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Tsunami-generated linear acoustic–gravity waves in the atmosphere with altitude-dependent vertical stratification and horizontal background winds are studied with the long-term goal of real-time tsunami warning. The initial-value problem is examined using Fourier–Laplace transforms to investigate the time dependence and to compare the cases of anelastic and compressible atmospheres. The approach includes formulating the linear propagation of acoustic–gravity waves in the vertical, solving the vertical displacement of waves and pressure perturbations numerically as a set of coupled ODEs in the Fourier–Laplace domain, and employing den Iseger’s algorithm to carry out a fast and accurate numerical inverse Laplace transform. Results are presented for three cases with different atmospheric and tsunami profiles. Horizontal background winds enhance wave advection in the horizontal but hinder the vertical transmission of internal waves through the whole atmosphere. The effect of compressibility is significant. The rescaled vertical displacement of internal waves at 100-km altitude shows an arrival at the early stage of wave development due to the acoustic branch that is not present in the anelastic case. The long-term displacement also shows an O(1) difference between the compressible and anelastic results for the cases with uniform and realistic stratification. Compressibility hence affects both the speed and amplitude of energy transmitted to the upper atmosphere because of fast acoustic waves.

On 14 July 2014 during the Deep Propagating Gravity Wave Experiment (DEEPWAVE), aircraft remote sensing instruments detected large-amplitude gravity wave oscillations within mesospheric airglow and sodium layers at altitudes z ~ 78–83 km downstream of the Auckland Islands, located ~1000 km south of Christchurch, New Zealand. A high-altitude reanalysis and a three-dimensional Fourier gravity wave model are used to investigate the dynamics of this event. At 0700 UTC when the first observations were made, surface flow across the islands’ terrain generated linear three-dimensional wave fields that propagated rapidly to z ~ 78 km, where intense breaking occurred in a narrow layer beneath a zero-wind region at z ~ 83 km. In the following hours, the altitude of weak winds descended under the influence of a large-amplitude migrating semidiurnal tide, leading to intense breaking of these wave fields in subsequent observations starting at 1000 UTC. The linear Fourier model constrained by upstream reanalysis reproduces the salient aspects of observed wave fields, including horizontal wavelengths, phase orientations, temperature and vertical displacement amplitudes, heights and locations of incipient wave breaking, and momentum fluxes. Wave breaking has huge effects on local circulations, with inferred layer-averaged westward flow accelerations of ~350 m s−1 h−1 and dynamical heating rates of ~8 K h−1, supporting recent speculation of important impacts of orographic gravity waves from subantarctic islands on the mean circulation and climate of the middle atmosphere during austral winter.

Tsunami-generated acoustic–gravity waves have been observed to propagate in the atmosphere up to the ionosphere, where they have an impact on the total electron content. The authors simulate numerically the propagation of two-dimensional linear acoustic–gravity waves in an atmosphere with vertically varying stratification and horizontal background winds. The authors’ goal is to compare the difference in how much energy reaches the lower ionosphere up to an altitude of 180 km, where the atmosphere is assumed to be anelastic or fully compressible. The authors consider three specific atmospheric cases: a uniformly stratified atmosphere without winds, an idealized case with a wind jet, and a realistic case with an atmospheric profile corresponding to the 2004 Sumatra tsunami. Results show that for the last two cases, the number and height of turning points are different for the anelastic and compressible assumptions, and the net result is that compressibility enhances the total transmission of energy through the whole atmosphere.

Mesospheric bores have been observed and measured in the mesopause region near 100-km altitude, where they propagate horizontally along a duct of relatively strong density stratification. Here, a weakly nonlinear theory is developed for the description of these mesospheric bores. It extends previous theories by allowing internal gravity wave radiation from the duct into the surrounding stratified regions, which are formally assumed to be weakly stratified. The radiation away from the duct is expected to be important for bore energetics. The theory is compared with a numerical simulation of the full Navier–Stokes equations in the Boussinesq approximation. Two initial conditions are considered. The first is a solitary wave solution that would propagate without change of form if the region outside the duct were unstratified. The second is a sinusoid that evolves into an undular bore. The main conclusion is that, while solitary waves and undular bores decay by radiation from the duct, they can survive as significant structures over sufficiently long periods (~100 min) to be observable.

Numerical transform solutions for hydrostatic gravity waves generated by both uniform and sheared flow over elliptical obstacles are used to quantify effects of horizontal geometrical spreading on amplitude evolution with height. Both vertical displacement and steepness amplitudes are considered because of their close connections to drag parameterizations in weather and climate models. Novel diagnostics quantify the location and value of the largest wavefield amplitudes most likely to break at each altitude. These horizontal locations do not stray far from the obstacle peak even at high altitudes. Resulting vertical profiles of wave amplitude are normalized to remove density and refraction effects, thereby quantifying the horizontal geometrical spreading contribution, currently absent from parameterizations. Horizontal geometrical spreading produces monotonic amplitude decreases with height through wave-action conservation as waves propagate into progressively larger horizontal areas. Accumulated amplitude reductions are appreciable for all but the most quasi-two-dimensional obstacles with long axes orthogonal to the flow, and even these are impacted appreciably if the obstacle is rotated by more than 20°–30°. Profiles are insensitive to the obstacle’s functional form but vary strongly in response to changes in its horizontal aspect ratio. Responses to background winds are captured by a vertical coordinate transformation that remaps profiles to a universal form for a given obstacle. These results show that horizontal geometrical spreading has comparable or larger effects on wave amplitudes as the refraction of vertical wavenumbers and thus is important for accurate parameterizations of wave breaking and drag.

