## 4 Discussion  
Here, various aspects related to the quality of the simulations and the interpretation of our results are discussed. This discussion is relevant to numerous other studies using similar radiative transfer systems. In Section 3.1, it is shown that our monthly SSR simulations are in good agreement with ground- and satellite-based observations exhibiting a negative bias. [PERSON] [98] stressed that the use of a daytime-average zenith angle may lead to high biases in the amount of radiation reflected by the clouds. Indeed, our clear-sky SSR values are very close to the corresponding clear-sky values from CM SAF and CERES. Other tests (e.g., the use of AERONET ground-based AOD observations instead of MODIS, and the use of artificial biases in other aerosol and cloud optical properties and atmospheric parameters) did not remove the negative bias. On the other hand, by running our system for the three evaluation stations on an hourly basis (24 simulations per month), we obtained a decreased bias (NMB of -3.5% relative to ground observations, the correlation still being very good). All these give us an indication that the systematic negative bias appearing in our SSR data, and in the data from similar radiative transfer systems [21], is largely due to the fact that our simulations are done on a monthly basis, assuming a monthly mean daily SZA and daylength. Another reason for the negative bias might be the representation of clouds within a day by using afternoon measurements (despite correcting for the diurnal variability). This systematic negative bias is not expected to affect the radiative effect calculations substantially, while, on the other hand, the implementation of monthly simulations is much less time consuming compared to daily or hourly simulations, allowing for more tests and easier fine-tunning of the radiative transfer system. While our study focuses on the average radiative effects on monthly timescales, the instantaneous radiative effects of the parameters examined here could be much higher or lower. For example, [PERSON] et al. [99], studying an extreme dust event, showed that the radiative effect induced by dust on SSR was up to \(-150\) W/m\({}^{2}\) over Southern Greece, which is more than 10 times the average all-aerosol radiative effect (\(-13\) W/m\({}^{2}\)) shown in this work. As far as clouds are concerned, [PERSON] et al. [100] showed that the instantaneous cloud radiative effect over Thessaloniki can reach values up to \(-900\) W/m\({}^{2}\). This is more than 15 times the average radiative effect of clouds that we calculate here for Thessaloniki (\(-54\) W/m\({}^{2}\)). It is obvious that by using monthly data as the input, one will rule out such extreme values. On top of that, the common practice to use of monthly means as input in the radiative transfer simulations, at some extent, will impact the relative importance of the various parameters, i.e., aerosols, tropospheric NO\({}_{2}\), and clouds, for the calculated solar radiation fields. For example, under cloudy conditions, satellite-based AOD retrievals are unavailable and hence the AOD monthly mean values come from cloud-free scenes, which could bias the RE\({}_{\text{aer}}\) values. This is an unavoidable limitation of satellite observations and will always exist, despite the fact that we follow the optimal way of aggregating the data here (temporal averaging of spatially aggregated observations), as discussed in [PERSON] et al. [101]. Another point that has to be stressed here is that the radiative effect of each parameter (see Equation (1)), except for the parameter per se, depends on the amount of solar radiation reaching the Earth's atmosphere, which in turn varies according to the season of the year and the geographical latitude. This means that even if a parameter was constant throughout the year, the radiative effect would be higher in the summer compared to the winter and over locations at lower latitudes, following the solar radiation variability.