水庫操作的不確定性分析：水庫水位的序率過程模型

Abstract

本研究提出了一個不同以往的水庫操作規則。在本研究中，操作規則是藉由建立未來水位的序率過程的模型而得，而非傳統的藉由建立最佳化模型而得。這包含了（１）雙變數伽碼隨機變數的統計性質的推導。特別是，本研究給出了一個重要的的規則，即由一對雙變數伽碼隨機變數的相加或相減所產生的新隨機變數依然近似於伽碼隨機變數。（２）將雙變數伽碼隨機變數推廣至伽碼時間序列，進而建立入流時間序列的模型。並建立伽碼時間序列建模及模擬的程序。（３）藉由入流及出流的水平衡和雙變數伽碼隨機變數的統計性質，建立未來水位的伽碼時間序列模型。（４）藉由模擬未來水位的伽碼時間序列的模型，評估風險水位的發生機率，進而給定最終的操作規則。 一但建立最終的操作規則後，規則本身是定義明確且容易執行。機率的機制已被引入，因此它可結合長期、短期及多目標操作於一個最佳化中。分析所需的唯一材料是入流資料，因此，它亦可被應用於在興建新水庫前，估計滿足需求所需的水庫容量大小。

A totally different reservoir operation rule is proposed here. In this study, the operation rule is obtained by modeling the stochastic process of future water levels instead of the traditional optimization modeling approaches. This involves (1) the derivation of statistical properties of bivariate gamma random variables, especially, this study gives an important rule that the random variable obtained by adding or subtracting a pair of gamma random variables is still approximately a gamma random variable, (2) extending bivariate gamma random variables to gamma time series to model the inflow time series, and establishing the modeling and simulation procedure of gamma time series, (3) establishing the gamma time series model for future reservoir water levels via the water balance between inflows and outflows and the statistical properties of bivariate gamma random variables, (4) the final operation rule is simply given by evaluating the probabilities of the occurrence of risk water levels via simulating realizations from the gamma time series model of the future water level. Once the final operation rule is established, the rule itself is well-defined and easy-to-implement. It is able to combine long term, short term, and multi-goals operations to one optimization because the probability mechanism has been given. The only needed material for the analysis is the inflow data, thus, it can also be applied to estimate the required storage size to fulfill needs before building a new reservoir.