Stratospheric sudden warming as a threshold behavior of Rossby waves

2020 ◽  
Author(s):  
Noboru Nakamura
Keyword(s):  
Zonal Wind ◽  
Rossby Waves ◽  
Vortex Breakdown ◽  
Finite Amplitude ◽  
Wave Activity ◽  
Reference State ◽  
Threshold Behavior ◽  
Mean Flow ◽  
Transient Wave ◽  
Wave Activity Flux

<p>We present evidence that stratospheric sudden warmings (SSWs) are, on average, a threshold behavior of finite-amplitude Rossby waves arising from wave-mean flow interaction. Competition between an increasing wave activity and a decreasing zonal-mean zonal wind sets a limit to the upward wave activity flux of a stationary Rossby wave.  A rapid, spontaneous vortex breakdown occurs once the upwelling wave activity flux reaches the limit, or equivalently, once the zonal-mean zonal wind drops below a certain fraction of the wave-free, reference-state wind obtained from the zonalized quasigeostrophic potential vorticity.  This threshold faction is 0.5 in theory and about 0.3 in reanalyses.  We use the ratio of the zonal-mean zonal wind to the reference-state wind as a local, instantaneous measure of the proximity to vortex breakdown, i.e. preconditioning.  The ratio generally stays above the threshold during strong-vortex winters until a pronounced final warming, whereas during weak-vortex winters it approaches the threshold early in the season, culminating in a precipitous drop in midwinter as SSWs form. The essence of the threshold behavior is captured by a semiempirical 1D model of SSWs, analogous to the “traffic jam” model of Nakamura and Huang for atmospheric blocking. This model predicts salient features of SSWs including rapid vortex breakdown and downward migration of the wave activity/zonal wind anomalies, with analytical expressions for the respective timescales. Model’s response to a variety of transient wave forcing and damping is discussed.</p><p> </p><p> </p><div> </div><p> </p>

scholarly journals Why Are Stratospheric Sudden Warmings Sudden (and Intermittent)?

2020 ◽  
Vol 77 (3) ◽  
pp. 943-964 ◽  
Author(s):  
Noboru Nakamura ◽  
Jonathan Falk ◽  
Sandro W. Lubis
Keyword(s):  
Zonal Wind ◽  
Vortex Breakdown ◽  
Finite Amplitude ◽  
Wave Activity ◽  
Threshold Behavior ◽  
Mean Flow ◽  
Transient Wave ◽  
Wave Forcing ◽  
Stratospheric Sudden Warmings ◽  
Wave Activity Flux

Abstract This paper examines the role of wave–mean flow interaction in the onset and suddenness of stratospheric sudden warmings (SSWs). Evidence is presented that SSWs are, on average, a threshold behavior of finite-amplitude Rossby waves arising from the competition between an increasing wave activity A and a decreasing zonal-mean zonal wind u¯. The competition puts a limit to the wave activity flux that a stationary Rossby wave can transmit upward. A rapid, spontaneous vortex breakdown occurs once the upwelling wave activity flux reaches the limit, or equivalently, once u¯ drops below a certain fraction of uREF, a wave-free, reference-state wind inverted from the zonalized quasigeostrophic potential vorticity. This fraction is 0.5 in theory and about 0.3 in reanalyses. We propose r≡u¯/uREF as a local, instantaneous measure of the proximity to vortex breakdown (i.e., preconditioning). The ratio r generally stays above the threshold during strong-vortex winters until a pronounced final warming, whereas during weak-vortex winters it approaches the threshold early in the season, culminating in a precipitous drop in midwinter as SSWs form. The essence of the threshold behavior is captured by a semiempirical 1D model of SSWs, similar to the “traffic jam” model of Nakamura and Huang for atmospheric blocking. This model predicts salient features of SSWs including rapid vortex breakdown and downward migration of the wave activity/zonal wind anomalies, with analytical expressions for the respective time scales. The model’s response to a variety of transient wave forcing and damping is discussed.

