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Use of special sensor microwave imager data for soil moisture estimation

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U se o f S p ecia l S en sor M icrow ave
Im ager D a ta
for S oil M o istu re E stim a tio n
Venkataraman Lakshmi
A DISSERTATION
PRESENTED TO THE FACULTY
OF PRINCETON UNIVERSITY
IN CANDIDACY FOR THE DEGREE
OF DOCTOR OF PHILOSOPHY
RECOMMENDED FOR ACCEPTANCE
BY THE DEPARTMENT OF
CIVIL ENGINEERING AND OPERATIONS RESEARCH
JANUARY 1996
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OMI Number: 9612892
Copyright 1996 by
Lakshmi, Venkataraman
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ii
©Copyright by Venkataraman Lakshmi, 1996. All rights reserved.
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A b stra ct
The use of satellite data in land surface modeling is of great importance, par­
ticularly if we want to move up in spatial scale, there is a definite lack of field
observations of soil moisture. The present research hopes to harness the available
satellite data from various sensors to help in estimating soil moisture over large ar­
eas compatible with grid sizes of climate models. This research uses the microwave
brightness temperatures from the Special Sensor Microwave Imager (SSM/I) at 19
and 37 GHz in both the horizontal and vertical polarizations.
A coupled soil-canopy-atmosphere model is used to study the processes that
affect the observation of the brightness temperatures by the SSM/I sensor. The
land surface hydrological model is used to simulate the water and energy balance
fluxes for the Kings Creek catchment for a period of ten years from 1980 to 1989.
The sensitivity of the simulated brightness temperatures to vegetation and soil
is investigated using a canopy radiative transfer model for the vegetation and an
atmospheric attenuation model.
The SSM/I brightness tem perature observations are over large areas, of the
order of 900-2500 km 2. At these scales, it is important to investigate the effect
of heterogeneities in land surface characteristics on the observed brightness tem ­
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peratures. Simulations are carried out using the coupled soil-canopy-atmosphere
model to assess the effect of vegetation distribution as well as distribution and
partial coverage of rainfall on the simulated brightness temperatures.
Soil moistures and the SSM/I brightness temperatures at 19 and 37 GHz are
simulated over the Red River basin area between 31.5 °N to 36 ° N latitude and
94.5 °W to 104.75°W longitude. This simulation is carried out for a tim e period
of one year (August 1, 1987 to July 31, 1988). The soil hydrology, radiative trans­
fer and atmospheric attenuation models use remotely sensed data for vegetation
and rainfall input. The vegetation input is derived using the NDVI (Normalized
Difference Vegetation Index) data from AVHRR (Advanced Very High Resolu­
tion Radiometer) observations and the rainfall input is obtained using Manually
Digitized Radar (MDR) data.
Comparisons between the model derived and SSM/I derived soil moisture are
analyzed. The monthly estimates of cumulative evapotranspiration derived using
SSM/I derived soil moisture and the hydrological model are compared with es­
timates derived using atmospheric budget analysis. The mean monthly surface
soil moistures derived using observed SSM/I data is analyzed in conjunction with
rainfall and vegetation information.
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A cknow ledgm ents
First and foremost, I thank my advisor Dr. Eric Wood for his guidance, input and
constant source of inspiration. It has been a very fruitful experience working with
him.
Dr. Bhaskar Choudhury at NASA has been very gracious in offering advice
and in helping out with numerous questions that I have had along the way. I
have benefited immensely from my discussions with him, and this thesis has been
improved thanks to his helpful comments.
Dr.
Jim Smith has been very helpful. His suggestions during the various
committee meetings have been very thought-provoking.
I am extremely grateful to all members of Prof. Wood’s research team past
and present, who have helped me with my work. Jay, Dom, Claudio, Christa,
Mark, Erik, Ying and Xu have provided valuable input and pleasant company.
Fellow graduate students in the Water Resources program, Saumyen, Wenjie, Al­
berto, Jon, Paul, Lan and Beverly, have been friendly and supportive. I thank
my friends in Civil Engineering, Ugur and Adam, and my office-mate, Paula, for
their encouragement. I would like to thank the Rapkins for their warm and loving
friendship.
I
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I am very pleased to have had the privilege of working with Dah-Syang Lin. I
knew Dah-Syang when we started graduate studies together in Iowa City in August
1987. It is a tremendous loss for science and hydrology that Dah-Syang will no
longer be with us.
My father was the greatest influence in my life. He was the first person to
introduce me to independent scientific thinking. He provided the intellectual nour­
ishment and constant support and advice without which I could have not gotten
this far. I only wish he could have read this work. I dedicate this thesis to the
memory of two departed souls, my father and Dah-Syang Lin. May their souls rest
in peace.
My mother and brother have been with me every step of the way. To my wife
Saraswati, thank you for all the loving support.
Research support from the NASA grant NAS5-31719 Global Hydrologic Pro­
cesses is gratefully acknowledged.
I
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To the memory of two departed souls ...
My father - my first teacher and the best teacher
My friend Dah-Syang - colleague, friend and confidant
and to
My mother and my brother
My wife Saraswati - my inspiration
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C o n ten ts
A b stra ct
1
2
iii
A ck n ow led gm en ts
v
In tro d u ctio n , M o tiv a tio n and L iterature R ev iew
1
1.1
In tro d u ctio n ...............................................................................................
1
1.2
Motivation : Importance of soilm o is tu re ..............................................
3
1.3
Science o b jectiv es......................................................................................
7
1.4
Previous Work - Literature R e v ie w .......................................................
8
1.5
Contributions of this th e sis......................................................................
11
1.6
Models and m e th o d s ...............................................................................
12
A S oil-C an op y-A tm osp h ere M od el for use in S S M /I H y d ro lo g ica l
In v estig a tio n s
17
viii
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2.1
In tro d u ctio n ...............................................................................................
17
2.2
Overview of modeling s tra te g y ................................................................
21
2.3
Thin layer soil hydrological m o d e l..........................................................
23
2.3.1 Hydrological model : Water balance...........................................
23
2.3.2 Hydrological model : Energy b a la n c e ........................................
35
Canopy radiative transfer m o d el.............................................................
37
...........................................................
38
2.4.2 Brightness tem perature.................................................................
48
2.4.3 Polarization difference in d e x ........................................................
50
2.5
Atmospheric attenuation m o d e l ............................................................
52
2.6
Hydrological model testing and validation
53
2.4
2.4.1 Canopy radiative transfer
2.7
2.8
.........................................
2.6.1 Site d e sc rip tio n ...................................................
54
2.6.2 D ata and p a ra m e te rs....................................................................
55
2.6.3 Results and discussions.................................................................
58
Sensitivity of radiative transfer to vegetation and soil moisture . . .
67
2.7.1
Effect of vegetation p a r a m e te rs .................................................
67
2.7.2 Sensitivity to leaf area index and soil m o istu re........................
70
C o n clu sio n s...............................................................................................
75
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3
In v estig a tio n o f th e Effect o f H etero g en eities in V eg eta tio n and
R ainfall on Sim ulated Soil M oistures and S S M /I B rig h tn ess T em ­
p era tu res
95
3.1 In tro d u ctio n ................................................................................................
96
3.2 Review of previous heterogeneity e x p e rim e n ts ....................................
97
3.3 Overview of a n a ly s is ................................................................................... 100
3.4 Description of experim ents..........................................................................101
3.5 The effect of heterogeneity on simulation of soil moisture and bright­
ness tem peratures............................
3.5.1
105
Heterogeneities in leaf area index and spatial variability and
coverage of r a in f a ll.........................................................................107
3.6 Effect of heterogeneity on soil moisture estim atio n ................................ 118
3.6.1
The effect of distributed soil moisture on soil moisture esti­
mation ...............................................................................................119
3.7 Interpretation of results in the context of SSM/I footprint
................. 122
3.8 C o n clu sio n s.................................................................................................. 123
4
E valu ation o f S S M /I S atellite D a ta for R eg io n a l Soil M o istu re
E stim a tio n
141
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4.1
In tro d u ctio n ........................................................................
4.2
Special Sensor Microwave Imager( S S M /I ) ............................................. 145
4.3
M e th o d s........................................................................................................146
4.3.1
Data sets
141
......................................................................
146
4.3.2 Description of study a r e a ................................................................ 152
4.3.3 Calibration of parameters and simulation m eth o d s....................154
4.4
Results and D iscussion...............................................................................156
4.4.1
Errors and correlations on different time scales.......................... 156
4.4.2 Pixel results for soil moisture and brightness temperatures . 161
4.4.3
SSM/I derived monthly soil moisture estimates
.......................163
4.4.4 SSM/I derived monthly evaporation e s tim a te s .......................... 165
4.4.5
4.5
5
Comparison of results with previous studies
............................. 169
Conclusions and Implications for future w o rk .......................................... 173
C on clu sion s and Future W ork
202
5.1
Summary of major r e s u l t s ........................................................................ 202
5.2
Strategy for future research
..................................................................... 206
5.2.1
SSM/I generated monthly climatology
.......................................207
5.2.2
Use in agricultural a p p lic a tio n s ....................................................207
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5.2.3
Field experiments in conjunction with SSM/I d a t a ...................208
5.2.4
Other instruments
........................................................................ 208
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L ist o f F igu res
2.1
Representation of the integrated soil-canopy-atmosphere process . . 81
2.2
Representation of the thin-layer model of soil hydrology...................
2.3
Observed (dotted line) and simulated (solid line) daily discharges
(mm) for the calibration period (1980-1984)
2.4
.......................................
.........................................................................................................
85
Mean observed (25mm depth; dots) and simulated (top layer - lines)
volumetric soil moisture for IFC-1 through I F C - 4 .............................
2.7
84
Precipitation (in mm) for the Kings Creek gauge for IFC-1 through
IFC-4
2.6
83
Observed (dotted line) and simulated (solid line) daily discharges
(mm) for the validation period (1985-1989)
2.5
82
86
Mean observed (75mm depth; symbols) and simulated (bottom layer
- lines ) volumetric soil moisture for IFC-1 through IF C -4 ................
87
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x iv
2.8
Time series plot of observed surface temperatures (dots) and simu­
lated top layer temperatures (lines) for IFC-1 through IFC-4 . . . .
2.9
88
Scatter plot of observed surface temperatures and simulated top
layer temperatures for IFC-1 through I F C - 4 ......................................
89
2.10 Scatter plot of 6:00 am observed surface temperatures and simulated
top layer temperatures for IFC-1 through I F C - 4 ................................
90
2.11 Sensitivity of 19 GHz polarization difference index (DY) to the leaf
area index (LAI) for different values of stem area index (SAI) and
canopy moisture content ( m e ) ................................................................
91
2.12 Sensitivity of 37 GHz polarization difference index (DY) to the leaf
area index (LAI) for different values of stem area index (SAI) and
canopy moisture content ( m e ) ................................................................
92
2.13 Sensitivity of 19 and 37 GHz polarization difference index (DY)
to leaf area index for different soil moisture contents between 0.02
(residual) and 0.50 (saturation) at increments of 0.048 for stem area
index and canopy moisture content at 0.3 and 0.35 respectively . . .
93
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xv
2.14 Sensitivity
Sensitivityofof1919and
and 3737GHz
GHzpolarization
polarizationdifference
differenceindex
index (DY)
(DY)
to volumetric soil moisture content for different leaf area indices
between 0.0 and 7.0 at increments of 0.5 for stem area index and
canopy moisture content at 0.3 and 0.35 respectively
......................
94
3.1 Schematic representation of the observation of heterogeneity in soil
moisture and the estimation of soil m o is tu r e ......................................... 129
3.2 Flow chart of the numerical experiment for investigation of hetero­
geneity of vegetation and rainfall on a 100 X 100 grid..........................130
3.3 Variation of leaf area index, soil moisture and polarization difference
index (19 and 37 GHz) for distributed leaf area index and lumped
rainfall for January 1 to December 31, 1987.......................................... 131
3.4 Variation of leaf area index, soil moisture and polarization difference
index (19 and 37 GHz) for lumped leaf area index and distributed
rainfall for January 1 to December 31, 1987
.............................. 132
3.5 Comparison of distributed versus lumped and distribution based
cases for soil moisture and 19 and 37 GHz polarization difference
index for distributed vegetation case (rainfall lu m p ed )......................... 133
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3.6
Comparison of distributed versus lumped and distribution based
cases for soil moisture and 19 and 37 GHz polarization difference
index for distributed rainfall case (vegetation lum ped)......................... 134
3.7
Rainfall difference in soil moisture and polarization difference index
for 19 and 37 GHz between the spatially distributed representation
and the lumped representation of rainfall for January 1 to December
31, 1987 ..................................................................................................... 135
3.8
Rainfall difference in soil moisture and polarization difference index
for 19 and 37 GHz between the spatially distributed representation
and the distribution based representation of rainfall for January 1
to December 31, 1987 ............................................................................... 136
3.9
Coefficient of variation (cv) for soil moisture and the 19 and 37 GHz
polarization difference index for the distributed vegetation, lumped
rainfall and the lumped vegetation distributed rainfall.......................... 137
3.10 Variability of polarization difference index and soil moisture for dif­
ferent leaf area indices. The leaf area indices are 0.02, 0.11, 0.30,
0.75 and 1.1, top to bottom. The dots indicate the mean and the
boxes are two standard deviations w id e .................................................. 138
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XVII
3.11 Flowchart for investigation of the effect of a spatial distribution of
rainfall, vegetation and soil moisture on the SSM/I estimated soil
m o istu re ........................................................................................................ 139
3.12 Average of the simulated volumetric soil moisture (dot) and two
standard deviations versus the the soil moisture derived from the
average 100X100 brightness tem perature (19 G H z)................................140
4.1 Location of the study area (denoted by a dotted rectangular box) . 182
4.2 Scheme for calibration, validation and comparison of soil moistures
and brightness tem p eratu res......................................................................183
4.3 Correlation coefficient (r) between the simulated soil moisture and
the SSM/I derived soil moisture using 19 and 37 GHz brightness
temperatures for monthly averaged, weekly averaged and daily valuesl84
4.4 Frequency distribution of the root mean squared difference between
the simulated soil moisture and the SSM/I derived soil moisture
using 19 and 37 GHz brightness temperatures for monthly averaged,
weekly averaged and daily values
............................................................ 185
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xvm
4.5
Frequency distribution of the root mean squared difference between
the simulated and the SSM/I derived average brightness temper­
ature using 19 and 37 GHz brightness temperatures for monthly
averaged, weekly averaged and daily v a lu e s............................................ 186
4.6
Frequency distribution of the root mean squared difference between
the simulated and the SSM/I derived polarization difference bright­
ness temperature using 19 and 37 GHz brightness temperatures for
monthly averaged, weekly averaged and daily v a lu e s............................ 187
4.7 Root mean squared difference between the daily simulated soil mois­
ture and the SSM/I derived soil moisture using 19 and 37 GHz
brightness te m p e ra tu re s ............................................................................ 188
4.8 Root mean squared difference between the weekly averaged simu­
lated soil moisture and the SSM/I derived soil moisture using 19
and 37 GHz brightness te m p e ra tu re s ...................................................... 189
4.9 Root mean squared difference between the monthly averaged sim­
ulated soil moisture and the SSM/I derived soil moisture using 19
and 37 GHz brightness te m p e ra tu re s ...................................................... 190
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4.10 Root mean squared difference between the simulated surface tem ­
perature at 6:00am and the observed surface tem perature assumed
to be equal to the minimum air temperature of the d a y ...................... 191
4.11 Good agreement between the simulated and 19 GHz SSM/I bright­
ness temperature derived soil moisture and average and polariza­
tion difference brightness temperature at the location 33.0°N and
1 0 4 .2 5 ° W ..................................................................................................... 192
4.12 Good agreement between the simulated and 37 GHz SSM/I bright­
ness temperature derived soil moisture and average and polariza­
tion difference brightness temperature at the location 31.5°IV and
104.75°W
..................................................................................................... 193
4.13 Bad agreement between the simulated and 19 GHz SSM/I bright­
ness tem perature derived soil moisture and average and polarization
difference brightness temperature at the location 35.0°IV and 95.75°W194
4.14 Bad agreement between the simulated and 37 GHz SSM/I bright­
ness tem perature derived soil moisture and average and polarization
difference brightness temperature at the location 35.0°N and 95.75°W195
4.15 Correlation coefficient (r) between the simulated soil moisture and
the SSM/I derived soil m o istu re ................................................................196
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XX
4.16 Distribution of correlation coefficient (r) between the simulated soil
moisture and the SSM/I derived soil moisture for the 0.25° pixel
and the averaged 0.75°p i x e l ....................................................................... 197
4.17 Mean monthly 0.25°X0.25° soil moisture derived from 19 GHz SSM/I
data between August 1987 to July 1988. The SSM/I was turned off
in December 1987........................................................................................ 198
4.18 Cumulative monthly 0.25°X0.25° precipitation (in m m ) between
August 1987 to July 1988
........................................................................ 199
4.19 Mean monthly 0.25°X0.25° leaf area index between August 1987 to
July 1988
................................................................................................... 200
4.20 Monthly total evapotranspiration computed using atmospheric wa­
ter vapor budgets and estimated using SSM/I and hydrological mod­
eling ...............................................................................................................201
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List o f T ables
2.1 Parameters for the thin layer hydrological model
..............................
79
2.2 Maximum simulated range residual to saturated soil moisture con­
tent (6,-6t ) for polarization difference index (A T X 100) leaf area
index (L ) = 0.75; branch to stem area ratio (rj) = 2.7 for 19 GHz
and 37 G H z ...............................................................................................
80
3.1 Comparison of different coefficient of variation (cv) of leaf area index
with the case of lumped leaf area index for mean and root mean
squared difference (rmsd) of the spatially distributed case with the
lumped case for soil moisture and polarization difference index . . . 126
xxi
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3.2
Comparison of different fractional coverage of rainfall (fi) with the
case of uniform rainfall for mean and root mean squared difference
(rmsd) of the spatially distributed case with the lumped case for
soil moisture and polarization difference i n d e x ......................................127
3.3
Variation of polarization difference index with leaf area index and
soil m o istu re..................................................................................................128
4.1 Parameters for the coupled soil-canopy-atmosphere model..................... 177
4.2 List of Surface Airways S ta tio n s ................................................................ 178
4.3
Summary of root mean squared differences between simulations and
observations for 19 and 37 GHz brightness temperatures and esti­
mated soil m o istu re ..................................................................................... 179
4.4
Effect of water bodies on the SSM/I observations - root mean squared
differences between simulated and observed brightness temperatures
and simulated and estimated soil moisture for 19 and 37 GHz . . .
180
4.5 Comparison of monthly evaporation estimates (in mm) from an at­
mospheric model and derived using 19 GHz SSM/I observations . . 181
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0
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C h ap ter 1
In tro d u ctio n , M o tiv a tio n and
L iteratu re R ev iew
1.1
In tro d u ctio n
The hydrological cycle is of extreme importance in determining the day to day
changes in the weather as well as the long term climate over a specific region. The
land surface plays a very important role in terms of feedback to the atmosphere.
Diurnal phenomena such as land and sea breeze are caused by uneven heating
of the earth’s surface and result in the redistribution of heat and moisture. The
land surface sustains mankind through its soil layer, which supports the growth of
1
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C H A P T E R 1. I N T R OD U CT IO N
2
plants. The plants serve as a source of food to the herbivore and to man. In short,
the food chain is highly dependent on the soil layer of the land surface. The land
surface acts as a link between the atmosphere and the deeper layers of the soil. It
controls the amount of infiltration that can occur, which makes its way to the water
table. This water from the water table serves as a source for human consumption.
The growth of plants depends on the moisture in the soil. In seasons of drought,
lack of rainfall is followed by the water table receding to deeper depths, making it
difficult for the plants to carry out photosynthesis. Evaporation from the soil and
transpiration from the plants move the moisture in the soil to the atmosphere.
The moisture in the atmosphere can condense and precipitate over the same
region from where it was evaporated or elsewhere. In addition, there is a time lag
between the evaporation process and the precipitation process. This time lag is
greater when the region from which the moisture evaporates is far away from the
region on which the moisture precipitates. A part of this precipitated moisture
enters the soil and a part of it constitutes runoff. The runoff may evaporate,
infiltrate into the soil or flow via a network of stream channels and/or rivers to
a lake or the sea. This runoff results in movement of the soil moisture from one
region to another. Hence, there is a feedback between the land surface and the
atmosphere as well as connections between regions far apart. The hydrological
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C H A P T E R 1. IN T R O D U C T IO N
3
cycle thereby affects the land surface and the atmosphere over a range of spatial
and temporal scales.
1.2
M o tiv a tio n : Im p o rta n ce o f soil m o istu r e
This section describes the role of soil moisture in land surface-atmosphere pro­
cesses and underlines its importance. The importance of soil moisture governs our
motivation for better estimations of soil moisture from observational data.
Surface soil moisture is an important variable in land surface hydrology. It
controls the partitioning of rainfall into runoff and infiltration. It affects (along
with the surface temperature) the depth of the planetary boundary layer, circu­
lation/wind patterns (Mahfouf et. ah, 1987, Lanicci et. al., 1987 and Zhang et.
al., 1989) and regional water and energy budgets. The study of the global climate
using GCMs has shown th at soil moisture is a very important factor (Walker et.
al., 1977; Rowntree et. al., 1983; Rind, 1982; Carson et. al., 1981; Mintz, 1984).
Evapotranspiration plays an important role in determining surface temperatures,
surface pressure, rainfall and motion (Shukla et. al., 1982). Evapotranspiration
in turn depends on soil moisture (together with incoming radiation and a host of
other meteorological factors). Soil moisture is very closely connected with hydrol­
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C H A P T E R 1. IN T R O D U C T IO N
4
ogy as well as climate (Yeh et. al., 1984). The surface soil moisture is an important
factor in agricultural applications. Soil moisture is an important output variable
from hydrological models. It can be compared against observations to determine
the validity of the parameterizations used in modeling.
Projects like the GCIP (Global Energy and Water Experiment - GEWEX Con­
tinental Scale International Project) involve the development and testing of hydrological models on a continental scale over the Southern Plains of the United States.
The availability of data sets for the validation of continental scale soil moisture
would be very useful. There can be two ways used to collect soil moisture data
: field sampling and remote sensing methods. There are many advantages to
remote sensing as a method of soil moisture determination as compared to field
sampling. Field sampling is point based and does not give a clear picture of the
variation of the soil moisture over an area. To find out the spatial variation in the
soil moisture, interpolation has to be carried out, whose accuracy (difference be­
tween the actual soil moisture pattern and the interpolated soil moisture pattern)
depends on the closeness of the sampled soil moisture data points and the homo­
geneity/heterogeneity of the soil moisture distribution. To be accurate, (a) more
points need to be sampled, and this means greater resources that may at times be
difficult to obtain and (b) the correlation lengths of the variation of soil moisture
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C H A P T E R 1. IN T R O D U C T IO N
5
is greater than the measurement spatial interval. In the case where the correlation
lengths of soil moisture are smaller than the measurement spatial interval, ground
based data collection may result in the biased sampling of the soil moisture. This
would result in a biased estimate of the areal mean of the soil moisture from field
sampling. It is for this reason that remote sensing is a more attractive proposition
than field-based sampling, since it gives a much better picture of the variation of
the soil moisture over an area.
Satellite remote sensing offers spatial coverage and a certain temporal fre­
quency in monitoring soil moisture from space. The microwave frequencies of the
electro-magnetic spectrum are the most sensitive to the variations of soil moisture
(Schmugge, 1985). This is due to the different response water and dry soil exhibit
toward electro-magnetic radiation in the microwave region. Water is a strongly
polar molecule. The dielectric constant of water (which measures the effect of the
interaction with electric field a function of frequency) is around 80 compared to
3 to 5 for dry soils at low microwave frequencies. Hence, a soil with higher mois­
ture content will have a higher dielectric constant compared to a soil with lesser
moisture content. This change in dielectric constant of the soil (caused by changes
in soil moisture) is recorded as changes in the radiation emitted by the soil in the
microwave region. Microwave remote sensing can be carried out in two ways :
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C H A P T E R 1. IN T R O D U C T IO N
6
active and passive (Ulaby et. al., 1986). In active remote sensing, a signal is trans­
m itted from the instrument to the ground and the reflected signal is measured.
In the case of passive remote sensing, the electromagnetic radiation emitted from
the ground is measured. Our choice here to use passive microwave remote sensing
was dictated by the presence of the Special Sensor Microwave Imager (SSM/I), a
microwave sensor with global coverage and daily temporal coverage. In addition,
the SSM/I is a very stable, sensitive and well-calibrated sensor (Hollinger et. al.,
1990), which makes it a very appealing choice.
The Special Sensor Microwave Imager is a four frequency (19.4, 22.0, 37.0, 85.0
GHz) seven channel (19V, 19H, 22V, 37V, 37H, 85V, 85H) microwave sensor aboard
the Defense Meteorological Satellite Program (DMSP) spacecraft F-8 (Hollinger et.
al., 1990). The polar orbiting satellite has equatorial overpass times (local time) at
0615 (ascending orbit) and 1815 (descending orbit). The resolution of the sensor
varies with frequency. The resolution is about 56 km at 19 GHz, 33 k m at 37 GHz
and 14 km at 85 GHz. There are some missing days due to the precession of the
orbits. The satellite travels at a speed of 6.6km/s at a height of 833 km above the
surface of the earth. The swath width is 1400 km, with an active scan angle of
102° and a zenith angle of 53.1° (Hollinger et. al., 1990). The SSM/I measures the
intensity of emitted radiance in terms of brightness temperatures, which is directly
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C H A P T E R 1. IN T R O D U C T IO N
7
proportional to radiation intensity using the Planck’s function and the RayleighJean’s approximation for the microwave portion of the electromagnetic spectrum.
The estimate of the standard error of the absolute calibration is ± 3 K. This has
been determined from comparisons using the SSM/I aboard an aircraft and flying
it over ocean areas, forest areas and desert areas (Hollinger et. al., 1990).
1.3
S cien ce o b jectiv es
The objectives of this thesis are :
(1) Set up a hydrological model for use in microwave remote sensing
(2) Investigate the sensitivity of surface soil moisture and brightness tempera­
tures to heterogeneities in vegetation and spatial distribution of rainfall
(3) Use observed SSM/I data for soil moisture estimation
The objectives are designed to help study soil moisture, which is a major fac­
tor in land surface-atmosphere interaction as seen in the previous section 1.2. A
hydrological model with a complete water and energy budget is to be put together
that can be used in microwave remote sensing. The investigation of the role of
heterogeneities in the measurement process of the SSM/I and in the estimation of
soil moisture from SSM/I data is carried out. The objectives also involve using
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C H A P T E R 1. IN T R O D U C TIO N
8
existing satellite SSM/I data to estimate soil moisture.
The science questions posed and answered in this thesis are :
(1) Can SSM/I data be used for soil moisture estimation ?
(2) W hat are the effects of heterogeneities in vegetation and a spatial distribu­
tion of soil moisture on SSM/I observations and inversion of the observed SSM/I
brightness temperatures to obtain soil moisture ?
This thesis attempts a critical evaluation of the SSM/I sensor for estimation of
soil moisture. The feasibility of using the SSM/I sensor for soil moisture estimation
is examined. The role of the heterogeneities in vegetation and soil moisture on the
SSM/I measurements and the effect the heterogeneities have in the inversion of
brightness temperatures to obtain soil moistures are also examined
1.4
P r e v io u s W ork - L itera tu re R e v ie w
This section lists the various applications of SSM/I data and the use of SSM/I data
for estimation and monitoring of land surface variables. Applications involving soil
moisture have been presented.
The data from the SSM/I has been used for various land surface, ocean surface
and atmospheric characteristics determination. The quantities derived from SSM/I
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C H A P T E R 1. IN T R O D U C T IO N
9
include oceanic total precipitable water (Alihouse et. al., 1990a), cloud liquid wa­
ter content (Alihouse et. al., 1990b), ocean surface wind speed (Goodberlet et.
al, 1990), land surface temperature (McFarland et. al., 1990), atmospheric water
vapor over oceans (Schluessel et. al., 1990) and sea ice classification (Steffen et.
al., 1990). Rainfall over oceans has been estimated using the 37 GHz brightness
tem perature measurements of the SSM/I and the SMMR (Scanning Multichannel
Microwave Radiometer) (Prabhakara, et. al., 1992a; Prabhakara et. al., 1992b).
The observed brightness temperature has been studied for the 19 and 37 GHz over
desert, rain forest and savanna locations for a period of two years to determine the
influence of the vegetation cover (Choudhury, 1993). This study has shown that
the reflectivities derived from the 19 and 37 GHz data exhibits a good correlation
with the seasonal cycle of biomass growth. This leads to the justification of the
use of SSM/I data for monitoring the seasonal cycle of biomass growth.
However, the influence of soil on SSM/I brightness temperatures has been recog­
nized in studies involving the effect of rainfall on SSM/I radiances (Heymsfield
et. al., 1992). Heymsfield et. al., (1992), Teng et. al, (1993) and Choudhury
et. al., (1988) have used the concept of antecedent precipitation index (API) as
a measure of the soil wetness (Saxton et. al., 1967; Choudhury et. al., 1983) to
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C H A P T E R 1. IN T R O D U C TIO N
10
develop a regression relation between soil wetness and brightness temperatures.
