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The authors prove the existence and the linear stability of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable x) of a 2-dimensional ocean with infinite depth under the action of gravity and surface tension. Such an existence result is obtained for all the values of the surface tension belonging to a Borel set of asymptotically full Lebesgue measure.

The National Aeronautics and Space Administration (NASA) Atmospheric Waves Experiment (AWE) instrument, launched in November 2023, provides direct observation of small‐scale (30–300 km) gravity waves (GWs) in the mesosphere on a global scale. This work examined changes in GW activity observed by AWE during two major Sudden Stratospheric Warmings (SSWs) in the 2023 and 2024 winter season. Northern Hemisphere (NH) midlatitude GW activity during these events shared similarities. Variations in mesospheric GW activity showed an evident correlation with the magnitude of zonal wind in the upper stratosphere. NH midlatitude GW activity at ∼ $\\mathit{\\sim }$87 km was reduced following the onset of SSWs, likely caused by wind filtering and wave saturation. The upward propagation of GWs was suppressed when the zonal wind reversed from eastward to westward in the upper stratosphere. In regions where the zonal wind weakened but remained eastward, the weakened GWs could be due to their refraction to shorter vertical wavelengths.

An exceptionally deep upper-air sounding launched from Kiruna airport (67.82∘ N, 20.33∘ E) on 30 January 2016 stimulated the current investigation of internal gravity waves excited during a minor sudden stratospheric warming (SSW) in the Arctic winter 2015/16. The analysis of the radiosonde profile revealed large kinetic and potential energies in the upper stratosphere without any simultaneous enhancement of upper tropospheric and lower stratospheric values. Upward-propagating inertia-gravity waves in the upper stratosphere and downward-propagating modes in the lower stratosphere indicated a region of gravity wave generation in the stratosphere. Two-dimensional wavelet analysis was applied to vertical time series of temperature fluctuations in order to determine the vertical propagation direction of the stratospheric gravity waves in 1-hourly high-resolution meteorological analyses and short-term forecasts. The separation of upward- and downward-propagating waves provided further evidence for a stratospheric source of gravity waves. The scale-dependent decomposition of the flow into a balanced component and inertia-gravity waves showed that coherent wave packets preferentially occurred at the inner edge of the Arctic polar vortex where a sub-vortex formed during the minor SSW.

The current standard version of the Whole Atmosphere Community Climate Model (WACCM) simulates Southern Hemisphere winter and spring temperatures that are too cold compared with observations. This “cold-pole bias” leads to unrealistically low ozone column amounts in Antarctic spring. Here, the cold-pole problem is addressed by introducing additional mechanical forcing of the circulation via parameterized gravity waves. Insofar as observational guidance is ambiguous regarding the gravity waves that might be important in the Southern Hemisphere stratosphere, the impact of increasing the forcing by orographic gravity waves was investigated. This reduces the strength of the Antarctic polar vortex in WACCM, bringing it into closer agreement with observations, and accelerates the Brewer–Dobson circulation in the polar stratosphere, which warms the polar cap and improves substantially the simulation of Antarctic temperature. These improvements are achieved without degrading the performance of the model in the Northern Hemisphere stratosphere or in the mesosphere and lower thermosphere of either hemisphere. It is shown, finally, that other approaches that enhance gravity wave forcing can also reduce the cold-pole bias such that careful examination of observational evidence and model performance will be required to establish which gravity wave sources are dominant in the real atmosphere. This is especially important because a “downward control” analysis of these results suggests that the improvement of the cold-pole bias itself is not very sensitive to the details of how gravity wave drag is altered.

The transition scale L t from balanced geostrophic motions to unbalanced wave motions, including near-inertial flows, internal tides, and inertia–gravity wave continuum, is explored using the output from a global 1/48° horizontal resolution Massachusetts Institute of Technology general circulation model (MITgcm) simulation. Defined as the wavelength with equal balanced and unbalanced motion kinetic energy (KE) spectral density, L t is detected to be geographically highly inhomogeneous: it falls below 40 km in the western boundary current and Antarctic Circumpolar Current regions, increases to 40–100 km in the interior subtropical and subpolar gyres, and exceeds, in general, 200 km in the tropical oceans. With the exception of the Pacific and Indian sectors of the Southern Ocean, the seasonal KE fluctuations of the surface balanced and unbalanced motions are out of phase because of the occurrence of mixed layer instability in winter and trapping of unbalanced motion KE in shallow mixed layer in summer. The combined effect of these seasonal changes renders L t to be 20 km during winter in 80% of the Northern Hemisphere oceans between 25° and 45°N and all of the Southern Hemisphere oceans south of 25°S. The transition scale’s geographical and seasonal changes are highly relevant to the forthcoming Surface Water and Ocean Topography (SWOT) mission. To improve the detection of balanced submesoscale signals from SWOT, especially in the tropical oceans, efforts to remove stationary internal tidal signals are called for.

