Four EARLINET stations affected by typical Saharan dust intrusions in the Mediterranean were selected (listed from west to east): Granada (Spain), Potenza (Italy), Athens (Greece) and Limassol (Cyprus). A 4-year (2014–2017) common period of aerosol depolarization Raman lidar data obtained at 532 nm was selected for this analysis. Table 1 summarizes the basic information about these lidar systems for each location. Except the Limassol station that provides data only at 532 nm, the other three stations are equipped with a multiwavelength lidar system able to provide extensive aerosol properties at multiple wavelengths, namely three βaer (355, 532, 1064 nm) and two αaer (355, 532 nm), as well as aerosol intensive properties, namely the backscatter and extinction-related Ångström exponents (AEα355/532, AEβ355/532, AEβ532/1064 nm), the lidar ratio (LR) and additionally the linear volume (δv532) and particle depolarization ratio (δp532) at 532 nm. By using the Raman technique, as proposed by Ansmann et al., (1992), the βaer and αaer vertical profiles can be retrieved with uncertainties of ∼ 5 %–15 % and ∼ 10 %–25 %, respectively (Ansmann et al., 1992; Mattis et al., 2002). Therefore, the corresponding uncertainty of the retrieved lidar ratio values is of the order of 11 %–30 %, while the uncertainty for AEβ and AEα ranges between 0.02–0.04 and 0.03–0.08, respectively, as estimated by propagation error calculations.

Dusty cases analyzed in this study were selected based on the values of the aerosol optical properties δp532 and LR532 measured by lidar (Groß et al., 2013). Since pure dust layers are rare over the Mediterranean cities due to continental contamination by urban pollution or even biomass burning (BB) aerosols, a sufficiently lower δp532 value with respect to the pure dust values (e.g., Freudenthaler et al., 2009) should be considered to characterize an aerosol layer as a dusty one. Based on previous studies, the respective LR532 values for long-range-transported mixtures over the Mediterranean area are expected to range between 35 and -75 sr (Mona et al., 2006; Papayannis et al., 2009; Tesche et al., 2009; Groß et al., 2011; Ansmann et al., 2012; Nisantzi et al., 2015; Soupiona et al., 2018). Consequently, from the total set of Saharan dust events per station listed in the EARLINET database for the period 2014–2017, we considered for further analysis only the data meeting three basic criteria: (a) δp532≥0.16 in the free troposphere, (b) 35 sr ≤ LR532≤75 sr in the free troposphere and (c) the thickness of the detected layer to be 500 m at least. The critical height (in m a.s.l.) in which the first criterion was met was considered to be the base of the dust layer. This assumption was deemed necessary to be made since, usually, the lofted dust layers cannot be distinguished from the top of the planetary boundary layer (PBL), while the presence of urban haze and pollution decreases the δp values drastically down to 0.03–0.10 (Gobbi et al., 2000; Groß et al., 2013). The top of the dust layer was estimated as the height where the signals were similar to the molecular scattering (both δp532 and β532 tending to zero) in the free troposphere. For some cases of the Athens station, where depolarization measurements were unavailable, the values of the base and top were calculated from the Raman lidar signals, following the procedure proposed by Mona et al. (2006).

Moreover, a careful investigation of the air mass origin and dust transport path was performed by means of backward trajectory analysis. This analysis was carried out using the HYbrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model (https://ready.arl.noaa.gov/HYSPLIT_traj.php, last access: 7 October 2020; Stein et al., 2015) together with the GDAS (Global Data Analysis System) meteorological files (spatial resolution of 1∘×1∘ , every 3 h) as data input. The kinematic back-trajectories were calculated using the vertical velocity component given by the meteorological model with a 96–120 h pathway (4–5 d back). MODIS/Terra information (https://firms.modaps.eosdis.nasa.gov/map, last access: 7 October 2020) was also taken into account for the corresponding hotspots of possible fires and thermal anomalies along the trajectories (https://firms.modaps.eosdis.nasa.gov/map, last access: 7 October 2020, not shown here).