scholarly journals Finite-Amplitude Wave Activity and Mean Flow Adjustments in the Atmospheric General Circulation. Part I: Quasigeostrophic Theory and Analysis

2010 ◽  
Vol 67 (12) ◽  
pp. 3967-3983 ◽  
Author(s):  
Noboru Nakamura ◽  
Abraham Solomon
Keyword(s):  
Zonal Wind ◽  
Finite Amplitude ◽  
Wave Activity ◽  
Reference State ◽  
The Arctic ◽  
Surface Boundary ◽  
Mean Flow ◽  
Amplitude Wave ◽  
Finite Amplitude Wave Activity ◽  
Mean State

Abstract A diagnostic relationship between finite-amplitude wave activity and the associated adiabatic adjustments to the zonal-mean zonal wind and temperature is developed in the quasigeostrophic (QG) framework and is applied to a 23-yr segment (1979–2001) of the 40-yr ECMWF Re-Analysis (ERA-40) data. Wave activity is defined in terms of an instantaneous areal displacement of QG potential vorticity (PV) from zonal symmetry. Unlike previous forms, the tendency of wave activity equals exactly the negative of the eddy PV flux (Eliassen–Palm flux divergence) in the conservative limit, even at finite amplitude. This allows one to integrate the transformed Eulerian mean (TEM) theory in time and quantify the departure (adiabatic adjustment) of the zonal-mean state from an eddy-free reference state in terms of the observed wave activity. The structure of wave activity identifies synoptic eddies in the extratropics and planetary waves in the high latitudes of winter-to-spring stratosphere. In addition, a thin layer of high wave activity is found at the top of the lowermost stratosphere (∼17 km) in the summer extratropics. The reference state is constructed by “zonalizing” the PV contours conservatively (preserving area) on the isobaric surface and by inverting the resultant PV gradient for the mean flow. The adjustment associated with wave activity depends on the assumed surface boundary condition for the reference state. With a no-slip condition, the observed zonal-mean temperature is on average ∼33 (90) K higher than the reference state in the troposphere (stratosphere) of the Arctic winter, while the zonal-mean zonal wind is ∼30 m s−1 slower in the upper stratosphere. Since the reference state filters out the advective eddy–mean flow interaction, it fluctuates less than the zonal-mean state, potentially improving the signal-to-noise ratio for climate diagnosis.

scholarly journals A Formulation of Unified Three-Dimensional Wave Activity Flux of Inertia–Gravity Waves and Rossby Waves

2013 ◽  
Vol 70 (6) ◽  
pp. 1603-1615 ◽  
Author(s):  
Takenari Kinoshita ◽  
Kaoru Sato
Keyword(s):  
Wave Propagation ◽  
Gravity Waves ◽  
Rossby Waves ◽  
Three Dimensional ◽  
Wave Activity ◽  
Storm Tracks ◽  
Mean Flow ◽  
Wave Activity Flux ◽  
Inertia Gravity Waves ◽  
Dimensional Wave

Abstract A companion paper formulates the three-dimensional wave activity flux (3D-flux-M) whose divergence corresponds to the wave forcing on the primitive equations. However, unlike the two-dimensional wave activity flux, 3D-flux-M does not accurately describe the magnitude and direction of wave propagation. In this study, the authors formulate a modification of 3D-flux-M (3D-flux-W) to describe this propagation using small-amplitude theory for a slowly varying time-mean flow. A unified dispersion relation for inertia–gravity waves and Rossby waves is also derived and used to relate 3D-flux-W to the group velocity. It is shown that 3D-flux-W and the modified wave activity density agree with those for inertia–gravity waves under the constant Coriolis parameter assumption and those for Rossby waves under the small Rossby number assumption. To compare 3D-flux-M with 3D-flux-W, an analysis of the European Centre for Medium-Range Weather Forecasts (ECMWF) Interim Re-Analysis (ERA-Interim) data is performed focusing on wave disturbances in the storm tracks during April. While the divergence of 3D-flux-M is in good agreement with the meridional component of the 3D residual mean flow associated with disturbances, the 3D-flux-W divergence shows slight differences in the upstream and downstream regions of the storm tracks. Further, the 3D-flux-W magnitude and direction are in good agreement with those derived by R. A. Plumb, who describes Rossby wave propagation. However, 3D-flux-M is different from Plumb’s flux in the vicinity of the storm tracks. These results suggest that different fluxes (both 3D-flux-W and 3D-flux-M) are needed to describe wave propagation and wave–mean flow interaction in the 3D formulation.

