## 3 Results and Discussion
### Geographical Distribution of DDREs  
The geographical distribution of the instantaneous (12:00 UTC) all-sky DDREs (at TOA, in the atmosphere, and at the surface), during the three days of the examined DAEC, are illustrated in Figure 4. The corresponding daily mean all-sky DDREs are shown in Figure S10. The spatial patterns of DDREs in the atmosphere (middle column of Figures 4 and S10) and at the region's surface (right column of Figures 4 and S10) are quite similar to those of the geographical distributions mainly of DOD (Figure 2i) as well as dust SSA (Figure S9), underlining the determinant role of DA loads for the perturbation of the solar radiation budget. Dust particles increase the absorption of solar radiation everywhere (positive values of DDREs in the maps of Figure 4 ii), by as much as 187 W/m\({}^{2}\) at 12:00 UTC and 70 W/m\({}^{2}\) on a daily mean basis (Figure 4 ii and Figure S10i), over areas with maximum DOD values (Figure 2i). This absorption leads to an atmospheric radiative heating effect, as discussed later (Section 3.5). Larger atmospheric DDREs are observed during the first day of the DAEC (values up to 168 W/m\({}^{2}\), Figure 4 ii-a and Figure S10 ii-a), when DOD is also largest (Figure 2i-a), than in the next two days (values up to 138 W/m\({}^{2}\)). This day-to-day decrease in the magnitude of atmospheric DDREs is due to the transport of dust from the source African areas to the MB and the consequent spreading out of their loads to areas as far as the northern Balkan peninsula and the Black Sea (Figure 2). At the surface, very similar geographical patterns, but with a negative sign and even greater magnitude, are observed over the entire MB (right column of Figures 4 and S10). The greater magnitude of the surface DDREs is attributed to the scattering of dust, which cuts off the downward solar radiation, as well as to dust absorption. The decreased surface solar radiation, caused by dust, produces a solar dimming and a subsequent SW radiative cooling. The surface DDREs take values between zero, over areas with zero or very low DOD, and down to \(-200\) W/m\({}^{2}\) at 12:00 UTC (\(-60\) W/m\({}^{2}\) on a daily basis) over dust export areas, e.g., over Tunisia's eastern coasts on the first day of the DAEC (16 June 2016, Figure 4 iii-a, deep blue colors). Again, as also found for the atmospheric DDREs, the surface DDREs gradually decrease from the first to the second and third days of the DAEC (largest values equal to \(-144\) and \(-113\) W/m\({}^{2}\), respectively). In another study [45] using WRF-Chem for estimating the net (SW + LW) clear-sky DDRE of a dust episode that took place on February 2015 over the MB, the researchers found an atmospheric radiative heating up to +147 W/m\({}^{2}\) and a surface radiative cooling as strong as \(-252\) W/m\({}^{2}\). The slightly different (mainly larger) values compared to those in the present study are mainly attributed to the cloud-free conditions considered in [45] as well as to differences in dust loads (up to 4.5 in [45] against 1.4 in the present study) and the used models (WRF-Chem against FORTH-RTM). Similar or even larger atmospheric and surface DDREs than those of the present study have been estimated by [8] with the NMMB-MONARCH model during 20 intense and widespread dust outbreaks, which affected the broader MB from 2000 to 2013. In addition, in [56], based on the chemical transport model (CTP) and RTM simulations, a reduction in the Global Horizontal Irradiance (GHI) as large as \(-200\) W/m\({}^{2}\) due to the presence of a dust plume that affected the MB on 1 st February 2015 was found. Apart from studies with large (regional) spatial coverage, there are also some local studies of DDREs. Thus, the DDRE during a dust intrusion on July 2002 at Lampedusa Island was estimated by [46], reporting lower values at the surface (maximum perturbation of 33 W/m\({}^{2}\) against 75 W/m\({}^{2}\) in this study). This difference is attributed to the lower AOD (up to 0.2) in [46] than in the present study (up to 1.4).