Exploring an ‘ideal hill': how lithology and transport mechanisms affect the possibility of a steady state during weathering and erosion

Abstract

We present a model of chemical reaction within hills to explore how evolving porosity (and by inference, permeability) affects flow pathways and weathering. The model consists of hydrologic and reactive‐transport equations that describe alteration of ferrous minerals and feldspar. These reactions were chosen because previous work emphasized that oxygen‐ and acid‐driven weathering affects porosity differently in felsic and mafic rocks. A parameter controlling the order of the fronts is presented. In the absence of erosion, the two reaction fronts move at different velocities and the relative depths depend on geochemical conditions and starting composition. In turn, the fronts and associated changes in porosity drastically affect both the vertical and lateral velocities of water flow. For these cases, estimates of weathering advance rates based on simple models that posit unidirectional constant‐velocity advection do not apply. In the model hills, weathering advance rates diminish with time as the Darcy velocities decrease with depth. The system can thus attain a dynamical steady state at any erosion rate where the regolith thickness is constant in time and velocities of both fronts become equal to one another and to the erosion rate. The slower the advection velocities in a system, the faster it attains a steady state. For example, a massive rock with relatively fast‐dissolving minerals such as diabase – where solute transport across the reaction front mainly occurs by diffusion – can reach a steady state more quickly than granitoid rocks in which advection contributes to solute transport. The attainment of a steady state is controlled by coupling between weathering and hydrologic processes that force water to flow horizontally above reaction fronts where permeability changes rapidly with depth and acts as a partial barrier to fluid flow. Published 2020. This article is a U.S. Government work and is in the public domain in the USA.

Relating land surface, water table, and weathering fronts with a conceptual valve model for headwater catchments

“…Other researchers have similarly assumed a steady state akin to our ideal hill formulation albeit with different assumptions (e.g., Harman & Cosans, 2019;Pavich, 1986;Rempe & Dietrich, 2014). Harman and Cosans (2019) (Lebedeva & Brantley, 2020). Permeability was assumed to change as a function of ϕ 3 for a hill with geometry set as described above.…”

“…For each lithology, an upper and lower flow channel forms. Figures were reproduced with permission from a previous publication (complete descriptions of simulations are given in Lebedeva and Brantley (2020) conclusions from the previously described models that treated water- New observations were also made. The infiltration rate at the hill surface was observed to affect both the elevation of the reaction front and the water The water table located either above or below the reaction front, F I G U R E 7 Simulations of reacting hills where both vertical and lateral flow are allowed, and an approximation for the water table is calculated (see text for additional explanation).…”

“…The water storage capacity increased by 37.6% (note difference in colour scale). All the simulations are shown for dimensionless variables where the hillslope width and elevation are normalized by L = 20 m. Simulations a,b,c,d were reproduced with permission from a previous publication where all simulation parameters are summarized (Lebedeva & Brantley, 2020) depending upon the parameters of the simulation. For the chosen boundary conditions, the water table was always above the reaction front at the valley, regardless of the infiltration rate at the surface.…”

“…This in turn mostly follows the treatment of Lichtner (1988) in that they do not explicitly include a term for dispersion. As discussed recently (Lebedeva & Brantley, 2020), the dispersion tensor is neglected under the assumption that the Darcy velocities are very low, or, that dispersion can be treated by increasing the effective diffusivity D , which in the absence of dispersion is equal to the molecular diffusion coefficient divided by tortuosity.…”

“…Simulations focused on albite transforming to kaolinite. Many of the (Lebedeva & Brantley, 2020) depending upon the parameters of the simulation. For the chosen boundary conditions, the water table was always above the reaction front at the valley, regardless of the infiltration rate at the surface.…”