Wayne Gibson, Christopher Daly and George Taylor
Oregon State University, Corvallis, Oregon
PRISM (Parameter-elevation Regressions on Indepedent Slopes Model) is an analytical model that uses point data and a digital elevation model (DEM) to generate gridded estimates of monthly and annual precipitation. PRISM is uniquely suited to regions with mountainous terrain, because it incorporates a conceptual framework that allows the spatial scale and pattern of orographic precipitation to be quantified and generalized.
The primary effect of orography on a given mountain slope face is to cause precipitation to increase with elevation. Orographic effects typically operate at large spatial scales, responding to smoothed topographic features rather than detailed variations in terrain. Relationships between measured precipitation and elevation are generally strengthened when the elevation of each data point is given in terms of its height on a smoothed terrain, termed its "orographic" elevation (OE). The relationship between precipitation and OE 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.
The orientation of a facet is determined by examining the adjacent points in a north-south and east-west direction at the current cell location. The orientation of the cell is assigned based on an 8 point compass with the directions wnw, wsw, ssw, sse, ese, ene, nne, and nnw. An additional orientation of "flat" is assigned if the gradient of the topography is below a threshold. Inspection of the facet grid at the highest smoothing level shows thin elongated features (e.g. ridge lines and valley bottoms) and small facets. Small facets will be less likely to have a sufficient number of data points from which to derive a precipitation estimate. Elongated facets that run along ridge lines or valley bottoms do not represent orographically distinct regions, but rather are transition zones between more meaningful topographic facets. Even after smoothing at larger scales, there are considerable undulations in the topographic surface.
A refined faceting method was developed to eliminate small or narrow facets at higher smoothing levels. Assigned orientations were based on some generalization of the area around each cell. The size of the area chosen at each facet level is the cutoff distance used to filter the terrain data at that level. By using a technique that accounts for orientations in the surrounding area, it was hoped that small facets and elongated facets along ridge lines and valley bottoms would be eliminated.
Each cell orientation within the specified area was assigned to a 9 bin frequency distribution, and the frequency of occurrence of each orientation was calculated. Based on the distribution of the orientations, a system of rules were devised to pick the best orientation for that cell. In order to facilitate inspection of the histograms, a "point and click" version of the faceting software was implemented.