CONICAL ELECTROMAGNETIC WAVES DIFFRACTION FROM SASTRUGI TYPE SURFACES OF LAYERED SNOW DUNES ON...
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Transcript of CONICAL ELECTROMAGNETIC WAVES DIFFRACTION FROM SASTRUGI TYPE SURFACES OF LAYERED SNOW DUNES ON...
CONICAL ELECTROMAGNETIC WAVES DIFFRACTION FROM SASTRUGI TYPE SURFACES OF LAYERED SNOW DUNES ON GREENLAND ICE SHEETS IN
PASSIVE MICROWAVE REMOTE SENSING
Wenmo ChangLeung Tsang
Department of Electrical EngineeringUniversity of Washington
Outline
• Motivation– Observations in passive microwave remote sensing– Large 3rd and 4th Stokes parameters
• Scattering physics– Rough surfaces : Large slope and large height– Total internal reflection in layered media
• Electromagnetic methodology– Maxwell equations for rough surface– Radiative transfer theory for layered media
• Results and discussion
Greenland’s snow profile
• Wind induced– Sastrugi surface
• Large RMS height– 20 cm– 7 wavelengths @ 10.7 GHz– 12 wavelengths @ 18.7 GHz
• Large slope
Photo courtesy of Quintin Lake www.quintinlake.com
Four Stokes parameters in passive microwave remote sensing
• Microwave polarimetric signatures
2
2
*
*
1
2 Re
2 Im
vv
hh
v h
v h
ETET
IU E E
V E E
Observations
• WindSat data over the Summit site
• Large 3rd and 4th Stokes parameters
• Up to 15 K for 10.7 GHz, 18.7 GHz and 37 GHz
Li, L.; Gaiser, P.; Twarog, E.; Long, D.; Albert, M.; , "WindSat Polarimetric View of Greenland," Geoscience and Remote Sensing Symposium, 2006. IGARSS 2006. IEEE International Conference on , vol., no., pp.3824-3827, July 31 2006-Aug. 4 2006
Outline
• Motivations• Scattering physics• Electromagnetic methodology• Results and discussion
Physical model• Large height and large slope coupled with
subsurface total internal reflection• 1-D roughness: azimuthal asymmetry
ki ks
θiφi
θs
φs
↑ Sastrugi surface
Underlying snow layer 1
Underlying snow layer 2
More underlying snow layers
Multilayered snow↓
Computer generation of Sastrugi surfaces
• Statistical data needed for Sastrugi profile
-1.5 -1 -0.5 0 0.5 1 1.5
-1
-0.5
0
0.5
1
1.5
-2 -1.98 -1.96 -1.94 -1.92 -1.9 -1.88 -1.86 -1.84 -1.82 -1.80
0.05
0.1
0.15
0.2
0.25Photo courtesy of Quintin Lake www.quintinlake.com
Large angle transmission
20°
15°
60.2°
Incident angle=55°
Total internal reflection
ε1=1.8, dense snow
ε2=1.3, less dense snow
ε0=1, air
2
2
*
*
1
2 Re
2 Im
vv
hh
v h
v h
ETET
IU E E
V E E
Critical angle=58.2°
Large slope
2 1 1 2
2 1 1 2
1 2
1 2
1 exp( )
1 exp( )
z zv v
z z
z zh h
z z
v h
k kR j
k k
k kR j
k k
• Phase shifts of v- and h-pol are different
• Non-zero U and V are generated
Scattering physics: results based on Maxwell equations
• Air to snow– Ɵi=55 deg
– ɸi=30 deg
– εrsnow =1.8
– εrunder =1.3
10 20 30 40 50 60 70 80 90-50
-40
-30
-20
-10
0
10
20
30
X: 37.6Y: 19.8
Bistatic transmission coefficients
Tra
nsm
itted
ene
rgy
/ dB
t / deg
X: 60.44Y: 16.62
vv
hv
Specular
• Two peaks in transmission• Specular transmission angle in snow: 37.6 deg• A secondary peak: around 60.4 deg
• Critical angle between snow and underlying layers: 58.2 deg• The 60.4-deg transmission will have total internal reflection
ki ks
θiφi
θs
φs
Underlying snow layers
kt
θt
Outline
• Motivations• Scattering physics• Electromagnetic methodology• Results and discussion
Challenges in electromagnetic model• Height of profile
– Past: small to moderate height– New: large height up to 7 wavelengths
• Fluctuations of microwave signatures in simulations– Past coherent 3-D MoM (Tsang et al., 2008)
• Fluctuations due to roughness• Fluctuations due to coherent multiple reflections of
layering
– Present model has less fluctuations
Present hybrid model
• Previous 3D MoM coherent model (Tsang et al., 2008) for comparisons
• (1) Maxwell equations for rough surface scattering to numerically derive rough surface’s bistatic coefficients
• (2) Radiative transfer theory for layered media• Combine (1) and (2) : rough surface’s bistatic
coefficients from Maxwell equations used as boundary conditions for radiative transfer
