Improvements to a lava flow simulation workflow with statistical and deterministic optimizations

Numerical modeling is a powerful tool for predicting the most likely paths that lava flows may follow during an ongoing eruption. In particular, 2D models represent an excellent compromise between execution time and accuracy in simulating lava flows. These models can assimilate, as input data for numerical simulations, physical parameters provided by remote sensing or field observations such as the time-averaged discharge rate (TADR), the vent position, and the extent of the active lava field.

However, uncertainties associated with these parameters, combined with the simplifications inherent in the adopted numerical approaches, make it challenging to define the optimal conditions that best reproduce the actual lava flow and to make a reliable forecast of its evolution. Furthermore, simple 2D modeling struggles to accurately reproduce composite lava fields, which are generated from the overlap of multiple lava flow units that induces changes in the original topography and from unpredictable eruptive dynamics (e.g., opening of new vents, formation of lava tubes, and fluctuations in effusion rates). More complex eruptive dynamics can be addressed by simulating the different lava flow units through a multistep approach that includes multiple vents; however, this strategy increases the dimensionality of the parameter space required to run the model, leading to higher computational costs.

In this regard, an optimization strategy is fundamental to identify the best-fit solution by exploring the parameter space within a relatively short time. In this study, two methods are adopted: i) the Metropolis–Hastings approach, part of the Markov Chain Monte Carlo (MCMC) family, which performs a sequential refinement of the input parameters; and ii) the Nelder–Mead approach, a direct search method that minimizes a nonlinear objective function. The two methods differ in their goals and outcomes. The Metropolis–Hastings approach is designed to fully explore the multidimensional parameter space and to provide probability distributions of the parameters, whereas the Nelder–Mead approach aims to identify a single optimal solution that minimizes the mismatch between simulated and observed lava flows. The latter method significantly reduces computational costs compared to the MCMC approach; however, its performance may be affected by the presence of local minima, potentially preventing convergence toward the global minimum.

Both methods are tested on two recent effusive Mt. Etna (Italy) eruptions: the 27 February–1 March 2017 eruption, during which a single lava flow unit was emplaced over three days, and the 13 May–14 June 2022 eruption, characterized by multiple lava flows emitted from several vents that opened sequentially during the eruptive activity. The development of workflows based on these methods represents an important step towards the accurate, near-real-time reproduction of lava flows, which is essential for rapid hazard forecasting during volcanic crises and can be a powerful tool in assisting the mitigation of volcanic risk.