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.

Volcanic activity occurring in tropical moist atmospheres can promote deep convection and trigger volcanic thunderstorms. Intense heating at ground surface and entrainment of moist air generates positive buoyancy, rapidly transporting volcanic gases and ash particles up to the tropopause and beyond. Volcanically-induced deep convection, however, is rarely observed to last continuously for more than a day and so insights into the dynamics, microphysics and electrification processes are limited. Here we present a multidisciplinary study on an extreme case, where this phenomenon lasted for six days. We show that this unprecedented event was triggered and sustained by phreatomagmatic activity at Anak Krakatau volcano, Indonesia from 22-28 December 2018. During this period, a deep convective plume formed over the volcano and acted as a ‘volcanic freezer’ producing ~3 × 10⁹ kg of ice on average with maxima reaching ~10¹⁰ kg. Our satellite analyses reveal that the convective anvil cloud, reaching 16-18 km above sea level, was ice-rich and ash-poor. Cloud-top temperatures hovered around -80 °C and ice particles produced in the anvil were notably small (effective radius from 20-30 μm). Our modelling suggests that ice particles began to form above 5 km and experienced vigorous updrafts (>30 m/s). These findings explain the impressive number of lightning strikes (~100,000) recorded near the volcano during this time. Our results, together with the unique dataset we have compiled, provide new insights into volcanic and meteorological thunderstorms alike.