## 3 Results
### MERRA-2 GDB (SSR Trends) and Its Evaluation
#### 3.2.1 Evaluation of MERRA-2 GDB (SSR Trends)
All examined 232 GEBA stations, indicate an average brightening of 3.95 W/m\({}^{2}\), while the BSRN stations indicate a somewhat weaker brightening of 1.83 W/m\({}^{2}\). Figure 6: Scatterplot comparison between MERRA-2 and GEBA (**a**), and MERRA-2 and BSRN (**b**) \(\Delta\)(SSR) or GDB (in W/m\({}^{2}\)). The linear regression fit, and the associated statistical metrics, namely the slope, the slope error, the correlation coefficient (R), the root-mean squared error (RMSE), the bias (MERRA-2 minus stations) and the total number of matched data pairs, are also shown. Figure 7: Time series of averaged SSR anomalies for GEBA stations ((**a**), blue curve) and BSRN stations ((**b**), blue curve) along with those for the corresponding MERRA-2 pixels (red curves). The number of available stations for each month is also shown in green color. 12-month moving averages for each time series are also shown in same colors. The computed \(\Delta\)(SSR) and the associated standard deviation along with the correlation coefficient (R) between the two sets of time series (1980–2017 for GEBA and 1992–2020 for BSRN) are given at the top of figure. According to the obtained trends of MERRA-2 pixels including the GEBA stations, over the same time period, the positive trends vary from 0.14 to 13.96 W/m\({}^{2}\), and the negative trends from \(-\)0.05 to \(-\)36.54 W/m\({}^{2}\), whereas the corresponding ranges for MERRA-2 pixels including the BSRN stations are 0.01-11.32 and \(-\)(0.00-11.55) W/m\({}^{2}\). The MERRA-2 pixels including the GEBA sites, all together, indicate an average dimming of \(-\)0.47 W/m\({}^{2}\) (Figure 8i-b), while the MERRA-2 pixels including the BSRN sites also indicate an even stronger dimming of \(-\)2.29 W/m\({}^{2}\) (Figure 8 ii-b), which are both of opposite sign to the corresponding GEBA/BSRN stations results. Yet, in spite of this average disagreement, there is partial agreement (for GEBA) between the respective average GDB computed only for cases, i.e., stations-pixels, with statistically significant trends. Specifically, the average MERRA-2 GDB for GEBA/BSRN sites is 0.51 and \(-\)3.45 W/m\({}^{2}\), while the corresponding mean GDB for GEBA/BSRN sites is 5.22 and 1.68 W/m\({}^{2}\). Moreover, both MERRA-2 pixels and GEBA stations indicate strong and statistically significant dimming over India and strong brightening over Europe, with a stronger brightening occurring at the GEBA stations than MERRA-2. On the contrary, a clear disagreement, with GEBA brightening versus MERRA-2 dimming, is found over Japan, which explains the opposite overall sign of GDB between MERRA-2 pixels and GEBA sites reported above. The priority in such a comparison between the MERRA-2 and GEBA/BSRN station-based trends of SSR, i.e., GDB, is the agreement/disagreement between their signs. This is better shown in Figure 9, which displays with blue/red bullets the stations for which  
Figure 8: Computed GDB (or \(\Delta\)(SSR), in W/m\({}^{2}\)) for GEBA (**i-a**) and BSRN (**ii-a**) stations and for the corresponding pixels of MERRA-2 containing the GEBA (**i-b**) and BSRN (**ii-b**) stations. Negative values, shown in blue and green colors, indicate dimming, and positive values, orange and red colors, indicate brightening. The embedded white x symbols indicate trends which are statistically significant (assessed at the 95% confidence level by applying the non-parametric Mann Kendall test). The trends are estimated over the periods covered by each station (shown in Figure S2). the trends of MERRA-2 and CEBA/BSRN stations SSR have the same/opposite sign. A satisfactory percentage of agreement (63.4%) between the signs of MERRA-2 and CEBA GDB is found, whereas the percentage is lower (50%) for BSRN stations. Furthermore, it is found that the percentage of agreement is somewhat better for cases (pixels) with statistically significant trends, being equal to 75.7% for GEBA and 66.7% for BSRN stations.