SAR AltimetryApplications overWater SurfacesCristina Martin-Puig(1), Jose Marquez(1), Giulio Ruffini(1), R. KeithRaney (2), Jérôme Benveniste(3)

(1) Starlab Barcelona S.L.(2) Johns Hopkins University APL(3) ESA - ESRIN

2

Presentation Contents

i. SAMOSA Project• SAMOSA Context & Background

• SAR Altimetry in Brief

• SAMOSA in Brief

• SAMOSA Project Description

• Current Status: TASK 2

ii. Reduced SAR mode• Cryosat Acquisitions Modes• Cryosat Data Types L1 data• What is reduced SAR mode? Why reduced SAR?• How can we achieve Reduced SAR mode data?• Cramer Raô-Bound to assess on reduced SAR mode performance• Conclusions and SAMOSA Future work

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SAMOSA context &background

• 2009, Cryosat-2 SIRAL altimeter apply SyntheticAperture Radar (SAR) techniques to classical radaraltimetry

• In addition to Cryospheric communities, Hydrosphere andOceanographic communities

• SAMOSA is the short name of Development of SARAltimetry Mode Studies and Applications overOcean, Coastal Zones and Inland Waters

© Cryosat - ESA

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SAR Altimetry in Brief

[Ref] Raney , R.K., The Delay / Doppler RadarAltimeter, IEEE Trans. Geosci. RemoteSensing, 36, 1 57 8-1 588, 1 998.

SAR ALTIMETRY

key innovation along trackprocessing for:

• increased resolution• multi-look processing betterspeckle reduction

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SAMOSA in Brief

• Main objectiveQuantification of the improvement of SAR altimetry toconventional altimetry over water surfaces COASTAL,OCEAN, and IN LAND

• Consortium:Leader: Satellite Observing Systems (SOS,UK)The Danish National Space Centre (NDSC, Denmark)De Montfort University (DMU,UK)The National Oceanography Centre (NOCS, UK)Starlab Barcelona S.L (STARLAB,Spain).

• ESA Project Officer:Jérôme Benveniste (ESRIN)

• External collaboration of:Dr. Keith Raney (Johns Hopkins University)

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SAMOSA ProjectDescription

Task 1State of the art assessment

Task 2Range Error As a fon of

ocean surface

Task 3Potential capabilities of SAR modedata ov er ocean. How the higher

resolution of SAR may enhance thecapability to prov ide info on short-wav elength greop. Signals in areas

of high wav es

Task 4SAR Altimeter echo ov er water

-Non circular ground resolution cell- Multiple looks

Task 5New re-tracking method

ov er water

Task 6Improv ement of

capabilities for coastalzones estuaries, riv ers

and lakes

Task 7Assessment of RA-2

indiv idual echoes ov erwater

Task 8Validation using ASIRAS

data

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Task 2

Three subtasks

• Theoretical modelling to characterize expected gainbetween high PRF reduced SAR mode data and LowPRF classical Low Resolution Mode (LRM) data

• Development of a software to reduce SAR FBR datato reduced SAR mode data

• Processing of simulated data sets over slowly varying openocean Numerical Simulations Using CRYMPS

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Cryosat Acquisition Modes

[Ref] Cy osat Mission and Data Description. Page 28th. ESA Doc No. CS-RP-ESA-SV-0059

PRF = 17.8KHz

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Cryosat Data Types L1data - FBR

A/D

fs

HeightTracker

ChirpGenerator

2DStore

ATFFT iFFT

Doppler Positon Maping

|·|2 Σ

DopplerShift

RCMCPhase

A/D IFFT

|·|2

Σ

fs

HeightEstimation

HeightTracker

ChirpGenerator

Controllable delay

Conventional Altimeter

SAR Altimeter

LRM data Level 1 FBR.

Multilooked echoes at a rate of ~20 Hz

SAR data Level 1 FBR

Individual complex I,Q echoes

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What is reduced SAR modedata? Why reduced SAR?

What?

Reduced SAR mode data intends to emulate LRM starting with FBRSAR.

Why?

• This data would let us achieve two different product types from thesame acquisition mode (SAR)• The resulting data would support quantitative comparison of themeasurement precision delivered by the two styles of altimeter overidentical sea states

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How can we achieveReduced SAR mode data?