Thus, we ended up with 51 individual cases in total, of 30 min to 1 h averaged lidar profiles each (15 for Granada, 18 for Potenza, 12 for Athens and 6 for Limassol). For the region of Cyprus, the situation is more complex since Middle East dust outbreaks also occur frequently in addition to the Saharan dust events (Nisantzi et al., 2015; Kokkalis et al., 2018; Solomos et al., 2019). On top of that, dust particles originating from the Middle East proved to have different lidar ratio values than the corresponding observations over the Saharan desert (Mamouri et al., 2013; Kim et al., 2020). Taking this into account, dust cases over the Limassol station originating from Middle East regions were excluded from our study.

The air mass trajectory analysis based on HYSPLIT for each station reveals the origin of each observed layer (Fig. 1). In the majority of cases, air masses originate from western and northwestern Africa (Morocco, Mauritania, Algeria and Tunisia). At first glance, two occurrences seem to dominate: (i) trajectories that travel directly from the source to the observation stations and (ii) trajectories that circulate over the Mediterranean or the Atlantic Ocean (for the Granada and Potenza cases), Europe and the Balkans or even Turkey (for the Limassol and Athens cases) before reaching the observation stations.

To retrieve the aerosol dust mass concentration profiles, we used the β532 and the δp532 coefficients. Furthermore, by assuming that we have two aerosol types (dust and non-dust) inside the calculated β532 values, we separated the backscatter profiles into two components: the first arising from the contribution of the weakly depolarizing particles (δnd=0.05 for non-dust particles) and the second from the contribution of strongly depolarizing particles (δd=0.31 for dust particles). Then, the dust-related backscatter coefficient βd at 532 nm was obtained, following the procedure described by Tesche et al. (2009). The estimation of the height-resolved mass concentration (in kg m-3) of dust particles was based on the procedure described by Ansmann et al. (2012), using the following equation: 1massd=ρdvd/τdβdLRd, where in our study the coarse-particle mass density (ρd) was assumed equal to 2.6 g m-3, and a mean-volume-to-AOT ratio for coarse-mode particles, vd/τd, was calculated from AERONET measurements (https://aeronet.gsfc.nasa.gov/, last access: 7 October 2020) for each station during the period 2014–2017. Table 2 summarizes these values for the entire studied period, since only few cases were common in EARLINET and AERONET database. Regarding the LRd parameter, the mean LR values per station, as calculated from the lidar measurements, were used (see Table 2; Fig. 4c). These values are in good agreement with findings in the literature for long-range-transported Saharan dust events (Tesche et al., 2009; Guerrero-Rascado et al., 2009; Ansmann et al., 2012; Groß et al., 2011; 2013; Bravo-Aranda et al., 2015).

The SphInX software tool provides an automated process to carry out calculations from lidar data to obtain the aerosol microphysical properties and further to statistically evaluate the inversion outcomes. It has been developed at the University of Potsdam (Samaras, 2016) within the Initial Training for atmospheric Remote Sensing (ITaRS) project (2012–2016). SphInX operates with expendable precalculated discretization databases based on spline collocation and on lookup tables of scattering efficiencies using T-matrix theory (Rother and Kahnert, 2009). This is to avoid the computational cost which would otherwise limit the microphysical retrieval to an impractical point. The complex refractive index (CRI) is fed to the software separately for the real and imaginary parts, which then constitutes a grid combining the following default values: real part (RRI) [1.33,1.4,1.5,1.6,1.7,1.8] and imaginary part (IRI) [0,0.001,0.005,0.01,0.03,0.05,0.1]. A range of values for the effective radius (Reff), which occurs from the ratio of the total volume concentration (ut) and the total surface-area concentration (at), reff=3ut/at, is also needed to be predefined. The methodology applied here for spheroid-particle approximation is the same as presented in Soupiona et al. (2019). More specifically, the Raman lidar profiles were used as inputs for specific heights within the observed dusty layers and were averaged to produce the six-point dataset of the so-called 3βpar+2αpar+1δ setup. All cases fulfilling this setup were treated in parallel for retrieving their microphysical properties. Here, the Reff ranged between 0.01 and 2.2 µm, and the CRI grid was narrowed down to include only the values 1.4 and 1.5 for the real part (RRI), and the values 0, 0.001, 0.005 and 0.01 for the imaginary part (IRI), providing a total of eight possible combinations for the CRI grid (instead of the initial total of 42 for the CRI grid). These ranges were used after a careful investigation of the values of the aerosol optical and microphysical properties found in the literature concerning transported Saharan dust events (Dubovik et al., 2006; Weinzierl et al., 2011; Mishra et al., 2014; Veselovskii et al., 2016, 2020; Benavent-Oltra et al., 2017) in order to avoid retrieving less realistic dust-related size distributions and CRI values and to minimize the computational time. The outputs presented here are the RRI and IRI, the single scattering albedo (SSA) and the Reff.

