Variation of the Surface Roughness of a Stream Channel Based on a Simple Cellular Automata Model Given an Initial Particle Distribution, Channel Width and Slope

The roughness of a stream channel boundary is an important control on the movement of sediment particles. The likelihood of a particle being entrained and transported from a surface composed of coarse-grained particles will depend in part on the local roughness geometry defined by the surface particles, i.e., particle motion will depend on a particle's size and elevation relative to the size and height of the surrounding particles. Over time, movement of particles can modify the shape of the channel boundary, and size-selective particle motion can change the distribution of surface particle sizes. These changes then modify the roughness of the boundary. We have constructed a cellular automata that models a simple version of this dependency of particle motion on the roughness of the surrounding surface. Cellular automata (CA) are models defined on a grid of cells, and changes in the state of a given cell depend solely on the current state of nearby cells. This CA evaluates the mobility of a given particle or group of particles based on whether or not the particles rise above or are sheltered by the surrounding particles. The CA results indicate the modeled sheltering mechanism can result in preferential transport of some particle sizes, a shift in particle size distributions over time, spatial sorting of particles to form convoluted patches of similarly-sized particles, and other effects. Previous CA models for simulating particulate surfaces, although not in the context of stream channels, have investigated roughening of particulate surfaces over time. Such studies identified scaling laws that describe the roughening of the evolved surfaces, and surface roughening in this model will be compared to the previously identified scaling. Roughening of surfaces with varying slope will also be evaluated. We plan further model variants using an evaluation of the forces on particles for different configurations of surrounding particle sizes to further characterize such effects of particle motion, surface roughening and evolution of channel form.