機率預報不確定性於水資源調配之影響

Abstract

臺灣在水資源的使用上，主要仰賴於水庫的水資源操作。雖然台灣的降雨量十分充沛，但因地形而導致空間與空間上的降雨不均，並使得大部分的水資源無法被利用。另外，各式各樣常用之預報，如定性預報、機率預報、甚至是系集預報的好壞在極大程度上影響決策者在許多方面的決定，例如入流預報對水庫的操作的影響。也因此許多方法被提出，用來判定是否預報能符合準確的要求，但在近年受到極端氣候影響，預報在不論降雨或及水庫入流的預估上已無法提供決策者準確的資訊，以至在面對如梅雨延後是缺水時常遭受重大損失。預報的校準通常藉由圖料精度表或是根據貝式定理的後測機率來執行，此雖可增加其準確度，但面對愈加嚴重的氣候變遷，其效果仍十分有限。 本研究旨在提供機率預報事前的不確定性，並運用於入流預報觀察對水庫操作的影響。在不確定性的事前預估中，採用的方法根據了(1)順序統計法以及(2)回歸週期。其概念為二項分配的抽樣概念以及根據某水文現象的統計特性,利用現有水文資料,分析水文變數設計值與出現頻率（或重現期）之間的定量關係。 考慮了未來不確定性後，假設檢定便會對操作產生影響。考慮第一型錯誤和第二型錯誤可能發生的情況，使預估的成本提高，但當預估越靠近需求時，成本卻會因事先考慮的錯誤而降低。將不確定性帶到避險準則(period hedging rule)中，發現在相信未來有不確定性的情況下，考慮事前不確定的操作在低水位時的可降低損失，尤其於面臨乾旱情況時。最後將不確定性應用於模擬乾旱年預報在石門水庫的實際操作，發現當水庫於平均水位下時，考慮事前不確定性的操作能有顯著效益。並且適當的不確定性預估，能有效在各時期水位以及各時期入流上將損失大幅度降低。近年來極端旱象頻率節節攀升，過去預報的精準度已跟不上日益顯著的氣候變遷，為此機率預報不確定性概念將未來真實機率納入考量以提高預報之準確性，協助決策者做出較為周全之決策，藉此降低整體操作損失。

In Taiwan, utilization of water resources mainly relies on the reservoirs. Although the precipitation is abundant, lots of water is unavailable due to steep landform and spatial-temporally unequal distribution of rainfall. Besides, the quality the probabilistic forecasts often used, for example deterministic forecast, probabilistic forecast or ensemble forecast, would strongly affect decision-maker to make the operation policy. For instance, the influence of inflow forecast in reservoir operation. Many methods are proposed to adjust the accuracy of forecasts. However, forecasts are more inaccurate because of the impact of extreme events occurring. Although forecast verifications could follow reliability diagram or Bayes' theorem - posterior probability, the limitation still exists due to severe climate change. This study aims to give the uncertainty of probabilistic forecast in reservoir operation before events occurring. The method estimating the uncertainty based on two concepts – Order Statistics Method and Return Period. The concepts are the random sampling of Binomial Distribution and the relationship between hydraulic coefficients and return period calculated by statistics characteristics of hydraulic events. The Hypothesis test would be proposed, and the influence in the operation would be considered. With type I error and Type II error, the cost of the forecast would increase. However, the cost would get lower when forecast approaches demand target because considering uncertainty beforehand. Next, we apply the uncertainty to hedging rule. The operating results represent that under the existing of future uncertainty, operating cost tends to decrease under the low water level, especially in drought. Moreover, the uncertainty is applied to a practical operation for Shihmen reservoir during drought. The efficiency of considering the uncertainty of probabilistic forecast is evident when the water level is low. Besides, the cost would reduce apparently when during each water level and inflow with proper uncertainty estimate. With the increasing frequency of extreme events during drought, the accuracy of the probabilistic forecast is not high as before. The concept of the uncertainty of probabilistic forecast provides the decision maker a different aspect of treating the future uncertainty. As a result, the total loss would be diminished.