The BSC-DREAM8b model (Basart et al., 2012), operated by the Barcelona Supercomputer Center (BSC-CNS; https://www.bsc.es/, last access: 7 October 2020) has provided operational forecasts since May 2009. The BSC-DREAM8b is a regional model designed to simulate and predict the atmospheric cycle of mineral dust aerosols. It is one of the most widely used and evaluated models for dust studies over northern Africa and Europe (see Jiménez-Guerrero et al., 2008; Papayannis et al., 2009; Basart et al., 2012; Amiridis et al., 2013; Tsekeri et al., 2017). The presented analysis includes vertical profiles of dust mass concentration simulations (0.3∘×0.3∘ horizontal resolution) and 24 vertical levels (from ground level to approximately 15 km in the vertical), corresponding to the studied cases and for time periods close to the measurement times, usually at 18:00 and 00:00 UTC, since the meteorological fields are initialized every 24 h (at 12:00 UTC) with the National Centers for Environmental Prediction (NCEP) global analysis (0.5∘×0.5∘), and the boundary conditions are updated every 6 h with the NCEP Global Forecast System (GFS) (0.5∘×0.5∘).

The aerosol effects on solar and terrestrial radiation are usually quantified through the so-called aerosol radiative forcing (ARF). The ARF defined here as the perturbation in flux in the atmosphere caused by the presence of the dusty layers in relation to that calculated under clear-sky conditions can be expressed as (Quijano et al., 2000; Sicard et al., 2014; Mishra et al., 2014) 2ARF(z)=ΔFdusty(z)-ΔFclear(z), where the net flux, ΔF, at a level z is the difference between the downwelling and upwelling flux, F↓ and F↑, respectively: 3ΔF(z)=F↓(z)-F↑(z). These fluxes (in W m-2) are calculated separately for SW and LW radiation sources and assuming that the amount of the incoming solar radiation at the top of the atmosphere (TOA) is equal for both cases with and without the presence of dust aerosols. Therefore, the net ARF, ARFNET(z), is expressed as 4ARFNET(z)=ARFSW(z)+ARFLW(z). Based on this definition, the ARF at a given altitude will be positive when the aerosols cause a heating effect and negative when they cause a cooling effect. Finally, the ARF within the atmosphere (ARFAtm) can be defined as the net difference between ARF at the top of the atmosphere (TOA) and the bottom of the atmosphere (BOA), denoted here as ARFTOA and ARFBOA, respectively: 5ARFAtm=ARFTOA-ARFBOA. Our analysis was based on these equations for estimating the radiative forcing by means of direct and diffuse irradiances of an accurate radiative transfer model combining lidar measurements and dust concentration simulations.

Before using the vertical dust mass concentrations profiles retrieved from (i) BSC-DREAM8b model simulations (Scheme A) and (ii) lidar measurements as calculated from Eq. (1) (massd), (Scheme B) as inputs to the libRadtran model, we performed a day-by-day comparison between them. Due to the different spatial and vertical resolution between the modeled and the lidar profiles, both profiles were degraded to the fixed height levels of the OPAC dataset (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 35 km).

Figure 3 shows a Taylor diagram of the mass concentrations simulated by the BSC-DREAM8b model against the lidar-retrieved ones. The azimuthal angle presents the correlation coefficient, the radial distance presents the normalized standard deviation (SD) of each point and the root mean square error (RMSE) is proportional to the distance from the point on the x axis identified as “calculated”, which, depicted by a black point at the (1,0) cross section, indicates the lidar-retrieved aerosol mass values representing the reference point. The normalization of the SD is performed with respect to the calculated values. In 66 % of the cases there is a good correlation (r>0.6), and, consequently, a good prediction of the shape of the vertical distribution is achieved, while in 96 % of the cases the model gives lower concentration values (normalized SD < 1), revealing an underestimation in the intensity and the mass concentration of the events. Therefore, we report a mean underestimation of the mean mass concentration values of the BSC-DREAM8b of the order of 31 %. However, we should take the following into consideration: (i) the spatial resolution, where the lidar observations are considered as point measurements, while the simulations represent uniform pixels of 0.3∘ resolution; and (ii) the temporal resolution, where the lidar-retrieved profiles are hourly averaged, while the model-derived profiles are instantaneous results, saved every 6 h.

