In this study, we detail a new prediction-oriented procedure aimed at volcanic hazard assessment based on geophysical mass flow models with heterogeneous and poorly constrained output information. Our method is based on an itemized application of the empirical falsification principle over an arbitrarily wide envelope of possible input conditions. In particular, instead of fully calibrating input data on past observations, we create and explore input values under more general requirements of consistency, and then we separately use each piece of empirical data to remove those input values that are not compatible with it, hence defining partial solutions to the inversion problem. This has several advantages compared to a traditionally posed inverse problem: (i) the potentially non-empty intersection of the input spaces of partial solutions fully contains solutions to the inverse problem; (ii) the partial solutions can provide hazard estimates under weaker constraints potentially including extreme cases that are important for hazard analysis; (iii) if multiple models are applicable, specific performance scores against each piece of empirical information can be calculated. We apply our procedure to the case study of the Atenquique volcaniclastic debris flow, which occurred in the State of Jalisco (MX), 1955. We adopt and compare three depth averaged models currently implemented in the TITAN2D solver, available from vhub.org. The associated inverse problem is not well-posed if approached in a traditional way. However, we show that our procedure can extract valuable information for hazard assessment, allowing the exploration of the impact of model flows that are similar to those which occurred in the past, but differ in plausible ways.

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.