A Lagrangian stochastic model of a volcanic eruption column

TL;DR

This paper introduces a Lagrangian stochastic model for volcanic plumes that incorporates fluctuations in vertical velocity, improving the accuracy of mass concentration profiles compared to traditional models and aligning well with large-eddy simulation results.

Contribution

The paper presents a novel Lagrangian stochastic model for volcanic plumes that includes velocity fluctuations and accounts for ambient wind and moisture effects.

Findings

The LSM captures the order of magnitude of LES mass concentrations.

Mass concentration from LSM decays towards the top of the plume, consistent with LES.

Presence of ash causes a peak in mass concentration at the transition level.

Abstract

We develop a Lagrangian stochastic model (LSM) of a volcanic plume in which the mean flow is provided by an integral plume model of the eruption column and fluctuations in the vertical velocity are modelled by a suitably constructed stochastic differential equation. The LSM is applied to the two eruptions considered by Costa et al. (2016) for the volcanic-plume intercomparison study. Vertical profiles of the mass concentration computed from the LSM are compared with equivalent results from a large-eddy simulation (LES) for the case of no ambient wind. The LSM captures the order of magnitude of the LES mass concentrations and some aspects of their profiles. In contrast with a standard integral plume model, i.e. without fluctuations, the mass concentration computed from the LSM decays (to zero) towards the top of the plume which is consistent with the LES plumes. In the lower part of the plume, we show that the presence of ash leads to a peak in the mass concentration at the level at which there is a transition from a negatively buoyant jet to a positively buoyant plume. The model can also account for the ambient wind and moisture.