By further comparing the modeled mass vertical profiles to the ones calculated by lidar, we report that the mean center of mass (in km) estimated from BSC-DREAM8b profiles is 0.6 km lower than the one calculated from the lidar measurements (2.6±1.0 km and 3.2±1.1 km respectively). The maximum concentration (peak) is usually found in the region 2–3 km, both in the modeled and the observed data. The BSC-DREAM8b, having a significantly lower vertical resolution compared to the lidar, predicts smoother profiles of dust layers by spreading the layer's base to lower altitudes (∼ 1 km, in 100 % of the cases) and the top at higher altitudes (in 86 % of the cases) compared to the observed ones. These remarks are in line with the previous studies of Mona et al. (2014) and Binietoglou et al. (2015), who reported discrepancies concerning the base, the top layer height and extinction profiles and good agreement in terms of profile shape between the BSC-DREAM8b and observations. However, since fixed height levels of the OPAC dataset were finally used in libRadtran for the ARF simulations of the three schemes, having significantly lower vertical resolution compared to the initial lidar profiles, these discrepancies in height were smoothed out.

The evaluation of the performance of the model was undertaken by statistical means. The relative root mean square error (rRMSE), the relative mean bias error (rMBE), the correlation coefficient (r) and the normalized SD were calculated in order to numerically quantify the performance of the global irradiance recorded by pyranometers and simulated from the three schemes. Table 3 shows the statistical results for the modeled global irradiance values versus the reference 1 min pyranometer measurements for both locations (Granada, Athens) and the three schemes at 25∘, 45∘ and 65∘ SZA. All scheme simulations perform remarkably well, with rRMSE values ranging from 8.3 % to 16.2 % and rMBE values between 0 % and 15.2 %. In general, the rRMSE is slightly higher at Granada, mainly for Scheme A. According to this statistic, the libRadtran outputs with the best performance are those obtained by Scheme C as input followed by Schemes B and A, respectively. This order is the same for the rMBE values with the exception of Scheme A at Athens. The correlation coefficient r depicts the good performance of the radiative transfer model for the three schemes and the two locations. All simulations present a value of r>0.95, with minor differences (below a 10 %) in the normalized SD values with respect to the pyranometer global irradiance values. A slight overestimation is observed for all scheme outputs at Granada (norm SD>1). Conversely, this overestimation is no longer evident in the modeled global irradiance for Athens. However, it is important to note the good performance of the Scheme B despite the high number of various parameters involved in it.

For each case studied, the mean δp532, mean LR532 and AOT532 values were calculated inside the dust layers (see Sect. 2.2) as shown in Fig. 4a–d. The corresponding SD values give an indication of the variability of these parameters from the base to the top of the dust layer. Figure 4a shows the aerosol geometrical properties for the detected layers one by one, per station and per year. The mean values of the base and top height of the dust layers per station, along with their SD, are marked with horizontal bounded lines. At the four sites (Granada, Potenza, Athens and Limassol) mean layer thicknesses of 3392±1458, 2150±1082, 1872±816 and 1716±567 m were calculated, respectively. We also found mean δp532 values of 0.24±0.05, 0.26±0.06, 0.28±0.05 and 0.28±0.04 (Fig. 4b) and indicative mean AOT532 values of 0.40±0.31, 0.11±0.07, 0.12±0.10 and 0.32±0.17 (Fig. 4d), respectively. Similar mean LR532 values of around 51 sr (Fig. 4c) were found for all stations. The Granada station has the minimum mean value for layers' base height (1567±788 m a.s.l.) and the maximum for top height (4960±975 m) and layers' thickness. Concerning the LR values, no remarkable deviations were observed among the four stations, having mean values around 51 sr, which are in very good agreement with findings in the literature (Tesche et al., 2009; Ansmann et al., 2012; Groß et al., 2011; 2013). The largest indicative mean AOT value, equal to 0.40±0.31, observed over Granada station for the total studied period is in accordance with the geometrical properties (Fig. 4a) that depict thick dust layers in the majority of the cases.

