Climatology of gravity waves in the middle atmosphere

An attempt is made at the statistical analysis of small-scale disturbances in the stratosphere and mesosphere with the aid of meteorological rocket observations at many stations from 77°N to 8°S for several years.By applying a high-pass filter to daily rocket data in the height range 20–65 km, wind and temperature fluctuations with characteristic vertical scales close to or less than 10 km are obtained, which are considered to be due to internal gravity waves. Results are expressed in terms of parameters which tend to emphasize smallscale vertical fluctuations and which should provide qualitative measures of gravity wave activity.It is found that the gravity wave activity shows a notable annual cycle in higher latitudes with the maximum in wintertime, while it shows a semiannual cycle in lower latitudes with the maxima around equinoxes. It is also found from the standard deviation around the monthly mean that the temporal variability of gravity waves is very large.     

Dynamic coupling between the lower and upper atmosphere by tides and gravity waves

Results of a General Circulation Model simulation of the dynamics of the middle atmosphere are shown focusing our attention to the tidal wave mean flow interaction and propagation of migrating diurnal and semidiurnal tides in the model. It is shown that migrating tidal waves are well simulated and the amplitude growth with height is effectively suppressed by the convective adjustment in the model. It is also shown that the dissipating solar diurnal tide plays an important role in inducing mean zonal winds in the low latitude region of the lower thermosphere. The behavior of non-migrating diurnal tides is also analyzed to show that non-migrating diurnal tides have significant amplitudes in the lower thermosphere. It is suggested that the non-migrating diurnal tide, which propagates against background mean zonal winds, has the possibility to propagate into the middle to high latitude region due to the Doppler effect.     

Radar studies of gravity waves and tides in the middle atmosphere: a review

This review deals with recent radar studies of gravity waves and tides in the middle atmosphere, roughly over regions of 10–30 and 60–90 km. The techniques are briefly discussed and their limitations are pointed out. In the troposphere-stratosphere region, buoyancy oscillations, gravity-wave critical-layer interactions, and gravity waves excited by cumulus convection have been observed. Pronounced short-period (10–20 min) waves have frequently been detected in the mesosphere, and in some cases these have been identified as evanescent and trapped gravity wave modes. Diurnal and semidiurnal tides have been observed in the stratosphere and mesosphere at low and mid latitudes, but the corresponding tidal modes are not unambiguously resolved. The need for obtaining more comprehensive data bases with the existing radar systems is emphasized for further tidal and wave studies in the middle atmosphere.     

Pseudosaturation of gravity waves in the middle atmosphere: an interpretation of certain lidar observations

Irregular winds of the middle atmosphere, commonly attributed to gravity waves, often exhibit a vertical-wavenumber (m) spectral form approximating to Km⁻³ at sufficiently large m, with K a constant found to be relatively unvarying with time, location and even height. This behavior is widely believed to result from some saturation process, but the physical mechanism remains a matter for debate. There now exist three theories:

• 1.(a) linear instability,
• 2.(b) nonlinear wave-induced diffusion, and
• 3.(c) nonlinear waveinduced Doppler spreading. Each has produced the Km⁻³ form (but only as an approximation in the case of Doppler spreading) and values of K within a factor of three of one another and of observed values.

New data have revealed circumstances in which an approximation to the form Km⁻³ is again found, suggestive of saturation, but with values of K that increase by a factor of 5 or 10 on moving from the stratopause to the mesopause region. This height variation is incompatible with theories (a) and (b) if the m⁻³ form is taken to be induced by the corresponding saturation process (rather than by source spectra), but is shown here to be compatible with the Doppler-spread theory. Because of the continued growth of K with height, which must ultimately cease, the observations and corresponding theory are taken to represent pseudosaturation rather than fully developed saturation per se.     

