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Show 7.2 Model with Conjunctive use of Surface and Groundwater The second model developed in this chapter specifically considers the conjunctive use of surface and groundwater as an integral part of the development of a regional water use plan. The model is still developed in the yield model framework, and derives from the discussion in sections 6.2 and 6.3 regarding yield reliabilities and operation of the water supply system. It is presumed that failures of the yields from individual reservoirs ( existing or proposed) are permissible. The total shortage resulting from these failures is made up through increased groundwater use, thus maintaining the system yield reliability at the desired levels. The degree of failure of each reservoir yield for each candidate year in the record, is introduced as a decision variable. While a general statement of this model considering irrigation, M& I, flood control, hydropower, and recreation uses is possible, a reduced formulation appropriate for the applications presented for the Jordan River Basin is presented in this section. Only a single use ( M& I) and a single level ( firm) of yield reliability is considered. Also, for simplicity of presentation, only a single demand area is considered for groundwater development. The water rights constraints introduced in Chapter 3, for the groundwater applications, are not reproduced here. Their inclusion is however possible. Similarly, none of the areas of groundwater contamination considered in Chapter 3 applications were near the candidate wells considered for Salt Lake City. Consequently, the groundwater quality maintenance constraints are not reproduced as part of this formulation. Their inclusion can however be readily accomplished. The 8 reservoir system and the aquifer section in the Salt Lake City area are considered the application site, and the model formulation is presented to correspond to the definition of this water system. As in the previous section the objective of the model was to minimize the total annual cost from reservoir and groundwater development for meeting the specified level of demand. The objective function of the model is stated as: s NY cio. S c2 MinOBJ = T c l T~ s + - ^ ^ jLmd S S s= l X2>.{ « ^> NY W NY XzwMvV NY ( 7.7) where the first term represents the annual cost of reservoir storage, the second term the annual cost of surface water treatment, the third term the annual cost of groundwater pumping, and qfy is the degree ( probability) of failure of the surface water yield in year y, and all other variables are as defined earlier. The total storage Ts at each site is computed following the procedures in Chapter 5. Since dead storage was not considered in the applications, the total storage Ts represents the active storage of the reservoir to supply the yield Ms. The variables qfy are not specified for each of the 55 years of simulation. They are specified only for the years in each critical period. For the Jordan River Basin applications, analysis of the streamflow data indicated that the streamflows at the 8 sites were highly correlated, and the region was hydrologically homogeneous in the sense that a joint critical period across all 8 sites could be readily identified. With this assumption, we need to only consider yield failures for the surface water system, rather than by reservoir. Hence, the specification of the yield failure 171 |