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Synoptic surface moisture retrieval using special sensor microwave imager (SSM/I) and advanced very high resolution radiometer (AVHRR) data

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SYNOPTIC
SURFACE
MICROWAVE
MOISTURE
IMAGER
RETRIEVAL
(SSM/I)
USING
AND ADVANCED
RESOLUTION RADIOMETER
(AVHRR)
SPECIAL
VERY
SENSOR
HIGH
DATA
by
Xin Qiu
A dissertation submitted in partial fulfillment
of the requirements for the degree
of
DOCTOR OF PHILOSOPHY
in
Electrical Engineering
Approved:
Robert W. Gunderson
Co-Major Professor
Christopher M.U. Neale
Co-Major Professor
CiJTood K. Moon
'ommittee Member
achard W. Harris
Committee Member
mes P. Shaver
fean of Graduate Studies
Gail E. Bfrigham
Committee Member
UTAH STATE UNIVERSITY
Logan, Utah
1995
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UMI Number: 9636998
U M I Microform 9636998
Copyright 1996, by U M I Company. All rights reserved.
This microform edition is protected against unauthorized
copying under Title 17, United States Code.
UMI
300 North Zeeb Road
Ann Arbor, M I 48103
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ii
ABSTRACT
Synoptic Surface Moisture Retrieval Using Special Sensor
Microwave Imager (SSM/I) and Advanced Very High
Resolution Radiometer (AVHRR) Data
by
Xin Qiu, Doctor of Philosophy
Utah State University, 1995
Major Professors:
Dr. Christopher M.U. Neale
Dr. Robert W. Gunderson
Department: Electrical and Computer Engineering
An Integrated framework was developed, which provides a
systematic approach for land surface moisture.retrieval over
large areas based on Special Sensor Microwave Imager (SSM/I)
brightness
temperatures.
The higher
spatial
Advanced Very High Resolution Radiometer
resolution
(AVHRR)
data in
conjunction with the existing U.S. weather data were used to
verify the methodology.
A
fuzzy logic-based clustering method with a newly
defined normalized fuzzy entropy was developed
surface classification using SSM/I data.
for land
This method allows
for the classification of nonuniform surface footprints and
thereby
increases
the accuracy and completeness
of land
surface identification for a given scene.
Multiple data resources, including the AVHRR data, the
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iii
U.S. soil classification map, and the Major Land Resource
Area
(MLRA)
database
Handbook,
that
provided
were used
useful
to develop
information
location and size of water bodies,
a parameter
such
as
the
soil properties,
and
vegetation properties used to improve the accuracy of the
moisture retrieval modelling.
A new empirically-based model was developed to describe
the relationship between the SSM/I brightness temperatures
and surface moisture in terms of the antecedent precipitation
index.
The single footprint-based physical model developed
in previous research was linked to the integrated framework
to retrieve surface moisture and temperature over large areas
at a practical level by using the dynamic database scheme.
The methodology was used to retrieve moisture resulting
from several large storm systems in the Central Plain and
Western Desert areas of the United States.
The simulated
results were compared to ground truth data visually and
statistically.
(181 pages)
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iv
To the ones,
Who supported in this work.
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v
ACKNOWLEDGMENTS
I would like to thank Dr. Christopher M.U. Neale, my co­
major professor, for his sound advice and financial support
throughout this research.
Gunderson,
guidance,
my
co-major
support,
I am grateful to Dr. Robert W.
professor,
for
his
invaluable
and encouragement in completion of my
entire Ph.D. study.
Special thanks also go to my other committee members.
I wish to thank Dr.
Richard W. Harris
for his generous
funding during the first two years of my study and for
unending support throughout all these years;
Dr. Tood K.
Moon, a valued advisor and a great friend, who provided me
with
his
understanding,
support
suggestions at various stages;
and
extremely
helpful
Dr. Gail E. Bingham for his
trust in me and his recommendation, through which I had a
chance to work on this project.
My appreciation also goes to Dr. John C. Kemp, Dr. Doran
J.
Baker,
and Dr.
Chen Ming Huang
for
their
inspiring
teaching and encouragement both in and out of the classroom.
I would like to thank Chang Yi Sun, Georghios A. Vassiliades,
and Chai Huat Chong for their invaluable discussions on my
dissertation topics;
Lynette Gittins and Kathy Peacock, who
gave me so much support and encouragement during my studies
at Utah State University.
I am also grateful to Ms. Daisy
Hughes, Ms. Rachel Murray, and their families, who helped me
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vi
get through some tough times I had during all these years.
Their encouragement and love warmed me up every day.
By far the most important source of support came from my
mother and father, thousands of miles away, in China.
Their
unconditional love and immeasurable sacrifices supported me
to pursue a higher education.
This
research
was
funded
in
part
by
NOAA
grant
NA26GP0342 and NASA grant NAG-2973 through a subcontract with
the University of Wisconsin.
I appreciate the funding from
these two agencies that made this research possible.
Xin Qiu
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v ii
CONTENTS
Page
ABSTRACT ......................
ii
ACKNOWLEDGMENTS .......................................
LIST OF TABLES .......................................
LIST OF FIGURES ............. * .....................
v
xi
xiii
CHAPTER
I. INTRODUCTION ...................................
1
A . Background ...............................
B. Statement of theProblem ...................
1
3
1) Moisture Retrieval Models Using the
SSM/I Data .............................
2) Land Surface Type Classification ........
3) Problems with Using SSM/I Data ..........
4) SSM/I and Climatic Data Processing ......
3
5
7
7
C. Objectives of Research .................... 8
D. Significance of Research ................. 10
II.
FUNDAMENTALS OFMICROWAVEREMOTE SENSING
AND LITERATURE REVIEW ......................... 12
A. Microwave Remote Sensing ................. 12
1) General Description .................... 12
2) Soil Dielectric Properties,
Surface Roughness, Reflectivity,
and Emissivity ....................... 14
3) Simple Radiative Transfer Model ........ 16
B. The Special Sensor Microwave/Imager
(SSM/I) System ......................... 17
1) Data Description ....................... 17
2) Instruments' Description and
Operational Status ................... 18
3) SSM/I Data Applications ................ 19
C. Land Surface Classification Using
SSM/I Data ............................
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20
v iii
1) Combinations of Brightness Temperatures . 20
2) Statistical Land Surface
Classification Methods ............... 22
D. Fuzzy C-Varieties (FCV) Classification .... 23
1) Mathematical Basis for the
FCV Algorithm .......................
2) Previous Applications in
Remote Sensing ......................
24
26
E. The Antecedent Precipitation
Index (API) ........................... 26
F. Factors Affecting Soil Moisture
Retrieval in the Microwave ............. 28
1) Radiometric Wavelength ................
2) Soil Texture and Surface Roughness ....
3) Effect of Vegetation Cover ............
28
29
30
SSM/I Moisture Retrieval Models .........
30
1) Empirically-Based Model ...............
2) Physically-Based Model ................
30
31
H. Advanced Very High Resolution
Radiometer (AVHRR) ....................
40
METHODOLOGY ..................................
44
G.
III.
A. The Ground Truth Data
Processing ............................
B. The Land Surface Classification
Using the SSM/I Brightness
Temperatures ..........................
1)
2)
3)
47
Classification Parameters ............. 48
Preprocessing ......................... 49
Fuzzy-Logic-Based Classification Method . 49
C. Data Merging and Gridding
Processes .............................
1)
2)
46
52
Data Merging Process .................. 52
Data Gridding Process ................. 54
D. Parameter Database ...................... 54
E. Dynamic Database ........................ 55
F. Surface Moisture Retrieval
Modelling ............................. 56
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ix
1) Empirically-Based Model ................ 56
2) Physically-Based Model.................. 60
IV.
FUZZY-LOGIC-BASED METHODOLOGY FOR
LAND SURFACE CLASSIFICATION ................... 62
A. Introduction ............................ 62
B. Fuzzy Clustering Algorithm ............... 64
1)
2)
3)
4)
The Basics of Fuzzy Set Theory ......... 64
Normalized Fuzzy Entropy ............... 65
Average Normalized Fuzzy Entropy(ANFE) . 69
The Most Representative Class Number .... 70
C. Clusters Assignment ...................... 75
1) Look-Up Table ......................... 75
2) Assignment of Cluster Center Types ..... 78
3) Assignment of Data Pixel Types ......... 78
D. Simulation and Results ..................
V.
PARAMETER DATABASE ............................ 89
A. Water Bodies ............................
B. Soils ...................................
C. Vegetation ..............................
VI.
79
89
92
95
EMPIRICALLY-BASED MODEL ...................... 100
A. Microwave Signature Responses
to Surface Moisture
...............
B. MLRA Regions Files .....................
C. Regression Analysis ....................
D.
100
105
107
1) Selection of API Ground Truth
Dependent Variable ..................
2) Selection of SSM/I Independent
Variables ..........................
3) Outliers and Influential Observation
Detection ..........................
4) The Effects of dslrf ..................
5) Regression Model for Surface
Moisture Prediction .................
110
Model Applications .....................
112
1) 1987 Summer Storm Analysis ..........
2) 1988 Spring Storm Analysis ..........
113
117
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107
108
109
109
X
3) 1992 California Winter Storm
Analysis .........................
118
E. Statistical Evaluations of
the Empirically-Based Model ........... 126
VII.
PHYSICALLY-BASED MODEL ......................
144
A. Preparation of Model
Parameters ........................... 144
B. Model Applications ...................... 149
C. Examples of Surface Moisture
and/or Temperature Retrievals ......... 150
1) 1987 August Storm--Moisture and
Temperature Retrievals ............ 150
2) 1988 Spring Storm--Moisture
Retrievals ....................... 158
VIII.
SUMMARY, CONCLUSIONS AND RECOMMENDATIONS ..... 163
A. Summary ................................
B. Conclusions ............................
C. Recommendations ........................
163
166
168
REFERENCES ..........................................
170
APPENDIX ............................................
177
CURRICULUM VITAE ....................................
180
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x i
LIST OF TABLES
Table
Page
I
C haracteristics an d Status of the DMSP
S a t e l l i t e ............................................ 18
II
C h a r a c t e r i s t i c s a n d Sta tu s of th e n o a a
A V H R R S y s t e m s ....................................... 42
III
E n t r o p y M e a s u r e m e n t f o r C = 3 ....................... 69
IV
V
VI
VII
VIII
IX
Ent r o p y M ea s u r e m e n t for C = 4
.....................
69
E n t r o p y M e a s u r e m e n t f o r C = 5 ....................... 70
L o o k -u p T a b l e f o r L a n d S u r f a c e
D e s c r i p t i o n s ................................
76
C e n t e r T y p e s o f U.S. W e s t e r n D e s e r t A r e a
w i t h F i r s t - L e v e l C l a s s i f i c a t i o n ’...................
80
C e n t e r T y p e s o f U.S. C e n t r a l P l a i n s A r e a
w i t h F i r s t - L e v e l C l a s s i f i c a t i o n ...................
80
C e n t e r T y p e s o f S o u t h A m e r i c a A r e a ................
81
X
C enter T ypes of A frica A re a for
T i m e S e r i e s O n e ...................................... 81
XI
C enter T ypes of A frica A r e a for
T i m e S e r i e s T w o ...................................... 82
XII
S o i l C h a r a c t e r i s t i c s ................................. 93
XIII
S o i l P a r t i c l e D e n s i t y a n d D i e l e c t r i c C o n s t a n t ........ 93
XIV
So i l O r d e r s a n d So i l C l a s s e s
......................
XV
MLRA Subregions description
....................
XVI
xvii
XVIII
94
106
CORRELATION COEFFICIENTS FOR
A P I S e l e c t i o n .......................................108
M ultiple L inear Correlation between
API], AND S S M / I V a r i a b l e s .......................... m
M ultiple L inear Correlation between
A P I 2 AND S S M / I V A R I A B L E S ........................
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H I
x ii
XIX
XX
XXI
XXII
S t a t i s t i c s f o r 1 9 8 7 S t o r m ...........................127
S t a t i s t i c s f o r 1 9 8 8 S t o r m .........................
127
S t a t i s t i c s f o r 1 9 9 2 S t o r m ...........................128
ANOVA TABLE FOR dslrf
= 1 OF
19 8 7 S u m m e r S t o r m .................................. 131
XXIII
XXIV
XXV
A N O V A Tab le for dslrf
= 2 of
1 9 8 7 S u m m e r S t o r m ................................
132
A N O V A Tab le for dslrf
= 3 of
1 9 8 7 S u m m e r S t o r m ................................
132
A N O V A Ta b l e for dslrf
= 1 OF
1 9 8 8 S p r i n g S t o r m ................................
136
XXVI
A N O V A TABLE FOR d s l r f
= 2 OF
1 9 8 8 S p r i n g S t o r m .................................. 136
XXVII
A N O V A T able for dslrf
= 3 of
1 9 8 8 S p r i n g S t o r m .................................. 137
XXIII
A N O V A Table for dslrf
= 4 of
1 9 8 8 S p r i n g S t o r m .................................. 137
xxix
A N O V A Table for dslrf
= 5 of
1988 S p r i n g S t o r m .................................. 138
XXX
A N O V A Ta b le for dslrf
= 1 of
1992 W i n t e r S t o r m .................................. 141
XXXI
A N O V A Tab le for dslrf
= 2 of
1 9 9 2 W i n t e r S t o r m .................................. 141
XXXII
A N O V A Ta b l e for dslrf
= 3 of
1 9 9 2 W i n t e r S t o r m .................................. 142
XXXIII
A NOVA Table for dslrf
= 4 of
1992 W i n t e r S t o r m .................................. 142
XXXIV
A N O V A Ta b le for dslrf
= 5 of
1992 W i n t e r S t o r m .................................. 143
XXXV
P r e d e t e r m i n e d P a r a m e t e r s of r
P h y s i c a l l y -b a s e d M o d e l ............................
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145
x iii
LIST OF FIGURES
Figure
1
Page
SSM/I scan geometry (from
Hollinger et al. [10])
19
Methodology for large-scale
moisture retrievals ............................
45
3
The overall classification logic ...............
51
4
ANFE and iterations vs. class number for
data set 1 .....................................
72
ANFE and iterations vs. class number for
data set 2 .....................................
72
ANFE and iterations vs. class number for
data set 3 .....................................
73
ANFE and iterations v s . class number for
data set 4 .....................................
73
Land surface classification for
U.S. Western Desert area .......................
84
Land surface classification for
U.S. Central Plains area .......................
85
Land surface classification for
South America area .............................
86
Land surface classification for
Africa area (time series one) ..................
87
Land surface classification for
Africa area (time series two) ..................
88
13
Structure of the parameter database ............
90
14
MPDI (SMMR) vs. NDVI (AVHRR) from
Becker and Choudury [30]
97
15
LAI (SSM/I) vs. NDVI (AVHRR) ...................
98
16
Normalized brightness temperature T19H/T37V
response to surface moisture at
44.75 lat., 97.50 long ........................
2
5
6
7
8
9
10
11
12
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102
xiv
17
T85H response to surface moisture
at 44.75 lat., 97.50long ......................
102
Seasonal variations of running average MPI
at 44.75 lat., 97.50.long......................
103
Normalized brightness temperature T19H/T3 7V
response to surface moisture
at 41.25 lat., 94.75 long......................
104
T85H response to surface moisture
at 41.25 lat., 94.75 long......................
104
Seasonal variations of running average MPI
at 41.25 lat., 94.75 long......................
105
22
Predicted API2 vs. actual API2 values ..........
112
23
Surface moisture retrieval for 1987 August
storm by using empirically-based model ......... 115
24
Ground truth measurement for 1987 August
storm from NOAA cooperative network ............ 116
25
Surface moisture retrieval for 1988 spring
storm by using empirically-based model ......... 119
26
Ground truth measurement for 1988
spring storm from NOAA cooperative network ..... 120
27
Surface moisture retrieval for 1992
California storm (from DOY 40-47) .............. 121
28
Ground truth measurement for 1992 California
storm from NOAA cooperative network
(from DOY 40-47)
18
19
20
21
122
29
Surface moisture retrieval for DOY 48, 1992
by using empirically-based model ............... 123
30
Surface moisture retrieval for DOY 49, 1992
by using empirically-based Model ..............
124
Boxplot for dslrf = 1 of 1987
summer storm ..................................
12 9
Boxplot for dslrf = 2 of 1987
summer storm ..................................
12 9
31
32
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XV
33
Boxplot for dslrf = 3 of 1987
summer storm ..................................
130
Boxplot for dslrf = 4 of 1987
summer storm ..................................
130
Boxplot for dslrf = 1 of 1988
spring storm ..................................
134
Boxplot for dslrf = 2 of 1988
spring storm ..................................
134
Boxplot for dslrf = 3 of 1988
spring storm ..................................
135
Boxplot for dslrf = 4 of 1988
spring storm ..................................
135
Boxplot for dslrf = 1 of 1992
winter storm ..................................
138
Boxplot for dslrf = 2 of 1992
winter storm ..................................
139
Boxplot for dslrf = 3 of 1992
winter storm ..................................
139
Boxplot for dslrf = 4 of 1992
winter storm ..................................
140
Boxplot for dslrf = 5 of 1992
winter storm ..................................
140
44
The flow chart of the retrievalprocess ........
148
45
Surface moisture retrieval for1987
August storm by using physically-based
model (for day 225, 226)
151
Surface moisture retrieval for1987
August storm by using physically-based
model (for day 227,228)
152
Surface moisture retrieval forKansas
and Oklahoma regions (for day 225, 226)
154
Surface moisture retrieval forKansas
and Oklahoma regions (for day 227, 228)
155
34
35
36
37
38
39
40
41
42
43
46
47
48
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xvi
49
50
51
52
53
Surface temperature retrieval for Kansas
and Oklahoma regions (for day 225, 226)
156
Surface temperature retrieval for Kansas
and Oklahoma regions (for day 227, 228)
157
"Air temperature" for Kansas and
Oklahoma regions (for day 225, 226)
159
"Air temperature" for Kansas and
Oklahoma regions (for day 227, 228)
160
Surface moisture retrieval for 1988 spring
storm by using physically-based model .......... 161
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CHAPTER
I
INTRODUCTION
A. Background
The
surface
soil-moisture
content
has
fundamental
importance in agriculture, hydrology, and meteorology.
agriculture,
soil
moisture
information
irrigation
planning
and
yield
hydrology,
soil
watershed
runoff
crop
moisture
is
estimation
an
and
is
needed
for
forecasting.
important
flood
In
In
variable
prediction.
in
In
meteorology, soil moisture determines the partitioning of net
radiation into latent and sensible heat components.
In
addition, soil moisture provides useful information on global
climatic
change.
accurately
and
It is of considerable significance to
dynamically
estimate
moisture
over
large
areas.
Conventionally,
there are two general approaches
surface moisture estimation,
i.e.,
methods and soil water modelling.
to
in situ point sampling
The in situ point sampling
methods provide reliable soil moisture information.
However,
to achieve a specified level of accuracy over large areas, a
large number of point measurements are needed.
This requires
significant manpower and high cost.
Soil water models have the capability of predicting soil
water conditions over a short time period.
However, there
are several disadvantages in using these models.
First,
large amounts of meteorological input data are required.
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These
data
Second,
are usually difficult
parameters
and
functions
and
used
costly
to obtain.
in the model
usually difficult to accurately determine.
Third,
are
errors
could be introduced from various sources in the modelling
process,
which
could
lead
to
significant
deviations
in
moisture prediction.
Recent attempts have been made to use remote sensing
techniques
in estimating surface
soil moisture.
Remote
sensing techniques can provide rapid data collection over
large areas on a repetitive basis.
.sensors provide
Data from space-borne
the opportunity for quantifying temporal
changes in soil moisture on continental and global scales.
Remote
sensing
measurement
reflected
promising
of
or
soil
electromagnetic
emitted
part
of
of
from
the
the
moisture
energy
soil
depends
that
surface.
electromagnetic
on
is
the
either
The most
spectrum
for
operational remote sensing of soil moisture is the microwave
spectrum.
The electromagnetic wavelengths of the microwave
lie between a few millimeters and a meter.
A significant
advantage of microwave remote sensing is that it is free of
the cloud cover effect.
At microwave wavelengths,
soil
moisture can be measured by radiometric (passive) or radar
(active) techniques.
The Special Sensor Microwave Imager (SSM/I), onboard the
Defense Meteorologic Satellite Program (DMSP) satellites (F8,
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F10, and Fll), is a seven-channel, four-frequency, linearlypolarized passive microwave radiometer.
The SSM/I system
first launched in 1987, and has been used by the U.S. Navy as
an operational all-weather oceanographic and meteorological
sensor.
The instrument measures surface and/or atmospheric
brightness temperatures to retrieve climatic and hydrologic
parameters such as ice edge and concentration, precipitation,
wind over ocean, land surface temperature, snow properties,
and surface moisture.
B. Statement of the Problem
Previous attempts have been made in using SSM/I data to
retrieve
surface moisture.
However,
many problems were
encountered in using the previous methods.
It is necessary
to develop a systematic approach capable of predicting the
surface moisture of a large area (at a practical level) with
reasonable accuracy and speed.
1)
Moisture Retrieval
Models Using the
SSM/I Data:
There are generally two types of surface moisture retrieval
models, physically-based models and empirically-based models.
The empirically-based model [1] is a regression function
between brightness temperature and surface soil moisture.
The model was developed on the basis
footprints,
such
as
deserts,
of
jungles,
simple uniform
savannas,
etc.
However, the original SSM/I data sets used in developing the
model
contained
footprints
contaminated
by
rain,
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or
footprints with significant water bodies.
and water .bodies
should
have
introduced
been
excluded
"noise"
from
developing the empirical model.
The precipitation
to the model,
the
data
set
which
prior
to
A parameter database for
inventory of the water body locations of the water bodies
within the study area could be very useful to solve this
problem.
The use of a dynamic database [2] could also be useful.
The dynamic database keeps track of the running average of
the
Microwave
Polarization
Index
(MPI)
and
the
running
average of the moisture indicator (T19H/T37V). The running
average of MPI is an important variable in the empiricallybased
model,
which
vegetation density.
takes
into
account
the
effect
of
The running average of T19H/T37V is
useful in determining when the model needs to be used for
moisture retrieval.
The physically-based model is an inversion of the Land
Surface Radiative Transfer Model (LSRTM) [3] . This model was
developed to simulate microwave radiation emitted from the
earth's surface and attenuated through the atmosphere before
being measured by the SSM/I instrument in space.
The model
is a single-footprint-based model and can be inverted to
retrieve
the
surface
moisture
using
the
SSM/I
seven
brightness temperatures over a variety of footprints.
SSM/I
footprints
are
represented
proportionally
The
by
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a
composite of different surfaces.
The use of this model requires a priori information
25 input parameters to characterize a footprint.
on
Among these
parameters, some need to be obtained by means of other data
sources, such as the Advanced Very High Resolution Radiometer
(AVHRR) data and the classified soil map.
It is necessary to
develop a parameter database for these parameters.
Since
the
physically-based
model
developed
by
Vassiliades [3] is single-footprint based and its inversion
is obtained by using an iterative procedure, it is very time
consuming to retrieve daily surface moisture
areas.
over large
The dynamic database [2] can be used to solve this
problem.
Moisture is retrieved only when the presence of
moisture is observed,
and the MPI indicates that surface
vegetation is not very dense.
This will greatly reduce the
number of footprints in requiring the model application and
make it possible to retrieve surface moisture over large
areas within a reasonable computation time.
2) Land Surface Type Classification:
The application of
both physically-based and empirically-based models requires
the proper surface type classification
within
the
directly
study area.
affects
of the footprints
The accuracy of
the performance
and validation
models, and the quality of the retrievals.
to
properly
identify
land
classification
surface
of
the
It is difficult
types
using
SSM/I
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brightness
temperatures
due
to
the
complexity
and
multivariable characteristics of the data, as well as the
large sizes of the footprints.
A great variety of land
surface types could occur within the large dimensions of an
SSM/I
footprint
footprint
cover,
could
(14-55 km,
include
depending
different
topographic features,
on
frequency).
degrees
of
A
vegetation
the presence of water bodies
such as lakes and reservoirs, and various uncertain climatic
and atmospheric effects
(such as precipitation,
moisture,
snow, and water vapor'.
Previous
research
[2],
[4]
on
land
surface
type
classification using SSM/I data focused mainly on statistical
analysis.
The
thresholding
values
of
SSM/I
brightness
temperatures and IF...THEN logic are used to differentiate
natural surface types.
general
thresholding
surface.
However, it is very difficult to use
values
Since a number
of
to
classify
a
combinations
complex
land
of brightness
temperatures of the SSM/I data need to be checked,
it is
inevitable that there are undefined gaps between the multiple
conditions.
There are always unclassified footprints when
using statistical methods.
In the real world, logic is not the traditional two­
valued or even multivalued logic, but rather it is fuzzy
logic.
In other words,
the membership of an object in a
class is gradual rather than abrupt.
The fuzzy logic theory
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seems
to be
a more
promising
solution
to
land
surface
classification.
3) Problems with Using SSM/I Data:
There are two major
disadvantages commonly encountered with the use of the SSM/I
data.
First,
the short wavelengths of the SSM/I system
result in small penetration depths.
The sensitivity of the
SSM/I to surface moisture will decrease due to overlying
vegetation.
It is physically impossible to retrieve soil
moisture using SSM/I data if the land surface is heavily
vegetated.
Second, the SSM/I footprints have a relatively
coarse spatial resolution.
land
surface
within
a
The heterogenous nature of the
large
SSM/I
footprint
makes
impossible to accurately characterize the footprint.
it
To
overcome the disadvantage of coarse spatial resolution of the
SSM/I data, the AVHRR (which has a resolution of 1 km [5] ) on
board the
NOAA operational satellites
can be used.
In
addition, the Major Land Resource Area (MLRA) maps and soil
maps can be used to develop a parameter database to store the
model parameters such as vegetation height, soil dielectric
properties, etc.
Vegetation density and the location ofthe
water bodies can be obtained from the AVHRR data.
4) SSM/I and Climatic Data Processing:
The data used in
developing surface moisture retrieval models are data merged
from SSM/I data and climatological data
previous research,
[6] - [7] .
In the
the SSM/I data and climatic data were
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first gridded into separate cells with a resolution of 0.25°
of. latitude
and
longitude
(quarter-degree
boxes) .
The
gridded SSM/I data were then merged with the gridded climatic
data.
The way in which data were processed in past research
could have introduced significant errors since footprints
were artificially re-geolocated( sometimes by as much as 15
km.
