A clarification and extension of our model of regolith formation on hillslopes

In this paper we clarify that our weathering model from 2013 did not explicitly describe weathering of soil moving downhill along hillslopes. In addition, we re-analyze the role of the term that we neglected that describes loss of regolith mass through mineral dissolution. We derive an equation for this term by including lateral flow of water inside the model hill. For the revised hill model, we define a dimensionless parameter that allows estimation of the effect of lateral flow on the steady-state hillslope. This parameter is equal to the ratio of averaged advective flux of dissolved species out of the hill to the rate of total denudation. The parameter also yields a criterion for the existence of a steady-state regolith thickness for systems experiencing unidirectional advection at a constant velocity: for a ridge, the rate of downward flow of water (q_y) must be less than the rate of upward movement of rock (E) after normalization by a small parameter, α. This parameter is equal to the equilibrium aqueous concentration divided by the concentration of the reacting mineral in the rock. Alternatively, a steady-state may exist for the case of both vertical and lateral flow in a hill for any value of erosion rate if the Darcy velocities decrease with depth. Subsurface flow systems play an essential role in the existence of both steady-state hillslopes and steady-state regolith thicknesses. Published 2018. This article is a U.S. Government work and is in the public domain in the USA.