Hydrologic and ecological studies in mountainous terrain are sensitive to the temporal and spatial distribution of precipitation. In this study, we introduce a geostatistic model, ASOADeK (Auto-searched Orographic and Atmospheric effects De-trended Kriging), to map mountain precipitation for arid and semi-arid regions using gauge data. ASOADeK model considers both precipitation spatial covariance and orographic and atmospheric effects in estimating precipitation distribution. The model employs a multivariate linear regression approach to auto-search regional and local climatic settings (spatial trend of atmospheric moisture distribution, effective moisture flux direction,), and local orographic effects (effective terrain elevation, effective slope aspect). The observed gauge precipitation data are then de-trended by the auto-searched regression surface. The de-trended gauge data are further interpolated by ordinary kriging, to generate a de-trended precipitation residual surface. The precipitation map is then constructed by adding the regression surface to the residual surface. We applied ASOADeK to map monthly precipitation for a mountainous area in semi-arid northern New Mexico. The effective moisture flux directions identified by the optimal multiple linear regression agree with the regional climate setting. ASOADeK gives a precipitation map with a spatial resolution of the smaller window-size of those for DEM elevation and slope aspect. When compared to a common precipitation mapping product, PRISM, the study area summer maps agree well with the PRISM estimates, and with higher spatial resolution. The study area winter maps improve upon PRISM estimates. ASOADeK gives better estimates than precipitation kriging and precipitation-elevation cokriging because it considers orographic and atmospheric effects more completely. Compared to PRISM, ASOADeK explicitly introduces both the moisture flux-dependent slope aspect and the spatial trend of the atmospheric moisture distribution in the precipitation regression, allowing auto-search and auto-parameterization of these effects. ASOADeK also auto-determines the optimal effective window size for orographical variables, leading to an optimal higher resolution precipitation map than PRISM.