Flipping the thin film model: Mass transfer by hyporheic exchange in gaining and losing streams

The exchange of mass between a stream and its hyporheic zone, or hyporheic exchange, is central to many important ecosystem services. In this paper we show that mass transfer across the streambed by linear mechanisms of hyporheic exchange in a gaining or losing stream can be represented by a thin film model in which (a) the mass transfer coefficient is replaced with the average Darcy flux of water downwelling into the sediment and (b) the driving force for mass transfer is flipped from normal to the surface (concentration difference across a boundary layer) to parallel to the surface (concentration difference across downwelling and upwelling zones). Our analysis is consistent with previously published analytical, computational, and experimental studies of hyporheic exchange in the presence of stream-groundwater interactions, and links stream network, advection-dispersion, and stochastic descriptions of solute fate and transport in rivers.