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Synthetic Aperture Radar Data Assimilation for Sea Ice Analysis
N. Gökhan Kasapoğlu
Dept. of Electronics and Communication Engineering İstanbul Technical University, Turkey
Outline
• Introduction• 0D-Var SAR Data Assimilation • SAR Features• SAR Forward Model• Sea Ice Open Water Discrimination• A Simple Forward Model• SAR 0D-Var Analysis Results• Optimal SAR Feature Selection
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R2 Dual PolarizedSCWA SAR DATA
Forecast
Analysis
Forecast
SAR Feature Extraction
AssimilatedObservations
SAR Forward Model
DATA Assimilation
Model
SAR Data Assimilation
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Variational data assimilation
• Basic idea: Bayes theorem is used to update pdf of model forecast (x) using all available observations (y)
• If all pdfs Gaussian, maximum likelihood estimate minimizes the function:
)()(2
1)][()][(
2
1])|[ln()( 11
bT
bT HHCpJ xxBxxyxRyxyxx
Jobs Jb• where:• xb is the short-term ice-ocean model forecast used as the background state• B is the background error (forecast error) covariance matrix• y is the vector of observations• R is the observation error covariance matrix• H maps the analysis vector into observation space
)(/)()()( yxx|yy|x pppp
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Variational method of solution
• Use an iterative descent algorithm to find the analysis increment ∆x = x-xb that minimizes the cost function J (requires gradient of J)
• If obs operator is linear, then J is quadratic and possible to easily find unique minimum
• Otherwise, obs operators can be periodically re-linearized during minimization
• Can be difficult to find the global minimum of a non-quadratic cost function (when H highly nonlinear)
• Grey is original J with nonlinear H, Red curves are from linearizing H
→
)()][(][
)(
)()(2/1)][()][(2/1)(
11
11
b
bb
HH
J
HHJ
xxByxRx
xx
xxBxxyxRyxx
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J
Analysis Variable
R2 Dual PolarizedSCWA SAR DATA
SAR Feature Extraction
AssimilatedObservations
SAR Forward Model H(x,)
DATA Assimilation (0D-Var), J(x)
0D-Var SAR Data Assimilation
Analysis
N.G. Kasapoğlu, IGARSS 2011, Vancouver,Canada July. 29, 2011
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Data Assimilation Formulation
)()(2
1),(),(
2
1)( 11 bTbT xxBxxxHyRxHyxJ
• y : the observed SAR features
• H : the forward model, H(x,) is the predicted SAR feature
• x : ice concentration
• : incidence angle
• R : observation error covariance matrix
• B : background error covariance matrix
N.G. Kasapoğlu, IGARSS 2011, Vancouver,Canada July. 29, 2011
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RadarSAT-2 ScanSAR data
• RadarSAT-2 SCWA Dual-polarized data– C Band, 5.6 GHz– HH and HV channels– 500 km2 coverage– 100 m pixel spacing
N.G. Kasapoğlu, IGARSS 2011, Vancouver,Canada July. 29, 2011
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SAR Features
r2_20090226_215200
• RadarSAT-2 SCWA SGF Product – HH channel
r2_20090301_220402
RADARSAT-2 Data and Products © MacDonald, Dettwiler and Associates Ltd. (2009) - All Rights Reserved.
N.G. Kasapoğlu, IGARSS 2011, Vancouver,Canada July. 29, 2011
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SAR Features
• RadarSAT-2 SCWA SGF Product – HV channel
r2_20090226_215200 r2_20090301_220402
RADARSAT-2 Data and Products © MacDonald, Dettwiler and Associates Ltd. (2009) - All Rights Reserved.