The brightness temperature has been related to API for the 6.6 GHz SMMR data
(Choudhury et. al., 1988) and the 19 GHz SSM/I data (Teng et. al., 1993).
The work of Teng et. al., (1995) follows a series of works (Choudhury et. al., 1987;
Becker et. al., 1988; Townshend, 1989) in investigating the dependence of the 37
GHz microwave polarization difference index (MPDI) (the difference between the
vertical and horizontal polarization brightness temperatures) on vegetation and
soil moisture. The MPDI is related to the NDVI (Normalized Difference Vegeta­
tion Index - a measure of the amount of vegetation) and the moisture content. The
relationship depends on the nature of the vegetation as well as the stage of growth
of the vegetation. The soil radiance gets modulated by the overlying canopy and
the atmosphere. As the vegetation amount increases, the sensitivity of the MPDI
to soil moisture decreases. The effect of the vegetation canopy increases with an
increase in the amount of vegetation and the observation frequency as seen from
studies using radiometers in a field site (Vyas et. al., 1990).
In another study, the 37 GHz and 85 GHz horizontal polarization channels of the
SSM/I are modeled to determine the difference between the day and the night soil
wetness (API) in the Great Plains (England et. al., 1992). These model simulation
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C H A P T E R 1. IN T RO D U CTIO N
11
results show that the SSM/I overpass time of 2:00am/pm is optimal.
1.5
C on trib u tion s o f th is th e sis
This thesis is based on certain specific extensions and improvements of prior work,
which are described in the previous section but referred to once again in this section
for the sake of completeness. This section will explain the specific contributions of
this thesis.
Previous work involving large scale hydrological modeling using microwave satellite
data are either at a coarse resolution (with the utilization of SMMR data) or have
simplified hydrological parameterizations (the API measure of soil wetness). For
example, surface soil moisture has been derived using the 6.6 GHz (resolution 150
km) frequency passive microwave data over a 150 k m area from the SMMR (Owe
et. al., 1992) and when compared to weekly field measurements for a period of
three years shows good agreement. Simplified hydrological models using API as
a surrogate for soil moisture and regression techniques has been used (Teng et.
al., 1993) along with 19 and 37 GHz SSM/I brightness temperature data for the
midwest region and using 6.6 GHz SMMR data for the U.S South Great Plains
region (Choudhury et. al., 1988) in order to estimate soil moisture.
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C H A P T E R 1. IN T R O D U C TIO N
12
The present work attempts to improve the previous methods by using the 19 and
37 GHz data, which is at a higher resolution (compared to the 6.6 GHz data),
along with a physically-based hydrological modeling framework that solves for the
complete water and energy budgets and computes the soil moisture instead of using
the API representation. The estimation of soil moisture is carried out by using the
radiative transfer model for the vegetation canopy (Choudhury et. al., 1990) and
the atmospheric attenuation model (Choudhury, 1993). These models have been
validated by comparing the simulated SSM/I brightness with the SSM/I observed
brightness temperatures.
The work presented in this thesis is in three parts (described in the next section),
each of which builds up to the ultimate goal of soil moisture estimation using the
observed 19 and 37 GHz SSM/I brightness temperature data.
1.6
M o d els and m eth o d s
A coupled soil-canopy-atmosphere model has been put together to answer the sci­
ence questions and fulfill the objectives of this thesis. The land surface model is a
thin-layer representation of the soil hydrology and is based on the work of Mahrt
et. al. (1986). The soil moisture and the surface temperature computed using
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C H A P TE R 1. IN T R O D U C T IO N
13
this hydrological model serves as the bottom boundary condition for the canopy
radiative transfer model (Choudhury, et. al., 1990). The canopy radiative transfer
model solves the radiative transfer equation for scattering and extinction in the
plant canopy. The canopy-top brightness temperatures computed from the canopy
radiative transfer model are attenuated in their passage through the atmosphere
by atmospheric oxygen and water vapor before reaching the satellite. This atten­
uation is quantified using the atmospheric attenuation model (Choudhury, 1993).
This coupled land surface-canopy-atmosphere model is used to study : (a) the sim­
ulation of brightness temperatures and its comparison with the observed brightness
temperatures; (b) the effect of the heterogeneities in vegetation and rainfall on the
simulated soil moistures and brightness temperatures and (c) the inversion of the
observed 19 and 37 GHz SSM/I brightness temperatures to obtain soil moisture
estimates.
The first part of the thesis deals with simulation of soil moisture and soil tem pera­
ture using a thin layer hydrological model. The thickness of the top layer is 1 cm.
This is necessary since the penetration depth of the SSM/I sensor is not more than
a few tenths (one-tenth to one) of the wavelength (Ulaby et. al., 1986). Therefore,
since the wavelengths in question are 1.5 cm (19.4 GHz) and 0.8 cm (37 GHz), a 1
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C H A P T E R 1. IN T R O D U C T IO N
14
cm upper layer would be closer to the SSM/I penetration depth rather than using
hydrological models that have the upper layer as the root zone (depth of about 50
cm) as in the case of Topographic Land Atmosphere Transfer Scheme (TOPLATS;
Famiglietti et. al., 1994), Variable Infiltration Capacity (VIC-2L; Liang et. al.,
1994) or Simple Biosphere Model (SiB; Sellers et. al., 1986). To use an upper
thin layer model, attention must be paid to the asymmetric difference caused by
a thin upper layer and a thicker lower layer. In this regard, the parameterizaC
tion of Mahrt and Pan (1984), which recognizes this problem and provides the
necessary correction to counter the truncation errors in a finite difference scheme,
is used. The scheme is tested by comparing with a very detailed finite element
model (Mahrt et. al., 1984). In addition, the moisture gradient driven upward
flux th at provides for soil evaporation from the 1 cm is included. This is neglected
in the other schemes mentioned above. The thin-layer hydrological model is used
to simulate at an hourly time step for a period of 10 years between 1980-89 for the
Kings Creek catchment in FIFE. The model is calibrated using the stream flow
data at Kings Creek gauging station for a period of five years (1980-1984) and is
validated using stream flows for the remaining five years (1985-89). The model
predicted soil moistures and temperatures are compared with the observed values
for the four intensive field campaigns (IFCs) in the summer and fall of 1987.
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C H A P T E R 1. IN T R O D U C T IO N
15
The second part investigates the effect of the heterogeneities in vegetation and
rainfall input on the simulated soil moistures and the 19 and 37 GHz SSM/I mi­
crowave brightness temperatures using the coupled soil-canopy-atmosphere model.
This study also involves the issue of inversion of observed SSM/I brightness tem ­
peratures to obtain soil moisture estimates. The SSM/I inherently averages over
the heterogeneities in soil moisture in its footprint and reports a single value. The
studies investigate if there is a bias in the estimated soil moisture using the SSM/I
observed brightness temperatures because of the averaging involved in the obser­
vation process.
The third part deals with the simulation and validation of the 19 and 37 GHz
brightness temperatures and estimation of soil moisture using observed SSM/I
brightness temperature data for a 5° (latitude) X 10° (longitude) box centered on
the Red River basin for a period of one year between August 1, 1987 and July 31,
1988 using the coupled land-canopy-atmosphere model. The region is completely
modeled hydrologically by using the hourly meteorological data from the surface
airways stations and the rainfall data from the Manually Digitized Radar (MDR).
The soil moisture and the surface temperature simulated using the hydrological
model are used to simulate the satellite brightness temperatures using a canopy
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C H A P T E R 1. IN T R O D U C T IO N
16
radiative transfer model (Choudhury et. al., 1990) and an atmospheric attenuation
model (Choudhury, 1993). The simulated brightness temperatures are compared
with the SSM/I observed brightness temperatures. The SSM/I observed bright­
ness temperatures are used to estimate soil moisture using the canopy radiative
transfer model and the atmospheric attenuation model. The SSM/I derived soil
moistures are compared with the hydrological model simulated soil moistures. The
SSM/I derived surface soil moisture is used in conjunction with the hydrological
model to estimate cumulative monthly evaporation, and this result is compared
with estimates derived using atmospheric budget analysis. The SSM/I derived
monthly mean surface soil moisture is discussed in conjunction with monthly rain­
fall accumulation and the monthly mean leaf area index.
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C h a p ter 2
A S o il-C a n o p y -A tm o sp h ere
M o d el for u se in S S M /I
H y d ro lo g ica l In v estig a tio n s
2.1
In tro d u ctio n
Surface soil moisture is the most important factor for partitioning rainfall into
infiltration and runoff. The land surface evaporation and transpiration depend
on the amount of soil moisture available. Together, surface temperature and soil
moisture determine the land surface heat and water balance. In large scale mod17
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C H A P T E R 2. A SO IL-CA N O PY-ATM O SPH E RE M ODEL
18
eling, the soil moisture and temperature are important in deciding the depth of
the planetary boundary layer, circulation/wind patterns (Mahfouf et. al., 1987,
Lanicci et. al., 1987 and Zhang et. al., 1989) and regional water and energy bud­
gets. It is therefore important for improved modeling of these quantities and the
use of observational data on scales comparable to the modeling scales. Satellite
data is useful in this regard. Research in, and utilization of remotely sensed data is
important for the purposes of understanding spatial variability and regional scales,
and in verifying land surface parameterizations (Wood, 1991).
The motivation for the development and testing of a thin layer model for land
hydrology stems from the desire to use satellite remote sensing for purposes of
soil moisture estimation. The Special Sensor Microwave Imager (SSM/I) is a four
frequency (19, 22, 37 and 85 GHz), dual polarization (horizontal and vertical,
except for 22 GHz, which has only horizontal polarization) sensor. The resolution
of the SSM/I is about 56k m at 19 GHz and 33km at 37 GHz, which are the
frequencies being used for soil moisture sensing. The surface tem perature and soil
moisture form the boundary conditions for microwave radiation emanating from
the soil. The penetration depth of the SSM/I sensor would be in the order of
one-tenth of the wavelength to a wavelength (Ulaby et. al. 1986), which means
the contribution thickness to the microwave radiation would be 0.1 to 1.5cm in the
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C H A P T E R 2. A SO IL-CANO PY-ATM O SPH ERE M O D EL
19
case of 19 GHz and 0.08 to 0.8cm in the case of 37 GHz. Hence, .if we wish to use
the SSM/I sensor data at 19 and 37 GHz for soil moisture sensing, the hydrological
model should have a thin upper layer and predict the surface tem perature and soil
moisture.
However, there is no such model readily available. Most of the hydrological
models have an upper layer of 50cm or so, which corresponds to the root zone
depth (Famiglietti et. al., 1994; Liang et. al., 1994). In addition, most of the
hydrological models validate their parameterizations with observed energy fluxes
(latent, sensible and ground heat fluxes) and some times surface temperature.
There has been no checking of both soil moisture and surface temperature in
the validation process. The TOPLATS model (Famiglietti et. al., 1994) has a
50cm upper layer and validates only the evapotranspiration flux. The VIC-2L
model (Liang et. al., 1994) also has a 50cm upper layer and compares the heat
fluxes (latent, sensible and ground) as well as surface tem perature as validation.
However, an omission in both these models is the lack of adequate parameterization
of moisture gradient driven flux from the lower layer to the upper layer to replenish
the soil moisture of the upper layer. This aspect of soil moisture dynamics is very
im portant when modeling the soil column, especially during the morning (6:00am)
overpass of the SSM/I sensor, prior to which the upper layer has been depleted by
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C H A P T E R 2. A SO IL-CA N O PY-ATM O SPH E RE M ODEL
20
evaporation during the previous day and is replenished during the nighttime hours
when the soil evaporation is low.
Therefore, a thin layer model of soil hydrology with a lcm upper layer thick­
ness created. The model is based on assumptions that have been validated by
comparison with a more detailed finite element approach (Mahrt et. al., 1984) to
minimize truncation errors.
The soil column is partitioned into two layers : a top lcm layer and a bottom
layer extending to a depth of 1.0m. The incoming shortwave and longwave radia­
tion is partitioned between the vegetation and the bare soil surface and provides
energy for the evapotranspiration process. Precipitation is divided into infiltration
and runoff depending on the top layer soil moisture. The runoff occurs as satu­
ration excess and infiltration excess. The baseflow is related non-linearly to the
bottom layer soil moisture. The movement of moisture in response to the evapora­
tive demand occurs from the top soil layer in the form of bare soil evaporation, the
canopy interception storage of water and the bottom soil layer through the root
extraction of moisture. The top layer and the bottom layer are coupled to each
other through flux exchanges that are driven by gravity and the diffusive gradient
of soil moisture.
To gain an understanding of the effect of vegetation and soil on the SSM/I ob­
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C H A P T E R 2. A SOIL-CA NO PY-ATM O SPH E RE M ODEL
21
served brightness, temperatures, a coupled soil-canopy-atmosphere model is used
(Figure 2.1. The lcm soil moisture and the surface temperature predicted by the
hydrological model serve as bottom boundary conditions for the canopy radiative
transfer model (Choudhury et. al., 1990). The canopy-top brightness temper­
atures computed by the canopy radiative transfer model are attenuated by the
atmospheric water vapor and oxygen, and modeled using the atmospheric atten­
uation model (Choudhury, 1993). This coupled soil-canopy-atmosphere system is
used to assess and describe the sensitivities of the simulated brightness tempera­
tures to vegetation and soil moisture.
2.2
O v erv iew o f m o d elin g str a te g y
The purpose of this chapter is to
(i) Develop a thin layer hydrological model for water and energy balance that can
be used to predict the top lcm layer soil moisture and the surface tem perature
(ii) Understand the processes and the sensitivities of the SSM/I brightness tem ­
peratures to vegetation and soil moisture
The thin layer model of soil hydrology is first tested in regard to the simula-
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C H A P T E R 2. A SO IL-CANO PY-ATM O SPH ERE M ODEL
22
tions of soil moisture and surface temperature. The hydrological model is used
to simulate hourly water and energy balance fluxes over a period of ten years
(1980-1989) over the Kings Creek catchment in Kansas. The model is calibrated
using daily streamflows over the first five year period (1980-1984) and validated
for streamflows over the next five year period (1985-1989). The soil moisture and
surface tem perature are validated against observations collected during FIFE in
the summer and fall of 1987.
The thin layer model of soil hydrology is coupled to the canopy radiative trans­
fer model through the soil moisture and the surface temperature, which serve as the
boundary conditions for the canopy radiative transfer process. The atmospheric
attenuation model deals with the attenuation due to atmospheric water vapor and
oxygen. The coupled model setup is shown in Figure 2.1.
This coupled soil-canopy-atmosphere model is used to study the sensitivity of
the polarization difference index (which is related to the difference in the vertical
and the horizontal polarization SSM/I brightness temperatures) to vegetation pa­
rameters (stem area index and canopy moisture content), the leaf area index and
the soil moisture content.
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C H A P T E R 2. A SO IL-CANO PY-ATM O SPH ERE M ODEL
2.3
23
T h in layer soil h yd rological m o d el
This section describes the thin layer hydrological model. The model is divided
into two layers - the top layer is lcm thick and the bottom layer is 99cm thick.
The model includes the following processes: infiltration of rainfall, runoff, bare
soil evaporation from the top layer, the exchange fluxes between the top layer and
the bottom layer, subsurface drainage from the bottom layer and transpiration by
vegetation from the bottom layer. All the processes mentioned above are described
in the following subsections.
2 .3 .1
H y d ro lo g ica l m o d e l : W a ter b a la n ce
The water balance for the two soil layers (1.0 cm top layer thickness) and the top
canopy interception storage is given by Figure 2.2
dC_
= P~Pn
dt
d6i
Z1
— Pn — E — R — ql t 2
d&2
Z2~q£ = 9i.2 - 12 - T - Qb
(2.1)
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C H A P T E R 2. A SOIL-CA NO PY-ATM O SPH E RE MODEL
24
(7(0 < C < S) is the amount of intercepted water on the canopy, S being the
canopy storage capacity; the units for S and C are in mm.
$2($r 5- 8 2 < <
8
8
\{ 8 r <
8 1
< 0a) and
a) are the volumetric soil moistures of layer 1 (with thickness zi)
and layer 2 (with thickness z2), qi<2 and q2 are the exchange fluxes from layer 1
to layer 2 and drainage from layer 2; Roots are present in the bottom layer and
extract moisture for transpiration from layer 2 only, T is the transpiration assumed
to come out of layer 2 only, R is the runoff and Pn is the net precipitation reaching
the soil surface, which is given by Pn = P — Sa, where P is the precipitation, if
P > Sa and Pn = 0 if P < Sa where Sa is the available storage in the canopy given
by Sa = S — C. The water table is assumed to lie below the bottom layer, and the
dynamics of the water table are not modeled. Also, the capillary rise from the water
table is not considered. Since the object of this study is to simulate the top lcm
layer soil moisture, it is assumed that the changes in the depth of the water table
do not affect the top layer soil moisture. However, when the water table is close
to the surface (such as an area adjacent to a stream channel), this assumption will
break down. The model is not being used at a fine spatial resolution to simulate
the soil moistures close to stream channels; it is used for a catchment in an average
sense.
The initial conditions for the above set of differential equations is given by C(t =
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CH APTER 2. A SOIL-CANOPY-ATMOSPHERE MODEL
25
0) = C°, 0i(t = 0) = 6\ and d2(t = 0) = 0f.
E v a p o ra tio n an d tra n sp ira tio n
In c o m in g ra d ia tio n
Given the observations at the top of the canopy for
incoming shortwave radiation R ,d and longwave radiation Rid (signifies shortwave
and longwave downward), the incoming shortwave and longwave radiation for the
soil ( R ad,s and Rid,, respectively) and vegetation (R,d,v and Rid,v respectively) are
given using Beer’s Law (Choudhury et. al., 1988)
Rad,, = Rad e x p ( - ^ L )
Rid,a
= Rid exp (~[lL)
Rad,v — Rad( 1
Rid,v
exp (
^X.Zy))
= Rid( 1 - exp(-/J.L))
(2.2)
where fi is the extinction coefficient, 0.35 for grasses (Eagleson, 1982; Larcher,
1975) and L is the leaf area index.
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C H A P T E R 2. A SO IL-CA N O PY-ATM O SPH E RE M ODEL
R e sista n ce
26
The aerodynamic resistance for the transfer of.heat (rah,s) and
water vapor (rav,s) for bare soil is given by (Brutsaert, 1982)
( 2 ' 3 )
and for vegetation canopy for heat (rah,v) and water vapor (rav>v) by
r- ' = - * - p s f e ) N
i S
r 11,
(2A)
where k is the Von Karman constant, u(za) is the air velocity at the reference level
za, d, is the zero plane displacement over bare soil, dv is the zero plane displacement
over vegetation, z0>, is the roughness length over bare soil and z0i„ is the roughness
length over vegetation. The canopy resistance rc is parameterized as a function of
leaf area index (Feyen et. al., 1980; Famiglietti et. ah, 1994) as
r mat■
tn
rc = - f L
'
(2.5)
r £ in is the minimum stomatal resistance.
P o te n tia l ev a p o ratio n and tra n s p ira tio n
The calculation of potential
bare soil evaporation (Ep), potential vegetation transpiration (Vp) and potential
evaporation from the canopy interception storage (Ev) is described below (Famigli­
etti, 1992). The bare soil temperature for potential evaporation (Tap), the vege­
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C H A P T E R 2. A S O IL-CA N O PY-AT M O SPH E RE M ODEL
27
tation canopy temperature for potential transpiration (Tvp) and the vegetation
canopy temperature for potential evaporation of intercepted water ( )
are com­
puted using the energy balances as follows:
(a) bare soil temperature Tap for potential evaporation
RsdAl-<Xs)+esRi'i,a- e 3*T?p— t ° ^ ( e*(Tap) - e a) - ^ ( T ap- T a) - ^ ( T ap- T 2) = 0
7^av,a
Tah,a
D
( 2 .6 )
(b) vegetation canopy temperature Tvp for potential transpiration
- a ,) + evR,d,v - evaTfp -
7(7c + r av,v )
Ae*(Tvp)- ea) -
Tvp - T„) = 0
r ah,v
(2.7)
(c) vegetation canopy temperature for potential evaporation of intercepted wa­
ter, Tap
R . d M -<*») + ^ R u , v ~ evaT,%-
'y7'av,v
- ea) -
r ah<v
- T a) = 0 (2.8)
The first three terms are the net radiation quantities, the fourth term is the latent
heat flux, the fifth term is the sensible heat flux and the last term is the ground
heat flux (in Equation 2.6 only) in all three equations (2.6-2.8) above. The various
quantities in the above equations are: a is the albedo, e the emissivity, a is the
Stefan-Boltzman’s constant, 7 is the psychometric constant, r av and r ah are the
aerodynamic resistance to water vapor transfer and heat transfer respectively, (the
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C H A P T E R 2. A SO IL-CA N O PY-ATM O SPH E RE M ODEL
28
subscripts s and v denote soil and vegetation respectively); rc is the canopy resis­
tance due to the opening and closing of the stomata, ea is the vapor pressure of
ambient air, e*(T) is the saturated vapor pressure corresponding to temperature T
given by e*(T) = 611 exp ((17.27T —4714.7)/(T —35.7)), T is the temperature in
degrees Kelvin (Raudkivi,1979), Cp is the specific heat corresponding to constant
pressure, D is the diurnal damping depth, T 2 is the temperature at D taken to
equal the average air temperature for the day (Deardorff, 1978), k is the thermal
conductivity (in J/( m sK )) , whose variation with soil moisture is given by Pielke
(1984) as k = 419 exp (—(Pf + 2.7)) for Pf < 5.1, and as k = 0.172 for Pf > 5.1,
where Pf = logw^l){6), ip(6) being the moisture potential in cm.
It can be noticed that the potential evaporation from the interception storage of
the vegetation proceeds with no resistance from the vegetation (Sellers et. al.,
1986). After knowing the temperatures corresponding to the potential rates, the
potential rates can be evaluated as
(a) bare soil potential evaporation Ep
E- =
<2 -9 )
(b) vegetation canopy potential transpiration Vp
p
( 2 - 1 0 )
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C H A P T E R 2. A SOIL-CA NO PY-ATM O SPH E RE M ODEL
29
(c) interception storage potential evaporation Ev
E' = V
T ^ e' ^
Pw-L' 7 r av
- «•)
(2-11)
where pw is the density of water and L is the latent heat of water for evaporation.
A c tu al ev a p o ra tio n an d tra n sp ira tio n
The actual bare soil evaporation
will attem pt to proceed at the maximum rate by letting the surface of the top soil
layer dry up to the residual value (0r ). When the soil is still unable to meet the
potential demand imposed on it by the atmosphere, the soil will evaporate at a
maximum rate at which the surface dries out to the residual soil moisture (0r ).
Mathematically, the bare soil evaporation E proceeds at a potential rate if the
surface soil moisture 6\a > 6r, so we calculate what the surface soil moisture ($ia)
would be for the imposed potential Ep when 6i is the soil moisture assigned to the
mid-level of the top layer (at depth of Zi/2),
6U = 91 - (Ep + K(9))(Zl/2)/D(6)
(2.12)
When the computed &is is less than 6r, the residual soil moisture content, the
evaporation is less than the potential, else it equals the potential (Mahrt et. al.,
1984). 6is takes into account the variations of hydraulic conductivity K and hy­
draulic diffusivity D with soil moisture 6. Hence, if the computed B\, is less than
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C H A P TE R 2. A SOIL-CA N O PY-ATM O SPH E RE MODEL
30
the residual soil moisture 0r there is not enough moisture in the top soil layer for
satisfying the potential evaporation rate.
The bare soil evaporation rates are given by
E -- Ep
E = £>(0X0!- 0r)/(* i/2) - K (0)
6ia > 0r
0l4 < 0r
(2.13)
where both K(0) and D(0) are computed as an average between the surface and
the mid-level of the top layer (0i). The soil resistance to evaporation is included
in the form of the decrease of soil conductivity K (0 ) and soil diffusivity D(0)
with decrease in soil moisture 0. These are parameterized using the Brooks-Corey
relations outlined in this section (Equation 2.16).
The actual transpiration from the vegetation should be a function of soil mois­
ture, which controls the osmotic potential at the roots. There will be some critical
value of soil moisture (0*) when the plant can no longer supply water for tran­
spiration at the potential rate. This has been observed by variousinvestigators
(Denmead et. al., 1962; Saxton et. al., 1974). The vegetation transpiration is
computed as (Neghassi, 1974),
0 2 - 0 „ lA
e*-0v
0 < 0*
V = Vp
0 > 0*
(2.14)
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C H A P T E R 2. A SOIL-CA NO PY-ATM O SPH E RE M ODEL
31
where A and 6* are parameters. The value of 6* is the transitional volumetric soil
moisture at which the transpiration drops off from the potential value; 0W is the
wilting point for the canopy.
The evaporation from the vegetation canopy storage is computed as (Rutter
et. al., 1975),
EC= EV^
EC= EV
C<S
C>S
(2.15)
where C is the amount of intercepted water on the canopy whose storage capacity
is S. The initial interception water in the canopy is given by C° and is a parameter
to be ascertained. The storage capacity (5 in m m ) is related to leaf area index
(L ) (Dickinson, 1984; Sellers et. al., 1986) by S = 0.2L (Dickinson, 1984). Leaves
covered with a film of water (having intercepted water on them) are assumed not
to transpire (Rutter, 1975). The intercepted water is first evaporated before the
vegetation starts to transpire. When C = 0, in which case there is no intercepted
water storage on the canopy, there is no interception storage evaporation Ec = 0.
If C > Evdt, then E c is given by the above expression and V — 0 as the potential
is satisfied by the intercepted water on the canopy. If C < Evdt, then the potential
is not satisfied completely by the intercepted water on the canopy and additional
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C H A P T E R 2. A SO IL-CA N O PY-ATM O SPH E RE M ODEL
32
transpiration by the canopy is needed. In this case, all the intercepted water would
be evaporated first, i.e., Ecdt = C, and the deficit of the potential Edef = Evdt —C
would equal the transpiration by the vegetation Vp = Edef to compute the actual
vegetation transpiration.
Soil m o istu re fluxes
Soil m o istu re versus h y d rau lic c o n d u c tiv ity relatio n s
The variation of
soil hydraulic conductivity with soil moisture is given by the Brooks-Corey relations
as (Brooks and Corey, 1964) given by
K{4,) = K . ( ^ jp j +
tP x
Pc
o ty) = oT + (oa - eT)
V’ > V’c
K(ip) = K a
ip <tf)c
6{xjj) = 0a
(2.16)
where 6a is the saturated soil moisture content, 0T is the residual soil moisture
content and m is the pore distribution index (Brooks-Corey parameter), ipc is
the air-entry suction head and K a is the saturated hydraulic conductivity. The
parameters for the above set of relations is obtained from Rawls et. al., 1982 for
various soil types.
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C H A P T E R 2. A SOIL-CA NO PY-ATM O SPH E RE M ODEL
E x ch an g e fluxes
33
The drainage from layer 1 to layer 2, qi;2 (if > 0, flux is
from layer 1 to layer 2, else vice-versa) is given by (Mahrt et. al., 1984)
d6
9i,2 = K{max(0u 02)) + D(max(0u 02)) —
(2-17)
where max(6i,62) is the larger of 6\ and 02. The usage of max(0i,02) follows
Mahrt et. al., (1984) to reduce the truncation errors caused by asymmetric finite
differencing between layer 1 and 2. This formulation follows the moisture move­
ment from ’’upstream” (where the movement) originates and helps in reducing
truncation errors. q2 is the drainage flux from layer 2,
92 = K{02)
R u n o ff an d su b su rface flow
(2.18)
The overland runoff (R ) is the sum of the
infiltration excess and the saturation excess,
R = R ie + Rse
(2.19)
Rie is the infiltration excess and R se is the saturation excess. The term satura­
tion excess here implies the runoff when the top soil layer is saturated (the bottom
layer need not be).The infiltration capacity of the soil is given by R ice as (Mahrt
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C H A P T E R 2. A SOIL-CA NO PY-ATM O SPH E RE M ODEL
34
et. al., 1984)
R cie = D(8a)(8a - * i)/(zi/2 ) + K(8a)
(2.20)
Equation 2.20 states that when precipitation occurs, the surface gets saturated,
and there are two forces that play a role in the infiltration of water : (a) gravity
at the saturation rate K{8„) and (b) the diffusion gradient between the saturated
surface and the unsaturated top soil layer D(83)((83—8i)/zi). Based on the infiltra­
tion capacity, the infiltration excess runoff is determined as the difference between
the net precipitation rate and the infiltration capacity over the time interval of
precipitation AtT as,
Rie = (Pn - J £ ) A t r
P > Rl
Rie — 0
P < R cie
(2.21)
The saturation excess runoff is given by the difference between the soil moisture
content and the saturation soil moisture content,
Rse = (01 - 8a) z !
8X > 8a
Rse = 0
81 < 8 a
(2 .2 2 )
There is no surface runoff or infiltration when the air temperature is less than
273K , as the precipitation is considered to be in the form of snow.
