*3.1. MODIS VCTH Estimation*

MODIS is a multispectral radiometer on board the NASA Terra and Aqua polar satellites. It has 36 spectral channels from visible (VIS) to thermal infrared (TIR), with a spatial resolution at sub-satellite of 1 km in the TIR and repetition cycle of 1–2 days. The VCTH is computed by exploiting the well known "dark pixels" procedure, based on the comparison between the brightness temperature at 11 μm of the coldest volcanic cloud pixel (Tb,11), with the atmospheric temperature profile of the same region at same time [2]. The temperature profile has been obtained from the National Centers for Environmental Prediction (NCEP)/National Center for Atmospheric Research (NCAR) [31], considering a box with 2.5◦ × 2.5◦ centred on Etna at 12:00 UTC. The left panel of Figure 5 shows the Tb,11 for the MODIS-Terra image collected the 26 October 2013 at 09:00 UTC. The volcanic cloud is clearly visible as dark signature on the right side of the image, while the cyan region indicates no data. The right panel of Figure 5 shows the NCEP temperature profile (grey line) and the Tb,11 of the dark pixel (red vertical line). Being Tb,11 = −37.4 ◦C, VCTH result 8.9 km with an uncertainty of +/− 500 m, computed considering Tb,11 +/− 2 ◦C [2,32].

**Figure 5. Left panel**: brightness temperature at 11 μm for the moderate resolution imaging spectroradiometer (MODIS)-Terra image collected the 26 October 2013 at 09:00 UTC. **Right panel**: National Centers for Environmental Prediction (NCEP) temperature profile (grey line) and dark pixel brightness temperature (red vertical line).

#### *3.2. SEVIRI VCTH Estimation*

The SEVIRI instrument on board METEOSAT Second Generation (MSG) geostationary satellites is a 12 channel VIS-TIR multi-channel imager, which operates from 15 min repeat cycle on entire hemisphere (Full Disk) to 5 min over Europe (Rapid Scan). The sub-satellite point spatial resolution is <sup>3</sup> × 3 km2, and the pixel dimension in the Etnean area is about 4.3 × 3.3 km. Exploiting the high data frequency of the SEVIRI images, the volcanic cloud speed can be retrieved by following the volcanic cloud centre of mass. By making a basic assumption that the estimated centre of mass speed is the whole volcanic cloud speed, VCTH can be obtained by comparing this value with the wind speed profile collected in the same time and position [26]. Also in this case the wind profile derive from NCEP/NCAR considering a box with 2.5◦ x 2.5◦ centred on Etna at 12:00 UTC. The upper panels of Figure 6 show the volcanic cloud ash mass maps obtained from the SEVIRI images collected at 09:00 UTC (left panel) and at 10:00 UTC (right panel). In these two images the different position of the volcanic cloud centre of mass is clearly identifiable. The distance of the centre of mass from the vents and the time of acquisition of the SEVIRI images, allows the computation of the volcanic cloud speed (see lower-left panel). This retrieved value is then compared with the wind speed NCEP/NCAR profile (see lower-right panel). In this case the wind speed of the volcanic cloud centre of mass is 18.0 m/s that yield to a VCTH of 10.5 km. An uncertainty of +/- 500 m is associated to take into account the uncertainty in the centre of mass identification. It is interesting to note that the P2E offset in Figure 3 corresponding to volcanic cloud velocities, is comparable to the wind speed measured by NCEP/NCAR (~18 m/s) shown in Figure 6.

**Figure 6.** Upper panels: volcanic cloud ash mass maps obtained from the spinning enhanced visible and infrared imager (SEVIRI) images collected at 09:00 UTC (**left panel**) and at 10:00 UTC (**right panel**). Lower panels: Computation of the volcanic cloud speed from SEVIRI images (**left panel**) and comparison between the value obtained and the wind speed NCEP/ National Center for Atmospheric Research (NCAR) profile (**right panel**).

#### **4. Discussion**

The simple cross comparison presented here indicates that VCTH retrievals from Landsat 8, SEVIRI, and MODIS are in good agreement, taking into account the different methodologies and the different times of images acquisition (9:37 UTC for Landsat, 9:00 UTC for MODIS and from 9 to 10:30 UTC for SEVIRI). The volcanic plume is a complex medium made of different materials and chemical species. Different materials (such as ash or ice) and different chemicals (such as SO2, H2O, and CO2, and halogens) are dispersed at different altitudes. As an example, sensors that capture or model SO2 dispersion in the atmosphere (such as the Infrared Atmospheric Sounding Interferometer, Iasi) will, therefore, measure a different plume altitude compared to sensors that measure visible plume particles (such as Landsat 8 and SEVIRI). This important distinction has to be taken into account when comparing results from different sensors. The PEM method works best for volcanic clouds made of ash particles and optically thick material.

The accuracy of the PEM extracted from Landsat 8 has been already assessed against ground cameras in de Michele et al. (2016) for the Holuraun fissural eruption (Iceland). They reported an accuracy of 300 m. Landsat 8 acquires data at a high spatial resolution (15/30 m grid) at the cost of a medium revisit time (every 14 days). Instead, SEVIRI has the advantage of acquiring data every half an hour everywhere in the globe. This is done at the cost of medium spatial resolution (1 km grid). Statistics performed over VCTH retrieved by Landsat 8 (PEM), SEVIRI and MODIS data on a common area show very good agreement with a maximum height value of 8 (with 1 km precision). The strength in the results show the complementarity between these systems. Assimilation models could benefit from complementary constraints brought by these sensors.

Some questions remain open to future studies. How large must the optical depth or concentration of the particles be to enable VCTH-assessment? How far from the source is the retrieval of VCTH typically possible with Landsat 8 ? We believe that this information would be essential for designing a new, dedicated mission. In general, in our approach, the plume height is not measureable if the plume is not visible in the image (Table 1).

**Table 1.** Summary of the comparison between the different volcanic cloud-top height (VCTH) retrievals derived from Landsat 8, MODIS and SEVIRI.

