• The Construction of a Probability Distribution for Rainfall on a Watershed by Simulation

      Williamson, Gary; Davis, Donald Ross; Systems & Industrial Engineering, University of Arizona, Tucson, Arizona 85721 (Arizona-Nevada Academy of Science, 1972-05-06)
      A raingage reading is a sample from the point rainfall population of an area. The actual average rainfall on the area (watershed) is a conditional probability distribution. For the case of thunderstorm rainfall this distribution is simulated by looking at all storms that could have produced the raingage reading. The likelihood of each storm is a function of its center depth. The amount of rain dumped on the watershed by each storm is weighted by the likelihood of its occurence and the totality of such calculations is used to produce a probability distribution of rainfall on the watershed. Examples are given to illustrate the versatility of the program and its possible use in decision analysis.
    • Input Specifications to a Stochastic Decision Model

      Clainos, D. M.; Duckstein, L.; Roefs, T. G.; Systems and Industrial Engineering Department, University of Arizona; Hydrology and Water Resources Department, University of Arizona (Arizona-Nevada Academy of Science, 1972-05-06)
      The use of discrete conditional dependency matrices as input to stochastic decision models is examined. Some of the problems and initial assumptions involved with the construction of the above mentioned matrices are discussed. Covered in considerable detail is the transform used to relate the gamma space with the normal space. A new transform is introduced that should produce reasonable results when the record of streamflow (data) has a highly skewed distribution. Finally, the possibility of using the matrices to provide realistic inputs to a stochastic dynamic program is discussed.
    • Objective and Subjective Analysis of Transition Probabilities of Monthly Flow on an Ephemeral Stream

      Dvoranchik, William; Duckstein, Lucien; Kisiel, Chester C.; Department of Systems and Industrial Engineering, University of Arizona; Department of Hydrology and Water Resources, University of Arizona, Tucson, Arizona (Arizona-Nevada Academy of Science, 1972-05-06)
      A critique of statistical properties of monthly flows on an ephemeral stream in Arizona is given. A subjective procedure, justified for managerial purposes not concerned with the variability of flow within the month, is proposed for sequential generation of monthly flow data. Ephemeral flows should be modeled by starting with at least historical daily flows for more meaningful monthly flow models. Stochastic properties of monthly streamflows and state transition probabilities are reviewed with regard to ephemeral streams. A flow chart for a streamflow model geared to digital computers, with a simulation of streamflow subroutine, is developed. Meaningful monthly flow models could serve as a check on alternative models (subjective matrix, lag-one auto regressive, harmonic, bivariate normal, bivariate log-normal models). Rules and guidelines are presented in developing meaningful probability matrices.
    • Role of Modern Methods of Data Analysis for Interpretation of Hydrologic Data in Arizona

      Kisiel, Chester C.; Duckstein, Lucien; Fogel, Martin M.; Department of Hydrology and Water Resources, University of Arizona, Tucson, Arizona 85721; Department of Systems and Industrial Engineering | Department of Watershed Management (Arizona-Nevada Academy of Science, 1972-05-06)
      Mathematical models, requiring substantial data, of hydrologic and water resources systems are under intensive investigation. The processes of data analysis and model building are interrelated so that models may be used to forecast for scientific reasons or decision making. Examples are drawn from research on modeling aquifers, watersheds, streamflow and precipitation in Arizona. Classes of problems include model choice, parameter estimates, initial condition, input identification, forecasting, valuation, control, presence of multiple objectives, and uncertainty. Classes of data analysis include correlation methods, system identification, stationarity, independence or randomness, seasonality, event based approach, fitting of probability distributions, and analysis for runs, range and crossing levels. Time series, event based and regression methods are reviewed. The issues discussed are applied to tree-ring analyses, streamflow gaging stations, and digital modeling of small watersheds and the Tucson aquifers.