Geomorphological changes in young soils with sparse vegetation: Mathematical modeling and numerical simulation

Abstract

This article presents an improved mathematical model and numerical simulation for weathering of large areas with complex topography. It uses the equations of momentum, temperature, and humidity in turbulent air and for heat and water infiltration into soils. A mathematical model is also presented to calculate the soil porosity fraction produced by physical rock weathering in areas where soil is produced from intrusive rocks (batholiths). An algorithm based on air velocity, humidity (rainfall), temperature variation, and soil topography was developed to quantify soil erosion and change of relief at each point and time step in air, at the ground surface, and within the soil. This results in a complete air-soil model based on conservation laws that have not previously been applied to large areas of the earth's surface. The mathematical model is solved using large-scale numerical simulations applied to an area of 6.6 km2 in the Sierra Nevada batholith of California, USA. The results show that the wind velocity and resulting erosion is greater in areas with steeper slopes and that moisture accumulates mainly in low and flat areas; therefore, erosion is not uniform throughout the study area. In addition, computer simulations localized calculations to discrete grid cells within the porous (saprolite) fraction of the soil produced by freezing and thawing of water in rock. Results indicate that this physical mechanism is the primary contributor to weathering of rock at the study area.