Primary weathering rates, water transit times, and concentration-discharge relations: A theoretical analysis for the critical zone

The permeability architecture of the critical zone exerts a major influence on the hydrogeochemistry of the critical zone. Water flow path dynamics drive the spatiotemporal pattern of geochemical evolution and resulting streamflow concentration-discharge (C-Q) relation, but these flow paths are complex and difficult to map quantitatively. Here we couple a new integrated flow and particle tracking transport model with a general reversible Transition State Theory style dissolution rate law to explore theoretically how C-Q relations and concentration in the critical zone respond to decline in saturated hydraulic conductivity (K-s) with soil depth. We do this for a range of flow rates and mineral reaction kinetics. Our results show that for minerals with a high ratio of equilibrium concentration (C-eq) to intrinsic weathering rate (R-max), vertical heterogeneity in K-s enhances the gradient of weathering-derived solute concentration in the critical zone and strengthens the inverse stream C-Q relation. As C-eq/R-max decreases, the spatial distribution of concentration in the critical zone becomes more uniform for a wide range of flow rates, and stream C-Q relation approaches chemostatic behavior, regardless of the degree of vertical heterogeneity in K-s. These findings suggest that the transport-controlled mechanisms in the hillslope can lead to chemostatic C-Q relations in the stream while the hillslope surface reaction-controlled mechanisms are associated with an inverse stream C-Q relation. In addition, as C-eq/R-max decreases, the concentration in the critical zone and stream become less dependent on groundwater age (or transit time).