New inversion approach to constrain tephra sedimentation from volcanic plumes applied to the 17 June 1996 Ruapehu eruption, New Zealand: Methodology and results for a single grain size

Particle density distribution in volcanic plumes and corresponding particle fallout are key parameters to forecast impacts of potential and ongoing explosive eruptions. We develop a new approach to constrain such mass loss rates along a volcanic plume from deposit data by directly inverting the tephra dispersion process. In contrast to previous tephra inversion studies, we do not specify mass loss relationships for the plume and instead treat tephra fallout along the plume as a set of free parameters. We apply our method to the Ruapehu eruption on June 17, 1996 in New Zealand, which was characterized by a strongly wind-advected (weak) plume and for which an exceptional dataset is available of isomass measurements and particle size distributions at 119 locations. Our model is parameterized as a set of equally-spaced point sources along the plume base, whose trajectory is constrained by satellite data and photographic images. Each point source releases tephra that is dispersed according to an advection-diffusion equation. This dispersion process can be expressed as a system of linear equations with nonlinear dependence on diffusivity and wind speed. We estimate the tephra mass released by each point source from the ground deposit by inverting the dispersion process. We implement Tikhonov regularization to obtain stable, meaningful results, and use the L-curve criterion to select an optimal regularization parameter. Furthermore we use profile log-likelihood plots to constrain the grain-size dependent nonlinear parameters of wind speed and diffusivity. We present an example of our analysis for the Ruapehu data at a single grain size of 0.35-0.5 mm, and find that our model predictions fit the measured deposit data. We also validate our approach using tests with synthetic data in the presence of realistic noise levels. We thus see great potential to evaluate and improve theoretical models of plume sedimentation using our approach.