Wavelet-based trend analysis of hydrological processes at different timescales

Abstract

This study analyzes involved trends in stream flow and precipitation data at monthly, seasonal and annual timescales observed at six precipitation and four stream flow stations of Tampa Bay using non-parametric Mann–Kendall (MK) and discrete wavelet transform (DWT) methods. The MK test and sequential MK analysis were applied to different combinations of DWT after removing the effect of significant lag-1 serial correlation to calculate components responsible for trend of the time series. Also, the sequential MK test was used to find the starting point of changes in annual time series. The results showed that negative trend is prevalent in the case study; generally, short-term periods were important in the involved trend at original time series. Thus, the precipitation data at three scales showed short-term periods of 2 months, 6 months and 2 years in monthly, seasonal and annual scales, respectively. In the greatest stream-flow time series at three timescales, wavelet-based detail at level 2 plus the approximations time series was conceded as the dominant periodic component. Finally, the results of Sen's trend analysis, applied to the original annual time series, also confirmed the results of the proposed wavelet-based MK test in most cases.

Understanding changes and trends in projected hydroclimatic indices in selected Norwegian and Polish catchments

“…The Mann-Kendall (MK) and modified MannKendall (MMK) tests belong to the family of nonparametric tests. The other two tests applied here are based on the discrete wavelet transform (DWT) (Nalley et al 2012;Nourani et al 2015) and dynamic harmonic regression (DHR) (Young et al 1999;Venier et al 2012).…”

“…Extraction of long-term trends in precipitation and streamflow has been studied by many researchers (e.g. Nalley et al 2013;Nourani et al 2015) by means of discrete wavelet transform (DWT). The wavelet transform is an effective decomposition method that provides a way of analysing signals in both time and frequency domains.…”

“…The DWT is used to isolate different periodicities embedded in a time series and to examine the composition of a signal. It helps to identify components that may be considered important in a signal, at their exact temporal location, which otherwise may not be clearly detected by the use of regular statistical tests alone (Nalley et al 2013;Nourani et al 2015). This is one of the most obvious strengths of the DWT because it gives a more complete picture of the dynamics contained in the signal being analysed.…”

“…This is one of the most obvious strengths of the DWT because it gives a more complete picture of the dynamics contained in the signal being analysed. Trend analyses of hydrological processes using discrete wavelet transform and nonparametric Mann-Kendall methods have become very popular recently (Nourani et al 2015, Nalley et al 2012. Dynamic harmonic regression (DHR) model is a powerful tool to extract nonstationary characteristics from analysed time series.…”

Spatiotemporal evaluation of drought trend during 1979–2019 in seven climatic zones of Bangladesh

“…Several methods were applied for drought analysis in various studies among them meteorological data based Standardized Precipitation Evapotranspiration Index (SPEI) and the Palmer Drought Severity Index (PDSI) are most common; however, SPEI is a new method, but it fulfills proper data utilization ( McKee et al., 1993 ; Palmer, 1965 ). Also, wavelet trans-form Mann–Kendall (WTMK) is also used as a recent method of hydroclimatic statistics ( Danandeh Mehr et al., 2013 ; Nourani et al., 2015 ). In a recent article, the new approaches of innovative trend analysis (ITA) and sequential average methodology (SAM) were also employed in conjunction with the optimization of the Mann-Kendall (MK) test and Sen's Slope estimator for trend analysis on different geological timescales ( Danandeh Mehr et al., 2021 ; Jerin et al., 2021 ).…”