On Estimation of Soil Moisture with SAR Jiancheng Shi ICESS University of California, Santa Barbara.
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Transcript of On Estimation of Soil Moisture with SAR Jiancheng Shi ICESS University of California, Santa Barbara.
![Page 1: On Estimation of Soil Moisture with SAR Jiancheng Shi ICESS University of California, Santa Barbara.](https://reader034.fdocuments.us/reader034/viewer/2022051821/5697bf8a1a28abf838c8a8a1/html5/thumbnails/1.jpg)
On Estimation of Soil Moisture with SAROn Estimation of Soil Moisture with SAR
Jiancheng Shi
ICESS
University of California, Santa
Barbara
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Importance of Water CircleImportance of Water Circle
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Electromagnetic SpectrumElectromagnetic Spectrum
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Why Synthetic Aperture Radar?Why Synthetic Aperture Radar?
• Advantages:
• All weather free
• All day free
• High resolution
• Penetration thickness information
•Very sensitive to Moisture
• Disadvantages:
• Expensive
• Large data volume
• More difficult in image analyses
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Synthetic Aperture Radar (SAR)Synthetic Aperture Radar (SAR)
10
1978 Seasat (Lhh)
CCRS, Canada
1984SIR-B (Lhh)
1981SIR-A (Lhh)
SIR-C/XSAR(L,C Quad pol, Xvv)
2000
SRTM, InSARC Wide SwathX Narrow, Hi Res
NASA, USA
NASDA, Japan
ESA, European
1991ERS-1Cvv
1996ERS-2Cvv
1992JERS-1Lhh
2001 ASARENVISAT-1C, Multi Pol
2002RADARSAT-2C, Multi Pol
1996RADARSAT-1Chh
200?
2002ALOS-PALSARL, Multi Pol
LightSARL Quad PolX Hi Res
1994
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OutlineOutline
1. Surface Backscattering On Modeling :
• Tradition Backscattering Models
• Integral Equation Model
• Dielectric and Roughness Properties
2. On Estimate Bare Surface Soil Moisture• Current Inverse Techniques
• Examples from AIRSAR and SIR-C
3. On Estimate Vegetated Surface Soil Moisture• Radar Decomposition Technique
• Proposed Technique Using Multi-Temporal Measurements and its demonstration
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Small Perturbation ModelSmall Perturbation Model
pq = vv or hh
is the fourier transform of the surface correlation function. 0,2 xkW
0),sin(2)(cos82424 kWsk pq
opq
22 ))sin((exp2
10),sin(2 kllkW
5.12
2
))sin(2(120),sin(2
kl
lkW
Exponential
Guass
Validity Condition: ks < 0.3, kl < 3 & rms slope < 0.3
hh
s
( )
(cos sin )
12 2 22
22
)sin(cos
)sin)sin1()(1(
ss
vv
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Physical Optical ModelPhysical Optical Model
is nth power of fourier transform of the surface correlation function. 0,2 xn kW
2
22
22
)sincos(
)sincos()(
vvR 2
)()( hhhhR
0),sin(2!
))cos(2())cos(2(exp)()(cos
1
2222 kW
n
ksksRk n
n
n
pqopq
n
kl
n
lkW n
22 ))sin((exp0),sin(2
5.122
2
))sin(2(0),sin(2
kln
nlkW n
Guass
Exponential
Validity Condition: 0.05λ < s < 0.15λ, l > λ, & m < 0.25
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Geometric Optical ModelGeometric Optical Model
)(cos)0("2
)0("2)(tanexp)0(
42
2
2
s
sRpq
opq
)0("22 sm
2
1
1)0()0(
hhvv RR
Validity Condition: s > λ/3, l > λ, & 0.4 < m < 0.7
rms slope - m
Reflectivity
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Dielectric Properties of Soil Dielectric Properties of Soil
Solid Material - 4.7
Water - frequency & temperature
Soil - frequency, moisture, temperature, and texture
Im D
C
Clay 80% & Sand 20%
Clay 20% & Sand 80%
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Surface Roughness Measurement Surface Roughness Measurement
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Surface Roughness PropertiesSurface Roughness Properties
• Stationary Random Rough Surface
• Description:• surface rms. Height
• correlation length
• correlation function
correlation function
1/e
GaussExponential
2/122 zzs
1)( el
dxxz
dxxzxz
)(
)()()(
2
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Surface Roughness Correlation Functions Surface Roughness Correlation Functions
Surface Roughness Measurements at Washita Site
n
l
xx exp)(
power spectral density function
Characteristics:
• Exponential function has higher frequency components
Power spectrum FT surface profile or correlation function
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Problems in Roughness MeasurementsProblems in Roughness Measurements
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Simulation of Surface RoughnessSimulation of Surface Roughness
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Effect of Multi-scale Surface roughness on Backscattering
Effect of Multi-scale Surface roughness on Backscattering
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Validity Regions of Classical Surface Backscattering Models
Validity Regions of Classical Surface Backscattering Models
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Measured Co-Polarization Ratio by ScatterometerMeasured Co-Polarization Ratio by Scatterometer
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Integral Equation Model (1)Integral Equation Model (1)
!
