- 學位論文
擾動差法應用於新店溪懸浮固體濃度之預測與其不確定性之討論
Application of Perturbance Moment Method to the prediction of suspended sediment concentration in Xindian river and its associated uncertainty
摘要
2015年，蘇迪勒颱風侵襲台灣，不僅帶來豪雨以及強風，更造成北勢溪以及翡翠水庫原水濁度飆升，飆升速度太快導致淨水廠處理不及造成新店溪濁度跟著飆高。此研究目的為提供一個快速的方法預測濁度中的懸浮固體濃度。在實際現象之模擬與預測方面，變數或參數會因為有不確定性導致濃度預測或是濃度模擬有誤差產生。因此此研究將不確定性分析納入考量並應用於Mike 21 HD和Mike 21 ST模式，研究區域為新店溪河段，以屈尺站作為上游邊界條件，秀朗站為率定驗證對應測站。 在不確定性分析法的應用中，此研究利用擾動差法。此方法的最大優點是可以省略繁瑣的計算過程並省下龐大的計算量，因此適用於模擬時間長的模式。首先我們利用Mike 21 HD&ST做模型的率定以及驗證，率定參數分別是曼寧係數以及延散係數。在HD模型率定驗證方面，上游邊界採用屈尺站之歷史資料；下游邊界則是利用曼寧公式計算正常水深與流量的關係，率定採用水利署提供之秀朗站於2009年1月21至2月20之流量水位率定曲線，驗證則採用2009年2月21至3月20之資料。ST模型方面上游邊界為屈尺站之流量濃度率定曲線，下游則是利用Engelund and Hansen method求平衡濃度。率定驗證方面利用水利署提供之秀朗站流量濃度率定曲線。 在應用中，此研究將主要率定參數，即曼寧係數與延散係數作為隨機變數，並將代表粒徑d_50作為隨機變數。首先先考慮所有隨機變數的不確定性，討論考慮不確定性後模擬改善的結果；接著我們討論不同的隨機變數對模擬輸出值的變異性做討論。最後假設濃度標準後，可以利用擾動差法決定超過此標準的風險。
並列摘要
The modeling of the concentration of suspended sediment necessarily involves with uncertainty. The main goal of this research is to predict the output concentration of suspended sediment in Xindian river in Taipei, Taiwan. Mike 21 Hydrodynamic Model (HD) and Mike 21 Sediment Transport (ST) model are utilized to the modeling, and the study area is focused on Xindian river watershed. First, under the boundary discharge and normal depth conditions, the output depth-averaged horizontal flow velocity can be obtained from the Hydrodynamic Model, then the output of Hydrodynamic Model input to ST to simulate the output concentration. Second, the historical stage-discharge rating curve data and concentration-discharge rating curve are used for calibration validation. The Manning number and dispersion coefficient are the main items to be calibrated. Finally, after calibration and validation, a flood design with 1000 cubic meter per second (cms) is adopted to predict the concentration using a state-of-the-art method for uncertainty analysis called the perturbance moment method (PMM). The PMM is more efficient than the Monte-Carlo simulation (MCS). In MCS, calculations may become cumbersome when they involve multiple uncertain parameters and variables. In the PMM, the entire probability distribution of a random variable is redistributed among three points., and the statistical moments (such as mean value and standard deviation) for the output can be presented by the representative points and perturbance moments based on the parallel axis theorem. With assumed independent parameters and variables, the computation time of the PMM is significantly lower than MCS for a comparable modeling accuracy. This research, takes natural and parameter uncertainty into account, with natural uncertainty grain size are considered since the grain size is the input data in the ST model and for the parameter uncertainty the Manning number and dispersion coefficient are considered since they are main parameters for the calibration in the HD model and ST model. After evaluating the moments of output suspended sediment concentration by PMM, the range of the suspended sediment concentration prediction will be obtained.