Tephra fallout hazard assessment is commonly undertaken with the development of probabilistic maps that rely on numerical models. Among the steps for map production, the definition of input parameters of the model (including atmospheric conditions), the physical approximations of the numerical simulations, and the probabilities of occurrence of different eruption types in specific time frames are among the most critical sources of uncertainty. In this paper, we present a tephra fallout hazard assessment study for two volcanoes (Cotopaxi and Guagua Pichincha) in Ecuador. We utilize the coupled PLUME-MoM/HYSPLIT models, and we develop a procedure for uncertainty quantification where: i) we quantify the uncertainty on eruptive source parameters and eruption type occurrence through expert elicitation; ii) we implement a new procedure for correlations between the different parameters, and iii) we quantify the uncertainty of the numerical model by testing it with past eruptions and by deriving coefficients of mean model overestimation/underestimation. Probability maps of exceedance, given a deposit thickness threshold, and thickness maps, given a probability of exceedence, are produced for eruption of sub-Plinian and Plinian types, which are then merged into single maps concerning the next eruption. These are described according to the uncertainty distribution of eruption type occurrence probabilities, in terms of their 5th percentile, mean and 95th percentile values. We finally present hazard curves describing exceeding probabilities in 10 sensitive sites within the city of Quito. Additional information includes the areal extent and the people potentially affected by different isolines of tephra accumulation.

We describe a new method for the reconstruction (or forecast) of probabilities that distal geographic locations were inundated by a large pyroclastic density current (PDC) in terms of the flow mass and related uncertainties. Using appropriate model input uncertainty distributions, derived from expert judgements using the equal weights combination rule, we can estimate the mass amount needed to reach a marginal locality at any given confidence level and compare this with ambiguous or inexact peripheral field data. Our analysis relies on different versions of the Huppert and Simpson (1980) integral formulation of axisymmetric gravity-driven particle currents. We focus on models which possess analytical solutions, enabling us to utilize a very fast functional approach for enumerating results and uncertainties. In particular, we adapt the ‘energy conoid’ approach to generate inundation maps along radial directions, based on comparison of the mass-dependent kinetic energy of the flow with the potential energy control by topography in the direction of flow at distal ranges. We focus on two alternative conceptual models: (i) Model 1 assumes the entire amount of solid material originates from a prescribed height above the volcano and flows as a granular current slowed by constant friction; (ii) Model 2 is a multi-phase formulation and includes, in addition to suspended particles, interstitial gas thermally buoyant with respect to surrounding cold air. In the latter case, the flow stops propagating at the surface when the solid fraction becomes less than a critical value, and there is lift-off of the remaining mixture of gas and small particulates. Our model parameters can be further constrained where there is reliable field data or information from analogue eruptions. Finally, we used a Bayes Belief Network related to each inversion model to evaluate probabilistically the uncertainties on the mass required, estimating correlation coefficients between input variables and the calculated mass. For any major magnitude ignimbrite PDC scenario, our method provides a rational basis for assessing the probability of distal flow inundation at critical peripheral locations when there is major uncertainty about the actual or predicted extent of flow runout. Example case histories are illustrated.

The study focuses on the estimation and modeling of the temporal rates of major explosions and paroxysms at Stromboli volcano (also named small-scale and large-scale paroxysms respectively). The analysis was further motivated by the paroxysm of July 3rd 2019, which raised, once again, the attention of the scientific community and civil protection authorities on the volcanic hazards of Stromboli. In fact, at the present state of knowledge, major explosions and paroxysms cannot be forecasted based on monitoring data, and a full probabilistic assessment based on past eruption data would be quite useful for scientific and civil protection purposes. In the study we perform a time series analysis either considering the last ~150 years of reconstructed activity and the most recent 35 years. We included the estimation of event rates and rate changes in time. Results clearly highlight that the activity is non-homogeneus in time, with a significant low of activity between about 1960 and 1990. Maximum values of event rates were computed during the first half of last century, for both major explosions and paroxysms, whereas the rate of paroxysms is significantly lower in the last decades with respect to maximum rates. We also accomplish a statistical analysis of the inter-event times, enabling us to determine if the data can be modeled as a Poisson process or not, e.g. if it shows time dependent distributions, recurring cycles, or temporal clusters. The uncertainty quantification on the current and future rates is mainly related to the choice of the modeling assumptions. The study represents a crucial progress towards quantitative hazard and risk assessments at Stromboli, which is particularly relevant for the thousands of people (e.g. tourists, guides and volcanologists) that regularly climb the volcano every year.

