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J. Vanneste and T. G. Shepherd

Abstract

The density and the flux of wave-activity conservation laws are generally required to satisfy the group-velocity property: under the WKB approximation (i.e., for nearly monochromatic small-amplitude waves in a slowly varying medium), the flux divided by the density equals the group velocity. It is shown that this property is automatically satisfied if, under the WKB approximation, the only source of rapid variations in the density and the flux lies in the wave phase. A particular form of the density, based on a self-adjoint operator, is proposed as a systematic choice for a density verifying this condition.

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G. J. Boer and T. G. Shepherd

Abstract

Global FGGE data are used to investigate several aspects of large-scale turbulence in the atmosphere. The approach follows that for two-dimensional, nondivergent turbulent flows which are homogeneous and isotropic on the sphere. Spectra of kinetic energy, enstrophy and available potential energy are obtained for both the stationary and transient parts of the flow. Nonlinear interaction terms and fluxes of energy and enstrophy through wavenumber space are calculated and compared with the theory. A possible method of parameterizing the interactions with unresolved scales is considered.

Two rather different flow regimes are found in wavenumber space. The high-wavenumber regime is dominated by the transient components of the flow and exhibits, at least approximately, several of the conditions characterizing homogeneous and isotropic turbulence. This region of wavenumber space also displays some of the features of an enstrophy-cascading inertial subrange. The low-wavenumber region, on the other hand, is dominated by the stationary component of the flow, exhibits marked anisotropy and, in contrast to the high-wavenumber regime, displays a marked change between January and July.

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J. F. Scinocca and T. G. Shepherd

Abstract

Exact, finite-amplitude, local wave-activity conservation laws are derived for disturbances to steady flows in the context of the two-dimensional anelastic equations. The conservation laws are expressed entirely in terms of Eulerian quantities, and have the property that, in the limit of a small-amplitude, slowly varying, monochromatic wave train, the wave-activity density A and flux F, when averaged over phase, satisfy F = c g A where c g is the group velocity of the waves. For nonparallel steady flows, the only conserved wave activity is a form of disturbance pseudoenergy; when the steady flow is parallel, there is in addition a conservation law for the disturbance pseudomomentum.

The above results are obtained not only for isentropic background states (which give the so-called “deep form” of the anelastic equations), but also for arbitrary background potential-temperature profiles θ 0(z) so long as the variation in θ 0(z) over the depth of the fluid is small compared with θ 0 itself. The Hamiltonian structure of the equations is established in both cases, and its symmetry properties discussed. An expression for available potential energy is also derived that, for the case of a stably stratified background state (i.e., 0/dz > 0), is locally positive definite; the expression is valid for fully three-dimensional flow.

The counterparts to results for the two-dimensional Boussinesq equations are also noted.

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P. H. Haynes, M. E. McIntyre, and T. G. Shepherd

Abstract

No abstract available

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D. Wirosoetisno, T. G. Shepherd, and R. M. Temam

Abstract

It is shown how a renormalization technique, which is a variant of classical Krylov–Bogolyubov–Mitropol'skii averaging, can be used to obtain slow evolution equations for the vortical and inertia–gravity wave components of the dynamics in a rotating flow. The evolution equations for each component are obtained to second order in the Rossby number, and the nature of the coupling between the two is analyzed carefully. It is also shown how classical balance models such as quasigeostrophic dynamics and its second-order extension appear naturally as a special case of this renormalized system, thereby providing a rigorous basis for the slaving approach where only the fast variables are expanded. It is well known that these balance models correspond to a hypothetical slow manifold of the parent system; the method herein allows the determination of the dynamics in the neighborhood of such solutions. As a concrete illustration, a simple weak-wave model is used, although the method readily applies to more complex rotating fluid models such as the shallow-water, Boussinesq, primitive, and 3D Euler equations.

