required to parameterize the vegetation
effect in the ESTAR based soil moisture retrieval model (Jackson and Schmugge, 1991).
The land-use classification data were aggregated based on the most commonly occurring
class in an ESTAR pixel (Fig. 5.9c).
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135
Average Value of NDVI
CMOS: C O U /IC E S
Figure 5.9a
Average value o f Normalized Difference Vegetation Index (NDVI) at
ESTAR resolution (800 m).
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136
Sub-pixel Variability of NDVI
CrADS: COLA/IGES
Figure 5.9b
Sub-pixel variability o fN D V I at ESTAR footprint (obtained by using 30
m Thematic Mapper data).
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137
Lcnduse Mop of SGP97
Landuse
Unelaeeified
Alfalfa
Bare
Com
1 1 :orcge
Legume
P asture
Tree
Urban
Wafer
Wheaf
Sum m er Corn
Summer Legume
Shrub
l----- 1
10 km
CM OS: C 0 l> /IG E S
Figure 5.9c
Land-use classification map o f SGP ‘97 domain obtained by using the
most commonly occurring land-use classification.
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138
Next, the relationship between the average value ofN D V I and sub-pixel variability
was investigated as a function o f land-use. The high resolution (30 m) NDVI imagery,
obtained from SGP ‘97 database, was aggregated to ESTAR resolution. The use o f a high
resolution imagery allows use to compute the sub-pixel variability ofN D V I (surrogate o f
vegetation characteristics) within the ESTAR pixel. The land use was aggregated based on
the most commonly occurring land characteristics with the ESTAR foot print. The sub-pixel
variability (as a function o f land-use) increases rapidly for low values o f average NDVI till
it reaches a maximum (mixed pixel) and decreases for high values o f average NDVI (Fig.
5.10a). For most o f the land-use classes the maximum spatial variability occurs between
NDVI values o f 0.3-0.4. Thus, the distribution function for NDVI with sub-pixel variability
ofN D V I is skewed to the left. The values ofN D V I are strongly related to the respective
land-use classification, and the range o f variability ofN D V I changes along this distribution
depending on the land-use class. This relationship was approximated here by a gamma
function for each land-use. Figure 5 .10b shows the gamma function for the most commonly
occurring land-use classes in the SGP ‘97 study area.
Using the mean NDVI values and the most commonly occurring land-use class, soil
moisture estimates were derived over the entire SGP ‘97 domain (Fig 5.1 la). Subsequently,
the mean NDVI values where perturbed by one-fold as a function o f the average NDVI value
and land-use classification present over that footprint. The results indicate that the sub-grid
scale variability o f vegetation w ater content has a significant effect on the ESTAR based soil
moisture retrievals. The absolute value of soil moisture can vary as much as 15% with
respect to the mean value (Table 5.2), and the increase in soil moisture due to an increase on
vegetation water content is greater than the respective decrease. The range o f variability o f
brightness temperature decreases with increase in vegetation water content (Fig. 5.11). Thus,
the soil moisture sensitivity to brightness temperature reduces with increase in vegetation,
at which point it is impossible to distinguish vegetation from soil moisture effects as
discussed previously. The effects are significant in regions o f higher vegetation (northern
parts o f SGP ‘97 domain) (Figs. 5.11 a-c).
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0.4
0.3
0.2
•9 0.1
0.0
0.0
F igure 5 .1 0 a
0.2
0.6
0.4
A verage NDVI
0.8
S u b -p ixel variab ility o f N D V I as a function o f average value o f N D V I for W inter W heat.
1.0
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0.3
•----- • Alfalfa
F orage
P a s tu re
H------ h W heat
x------x S h ru b
t'
^
- X- ' ~x-
80.1
¥
0.0
0.0
Figure 5.10b
0.2
0.4
0.6
A verage NDVI
v.
0.8
1.0
Sub-pixel variability ofN D V I as a function o f average value ofN D V I for most prevalent landuses in SGP ‘97 domain.
141
July 2
July 12
Soil Moisture
(X)
44 —
40 —
I----- 1
10 km
GrADS: COU/IGES
Figure 5.11a
Soil moisture imagery for SGP ‘97 domain obtained by using the average
value ofNDVI.