Volcanoes can produce tsunamis by means of earthquakes, caldera and flank collapses, pyroclastic flows or underwater explosions 1 – 4 . These mechanisms rarely displace enough water to trigger transoceanic tsunamis. Violent volcanic explosions, however, can cause global tsunamis 1 , 5 by triggering acoustic-gravity waves 6 – 8 that excite the atmosphere–ocean interface. The colossal eruption of the Hunga Tonga–Hunga Ha’apai volcano and ensuing tsunami is the first global volcano-triggered tsunami recorded by modern, worldwide dense instrumentation, thus providing a unique opportunity to investigate the role of air–water-coupling processes in tsunami generation and propagation. Here we use sea-level, atmospheric and satellite data from across the globe, along with numerical and analytical models, to demonstrate that this tsunami was driven by a constantly moving source in which the acoustic-gravity waves radiating from the eruption excite the ocean and transfer energy into it by means of resonance. A direct correlation between the tsunami and the acoustic-gravity waves’ arrival times confirms that these phenomena are closely linked. Our models also show that the unusually fast travel times and long duration of the tsunami, as well as its global reach, are consistent with an air–water-coupled source. This coupling mechanism has clear hazard implications, as it leads to higher waves along land masses that rise abruptly from long stretches of deep ocean waters. By analysing sea-level, atmospheric and satellite data captured after eruption of the Hunga Tonga–Hunga Ha’apai volcano, as well as numerical and analytical models, it is shown that global tsunamis can be triggered by acoustic-gravity waves.

Orographic gravity waves (OGWs) are an important mechanism for coupling of the free atmosphere with the surface, mediating the momentum and energy transport and influencing the dynamics and circulation especially in the middle-atmosphere. Current global climate models are not able to resolve a large part of the OGW spectrum and hence, OGW effects have to be parameterized in the models. Typically, the only parameterized effect is the OGW induced drag. Despite producing the same quantity as an output and relying on similar assumptions (e.g. instantaneous vertical propagation), the individual OGW parameterization schemes differ in many aspects such as handling of the orography, the inclusion of non-linear effects near the surface and the tuning of the emergent free parameters. In this study, we have reviewed 7 different parameterizations, which are used in 9 different CMIP6 models. We report pronounced differences in the vertical distribution and magnitude of the parameterized OGW drag between the models and study to what extent the inter-model differences can be traced back to the difference in the type and tuning of the schemes. Finally, we demonstrate how the OGW drag differences project to the intermodel differences in the stratospheric dynamics. The study can pave the way for a more systematic research of the OGW parameterizations in the future, with an ultimate goal of lowering the amount of uncertainty of the future climate projections connected with the parameterized effects of unresolved orography.

Large volcanic eruptions produce various atmospheric wave perturbations. One of these wave manifestations is atmospheric gravity waves (AGWs), which can be observed through remote sensing satellite measurements. Based on multisensory instruments on board Aqua, Suomi NPP, and Thermosphere Ionosphere Mesosphere Energetics Dynamics satellites, we discuss the propagation of AGWs across stratospheric and mesospheric altitudes following three large volcanic eruptions of 15 January 2022 Hunga Tonga‐Hunga Ha'apai, 11 April 2021 La Soufrière, and 13 February 2014 Kelud. Following the events, the mechanical updraft of air, observed as tropopause overshooting and the enhanced H2O in Microwave Limb Sounder measurements, contributed to the convective generation of AGWs through mechanical oscillator effect and thermal forcing. The present study is an important and useful contribution in compiling the propagation of AGWs across various atmospheric layers and substantiating their convective generation, for large volcanic eruptions. Thereby, strengthening our understanding of lithosphere‐atmosphere coupling through wave‐dynamic pathways by reinforcing the existing knowledge.

The characteristics and mechanisms of diurnal rainfall and winds near the south coast of China are explored using satellite data (CMORPH), long-term hourly WRF Model data (Du model data), a simple 2D linear model, and 2D idealized simulations. Both the CMORPH and Du model data indicate that the diurnal cycle of rainfall has two propagation modes near the coast: onshore and offshore. The diurnally periodic winds (vertical motions) also show a similar propagation feature. Analysis of the rainfall budget indicates that vertically integrated vertical vapor advection plays a key role in the diurnal cycle of rainfall and thus provides a physical connection between winds and rainfall in the diurnal cycle. It was found that a simple 2D linear land–sea breeze model with a background wind can well capture the two propagation modes, which are associated with inertia–gravity waves, in terms of speed and phase. The background wind changes the pattern of the inertia–gravity waves and further affects the diurnal propagation. The effect of the background wind on the diurnal propagation was verified through idealized simulations using a simplified version of the WRF Model that can also capture the diurnal features.

A multi-group of strong atmospheric waves (wave packet nos. 1–5) over China associated with the 2022 Hunga Tonga–Hunga Ha′apai (HTHH) volcano eruptions were observed in the mesopause region using a ground-based airglow imager network. The horizontal phase speed of wave packet nos. 1 and 2 is approximately 309 and 236 m s−1, respectively, which is consistent with Lamb wave L0 mode and L1 mode from theoretical predictions. The amplitude of the Lamb wave L1 mode is larger than that of the L0 mode. The wave fronts of Lamb wave L0 and L1 below the lower thermosphere are vertical, while the wave fronts of L0 mode tilt forward above the lower atmosphere, exhibiting internal wave characteristics which show good agreement with the theoretical results. Two types of tsunamis were simulated; one type of tsunami is induced by the atmospheric-pressure wave (TIAPW), and the other type of tsunami is directly induced by the Tonga volcano eruption (TITVE). From backward ray-tracing analysis, the TIAPW and TITVE were likely the sources of wave packet nos. 3 and 4–5, respectively. The scale of tsunamis near the coast is very consistent with the atmospheric AGWs observed by the airglow network. The atmospheric gravity waves (AGWs) triggered by TITVE propagate nearly 3000 km inland with the support of a duct. The atmospheric-pressure wave can directly affect the upper atmosphere and can also be coupled with the upper atmosphere through the indirect way of generating a tsunami and, subsequently, tsunami-generating AGWs, which will provide a new understanding of the coupling between ocean and atmosphere.