Advances in Water Resources
Optimal perennial groundwater yield pumping strategies were computed for a complex multilayer aquifer with: (i) confined and unconfined flow, and (ii) many flows typically described by piecewise-linear (nonsmooth) equations. The latter flows account for over 50% of the aquifer discharge from the test area, the eastern shore of the Great Salt Lake in Utah. Normally utilized response matrix (RM) and embedding (EM) simulation/optimization modelling procedures did not converge to optimal solutions for this area; they diverged or oscillated. However, the newly presented linear RM and EM approaches satisfactorily addressed the nonlinearities posed by over 2000 piecewise-linear constraints for evapotranspiration, discharge from flowing wells, drain discharge, and vertical interlayer flow reduction due to desaturation of a confined aquifer. Both presented modelling approaches converged to the same optimal solution. Superposition was applied to the nonlinear problem by: making a cycle within the RM analogous to an iteration in a simulation model (such as MODFLOW); and using a modified MODFLOW to develop influence coefficients. The EM model contained about 40 000 nonzero elements and 12 000 single equations and variables, demonstrating its suitability for large scale planning.
Takahashi, S. and R.C. Peralta. 1995. Optimal perennial groundwater yield planning for complex nonlinear aquifers: methods and examples. Advances in Water Resources, 18: 49-62