Analytical and numerical adjoint solutions for cumulative streamflow depletion
Scholarly Edition
Overview
abstract
The traditional metric of streamflow depletion represents the; instantaneous change in the volumetric rate of aquifer–stream exchange; after a finite period of continuous groundwater extraction. In the; present study an alternative metric of streamflow depletion was; considered: cumulative stream depletion (CSD), which described the total; volumetric reduction in flow from an aquifer to a stream resulting from; continuous groundwater extraction over a finite period, at the final; time of extraction. A novel analytical solution for the prediction of; CSD was derived, based upon a forward solution that accounted for; streambed conductance and partial stream penetration. Separately, a; novel numerical solution for prediction of CSD was derived, based on the; derivation and calculation of an adjoint state solution. The accuracy of; these methods was demonstrated through benchmarking against existing; analytical solutions and perturbation-based results, respectively. The; derivation of the adjoint state solution identified three parameters of; relevance to CSD prediction: streambed hydraulic conductivity and; thickness, both of which contribute to the lumped parameterization of; streambed conductance, as well as aquifer specific yield, which controls; the rate at which hydraulic perturbations propagate through an aquifer.; The computational advantage of the numerical adjoint solution was; highlighted, where a single numerical model can be used to predict CSD; resulting from any potential groundwater extraction location. The; reduction in computational time required was proportional to the number; of potential extraction well locations. If the number of potential; locations is large then a reduction in model run time of nearly 100 %; can be achieved.
