Introduction
A major sudden stratospheric warming (major SSW) is a dramatic phenomenon
with strong wind disturbance and polar temperature rise in the winter
stratosphere, associated with transport of air from low to high latitudes
see e.g.. The mechanism of SSWs has been understood as
a result of tropospheric waves propagating upwards into the stratosphere and
breaking at a certain level . Planetary-scale waves can be
diagnosed by the Eliassen–Palm (EP) flux and its divergence
e.g.. In particular, positive and negative
values of the EP flux divergence quantify the acceleration and deceleration
of the westerly zonal flow, respectively, driving the Brewer–Dobson (BD)
circulation e.g..
Resolving filamentary structures explicitly and realistically, representing
the dissipation/mixing processes in models, is important for simulating
non-linear chemical reactions accurately
. However, resolving
these structures accurately is a general difficulty for chemical transport
models e.g.. During a SSW
event, strong large-scale planetary waves propagate, break and finally
dissipate – a process that occurs almost isentropically, i.e. on levels with
a constant potential temperature. In the stratospheric chemical tracer
fields, the SSW itself is characterized by the existence of filamentary
structures on a broad range of spatial scales see
e.g. . Therefore,
quantitative understanding of SSWs is a challenge for current chemical
transport models in particular in terms of coupling between dynamics,
transport and chemistry.
To improve the understanding of SSWs, many case studies based on reanalysis
data, modelling and/or satellite data have been performed.
described the synoptic evolution during the
2004 and 2006 sudden stratospheric warmings (SSW). Based on the Aura
Microwave Limb Sounder (MLS) observations, the meteorology and trace gases
from the UTLS (upper troposphere and lower stratosphere) to the lower mesosphere during the 2006 and 2009 SSWs were
extensively studied . Using satellite
temperature measurements during three major SSWs, an anomalously strong
descent of mesospheric air into the upper stratosphere was found, along with
the stratopause breaking down and then reforming above 75 km
. The major SSW in 2009
was the most intensive and prolonged case on record
and this event happened although typical known external factors, e.g. the
quasi-biennial oscillation, the Southern Oscillation and the 11-year sunspot
cycle, were all unfavourable for the occurrence of a SSW .
and studied this event from the
perspective of tropospheric forcing. Both studies pointed out that the
pronounced planetary wave-2 in the stratosphere, which triggered the 2009 SSW, is
associated with a high-pressure ridge over the Pacific.
The remarkable stratospheric warming event in 2009 strongly influenced the
distribution of chemical species. The amount of air transported out of the
polar vortex into the mid latitudes in the mid stratosphere was weak until 1
week before the onset of the major SSW and became strong with a weak vortex
transport barrier within a month after SSW onset until the reestablishment of
a vortex barrier . diagnosed an
increasing trend of occurrence of NH (Northern Hemisphere) major SSWs in recent years (1999–2011).
They confirmed a weakening in the chlorine-induced ozone loss after the onset
of major SSWs during the winters of 2003/04, 2005/06 and 2008/09.
used Global Ozone Monitoring by Occultation of Stars
(GOMOS) satellite measurements to study the O3, NO2 and NO3
distribution during the three major SSWs and found that changes in chemical
composition due to major SSWs can extend into the mesosphere and even into
the lower thermosphere. studied the winter of 2012/13 and
pointed out that, although the chlorine-induce ozone loss became weak after
the onset of SSW, the ozone loss was still significant due to the unusual low
temperature in the lower stratospheric polar vortex and continued confinement
of air in the vortex mainly in December and January.
From the Lagrangian perspective, modelling of transport can be divided into
advection and mixing. Advection is the reversible part of transport which
describes transport of an air parcel along a 3-D trajectory. Mixing, the
irreversible part of transport, makes the representation of transport
barriers in Eulerian models difficult
. Compared to Eulerian transport
models with an implicit numerical diffusion, Lagrangian transport models have
advantages in separating mixing from advection, and thus explicitly describe
the mixing process in the atmosphere. Here, we use the Chemical Lagrangian
Model of the Stratosphere (CLaMS), which is a chemistry transport model with
Lagrangian transport and parametrized mixing induced by atmospheric
deformation . The concept of
deformation-induced mixing parameterization is based on the concept that horizontal flow
deformation produces pronounced filaments and streamers in the stratosphere,
which induce non-linear behaviour on small scales with subsequent mixing.
Advection in CLaMS is driven by the European Centre for Medium-range Weather
Forecasts (ECMWF) ERA-Interim reanalysis horizontal winds u,v, and cross-isentropic
vertical velocity is deduced from diabatic heating rates
.
An appropriate representation of mixing in the models is one main difficulty
for an accurate description of the permeability of transport barriers like
the polar vortex edge or the tropical pipe
. Mixing itself is an
irreversible process which, in a stably stratified stratosphere, is mainly
driven by isentropic stirring that is associated with large-scale wave
breaking and wind shear . assessed the
influence of uncertainties in the atmospheric mixing strength on the global
distribution of the greenhouse gases H2O, O3, CH4 and N2O in the
upper troposphere and lower stratosphere (UTLS) and on the associated
radiative effects. Their results show that simulated radiative effects of
H2O and O3, both characterized by steep gradients in the UTLS, are
particularly sensitive to the atmospheric mixing strength.
To separate and quantify the impact of mixing on transport and chemistry of
stratospheric constituents during a SSW, we utilize tracer–tracer
correlations. Chemical constituents in the stratosphere whose chemical
sources and sinks are slow compared with dynamical timescales, are influenced
by the Brewer–Dobson circulation and by quasi-isentropic mixing (which is
most efficient within the extratropical surf zone in winter) and show compact
tracer–tracer relations . Mixing is suppressed at the edge
of the winter polar vortex and at the edges of the tropics, so that tracer
relationships distinct from those of middle latitudes occur in the tropics
and in the polar vortices
e.g.. Here,
we focus on the relationship of O3 with the long-lived tracer N2O.
Because chemical production and loss terms of O3 increase strongly with
altitude in the stratosphere, ozone can not be considered long-lived at
altitudes above ≈ 20 km and relations with N2O are not
necessarily compact . Conditions are different in the
polar vortex in winter, where the lifetime of ozone exceeds half a year in
the absence of chlorine-catalyzed ozone loss in the lower stratospheric
vortex . However, the transport barriers in the
stratosphere are sufficiently strong to allow distinct tracer–tracer
relationships, in particular different O3–N2O relationships to develop
in the polar vortex, the mid latitudes and in the tropics
.
