A low‐dimensional model of bedrock weathering and lateral flow coevolution in hillslopes: 2. Controls on weathering and permeability profiles, drainage hydraulics, and solute export pathways

Abstract

Funding information National Science Foundation, Grant/Award Number: EAR-1344664, CBET-1360415 and EAR-90072546 Abstract The advance of a chemical weathering front into the bedrock of a hillslope is often limited by the rate weathering products that can be carried away, maintaining chemical disequilibrium. If the weathering front is within the saturated zone, groundwater flow downslope may affect the rate of transport and weathering—however, weathering also modifies the rock permeability and the subsurface potential gradient that drives lateral groundwater flow. This feedback may help explain why there tends to be neither ‘‘runaway weathering’’ to great depth nor exposed bedrock covering much of the earth and may provide a mechanism for weathering front advance to keep pace with incision of adjacent streams into bedrock. This is the second of a two-part paper exploring the coevolution of bedrock weathering and lateral flow in hillslopes using a simple low-dimensional model based on hydraulic groundwater theory. Here, we show how a simplified kinetic model of 1-D rock weathering can be extended to consider lateral flow in a 2-D hillslope. Exact and approximate analytical solutions for the location and thickness of weathering within the hillslope are obtained for a number of cases. A location for the weathering front can be found such that lateral flow is able to export weathering products at the rate required to keep pace with stream incision at steady state. Three pathways of solute export are identified: ‘‘diffusing up,’’ where solutes diffuse up and away from the weathering front into the laterally flowing aquifer; ‘‘draining down,’’ where solutes are advected primarily downward into the unweathered bedrock; and ‘‘draining along,’’ where solutes travel laterally within the weathering zone. For each pathway, a different subsurface topography and overall relief of unweathered bedrock within the hillslope is needed to remove solutes at steady state. The relief each pathway requires depends on the rate of stream incision raised to a different power, such that at a given incision rate, one pathway requires minimal relief and, therefore, likely determines the steady-state hillslope profile.