Volcanic eruption time forecasting using a stochastic enhancement of the
Failure Forecast Method
Abstract
In this study, we use a doubly stochastic model to develop a short-term
eruption forecasting method based on precursory signals. The method
enhances the Failure Forecast Method (FFM) equation, which represents
the potential cascading of signals leading to failure. The reliability
of such forecasts is affected by uncertainty in data and volcanic system
behavior and, sometimes, a classical approach poorly predicts the time
of failure. To address this, we introduce stochastic noise into the
original ordinary differential equation, converting it into a stochastic
differential equation, and systematically characterize the uncertainty.
Embedding noise in the model can enable us to have greater forecasting
skill by focusing on averages and moments. In our model, the prediction
is thus perturbed inside a range that can be tuned, producing
probabilistic forecasts. Furthermore, our doubly stochastic formulation
is particularly powerful in that it provides a complete posterior
probability distribution, allowing users to determine a worst-case
scenario with a specified level of confidence. We verify the new method
on simple historical datasets of precursory signals already studied with
the classical FFM. The results show the increased forecasting skill of
our doubly stochastic formulation. We then present a preliminary
application of the method to more recent and complex monitoring signals.