Stromboli’s “memory”

by Andrea Bevilacqua, Antonella Bertagnini, Massimo Pompilio, Patrizia Landi, Paola Del Carlo, Alessio Di Roberto, Willy Aspinall, and Augusto Neri
(English translation courtesy of Boris Behncke)

Reliable forecasting of volcanic eruptions remains a major scientific challenge at volcanoes all over the world. Many eruptions appear to occur in a completely random way, “out of the blue”, without any apparent “memory” of the behavior that the volcano showed in the past. Is this really so, or could the reverse be possible: to identify recurrent patterns of behavior? A new study tries to answer this quandary for Stromboli.

Stromboli is famous for its persistent, low-energy explosive activity, known as Strombolian activity, characterized by continuous degassing punctuated, at intervals of about 10-20 minutes, by small explosions, which can eject lapilli, bombs and blocks over the crater terrace. Thanks to these manifestations of regular, frequent volcanic activity, Stromboli has always attracted visitors and volcanologists from all over the world. However, every now and then there are more intense explosions, which present a serious potential danger. These explosions were described early in the last century by Giuseppe Mercalli as the “bursts of the volcano”, and he called them “Strombolian paroxysms”. During such explosions, several of the craters of the volcano act simultaneously, and major volumes of hot and dangerous pyroclastic material are ejected. Recent examples are the paroxysms of 3 July and 28 August 2019.

However, Stromboli’s violent explosions are not all the same, but can vary in intensity from so-called major explosions to true, proper paroxysms. Major explosions eject bombs and blocks onto the summit portion of the volcano and onto the Sciara del Fuoco, whereas paroxysms can produce eruption columns several kilometers high, with bombs and blocks flying far and wide, coming down over great portions of the island, sometimes extending beyond the shoreline, out to sea (Figure 1).

Figure 1 – At center, an aerial view of Stromboli. Frames (a) to (i) show five different paroxysms of Stromboli: those of 1915, 1959, 2003 e 2019 (3 July and 28 August).

So, how likely is one of these more violent explosive events to occur and within what timescale? How much does the probability of a repeat increase after one of them has just occurred, and for how long does this increased likelihood last? The two recent paroxysms, on 3 July and 28 August 2019, provided a new stimulus to seek answers to these questions.

During the past few decades, besides the two events in 2019 only two other paroxysms have occurred at Stromboli, in 2003 and 2007. Yet, such events are nothing new for this volcano; as a matter of fact, they were rather frequent before 1960. It is thus important to estimate the frequency of occurrence of major explosions and paroxysms to check if Stromboli does have a “memory” – that is, whether there is statistical evidence for this volcano to exhibit a tendency to repeat itself with further major explosions or paroxysms, if one has just occurred. As a first step to tackling these questions, we have constructed a new catalog with descriptions of 180 major explosions and paroxysms that took place at Stromboli between 1879 and 2020. This review also includes a reclassification of numerous events through critical analysis of the historical sources.

In particular, 36 of the assessed explosive events are now classed as paroxysms and 99 as major explosions. In addition, 45 events are classified as uncertain due to the difficulty in distinguishing between major explosions and other intense but more ordinary eruptive activity because of insufficient historical information. During the past 140 years there have been, on average, a paroxysm for every 3 – 4 major explosions; in contrast, over the past 35 years, the ratio has been much lower: one paroxysms for every 14 major explosions.

Figure 2 – Cumulative number of major explosions and paroxysms between 1879 and 2020. Red dots indicate paroxysms; black dots are major explosions, including uncertain events. In contrast, gray dots are major explosions and paroxysms excluding uncertain events. For the temporal interval between 1960 and 1985, the catalog of major explosions might be incomplete.

Figure 2 shows the count of violent explosive events (major explosions or paroxysms) through time historically. From the analysis of the catalog, the mean annual rate of major explosions and paroxysms in the past 140 years is 1.3 events per year and, if we exclude uncertain events, it is 1.0 per year. The average annual rate has exhibited significant fluctuations – for example, the rate was relatively high from 1879 to 1908, then it was lower from 1908 to 1960, but it rose again during the past 35 years of activity. In particular, the annual rate of major explosions and paroxysms in the past 10 years – 2.8 events per year – is 2-3 times higher than the mean rate in the past 140 years, and similar to that of the early 20th century. Therefore, although paroxysms as compared to major explosions have been less frequent than in the past, in terms of violent explosive phenomena, Stromboli is currently experiencing one of the most intense phases of activity in its recent history.

Figure 3 – Cumulative count of the number of paroxysms between 1879 and 2020. Blue dashed lines highlight groups with inter-event intervals of less than a year. The years of six sequences of paroxysms separated by intervals of more than 9 years are indicated. On the right side, the shortest and longest periods between paroxysms are reported.

Figure 3 shows the count of paroxysms with time. In this case, due to their greater scale, all paroxysmal events have been considered as certain. From the analysis it appears that the short interval of 56 days between the two paroxysms in the summer of 2019 is not a rare situation. In five cases in the past 140 years, the time intervals between two paroxysms were even shorter. In contrast, there have been many periods without paroxysms, of which four lasted between 9 and 15 years, and one as long as 44 years (from 1959 until 2003). Seven paroxysms in the past 140 years have been single events, 5 occurred as couples within 12 months, 5 were clusters of 3 events in 12 months, and one was a group of four events within two years. It is thus apparent that paroxysms tend to occur in groups or bursts.

