Spatially distributed estimations of precipitation are required as inputs to many environmental models. It is necessary to find methods to estimate precipitation in areas where precipitation has not been measured. As a high accuracy surface modeling method, HASM has been widely used in many areas. However, its performance in interpolating precipitation has not been satisfactory. 

In China, the monsoon system, together with the effects of topography, yields a remarkable change in annual total precipitation, from less than 25 mm in the northwest to more than 2,000 mm in the southeast, thus representing an increasing precipitation pattern from northwest to southeast over China.  

Based on the spatial distribution of precipitation in China, Dr. ZHAO Na and Prof. YUE Tianxiang from Institute of Geographic Sciences and Natural Resources Research (IGSNRR), Chinese Academy of Sciences gave a modification of HASM (HASM-PRE) to improve its simulation skills in interpolating precipitation. 

They added the mixed derivative of the surface theory into HASM and proposed a specific discrete scheme of it according to the spatial distribution pattern of precipitation in China. They used the neighboring observations located in the southeast and northwest to predict attributed values at unsampled locations (i, j). 

The effectiveness of HASM-PRE was validated by comparing it with HASM and other popular interpolators. Studies showed that the proposed technique is more accurate for predicting the spatial patterns of precipitation than other methods. The proposed method can be used for calculating precipitation for other areas in other temporal scale by taking into account the different difference schemes for the respective area.