Probabilistic modeling of future volcanic eruptions at Mount Etna
Annalisa Cappello,1 Giuseppe Bilotta,1,2 Marco Neri,1 and Ciro Del Negro1
Received 4 December 2012; revised 20 February 2013; accepted 11 April 2013.
[1] The statistical analysis of volcanic activity at Mt Etna was conducted with the twofoldaim of (1) constructing a probability map for vent opening of future flank eruptions and(2) forecasting the expected number of eruptive events at the summit craters. Thespatiotemporal map of new vent opening at Etna volcano is based on the analysis of spatiallocations and frequency of flank eruptions starting from 1610. Thanks to the completenessand accuracy of historical data over the last four centuries, we examined in detail the spatialand temporal distribution of flank eruptions showing that effusive events follow anonhomogenous Poisson process with space-time varying intensities. After demonstratingthe spatial nonhomogeneity and the temporal nonstationarity of flank eruptions at Etna, wecalculated the recurrence rates (events expected per unit area per unit time) and produceddifferent spatiotemporal probability maps of new vent opening in the next 1, 10 and50 years. These probabilistic maps have an immediate use in evaluating the future timingand areas of Etna prone to volcanic hazards. Finally, the results of the analysis of thepersistent summit activity during the last 110 years indicate that the hazard rate for eruptiveevents is not constant with time, differs for each summit crater of Mt Etna, highlighting ageneral increase in the eruptive frequency starting from the middle of last century andparticularly from 1971, when the SE crater was formed.
Citation: Cappello, A., G. Bilotta, M. Neri, and C. D. Negro (2013), Probabilistic modeling of future volcanic eruptionsat Mount Etna, J. Geophys. Res. Solid Earth, 118, doi:10.1002/jgrb.50190.
1. Introduction
[2] Mt Etna (Italy) is one of the most active and hazardousvolcanoes in the world [Behncke et al., 2005]. It is well knownfor the persistent activity from the summit craters, frequentlava flow-forming eruptions from vents situated on the flanksof the volcano, and the large population settled on and aroundthe sides of the volcano that is at risk [Guest and Murray,1979; Bisson et al., 2009]. The ever-expanding use of areasnear the volcano increases the potential impact of future erup-tions of Mt Etna on the regional economy and on the healthand safety of its citizens (Figure 1). Eruptions can neither beprevented nor interrupted, but actions can be taken to mini-mize damage from them [Ganci et al., 2012b]. Reduction ofrisk to life and property can be undertaken by avoiding threat-ened areas and by taking protective measures to reduce the ef-fects when and where vulnerable areas cannot be avoided[Scifoni et al., 2010]. Etna is continuously monitored usingseismology, deformation, gravity, magnetism, gas emissionstudies, and petrology by Istituto Nazionale di Geofisica eVulcanologia (INGV) and its observatory in Catania [Napoli
et al., 2008; Greco et al., 2010; Bonaccorso et al., 2011].Detection of volcanic precursors can generally identify thelocality of impending volcanic activity, even though it oftendoes not determine exactly the typology or timing of an erup-tion or even its certainty. Hazard-zonation maps can then beused for risk-based decision making in land-use planningand emergency management, as well as addressing the moregeneral problem of quantitative volcanic hazards assessment[Wadge et al., 1994; Newhall, 2000; Sparks, 2003; Magillet al., 2005; Behncke et al., 2005; Favalli et al., 2009; Bissonet al., 2009; Crisci et al., 2010; Cappello et al., 2011a; Vicariet al., 2011a, 2011b]. Thus, effective monitoring of Etnavolcano, combined with the preparation of emergency plansto face future eruptions, can help reduce the risk to lives andproperty in an area densely urbanized, where about 0.8 millionpeople live [Behncke et al., 2005].[3] Our purpose is to give a proper statistical treatment of
the records of volcanic eruptions at Mt Etna to allow key at-risk areas to be rapidly and appropriately identified. In termsof hazard, persistent summit activity does not represent a sig-nificant threat to the towns located on Etna’s slopes, althoughimportant tourist facilities and infrastructures close to the cen-tral craters have been repeatedly destroyed. However, periodicflank eruptions pose a serious danger to the lives and the prop-erty of the local populace [Behncke et al., 2005], especiallywhen the eruptive vents open up at very low altitudes (up to200–300m above sea level). In terms of volcanological data,the catalog of Etna flank eruptions is fully reliable only forthe last ~400 years, while summit eruptions are sufficientlydocumented starting from the first decades of the 20th century[Mulargia et al., 1985; Behncke et al., 2005; Tanguy et al.,
1Istituto Nazionale di Geofisica e Vulcanologia, Sezione di Catania,Osservatorio Etneo, Catania, Italy.
