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.

/pdf/gravity-wave-dynamics-and-effects-in-the-middle-atmosphere-4huexaq7y8.pdf

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

Whether radar meteor echoes occur at high altitudes (above ~130 km) in the Earth's atmosphere is a long-standing question within the meteor radar community. Using observations from the Sanya VHF coherent radar interferometer during 11 July to 10 August 2013, we have found a new class of range-spread high-altitude meteor trail echoes (HAMEs), some of which appeared at ~170 km altitude lasting more than 10 s. A statistical analysis on the local time dependence of the identified HAME events shows a maximum around 00–04 LT. The results imply that there could be much more meteor mass input due to meteoroid sputtering at high altitudes in the Earth's atmosphere than previously thought.

/pdf/observational-evidence-of-high-altitude-meteor-trail-from-36q2ygzb65.pdf

Observational evidence of high-altitude meteor trail from radar interferometer

Lidar measurements of mesospheric gravity wave characteristics are simulated using a simple numerical model. Simple theory is used to superimpose gravity wave fluctuations upon typical background densities and sodium abundances in the height range 80–100 km, which we then assume are perfectly observed by a Rayleigh and Na lidar, respectively. These lidar “data” are then analyzed for their gravity wave content using the standard reduction and analysis methods which are routinely applied to these data sets. Our goal is to assess whether this analysis of lidar data faithfully recovers the underlying wave field. In both quasi-monochromatic and spectral wave studies, the height range over which Na number density can be measured and the shape of the background Na profile impose a limit on the gravity wave information which can be extracted from Na lidar data. The limitations due to background layer shape do not exist for Rayleigh lidar measurements. The simulations reveal that quasi-monochromatic gravity waves with vertical wavelengths larger than approximately 10 km may not be reliably retrieved from Na lidar data. It is also shown that there are limitations on the accurate extraction of spectral parameters from Na lidar data due to the limited vertical extent of the mesospheric Na layer.

Simulation of lidar measurements of gravity waves in the mesosphere

. In recent years, the concept of multistatic meteor radar systems has attracted the attention of the atmospheric radar community, focusing on the
mesosphere and lower thermosphere (MLT) region. Recently, there have been some notable experiments using such multistatic meteor radar systems. Good
spatial resolution is vital for meteor radars because nearly all parameter inversion processes rely on the accurate location of the meteor trail
specular point. It is timely then for a careful discussion focused on the error distribution of multistatic meteor radar systems. In this study, we
discuss the measurement errors that affect the spatial resolution and obtain the spatial-resolution distribution in three-dimensional space for the
first time. The spatial-resolution distribution can both help design a multistatic meteor radar system and improve the performance of existing radar
systems. Moreover, the spatial-resolution distribution allows the accuracy of retrieved parameters such as the wind field to be determined.

/pdf/error-analyses-of-a-multistatic-meteor-radar-system-to-or01yrkj4s.pdf

Error analyses of a multistatic meteor radar system to obtain a three-dimensional spatial-resolution distribution

Radar studies of atmospheric gravity waves

This study compares the hourly mesospheric horizontal winds observed by two collocated and independent low-latitude meteor radars operating at 37.5 MHz and 53.1 MHz in Kunming, China (25.6°N, 103.8°E). Upon analyzing simultaneously detected meteor echoes, we find a fixed angular deviation between the baselines of the two meteor radar antenna arrays within the east–north–up coordinate system. Then, we correct the deviation in the antenna azimuth direction using a novel method and recalculate the horizontal zonal and meridional winds. A comparison of the results before and after the correction shows strong consistency between the winds observed by both meteor radars within the entire detection altitude range. Furthermore, we summarize the performance of different techniques for measuring mesospheric winds. Ultimately, our statistical analysis approach allows the uncertainties associated with meteor radar wind observations to be more precisely estimated.

https://www.mdpi.com/2072-4292/14/10/2354/pdf?version=1652428195

Iain M. Reid

Papers

Observational evidence of high-altitude meteor trail from radar interferometer

Simulation of lidar measurements of gravity waves in the mesosphere

Error analyses of a multistatic meteor radar system to obtain a three-dimensional spatial-resolution distribution

Radar studies of atmospheric gravity waves

Comparison between the Mesospheric Winds Observed by Two Collocated Meteor Radars at Low Latitudes