Uniform discrete wavelet spectrum for detection of hydrologic variability at multiple timescales

Abstract

Detecting the signals of hydrologic variability, including both periodicities and trends, at multi-timescales with evaluation of their statistical significance is one of the primary goals in hydrology studies, but it is also a challenging task. While the discrete wavelet spectrum (DWS) has been widely used to meet this purpose, it has limitations in practical applications, especially with the difficulty in detecting the spatial heterogeneity in hydrologic variability. In this study, a uniform DWS method is developed by determining the spectral values of the reference DWS, which are used as a uniform criterion for significance evaluation to identify hydrologic signals and compare their spatial heterogeneity. Application of the uniform DWS method to three annual runoff (and the corresponding precipitation) time series in the Yarlung Tsangpo River basin indicates that the significance of the runoff variability increases from down- to up-streams. It is shown that the uncertainty becomes large when the variability at small timescales is considered in short hydrologic time series. It is also demonstrated that hydrologic variability at long timescales usually tends to have a non-monotonic trend and that a monotonic trend would misrepresent the true underlying behavior. The uniform DWS method proposed here, by identifying the periodicities, non-monotonic and monotonic trend with significance evaluation, has the potential for a much wider use in hydrologic and climate sciences.