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I. Polichtchouk, T. G. Shepherd, R. J. Hogan, and P. Bechtold

Abstract

The role of parameterized nonorographic gravity wave drag (NOGWD) and its seasonal interaction with the resolved wave drag in the stratosphere has been extensively studied in low-resolution (coarser than 1.9° × 2.5°) climate models but is comparatively unexplored in higher-resolution models. Using the European Centre for Medium-Range Weather Forecasts Integrated Forecast System at 0.7° × 0.7° resolution, the wave drivers of the Brewer–Dobson circulation are diagnosed and the circulation sensitivity to the NOGW launch flux is explored. NOGWs are found to account for nearly 20% of the lower-stratospheric Southern Hemisphere (SH) polar cap downwelling and for less than 10% of the lower-stratospheric tropical upwelling and Northern Hemisphere (NH) polar cap downwelling. Despite these relatively small numbers, there are complex interactions between NOGWD and resolved wave drag, in both polar regions. Seasonal cycle analysis reveals a temporal offset in the resolved and parameterized wave interaction: the NOGWD response to altered source fluxes is largest in midwinter, while the resolved wave response is largest in the late winter and spring. This temporal offset is especially prominent in the SH. The impact of NOGWD on sudden stratospheric warming (SSW) life cycles and the final warming date in the SH is also investigated. An increase in NOGWD leads to an increase in SSW frequency, reduction in amplitude and persistence, and an earlier recovery of the stratopause following an SSW event. The SH final warming date is also brought forward when NOGWD is increased. Thus, NOGWD is still found to be a very important parameterization for stratospheric dynamics even in a high-resolution atmospheric model.

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H-R. Cho, T. G. Shepherd, and V. A. Vladimirov

Abstract

The problem of symmetric stability is examined within the context of the direct Liapunov method. The sufficient conditions for stability derived by Fjørtoft are shown to imply finite-amplitude, normed stability. This finite-amplitude stability theorem is then used to obtain rigorous upper bounds on the saturation amplitude of disturbances to symmetrically unstable flows.By employing a virial functional, the necessary conditions for instability implied by the stability theorem are shown to be in fact sufficient for instability. The results of Ooyama are improved upon insofar as a tight two-sided (upper and lower) estimate is obtained of the growth rate of (modal or nonmodal) symmetric instabilities.The case of moist adiabatic systems is also considered.

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P. H. Haynes, M. E. McIntyre, T. G. Shepherd, C. J. Marks, and K. P. Shine

Abstract

The situation considered is that of a zonally symmetric model of the middle atmosphere subject to a given quasi-steady zonal force , conceived to be the result of irreversible angular momentum transfer due to the upward propagation and breaking of Rossby and gravity waves together with any other dissipative eddy effects that may be relevant. The model's diabatic heating is assumed to have the qualitative character of a relaxation toward some radiatively determined temperature field. To the extent that the force may be regarded as given, and the extratropical angular momentum distribution is realistic, the extratropical diabatic mass flow across a given isentropic surface may be regarded as controlled exclusively by the distribution above that surface (implying control by the eddy dissipation above that surface and not, for instance, by the frequency of tropopause folding below). This “downward control” principle expresses a critical part of the dynamical chain of cause and effect governing the average rate at which photochemical products like ozone become available for folding into, or otherwise descending into, the extratropical troposphere. The dynamical facts expressed by the principle are also relevant, for instance, to understanding the seasonal-mean rate of upwelling of water vapor to the summer mesopause, and the interhemispheric differences in stratospheric tracer transport.

The robustness of the principle is examined when is time-dependent. For a global-scale, zonally symmetric diabatic circulation with a Brewer-Dobson-like horizontal structure given by the second zonally symmetric Hough mode, with Rossby height HR = 13 km in an isothermal atmosphere with density scale height H = 7 km, the vertical partitioning of the unsteady part of the mass circulation caused by fluctuations in confined to a shallow layer L is always at least 84% downward. It is 90% downward when the force fluctuates sinusoidally on twice the radiative relaxation timescale and 95% if five times slower. The time-dependent adjustment when is changed suddenly is elucidated, extending the work of Dickinson (1968), when the atmosphere is unbounded above and below. Above the forcing, the adjustment is characterized by decay of the meridional mass circulation cell at a rate proportional to the radiative relaxation rate τr−1 divided by {1 + (4H2/HR2)}. This decay is related to the boundedness of the angular momentum that can be taken up by the finite mass of air above L without causing an ever-increasing departure from thermal wind balance. Below the forcing, the meridional mass circulation cell penetrates downward at a speed τr−1HR2/H. For the second Hough mode, the time for downward penetration through one density scale height is about 6 days if the radiative relaxation time is 20 days, the latter being representative of the lower stratosphere. At any given altitude, a steady state is approached. The effect of a rigid lower boundary on the time-dependent adjustment is also considered. If a frictional planetary boundary layer is present then a steady state is ultimately approached everywhere, with the mass circulation extending downward from L and closing via the boundary layer.

