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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.

In previous work (Knight et al., 2019) a multilayer Fourier method was introduced for obtaining solutions for a partial differential equation (PDE) associated with a dispersion relation for linear gravity waves in a vertically varying, anelastic, nonhydrostatic, viscous, and thermally diffusive atmosphere over some altitude range, given boundary conditions that allow waves to enter at the lower boundary and exit at the top. The previous work described an exact solution method for the dispersion-relation PDE using all wave modes. The current work describes a type of approximate solution, based on a single upgoing gravity-wave mode for each Fourier component, which is computationally cheaper and simpler to implement. Two different approaches to defining the single-mode solution are presented, one based on the Wentzel–Kramers–Brillouin (WKB) method and the other based on a simplified version of the multilayer approximation. The two approaches are shown to be mathematically equivalent. The accuracy of the single-mode approximation is investigated through comparison with the all-mode solution for a realistic example in which gravity waves generated by a convective storm in the troposphere propagate into the upper thermosphere and for which the single-mode approximation gives reasonably accurate results. It is necessary to include imaginary frequency shifts in some Fourier components in order for the different types of modes (e.g., upgoing vs. downgoing and gravity-wave vs. dissipative) to be well-defined in the presence of molecular viscosity. A systematic approach to determining the smallest possible imaginary frequency shift for any given Fourier component is introduced. The new method efficiently suppresses a specific type of numerical artifact associated with large imaginary frequency shifts.

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.

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 Deep Propagating Gravity Wave Experiment (DEEPWAVE) project was conducted over New Zealand and the surrounding regions during June and July 2014, to more fully understand the generation, propagation, and effects of atmospheric gravity waves. A large suite of instruments collected data from the ground to the upper atmosphere (~100 km), with several new remote-sensing instruments operating on board the NSF Gulfstream V (GV) research aircraft, which was the central measurement platform of the project. On 14 July, during one of the research flights (research flight 23), a spectacular event was observed as the GV flew in the lee of the sub-Antarctic Auckland Islands (50.7°S). An apparent "ship wave" pattern was imaged in the OH layer (at ~83.5 km) by the Utah State University Advanced Mesospheric Temperature Mapper and evolved significantly over four successive passes spanning more than 4 h. The waves were associated with orographic forcing generated by relatively strong (15-20 m/s) near-surface wind flowing over the rugged island topography. The mountain wave had an amplitude T_ ~ 10 K, a dominant horizontal wavelength ~40 km, achieved a momentum flux exceeding 300 m2 s-2, and eventually exhibited instability and breaking at the OH altitude. This case of deep mountain wave propagation demonstrates the potential for strong responses in the mesosphere arising from a small source under suitable propagation conditions and suggests that such cases may be more common than previously believed. © 2016. American Geophysical Union. All Rights Reserved.

Mesoscale model simulations of representative trade winds impinging upon the Big Island of Hawaii are diagnosed for their mountain-wave characteristics by coupling a mesoscale model to a Fourier method. Localized phase-averaged wave momentum fluxes are calculated, which facilitates the study of wave generation from fine-scale topographic features. We find that the wave momentum fluxes are dominated by forcing from subsidiary topographic peaks, with the broader island topography controlling flow splitting and lee vortex generation. Waves also arise at the far northern and southern extremities of the island by acceleration of split flow. The strength of the local momentum fluxes proves to be sensitive to a small change in the incident flow direction. Areally integrated fluxes (wave drag) align closely with the incident flow direction and are an order of magnitude smaller than linear predictions and an order of magnitude larger than corresponding dividing streamline predictions. We briefly discuss the relevance of these results to the parameterization of subgrid-scale mountain-wave drag in climate and weather models.

Ray theory is used to study the refraction of short oceanic internal waves by a spectrum of large amplitude inertia waves superimposed on a weakly sheared steady current. The results suggest that the steady current has a significant cumulative effect on short-wave propagation over the timescale of a few inertia periods. The strength of ray convergence is also computed, as this affects short-wave amplitudes. Typically we find weak ray convergence and much slower growth toward instability with increasing vertical wavenumber than in a steady-shear critical-layer model.

Present Doppler-spreading models for short internal waves in the atmosphere and the ocean either neglect the time dependence of the background long-wave shear entirely, or ignore time-dependent effects in their parameterization of dissipation. We use ray and numerical simulations to examine the Doppler spreading of a short internal-wave packet by an inertia-wave packet. The results are enough to show that time dependence in the long-wave shear can make a significant difference to short-wave behavior, and will need to be taken into account in future modelling efforts.