0,22exp
2
/,cos4)(2
1
222
0
n
kWIk
k
II
xn
n
nppz
ipsspspp s
where kZ = k cos, kX = k sin, and pp = vv or hh,
2
0,0,exp2 22 xppxpp
nz
zppn
znpp
kFkFkkfkI
the symbol is the Fourier transform of the nth power of the surface correlation coefficient.
0,2)(x
n kW
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Integral Equation (2)Integral Equation (2)
cos/2cos/2 || RfRf hhvv
22
222||
2
cos
cossin11
cos
1sin20,0,
r
rrr
rxvvxvv
RkFkF
22
2222
cos
cossin11
cos
1sin20,0,
r
rrr
rxhhxhh
RkFkF
where, are the Fresnel reflection coefficients for horizontal and vertical polarization.
RR ,||
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Comparing IEM Model with SIR-C & AIRSAR Measurements
Comparing IEM Model with SIR-C & AIRSAR Measurements
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Summary on Surface Scattering ModelsSummary on Surface Scattering Models
• Surface roughness parameters are described by the surface
auto-correlation function, rms height, and correlation length
• Tradition surface scattering models (SP, PO, and GO) are
outside of application range due to restrictions on surface
roughness parameters
• Recently developed IEM model has much wider application
range for surface roughness parameters
• Research is needed for better techniques to describe natural
surface properties
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Current Concept on Using Repeat-pass Measurements Current Concept on Using
Repeat-pass Measurements
Basic Concept
•
• Two measurements => the relative change in
dielectric properties
• The absolute dielectric properties <= one
measurement is known
),,()( 21 rrpp sorsff
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Problem of Repeat-pass Measurements
Problem of Repeat-pass Measurements
Problems:
• Large dynamic range ks & kl
=> a different response of
dielectric properties
• Roughness effects can not be
eliminated
•Effect is greater
• VV than HH
• large incidence than small incidence
Normalized Polarization functions - R/min(R)
SP-VV
SP-HH
GO
Relative moisture change in %
23°
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Current Techniques Using Polarization Measurements
Current Techniques Using Polarization Measurements
Basic understanding on HH and VV difference:
• As dielectric constant , the difference
• As roughness (especially rms height) , the difference
• As incidence angle , the difference
Common idea of the current algorithms
•
• Inverse - two equations two unknowns.
),,()( 21 rrpp sorsff
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Current Algorithms for Bare Surface (1) Current Algorithms for Bare Surface (1)
p kshh
vv
{ ( ) exp( )}/12 1 3 20
q kshv
vv
0 23 10. [ exp( )]
0
21
1
Oh et al., 1992.
•Semi-empirical model ground scatterometer measurements
•Using 3 polarizations 2 measurements
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Current Algorithms for Bare Surface (2) Current Algorithms for Bare Surface (2)
Dubios et al., 1995
hh ks 10 102 75
1 5
50 028 1 4 0 7.
.. tan . .(
cos
sin) ( sin )
vv ks 10 102 35
3
30 046 11 0 7. . tan . .(
cos
sin) ( sin )
• Semi-empirical model ground scatterometer measurements
• Using 2 co-polarizations 2 measurements
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Current Algorithms for Bare Surface (3) Current Algorithms for Bare Surface (3)
Shi et al., 1997.