Because different O3–N2O relationships prevail in the polar
vortex, in mid latitudes and in the tropics, mixing of air masses from these
different regions will change O3–N2O relationships, even if
relations in a particular region are linear (Fig. , top panel).
Mixing between the polar vortex and mid latitudes and between mid latitudes
and the tropics occurs along quasi-isentropic surfaces
. Because of the location of the isentropes in
O3–N2O space, mixing of mid-latitude and polar air will lead
to higher ozone and higher N2O in the polar region, and mixing of
mid-latitude and tropical air will lead to lower N2O and lower ozone
in the tropics (Fig. , top panel). The effect of mixing between
polar and mid-latitude air on O3–N2O relationships and the
occurrences of this process along quasi-isentropic surfaces is also clearly
visible in model simulations .
However, the strength of the transport barrier at the vortex edge is likely
underestimated in model simulations so that the intensity
of mixing will be overestimated.
Schematic diagram showing the influences of (a) mixing,
(b) up- and downwelling and (c) chemistry on N2O–O3
correlations.
Upwelling and downwelling of stratospheric air changes tracer mixing ratios
at a particular altitude (or potential temperature level) but does
not change the tracer–tracer correlation . Therefore
O3–N2O relationships will not be affected by up- and
downwelling (Fig. , middle panel), while however the location of
the potential temperature surfaces in O3–N2O space will
change. Because of the vertical profile of ozone and N2O below
altitudes of ≈700 K, downwelling in the polar region will lead to
an upward bending (more ozone, less N2O) of the isentropes, while
upwelling in the tropics will lead to downward bending (less ozone, more
N2O) of the isentropes (Fig. , middle panel, grey
lines).
Finally, chemistry will impact O3–N2O relationships;
indeed ozone–tracer relations have been used extensively to examine
lower stratospheric ozone loss in the polar regions
e.g.. On the
timescales and for the altitudes of interest here, only chemical
change for ozone needs to be taken into account. Thus, chemical loss
of ozone in the polar regions shifts the O3–N2O
relationship downward, towards lower ozone mixing ratios and chemical
production of ozone in the tropics will shift the
O3–N2O relationship upwards towards higher ozone
mixing ratios (solid and dashed black lines in Fig. , bottom panel).
In a model simulation the impact of chemistry on
ozone–tracer relations can be investigated further through simulations using
passive (i.e. chemically inert) ozone; this point will be discussed below in
Sect. 5.
The motivation of this work is to improve our understanding of transport and
its impact on chemistry in the stratosphere under strongly disturbed dynamical
conditions. In particular, the 2009 major SSW is an excellent case for
studying: (1) the multi-timescale (days to months) responses to the wave
forcing; (2) the evolution of mixing and its effect on distribution of
chemical composition; and (3) the observed tracer–tracer correlations using CLaMS
simulations. In Sect. , we will present an overview of the
dynamical background of the stratospheric winter 2008/09. The CLaMS setup and
validation of CLaMS result with the MLS observations of N2O and O3 will
be presented in Sect. 3. Section 4 will discuss the simulated mixing
intensity in relation to wave forcing. Finally, Sect. 5 will present the
N2O–O3 correlations and their interpretation in terms of mixing,
advection and chemistry caused by the major SSW in January 2009. Finally, the
main results will be concluded in Sect. 6.
Dynamical background
The definitions for SSW and classifications are extensively discussed by
. According to commonly used criteria
, we identify the warming event on 24
January by the reversal of 60∘ N westerly zonal-mean wind at
10 hPa. As has been pointed out , use of the
highest polar cap temperature instead of the zonal wind reversal at
60∘ N and 10 hPa, characterizes the response of the BDC to SSWs
better. Thus, we identify the central SSW day as the date when 5-day smoothed
polar cap temperature at 10 hPa reach its peak within ±5 days of the
wind reversal date. 23 January is used as the central day in our study
because the polar cap temperature reached its peak on 23 January.
(a) Polar cap area weighted mean temperature
(60–90∘ N) overlaid with zonal mean easterlies at 60∘ N (black contours in m s-1),
(b) tropical zonal mean temperature anomaly from the 24-year climatology (0–20∘ N),
(c) eddy heat flux (40–70∘ N, black) on 100 hPa and its
decomposition into wave-1 (blue) and wave-2 (red) components
(d) polar mean (60–90∘ N) anomaly of the heating rates from
the 24-year climatology Q=dθ/dt=θ˙ (for more details see the text),
(e) same as (d) but for 0–30∘ N.
The figures are based on the ERA-Interim reanalysis.
Figure gives an overview of the dynamical background during the
boreal winter 2008/09 based on ERA-Interim reanalysis. Figure a
shows that the sudden rise of the polar cap temperature started in the upper
stratosphere, around 10 January at 1 hPa. Thereafter, the warming propagated
downward, arriving at 10 hPa and descended to the lower stratosphere until
late January. The increase of polar temperature was accompanied by the
generation of easterlies, which are also shown in Fig. a (black
contours). The rise in easterlies and temperature lasted only 10 days at
1 hPa followed by a strong polar vortex cooling while the disturbance of
wind and temperature in the lower stratosphere lasted more than 1 month
without a complete recovery until the final warming in the spring of 2009.
Before the major SSW, the lower stratosphere in the tropics was slightly
warmer than the long-term average due to the westerly phase of the QBO in
this winter. Similar to the warming in the high latitudes, the tropical
cooling (Fig. b) also started at about 15 January at 1 hPa and
descended from the upper to the lower stratosphere over 2 weeks. As discussed
in , time-dependent upwelling in the tropical lower
stratosphere is correlated with transient extratropical planetary waves,
which transport heat from the tropics to high latitudes and, in turn, drive
the BD-circulation.
A widely used diagnostic of the upward-propagating planetary waves is the
vertical component of the EP flux, for which the strongest contribution
results from the horizontal eddy heat flux v′T′‾ with
v′=v-v¯, T′=T-T¯ and with the overbar denoting zonal mean and
primes describing the deviations (i.e. fluctuations) for the temperature T
and for the meridional velocity v .
