dc.contributor.author Mills, William Carlisle dc.date.accessioned 2016-07-26T19:23:23Z dc.date.available 2016-07-26T19:23:23Z dc.date.issued 1980-06 dc.identifier.uri http://hdl.handle.net/10150/617601 dc.description.abstract 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. dc.description.sponsorship The work upon which this publication and the associated en dissertation are based was supported by the Science and Education Administration of the United States Department of Agriculture. The author is employed as a Research Hydraulic Engineer in the Agricultural Research function of that Agency. dc.language.iso en_US en dc.publisher Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ) en dc.relation.ispartofseries Technical Reports on Hydrology and Water Resources, No. 36 en dc.rights Copyright © Arizona Board of Regents en dc.source Provided by the Department of Hydrology and Water Resources. en dc.subject Hydrologic models. en dc.subject Water resources development -- Decision making. en dc.subject Stochastic processes. en dc.title COUPLING STOCHASTIC AND DETERMINISTIC HYDROLOGIC MODELS FOR DECISION-MAKING en_US dc.type text en dc.type Technical Report en dc.contributor.department Department of Hydrology & Water Resources, The University of Arizona en dc.description.collectioninformation This title from the Hydrology & Water Resources Technical Reports collection is made available by the Department of Hydrology & Atmospheric Sciences and the University Libraries, University of Arizona. If you have questions about titles in this collection, please contact repository@u.library.arizona.edu. en refterms.dateFOA 2018-09-11T14:38:53Z html.description.abstract 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.
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