Chaos hides and generates order: An application to forecasting the next eruption of Vesuvius

The poissonian and non-fractal characters generally exhibited by the most intense natural events do not allow the application of the current exponential and power law long-term hazard predictive models, and have suggested searching for a new model. This has been set up also taking into account that the random sequence (representing disorder) of these events is linked to the duration of the stationary small ones (representing order). The model, proposed in terms of the orbit of a simple non-linear hazard function, simulates the large eruptions of Vesuvius quite well and permits estimation of the next subplinian eruption to occur there around A.D. 2030. A short range forecasting model based on the tidal triggering is also provided and discussed. When large tidally triggered M2 term in the earthquakes at Vesuvius become significant at the 0.01 level the proposed long-term hazard model will yield a more accurate estimate of the above prediction.