指導教授：蔡宛珊臺灣大學：土木工程學研究所林彥廷Lin, Yen-TingYen-TingLin2014-11-252018-07-092014-11-252018-07-092014http://ntur.lib.ntu.edu.tw//handle/246246/260733It 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.口試委員會審定書 # 中文摘要 i ABSTRACT ii CONTENTS iv LIST OF FIGURES vii LIST OF TABLES ix Chapter 1 Introduction 1 1.1 Problem Statement 4 1.2 Research Hypotheses 5 1.3 Objectives of Study 7 1.4 Overview of Thesis 7 Chapter 2 Literature Review 8 2.1 Particle Tracking Models 9 2.1.1 Hunter et al. (1993) 9 2.1.2 Pope (1994) 11 2.1.3 Spivakovskaya et al. (2005) 12 2.1.4 Spivakovskaya et al. (2007) 13 2.2 Summary 14 Chapter 3 Stochastic Theories 16 3.1 Brownian Motion 17 3.2 Wiener Process 18 3.3 Poisson Process 19 3.4 Exponential Distribution 20 3.5 Summary 21 Chapter 4 Stochastic Particle Tracking Model using Extreme Value Generator in Jump Term 22 4.1 Introduction 23 4.2 Stochastic Jump Diffusion Particle Tracking Model 24 4.2.1 Governing Equation 24 4.2.2 Determination of Jump Terms 26 4.2.3 Extreme Value Distribution 29 4.2.4 Poisson Jump Processes 30 4.3 Applications in Open Channel Flows 33 4.3.1 Hydraulic Parameters 34 4.4 Simulation Results 37 4.4.1 Example 1: Two-Dimensional 37 4.4.2 Example 2: Open Channel Flow 40 4.4.3 Example 3: Forecast Model 43 4.5 Summary and Conclusions 47 Chapter 5 Trend Analysis of Large Flow Perturbations and Applications to Stochastic Particle Tracking Model 49 5.1 Introduction 50 5.2 Logistic Trend model 52 5.3 Analysis of Trends of Large Flow Perturbations 54 5.3.1 Case 1: Large Timescales Flow Events 54 5.3.2 Case 2: Small Timescales Flow Events 57 5.3.3 Conclusions 58 5.4 Poisson Jump Processes 59 5.5 Applications in Stochastic Jump Particle Tracking Model 62 5.6 Simulation Results 63 5.6.1 Case 1: Large Timescales Flow Events 63 5.6.2 Case 2: Small Timescales Flow Events 66 5.7 Discussions 68 5.8 Summary and Conclusions 69 Chapter 6 Summary and Recommendations 71 6.1 Summary and Conclusions 72 6.2 Recommendations for Future Research 73 REFERENCES 75 APPENDIX 781653562 bytesapplication/pdf論文公開時間：2016/08/21論文使用權限：同意有償授權(權利金給回饋學校)隨機微分方程序率模式顆粒軌跡模型泥砂運動極端流動事件氣候變遷[SDGs]SDG13thesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/260733/1/ntu-103-R01521317-1.pdf