## 4 Materials and Methods
### Data and Methodology
#### 4.2.1 Meteorological Data (Temperature, Humidity, Pressure)  
Temperature, humidity, and pressure data were sourced from Meteomanz [82]. Meteomanz delivers observed meteorological data from global sites sourced from surface synoptic observations (SYNOP) and Binary Universal Form for the Representation of meteorological data (BUFR) information supplied by accredited meteorological stations as well as forecast atmospheric information derived from Global Forecast System (GFS) models and European Centre for Medium-Range Weather Forecasts (ECMWF). The data were accessible as 3-h averages; the linear interpolation method was used to obtain hourly averages from the 3-h averages.  
Observation data were sourced for the eight-year period of 2014-2021. Quality control of raw datasets was provided based on the semiempirical method [83]. Missing data were filled in. Minor data gaps (up to six measurement cycles missing) were filled in using the linear regression method; for longer data gaps, gap-filling was performed using data from the preceding method and 1-3 days prior to the data gap, leaving a maximum of three hours of adjustment time to fit the measured and interpolated data. It is noted that the distribution of the SYNOP stations and quality of observations in Morocco are better than in most other parts of Africa [84; 85]. Water vapour was calculated from hourly temperature and hourly humidity data using a methodology given by [45; 86; 87; 88; 89]. The methodology used is summarised by Equations (8) to (12):  
\[P_{bv}=0.1\cdot H_{V},P_{V} \tag{8}\]  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Input/Model** & **[PERSON]** & **Simple Solis** & **Ineichen–Perez** & **[PERSON]** & **[PERSON]** & **Berger-Duffie** & **ABCG** \\ \hline Zenith Angle & X & X & X & X & X & X & X \\ \hline Albedo & X & - & - & X & - & - & - \\ \hline AOD1240 nm & X & X & - & - & - & - & - \\ \hline AOD550 nm & X & X & - & X & - & - & - \\ \hline AOD380 nm & X & - & - & - & - & - & - \\ \hline AOD500 nm & X & - & - & - & - & - & - \\ \hline AOD700 nm & - & X & - & - & - & - & - \\ \hline Temperature & X & X & - & X & - & - & - \\ \hline Humidity & X & X & - & X & - & - & - \\ \hline \(DNI_{TOA}\) & X & X & X & X & - & X & X \\ \hline D (Julian day) & X & X & X & X & X & X & X \\ \hline Solar constant & X & X & X & X & - & - & - \\ \hline Pressure & X & X & X & X & - & - & - \\ \hline Altitude & X & X & X & X & X & X & X \\ \hline Linke Turbidity & - & - & X & - & - & - & \\ \hline Ozone & X & - & - & X & - & - & - \\ \hline Absolute airmass & - & - & X & - & - & - & - \\ \hline Relative airmass & X & - & X & - & - & - & - \\ \hline Apparent Elevation & - & X & - & - & - & - & - \\ \hline Asymmetry & X & - & - & - & - & - & - \\ \hline Total inputs & 16 & 12 & 9 & 11 & 3 & 4 & 4 \\ \hline \end{tabular}
\end{table}
Table 3: A table summarising different inputs required by different models.  
where \(H_{V}\) is the apparent water vapor scale height (in km) and \(P_{V}\) is the surface water vapor density \(\left(\text{in}\ \frac{\mathcal{S}}{m^{3}}\right)\). These are given by Equations (9) and (11), respectively:  
\[H_{V}=0.4976+1.5265\cdot X+e^{(13.68\cdot X-14.9188\cdot X^{3})} \tag{9}\]  
\[\text{With}\ X=\frac{T}{273.15} \tag{10}\]  
\[P_{V}=216.7\cdot RH.\frac{e_{s}}{T} \tag{11}\]  
\[\text{With}\ e_{s}=e^{(22.33\cdot\frac{8914}{7}-\frac{109220}{7^{2}}-0.0039015 \cdot T)} \tag{12}\]  
where \(T\) is the temperature (in \({}^{\circ}\)C) and \(RH\) is the relative humidity (in %).