A review of CLS retracking Page 1 solutions for coastal altimeter waveforms P.Thibaut, J.C.Poisson : Collecte Localisation Satellite, France A.Halimi, C.Mailhes.Y.Tourneret : University of Toulouse / IRIT-ENSEEIHT-TESA, France F.Boy, N.Picot : Centre National d Etudes Spatiales, France San Diego, CA, USA : October 2011
Coastal waveforms Page 2
Retracking solutions Page 3 Brown ocean waveforms Brown corrupted ocean waveforms Current ocean retracking MLE3 or MLE4 SVD before MLE3/4 to denoise the estimations Oce3 in Pistach products
Retracking solutions Page 4 Brown ocean waveforms Brown corrupted ocean waveforms Current ocean retracking MLE3 or MLE4 SVD before MLE3/4 to denoise the estimations Oce3 in Pistach products Retracking on troncated window Red3 in Pistach products
Retracking solutions Page 5 Brown ocean waveforms Brown corrupted ocean waveforms Current ocean retracking MLE3 or MLE4 SVD before MLE3/4 to denoise the estimations Oce3 in Pistach products Red3 Retracking on troncated window Brown + Gaussian Peak
Retracking solutions Page 6 Focus on two retracking solutions Retracking dedicated to Brown + Gaussian peak waveforms (A.Halimi from the University of Toulouse) Denoised estimations with Singular Value Decomposition cf S.Labroue talk with validation results on the Alghulas current
Brown s model Page 7
Jason-2 waveform classification Page 8
Jason-2 waveform classification Page 9
Example of Jason-2 waveforms Page 10 Waveforms observed on coastal areas but also on hydrological areas
Brown with Gaussian Peak (BGP) This model has been already presented in Porto Coastal meeting last year (P.Thibaut) Page 11 Well adapted for echoes of class 13 Not appropriate for asymmetric peaks located near at the end of the leading edge (class 7)
Brown with Asymmetric Gauss. Peak Page 12 (BAGP)
Maximum Likelihood Estimator Page 13
Estimation Performance Page 14
RMSE for class 13 Page 15
RMSE for class 7 Page 16
Real and estimated Jason-2 WFs Page 17
Conclusions on peaky models Page 18 The BAGP is a generalization of the BGP model BGP well adapted to class 13 BAGP well adapted to coastal altimetric waveforms (classes 13 and 7)
Retracking solutions Page 19 Focus on two retracking solutions Retracking dedicated to Brown + Gaussian peak waveforms (A.Halimi from the University of Toulouse) Denoised estimations with Singular Value Decomposition cf S.Labroue talk with validation results on the Alghulas current
Truncated Singular Value Decomposition for Noise Reduction The denoising process consists in : J1 Ku band raw waveforms Taking the S matrix representing the noisy signal (Wfs matrix) S= S + B Computing the Singular Value Decomposition S (m,n) : WF matrix (m= 104; n=300) U (m,m), V*(n,n): unit matrices S (m,n) : diagonal matrix S= USV* J1 Ku band filtered waveforms SVD filtering S= l 1 VS 1 +.+l k VS k +..l r VS r signal + noise noise Discarding small singular values of S (which mainly represent the additive noise) The rank-k matrix Ak represents a filtered signal
Truncated Singular Value Decomposition for Noise Reduction Raw waveforms Filtered waveforms
Parameters used for the SVD filtering Determination of the truncature threshold Investigations on the frequential spectrum of the SLA residuals (SLA Products SLA SVD ) 96 % threshold - SLA Products - SLA SVD - Residuals 10km 700m
Parameters used for the SVD filtering Determination of the truncature threshold Investigations on the frequential spectrum of the SLA residuals (SLA Products SLA SVD ) 92 % threshold - SLA Products - SLA SVD - Residuals 10km 700m Page 23
Parameters used for the SVD filtering Determination of the truncature threshold Investigations on the frequential spectrum of the SLA residuals (SLA Products SLA SVD ) 90 % threshold - SLA Products - SLA SVD - Residuals 10km 700m
Parameters used for the SVD filtering Determination of the truncature threshold Investigations on the frequential spectrum of the SLA residuals (SLA Products SLA SVD ) 88 % threshold - SLA Products - SLA SVD - Residuals 10km 700m
Parameters used for the SVD filtering Determination of the truncature threshold Investigations on the frequential spectrum of the SLA residuals (SLA Products SLA SVD ) 84 % threshold - SLA Products - SLA SVD - Residuals 10km 700m
Parameters used for the SVD filtering Determination of the truncature threshold Investigations on the frequential spectrum of the SLA residuals (SLA Products SLA SVD ) 80 % threshold - SLA Products - SLA SVD - Residuals 10km 700m
Impact on range (threshold of 84 %) SLA spectrum Ku band SLA variation MLE4 SVD+MLE4 MLE4 SVD+MLE4 latitude 10km 700m 8 cm at 20 Hz 5 cm at 20 Hz
Impact on range (threshold of 90 %) SLA variation SLA spectrum Ku band - SLA Prod - SLA SVD 10km 700m 8 cm at 20 Hz 7 cm at 20 Hz
SWH variation Impact on SWH (threshold of 84%) SWH spectrum Ku band MLE4 SVD+MLE4 MLE4 SVD+MLE4 10km 700m latitude 54 cm at 20 Hz 12 cm at 20 Hz
Impact on SWH (threshold of 90 %) SWH SWH spectrum Ku band SWH SVD SWH Prod 54 cm at 20 Hz Bias : SWH SVD = SWH Prod - 3 cm (Ku) 40 cm at 20 Hz Two SWH populations appear in the SWH distribution
Performances on noise level Synthesis of the noise levels obtained (for threshold 90%) 20 Hz 1 Hz Ku C Ku C Range 7.07 cm (products = 8.02) 16.6 cm (products = 20.14) 2.64 cm (products = 2.81) 4.6 cm (products = 5.34) SWH 38.27 cm (products = 50.7) 100 cm (products = 120) 11 cm (products = 14) 25.35 cm (products = 32.73) Sigma0 0.307 db (products = 0.376) 0.13 db (products = 0.13) 0.14 db (products = 0.16) 0.11 db (products = 0.11) Observed gains at 20 Hz are reduced at 1 Hz. The 20 Hz denoising allows to increase the number of elementary measurements
Applications on a track that crosses the Alghulas current (South Africa) Jason-2 pass 96 has been processed : SVD (84%)+MLE4. Page 33 SLA SWH
Conclusions SVD allows a strong noise reduction on SWH and range.this reduction depends on the rank truncation and can be adapted to the application SVD allows a gain in SLA rms measurements by a factor between 1.2 (weak waves) to 2 (strong waves). SVD allows to pass from a 7 km resolution (corresponding to 1 Hz products) to a 1.2 km (6 Hz) with an equivalent noise (precision of the SLA). We are testing SVD processing on different zones where small structures now hidden in the noise level for current products, will clearly appear.
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