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C H A P T E R 2. A SO IL-CA N O PY-A TM O SPH E RE MODEL
35
The subsurface flow from the lower layer constitutes the base flow and is ex­
pressed using the ARNO non-linear flow equations (Francini, et. al., 1991; Liang
et. al., 1994).
Qb = Q &
Ob
Q* = Q l ~ + ( « “" - Q -JW /e.))
02 < e*h
> et
(2 .23)
where Q™ax represents the maximum baseflow, 61 is the soil moisture acting as a
cutoff between the linear and non-linear base flow dependence on lower layer soil
moisture and Q l is the maximum value of the baseflow in the linear region are
parameters that must be ascertained.
The total discharge (Q) is given by the sum of the overland runoff (R ) and the
base flow (Qb),
Q = R + Qb
2 .3 .2
(2.24)
H y d r o lo g ic a l m o d e l : E n er g y b a la n ce
After the water balance is computed, the energy balance is re-solved to yield the
temperatures of the bare soil surface, vegetation and the composite of the soil and
vegetation canopy as follows :
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C H A P T E R 2. A SO IL-CA N O PY-ATM O SPH E RE MODEL
36
(a) bare soil temperature Ts
R, dA 1 - a s) + e,Rldi3 - EgcrT* - EpwL - ^ ( T a - Ta) - ^ ( T 3 - T2) = 0 (2.25)
r ah,n
D
(b) vegetation temperature Tv
n
i2ad,v(l - o„) + evRid>v - evaT^ - VpwL - ^ _ £ ( Tv - T a) = 0
(2.26)
r ah,v
(c) composite soil-vegetation tem perature T3V
R 3d( 1 - a ) + eRld - ecTt, - E T p wL - ^
( Tav - Ta) - ^ ( T3V - T 2) = 0 (2.27)
Tah
D
The first three terms are the net radiation quantities, the fourth term is the
latent heat flux, the fifth term is the sensible heat flux and the last term is the
ground heat flux (in Equation 2.25 only) in all three equations (2.25-2.27) above.
The vegetation temperature could be a result of evaporation from the intercepted
storage alone, in which case V is replaced by Ec, or if there is a combination of
evaporation from the intercepted storage as well as transpiration, V = V + Ec
in the above equation. Depending on the scenario, the evapotranspiration E T is
given by E T = E -f V or E T = E + Ec or E T = E + V + E c.
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C H A P T E R 2. A SOIL-CA N O PY-ATM O SPH E RE MODEL
2 .4
37
C an op y ra d ia tiv e tran sfer m o d e l
The radiative transfer model for the vegetation canopy is a part of the coupled
soil-canopy-atmosphere model used in the brightness temperature simulations as
well as in the sensitivity studies examining the role of heterogeneities on bright­
ness temperatures. The canopy radiative transfer model described in this section
follows the description of Choudhury et. al., 1990. The land surface hydrological
model (described above) computes the soil moisture and surface temperature of a 1
cm layer, which serves as the bottom boundary conditions for the canopy radiative
transfer model. The microwave radiation originating from the soil surface is mod­
ulated by the overlying vegetation canopy, resulting in the canopy-top brightness
tem perature values. This canopy-top brightness temperature is attenuated by the
atmospheric water vapor before it reaches the satellite sensor.
The following sections describe the theoretical basis for the expressions of bright­
ness temperature, which is derived from the equations for radiative transfer. The
various approximations and parameterizations for the variables involved are also
described.
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C H A P T E R 2. A S O IL-CA N O PY-AT M O SPH E RE M ODEL
2 .4 .1
38
C a n o p y r a d ia tiv e tra n sfe r
The surface temperature T0 and the top layer soil moisture 6\ are used in the
canopy scattering model (Choudhury et. al., 1990) to compute the canopy-top
horizontally and vertically polarized brightness temperatures.
The radiative transfer model treats the interaction of microwave radiation from
the soil with the vegetation branches, stems and leaves. The model is based on a
high frequency approximation - the extinction cross section area of the scatterer
equals their geometrical shadow area. The model also assumes that there is no
transmission of radiation by the stems and the branches. All radiation on the stems
and branches is absorbed. The model is analytic and provides an expression for
the canopy-top brightness temperature using the two-point Gaussian quadrature,
which results in a system of two coupled ordinary differential equations with the
bottom boundary condition dictated by the soil moisture and surface tem perature
and the top boundary condition dependent on the radiation from the sky incident
on the canopy. This brightness tem perature is then attenuated by the atmospheric
water vapor before it reaches the satellite.
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C H A P T E R 2. A SO IL-CA N O PY-ATM O SPH E RE M ODEL
E q u a tio n s an d b o u n d a ry co n d itio n s
39
The canopy top brightness temperature
Ts(7 ,p) is related to the at-satellite brightness temperature Tg(.A,7 ,p) for zenith
angle 7 of the sensor, polarization p (horizontal or vertical) and A (the altitude of
the radiometer) by
Tb ( A , 7 , p) = ra(A, ~r)TB(7 , P) + Tatm(A, 7 ) •
(2.28)
where ra(A, 7 ) is the transmissivity of the atmosphere, and Tatm(A, 7 ) is the radi­
ation entering the radiometer from the atmosphere.
The canopy-top brightness temperature T b (j , p ) will be derived followed by the
derivation and discussion of Ta{A,"f) and Tatm(i4, 7 ). The radiative transfer equa­
tion is given by (Choudhury et. al., 1990, Stephens et. al., 1988) as
=W b
P) +
P (P>
p ) dP + (1 ~ wb ) ) r o] (2.29)
where I(x, p) is the radiance at depth x within the canopy (the top of the canopy
is taken as x = 0, and the bottom of the canopy is taken to be x = 1) at an
angle whose cosine is p (p = cos(7 ), p > 0 for radiation direction towards soil and
p < 0 for radiation direction away from soil), k(p) is the extinction coefficient,
u>(p) is the single scattering albedo, P(p, p ) is the phase function (the probability
that the element will scatter incident radiation at p to direction p) and To is the
soil/canopy temperature (both soil and canopy are assumed to be at the same
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C H A P T E R 2. A SOIL-CA NO PY-ATM O SPH E RE M ODEL
40
temperature).
The boundary conditions are given by
1(0, fJ.)
7(1,- f i )
= T aky
= R ( n ) I( l ,n ) + (1 - R(fi))T0
(2.30)
where Taky is the intensity of atmospheric radiation incident on the top of the
canopy and R(fJ.) is the reflectivity of the soil. The first condition states that the
downwelling radiation at the top of the canopy is the sky radiation, and the second
condition states that the upwelling radiation at the bottom of the canopy equals
the emissivity of the soil plus the incident radiation reflected at the soil surface.
The canopy-top brightness temperature is given by
TB(l t p) = I ( 0 , - f i )
E x tin c tio n coefficient an d single s c a tte rin g alb ed o
(2.31)
We now proceed to
calculating the extinction coefficient and the single scattering albedo, which are
functions of vegetation characteristics.
The extinction coefficient for leaves (Ajj(/x)) is given by
kti/i) = WeNH}i
(2.32)
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C H A P TE R 2. A SOIL-CA NO PY-ATM O SPH E RE MODEL
41
where cre is the scattering cross-section, N and H are the number densities of
scattering elements and canopy height respectively. The approximation for the
high frequency case (van de Hulst, 1962) is \/2ir << size of scattering elements
and the previous equation simplifies to (using the fact that the extinction crosssection equals the geometrical area of the element),
[aeNH}t = atNiHGi(ii)
(2.33)
where cre = aiGi(fi.), Gi(fi) is the cosine of the acute angle between the leaf normal
and the radiation incidence direction, and a/ is the area of the leaves. Using the
simplifications aiNiH = L, where L is the leaf area index, we get
[aeNH], = LGi(fi)
(2.34)
where Gi(fi) is taken equal to 0.5, which is the case for uniform distribution of
leaves.
The extinction coefficient of the stems and branches (i.e the woody components)
is given by
[aeNH]w = [aeNH] stems 4" W e N H } ^ ^ ,
(2.35)
In a similar fashion to the expressions for leaves, we can write the expressions for
the stems and branches as
[aeNH }atem, = aaN aH{ 1 - /z2)1/2
(2.36)
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C H A P T E R 2. A SOIL-CA NO PY-ATM O SPH E RE M ODEL
42
The geometrical shadow area of stems (modelled as cones) is give by a„ = S5/ir,
where S3 is the surface area of the stems. If we define 77 as the ratio of the branch
and stem areas (aiNbH/ a , N , H ) and % as the ratio of stem surface area to ground
area (x = S , N sH ), the extinction coefficient for the woody components is given
by
[aeN H ) w = %
7r
- /z2)1/2 + r j G M )
(2.37)
The value of x varies from 0.2 to 0.6 for temperate deciduous forests and that of 77
from 1.8 to 3.6 for shrubs and 5 to 6 for mature closed temperate deciduous forests
(W hittaker et. al., 1967; W hittaker et. al., 1974; Cannell, 1982). The canopy
extinction coefficient is given by
fc(p) = L G f o ) + -[(1 - V2)1' 2 + vGb(fi)}
(2.38)
The single scattering albedo tu(/i) is the ratio of the scattering and extinction
coefficients
/ \ _ LGi(fi)Qi + (x/tQ[( 1 ~ P2Y /2Qs + 77Gb(n)Qb]
~
LGi(fi) + ( x /7r)[(l - P2)1/2 + r,Gb{p)
,
[
.
where Qi, Qs and Qb are the scattering efficiencies of the leaves, stems and branches
respectively.
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C H A P T E R 2. A SOIL-CANO PY-ATM O SPH ERE M OD EL
P h a s e fu n ctio n
p((
43
The effective phase function (P((/x,//)) is given by,
'n = LGi(fi)QiPi(fi, fi') + (xftr)[(l - /J.2)1/2Q3Pa{n, fi') + 7]Gb(ix)QbPb(fi, //)]
}
LGi(fj,)Qi + ( x /7r)[(l - ^
2Qs + vGb{ii)Qb]
(2.40)
The phase functions for the leaves (Pz(/x, //)), stems (P4(/x,/x*)) and branches
(Pb(/JL, fj,')) and the effective phase function satisfy the normalization as
1
2J
1
,
rl
Pl{p>
Z*1
,
=1
i
2
=
1
1 p
/
2 7-i Pb^ ’M^
= 1
=1
(2.41)
The scattering efficiency of the leaf Qi is given as
Qi = Ri + Ti
(2.42)
where Pj (effective reflection coefficient of leaf) and TJ (effective transmission co­
efficient of leaf) are given by Ulaby et. al., 1981 as
Ri
= ri[ 1 +
rp
T‘
-
i,a( l-r ? ).
1 - tfrf
^(1
Ti) )
1 - ifr f
/D in’!
(2 '43)
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C H A P T E R 2. A SO IL-CA N O PY-ATM O SPH E RE M ODEL
44
where ri and f; are the single reflectivity and single transmissivity, of a leaf.
The single transmissivity of a leaf i/is given by
t / = exp(—47rdn2/A)
(2.44)
where d is the effective leaf thickness, n 2 is the imaginary part ofthe refractive
index (square root of dielectric constant e*) of leaf i.e 712 = Im(el)/2)and A is the
radiation wavelength.
The reflection coefficient for the horizontal polarization ( r f ) and vertical polariza­
tion (rj/') is given by, (using Fresnel relations)
rf
v
D
= Qirfo(P)
+
(1
-
qi)rfo(P)
qirfoW) +(!- ®)rS
rfM
cos (3 — (ei — sin2/3)1/2 '2
cos /3 —(e/ + sin2/3)1/2
rfM
e/ cos /3 —(e/ —sin2 /3)1/2
e/ cos /3 —(ei + sin2 /3)1/2
(2.45)
where qi is the polarization mixing coefficient used to account for the depolarization
of radiation due to the coordinate system of the leaves not being identical to that
of the smooth ground surface (in the case of random leaf orientation qi = 0.5,
which is adopted for this study), cos((3) = G/(/i) (Gi(fi) has been discussed earlier)
and et is the leaf dielectric coefficient. The dielectric constant of the leaf e; (for 37
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C H A P TE R 2. A SOIL-CA NO PY-ATM O SPH E RE M ODEL
45
GHz) is computed using the formulation of Ulaby et. al., 1987 as •
ei
= er + ef vf + envn
er
= 1.7 + 3.2mc + 6.5m?
ef
= 20.0 + i30.5
en
= 5.5 + i2.5
Vf
Jn
= m c(0.82mc + 0.166)
31.4m?
1 + 59.5m?
(2.46)
where er is the non-dispersive residual dielectric component, ey and en are the
free-water and the bound water dielectric components uy and vn are the free and
bound watervolume fractions, i = y/—l and mcis the leaf volumetric moisture.
When, 19 GHz, ey = 39.6 + i37.4 and en = 6.6 + z3.3. The effective thickness of
the leaf (d) is related to its oven dry thickness (d0) and moisture content m c as,
an
d= r-2 1 —mc
(2.47)
The scattering in the forward direction a/ is given by
a' = w tr L
<2'48>
The phase function for the leaf is given by
Pi(fi, fi) = 2aiS(fi - i i ) + (1 - a t)
(2.49)
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C H A P T E R 2. A SOIL-CA N O PY-ATM O SPH E RE M ODEL
46
The scattering efficiency for the stem for horizontal and vertical polarizations (hpol and v-pol) is given by
Q* =
t %o{P')
h-pol
Q* = rlo(P') V - P°l
(2-50)
The stem phase function is given by
=
(2.51)
where r ^ 0(/3') and r^ 0(/3,) are the horizontal and vertical polarization Fresnel re­
flectivities and fl' = 7r/2 —7 , where 7 is the zenith angle. The scattering efficiency
for the branches for horizontal and vertical polarizations (h-pol and v-pol) is given
by
Qb = r t
Qb
= t'X
h — pol
v ~ P°l
(2.52)
The branch phase function is given by
Pb(p,v) = 1
(2.53)
The phase functions and the scattering efficiencies of the leaves, stems and branches
can be substituted into the expression for the effective phase function P ((fi, p ).
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CH A P T E R 2. A SOIL-CANO PY-ATM O SPHERE MODEL
Soil r eflec tiv ity
The reflectivity of the soil
47
R(n) is determined by the soil mois­
ture and content using the mixing formula for soils (Wang et. al., 1980).
The wilting point {WP) volumetric soil moisture is determined as
W P = 0.06774 - 0.000645^41VD + O M m C L A Y
(2.54)
where S A N D and C L A Y are the sand and clay contents in percent dry weight of
the soil. The transition soil moisture content (9t) is related to the wilting point
soil moisture as
9t = 0.49WP + 0.165
(2.55)
The dielectric constant for soils is given by
=
+ (P — 9i)ea + (1 —P)er 6\ <
Q
— £»-}-(
Ot
At
= 9t ex + (0j — 6t)ew + (P — Qi)ea + (1 —P )er
ex = e» + (cu, - e,)A
> 6t
(2.56)
where A is a best fit parameter and is given by A = —0.57WP + 0.481; ew, ea,
ei and er are the dielectric constants of water, air, ice and rock respectively. The
dielectric constant of water is given by the Debeye relaxation formula (Ulaby et.
al., 1986) and the complex dielectric constant (denoted as (real part, imaginary
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C H A P T E R 2. A SO IL-CA N O PY-ATM O SPH E RE M ODEL
48
part)) is (39.6, 37.4) at 19 GHz and (19.3, 29.5) at 37 GHz frequencies. The
dielectric constants of air, rock and ice are taken to be (1,0), (5.5, 0.2) and (3.2,0.1)
respectively (Wang et. al., 1980).
The reflectivity is evaluated using the Fresnel relations, which were applied in the
previous section to determine the leaf reflectivity, by replacing the leaf dielectric
constant ej with the soil dielectric constant e3. The reflectivity of a rough surface
was related to the reflectivity of a smooth surface by (Choudhury et. al., 1979;
Wang, 1983)
R(ti0) = R ^ mooth\ f i 0) exp( - h )
(2.57)
where h is the roughness parameter which varies between 0 for a smooth field and
0.5 for a rough field.
2 .4 .2
B r ig h tn e s s te m p e r a tu r e
Substituting the above expressions for extinction coefficient, single scattering albedo
and phase function into the canopy radiative transfer equation we get,
= - K (fJ')I(x ^P) + S(fi)
where the variables
K M
=
l g lM
J
^I(x,fi)dfj! + E(fj.)T0
(2.58)
S(n) and E(fi) are defined as
( 1 - r,) + %
7r
-
l -
q
. ) + v G bM }
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CHAPTER 2. A SOIL-CANOPY-ATMOSPHERE MODEL
SM
= LG^
E(it)
= £G|(/*)(1 - <30 + -[(1 7T
49
R' +
- Q .) +
1 - Qt )(2.59)
Using the two-point Gaussian quadrature (Chandrashekar, 1960) and defining
Ii(x)
= I ( x , f i 0)
I2{x)
= I(x,-no)
fi0
=
(2.60)
The above equation of radiative transfer can be written in terms of the downwelling
I\(x) and upwelling J2(o;) radiances (at depth a;) as
= —K(no)h
+ S{po)(h + h )
+
E(/ j,0)To
= ~K(no)l2 + S(fi0) (h + h )
+
E(fio)T0
The above set of simultaneous ordinary differential equations are solved to yield
the brightness tem perature as
TB(T,p)
= h { x = 0)
(2.62)
The brightness tem perature is given by a linear combination of Taky and T0 as
T b = ATaky + (1 - A)T0
(2.63)
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(2.61)
C H A P T E R 2. A SO IL-CANO PY-ATM O SPH ERE M ODEL
50
where A is defined as the effective reflectivity of the soil-canopy system and is
defined using the reflectivity of the canopy A c as
l + 64c
_ 1 - (E(no)/K(no)y/2
c 1 + (E(fi0)/K(iJ,0))1/2
_ (Ac - R(/j,0)) ex p (-2 a)
R(fi0)Ac — 1
a = (3E(fio)K(p0))1/2
2 .4 .3
(2.64)
P o la r iz a tio n d ifferen ce in d e x
The polarization difference index A y is defined as follows.
The atmospheric
transmissivity and the sky temperature are used in determining the at-satellite
brightness temperatures (Tb (A, "f,p)) from the canopy-top brightness tem pera­
tures (Tb(7 ,p)) for polarization p (horizontal or vertical), altitude A, atmospheric
attenuation ra( A , ^ ) and atmospheric radiation entering the radiometer T3ky as
(Choudhury et. al., 1990)
Tb ( A , j , p ) = r 0( ^ 7 ) T B(7>p) -I- Taky
(2.65)
The canopy top brightness temperature can be written as a weighted sum of the
sky contribution and the surface expressed through the surface tem perature T,
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C H A P T E R 2. A SO IL-CANO PY-ATM O SPH ERE MODEL
51
(Choudhury, et. al., 1990),
T b (j , p )
= x(p)Tsky + y
(
p
)
T
(2.66)
where x(p) = 1 —y(p) the coefficient y(p) is a function of the vegetation and soil
moisture and Ta is the surface temperature. The variable y(p) is a function of
frequency and polarization. The polarization difference index is defined as the
difference between the vertical polarization (p = v ) value of the coefficient y and
the horizontal polarization (p = h) value of coefficient y as A F = y ( v ) —y(h). All of
the above variables are a function of frequency. Hence, they would be different for
the 19 GHz frequency than for the 37 GHz frequency. The polarization difference
index is a measure of the difference in the vertical effective reflectivity and the
horizontal effective reflectivity of the soil-canopy system. The effective reflectivity
has been defined (Choudhury, et. al., 1990) to depend on the canopy reflectivity
(which is determined by the vegetation parameters) and the soil reflectivity (which
is determined by the soil type and moisture). The polarization difference index
is a better estimate of soil moisture than the polarization difference of brightness
temperatures since it does not depend on surface temperature, air temperature or
precipitable water. Therefore, variations in polarization index reflect changes in
soil moisture and not in the other variables listed above.
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C H A P T E R 2. A SO IL-CANO PY-ATM O SPH ERE M OD EL
52
The values of the polarization difference index are multiplied by 100 in all
figures, tables and discussions. This is done for the sake of convenience and does
not change the results in any way.
2.5
A tm o sp h eric a tten u a tio n m o d e l
The canopy-top brightness temperatures undergo atmospheric attenuation due to
atmospheric oxygen and water vapor before resulting in the at-satellite brightness
temperatures. The optical thickness was computed based on the total precipitable
water vapor in the atmospheric column V (in mm) (Choudhury, 1993). The op­
tical thickness is related to the atmospheric transmissivity (ra = exp(—Topt/fi).
The effective radiating temperature of the atmosphere Te is related to the air tem ­
perature Ta and the total precipitable water. The total precipitable water and
the effective radiating temperature are used to compute the sky tem perature T,ky,
which serves as the upper boundary condition on the canopy.
Topt = 0.011 + 0.0026V
19GHz
Topt = 0.037 + 0.0021V
2,1GHz
Te = Ta —(8 + 0.06)V
19GHz
Te = Ta - (18 + 0.12)V
2,1GHz
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C H A P T E R 2.
A SOIL-CANOPY-ATM OSPHERE M ODEL
Taky = Te(l —Ta )
53
(2.67)
The atmospheric transmissivity and the sky temperature are used in determining
the at-satellite brightness temperatures (TB(A, 7 ,p)) from the canopy-top bright­
ness temperatures (Tb(7 ,p)) for polarization p (horizontal or vertical), altitude A,
atmospheric attenuation ra(yl,7 ), and atmospheric radiation entering the radiome­
ter TatTn{A ,7 ) (approximated to be equal to T,ky) (Ulaby et. al., 1981) as
TB(A ,7 ,p) = ra(A,'y)TB('y,p) + Taky
(2.68)
The average (T B) and polarization difference (AT) brightness tem perature are
defined as
T b = -1{T b ( A , 1 , V ) + T b {A,1 ,H))
A T = Tb ( A , 1 , V ) - T b (A ,1 , H )
2.6
(2.69)
H y d ro lo g ica l m o d el te stin g an d v a lid a tio n
This section describes the application of the thin layer hydrological model described
earlier. The description of the catchment, the sources of the data, the calibration
of the parameters and the validation using observed data are described below.
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C H A P T E R 2. A SOIL-CA NO PY-ATM O SPH E RE M ODEL
2 .6 .1
54
S ite d e sc r ip tio n
The purpose of the modeling effort was to carry out a ten year simulation over the
Kings Creek catchment along with validation. The calibration of the parameters
was done using the first five years (1980-1984) of the daily streamflow data, and the
simulated streamflow over the next five years (1985-1989) was compared on a daily
basis. Also, comparisons of soil moisture and soil temperature were carried out
over the catchment for data available during the FIFE in the summer of 1987. The
First International Satellite Land Surface Climatology Project Field Experiment
(FIFE) was a land-surface-atmosphere experiment carried out on a 15 X 15 k m site
near M anhattan, Kansas (Sellers et. al., 1992). This area is covered by tallgrass
prairie, and it consists of rolling hills. The goals of the experiment (as outlined
in Sellers et. al., 1992) were to carry out upscale integration of models from a
plant scale to a scale amenable to the use of remotely sensed satellite data, and to
test applications of satellite data and validate hydrological models of land surface
processes. The hydrological model described above is applied to the 11.7 k m 2 Kings
Creek catchment located in the northwestern corner of the FIFE site. The field
experiment was carried out in four distinct durations (termed as IFCs - Intensive
Field Campaigns) during IFC-1 (June 1- June 6, 1987), IFC-2 (June 25 - July 11,
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C H A P T E R 2. A SO IL-CA N O PY-ATM O SPH E RE MODEL
55
1987), IFC-3 (August 6 - August 21, 1987) and IFC-4 (October 5 - October 16,
1987). The simulated surface soil moistures and temperatures are compared with
the observations during these periods on an hourly basis.
2 .6 .2
D a ta and p a r a m e te r s
The surface airways data from the Topeka, Kansas are on a hourly basis are EarthInfo’s NCDC (National Climate Data Center) surface airways data product. The
variables used here from that database are air temperature, dew point tempera­
ture, air pressure, wind speed, cloud height (defined as the height of the lowest sky
cover layer more than 1/2 opaque), total sky cover and wind speed. The ten year
(1980-89) hourly rainfall data was obtained from the Tuttle Creek rain gauge. The
rainfall data for the duration of the FIFE was obtained from the FIFE Information
System and used in the simulations. The same was the case for the meteorological
data for the periods during the Intensive Field Campaigns where observed data
was available for Kings Creek, those data were used in place of the Topeka Surface
Airways data. The incoming shortwave radiation is modeled using the two-stream
approach outlined in Dubayah et. al., 1990 and Dubayah, 1992. It is corrected
for cloud cover effects using an empirical correction factor 1 —(1 —K ) N , where
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C H A P T E R 2. A SOIL-CA NO PY-A TM O SPH E RE M ODEL
56
K = 0.18 + 0.08532, z is the cloud base altitude in k m and N is the fraction of sky
covered with clouds (Eagleson, 1970). The incoming longwave radiation is given by
SaO’T^, where ea is the clear sky atmospheric emissivity dependent on atmospheric
water content (Idso, 1981) given by ea = 0.74 + 0.0049e (Bras, 1990) and e is the
vapor pressure in mb, Ta is the air temperature and a is the Stefan-Boltzmann
constant. The incoming longwave radiation is corrected for cloud effects using the
fraction of cloud cover N as 1 + 0.177V2 (TVA, 1972). The data for the air temper­
ature, vapor pressure, cloud cover and cloud base altitude are obtained from the
Earthlnfo surface airways data set for Topeka, KS.
The vegetation data has been obtained from the University of Maryland repro­
cessed NOAA Global Vegetation Index Data Product (Goward et. al., 1993). This
NOAA-GVI has been put together from measurements made by the Advanced Very
High Resolution Radiometer (AVHRR) on board NOAA polar orbiting satellites.
The data comprises three years (1983,1987,1989) of bi-weekly composite observa­
tions. The leaf area index is computed using the Normalized Difference Vegetation
Index using a Beer’s law kind of variation (Baret et. al., 1991). The values of
the leaf area index for the years other than 1983, 1987 and 1989 are taken as the
average of the values from 1983, 1987 and 1989 data. Missing periods embedded
in the 1983, 1987 and 1989 data are estimated by simple interpolation. The data
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C H A P T E R 2. A SOIL-CA NO PY-ATM O SPH E RE M ODEL
57
used in this study has been tabulated in Table 2.1.
The soil type at Kings Creek is silt loam. The values of the residual (0r ) and
saturated (0B) volumetric soil moisture contents are taken to be 0.02 and 0.50
respectively; the Brooks-Corey parameter equals 0.2; the air-entry suction head
(V>(0,)) is 0.20m; and the saturated hydraulic conductivity (K s) for silt loam is
6.8m m / h r (Rawls et. al., 1982). The albedo of bare soil (a a) and vegetation (a„)
is taken as 0.15 and 0.20; the emissivity of bare soil (e, ) and vegetation (es) is
taken to be unity (Famiglietti et. al., 1994). The zero plane displacement for
bare soil (da) and vegetation (dv) are zero and 25cm respectively; the roughness
lengths for bare soil (zo,«) and vegetation (zo,v) are 1mm and 7cm respectively.
The average daily air temperature computed using the Earthlnfo data set is taken
to be the soil temperature at 5cm depth. The initial interception storage is taken
to be zero. The values of 0*and 9W are taken to be 0.12 and 0.045. The minimum
stomatal resistance r£in equals 100s /m . The baseflow parameters for the ARNO
model Q™ax, 61 and Ql, and the exponent A in the transpiration relationship, are
calibrated using the observed daily flows at Kings Creek USGS stream gauge data.
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C H A P T E R 2. A SO IL-CANO PY-ATM O SPH ERE MODEL
2 .6 .3
58
R e s u lts an d d iscu ssio n s
The hydrological model described in the previous sections is used to simulate the
water and energy fluxes for the Kings Creek catchment for a period of ten years
(1980-1989) on a hourly time step. The parameters are calibrated using the first
five years (1980-1984), and the validation is done for the 1985-1989 streamflows
as well as the soil moistures and surface temperatures for the four Intensive Field
Campaign (IFCs) in FIFE 1987. There has been no adjustment or initialization
of the soil moistures at the start of the IFCs. The calibrated parameter values are
used to generate the streamflows, soil moistures and surface temperatures at an
hourly time step for the entire ten year period.