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SAR Features
N.G. Kasapoğlu, IGARSS 2011, Vancouver,Canada July. 29, 2011
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Observed HH-Variance from r2_20090226_215200
Observed HH-Dissimilarity from r2_20090301_220402
SAR Features
• Texture Feature Examples
N.G. Kasapoğlu, IGARSS 2011, Vancouver,Canada July. 29, 2011
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Observed HV-Lee Filtered Image from R2_20090226_215200
Observed HV-Entropy from R2_20090301_220402
SAR Features
• Texture Feature Examples
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Forward Model
0123
456789
2cos..).1(
...SAR
aaICaWSaIC
SATSDaSATaSDaIThaIThaaICfeature
ITh = ice thickness (from CIS image analysis chart)IC = ice concentration (from CIS image analysis chart) = incidence angle (know)SAT = surface air temperature (from GEM)SD = snow depth (from GEM)WS = wind speed (from GEM) = angle between instrument angle (know) and wind direction (from GEM)
= “optimal” model coefficients estimated from “training data”
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Predicted HH from obs operator and image analysis
Observed HH from RadarSAT-2 image
Simulated SAR Features
• r2_20090301_220402
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Predicted HV-Entropy from obs operator and image analysis
HV-Entropy from RadarSAT-2 image
Simulated SAR Features• r2_20090301_220402
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Sea-Ice Open Water DiscriminationMean and Standard deviation of SAR feature (0 HH Mean) for Sea ice (Red) with IC>%95 and Open Water (Blue) versus incidence Angle
19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49-20
-10
0
10
20
30
40
50
60
70
0 H
H M
ea
n
Incidence Angle (deg)
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19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 490.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0 HV
Incidence Angle (deg)
Sea-Ice Open Water DiscriminationMean and Standard deviation of SAR feature (0 HV) for Sea ice (Red) with IC>%95 and Open Water (Blue) versus incidence Angle
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19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 490.5
1
1.5
2
2.5
3
3.5
0 H
V E
ntr
op
y
Incidence Angle (deg)
Sea-Ice Open Water DiscriminationMean and Standard deviation of SAR feature (0 HV Entropy) for Sea ice (Red) with IC>%95 and Open Water (Blue) versus incidence Angle
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19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 490
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0 H
V D
ata
Ra
ng
e
Incidence Angle (deg)
Sea-Ice Open Water DiscriminationMean and Standard deviation of SAR feature (0 HV Data Range) for Sea ice (Red) with IC>%95 and Open Water (Blue) versus incidence Angle
N.G. Kasapoğlu, IGARSS 2011, Vancouver,Canada July. 29, 2011
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Simple Forward Model
)1()()(SAR ICαtpICαtpfeature)H(IC,α OowOiceO
H : Observation operator (forward model operator)IC : Ice Concentration i : Incidence Angle
o = floor (i) o : Rounded Incidence Angle o = 19,20,...,49 for SCWA
Number of Incidence Angle quantization level: 31
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-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0D-Var Analysis Results
Background_Bias Background_Std Analysis_Bias Analysis_std -0.0744 0.199 -0.0667 0.194
F_ID: 3_4_7_8_9_11_13_23
Xa =Xb+ x0D-Var Analysis ResultXb: Background State; PM data only
R2_20090226_215200
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-0.1
0
0.1
0.2
0.3
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0.6
0.7
0.8
0.9
Analysis Increment: x
R2_20090226_215200R: HH Lee-Filtered ImageG: HH VarianceB: HV Mean
0D-Var Analysis Results
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0
0.1
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Analysis Increment: x
R2_20090226_215200
0D-Var Analysis Results
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-0.1
0
0.1
0.2
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0.6
0.7
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Background_Bias Background_Std Analysis_Bias Analysis_std 0.1471 0.3057 0.0889 0.2645
R2_20100221_103028
Xa =Xb+ x
0D-Var Analysis Results
Xb: Background State; PM data only
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-0.1
0
0.1
0.2
0.3
0.4
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0.6
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0.9R
2_20
1002
21_1
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Analysis Increment: x0D-Var Analysis Results
HH
HV
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0D-Var Analysis Results
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Optimal SAR Feature Selection
• Statistically independent features • Forward model generalization capability • Sea-Ice and open water tie points distributions • Analysis results statistics • Weights of factors listed above x
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Separability Measures and Discrimination Analysis
Tk
ii
Cxiw xxkS
i
1
)()()(
k
i
TiiiB nkS
1
))(()(
11 )( bwSStrd
)(
)(2
w
b
Str
Strd
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Tjijijiijjiij mmmmTrTrdd 1111
3 2
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)1(2 8/4
ijdTij edd
ji
ji
jijiT
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ln2
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BDij eJJM 12
SAR Feature Selection
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Best SAR feature combination selection
Top-Down & Bottom-Up Strategies
Analysis Bias as a selection criteria
Feature Selection for Incidence Angle Intervals
Feature Selection for Incidence Angle Intervals
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Acknowledgements
•Canadian Ice Service (CIS)
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Synthetic Aperture Radar Data Assimilation for Sea Ice Analysis
N. Gökhan Kasapoğlugokhank@itu.edu.tr
Thank you for your attention!
N.G. Kasapoğlu, IGARSS 2011, Vancouver,Canada July. 29, 2011
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