Project Participants
Nikolay A. Zabotin (PI) Oleg A. Godin Terence W. Bullett Catalin Negrea
Motivation
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 airwater 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 airsea interface.
Godin O. A. Sound transmission through waterair interfaces: New insights into an old problem, Contemporary Physics, 49, p. 105–123 (2008). DOI: 10.1080/00107510802090415.
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Oleg A. Godin and Iosif M. Fuks (2012). Transmission of acousticgravity waves through gas–liquid interfaces. Journal of Fluid Mechanics, 709, pp 313340. doi:10.1017/jfm.2012.336.
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Zabotin, N.A., J.W. Wright, and G.A. Zhbankov (2006), NeXtYZ: Threedimensional electron density inversion for dynasonde ionograms, Radio Sci., 41, RS6S32, doi:10.1029/2005RS003352.
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Results
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 nonlinear 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 oceangenerated 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 oceanatmosphere 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 0.14.14 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 / SouthEast). 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 selfconsistent 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 betterstudied 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 nonnegligible for acousticgravity 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 acousticgravity 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 acousticgravity 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 acousticgravity waves in threedimensionally inhomogeneous atmosphere. Huygens’ wavefronttracing 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.
Publications
Oleg A. Godin, Nonlinear progressive acousticgravity waves: Exact solutions, Geophysical Research Abstracts, Vol. 15, EGU20131820, 2013, (EGU General Assembly, Vienna, Austria, 812 April 2013).
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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.
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Nikolay A. Zabotin and Oleg A. Godin, Infragravity waves in the ocean as a source of acousticgravity waves in the atmosphere, Geophysical Research Abstracts, Vol. 15, EGU20132118, 2013, (EGU General Assembly, Vienna, Austria, 812 April 2013).
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Nikolay A. Zabotin, Oleg A. Godin and Anne Sheehan, Interferometry of background acousticgravity waves, Geophysical Research Abstracts, Vol. 15, EGU20132117, 2013, (EGU General Assembly, Vienna, Austria, 812 April 2013).
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Catalin Negrea, Nikolay A. Zabotin, and Terence Bullett, Spectral Characteristics of Ionospheric Plasma Density and Tilt Variations from the Dynasonde Data, Vol. 15, EGU2013954, 2013, (EGU General Assembly, Vienna, Austria, 812 April 2013).
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Catalin Negrea, Nikolay A. Zabotin, and Terence Bullett, Wave activity in the ThermosphereIonosphere system as determined from Dynasonde data, CEDAR Meeting, Boulder, Colorado, 2228 June 2013, IT Poster ITTI13.
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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), Finiteamplitude acousticgravity waves: exact solutions, J. Fluid Mech.,
767, 5264, doi:10.1017/jfm.2015.40. link
Godin, O. A., N. A. Zabotin, and T. W. Bullett (2015), Acousticgravity waves in the atmosphere generated by infragravity waves in the ocean, Earth, Planets and Space, 67, Art. 47, doi: 10.1186/s4062301502124. link
Godin, O. A. (2016), Diffraction of acousticgravity waves in the presence of a turning point, J. Acoust. Soc. Am., 140, 283295, doi: 10.1121/1.4955283. link
Negrea, C. (2016), Characteristics, Variability and Impact of Atmospheric Gravity Waves in the ThermosphereIonosphere 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 thermosphereionosphere determined from Dynasonde data, Radio Sci., 51, 213222,
doi:10.1002/2015RS005823. link
Negrea, C., N. Zabotin, T. Bullett, T. FullerRowell, T.W. Fang, and M. Codrescu (2016a),
Characteristics of acoustic gravity waves obtained from Dynasonde data, J. Geophys. Res. Space
Physics, 121, 36653680, doi:10.1002/2016JA022495. link
Negrea, C., N. Zabotin, T. Bullett, M. Codrescu, and T. FullerRowell (2016b), Ionospheric
response to tidal waves measured by dynasonde techniques, J. Geophys. Res. Space Physics, 121,
602611, 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, 34523463, doi:10.1002/2016JA022357. link
Marine Sensors
DART Stations
CTBTO Monitoring System
