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Show may be deterministically and exogenously specified. The stochastic nature of demands and of natural recharge is ignored. For model applications to drought situations, it is desirable to establish a data base of demands and recharge for the critical period to conduct at least an implicitly stochastic analysis of the management problem. Paucity of data ( groundwater records available did not consistently extend beyond 1969), curtailed such an assessment for the Salt Lake County applications. The 10 most critical years ( 1973- 1982) of the 1969- 1982 record available were used to specify demands and natural recharge. ( 3) While the model presented offers considerable savings in terms of computation resources ( both memory and time) over other groundwater management models presented in the literature, these requirements are still significant, and curtail attempts to make applications at a level of detail that would exhaustively consider and pinpoint candidate well locations for a number of water supply agencies in a region. Further work on developing techniques for the analytical approximation and convolution of the discrete kernels for drawdown as a response to point or line sources of pumping may be helpful in overcoming this hurdle. ( 4) The specification of the water rights structure through constraints on flow across interagency boundaries is in some ways a limitation. If these constraints are computed from the historical data set and strictly enforced and upper bounds on the quantity of water to be pumped for each agency are also enforced, it is likely that the problem solution will have a very restricted feasible space, and the optimal solution obtained will fail to be significantly different from the historical pumping record. This is a limitation of the model, since it is possible to explore various avenues for maintaining the water rights while significantly altering the pumping strategy. The Salt Lake County applications with no upper bounds on the quantity to be pumped for each agency, yielded optimal solutions calling for pumping well in excess of demand for agencies with low unit costs. While this is practically meaningless from an individual agency's perspective, it indicates that the system wide optimal solution is to perhaps export water from the agency pumping the excess water to agencies with high costs. The model does not indicate the direction and extent of such transfers. An extension of the model to directly consider such exchanges and logically assign monetary values to the exchanges ( perhaps using the solution for the dual variables associated with the water rights constraints) is in order. ( 5) Artificial recharge to increase the aquifer yield, improve the pumping lift, and/ or control contamination was not explicitly considered in the formulation presented or the applications. It is , however, possible to include the consideration of artificial recharge without any modification of the model, by defining candidate well nodes for artificial recharge, and developing response matrices for recharge in the same way as for a pumping well. Where artificial recharge is promulgated, it may be possible to extend the model presented to devise a scheme for the simultaneous and optimal allocation of the cost of recharge among the agencies that would either benefit from recharge, or are responsible for increasing the spread of contamination. Several extensions of the model formulated, and of the applications performed, are possible as indicated above. It would be most fruitful to pursue these in the context of ( 1) developing a strategy for the conjunctive management of surface and ground water, with interacting but independent models of ground and surface water management ( possibly formulated as an optimal control problem), and ( 2) a flexible, hierarchical modeling strategy that allows consistent solutions to be generated at different time scales of operation. 91 |