• Semi-empirical model IEM simulated most possible conditions
• Using 2 combined co-polarizations 2 measurements
pp
opp
R
pp pp R
S
a b S
2
( ) ( )
10 1010
2 2
10log ( ) ( ) log
vv hh
vvo
hho vh vh
vv hh
vvo
hho
a b
S ks WR ( )2
hh
o
vvo
hh
vv
r r ra ks b c W 2
2exp[ ( ) ( ( ) ( ) ]
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Study Site Description Study Site Description
1992 Soil Moisture Experiment
1992 Soil Moisture Experiment
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0
-12
-9
-3
-6
dB
Experimental Description JPL L-band AIRSAR (June 10 – 18, 1992)
Experimental Description JPL L-band AIRSAR (June 10 – 18, 1992)
VV
HH
HV
Ju
ne
12
Ju
ne
18
Ju
ne
16
Ju
ne
13
VV
dif
fere
nce
to
firs
t d
ay
Ju
ne
15 J
un
e 10
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Estimated Surface Soil Moisture MapsEstimated Surface Soil Moisture Maps
vegetation
<4 %
8-12
12-16
4-8
28-32
32-36
20-24
16-20
24-28
> 36 %
June
10
Jun
e 15
Jun
e 18
Jun
e 13
Jun
e 16
Jun
e 12
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Estimated Surface Roughness ParameterEstimated Surface Roughness Parameter
vegetation
< -24 dB
-22--20
-20--18
-24--22
-12--10
-10--8
-16--14
-18--16
-14--12
> -8 dB
Jun
e 12
Jun
e 10
Jun
e 13
Jun
e 15
Jun
e 16
Jun
e 18
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Estimated Surface Soil Moisture Maps Using SIR-C’s L-band in April, 1994
Estimated Surface Soil Moisture Maps Using SIR-C’s L-band in April, 1994
vegetation
<4 %
8-12
12-16
4-8
28-32
32-36
20-24
16-20
24-28
> 36 %
12 13 15
16 17 18
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Comparing Field MeasurementsComparing Field Measurements
Standard Error (RMSE) 3.4% in Soil Moisture estimation
Standard Error (RMSE) 1.9 dB in roughness estimation
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Basic Consideration (1)Basic Consideration (1)
Common idea of the current algorithm
•
• Inverse - two equations two unknowns. It can be
re-ranged to one equation for one unknown.
Disadvantages:
• Requires both formula all in good accuracy
• Error in the estimated one unknown the other
),,()( 21 rrpp sorsff
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Basic Consideration (1) - continueBasic Consideration (1) - continue
)log(36.3)log(09.3)log(
)log(78.4)log(79.319.2))(log(
)log(57.2)log(09.203.2)log(2
hhvvh
hhvvr
hhvv
R
WksS
ks
in (a)
in (b)
in (c)
• Different weight sensitive to different surface parameter
• Independent direct estimation of soil moisture and RMS height
(a) ks (b) Sr (c) Rh
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Basic Consideration (2)Basic Consideration (2)
IEM -- Power expansion and nonlinear relationships
!
)0,2(||2exp
2 1
22222
n
kWIssk
k x
n
n
n
pp
n
z
o
pp
Higher order inverse formula improve accuracy
Example: estimate surface RMS height
28.0
),()2(
RMSE
f hhvv
36.0
),()1(
RMSE
f hhvv
ss
s’ s’
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Basic Consideration (3)Basic Consideration (3)
Polorization Magnitude Roughness function
SP
PO
GO
Tradition Backscattering Models
222 )sin(exp)()( klklks
2
2
sincos
sincos
rr
rr
)1()1(rr )
2
tanexp(
2
1 2
mm
n
kl
nn
kl
klkl
n
n
4
)(exp
!
