貝氏超圖分析於跨流域水源調度之水資源風險評估：以曾文—烏山頭系統與南化水庫串聯為例

Abstract

臺灣降雨的時空分布高度不均，跨流域水源調度因而成為枯水期供水保障之關鍵手段，惟既有缺水風險研究仍存在兩項方法論缺口：Tsai et al.（2023）以水庫初始蓄水量與累積入流量推導可供水量、並以其低於需水量之機率定義缺水風險的解析型框架，尚未延伸至涉及水量交換之跨流域情境；而 Javidian et al.（2020）以可連接任意數量頂點之超邊顯式表達多變數聯合影響機制的貝氏超圖，於水資源領域之應用亦近乎空白。 本研究以貝氏超圖為方法論核心，首先將水量平衡方程式與缺水風險定義轉譯為超邊形式，建立單水庫缺水風險模組；接著以曾文—烏山頭水庫系統與南化水庫為實證對象，蒐集共11年（2013 ~ 2023）之旬營運紀錄資料，以L-動差比圖95%接受區域方法進行適合度檢定，並就1月1日~ 5月底之決策期，依卷積積分關係推導可供分配水量與單水庫缺水風險；最後以聯通管是否啟用區分基準情境與聯合調度情境，加入聯合調度超邊與調度後缺水狀態超邊，完成由13個節點與7條超邊所組成之整體架構。 除曾文系統之初始可分配蓄水量服從常態分佈外，其餘三項水文量均以Gumbel分佈為最適分佈，基準情境下兩座水庫之缺水風險分別為48.49%與5.00%。以雙缺水狀態為例，在四種調度水量之截斷常態分佈設定下，南化水庫之缺水風險下降1.96% ~ 2.63%、曾文系統則上升3.40% ~ 5.12%，其轉移幅度主要受調度規模影響而對變異程度不敏感。本架構在保留計算效率與決策直觀性之前提下顯式刻劃多水源共同決定缺水風險之條件獨立結構，對「珍珠串計畫」下其他經串接形成之多水庫系統應具移植與推廣之潛力。

Taiwan's uneven rainfall makes inter-basin water allocation central to dry-season supply security, yet two gaps remain in the shortage risk literature. The analytical framework of Tsai et al. (2023), which derives available water from initial storage and cumulative inflow and defines shortage risk as the probability that it falls below demand, has not been extended to inter-basin settings involving water exchange; and the Bayesian hypergraph of Javidian et al. (2020), whose hyperedges connect arbitrarily many vertices and thus express joint multi-variable influence explicitly, remains almost unapplied. This study takes the Bayesian hypergraph as its methodological core. The water balance equation and the shortage risk definition are first translated into hyperedge form as a single-reservoir module. With the Tsengwen–Wushantou system and Nanhua Reservoir as the empirical case, eleven years of ten-day records (2013-2023) are compiled, goodness of fit tested by the L-moment ratio diagram 95% acceptance region method, and allocatable water and shortage risk derived by convolution over a decision period from 1 January to the end of May. Baseline and joint operation scenarios are distinguished by whether the pipeline is activated, a joint operation hyperedge and a post-transfer shortage state hyperedge completing an architecture of thirteen nodes and seven hyperedges. Apart from the Tsengwen system's initial allocatable storage, which follows a normal distribution, the three remaining variables follow Gumbel distributions, and baseline shortage risks for the two reservoirs are 48.49% and 5.00%. Under four truncated normal specifications of the transfer volume in the dual-shortage state, the shortage risk of Nanhua Reservoir falls by 1.96% to 2.63% while that of the Tsengwen system rises by 3.40% to 5.12%, the shift depending mainly on transfer scale rather than variability. The architecture makes explicit the conditional independence structure by which multiple sources jointly determine shortage risk, preserves computational efficiency and decision transparency, and should transfer to other linked systems under the (珍珠串計畫).