以隨機微分方程法探討極端事件下泥砂運動機制

Abstract

It is important to develop a forecast model to predict the trajectory of sediment particles when extreme flow events occur. In extreme flow environments, the stochastic jump diffusion particle tracking model (SJD-PTM) can be used to model the movement of sediment particles in response to extreme events. This proposed SJD-PTM can be separated into three main parts — a drift motion, a turbulence term and a jump term due to random occurrences of extreme flow events. The study is intended to modify the jump term, which models the abrupt changes of particle position in the extreme flow environments. Firstly, considering the probabilistic occurrences of extreme events, both the magnitude and occurrences of extreme flow events can be simulated by the extreme value type I distribution (EVI) and the Poisson process, respectively. The evidence shows that the proposed model can more explicitly describe the uncertainty of particle movement by taking into considerations both the random arrival process of extreme flows and the variability of extreme flow magnitude. Secondly, the frequency of extreme flow occurrences might change due to many uncertain factors such as climate change. The study also attempts to use the concept of the logistic regression and the parameter of odds ratio, namely the trend magnitude to investigate the frequency change of extreme flow event occurrences and its impact on sediment particle movement. With the SJD-PTM, the ensemble mean and variance of particle trajectory can be quantified via simulations. The results show that by taking into the effect of the trend magnitude, the particle position and its uncertainty may undergo a significant increase. Such findings will have many important implications to the environmental and hydraulic engineering design and planning. For instance, when the frequency of the occurrence of flow events with higher extremity increases, particles can travel further and faster downstream. And more likely flow events with higher extremity can induce a higher degree of entrainment and particle resuspension, and consequently more significant bed and bank erosion.