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- Author or Editor: Timothy J. Dunkerton x
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Abstract
The variability of zonally averaged stratospheric circulation is examined using daily gridded analyses from the U.K. Met. Office for 1991–99, corresponding to the period observed by the Upper Atmosphere Research Satellite. Application of rotated principal component analysis to the dataset reveals dominant modes of variability consisting of annual, semiannual, and quasi-biennial oscillations, together with intraseasonal and interannual variability in the winter hemisphere. In the upper stratosphere during northern winter, poleward propagating zonal wind anomalies at the stratopause and a sudden deceleration of the subtropical mesospheric jet in each midwinter are observed. The high-latitude flow is more variable, and the data suggest two contrasting types of wintertime evolution in the polar stratosphere. One is characterized in high latitudes by relatively strong flow in early winter and a significantly weakened flow after solstice, the other by relatively weak flow in early winter and a strong positive flow anomaly after solstice. In both, the subtropical deceleration is accompanied by high-latitude acceleration. In the second type, polar westerlies remain long after solstice, decaying gradually, while in the first type, polar easterlies appear after 10–30 days. In two winters of the first type, the subtropical deceleration is unusually abrupt, followed by brief reacceleration of the polar vortex and a spectacular breakdown after 30 days. Multivariate EOF analysis incorporating temperature data separates deceleration events in northern winter affecting the subtropical jet, with midlatitude warming, from those affecting the polar night jet, with polar warming.
Abstract
The variability of zonally averaged stratospheric circulation is examined using daily gridded analyses from the U.K. Met. Office for 1991–99, corresponding to the period observed by the Upper Atmosphere Research Satellite. Application of rotated principal component analysis to the dataset reveals dominant modes of variability consisting of annual, semiannual, and quasi-biennial oscillations, together with intraseasonal and interannual variability in the winter hemisphere. In the upper stratosphere during northern winter, poleward propagating zonal wind anomalies at the stratopause and a sudden deceleration of the subtropical mesospheric jet in each midwinter are observed. The high-latitude flow is more variable, and the data suggest two contrasting types of wintertime evolution in the polar stratosphere. One is characterized in high latitudes by relatively strong flow in early winter and a significantly weakened flow after solstice, the other by relatively weak flow in early winter and a strong positive flow anomaly after solstice. In both, the subtropical deceleration is accompanied by high-latitude acceleration. In the second type, polar westerlies remain long after solstice, decaying gradually, while in the first type, polar easterlies appear after 10–30 days. In two winters of the first type, the subtropical deceleration is unusually abrupt, followed by brief reacceleration of the polar vortex and a spectacular breakdown after 30 days. Multivariate EOF analysis incorporating temperature data separates deceleration events in northern winter affecting the subtropical jet, with midlatitude warming, from those affecting the polar night jet, with polar warming.
Abstract
Observations of ascending water vapor anomalies in the tropical lower stratosphere—the so-called tape recorder effect—have been used to infer profiles of vertical mean motion, vertical constituent diffusivity, and lateral in-mixing rate in this region. The magnitude of vertical wave flux required to drive the quasi-biennial oscillation (QBO) in the presence of mean upwelling, along with other related aspects of QBO dynamics, is examined in light of the tape recorder results using a simple one-dimensional model. As found in a previous study, it is necessary that wave fluxes significantly exceed the “classic” values associated with long-period Kelvin and Rossby-gravity waves; the extra fluxes are presumably associated with a continuous spectrum of short-period gravity and inertia–gravity waves. Larger wave fluxes, when used in connection with traditional wave-transport parameterizations developed for the QBO, require a larger vertical diffusivity of momentum in order to prevent the formation of unrealistically strong vertical wind shear. The profile of constituent diffusivity derived from the tape recorder effect, however, is much smaller everywhere than the momentum diffusivity assumed in previous QBO modeling studies.
Realistic shear is obtained in the model using a momentum-conserving “shear adjustment” scheme representing the effect of unresolved shear instabilities and other processes not included in the wave-transport parameterization. This device, together with a QBO amplitude profile based on the equatorial-wave phase speeds, motivates an (otherwise inviscid) analytic QBO solution in the underdamped, quasi-compressible case. The simple analytic solutions replicate most aspects of the numerical solution, display a similar dependence on wave flux at the lower boundary, and provide reasonably accurate estimates of QBO period in the inviscid limit.
