Forecasting explosion repose intervals with a non-parametric Bayesian survival model: Application to Sakura-jima volcano, Japan

Forecasting the repose between eruptions at a volcano is a key goal of volcanology for emergency planning and preparedness. Previous studies have used the statistical distribution of prior repose intervals to estimate the probability of a certain repose interval occurring in the future, and to offer insights into the underlying physical processes that govern eruption frequency. However, distributions are only decipherable after the eruption, when a full dataset is available, or not at all in the case of an incomplete time-series. Thus there is value in using an approach that does not assume an underlying distribution in forecasting likely repose intervals, and that can make use of additional information that may be related to the duration of repose. The use of a non-parametric survival model is novel in volcanology, as the size of eruption records is typically insufficient. Here, we apply a non-parametric Bayesian grouped time Markov Chain Monte Carlo (MCMC) survival model to the extensive 58-year eruption record (1956 to 2013) of Vulcanian explosions at Sakura-jima volcano, Japan. The model allows for the use of multiple observed and recorded data sets, such as plume height or seismic amplitude, even if some of the information is incomplete. Thus any relationships between explosion variables and subsequent or prior repose interval can be investigated. The model was successfully able to forecast future repose intervals for Sakura-jima using information about the prior plume height, plume colour and repose durations. For plume height, smaller plumes are followed by shorter repose intervals. This provides one of the first statistical models that uses plume height to quantitatively forecast explosion frequency.