The deterministic approach to the analysis of river channel instability has not proved to be a completely useful basis for geographic predictions of channel behavior. Economic estimates for benefits of structural channel control projects commonly account for flood inundation, but in arid and semiarid regions these estimates are incomplete because they fail to take into account destructive channel migration and erosion. As a solution, a method whereby historical records of channel locations are reduced to spatially defined probabilistic functions allows calculation of the probability that given parcels of near-channel terrain will be destroyed by erosion. The probability of erosion for any given parcel over a given period of time is directly proportional to the sizes of the annual floods during the period and inversely proportional to two distance measures: distance upstream and distance laterally to the channel. In a test of the probabilistic geographic method using data on the locations of Rillito Creek, Arizona, from 1871 to 1978, erosion probability maps accurately characterized the locations of observed changes. In a 50-year simulated period, erosion ultimately produced economic losses that were 5 times greater than potential inundation losses