Dominant vertical scales of gravity waves in the middle atmosphere observed with the MU radar and rocketsondes

We have simultaneously observed wind motions in the altitude range of 5–90 km by means of the MU radar, rocketsondes and radiosondes. Dominant vertical scales of wind fluctuations due to gravity waves were 2–5 km in the lower stratosphere, about 5–15 km in the upper stratosphere and longer than 15 km in the mesosphere. The increase in the vertical scale with altitude is interpreted in terms of the saturation of upward propagating gravity waves. In the stratosphere, the observed vertical wavenumber spectra showed smaller amplitudes and more gradual slopes than the model values. Furthermore, the wind velocity variance in the stratosphere increases exponentially with an e-folding height of about 9 km, implying that the gravity waves were not fully saturated. On the other hand, the spectra in the upper stratosphere and mesosphere agreed fairly well with the model spectra. The variance in the mesosphere seems to cease increase of the wave amplitudes and agrees reasonably well with the model value.     

Net radiative heating in the middle atmosphere

The meridional distributions of both total solar and net radiative heating rates have been obtained between 30 and 110 km at both the solstice and equinox using Fomichev et al.'s total radiative long wave cooling data in the calculations of the net radiative heating. The contributions to the solar heating of O₃, O₂, CO₂ and H₂O have been investigated. For the ozone heating, the absorption of diffusive solar radiation from the ground and troposphere has been estimated. The 50–90 km layer is close to radiative equilibrium on a globally averaged basis. The importance of radiative cooling as an energy sink in the 90–110 km layer is apparently not less than that of the vertical eddy heat conduction. The ordered meridional circulation has been obtained under the assumption that the temperature variation, due to net radiative heating, is balanced by the adiabatic and temperature variations due to vertical air motion. The circulation model obtained is compared with other empirical models, which are reviewed. For the hemisphere and the 60–80 km layer, the two-cell circulation with the rising motion near the equator and pole from spring to autumn and above 80 km, the one-cell circulation with the sinking motion near the equator and equinox, seem to be most realistic. Also quite realistic for the period near the solstice is the same type of two-cell circulation in the 40–50 km layer and the sinking motion at low latitudes in the 50–60 km layer.     

The nonlinear mechanism of gravity wave generation by meteorological motions in the atmosphere

Using asymptotic expansions of the hydrodynamic equations in the Rossby number and the method of multiple time scales, we derive approximate expressions for the inhomogeneous “forcing” terms which describe the continuous generation of inertio-gravity waves by quasi-geostrophic motions. As a result of numerical modelling applied to the evolution of tropospheric meso- and macro-scale wave sources, the values of these forcing terms are estimated. A three-dimensional numerical simulation of wave propagation from a mesometeorological tropospheric eddy into the upper atmosphere was done to estimate the gravity wave response to the sources described. The results of the calculations show that the most part of the wave energy propagates quasi-horizontally carried by two-dimensional inertio-gravity waves. At the same time, a part of the energy is transported into the upper atmosphere by internal-gravity waves which can create regions of wave disturbance in the upper atmosphere at considerable distances from the source site. The amplitudes of these waves increase with increasing intensity and decreasing time scales of the wave sources and can reach the values observed in the upper atmosphere.     

Atmospheric gravity waves and sporadic-E

Observations of atmospheric gravity waves have identified several occasions when a wave-group propagating upwards can be associated first with a sporadic-E layer whose total electron content varies periodically, and later with a disturbance in the F-region varying with the same period. This paper reports four examples of such behaviour.     

Fractal analysis of gravity wave spectra in the middle atmosphere

Wind fluctuations in the middle atmosphere behave like colored noise processes. They have a continuum of scales without dominant features and a power spectrum density (PSD) that often decays with frequency ƒ as ƒ^−β. Spectral index β is generally obtained through least-square fit to PSD estimated by Fourier methods. Graphs of colored noise have fractal plane-filling properties depending on β. An efficient method for finding β using the fractal dimension (D), based on analysis of 1/ƒ noise in galactic X-ray luminosities by McHardy I. and Czerny B., (1987, Nature325, 696), is described. An empirical relation is found between D and β and its validity is confirmed in limiting cases. Then D is obtained from power-law dependence of a length metric L(μ) on scale μ. The method is applied to middle-atmospheric velocity data from the Poker Flat radar in Alaska. Variations of D follow those in β, from an earlier analysis by Bemraet al., (1986, Handbook for MAP20, 216), but show an offset of 0.1–0.2 even after corrections for outliers, gaps, and additive noise. Usefulness of this method for screening data as an aid to spectral analysis is examined.     

