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We develop a Lagrangian stochastic model (LSM) of a volcanic plume in whichthe mean flow is provided by an integral plume model of the eruption column andfluctuations in the vertical velocity are modelled by a suitably constructedstochastic differential equation. The LSM is applied to the two eruptionsconsidered by Costa et al. (2016) for the volcanic-plume intercomparison study.Vertical profiles of the mass concentration computed from the LSM are comparedwith equivalent results from a large-eddy simulation (LES) for the case of noambient wind. The LSM captures the order of magnitude of the LES massconcentrations and some aspects of their profiles. In contrast with a standardintegral plume model, i.e. without fluctuations, the mass concentrationcomputed from the LSM decays (to zero) towards the top of the plume which isconsistent with the LES plumes. In the lower part of the plume, we show thatthe presence of ash leads to a peak in the mass concentration at the level atwhich there is a transition from a negatively buoyant jet to a positivelybuoyant plume. The model can also account for the ambient wind and moisture.

A Lagrangian Stochastic Model of a Volcanic Eruption Column