Detecting trends in hydrometerological data through the commonly used Mann-Kendall test is misleading in the presence of data autocorrelation. Autocorrelation seriously interferes with type I errors and power of trend detection. To mitigate this effect, the authors introduce a variance correction prewhitening method. It addresses two important issues that lacked appropriate attention in the past application of trend-free prewhitening method: inflationary variance of slope estimator and deflationary serial variance. After serial and slope variances correction, the new method keeps a better balance between maintaining a low type I error and a relatively strong power of trend detection. In comparison, other methods for the same purpose only address one of these two characteristics. The new method bears some resemblance to the block-bootstrap method; however, it is superior in its simplicity for implementation. Case studies reveal that uncertainties arising from autocorrelation are substantial. Applying more than one test is helpful to interpret results with uncertainties information. The new method provides a robust choice to this strategy.

To understand the changing rainfall–runoff relationship, this study examined climate and streamflow data in the Milwaukee River Basin in southeastern Wisconsin, of which four catchments with different degrees of urbanization were selected for analysis. This study analyzed temperature, precipitation, and streamflow data with a range of statistical methods, including the Mann–Kendall test, double-mass technique, and quantile regression. Runoff ratios and extreme flow indexes were higher in more urbanized catchments. Catchments with long-term data (>forty years) showed significantly increasing runoff ratios and slopes in double-mass curves. Overall, there are signs of changes in the rainfall–runoff relationship, but how much they can be attributed to land use changes is uncertain.

Hydrometeorological data are commonly serially dependent and thereby deviate from the assumption of independence that underlies the Spearman rho trend test. The presence of autocorrelation will influence the significance of observed trends. Specifically, the positive autocorrelation inflates Type І errors, while it deflates the power of trend detection in some cases. To address this issue, we derive a theoretical formula and recommend an appropriate empirical formula to calculate the rho variance of dependent series. The proposed procedure of the variance correction for the Spearman rho method is capable of mitigating the effect of autocorrelation on both, Type І error and power of the test. Similar to the Block Bootstrap method, it has the advantage that it does not require an initial knowledge of the autocorrelation structure or modification of the series. In comparison, the capability of the Pre-Whitening method is sensitive to model misspecification if the series are whitened by a parametric autocorrelation model. The Trend-Free Pre-Whitening method tends to lead to an overestimation of the statistical significance of trends, similar to the original Spearman rho test. The results of the study emphasize the importance of selecting a reliable method for trend detection in serially dependent data.