The fate of volcanic ash: premature or delayed sedimentation?

A large amount of volcanic ash produced during explosive volcanic eruptions has been found to sediment as aggregates of various types that typically reduce the associated residence time in the atmosphere (i.e., premature sedimentation). Nonetheless, speculations exist in the literature that aggregation has the potential to also delay particle sedimentation (rafting effect) even though it has been considered unlikely so far. Here, we present the first theoretical description of rafting that demonstrates how delayed sedimentation may not only occur but is probably more common than previously thought. The fate of volcanic ash is here quantified for all kind of observed aggregates. As an application to the case study of the 2010 eruption of Eyjafjallajökull volcano (Iceland), we also show how rafting can theoretically increase the travel distances of particles between 138–710 μm. These findings have fundamental implications for hazard assessment of volcanic ash dispersal as well as for weather modeling.

The aggregate porosity " is defined as the ratio of all the voids $%&'( and the total aggregate volume " : The right-hand side of Eq. 1.1 can be rearranged as: (1.2) Eq. 1.1 can be rearranged as: (1. 3) The overall aggregate density " can be expressed as a function of the coating mass + and the core mass , , regardless of the shape of the inner core: where + is the density of the ash coating, , is the density of the inner core and " the mass of the overall aggregate. Under the assumption that the coating and the inner core have similar densities, i.e. + ≈ , , Eq.1.4 becomes: Combining Eq.1.3 and Eq.1.5 we get an explicit relationship between the aggregate density and its porosity, as a function of , : (1.6) It is worth noticing that Eq.1.6 neither depends on the shape of the inner core nor is strictly related to cored clusters. Its validity is general, such as it can be easily proven defining the solid volume of the aggregate as ( = + + , . Let us evaluate the maximum aggregate porosity, noticing how Eq.1.2 provides the maximum aggregate porosity in the limit of an infinitesimal mass in the coating volume, i.e. for + → 0. (1.7) Two cases are analysed in the following: i) spherical core; ii) ellipsoidal core.
Sphere: maximum aggregate porosity for an inner spherical core as a function of the aggregateto-core size ratio Λ (i.e. Λ = " / , ): Therefore, the final formula for the maximum porosity has the same formal expression regardless of the shape of the inner core, once the diameter ratio is properly defined.

Supplementary Note 2 -Comparison of the sedimentation charts for Stokes drag coefficient
In Supplementary Figure 2 we show the difference in rafting for different core sizes using Stokes' law, a Ob (Eq. 4 in methods) and Bagheri and Bonadonna's law 3 for drag, a cc (Eq. 5 in methods).

Supplementary Note 3-Rafting as a function of core density and altitude of release
In this section the rafting parameter e is calculated for core sizes from 10 to 1000 and densities of 2500

Supplementary Note 4 -Characteristics of aggregates and associated aggregate cores used as input data for Lagrangian simulations with NAME.
In the following tables we summarize the most important parameters used for the simulations in NAME. It is worth noticing that particle axes L, I, S are determined as defined in literature 3 .
Supplementary Table 1. Cores dynamical properties. Shape factors and density values for single cores for ash collected at 9.7 km from the vent during the 2010 Eyjafjallajökull eruption (Iceland). The values reported in row 1 and row 3 belong to those particles whose diameter is equal to the median of uv for the two bins = 2 and = 3 respectively. The elongation and flatness are the ones proper of these two specific particles as observed for the Eyjafjallajökull ash 4 . In the simulation the statistical descriptor "median" guarantees the use of shape parameters that really occurred during the eruption. In row 2 and row 4 we reported the same particles but assumed spherical.