Quantifying the Ocean Coupling of Air Waves, and Why DART Data Reporting Can Be Deceptive

In the context of the 2022 volcanic explosion in Tonga, we investigate the structure of the fundamental elasto-gravitational branch GR₀ of air waves, and especially their coupling to an oceanic column of variable depth. We find that the structure of the wave in the atmosphere, in particular the overpressure component of its eigenfunction, is essentially independent of the presence and depth of an oceanic layer; normal mode theory predicts that its excitation by an explosive source in the atmosphere is also independent of water depth. The impedance of GR₀, defined as the ratio of vertical displacement of the sea surface to overpressure at the base of the atmosphere, increases strongly with water depth and varies only marginally with frequency. It can become negative for very shallow depths and very low frequencies, but takes its classical hydrostatic value of 1 cm/mbar only for a ∼5-km deep ocean. This results in minimal maregraphic amplitudes, and hence flooding hazard, during the passage of GR₀ over very shallow seas. Finally, we find that the ratio of the sea surface displacement to the pressure signal on the seafloor, as measured for example by sensors of the DART network, increases strongly with ocean depth, but never reaches its hydrostatic value (1 cm/mbar or 10^-4 m/Pa). In this respect, the present DART protocol in which the hydrostatic ratio is hardwired into the reporting algorithm could be considered deceptive, and should be revised.