台灣地區位處熱帶與亞熱帶之間，平均年降雨量豐沛，但由於降雨時空分布不均以及地形因素，導致台灣本島河川乾濕季分明、且水資源僅有短暫時間停留地表，難以被有效利用。因此，為提供穩定水源，台灣地區以興建水庫之方式蓄存河川豐水期流量以供枯水期使用，然而由於乾旱、水庫淤積、城市發展等各種因素，導致水庫供水有時無法完全滿足需求量。因此本論文首先以水庫歷史入流量資料建立入流量機率分布，並加上蓄水量定義為水庫可供水量的機率分布，透過比較其與計畫需水量之間關係，即可逐旬推導供水水庫未來前置時期之缺水機率以及缺水量機率分布。本論文以台灣南部區域的南化水庫以及甲仙攔河堰系統為例，探討所提出之方法應用於實際水庫之情形。研究結果顯示南化水庫於各旬不同前置時期的缺水狀況呈現明顯差異，當具有相同起始有效蓄水量時，枯水期月份(11月至4月)的缺水機率較高；而豐水期月份(5至10月)的缺水機率較低。於相同前置時期時，缺水機率隨著起始有效蓄水量之增加而逐漸降低，且缺水量分布於較小範圍內，意即當起始有效蓄水量較高時，發生缺水之機率不高且缺水量機率分布集中於小幅缺水量處。本論文所得之研究結果可初步提供水庫營運單位預判供水水庫未來發生缺水之機率，期望未來可作為水庫缺水風險以及水庫即時操作之參考。

Although Taiwan receives plenty of rainfall normally, water shortages frequently threaten Taiwan due to unevenly spatio-temporal rainfall distribution. Reservoirs are the most important and efficient facilities for providing stable water supplies in Taiwan. The main aim of this study is to theoretically derive future lead-time water-shortage probability and probability distribution for a water-supply reservoir. This study uses water availability, defined as the sum of the useful storage and inflow, to represent water-supply capability of a water-supply reservoir. Water shortages are determined by comparing the relationship between water availability and demand. Inflows during the future lead times are unknown in advance, but distributions of inflows can be estimated from the historical data. The probability distribution of water availability is then constructed by convolution. Comparing probability distribution of water availability and demands, the water-shortage probability and distribution are constructed theoretically. The Nanhua Reservoir and the Chiahsien Weir located in southern Taiwan is used as an example to illustrate the proposed methodology. The results indicate that the water-shortage probability is high during the dry season (November to April) in Taiwan. In contrast, low water-shortage probability is observed during the wet season (May to October). The water-shortage probability decreases with increasing useful storage. The results of this study provide useful information for real-time reservoir operation.

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