Optimal perennial groundwater yield planning for complex nonlinear aquifers: methods and examples

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