Author’s Reply

Abstract

We thank Dr. Hunt for giving us this opportunity to expand briefly on our paper. Dr. Hunt makes two points: (1) the solution described in our paper does not reproduce the delayed-yield behavior commonly observed in unconfined aquifers and (2) the zero-drawdown assumption is unrealistic. We will briefly respond to each of his points. We agree with Dr. Hunt that our solution does not consider the delayed-yield behavior commonly observed in the initial drawdown in unconfined aquifers. Thus, the solution is not appropriate for analysis of drawdown in the early stages of pumping an unconfined aquifer that displays delayed-yield behavior. However, the larger-time drawdown, which is the primary driver of stream depletion and/or leakage through an underlying aquitard, is well represented. Thus, our solution should be a reasonable tool for calculating pumping-induced stream depletion and leakage in unconfined systems. We agree with Dr. Hunt that the zero-drawdown assumption, which was originally invoked by Hantush (1955, 1964), is never rigorously met in actual field systems. However, as has been shown by countless pumping tests in leaky aquifer systems, this assumption is often quite reasonable for pumping periods of limited durations (periods of a few to several days—typical durations used for pumping in support of irrigated agriculture). Although the simulation results presented by Dr. Hunt are not consistent with the large body of field evidence from pumping tests in leaky aquifer systems, his results do emphasize the need to check the viability of key model assumptions in the field. We agree and, in the last two paragraphs of our paper, we remind the reader that the viability of the zero-drawdown assumption must always be checked in the field. Let us just repeat that reminder here: However, two points are worthy of further emphasis. First, as a result of the constant-head condition of Equation (14), the lower aquifer is assumed to be able to provide an unlimited amount of water without significant changes in head. An observation well is therefore needed in the lower aquifer to verify that large head changes, which would greatly diminish the upward flux, are not induced by pumping in the overlying unconfined aquifer. The viability of the constant-head condition may deteriorate as the duration of pumping increases. Batu (1998) summarizes past work on the dependence of this assumption on pumping duration for leaky aquifer systems in the absence of a stream. That previous work should be equally appropriate for the stream-aquifer systems considered here. Second, prior to invoking aquitard leakage as an important recharge mechanism, one must demonstrate the existence of the assumed pumping-induced head gradient within the aquitard. The solution presented here should not be used for practical assessments of pumping impacts on nearby streams without site-specific data indicating both relatively stable heads in the lower aquifer and a pumping-induced gradient within the aquitard. Finally, we want to emphasize that the major goal of our paper was to use this simple solution to demonstrate that pumping-induced leakage through an underlying aquitard, a commonly ignored mechanism in stream depletion calculations, can be an important source of recharge. We should also point out that our model yields a lower-bound estimate of stream depletion, while most existing analytical models, such as the Glover-Balmer-Theis model, provide upper-bound estimates (Zlotnik 2004). Thus, one can use these different models for rapid bounding case analyses to assess when the possibility of pumping-induced leakage through an underlying aquitard should be further explored.