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.