to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

[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

인공고관절의 세라믹 볼 헤드의 기계적 안정성 평가를 위한 3 차원 유한요소 해석

The potential for sea ice-albedo feedback to give rise to nonlinear climate change in the Arctic Ocean – defined as a nonlinear relationship between polar and global temperature change or, equivalently, a time-varying polar amplification – is explored in IPCC AR4 climate models. Five models supplying SRES A1B ensembles for the 21 st century are examined and very linear relationships are found between polar and global temperatures (indicating linear Arctic Ocean climate change), and between polar temperature and albedo (the potential source of nonlinearity). Two of the climate models have Arctic Ocean simulations that become annually sea ice-free under the stronger CO 2 increase to quadrupling forcing. Both of these runs show increases in polar amplification at polar temperatures above-5 o C and one exhibits heat budget changes that are consistent with the small ice cap instability of simple energy balance models. Both models show linear warming up to a polar temperature of-5 o C, well above the disappearance of their September ice covers at about-9 o C. Below-5 o C, surface albedo decreases smoothly as reductions move, progressively, to earlier parts of the sunlit period. Atmospheric heat transport exerts a strong cooling effect during the transition to annually ice-free conditions. Specialized experiments with atmosphere and coupled models show that the main damping mechanism for sea ice region surface temperature is reduced upward heat flux through the adjacent ice-free oceans resulting in reduced atmospheric heat transport into the region.

Geophysical fluid dynamics.

The implementation of the Global Positioning System (GPS) network of satellites and the development of small, high-performance instrumentation to receive GPS signals have created an opportunity for active remote sounding of the Earth's atmosphere by radio occultation at comparatively low cost. A prototype demonstration of this capability has now been provided by the GPS/MET investigation. Despite using relatively immature technology, GPS/MET has been extremely successful [Ware et al., 1996; Kursinski et al., 1996], although there is still room for improvement. The aim of this paper is to develop a theoretical estimate of the spatial coverage, resolution, and accuracy that can be expected for atmospheric profiles derived from GPS occultations. We consider observational geometry, attenuation, and diffraction in defining the vertical range of the observations and their resolution. We present the first systematic, extensive error analysis of the spacecraft radio occultation technique using a combination of analytical and simulation methods to establish a baseline accuracy for retrieved profiles of refractivity, geopotential, and temperature. Typically, the vertical resolution of the observations ranges from 0.5 km in the lower troposphere to 1.4 km in the middle atmosphere. Results indicate that useful profiles of refractivity can be derived from ∼60 km altitude to the surface with the exception of regions less than 250 m in vertical extent associated with high vertical humidity gradients. Above the 250 K altitude level in the troposphere, where the effects of water are negligible, sub-Kelvin temperature accuracy is predicted up to ∼40 km depending on the phase of the solar cycle. Geopotential heights of constant pressure levels are expected to be accurate to ∼10 m or better between 10 and 20 km altitudes. Below the 250 K level, the ambiguity between water and dry atmosphere refractivity becomes significant, and temperature accuracy is degraded. Deep in the warm troposphere the contribution of water to refractivity becomes sufficiently large for the accurate retrieval of water vapor given independent temperatures from weather analyses [Kursinski et al., 1995]. The radio occultation technique possesses a unique combination of global coverage, high precision, high vertical resolution, insensitivity to atmospheric particulates, and long-term stability. We show here how these properties are well suited for several applications including numerical weather prediction and long-term monitoring of the Earth's climate.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/97JD01569

Observing Earth's atmosphere with radio occultation measurements using the Global Positioning System

Spectra of atmospheric motions as a function of observed frequency may depart significantly from the spectra as a function of intrinsic frequency due to a nonzero mean wind. In this paper we examine the effects of Doppler shifting on a model spectrum of atmospheric gravity waves. In order to gain insight into the effects of Doppler shifting, we have derived analytic solutions by approximation of the intrinsic frequency spectra and the gravity wave dispersion relation. Our results reveal that Doppler shifting can have major effects on the observed frequency spectrum of both horizontal and vertical gravity wave energy. For levels of Doppler shifting representative of the lower and middle atmosphere, possible effects include a substantial enhancement of horizontal energy density at higher observed frequencies, a corresponding reduction of the vertical energy density at higher frequencies, and a significant transfer of vertical energy to observed frequencies above the buoyancy frequency. The predicted effects are found to be consistent with some of the features of the observed frequency spectra.

Effects of Doppler shifting on the frequency spectra of atmospheric gravity waves

Global study of northern hemisphere quasi-2-day wave events in recent summers near 90 km altitude

Unstable Velocity shears are a Common source of vertically propagating gravity waves in the atmosphere. However, the growth rates of unstable modes predicted by linear theory cannot always amount for their observed importance. We examine in this paper, using a numerical model, the nonlinear excitation and evolution of atmospheric gravity waves. It is found that such waves can reach large amplitudes and induce significant accelerations of the mean velocity profile, resulting in shear stabilization and jet formation. Unstable modes that are vertically propagating above and below the shear layer may, when growing in isolation, achieve a state of quasi-sustained radiation. The nonlinear excitation of vertically propagating gravity waves via the interaction of two KH modes is found to be very rapid, providing an explanation for their occurrence in the atmosphere.

Shear Excitation of Atmospheric Gravity Waves

Wind and temperature data collected on commercial aircraft during the Global Atmospheric Sampling Program (GASP) are used to investigate the effects of underlying terrain on mesoscale variability, and the observational results are interpreted within the theories of gravity wave motions and quasi-two-dimensional turbulence. The data show the variances are up to six times larger over mountainous terrain than over oceans or plains, with the most striking differences at horizontal scales from 4 to 80 km. Results were subdivided between the stratosphere and troposphere, and between high- and low-background wind speed cases, and show basically the same response to topography in all cases. The linear theory of gravity waves is found to predict correctly the scaling of wave amplitude with background stability in the case of low-background wind speeds, while the two-dimensional turbulence theory correctly predicts the shape of the variance spectrum and the observed amplitude scales with ϵ as required by t...

David C. Fritts

Papers

Effects of Doppler shifting on the frequency spectra of atmospheric gravity waves

Global study of northern hemisphere quasi-2-day wave events in recent summers near 90 km altitude

Shear Excitation of Atmospheric Gravity Waves

An Investigation of Terrain Effects on the Mesoscale Spectrum of Atmospheric Motions

The effects of Doppler shifting on the frequency spectra of atmospheric gravity waves