Considering Granada's station as representative of the western Mediterranean region, Potenza of the central Mediterranean region and Athens and Limassol stations of the eastern Mediterranean region, a dust aerosol mode classification per region can be made. For this purpose, the mean AOT532 versus the AEβ532/1064, giving an indication of the aerosol particle size in the atmospheric column for each region, is shown in Fig. 5. A wide spread of the AOT values at moderate to low AEβ532/1064 values (between 0 and 0.6) observed in the western Mediterranean region demonstrates that the dust size distribution in this area is dominated by coarse-mode particles during events of different intensities. On the other hand, the presence of dusty layers in the central and eastern Mediterranean regions can be associated with higher AEβ532/1064 values (even up to 1.5) and, consequently, with the presence of fine-mode particles and lower dust loads. Our findings verify that the longer the time and distance of dust transport is, the more likely it is for the dust aerosols to be mixed with background ones in the eastern Mediterranean (Groß et al., 2019; Soupiona et al., 2019).

In terms of the aerosol size distribution, the scatter plot of Fig. 5 allowed k-means clustering to be performed (Arthur and Vassilvitskii, 2007) in order to define three physically interpretable aerosol size distributions: (a) fine mode, with AEβ532/1064>0.6; (b) coarse mode, with AEβ532/1064≤0.6 and AOT532 between 0 and 0.2; and (c) AEβ532/1064 values smaller than 0.6 attributed to large AOTs (between 0.2 and 0.8), representative of extreme dust events. It seems that the majority of these extreme dust outbreaks occur over the western Mediterranean region, more likely due to its location close to the African continent. For example, Fernández et al. (2019) recently reported an unprecedented extreme wintertime Saharan dust event during February 2017 over the whole Iberian Peninsula, with AOTs > 0.2 (675 nm) and AE values around zero. More studies referring to the occurrence of extreme dust events over the aforementioned area can be found in literature (Cachorro et al., 2008; Guerrero-Rascado et al., 2009).

Based on the High Spectral Resolution Lidar (HSRL) classification presented by Groß et al. (2013), the intensive aerosol quantities LR532 versus δp532 were plotted, identifying three of the six existing clusters in our data (Fig. 6). The first cluster (green marks and error bars) represents a mixing state of Saharan dust and BB aerosols, with a large spread in mean LR values and low mean δp532 values (40 sr ≤ LR532≤75 sr, 0.16≤δp532≤0.19). The second one (red marks and error bars) is attributed to mixed Saharan dust, where dust aerosols are dominant, but urban/continental, marine or even pollen aerosols are also possibly present (40 sr ≤LR532≤ 65 sr, 0.20≤δp532≤0.29). The third cluster (orange marks and error bars) is attributed to pure Saharan dust aerosols (45 sr ≤ LR532≤60 sr, 0.30≤δp532≤0.36). The most populated and, consequently, the most common among those three clusters is the red one, as expected, due to the frequent mixing of dust aerosols with continental ones (Papayannis et al., 2009). The range of our measured δp532 values as indicated by the horizontal error bars in Fig. 6 shows an overlap between the three identified aerosol clusters, evidencing a more realistic transition from one cluster to the other and bridging the gap especially between green and red clusters from the HSRL classification.

Table 4 summarizes the mean values of the aerosol geometrical, optical and microphysical properties of the three identified clusters along with their SD (5 cases for BB and Saharan dust, 8 cases for Saharan dust, 29 cases for mixed Saharan dust). A synergistic approach of HYSPLIT (trajectories of 120 h backward for each case) and Google Earth (distance calculator) tools allowed us to estimate the distance traveled (in km) to the respective sites and the mixing hours per cluster. Specifically, the term of mixing refers to the hours the air masses traveled after leaving the African continent. We can see that the Saharan dust cluster presents the lowest mixing with other air masses (26±13 h), compared to the other clusters (41±26 h for the BB and mixtures and 66±41 h for the mixed Saharan dust cluster). Moreover, the air masses of the Saharan dust cluster seem to travel faster than those of the other two clusters, although covering a greater distance (4845±2825 km) at the same time (within 120 h). Now, the main difference between the two remaining clusters (BB and mixtures and mixed Saharan dust) is attributed to the mixing hours. The air masses of the latter cluster remain 15 h longer and circulate over the Mediterranean and Europe, so they are probably enriched with other types of aerosols.