The reason is because that if the center of an SSM/I
footprint is located within a quarter-degree cell, the whole
footprint is considered within the box even though its real
boundaries may spill over outside the box.
When the gridded
SSM/I data and the gridded climatic data are merged, it is
very possible they do not cover the same area.
These errors
can be reduced by first merging SSM/I data with climatic data
and then gridding the merged data.
The gridding process is
still a necessary process after merging.
dynamic
database
vegetation
density
needs
position
and
moisture
This is because the
references
indicators
consecutive overpass covering the same area.
to
check
for
the
There are also
some problems in the climatic data process, which will be
discussed in the Chapter III.
C. Objectives of Research
The general objective of this research was to develop an
integrated framework for large-scale retrieval of surface
moisture from remotely sensed data.
clustering
method
was
developed
for
A fuzzy logic-based
land
surface
type
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9
classification.
This
moisture retrieval.
1.
is
an
essential
step
in
surface
Specific objectives include:
To develop a fuzzy logic-based clustering method
for land surface classification using the SSM/I
data.
The major feature of this method is to use
fuzzy sets as a presentation framework.
The model
includes two levels: unsupervised and supervised
classification.
A new criterion will be defined
in the method to determine the most "plausible"
number
of
classes
for
classification problem.
an
unsupervised
The membership values,
cluster centers, and normalized fuzzy entropy will
be used to interpret the nature of each footprint.
2.
To
develop
include
a
parameter
information
on
database,
vegetation,
which
will
soils,
and
water bodies as well as the dielectric properties
of the constituents of land surface.
The database
will be very useful in reducing the noise in the
moisture retrieval process.
3.
To develop a new empirically-based model by using
multiple linear regression analysis together with
the parameter database and the fuzzy logic-based
classification method.
The resulting model will
then be used for moisture retrieval over large
areas.
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10
4.
To
determine
the
input
parameters
for
the
physically-based model based on the information
from
the
parameter
physically-based
framework
database,
model
for
within
large-scale
and
apply
the
integrated
surface
the
moisture
retrievals.
5.
To evaluate the performance of the two models by
applying them to three major storm systems,
comparing
simulated
results
with
ground
and
truth
climatic data.
D. Significance of Research
To accurately retrieve surface moisture and produce
synoptic maps over large areas is of great hydrologic and
climatic importance.
The research conducted in this study is innovative in
several respects.
First,
method
defined
with
newly
a fuzzy logic-based clustering
normalized
fuzzy
entropy
is
developed for land surface classification using the SSM/I
data.
This is a first attempt to apply fuzzy set theory to
multi-frequency
passive
microwave
data.
Second,
an
integrated framework, which has the capability to retrieve
updated surface soil moisture over large areas based on SSM/I
brightness
temperatures,
is
developed
by
using
higher
spectral resolution AVHRR data in conjunction with existing
U.S. weather data.
Third, a new empirically-based model is
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developed
to
describe
the
relationship
between
SSM/I
brightness temperatures and surface moisture in terms of the
antecedent precipitation index. Fourth, the physically-based
model on a single footprint basis can be linked to the
integrated framework to retrieve surface moisture over large
areas at a practical level.
Finally, the results obtained in
this research could be applied to other areas in which there
are
no
ground-based
weather
stations
for
moisture
measurements.
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12
CHAPTER II
FUNDAMENTALS OF MICROWAVE REMOTE
SENSING AND LITERATURE REVIEW
The fundamentals of microwave remote sensing will be
discussed in this chapter, which includes basic terminology,
definitions,
Special
properties of microwave remote sensing,
Sensor Microwave
Imager
(SSM/I)
Advanced Very High Resolution Radiometer
System,
(AVHRR)
the
and the
system.
Literature will also be reviewed with respect to land surface
type classification, and surface moisture retrieval models
and their application using SSM/I data.
A. Microwave Remote Sensing
1) General Description:
Remote sensing is based on the
premise that all earth surface features reflect, emit, or
absorb
electromagnetic
(EM)
radiation.
Sensors
onboard
satellites can simultaneously scan several wavelengths, or
bands, of the electromagnetic spectrum and record reflected
or emitted electromagnetic energy radiating from the earth's
surface.
The data are then transmitted to a ground receiving
station for processing.
Most remote sensing applications are limited to the
ultraviolet, visible, infrared, and microwave portions of the
EM spectrum.
Since the early seventies,
sensors in the
visible and near-infrared portion of the electromagnetic
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13
spectrum have been used to provide information on land use
patterns, vegetation, and snow.
But remote sensing at these
wavelengths is severely restricted by cloud cover.
Microwave (wavelength ranging from about 1 m to 1000 mm,
frequency
from
0.3
GHz
to
300
GHz)
remote
sensing
unrestricted by cloud cover to a considerable degree.
is
It can
provide information about hydrologic variables such as soil
moisture, seasonal inundation, vegetation, snow depth and its
water
equivalent,
and
rainfall.
atmospheric attenuation is small,
At
these
wavelengths,
and data collected are
generally reliable under cloud conditions.
There are some
specific bands that are subject to rain or fog attenuation.
There are two different modes through which microwave
remote sensing can be conducted,
radars)
and passive
namely active
(microwave
(microwave radiometers).
In active
microwave remote sensing, the sensor system observes a self­
generated signal reflected by the surface-atmosphere system,
while in the passive microwave remote sensing the sensor
system observes naturally emitted microwave radiation.
The
passive
microwave
radiation
measured
at
the
satellite consists of three components: (1) radiation emitted
from a surface and attenuated through the atmosphere;
(2)
radiation emitted downwards from the atmosphere, reflected by
the surface, then attenuated through the atmosphere before
reaching the satellite; and (3) radiation emitted upwards
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14
from the atmosphere and measured directly by satellite.
2)
Soil
Dielectric
Reflectivity, and Emissivity:
represented by
constant
has
real
part
called
the
Surface
Roughness.
Soil dielectric properties are
the dielectric
a
imaginary part
Properties.
constant.
called
The dielectric
permittivity,
dielectric
loss
and
factor.
dielectric constant is dependent on wavelength.
an
The
An increase
in the dielectric constant will result in an increase in
reflectivity
and
a
decrease
in
emissivity.
Since
the
dielectric constant of water is much larger than that of dry
soil,
it is possible to monitor soil moisture based on the
differences in brightness temperatures resulting from the
dielectric properties of soil and water.
The earth's surface can be considered smooth or rough,
depending on the wavelength of the energy being reflected.
When the surface is smooth, specular reflection occurs.
it
is
rough,
scattered
or
diffused
reflections
When
occur.
Clearly, the principles of reflection by a perfectly smooth
surface
cannot
be
directly
surfaces are usually rough.
applied
to
earth
where
the
Rayleigh's criterion defines the
surface roughness, which is given by:
h £ -----(8cos0)
(2 .i)
where:
h = height variations above a plane in wavelengths;
X = wavelength;
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15
8 - incident angle.
The incident angle is the angle between the direction of
propagation to the detector and nadir, and equals 53.1° for
SSM/I.
What is important here is that the wavelength of the
incident or emitted EM radiation determines the roughness.
Reflectivity is defined as the reflective property of a
material meeting the Rayleigh criterion for a smooth surface.
The specular reflectivity
(rsp) describes how effectively
radiation is reflected by smooth surface.
In the horizontal
(h) and vertical (v) planes, they can be calculated from the
surface dielectric constant by [8]:
cos0-v/£s-sm0
Tsp{9,h) =
cos8 +v/es-sin0
rsp(e,v) =
(2 .2 )
£scos0 -^/Eg-sin©
£scos0 +\/£s-sin0
(2.3:
where:
8 = the incidence angle;
es is soil dielectric constant.
Emissivity is defined as the ratio of the spectral
excitance
of a material
blackbody
at
difference
emissivity,
the
between
same
to the
spectral
temperature.
emissivity
and
excitance of a
There
is
a
basic
reflectivity.
For
any substance at temperature T has a state of
thermal energy and emits EM radiation based upon the level of
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16
this energy, or simply its temperature.
is an EM radiation generator.
Briefly, the source
For reflectivity, a substance
reflects all or part of the EM radiation incident on its
surface.
3)
Simple
Radiative
Transfer
Model:
A
radiative
transfer model (RTM) [9] predicts the brightness temperature
emitted by a surface.
For vegetation-covered soil,
vegetation canopy (besides its own emission)
the
scatters and
depolarizes radiation that is initiated by the underlying
soil.
The radiative transfer equation that describes the
emission from vegetation-covered soil can be written as [8] :
(2.4)
where:
6 = incident angle;
p = polarization, vertical (v) or horizontal (h) ;
Tcan = brightness temperature of the canopy;
r3 = reflectivity of the soil surface;
a = single scattering albedo for vegetation;
Tg = physical soil temperature;
Tv = physical canopy temperature;
L (0) = loss factor of vegetation canopy.
For very dense vegetation, L(0) >1, the contribution of
the soil surface becomes very small.
Thus, it is impossible
to retrieve soil moisture under dense vegetation.
other hand, in bare soil condition,
On the
L (8) <= 1, the soil term
is the only contributor to the brightness temperature.
Thus,
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17
the degree of vegetation cover becomes critical in surface
moisture retrieval.
B. The Special Sensor Microwave/Imager
(SSM/I) System
1)
Data Description:
The Special
Sensor Microwave
Imager (SSM/I) measures microwave brightness temperatures at
19.35, 22.235, 37.0, and 85.5 GHz with footprint resolution
areas of approximately 2.5 x 103, 1.6 x 103, 0.86 x 103, and
0.14 x 103 Km2, respectively [6].
37.0,
and
85.5
GHz,
both
.polarizations are observed.
from
antenna
vertical
Brightness
temperatures
antenna pattern correction,
and
horizontal
Only the vertical polarization
is observed at 22.235 GHz.
computed
At frequencies of 19.35,
temperatures are
using
the
published
including dynamics adjustments
for antenna side lobe, antenna efficiencies, and neighboring
pixel contributions [6].
Computer tapes containing SSM/I data were obtained from
the Naval
dates.
Research Laboratory
(NRL)
for the appropriate
Data over the area of interest were downloaded to
disk, and submitted to a set of programs that remove header
records and other nonrelevant information.
The resulting
SSM/I data files consisted of the seven channels of microwave
brightness temperatures, with the latitude and longitude tags
for each pixel.
longitude
With the specification of latitude and
coordinates, all SSM/I and ground truth data can
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18
be assembled as one file.
2)
Instruments'
Description and Operational
Status:
Table I contains several DMSP satellites' characteristics and
operational status.
DMSP satellites are in a circular sun-synchronous nearpolar orbit at an altitude of approximately 833 Km [6].
orbit produces 14.1 full orbit revolutions per day.
direction
is
from
left
to
right
with
the
The
The scan
active
scene
measurements lying ±51.2° about the aft direction, resulting
in a swath width of 1400 Km as shown in Fig. 1 [6].
The scan
angle from nadir is 45.0°, and incident angle from nadir is
53.1°.
Radiometer data are sampled over each A or B scan
alternately.
Scan A denotes scans in which all channels are
sampled concentrically while Scan B denotes scans in which
only 85.5 GHz data are taken.
Because the size of the 85.5
GHz footprints is approximately 12.5 km, on each A or B scan,
it is sampled 128 times, while the other frequencies with
larger footprints are sampled 64 times in the A scan.
TABLE I
Characteristics and
F-8
Sta t u s of th e
DMSP
Sa t e l l i t e
launched June 1987, problems with 85 GHz vertical
channel after March 1988;
local ascending node time is 06:19.
F- 10
launched February 1988, all channels are normal;
local ascending node time is 21:17.
F- 11
launched November 1991, all channels are normal;
local ascending node time is 17:30.
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19
(CM
*
SCCNC t T A T I O W ir t C A *
flX C L I« C A * l
s7t
S C IN I
S C C N t S T A .T I0 N V S C 4 .N 1 J *
r i X E '. l/ S C A N
2S€
S C t« C S T A T IO W /O R 6 IT
* 0 * .M
1 313.721
f lX E L i/ O R B lT
.
IIS'* '
1JOSto
Fig. 1.
SSM/I scan geometry (from Hollinger et al. [10]).
3) SSM/I Data Applications:
derive geophysical parameters,
SSM/I data are used to
such as ocean surface wind
speed, snow cover, area covered by ice, ice concentration,
ice edge, precipitation over land, precipitation over water,
cloud liquid water, integrated columnar water vapor, surface
soil moisture, and land surface temperature.
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20
C. Land Surface Classification
Using SSM/I Data
1)Combinations of Brightness Temperatures:
There are
several possible combinations of the seven SSM/I brightness
temperatures commonly used for land surface classification,
including T22V-T19V, (T19V+T37V)/2- (T19H+T37H)/2, T37V-T19V,
T37V, T85H-T37H, and T85V-T37V [2].
T22V-T19V is used to detect large bodies of water or
standing water due to flooding.
The brightness temperatures
at all frequencies decrease when there is a large amount of
standing water in a footprint.
This is because water has a
high permittivity, resulting in low emissivities. However,
the microwave emissivity of water increases with frequency.
Brightness temperature will be higher at 22.235 GHz than at
19.35 GHz.
In addition, since both 19.35 GHz and 22.235 GHz
channels have approximately the same footprint size, and the
22.235 GHz channel is more sensitive to water vapor [3],
the
difference between T22V and T19V can be used to detect large
bodies of water such as lakes or reservoirs and areas flooded
by large precipitation events.
(T19V+T37V)/2-(T19H+T37H)/2
vegetation density,
and
is
is
commonly
an
indicator
referred
to as
of
the
Microwave Polarization Index (MPI). The higher the value of
the average polarization difference between the frequencies
of 19.35 GHz and 37.0 GHz,
the less the vegetation cover
and/or density for an SSM/I footprint.
The MPI usually has
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21
a positive value since the vertical polarization is usually
greater than horizontal polarization.
However, it could be
a negative value due to noise, as discussed by Neale [2].
T37V - T19V can be used to detect rain or snow over land
surface.
At the wavelength of the 37.0 GHz channels (0.8cm),
the size and quantity of rain drops or snow crystals are
sufficient to scatter microwave radiation.
The brightness
temperatures are lower at 37.0 GHz channels than at 19.35 GHz
channels due to differences in wavelength.
The problem of
using this combination is that the 19.35 GHz and 37 GHz
channels sense different areas.
For complex footprints,
additional noise could be included by using this combination.
T37V has been used for many studies.
indicate
that
the
detecting snow.
37.0
GHz
channels
Ulaby et al. [8]
are
the
best
for
It has also been found that brightness
temperatures at 37 GHz channels are closer to the surface
skin
temperature
Therefore,
than
those
of
when T37V is very low,
the
other
channels.
snow covered or frozen
surfaces can be detected.
T85H-T37H and T85V-T37V can be used to detect rain and
surface moisture.
As discussed above, the size and quantity
of rain drops and other hydrometeors is sufficient to scatter
microwave radiation when the wavelengths are on the same
order
or
smaller
than
these particles.
The
brightness
temperatures of the 85 channels are scattered more than those
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22
of the 37 channels.
In the presence of rain, brightness
temperatures of the 85 channels are lower than those of the
37 channels.
These two combinations can also be used to differentiate
moist footprints and composite water with soil waterbodies
from dry soil. This is because the brightness temperatures
from standing water at 85.5 GHz are greater than that of 37.0
GHz,
since both the permittivity and the dielectric loss
factor of water are smaller at 85.5 GHz than at 37.0 GHz.
In previous research [1]-[3] , [7] , the resolution of the
85.5 GHz channels (approximately 14 Km) was decreased through
an
averaging
scheme
to
that
of
the
37.0
GHz
channels
(approximately 33 Km) . With this scheme, both channels sense
approximately
approximately
the
the
same
same
area.
Therefore,
proportions
of water,
they
have
soil,
and
vegetation within the concentric footprints.
2)
Statistical
Land Surface Classification Methods:
Classification of the multifrequency scenes observed by the
SSM/I System is a fundamental step in the application of
retrieval algorithms over land.
Several efforts have been
made in using the microwave brightness temperatures of the
SSM/I to conduct land classification.
Hollinger et al. [10]
discussed a set of IF..THEN ad hoc binary categorization
rules used to retrieve parameters of land surface types.
However, as indicated in the final report entitled DMSP SSM/I
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23
Calibration and Validation [6] , numerous misclassifications
occurred by using this prelaunch algorithm.
Neale
et
al.
[2]
developed
a
physical/statistical
combined land surface type classification scheme.
Channel
brightness temperatures and polarization differences were
incorporated with statistically determined threshold values
to derive a set of independent classification rules.
Another classification scheme was developed by Heinrich
et al. [4] . This method uses principal component analysis to
extract information on surface types and different microwave
properties.
A set of two-year manually classified SSM/I
observations was used to reduce the seven SSM/I brightness
temperatures to three discriminant scores.
A look-up table
translates the discriminate scores into 23 surface types,
which are then classified in three major categories of ocean,
land, and "unknown" (points outside the discriminate bounds) .
In one sense or another, the previous algorithms for land
surface classification with microwave brightness temperatures
are all based on statistical theory.
D. Fuzzy C-Varieties (FCV)
Classification
Fuzzy
set
is
a
plausible
tool
for
modelling
and
mimicking cognitive processes of the human being, especially
those concerning recognition aspects. The main advantage of
all fuzzy clustering methods is that a partition matrix can
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24
be
generated
with
entries
taking values
in
the
[0,
1]
interval, instead coming from the two-valued set, {0, l} as
is the case with obtained by "hard" clustering algorithms.
In
other
words,
fuzzy
clustering
algorithms
provide
partitioning results with additional information, supplied by
the cluster membership values.
potentially
more
classification.
flexible
Problems
As such,
tool
of
for
the user has a
interpretation
of
significance
and
cluster
validity can be tackled by using cluster membership values as
a
criterion
for
the
determination
of
cluster
overlap,
clustering performance, and number of clusters.
1) Mathematical Basis for the FCV Algorithm:
Perhaps
the best known "fuzzy" clustering method is the Fuzzy CVarieties (FCV) family of algorithms, introduced by Bezdek et
al. in
[11].
It is assumed
(in
[11],)
that data space
consists of n measurement vectors, X = {xlf ...,xn}, each with
d attributes, xk = (xkl, ...,xkd). The algorithms were derived
by minimizing the objective function:
c
n
minimize J{U,V) = £
£ ulk II** ~ v±II2
1=1 k =1
(2.5)
0 £ uik £ 1, 1 < i < c, 1 £ k £ n,
over all possible values of the parameters uik and Vi( subject
to the constraints:
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25
E ui*=1
where:
n = the number of measurementvectors;
c = the number of clusters;
uik =
the membership grade for data vector
belonging to cluster k; the larger the uik,
the more the confidence that
belongs to
cluster k;
u =(uik) is an
n x c matrix;
V = [V1( V2,..
VJ , where
is the "center" of the
ith class.
The FCV algorithm,
via iterative optimization of J,
produces a fuzzy set of c partitions for the data set.
The
basic steps of the algorithm are as follows:
(1) Guess the number of classes, c.
(2) Guess starting centers {v1( V,, ..., Vc} .
(3) Compute "membership coefficients" using:
U,u
■1
1K
jr =
~
y'
Pi
^ ik
V
c
y
pi llx.-^ll2
(2-6)
if Dik=Djk=0 then uik=l, and uik=0 for j^i.
(4) Compute new centers using:
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26
n
E
V,
=
u ik2 x k
k = l ________
n
E
k =1
(5)
Stop,
(2.7)
u ik
if the maximum of ||uik(j)
where e > 0 is a small scaler.
- uik(j-l)|| s e,
In this study, e is set
to 0.005; otherwise return to step (3) with the updated
Vi2) Previous Applications in Remote Sensing:
A lot of
scientific effort has been done applying FCV algorithms to
the
field
of
pattern
recognization,
such
as
speech
recognition, intelligent robots, image processing, and signal
classification, etc.
FCV
algorithms
for
Recent attempts have been made to use
remotely
sensed
data
classification,
particularly for the LANDSAT Thematic Mapper (TM) data with
a noteworthy success.
Jakowski
[12] and Sikka
[13],
for
example, applied FCV algorithms to classify ground cover into
the desired number of spectral classes based on subsequent
field
observations,
information.
However,
aerial
fuzzy
photos,
set
and
theory
some
is
field
relatively
untested for passive multi-frequency microwave data.
E. The Antecedent Precipitation
Index (API)
Since the late 1970's, many studies have been conducted
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27
in soil moisture sensing using passive microwave signatures.
One of the important findings is that microwave brightness
temperatures
are
correlated
with
estimates
of
surface
moisture such as the antecedent precipitation index
(API)
(14] -[16] .
With
daily
maximum/minimum
temperatures
and
precipitation information, spatial and temporal variations of
surface
moisture
can be
estimated
using
Precipitation Index (API) as a surrogate.
the Antecedent
Models proposed by
Choudhury et al . [17] and Owe et al. [18] incorporated soil
evaporation in the estimation of the recession coefficient.
The surface moisture
at
the current day i, APIi( is related
to the moisture at the preceding day i-1, API^, by:
A P I,
1
= K, (API. .
►P.)
1-1
1
(2 . 8 )
1
where:
Pi = total (mm) precipitation on day i;
Kj. = soil water recession coefficient, defined as:
/ ETP )
,
K l = exp(-—
(2.9)
where:
ETP = potential evapotranspiration (mm/day);
Wm = maximum depth of soil water available
evaporation (mm) at the soil surface.
The
potential
evapotranspiration
can
be
computed
Hargreaves equation [19], which can be written as:
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
for
by
ETP
= 0.0023
R a (TC
+ 17.8)
TD
0<5
(2.10)
where:
Ra = extraterrestrial solar radiation inmm/day;
TC = (Tmax+Tmin)/2 (average dailytemperature)
in °C;
TD = T■‘•max -Tmin
• °C^ '
Tmax = maximum daily temperature;
Tmin = minimum daily temperature.
The extraterrestrial radiation Ra can be expressed as:
_9167.32ES(OMsin(Lat)sin(DEC)+cos(lat)cos(DEC)sin(OM)
5.96-0.55 TC
(2 .1 1 )
where:
Lat is the latitude of the location in radians;
DEC = 0.40876cos(0.0172142(J 192));
J = day of year;
ES = 1.00028 + 0.03269COS(0.0172142 (J+192));
OM = Arc.cos(-tan(Lat)/tan(DEC)).
F. Factors Affecting Soil Moisture
Retrieval in the Microwave
There are various
retrievals
using
the
factors influencing soil moisture
SSM/I.
The
key
factors
include
radiometric wavelength, soil texture, vegetation cover, and
surface roughness.
1) Radiometric Wavelength: The effect of wavelength for
soil surface moisture sensing has been discussed by different
authors [9],
[20]- [22] .
All these studies have shown that
there is a decrease in sensitivity to soil moisture as the
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29
wavelength
decreases
(and
frequency
increases).
The
thickness of the emitting top soil layer contributing to the
brightness temperature is inversely related to the frequency
and
soil
moisture
content.
The
contributing
layer
is
estimated as 10 percent of the wavelength for a moist soil
[8] . At the SSM/I frequencies, this represents an emitting
layer of only a couple of millimeters at the 19.35 GHz
(1.55cm) channels.
The 19.35 horizontal channel was found to
be the most sensitive to surface moisture [1].
2) Soil Texture and Surface Roughness:
The soil texture
affects the microwave emissivity [23]- [24] . This is because
water molecules that are held tightly on soil particles are
not as free to move and align themselves with an applied EM
field, and the permittivity of this type of water is not as
large.
Clay-like soils have a larger effective surface area
than sandy soil, and can hold more water in a tightly bound
stage.
Previous research also found that sensitivity to soil
texture in the microwave frequency region is less marked for
shorter wavelengths [23]- [24] .
As
the
scattering
surface
also
roughness
increases
with
sensitivity to surface moisture.
increases,
a
resulting
the
decrease
by Vassiliades
[3]
have
in
This was shown to be the
case by Wang et al. [25], and Newton et al. [26].
studies
surface
taken
Recent
into account
the
surface roughness in a physically-based moisture retrieval
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30
model for SSM/I data by simulating a rough surface as an
arrangement of dielectric slabs on top of a quasi-specular
surface.
3) Effect of Vegetation Cover:
Vegetation cover will
also decrease the sensitivity to soil moisture due to self­
emission
as
well
as
scattering
and
depolarization
microwave radiation emitted by the soil.
of
Several studies
have indicated that longer wavelengths can better penetrate
vegetation cover and are therefore better suited for soil
moisture
sensing.
Vegetation
effects
on
microwave
sensitivity to soil moisture have been studied and discussed
by Wang et al. [27], Burke and Schmugge
[28], Theis and
Blanchard [29] , and Ulaby et al. [9] . The attenuation of the
microwave radiation in a vegetation canopy for the SSM/I was
modelled using Mie-Scattering theory in the Land Surface
Radiative Transfer Model (LSRTM) by Vassiliades [3].
G. SSM/I Moisture Retrieval Models
There are generally two types of models, empiricallybased
and physically-based models,
for
surface moisture
retrieval using SSM/I data.
1) Empiricallv-Based Model:
developed by Gerard [1] .
using
regression
An empirical model was
Three linear models were developed
analysis
to determine
the
relationship
between the Antecedent Precipitation Index (API) and SSM/I
brightness
temperatures
for
three
different
vegetation
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31
densities.
Vegetation density was obtained by computing the
polarization average of the 19 GHz and 37 GHz channels over
dry soil.
For relative dense vegetation, 4 < MPI <= 6, the
model is given by [1]:
API = 1707.24-1724.14
T19H
T3 7V
(2 . 1 2 ]
For medium dense vegetation, 6 < MPI <= 8, the model is given
by:
API = 1126.58-1145.48 T19H
T3 7V
,
(2.13)
For sparse dense vegetation, MPI > 8, the model is given by:
API = 659.35 -675.22-^!^
T37V
(2.14)
These empirical models are limited to API value of 70 mm
since for large API values the relationship between API and
T19H/T37V is not linear.
The models were developed using
data for the year 1988.
2) Physically-Based Model:
developed by Vassiliades
[3]
A physically-based model
is called the Land Surface
Radiative Transfer Model (LSRTM). The model can be used to
simulate the microwave radiation emitted from the earth's
surface and attenuated through the atmosphere.
However, the
inverse of this model can be used to retrieve surface soil
water content within a composite individual footprint.
a) LSRTM:
The Land Surface Radiative Transfer Model
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32
(LSRTM) was developed as a tool for understanding microwave
emissions from complex footprints from the earth's surface.
