A unified probabilistic framework for volcanic hazard and eruption forecasting

The main purpose of this article is to emphasize the importance of clarifying the probabilistic framework adopted for volcanic hazard and eruption forecasting. Eruption forecasting and volcanic hazard analysis seek to quantify the deep uncertainties that pervade the modeling of pre-, sin-, and post-eruptive processes. These uncertainties can be differentiated into three fundamental types: (1) the natural variability of volcanic systems, usually represented as stochastic processes with parameterized distributions (aleatory variability); (2) the uncertainty in our knowledge of how volcanic systems operate and evolve, often represented as subjective probabilities based on expert opinion (epistemic uncertainty); and (3) the possibility that our forecasts are wrong owing to behaviors of volcanic processes about which we are completely ignorant and, hence, cannot quantify in terms of probabilities (ontological error). Here we put forward a probabilistic framework for hazard analysis recently proposed by Marzocchi and Jordan (2014), which unifies the treatment of all three types of uncertainty. Within this framework, an eruption forecasting or a volcanic hazard model is said to be complete only if it (a) fully characterizes the epistemic uncertainties in the model's representation of aleatory variability and (b) can be unconditionally tested (in principle) against observations to identify ontological errors. Unconditional testability, which is the key to model validation, hinges on an experimental concept that characterizes hazard events in terms of exchangeable data sequences with well-defined frequencies. We illustrate the application of this unified probabilistic framework by describing experimental concepts for the forecasting of tephra fall from Campi Flegrei. Eventually, this example may serve as a guide for the application of the same probabilistic framework to other natural hazards.