有限区域内球谐展开的误差分析

THE ERROR ANALYSIS OF A SPHERICAL HARMONIC EXPANDING IN LIMITED REGIONS

以500hPa 高度场为例在有限区域内进行球谐函数的展开。结果表明:当纬向截点数 L 为64,且经圈截点为32时,对应于波数 M =L/2=32的球谐展开误差最小。这时对4种有限区域计算的谱展前后的均方根误差都小于2.5位势米(0.04%),最大绝对误差都小于14位势米(0.23%)。有限区域谱展前后的均方根误差比全球范围的相应值要小2—3位势米,这主要是由于在有限区域内纬向格距较小的缘故。

The numerical computation of expanding a meteorological element in terms of spherical har-monic functions for five regions is carried out by using 500hPa height observations.The calculat-ed results show that all root-mean-square errors(RMSE)of spherical harmonic expansion are lessthan 2.5 gpm(0.04%) and the maximums of absolute error are less than 14 gpm(0.23%)forfour limited regions with the number of of longitudinal grid points L=64,while the number ofGauss discrete points in the latitudinal direction is 32 and the wave number M=L/2=32.TheRMSE of the spherical harmonic expansion for limited areas are 2—3 gpm less than that for theglobe.This is principally due to the longitudinal gridlength is shorter for the limited areas than thatfor the globe.