- 期刊
小波去噪演算法及其應用於線性擾動響應模式之研究
Algorithm of Wavelet Denoise and Its Application to the Linear Perturbation Response Model
摘要
小波分析爲一種多尺度分析方法，能有效分離主訊號與噪音。小波去噪演算法能滿足各種去噪要求，且與傳統之去噪方法相比較，小波去噪具有無可比擬之優點。而線性擾動響應模式（Linear Perturbation Response Model，簡稱LPRM）爲常見之水文模式，主要應用於水文模擬與預報。該模式依據觀測之降雨－逕流資料，分別計算其平滑之季節平均值及相對應之擾動項。傳統上常採用傅立葉級數使季節平均值平滑化，但由於傅立葉分析方法適用於平穩之水文時間序列，但像暴雨與洪水等水文時間序列常爲非平穩隨機過程，傅立葉分析的去噪範圍有限。因此本研究改採用小波去噪方法，來計算降雨－逕流之平滑季節平均值及相對應之擾動項。研究結果顯示，由於小波分析能分離出訊號之高頻成分與低頻成分，可以有效地計算季節平均值及相對應之擾動項，進而提高降雨－逕流歷程模擬與預報之精確度。
並列摘要
The wavelet analysis is a multi-scale method. The approximate signal and noise can be effectively separated by wavelet decomposition. The algorithm of wavelet denoise can satisfy requests for different kinds of denoise. Wavelet denoise possesses matchless advantages compared with traditional denoise method. Linear perturbation response model (LPRM) is one kind of hydrological models and applied to hydrological modeling and forecasting. The smooth seasonal average and corresponding perturbation term are obtained from observed rainfall-runoff data. Conventionally, the Fourier series is applied to smooth the estimate of seasonal average. The Fourier analysis is suitable for stationary hydrological time series. The hydrological time series such as storm and flood belong to non-stationary process. The denoise effect of application of Fourier analysis to non-stationary process is limited. In this paper, the wavelet denoise is applied to obtain the smooth seasonal average and corresponding perturbation term from rainfall-runoff data. The results illustrate that wavelet analysis can effectively calculate the smooth seasonal average and corresponding perturbation term by separating high frequency composition and low frequency composition, so as to enhance the accuracy of modeling and forecasting of rainfall-runoff processes.
延伸閱讀
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