Propagation of Source Grain-size Distribution Uncertainty by Using a Lagrangian Volcanic Particle Dispersal Model

Lagrangian particle dispersal models are commonly used for tracking ash particles emitted from volcanic plumes and transported under the action of atmospheric wind fields. In this work, we adopted a Lagrangian particle model to carry out an uncertainty quantification analysis of volcanic ash dispersal in the atmosphere focused on the uncertainties affecting particle source conditions. To this aim the Eulerian fully compressible mesoscale non-hydrostatic model WRF was used to generate the driving wind field. The Lagrangian particle model LPAC (de'Michieli Vitturi et al., JGR 2010) was then used to simulate the transport of mass particles under the action of atmospheric conditions. The particle motion equations were derived by expressing the Lagrangian particle acceleration as the sum of the forces acting along its trajectory, with drag forces calculated as a function of particle diameter, density, shape and Reynolds number. The simulations were representative of weak plume events of Mt. Etna and aimed to quantify the effect on the dispersal process of the uncertainty in the mean and variance of a Gaussian density function describing the grain-size distribution of the mixture and in the particle sphericity. In order to analyze the sensitivity of particle dispersal to these uncertain parameters with a reasonable number of simulations, and therefore with affordable computational costs, response surfaces in the parameter space were built by using the generalized polynomial chaos technique. The uncertainty analysis allowed to quantify the most probable values, as well as their pdf, of the number of particles as well as of the mean and variance of the grain size distribution at various distances from the source, both in air and on the ground. In particular, results highlighted the strong reduction of the uncertainty ranges of the mean and variance of the grain-size distribution with increasing distance from source and the significant control of particle sphericity on the dispersal process.