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.     

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).     

Inertio-gravity waves and subtropical multiple tropopauses: Vertical wavenumber spectra of wind and temperature observed by the MU radar,radiosondes and operational rawinsonde network

We have carried out continuous observations of the tropopause region over Japan for three weeks during the Baiu (early summer rain “in Japan”) season in 1991, by using a VHF Doppler radar (the MU radar), radiosondes launched at the radar site and operational rawinsondes at five meteorological stations. Based on these observations, we try to examine the hypothesis that the multiple tropopauses and the dominant inertio-gravity waves are one and the same feature, and obtain some interesting results that are not inconsistent with this hypothesis. First, vertical wavenumber spectra and hodographs analyzed from the radar wind data in the tropopause region suggest that inertio-gravity waves with vertical wavelengths of ∼ 2 km are quasi-monochromatically dominant (with 2–3 day scale variabilities of 10–20%), and are in accordance with activities of the subtropical jet stream and mesoscale cyclone-front system activities observed by the operational network. Second, striking (potential) temperature fluctuations are detected simultaneously by the radiosondes and rawinsondes, which appear as multiple tropopauses in meridional cross-section analysis. Third, vertical wavenumber spectra analyzed from the radiosonde temperature data are consistent with the radar wind spectrum, if we assume that both wind and temperature fluctuations are mainly induced by the dominant inertio-gravity waves. Finally, we confirm that the dominant interio-gravity waves can be barely detected also from routine rawinsonde (1.5-km running-mean) wind data if the amplitude is larger than 1.5 m/s. However, the monochromatic wave structures are generally quite localized in space and time.     

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.     

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.     

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.     

Source regions of medium scale travelling ionospheric disturbances observed at mid-latitudes

The characteristics of medium scale travelling ionospheric disturbances (MSTIDS) have been determined from observations carried out between 1972 and 1975 at Leicester U.K. (52°32′N, 1°8′W) using the HF Doppler technique. By reverse ray tracing through a model atmosphere an estimate of the source locations of these waves can be obtained. Auroral sources do not appear to represent an important generation mechanism for MSTIDs observed at mid-latitudes. The majority of waves originate at tropospheric altitudes at ground ranges of less than 1500 km from the observation point, and a moderate correlation is found between the occurrence frequency of MSTIDs and the intensity of the meteorological jet stream.     

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.     

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.     

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.     

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.     

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.     

Wave characteristics in the troposphere and stratosphere over the Indian Tropics during the DYANA period

One of the important scientific objectives of the international DYANA campaign was to obtain the characteristics of planetary scale waves in the low-latitude middle atmosphere. India participated in this campaign by way of launching several rockets and high-altitude balloons from a number of locations to determine the vertical structure of different wave modes present during January–March 1990. Rocket launchings were conducted from two stations, namely Thumba (8.5°N, 77.0°E) with M-100 rockets and Balasore (21.5°N, 87.0°E) with RH-200 rockets, while balloons were launched from three stations, i.e. Trivandrum near Thumba, Minicoy (8.2°N, 73.0° E) and Port Blair (11.7°N, 92.7°E). In addition, there were balloon flights from Hyderabad (17.3°N, 78.3°E) and Bhubaneshwar (20.2°N, 85.5°E). The results of the synoptic scale wave activity as obtained from various data sources are given here.Three prominent peaks with wave periods near 6–8 days (short periods), 10–12 days (medium periods) and 30–45 days (long periods) are found to occur at all the stations. The medium- and long-period waves appear to be forced Rossby modes penetrating from midlatitudes while short period waves all have characteristics matching those of mixed Rossby-gravity waves. A very interesting result is the presence of long-period oscillations in the upper stratosphere and mesosphere, with very large amplitude, contrary to earlier observations.     

