A New Look at Stratospheric Sudden Warmings. Part I: Climatology and
Modeling Benchmarks
ANDREW J. CHARLTON*
Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York
LORENZO M. POLVANI
Department of Applied Physics and Applied Mathematics, and Department of Earth and Environmental Sciences,
Columbia University, New York, New York
(Manuscript received 13 October 2005, in final form 28 March 2006)
ABSTRACT
Stratospheric sudden warmings are the clearest and strongest manifestation of dynamical coupling in the
stratosphere–troposphere system. While many sudden warmings have been individually documented in the
literature, this study aims at constructing a comprehensive climatology: all major midwinter warming events
are identified and classified, in both the NCEP–NCAR and 40-yr ECMWF Re-Analysis (ERA-40) datasets.
To accomplish this a new, objective identification algorithm is developed. This algorithm identifies sudden
warmings based on the zonal mean zonal wind at 60°N and 10 hPa, and classifies them into events that do
and do not split the stratospheric polar vortex.
Major midwinter stratospheric sudden warmings are found to occur with a frequency of approximately six
events per decade, and 46% of warming events lead to a splitting of the stratospheric polar vortex. The
dynamics of vortex splitting events is contrasted to that of events where the vortex is merely displaced off
the pole. In the stratosphere, the two types of events are found to be dynamically distinct: vortex splitting
events occur after a clear preconditioning of the polar vortex, and their influence on middle-stratospheric
temperatures lasts for up to 20 days longer than vortex displacement events. In contrast, the influence of
sudden warmings on the tropospheric state is found to be largely insensitive to the event type.
Finally, a table of dynamical benchmarks for major stratospheric sudden warming events is compiled.
These benchmarks are used in a companion study to evaluate current numerical model simulations of the
stratosphere.
1. Introduction
Over the last decade our understanding of the rela-
tionship between the stratosphere and troposphere has
been radically altered. While the influence of tropo-
spheric waves on the stratospheric circulation has been
recognized since Matsuno’s early models of strato-
spheric sudden warmings (SSWs; Matsuno 1971), the
influence of stratospheric conditions on the tropo-
spheric flow has only recently become widely accepted.
Both observational studies (Baldwin and Dunkerton
2001; Thompson et al. 2002; Thompson and Solomon
2002) and modeling studies (Shindell et al. 1999; Sexton
2001; Polvani and Kushner 2002; Gillett and Thompson
2003; Norton 2003; Charlton et al. 2004) have provided
strong evidence that the stratospheric state is able to
influence the tropospheric circulation. As a conse-
quence, the stratosphere is coming to be seen as more
than a passive absorber of tropospheric planetary
waves, and the emerging paradigm is one of a two-way
coupled system.
SSW events are the clearest and strongest manifes-
tation of the coupling of the stratosphere–troposphere
system. Recent work has shown that the influence of
SSWs on the tropospheric flow can last for many weeks
(Baldwin and Dunkerton 2001; Polvani and Waugh
2004). It is therefore important to correctly represent
* Current affiliation: Department of Meteorology, University of
Reading, Reading, United Kingdom.
Corresponding author address: Andrew J. Charlton, Depart-
ment of Meteorology, University of Reading, Reading, Berkshire,
RG6 6BB, United Kingdom.
E-mail: a.j.charlton@reading.ac.uk
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EBRUARY 2007 CHARLTON AND POLVANI 449
© 2007 American Meteorological Society
JCLI3996
stratospheric dynamics, and its coupling to the tropo-
sphere in numerical models of the climate system. A
useful analogy might be drawn at this point with the
atmosphere–ocean system: in the same way as under-
standing and successfully modeling the El Niño–Southern
Oscillation phenomenon is of primary importance for
the atmosphere–ocean system, understanding and suc-
cessfully modeling stratospheric sudden warming
events is of primary importance for the stratosphere–
troposphere system.