Figure e shows the time evolution of the eddy heat flux at
100 hPa averaged between 40 and 70∘ N, which explains more than
80 % of the variability of the total vertical component of the EP flux. In
addition, contributions of the wave-1 and wave-2 components to the mean eddy
heat flux are also shown.
pointed out that the eddy heat flux measures activity of
the waves and is highly correlated with the time evolution of the
stratospheric polar temperature. As can be deduced from Figs. e
and a (or Fig. b), the mean eddy heat flux at
100 hPa was well correlated with warming at the North Pole and cooling in
the tropics. It shows a 1–2 weeks oscillation ranging within
0–25 K m s-1 in December and it began to increase from 6 January
reaching the first peak on 18 January. After several days of a slight decay,
it rose up to the second peak on 27 January and then gradually declined to
zero around mid-February with some small fluctuations afterwards. The
dominant wave number before and during the major SSW was wave-2, which led to
the vortex split. The dominant and extraordinary planetary wave-2 is
associated with unusual development of the upper tropospheric ridge over
Alaska . However, after the major SSW, the
main contribution to the total eddy heat flux resulted from higher wave
numbers.
Large-scale tropospheric waves can propagate upward into the stratosphere
through weak westerlies and break at the critical level, disturbing the mean
flow . Such a transient wave breaking
converts the zonal flow momentum to mean meridional circulation, and thus
drives the extra-tropical downwelling and tropical upwelling of the BD
circulation e.g. . The temperature perturbations
discussed above and shown in Fig. a, b result directly from
diabatic heating and cooling caused by these wave-driven vertical motions.
Subsequently, temperatures gradually relax toward their radiative equilibrium
values by additional radiative cooling or heating, causing vertical motion,
i.e. down- or upwelling, through isentropic surfaces. The polar and tropical
(total) diabatic heating rate anomalies from the 24-year mean of ECMWF
meteorological ERA-Interim reanalysis are shown in
Fig. d, e. As expected, diabatic polar downwelling and tropical
upwelling (quantified by these heating rates) were both accelerated after the
onset of the major SSW. The polar vortex descent rate strongly increased
around 25 January up to 15 K day-1 on 1000 K and only around
3 K day-1 on 500 K during the late January. The variability of polar
vortex descent rate reported here is consistent with findings by
and where the tracer isopleths method
based on MLS observations of N2O, CO and H2O was used. The onset of the
heating rate anomalies at each altitude, and thus their downward propagation,
is roughly synchronous with the temperature anomalies shown in
Fig. a, b. The radiative decay of the anomalies takes only about
10 days at 1000 K, but more than 1 month below 500 K. This is consistent
with the stratospheric radiative relaxation time inferred from satellite
measurements , which was found to increase from 10 days
at 1 hPa to about 100 days at 50 hPa. This is also consistent with a strong
suppression of planetary-wave propagation into the vortex after the major SSW
.
Model description and validation
Model setup
CLaMS is a Lagrangian chemistry transport model that can be run with or
without mixing, so that the whole transport is carried out only along 3-D
forward trajectories. However, a pure Lagrangian transport approach gives
rise to many unrealistic small-scale structures due to lack of mixing
. Hence, irreversible small-scale mixing
between air parcels (APs) should be considered. With the concept that
(small-scale) mixing is driven by large-scale flow deformation, the CLaMS
mixing procedure is realized through adaptive re-gridding of the irregular
grid. More specifically, the APs are inserted or merged when the distances
between the next neighbours increase above or decrease below a critical
distance. The critical deformation γc is defined as
γc=λcΔt, with the critical Lyapunov
exponent λc and the advective time step Δt set to
1.5 day-1 and 24 h, respectively for more details
see.
PDFs (probability distribution functions) of MLS observations and CLaMS reference simulation for the
entire simulation period from 1 December 2008 to 1 April 2009
for APs in the Northern Hemisphere with 400 K <θ< 1000 K
(left: N2O, right: O3).
CLaMS simulations cover the 2008/09 boreal winter from 1 December 2008 to 1
April 2009 and extend between the Earth's surface and the potential
temperature θ=2500 K (i.e. roughly around the climatological position
of the stratopause with p≈0.3 hPa). The horizontal separation of
the APs, which was initialized on 1 December, is 70 km in the NH, where all our results
are obtained, and 200 km in the SH. During the course of the simulation,
this irregular grid of APs undergoes advection along the trajectories,
chemistry and mixing every time step, with Δt=24 h
.
The horizontal winds are prescribed by the ECMWF ERA-Interim reanalysis
. To resolve both transport processes in the troposphere
influenced by the orography and in the stratosphere where adiabatic
horizontal transport dominates, a hybrid coordinate is used as proposed by
. In the stratosphere and in the UTLS, potential
temperature θ is employed as the vertical coordinate of the model
above 300 hPa and the cross-isentropic velocity θ˙=Q is deduced
from the ERA-Interim forecast total diabatic heating rates Q, including the
effects of all-sky radiative heating, latent heat release and diffusive
heating as described by . The time evolution of the
anomaly of θ˙ averaged over the polar cap and over the tropics is
shown in Fig. c, d and was discussed in the previous section.
N2O and O3, the most important species for this work, are initialized
from the MLS data (more details on MLS can be found in the next subsection).
The other chemical species are initialized from a multi-annual CLaMS
simulation with simplified chemistry as well as from
gridded MLS data of HCl, H2O and CO. The employed method uses
tracer–tracer correlations for more details see. At the
upper boundary (2500 K) O3 is set to the HALOE climatology after every
24 h time step. However, the impact of the upper boundary condition on the
chemical tracers is not significant below 1000 K and our following analyses
are for levels below 1000 K. The chemistry module of CLaMS is described in
detail in .
By switching the mixing module off and on, we get two sets of simulations:
full chemistry without mixing and full chemistry with mixing. The simulation
with full chemistry and with mixing is the reference as the best model
representation of the real atmosphere. Both simulations include ozone
calculated with full chemistry (O3) and passively transported O3
without any chemistry (pO3).
Validation with the MLS observations
MLS observes microwave emission from the limb of the Earth's atmosphere in
the direction of the Aura orbit. The instrument measures vertical profiles
every 165 km (1.5∘ along the Aura orbit), providing about 3500
profiles per day. We use version 3.3 N2O and O3 from the MLS product
both to initialize and to validate the CLaMS reference
simulation. The vertical resolution of O3 is about 2.5–3 km in the
stratosphere with a 5–10 % uncertainty . The vertical
resolution of N2O is about 4–6 km with a 9–25 % uncertainty for the
region of interest in this study . Averaging kernels are
applied in the retrieval of the MLS profiles, which relate the retrieved MLS
profiles to the true atmospheric state.
