Relationships between the Transit Time of Water and the Fluxes of Weathered Elements through the Critical Zone

Abstract

The movement of water is a widely recognized control on chemical weathering rates. However, the extent to which chemical weathering rates are controlled by subsurface structure and heterogeneity remains poorly quantified. As a result, most geochemical models of solute fluxes from catchments cannot uniquely predict commonly observed relationships between concentrations of reactive solutes and stream discharge. The reactive solute composition of waters in the stream is the flux-weighted average of the ensemble of flow paths and is thus strongly linked to the transit time distribution, which is in turn a complex measure of physical heterogeneity. To quantify the effect of physical heterogeneity on chemical weathering rates and fluxes, we present simplified two-dimensional reactive transport simulations of chemical weathering reactions in heterogeneous domains and link the extent of reaction progress to the transit time distribution. We show that the importance of heterogeneity, measured by dilution of solute relative to homogeneous models, is a function of the Damköhler number (Da). At low flow rates or for rapid reaction rates (high Da), physical heterogeneity is less important because solute gradients are minimal. Similarly, at high flow rates or slow reaction rates (low Da), physical heterogeneity has little effect on the solute fluxes or weathering rates. At moderate Da, the effect of heterogeneity is most pronounced based on the maximum dilution from the homogenous case. Here, the effective reaction rates are also at a minimum relative to homogeneous case because of variable departures from equilibrium throughout the domain, resulting in a scale dependence of the effective reaction rates. Most weathering in the critical zone probably occurs within the range associated with high to moderate Da, suggesting that transit time distributions will have a moderate to substantial influence on the observed chemical fluxes and effective reaction rates. 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.