Samples were collected and tephra loading per unit area measured at seven locations (Fig. 1 and Table 1). They were oven-dried at 110 ∘C for 12 h and analysed in the sedimentology laboratory at INGV-OE, in Catania (Italy). The individual grain-size distributions (GSDs; available in the Supplement in Fig. S1) were measured optically at a 1Φ-interval through the CAMSIZER^® (Retsch Technology), covering the range from -5 to 5Φ (where d = 2-Φ, with the diameter d in millimetres). Although field measurements are commonly used for determining the total erupted mass (TEM) by integrating the isomass lines (Bonadonna and Costa, 2012, 2013), the paucity of samples with their wide dispersion (Fig. 1) limits the reliability of the estimation based on field observations only. However, on the basis of the field data analysis, Andronico et al. (2015) estimated a TEM of 1.3 ± 1.1 × 109 kg making use of the Weibull distribution method (Bonadonna and Costa, 2012, 2013). Then, combining the field-derived TEM with the paroxysmal duration (∼ 50 min), they calculated an average MER of 4.5 ± 3.6 × 105 kg s-1. Furthermore, considering the climax phase only (i.e. from 09:55 to 10:14), the MER reached 106 kg s-1, ejecting more than 80 wt % of the erupted mass (Donnadieu et al., 2017). It is worth noting that such MER estimations represent average (or peak) values for the entire duration of the paroxysmal phase without considering its time evolution (i.e. the variation of eruption intensity). Indeed, the time-series MER can be assessed from the relationships between MER and the column height (e.g. Mastin et al., 2009; Degruyter and Bonadonna, 2012; Woodhouse et al., 2013; Folch et al., 2016) and from velocity variations at the vent recorded by VOLDORAD 2B.

The simultaneous record of the eruption from both satellites and ground-based instruments permits retrieval, on the one hand, of the plume spreading and airborne ash mass dispersal (see Animation A1 in the Supplement), collected by the Spinning Enhanced Visible and Infrared Imager (SEVIRI) on board the geostationary Meteosat Second Generation (MSG) satellite. The Moderate Resolution Imaging Spectro-radiometer (MODIS) aboard the NASA-Aqua polar-orbit satellite was also used to describe the eruption features (Corradini et al., 2016). On the other hand, concerning ground-based instruments, the X-Radar (Montopoli, 2016; Vulpiani et al., 2016) and the visible/thermal cameras (Corradini et al., 2016) provided time-series data of the plume height and the erupted mass.

The available data mentioned above were integrated through a multi-disciplinary approach in Corradini et al. (2016) to improve the volcanic cloud retrievals and the source characterization, and to generate new products. In particular, the satellite observations (Fig. 3) showed the formation of the two distinct volcanic clouds described in Sect. 2. Although both spread north-eastwards, one reached ∼ 6 km a.s.l., being mainly made of ash (ash cloud – AC), and therefore retrieved in terms of airborne ash mass and cloud altitude. The second cloud was higher (∼ 11 km a.s.l.) with enough ice/gas droplets (ice/gas cloud – IC) to significantly alter the cloud characteristics, blinding the satellite from any ash mass measurement (Prata and Kerkmann, 2007). Initially, the clouds were united and split out over the Calabria region (around 11:00). In a final stage, the AC reached the Apulia region, whereas the IC moved over the Ionian Sea towards Albania (around 14:00). In terms of mass, Fig. 4 shows ash was dominant from the onset of the eruption until 11:30, and then ice replaced ash. In fact, from SEVIRI retrievals, ash was likely released between 10:00 and 12:00 prior the emitted water vapour being transformed into ice (i.e. 11:00–12:45). This is also shown in Fig. 4, where ice formation starts later than SO2 and ash emission. SO2 was released all along the eruption (i.e. 10:00–12:30), although with a lower contribution than ash and ice.