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142
July 2
July 1 2
Soil Moisture
(X increase)
CrADS: CO W /IGES
Figure 5.1 lb
Soil moisture imagery over SGP ‘97 dom ain obtained by using a one-fold
increase in vegetation water content.
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143
July 2
July 12
Soil Moisture
(X decrease)
CrADS: C O U /W E S
Figure 5.11c
Soil moisture imagery over SGP ‘97 domain obtained by using a one-fold
decrease in vegetation water content.
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144
Table 5.2
Statistics o f the difference in Soil Moisture (%) due to vegetation uncertainty
June 18
Max.
increase
(%)
14.74
Max.
decrease
(%)
9.71
Mean
increase
(%)
0.89
Mean
decrease
(%)
0.69
Variance
of
increase
0.55
Variance
of
decrease
0.37
June 19
14.24
8.57
0.79
0.62
0.41
0.26
June 20
14.77
8.05
0.70
0.57
0.28
0.20
June 25
10.15
5.89
0.55
0.44
0.17
0.12
June 26
11.41
10.45
0.92
0.71
0.62
0.41
June 27
14.51
9.24
1.07
0.83
0.90
0.58
June 29
15.18
14.70
0.85
0.66
0.58
0.42
June 30
14.02
9.87
1.00
0.78
1.00
0.68
July 1
13.89
8.43
0.97
0.76
1.00
0.65
July 2
13.66
12.42
0.84
0.68
0.57
0.39
July 3
7.38
6.90
0.58
0.46
0.26
0.18
July 11
9.24
8.03
0.87
0.68
0.46
0.32
July 12
12.43
8.12
1.02
0.84
0.92
0.68
July 13
9.53
8.61
0.56
0.45
0.20
0.15
July 14
8.24
8.00
0.52
0.43
0.17
0.13
July 16
7.75
5.73
0.62
0.52
0.22
0.17
Date
Overall, the mean error due to sub-pixel variability is below the noise level o f the
instrument. From these results it can be concluded that ESTAR soil moisture retrieval
algorithm scales linearly for mixed vegetation pixels, thus it is the amount o f biomass and
not its spatial distribution within the pixel that is important in determining microwave
response. Liou et al. (1998) arrived at the same conclusion by comparing the soil moisture
estimates obtained by using the 200 m ESTAR imagery, and then aggregating the same to
coarser resolutions.
5.7
Error Analysis for ESTAR Estim ated Soil M oisture
The sensitivity o f the ESTAR estimated soil moisture retrieval algorithm to different
land surface properties (vegetation, soil texture and soil temperature) was demonstrated
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145
earlier. The error in the estimation o f any o f these properties leads to an error in soil
moisture estimation. The differences in observed soil moisture and ESTAR estimated soil
moisture can be classified in three different categories: (1) error in ESTAR based soil
moisture estimates due to error in estimation o f land surface parameters, (2 ) error (noise) in
ESTAR observations, and (3) difference in soil moisture estimates due to ground
observations. These three types o f errors can be considered to be additive in nature.
The error in ESTAR based soil moisture estimates due to error in land surface
parameters are expected to be correlated to one another.
The effect o f incorrect
representation o f vegetation, soil temperature and soil texture on soil moisture estimates was
investigated. Vegetation water content was varied from 0 to 4 kg/m2, with a variability o f
± 0.5 kg/m2. The highest value o f vegetation water content observed at the test sites during
the Washita ‘94 experiment was 2 kg/m2. A value o f 4 kg/m 2 represents densely vegetated
areas, typically forests.
The soil temperature was varied from 5° C to 35° C, with a
variability o f o f ± 5° C. The ESTAR brightness temperature was varied from 150 K. to 300
K, which covers the entire range o f vegetation, soil temperature and brightness temperatures.
The effect of variability in land surface parameters was used to estimate the maximum
absolute error in soil moisture estimates. This analysis was conducted for the 12 soil textures
listed in Table 5.2. A variability o f ± 15% in percent sand and clay was used for each soil
texture. Figures 5.12 (a-b) show the absolute error in soil moisture estimates for sand and
clay. As the vegetation water content increases, the viewing window for soil moisture
monitoring decreases, and so does the error. Increase in vegetation attenuates the ESTAR
signal and the sensitivity to soil moisture variations reduces. The viewing window for soil
moisture estimation translates towards higher brightness temperatures with the increase in
soil temperature. There is no significant change in absolute errors with the increase in soil
temperature. Although, the absolute error in soil moisture estimation for clay is higher than
for sand, but the differences are small (Fig. 12 a and b).
