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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

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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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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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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William Turner IV
and
Terrence R. Nathan

Abstract

The relationship between El Niño–Southern Oscillation (ENSO) and the transatlantic slave trade (TAST) is examined using the Slave Voyages dataset and several reconstructed ENSO indices. The ENSO indices are used as a proxy for West African rainfall and temperature. In the Sahel, the El Niño (warm) phase of ENSO is associated with less rainfall and warmer temperatures, whereas the La Niña (cold) phase of ENSO is associated with more rainfall and cooler temperatures. The association between ENSO and the TAST is weak but statistically significant at a 2-yr lag. In this case, El Niño (drier and warmer) years are associated with a decrease in the export of enslaved Africans. The response of the TAST to El Niño is explained in terms of the societal response to agricultural stresses brought on by less rainfall and warmer temperatures. ENSO-induced changes to the TAST are briefly discussed in light of climate-induced movements of peoples in centuries past and the drought-induced movement of peoples in the Middle East today.

Significance Statement

The transatlantic slave trade was driven by economic and political forces, subject to the vagaries of the weather; it spanned two hemispheres and four continents and lasted more than 400 years. In this study we show that El Niño–Southern Oscillation, and its proxy association with West African rainfall and temperature, are significantly associated with the number of enslaved Africans that were transported from West Africa to the Americas. Lessons learned from the effects of weather and climate on the transatlantic slave trade reverberate today: extreme weather and climate change will continue to catalyze and amplify human conflict and migrations.

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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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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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Gloria L. Manney
and
Terrence R. Nathan

Abstract

The stability of a basic state composed of a westward-moving wave and a zonal mean jet is examined in a linearized barotropic nondivergent model on a sphere. The sensitivity of the stability to the strength and structure of the zonal jet is emphasized. For certain westward-moving basic state waves, inclusion of a very weak jet in the basic state can dramatically alter the stability of the flow. Examination of the energetics shows that some unstable disturbances depend almost entirely on zonal variations in the basic state for their existence. In cases where meridional variations of the basic state dominate the energy transfer, examination of basic state meridional vorticity gradients is useful in understanding the stability characteristics. At subcritical basic state wave amplitudes, addition of a weak jet, which by itself is stable, can change the meridional absolute vorticity gradient to resemble that for a supercritical basic state wave alone. Unstable disturbances then occur that have spatial structures and propagation characteristics similar to those for the supercritical wave alone.

For a basic state wave resembling the observed “2-day” wave, inclusion of an easterly (summer) jet in the basic state has a strong stabilizing influence. Unstable disturbances occur when a strong easterly jet is included that have structures similar to waves observed concurrently with the “2-day” wave.

Evidence is shown for seasonal dependence in the stability of several westward-moving basic state waves. Implications of these results on the observation of westward-moving waves in the stratosphere are briefly discussed.

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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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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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