Abstract
Observations of ascending water vapor anomalies in the tropical lower stratosphere—the so-called tape recorder effect—have been used to infer profiles of vertical mean motion, vertical constituent diffusivity, and lateral in-mixing rate in this region. The magnitude of vertical wave flux required to drive the quasi-biennial oscillation (QBO) in the presence of mean upwelling, along with other related aspects of QBO dynamics, is examined in light of the tape recorder results using a simple one-dimensional model. As found in a previous study, it is necessary that wave fluxes significantly exceed the “classic” values associated with long-period Kelvin and Rossby-gravity waves; the extra fluxes are presumably associated with a continuous spectrum of short-period gravity and inertia–gravity waves. Larger wave fluxes, when used in connection with traditional wave-transport parameterizations developed for the QBO, require a larger vertical diffusivity of momentum in order to prevent the formation of unrealistically strong vertical wind shear. The profile of constituent diffusivity derived from the tape recorder effect, however, is much smaller everywhere than the momentum diffusivity assumed in previous QBO modeling studies.
Realistic shear is obtained in the model using a momentum-conserving “shear adjustment” scheme representing the effect of unresolved shear instabilities and other processes not included in the wave-transport parameterization. This device, together with a QBO amplitude profile based on the equatorial-wave phase speeds, motivates an (otherwise inviscid) analytic QBO solution in the underdamped, quasi-compressible case. The simple analytic solutions replicate most aspects of the numerical solution, display a similar dependence on wave flux at the lower boundary, and provide reasonably accurate estimates of QBO period in the inviscid limit.
Abstract
Interannual variability of trace constituents in the stratosphere is examined using methane, water vapor, and ozone data from the Halogen Occultation Experiment aboard the Upper Atmosphere Research Satellite in 1992–99. Application of rotated principal component analysis to the dataset reveals dominant modes of variability consisting of annual, semiannual, and quasi-biennial oscillations (QBOs), together with “subbiennial” variations evidently due to nonlinear interaction between the annual cycle and QBO. The structure of quasi-biennial variability is approximately symmetric about the equator, while subbiennial variability, with certain exceptions, is approximately antisymmetric and confined mostly to the subtropics. The vertical structure and downward propagation of the ozone QBO at the equator is described by a pair of symmetric EOFs having separate amplitude maxima in the lower and upper stratosphere. A second pair of EOFs explains the seasonal dependence of subtropical ozone anomalies. For each tracer, the subtropical anomaly is larger in the Northern Hemisphere.
A novel “phase diagram” illustrates the joint seasonal and QBO dependence of tracer anomalies. A pair of principal components are used to define the phase of the dynamical QBO. When plotted against the phase of the annual cycle, the QBO follows a diagonal trajectory with regular phase progression except for an occasional slowing of easterly shear-zone descent near 50 hPa. Tracer principal components of symmetric and antisymmetric EOFs, plotted along this trajectory, display the distinct signatures of quasi-biennial and subbiennial variation. Tracer anomalies reconstructed using an idealized representation of QBO and subbiennial harmonics display the seasonal synchronization and decadal modulation characteristic of QBO–annual cycle interaction.
Abstract
Interannual variability of trace constituents in the stratosphere is examined using methane, water vapor, and ozone data from the Halogen Occultation Experiment aboard the Upper Atmosphere Research Satellite in 1992–99. Application of rotated principal component analysis to the dataset reveals dominant modes of variability consisting of annual, semiannual, and quasi-biennial oscillations (QBOs), together with “subbiennial” variations evidently due to nonlinear interaction between the annual cycle and QBO. The structure of quasi-biennial variability is approximately symmetric about the equator, while subbiennial variability, with certain exceptions, is approximately antisymmetric and confined mostly to the subtropics. The vertical structure and downward propagation of the ozone QBO at the equator is described by a pair of symmetric EOFs having separate amplitude maxima in the lower and upper stratosphere. A second pair of EOFs explains the seasonal dependence of subtropical ozone anomalies. For each tracer, the subtropical anomaly is larger in the Northern Hemisphere.
A novel “phase diagram” illustrates the joint seasonal and QBO dependence of tracer anomalies. A pair of principal components are used to define the phase of the dynamical QBO. When plotted against the phase of the annual cycle, the QBO follows a diagonal trajectory with regular phase progression except for an occasional slowing of easterly shear-zone descent near 50 hPa. Tracer principal components of symmetric and antisymmetric EOFs, plotted along this trajectory, display the distinct signatures of quasi-biennial and subbiennial variation. Tracer anomalies reconstructed using an idealized representation of QBO and subbiennial harmonics display the seasonal synchronization and decadal modulation characteristic of QBO–annual cycle interaction.
