Do the Mann-Kendall Test and Theil-Sen Slope Fail to Inform Trend Significance and Magnitude in Hydrology?

The Mann-Kendall (MK) test is frequently used for trend detection in hydrological time series although its power has not been systematically studied under the influence of both missing data and aggregation of data (daily, monthly averages). We used Monte Carlo experiments to examine how the power of the MK test and the accuracy/precision of the Theil-Sen (TS) estimator are affected by missing data and taking averages of the data. A case study using real measurements is presented to evaluate whether the results of the MK test and TS estimates are consistent with different averaging window sizes. Results show interactive effects of missing data and averaging window size on the power of the MK test. The TS slope was accurate; however, its precision was low for minor trends. Our case study showed the TS slope was stable against different averaging window sizes, while the results of the MK test were not.