Long-term forecasting of volcanic explosivity

It has been 30 years since the terms time-predictable (repose length increases with previous eruption size) and size-predictable (eruption size increases with repose length) entered the volcanological lexicon. While much evidence of, and models for, the former have emerged, the latter is still largely unsubstantiated. Statistical tests for size-predictability from individual volcanoes suffer from insufficient power and the inherent non-normality and non-linearity in the relationship. Aggregating data from several volcanoes is difficult due to the different temporal and size scales involved. Here, we consider characterizing the volcanic explosivity index (VEI) distribution by a parameter, which is itself influenced by the length of the previous repose, the state of the conduit (open or closed) and possibly other factors. Dependency between the parameters for different eruptions at the same volcano is introduced using a multilevel (hierarchical) Bayesian formulation. Using data from Indonesia, largely since AD 1800, we find that there is a significant probability (>0.999) that the VEI of the next eruption from closed conduit volcanoes increases with increasing repose length. For example, a further 10-yr wait for the next eruption from Kelut increases the probability of a VEI > 2 by approximately 11 per cent. On the other hand, open conduit volcanoes show no evidence of an increase in VEI with repose length. The results are insensitive to the details of the VEI distribution, prior distributions or number of levels in the Bayesian structure.