The data integration presented in Corradini et al. (2016) permits us to reduce the uncertainties associated with the volcanic cloud top height, the ash/ice/SO2 masses (Fig. 4), and the aerosol optical depth (AOD) retrievals. On the basis of the satellite and X-Radar data, Corradini et al. (2016) improved the mass estimation of 30 % and reported a X-Radar-derived TEM of ∼ 3.0 × 109 kg with a PM20 fraction between 1 and 2 wt %, that is ∼ 30–60 t. The source characterization can also be better described by means of the ESP and the eruptive phases. The plume height time series was recorded from the visible cameras at INGV-OE, indicating values from the NSEC (∼ 3300 m a.s.l.) to ∼ 11 km a.s.l., with a rapid increase around 09:30 followed by a decay at 10:20.

The VOLDORAD 2B radar is a pulsed Doppler radar operating at 23.5 cm wavelength (L-band) allowing tephra from block-sized to lapilli-sized to be detected. VOLDORAD 2B has continuously monitored Etna's summit craters since 2009 (Donnadieu et al., 2015, 2016) at 3 km from the NSEC (La Montagnola station). Inferred radar parameters (e.g. backscattered echo power) are proportional to the quantity of tephra detected through the radar beam. In addition, the along-beam radial velocities permit lava fountains from being observed at high time resolution (i.e. 0.2 s), inferring near-source detection of the ejection velocities by means of the following equation (Freret-Lorgeril et al., 2016; Donnadieu et al., 2017): Ve=vr+sin⁡θ≈3.89vr+, where Ve is the ejection velocities (in m s-1), vr+ is the radial velocity (in m s-1), and θ is the elevation angle of the radar beam (here θ = 14.9∘). Such an approach is relevant for integrating the time-dependent ejection velocities with the corresponding observed eruptive column heights. In particular, we used the VOLDORAD 2B data associated with the 23 November 2013 eruption to better constrain the eruption phases' characterization.

The seven field samples are not sufficient for assuming the field-derived TGSD as the full spectrum TGSD (Andronico et al., 2014; Beckett et al., 2015; Bonadonna et al., 2015; Costa et al., 2016a; Spanu et al., 2016). Although such a field-based TGSD is being biased toward coarse ash, we first estimated the TGSD (hereinafter Field TGSD; Fig. 5) from the individual GSDs using the Voronoi tessellation method (Bonadonna and Houghton, 2005). However, the Field TGSD needs to be better characterized prior to being used within atmospheric ash dispersal models. Considering the Field TGSD representativeness on the grain-size spectrum (i.e. -5 to 5Φ; Sect. 2.1), we used the X-Radar retrievals to constrain the mass relative to coarse and fine ash (i.e. -1 to 5Φ; Corradini et al., 2016). The X-Radar-derived TGSD is inverted from the particle-size distribution (PSD), given as ash number density distribution (Corradini et al., 2016). It is worth noting that we considered a spatial and temporal average of the X-Radar-based PSD for the whole event. The average takes in input each PSD estimated from each single radar resolution volume delineated by horizontal angle, vertical angle, and range distance at each available time step for the airborne ash mass seen by the radar. We converted the PSD into number of particles per unit of volume with the particle-size bins. Then, by means of the volume and density associated with the size bins, we calculated the mass density distribution (hereinafter Radar TGSD; Fig. 5). However, we would like to highlight that retrieval of Radar data is done assuming a Gamma distribution for the number particles per unit of volume for each particle size interval. Then this distribution is converted to express the mass fraction as a function of Φ. In particular, since a single Gamma distribution is not able to adequately describe large size spectra, a Gamma distribution, with different parameters, is assumed in each particle size range of fine ash, coarse ash, small lapilli, and large lapilli, so the final total distribution is a combination of several gamma distributions. However, such an empirical derived distribution can be approximated using other distributions, such as a lognormal or a Weibull distribution. The latter point will be investigated in future studies.

It is worth noting that the Field and Radar TGSDs are distributions observed through their own grain-size window, which explains the substantial difference in shape (Fig. 5). It follows that assessing accurately the TGSD covering both windows can be done by integrating the Field and Radar TGSDs only. Although, in principle, their integration is possible, the grain-size windows' discrepancy prevents merging of the Field and Radar TGSDs without knowing their relative weighting averages. We determined empirically the weight combination by integrating the distributions at regular intervals (i.e. from full Field TGSD to full Radar TGSD). The resulting distribution (i.e. -5 to 5Φ; hereinafter Integrated TGSD; Fig. 5) is obtained, best fitting the tephra loading at the sampled sites.