Given the prominent role of SSW events, it is some-
what surprising that relatively few attempts have been
made to establish a comprehensive climatology of
SSWs; this is the aim of the current work which, en-
compasses two related papers. In this first paper we
construct a climatology of major, midwinter, strato-
spheric sudden warmings, together with a set of dy-
namical benchmarks for their simulation in numerical
models. In the second paper we examine a number of
stratosphere resolving GCMs and assess their ability to
simulate the observed characteristics of SSWs.
Since the discovery of SSWs by Scherhag (1952),
many studies have examined the dynamics of individual
major warming events. Only a few studies, however,
have attempted to establish a climatology of SSWs, in-
cluding those by Labitzke (1977) and Manney et al.
(2005). This study builds on those earlier works and is
novel and distinctive in three important respects. First,
we provide full dating information for SSWs, including
the day of occurrence, and tabulate all events from the
late 1950s to the present in a single table. Second, our
climatology is established from two widely used re-
analysis datasets, which to our knowledge have not
been examined for SSW activity before. Third, we use
a new analysis technique that, for the first time, classi-
fies the SSWs into vortex displacement and splitting
events.
This study is also closely related to that of Limpasu-
van et al. (2004, hereafter LIM04). However, while the
latter used the 50-hPa annular mode to define SSWs
and considered only the National Centers for Environ-
mental Prediction–National Center for Atmospheric
Research (NCEP–NCAR) reanalysis dataset, we here
adhere to the more widely used World Meteorological
Organization (WMO) definition of SSWs (easterly
winds at 10 hPa and 60°N), and we examine both the
NCEP–NCAR and the 40-yr European Centre for
Medium-Range Weather Forecasts (ECMWF) Re-
Analysis (ERA-40) datasets.
In this study we also distinguish between different
types of SSWs, based on the synoptic structure in the
middle stratosphere. Following O’Neill (2003), one
type, a vortex displacement, is characterized by a clear
shift of the polar vortex off the pole, and its subsequent
distortion into a “comma shape” during the extrusion
of a vortex filament; an example is given in Fig. 1a. The
other type, a vortex split, is easily recognizable in that
the polar vortex breaks up into two pieces of compa-
rable size (Fig. 1b). While these two types of SSWs are
often associated with large amplitudes of longitudinal
wavenumbers 1 and 2, respectively, a simple Fourier
decomposition is not sufficient to identify them (Waugh
1997, their appendix): a more sophisticated algorithm is
needed.
In section 2 this new algorithm is described in detail.
In sections 3 to 6, using this new tool, we then attempt
to answer the following key questions:
• How often do SSWs occur, and what is the ratio of
vortex displacements to vortex splits?
• What is the temporal distribution of SSWs?
• 〈re vortex displacements and vortex splits dynami-
cally different? If so how?
• Do vortex displacements and vortex splits differ in
their impacts on the tropospheric flow?
In section 7, we construct a set of modeling bench-
marks for SSWs, and we conclude with a brief summary
of our findings in section 8.
2. Sudden warming identification and classification
algorithm
In this section we describe the key tool that we have
developed for the present study: an algorithm for au-
tomatically identifying and classifying SSWs. This tool
is needed because we intend to examine SSWs in many
different datasets (both reanalyses and model outputs)
and, for validation purposes, it is essential that such an
examination be done objectively. Also, the task of iden-
tifying and classifying SSWs is, de facto, humanly im-
possible as many, large datasets need to analyzed.
In view of this, special care is needed in designing the
detection/classification algorithm. In particular the al-
gorithm should use only those variables that are typi-
cally archived on at least daily time scales by general
circulation model (GCM) simulations and should not
involve diagnostics that require fine vertical resolution
to be calculated offline. In addition, the algorithm has
been designed to minimize the number of variables that
need to be derived from the direct GCM output, in
order to avoid introducing unnecessary interpolation
and differentiation errors, as well as to simplify the
analysis.
The algorithm consists of two parts: first SSWs are
identified, and second they are classified as vortex dis-
placement or vortex splitting events. These two steps
450 JOURNAL OF CLIMATE VOLUME 20
are described, separately, in the following subsections.
