Forecasting the duration of volcanic eruptions: an empirical probabilistic model

Gunn, L. S.; Blake, S.; Jones, M. C. and Rymer, H. (2014). Forecasting the duration of volcanic eruptions: an empirical probabilistic model. Bulletin of Volcanology, 76(1), article no. 780.



The ability to forecast future volcanic eruption durations would greatly benefit emergency response planning prior to and during a volcanic crises. This paper introduces a probabilistic model to forecast the duration of future and on-going eruptions. The model fits theoretical distributions to observed duration data and relies on past eruptions being a good indicator of future activity. A dataset of historical Mt. Etna flank eruptions is presented and used to demonstrate the model. The data has been compiled through critical examination of existing literature along with careful consideration of uncertainties on reported eruption start and end dates between the years 1300 AD and 2010 and data following 1600 is considered to be reliable and free of reporting biases. The distribution of eruption durations between the years 1600 and 1670 is found to be statistically different from that following 1670 and represents the culminating phase of a century-scale cycle. The forecasting model is run on two datasets ofMt. Etna flank eruption durations; 1600-2010 and 1670-2010. Each dataset is modelled using a log-logistic distribution with parameter values found by maximum likelihood estimation. Survivor function statistics are applied to the model distributions to forecast (a) the probability of an eruption exceeding a given duration, (b) the probability of an eruption that has already lasted a particular number of days exceeding a given total duration and (c) the duration with a given probability of being exceeded. Results show that excluding the 1600-1670 data has little effect of the forecasting model result, especially where short durations are involved. By assigning the terms ‘likely’ and ‘unlikely’ to probabilities of 66 % and 33 %, respectively the forecasting model is used on the 1600-2010 dataset to indicate that a future flank eruption on Mt. Etna would be likely to exceed 20 days (± 7 days) but unlikely to exceed 68 days (± 29 days). This model can easily be adapted for use on other highly active, well-documented volcanoes or for different duration data such as the duration of explosive episodes or the duration of repose periods between eruptions.

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