We describe and then model satellite-inferred severe (stand-replacing) fire occurrence relative to topography (elevation, aspect, slope, solar radiation, Heat Load Index, wetness and measures of topographic ruggedness) using data from 114 fires > 40 ha in area that occurred between 1984 and 2004 in the Gila Wilderness and surrounding Gila National Forest. Severe fire occurred more frequently at higher elevations and on north-facing, steep slopes and at locally wet, cool sites, which suggests that moisture limitations on productivity in the southwestern US interact with topography to influence vegetation density and fuel production that in turn influence burn severity. We use the Random Forest algorithm and a stratified random sample of burn severity pixels with corresponding pixels from 15 topographic layers as predictor variables to build an empirical model predicting the probability of occurrence for severe burns across the entire 1.4 million ha study area. Our model correctly classified severity with a classification accuracy of 79.5% when burn severity pixels were classified as severe vs. not severe (two classes). Because our model was derived from data sampled across many fires over a 20-year period, it represents average probability of severe fire occurrence and is unlikely to predict burn severity for individual fire events. However, we believe it has potential as a tool for planning fuel treatment projects, in management of actively burning fires, and for better understanding of landscape-scale burn severity patterns.