For comparison, we map CLaMS mixing ratios to the observed MLS profiles using
a back and forward trajectory technique and apply the MLS
averaging kernels to CLaMS output in order to get comparable quantities (see
Appendix). Because CLaMS APs are saved every day only at 12:00 UTC, we
calculate the noon-positions of the MLS observations within a 1-day window
using back and forward trajectories, and then select the nearest CLaMS AP to
the corresponding MLS observation. The mixing ratios at this AP are then
compared with the respective MLS observations.
Hereby, a one-to-one MLS-CLaMS data set for N2O and O3 is established
that is plotted in Fig. as probability distribution functions
(PDFs) calculated for the whole NH and for the entire simulation period
(around 10 thousand points). According to a high correlation coefficient both
for N2O (0.957) and for O3 (0.989), our reference simulation matches
the MLS observations fairly well. The largest difference was diagnosed in the
θ-range between 650 and 1000 K where CLaMS O3 slightly
overestimates the MLS observations. Three possible explanations for this small
bias are: (1) there was not enough NOx-induced ozone loss; (2) there was too much photolytical
ozone production; (3) poleward transport from the tropics was too fast.
For a further comparison, we investigate the horizontal distribution of
N2O. Figure shows the comparison between the CLaMS simulation
and MLS observations for five selected days at θ=800 K (top 2 panels)
and 475 K (bottom 2 panels). On 9 January, the vortex was centred around
the North Pole and the vortex edge was well defined and not changing rapidly
in the middle and lower stratosphere. Mainly influenced by the planetary
wave-2, the polar vortex stretched to North America and Asia on both heights
during the following days. Around the central day of the major SSW at 23
January, a double centre structure formed which split up until 25 January at
475 K and until 28 January at 475 K (not shown).
N2O distribution at θ=800 K (top 2 rows) and 475 K
(bottom 2 rows) interpolated from CLaMS simulation and MLS observations for
five selected days in 2009 before and after the major SSW event. Nash's
criteria is applied to define the edge of the polar vortex
shown as the black contours. According to this method, the vortex edge is
identified as the maximum PV (potential vorticity) gradient with respect to equivalent latitude
constrained by the location of the maximum wind jet calculated along
equivalent latitudes.
In the following days, an increasing number of filaments could be observed
outside of the vortex characterized by low N2O values. The two vortex
centres slowly rotated anticlockwise. One of the vortex remnants over eastern
North America and the Atlantic stretched further, split and dissolved,
releasing its content to mid latitudes, while another one stayed over
northern Asia and the Pacific Ocean. Although in the following weeks most of
the vortex fragments were mixed with mid-latitude air, a part of them, like
those over northern Asia and the Pacific Ocean, re-organized as a new and
relatively weak vortex. However, this top-down process that started in
late February at 800 K (a weak, circumpolar vortex edge can be diagnosed at
θ=800 K at 20 February, see Fig. ) and was finished in
mid March at 475 K (not shown), is excluded from our analysis, which ends with 28
February.
The distribution of simulated N2O accurately represents the MLS
observations, although more filamentary structures are resolved in CLaMS
simulations than MLS observations. It should be noted that applying averaging
kernels to model result also smoothes out some valuable information, e.g.
filamentary structures, and, consequently, may result in a misinterpretation
of the stratospheric composition, especially for high-latitude N2O. More
details are discussed in the Appendix.
Planetary waves and mixing
Transport and mixing barriers in the winter hemisphere
In the winter stratosphere, two main barriers to transport exist, shown
by the two thick blue lines in Fig. . One is
the polar vortex edge, which can be identified as the maximum gradient of
potential vorticity (PV) with respect to equivalent latitude within a certain
range where maximum of wind speed along equivalent latitudes (in the
following eq. latitude) occurs . The second barrier (around
10–30∘ N eq. latitude, varying with altitude) separates the
mid-latitude surf zone from the region of tropical
upwelling, the so-called tropical pipe .
Schematic diagram of transport and mixing processes in the winter
stratosphere. The thick blue lines show the barriers, the grey arrows
indicate the direction of the BD circulation. Yellow shaded areas stand for
strong westerlies. Red two-headed arrows indicate isentropic mixing, with
thicker and thinner arrows showing stronger mixing in the surf zone and
weaker mixing across the transport barriers, respectively. For a better
overview, the tropopause with the subtropical jet are also marked.
This subtropical barrier is not as well-defined as the polar vortex edge and
is usually characterized by a much weaker PV gradient between tropics and
mid latitudes although large meridional tracer gradients
can be diagnosed . While the
polar vortex edge is considered as a meridional transport barrier due to a
strong polar jet, the subtropical barrier is only weakly influenced by the
jets and is usually understood as a barrier for propagation of planetary
waves. This barrier is strongly related to the phase of the quasi-biennial
oscillation (QBO): during the westerly QBO, planetary waves generated in the
winter hemisphere can propagate across the equator to dissipate at the summer
hemisphere easterlies, whereas such propagation is suppressed during the
easterly QBO phase . Thus, during
the 2008/09 winter, the subtropical transport barrier was weakened by the
westerly QBO phase (dashed thick blue line in Fig. ).
In a winter with weak activity of planetary waves and a strong vortex, the
exchange and mixing of air across the vortex edge is suppressed. However,
once a strong sudden warming event happens that usually follows a significant
weakening of vortex edge with exceptions e.g. 2013 SSW,
enhanced wave forcing drives significant isentropic, two-way mixing (red
curved arrows) as well as the large-scale BD circulation (grey arrows). The
evolution of the dynamical fields, including cross-isentropic vertical
velocity θ˙ and zonal wind, was discussed in the previous section
(Fig. ). But isentropic mixing and its relation to wave forcing
need further investigation.
CLaMS mixing versus wave forcing
Mixing between the Lagrangian APs is parametrized in CLaMS through adaptive
re-gridding. During this process, the involved APs (i.e. APs, which were
generated by the mixing algorithm), are marked after every 24 h time step.
Here we use the statistics of these events, i.e. the percentage of mixed APs
relative to all transported APs, in the following denoted as mixing
intensity. In this way, we illustrate the impact of the major SSW on the
distribution and evolution of mixing resolved by the model.
CLaMS zonal mean mixing intensity within three layers:
(a) 700–850 K, (b) 500–700 K and (c) 400–500 K
overlaid by the location of the vortex edge (thick black lines
). The white contours indicate the mixing intensity of
40 %. The letters mark the regions of high mixing intensity and correspond
to the letters in Fig. .
