A mathematical model for steady‐state regolith production at constant erosion rate

It has been hypothesized that many soil profiles reach a steady‐state thickness. In this work, such profiles were simulated using a one‐dimensional model of reaction with advective and diffusive solute transport. A model ‘rock’ is considered, consisting of albite that weathers to kaolinite in the presence of chemically inert quartz. The model yields three different steady‐state regimes of weathering. At the lowest erosion rates, a local‐equilibrium regime is established where albite is completely depleted in the weathering zone. This regime is equivalent to the transport‐limited regime described in the literature. With an increase in erosion rate, transition and kinetic regimes are established. In the transition regime, both albite and kaolinite are present in the weathering zone, but albite does not persist to the soil–air interface. In the weathering‐limited regime, here called the kinetic regime, albite persists to the soil–air interface. The steady‐state thickness of regolith decreases with increasing erosion rate in the local equilibrium and transition regimes, but in the kinetic regime, this thickness is independent of erosion rate. Analytical expressions derived from the model are used to show that regolith production rates decrease exponentially with regolith thickness. The steady‐state regolith thickness increases with the Darcy velocity of the pore fluid, and in the local equilibrium regime may vary markedly with small variations in this velocity and erosion rate. In the weathering‐limited regime, the temperature dependences for chemical weathering rates are related to the activation energy for the rate constant for mineral reaction and to the ΔH of dissolution, while for local equilibrium regimes they are related to the ΔH only. The model illustrates how geochemical and geomorphological observations are related for a simple compositional system. The insights provided will be useful in interpreting natural regolith profiles. Copyright © 2010 John Wiley & Sons, Ltd.