Trend Analysis by Using Wavelets

Wavelet analysis has been introduced during the past ten years in which a different type of basis functions, called Wavelets, are used. Wavelets are localized in time as well as in frequency. In the theory of Wavelet transforms, the notion of ‘frequency' is changed to an equivalent one of ‘scale', where large scales correspond to low frequencies and small scales correspond to high frequencies. By using Wavelet analysis, longer time windows can be used to detect low frequency (large scale) information, while shorter time windows can be used to detect high frequency (small scale) information. Wavelet analysis offers a different approach to investigating signals. In effect, by using the Wavelet transform the signal is decomposed into components of different scales. Wavelet analysis can be used as a tool for performing a wide range of tasks which include: detecting discontinuities in signals, detecting long-term evolution (trends), detecting self similarity (fractal signals), identifying pure frequencies (time-frequency analysis), suppression, and compression of signals. In this paper Wavelet analysis is used to investigate the trends in hydrologic time series. This new method of trend analysis appears to be quite robust and useful.