Improvement of the Spectral Representation of the Earth Topography with a Variational Method

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Abstract
The orography representation in spectral models has always led to problems. These problems become critical in high-resolution models, like the variable-resolution spectral model used at Météo-France, because they interact with the physical fields. The author describes a variational process to compute a spectral approximation of a gridpoint field. The method is used to improve the representation of the earth topography, and it is compared to a simple spectral filter. The author presents first, in the variable-resolution model, some unsuccessful attempts to show that it is not easy to find the more relevant cost function and then describes the best results obtained. In the variable-resolution case, Gibbs waves are eliminated from the high-resolution area. In the constant-resolution model, Gibbs waves are eliminated from all of the flat areas. In the two cases, the improvement of the orography representation is better with the variational process than with the spectral fitter.

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