The noise levels in the ESTAR observed brightness temperature are o f the order o f
2K. This error in ESTAR observations can result in an absolute error in soil moisture o f
about 2% (Jackson et al., 1995). As seen earlier, the error in soil moisture estimates would
depend on the land surface parameters.
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146
a) Sand
Soil Tem p = 5
Soil Temp = 3 5
CM
<
cn
150 170 190 210 230 250 270 290
150 170 190 210 230 250 270 290
B r ig h tn e ss Temp (K)
B rightness Tem p (K)
Soil Temp
Soil Temp =
V®
150 170 190 210 230 250 270 290
150 170 190 210 230 250 270 290
B r ig h tn e ss Tem p (K)
4
5
B righ tn ess Tem p (K)
6
7
8
10
11
12
Absolute Error (%)
Figure 5.12
Error analysis for ESTAR estimated soil moisture retrieval algorithm for
sand and clay for different levels o f soil temperature, vegetation water
content and brightness temperature.
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147
Finally, differences in soil moisture observations and ESTAR estimates could be
present in spite o f a perfect algorithm and sensor. These differences could be due to the fact
that the ESTAR and ground observations may not be representing the same thing.
The
ground based soil moisture sampling procedure for the test sites is documented in Jackson
and Schiebe (1993). In a test site 14 ground samples were taken and the mean o f these
observations is used as soil moisture observation for the ESTAR pixel.
The spatial
variability o f soil moisture within the ESTAR pixel, may result in errors is ground based soil
moisture observations. The sampling depth for ground observations was 5 cm, but the
penetration depth for ESTAR is dependent on the land surface conditions. For very wet soils
the penetration depth is lower. Also, the ESTAR signal attenuates with soil depth, thus soil
moisture estimation errors could be introduced, if the upper soil moisture profile in not
uniform.
5.8
ESTAR Aggregation Kernel and Land Surface Properties
Next, we investigated the relationship between the ESTAR aggregation kernel as a
function o f land surface properties. The use o f two independent soil moisture estimates at
two different resolutions enables us to estimate empirically the effect o f sub-pixel variability
and the aggregation kernel as a function o f land surface parameters for the coarse resolution
sensor. The SAR estimated soil moisture at 30 m was used in the ESTAR retrieval model
to estimate brightness temperature fields at 30 m resolution. These estimates were used as
‘ground truth’ for this application. Using the brightness temperature field at two different
resolutions the sub-grid scale variability was then quantified as a function o f relative soil
hydraulic conductivity, land-use, and NDVI. Multi-linear regression based on ESTAR
observed and SA R derived brightness temperatures was used to estimate sub-grid scale
variability within the ESTAR pixel.
W VEEW W ^M ]
i=l1 M
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(5-1)
148
where & (ij) is the land surface variable, is a linear combination (/') ofNDVI and relative soil
hydraulic conductivity (Krd) as a function o f land-use (/). In this formulation three different
K.n r
(5.2)
sand
sat
combinations
( m
=
3) where used: (1) NDVI, (2)
K
r d ,
and (3)
N
D
V
I
*
K
r d .
The coefficient
[a(i,j)] represents the sub-grid scale variability as a function o f land use and different
combinations o f NDVI and relative soil hydraulic conductivity. The use o f relative soil
hydraulic conductivity results in the use of normalized land surface parameters in the
formulation.
The relative error in the estimation o f each one o f these kernels is given by (Draper
and Smith, 1981; Wilks, 1995):
[£ r2
r - 2 t-i
-
- O tttf [ £ <1>(V,*)2 - r . i f t p ) 2]]
k- 1
(5.3)
The ratio o f the multi-linear regression coefficient [a(i,j)] to the standard error is
shown in Table 5.3. The ratio provides the significance level o f the relative land surface
parameters in the aggregation kernel. It can be seen that the relative hydraulic conductivity
governs the sub-grid scale variability for all the land uses in the Little Washita watershed,
whereas the effect ofNDVI is significant only for rangeland. The ESTAR resolution is less
that the field resolution (typically the field size is 800 m), therefore the sub-pixel variability
effects ofN D V I during Washita ‘94 were minimal.
