Tracing Acoustic-Gravity Waves from the Ocean into the Ionosphere: ONR BRC Project
 2013 - 2017
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Project Participants

Nikolay A. Zabotin (PI)
Oleg A. Godin
Terence W. Bullett
Catalin Negrea


Theory predicts strong coupling between waves in the atmosphere and the ocean at low frequencies where mechanical waves in both fluids should be treated as acoustic gravity waves (AGWs). It has been shown recently that for an underwater source, the power transmitted into the atmosphere through air-water interface can exceed the total power emitted by the same source in unbounded water by an order of magnitude or more, depending on wave frequency. Under somewhat idealized conditions, particularly strong transmission of AGWs from a compact underwater source into atmosphere has been predicted to occur in two narrow frequency bands with central frequencies of several mHz. Exact values of the central frequencies depend on the ocean depth and atmospheric conditions. These frequency bands can be called Transparency Windows. At a similar frequency, a transition in behavior of oceanic infragravity waves occurs; at higher frequencies the infragravity waves penetrate into the atmosphere only up to heights of the order of their wavelength, but below the transition frequency, the energy and momentum of infragravity waves are radiated into the atmosphere and are expected to reach the upper atmosphere, including thermosphere and ionosphere. This second effect may be called Wideband Transparency of the air-sea interface.

Godin O. A. Sound transmission through water-air interfaces: New insights into an old problem, Contemporary Physics, 49, p. 105–123 (2008). DOI: 10.1080/00107510802090415. link

Oleg A. Godin and Iosif M. Fuks (2012). Transmission of acoustic-gravity waves through gas–liquid interfaces. Journal of Fluid Mechanics, 709, pp 313-340. doi:10.1017/jfm.2012.336. link

Zabotin, N.A., J.W. Wright, and G.A. Zhbankov (2006), NeXtYZ: Three-dimensional electron density inversion for dynasonde ionograms, Radio Sci., 41, RS6S32, doi:10.1029/2005RS003352. link


Significant correlation between spectral amplitudes of infragravity waves in the ocean and acoustic gravity waves in the thermosphere has been revealed as a result of analysis of the data from Wallops Island Dynasonde and the two DART stations (#44402 and #41424) [Zabotin et al., 2016]. Maximum values of the correlation coefficients reach 0.43. 9 month duration of the data series has ensured a high statistical significance of the correlation values. Correlation remains predominantly positive within the high confidence bounds, on the average decreasing with the altitude from the maximum values to zero, in a very broad frequency band (~0.2–3.2 mHz) and in the altitude range from 140 to 190 km). At the same time the correlation coefficient demonstrates highly uneven structure in the spectral domain with several prominent peaks. These common tendencies are stronger for the closer (and located in the shallower ocean) DART 44402 than the DART 41424.

The result can be considered as a direct confirmation of the theoretical concept of coupling between the infragravity waves in the ocean and acoustic gravity waves in the thermosphere [Godin et al., 2015]. The experimentally observed peaks of the correlation occur at the altitudes as low as 140–150 km, where dissipative (linear) attenuation of AGWs is only starting to manifest itself. At higher altitudes, temporal variations of the atmospheric attenuation and non-linear processes serve as natural decorrelation factors for waves originating at the sea level.

The observed peak values of the correlation between normalized spectral amplitudes of IGWs in the ocean and AGWs in the thermosphere is high enough. While the question of relative significance of the ocean-generated waves remains open, our results call for a change in the existing paradigm, which ignores completely the role of IGWs in supporting background thermospheric wave activity. The empirical findings reveal a previously unrecognized, important link in the coupled ocean-atmosphere system. Adjustments may be necessary in estimates of the momentum deposition by AGWs in the thermosphere.

Further development of Dynasonde’s ability to measure characteristics of acoustic gravity waves [Negrea, 2016; Negrea and Zabotin, 2016; Negrea et al., 2016a,b] resulted in the first empirical estimates of the body forcing rendered on the neutral component of the thermosphere over Walops Island, VA. The total momentum flux is obtained by integrating over the frequency range 0.1-4.14 mHz. The magnitude and direction of the momentum flux vector are determined. Within the altitude ranges and during periods when the momentum flux magnitude was high, a clear direction of the vector can be observed (South / South-East). For most of the remainder of the interval, the momentum flux vector was oriented westward, with a magnitude up to 2 orders smaller, but much more variable.

Ray and WKB approximations have long been important tools of understanding and modeling propagation of atmospheric waves. However, contradictory claims regarding the applicability and uniqueness of the WKB approximation persist in the literature. We have resolved the contradictions through a rigorous mathematical analysis of the problem [Godin, 2015a]. A self-consistent version of the WKB approximation has been systematically derived from first principles and compared to ad hoc approximations proposed earlier. The parameters of the problem have been identified that need to be small to ensure the validity of the WKB approximation. Contrary to the better-studied cases of acoustic waves and internal gravity waves in the Boussinesq approximation, the WKB solution contains the geometric, or Berry, phase. The Berry phase is generally non-negligible for acoustic-gravity waves (AGWs) in a moving atmosphere. In other words, knowledge of the AGW dispersion relation is not sufficient for calculation of the wave phase [Godin, 2015a].

