Incorporation of constraints on hydraulic head gradients near no‐flow boundary conditions in the determination of spatial drift and their use in an inverse groundwater flow model

Abstract

Transmissivities determined by an inverse groundwater model are dependent on the prior hydraulic heads used to calibrate the model. It has been observed in a previous case study of the Avra Valley aquifer in southern Arizona that when gradients in the prior head distribution obtained by kriging do not match assumed no‐flow boundary conditions, the inverse model produced low transmissivity values along these boundaries in an attempt by the model to reconcile inconsistencies in the head gradient and the boundary conditions. To alleviate this problem, an estimation method that includes constraints on the hydraulic head gradient across no‐flow boundaries is presented and used to obtain prior heads estimated at node points for the Avra Valley aquifer. The method involves estimating the drift in the hydraulic head data and then kriging the hydraulic head residuals. The method is multiobjective in that the goal in the drift estimation is to fit simultaneously both the measured 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 the 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 modeling 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 errors on the prior heads and the subsequent lower estimation error of the transmissivities in regions of the aquifer in the vicinity of a no‐flow boundary where few head measurements exist. Including boundary conditions in estimating prior heads for use in inverse modeling yielded more realistic transmissivities with lower estimation errors.