There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

[1] Atmospheric gravity waves have been a subject of intense research activity in recent years because of their myriad effects and their major contributions to atmospheric circulation, structure, and variability. Apart from occasionally strong lower-atmospheric effects, the major wave influences occur in the middle atmosphere, between ∼ 10 and 110 km altitudes because of decreasing density and increasing wave amplitudes with altitude. Theoretical, numerical, and observational studies have advanced our understanding of gravity waves on many fronts since the review by Fritts [1984a]; the present review will focus on these more recent contributions. Progress includes a better appreciation of gravity wave sources and characteristics, the evolution of the gravity wave spectrum with altitude and with variations of wind and stability, the character and implications of observed climatologies, and the wave interaction and instability processes that constrain wave amplitudes and spectral shape. Recent studies have also expanded dramatically our understanding of gravity wave influences on the large-scale circulation and the thermal and constituent structures of the middle atmosphere. These advances have led to a number of parameterizations of gravity wave effects which are enabling ever more realistic descriptions of gravity wave forcing in large-scale models. There remain, nevertheless, a number of areas in which further progress is needed in refining our understanding of and our ability to describe and predict gravity wave influences in the middle atmosphere. Our view of these unknowns and needs is also offered.

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Gravity wave dynamics and effects in the middle atmosphere

The influence of breaking gravity waves on the dynamics and chemical composition of the 60- to 110-km region has been investigated with a two-dimensional dynamical/chemical model that includes a parameterization of gravity wave drag and diffusion. The momentum deposited by breaking waves at mesospheric altitudes reverses the zonal winds, drives a strong mean meridional circulation, and produces a very cold summer and warm winter mesopause, in general agreement with observations. The seasonal variations of the computed eddy diffusion coefficient are consistent with the behavior of mesospheric turbulence inferred from MST radar echoes. In particular, it is found that eddy diffusion is strong in summer and winter but much weaker at the equinoxes and that this seasonal behavior has important consequences for the distribution of chemical species. Comparison between computed atomic oxygen and ozone, and the abundances of these constituents inferred from the 557.7-nm and 1.27-μm airglow emissions, reveals excellent agreement. The consistency between model results and these diverse types of observations lends strong support to the hypothesis that gravity waves play a very important role in determining the zonally averaged structure of the mesosphere and lower thermosphere.

The effect of breaking gravity waves on the dynamics and chemical composition of the mesosphere and lower thermosphere

Systematic westerly biases in the northern hemisphere wintertime flow of the Meteorological Office 15-layer operational model and 11-layer general circulation model are described. Evidence that the failure to parametrize subgrid-scale orographic gravity wave drag may account for such biases is presented. This evidence is taken from aircraft studies, surface pressure drag measurements, and studies of the zonally averaged momentum budget. A parametrization scheme is described in which the surface stress is proportional to the near-surface wind speed and static stability, and to the variance of subgrid-scale orography. The stress is absorbed in the vertical by considering the influence of such gravity wave activity on static stability and vertical wind shear. A Richardson-number-dependent wave breaking formulation is devised, and the vertical stress profile determined by a saturation hypothesis whereby the breaking waves are maintained at marginal stability. It is shown that wave breaking preferentially occurs in the boundary layer and in the lower stratosphere.

Results from a simple zonally symmetric model show how the adjustment to thermal wind balance with a wave drag in the stratosphere, warms polar regions by adiabatic descent, and decelerates the mean westerlies in the troposphere.

The influence of the parametrization scheme on integrations of the 11-layer model is described, and found to be generally beneficial.

In a discussion of the reasons why this problem has only recently emerged, it is suggested that the satisfactory northern hemisphere winter circulations of previous, coarser general circulation models were due to a compensation implied by underestimating both the surface drag, and the horizontal flux of momentum by explicitly resolved large-scale eddies.

Alleviation of a systematic westerly bias in general circulation and numerical weather prediction models through an orographic gravity wave drag parametrization

This paper provides a review of recent advances in our understanding of gravity wave saturation in the middle atmosphere. A brief discussion of those studies leading to the identification of gravity wave effects and their role in middle atmosphere dynamics is presented first. This is followed by a simple development of the linear saturation theory to illustrate the principal effects. Recent extensions to the linear saturation theory, including quasi-linear, nonlinear, and transient effects, are then described. Those studies addressing the role of gravity wave saturation in the mean circulation of the middle atmosphere are also discussed. Finally, observations of gravity wave motions, distribution, and variability and those measurements specifically addressing gravity wave saturation are reviewed.

Gravity wave saturation in the middle atmosphere: A review of theory and observations

A preliminary long-term comparison of MF SA and meteor wind determinations with collocated radar systems

In order to test whether the chosen Doppler peaks represent localized scatters in motion, as opposed to some sort of integrated composite, an attempt was made to determine the change in position of single scatterers over a series of sequential records. A four-antenna system was employed which had 1 degree of freedom in phase. Due to limitations N-S linear transmission and E-W linear reception were used. The Doppler frequency peak selection criteria were that at least two of the four power spectra should have a local peak, and that normalized phase discrepancy, should be less than 0.3. The lack of success in tracking individual scatters seems to suggest a short lifetime. If this is the case, then the present experiment is not able to resolve the difference found between the correlation analysis true velocity and the interferometer value. On the other hand, it appears that the interferometer may be of some use in tracking waves.

/pdf/comparison-of-medium-frequency-pulsed-radar-interferometer-21a3u3197d.pdf

Comparison of medium frequency pulsed radar interferometer and correlation analysis winds, part 2

In principle, the interferometer analysis determines the radial velocity and direction of single scatterers provided that each has a sufficiently different Doppler frequency to permit separation by spectral analysis. In fact, scatterers will not have constant radial velocity, and their Doppler frequencies as well as their directions will be modulated by their horizontal motion. Thus, there is a tradeoff between the poorer resolution but less smeared scatterers on shorter records and the higher resolution (longer) records. Three or more non-collinear scatterers are sufficient to determine the wind. It appears that the velocity found from the combined interferometer peaks agrees well with the apparent velocity from correlation methods, but the true velocity is a factor of 2 smaller. This difference might be resolved by searching for scatters showing regular movement between adjacent records.

/pdf/comparison-of-medium-frequency-pulsed-radar-interferometer-21uvmoao56.pdf

Comparison of medium frequency pulsed radar interferometer and correlation analysis winds, part 1

/pdf/radar-and-optical-studies-of-the-atmosphere-1jvitfyb4r.pdf

Radar and optical studies of the atmosphere.

Radar is used to make measurements of the dynamics and structure of the atmosphere by detecting irregularities in refractive index due to variations in humidity and temperature in the lower atmosphere (0 - 20 km), and due to variations due to fluctuations in electron density in the Mesosphere Lower Thermosphere (MLT) region of the upper atmosphere (50 - 110 km). Wind Profiling Radars operating in the lower VHF band have been used for about 25 years to investigate the Stratosphere Troposphere (ST) region, but only routinely in the last 15 years. Considerable development has occurred within the past decade and a number of rocket launch sites now utilize Wind Profilers for launch support. They are also becoming increasingly common for airport operations. Here we provide a very brief overview.

/pdf/ground-based-vhf-radar-for-observations-of-the-atmosphere-vvj6v9rj25.pdf

Iain M. Reid

Papers

A preliminary long-term comparison of MF SA and meteor wind determinations with collocated radar systems

Comparison of medium frequency pulsed radar interferometer and correlation analysis winds, part 2

Comparison of medium frequency pulsed radar interferometer and correlation analysis winds, part 1

Radar and optical studies of the atmosphere.

Ground based VHF radar for observations of the atmosphere