## 2 Materials and Methods
### Methods
#### 2.3.3 Estimation of Aridity Index  
The aridity index (AI) was calculated as the ratio of potential evapotranspiration (PET) and precipitation (Prec) as defined by the Penman-Monteith [49] method (Equation (14)).  
\[AI=\frac{PET_{(x,t)}}{Prec_{(x,t)}} \tag{14}\]  
where \(PET_{(x,t)}\) stands for potential evapotranspiration (mm) and \(Prec_{(x,t)}\) for precipitation (mm) at timescale t and grid position x, respectively. The \(PET_{(x,t)}\) was estimated by using the following equation (Equation (15)):  
\[PET_{(x,t)}=\frac{0.408\Delta(R_{n}-G)+\rho\frac{900}{T_{air}+273}Ws_{2}(es-ea) }{\Delta+\rho(1+0.34 Ws_{2})} \tag{15}\]  
\(R_{n}\) is the net radiation at the canopy (MJ\(\cdot\)m\({}^{-2}\)-timescale\({}^{-1}\)), \(G\) is the soil heat flux density (MJ\(\cdot\)m\({}^{-2}\)-timescale\({}^{-1}\)), which was calculated by the difference of mean daily air temperature between two continuous days as estimated by Penman-Monteith and by Thorthwaite [50; 51] methods. \(T_{air}\) stands for the mean daily air temperature at 2 m of height (\({}^{\circ}\)C), \(Ws_{2}\) is the wind speed at 2 m of height (m\(\cdot\)s\({}^{-1}\)) and \(es-ea\) are the saturation and the actual vapor pressure (kPa), while \(\Delta\) is the slope of saturated vapor pressure in relation to air temperature (kPa\(\cdot\)\({}^{\circ}\)C\({}^{-1}\)) and \(\rho\) is the psychometric constant (kPa\(\cdot\)\({}^{\circ}\)C\({}^{-1}\)), respectively. The \(R_{n}\) was estimated from the difference between the net shortwave radiation (\(R_{ns}\)) and the net longwave radiation (\(R_{nl}\)) (Equation (16)):  
\[R_{n}=R_{ns}-R_{nl} \tag{16}\]  
Generally, AI is expressed on the annual basis as the fact that the degree of dryness cannot be determined at daily or monthly time scales, which differentiates the aridity and drought concepts [21; 51]. To optimize our AI estimation onto the GLR-SSA tropical climate [52], we have applied the mean annual values of PET and Prec to calculate the AI from 2001 to 2020. Moreover, the AI values were classified in accordance with UNEP and UNESCO aridity classification limits based on Thornthwaite (UNEP 1992) and Penman (UNESCO 1978) methods, respectively (Table 3 and Figure 3).  
The GLR-SSA was dominated by humid climate (70%), while the other climate zones were extended over the remaining 30% of the GLR-SSA in which semi-humid, semi-arid and arid climate zones are extended over approximately 10%, 2.79% and 11.23%, respectively as the UNEP and UNESCO classifications (Figure 3).  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Climate Zones**} & **UNESCO (1979)** & **UNEP (1992)** \\ \cline{2-3}  & **Penman Method** & **Thornthwaite Method** \\ \hline Hyper-Arid & \textless{}0.03 & \textless{}0.03 \\ Arid & 0.03–0.20 & 0.03–0.20 \\ Semi-Arid & 0.20–0.50 & 0.20–0.50 \\ Sub-Humid & 0.50–0.75 & 0.50–0.65 \\ Humid & \textgreater{}0.75 & \textgreater{}0.65 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Aridity classification limits according to the UNEP and UNESCO international conventions.  
Figure 3: Spatial and patterns distribution of climate zones based on Aridity index classification using both UNEP (PenMan) and UNESCO (Thornthwaite) Methods.