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September 12, 2022


Discovery of the “Pekeris Wave” — Special Atmospheric Wave Caused by the 2022
Hunga Tonga–Hunga Ha’apai Volcanic Eruption

1. Key Points

A major eruption of the Hunga Tonga–Hunga Ha’apai volcano in 2022 triggered a special atmospheric wave that had not been revealed for the past 85 years.
State-of-the-art observational data and simulation model, as well as simulation environments were critical to this discovery.
Fluctuations in atmospheric pressure associated with the “Pekeris wave” may have been involved in the meteorological tsunami observed near Japan after the volcanic eruption in Tonga.

2. Overview

Shingo Watanabe and Masuo Nakano of the Research Center for Environmental Modeling and Application, Japan Agency for Marine–Earth Science and Technology (JAMSTEC), along with Kevin Hamilton of the International Pacific Research Center, University of Hawaii and Takatoshi Sakazaki from the Graduate School of Science, Kyoto University, have discovered that the Hunga Tonga–Hunga Ha’apai volcanic eruption on January 15, 2022 (hereafter, the “Tonga eruption”) generated a special atmospheric wave. The existence of this wave, which the research team proposes calling the “Pekeris wave,” have not been detected for the past 85 years. Pekeris waves are resonance oscillations inherent to Earth’s atmosphere that were theoretically derived by Dr. Chaim Leib Pekeris in 1937, and their existence has long been a question in meteorological dynamics.

In the study reported here, the research team analyzed brightness temperature data observed by the Himawari-8 meteorological satellite over the first ~12 hours after the Tonga eruption and identified the Pekeris wave moving away from the volcano at a speed of ~245 ms-1, along with the Lamb wave moving away from the volcano in concentric circles at approximately Mach 1 (~315 ms-1). A numerical simulation of atmospheric response to the Tonga eruption was able to reproduce pressure fluctuations with vertical structures consistent with the theoretical calculations of the Lamb and Pekeris waves spreading over the Pacific Ocean at the same speed as those signatures observed by the Himawari-8. Data from the SORATENA*1 barometer array clearly captured the horizontal structures of the Lamb and Pekeris waves crossing Japan, which were consistent with the simulation results. The results of this research not only have significance as a historical discovery in meteorological dynamics but also suggest that the Pekeris wave may have caused "meteorological tsunamis," large sea-level changes caused by resonance phenomena between the atmosphere and the ocean at the sea surface. The research team plans to investigate such a possibility in the future by combining ocean models and the simulation results of this study to gain a better understanding of these special waves, which will contribute to coastal disaster prevention.

SORATENA: A network of weather sensors installed across Japan by Weathernews, Inc. In this study, data recorded at one-minute intervals from barometers at ~1,600 locations were provided.

This study was supported by the Integrated Research Program for Advancing Climate Models (TOUGOU) (JPMXD0717935715) and the Grant-in-Aid for Scientific Research program (JP20H01973, JP21K03661, and JP20H05728) of the Ministry of Education, Culture, Sports, Science, and Technology of Japan. The Himawari-8 gridded data were provided by the Center for Environmental Remote Sensing (CEReS), Chiba University, Japan. The barographic pressure data of the SORATENA array were provided by Weathernews, Inc. The Visualization and Analysis Platform for Ocean, Atmosphere, and Solar Researchers (www.vapor.ucar.edu) was used to create the explanatory video accompanying this press release.

The results will be published in the Journal of the Atmospheric Sciences on September 12, 2022 (JST).

First Detection of the Pekeris Internal Global Atmospheric Resonance: Evidence from the 2022 Tonga Eruption and from Global Reanalysis Data
Shingo Watanabe1, Kevin Hamilton2, Takatoshi Sakazaki3, and Masuo Nakano1


Japan Agency for Marine–Earth Science and Technology (JAMSTEC)
Department of Atmospheric Sciences and International Pacific Research Center, University of Hawaii
Graduate School of Science, Kyoto University

3. Background

The question of whether or not Earth’s atmosphere resonates at a certain frequency, like the strings of a violin or the skin of a drum, is fundamental in meteorological dynamics. At the end of the 18th Century, Pierre-Simon Laplace formulated the mathematical system known today as the “classical theory.” One possible solution to Laplace’s classical theory was the Lamb wave, first proposed in 1911 by Sir Horace Lamb. Far-traveling Lamb waves move horizontally at nearly the speed of sound; the phenomenon was first described following the 1883 eruption of Krakatoa. Similar pulses in pressure were observed after the explosion of the Tunguska meteorite in 1907 and during later nuclear tests; to-date Lamb waves have been observed worldwide during the monitoring of nuclear tests.

In 1937, Dr. Chaim Leib Pekeris theorized that, in addition to Lamb waves, Earth’s atmosphere might exhibit another unique resonance oscillation that travels horizontally at a slower speed. Unlike Lamb waves, which do not change phase in the vertical direction, these oscillations are characterized by a 180° phase shift in the lower stratosphere. It has been argued that they have large amplitudes in the upper stratosphere because of energy trapping between two temperature minima, called the tropopause and the mesopause, but the existence of such waves has not been confirmed until now.

On January 15, 2022, 85 years after Dr. Pekeris' theoretical study, the Hunga Tonga-Hunga Ha'apai volcano erupted, suggesting that there may have been an atmospheric wave that traveled ~20% slower than the Lamb wave. This study attempted to elucidate the Pekeris wave by analyzing observation data from the Himawari-8 meteorological satellites and the barometer arrays of SORATENA, and then conducting and analyzing simulations using a high-resolution whole neutral atmosphere model. The Earth Simulator, a multi-architecture supercomputer owned by JAMSTEC, was used to analyze the observational data and to perform and analyze the simulations in this study.

