The radial spreading of volcanic umbrella clouds deduced from satellite measurements

Abstract

Analysis of thermal infrared satellite measurements of umbrella clouds generated by volcanic eruptions suggests that asymptotic gravity current models of the temporal (t) radial (r) spreading (r ~t_f, f < 1) of the umbrella-shaped intrusion do not adequately explain the observations. Umbrella clouds from 13 volcanic eruptions are studied using satellite data that have spatial resolutions of ~4–25 km² and temporal resolutions of 1–60 minutes. The umbrella cloud morphology is evaluated using digital image processing tools in a Lagrangian frame of reference. At the onset of neutral buoyancy, the radial spreading is better explained by a stronger dependence on time of r ~ t, rather than t^2/3, t^3/4, or t^2/9. This flow regime exists on the order of minutes and has not been observed previously in satellite data. This may be of significance as it provides a means to rapidly (within the first 2–3 observations) determine the volumetric eruption rate. A hyperbolic tangent model, r ~ tanh(t) is presented that matches the entire radial spreading time history and has a conserved torus-shaped volume in which the intrusion depth is proportional to sech(t). This model also predicts the observed radial velocities. The data and the model estimates of the volumetric flow rate for the 15 January 2022 Hunga eruption are found to be 3.6–5 × 10¹¹ m³s⁻¹, the largest ever measured.