## 4 Discussion  
In order to assess the accuracy of the maps produced by machine learning techniques, we compare them to the maps of actual lava flow fields of the three investigated Etna eruptions manually retrieved from multi-view PlanetScope images (four bands: Blue, Green, Red plus Near Infrared with a ground sampling distance of \(\sim\)3.7 m). To determine the robustness of our results, we computed three different performance indices, which have been extensively used to quantify the goodness of fit between real and simulated lava flows [(80; 62; 81; 82)]:  
* **accuracy** (ACC) = \(\sqrt{\frac{A(\text{test}\cdot\text{ref})}{A(\text{test}\cdot\text{ref})}}\)
* **precision** (also known as the _positive predictive value_, \(\text{PPV}\)) = \(\sqrt{\frac{A(\text{test}\cdot\text{ref})}{A(\text{test})}}\)
* **sensitivity** (also known as the _true positive rate_, \(\text{TPR}\)) = \(\sqrt{\frac{A(\text{test}\cdot\text{ref})}{A(\text{ref})}}\)  
where \(A(\text{test})\) and \(A(ref)\) are the testing and reference areas, respectively.  
A comparison between the ACC, PPV and TPR provides insights on how the testing emplacements change compared to the actual areas. Specifically, the testing area underestimates the actual one if PPV is higher than ACC, while it overestimates if TPR is greater than ACC [(83; 84)].  
Table 1 shows the areal extent of lava flows for the investigated eruptions extracted from Sentinel-2 MSI data (BNN), ground-based measurements (GROUND), and PlanetScope images (REAL). Results for ACC, PPV and TPR calculated for BNN and GROUND (as testing) and REAL (as reference) are also reported.  
Figure 7: Lava flow map resulting from the BNN and the post-processing stages (red) and the contour of the real lava flow (white) observed during the Etna eruption that occurred in December 2018.  
BNN mapping is more accurate than the ground-based one and fully in agreement with the real lava flows in all the presented cases of study. Indeed, the values for ACC, PPV and TPR are always higher than 0.60 for all the three case studies, meaning that the real lava flow field is always well reproduced.  
The best fits (ACC = PPV = 0.88, TPR = 0.86) are obtained for the lava flow of February-April 2017, while the worst case is August 2018 (ACC = 0.73, PPV = 0.60, TPR = 0.81). The performances get worse when the closest available images are recorded weeks after the lava eruption ends, thus reducing the information available to infer the lava flow map. In fact, after several days, it gets harder to distinguish older and newer lava flows. For instance, this happened for the lava flow of 27 August 2018, when one of the clouds and snow-free Sentinel 2-MSI datasets used as post-eruptive images are recorded nearly 45 and 30 days later, respectively. On the other hand, for April 2017, the farthest image used as post-eruptive image is recorded nine days after the volcanic eruption ends, thus leading to good performances; similarly, for the northern lava flow of the August 2018 case study.  
Another major factor that can reduce the BNN performance is the presence of ice, snow, atmospheric clouds, ash and/or tephra plumes. For example, the images we used for December 2018 were affected by clouds, plumes/ash, and snow, resulting in noisy pixels that represented a source of error for our classifier. The combination of all these factors can increase uncertainty, worsening overall performance.  
It is worth noting that different lava flow morphologies (Kal  
close enough to the eruption ending date worsens the performance of the algorithm, as shown in the southern lava flow of the August 2018 case study.  
Further development to improve the overall performance could enable the clustering stage to set the number of clusters automatically. Moreover, the availability of a far bigger dataset could allow the formation of a unique BNN, trained just once and applicable to all the other cases.