scholarly journals Finite-Amplitude Wave Activity and Mean Flow Adjustments in the Atmospheric General Circulation. Part II: Analysis in the Isentropic Coordinate

2011 ◽  
Vol 68 (11) ◽  
pp. 2783-2799 ◽  
Author(s):  
Noboru Nakamura ◽  
Abraham Solomon
Keyword(s):  
General Circulation ◽  
Equation System ◽  
Finite Amplitude ◽  
Wave Activity ◽  
Reference State ◽  
Mean Flow ◽  
Negative Wave ◽  
Amplitude Wave ◽  
Upper Troposphere ◽  
Finite Amplitude Wave Activity

Abstract The finite-amplitude wave activity diagnostic developed for quasigeostrophic (QG) flows in Part I is extended to the global primitive equation system in the isentropic coordinate. The Rossby wave activity density A is proportional to Kelvin’s circulation around the wavy potential vorticity (PV) contour minus that around the zonal circle that encloses the same isentropic mass. A quasi-conservative, eddy-free reference state flow uREF is constructed from the observed Kelvin’s circulation by zonalizing the PV contours conservatively while enforcing gradient balance. The departure of the observed zonal-mean flow of the atmosphere from the reference state is defined as the net adjustment by the eddies. Then Δu is further partitioned into the direct eddy drag −A and the residual impulse ΔuR consistent with the time-integrated transformed Eulerian mean (TEM) zonal-wind equation. The analyzed climatological-mean wave activity in the 40-yr European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-40) is similar to that in Part I. The net adjustment Δu is mainly due to the direct eddy drag (Δu ≈ −A) in the winter polar stratosphere and can reach approximately −60 m s−1 in the Northern Hemisphere. In the extratropical troposphere Δu is a small residual (ΔuR ≈ A), yet it clearly reveals a 5–6 m s−1 eddy driving of the Southern Hemisphere jet as well as a 7–8 m s−1 eddy drag in the subtropical upper troposphere of both hemispheres. The local maxima in wave activity in the equatorial upper troposphere and the extratropical lower stratosphere found in Part I are undetected, while negative wave activity is found where the isentropes intersect the ground. As in the QG case, uREF exhibits significantly less transient and interannual variability than , implying a better signal-to-noise ratio as a climate variable.

scholarly journals Quasigeostrophic Transient Wave Activity Flux: Updated Climatology and Its Role in Polar Vortex Anomalies

2010 ◽  
Vol 67 (10) ◽  
pp. 3164-3189 ◽  
Author(s):  
Mototaka Nakamura ◽  
Minoru Kadota ◽  
Shozo Yamane
Keyword(s):  
Lower Troposphere ◽  
Polar Vortex ◽  
Wave Activity ◽  
Vertical Flux ◽  
Storm Tracks ◽  
Mean Flow ◽  
Transient Wave ◽  
Upper Troposphere ◽  
Wave Flux ◽  
Wave Activity Flux

