Transient Theory of Pumping Induced Depletion and Drawdown of a Stream with Finite Channel Storage
Abstract. Mathematical models for stream depletion with stream stage decline or drawdown are developed to overcome the deficiency in existing models that typically use the constant-head (Dirichlet) or general (Robin) boundary condition and source terms at the stream-aquifer interface. Existing approaches assume a fixed stream stage during pumping, implies that the stream is an infinite water source, with depletion defined as a decrease in stream discharge. We refer to this depletion without drawdown as the ``stream depletion paradox.'' It is a glaring model limitation, ignoring the most observable adverse effect of long-term groundwater abstraction near a stream, namely stage declines that eventually lead to dry streambeds. Field data are presented to demonstrate that stream stage responds to pumping near the stream, motivating the development of an alternative theory predicts transient stream drawdown based on the concepts of finite stream storage and mass continuity at the stream-aquifer interface. Based on this alternative theory, models are developed for the cases of a non- and a fully-penetrating stream. The proposed model reduces to the fixed-stage model in the limit as stream storage becomes infinitely large and to the limiting case of confined aquifer flow with a no-flow boundary at the streambed when the stream storage vanishes. The model is applied to field observations of both aquifer and stream drawdown from tests conducted in a confined aquifer over which a shallow stream flows. Model fits and parameter estimates are obtained both aquifer and stream drawdown data. Model predicted and observed transient drawdown behavior indicate that fixed-stage models (a) underestimate late-time aquifer drawdown and (b) overestimate the available recharge from streams to pumping wells. This has significant implications for the sustainable management of water resources in hydraulically connected stream-aquifer systems with heavy groundwater abstraction.
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