RESEARCH LETTER

How Well Do We Know the Surface Impact of Sudden
Stratospheric Warmings?

Key Points:

Jessica Oehrlein1,2

10.1029/2021GL095493• U
 ncertainty in the surface climate
response to sudden stratosphericwarmings is assessed frombootstrapped composites of 39
observed events• The bootstrapped composites showrobust but highly variable patterns
over the Northern Hemisphere• The spread across the composites isdue to tropospheric variability thatis independent of the stratosphericconditions sampled
Supporting Information:
Supporting Information may be foundin the online version of this article.
Correspondence to:J. Oehrlein,jessica.oehrlein@columbia.edu
Citation:
Oehrlein, J., Polvani, L. M., Sun, L.,& Deser, C. (2021). How well do weknow the surface impact of sudden
stratospheric warmings? GeophysicalResearch Letters, 48, e2021GL095493.
https://doi.org/10.1029/2021GL095493
Received 29 JUL 2021
Accepted 27 OCT 2021

, Lorenzo M. Polvani2,3,4, Lantao Sun5

, and Clara Deser6

1
Department of Mathematics, Fitchburg State University, Fitchburg, MA, USA, 2Department of Applied Physics andApplied Mathematics, Columbia University, New York, NY, USA, 3Department of Earth and Environmental Sciences,
Columbia University, New York, NY, USA, 4Lamont-Doherty Earth Observatory, Palisades, NY, USA, 5Department ofAtmospheric Sciences, Colorado State University, Fort Collins, CO, USA, 6National Center for Atmospheric Research,
Boulder, CO, USA

Abstract Sudden stratospheric warmings (SSWs) are key to understanding and predicting
subseasonal Northern Hemisphere winter climate variability. Here we study the uncertainty in thesurface response to SSWs in reanalysis data by constructing synthetic composites based on bootstrapping
the 39 events observed during the 1958–2019 period. We find that the well-known responses in the
North Atlantic and European regions following SSWs are consistently present, but their magnitude andspatial pattern vary considerably across the synthetic composites. We further find that this uncertainty
is unrelated to stratospheric polar vortex strength and is instead the result of independent troposphericvariability. Our findings provide a basis for evaluating the fidelity of the surface response to SSWs inmodels.
Plain Language Summary In winter, the average winds about 30 km above the Arctic areusually west-to-east. When they are disrupted and reverse directions in an event known as a sudden
stratospheric warming, particular surface climate patterns tend to develop over the following 60 days,
especially in the North Atlantic and European regions. However, there is a great deal of variation or
uncertainty in this response, and that variation can be difficult to measure. We study this uncertainty
by building composites or averages of different combinations of observed events, assuming they areinterchangeable. Using these synthetic composites, we find that the responses in the North Atlantic andEuropean regions are always present, but they vary in magnitude, location, and shape. We further findthat this variation is not a result of how strong or weak the 30 km winds are in each synthetic composite;rather, it results from unrelated noise in the atmospheric system. Our results can be used to informweather and climate forecasts of the surface impacts associated with these high-altitude disruptions of theatmospheric circulation.

1. Introduction
The state of the stratospheric polar vortex is an important driver of wintertime climate variability in the
Northern Hemisphere troposphere. In particular, the extreme weak state of the vortex seen during sudden stratospheric warmings (SSWs) has been connected to negative phases of the Northern Annular Mode
(NAM) and North Atlantic Oscillation (NAO) with effects at the surface for two months after the SSW (Baldwin & Dunkerton, 2001). Effects on temperature include below-normal values in Northern Europe and theEastern United States and above-normal values in North Africa, Central Asia, and Eastern Canada in theaftermath of SSWs (e.g., Butler et al., 2017; Domeisen & Butler, 2020; King et al., 2019; Kolstad et al., 2010;
Scaife et al., 2008; D. W. J. Thompson & Wallace, 2001). Common precipitation anomalies following SSWs
include dry spells in northern Europe and increased precipitation in southern Europe (e.g., Ayarzagüena
et al., 2018; Butler et al., 2017; Domeisen & Butler, 2020; King et al., 2019).