Abstract
For barotropic flow in spherical geometry, the ideal potential vorticity staircase with flat steps and vertical risers exhibits a relationship between prograde jet strength and spacing such that, for regular spacing, the distance between adjacent jets is given by a suitably defined “Rhines scale” multiplied by a positive constant equal to 
Abstract
For barotropic flow in spherical geometry, the ideal potential vorticity staircase with flat steps and vertical risers exhibits a relationship between prograde jet strength and spacing such that, for regular spacing, the distance between adjacent jets is given by a suitably defined “Rhines scale” multiplied by a positive constant equal to
Abstract
The decelerating effect of enhanced upper tropospheric wavedriving (DF ) in winter and early spring induces a “reverse” component of the residual mean meridional circulation in the polar lower stratosphere opposite to that induced by radiative cooling. The cooling, in turn, is maintained by the decelerating effect of stratospheric DF . If the upper-tropospheric wavedriving is increased, and the stratosphere wavedriving is sufficiently reduced, the change in the mean circulation will include upwelling in the polar lower stratosphere. Analytic and numerically derived properties of this generalized residual mean “body form” circulation are discussed.
Abstract
The decelerating effect of enhanced upper tropospheric wavedriving (DF ) in winter and early spring induces a “reverse” component of the residual mean meridional circulation in the polar lower stratosphere opposite to that induced by radiative cooling. The cooling, in turn, is maintained by the decelerating effect of stratospheric DF . If the upper-tropospheric wavedriving is increased, and the stratosphere wavedriving is sufficiently reduced, the change in the mean circulation will include upwelling in the polar lower stratosphere. Analytic and numerically derived properties of this generalized residual mean “body form” circulation are discussed.
Abstract
The subtropical mesospheric jet observed by the Nimbus 7 Limb Infrared Monitor of the Stratosphere in late 1978 was flanked to the north and south by regions of reversed potential vorticity gradient. In mid-December, enhanced planetary wave activity propagating upward into the mesosphere led to visible overreflection from the low-latitude reversed gradient region and rapid deceleration of the jet. It is argued, first, that the overreflection visible in the geopotential height field was probably genuine, and not likely to have been due to Rossby waves incident on an inertially unstable region. Nor was it due to the opposing mean meridional circulation. Second, the observed dominance of wave 1 in the overreflected flux may have been attributable to hemispheric barotropic instability: a low-wavenumber type of instability on the sphere related to the midlatitude modes discovered by Hartmann. In comparison to the barotropically unstable eigenmodes for higher zonal wavenumbers, the wave 1 mode has a slower growth rate but larger spatial extent. For practical purposes, it is a radiating mode excitable by sources in the far field. Equally important, the phase speed of the eigenmodes can be made exactly zero when the mean flow vanishes just within this region, as observed in mid-December 1978. Resonant excitation is therefore possible.
Realistic opposing mean meridional advection has only a slight effect on the barotropic eigenmode, provided that high-wavenumber oscillations are filtered out of the calculation, acting to reduce the growth rate and shift the subtropical secondary amplitude maximum a few degrees towards the pole.
Abstract
The subtropical mesospheric jet observed by the Nimbus 7 Limb Infrared Monitor of the Stratosphere in late 1978 was flanked to the north and south by regions of reversed potential vorticity gradient. In mid-December, enhanced planetary wave activity propagating upward into the mesosphere led to visible overreflection from the low-latitude reversed gradient region and rapid deceleration of the jet. It is argued, first, that the overreflection visible in the geopotential height field was probably genuine, and not likely to have been due to Rossby waves incident on an inertially unstable region. Nor was it due to the opposing mean meridional circulation. Second, the observed dominance of wave 1 in the overreflected flux may have been attributable to hemispheric barotropic instability: a low-wavenumber type of instability on the sphere related to the midlatitude modes discovered by Hartmann. In comparison to the barotropically unstable eigenmodes for higher zonal wavenumbers, the wave 1 mode has a slower growth rate but larger spatial extent. For practical purposes, it is a radiating mode excitable by sources in the far field. Equally important, the phase speed of the eigenmodes can be made exactly zero when the mean flow vanishes just within this region, as observed in mid-December 1978. Resonant excitation is therefore possible.
Realistic opposing mean meridional advection has only a slight effect on the barotropic eigenmode, provided that high-wavenumber oscillations are filtered out of the calculation, acting to reduce the growth rate and shift the subtropical secondary amplitude maximum a few degrees towards the pole.
