Stochastic Modelling of Soil Erosion and Deposition

The rate of erosion is the product of the concentration of active soil aggregates and their mean vertical velocity. The sediment concentration for a given time is proportional to the probability of detachment of first-time mobilized soil aggregates and to the probability of the deposited sediments’ redetachment. The probability of soil aggregate activation is equal to the probability of the driving forces exceeding the resistance forces. These forces are stochastic variables, and any excess value of the driving forces above the resistance forces is a probability function of these stochastic variables. Five characteristics are used as stochastic variables: flow velocity; soil cohesion; aggregate size for the native soil and deposited sediments; and soil consolidation (or soil fatigue). The vertical velocity of soil aggregates at the moment of detachment is derived from the momentum continuity equation for the stable particle at the flow bed. The proposed theory explicitly describes differences in types of relationships between detachment rates and flow velocities; the different shapes of the probability density curves of soil properties (cohesion, aggregate size and soil consolidation) cause this difference. The detachment rate increased with flow velocity more rapidly for more consolidated soils with high cohesion, and large aggregates.