…LRM

tPRFLRM = 1970 Hz

Echo wav eforms

How do we will analyze theperformance?

CRAMÉR-RAO BOUND

92 echoes at a rate of ~ 20 Hz

How many waveforms can we achieve for a reduced SAR mode?

8-pulsepre-sum . . .

Pre-summing of n pseudo-LRMwaveforms after pre-sum

SAR

t

64 Echo wav eforms.

PRFSAR = 17.8KHz

9SAR

LRM

PRFn

PRF= =

8n =

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Cramér-Rao Bound (CRB) I

• N point dataset X = {X[0], X[1], …, X[N-1]} and X = fon(θ) weare interested in determine θ from X, or define a goodestimator of θ

• Provided that the data are inherently random

• CRB help us find the minimum variance of anunbiased estimator if it exists.

CRB theorem

If satisfies:

ˆ ( )g X! =

( ; )p X !

( ; )p X !

ln( ( ; ))0

d p XE for

d

!!

!

" #= $% &' (

2

2

1ˆvar( )ln ( ; )p X

E

!!

!

"# $%

& ' (%) *

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CRB II – decorrelatedsignal simplification

Focusing on complex, vectorial Gaussian-distributedsignals

Being г the covariance matrix

CRB ugly expression ; de-correlated signal as is the case

*( [ ]) ( [ ])

( )

1( , )

X E X X E X

card Xp X e!

"

# $% % &'& %( )='

( )( )*

[ ] [ ]ij i i j jE X E X X E X! "# = $ $% &' (

2

2

2

ˆvar( )

[ ]1 2i i

i i i

CRB

E XCRB

!

! !"

#

$% $& '= + ( )% $ % $* +,

14

Conventional AltimetryComplex Waveform

A/D( )Rs t

( )n t ( )ds t

IFFT

i R d d

d

X S S N S

u N S

! "

! "

= # + # =

= + #

( )*

1/32

1

[ ] 0

1[ ] ;

4

i

ij i j

E X

E u u HSNR

!" #

!

=

$ = +%

Trickypart

dS S! = "

Sea surface scatteringSpeckle statistics

Complex, Vectorial, zero mean,Gaussian PDF

Thermal noiseComplex, Vectorial, with Im

and Re components bothGaussian, zero mean and stdev

1

The reflected waveform will also be Gaussian with:

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Reduced SAR mode vs LRM

• The main difference of both modes is the term SNR1

• With reduced SAR for approximately 20Hz rate we willachieve 32 pseudo-LRM de-correlated echoes, while for LRMwe will have 92 de-correlated echoes.

• This means that the reduce SAR mode SNR1 will beapproximately 10 log (sqrt(32/92)) = -2.29 dB worse thana conventional altimeter.

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How much will be the previousdegradation in precision?

Considering that

CRB simplifies to:

is related to θ and SWH, and θ related to “r”

[ ] 0i

E X =

2

2

ˆvar( )

1i

i i

CRB

CRB

!

!

"

#

$%=

% $&

( )( )1/3;i fon H! "# =

( )1/3;H! "

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Conclusions & future work

• The main difference in both acquisition modes is a -2.29SNR1 degradation

• Future work needs to be done in numerically simulate theperformance of range vs SWH. The theoretical work iscompleted

• A software to transform FBR data into pseudo-LRM data isalmost completed

• This software will permit numerical simulations withCRYMPS data to assess on range precision (NOCS) Jensen& Raney DDA: Better Measurement Precision 1998

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Acknowledgements

• My collaborators: Jose Marquez, Giulio Ruffini and Dr. KeithRaney

• The SAMOSA team

• Jérôme Benveniste (ESRIN)

• Maria Milagro (ESRIN)

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Thanks!

Contact:Cristina Martin-PuigStarlab Barcelona S.L.Camí de l’Observatori s/n08035 – Barcelona – Spain+34 93 254 03 69http://starlab.escristina.martin@starlab.es

SAMOSA Project Contact:David Cotton; d.cotton@satobsys.co.uk

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De-correlated Signal

• Signal BW = 350 MHz

• Sampling rate approx 638.3MHz

• Nyquist = 2*BW = 700MHz

• Under-sampling, de-correlated signal

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Coherence time

d

2f

1f

Along trackAcross

track

1/2

1/3 01

0

( 2 )

1 /e

c H Rr

R R

!" #+= $ %

+& '