The discussion is somewhat technical in nature and is
included here for the sake of completeness and repro-
ducibility. Some readers may wish to skip directly to the
next section, where we present the results obtained by
applying the algorithm to the NCEP–NCAR and ERA-
40 datasets.
a. Identifying sudden warming events
We have decided to follow the WMO definition (An-
drews et al. 1985, p. 259), also used for the widely
known STRATALERT messages (Labitzke and Nau-
jokat 2000) in order to detect the occurrence of the
SSWs: a major midwinter warming occurs when the
zonal mean zonal winds at 60°N and 10 hPa become
easterly during winter, defined here as November–
March (NDJFM). Note that our definition differs from
that used by Labitzke and others in several studies in
that we do not attempt to exclude Canadian warmings
from our definition and that we also include events in
March that would be rejected by some authors. The
first day on which the daily mean zonal mean zonal
wind at 60°N and 10 hPa is easterly is defined as the
central date of the warming. Note that this definition
differs from that of LIM04, who identify warmings by
reduction in strength of a stratospheric zonal index,
based on the first empirical orthogonal function of 50-
hPa geopotential height.
We note that the WMO definition, in addition to the
reversal of the winds at 60°N and 10 hPa, requires that
the 10-hPa zonal mean temperature gradient between
60° and 90°N be positive (Kruger et al. 2005) for an
event to be designated as a major midwinter warming.
Including this additional constraint makes only a small
difference to the number of SSWs identified (only three
events in the NCEP–NCAR dataset and one in the
ERA-40 dataset do not meet this criterion). Thus, to
avoid unnecessary complexity, we have not included
the temperature gradient criterion
1
in our algorithm.
Once a warming is identified, no day within 20 days
of the central date can be defined as an SSW. The
length of the interval is chosen to approximately equal
two radiative time scales at 10 hPa (Newman and
1
There also appears to be some ambiguity as to the exact speci-
fication of the temperature gradient criterion for defining major
stratospheric warmings. Contrast, for instance, Limpasuvan et al.
(2004, p. 2587) with Kruger et al. (2005, p. 603).
FIG. 1. Polar stereographic plot of geopotential height (contours) on the 10-hPa pressure surface. Contour
interval is 0.4 km, and shading shows potential vorticity greater than 4.0 ⫻ 10
⫺6
Kkg
⫺1
m
2
s
⫺1
. (a) A vortex
displacement type warming that occurred in February 1984. (b) A vortex splitting type warming that occurred in
February 1979.
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EBRUARY 2007 CHARLTON AND POLVANI 451
Rosenfield 1997). This condition prevents the algo-
rithm from counting the same SSW twice, as the zonal
mean zonal winds might fluctuate between westerly and
easterly values following the onset of the warming.
Finally, it is important to highlight that only midwin-
ter warmings are considered in this study. To ensure
this, cases where the zonal mean zonal winds become
easterly but do not return to westerly for at least 10
consecutive days before 30 April are assumed to be
final warmings, and as such are discarded. This criterion
ensures that following SSWs, a coherent stratospheric
vortex is reestablished.
b. Classifying sudden warming events
Once an SSW has been identified, the second part of
the algorithm classifies it as a vortex displacement or a
vortex split. This involves identifying the number and
relative sizes of cyclonic vortices during the evolution
of the warming. Ideally, one would want to work with
Ertel potential vorticity (EPV) on an isentropic surface,
as in Waugh and Randel (1999), to identify strato-
spheric vortices. In practice, however, EPV is not fre-
quently archived in model output datasets.
We have therefore decided to work with
p
, the ab-
solute vorticity on pressure surfaces, as a substitute for
EPV. This presents several advantages:
p
is readily
computed from the velocity field, and this can easily
2
be
done with spectral accuracy. Furthermore, no vertical
interpolation is needed, as most model levels in the
middle atmosphere are in fact pressure levels. As Bald-
win and Holton (1988) have shown,
p
is well suited for
looking at the outer contours of the polar vortex and
defining the vortex edge.
