Inertio-gravity Waves Research Articles

The Impacts of Convective Parameterization and Moisture Triggering on AGCM-Simulated Convectively Coupled Equatorial Waves

Abstract This study examines the impacts of convective parameterization and moisture convective trigger on convectively coupled equatorial waves simulated by the Seoul National University (SNU) atmospheric general circulation model (AGCM). Three different convection schemes are used, including the simplified Arakawa–Schubert (SAS) scheme, the Kuo (1974) scheme, and the moist convective adjustment (MCA) scheme, and a moisture convective trigger with variable strength is added to each scheme. The authors also conduct a “no convection” experiment with deep convection schemes turned off. Space–time spectral analysis is used to obtain the variance and phase speed of dominant convectively coupled equatorial waves, including the Madden–Julian oscillation (MJO), Kelvin, equatorial Rossby (ER), mixed Rossby–gravity (MRG), and eastward inertio-gravity (EIG) and westward inertio-gravity (WIG) waves. The results show that both convective parameterization and the moisture convective trigger have significant impacts on AGCM-simulated, convectively coupled equatorial waves. The MCA scheme generally produces larger variances of convectively coupled equatorial waves including the MJO, more coherent eastward propagation of the MJO, and a more prominent MJO spectral peak than the Kuo and SAS schemes. Increasing the strength of the moisture trigger significantly enhances the variances and slows down the phase speeds of all wave modes except the MJO, and usually improves the eastward propagation of the MJO for the Kuo and SAS schemes, but the effect for the MCA scheme is small. The no convection experiment always produces one of the best signals of convectively coupled equatorial waves and the MJO.

Abrupt transitions between gyroscopic and internal gravity waves: the mid-latitude case

The large-scale vertical density stratification, represented by buoyancy frequency N, is generally very stable in the upper half of the ocean, and relatively weak in the lower half. However, closer inspection of density profiles demonstrates steps rather than a smooth increase with depth. As is demonstrated here using Richardson number, geostrophic balance and slantwise convective mixing arguments, these layers have a limited set of minimum, weak stratification, N-values Nmin indicating the transition between stably stratified and convective ‘homogeneous’ layers. Adopting the viewpoint that the transition occurs for neutral stability in the direction of Earth's rotation Ω instead of gravity g, three discrete states are hypothesized for mid-latitudes: (i) Nmin = 2fh under linear stability conditions, (ii) Nmin = fh(|ϕ| < 45°) and (iii) Nmin = 4fh, both under nonlinear stability, where horizontal component fh = 2Ω cos ϕ at latitude ϕ. The Nmin are not in terms of inertial frequency f = 2Ω sin ϕ, because the effect of fh is the tilting of vortex tubes away from the local vertical in the direction of Ω. The above explains very well deep-ocean North-Atlantic and Mediterranean observations on transitions in conductivity-temperature with depth profiles, inertial polarization and near-inertial shear. The latter peaks at sub-inertial 0.97f, which is associated with the lower inertio-gravity wave limit for Nmin = 4fh, thereby stressing the importance of fh for the dominant physics associated with mixing in the ocean.

Electromagnetic inertio-gravity waves in the ionospheric E-layer

The effect of the Ampére force on inertio-gravity (IG) waves in the partially ionized ionospheric E-layer is considered. Electromagnetic IG waves are then studied. It is shown that the free energy necessary for linear instability of electromagnetic IG waves arises from the field-aligned current. Furthermore, it is found that atmospheric vortex motions can induce substantial variations in the geomagnetic field and field-aligned currents.

Characteristics of inertio‐gravity waves revealed in rawinsonde data observed in Korea during 20 August to 5 September 2002

Characteristics of inertio‐gravity waves (IGWs) observed at six operational rawinsonde stations in Korea from 20 August to 5 September 2002 and their relationship with convective sources are investigated. Several types of convective systems, including mesoscale convective complexes and Typhoon Rusa, passed the Korean peninsula during the observing period. To categorize the observed waves with and without convective sources, wet and dry periods are defined at each observing site using hourly precipitation and satellite data. Although waves with extremely large values of intrinsic frequency and vertical wavelength are observed mostly in wet periods, the mean values of wave parameters for wet and dry periods are similar. Low‐frequency IGWs can originate far from and long before the observing sites, implying that it is unreasonable to correlate convective sources and observed waves at the same location and time. For better correlation of the observed waves and their sources, a three‐dimensional ray‐tracing model is used. A new wet case is defined on the basis of the occurrence of convection when and where a ray locates in mid‐to‐upper troposphere. Characteristics of the observed waves for new wet and dry cases differ significantly: the intrinsic frequency is larger but the horizontal wavelength is much smaller for wet than dry cases. Sources for wet cases are mostly convective clouds located northeast and southeast of the observing sites below 5 km. This is clearly distinguished from dry cases, where sources are located mostly in the northwest above 15 km and southeast far from the observing sites below 5 km.

