Gravity waves from O2 nightglow during the AIDA '89 campaign III: effects of gravity wave saturation

The O₂ atmospheric (0–1) night airglow emitted within the gravity wave saturation region at ∼90–100 km can serve as a means of studying the wave activity. In this analysis, the atmospheric motions were described by a mean spectral model and an algorithm was developed to infer the wave kinetic energy density and momentum flux from variations in O₂ (0–1) airglow emission rate and rotational temperature. The method was applied to eight nights of data collected by MORTI, a mesopause oxygen rotational temperature imager, during the AIDA campaign of 1989 in Puerto Rico (18°N, 67°W). The observed r.m.s. fractional fluctuations of airglow emission rate and rotational temperature were of the order of ∼0.07–0.15 and ∼0.02–0.04, respectively, and the characteristic vertical wavelengths were estimated at ∼10 2 -20 km. The inferred r.m.s. horizontal velocities and velocity variances were found to be ∼12–25 m/s and ∼150–600 m²/s², with the majority of the horizontal velocity and its variance associated with low-frequency, large-scale wave motions. The estimated momentum fluxes, mainly contributed by high-frequency, small-scale waves, were ∼2–10 m²/s². These results are in good agreement with those obtained from other measurements using different observational methods at low and mid-latitudes.     

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).     

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.     

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.     

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.     

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.     

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.     

Interference of tidal and gravity waves in the ionosphere and an associated sporadic E-layer

Observations made on 10 July 1987 with the EISCAT UHF radar are presented. The F-region measurements of both electron density and field-aligned ion velocity show that an upward propagating gravity wave with a period of about 1 h is present. The origin of the gravity wave is probably auroral. The E-region ion velocities show a tidal wave and both upward and downward propagating gravity waves. The gravity waves have three dominant periods with a possible harmonic relationship and similar vertical wavelengths. These waves are either reflected at a single reflection level, ducted between two levels, or they are generated in a non-linear interaction between gravity and tidal waves. The E-region electron density is dominated by particle precipitation. After a short burst of more intense precipitation, a sporadic E-layer forms at 105km and then disappears 40min later. Within this time, the layer rises and falls by a few kilometres, following closely the motion of a convergent null in the velocity profile. We suggest that the formation and destruction of this layer is controlled by both the precipitation, which indirectly provides a source of metal ions through charge exchange, and the superposition of gravity waves and the tidal wave.     

Gravity wave activity in the upper mesosphere over Urbana,Illinois: lidar observations and analysis of gravity wave propagation models

We analyze 375 h of Na Wind/Temperature lidar measurements of the mesopause region (≈ 80–105 km) Na density and temperature profiles on 57 nights distributed over 2 yr at Urbana, Illinois. These observations yield a high-resolution seasonal data set of gravity wave activity in the upper mesosphere. From this data, we present measurements of the Brunt-Väisälä period, the relative atmospheric density perturbations and their spectra, and the parameters of 143 quasi-monochromatic gravity waves. The direct measurement of the Brunt-Väisälä period allows accurate calculation of the horizontal velocity perturbations and vertical displacement perturbations from the density measurements. The horizontal velocity and vertical displacement vertical wave number spectrum magnitudes and indices show considerable seasonal and nightly variability. The gravity wave amplitudes, wavelengths, and observed periods exhibit systematic relationships similar to those found in previous studies, and are consistent with the MU radar measurements of intrinsic gravity wave parameters. Here, we present a detailed analysis of the observations in terms of Diffusive-Filtering Theory models of gravity wave propagation. The magnitudes of the vertical wave number spectrum, the form of the joint vertical wave number and frequency spectrum, and the systematic relationships between the monochromatic gravity wave parameters are consistent with the Diffusive-Filtering model. We compare these results with a variety of radar, lidar, and airglow observations from other sites. This observational study suggests that the complex nonlinear interactions of the gravity wave field may be modeled successfully as a diffusive damping process, where the effective diffusivity is a function of the total wave variance.     

Transmission of large-scale TIDs in the ionospheric F2-region

Large-scale travelling ionospheric disturbances (1.s. TIDs) have been investigated in order to derive the horizontal velocity dispersion by using f₀F2 data from four ionospheric observatories in Japan. It was found that the horizontal phase trace velocity lies between 300 and 1000ms⁻¹ with periods in the range 50 to 150 min. There is evidence that the derived velocity generally increases with increase of wave period. This is consistent with the dispersion predicted by the theory of the internal gravity waves. The azimuthal angles are distributed in ±35° sectors centered around 197° (measured clockwise from north), indicating that 1.s. TIDs may be obtainable when they are excited along the auroral zone of the same sector in longitude as that of the observatories. The average propagation direction shifts by 17° from south towards west. This clockwise shift is consistent with the rotation caused by the Coriolis effect. This means that the Coriolis effect cannot be ignored for the wave propagation of 1.s. TIDs. In addition to the positive correlation between TID speed and geomagnetic activity, the direction of wave propagation is found to be correlated with polar magnetic activity. The propagation direction is mostly southward during the period of large polar magnetic disturbances, while during the period of low magnetic activity the direction scatters considerably.     