Identifying vortices in the
p
field involves determin-
ing the value of
p
at each vortex edge. We tested a
variant of the Nash et al. (1996) algorithm, using
p
instead of EPV, but found it to be unreliable during
SSWs when two or more vortices were present. In these
SSWs the equivalent latitude averaging procedure had
a tendency to mix the EPV gradient structure of the
two vortices together and make it difficult to identify
the vortex edge. To avoid such averaging, we have
adopted an algorithm from early computer vision stud-
ies (Castleman 1996). Specifically, the edges of each
vortex are identified as the location of the maximum
horizontal gradient in
p
, and these are computed by
finding locations of the zeros in the Laplacian of
p
. Our
algorithm, therefore, follows Nash et al. (1996) in that it
identifies the vortex edges as the locations of maximum
vorticity gradients, but it accomplishes this with no
horizontal averaging.
In detail, our algorithm proceeds as follows: for each
of the days between 5 days before the central date and
10 days after the central date one executes the steps
below. If at least one day meets all of the criteria in the
loop, the SSW is classified as a vortex split. Otherwise
the SSW is classified as a vortex displacement.
1) Compute
p
at 10 hPa and smooth it. If not directly
available,
p
is easily obtained from the horizontal
wind components. To reduce noise, filter
p
with a
triangular truncation of the spherical harmonic co-
efficients and retain up to total wavenumber n
T
.
2) Compute the Laplacian of
p
. The field ⵜ
2
p
is
needed to find the value of
p
that defines the edge
of the vortex (Castleman 1996).
3) Construct n
C
contours, C(
p
), which enclose the
maximum
3
of
p
. The algorithm aims to find the
vortices using the vortex edge defined from the big-
gest vortex.
4) Compute the mean absolute value of ⵜ
2
p
on C(
p
).
For a very smooth field, the Laplacian itself would
identify the closed region corresponding to the big-
gest vortex. This extra smoothing is required be-
cause the
p
field is noisy.
5) Define the vortex edge Z
E
. This is the value of
p
on
the contour in C(
p
) with minimum mean absolute
value of ⵜ
2
p
, and closest to the maximum
p
.
6) Compute the number of closed contours with value
Z
E
in the
p
field. If two or more such contours of Z
E
exist, proceed to the next step. Otherwise skip it.
7) Calculate the circulation around the two largest con-
tours of Z
E
. This is done using Stokes’ theorem, and
the aim is to compare the strength of the two largest
vortices. If the ratio of their circulations is greater
than a given threshold, R
, classify this SSW as a
vortex split.
The algorithm includes a number of tunable param-
eters, which were chosen to give the best possible per-
formance. The values used to produce the results dis-
cussed in this and the following paper are as follows:
n
T
⫽ 11, n
C
⫽ 11, and R
⫽ 0.5. These values were
empirically determined, to give the best agreement be-
tween the output of the algorithm (in terms of detected
SSWs and their type) and a subjective analysis of the
2
For instance, absolute vorticity could be calculated with the
SPHEREPACK routines (Adams and Swarztrauber 1999).
3
In our algorithm, contours that enclose the maximum absolute
vorticity are found by considering the 8-point adjacency of grid
points to the maximum absolute vorticity, making binary images
of these grid points and then contouring the binary images. Other
methods, such as winding number contour based methods, could
be used.
452 JOURNAL OF CLIMATE VOLUME 20
fields on the 10-hPa pressure surface, using both the
NCEP–NCAR and ERA-40 datasets, as described in
the next section.
3. Stratospheric sudden warmings and their
classification: 1958–2002
We start by presenting, in Table 1, the results of our
new algorithm when applied to two widely available
reanalysis datasets: the first is from the NCEP–NCAR
reanalysis project (Kistler et al. 2001), and the second is
from the ERA-40 reanalysis project (Kallberg et al.