However, due to the instrument/method grain-size limit, none of the three TGSDs (Field, Radar, or Integrated TGSD; Fig. 5) contains enough PM20 to reproduce the far-travelling airborne ash mass retrieved by satellite. We assessed the tail of the Integrated TGSD (i.e. Φ ≥ 6) by modifying empirically the PM20 fraction, adding mass into the corresponding classes. We calculated the fractions based on an empirical power-law dependence of the classes with Φ through the following parameterization: XΦi=XΦ5×γΦi-Φ5, where X(Φi) is the fraction (in wt %) allocated to the ith bin, X(Φ5) is the fraction obtained for Φ = 5, and γ is the empirical factor (γ < 1). The explored γ values span from 0.1 to 0.7, giving, respectively, PM20 fractions between ∼ 0.6 and 10.7 wt % of the TEM. The best fraction to use within the TGSD (hereinafter Whole TGSD; Fig. 5) is chosen as best fitting the satellite retrievals.

To furnish the ESPs required by the FALL3D tephra dispersal model, we used the FPlume integral plume model (Folch et al., 2016) describing the eruptive column based on the buoyant plume theory (Morton et al., 1956). FPlume solves a set of 1-D cross-section-averaged equations for mass, momentum, and energy conservation in the eruption column, accounting for wind coupling, air moisture, particle re-entrainment, and ash aggregation effects (Folch et al., 2016). Among the source conditions, FPlume feeds into FALL3D by describing the mass flow rate for each particle bin and the vertical distribution within the column. As inputs, FPlume uses the TGSD, initial magma temperature, and water content (Table 2) to calculate the mass released per unit of time within the column. Indeed, FPlume uses the TGSD to solve the mass conservation equation for each class distributing along the column. Then, the mass for each particle class at each level is transported laterally using FALL3D.

In our case, Etna's magmas have a temperature of 1300 K with ∼ 2.5 wt % of water (Carbone et al., 2015; Spilliaert et al., 2006). FPlume calculates MER from the column height (or vice versa) for a given wind profile (Folch et al., 2016) by describing the air mixing within the plume through two turbulent air entrainment coefficients (i.e. radial – α and cross-flow – β; Bursik, 2001; Kaminski et al., 2005; Suzuki and Koyaguchi, 2015; Folch et al., 2016; Costa et al., 2016b). Here, α and β are obtained empirically through the solution of an inverse problem best-fitting the erupted mass derived from the field measurements (Poret et al., 2017). Ash aggregation can be considered negligible during Etna eruptions, with less than 2 wt % of the fine ash removed by aggregation. For this reason, we did not consider such a process in this study. The effects of the typical uncertainties associated with the input parameters of FPlume on the source term characterization are described in Macedonio et al. (2016).

FALL3D is used for simulating tephra dispersal and is a 3-D time-dependent Eulerian model based on the advection–diffusion–sedimentation equation computed over a terrain-following domain (Costa et al., 2006; Folch et al., 2009). Besides the ESPs, FALL3D needs the time-dependent meteorological fields over the computational domain for the corresponding period (i.e. from 00:00 on 23 November up to 00:00 on 29 November 2013). The first series of simulations are run by means of a local high-resolution meteorological database (ARPAE from INGV-OE) to better constrain the computed tephra loadings against the field measurements in proximal and medial areas (Fig. 1 and Table 1). Indeed, ARPAE provides a 7 km × 7 km spatial and 15 min temporal resolution over the domain highlighted in Fig. 1. Then, FALL3D internally interpolates the meteorological data over a grid set at 1 km × 1 km resolution. The parameterizations used for the simulations with the ARPAE database are summarized in the Appendix. The related main atmospheric profiles (e.g. temperature, air moisture, and wind speed) over the NSEC are displayed in Fig. 6.

