Sigma Coordinate Pressure Gradient Errors: Evaluation and Reduction by an Inverse Method

F. Auclair Laboratoire d’Aérologie, UMR CNRS/UPS 5560, Observatoire Midi-Pyrénées, Toulouse, France

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P. Marsaleix Laboratoire d’Aérologie, UMR CNRS/UPS 5560, Observatoire Midi-Pyrénées, Toulouse, France

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C. Estournel Laboratoire d’Aérologie, UMR CNRS/UPS 5560, Observatoire Midi-Pyrénées, Toulouse, France

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Abstract

Sigma coordinate models currently suffer from the difficulty encountered in specifying the horizontal pressure gradient. Most of the efforts to reduce this truncation error lead to the loss of at least one integral constraint in the pressure gradient scheme (energy, tracer balance, etc.). Starting from a usual Arakawa-based scheme, it is shown that judicious adjustment of the sigma surfaces together with control of the bottom topography slope parameter and an “optimal modification” of the measured initial pressure field lead to a drastic reduction in the truncation errors. The first experiment is based on a coastal academic domain in order to compare the results of the proposed inverse method with published data. A few experiments are then conducted on the eastern part of the Gulf of Lions in the Mediterranean using data from the Suivilion experiment.

Corresponding author address: Dr. Francis Auclair, Laboratoire d’ Aérologie UMR CNRS/UPS 5560, Observatoire Midi-Pyrénées, 14, Av. E. Belin, 31400 Toulouse, France.

Email: aucf@aero.obs-mip.fr

Abstract

Sigma coordinate models currently suffer from the difficulty encountered in specifying the horizontal pressure gradient. Most of the efforts to reduce this truncation error lead to the loss of at least one integral constraint in the pressure gradient scheme (energy, tracer balance, etc.). Starting from a usual Arakawa-based scheme, it is shown that judicious adjustment of the sigma surfaces together with control of the bottom topography slope parameter and an “optimal modification” of the measured initial pressure field lead to a drastic reduction in the truncation errors. The first experiment is based on a coastal academic domain in order to compare the results of the proposed inverse method with published data. A few experiments are then conducted on the eastern part of the Gulf of Lions in the Mediterranean using data from the Suivilion experiment.

Corresponding author address: Dr. Francis Auclair, Laboratoire d’ Aérologie UMR CNRS/UPS 5560, Observatoire Midi-Pyrénées, 14, Av. E. Belin, 31400 Toulouse, France.

Email: aucf@aero.obs-mip.fr

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