C a lib ratio n an d v alid atio n of stream flow s
The hourly streamflows are sim­
ulated over the first five year period (1980-84) and aggregated to daily values. The
parameters are optimized using the root mean square of the difference between
the observed flows (obtained using the daily discharge values at Kings Creek) and
simulated values over the five year period. This results in the values of Q™ax,
61, Q£ and A as 3.38m m / h r , 0.15, O.OQmm/day and 0.50 respectively. The root
mean squared of the error of the streamflow over the 1980-84 period is 1.7mm and
1.6mm over the 1985-89 period (see Figure 2.3 and Figure 2.4). The results of the
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C H A P T E R 2. A SO IL-CANO PY-ATM O SPH ERE MODEL
59
streamflow calibration and the validation are plotted as time series for 1980-1984
and 1985-1989 in Figure 2.3 and Figure 2.4 respectively. The agreements between
the simulated (solid lines) and the observed streamflows (dotted lines) at the Kings
Creek gauging station show reasonable agreements. The disagreements could be
due to the use of rainfall data from the Tuttle Creek rain gauge caused by the
non-availability of the hourly rainfall data at the Manhattan rain gauge for the pe­
riod under study. In general, the simulated streamflow overestimates the observed
streamflow, but it shows good qualitative agreement. Since the objective of the
study is not to match the simulated and the observed runoffs but to simulate a
realistic variation of the top soil layer moisture, the streamflow results are accept­
able. In the case of the calibration years (Figure 2.3), it can be seen in 1982 (June
24 and July 1 - Julian day 175, 182 respectively) that the observed streamflows are
8.6 and 50.3mm respectively. On examination of the rainfall records of the Tuttle
Creek gauge, there is no rain from June 16 (Julian day 167) to June 25 (Julian
day 175), and the total rain on July 1 is 7.8mm (there is no rain on June 28, 29
and 30 - Julian day 179-181). This shows that the rain gauge at Tuttle Creek
does not record the storm that results in these large streamflows. The other plots
in Figure 2.3 show better agreement. The same is the case in Figure 2.4, where
the observed streamflow on May 17, 1986 (Julian day 137) is 18.1mm and there
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C H A P TE R 2. A SO IL-CA N O PY-ATM O SPH E RE M ODEL
60
is no rainfall observed at the rain gauge between April 28 (Julian day 118) and
May 31, 1986 (Julian day 151). On the other hand, between August 20 (Julian
day 232) and October 1, 1989 (Julian day 274), there is a huge overestimation of
the streamflow. This is because of a very large baseflow estimation that results
from the increase in soil moisture of the bottom layer due to 297m m of rain that
is recorded by the rain gauge. In summary, the hydrological model estimates the
streamflow with reasonable accuracy as consistent with the rainfall data.
Soil m o istu re co m p ariso n s
The average of the soil moistures observed over
the Kings Creek catchment (obtained using the FIFE Information System - FIS
database) is plotted against the simulated soil moisture for IFC-1 through 4 for
both the top (Figure 2.6) and the bottom (Figure 2.7) layers. The observations
are made at a depth of 25m m and 75mm at the Bowen ratio stations (2, 8, 10,
12, and 14 corresponding to grid numbers 1916, 3129, 3414, 2915 and 2516). At
each station, there are five measurements of soil moisture corresponding to the
center, north, south, east and west (distance approximately 30m in each case).
These are averaged to obtain the catchment averaged soil moisture for comparison
with the simulated soil moisture. The simulated soil moistures correspond to a top
layer of 10mm (1cm) thickness and a bottom layer of 990mm (99cm) thickness.
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C H A P T E R 2. A SOIL-CANO PY-ATM O SPH ERE M ODEL
61
The 25m m observed soil moistures are plotted against the top layer simulated soil
moisture and the 75m m observed soil moistures are plotted against the bottom
layer simulated soil moisture. The observed soil moistures are plotted individually
at the beginning of the day (i.e., if the observations are on Julian day 152 - June 1,
1987, they are plotted corresponding to hour 1, day 152) since the time of day at
which the observations are made is not available. However, since the observations
are made only once daily, they do not capture the temporal dynamics of the soil
moisture variation. The temporal variation is reflected in the simulated soil mois­
ture. However, note that the x-axis (in days) is over a range of 6 days for IFC-1,
17 days for IFC-2, 16 days for IFC-3 and 12 days for IFC-4. Therefore, temporal
variations will appear emphasized in IFC-2 and 3 and appear much more gradual
in IFC-4 and IFC-1.
The four panels in Figure 2.6 are for IFC-1 through IFC-4. It is interesting
to note that each of them displays different nuances associated with soil moisture
dynamics. In the case of IFC-1, there is virtually no rainfall as seen from the
rainfall data for the IFCs in Figure 2.5 (only one hour with 0.2mm of rain on the
June 2nd at 0900 hrs). The observed soil moisture exhibits a slow decrease over
time. The simulated soil moisture remains relatively constant for the duration of
the IFC. This is because there is replenishment of the loss in soil moisture (due
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C H A P T E R 2. A SOIL-CA NO PY-A TM O SPH E RE M ODEL
62
to bare soil evaporation) of the upper layer by diffusive flux from the bottom
layer. The bottom layer holds a larger amount of moisture compared to the top
layer (capacity of the top layer = 10mmX0.50(porosity)=5mm; capacity of the
bottom layer = 990mmX0.50(porosity)=495mm), and therefore the bottom layer
soil moisture shows little decrease when it supplies the top layer with moisture
(even if there is a 5m m flux of moisture from the bottom layer to the top layer,
the bottom layer soil moisture content decreases by only 0.005). In the case of IFC2, there is no rainfall on June 25 and 26 (Julian day 176 and 177), and the top layer
soil moisture shows a decrease. There is rainfall on June 27, and the soil moistures
increase. On June 27 at 2200 hrs there is a 9.65m m rainfall, and the top layer soil
moisture increases from 0.135 to 0.401. This is expected since the rainfall wets the
top layer of the soil almost instantly. The total rainfall on June 27 is 30.98mm.
This rainfall is reflected in the observed 25mm soil moisture the next day (June
28), which increases from 0.22 on June 27 to 0.31 on June 28. There are two
im portant observations here. The immediate increase in the 25mm soil moisture
is less than the increase seen in the 1cm soil moisture. The 25mm soil moisture
shows a more gradual change as opposed to the 1cm soil moisture. On the other
hand, the 1cm soil moisture on responds on much shorter time scales. This cannot
be completely verified since only daily observations “of the 25mm soil moisture are
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C H A P T E R 2. A SOIL-CANO PY-ATM O SPHERE M OD EL
63
available. After the top layer gets wet in response to the rainfall input, gravity and
the soil moisture gradient between the top layer and the bottom layer results in
movement of the moisture to the bottom layer. However, since the bottom layer is
99cm thick, the increase in soil moisture of the bottom layer due to this incoming
soil moisture is very slight as seen in the second panel of Figure 2.7. There is
rainfall between June 27 (178) to June 30 (181), after which there is no rain for
a period of three days between July 1 to July 3 (182-184). We can observe the
drydown in the top layer soil moisture from 0.237 on July 1 to 0.139 on July 4.
There are again periods of rain on July 4 (about 0.2mm) and July 5 (8.9mm),
after which there is no rain till the end of the IFC and the soil moisture of the top
layer exhibits a drydown (there is an hour of 1.5mm of rain on July 7, hence the
spike around day 187). The 25mm observed soil moisture exhibits behavior that
agrees with the rainfall input and the simulated 1cm soil moisture.
IFC-3 behaves similar to IFC-2 in that there are periods of rain and periods
of drydown when the soil moisture decreases. The 25mm observed soil moisture
shows a gradual behavior consistent with the rainfall pattern, whereas the 1cm
simulated soil moisture shows a greater temporal variation that agrees very well
with the rainfall input pattern as shown in the third panel of Figure 2.5 and
Figure 2.6. The bottom soil moisture shows a slight increase on August 12 in
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C H A P T E R 2. A SO IL-CANO PY-ATM O SPH ERE MODEL
64
response to the rainfall on August 12 (third panel in Figure 2.7). This rainfall
increases the top layer soil moisture from 0.126 in the early morning of August 12
to 0.369 at 0400hrs (12.7mm rain at 0400hrs) and from 0.251 at 1400hrs to 0.402
at 1500hrs (12.2mm rain at 1500hrs). The soil moisture in the lower layer increases
from 0.188 at 1400hrs to 0.199 at 1500hrs; 0.214 at 1600hrs; 0.228 at 1700hrs and
0.232 at 1800hrs. The lower layer soil moisture attains a value of 0.235 at 2200hrs
of August 12 and changes very little thereafter. The same observation can be
made comparing the 25m m observed soil moisture and the 75mm observed soil
moisture. The increases in the 75mm soil moisture in response to rainfall events
are less than those in the 25mm soil moisture. The case for IFC-4 is similar to the
ones discussed above. There is no rain between October 5 and October 13, but
there is rainfall in two hours of October 13 and October 14. Though this rainfall
is very slight (1.27mm and 0.51mm), it does increase the soil moisture of the top
layer. The rainfall on October 15 increases the soil moisture, after which it drops
off due to drainage into the bottom layer.
The simulated soil moisture shows consistent agreement with the observed rain­
fall and the observed 25mm and 75mm soil moistures. Since the top 1cm layer soil
moisture is affected by rainfall almost instantaneously, it is important that the soil
moisture accounting scheme operates on hourly time steps (as in the case here) so
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CHAPTER 2. A SOIL-CANOPY-ATMOSPHERE MODEL
65
that the temporal variability is captured.
S urface te m p e r a tu re com parisons
The observed surface temperatures from
the stations (3 - Super Automated Mesonet Station; 31, 3, 7 - AMS Stations) in
grid numbers 2123, 2139, 2428 and 3221 respectively are half hourly observations
averaged to hourly values. The observed (dots) and simulated (solid line) are
plotted in Figure 2.8. However, during the midday hours the simulated values of
surface temperatures are larger than the observed values. The IFC-1 comparisons
show reasonable agreements for most of the hours except for a few hours of June
4 (Figure 2.8) (the fourth peak in panel 1 of Figure 2.8). There are disagreements
between the observed and the simulated surface temperatures of 5K or more be­
tween 10:00am and 6:00pm on that day. The wind speed controls the resistance
of the bare soil evaporation and the vegetation transpiration. The aerodynamic
resistances are inversely proportional to wind speed. The lower the wind speed,
the higher the value of the aerodynamic resistance for bare soil and vegetation.
During the day of June 4, 1987, the wind speeds between 10:00am and 6:00pm
ranged from 1.4 to 2.1m /s . This range, when compared to the wind speed vari­
ation during the same time on June 5 (4.7 to 11.2m/s) results in a much larger
aerodynamic resistance, thereby reducing the evapotranspiration. It is because of
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C H A P T E R 2. A SO IL-CA N O PY-ATM O SPH E RE MODEL
66
this that the simulated surface temperatures on June 4 show a marked disagree­
ment with the observations. The same explanation holds for July 1, 2 and 3 (panel
2, Figure 2.8); August 10, 11 and 13 (panel 3, Figure 2.8) and October 11 and 12,
1987 (panel 4 in Figure 2.8). The hours of overestimation coincide with low values
of wind speed (which reduce the simulated evapotranspiration) coupled with high
values of incoming solar radiation (at midday hours). The high solar radiation
(and hence net radiation) results in large values of sensible and ground heat fluxes
(since the latent heat heat is small), and this increases the surface temperature to
preserve the energy budget. However, for most part, the simulated surface tem ­
peratures do agree well with the observed values. Figure 2.9 shows the scatter
of the simulated surface temperatures with the observed values. The root mean
square error over IFC-1 is 5.7K\ IFC-2 is 5.5K\ IFC-3 is 5.9K and IFC-4 is 3.6K .
On examining Figure 2.9, we can observe that there is more overestimation of the
observed temperatures than underestimation.
Since we are especially interested in the 6:00am observations, which coincides
with the SSM/I ascending orbit overpass comparisons between the observed and
the simulated values are meaningful. The root mean square error for the 6:00am
surface temperatures are 1.8K , 0.8K , 1.5K and 1.2K for IFC-1, IFC-2, IFC-3
and IFC-4 respectively. The root mean square error for all the 6:00am surface
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C H A P T E R 2. A SOIL-CA NO PY-ATM O SPH E RE M ODEL
67
temperatures lumped together from all the IFCs is 1.3K. Figure 2.10 shows the
scatter plot between the observed and the simulated 6:00am surface temperatures.
The agreement is very good.
2.7
S e n sitiv ity o f ra d ia tiv e tran sfer to v e g e ta ­
tio n an d so il m o istu re
2.7 .1
E ffect o f v e g e ta tio n p a r a m e te r s
The effect of the stem area index (77) and the canopy moisture content (mc) for the
range of the polarization difference index A Y (X100 as explained earlier; denoted
by DY in all figures), the leaf area index (LAI) and the soil moisture range (between
residual and saturation) is shown in Figure 2.11 for the 19 GHz case, and in
Figure 2.12 for the 37 GHz case. The figures are organized into nine panels. The
stem area index varies across from 0 to 0.6 from left to right, and the canopy
moisture content varies from 0.65 at the top (corresponding to a turgid leaf) to
0.05 at the bottom (corresponding to a dry leaf). The branch to stem area ratio (x)
is set to 2.7, corresponding to the vegetation type shrubs (W hittaker et. al., 1967
and 1974). The lines drawn in the figures (obtained by simulation) correspond to
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C H A P T E R 2. A SOIL-CA NO PY-ATM O SPH E RE MODEL
68
soil moisture at saturation (the line to the right, i.e., greatest value of DY for a
given LAI) and at residual (least value of DY for a given LAI). These lines form
the bounding curves in between which values for other soil moistures lie. The
figures show the effect of stem area index as one moves from left to right across
the page. The stem area increases and the range between the simulated saturation
soil moisture content and the residual soil moisture content curves decreases for
a given leaf area index. There is a greater decrease in the polarization difference
index for the saturation soil moisture than for the residual soil moisture.
The polarization difference signal originates at the soil surface and propagates
through the vegetation. This polarization difference signal caused by the dipolar
nature of the water molecule is greatest for a saturated soil. The increase in leaf
area index and/or stem area index attenuates this signal. This attenuation of the
polarization difference index is greater for the saturated soil moisture curve as
opposed to the residual soil moisture curve for both the increase in leaf area index
and the stem area index. At sufficiently high leaf area index (in this case 7.0), the
polarization difference index of the residual and the saturation soil moisture curves
(for all stem area indices and leaf moisture contents of 0.65 and 0.35) coincide.
Increasing canopy moisture content also decreases the polarization difference
signal, as seen from the figures moving bottom to top. When the leaf is dry
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CH A P TE R 2. A SO IL-CANO PY-ATM O SPH ERE MODEL
69
(mc=0.05), the polarization difference index stays high, even at High leaf area in­
dices. Turgid leaves absorb the microwave radiation and polarization difference
emitted from the surface of the soil (Choudhury et. al., 1990). Therefore, an in­
crease in the canopy moisture content attenuates the polarization difference index.
The above observations are common to both 19 and 37 GHz polarization difference
indices.
Table 2.2 shows the variation of the simulated maximum range of the polar­
ization index (A F ), i.e., the difference between the polarization index for the soil
saturated case and the soil dry case for varying the stem area index and the canopy
moisture content. As the observations from Figure 2.11 and Figure 2.12 showed,
the range decreases with increasing stem area index and increasing canopy mois­
ture content. Furthermore, the range is greater for the 19 GHz case as opposed
to the 37 GHz case, but for a dry leaf (mc=0.05) they are almost identical. This
shows that the vegetation exerts greater influence in modulating the polarization
difference signal for 37 GHz as opposed to 19 GHz. In addition, for the case of
a dry leaf and stem area index equal to zero, the polarization difference index is
identical (13.0) for both the 19 and the 37 GHz frequency. In this case, there is
almost no influence exerted by the vegetation on the polarization difference signal
originating from the soil. Hence for the case of zero stem area index and zero
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C H A P T E R 2. A SO IL-CANO PY-ATM O SPH ERE MODEL
70
canopy moisture content, the polarization difference index for the 19 and 37 GHz
differs only due to the difference in the dielectric properties of water, which are a
function of frequency. Using the mixing formula for computing the dielectric coef­
ficient of the soil and the Fresnel relation for evaluating reflectivity for a mixture
of soil and water (Wang et. al., 1980), the difference in the reflectivity between
horizontal and vertical polarization for saturated soil moisture content of 0.50 for
silt loam is 0.209 for 37 GHz and 0.2124 for 19 GHz. Therefore, since the differ­
ences in reflectivity are small, the differences in the polarization difference index
would also be small.
2 .7 .2
S e n s itiv ity to le a f a rea in d e x an d so il m o is tu r e
The sensitivities of the polarization difference index A Y to leaf area index L and
soil moisture 6 can be expressed as
and
respectively. They will both
be a function of the vegetation parameters - the stem area index and the canopy
moisture content that were examined in the previous subsection. This section will
examine these sensitivities for a stem area index of 0.3 and a canopy moisture
content of 0.35.
The sensitivity of the polarization difference index to the leaf area index
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CH A P T E R 2. A SO IL-CA N O PY-ATM O SPH E RE MODEL
71
has to be evaluated at a fixed value of soil moisture. It will be a function of the
soil moisture and the leaf area index (in the neighborhood of which it is being
evaluated). This can be seen in Figure 2.13, in which the variation of polarization
difference index for 19 and 37 GHz has been plotted against the leaf area index for
different values of the soil moisture content ranging from 0.02- (residual) to 0.50
(saturation) for ten increments. It can be seen from the figure that as the soil
moisture decreases,
decreases, i.e.,
In the case of 19 GHz (Figure 2.13), for L —1.0,
is 1.1 for 5=0.02 (residual
soil moisture) and 3.5 for 5=0.5 (for saturation soil moisture). The value of
is computed using the A Y values for the leaf area index L of 0.5 and 1.5. In the
case of 5 taking up intermediate values between 0.02 and 0.5, the value of
lies
between 1.1 and 3.5; 1.8 for 5=0.12; 2.7 for 5=0.21 and 3.3 for 5=0.31. In the case
of 37 GHz, the values are similar but slightly higher for 5=0.5,
— 3.6. This
shows that the 37 GHz frequency has an increased sensitivity to leaf area index.
The sensitivity to leaf area index of the polarization difference is maximum
for the case of saturation soil moisture and minimum for the case of residual soil
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C H A P T E R 2. A SOIL-CANO PY-ATM O SPHERE M OD EL
72
moisture. Hence we can write,
(d A Y \
^ fd A Y \
fd A Y \
„
, '
(2 7 1 )
In addition, as the leaf area index increases the sensitivity to leaf area index de­
creases (at a fixed value of soil moisture) i.e.,
fd A Y \
(d A Y \
Using the above values, for a value of 0=0.21, the value of
js 2.7 for A=1.0;
1.5 for A=2.0; 0.9 for L = 3.0 and 0.4 for Z=5.0.
However, for higher soil moisture contents, the sensitivity of the polarization
difference index to leaf area index still remains significant even when the leaf area
index increases. This can be seen in Figure 2.13, e.g., for 0=0.12, for L=1.0,
^ = 1 . 8 ; L = 2.0, ^ = 1 . 0 and for £=3.0, ^ = 0 . 6 for the 19 GHz case. In the
case for 0=0.31, the corresponding values are 3.3, 1.9 and 1.1 for L = 1, 2 and 3
respectively. So, for the leaf area index of 3,
is 1.0 for 0=0.31, but only 0.6
for 0=0.12. The corresponding values for the 37 GHz case are 1.7, 0.8 and 0.5
for Zr=l,2 and 3 respectively (for 0=0.12) and 3.3, 1.7 and 1.0 for L = 1,2 and 3
respectively (for 0=0.31).
At higher values of leaf area index, the polarization difference signal gets atten­
uated by the vegetation canopy. The strength of the polarization difference signal
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C H A P T E R 2. A SOIL-CA NO PY-ATM O SPH E RE M ODEL
73
is a function of the soil moisture content. At higher soil moisture contents, the
polarization difference signal does not get completely attenuated at larger values
of leaf area index, and therefore there is still sensitivity of the leaf area index. On
the other hand, for low soil moisture contents, the polarization difference signal is
low to begin with and gets attenuated with increasing leaf area index to a degree
that further changes in leaf area index do not affect the signal, hence reducing the
sensitivity.
The sensitivity of the polarization difference index to the soil moisture
evaluated at a fixed value of leaf area index. The sensitivity of
is
is a function of
the leaf area index and the soil moisture content in the neighborhood in which it
is evaluated. The variation of the polarization difference index with soil moisture
for different leaf area index values ranging between 0 and 7 at increments of 0.5 is
presented in Figure 2.14. It can be seen that as the leaf area index increases, the
sensitivity of the polarization difference to the soil moisture ( ^ n ) decreases (for
a given 6) i.e.,
L' < L ^
The value of the 19 GHz
fd A Y \
[
~
fd A Y \
b
t
(2 -73)
for 5=0.12 is 31.25 for L= 0; 17.7 for Z=1.0; 11.5
for L = 2.0 and 4.2 for L= 4.0. It can be seen that as the leaf area index increases,
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C H A P T E R 2. A SO IL-CANO PY-ATM O SPH ERE M ODEL
74
the sensitivity rapidly decreases. This is expected since increasing leaf area index
masks the polarization difference signal of the soil moisture. The 37 GHz
behaves similarly. The values of
also
are 22.9, 10.4, 6.25 and 1.0 corresponding to
L of 0, 1.0, 2.0 and 4.0 respectively for 0=0.12. It can be seen that the sensitivity
values of
are lower for the 37 GHz than for the 19 GHz. This is expected, as
the 19 GHz has greater sensitivity to the soil moisture due to its longer wavelength.
The decrease of
with leaf area index results in almost zero sensitivity when
high values of leaf area index (like L = 7.0) are approached. This can be seen in
Figure 2.14; the A Y vs 6 curves for £=7.0 are almost straight vertical lines for
both the 19 and the 37 GHz cases. As the soil moisture increases from residual
soil moisture content,
first increases and then decreases. This can be seen
by observing the slope
of the A Y versus 0 curve (for a fixed L). As the soil
moisture increases (for a given leaf area index), the sensitivity of the polarization
difference to the soil moisture increases. After a certain soil moisture content, the
polarization difference signal gets saturated, and further increases do not result in
corresponding increases in polarization difference index.
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C H A P T E R 2. A SOIL-CANO PY-ATM O SPHERE M ODEL
2.8
75
C on clu sion s
A thin layer model of hydrology with complete water and energy budgets has been
presented here. The model is built on the framework of Mahrt et. al., (1984)
for inclusion of a thin upper layer. The parameterizations include the moisture
gradient driven flux for diffusion of water from the lower layer to the upper layer
to replenish the moisture lost during evaporation. This is an important process
th at is not dealt with in some other hydrological models, partly because they
consider a 50cm upper layer to form the root zone and the lower layer is very thick
(250cm or so). Hence, the moisture gradient would be low. The parameterizations
for between layer fluxes driven by gravity and moisture gradient use the values of
hydraulic conductivity and diffusivity of the layer from which they originated (i.e
the ’’upstream ” condition). This is shown to result in decreased truncation errors
(Mahrt et.
al., 1984) that are associated with an asymmetric finite difference
scheme.
The hydrological model is applied over a ten year period. The observed daily
streamflows from 1980-1984 are used to calibrate the model parameters.
The
simulated streamflows are validated over the 1985-1989 period. The comparisons
between observed and simulated streamflows have been good. It must be noted
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C H A P T E R 2. A SOIL-CA NO PY-ATM O SPH E RE M ODEL
76
that the rain gauge for the rainfall observations was about 16km away from the
catchment. This does result in some discrepancies between the rainfall and the
streamflow time series. The results when viewed in the light of these discrepancies
show good qualitative and decent quantitative agreements. However, the aim of
this chapter was not to develop a model for accurate streamflow prediction. The
aim of this chapter is to develop a scheme to predict the surface tem perature and
soil moisture with a sufficient degree of accuracy for the 1cm surface layer. The
streamflow is compared to determine that the hydrological model behaves properly
with the rainfall process. Further, the model simulated soil moistures and surface
temperatures are compared for the time periods during the four IFCs in FIFE.
The 19 GHz and 37 GHz polarization difference indices have a greater range
between the residual and the saturated soil moisture levels, showing greater sen­
sitivity to soil moisture variations. The sensitivity of the polarization difference
index to leaf area index decreases with a reduction in soil moisture and an increase
in leaf area index. The sensitivity of the polarization difference index to the soil
moisture is affected by the leaf area index; an increase in leaf area index decreases
this sensitivity; an increase in soil moisture results in increased sensitivity followed
by a decrease in sensitivity at high soil moistures. Among the vegetation parame­
ters, the stem area index and the canopy moisture content affect the polarization
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CH A P T E R 2. A SOIL-CA NO PY-A TM O SPH E RE M ODEL
77
difference the greatest. An increase in the stem area index and/or the canopy mois­
ture content results in a masking of the polarization difference signal originating
at the soil surface.
It is proposed that this model can be used in conjunction with passive mi­
crowave satellite data for soil moisture estimation. The 19 and 37 GHz Special
Sensor Microwave Imager (SSM/I) brightness temperature data is proposed to be
used for the study. Microwave satellite data at lower frequency (6.6 GHz) has been
used in the past to infer soil moisture (Owe et. al., 1992) and soil wetness (Choudhury, et. al., 1988). These, however, use simple regression based relations between
soil moisture (or antecedent precipitation index API) and brightness temperature.
In the case of higher frequencies (such as the 19 and 37 GHz frequencies that we
propose to use), a simple inversion may not be very effective. It is desired that a
complete model of soil hydrology providing the surface tem perature and soil mois­
ture along with a radiative transfer model for the plant canopy and an attenuation
model for the atmosphere would be used to simulate the SSM/I brightness temper­
ature and subsequently help in retrieving soil moistures from observed brightness
temperatures. The model of thin-layer soil hydrology will help in this regard.
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C H A P T E R 2. A SOIL-CA NO PY-ATM O SPH E RE MODEL
parameter
78
value
albedo (soil) a a
0.15
albedo (vegetation) a v
0.20
emissivity (soil) ea
1.00
emissivity (vegetation) e„
1.00
roughness length (soil) z0<a
0.001m
roughness length (vegetation) z0,a
0.07m
zero plane displacement (soil) da
0.0
zero plane displacement (vegetation) dv
0.25m
top layer thickness z\
0.01m
bottom layer thickness z2
0.99m
leaf area index L
minimum stomatal resistance r£ in
biweekly LAIs
lOOs/m
porosity 6a
0.50
residual soil moisture 0r
0.02
Brooks Corey parameter m
0.2
air entry suction head i})c
saturated hydraulic conductivity K a
0.2m
1.89X10"6m s-1
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C H A P T E R 2. A SO IL-CA N O PY-ATM O SPH E RE MODEL
parameter
value
transition soil moisture 6*
0.12
wilting soil moisture (volumetric) 9W
0.05
meteorological data
hourly data, Topeka, KS
rainfall data
hourly data, Tuttle Creek
streamflow data
79
daily, Kings Creek
Table 2.1: Parameters for the thin layer hydrological model
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CH A P TE R 2. A SOIL-CA NO PY-ATM O SPH E RE MODEL
80
stem area index
canopy moisture
A Y (X 100)
A Y (X 100)
(x)
(me)
(19 GHz)
(37 GHz)
0.0
0.65
8.3
7.3
0.3
0.65
4.4
3.9
0.6
0.65
2.4
2.1
0.0
0.35
10.1
9.4
0.3
0.35
5.5
5.0
0.6
0.35
3.1
2.7
0.0
0.05
13.0
13.0
0.3
0.05
7.1
7.0
0.6
0.05
3.9
3.7
Table 2.2: Maximum simulated range residual to saturated soil moisture content
(9a-Qr) for polarization difference index (A Y X 100) leaf area index (L ) = 0.75;
branch to stem area ratio (tj) — 2.7 for 19 GHz and 37 GHz
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C H A P T E R 2. A SO IL-CANO PY-ATM O SPH ERE M ODEL
81
SSM/I
atmospheric attenuation
canopyradiative transfer
soil hydrology'
Figure 2.1: Representation of the integrated soil-canopy-atmosphere process
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C H A P T E R 2. A SOIL-CANO PY-ATM O SPHERE M ODEL
82
Figure 2.2: Representation of the thin-layer model of soil hydrology
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C H A P T E R 2. A SO IL-CANO PY-ATM O SPH ERE MODEL
0
100
200
Day(I960)
300
0
100
200
Day(iMi)
300
83
:
•
0
100
200
Day(1962)
300
300
.
0
100
200
Day(1983)
0
100
200
Day(1964)
_
,-----<Vw
300
Figure 2.3: Observed (dotted line) and simulated (solid line) daily discharges (mm)
for the calibration period (1980-1984)
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C H A P T E R 2. A SOIL-C A N O PY-A T M O SPH E R E MODEL
L.
0
84
^
100
200
300
Day (1985)
!
0
100
200
300
Day (1986}
•
0
i
^
100
200
300
Day (1907)
0
100
200
300
Day (1968)
_____________ 0
10Q
200
300
Day (1989)
Figure 2.4: Observed (dotted line) and simulated (solid line) daily discharg* (mm)
for the validation period (1985-1989)
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C H A P T E R 2. A SOIL-CA NO PY-ATM O SPH E RE MODEL
85
rainfal (rr»n)
IF C -1
152
153
154
155
158
157
Julan Day Juna i-0.1W 7
rainfall (mm)
IF C -2
I
.
i
. .
t»
165
100
Jiiian Day Juna 25>kiy 11.1087
riinlan (mm)
IF C -3
1
218
1
i
220
222
1
L
224
228
228
230
232
JUtan Day Augual 0-21.1087
n'Rfal (mm)
IF C -4
. ----------------------------------------------------------------------------------------------------------------------------------- . . . .
