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.

Parametric Assessment of Trend Test Power in a Changing Environment

“…These results are in perfect agreement with the findings of Yue et al [15], who analyzed the MK test power from generation performed with GEV parent distribution, with different values of the trend, coefficient of variation, and sample size. They are also consistent with the results shown by Wang et al [16] and extend the range of climatic variability explored by Totaro et al [14].…”

“…They followed the approach proposed by Yue et al [15] that produced a numerical evaluation of the MK test power for Generalized Extreme Value (GEV) distributed samples. Wang et al [16] provided a practical relationship for a proper power assessment of specific time series.…”

“…In environmental applications in particular, the length of the observed series required to reach an acceptable power value could be very different according to the variable's parent distribution and the strength of the trend [10,[14][15][16]. It could be much shorter for temperature and humidity time series than for runoff and precipitation time series that usually show higher space-time variability.…”

Spatiotemporal Variation in Relative Humidity in Guangdong, China, from 1959 to 2017

“…Some studies found that the M-K test results of pre-whitening processed sequences were not accurate because of the loss of important information [85]. It is also suggested that the M-K test results can be improved by improving the significance test level and increasing the time series length of samples [64]. In the current study, the variation trend of relative humidity series was obvious, the sample size was large (1959-2017), and the confidence level of 95% was adopted.…”

“…This study found that the autocorrelation of the time series of hydrological and meteorological elements had an impact on the M-K test results. Therefore, the autocorrelation of the relative humidity time series was tested before the M-K test, and the influence of significant correlation was eliminated by the means of variance correction [64,65].…”