It is capable
of simulating SSM/I brightness temperatures
subject to changes of one of several major parameters, such
as incident angle, soil moisture, leaf area index, proportion
of bare soil in a footprint, proportion of vegetation in the
footprint,
proportion
of
water
bodies
frequency,
or surface temperature.
in
a
footprint,
The model includes a
total of 21 input parameters, such as apparent angle (0app)»
temperature of bare soil, vegetation and water body (Ts, Tv,
-Tw), permittivity and loss factor of soil particles
(£s',
£s''), vegetation bulk material (£b', £b''), volume fraction
of free water (Vfw), bound water (Vbw), soil particles (Vs),
leaves in the canopy (VJ , leaf water content (Vwl), height of
vegetation canopy
vegetation
surface
(h) ,. area fraction of bare soil
(Acan), water body
roughness
factor
(Agmx),
(AWB) in the footprint,
(RoughF), slab
factor
soil
(SLBF),
relative humidity (RH), and lapse rate (LpsRt). The concepts
of this model are explained below.
First it was assumed that an SSM/I footprint consisted
of bare soil, vegetation-covered soil, and water bodies.
The
microwave radiation is the summation of the three emissions,
weighted according to their proportions in that footprint.
SSM/I brightness temperatures are simulated by initially
calculating the dielectric constant of each surface type in
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33
the model.
The dielectric constant of the soil matrix (£max)
can be calculated [30] by the dielectric constants
(£) of
various components as:
_
_ 3es+2Vfw(
+
2Vbu(Ebu-£s) +2Va(za-zs)
smx
+Vb„(-^-l)+ya(£s-£a)
£ fur
(2.15)
£ bw
The soil matrix is considered as a mixture of soil particles
(s) , comprising the host material, with the inclusions of
free water (fw) in the pores, bound water (bw) held tightly
on the solid particles, and air (a).
The vegetation canopy consists of air (a) and leaves
(1) .
Air is the host material.
The dielectric constant
(£can) of vegetation canopy [9] is defined by the following
equation:
^can
£I[3£a+27i(£1-£a)]
3£,-V, (e, -£ )
1 iy 1 a>
(2.16)
where £, is the dielectric constant of the leaf, which is
defined as [9]:
fw
(2.17)
The leaf is a mixture of vegetation bulk material and free
water.
The vegetation bulk material is the host material in
the leaf.
The dielectric constant for air £a is one.
Based on the dielectric constant of each surface, the
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34
specular reflectivities then can be calculated by the Fresnel
equations
(2.2) and (2.3) in both vertical and horizontal
polarizations.
frequencies
However,
most
surfaces
are considered rough.
at
the
SSM/I
For a bare soil, a rough
surface can be simulated as an arrangement of dielectric
slabs on the top of a quasi-specular surface
[3] .
The
overall emissivity (eamxp) or reflectivity (rDmxp) of a rough
surface in the p-polarization is the summation of the two
emissivities, or
reflectivities
(of
slabs
weighted according to their proportion
and
surface),
in the
simulated
surface, i.e.:
epsmx = Qslb epSLB ♦ (1 ~Qslb )(1 -rp*-»P)
(2.18)
p s/nx - n
p SLB + / i _r\
v p q-sp
ip
SLB p
\ A ^ SLBlx p
(2 .19)
where:
eSLBp = emissivity of slabs;
rSLBp = reflectivity of slabs;
Qslb = density of the dielectric slabs.
Qslb is used to represent the degree of roughness, which in
turn influences the loss factor of soil layer (L2) . L2 is a
function of the thickness of the slabs, which is determined
by the wavelength (X) and moisture level
reflectivity of
a quasi-space
[8]
is
(Vfw + Vbw) .
The
considered as
the
specular reflectivity attenuated by a roughness parameter,
h' :
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35
Tp"sp = TpP .exp(-h /cos29app)
(2.20)
The reflectivity of a slab at p-polarization (rSLBp) [8] and
corresponding emissivity
(eSLBP)
[3]
can be calculated by
equations as follows:
' (i-r|p)2'
,SLB
■pSP
1P
(2 .2 1 )
(r f )2
/
i 'i
(l -r|p)
ePSLB
J2
1\'
For canopy-covered soils,
calculated
from
pSP N
1.H
the
(2 .2 2 !
(r;/ J
the reflectivity
specular
canopy
(rcanp) can be
reflectivity
(rspp)
attenuated by the roughness parameter h', i.e.:
r can = T sp _ e x p ( _h /c o s 20 j
(2.23)
where 8 is the incidence angle.
Water body reflectivities in the horizontal
(TWBH) and
vertical (r^) were obtained [3] from regression analysis of
selected
footprints
in the middle of large
lakes.
The
results are:
rr = (0.84037-0.00191f)
(2.24)
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36
and:
r ™ = r£p (0. 83383-0.00080f)
(2.25)
where f is frequency in GHz.
The emissivity of the surface
eSFCp is equal to 1 - rSFCp (the reflectivity of the surface) .
Based
on
equations
(2.15)-(2.22),
the
temperatures for each surface can be computed.
radiation measured at the satellite
temperature
considered
(b)
[8]
radiation that
units
as
the
(K)
for
The microwave
(Tbsur) in brightness
each
combinations
brightness
of
surface
(sur)
three parts:
is
(1)
is emitted from a surface and attenuated
through the atmosphere (Taur) ; (2) radiation that is emitted
downwards from the atmosphere (TDN), reflected by the surface,
and attenuated through the atmosphere before reaching the
satellite, and (3) radiation that is emitted upwards from the
atmosphere (Tup) and measured directly by the satellite.
The
relationship was defined as in [8] :
r(b,SUr) = (epUrTsur)TrAtm+ (TpUrTDN)TrAtm +Tup
(2.26)
where TrAtm is the transmissivity of the
atmosphere, and is
defined [10] as:
TrAtm = exp
' (kH,o+ko,) kmAtm)
COS0
(2.27)
where:
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37
kH.o+ k 02 = total atmospheric absorption coefficient;
kmiAtm = thickness of atmosphere.
Tdn and Tup in equation (2.26) are defined [8] as:
TDN - TyP - Te(j •
(1
-TrAtm)
(2.28)
The equivalent radiating temperature Teq is approximately
equal to average footprint temperature reduced by the lapse
rate (LpsRt)
T eq
=
[31], as defined as:
(AsmxTsmx +AcattTcan +Am Tm ) - ( L p s R t )
1Q
(2.29)
where:
A
smx
-
A can =
A WB =
Tsmx
T can =
^WB “
The
area fraction of footprint covered with bare soil ;
with
area
fraction
of
footprint
covered
vegetation;
area fraction of footprint covered with open
water;
temperature of bare soil;
temperature of vegetation canopy;
temperature of water body.
radiation
for
bare
soil
in
equation
(2.23)
in
p-
polarization (both horizontal and vertical) is:
oPsurT
= PPsrax<rsmx = 'n -rsmx^
'r
■L sur
P
I smx
(2.30)
and for water body is:
epUrTsur -
= (1-rf )Tm
(2.31)
For vegetation canopy, radiation emitted from canopy surface
was defined in [8] as:
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38
(
l -r£an
•pcan .pS/nx
psmx \
1- P
(l- 1
L(G)j \ L { 9 )
/ 1 -psmx v
J- J-p
L ( 9 ) )\
1
L ( 9)2
Equation (2.4) is a simplification of equation (2.29) if rcanp
is set to zero.
The brightness temperatures observed by the SSM/I can be
computed by weighting the brightness temperatures from each
surface according to the proportion that each surface has in
the footprint as:
7
1
= **smx
A * T (b,smx) +Acan * I1(b,can) +A •m * ±71(b, MB)
J> (b,p)
(2.33)
where p denotes polarizations (h-horizontal, v-vertical).
b) The inverse LSRTM:
(LSRTM)
was
inverted
[3]
The Land Surface Transfer Model
by
entering
seven
brightness
temperatures to retrieve surface moisture and temperatures
(etc.) over a single footprint.
nonlinearity
of
the
equations
Due to the complexity and
of
LSRTM,
brightness
temperatures cannot be explicitly written in terms of the
input parameters.
Search
Therefore, the Parabolic Golden-Section
(PGSS) Optimization technique
[32] was employed to
find the combination of the input parameters that minimize
the difference between the brightness temperatures calculated
by the model and those recorded by the SSM/I in inverting the
LSRTM.
The
sum of the squared differences between the
brightness temperatures observed by the SSM/I instrument and
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39
the ones calculated by the LSRTM was chosen as the objective
function (OBJF),
and is written as:
OBJF = (T19vs -T19v m)2+ (Tl9hs -T19hH)2+ (T22vs -T22vM)2
= (T37vs -T37v m)2+ (T37hs -T37hM)2
= (T85vs-T85v m)2+ (T85hs-T85hH)2
where
"T19vs" is
the
brightness
temperature
at
(2.34)
19
GHz
vertical polarization measured by the SSM/I instrument, and
" T 1 9 v h"
is the corresponding temperature calculated by the
LSRTM, with similar nomenclature used for all other channels.
Since the PGSS technique only guarantees a local minimum
[32],
depending
parameters,
on
the
initial
values
of
to achieve the global minimum,
approach was used
[3] .
the
input
an iteration
A set of guessed initial
input
parameters was used, within their allowable ranges, and the
PGSS technique was applied to each of parameters in sequence.
A new set of parameters was obtained at the end of the
procedure, which resulted in a local minimum OBJF.
The new
resulted parameters were then used as the initial conditions
for the next run of the PGSS, and, with the allowable ranges
of parameters
restored
to
the original
values,
the new
parameters resulted in an OBJF smaller than the previous one.
This process iterates until OBJF is smaller than 2 K [10]
(the sum of the squares of the noise equivalent errors of all
the SSM/I channels), and the searching step is smaller than
a certain value (c) of 0.0001.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The
inverse
model
is
capable
of
retrieving
seven
parameters, including soil moisture, footprint temperature,
relative humidity, and the three factors used in LSRTM to
characterize the roughness of the surface, which are apparent
angle,
roughness
factor,
and slab factor.
However,
the
inverse model requires many parameters to characterize a
footprint as model input, including the area fractions of
bare
soil
(Asmx) , vegetation-covered
soil
(Acan) , water
bodies (A^), estimates of the dielectric properties of the
solid particles,
type of vegetation material,
density of the vegetation canopy,
water in the leaves.
height and
and volume fraction of
The temperatures of the three possible
footprint constituents (soil, vegetation, water) were assumed
the same for simplicity.
Since the satellite does not align
the same area during every overpass, some variations (± 0.05)
in the estimated values of Asmx, Acan, and A^ were allowed
in the inverting process.
is
nonuniqueness
variables
in
the
of
It is important to note that there
the
model
solution
are
more
because
than
the
the
unknown
independent
equations.
H. Advanced Very High Resolution
Radiometer (AVHRR)
Because of the very coarse spatial resolution of the
SSM/I, it is difficult to interpret the microwave signatures
and
thus
characterize
the
footprints.
For
large-scale
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41
moisture retrieval, AVHRR can be used to resolve more surface
features due to higher spatial resolution, and spectral bands
suitable for sensing vegetative soil and water.
The
AVHRR
data
from
polar
orbiting
meteorological
satellites (NOAA-6, -7, -8, and -11) of the National Oceanic
and Atmospheric Administration (NOAA) have been used to studyseasonal fluctuations in the extent of vegetation [33]- [35],
classify land cover type [36], monitor monthly variations in
globally
averaged
atmospheric
C02
[37],
and
monitor
vegetation development and the length of crop growing seasons
[38]- [39] . The NOAA AVHRR collects data in various regions
of the electromagnetic spectrum, ranging from the visible to
the thermal infrared [5] . The primary spacecraft and sensor
characteristics for NOAA AVHRR systems currently in orbit are
described in Table II.
The standard NOAA AVHRR product, collected worldwide on
a daily basis since 1979, is the GAC (Global Area Coverage)
data with a 5 km x 3 km resolution element [40]- [41] . It is
produced by onboard processing of the raw 1.1 km x 1.1 km LAC
(Large Area Coverage) data, which for sample areas may be
transmitted to earth by special request.
During the past decade the AVHRR-derived vegetation
indices have proved to be a useful tool in depicting the
large-scale
distribution
and
phenological
changes
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of
42
TABLE II
Characteristics and
NOAA-6
NOAA AVHRR
Systems
la u n c h e d June 1979, N O A A funded;
T a k e n out of operational service 5 M a r c h 1983,
r e i n s t a t e d 22 June 1984.
NOAA-7
l a u nched June 1981,
Operational.
NOAA-8
l a u n c h e d M a r c h 1983, N O A A funded;
T a k e n out of operational service 12 June 1984.
N O A A - 11
9 days.
S c a n angle range
±55.4°.
G r o u n d Coverage
i n clination
98.8°.
833 km.
Orbit p e r i o d
102 min.
E q u a torial
crossing
S p ectral channels
S p ectral range (|tm)
N O A A funded;
2700 km.
O rbit height
G r o u n d res o l u t i o n
and
N O A A funded;
launc h e d S e p t e m b e r 1988,
Operational.
C o v e r a g e cycle
Orbit
St a t u s o f t h e
1.1 k m
6.9 k m
(nadir); 2.4 km (max. o f f-angle al o n g track);
(max. off-angle cross track)
Descending
07:30
02:30
01:40
1
0.58-0.68
Ascending
19:30 (NOAA-6 & NOAA-8)
14:30 (NOAA-7)
13:40 (NOAA-11)
2
3
4
0.70-1.10 3.60-3.90 10.3-11.3
vegetation over particular regions.
5
11.5-12.5
The contrast between the
near-IR and visible AVHRR reflectance is an indicator of the
amount and state of the vegetative cover.
Two vegetation
indices are usually considered and are represented by:
DVI = R x-R2
NDVI = (J?2
(2 .35)
)
(2.36)
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43
where Rx and R2 correspond to visible and near-IR reflectance,
respectively; DVI denotes the difference vegetation index;
and
NDVI
denotes
the
normalized
difference
vegetation
index.
The NDVI equation produces values in the range of -1.0
to 1.0, where increasing positive values indicate increasing
vegetation density and negative values indicate nonvegetated
surface features such as water, ice, snow, or clouds.
The
computed NDVI value from the AVHRR, ranging from -1.0 to 1.0,
was scaled to the range of 0 to 200 in the CD-ROM (compact
disc read only memory).
The computed values -1.0, 0, 1.0
correspond to the values of 0, 100, 200, respectively.
Since remote sensing at AVHRR wavelength is severely
restricted by cloud cover, the method for determining the
portion of each overpass was
highest NDVI values.
to retain pixels with the
The NDVI was examined for each overpass
within the weekly or biweekly compositing period to determine
the maximum values.
In 1987, the U.S. Geological Surveys
EROS Data Center (EDC) began receiving AVHRR data from NOAA
polar-orbiting satellites.
Early in the 1990 growing season
the EDC started acquiring NOAA-11 AVHRR 1-km resolution daily
observations
to
produce
weekly
and
biweekly
maximum
normalized difference vegetation index (NDVI) composites of
the conterminous United States [42].
Beginning in 1993,
also published water-body information in CD-ROM series.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
EDC
44
CHAPTER
III
METHODOLOGY
To accomplish the objectives of this study, a systematic
approach for large-scale moisture retrievals using the SSM/I
and AVHRR data was developed, and is schematically shown in
Fig. 2.
The methodology can be viewed as a six-step process: (1)
The ground truth processing was used to determine the values
of an Antecedent Precipitation Index
(API), which was a
surrogate variable for the ground truth surface moisture; (2)
the land surface classification method was used to identify
the land surface types in terms of rain over soil, vegetated
soil,
desert,
and moist
soil,
etc.;
(3)
the multilayer
parameter database was used to store information on water
bodies and vegetation density, and soil porosity, which are
important to the moisture retrieval models;
merging-then-gridding
approach
was
used
to
(4) the data
combine
the
classified SSM/I footprints and the ground truth climate
data, and to provide positional references for the dynamic
database;
(5) the dynamic database was used to store the
running average values of T19H/T37V and MPI, which are two
important parameters in developing and/or running of the
moisture retrieval models;
and (6) both the empirically-
based model and the physically-based model were used to
predict the surface moisture over selected areas.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Fuzzy Logic-Based
Classification
Generation of
Daily Max, Min
Temperatures and
Precipitation
Files
Compute API
EBM £ PBM
Multi-Layer
Parameter Database
• Waterbody
• Soil
• Vegetation
• MLRA Code
Data Merging
Process
1!§B
1r
Data Gridding
Process
&
H
Dynamic Database
|
PBM
Moisture Prediction Modelling
Empirically-Based Model (EBM)
Physically-Based Model (PBM)
Fig. 2.
Methodology for large-scale moisture retrievals.
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46
A. The Ground Truth Data
Processing
To test the validity of the moisture retrieval models,
it was necessary to obtain measured ground truth data.
the SSM/I spatial resolution
At
(on the order of dozens of
kilometers), surface moisture was not available from direct
measurements, so a surrogate variable called the Antecendent
Precipitation Index
variables
from
Administration
(API) was estimated based on climatic
the
(NOAA)
National
Oceanic
cooperative
and
network
Atmospheric
of
weather
stations.
The data arrived on tapes and daily files were
generated
that
included
daily
maximum
and
minimum
temperatures and precipitation.
In the previous ground truth data processing [1] , it was
assumed that weather stations recorded data in the early
morning, and thus the maximum temperature recorded was for
the previous day.
Although most measurements were made in
the early morning hours, some weather stations' data could
have been recorded at other times.
It is sensible to check
the recording time to determine the maximum temperatures.
If
a record was measured between noon and midnight, it can be
assumed that the value represents the maximum temperature of
the
current
day;
otherwise
it
temperature of the previous day.
represented
the
maximum
The minimum temperature
always represents the minimum temperature of the current day
because it usually occurs early in the morning.
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47
Many stations measure precipitation but not temperature.
Temperature
values
for
a
weather
station
with
missing
temperature were obtained by averaging temperatures
from
neighboring weather stations.
It was also assumed, in the previous data processing,
that
the
precipitation
value
was
zero
when
the
data
measurement flag indicated there were several days without
reported
values,
precipitation value.
parameter.
followed
by
a
Precipitation
large
accumulated
is a more uncertain
It is more reasonable to use an averaged value of
the accumulated precipitation to replace a zero value for
days that have no recorded precipitation values. It is very
possible that the large precipitation value is an accumulated
value.
Based on the daily precipitation amount, daily minimum
and maximum temperatures, the antecedent precipitation index
(API) was calculated by equations (2.8)-(2.11) as the surface
moisture ground truth measurements.
B. The Land Surface Classification
Using the SSM/I Brightness
Temperatures
The SSM/I brightness temperature data were obtained from
the Naval Research Laboratory (NRL).
The SSM/I data were
averaged in such a way that three rows of 85.5 GHz footprints
were assigned to the concentric 19.35 GHz
footprints.
and 37.0 GHz
Nine 85.5 GHz footprints covered about the same
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48
area as one 37.0 GHz footprint and represented an averaged
value at 85.5 GHz.
The SSM/I data files contained seven
brightness temperatures corresponding to the seven channels
and the latitude and longitude locations of the centers of
the SSM/I concentric footprints.
1) Classification Parameters:
To use the SSM/I data to
retrieve surface moisture, it is a essential step to classify
the land surface types within the study area.
The
combinations
of
SSM/I
brightness
temperatures
commonly used to classify a land surface are T22V-T19V, MPI,
T37V-T19V, T85H-T37H, T85V-T37V, T19V, T37V, and T19V-T19H.
As discussed in Chapter II, the IF...THEN logic approach was
conventionally used, using these combinations, to determine
the
land
surface
types.
However,
the
use
of multiple
conditions increased the complexity of the classification
process and resulted in unclassified cases.
There
were
only
four
combinations
of
the
brightness temperatures used in this research.
SSM/I
They are
(T19V+T37V)/2-(T19H+T37H)/2
(Microwave Polarization Index,
MPI) , T85H-T37H,
and T37V.
T85V-T37V,
The parameter MPI
indicates vegetation density as MPI decreases with increased
density.
The combination of T85H-T37H provides the most
information concerning rain or snow, extent of soil surface
moisture (moist or dr4) and
water bodies.
of
to
T85V-T37V
can
be
used
The combination
differentiate
desert
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from
49
moist/composite water with soil.
Parameter T37V can be used
to detect frozen ground and snow since it is physically close
to the soil skin temperature [1] .
parameters,
Based on the above four
a look-up table, as shown in Chapter IV, was
developed to describe land surface types.
2} Preprocessing:
To learn the characteristics of the
combinations of brightness temperature of the SSM/I data,
ERDAS software was used to produce land surface images for
selected time sequences from the 1987 storm data,
covered different
areas
of the world.
compared to the ground truth information.
The
which
images were
Many iterations of
producing images and comparisons were made by trial and error
for different values of each combination.
conclusions were obtained:
The following
(1) values of T37V less than 225
indicate frozen ground and/or snow; (2)
values of T85H-T37H
less than negative 20 indicate heavy rain;
(3) values of
T85H-T37H greater than positive 20 indicate a large waterbody
or flooding land; and (4) MPI values greater than positive 30
indicate a land surface free of vegetation.
These four
conditions were first used to identify the surface types.
This was named as the preprocessing in this study.
3) Fuzzy Logic-Based Classification Methods:
Following
the preprocessing, a two-level structured fuzzy logic-based
method was used to further classify the remaining undefined
footprints.
MPI and T85H-T37H were used in the first level,
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50
which identified most of the land surface types, such as rain
over soil, vegetated soil, and moist soil, etc.
Since the
number of land surface classes is unknown, the first-level
classification is an unsupervised classification problem.
the second level,
In
T85V-T37V was used to differentiate a
desert from moist/composite water with soil.
a supervised problem with two classes.
It is therefore
Since there are only
two parameters used in the first level and one parameter in
the second level,
this two-level
classification approach
greatly reduces the complexity of the classification process.
The overall classification logic is illustrated in Fig. 3.
There were two operations in each level:
assignment.
A
fuzzy
logic-based
clustering and
clustering method
applied for partitioning a SSM/I data set.
was
The use of FCV
requires the user to prespecify the number of clusters for a
data set. The FCV method is ready to be used in the second
level classification since it is a supervised problem with
known class number.
problem
to
use
the
However,
FCV
it is not a straightforward
algorithm
in
the
first-level
classification since the class number is unknown.
In order
to use FCV in this unsupervised problem, a Normalized Fuzzy
Entropy
(NFE)
definition was
discussed in Chapter IV.
introduced,
which
Fuzzy
be
The NFE determines the ambiguity or
impreciseness of a partition for a data element.
Normalized
will
Entropy
(ANFE)
was
then
The Average
calculated
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
to
51
SSM/I Data
Yes
T85H-T37H > 20 ?
Waterbody or
Flooding
.No
Yes
Heavy Rain or Snow
over Soil
T85H-T37H < -20 ?
Preprocessing
No
Yes
Frozen Surface
T37V < 225 ?
No
MPI > 30 ?
Yes
No
First-Level
Classification
Fuzzy CVaricfcuas
Clustering
No
Are There
Uncertain Cases ?
Yes
Second-Level
Classification
No
Classified Land
Types
Fig. 3.
The overall classification logic.
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52
in determining the most representative number of clusters for
determine
the
fuzziness
of
one data
set.
The
minimum
criterion for the ANFE was used in an unsupervised data set.
To determine
the minimum ANFE,
a minimization searching
algorithm was developed.
The physical meanings of each class were assigned based
on the information of normalized point fuzzy entropy (NFE),
cluster centers, and the look-up table.
C. Data Merging and Griddina
Processes
As
mentioned
in
Chapter
I,
the
conventional
data
gridding-then-merging process introduced significant noise,
due to the possible spatial mismatch between gridded weather
stations and SSM/I
concentric footprints centers falling
randomly within the grid cells.
To deal with this problem,
a data merging-then-gridding approach was used.
The merging
process was used to combine the classified SSM/I footprints
and the point ground truth climatic data within the same
area.
The gridding process was used to provide a positional
reference for the dynamic database [2] , providing information
on vegetation density and moisture for consecutive SSM/I
overpasses also within the same area.
1) Data Merging Process:
The SSM/I data from satellites
F8 and Fll were used in this research.
The satellites that
carry the SSM/I instrument pass roughly over the same area
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53
twice per day, once heading from south to north (about 6 a.m.
for F8 and about 6 p.m. for Fll [ascending overpass]), and
the second time heading from north to south (about 6 p.m. for
F8
satellite
overpass]).
and
6 a.m.
for
Fll
satellite
[descending
It was assumed in calculating API values that
there was no evapotranspiration during the night, and the
precipitation events occurred between 12 a.m. and 6 p.m. for
a particular day.
The F8 ascending overpasses
and Fll
descending overpasses were merged with point "ground truth"
API
files
from
the
previous
day.
The
F8
descending
_ overpasses and Fll ascending overpasses were merged with the
point API files from the same day.
In the merging process, the SSM/I footprint was used as
a key element
in searching API
files.
Since the SSM/I
footprints "look" at a different areas for each overpass and
day,
their positions
are not
fixed
(while positions
of
weather stations are fixed). A binary search, which uses the
divide-and-conquer approach,
was employed to find matches
between the SSM/I location and the ground truth location.
If
the distance between a weather station and the center of a
SSM/I footprint was less than 15-Km (a circle with radius of
15 Km has about the same area of a quarter-degree box cell
and a 37 GHz footprint), the records of the weather station
were considered matches.
If more than one match was found
within the 15-Km circle of the SSM/I footprint,
the API
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54
values for all of the matches recorded from the corresponding
weather stations were averaged.
Otherwise a special flag was
used to indicate that there were no corresponding API values
for
the particular SSM/I
footprint.
From this merging
process, a merged data file was developed, which consisted of
latitude and longitude (in terms of the center of the SSM/I
footprint),
seven
brightness
temperatures,
surface
type
classification code, four API values, minimum and maximum
daily temperatures,
the number of days since last missing
record, and the number of days since last rain fall event.
2) Data Gridding Process:
The merged data was then
assigned to a particular cell with a resolution of 0.25°
latitude/longitude (quarter-degree boxes) if the center of
the
SSM/I
footprint
fell
within
the
cell.
The
latitude/longitude designation of a quarter-degree box refers
to its lower right corner.
If more than one footprint was
present in a particular box, the values were averaged.
D . Parameter Database
Water bodies,
greatly
affect
wavelengths.
vegetation density,
microwave
emissions
of
and soil porosity
SSM/I
brightness
The development and application of moisture
retrieval models, using SSM/I brightness temperature, require
information
footprint.
on
these
surface
features
within
an
SSM/I
Remotely sensed imagery by the AVHRR onboard the
NOAA series of satellites, soil maps, and the MLRA handbook
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
55
(published by the U.S.
provided
information
spatial resolution.