278
280
283
284
n.
288
IL/h.
288
JiA tn Day Oclotw r 6-18.1887
Figure 2.5: Precipitation (in mm) for the Kings Creek gauge for IFC-1 through
IFC-4
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86
CH A P TE R 2. A SO IL-CA N O PY-ATM O SPH E RE M ODEL
IFC-1
JiJian Day Ju n a 1*6.1907
IFC-2
o
*
aZ
°
i3
i:
Julian Day Ju n a 2 5 -Jiiy u , 1907
IFC-3
£
Bn
i „
3d
8^
56
a
z
*
°
* so
225
220
2X
Ju fa n Oay Augutt 0 -2 1,1907
IFC-4
t
e
i
$
1I
a
z
»
°
i
°
9°
270
200
204
200
208
200
Jiiian Day OctoOar 5-10.1907
Figure 2.6: Mean observed (25mm depth; dots) and simulated (top layer - lines)
volumetric soil moisture for IFC-1 through IFC-4
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C H A P T E R 2. A SOIL-CA NO PY-ATM O SPH E RE M ODEL
87
IFC-1
|
i 6
3I
g
I
?
°:
..
6
2
JUian Day J n w 1-6. 1967
IFC-2
Julian Day Ju n a 25-Jufy 1 1 .1967
IFC-3
230
325
320
JU ian Day August 6-21 .1 9 6 7
IFC-4
”
a
•
•
•
'
•
JU ian Day Octotwr 6-16.1967
Figure 2.7: Mean observed (75mm depth; symbols) and simulated (bottom layer
lines ) volumetric soil moisture for IFC-1 through IFC-4
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C H A P T E R 2. A SO IL-CA N O PY-ATM O SPH E RE M ODEL
88
IFC-1
o
N
n
* o©
~
►-
o
o
N
152
155
154
153
156
157
158
Julian Day June 1*6,1987
IFC-2
160
185
Julian Oay June 25-Juty 11.1987
IFC-3
225
230
Jiiian Oay August 6-21,1987
IFC-4
n
Figure 2.8: Time series plot of observed surface temperatures (dots) and simulated
top layer temperatures (lines) for IFC-1 through IFC-4
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C H A P T E R 2. A SOIL-C A N O PY-A T M O SPH E R E MODEL
IFC-1
IFC-2
<u
3
0
43-4
CO
w
0
a
E
CO
o
i_
0a
CN
J
CO
E
0
h o
oo oCO
CO
■3t
w o
*0D CD
CM
3
w
aj
300
320
3
E
c/5
320
IFC-4
2
3
0
0
a
3
E
300
IFC-3
L.
£
cu
o
to
t
3
w
eg
ra
280
E
c/5
Observed Surface Tem perature (K)
0)
a
3
Observed Surface Temperature (K)
4-4
4-4
0
CM
CO
w
*D
280
E
o
a)
I- O
0o) O
CO
(0
•c
3
+4
ra
CO
89
o
k.
CM
CO
E
o
CVJ
CO
0
H
0o
0
t:
O
O
CO
o
o
CO
3
CO
•o
0
o
CO
CVJ
0
280
300
320
Observed Surface Tem perature (K)
3
E
55
280
300
320
Observed Surface Tem perature (K)
Figure 2.9: Scatter plot of observed surface temperatures and simulated top layer
temperatures for IFC-1 through IFC-4
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C H A P T E R 2. A S O IL-CA N O PY-ATM O SPH E RE MODEL
IFC-1
90
IFC-2
0)
0
u.
u.
3
3
co
o o
a CM
E CO
0
h o
oo o
(0 CO
t:
2 o
aQ) CM
E CO
0
H O
0
o
O
CO
CO
t:3
CO
oco
T
03) CM
J2
3
E
3
CO
T>
0
0
o
CO
CM
3
280
300
320
CO
E
co
280
300
320
Observed Surface Tem perature (K)
Observed Surface Temperature (K)
IFC-3
IFC-4
a)
0
v.
L.
3
3
(0
k.
(3
u
0
a
E
0a)
E
|2 o
0o) o
(0 CO
“C
3
w o
03
•o
<1) CM
|2
o
m
•c
3
w
•o
o
oCM
CO
O
O
CO
oCO
CM
ffl
3
E
m
3
280
300
320
Observed Surface Tem perature (K)
E
w
280
300
320
Observed Surface Temperature (K)
Figure 2.10: Scatter plot of 6:00 am observed surface temperatures and simulated
top layer temperatures for IFC-1 through IFC-4
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91
C H A P TE R 2. A SO IL-CA N O PY-ATM O SPH E RE MODEL
«
2
2
o
0
5
10
15
20
0
25
5
10
IS
20
25
DY (IB urU )
D Y (IO G H J)
OY (10 GH2)
o
ID
SAWi.fi
m o O .3 5
2
2
o
0
5
10
15
20
25
0
5
10
IS
DY (10 GHz)
DY(10G H 2)
20
25
0
5
10
15
20
25
0Y (19 GH2)
o
SAI-0.6
m c-0.05
2
0
5
10
15
o y o b g h j)
20
25
DY (19GH2)
Figure 2.11: Sensitivity of 19 GHz polarization difference index (DY) to the leaf
area index (LAI) for different values of stem area index (SAI) and canopy moisture
content (me)
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92
C H A P T E R 2. A SO IL-CA N O PY-ATM O SPH E R E MODEL
SAlaO.6
m c*0.65
3
3
o
o
15
20
0
25
5
10
15
20
25
0Y (37G H I)
<o
3
S A M .6
m o 0 .3 5
3
o
5
10
15
20
25
0
5
10
15
20
25
DY (37 OKU)
DY (37 OKU)
e
3
0
5
10
15
220
0
225
5
0
5
10
15
SAI-0.3
SAI>0.e
m o O .0 5
m o 0 .0 5
20
25
0
5
10
15
20
25
Figure 2.12: Sensitivity of 37 GHz polarization difference index (DY) to the leaf
area index (LAI) for different values of stem area index (SAI) and canopy moisture
content (me)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
C H A P T E R 2. A SOIL-CANO PY-ATM O SPH ERE M ODEL
93
CO
S A I=0.3
m c=0.35
3
OJ
0.50
0.02
0
5
10
15
20
25
DY (19 G H z)
co
S A I=0.3
m c=0.35
CM
o
0.50
0.02
0
5
10
15
20
25
DY (37 G H z)
Figure 2.13: Sensitivity of 19 and 37 GHz polarization difference index (DY) to
leaf area index for different soil moisture contents between 0.02 (residual) and
0.50 (saturation) at increments of 0.048 for stem area index and canopy moisture
content at 0.3 and 0.35 respectively
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C H A P T E R 2. A SOIL-CANO PY-ATM O SPH ERE M ODEL
94
in
o
r t-
LD
S A I=0.3
m c=0.35
o
DC
[—
o
CO
oCO
co
©
CM
O
o
o
o
5
10
15
20
25
D Y (19 G H z)
in
o
S A l=0.3
m c=0.35
o
co
o
CM
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10
15
20
25
D Y (3 7 G H z)
Figure 2.14: Sensitivity of 19 and 37 GHz polarization difference index (DY) to
volumetric soil moisture content for different leaf area indices between 0.0 and 7.0
at increments of 0.5 for stem area index and canopy moisture content at 0.3 and
0.35 respectively
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C h a p ter 3
In v estig a tio n o f th e E ffect o f
H e te r o g e n e itie s in V eg e ta tio n
an d R ain fall on S im u la ted Soil
M o istu res and S S M /I B r ig h tn e ss
T em p era tu res
95
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
3.1
96
In tro d u ctio n
The Special Sensor Microwave Imager (SSM/I) has a resolution of about 56km at
19 GHz and 33km at 37 GHz (Hollinger et. al., 1990). At this spatial coverage,
there are bound to be heterogeneities in vegetation cover and variability in soil
moisture caused by spatial variations in rainfall input, among other factors. The
microwave brightness temperatures reported at these frequencies will have to be
interpreted in the context of the diverse hydrological characteristics at the land
surface. This chapter intends to investigate the effect of these heterogeneities on
the computed microwave brightness temperatures via simulations performed using
a coupled land-canopy-atmosphere model consisting of a thin layer model of soil
hydrology (based on Mahrt et. al., 1984); canopy radiative transfer model (Choudhury et. al., 1990) and an atmospheric attenuation model (Choudhury, 1993) The
physical location chosen here for the numerical simulation experiments corresponds
to the Kings Creek catchment in the First ISLSCP (International Satellite Land
Surface Climatology Project) Field Experiment (FIFE) area in Kansas. The time
period of January 1 through December 31, 1987 was chosen, even though the SSM/I
instrument itself became operational beginning in June 1987, with the intention
to include an annual cycle of soil moisture as well as brightness temperatures.
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C H A P T E R 3. THE EFFECT OF H ETEROGENEITIES
97
The simulation study over a time period of one year will help in interpreting the
seasonal dependence of the sensitivities.
The results of this study hold up well no m atter what the physical location of
the study area or the time duration of the study. The broad applicability of this
study stems from the fact that the range of parameters have been investigated
and the conclusions are not based on the parameters corresponding to the FIFE
site. In addition, the effect of varying the vegetation variability and the spatial
coverage of rainfall has been investigated. The vegetation parameters that are
investigated in the sensitivity analysis are the stem area index and the canopy
moisture content. The other vegetation parameters do not affect the simulated
brightness temperatures to the same extent as the stem area index and the canopy
moisture content.
3.2
R e v ie w o f p rev io u s h e te r o g e n e ity e x p e r i­
m en ts
The role of heterogeneities in vegetation and rainfall (and hence soil moisture) in
the simulation of satellite microwave brightness temperature is investigated. The
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
98
study of the effect of heterogeneity in land surface and input on the observed
hydrological variables and development of adequate representation techniques for
heterogeneity has been studied in the past (Wood, 1991). The main motivation
for these studies stems from : (a) the lack of data sets at fine spatial resolutions
and/or (b) the computational burden encountered in attempting to carry out the
modeling effort at fine spatial resolutions over large areas.
Previous representations of heterogeneity have been carried out using frequency
distributions of topographic parameters governing soil moisture movement (Famiglietti et. al., 1994); frequency distributions of the soil moisture (Entekhabi et. al.,
1989) or frequency distributions of stomatal conductance (Avissar et. al., 1992).
All of the frequency distribution representations (Famiglietti et. al., 1994; En­
tekhabi et. al., 1989 and Avissar ., 1992) result in the computation of a frequency
distribution of energy fluxes and compare them with a lumped representation
(Avissar, 1992); examine its sensitivity to the choice of frequency distribution
(Entekhabi et. al., 1989) or examine the areal average and the spatial variability
of the evaporation fluxes (Famiglietti et. al., 1994a, 1994b). The work of Avissar
et. al., (1989) divides the heterogeneous land surface areas into homogeneous subareas. The total flux and/or hydrological effect is determined as an area-weighted
average. Two different representations of subgrid vegetation variability were com-
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CH A P TE R 3. THE EFFECT OF HETEROGENEITIES
99
pared by Koster et. al., 1992, to investigate the effect of vegetation representation
on energy balance computations. It was found that the two representations (as a
mosaic, i.e., partitioning off into homogeneous subareas of vegetation types or a
mixture i.e. allowing for interacting between vegetation types) showed the same
behavior in energy balance studies. The study of aggregation on the simulated
areal average fluxes using biospheric models and satellite data shows that the land
surface characteristics as well as fluxes can be scaled, and that effective parameters
would suffice for representation of heterogeneities (Wood et. al., 1993).
The effect of spatial variability of precipitation on the hydrological processes
and variables such as evaporation, runoff and soil moisture has been determined
as significant (Eltahir et. al., 1993; Entekhabi et. al., 1989; Liang, 1994; Pitm an
et. al., 1990; Shuttleworth, 1988; and Warrilow et. al., 1986). The inclusion
of a frequency distribution of precipitation (Warrilow et. al., 1986) resulted in
sensitivity of evaporation and runoff to the fractional coverage of precipitation
(Pitm an et. al, 1990). The soil moisture was higher and the evaporation lower for
small storms, and the soil moisture was lower and the runoff higher for large storms
for a spatial representation of the rainfall variability using a frequency distribution
(Liang, 1994).
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
3.3
100
O verview o f an aly sis
The above discussion of the role of heterogeneities warrants further study. It is
not possible for us to directly incorporate the results from the literature without
trying to understand the role played by the heterogeneities in our context. The
non-linearity of the response of the land-surface to rainfall input raises a lot of
questions about the behavior of hydrological variables. Each hydrological variable
exhibits a different sensitivity to different heterogeneities in land surface and input
data. In the present study, we are specifically interested in deriving estimates of
soil moisture using satellite microwave brightness temperature data. Therefore,
we investigate the effect of heterogeneities in vegetation and the effect of spatial
distribution and coverage of rainfall on the simulated soil moisture and the SSM/I
brightness temperatures. Since the relationship between the SSM/I brightness
temperatures, the soil moisture and vegetation is non-linear, this study is required
to examine the degree of non-linearity in this relationship. Figure 3.1 explains
the central theme of this study. Soil moisture and vegetation are distributed over
the SSM/I field of view. Since the radiance originating from the land surface is
dependent on these quantities, we have a distributed radiance pattern observed
by the SSM/I in an averaged fashion over the field of view. Using the SSM/I
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
101
observed brightness temperatures, we wish to estimate soil moisture. In this study,
two aspects of the role of heterogeneities in soil moisture and vegetation on the
SSM/I brightness temperature are examined. First, the effect of distributed soil
moisture and vegetation on the SSM/I simulated polarization difference index is
studied. Second, the effect of spatial distributions of soil moisture and vegetation
on the estimation of soil moisture from the observed SSM/I brightness tem perature
is examined. The two studies together give us a complete picture of the role of
the heterogeneities in soil moisture and vegetation on the observation, and on the
estimation aspects of using the SSM/I for soil moisture. Such a study has not yet
been attem pted, though the sensitivity of some of the land surface and atmospheric
variables on the simulated brightness temperatures has been examined (Choudhury
et. al., 1990).
3.4
D e sc r ip tio n o f e x p e r im e n ts
The location of the study area is the Kings Creek catchment, FIFE area in Kansas.
The hourly input meteorological data, such as cloud height, wind speed, relative
humidity, air temperature, percentage sky cover and the atmospheric pressure,
are all obtained from the surface airways data for Topeka, Kansas. The input
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C H A P T E R 3. THE EFF E C T OF HETEROGENEITIES
102
shortwave and longwave radiation are generated according to the scheme outlined
in Chapter 2. The hourly rainfall data is obtained from the Tuttle Creek rain gauge
(about 16.5km from Kings Creek). The vegetation data has been obtained from the
University of Maryland reprocessed NOAA Global Vegetation Index Data Product
(Goward et. al., 1993). The NOAA-GVI is a biweekly product comprised from
measurements made by the Advanced Very High Resolution Radiometer (AVHRR)
on board NOAA polar orbiting satellites. The parameters of the hydrological model
are given in Table 2.1. The vegetation parameters for the canopy radiative transfer
model correspond to a tallgrass prairie grassland. The branch to stem area ratio
for shrubs ranges from 1.8 to 3.6 (Choudhury.et. al., 1990). Sensitivity analysis
of the brightness temperatures for the branch to stem area ratio showed that the
effect was minor. As a result, the branch to stem area ratio was fixed at 2.7 for
this study.
The hydrological model has been calibrated using the observed streamflow for
a five year period from 1980 to 1984 as explained in Chapter 2. The hydrological
model is used to simulate the surface temperature and the soil moisture on an
hourly time step from January 1, 1980 through December 31, 1989. The period
considered for the simulation of brightness temperatures is January 1 to December
31, 1987. The brightness temperatures are simulated using the canopy radiative
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
103
transfer model (Ch.oudh.ury et. al., 1990) and the atmospheric attenuation model
(Choudhury, 1993) corresponding to the SSM/I ascending orbit at 6:00am.
The leaf area index is distributed using a normal distribution on a 100 X 100
grid (10000 grid cells) with a coefficient of variation c„ = 0.655 (Walthall et. al.,
1992) consistent with the FIFE site area. Also, a range of the coefficient of varia­
tion for vegetation (c„=0.0,1.0 and 2.0) was used to study the effect of increased
variation of vegetation on surface temperature, soil moisture and brightness tem ­
perature. The rainfall was distributed using an exponential distribution (Warrilow
et. al., 1986), with the fraction of the grid cells over which rainfall occurs given by
fi = 0.3 that corresponds to convective rainfall in GCM grids (Liang, 1994). This
value has been used by the U.K. Meteorological Office for the case of convective
rainfall in their GCM. In addition, examination of the fractional rainfall coverage
versus rainfall rate using Manually Digitized Radar data (Fan, 1995) shows that
at the grid size of 16km (equal to the grid size to be used for the simulations on
the Red River basin), the fractional coverage is always greater than 0.3. The sen­
sitivity obtained by increasing fractional coverage of rainfall has also been studied
by varying \l = 0.3, 0.5 and 0.8.
The representation of rainfall and vegetation was done explicitly over 100X100
(10000) pixels. In addition, a distribution based representation in which eleven
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C H A P T E R 3. THE E F FE CT OF HETEROGENEITIES
104
classes were created (ten corresponding to rain or LAI and one corresponding to
no rain or LAI=0) was studied. In this case, the soil moisture and brightness
tem perature for each class in the distribution is modeled separately, and after the
end of the time step (of one hour), the soil moisture of the top and bottom layers
is averaged across all the classes for the next time step. In the next time step, the
classes are formed again based on input data (vegetation or rainfall), and all the
classes have the same soil moisture at the start.
The experiment was run to compare a distributed versus a lumped representa­
tion and a distribution into classes representation of either vegetation or rainfall,
or both, as depicted in Figure 3.2. The distributed representation input to a thin
layer hydrological model (described in Chapter 2) based on the Mahrt and Pan
(1984) representation of the thin top layer of soil leads to a distributed output of
the 1cm layer soil moisture and soil temperatures (on a 100X100 grid). This is
input to the canopy radiative transfer model (Choudhury et. al., 1990) and the at­
mospheric attenuation model (Choudhury, 1993) to compute the at-satellite 19 and
37 GHz brightness temperatures at both the horizontal and vertical polarizations
on a 100X100 grid.
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C H A P T E R 3. TH E E F FECT OF HETEROGENEITIES
3.5
105
T h e effect o f h etero g en eity on sim u la tio n o f
so il m o istu r e and b rig h tn ess te m p e r a tu r e s
The effect of heterogeneity in vegetation and rainfall gives rise to a distribution of
soil moisture. The effect of vegetation and rainfall are examined individually on the
soil moisture and the polarization difference index to see if the averaging process or
simplified representation of this heterogeneity using frequency distribution classes
causes a bias in the simulated soil moisture and/or the polarization difference
indices for the 19 and 37 GHz frequencies. This is investigated for the FIFE
region for the duration of one year between January 1 and December 31, 1987, and
corresponds to the ascending SSM/I overpass. The procedure is outlined in the
flowchart (Figure 3.2) and described below.
The leaf area index is distributed using a normal distribution with a coefficient
of variation of 0.655 (Walthall et. al., 1992). The rainfall is distributed according
to an exponential distribution (Warrilow et. al.,, 1986) with a fractional coverage
of 0.3. The vegetation and rainfall are distributed on a 100X100 grid. The veg­
etation is distributed according to the same variability, i.e., the 100X100 normal
IV(0,1) distribution field is created at the first time step, and the leaf area in­
dices for the 100X100 grid are computed using the current value of leaf area index
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
106
over the area and a coefficient of variation of 0.655. The rainfall is distributed
using the exponential distribution with fractional area coverage of 0.3 for the rain
time steps; in case of no rain, the entire 100X100 grid has no precipitation input.
The distributed values are used to compute a distributed (on a 100X100 grid)
soil moisture, 19 GHz and 37 GHz polarization difference indices. This value is
averaged and referred to as the distributed case. The 100X100 distributed vege­
tation and rainfall are averaged, and the soil moisture and polarization difference
index is computed. This is termed as the lumped case. The 100X100 distributed
vegetation and rainfall are classified into eleven classes to construct a frequency
distribution. In the case of vegetation leaf area index, there are ten classes and a
bare soil class; for rainfall there are ten classes of rain and one class of no rain. The
soil moisture and polarization difference index for 19 and 37 GHz is evaluated for
each class and then averaged. This is referred to as the distribution case (meaning
a frequency distribution rather than the entire distributed input is being used).
The lumped case and the distribution case are compared to the distributed case.
The effect of the heterogeneities in vegetation on soil moisture and polarization
difference index is compared to the corresponding effect of the spatial variability
and coverage of rainfall on soil moisture. This is carried out to give an idea of the
relative importance of each variable in our analysis of heterogeneities.
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
3 .5 .1
107
H e te r o g e n e itie s in le a f a rea in d e x a n d sp a tia l vari­
a b ility an d co v era g e o f ra in fa ll
S easo n ality an d sen sitiv ity
The leaf area index (LAI), soil moisture and po­
larization difference index for 19 and 37 GHz for the distributed vegetation and
lumped rainfall case, and the lumped vegetation and distributed rainfall case, are
displayed in Figure 3.3 and Figure 3.4 respectively. The figures shows that the
computed polarization difference index reflects the variations of the soil moisture.
This variation is greater (over time) for the distributed vegetation and lumped
rain case (bottom panel in Figure 3.3) compared to the lumped vegetation and
distributed rainfall case (bottom panel in Figure 3.4). The 37 GHz polarization
difference index behaves as expected - it is smaller in magnitude than the 19 GHz
polarization difference index. This is because the 19 GHz has a better penetration
into the soil layer as compared to the 37 GHz frequency and has a greater contri­
bution from the soil layer. Both the polarization indices show a correlation with
the leaf area index. The polarization difference index decreases during the periods
of increased LAI from around Julian day 100 (April) to Julian day 300 (Novem­
ber). This can be seen by comparing the top and the bottom panels of Figure 3.3
and Figure 3.4. The polarization difference index depends on soil moisture and
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
108
vegetation properties. An increase in LAI results in the polarization difference
signal originating at the soil surface being attenuated during its passage through
the plant canopy. This attenuation accounts for the decrease in the polarization
difference index, with an increase in LAI for a range of vegetation parameters
(Figure 2.11 and Figure 2.12). In addition, there is also a decreased sensitivity
to the changes in the soil moisture for an increase in leaf area index. An increase
in the soil moisture from 0.16 to 0.4 between March 3 and March 4, 1987 (Julian
day 81 and 82) resulted in an increase in the 19 GHz polarization difference index
from 6.7 to 10.5 (Figure 3.3) for a leaf area index of 0.18. Defining polarization
difference sensitivity as a ratio of change in polarization difference index to change
in soil moisture,
we have a polarization difference sensitivity of 15.83 for this
case. A change in soil moisture from 0.25 to 0.41 between August 25 and 26, 1987
(Julian day 237 and 238), resulted in the 19 GHz polarization difference indices of
6.4 and 7.5 respectively (Figure 3.3) for a leaf area index of 0.92. The polarization
difference sensitivity is 6.9 for this case. Hence, as the leaf area index increases, the
polarization difference index decreases and becomes less sensitive to soil moisture
changes.
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
S im plified re p re se n ta tio n s o f v eg etatio n an d rainfall
109
The comparison of
the representation of vegetation and its effects on the computed soil moisture and
the polarization difference index is made in Figure 3.5. The figure shows that
there is no major bias between the different representations of vegetation, i.e.,
distributed, lumped or frequency distribution representation using classes. There
appears to a very slight underestimation of soil moisture and the polarization
difference indices for the case of the lumped representation of vegetation. In the
case of the frequency distribution representation, there appears to be no bias at
all. Vegetation heterogeneity does not seem to bias the computed soil moisture
and polarization difference indices. The vegetation affects the surface soil moisture
indirectly. Transpiration occurs from the lower layer of the soil. The increase or
decrease in vegetation results in an increase or decrease in transpiration, which
affects the soil moisture of the lower layers. This in turn would affect the surface
soil moisture by moisture gradient driven flux between the lower layer and the top
layer. This gradient also depends on the top layer soil moisture, which is affected
by the evaporation. During the hours of the day when transpiration is large, soil
evaporation is also large and the upper layer is normally drier than the lower layer
and dictates the direction of the moisture gradient, i.e., lower layer to upper layer.
A change in transpiration over the layer from which the roots take up moisture
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
110
for transpiration (in this case 99cm) changes the soil moisture content of the lower
layer by a very small quantity.
The comparison of the representations of spatial variability in rainfall is more
interesting. The lumped and the distribution based representations show signifi­
cant biases towards higher values of soil moisture and polarization difference index
(Figure 3.6). The bias towards higher values is lesser in the distribution representa­
tion as compared to the lumped representation of rainfall. The spread measured as
a root mean squared difference between the distributed representation case and the
lumped representation case for soil moisture is 0.04 (top left panel in Figure 3.6);
for the distribution representation case (i.e., root mean squared difference between
the distributed and the distribution representation case), it is 0.03. The corre­
sponding spread values for the polarization difference are 0.8 for 19 GHz and 0.7
for 37 GHz for the lumped case, and 0.7 for 19 GHz and 0.6 for 37 GHz for the
distribution representation. The spread decreases when the spatial distribution of
rainfall is represented by distribution into classes as opposed to a lumped input.
The soil moisture is related in a non-linear way to the input rainfall. The inter­
action is two-way, i.e., a high soil moisture content of the upper layer results in
lesser infiltration, and a lower soil moisture content of the upper layer results in a
higher infiltration due to a higher infiltration capacity. The infiltration of rainfall
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
111
depends also on the soil moisture of the lower layer, since the lower layer and the
upper layer are coupled. The increase in soil moisture content of the upper layer
would increase the soil moisture of the lower layer due to moisture gradient and
gravity. A smearing of the rainfall over all the grids, as in the case of the lumped
representation of rainfall results in uniform wetting of the soil. This increases the
soil moisture of the surface layer uniformly over all the grids. In the case of a spa­
tial distribution of rainfall, there are some grids that get greater rainfall and some
that get lesser rainfall than the mean. There is also a fraction of grids that get no
rainfall. The greater than mean rainfall in most of the cases does not infiltrate,
and a portion of it constitutes runoff. The top panel in Figure 3.7 and Figure 3.8
shows the rainfall accumulation at 6:00am (from 6:00am of the previous day). This
can be seen in the context of the error (difference between the actual spatially dis­
tributed rainfall computed soil moisture and polarization difference index and the
lumped and the distribution representations of rainfall). The overestimation of
the ’’true” soil moisture (given by the distributed soil moisture) by the lumped
or the distribution representation of rainfall is greater for days with lower rain
accumulations and vice-versa. This can be seen by comparing the top panel and
second panel for the lumped representation case (in Figure 3.7) and the top panel
and second panel for the distribution based representation (Figure 3.8). The po­
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
112
larization difference index reflects the increased soil moisture in both the lumped
and the distribution based representations as seen in Figure 3.6 as a scatter plot,
and the overestimation of the spatially distributed rainfall polarization difference
index in Figure 3.7 and Figure 3.8 as a time series.
The spatial variation of the soil moisture and the 19, 37 GHz polarization
difference index is examined for the distributed vegetation, lumped rainfall, and
the lumped vegetation, distributed rainfall, in Figure 3.9. The spatial variability
is presented as the coefficient of variation. It can be seen th at the coefficient of
variation of the soil moisture in the distributed rainfall, lumped vegetation case is
far greater than that in the lumped rainfall, distributed vegetation case. The soil
moisture is affected to a greater extent by the spatial distribution of rainfall than by
the spatial distribution of vegetation as explained in the previous paragraphs. The
coefficient of variation of the polarization difference index for the case of distributed
vegetation, lumped rainfall shows a large degree of seasonal dependence. The
coefficient of variation is large during the growing season - April to September and is small in the remaining months. The coefficient of variation in the case of the
lumped vegetation and distributed rainfall case shows no seasonal dependence. The
polarization difference index is affected by changes in soil moisture and vegetation.
During the growing season, when the leaf area index is high, there is a greater
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
113
degree of variability in the leaf area index over the 100X100 grid, since the standard
deviation equals the mean leaf area index times the coefficient of variation.
