2.5.4. Trend Analysis

The Mann Kendall (MK) test, which is a non-parametric test used to analyze monotonic trends of changes in hydro-meteorological data, was used to examine trends in seasonal and annual temperature and rainfall as well as temperature and rainfall extremes [35,36]. Positive and negative values of MK test results indicate increasing or decreasing monotonic trends, respectively. The magnitude of changes in the trends of rainfall and temperature data was determined using Theil-Sen's slope estimator. The MK test statistic, S, was calculated as:

$$s = \sum\_{i=1}^{n-1} \sum\_{j=i+1}^{n} s g n \left(X\_j - X\_i\right)$$

where *Xi* and *Xj* refer to the annual values of the climate variables in years *i* and *j*, respectively. For time-series data with significant autocorrelation, the modified MK test was used. In this procedure, bias-corrected prewhitening, involving transformation of an autocorrelated sequence into an uncorrelated one before trend testing, was used [37]. This technique enhances the effectiveness of prewhitening in trend analysis by eliminating under- or overestimation of the autocorrelation parameter within the limits of sampling variations [37].
