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[1] We introduce a new inversion approach to constrain eruption source parameters and the distribution of tephra sedimentation from a weak plume. Our model is parameterized as a set of point sources along the plume base, whose trajectory is constrained by satellite and photographic images. Each point source releases tephra that is dispersed according to an advection-diffusion equation. This dispersion process is expressed as a system of linear equations with nonlinear dependence on diffusivity and wind speed. We employ inversion techniques to estimate the tephra mass released by each point source as well as diffusivity, stabilizing the inversion by regularization. We apply our method to the Ruapehu eruption on 17 June, 1996 in New Zealand, which was characterized by a strongly wind-advected plume that can be studied via tephra isomass measurements and particle size distributions at 119 locations. We demonstrate that the approach is feasible by performing analyses with real and synthetic data at a single grain size, and gain insight into the effects of data gaps, presence of noise, and nonlinear parameters on the inversion results. The best fit value of diffusivity yields tephra fallout that decreases steadily with distance to vent, and the predicted deposit is a good fit to the field measurements. This study illustrates the potential of a direct inversion approach to constrain diffusivity, as well as to recover the tephra fallout, without assuming a physical model for mass transport inside the plume.

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Weak subplinian-plinian plumes pose frequent hazards to populations and aviation, yet many key parameters of these particle-laden plumes are, to date, poorly constrained. This study recovers the particle size-dependent mass distribution along the trajectory of a well-constrained weak plume by inverting the dispersion process of tephra fallout. We use the example of the 17 June 1996 Ruapehu eruption in New Zealand and base our computations on mass per unit area tephra measurements and grain size distributions at 118 sample locations. Comparisons of particle fall times and time of sampling collection, as well as observations during the eruption, reveal that particles smaller than 250 μm likely settled as aggregates. For simplicity we assume that all of these fine particles fell as aggregates of constant size and density, whereas we assume that large particles fell as individual particles at their terminal velocity. Mass fallout along the plume trajectory follows distinct trends between larger particles (d ≥ 250 μm) and the fine population (d < 250 μm) that are likely due to the two different settling behaviors (aggregate settling versus single-particle settling). In addition, we computed the resulting particle size distribution within the weak plume along its axis and find that the particle mode shifts from an initial 1 mode to a 2.5 mode 10 km from the vent and is dominated by a 2.5 to 3 mode 10-180 km from vent, where the plume reaches the coastline and we do not have further field constraints. The computed particle distributions inside the plume provide new constraints on the mass transport processes within weak plumes and improve previous models. The distinct decay trends between single-particle settling and aggregate settling may serve as a new tool to identify particle sizes that fell as aggregates for other eruptions.

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