Improving Nonparametric Estimates of the Sea State Bias in Radar Altimeter Measurements of Sea Level

Philippe Gaspar Collecte Localisation Satellites, Space Oceanography Division, Ramonville, France

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Sylvie Labroue Collecte Localisation Satellites, Space Oceanography Division, Ramonville, France

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Françoise Ogor Collecte Localisation Satellites, Space Oceanography Division, Ramonville, France

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Guillaume Lafitte Institut National des Sciences Appliquées, Département Génie Mathématique et Modélisation, Toulouse, France

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Laurence Marchal Institut National des Sciences Appliquées, Département Génie Mathématique et Modélisation, Toulouse, France

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Magali Rafanel Institut National des Sciences Appliquées, Département Génie Mathématique et Modélisation, Toulouse, France

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Abstract

A fully nonparametric (NP) version of the sea state bias (SSB) estimation problem in radar altimetry was first presented and solved by Gaspar and Florens () using the statistical technique of kernel smoothing. This solution requires solving a large linear system and thus comes with a significant computational burden. In addition, examination of SSB estimates reveals a marked bias close to the boundaries of the estimation domain. This paper presents efforts to improve both the skill and the computational efficiency of the SSB estimation method. Computational efficiency is rather easily improved by an appropriate kernel choice that transforms the linear system to be solved into a very sparse system for which fast solution algorithms exist. The estimation bias proves to be due to the choice of a rudimentary NP estimator for conditional expectations. Use of a more elaborate estimator appears to be possible after a slight adaptation of the method. This solves the bias problem. Further improvement of the estimation skill is obtained by a local tuning of the kernel bandwidth. The refined estimation method is finally used to obtain a new NP estimate of the TOPEX SSB. This estimate yields larger SSB values than most previous estimates, in better agreement with recent in situ observations.

Corresponding author address: Dr. Philippe Gaspar, Collecte Localisation Satellites, Space Oceanography Division, 8-10 rue Hermes, Parc Technologique du Canal, Ramonville Cedex 31526, France. Email: philippe.gaspar@cls.fr

Abstract

A fully nonparametric (NP) version of the sea state bias (SSB) estimation problem in radar altimetry was first presented and solved by Gaspar and Florens () using the statistical technique of kernel smoothing. This solution requires solving a large linear system and thus comes with a significant computational burden. In addition, examination of SSB estimates reveals a marked bias close to the boundaries of the estimation domain. This paper presents efforts to improve both the skill and the computational efficiency of the SSB estimation method. Computational efficiency is rather easily improved by an appropriate kernel choice that transforms the linear system to be solved into a very sparse system for which fast solution algorithms exist. The estimation bias proves to be due to the choice of a rudimentary NP estimator for conditional expectations. Use of a more elaborate estimator appears to be possible after a slight adaptation of the method. This solves the bias problem. Further improvement of the estimation skill is obtained by a local tuning of the kernel bandwidth. The refined estimation method is finally used to obtain a new NP estimate of the TOPEX SSB. This estimate yields larger SSB values than most previous estimates, in better agreement with recent in situ observations.

Corresponding author address: Dr. Philippe Gaspar, Collecte Localisation Satellites, Space Oceanography Division, 8-10 rue Hermes, Parc Technologique du Canal, Ramonville Cedex 31526, France. Email: philippe.gaspar@cls.fr

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