Effects of Spatio-Temporal Variations in Streambed Conductance on Stream Depletion

Abstract:

Stream depletion is the reduction in flow rate in a stream due to pumping in an aquifer that is hydraulically connected to the stream. The amount of stream depletion is related to the pumping rate, the distance between the well and the stream, and the hydraulic properties of the aquifer and streambed. If the conductance of the streambed sediment is high, water is exchanged easily between the aquifer and the stream, leading to high stream depletion; while if the sediment has low conductance, water cannot be exchanged easily, so stream depletion is lower. While sediment transport occurs continuously in natural stream channels, features of the channels create patterns of sediment transport behavior that lead to alternating reaches of higher conductance and lower conductance. Furthermore, these patterns of streambed heterogeneity vary temporally due to scour and deposition during high flow and low flow periods. Through numerical simulations, we demonstrate that temporal variations in heterogeneity patterns lead to exaggerated amounts of stream depletion. Specifically, if a well is pumping near a stream stretch that alternates between periods of high conductance and periods of low conductance, the amount of stream depletion during the high conductance periods will be higher than the amount of stream depletion that would be expected if the streambed sediment permanently had high conductance. Similarly, the amount of stream depletion during the low conductance periods will be lower than the amount of stream depletion that would be expected if the stream bed sediment permanently had low conductance. This behavior results from the cumulative effect of the temporally-varying conductance on drawdown in the aquifer in the vicinity of the stream. More drawdown occurs during periods of low conductance than during periods of high conductance. Thus, when a period of high conductance follows a period of low conductance, the drawdown in the aquifer near the stream, and therefore the hydraulic gradient between the aquifer and the stream, is larger than it would be if high conductance was assumed for the entire simulation. Consequently, stream depletion during the high conductance period is higher if the streambed conductance varies temporally than if it is always high.