Mass estimations of ejecta from Strombolian explosions by inversion of Doppler radar measurements

We present a new method for estimating particle loading parameters (mass, number, volume) of eruptive jets by inversion of echo power data measured using a volcano Doppler radar (VOLDORAD) during typical Strombolian activity from the southeast (SE) crater of Mount Etna on 4 July 2001. Derived parameters such as mass flux, particle kinetic and thermal energy, and particle concentration are also estimated. The inversion algorithm uses the complete Mie (1908) formulation of electromagnetic scattering by spherical particles to generate synthetic backscattered power values. In a first data inversion model (termed the polydisperse model), the particle size distribution (PSD) is characterized by a scaled Weibull function. The mode of the distribution is inferred from particle terminal velocities measured by Doppler radar for each explosion. The distribution shape factor is found to be 2.3 from Chouet et al.'s (1974) data for typical Strombolian activity, corresponding to the lognormal PSDs commonly characteristic of other Strombolian deposits. The polydisperse model inversion converges toward the Weibull scale factor producing the best fit between synthetic and measured backscattered power. A cruder, alternative monodisperse model is evaluated on the basis of a single size distribution assumption, the accuracy of which lies within 25% of that of the polydisperse model. Although less accurate, the monodisperse model, being much faster, may be useful for rapid estimation of physical parameters during real‐time volcano monitoring. Results are illustrated for two explosions at Mount Etna with contrasted particle loads. Estimates from the polydisperse model give 58,000 and 206,000 kg as maxima for the total mass of pyroclasts, 26,400 and 73,600 kg s −1 for mass flux rates, 38 and 135 m 3 (22 and 76 m 3 equivalent magma volume) for the pyroclast volumes, and 0.02–0.4 and 0.06–0.12 kg m −3 for particle concentrations, respectively. The time‐averaged kinetic energy released is found to be equal to 4.2 × 10 7 and 3.9 × 10 8 J, and thermal energy is estimated at 8.4 × 10 10 and 3 × 10 11 J.