The modified Mann-Kendall test: on the performance of three variance correction approaches

The Mann-Kendall test has been used to detect climate trends in several parts of the Globe. Three variance correction approaches (MKD, MKDD and MKRD) have been proposed to remove the influence of serial correlation on this trend test. Thus, the main goal of this study was to evaluate the probability of occurrence of types I and II errors associated with these three approaches. The results obtained by means of Monte Carlo simulations and from a case of study allowed us to drawn the following conclusions: All approaches are capable of meeting the adopted significant level when they are applied to trend-free uncorrelated series. The approaches are as powerful as the original MK test when they are applied to uncorrelated series. Regarding serially correlated series it was verified that: (i) the performance of the MKDD and MKRD are comparable; (ii) both approaches may not be able to preserve the adopted significance level and (iii) although the MKD is capable of preserving the adopted significance level, it is less powerful than the MKDD and MKRD. Thus, there is a trade-off between the power of the three approaches and their capability of meeting the nominal significance level. Accordingly, we recommend the use of at least two approaches -MKD and MKDD(MKRD)- to evaluate the presence of trends in a given dataset.