10/11-04-2011Progress meetingOTT correction

Jean-Luc Vergely (ACRI-ST)Jacqueline Boutin (LOCEAN)

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10/11-04-2011Progress meetingIntroduction General problematic of the OTT : what kind of correction should be applied ? How to compute the best estimator of the correction ?

1/ Robustness of the OTT estimators : L1, L2, Lp, meAdian ?

2/ Additive/multiplicative ?

3/ OTT resolution

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10/11-04-2011Progress meetingRobustness : general problemDifferent ways to obtain OTT estimation assuming a OTT law (additive, multiplicative )

=> What are the principal estimators we could be used ?

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10/11-04-2011Progress meetingDifferent estimators : central distribution caseMEAN (L2)MEDIAN (L1)WEIGHTED L1 NORMM which minimizesSet of dataWEIGHTED L2 NORM which minimizes

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10/11-04-2011Progress meetingDifferent estimators : central distribution caseSIMPLE MEADIANJosselin et al.2004

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10/11-04-2011Progress meetingDifferent estimators : central distribution caseLAPLACE MEADIANLaplace 1818

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Different estimators : adaptation to OTT caseEasy to adapt to additive and multiplicative cases.

Difficult to deal with L1 norm for convolutive case.

(and for SSS case ?)

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10/11-04-2011Progress meetingRobustness of the estimatorCase of the meAdian which is a weighting between mean and median

The weight depends on the variance of the median V(M) and the variance of the mean V(x)

If mean robust -> MeAdian converge to mean (m)If median robust -> MeAdian converge to median

How to compute the variances V(M) and V(x) ?

Boostrap approach

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10/11-04-2011Progress meetingmeAdian estimation : bootstrap approachX=(x1,x2,,xN)X*1X*2X*bF (X*1)F (X*2)F (X*b)F(X*) : estimator of a parameter (central value, multiplicative coefficient )X : set of realizations of a random variable X* : subset of Xs2F(X) : variance of F(X) from the subsets X*

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10/11-04-2011Progress meetingmeAdian estimation : bootstrap approach for SMOS OTT estimationData : 200 snapshots

Cosdir plan discretisation in cells of (dxi,deta).

For each cell, a set of TBs is available. Ndata is available.

Random drawing of 300 subsets of Ndata/2. Computation of mean and median indicator for each subset.

The dispersion of the mean and median gives an estimation of the robustness. If the dispersion of the mean is lower than the dispersion of the median, then the mean is more robust (resistant) than the median. And vice versa.

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Additive OTT10/11-04-2011Progress meetingPolar X, ascending orbit, August 2010

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Additive OTT10/11-04-2011Progress meetingPolar X, ascending orbit, August 2010

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Additive OTT10/11-04-2011Progress meetingPolar X, ascending orbit, August 2010

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Additive OTT10/11-04-2011Progress meetingPolar X, ascending orbit, August 2010

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Additive OTT10/11-04-2011Progress meetingPolar X, ascending orbit, August 2010

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Additive OTT10/11-04-2011Progress meetingPolar X, ascending orbit, August 2010

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Additive OTT10/11-04-2011Progress meetingPolar X, ascending orbit, August 2010

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Additive OTT10/11-04-2011Progress meetingPolar X, ascending orbit, August 2010

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Additive OTT10/11-04-2011Progress meetingPolar Y, ascending orbit, August 2010

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10/11-04-2011Progress meetingConclusions for robustnessDifferent estimators show significant different results for additive OTT (mean difference is about 0.2 K).

Bootstrap approach allow to build indicators of the estimator robustness

Best estimator should be the Laplace meAdian estimator which weighted the L1 and L2 estimator accordingly to their respective robustness

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10/11-04-2011Progress meetingMultiplicative or additive OTT : how to choose ?Numerical experimentation is required.

Imagine that the true data is affected by an multiplicative OTT and that we think by error that the data is affected by an additive OTT.Or vice et versa

-> simulated data using additive OTT and process using the multiplicative OTT hypothesis.

-> simulated data using multiplicative OTT and process using the additive OTT hypothesis.