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149
Table 5.3
Ratio o f multi-linear regression aggregation kernel to the standard error for
____________ different land surface properties as a function o f land-use._______________
-----------Kre,
"" NDVI
ND V I*^,
Urban
64.13
4160.38
-486.15
Agricultural Land
28.63
2696.98
-352.41
Rangeland
160.04
3257.98
-993.51
Forest Land
93.28
1494.58
-538.27
Water
22.58
61.64
-138.57
Barren Land
16.55
329.80
-140.70
5.9
Scaling Behavior o f SAR and ESTAR
The spatial variability within the SAR and ESTAR observations can be studied in the
framework o f fractal geometry. Self-similar fractals exhibit isotropic scaling: a generalized
function f(x,y) is statistically similar to f ( Lx.lv), where / is a scaling factor. Fractal sets that
exhibit anisotropic scaling are called self-affine: for example, the generalized function f(x,y)
is statistically similar to the function f(ax,aHy), where the power coefficient H is known as
the Hurst coefficient (Mandelbrot, 1977; Bindlish and Barros, 1996).
The power law
distribution does not include a characteristic length scale, so it is applicable to scale invariant
phenomena.
Self-affine fractals can be analyzed using spectral techniques (Le Mehaute, 1991).
A standard approach to the analysis o f self-affine fractals is to determine the power density
function as a function o f wave number k. Graphically, the slope o f the log-log plot o f the
spectral density function against the radial wave number is a function o f the fractal
dimension o f the variable.
The linear scaling property o f self-affine fractals in the frequency domain can be used
to aggregate or disaggregate microwave observations (SAR or ESTAR). The spectral density
function for the SAR estimated soil moisture can be divided into three linear parts (Fig.
5.13). For high resolutions (up to 800 m) (region A) and intermediate resolutions (800 m 8 km) (region B), the spectral density function for L-band (both HH and VV) data has similar
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4
LHH
— SAR estimated mv
- — ESTAR observed Tb
x ESTAR estimated mv
2
0
c
&
7
c
"< >
0)
a
2
Region C
Region A
I
Q_
Region B
-4
6
10
Figure 5,13
100
1000
Resolution (m)
10000
Plot o f spectral density function at different resolutions for ESTAR and SAR imagery.
100000
LA
o
151
characteristics as the SAR estimated soil moisture. Both the ESTAR observed brightness
temperature and estimated soil moisture exhibit linear scaling characteristics, and the spectral
density functions for the two are almost parallel to each other (Fig. 5.13). This indicates that
the spatial variability o f soil moisture and brightness temperature fields is very similar,
which is expected since the ESTAR soil moisture retrieval algorithm can be represented by
a set of simple equations.
The linear scaling properties exhibited by SAR and ESTAR were used as a basis to
disaggregate the ESTAR brightness temperature from 200 m to 40 m. It was observed that,
the slope o f L-band spectral density function and the ESTAR brightness temperature are the
same in region A (Fig. 5.13). Based on this, the L-band imagery was used as an interpolating
surface to obtain finer resolution (40 m) ESTAR brightness temperature.
Ideally, it is
recommended that a fractal interpolating surface with the same fractal dimension as that o f
ESTAR brightness temperature be generated. This interpolating surface along with the high
resolution SAR imagery is then used to disaggregate brightness temperature observations
(Bindlish and Barros, 1996).
The disaggregated ESTAR brightness temperatures were then used to retrieve high
resolution soil moisture estimates.
The soil moisture estimates using the downscaled
ESTAR brightness temperatures show a greater spatial variability than the coarse resolution
(200 m) soil m oisture estimates, which is consistent with the SAR derived field (Fig. 5.14).
In particular, the soil moisture estimates in the central part o f the watershed have a stronger
soil texture signature. Lake Burtschi can be located in the north-west com er o f the imagery.
