## 1 Introduction  
Dust Aerosols (DAs) are very important, since they largely contribute to the global aerosol mass in the atmosphere by more than 50% [1; 2]. They perturb the Earth's radiation budget through their direct interaction with solar and terrestrial radiation, but also indirectly through modification of the cloud properties. Specifically, DAs absorb and scatter the shortwave radiation [3] and absorb and re-emit longwave radiation [4]. The interaction of DAs with SW radiation results in a positive anomaly of the atmospheric absorbed solar radiation (atmospheric heating effect) and a (greater over most regions) negative anomaly of the net surface solar radiation (surface cooling effect). The sum of these two opposite-sign effects results in an overall cooling effect of Dust Radiation Interaction (DRI) at the Top of Atmosphere (TOA), which is estimated to be equal to \(-0.83\) W/m\({}^{2}\) on a climatological (for the years 1980-2018) annual global mean basis, arising from global mean surface cooling and atmospheric heating radiative effects equal to \(-1.98\) W/m\({}^{2}\) and \(1.15\) W/m\({}^{2}\), respectively [5]. The annual mean SW Dust Direct Radiative Effects (DDREs) are greater over regions with high dust loads, namely world deserts, and especially the Sahara and Arabian deserts, where dust-induced strong surface cooling (down to \(-32.9\) W/m\({}^{2}\)) and an equally strong atmospheric heating (up to 33.0 W/m\({}^{2}\)) occur [5]. These values are even greater in spring (\(-39.3\) W/m\({}^{2}\) and \(39.8\) W/m\({}^{2}\) at the surface and in the atmosphere, respectively) and summer (\(-54.5\) W/m\({}^{2}\) and \(38.0\) W/m\({}^{2}\) at the surface and in the atmosphere, respectively) when dust loads are maximum over these regions [5]. These opposite DA radiative effects in the atmosphere and at the Earth's surface nearly cancel out, resulting in a small cooling or even heating effect at the TOA, over desert areas such as those included in the Mediterranean region. The change in sign of the SW DDRE at the TOA is attributed to the multiple scattering between the absorbing DA and the highly reflective underlying desert surfaces, thus highlighting the important role of surface albedo. On the other hand, the LW DDREs are generally smaller in magnitude and of opposite sign compared to the SW DDREs [6; 7; 8] and, for this reason, many studies do not take it into account [9; 10; 11]. The magnitude of LW DDREs depends on dust radiative properties [12], but also on several other parameters, such as dust load, coarse/fine mode ratio, dust vertical distribution, and surface temperature and albedo [13]. Albeit smaller than the SW DDREs, the LW DDREs can be significant (reaching up to 26% of the SW DDREs) and counteract the SW cooling effect at the TOA [13]. Apart from their DDRE, DAs play a significant role in the Earth-atmosphere system through their interaction with clouds, since they act as Cloud Condensation Nuclei (CCN) and Ice Nuclei (IN), thus modifying the cloud composition and number of droplets and ice crystals and altering their physical and optical properties. Indeed, as shown by several measurement campaigns [14] and confirmed by laboratory studies [15], dust particles can modify several cloud properties (i.e., liquid water path, cloud fractional coverage) [16] by influencing the particle size distribution, cloud thickness, spatial extent, lifetime, and precipitation [17]. Although near to their sources, DAs contain insoluble materials (such as aluminosilicate clays and carbonates), and field observations have shown that many of the transported dust particles contain nitrates, which are formed during their transport in the troposphere [18; 19]. In addition, DAs free of any coatings enhance ice formation through the deposition nucleation mechanism at low supersaturations (10-20%, [20]). On the other hand, for DAs coated with chemically insoluble materials, the nucleation tends to occur at higher supersaturations through the adsorption mechanism [20].