INCORPORATION OF CONSTRAINTS ON HYDRAULIC-HEAD GRADIENTS NEAR NO-FLOWBOUNDARY-CONDITIONS IN THE DETERMINATION OF SPATIAL DRIFT AND THEIR USE IN AN INVERSE GROUNDWATER-FLOW MODEL

Transmissivities determined by an inverse groundwater model are depend ent on the prior hydraulic heads used to calibrate the model. It has b een observed in a previous case study of the Avra Valley aquifer in so uthern Arizona that when gradients in the prior head distribution obta ined by kriging do not match assumed no-flow boundary conditions, the inverse model produced low transmissivity values along these boundarie s in an attempt by the model to reconcile inconsistencies in the head gradient and the boundary conditions. To alleviate this problem, an es timation method that includes constraints on the hydraulic head gradie nt across no-flow boundaries is presented and used to obtain prior hea d's estimated at node points for the Avra Valley aquifer. The method i nvolves estimating the drift in the hydraulic head data and then krigi ng the hydraulic head residuals. The method is multiobjective in that the goal in the drift estimation is to fit simultaneously both the mea sured heads at well locations and the head gradient along the no-flow boundary conditions. The appropriate weighting of the no-flow boundary constraints is investigated by examining the tradeoff in fitting head measurements and fitting the no-flow boundary conditions. Changes in the semivariogram of the head residuals and the estimation error of th e heads are also considered. It is found that boundary constraints can improve the fit of the estimated heads to the no-flow boundaries with little deterioration of the fit to the head measurements. Inverse mod eling of the Avra Valley aquifer based on these estimated prior heads did not produce the low transmissivities along the no-flow boundaries. The constraints on the head gradient resulted in lower estimation err ors on the prior heads and the subsequent lower estimation error of th e transmissivities in regions of the aquifer in the vicinity of a no-f low boundary where few head measurements exist. Including boundary con ditions in estimating prior heads for use in inverse modeling yielded more realistic transmissivities with lower estimation errors.