A Statistical-Topographic Model for Mapping Climatological Precipitation over Mountainous Terrain

TLDR

The growing need for climatological precipitation fields on regular grids drives the development of models that integrate geographic information systems with ecological and hydrological applications. This paper introduces an analytical model that distributes point measurements of monthly and annual precipitation to regularly spaced grid cells in midlatitude regions. PRISM employs a digital elevation model to estimate station elevations, groups stations into topographic facets, and performs a regression of precipitation versus elevation for each facet to estimate grid‑cell precipitation—optionally providing prediction intervals—and was applied to northern Oregon and the western United States where kriging methods could not be used. PRISM achieved the lowest cross‑validation bias and absolute error compared to kriging, detrended kriging, and cokriging in the Willamette River basin, and maintained low errors across northern Oregon and the western U.S.

Abstract

The demand for climatological precipitation fields on a regular grid is growing dramatically as ecological and hydrological models become increasingly linked to geographic information systems that spatially represent and manipulate model output. This paper presents an analytical model that distributes point measurements of monthly and annual precipitation to regularly spaced grid cells in midlatitude regions. PRISM (Precipitation-elevation Regressions on Independent Slopes Model) brings a combination of climatological and statistical concepts to the analysis of orographic precipitation. Specifically, PRISM 1) uses a digital elevation model (DEM) to estimate the “orographic” elevations of precipitation stations; 2) uses the DEM and a windowing technique to group stations onto individual topographic facets; 3) estimates precipitation at a DEM grid cell through a regression of precipitation versus DEM elevation developed from stations on the cell's topographic facet; and 4) when possible, calculates a prediction interval for the estimate, which is an approximation of the uncertainty involved. PRISM exhibited the lowest cross-validation bias and absolute error when compared to kriging, detrended kriging, and cokriging in the Willamette River basin, Oregon. PRISM was also applied to northern Oregon and to the entire western United States; detrended kriging and cokriging could not be used, because there was no overall relationship between elevation and precipitation. Cross-validation errors in these applications were confined to relatively low levels because PRISM continually adjusts its frame of reference by using localized precipitation-DEM elevation relationships.