Trend detection in hydrologic data: The Mann–Kendall trend test under the scaling hypothesis

Abstract

The subject of trend detection in hydrologic data has received a great deal of attention lately, especially in connection with the anticipated changes in global climate. However, climatic variability, which is reflected in hydrologic data, can adversely affect trend test results. The scaling hypothesis has been recently proposed for modeling such variability in hydrologic data. In this paper, the Mann–Kendall test, which is widely used to detect trends in hydrologic data, is modified to account for the effect of scaling. Exact expressions for the mean and variance of the test statistic are derived under the scaling hypothesis, and the Normal distribution is shown to remain a reasonable approximation. A procedure for estimating the modified variance from observed data is also outlined. The modified test is applied to a group of 57 worldwide total annual river flow time series from the database of the Global Runoff Data Centre in Koblenz, Germany, that were shown in an earlier study to exhibit significant trends in annual maximum flow. The results show a considerable reduction in the number of stations with significant trends when the effect of scaling is taken into account. These results indicate that the evidence of real trends in hydrologic data is even weaker than suggested by earlier studies, although highly significant increasing trends seem to be more common than negative ones. It is also shown that admitting scaling in the modified test helps to avoid discrepancies found in some previous studies, such as the existence of significant opposite trends in neighboring stations, or in different segments of the same time series.