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應用小波轉換於水文時間序列趨勢預測之研究

Application of Wavelet Transform to the Trend Forecasting of Hydrological Time Series

摘要


水文時間序列之分析及模擬已有多種新穎方法與模式,然而大多數方法與模式均由水文時間序列自身進行分析處理。實際之水文時間序列,由於受各種複雜因素之制約與影響,難以掌握與研究。就時間-頻率觀點而言,任一水文時間序列均含有多種頻率成分,每一成分皆有其自身之制約因素與發展演變規律。單從水文時間序列本身出發建構模式,勢必難以詳細掌握水文時間序列之內在動力機制,因此實有必要對水文時間序列執行進行多分辨層研究,而小波分析適可提供一種便捷之多分辨分析技術。此外,長時期之水文時間序列具有長期相依性,其可用赫斯特係數加以鑑別。應用小波分析之特性,可有效地計算長時程水文時間序列之赫斯特係數,據以提供未來從事全球變遷分析研究之應用。本研究蒐集淡水河流域及曾文溪流域具代表性之雨量站資料,加以建檔、研析,並建立資料庫。研究中應用具有多分辨分析功能之小波轉換理論,以探討長時程降雨量資料之多分辨結構。此外,長時期之水文時間序列具有持續性,應用小波分析可計算水文時間序列之赫斯特係數。而應用小波轉換,亦可進行長時程水文時間序列之多分辨分析,並分析台灣地區近年來不同分辨層水文時間序列變化之空間差異,進而針對長時程水文時間序列之趨勢進行預測,期能作爲水資源規劃應用之參考。

並列摘要


There are many new methods and models to analyze and simulate the hydrological time series. However, most of the methods and models applied hydrological time series themselves to carry out research. In practice, it is difficult to grasp and study hydrological time series because they were controlled and affected by complex factors. From the standpoint of time-frequency, each hydrological time series contained many frequency components which had their restricted factors and developed rules. Using only one resolution component to model the hydrological time series is difficult to understand the internal mechanism. It is necessary to apply the wavelet-based multi-resolution analysis to the modeling of hydrological time series. In addition, long term time series had long term dependency which could be identified by Hurst coefficients. The Hurst coefficients could be computed effectively by applying the characteristics of wavelet analysis, so as to provide the application for the analysis of global change. This study collects the data of representative rainfall gages in Taiwan. The rainfall data can be employed to establish files and study so as to construct the database. Applying the wavelet theory with multi-resolution characteristics can probe into the multi-resolution structure of rainfall in Taiwan. In addition, wavelet analysis can be employed to calculate the Hurst coefficients, which represents the long term dependency of hydrological time series. Application of wavelet transform can proceed to carry out the multi-resolution analysis of hydrological time series and analyze the differences of varying hydrological time series in different areas. The above results can be applied to the trend forecasting of the hydrological time series in Taiwan, so as to provide the reference for water resource planning and application.

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