*3.2. Trend Analysis for Temperature, Precipitation and River Discharge*

Linear trends in the time series were analyzed using the Mann–Kendall test [32]. It was chosen, because it is a robust nonparametric test and it can handle missing data as well as it has higher power for non-normally distributed data, which are common in hydrological and meteorological data [33]. Each element is compared with its successors and ranked as larger, equal, or smaller. Based on this analysis, the statistical significance of rejecting the null hypothesis that there is no monotonic trend is tested (for all tests α = 0.05). The R package "Kendall" was used for the calculation [34].

The Theil–Sen approach was used in order to quantify the linear trend [35,36]. It computes the slope for all pairs of the ordinal time points of a time series and then used the median of these slopes as an estimate of the complete slope. This approach is commonly combined with the Mann–Kendall test and estimates the trend slope of a time series in its original unit. The R package "zyp" was used in order to calculate the Theil–Sen trend and includes a pre-whitening according to Ye et al. (2002) [37] if autocorrelation occurs [38].