2Dipartimento di Matematica e Informatica, Università di Catania,Catania, Italy.
Corresponding author: C. D. Negro, Istituto Nazionale di Geofisica eVulcanologia, Sezione di Catania, Osservatorio Etneo, Italy.([email protected])
2007]. Therefore, the statistical analysis of volcanic activity ofMt Etna was conducted with the dual aim of (1) constructing aspatiotemporal probability map for vent opening of futureflank eruptions and (2) forecasting the expected number oferuptive events at the summit craters.[4] Different approaches have been used to evaluate the
probability of vent opening at Etna volcano by analyzingthe distribution of spatial location of flank eruptions andtheir temporal frequency.[5] For the spatial distribution, the density of vents has
been calculated to identify areas where the highest concen-tration is located, which correspond to the zones known asNE, S, and W Rifts [Guest and Murray, 1979; Acocellaand Neri, 2003; Salvi et al., 2006; Crisci et al., 2010; Rongoet al., 2011; Neri et al., 2011; Cappello et al., 2012].[6] For the temporal distribution of flank eruptions,
Mulargia et al. [1985] concluded that Etna’s lateral eruptionsfollow a stationary Poisson process with a constant intensity.Salvi et al. [2006] refuted this result, proving that flank erup-tions at Etna do not follow a simple Poisson distribution butare more likely represented by a nonhomogeneous Poissonprocess with power law intensity. Recently, Bebbington[2007] applied the Hidden Markov Models (HMM) to volca-nic occurrences to identify the activity state (hidden) of thevolcano most consistent with the observations and to forecastthe next eruptions. However, the stationary distributionassumed by HMM cannot properly model the increasing trendof flank eruptions observed over the last 40 years at Etna
[Allard et al., 2006]. Finally, the temporal analysis performedby Smethurst et al. [2009] revealed that flank eruptions followa nonhomogeneous Poisson process with a piecewise intensityincreasing nearly linearly since the mid-1900s.[7] In this paper, we carefully assess the distribution of
future vent locations using a probabilistic modeling thatcombines both the temporal and spatial analysis of flank erup-tions in the past four centuries. Spatiotemporal probabilitymaps for future vent opening on the flanks of Mt Etna in thenext few years/decades are presented and discussed. Weassume that the temporal patterns extracted from the recordsof past eruptions are useful to predict the future behavior of avolcano; likewise, we consider the regions with a high densityof volcanic structures to be the most probable emission zonesof future lava flows. Clearly the resulting map does not repre-sent a deterministic forecast of future eruptions but a probabi-listic estimate originating from a statistical analysis of the flankeruptive activity of Etna since 1600. Moreover, we show theresults of the statistical modeling of the persistent summitactivity during the last 110 years, considering Etna’s summitcraters both separately or as a whole.
2. Etna Volcanic Eruptions: Types, Frequencies,and Structural Features
2.1. Flank Eruptions in the Last Four Centuries
[8] Before the beginning of the 17th century, the catalog ofEtna flank eruptions is fragmentary and incomplete, but since
Figure 1. Map of Etna, showing the spatial distribution of eruptive fissures (in dark gray) produced by theflank eruptions occurring from 1610 to 2012. The dashed black line delineates the area of 1170 km2
containing the 500m spaced grid of potential vents. (a) Rose diagram representing the geometric orientationof the eruptive fissures; (b) frequency of the eruptive fissures during the last four centuries (the last column onright cumulates the fissures opened in the period 1900–2012).
