Simulation of gravity wave effects under solstice conditions using a 3-D circulation model of the middle atmosphere

Vertically propagating gravity waves can transport momentum and energy from the troposphere up to the mesosphere and thus modify the circulation of the middle atmosphere. The effects of regional gravity wave sources, together with temporal changes of gravity wave activity, are studied under solstice conditions in a 3-D circulation model using a simplified parameterization scheme for the gravity momentum deposition. In this way we can reproduce the reversal of the mean zonal wind with height and very low temperatures at the summer mesopause region. Using a stochastic forcing by taking the gravity wave parameters at random, characteristic oscillations are found with periods in the planetary scale range (2, 4 and 5 days) and in the tidal range (1 day, 16 h and 12 h).     

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.     

A simple model of gravity-wave momentum and energy fluxes transferred through the middle atmosphere to the upper atmosphere

Vertical fluxes of momentum and energy through the middle atmosphere are calculated by using a simple semi-empirical model of quasi-monochromatic internal gravity waves with dominant vertical wavenumbers. In this model those dominant gravity waves are assumed to saturate and break at each observational altitude by an effective critical-layer mechanism. The dominant value of the vertical wave-number is expressed by an exponential function of altitude, decreasing upward with a scale height of 34 km. This expression gives the momentum and energy flux densities decreasing upward with scale heights of 12 and 18 km, respectively, and typical values at 100 km altitude are estimated as 4 × 10⁻⁵ Pa and 4 × 10⁻³ W/m². A heat flux induced by wavebreaking turbulence also has an order of magnitude similar to that of the wave energy flux. Variabilities around these values and comparisons with other momentum and heat inputs to the upper atmosphere are only briefly discussed.     

Variations of the gravity wave characteristics with height,season and latitude revealed by comparative observations

This paper reviews some recent observations of gravity wave characteristics in the middle atmosphere, revealed by co-ordinated observations with the MU radar in Shigaraki (35°N, 136°E) and nearby rocketsonde experiments at Uchinoura (31°N, 131°E). We further summarize the results of comparative studies on the latitudinal variations of the gravity wave activity, which were detected by additionally employing data obtained with MF radars at Adelaide (35°S, 139°E) and Saskatoon (52, 107W) and lidar observations at Haute Provence (44, 6E).The seasonal variation of gravity wave activity detected with the MU radar in the lower stratosphere showed a clear annual variation with a maximum in winter, and coincided with that for the jet-stream intensity, indicating a close relation between the excitation of gravity waves and jet-stream activity at middle latitudes. The long-period (2–21 h) gravity waves seemed to be excited near the ground, presumably due to the interaction of flow with topography, and the short-period (5 min 2 h) components had the largest kinetic energy around the peak of jet-stream.We found an increase with height in the vertical scales of dominant gravity waves, which can be explained in terms of a saturation of upward propagating gravity waves. The values of the horizontal wind velocity variance generally increased in the stratosphere and lower mesosphere, but they became fairly constant above about 65 km due to the wave saturation, resulting in the active production of turbulent layers.Although the gravity wave energy showed an annual variation in the lower atmosphere, it exhibited a semiannual variation in the mesosphere, with a large peak in summer and a minor enhancement in winter. Lidar observations reasonably interpolated the seasonal variations in the intermediate height regions.The gravity wave energy in the mesosphere, with periods less than about 2 h, was consistently larger in summer than in winter at all the stations, i.e. at 35N, 44N,52 N and 35 S. However, the values were generally larger at 35 N than at 52 N. which was found from a comparison of l-yr observations at Shigaraki and Saskatoon. Furthermore, a comparison between Shigaraki and Adelaide, located at the conjugate points relative to the equator, revealed that the gravity-wave energy in the mesosphere was found to be fairly similar, when we compared the values in summer/winter in each hemisphere.     

A nonlinear simulation of the thermal diurnal tide

A simplified middle atmosphere general circulation model is used to investigate the nonlinear behavior of the thermal diurnal tidal waves. In the model, only a westward moving diurnal tide generated by heating with zonal wavenumber 1 is considered. The tidal wave propagation is simulated by a full nonlinear calculation with a convective adjustment scheme and a Richardson number dependent vertical eddy diffusion.The numerical results show that the growth of the diurnal tide due to the density stratification is effectively suppressed and a relatively constant amplitude distribution with height is realized by the convective adjustment in the lower thermosphere. It is also shown that mean zonal winds and mean meridional circulations are induced by the diurnal tidal waves in the region where the tidal waves are breaking by convective instability, in accordance with the wave-mean flow interaction theorem.     