Abstract
Internal gravity waves, and the stress divergence and turbulence induced by them, are essential components of the atmospheric and oceanic general circulations. Theoretical studies have not yet reached a consensus as to how gravity waves transport and deposit momentum. The two best-known theories, resonant interaction and Eikonal saturation, yield contradictory answers to this question. In resonant interaction theory, an energetic, high-frequency, low-wavenumber wave is unstable to two waves of approximately half the frequency and is backscattered by a low-frequency wave or mean finestructure of twice the vertical wavenumber. By contrast, the Eikonal saturation model, as it is commonly used, ignores reflection by assuming a slowly varying basic state and does not question the longevity of the primary wave in the presence of local Kelvin–Helmboltz or convective instabilities. The resonant interaction formalism demands that the interactions be weakly nonlinear. The Eikonal saturation model allows strong, “saturated” waves but ignores reflection and eliminates nonlinear instability with respect to other horizontal wavenumbers by invoking the linear or quasi-linear assumption.
To help bridge the gap between the two theories, results from prototype, nonlinear numerical simulations are presented. Attention is directed at the nonlinear instability of gravity waves in a slowly varying basic state. Parametric instability theory yields a group trajectory length scale for the primary wave expressed in terms of the dominant vertical wavelength and degree of convective saturation. This result delimits the range of validity for the Eikonal saturation model: a low-amplitude wave introduced into an undisturbed slowly varying basic state easily traverses many vertical wavelengths; conversely, a convectively neutral wave soon undergoes decay through nonlinear instability provided that some noise is present initially or created in situ by off-resonant interactions.
The numerical results establish the existence of a cascade in wavenumber space, which for hydrostatic waves proceeds toward both higher and lower horizontal wavenumbers, in accord with theory. Substantial reductions in momentum flux are found relative to the linear values.
Abstract
Internal gravity waves, and the stress divergence and turbulence induced by them, are essential components of the atmospheric and oceanic general circulations. Theoretical studies have not yet reached a consensus as to how gravity waves transport and deposit momentum. The two best-known theories, resonant interaction and Eikonal saturation, yield contradictory answers to this question. In resonant interaction theory, an energetic, high-frequency, low-wavenumber wave is unstable to two waves of approximately half the frequency and is backscattered by a low-frequency wave or mean finestructure of twice the vertical wavenumber. By contrast, the Eikonal saturation model, as it is commonly used, ignores reflection by assuming a slowly varying basic state and does not question the longevity of the primary wave in the presence of local Kelvin–Helmboltz or convective instabilities. The resonant interaction formalism demands that the interactions be weakly nonlinear. The Eikonal saturation model allows strong, “saturated” waves but ignores reflection and eliminates nonlinear instability with respect to other horizontal wavenumbers by invoking the linear or quasi-linear assumption.
To help bridge the gap between the two theories, results from prototype, nonlinear numerical simulations are presented. Attention is directed at the nonlinear instability of gravity waves in a slowly varying basic state. Parametric instability theory yields a group trajectory length scale for the primary wave expressed in terms of the dominant vertical wavelength and degree of convective saturation. This result delimits the range of validity for the Eikonal saturation model: a low-amplitude wave introduced into an undisturbed slowly varying basic state easily traverses many vertical wavelengths; conversely, a convectively neutral wave soon undergoes decay through nonlinear instability provided that some noise is present initially or created in situ by off-resonant interactions.
The numerical results establish the existence of a cascade in wavenumber space, which for hydrostatic waves proceeds toward both higher and lower horizontal wavenumbers, in accord with theory. Substantial reductions in momentum flux are found relative to the linear values.
Abstract
The propagation and refraction of stationary inertia–gravity waves in the winter stratosphere is examined with ray tracing. Due to their smaller vertical group velocity these waves experience more lateral ray movement and horizontal refraction that the simple gravity waves recently discussed by Dunkerton and Butchart. Stationary waves are rotated by the transverse horizontal shear and propagate into the polar night jet. Circumstances are found in which the mean flow shear has enhanced unstable wavebreaking by compressing, the wave packet and decreasing the absolute value of wave action density required for breaking. In some other places, reflection from the caustic is more likely.
Abstract
The propagation and refraction of stationary inertia–gravity waves in the winter stratosphere is examined with ray tracing. Due to their smaller vertical group velocity these waves experience more lateral ray movement and horizontal refraction that the simple gravity waves recently discussed by Dunkerton and Butchart. Stationary waves are rotated by the transverse horizontal shear and propagate into the polar night jet. Circumstances are found in which the mean flow shear has enhanced unstable wavebreaking by compressing, the wave packet and decreasing the absolute value of wave action density required for breaking. In some other places, reflection from the caustic is more likely.
