• BAYESIAN DECISION ANALYSIS OF A STATISTICAL RAINFALL/RUNOFF RELATION

      Gray, Howard Axtell; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1972-10)
      The first purpose of this thesis is to provide a framework for the inclusion of data from a secondary source in Bayesian decision analysis as an aid in decision making under uncertainty. A second purpose is to show that the Bayesian procedures can be implemented on a computer to obtain accurate results at little expense in computing time. The state variables of a bridge design example problem are the unknown parameters of the probability distribution of the primary data. The primary source is the annual peak flow data for the stream being spanned. Information pertinent to the choice of bridge design is contained in rainfall data from gauges on the watershed but the distribution of this secondary data cannot be directly expressed in terms of the state variables. This study shows that a linear regression equation relating the primary and secondary data provides a means of using secondary data for finding the Bayes risk and expected opportunity loss associated with any particular bridge design and single new rainfall observation. The numerical results for the example problem indicate that the information gained from the rainfall data reduces the Bayes risk and expected opportunity loss and allows for a more economical structural design. Furthermore, the careful choice of the numerical methods employed reduces the computation time for these quantities to a level acceptable to any budget.
    • A STOCHASTIC SEDIMENT YIELD MODEL FOR BAYESIAN DECISION ANALYSIS APPLIED TO MULTIPURPOSE RESERVOIR DESIGN

      Smith, Jeffrey Haviland; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1975-07)
      This thesis presents a methodology for obtaining the optimal design capacity for sediment yield in multipurpose reservoir design. A stochastic model is presented for the prediction of sediment yield in a semi -arid watershed based on rainfall data and watershed characteristics. Uncertainty stems from each of the random variables used in the model, namely, rainfall amount, storm duration, runoff, peak flow rate, and number of events per season. Using the stochastic sediment yield model for N- seasons, a Bayesian decision analysis is carried out for a dam site in southern Arizona. Extensive numerical analyses and simplifying assumptions are made to facilitate finding the optimal solution. The model has applications in the planning of reservoirs and dams where the effective lifetime of the facility may be evaluated in terms of storage capacity and of the effects of land management on the watershed. Experimental data from the Atterbury watershed are used to calibrate the model and to evaluate uncertainties associated with our knowledge of the parameters of the joint distribution of rainfall and storm duration used in calculating the sediment yield amount.