The Remarkable Generality of the Transient Storage Model with Residence Time Dependence: Temporal Moments.

Several distinct approaches to the one-dimensional modeling of river corridor transport at the macroscale have been developed as generalizations of the original Transient Storage Model (TSM).  We show that essentially all of them can be captured by simply restructuring the TSM so that the exchange coefficients are functions of residence time, because doing so converts the TSM to a general memory function form.  We use this generalized TSM approach to find novel closed-form expressions for the temporal moments of breakthrough curves resulting from river corridor tracer tests, when hyporheic zone exchange is governed by a memory function.  These expressions are useful because they can be used to test different hypotheses about the hyporheic zone residence time distribution based on analyses of the temporal moments of the tracer test breakthrough curves prior to detailed modeling work.  We demonstrate the application with a case study, and present extensions of the notion of making rate coefficients depend on residence time.