Electromagnetic Models In Active And Passive Microwave Remote Sensing of Terrestrial Snow Leung Tsang 1 , Xiaolan Xu 2 and Simon Yueh 2 1 Department of Electrical Engineering, University of Washington, Seattle, WA 2 Jet Propulsion Laboratory, Pasadena, CA
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Electromagnetic Models In Active And Passive Microwave Remote Sensing of Terrestrial Snow
Electromagnetic Models In Active And Passive Microwave Remote Sensing of Terrestrial Snow. Leung Tsang 1 , Xiaolan Xu 2 and Simon Yueh 2 1 Department of Electrical Engineering, University of Washington, Seattle, WA 2 Jet Propulsion Laboratory, Pasadena, CA. Radiative Transfer Equation. - PowerPoint PPT Presentation
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Electromagnetic Models In Active And Passive
Microwave Remote Sensing of Terrestrial Snow
Leung Tsang1, Xiaolan Xu2 and Simon Yueh2
1Department of Electrical Engineering, University of Washington, Seattle, WA2Jet Propulsion Laboratory, Pasadena, CA
Radiative Transfer Equation
2
' ' '
'
' '
ˆ,ˆ ˆ ˆ ˆ ˆ, , ,
ˆ ˆ, : Intensity at in direction
: extinction coefficient
ˆ ˆ ˆ ˆ, : scattering from direction to direction
e
e
dI r sI r s ds P s s I r s
dsI r s r s
P s s s s
'ˆ ˆ,P s s
Dense Media Radiative Transfer Equation (DMRT)Model 1) QCA
◦ Analytical Approximate Solution of Maxwell Equations
Model 2) Foldy Lax equations◦ Numerical Maxwell Equation Model (NMM3D)
Since 2009, Model 3) Bicontinuous medium: ◦ Numerical Maxwell Equation Model (NMM3D)◦ Bicontinuous media; Realistic microstructure of
snow◦ Comparisons With SnowSCAT
3
DMRT Models
4
QCA Foldy Lax BicontinuousModel Spheres, pair
distribution functions
Computer generation of spheres
Computer generation of
snow microstructures
2 Size parameters
Particle diameter (2a);
Stickiness (τ)
Particle diameter (2a);
Stickiness (τ)
<ζ>; b
Solution method
Analytical QCA Numerical solution of Maxwell equation using Foldy-Lax
equations
Numerical solutions of
Maxwell equations using DDA / FFT
Quasi-Crystalline Approximation (QCA)
Lorentz-Lorenz law; Generalized Ewald-Oseen theorem Phase matrix, pair distribution function and
structure factor Structure factor is the Fourier transform of
5
3
1( ) ( ( ) 1)(2 )
ip rH dr g r e
g r
1h r g r
)()()( 21111 qfP
)()()( 22222 qfP
max( ) ( ) ( ) ( )
111
1 2 1( ) (cos ) (cos )( 1)
NM M N N
n n n n n nnr
nf T X T XkK n n
max
( ) ( ) ( ) ( )22
1
1 2 1( ) (cos ) (cos )( 1)
NM M N N
n n n n n nnr
nf T X T XkK n n
))()2(1()( 300 Hnnq
Diameter = 1.4 mm; Stickiness parameter τ=0.1; stickiness, adhere to form aggregates QCA sticky has weaker frequency dependence than
Mie scattering
101
102
10-4
10-3
10-2
10-1
100
101
102
103
Frequency [GHz]
s [1 /
m]
Scattering Coefficient
s By Mie Scattering
s By QCA Sticky Particles
s By Non-Sticky Particles
Scattering Rate: QCA Compared With Classical Mie Scattering
Brightness temperature increases with for the same κS
◦ Physical temperature is 250 K◦ Optical thickness = κSd; All curves have same κS
Passive remote sensing: Effects Of ‘Mean Cosine’
29
Mean Cosine ComparisonsMean cosine > 0, means forward
scattering is stronger than backward scattering
Models Mean cosine μ
1-μ Meaning
Bicontinuous
0.1 ~ 0.6 0.4 ~ 0.9
Forward scattering
Rayleigh Phase Matrix
0 1.0 Dipole scattering
HUT 0.96 0.04 Strong forward scattering
30
Data Validation With SnowSCATData collected
◦At IOA snow pit◦Radar backscattering and ground data:
Dec. 28, 2010~Mar. 1, 2011Data
◦Time series backscattering◦Time series SWE◦SSA◦Density◦Depths of multilayer structure◦Grain sizes
31
Comparisons With SnowSCAT Time series data for 9 different days in the same IOA snow pit
Ground truth of data point #8◦ Bottom layer is the thickest layer◦ Bottom layer has the largest grain size
Typical values of measured SSA◦ SSA measured in a different year from snow depth, density and grain size◦ Bottom layers : 59 ~ 124 [cm2/g]◦ Top and intermediate layers : 100 ~ 790 [cm2/g]
Data Validation With SnowSCATBicontinuous extracted
parametersLaye
r<ζ> [m-1] b Optical
thicknessMean
cosine μCorrelation length [mm]
Analytical SSA [cm2/g]
Numerical SSA
[cm2/g]1 30000 1.0 1.6×10-4 0.19 0.051 309 222
2 20000 1.0 8.7×10-3 0.14 0.080 228 200
3 20000 1.5 0.015 0.05 0.085 238 188
4 10000 1.5 0.012 0.11 0.17 117 95.2
5 6000 1.2 0.17 0.31 0.28 72 57.4
34
Data Validation With SnowSCATCo-polarization at 16.7 GHz
60 80 100 120-11
-10
-9
-8
-7
SW E [mm]
vv [d
B]
Co-polarization @ 16.7 GHz
MeasurementDMRT
DMRT Models Comparison
35
Scattering
properties
Independent scattering
QCA Foldy Lax Bicontinuous
Frequency dependen
ce
4.0 As low as 2.8
Consistent with QCA
As low as 2.5
mean cosine
0, dipole pattern
Up to 0.3 Consistent with QCA
Up to 0.6
Cross-pol in phase matrix
0 0 NonzeroDipole
interactionsUp to 15 dB
below like-pol
NonzeroDipole
interactionsUp to 7 dB below
like-pol
QCA Foldy Lax BicontinuousModel Spheres, pair
distribution functions
Computer generation of spheres
Computer generation of
snow microstructures
Size parameters
Particle diameter (2a);
Stickiness (τ)
Particle diameter (2a);
Stickiness (τ)
<ζ>; b
Solution method
Analytical QCA Numerical solution of Maxwell equation using Foldy-Lax
equations
Numerical solutions of
Maxwell equations using DDA / FFT
36
Summary Bicontinuous model
◦ Computer Generation of snow microstructures◦ Three parameters α, <ζ>, b◦ Correlation function close to exponential◦ correlation function and SSA◦ Grain size indirectly, empirically related to correlation
function and SSA◦ Computer Generate structures and solve Maxwell
equations numerically using DDA Compare with SnowSCAT scatterometer data Using ground