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 𝜔𝑋 and 𝜏𝑋

C. Physical model based SWE retrieval algorithm i. Radar retrieval algorithmii. Classify backscatter w.r.t. 𝜔𝑋

iii. SWE retrieval performance Using SnowSARbackscatter 𝜎𝑉𝑉 (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

𝜎pqvolume: volume scattering from snowpack

𝜎pqsurface: surface scattering from ground

𝜎pqvolume

𝜎pqsurface

Give SWE

Poster 20Shurun Tan et al., “Assessment of Background Scattering at X-and Ku-band in Snow Remote Sensing”.

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

Retrieved𝜔𝑋, 𝜏𝑋

Radiation

Laboratory

SnowSAR (Canada TVC 2013) X- and Ku-band backscatter: raw data

• 𝜎𝑉𝑉𝑋 : ranged from -18dB to -11dB

• 𝜎𝑉𝑉𝐾𝑢: ranged from -11dB to -6dB

Radiation

Laboratory

• Model: volume scattering• 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

Retrieved𝜔𝑋, 𝜏𝑋

SWE retrieval algorithm flow chart

Radiation

Laboratory

Computer Generated Snow: BicontinuousMedium

A. Wiesmann, C. Mätzler, 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., “DMRT Models for Active and Passive Microwave Remote Sensing”

Radiation

Laboratory

Snow homogeneous: Bicontinuous Dense Media Radiative Transfer (Bic/DMRT)

10

ˆ ˆ: Intensity in directionI s s

𝜅𝑒: extinction coefficient

'ˆ ˆ, : phase matrix P s s

coherent incoherent

Solve Maxwell’s Eq. over a block of computer snow (3𝜆 − 5𝜆) with DDA:

get effective 𝑃, 𝜅𝑒, 𝜀eff

Substitute the effective parameters into & Solve RTE:

Backscatter: 𝜎

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

'ˆ'ˆ,ˆ'ˆˆ

ˆsIssPsdsI

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 𝜻 , 𝒃, 𝝆𝒔𝒏𝒐𝒘, 𝒅 𝜎𝑉𝑉𝑋 , 𝜎𝑉𝑉

𝐾𝑢 dB 𝝎𝑿 𝝉𝐗 …

55.02 (9000, 1.2,10%,0.6) (-15.3, -10.6) 0.6805 0.0166 …

64.19 (9000, 1.2,10%,0.7) (-14.9, -10.1) 0.6805 0.0194 …

73.36 (9000, 1.2,10%,0.8) (-14.6, -9.7) 0.6805 0.0221 …

… … … … … …

Parameters MinimumMaximu

mInterval

Volume fraction 𝒇𝒗

10% 45% 5%

𝑏 parameter 0.6 1.6 0.2

𝜁 parameter (m−1)

5000 15000 2000

Snow depth 𝑑(m)

0.1 1.2 0.1

Radiation

Laboratory

12

Parameterization: scattering albedo 𝜔 and optical

thickness 𝜏, retrieve 𝜏𝑎

s s

s a e

Scattering albedo:

Optical thickness: ed

Absorption loss is proportional to SWE

𝜏𝑎 = 1 − 𝜔 τ = 𝜅𝑎 𝑑 ∝ SWE Two frequencies, four parameters: 𝜔𝑋, 𝜏𝑋; 𝜔Ku, 𝜏Ku

1T

2T

0ice

0

d d

e a s

𝜅𝑠: scattering coefficients𝜅𝑎: absorption coefficients𝜅𝑒: extinction coefficients

Radiation

Laboratory

Regression training: reduce 𝜔𝐾𝑢, 𝜔𝑋, 𝜏𝐾𝑢, 𝜏𝑋to 𝜔𝑋, 𝜏𝑋

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 𝜏𝐾𝑢 and 𝜏𝑋, 𝜛𝐾𝑢 and 𝜛𝑋: based on LUT

14

Correlation between (𝜏X, 𝜏Ku) Correlation between (𝜔X, 𝜔Ku)

Radiation

Laboratory

Regression between single and multiple scattering

15

Backscatter for X band 𝜎X 𝜎X1

𝜛x, 𝜏X Backscatter for Ku band 𝜎Ku 𝜎Ku1

𝜛Ku, 𝜏Ku

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

Retrieved𝜔𝑋, 𝜏𝑋

SWE retrieval algorithm flow chart

Radiation

Laboratory

Background scattering subtraction & backscatter classification w.r.t. 𝝎𝑿

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

Sodankylӓ, Finland Mar. 17th, 2011 X and Ku band VV&HV

Finland SnowSAR2

Sodankylӓ, 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 𝜔𝑋

(or effective grain size)

Radar observation 𝜎𝑜𝑏𝑠 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

(𝜔𝑋 and 𝜏𝑋)ii. Validated against SnowSAR data

C. Retrieval algorithm: SWE ∝ 𝜏𝑎,𝑋 = 1 − 𝜔𝑋 𝜏𝑋i. A priori 𝜔𝑋

ii. Classify backscatter w.r.t. 𝜔𝑋 restores its high sensitivity to SWE

iii. Performance: RMSE <30mm for SWE up to 300mm

Radiation

Laboratory

24