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- Author or Editor: Timothy J. Dunkerton x

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## 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

Local shear and convective instabilities of internal inertia-gravity waves (IGW) are examined assuming a steady, plane-parallel flow with vertical profiles of horizontal velocity and static stability resembling an IGW packet in a basic state at rest, without mean vertical shear. The eigenproblem can be described in terms of a nondimensional rotation rate *R* = *f*/*ω̂*_{0} < 1*f* is the Coriolis parameter, *ω̂*_{0}*a,* such that *a* = 1 for convectively neutral waves. In the nonrotating case, shear instability is possible only for convectively supercritical waves, with horizontal wavevector aligned parallel or nearly parallel to the plane of IGW propagation. Transverse convection, with wavevector aligned perpendicular to the plane of IGW propagation, displays faster growth than parallel shear or convective instability at any horizontal wavenumber. For intermediate *R,* eigenmodes in supercritical IGW are characterized at small horizontal wavenumber *k* by a transverse mode of convective instability and a parallel mode of shear instability. The transverse mode again has larger growth rate at small *k* but is suppressed at high wavenumbers where parallel convection prevails. Shear production of perturbation kinetic energy in transverse instability is positive (negative) at intermediate or large (small) *R.* For *R* approaching unity, shear instability takes precedence over convective instability at all azimuths regardless of *a.* In this limit, growth of the most unstable mode is almost independent of azimuth. It is shown that the parallel shear instabilities of an IGW are analogous to the unstable modes of a stratified jet.

## Abstract

Local shear and convective instabilities of internal inertia-gravity waves (IGW) are examined assuming a steady, plane-parallel flow with vertical profiles of horizontal velocity and static stability resembling an IGW packet in a basic state at rest, without mean vertical shear. The eigenproblem can be described in terms of a nondimensional rotation rate *R* = *f*/*ω̂*_{0} < 1*f* is the Coriolis parameter, *ω̂*_{0}*a,* such that *a* = 1 for convectively neutral waves. In the nonrotating case, shear instability is possible only for convectively supercritical waves, with horizontal wavevector aligned parallel or nearly parallel to the plane of IGW propagation. Transverse convection, with wavevector aligned perpendicular to the plane of IGW propagation, displays faster growth than parallel shear or convective instability at any horizontal wavenumber. For intermediate *R,* eigenmodes in supercritical IGW are characterized at small horizontal wavenumber *k* by a transverse mode of convective instability and a parallel mode of shear instability. The transverse mode again has larger growth rate at small *k* but is suppressed at high wavenumbers where parallel convection prevails. Shear production of perturbation kinetic energy in transverse instability is positive (negative) at intermediate or large (small) *R.* For *R* approaching unity, shear instability takes precedence over convective instability at all azimuths regardless of *a.* In this limit, growth of the most unstable mode is almost independent of azimuth. It is shown that the parallel shear instabilities of an IGW are analogous to the unstable modes of a stratified jet.

## 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

A semiannual oscillation in monthly mean wind has been observed in the upper mesosphere over Ascension Island (8°S) and Kwajalein (9°N). It is suggested that the selective transmission of gravity and Kelvin waves through the lower-level stratopause semiannual oscillation is responsible for this “mesopause” semiannual oscillation. No *in situ* semiannual forcing is required at the mesopause.

The theoretical model developed here also illustrates the importance of the time-mean component of the mean zonal flow as it affects wave propagation through the equatorial middle atmosphere.

## Abstract

A semiannual oscillation in monthly mean wind has been observed in the upper mesosphere over Ascension Island (8°S) and Kwajalein (9°N). It is suggested that the selective transmission of gravity and Kelvin waves through the lower-level stratopause semiannual oscillation is responsible for this “mesopause” semiannual oscillation. No *in situ* semiannual forcing is required at the mesopause.

The theoretical model developed here also illustrates the importance of the time-mean component of the mean zonal flow as it affects wave propagation through the equatorial middle atmosphere.

