On the Lagrangian formulations of reactive solute transport in the hydrologic response

We address Lagrangian dispersion of reactive solutes in the framework of the formulation of transport by travel time distributions, specifically aiming at models of basin-scale, nonpoint transport applicable to complex geomorphological settings. We revisit existing exact solutions of the reactive transport problem derived in the convective stochastic framework and extend them to the case of transport of mass arbitrarily distributed (in time and space) within the immobile phase, a situation which is arguably suited to better describe nonpoint source solute transport driven by the hydrologic response. The initial conditions and, particularly, the mass initially stored in immobile rather than mobile phases bear a pronounced effect on the spatial and temporal moments of the solute plume. We also show that in many nonpoint source cases of interest (typically when heterogeneous conditions prevail) a simpler model of reaction kinetics, where spatial gradients in the immobile concentration are neglected, does well. Such a class of models, termed mass response functions, is known from the literature and has the property, beside being simplified in the mass exchange terms, of embedding unsteady flow forcing of the type typically employed in the theory of the hydrologic response. Thus, in the range of cases where the well-mixed assumption proves meaningful, we suggest a natural extension of current geomorphological models of the hydrologic response to generic transport phenomena.