Temporal models for the occurrence of Etna eruptions and implications for hazard assessment

Sandri, Laura; Garcia, Alexander; Scollo, Simona; Mereu, Luigi; Prestifilippo, Michele

doi:10.5194/egusphere-2025-5875

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https://doi.org/10.5194/egusphere-2025-5875

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04 Dec 2025

| 04 Dec 2025

Temporal models for the occurrence of Etna eruptions and implications for hazard assessment

Laura Sandri, Alexander Garcia, Simona Scollo, Luigi Mereu, and Michele Prestifilippo

Abstract. Mt Etna volcanic activity is broadly divided into flank eruptions and summit paroxysms. Here, building on previously-available literature and data on the start time of these events, we collate two separate catalogs of the two activity types. Then we separately model their temporal occurrence. The catalog of flank eruptions, spanning the last 400 years, has been modelled by means of the most widely used renewal models, among which the best one (through Akaike Information Criterion) is the Brownian Passage Time. The catalog of summit paroxysms, covering the period 1986–2022, according to our cluster analysis is best characterized by 12 clusters of paroxysms. We separately analyze the inter-event times between onset times of successive clusters of paroxysms (inter-cluster inter-event times) and the inter-event times between successive paroxysms within clusters (intra-cluster inter-event times). Again, the Brownian Passage Time is the best-fitting model, obviously with very different parameters in the two cases. We test the best-fitting models by checking their ability to reproduce features of the real catalogs. Finally, we provide an example of how to use in practice such temporal models in the context of probabilistic hazard assessment, showing a possible use in the case of tephra fallout hazard from summit paroxysms.

Received: 27 Nov 2025 – Discussion started: 04 Dec 2025

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Laura Sandri, Alexander Garcia, Simona Scollo, Luigi Mereu, and Michele Prestifilippo

Status: final response (author comments only)

RC1:
'Comment on egusphere-2025-5875', Ian Main, 24 Feb 2026
Temporal models for the occurrence of Etna eruptions and implications for hazard assessment
by Laura Sandri, Alexander Garcia, Simona Scollo, Luigi Mereu, and Michele Prestifilippo
This manuscript develops a new database for eruptions at Mount Etna, separates it into flank and summit eruptions, and analyses the data to determine the best fitting model in the two cases. There are many examples of good practice in the analysis, including the testing of multiple hypotheses, the use of an appropriate information criterion to choose the best one, and the simulation of model variability and averaging by running an ensemble of models, not just using the best fit. The results show a clear difference between the two types of eruption, with summit eruptions showing clear evidence of short-term clustering, even in the primary data, and the best fit model for flank eruptions consistent with long-term anti-clustering indicating a renewal process with some memory. The results could in principle be used in managing the future risk of eruptions of the different types in operational forecasting mode for a time varying hazard rate, and some examples of this are given to illustrate this.
The paper is of a suitable standard for publication, and I recommend publication after addressing the following mostly minor points.
The abstract could be more specific about the example application to hazard forecasting.

Section 2.1. Can you say something about the uncertainty in dating events in such a long catalogue, and how this varies in time?

Line 50. Can you also demonstrate and justify the statement of completeness and how this was determined? (In any case you change the completeness starting date later and explain why, so this is an initial guess, not the final version). In fact, the completeness is determined effectively by trial and error with stationarity as a criterion.

Line 58. How was the catalogue merging done? Was this simply by combining these databases, or did it involve some recalibration and/or decisions on which to use in the case of overlapping events? Would you say this resulted in a homogeneous catalogue after the merger, and why?

Line 70. ‘does not show evident clustering’. Where is the evidence for this statement? This assertion (in fact all unsupported assertions) should be justified by a logical narrative and cross-reference to the evidence.

Line 82. ‘due to their tendency to cluster’ - see previous comment. This assertion should be justified.

Line 93. Can you explain how the compound model works? Is this a sum of two different processes or is this a temporary change where one process switches off and another switches on?

Line 121. Can you compare these annual rates with what you would get from a standard Poisson model? What is the probability gain on the forecasts compered to this null hypothesis?

