Re-evaluation of the Power of the Mann-Kendall Test for Detecting Monotonic Trends in Hydrometeorological Time Series

Abstract

The Mann-Kendall (MK) statistical test has been widely applied in the trend detection of the hydrometeorological time series. Previous studies have mainly focused on the null hypothesis of “no trend” or the “Type I Error”. However, few studies address the capability of the MK test to successfully recognize the trends. In some cases, especially when the trend test is jointly applied with hydropower station design, flood risk assessment, and water quality evaluation, the “Type II error” is equally important and should not be neglected. To cope with this problem, we carry out Monte Carlo simulations and the results indicate that in addition to the significance level and the sample length, the MK test power has a close relationship with the sample variance and the magnitude of the trend. For a given time series with fixed length, the power of the MK test increases as the slope increases and declines with increasing sample variance. A deterministic relationship between the slope and the standard deviation of the white noise that can be used for evaluating the power of the MK test has also been detected. Furthermore, we find that a positive autocorrelation contained in the time series will increase both the Type I and the Type II errors due to the enlargement of the variance in the MK statistics. Finally, we recommend that researchers slightly increase the significance level and lengthen the time series sample to improve the power of the MK test in future studies.