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

Area of Science:

• Earth and Environmental Science
• Geomorphology
• Soil Science

Background:

• Understanding large-scale weathering and erosion is crucial for predicting landscape evolution.
• Existing models often lack the complexity to capture intricate air-soil interactions in diverse topographies.
• Physical weathering processes, particularly freeze-thaw cycles, are significant but often simplified in large-scale simulations.

Purpose of the Study:

• To develop and validate an improved mathematical model and numerical simulation for weathering and erosion in large, complex topographic areas.
• To integrate air-soil dynamics, heat and water transfer, and soil porosity calculations into a unified conservation-law-based model.
• To quantify the impact of topographic variations and physical weathering mechanisms on soil erosion and relief change.

Main Methods:

• Developed a comprehensive air-soil model incorporating equations for momentum, temperature, and humidity in turbulent air, and heat/water infiltration into soils.
• Created a mathematical model to calculate soil porosity fraction from physical rock weathering, specifically for intrusive rocks (batholiths).
• Employed large-scale numerical simulations on a 6.6 km² area in the Sierra Nevada batholith, California, using an algorithm based on air velocity, humidity, temperature, and topography.

Main Results:

• Demonstrated that wind velocity and soil erosion are significantly higher on steeper slopes.
• Observed preferential moisture accumulation in low and flat areas, leading to non-uniform erosion patterns.
• Confirmed that freeze-thaw cycles within the soil's porous (saprolite) fraction are the primary driver of physical rock weathering in the study area.

Conclusions:

• The developed air-soil model provides a robust framework for simulating weathering and erosion dynamics across large, complex landscapes.
• Topographic features exert a strong control on erosion and moisture distribution, highlighting the importance of spatial heterogeneity.
• Physical weathering, particularly freeze-thaw, plays a dominant role in rock breakdown and soil formation in granitic environments like the Sierra Nevada.