A rudimentary mechanistic model for soil production and landscape development

A rudimentary mechanistic model for soil production and landscape development is proposed. The continuity equation of the model assumes that the change in soil thickness over time depends on the production of soil from the weathering of bedrock and the transport of soil through natural surface erosion. The parameters for the model include the weathering rate, and erosive diffusivity. Weathering rate is expressed as an exponential decay function of soil thickness, which represents mechanical weathering. Erosive diffusivity can be estimated from soil erosion models. The model is solved numerically using the finite-difference approach and is applied to a numerical example. Simulation is performed for a hypothetical landscape with a series of hills and valleys. Results show the development rate of soil initially is very large, and slows down until it reaches a steady-state, defined by a constant change in soil thickness. The model also exhibits the characteristics of a nonlinear dynamic system: nonlinearity of soil thickness and curvature, and initial randomness appears to cause chaos (instability) in the system. The results show promising progress in quantitative modelling of pedogenesis. The limitations and suggested improvements of the model are also presented.

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