Many planning decisions related to the land phase of the
hydrologic cycle involve uncertainty due to stochasticity of rainfall
inputs and uncertainty in state and knowledge of hydrologic processes.
Consideration of this uncertainty in planning requires quantification
in the form of probability distributions. Needed probability distributions,
for many cases, must be obtained by transforming distributions
of rainfall input and hydrologic state through deterministic models of
hydrologic processes.
Probability generating functions are used to derive a recursive
technique that provides the necessary probability transformation for
situations where the hydrologic output of interest is the cumulative
effect of a random number of stochastic inputs. The derived recursive
technique is observed to be quite accurate from a comparison of
probability distributions obtained independently by the recursive
technique and an exact analytic method for a simple problem that can
be solved with the analytic method.
The assumption of Poisson occurrence of rainfall events, which
is inherent in derivation of the recursive technique, is examined and
found reasonable for practical application. Application of the derived technique is demonstrated with
two important hydrology- related problems. It is first demonstrated
for computing probability distributions of annual direct runoff from
a watershed, using the USDA Soil Conservation Service (SCS direct
runoff model and stochastic models for rainfall event depth and
watershed state. The technique is also demonstrated for obtaining
probability distributions of annual sediment yield. For this
demonstration, the-deterministic transform model consists of a parametric
event -based sediment yield model and the SCS models for direct
runoff volume and peak flow rate. The stochastic rainfall model
consists of a marginal Weibull distribution for rainfall event duration
and a conditional log -normal distribution for rainfall event depth,
given duration. The stochastic state model is the same as used for
the direct runoff application.
Probability distributions obtained with the recursive technique
for both the direct runoff and sediment yield demonstration examples
appear to be reasonable when compared to available data. It is,
therefore, concluded that the recursive technique, derived from
probability generating functions, is a feasible transform method
that can be useful for coupling stochastic models of rainfall input
and state to deterministic models of hydrologic processes to obtain
probability distributions of outputs where these outputs are cumulative
effects of random numbers of stochastic inputs.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/617601 |
| Date | 06 1900 |
| Creators | Mills, William Carlisle |
| 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. 36 |
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