Using discrete wavelet transforms to analyze trends in streamflow and precipitation in Quebec and Ontario (1954–2008)

Abstract

Summary This paper aims to detect trends in mean flow and total precipitation data over southern parts of Quebec and Ontario, Canada. The main purpose of the trend assessment is to find out what time scales are affecting the trends observed in the datasets used. In this study, a new trend detection method for hydrological studies is explored, which involves the use of wavelet transforms (WTs) in order to separate the rapidly and slowly changing events contained in a time series. More specifically, this study co-utilizes the Discrete Wavelet Transform (DWT) technique and the Mann–Kendall (MK) trend tests to analyze and detect trends in monthly, seasonally-based, and annual data from eight flow stations and seven meteorological stations in southern Ontario and Quebec during 1954–2008. The combination of the DWT and MK test in analyzing trends has not been extensively explored to date, especially in detecting trends in Canadian flow and precipitation time series. The mother wavelet type and the extension border used in the wavelet transform, as well as the number of decomposition levels, were determined based on two criteria. The first criterion is the mean relative error of the wavelet approximation series and the original time series. In addition, a new criterion is proposed and explored in this study, which is based on the relative error of the MK Z -values of the approximation component and the original time series. Sequential Mann–Kendall analysis on the different wavelet detail components (with their approximation component added) that result from the time series decomposition was also used and found to be helpful because it depicts how harmonious each of the detail components (plus approximation) is with respect to the original data. This study found that most of the trends are positive and started during the mid-1960s to early 1970s. The results from the wavelet analysis and Mann–Kendall tests on the different data types (using the 5% significance level) reveal that in general, intra- and inter-annual events (up to 4 years) are more influential in affecting the observed trends.