[2024]Digital Global Overview Report 2024 Meltwater.pdf
ShaowuHuang_IGARSS2011_final.pdf
1. Like polarization and Cross polarization of Radar remote
sensing of soil moisture at L band: 3D numerical simulations
of Maxwell equations, Analytical models, and Retrieval
Performance in Soil Moisture Retrieval
Shaowu Huang1, Xueyang Duan2, Jeff Ouellette3, Xiaolan Xu1, Tien-hao Liao1,
Joel Johnson3, Mahta Moghaddam2, Leung Tsang1
1Dept. of Electrical Engineering, Univ. of Washington, Seattle, WA
2Dept. of Electrical and Computer Engineering, Univ. of Michigan, Ann Arber, MI
3 Dept. of Electrical and Computer Engineering, Ohio State Univ., OH
2. Outline
Forward model
– 5 Tests of Accuracies for Numerical Model (NMM3D):
– Model Comparisons for full bistatic patterns:
– Model Comparisons with In-Situ Measurements
3 to 3 Retrieval algorithm for bare soil surfaces
– VV, HH and VH to retrieve permittivity, rms height and
correlation lengths
– Results and comparisons with other algorithms:
Dubois’, Oh’s, and Shi’s 2 to 2 approaches
3. Surfaces with Exponential Correlation
Functions are Used in the Study
2
Exponential Correlation Function:
Gaussian Surface
1.5 Expoential Surface
1
x2 y2
C ( x, y) h exp(
2
)
z = f(x) (wavelengths)
l 0.5
Spectral density : 0
-0.5
h 2l 2
W (k ) -1
2 [1 (kl) 2 ]
3
2
-1.5
-30 -20 -10 0 10 20 30
x (wavelengths)
Land surface (soil surfaces): (a) Comparison of 1D Exponential and
large slope , Gaussian Surfaces used in 2D simulations
fine scale features,
small to moderate height
(b) 2D Exponential Surface Used in 3D 3
Simulations
4. Model Comparisons for Bare Soil Surfaces
Numerical Models:
Hybrid UV/PBTG/SMCG method based on NMM3D
Stabilized Extended Boundary Condition Method (SEBCM)
Analytical Models
Small perturbation method (SPM)
Advance Integral equation Model (AIEM)
Small Slope Approximation (SSA)
Reduced Local Curvature Approximation (RLCA)
Empirical Models:
Dubois formulas
4
5. 5 Tests of Accuracies of NMM3D
1) Convergence with discretization sampling
2) Convergence with respect to surface area
– Physical Results for incoherent wave convergence as surface
area increases
– Unique test for random rough surface
3) Convergence with respect to realizations
– Maxwell Equations give coherent solution and have speckle
– Unique test for random rough surface
4) Energy conservation test for each realization
5) Reciprocity test for each realization
6. Tests of Reciprocity for Each Realization
To Verify the Accuracy of Cross-pols
Reciprocity means
σvh =σhv
Notes:
Exchange transmitter and receiver means same result
Not obeyed in some analytic models
6
7. Tests of Reciprocity for Each Realization
To Verify the Accuracy of Cross-pols
32 by 32 square wavelengths 16 by 16 square wavelengths
0 0
-5 -5
Cross-pol Bistatic Coefficients in dB
Cross-pol Bistatic Coefficients in dB
-10 -10
-15 -15
-20 -20
-25 -25
-30 -30
-35 -35
2
-40 2 -40 HV 16 by 16
HV 32 by 32
2
-45 2 VH 16 by 16
VH 32 by 32 -45
-50
-80 -60 -40 -20 0 20 40 60 80 -50
-80 -60 -40 -20 0 20 40 60 80
Scattering angles in degree Scattering angles in degree
Notes:
Backscattering (-40 degrees): HV = VH
other directions do not have reciprocity condition
7
8. Co-pol Full Incoherent Bistatic Patterns
RMS height = 1cm, NMM3D
Notes:
Strong bistatic values in specular region
Weak bistatic values in backscattering region
Minimum bistatic values in rotated 90o region 8
9. Cross-pol Full Incoherent Bistatic Pattern
