Cellular automata models of particle interactions in sediment entrainment

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 particle may be complex and highly variable, and tends to include multiparticle structures. These textural and structural characteristics influence whether an individual particle 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 particle sizes that result with these different entrainment rules. The extremal rule results in a patchy distribution of particles sizes, in which groups of adjacent cells tend to have the same particle size. The effect of the extremal rule is roughly analogous to considering a sequence of flow events that progressively increase the overall stability of particles on the channel bed, so that over time successively higher flows are required to mobilize particles. In contrast, the threshold rule results in a channel bed that tends to coarsen with time.