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Utilizing SAR Images to Constrain Internal Wave

ModelsChris WackermanChris Wackerman

General Dynamics [email protected]

734-480-5413

SW06 Workshop 12-14 February 2008

Overall Program Goal: Provide Characterization of Internal Waves to Constrain Forward Prediction Models

• number of waves• wave length• radii of curvature• surface current statistics• phase speed (from single image)

Spatial Map of:

Designed to measure “statistics” of IWs, not to match to individual waves

single image)

IW Future Characteristics

Modify model inputs to match

SAR characterization

now

IW Model•simple 2 layer model•full-up model

ESA 2006ENVISAT 07/23/06 C-VV

Use model inputs to predict future IW

characteristics

Hard Problem is to Characterize Surface Currents From SAR Intensity => Alternative Title: Surface Current Characterization From SAR Images via Inversion

Estimating Surface Currents and Phase Speed from SAR Imagery

• Find surface currents such that forward SAR image predictionmodel matches internal wave signature

• Use normalized observation (RCS-Mean)/Mean to avoidcalibration issues

Solve wave action balance equation

Surface current

field

Wave spectra

field

Apply 2-scale RCS model with hydro

term, breaking, PO

Forward Model

Normalized RCS Field

SAR image signature

Error

Estimate gradient of the error with respect to

surface current and phase speed

Find step in conjugate gradient direction to minimize

error

Next current estimate

Forward Model

Inverse Model





Surface current gradient

field

Wave spectra

field


term, breaking, PO

Forward Model


SAR image signature

Error




error


Forward Model

Inverse Model

(((( )))) Sx

xgx Fk

A

x

uk

t

Acu

t

A====

∂∂∂∂

∂∂∂∂

∂∂∂∂

∂∂∂∂−−−−

∂∂∂∂

∂∂∂∂++++++++

∂∂∂∂

∂∂∂∂

Wave Action Balance Equation (x-variation only)

• Solved for wave scales from 1/10 to 100 meters• Uncertainties in FS terms with wind growth rate, sources/sinks of wave energy, wave equilibrium spectrum






field

Wave spectra

field


term, breaking, PO

Forward ModelRCS Model


SAR image signature

Error




error


Forward Model

Inverse Model

(((( )))) (((( ))))[[[[ ]]]] (((( )))) cucucucubo dsdss,ss,sh1s,s ρρρρ++++σσσσ====σσσσ ∫∫∫∫∫∫∫∫Tilted Bragg

“Hydrodynamic” Modulations

[[[[ ]]]](((( ))))

(((( ))))sc

su

I4

22sm

2ePO s,s

cos

)0(Rk4exp ρρρρ

θθθθ

ππππσσσσ−−−−====σσσσ

(((( )))) da,0NAT

2a

BR0BR ∫∫∫∫

∞∞∞∞−−−−

σσσσσσσσ====σσσσ

Physical Optics specular reflections

Breaking waves

RCS Model






field

Wave spectra

field


term, breaking, PO

Forward Model

Error Gradient wrt. current gradient

(((( )))) (((( )))) (((( ))))

(((( ))))

sswsf

xdu

x,kfkSkS

r

rrrr

∂∂∂∂

∂∂∂∂====

(((( ))))(((( )))) (((( )))) (((( )))) (((( ))))[[[[ ]]]] (((( )))) xdsdspkSkSsG

1xE2

xdx

du

Msfsf

0o

rrrrrrr

r∫∫∫∫∫∫∫∫ −−−−++++

σσσσ====

∂∂∂∂

∂∂∂∂

Tilted Bragg Scattering


SAR image signature

Error




error


Forward Model

Inverse Model

(((( ))))oxdx

du r∂∂∂∂

(((( ))))

(((( ))))(((( ))))

(((( ))))(((( ))))(((( ))))sr

sko

o

s

k

5.0kpcosxx

xdx

du

x,kf s r

r

rr

r

rr r

ββββ

++++ϕϕϕϕ−−−−δδδδ====

∂∂∂∂

∂∂∂∂“Lossy” Limit => Large

relaxation rate ββββr => no spatial “memory” in solution

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

0 50 100 150 200 250 300 350 400

Distance Across IW (m)(R

CS

-Me

an

)/M

ean

Iteration 1 Result

Iteration 2 Result

Iteration 3 Result

Iteration 4 Result

Iteration 5 Result

Observation

0.015

Previously showed that we could reconstruct input current gradient from simulated RCS values using these approximation…

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

0 50 100 150 200 250 300 350 400

Distance Across IW (m)

Cu

rren

t G

rad

ien

t (d

ud

x)

(s**

-1)

Iteration 1 Result

Iteration 2 Result

Iteration 3 Result

Iteration 4 Result

Iteration 5 Result

Truth

Initial Guess

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

0 100 200 300 400 500 600

(RC

S-M

ean

)/M

ean

Iteration 1 Result

Iteration 2 Result

Iteration 3 Result

Observation

0.015

… although we miss the last bit of current at the end (probably

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

0 100 200 300 400 500 600

Distance Across IW (m)

Cu

rren

t d

u/d

x (

s**

(-1))

Iteration 1 Results

Iteration 2 Result

Iteration 3 Result

Truth

Initial Guess

at the end (probably due to the approximations)

=> The current1 question is whether the forward model is generating the correct SAR image modulations for the actual surface currents and surface wave spectra

• Would like to validate the choices for the sources/sinks in the wave action balance equation from measurements of surface wave spectra over the required scales

• may be able to use buoy data for large-scale waves as

1Pardon the pun

• may be able to use buoy data for large-scale waves as the IW passes by?

