## 2 Data and Methods
### Data
#### 2.1.4 CM SAF, CERES and Ground-Based SSR Data  
For evaluation purposes, SSR satellite-based observations were acquired from the Satellite Application Facility on Climate Monitoring Surface Solar Radiation Data Set--Heliosat--edition 2.1 (CM SAF SARAH-2.1) product [65]. SARAH-2.1 is an extension of SARAH-2 [66], being the latest release of a series of CM SAF SSR products, which are based on observations from the Meteosat First and Second Generation (MFG/MSG) geostationary satellite series covering Africa, Europe, and the Atlantic Ocean ([PERSON] et al., [18] and references therein). The effective cloud albedo calculated with the Heliosat algorithm is used in combination with the clear-sky surface radiation model SPECMAGIC to derive SSR (in the 200-4000 nm wavelength region) from the Meteosat Visible-InfraRed Imager (MVIRI) and Spinning Enhanced Visible and Infrared Imager (SEVIRI) sensors onboard MFG and MSG satellites based on a modified Monitoring Atmospheric Composition and Climate (MACC) aerosol climatology [18]. The CM SAF SARAH-2.1 SSR data are available on a 30 min, daily and monthly basis at a spatial resolution of 0.05\({}^{\circ}\)\(\times\) 0.05\({}^{\circ}\) spanning the period 1983-2017. In this work, monthly data are used for the period 2005-2017. Evaluation of the SARAH-2.1 monthly product over Europe [66] has shown good agreement with ground-based pyranometric observations (mean bias of +2.7 W/m\({}^{2}\), mean absolute bias of 6.9 W/m\({}^{2}\) and a Pearson's correlation coefficient R of 0.89). Another satellite-based SSR dataset used here for evaluation comes from the Clouds and the Earth's Radiant Energy System Energy Balanced and Filled edition 4.1 (CERES EBAF edition 4.1) level-3b product [67; 68]. The data are available on a monthly basis at a 1\({}^{\circ}\)\(\times\) 1\({}^{\circ}\) spatial resolution. The product is mostly based on measurements from the CERES sensors onboard Terra and Aqua satellites, MODIS measurements from the same satellites and geostationary imagers. CERES measures filtered radiances in the shortwave (SW; 0.3-5 \(\upmu\)m), total (TOT; 0.3-200 \(\upmu\)m) and window (wavelengths between 8 and 12 \(\upmu\)m) spectral regions with a spatial resolution of \(\sim\)20 km at nadir [69]. Unfiltered SW, longwave (LW) and window radiances are calculated [70] and finally are converted to fluxes using empirical angular distribution models (ADMs) [71]. For the calculation of surface fluxes cloud data from MODIS and geostationary satellites are utilized along with aerosol properties from MATCH (Model of Atmospheric Transport and Chemistry) that assimilates MODIS AODs, atmospheric profile data from the Goddard Earth Observing System version 5.4.1 (GEOS-5.4.1) reanalysis, and ancillary atmospheric profile data from other satellite sensors (i.e., CALIPSO, Cloudsat and AIRS/Aura) [68]. The radiative transfer calculations are constrained by the CERES TOA fluxes. The uncertainty of the 1-degree CERES EBAF edition 4.1 SSR product used here is less than 5 W/m\({}^{2}\), which is within the uncertainty of ground measurements [68]. Finally, for evaluation purposes, hourly pyranometric data from three ground stations with quality-assured long time series [27] are utilized here. The first station (urban) is located in the center of Thessaloniki within the university campus of the Aristotle University of Thessaloniki (40.63\({}^{\circ}\) N, 22.96\({}^{\circ}\) E). The measurements come from a CM21 pyranometer (Kipp and Zonen, Delft, the Netherlands) [72]. The instrument measures solar radiation in the spectral range 305-2800 nm with an uncertainty of \(\pm\)2%. The second station (urban) is located in the center of Athens, Greece at the facilities of the National Observatory of Athens (37.97\({}^{\circ}\) N, 23.72\({}^{\circ}\) E). The measurements were taken from an Eppley precision spectral pyranometer that measures solar radiation in the wavelength range from 285 to 2800 nm with an uncertainty of \(\pm\)1-2% [73].