The soil moisture estimates are comparable to the ground based observations (Fig. 5.15). On
a point-by-point basis, the soil moisture estimates improved for fields which had low
observed soil m oisture content. Overall, the absolute RMS error improved to 2.79% from
an earlier value o f 3.16%.
These results suggest that it is possible to improve on the spatial resolution of
ESTAR data by using one SAR frequency only. This finding is especially relevant for
operational hydrologic and climate applications. The use o f the concept enables us to
overcome the data overload problems associated with multi-frequency radar observations,
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152
ESTAR e s t i m a t e d Soil Moisture
Soil
M oisture
D o w n s c a l e d ESTAR e s t i m a t e d Soil Moisture
Figure 5.14
Soil moisture estimate obtained by using downscaled ESTAR brightness
temperature.
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153
C om p ariso n of SAR a n d ESTAR E stim ated Soil Moisture with M e a su re m e n ts
0 .4 0
r
-j.
SAR Ooto (30 m)
o
O
ESTAR Ooto (200 m)
*
*
ESTAR Ooto (40 m)
0.20 r
Estimated
Soil M oisture
0.30 r
0.00
0.00
0.10
0.20
0.30
0.40
Measured Soil Moisture
Figure 5.15
Comparison between measured and estimated volumetric soil moisture using
SAR, ESTAR, and downscaled ESTAR data at the test sites for April 11,
1994.
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154
and provides high resolution soil moisture estimates using coarse resolution ESTAR
observations.
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155
Chapter 6
Contributions and Research Needs
6.1
Sum m ary and Research Findings
Soil moisture has a significant influence on the interactions between the land surface
and the atmosphere, specifically through the exchange o f w ater vapor and sensible beat, and
this in turn influences the prediction o f hydro-meteorological state variables. Soil moisture
also controls the partitioning o f precipitation into runoff and infiltration, and plays a pivotal
role in ecological and biogeochemical cycles.
In this work we developed two independent operational soil moisture retrieval
algorithms using remotely sensed active (SAR) and passive (ESTAR) microwave
observations. The summary o f the research findings is presented below:
6.1.1
Multi-frequencv.
Multi-polarization
Soil
Moisture
Model
from SAR
Measurements
This work demonstrated the possibility o f using
multi-frequency and multi­
polarization instruments to derive soil moisture fields from the remotely sensed images
without prescribing time-varying land-surface parameters such as roughness height and
correlation length as input, and without conducting site specific calibration. This case-study
provides a proof-of-concept for using the inverse problem approach to evaluate soil-water
functional relationships at the scale o f remote-sensing instruments over large areas, and to
facilitate the operational use o f satellite data for hydrologic applications in data-sparse
regions.
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156
6.1.2
Parameterization of Vegetation Effects in Radar Based Soil Moisture Estimates
A semi-empirical vegetation parameterization model was coupled to the multi­
frequency soil moisture inversion algorithm. It was demonstrated that the use o f an explicit
vegetation calibration in the multi-frequency radar based soil moisture retrievals improves
the soil moisture retrieval for vegetated regions. The results improved considerably when
land use was introduced explicitly as an independent parameter. Radar based soil moisture
is a function o f not only the amount o f vegetation present, but also the structure o f the
vegetation canopy. This study suggests that land-use can be used as a surrogate measure o f
overall vegetation structural effects on a regional basis.
6.1.3
Sensitivity and Sub-pixel Variability of ESTAR Soil Moisture Estimates
The ESTAR retrieval algorithm is insensitive to moderate values o f sub-pixel
variability o f various soil surface properties (soil moisture, soil texture, and soil
temperature). The sub-pixel variability observed within the ESTAR pixel was quantified in
term o f land surface characteristics (topography, geology, vegetation, soils), which govern
the soil moisture regime. The knowledge o f the dependence o f soil moisture on the land
surface kernels would enable us to disaggregate ESTAR imagery at a finer resolution based
on these kernels. Nevertheless, these conclusions maybe valid only for regions similar to
Little Washita. It is expected that for regions with a wider range ofN D V I values, would
show a stronger sensitivity to vegetation. Thus, the spatial variability o f vegetation would
be more significant parameter.