Soil
on
Conservation Services
these
surface
features
at
[43])
high
A database was developed to store the
information of these parameters
(discussed in detail
in
Chapter V ) .
E. Dynamic Database
It was
observed
[1]
that
the normalized brightness
temperature (T19H/T3 7V) did not vary considerably from day to
day over dry .soil conditions.
When soil surface was wet
(after a rain), there was an abrupt temperature decrease, if
the vegetation was not too dense, and gradually returned to
the value prior to the rain event over a period of time.
Thus,
the running average of T19H/T3 7V can be used as a
moisture indicator.
Vegetation
density
is
retrieval using the SSM/I.
a major
factor
for moisture
The average polarization in 19
GHz and 37 GHz channels is referred to as the Microwave
Polarization Index (MPI) . The running average of the MPI can
be
used
to
monitor
growing
vegetation
and
senescence
throughout the season indicating vegetation density.
The
running
average
of T19H/T37V and
the MPI
were
calculated and stored in the dynamic database [2] . The most
recent overpass value T19H/T37V was compared to its own
running average before including it in the running averages.
If T19H/T37V was
significantly smaller than its running
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56
average and the classification code indicated moisture, the
surface was considered moist.
The most recent T19H/T37V and
MPI were consequently not included in the running averages.
If T19H/T37V was not significantly different from the running
average in the dynamic database and the classification code
did not indicate moisture, the soil surface was considered as
dry.
The information for the most recent values of T19H/T3 7V
and the MPI was then included in the running averages.
The dynamic database was used in the development and
application of the empirically-based and physically-based
models.
The running average of the MPI was included as an
independent
variable
in
the
empirically-based
represent the effects of vegetation density.
model
to
The dynamic
database was also used to apply the footprint-based physical
model for surface moisture retrieval over large areas.
The
physically-based
was
model
was
only
used
when
moisture
detected and the surface was not heavily vegetated.
considerably
reduced
the
number
of
times
in
which
This
the
physical model was in use, making retrieval of moisture over
large areas realistic.
F. Surface Moisture Retrieval
Modelling
1)
Empirically-Based Model: The ideal surface moisture
retrieval model
should be
one that uses
only
the SSM/I
brightness temperatures, without requiring additional surface
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57
feature information.
Gerard [1] developed an empirically-
based
based
linear
model,
on
three
vegetation
density
classes, and linear relationships between API and the SSM/I
normalized brightness temperature, T19H/T37V.
The model can
provide simple and fast prediction of surface moisture for
relatively small API values.
However, a lot of noise was
introduced in the regression data sets due to the datagridding process as well as the inclusion of water bodies and
rain footprints.
This section will discuss the approach used
in developing the empirically-based model introduced in this
study by using multiple nonlinear regression analysis.
a) Preparation of regression data set:
SSM/I files with
potential surface moisture were selected from overpasses
of
the Central Plains and Western Desert areas of the United
States by locating storms with significant precipitation on
daily weather maps (published by NOAA.)
The SSM/I data files
used to generate regression data set were ordered to cover a
time period of 1 or 2 days before and several days after a
storm.
This made it possible to detect abrupt changes in
surface moisture on the day of the storm and follow the
subsequent dry-out period.
For the appropriate dates and overpasses,
footprints
were
classified
using
the
fuzzy
the SSM/I
logic-based
classification method as discussed earlier in this chapter.
The classified footprints were then merged with ground truth
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58
API data files, including precipitation amount, maximum and
minimum daily temperatures, days after last rainfall, days
after last missing record, and four API values.
The minimum
number of days after last missing record was later used in
the regression analysis for an outlier analysis.
If there
was no API data available for a particular footprint, the
footprint
data
were
omitted
in
the
data
set
used
for
regression analysis.
Based on sensitivity analysis by using a radiative
transfer model by Vassiliades [3], 1.5 percent of standing
water within a footprint would result in significant change
in the SSM/I brightness temperatures.
Therefore, footprints
with significant standing water (more than 1.5 percent) were
excluded from regression files.
The percentage of standing
water was calculated based on the water-body layer of the
parameter database obtained from the AVHRR data set.
To
reduce searching time, footprints recorded under rain and/or
snow
condition
were
previously
excluded,
by
the
classification process, or by checking whether the normalized
temperature (T19H/T37V) was greater than 1.
b) Multiple regression analysis:
model
was
developed
by
An empirically-based
statistically
analyzing
the
relationship between the API data and the SSM/I brightness
temperatures,
normalized brightness temperatures,
running average of MPI.
and the
Previous study [1] has shown that
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59
parameter T19H/T37V has the most correlation with API values.
This is because the 37 GHz channel vertical polarization
channel is closer to the emitting skin temperature due to its
smaller penetration depth [1].
A multivariate nonlinear model structure was used in
this study, as written by:
A P I 3 = Po +Pix i +P 2X 2 + • • • +Pqx q +aif (Yi) +a2f(Y2) + . . .a f (Y )
(3.2)
where:
X± (i=l, 2, ..., q) and Yj (j=l, 2, ..., p) is the
explanatory or independent variables;
p and q are the number of explanatory variables;
/Si and
are the regression coefficients, and
f(.) is the simple or power transformation function.
The foundation for a multiple linear regression analysis
is that the underlying variables have linear relationships.
This
was
variable.
line.
checked
by
plotting
the
distribution
of
each
Normally distributed data results in a straight
If the data were not normally distributed, appropriate
power or nonlinear transformations were used, transforming
skewed distributions to be more symmetrical.
A multiple linear regression model can include a large
number of independent variables.
Each independent variable
contributes a variance portion of the dependent variable.
stepwise
regression
technique
was
used
to
find
A
the
combination of the independent variables, which give the best
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60
prediction
of
the
dependent
variable
(API).
Stepwise
regression usually avoids irrational coefficients because the
statistical
criteria
used
in
selecting
the
independent
variables usually eliminate predictor variables that have
high intercorrelation [44].
The SAS statistical package on
the VAX computer was used in this study.
2)
Physically-Based Model:
The LSRTM was developed by
Vassiliads [3] . This model simulates the microwave radiation
emitted by complex footprints and measured by the SSM/I.
Since the model is based on physically-derived equations, it
is
more
flexible
than
the
empirically-based
applied to complex footprints.
model
when
Part of the "noise," when
developing and using the empirical algorithms, was modelled
as
radiation
emissions
from
heterogeneous
patches
of
vegetation, bare soil, or water bodies occupying portions of
the total footprint area.
all
SSM/I
channels
were
The brightness temperatures for
simulated
by modelling
surface
roughness with apparent angle and dielectric slabs.
The
attenuation of the microwave radiation in a vegetation canopy
was modelled using the Mie-Scattering theory.
The Inverse-LSRTM was developed for estimating surface
moisture and temperature from SSM/I data over a variety of
footprints.
retrieve
The parameters
include:
temperature,
(a)
soil
that
the
inverse LSRTM
moisture,
(c) relative humidity, and
(b)
can
footprint
(d) three factors
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(apparent angle,
roughness factor, and slab factor) that are
used to characterize the roughness of the surface.
the
model
requires
many
characterize a footprint.
input
parameters
in
However,
order
to
The inverse iterative procedure is
a time-consuming process.
The parameter database was used to determine the input
parameters
to
the
model,
in
order
to
retrieve
surface
moisture over large areas using this physically-based model.
The dynamic database [2] was used to detect footprints that
the model
requires
to retrieve moisture.
All
of
these
aspects will be discussed in detail in Chapter VII.
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62
CHAPTER IV
FUZZY LOGIC-BASED METHODOLOGY FOR
LAND SURFACE CLASSIFICATION
A. Introduction
In order to use the brightness temperatures (TB) from the
SSM/I
to
retrieve
surface
properly
classify
Chapters
I and II,
the
methods
[2] ,
were
classification.
the
[4]
land
moisture,
it
surface
type.
is
necessary
As
stated
statistical discriminant
used
for
SSM/I
to
in
analysis
land
surface
However, it is difficult to achieve accurate
classification results using these statistical methods for
mixed and complex surface types.
One of the major problems when using the conventional
classification
procedures
traditional "hard" logic,
is
that
they
are
based
on
requiring that every object must
belong to one (and only one) of the predefined object classes.
This requirement is clearly in opposition to the land surface
classification problem,
where a continuum of land surface
types often only has a subtle difference between them.
order
to
technique,
use
the
traditional
statistical
In
classification
it is necessary to assume an arbitrarily large
number of classes.
When a footprint is not sufficiently
similar to one of the expected surface types, the method must
be
programmed
to
reject
classification,
to
avoid
misclassification.
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63
A promising solution of the above problem is to employso-called fuzzy logic [11], [45]- [46] rather than traditional
binary logic.
approach,
Fuzzy logic provides a continuous multi-valued
not
available
with
traditional
(yes-no)
logic,
introducing the concept of degree-of-membership of an object
in a class.
A fuzzy logic-based method has been first developed for
land surface classification using SSM/I data in this study.
The method includes the following major processes:
(1) The
Fuzzy C-Varieties (FCV) family of clustering algorithm [11]
was used to classify the SSM/I data in terms of membership
functions; (2) a normalized fuzzy entropy definition was used
as a criterion
a
data
element;
determine
entropy
to determine the fuzziness of a partition for
(3)
a
"local"
for
the
a
searching
minimum
data
of
set,
algorithm
average
which
was
used
normalized
defines
the
to
fuzzy
most
representative class number; (4) a cluster assignment approach
was used to interpret the identified classes in terms of
physical and environmental meanings.
The new classification
method allows classification of nonstandard surface footprints
and
thereby
increases
the
identification
accuracy
and
completeness for a given scene.
B. Fuzzy Clustering Algorithm
This section will discuss the fuzzy clustering algorithm,
the concept of normalized fuzzy entropy, and the minimum ANFE
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64
searching algorithm.
Numerical examples are used to show the
validation of the normalized fuzzy entropy concept.
1) The Basics of Fuzzy Set Theory:
fuzzy
set
is
the
membership
The basic concept of
function,
which
numerically
represents the degree to which an element belongs to a set.
If an element is a member of a set to some degree, the value
of its membership function can be between 0 and 1.
fuzzy
set
is
always
defined
as
a
subset,
the
Since a
"sub"
is
frequently ignored, and it is referred to as a fuzzy set.
A fuzzy set A can be defined as a vector [45]:
A = (U A
t UA f ... r UA f ... f UA )
(4.1)
where:
uAj is the membership value of jth element in subset A;
n is the number of elements in the universe of discourse
X, or:
X = {xirx 2,
(4.2)
Assuming there are two subsets A and B,
with membership value
vectors A = (u^u*2, ...,uAn) and B = (Ug1, ^ 2, ...,uBn), there are
the following basic fuzzy set operations [11]:
(a) The complement of A, A°
u/c(x) = l-uAJ(x)
(4.3)
(b) The union of A and B (A u B)
illjfl(x) = max(u/(x) ,uBJ(x))
(4.4)
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65
(c) The intersection of A and B (A n B)
uaTib(x ) = min(uAJ(x) , uBJ(x))
11
(4.5)
(d) The size or cardinality of A, M(A)
M (A
2) Normalized
)= £
j= 1
u*(x) = £
j= 1
\uj(x) -01
(4.6)
Fuzzy Entropy: Thefuzziness of a fuzzy
set A arises from the ambiguity or vagueness between itself
and its complement (Ac) .
also.
If A is uncertain, Ac is uncertain
The amount of fuzziness in A can be measured by fuzzy
entropy.
Kosko [47] introduced a fuzzy entropy definition, as
given by:
E (A) = M
M (aUa c)
(4.7)
Fuzzy entropy, as defined above, measures the fuzziness
of
set A, which includes n elements
(each of which has a
membership value to A with range [0,1]).
To evaluate the validity of a partition, or the ambiguity
of
the partition with class number
c, a normalized fuzzy
entropy definition was introduced in this study.
Assume a universe of discourse X:
X — i x^ fX 2 1 • • • f
)
(4.8)
where c is the number of classes.
The membership values, with
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66
class number c for a given data element, are represented by a
vector:
G(Xj) = (uA\ r ui2, ... ,ulc)
(4.9)
where j = 1, 2, ..., n, and n is the number of data elements.
Based on the FCV algorithm, the sum of the membership values
over all classes for a given data element is equal to 1, or:
C
]£ uAi(*j) =1 ;
j =1,2, ... ,n
•i=l
(4.10)
However, Gc(xj) does not meet the above constraint.
The sum
of the attributes of vector Gc(xj) is not equal to 1.
To keep
both
G(xj)
and
Gc(xj)
within
the
same
normalization must be conducted for Gc(xj).
constraint,
The normalized
Gc(xi) is defined as:
/
G„C(X.) =
1 -ui^Xj)
iTl
l - u i a(Xj)
'
c^-1
1-uijXj)
'■**#
(4.11)
c^l
Based on vector G(Xj) and Gc(xj), the ambiguity of a partition
with class number c for a data element xj can then be defined
by:
E(x ) 4 m (s(x,)ns„°(^))
1
~ M ( G(x) )Ue°(xJ))
which is called as Normalized Fuzzy Entropy
(4.12)
(NFE).
properties of NFE are:
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The
67
1)
A
partition
imprecise),
is
maximally
ambiguous
(most
if uAi(x.j) = 1/c, i = 1, 2,
any data element j = 1, 2, ...,n.
c for
In this case,
E(Xj) = 1;
2)
A partition is minimally ambiguous if one of its
membership values is equal to 1, or E(Xj) =0.
Validation of the normalized fuzzy entropy definition has
been supported by many numerical
experiments.
A typical
example is shown by the following:
Example:
Assume the class number is c = 3.
For a
partition with class number c = 3 and a data element x1 with
shared equal membership values:
G(x:) = (0.333,0.333,0.333)
G c(x1) = (1-0.333,1-0.333,1-0.333) = (0.667,0.667,0.667)
G(x:)UGnc(x1) = {0.333,0.333,0.333}
G(xx)flG„c(x1) = {0.333,0.333,0.333}
C c(
't ) - ( °-667
\x l)
C ~ 1
G n
0.667 , 0j_667 ) = (0 .333 ,0 .333 ,0 .333 )
Under this partition, the entropy value of this data element
is:
c ,„ x _ 0.333 + 0.333 + 0.333 _ , n
( 1;
0.333 + 0.333 + 0.333
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68
Under the same partition,
a data element x2 with membership
values:
G(x2) = (0.25,0.50,0.25)
G c(x2) =(1-0.25,1-0.50,1-0.25) =(0.75,0.50,0.75)
G(x2)flGc(x2) = (0.25,0.25,0.25}
G(x2)U G c(x2) =(0.375,0.50, 0.375}
,c - 1 2c^-2^1 ) = (0.375,0.25, 0.375)
2^21
c -1
Gn{ x 2) = (
The entropy value of x2 is:
E (x \ - 0-25 + 0.25 + 0.25 _
1 2'
0.375 + 0.50 « 0.375
The above
calculations
show that data element x2 is less
precise than x2 since its entropy value is larger than that of
x2. This is consistent with the conclusion of the membership
function concept.
Since x1 has an equally shared membership
function, it has an entropy value of one. The entropy value
i
of element x2 is smaller than that of element x2 since it has
only shared membership between class 1 and class 3.
Tables III, IV, and V include other typical examples with
different class numbers.
It can be seen that the NFE does not
depend on the number of classes.
In other words,
the NFE
definition is applicable to measure the ambiguity of a
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69
TABLE III
E nt r o p y M ea su rem en t for c = 3
Data
M e m b e r s h i p Value
Sam p l e Point
Class
1
No r m a l i z e d
Class 2
Class 3
Fuzzy Entropy
1
0.0113
0.0803
0.9085
0.0737
2
0.7526
0.2327
0.0147
0.2278
3
0.2355
0.6166
0.1479
0.4036
4
0.5212
0.2394
0.2394
0.6889
5
0.2915
0.4000
0.3085
0.8181
6
0.3333
0.3333
0.3333
1.0000
TABLE IV
entropy
Data
Sample Point
M easurement for c = 4
M e m b e r s h i p Value
No r m a l i z e d
Fuzzy Entropy
Class 1
Class 2
Class 3
Class 4
1
0.0115
0.0640
0.0182
0.9063
0.0666
2
0.7141
0.0152
0.2274
0.0433
0.2354
3
0.0374
0.4608
0.3094
0.1925
0.4703
4
0.3015
0.1771
0.3342
0.1872
0.6934
5
0.1871
0.2715
0.3042
0.2372
0.8165
6
0.2500
0.2500
0.2500
0.2500
1.0000
partition with any number of classes.
3)
Average
Normalized
previously discussed,
Fuzzy
the NFE can be
Entropy
(ANFE):
As
usedto measure
the
fuzziness of a partition for a data element.
fuzziness of a partition
To measure
the
for a data setwith n data elements,
the ANFE can be used, as given by:
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70
TABLE V
En t ro py M ea su rem en t for c = 5
Data
Sample
Point
C lass 1
Class 2
Class 3
Class 4
Class 5
Normalized
Fuzzy
E ntropy
1
0.0199
0.8211
0.1359
0 .0047
0.1259
0.1259
2
0.5403
0 .2816
0.1160
0.0446
0.0174
0.3094
3
0.1134
0.2719
0.4352
0.1451
0.0344
0.4452
4
0.3152
0.1401
0.1384
0.2700
0.1363
0.6240
5
0.2250
0.1000
0.2250
0.2250
0.2250
0.8750
6
0.2000
0.2000
0.2000
0.2000
0.2000
1.0000
M e m b e r s h i p Value
n
E £<*j>
ANFE
(C
) = -i-li----n
(4.13)
where E(xj) is the normalized fuzzy entropy
(NFE)
individual data element Xj with class number c
(1
for an
s c < n) .
A class number that gives the minimum ANFE value is the most
representative class number for the data set.
4) The Most Representative Class Number:
A prespecified
number of classes needs to be given in order to use the FCV
algorithm to cluster a data set.
The conventional approach
used in determining class number for a particular data set is
to repeat the FCV algorithm for different class numbers.
The
one that seems to make "sense" for the data set is selected.
It is arbitrary to use this method to determine the cluster
number of the data set.
Theoretically, the FCV algorithm can be repeated for all
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71
the class number c in order to determine a "global" minimum
ANFE.
However, when the number (n) of elements in the data
set is large, finding a "global" minimum ANFE is a very timeconsuming procedure.
The FCV procedure would have to be
repeated from c = 2 t o c = n - l .
To run the FCV n-2 times is
a very slow process because an SSM/I overpass usually includes
thousands of footprints.
Therefore,
it was necessary to
develop an efficient searching approach that can identify a
"local" minimum ANFE without searching for all the potential
classes.
To
develop
an
efficient
searching
approach
for
determining the most representative class number of the data
set, many experiments were conducted to examine the responses
of ANFE with the class number.
shown in Figs. 4, 5,
6
, and 7.
A few example results are
The relationship between ANFE
and the speed of the convergence of the FCV algorithm was also
examined.
The number of iterations of using FCV is plotted in
the same figures.
It can be seen, from the above figures, that there is a
relatively small number of iterations when ANFE approaches its
"local" minimum value. This implies that the "local" minimum
ANFE not only defines the most representative class number,
but also assures a relatively fast convergence.
Many other experiments were conducted in this research
with the 1987 storm time series data from different areas of
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0.25-
2500
0.240.23-
■2000
TANFE
0.22-
1500
0 . 21Iterations
0. 2-
•1000
“
0.19■500
0.180.17Class Number
Fig. 4.
ANFE and iterations vs. class number
for data set 1 .
.-
250
0 22
0 . 21 -
0.2-
■200
Iterations
•150
U.
0.19■100
“
TANFE
0.18-
•50
0.170.16Class Number
Fig. 5.
ANFE and iterations vs. class number
for data set 2 .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0.225-
450
0.22-
400
0.215-
350
Iterations
•300
0 .2 1 -
(JU 0.205-
•250
J
•200 1
0.195-
ISO
0.19-
100
TANFE
0.185-
•50
0.18
Class Number
Fig.
6
. ANFE and iterations vs. class number
for data set 3.
0.19-
•450
0.18-
-400
0.17-
■350
•300
0.16-
■250 S
2 0.15-
TANFE
Iterations
0.14-
•200 £
■150
0.13-
•100
0 .12-
■50
0.11
Class Number
Fig. 7. ANFE and iterations vs. class
number for data set 4.
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74
the world.
The following observations were obtained regarding
the "local" minimum ANFE point: (1) a "local" minimum ANFE is
followed by two consecutive points with ascending ANFE values
as shown in Figs. 4, 5, and
6
; (2) a "local" minimum ANFE is
followed by two consecutive points with much higher ANFE
values, as shown in Fig. 7.
A "local" minimum ANFE point could be determined when
either of the above two cases occur.
The procedure of the
search approach can be summarized as follows:
Step 1)
Step 2)
Step 4)
Start with c = 2, run FCV to compute ANFE(c):
let min_ANFE (minimum ANFE) = ANFE(c);
opti_class (optimal class number) = c;
pre_ANFE (previous ANFE) = ANFE(c) (pre_ANFE
is used to compare with ANFE value in the next
step);
go_flag (program repeating flag) = 1 ;
c = c + 1 , go to next step =>
Run FCV to computeANFE(c);
If ANFE(c) < min_ANFE:
min_ANFE = ANFE(c); pre_ANFE = ANFE(c);
opti_class = c; go_flag = 1 ;
Else If (ANFE(c)-min_ANFE) > THRESHOLD value
go_flag = 0 ;
Else
pre_ANFE = ANFE(c);
go_flag ++;
c = c + 1 , go to next step =>
If c < n,go_flag s 1
go to step 2 ) .
else
Stop program.
and go_flag <=
6
:
There are a number of advantages when using this fuzzy
clustering algorithm: (1 ) the number of land surface types can
be determined without prior information;
(2 ) each pattern is
characterized by a degree of membership to the given cluster;
(3) a data set is partitioned into a certain number of natural
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75
and homogeneous sets where the elements of each set are as
similar as possible and dissimilar from those of the other
sets;
(4) at minimum ANFE there is a relatively high FCV
convergence speed; and (5) the numbers of repeating FCV are
considerablely reduced.
C.
Clusters Assignment
Once
the data
set
has been
clustered,
the
obtained
clusters need to be interpreted in terms of their physical
and/or environmental meanings.
An assignment approach is
introduced in this section.
1) Look-Up Table:
To understand the physical meanings of
the combinations of the SSM/I brightness temperatures (MPI,
T85H-T37H, T85V-T37V, and T37V), ERDAS software has been used
to produce images for different values of these combinations
for the 1987 and 1988 SSM/I data.
The resulting images were
compared
information
with
the
ground
truth
in
order
to
determine a set of parameters that correctly represents land
surface physical
features.
conducted by trial and error.
developed
based
on
the
Many of these processes were
A look-up table (Table VI) was
obtained
parameters
combinations of SSM/I brightness temperatures.
of
the
four
There are
total 14 categories of land surface types.
As shown in Table VI, the MPI and T85H-T37H define most
of the land surface types except the case of 3, 17, and 18.
As in case 3, MPI values greater than 30.0 indicate a land
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76
TABLE VI
L o o k -u p T a b l e f o r L a n d S u r f a c e D e s c r i p t i o n s
Case
Co m b i nations
MPI T 8 5 H - T 3 7 H
S urface
type
Descriptions
1
< -20.0
8
2
>
7
Water Bod y and/ o r Flooding
0
unce r t a i n
Check T 8 5 V - T 3 7 V
(Second-Level Classification)
20.0
H e a v y Rai n a n d /or Snow
3
>30.0
4
0 .0
-10.0
4
Rai n a n d / o r Sno w ove r Ve g e t a t i o n
5
0 .0
8 .0
1
Dense V e g e t a t i o n
6
0 .0
13 .0
10
7
3.0
-10 .0
4
Rai n a n d / o r S now o ver V e g e t a t i o n
8
3 .0
8.0
2
M e d i u m Dense V e g e t a t i o n
9
3 .0
13 .0
11
M oi s t / C o m p o s i t e Water w ith M e d i u m dense
Vegetation
10
7.0
-10 .0
5
11
7 .0
8 .0
3
Arable Soil
12
7 .0
13 .0
18
M o i s t / C o m p o s i t e Water wit h Arable Soil
13
15 .0
-10.0
14
15 .0
8.0
12
S e m i - A r i d Soil
15
15.0
15.0
9
M oi s t / C o m p o s i t e Water wit h Bare Soil
16
25.0
-10 .0
5
Rain and/ o r Sno w o ver Soil
17
25 .0
8 .0
0a
unce r t a i n
C h e c k T85 V - T3 7V
(Second-Level Classification)
18
25 .0
15 .0
0
u nce r t a i n
C heck T85 V - T3 7V
(Second-Level Classification)
14
D r y S n o w and/ o r Frozen Grou n d
19
if T 37V < 225.0
5 .
M o i s t / C o m p o s i t e Water w i t h Veg e t a t i o n
Rain and/ o r S now o ver Soil
R ain a n d/or Snow ove r Soil
■’ If soil is classified as a desert in the second-level classification,
surface type is 13, otherwise is 9.
surface free of vegetation.
A second-level classification is
needed to further differentiate desert from
water with soil.
moist/composite
In cases 17 and 18, high values of the MPI
(25.0) indicate that land surface includes little vegetation.
Since
there is a relatively high value of T85H-T37H,
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as
77
discussed above,
the land surface could be soil with high
water content or a flat desert.
These characteristics cannot
be identified in the first level of classification. Further
classification is needed based on the brightness temperatures
O f T85V-T37V.
In second-level classification, the combination of T85VT37V has a high negative value for a desert (which increases
as water content increases.)
For a "perfect" desert,
the
value of T85V-T37V is approximately -4.0, while the value for
"perfect" moist/composite water with soil is approximately 5.0
(or greater).
In mid-March of 1988, there was an increase in the noise
level of the 85.5 GHz vertical polarization channel on F8 .
This channel continued to deteriorate until the data were
rendered useless by the middle of 1988.
second-level
Due to this fact,
classification for data recorded during this
period was not used, and misclassification would occur between
a desert surface and a surface of moist/composite water with
soil.
desert
However, it was assumed that these data fell into the
category.
moisture detection.
horizontal
Thus,
results
are
less
sensitive
to
Later, similar problems with the 85.5 GHz
polarization
channel
occurred.
Because
of
disability of 85.5 GHz channels, land surface classification
is very difficult to conduct correctly.
