Evaluating the efficiency of catchments as chemical reactors

Catchments can be viewed as biogeochemical reactors that moderate the transfer of reactive gases and solutes according to the movement of water through the subsurface. A simple measure of the efficiency of a reactor is the Damköhler number (Da), which compares the characteristic fluid travel time to the characteristic time scale for the reaction of interest. However, the mixture of unsaturated and saturated flow conditions combined with complex subsurface heterogeneity results in an ensemble of travel times that is variable in space and time. Because most chemical reactions of interest are kinetically controlled and thus a non-linear function of time, the interaction between the travel time distribution and the reaction progress curve dictates the efficiency of chemical conversion within the catchment. This interaction is ultimately reflected in the relationship between concentration of a solute and discharge in wells and rivers.

To evaluate the coupling between transport dynamics and chemical reactions, we conducted a series of reactive transport simulations of heterogeneous domains at multiple scales, ranging from soil profile to hillslope scale, and evaluated rates of chemical transformations and fluxes under both steady-state and transient flow conditions. Travel time distributions are evaluated for each realization. For both heterogeneous and homogenous kinetic reactions considered, mixing further reduces the efficiency of chemical conversion to an extent that is determined by the average Da: at moderate Da, corresponding to pronounced solute gradients, the variability in local reaction rates is most pronounced. At the soil profile scale, characterized by dominantly vertical flow, concentrations scale with mean travel time. For a hillslope geometry, the travel time distribution is more complex and the nature of mixing can shift the trajectory of the reaction progress curve towards different endpoints, obscuring the relationship between concentration, water flux and travel time. Despite the inherent challenges, coupling measures of water age to reactive geochemical tracers in models and in applied settings presents many new opportunities to evaluate the factors that control the water, solute and energy fluxes into and out of catchments.