Abstract
The quasi-biennial oscillation is simulated in two dimensions using a WKB approach for the equatorial waves in which analytic approximations to the wave-induced body forces are inserted as forcing terms in a primitive equation model of the zonally-averaged flow. Realistically large amplitude oscillations are obtained with this method.
Examination of one such oscillation in this paper clarifies the linear and nonlinear role of the residual mean meridional circulation: at low latitudes due to its vertical advection of momentum, and at higher latitudes on account of the Coriolis torque. Because this circulation also advects ozone, the primary source of radiative heating in this region, coupling between the ozone and dynamical oscillations will be significant in determining the strength of this meridional circulation.
Also of importance for the waves themselves are the scale-dependent radiative damping rate and, in the Rossby-gravity wave, the effect of latitudinal shear.
Abstract
The quasi-biennial oscillation is simulated in two dimensions using a WKB approach for the equatorial waves in which analytic approximations to the wave-induced body forces are inserted as forcing terms in a primitive equation model of the zonally-averaged flow. Realistically large amplitude oscillations are obtained with this method.
Examination of one such oscillation in this paper clarifies the linear and nonlinear role of the residual mean meridional circulation: at low latitudes due to its vertical advection of momentum, and at higher latitudes on account of the Coriolis torque. Because this circulation also advects ozone, the primary source of radiative heating in this region, coupling between the ozone and dynamical oscillations will be significant in determining the strength of this meridional circulation.
Also of importance for the waves themselves are the scale-dependent radiative damping rate and, in the Rossby-gravity wave, the effect of latitudinal shear.
Abstract
Instabilities arising on a latitudinally sheared mean flow fall into one of at least two classes: inertial instabilities associated with a reversed potential vorticity and barotropic instabilities associated with a reversed meridional gradient of potential vorticity. Both types of instability are described by the generalized Laplace tidal equation, a horizontal structure equation that explicitly includes the effect of horizontal divergence on the disturbances. The effect of horizontal divergence on barotropic instability has not been extensively studied. A systematic investigation of the eigenfunctions of the generalized Laplace tidal equation for monotonic mean zonal wind profiles having a single, narrow region of reversed vorticity gradient in tropical latitudes reveals that, in the limit of low planetary zonal wavenumber, the modes of barotropic instability bifurcate into weakly divergent modes of hemispheric scale, and strongly divergent, “internal” modes trapped about the source region, i.e., equatorially trapped. Disturbances in the second category penetrate into the deep tropics—the side of the critical latitude with positive intrinsic frequency—as a Kelvin wave type of behavior not previously seen in this context.
These results suggest, first, that hemispheric barotropic instability need not be purely nondivergent. In fact, the growth of weakly divergent modes is preferred. Their equivalent depth is similar to that of free neutral modes of the homogeneous vertical structure equation. Second, the existence of equatorially trapped divergent barotropic instability may be of interest in the tropical troposphere and mesosphere. The equatorial amplitude of these disturbances can be significant, and their frequency, which is generally less than that of a dry Kelvin wave, is determined by a critical latitude in the region of reversed vorticity gradient.
Abstract
Instabilities arising on a latitudinally sheared mean flow fall into one of at least two classes: inertial instabilities associated with a reversed potential vorticity and barotropic instabilities associated with a reversed meridional gradient of potential vorticity. Both types of instability are described by the generalized Laplace tidal equation, a horizontal structure equation that explicitly includes the effect of horizontal divergence on the disturbances. The effect of horizontal divergence on barotropic instability has not been extensively studied. A systematic investigation of the eigenfunctions of the generalized Laplace tidal equation for monotonic mean zonal wind profiles having a single, narrow region of reversed vorticity gradient in tropical latitudes reveals that, in the limit of low planetary zonal wavenumber, the modes of barotropic instability bifurcate into weakly divergent modes of hemispheric scale, and strongly divergent, “internal” modes trapped about the source region, i.e., equatorially trapped. Disturbances in the second category penetrate into the deep tropics—the side of the critical latitude with positive intrinsic frequency—as a Kelvin wave type of behavior not previously seen in this context.
These results suggest, first, that hemispheric barotropic instability need not be purely nondivergent. In fact, the growth of weakly divergent modes is preferred. Their equivalent depth is similar to that of free neutral modes of the homogeneous vertical structure equation. Second, the existence of equatorially trapped divergent barotropic instability may be of interest in the tropical troposphere and mesosphere. The equatorial amplitude of these disturbances can be significant, and their frequency, which is generally less than that of a dry Kelvin wave, is determined by a critical latitude in the region of reversed vorticity gradient.