The second series of simulations aims at reproducing the satellite retrievals, expanding the computational domain to Albania. The ARPAE data do not cover such a domain, for which we use the meteorological fields from the European Center for Medium-Range Weather Forecasts (ECMWF, ERA-Interim-Reanalysis; hereinafter ERA-Interim). They provide a 6 h interval for 37 pressure levels of data at 0.75∘ horizontal resolution. For computational cost reasons, the internal grid resolution into FALL3D is set at 5 km × 5 km, which is still consistent with the satellite data resolution (3 km × 3 km at nadir). The parameterization used with the ERA-Interim database is summarized in the Appendix.

The consistency between the two databases is checked by adding the profiles retrieved over the NSEC with ERA-Interim in Fig. 6. Although ARPAE and ERA-Interim tend to have the same temperature and wind speed patterns, the air moisture from ERA-Interim is slightly lower than ARPAE for 3–6 km a.s.l. and higher for 7–11 km a.s.l. These observations are not significant to produce a substantial effect on the simulations. Moreover, Fig. 6 also shows the conditions over the Albanian capital (Tirana). With such meteorological conditions, airborne tephra needs 4.5 h to be transported from Etna to Albania (Fig. 6), being consistent with the pilot report mentioning ash. Wind speed is moderate to strong, with higher velocities near the volcano than at Tirana. As indicative values at 9 km a.s.l., we report ∼ 48 and ∼ 45 m s-1 over the NSEC (at 09:30) for ERA-Interim and ARPAE, respectively, and ∼ 34 m s-1 over Tirana at 14:00. Besides the velocities, the wind direction (Fig. 6) shows a strong north-easterly orientation over the NSEC, which is consistent with the tephra dispersion towards Calabria. The profiles indicate a substantial variation between middle (5–6 km a.s.l.) and high altitudes (> 7 km a.s.l.), which probably resulted in the different spreading orientations for the two volcanic clouds (AC and IC) at their own altitudes (Fig. 3). Besides the profiles, the consistency for using alternatively the two meteorological databases is checked by constraining the simulations with ERA-Interim to converge the TEM towards the same value as for the Integrated TGSD and the ARPAE database.

Tephra dispersal simulations are commonly carried out using the field-based TGSD and assuming a constant average column height (or MER) for the entire duration of the paroxysmal phase (Fig. 7a). However, it is evident that eruption intensity varies substantially with time and consequently the column height (e.g. Scollo et al., 2014, 2015). To account for such variability, we discretized the eruption into a set of phases consistent with (i) the plume height observations from the remote sensing measurements (Corradini et al., 2016) and (ii) the exit velocities retrieved by VOLDORAD-2B (Donnadieu et al., 2015, 2016, 2017). The improved simulation scheme (Fig. 7b and c) is achieved by coupling this discretization with the ARPAE or ERA-Interim databases and the Integrated TGSD or Whole TGSD, respectively, depending on the inversion purpose.

Simulation optimization is carried out to assess the ESP, and among them the TGSD, leading to the numerical reconstruction of the tephra loading and airborne ash mass dispersal. Input parameters in Table 2 were varied at constant steps within their ranges facing the inherent non-uniqueness solution for assessment purposes (e.g. Anderson and Segall, 2013). Starting by inverting the Integrated TGSD, we tested each weighting average combination of the Field and Radar TGSDs, ranging from 100 wt % Field TGSD to 100 wt % Radar TGSD, with a step of 5 wt %. To select the best combination, we compared the tephra loadings computed at the sampled sites until we best fit the field measurements.

Considering the simulations, we used the scheme described in Sect. 3.2 (Fig. 7b and c), which implies a set of column height values (and hence the corresponding MERs) with the average exit velocity. Therefore, neither the column height, the MER, nor the exit velocity were changed in each simulation. However, we inverted the plume parameters (i.e. α and β) from 0.05 to 0.15 and 0.05 to 1.0, respectively (Costa et al., 2016b), by means of the following goodness-of-fit procedure.

