Development of a new method of wavelet aided trend detection and estimation

The detection and estimation of trends in the presence of noise, periodicities, or discontinuous patterns is important in hydrology and climate research studies. The basic idea of currently available trend estimation techniques (tests) is that the trends should be smooth and monotonic; however, hydro-climatologic variables contain multiple signals, and have segments of increasing and decreasing trends. As a result, estimating trends in time series is an essential but arcane art and it is therefore important to continue developing the theory and practice of trend analysis. In this paper, a new technique is proposed based on the continuous wavelet transform (CWT). CWT permits the transformation of observed time series into wavelet coefficients according to time and scale simultaneously. These coefficients can be used to detect and estimate trends or to reconstruct signals that are of interest. The proposed CWT method was first tested on computer-generated data exhibiting both periodic and noise components. It was then applied to observed monthly minimum streamflow observations extracted from the Reference Hydrometric Basin Network (RHBN) for five different eco-zones in Canada. It was concluded that the proposed wavelet transform (WT) based method provides a very flexible and accurate tool for detecting and estimating complicated signals. The results from monthly minimum observations indicate that short period fluctuations are decreasing, while multi-annual variability is increasing in Canada. And finally, a persistent ~55-year signal is well correlated with the Pacific Decadal Oscillation in all records, which indicates that trends are not controlled by a single factor.