The F10 and Fll
satellites, launched later, had SSM/I instruments to replace
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78
the F8 instrument because of its faulty 85.5 GHz channels.
2) Assignment of Cluster Center Types:
represents the prototype of the class.
A cluster center
It is necessary to
first determine the types of class centers.
This can be done
by computing the Euclidian distances between each class center
and the entries of the look-up table.
The shortest distance
will determine the surface type of the class center.
3) Assignment of Data Pixel Types:
pixels
can
be
determined
based
on
The types of data
information
from
the
normalized fuzzy entropy and membership values, the types of
class centers, and the look-up table.
By examining the 1987 and 1988 storm data set, it was
discovered that if the NFE of a data element Xj. is less than
0.3,
it belongs to a class with differentiated membership
values.
Assuming data element xt has the maximum membership
value nitl Xi belongs to class j with the largest degree.
The
surface type of x* will be determined by the type of center of
class j .
If data element xA has shared membership values between
classes,
its NFE will be greater than 0.3.
Assuming the
largest membership value for x± is fiik, and the second largest
membership
value
for
Xi
is
/uil(
if
x± falls
within
a
rectangular range with diagonal between the centers of cluster
k and
1
, x± will belong to class k with the largest membership
being fiik. The surface type of data pixel xA was determined by
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79
the
center
type
of
class
k.
If
x*
falls
beyond
the
rectangular range, the Euclidian distances between
and the
entries of
and the
the look-up table have
to be computed,
shortest one determines the type of the data pixel.
D. Simulation and Results
SSM/I
data
methodology.
were
used
to
verify
the
classification
Each data file included many footprints,
and
each footprint had seven brightness temperature measurements
(located by latitude and longitude.)The selected data files
recorded in 1987 include four areas:
the U. S. Western Desert
(WD) area and the Central Plains (CP) area, South America (SA)
area, and Africa (AF) area.
Time series were selected from
each test area to test the model consistency.
The most "plausible" number of clusters (c), centers of
clusters, and"class center types for two of the four selected
areas
(U.S. Western Desert and Central Plains areas)
determined and are shown in Tables VII and VIII.
the
footprints
were
classification,
classified
in
the
were
Since all
first-level
there were no results for the second-level
classification.
In files for South America and Africa, the second level
classification
was
applied
to
differentiate
moist/composite water with soil footprints.
desert
from
Tables IX, X, and
XI show the results.
The
results
show
the
fuzzy
classification
technique
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80
provides consistent land surface types.
In most cases, the
same center types occur during consecutive days.
Since the
data files may be recorded for different areas on different
days, atmospheric effects may lead to generating new clusters
such as "rain over soil" or "rain over vegetation."
TABLE VII
C enter
T ypes
U.S.
of
W estern D esert A rea
Classification
Cluster
C e nters
F i r s t -Level
File
W D 2 2 2 D .D I N a
1
Type
with
3.33
-0.15 b
WD223A.DIN
13.18
2
2
Type
8.45
3
Type
13.48
WD2 2 4 A . D I N
8.00
12.68
7.76
12
1.59
3.39
12
0.91
3
5.82
2.12
3
2
6.11
8.39
2.76
12
3
' Data file name, the number followed by "WD" indicates Julian day in a
year. "D" and "A" represent descending and ascending overpasses.
D The data used to run FCV in the first-level classification are twodimensional data: the first dimension is MPI, and the second is T85HT37H.
TABLE VIII
C enter
T ypes
U.S.
of
C entral Plains A r e a
Classification
with
F i r s t -Level
File
Cluster
C e n t ers
C P 2 5 2 D .DIN
1
Type
5 .89
2
Type
5 .10
3
Type
5.46
4
Type
10 .98
-11.38
C P 2 5 3A.DIN
0.33
4
1 .74
4 .80
11 .62
3 .46
11 .24
11 .01
6 .68
5 .81
5 .74
3
5 .96
3
12
7 .19
11.31
12
2
3
-9.01
4.62
4
3
12
-9.66
4 .39
5
CP2 5 4 A .DIN
4 .35
2 .56
2
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81
TABLE IX
C e n t e r T yp e s o f So u t h A m e r i c a A r e a
File
First
Level
Clu s t e r
C enters
SA056D.DIN
S A 0 5 7 D .DIN
S A 0 5 8 D .DIN
SA059A.DIN
1
Type
14.39 2.89
12
13.07 4.57
12
2.36
-8.49
4
2.04
2
Type
2.96
2.42 -8.91
4
1.96
2.93
1.59
3
Type
2.14
-6.42
4
3.89
11.43 5.76
12
4
Type
1
4.82
6.77
2
11.58
12.73
9
5
Type
Second
Level
3.08
2
2.23 3.54
2
2
-6.67
4
13.77 3.97
12
1
Type
-3.58 J
13
2
Type
1.94
9
-2.87
13
-2.59
13
0 .06
13
3.25
9
5 .70
9
2 .97
9
The data used to run FCV
dimensional data (T85V-T37V.)
in second-level
classification
are
one­
TABLE X
C e n t e r T yp es o f A f r i c a A r e a for T ime S er ie s O ne
File
Cluster
Centers
First
Level
Second
Level
AF056A.DIN
1
Type
21.03
2
Type
12.64
3
Type
1.64
8.04
AF057A.DIN
21.47
0
7.95
A F 0 5 9 A .DIN
21.56
0
0.46
12.44
12
1.02
11.48
1.69
2.16
12
12
4.55
7.95
0
4.93
1.82
5.07
2
2
2
1
Type
-7 .70
13
-8.11
13
-8 .58
13
2
Type
-0 .65
13
-1.09
13
-2 .17
13
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
82
TABLE XI
C e n t e r t y p e s of A f r i c a A r e a for T ime S eries T wo
File
Cluster
Centers
First
Level
AF232D.DIN
1
Type
21.64
2
Type
11.98
3
Type
2.07
19.30
0
AF233D.DIN
9.29
18.94
12
7.25
3.95
3.25
-8.39
2
4
-9.23
2.52
3.61
4
2.18
9.09
12
2.24
12
4
Type
Second
Level
9.21
AF233A.DIN
2
3.62
2
1
Type
-7 .32
13
-7.38
13
-7 .75
13
2
Type
-1 .22
13
-0 .83
13
-1 .54
13
Since it is impossible to numerically show all of the
results for all the data points, ERDAS software has been used
to produce the images of the results shown in Figs.
1 1
, and
1 2
8
, 9, 10,
.
Ground truth information has been used to verify the
simulated results.
The sources of ground truth information
used in this research include: (1 ) the natural resource atlas
for
the
world;
(2)
the Major Land Resource Area
(MLRA)
classification of the Soil Conservation Service [43], which
list regions that combine similar characteristics with respect
to topography, natural vegetation, land use, climate, soil,
and water resources; and (3) the climatic data (which included
daily precipitation amount,
snow,
maximum
collected
temperature)
were
minimum temperature and
through
the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
NOAA
cooperative network of stations.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
84
XsctMi.iini; Overpass, I'OV. 22 t.
vt'gV’ t'4 'U n i . . ;
yS Mi^ili.vun lio n s a Vf'LH' i at ion
’ i | A r «">-■>11>. S oil :.
R uin iiV or
aLioiv ■■■"''.’ ■ ■
, _ ...Rain' o v o r'S o il.
/' ■ ■ ■ .
, tVai.iM\lin<iy .'uni / o r F K u u liii^
.
H ru v v R a in t iy r r IiU u ilj.
.M iii.s t,/C o jn p in iilv l);\iy r->oil :
vlloist/’l/Oi'uposiii* faojisiv.Vog.
;£§il '.lo is l /.C o m p o si tv M o tlh n n Vo
7- •®.St?in(u A rid S oil . ■■
...
:; . ' •
V'/S--'
.-.H Moist /(Vinposito ••Aral>U> Soil
Fig.
8 .
Land surface classification
for U.S. Western Desert area.
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission
85
Iim d S u rfa ce C lassificatio n fo r U.S. C e n tra l Plains Area
lie s c o n d in g
O v e r p a R s , ij.OY-
•'
Ascending Overpass, IJOY 25rt
H
■
tU R H B
IH H H H
-^JHH^HH H
HL
tF
B
B
B
B
H
B
B
.
■
SHBjB n
B B I HflB
H H m m
B H B j
SHEH H
m bmB H
■H
H H
H H
h
Fig. 9. Land surface classification
for U.S. Central Plains area.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission
86
Lanxi S u rfa c e C la .s s itic a tio u t a r S o u th A m e r ic a Area
Pesceudiiig
0vt*rim3s, DOV. 00'
-t^u-
■’I'oai*.-■endingDOV; 57- '’•
Ovtvrpuiw,
y&Wg'i'
■■■■MSS-r
:
'■•
■
/■■ IX-iiSi’fVogol at ion
" ^ -\1 r ‘ I i 1 1 n v ; n « f . V t ’ f M . i i f i i i j i
• ■HAr/iljlt'*. Sn.il.
■
ISani-.oviH-'
• V
V«*«5»»bit.i<viV'
;; p.riiri -nTr.r -Srti
•:
Walo.r. |!o(ly anrf--W".-1' Ii?o«iipjj
v • ■
•.
Mlt-aiH' .lliiin
' V' ;■
<? T ia ra .S a il. ■
Mfist/rrinijiii.-ito
. .
•'
\'f«.
V^g;'
■'•^ISnini- Ai'i.l -Soil •
'
■’
lVi'ort ../. "
'j ;l|Mo.itft/C«i'i.hutfiut.«‘ )\rabl»* .Siiii
Fig. 10. Land surface classification
for South America area.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission
87
Land .S u rfa c e C la s s ific a tio n fo r A fric a A rea (T im e .Series One)
Ascending OvcrpiiVs; DuV 07.
A s c e n d in g O v e rp a s s , Du,Y or) '
-V
.'
Tja-.-
Ascending Overpass, DuV 50
' '«m.
:
. litM itie ,V e g e ta tio n
■
"
iiMediurii.iHiiise..Vegetation; BArablc Soil
. (ta in o v e r V
egetatjiin ;.
■ -.
o v e r Soil.-. .
: W ilie r H n r |\\|in r l f o r ['’l.n.ocling .
•Ilr:r.y Humv ■
■ '' V-.;
.B a r e S o il'
..Ato.i.si /C o m p c iM I<• Urns'' Vcg.. •
■\ j | | M o is t /C 'i)tii|i()k itC M im Ih h ii Yeg.'
. ^ S e i i r i - A r i i l H oil
Poserl. :
^ M o i s l / C o M i p o s i l c A r a b ic S o li "
Fig. 11. Land surface classification
for Africa area (time series one).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
88
Land S urface C la ss ifica tio n fo r 'A fr ic a Area (T im e Series Two)
... . D e s c e n d in g O v e rp a s s , DOY
• D e s c e n d in g O v o rp a s s , D O Y
Ascen.diug uverjiiiss, fl.OY; 2 3 3
232-
233
i>enr.e Yegetnlipn "■ ■■■■ .' :
: ^Yipdiuui'..DenSe..Vt'ge.tat'iorr. v
BArable Soil •. ■
•' Rain nyer .Yegetcvtion .■
liain o'. er Soil v ■-I
"' Water. Body" and /orFlooding ••/'
Heavy Rain .
■
. •Moisil/Coitij) oai t'e Bare .Soil...
M o is.(Aon ip oyi tv./De l'ise Veg .•.
■
B -M o ja l/C u tu p o a i Ire- -M id i win Teg .
B'Se.mi :Add'- Soil . .
Desorl
■.■.
l| Moist/Composite Arable Soil ..
Fig. 12. Land surface classification
for Africa area (time series two).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
89
CHAPTER V
PARAMETER DATABASE
This chapter discusses the development
database,
which
framework.
water
is an
important
part
of
of a parameter
the
integrated
Information contained in the database includes
bodies,
vegetation
cover
conditions,
and
soil
conditions.
The presence of water bodies,
lakes,
and
reservoirs,
temperatures.
model,
such as large rivers,
contaminates
To properly
develop
SSM/I
brightness
an empirically-based
or apply the physically-based model,
water bodies
should be excluded or accounted for prior to using the SSM/I
data.
However, as discussed in Chapter II, data used for the
development of the existing empirical model
[1 ] included a
significant number of water bodies.
The use of the physically-based model requires the area
percentages of water bodies,
covers,
as
well
as
vegetation covers,
information
on
properties
and soil
of
the
vegetation canopy and soils within the study area.
Fig. 13 illustrates the overall process in developing
the parameter database, including the layer of water body,
soil, and vegetation.
A. Water Bodies
Because of the very coarse spatial resolution of the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
90
Soil Type
Maps
MLRA
Handbook
AVHRR
Regression Analysis
LAI vs.
Water-body Layer
•
Locations
Estimation
NDVI
Vegetation Height h
Vegetation Layer
Soil Layer
Vegetation Height h
Soil
Volume
Dielectric Constan
F r a c t i o n Vi
Porosity
Multi-Layer Parameter Database
Fig. 13.
Struture of the parameter database,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
91
SSM/I data, variations of surface features within an SSM/I
footprint can not be characterized.
Chapter II,
However, as discussed in
the AVHRR can resolve more of these surface
features (such as standing water) than the SSM/I, due to its
higher spectral and spatial resolution.
Water bodies were separated from daily AVHRR scenes by
using channel 2 (near IR) of its five channels.
Since remote
sensing at AVHRR frequencies is severely restricted by cloud
cover,
cloud-free scenes were selected by visual quality
assessment of approximate 50 AVHRR images [5].
These cloud-
free AVHRR images were then used to determine the threshold
value between land and water
(based on prior geographic
information of land surface covers, ) and a binary water-body
mask (where water had a value of
in the CD ROM) was computed.
1
and land had a value of
0
,
Based on the water-body mask,
the position of water bodies can be extracted.
Since the
AVHRR data are registered in Lambert Azimuthal Equal Area
projection coordinates,
a computer program was written to
convert these data into latitude and longitude coordinates
(compatible
with
the
SSM/I
data.)
The
information
Azimuthal Equal Area projection is shown Appendix A.
position
of
the
water
bodies
obtained
provided
of
The
aerial
percentage information within an SSM/I footprint, to be used
in
the
development
of
empirically-based
model
and
application of the physically-based model.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the
92
B. Soils
The physically-based model requires information on the
dielectric constant of land surface constituents.
The soil
dielectric constant can be computed by [3]:
£_ = (1.01 + 0. 44 q )2 - 0.062
(5.1)
where p g is the density of solid particles (g cm'3), which
can be further calculated by [48]:
Particle Density -
? ulk D ^ a i t y
1 - Pore Space
2)
Particle density and bulk density are two common density
measurements of soils.
Particle density is the density of
only the solid soil particles;
include water and air space.
the measurement does not
Bulk density is the density of
a volume of soil as it exists naturally,
space.
space
Pore space, usually measured by porosity,
in
a
particles.
and
including pore
soil
volume
that
is not
occupied by
is the
solid
Typically, the pore space is occupied by water
air,
which
be
determine
used
to
the
limit
water-holding
the
capacity.
Porosity
will
retrieved moisture
content.
Table XII gives representative bulk densities and
percentages of pore space of typical texture soil classes.
Table
XIII
gives
the
calculated
representative
particle
densities and dielectric constants of the soils, as given in
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
93
Table XII.
In the latest U.S. soil classification (soil taxonomy)
system [48], officially adopted in 1965, soils are fitted
into 10 orders.
The 10 soil orders include four which exist
in a wide variety of climates:
Histosols (organic soil), the
undeveloped Entisols , the slightly developed Inceptisols, and
swelling
clayey
Mollisols,
Vertisols .
Alfisols,
The
Ultisols,
other
Aridisols,
six
orders
are
Spodosols,
and
TABLE XII
Soil Characteristics
Soil
Ident i f i c a t i o n
Bulk Density
[48]
(g cm'5)
Pore Space
Loam
1.65
38
C l a y Loam
1.50
43
Silt Loa m
1.47
45
S a n d y Loam
1.15
57
Loamy Sandy
1.50
43
Clay
0 .66
75
Peat
0.66
about 65
(%)
TABLE XIII
So i l p a r t i c l e D e n s i t y a n d D i e l e c t r i c C o n s t a n t
Soil Classes
Particle Density
(g c m ’5)
Die l e c t r i c Constant
Loam
2.66
4 .69
C la y Loam
2.63
4 .64
Silt Loa m
2 .67
4.71
S a n d y Loa m
2 .67
4.71
L o a m y Sandy
2 .63
4 .64
Clay
2 .64
4 .65
Peat
1.89
about 3.32
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Oxisols.
The
10
soil
orders
were
shown
generalized soil map of the United States
study, the
10
in
a
[43] .
colored
In this
soil orders were characterized approximately by
the soil classes described above, and are shown in Table XIV.
TABLE XIV
So i l O r d e r s a n d So i l C l a s s e s
Soil Orders
Soil Classes
Alfisols
Sandy Loam
Aridisols,
Entisols,
Mollisols
Spodosols,
Loam
Ultisols
Loamy Sand
Histosols
Decomposed Peat
Inceptisols
Silt Loam
Oxisols
Clay Loam
Vertisols
Clay
A Major Land Resource Area (MLRA) [43] is geographically
associated
in land resource units
(designated by Arabic
numbers and identified by descriptive geographic name.)
For
example, MLRA 1 (Northern Pacific Coast Range, Foothills, and
Valleys) is on the west coast; MLRA 157 is on the east coast;
and MLRA 175 is in Alaska.
The MLRA has been gridded into
quarter-degree cells, which are about the size of a 3-dB
SSM/I footprint.
Each MLRA code number is referenced by
latitude and longitude coordinates.
By comparing the MLRA
map with the colored soil map, the soil classes for each MLRA
unit were determined based on Table XIV.
Porosities and
dielectric constants were then determined based on Tables XII
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
95
and XIII.
Due to small penetration characteristics at SSM/I
frequencies, moisture information about the eastern area of
the United States is unable to be retrieved because of the
heavily vegetated surfaces.
Soil porosities and dielectric
constants included in the parameter database in this research
are only for the U.S.
Central Plains and Western Desert
areas.
C. Vegetation
The
physically-based
model
requires
vegetation
parameters such as volume fraction of vegetation, height of
vegetation, permittivity of vegetation bulk material (Bb'),
the loss factor of vegetation bulk
content (Vwl) .
(sb'')( and leaf water
However, the model is not very sensitive to
the last three parameters listed above
[3] , and were set
equal to 3, 0.05, and 0.65 in this study.
Since an SSM/I footprint covers a large area, the height
of the vegetation canopy can vary greatly within a footprint.
The average height of vegetation for a footprint can be
roughly estimated based on the vegetation type descriptions
of the MLRA units from the MLRA book [43].
The volume fraction can be determined from the following
relationship:
h*V,
----LAI = -- —
leaf thickness
(5
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3
)
96
where LAI is leaf area index, and leaf thickness is set to
0.002.
Based on the estimated vegetation height, if LAI is
known,
the value of Vx can be calculated from the above
equation.
Previous studies have shown relationships between leaf
area index and AVHRR Normalized Difference Vegetation Index
(NDVI)
for
certain
vegetation
conditions
and
different
satellite instruments [30]- [32] . A new relationship between
LAI defined in the SSM/I resolution scale and AVHRR NDVI was
developed in this study.
Becker
and
Choudhury
[30]
proposed
a
relationship
between the Microwave Polarization Difference Index (MPDI)
and the AVHRR NDVI.
brightness
MPDI is the normalized difference of
temperatures
in
horizontal
and
vertical
polarization measured at 37 GHz by the Scanning Multichannel
Microwave
Radiometer
(SMMR)
onboard
Nimbus
7
and
is
represented by:
_ 20 . (T37V-T37H)
(T37V +T37H)
The relationship between MPDI
(SMMR)
(5 .4 )
and NDVI
(AVHRR)
is
shown in Fig. 14.
Since SSM/I also measures brightness temperatures at 37
GHz, the relationship between SSM/I brightness temperatures
and AVHRR NDVI
can be
determined
from the
relationship
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
97
LEGEND
1-SAHARA
2-SENEGAL
3-MAURITANIA
4-UPPER VOLTA
5-U.S. SO. GT. PLAINS (W)
6-U .S. SO. GT. PLAINS (E)
(APR. 1982 TO JAN. 19851
IE
2 0.8
co
UJ
o
2
UJ
CC
UJ
U.
t
Q
Z
0.6
o
H
<
N
IT
<
146
0.4
O
CL
Q
UJ
N
_1
<
66
cr 0.2
O
2
0.0
0.0
0.1
0.2
0.3
0 .4
N O R M A L I Z E D DIFFERENCE (AVHRR)
Fig. 14.
MPDI (SMMR) vs. NDVI (AVHRR) from Becker and
Choudury [30].
between MPDI and NDVI.
The physically-based model
(LSRTM)
[3] was used to determine brightness temperatures at 37 GHz
for a given LAI and a certain soil condition.
The MPDI value
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
98
was then calculated.
By changing the input parameters to the LSRTM (fixing
the LAI value equal to zero) it was possible to match the
MPDI value with the "Sahara" desert data of 0.92 (shown in
Fig. 14).
After matching the MPDI value to 0.92 (under a
desert condition,) the input parameters became fixed values.
The LAI values in the model were changed to simulate other
vegetation densities
(resulting in new MPDI values.)
The
NDVI values corresponding to the new MPDI values were then
obtained, based on Fig. 14, resulting in a link between the
LAI values and NDVI values (shown in Fig. 15).
LAI vs. NDVI
1.6 -
1.412
LAI=1.716 Log(NDVI) +2.334
-
3 0.80.60.4-
020.05
Fig. 15.
0.1
0.15
NDVI
0.2
0.3
LAI (SSM/I) VS. NDVI (AVHRR).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
99
The equation relating LAI and NDVI was determined by
using regression analysis (where R2 = 0.99) given by:
LAI = 1.7161og(NDVI)+2.334
(5.5)
Based on the LAI value it was possible to compute the leaf
volume fraction (V^ by using equation (5.3).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
100
CHAPTER VI
EMPIRICALLY-BASED MODEL
This chapter will describe the improvements made by this
study to an empirically-based model, and how the model is
used to retrieve
surface moisture.
Statistical analysis was
in developing the model using 1988 sub-MLRA region files
(including large storms).
The model was then applied to
other storm data for the purpose of moisture retrieval.
Images of the simulated results were generated by ERDAS
software to verify the performance of the model.
A. Microwave Signature Responses
to Surface Moisture
In order to determine the relationships between API,
SSM/I brightness temperatures, and precipitation, it is very
useful
to
plot
variations
of
locations and vegetation cover.
the
data
under
different
From these plots, one could
see how variables respond to each others.
Figs. 16, 17, and 18 illustrate typical time series of
API2, precipitation, and running average MPI for 1988 SSM/I
data, which correspond to the quarter-degree box
(latitude
44.75°, and longitude 97.50°, ) and the normalized temperatures
of T19H/T37V and T85H.
The
selected area
vegetation located in South Dakota.
API2
other
than
API1(
API3, and
is of grass
One reason in choosing
API4
is
that
API2
was
calculated by restricting the maximum depth of the soil water
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
101
available for evaporation to
mm (close to the moisture
10
sensing depth of the SSM/I). Another reason is because API.,
has
better
correlation
with
the
SSM/I
brightness
temperatures, which will be shown later in this chapter.
MPI
decreases
as
evidenced in Fig. 18).
the
first
of
vegetation
density
increases
(as
The value of the MPI is high during
spring,
and decreases
increasing again in late fall.
until
early
fall,
The reason for this is the
low vegetation during the beginning of the spring season,
which increases until the summer, decreasing in late fall.
Fig. 18 shows that MPI has the lowest -values for days 180
through
(during that period of time vegetation was the
220
most dense).
Both
normalized
temperatures
of T19H/T37V
and T85H
decrease as surface moisture increases (shown in Fig. 16 and
17).
2 2 0
in
Since precipitation events occurred around days
140,
, and 260, surface moisture largely increased (resulting
abrupt
decreases
in
the
brightness
temperatures
of
T19H/T37V and T85H).
The change in the T19H/T37V value is larger on day 12 0
than on day 140, although there was larger precipitation on
day 140, because vegetation was denser on day 140.
The T85H
channel had a small penetration through the vegetation (shown
in Fig. 18).
220
The response of the T85H to a storm around day
is much smaller than its response to a similar storm
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Response o f T 19H /T 37V to Moisture
350
0.99-
300
0.980.97-
250
0.96-
•200 e
0.95C 0.94-
•150 a
0.93-
100 <
0.92-
■50
0.910.9-
Day of the Year
T19W37VAPI2
“
Rain
Fig. 16.
Normalized brightness temperature
T19H/T37V response to surface moisture at
44.75 lat., 97.50 long.
Response o f T85H to Moisture
350
290'
285
•300
280
250
275
270
^ . ' 200i
265-
'15 0 |
260'
-100
255'
^
250
■50
245240
Day of the Year
T85H
Fig. 17.
API2
*
Rain
T85H response to surface moisture at
44.75 lat., 97.50 long.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
103
Variations o f Running Average M PI
00
v 10-
100
120
140
160
180
200
220
Day of the Year
Fig. 18. Seasonal variations of running
average MPI at 44.75 lat., 97.50 long.
around day 140, due to the higher vegetation density on day
220 (Fig. 18).
A well vegetated footprint with latitude/longitude of
41.25°/ 94.75° was also selected.
The time series for this
area is shown in Figs. 19, 20 and 21.
Fig. 21 shows that
this area reached a higher vegetation density than the area
previous discussed.
Responses of both T19H/T37V and T85H to
surface moisture are much less than those for the previous
area (44 .75°/97 .5°) . Although there was a large storm around
day 2 60,
there was no decrease in either the T19H/T37V or
the T85H due to the very high vegetation density at the time.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0.990.980.97£ 0.96S 0.95= 0.94-
Response o f T19H /T37V to Moisture
1
160
140
V”
S•
120
100
II
A
§,
JU
rr
-80
60 “
%
40
M
....... -
100 120 140 160 180 200 220 240 260 280 300
Day ofthe Year
•T19H/T37V • ■API2
*
Rain
Fig. 19.
Normalized brightness temperature
T19H/T37V response to surface moisture
at 41.25 lat., 94.75 long.
Response of T85H to Moisture
285
160
140
280
120
275-
100
290
| 270
cc
265-
S’
260
20
255250
Day ofthe Year
■T85H '
Fig. 20.
■API2
“
Rain
T85H response to surface moisture at
41.25 lat., 94.75 long.
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
105
Variations o f Running Average MPI
CO
100
120
140
160
Day ofthe Year
Fig. 21. Seasonal variations of running
average MPI at 41.25 lat., 94.75 long.
