Probabilistic reconstruction (or forecasting) of distal runouts of large magnitude ignimbrite PDC flows sensitive to topography using mass dependent invasion models.

Abstract

We describe a new method for the reconstruction (or forecast) of probabilities that distal geographic locations were inundated by a giant 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 particular distal locality at any given confidence level and compare this with ambiguous or inexact 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 different 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 down 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 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 with 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 the input variables and the calculated mass. For any major magnitude ignimbrite PDC scenario, our method provides a rational basis for assessing the probability of flow inundation at critical geographic locations within distal areas when there is major uncertainty about the actual or predicted extent of flow runout. Example case histories are illustrated.