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Show Constraints: H) He3< 3 Computation The head at any node of interest is determined in terms of the initial head at the node and aquifer pumping using a unit response formulation. The USGS 3- D Finite Difference flow model of Mcdonald and Harbaugh ( 1982) is used to first estimate the steady state drawdown ajft, due to unit pumping at each of the wells k ( one at a time), at the location of interest ( i, j). The steady state simulation considered the seasonally variable natural recharge, as well as the pumping at the background wells ( non- municipal and small scale). The drawdown at a node ( ij) due to unit pumping at well k is termed the response coefficient a^. The resulting head at node ( i j) may then be computed through equation ( 4.2) as A na H°. - y y , a.-. Q, - rf. = H.. ( 4.2) a- 1 k- 1 © where H^ is the initial head at the node ( ij), and Hby is the change in head at node ( ij) due to natural recharge and background pumping activity. The number of constraints of the type specified by equation ( 2) is equal to the total number of nodes where heads are of interest. These include the well nodes, and nodes used for the computation of flow rates for water rights and water quality maintenance. For the Salt Lake County application, there were 181 such nodes. ( 2) Water Demands: Constraints are specified to ensure that the base annual demand WDa of each water supply agency is satisfied. The sum of the total annual pumpage for each agency should thus be at least equal to the agency's base annual demand. These are stated for each agency a as: na X Qka * WDa < 4' 3) k- 1 One such constraint was specified, for each of the ten water agencies identified for Salt Lake County. Due to the large number of wells in Salt Lake County, only 46 nodes with wells pumping at rates greater than 0.6 cubic feet per second ( cfs), were considered. It was presumed that nodes where no wells pumped at a rate greater than 0.6 cfs were not productive areas of the aquifer, and were not optimizable. These nodes were designated as background pumping nodes - a classification similar to that accorded the non- municipal wells. A reduced water demand for each agency was estimated by adding the historical pumping from only the well nodes considered. Parametric runs of the optimization model at varying levels of the estimated water district demands were made to observe their effect on the optimal yield. ( 3i) Drawdown restriction Drawdown in the aquifer may need to be restricted for a number of reasons. A 94 |