An empirical relation between velocity, mass discharge rate and vent area for normal through paroxysmal eruptions at Stromboli

Based on published and new data for explosive events at Stromboli (Italy), we propose an empirical relation that links mass discharge rate (MDR) and at-vent gas jet velocity (G_v). We use 65 simultaneous measurements of MDR and G_v and find two trends in both the cross-correlation and rank order statistics. Cross-correlation gives a power law relation: \(MDR= {10}^{(0.015{G}_{v}+2.434)}\) $MDR={10}^{(0.015G_v+2.434)}$ kg/s, R² = 0.81, and applies to ash-dominated emissions. Combining this relation with the conservation of mass equation allows at-vent plume density and/or vent area to be derived from MDR = G_v ρ A, ρ being plume density and A being vent cross-sectional area. We find that while a vent radius of 2 m and plume density of 0.35 kg/m³ fits with the “normal” activity at Stromboli, a 290 × 2.5 m vent area likely feeds a 10 kg/m³ jet during paroxysmal activity. Initial tests on available data shows promise in extending the correlation beyond Stromboli and/or to events with higher MDR (> 10⁷ kg/s). However, the exact relation will depend on magma composition, temperature and volatile content, as well as conduit radius and vent overpressure.