The impact of particle shape on fall velocity: Implications for volcanic ash dispersion modelling

Modelling atmospheric volcanic ash dispersion is a critical tool in mitigating the impact of large explosive eruptions; it is also useful for understanding and reconstructing past events. Most atmospheric dispersion models include a sedimentation velocity term that is sensitive to the physical properties of the particle, but many do not use particle shape as an input parameter; instead particles are assumed to be spherical. There are many empirical and semi-empirical shape-dependent drag laws. We measure the velocity of scaled analogue particles over the range of flow conditions anticipated for volcanic ash dispersion to test published formulae against an independent dataset. We use a semi-empirical formula we determined to be accurate for non-spheres to investigate the sensitivity of the modelled transport of an ash cloud to particle shape, using the atmospheric dispersion model NAME and a shape parameter we measure for non-spherical ash particles from Katla volcano, Iceland. We find that model particle trajectories are sensitive to particle shape for particles >1–3 μm diameter; the sedimentation velocity of smaller particles is low compared to atmospheric vertical velocities. Sensitivity to shape increases with size such that 100 μm particles can travel 44% further from the source when they are highly non-spherical (sphericity = 0.5). Despite the sensitivity of the fall velocity of large particles to their shape, however, forecasts of distal ash concentration using particle size distributions of 0.1–100 μm and 0.1–250 μm show relatively good agreement between a spherical and non-spherical case for the first 36 h after an eruption. The vertical structure of an ash cloud is more sensitive to particle shape than the horizontal extent. Model particle trajectories are also sensitive to particle size, and we find a discrepancy between different particle size parameters for non-spherical ash: particle long axis L, used in cryptotephra studies, was on average twice the equivalent-volume sphere diameter d_v, used in dispersion modelling, for tephra samples from Katla volcano, Iceland. This discrepancy in size measurements could explain the observed travel distance of large distal cryptotephra shards.