© 2021. American Geophysical Union.
All Rights Reserved.

OEHRLEIN ET AL.

However, there is a great deal of uncertainty in this response, and in observational studies, we do not havethe luxury of a large ensemble to isolate the forced response from unrelated noise. The record of SSW
observations is under 70 years long (Baldwin et al., 2021), and the typical surface response is not foundin all events. This raises the question of whether the set of SSWs we have observed is representative andwhy a surface signal is seen following some events and not others. Studies of this uncertainty have focused

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on variability across individual SSW events or types of events. Only two-thirds of SSWs propagate downward to the surface and are followed by a negative NAO (Afargan-Gerstman & Domeisen, 2020; Butler
et al., 2020; Domeisen, 2019; Karpechko et al., 2017). Suggested stratospheric causes for the spread in surface response include lower stratospheric anomalies and magnitude of wave activity following the central
date (Karpechko et al., 2017), persistence of these anomalies (Runde et al., 2016), and differences in type of
SSW event (i.e., split/displacement, absorbing/reflecting) (Kodera et al., 2016; Mitchell et al., 2013; Seviour
et al., 2016). However, these may not determine the following surface responses (Karpechko et al., 2017;
Maycock & Hitchcock, 2015; White et al., 2019). Suggested tropospheric causes for the uncertainty in thesurface response following SSWs include the state of the jet or North Atlantic prior to the event (Chan &Plumb, 2009; Charlton-Perez et al., 2018; Domeisen et al., 2020; Garfinkel et al., 2013) or other phenomena
affecting the troposphere, such as ENSO and the MJO (Baldwin et al., 2021, and references therein).
One possible approach to studying SSWs with relatively few observed events is to use large-ensemble models, as is done in Wang et al. (2020) for Southern Hemisphere SSWs. Here, we instead use the observed set of
SSWs that we have and follow Deser et al. (2017, 2018), which addressed similar challenges in understanding the extratropical circulation response to the El Niño-Southern Oscillation (ENSO). Using a bootstrap resampling method, they constructed synthetic, observationally based El Niño and La Niña composites comparable to the observed composite. Because these synthetic composites were built of resampled observed
events, it is plausible that they could have occurred given different atmospheric variability unrelated to
ENSO. This approach captures the uncertainty in both spatial pattern and magnitude of impacts of ENSO.
They found that sea level pressure (SLP), temperature, and precipitation anomalies in some regions wererobust across the synthetic composites but nevertheless varied in magnitude by up to a factor of 2; otherregions showed less robust responses across the composites. The spread in the circulation responses in all
regions was found to be largely unrelated to ENSO diversity, and instead to be due to internal atmosphericnoise.
The goal of this study, using the method of Deser et al. (2017), is to answer two questions related to uncertainty in the tropospheric response to SSWs. First, how robust to sampling variability are the observed
composite surface responses to SSWs? Second, is the spread that we see in the composite surface response a
result of differences in the SSWs that make up each synthetic composite, or is it due to unrelated tropospheric variability? Our analysis proceeds as follows. After describing our methods (Section 2), we examine asubset of the observationally based synthetic composites, as well as the observed composite, to qualitatively
illustrate the spread in both pattern and amplitude in the mean surface response following SSWs (Section
3a). Then, focusing on particular regions identified from those composites, we confirm that the well-known
observed responses are robust and distinct from what is seen in a climatological winter composite (Section
3b). Finally, we attempt to relate the spread in surface anomalies to the spread in stratospheric anomalies
across the 2,000 synthetic composites (Section 3c). We find that there is little relationship between thecomposite stratospheric anomalies and the magnitude of anomalies at the surface, and we deduce that theuncertainty in the surface response is largely due to unrelated internal tropospheric variability. We conclude
with a brief discussion of the use of these results for model evaluation (Section 4).

