The non-parametric Mann-Kendall (MK) statistical test has been popularly used to assess the significance of trend in hydrological time series. The test requires sample data to be serially independent. When sample data are serially correlated, the presence of serial correlation in time series will affect the ability of the test to correctly assess the significance of trend. To eliminate the effect of serial correlation on the MK test, effective sample size (ESS) has been proposed to modify the MK statistic. This study investigates the ability of ESS to eliminate the influence of serial correlation on the MK test by Monte Carlo simulation. Simulation demonstrates that when no trend exists within time series, ESS can effectively limit the effect of serial correlation on the MK test. When trend exists within time series, the existence of trend will contaminate the estimate of the magnitude of sample serial correlation, and ESS computed from the contaminated serial correlation cannot properly eliminate the effect of serial correlation on the MK test. However, if ESS is computed from the sample serial correlation that is estimated from the detrended series, ESS can still effectively reduce the influence of serial correlation on the MK test.
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Yue, S., Wang, C. The Mann-Kendall Test Modified by Effective Sample Size to Detect Trend in Serially Correlated Hydrological Series. Water Resources Management 18, 201–218 (2004). https://doi.org/10.1023/B:WARM.0000043140.61082.60