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