A new approach to implement sigma coordinate in a numerical model

Duration: 27 mins 53 secs

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Description:	Li, Y (Chinese Academy of Sciences) Friday 24 August 2012, 11:00-11:30


Created:	2012-08-28 14:15
Collection:	Multiscale Numerics for the Atmosphere and Ocean
Publisher:	Isaac Newton Institute
Copyright:	Li, Y
Language:	eng (English)


Abstract:	This study shows a new way to implement terrain-following σ-coordinate in a numerical model, which does not lead to the well-known “pressure gradient force (PGF)” problem. First, the causes of the PGF problem are analyzed with existing methods that are categorized into two different types based on the causes. Then, the new method that bypasses the PGF problem all together is proposed. By comparing these three methods and analyzing the expression of the scalar gradient in a curvilinear coordinate system, this study finds out that only when using the covariant scalar equations of σ-coordinate will the PGF computational form have one term in each momentum component equation, thereby avoiding the PGF problem completely. A convenient way of implementing the covariant scalar equations of σ-coordinate in a numerical atmospheric model is illustrated, which is to set corresponding parameters in the scalar equations of the Cartesian coordinate. Finally, two idealized experiments manifest that the PGF calculated with the new method is more accurate than using the classic one. Specifically, the relative error of PGF in the new method is reduced by orders of magnitude compared with the result obtained by the classic method; and the pattern of PGF in the new method is more consistent with the analytical PGF pattern than using the classic method. This new method can be used for oceanic models as well, and needs to be tested in both the atmospheric and oceanic models.

Abstract:

This study shows a new way to implement terrain-following σ-coordinate in a numerical model, which does not lead to the well-known “pressure gradient force (PGF)” problem. First, the causes of the PGF problem are analyzed with existing methods that are categorized into two different types based on the causes. Then, the new method that bypasses the PGF problem all together is proposed. By comparing these three methods and analyzing the expression of the scalar gradient in a curvilinear coordinate system, this study finds out that only when using the covariant scalar equations of σ-coordinate will the PGF computational form have one term in each momentum component equation, thereby avoiding the PGF problem completely.

A convenient way of implementing the covariant scalar equations of σ-coordinate in a numerical atmospheric model is illustrated, which is to set corresponding parameters in the scalar equations of the Cartesian coordinate. Finally, two idealized experiments manifest that the PGF calculated with the new method is more accurate than using the classic one. Specifically, the relative error of PGF in the new method is reduced by orders of magnitude compared with the result obtained by the classic method; and the pattern of PGF in the new method is more consistent with the analytical PGF pattern than using the classic method. This new method can be used for oceanic models as well, and needs to be tested in both the atmospheric and oceanic models.

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