The ray theory predicts unphysical, divergent values of the wave amplitude and needs to be modified in the vicinity of caustics. We have developed an asymptotic theory that describes diffraction, focusing and increased dissipation of acoustic-gravity waves in the vicinity of caustics and turning points [Godin, 2016]. Uniform asymptotics of the wave field have ben expressed in terms of Airy functions and their derivatives. The geometrical, or Berry, phase, which arises in the consistent WKB approximation for acoustic-gravity waves, plays an important role in the caustic asymptotics. In addition to the wave field in the vicinity of the caustic, these asymptotics describe wave reflection from the caustic and the evanescent wave field beyond the caustic. The evanescent wave field have been found to play an important role in ionospheric manifestations of gravity waves.

Using the ray theory and its caustic extensions, we have modeled propagation of acoustic-gravity waves in three-dimensionally inhomogeneous atmosphere. Huygens’ wavefront-tracing was used to simulate wave propagation from an earthquake hypocenter through the earth’s crust and ocean to the upper atmosphere. We have quantified the influence of temperature stratification and winds, including their seasonal variability, and air viscosity and thermal conductivity on the geometry and amplitude of ionospheric disturbances. We have found, in particular, that
- to relate quantitatively the characteristics of the observed ionospheric disturbances and the underlying natural hazard, it is imperative to accurately model AGW propagation through the actual atmosphere;
- at propagation from ground level to the ionosphere, the differences between AGW attenuation, which is predicted by ad hoc and consistent asymptotic models, are significant and can exceed 10 dB for tsunamigenerated AGWs;
- absorption of waves in the upper atmosphere is strongly anisotropic. Critical levels in the atmosphere limit the geographical extent of possible ionospheric manifestations of tsunamis. Both the AGW absorption and attenuation due to diffraction affect the magnitude of the ionospheric signatures of tsunamis;
- variability of the neutral atmosphere affects the intensity of ionospheric signatures of earthquakes primarily through the variations in the AGW absorption at ionospheric heights.


Oleg A. Godin, Nonlinear progressive acoustic-gravity waves: Exact solutions, Geophysical Research Abstracts, Vol. 15, EGU2013-1820, 2013, (EGU General Assembly, Vienna, Austria, 8-12 April 2013). Image

Godin O. A., N. A. Zabotin, A. F. Sheehan, Z. Yang, and J. A. Collins (2013), Power spectra of infragravity waves in a deep ocean, Geophys. Res. Lett., 40, 2159–2165, doi:10.1002/grl.50418. link

Nikolay A. Zabotin and Oleg A. Godin, Infragravity waves in the ocean as a source of acoustic-gravity waves in the atmosphere, Geophysical Research Abstracts, Vol. 15, EGU2013-2118, 2013, (EGU General Assembly, Vienna, Austria, 8-12 April 2013). Image

Nikolay A. Zabotin, Oleg A. Godin and Anne Sheehan, Interferometry of background acoustic-gravity waves, Geophysical Research Abstracts, Vol. 15, EGU2013-2117, 2013, (EGU General Assembly, Vienna, Austria, 8-12 April 2013). Image

Catalin Negrea, Nikolay A. Zabotin, and Terence Bullett, Spectral Characteristics of Ionospheric Plasma Density and Tilt Variations from the Dynasonde Data, Vol. 15, EGU2013-954, 2013, (EGU General Assembly, Vienna, Austria, 8-12 April 2013). Image

Catalin Negrea, Nikolay A. Zabotin, and Terence Bullett, Wave activity in the Thermosphere-Ionosphere system as determined from Dynasonde data, CEDAR Meeting, Boulder, Colorado, 22-28 June 2013, IT Poster ITTI-13. Image

Godin, O. A. (2015a), Wentzel–Kramers–Brillouin approximation for atmospheric waves, J. Fluid Mech., 777, 260–290, doi: 10.1017/jfm.2015.367. link

Godin, O. A. (2015b), Finite-amplitude acoustic-gravity waves: exact solutions, J. Fluid Mech., 767, 52-64, doi:10.1017/jfm.2015.40. link

Godin, O. A., N. A. Zabotin, and T. W. Bullett (2015), Acoustic-gravity waves in the atmosphere generated by infragravity waves in the ocean, Earth, Planets and Space, 67, Art. 47, doi: 10.1186/s40623-015-0212-4. link

Godin, O. A. (2016), Diffraction of acoustic-gravity waves in the presence of a turning point, J. Acoust. Soc. Am., 140, 283-295, doi: 10.1121/1.4955283. link

Negrea, C. (2016), Characteristics, Variability and Impact of Atmospheric Gravity Waves in the Thermosphere-Ionosphere as determined from Dynasonde Data, PhD Dissertation, U. of Colorado, Boulder, 169 pp.

Negrea, C., and N. A. Zabotin (2016), Mean spectral characteristics of acoustic gravity waves in the thermosphere-ionosphere determined from Dynasonde data, Radio Sci., 51, 213-222, doi:10.1002/2015RS005823. link

Negrea, C., N. Zabotin, T. Bullett, T. Fuller-Rowell, T.-W. Fang, and M. Codrescu (2016a), Characteristics of acoustic gravity waves obtained from Dynasonde data, J. Geophys. Res. Space Physics, 121, 3665-3680, doi:10.1002/2016JA022495. link

Negrea, C., N. Zabotin, T. Bullett, M. Codrescu, and T. Fuller-Rowell (2016b), Ionospheric response to tidal waves measured by dynasonde techniques, J. Geophys. Res. Space Physics, 121, 602-611, doi:10.1002/2015JA021574. link

Zabotin, N. A., O. A. Godin, and T. W. Bullett (2016), Oceans are a major source of waves in the thermosphere, J. Geophys. Res. Space Physics, 121, 3452-3463, doi:10.1002/2016JA022357. link

Marine Sensors

DART Stations
CTBTO Monitoring System