不同水文條件下泥砂輸出與水庫淤積之數值模擬研究-以石門水庫為例

Abstract

臺灣多數水庫因上游地質脆弱與極端豪雨頻繁而面臨嚴重淤積，石門水庫尤甚，長年影響北部供水與庫容安全。為量化未來百年石門水庫的淤積風險，本研究整合「土壤沖蝕、崩塌產砂、二維輸砂、長期機率推估」四大模組，建構涵蓋產生、遞移至入庫的多源泥砂預測框架。研究方法利用改良之 USLE 融合 Landsat-8，經 GIS 空間運算取得坡地土壤沖蝕量，並使用全臺測站雨量行資料透過反距離權重法推算降雨沖蝕指數，提高空間推估一致性。再以 2004–2019 年航測崩塌資料與歷史沖蝕崩塌比例計算崩塌體積，並建立崩塌面積-體積關係，配合坡度百分比、順向坡率、累積崩塌率及降雨能量，以羅吉斯回歸求得各子集水區崩塌失效機率；後使用近十年雨量站資料計算流量歷線，並以 1 m DEM 建立 SRH-2D 動床模型，模擬 Q2、Q5、Q10、Q25、Q50、Q100洪水情境下白石溪的輸砂行為，估算泥砂遞移率（SDR），最後帶入 Poisson 反累積分布抽樣百年降雨事件，預測未來百年入庫泥砂量。 本研究區之 Rm 整體高於歷年文獻，而 Km 在白石溪支流顯著偏高，這突顯該區為高潛勢土壤流失熱點；坡度因子與作物管理因子於裸岩與人工構造物上仍有高估風險。羅吉斯模型顯示坡度 (SN) 與累積崩塌因子 (ELN) 為主要控制變數，三大子集水區崩塌風險皆超過 50%。SRH-2D 水位校準與觀測吻合（R²＝0.9985），六組洪水情境下 SDR 均大於 0.3，證明上游泥砂流通性強。進一步將土壤沖蝕量、崩塌產砂量與 SDR 結合卜瓦松隨機抽樣百年降雨序列，預測未來百年年均入庫泥砂量約 1.5×10⁴ m³；若未搭配清淤或攔砂措施，庫容衰減仍具威脅。 創新之處在於結合坡面沖蝕、崩塌機率與二維輸砂，並透過 Poisson 降雨抽樣預測未來入庫泥砂量，讓泥砂預報兼具空間與時間解析力；資料來源如衛星影像、DEM、雨量網格等皆可定期更新，使本研究框架可移植至翡翠、曾文、鯉魚潭等高山水庫，或結合雷達雨量、UAV-LiDAR 升級為半即時泥砂預警與 AI 排砂決策系統。研究成果為石門水庫長期減淤與供水韌性提供量化依據，也為臺灣水庫在極端氣候下的治理策略開啟整合科學、工程及管理的新途徑。

Most Taiwanese reservoirs suffer from severe sedimentation due to fragile mountain geology and frequent typhoon downpours; Shimen Reservoir is among the most affected, jeopardizing both storage capacity and water-supply reliability in northern Taiwan. To quantify its centennial siltation risk, this study integrates four modules—hillslope soil erosion, landslide‐derived yield, two-dimensional sediment transport, and long-term probabilistic projection—into a multi-source sediment-forecasting framework that spans production, delivery, and deposition. First, an enhanced Universal Soil Loss Equation( USLE), combined with Landsat-8 was applied in a GIS to map spatially distributed soil erosion, and nationwide rain-gauge data (interpolated using inverse-distance weighting), provides spatially consistent soil-erosion estimates. Secondly, aerial-photography landslide inventories (2004–2019) is converted to volumes via a new area–volume relation; together with slope percentage, dip-slope ratio, cumulative landslide rate, and rainfall energy feed a logistic model that yields failure probabilities for each sub-watershed. Third, ten-year rainfall data was converted into flood hydrographs, and a 1-m DEM supports an SRH-2D movable-bed model that simulates Q2, Q5, Q10, Q25, Q50, and Q100 floods on Baishih Creek to derive sediment-delivery ratios (SDR). Finally, a Poisson inverse CDF was sampled to create a 100-year stochastic rainfall series, from which future reservoir sediment inflow was estimated. Results show rainfall erosivity (Rm) is higher than previously reported and an exceptionally high soil-erodibility factor (Km) in the Baishih tributary, marking it as an erosion hotspot. Slope (SN) and cumulative landslide factor (ELN) dominate the logistic model, with failure probabilities exceeding 50 % in all three major sub-basins. SRH-2D calibration matches observed water levels (R² = 0.9985), and SDR remains above 0.3 across scenarios, indicating efficient sediment export. Combining soil-erosion and landslide yields with SDR and Poisson-sampled centennial rainfall sequences predicts a mean annual sediment inflow of roughly 1.5 × 10⁴ m³ over the next century; without dredging or check-dam intervention, storage loss will persist. The study’s novelty lies in unifying slope-scale erosion, landslide probability, and 2-D sediment transport, while introducing future climate variability via Poisson rainfall sampling, thereby delivering both spatial and temporal resolution.. By inputing such as satellite imagery, DEMs, and rainfall grids can be periodically updated, allowing rapid transfer to other mountain reservoirs (e.g., Feitsui, Zengwen, Liyutan) and integration with radar rainfall and UAV‐LiDAR for semi-real-time warning and AI-assisted desiltation. The results provide quantitative support for long-term sediment management and water-supply resilience at Shimen and open a science-based pathway for Taiwan’s reservoir governance under extreme climate change.