Parameter estimation of the transient storage model for stream-subsurface exchange

The transient storage model (TSM) is the most commonly used model for stream-subsurface exchange of solutes. The TSM provides a convenient, simplified representation of hyporheic exchange, but its lack of a true physical basis causes its parameters to be difficult to predict. However, the simple formulation makes the model a useful practical tool for many applications. This work compares the TSM with a physically based pumping model. This comparison is advantageous for two reasons: Advective pumping is known to be an important hyporheic exchange process in many streams, and the pumping model can be used to derive dimensionless transient storage parameters that are properly scaled with important physical stream parameters. Transient storage model parameters are shown to be dependent on both the timescale of observation and the shape of the breakthrough curve, i.e., on the temporal evolution of the solute concentration in the surface water. This indicates that the transient storage model can, in practice, lead to incorrect predictions when model parameters are obtained without consideration of the stream flow dynamics, the properties of the stream bed, or the process timescale. This work emphasizes the limitations of simplified models for hyporheic transport, and indicates that such models need to be carefully applied.