The influence of autocorrelation on the ability to detect trend in hydrological series

Abstract

Abstract:This study investigated using Monte Carlo simulation the interaction between a linear trend and a lag-one autoregressive (AR(1)) process when both exist in a time series. Simulation experiments demonstrated that the existence of serial correlation alters the variance of the estimate of the Mann-Kendall (MK) statistic; and the presence of a trend alters the estimate of the magnitude of serial correlation. Furthermore, it was shown that removal of a positive serial correlation component from time series by pre-whitening resulted in a reduction in the magnitude of the existing trend; and the removal of a trend component from a time series as a first step prior to pre-whitening eliminates the influence of the trend on the serial correlation and does not seriously affect the estimate of the true AR(1). These results indicate that the commonly used pre-whitening procedure for eliminating the effect of serial correlation on the MK test leads to potentially inaccurate assessments of the significance of a trend; and certain procedures will be more appropriate for eliminating the impact of serial correlation on the MK test. In essence, it was advocated that a trend first be removed in a series prior to ascertaining the magnitude of serial correlation. This alternative approach and the previously existing approaches were employed to assess the significance of a trend in serially correlated annual mean and annual minimum streamflow data of some pristine river basins in Ontario, Canada. Results indicate that, with the previously existing procedures, researchers and practitioners may have incorrectly identified the possibility of significant trends.

Precipitation Trends over Slovakia in the Period 1981–2013

“…The trend-free pre-whitening (TFPW) procedure [73] was applied to detect a significant trend in a serially correlated time series, although it shows very high Type I error rates with increasing autocorrelation [74]. The original sample data X t were unitized by dividing each of their values by the sample mean E(X t ) prior to conducting the trend analysis.…”

Oasis Irrigation-Induced Hydro-Climatic Effects: A Case Study in the Hyper-Arid Region of Northwest China

“…However, serial correlations may increase the probability of significant trends and they should be removed [43,44]. The trend-free pre-whitening method was used to eliminate the effect of serial correlation on the Mann-Kendall test [45]. The relationship between the trends in ET0 and the sum of cultivated land and urban land, barren or sparsely vegetated lands within a certain radius were obtained using linear regression.…”

Changes in runoff time series in Thuringia, Germany – Mann-Kendall trend test and extreme value analysis

“…An important requirement for the correct interpretation of significance levels of MannKendall test results is serial independency of the time series (Helsel and Frans, 2006). Hydrological mean and low flow time series "may frequently display statistically significant serial correlation" (Yue et al, 2002). To account for this, the procedure of trend-free-pre-whitening was applied, which consists of 5 steps and is described in detail in Yue et al (2002) and Petrow and Merz (2009): first, linear trends are estimated for all time series, applying a robust slope estimator (after Sen, 1968, cited in Petrow andMerz, 2009).…”

“…Hydrological mean and low flow time series "may frequently display statistically significant serial correlation" (Yue et al, 2002). To account for this, the procedure of trend-free-pre-whitening was applied, which consists of 5 steps and is described in detail in Yue et al (2002) and Petrow and Merz (2009): first, linear trends are estimated for all time series, applying a robust slope estimator (after Sen, 1968, cited in Petrow andMerz, 2009). The linear trend is removed from the series in a second step by subtraction of the trend value in each time step.…”