Analyzing trends in temperature, streamflow and precipitation over Southern Ontario and Québec using the discreet wavelet transform

Analysis on hydroclimatic variables can provide information on how the climate has evolved over time. This can be accomplished through time series analysis. Trend analysis in hydroclimatic variables is challenging due to their non-stationary nature and the presence of noise and stochastic components in them. The principal objective of this study is to detect and analyze trends in mean surface air temperature, total precipitation and mean streamflow obtained from several stations in Ontario and Quebec, Canada. To accomplish this, we co-utilized the wavelet transform (WT) technique (more specifically, the discrete wavelet transform (DWT)) and the Mann-Kendall (MK) trend test. The time series used were decomposed via the DWT in order to separate their high-frequency and low-frequency components, prior to testing their statistical significance with the MK trend test. The trend (i.e. slowly changing processes) is assumed to be contained in the low-frequency component of the data. The trends in temperature, precipitation and flow are assessed on different bases: monthly, seasonal, and annual. Temperature trends for the different seasons (i.e. winter, spring, summer, and autumn) were also assessed. In this study, we demonstrated the use of WT in extracting information contained in the time series that is not obvious in the raw data. The advantages of the WT technique are highlighted by its ability to extract time-frequency information contained in the analyzed time series manifested in the form of periodicities ranging from intra-annual to decadal events. A new criterion is also proposed in this study where the relative error of the MK Z-values between the approximation component of the last decomposition level and the original data was used to determine the number of decomposition levels of the analyzed time series, the type of Daubechies (db) mother wavelet, and the border condition to be used in the DWT procedure.The procedures contained in the methodology for trend analysis outlined in this study have not been explored in the existing literature. First of all, we tested for the presence of a significant autocorrelation in a time series prior to applying the MK test, which is often ignored in many trend detection studies. The time series were then decomposed via the DWT; the MK trend test and sequential MK test were then applied in order to determine the most significant periodic mode affecting the observed trends. In this study, three versions of MK test were used, depending on the characteristics of the analyzed data. The original MK test was used on data that exhibit neither seasonality patterns nor significant autocorrelations. Seasonal MK test by Hirsch and Slack (1984) was used on the time series exhibiting seasonality cycles (with or without significant autocorrelations). Modified MK test by Hamed and Rao (1998) was used on data with significant autocorrelations. Finally, combining the application of the DWT and MK test in trend assessment in hydroclimatic time series (especially in the context of Canadian studies) has not been explored. Therefore, the results obtained in this study contribute to furthering the overall understanding of climatic change in Southern Ontario and Quebec. Although the trends in the different variables studied are affected by different time periodicities, the study found that generally positive trends are more dominant. Among the most important findings of this study are: (i) all temperature data show positive values, which implies warming trends (ii) precipitation and flow trends are affected by fluctuations of up to four years, and (iii) annual positive trends in temperature may be attributed mostly by winter and summer warming. This suggests that if the temperature trends remain in the positive direction, other hydroclimatic indices may also experience significant changes in the future.

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