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On the use of gridded data to estimate potential coefficients

Federica Migliaccio(1), Mirko Reguzzoni(2), Fernando Sansò(3) and Nikolaos Tselfes(3)

(1) Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133, Italy
(2) OGS - c/o Politecnico di Milano, Via Valleggio, 11, 22100 Como, Italy
(3) Politecnico di Milano, Via Valleggio, 11, 22100, Italy

Abstract

In the framework of the space-wise approach for the GOCE data analysis an intermediate step of prediction of functionals of the gravitational potential on a regular spherical grid has to be performed. The scope of this procedure is to filter the observations in a space-wise sense. The gridding procedure is made by collocation over local patches of observations, while a global collocation would be numerically unfeasible because of the large number of data. The gridded values are then used for the estimation of the spherical harmonic coefficients of the gravitational potential.

Once such a procedure is envisaged, several questions arise. Is there loss of information within this step-wise procedure, with respect to a direct collocation estimate of the coefficients from the original data? What should the size of the grid be and which intermediate functional should be predicted? What is the impact of the local application of collocation? These questions, connected to the concept of sufficient statistics, are studied. Some of them (the simplest ones) are answered from the theoretical point of view, while others are investigated numerically.

A realistic GOCE simulation scenario is also used for numerical tests, since the final scope is to identify the optimal procedure with respect to the space-wise approach performance. One of the results of these tests is that the error in the final estimate of the coefficients is almost invariant with respect to the choice of the intermediate functional. Moreover the specific features of the final coefficients estimation step, i.e. by collocation versus exact spherical Fourier analysis, are demonstrated and the results are discussed.

 

Workshop poster

Keywords: ESA European Space Agency - Agence spatiale europeenne, observation de la terre, earth observation, satellite remote sensing, teledetection, geophysique, altimetrie, radar, chimique atmospherique, geophysics, altimetry, radar, atmospheric chemistry