EP flux (arrows) and its divergence (coloured bluish). Black contours
indicate the mixing intensity larger
than 0.4. The panels (a)–(d) show mean values averaged over four time periods: (a) 3–13
January,
(b) 14–23 January, (c) 24 January–3 February and (d) 4–13 February.
Figure shows the time evolution of the zonally averaged mixing
intensity derived from CLaMS versus eq. latitude. Figure
illustrates the relationship between the EP flux divergence and the CLaMS
mixing intensity averaged over several stages of the polar vortex during the
winter of 2008/09: (a) strong vortex conditions in January between 3rd and 13th,
(b) 10-day period before the major SSW, i.e. between 14 and 23 January,
(c) 10-day period after the major SSW, i.e. between 24 January and 3
February, and (d) weakened wave activities after the major SSW between 4 and
13 February.
We notice that before mid January, maximum mixing remains equatorward of
65∘ N and generally outside the polar vortex boundary as defined by
the Nash criterion (Fig. ). In particular, above 700 K the rather
abrupt poleward decrease in mixing strength clearly marks the polar mixing
barrier isolating the core of the stable polar vortex from the surf zone.
Note that the Nash criterion is not necessarily a perfect proxy for the
mixing barrier, thus mismatch to within a few degrees latitude, as apparent
in Fig. a. In mid January the picture changes drastically. With the
intensified wave activity disturbing the polar vortex, the westerlies
decelerated. Consequently, the EP flux increased and its divergence became
strongly negative, meaning an enhanced convergence of the EP flux
(Fig. ). Furthermore, the pattern of mixing intensity separated
into two branches above 700 K after 24 January (Fig. a): one in
high and another one in mid eq. latitudes (marked as A1 and A2 in
Figs. a and c, respectively).
This distribution of mixing intensity indicates that both the polar and
subtropical barrier (the latter above 700 K) are weakened by the major SSW.
Furthermore, daily PV or tracer distributions over the NH (cf. Fig. 3)
exhibit that at this time several vortex fragments move equatorward and mix
with mid-latitude air. At the same time, several fragments of tropical air
masses which are generated at low latitudes, are transported poleward and
mixed with mid- or high-latitude air.
Mixing intensity diagnosed in Fig. shows some interesting,
altitude-dependent patterns: At the highest levels (θ between 700 and
850 K) after the major SSW, the mid- and high-latitude mixing is comparable
(cf. A1 versus A2 in Fig. a). At the levels between 500 and 700 K,
the high-latitude mixing branch within the vortex dominates. Finally, in the
lower stratosphere between 400 and 500 K, mixing has intensified in the
polar region after the major SSW, while the mixing intensity in the surf zone
(marked by B in Fig. c) has slightly increased during and after the
major SSW. Note that the subtropical barrier can be identified as a minimum
in mixing intensity between 10 and 20∘ N eq. latitude
(Fig. b). The position of this minimum does not significantly
change during the time shown although the impact of the major SSW can be seen
around 1 February, mainly at highest levels between 700 and 850 K.
From the vertical cross sections of EP flux shown in Fig. , we
infer that in the first half of January, there were three intensive mixing
regions (marked as A, B and C) with only weak, vertically propagating waves.
As mentioned above, region A became stronger during the course of the winter
and then divided into two branches (A1 and A2). Region B is related to the
mid-latitude (surf zone) mixing in the lower stratosphere (400–500 K) that
is influenced by the subtropical jet and the QBO. Region C is associated with
strong vertical shear in the transition layer between the westerlies and
easterlies of the QBO.
It is obvious that although high mixing intensities can be diagnosed in
the surf zone outside of the polar vortex (region A) before the major SSW, this
signature intensifies after the onset of the major SSW (regions A1 and A2).
Convergence of the EP flux indicates breaking of waves and thus leads to
wave and mean-flow interaction. Once the local wind field is significantly
disturbed by transport of momentum and heat flux, subsequent stirring and
stretching of eddies (resolved by the ECMWF winds) drives the mixing
parameterization in CLaMS. Note that after 10 February (20 days after the
SSW), the mixing intensity quickly dropped as the vortex started to recover
with a weak vortex edge between 50 and 60∘ N eq. latitude at 800 K
and 50∘ N eq. latitude at 600 K (i.e. with a weak PV gradient
according to the Nash criterion).
Based on the analysis of the temporal and spatial evolution of the mixing
intensity resolved in CLaMS and the EP flux divergence, the simulated
patterns show a clear and reasonable physical picture how mixing responds to
large-scale wave forcing: when the transport barriers stay strong, the mixing
pattern does also not change dramatically (Fig. a); when the
general circulation is disturbed and the transport barriers are weakened, the
pattern of mixing is highly associated with the local wave activities
(Fig. b and c). However, the question still arises whether mixing
resolved by the model can also be seen in the observations. This would help
to provide a more quantitative understanding of how the major SSW influences
the chemical composition of the stratosphere.
Impact of the major SSW on transport and chemistry
N2O–O3 correlations: MLS versus CLaMS
As discussed in the last section, the subtropical barrier and even more so
the polar vortex barrier suppress the exchange of air across those barriers
before the major SSW. Hence, long-lived species are well-mixed in the regions
separated by these barriers and strong isentropic gradients of these species
are expected across such barriers. In the tracer–tracer space (in the
following abbreviated as tracer space), these well-mixed regions manifest as
compact correlations; however correlations between the tracers are different
in the regions separated by barriers for a review of this method
see.
Figure a1–c1 show the N2O–O3 correlations of MLS
observations plotted as probability distribution functions (PDFs). The data
cover the NH with eq. latitudes between 0 and 90∘ N and within the
potential temperature range between 450 and 700 K. The MLS observations are
selected for three periods: 18–28 December (1 month before the major SSW),
18–28 January (during the major SSW) and 18–28 February (1 month after the
major SSW). The grey lines in Fig. a1–c1 indicate the
isentropes calculated from the pressure altitude of the observations and
corresponding ECMWF temperature.
Under relatively strong vortex conditions before the major SSW, two stronger
and one weaker branch of N2O–O3 correlations with enhanced PDF values
can be distinguished in Fig. a1. These branches describe the
well-mixed air masses within the polar vortex, the surf zone and the tropics
(thin black lines from bottom to the top, respectively). The corresponding
barriers in the physical space, i.e. the vortex edge and the subtropical
barrier, manifest in tracer space as regions with lower PDF values separating
the correlation branches (a detailed discussion follows in the next
subsection). After the major SSW (see Fig. c1), the polar
correlation totally disappears in tracer space and the tropical correlation
becomes slightly weaker. Conversely, the PDF of the mid-latitude correlation
strengthens in the time period after the major SSW.
