ESTIMATES OF THE AMOUNT OF WATER IN THE HUNGA TONGA-HUNGA HA’APAI PLUME
For plume volume, we used a cylinder 58 km high (maximum) with a radius of 5 km for the core area near the volcano, then a disk 10 km thick to represent the umbrella cloud. To get the amount of water, we used 15 g/m3 for the core (based on calculations on Alaskan volcanoes) and 1.5 g/m3 for the umbrella cloud (a published value from thunderstorms). Note that the core concentration is an order of magnitude higher. We deliberately used simple geometries to establish a baseline.
We note that: 1) The two parts are not synchronous. The 58 km high part was early and transient, and the huge umbrella cloud was 30-60 min later; 2) The thickness of the umbrella cloud is not well known. It is likely thicker near the volcano and thinner near the leading edges; and 3) The water concentrations are likely on a spectrum between these two endmember values
Hence, plume volume estimates were made every 10 minutes coincident with satellite images. Umbrella thicknesses were assumed to be 10 km. Areas are measured from the satellite images. A lidar image (Calypso) shows thickness of the ash-rich part of the plume (2-2.5 km). Topography of the plume top is variable but we used average values. The estimates for the amount of water range from 3-9 x 1015 g.
As an independent check, a published paper uses the number of lightning flashes to determine water content of thunderstorms. Each flash represents a unit of electrical energy, corresponding to an amount of water. These estimates (based on 400,000 flashes) are 1-3 orders of magnitude higher at 2 x 1016 to 4 x 1018 g. We speculate that the large number of fine ash particles in the plume may have contributed to higher lightning efficacy.
Estimates of the amount of water in the magma, using 2600 Kg/m3 for magma density, 5 wt % water, and 6 km3 of magma, are 8 x 1014 g, an order of magnitude lower than the plume estimates. We thus infer that 90 percent of the plume is from seawater flashed to steam.