A smoothed-particle hydrodynamic automaton of landform degradation by overland flow

Abstract

A novel model for calculating hillslope degradation by overland flow is based on a coupling of the cellular automaton and smoothed-particle hydrodynamics theories.Simulated debris-laden floods were initiated on digital elevation models (DEMs). The flows were created by solving equations for diffusion routing, and erosion and deposition. We separated advection and diffusion terms using operator splitting, then solved the advection term via automaton and the diffusion term via smoothed-particle hydrodynamics.The technique was tested on geometrically simple synthetic slopes, against data for erosion and deposition by debris-laden flows in a gully developing on a scoria cone (Arizona), and against data on a recent moderate-sized debris-laden flood generated by possible partial glacier melting at Popocatépetl volcano (Mexico). The flow and erosion/deposition patterns on the simple synthetic slopes appear intuitively reasonable. On the synthetic scoria-cone slope, the model reproduced some of the observed spatial patterns of event-scale erosion and deposition. Reasonable flow speeds, runup heights, and runout lengths were produced for the debris-laden flood at Popocatépetl.The coupled cellular automaton–smoothed-particle hydrodynamics technique represents some advance in the modeling of landform degradation and channel development by cellular automata (CA). Use of the technique may aid our understanding of the link between hillslope-scale and landform-scale degradation patterns.