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Terrence R. Nathan

Abstract

The role of ozone in the linear stability of Rossby normal modes is examined in a continuously stratified, extratropical baroclinic atmosphere. The flow is described by coupled equations for the quasi-geostrophic potential vorticity and ozone volume mixing ratio. A perturbation analysis is carded out under the assumption of weak diabatic heating, which is generated by Newtonian cooling and dynamics–ozone interaction. An expression for the propagation and growth characteristics is obtained analytically in terms of the vertically averaged wave activity, which depends explicitly on the wave spatial structure, photochemistry, and basic state distributions of wind, temperature, and ozone mixing ratio. Calculations show that stationary internal modes, whose amplitudes are largest in the stratosphere, are destabilized by dynamics–ozone interaction and Newtonian cooling, with e-folding times on the order of 20–40 days.

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Terrence R. Nathan

Abstract

Weakly nonlinear interactions between an unstable baroclinic wave and resonant topographic wave are investigated using asymptotic methods in a two-layer, quasi-geostrophic channel model on a midlatitude beta plane in the presence of sinusoidal topography and dissipation. The asymptotic analysis pivots about slightly supercritical, vertically sheared zonal flows for which the baroclinic wave is weakly unstable and the topographic wave nearly resonant. Two long time scales are required to describe the evolution of the baroclinic wave and zonal flow connections, while the topographic wave evolves only on the longest time scale. To facilitate the numerical analysis, the method of reconstitution is used to form amplitude and zonal flow equations on a combined time scale.

Examination of the analytically derived amplitude evolution equations shows that the phase of the topographic wave relative to the mountain explicitly affects the nonlinear evolution of the baroclinic wave. In contrast, phase changes in the baroclinic wave have no direct effect on the evolution of the topographic wave.

Numerical integrations of the reconstituted evolution equations reveal two distinct asymptotic states of the system: 1) a single (stationary) topographic wave state where the wave trough is upstream of the mountain ridge, or 2) a mixed wave state where the baroclinic wave propagates with fixed amplitude, while the topographic wave remains stationary with its trough upstream of the mountain ridge. Single wave states, or mixed wave states dominated by the topographic wave, are, relatively speaking, favored for large zonal scales, large topographic heights, small beta and weak dissipation. However, for sufficiently small zonal scales only mixed wave states exist which are dominated by the baroclinic wave.

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Terrence R. Nathan and Long Li

Abstract

A simple β-plane model that couples radiative transfer, ozone advection, and ozone photochemistry with the quasi-geostrophic dynamical circulation is used to study the diabatic effects of Newtonian cooling and ozone–dynamics interaction on the linear stability of free planetary waves in the atmosphere. Under the assumption that the diabatic processes are sufficiently weak, an analytical expression is derived for the eigenfrequencies of these waves valid for arbitrary vertical distributions of background wind and ozone volume mixing ratio (&gamma¯). This expression shows the following: 1) the influence of meridional ozone advection on wave growth or decay depends on the wave and basic state vertical structures; 2) vertical ozone advection is locally (de)stabilizing when d&gamma¯/dz (>0) < 0, irrespective of the wave or basic state vertical structures; 3) photochemically accelerated cooling, which predominates in the upper stratosphere, augments the Newtonian cooling rate and is stabilizing.

The one-dimensional linear stability problem also is solved numerically for a Charney basic state (constant vertical shear and constant stratification) and for zonal mean basic states constructed from observational data characteristic of each season. It is shown that ozone heating generated by ozone–dynamics interaction in the stratosphere can reduce (enhance) the damping rates due to Newtonian cooling by as much as 50% for planetary waves of large vertical scale and maximum amplitude in the lower (upper) stratosphere. For waves with relatively large density-weighted amplitude in the lower to midstratosphere and small Doppler-shifted frequency, ozone-dynamics interaction in the stratosphere can significantly influence the zonally rectified wave fluxes in the troposphere.

For the summer basic state, adiabatic eastward- and westward-propagating neutral modes having the same zonal scale emerge; both are confined to the lower stratosphere and troposphere. For these modes ozone heating dominates over Newtonian cooling, and the modes amplify with growth rates comparable to those of baroclinically unstable waves of similar spatial scale.

