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Radiation
Laboratory
Physical Model based SWE Retrieval Algorithm Using X- and Ku- band Radar
Backscatter
Jiyue Zhu1, Shurun Tan1, and Leung Tsang1
Joshua King2, and Chris Derksen2
Juha Lemmetyinen3
1 Radiation Laboratory, Department of Electrical Engineering and Computer Science, The University of Michigan, Ann Arbor, 48109-2122 MI USA
2Climate Research Division, Environment and Climate Change Canada, Toronto, ON M3H 5T4, Canada
2Arctic Research Centre, Finnish Meteorological Institute P.O.Box 503, Fin-00101 Helsinki Finland
Wednesday, August 9th, 8:45 - 9:00AMSession: Modeling and Snow Measurements
Radiation
Laboratory
Outlines
2
A. Background scattering subtraction
B. Forward model: i. Bicontinuous / DMRT model and regression trainingii. Parameterized model: only 2 parameters ๐๐ and ๐๐
C. Physical model based SWE retrieval algorithm i. Radar retrieval algorithmii. Classify backscatter w.r.t. ๐๐
iii. SWE retrieval performance Using SnowSARbackscatter ๐๐๐ (9.6 GHz and 17.2GHz)
Radiation
Laboratory
0ice
Radar
Air
Snow
Soil
d
g
t
i
Radar backscattering: volume and surface scattering
3
volume surfactotal
pq pq pq
e 2exp
cos t
๐pqvolume: volume scattering from snowpack
๐pqsurface: surface scattering from ground
๐pqvolume
๐pqsurface
Give SWE
Poster 20Shurun Tan et al., โAssessment of Background Scattering at X-and Ku-band in Snow Remote Sensingโ.
Radiation
Laboratory
Background scattering subtraction in the SWE retrieval algorithm
4
Retrieval algorithm
,mod
1
,
2,
,
2,
,
mod
2
2,
3
,
,X X
X obs
VV vol X X
Ku obs
VV vol X
X el
V
X
V
Ku
X
VV
X
el
w
F MIN w
w
Radar observations
A priori information
Forward model
EstimatedVariables
SWE
Parameterized Bic/DMRT model
,mod ,Ku el
VV X X ,mod ,X el
VV X X
X
Extract volume scattering
,X obs
VV ,Ku obs
VV ,X ground
VV ,Ku ground
VV
Extract volume scattering
,
,
X obs
VV vol ,
,
Ku obs
VV vol
Snow free measurements /
Surface scattering model
X
Snow on measurements
Retrieved๐๐, ๐๐
Radiation
Laboratory
SnowSAR (Canada TVC 2013) X- and Ku-band backscatter: raw data
โข ๐๐๐๐ : ranged from -18dB to -11dB
โข ๐๐๐๐พ๐ข: ranged from -11dB to -6dB
Radiation
Laboratory
โข Model: volume scatteringโข SnowSAR data: volume scattering + background scattering
Bic/DMRT LUT compare with Canada SnowSAR
Radiation
Laboratory
Volume scattering of SnowSAR within model predictions Shift data more in X band than Ku band Larger dynamic range in volume scattering
Background scattering subtracted from raw data
Radiation
Laboratory
8
Retrieval algorithm
,mod
1
,
2,
,
2,
,
mod
2
2,
3
,
,X X
X obs
VV vol X X
Ku obs
VV vol X
X el
V
X
V
Ku
X
VV
X
el
w
F MIN w
w
Radar observations
A priori information
Forward model
EstimatedVariables
SWE
Parameterized Bic/DMRT model
,mod ,Ku el
VV X X ,mod ,X el
VV X X
X
Extract volume scattering
,X obs
VV ,Ku obs
VV ,X ground
VV ,Ku ground
VV
Extract volume scattering
