## 2 Materials and Methods
### Methodology  
The evaluation of MERRA-2 GDB is examined through comparisons against GEBA and BSRN measurements using monthly mean SSR fluxes and deseasonalized anomalies, which were computed by subtracting from each monthly SSR value the corresponding long-term (different for each station) averaged value. SSR anomalies were preferred to corresponding absolute fluxes in the computation of either the correlation coefficients or the trends of time series, since the use of deseasonalized anomalies minimizes the seasonal component of variability, which is assumed to be periodic with constant amplitudes and thus does not have much impact on the long-term variability [90]. On the other hand, the computation of other evaluation statistical metrics, such as the absolute and relative percent bias and root mean squared error (RMSE), were done using the absolute monthly SSR fluxes. Specific data availability criteria have been applied in the analysis in order to ensure the maximum possible robustness of the obtained results and conclusions. Thus, in the comparison between MERRA-2 and GEBA/BSRN SSR fluxes and anomalies, each year was required to have more than 10 months of measurements available, in order to exclude years with poor seasonal representativeness, which would degrade the comparison quality. The application of this criterion resulted in availability of 1099 GEBA and 70 BSRN stations (out of the originally available 1397 GEBA and 73 BSRN stations). These stations, shown inFigure 1, still ensure a satisfactory geographical coverage of the world's continental areas, of course more for GEBA than BSRN. The different steps of the applied methodology are outlined in Figure 2.  
Figure 1: Global Distribution of: (**a**) Global Energy Balance Archive (GEBA) 1099 stations and (**b**) Baseline Surface Radiation Network (BSRN) 70 stations, whose surface solar radiation (SSR) data (availability in years indicated in the colorbar) have been used in this study. Four (4) statistical indices were used to quantify the degree of agreement/disagreement between the MERRA-2 and reference stations' GDB: the Pearson's correlation coefficient (R), the Root Mean Squared Error (RMSE) and percent relative RMSE (RRMSE), the bias and relative bias; whose equations are:  
\[R=\frac{\sum_{i=1}^{n}(M_{i}-M)(G_{i}-G)}{\sqrt{\sum_{i=1}^{n}(M|i-M)^{2}\sqrt{ \sum_{i=1}^{n}(G_{i}-G)^{2}}}} \tag{1}\]  
\[RMSE=\sqrt{\frac{1}{n}\sum_{i=1}^{n}(M_{i}-G_{i})^{2}} \tag{2}\]  
\[RRMSE=\frac{\sqrt{\frac{1}{n}\sum_{i=1}^{n}(M_{i}-G_{i})^{2}}}{G}100\% \tag{3}\]  
\[BIAS=M-G \tag{4}\]  
\[BIAS(\%)=\frac{M-G}{G}100\% \tag{5}\]  
where \(n\) is the number of monthly data, \(M_{i}\) and \(G_{i}\) are the monthly (for the -\(i\) month) values of MERRA-2 and ground-based station, respectively, and \(M\) and \(G\) are the mean values of MERRA-2 and ground-based stations. The R (Equation (1)) value measures how strongly the two variables correlate (covariate), whereas RMSE (Equation (2)) measures the average magnitude of the error, i.e., the difference between the Reanalysis and ground station. Since the errors are squared before being averaged, the RMSE gives a relatively high weight to large errors, thus it is most useful when large errors are particularly undesirable. The normalized RMSE (Equation (3)) is also computed. BIAS quantifies the difference between the mean value of predictions and the mean value of observations, as shown in Equation (4). Emphasis, however, is also placed on relative bias, which better represents the difference (Equation (5)). In order to evaluate the GDB of MERRA-2, a linear regression was applied to the time series of deseasonalized monthly anomalies, and the slopes were computed either for each station or the corresponding MERRA-2 pixels, where the stations are located.