A MICROWAVE SCATTERING MODEL OF VEGETATED SUFACES BASED ON BOR & NMM3D FOR SMAP MISSION
Xiaolan Xu, Shaowu Huang, Leung Tsang
EE, University of Washington, Seattle, WA
Seung-Bum Kim, Eni Njoke
JPL, California Institute of Technology, Pasadena, CA
IGARSS 2010, Honolulu, HawaiiJuly 25 -30
Outline
Background - SMAP mission Baseline Algorithm - Flow Chart Data Cube Representation
Soil - Rough Surface Scattering Vegetation – Volume Scattering Interaction
Data Comparison Summary
Background – SMAP mission
Soil Moisture Active/Passive (SMAP) mission
L-band (1.26GHz) combined microwave system
Global maps of the Earth’s soil moisture
Radar Backscatter product with 3 km resolution
Requirements
Estimates of top 5-cm soil moisture
Excluding regions of snow and ice, mountainous topography, open water, and VWC > 5kg/m2
3D DATA CUBE(N classes)
Physical Forward Model
Vegetation Layer
Interaction
Soil Surface
Corn Field
GrassLand
SoybeanField
Snapshot
Time-SeriesR
ad
ar
Le
vel O
ne
Da
ta
HH
VV
HV
Cla
ssifi
catio
nC
lass
ifica
tion
••••
• ••
•••
Class 1
Class n
InvertInvertSoil Moisture
Soil Moisture
To Archive
Topography
(SRTM)
NDVI
Ra
da
r L
eve
l On
e D
ata
HH
VV
HV
Cla
ssifi
catio
nC
lass
ifica
tion
••••
• ••
•••
InvertInvert
Invert
Re
ass
em
ble
Sp
atia
l Ma
p
Flag DataNot valid
To Archive
Unable to invert
),( nW
),,,,( lhnW
),,( lh
Flow Chart
Baseline Retrieval Algorithm
An optimization process applied to a robust physical forward model
d(iksrtr ,imvrtr ) wich ich0 (iksrtr ,imvrtr )
ich
HH ,VV
ich0 (iksrtr ,imvrtr ) ( ich,mea
0 (ikstrue,imvtrue,ivwctrue ) ich,rtr0 (iksrtr ,imvrtr ,ivwctrue ))2
Data Cube – Generate according to the vegetation type
Retrieval Algorithm – Least squared Method
Minimize d
Data Cube - Advantages
Accuracy 3D Numerical solution of Maxwell’s Equations for
both rough surface scattering and volume scattering to ensure accuracy
Time Fast algorithm has been applied for scattering
calculation. (Surface: PBTG/SMCG; Volume: BOR) Pre-calculated Look-up table
Interpolation
Robust
Outline
Background - SMAP mission Baseline Algorithm - Flow Chart Data Cube Representation
Soil - Rough Surface Scattering Vegetation – Volume Scattering Interaction
Data Comparison Summary
eff effk
soil soilk
0z
z d
'z z
Region 0
Region 1
Region 2
pr
Soil - Rough Surface Scattering
Bared surface – Numerical Method (NMM3D) Generate profile of 3D random rough surface for
each realization, using exponential correlation functions
Solve Maxwell Equations Based on Method of Moment (MoM) solution of
Maxwell Equations Accelerated by fast algorithm
S. Huang et, al. TGARSS vol.48, no.6, pp.2557-2568, 2010 Implemented on parallel computing
Surface roughness parameters of rms height and correlation length and moisture
condition of soil permittivity were measured in Michigan’s experiment.
Bare Soil ValidationCompared with Michigan’s POLARSCATTER Data-3
9
Cross-pol Backscattering Coefficients
10
-40 -30 -20 -10
-40
-30
-20
-10
(HV+VH)/2 NMM3D(dB)
(HV
+V
H)/2
Mic
hgan
(dB
)
Notes:Cross-pol agree with Michigan’s data
Relative permittivity = 15.14+i*1.27,
rms height are normalized in wavelength
correlation length = 10*rms height.