This is consistent with the findings by McFarland et al. [71
which state that surface moisture retrievals for MPI values
less than 4 k are physically impossible due to lack of
sensitivity to surface moisture.
B. MLRA Region Files
MLRA region files selected for this study cover the same
area as the files used by Gerard [1] (the U.S. Central Plains
areas).
The information of MLRA subregions includes large
storms for 1988 data shown in Table XV.
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106
TABLE XV
MLRA
Subregions D escriptions
MLRA Areas
54,
55B,
Descriptions
Northern Great Plain Spring Wheat Region:
Vegetation is relative low in spring, high in
summer, low again in fall.
56
70, 71, 73, 77,
78, 80A, 8 OB
102A,
102B,
106
Central Feed Grains and Livestock Region:
Vegetation is relative low in spring, high in
summer, low again in fall.
Edwards Plateau in Texas:
A wide range of vegetation density occurs for all
seasons.
81
42
65,
Central Great Plains Winter Wheat and Range Region:
Vegetation is relative low in spring, high in
summer, low again in fall.
Desert Basins, Plains:
Vegetation density is low.
67,
69,
118,
119
70
Western Great Plains and Irrigated Region:
Vegetation is relative low in spring, high in
summer, low again in fall.
East and Central Farming and Forest Region:
Vegetation density is high (70 % is f o r e st ).
The large storms occurred during DOY (day of year) 93
through 154 (spring season), 180 through 227 (summer season),
and 254 through 294 (fall season). The model by Gerard [1]
includes
three
regression
equations,
each
corresponds to a certain vegetation density.
of
which
As discussed
above, vegetation density has a major effect on the response
of surface moisture.
It is necessary to include vegetation
density as a variable in the model to improve retrievals,
which
will
avoid
discontinuities
in
the
model
output.
Combined files, which included different vegetation classes
and MLRA
regions,
were
used
in developing
the
improved
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107
empirical model in this study.
C. Regression Analysis
1)
Selection of API Ground Truth Dependent Variable:
There are four API data files, including API1( API2,
API3,
and API4, each of which corresponds to a soil water depth
available for evaporation of 7.5 mm, 10 mm, 15 mm, and 20 mm,
respectively.
Correlation analyses were conducted using the
SAS package on the VAX computer to evaluate the correlation
between
each
temperatures.
API
data
file
and
the
SSM/I
brightness
The resulting correlation coefficients are
presented in Table XVI.
The API data files used for this
analysis include data recorded with different "days since
last rain fall (dslrf)" values (the effect of the dslrf will
be
discussed
in
the
following
section).
Brightness
temperatures of T19H and T37V are not included in Table XVI
since they are highly correlated with T19H/T37V, which is a
good moisture indicator as discussed by Gerard [1].
Table
XVI shows that both API3 and API2 have higher correlation with
the most SSM/I variables (there are not many differences),
except T19H/T37V.
Also, SSM/I sensing depth is restricted to
the top soil layer, which is close to the depth of available
water
evaporation
used
equations 2.8 and 2.9).
to
calculate
API3
and
API,
(in
The stepwise procedure, in the SAS
software, was used further to choose either API3 or API2 for
selected SSM/I variables.
This will be shown in a later
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
108
TABLE XVI
Correlation
Coefficients
API
for
Selection
SSM/I Variables
API,
API,
API,
API,
MMPI1’
-0 .1791
-0.1755
-0.1656
-0.1558
T19V
-0 .4498
-0.4426
-0 .4328
-0.4255
T22V
-0.4068
-0 .3980
-0.3866
-0 .3786
T37H
-0 .3756
-0.3758
-0.3760
-0.3753
T85V
-0 .2541
-0.2425
-0.2258
-0.2139
T85H
-0.2591
-0.2473
-0.2304
-0 .2166
T19H/T37V
-0.3677
-0.3808
-0 .3954
-0.4022
1 MMPI is the running average of the microwave polarization index.
section.
API2 was finally selected as the dependent variable
' in the model.
2) Selection of SSM/I Independent Variables:
regression
analysis
was
used
to
develop
a
Multiple
relationship
between API2 (or APIX) and other significant SSM/I variables.
As discussed in Chapter II,
a nonlinear trend was observed
in the 1987 data by Neale et al. [2] and in the 1988 data by
Gerard [1].
In this study, a logarithmic transformation was
conducted on T19H/T37V to match the nonlinear trend.
For the
continuity of modelling the effects of vegetation density,
the running average of MPI was included as an independent
variable.
Stepwise regression technique was used to select
the optimal
combination of
independent variables
in the
multiple regression analysis.
The R-square statistic, C(p),
and
criteria
RMS
were
used
as
the
for
selecting
combination of variables.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the
109
3)
Outliers
and
Influential
Observation
Detection:
Improperly recorded data may be found, even though the sample
data
were
selected
very
carefully.
The data
misleading when using the regression analysis
prediction.
may
be
and model
The Cook's D distance measurement [44] was used
to test
the
influence of an observation and detect
possible
outliers.
outliers:
(1)
Snow
There
are
cover had
reasons
a
the
for the detected
significant
effect
on
moisture retrieval. Since snow microwave emissions are very
complicated,
and the SSM/I footprint sizes are very large
(and may be partially snow covered,) the
classification
scheme is sometimes unable to make the correct decision
regarding wet snow cases.
It was estimated that 53 percent
of the outliers resulted from this reason;
(2 ) many outliers
occurred when the flag indicated that a large precipitation
occurred on that day.
This can be explained by the fact that
the large precipitation event may have occurred after the
SSM/I overpass, or there might have been a light rain event
far before the SSM/I overpass and soil surface dried out
during the day, before the SSM/I overpass.
4)
The Effects of dslrf:
The "days since last rain
fall" (dslrf) flag is a very important factor affecting the
hydrologic response of a soil surface to precipitation.
This
parameter takes into account the time period, in days, since
the last precipitation event.
For example, dslrf = 1 means
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
110
that there was a rain event occurring on the same day as the
SSM/I overpass.
For different dslrf,
the depth of water
remaining on the top soil will be significantly different.
Several days after a rainfall, water has infiltrated into
deeper layers and the surface has dried due to evaporation.
As dslrf increases, the sensitivity of the SSM/I to surface
moisture will decrease since the SSM/I sensing depth is only
10 mm.
Therefore, the parameter dslrf was used as a filter
to delete data records with dslrf greater than one for the
model development.
5)
Regression Model for Surface Moisture Prediction:
The SSM/I regression data set was prepared with consideration
of the dslrf effect.
The stepwise regression technique
provided by SAS software was used to generate the model.
A
set of regression models for APIX and API2, with different
combinations of independent variables, was evaluated.
The
resulting models and corresponding statistics for APIX and
API2 are shown in Tables XVII and XVIII.
When adding the MMPI
and T85H variables, the R-square increased and C(p) and RMS
(root-mean-square) error decreased dramatically.
However,
there was not much improvement by adding further variables.
API, was selected as a dependent variable in the final
model, since API2 has a larger R-square value and a smaller
C(p) value than APIX does.
The best combination of SSM/I
variables for the model consists of the running average of
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I l l
TABLE XVII
M u ltiple L inear Cor re lat io n between A P ^
and
SSM/I
Variables
N o . of
.ariables in
Model
SSM/I variables
in Subset
R‘
C(p)
RMS
1
LoglO(T19H/T37V)
0.5534
177 .18
24.96
2
MMPI,
LoglO(T19H/T37V)
0.7152
61 .00
18 .20
3
MMPI, T85H
LoglO(T19H/T37V)
0.7993
1.61
16 .84
4
MMPI, T22V, T85H
LoglO(T19H/T3 7V)
0.7998
1.45
16 .21
TABLE XVIII
API2
M ultiple L inear Correlation between
and
SSM/I VARIABLES
N o . of
Variables in
Model
SSM/I variables
in Subset
R‘
C(p)
RMS
1
LoglO(T19H/T37V)
0 .5858
176.06
21 .51
2
MMPI,
LoglO(T19H/T37V)
0.7355
60.57
22 .57
3
MMPI, T85H
LoglO(T19H/T37V)
0.8143
0.76
18 .98
4
MMPI, T22V, T85H
LoglO(T19H/T37V)
0.8151
0.74
17 .93
MPI, T85H and log10 (T19H/T37V) , as given by Equation (6.1).
API2 = -3429.20631og10(-||||) -13 .4027 (MMPI)
-2.0409(T85H) +639.0594
(6.1)
where API2 is the retrieved surface moisture in mm and MMPI
is the moving average microwave polarization difference prior
to a storm event.
The predicted API2 values and actual API2
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112
data points were compared and are shown in Fig. 22 for the
1988 independent data.
This
new equation
is capable of
moisture values up to 250 mm.
retrieving surface
The original linear algorithm
[1] was limited to 70 mm of surface moisture.
Surface Moisture Prediction
200
CL
180160140
120'
a 100-
806040-
■©
Ground Truth API2
Fig. 22.
Predicted API2 vs. actual API2 values.
D. Model Applications
The empirically-based model was incorporated into the
proposed framework to retrieve surface moisture over the
Central Plains and Western Desert areas of the United States.
In most of these areas, vegetation density is not too high
for SSM/I surface moisture retrievals.
In the eastern area
of the United States, vegetation is too dense to retrieve
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
113
surface moisture by using the SSM/I instrument.
The overall procedures in application of the model are
listed as follows:
1.
The
SSM/I
seven
brightness
temperatures
were
classified.
2.
The resulting classified data were merged with the
generated
API
files
from
the
ground
weather
station network.
3.
The merged files were gridded into quarter-degree
cells as inputs to the dynamic database.
4.
The empirically-based model was used to retrieve
moisture when the dynamic database indicated that
(1 )
the
vegetation
was
not
too
dense,
(2 )
brightness temperatures were not scattered by rain
or
snow,
and
(3)
there
was
moisture
detected
within the study area.
To compare
the predicted moisture
results with the
ground truth data, images were produced by using the Earth
Resources Data Analysis System (ERDAS) Software.
1) 1987 Summer Storm Analysis:
A time sequence of the
SSM/I data with a storm from day 223 through 229 was selected
from the 1987 data recorded from the F8 satellite
(which
covers the Central Plains areas of the United States) . There
was a dense network of weather stations for the area, which
provided better
ground
truthing
for model
verification.
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114
Images were produced based on the model applications results
and are
shown
in Figs.
23 and 24.
Fig.
23
shows
predicted moisture from day 223 through day 229.
the
Fig. 24
shows the corresponding ground truth API values from the NOAA
Cooperative Network.
Empty grid cells are 0.25 x 0.25 degree
latitude/longitude cells with no weather stations.
Images from both model and ground truth data for day 223
show that the surface was dry before that Storm.
The ground
truth image for day 225 in Fig. 24. shows that a large storm
occurred in the Kansas and Oklahoma regions on that day.
The
predicted moisture in Fig. 23, from the empirically-based
model, shows a moisture pattern similar to that of Fig. 24
for the same day.
Moisture was unable to be retrieved from
the eastern area of Oklahoma during late July because of
heavy vegetation.
simulated image.
classified by the
These regions are shown in green on the
Precipitation,
shown in gray color, was
fuzzy logic-based scheme described in
Chapter IV, and no surface moisture retrievals were attempted
for
the
same
surface
type.
The
moist
soil
category,
represented by avocado green, corresponded to the soil where
only one of the criteria was met (i.e., either a moist soil
surface type from the classification scheme, or a significant
change in the value of T19H/T37V with respect to the moving
average).
There was a second smaller storm that occurred the next
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115
SSM/I Surface "Moisture Retrieval Algorithm
. , U sin g D’v iianiivv D a la b a y ie /M e th o d
■ ’.
./
T O *
2
1«
«
WKWfl
H n =' mni'
Brafl9 =■a :inlii
Bra™ = 40 m m '
Q M = fiO;.mm'.’-•
1m
= 7r>. nini
B
B R I ^ .1lit)m.rn ,
B
BBS B
Vnrri
w m | . = 200 nun
1 Bj
m s a ;=■ 250 nuri
H Bn
/ ;\F'I2 - 250 Him
H-Moist
.
D e n s e y e g e t iit io n
B fP r e e ip ita tie n ;
Fig. 23.
Surface moisture retrieval for 1987 August storm
by using empirically-based model.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
116
Antece'dent Precipitation Index (API)
" Frpni ^OAA/C'oo^t'rative N e t w o r k
>1 •:■ «*■ J
’io“.Tjra,'
v . v
"■*w"y^ ■
iff-:,
vlfiv
f**v.«V ■
.
^y4<
av.-*'-'.
; . , V
Fig. 24.
Ground truth measurement for 1987 August storm
from NOAA cooperative network.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
117
day (day 226) in the same area (shown by the ground truth
image of DOY 226 in Fig. 24) .
over wet soil,
This precipitation occurred
causing a standing water and producing a
microwave signature of high moisture (shown in the image of
day 226 in Fig. 23).
Images of day 227 show that there was less surface
moisture.
This is because two days had passed since the big
storm (day 225) and the soil surface had started to dry from
evaporation.
However, the ground truth image shows a higher
moisture signature than that was sensed by the SSM/I, because
the
higher
values
of
API
would
percolated deeper into the soil
represent
water
that
(beyond the SSM/I sensing
depth), and does not affect the surface microwave signatures.
On the same day, in the upper area of North Dakota, there was
another big storm.
This is evidenced by both images of day
227 in Figs. 23 and 24.
Images of day 229 show that four
days after the big storm of day 225, surface moisture had
dried out.
The above sequence of images shows the pattern from the
wetting of the surface on day 225 through the drying of the
following days.
2) 1988 Soring Storm Analysis:
A storm during late
spring of 1988 recorded from the F8 satellite was used as
another example to test the model.
vegetation was at its peak.
During the late spring,
If the vegetation is not too
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
118
dense,
it is still possible for the SSM/I instrument to
detect moisture.
Figs. 25 and 26 show the SSM/I retrievals
of surface moisture and ground truth observations.
The storm began on day 140.
that day.
The bigger one
There were two storms on
(storm one) was located in the
intersection area of Wyoming, Nebraska, and Colorado, with
storm intensity reducing in the northeast direction.
The
smaller storm (storm two) appeared in the eastern region of
New Mexico.
on day 140.
The storms on day 141 were stronger than those
On day 142,
ground truth observation still
showed moisture in the eastern region of New Mexico, where
storm two was drying up in the SSM/I image because the water
had infiltrated to the deeper soil and evaporated.
Storm
two, on day 141, was heading in the northeast direction, the
center of the storm being in the Nebraska area.
The storm
also appeared on both images of day 143 and day 144 in parts
of areas of Wyoming, South Dakota, and Nebraska.
Images for
both ground truth and SSM/I observations on day 148 show it
was dry and clear.
3) 1992 Winter California Storm Analysis:
In Figs. 27
through 30, the ground truth measurements and the retrievals
of surface moisture are shown from a time series of SSM/I
data within the Western Desert area of the United States
during the 1992 winter season.
The SSM/I data were recorded
from the Fll satellite, whose local ascending time is at
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119
S S M y1 .S iii'fa co M o is tu re ' Kot.rie.va 1 A lg o i’iH im
I ’si up D y n a m i c D a ta b a s e Method: •
■ API,’ ■= 10 iiiui
B 10 Him \F-Ti' • 2 i;’ in ii i ./.
■A‘0 mm-T'AFTS''' i.'OG-mi'n
mm
•II: m nr | 3 ‘l.0.iiiiii- T .API 11 )
5 0 i n in
APIS •■
APIS .
a mm
100 uiin ■
; A
P
IS
01) in iri
V
5 inin
TOO liin i.
■loD.mii)
-^
150 limy. •: APIS
1111.111111
SOU liim
A P IS'' - S50, in n i
M
' Arosfiii. nim
■ M .'is t Soil'
■■iv .ii.mi Vi.i'ii*.*t,ni.)vi11
Fig. 25.
Surface Moisture retrieval for 1988 spring storm
by using empirically-based model.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
120
Antecedent J^recipitation Incl^x (API)
. : T r o n i - N O A A ;€ooperath:p -N;p(wDrt
■ APl-i
= 10 m m
■ 1o H u n
P |P U ' rn.rri .
API:.’
A P IS -
> ■API2
22-1-0 .11)111 '
'APIS
20' a iu i
SOm m
■10 n u n . ;
’5 0 -,111111
£|to m m A'APIS ■' 73 aim;
]f)0 mini
1.75 inni. A AI’12
■100 iiini
•'1(H ), mill. ■ ■APIS-.
■■.10p.;iuin: v./A P lS
.ZOO rum
•\ APIS,::
Fig. 26.
APIS
' 2 0 0 in in
SfjCrhim
2 3 0 in m -
Ground truth measurement for 1988 spring storm
from NOAA cooperative network.
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121
Surface M o is lure Retrieval
C a lifo rn ia
S Io 'rrr i,
1SJOil’
'-V°Zd
B :\R I1
•.-• 10 mm
APIS20 nim
■B-d liiin !v4$K •',=■yOU'mill
„ iU in n i . .A P12. '■;?=•. 40 illhi
10 mm - : APi~ '.- 5; .50: m m .
jO mui .. AP12 =: 75 iniii
tv mm A P I2 \ r 100 iiim
(
lOOAiiiif AP12-v:=. 150 mlij
lao .mni ^ APia;< =: 20Q iniii
.'-•(id turn AIM.7 = 25.0 m m
API.1
,250.;m'iii
BMni^t
■ bens'? .vegetal ion,
B PrFi ijiiliil i.o11 •
Fig. 27.
Surface moisture retrieval for 1992 California
storm (from DOY 40-47) .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
122
. Antecedent ri’.ecipitation Index (Al'l) '• ;
. Fi u m N’ OAA C o o p e ra tiv e . N’ e tiv o r k
A:
■
■ t f * . :.< ■>
i- J
,.
:■'■■■ ".v ^ •• • V -
2
• y
v
■
>1
It ■ =
;•!
;T\
i,
'■■'.’ey •:- ■:■■
■ ‘
, •!
.
,■■
-
L-C? £ * . ■A,A
A"**!
' > , „ ! ■ « . . ''.-..■
’■
:.' A; " HlO bim •
' i r . V " * y . ~ -A
A
■
;
; A
A
. ' / V
1
* * V
a .••
API2
.- 20 mm
■•;. ■■' 'B ^ d iu im ,--A P IA ""-'A
•■ .^ 3
A
1
■i, :S.'■ .
Aa ^ - ^
'A'- . y
30
- ' . i i m V A ‘.'; ' A I : i j
A
’ :
- l. U - 'h in i. -
u liiin
A I‘ 12
-
inni
• .
■'’■■A.- ' io uim
A; ISO
•
-'
4u Liiin ■ At'12 =. 10 m l u
;
■' I 0 0
*A
2
■. '•'/ ' 2 0 0
\ A P I2
Al’l^ - 11)0 ihm
l i i i n A APIS •■'■'-I *>()■ " I ill.
inri;: :' API1 ; 201) m m
■
'nm
. A PI 2 A
'-- 250. m r ii •
25.0 m m
-
Fig. 28. Ground truth measurement for 1992 California
storm from NOAA cooperative network (from DOY 40-47).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
123
Surface
' ;
Moisture
C a l i f o r n i a S’t o r n i i
Retrieval
1 9 9 2 ( I) O Y -10)
■
aP
1
10 i u u i
I2 '< =
10 m m
.
< . A P I2 < = .2 0 l i i m -
■ 20 m m < AF“,I2 <=: 30 men
H 30.'.m m -'•v.:AFI3 < = -10 m rn
'S W a iim ,- '. API2
'50 m in '
' '• A , :
■
. :j}. ■8V
-
r ■■^ 'V.':
S '50- h im
7‘5 m m
.1 0 0 n u n
1 5 0 jn m i
-0 A P I2
< = ; 15m n l'v ,1
•. A P I2 =
• .250 m i n
•-
,
I HO i n n i
, ;■AT:,13 . ' 2 ( 1 0
2 0 0 n u i i . A I ’ 12
.A P I2
100 m m
. A P I2 U -
mm
2 0 0 in n i
■■;
■ Mi isl ' :
.a* ••M.'
Dense, vegetation
■ P roeipitation
Fig. 29. Surface moisture retrieval for DOY 48, 1992
California storm by using empirically-based model.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
124
S u T f a e e 'M n i s Li i r e
HeLriaval
Maiti, 1■='-n\ nnu.
H it lT in u ' "■ .A1*I
Al’l t
II
M
O min
..
-
A
O.inni . •
AO mtii •
Al’l -
10 mm
HI-li). iiiiii Al’I'J
At) inni
| .‘ O.inln. \
'
M’l ' l
7\t til M
I : ,.Al'IM. •
.
il/i
ioi)'.tn ui ■■
11
. ) 0 0 : i l l 111
. Hid 'mm. .Al'lV
',• iAu inin • \r’i~-i
.'.'(10 .lViiit
'.'ini 11t.ui ’ U'i:i ■ '
ni nr
v api:. ',. ''-fit) m m
Ai;<>-V.si"A S I;■;■•'
H i 1}
.i |< i i si t i o i i ’
Fig. 30. Surface moisture retrieval for DOY 49, 1992
California storm by using empirically-based model.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
125
15:00
(different from F8 ) .
In this area,
the vegetation
cover is light enough for surface moisture retrievals.
But,
compared to the Central Plains area of the United States,
there is a relatively sparse network of weather stations.
However, in the California area, where a big storm appeared,
there are enough weather stations to provide the pattern of
the ground truthing.
Fig. 27 shows the images of SSM/I measurements for days
40, 42, 46, and 47.
Fig. 28 shows the corresponding ground
truth observations.
The moisture peak was retrieved on days
46 and 47 in the California area, agreeing with the high API
values of those two days.
moisture was present.
in both
SSM/I
Before the storm, on day 40, no
On day 42, surface moisture appeared
measurement
and
ground
truth
observation
images.
Figs. 29 and 30 show the images for day 48 and 49, which
occur days after the peak of the storm.
of
the
SSM/I
data
does
not
The drying pattern
correspond
continuously high API ground truth values.
well
with
the
One possibility
might be because it occurred during the winter time; the
evaporation is relatively small, which results in a small
recession coefficient K in equation (2.10).
Therefore, the
calculated API values decrease slower in the winter than
during the summer when evaporation rates are much higher.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
126
E. Statistical Evaluations of
the Empiricallv-Based Model
Statistical analyses were conducted to further evaluate
simulation results from the empirically-based model.
First,
pixels with detected moisture were selected from the 1987,
1988, and 1992 storms.
software)
was
The univariate procedure [44]
applied
to
these
pixels
to
(SAS
determine
statistical values such as standard deviation, mean, median,
minimum (min), maximum (max), and upper (%75) and lower (25%)
quartiles for both ground truth API (T_API) and predicted API
(P_API).
ANOVA (analysis of variance) was then conducted to
test the equality of the means and variation between and
within the ground truth API and predicted API values.
Tables XIX, XX, and XXI summarize,
respectively,
the
results from the univariate procedures for the 1987, 1988,
and 1992 storms. These results show that the predicted API
values were close to the ground truth API values for the day
of the storm (dslrf =
=2)
1
), and the day after the storm (dslrf
as the SSM/I overpasses.
The statistical values for
those two days are fairly close between predicted API and
ground truth API for most of cases.
from
the
precipitation
event
As the number of days
(dslrf)
increases,
the
statistical differences between T_API and P_API increase.
To statistically test the equality of the means and to
compare the similarity of the predicted and ground truth API
values, the analysis of variance (ANOVA) was conducted.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
127
TABLE XIX
STATISTICS FOR 1987 STORM
dslrf
Vara
StdDb
Means
Max
%Q,
Med
%Q,
Min
1
T_API
39.5
69.4
211.8
91.2
64 .9
39.7
2.9
210plsc
P_API
22.3
60.5
124.0
74 .2
59.1
45.8
0.6
2
T_API
27.4
45.4
116 .4
56 .4
39.3
26 .7
0.9
106pls
P_API
23.0
56.0
131.7
69.0
54 .4
42.8
3.8
3
T_API
14.3
28.0
67.3
34 .3
26.1
18 .7
0.5
4 Opls
P_API
17.0
52.2
95.1
63 .3
49.3
40.5
23.0
4
T_API
9.1
14 .2
32.0
18.5
13 .7
8.7
0.2
24pls
P_API
13.4
53.8
82.3
62 .7
55 .2
42.6
30.0
5
T_API
6.4
9.3
17.8
10.7
10 .5
7.4
0.1
5pls
P_API
9.2
59 .0
72.4
59.8
59.1
57.2
46 .7
* Variable.
n Standard Deviation.
Pixels.
TABLE XX
Statistics for 1988 Storm
dslrf
Var
StdD
Means
Max
%Q,
Med
%Q,
Min
1
987pls
T_API
53 .0
76.9
240.8
109.4
62.3
34 .3
1. 0
P_API
27.7
79.1
198.3
96.9
77.2
60.8
2.6
T_API
45 .9
51.8
192 .4
79.4
32.3
18 .9
0.8
P_API
30.9
64 .8
171.0
81.5
60.8
41.6
0.6
T_API
37.2
49.2
111.4
78.9
37 .9
15.9
0.5
P_API
22 .4
63.7
126.6
73 .9
69.5
44 .3
25 .3
T_API
13 .4
10.8
45.3
12 .4
5.4
3.6
0.7
P_API
42.3
60.4
133 .8
71.7
44 .8
32 .8
17 .2
T_API
4.7
5.5
13.5
8.9
5.2
0.9
0.9
P API
37.3
57.6
114 .3
96.8
45.2
30.5
10.0
2
115pls
3
24pls
4
lOpls
5
7pls
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128
TABLE X X I
S t a t is t i c s fo r 1 9 9 2
S to rm
dslrf
Var
StdD
Means
Max
%Q,
%Med
%Q,
%Min
1
T_API
78 .7
88.3
310.9
140.2
61.7
24.6
1.6
307pls
P_API
49.3
81.7
316.1
102 .2
68.3
52 .2
1.4
2
T_API
78 .1
80.7
276.3
132 .7
52.2
19.9
3.0
116pls
P_API
41.6
71.9
289.7
98.6
68 .2
46.1
1.2
3
T_API
65.0
49.4
251.5
56.9
28.4
11.8
2.3
62pls
P_API
32.5
62.5
184 .4
73 .2
57.4
47.5
3.1
4
T_API
38.1
34.1
167.3
47 .1
2.7
10.5
1.9
18pls
P_API
35.6
52.7
167.0
65 .1
52.3
36.6
3.9
5
T_API
17.2
24 .5
49.4
38.5
24 .3
7.3
5.2
lOpls
P_API
25.3
56.3
91.1
73.9
60.1
33.4
12.7
Boxplots were first used to graphically examine the
differences of the statistics between ground truth API and
predicted API for different dslrf values.
