TU4.L09 - RETRIEVAL OF SOIL MOISTURE UNDER VEGETATION USING POLARIMETRIC SCATTERING CUBES

National Aeronautics and Space Administration

Jet Propulsion LaboratoryCalifornia Institute of Technology

Pasadena, California




Retrieval of Soil Moisture under Vegetation using Polarimetric

Scattering CubesMotofumi Arii ([email protected])Mitsubishi Space Software Co., Ltd.,

792 Kami-machiya, Kamakura,Kanagawa 247-0065

Jakob J. van Zyl and Yunjin KimJet Propulsion Laboratory,

California Institute of Technology,Pasadena, California, USA

1







x,y : Polarization state for transmitting/receiving

( )roughvxyxy pmf ,0 =σ

( )gvm ε

Many ways to invert soil moisture from radar backscattering from bare surfaces have been proposed as summarized in [1].

[1] J. J. van Zyl and Y. Kim, "A quantitative comparison of soil moisture inversion algorithms," Proc. of IGARSS01, Sydney, Australia, Jul. 2001.

2

Soil Moisture Retrieval from Bare Surface







( )vnvvroughvxyxy ppppmf ,,,, 210 =σ

pvi : Parameters to characterize vegetation

More than 76% [2-3] of the earth surface is covered by vegetation.

Surface

Volume(Canopy)

Double bounce(Ground-trunk, ground-canopy)

3

Volume(Trunk)

vm

Soil Moisture Retrieval from Vegetated Terrain

[2] R. T. Watson, I. R. Noble, B. Bolin, N. H. Ravindranath, D. J. Verado, and D. J. Dokken, Land use, land-use change and forestry, Cambridge, UK: Cambridge University Press, 2000.

[3] E. Ezcurra, Global Desserts Outlook, Nairobi, Kenya: DEWA, UNEP, 2006.







Polarimetric Decomposition

4

0,ˆ vxyσ 0

,ˆ dxyσ 0,ˆ sxyσ

Soil Moisture

0xyσ

One may try to decompose the Observation







-Inversion algorithm: A simple but robust technique proposed by Dubois et al.[4] for bare surfaces assuming L-band (24cm)

5

Preparation for the Demonstration

[4] P. C. Dubois, J. van Zyl, and T. Engman, “Measuring Soil Moisture with Imagin Radars,” IEEE Trans. Geosci. Remote Sensing, vol 33, no. 4, Jul. 1995. [5] J. J. van Zyl, M. Arii, and Y. Kim, “Model Based Decomposition of Polarimetric SAR Covariance Matrices Constrained for Non-Negative Eigenvalues,”

IEEE Trans. on Geosci. Remote Sensing, 2010 (in press)

{( ) ( ) }48.2sinlog130coslog255

log110log140tan36.3

1ˆ

−−−

−=

ii

hhvvi

bare

θθ

σσθ

ε

-Polarimetric Decomposition: Non-Negative Eigenvalue Decomposition proposed by van Zyl et al.[5] assuming cosine squared distribution which is suitable for agricultural area

[ ] [ ] [ ] [ ] [ ]remainderssddv CCCCxC +++= λλAfter the decomposition, only HH and VV of the surface scattering component, Cs, are utilized to estimate soil moisture by (1).

(1)

(2)







6

Iowa, at L-band Walnut creek watershed, Iowa observed by AIRSAR in July 2002. The

area is widely covered by soy beans and corns.

Residential areaDensely vegetated area

along the river Snapshot






Pasadena, California Inversion Results

-200

0

Maps of Negative ε

The more vegetation, the smaller ε.Of course, negative ε is not physically acceptable!

Dubois et al. algorithm with decomposition

Dubois et al. algorithm only




ψ

δspqrsσ

( ) δψψδψρσ ddpSS jrs

jpq

jpqrs sin,*∫∫=

Discrete Scatterer Model (DSM)[6-7]

[6] S. L. Durden, J. J. van Zyl, H. A. Zebker, “Modeling and Observation of the radar polarization signature of forested areas,” IEEE Trans. Geosci. Remote Sensing, vol. 27, no. 3, May 1989.