Unpredictability of internal M<sub>2</sub>

Abstract. Current observations from a shelf sea, continental slopes and the abyssal North-East Atlantic Ocean are all dominated by the semidiurnal lunar (M2) tide. It is shown that motions at M2 vary at usually large barotropic and coherent baroclinic scales, >50 km horizontally and >0.5 H vertically. H represents the waterdepth. Such M2-scales are observed even close to topography, the potential source of baroclinic, "internal" tidal waves. In contrast, incoherent small-scale, ~10 km horizontally and ~0.1 H vertically, baroclinic motions are dominated around f, the local inertial frequency, and/or near 2Ω≈S2, the semidiurnal solar tidal frequency. Ω represents the Earth's rotational vector. This confirms earlier suggestions that small-scale baroclinic M2-motions generally do not exist in the ocean in any predictable manner, except in beams very near, <10 km horizontally, to their source. As a result, M2-motions are not directly important for generating shear and internal wave induced mixing. Indirectly however, they may contribute to ocean mixing if transfer to small-scale motions at f and/or S2 and at high internal wave frequencies can be proven. Also far from topography, small-scale motions are found at either one or both of the latter frequencies. Different suggestions for the scales at these particular frequencies are discussed, ranging from the variability of "background" density gradients and associated divergence and focusing of internal wave rays to the removal of the internal tidal energy by non-linear interactions. Near f and S2 particular short-wave inertio-gravity wave bounds are found in the limits of strong and very weak stratification, which are often observed in small-scale layers.

Latitudinal Variations of the Convective Source and Propagation Condition of Inertio-Gravity Waves in the Tropics

Abstract Latitudinal variations of the convective source and vertical propagation condition of inertio-gravity waves (IGWs) in the tropical region (30°S–30°N) are examined using high-resolution Global Cloud Imagery (GCI) and 6-hourly NCEP–NCAR reanalysis data, respectively, for 1 yr (March 1985–February 1986). The convective source is estimated by calculating the deep convective heating (DCH) rate using the brightness temperature of the GCI data. The latitudinal variation of DCH is found to be significant throughout the year. The ratio of the maximum to minimum values of DCH in the annual mean is 3.2 and it is much larger in the June–August (JJA) and December–February (DJF) means. Spectral analyses show that DCH has a dominant period of 1 day, a zonal wavelength of about 1600 km, and a Gaussian-type phase-speed spectrum with a peak at the zero phase speed. The vertical propagation condition of IGWs is determined, in the zonal wavenumber and frequency domain, by two factors: (i) latitude, which determines the Coriolis parameter, and (ii) the basic-state wind structure in the target height range of wave propagation. It was found that the basic-state wind significantly influences the wave propagation condition in the lower stratosphere between 150 and 30 hPa, and accordingly a large portion of the source spectrum is filtered out. This is prominent not only in the latitudes higher than 15° where strong negative shear exists, but also near the equator where strong positive shear associated with the westerly phase of the quasi-biennial oscillation (QBO) filters out large portions of the low-frequency components of the convective source. There is no simple relationship between the ground-based frequency and latitude; lower latitudes are not always favorable for low-frequency IGWs to be observed in the stratosphere. The basic-state wind in the Tropics, which has seasonal, annual, and interannual variations, plays a major role not only in determining the wave propagation condition in the stratosphere but also in producing convective sources in the troposphere.