## Abstract

Rawinsonde data from tropical Pacific stations were examined for westward-propagating 3–6-day meridional wind oscillations in the troposphere and lower stratosphere, 1973–1992. Four types were identified from cross- spectrum and principal component analysis. 1) The dominant oscillation, near 250 mb, had a period slightly greater than 5 days, zonal wavenumber 4–6, and modified Rossby-gravity structure near the date line. 2) In the western Pacific lower troposphere there was broadband activity with short zonal scale, coupled to upper- tropospheric waves in NH summer. 3) In the central Pacific, during NH autumn, there was a well-defined ∼4½-day oscillation with maximum amplitude in the lower troposphere and baroclinic phase tilt above. The vertical structure suggested coupling to deep tropical convection; this interpretation was supported by correlation of meridional wind with antisymmetric outgoing longwave radiation. 4) In the stratosphere, Rossby-gravity waves had periods ≤4 days and zonal wavenumber 3-4. Unlike tropospheric waves, these disturbances were coherent in a *shallow* layer, largest in west phase of QBO and annual cycle (NH winter-spring).

## Abstract

Rawinsonde data from tropical Pacific stations were examined for westward-propagating 3–6-day meridional wind oscillations in the troposphere and lower stratosphere, 1973–1992. Four types were identified from cross- spectrum and principal component analysis. 1) The dominant oscillation, near 250 mb, had a period slightly greater than 5 days, zonal wavenumber 4–6, and modified Rossby-gravity structure near the date line. 2) In the western Pacific lower troposphere there was broadband activity with short zonal scale, coupled to upper- tropospheric waves in NH summer. 3) In the central Pacific, during NH autumn, there was a well-defined ∼4½-day oscillation with maximum amplitude in the lower troposphere and baroclinic phase tilt above. The vertical structure suggested coupling to deep tropical convection; this interpretation was supported by correlation of meridional wind with antisymmetric outgoing longwave radiation. 4) In the stratosphere, Rossby-gravity waves had periods ≤4 days and zonal wavenumber 3-4. Unlike tropospheric waves, these disturbances were coherent in a *shallow* layer, largest in west phase of QBO and annual cycle (NH winter-spring).

## Abstract

This paper investigates the occurrence, formation, and maintenance of eyes in idealized axisymmetric balanced vortices with diabatic forcing. Two key elements of the model setup are temperature relaxation toward a specified equilibrium temperature *T _{e}* and Ekman pumping from a turbulent boundary layer. Furthermore, the flow is assumed to be almost inviscid in the interior. The model does not attempt any closure for moist convection. Previous work by the authors has shown that there is a continuous transition from monsoonlike vortices to hurricane-like vortices. This transition is governed by the ratio

*α*/

_{T}*c*, where

_{D}*α*is the thermal relaxation rate and

_{T}*c*the surface drag coefficient.

_{D}An eye is defined in terms of the vertical wind with maximum upwelling occurring at some finite radius rather than at the origin. It is possible to obtain an eye even though *T _{e}* maximizes at the origin, that is, even though

*T*does not directly predispose upwelling at some finite radius. The occurrence of an eye is controlled by

_{e}*T*. The key role of

_{e}## Abstract

This paper investigates the occurrence, formation, and maintenance of eyes in idealized axisymmetric balanced vortices with diabatic forcing. Two key elements of the model setup are temperature relaxation toward a specified equilibrium temperature *T _{e}* and Ekman pumping from a turbulent boundary layer. Furthermore, the flow is assumed to be almost inviscid in the interior. The model does not attempt any closure for moist convection. Previous work by the authors has shown that there is a continuous transition from monsoonlike vortices to hurricane-like vortices. This transition is governed by the ratio

*α*/

_{T}*c*, where

_{D}*α*is the thermal relaxation rate and

_{T}*c*the surface drag coefficient.