V ariation s in th e variability of veg eta tio n and rainfall
The effect of change
in the coefficient of variation of the leaf area index and the fractional rainfall cover­
age is investigated. The coefficient of variation of the leaf area index was increased
from 0.655 to values of 1.0 and 2.0. The fractional rainfall coverage values of 0.5
and 0.8 were examined in addition to the value of 0.3. The results are summarized
in Table 3.1 for the case of the variation of vegetation heterogeneity, and in Ta­
ble 3.2 for the case of the fractional rainfall coverage variability. The results are
presented as the difference between the distributed case (of vegetation or rainfall)
and the lumped case (no spatial variation in vegetation and rainfall). The mean
difference and the root mean squared difference between the spatially distributed
and the lumped case are presented. This gives us an idea of the effect of spatial
variation of leaf area index and rainfall on soil moisture and polarization difference
index. The larger the mean difference, the larger the bias, and the higher root
mean squared difference corresponds to larger scatter between the two cases. In
the case of the soil moisture, the mean difference between the spatially distributed
and the lumped cases is low for both the vegetation and the rainfall cases. The
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C H A P T E R 3. THE EFFECT OF H ETEROGENEITIES
114
bias in the soil moisture caused by vegetation distribution is three orders of mag­
nitude smaller than that caused by the rainfall distribution. Both the biases are
very small. The root mean squared difference in soil moisture between the spa­
tially distributed and the lumped vegetation cases is extremely small. The mean
difference (bias) in the case of the polarization difference index is larger for the
case of the partial rainfall coverage cases than for the vegetation heterogeneity
cases. The bias for A T (polarization difference index) is very small for all three
cases of vegetation heterogeneity. The root mean squared difference (rmsd) be­
tween the spatially distributed vegetation case and the lumped vegetation case for
the polarization difference increases as the coefficient of variation of leaf area in­
dex increases (Table 3.1); cv=0.655, rmsd=0.13, cv=1.0, rmsd=0.18 and cv=2.0,
rmsd=0.22 for 19 GHz and cv=0.655, rmsd=0.14, cv=1.0, rmsd=0.19 and cv=2.0,
rmsd=0.24 for 37 GHz. Also, the root mean squared difference is higher for the
37 GHz frequency compared to the 19 GHz frequency due to greater interaction
of the 37 GHz radiation with vegetation as compared to the 19 GHz radiation.
The bias for soil moisture and AY for the partial rainfall coverage decreases as
the fraction (fi) increases and the heterogeneity in rainfall distribution decreases
(Table 3.2). The bias for the case of soil moisture is very small. The bias for
A T is -0.43 for /x=0.3, -0.31 for fi=0.5 and -0.20 for fi=0.8 for 19 GHz and -0.36
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
115
for fi=0.3, -0.26 for //=0.5 and -0.16 for pb=0.8 for 37 GHz. The effect of partial
rainfall coverage is greater on the 19 GHz frequency than on the 37 GHz frequency
due to the greater ability of the 19 GHz to penetrate to the soil layer. The root
mean squared difference for soil moisture and polarization difference index also
shows a decrease with an increase in the spatial coverage fi of rainfall at both 19
and 37 GHz frequencies. The spatial variability in rainfall has an effect on the soil
moisture. This is reflected in the polarization difference index for the 19 and 37
GHz frequencies. Since the 19 GHz is effected by soil moisture to a greater degree
than the 37 GHz frequency, the bias and rmsd values for polarization difference
index for the 19 GHz are greater than that for 37 GHz.
E ffects of lea f a re a in d ex an d soil m o istu re on th e v ariab ility of p o la r­
izatio n d ifference in d ex
The effect of the leaf area index on the polarization
difference variability for soil moisture variation over the 100X100 grid is shown
in Figure 3.10 for the 19 and 37 GHz cases, as well as tabulated in Table 3.3. In
Figure 3.10, the mean polarization difference index is plotted against the mean soil
moisture (as dots), and the width of the box drawn around the mean values (two
standard deviations) gives an idea of the extent of the variability of polarization
difference index in response to the variability to soil moisture and the leaf area
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C H A P T E R 3. THE EFFECT OF H ETEROGENEITIES
116
index. These boxes are drawn for two soil moisture contents, 0.12 and 0.21 and
for five values of leaf area index, 0.02, 0.11, 0.30, 0.75 and 1.15. As the leaf area
index increases from 0.02 to 1.15, the mean polarization index (denoted by the
dots in Figure 3.10) decreases, as does the standard deviation of the polarization
difference index for both the 0.12 and 0.21 mean soil moisture contents. The stan­
dard deviation of polarization diiference index for the mean soil moisture of 0.21
is greater than that corresponding to the mean soil moisture content of 0.12 for
all values of the leaf area index for both 19 and 37 GHz frequency cases. The
decrease in the mean polarization index with an increase in leaf area index is due
to the attenuation of the polarization difference signal by the vegetation canopy.
The decrease in the standard deviation or the spread of the polarization difference
values with a decrease in soil moisture is due to the lower variability of the lower
mean soil moistures. The standard deviations of the soil moistures are higher for
the higher mean soil moisture case than for the lower mean soil moisture case as
seen from Table 3.3. This is why the standard deviations of polarization difference
index for the mean soil moisture of 0.21 are greater than that corresponding to
the mean soil moisture content of 0.12 for all values of the leaf area index for 19
and 37 GHz. The decrease in the standard deviation of the polarization differ­
ence index with an increase in the leaf area index is due to masking of the signal
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
117
by the vegetation in a way that, even though the standard deviation of the soil
moisture is still large at leaf area index of 1.15 (compared to at leaf area index of
0.30), the higher leaf area index reduces the variability. This can also be seen in
the sensitivity of the range of polarization difference index between the residual
and saturation soil moisture in response to the leaf area index in Figure 2.13. As
the leaf area index increases, the range between the polarization difference index
corresponding to saturation soil moisture and residual soil moisture decreases.
E ffects on surface te m p e ra tu re
The polarization difference index derived
from the SSM/I observed data depends on the surface temperature. In this study,
comparison of surface temperatures obtained for various vegetation and rainfall
distributions show that surface temperature is a very robust variable. Simulation
experiments were carried out to see the differences in the simulated surface tem­
peratures for the various representations of vegetation heterogeneity and spatial
distribution of rainfall. The differences were very small. The root mean squared
difference between the lumped representation and a distributed representation for
leaf area index for coefficients of variation 0.655, 1.0 and 2.0 were 0.09, 0.24 and
0.47 K respectively, and for a rainfall fractional coverage of 0.3, 0.5 and 0.8 were
0.028, 0.023 and 0.021 K respectively. This shows that using a lumped representa­
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
118
tion of the leaf area index or input rainfall does not result in any significant errors
in surface temperature. The root mean squared difference between the air tem per­
ature and the surface temperature corresponding to cv=2.0 for leaf area index is
2.6 K , and between the air temperature and the case of rainfall fractional coverage
of 0.3 is 2.4 K . This shows that the surface temperature is quite stable and can be
approximated by the air temperature during the inversion of the SSM/I brightness
tem perature to obtain soil moisture. This result will be used in the next section.
3.6
E ffect o f h ete r o g e n e ity on soil m o istu r e e s­
tim a tio n
This section will examine if the soil moisture estimated from the SSM/I bright­
ness tem perature is biased compared to the actual average soil moisture derived
by simulation. This section uses the simulation framework to investigate the effect
of heterogeneities in soil moisture and leaf area index on the estimation of soil
moisture using the simulated SSM/I brightness temperatures. The SSM/I esti­
mated soil moisture will be compared to the simulated soil moisture to examine
if it is biased due to the non-linearities in the inversion process. The simulation
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
119
of the polarization difference index was seen to exhibit certain biases with respect
to spatial distribution of rainfall. The study in this section will help determine if
those biases affect the inversion process in the estimation of soil moisture. The
knowledge gained from this study will greatly help in the estimation of regional
soil moisture using SSM/I data.
3 .6 .1
T h e effect o f d istr ib u te d so il m o is tu r e o n s o il m o is ­
tu r e e s tim a tio n
The examination of the effects of the heterogeneity on the process of inverting
the brightness temperatures to estimate soil moisture is outlined in the flowchart
(Figure 3.11). Since the representation of the spatial distribution of rainfall using
a lumped representation resulted in significant biases in soil moisture and the po­
larization difference index, the distributed rainfall field and a distributed leaf area
index with a coefficient of variation of 1.0 was chosen to simulate a distributed
soil moisture field on a 100X100 grid. This simulation is similar to the simulation
described in the previous section, with rainfall described by an exponential dis­
tribution (Warrilow et. al., 1986) and a fractional coverage of 0.3. This is used
to carry out simulations on a hourly time step and compute the 19 GHz bright­
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C H A P T E R 3. THE EFFECT OF H ETEROGENEITIES
120
ness temperatures corresponding to a 6:00am satellite overpass. .The distributed
(100X100) soil moisture is used to compute the 19 GHz SSM/I horizontal and
vertical polarization distributed brightness temperatures fields (100X100). The
distributed brightness temperature field (100X100) is averaged. In this simulation
experiment, we shall assume that the SSM/I sensor observes this average value
over the area, i.e., radiances from each of the 10000 areas are equally weighted
by the sensor to give an observed brightness temperature that equals an average
of all the radiances. In addition, it is assumed that the radiances (or brightness
temperatures) simulated by using the canopy radiative transfer model (Choudhury
et. al., 1990) and the atmospheric attenuation model (Choudhury et. al., 1993)
are realistic representations of the radiative processes affecting the SSM/I sensor.
This is a reasonable assumption, as the canopy radiative transfer model (Choud­
hury et. al., 1990) is based on the physics of scattering elements (leaves, stems and
branches) and the atmospheric attenuation model (Choudhury, 1993) is based on
observed upper air sounding data. We shall refer to this brightness tem perature as
the SSM/I ’’observed” brightness temperature. This SSM/I observed brightness
tem perature is used to estimate the soil moisture. The soil moisture is derived
by minimizing the absolute difference between the brightness temperature simu­
lated using the various soil moistures between the residual soil moisture and the
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
121
saturated soil moisture levels (using the radiative transfer model for the canopy
and an attenuation model for the atmosphere) and the SSM/I ’’observed” bright­
ness temperature. In the inversion process, the air temperature is used instead
of the surface temperature. This is because : (a) we have no knowledge of the
surface temperature during the inversion process and (b) as seen from the results
of the previous section, air temperature is a good approximation of the surface
tem perature as the root mean squared differences are around 2.5 K (less than 1%
of the surface temperature). The derived soil moisture is compared to the aver­
age of distributed soil moisture field (obtained by simulation). The averaged soil
moisture and one standard deviation on each side of the average is plotted versus
the SSM/I brightness temperature derived soil moisture in Figure 3.12. It can be
seen that despite the averaging, there is good agreement between the two sets of
soil moisture values. In fact, the largest of the differences between the average of
the simulated soil moisture field and the SSM/I derived soil moisture is 0.1, and a
root mean squared difference of 0.02. The corresponding results using the 37 GHz
frequency have not been displayed, but show similar behavior. The root mean
squared difference between the estimated and the simulated soil moisture content
is 0.021, and the maximum error is around 0.1. This shows that the heterogene­
ity in soil moisture does not cause a bias in the estimation process. However, it
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
122
does not tell us the variability of the soil moisture. In the case of SSM/I coverage
wherein the soil moisture can exhibit variability, the data from the SSM/I is an
average from the field of view of the sensor.
3 .7
In terp reta tio n o f resu lts in th e c o n te x t o f
S S M /I footp rin t
In the above discussions of the effects of heterogeneity on the simulated soil mois­
ture and polarization difference index, no reference has been made to the actual
variations of leaf area index or spatial distribution and coverage of rainfall in the
SSM/I field of view. The SSM/I field of view is 56kmX56km for the 19 GHz fre­
quency and 33kmX33km for the 37 GHz frequency. There are variations in leaf
area index and rainfall at these scales. However, instead of explicitly investigating
for a particular set of variations, an entire spectrum of variations were investigated
in this chapter. The coefficient of variation for the leaf area index of 0.655 (corre­
sponding to the FIFE site), 1.0 and 2.0 results in a range of standard deviations up
to 2.2. The mean leaf area index in this study varies between 0.02 and 1.5. This
is a range of variation for the Midwestern United States, corresponding to Kansas.
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C H A P TE R 3. THE EFFECT OF HETEROGENEITIES
123
The studies carried out in this chapter are not tied to any particular geographical
location, but are intended to investigate the various effects on SSM/I observation
and estimation. The results of this study hold up well for the presented range of
leaf area index data and its variability. Different fractional coverages of rainfall
have been studied, and the results are interpreted over the range of these values.
Therefore, the results from the effect of spatial distribution and coverage of rainfall
also hold up well for other situations. Hence, even without explicit reference to
the SSM/I field of view, the findings of this study hold applicability to a broad
array of cases.
3.8
C on clu sion s
The resolution of the Special Sensor Microwave Imager (SSM/I) is of the order of
56km at 19 GHz and 33A:m at 37 GHz. At these resolutions, there is an existence
of heterogeneity in land surface variables that affect the sensor (vegetation and
soil moisture). Polarization difference index is a measure of the soil moisture. The
sensitivity of the polarization difference index to the soil moisture is affected by the
leaf area index; an increase in leaf area index decreases this sensitivity. The effect
of heterogeneity of leaf area index and the spatial variability of rainfall on the sur­
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
124
face soil moisture and the SSM/I observations through the use of the polarization
difference index is examined. The results show that different representations of
vegetation variability (variability of leaf area index) do not show different results
for the soil moisture or polarization difference index. An average value of leaf area
index would be a sufficient representation. On the other hand the spatial distri­
bution of rainfall has to be properly represented, as soil moisture and polarization
difference index show sensitivity to the spatially distributed rainfall representa­
tion. In addition, spatial variability in rainfall causes a spatial variability in soil
moisture and the polarization difference index. This is less pronounced for the
spatial variations in vegetation. An increase in the coefficient of variation of the
leaf area index does not affect the soil moisture and the polarization difference in­
dex. The increase in fractional coverage of rainfall decreases the bias as well as the
root mean squared differences between the lumped and the spatially distributed
representation of rainfall. The surface temperature is a very stable variable and
shows almost no change for the different cases of heterogeneity. Also, the differ­
ences between the surface temperature and the corresponding air temperatures are
very small, and the air temperatures are used in place of surface temperatures in
the soil moisture estimation from SSM/I brightness tem perature data. In the case
of using the SSM/I observations for soil moisture estimation, the heterogeneity in
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
125
vegetation and spatial distribution and coverage of rainfall (hence distributed soil
moisture) is seen not to introduce a bias. Therefore, it is concluded that for this
case study, the relationship between the SSM/I brightness tem perature and the
soil moisture and vegetation leaf area index is only weakly non-linear. This weak
non-linearity does not introduce a bias in the soil moisture estimation using the
SSM/I brightness temperature data. This is very encouraging for the use of the
SSM/I sensor for the estimation of soil moisture.
i
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126
C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
cv
mean 6
rmsd 0
mean A Y
rmsd A 7
mean A y
rmsd A y
(19 GHz)
(19 GHz)
(37 GHz)
(37 GHz)
0.655
-.00006
0.00262
0.07562
0.13467
0.07808
0.13658
1.0
-.00002
0.00395
0.08063
0.18117
0.08866
0.18814
2.0
0.00071
0.00637
-.03044
0.22427
0.00071
0.23513
Table 3.1: Comparison of different coefficient of variation (cv) of leaf area index
with the case of lumped leaf area index for mean and root mean squared difference
(rmsd) of the spatially distributed case with the lumped case for soil moisture and
polarization difference index
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
p
mean 6
rmsd 9
127
mean A Y
rmsd A F
mean A F
rmsd A F
(19 GHz)
(19 GHz)
(37 GHz)
(37 GHz)
0.3
-.02026
0.03914
-.43192
0.77532
-.35649
0.70524
0.5
-.01462
0.02980
-.30967
0.58493
-.25679
0.53871
0.8
-.00930
0.01996
-.19540
0.38139
-.15973
0.35688
Table 3.2: Comparison of different fractional coverage of rainfall (/x) with the
case of uniform rainfall for mean and root mean squared difference (rmsd) of the
spatially distributed case with the lumped case for soil moisture and polarization
difference index
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128
C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
e
L
ere
AF
OAY
AF
O'AY
19 GHz
19 GHz
37 GHz
37 GHz
0.12
0.02
0.02
6.17
0.56
5.22
0.40
0.12
0.11
0.02
5.91
0.52
4.97
0.36
0.12
0.30
0.01
5.28
0.35
4.38
0.24
0.12
0.75
0.01
4.20
0.30
3.36
0.20
0.12
1.15
0.01
3.43
0.25
2.66
0.16
0.21
0.02
0.05
8.79
1.44
7.53
1.29
0.21
0.11
0.06
8.21
1.68
7.03
1.45
0.21
0.30
0.05
7.68
1.26
6.47
1.07
0.21
0.75
0.07
5.92
1.21
4.83
1.03
0.21
1.15
0.07
4.80
1.09
3.80
0.91
Table 3.3: Variation of polarization difference index with leaf area index and soil
moisture
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
129
SSM /I observed brightness temperature
distributed radiance
distributed soil m oisture and vegetation
OBSERVATION
SSM /I estim ated soil m oisture
ESTIMATION
Figure 3.1: Schematic representation of the observation of heterogeneity in soil
moisture and the estimation of soil moisture
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
130
lumped case
vegetation and
soil moisture
polarization difference
rain
index - 19, 37 GHz
100 X 100
average
frequency
distribution case
11 classes
soil m oisture
distribu :ed case
100X 100
polarization difference
soil moistiare
index, 19, 37 GHz
polarizatic >n difference
index - 19 37 GHz
average
average
compare
compare
Figure 3.2: Flow chart of the numerical experiment for investigation of heterogene­
ity of vegetation and rainfall on a 100 X 100 grid.
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
131
o
in
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0
100
200
o
300
distributed v eg e ta tio n ; lu m p ed rainfall
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Figure 3.3: Variation of leaf area index, soil moisture and polarization difference
index (19 and 37 GHz) for distributed leaf area index and lumped rainfall for
January 1 to December 31, 1987
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
132
in
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Julian D ay (Jan u ary 1 • D e c e m b e r 3 1 , 1 9 8 7 )
Figure 3.4: Variation of leaf area index, soil moisture and polarization difference
index (19 and 37 GHz) for lumped leaf area index and distributed rainfall for
January 1 to December 31, 1987
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
133
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Figure 3.5: Comparison of distributed versus lumped and distribution based cases
for soil moisture and 19 and 37 GHz polarization difference index for distributed
vegetation case (rainfall lumped)
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
(0
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Figure 3.6: Comparison of distributed versus lumped and distribution based cases
for soil moisture and 19 and 37 GHz polarization difference index for distributed
rainfall case (vegetation lumped)
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135
C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
to
daily a c c u m u la te d
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200
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Figure 3.7: Rainfall difference in soil moisture and polarization difference index for
19 and 37 GHz between the spatially distributed representation and the lumped
representation of rainfall for January 1 to December 31, 1987
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
136
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Figure 3.8: Rainfall difference in soil moisture and polarization difference index
for 19 and 37 GHz between the spatially distributed representation and the distri­
bution based representation of rainfall for January 1 to December 31, 1987
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
137
distributed v e g e ta tio n ; lu m p ed rainfall
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distributed v e g e ta tio n ; lu m p e d rainfall
polarization d iffe re n c e index
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lu m p ed v o g e ta tio n ; d istributed rainfall
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Figure 3.9: Coefficient of variation (cv) for soil moisture and the 19 and 37 GHz
polarization difference index for the distributed vegetation, lumped rainfall and
the lumped vegetation distributed rainfall
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
138
oT*
a
19 GHz
to
no
Cl
o
0.0
soil moisture
0.0
0.1
0.2
0.3
0.4
0.5
soil moisture
Figure 3.10: Variability of polarization difference index and soil moisture for dif­
ferent leaf area indices. The leaf area indices are 0.02, 0.11, 0.30, 0.75 and 1.1, top
to bottom. The dots indicate the mean and the boxes are two standard deviations
wide
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
139
rain, L A I
d istrib u ted
soil m oisture
average
distributed
soil m oisture
average
brightness
tem perature
com pare
distributed
average
a v erag e
LAI
SSM /I
derived
soil m oisture
average
brightness
SSM /I
tem perature
observed
Figure 3.11: Flowchart for investigation of the effect of a spatial distribution of
rainfall, vegetation and soil moisture on the SSM/I estimated soil moisture
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C H A P T E R 3. THE EFFECT OF HETEROGENEITIES
140
Soil moisture
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Average simulated
Figure 3.12: Average of the simulated volumetric soil moisture (dot) and two
standard deviations versus the the soil moisture derived from the average 100X100
brightness temperature (19 GHz)
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C h a p ter 4
E v a lu a tio n o f S S M /I S a te llite
D a ta for R egion al Soil M o istu re
E stim a tio n
4.1
In tro d u ctio n
Soil moisture is an important hydrological variable in a variety of land surfaceatmosphere interactions. Soil moisture controls the partitioning of rainfall into
runoff and infiltration. It affects (along with the surface temperature) the depth
of the planetary boundary layer, circulation/wind patterns (Mahfouf et. al., 1987,
141
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C H A P T E R 4. S S M /I REGIONAL SOIL M OISTU RE E STIM A T IO N
142
Lanicci et. al., 1987 and Zhang et. al., 1989) and regional water and energy bud­
gets. The study of global climate using GCMs has shown that soil moisture is a
very im portant factor (Walker et. al., 1977; Rowntree et. al., 1983; Rind, 1982;
Carson et. al., 1981; Mintz, 1984). Evapotranspiration plays an im portant role
in determining surface temperatures, surface pressure, rainfall and motion (Shukla
et. al., 1982). Evapotranspiration in turn depends on soil moisture (together with
incoming radiation and a host of other meteorological factors). Soil moisture is
very closely connected with hydrology and climate (Yeh et. al., 1984). Surface soil
moisture is an im portant factor in agricultural applications. Soil moisture is an im­
portant output variable of hydrological models, and simulated soil moisture can be
compared against observations to determine the validity of the parameterizations
used in modeling.
The variations of soil moistures over different spatial and temporal scales make
soil moisture difficult to characterize. Field measurements of soil moisture are
not a practical choice due to resource constraints when soil moisture over large
areas is to be ascertained. In addition, field measurements have to be carried
out at spatial intervals smaller than the correlation lengths of the soil moisture.
Therefore, in characterizing soil moisture over large areas, remote sensing is an
attractive proposition. Microwave remote sensing is very suitable, since there is a
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C H A P T E R 4. S S M /I REGIONAL SOIL M OIS TU RE ESTIMATION
143
sensitivity of the sensor to moisture due to the dipolar nature of the water molecule.
Numerous efforts using remotely sensed satellite data to yield estimates of soil
moisture have been carried out. The 6.6 GHz data from the Scanning Multichannel
Microwave Radiometer (SMMR) has been used to estimate soil moisture and com­
pared with weekly field measurements (Owe et. al., 1992) fpr a 150km X 150A:m
region in Africa. The 6.6 GHz SMMR has also been used over the Southern Great
Plains region of U.S for estimating soil wetness using the antecedent precipitation
index (API) formulation (Choudhury et. al., 1988). Teng et. al., (1993) use the
19 GHz data from the Special Sensor Microwave Imager (SSM/I) to estimate the
API using regression techniques. Heymsfield et al., (1992) study the effect of soil
moisture on SSM/I observed radiances. The previous studies use simplified hy­
drological modeling in their investigations of the correlation between the satellite
observed SSM/I brightness temperatures and soil moisture. The present study
uses a detailed hydrological model for water and energy balance to compute both
the surface temperature and soil moisture.
Our effort here is to use the data from the Special Sensor Microwave Imager
(SSM/I) to estimate soil moisture.
Successful simulation of SSM/I brightness
temperatures is the first step in using SSM/I data for continental-scale hydrologic
modeling. This would help in understanding how satellite data can be used for
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CH A P T E R 4. S S M / I R E G IO N AL SOIL M OIS TU RE ESTIMATION
144
water and energy budget modeling. The coupled soil-canopy-atmosphere model
that has been described in Chapter 2 is used to carry out these simulations. The
thin-layer model of soil hydrology (based on Mahrt et. al., 1984) uses meteorologi­
cal input (both longwave and shortwave incoming radiation, air temperature, dew
point temperature, wind speed and rainfall) and vegetation data to carry out water
and energy budgets for two layers : a 1cm top layer, and a second layer extending
from the bottom of the top layer to a depth of 1.0m. The top layer volumetric soil
moisture and temperature serve as boundary conditions for the canopy radiative
transfer model. The canopy radiative transfer model (Choudhury et. al., 1990)
solves the radiative transfer equation using Gaussian quadrature for the canopytop horizontally and vertically polarized brightness temperatures. The model is
based on a high frequency approximation and assumes that there is no transmission
of radiation by the stems and branches. The canopy-top brightness temperatures
undergo atmospheric attenuation (Choudhury et. al., 1993) due to atmospheric
oxygen and water vapor before resulting in the at-satellite brightness tem pera­
tures. This coupled soil-canopy-atmosphere model has been used to simulate the
brightness temperature for the Red River basin area that extends from 31.5°N to
36° N and 94.5°W to 104.75°W for a period of one year (August 1, 1987 - July
31, 1988) for horizontal and vertical polarizations of the 19 and 37 GHz brightness
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CH A P TE R 4. S S M / I REG IONAL SOIL MOISTURE EST IM ATI ON
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temperatures. The observed brightness temperatures have been used to derive the
soil moistures, which are compared to the simulated values. The results have been
encouraging.
4.2
S p ecia l Sensor M icrow ave Im a g er (S S M /I )
The Special Sensor Microwave Imager (SSM/I) provides a measure of the bright­
ness temperature at four frequencies (19.4, 22.2, 37.0 and 85.5 GHz) and two
polarizations (horizontal and vertical) for each of the four frequencies (except for
22.2 GHz, which has only vertical polarization). The SSM/I is flown on the Defense
Meteorological Satellite Program (DMSP) spacecraft at an altitude of 833 km with
an orbit period of 102 minutes and an inclination of 98.8° and an equatorial cross­
ing of 0613 local time during the ascending orbit. The swath width of the sensor
is 1400 km, and the zenith angle is 53.1°. The beam resolution is approximately
12.5 km in the along-track and cross-track directions. The resolution of the sensor
varies with frequency. The footprint size is about 56 km at 19 GHz and 33 k m at
37 GHz. The data was gridded on a 0.25° X 0.25° grid and used for comparing the
simulated values. The ascending orbit of the SSM/I was used because during this
time, the land surface conditions are relatively homogeneous and the analysis and
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C H A P T E R 4. SS M/ I REGIONAL SOIL M OIS TU RE ESTIMATION
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interpretation of the SSM/I data is easier. The data is between August 1, 1987
and July 31, 1988. There are missing days - all of December 1987, the first twelve
days of January 1988, a day in October 1987 and three days in May 1988. The
SSM/I overheated and was turned off during December 1987 and up to January
12, 1988. There are some missing days over individual pixels due to the precession
of the orbits. The standard error of the determination of the absolute calibration
of SSM/I is ± 3 K (Hollinger et. al., 1990). This has been determined from com­
parisons using the SSM/I aboard an aircraft and flying it over ocean, forest and
desert areas.
4 .3
M eth o d s
4 .3 .1
D a ta se ts
The summary of the data sets and the parameters used in this study is presented
in the following paragraphs as well as tabulated in Table 4.1.
S u rface A irw ays M eteorological D a ta
The surface airways data (17 stations
on a hourly basis) are from Earthlnfo’s NCDC (National Climate Data Center)
surface airways data product. The variables used here from that database are
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C H A P T E R 4. S S M / I REG ION AL SOIL MOISTURE ESTIM ATION
147
air temperature, dew point temperature, air pressure, wind speed, cloud height
(defined as the height of the lowest sky cover layer more than 1/2 opaque), total
sky cover and wind speed. Table 4.2 gives a list of the surface airways stations as
well as their geographical location.
R a d ia tio n
The incoming longwave radiation is given by
h = K E acxT*
(4.1)
where i f is a factor th at accounts for cloud cover effects and is given by i f =
1 + 0.17N 2 (TVA, 1972), N is the fraction of the sky covered by clouds, E a is the
atmospheric emissivity given by (Idso, 1981) Ea = 0.740 + 0.0049e, e is the vapor
pressure in millibars, a is the Stefan Boltzmann constant (5.67-X10-8 J m -25-1i f -4)
and Ta is the surface air temperature.
The Image Processing Workbench (IPW) (Frew, 1990; Dozier et. al., 1989)
is used to generate incoming clear-sky shortwave radiation based on the digital
elevation map of the area. This value is corrected for cloud cover effects (Eagleson,
1970)
i
f = l-{l-K )N
(4.2)
-*C
where l's is the corrected incoming shortwave radiation, Ic is the clear-sky incoming
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C H A P T E R 4. S S M / I REG IONAL SOIL MOIS TU RE ES TI M AT IO N
148
shortwave radiation and K is a factor that accounts for the cloud height ( K =
0.18 + 0.0853z, where z is cloud base altitude in kilometers).
V e g eta tio n
The vegetation data has been obtained from the University of Mary­
land reprocessed NO AA Global Vegetation Index Data Product (Goward et. al.,
1993). This NOAA-GVI has been created from measurements made by the Ad­
vanced Very High Resolution Radiometer (AVHRR) on board NOAA polar orbiting
satellites. The data comprises three years (1983, 1987, 1989) of bi-weekly compos­
ite observations. The observations were mapped to a Plate Carree’ projection and
calibrated radiometrically for spectral reflectance. Biweekly composites of Normal­
ized Difference Vegetation Index (N D V I ) were used to minimize the amount of
cloud contamination. The Plate Carree’ projection (between 75°N and 55°S) has a
resolution of about 16km at the equator. The apparent reflectance was calculated
by using the digital number (NOAA-GVI), preflight gain and degradation ratio.
