基於馬可夫鏈架構之河川時流量序列合成方法

目前國內外研究多偏向於較長時間尺度之流量合成方法，尚無應用於時流量合成方面，本研究將前人研究曾採用之日流量合成方法運用於時流量合成，除參考前人研究使用一階馬可夫鏈，另利用AIC求得馬可夫鏈之最適階數，並分別直接進行時流量合成，同時基於馬可夫鏈配合前人研究曾採用之Gamma分布函數模擬流量上升段，並以條件對數常態分布函數進行改良修正，而流量下降段則皆以指數函數進行模擬，最後選定淡水河、大安溪、大甲溪、濁水溪、曾文溪、高屏溪及卑南溪流域之49個流量站進行案例分析，並以流量延時曲線、時流量檢定參數及水文改變概念指標之統計檢定等方法進行模擬結果分析比較，以瞭解不同模式組合之優劣程度。研究結果顯示整體表現係以最適階數馬可夫鏈配合條件對數常態分布函數模擬流量上升段之結果較佳，在高流量方面，可有效改善Gamma分布函數之低估情形，同時兼顧合成流量之重現性及變異性，可滿足防洪治理規劃需求，另對於水文生態影響較大之低流量方面，大部分流量站有略為高估之情形，重現性尚有改善空間。

關鍵字

序率過程；合成時流量模式；最適階數馬可夫鏈；水文改變概念指標；流量延時曲線

並列摘要

This study applies the synthetic daily flow sequence simulation method used by previous studies to the synthetic hourly flow sequence simulation, except using the first-order Markov chain refered to previous studies, and the optimal-order Markov chain obtained by the Akaike information criterion to generate the hourly flow data directly. At the same time, Markov chain-based method with the Gamma distribution function used by previous studies is applied to simulate the ascension curve of the flow, and improved by the conditional lognormal distribution function, while simulating the recession curve of the flow by exponential function. Finally, 49 discharge stations of seven river basins including Tamsui River, Daan River, Dajia River, Zhuoshui River, Zengwen River, Gaoping River and Beinan River were selected to be case study, and this study applies flow duration curves(FDC) and three performance indices as well as a method of statistical testing to identify whether Indicators of Hydrologic Alteration(IHA) derived from historical and synthetic flow data have the same distribution. This enabled us to evaluate and examine the capacity of the synthetic hourly flow models, as a reference for future related research. The results show that the overall performance is better with the optimal order Markov chain based on the conditional lognormal distribution function to simulate the ascension curve of the flow. In the high-flow data, the Gamma distribution function underestimation can be effectively improved, and the variability of synthetic hourly discharge can be availabled, should meet the needs of flood prevention planning. In addition, for the low-flow data with great impact on hydrology and ecology, most of the stations have a slightly overestimated situation, and its reproducibility remain problematic for improvement.

並列關鍵字

Stochastic processes ； Synthetic hourly streamflow model ； Optimal order of Markov chain ； Indicators of Hydrologic Alteration (IHA) ； Flow duration curve (FDC)