Generalized Exner equation for the conservation of sediment mixtures

The Exner equation of sediment conservation is the basis upon which river morphodynamics stands. In the case of mixtures of different sediment sizes it is customary to formulate sediment conservation in terms multiple discrete layers stacked in the vertical. In the simplest of these formulations, the bed is divided into two layers; an "active" ("surface," "exchange") layer, which directly exchanges sediment with the water column and a "storage" ("substrate") layer below which exchanges sediment with the active layer by means of aggradation and degradation. The discrete layers of such active layer formulations, however, are a gross simplification of the vertical structure of a bed deposit, which should show a continuous variation in the vertical when averaged over area. Here the discrete active layer formulation is replaced by a fully continuous probabilistic formulation. Copyright ASCE 2004.