Winds in the ionosphere—A review

Winds in the upper atmosphere, and their effect on the ionosphere, are reviewed with an emphasis on information useful to ionospheric studies. The winds are driven by pressure gradients from solar and auroral heating, with some forcing by tidal energy from below. Simple calculations which balance the pressure gradient by ion drag and Coriolis forces are generally unreliable, so large-scale numerical models of the coupled atmosphere and ionosphere are required. The accuracy of these global models is limited by uncertainties in the energy inputs at high latitudes and at the lower boundary (about 90 km). The best current wind data come from incoherent scatter radar or airglow installations, at a few sites and for only a few nights per month. Satellite data are also available for several years, and results to 1989 are incorporated in the global HWM90 model. This seems acceptable for determining mean winds at night, less good during the day, and least good in the southern hemisphere where few data were available. Plots are given to show the mean winds at different latitudes and longitudes, for use in ionospheric calculations.Meridional winds alter the height of the mid-latitude F layer, causing large changes in the effective loss rate. This is the major cause of observed seasonal changes, of differences between the hemispheres, and of changes at different longitudes. An increased knowledge of the winds is essential for further progress in F region studies. Ionospheric data provide the most promising route, using routinely scaled parameters. The simplest calculations compare observed peak heights, obtained from M (3000)F2, with the value h_o predicted by simplified “servo” equations. Errors occurring for some hours after sunrise can be overcome using model results to define h_o this allows rapid and accurate wind calculations at dip latitudes of 23–62°. Winds can also be obtained from full model calculations, designed to match observed values of peak height or density.     

Lightning transient fields in the atmosphere—low ionosphere

The complexity of the electric properties of the atmosphere, which influences the excitation and propagation of electromagnetic signals generated by lightning discharges, gives rise to a diversity of the typical signal wave forms and amplitudes in the various space-time domains. This causes difficulties and controversies in the interpretation of the experimental data. In geophysical problems of such a kind, considerations accounting for a broadband spectrum are particularly important.In the present paper, lightning induced ULF-VLF fields in the daytime inhomogeneous atmosphere and D-region of the ionosphere above the thundercloud are analyzed for a standard model of the vertical return stroke. The developed analytical approach makes it possible to unite the canonical model of the electromagnetic radiation into a free-half-space, the discharge (ELF-VLF spectrum) and ‘post-discharge’ (ULF spectrum) low-frequency models and to clarify the temporal scales in the mechanism of lightning coupling with the atmosphere and low ionosphere with respect to the local relaxation time, discharge characteristic time scales and observer location.     

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.     

Equatorial spread-F: recent results and outstanding problems

Recent results and outstanding problems in the field of equatorial spread-F are reviewed. The discussion is organized about four distinct wavelength regimes: long (≳ 20 km). intermediate (20 km–100 m). transitional (100 m–10 m) and short (≲ 10 m). The intermediate waves are best understood, although the enhanced turbulent power near 1 km wavelength needs explanation, as does the saturation mechanism itself. The role of shear flow and irregularity seeding by ‘geophysical noise’ in the neutral atmosphere form important future research topics at the longest scales. Identification of drift waves in the transitional wavelength range has been a major new step in explaining the full spread-F phenomenon. This drift wave turbulence in the transition regime will be actively studied in the near future, particularly with regard to its role in determining the saturated amplitude of the intermediate waves, as well as in the anomalous diffusion of plasma at high altitudes. Although waves as short as 11 cm have been unambiguously detected and linear theories exist, the origin and amplitude spectra of these short wavelength waves inside topside plumes remain in some doubt and should also be examined in more detail.     

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.     

Role of Infragravity Energy in Bar Formation in a Strong‐Wind Bay: Observations from Seaford Beach,Port Phillip Bay,Australia

Measurements of the surf zone wave field and morphology were obtained from a multi‐barred beach in a fetch‐limited, strong‐wind bay (Seaford, southeastern Australia) during both low‐ and high‐energy conditions. Analysis of the infragravity energy present during high‐energy events (onshore winds >7 ms^?1) revealed that it was broad‐banded, consisting of a mixture of standing and progressive motions and displaying daily variations in standing wave length scales. Infragravity standing waves were therefore not considered significant to the formation and migration of bars at Seaford during this study, with bar behaviour during high energy events potentially attributable to either breaking wave‐bed return flow and/or self‐organisational mechanisms.