• Basin Scale and Runoff Model Complexity

      Goodrich, David Charles; Department of Hydrology & Water Resources, The University of Arizona; Southwest Watershed Research Center (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1990-06)
      Distributed Rainfall-Runoff models are gaining widespread acceptance; yet, a fundamental issue that must be addressed by all users of these models is definition of an acceptable level of watershed discretization (geometric model complexity). The level of geometric model complexity is a function of basin and climatic scales as well as the availability of input and verification data. Equilibrium discharge storage is employed to develop a quantitative methodology to define a level of geometric model complexity commensurate with a specified level of model performance. Equilibrium storage ratios are used to define the transition from overland to channel -dominated flow response. The methodology is tested on four subcatchments in the USDA -ARS Walnut Gulch Experimental Watershed in Southeastern Arizona. The catchments cover a range of basins scales of over three orders of magnitude. This enabled a unique assessment of watershed response behavior as a function of basin scale. High quality, distributed, rainfall -runoff data was used to verify the model (KINEROSR). Excellent calibration and verification results provided confidence in subsequent model interpretations regarding watershed response behavior. An average elementary channel support area of roughly 15% of the total basin area is shown to provide a watershed discretization level that maintains model performance for basins ranging in size from 1.5 to 631 hectares. Detailed examination of infiltration, including the role and impacts of incorporating small scale infiltration variability in a distribution sense, into KINEROSR, over a range of soils and climatic scales was also addressed. The impacts of infiltration and channel losses on runoff response increase with increasing watershed scale as the relative influence of storms is diminished in a semiarid environment such as Walnut Gulch. In this semiarid environment, characterized by ephemeral streams, watershed runoff response does not become more linear with increasing watershed scale but appears to become more nonlinear.
    • 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.
    • CALIBRATION OF RAINFALL-RUNOFF MODELS USING GRADIENT-BASED ALGORITHMS AND ANALYTIC DERIVATIVES

      Hendrickson, Jene Diane,1960-; Sorooshian, Soroosh; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1987-05)
      In the past, derivative-based optimization algorithms have not frequently been used to calibrate conceptual rainfall -riff (CRR) models, partially due to difficulties associated with obtaining the required derivatives. This research applies a recently- developed technique of analytically computing derivatives of a CRR model to a complex, widely -used CRR model. The resulting least squares response surface was found to contain numerous discontinuities in the surface and derivatives. However, the surface and its derivatives were found to be everywhere finite, permitting the use of derivative -based optimization algorithms. Finite difference numeric derivatives were computed and found to be virtually identical to analytic derivatives. A comparison was made between gradient (Newton- Raphsoz) and direct (pattern search) optimization algorithms. The pattern search algorithm was found to be more robust. The lower robustness of the Newton-Raphsoi algorithm was thought to be due to discontinuities and a rough texture of the response surface.
    • Improving the Reliability of Compartmental Models: Case of Conceptual Hydrologic Rainfall-Runoff Models

      Sorooshian, Soroosh; Gupta, Vijai Kumar; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1986-08)