Rough surface’s boundary conditions
• Numerical methods to solve Maxwell equations (integral equations)– Conical diffraction– Field components obtained
( )
( )
( , ( ))
ˆ · ( , )
( , ( ))
ˆ · ( , )
y
t t y z f x
y
t t y z f x
H x z f x x
n H x z x
E x z f x x
n E x z x
1
1
1
1
( , ) ( , )
ˆ ˆ· ·
(x, z) ( , )
ˆ ˆ· ·
=y y
t t y t t y
y y
t t y t t y
E x z E x z
n E n E
H H x z
n H n H
Four types of surface unknowns Continuity boundary conditions
Numerical solutions• Numerical methods to solve Maxwell
equations (integral equations)– Conical diffraction– Field components obtained
( )
( )
, , for r in region 0ˆ, · , ; , , ; ,
0, for r in region 1
, , for r in region 0ˆ, · , ; , , ; ,
0, for r in region 1
yyi t t
z f x
yyi t t
z f x
E x zE x z ds x n g x z x z g x z x z x
H x zH x z ds x n g x z x z g x z x z x
1 1 1 1( )
1
1 1 1 1
1
0, for r in region 0, ; , , ; ,
, for r in region 1
0, for r in region 0ˆ · , ; , , ; ,
, , for r in region 1
tz f x
y
t t
y
ds x g x z x z g x z x z xE x z
ds x n g x z x z g x z x z xH x z
Numerical requirements• Physical Parameters
– RMS height: 20 cm• 7.1 wavelengths @ 10.7 GHz• 12.4 wavelengths @ 18.7 GHz
• Numerical parameters– Surface length: 4 m
• 142 wavelengths @ 10.7 GHz• 249 wavelengths @ 18.7 GHz
• Number of surface unknowns: up to 20,000• Linear solver
– Direct solver based on LU decomposition– In the future: multi-level UV
Bistatic coefficients
• Bistatic scattering and transmission coefficients
2 22
2
4 2, ; , lim
coscos
s s
s s i ir s
i inc ii
r E E
PE A
/2 /2* * *
/2 /2 00
1 1Re Re 2 cos
2 2 4
L L Linci i xi yi yi xi iL L zz
g kP dx E H dx E H E H
01( , ,0)cos ( , , , ) ( , ,0)cost
t t t t i t t i i u i i iI d I
11( , ,0) cos ( , , , ) ( , ,0)cosr
d s s s i s s i i u i i iI d I
Boundary conditions for radiative transfer
• ‘Boundary condition’ for radiative transfer of layered media
• Multiple reflection– Iterative scheme
• Solid angle integral
Matrices formed by the numerical bistatic coefficients
t rFlatSurface Subsurface FlatSurfau ce dI I I
At upper rough boundary
At lower flat subsurface
Periodic profile• Single realization• Hybrid model compared with coherent 3-D MoM
0 10 20 30 40 50 60 70 80 900
50
100
150
200
250
Azimuthal angle /
T v / K
Hybrid
Coherent 3-D MoM
0 10 20 30 40 50 60 70 80 900
50
100
150
200
250
Azimuthal angle /
T h / K
Hybrid
Coherent 3-D MoM
0 10 20 30 40 50 60 70 80 90-20
-15
-10
-5
0
5
10
15
20
Azimuthal angle /
U /
K
Hybrid
Coherent 3-D MoM
0 10 20 30 40 50 60 70 80 90-20
-15
-10
-5
0
5
10
15
20
Azimuthal angle /
V /
K
Hybrid
Coherent 3-D MoM
Geometry
Outline
• Motivations• Scattering physics• Electromagnetic methodology• Results and discussion
Sastrugi surface at 10.7 GHz
• Averaging over 5 realizations
Geometry
0 10 20 30 40 50 60 70 80 90150
160
170
180
190
200
210
220
230
240
250
Azimuthal angle /
10.7 GHz
T v
0 10 20 30 40 50 60 70 80 90140
150
160
170
180
190
200
210
220
230
Azimuthal angle /
10.7 GHz
T h
0 10 20 30 40 50 60 70 80 90-20
-15
-10
-5
0
5
10
15
Azimuthal angle /
10.7 GHz
U
0 10 20 30 40 50 60 70 80 90-10
-8
-6
-4
-2
0
2
4
6
8
10
Azimuthal angle /
10.7 GHz
V • 3rd and 4th Stokes parameters up to -15 K / +10 K
Sastrugi surface at 18.7 GHz
• Averaging over 5 realizations
0 10 20 30 40 50 60 70 80 90120
140
160
180
200
220
240
260
Azimuthal angle /
18.7 GHz
T v
0 10 20 30 40 50 60 70 80 90120
140
160
180
200
220
240
Azimuthal angle /
18.7 GHz
T h
0 10 20 30 40 50 60 70 80 90-4
-2
0
2
4
6
8
Azimuthal angle /
18.7 GHz
U
0 10 20 30 40 50 60 70 80 90-2
0
2
4
6
8
10
12
Azimuthal angle /
18.7 GHz
V
• 3rd and 4th Stokes parameters up to -2 K / +10 K
Geometry
Summary• Hybrid model
– 2-D MoM for rough surface– Radiative transfer for layer media– Combine rough surface boundary conditions with
radiative transfer
• Numerical results of the model– Large 3rd and 4th Stokes parameters up to -15 K / 10 K– Less fluctuations– Both 10.7 GHz and 18.7 GHz show up to 15K
Thank You for Your Attention!