Initial-value approach to study the inertio-gravity waves without the ‘traditional approximation’

An initial-value problem is formulated with linear Boussinesq equations to study the inertio-gravity waves without the “traditional approximation” that is to include a complete effect of rotation. Motions are assumed to be horizontally periodic, but bounded vertically at the top and bottom. The evolution of the vertical structure of wave motions can be calculated from given initial conditions with a one-dimensional finite-difference version of the model with or without forcing/dissipation under a variable thermal buoyancy condition in height. This program is intended to use as a simple numerical laboratory to study the time-evolution of inertio-gravity waves. Examples show for (1) the free oscillations using the normal mode solutions as initial conditions, and (2) the forced oscillations as a simulation of near-inertial currents in the oceans generated by atmospheric storms. An emphasis is made to asses the role of the horizontal component of the earth’s rotation which has been traditionally neglected in the study of inertio-gravity waves.

Shear at the critical diurnal latitude

[1] Around latitudes ∣ϕ∣ ≈ 30° where diurnal D1 equals the local inertial frequency f = 2Ωsinϕ, Ω denoting the Earth's rotational vector, several mechanisms can enhance shear at f due to a reduction in vertical scales. This would imply locally enhanced deep-ocean mixing. Here, recent 1.5 years of acoustic Doppler current profiler (ADCP) observations from the Canary Basin demonstrate largest kinetic energy at semidiurnal tides (D2), but a complete absence of D2-shear. Instead, shear is peaking at subinertial 0.97 ± 0.01f and terdiurnal 3f(≈D2 + f ≈ D3 here), and vertical scales Δz(f) < 0.1Δz(D2). However, the f-band is broader than deterministic tidal frequencies and the smallest vertical scales, organizing shear in thin layers, are found at the lower inertio-gravity wave limit, which equals 0.97f for the weakest stratification observed (N = 6f, using Δz = 10 m). Hence, besides possibly subharmonic resonance, other mechanisms must be involved in enhancing f-shear, including non-linear harmonic interactions and wave trapping at the critical latitude's poleward shift.

Inertial and tidal shear variability above Reykjanes Ridge

Yearlong 75 kHz acoustic Doppler current profiler (ADCP) data were obtained well above Reykjanes Ridge (northern extension of the Mid-Atlantic Ridge (MAR)). The area is characterized by relatively large semidiurnal tidal (‘ D 2’) currents that have (at lunar M 2) more than half a decade larger variance than inertial ( f) currents. However, despite the relatively weak near-inertial kinetic energy, its vertical current shear shows larger magnitudes than at M 2 in an otherwise flat f− D 2 band limited between frequencies 0.74 and 1.35 f, which equals the inertio-gravity wave bounds [ σ min, σ max]( N= f). N represents the buoyancy frequency. The shear in this band dominates all shear computed at 20 m effective vertical scale. As the kinetic energy spectrum peaks at M 2, but not (significantly) at S 2 and N 2, a difference in tidal (and inertial) scales and hence sources is observed. M 2-tides contribute mostly to large-scale coherent motions. The dominant incoherent f− D 2 shear is highly variable in time (∼2-day periodicity). Furthermore, inertial and tidal shear are more or less completely separated in space and time, each occurring in different layers in the vertical. The thin shear layers reflect the rapidly varying short vertical scale N s profile, to within the ∼20 m limitation of ADCP data, rather than the large-scale smooth N L. In each of large- N s layers Ri≈1, probably. The yearlong smoothed shear magnitude follows N L, but only as stable Ri≈5. The shear polarization is more circular than rectilinear, albeit varying with time, and highly symmetric around f. During transitions, e.g., between stratified and homogeneous layers and between waves from varying sources, near-circular motions can generate near-rectilinear shear in the direction of wave propagation (in the direction of the minor axis of the current ellipse). This contrasts with the possibility of near-rectilinear barotropic oscillatory motions generating near-circular shear under viscosity in shallow seas.