The effects of radiative–photochemical feedbacks on the transient time scales of observed waves in the atmosphere also are discussed.

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Terrence R. Nathan and Albert Barcilon

Abstract

Jin and Ghil demonstrate that for topographically resonant flow, low-frequency finite-amplitude oscillations may arise from wave–wave interactions and topographic form drag. Their model is extended to include a zonally asymmetric vorticity source, which is shown to interact with the perturbation field to produce zonally rectified wave fluxes that dramatically alter the Hopf bifurcation from stationary solutions to low-frequency oscillations. The frequency, intensity, and general character of these oscillations are shown to depend crucially upon the phasing and relative strength of the forcings.

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Daniel Hodyss and Terrence R. Nathan

Abstract

A theory is presented that addresses the connection between low-frequency wave packets (LFWPs) and the formation and decay of coherent structures (CSs) in large-scale atmospheric flow. Using a weakly nonlinear evolution equation as well as the nonlinear barotropic vorticity equation, the coalescence of LFWPs into CSs is shown to require packet configurations for which there is a convergent group velocity field. These LFWP configurations, which are consistent with observations, have shorter wave groups with faster group velocities upstream of longer wave groups with slower group velocities. These wave group configurations are explained by carrying out a kinematic analysis of wave focusing, whereby a collection of wave groups focus at some point in space and time to form a large amplitude wave packet having a single wave front. The wave focusing and the subsequent formation of CSs are enhanced by zonal variations in the background flow, while nonlinearity extends the lifetimes of the CSs. These results are discussed in light of observed blocking formation in the Atlantic–European and South Pacific regions.

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Long Li and Terrence R. Nathan

Abstract

The extratropical response to localized, low-frequency tropical forcing is examined using a linearized, non-divergent barotropic model on a sphere. Zonal-mean basic states characterized by solid-body rotation or critical latitudes are considered. An analytical analysis based on WKB and ray tracing methods shows that, in contrast to stationary Rossby waves, westward moving, low-frequency Rossby waves can propagate through the tropical easterlies into the extratropics. It is shown analytically that the difference between the stationary and low-frequency ray paths is proportional to the forcing frequency and inversely proportional to the zonal wavenumber cubed. An expression for the disturbance amplitude is derived that shows the ability of the forced waves to maintain their strength well into middle latitudes depends on their meridional wave scale and northward group velocity, both of which are functions of the slowly varying background flow.

A local energetics analysis shows that the combination of energy dispersion from the forcing region and energy extraction from the equatorward flank of the midlatitude jet produces disturbances that have the greatest impact on the extratropical circulation. Under the assumption that the forcing amplitude is independent of frequency, this impact is largest when the tropical forcing period is in the range 10–20 days.

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Long Li and Terrence R. Nathan

Abstract

A spherical nondivergent barotropic model, linearized about a 300-mb climatological January flow, is used to examine the extratropical response to low-frequency tropical forcing. A two-dimensional WKB analysis shows that the energy propagation depends on the sum of three vectors: the basic state wind vector, a vector that is parallel to the absolute vorticity contours, and the local wave vector. The latter two vectors are functions of the slowly varying background flow and forcing frequency ω. As ω decreases, the ray paths approach that of the local wave vector, so that the energy propagates in a direction perpendicular to the wave fronts. The extratropical jet streams have a stronger influence on the long period (>30 day) ray paths than on those of intermediate period (∼10–30 day).

Global and local energetics calculations show that the energy conversion from the zonally varying basic flow increases as ω decreases. The local energetics show that for the long period disturbances, both the energy conversion and energy redistribution due to advection and pressure work are significant along the North African–Asian jet stream. The long period disturbances are less sensitive to the location of the tropical forcing than those of intermediate period. This provides a plausible explanation for the observations showing that the long period oscillations tend to be geographically fixed at the exits of the extratropical jet streams, whereas those of intermediate period are zonally mobile wave trains. The long (intermediate) timescale disturbances dominate in the Northern (Southern) Hemisphere, where the zonal variations in the basic flow are more (less) pronounced.