Numerical simulations of the saturated gravity wave spectra in the atmosphere

A two dimensional numerical model is used to compute the saturation of small scale gravity waves in the region near the critical level. The vertical wave number spectrum of horizontal velocity fluctuations in the unstable region (USR) where shear instability develops is found to be governed by wave-shear interaction and follows a theoretical saturation spectrum ~ω_b²/2m³. Wave-shear interaction is also found to be responsible for the observed fact that the variance of vertical velocity fluctuations is significantly lower than the level predicted by linear gravity wave theory. On the other hand, the corresponding spectrum in the stable region (SR) following a much shallower spectrum ~m⁻² is found to result from the combined effects of wave-wave interactions and eddy diffusion. The key step in our simulation is the separate parameterization of horizontal and vertical eddy diffusion coefficients instead of a constant molecular viscosity coefficient.     

Equatorial spread-F by electric fields and atmospheric gravity waves generated by thunderstorms

It is assumed that atmospheric gravity waves, resulting in travelling ionospheric disturbances (TIDs), and electric fields, generated by convective thunderstorms, have a reasonable influence on the large-scale structure of premidnight equatorial spread-F irregularities. The responsible mechanisms, viz the superposition of thunderstorm generated electric fields on the ionospheric electric fields being the determining factor for irregularity generation and the steepening of TID structures due to spatial resonance, are briefly outlined. It is recalled that convective activity is most pronounced in the intertropical convergence zone over the African and South American continents. A model based on the typical features of seasonal and geographical variation of tropical convection generating the TIDs is presented which can explain seasonal and geographical variations of premidnight equatorial spread-F occurrence.     

Optical observations of gravity waves in the auroral zone

Night-time observations of O(¹D) λ630 nm and O(¹S) λ558 nm thermospheric emissions were made at Mawson, Antarctica (67.6°S, 62.9°E) from 1982 to 1989, using a three-field photometer. Crossspectral analysis of the data was used to extract frequencies and horizontal trace velocities of periodic structures. Structures in the λ630 nm emission were characteristic of large-scale waves, and those in the λ558 nm emission were characteristic of medium-scale waves. The results showed distinct polarisation of the propagation azimuths; waves in the λ630 nm emission propagated approximately northwestward throughout the 8 yr period, whilst propagation azimuths of waves in the λ558 nm emission appeared to be solar-cycle-dependent. It is suggested that waves observed in the λ630 nm emission were of predominantly auroral electrojet origin, whilst those observed in the λ558 nm emission were of both auroral and tropospheric origin.     

Large-scale TIDs and upper atmospheric gravity waves

Excitation of the guided acoustic-gravity waves in the upper thermosphere in response to enhanced auroral electrojets is calculated in the absence of dissipation under a fully ducted condition. It is shown that a model atmosphere terminated with an isothermal half-space supports a long-period, high-speed mode, which is the interface mode guided along the half-space termination of the atmosphere. The dispersion properties and the vertical distributions of the kinetic energy density of this mode are similar to those of the so called ‘gravity pseudomode’. The excitation of this mode is computed to show how the wave generation depends on the source mechanism (the Lorentz force and joule heating) and on the source altitude. Joule heating can generate the waves with appreciable amplitudes. On the other hand, the Lorentz force prevailing in the lower region cannot excite the waves with any observable amplitudes. The waves are intensified with increasing the heat source altitude. The gross features of the calculated waves indicate that the ducted thermospheric gravity waves are capable of producing observable thermospheric waves. It is therefore suggested that further examination of the excitation of the ducted acoustic-gravity waves undergoing partial reflections due to viscosity and thermal conduction should be useful for the theory of large-scale travelling ionospheric disturbances.     

