Exaggerated Stream Depletion in Streams with Spatiotemporally Varying Streambed Conductance

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. We developed a semianalytical expression for stream depletion for pumping in a homogeneous aquifer, with an infinitely long, straight stream with a streambed conductance, C, that varies cosinusoidally in space and time in the range CL≤C≤CH. The wavelength of the spatial variations is equal to twice the distance between adjacent pools in a pool and riffle sequence, and the period of the temporal fluctuations represents alternating high and low flows. These spatiotemporal variations in streambed conductance produce temporal fluctuations of stream depletion superimposed on a trend that increases at a decreasing rate. Certain combinations of streambed and aquifer hydraulic parameters lead to exaggerated stream depletion, in which the temporally fluctuating stream depletion is not bracketed by the amount that would be obtained with steady, homogeneous streambed conductance of CL and CH. After sufficient time has passed, the same parameter sets produce excessive stream depletion, in which stream depletion exceeds the pumping rate at certain times. The degree of exaggerated stream depletion increases with the distance between pools, and is high if the temporal period of fluctuation matches the times of high rate of change of stream depletion.