以基於可靠度之最佳化河川流量分配模式評估流域可用水量

Abstract

由於天然流量與人為取水之隨機性，河川可用水量及其可靠度不易採用確定性方法加以模擬。本研究利用流量延時曲線(flow duration curve, FDC)之特性建立一基於可靠度之最佳化河川流量分配模式，以評估河川上各取水位置之分配流量及其可靠度，進而推求流域剩餘之可用水量。本最佳化模式為一具有機率限制式之規劃模式，以混合整數線性規劃求解。 為推估未設站位置之流量延時曲線，首先進行水文區域劃分，作為流量選擇流量站之依據；應用主成分分析、集群分析及判別分析等方法對臺灣主要22水系進行水文區域劃分，透過將相鄰水系結合為若干連續區域方式，並比較其分群結果，使水系間之劃分界線更易於辨識。其次，應用三種迴歸方法建立流量延時曲線推估模式，包括傳統多元線性迴歸方法、主成分迴歸方法及偏最小二乘迴歸方法。利用交叉驗證比較模式表現，結果顯示傳統多元線性迴歸方法推估結果之不穩定現象，此乃由於其於不同流量超越機率值選入不同變數所致，主成分迴歸方法及偏最小二乘迴歸方法則可解決其選擇變數之困難，獲得更穩定之流量延時曲線推估結果。 最佳化河川流量分配模式應用於臺灣中部地區之烏溪，首先劃分661個次集水區作為流量分配之水文單元，利用烏溪所在水文區之流量站，以偏最小二乘迴歸方法建立未設站位置流量延時曲線推估模式；其次，以流域各水文單元之流量延時曲線推估結果作為未分配流量前之初始值，依據水文單元之上、下游關係建立最佳化河川流量分配模式，求解水系上130個既有取水申請之分配流量及其可靠度，與分配流量後各水文單元之剩餘可用水量。最後，利用最佳化河川流量分配模式評估新增水庫壩堰設施時，採用不同保留流量對下游既有取水之影響。

Deterministic approaches are difficult to apply when simulating water availability and reliability because of the natural stochastic variability of streamflow and water withdrawals. A reliability-based optimal streamflow allocation model was developed in this study using flow duration curves (FDCs) to evaluate allocations of streamflow and their associated reliabilities for each water abstraction location and water availability in the basin. The developed model is a chance constraint programming model, which was solved by mixed integer linear programming. In order to estimate the FDCs at ungauged locations, hydrologic regions were delineated to select streamflow gaging stations in the first place. Twenty-two river basins in Taiwan with major demands were grouped into homogeneous regions using principal component analysis (PCA), cluster analysis (CA), and discriminant analysis (DA). The dividing line between two adjacent river basins was easier to differentiate by combining adjacent river basins to form several contiguous regions and comparing their clustering results. Second, models were built for FDC estimations, applying three regression methods including the traditional multiple linear regression (MLR), principle component regression (PCR), and partial least squares regression (PLSR). A comparison of the model performances obtained using a cross-validation procedure showed some unstable conditions for MLR in the regional regression models for estimating the FDC; this was due to the variation of selected variables among percentile flows. The PCR and PLSR approaches can address the difficulties of variable selection and achieve a more robust model of FDC estimation. Optimal streamflow allocation model was applied to the Wu River, situated in the central part of Taiwan. First, Wu River catchments were divided into 661 sub-catchments as hydrological units for allocating streamflow. Based on the streamflow gaging stations in the hydrologic homogeneous region, regional regression models for estimating the FDC were built using PLSR method. The FDC estimation results of each hydrological unit in the river basin were taken as the initial values before allocating streamflow. Second, optimal streamflow allocation model was developed according to the upstream and downstream relationships of hydrological units. The allocation of streamflow and their associated reliabilities for 130 existing withdrawal sites and water availability for each hydrological units were solved by the optimal model. Finally, optimal streamflow allocation model was applied to evaluate the instream flow reserved by a new reservoir and their influence on the downstream existing withdrawal sites.