4. Results

The research team initially focused on the brightness temperature data of the Himawari-8 satellite, which is capable of observing various phenomena on the Earth using electromagnetic waves. It provides irradiance data in 16 wavelength bands, from visible light to infrared, which is converted to the brightness temperature data. When visualizing the data from the 9.6-μm band, which is the absorption wavelength of ozone and captures variations in stratospheric temperature and ozone density, the Lamb wave was identified moving away from the Tonga eruption in concentric circles at approximately Mach 1 (~315 ms-1). The Pekeris wave was also discovered moving away from the volcano at a slower velocity of ~245 ms-1 (Fig. 1).


Figure 1 Ten-minute difference in the 9.6-μm brightness temperature observed by the Himawari-8 satellite plotted ~4 h after the Tonga eruption (difference between 08:40 and 08:30 on January 15, 2022). Abbreviation: TBB, the brightness temperature.

To determine whether or not the Pekeris wave observed in the Himawari-8 data was consistent with the resonance oscillations proposed by Pekeris in 1937, the vertical structure was also examined. As no observational method yet exists to confirm the vertical structure of the Pekeris wave, a realistic atmospheric field was input to a high-resolution whole neutral atmospheric model (the Japanese Atmospheric General circulation model for Upper Atmosphere Research, JAGUAR), including the vertical temperature structures of the troposphere, stratosphere, mesosphere, and lower thermosphere, which were considered necessary for the Pekeris wave to resonate in the atmosphere. Numerical simulations were performed to simulate a far-field response of atmosphere to the Tonga eruption. To reproduce Pekeris wave, horizontal (~5 km) and vertical (~300 m) resolutions several times finer than the global weather forecast model of the Japan Meteorological Agency were needed. Consequently, pressure variations were reproduced with vertical structures that were consistent with the theoretical calculations of the Lamb and Pekeris waves, and which spread over the Pacific Ocean at the same speeds observed by Himawari-8 (Fig. 2).


Figure 2 Pressure anomalies at sea level simulated by the high-resolution whole neutral atmospheric model. The difference between the “eruption” and the “no-eruption” experiments is shown. (a) time in Fig. 1 (08:40 UTC on January 15, 2022); (b) time when Lamb waves began arriving in Japan (11:20 UTC); (c) simulation of the global atmosphere after the Tonga eruption (JAMSTEC).

The good agreement of the JAGUAR simulation results with the pressure pulses recorded by barometers in Honolulu and Yokohama, as well as the data from the SORATENA barometer array allowed for the horizontal structures of Lamb and Pekeris waves that crossed Japan and the temporal variations in pressure pulses to be captured clearly, demonstrating their consistency with the simulation results. According to the SORATENA barometer data, the Lamb wave caused an increase in pressure of ~2 hPa during the first 20 minutes after they began arriving at each location; the Pekeris wave, which arrived ~2 hours later, caused pressure to decline by approximately 0.1–0.2 hPa during the following ~10 minutes (Fig. 3). It is possible that the increase (Lamb) or decrease (Pekeris) in atmospheric pressure caused by the passage of these waves may have contributed to the changes in sea level observed during the same time period. This point has important implications for disaster prevention and should be clarified in future studies.


Figure 3 (a) Distribution of SORATENA stations. Color-coded points are classified according to the arrival time of the peak of the pressure increase caused by the Lamb wave. Contours indicate the great circle distance [km] from the Hunga Tonga volcano (20.5°S, 175.4°E). Time series of (b) SORATENA surface and (c) JAGUAR sea-level pressures, which show the differences between the “eruption” and “no-eruption” experiments.

After carefully analyzing 67 years of hourly surface pressure data from the reanalysis data, the research team succeeded in finding signals of surface pressure fluctuations corresponding to the Pekeris and Lamb waves (Fig. 4). This finding indicates that the Pekeris wave is not unique to the Tonga eruption, but is a resonance phenomenon that exists on a regular basis (Ref.) Thus, the existence of Pekeris waves, which has been debated for 85 years, was conclusively demonstrated.


Figure 4 Power spectral density (abscissa: time period in daily cycles) of the eastward component at zonal wavenumbers 1 (E1) and 2 (E2), calculated from 67 years (1950–2016) of equatorial (20°S–20°N) surface pressure data. The positions of the vertical bars marked with solid and dashed gray lines indicate the theoretically predicted resonance oscillation frequencies of the Pekeris (P) and Lamb (L) waves, respectively. The observed spectral peaks are close to these theoretical values, indicating that resonance occurs at this period; however, the sharp peak near 1.0 cpd is due to the daily period and not resonance oscillations.

5. Future Prospects

The results reported here mark a historic discovery in meteorological dynamics and suggest that the Pekeris wave, which has been considered a “phantom atmospheric wave” due to a lack of real-world evidence to support that, arrived in Japan approximately two hours after Lamb waves, and may have caused unexpectedly large changes in sea-level, called meteorological tsunami, through resonance between the atmosphere and ocean at the sea surface. To reproduce these changes in sea level, it was necessary to input data on atmospheric pressure fluctuations over the Pacific Ocean to ocean models that can represent meteorological tsunamis. JAMSTEC researchers have begun incorporating the results of this simulation into ocean models. Through such research, it will be possible to determine when, where, and how much sea levels might change in response to strong volcanic eruptions somewhere in the world, and thus to prepare for such an event, thereby contributing to coastal disaster prevention.


(For this study)
Shingo Watanabe, Principal Researcher, Research Center for Environmental Modeling and Application (CEMA), Research Institute for Global Change (RIGC), JAMSTEC
(For press release)
Press Office, Marine Science and Technology Strategy Department, JAMSTEC
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