The manuscript present an updated and more complete approach, with regard to previous ones, to evaluate the probability of opening of new vents at Etna.

The manuscript is overall well written, clear and scientifically robust.

I have only minor formal concerns, largely devoted at clarifying several aspects (including the novelties) , mostly in the abstract and introduction. The latter would benefit from introducing a general scientific problem of interest to a broad auidence.

I attach a pdf with my annotations.

The article is clear, very well written and is of interest for the community. As a general comment the authors could emphasis a bit more on the utility of reassessing hazard on Mont Etna (as there are already a great number of contributions about it) and why their work is of importance. This could in part be done by giving more background on the importance of considering effect of edifice deformation and justification of the scenario they choose.

I provide number of minor but important comments on the attached pdf to hopefully improve the article.

The manuscript shows an updated probability cartography for vent opening related with flank eruptions. The manuscript is clear and the methodology employed is very robust.

Nevertheless, I have some minor concerns (mainly about presentation style) the authors should take into account before publication to emphasize manuscript objectives and results. 

Abstract 

Abstract should be overall re-written to emphasize the importance of good probability estimates of lateral eruptions. 

The a priori assumption considered about how the past and present eruptive volcanic fissures can be used to estimate future spatial distribution of flank eruptions over long-term should be briefly described in the abstract to focus the work purposes as well as emphasize differences with previous works. 

The difference of previous studies should be highlighted: time window extension that allows to increase the number of fissure (even the data incompleteness seems to not promote a substantial or change on forecasting capability) and therefore, to consider training and test sets to estimate density functions following a machine learning approach as well as the inclusion of the interconnectivity (induce stress) of flank fissures opening with deformation sources as the volumetric source that feeds eruptions and/or flank slip. 

Before the training and test models description authors should describe that, for probability estimations, a kernel technique is used to obtain the unknown probability density function at the sampling points of the target area. For such a purpose different kernel functions are tested to construct probability maps (instead of directly talking about kernel functions) splitting data on to training and test sets. 

The term ‘unclamping’ should be removed from the abstract. Instead a brief introduction over induce stress should be included in the section 3.4.2.

Nomenclature about ‘canonical map’ should be defined after first use (line 16).

1.Introduction

The power of the work should be enhanced in the introduction. I recommend a carefully rewritten, removing some parts that could be better merged onto other manuscript sections. Some suggestions the authors should take into account could be:

Focus lateral eruptions, main subject of the manuscript: paragraph containing line 25 would be better removed; the paragraph that starts on line 45 should be merged with the paragraph from lines 30 to 45. Then continue with the paragraph that starts on line 65 and the one that starts on line 74. The introduction should finish with a brief mention of the training and test procedure and the sensitivity analysis.  

Paragraphs that start on lines 49, 82 and 89 have too much information for the introduction. I recommend cutting the methodological descriptions and merge such descriptions in the next sections. 

1. Data

This section should be the emplacement of the information presented in paragraphs that start on line 49 and 83 (subsection 2.1). 

1. Method

Unified notation should be used to name time windows: example, CE vs BP. CE is before/after 1971 or are the authors using the Gregorian Calendar?

Authors should describe here that assumption of the first stage of the analysis is that the past and present eruptive fissures can be used to estimate future spatial distribution of lateral eruptions over the long-term. The stochastic model they are using where a spatial point process where fissures are considered as random points within a set should be briefly described. 

 What is the role of the major and minor fissure sets classification for the computation of the spatial probability? I think they are used for train-test exercises because later on (lines 184-185) the authors refer to the assumption that future opening will be influenced by how close a point is from a fissure system.

I do not have a good understanding of the way authors estimate the rate of flank opening. My intuition is that the kernel function to estimate the rate of flank opening in a given cell point (every cell of the mesh assimilates to a point) of the domain (expression 1) takes into account the distance between the cell point of flank opening following expression 1. That is the way authors take into account the length and fissures orientation. However, they refer to the minimum distance between a point to a linear fissure element. Authors should define minimum distance. Is it the euclidean distance between two points on a plane? In this case the point of the linear fissure element is the one that accomplishes for the minimum euclidean distance. Is the elevation of the points taken into account? If not, what is the topography effect? From the physical point of view, the regional stress field caused by Etna topography could influence fissure opening. Maybe considering a topography zoning of the target domain given areas with different elevation and three dimensional euclidean distance could be a way to consider the topography effect.

3.2. Identification of the best kernel

The choice of kernel function with appropriate values of h has some consequences for the parameter estimation because it controls how expression (3) varies with distance from existing fissures. Gaussian and Cauchy  kernels are based on the intuition that the next fissure to form will not be far from an existing one. What are the assumptions to consider exponential or uniform kernels? Do the authors choose a pair or just one kernel function to generate the probability map? How do the authors find the best? What kind of norm (measure) are they using? 

3.4.2. Inclusion of stress changes due to different deformation sources

Lines 228-229: some reference should be included as Walter and Amelung (2004), Walter et al. (2005), Dieterich et al. (2003), Thatcher and Savage (1982), Stein (1999) or the classical King et al. (1994) (Static stress changes and the triggering of earthquakes, BSSA, 84 (3): 935–953. https://doi.org/10.1785/BSSA0840030935

Please, define clump or unclump through the sign of normal stresses to the plane of fracture.

Line 250 should be merged with the paragraph that starts on line 241 (in this way, there are more single sentences along the manuscript the authors should be take into account).

4.1 Reference model on training data

Lines 271-274: How do you measure that the Exponential model is always the best?

Can the null hypothesis be rejected for the rest of the distributions? Visual inspection of Figure 5 for 1600 CE training subset does not allow to distinguish the Gaussian and exponential distribution.

1. Discussion 

A flank eruption implies a fissure where magma is extruded as defined by the authors; however a fissure could be not related to a flank eruption. I think special attention should be given to this fact, including in the discussion a few lines about the effect of possible fissures not related to lateral eruptions. I assume there must be some kind of uncertainty on the fissure dataset consider by the authors.

Some lines about the fidelity or not of the probability map with the physic principles of the lateral eruptions should be included in the discussion.

Lines 320-322: “10-5” should be replaced by 10^-5 and so on.

1. Conclusions

Instead of a canonical map, I would refer to a canonical cartography set that takes into account different future scenarios. 

Finally:

There are some missing single sentences across the manuscript that should be merged with paragraphs.

In general, the quality of figures should be improved. Furthermore, I would merge Figure 2, 3 and 4;  Figures 7 and 8; and Figures 9 and 10. 

Figure 6b seems cut.

Data and figures on the Appendix are not properly cited on the overall manuscript instead of it is cited supplementary material.