Coupling mechanisms between equatorial waves and cumulus convection in an AGCM

In this study, we focused on the difference in appearances of the convectively coupled equatorial waves (CCEWs) in a simulation with the CCSR/NIES/FRCGC AGCM, between two experiments, one with and the other without implementation of the convective suppression scheme (CSS) in the prognostic Arakawa–Schubert cumulus parameterization. Realistic CCEW modes, i.e., Kelvin, Rossby, mixed Rossby-gravity (MRG), and n = 0 eastward inertio-gravity (EIG) wave modes, were reproduced in the with-CSS experiment, while only Rossby-wave-like signals appeared in the without-CSS experiment. By comparing the structures of the Kelvin wave mode and the Rossby wave mode in two runs, it was suggested that the structural difference between these two modes in conjunction with the difference in the controlling factor of cumulus convection determines the CCEW features. The CSS implemented here is such that cumulus convection is suppressed until the cloud-layer-averaged relative humidity exceeds the threshold of 80%. In the without-CSS model, only Rossby wave modes are coupled with the convection. This is because CAPE controls cumulus convection in this model, and the larger frictional convergence of Rossby wave mode prepares CAPE to generate favorable condition for cumulus convection. In the case of the with-CSS model, on the other hand, cumulus convection is largely controlled by the humidity in the free atmosphere. The convergence associated with the equatorial waves can produce the moisture anomaly to overcome the relative humidity threshold, and maintains the favorable condition for cumulus convection once it starts. In this case, not only Rossby waves but also Kelvin, MRG, and n = 0 EIG waves are reproduced more realistically. It is suggested that inclusion of some kind of mechanism connecting the free tropospheric moisture with the convection under the condition of abundant convective available potential energy could be a key factor for realistic coupling between large-scale atmospheric waves and convection.

Meridional Propagation of Planetary-Scale Waves in Vertical Shear: Implication for the Venus Atmosphere

Abstract It is shown that planetary-scale waves are inherently accompanied by latitudinal momentum transport when they propagate vertically in vertically sheared zonal flows. Because of the dependence of the wave's latitudinal scale on the intrinsic phase speed, positive (negative) vertical shear should force prograde (retrograde) waves to focus equatorward and retrograde (prograde) waves to expand poleward in the course of upward propagation. Consequently, Eliassen–Palm (EP) flux vectors are tilted from the vertical and nonzero latitudinal momentum fluxes occur. The direction of momentum transport should always be equatorward (poleward) in positive (negative) vertical shear irrespective of the zonal propagation direction. The idea was applied to upwardly propagating waves in the Venusian middle atmosphere, where vertical shear of strong midlatitude jets and equatorial superrotation exist. Numerical solutions showed that Kelvin and prograde inertio-gravity waves focus equatorward and mixed Rossby–gravity and Rossby waves expand poleward below the cloud top. The former is attributed primarily to the vertical shear of the superrotation, while the latter to the vertical shear beneath the midlatitude jets. Such characteristics of planetary-scale waves will cause angular momentum separation between high and low latitudes and, at least partly, contribute to the maintenance of the superrotation.

A Three Dimensional Wave Activity Flux Applicable to Inertio-Gravity Waves

A three dimensional wave activity flux applicable to non-hydrostatic inertio-gravity waves in a time mean flow in a Boussinesq fluid is derived. It is shown that the flux gives the wave-action density flux relative to the local time mean flow, and additive terms in residual circulation are equal to Stokes drift under the WKB limit. The flux is a generalization of three dimensional wave activity fluxes that have been used to analyze quasi-geostrophic wave disturbances. A flux under the log-pressure coordinate system on spherical geometry applicable to global hydrostatic inertio-gravity waves is also derived.

Dynamical structures for southwesterly airflow over southern Norway: the role of dissipation

Earlier studies have revealed mesoscale structures in southwesterly flows over the mountains of southern Norway (Rossby number ∼1): a left-side jet and an upstream wind minimum as signs of the influence of rotation; a downstream wind shadow connected to inertio-gravity waves; a weak jet on the right side of the wind shadow and a shallow coastal wind shadowbetween the left-side jet and the main wind shadow. In the present study, the dynamics of the structures have been further examined from the results of experiments performed by a mesoscale numerical model and computations using a linear model with rotation included. Ideal atmospheric conditions for a large-scale wind direction from southwest have been used to initialize the numerical model. The sensitivity of mesoscale structures was studied with respect to dissipation from wave breaking and surface friction. Nonlinearity and dissipation in breaking waves are needed to explain the location, depth and strength of the downstream wind shadow. Increased wind to the right of the shadow was found to be generated by the effect of the Coriolis force as air was pulled towards the low-pressure perturbation behind the mountains. The coastal wind shadow was found to be a direct result of differential friction between land and ocean. Nonlinear experiments and an attempt to include boundary layer effects in linear theory showed that friction is reducing the effective height of the mountain and the signal of the mesoscale structures.

