Modeling Bed-Load Transport by a Three-State Continuous-Time Markov Chain Model

Abstract

A three-state continuous-time Markov chain is proposed to model the movement of sediment particles across three different states, i.e., bed material, bed load, and suspended load layer. The proposed model incorporates an exchange process between the bed load and the suspended load layer, in addition to the interface between the bed-load layer and the bed material, as normally considered in most of the existing sediment transport studies. In this study the mathematical treatment of the continuous-time Markov chain is clarified to stress the difference in definitions of the continuous-time and discrete-time Markov chains. With the employment of the continuous-time Markov model, the bed-load transport capacity in the long run and the time-varying transport rates can be derived. On the other hand, the three-state model can assist in distinguishing whether the flow is subject to significant suspended load or not. Furthermore, the distribution of particles in each of the three layers can be quantified. The proposed model is validated against natural river data. The comparison has shown a reasonably good agreement and thus the validity of the proposed model is confirmed.