6.1.4
Compatibility of SAR and ESTAR
The results o f this study suggest that the two microwave remote sensing systems are
compatible, and could be used to complement each other operationally. It is possible that
a SAR system could contribute to the advanced higher resolution soil moisture mission as
a complement to the prim ary passive instrument system. The work demonstrated the
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157
possibility o f using the high resolution SAR imagery to quantify spatial variability o f soil
moisture in the ESTAR imagery.
6.1.5
Scaling and Disaggregation of ESTAR Imagery
Both the SAR and ESTAR observations as well as the soil moisture estimates
exhibited fractal behavior. Based on the scaling behavior o f SAR and ESTAR observations,
it is possible to obtain high resolution soil moisture estimates using ESTAR and a single
polarization, single frequency radar data. This has tremendous implications to small and
regional scale climate and hydrology operational applications. This finding also addresses
the data transmission problem associated with multi-frequency, multi-polarization SAR
systems. It is essential to conduct extensive study (over different areas) to validate these
results.
6.2
Research Needs and Recommendations for Future W ork
6.2.1
Transportability of Soil Moisture Estimation Algorithms
In this work the use o f both SAR and ESTAR based soil moisture algorithms over
the Little Washita watershed was investigated. There is a strong need to conduct more field
experiments or pilot studies at a variety o f climatic environments. The results obtained in
this work must be cross-validated for other sites to access their true validity. The algorithms
should be validated in different land surface characteristic regions. In order to conduct a
comprehensive analysis o f existing and planned sensors, it is essential to carry out field
experiments where all sensors are used synchronously. These field experiments should have
a greater and diverse ground based sampling plan covering a wide range o f vegetation and
soil geomorphologic features in different parts o f the experimental area.
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158
6.2.2
Optimal Estimates of Soil Moisture using Hvdrologic Models and its Use in
Climate Models
Ideally, the soil moisture estimation algorithms should be coupled with a Iand-surface
model, which accounts for root zone infiltration (Capehart and Carlson, 1994; Burke et al.,
1997). The use o f a complete land surface model will enable us to obtain optimum estimates
of soil moisture and other land surface properties. Also, this would provide us with an
opportunity to study the effect of spatial variability and the interaction between soil moisture
and other variables. These soil moisture estimates should be used in operational climate and
hydrologic models to quantify the effect o f soil moisture, and to improve the quality o f
current forecasts.
6.2.3
Operational Soil Moisture Monitoring from Space
One possible outcome of this work is to design a stategy to integrate SAR and
ESTAR data: the high resolution estimates for pilot sites could be made using a multi­
frequency, multi-polarization SAR system, whereas large scale and global coverage for soil
moisture could be made using ESTAR. SAR and ESTAR can be used to complement each
other. ESTAR can be used to provide global soil moisture coverage, whereas SAR can be
used over long term experimental research watersheds in different climatic conditions to
quantify sub-pixel variability. SAR systems have flown in space since 1978, and thus have
proven technology which provides much higher resolution, and consequently data rates, than
the passive system. The repeat cycles o f the SAR system would be o f the order o f 30 days
or more, making the independent data o f limited value for hydrologic process studies.
Currently, there are no operational satellite systems truly capable o f reliable soil
moisture measurement. Based on the results obtained, it is recommended to design an
instrument w hich consists on a L-band radiometer, a L-band radar, and an infrared sensor.
Single frequency data from JERS-1 (L-band radar) or RADARS AT (C-band radar) can be
used in conjunction with a L-band radiometer. This combination can provide high resolution
soil moisture estimates.
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159
Appendix
Sensitivity of SAR based Soil Moisture Estimation Algorithm
to Initial Guess
A .l
Sensitivity to Soil M oisture
The mean of the typical values o f surface soil moisture observed during the Washita
‘94 experiment were used as an initial guess in the inversion algorithm. The initial guess for
volumetric surface soil moisture was 20.0%. This fall in the middle o f the dynamic range
o f soil moisture values. The value o f the initial guess was uniform all over the watershed and
did not change from day to day, during the dry-down process.
