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Digitized by Kansas Correctional Industries

Typescript (photocopy). / Digitized by Kansas Correctional Industries

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FLUMP, a recently developed mixed explicit -implicit finite -element program, was calibrated against a data base obtained from a portion of the Tucson Basin aquifer, Arizona, and represents its first application to a real -world problem. Two previous models for the same region were constructed (an electric analog and a finite -difference model) in which calibration was based on prescribed flux boundary conditions along stream courses and mountain fronts. These fluxes are not directly measured and estimates are subject to large uncertainties. In contrast, boundary conditions used in the calibration of FLUMP were prescribed hydraulic heads obtained from direct measurement. At prescribed head boundaries FLUMP computed time - varying fluxes representing subsurface lateral flow and recharge along streams. FLUMP correctly calculated fluctuations in recharge along the Santa Cruz River due to fluctuations in storm runoff and sewage effluent release rates. FLUMP also provided valuable insight into distributions of recharge, discharge, and subsurface flow in the study area.Properties of FLUMP were compared with those of two other programs in current use: ISOQUAD, a finite -element program developed by Pinder and Frind (1972), and a finite- difference program developed by the U.S. Geological Survey (Trescott, et al., 1976). It appears that FLUMP can handle a larger class of problems than the other two programs, including those in which the boundary conditions and aquifer parameters vary arbitrarily with time and /or head. FLUMP also has the ability to solve explicitly when accuracy requires small time steps, the ability to solve explicitely in certain parts of the flow region while solving implicitly in other parts, flexibility in mesh design and numbering of nodes, computation of internal as well as external fluxes, and global as well as local mass balance checks at each time step.

A model for real -time control of a multipurpose reservoir under the conditions of uncertainty is developed. The control model is formulated as a multistage decision process. It is conceptualized in the form of two sub -processes. The first level process is a Forecast - Strategy Process which performs as an open-loop feedback controller. It is defined by a sequence of forecasts and optimal release strategies against these forecasts. At each forecast time (time of issuing the forecast), the optimal release strategy is computed for the time period equal to the lead time of the forecast, and it remains in execution until the next forecast time. The second level process, defined for each forecast time, is a Control Process which for the given forecast generates the release strategy satisfying the preference criterion (minimization of expected disutility). This process is formulated as a truncated Markovian adaptive controller performing on a finite set of discrete times --the same set which indexes the forecast inflow process. To evaluate the past performance of the control, a set of measures of effectiveness is proposed. Computational aspects of the control model are analyzed. Structural properties of the reservoir control process are explored in the main theorem which assures the monotonicity of the optimal strategy with respect to one of the state variables. Also, the properties of the optimal strategy for the case of a categorical forecast are proven. Next, two suboptimal strategies are derived: (1) partial open -loop strategy and (2) naive /partial open-loop strategy. Finally, a'discretization procedure which guarantees convergence of the numerical solution is discussed, and the computational requirements of the optimal and two suboptimal strategies are compared.