Weak nonlinear theory of the ionospheric response to atmospheric gravity waves in the F-region

The nonlinear ionospheric response to atmospheric gravity waves is studied in an approximate fashion using a new approach. The concept of nonlinear travelling ionospheric disturbances (TIDs) is outlined, and the nonlinear behaviour of atmospheric gravity waves is calculated. A principal result is that harmonics are generated which cause the wave velocity perturbation to deform. The ionospheric response is investigated by solving the continuity equation for ionization in the F-region. The distortion of the TIDs waveform produced by the nonlinear interactions is depicted. The nonlinear TIDs depart seriously from a cosinusoidal wave described by previous linear TID theory. The distorted TIDs appear as ‘sharp peak’ and ‘sawtooth’ waveform shapes. The ‘peaks’ can be upward or downward, and the ‘sawteeth’ forward or backward, depending on the wave parameters. The nonlinearly distorted TIDs show a good agreement with various observed ionospheric irregularities produced by atmospheric gravity waves.     

Comprehensive meteorological modelling of the middle atmosphere: a tutorial review

This paper reviews the current state of comprehensive, three-dimensional, time-dependent modelling of the circulation in the middle and upper atmosphere from a meteorologist's perspective. The paper begins with a consideration of the various components of a comprehensive model (or general circulation model, GCM), including treatments of processes that can be explicitly resolved and those that occur on scales too small to resolve (and that must be parameterized). The typical performance of GCMs in simulating the tropospheric climate is discussed. Then some important background on current ideas concerning the general circulation of the stratosphere and mesosphere is presented. In particular, the transformed-Eulerian mean flow formalism, the role of vertically-propagating internal gravity waves in driving the large-scale circulation, and the notion of a stratospheric surf zone are all briefly reviewed. Using this background as a guide, some middle atmospheric GCM results are discussed, with a focus on simulations made recently with the GFDL ‘SKYHI’ troposphere-stratosphere-mesosphere GCM. The presentation attempts to emphasize the interaction between theory and comprehensive modelling. Many theoretical notions cannot be confirmed in detail from observations of the real atmosphere due to the various limitations in the observational methods, but can be very completely examined in GCMs in which every atmospheric variable is known perfectly (within the limits of the numerical methods). It will be shown that our understanding of both the role of gravity waves in the general circulation and the nature of the stratospheric surf zone has benefited from analysis of GCM results.From the point of view of the upper atmosphere, one of the most interesting aspects of GCMs is their ability to generate a self-consistent field of upward-propagating gravity waves. This paper concludes with a discussion of the gravity wave field in the middle atmosphere of GCMs. Comparisons of the explicitly-resolved gravity wave field in the SKYHI model with observations are quite encouraging, and it seems that the model is capable of producing a gravity wave field with many realistic features. However, the simulated horizontal spectrum of the eddy momentum fluxes associated with the waves is quite shallow, suggesting that much of the spectrum that is important for maintaining the mean circulation is not explicitly resolvable in current GCMs. A brief discussion of current efforts at parameterizing the mean flow effects of the unresolvable gravity waves is presented.     

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.     

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.     

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.     

Angle-of-arrival oscillations in the mesosphere as seen by medium frequency (MF) radar

The Saskatoon MF radar operates continuously in the spaced antenna mode with 5 min resolution, primarily for horizontal wind analysis at mesospheric heights. Mean Doppler frequency and antenna-pair phase difference are available as byproducts. Clear oscillations are sometimes seen in the latter. Spectral analysis shows that these also occur in the Doppler and extend over a range of heights. The two cases shown are almost certainly perturbations in specular reflecting layers moving with horizontal velocity close to that of the wind. Downward phase propagation is apparent, and when the oscillations are present, the wind appears to be decelerating. The tentative explanation of a breaking gravity wave decelerating the mean flow is put forward, although the relations between frequency, and horizontal and vertical wavelengths, contradict linear gravity wave theory.     

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.     

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 wave guide model of lightning currents

In this paper, a lightning channel is simulated by a vertical wire of finite length and of moderate electric conductivity. At low frequencies, such a wire behaves like a resonant wave guide cavity in which only discrete resonant wave modes can be generated. The theory of resonant waves in a wire of finite diameter is outlined and applied to the return stroke with electric contact to the earth and to intracloud K-strokes without electric contact to the earth. Two types of current wave forms exist: aperiodic waves of the Bruce-Golde type and damped oscillations. The configurations of the electric charge density and the electric current in the wire are presented for the various wave modes as functions of height and time. From the observations of lightning current and of sferic wave forms, it is apparent that the first mode dominates, and that both types of wave forms can be identified. From these wave forms, the channel parameters-length and diameter can be derived. For the higher order modes, the resonance model loses its validity and freely propagating waves are expected during the whole lightning flash. These waves contribute to the observed continuous spectrum. The skin effect becomes important increasing the effective resistance of the wire with frequency. Since these waves interfere destructively, they do not contribute significantly to an effective charge transport.