A Threshold Based Wavelet Denoising Method for Hydrological Data Modelling

Abstract

This work developed a novel framework for considering wavelet denoising in linear perturbation models (LPMs) and simple linear models (SLMs). Rainfall and runoff time series data were decomposed using wavelet transforms to acquire approximate and detailed rainfall and runoff signals, respectively, at various resolution levels. At each resolution level, threshold quantifications were performed by setting the values of a detailed signal below a certain threshold to zero. The denoised rainfall and runoff time series data were obtained from the approximation at the final resolution level and processed detailed signals using threshold quantification at all resolution levels of rainfall and runoff, respectively, by wavelet reconstruction. The data were then applied to the SLM and regarded as the smooth seasonal mean employed in the LPM. The noise, i.e., original time series value minus denoised time series value, was employed as the perturbation term in the LPM. Moreover, a linear relationship between input and output noise was assumed. The denoised runoff and estimated noise of runoff were summed to estimate overall runoff in the LPM. To verify the accuracy of the proposed method, daily rainfall–runoff data were analyzed for an upstream area of the Kee-Lung River. The analytical results demonstrate that wavelet denoising enhances rainfall–runoff modelling precision for the LPM.