The representative stream length for estimating surface water-groundwater exchange using Darcy's Law

Groundwater discharge to streams is spatially variable. We often estimate this flux based on an averaged measurement of hydraulic gradient and local estimate of hydraulic conductivity. It is important to understand how this estimated flux value relates to the flux into the stream. In this study we introduce the concept of representative stream length. The estimated flux value best represents the groundwater discharge over the representative stream length. We simulated groundwater discharge to a stream using synthetic stochastic hydraulic conductivity fields to investigate the impact of heterogeneity (variance and correlation length) on the estimated groundwater discharge and the representative stream length of this discharge. To obtain estimates of hydraulic conductivity between the stream and piezometer, the groundwater head response to a known change in stream stage was simulated and analyzed using a well-known analytical solution. The results of the theoretical investigation showed that the representative stream length of the groundwater discharge estimate was approximately equal to the distance of the piezometer from the stream, that is, groundwater discharge estimated using Darcy's law from a piezometer 50. m from a stream will approximately represent the discharge occurring over a 50. m length of the stream. Furthermore, the results suggest that the variability in the estimated groundwater discharge significantly reduced when the distance of the piezometer from the stream increased. A field experiment was conducted using two controlled stream-stage change tests and found that results were consistent with the theoretical experiment. That is, as the distance of the piezometer from the stream increased, the variability in discharge estimates reduced. The implication of this finding is that future studies estimating groundwater discharge to streams applying Darcy's law need to consider the representative stream length, as this will impact the spatial scale over which the discharge estimate can be applied.