Tracer and physical space
Before transport and chemistry triggered by the major SSW in January 2009
is described more quantitatively, Fig. shows schematically
how these physical processes can be interpreted and separated by using
N2O–O3 correlations. The left column in Fig. show the APs in
physical space using eq. latitudes as the meridional axis. On the right
side, the corresponding tracer space is shown in the same way as discussed in
Fig. .
Schematic diagram of transport processes shown in physical space
(left column) and tracer space (N2O–O3, right column) before (top),
during (middle) and after (bottom) the major SSW. In the physical space (left
column), equivalent latitudes are used as the horizontal coordinates to
illustrate isentropic mixing (curved red arrows) and cross-isentropic
transport (grey vertical arrows). The thickness of the grey arrows indicates
the intensity of vertical motion. The characters denote exemplarily the vortex
and tropical air masses which interact with the mid-latitude air. Black
curves in (a2)–(c2) show respective N2O–O3 correlations. Grey lines
denote the isentropic levels. In the tracer space, the position of isentropes
before (dashed) and after (solid) the major SSW is also marked. The change of
the position of a prescribed point in the tracer space along the isentropes
quantifies isentropic mixing, whereas motion relative to these isentropes
describes the effect of an idealized (mixing-free) cross-isentropic motion
(up- or downwelling). Changes of the relative thickness of the different
correlation branches mean their enhanced or weakened relative contributions
to the composition of the considered part of the atmosphere (dashed lines indicate
a possible missing part).
PDFs of N2O–O3 correlations (tracer space) shown for three
periods: (a) 18–28 December, (b) 18–28 January and
(c) 18–28 February. The top row (a1–c1) is based on the MLS
observations within eq. latitudes 0–90∘ N and potential temperature
range between 450 and 700 K. The black lines in (a1–c1) represent the
respective correlation branches (polar, surf-zone, tropics). The middle and
bottom rows show CLaMS simulations without ozone chemistry but with and
without mixing, respectively. CLaMS PDFs are calculated from the APs with the
same potential temperature range but with eq. latitudes between 40 and
90∘ N. The grey lines mark the isentropes (450, 500, 550, 600, 650,
and 700 K). For better comparison between CLaMS with and without mixing, the
dashed black curves in (a2–c2) show the estimated N2O–O3 correlation
line from the case without mixing (i.e. from a3–c3). Reversely, dashed lines
in (a3–c3) depict schematically transferred correlation branches from CLaMS
with mixing (i.e. from a2–c2).
Through isentropic mixing, the APs in the mid latitudes change their
composition as they mix with other APs isentropically transported from higher
or lower latitudes (like fragments B, E and F in Fig. a1, b1).
Consequently, mixing lines connecting the isolated correlations may appear
or, when intensive and persistent mixing happens, the whole correlation line
inclines to one side (e.g. the thick black correlations in
Fig. b2). Moreover, the enhanced mixing also results in a decay
or growth of certain correlation branches (shown as thinned or thickened
black curves in Fig. b2 and c2) and expressing the shrinking or
expanding of corresponding regions.
Conversely, if the APs are affected purely by vertical transport like strong
cross-isentropic motion during the SSW (i.e. by up- or downwelling), the
composition of the APs (and thus their position in tracer space) stays the
same although their θ-coordinate significantly changes. As discussed
in Fig. a, b, in the absence of mixing and chemistry, an AP will
not change its coordinates in the tracer space although it will move in the
physical space (e.g. vertical displacement of APs shown in
Fig. b1). Furthermore, if only APs within a limited range of
potential temperature are considered, the cross-isentropic transport results
in an additional flux of the APs out of (export) or into (import) the
considered domain in tracer space. Such vertical export or import of APs
reflects in tracer space as vanishing or growing of certain part of the
correlation line (vanished parts of vortex correlation are shown as dashed
black curves in Fig. b2/c2). In the same way, export or import of
APs from a limited range of latitudes (or eq. latitudes) may influence the
tracer–tracer correlation, e.g. if the subtropical barrier moves toward the
equator.
Generally, the major SSW itself creates vortex fragments which in the
time following can either merge and reform a new polar vortex, or can be
isentropically mixed with the mid-latitude air. These two possibilities are
exemplarily shown in Fig. b1 and c1 (mixing – fragments B and E;
recovery – fragments A, C and D). Note that in the eq. latitude space, the
spatially separated vortex remnants form a compact and coherent circumpolar
structure although smaller than the vortex at the beginning of the winter.
Finally, also chemistry can influence the N2O–O3 correlations as
discussed in Fig. c. Particularly, halogen or NOx-induced
ozone loss would shift the polar or the surf zone correlations downwards,
whereas ozone production in the low latitudes would steepen the tropical or
the surf zone correlations.
Spatial distribution in the eq. latitude-θ space of the APs,
defined by the mixing
ratios of N2O and pO3 inside the square in Fig. a3,
i.e. with N2O and pO3 values from 80 to 130 and
from 2.7 to 3.5 ppmv, respectively, calculated from the CLaMS run without mixing.
(a) 23 December 2008; (b) 23 January 2009 and (c) 23 February 2009.
Colours indicate different ranges of pO3 values and are defined in the box.
The PDFs along the eq. latitude and
potential temperature axes are shown as red lines.
Thick black lines denote the edge of the polar vortex.
Our first goal is to understand the changes in the N2O–O3 correlations
observed by MLS before and after the major SSW (Fig. a1 to c1)
as a result of different transport mechanisms (isentropic mixing, meridional
transport). In particular, we would like to figure out why the polar and the
tropical N2O–O3 correlations weakened after the major SSW and the
mid-latitude correlation became stronger. First, we rule out ozone chemistry
by using CLaMS simulations with passively transported O3 (pO3). At
the end of this section, we will also include CLaMS results with the full
stratospheric ozone chemistry.