_{D}An eye is defined in terms of the vertical wind with maximum upwelling occurring at some finite radius rather than at the origin. It is possible to obtain an eye even though *T _{e}* maximizes at the origin, that is, even though

*T*does not directly predispose upwelling at some finite radius. The occurrence of an eye is controlled by

_{e}*T*. The key role of

_{e}## Abstract

Horizontal wind and temperature data obtained from operational radiosondes over Japan have recently been available with high vertical resolution. Analyzing these data over 4 yr has indicated horizontal velocity layers with vertical scales of about 5 km lasting for a week or more. The layers appear frequently in winter at several stations simultaneously and are dominant in the height range of 8–16 km. An empirical orthogonal function (EOF) analysis for the time series of layered disturbance amplitude in winter indicates that there are two dominant principal components. The first component (EOF1) describes layered disturbances in the middle of Japan (30°–37°N) and the second one (EOF2) describes disturbances in the south of Japan (23°–30°N). Using global analysis data, the background field of the layered disturbances was examined. An interesting result is that the background potential vorticity (PV) is approximately zero or negative for EOF2 disturbances even though located in a relatively high-latitude region. This fact suggests that the EOF2 disturbances are due to inertial instability. It is also shown that negative PV occurs more than 30% of the time in winter, in a zonally elongated region of 23°–29°N in the western Pacific, on an isentropic surface of 345 K (∼10 km altitude). Such a high frequency of negative PV is not observed at other longitudes in this latitude band. To determine the origin of the anomalous PV, backward trajectories were analyzed. For EOF2 disturbances, air parcels having mostly negative PV are traced back to the equatorial region in the longitude band 20°W–140°E within a few days. This is due to a strong northward branch of the Hadley circulation associated with deep convection over the Maritime Continent and a strong northeastward subtropical jet stream. On the other hand, the background PV is low but scarcely negative for EOF1 disturbances. Air parcels at EOF1 stations are traced back to the far west because they are advected mostly by a strong eastward jet stream. Thus, it is inferred that the EOF1 disturbances may be due to inertia–gravity waves trapped in a duct of the westerly jet core.

## Abstract

Horizontal wind and temperature data obtained from operational radiosondes over Japan have recently been available with high vertical resolution. Analyzing these data over 4 yr has indicated horizontal velocity layers with vertical scales of about 5 km lasting for a week or more. The layers appear frequently in winter at several stations simultaneously and are dominant in the height range of 8–16 km. An empirical orthogonal function (EOF) analysis for the time series of layered disturbance amplitude in winter indicates that there are two dominant principal components. The first component (EOF1) describes layered disturbances in the middle of Japan (30°–37°N) and the second one (EOF2) describes disturbances in the south of Japan (23°–30°N). Using global analysis data, the background field of the layered disturbances was examined. An interesting result is that the background potential vorticity (PV) is approximately zero or negative for EOF2 disturbances even though located in a relatively high-latitude region. This fact suggests that the EOF2 disturbances are due to inertial instability. It is also shown that negative PV occurs more than 30% of the time in winter, in a zonally elongated region of 23°–29°N in the western Pacific, on an isentropic surface of 345 K (∼10 km altitude). Such a high frequency of negative PV is not observed at other longitudes in this latitude band. To determine the origin of the anomalous PV, backward trajectories were analyzed. For EOF2 disturbances, air parcels having mostly negative PV are traced back to the equatorial region in the longitude band 20°W–140°E within a few days. This is due to a strong northward branch of the Hadley circulation associated with deep convection over the Maritime Continent and a strong northeastward subtropical jet stream. On the other hand, the background PV is low but scarcely negative for EOF1 disturbances. Air parcels at EOF1 stations are traced back to the far west because they are advected mostly by a strong eastward jet stream. Thus, it is inferred that the EOF1 disturbances may be due to inertia–gravity waves trapped in a duct of the westerly jet core.

## Abstract

This paper provides a unified perspective on the dynamics of hurricane- and monsoonlike vortices by identifying them as specific limiting cases of a more general flow system. This more general system is defined as stationary axisymmetric balanced flow of a stably stratified non-Boussinesq atmosphere on the *f* plane. The model is based on the primitive equations assuming gradient wind balance in the radial momentum equation. The flow is forced by heating in the vortex center, which is implemented as relaxation toward a specified equilibrium temperature *T _{e}*. The flow is dissipated through surface friction, and it is assumed to be almost inviscid in the interior. The heating is assumed supercritical, which means that

*T*does not allow a regular thermal equilibrium solution with zero surface wind, and which gives rise to a cross-vortex secondary circulation. Numerical solutions are obtained using time stepping to a steady state, where at each step the Eliassen secondary circulation is diagnosed as part of the solution strategy.