This apparent planetary reflectance is corrected based on the distance between the
sun and the earth and the solar zenith angle to give the true planetary reflectance
is used to calculate the N D V I as
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C H A P T E R 4. S S M /I REGIONAL SOIL M OI S TU RE ESTIMATION
149
where N I R and V I S are the near infra-red and the visible planetary reflectances.
The values of the N D V I computed as above were corrected by Goward et. al.,
(1993) (in a linear fashion) to account for the off-nadir and backscatter views
preference of the GVI processing and the effect of atmospheric attenuation on
spectral measurements (Goward et. al., 1993). The resulting N D V I values were
converted to leaf area index {LAI) using a Beer’s law kind of variation (Baret et.
al.,1991) as
N D V I = N D V I oo + { N D V I g - N D V I «*,)exp( ~ K NDVIL A I )
(4.4)
where N D V I g corresponds to bare soil (0.193), NDVIqo is the asymptotic value
when L A I tends to infinity (limit reached when L A I greater than 8.0) and
K ^
dvi
controls the slope (an extinction coefficient). The values of K ^ d v i and NDVIoa
depend on the average leaf inclination (equal 0.93 and 0.965 for average leaf incli­
nation of 50°) (Baret et. al., 1991).
The other vegetation parameters for the simulation used by the canopy radiative
transfer model are thickness of the leaf (0.1mm), volumetric stem moisture content
(0.1) and volumetric branch moisture content (0.1). The stem to ground area ratio,
branch to stem area ratio and the volumetric moisture of the leaf are estimated as
described in a later section.
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CH A P T E R 4. S S M / I REGIONAL SOIL M OI S TU RE ESTI MA TI ON
R ain fall
150
The Manually Digitized Radar is a program that produces a complete
computer generated composite map of the echo characteristics. The MDR data
has been generated using information from all the 100 radars around the country
(Moore et. al. 1979). The data is presented as VIP (Video Integrator and Proces­
sor) levels, which are the maximum levels for that particular grid box. The VIP
levels are related to the rainfall rate (echo intensity is a function of precipitation)
and MDR VIP levels 1, 2, 3, 4, 5 and 6 correspond to an echo intensity of light,
moderate, heavy, very heavy, intense and extreme. The VIP levels are converted
into rain rates using conversion tables (Fan et. al., 1995), which take into account
the geographical position of the MDR pixel, the month of the year and the time of
the day. The spatial resolution of the MDR data is 40km. Climatological studies
using the MDR data (Baeck et. al., 1994) have shown that the data is useful in
hydroclimatological studies. The data is described in more detail in Baeck et. al.,
1994.
V ap o r P re s s u re
The saturation vapor pressure (es in Pa = N m ~ 2) is related
to air tem perature (Ta in K ) as (Raudkivi, 1979)
_
,17.27T0 - 4717.47,
e, = 611 exp(
)
(4.5)
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CH A P TE R 4. S S M /I REGIONAL SOIL MOISTU RE ESTIMATION
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The saturation vapor pressure at the dew point temperature (Tj) equals the vapor
pressure of the ambient air (ea).
P re c ip ita b le W a te r
The precipitable water content was compiled using the
Hydrologic Research Laboratory, National Weather Service radiosonde data for
stations in North America for 1972-1988 (Bradley et. al., 1993). The original
source of this data is from the National Climatic Data Center. The data was
corrected for errors resulting in radiosonde equipment changes, reporting methods
for relative humidity data and degradation of quality of data due to automation, as
well as for the existence of unrealistic superadiabatic layers (Bradley et. al., 1993).
The precipitable water is defined as the liquid equivalent of the water vapor in the
atmospheric column and is computed as
y = -------- /
qdp
(4.6)
g p w J po
where g is the acceleration due to gravity (9.8ms-2), pw is the density of water
(lOOOgcm-3 ), q is the specific humidity and p is the pressure, where pQ is chosen
to be 300mb and pa is the surface pressure. The precipitable water was computed
for the OZ radiosonde soundings and used for the whole day, so a field of 32 X
71 values were extracted from the North America data set for each day between
August 1, 1987 and July 31, 1988.
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CH A P TE R 4. S S M /I REG IO N AL SOIL MOISTURE ESTIMATION
Soils D a ta
152
Soil type data for the Red River basin was available (Abdulla, 1995).
Most of the Red River basin is composed of silt loam and loam soil. The soil for
the region outside the Red River basin was considered as a uniform silt loam (in
the absence of a distributed data set). The Brooks-Corey parameters for a silt
loam soil are #r=0.02, 0a=O.5O, ^){6S)= 0.2m ,K , = 1.89X10_6m s_1 and m=0.2
(Rawls et. al., 1982).
4 .3 .2
D e sc r ip tio n o f s tu d y area
The present study is carried out over an areal extent of 4.75° in latitude and 10.5°
in longitude in the southwestern plains of United States (Figure 4.1). The study
area includes 19 rows and 42 columns of 0.25° boxes or grid cells of observed
SSM/I data. The study area includes a small part of eastern New Mexico, most of
Oklahoma (except a small part in the north) and northern Texas (a small portion
of the panhandle is left out). The study area has a topographic relief between 6001500m in the High plains of eastern New Mexico and western Texas, 300-600m in
Mid-continent plains of north central Texas and central Oklahoma, 150-300m in
eastern Oklahoma and 0-150m in the Gulf Atlantic rolling plains of southeastern
Texas. The area is made up of gently sloping plains in the eastern Texas and
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C H A P T E R 4. S S M / I REG IONAL SOIL MOIS TURE ESTI MA TIO N
153
western New Mexico region; irregular plains in the eastern Texas and Oklahoma
region and the central part consists of mostly moderate relief tablelands. The
vegetation ranges from Grama-buffalo grass in eastern New Mexico and Western
Texas to Mesquite-buffalo grass in south central Texas; cross timbers in north
central Texas and oak hickory pine forests in south eastern Oklahoma and eastern
Texas. The land types in the study area include sub humid grassland, semiarid
grazing land, crop land, irrigated land, crop land pasture, woodland and forests.
The land use in the Central Great Plains is winter wheat cultivation and range
(east New Mexico, Western Texas and western Oklahoma); cotton and forage in
the Southwestern prairie (central Texas and Central Oklahoma); South Atlantic
and Gulf slope cash crops in east Texas; and general farming, forests and livestock
in eastern Oklahoma. Winter wheat is grown in northwest Texas and most of
Oklahoma; barley in central Oklahoma and cotton in eastern Texas. There are no
forests in eastern New Mexico and western Texas. The remaining area consists of
oak hickory, oak pine and small leaf pine trees in the forested areas. The mean
annual precipitation ranges from around 40cm in the western regions to 120cm in
the eastern regions of the study area. The eastern part of the study area (eastern
Oklahoma and eastern Texas) have many reservoirs : Lake Texoma at the TexasOklahoma border, the Garza-Little Elm reservoir and the the Whitney Reservoir
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C H A P T E R 4. S S M / I REGIONAL SOIL MOIS TU RE E S TI M AT IO N
154
in eastern Texas and the Eufaula reservoir in western Oklahoma.
4 .3 .3
C a lib r a tio n o f p a ra m eters an d s im u la tio n m e th o d s
The coupled soil-canopy-atmosphere model is used to compute the brightness tem ­
peratures coinciding with the time of the satellite 6:00am ascending overpass. The
scheme for calibration and validation is outlined in Figure 4.2. The spatial resolu­
tion of the simulations is the same as that of the Global Vegetation Index (GVI)
data set, which is approximately 16A:m at the equator. This results in 32X71 grid
cells over the study area for the simulations. In the calibration, the coupled soilcanopy-atmosphere model is used to simulate the soil moisture, surface tem pera­
ture and the 19 GHz polarization difference index for a period of 90 days beginning
August 1, 1987. The observed polarization difference index corresponding to the 19
GHz SSM/I data is computed by using the surface tem perature (computed using
the hydrological model), the precipitable water (derived from radiosonde data) and
the air tem perature (obtained from the surface airways stations). This observed 19
GHz polarization difference index is resampled from the 19X42 grid to the simula­
tion grid of 32X71 grid cells. The simulated 19 GHz polarization difference index
and the resampled SSM/I observed 19 GHz polarization difference index are used
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C H A P T E R 4. S S M / I REGIONAL SOIL M OI S TU RE ES TI M AT IO N
155
to estimate the vegetation parameters, namely the stem area ratio, the branch to
stem area index and the volumetric moisture content of the leaf. The parameters
are computed by minimizing the root mean square difference between the observed
and the simulated 19 GHz polarization difference index over a 90 day period for
each of the 32X71 grid cells.
The resulting set of 32 rows by 71 columns of parameter values for each grid
cell is used to carry out the simulations for the remainder of the duration from
October 30, 1987 to July 31, 1988. The coupled soil-canopy-atmosphere model is
used to perform simulations at an hourly time step and to obtain hourly values
of soil moisture and the 19 and 37 GHz brightness temperatures corresponding
to the 6:00am SSM/I ascending overpass. The simulated soil moisture and the 19
and 37 GHz brightness temperatures are resampled to the SSM/I observation grid,
i.e., from 32X71 to 19X42 for purposes of comparison with the SSM/I brightness
tem peratures and the SSM/I estimated soil moisture. In addition, the simulated
surface tem perature at 6:00am during the SSM/I ascending overpass is compared
with the minimum air temperature used as a surrogate for the observed surface
tem perature (McFarland et. al., 1990). The observed brightness temperatures are
used to derive the polarization difference index for the 19 and 37 GHz frequency by
using the atmospheric data and approximating the surface tem perature with the
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C H A P T E R 4. S S M /I REGIONAL SOIL MOISTU RE ESTIMATION
156
observed air temperature since the surface temperature is unknown. The canopy
radiative transfer model is iterated for the soil moisture so that the error between
the computed and the observed polarization difference index is minimized. The
soil moisture corresponding to this minimum difference between the simulated and
the observed polarization difference index is the SSM/I estimated soil moisture.
4 .4
R e su lts and D iscu ssio n
4 .4 .1
E rrors an d co r re la tio n s o n d ifferen t t im e sc a le s
The simulated values of soil moisture and average and polarization difference
brightness temperatures are compared with the SSM/I derived soil moistures and
average and polarization difference brightness temperatures. The root mean squared
differences between the simulated and observation derived quantities is computed
on a daily basis and averaged on a weekly and monthly basis for the entire area of
19 X 42 grid cells or pixels. The sum of squared difference for each pixel (i , j ) is
computed over the time steps of the entire year n as
S(X"(i,i)) =
(4.T)
J=1
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C H AP TE R 4. S S M / I REG IONAL SOIL MOISTURE ESTIM ATION
157
where X,im is the simulated and X Dba is the observed quantity X (soil moisture 0\
average brightness temperature T b ] polarization difference brightness tem perature
A Tb ) and v is the frequency of the SSM/I (19 or 37 GHz).
The root mean square difference is determined as
E { X " ( i tj ) ) = ( S ( X " ( i , j ) ) / N ( i , j ) ) ' l 2
(4.8)
where N ( i , j ) is the number of the time steps for each pixel ( i, j) for which the
SSM/I observations are available to compute X . The mean and standard deviation
of this error E ( X ) and
cte(X )
is determined. The soil moisture derived from
the 19 GHz SSM/I observations is different from that derived from the 37 GHz
observations. However, both the observation derived quantities are compared with
the same set of simulated soil moistures, i.e., 9]fm and 6^Jm are the same. In the
case of the weekly averaged quantities, X aimv(i,j) and X 0h3v{i,j) are averaged
over a week and a month for the frequency v and the pixel location (i, j). The
results of the root mean squared differences are given in Table 4.3. As expected,
the mean of the errors decreases as the averaging of the quantities is carried out.
On the other hand the standard deviations do not show any consistent trend. The
correlation between the simulated and the SSM/I observation derived soil moistures
(Figure 4.3) reveals that the monthly averaged values show a correlation coefficient
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C H A P TE R 4. S S M / I REGIONAL SOIL MOISTURE ES TIM ATI ON
158
(r) between 0 and 0.5 (for both the 19 and 37 GHz derived soil moistures). The
values range from 0.0 in June 1988 to 0.59 in March 1988 for the 19 GHz derived
soil moistures, and from 0.17 in August 1987 to 0.59 in March 1988. The variation
of r for the monthly averaged case is much smoother than the weekly averaged
r variation or the daily r variation as seen in Figure 4.3. The r values for the
weekly averaged case vary between -0.1 to 0.63 for the 19 GHz case and between
-0.15 and 0.60 for the 37 GHz case. In the case of r based on the daily values, the
variations are much larger than the previous two cases and range between -0.4 to
0.75 for the 19 GHz case and between -0.5 to 0.63 for the 37 GHz case. As the
time period for the averaging decreases from monthly to daily, the range of the
correlation coefficient increases.
The distribution of errors for soil moisture and average and polarization differ­
ence brightness temperatures are shown in Figure 4.4, Figure 4.5 and Figure 4.6
respectively for the 19 and 37 GHz frequencies. They show results similar to that
in Table 4.3, i.e., as the averaging time frame increases (daily to weekly to monthly
averages), the peak frequency of the root mean squared differences moves to lesser
values of error. The peak frequency of 0.36 at 0.125 root mean squared difference
for soil moisture for the daily comparison versus 0.35 for the peak frequency at
0.075 for the weekly comparison versus 0.36 for the peak frequency at 0.075 for the
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C H A P T E R 4. S S M / I REGIONAL SOIL M OI S TU RE ES TI M ATI ON
159
monthly comparison for the 19 GHz case. The difference between the weekly and
monthly cases is such that there is more mass under the frequency distribution at
the lower values of error for the monthly averaged case as opposed to the weekly
averaged case. This can be seen by comparing the solid lines in the middle and
bottom panels in Figure 4.4. A similar trend is seen for the 37 GHz frequency
case. In the case of the average brightness temperatures (Figure 4.5), it can be
seen th at the the peak frequency is 0.28 corresponding to a root mean squared
difference 6.75 K for the daily case, peak frequency is 0.25 corresponding to a root
mean square error of 6.75 K for the weekly averaging case and the peak frequency
of 0.27 corresponding to a root mean square error of 3.75 K for the monthly av­
eraged case. The peak frequency may occur at the same location for the daily
and weekly cases, however, there is much more mass at the lower values in the
weekly averaged case as opposed to the daily case. The monthly averaged case
has greater frequencies at lower values than both the weekly and daily cases. The
same behavior is seen for the 37 GHz frequency case as well as for the distribution
of the root mean squared errors for polarization difference brightness temperature
(Figure 4.6).
The spatial distribution root mean squared differences for the soil moisture (19
and 37 GHz frequencies) are shown as images for the daily case, weekly averaged
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C H A P T E R 4. S S M /I REGIONAL SOIL M O I S T U R E ESTIMATIO N
160
case and monthly averaged case in Figure 4.7, Figure 4.8 and Figure 4.9 respec­
tively. It can be seen that the root mean squared differences are highest for the
daily case and the lowest for the monthly case, with the weekly case falling in
between. This is expected from temporal averaging, which smoothes out some of
the differences between the simulated and the SSM/I estimated values. This is
demonstrated in the previous paragraphs in the discussion of correlation coeffi­
cients between the simulated and the estimated soil moistures and the frequency
distribution of the root mean squared differences between the simulated and the
estim ated soil moisture.
The comparison between simulated surface tem perature at 6:00am correspond­
ing to the SSM/I ascending overpass and the minimum air temperature of the
day (obtained from Surface Airways station observations), which can be used as
a surrogate for the surface temperature (McFarland et. al., 1992), shows a root
mean square difference ranging from I K to 4K (Figure 4.10). The surface tem­
perature observations can be derived from AVHRR channel 4 and channel 5 mea­
surements. However, the AVHRR equatorial overpass is 0230 hrs (descending) and
1430 (ascending). These times do not coincide with the SSM/I overpass. Hence,
the minimum air temperature during the day was taken to be the observed sur­
face tem perature during the SSM/I ascending overpass for comparison with the
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CH APTER 4. SS M /I REGIONAL SOIL MOISTURE ESTIMATION
161
simulated surface temperature.
4 .4 .2
P ix e l r e su lts for so il m o istu r e an d b r ig h tn e s s t e m ­
p e r a tu r e s
The comparison of simulated and SSM/I estimated soil moisture for individual
grid cells or pixels is discussed below. The following discussion intends to describe
agreements and disagreements between the two. Figure 4.11 and Figure 4.12 show
the daily time series of good agreement between simulated and SSM/I derived
soil moisture and average and polarization difference brightness temperatures for
the 19 and 37 GHz frequencies respectively for a particular pixel. Figure 4.11
corresponds to a 0.25° X 0.25° pixel located at 33.0°N, 104.25°W. The root mean
squared differences for the soil moisture and average and polarization difference
brightness temperatures are 0.03, 6.18 K and 1.71-K" respectively. Figure 4.12
shows the variation of the simulated and the 37 GHz observation derived quantities
for good agreement at location 31.5°N, 104.75°W. In Figure 4.12, it can be seen
th at the 37 GHz observed polarization difference temperature is very high (much
higher than the simulated value) on day 190 (February 6, 1988). The reason for
this is the melting of snow, which causes a large increase in polarization difference
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C H A P T E R 4. S S M / I REG ION AL SOIL MOISTURE ESTIMATIO N
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brightness temperature. The Atmospheric Environment Service of Canada has
developed an algorithm to detect melting snow (Szeliga, 1995). Their algorithm is
based on A T (for 37 GHz) > 10 K for a melting snow layer. The A T for the 37 GHz
frequency on day 190 is 16.5 K. (There is also a low value of the average brightness
tem perature 241.4 K and a high value of the SSM/I derived soil moisture 0.31).
This indicates a possibility of melting snow. The corresponding A T for the same
location and same day for the 19 GHz frequency is 28.2 K , T b is 239.2 K and
the SSM/I derived soil moisture is 0.46. The hourly air temperature records of
the Surface Airways station closest to the above location in El-Paso, TX (31.8°,
106.4°) shows a warming trend increasing upto 296 K at 3pm on February 3, 1988.
The air tem perature continued to stay above 280 K for most of February 4, 1988
and around 274 K on February 5, 1988. This may have caused the melting of the
snow accumulated on the ground surface at this location.
Examples of poor agreements between the simulated and the observation de­
rived quantities are shown in Figure 4.13 for the 19 GHz frequency and Figure 4.14
for the 37 GHz frequency. Both these Figures correspond to the same location of
35.0°N, 95.75°W. A good part of this 0.25°AT0.25° pixel is occupied by the Eufaula
Reservoir located on the Canadian River. The presence of a large water body in
the pixel reduces the average brightness temperature and increases the polariza­
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C H A P T E R 4. S S M / I REGIONAL SOIL MOISTURE ES TI M A TI O N
163
tion difference brightness temperature. A consequence of the increase in A T is
large values (equal to saturation) of the SSM/I derived soil moisture. The same is
observed for a few other pixels of the SSM/I observations in the same area. There
is a presence of water bodies in parts of the pixels that result in large root mean
squared differences between the simulated and the observed soil moistures and
average and polarization difference brightness temperatures (see Table 4.4). The
Eufaula Reservoir affects the first four locations, and the Short Mountain Reservoir
(located northeast of the Eufaula Reservoir, also on the Canadian River) affects
the fifth location.
4 .4 .3
S S M /I d e r iv e d m o n th ly so il m o is tu r e e s tim a t e s
The monthly mean surface soil moisture created using the 19 GHz SSM/I estimated
soil moisture is shown in Figure 4.17. This section interprets the mean monthly
soil moisture derived from SSM/I 19 GHz data and points out the variations due
to rainfall and leaf area index. It can be seen that the monthly mean soil moisture
is greater in the eastern regions than in the western regions of the study area. This
is especially true for January, February and March 1988. This can be attributed to
greater rainfall in the east compared to the west as seen in Figure 4.18. Figure 4.18
l
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C H A P T E R 4. S S M / I REGIONAL SOIL MOISTURE ES TI M AT IO N
164
gives the monthly rainfall accumulations (in mm) for the study area. In the case
of March 1988, the rainfall can be seen as greater from Figure 4.18; however, the
cases of February and March 1988 are not so clear, due to the scale of the rainfall
images designed to span between the minimum and the maximum, which does not
give adequate grey scale variation for these months. For the months of February
and March 1988, the rainfall is greater on the eastern edge compared to the western
edge of the study area. The eastern edge receives around 8-10mm of rain in the
northeastern corner and around 20-25mm of rain in the southeastern corner in
January 1988 and around 5-10mm in the northeastern corner and 20-30mm in
the southeastern corner in February 1988. The western edge receives 0-5mm in
January 1988 and February 1988. Since, in these months, the evaporation from
the soil is low, the rainfall is reflected in the increased surface soil moisture, and
the greater soil moisture in the eastern edge compared to the western edge can
be attributed to greater rainfall. For the months of April through July 1988, the
mean monthly soil moisture tends to follow the rainfall pattern and the pattern of
leaf area index. The mean monthly leaf area index is shown in Figure 4.19. The
increase in the leaf area index in the eastern region of the study area results in an
increase in evapotranspiration losses, and surface soil moistures are consequently
not as high as they were in the first three months of 1988.
Also, the rainfall
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C H A P T E R 4. S S M / I REG IONAL SOIL M OIS TU RE ESTIMATION
165
distribution is not biased as much towards higher values in the east as in January
through March 1988. The higher values of rainfall in the west and central regions,
together with lower leaf area index values (than for the eastern region), results in
values of soil moisture that are higher than the first three months of 1988 and that
are comparable to the eastern region. Examination of Figure 4.17 clearly shows
greater uniformity of soil moisture in the months of April through July 1988. The
soil moisture of August through November 1987 can be explained in a similar
fashion. The variation of mean monthly soil moisture across the study area can
be viewed as a reflection of the monthly accumulated rainfall patterns. The area
of high soil moisture in the east-central area in November 1988 corresponds to a
higher rainfall accumulation.
4 .4 .4
S S M /I d eriv ed m o n th ly e v a p o r a tio n e s tim a te s
The evapotranspiration derived using SSM/I data was compared with the estimates
using an atmospheric model. The atmospheric water budget is written as (Abdulla,
1995)
dW
— + V.Q = E - P
(4.9)
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CH A P TE R 4. S S M / I REG IO N AL SOIL MOISTURE ESTIMATION
166
where W is the precipitable water in the atmospheric column computed using
radiosonde data; E is the evapotranspiration estimated as a residual; P is the
precipitation and
is the divergence of moisture flux. The water vapor flux Q
is computed as
Q = j P‘
J3 0 0 m b
qU—
(4.10)
(j
where q is the specific humidity, U is the horizontal wind velocity, g is the acceler­
ation due to gravity and p is the pressure. The limits of integration p„ corresponds
to surface pressure, and 300m6 corresponds to a point sufficiently high enough in
the atmospheric column above which there is insignificant water vapor present.
The atmospheric budget computations were carried out over a box extending
between 32° N to 40° N in latitude and 92° W to 108° W longitude. This box is
bigger than the present study area. This is reasonable since the values of conver­
gence derived using a smaller area will be based on a lesser number of radiosonde
data sources, and these estimates of water vapor convergence may not be that
precise. In addition, the atmospheric budget computations are carried out over a
sixteen year period extending between 1973 and 1989. This time period includes
the time period of the present simulation study. Therefore, the estimates derived
from this atmospheric budget analysis do hold relevance to the present study area
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C H A P T E R 4. S S M / I REGIONAL SOIL MOISTU RE ES TI MA TI ON
167
and time period. However, the variations between the actual atmospheric budget
estimates for August 1987 - July 1988 and this sixteen year average may be slight,
considering that the averages are over a sixteen year period and they include vari­
ations during the 1987-88 year period. Therefore, the results of the atmospheric
budget analysis in the form of mean monthly evapotranspiration estimates have
been adopted for comparison with the SSM/I estimated evapotranspiration.
The water vapor convergence values were used to derive the evapotranspiration
estimate (Abdulla, 1995) over the box using observed precipitation values and the
radiosonde data interpolated onto 1° grids (Bradley, et. al., 1995; Abdulla, 1995).
The mean monthly values of the evapotranspiration estimates are presented in
Table 4.5.
The evapotranspiration is estimated using the SSM/I derived surface soil mois­
ture and the thin layer hydrological model derived water fluxes using Equation 2.1,
i.e.,
d6\
dd2
E T = P — R — q2Qb - Zx- ± - z 2- ±
(4.H )
where P is the cumulative monthly precipitation, R, q2 and Qb are the cumulative
monthly surface runoff, drainage from the lower layer and the base flow from the
lower layer computed using the hydrological model,
is the monthly change
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C H A P T E R 4. S S M /I REGIONAL SOIL M O I S TU R E ES TI MA TI ON
168
in the upper layer storage estimated from the SSM/I derived soil moisture, ^ L
is the change in the lower soil moisture storage derived from the hydrological
model estimates and Zi and Z2 are the thicknesses of the upper and lower layers
respectively.
The evapotranspiration estimated using the SSM/I soil moisture estimates in
conjunction with the hydrological model is tabulated in Table 4.5. The monthly
variation of the cumulative evapotranspiration is shown in Figure 4.20. The evap­
otranspiration totals estimated using the SSM/I soil moisture and the hydrological
model shows good agreement with the atmospheric water vapor budget estimates.
There is, however, a consistent underestimation of the atmospheric model derived
evapotranspiration by the SSM/I and the hydrological model estimated values.
The underestimation is low for August, September and October of 1987 (14, 5
and 6mm respectively). There is no estimation from the SSM/I and hydrological
model for the months of December 1987 and January 1988, since the SSM/I was
not functional between December 1987 and January 12, 1998. The underestima­
tion is larger in 1988 with 10mm in February, and 14mm in March, decreasing to
6mm in April 1988. The underestimation is large for May and June (42mm and
47m m ) and show good agreement for July 1988 with an underestimation of only
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C H A P T E R 4. S S M /I REGIONAL SOIL MOISTURE E STI M ATI ON
169
2mm. The SSM/I and hydrological model derived evapotranspiration totals show
the proper seasonal variation with a maximum of 60mm in August 1987 and July
1988 and a minimum of 12mm in February 1988. The monthly variation of the
two evapotranspiration estimates follow the same trend, with the exception of a
decrease in evapotranspiration from June (100mm) to July (63mm) in the case of
the atmospheric budget estimates, and an increase in the evapotranspiration from
53mm (June 1988) to 61mm (July 1988) according to the SSM/I and hydrologi­
cal model estimates. The evapotranspiration shows a decrease between August to
January, and an increase till July.
4 .4 .5
C o m p a r iso n o f r e su lts w ith p r e v io u s s tu d ie s
The correlation coefficients and the root mean squared differences are computed
between the simulated and the SSM/I estimated values for soil moistures and the
average and polarization difference temperatures for 19 and 37 GHz. There is an
im portant point to be made here. There is no connection between the SSM/I
estim ated values of soil moisture and the simulated values. The two sets of soil
moisture values (simulated and SSM/I estimated) are derived independently of
each other. The correlation coefficients and the root mean squared differences
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C H A P T E R 4. S S M /I REGIONAL SOIL M OIS TU RE ES TI MA TI ON
170
interpreted in this perspective show extremely good characteristics, i.e., the cor­
relations are quite good and the root mean squared differences are not that high.
The comparison of the above computed correlation coefficients to those computed
by previous investigators is carried out in this subsection to put this study in
perspective of studies on this topic carried out in the past.
.
The correlation coefficient between the estimated antecedent precipitation in­
dex (API) using 6.6 GHz SMMR brightness temperature data (Choudhury et. al.,
1988) and the simulated API is 0.87. Their correlations are higher because (a)
the lower frequency (6.6 GHz in their case) is much more sensitive to soil wetness
and (b) a longer span (5 years - 1979-1983) of data for a selected period in the
year (days 121-243) was used. The 19 GHz data used by Teng et. al., (1993) have
lower r between the simulated and estimated API than in the previous study of
Choudhury et. al., (1988). The 0.25°A’0.25° SSM/I data in their study has been
averaged to 0.75°X0.75° pixels. The correlation coefficients have been reported
for yearly averaged values and for two distinct regions (the semi-arid western part
and the humid eastern part). The correlation coefficient is lower for the eastern
part than for the western part. Since their study uses the 19 and 37 GHz SSM/I
observations used in this study, it is worthwhile comparing their r (between cal­
culated and 19 GHz SSM/I estimated API) and the r (between simulated and 19
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C H A P T E R 4. S S M / I REGIONAL SOIL M OIS TU RE E S TI M AT IO N
171
GHz SSM/I derived soil moistures) from this study. The values for the coefficient
of correlation between the 19 GHz SSM/I estimated API and the calculated API
were reported for different geographical locations to range between a maximum of
0.7 in the semi-arid western region to a minimum of 0.35 for the humid central part
of western Iowa and western Missouri for 1987. The corresponding values for 1988
were 0.7 and 0.45. In this study, the average correlation coefficient between the
SSM/I estimated soil moisture and the simulated soil moisture (computed from
daily correlation values between August 1, 1987 and July 31, 1988) is 0.131 for 19
GHz and 0.128 for 37 GHz. The lower values could be attributed to stricter pro­
cedures adopted in this study to simulate and estimate the soil moisture. The soil
moisture has been simulated using a complete water and energy balance model,
and the estimation has been carried out using a physically based radiative transfer
model. In the study of Teng et. al., (1993), the antecedent precipitation index
method has been used which is an approximation for soil moisture, and the esti­
mation is done through regression analysis. The regression relations between the
horizontally polarized 19 GHz brightness temperatures and the antecedent precipi­
tation index are different for the arid western region and the humid eastern region.