,
,
X obs
VV vol ,
,
Ku obs
VV vol
Snow free measurements /
Surface scattering model
X
Snow on measurements
Retrieved๐๐, ๐๐
SWE retrieval algorithm flow chart
Radiation
Laboratory
Computer Generated Snow: BicontinuousMedium
A. Wiesmann, C. Mรคtzler, and T. Weise, "Radiometric and structural
measurements of snow samples," Radio Sci., vol. 33, pp. 273-289, 1998.X
Z
Vertical Plane
5mm
10mm
15mm
20mm
X
Y
Horizontal Plane
5mm
10mm
15mm
20mm
Real snow cross
section image
9
Traditional exponential correlation function
Same behavior for
short separation
Large tails in long separation
Computer-generated
Comparison through
correlation function
Poster 7Weihui Gu et al., โDMRT Models for Active and Passive Microwave Remote Sensingโ
Radiation
Laboratory
Snow homogeneous: Bicontinuous Dense Media Radiative Transfer (Bic/DMRT)
10
ห ห: Intensity in directionI s s
๐ ๐: extinction coefficient
'ห ห, : phase matrix P s s
coherent incoherent
Solve Maxwellโs Eq. over a block of computer snow (3๐ โ 5๐) with DDA:
get effective ๐, ๐ ๐, ๐eff
Substitute the effective parameters into & Solve RTE:
Backscatter: ๐
Discrete Dipole Approximation (DDA)
2
1
( ) ( )
( , ) ( ( ) 1) ( )
i inc i
N
i j j r j j
j
E r E r
kG r r V r E r
'ห'ห,ห'หห
หsIssPsdsI
ds
sdIe
Radiative Transfer Equation
Poster 7Weihui Gu et al.
Radiation
Laboratory
Look-up table (LUT) of Bic/DMRT
11
Physical Model
(Bic/DMRT)Snowpack
ParametersLUTs
SWE ๐ป , ๐, ๐๐๐๐๐, ๐ ๐๐๐๐ , ๐๐๐
๐พ๐ข dB ๐๐ฟ ๐๐ โฆ
55.02 (9000, 1.2,10%,0.6) (-15.3, -10.6) 0.6805 0.0166 โฆ
64.19 (9000, 1.2,10%,0.7) (-14.9, -10.1) 0.6805 0.0194 โฆ
73.36 (9000, 1.2,10%,0.8) (-14.6, -9.7) 0.6805 0.0221 โฆ
โฆ โฆ โฆ โฆ โฆ โฆ
Parameters MinimumMaximu
mInterval
Volume fraction ๐๐
10% 45% 5%
๐ parameter 0.6 1.6 0.2
๐ parameter (mโ1)
5000 15000 2000
Snow depth ๐(m)
0.1 1.2 0.1
Radiation
Laboratory
12
Parameterization: scattering albedo ๐ and optical
thickness ๐, retrieve ๐๐
s s
s a e
Scattering albedo:
Optical thickness: ed
Absorption loss is proportional to SWE
๐๐ = 1 โ ๐ ฯ = ๐ ๐ ๐ โ SWE Two frequencies, four parameters: ๐๐, ๐๐; ๐Ku, ๐Ku
1T
2T
0ice
0
d d
e a s
๐ ๐ : scattering coefficients๐ ๐: absorption coefficients๐ ๐: extinction coefficients
Radiation
Laboratory
Regression training: reduce ๐๐พ๐ข, ๐๐, ๐๐พ๐ข, ๐๐to ๐๐, ๐๐
13
Parameterize Model
Regression Training
Look up table of Bic/DMRT outputs
Snow Parameter
: snow density : snow depth :related to correlation length/snow grain size
:related to the tail of correlation function
Bicontinous DMRT (Multiple scattering)
b
X Ku KuX X
VV Ku
VV
snow d
Non-linear regression
vs. Ku X
Non-linear regression
vs. Ku X
Linear regression
,1 vs. ,X X st
VV VV X X
Linear regression
,1 vs. ,Ku Ku st
VV VV Ku Ku
Two unknowns and two equations: ,Ku
VV X X ,X
VV X X
Four parameters Two observations
Two parameters Two observations
Radiation
Laboratory
Regressions between ๐๐พ๐ข and ๐๐, ๐๐พ๐ข and ๐๐: based on LUT
14
