1_kasapoglu_igarss11.ppt

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

N.G. Kasapoğlu, IGARSS 2011, Vancouver,Canada July. 29, 2011

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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


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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


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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


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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.


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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


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Observed HH-Variance from r2_20090226_215200

Observed HH-Dissimilarity from r2_20090301_220402

SAR Features

• Texture Feature Examples


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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


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


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

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0.09

0 H

V D

ata

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ng

e


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


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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

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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

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Analysis Increment: x

R2_20090226_215200R: HH Lee-Filtered ImageG: HH VarianceB: HV Mean



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Analysis Increment: x

R2_20090226_215200



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0.9

Background_Bias Background_Std Analysis_Bias Analysis_std 0.1471 0.3057 0.0889 0.2645

R2_20100221_103028

Xa =Xb+ x


Xb: Background State; PM data only


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-0.1

0

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0.9R

2_20

1002

21_1

0302

8

Analysis Increment: x0D-Var Analysis Results

HH

HV


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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

1

2

1

)1(2 8/4

ijdTij edd

ji

ji

jijiT

ji mmmmBD2

ln2

1

28

11

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 Kasapoğ[email protected]

Thank you for your attention!


1_kasapoglu_igarss11.ppt

Technology

training data

analysis vector

analysis incrementx

jx analysis

sar features r2

sar features radarsat

scansar data radarsat

ice concentration