Concerning the aerosol optical properties, the β532 and α532 show lower values for BB and dust and for mixed Saharan dust cases (1.10±0.15×10-3 km-1 sr-1, 0.47±0.28 km-1 and 1.24±0.80×10-3 km-1 sr-1, 0.74±0.48 km-1, respectively) and higher values (1.54±1.05×10-3 km-1 sr-1, 0.80±0.27 km-1) for the Saharan dust cluster. Therefore, higher AOT532 values (0.32±0.25) were found for the latter cluster compared to the others, due to the higher dust burden of these events over the affected sites. The highest δp532 values (0.32±0.02) indicate the arid origin and the coarse mode of pure Saharan dust layers (Freudenthaler et al., 2009) of the corresponding cluster. No direct information can be extracted from the similar LR532 values about the mixing state of the aerosol layer, except that the range of the SD narrows as the mixing decreases. However, for the cases for which observations at 355 nm were available, it seems that the color ratio (namely the LR35/LR532) converges to unity for the Saharan dust cluster, indicating the absence of spectral dependence for the case of pure dust (Müller et al., 2007; Veselovskii et al., 2020). For these cases also, the AEβ355/532 becomes closer to zero, having a mean value of 0.35±0.45.

We also summarize the changes in mean microphysical properties estimated with the SphInX tool for all the cases of each of the three identified clusters. The BB and Saharan dust cluster has a lower mean Reff value (0.293±0.074 µm) due to the fine structure of BB aerosols included in the layer, while a mean Reff of 0.360±0.081 µm corresponds to the cluster of mixed Saharan dust and a slightly larger value (0.387±0.070 µm) corresponds to the Saharan dust cluster. The values for RRI, IRI and SSA at 532 nm were similar for the two clusters that do not include BB aerosols, whilst the presence of BB aerosols of the first cluster leads to higher RRI and IRI values and lower SSA, results that are in good agreement with the ones reported in Petzold et al. (2011) over Dakar, for mineral dust and dust mixed with anthropogenic pollution.

As mentioned previously, there is a shortage of papers in the literature about the role of dust in the Earth's radiation budget. Since very few in situ measurements of ARF effects and heat fluxes are available, especially in the Mediterranean (Bauer et al., 2011; Meloni et al., 2018), we are restricted to performing simulations to quantify the role of dust aerosols in radiative forcing in the studied regions. The mean ARF is calculated during this simulation, running the libRadtran radiation code twice: with (index “dusty” in Eq. 2) and without (index “clear” in Eq. 2) the presence of free tropospheric dusty aerosol layers. For all cases, the vertical profiles of ARF starting from ground level/bottom of atmosphere (BOA) up to the top of atmosphere (TOA) in the SW and LW ranges were simulated using the three aforementioned schemes.

A negative forcing of aerosols both at the BOA and TOA is noted in the SW range, as presented in Fig. 7a, which depicts the mean ARF of all cases per scheme, over the Mediterranean Basin. Our results indicate a presence of less absorbing aerosols, thus having a cooling behavior. Depending on the dust optical properties and load intensity, ARF values at the BOA range from -40 to -13 W m-2 at SZA 25∘, from -43 to -14 W m-2 at SZA 45∘ and from -44 to -15 W m-2 at 65∘. At the TOA, the corresponding ranges per SZA are -9.5 to -1.4 W m-2 (25∘), -16 to -3.3 W m-2 (45∘) and -24.3 to -6.9 W m-2 (65∘). Similarly, in the SZA independent LW range (thermal spectral range), the ARF values range from +1.6 to +4.6 W m-2 for the BOA and from +0.8 to +3.6 W m-2 for the TOA. Our estimations are consistent with results obtained by other findings in the literature for Saharan dust aerosols over the Mediterranean region. Specifically, Sicard et al. (2014) found that the SW radiative forcing (RF) at the BOA always has a cooling effect, varying from -93.1 to -0.5 W m-2 while the corresponding LW RF always has a heating effect, varying from +2.8 to +10.2 W m-2. They also concluded that dust aerosols have a cooling effect in the SW spectral range at the TOA, with a RF ranging from -24.6 to -1.3 W m-2, while at the TOA the LW RF varies between +0.6 and +5.8 W m-2. Meloni et al. (2003) found at the island of Lampedusa instantaneous RF of -70.8 W m-2 at the BOA and -7.5 W m-2 at the TOA within the range 300–800 nm for an event with an AOT of 0.51 at 415 nm. For the same location and for another strong Saharan dust outbreak (AOT500=0.59), Meloni et al. (2015) reported a total (SW + LW) radiative forcing of -48.9 W m-2 at the BOA, -40.5 W m-2 at TOA and +8.4 W m-2 within the atmosphere for SZA = 55.1∘. A negative radiative effect reaching down to -34.8 W m-2 at the BOA in the Mediterranean area was also recently reported by Gkikas et al. (2018) for the studied period March 2000–February 2013.