Isentropic mixing versus cross-isentropic transport
Two sets of CLaMS simulations, with and without mixing, are used to study the
mixing-induced differences between the PDFs of the pO3–N2O
correlations. The results are shown in Fig. (middle/bottom row
for mixing/non-mixing cases). As in Fig. a1–c1, the PDFs are
calculated for the same time periods before, during and after the major SSW
(from a to c). However, the range of the considered eq. latitudes is confined
to 40–90∘ N (instead of 0–90∘ N shown in
Fig. a1 to c1) to separate more clearly the effect of transport
from the tropics on the composition of air in the mid latitudes (see
discussion below). To provide better comparability, correlation branches of
the non-mixing experiment are also depicted in the mixing case as dashed
lines (and vice versa).
Transport from the tropics
By using such a limited range of eq. latitudes, we exclude the APs on the
tropical side of the subtropical barrier (that is around 20∘ N
eq. latitude) and it is obvious that the PDFs of the CLaMS run with mixing
do not show any tropical correlation in the eq. latitude 40–90∘ N
(Fig. a2 to c2). However, a tropical correlation was found in
the non-mixing run during and after the major SSW (Fig. b3/c3)
because in this idealized simulation, tropical air was transported into the
mid latitudes but it had not been mixed. For a better comparison, this
“artificial” tropical correlation (i.e. from Fig. b3/c3) is
also shown in Fig. b2/c2 (solid dashed line).
Thus, a clear difference in the result of the mixing and non-mixing case
indicates that the tropical APs are transported from lower latitudes to
mid latitudes where they mix with the mid-latitude APs. Consequently, the
slope of the surf-zone correlation moves towards the tropical correlation
branch, especially between 550 to 650 K (cf. Fig. from a2 to
c2 and c2 with c3). This isentropic mixing in mid latitudes is also
consistent with the increased mixing intensity marked as A2 in
Figs. and . In contrast, an idealized, pure trajectory
calculation (i.e. CLaMS without mixing) completely neglects this effect and
produces N2O-O3 correlations which cannot be reconciled with MLS
observations (i.e. for eq. latitudes 40–90∘ N, not shown).
Vortex breakup and decay
All APs which are transported along the trajectories without mixing do not
change their composition and thus keep the same position in the N2O–O3
space unless they leave the considered range of eq. latitudes or potential
temperatures. Besides the almost isentropic import of tropical APs that was
mentioned in the last subsection, strong downwelling within the polar vortex,
mainly during the major SSW itself, can also be diagnosed in the tracer
space.
The isentropes move upwards in tracer space during the major SSW
(Fig. from column a to b), as a consequence of diabatic
cooling (downwelling) associated with warming in mid and high latitudes
(see also Fig. ). As a result of this cross-isentropic transport,
the APs transported without mixing may be exported (or imported) from (or
into) the considered θ-range between 450 and 700 K. For example, the polar
APs within the black solid squares in Fig. a3 are missing in
the box of Fig. c3. The box is defined by the N2O values
between 80 and 130 ppbv and O3 between 2.7 and 3.5 ppmv. Note that for CLaMS
with mixing these regions are filled with APs indicating that mixing in the
model re-establishes parts of the correlation.
To shed more light on the ongoing processes, in Fig. we plot the
eq. latitudes and the potential temperature coordinates of these missing APs
at the end of each of the considered time periods (from the CLaMS run without
mixing). Furthermore, the APs are coloured by different ranges of pO3 and
the PDFs of their eq. latitudes and θ coordinates describe their mean
horizontal and vertical position during the course of the winter.
Impact of O3-chemistry on the temporal evolution of the
N2O-O3 correlations. The PDFs are calculated from the N2O-pO3
correlations of APs with eq. latitudes 0–90∘ N and potential
temperatures 450–700 K. The considered time periods are the same as in
Fig. . The dashed black curves fit the maxima of the
N2O-O3 correlations (PDFs) derived from a CLaMS run with a full
stratospheric ozone chemistry. The correlation for passive ozone (pO3)
marked as A (N2O near 140 ppbv and pO3 near 7400 ppbv) and the
correlation marked as B (N2O near 140 ppbv and pO3 near 7400 ppbv)
show clear differences from the dashed curves showing simulation with full
chemistry. The two groups of APs marked by those correlation features have
been investigated in more detail of their ozone chemistry (see text).
Figure shows that after the major SSW onset, most of the APs
which were originally located above 450 K, have been transported downwards
below 450 K. Therefore, the downward cross-isentropic transport within the
vortex (diabatic descent) with subsequent export of the APs out of the
considered potential temperature range 450–700 K is the main reason for the
missing correlation inside the square of Fig. c3. Moreover,
most of the APs were confined inside the polar vortex before the major SSW,
while after the major SSW these APs were spread almost uniformly between 40
and 90∘ N eq. latitude (Fig. c) due to chaotic advection
with pronounced streamers and filaments after a complete breakup of the two
vortices over eastern North America and the Atlantic (see N2O distribution
at 475 K in Fig. ).
In the CLaMS run with mixing, the situation is stable as long as the
well-defined vortex edge constitutes an effective mixing barrier
(Fig. , column a). Later, during the major SSW, descent and
chaotic advection have the same effect as in the idealized CLaMS simulation
without mixing, i.e. part of the APs carrying the signature of the polar
correlation are again eventually exported from the considered θ-range
as they descend below 450 K.
However, increased mixing between these descending polar APs with the APs
outside the vortex have two additional effects: (i) the signature of the
polar correlation is spread to mid-latitude APs that do not descend beyond
the considered θ-range, such that the signature remains visible (like
vortex fragment D in Fig. b1/c1), and (ii) the mixing with
mid-latitude (and even tropical) APs causes the polar correlation branch to
become less compact and shift toward the mid-latitude correlation branch
along the plotted isentropes (like air masses C and E in
Fig. b1/c1). These effects can be well discerned by comparing the
vortex branch of the correlation for the mixed case
(Fig. b2/c2) with the non-mixed case
(Fig. b3/c3), also denoted as dashed black curves in Fig. b2/c2.
After the breakup of the two vortices over eastern North America and Atlantic
in mid February, spreading of the polar APs across the hemisphere along with
intense mixing with mostly mid-latitude and some tropical APs leads to an
almost complete loss of the polar correlation branch (Fig. c2),
which remains preserved only in a few unmixed vortex remnants (like fragments
A, B and D in Fig. c1). As explained by , the
fast and nearly hemisphere-wide isentropic mixing (as promoted by the major
SSW) leads to a single compact extratropical correlation.
Note that the weak polar correlation which is present in CLaMS (see
Fig. c2) is not resolved in the MLS observations. A potential
explanation is the limited spatial resolution of the MLS instrument with
vertical resolution of 4–6 km for N2O and 2.5–3 km for O3,
respectively, and horizontal resolution of 200 km for both species. This
means that physical structures below these spatial scales are smoothed out by
the MLS instrument (an effect sometimes called optical mixing, see Appendix).
