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研究生： 李政哲
Li, Cheng-Che
論文名稱： 以隱藏馬可夫模式與自迴歸移動平均模式序率模擬臺灣地區之月流量系列
Stochastic simulation of monthly streamflow series using the hidden Markov model and the autoregressive moving average model in Taiwan
指導教授： 蕭政宗
Shiau, Jenq-Tzong
學位類別： 碩士
Master
系所名稱： 工學院 - 水利及海洋工程學系
Department of Hydraulic & Ocean Engineering
論文出版年： 2022
畢業學年度： 110
語文別： 中文
論文頁數： 78
中文關鍵詞： 隱藏馬可夫模式 、自迴歸移動平均模式 、序率模擬 、月流量
外文關鍵詞： hidden Markov model, autoregressive moving average model, stochastic simulation, monthly streamflow
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    • 受到全球氣候變遷的影響，臺灣河川流量因時間與空間分布不平均的情況將越加惡化，同時社會發展整體需水量增加，使得臺灣地區水資源管理系統受到嚴峻的挑戰。本研究目的為利用隱藏馬可夫模式及自迴歸移動平均模式建立流量序率模擬模式，本研究選取臺灣地區北、中、南、東部區域共七個流量站，先以對數轉換與Box-Cox轉換使月流量資料接近常態分布，建立七個流量站的隱藏馬可夫模式及自迴歸移動平均模式，以繁衍與實測資料等長之繁衍流量50組。結果顯示隱藏馬可夫模式能良好的辨識流量之型態，並以百分誤差(%difference)分析各繁衍分位流量與實測流量之誤差，研究顯示各站第10至第90分位間流量百分誤差幾乎都小於10%誤差內，兩個模式在小於第10分位數及大於第90分位數流量普遍呈現高估的現象。最後以相對平均絕對誤差(RMAD)判定，以對數轉換後隱藏馬可夫模式為最佳，隱藏馬可夫模式搭配Box-Cox轉換與自迴歸移動平均模式搭配對數轉換次之，Box-Cox轉換搭配自迴歸移動平均模式模擬結果較差。

    Spatio-temporal uneven distributed streamflow would be deteriorated due to impact of climate change. Meanwhile, rapid economic development leads to increasing water demand in Taiwan. Efficient water use in Taiwan is a challenge task. The purpose of this paper is using the hidden Markov model (HMM) and the autoregressive moving average (ARMA) model for streamflow stochastic simulation. This study selects seven streamflow gauge stations in the northern, central, southern and eastern regions of Taiwan. The monthly streamflow is log-transformed and Box-Cox-transformed first to improve data symmetry. The models generate 50 sequences with the same length of the recorded streamflow data. The results indicate that the HMM efficiently recognizes the patterns of monthly streamflow in Taiwan. The differences between the synthetic sequences and the corresponding recorded data are evaluated in terms of percentage difference. The HMM and ARMA model can reproduce the streamflow series which are close to the recorded data with less than 10% difference when streamflow are within 10th and 90th percentiles. When streamflow less than 10th and greater than 90th percentiles, the generated data are generally overestimating. Using the relative mean absolute difference (RMAD) to evaluate the model performance, the log-HMM is the best model, BC-HMM and log-ARMA rank second, and BC-ARMA has the worse performance.

    摘要 .............................................................................................................................I Extended Abstract.......................................................................................................II 誌謝 ..........................................................................................................................IX 目錄 ........................................................................................................................... X 表目錄 ................................................................................................................... XIII 圖目錄 ...................................................................................................................XIV 第一章 緒論.......................................................................................................... 1 1.1 研究動機 .............................................................................................. 1 1.2 研究目的 .............................................................................................. 2 1.3 相關文獻回顧...................................................................................... 3 1.3.1 序率模式....................................................................................... 3 1.3.2 自迴歸移動平均模式相關文獻.................................................. 3 1.3.3 隱藏馬可夫模式相關文獻.......................................................... 4 1.4 論文架構 .............................................................................................. 7 第二章 研究方法.................................................................................................. 8 2.1 隱藏馬可夫模式.................................................................................. 8 2.1.1 模式特性....................................................................................... 8 2.1.2 參數估計..................................................................................... 10 2.1.3 前向後向演算法......................................................................... 12 2.1.4 最佳狀態序列............................................................................. 13 2.1.5 序率模擬..................................................................................... 13 2.2 自迴歸移動平均模式........................................................................ 14 2.2.1 模式特性..................................................................................... 14 2.2.2 序率模擬..................................................................................... 16 2.3 模式選取準則.................................................................................... 16 2.4 資料處理 ............................................................................................ 17 2.4.1 資料轉換..................................................................................... 17 2.4.2 去季節化..................................................................................... 18 第三章 研究地區與資料.................................................................................... 19 3.1 研究區域概述.................................................................................... 19 3.2 流量測站概述.................................................................................... 22 第四章 結果與討論............................................................................................ 25 4.1 資料轉換 ............................................................................................ 25 4.2 隱藏馬可夫模式................................................................................ 25 4.2.1 各測站狀態數............................................................................. 25 4.2.2 各測站隱藏馬可夫模式之隱藏狀態變化................................ 26 4.2.3 隱藏狀態發生機率..................................................................... 28 4.3 自迴歸移動平均模式........................................................................ 34 4.3.1 各測站(p, q)階數........................................................................ 34 4.4 序率模式繁衍之結果比較................................................................ 34 4.4.1 模擬流量系列之機率密度圖.................................................... 34 4.4.2 模擬流量系列之基本統計量.................................................... 35 4.4.3 誤差指標..................................................................................... 37 4.4.4 序率模擬之誤差指標比較........................................................ 37 4.4.5 模式比較..................................................................................... 43 第五章 結論與建議............................................................................................ 44 5.1 結論 .................................................................................................... 44 5.2 建議 .................................................................................................... 45 參考文獻.................................................................................................................. 46 附錄A 各測站隱藏馬可夫模式AIC及BIC值隨狀態數變化圖...................... 52 附錄B 各測站流量系列對應之隱藏馬可夫模式隱藏狀態系列........................ 56 附錄C 各測站隱藏馬可夫模式隱藏狀態對應流量之盒狀圖............................ 60 附錄D 各測站隱藏馬可夫模式之推估參數........................................................ 64 附錄E 各測站自迴歸移動平均模式之推估階數及參數..................................... 66 附錄F 各測站隱藏馬可夫模式繁衍流量與實際流量機率密度函數圖............. 67 附錄G各測站自迴歸移動平均模式繁衍流量與實際流量機率密度函數圖..... 71 附錄H 各測站模擬流量系列基本統計量盒狀圖................................................ 75

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