A numerical study of gravity waves induced by convection associated with Typhoon Rusa

Typhoon Rusa (2002) is simulated using a three‐dimensional mesoscale model (MM5), and the characteristics of gravity waves generated by convection associated with the typhoon are investigated. The gravity waves in the stratosphere propagate in two directions, northwestward and southeastward according to the convective bands propagating in the same directions, although the typhoon itself moves north‐northeastward. Spectral analyses show that the inertio‐gravity waves (IGWs) in the stratosphere generated by Rusa have a dominant horizontal wavelength of 300–600 km, a vertical wavelength of 3–11 km, and a period of 6–11 hrs. A large fraction of the IGWs is filtered out in the upper troposphere and stratosphere mainly due to the critical‐level filtering process. The decreased magnitude of the momentum flux with height in a non‐filtered region is likely due to the damping process, with a minor contribution by the wave breaking process that can occur exclusively near the critical‐level phase speeds.

Large-Scale Modes in a Rotating Atmosphere with Radiative–Convective Instability and WISHE

Abstract A highly simplified parameterization of diabatic processes is applied to linearized equations on a equatorial beta plane. The diabatic processes include moist convection, cloud–radiation interactions (CRI), and wind-induced surface heat exchange (WISHE). The precipitation rate is assumed to increase linearly as the vertically averaged saturation deficit decreases. The modeled modes are Matsuno’s normal modes, that is, Kelvin waves, mixed Rossby–gravity waves, Rossby waves, and inertio–gravity waves, and an additional mode called here a slow moisture mode. All of the Matsuno modes are damped and remain stable even when CRI and WISHE are turned on. Their phase speeds do not vary much from Matsuno’s adiabatic values except for very long wavelength Kelvin and Rossby modes, for which the phase speeds are reduced compared to the adiabatic values. The slow moisture modes are stationary and unstable under CRI, while WISHE causes them to propagate. Under CRI and WISHE together the slow moisture modes are unstable and eastward propagating for long wavelengths and slowly moving relative to the mean flow for short wavelengths. The dispersion relations of the slow moisture modes are one of nearly constant or decreasing frequency with increasing wavenumber. The most important model parameter is the tropospheric moisture relaxation time scale, which is chosen to be 1 day. The model failed to explain the observed phase speeds of convectively coupled Matsuno modes. Following Mapes, the authors suggest that other dynamics, more realistic than the one including only the first baroclinic mode, may be responsible for these modes.

Gravity waves above Andes detected from GPS radio occultation temperature profiles: Mountain forcing?

A significant wave activity in the upper troposphere and lower stratosphere at midlatitudes (30–40S) above the Andes Range was recently detected from Global Positioning System Radio Occultation (GPS RO) temperature profiles, retrieved from SAC‐C (Satélite de Aplicaciones Cientficas‐C) and CHAMP (CHAllenging Minisatellite Payload) satellites. Previously, large amplitude, long vertical wavelength structures have been reported in this region, as detected from other limb‐sounding devices and have been identified as mountain waves (MWs). The capability of GPS RO observations to detect typical MWs with horizontal wavelengths shorter than 150 km, as well as the proper association of the observed wave activity to mountain forcing is put in doubt. Other three possible sources are discussed. In particular, the generation of inertio‐gravity waves by geostrophic adjustment near to a permanent jet situated above the mountains, may constitute another important mechanism in this region. These waves may possess longer horizontal and perhaps shorter vertical wavelengths than those typically expected in MWs and could be more easily detected from limb‐sounding profiles. The “jet” mechanism will be discussed in a second paper.

The dynamical background of polar mesosphere winter echoes from simultaneous EISCAT and ESRAD observations

Abstract. On 30 October 2004 during a strong solar proton event, layers of enhanced backscatter from altitudes between 55 and 75km have been observed by both ESRAD (52MHz) and the EISCAT VHF (224MHz) radars. These echoes have earlier been termed Polar Mesosphere Winter Echoes, PMWE. After considering the morphology of the layers and their relation to observed atmospheric waves, we conclude that the radars have likely seen the same phenomenon even though the radars' scattering volumes are located about 220km apart and that the most long-lasting layer is likely associated with wind-shear in an inertio-gravity wave. An ion-chemistry model is used to determine parameters necessary to relate wind-shear induced turbulent energy dissipation rates to radar backscatter. The model is verified by comparison with electron density profiles measured by the EISCAT VHF radar. Observed radar signal strengths are found to be 2-3 orders of magnitude stronger than the maximum which can be expected from neutral turbulence alone, assuming that previously published results relating radar signal scatter to turbulence parameters, and turbulence parameters to wind shear, are correct. The possibility remains that some additional or alternative mechanism may be involved in producing PMWE, such as layers of charged dust/smoke particles or large cluster ions.