2. Data and Methods
To study the anomalies following sudden stratosphere warmings, we use data from the Japanese 55-Year
Reanalysis (JRA-55) (Japan Meteorological Agency, Japan, 2013; Kobayashi et al., 2015), chosen for a top
above the stratopause (0.1 hPa), fine vertical resolution (60 levels) (Fujiwara et al., 2017), and suitability
for use in studying SSWs (Gerber et al., 2021). We analyze winds, SLPs, temperatures, precipitation, andgeopotential heights from this data set over the 1958–2019 period, calculating daily anomalies by removingfrom daily mean fields a climatology calculated as the mean value of each calendar day over the full period.
We detect SSWs using the definition of Charlton and Polvani (2007) (see the corrigendum Charlton-Perez& Polvani, 2011). An event is considered an SSW if the zonal mean zonal winds at 10 hPa and 60°N reverse
from westerly to easterly during extended boreal winter (NDJFM). The first date when the daily zonal mean
zonal winds are easterly is defined as the “central date,” and no day within 20 days following the central dateis considered a separate SSW. If the daily zonal mean zonal winds do not return to westerly for at least 10
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consecutive days before April 30th, the event is classified as a final stratospheric warming and is excluded.
This definition is among those described in Butler and Gerber (2018) as optimal for identifying SSWs. This
procedure identifies 39 SSWs, listed in the leftmost column of Table S1 in Supporting Information S1, in
JRA-55 over the 1958–2019 period.
Following Deser et al. (2017), we form synthetic SSW composites by randomly sampling with replacement(bootstrapping) from the 39 SSW events to form new sets of 39 events. With this procedure, we generate
2,000 synthetic composites. This bootstrap distribution allows us to study variability across SSW composites
as opposed to event-to-event SSW variability. To confirm that the results of this process are in agreementwith probabilistic predictions, we examine two characteristics: the distribution of the number of unique
SSW events across the 2,000 synthetic composites, and the distribution of the maximum number of times
a single event is repeated in a composite. These are shown in Figure S1 in Supporting Information S1 andindeed correspond to what is expected of a multinomial process.
We compare the distributions of composite responses to SSWs to distributions of these fields over comparable climatologies. We construct these 2,000 climatology composites by randomly choosing 39 60-day
periods of the year, each of which corresponds to 60-day periods of an SSW in the reanalysis, and separately,
randomly choosing a year from the 1958–2019 period for each of these periods. This preserves seasonality
effects by sampling from winter periods according to the seasonal distribution of SSWs but forms a climatology by choosing from all years without regard for vortex state.
We calculate the NAM, following Oehrlein et al. (2020), at each pressure level as a deseasonalized anddetrended daily mean of geopotential height, which is then averaged over 65°–90°N. This quantity is normalized to have unit variance with a sign convention such that a negative stratospheric NAM indicates a
weak polar vortex.
Throughout the paper, we focus on six regional surface responses. Region boundaries for these quantities
were chosen to capture variability across composites. The results are robust to changes in the exact boundaries of the region. These climate indices are computed as below:
1. NAO: The difference between normalized, area-weighted averages of SLP anomalies over 62.5°–90°N,
45°W–10°E and 35°–50°N, 45°W–10°E.
2. North Atlantic Precipitation: The area-weighted average over 30°–50°N, 40°W–10°E.
3. North Pacific SLP: The area-weighted average over 30°–60°N, 175°E–135°W.
4. Northern Eurasian Surface Temperature (Ts): The area-weighted average over 60°–75°N, 30°–120°E (Polvani et al., 2017).
5. Eastern Canadian Ts: The area-weighted average over 45°–70°N, 45°–90°W.
6. Eastern United States Ts: The area-weighted average over 25°–42.5°N, 65°–90°W.

3. Results
Figure 1 shows SLP, Ts, and precipitation anomalies for the 60 days following SSW central dates both forthe observed composite (a–c) and for six of the 2,000 synthetic composites (a1–a6, b1–b6, c1–c6); the same
synthetic composites are shown for all fields. These composites were selected as a qualitative illustration of
the spread in anomaly patterns and magnitudes across the entire bootstrapped sample. A systematic quantification of the spread across the entire bootstrapped sample will also be given.
Let us first consider the SLP anomalies (Figures 1a and a1–a6). While a negative NAO is present in allof these composites, it varies from strong (a2) to much weaker (a1) by a factor of two in both centers ofaction. The spatial pattern also varies significantly, with the southern lobe sometimes centered over the
North Atlantic (a4) and sometimes shifted toward western Europe (a5). The other region of interest in thesecomposites is the North Pacific. The observed composite and many of the synthetic composites show ahigh-pressure anomaly in this region, but it is often not statistically significant at the 95% level and is much
weaker than the NAO-related anomalies.
Turning to the corresponding Ts anomalies (Figures 1b and b1–b6), we again see features common acrossall seven composites: northern Eurasian cooling, Central Asian and Middle Eastern warming, and EastOEHRLEIN ET AL.