The goodness of fit between simulations and field observations was evaluated through different statistical metrics (see Poret et al., 2017). In particular, we used the normalized root mean square error (i.e. RMSE) assuming three different error distributions (i.e. RMSE1, RMSE2, and RMSE3) described in Folch et al. (2010). We also used the Aida (1978) indexes K (i.e. geometric average of the distribution) and k (i.e. geometric standard deviation of the distribution). K=exp⁡1N∑iNlog⁡ObsiSimi,k=exp⁡1N∑iNlog⁡ObsiSimi2-1N∑iNlog⁡ObsiSimi2, where i refers to the ith sample over N, and Sim and Obs are the simulated and observed tephra loadings, respectively. For a given set of ESPs, K gives the gap between the theoretical optimal tephra loading samples and the simulated ones. The reliability of the simulation is obtained for K between 0.95 and 1.05, which means a threshold of ±5 wt % from the derived theoretical optimal TEM. It follows that the best simulations are selected for K close to 1 with k and the three RMSEs minimized. Additionally, we estimated the bias, the correlation, and the Student T test (Folch et al., 2010).

After the Integrated TGSD, the Whole TGSD is inverted by quantitatively analysing the effect of different PM20 fractions (i.e. 0.6–10.7 wt %; Sect. 3.1) on the computed airborne ash dispersal. The best fraction is selected by means of the following three statistical metrics. The mass difference (i.e. ΔMass) between the satellite measurements and the FALL3D estimates. We compared the masses over the number of pixels given by the plume mask (obtained for the threshold of 0.1 t km-2) retrieved from SEVIRI: ΔMass=1ΔT∫t0tfMObs-MSimdt, where MObs and MSim are the observed and simulated masses integrated over the whole event (i.e. from t0 = 09:30 to tf = 14:30, with ΔT = tf - t0). This index gives the discrepancy (in t) for each γ factor (i.e. PM20 fractions). Additionally, we also calculated for each γ factor the absolute average difference of mass per unit area (Sum(Δ)‾ in t km-2) for the entire volcanic cloud by the following: Sum(Δ)‾=1ΔT∫t0tf∑NMObs(N)-MSim(N)AreaPdt, where N is the number of pixels (i.e. plume mask), and MObs(N) and MSim(N) are the observed and modelled masses associated with the Nth pixel for SEVIRI and FALL3D, respectively. AreaP refers to the area covered for the related time interval, which is calculated by means of N and the pixel resolution (i.e. 9 km2). This index indicates the uncertainty of the simulated airborne ash mass per unit area with respect to the satellite retrieval.

Considering that ΔMass and Sum(Δ)‾ are discrepancy estimates, the selection is done on the basis of their minimization. Nonetheless, Sum(Δ)‾ gives absolute values preventing any over- or under-estimation characterization. It follows that we also evaluated the following index: ε=1ΔT∫t0tf∑NMObs(N)-MSim(N)<0+∑NMObs(N)-MSim(N)>0AreaPdt, where ε refers to an over-estimation per pixel when ε < 0 and an under-estimation per pixel for ε > 0, with a best fit for ε = 0. Moreover, the index indicates the average mass difference per unit area (i.e. t km-2) between the satellite measurements and the simulation. The synergic use of these metrics aims at providing a simple way of comparing spatially and temporally the simulation outputs with the field and remote system measurements.

Regarding the Integrated TGSD inversion (Sect. 3.3), Table 3 shows the statistical analysis for the best simulation (i.e. K ≈ 1, RMSE1, RMSE2, RMSE3, and k minimized) for each weighting average combination. Regardless of the weights, RMSE1 and RMSE3 have flat patterns, motivating us to rely on the RMSE2 and k. They show relevant combinations from (65, 35; i.e. 65 and 35 in wt % for the Field and Radar TGSDs, respectively) to (85, 15). Although RMSE2 ranges between 1.56 and 1.85 from (65, 35) to (85, 15), k is minimized at 2.95 for (75, 25), being selected as the best weighting average combination for composing the Integrated TGSD (Table 3 and Fig. 8). It is worth noting that RMSE2 and k indicate relatively high values yielding a mean error factor nearby 3, which is comparable to uncertainties associated with other classical methods (Bonadonna and Costa, 2012, 2013; Bonadonna et al., 2015).

