## 3 Results
### Satellite-Derived Lava Flow Field Retrievals  
During the effusive phase that occurred between 30 March and 1 April, we converted the radiant heat flux (Figure 3e) into Time-Averaged Discharge Rate (TADR), which is an estimation of the effusion rate averaged over a certain duration ([87]; Figure 5). Integrating the TADR curve, we obtained an upper and lower bound for the erupted Dense Rock Equivalent (DRE) lava volume that can be placed between 37 and \(69\times 10^{3}\) m\({}^{3}\). This compares to the volume of the NEC eroded during the overflows, which was estimated at \(13.4\times 10^{3}\) m\({}^{3}\).  
The mapping of the lava overflow that occurred between 28 March and 1 April was performed through the ML classifier [72], using the Sentinel-2 MSI image acquired on 13 March as representative of the pre-eruptive, and the two images of 7 and 12 April 2020 as post-eruptive. As pre-eruptive topography, we used a 1-m Digital Elevation Model (DEM) that was generated by very high-resolution tri-stereo optical imagery acquired by the Pleiades-1 satellite constellation on 8 October 2019 [88]. Following the same steps that are discussed in [72], pixels with similar spectral properties were grouped in 50 clusters by the k-medoids unsupervised classifier. Subsequently, three pixels for each cluster were labelled to train the BNN, i.e., 150 pixels were used overall. To improve the accuracy, the lava flow field was then refined using the Pleiades image acquired on 7 April 2020, which provides a pixel resolution of 0.5 m.  
Figure 6 shows the lava flow map resulting from the ML classifier. The area measures \(94{,}500\pm 3380\) m\({}^{2}\). The uncertainty was calculated by multiplying the satellite-derived perimeter (6760 m) by the pixel resolution of the Peiades-1 imagery (0.50 m) [69].  
Figure 4: (**a**) 28 February 2020–27 March 2020, representing the pre-effusive period. Measured displacement was restricted to the NEC area and related to the accumulation and gravitational instability of the newly emplaced volcanic material; and, (**b**) 31 March 2020 cumulative displacement, highlighting the syn-eruptive deflation that occurred between 00:35 and 05:09.  
In the area that was identified thanks to the ML classification (Figure 6), we found a thickness of volcanic deposits that goes from \(-\)14 m (due to the coastal erosion) to 14 m (in proximity of the NE crater) (Figure 7). The volume of the deposits accumulated near the NE crater amounts to 34,600 \(\pm\) 9700 m\({}^{3}\). For calculating the volume of the main lava flow spreading on the SdF, we analyzed the histogram of the thicknesses (inset in Figure 7), finding a peak to 0.8 m. Being the most frequent value, we assigned it to the pixels where the DEM difference was negative, thus estimating a volume of 144,400 \(\pm\) 79,000 m\({}^{3}\). Consequently, the total bulk volume of deposits thus amounts to 179,000 \(\pm\) 89,000 m\({}^{3}\). The uncertainty was computed by multiplying the areas by the residual vertical accuracy outside the margins of the deposits, i.e., the standard deviation (\(\sim\)1.7 m) of the DEM difference in the area that was not covered by deposits.  
Figure 5: Minimum, mean, and maximum estimates for Time-Averaged Discharge Rate (TADR) and volume estimated during the effusive phase occurred from 30 March to 1 April 2020.  
Figure 6: Google Earth view of the satellite-derived lava overflows from the NE crater rim spreading along the Sciara del Fuoco. The lava flow field (red contour) has been superimposed from the Pleiades image acquired on 7 April 2020.