We present two models using monitoring data in the production of volcanic eruption forecasts. The first model enhances the well-established failure forecast method introducing an SDE in its formulation. In particular, we developed new method for performing short-term eruption timing probability forecasts, when the eruption onset is well represented by a model of a significant rupture of materials. The method enhances the well-known failure forecast method equation. We allow random excursions from the classical solutions. This provides probabilistic forecasts instead of deterministic predictions, giving the user critical insight into a range of failure or eruption dates. Using the new method, we describe an assessment of failure time on present-day unrest signals at Campi Flegrei caldera (Italy) using either seismic count and ground deformation data. The new formulation enables the estimation on decade-long time windows of data, locally including the effects of variable dynamics. The second model establishes a simple method to update prior vent opening spatial maps. The prior reproduces the two-dimensional distribution of past vent distribution with a Gaussian Field. The likelihood relies on a one-dimensional variable characterizing the chance of material failure locally, based, for instance, on the horizontal ground deformation. In other terms, we introduce a new framework for performing short-term eruption spatial forecasts by assimilating monitoring signals into a prior (“background”) vent opening map. To describe the new approach, first we summarize the uncertainty affecting a vent opening map pdf of Campi Flegrei by defining an appropriate Gaussian random field that replicates it. Then we define a new interpolation method based on multiple points of central symmetry, and we apply it on discrete GPS data. Finally, we describe an application of the Bayes’ theorem that combines the prior vent opening map and the data-based likelihood product-wise. We provide examples based on either seismic count and interpolated ground deformation data collected in the Campi Flegrei volcanic area.

Episodes of slow uplift and subsidence of the ground, called bradyseism, characterize the recent dynamics of the Campi Flegrei caldera (Italy). In the last decades two major bradyseismic crises occurred, in 1969/1972 and in 1982/1984, with a ground uplift of 1.70 m and 1.85 m, respectively. Thousands of earthquakes, with a maximum magnitude of 4.2, caused the partial evacuation of the town of Pozzuoli in October 1983. This was followed by about 20 years of overall subsidence, about 1 m in total, until 2005. After 2005 the Campi Flegrei caldera has been rising again, with a slower rate, and a total maximum vertical displacement in the central area of ca. 70 cm. The two signals of ground deformation and background seismicity have been found to share similar accelerating trends. The failure forecast method can provide a first assessment of failure time on present‐day unrest signals at Campi Flegrei caldera based on the monitoring data collected in [2011, 2020] and under the assumption to extrapolate such a trend into the future. In this study, we apply a probabilistic approach that enhances the well‐established method by incorporating stochastic perturbations in the linearized equations. The stochastic formulation enables the processing of decade‐long time windows of data, including the effects of variable dynamics that characterize the unrest. We provide temporal forecasts with uncertainty quantification, potentially indicative of eruption dates. The basis of the failure forecast method is a fundamental law for failing materials: ẇ-α ẅ = A, where ẇ is the rate of the precursor signal, and α, A are model parameters that we fit on the data. The solution when α >1 is a power law of exponent 1/(1 − α) diverging at time Tf , called failure time. In our case study, Tf is the time when the accelerating signals collected at Campi Flegrei would diverge if we extrapolate their trend. The interpretation of Tf as the onset of a volcanic eruption is speculative. It is important to note that future variations of monitoring data could either slow down the increase so far observed, or suddenly further increase it leading to shorter failure times than those here reported. Data from observations at all locations in the region were also aggregated to reinforce the computations of Tf reducing the impact of observation errors.