應用多重碎形理論於雨量預測之研究

Abstract

過去二十年來多重碎形理論的發展已逐漸成熟，相關的研究成果已顯示出自然界的許多時間歷程資料存在著多重碎形的現象，這些研究成果指出時間序列所表現出的統計自相似性是與尺度有關的。有別於單一碎形，多重碎形理論可以描述時間序列與尺度變化的關係，一般學者相信從多重碎形理論的本質可以用來合成與預測具有高解析度的雨量時間序列，然而，相關的研究主要還停留於降雨結構的分析。 有鑑於此，本研究提出整合多重碎形理論及非線性動力學的方法，結合非線性動力學在動態預測的優勢，以及多重碎形理論描述時間序列尺度與統計自相似性的能力，以雨量時間序列為研究對象，從歷史雨量資料建立多重碎形譜，進而求取相對應的動力方程組。並且依照此方法的特性，本研究亦設計出融合知識庫概念的雨量預測系統架構，並且依循此架構實作出雨量預測系統之雛型。 經由實際案例分析的過程，本研究亦對此架構可能遇到的問題提出解決的方法；並且分析預測的結果，驗證此方法及架構之可行性；最後，並提出與本研究相關的議題，作為未來研究的參考。

The theory of Multifratals has been evolved successfully during the last two decades. Many research reports have indicated that time-series in nature exhibits multifractal behaviors. This means that the statistical self-similarity of the time-series is related to the measured scales. From the mathematical point of view, many researchers believe that Multifractals has the ability to synthesize and forecast high resolution time series of rainfalls. However, the related research still only focuses its efforts on analyzing the structure of rainfall rather than on forecasting or synthesizing it. Therefore, this research proposes an approach for forecasting high resolution rainfall data through combining the theory of Nonlinear Dynamics and Multifractals. The proposed approach estimates the corresponding multifractal spectra from the historical rainfall data, and then determines the best values for the parameters of the corresponding dynamic systems based on these multifractal spectra. This research, based the proposed approach, also designs a rainfall forecast framework, intergrating the Multifractals with the concept of Konwledge Base, and then implements a prototype system from this framework. Finally, through applying the prototype system on forecasting the rainfall in a given rain event, this research conducts a feasibility and accuracy study on the proposed approach and framework.