Sudden Stratospheric Warmings (SSWs) in WACCM


Although many of the changes to the climate that develop are from negative radiation anomalies, variability in the stratosphere creates notable regional signatures in the aftermath of a soot injection into the lower stratosphere / upper troposphere. Sudden Stratospheric Warmings (SSWs) are one of the major manifestations of natural variability which influences weather from the poles to the mid-latitudes. SSWs are usually defined as zonal-mean zonal wind reversal at 10 hPa and 60N. (Kim et al., 2017) This definition can be influenced by bias, such that models with a weaker climatological polar vortex has more frequent SSWS. A model could simulate a higher frequency of SSWs by having a weaker vortex, because it is easier to decelerate the zonal winds from 10 to <0, compared to 20 to <0.

SSWs are characterized by a reversal of the zonal winds as well as a warming of stratospheric temperatures by tens of degrees within a few days, reversing the climatological temperature gradient. In modeling studies, it has been found that a warmer climate will have more frequent SSWs, as SSWs occur due to the upward flux of wave activity into the stratosphere.


'To ensure a focus on midwinter SSWs, final warming events are excluded by adopting the method proposed by Charlton and Polvani (2007).'

'Polvani and Waugh (2004) showed that the upward wave activity entering the stratosphere, integrated over 20 days or longer, leads to a marked weakening of the polar vortex' Analysis of reanalysis finds that there are an average of 0.46 events per year in the northern hemisphere. 'de la Torre etal. [2012] found that the frequency of major SSW events in WACCM is very similar to that found in reanalysis data,although the major SSW events are generally prolonged in WACCM and occur disproportionately often in December.'
(Holt et al., 2013)




Advanced literature review

A New Look at Stratospheric Sudden Warmings. Part I: Climatology and Modeling Benchmarks
Charlton and Polvani, 2007

SSWs clearest and strongest manifestation of dynamic coupling in stratosphere-troposphere system.
--> focus on major midwinter warming events ... major events occur 6 times per decade.
--> separate events that do and do not split the stratosphere polar vortex (splitting vs displaced from pole)
Vortex splitting occurs after clear preconditioning of polar vortex.
--> influence on mid stratosphere temperatures lasts 20+ days, longer than vortex displacement
--> influence on troposphere insensitive to event type

Matsuno, 1971: Early Models of SSWs

A dynamical model of the SSW, discussed in terms of interaction of vertically propagating planetary waves with zonal winds.

*Global scale disturbances are generated in troposphere, propagate upward into stratosphere
-->waves act to decelerate polar night jet through 'induction of a meridional circulation'.
*'Critical layer interaction' occurs at layer where zonal winds reverse
Vertical propagation of planetary waves and interaction with zonal winds...
3 Major Features
1) Distortion and breakdown of stratospheric polar vortex.
2) Sudden warming of polar air reverses meridional temperature gradient.
3) Circumpolar easterly winds.

Polar night jet is NOT stable to wave disturbances.
Wexler (1959): not enough evidence that breakdown occurs spontaneously due to instability because it does not occur in the Southern Hemisphere. However, the inhomogeneity of the Earth's surface is far greater in Northern Hemisphere, influencing planetary scale disturbance.
* Growth of planetary waves in stratosphere is thus supplied by the troposphere -- weakening of polar night jet can not be attributed to energy conversion to eddies.

Miyakoda et al., (1970) : found that SSW caused by penetration of wave disturbances from lower part of atmosphere -- mechanisms details not clear.

Matsuno 1971 model: planetary wave propagation and interaction with zonal winds.

Charney-Drazin Theorem (1961):: the change of zonal mean fields by vertically propagating plentary waves should vanish.
Planetary scale geostrophic disturbances can propagate from troposphere to stratosphere if prevailing winds are moderate westerlies (relative to phase velocity of waves).

Zonal wave numbers 1 and 2 can propagate vertically (at the limit of what is possible, however).
--> planetary waves can not propagate in easterly winds ...
--> when waves reach the critical level, wave amplitude decreases rapidly and wave energy flow vanishes.
Implication is wave energy is absorbed where zonal velocity becomes zero.



The expression (dB/dz) - (dM/dy) is identically zero - if wave is stationary and u is not 0. (Eliassen and Palm, 1961).
--> if critical level or dissipative effects not incorporated, RHS of (1) does not vanish.
Although conditions under which RHS of (1) vanishes are not fulfilled in winter stratosphere, C-D theorem valid to a first approximation in the following sense:
Planetary waves in general, transport heat and momentum, theorem would mean effects of eddy fluxes and mean meridional circulation cancel each other ... zonal mean field unchanged.
Hiroto and Sato (1969) found the actual change of zonal wind velocity is very poorly correlated with convergence of eddy momentum flux, suggested C-D theorem may hold in ordinary situations.
Where the C-D theorem can not be applied will explain SSW within the framework of planetary wave-zonal interaction.