The correlation coefficients derived in this study are for the whole study region.
The present study is more physically based, and it analyzes the physically based
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C H A P T E R 4. S S M / I REGIONAL SOIL MOISTURE ES TI M A TI O N
172
relationships between the SSM/I observed brightness temperatures and the soil
moisture, rainfall and vegetation. The average correlation coefficient between the
simulated and the estimated soil moisture computed on a weekly averaged basis is
0.255 and 0.247 for the 19 and 37 GHz frequency respectively, and on a monthly
basis is 0.379 and 0.378 for the 19 and 37 GHz respectively. Again averaging helps
increase the agreement between the two sets of soil moisture.
The coefficient of correlation between the daily simulated and the SSM/I obser­
vations derived soil moistures for each of the 19X42 pixels is shown in Figure 4.15.
The distribution of the daily correlation coefficients between the simulated and
SSM/I derived 6 (derived from Figure 4.15) is shown in Figure 4.16. The fig­
ure also shows the distribution of correlations between the 0.75oAT0.75° averaged
simulated and SSM/I derived 9. There does not seem to be much difference be­
tween the two. The correlation coefficient ranges from -0.4 to 0.65 for both the 19
GHz and the 37 GHz frequency SSM/I derived soil moistures and the simulated
soil moistures. The aggregation of 0.25° pixels to 0.75° pixels, however, does not
change the magnitude of the correlation coefficient between the simulated and the
estim ated soil moisture.
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CH APTER 4. S SM /I REGIONAL SOIL MOISTURE ESTIM ATION
4.5
173
C on clu sion s and Im p lica tio n s for fu tu re w ork
The coupled soil-canopy-atmosphere model has been used to simulate soil moisture
and brightness temperatures for a region in the Red River basin of the southern
United States. The simulations and comparisons with observed values were car­
ried out on a 0.25° X 0.25° grid for a period of one year between August 1, 1987
and July 31, 1988. The simulated brightness temperatures at 19 and 37 GHz
were compared against the SSM/I observed brightness temperatures. The root
mean squared difference between the simulated and the observed average and po­
larization difference brightness temperatures decreases as the comparison period
for which the averaging is done is increased, i.e., the monthly average brightness
temperatures show a lower root mean squared difference than the weekly values,
and the weekly values exhibit a lower error than the daily values. The errors for
the 19 GHz range between 6.2 (daily) and 4.9K (monthly) for the average bright­
ness tem perature, and between 2.6 (daily) and 1.8K (monthly) for the polarization
difference brightness temperatures. The errors for the 37 GHz are between 5.1 to
3.7K for the average brightness temperature, and between 2.4 to l.QK for the
polarization difference. The simulated surface temperatures were compared with
the observed surface temperatures derived from air temperature measurements.
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C H A P T E R 4. S S M / I REGIONAL SOIL M OI S TU RE ES TIM ATI ON
174
These results showed that the root mean squared error of the surface temperature
at the time of the SSM/I overpass ranged between 1 to 4K. The SSM/I estimated
soil moisture was compared with the simulated soil moisture. The comparisons
between the simulated and the 19 GHz SSM/I estimated show reasonable correla­
tions between 0 and 0.6 for a monthly basis; -0.1 and 0.6 for a weekly basis and
-0.4 to 0.75 for a daily basis. The corresponding ranges for the 37 GHz frequency
are 0.17 to 0.6, -0.15 to 0.6 and -0.5 to 0.63 for the monthly, weekly and daily
comparisons. The range of the correlation coefficient increases as the time period
of averaging for the soil moisture comparison decreases. The monthly average es­
tim ates of surface soil moisture derived from the SSM/I are interpreted in context
with the monthly rainfall and the monthly averaged leaf area index. The SSM/I
derived monthly average surface soil moisture shows a very strong relationship
with the cumulative monthly rainfall. The cumulative monthly estimates of evap­
otranspiration computed using the SSM/I estimates of soil moisture in conjunction
with the hydrological model yielded good comparisons with the monthly estimates
obtained via the atmospheric budget analysis.
The study described in this chapter can be extended in time and space to
achieve better understanding of more diverse situations. Extension of this study
to a tim e period of five years would help in explaining some of the inter-annual
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C H A P T E R 4. S S M / I REGIONAL SOIL M O I S TU R E ES TI MA TI ON
175
variations as observed by the SSM/I. This is very relevant in the discussions of
SSM/I monthly climatology for the calculation of the mean monthly SSM/I es­
tim ated soil moisture and the cumulative monthly evapotranspiration computed
using the SSM/I and the hydrological model. Extension of this analysis to a larger
area (the Mississippi river basin or the Red-Arkansas river basin) would definitely
help in interpreting the results in the context of varying geographical regions.
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CH A P T E R 4. S S M / I REG IONAL SOIL MOISTURE ESTIM ATION
value
parameter
albedo (soil) a a
0.15
albedo (vegetation) a„
0.20
emissivity (soil) e,
1.00
emissivity (vegetation) e„
LOO
roughness length (soil) z0i3
0.001m
roughness length (vegetation)
176
zq<
3
zero plane displacement (soil) ds
0.07m
0.0
zero plane displacement (vegetation) dv
0.25m
top layer thickness z\
0.01m
bottom layer thickness z2
0.99m
leaf area index L
minimum stomatal resistance r ^ in
biweekly LAIs
lOOs/m
transpiration parameter A
0.5
porosity 6a
0.50
residual soil moisture 6r
0.02
Brooks Corey parameter m
0.2
air entry suction head t/jc
saturated hydraulic conductivity K a
0.2m
1.89X10-6m s-1
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CH A P T E R 4. S S M / I REGION AL SOIL MOI STURE ES TIM ATI ON
parameter
value
transition soil moisture 6*
0.12
wilting soil moisture (volumetric) 6W
0.05
baseflow parameter Q™ax
3.38m m /h r
baseflow param eter 9%
0.15
baseflow param eter Q£
0.06m m j day
meteorological data
rainfall data
oven dry thickness of leaf d0
precipitable water
177
hourly data, surface airways stations
hourly data, MDR data
0.1mm
radiosonde data (derived)
Table 4.1: Parameters for the coupled soil-canopy-atmosphere model
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C H A P T E R 4. S S M / I REGIONAL SOIL MOISTURE ESTIM ATION
No.
Name
Latitude
Longitude
Height (f t )
1
Abilene, TX
32°25'
99°4l'
21
2
Amarillo, TX
35°14'
101°42'
23
3
Dallas-Fort Worth, TX
32°54'
97°02'
22
4
Lubbock, TX
33°39'
101°49'
25
5
Midland, TX
31°57'
102°ll'
22
6
Oklahoma City, OK
35°24'
97°36'
20
7
Roswell, NM
33°18'
104°32'
20
8
Stephenville, TX
32°13'
98°ll'
20
9
W ichita Falls, TX
33°58'
98°29'
21
10
Longview, TX
32°2l'
94°39'
22
11
Tucumcari, NM
35°ll'
103°36'
22
12
San Angelo Mathis, TX
31°22'
100°30'
20
13
Clayton, NM
36°27'
103°09'
33
14
Fort Smith, AR
35°20'
94°22'
23
15
Dodge City, KS
37°46'
99°58'
33
16
El Paso, TX
31°48'
106°24'
32
17
Lufkin Angelina, TX
31°14'
94°45'
22
178
Table 4.2: List of Surface Airways Stations
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179
C H A P T E R 4. S S M / I REGIONAL SOIL MOISTURE ES TIM ATI ON
daily
weekly
monthly
mean
sdev
mean
sdev
mean
sdev
19 GHz soil moisture
0.14
0.059
0.12
0.059
0.11
0.063
37 GHz soil moisture
0.13
0.053
0.11
0.052
0.09
0.054
19 GHz avg. bri. temp. (K )
6.2
1.92
5.7
2.04
4.9
2.0
19 GHz pol. diff. bri. temp. ( K)
2.6
0.84
2.2
0.83
1.8
0.82
37 GHz avg. bri. temp. ( K)
5.1
1.42
4.5
1.61
3.7
1.49
37 GHz pol. diff. bri. temp. (K )
2.4
0.84
1.9
0.79
1.6
0.76
Table 4.3: Summary of root mean squared differences between simulations and ob­
servations for 19 and 37 GHz brightness temperatures and estimated soil moisture
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C H A P T E R 4. S S M / I REGIONAL SOIL MOISTURE E STI M AT IO N
180
37 GHz
19 GHz
location
Tb
AT
e
Tb
AT
0
35.25°N, 95.75° W
0.30
6.9
4.7
0.32
9.6
7.5
35.25°N, 96.0° W
0.29
7.9
3.8
0.29
5.7
4.0
35.5°N, 95.75°W
0.24
7.3
3.2
0.29
7.1
5.6
35.5°N, 96.0° W
0.25
8.7
3.4
0.25
5.8
3.8
35.5° IV, 95.25°W
0.21
7.3
2.8
0.26
5.9
3.8
Table 4.4: Effect of water bodies on the SSM/I observations - root mean squared
differences between simulated and observed brightness temperatures and simulated
and estimated soil moisture for 19 and 37 GHz
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CH A P TE R 4. S S M / I REGIONAL SOIL MOISTURE ESTIM ATION
Month
181
Evaporation (mm)
Atmospheric
SSM/I
August
74
60
September
56
51
October
49
43
November
44
27
December
27
January
7
February
22
12
March
45
31
April
53
47
May
85
43
June
100
53
July
63
61
Table 4.5: Comparison of monthly evaporation estimates (in m m ) from an atmo­
spheric model and derived using 19 GHz SSM/I observations
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C H A P T E R 4. S S M / I REGIONAL SOIL M O I S T U R E ES TIM ATI ON
182
Colorado i Kansas
Oklahoma
N 3w Mexico
Texas
Figure 4.1: Location of the study area (denoted by a dotted rectangular box)
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C H A P T E R 4. S S M / I REGIONAL SOIL MOIS TU RE E STI M ATI ON
183
CALIBRATION
soils/rad/m et/rain/lai
distributed input
soil m oisture
H ydrologic and B rightness
T em p eratu re S im ulator
3 2 X 7 1 g rid / 90 days
p recip itab le w ater
a ir tem p eratu re
surface tem perature
Subtraction o f A tm ospheric
E stim atio n o f V eg etatio n
E ffects from S S M /I
P aram eters
3 2 X 7 1 g rid / 9 0 days
B rightness T em p eratu res
H y d ro lo g ic an d B rightness
In v ert S S M /I B rig h tn ess
T em p eratu re S im u lato r
T e m p e ra tu re s
3 2 X 7 1 g r i d / 365 days
surface
temperature
19 X 4 2 g rid / 36 5 d ay s
com pare
Soil m o istu re sim u lated on
3 2 X 71 g rid resam p led
Soil m o istu re d eriv ed
o b se rv ed surface
tem perature
to 1 9 X 4 2 grid
from SSM /1 d ata
sim u lated brightness
o b se rv ed b rig h tn e ss
tem p eratu re
tem p eratu re
com pare
VALIDATION
Figure 4.2: Scheme for calibration, validation and comparison of soil moistures
and brightness temperatures
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C H A P T E R 4. S S M / I REGIONAL SOIL MOIS TU RE ES TI M A TI ON
184
m onth
©
i/i
9
0
10
20
30
40
50
w e e k (w e e k 1 sta r ts A u g u st 1 ,1 9 8 7 )
o
©
in
9
0
100
200
300
d a y (d a y 1 sta rts A u g u st 1 ,1 9 8 7 )
Figure 4.3: Correlation coefficient (r) between the simulated soil moisture and
the SSM/I derived soil moisture using 19 and 37 GHz brightness temperatures for
monthly averaged, weekly averaged and daily values
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C H A P T E R 4. SS M/ I REGIONAL SOIL M OI S TU R E ESTIMATION
185
o
daily
CO
o
o
to
d
a
19 G H z
37 GHz
o
©
d
0.0
0.1
0.2
0 .3
0 .4
0 .5
0.1
0 .2
0 .3
0 .4
0 .5
0 .2
0 .3
0 .4
0 .5
o
w ee k ly
CD
d
to
d
*r
d
C\J
o
p
0 .0
p
m onthly
to
o
to
d
d
o
d
0 .0
0.1
volum etric s o il m oistu re
Figure 4.4: Frequency distribution of the root mean squared difference between the
simulated soil moisture and the SSM/I derived soil moisture using 19 and 37 GHz
brightness temperatures for monthly averaged, weekly averaged and daily values
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C H A P T E R 4. S S M / I REGIONAL SOIL M O I S TU R E ESTIMATION
186
o
CO
©
O
A
co
19G H z
37 GHz
o
©
o
©
o
0
5
10
15
0
5
10
15
5
10
15
o
CO
o
CO
o
©
cy
©
o
o
o
m onthly
°o
©
CO
o
o
cvt
o
o
o
0
a v e r a g e b r ig h tn e ss tem p oratu re (K)
Figure 4.5: Frequency distribution of the root mean squared difference between
the simulated and the SSM/I derived average brightness temperature using 19 and
37 GHz brightness temperatures for monthly averaged, weekly averaged and daily
values
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C H A P T E R 4. S S M /I REGIONAL SOIL M OI S TU R E ESTIMATION
187
©
daily
CO
□
|
I
o
A
CO
19 GHz
3 7 GHz
©
v
o
CM
d
o
d
o
2
4
6
e
10
6
8
10
6
6
10
o
w ee k ly
p
d
I
I
CO
d
d
CM
o
e
d
0
2
o
m onthly
CD
d
I
d
CM
d
o
d
0
2
i
p olarization d iffer en ce b r ig h tn e ss tem p oratu ro (K)
Figure 4.6: Frequency distribution of the root mean squared difference between
the simulated and the SSM/I derived polarization difference brightness tempera­
ture using 19 and 37 GHz brightness temperatures for monthly averaged, weekly
averaged and daily values
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CH A P T E R 4. S S M /I REGIONAL SOIL M OI S TU RE ESTIMATION
188
19 GHz
0.0
0.50
Figure 4.7: Root mean squared difference between the daily simulated soil moisture
and the SSM/I derived soil moisture using 19 and 37 GHz brightness temperatures
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CHAPTER 4. S SM /I REGIONAL SOIL MOISTURE ESTIM ATION
189
19 GHz
0.0
0.50
Figure 4.8: Root mean squared difference between the weekly averaged simulated
soil moisture and the SSM/I derived soil moisture using 19 and 37 GHz brightness
tem peratures
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C H A P T E R 4. S S M / I REGIONAL SOIL M OI S TU RE ESTIM ATION
190
19 GHz
0.0
0.50
Figure 4.9: Root mean squared difference between the monthly averaged simulated
soil moisture and the SSM/I derived soil moisture using 19 and 37 GHz brightness
temperatures
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C H A P T E R 4. S S M /I REGIONAL SOIL M OIS TU RE ESTIMATION
191
Figure 4.10: Root mean squared difference between the simulated surface temper­
ature at 6:00am and the observed surface tem perature assumed to be equal to the
minimum air temperature of the day
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C H A P T E R 4. S S M /I REGIONAL SOIL M OIS TU RE ESTIMATION
192
in
o
l o c a t io n : ( 3 3 .0 N . 1 0 4 .2 5 W )
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200
300
a v e r a g e b r ig h t n e s s t e m p e r a t u r e (K )
s H
p o la r iz a t io n d i f f e r e n c e b r i g h t n e s s t e m p e r a t u r e (K )
0
100
200
300
d a y ( d a y 1 c o r r e s p o n d s to A u g u s t 1 , 1 9 8 7 )
Figure 4.11: Good agreement between the simulated and 19 GHz SSM/I bright­
ness tem perature derived soil moisture and average and polarization difference
brightness tem perature at the location 33.0°IV and 104.25°W
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C H AP TE R 4. S S M /I REG IONAL SOIL M OIS TU RE ESTIMATION
lo c a t i o n : ( 3 1 .5 N . 1 0 4 .7 5 W )
o
•
193
s im u la tio n
3 7 G H z S S M /I
s
n
a v e r a g e b r i g h t n e s s t e m p e r a t u r e (K )
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100
200
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p o la r iz a tio n d if f e r e n c e b r ig h t n e s s te m p e r a t u r e (K )
0
100
200
300
d a y (d a y 1 c o r r e s p o n d s to A u g u st 1, 1 9 8 7 )
Figure 4.12: Good agreement between the simulated and 37 GHz SSM/I bright­
ness tem perature derived soil moisture and average and polarization difference
brightness temperature at the location 31.5°iV and 104.75°W
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C H A P T E R 4. S S M/ I R E G IO N AL SOIL MOIS TU RE ESTIMATION
194
m
d
location: (35.0N.e5.75W)
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0
100
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200
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p o la r iz a tio n d if f e r e n c e b r ig h t n e s s t e m p e r a t u r e (K )
m
o
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o
0
100
200
300
d a y (d a y 1 c o r r e s p o n d s to A u g u st 1 . 1 9 8 7 )
Figure 4.13: Bad agreement between the simulated and 19 GHz SSM/I brightness
tem perature derived soil moisture and average and polarization difference bright­
ness temperature at the location 35.0°iV and 95.75°W
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C H A P T E R 4. S S M / I REG IONAL SOIL MOIS TU RE E S TI M A TI ON
195
in
©
lo c a t io n : ( 3 5 .0 N . 9 5 .7 5 W )
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s im u la t io n
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0
100
200
300
a v e r a g o b r ig h t n e s s t e m p e r a t u r e (K )
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8
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0
100
200
300
p o la r iz a tio n d if f e r e n c e b r ig h t n e s s t o m p e r a t u r o (K )
0
100
200
300
d a y ( d a y 1 c o r r e s p o n d s to A u g u s t 1 , 1 9 8 7 )
Figure 4.14: Bad agreement between the simulated and 37 GHz SSM/I brightness
tem perature derived soil moisture and average and polarization difference bright­
ness tem perature at the location 35.0°N and 95.75°W
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C H APTER 4. SSM /I REGIONAL SOIL MOISTURE ESTIM ATION
196
19 GHz
-0 .4 5
0.75
Figure 4.15: Correlation coefficient (r) between the simulated soil moisture and
the SSM/I derived soil moisture
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CH A P T E R 4. S S M/ I REGIONAL SOIL M OI S TU R E ESTIMATION
197
daily 19 GHz
0
o
o
0.25 deg
a
0.75 deg
o
o
-0.4
-
0.2
0.0
0.2
0.4
0.6
0.4
0.6
daily 37 GHz
0
d
o
o
-0.4
-
0.2
0.0
0.2
Figure 4.16: Distribution of correlation coefficient (r) between the simulated soil
moisture and the SSM/I derived soil moisture for the 0.25° pixel and the averaged
0.75° pixel
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C H A P T E R 4. S S M / I REGIONAL SOIL MOIS TU RE ESTIMATION
August 1987
September 1987
O cto b er 1987
N o v em b er 1987
198
rv«HT> m
J a n u a ry 1988
„ra
F eb ru a ry 1988
M arch 1988
A p ril 1988
M ay 1988
J u n e 1988
J u ly 1988
0.0
0.5
Figure 4.17: Mean monthly 0.25°X0.25° soil moisture derived from 19 GHz SSM/I
data between August 1987 to July 1988. The SSM/I was turned off in December
1987.
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C H A P TE R 4. S S M /I R E G IO N AL SOIL M OISTU RE ESTIM ATION
A u g u st 1987
S ep tem b er 1987
O ctob er 1987
N o v em b er 1987
D ecem b er 1987
Ja n u a ry 1988
F eb ru ary 1988
M arch 1988
A pril 1988
M ay 1988
J u n e 1988
J u ly 1988
0
5 00 m m
199
Figure 4.18: Cumulative monthly 0.25°X0.25° precipitation (in m m ) between Au­
gust 1987 to July 1988
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C H A P T E R 4. S S M /I REGIONAL SOIL M O ISTU R E ESTIM ATION
A u g u st 1987
200
S ep tem b er 1987
O cto b er 1987
N o v em b er 1987
D ecem b er 1987
J a n u a ry 1988
F eb ru a ry 1988
M a rch 1988
A p ril 1988
M a y 1988
J u n e 1988
J u ly 1988
HU
0.0
2.5
Figure 4.19: Mean monthly 0.25°X0.25° leaf area index between August 1987 to
July 1988
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C H A P T E R 4. S S M /I REG ION AL SOIL M O ISTU R E E STIM ATIO N
o
O
O
a
201
Atmospheric model
SSM/I and hydrological model
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1988
oct
dec
feb
apr
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month
Figure 4.20: Monthly total evapotranspiration computed using atmospheric water
vapor budgets and estimated using SSM/I and hydrological modeling
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C h ap ter 5
C on clu sion s an d F u tu re W ork
5.1
S u m m ary o f m a jo r r esu lts
This thesis describes an attem pt to develop a coupled soil-canopy-atmosphere mod­
eling framework for simulating surface soil moisture and Special Sensor Microwave
Imager (SSM/I) brightness temperatures and for estimating the soil moisture using
19 and 37 GHz observed SSM/I brightness temperature data.
The coupled soil-canopy-atmosphere model consists of the thin layer model of
land surface hydrology, the radiative transfer model for the vegetation canopy and
the attenuation model for the atmosphere. The thin layer model of land surface
hydrology is based on the thin layer model of Mahrt and Pan (1984). The water and
202
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C H A P T E R 5. CONCLUSIONS
203
energy budgets, as well as the surface soil moisture and temperature, are computed
using the thin layer hydrological model.
The canopy radiative transfer model
developed by Choudhury et. al., (1990) is used to solve the coupled differential
equation for radiative transfer through a scattering canopy with the boundary
conditions of the land surface at the bottom and the atmosphere at the top. The
brightness temperatures at the canopy top are then attenuated by the atmospheric
oxygen and atmospheric water content, which is quantified by the atmospheric
attenuation model (Choudhury, 1993).
Chapter 2 concerns the description of the coupled soil-canopy-atmosphere model,
testing of the thin layer model of soil hydrology and using the coupled model for
studying the sensitivity of the simulated brightness temperatures to changes in
soil moisture, leaf area index and vegetation parameters. The thin layer model is
calibrated and validated over the Kings Creek Catchment for a ten year period
between 1980 and 1989. The calibration is done using the observed daily streamflows at the Kings Creek gauging station for the first five year period between 1980
and 1984. The validation is done by comparing the simulated and observed daily
streamflows for the second five year period between 1985 and 1989. The surface
soil moisture and the temperature are compared with the observations collected
during the First International Satellite Land Surface Climatology Project Field
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C H A P T E R 5. CONCLUSIONS
204
Experiment (FIFE) in the summer and fall of 1987. The analysis of the simulated
soil moisture is carried out in conjunction with the observed rainfall data. The
coupled soil-canopy-atmosphere model is used to study the sensitivity of the radia­
tive transfer and the brightness temperatures to soil moisture, leaf area index and
other vegetation parameters. The sensitivity of the polarization difference index to
soil moisture decreases with an increase in leaf area index. The sensitivity of the
polarization difference index to changes in leaf area index is greater at higher soil
moisture values. The stem area index and the canopy moisture content play an
important role in modulating the polarization difference signal originating at the
soil surface. An increase in stem area index or canopy moisture content decreases
the polarization difference index.
Chapter 3 involves the use of the coupled soil-canopy-atmosphere to study the
effect of heterogeneities in leaf area index and rainfall on the simulated surface
soil moisture and brightness temperatures and on the SSM/I estimated soil mois­
ture. The representation of the leaf area index using an average value seems to
be sufficient for computing the soil moisture and the polarization difference in­
dex. On the other hand the spatial distribution of rainfall has to be represented
in a distributed manner using lumped input rainfall results in biased values of
soil moisture and polarization difference index to higher values. The estimation
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C H A P T E R 5. CONCLUSIONS
205
of soil moisture using SSM/I brightness temperatures in a simulation framework
yielded very good results. It demonstrated the fact that for the given set of con­
ditions, the non-linearity of the transformation between soil moisture, leaf area
index and brightness temperature is not large enough to cause a substantial bias
in the estimation of the soil moisture from the brightness temperatures.
Chapter 4 describes the use of the coupled soil-canopy-atmosphere model for
simulation of soil moisture and 19 and 37 GHz SSM/I brightness tem peratures for
the region around the Red River basin in the southern United States for a period
of one year between August 1, 1987 and July 1, 1988. The simulated values of av­
erage and polarization difference brightness temperatures are compared with the
SSM/I observations. The SSM/I estimated soil moisture is compared with the soil
moisture simulated using the hydrological model. The comparisons (for brightness
temperatures and soil moisture) are quantified by the correlation coefficient and by
the root mean squared differences. The SSM/I estimated monthly average values
of surface soil moisture are discussed along with the cumulative monthly rainfall
and the mean monthly leaf area index. It is seen that the mean monthly surface
soil moisture estimated from the SSM/I shows a strong correlation with the cu­
mulative monthly rainfall. The cumulative monthly evapotranspiration estimated
using the SSM/I derived surface soil moisture and the hydrological model is com­
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C H A P T E R 5. CONCLUSIONS
206
pared with estimates obtained using the atmospheric budget analysis. The results
of the comparison show that the monthly evapotranspiration estimates obtained
using SSM/I and the hydrological model underestimate the estimates using the
atmospheric budget.
5.2
S tr a te g y for fu tu re research
This thesis provides a basic framework/strategy to study land surface hydrology via
remote sensing. This framework involves assembling a physically based modeling
setup for the simulation and study of sensitivities of the system. The modeling
system is validated and then used in an inversion mode for estimation of the
variable of interest. In this thesis, the variable of interest is soil moisture.
Soil moisture is an important variable in climate modeling. Information about
soil moisture is relevant in the computation of circulation patterns, planetary
boundary layer and water and energy budgets. In the area of land surface hy­
drological modeling, surface soil moisture is important in partitioning the rainfall
into infiltration and runoff.
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C H A P T E R 5. CONCLUSIONS
5 .2 .1
207
S S M /I g e n e r a te d m o n th ly c lim a to lo g y
The SSM/I mean monthly soil moisture generated using the SSM/I estimated
surface soil moisture in Chapter 4 can be extended to a longer time period, using
SSM/I data for a period of five years, and over a larger geographical area. The
analysis of the surface soil moisture estimated over this longer time period and
larger area will provide a soil moisture climatological data set. This information
can be used by investigators as input to models that require specification of the
surface soil moisture.
5 .2 .2
U s e in a g ricu ltu ra l a p p lic a tio n s
The use of SSM/I data in conjunction with AVHRR NDVI data can help in moni­
toring crop development and detecting early stages of drought (Teng et. al., 1995).
Studies have shown that vegetation indices like NDVI are good indicators of the
onset of drought (Tucker, 1989). The use of surface soil moisture information es­
tim ated using SSM/I in conjunction with the NDVI estimates from AVHRR may
provide a better indicator of the vegetation information.
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C H A P T E R 5. CONCLUSIONS
5 .2 .3
208
F ie ld e x p e r im e n ts in c o n ju n c tio n w ith S S M /I d a ta
The spatial resolutions of the SSM/I at 19 and 37 GHz are about 56km and 33A:m
respectively. It is very difficult to plan field experiments at such large scales.
However, if homogeneous areas (with respect to vegetation type) are chosen and a
field experiment carried out to measure soil moisture, a valuable data set will be
provided with which the results of modeling and estimation of soil moisture can be
compared. Field experiments on large scales, such as the SSM/I resolution scale,
will help bridge the gap that exists between small scale field experiments and large
scale modeling.
5 .2 .4
O th er in str u m e n ts
The data from the MIMR (Multi-frequency Imaging Microwave Radiometer) would
greatly help in land surface hydrological modeling. The MIMR is expected to be
mounted on the Earth Observing System (EOS) PM satellite series. The status of
MIMR is now in doubt. MIMR would operate at six frequencies (6.8, 10.7, 18.7,
23.8, 36.5 and 89 GHz) and at two polarizations (horizontal and vertical) at each
frequency. The three low frequencies could provide us with valuable soil moisture
information. The resolution of the MIMR would be better than the SSM/I both
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C H A P T E R S . CONCLUSIONS
209
spatially and temporally.
The studies using the SSM/I for soil moisture estimation undertaken in this
thesis and the results obtained by using these approaches demonstrate that avail­
ability of lower frequency and higher spatial resolution would greatly help in soil
moisture estimation. The lower frequency would mean lesser modulation of the
soil moisture signal by vegetation and the use of simplified models for quantifying
those interactions. This would be similar to the studies using SMMR (Owe et. al.,
1992; Choudhury et. al., 1988). The higher spatial resolution would aid in plan­
ning field studies for validating the estimation procedures and modeling strategies.
The basic framework of this thesis, i.e, the use of a physically based model for
simulation of satellite data for the purposes of simulation and estimation, can still
be used.
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