Variations among these values are expected since they strongly depend on the different AOTs, mass estimations and extinction profiles. Estimations retrieved from Scheme B are expected to give higher values compared to those given from Scheme A, as also revealed by Fig. 3. The ARF in the LW spectral region is opposite in sign and significantly lower in absolute values than in the SW region. The difference between the TOA and BOA ARF, with the former only weakly perturbed and the latter much stronger, can be attributed to the heating within the troposphere, since the presence of the dust aerosols mainly leads to a displacement of the surface's radiative heating into the dusty layer. We also noticed that the low values of the reflected solar flux are partially offset by the absorption of upwelling LW radiation. Finally, in the LW spectral region, the mean ARF values at the BOA (Scheme A: +1.6±1.6 W m-2, Scheme B: +4.6±4.7 W m-2 and Scheme C: +2.9±9.4 W m-2) are close to those at the TOA (Scheme A: +0.8±0.9 W m-2, Scheme B: +3.6±4.4 W m-2 and Scheme C: +1.2±6.2 W m-2) but moved a little to more positive values. As a result, the ARFAtm (Eq. 5) is positive during the diurnal circle, yielding net radiative heating of the dust layers.

The mean net heating rate within the atmosphere, calculated by adding algebraically both rates in the SW and LW spectral ranges, is presented in Fig. 7b. Here, the net heating rate is clearly dependent on the available solar radiation and increases with SZA due to the low incoming solar radiation reaching the BOA during afternoon hours (SZA 65∘). Our estimations are in accordance with the fact that as the SZA increases, the optical path of the SW radiation grows significantly, increasing the attenuation of the direct radiation while generating a higher fraction of the diffuse radiation. This effect is more pronounced at the BOA, where the intensity of the heating rate is reduced with increasing SZA, since fewer photons are available to heat the dust layers. The net heating rate values for Scheme A are as follows: -0.05±0.04 K d-1 (25∘), -0.04±0.03 K d-1 (45∘) and 0.00±0.02 K d-1 (65∘). Similar to slightly higher values are observed for Scheme B as follows: -0.07±0.06 K d-1 (25∘), -0.04±0.03 K d-1 (45∘) and -0.02±0.02 K d-1 (65∘). For Scheme C, we report higher values of this parameter during the diurnal circle. More precisely, the net heating rate is almost 1.5 times higher at 25∘, 2 times higher at 45∘ and around 0.8 times higher at 65∘, compared to the aforementioned schemes. Greater sensitivity in the SZA appears in Scheme B as it results from the line slope.

In order to further explain the difference of sign in the net heating rate of Scheme C, compared to the two others presented in Fig. 7b, we plotted the aforementioned parameter along with the base layer height, the AOT532 and the layer thickness of each case as presented in Fig. 8. Taking into account that the effect of net heating rate occurred by the dusty cases, from negative to positive values, is more pronounced close to the surface at small SZA values, the estimations of the net heating rate at the BOA at 25∘ SZA were selected to be presented in this graph. It becomes clear that the sign of the net heating rate at BOA depends on the dust vertical structure and the AOT. More precisely, the majority of the cases with low AOT532 values (≤0.2) and low layer thickness (≤2 km) give negative net heating rate values. Additionally, the higher the AOT is, the higher the absolute value of the net heating rate is. Concerning the base layer height, it plays a key role in the absolute net heating rate of each case, since dust layers close to the ground have higher absolute net heating rate values. For example, let us examine two dust events that occurred during the same month (August). The first one with a base of 2.8 km, 0.73 km thickness and AOT532 equal to 0.01 has a heating rate of -0.17 K d-1, while the second with a base of 3.8 km, 0.66 km thickness and AOT532 equal to 0.02 has a net heating rate of almost zero (-0.03 K d-1). In another comparison, net heating rate values of -0.02 K d-1 versus +0.09 K d-1 are reported for two layers during summertime that almost have the same base (2.6 and 2.5 km) and thickness (2.3 and 2.4 km) but different AOT532 values (0.08 and 0.34, respectively). Finally, a combination of high AOT532 (0.21–0.83) and high thickness (2.1–5.5 km), along with low base height (1.0–1.5 km), gives high net heating rate values with a positive sign, ranging from +0.06 to +0.26 K d-1.