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Figure 1. The observed composite and six synthetic composites for sea level pressure (SLP) (a, a1–a6), Ts (b, b1–b6), and precipitation (c, c1–c6) in the 60 days
following the sudden stratospheric warming central date, with stippling for significance at the 95% level based on a two-tailed Student's t-test. Black boxes on
the observed composites show regions used to define the climate indices.

Canadian warming. However, as with SLP, there is large spread in magnitude and pattern of these anomalies. For example, the northern Eurasian cooling varies greatly in strength (b3 vs. b4) and extent (b1 vs.
b5). We also note that the observed composite and five synthetic composites show statistically significant
cooling in the Eastern United States, sometimes confined to the coast (b5) and sometimes stretching to the
US Midwest (b6).
Finally, let us examine the associated precipitation anomalies (Figures 1c and c1–c6). Following SSWs, weconsistently see increased precipitation over the North Atlantic and western and southern Europe, withOEHRLEIN ET AL.

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Figure 2. The observed composite and six synthetic composites of the Northern Annular Mode, from 30 days before to 60 days after the sudden stratosphericwarming central date.

spread in magnitude and pattern generally following those of the associated negative SLP anomaly. This isoften accompanied by a dry anomaly in northern Europe and eastern North America.
Together with the surface patterns following SSWs, we now consider the corresponding composite stratospheric conditions. The descent of anomalies from the upper stratosphere to the troposphere is commonly
examined using “dripping paint” plots of the NAM, following Baldwin and Dunkerton (2001). We note awide range of NAM indices in the stratosphere and troposphere in the 30 days preceding and 60 days following the central date. This is illustrated in Figure 2, showing the same synthetic composites as in Figure 1.
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Some composites have a more negative NAM at 10 hPa (b4 and b6) or over a longer period of time andgreater range of levels (b3). These differences amplify as the anomalies descend. For example, the durationof a strong negative NAM at 100 hPa varies substantially (b1 vs. b3), and while all composites show somedescent of the negative NAM to the surface, this also varies in strength (b1 vs. b2) and longevity (b5 vs. b2).
We now address the key question of this study: is the spread in surface response across the synthetic composites explained by the spread in the stratospheric conditions? To answer this, we make use of the entire setof 2,000 synthetic composites. For each of the regional indices listed in Section 2, we identify the compositesthat correspond to the 10th percentile and the 90th percentile values of the index. In this way, we can quantify the 10th-to-90th percentile range of patterns and amplitudes in the synthetic composites that occurs as
a result of internal variability and (potentially) differences in the stratospheric conditions sampled. Figure 3
shows the SLP and NAM anomaly fields for the synthetic composites corresponding to the 10th and 90th
percentile values of the NAO (Figures 3a–3d) and East Canadian Ts (Figures 3e–3h) indices. The SSW events
included in each composite here are listed in Table S1 in Supporting Information S1, and results from otherregional indices are shown in Figures S2 and S3 in Supporting Information S1. For the regions here, we see
two opposite relationships between the negative NAM index in the stratosphere and the anomaly at thesurface. The stronger NAO at the surface in Figure 3a is associated with a stronger negative NAM in theupper stratosphere (Figure 3b), compared to the weaker NAO associated with the weaker NAM (Figures 3c
and 3d). However, the opposite relationship holds for East Canadian Ts (Figures 3e–3h). This suggests thatthe spread in the composite stratospheric NAM due to the different constituent SSW events does not explain
the spread of the composite surface anomalies.
We now consider the full distributions of 2,000 bootstrapped composites. We begin by showing the uncertainty in the composites for our surface climate indices, comparing the bootstrapped composites to a baseline of 2,000 climatological composites (Figure 4). In all cases except that of North Pacific SLP (Figure 4c),there are large shifts in anomalies in these regions following composite SSWs, with little overlap with thebaseline distributions. Further, for all composite SSW distributions except the North Pacific SLP and theEastern US Ts (Figures 4c and 4f), the anomalies across all composites are of the same sign. The Eastern US
