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

Studies of high latitude mesospheric turbulence by radar and rocket. I - Energy deposition and wave structure

. The mesosphere and lower thermosphere (MLT) is a dynamic layer of the earth’s atmosphere. This region marks the interface at which neutral atmosphere dynamics begin to inﬂuence the upper atmosphere and ionosphere. However, our understanding of this region and our ability to accurately simulate it in global circulation models (GCMs) is limited by a lack of observations, especially in remote locations. To this end, a meteor radar was deployed from 2016 to 2020 on the remote mountainous island of South Georgia (54 ◦ S, 36 ◦ W) in the Southern Ocean. In this study we use these new measurements to characterise the fundamental dynamics of the MLT above South Georgia including large-scale winds, solar tides, planetary waves (PWs), and mesoscale gravity waves (GWs). We ﬁrst present an improved method for time–height localisation of radar wind measurements and characterise the large-scale MLT winds. We then determine the amplitudes and phases of the diurnal (24 h), semidiurnal (12 h), terdiurnal (8 h), and quardiurnal (6 h) solar tides at this latitude. We ﬁnd very large amplitudes up to 30 m s − 1 for the quasi 2 d PW in summer and, combining our measurements with the meteor SAAMER radar in Argentina, show that the dominant modes of the quasi 5, 10, and 16 d PWs are westward 1 and 2. We investigate and compare wind variance due to both large-scale “resolved” GWs and small-scale “sub-volume” GWs in the MLT and characterise their seasonal cycles. Last, we use our radar observations and satellite temperature observations from the Microwave Limb Sounder to test a climatological simulation of the Whole Atmosphere Community Climate Model (WACCM). We ﬁnd that WACCM exhibits a summertime mesopause near 80 km altitude that is around 10 K warmer and 10 km lower in altitude than observed. Above 95 km altitude, summertime meridional winds in WACCM reverse to poleward, but this not observed in radar observations in this altitude range. More signiﬁcantly, we ﬁnd that wintertime zonal winds between 85 to 105 km altitude are eastward up to 40 m s − 1 in radar observations, but in WACCM they are westward up to 20 m s − 1 . We propose that this large discrepancy may be linked to the impacts of secondary GWs (2GWs) on the residual circulation, which are not included in most global models, including WACCM. These radar measurements can therefore provide vital constraints that can guide the development of GCMs as they extend upwards into this important region of the atmosphere.

Radar observations of winds, waves and tides in the mesosphere and lower thermosphere over South Georgia island (54 ◦ S, 36 ◦ W) and comparison with WACCM simulations

Gravity waves in the southern hemisphere exhibit many of the same characteristics as those in the northern hemisphere in terms of their scales, amplitude growth with height, and influences on the lower and middle atmosphere. Yet there are likely to be significant differences in the wave spectra and their effects as well, due to differing source distributions and strengths in the two hemispheres. Presented here will be a brief review of our current understanding of gravity wave saturation processes and effects, and of the evidence for and likely sources of wave variability, in both hemispheres. We will then examine some of the evidence for hemispheric differences in gravity wave sources, energies, drag, and induced diffusion.

Gravity Waves in the Middle Atmosphere of the Southern Hemisphere

Thorpe analysis has been used to study turbulence in the atmosphere and ocean. It is clear that Thorpe analysis applied to individual soundings cannot be expected to give quantitatively rel...

Direct Numerical Simulation Guidance for Thorpe Analysis to Obtain Quantitatively Reliable Turbulence Parameters

The Polar Mesospheric Cloud (PMC) Turbulence experiment performed optical imaging and Rayleigh lidar PMC profiling during a 6‐day flight in July 2018. A mosaic of seven imagers provided sensitivity to spatial scales from ∼20 m to 100 km at a ∼2‐s cadence. Lidar backscatter measurements provided PMC brightness profiles and enabled definition of vertical displacements of larger‐scale gravity waves (GWs) and smaller‐scale instabilities of various types. These measurements captured an interval of strong, widespread Kelvin‐Helmholtz instabilities (KHI) occurring over northeastern Canada on July 12, 2018 during a period of significant GW activity. This paper addresses the evolution of the KHI field and the characteristics and roles of secondary instabilities within the KHI. Results include the imaging of secondary KHI in the middle atmosphere and multiple examples of KHI “tube and knot” (T&K) dynamics where two or more KH billows interact. Such dynamics have been identified clearly only once in the atmosphere previously. Results reveal that KHI T&K arise earlier and evolve more quickly than secondary instabilities of uniform KH billows. A companion paper by Fritts et al. (2022), https://doi.org/10.1029/2021JD035834 reveals that they also induce significantly larger energy dissipation rates than secondary instabilities of individual KH billows. The expected widespread occurrence of KHI T&K events may have important implications for enhanced turbulence and mixing influencing atmospheric structure and variability.

David C. Fritts

Papers

Studies of high latitude mesospheric turbulence by radar and rocket. I - Energy deposition and wave structure

Radar observations of winds, waves and tides in the mesosphere and lower thermosphere over South Georgia island (54 ◦ S, 36 ◦ W) and comparison with WACCM simulations

Gravity Waves in the Middle Atmosphere of the Southern Hemisphere

Direct Numerical Simulation Guidance for Thorpe Analysis to Obtain Quantitatively Reliable Turbulence Parameters

Multi‐Scale Kelvin‐Helmholtz Instability Dynamics Observed by PMC Turbo on 12 July 2018: 1. Secondary Instabilities and Billow Interactions