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1610 an almost complete account of eruptions is available,which has since been summarized by Sartorius vonWaltershausen [1880], Imbo [1928, 1965], and more recentlyby Wadge [1977]. The eruptive behavior of Etna in the last400 years is undoubtedly irregular, with important fluctuationsin eruption frequencies, type of eruptions, and output rates,both in the long (centuries) and short terms (decades) [Hugheset al., 1990; Behncke and Neri, 2003; Allard et al., 2006].[9] The period spanning from 1600 to 1669 was character-
ized by very high output rates (mean of ~1.4m3 s�1;Behncke and Neri, 2003) and represents the culminatingstage of an earlier long cycle lasting several centuries [Tanguyet al., 2003; Clocchiatti et al., 2004].[10] After 1669, a new long cycle began that continues
today. This cycle is made up of a first phase (up to mid-1700 s) characterized by very few, low-fed eruptions (meaneffusion rate less than 0.03m3 s�1), occurring mostly at thevolcano summit. Then, a second phase (up to 1865) markedan increase in the mean output rate (~0.2 m3 s�1) and theresumption of a frequent flank eruptive activity (16 events).Flank eruptions and erupted volumes further increasedin the third phase (mean output ~0.47m3 s�1), up to thepresent [Wadge et al., 1975; Guest and Murray, 1979;Allard et al., 2006].[11] Moreover, short-term eruptive cycles have been
observed since 1865 to date, a period during which flankeruptions have occurred in clusters separated by intervals ofquiescence and summit activity [Behncke and Neri, 2003].These short cycles consist of three phases too: (1) a period oferuptive quiescence lasting less than 3.5 years, (2) a period
of continuous summit activity lasting 6–16 years, and finally(3) a period marked by flank eruptions alternating withsummit activity, lasting 9–22 years. Each short cycle ends witha high flux and/or voluminous flank eruption.[12] An evident increase in the lava output and frequency
of eruptions began in 1950, although the behavior remainedcyclic [Allard et al., 2006]. Effectively, more than 1.6 km3
of volume of products have been erupted starting from1950 at an average rate higher than 0.83m3 s�1. The lastshort eruptive cycle began after the 1991–1993 flank erup-tion (~235� 106m3 volume of erupted products), evolvinginto a couple of years of quiescence, 6 years of graduallymore frequent summit activity, followed by a series of flank(5) and summit (33) eruptions [Behncke et al., 2005; Allardet al., 2006; Neri et al., 2009, 2011; Vicari et al., 2011b].[13] Based on numerous and detailed studies conducted on
the structural features of flank eruptions at Etna [Neri et al.,2011, and references therein], we examined the eruptivefissure systems occurring between 1610 and 2012 (Figure 1).Specifically, we analyzed a total of 61 flank eruptions, whichformed 130 segments of eruptive fissures (Figure 1; in somecases, the same eruption produced multiple eruptive systemswith different orientations), propagated mainly southwardand SSE-ward (38% of the fissures), NE-ward and ENE-ward (22%), eastward (9%), and westward (7%) directions(Figure 1a). During the 17th and 18th centuries, the eruptionsgenerated 22 fissures; 27 eruptive fissures opened during the19th century; and finally, 81 fissures formed during the 20thand 21st centuries (Figure 1b). The increased number oferuptive fissures in the 20th and 21st centuries is significant.[14] The length of eruptive systems ranged from a few hun-
dred meters to about 11.5 km, with an average of ~3 km.About 60% of the eruptive fissures were located above2400m altitude; they were mainly radial with respect to thevolcano summit, even if most follow a ~N-S trend, namelyperpendicular to the direction of regional extension in the areaof Mt Etna volcano [McGuire and Pullen, 1989; Lanzafameet al., 1996; Monaco and Tortorici, 2000; Solaro et al.,2010]. At lower altitude (below 2400m), the eruptive fissureswere clustered in SE, SSE, NE, ENE, east, and west align-ments, following the rift zones. The minimum altitude(~650m above sea level) of an eruptive vent was reachedduring the 1669 eruption, close to Nicolosi town (southernflank, Figure 1). In many cases, eruptive fissures do not eruptalong their entire lengths (except at the very beginnings ofthe event); during the propagation of the fissure, the eruptiveactivity migrates downward, and the main vents arecommonly located on the lower portions of the fissure itself.
Figure 2. Topographic map of Etna’s summit area carriedout in 2007 (from Neri et al. [2008], modified). Contourinterval = 10m. Dashed black line indicates the rim of theformer central crater mapped in 1932 [Istituto GeograficoMilitare, 1934]. Light gray numbers indicate the age of themain lava flows in the period 1996–2007.
Table 1. Number and Type of Eruptions for Each Summit Cratera
aThe central crater includes the activity of Voragine and Bocca Nuova.The last column (Lava Flows) indicates the number of paroxysmal andstrombolian events that were also characterized by (1) rheomorphic lavasformed during highly fed explosive activity; (2) lava overflows emergingfrom one of the summit crater; and (3) lavas erupted from short fissuresopened along the external slope of the summit cone (above ~3000m asl).
2.2. Persistent Summit Activity During the Last110Years
[15] The summit area of Mt Etna has frequently undergonemajor morphological changes due to its persistent eruptiveactivity, both effusive and explosive [Neri et al., 2008]. Foursummit craters are active today: the Voragine, the NE crater,the Bocca Nuova, and the SE crater (Figure 2). Their erup-tive activity consists of the following: (1) continuousdegassing; (2) mild Strombolian explosions accompaniedby low rate (~0.1–1m3 s�1) lava effusion from vents insideor on the flanks of the summit craters; and (3) high-rateparoxysmal (up to 300–400m3 s�1) eruptions, characterizedby lava fountains, lava overflows, and tephra-rich eruptioncolumns several kilometers high.[16] This morphology has not always been as it is today.