Figs. 31, 32, 33,
and 34, respectively, show boxplots for the 1987 summer storm
with dslrf of 1 to 4.
medians,
Data points for means, quartiles,
and minimum and maximum values for predicted API
values spread within the same range as those for ground truth
API when dslrf is small. The differences between mean values
are smaller than the random fluctuations within the range of
their %25 quartiles to %75 quartiles.
the
overlap
of
the
boxplots
for
As dslrf increases,
ground
truth API
and
predicted API decreases until there is no overlap between
them.
To quantify the differences
as identified from the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
220
170
120
70
20
-30
Tru_API
OMin
Fig. 31.
+ Quantiles
Pre_API
xMedian
(Mean
AMax
Boxplot for dslrf = 1 of 1987 summer storm.
170
120
70
20
-30
Tru API
OMin
Fig. 32.
d-Quantiles
Pre API
xMedian
*Mean
flMax
Boxplot for dslrf = 2 of 1987 summer storm.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
130
120
20
-30
Tru API
OMin
Fig. 33.
-fQuantiles
Pre API
xMedian
(Mean
^Max
Boxplot for dslrf = 3 of 1987 summer storm.
120
70
-30
Tru API
^Min
Fig. 34.
Quant iles
Pre API
^ Median
fMean
^ Max
Boxplot for dslrf = 4 of 1987 summer storm.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
boxplots, ANOVA was used to determine the variation between
and within groups (predicted API group and ground truth API
group). The results, including the sums of squares between
and within groups, the mean squares, and the
F*-statistics
are summarized in Table XXII for dslrf = 1 of the 1987 summer
storm.
ANOVA
Table
for
TABLE XXII
dslrf = l o f 1987
Summer
Stor m
Sum of squares,
SS
Degrees of
freedom, d.f.
Mean square,
MS
Between
8339.58
1
8339.58
groups
(SSB)
(k-1)
Within
754294 .74
418
groups
(SSW)
(n-k)
762634 .32
419
(SST=SSB+SSW)
(n-1)
Total
fSB
( MSB -
k -1
)
1804.53
( MSW = SSiY )
n -k
8339.58 M 6,_ MSB
1804.53
MSW
d.f.=(l,4l8)=(k-l,n-k)
c = Fa = F0.01= 6.63
F ._
In Table XXII, n represents the total number of records
of data
(the number of records of predicted API plus the
number of records of ground truth API); k is the number of
groups (k =
2
); a is the significant level (a =
is the critical value for the F-distribution.
the two groups have the
difference)
0
.0 1 ); and c
When F* s c,
same means, andthe variation (or
between groups
is not large relative
to the
variation within groups.
In Table XXII, F* = 4.62 and c =
6.63, statistically, the
model correctly estimates API for
dslrf =
1
.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
132
TABLE
ANOVA
Between
Table for d s l r f
=
X X III
2 of 1 9 8 7
Sum of squares,
SS
Degrees of
freedom, d.f.
5987.14
1
groups
(SSB)
(k-1)
Within
134913.57
210
groups
(SSW)
(n-k)
140900.71
211
(SST=SSB+SSW)
(n-1)
Total
ANOVA
Ta b l e for
Summer Storm
Mean square,
MS
5987.14
( MSB =
k
)
-1
639.59
( MSW - S S ^ )
n -k
5987 .14 ^ 36 _ MSB
639.59
'
MSW
d.f.=(l,210)=(k-l,n-k)
c = Fa = F0 01= 6.63
F ._
TABLE XXIV
dslrf = 3 o f 1987
Summer
St o r m
Sum of squares,
SS
Degrees of
freedom, d.f.
Mean square,
MS
Between
11713.77
1
11713.77
groups
(SSB)
(k-1)
Within
19196.33
78
groups
(SSW)
(n-k)
30910.00
79
(SST=SSB+SSW)
(n-1)
Total
( MSB -
SSB )
K~ i
246.11
( MSW =
n -k
)
11713.77
MSB
246.11
'
MSW
d.f.=(l,78)=(k-l,n-k)
C = F0 = F0„,= 6.85
F ._
Tables XXIII and XXIV are two ANOVA tables for dslrf =
2 and dslrf = 3 of the 1987 summer storm.
For dslrf = 2, F* is larger than the critical value, but
they are still on the same magnitude.
much larger than the critical value.
For dslrf =3, F* is
This implies that the
predicted API values do not correctly represent the actual
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
133
API values when dslrf is greater than 2 for this particular
storm.
This is not surprising because the empirical model
used was based only on points with dslrf = 1.
The ground
truth API values were estimated using a depth of water
available for evaporation of
10
mm (see results on page
1 1 0
),
which is almost depleted by the third and fourth day after a
precipitation
event
during
the
summer
time
when
the
evaporation is high.
Similar analyses (boxplot and ANOVA) were conducted for
the 1988 spring storm.
The boxplots for dslrf of 1 to 5 are
shown in Figs. 35 to 38, respectively.
These figures show
that the difference of mean values from ground truth and
predicted API values are relatively small,
and the data
points of means, quartiles, medians, and minimum and maximum
values spread within the same range for predicted and ground
truth API when dslrf equals 1, 2, and 3.
However, there are
big differences when dslrf increases to 4 and 5 (the results
for dslrf = 5 are not shown) .
The results of ANOVA are
summarized in Tables XXV to XXIX
for dslrf of
1 to 5,
respectively.
When dslrf equals 1, 2 and 3, for each case, the F*
value is less than its critical value c.
Based on the
criterion of F* s c, statistically, the simulated API values
represent the ground truth API values when dslrf is less than
4.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
134
270
t
220
170
120
.. d
0
..X
70
.. %\..
dj
20
4
<►
Tru_API
Pre_API
-30
0Min
Fig. 35.
^.Quantiles ^Median ^Mean
^Hax j
Boxplot for dslrf = 1 of 1988 spring storm.
220
170
120
70
20
-30
Tru API
.Min
Fig. 36.
^.Quantiles
Pre API
^Median
^Mean
Boxplot for dslrf = 2 of 1988 spring storm.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
135
170
120
70
20
-30
Tru API
Pre A P I
0Min + Quantiles ^Median # Mean ^Max
Fig. 37.
Boxplot for dslrf = 3 of 1988 spring storm.
170
120
..
70 --
20
..
-30
Tru API
Pre API
^Min +Quantiles ^Median ^Mean ^Max
Fig. 38.
Boxplot for dslrf = 4 of 1988 spring storm.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
136
In the case of the 1988 spring storm, the predicted API
values were close to the ground truth API values up to the
third day after the precipitation event.
This is because the
depletion of moisture in the surface layer was slower due to
a lower evaporation rate.
winter
storm were
Similar results for the 1992
obtained
as
discussed
later
in
this
chapter.
TABLE XXV
ANOVA
Between
Table
for
dslrf
=
l
of
Sum of squares,
SS
Degrees of
freedom, d.f.
2923.29
1
groups
(SSB)
(k-1)
Within
354507.98
1990
groups
(SSW)
(n-k)
357431.27
1991
Total
1988
S pring
St or m
Mean square,
MS
2923.29
( MSB =
)
k -l
1781.71
( MSW =
)
n -k
C _ 2923.29 ., r„ _ MSB
"1781.71
MSW
d.f.= (1,1990) = (k-1,n-k)
c = F„ = F0.oi= 6.63
F
(SST=SSB+SSW)
ANOVA
Table
for
(n-1)
TABLE XXVI
dslrf = 2 o f 1988
Spring
St or m
Sum of squares,
SS
Degrees of
freedom, d.f.
Mean square,
MS
Between
9635.77
1
9635.77
groups
(SSB)
(k-1)
Within
348750.72
228
groups
(SSW)
(n-k)
358386.49
229
(SST=SSB+SSW)
(n-1)
Total
( MSB =
K L
)
1529.61
( MSW =
n -k
)
9635.77
MSB
1529.61
'
MSW
d.f.=(l,228)=(k-l,n-k)
C = F„ = F0 01= 6.63
F ._
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
137
ANOVA TABLE
FOR
TABLE XXVII
dslrf = 3 OF 1988
SPRING STORM
Sum of squares,
SS
Degrees of
freedom, d.f.
Mean square,
MS
Between
2510.69
1
groups
(SSB)
(k-1)
2510.69
( MSB = S SB )
Within
43396.66
46
groups
(SSW)
(n-k)
45907.35
47
(SST=SSB+SSW)
(n-1)
Total
k -l
943 .41
( MSW -
SSIf
n -k
)
_ 2510.69 ..., ££ _ MSB
94 3.41
'
MSW
d.f.=(l,210)=(k-l,n-k)
C = FQ = F001= 7.08
F.
TABLE XXIII
ANOVA
Between
Ta b l e fo r d s l r f
= 4 of 1988
Sum of squares,
SS
Degrees of
freedom, d.f.
12296 .34
1
groups
(SSB)
(k-1)
Within
17761.01
18
(SSW)
(n-k)
30057.35
19
(SST=SSB+SSW)
(n-1)
groups
Total
S pring Storm
Mean square,
MS
12296.34
( MSB -
SSB
k -1
)
1781.986.72
( MSW ~ SSW )
n -k
_ 12296 .34 ^
_ MSB
986.72
'
MSW
d.f.=(l,18)=(k-l,n-k)
C = Fa = F0.01= 8.29
r..
Boxplot and ANOVA analyses were conducted for the 1992
winter storm.
Figs. 39 to 43 are boxplots, respectively, for
dslrf of 1 to 5.
The corresponding ANOVA tables are shown in
Tables XXX to XXXIV.
Tables XXX to XXXII show that the simulated API values
well represent the actual API values when dslrf equals 1, 2,
and 3 since for each case F* < c.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
138
TABLE
ANOVA
X X IX
T able for dslrf = 5 of 1988 S pring Storm
Sum of squares,
SS
Degrees of
freedom, d.f.
Mean square,
MS
Between
9493 .66
1
9493.66
groups
(SSB)
(k-1)
Within
8493 .62
12
groups
(SSW)
(n-k)
17987.28
11
(SST=SSB+SSW)
(n-1)
( MSB -
SSB
k-1
)
707.80
( MSN =
SSW )
n~k
9 6 3.
"6.30= MSB
152 9.61
MSN
d . f .=(1,12)=(k-1,n-k)
C = F0 = F001= 9.37
F-=
Total
320
2 7 0 --
220
170 t
120
-
7 0 --
20
--
-30
Tru API
Min
Fig. 39.
Quantiles
Pre API
Median
Mean
Max
Boxplot for dslrf = 1 of 1992 winter storm.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
139
320
270 -
220
1 7 0 --
120
--
7 0 --
20
-
-30
Tru API
^Min
Fig. 40.
_|_Quantile8
Pre API
^Median
# Hean
A Max
Boxplot for dslrf = 2 of 1992 winter storm.
270
220
--
1 7 0 --
120
--
7 0 --
20
--
-30
Tru API
^Min
Fig. 41.
_|_Quantiles
Pre API
^Median
^Mean
^ Max
Boxplot for dslrf = 3 of 1992 winter storm.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
140
170
120
70
20
-30
Tru API
^Min
Fig. 42.
^.Quantiles
Pre API
^Median
^Mean
^K a x
Boxplot for dslrf = 4 of 1992 winter storm.
120
70 -
-30
Pre API
Tru API
^Min
Fig. 43.
^.Quantiles
^Median
^Mean
^Max
Boxplot for dslrf = 5 of 1992 winter storm.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
141
ANOVA
Table for
TABLE XXX
d s l r f = l of
1992
W inter Storm
Sum of squares,
SS
Degrees of
freedom, d.f.
Mean square,
MS
Between
6427.01
1
6427.01
groups
(SSB)
(k-1)
( MSB = f B )
Within
2649852.97
616
groups
(SSW)
(n-k)
4301.71
( MSW - SSlf )
2656279.98
617
(SST=SSB+SSW)
(n-1)
Total
ANOVA
Between
Tabl e
for
TABLE XXXI
dslrf = 2 o f
Sum of squares,
SS
Degrees of
freedom, d.f.
4536.25
1
groups
(SSB)
(k-1)
Within
900946.50
230
groups
(SSW)
(n-k)
904863.66
231
(SST=SSB+SSW)
(n-1)
Total
n -k
_ 6427.01 ,
_ MSB
4301.71
'
MSW
d.f.=(l,616)=(k-l,n-k)
c =
= F„.ol= 6.63
1992
W
inter
Storm
Mean square,
MS
4536.25
( MSB = SIf B )
A
3917.16
( MSW =
1
n -k
)
4536.26 . ,
_ MSB
3917.16
'
MSW
d.f.=(l,230)=(k-l,n-k)
C — Fa = Fq.oi= 6.63
p. _
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
142
TABLE X X X II
A N O V A Table for d s l r f = 3 of 1 9 9 2
Between
Sum of squares,
SS
Degrees of
freedom, d.f.
5296.88
1
groups
(SSB)
(k-1)
Within
321941.57
122
groups
(SSW)
(n-k)
327238.45
123
(SST=SSB+SSW)
(n-1)
Total
ANOVA
Between
Table
for
Degrees of
freedom, d.f.
12296.34
1
groups
(SSB)
(k-1)
Within
17761.01
18
groups
Mean square,
MS
5296.88
( MSB - S SB )
k -1
2638.87
( MSW - SSW. )
n -k
o. - 5296.88 .0 Q1_ MSB
26 38.87
'
MSW
d.f.=(l,122)=(k-l,n-k)
C = F„ — Fq q^ 7.08
TABLE XXXIII
dslrf = 4 o f 1992
Sum of squares,
SS
(SSW)
(n-k)
30057.35
19
(SST=SSB+SSW)
(n-l)
Total
Winter Storm
W
inter
Storm
Mean square,
MS
12296.34
( MSB =
K
1
)
1781.986.72
( MSW ~ SSM )
n -k
p. _ 12296 .34
. 6 _M SB
986.72
'
MSW
d.f.=(l,18)=(k-l,n-k)
c = F„ = F0-01= 8.29
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
143
TABLE
ANOVA
X X X IV
Table for dslrf = 5 of 1992 S pring Storm
Sum of squares,
SS
Degrees of
freedom, d.f.
9493.66
1
Between
groups
(SSB)
(k-1)
Within
8493.62
12
groups
(SSW)
(n-k)
17987.28
11
(SST=SSB+SSW)
(n-1)
9493.66
( MSB -
a
result
of
the
f SB
k -i
)
707.80
( MSW ~ SSW )
n -k
_ 9635 .77
MSB
1529.61
'
MSW
d.f.=(l,12)=(k-l,n-k)
C =
= Fo.oi= 9-37
F.
Total
As
Mean square,
MS
above
example
analyses,
the
empirically-based model, along with dynamic database schemes,
provides a good detection for surface moisture on the day
when a rainfall event occurs.
The model also provides a
fairly good estimation for the second day after the rainfall
during the period when water is still on the top layer of the
soil.
As the dslrf increases, surface water infiltrates to
deeper soil layers and evaporates from the surface layers.
Because of the limitation of the SSM/I sensing depth (2-20
mm), the accuracy of the SSM/I model estimations decrease.
This is also corroborated in the results above as indicated
by the decreasing number of data points for which surface
moisture was detected with the SSM/I as the days after the
storms or precipitation event increases.
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144
CHAPTER VII
PHYSICALLY-BASED MODEL
This chapter includes the preparation of the parameters
needed by the physically-based model,
and the process of
linking the Inversed Land Surface Radiative Transfer Model to
the
integrated
framework
of
the
fuzzy
logic-based
classification method, the merging-then-gridding process, and
the dynamic database for moisture retrieval over large areas,
such as the United States. The parameters preparation and the
integrated framework are first developed in this study.
A. Preparation of Model
Parameters
Use of the physically-based model requires 25 input
parameters to characterize the SSM/I footprints of interest.
As discussed by Vassiliades in [3], the model is relatively
insensitive to some of the parameters.
These parameters were
fixed as constants in the model to avoid complexity.
Values
of these parameters are listed in Table XXXV.
The height of vegetation (h) and permittivity of soil
particles
(£„' ')
were
predetermined,
based
descriptions and soil texture classes,
on
the
MLRA
and stored in the
parameter database.
The area fraction of water bodies within each footprint
was calculated from the water-body mask information from the
AVHRR data as described in Chapter V.
The area fraction of
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145
vegetation in the footprint and volume fraction of the leaves
in the canopy (Vx) were computed, based on NDVI values from
the AVHRR.
Since the spatial resolution of the AVHRR is 1
km2, and the 37 GHz SSM/I footprint is about n x 15 x 15 km2,
a transformation was necessary to get an NDVI value for the
SSM/I footprint from each of the AVHRR pixels within the 15km radius of this SSM/I footprint.
TABLE XXXV
PREDETERMINED PARAMETERS FOR PHYSICALLY-BASED MODEL
Parameters
Acronym
Loss factor of soil particles
'
Volume fraction of soil particles
Volume fraction of bound water
Values
5 .0
V8
0 .5
Vbw
0 .022
Permittivity of vegetation bulk material
3 .0
Loss factor of vegetation bulk material
'
Leaf water content
V.i
0 .05
0 .65
As discussed in Chapter II, NDVI values less than 100
represent
surfaces.
clouds,
snow,
water,
and
other
nonvegetative
Values equal to or greater than 100 represent
vegetative surface.
The NDVI value for an SSM/I footprint
SSMIndvi can be calculated by:
£
SSMI™
NuPlOO
- TotNk t N u
(7-1)
where NuPlOO is the number of AVHRR pixels with NDVI values
greater than 100, and TotNu is the total number of AVHRR
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146
pixels in a SSM/I footprint.
Based on this value, the volume
fraction of leaves, V1# can be calculated by equation (5.5) .
Since
the
NDVI
value
is
a
continuous
function
of
vegetation density, an SSM/I footprint with an NDVI value of
170, for example, has greater vegetation than a footprint
with an NDVI value of 110.
In order to determine the area
fraction of vegetation, a visual assessment was made using
ERDAS software to produce an image for the AVHRR data.
A
fully vegetated pixel was found to have an NDVI value of 173,
and the
footprint was considered to have a
vegetation cover.
to have
100
percent
The pixel with NDVI value of 100 was found
no vegetation
cover,
and
the
vegetation of the footprint was zero.
between the NDVI value
area
fraction
of
Thus, the relationship
(SSMIndvi) and vegetation percent
(VegPer) for a pixel was represented by:
1 7 3 -1 0 0
1 0 0 -V e g r per
100
(7.2)
The percentage of vegetation, VegPer, can be calculated by:
Then, the area fraction of bare soil can be obtained by:
%soil = 1 -%water - ^Vegetation
(7.4)
Since the satellite does not align itself exactly on
every overpass,
a procedure was conducted to merge SSM/I
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147
data, the water-body database, the NDVI database from AVHRR,
and API files before gridding process.
The parameters (such
as water percentage, soil percentage, vegetation percentage,
and NDVI value, which were used to calculate LAI as required
by the physical model)
were obtained during the merging
process.
The soil moisture retrieved by the model, or the volume
fraction of free water, was limited [3] to the range of 0 to
0.5,
where
sometimes
0.5 was
considered
soil porosity.
However,
the retrieved value was greater than the soil
porosity, or the potential water-holding capacity.
this problem,
To solve
soil porosity was stored in the parameter
database as an upper limit of soil moisture in retrieval.
When
retrieved moisture
was
greater
than
the
porosity,
moisture was set at the value of soil porosity, the standing
water percentage was increased in the footprint,
model was executed again for the same footprint.
then set to indicate flooding,
and the
A flag was
as this is a significant
parameter in many areas such as agriculture, hydrology, etc.
The Inverse-LSRTM, which was coded in the QuickBasic
programming language on the PC by Vassiliades [3], was
re­
coded in the C language and is currently running on the SGI
workstation.
Fig. 44 shows a general flow chart of the
retrieval process.
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148
Next Data Record
Input Data
Latitude, Longitude, Surft,
7BT, PRCP, 4API, %wt, %veg,
%soil, NDVI, MRF (Model
Running Flag), MLRA Class
Code
No
MRF = 99?
Yes
Use MLRA Class Code as a
Reference to Search Parameter
Database to Obtain:
MRF = 1
Standing Water
MRF = 0
Dry Surface
MRF = -1
Dense Vegetation
MRF = -2
Atmospheric
Scatter
MRF = -3
Moist Surface
Porosity' (moisture limit)
Parameter
Database
Soil Dielectric Constant (Es)
Vegetation Height (h)
Run Inverse LSRTM
r
If Retrieved Surface g
Moisture > Porosity ?
no
Yes
End
Modification of Initial
Parameters
• Set Surface Moisture
at Porosity
• Increase %wt by 2%
• Decrease %veg by 1%
• Decrease %soil by 1%
Notes
•
•
•
Surft - Soil surface type
PRCP - Precipitation
BT - Brightness temperature
•
API - Antecedent Precipitation Index
•
•
%wt - Water body percentage
%veg - Vegetation percentage
Fig. 44.
The flow chart of the retrieval process.
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149
B. Model Applications
The physically-based model was used to retrieve surface
moisture and/or
temperature over the
Central
Plains and
Western Desert areas of the United States.
The overall procedures using this model are listed as
follows:
1.
The
SSM/I
seven
brightness
temperatures
were
classified for surface type.
2.
The resulting classified data were merged with the
API files generated from the ground truthing data
and parameter database, based on the AVHRR.
The
resulting merged data file includes: latitude and
longitude
coordinates,
seven
brightness
temperatures, classification codes, precipitation
and four API values, %water, %Vegetation, %soil,
and NDVI values.
3.
The merged files were gridded into quarter-degree
cells as input to the dynamic database.
4.
The dynamic database was used to select footprints
that would be used for moisture retrieval.
MLRA file,
degree
The
which was also gridded in quarter-
latitude
and
longitude
coordinates,
was
merged with the resulting file from step 3.
The
MLRA code is used as entry reference to parameter
database for obtaining soil dielectric constant
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150
(£s) , soil porosity,
and vegetation height
(h) .
The volume fraction of the leaf (V^ was calculated
using the vegetation (h) value and NDVI value for
a particular footprint.
5.
The inverse LSRTM was used to retrieve surface
moisture and/or temperature.
moisture
(moisture
value was
was
percentage was
greater
set
to
increased
If the retrieved
than
soil
porosity),
and
the
porosity
water-body
model
was
executed again to obtain the real standing water
percentage.
Images were produced by ERDAS Software to compare the
simulated results with the ground truth data.
C. Examples of Surface Moisture
and/or Temperature Retrievals
1)
1987
August
Storm--Moisture
and
Temperature
Retrievals: The resulting images for SSM/I data and ground
truth data are shown in Figs. 45 and 46.
These results were
similar to the results from the empirically-based model.
Moisture from the storm (which occurred on day 225) appeared
in
thesouth-central
plains (Kansas and Oklahoma area)
driedupin the following days.
The
and
predicted moisture had
similar patterns as shown by ground truth data.
In order to further verify the model, subregion files
were prepared for the Kansas and Oklahoma area in which large
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151
(V o l i i m m e t r i e W a t e r ' C on t e i i t , Y l ' T )
3
k
■ 0 .0
V .\iC > =
0 .0 5
Bo,Of>' w c •>.= b.i .V'.\
■o.l < V1VC <= 0,15 .7
®0.;t5< VtVC ^-- 0,20 \ :
110*2.0■'%..WC;:d= •0;S:5|'-;•
> o !25 -<,\nvc V = 0.30
.
0 .3 0 V: W C < = 0 . 3 5
■ 0 .3 5 < : W C ■.<= 0,4-
o.i < \nvc :<= 0.45
■ 0.45 'ivwc <= 0.5
i V a t e r b o d V
( b
o
y ; c l a s s i f i c a t i o n
) „
B.Ona of. two .conditions, show dry
t-”;!dense vegetaUoh.' '
Ht'Rain or show :■<,: /
Flooding (by model)
Fig. 45. Surface moisture retrieval for 1987 August storm
by using physically-based model (for day 225, 226).
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152
(V p lu jiu n e L rie Water: C oh.tent, ■V W )
B O . 0 * V'tVC - = 0 .0 5 \
B o . 05 . V H V ;= 0.1 ■
B O .l
vw e
■ - :0 . 1 5 . •
;,v- .
§|bvi5vxg.ig.'tt.V.
0 ?• : V-.VC • • =• 0.:25
0 25
0 3 -
y;.vc . - 0 ,3 1
V1VC
0 .3 5 '
0 35, . VWf’ • - O. j ■ ■
0
i..v.yc .- o.if>
' 0.-15 : VW' ' . - I>.;7
Waloi'lAiily ( |.iv. lia s sih o a t io n ) .
■ One of- two ..om litions show 0 r v
. Di'iVrit' vi>«et.iitlon
»K«»
'MVC •
Porosity . V-
Fig. 46. Surface moisture retrieval for 1987 August storm
by using physically-based model (for day 227, 228).
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153
moisture was detected on day 225.
The Inverse LSRTM was used
to retrieve surface moisture for each pixel within this
region
(the Kansas-Oklahoma
area:
the
northwest
located at 39.60 latitude and 101.60 longitude,
southeast
corner,
located
at
36.80
latitude
corner,
and the
and
97.40
longitude) . The moisture images for the subregion of day 225
to 228 are shown in Figs. 47 and 48.
The SSM/I signature for
day 225 resulted in a retrieval of high surface moisture
values, which decreased throughout the following days.
The
retrieved moisture values for some footprints on day 225
exceeded soil porosity,
holding capacity.
which determines the soil water-
In this case, there was standing water on
the surface due to very high moisture.
By introducing soil
porosity as a parameter into the model, standing water could
be predicted.
In these figures, one can see that the model
follows the trend of the ground observations.
In order to show the consistency of the physically-based
model in retrieving surface moisture and temperature,
the
surface temperature retrievals from the footprints within the
Kansas and Oklahoma areas are shown in Figs.
49 and 50.
Since moisture and air temperature are two major factors
affecting surface temperature, the daily maximum and minimum
temperature
(daily minimum temperature can be considered
close to the temperature of the SSM/I ascending overpass
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154
( f u r Ivaiisa^^'aYid^Old'ahtiilia-'AKK.A;)';
H O .O
I I
c k o Ov
V1VC •: = 0 .0 5
.
