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Characteristics of a Terrain-Following Sigma Coordinate

Atmospheric and Oceanic Science Letters 2011年第3期4卷 157-161页

作者： LI Yi-Yuan WANG Bin WANG dong-Hai State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluiddynamics Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China Center for Earth System Science Tsinghua University Beijing 100084 China State Key Laboratory of Severe Weather Chinese Academy of Meteorological Sciences Beijing 100081 China

This study quantifies the main characteristics of a terrain-following, G-coordinate through mathematical analyses of its covariant and contravariant basis vectors as well as the vertical coordinate of σ. A 3-d schematic of the σ-coordinate in a curvilinear coordinate system is provided in this study. The characteristics of the basis vectors were broken down into their ＂local vector charac- teristics＂ and ＂spatial distribution characteristics＂, and the exact expressions of the covariant; in addition, the con- travariant basis vectors of the G-coordinate used to eluci- date their detailed characteristics were properly solved. Through rewriting the expression of the vertical coordi- nate of G, a mathematical expression of all the cr-coor- dinate surfaces was found, thereby quantifying the so- called terrain-following characteristics and lack of flexi- bility to adjust the slope variation of G-coordinate sur- faces for the classic definition of G. Finally, an analysis on the range value of the vertical coordinate demonstrated that the general value range of G could be obtained by eliminating the G-coordinate surfaces below the Earth＇s surface. All these quantitative descriptions of the charac- teristics of G-coordinate were the foundation for improv- ing the G-coordinate or creating a new one.

关键词： quantitative description sigma coordinate 3-d schematic basis vectors non-orthogonal

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