The Total Grain-Size Distribution (TGSD) of tephra deposits is crucial for hazard assessment and provides fundamental insights into eruption dynamics. It controls both the mass distribution within the eruptive plume and the sedimentation processes and can provide essential information on the fragmentation mechanisms. TGSD is typically calculated by integrating deposit grain-size at different locations. The result of such integration is affected not only by the number, but also by the spatial distribution and distance from the vent of the sampling sites. In order to evaluate the reliability of TGSDs, we assessed representative sampling distances for pyroclasts of different sizes through dedicated numerical simulations of tephra dispersal. Results reveal that, depending on wind conditions, a representative grain-size distribution of tephra deposits down to ∼100 μm can be obtained by integrating samples collected at distances from less than one tenth up to a few tens of the column height. The statistical properties of TGSDs representative of a range of eruption styles were calculated by fitting the data with a few general distributions given by the sum of two log-normal distributions (bi-Gaussian in Φ-units), the sum of two Weibull distributions, and a generalized log-logistic distribution for the cumulative number distributions. The main parameters of the bi-lognormal fitting correlate with height of the eruptive columns and magma viscosity, allowing general relationships to be used for estimating TGSD generated in a variety of eruptive styles and for different magma compositions. Fitting results of the cumulative number distribution show two different power law trends for coarse and fine fractions of tephra particles, respectively.
Our results shed light on the complex processes that control the size of particles being injected into the atmosphere during volcanic explosive eruptions and represent the first attempt to assess TGSD on the basis of pivotal physical quantities, such as magma viscosity and plume height. Our empirical method can be used to assess the main features of TGSD necessary for numerical simulations aimed to real-time forecasting and long-term hazard assessment when more accurate field-derived TGSDs are not available.