PROMETHEUS: Probability in the Mediterranean of Tephra dispersal for various grain sizes. A tool for the evaluation of the completeness of the volcanic record in medial-distal archives.

PROMETHEUS is a statistical tool that allows creating maps showing the probability of finding tephra deposits of different grain sizes, originating from eruptions of a specific volcanic source, at any location around the vent. It couples wind profiles at different heights in the Mediterranean area with terminal velocity of volcanic particles. The input parameters include the height of the eruption column (which characterizes the intensity of the eruption), wind statistics (directions and intensities), and tephra deposits of a selected grain size. In particular, we used the parameterizations provided by Costa et al. (2016) and performed simulations using the HAZMAP tephra dispersal model to determine the maximum reachable distances that tephra can cover under weak, medium, and strong wind conditions (e.g. 7, 30, and 70 m/s velocities at the tropopause) and with column heights of 10, 20, and 30 km, depositing of at least the loading corresponding to 0.1 mm (corresponding to cryptotephra). Three alternative configurations of the model are validated analyzing first the eruptive source of Somma Vesuvius, with the related explosive eruptions from 22 ka Pomici di Base to the 1944 eruption. A further validation is made by comparing the probabilistic maps with the tephrostratigraphy of known marine and terrestrial cores using standard test of proportions (binomial distributions) and the binary logistic regression model, statistically quantifying the effectiveness of the model against the tephrostratigraphy recorded within this time frame. Based on this validation, a preferred configuration of PROMETHEUS is selected. PROMETHEUS probability maps will guide the selection of sampling sites for specific tephra deposits and could also support the study of the completeness of overall eruption catalogs over time.