Cellular Automata Models of Particle Interactions in Sediment Entrainment

Nancy E. Brown, Jorge A. Ramírez , and Ellen E. Wohl

Colorado State University

The geometry of a river bed surface is determined by the arrangement and size of the particles that form the bed.  In gravel-to-boulder bed rivers, the surface geometry around any individual grain may be complex and highly variable, and tends to include multi-grain structures. These textural and structural characteristics influence whether an individual grain is entrained. The effect on entrainment is generally described as particle hiding and protrusion, which together define the degree to which an individual particle is sheltered by surrounding particles.

Two variants of a cellular automata (CA) model are used here to investigate the effect of controls on sediment entrainment resulting from particle sheltering. One model variant uses the degree of sheltering as a threshold constraint; the other variant uses the degree of sheltering as an extremal condition. There is a striking contrast in the spatial pattern of grain sizes that result with these different entrainment rules.  The extremal rule results in a patchy distribution of grains sizes, in which groups of adjacent cells tend to have the same grain size. The effect of the extremal rule is roughly analogous to considering a sequence of flow events which progressively increase the overall stability of grains on the channel bed, so that over time successively higher flows are required to mobilize grains. In contrast, the threshold rule results in a channel bed that tends to coarsen with time.