_{e}Reality and regularity of the solution is discussed, putting this work in relation to previous work. Scaling analysis suggests that for a given geometry, essential vortex properties are controlled by the ratio *α _{T}*/

*c*, where

_{D}*α*is the rate of thermal relaxation and

_{T}*c*quantifies the strength of surface friction for a given surface wind. For large

_{D}*T*and the vortex shows properties that can be associated with a hurricane including strong cyclonic surface winds. On the other hand, for small

_{e}*T*. The scaling analysis is verified by numerical solutions spanning a wide range of the parameter space. It is shown how the two limiting cases correspond with the respective approximate semianalytical theories presented previously. The results imply an important role of

_{e}*α*for hurricane formation.

_{T}## Abstract

This paper provides a unified perspective on the dynamics of hurricane- and monsoonlike vortices by identifying them as specific limiting cases of a more general flow system. This more general system is defined as stationary axisymmetric balanced flow of a stably stratified non-Boussinesq atmosphere on the *f* plane. The model is based on the primitive equations assuming gradient wind balance in the radial momentum equation. The flow is forced by heating in the vortex center, which is implemented as relaxation toward a specified equilibrium temperature *T _{e}*. The flow is dissipated through surface friction, and it is assumed to be almost inviscid in the interior. The heating is assumed supercritical, which means that

*T*does not allow a regular thermal equilibrium solution with zero surface wind, and which gives rise to a cross-vortex secondary circulation. Numerical solutions are obtained using time stepping to a steady state, where at each step the Eliassen secondary circulation is diagnosed as part of the solution strategy.

_{e}Reality and regularity of the solution is discussed, putting this work in relation to previous work. Scaling analysis suggests that for a given geometry, essential vortex properties are controlled by the ratio *α _{T}*/

*c*, where

_{D}*α*is the rate of thermal relaxation and

_{T}*c*quantifies the strength of surface friction for a given surface wind. For large

_{D}*T*and the vortex shows properties that can be associated with a hurricane including strong cyclonic surface winds. On the other hand, for small

_{e}*T*. The scaling analysis is verified by numerical solutions spanning a wide range of the parameter space. It is shown how the two limiting cases correspond with the respective approximate semianalytical theories presented previously. The results imply an important role of

_{e}*α*for hurricane formation.

_{T}## Abstract

Singular value decomposition (SYD) analysis is frequently used to identify pairs of spatial patterns whose time series are characterized by maximum temporal covariance. It tends to compress complicated temporal covariance between two fields into a relatively few pairs of spatial patterns by maximizing temporal covariance explained by each pair of spatial patterns while constraining them to be spatially orthogonal to the preceding ones of the same field. The resulting singular vectors are sometimes complicated and difficult to interpret physically. This paper introduces a method, an extension of SVD analysis, which linearly transforms a subset of total singular vectors into a set of alternative solutions using a varimax rotation. The linear transformation (known as “rotation"), weighting singular vectors by the square roots of the corresponding singular values, emphasizes geographical regions characterized by the strongest relationships between two fields, so that spatial patterns corresponding to rotated singular vectors are more spatially localized. Several examples are shown to illustrate the effectiveness of the rotation in isolating coupled modes of variability inherent in meteorological datasets.

## Abstract

Singular value decomposition (SYD) analysis is frequently used to identify pairs of spatial patterns whose time series are characterized by maximum temporal covariance. It tends to compress complicated temporal covariance between two fields into a relatively few pairs of spatial patterns by maximizing temporal covariance explained by each pair of spatial patterns while constraining them to be spatially orthogonal to the preceding ones of the same field. The resulting singular vectors are sometimes complicated and difficult to interpret physically. This paper introduces a method, an extension of SVD analysis, which linearly transforms a subset of total singular vectors into a set of alternative solutions using a varimax rotation. The linear transformation (known as “rotation"), weighting singular vectors by the square roots of the corresponding singular values, emphasizes geographical regions characterized by the strongest relationships between two fields, so that spatial patterns corresponding to rotated singular vectors are more spatially localized. Several examples are shown to illustrate the effectiveness of the rotation in isolating coupled modes of variability inherent in meteorological datasets.