Stratospheric and tropospheric wave measurements near the Andes mountains

Experimental results and interpretation of temperature, pressure and wind velocity measurements, performed with an instrumented balloon, are presented. The balloon, an open-type stratospheric one was launched from Mendoza (Argentina), near the Andes mountains. The data analysis suggests the presence of a large amplitude quasi-inertial gravity wave, with intrinsic period close to 0.5 days, and vertical wavelength of around 1.7 km just below the tropopause. The possible orographic origin of this wave is discussed. A Fourier analysis confirms the existence of this mode, simultaneously in the temperature and in the wind velocity components. A hodograph of the zonal and meridional wind components shows the expected counterclockwise sense of rotation of the horizontal velocity with increasing altitude, corresponding to a long period gravity wave, in the southern hemisphere.It is found that the vertical wind velocity variations measured by the anemometer, are mainly due to buoyancy force variations induced by the wave on the open stratospheric balloon. The vertical profile obtained by the anemometer is anticorrelated with the rate of ascent or descent of the gondola. As a consequence, the wave induced velocity is very difficult to obtain using these balloons, contrary to the case of radiosonde balloon data. The differences in the response of open stratospheric and radiosonde-type balloons to the presence of internal gravity waves may be explained by their different design and material characteristics.     

Gravity wave saturation and eddy diffusion in the middle atmosphere

A discussion is given of gravity wave saturation and its relation to eddy diffusion in the middle atmosphere. Attention is focused on the saturation process and some of its observable manifestations. It does not serve as a review of all related work. Although a theoretical point of view is taken, the emphasis is on which wave parameters need be measured to predict quantitatively the influence of gravity waves on eddy transport. The following considerations are stressed: the variation of spectra with observation time T; that eddy diffusivities are determined by velocity spectra; the anisotropic nature of diffusivity; a unified approach to saturation; an attempt to make eddy diffusivity more precise; the relationship between eddy diffusivity and wave dissipation.The subjects of ‘wave drag’ (momentum flux deposition) and heat flux need only be treated briefly, because they are related to eddy diffusivity in simple ways. Consideration is also given to two different theoretical mechanisms of wave saturation—wave induced convective instability and strong nonlinear wave interactions. The saturation theory is then used to predict a globally averaged height profile of vertical diffusivity in the middle atmosphere. This calculation shows that gravity waves are a major contributor to eddy diffusion from heights of 40–110 km, and that they are significant down to 20 km. A more detailed calculation of wave induced eddy diffusion, including latitudinal and seasonal variations, can be made if wave velocity spectra become available. The paper closes with recommendations for future research.     

The non-linear interaction of a gravity wave with the vortical modes

The wave-wave interaction theory has been used successfully in describing one class of weakly non-linear wave phenomena. The application of this theory to the atmosphere shows the possibilities of energy and momentum transfer among three interacting gravity waves, as well as from the gravity wave to the other modes of motion. It has been found that the non-resonant interaction of a gravity wave with two vortical modes can proceed at a reasonably rapid rate. With the gravity wave viewed as the primary wave and the two vortical modes as the secondary waves, the interaction equation can be linearized and solved. The resulting analytic formula gives the growth rate of the interaction. In the absence of the Earth's rotation, the growth is limited to a threshold effect. The theory shows that whenever the horizontal air parcel velocity of a gravity wave exceeds a factor of √2 times the horizontal trace velocity of the wave, energy and momentum transfer from the gravity wave to the vortical modes can proceed. The rotation of the Earth will blur this threshold effect by making the interaction more likely to occur. Thus, through this mechanism, a gravity wave can transfer its energy and momentum to the horizontal velocity field in the vortical mode. In this sense, the small scale vortical motions would serve as the sink of both energy and momentum of a propagating gravity wave. When scales of vortical modes reach sufficiently small values, dissipation through viscosity becomes important. At this scale and smaller, the vortical modes are damped out quickly and its energy spectrum must exhibit a sharp decay.     

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.     

Dynamical coupling processes between the middle atmosphere and lower ionosphere

A variety of dynamical processes are important in coupling motions within the middle atmosphere and lower ionosphere. These processes can generally be classified as either advective, wave-like or diffusive. Within the middle atmosphere, wave-like processes, and especially gravity waves, are of crucial importance. Turbulent diffusion and advection probably play lesser, but not insignificant, roles. However, whether these same concepts apply to coupling for regions outside the middle atmosphere—and especially between the upper middle atmosphere and the lower ionosphere—is not clear. In this paper the current knowledge about coupling processes between these important regions is reviewed. We discuss coupling processes in the middle atmosphere with the objective of examining how well these concepts may be extended to the topic of middle atmosphere to ionosphere coupling. Different approaches to understanding, and the different experimental procedures used by workers studying the middle atmosphere and ionosphere, also make comparisons difficult. The importance of the measurement of common parameters is highlighted, and the need for coordinated campaigns to examine the interactions between the regions is emphasized.     

