[ Introduction | Background | Overview | Evaluation | Applications | Epilogue | Reference ]
PRISM (Parameter-elevation Regressions on Independent Slopes Model) is an expert system that uses point data and a digital elevation model (DEM) to generate gridded estimates of climate parameters (Daly et al., 1994). Unlike other statistical methods in use today, PRISM was written by a meteorologist specifically to address climate. PRISM is well-suited to mountainous regions, because the effects of terrain on climate play a central role in the model's conceptual framework. We call it an expert system, because it attempts to mimic the process an expert would use to map climate parameters. The user interacts with the process through a graphical interface.
Although PRISM was originally developed for precipitation mapping, it was quickly recognized that the model philosophy, i.e., the topographic facet is an important climatic unit and elevation is a primary driver of climate patterns, could be extended to other climate parameters. PRISM has since been used to map temperature, snowfall, weather generator statistics, and others. Below, we give a brief overview of PRISM as it pertains to precipitation.
Estimates of the amount and spatial distribution of precipitation are critical inputs to a variety of ecological, agricultural, and hydrological models. These include models of vegetation, water supply, water quality, drought severity, fire risk, crop production, and others. The demand for precipitation fields on a regular grid and in digital form is growing dramatically as models become increasingly linked to geographic information systems that spatially represent and manipulate model output.
There are many methods of interpolating precipitation from monitoring stations to grid points. Some provide estimates of acceptable accuracy in flat terrain, but few have been able to adequately explain the extreme, complex variations in precipitation that occur in mountainous regions. Inadequacies in these methods typically must be overcome by adding numerous estimated "pseudo- stations" to the data set and tediously modifying the resulting output by hand. Even then, there is no provision for easily updating the precipitation maps with new data or developing maps for other years or months. PRISM was developed to overcome these deficiencies, and provide the user with a flexible system by which detailed, state-of-the-art precipitation maps could be produced.
The primary effect of orography on a given mountain slope is to cause precipitation to vary strongly with elevation. Orographic effects may operate at relatively large spatial scales, responding to smoothed topographic features rather than detailed variations in terrain. Relationships between measured precipitation and elevation are sometimes strengthened when the elevation of each data point is given in terms of its height on a smoothed terrain. The relationship between precipitation and elevation varies from one slope face to another, depending on location and orientation. Thus, a mountainous landscape can be thought of as a mosaic of smoothed topographic faces, or "facets," each experiencing a different orographic regime. A topographic facet is a contiguous area over which the slope orientation is reasonably constant.
In operation, PRISM gives the user the option to use the DEM to estimate the elevations of precipitation stations at the proper orographic scale, and uses the DEM and a windowing technique to group stations onto individual topographic facets. For each DEM grid cell, PRISM develops a weighted precipitation/elevation (P/E) regression function from nearby stations, and predicts precipitation at the cell's DEM elevation with this function. In the regression, greater weight is given to stations with location, elevation, and topographic positioning similar to that of the grid cell. Whenever possible, PRISM calculates a prediction interval for the estimate, which is an approximation of the uncertainty involved.
PRISM has been compared to kriging, detrended kriging, and cokriging in the Willamette River Basin, Oregon (Daly et al., 1994). In a jackknife cross-validation exercise, PRISM exhibited lower overall bias and mean absolute error. PRISM was also applied to northern Oregon and to the entire western United States. Detrended kriging and cokriging could not be used in these regions because there was no overall relationship between elevation and precipitation. PRISM's cross-validation bias and absolute error in northern Oregon increased a small to moderate amount compared to those in the Willamette River Basin; errors in the western United States showed little further increase. PRISM has since been applied to the entire United States with excellent results, even in regions where orographic processes do not dominate precipitation patterns.
By relying on many localized, facet-specific P/E relationships rather than a single domain-wide relationship, PRISM continually adjusts its frame of reference to accommodate local and regional changes in orographic regime with minimal loss of predictive capability.
The PRISM methodology and output products underwent extensive evaluation early in a project with the National Resources Conservation Service to develop state-of-the-art isohyetal maps of monthly and annual precipitation for all 50 states. A panel of State Climatologists from several western states, plus additional experts, critically reviewed PRISM methods and maps of precipitation in their areas of interest. The panel concluded that PRISM produced precipitation maps that equaled or exceeded the quality of the best manually-prepared (hand-drawn) maps available.
PRISM is an evolving research tool. Improvements are being made continually as we learn from the model, and the model learns from us. We invite you to contact us if you wish to learn more about PRISM.
Daly, C., R.P. Neilson, and D.L. Phillips. 1994. A statistical-topographic model for mapping climatological precipitation over mountainous terrain. Journal of Applied Meteorology, 33, 140-158.