A Lagrangian Stochastic Model of a Volcanic Eruption Column

Abstract

AbstractWe present 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 modeled by a suitably constructed stochastic differential equation. This model is based on that of Bisignano and Devenish (2015, http://doi.org/10.1007/s10546-015-0055-3) with the mean flow provided by the integral plume model of Devenish (2013, http://doi.org/10.1016/j.jvolgeores.2013.02.015). The LSM is applied to the two eruptions considered by Costa et al. (2016, http://doi.org/10.1016/j.jvolgeores.2016.01.017) for the volcanic‐plume intercomparison study with no ambient wind and to the hypothetical cases with ambient wind considered by Aubry et al. (2019, http://doi.org/10.1029/2019GL083975). Vertical profiles of the mass concentration computed from the LSM are compared with equivalent results from large eddy simulations (LES). The LSM captures the order of magnitude of the LES mass concentrations and aspects of their profiles: for example, in contrast with a standard integral plume model, that is, without fluctuations, the mass concentration computed from the LSM decays (to zero) toward the top of the plume 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. A quantitative analysis of the cases with ambient wind shows generally good agreement between the LSM and the LES for a number of quantities including the maximum concentration, the level at which it occurs, the maximum rise height, and the total erupted mass.