RMS height = 1cm, NMM3D
Notes:
Strong bistatic values in rotated 90o region
(important for double bounce of vegetated surfaces)
Weak bistatic values in specular region
Minimum bistatic values at backscattering region 9
10. Cross-pol Full Incoherent Bistatic Pattern
RMS height = 1cm, NMM3D
(a) y=0 plane Incident on (b) x=0 plane
y=0 plane
Notes:
Cross-pols are smaller than co-pols in y=0 plane
15 dB smaller at backscattering direction
10
Cross-pols are stronger than co-pols in x=0 plane
15. Comparison with Michigan’s experimental data
POLARSCATTER Data-3 observed by truck-mounted
polarimetric scattermeter
Including1.25 GHz and incident angle 40 degrees
Surface roughness (rms heights and correlation) and soil
permittivities were measured
Measured autocorrelation function was found to be
closer to exponential for most soil surfaces
19. Backscattering Coefficients:
NMM3D rms heights up to 8 cm
-4
-5
-6
Backscattering Coefficients
-7
-8
-9
VV =22.0+i4.0
-10 r
HH =22.0+i4.0
-11 r
VV =9.0+i2.5
-12 r
HH =9.0+i2.5
-13 r
-14
-15
2 3 4 5 6 7 8
RMS height in centimeters
20. Backscattering Coefficients:
NMM3D permittivities 3 to 30 cm
-4
-5
-6
Backscattering Coefficients
-7
-8
-9
-10
VV rms height=6cm
-11
HH rms height=6cm
-12 VV rms height=4cm
HH rms height=4cm
-13
-14
-15
0 5 10 15 20 25 30
Real part of permittivities
21. Retrieval Algorithm
for Bare Soil Surfaces without Vegetations
• Michigan Data Set: Many soil moistures, but only 4
sets of rms height/correlation lengths
roughness parameters of rms
heights and correlation
lengths: Michigan data only
have four points in the range
The NMM3D simulations were
performed in the blue dot
range
22. Past retrieval algorithms: 2 to 2
• Dubois
– Using two co-pol, directly solve for soil moisture
• Oh’s Method rms,
mv
• Shi’s Method
Many cases of AIEM model statistically fit by the following eqn for
coefficients avh and bvh; alpha’s are Fresnel coeffcients;
Use backscattering data to get permittivity
Inverse
23. Performance of retrieval algorithms on
Michigan data
All these algorithms work for that specific
combination of cl and rms
24. Performance of retrieval algorithms on
NMM3D datasets
All these method shows problems when
considering more rough surface condition.
25. Retrieval algorithm: 3 to 3 using Look-Up
Table (LUT) of NMM3D
• Use all 3 channels: VV, HH, VH
• Three parameters: soil moisture, rms height
and correlation length
• Least squared method to search for the
closest solution.
vv , hh , hv
min(d (vv, hh, hv)) pq
0 (ms, rms, cl )
pq
26. Test data separation
From the
NMM3D and Two sets Add noise
interpolation
0 SNR
Test Data
Original 2dB SNR
LUT
Validation Perform
Table Retrieval
27. LUT retrieval algorithm validation
Test data without noise Test data with 2dB noise
Retrieval good performance;
Cross pol strongly dependent on rms height/correlation
28. Summary
Forward model:
• 5 accuracy tests were performed to validate the NMM3D (UV/PBTG/SMCG)
• NMM3D, SSA and SEBCM were compared for both Co-pol and Cross-pol full
bistatic patterns:
• NMM3D backscattering coefficients up to rms height 8cm
• Model Comparisons with Michigan experimental data
Co-pols agree better than cross-pols
NMM3D using 16 by 16 square wavelengths have the best comparisons
Retrieval algorithm for bare soil
• 3 to 3 algorithm based on NMM3D LUT (Look up Table)
• Past 2 to 2 algorithms: Oh’s, Dubois’, and Shi’s
• 3 to 3 algorithm has good performance on test data of NMM3D
