由雙向隨機顆粒軌跡模型辨認明渠流中泥砂沈積物潛勢來源區域

Abstract

泥砂傳輸在自然界屬於正常現象，然而，當過量泥砂傳輸至水庫時，將可能導致大量泥砂沉積並影響水庫蓄水功能。目前工程實務界尚未發展出有效、可行、成熟的方式以解決泥砂沉積問題（sedimentation problem），逆向追蹤顆粒軌跡模型（Backward Particle Tracking Model）可辨認沉積泥砂顆粒來源，然而，由於缺乏逆向顆粒追蹤之理論，研究者對於純逆向追蹤顆粒的可行性與精確度仍存疑，因此，本研究致力於發展一雙向隨機顆粒軌跡模型（Backward-forward Stochastic Particle Tracking Model）並應用於辨認泥砂沈積物潛勢來源區域。除此之外，本研究也改進前述模型中的水面之擴散度（diffusivity）之精確性。 受過去研究啟發（Lin et al., 2003），此研究應用Uliasz和Pielke於1990年所提出之「影響函數（influencen function）」定量描述上游區域對下游沈積區域之影響程度，並藉此將逆向與順向顆粒追蹤之結果連結。首先，此研究探討不同擴散度估計公式、不同數值方法在純順向及純逆向隨機顆粒軌跡追蹤過程之表現，接著，應用雙向隨機軌跡模型於辨認泥砂沈積物潛勢來源區域，結果發現顯式數值模式（explicit method）較隱式數值模式（implicit method）更能夠辨認出高影響函數之可能來源區域，且證實純逆向隨機顆粒軌跡模擬的結果不一定可信，由純逆向隨機顆粒軌跡模擬所推估之高濃度區域，並不一定是泥砂沈積物潛勢來源。 此外，本研究建議推算泥砂顆粒濃度時不能僅以一組（一萬個隨機顆粒軌跡）蒙地卡羅試驗（Monte Carlo Simulation）決定，因為只以一組蒙地卡羅試驗所推估之空間泥砂分布僅是一萬顆泥砂顆粒分布的其中一種分布狀況，而非一萬顆泥砂顆粒濃度分布的系集平均值（ensemble mean），因此，此研究藉由一百組蒙地卡羅試驗，估計由雙向隨機顆粒軌跡模型所辨認出之沉積物潛勢來源區域，釋放出之一萬顆顆粒產生的濃度分佈的系集平均值、系集標準差，由此結果可再次觀察到應用顯式數值方法於雙向隨機顆粒軌跡模型所辨認出之沉積物潛勢來源區，比應用隱式數值方法的結果較能辨識出高影響函數的區域。

Sediment transport is no more than a usual phenomenon in nature. However, when a large volume of sediment particles enters a reservoir, severe sedimentation would occur. There is rarely an efficient, practical, mature measure to solve the aforementioned problem. Moreover, due to the lack of theoretical calculations of backward tracking, the concentration distribution determined by backward tracking may be questionable. Therefore, we aim at discovering the probable source regions of deposited sediments by a Backward-Forward Stochastic Diffusion Particle Tracking Model (Backward-Forward SD-PTM) in this research. In addition, the accuracy of the diffusivity at the water surface is also improved. Inspired by Lin et al. (2003), the concept of the “influence function” (Uliasz and Pielke, 1990) is introduced to couple the backward and forward stochastic particle tracking models together. The influence function is a quantitative indicator of the influence of an upstream region to the downstream receptor (sedimentation region). Some pure backward simulations and pure forward simulations are computed first in order to compare the model performance with different diffusivity formulas and different numerical algorithms. Then, the forward-backward stochastic particle tracking model is applied to identifying probable sedimentation sources. It is found that the explicit method performs better in identifying probable sources with higher values of influence functions. Moreover, the pure backward simulation is unreliable. The high concentration area suggested by a pure backward simulation may not be a probable source region. Furthermore, we suggest that the spatial concentration distribution should be estimated by conducting many numerical experiments of Monte Carlo simulations. If the simulation is only by one round of Monte Carlo simulation, the derived spatial concentration distribution represents only one scenario rather than the ensemble mean of sediment spatial concentration distributions. Thus, the probable sources selected by the stochastic particle tracking model (including the explicit method and the implicit method) are discussed with the ensemble statistics of spatial concentration distributions. Ten thousand particles are released from each probable source for forward simulation and the corresponding ensemble statistics of spatial concentration distributions are discussed. The results again illustrate that the explicit method is better in selecting probable sources with higher values of influence functions.