- A iv c :;;, =. a . i
\
':
.-= d r i 5
\ U
•
lo•■\>vt'. =:;0;c'0 ''
o 2.0
v iv r
- 0 .2 0
0 25
V\Vt:'
= O.OO
o .jo
'v « C ;
- • o '.o o
.
0 .0 5 - ;V W r . . - . 0 .4 0
b . :10 ■ V.WC • = 0 .1 5
,• 0 .1 5
\ WC.
= 0 .5 0
5
■■.;'■•/■■
:
: ">:d
:
..
- d./ •'(
■ '• : d /
■7 ? •
' 4 V i \t u r h iH lv ‘ ( b v o Ir t > s if i y a t i o n ).
|0 .I
k’
o f ;•1 w o c;ori d iI. id ri.s s h o w d r y
• l i e r i s e * :v u g d t a f i o n
R a in
: \" U V
o r 5 now .
-
1’ o r o a i t v
• '."V ;
• ;
4"
Fig. 47. Surface moisture retrieval for Kansas and
Oklahoma regions (for day 225, 226) .
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
155
( f o r Kansas arid O k lo h o m a A rea)
rMiSSgJ®
0 0 .0
, \1VC
a, Of;
.0 :d ;0 5 - 1Ywo-: -
■
o .i
H il-!■ .v VOC Vo.l5
S3 0 0 5
YWC
= 0.2(1
0.20 •'. : w e ;
0.25..
0.25
Y1U'
- 0.30
. > .
0,30 . \WV(\
- 0.3;' "W : : : 0 .3fr : \ iv r .
Q..|Q:
:
■
0.10
YWC 5 = 0.-15 • V Y / J
ro.-io:
YWC'■>:=■■ 0,50
W aterbody (by. ;qlassil'ieatibn:) '
IS O ne; o f -twiv. eb n d i f i’b n s . ih ib v dby
bense veg etatio n ;
'R a i n
VWC
o r •■bn'n
=
•;■ "•
P o ro s ity
Fig. 48. Surface moisture retrieval for Kansas and
Oklahoma regions (for day 227, 228).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Fig. 49.
Surface temperature retrieval for Kansas and
Oklahoma regions (for day 225, 226).
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157
S
u r l ' a r c
i :v . '
^l'< i r , K • > i
I h - 1
r ; .
'
a
!
i
1 ; V
. [
'Ji\>'i',. ■ • a r l . h H
.
‘ JY: -
.■
f a
I
; ; ;;
;M h if a l
■'■■■
i t;i !n
■ j : , M . I- i
Fig. 50.
I ) '.-. ■■ ' .
Surface temperature retrieval for Kansas and
Oklahoma regions (for day 227, 228).
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158
time, and daily maximum temperature is close to the SSM/I
descending overpass temperature) were used to provide ground
truthing on the surface temperature (shown in Figs. 51 and
52) . During the first days after the storm, surface moisture
played a dominate role in affecting skin temperature.
From
day 225 to 227, the surface temperature was increased due to
the decrease in moisture.
moisture
was
lower
on
However, even though the surface
day
228
than
day
227,
temperature on day 228 was lower than on day 227.
surface
This can
be explained in that if there is not much moisture on the
surface, the air temperature plays a major role in affecting
skin temperature.
The "air temperature" was lower on day 228
than that on day 227, as shown on Fig. 52.
It is obvious from analyzing these figures that the
model interpreted the SSM/I signatures in a consistent way
and generated similar spatial trends of surface moisture and
temperature.
2) 1988 Spring Storm--Moisture Retrievals:
storm in the late spring of 1988
The same
(used as a example in
Chapter VI) was also used to test the physically-based model.
Fig. 53 shows the retrievals of surface moisture.
The ground
truth measurements were previously shown in Fig. 27.
A similar pattern of surface moisture was obtained as
with the empirically-based model retrieval and is evidenced
by comparing Fig.
25 and Fig.
53.
The surface moisture
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159
Fig. 51.
"Air temperature" for Kansas and Oklahoma regions
(for day 225, 226).
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160
Fig. 52.
"Air temperature" for Kansas and Oklahoma regions
(for day 227, 228).
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161
^ 0 i 5 . ' , W c v -j/il.t iil
i vo
i
■ u.isu'
ivii
w
. - U ..tin
'■= il'.iifi.
'.v h y - - o hi
• . II. Ill
. 7 ii i;.
. =.'i
'» ''
VWi.
... =
\ t .i -
-
iv-.n
Im .|\'
IBMmsst Vqiii
.... l u ji.-o
91i*ft*v fpi-uxi
VIVC;
Fig. 53.
.
l a t i 'Ji
•
,
■' ' Ian naif V .
Surface moisture retrieval for 1988 spring storm
by using physically-based model.
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162
retrieved by the physically-based model
shows a very dry surface on day 138,
(Fig. 53) clearly
the wetting of the
surface from the storm on day 140, and a dry surface again on
day 148.
The peak of surface moisture was retrieved on day
141 and 142, which is supported by the high API values of
these days.
There are many pixels with surface moisture
above soil porosity on days 141 and 142, and a decreased
number of pixels with standing water on the following days.
From
these
figures,
one
can
see
that
the model
mostly
followed the trend of the ground observations.
Since the physically-based model
retrieved the soil
Volummetric Water Content (VWC) of the surface layer, which
has different units than the Antecedent Precipitation Index
(API) , it is hard to make a numerical comparison between VWC
and API at this stage.
However, the relationship between VWC
and API could be developed through future research.
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163
CHAPTER VIII
SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
A . Summary
A framework was developed, which provides a systematic
approach for land surface-moisture retrieval over large areas
(such
as
the
temperatures.
United
States)
using
SSM/I
brightness
The methodology was applied to the Central
Plains and Western Desert areas of the United States for
moisture retrieval.
The framework can be viewed as a six-step process:
(1)
the ground truth processing; (2 ) the fuzzy logic-based land
surface
database;
classification;
(3)
the
multi-layer
parameter
(4) the data merging-then-gridding approach;
(5)
the dynamic database; and (6 ) the empirically-based model and
the physically-based model.
1.
The Ground Truth Data Processing:
The Antecedent
Precipitation Index (API) was estimated based on climatic
variables
from
Administration
stations.
the
(NOAA)
National
Oceanic
cooperative
and
network
Atmospheric
of
weather
The API values were used as a surrogate moisture
variable to evaluate and test the validity of the proposed
moisture retrieval methodology.
API were computed based on
daily maximum, minimum temperature and precipitation.
To
properly use these weather station data, the recording time
of daily maximum temperature was first checked because it
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164
could represent
current day's
or previous
temperature, depending on recording time.
day's maximum
Second, if there
were missing precipitation records for several consecutive
days, followed by a large accumulated precipitation value,
averaged values were used for missing records.
2.
Method:
The Fuzzy Logic-Based Land Surface Classification
A land surface classification method was developed,
which provides an efficient approach to classify land surface
types based on the SSM/I brightness temperatures.
The model
is a combination of the FCV algorithm, the NFE definition,
the algorithm for searching a local minimum average of NFE
values, and the cluster assignment algorithm.
be divided
into two levels:
The model can
an unsupervised first-level
classification and a supervised second-level classification.
Each of the classification levels included clustering and
cluster assignment.
An NFE definition was first introduced in this study to
define the fuzziness of a partition with class number c for
a
data
point.
Unlike
the
conventional
fuzzy
entropy
definition that deals with the membership values of n data
points within a given class, the NFE definition deals
with
a subset that consists of the membership values of one data
point with class number c . The average of the NFE values for
all
the
data
points
was
used
in
determining
the
most
representative class number of a data set in the unsupervised
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165
second-level classification.
3.
The Parameter Database:
A parameter database was
first developed by using multiple data resources,
such as
AVHRR data, classified soil map and Major Land Resource Area
Handbook,
to provide useful information on water bodies,
properties of soils,
and properties of vegetation to the
development of the empirically-based model and application of
the physically-based model.
4.
The
Data
Merging-Then-Gridding
Process:
Data
merging approach that searched for weather stations within
- the
SSM/I
footprints
was used
to combine
the resulting
classified SSM/I data with the computed ground truth API
files, and the parameter database.
have been done,
Once the data merging
the merged data were gridded to provide
position references for the dynamic database
vegetation
density
and
moisture
[2 ] to check
indicators
for
the
consecutive overpasses over the same area.
5.
The Dynamic Database:
The dynamic database was
used to compute and store the running averages of MPI and
T19V/T37V
for the development
empirically-based model
and/or application of the
and physically-based model.
The
running average of MPI was used as a vegetation density
indicator, and the running average of T19H/T37V was used as
a moisture indicator.
6
.
Development and Application of Moisture Retrieval
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166
Models:
An empirically-based model was developed and used to
retrieve surface moisture using the 1987,
SSM/I storm data.
1988,
and 1992
The physically-based model was also used
to retrieve land surface moisture for the 1987 and 1988 SSM/I
storm data.
The results were represented by images generated
by ERDAS software for verification purposes.
B. Conclusions
The results from example applications indicate that the
proposed
methodology
achieved
good
surface
moisture
prediction. On all the example applications, the predicted
surface moisture is close to the ground truth measurements.
The newly defined Normalized Fuzzy Entropy (NFE) is a
viable definition in evaluating the fuzziness of a partition
with class number c for a data point.
The Average Normalized
Fuzzy Entropy (ANFE) over all the data points within a data
set
is
an
effective
criterion
in determining
the
most
representative cluster number of the data set.
The fuzzy logic-based land classification method is an
effective method in identifying land surface types from SSM/I
brightness temperature data.
This method has overcome the
problem of missing classification by using the traditional
statistical threshold value method.
The use of the merging-then-gridding approach improved
the quality of moisture retrieval by reducing errors and
noise induced by the previously used gridding-then-merging
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167
approach.
The parameter database provided valuable information in
the
development
of
the
empirically-based
model
application of the physically-based model.
developing
the
empirically-based model
and
the
Data used for
were
improved by
removing the footprints, which contained significant water
bodies
(based
on
information
on
locations
percentages of water bodies) from the database.
and
area
The database
made it possible to apply the single-footprint-based physical
model
to
large-scale
information
on
water
moisture
bodies,
retrieval
properties
by
of
providing
soils,
and
properties of vegetation covers.
The empirically-based model was improved by including
vegetation density as an independent variable.
be used to retrieve moisture over 70 mm
The model can
(which was the
limitation of previous empirical models). Since water bodies
and precipitation were
removed from the data
regression
analysis, this model is more reliable than previous models.
The single-footprint-based physical model was extended
to retrieve moisture over large areas (such as the Central
Plains and Western Desert areas of the United States) by
incorporating
framework.
it
into
the
integrated moisture
retrieval
Since soil porosity was used as an upper limit to
the predicted moisture, flooding can be detected.
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168
C. Recommendations
1.
The fuzzy logic-based classification method cannot
be used
to differentiate
between different
snow-covered
surfaces (such as wet snow, melting snow, snow with soil, or
snow with vegetation.)
More ground truth measurements are
needed
snow
for
different
or
snow-covered
conditions.
Further study can be done to understand the responses of
SSM/I brightness temperatures to different snow conditions,
and the classification method can be expanded to include land
surface with snow covers.
2.
The
physically-based
model
retrieve volume fraction of water.
done to
was
developed
to
Further research can be
develop the relationship between the Antecedent
Precipitation Index (API) and the volume fraction of water.
3.
Field
experiments
for
different
vegetation
conditions can be conducted to develop a relationship between
the Microwave Polarization Index (MPI) from SSM/I and the
Normalized Difference Vegetation Index
(NDVI)
from AVHRR.
This relationship is very useful in monitoring deforestation
and reforestation over large agricultural areas.
4.
developed
The
for
surface
the
moisture
continental
retrieval
United
extended to other regions of the world.
methodology,
States,
could
be
To implement this,
globe AVHRR data could be used to expand the water-body layer
in the parameter database. The other available soil resource
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
maps for the world are needed to extend soil layer.
The
vegetation conditions could be obtained based on the NDVI
from AVHRR data.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
170
REFERENCES
[1]
B. G. Gerard,
"Development of surface moisture
algorithms using Special Sensor Microwave/Imager (SSM/I)
s i g n a t u r e M.S. thesis, Utah State University, Logan,
UT, 1990.
[2]
C. M. U. Neale, M. J. McFarland, and K. Chang, "Landsurface-type classification using microwave brightness
temperatures from the Special Sensor Microwave/Imager,"
IEEE Trans. Geosci. Remote Sensing, vol. GE-28, no. 5,
pp. 829-838, Sept. 1990.
[3]
G. A. Vassiliades, "Development of a radiative transfer
model for the Special Sensor Microwave Imager (SSM/I)
and its application for retrieving surface moisture and
temperature."
Ph.D.
dissertation,
Utah
State
University, Logan, UT, 1993.
[4]
J. F. Heinrich, A. J. Koscielny, and R. C. Savage, "A
statistical surface type classifier for SSM/I data,"
presented at Shared Processing Network DMSP SSM/I
Algorithm Symposium, Monterey, CA, 1993.
[5] K. B. Kidwell,
NOAA Polar Orbiter Data User's Guide,
Washington,
DC: National Oceanic and Atmospheric
Administration, 1984.
[6 ] J. Hoilinger,
DMSP Special Sensor Microwave/Imager
Calibrations/Validation, Vol. I, Washington, DC: Naval
Research Lab., 1991.
[7]
M. J. McFarland, R. L. Miller, and C. M.U. Neale, "Land
surface temperature derived from SSM/I passive microwave
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
171
brightness temperature,"
IEEE Trans. Geosci. Remote
Sensing, vol. GE-28, no. 5, pp. 839-845, Sept. 1990.
[8 ]
F. T. Ulaby, R. K. Moore, and A. K. Fung,
Microwave
Remote Sensing: Active and Passive, Vol. I, II, and III.
Norwood, MA: Artech House, 1986.
[9]
F. T. Ulaby, M. Razani, and M. C. Dobson, "Effects of
vegetation cover on the microwave sensitivity to soil
moisture," IEEE Trans. Geosci. Remote Sensing, vol. GE21, no. 1, pp. 51-61, 1983.
[10] J. Hollinger, R. Lo. Poe, R. Savage, and J. Piece,
Special
Sensor
Microwave/Imager
User's
Guide,
Washington, DC: Naval Research Lab., 1987.
[11] J. C. Bezdek, C. Coray, R. W. Gunderson, and J. D.
Watson, "Detection and characterization of cluster
substructure," SIAM J. of Appl. Math., vol. 40, No. 2,
pp. 339-372, 1981.
[12] M. A. Jadkowski,
"Multispectral remote sensing of
landslide susceptible." Ph.D. dissertation, Utah State
University, Logan, UT, 1987.
[13] A. K. Sikka,
"A hydrologic model for studying the
influence of climate change on evapotranspiration and
water yield."
Ph.D.
dissertation,
Utah
State
University, Logan, UT, 1993.
[14] M. J. McFarland,
"The correlation of Skylab L-Band
brightness temperatures with antecedent precipitation,"
presented at Conference on Hydrometeorology, AMS,
Boston, MA, 1976.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
172
[15] M. J. McFarland, and B. J. Blanchard,
"Temporal
correlations of antecedent precipitation with Nimbus 5
ESMR brightness temperatures,"
presented at Second
Conference on Hydrometeorology, AMS, Boston, MA, 1977.
[16] G. D. Wilke, and M. J. McFarland, "Correlations between
Nimbus 7 scanning multichannel microwave radiometer
(SMMR) data and an antecedent precipitation index,"
JCAM, vol. 25, pp. 227-238, September, 1986.
[17] B. J. Choudhury, M. Owe, S. N. Goward, R. E. Golus,
J. P. Ormsby,
A. T. C. Chang,
and J. R. Wang,
"Quantifying spatial and temporal variabilities of
microwave brightness temperature over the U.S. Southern
Great Plains," Int. J. Remote Sens., vol. 8 , no. 2, pp.
177-191, 1987.
[18] M. Owe, A. Chang, S. N. Goward, and R. E. Golus,
"Estimating surface moisture from satellite microwave
measurements and a satellite derived vegetation index,"
Remote Sensing Envirom., vol. 24, pp. 331-345, August,
1988.
[19] G. H. Hargreaves, and Z. A. Samani,
"Reference crop
evapotranspiration from temperature," Trans. AM. Soc.
Agric. Eng., vol. 1, no. 2, pp. 96-99, 1985.
[20] B. J. Choudhury, T. J. Schmugge, A. Chang, and R. W.
Newton, "Effect of surface roughness on the microwave
emission from soils," J. Geophys. Res., vol. 84, no.
C9, pp. 5699-5706, 1979.
[21] H. K. Burke, and T. J. Schmugge,
"Effects of varying
soil moisture contents and vegetation canopies on
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
microwave emissions,"
IEEE Trans. Geosci.
Sensing, vol. GE-20, no. 3, pp. 268-274, 1990.
Remote
[22] A. D. Vyas,
A. J.
Trivedi,
0. P. N.
Calla, S. S.
Rana,
and S. B. Sharma,
"Remote sensing of soil
moisture over bare soil at microwave frequencies," Int.
J. Remote Sensing,vol. 9, no. 2, pp. 341-347, 1988.
[23] F. T. Ulaby,
P.
P. Batlivals,
and M. C. Dobson,
"Microwave backscatter dependence on surface roughness,
soil moisture, and
soil texture: Part I--bare soil,"
IEEE Trans. Geosic.
Remote Sens., vol. 16, no. 4, pp.
286-295, 1978.
[24] M.
C. Dobson,
F.
Kouyate,
and
F.
T.
Ulaby,
"A
reexamination of soil textural effects on microwave
emission and backscattering,"
IEEE Trans. Geosic.
Remote Sens., vol. 22, no. 6 , pp. 530-535, 1984.
[25] J. R. Wang, P. E. O'Neill, T. J. Jackson, and E. T.
Engman, "Multifrequency measurements of the effects of
soil moisture, soil
texture and surface roughness,"
IEEE Trans. Geosci. Remote Sensing, vol. GE-21, no. 1,
pp. 44-51, 1983.
[26] R. W. Newton,
and J. W. Rouse,
Jr.,
"Microwave
radiometer measurements of soil moisture content, " IEEE
Trans. Antennas and Propag., vol. AP-28, no. 5, pp. 6806 8 6 , 1980.
[27] J. R. Wang, J. C. Shiue, and J. E. McMurtrey,
"Microwave remote sensing of soil moisture content over
bare and vegetated fields," Geophys. Res. Letters, vol.
7, no. 10, pp. 801-804, 1980.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
174
[28] H. K. Burke, and T. J. Schmugge,
"Effect of varying
soil moisture contents and vegetation canopies on
microwave emissions,"
IEEE Trans. Geosci.
Sensing, vol. 20, no. 3, pp. 268-274, 1982.
Remote
[29] S. W. Theis, and A. L. Blanchard,
"The effect of
measurement error and confusion from vegetation on
passive microwave estimates of soil moisture," Int. J.
Remote Sens., vol. 9, no. 2, pp. 333-340, 1988.
[30] F. Becker, and B. J. Choudhury, "Relative sensitivity of
Normalized Difference Vegetation Index (NDVI) and
Microwave Polarization Difference Index (MPDI) for
vegetation and desertification monitoring," Remote
Sensing Envirom., vol. 24, pp. 297-311, August, 1988.
[31] K. P. Gallo, and C. S. T. Daughtry, "Differences in
vegetation indices for simulated Landsat-5 MSS and TM,
NOAA-9, AVHRR, and Spot-1 Sensor Systems,"
Remote
Sensing Envirom., vol. 23, pp. 439-452, August, 1987.
[32] C. L. Wiegand, A. J. Richardson, and E. T. Kanemasu,
"Leaf area index estimates for wheat from LANDSAT and
their implications for evaportranspiration and crop
modeling," Agronomy Journal, vol. 71, pp. 179-182,
February, 1979.
[33] C. 0. Justice, J. R. G. Townshend, B. N. Holben, and
C. J. Tucker,
"Analysis of the phenology of global
vegetation using meteorological satellite data," Int.
J. Remote Sensing, vol. 6 , no. 8 , pp. 1271-1318, 1985.
[34] S. N. Goward, C. J. Tucker, and D. G. Dye,
American vegetation patterns observed with
"North
NOAA-7
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
175
advanced very high resolution radiometer," Vegetation,
vol. 64, no. 1, pp. 3-14, 1985.
[35] S. R. Schneider, Jr. McGinnis, D. F., and G. Stephens,
"Monitoring Africa's Lake Chad basin with LANDSAT and
NOAA satellite data,11 Int. J. Remote Sensing, vol. 6 ,
no. 1, pp. 59-73, 1985.
[36] C.
J.
Tucker,
J.
R. G. Townshend,
and T.
E. Goff,
"African land-cover classification using satellite
data," Science, vol. 227, pp. 369-375, July, 1985.
[37] C. J. Tucker,
I. Y. Fung,
C. D. Keeling, and R. H.
Gammon,
"Relationship
between
atmospheric
C02
variations and a satellite-derived vegetation index,"
Nature, vol. 319, pp. 195-199, November, 1986.
[38] K. P. Gallo, and T. R. Heddinghaus,
"Large area crop
monitoring with the NOAA AVHRR: Estimating the silking
stage of corn development," Remote Sensing Envirom.,
vol. 27, pp. 73-80, September, 1989.
[39] J. P. Malingreau,
"Global vegetation dynamics:
satellite observations over Asia,"
Int. J. Remote
Sensing, vol. 7, no. 9, pp. 1121-1146, 1986.
[40] J. A. Gatin, R. J. Sullivan, and C. J. Tucker,
"Monitoring global vegetation using NOAA AVHRR data,"
in Proc. of the IGAARS Symposium, San Francisco, 1990,
p. 23.
[41] A. Schwalb, "The Tiros-N/NOAA-A to G satellite series,"
National Technical Information Service, U.S. Dep.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
176
Commerce,
1978.
Springfield, VA, NOAA Tech. Memo. NESS 95,
[42] J. C. Eidenshink,
"The 1990 conterminous U. S. AVHRR
data set,"
Photogrammetric Engineering and Remote
Sensing, vol. 58, no. 6 , pp. 809-813, 1982.
[43] SCS Agricultural Handbook, Land Resource Regions and
Major Land Resources Regions and Major Land Resource
Areas of the United States. Washington, DC: USDA-SCS,
1981.
[44] L. Ott, An Introduction to Statistical Methods and Data
Analysis, North Scituate, MA: Duxbury Press, 1977.
[45] R. W. Gunderson,
"Adaptive FCV clustering algorithm,"
Int. J. Man-Machine Studies, vol. 19, no, 2, pp. 97-104,
1983 .
[46] R. W. Gunderson,
and R.
Canfield, "Piece-wise
multilinear prediction from FCV disjoint principal
component models,"
Int. J.General Systems, vol. 16,
no. 1, pp. 373-383, 1990.
[47] B. Kosko, Neural Networks and Fuzzy Systems: A Dynamical
Systems Approach to Machine Intelligence, Englewood
Cliffs, N J : Prentice-Hall, Inc., 1992.
[48] R. L. Donahue, R. W. Miller, J. C. Shickluna, and J. U.
Miller, Soil: An Introduction to Soil and Plant Growth.
Englewood Cliffs, NJ: Prentice-Hall, Inc., 1983.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
177
APPENDIX
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
178
LAMBERT AZIMUTHAL EQUAL AREA PROJECTION
Parameters:
Radius of sphere
6,370,997.0 meters
Longitude od central merdian
100 00 00 West
Latitude of origin
45 00 00 North
False easting
0
Unites of measure
meters
Pixel size
1,000 meters
For the conterminous United States:
Center of pixel (1,1)
(-2050500,
Number of lines
2,889
Number of samples
4,587
752500)
LAZEA minimum bounding rectangle:
In projection meters:
Lower Left
(-2050500,
-2136500)
Upper left
(-2050500,
752500)
Upper right
( 2536500,
752500)
Lower right
( 2536500,
-2136500)
In decimal degrees of latitude and longitude:
Lower
left
(-119.9722899 23.5837576)
Upper
left
(-128.5300591 48.4030555)
Upper
right
( -65.3946489 46.7048989)
Lower
right
(-75.4163527 22.4793919)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
179
In degrees, minutes, and seconds of latitude and
longitude:
Lower left
(-119 58 24
23 35
0 2
)
Upper left
(-128 31 48
48 24
1 1
)
Upper left
( -65 23 41
46 42 18)
Upper right
( -75 24 59
22
28 46)
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
180
CURRICULUM VITAE
Xin Qiu
CAREER OBJECTIVE:
An electrical engineer with emphasis in Communication,
Signal and Image Processing.
EDUCATION:
Ph.D. in Electrical and Computer Engineering, Utah State
University (1995).
M.S. in Electrical Engineering, Hunan University, China
(1987).
B.S. in Electrical Engineering, Hunan University, China
(1984) .
EXPERIENCE:
Research Assistant at Remote Sensing Service, Utah State
University (3/9 - 8/95) .
- developed different algorithms for remote sensing
applications based on SSM/I and AVHRR data.
- developed an algorithm for automatically performing
image registration on natural color and
multispectral digital video imagery from airborne
system.
Research
Assistant at Electrical
and Computer
Engineering Department, Utah State University (6/91 3/93) .
- performed research on error correction coding for bans
limited channels.
Teaching
Assistant
at
Electrical
and
Computer
Engineering Department, Utah State University (9/90 6/91).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
181
- was responsible for preparing homework solutions,
grading homework and answering students' questions for
signal analysis and stochastic signal processing
classes.
Assistant Professor at Radio Engineering Department,
Southeast University, China (12/86 - 12/89).
- involved in research on Switched Capacitor Circuit
Design and Adaptive Signal Processing.
- developed and taught undergraduate courses on Signal
Analysis, Circuit Theory, and Computer-aided Circuit
Analysis and Design.
SELECTED PUBLICATIONS:
1.
"Computation-efficient
algorithms
for
image
registration," X. Qiu, C. H. Chong, C. M. Huang
and C. M. U. Neale,
Proc.SPIE Conference on
Visual Communications and Image Processing, Oct.
1994.
2.
"Image enhancement and processing video imagery,"
C. M. U. Neale, J. Kuiper, T. K. Tarbet and X.
Qiu, Proc. of the 14th Biennial Workshop on Color
Aerial Photography and Videography for Resource
Monitoring, May 1993.
3.
"Image compression with the Wavelet transform," J.
Argest, M. Rampton, X. Qiu and T. Moon, Proc. SPIE
Conference on VisualCommunications and Image
Processing, Oct. 1993.
4.
"New structure of switched-capacitor circuit with
reduced
GB
effect,"
X. Qiu,
Electronics, Vol. 6 , China, 1989.
Journal
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