Abstract
Forecasting eruption onsets has received much attention, in both the short and long term. However, an eruption is not easily reduced to an instant in time, and forecasting what happens after eruption onset has received little attention. Any useful definition of an eruption has to allow for activity over scales ranging from days to decades, and can do so only by allowing for multiple eruptive phases. These phases can be defined by having different styles (e.g. effusive and/or explosive) of activity and/or quiescent periods between them. A vital question then presents itself: given what we have seen so far of the eruption, what is likely to happen next? We have recoded a global database of multiple-phase eruptions provided by the Smithsonian Institution’s Global Volcanism Program and the USGS into eight major styles of activity. The resulting database contains c. 700 multi-phase eruptions, with each eruption having up to 50 non-quiescent phases. The resulting record of transitions between states is relatively dense, and a probability tree that models 850 possible phase sequences is infeasible. Thus, we use (semi-)Markov chain models in order to assess the probability of transitioning from one phase of activity to another, as a function of the recent eruption activity. Markov chains describe the path from state to state i.e. from one style of activity to another, under the assumption that only the present state determines the probability of the next state, but the definition of ‘state’ can be extended. The ‘order’ of a Markov chain is the number of previous consecutive phases that are considered to define the current state controlling the next transition, and thus higher order Markov chains can account for a greater degree of memory. A semi-Markov chain is one in which the duration in a given state is not necessarily memoryless. We show how a second-order semi-Markov chain can be used to calculate likelihoods for the next style of activity during an eruption, conditional on the type and elapsed duration of the current phase, and the type and duration of the one preceding it. We find that solely effusive behaviour is unlikely to precede violent explosions, and that Plinian eruptions only become more likely during a sequence once a major eruption occurs. A quantitative method for forecasting intra-eruptive activity supports long-term and short-term decision making. To further refine the model, we discuss possible future developments to differentiate between volcanoes, and to incorporate monitoring data in real time to update forecasts.