應用小波轉換於降雨－逕流歷程之模擬

Application of Wavelet Transform to the Modeling of Rainfall-Runoff Processes

王如意(RU-YIH WANG) ； 周建明(CHIEN-MING CHOU)

《台灣水利》 49卷3期 (2001/09) Pp. 1-13

摘要

本文應用小波轉換於降雨－逕流歷程之模擬。首先針對實際觀測之有效降雨及直接逕流時間序列資料進行＂à trous＂小波轉換，獲致相對應於不同尺度之小波係數。其次應用不同尺度之小波係數於離散系統線性黑盒模式與微分擬合之水文灰色模式，以分別模擬各尺度降雨－逕流之歷程。應用不同尺度之小波係數於離散系統線性黑盒模式之辨識時，係根據各尺度有效降雨及直接逕流之小波係數，以辨識各尺度之系統響應函數，由檢定結果可獲得代表各尺度之平均系統響應函數。再者，將驗證颱洪場次分解之有效降雨資料與不同尺度檢定之平均響應函數進行褶合積分，可獲致各尺度之逕流推估值。最後，運用＂à trous＂完全重構公式，得到組合之原尺度推估逕流歷線。文中亦應用不同尺度之小波係數的微分擬合之水文灰色模式中，係將各尺度之降雨－逕流之歷程，以微分擬合之水文灰色模式模擬之；再利用不同尺度有效降雨及直接逕流之小波係數，以推估各尺度微分擬合之水文灰色模式灰參數值。模擬結果可證實本文所倡議之方法適用於台灣小集水區降雨－逕流歷程之模擬分析，並可改善台灣小集水區逕流推估之準確性。

關鍵字

小波轉換 ； 降雨－逕流 ； 系統響應函數 ； 具偶序列微分擬合之水文灰色模式DHGM（2,2）

並列摘要

This paper proposed the application of wavelet transform to the modeling of rainfall-runoff processes in a hydrological system. Firstly, ＂à trous＂ wavelet transforms were applied to the observed effective rainfall and direct runoff time series to obtain the wavelet coefficients at each resolution level. Then, these wavelet coefficients were applied to the modeling of rainfall-runoff processes using the linear black box model of discrete system and differential hydrological grey models with dual series DHGM(2,2) at each resolution level. The wavelet coefficients of effective rainfall and direct runoff were used to identify the linear black box model of discrete system at different resolution levels to achieve the system response functions at each resolution level. The representative average system response functions were achieved from the calibration results. Then, taking convolution integral of the identified average system response functions with the decomposed effective rainfall of validated typhoon events, resulting direct runoff at each resolution level was estimated. ＂à trous＂ reconstructed formula was finally applied to obtain the combination estimate of direct runoff. The wavelet coefficients of effective rainfall and direct runoff were also used in this paper to differential hydrological grey models with dual series DHGM(2,2) at different resolution levels for modeling the rainfall-runoff processes. These wavelet coefficients were then used to the parameter estimation of differential hydrological grey models with dual series DHGM(2,2). The results demonstrated that the analytical method is suitable for the modeling of the rainfall-runoff process and can improve the accuracy of the runoff estimation for small watersheds in Taiwan.

並列關鍵字

Wavelet transform ； Rainfall-runoff ； System response function ； Differential hydrological grey models with dual series DHGM(2,2)