[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.

We use numerical simulations based on the shallow water equations for a homogeneous fluid on an f-plane to study the evolution of a cyclonic eddy over a topographic slope. The results are compared with analogous simulations using the nondivergent approximation in order to determine the effect of the free-surface vortex stretching terms. The simulations use a geometry and parameters related to the experimental results of Carnevale et al. (1991). We find that this vortex stretching produces a significant reduction in the eddy speed. Our numerical results are supported by theoretical analyses, largely set in the quasi-geostrophic context.

We show high-resolution satellite observations of mountain wave events in the stratosphere above South Georgia Island in the remote southern Atlantic Ocean and compute the wave momentum fluxes for these events. The fluxes are large, and they imply important drag forces on the circulation. Small island orography is generally neglected in mountain wave parameterizations used in global climate models because limited model resolution treats the grid cell containing the island as ocean rather than land. Our results show that satellite observations can be used to quantitatively constrain mountain wave momentum fluxes, and they suggest that mountain waves from island topography may be an important missing source of drag on the atmospheric circulation.

Results are presented from a numerical model for barotropic, nondivergent flow in a region with the typical geometry and topography for a strait connecting two ocean basins. The study is motivated by questions concerning the transmission, or generation, of energy through, or in, Bass Strait. The numerical model is a spectral collocation method developed specifically to handle regions with steep and complex topography. Two basic problems are considered, these being the forcing of flow in the strait by a coastally-trapped wave incident at one side, and the forcing by wind stress in the strait, either stationary, or steadily propagating. For the first problem we find that the transmission of energy is enhanced when the boundary conditions allow an oscillatory flux in the strait, as opposed to the case when no such flux is permitted. Mode 2 is more readily transmitted than mode 1 but this is largely counterbalanced by its greater decay due to friction. For the second problem when the forcing is due t...

We describe the high-resolution spectral modelling of nondivergent barotropic linearized flow over steep irregular topography. We use collocation to evaluate spatial derivatives in the barotropic vorticity equation, and a spectral multigrid technique to accelerate the iterative solution of the vorticity—stream function relation. The computational domain is a rectangular channel, which can be conformally mapped into more interesting shapes, as we also discuss. A Fourier-series representation is used in the (periodic) direction parallel to the walls of the channel, and a sine series in the cross-channel direction. For much of the paper we concentrate on the numerical techniques, though results are provided, including an application to the Bass Strait region of southeast Australia.

The atmosphere s response to the total solar eclipse of 4 December 2002 is studied using a prototype high-altitude global numerical weather prediction model (NOGAPS-ALPHA). Local reductions in solar ultraviolet (UV) radiation during the eclipse are estimated using astronomical calculations of umbral and penumbral surface trajectories and observed solar limb darkening at ~ 200-300 nm. In NOGAPS-ALPHA these UV eclipse shadows yield stratospheric radiative cooling rate footprints peaking near 27 K day 1, a value 2 3 times larger than assumed in previous modeling. Difference fields between NOGAPS-ALPHA runs with and without this eclipse forcing reveal vertically deep middle atmospheric responses, with three-dimensional horizontal structures very similar to the large-scale bow-wave response first proposed by Chimonas (1970). Such structure appears clearly only at later times when total eclipses have abated and gravity waves generated in the stratosphere have had time to propagate vertically. Bow-wave amplitudes and direct thermal cooling responses are both small (]1 K for temperature and ]2 3 m s 1 for horizontal winds), contradicting some rocketsonde measurements that suggest much larger responses near 50 60 km altitude. We also find clear evidence of a bow-wave-like response in the model s surface pressure fields, with an amplitude 0.1 0.5 hPa, while surface air temperatures in NOGAPS-ALPHA show 4 K cooling over Africa during the eclipse. Both findings are consistent with surface atmospheric data acquired during previous eclipse passages.

[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).

Ray calculations are used to examine short-wave propagation through an inertial current. The results exhibit differences from theories of short-wave refraction based on steady shears. Caustics take the place of critical layers as the locations of ray focusings and form for short waves at all intrinsic frequencies and at all phases of the inertial oscillation. Conversely, short waves that refract to, and remain at, high vertical wavenumber can escape instability altogether. Similarities with the steady-shear model of Hartman (1975) and contrasts with the Taylor-Goldstein model are emphasised. Checks on the validity of the slowly-varying approximation are also made.