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

The theory developed by Briggs (1995) is extended to explain the measurement of a wind velocity equivalent to the spaced antenna apparent wind by imaging Doppler interferometer-like (IDI-like) interferometric analyses. The point is made that the presence of turbulence, or random change in the diffraction pattern on the ground, is directly responsible for the difference between the true and apparent velocities in the spaced antenna analysis, and also for the overestimation of the wind velocity by the IDI technique. An experiment is conducted to determine whether the “effective” scattering points resolved by IDI-like analyses tend to lie upon the azimuth predicted by theory. This is found to be the case, even for unsmoothed cross spectra for which the theory was not explicitly derived. An averaging mechanism is proposed which may explain the extent to which the unsmoothed experimental data conform to the behavior predicted by theory.

On the spaced antenna and imaging Doppler interferometer techniques

An investigation of biases in the full correlation analysis technique

A method has been developed to determine the angle-of-arrival (AoA) of incident radiation using pre-computed lookup tables. The phase difference between two receiving antennas can be used to infer AoA as measured from the pair baseline, but there will be more than one possible solution for antenna spacings greater than or equal to half a wavelength. Larger spacings are preferable to minimize mutual coupling of elements in the receive array and to decrease the relative uncertainty in measured phase difference. We present a solution that uses all unique antenna pairs to determine probabilities for all possible azimuth and zenith values. Prior to analysis, the expected phase differences for all AOAs are calculated for each antenna pair. For a received signal, histograms of possible AoAs for each antenna pair phase difference are extracted and added to produce a two dimensional probability density array that will maximize at the true value of the AoA. A benefit of this method is that all possible antenna pairs are utilized, rather than the restriction to specific pairs along baselines used by some interferometer algorithms. Numerical simulations indicate that performance of the suggested algorithm exceeds that of existing methods, with the benefit of additional flexibility in antenna placement. Meteor radar data has been used to test this method against existing methods, with excellent agreement between the two approaches. This method of AoA determination will allow the construction of low-cost interferometric direction finding arrays with different layouts, including construction of difficult terrain and three-dimensional antenna arrangements.

/pdf/interferometer-angle-of-arrival-determination-using-2y9kbpqllz.pdf

Interferometer angle-of-arrival determination using precalculated phases

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2017JA025059

Estimation of Mesospheric Densities at Low Latitudes Using the Kunming Meteor Radar Together With SABER Temperatures

This paper describes a comparison of two meteor radar systems operated simultaneously from June 29 to July 15, 1994, at the Buckland Park field station near Adelaide, Australia (35°S, 138°E). Both meteor systems operate on a narrow-beam VHF wind profiler. The first meteor system was developed by the atmospheric physics group at the University of Adelaide. The second meteor system was the University of Colorado's meteor echo detection and collection (MEDAC) system. The goal of the campaign was to determine how closely the two similar meteor systems performed with regards to the detection of meteor trail echoes and the estimation of the Doppler frequencies. Classification of the signals in the resulting data set showed that a number of the echoes, including a class of echoes that appear to be from meteors traveling straight down the beam, were from sources other than under dense meteor trails. When the nonunder dense echoes were operated on by the Doppler frequency estimators, widely varying estimates between the two systems were produced. Only when taking into careful consideration the details of the detection routines, the signal composition of the data set, and performance characteristics of the Doppler estimators was the comparison satisfactory.

Iain M. Reid

Papers

On the spaced antenna and imaging Doppler interferometer techniques

An investigation of biases in the full correlation analysis technique

Interferometer angle-of-arrival determination using precalculated phases

Estimation of Mesospheric Densities at Low Latitudes Using the Kunming Meteor Radar Together With SABER Temperatures

A comparison of meteor radar systems at Buckland Park