Eruption source parameters (in particular erupted volume and column height) are used by volcanologists to inform volcanic hazard assessments and to classify explosive volcanic eruptions. Estimations of source parameters are associated with large uncertainties due to various factors, including complex tephra sedimentation patterns from gravitationally spreading umbrella clouds. We modify an advection-diffusion model to investigate this effect. Using this model, source parameters for the climactic phase of the 2450 BP eruption of Pululagua, Ecuador, are different with respect to previous estimates (erupted mass: 1.5–5 × 1011 kg, umbrella cloud radius: 10–14 km, plume height: 20–30 km). We suggest large explosive eruptions are better classified by volume and umbrella cloud radius instead of volume or column height alone. Volume and umbrella cloud radius can be successfully estimated from deposit data using one numerical model when direct observations (e.g., satellite images) are not available.

Uncertainty quantification (UQ) in eruption source parameters, like tephra volume, plume height, and umbrella cloud radius, is a challenge for volcano scientists because tephra deposits are often sparsely sampled due to burial, erosion, and related factors. We find that UQ is improved by coupling an advection‐diffusion model with two Bayesian inversion approaches: (a) a robust but computationally expensive Generalized Likelihood Uncertainty Estimation algorithm, and (b) a more approximate but inexpensive parameter estimation algorithm combined with first‐order, second‐moment uncertainty estimation. We apply the two inversion methods to one sparsely sampled tephra fall unit from the 2070 BP El Misti (Peru) eruption and obtain: Tephra mass 0.78–1.4 × 1011 kg; umbrella cloud radius 4.5–16.5 km, and plume height 8–35 km (95% confidence intervals). These broad ranges demonstrate the significance of UQ for eruption classification based on mapped deposits, which has implications for hazard management.

A Correction to this paper has been published: https://doi.org/10.1038/s43247-021-00096-9.