Southwesterly flows over southern Norway—mesoscale sensitivity to large-scale wind direction and speed

Mesoscale structures have been identified and studied for simulations of ideal flows passing southern Norway. The large-scale wind direction was between south and west and the wind speed between 10 and 22.5 m s—1. Flow data have been provided from simulations with a mesoscale numerical model with 10 km between the grid points horizontally. The results are found to be qualitatively in accordance with observational findings, including old forecasting rules for southern Norway. As expected, the influence of rotation is considerable. Accordingly, the flows are characterized by a jet on the left side of the mountains and a minimum on the right upstream side. In addition, a wind shadow extends far downstream of the main mountains, with signs of increased winds on the right side of the wind shadow. The wind shadow is connected to an inertio-gravity wave with downstream signatures caused by rotation. When the background wind direction was turned, the alignment of the structures was turned accordingly. For flows in the sector 200–270°, the action of the Coriolis force gave an efficiently narrower mountain (than without rotation). A similar action for southerly flows, on the other hand, resulted in an efficiently wider mountain. Different mountain widths resulted in different shape of the gravity waves and different acceleration of the jet on the left side. When the wind speed is increased, the amplitudes of the mesoscale structures are decreased with no abrupt change in the character of the flow.

Properties of internal planetary-scale inertio gravity waves in the mesosphere

Abstract. At high latitudes in the upper mesosphere, horizontal wind oscillations have been observed with periods around 10h. Waves with such a period are generated in our Numerical Spectral Model (NSM), and they are identified as planetary-scale inertio gravity waves (IGW). These IGWs have periods between 9 and 11h and appear above 60km in the zonal mean (m=0), as well as in m=1 to 4, propagating eastward and westward. Under the influence of the Coriolis force, the amplitudes of the waves propagating westward are larger at high latitudes than those propagating eastward. The waves grow in magnitude at least up to about 100km and have vertical wavelengths around 25km. Applying a running window of 15 days for spectral analysis, the amplitudes in the wind field are typically between 10 and 20m/s and can reach 30m/s in the westward propagating component for m=1 at the poles. In the temperature perturbations, the wave amplitudes above 100km are typically 5K and as large as 10K for m=0 at the poles. The IGWs are intermittent but reveal systematic seasonal variations, with the largest amplitudes occurring generally in late winter and spring. Numerical experiments show that such waves are also generated without excitation of the migrating tides. The amplitudes and periods then are similar, indicating that the tides are not essential to generate the waves. However, the seasonal variations without tides are significantly different, which leads to the conclusion that non linear interactions between the semidiurnal tide and planetary waves must contribute to the excitation of the IGWs. Directly or indirectly through the planetary waves, the IGWs are apparently excited by the instabilities that arise in the zonal mean circulation. When the solar heating is turned off for m=0, both the PWs and IGWs essentially disappear. That the IGWs and PWs have common roots in their excitation mechanism is also indicated by the striking similarity of their seasonal variations in the lower mesosphere. Compared to the PWs, however, the planetary-scale IGWs propagate zonally with much larger phase speeds. In contrast to the PWs, the IGWs thus are not affected much by interactions with the background zonal winds whose seasonal variations drastically change with altitude in the mesosphere. Since the IGWs can propagate through the mesosphere without much interaction, except for viscous dissipation, one should then expect that they reach the thermosphere above with significant and measurable amplitudes.

Dynamics of 2-Day Equatorial Waves

Abstract The dynamics of the 2-day wave, a type of convectively coupled disturbance that frequents the equatorial western Pacific, is examined using observations and a linear primitive equation model. A statistical composite of the wave's kinematic and thermodynamic structure is presented. It is shown that 1) the wave's wind and temperature perturbations can be modeled as linear responses to convective heating and cooling, and 2) the bulk of the wave's dynamical and convective structure can be represented with two vertical modes. The observations and model results suggest that the 2-day wave is an n = 1 westward-propagating inertio–gravity wave with a shallow equivalent depth (14 m) that results from the partial cancelation of adiabatic temperature changes due to vertical motion by convective heating and cooling.