E-mail: edward.bolton@yale.edu

Computational Landform Evolution

Land surface material is transported overland by both flowing water and gravity. The combination of tectonic and erosive forces creates the observed topography. We have incorporated simple erosion laws into a numerical finite-difference model which simulates the appearance of typical badlands topography. We solve the shallow-water equations for flow down arbitrary topography, along with an equation for mass continuity. Sediment fluxes are calculated from the water slope, depth, and velocity. The approach is more fundamental than the water-passing models which have up to now dominated the literature in dynamic geomorphology. Initial results of this work, with computer scientist Kenton Musgrave, appear realistic. Water and sediment masses are conserved; and erosion, transport, and deposition are calculated. Quantitative comparison of landform types with model results is one goal of this work, but will require an extension of wavelet analysis in order to allow basis functions of nonzero mean. This alternative to Fourier methods should have important applications to pattern recognition, especially when the structure to be analyzed is composed of a superposition of a particular geometric form at many different scales. In a complementary study, with graduate student Wenjie Zhao, we investigated the onset of the channeling instability. Flow down a sloping land surface creates channels when the hydraulic erosive effects dominate the diffusive effects.