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Lesley J. Gray and Timothy J. Dunkerton

Abstract

Satellite and station data have shown that the quasi-biennial oscillation (QBO) in total column ozone is asymmetric about the equator, unlike the zonal wind oscillation. There is an asymmetry in phase, as subtropical ozone anomalies maximize in the winter–spring season in both hemispheres, showing strong synchronization with the seasonal cycle irrespective of the phase of the equatorial QBO. There is also an asymmetry in amplitude, which we suggest is due to the timing of the equatorial QBO relative to the seasonal cycle and possible seasonal variation of the Hadley circulation. These asymmetries change with time as the phase relationship between the equatorial QBO and seasonal cycle changes, producing a slow modulation of the subtropical ozone QBO.

Numerical simulations of the ozone QBO with a two-dimensional radiative–dynamical–photochemical model successfully reproduce these features of the ozone QBO and show that mean motions near the base of the equatorial stratosphere are largely responsible for the asymmetry of the oscillation. The column oscillation is a complex superposition of number densities at various levels due to phase descent of the dynamical QBO and strong spatial gradients in the strength and direction of the Hadley circulation. The role of ozone photochemistry is also discussed, and comparison is made to the simulated quasi-biennial oscillation of NOy.

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M-Pascale Lelong and Timothy J. Dunkerton

Abstract

The three-dimensional breakdown of a large-amplitude, convectively unstable inertia–gravity wave is examined numerically as a function of primary-wave frequency and amplitude. The results confirm that near-inertial waves break down preferentially via shear instability even when the primary wave is initially overturned. As in the convectively stable near-inertial regime, the spectrum of instability energy is approximately isotropic in azimuthal orientation. At intermediate frequencies, wave breakdown is triggered by a transverse shear instability in the region of overturning. This behavior, displaying a clear preference for instability with horizontal component of wavevector in the transverse direction, is different from the breakdown of convectively stable waves at intermediate frequency examined in Part I. As the primary-wave frequency is increased further, shear instabilities once again develop in the transverse direction, but they are modified by convective instability as the billows reach finite amplitude. The influence of transverse vertical shear becomes progressively weaker as the wave frequency approaches the buoyancy frequency. In this limit, transverse convection leads to wave collapse, and there is no preferred scale of instability.

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Mark P. Baldwin and Timothy J. Dunkerton

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The stratospheric major warming of early December 1987 is analyzed using NMC observations of temperature and geopotential. This warming is distinguished as the earliest major warming ever recorded in the Northern Hemisphere winter. The observed mean zonal wind reversal and reversed poleward temperature gradient at 10 mb were preceded by the anomalous amplification of a zonal wavenumber 1 planetary wave emanating from the troposphere. This planetary wave event, similarly, is distinguished for having produced the second largest sustained flux of wavenumber 1 activity ever observed to propagate upwards from the troposphere at such an early time in the winter. Within the troposphere, the amplification of wave 1 was accompanied by several simultaneous blocking episodes, but it is unclear whether this blocking caused the anomalous formation of the planetary wave (or vice versa, or neither). Amplification of the planetary wave within the stratosphere led to a significant off-polar displacement of the circumpolar vortex and a reduction in vortex area, as observed in connection with other warmings. However, in the present case there is less significant evidence of a preconditioned stratospheric vortex, except for a small precursor event in late November which may have slightly retarded the normal, climatological expansion of the vortex. Therefore, it appears that this unusually early major warming was mainly attributable to an anomalously large tropospheric forcing.

After the climax of the warming, the midstratosphere vortex was observed to split into a double-vortex pattern. This feature is quite striking when viewed three-dimensionally, as the two 850 K vortex components remained contiguous, respectively, with single vortices in the upper and lower stratosphere. Thereafter, the stratosphere returned to a cold, undisturbed pattern until the beginning of March, when an early final warming occurred. The relatively cold January-February period coincided with the deep westerly phase of the equatorial quasi-biennial oscillation (QBO), as observed in connection with other cold, undisturbed winters. However, the QBO had already attained this phase by early December 1987, suggesting that the phase of the QBO per se is insufficient to prevent the occurrence of a major warming.

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Timothy J. Dunkerton and David C. Fritts

Abstract

Numerical simulations of vertically-propagating gravity waves interacting with critical layers are presented. For nearly monochromatic wave events, the wave amplitude behavior and mean zonal acceleration agree substantially with the predictions of the semi-analytic models of Grimshaw in 1975, Dunkerton in 1981–82 and Coy in 1983. A mean zonal wind “shock,” or steep sheer zone, forms at the base of a convectively unstable critical layer in these cases.