Correlation between (๐X, ๐Ku) Correlation between (๐X, ๐Ku)
Radiation
Laboratory
Regression between single and multiple scattering
15
Backscatter for X band ๐X ๐X1
๐x, ๐X Backscatter for Ku band ๐Ku ๐Ku1
๐Ku, ๐Ku
Radiation
Laboratory
16
Validation of parameterized Bic/DMRT model: Canada SnowSAR
Good agreement: achieve RSME < 0.28dB
X band Ku band
Radiation
Laboratory
17
Retrieval algorithm
,mod
1
,
2,
,
2,
,
mod
2
2,
3
,
,X X
X obs
VV vol X X
Ku obs
VV vol X
X el
V
X
V
Ku
X
VV
X
el
w
F MIN w
w
Radar observations
A priori information
Forward model
EstimatedVariables
SWE
Parameterized Bic/DMRT model
,mod ,Ku el
VV X X ,mod ,X el
VV X X
X
Extract volume scattering
,X obs
VV ,Ku obs
VV ,X ground
VV ,Ku ground
VV
Extract volume scattering
,
,
X obs
VV vol ,
,
Ku obs
VV vol
Snow free measurements /
Surface scattering model
X
Snow on measurements
Retrieved๐๐, ๐๐
SWE retrieval algorithm flow chart
Radiation
Laboratory
Background scattering subtraction & backscatter classification w.r.t. ๐๐ฟ
enhances sensitivity of backscatter to SWE SWE doubles, Backscatter increases about 2-3dB
Classification: two classes of backscatter, Canada SnowSAR
19
X band Ku band
Radiation
Laboratory
Radar datasets used
Dataset Loacation Date Frequency Polarization
Finland SnowSAR1
Sodankylำ, Finland Mar. 17th, 2011 X and Ku band VV&HV
Finland SnowSAR2
Sodankylำ, Finland December 19th, 2011 to March
24th, 2012X and Ku band VV&HV
Canada SnowSAR
Trail Valley Creek (TVC), the Northwest
Territories, Canadawinter 2012~2013 X and Ku band VV&HV
Radiation
Laboratory
20
Performance of SWE retrieval algorithm: Canada SnowSAR
Achieves RMSE = 26.98mm, and r = 0.7 For SWE < 200 mm, RMSE = 24.31mm
SCLP requirement: RMSE < 20mm for SWE < 200mm and RMSE < 10% of total SWE for SWE > 200mm
Radiation
Laboratory
21
Performance of SWE retrieval algorithm: Finland SnowSAR1 and SnowSAR2
Achieves RMSE = ~24 mm Achieves RMSE = ~18 mm
SnowSAR1 SnowSAR2
Radiation
Laboratory
Methods to improve the algorithm
22
Solution 1: snow thermodynamics model with ancillary meteorological data
Solution 2: combine active and passive microwave measurements
A priori information X
Better background scattering subtraction
Better a priori estimate of ๐๐
(or effective grain size)
Radar observation ๐๐๐๐ from snow free conditions
Polarimetry: volume / surface scattering decomposition
Combine active and passive measurements to retrieve both soil and snowpack parameters
Radiation
Laboratory
Summary
23
A. Background scattering subtraction: i. Affects more in X band than Ku bandii. Volume backscatter sensitive to SWE
B. Forward model: parameterized Bic/DMRTi. Regression training: 2 observations vs. 2 unknowns
(๐๐ and ๐๐)ii. Validated against SnowSAR data
C. Retrieval algorithm: SWE โ ๐๐,๐ = 1 โ ๐๐ ๐๐i. A priori ๐๐
ii. Classify backscatter w.r.t. ๐๐ restores its high sensitivity to SWE
iii. Performance: RMSE <30mm for SWE up to 300mm
Radiation
Laboratory
24