Just 100 years ago, there was only one summit crater:the central crater (CC; Guest [1973]). Indeed, during the17th–18th centuries, the summit of the volcano had a singledeep and wide crater depression, which was formed becauseof the collapse of the summit area triggered by the huge1669 eruption. Later on, during the 19th–20th centuries,the volcanic activity resumed within this crater, causing itsgradual filling.[17] During the almost persistent activity of the central
crater (CC), the NE crater (NEC) formed in 1911. At thebeginning, it was a pit located ~3160m above sea level(asl) on the northern slope of the CC cone [Guest, 1973]and characterized mainly by Strombolian activity. NECbecame very active in the second half of the 20th century,producing numerous and occasionally violent and longeruptions (especially in 1947–1960, 1974–1986, and
1995–1998), up to becoming a major pyroclastic cone aswell as the highest point of the volcano (3330m asl in2007; Neri et al., 2008).[18] Starting from the middle of the 20th century, the CC
changed its internal morphology frequently due to theintracrater volcanic activity alternating with subsidence andcollapse phenomena. One of these events led to the creationof the Voragine (VOR; also known as “The Chasm”) in1945. VOR formed in the northeastern portion of the fairly flatfloor of CC [Guest, 1973]. Major eruptive phases occurred atCC in 1960–1964, which culminated in the opening of erup-tive fissures, several paroxysmal events accompanied by hugetephra emissions, continuous lava overflows, and the growthof some pyroclastic intracrater cones [Behncke et al., 2004].Four years later, in 1968, the Bocca Nuova (BN) was formed,still inside the CC, a few tens of meters west of the VOR[Behncke et al., 2003]. BN widened and deepened gradually,always within the CC, becoming even larger than the VOR.Later, in 1998, the Strombolian activity resumed at the craterfloor, generating several lava fountaining episodes (in 1999)that filled the crater and triggered numerous lava overflows[Behncke et al., 2003; Calvari et al., 2003]. After the 2001flank eruption, BN and VOR were involved in subsidenceand sporadic phreatomagmatic explosions, and progressivelythey collapsed, becoming almost a single crater depressionwhose edges are, in part, coincident with those of the CC[Giammanco et al., 2007]. Therefore, it is evident that VORand BN are internal, minor vents of the CC itself (see dashedblack line in Figure 2).[19] The SE crater (SEC) formed during the 1971
eruption. Since its creation, SEC has been the most active
Figure 3. Kolmogorov-Smirnov test of stationarity for Etna’s flank eruptions over the last four centuries.The green step function is the empirical distribution of the eruption onsets, the blue straight line is thetheoretical uniform distribution, and the light blue stripes are the 95% confidence bands. Red dots indicatethe repose times in years (see secondary Y axis on the right side) between the openings of successiveeruptive fissures. The straight red line highlights the decreasing trend of repose times, i.e., eruptionsoccurring more frequently in recent years than in the past centuries.
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of the summit craters of the volcano. At first, it was adegassing pit located close to the southeast base of the CCcone, at ~3070m asl [Behncke et al., 2006]. During the first25 years of activity, SEC erupted quite frequently and built acone about 100m high. The cone has grown dramatically inthe periods 1996–2001 and 2006–2012, through over 143paroxysmal episodes and effusive eruptions. Today it hasreached an elevation of ~3300m, forming also a huge newpyroclastic cone on its eastern slope [Alparone et al.,2005; Behncke et al., 2006; Neri et al., 2008; Vicari et al.,2011b; Ganci et al., 2012a].[20] The progressive increase in eruptive activity charac-
terizing the Mt Etna summit area during the last 110 yearscan be readily seen in Table 1. What is most striking isthe fact that the appearance of the SEC marks a real changein the eruptive frequency. Over the past 41 years, the SEChas produced a number of eruptive events that correspondto more than double the events produced jointly by the CCand NEC in 110 years. Never in the recent past has Mt Etnabeen so active; to find similar levels of activity, wewould probably have to go back several hundred years,when the historical chronicles, however, were certainly notas accurate as today.
3. Statistical Analysis of Flank Eruptions
[21] Over the last four centuries, the completeness andaccuracy of historical data at Mt Etna provides a robustbasis for conducting a statistical analysis to detect spatialand temporal patterns in the distribution of past eventsand hence to formulate the appropriate spatiotemporalprobabilistic model for future flank eruptions.
[22] We analyzed the spatial pattern of eruptive fissuresusing the Clark and Evans [1954] aggregation index R thatmeasures the ratio between the expected nearest-neighbordistances under complete spatial randomness (CSR) andthe observed mean nearest-neighbor distances:
R ¼XNi¼1
dmin ið Þ=Nð Þ !
