Long-term forecasting of the extreme eruptions of Etna

Journal of Volcanology and Geothermal Research 83 Ž1998. 167–171

Long-term forecasting of the extreme eruptions of Etna A. Palumbo

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Department of Geophysics and Volcanology, UniÕersity of Naples Federico II, Largo S. Marcellino, 10, 80138 Naples, Italy Received 27 February 1997; accepted 20 November 1997

Abstract Until now, the widely used predictive long-term hazard models of the most intense natural phenomena do not yield predictions other than the mean return period. To achieve less uncertain estimates, an alternative model is proposed. The analysis of the eruptions of Etna from 1868 to 1993 shows that the time interval Dt between consecutive large eruptions is clearly random, whereas the total volume of tephra ejected during Dt is roughly constant. Taking into account the above evidence, the model yields significant long-term forecasts both of the time and of the intensity of future large eruptions. The large volume of tephra ejected by the volcano since the last intense eruption in 1980 allows the model to estimate that the next large eruption will not to take place soon. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Etna; volcanic eruptions; long-term forecasting model

1. Introduction Many papers have dealt with the historical series of the eruptions of Etna ŽRodwell, 1878; Rittmann, 1964; Wadge, 1977; Kieffer, 1982; Tanguy, 1979; Mulragia et al., 1985.. Simkin and Siebert Ž1994. provided a list of eruptions from 1816 BP until 1993 AD. None of these papers provides long-term forecasting estimates of the largest eruptions of Etna. Since the first model provided by Gumbel Ž1958., many authors have proposed alternative statistical techniques for severe event frequency-correlations: the two-parameter gamma, log Gumbel, log normal Hazen, log Pearson type III, and Weibull distributions ŽTurcotte and Green, 1993.. The time distributions of many natural phenomena, like volcanic erup)

Corresponding author.

tions, earthquakes etc., do not exhibit a Poissonian character and so do not allow the application of Poissonian models such as the exponential ones. Turcotte Ž1992. has proposed a scale-invariant approach which requires the cumulative distribution of events with different sizes to follow a power law which, very often, does not fit the observed distributions. Non-Poissonian slip predictable and time predictable models based on a renewal process with a mixture failure time density have been proposed by Shimazaki and Nakata Ž1980.. The results of these models have poor practical forecasting utility because of the large uncertainty of the computed values of the return period ŽRikitake, 1976., and also because the return period indicates, for an event of intensity greater than a fixed threshold, only a large interval during which the event will probably occur. Simkin and Siebert Ž1994. comment that statistical

0377-0273r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 3 7 7 - 0 2 7 3 Ž 9 8 . 0 0 0 1 3 - 4

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investigations of the frequency of volcanic eruptions have been applied with seeming success, only to be contradicted by other workers using different approaches and different data sets. The main reason for the failure of these models is related to the unpredictability and to the complexity of the evolution of many natural systems Žvolcanic, tectonic, climatic, oceanic, biological etc.. that make both their physical modelling and the long-term forecasting of their extreme events unreliable. To contribute to this problem, a simple long-term predictive hazard model is proposed for the long-term forecasting of large eruptions of Etna.

2. Analysis of the data In the present paper, I examine the eruptions of Etna reported by the catalogue of Simkin and Siebert Ž1994. which uses the VEI Žvolcanic explosively index. as a quantitative measure of the intensity of volcanic activity ŽNewhall and Self, 1982.. Since, according to the authors, the reliability of the catalogue is very poor before 1850, and since no eruptions with VEI G 4 have taken place since 1787, I have searched for the long-term forecasting of eruptions with VEI s 3 after 1868. From Table 1, the number x of eruptions with VEI s 1 which occurred during each 20 years inter-

Table 1 Time interval

1790–1809 1810–1829 1830–1849 1850–1869 1870–1889 1890–1909 1910–1929 1930–1949 1950–1969

Number of events with VEIs1a

VEI s 2 b

VEIs 3 c

0 3 0 1 1 4 10 6 3 x s 3.1 SDs 3.3 SDr x s1.1

6 2 5 4 4 3 6 5 6 x s 4.6 SDs1.4 SDr x s 0.30

1 1 0 1 2 1 1 1 1

a,b,c Number of eruptions with VEIs1, VEIs 2 and VEIs 3 occurring during each 20-year interval; x and SD denote, respectively, the mean value and the population standard deviation.