Assumptions: beta plane, atmosphere bounded laterally by vertical walls at 2 lattitudes, extending infintely in vertical direction.
Wave has no phase variation in latitudinal direction. Wave transports no momentum, forcing to mean height change occurs only when heat transport varies with height.

First: consider a situation in which basic wind profile has critical level at height zc.
--> heat flux jumps from positive to 0 in crossing zc. Equation 1 becomes:



The zonal mean heights tend to rise in higher latitudes and fall in lower. Mean meridional circulation is implicit in the sollution.
Since upward propagating planetary waves accompany poleward heat transport (Eliassen and Palm, 1961), there is a heating tendency at higher latitudes and cooling at lower as a result of flux divergence.
Effect forces zonal mean upward motion at higher latitudes and downard motion at lower latitudes.
--> forced vertical motions diminish above critical level because heat transport vanishes there..
--> to satisfy continuity of mass flux, must be a flow from higher to lower latitudes near critical level.
The coriolis force acts on this 'wave-induced meridional circulation' and is the origin of easterly acceleration.
temperature change results from balance between eddy heating and effect of mean vertial motion. --> below the critical level, the eddy heating exceeds the effect of the mean vertical motion.
--> above the critical level, only vertical motion causes temperature changes.

The solution to (2) is consistent with statement 'rossby waves incident on critical level force southward transport of potential vorticity' (Dickinson, 1970).

Consider the following situation: basic wind is westerly everywhere, planetary waves in transient state of upward propagation ... waves generated from far below and leading edge of waves has reached a certain height zf.
--> wave amplitude as well as heat flux due to waves (B) may decrease with height in vicinity of zf.
Conclusion: upward propagating planetary waves accompany easterly acceleration of zonal winds and warming of the air in the higher latitude side, when the waves are in a building up state.

Contrast: when waves are decaying, second-order effects may act in opposite way.

previous discussion predicated on cases with no momentum transport associated with waves)
If a horizontal flux of zonal momentum exists, can contribute to redistribution of momentum in horizontal layer, but can not cause changes to total momentum in layer.

The model of the sudden warming
Assume: zonally asymmetric circulation with normal winter profile, planetary-scale disturbances (wn 1 and 2) grow with time to reach large amplitude and persist for long time.
--> blocking is observed in parallel with breakdown of polar night jet, reasonable assumption.
Response of the stratosphere
Phase 1
Wave may propagate upward, giving rise to deceleration of westerly jets, weakening polar night jet at same time the disturbance increases its amplitude.
Total flow pattern appears as a deformation, then breakdown of PV.
--> temperature disturbance due to waves becomes significant and zonal mean temperature at high latitudes rises.
Phase 2
eASTERLY ACCELERATION INCREASES with increasing height due to wave amplitude increasing with decrease of air density. At a certain level, wave-induced acceleration destroys westerly jet, creates an easterly jet.
--> once easterly jet appears, critical layer interaction appears
--> planetary waves inhibited from propagating further upward and are absorbed, reducing their amplitude.
Intense warming occurs just below the critical level, easterly winds near critical level accelerated by the waves, lowering the level.
Warming and wind reversal shift downward.
Lindzen-Holton hypothesis (1968): process of absorption of waves at a critical level and consequent descent of the level is consistent with LH 1968 on QBO of equatorial winds.
--> different acceleration mechanisms.
LH scheme: zonal winds accelerated by deposition of zonal momentum transported vertically by equatorial waves.
SSWs: acceleration attributed to coriolis force due to secondary circulation induced by heaet transport by planetary waves.
(Discussions on these two types of zonal wind acceleration by waves have been made by Bretherton (1969), Lindzen (1970), Hayashi (1970).

Model used consists of 1) planetary wave propagation in a zonal wind system and 2) chagne of zonal winds forced by waves.
Adiabatic, geostrophic, potential vorticity equation split into zonal mean and deviation from it. <<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>


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The following definitions are used below, with the temperature condition turned on/off for sensitivity tests. #MAJOR SSW: westerly winds at 60N, 10 hPa reverse (become easterly (positive to negative))
# *zonal mean temperature increases poleward from 60 degrees latitude
#MINOR SSW: westerly winds are slowed but do not reverse
# *significant temperature increase (25 degrees in a period of a week or less)
#FINAL SSW: becomes easterly for the summer
#
# https://journals.ametsoc.org/doi/abs/10.1175/JCLI-D-16-0465.1


Based on reanalysis, an average of 0.46 SSW events occur during DJF when averaged over 50 years. During this 20 year analysis, we found an average of 0.50 SSW events during DJF. #http://scholarworks.sjsu.edu/cgi/viewcontent.cgi?article=8344&context=etd_theses #Based on the reanalysis results, 26 SSW events were identified and occurred with an average of 0.46 events per #winter over the 56 year period. #at 0.50 events per year, control run is PERFECT https://journals.ametsoc.org/doi/pdf/10.1175/JCLI-D-16-0465.1