Power of the Mann-Kendall Test for Detecting Trends in Hydro-meteorological Time Series

The Mann-Kendall (MK) statistical test has been widely used for detecting trends in hydro-meteorological time series. However, previous studies focus more on the null hypothesis of “no trend”, or the “Type I Error”, but few study addresses on its ability of successfully recognizing the trend. In specific cases, the “Type II error” are equally important, especially when the trend test is associated with hydropower design, flood risk assessment and water quality evaluation. Results of Monte Carlo simulations indicate that the power of the MK test is closely associated with the sample variance and the magnitude of the trend. For a given length of time series, the power of the MK test increases as the slope value increases and decreases with the rising of the sample variance. Meanwhile, there exists a deterministic relation between the slope and the standard deviation of white noise, which can be used for evaluating the power of the MK test. Therefore the threshold of slope for judging the effectiveness of MK test can be estimated by the time length and the variance of the samples approximately. A positive autocorrelation existing in the time series will increase the Type I and Type II errors due to enlarging the variance of the MK statistics. The power of the MK test is a function of the specific sample variance and range of trend slope.