Because the semi-analytic model is based on the WKB approximation, the gravity wave, mean-flow interaction proceeds somewhat differently when this approximation is not accurate. For highly transient wave packets containing a broad frequency spectrum, momentum deposition and convective instability occurs over a much broader range of heights than predicted by the semi-analytic model. For nearly monochromatic waves, on the other hand, partial reflection from the internal mean flow shock is observed.

The inviscid gravity wave critical layer is inherently turbulent since overturning rapidly develops in the potential temperature field. Negative local Richardson numbers (Ri) are contemporaneous with the development of the internal shock in the monochromatic wave events, are coincident with Lagrangian zonal perturbation velocities exceeding the intrinsic phase speed, and occur very soon after the appearance of regions with Ri<¼. To account for convective wavebreaking a simple, local turbulence parameterization is advanced, which is not based upon turbulent eddy diffusion. Instead, the total wave plus mean flow profile, when required is frictionally relaxed to a convectively neutral equilibrium which conserves potential temperature and total vorticity, analogous to the familiar “convective adjustment” procedure in general circulation models. Despite being a local adjustment within the wave, this turbulence parameterization seems to confirm the amplitude-limiting effects predicted by Lindzen's global amplitude balance model in the relatively simple case studies presented here.

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Francis X. Crum and Timothy J. Dunkerton

Abstract

Wave-CISK with conditional heating is investigated in the equatorial zonal-height plane by analytic and numerical techniques. For two- and three-level models, previous results are extended to give additional evidence that the most unstable mode has a single wet region of infinitesimal width. A three-level model has qualitatively similar behavior as the two-level model except that propagating solutions are possible due to coalescence of internal vertical modes. Phase speeds with conditional heating are found to be slightly greater than those for unconditional heating. The structure has one circulation cell in the vertical and is asymmetric in longitude with stronger motion on the leading edge. Growth rate is inversely proportional to the width of the single wet region. That width can be limited by second-order diffusion. A general integral relationship between growth rate, viscosity, phase speed, and heating is derived.The main conclusion is that the linear wave-CISK catastrophe is modified by conditional heating but not eliminated. The preferred mode of instability has one wet region, but it occurs on the smallest possible scale. It is likely that numerical models that use conditional heating are sensitive to resolution, especially for the commonly used spectral truncations, unless there is sufficiently strong damping at the smallest scales.

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Timothy J. Dunkerton and Mark P. Baldwin

Abstract

Twenty years of rawinsonde data (1973–1992) were examined in conjunction with European Centre for Medium-Range Weather Forecasts (ECMWF) analyses and outgoing longwave radiation (OLR) in 1980–1989 to determine the horizontal structure, propagation, and convective coupling of 3–6-day meridional wind oscillations over the tropical Pacific. Wave properties from ECMWF data, determined by lag correlation with respect to rawinsonde or ECMWF principal components, were consistent with what could be determined from the sparse rawinsonde network alone. Gridded analyses allowed a clearer distinction between equatorially trapped Rossby-gravity waves (RGW) and off-equatorial “tropical-depression” (TD) disturbances, so that the contrasting properties of these waves, including their seasonal and interannual variation, could be studied in better detail. Significant correlations with OLR were found, increasing in magnitude from eastern to western Pacific.

The apparent group propagation of disturbances was equatorward in the western Pacific, eastward across the central and eastern Pacific, and upward-downward out of the 150–300-mb layer. Vertical propagation was evident primarily at higher frequencies, implying that only a fraction of the kinetic energy associated with Rossby-gravity waves in the upper troposphere was involved either in convective coupling to the lower troposphere or vertical momentum transport to the lower stratosphere. It is suggested that in addition to convective and lateral forcings, Rossby-gravity waves are sometimes excited by energetic TD disturbances in the western Pacific.

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Timothy J. Dunkerton and Robert E. Robins

Abstract

This paper presents results obtained with high-resolution numerical models of the gravity-wave critical layer. The structure and growth rates of preferred modes of secondary instability—within or near regions of potential temperature overturning in the wave field—are discussed. Model instabilities, which appear to be primarily convective, are of two kinds. The expected mode of convective instability is nonradiating, trapped within the region of overturning. A new “radiating” mode of instability was also obtained that has a preferred zonal scale, grows to observable amplitude prior to the nonradiating mode, and extends into the adjacent stable regions of the wave field. As a result, this mode is important in the transition to turbulence and may affect momentum deposition and turbulent mixing due to gravity-wave breaking.

