The impact of depth-dependent water content on steady state weathering and eroding systems

Models for weathering and regolith formation are generally built on the assumption of constant rates of water advection in the zone of water-saturated pores, and constant water content of those pores, but it is common that weathering occurs in the water-unsaturated zone where lateral flow occurs. Thus, water content in pores varies with depth. Here we model mineral weathering profiles while accounting for depth-dependent water content. Like previous models, a mineral equilibrates with water over a length ξ that depends on dissolution and advection rates, but a new lengthscale λ is introduced to describe the decrease of water content with depth. Steady states of the regolith thickness can be attained for any finite λ and non-zero velocity v_E of erosion at the land surface. The type of mineral depletion profile developed over geological timescales depends on coupling between weathering and erosion: for slow erosion, a completely developed profile (CDP) is observed, in which the mineral-depleted zone at the top of the regolith has thickness of order λ; as v_E increases, there is a transition to an incompletely developed profile (IDP), in which partial mineral depletion at the land surface is constrained to a narrow range of velocities; when v_E exceeds the advance rate of weathering under far from equilibrium conditions, the profile transitions to an unstable regime that exposes bedrock. In general, the reaction front (RF) thickness and the velocity where CPD transitions to IDP depend on the interplay of both water infiltration and chemical equilibration over the timescale of water residence in regolith. The RF thickness roughly equals a correlation length χ defined as half the harmonic average of ξ and λ. In cases of limited water infiltration, water-mineral equilibration is achieved within the length λ, so that the RF thickness is controlled by hydrological properties and is independent of dissolution and advection rates. In the opposite endmember, water infiltrates to large depths and the effects of physical and chemical parameters on RF thickness are the same as in previous geochemical models. The relaxation time for reaching a steady state is shown to be ∼χ/v_E. We discuss the effects of physical and chemical parameters in CDPs and IDPs in those endmembers and show an application to a CDP in granitic regolith.