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OTT correction

OTT correction. Jean-Luc Vergely (ACRI-ST) Jacqueline Boutin (LOCEAN). Introduction. 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 ?

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OTT correction

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  1. OTT correction Jean-Luc Vergely (ACRI-ST) Jacqueline Boutin (LOCEAN) Progress meeting

  2. Introduction 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 Progress meeting

  3. Robustness : general problem Different ways to obtain OTT estimation assuming a OTT law (additive, multiplicative …) => What are the principal estimators we could be used ? Progress meeting

  4. Different estimators : central distribution case Set of data MEAN (L2) MEDIAN (L1) which minimizes WEIGHTED L2 NORM M which minimizes WEIGHTED L1 NORM Progress meeting

  5. Different estimators : central distribution case Josselin et al.2004 SIMPLE MEADIAN Progress meeting

  6. Different estimators : central distribution case Laplace 1818 LAPLACE MEADIAN Progress meeting

  7. Different estimators : adaptation to OTT case • Easy to adapt to additive and multiplicative cases. • Difficult to deal with L1 norm for convolutive case. • (and for SSS case ?) Progress meeting

  8. Robustness of the estimator Case 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 Progress meeting

  9. meAdian estimation : bootstrap approach X : set of realizations of a random variable X=(x1,x2,…,xN) X*1 X*2 X*b … X* : subset of X F(X*) : estimator of a parameter (central value, multiplicative coefficient …) F (X*1) F (X*2) … F (X*b) s2F(X): variance of F(X) from the subsets X* Progress meeting

  10. meAdian estimation : bootstrap approach for SMOS OTT estimation Data : 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. Progress meeting

  11. Additive OTT Polar X, ascending orbit, August 2010 Progress meeting

  12. Additive OTT Polar X, ascending orbit, August 2010 Progress meeting

  13. Additive OTT Polar X, ascending orbit, August 2010 Progress meeting

  14. Additive OTT Polar X, ascending orbit, August 2010 Progress meeting

  15. Additive OTT Polar X, ascending orbit, August 2010 10/11-04-2011 Progress meeting

  16. Additive OTT Polar X, ascending orbit, August 2010 Progress meeting

  17. Additive OTT Polar X, ascending orbit, August 2010 Progress meeting

  18. Additive OTT Polar X, ascending orbit, August 2010 Progress meeting

  19. Additive OTT Polar Y, ascending orbit, August 2010 Progress meeting

  20. Conclusions for robustness Different 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 Progress meeting

  21. Multiplicative 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. Progress meeting

  22. Multiplicative or additive OTT : how to choose ? Simulated data with radiometric noise = 0.01K and low dynamic in the TBs Progress meeting

  23. Multiplicative or additive OTT : how to choose ? Simulated data with radiometric noise = 1K and low dynamic in the TBs Mean and std of residues cannot allow us to conclude if radiometric noise is too large Progress meeting

  24. Multiplicative or additive OTT : how to choose ? Simulated data with radiometric noise = 1K and high dynamic in the TBs Mean and std of residues cannot allow us to conclude even if the dynamic in the TBs is high Progress meeting

  25. Multiplicative or additive OTT : how to choose ? Progress meeting

  26. Comparison between multiplicative/additive OTT Full pacific half orbit (25/08/2010) Part of the orbit for OTT estimation Whole orbit for performances Progress meeting

  27. Multiplicative or additive OTTapplied to SMOS data Polar X : part of the orbit for OTT estimation Progress meeting

  28. Multiplicative or additive OTTapplied to SMOS data Polar X : whole orbit for validation Progress meeting

  29. Multiplicative or additive OTTapplied to SMOS data Polar X : whole orbit for validation (High value because using weighted L1 norm for OTT estimation) 10/11-04-2011 Progress meeting

  30. Multiplicative or additive OTTapplied to SMOS data Polar X : whole orbit for validation 10/11-04-2011 Progress meeting

  31. OTT resolution Polar X : ascending orbit 10/11-04-2011 Progress meeting

  32. Multiplicative or additive OTTapplied to SMOS data Polar Y : part of the orbit for OTT estimation Progress meeting

  33. Multiplicative or additive OTTapplied to SMOS data Polar Y : whole orbit for validation Progress meeting

  34. Multiplicative or additive OTTapplied to SMOS data Polar Y : whole orbit for validation (High value because using weighted L1 norm for OTT estimation) 10/11-04-2011 Progress meeting

  35. Multiplicative or additive OTTapplied to SMOS data Polar Y : whole orbit for validation 10/11-04-2011 Progress meeting

  36. OTT resolution Polar Y : ascending orbit 10/11-04-2011 Progress meeting

  37. Multiplicative or additive : conclusions • Histograms 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 large • The 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 ? Progress meeting

  38. OTT resolution • What 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 (ξ,η) cell at each resolution : • Cost(ξ,η) =∑(|TBsmos(ξ,η) – OTT(ξ,η) |/σTB(ξ,η) ) / ndata • If resolution adequate : Cost(ξ,η) should be close to 1 • Indicator : cost function versus resolution. Progress meeting

  39. OTT resolution Polar X : ascending orbit Resolution: 0.005 Progress meeting

  40. OTT resolution Polar X : ascending orbit Resolution: 0.015 Progress meeting

  41. Polar X : ascending orbit OTT resolution Progress meeting

  42. OTT resolution Polar Y : ascending orbit Resolution: 0.005 Progress meeting

  43. OTT resolution Polar Y : ascending orbit Resolution: 0.015 Progress meeting

  44. Polar Y : ascending orbit OTT resolution Progress meeting

  45. OTT resolution Polar Y : ascending orbit Center of the FOV 10/11-04-2011 Progress meeting

  46. OTT resolution Polar X : ascending orbit 10/11-04-2011 Progress meeting

  47. OTT resolution Polar X : ascending orbit Center of the FOV SIGNAL FLATTER THAN IN POLAR Y 10/11-04-2011 Progress meeting

  48. Conclusion OTT resolution Resolution of 0.02 in (ξ,η) plan should be sufficient At the centre of the FOV : could be 0.1 in (ξ,η) Polar X and polar Y behave differently Progress meeting

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