Figure 9a–c depict the same results as in Fig. 7a but for each of the three identified clusters: BB and dust, mixed Saharan dust and Saharan dust. The ARF in the SW range is negative both in the BOA and TOA for all clusters and is dominated by large dust particles for the cluster of the Saharan dust episodes (see Table 4; Fig. 9c), (Scheme A: -22.5±16.7 W m-2, Scheme B: -38.3±29.0 W m-2 and Scheme C: -49.2±50.9 m-2 for BOA and Scheme A: -2.5±2.1 W m-2, Scheme B: -4.9±4.1 W m-2 and Scheme C: -12.1±14.4 m-2 for TOA; SZA 25∘), whereas dust layers mixed with biomass burning aerosols have a significantly lower cooling effect (Fig. 9a; Scheme A: -6.2±4.0 W m-2, Scheme B: -18.2±11.3 W m-2 and Scheme C: -4.8±3.5 W m-2 for BOA and Scheme A: -0.5±0.4 W m-2, Scheme B: -2.0±1.6 W m-2 and Scheme C: -0.7±0.5 m-2 for TOA; SZA 25∘) for each of the three applied schemes. ARF seems to be inversely proportional to the mixing ratio, since higher absolute values are estimated for less mixed dust layers. This can directly be linked to the fact that ARF values strongly depend on αpar, βpar and AOT that have much higher values for the Saharan dust cluster, as already reported (Table 4). Focusing on the SW range, the cooling effect for Scheme A of the Saharan dust cluster is up to 3 times higher compared to the BB and Saharan dust one, whilst the cooling effect for Scheme C of the former cluster is up to 10 times higher compared to the latter. The cooling effect of Scheme B also becomes stronger with the decreasing mixing state but at a lower magnitude (the former cluster is almost 2 times higher compared to the latter).

Hence, even though the studied cases included in the Saharan dust cluster usually have higher mass concentration values than the other cases, as predicted by BSC-DREAM8b (Scheme A), the model still seemingly underestimates the intensity of strong transported dust episodes over the observation stations. In contrast, Scheme C is the most sensitive to the mixing state of the aerosol layers. To explain this result one should consider that on the one hand, spheroidal particles such as dust have larger dimensions than spherical ones such as BB aerosols and thus lead to larger AOTs (Haapanala et al., 2012) and consequently to increased negative ARF, and on the other hand, Schemes A and B involve greater assumptions concerning dust particles than Scheme C.

Finally, our interest is focused on the vertical ARF profiles from the surface (a.s.l.) up to 10 km height in the free troposphere, where airborne dust is usually found, as estimated by Scheme C at 45∘ SZA per station. The ARF profiles in the SW region, presented in Fig. 10a–d, follow the aerosol extinction vertical structure. The ARF values at the BOA are high in absolute values with a cooling behavior and decrease with increasing height, while the magnitude is proportional to the aerosol load in the whole atmospheric column. Specifically, the ARF ranges from -150.0 to -1.9 W m-2 for Granada, from -38.1 to -3.7 W m-2 for Potenza, from -64.8 to -13.2 W m-2 for Athens and from -90.3 to -28.4 W m-2 for Limassol. The corresponding ranges of α532 are 0.286–0.029, 0.268–0.088, 0.135–0.078 and 0.547–0.214 km-1, respectively. Peaks in α532 are observed usually between 2 and 6 km a.s.l., indicating the intrusion of dust that corresponds to a decrease in the solar radiation reaching the surface.