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Donal O'Sullivan and Timothy J. Dunkerton

Abstract

The seasonal (wintertime) development of middle atmosphere circulation in opposite phases of the equatorial quasi-biennial oscillation (QBO) was simulated with a three-dimensional nonlinear numerical model. In the stratosphere, the effect of equatorial QBO was generally consistent with the extratropical QBO observed by Holton and Tan, namely, a stronger midwinter polar vortex in the westerly phase, and vice versa. However, the extratropical response to the QBO was sensitive to other factors such as mesospheric gravity wave drag and the amplitude of Rossby waves specified at the model's lower boundary. The extratropical QBO was realistic only when a drag parameterization was included and Rossby wave amplitudes lay in an intermediate range close to the observed. At somewhat stronger forcing, the model's response was largest in the mesosphere where (in this case) westerlies were stronger in the easterly phase of equatorial QBO. This was apparently due to a shielding effect.

The theory of planetary wave–mean flow interaction suggests that the sensitivity to equatorial QBO should be greatest for wave forcings near a “bifurcation” point. Below this threshold the stratosphere approaches radiative equilibrium, shutting off vertical propagation of planetary waves. Supercritical forcing leads to a major warming. The model's sensitivity to forcing, while consistent with this idea, was most apparent in perpetual solstice runs without parameterized wave drag. Seasonal integrations with wave drag produced a more realistic extratropical QBO, making the bifurcation less conspicuous.

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Donald P. Delisi and Timothy J. Dunkerton

Abstract

Observations of zonally averaged temperature from the Nimbus 7 Stratospheric and Mesospheric Sounder (SAMS) in 1979–82 demonstrate that a significant seasonal variation or asymmetry exists in the equatorial semiannual oscillation (SAO) in the sense that the “first” semiannual cycle beginning in the Northern Hemisphere winter (December–May) is much stronger than the “second” cycle beginning six months later (June–November). Calculation of balanced winds from the satellite data indicates a corresponding seasonality in SAO wind regimes; equatorial easterlies are stronger in December–February than in June–August and are followed by stronger westerly mean flow accelerations and, as a result, stronger westerlies in March–May than in September–November. This observation is in agreement with previous studies of the semiannual oscillation.

Strong coupling is observed during the first SAO cycle between equatorial and North Polar temperature. A model of this coupling via a mean meridional circulation suggests that planetary Rossby wave momentum deposition in the northern winter is the Underlying cause of the seasonal variation in the easterly phase of the SAO, This circulation can produce significant horizontal advection of angular momentum in the tropics even when the body force is confined to midlatitudes. At higher levels, the reverse component of the circulation or a reduced diabatic circulation combine with equatorial Kelvin and westerly gravity waves to produce the large westerly mean flow accelerations in the first SAO cycle.

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Timothy J. Dunkerton and Richard K. Scott

Abstract

An idealized analytical model of the barotropic potential vorticity (PV) staircase is constructed, constrained by global conservation of absolute angular momentum, perfect homogenization of PV in mixing zones between (prograde) westerly jets, and the requirement of barotropic stability. An imposed functional relationship is also assumed between jet speed and latitudinal separation using a multiple of the “dynamical Rossby wave” Rhines scale inferred from the strength of westerly jets. The relative simplicity of the barotropic system provides a simple relation between absolute angular momentum and PV (or absolute vorticity). A family of solutions comprising an arbitrary number of jets is constructed and is used to illustrate the restriction of jet spacing and strength imposed by the constraints of global conservation of angular momentum and barotropic stability. Asymptotic analysis of the theoretical solution indicates a limiting ratio of jet spacing to the dynamical Rhines scale equal to the square root of 6, meaning that westerly jets are spaced farther apart than predicted by the dynamical Rhines scale. It is inferred that an alternative “geometrical” Rhines scale for jet spacing can be obtained from conservation of absolute angular momentum on the sphere if the strength of zonal jets is known from other considerations. Numerical simulations of the full (nonaxisymmetric) equations reveal a pattern of zonal jet evolution that is consistent with our construction of ideal PV staircases in spherical geometry (which can be considered as limiting cases), as well as with the asymptotic analysis of a geometrical Rhines scale. The evolution of the PV staircase originating from an upscale cascade of energy in the barotropic model is therefore seen to depend on conservation of energy (for the strength of jets) and conservation of absolute angular momentum (for the spacing and number of jets). Further analysis of the numerical results confirms a “Taylor identity” relating the flux of eddy potential vorticity to mean-flow acceleration. Eddy fluxes are responsible for the occasional transitions between mode number as well as for maintaining the sharp westerly jets against small-scale dissipation. Suggestions are made for extending the theoretical model to PV staircases that are asymmetric between hemispheres or with latitudinal variation of amplitude, as modeled in the shallow-water system.

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