- 學位論文
灰馬可夫鏈模式於水文時間序列之預測探討
Prediction of Hydrological Time Series based on Grey Markov Chain Model
摘要
台灣地區幅員不寬，河川流域面積普遍狹小，河道源短流急，水資源蓄積不易，降雨量在時間及空間上分布不均，因此如何有效控制及掌握水資源的動向成為備受重視之議題。 本研究採用結合灰色理論與馬可夫鏈觀念之灰馬可夫鏈MRGM (1,1)模式，以長時間尺度資料之月地下水位、河川逕流量，及短時間尺度資料之颱風時雨量為研究對象，進行預測分析研究，並和已被廣泛使用之時間序列分析方法ARIMA模式進行相互探討及分析，以瞭解各模式在分析不同長短時間尺度資料上之適用性。在灰馬可夫鏈模式中，利用馬可夫鏈之狀態轉移機率矩陣，可提高對隨機波動較大的數據之預測精度，而疊加相當步長之狀態轉移機率矩陣對預測結果會有顯著影響，且在資料數據的長度上，越長的資料筆數對於疊加型MRGM(1,1)模式越有優勢，可使狀態轉移機率矩陣的預測功能發揮的更為完整或更有規律性。而在ARIMA模式及加入季節性因子之SARIMA模式預測結果中，對於時間序列內較大序列值之預測則有較佳之效果。
並列摘要
Water is essential to life, but the water resource of Taiwan is limited and hard to retain for most of the rivers run from high mountains in short and steep courses. In addition, the temporal and spatial distribution of rainfall is very uneven. How to utilize the water resources rationally becomes an important issue in Taiwan recently. This research adopts the MRGM(1,1) model which combines the grey theory with the concept of gray Markov chain to analyze the data of groundwater level and river runoff for long-time scale and typhoon rainfall for short-time scale. The traditional ARIMA and SARIMA models are also used to analyze the time series data in order to compare the applicability of different models for different time-scale data. It is found that the status transition matrix of MRGM (1,1) model can improve the prediction accuracy for data with large fluctuations, and the overlaying of several steps in status transition matrix will affect forecast results obviously. In addition, the status transition matrix can play an important role and will facilitate the prediction if the data length is sufficiently long. On the other hand, the SARIMA model can perform well for the larger value portions of the original time series.