Vertical propagation characteristics of internal gravity waves around the mesopause observed by the Arecibo UHF radar

A high resolution wind observation of the mesosphere and lower thermosphere (73–95 km) was conducted with the aid of the high power UHF Doppler radar at Arecibo (18.4°N, 66.8°W). Zonal wind velocities were continuously observed during day-time hours on 1–15 August 1980. We discuss here the observed wind fluctuations with periods of 1–4 h in the light of internal gravity waves. The phase propagation associated with these fluctuations is, on average, shown to be downward, indicating an upward energy flux. A space-time spectral analysis shows that waves with vertical wavelengths shorter than 10 km disappear around the mesopause (about 85km), while those with longer vertical wavelengths exist throughout the observational height. This result is explained in terms of wave absorption at a critical layer where the mean zonal wind has a westerly shear with height. This feature is consistent with the behavior expected for internal gravity waves around the summer mesopause in order to explain general circulation models.     

Nonlinear disturbances in the ionosphere due to acoustic gravity waves

The influence of the higher harmonics of an internal gravity wave on the formation of nonlinear quasi-periodic disturbances in the F-region of the Earth's ionosphere is considered. It is shown that the Boussinesq approximation cannot be used in describing a plane nonlinear gravity wave as nonlinearities associated with the compressibility of the atmosphere have to be taken into account.     

A test of the Hines dispersion equation for atmospheric gravity waves

Simultaneous observations of an ionospheric wave by two incoherent scatter facilities and three Faraday-rotation polarimeters have provided measurements of the frequency, vertical wavelength, horizontal wavelength and direction of propagation of the wave. These measured values confirm the Hines dispersion equation for atmospheric gravity waves.     

Measurement of vertical phase and group velocities of atmospheric gravity waves by VHF radar

A systematic method of deriving from MST radar data the group velocity and phase velocity of the atmospheric wave along the radar beam direction is proposed and verified by a series of numerical simulations. We apply the method to two data sets measured by Chung-Li radar under different background wind conditions. It is found that the vertical group velocity and phase velocity are mostly in the opposite direction when the background wind is weak. The energy source of downgoing wave packets was evidently related to the instability in the upper height range (10.5–11.7 km) where strong wind shear existed. When the background wind and wind shear are stronger, the vertical group and phase velocities may propagate in the same direction. We also found from numerical simulation and data analysis that the wave packet of gravity waves following power law spectrum are short-lived. A by-product of the group velocity measurement is that the horizontal wavelength may also be deduced from a vertical radar beam measurement from the dispersion relation if it is valid.     

A quartic dispersion equation for internal gravity waves in the thermosphere

A new quartic dispersion equation in the square of the complex vertical wave number is derived by employing the ‘shallow atmosphere’ approximation and an ion drag approximation. These approximations allow the coefficients of the quartic equation to be given in terms of the corresponding cubic equation, which neglects the Coriolis force and the zonal ion drag component, but modified to take into account these neglected effects. Coupling between the extraordinary viscosity wave mode and the other three wave modes is highlighted and numerical solutions are compared for this quartic equation, an exact eighth order equation and the cubic equation. For the first time the validity of using the ‘shallow atmosphere’ approximation to describe internal gravity wave motions is demonstrated.     

Interactions between diurnal tides and gravity waves in the lower thermosphere

Recent progress on interactions between breaking gravity waves and the diurnal tide in the upper mesosphere and lower thermosphere is reviewed, mainly based on the recent results of our numerical models.     

The impact of gravity waves on nitric oxide in the lower thermosphere

Observations of nitric oxide (NO) by the Solar Mesosphere Explorer (SME) during equinox indicate a lower-thermosphere equatorial minimum which is at variance with theoretical predictions. To address this discrepancy a zonally averaged model of the thermosphere and upper mesosphere is used to evaluate the influence of a latitude variation in turbulence. Five numerical simulations were performed with different latitude structures of eddy diffusion (K_T), ranging from uniform in latitude, peaks at low, mid-, or high-latitude, to a hemispherically asymmetric distribution. A local increase in eddy diffusion causes the lower thermosphere to cool and induces a latitude pressure gradient that drives horizontal and vertical winds. The circulation, turbulent transport and temperature dependent chemistry act to change the distribution of species. Comparison of the model predictions of NO with SME data, and simulated wind and temperature structure with empirical climatology, indicates a preference for a midlatitude peak in K_T.