臺灣地區降雨量豐沛，但因降雨過於集中導致乾濕季分明，且因地形坡陡流急，水資源容易流失，無法妥善被利用。因此調節河川豐枯不均的流量及提供穩定水資源為臺灣地區水庫營運重要的課題之一。然而無法預期且嚴重的乾旱可能使得水庫供水無法滿足需水量。水庫的供水主要來自水庫內的蓄水量及入流量，其中入流量具有高度不確定性，雖然由過去的水文紀錄可以了解入流量的季節性分布及各時刻入流量的機率分布，但要準確預測未來入流量的大小仍有一定程度的困難。因此本研究提出以歷史流量紀錄建立入流量的機率分布，並與水庫有效蓄水量建立水庫可供水量的機率分布，經與已知的需水量比較即可推估缺水機率及缺水量機率分布。本研究以臺灣南部地區的南化水庫與甲仙攔河堰系統為例，首先建立系統之入流量機率分布，以探討不同前置時期與不同有效蓄水量下各時刻的缺水機率及缺水量機率分布。研究結果顯示南化水庫在不同前置時期的缺水機率於不同月份的缺水狀況呈現明顯差異，枯水期月份(1至2月及11至12月)的缺水況較為類似，且其缺水機率較高，而豐水期月份(6至9月)的缺水情況亦較為類似，但其缺水機率較低。在相同前置時期下，隨著有效起始蓄水量逐漸增加，缺水機率會逐漸降低，且缺水量機率分布會逐漸往左偏移，即缺水量會分布在較小範圍內。整體而言，本研究所提出之方法可作為水庫即時操作評估缺水機率及缺水量機率分布的參考。

Inefficient uses of water resources in Taiwan are caused by uneven distributed rainfall and steep terrain. Reservoirs become important facilities to regulate highly fluctuating streamflow and provide stable water supplies in Taiwan. The purpose of this study is to theoretically derive water-shortage probabilities and distributions of future lead times for a water-supply reservoir. The reservoir supply ability is represented by water availability, which is defined as the sum of useful storage and inflow. The water-shortage probability is the probability when the demand is less than the water availability. The water-shortage distribution is a flip of the water-availability distribution. The Nanhua Reservoir and the Chiahsien Weir located in southern Taiwan is used as an example to illustrate the proposed methodology. The water-shortage probabilities and distributions of 1 to 18 10-day periods for various initial useful storage (from empty to full capacity) are constructed. The results indicate that the water-shortage probabilities are different in various periods, which reflect inherent differences of inflow distributions. The water-shortage probabilities generally decrease with increasing initial useful storage for the same lead time. Furthermore, the water-shortage distributions leftward shift, distributed in a smaller range, with increasing initial useful storage. The proposed methodology is useful for real-time reservoir operation since it provides decision-makers future lead-time water-shortage probability and distribution for triggering water rationing measures.

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