Ts anomaly is positive in only 10 SSW composites out of 2,000. The North Pacific anomaly shows both lessseparation from the baseline and a less consistent sign across the composites, with 20% showing negativevalues.
To investigate the North Pacific region further, we separate the observed events by ENSO phase (NOAA(National Oceanic and Atmospheric Administration), n.d.) due to the influence of ENSO in the region andknown interactions between ENSO and the stratospheric polar vortex (e.g., Butler & Polvani, 2011; Domeisen et al., 2019; Polvani et al., 2017). We use a similar bootstrapping process as above, forming composites of
10 SSW events for each ENSO phase (El Niño, La Niña, and neutral); the number of SSW events is reduced
due to the sampling available for each ENSO phase. In El Niño and La Niña, North Pacific SLP anomalies(Figure S4 in Supporting Information S1) are shifted positively following SSW composites compared tothe baseline composites (+1.3 hPa and +0.59 hPa respectively), but we see the opposite in neutral-ENSO(−0.71 hPa). These results do not suggest a clear influence of SSWs modulated by ENSO in the North Pacific.
Unlike the clear shifts in the mean, there is little difference in the width and shape of the distributions
between the climatological and SSW composites. This implies that most of the spread is not a result of differences in composite SSW strength. To demonstrate this, we directly consider the relationship between thesurface climate indices and vortex strength as measured by the 10 hPa polar cap (65°–90°N) geopotential
height anomaly in the first 5 days after the SSW central date, denoted z10-5 day (Figure 5). This period ischosen to capture the strongest anomaly at 10 hPa. We highlight in blue and red respectively the 10th and90th percentile composites (spatial patterns shown in Figures 3, S2 and S3 in Supporting Information S1). In
all cases, there is no sizable correlation between the surface anomaly and z10-5 day (correlation coefficients
ranging from 0.0 to 0.26 in absolute value). Thus, the spread in the composite surface responses is not theresult of spread in the composite strength of SSWs as measured by z10-5 day. There is a stronger relationship (correlation coefficients ranging from 0.25 to 0.49 in absolute value) between the surface anomalies
and the stratospheric anomalies at 100 hPa in the 5 days following the central date (Figure S5 in Supporting
Information S1), suggesting that strong and rapid descent of the NAM signal to the lower troposphere isassociated with larger anomalies at the surface. However, 100 hPa is too low to measure the strength of theOEHRLEIN ET AL.

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Figure 3. Surface anomaly and Northern Annular Mode (NAM) fields for days 0–60 following the sudden stratospheric warming (SSW) central date for thesynthetic SSW composites corresponding to the 10th and 90th percentile values of the North Atlantic Oscillation (NAO) (a–d) and East Canadian Ts (e–h)
indices. SLP, sea level pressure.

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Figure 4. Unfilled: histograms of the composite surface responses in the 60 days following the sudden stratospheric warming central date for (a) North
Atlantic Oscillation (NAO), (b) North Atlantic precipitation (mm/day), (c) North Pacific sea level pressure (SLP) (hPa), (d) Eurasian Ts (K), (e) Eastern
Canadian Ts (K), and (f) Eastern United States Ts (K), from the 2,000 synthetic composites. Hatched: histograms from the corresponding 2,000 climatologicalsynthetic composites.

main stratospheric vortex; further, the composite NAM anomaly at 100 hPa explains less than 25% of thevariance in the composite surface climate indices. Correlations between the 60-day surface anomalies andsliding windows of z-5 day across pressure levels and lag (Figure S6 in Supporting Information S1) showthat persistence of lower stratospheric anomalies to days 40–50 may be related to the strength of surface
anomalies. However, there are no instances in which the stratospheric spread explains more than 25% of
the surface variability. Therefore, we conclude that the vast majority of the spread in the surface composite
responses is a result of tropospheric internal variability, independent of the stratosphere.

