以賭徒問題與多態離散時間馬可夫鏈探討泥砂運動機制

Abstract

In this study, the transport process of uniform size sediment particles under steady and uniform flow is described by two different stochastic process approaches: the Gambler’s ruin problem and the multi-state discrete-time Markov chain. Firstly, the Gambler’s ruin model is employed to estimate the probability of reaching the designated capacity such as the pre-established water quality standard or maximum sediment carrying capacity in different flow conditions. Secondly, for application to the Shihmen reservoir and the Shi Lin weir in Taiwan, the Gambler’s ruin model is employed to simulate the daily effective risk of reaching to the limitation of the established water quality standard that can be handled by the water treatment plant. Finally, the uncertainty analysis is introduced to evaluate the effective risk variation of violating the pre-established water quality standard when considering the variability of the daily water level. On the other hand, the multi-state discrete-time Markov chain is employed to describe the suspended sediment concentration distribution versus water depth for different steady and uniform flow conditions. Model results are validated against available measurement data and Rouse profile. Moreover, multi-state discrete-time Markov chain can be used to estimate the average time spent for the flow to reach the dynamic equilibrium of particle deposition and entrainment processes.