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.     

Large scale coherence of the mesospheric and upper stratospheric temperature fluctuations

A large set of temperature profiles has been obtained in the upper stratosphere and the mesosphere over Europe during the MAP/WINE compaign by the use of different techniques: datasondes and falling spheres launched by metrockets, ground-based OH spectrometers and a Rayleigh lidar. These data have been used to study the large scale variability of the middle atmosphere during the winter 1983–1984. The temperature variations with periods longer than 25 days are clearly related to the succession of minor upper stratospheric warmings observed during this winter. The variations in the period range 10–20 days are at least partially due to westward propagating Rossby waves, of which one mode, with a 12.5 days period, is tentatively identified as the second symmetric mode of the wave number 2.     

A numerical model for gravity wave dissipation in the thermosphere

Two simplified models of internal gravity wave dissipation due to viscosity, thermal conduction and ion-drag, in a multilayered, isothermal thermosphere are developed. Each of these models uses the WKB approximation, ray theory and the time-averaged equation of energy conservation, but whereas one of the models (A) employs all of the gravity wave equations appropriate to a dissipative atmosphere, the other (B) does not. Results derived from these models for one particular wave are compared to each other and also to some previously published results of Klostermeyer, which employed a full-wave, model. A breakdown of the WKB approximation in the lower, non-isothermal thermosphere leads to models A and B underestimating the total dissipation there. In the middle thermosphere model A estimates the dissipation reasonably well, while model B grossly overestimates the dissipation. In the upper thermosphere model A underestimates the total upward energy flux, probably as a result of the neglect of coupling into the dissipative waves at these levels, while no energy remains in model B. Results from model A show that when dissipation due to viscosity and thermal conduction are included correctly and simultaneously, the dissipation due to viscosity can exceed that due to thermal conduction by a factor of three. It is argued that ray theory may either overestimate or underestimate the energy flux reaching the upper boundary of a thermospheric model depending on both its height and the particular thermospheric model used.     

A spectral approach for studying middle and upper atmospheric phenomena

We report on the application of a newly developed spectral code to the study of the middle/upper atmosphere. The spectral approach offers conceptual and practical convenience for analyzing the generation and interaction of different components of atmospheric activity through the decomposition of the dynamical fields into components with different zonal wave numbers (m). As examples and tests, we obtain solutions for the m = 0 (the mean circulation) and 1 (the diurnal tides) components separately (no mutual interactions), as well as the m = 1 component under the influence of the mean circulation. By simulating gravity wave effects with Rayleigh friction and eddy diffusion peaking near 90 km altitude, the mean circulation thus generated can reproduce the observed mesospheric temperature anomaly under solstice conditions. The computed diurnal tides are in good agreement with results obtained earlier by other authors. The large temperature gradient (associated with the m = 0 component) set up by the mesospheric temperature anomaly under solstice conditions creates a condition favorable for the development of baroclinic instabilities in the mesopause layer, especially near the summer pole. In our time dependent calculation, waves with approximately 4-day period are generated in the m = 1 component, superimposing with the 1-day period tides.     

Permanent monitoring of the upper mesosphere and lower thermosphere wind fields (prevailing and semidiurnal tidal components) obtained from LF D1 measurements in 1991 at the Collm Geophysical Observatory

The wind field of the upper mesosphere and lower thermosphere region (85–105 km) over Central Europe (52°N, 15°E) has been continually and reliably recorded by regular daily D1 radio wind measurements in the LF range (177, 225 and 270 kHz) using commercial radio transmitters. These measurements show the prevailing winds, the tidal wind components and the effects of internal gravity waves, as well as the seasonal and irregular variations of these parameters. The height of the wind measurements is determined by measuring the travel time differences between corresponding modulation bursts in the sky wave and in the ground wave. Using a quasi-online calculation procedure, the results are available immediately. Therefore they are useful for monitoring the upper atmospheric circulation with regard to upper atmosphere meteorology in the future. Vertical profiles of the wind field parameters can be derived with the aid of the combined wind and height measurements. Height-time cross-sections of the monthly mean prevailing winds and semidiurnal wind components have been calculated almost continuously for the last 10 years. The present paper deals with recent results for the year 1991.     

