Fig. 4: The inversion results for plume umbrella volume and total energy and comparison with observed event plumes.

(A) The total volume and (B) total energy predicted by our model as functions of the observed tephra dispersal lengthscale (L), defined as the decay scale of the Gaussian model of Eq. (1) (and equal to the distance from the center encompassing ~93% of the mass of tephra dispersed by the umbrella of the particle group under consideration). The value used for the Brunt-Väisälä frequency is N = 10⁻³ s⁻¹ and the eruptive timescale used to convert our energy flux into a total energy is taken here as the representative value τ = 15 h (as derived in our results section, where a range of 10–20 h is inferred based on the lava volume and morphology). The thick curves are evaluated for a settling speed of w_s = 3 cm s⁻¹, for the particle range 250–500 μm used in the inversion. The other curves (gray) represent the minimal and maximal inferences that would apply for settling speeds of w_s = 2 cm s⁻¹ and duration τ = 10 h, and w_s = 4 cm s⁻¹ and duration τ = 20 h, covering ranges of uncertainty in these parameters. Bands represent the inferred values based on the fitted dispersal length scale L = 4.9 ± 0.4 km determined by our fitting to the observed data for the Northern Escanaba (NESCA) eruption (Fig. 2). The range of volumes and heat energies of observed megaplumes (volume ≥10 km³)⁵ are indicated by the green bars along the vertical axes, showing consistency with both of our predictions. This indicates that a megaplume was produced during the NESCA eruption. The volume range of the considerably smaller group of event plumes observed at the Lau Basin⁶ are indicated by the orange bar in (A), potentially forming a distinct category of event plume.