On the basis of the evaluation of recent Greenland precipitation studies, some of the deficiencies in the modeled precipitation are probably related to the topographic data employed in modeling. In this paper the modern digital elevation data of Ekholm <1996> is used. If the horizontal pressure gradient force in &sgr; coordinates is separated into its irrotational and rotational parts, which are expressed by the equivalent geopotential and geo-stream-function, respectively, the topographic effect on the precipitation can be accurately modeled. The equivalent geopotential and geo-stream-function are implemented in a fully consistent manner in the generalized ω-equation in this paper. A simplified large-scale condensation without evaporation of condensate is also used. These improvements are combined to yield an improved dynamic method. Two aspects of the precipitation distribution are refined by the improved dynamic method. One is the 10 cm yr-1 contour near Summit, Greenland, and the other is a relative large precipitation area centered near the point (70 ¿N, 49 ¿W). Extensive comparisons are made between the retrieved precipitation and the observed annual accumulation time series from 11 ice core sites on the ice sheet. The modeled precipitation from the original method must use scalers to have a high degree of interannual correspondence between the measured accumulation and the retrieved precipitation, but the retrieved precipitation from the improved method increases at all ice core sites and a good correspondence is obtained without any scaler being required. The spatial average of multiyear mean error (ϵ¿j) is 11.5 cm yr-1 for the modeled precipitation from the improved method, while that for P from ERA-15 is 14.5 cm yr-1. The total mean error(ϵM) is 3.0 cm yr-1 for the improved method, while ϵM for the P from ERA-15 is 4.0 cm yr-1. These two errors show that the precipitation modeled by the improved method is better than the P from ERA-15. Thus the distribution of precipitation over the 11 sites retrieved by the improved dynamic method is considerably refined. Large downward trends in annual amounts are present in the precipitation retrieved by the improved dynamic method for all of Greenland and its southern and central west coastal regions. The modeled precipitation from the improved dynamic method and observed accumulation from ice cores are all in agreement with the Thomas et al. <1999> result that the southern Greenland ice sheet above 2000 m is approximately in balance. Italso shows that local thickening and thinning areas of the ice sheet derived by airborne laser altimetry from 1993 to 1999 over the entire Greenland above 2000 m <Krabill et al., 2000> are approximately consistent with precipitation change retrieved by the improved dynamic method. ¿ 2001 American Geophysical Union