Satellite observations of temperature and ozone are used in conjunction with a radiative transfer scheme to estimate the altitudes from which the lower stratospheric diabatic vertical velocity is controlled by the effective in the real atmosphere. The data appear to indicate that about 80% of the effective control is usually exerted from below 40 km but with significant exceptions up to 70 km (in the high latitude southern hemispheric winter). The implications for numerical modelling of chemical transport are noted.

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V. I. Fomichev, A. I. Jonsson, J. de Grandpré, S. R. Beagley, C. McLandress, K. Semeniuk, and T. G. Shepherd

Abstract

The Canadian Middle Atmosphere Model (CMAM) has been used to examine the middle atmosphere response to CO2 doubling. The radiative-photochemical response induced by doubling CO2 alone and the response produced by changes in prescribed SSTs are found to be approximately additive, with the former effect dominating throughout the middle atmosphere. The paper discusses the overall response, with emphasis on the effects of SST changes, which allow a tropospheric response to the CO2 forcing. The overall response is a cooling of the middle atmosphere accompanied by significant increases in the ozone and water vapor abundances. The ozone radiative feedback occurs through both an increase in solar heating and a decrease in infrared cooling, with the latter accounting for up to 15% of the total effect. Changes in global mean water vapor cooling are negligible above ∼30 hPa. Near the polar summer mesopause, the temperature response is weak and not statistically significant. The main effects of SST changes are a warmer troposphere, a warmer and higher tropopause, cell-like structures of heating and cooling at low and middlelatitudes in the middle atmosphere, warming in the summer mesosphere, water vapor increase throughout the domain, and O3 decrease in the lower tropical stratosphere. No noticeable change in upward-propagating planetary wave activity in the extratropical winter–spring stratosphere and no significant temperature response in the polar winter–spring stratosphere have been detected. Increased upwelling in the tropical stratosphere has been found to be linked to changed wave driving at low latitudes.

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V. Eyring, N. R. P. Harris, M. Rex, T. G. Shepherd, D. W. Fahey, G. T. Amanatidis, J. Austin, M. P. Chipperfield, M. Dameris, P. M. De F. Forster, A. Gettelman, H. F. Graf, T. Nagashima, P. A. Newman, S. Pawson, M. J. Prather, J. A. Pyle, R. J. Salawitch, B. D. Santer, and D. W. Waugh

Accurate and reliable predictions and an understanding of future changes in the stratosphere are major aspects of the subject of climate change. Simulating the interaction between chemistry and climate is of particular importance, because continued increases in greenhouse gases and a slow decrease in halogen loading are expected. These both influence the abundance of stratospheric ozone. In recent years a number of coupled chemistry–climate models (CCMs) with different levels of complexity have been developed. They produce a wide range of results concerning the timing and extent of ozone-layer recovery. Interest in reducing this range has created a need to address how the main dynamical, chemical, and physical processes that determine the long-term behavior of ozone are represented in the models and to validate these model processes through comparisons with observations and other models. A set of core validation processes structured around four major topics (transport, dynamics, radiation, and stratospheric chemistry and microphysics) has been developed. Each process is associated with one or more model diagnostics and with relevant datasets that can be used for validation. This approach provides a coherent framework for validating CCMs and can be used as a basis for future assessments. Similar efforts may benefit other modeling communities with a focus on earth science research as their models increase in complexity.

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