臺灣博碩士論文加值系統

台灣地區年平均降雨量約為世界平均值的2.6倍，但由於地狹人稠以及降雨空間與時間分布不均，且因氣候變遷的影響，極端暴雨及乾旱的頻率和強度都有明顯的增加，因此水資源管理顯得更加重要。透過具歷史資料統計特性之流量序率模擬模式，可繁衍多組水文時間序列，將繁衍序列輸入至水資源系統模擬模式中，得以評估系統設計、水庫營運決策的性能和可靠性。因此本研究使用隱藏馬可夫模式(Hidden Markov Model)進行月流量序率模擬，探討四種影響因子包括資料轉換、狀態數、狀態決定方式以及繁衍組數，對序率模擬結果準確性的影響。本文選用位於臺灣北部區域蘭陽溪流域的蘭陽大橋測站1950到2021年的觀測月流量資料以及南部區域高屏溪流域中的荖濃測站1959到2008年的觀測月流量資料為分析案例，分別將原始月流量資料與以對數轉換或Box-Cox轉換過之月流量資料建立隱藏馬可夫模式，改變不同狀態數、狀態決定方式及繁衍組數以繁衍與實際觀測流量等長之月流量序列。繁衍流量則以百分誤差(%difference)和相對平均絕對誤差(relative mean absolute difference, RMAD)分析與實際流量之差異程度和誤差改變率，選擇最具影響力之影響因子。研究結果顯示，蘭陽大橋測站以及荖濃測站影響因子由大至小的排序皆為資料處理、狀態數、狀態決定方式、繁衍組數。

Due to the dense population, spatio-temporal uneven distributed rainfall, and the reduced reliability of water supply caused by global climate change, the frequency and intensity of extreme events such as floods and droughts have significantly increased. Consequently, water resource management has become increasingly important. Stochastic simulation model can be used to generate streamflow series, which possesses the statistical properties of historical data. The reproduced streamflow series provides alternative data instead of historical data to evaluate performance and reliability of water-resources systems. This study employs a Hidden Markov Model (HMM) for simulating monthly streamflow sequences and investigates four influencing factors: data processing, number of states, state determination method, and number of simulated sequences, on the accuracy of the simulation results. Monthly streamflow data from the LAN-YANG BRIDGE gauge station and the LAO-NUNG gauge station in Taiwan are selected as case studies. The simulated streamflow is then compared to the observed streamflow using the percentage difference (% difference) and relative mean absolute difference (RMAD) to analyze the degree of differences and error change rate. The results of this study indicate that the order of the influencing factors, from most to least, are data processing, number of states, state determination method, and number of generated sequences for both the Lan-Yang Bridge and Lao-Nong gauge stations.

摘要 I
Extended Abstract II
致謝 XI
目錄 XII
表目錄 XV
圖目錄 XVII
第一章 緒論 1
1.1 研究動機 1
1.2 研究目的 3
1.3 論文架構 3
第二章 文獻回顧 5
2.1 序率模式 5
2.2 隱藏馬可夫模式相關文獻 6
2.2.1 隱藏馬可夫模式應用 6
2.2.2 隱藏馬可夫模式水文領域應用 6
2.2.3 隱藏馬可夫模式與其他模式比較 7
第三章 研究方法 9
3.1 隱藏馬可夫模式 9
3.1.1 模式概述 9
3.1.2 參數推估 11
3.1.3 前向後向演算法 14
3.1.4 維特比動態演算法(Viterbi algorithm) 15
3.2 序率模擬 16
3.3 影響因子 16
3.3.1 資料處理 17
3.3.2 狀態個數 18
3.3.3 狀態決定 18
3.3.4 繁衍組數 19
3.4 評估指標 20
3.4.1 百分誤差(%difference) 20
3.4.2 相對平均絕對誤差(relative mean absolute difference, RMAD) 20
第四章 研究地區與研究資料 21
4.1 研究區域概述 21
4.2 研究流量測站統計特性 24
4.3 隱藏狀態分組 28
第五章 結果與討論 29
5.1 資料處理 29
5.2 HMM參數推估 29
5.2.1 EM法決定狀態 29
5.2.2 事先指定狀態 31
5.3 繁衍結果比較 32
5.3.1 資料處理的影響 33
5.3.2 狀態數的影響 41
5.3.3 狀態決定方式的影響 44
5.3.4 繁衍組數的影響 48
5.4 模式比較 51
5.4.1 影響因子比較 51
5.4.2 蘭陽大橋及荖濃測站比較 52
第六章 結論與建議 54
6.1 結論 54
6.2 建議 55
參考文獻 56
附錄A 蘭陽大橋測站及荖濃測站隱藏馬可夫模式之推估參數 60
附錄B 蘭陽大橋測站繁衍流量與實際流量機率密度函數圖 68
附錄C 荖濃測站繁衍流量與實際流量機率密度函數圖 74
附錄D 蘭陽大橋測站繁衍流量序列百分誤差圖 80
附錄E 荖濃測站繁衍流量序列百分誤差圖 83
附錄F 蘭陽大橋站繁衍月流量盒狀圖 86
附錄G 荖濃站繁衍月流量盒狀圖 92

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