Exaggerated stream depletion due to spatio-temporal periodic variations in streambed conductance

Abstract:

Stream depletion, which is the reduction in flow rate in a stream due to pumping in an aquifer that is hydraulically connected to the stream, is related to the streambed conductance. Natural streambeds are heterogeneous, with stretches of coarse sediment with higher conductance alternating with stretches of fine sediment with lower conductance. Pumping near a section with high conductance produces more stream depletion than pumping near a section with low conductance. In natural channels, the patterns of streambed heterogeneity can vary temporally due to scour and fill during high flow and low flow periods. As a first-order approximation, we assume streambed conductance varies periodically in space along a straight, infinite stream channel. At each point in space, we assume that streambed conductance varies co-sinusoidally in time, representing an annual cycle of high flows and low flows that leads to corresponding scour and fill events. We use a semi-analytical expression for stream depletion under conditions of spatio-temporal variations in streambed conductance to demonstrate that temporal variations in streambed heterogeneity patterns lead to temporal fluctuations of stream depletion. We show that some scenarios lead to exaggerated stream depletion, in which the temporally fluctuating stream depletion is not bracketed by end-member scenarios of steady, homogeneous streambed conductance. We show that the degree of exaggerated stream depletion increases with the period of the spatial variation and with the mean streambed conductance. We also demonstrate that scenarios that exhibit exaggerated stream depletion also experience periodic occurrences of excessive stream depletion in which the reduction in the stream flow rate exceeds the rate of pumping at the well.