Stochastic components in the gully erosion modelling

The great complexity of the geo-mechanical, structural, and electro-chemical forces in soil, as well as of initial and boundary conditions in the equations of hydrodynamics, leads to a necessity of spatial/temporal averaging of deterministic equations related to soil behaviour. The stochastic terms, which appear in the equations after averaging procedures, must be incorporated into the modelling of erosion features. In this study, a new method of estimating detachment rate was used in stochastic gully erosion modelling. It is based on estimation of the probability of excess of driving forces above resistance forces in the interaction of water flow and structured soil. Knowledge of the probability density functions for the flow and soil main characteristics (as flow velocity, soil cohesion, aggregate size and others) makes it possible to calculate theoretically the rate of cohesive soil erosion for any combination of these stochastic variables. The proposed theory allows explicit explanation of relationships between detachment rate and flow/soil characteristics. Detachment rate increases with flow velocity more rapidly for soil with higher cohesion and larger aggregates. This theory also shows great difference in type of soil erosion for relatively high and relatively low flow velocities, and explains rather high errors in calculating of soil erosion rate even with detailed models.