Impact of chemistry
In general, Arctic O3 loss triggered by activated chlorine mainly occurs
in late winter and spring within a sufficiently cold polar vortex. The
chlorine-induced ozone-loss also requires sunlight exposure see
e.g.. The NOx-induced O3 chemistry roughly follows the
halogen chemistry after the vortex breakup with highest values occurring in
the middle and lower stratosphere see e.g.. To
quantify the chemical effect on the N2O–O3 correlation,
Fig. shows the pO3–N2O correlation within
0–90∘ N and 450–700 K range, overlaid with the correlations from
the full chemistry run (dashed curves).
In the early winter, we found a small but significant amount of ozone loss in
the lower stratosphere (cf. dashed curve and PDFs between 450 and 550 K in
Fig. b), which is consistent with the results of
. After the onset of the warming event, only few polar stratospheric clouds (PSCs) were
formed and, consequently, the subsequent, chlorine-induced ozone-loss within
the polar vortex was very limited . This
can also be inferred from the CLaMS-based correlation with pO3 (PDFs in
Fig. c) that is very close to the correlation based on
full-chemistry O3 (dashed curve in Fig. c). Besides the
chlorine-catalyzed ozone loss, the remaining O3 chemistry is of importance
in our interpretation of the N2O–O3 correlations, especially when the
temperature rises after the major SSW and thus the chemical reactions are
accelerated.
Two regions (marked in Fig. 11 as A and B) of this correlation plot have been
investigated in more detail regarding the chemical change of ozone. Region
(A) has N2O mixing ratios near 140 ppbv and passive ozone near 7.4 ppmv
on 23 January, corresponding to a most probable location of 35∘ N
and 650 K (using a similar method as discussed in Fig. ). It is
evident that here the chemistry causes ozone depletion. From the locations of
120 air parcels in this area, back trajectories were calculated for 1 month
along which the chemistry, which was calculated using the CLaMS chemistry module, and
additional output to analyse and quantify the contribution of the individual
ozone depletion cycles as defined by to the ozone loss
term. The average ozone production over this month through oxygen photolysis
was 0.85 ppmv which was outweighed by ozone loss of 1.45 ppmv, of which
about half could be attributed to NOx-catalyzed ozone loss cycles and the
remaining half equally distributed to HOx, ClOx and Ox cycles.
In contrast, region (B) with N2O mixing ratios of 260 ppbv and passive
ozone mixing ratios of 3.8 ppmv corresponds to a most probable location of
11∘ N and 575 K. Here, the chemistry causes an ozone increase. A
similar chemistry simulation along 132 1-month back trajectories showed an
ozone production through oxygen photolysis of 800 ppbv and net ozone
depletion by 260 ppbv. Therefore ozone production dominates in this part of
the tropics. Since gas-phase chemical reactions are temperature-dependent, we
investigated whether the temperature anomaly (see Fig. 1b) had a significant
effect on ozone. An identical run along the 132 trajectories, however, with
temperatures set 3 K higher, increased the ozone loss by 0.03 ppmv. The
ozone production is not temperature-dependent. A change in the ozone loss
rate of 1 ppbv per day is negligible compared to the changes caused by
dynamics that are discussed here. Complementary to our discussion above, we
find that in polar latitudes, the differences between correlations with or
without chemistry are negligible, indicating minor importance of the
chlorine-induced ozone-loss during the 2008/09 winter.
Conclusions
A remarkable major SSW in January 2009 led to strongly disturbed
stratospheric dynamics which manifested in both accelerated polar descent and
tropical upwelling. During the following 2 weeks up to the end of January,
this transient signal of cross-isentropic transport propagated down from
around 1 to 100 hPa. The radiative relaxation of this anomaly in diabatic
heating was relatively fast (∼ 10 days) in the upper stratosphere, but
took more than a month in the lower stratosphere, which resulted in
accelerated polar descent and accelerated tropical upwelling through late
March (Fig. ).
Associated with the disturbed dynamical background during the major SSW,
strong variability of N2O and O3 was observed by the MLS instrument. We
used CLaMS to simulate transport, mixing and chemistry to interpret the
observed change of stratospheric composition. By comparison with MLS
observations of N2O–O3 correlations, we showed how the polar vortex
edge weakened and how the subtropical mixing barrier was affected by poleward
transport followed by mixing in mid latitudes during and after the major SSW.
As an important but uncertain piece of atmospheric modelling, the mixing
process could be explicitly and reasonably described in CLaMS simulations.
The distribution of simulated mixing intensity showed that mixing across the
vortex edge and also across the subtropical barrier (above 700 K) was
enhanced after the onset of the major SSW, associated with wave forcing,
quantified in terms of the EP flux divergence.
The observation- and model-based O3–N2O correlations have been shown to
be a useful diagnostic to separate dynamical and chemical effects. Model
results show that isentropic mixing is a key process to understand the
drastic change of stratospheric composition triggered by the major SSW: the
decay of the polar O3–N2O correlation and the strengthening of the
mid-latitude correlation. One month after the major SSW, almost half of the
polar vortex correlation dissolved due to isentropic mixing, whereas the
other part constituted the germ for the formulation of a new and relatively
weak vortex. Halogen-induced ozone loss within the polar vortex was
negligible in the late winter of 2008/09 and the dominant ozone
chemistry during and after the major SSW was the extra-tropical ozone loss
due to NOx catalytic cycles mainly at 600–800 K and ozone production in
the tropics.
However, there is also a limitation of the applicability of the MLS satellite
data with a vertical resolution of a few kilometres. As shown in the
Appendix, due to this limited spatial resolution, physical structures below
these spatial scales and resolved by the model are smoothed out by the
satellite's averaging kernel (an effect sometimes called optical mixing).
Thus, although MLS satellite data offer a very good coverage, their poor
vertical resolution does not allow us to narrow the possible range of the
mixing parameters in CLaMS (i.e. of the critical Lyapunov exponent).
Finally, we can speculate that for a winter with significant,
chlorine-induced ozone loss, followed by a strong major SSW and/or a final
warming, the mid-latitude air can be influenced by processed, ozone-depleted
air. Conversely, mid-latitude air (also O3-rich air compared to polar
vortex air in mid stratosphere) can be effectively transported into the high
latitudes.