Wind and temperature effects on F-region medium-scale gravity waves estimated using a multi-layer atmospheric model

Diurnal variations in the propagation direction of atmospheric gravity waves, and the travelling ionospheric disturbances to which they give rise, have been observed in many experimental observations and several modelling studies have demonstrated that this is primarily due to the corresponding diurnal rotation in the direction of the thermospheric wind. Other variations have been attributed to seasonal or other effects, but the effects of variations in the thermospheric temperature have not previously been analysed in detail. We present results from a study of the propagation of gravity waves through a layered atmosphere in which the thermospheric wind and temperature are derived from a three-dimensional time-dependent model. The analysis has been carried out for a range of wave speeds and periods, and for a range of times, seasons and propagation azimuths. Results suggest that a significant diurnal variation in the transmission coefficient for waves propagating through the thermosphere exists with seasonally dependent maxima. Transmission increases for increasing wave period up to about 50 min, after which it remains approximately constant. Maximum transmission occurs for wave phase speeds around 200–250 m/s and falls to zero for speeds less than about 100 m/s. An exception to this rule occurs for waves with periods less than 40 min and speeds less than 50 m/s for which significant transmission appears to be theoretically possible.     

Summertime stratospheric wind measurements above the South Pole

Observations of the mean wind flow and wave motions in the stratosphere at the South Pole are presented. The atmospheric motions are determined from the tracking of a high altitude, zero-pressure balloon launched from Amundsen-Scott Station during the austral summer of 1985–1986. The balloon position was precisely monitored by an optical theodolite for a large portion of the flight so that small scale motions could be resolved. The mean flow above the pole was approximately 3ms⁻¹. Atmospheric motions characteristic of internal gravity waves were observed with an intrinsic period of approximately 4.5 h and vertical and horizontal wavelengths of approximately 2.5km and 125km, respectively. The horizontal perturbation velocity of the observed waves was large compared to the mean horizontal flow velocity. The implication is that wave motions play a dominant role in the transport of stratospheric constituents in regions where the mean winds are light, such as over the South Pole during austral summer.     

Field Measurements of Wave Characteristics on a Near‐Horizontal Shore Platform,Mahia Peninsula,North Island,New Zealand

Waves are an important process responsible for the initiation and subsequent development of intertidal shore platforms. However, few field studies to date have described wave processes on shore platforms. A field experiment was conducted using an across‐shore array of wave gauges, including a directional sensor, on a near‐horizontal platform at Mahia Peninsula, North Island, New Zealand. Results show that the platform is very efficient in filtering wave energy at gravity wave frequencies (>0.05 Hz), with 40–80% reduction in wave height measured across the 140 m wide platform. By contrast, infragravity waves are present on the platform and increase in magnitude towards the cliff toe. Directional wave analysis indicates that wave reflection is mainly restricted to infragravity wave frequencies, demonstrating the differences in gravity and infragravity wave behaviour on the platform studied. Results indicate that, under fair weather conditions, the role of waves as an agent of cliff toe erosion is likely to be limited at present, although they are probably important for removing sediments accumulated at the cliff toe. The observed increase in infragravity wave energy towards the cliff toe implies that these long‐period waves may be important geomorphic agents on shore platforms.     

Some aspects of Doppler radar measurements of the mean and fluctuating components of the wind field in the upper middle atmosphere

The basic assumptions made when a Doppler radar is used to measure the mean and fluctuating components of the wind field in the middle atmosphere with various beam configurations are examined. Particular reference is made to the measurement of the various components of the Reynolds stress tensor associated with short period internal gravity waves. It is shown that it is not generally possible to measure the upward flux of horizontal momentum with the conventional Doppler radar beam configuration in the upper middle atmosphere and that an optimum beam configuration is that in which beams are directed at +θ,0 and − θ to the zenith in both the zonal and meridional planes. This allows five of the six components of the Reynolds stress tensor (all those except the horizontal transport of momentum) to be obtained directly from the mean square radial velocities. In addition, the mean wind components and, in principle, the horizontal divergence and stretching deformations may be obtained. The power spectrum of the horizontal velocity may also be calculated using only the assumption that the statistics of the motions are horizontally homogeneous.     

Contributions of gravity waves to the momentum,heat and turbulent energy budget of the upper mesosphere and lower thermosphere

The role of gravity waves for the momentum and heat budget of the atmosphere between approximately 70 and 110 km height is considered. Parameterization schemes for vertical gravity wave diffusivity, generalized Rayleigh friction, viscous force, heat conduction and kinetic energy dissipation are reviewed. Eddy diffusion parameterization and its relation to the gravity wave approach is also discussed and it is shown that principal similarities exist in both concepts, especially when irregular (stochastic) contributions to the perturbations are modeled. Special attention is paid to the dissipation of perturbation kinetic energy and its contribution to the heat budget of the mesopause region. It is concluded that the amount of energy which can be attributed to the part of the gravity wave spectrum contributing to generalized Rayleigh friction above the mesopause is of the order of 10% of the total perturbation energy.