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

The decay times of VHF radar echoes from underdense meteor trails are reduced in the lower portions of the meteor region. This is a result of plasma neutralization initiated by the attachment of positive trail ions to neutral atmospheric molecules. Decreased echo decay times cause meteor radars to produce erroneously high estimates of the ambipolar diffusion coefficient at heights below 90 km, which affects temperature estimation techniques. Comparisons between colocated radars and satellite observations show that meteor radar estimates of diffusion coefficients are not consistent with estimates from the Aura Microwave Limb Sounder satellite instrument and that colocated radars operating at different frequencies estimate different values of the ambipolar diffusion coefficient for simultaneous detections of the same meteors. Loss of free electrons from meteor trails due to attachment to aerosols and chemical processes were numerically simulated and compared with observations to determine the specific mechanism responsible for low-altitude meteor trail plasma neutralization. It is shown that three-body attachment of positive metal ions significantly reduces meteor radar echo decay times at low altitudes compared to the case of diffusion only that atmospheric ozone plays little part in the evolution of low-altitude underdense meteor trails and that the effect of three-body attachment begins to exceed diffusion in echo decay times at a constant density surface.

/pdf/the-effects-of-deionization-processes-on-meteor-radar-2fzaoc6jfm.pdf

The effects of deionization processes on meteor radar diffusion coefficients below 90 km

[1] Interferometry measurements of range spread meteor trail echoes (RSTEs; also known as nonspecular echoes) have provided new insights into both the irregularity structures in meteor trails and lower-thermospheric winds (LTWs). In this study, we used trail echoes observed with the newly installed Sanya (18.4°N, 109.6°E) 47.5 MHz VHF coherent radar and the Sanya all-sky meteor radar to estimate instantaneous zonal and hourly averaged meridional winds from RSTEs and hourly averaged zonal and meridional winds from large numbers of specular meteor echoes. The mean height variations in both the zonal and meridional winds estimated from the RSTEs were generally consistent with those estimated from specular meteor echoes below 96 km. This gives validity to the technique proposed recently by Oppenheim et al. (2009) and suggests that RSTE measurements made with a small radar can be used to investigate LTWs, whereas this had previously been limited to larger radars such as the Jicamarca radar. However, some observations show significant differences in wind magnitude at individual heights at times. The results of RSTE measurements show the presence of an intense westward wind with a speed near 100 ms−1. In contrast, the specular meteor zonal winds were generally less than 50 ms−1. On the other hand, the meridional drift of RSTEs derived from the meridional Doppler velocity at higher altitudes shows a very poor correlation with the specular meteor meridional wind. Potential causes for the discrepancy in wind estimates obtained from RSTE and specular meteor trail echoes are discussed.

/pdf/a-comparison-of-lower-thermospheric-winds-derived-from-range-lkwnax581x.pdf

A comparison of lower thermospheric winds derived from range spread and specular meteor trail echoes

This paper investigates turbulent velocity esti- mation using the full correlation analysis (FCA) of spaced antenna (SA) data, and its application to the routine FCA observations of the Buckland Park MF (BPMF) radar. The effects of transmitter beamwidths are investigated, confirm- ing the suggestions of previous authors that wide transmit beam widths lead to an overestimation of the turbulent veloc- ity. The annual variation of the turbulent velocity is investi- gated, revealing an increase in turbulent velocity with height, and equinoctal minima and solstice maxima observed below 80 km. Investigations of the turbulent velocities about the March diurnal tide maximum reveals a diurnal variation in phase with the zonal velocity. Harmonic analysis reveals this relationship exists between February and September. De- scending power layers are also observed during this period. A number of mechanisms are proposed to describe these ob- servations.

/pdf/mesospheric-turbulent-velocity-estimation-using-the-buckland-160bub8brf.pdf

Mesospheric turbulent velocity estimation using the Buckland Park MF radar

We present results from three years of mesospheric and thermospheric wind measurements obtained using full correlation analysis (FCA) and imaging Doppler interferometry (IDI) for the Buckland Park MF radar. The IDI winds show excellent agreement with the FCA winds, both for short (2-min) and longer term (hourly, fortnightly) comparisons. An extension to a commonly used statistical analysis technique is introduced to show that the IDI winds are approximately 10% larger than the FCA winds, which we attribute to an underestimation of the FCA winds rather than an indication that IDI overestimates the wind velocity. Although the distribution of IDI effective scattering positions are shown to be consistent with volume scatter predictions, the velocity comparisons contradict volume scatter predictions that the IDI velocity will be overestimated. However, reanalysis of a 14-day data set suggests the lack of overestimation is due to the radial velocity threshold used in the analysis, and that removal of this threshold produces the volume scatter predicted overestimation of the IDI velocities. The merits of using hourly IDI estimates versus hourly averaged 2-min IDI estimates are presented, suggesting that hourly estimated turbulent velocities are overestimated.

/pdf/comparisons-of-full-correlation-analysis-fca-and-imaging-2zf1dkz97j.pdf

Comparisons of full correlation analysis (FCA) and imaging Doppler interferometry (IDI) winds using the Buckland Park MF radar

A simple computer model of atmospheric radar backscatter is used to investigate and compare various spaced antenna (SA) techniques, including the full correlation analysis (FCA) and a number of imaging interferometry techniques. The results illustrate that the FCA true velocity proves to be an excellent estimate of the model input velocity for all magnitudes of model turbulent motions. On the other hand, the interferometric velocities increase as the magnitude of the turbulent motions are increased, providing a poor estimate of the model input velocity for large turbulent motion magnitudes. Maps illustrating the interferometry-estimated scattering positions superimposed upon the actual model scatterer positions reveal the estimated positions to be inaccurate. The estimated positions are shown to approach the zenith as the magnitude of the turbulent motions increases, confirming the volume scatter derived suggestions of Briggs (1995). Furthermore, the estimated positions have a preferred azimuth angle agreeing with volume scatter derived suggestions. The effects of receiver noise upon the interferometric techniques are investigated, revealing an effect analogous to the FCA triangle size effect whereby the estimated velocity decreases with increasing noise level. The effects of the thresholds used to preclude individual Doppler frequencies from the analyses are illustrated. The results are in excellent agreement with the experimental results obtained in a number of different studies.

Iain M. Reid

Papers

The effects of deionization processes on meteor radar diffusion coefficients below 90 km

A comparison of lower thermospheric winds derived from range spread and specular meteor trail echoes

Mesospheric turbulent velocity estimation using the Buckland Park MF radar

Comparisons of full correlation analysis (FCA) and imaging Doppler interferometry (IDI) winds using the Buckland Park MF radar

Spaced antenna analysis of atmospheric radar backscatter model data