= 0:5 A=Nð Þ1=2� �
(1)
where dmin(i) is the distance between the ith eruptive fissureand its nearest neighbor, A is the area of the region, and N isthe number of structures considered in the calculation.In order to consider the eruptive fissures in full, dmin is cal-culated as the “minimax distance,” that is, the minimumvalue of the maximum distances between each end pointof the ith eruptive fissure and all the end points of the jtheruptive fissure [Cappello et al., 2012].
Table 2. Estimates of the Parameters d and θa
Parameters Minimum Estimates Best Estimates Maximum Estimates
aCalculated by minimizing the square differences of residuals betweenthe expected and actual number of eruptions over time (best estimates), withthe 95% confidence intervals (minimum and maximum estimates).The eval-uations of d and θ are then used to calculate the recurrence rate l(T2+p)with T2= 2012 and p= 1, 10, 50.
Figure 4. Centroids of the eruptive fissures opened in the last 400 years, grouped in short periods of50 years. A spatial shift is evident over time in the location of the eruptive activity, which becomes progres-sively closer to the summit of the volcano, on the high eastern side. Coordinates are in Universal TransverseMercator (UTM) projection, zone 33N.
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[23] R values less than 1 highlight a cluster tendency,since the observed mean distance between neighboringfissures is less than that expected in random patterns. Requal to 1 points out that casualness is present among data,while R greater than 1 indicates uniformity. The theoreticalmaximum of R is 2.149 occurring when data are maximallydispersed. With historical data at Etna, we obtained an Rvalue equal to 0.027, which proves the nonhomogeneousspatial distribution of eruptive fissures.[24] In addition to the spatial analysis, we examined the
historical records during the last four centuries to detectthe presence of trends or patterns characterizing the tempo-ral distribution of eruption occurrences. We calculated thecumulative number of eruptive fissure systems linked toflank eruptions over time and the inter-event periods, i.e.,the repose times between subsequent eruptions (Figure 3).Both distributions underline the temporal nonstationarityof eruption occurrences, since a growing trend is evidentfor the number of flank eruptions, while a mainly decreasingtendency stands out for repose times during the last30 years. This highlights that volcanic eruptions occurredwith a higher frequency in this last period than in theprevious ~370 years of activity. To formally prove thatthe sequence of eruptive events is not a stationary process,we applied the Kolmogorov-Smirnov test statistic Dn
[Mulargia et al., 1985], which is based on the maximumdifference between the theoretical (uniform) and the empir-ical cumulative distribution functions. Since the historicalrecords of Etna’s flank eruptions provided Dn = 0.267,which is higher than the critical value at a 5% significancelevel (0.174 = 1.36/√n for a large number n of events), wecan reject the null hypothesis of uniform distribution(Figure 3).[25] In order to evaluate the possible shift during time
of the location of the eruptive activity, we also calculatedthe centroids closer to the eruptive fractures in the last400 years, grouping them every 50 years (Figure 4). Theresult indicates that the increasing trend in volcanic activityis accompanied by a migration of the centroids that becameprogressively closer to the summit of the volcano, on thehigh eastern side. This fact is testified by the rapidmorphostructural evolution of the summit area during thelast decades: the former central crater (the single summitcrater existing up to early 1900) was modified by thegrowth of the NE crater (formed in 1911 on the northernside), the Bocca Nuova (formed in 1968 inside the centralcrater and close to the its western rim, see Figure 2), andthe SE crater (formed in 1971 on the southeastern side),which represent the connections of the three main volcanicrifts in the summit area [Neri et al., 2011].
Figure 5. (a) Cumulative number of eruptions (black curve); best estimate calculated by minimizing thesquare differences of residuals between the expected and actual number of eruptions over time (red curve);and the 95% confidence interval (blue curves) of the best estimate. (b) The corresponding power intensityfunctions l(t). The future rates (listed in detail in Table 2) are obtained by extending the curves for thedifferent forecasting periods highlighted by the dashed lines over the gray bar, i.e., 2013 and the next10 and 50 years.
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[26] The statistical analysis conducted on flank eruptions inthe last four centuries demonstrates the spatial nonhomogeneityand the temporal nonstationarity of flank activity, hencesuggesting that the most appropriate space-time probabilisticmodel for future flank eruptions at Etna volcano is anonhomogenous Poisson process (NHPP) with a time-varying intensity function.
