On Estimation of Soil Moisture with SAR Jiancheng Shi ICESS University of California, Santa Barbara.
-
Upload
jack-george -
Category
Documents
-
view
215 -
download
0
Transcript of On Estimation of Soil Moisture with SAR Jiancheng Shi ICESS University of California, Santa Barbara.
On Estimation of Soil Moisture with SAROn Estimation of Soil Moisture with SAR
Jiancheng Shi
ICESS
University of California, Santa
Barbara
Importance of Water CircleImportance of Water Circle
Electromagnetic SpectrumElectromagnetic Spectrum
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
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
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
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
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
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
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%
Surface Roughness Measurement Surface Roughness Measurement
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
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
Problems in Roughness MeasurementsProblems in Roughness Measurements
Simulation of Surface RoughnessSimulation of Surface Roughness
Effect of Multi-scale Surface roughness on Backscattering
Effect of Multi-scale Surface roughness on Backscattering
Validity Regions of Classical Surface Backscattering Models
Validity Regions of Classical Surface Backscattering Models
Measured Co-Polarization Ratio by ScatterometerMeasured Co-Polarization Ratio by Scatterometer
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
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 ,||
Comparing IEM Model with SIR-C & AIRSAR Measurements
Comparing IEM Model with SIR-C & AIRSAR Measurements
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
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
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°
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
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
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
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[ ( ) ( ( ) ( ) ]
Study Site Description Study Site Description
1992 Soil Moisture Experiment
1992 Soil Moisture Experiment
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
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
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
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
Comparing Field MeasurementsComparing Field Measurements
Standard Error (RMSE) 3.4% in Soil Moisture estimation
Standard Error (RMSE) 1.9 dB in roughness estimation
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
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
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’
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
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
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
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
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
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
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
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
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
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?
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