Estimating the 3D shape of volcanic ash to better understand sedimentation processes and improve atmospheric dispersion modelling

Abstract The sedimentation rate of volcanic ash through the atmosphere influences its travel distance, with important implications for aviation and health. The fall velocity of a particle depends on its size and density, but also shape, and volcanic ash is not spherical. To capture the sedimentation of ash, atmospheric dispersion models use empirical drag equations calibrated using geometric shape descriptors. However, particle shape data are scarce and there is no standard method of shape measurement. In addition, shape measurements are not always available during an eruption, when dispersion models are used operationally to forecast ash hazard. We assess the variability in the shape of volcanic ash from Icelandic eruptions using X-ray computed tomography. To consider how good different drag equations and shape descriptors are at representing the sedimentation of volcanic ash we compare calculated fall velocities to measured fall velocities of volcanic ash in air in a settling column. We then suggest the best drag equations and shape descriptors for use in atmospheric dispersion models. We find that shape-dependent drag equations produce more accurate results than a spherical approximation. However, accurate drag calculations based on the shape descriptor sphericity, which is a function of surface area, require the imaging resolution to be within the range of 102 - 105 voxels per particle (where a voxel is a volumetric pixel) as surface area is sensitive to imaging resolution. We suggest that the large-scale form of the particle impacts sedimentation more than small-scale surface roughness. Shape descriptors based on ratios between principal axis lengths are more practical as they are less variable among particle size classes and much less sensitive to imaging resolution. Finally, we use particle shape data from this study and literature sources to make recommendations on default values for use with atmospheric dispersion models where no shape data are available.