Coherent reflectivity
Vegetation Layer - Single Scatterer
Numerical method of solving the Max well’s equations rigorously for the rotationally symmetric, 3D objects
Originally developed by Harrington and Mautz. Matthaeis & Lang applied to vegetation scattering
over flat surface
Body of Revolution
LeafBranch
Benchmark with mie scattering
For sphere ka = 6.28, epsr = 6-2i
Backscattering Comparison between BOR & Infinite Cylinder Approx.
Distribution function of a group of cylinders
The bistatic function depends on the orientation angles of the cylinders. The averaging is taken as followed,
2 2
1 1
2
1
1 2
2
01 2
( , ) sin ( , ) ( , )
Usually, and are independent, ( , ) ( ) ( )
For uniform distribution,
1 1( ) ( )=
2 cos cos
1( , ) sin ( , )
2 (cos cos )
For cosine sq
g d d p g
p p p
p p
g d d g
23 3
1 2
uared distribution,
1 3( ) ( )= cos
2 cos cosp p
Vegetated rough surface
Half Space Greens’ Function
( , ') ( , ') ( , ')P RG r r G r r G r r
exp( ) ˆ ˆ( , ') [ ( ) ( ) ( ) ( )]exp( ') exp( ')4P sz sz sz sz sz s
ikrG r r v k v k h k h k ik z ik
r
exp( ) ˆ ˆ( , ') [ ( ) ( ) ( ) ( )]exp( ') exp( ')4
,
ˆ ˆsin cos sin sin
cos
R v sz sz h sz sz sz s
s eff s s eff s s
sz eff s
ikrG r r R v k v k R h k h k ik z ik
rwhere
k k x k y
k k
2 '( 1) ( , ') ( ')p
s rVE k dr G r r E r
The coherent reflectivities Rv and Rh is calculated by NMM3D
eff effk
soil soilk
0z
z d
'z z
Region 0
Region 1
Region 2
pr
Backscattering Coefficient
2( )(1)
_ _1
2( )(2)
_ _
2( )(3)
_ _
2( )(4)
_ _
4 { exp(2 Im( ) )
( ) exp( 2 Im( ) )
( ) exp(2 Im( ) )
( ) ( ) exp( 2 Im( ) ) }
pq
pq
pq
pq
Nj
pq zeff q zeff p jj
jq i zeff q zeff p j
jp i zeff q zeff p j
jp i q i zeff q zeff p j
f k k z
f R k k z
R f k k z
R f R k k z
Four mechanisms
exp( )t v sv spq pq pq pq pq
Born Approx.
Foldy Approx.
Grass Land Comparison
Typical Condition in Grass land
Thin cylinders,
more uniform distribution
Southern Great Plains (SGP) 1999 Experiment
Passive and Active L & S System (PALS)
L-band VV, HH, VH channel Incident angle 40
Input Measurement from SGP 99
site #incidentangle
bulk density
VWCsample
Rms (mm) Cl (mm) Clay(%) Sand(%)
2 37.9 1.27 0.16 4 100 15 37
3 38.2 1.33 2.38 6 67 10 60
4 38 1.41 0.48 3 38 6 79
5 38 1.42 0.34 3 67 6 79
6 39.4 1.13 0.33 4 86 6 79
7 39.7 1.36 0.57 8 116 13 21
Grass data comparison at SGP 99
Data matching against soil moisture
Backscattering co-pol difference (vv/hh)
Site 5: Discussion
mv is low, hh > vv
mv increase, hh < vv
HH dominant by vegetation effect (volume scattering + double bounce)
VV dominant by soil effect (surface scattering)
Further more… how about cross-pol?
Cross-pol from soil is done by Oh. Model.
Cross-pol is underestimated
1. Distribution of vegetation
2. Accurate cross-pol from soil
Summary
SMAP Baseline Algorithm Data cube representation
More accurate by using numerical method Fit into the retrieval algorithm by using Look up
table with interpolation Robust tune up
Good Agreement with SGP 99 measurement
Ongoing Research
Rough Surface Accurate cross-polarization
Vegetation Multilayer to include more complicate structure
Interaction Include incoherent reflection
Data validation of more types of crops
Acknowledgement
Shaowu Huang, Prof. Leung Tsang
Dr. Seung-Bum Kim, Dr. Eni Njoke
NASA, JPL
Thanks for your attention!
QUESTION?
