Applications of Wavelet Transform Technique in Hydrology—A Brief Review

Abstract

Recently, wavelet transform analysis has become a popular analysis tool due to its ability to elucidate simultaneously both spectral and temporal information within the signal. This overcomes the basic shortcoming of Fourier analysis, which is that the Fourier spectrum contains only globally averaged information. Therefore, a data preprocessing can be performed by time series decomposition into its subcomponents using wavelet transform analysis. Wavelet transforms provide useful decompositions of the main time series, so that wavelet-transformed data improve the ability of a forecasting model by capturing useful information on various resolution levels. The wavelet decomposition of a nonstationary time series into different scales provides an interpretation of the series structure and extracts significant information about its history, using few coefficients. For these reasons, this technique is largely applied to time series analysis of nonstationary signals. In terms of hydrologic applications, this modeling tool is still in its nascent stages. The practicing hydrologic community is just becoming aware of the potential of wavelet transform as an analyzing tool. This paper is intended to serve as an introduction to wavelet transformation for hydrologists. Apart from descriptions of various aspects of wavelet transform and some guidelines on their usage, this paper offers brief comparisons of the nature of wavelet transformations and other modeling philosophies in hydrology. The merits of wavelet transform applications have been discussed.