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The Slepian approach revisited: dealing with the polar gap in satellite based geopotential recovery

Nico Sneeuw(1) and Oliver Baur(1)

(1) Universit├Ąt Stuttgart, Geschwister-Scholl-Str. 24D, 70174 Stuttgart, Germany


Gravity field modelling is typically based on spherical harmonic expansion of the potential function. Surface spherical harmonics are globally defined and satisfy the orthogonality relations on the sphere. However, satellite ground tracks often leave out polar areas. Especially regarding the GOCE mission, a double polar cap with a radius of more than six degrees will not be covered by observation data. Conventionally, this problem is tackled by adjusting the data situation to the model, e.g. by introducing terrestrial measurements. As an alternative we investigate the adaptation of the geopotential modelling to the observations. In particular we introduce band limited base functions that are optimally concentrated within the spherical belt. This approach goes back to David Slepian who referred them to as prolate spheroidal wave functions. Already in Albertella et al. (1999) the method has been applied in satellite geodesy. However, they only succeeded in the calculation of random band limited functions. Recently an analytical expression has been found for the unique transformation to the Slepian base when neglecting an axisymmetric double polar cap. We apply that approach to a simulated GOCE data set to investigate its benefit for geopotential recovery.


Workshop presentation

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