一种新水平网格的Rossby波计算特性

Computational properties of a new horizontal staggered grid for Rossby waves

提出了一个新的水平跳点网格(LE网格),这种网格将h放置在格点上,u,v同时放置在x方向和y方向格点中间.并采用一种推导频散关系的通用方法,研究在该LE网格上与Arakawa A-E网格上描述Rossby波产生误差的情况,分可分辨和不可分辨两种情况.采用二阶中央差或四阶紧致差分格式从频率和群速度两个方面进行对比分析,结果表明不论在可分辨或不可分辨情况下,还是采用二阶中央差或四阶紧致差分格式,在频率和群速度两方面,LE网格在描述Rossby波产生的误差均较Arakawa A-E网格要小,同时也表明不论在可分辨还是不可分辨的情况下,采用高精度的四阶紧致差分格式,LE网格和Arakawa A_E网格在描述Rossby波时产生的频率误差和x、y方向群速度误差并非必然减少.

This paper presents a new horizontal staggered grid （LE grid）, which defines h at a gridpoint, and both u and v at the same mid-gridpoint along x and y directions. A general method is used to deduce the dispersion relationships describing Rossby waves on the LE grid and Arakawa A-E grids, which are then compared with the analytical solution in resoluble or unresoluble cases, using the two-order central difference or four-order compact difference scheme in the frequency and group velocity. The results show that in both resoluble and unresoluble cases, no matter whether the two-order central difference or four-order compact difference scheme is used, the frequency and group velocity discrete errors on the LE grid in describing Rossby waves are smaller than those of Arakawa A-E grids. At the same time, for the LE grid and Arakawa A-E grids the employment of a four-order compact difference scheme with higher difference precision can not inevitably improve their accuracy of frequency and group velocity in x and y directions in describing Rossby waves.