The sign of the z-statistic indicates the direction of the trend. Thus, positive, negative and zero z-statistics indicate an upward, a downward and no trend, respectively. The MK test assumes that the time series data is uncorrelated. However, most hydrological data exhibits positive autocorrelation. Therefore, \citet{von_Storch_1999} suggested pre whitening method, which transforms the time series data to remove autocorrelation. This method, which employs the lag-1 serial correlation coefficient (r1) of the sample data Xi, has been widely used by researchers since its introduction \citep{Douglas_2000,Kulkarni_1992,yazdan2021,Zhang_2000}: