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.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/620103 |
| Date | 06 1900 |
| Creators | Price, Williams Evans, Jr. |
| Contributors | Department of Hydrology & Water Resources, The University of Arizona |
| Publisher | Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ) |
| Source Sets | University of Arizona |
| Language | en_US |
| Detected Language | English |
| Type | text, Technical Report |
| Source | Provided by the Department of Hydrology and Water Resources. |
| Rights | Copyright © Arizona Board of Regents |
| Relation | Technical Reports on Hydrology and Water Resources, No. 7 |
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