4. The Space-Time Probabilistic Modeling ofFlank Eruptions
[27] Probabilistic modeling provides a powerful toolto estimate the timing and location of future eruptions.Typically, modeling exploits statistical analysis on histori-cal information to calculate probability estimates overa particular area of interest and construct a spatiotemporalmap furnishing detailed recurrence rates, i.e., events expectedper unit area per unit time.[28] Here the area of interest on Etna volcano is 1170 km2
(rectangular dotted area of 32.5� 36 km in Figure 1),over which we superimposed a regular grid of potentialvents yielding a resolution of 0.5 km. For each potentialvent (x, y), the probability of at least a new vent openingin the unit area ΔxΔy (0.5 km� 0.5 km) within time Δt iscalculated with the NHPP model as follows:
pa x; y;Δtð Þ ¼ 1� exp �lx y tΔxΔyΔt� �
(2)
with lxyt the space-time varying intensity function calculated as
lxyt ¼XNi¼1
exp �d2i = 2h2� �� �� exp ktið Þ� �
(3)
where di is the distance between the point (x, y) and the itheruptive fissure, h is the smoothing factor, ti is the elapsedtime since the eruption at the ith fissure, N is the total numberof fissures, and k is a constant that assigns larger weights tomore recent events with respect to older ones.
[29] The smoothing factor h (also called bandwidth orwindow width) strictly influences the result of equation (3),controlling how lxyt varies with distance from historicaleruptive fissures. We assigned it a value of 1 km by applyingthe explicit version of the Least Squares Cross-Validation(LSCV) proposed by Worton [1995], which is based onminimizing the integrated square error between the trueand the estimated distribution:
LSCV hð Þ ¼ 1
ph2Nþ 1
4ph2N2
�XNi¼1
XNj¼1
exp �d2ij= 4h2� �� �
� 4 exp �d2ij= 2h2� �� �� �
(4)
where N is the total number of structures considered in thecalculation and dij is the minimax distance.[30] In order to calculate the constant k, we conducted a
retrospective search to quantify how the distribution of theoldest eruptive fissures has affected the formation of themost recent ones. The approach used, called back analysis[Cappello et al., 2011b], allowed us to empirically retrievethe best value of the parameter k using only the known pastdata. We divided all eruptive fissures according to the age oftheir formation in two parts and used the first one as a learning
Figure 6. Spatiotemporal probability maps of flank vent opening for the next (a) 1 , (b) 10, and(c) 50 years. A gradual increase in the probabilities is evident as the forecasting period increases. Thehighest value estimated with our model is very low for 2013 (0.00178), reaches a medium peak for thenext 10 years (0.018), and attains the top value in the spatiotemporal probability map for the next 50 years(0.091). Summit craters are masked because their activity was separately investigated.
Table 3. Estimates of the Best Values for d, θ (Best Estimates), andthe 95% Confidence Intervals (Minimum and Maximum Estimates)and the Relative Recurrence rates l(T2+p) with T2= 2012 andForecasting Periods p = 1, 10Yearsa
Parameters Minimum Estimates Best Estimates Maximum Estimates
aThe estimates are calculated considering the activity of summit craters asa whole.
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data set and the second one as a testing data set. The cutofftime we chose to divide the eruptive fissures is 1981, sinceit determines two meaningful sets from a statistical point ofview: 50 fissures were used for learning and 11 for testing(i.e., the 1983, March 1985, December 1985, 1986–1987,1989, 1991–1993, 2001, 2002–2003, 2004–2005, 2006,and 2008–2009 eruptions). Moreover, from a volcanologicalpoint of view, activity at Etna since 1981 shows a consider-ably increasing trend that further justified our choice[Behncke and Neri, 2003; Behncke et al., 2005; Allardet al., 2006; Salvi et al., 2006; Neri et al., 2008, 2009;Cappello et al., 2011b].[31] The best fit for the constant k was retrieved by evalu-
ating the mean square error of each probability forecast withthe Brier score [Brier, 1950]:
BS ¼ 1
N
XNi¼1
pi � oið Þ2 (5)
where pi is the forecast probability of each grid cell and oiindicates whether an eruptive fissure has been formed in thatcell after 1981 (oi= 1 if at least a fissure has occurred, andoi= 0 if not). The Brier score runs from 0 to 1, with smallervalues indicating better forecasts. We found that the value fork that minimizes BS is �0.00107 and used it in equation (3)for all eruptive fissures.