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John R. Albers and Terrence R. Nathan

Abstract

A mechanistic chemistry–dynamical model is used to evaluate the relative importance of radiative, photochemical, and dynamical feedbacks in communicating changes in lower-stratospheric ozone to the circulation of the stratosphere and lower mesosphere. Consistent with observations and past modeling studies of Northern Hemisphere late winter and early spring, high-latitude radiative cooling due to lower-stratospheric ozone depletion causes an increase in the modeled meridional temperature gradient, an increase in the strength of the polar vortex, and a decrease in vertical wave propagation in the lower stratosphere. Moreover, it is shown that, as planetary waves pass through the ozone loss region, dynamical feedbacks precondition the wave, causing a large increase in wave amplitude. The wave amplification causes an increase in planetary wave drag, an increase in residual circulation downwelling, and a weaker polar vortex in the upper stratosphere and lower mesosphere. The dynamical feedbacks responsible for the wave amplification are diagnosed using an ozone-modified refractive index; the results explain recent chemistry–coupled climate model simulations that suggest a link between ozone depletion and increased polar downwelling. The effects of future ozone recovery are also examined and the results provide guidance for researchers attempting to diagnose and predict how stratospheric climate will respond specifically to ozone loss and recovery versus other climate forcings including increasing greenhouse gas abundances and changing sea surface temperatures.

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John R. Albers and Terrence R. Nathan

Abstract

A mechanistic model that couples quasigeostrophic dynamics, radiative transfer, ozone transport, and ozone photochemistry is used to study the effects of zonal asymmetries in ozone (ZAO) on the model’s polar vortex. The ZAO affect the vortex via two pathways. The first pathway (P1) hinges on modulation of the propagation and damping of a planetary wave by ZAO; the second pathway (P2) hinges on modulation of the wave–ozone flux convergences by ZAO. In the steady state, both P1 and P2 play important roles in modulating the zonal-mean circulation. The relative importance of wave propagation versus wave damping in P1 is diagnosed using an ozone-modified refractive index and an ozone-modified vertical energy flux. In the lower stratosphere, ZAO cause wave propagation and wave damping to oppose each other. The result is a small change in planetary wave drag but a large reduction in wave amplitude. Thus in the lower stratosphere, ZAO “precondition” the wave before it propagates into the upper stratosphere, where damping due to photochemically accelerated cooling dominates, causing a large reduction in planetary wave drag and thus a colder polar vortex. The ability of ZAO within the lower stratosphere to affect the upper stratosphere and lower mesosphere is discussed in light of secular and episodic changes in stratospheric ozone.

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Eugene C. Cordero and Terrence R. Nathan

Abstract

The effects of wave and zonal mean ozone heating on the evolution of the quasi-biennial oscillation (QBO) are examined using a two-dimensional mechanistic model of the equatorial stratosphere. The model atmosphere is governed by coupled equations for the zonal mean and (linear) wave fields of ozone, temperature, and wind, and is driven by specifying the amplitudes of a Kelvin wave and a Rossby–gravity wave at the lower boundary. Wave–mean flow interactions are accounted for in the model, but not wave–wave interactions.

A reference simulation (RS) of the QBO, in which ozone feedbacks are neglected, is carried out and the results compared with Upper Atmosphere Research Satellite observations. The RS is then compared with three model experiments, which examine separately and in combination the effects of wave ozone and zonal mean ozone feedbacks. Wave–ozone feedbacks alone increase the driving by the Kelvin and Rossby–gravity waves by up to 10%, producing stronger zonal wind shear zones and a stronger meridional circulation. Zonal mean–ozone feedbacks (ozone QBO) alone decrease the magnitude of the temperature QBO by up to 15%, which in turn affects the momentum deposition by the wave fields. Overall, the zonal mean–ozone feedbacks increase the magnitude of the meridional circulation by up to 30%. The combined effects of wave–ozone and ozone QBO feedbacks generally produce a larger response then either process alone. Moreover, these combined ozone feedbacks produce a temperature QBO amplitude that is up to 30% larger than simulations without the feedbacks. Correspondingly, significant changes are also observed in the zonal wind and ozone QBOs. When ozone feedbacks are included in the model, the Kelvin and Rossby–gravity wave amplitudes can be reduced by ∼10% and still produce a QBO similar to simulations without ozone.

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