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A New Approach to Implement Sigma Coordinate in a Numerical Model

Published online by Cambridge University Press:  20 August 2015

Yiyuan Li ,
Donghai Wang  and
Bin Wang
Yiyuan Li*
Affiliation:
State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China
Donghai Wang*
Affiliation:
State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing, China
Bin Wang*
Affiliation:
State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China Ministry of Education Key Laboratory for Earth System Modeling, and Center for Earth System Science, Tsinghua University, Beijing, China
*
Email:liyiyuan@mail.iap.ac.cn
Corresponding author.Email:d.wang@hotmail.com
Email:wab@lasg.iap.ac.cn
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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. This method can be used for oceanic models as well, and needs to be tested in both the atmospheric and oceanic models.

Keywords

86-0886A0586A10Pressure gradient force (PGF)terrain-following sigma coordinatenon-orthogonalbasis vectorsnumerical modelingcomputational errors
Type
Research Article
Information
Communications in Computational Physics , Volume 12 , Issue 4 , October 2012 , pp. 1033 - 1050
Copyright
Copyright © Global Science Press Limited 2012

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