• Would like to validate final model from measurements of surface currents coincident with IW SAR signature

• WamOS data may be best for this when it becomes available• OSU have graciously put out their ADCP data from the Oceanus (multiple thanks!)

Track

Oceanus ADCP Data from 08/18/06 Courtesy of OSU


Start

Shallowest depth is 3.5m – what is a better way to extrapolate to surface currents other than linear interpolation?


Linear interpolation region


Linear interpolation region

4 waves, ~ 0.5 m/s peak current, varying widths => du/dx increases left to right


EnvisatAug 18 20062:37 GMTC-VV

N

Wind To

SAR

Look

Wind To

5 m/s

Oceanus Track (blue) and SAR Image Locations (red)

EnvisatAug 18 20062:37 GMTC-VV

Envisat0818

0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

1000 2000 3000 4000 5000

Distance (m)

Delt

a-R

CS

=> SAR Image modulations are from ±0.1 to 0.4, spacing is ~ 300 – 370 m

ERSAug 18 20093:06 GMTC-VV

ERS0818

ERSAug 18 20093:06 GMTC-VV

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

2000 3000 4000 5000 6000 7000

Distance (m)

Delt

a-R

CS

=> ½ hour later, SAR Image modulations are ~ ±0.1 to 0.3, spacing is ~ 300 – 370 m

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 1000 2000 3000 4000 5000 6000 7000 8000

Distance Along Plot (m)

(RC

S-M

ean

)/M

ean

RADARSAT 08/23 CHH

SAR Look

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0 1000 2000 3000 4000 5000 6000 7000 8000


(RC

S-M

ea

n)/

Me

an

ENVISAT 07/23 CVV

SAR Look

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0 1000 2000 3000 4000 5000 6000 7000 8000


(RC

S-M

ean

)/M

ea

n

Distance Along Plot (m) SAR Look

Wind Direction

Wind Speed 3 m/s

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0 1000 2000 3000 4000 5000 6000 7000 8000


(RC

S-M

ea

n)/

Me

an

Wind Direction

Wind Speed 5 m/s

WABE Runs

-4.0

-2.0

0.0

2.0

RC

S (

dB

)

VV Full Model

HH Full Model

VV no PO

CMOD4 RCS

HH no PO

VV With Breaking

-12.0

-10.0

-8.0

-6.0

-600 -400 -200 0 200 400 600

Distance (m)

RC

S (

dB

)

Wabe Forward Runs

1

1.5

2

2.5

3

De

lta

-RC

S

0.6 m/s peak, -0.4 m/s cp

0.6 m/s peak, 0.0 m/s cp



-1

-0.5

0

0.5

1

-600 -400 -200 0 200 400 600

Distance (m)

De

lta

-RC

S

Wabe Run 4 Waves

-4.0

-2.0

0.0

2.0

VV

RC

S (

dB

)

0.3 m/s peak

0.6 m/s peak

-10.0

-8.0

-6.0

-4.0

-2000 -1500 -1000 -500 0 500 1000 1500 2000

Distance (m)

VV

RC

S (

dB

)

WABE Run 4 Waves

0.5

1

1.5

2

De

lta

-RC

S V

V

0.6 m/s peak

0.3 m/s peak

-1

-0.5

0

0.5

-1000 -800 -600 -400 -200 0 200 400 600 800 1000

Distance (m)

De

lta

-RC

S V

V

Summary of WABE Run Modulations

0.5

1

1.5

2

Ma

x (

bla

ck

) o

r M

in (

red

) D

elt

a R

CS

Max Delta-RCS Modulations

Min Delta-RCS Modulations

4 wave Min Delta-RCS

4 wave Max Delta-RCS

-1

-0.5

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Peak Current (m/s)

Ma

x (

bla

ck

) o

r M

in (

red

) D

elt

a R

CS

=> With 4 wave runs, peak modulations are consistent with observations but minimum are too low

Observed Modulations

Summary• Forward model appears to be consistent with max RCS modulations

when including 4 waves, but too low for min RCS modulations– May be a noise floor problem with the SAR?

• Questions I would like to discuss during the workshop– Are the units rights for the ADCP?– What is a better way to extrapolate to a surface current?– Can I get IW modulations wavelength from the current data (i.e. do we

know the ship velocity and the IW phase speed)?– Are there other surface current observations available?– Does anyone want the SAR images and/or interpretations of them for their – Does anyone want the SAR images and/or interpretations of them for their

analysis?

• We have derived the adjoint of the WABE for RCS errors as a function of current to avoid the simplifying assumptions used in the gradient estimate

– It should converge faster and be more accurate close to the solution

• Now need to use this forward model in the new inversion and derive the current

RADARSATAug 18 200622:58 GMTC-HH

ENVISATCVV

July 23 2006

SAR Look

Line 1

Wind Direction

Wind Speed5 m/s Line 2

RADARSATCHH

August 23, ‘06

SAR Look

Wind Direction

Line 1

Wind Direction

Wind Speed3 m/s

Plot Locations

Line 2

RSI 2006

utilizing sar images to constrain internal wave modelsacoustics.whoi.edu › sw06 ›...

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