Solute transport through unsteady hydrologic systems along a plug flow-to-uniform sampling continuum

Abstract

Transit time distribution (TTD) theory elegantly addresses many long-standing challenges associated with modeling the age and transit times of water and solute in spatially heterogeneous hydrologic systems (McDonnell et al., 2010;McGuire & McDonnell, 2006;Kirchner, 2016). Recently the theory has been extended to rigorously account for unsteady flow through the use of StorAge Selection, or SAS, functions (Botter et al., 2011, Rinaldo et al., 2015. A few definitions are in order. Here, "age" is the elapsed time a water parcel has spent in a hydrologic system, "transit time" is the age of a water parcel as it exits the system, and the SAS function approximates how water parcels exiting the system are biased by age. Because water parcels enter and exit a system at various times, all three quantities (i.e., age, transit time, and SAS function) are represented by probability distributions. Further, in unsteady hydrologic systems, the age and TTDs vary with time in accordance with an age conservation equation (ACE). The ACE, in turn, builds on the M'Kendrick-von Foerster (MKVF) equation (M'Kendrick, 1925;