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Show Based on the above discussion, it was felt that the response matrix methods offered the best hope for the development of models that would be flexible and controllable for reasonably large scale practical applications. Even with decomposition, the embedding formulations tend to grow in size very rapidly as a finer discretization in time and/ or space of the governing equations of flow is considered. Efforts in this study were focused on the development of distributed parameter, groundwater management models, that consider water quality, water rights and yield issues, and utilize the response matrix approach to develop relationships between pumping and aquifer heads, flows across regional boundaries, and flows near areas of contamination. Both confined and stratified aquifer systems are considered. Further, the models in the literature predominantly considered the groundwater management problem in an agrarian context. The focus of the effort in this study was on models in a metropolitan setting where identifiable water supply agencies compete for the groundwater resource. Water rights issues relevant to bulk or large users, rather than individual well operators were of concern. 1.2.2 Conjunctive Use Models Table 1.1 reviews some the other models reported on in the literature. Some of the studies most pertinent to this study are reviewed here. Yu and Haimes ( 1974) describe a multi- level hierarchical model for improving the efficiency of regional groundwater allocation. The problem is decomposed into subproblems, each of which was formulated as a nonlinear programming model for minimizing net water supply costs. Subregional models provided inputs into a second level representing coordination by a regional authority. This authority assures consistent boundary water levels across subregions, determines tax rates and artificial recharge operation to minimize total regional water supply costs. A two dimensional representation of the aquifer with adjoining subregions and a single confined aquifer was considered. The main limitations of this model were ( a) a lack of surface water representation, ( b) no stream- aquifer interaction, ( c) no system reliability consideration, ( d) no development issues were addressed, only operation, ( e) no consideration of costs of distribution within a region, ( f) no water quality consideration, ( g) no bounds on artificial recharge based on groundwater uplift, and ( g) no point by point well drawdowns were considered. Initial experiments with formulations similar to Yu and Haimes ( 1974) also showed that if a more detailed representation of the groundwater system is desired, their model is inordinately complex, and convergence problems in managing the decomposition are likely. A direct solution of the regional problem with subregional boundaries is feasible with response matrix formulations, and is computationally more attractive. Haimes and Dreizen ( 1977) present the most comprehensive conjunctive management model reported on. A multilevel, hierarchical structure similar to that of Yu and Haimes ( 1974) is used. A reservoir, an aquifer and streams in each subregional cell are considered. A response matrix approach is used for the groundwater system. Decisions on operational aspects of pumping, artificial recharge, and surface water use are considered in addition to decisions on tax rates and reservoir storage. Constraints on water requirements, lift, drawdown, pumping at each well, recharge capacity and surface water allocations are specified. Stream- aquifer interactions were considered, and a three stage solution procedure was used for the solution of the multilevel problem. The limitations of the model are ( a) a lack of consideration of prior water rights, level of detail of the groundwater representation is of limited utility for a local agency, and limitations ( c), ( d), ( e) and ( f) reported for Yu and Haimes ( 1974). Exploration of the structure of this model as a candidate for the developments in this study, revealed that ( a) the problem size and decomposition approach used got intractable as multiple reservoirs with multiple uses were 9 |