• 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.
    • Transmissivity Distribution in the Tucson Basin Aquifer

      Supkow, D. J.; Department of Hydrology and Water Resources, University of Arizona (Arizona-Nevada Academy of Science, 1972-05-06)
      The distribution of transmissivity within the Tucson basin aquifer, as determined by pumping tests and reviewed in the construction of a digital model of the aquifer, was not totally random in space. Data tended to be distributed normally or log-normally for biased samples of developed wells. A frequency distribution of transmissivity derived from a calibrated digital model is more nearly representative of the real world because the aquifer sample is without bias as the sample constitutes the entire aquifer. Geohydrologic setting, electric analog, and digital models of the basin are discussed. The theory of transmissivity distribution in an arid land alluvial aquifer is developed from Horton's laws of exponential relationship between stream order and drainage network parameters. It is hypothesized that there is an exponential relationship between transmissivity of an alluvial aquifer. A statistical study was made of values derived from the digital model to test the probability density function hypothesized for transmissivity. The mean value is a function of climate and drainage area. These hypotheses require further validation.