Figure 9 illustrates the statistical analysis of the Whole TGSD inversion (Sect. 3.3) for the best simulation for each PM20 fraction. Considering the whole airborne ash mass, the results yield a best value for ΔMass at γ = 0.65 (i.e. PM20 = 9.0 wt %), indicating an overall under-estimation of ∼ 76 t of ash by FALL3D for the entire eruption. Then, Sum(Δ)‾ shows a minimum for γ = 0.40 (i.e. PM20 = 3.6 wt %), giving an absolute average difference of mass per unit area of ∼ 0.37 t km-2 for the whole sequence. The third index returns a best value of ε = -0.03 t km-2 for γ = 0.65 (i.e. PM20 = 9.0 wt %), being consistent with ΔMass. ε likely reflects that FALL3D slightly over-estimates the average mass per pixel of 0.03 t km-2. By integrating the results (Fig. 9), the Whole TGSD required the minimum PM20 fraction of 3.6 wt % to best reproduce in absolute terms the average ash mass per unit area. However, such a fraction is not sufficient for best simulating the whole airborne ash mass released during the eruption, and minimizing the over- or under-estimation, which tends to be satisfied with higher PM20 fractions (i.e. 9.0 wt %). The corresponding input TGSD is displayed in Fig. 5. Moreover, ΔMass and ε in Fig. 9 both indicate that FALL3D under-estimates substantially the airborne mass for PM20 fractions lower than ∼ 7 wt % and over-estimates it above ∼ 10 wt %.

Regarding the other ESPs, although the column height values were not changed throughout the simulations (Fig. 7b and c), we report here the MER inverted by FPlume for the climax phase only, which is ∼ 7.0 × 105 kg s-1. The calibration of α and β returns values ranging from 0.06 to 0.15 and from 0.21 to 1.00, respectively, depending on the weighting average combination (Table 3). The latter ranges are consistent with the literature (Devenish et al., 2010; Suzuki and Koyaguchi, 2015).

During the Integrated TGSD inversion, the six proximal samples were relatively stable when varying the weighting average combination, whereas the farthest sample (i.e. TER) was substantially affected. Figure 8 shows the comparison between the computed and measured tephra loadings with the Integrated TGSD (details in Table 1). It is worth noting that making use of the Field TGSD prevents FALL3D from capturing the TER sample, while the Radar TGSD fails on most of the samples as indicated in Table 1. These observations argue the necessity of combining the two different distributions through the Integrated TGSD, especially when field measurements are few. Figure 8 shows the seven samples lying within the 1/5–5-times threshold of the measured tephra loadings, especially the unique medial sample (i.e. TER). As indicative values from Table 1, the six proximal samples indicate tephra loadings ranging from 1 to 17 kg m-2. In contrast, FALL3D computed them between 3 and 7 kg m-2 for the Integrated TGSD. Such narrower ranges compared to the field data can be attributed to the complexity for modelling in proximal areas (< 20 km from the source) and the field samples' location with respect to the main plume axis.

Besides the tephra loadings, we also compared the field-derived GSD at the sampled sites with the numerical results for the Integrated TGSD (see Fig. S1). Although FALL3D reproduces accurately three of the seven samples by peaking at the same modes, four proximal samples (i.e. CRT, PDM, FFD, and GDN) are shifted by 1Φ, indicating the field measurements being slightly finer than the computed ones. This discrepancy argues for the difficulty in computing accurately at such proximal areas due to plume dynamic complexities (e.g. Cerminara et al., 2016). Nonetheless, the mode shift can also be attributed to the sampling distance from the source as explained in Spanu et al. (2016). Indeed, in proximal areas the coarse tephra (-4 ≥ Φ ≥ -2) deposits rapidly, increasing the difficulty in estimating accurately this part of the TGSD with the Voronoi tessellation method together with a paucity of field measurements (Andronico et al., 2014). Moreover, we cannot exclude partial breakages of a few coarse-grained clasts when impacting the ground (Andronico et al., 2015), which also may result in grain sizes slightly finer than expected.

