A Stochastic Diffusion Jump Model of Suspended Sediment Transport in Hydrologic Extreme Events

Movement of sediment particles in surface water can be described by a stochastic diffusion jump process. The proposed approach simulates sediment transport in hydrologic extreme flows by introducing the Poisson jump process. The stochastic differential equation (SDE) in the proposed stochastic model classifies the movement of particles using three major terms including a mean drift motion, a random Brownian type turbulent motion and jumps due to the hydrologic extreme events. The random term is represented by the Wiener process. The jump term is modeled as the Poisson process. The magnitude of particle movement in response to extreme flow events, characterized as the Poisson jump, depends on the characteristics of the extreme events and the properties of the sediment particles. The frequency of occurrence of the extreme events in the proposed model can be explicitly accounted for in the evaluation of movement of sediment particles. In the proposed SDE model for particle movement, the relaxation time, defined as the time needed for a particle to move from the regular flow state to the extreme flow state, is introduced. One example is presented to illustrate the realizations of sediment transport. The ensemble mean and variance of particle trajectory can be obtained from the proposed model via simulations.