Lines 169-171. The evidence and chain of logic behind this inference on the hazard function is not presented, but it should be. Do you mean a steady increase, or a temporary increase and transient decay to the background level after the cluster stops? I think you should cross-refer to the relevant figure for the hazard functions here for both types of eruption from the two variants of the BPT model, and compare and contrast these with each other rather than simply assert the inference. It would also be useful to add a time-independent rate to the relevant figure and discussion for comparison.

Figure 1. It would be good to see the incremental probability function here as well as the cumulative version.

Figure 3. There is clear evidence of clustering here, but you don’t refer to this in the main text as evidence when you introduce the notion of clustering.

Figure 4. I think it would be useful to also show the variability or uncertainty in the best fit curves (red) from the simulations, similar to Figure 1.

Figure 8. Can you explain why the lower percentile curve is shorter than the upper one?

Ian Main, University of Edinburgh, 24 February 2026
Citation: https://doi.org/10.5194/egusphere-2025-5875-RC1
RC2: 'Comment on egusphere-2025-5875', Anonymous Referee #2, 24 Apr 2026

The paper aims to provide reliable statistical distributions of different styles of eruptive activity at Mt. Etna, an important topic for volcanic hazard analysis.
Overall I found the manuscript interesting and readable. However, several issues need to be addressed in a revised version.
- Completeness of the flank-eruption catalog. The manuscript is inconsistent about the catalog’s completeness: line 50 states eruptions since 1600 are considered “for reasons of completeness,” while line 110 claims completeness only since 1763. Beyond correcting this contradiction, the authors should clearly explain how they assessed completeness. Section 4.1 gives the impression that a cutoff date was chosen to produce a “coherent” distribution (e.g., starting from 1660 would yield a different distribution), which is not an appropriate justification. The long quiescence after the 1669 eruption might reflect a time‑predictable behavior suggested in previous work (e.g., Marzocchi and Zaccarelli, JGR, 2006). That possibility is not necessarily inconsistent with the authors’ results, but the paper needs a more thorough discussion of the completeness issue and its implications for the analysis.
- AIC is known to favor models with more parameters. Here all distributions have two parameters except the exponential, which has one. Would the results change if you used AICc (the small-sample corrected AIC) to account for this bias?
- The use of the KS1 test may be inappropriate here. KS1 assumes the model parameters are known a priori, not estimated from the data; ignoring parameter estimation can substantially bias goodness‑of‑fit results. Use an alternative that accounts for fitted parameters (e.g., the Lilliefors modification for KS1 with normal or exponential distributions) or adjust KS via a parametric bootstrap to obtain correct p‑values. Other robust options include the Anderson–Darling test, which IS LESS sensitive to this problem.
- The authors use the term "hazard function." While statistically correct, this can be confused with the "hazard curve" (often a survival or exceedance function). I suggest defining both terms explicitly when first used.
- Many volcanologists may be unfamiliar with the BPT distribution. I suggest citing Matthews et al. (BSSA, 2002) and referencing their Figure 2 to illustrate the distinction between a “periodic” BPT and a “clustered” BPT. This will help readers visualize and understand the different behaviors.

Citation: https://doi.org/10.5194/egusphere-2025-5875-RC2

Laura Sandri, Alexander Garcia, Simona Scollo, Luigi Mereu, and Michele Prestifilippo

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https://doi.org/10.5194/egusphere-2025-5875-supplement

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OTETNA Laura Sandri et al. https://doi.org/10.13127/etna/otetna

Laura Sandri, Alexander Garcia, Simona Scollo, Luigi Mereu, and Michele Prestifilippo

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Short summary

We model how eruptive events occur in time at Mt Etna. We distinguish between eruptions from flank fissures and paroxysmal eruptions from the summit craters. Our model allows to compute the expected annual frequency of flank events and the expected number of summit paroxysms in a future period of time, with uncertainty estimates. We show how this model can improve the assessment of probabilistic hazard from these eruptions.


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