val averages 3.1 with a population standard deviation ŽSD. equal to 3.3 and hence SDrx s 1.1. The corresponding values for the eruptions with VEI s 2 are x s 4.6, SD s 1.4 and hence SDrx s 0.30. The scattering relative to the number of eruptions with VEI s 2 is smaller than that corresponding to the events with VEI s 1 but still large. The mean number n of these events occurring after 1910 Ž n s 12.0. is about two times larger than the pre-1910 ones Ž n s 5.5., markedly contributing to the above observed large scattering. The apparent increase in the number of events may be due to increasingly accurate records rather than to any real change in the number of these events, so that the post-1910 period is more representative of the activity of Etna. This is also supported by the absence of an increase in the corresponding number of events with VEI s 3, since a large event could hardly pass unnoticed by observers, and is moreover supported by the largest increase in the number of events with VEI s 1 which are more likely to pass unnoticed. In 1883, an intense earthquake took place around the volcano Epomeo on the Island of Ischia, claiming numerous victims. This event suggested to the National Institute of Geodynamics to set up a volcanological observatory on the Island. After the catastrophic earthquake occurred in Messina, Sicily, near Etna in 1908, the authorities realised the importance of improving the volcanological survey by increasing the number of personnel and of instruments at the observatory of Etna. One of the effects was the higher accuracy of the observations. It follows that the most reliable data are those recorded during this century. Table 1 shows that the number of eruptions recorded each 20 years suddenly increased after 1910: namely those with VEI s 1 from 1.5 to 6.3 Žfactor 4.2., those with VEI s 2 from 4.0 to 5.7 Žfactor 1.4. and those with VEI s 3 from 1 to 1 Žfactor 1. indicating, as expected, a major increase for the events with VEI s 1. To compute the pre-1910 data for the events missing from these records, I, therefore, multiplied the number of these eruptions by the factors 4.2 and 1.4, respectively, for those with VEI s 1 and VEI s 2, reducing the scattering of the data. It is worth noting that the above normalisation has not markedly influenced the results of the proposed forecasting model ŽTables 2 and 3..

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Table 2 Years of occurrence of eruptions with VEI s 3 Year

1868 1879 1886 1899 1912 1940 1959 1980

Dt

10.5 7.0 13.2 13.1 27.1 19.6 20.8

Number of events with

Normalised

VEI s 1

VEI s 2

VEI s 1

VEI s 2

VEI s 1

Volume VEI s 2

VEI s 3

0 1 2 3 10 7 1

3 1 2 3 6 8 11

0 4.2 8.4 12.6 10 7 1

4.2 1.4 2.8 4.2 6 8 11

0 1.7 3.4 5.0 4 2.8 0.4

4.2 1.4 2.8 4.2 6 8 11

2.5 2.5 2.5 2.5 2.5 2.5 2.5

Total V

Vc

VrDt

6.7 5.6 8.7 11.7 12.5 13.3 13.9

6.7 12.3 21.0 32.7 45.2 58.5 72.4

0.64 0.80 0.68 0.89 0.46 0.68 0.67

Inter-arrival time is denoted by Dt ; V denotes the total volume of tephra ejected by all the events that occurred during the interval Dt including the final events with VEI s 3; Vc indicates the cumulate volume of V. Dt is measured in years and all volumes are in units of 10 5.7 m3.

The catalogue does not report the volume of the lava and of the tephra for all the events, but only for some of them. I have computed the mean values of these available values, which yields for the average volumes of tephra ejected by eruptions with VEI s 1, 2 and 3 the values 10 5.3, 10 5.7 and 10 6.1 m3, respectively. The series of all the eruptions Žafter normalisation. was analysed following the method of Gumbel Ž1958.. In his widely used traditional method the size m of an event Žin this case the VEI. is hypothesised to be a random variable distributed with a cumulative distribution N s ceyb m . The identification of the specific limits, inside which the cumulate number is related to m according to the exponential law, is

easily obtained by verifying the degree of linearity of the relationship ln N s ln c y bm. The mean return period P computed according to this model for the eruptions with VEI G 3 was found to be equal to 18.6 years. Palumbo Ž1997a. has shown that natural systems controlled by the principle of self-organised criticality, like volcanic systems, reach their critical state after a time lag from the last large event longer than one half of the mean return period. The mean return period represents only a time interval within which the eruption will probably take place without, however, providing any information on the year when the event will more probably occur. To contribute to the solution of this problem, I have related the inter-arrival times of the large erup-

Table 3 Years of occurrence of eruptions with VEI s 3 Year

1868 1879 1886 1899 1912 1940 1959 1980

Dt

10.5 7.0 13.2 13.1 27.1 19.6 20.8

Number of events with

Volume

VEI s 1

VEI s 2

VEI s 1

VEI s 2

VEI s 3

0 1 2 3 10 7 1

3 1 2 3 6 8 11

0 0.4 0.8 1.2 4.0 2.8 0.4

3.0 1.0 2.0 3.0 6.0 8.0 11.0

2.5 2.5 2.5 2.5 2.5 2.5 2.5

Total V

VrDt

Vc

5.5 3.9 5.3 6.7 12.5 13.3 13.9

0.52 0.56 0.40 0.51 0.46 0.68 0.67

5.5 9.4 14.7 21.4 33.9 47.2 61.1

Inter-arrival time is denoted by Dt ; V denotes the total volume of tephra ejected by the number Žnon-normalised. of all the events that occurred during the interval Dt including the final events with VEI s 3; Vc indicates the cumulate volume of V. Dt is measured in years and all volumes are in units of 10 5.7 m3.