Although we used the improved simulation scheme (Sect. 3.2; Fig. 7b), we run a simulation through the simplified procedure (Fig. 7a) to highlight the effect on the tephra loading, and therefore the statistical analysis. The results show that making use of a constant plume height (here ∼ 11.3 km a.s.l.) for the entire paroxysmal phase gives K = 1.01 and k = 5.76 with RMSE1 = 0.80, RMSE2 = 3.36, and RMSE3 = 1.33, which are significantly higher than for the improved procedure (details in Table 3). Regarding the TEM, the simplified scheme returns 1.5 × 109 kg, which is ∼ 34 % higher than for the integrated approach with 1.2 × 109 kg. The latter TEM is in good agreement with the estimation of 1.3 × 109 kg reported in Andronico et al. (2015). It is worth noting that varying the weighting average from 100 wt % Field TGSD towards 100 wt % Radar TGSD yields an increasing TEM going from 1 to 6 × 109 kg, respectively (Table 3). This observation of TEM is consistent with the results described in Corradini et al. (2016), which indicates a X-Radar-derived total mass of 3.0 × 109 kg compared to the field-derived TEM of 1.3 × 109 kg from Andronico et al. (2015). Such a difference between X-Radar and field-based TEM estimates can be explained by considering the following aspects: (i) X-Radar samples airborne particles during their fallout, whereas the field measurements are based on deposited tephra; (ii) the operative window focuses the X-Radar retrievals on detecting the ash particles (-1 to 5Φ), while the field sampling method expands the measurements to block-sized (-5 to 5Φ); (iii) the Radar TGSD refers to the average over the duration observed from the radar at the sampled grid points, which does not necessarily coincide with the duration and location characterized by the Field TGSD; (iv) as explained in Sect. 3.1, the X-Radar measurements are made with assumptions using a regression model of radar simulations, which can add a further degree of uncertainty. The assumptions mainly affecting the final radar retrieval involve the radar forward model used to set up the radar retrieval scheme. It follows that assumptions made about particle shape, density, orientation, and PSD play the key role. However, the presented integrated approach by weighting the distributions issued from different methods aims at preventing the resulting Integrated TGSD from being associated with the full uncertainty of a single source.

The use of the different distributions (i.e. Field, Radar, Integrated, and Whole TGSDs) presented in this study permits comparison of the resulting tephra loading maps (Fig. 10). The tephra loading scale reported in Fig. 10 refers to the use of the ERA-Interim database, indicating slightly different tephra loadings than the values in Table 1 (ARPAE). Here, Fig. 10 is used as indicative tephra loading maps to display the effect of the input TGSD on the resulting tephra dispersal, showing the affected areas (e.g. the Calabria and Apulia regions). In particular, the use of the Field TGSD (Fig. 10a) permits FALL3D to compute the tephra loadings at the sampled sites up to Calabria, but not in the Apulia region where ash was reported. The Radar TGSD (Fig. 10b) operates in the ash window, preventing its use from reproducing any tephra loading and airborne ash data. In contrast, the Integrated and Whole TGSDs (Fig. 10c and d) capture all the tephra loading samples, but only the Whole TGSD succeeds in simulating the far-travelling airborne ash mass retrieved from the satellite. The corresponding time-series animation of the tephra loading associated with the Whole TGSD is available as the Supplement (Animation A2).

As mentioned in Sect. 2, large quantities of ash, water vapour (transformed into ice), and SO2 gas (Fig. 4) were released from Etna, preventing the remote systems from quantifying the whole event easily. The formation of two volcanic clouds (AC and IC) following their own trajectory at different altitudes (Fig. 3) increased substantially the complexity of comparing quantitatively the far-travelling airborne ash masses (i.e. SEVIRI and FALL3D). Indeed, the columnar satellite measurements and FALL3D results prevent the two clouds from being isolated, which motivated this study to focus on the plume mask retrieved by SEVIRI for each time (Fig. 11). Figure 11 illustrates the comparison between the retrieved and computed airborne ash mass. By means of the inverted PM20 range (i.e. 3.6–9.0 wt %), we displayed the airborne ash mass maps. The left column refers to the minimum PM20 fraction (i.e. 3.6 wt %) required to capture accurately the absolute average difference of mass per unit area (i.e. Sum(Δ)‾), whereas the right column corresponds to the fraction (i.e. 9.0 wt %) best reproducing the whole airborne ash mass (i.e. ΔMass and ε). Each panel in Fig. 11 (i.e. a, b, and c) shows the overlapping between the SEVIRI retrievals and the FALL3D outputs for a given time. Although the overlap tends to decrease with time (i.e. 12:00, 13:00, and 14:00, respectively), the results for γ = 0.65 (i.e. PM20 = 9.0 wt %) indicate a better performance than for γ = 0.40 (i.e. PM20 = 3.6 wt %). The entire time-series animations are available in the Supplement (Animations A3 and A4 for γ = 0.40 and γ = 0.65, respectively).

