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Show h is the vector of hydraulic head above the base of the aquifer. 8(.) is the Diiac Delta function. Q is a pumpage vector. x*, y* is a set of well locations. R is a vector of natural recharge. Sy is the specific yield. The variables R, Q and h are spatially and temporally variable, while K and Sy are spatially variable. The partial differential equation above is nonlinear in the dependent variable h. This precludes the use of the principle of linear superposition for its solution. Consequently, the unit response approach for formulating groundwater optimization models appears unsuitable. This problem is even more acute when a stratified aquifer system is considered. In a stratified aquifer system, non- homogenieties in the hydraulic conductivity field result from layering of aquifer deposits. Each layer is likely to homogeneous ( but possibly anisotropic), with a discontinuity in conductivity at its boundary. Additional boundary conditions are thus imposed on the solution of the partial differential equation presented in equation ( 2.1). Reformulation of the problem using the Girinski Potential allows its reduction to a form suitable for a unit response formulation of the management model. The basic concepts relating to the Girinski potential are first reviewed. This is followed by the representation of the flow equations in terms of the Girinski Potential. The Girinski potential G( x, y), along the line ( 0 < z < h), flow ( unconfined) condition in a stratified aquifer system is defined as ( Halek & Svec, 1979): h G = J K( z)( h- z) dz ( 2.2) Halek & Svec ( 1979) show that the gradient of G yields the specific discharge q through the aquifer. 9G _ 9G_ ( 2 3) qx-" ax~;( ix- a7 The Girinski potential for a layered system may then be stated with reference to Figure 2.1 as ( Yeh, 1982): d l d 2 n G= f K1( h- z) dz+ f K2( h - z) dz + ... + J Kn + 1( h- z) dz ( 2.4) o d « d„ 1 n 12 |