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