The PM20 range obtained for the 23 November 2013 Etna paroxysm tends to be relatively high with respect to the literature (1–2 wt %; Corradini et al., 2016), eventually attributed to the observational data used and the instrument properties. However, in terms of mass to the TEM, the estimated PM20 fractions indicate consistent values. Indeed, 1–2 wt % of the X-Radar TEM (3.0 × 109 kg) refers to 30–60 t, while 3.6–9.0 wt % of the integrated TEM (1.2 × 109 kg) gives 43–108 t. In fact, Corradini et al. (2016) integrated X-Radar data with satellite retrievals to assess the PM20 fraction. However, the satellite cannot quantify any ash mass from pixels mainly filled by ice or gas (e.g. SO2). In other words, although the volcanic ice/gas clouds (i.e. IC) are assumed to be produced from ash nucleus (Corradini et al., 2016), the probable presence of ash within such clouds will be missed from SEVIRI.

Being the airborne ash mass spreading downwind towards the far field, the very fine ash fraction (i.e. here 3.6–9.0 wt % of the erupted mass) is a critical input into operational tephra dispersal models (e.g. HYSPLIT, Stunder et al., 2007; NAME, Witham et al., 2007; FALL3D, Folch et al., 2012), which are widely used for aviation safety. Although few studies have attempted to better constrain the fraction estimation, eruptions from different volcanoes are not comparable, as such a fraction is very different from one case to the other, ranging from 50 wt % to a few wt % (Rose and Durant, 2009). As discussed by Costa et al. (2016a, 2017), the very fine ash fraction varies with eruption intensity, magma composition, and eruption style. In particular, at the Spurr 1992 eruption, Wen and Rose (1994) estimated ∼ 2 wt % dispersed into the distal area. At the 2010 Eyjafjallajökull eruption, the estimated range spans from ∼ 0.9 to 11 wt % (Bonadonna et al., 2011; Dacre et al., 2011; Devenish et al., 2012). However, some operational models assume a fraction of ∼ 5 wt %, which is not related to our estimate for the Etna eruption. In fact, assuming a constant fraction (e.g. 5 wt %) would represent the very fine ash fraction that escapes to aggregation processes and travels in the far field. In the case of basaltic eruptions, like at Etna, the eruption intensity and the very fine ash content are low, and hence aggregation less efficient (Costa et al., 2010), implying that most of the fraction can be transported distally. These observations yield the necessity for better considering such a fraction as input, suggesting further investigations on both basaltic and silicic volcanoes.

Regarding the FALL3D results in Fig. 11, the airborne ash maps show the two volcanic clouds (AC and IC) observed from the satellite (Corradini et al., 2016), although they are still connected to each other. Dispersing simultaneously from the source, the FALL3D simulations yield the presence of volcanic ash following the trajectory of AC below FL 250. In addition, FALL3D also indicates a major contribution of the airborne mass associated with the IC trajectory spreading over FL 250. The results in terms of temporal dispersal (Animation A3) are corroborated by the SEVIRI retrievals (Animation A1) and the pilot report, which mentioned volcanic ash and probably gas near Albania at FL 360–380 (Crompton and Husson, 2015).

As a consequence of being blind to any ash within the IC, the comparative study results represent partially the whole airborne ash. This raises questions related to volcanic hazards, such as the air traffic safety. In fact, on the basis of the FALL3D results, the IC appears to have a significant amount of erupted material (i.e. PM20, ice, and gas). This observation highlights the necessity for quantifying entirely the far-travelling airborne tephra, perhaps benefitting from other sensors capable of characterizing such aerosol clouds. In particular, this study inferred from quantitative analysis based on the observations in terms of tephra loading and airborne ash mass the interest in integrating retrievals from diverse instruments to assess accurately the initial magma fragmentation (i.e. TGSD of the whole erupted tephra).