The tephra transport and fallout during the Plinian phase of the 79 A.D. eruption of Vesuvius has been numerically simulated by using an advection-diffusion model based on a continuity equation for the mass concentration in which wind field, atmospheric diffusion, and gravity settling are considered. The solution of the equation has been obtained on a nonuniform three-dimensional grid to optimize the computation time and to reduce the errors. The input data are (1) the total erupted mass, (2) the variation with time of the column height, (3) the particle population in terms of the settling velocity, and (4) the wind field. The vertical mass distribution of the particles which leave the column is given by an empirical formula (Suzuki, 1983), whose parameters are obtained from data of Carey and Sigurdsson (1987) and best fitting with field data.

Two distinct phases have been distinguished in the eruption: (1) related to white phonolitic pumice fallout and (2) dominated by the emission of gray tephritic-phonolite pumice. According to the literature the total duration of the pumice fallout was about 19 hours with column height ranging between about 14 and 32 km. The ''white phase'' has been estimated to have had 9 hours duration, while the ''gray phase'' lasted 10 hours. Magma discharge rate has been calculated assuming a fourth power relationship with column height. Total erupted volumes of 1.0 and 2.6 km3 of dense rock equivalent products have been assumed for the white and the gray phases, respectively (Sigurdsson et al., 1985). The particle population of the cloud has been assumed to correspond to that of a pyroclastic flow deposit related to a nearly total column collapse. The wind field results from a 60¿ clockwise rotation of the presently most frequent wind distribution field during the summer reduced in speed module of about 40%. The simulated ground thicknesses generally agree with the actual ones. The computed granulometric spectra at specific localities are in excellent agreement with the measured ones. As a whole, the simulation was successful. This fact emphasizes the significant consequences that the used model with a suitable choice of the input parameters can have for the establishment of truly probabilistic air fall hazard map of Vesuvius. ¿ American Geophysical Union 1988