Price, Williams Evans, Jr.; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1972-06)
      A digital model based on a random walk was used in an experiment to determine how well such a model is able to simulate alluvial - fan deposition. The model is in three dimensions and is dynamic with respect to both time and space. Two principal stochastic events were employed, (1) a relative uplift of the mountain area that is the source of the fan sediments, and (2) a storm event of sufficient magnitude to result in the deposition of material on the fan. These two events are assumed to follow independent Poisson processes with exponentially distributed interoccurrence times. The pattern of deposition is determined by a random walk from the canyon mouth at the mountain front, and each depositional event is assumed to occur instantaneously. The direction that each step in the walk takes is determined probabilistically by the gradient in the direction of flow, the momentum of flow, and the boundary conditions stipulated in the model. The type of flow, whether a depositing debris or water flow, or eroding water flow, depends upon the thickness of erodible material in the source basin. Deposition is assumed to occur over the entire route of flow either as a bed tapered in the direction of flow or as a bed of uniform thickness. The particle -size distribution of the water -flow deposits is governed by the slope in the direction of flow. Erosion is considered negative deposition and results from the exponential decline in elevation of the main stream channel at the fan apex during periods of no uplift, or from water flows containing little basin sediment. Results from the computer runs were printed as geologic maps of the fan surface, and geologic sections through the deposits; these indicate that, at least qualitatively, a random -walk model provides a reasonable basis for simulating alluvial -fan deposition.