)cos(
)sin(exp)(
2
1
22
22
22
sincos
sin1sin)1(
rr
rr
• Inverse model for different roughness region improve accuracy
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Validation Using Michigan's Scatterometer DataValidation Using Michigan's Scatterometer Data
Correlation: mv - 0.75, rms height - 0.96
RMSE: mv - 4.1%, rms height - 0.34cm
mv SRMSE for S
Measured parameters
Est
imat
ed
incidence
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Characteristics of Backscattering ModelCharacteristics of Backscattering Model
(4)
)()( ppsvv
ppvv
ppt ff
)()1()( 2 ppsvpp
ppsv fLf
First-order backscattering model
•Surface parameters – surface dielectric and roughness properties
•Vegetation parameters – dielectric properties, scatter number densities, shapes, size, size distribution, & orientation
2
)(
)(
)(
pp
ppsv
pps
ppv
v
L
f
Fraction of vegetation cover
Direct volume backscattering (1)
Direct surface backscattering (4 & 3)
Surface & volume interaction (2)
Double pass extinction
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Radar Target Decomposition Radar Target Decomposition
Covariance (or correlation) matrix
000
01
*
cT
Decomposition based on eigenvalues and eigenvectors
'331
'221
'111 kkkkkkT
where, are the eigenvalues of the covariance matrix, k are the eigenvectors, and k’ means the adjoint (complex conjugate transposed ) of k.
*hhhh SSc *
*
hhhh
vvhh
SS
SS
*
*2
hhhh
hvhv
SS
SS
*
*
hhhh
vvvv
SS
SSand
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Radar Target Decomposition TechniqueRadar Target Decomposition Technique
Total Power:
single, double, multi
Total Power:
single, double, multiVV:
single, double, multi
VV:
single, double, multi
HH
Correlation or covariance matrix -> Eigen values & vectors
Correlation or covariance matrix -> Eigen values & vectors
TTT *333
*222
*111 KKKKKKT
VV
, HH
, VH
VV
, HH
, VH
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Relationships in scattering components between
decomposition and backscattering model
Relationships in scattering components between
decomposition and backscattering model
1. First component in decomposition (single scattering) – direct volume, surface & its passes vegetation
2. Second component (double-bounce scattering) – Surface & volume interaction terms
3. Third component – defuse or multi-scattering terms
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Properties of Double Scattering Component
under Time Series Measurements
Properties of Double Scattering Component
under Time Series Measurements
1. Variation in Time Scale
• surface roughness
• vegetation growth
• surface soil moisture
2. In backscattering Model
3. Ratio of two measurements• independent of vegetation
properties
• depends only on the reflectivity ratio
)()()(2)( 2 ppppspp
ppsv dLR
npp
mpp
npp
mpp
R
R
2
2
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Comparison with Field MeasurementsComparison with Field MeasurementsV
V, H
H, V
HV
V, H
H, V
H
Two Corn Fields Dielectric Constant
Date
nhhnvv
mhhmvv
RR
RR
nhhnvv
mhhmvv
22
22
nhhnvv
mhhmvv
22
22
Normalized VV & HH cross
product of double scattering components for any n < m
Corresponding reflectivity ratio
nhhnvv
mhhmvv
RR
RR
Correlation=0.93, RMSE=0.42 dB
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Estimate Absolute Surface Reflectance Estimate Absolute Surface Reflectance
A)
B)
C)
2
2
||
||
mvv
nvvvnmA
2
2
||
||
mhh
nhhhnmA
mhh
nhh
mvv
nvvcnmA
||
||
||
||
)( cnm
vnm AfA )( c
nmhnm AfA
2
2222
||
||1||||||
mhh
nhhnhhmhhnhh
hnm
mhhnhhnhh A
1
||||||
222
hnm
vnm
hnm
vnm
mhhnhh AA
AAf22 ||||
A)
)log()log( cnm
vnm AA
B)
C) estimation
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Current EvaluationsCurrent Evaluations
• Validity range of the second component measurements
– Effect of radar calibration and system noise
– What type and vegetation condition?
• How to obtain vegetation and surface roughness information
– What we can do with the first component measurements?
• What to do with sparse vegetated surface?
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SummarySummary
• Time series measurements with second decomposed
components (double reflection) – A promising (direct and simple technique) to estimate the
relative change in dielectric constant for certain type of the vegetated surfaces
– A great possibility to derive soil moisture algorithm for the vegetated surface
• Advantages of this technique– Do not require any information on vegetation
– Can be applied to partially covered vegetation surface