[7] M. Arii, “Soil moisture retrieval under vegetation using polarimetric radar,” Ph.D. dissertation California Institute of Technology, Pasadena, CA, pp. 68-101, 2009.

[8] M.Arii, J. J. van Zyl, and Y. Kim, "Adaptive decomposition of polarimetric SAR covariance matrices," Proc. of IGARSS09, Cape Town, South Africa, Jul. 2009.

[9] M. Arii, J. J. van Zyl and Y. Kim, “Adaptive model-based decomposition of polarimetric SAR covariance matrices,” IEEE Trans. on Geosci. Remote Sensing, 2010 (in press)

spqrs

dpqrs

vpqrspqrs σσσσ ++=0

H

vm

( )εcW

kh

jxyS

dpqrsσ

vpqrsσ

π2

A

1

πψ

( )ψp

ψσ

91.00 ≤≤ ψσ

σψ = 0.00 : Delta func. (methodical)σψ = 0.57 : Cosine squared (medium)σψ = 0.91 : Uniform (most complicated)

dvj ,=

Standard deviation of ψ [8-9]




9

.deg40=iθ

mm2

cm50

2~1.0

/5~0

%60~02

==

=

kh

mkgW

m

c

v

3/900

1

mcylinders

mH

=

=

ρ

Cosine squared distribution

L-band (24cm)

π2

π1

ψ

DSM for Grassland

Variables







10

Inversion without Decomposition

€

Wc[kg/m2]

Backscatters from the grassland having specific soil moisture (10 to 60%) are generated as a test data in terms of vegetation water content. Then Dubois et al.’s algorithm estimates dielectric constant using co-polarizations of the simulated data.

mv (%)

truebare εε −ˆ







11

What’s going on?

€

Wc[kg/m2]

Bac

ksca

tter

ing

Cro

ss S

ectio

n [d

B]

{ } 44.18log11log1455.3ˆ +−= hhvvbare σσε

mv = 40%

Double-Bounce VolumeVVHH > ./ constHHVV ≈

truebare εε −ˆ







12

with Decomposition

€

Wc[kg/m2]

The ideal decomposition technique, which perfectly extracts the surface scattering component, makes the inversion even worse! Note that the DSM allows us to directly use the surface scattering.

mv (%)

truebare εε −ˆ




{ }fwdxxxx S

kIm

4 ρπα =

13

iθ

x = h , v

ivv

ihh

Hvv

vvv

Hhh

vhh

e

eθα

θα

σσσσ

cos/2

cos/2

−

−

=

=

Bare Surface Vegetated Terrain

vvhh σσ , vvv

vhh σσ ,

H

vvhh αα ,

Attenuation coefficients are calculated by Optical Theorem as

Then the scattering from bare surface are attenuated as

Why?




Taking into account the attenuation, the inversion model is rewritten as

14

+

+= −

−

−ihh

ihh

ivvH

H

H

barev ee

e θαθα

θα

εε cos/2cos/2

cos/2

log3log1455.3ˆˆ

ihhbarev H θαεε cos/2355.3ˆˆ lnln ⋅⋅−≈

For simplicity, let us take logarithm natural and assume same attenuation coefficients between co-polarizations.

The inferred dielectric constant decreases in terms of the amount of vegetation.

A new inversion algorithm which explicitly includes the attenuation effect is required!

44.18log3log1455.3ˆ +

+= hhhh

vvbare σ

σσε




( )( )( ) ( )

+=

cvrefjcv

refj

cvrefi

cvref

WkhmWkhm

WkhmWkhm

,,,,ln

,,ln,,ln

φσ

σσ

khvm

cW

hhσln hvσln

€

lnσhhvv

vvσln

hhvvφ

From DSM, we can form the following cubes for backscattering cross sections.

j = hhhv, hhvv, hvvv

15

i = hh, hv, vv

Polarimetric Scattering Cubes (PSC)

.deg




The same transformation is applied to measured data.