Abstract The climatology of transient wave activity flux defined by Plumb has been calculated for each calendar month, for high-frequency (HF) and low-frequency (LF) waves, using the NCAR–NCEP reanalyses for both hemispheres. Wave activity flux of both HF and LF waves shows upward propagation of waves from the lower troposphere into the upper troposphere, then into the lower stratosphere during the summer and at least up to the midstratosphere during other seasons. While the upward flux emanating from the lower troposphere is particularly large in the two storm tracks in the Northern Hemisphere (NH), it is large in most of the extratropics in the Southern Hemisphere (SH). The HF waves radiate equatorward most noticeably in the upper troposphere, whereas the LF waves do not show visible signs of equatorward radiation. The total horizontal flux is generally dominated by the advective flux that represents the eddy enstrophy advection by the mean flow and appears predominantly pseudoeastward. Divergence of the wave activity flux exhibits discernible large-scale characteristics at the lowest level in both hemispheres and in the upper troposphere in the NH. The divergence field indicates acceleration of the pseudoeastward mean flow near the surface in both hemispheres. In the NH, acceleration and deceleration, respectively, of the pseudoeastward mean flow in the storm tracks and downstream of the storm tracks in the upper troposphere are found. Seasonal variations in the wave flux are substantial in the NH but relatively minor in the SH. In the NH, the wave flux fields exhibit generally larger values during the cold months than during warm months. Also, the latitudes at which large wave flux values are seen are higher during warm months, as the jets and storm tracks shift northward from the winter to the summer. Anomalously large vertical flux of both HF and LF wave activity propagating up from the lower troposphere throughout the troposphere and stratosphere in the northern flank of the North Atlantic storm track is found to precede anomalous deceleration in the NH winter polar vortex, while anomalously small vertical flux in the same area precedes anomalous acceleration of the vortex. The accompanying horizontal flux anomalies tend to counteract the action of the anomalous vertical flux. These cases are found to be dissipation of strong anomalies in the polar vortex. The anomalous flux divergence does not prove the active role of the waves in the anomalous change in the polar vortex, however. No signs of the wave flux originating from specific areas preceding anomalous change in the polar vortex are found for the SH.

The influence of surface topography on rotating convection

1996 ◽  
Vol 313 ◽  
pp. 147-180 ◽  
Author(s):  
Peter I. Bell ◽  
Andrew M. Soward
Keyword(s):  
Surface Topography ◽  
Rossby Waves ◽  
Finite Amplitude ◽  
Length Scale ◽  
Mean Flow ◽  
Radial Temperature ◽  
Static State ◽  
Geostrophic Flow ◽  
Bump Height ◽  
Geostrophic Flows

Busse's annulus is considered as a model of thermal convection inside the Earth's liquid core. The conventional tilted base and top are modified by azimuthal sinusoidal corrugations so that the effects of surface topography can be investigated. The annulus rotates rapidly about its axis of symmetry with gravity directed radially inwards towards the rotation axis. An unstable radial temperature gradient is maintained and the resulting Boussinesq convection is considered at small Ekman number. Since the corrugations on the boundaries cause the geostrophic contours to be no longer circular, strong geostrophic flows may be driven by buoyancy forces and damped by Ekman suction. When the bumps are sufficiently large, instability of the static state is dominated by steady geostrophic flow with the convection pattern locked to the bumps. As the bump size is decreased, oscillatory geostrophic flow is possible but the preferred mode is modulated on a long azimuthal length scale and propagates as a wave eastwards. This mode only exists in the presence of bumps and is not to be confused with the thermal Rossby waves which are eventually preferred as the bump height tends to zero. Like thermal Rossby waves, the new modes prefer to occupy the longest available radial length scale. In this long-length-scale limit, two finite-amplitude states characterized by uniform geostrophic flows can be determined. The small-amplitude state resembles Or & Busse's (1987) mean flow instability. On losing stability the solution jumps to the more robust large-amplitude state. Eventually, for sufficiently large Rayleigh number and bump height, it becomes unstable to a long-azimuthal-length-scale travelling wave. The ensuing finite-amplitude wave and the mean flow, upon which it rides, are characterized by a geostrophic flow, which is everywhere westward.