[32] The function lxyt is then rescaled so that its integralacross the whole area equals the temporal intensity calcu-lated with the power intensity function [Smethurst et al.,2009; and reference therein]:
l tð Þ ¼ dθ
t � T1θ
� �d�1
for t≥T1 (6)
where T1 is the year of the oldest eruptive fissure, t is the yearof interest, and d and θ are unknown positive parameters. Theparameter d determines the shape of the power function: d> 1(resp. d< 1) corresponds to an increasing (resp. decreasing)intensity with time, while d =1 reduces equation (6) to ahomogenous process. The best estimates of d and θ (Table 2)are found by minimizing the square differences of residualsbetween the expected amount (computed as the integral of lfrom T1 to t) and the actual number of eruptions over time(estimated as the cumulative number of events observed upto t) on the entire catalog (from T1 = 1610 to T2 = 2012; seeFigure 5a). In order to indicate the reliability of the estimatesof d and θ, we also listed the 95% confidence intervals(minimum and maximum estimates in Table 2). Using theobtained values of d and θ, we extrapolated the curvesof annual recurrence rates for different forecasting periodsp (1, 10 or 50 years) and calculated the minimum, best,and maximum temporal intensities evaluating equation (6)
Figure 7. Actual cumulative number of summit eruptions (black curve) compared with the best estimate(red curve) and its 95% confidence interval (blue curves). The formations of the NE crater in 1911 and ofthe SE crater in 1971 are highlighted. (b) Power intensity functions l(t) calculated with the temporal ratesfor the next 1 and 10 years reported in Table 3.
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for t=T2+ p (Figure 5b). Obviously, the estimated values ofd> 1 (Table 2) are only representative of the increasing phaseof the current eruptive cycle. Indeed, it is not physically plau-sible that the intensity will increase continuously in the nextyears due to the cyclic variations in output rate and frequencyof Etna’s eruptive activity [Wadge et al., 1975; Hughes et al.,1990; Behncke and Neri, 2003; Allard et al., 2006].
5. Spatiotemporal Probability Maps for FutureVent Opening
[33] The spatiotemporal probability hazard maps for futurevent opening for the three different forecasting periods (1, 10or 50years) are reported in Figure 6. The temporal recurrencerates are those obtained with the best estimates of d and θ(Table 2). The highest value reached by the probability mapof vent opening for the coming year is fairly low, at 0.00178.This is bounded by the temporal recurrence rate (0.216), whichpredicts about one eruption every 5 years. As is evident inFigures 6b and 6c, the probability estimates gradually increasewhen the forecasting periods are 10 years (maximum value of0.018) and 50 years (maximum value of 0.091). Nevertheless,the global trend of the probability distributions is kept, showingthat the areas closer to the summit of the volcano, above2500m above sea level, are where it is very probable that anew eruption will take place. Dissimilarity in the probabilityestimates can be noticed also in the areas at lower altitude,between 2500 and 1800m above sea level. Below 1000m,the expectation of at least a new eruption is very low, exceptin the South Rift, where the probabilities slowly decrease untilthe altitude of ~600m above sea level. This effect is caused bythe presence of the 1669 eruptive fissure.
6. Statistical Modeling of Summit Eruptions
[34] The persistent summit activity documented at Etnafrom the first decades of the 20th century until today representsa good source for a statistical analysis. Thus, here we provide a
more comprehensive and accurate study in forecastingvolcanic eruptions, estimating also the space-time annual rateof eruptive events at the summit craters (Figure 2): the CC(comprising VOR and BN), the NEC, and the SEC (includingthe new cone recently formed on its eastern slope).[35] The data set for the statistical analysis comprises
the various types of eruptions occurring since 1900 at thesummit craters of Etna, including paroxysmal episodes andStrombolian activities (see Table 1). We conducted twokinds of analysis on this data set. First we calculated therecurrence rate of the summit activity considering the wholecatalog of eruptions. Next we divided the data set into threeand estimated space-time forecasts for each summit crater(CC, NEC, and SEC).[36] As for the recurrence rate of the summit activity as a
whole (without distinguishing the activity of each summitcrater), we estimated the best values for the parameters dand θ (Table 3) minimizing the square differences of resid-uals between the expected and the actual number of erup-tions over time (Figure 7a). These best estimates were thenused in the power intensity function described by equation(6) to obtain the curves of recurrence rates with the expectednumber of eruptions for the next 1 and 10 years (Figure 7b).Unlike the analysis of flank eruptions, we decided not to useforecasting periods longer than 10 years since they might
Figure 8. Actual (blue curve) and modeled (red curve) cumulative number of eruptions for the (a) centralcrater (CC), (b) the NE crater (NEC), and (c) the SE crater (SEC). The power intensity functions calculatedwith the best rates for the next 1 and 10 years are also shown respectively for (d) CC, (e) NEC, and (f ) SEC.
Table 4. Best Values Obtained for d and θ and the RelativeRecurrence Rates l(T2+p) with T2= 2012 and Forecasting Periodsp= 1, 10Yearsa
aThe estimates are calculated considering the activity of the centralcrater (since 1900), of the NE crater (since 1911), and of the SE crater(since 1971), separately.
