Discrete wavelet-based trend identification in hydrologic time series

Trend identification is a substantial issue in hydrologic series analysis, but it is also a difficult task in practice due to the confusing concept of trend and disadvantages of methods. In this article, an improved definition of trend was given as follows: a trend is the deterministic component in the analysed data and corresponds to the biggest temporal scale on the condition of giving the concerned temporal scale'. It emphasizes the intrinsic and deterministic properties of trend, can clearly distinguish trend from periodicities and points out the prerequisite of the concerned temporal scale only by giving which the trend has its specific meaning. Correspondingly, the discrete wavelet-based method for trend identification was improved. Differing from those methods used presently, the improved method is to identify trend by comparing the energy difference between hydrologic data and noise, and it can simultaneously separate periodicities and noise. Furthermore, the improved method can quantitatively estimate the statistical significance of the identified trend by using proper confidence interval. Analyses of both synthetic and observed series indicated the identical power of the improved method as the Mann-Kendall test in assessing the statistical significance of the trend in hydrologic data, and by using the former, the identified trend can adaptively reflect the nonlinear and nonstationary variability of hydrologic data. Besides, the results also showed the influences of three key factors (wavelet choice, decomposition level choice and noise content) on discrete wavelet-based trend identification; hence, they should be carefully considered in practice. Copyright (c) 2012 John Wiley & Sons, Ltd