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The ever-increasing population living near active volcanoes highlights the need for the implementation of effective risk reduction measures to save lives and reduce the impact of volcanic unrest and eruptions. To help identify volcanic systems associated with potential high risk and prioritize risk reduction strategies, we introduce a new Volcanic Risk Ranking (VRR) methodology that integrates hazard, exposure, and vulnerability as factors that increase risk, and resilience as a factor that reduces risk. Here we present a description of the methodology using Mexican volcanoes as a case study, while a regional application to Latin American volcanoes is presented in a companion paper (Guimarães et al., submitted). With respect to existing strategies, the proposed VRR methodology expands the parameters associated with hazard and exposure and includes the analysis of 4 dimensions of vulnerability (physical, systemic, social, economic) and of resilience. In particular, we propose 41 parameters to be analyzed, including 9 hazard parameters, 9 exposure parameters, 10 vulnerability parameters and 13 resilience parameters. Since the number of parameters evaluated for each risk factor is different, they are normalized to have the same weight based on dedicated sensitivity analyses. In order to best illustrate the methodology, the proposed VRR is here applied to 13 Mexican volcanoes and compared with other approaches. We found that the volcanoes associated with the highest combination of hazard, exposure and vulnerability (3-factor VRR) for this geographic area are Tacaná and El Chichón regardless of the analyzed time window of eruption occurrence (i.e., <1 and <10 ka). Nonetheless, the volcanoes with eruption <1 ka that require the most urgent actions as associated with no or few resilience measures in place are Michoacán-Guanajuato Volcanic Field and San Martín Tuxtla (4-factor VRR); the top volcanoes in the 4-factor VRR with eruption <10 ka are Michoacán-Guanajuato Volcanic Field and Las Cumbres.

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Volcanic Risk Ranking (VRR) methods have been developed worldwide as a way to hierarchize the volcanic systems and help target strategies for risk reduction. Such hierarchization is especially important in areas characterized by a large number of active volcanoes but limited resources. This is the case of Latin America, where large populations live nearby almost 300 active volcanoes. Here we assess the volcanic systems in Latin America with at least one eruption in the last 1,000 years based on the VRR strategy presented in a companion paper that accounts for the 4 main risk factors: hazard, exposure, vulnerability and resilience. Our results reveal that, among the 123 volcanoes analyzed, Santiaguito, Tacaná and Fuego are those with the highest score in the 3-factor VRR (H×E×V), while Ecuador, Marchena and Santiago are among the systems with the lowest score. Bárcena and Pinta score zero as there is no exposure. Although vulnerability significantly contributes to the VRR score, hazard and exposure are the main factors that define the risk of Latin American volcanic systems in the proposed 3-factor VRR, while resilience contributes to its reduction in the proposed 4-factor VRR strategy. In this regard, Arenal, Copahue, Villarrica, Ubinas, Irazú and Poás are the systems with the highest number of risk reduction strategies in place. Atitlán, Almolonga and Tecuamburro are the volcanic systems with the highest score in the 4-factor VRR [(H×E×V)/(Res+1)], combining moderate hazard, exposure and vulnerability and low resilience; Bárcena, Pinta, Ecuador, Marchena and Santiago receive the lowest scores due to no or low exposure. Santiaguito, Tacaná, El Chichón and Ceboruco are characterized by high scores in the 3-factor VRR and also stand out as some of those with few risk reduction strategies implemented; thus they have intermediate to high scores also in the 4-factor VRR. Recognizing that hazard is difficult to mitigate and reducing exposure may depend on hardly feasible relocation of infrastructure and already established communities, we emphasize that measures to reduce vulnerability and increase resilience should be promoted (e.g., creating redundancy/accessibility to infrastructure, carrying out risk assessment studies, implementing early warning systems, developing emergency plans and promoting educational activities).

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Accurate predictions of volcanological phenomena, such as the trajectory of blocks accelerated by volcanic explosions, require quantitative skills training. Large outdoor experiments can be useful to convey concepts of volcanic processes to students in an exciting way. Beyond the fun aspects, these experiments provide an opportunity to engage with the physics of projectile flight and help promote mathematical learning within the Earth Sciences. We present a quantitative framework required to interpret ballistic trajectories and the outdoor experiment known commonly as "trashcano", taking a step-by-step approach to the physics of this problem, and deriving a range of mathematical solutions involving different levels of complexity. Our solutions are consistent with the predictions from established computer programs for volcanic ballistic trajectory modelling, but we additionally provide a nested set of simplified solutions, useful for a range of teaching scenarios as well as downloadable simulated datasets for use where the full experiment may not be possible.

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