2.5. Linear rates, correlations, and cumulative departures
A non-parametric method such as the Sen’s slope (Sen, 1968) estimator was used to estimate the linear rates in rainfall since it is robust and resistant to outliers. Sen slope (Sk ) is the median overall values of the whole data and is estimated as,
\begin{equation} S_{k}=Median\left(\frac{Y_{j}-Y_{i}}{j-i}\right),\ for\ \left(1\ \leq i<j\leq n\right)\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 4\nonumber \\ \end{equation}
where Yj and Yi represents data values at time j and i (j > i ), respectively while n is the number of data. The slope can be positive indicating increasing trend or negative, indicating decreasing trend. Trend analysis for precipitation grids used a 20-year window different from the MLRA of GPCC-based precipitation (Section 2.4), which focused on trends based on 30-year climatological windows. Detecting changes in rainfall in a relatively short window is crucial for better understanding of significant climate trends and developing adaptation and mitigation measures at a regional and local scale. Given that the assessment of linear rates in rainfall is a key aspect of long-term water resource evaluations strategy, cumulative rainfall departure (Weber and Stewart, 2004) was estimated. The concept of cumulative rainfall departures (Weber and Stewart, 2004) was also applied to estimate cumulative departures of river discharge. Generally, cumulative departures are useful when employed as a general indicator of rainfall/discharge trends, with the upward and downward gradient indicating relatively a rise and decline in rainfall, respectively (e.g., Ndehedehe et al., 2017). Cumulative departures were both employed to evaluate trends in river discharge against those of rainfall. All temporal relationships between rainfall and discharge were based on the Pearson’s correlation coefficient and are deemed significant at α= 0. 05. Although it was not the main stay of this study, the
grid based comparison of GPCC and CRU precipitation data was also undertaken. Using correlation
and ANOVA in this regard provided a bit of perspective as to the inherent differences and similarities between the widely used GPCC observational reference and the CRU data over the region.