A vertical eigenfunction equation is solved to examine the partial reflection and partial transmission of tsunami-generated gravity waves propagating through a height-dependent background atmosphere from the ocean surface into the lower thermosphere. There are multiple turning points for each vertical eigenfunction (at least eight in one example), yet the wave transmission into the thermosphere is significant. Examples are given for gravity wave propagation through an idealized wind jet centered near the mesopause and through a realistic vertical profile of wind and temperature relevant to the tsunami generated by the Sumatra earthquake on 26 December 2004.

The Fourier-ray method involves ray tracing in a Fourier-transform domain. The ray solutions are then Fourier synthesized to produce a spatial solution. Here previous steady-state developments of the Fourier-ray method are extended to include a transient source of mountain waves. The method is illustrated with an initial value problem in which the background flow is started abruptly from rest and then maintained at steady velocity. The resulting wave transience is modeled in a simple way. All rays that radiate from the mountain, including the initial rays, are assigned the full amplitude of the longtime steady-state solution. Time dependence comes in through the changing position of the initial rays. This is sufficient to account for wave transience in a test case, as demonstrated by comparison with simulations from a mesoscale numerical model.

The ray solution for stationary hydrostatic mountain waves has a singularity along the vertical axis directly over the mountain. We use Maslov's method to improve the ray prediction. The ray solution is determined in the wave-number domain and is then mapped by inverse Fourier transform to give a spatial description of the wave field that approximates the linear solution over the mountain and elsewhere. We develop Maslov's method for a medium with a height-dependent mean wind and mean buoyancy, and we compare it with the traditional transform method and with the results of a numerical simulation. Copyright © 2002 Royal Meteorological Society

[1] The Vadas-Fritts ray-tracing model for convectively generated gravity waves is analyzed using the stationary phase approximation and is interpreted in terms of a ray Jacobian approximated by the density of rays. The Vadas-Fritts model launches rays from the convective source region, with initial conditions for the ray-tracing deduced from a near-field integral representation. In the far-field the rays are binned in space-time grid cells. The contribution of each ray to the spatial wave amplitude is determined by its spectral amplitude and by the local density of rays within the grid cells. The present analysis accomplishes two things. First, the stationary phase analysis gives the formal initial conditions for the ray-tracing, which mostly agree with the Vadas-Fritts initialization but also suggest some refinements. Secondly, the Jacobian and ray-density analysis shows how the Vadas-Fritts model can be generalized to follow a beam of rays with a single moving grid cell.

The refraction of a spectrum of short internal waves by a packet of inertia waves is considered. It is found that a short inertia-wave packet produces a larger net change in a spectrum of short waves than a long inertia-wave packet, provided the short waves are trapped at some time during the interaction. Specifically, an incident narrow-banded short-wave spectrum broadens more quickly and more fully when refracted by the short inertia-wave packet. The results are explained in terms of a frequency conservation law, which constrains short-wave change in the limit of a long inertia-wave packet.

[1] The Cryogenic Infrared Spectrometers and Telescopes for the Atmosphere (CRISTA) instrument measured stratospheric temperatures and trace species concentrations with high precision and spatial resolution during two missions. The measuring technique is infrared limb-sounding of optically thin emissions. In a general approach, we investigate the applicability of the technique to measure gravity waves (GWs) in the retrieved temperature data. It is shown that GWs with wavelengths of the order of 100–200 km horizontally can be detected. The results are applicable to any instrument using the same technique. We discuss additional constraints inherent to the CRISTA instrument. The vertical field of view and the influence of the sampling and retrieval imply that waves with vertical wavelengths ∼3–5 km or larger can be retrieved. Global distributions of GW fluctuations were extracted from temperature data measured by CRISTA using Maximum Entropy Method (MEM) and Harmonic Analysis (HA), yielding height profiles of vertical wavelength and peak amplitude for fluctuations in each scanned profile. The method is discussed and compared to Fourier transform analyses and standard deviations. Analysis of data from the first mission reveals large GW amplitudes in the stratosphere over southernmost South America. These waves obey the dispersion relation for linear two-dimensional mountain waves (MWs). The horizontal structure on 6 November 1994 is compared to temperature fields calculated by the Pennsylvania State University (PSU)/National Center for Atmospheric Research (NCAR) mesoscale model (MM5). It is demonstrated that precise knowledge of the instrument's sensitivity is essential. Particularly good agreement is found at the southern tip of South America where the MM5 accurately reproduces the amplitudes and phases of a large-scale wave with 400 km horizontal wavelength. Targeted ray-tracing simulations allow us to interpret some of the observed wave features. A companion paper will discuss MWs on a global scale and estimates the fraction that MWs contribute to the total GW energy (Preusse et al., in preparation, 2002).