A Formulation of Three-Dimensional Residual Mean Flow and Wave Activity Flux Applicable to Equatorial Waves

2014 ◽  
Vol 71 (9) ◽  
pp. 3427-3438 ◽  
Author(s):  
Takenari Kinoshita ◽  
Kaoru Sato
Keyword(s):  
Large Scale ◽  
3D Structure ◽  
Three Dimensional ◽  
Wave Activity ◽  
Stokes Drift ◽  
Equatorial Waves ◽  
Mean Flow ◽  
Wave Forcing ◽  
Meridional Cross Section ◽  
Wave Activity Flux

Abstract The large-scale waves that are known to be trapped around the equator are called equatorial waves. The equatorial waves cause mean zonal wind acceleration related to quasi-biennial and semiannual oscillations. The interaction between equatorial waves and the mean wind has been studied by using the transformed Eulerian mean (TEM) equations in the meridional cross section. However, to examine the three-dimensional (3D) structure of the interaction, the 3D residual mean flow and wave activity flux for the equatorial waves are needed. The 3D residual mean flow is expressed as the sum of the Eulerian mean flow and Stokes drift. The present study derives a formula that is approximately equal to the 3D Stokes drift for equatorial waves on the equatorial beta plane (EQSD). The 3D wave activity flux for equatorial waves whose divergence corresponds to the wave forcing is also derived using the EQSD. It is shown that the meridionally integrated 3D wave activity flux for equatorial waves is proportional to the group velocity of equatorial waves.

scholarly journals Formulation of Three-Dimensional Quasi-Residual Mean Flow Balanced with Diabatic Heating Rate and Potential Vorticity Flux

2019 ◽  
Vol 76 (3) ◽  
pp. 851-863
Author(s):  
Takenari Kinoshita ◽  
Kaoru Sato ◽  
Kentaro Ishijima ◽  
Masayuki Takigawa ◽  
Yousuke Yamashita
Keyword(s):  
Potential Vorticity ◽  
Diabatic Heating ◽  
Three Dimensional ◽  
Wave Activity ◽  
Stationary Waves ◽  
Vertical Flow ◽  
Mean Flow ◽  
Material Transport ◽  
Mean State ◽  
Wave Activity Flux

Abstract Three-dimensional (3D) quasi-residual mean flow is derived to diagnose 3D dynamical material transport associated with stationary planetary waves. The 3D quasi-residual mean vertical flow does not include the vertical flow due to tilting of the potential temperature caused by stationary waves, which is apparent but not seen in the mass-weighted isentropic mean state. Thus, the quasi-residual mean vertical flow is balanced with the term of diabatic heating rate. The 3D quasi-residual mean horizontal flow is balanced with the sum of the forcing due to transient wave activity flux divergence and the forcing associated with fluctuation of the potential vorticity due to stationary waves (defined as the effective Coriolis forcing). The zonal mean of the effective Coriolis forcing corresponds to the divergence of stationary wave activity flux. Thus, the zonal mean of derived 3D quasi-residual mean flow is exactly equal to the traditional residual mean flow. To demonstrate the usefulness of this quasi-residual mean flow, we analyze material transport of atmospheric sulfur hexafluoride (SF6) by using an atmospheric chemistry transport model. Comparison between the derived 3D quasi-residual mean flow and traditional residual mean flow shows that the zonal mean of advection of SF6 associated with the 3D quasi-residual mean flow derived is almost equal to that of the traditional residual mean flow. Next, it is confirmed that the horizontal structure of advection of SF6 associated with the 3D quasi-residual mean flow is balanced with the transport because of the nonlinear, nonconservative effects of disturbances. This relation is similar to the results for traditional residual mean flow in the zonal-mean state.

scholarly journals Stratospheric Wave–Mean Flow Feedbacks and Sudden Stratospheric Warmings in a Simple Model Forced by Upward Wave Activity Flux