2004). For simplicity and ease of comparison, we here
consider only the time period over which data are
available in both datasets, that is, from 1 September
1957 to 31 August 2002, a total of 45 winter seasons
(November–March) in the Northern Hemisphere. Dur-
ing that period, about 30 SSWs were detected by our
algorithm. Some of these SSWs have been analyzed
individually in earlier studies; however, such a summary
table
4
has not, to the best of our knowledge, appeared
in the literature to date. In the last column of Table 1,
we give references for many of the SSWs in the litera-
ture, if available; some SSWs, notably those in Febru-
ary 1979, have been extensively studied (see, e.g., An-
drews et al. 1985), and only an example reference is
included. We wish to emphasize that none of the SSWs
in this table are final warmings, as our algorithm was
specifically designed to exclude those.
In the second and third column of Table 1, we report
the central date for all SSWs identified by our algo-
rithm in either dataset. When SSWs are identified in
both datasets and obviously refer to the same event,
they are listed on the same line, even though the central
4
We note that the yearly published Arctic winter reports in the
“Beilage zur Berliner Wetterkarte” mention many of the events
described here. Short summaries can be found in Labitzke (1977)
and Naujokat and Labitzke (1993).
T
ABLE 1. SSWs identified in NCEP–NCAR and ERA-40 datasets. D indicates a vortex displacement and S indicates a vortex split.
⌬T
10
shows the mean area-weighted polar cap temperature anomaly at 10 hPa ⫾5 days from the central date. Warmings that are also
ESEs [in the sense of Baldwin and Dunkerton (2001), see text] are in bold.
No.
Central date,
NCEP–NCAR
Central date,
ERA-40
Type
subject
Type
NCEP–NCAR
Type
ERA-40
⌬T
10
(°K) References
1 30 Jan 1958 31 Jan 1958 S S S 7.8 Teweles and Finger (1958)
2 30 Nov 1958 D D 7.7 Hare (1960)
3 16 Jan 1960 15 Jan1960 D D D 5.9
4 28 Jan 1963 S S 10.5 Finger and Teweles (1964)
5 23 Mar 1965 S S 4.4
6 8 Dec 1965 16 Dec 1965 D D D 6.7 Johnson et al. (1969)
7 24 Feb1966 23 Feb 1966 S S S 3.1 Quiroz (1969)
8 8 Jan 1968 7 Jan 1968 S S S 12.0 Johnson et al. (1969)
9 27 Nov 1968 28 Nov 1968 D S D 5.3
10 13 Mar 1969 13 Mar 1969 D D D 4.3
11 2 Jan 1970 1 Jan 1970 D D D 6.8 Quiroz (1975)
12 17 Jan 1971 18 Jan 1971 S S S 9.6 Quiroz (1975)
13 20 Mar 1971 19 Mar 1971 D D S ⫺2.9
14 2 Feb 1973 31 Jan 1973 S S S 6.6 Quiroz (1975)
15 9 Jan 1977 S S 9.1 O’Neill and Youngblut (1982)
16 22 Feb 1979 22 Feb 1979 S S S 3.7 Palmer (1981)
17 29 Feb 1980 29 Feb 1980 D D D 11.5 Baldwin and Holton (1988)
18 4 Mar 1981 D D ⫺2.9
19 4 Dec 1981 4 Dec 1981 D D D 0.1
20 24 Feb 1984 24 Feb 1984 D D D 11.1
21 2 Jan 1985 1 Jan 1985 S S S 13.0 Randel and Boville (1987)
22 23 Jan 1987 23 Jan 1987 D D D 10.2 Manney et al. (2005)
23 8 Dec 1987 7 Dec 1987 S S S 14.1 Baldwin and Dunkerton (1989)
24 14 Mar 1988 14 Mar 1988 S D S 11.7
25 22 Feb 1989 21 Feb 1989 S S S 12.8 Kruger et al. (2005)
26 15 Dec 1998 15 Dec 1998 D D D 12.7 Manney et al. (1999)
27 25 Feb 1999 26 Feb 1999 S S S 11.0 Charlton et al. (2004)
28 20 Mar 2000 20 Mar 2000 D D D 5.3
29 11 Feb 2001 11 Feb 2001 S D D 6.3 Jacobi et al. (2003)
30 2 Jan 2002 30 Dec 2001 D D D 12.9 Naujokat et al. (2002)
31 17 Feb 2002 D D 5.6
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