• 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.
    • Water Disposition in Ephemeral Stream Channels

      Sammis, T. W.; Hydrology and Water Resources, University of Arizona (Arizona-Nevada Academy of Science, 1972-05-06)
      The contribution of flows from small watersheds to groundwater recharge is of interest. Water disposition depends on infiltration and evaporation characteristics. This study had the objective of developing an infiltration equation for estimating transmission losses during a flow event in an ephemeral stream near Tucson, Arizona, in the rocky mountain forest and range experiment station. Palo Verde, desert hackberry, cholla, marmontea and mesquite are the major bank species of the sandy channels. A climatic section consisting of a hydrothermograph recording rain gage and class a evaporation pan was installed. A water balance method was used to estimate evapotranspiration. A specially designed infiltrometer was used to simulate flow events. The data allowed the following conclusions: Philip's infiltration equation is an excellent mathematical model, initial moisture affects initial infiltration rate, the Philip coefficients are determinable by the infiltrometer constructed, soil moisture affects infiltration rates, and transpiration rates diminish linearly proportional to the ratio of available water to field capacity.