2014 ◽  
Vol 71 (11) ◽  
pp. 4055-4071 ◽  
Author(s):  
Jeremiah P. Sjoberg ◽  
Thomas Birner
Keyword(s):  
Wave Propagation ◽  
Inversion Layer ◽  
Wave Activity ◽  
Mean Flow ◽  
Stable States ◽  
Mass Model ◽  
Incoming Wave ◽  
Wave Forcing ◽  
The Mean ◽  
Wave Activity Flux

Abstract A classic result of studying stratospheric wave–mean flow interactions presented by Holton and Mass is that, for constant incoming wave forcing (at a notional tropopause), a vacillating stratospheric response may ensue. Simple models, such as the Holton–Mass model, typically prescribe the incoming wave forcing in terms of geopotential perturbation, which is not a proxy for upward wave activity flux. Here, the authors reformulate the Holton–Mass model such that incoming upward wave activity flux is prescribed. The Holton–Mass model contains a positive wave–mean flow feedback whereby wave forcing decelerates the mean flow, allowing enhanced wave propagation, which then further decelerates the mean flow, etc., until the mean flow no longer supports wave propagation. By specifying incoming wave activity flux, this feedback is constrained to the model interior. Bistability—where the zonal wind may exist at one of two distinct steady states for a given incoming wave forcing—is maintained in this reformulated model. The model is perturbed with transient pulses of upward wave activity flux to produce transitions between the two stable states. A minimum of integrated incoming wave activity flux necessary to force these sudden stratospheric warming–like transitions exists for pulses with time scales on the order of 10 days, arising from a wave time scale internal to the model at which forcing produces the strongest mean-flow response. The authors examine how the tropopause affects the internal feedback for this model setup and find that the tropopause inversion layer may potentially provide an important source of wave activity in the lower stratosphere.

scholarly journals Toward the Dynamical Convergence on the Jet Stream in Aquaplanet AGCMs

2015 ◽  
Vol 28 (17) ◽  
pp. 6763-6782 ◽  
Author(s):  
Jian Lu ◽  
Gang Chen ◽  
L. Ruby Leung ◽  
D. Alex Burrows ◽  
Qing Yang ◽  
...  
Keyword(s):  
Wave Breaking ◽  
Effective Diffusivity ◽  
Finite Amplitude ◽  
Wave Activity ◽  
Jet Stream ◽  
Mean Flow ◽  
A Value ◽  
Poleward Shift ◽  
Finite Amplitude Wave Activity ◽  
Large Peclet Number

Abstract Systematic sensitivity of the jet position and intensity to horizontal model resolution is identified in several aquaplanet AGCMs, with the coarser resolution producing a more equatorward eddy-driven jet and a stronger upper-tropospheric jet intensity. As the resolution of the models increases to 50 km or finer, the jet position and intensity show signs of convergence within each model group. The mechanism for this convergence behavior is investigated using a hybrid Eulerian–Lagrangian finite-amplitude wave activity budget developed for the upper-tropospheric absolute vorticity. The results suggest that the poleward shift of the eddy-driven jet with higher resolution can be attributed to the smaller effective diffusivity of the model in the midlatitudes that allows more wave activity to survive the dissipation and to reach the subtropical critical latitude for wave breaking. The enhanced subtropical wave breaking and associated irreversible vorticity mixing act to maintain a more poleward peak of the vorticity gradient, and thus a more poleward jet. Being overdissipative, the coarse-resolution AGCMs misrepresent the nuanced nonlinear aspect of the midlatitude eddy–mean flow interaction, giving rise to the equatorward bias of the eddy-driven jet. In accordance with the asymptotic behavior of effective diffusivity of Batchelor turbulence in the large Peclet number limit, the upper-tropospheric effective diffusivity of the aquaplanet AGCMs displays signs of convergence in the midlatitude toward a value of approximately 107 m2 s−1 for the ∇2 diffusion. This provides a dynamical underpinning for the convergence of the jet stream observed in these AGCMs at high resolution.

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