4. Conclusions
Using over 60 years of data comprising 39 SSW events and applying a bootstrapping procedure to construct 2,000 synthetic SSW composites, we find that the Northern Hemisphere composite surface climate
anomalies following a composite SSW exhibit considerable uncertainty in both pattern and magnitude.
Well-known SSW responses such as a negative NAO and cooling across Northern Eurasia are robust, as aretemperature anomalies in Eastern Canada and the Eastern United States. However, these responses vary bya factor of 3 in magnitude, and the spatial extent of the anomalies also varies widely.
The key finding of this study is that, though the sign of the response is robust, the uncertainty in surface
response to SSWs is largely unrelated to polar vortex conditions; that is, a more disrupted polar vortex in agiven composite of SSW events does not correspond to stronger-magnitude surface anomalies in general.
This suggests that the range of patterns and amplitudes seen at the surface across the bootstrapped SSW
composites is the result of unrelated tropospheric variability. There is some relationship between descentand persistence of geopotential height anomalies to the lower stratosphere and the strength of anomalies
at the surface, in agreement with previous studies on variability across SSW events (Baldwin et al., 2003;
Christiansen, 2005; Gerber et al., 2009; Karpechko et al., 2017; Rao et al., 2020; Runde et al., 2016;
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Figure 5. Scatterplots of the composite anomalies of (a) North Atlantic Oscillation (NAO), (b) North Atlantic precipitation, (c) North Pacific sea levelpressure (SLP), (d) Eurasian Ts, (e) Eastern Canadian Ts, and (f) Eastern United States Ts in the 0–60 days following sudden stratospheric warmings versus thestrength of the composite stratospheric polar vortex in days 0–5 (z10-5 day), for each of the 2,000 synthetic composites. Blue and red dots denote the 10th and90th percentile composites respectively, for each surface climate index. The value r shown in each panel is the linear correlation coefficient between the twoquantities.

Siegmund, 2005). However, we find that this descent to the lower stratosphere makes only a minor contribution to the variability at the surface, leaving 75% or more of the spread across the synthetic SSW composites
to independent tropospheric sources. This is also in agreement with previous work (Baldwin et al., 2021;
Chan & Plumb, 2009; Charlton-Perez et al., 2018; Domeisen et al., 2020; Garfinkel et al., 2013).
Large ensembles of model simulations are often used to study phenomena with few observed events (i.e.,
V. Thompson et al., 2017; Wang et al., 2020). The observational results shown in this study can be used
to benchmark such climate model simulations of SSW responses. In models for which a large number ofsimulations under the same radiative forcing scenario are available (“initial-condition Large Ensembles”
Deser et al., 2020), the bootstrapping procedure can be bypassed and the SSW composites can be derived
directly for each ensemble member. Such an analysis will be helpful for distinguishing between true model biases and apparent biases due to sampling different tropospheric variability unrelated to SSWs. Thisapproach was applied to the evaluation of ENSO composite responses simulated by three climate model
Large Ensembles by Deser et al. (2017, 2018). Some models overpredict the strength or persistence of thenegative NAO response after SSWs (Kolstad et al., 2020), hampering their effective usage in NAO prediction
for government, industry, and health applications in Europe (Charlton-Perez et al., 2021; Domeisen & Butler, 2020). Thus, a careful evaluation of model response to SSWs that accounts for sampling fluctuations due
to independent tropospheric variability would be of societal benefit.

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Data Availability Statement
Japanese 55-Year Reanalysis (JRA-55) data are available from the Research Data Archive at the National
Center for Atmospheric Research (Japan Meteorological Agency, Japan, 2013).

Acknowledgments
The authors thank two anonymous reviewers for their constructive comments
and suggestions. J. Oehrlein is fundedby National Science Foundation (NSF)
grant DGE 16-44869. L. M. Polvani isfunded by NSF grant 1914569 to Columbia University. This material is based
upon work supported by the National
Center for Atmospheric Research,which is a major facility sponsored by
the National Science Foundation undercooperative agreement 1852977.

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