The value o f the initial guess was changed to 10.0% and the soil moisture values for
each pixel within the watershed was re-computed. The results obtained for the two runs were
similar (Fig. A l). The specification for a low initial soil moisture does tend to under­
estimate the soil moisture values. This is because for low value o f soil moisture, the
sensitivity o f dielectric constant to soil moisture reduced. The small difference in the soil
moisture estimates are due to the high convergence rates. Over the entire watershed, about
95% o f the pixels attained convergence.
A.2
Sensitivity to Soil Roughness
Like the volumetric soil moisture an average value o f the observable soil roughness
was used as an initial guess (=1.5 cm). This is a typical value for soils found in nature. For
agricultural fields during the growing season, the soil roughness can be much higher due to
tillage (~5 cm).
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160
SAR estimated
soil moisture
(SM=10.0) (%)
Comparison between SAR soil moisture with different initial guesses
SAR estim oted soil m oisture (S M -2 0 .0 ) (%)
Figure A l
Sensitivity o f SAR based soil moisture estimates to initial soil moisture.
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161
The soil roughness was decreased to 0.5 cm and the soil moisture estimates obtained
were very close to initial results obtained with an initial roughness o f 1.5 cm (Fig. A2).
There is much less scatter in the soil moisture estimates due to change in initial guess o f soil
roughness, than that seen for soil moisture. Again, the high convergence rates could result
in small errors. These results lead us to believe that the SAR based soil moisture estimates
are robust to initial guesses of land surface parameters.
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162
Comparison between SAR soil moisture with different initial guesses
50
1 1 * ' 1 1 1 1 ' I 1 1 1 1 1 1 1 1 1 I 1 1 1 1 ‘ 1 1 ' 1 j :' 1 ' 1 1 1 1 1 1 | 1 1 1 1 1 1 1 1 *7
30
SAR estimoted
soil moisture
(Sigmo=0.5) (%)
40
§»
10
0
•
20
30
40
SAR estim oted soil moisture (Sigm a= 1.5) (%)
Figure A2
50
Sensitivity o f SAR based soil moisture estimates to initial soil surface
roughness.
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163
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V it a
R a j a t B in d l is h
E d u c a t io n
1996 - 2000
1994 - /996
1989 - 1993
Ph.D., Department of Civil and Environmental Engineering, The Pennsylvania State University
M aster of Science, Department o f Civil and Environmental Engineering, The Pennsylvania State
University
Bachelor of Technology, Department of Civil Engineering, Indian Institute o f Technology,
Bombay. India
W o r k .a n d R e s e a r c h E x p e r i e n c e
2000-present
R esearch Scientist, SSAI located at USDA ARS Beltsville, under the guidance of Dr. T.J.
Jackson
/ 994-2000
G rad u ate Research Assistant, The Pennsylvania State University. Advisor: Dr. Ana P.
B arros
Summer 1998
Visiting Research Scientist at US D epartm ent of Agriculture, under the guidance of Dr. T.J.
Jackson
Summer 1997
Participated in Southern G reat Plain ‘97 experiment.
Summer 1996
Visiting Research Scientist at NASA under the guidance o f Dr. B.J. Choudhury
7/93-5/94
R esearch Assistant on the N atural H azards Mitigation project in n T , Bombay
H o n o r s and A f f il ia t io n s
1989 - 1993
Since 1998
Since 1994
Since 1997
Recipient o f the National Talent Search Scholarship from NCERT, India
Member o f Institute of Electrical and Electronics Engineers (IEEE)
Member o f American Geophysical Union (AGU)
Member o f Chi Epsilon (Civil Engineers honor society)
L i s t o f P u b l i c a t io n s
Barros, A.P. and R. Bindlish, 1999. Using image analysis techniques for intercomparison o f spatial variables: an
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Remote Sensing o f Environment, 71 (1), pp. 67-88.
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hydrologic models in regions o f complex terrain. Journal o f Global and Planetary Studies (in press).
Bindlish, Rajat and A.P. Barros, 2000. Incorporation o f Vegetation effect in Radar based Soil Moisture estimation
model. LAHS, Remote Sensing and Hydrology, 2000 (in press).
Bindlish, Rajat and A.P. Barros, 2000. Sub-pixel variability o f remotely sensed soil moisture: An intercomparison
study o f SAR and ESTAR. (in preparation).
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