Then the distance between the measured data and each point of the cubes are defined as

( ) ( )( )

( )( ) ( )( )∑∑

∑

−+−+

−=

kcv

refk

mkk

jcv

refj

mjj

icv

refi

miicv

WkhmwWkhmw

WkhmwWkhmd

22

2

,,,,lnln

,,lnln,,

φφσσ

σσ

where, w’s are weighting functions.

+=

mj

mj

mim

φσ

σσ

ln

lnln

i = hh, hv, vvj = hhhv, hhvv, hvvv

16

Minimum Distance

dcv Wkhm ,,

min

Finally, we can determine the variables which minimize the distance.




RMSE(k

h)

RMSE(m

v)[%

]

RMSE(W

c)[kg/m

2 ]

]/[ 2mkgWc ]/[ 2mkgWc ]/[ 2mkgWc

The reference cubes (280x280x280 samples) for the grassland is applied to the area that has the same baseline parameters. The 300 test data sets for each plot are generated with randomly chosen mv, kh and Wc. Note that the Wc has a range between 0 and a number specified in the x axis.

The error comes from the number of samples of the cubes. The HHVV plays an important role to remove the vegetation effect.

0

1

=====

hvvvhhhv

vvhvhh

ww

www

17

Soil Moisture Vegetation water contentRoughness

Inversion by PSC

0=hhvvw

1=hhvvw

0=hhvvw

1=hhvvw

0=hhvvw

1=hhvvw




RMSE(m

v)[%

]



RMSE(k

h)

RMSE(W

c)[kg/m

2 ]

18

0

1

======

hvvvhhhv

hhvvvvhvhh

ww

wwww

Sensitivity to Cylinder Radius




RMSE(k

h)

RMSE(m

v)[%

]

RMSE(W

c)[kg/m

2 ]


19


0

1

=====

hvvvhhhv

hhvvvvhh

ww

www

Sensitivity to Distribution, σψ

π2

A

1

πψ

pdf

ψσσψ = 0.00 : Delta func. (methodical)σψ = 0.57 : Cosine squared (medium)σψ = 0.91 : Uniform (most complicated)

ψσ ψσ ψσ




Now noise equivalent σo = -30 dB, is randomly added to the test data. The lower accuracy is achieved for smaller vegetation water content since smaller HV can be easily affected by the noise.

RMSE(k

h)

RMSE(m

v)[%

]

RMSE(W

c)[kg/m

2 ]


20


Sensitivity to Noise

0=hvw

1=hvw

0

1

=====

hvvvhhhv

hhvvvvhh

ww

www

0=hvw

1=hvw

0=hvw

1=hvw




Cube Technique

0pqrsσ

Cube Library

Vegetation Type 1

Vegetation Type 2

Vegetation Type n

DecompositionTechnique

Classification

Inversion

VegetationType

WeightingFunctions

Cubes

21cv Whkm ˆ,ˆ,ˆ

vm

cW

kh

Comprehensive Inversion Strategy




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Summary

We proposed a technique using PSC to invert soil moisture, surface roughness, and vegetation water content, simultaneously. The technique has several characteristics such as Easy implementation Including attenuation effect Higher applicability to various vegetated terrains Easily extended by increasing axis (no reason to be limited to 3 axes!) Considering an effect of Brewster angle which is NOT taken into

account by most of current polarimetric decomposition techniques.

Systematic inversion strategy was also proposed.

Nevertheless, the key to let the technique meaningful should be on a validation of DSM (or other forward scattering models) by experimental data. We are planning to collaborate with Prof. Yamaguchi’s group in Niigata University, who are currently installing the brand-new indoor full polarimetric radar system.

TU4.L09 - RETRIEVAL OF SOIL MOISTURE UNDER VEGETATION USING POLARIMETRIC SCATTERING CUBES

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