If we consider only the most energetic events – the paroxysms – the mean annual rate in the past 140 years has been 0.26 events per year, or approximately one event every four years on average. This rate is close to that calculated for the past ten years, but much lower than that of the 1940s, when the rate was averaging 0.8 events per year. The analysis of the data also shows that major explosions lead to a higher probability of paroxysms in the following days – the annual rate of paroxysms that occurred within the first 15 days after a major explosion is 5-6 times higher than the baseline rate.

All this information is useful also in a context of forecasting, which means estimating the probability that these phenomena will occur in the future. If a phenomenon, such as a volcanic explosion in our case, takes place at irregular intervals in time, typically we study the distribution of the “inter-event times”: those time intervals that have been observed in the past between one explosion and the next.

In the case of Stromboli, based on the past 140 years, there is a probability of about 50% that a major explosion or a paroxysm will follow its predecessor within less than 3-5 months, and a 20% probability that this will happen within less than 2-3 weeks. If, on the other hand, we consider only paroxysms, there is a 50% probability that one paroxysm follows a preceding one within less than 12 months, and a 20% probability that this will occur within less than 2 months; in contrast, there is a probability of 10% that 10 years will pass without further paroxysms.

Assuming that the inter-event times are independent from each other, and thus that the volcano resets its state after each explosion, we can statistically forecast how much time can be expected to elapse until the next explosion. In particular, the development of inter-event models allows us to calculate the probability of occurrence of an explosion as a function of the time that has passed since the most recent event of that type. In other words, this is the probability that an explosion will happen on any day that dawns after an event – if, so far, that event has not been followed by a new explosion.

The simplest possible model for such a situation is one that is based on the assumption that the rate of occurrence is constant in time, and not influenced by how many days have passed since the last explosion. Such a renewal process (universally known as a one-parameter “Poisson process”) thus does not have any memory, and the probability that a repeat event will take place remains always constant.  A model of this type associates a low likelihood with the sequence of past events registered at Stromboli, and considers groups of paroxysms, such as those that have been observed, as statistically unlikely. Vice versa, an analysis of the sequence of major explosions and paroxysms at Stromboli, carried out using statistical models that better represent the available data, clearly indicate that the volcano presents a memory or persistence effect in the time elapsed between new explosive events.

Figure 4 – Example for the probability of (a) hourly occurrence of major explosions and paroxysms, and (b) daily occurrence of paroxysms, in function of the number of months elapsed since the last event of the same type. Colored bands show uncertainty related to the major explosions of difficult characterization (graph a), and for two different statistical models used (graphs a and b). Horizontal lines indicate probability of hourly or daily occurrence (dotted lines), and mean rates of occurrence in the past 10 and 25 years, in the hypothesis that the volcano has no memory, according to a Poisson model (continuous lines). Note the different time scales shown on the x-axis of the two graphs.

Figure 4 shows the hourly probability of major explosions and paroxysms as a function of time elapsed since the last event. On the x-axis, the graph represents the time elapsed in months since the last explosion, whereas the y-axis shows the probability of occurrence on a logarithmic scale. The figure also displays the mean rates in the past 10 and 25 years, which correspond to a Poisson model, with no memory.

The new models of occurrence shown in the figure, which were constructed from the new historical catalog described above, clearly show that Stromboli is a volcano that possesses a strong “behavioral memory” pattern. In the weeks and months after a previous event of the same type, the rates of occurrence of major explosions and paroxysms are, in fact, rather high (well above the average rate)  before they diminish gradually by 5-10 times within 3-9 months for major explosions, and within 12-15 months for paroxysms. In other words, the statistical analyses described here suggest the existence of an underlying physical process that, in some measure, influences the frequency of the explosions of the volcano, and thus makes them not entirely random events.

This recognition of Stromboli’s “memory” represents a significant contribution to our ability to quantify the probability of dangerous, violent explosions of this volcano, and thus to help reduce associated risks. This said, understanding the physical processes in the volcano which determine the “Stromboli memory effect” remains a major scientific challenge, and one that merits being tackled.

The results described in this post are presented in more detail in a new study published in the journal Nature Scientific Reports.

Bevilacqua, A., Bertagnini, A., Pompilio, M., Landi, P., Del Carlo, P., Di Roberto, A., Piccione, C. & Neri, A. (2020a) Historical catalog of major explosions and paroxysms at Stromboli (Italy). (Version 1.0) [Data set]. Istituto Nazionale di Geofisica e Vulcanologia (INGV).
Bevilacqua, A., Bertagnini, A., Pompilio, M., Landi, P., Del Carlo, P., Di Roberto, A., Aspinall, W. & Neri, A. (2020b) Major explosions and paroxysms at Stromboli (Italy): a new historical catalog and temporal models of occurrence with uncertainty quantification, Scientific Reports.
Bollettini multidisciplinari monitoraggio Stromboli.
Mercalli, G. (1907), I vulcani attivi della Terra, 412 pp, Hoepli, Milan, Italy.
Rosi, M., Pistolesi, M., Bertagnini, A., Landi, P., Pompilio, M. & Di Roberto, A. (2013) Stromboli volcano, Aeolian Islands (Italy): present eruptive activity and hazards. In: Geological Society of London Memoir 37, 475-492.

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