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10/11-04-2011Progress meetingMultiplicative or additive OTT : how to choose ?Simulated data with radiometric noise = 0.01K and low dynamic in the TBs

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10/11-04-2011Progress meetingMultiplicative or additive OTT : how to choose ?Mean and std of residues cannot allow us to conclude if radiometric noise is too largeSimulated data with radiometric noise = 1K and low dynamic in the TBs

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10/11-04-2011Progress meetingMultiplicative or additive OTT : how to choose ?Mean and std of residues cannot allow us to conclude even if the dynamic in the TBs is highSimulated data with radiometric noise = 1K and high dynamic in the TBs

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10/11-04-2011Progress meetingMultiplicative or additive OTT : how to choose ?

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10/11-04-2011Progress meetingComparison between multiplicative/additive OTT

Full pacific half orbit (25/08/2010)Part of the orbit for OTT estimationWhole orbit for performances

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10/11-04-2011Progress meetingMultiplicative or additive OTTapplied to SMOS dataPolar X : part of the orbit for OTT estimation

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10/11-04-2011Progress meetingMultiplicative or additive OTTapplied to SMOS dataPolar X : whole orbit for validation

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10/11-04-2011Progress meetingMultiplicative or additive OTTapplied to SMOS dataPolar X : whole orbit for validation (High value because using weighted L1 norm for OTT estimation)

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10/11-04-2011Progress meetingMultiplicative or additive OTTapplied to SMOS dataPolar X : whole orbit for validation

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10/11-04-2011Progress meetingOTT resolutionPolar X : ascending orbit

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10/11-04-2011Progress meetingMultiplicative or additive OTTapplied to SMOS dataPolar Y : part of the orbit for OTT estimation

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10/11-04-2011Progress meetingMultiplicative or additive OTTapplied to SMOS dataPolar Y : whole orbit for validation

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10/11-04-2011Progress meetingMultiplicative or additive OTTapplied to SMOS dataPolar Y : whole orbit for validation (High value because using weighted L1 norm for OTT estimation)

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10/11-04-2011Progress meetingMultiplicative or additive OTTapplied to SMOS dataPolar Y : whole orbit for validation

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10/11-04-2011Progress meetingOTT resolutionPolar Y : ascending orbit

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10/11-04-2011Progress meetingMultiplicative or additive : conclusionsHistograms of residues do not help to distinguish between additive or multiplicative OTT if :The number of data is small, There is a low dynamic in the data (no sensitivity for the multiplicative parameters) The radiometric noise is too largeThe correction is very low

Histograms of residues could help if selection of low and large TB values is performed. Land to be added ?

Performance seems to depend on the FOV positions. In front of the FOV, multiplicative OTT seems better. In back position, additive OTT seems better.

Neither additive OTT nor multiplicative OTT is adapted ?

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10/11-04-2011Progress meetingOTT resolutionWhat resolution should be applied in order to define OTT ?

This depends on : TB spatial variations. If TBs vary slowly, OTT varies slowly too.OTT spatial correlation length.

Computation of OTT using different resolution

Cost function defined for each (,) cell at each resolution : Cost(,) =(|TBsmos(,) OTT(,) |/TB(,) ) / ndata

If resolution adequate : Cost(,) should be close to 1

Indicator : cost function versus resolution.

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10/11-04-2011Progress meetingOTT resolutionPolar X : ascending orbitResolution: 0.005

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10/11-04-2011Progress meetingOTT resolutionPolar X : ascending orbitResolution: 0.015

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10/11-04-2011Progress meetingOTT resolutionPolar X : ascending orbit

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10/11-04-2011Progress meetingOTT resolutionPolar Y : ascending orbitResolution: 0.005

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10/11-04-2011Progress meetingOTT resolutionPolar Y : ascending orbitResolution: 0.015

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10/11-04-2011Progress meetingOTT resolutionPolar Y : ascending orbit

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10/11-04-2011Progress meetingOTT resolutionPolar Y : ascending orbit Center of the FOV

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10/11-04-2011Progress meetingOTT resolutionPolar X : ascending orbit

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10/11-04-2011Progress meetingOTT resolutionPolar X : ascending orbit Center of the FOVSIGNAL FLATTER THAN IN POLAR Y

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10/11-04-2011Progress meetingConclusion OTT resolutionResolution of 0.02 in (,) plan should be sufficient

At the centre of the FOV : could be 0.1 in (,)

Polar X and polar Y behave differently

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