CAPPELLO ET AL.: PROBABILISTIC HAZARD MAPPING
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provide inconsistent results starting from the short timeseries of documented summit eruptions (~110 years). Thebest values of recurrence rates for the coming year (12.327eruptions/year) and the next 10 years (17.030 eruptions/year)estimate that slightly more than one eruption per month isexpected in the entire summit area. In the worst cases, morethan two (25.530) and about three eruptions (35.268) permonth could occur, respectively, in the next 1 and 10 years.These estimates are strongly influenced by the extraordinaryactivity that took place at SEC in 2000 (66 short-term lavafountains) and recently between 2011 and 2012 (25 midtermlava fountains).[37] For the space-time forecasts, we divided the catalog
in three data sets selecting the eruptions occurring at CC,NEC, and SEC. With these three data sets, we used the samemathematical modeling, calculating the best expectednumber of eruptions on the basis of the historical catalogs(Figures 8a–8c), from which we derived the best estimatesfor parameters d and θ (Table 4). The recurrence rates wereagain estimated for the coming year and the next 10 years(Figures 8d–8f). The spatiotemporal analysis suggests thatthe expected number of eruptions at the CC (from 0.461 to0.484) is comparable with the rates obtained for the flankeruptions (from 0.216 to 0.219). Unlike those of the NECand of the SEC, the curve of the annual rate for the CCshows a decrease in the speed of growth. At the NEC,the expected number of eruptions reaches annual rates of1.453 and 1.641, respectively, for the next 1 and 10 years.But the summit crater showing the most exceptionalactivity is undoubtedly at the SEC. On the basis of thehistorical eruptions since its formation in 1971, weexpected a number of eruptions equal to 14.582 for thecoming year, that is, more than one eruption per month,and 22.010 eruptions in the next 10 years, namely slightlyless than two events per month.
7. Conclusive Remarks
[38] We have demonstrated a new way to construct thespatiotemporal probability map of vent opening over aspecific time period. The spatiotemporal probability mapfurnishes detailed recurrence rates, estimating the numberof expected events per unit area per unit time. In order tofind the areas where it is more likely that a new eruption willoccur, the best approach consists in analyzing the pasteruptive history of a volcano to deduce the possible locationof future eruptions.[39] We based the construction of the spatiotemporal
probability map of vent opening on an exhaustive statisticalanalysis and a NHPP model applied to the Etna flankeruptions of the last 400 years. The spatial distribution ofpast eruptive fissures is studied, as well as the spatial shiftin the effusive eruptions, which appears evident in the last30 years of Etna activity. An innovation of our approachconsists in forecasting the location of new eruptive ventsby weighting the most recent events more heavily than theolder ones. If a new eruption occurs, the map can simplybe updated by merging past information with the timingand location of the new vent. In order to make majorchanges to the map, a statistically significant number oferuptions would have to occur at different unexpectedlocations in the study area. The spatiotemporal probability
maps of vent opening are quite different in content andmeaning from the susceptibility map produced by Cappelloet al. [2012], which estimates only the most likely emissionzones. Here, we also considered the frequency of flank erup-tions to evaluate the future timing and areas of Etna prone tovent opening for the coming year and the next 10 and50 years. We chose three different forecasting periods tohighlight how the probability estimates change over time.Since the catalog of flank eruptions at Etna is well studiedand documented only for the last four centuries, forecastingperiods longer than 50 years would provide results lacking insignificance from a statistical point of view.[40] Even though the focus of this study is Mt Etna,
the approach used to assess the most exposed areas to beaffected by new eventual eruptions is meant to be generaland applicable to any volcanic region, if available data aresignificant from a statistical point of view. The spatiotemporalprobability map is extremely important in volcanic hazardsassessment because the degree of danger presented by ahazardous event strongly depends on the eruption ventlocation. Hence, the more rigorous the evaluation of thespatiotemporal probability map of vent opening, then thegreater the accuracy of the hazard map.[41] Finally, the results of the analysis of the persistent
summit activity during the last 110 years highlight that thehazard rate for eruptive events is not constant with timeand differs for each summit crater of Mt Etna. The variationsin the recurrence rates at the summit craters indicate that inthe last century the main eruptive activity was initiallylocated at the central crater, then migrated to the NE craterand later to the SE crater, as the new summit craters wereformed. Most likely, the SE crater will remain the mostactive crater in the summit area for the near future.
[42] Acknowledgments. This work was developed in the frame ofthe TecnoLab, the Laboratory for the Technological Advance in VolcanoGeophysics organized by INGV-CT, DIEES-UNICT, and DMI-UNICT.We thank Geoff Wadge and an anonymous reviewer for constructive andsupportive comments that helped to improve the manuscript.
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