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tions to the volume of tephra ejected during such time intervals.

3. Results I have denoted the inter-arrival time between successive major events by Dt Žyears. and have computed the total volume V Žin units of 10 5.7 m3 . of tephra ejected by small eruptions ŽVEI s 1 and VEI s 2. which occurred during Dt including the contribution of the last large one, assuming V s 10 5.3, 10 5.7 and 10 6.1 m3, respectively, for an eruption with VEI s 1, 2 and 3. The cumulative number Vc has been plotted vs. t in Fig. 1. Reported in Table 2 are: Ža. the year of occurrence of the largest eruptions; Žb. the inter-arrival times between successive large eruptions Dt Žyears.; Žc. the total volume V ejected during Dt ; Žd. the ratio VrDt and Že. the cumulative value of the volumes Vc . Table 3 gives the data of Table 2 without normalising the number of eruptions. Because of the highest reliability of the eruptions recorded during this century, it seems more profitable to analyse only the data since 1899. The main

Fig. 1. Cumulate value Vc Ž10 5.7 m3 . of the volume of tephra erupted by the volcano vs. the time Žin years.. The terminal point has coordinates Žyear 2000; Vc s85.2=10 5.7 m3 . indicating for the year 2000 the predicted occurrence of the next large eruption.

results of this analysis are: Ža. The fairly constant value of the volume V ejected during any Dt Ž V s 12.8 " 0.8 = 10 5.7 m3 .; Žb. the high significance level of the linear relationship of the Vc –t plots Žcoefficient of correlations 1, significant at 0.01 level.; Žc. the large scattering of the series of all Dt which does not allow any prediction ŽDts 15.9 " 6.4 years.; Žd. the significant mean value of all the ratios DtrV s 0.69 " 0.12.

4. Long-term prediction of the extreme eruptions From the fairly constant value of V during any Dt ŽTable 2. and from the very significant linear relationship between Vc and Dt ŽFig. 1. one may estimate the date of the next large eruption as follows. Assume that, after a time interval DXt larger than one-half of the mean return period, i.e., DXt ) 9.3 years from the last large eruption, precursors indicate that the volcano is becoming more active. From the volcanic records one computes the volume of tephra ejected since the last large eruption denoted VcX . If VcX is smaller than the volume VcY given by Fig. 1 as corresponding to DXt , two alternatives hold: Ži. several relatively intense eruptions could occur in the near future; or Žii. an extreme eruption might take place. The first hypothesis is not realistic since the data show that VrDt does not vary much during any time interval, and so an extreme eruption with ejection of tephra approximately equal in volume to Õ s VcY y VcX is expected to occur in the near future. In any case Õ will increase with t, especially if the rising rate of VcX continues to be smaller than the slope of the straight line of Fig. 1. When Õ G 10 6.1 m3 , an eruption with VEI G 3 may be expected to take place soon. The contrary holds if VcY - VcX , in which case a large eruption is not expected soon. It is obvious that the significance level of these estimates increases with DXt since it coherently decreases the time interval Ž Dt y DXt . within which we have no information on the future of V. The uncertainty of the estimate is related to the significance level of the linear relationship obtained for the V–Dt plots of Fig. 1 which is very high. The actual volume of tephra ejected during the 17-year interval from 1980 to the present is 12.8 =

A. Palumbor Journal of Volcanology and Geothermal Research 83 (1998) 167–171

10 5.7 m3 which yields at present Vc s 72.4 q 12.8 s 85.2 = 10 3. The abscissa of such a value on the straight line of Fig. 1 is 132, so that the next large eruptions of Etna is predicted to occur in the year 1868 q 132 s 2000, and probably later, since further small eruptions will very probably take place up to that year. From 2000 it would be practically profitable to search for tidal terms in the seismicity around the volcano following Palumbo Ž1986. and verify the physical explanation of the suggested tidal triggering mechanism ŽPalumbo, 1997b..

5. Conclusion The main result of the present investigation is the finding of the fairly constant value of the volume of tephra ejected by the volcano during any time-interval between subsequent large events, which has helped their long-term forecasting. Moreover, since such volumes may represent an index of the energy released by the volcano, the small ranges of variability of the ratios VrDt would indicate a small variability of the average power output, confirming the similar finding for the eruptions of Vesuvius ŽPalumbo, 1997b. and of the largest eruptions of the world ŽPalumbo, 1997c..

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