A CMIP6 Analysis of Past and Future Arctic Winter Stratospheric Temperature Trends

Reanalysis data reveal a weak warming trend in the midwinter Arctic stratosphere, contrary to the cooling expectation based on the greenhouse gas effect. This trend is also influenced by the occurrence of sudden stratospheric warmings (SSWs). Using Phase 6 of the Coupled Model Intercomparison Project (CMIP6) we investigate temperature trends over a similar timescale as ERA5 and find that CMIP6 models can replicate the positive midwinter temperature trend in the mid‐lower stratosphere. However, when considering the multi‐model mean, this positive temperature trend is much weaker than ERA5. Extrapolating to the future, we find that the SSW‐driven positive temperature trend will likely not continue in the future based on the SSP2‐4.5 and SSP5‐8.5 climate scenarios. Instead, the models project there will be widespread cooling throughout the Arctic winter stratosphere regardless of the occurrence of SSWs. Using a subsample of CMIP6 models which replicate the seasonality of the Arctic winter stratosphere most similarly to that of ERA5, we also find that the zonal wind strength during SSWs correlates the most with the temperature trends found there. However, trends in the zonal wind strength alone cannot account for the observed temperature trends among the CMIP6 models.

10.1029/2023JD039866 2 of 17 While most of the stratosphere has been cooling, there has been an unexpected weak dynamically induced warming trend in the mid-lower Arctic winter (December-February) stratosphere leaving a noticeable "cooling hole" (e.g., see Bloxam & Huang, 2022;Bohlinger et al., 2014;Ivy et al., 2016).More specifically, as Bloxam and Huang (2022) reveal, it is changes in the residual adiabatic motions that are largely responsible for the trend.Though the authors document that positive trends in surface temperature have also acted to warm the stratosphere, this alone cannot account for the observed temperature trends in the Arctic winter stratosphere.Bloxam and Huang (2022) also demonstrate that sudden stratospheric warmings (SSWs) play a substantial role in dictating this warming trend.When the 1980-2019 period is filtered according to years with and without SSWs, as seen in Figures 1a-1c, the connection between mid-lower stratospheric temperature trends and the occurrence of SSWs is evident.SSWs are associated with large-scale disturbances of the winter stratospheric polar vortex which can split in two or become displaced from its typical climatological configuration (see Baldwin et al. (2021) for an overview).Associated with this disruption of the polar vortex is a rapid heating of the stratosphere with temperatures reaching upwards of +50°K above normal, often within a matter of days (Baldwin et al., 2021;Butler et al., 2017;Limpasuvan et al., 2004).Following the onset of SSWs, the dynamical heating rates decrease, particularly in the case of long-lasting stratospheric warmings (Hitchcock, Shepherd, Taguchi, et al., 2013).As such, the rate at which the stratosphere cools following these events is based on the radiative relaxation timescales of the stratosphere which is the shortest in the upper stratosphere and increases as you approach the tropopause (Bloxam & Huang, 2021;Hitchcock et al., 2010;Newman & Rosenfield, 1997).In fact, as Baldwin et al. (2021), Bloxam and Huang (2021), and Butler et al. (2017) demonstrate, positive temperature anomalies can persist up to 60 days in the lowermost stratosphere following an SSW.Bell et al. (2010) mention that the negative temperature anomalies that occur before and after SSWs in the upper stratosphere approximately balance and the time-integrated response is equal to zero, having little impact on the mean-state temperature field.Meanwhile in the lower stratosphere the lingering temperature anomalies will dominate the time-integrated distribution and  (d-f) are displayed in (g-i), except using a subsample of CMIP6 models (see Table 1).CMIP6 data has been interpolated to match the latitudinal and pressure range of ERA5.Note that for the 10-250 hPa and 75°-90°N region the CMIP6 temperature trends are mostly insignificant at 95% (not shown).
3 of 17 will thus have a non-zero effect on the mean-state temperature.As such, the lingering temperature anomalies in the mid-lower stratosphere following SSWs is a possible reason why the positive temperature trend appears in the data.However, given that the historical analysis period presented here is only 40 years, it is possible that the SSW-induced warming trend is due to the limited number of years included in the analysis.In fact, we have determined that the Time of Emergence (ToE) of a statistically significant SSW-driven trend to appear will take between 40 and 80 years (see Supporting Information S1 and note that the ToE relies on both the trend and standard deviation).It is possible that with more years of data, this warming trend may decrease with time meaning that the variability introduced by the SSW-occurring years will stop impacting the trends as much.
Given the importance of understanding stratospheric temperature trends, it is important to ask, what will future Arctic winter stratospheric temperature trends look like?Will radiative cooling induced by the continued anthropogenic emissions of CO 2 dominate the trends as revealed by Maycock (2016) in their analysis of middle and higher climate forcing scenarios?Or will stratospheric variability play a role in at least partially offsetting the widespread cooling of the stratosphere by warming the lower Arctic stratosphere as mentioned by Bell et al. (2010) and Shepherd (2008)?To address this question, we use Phase 6 of the Coupled Model Intercomparison Project (CMIP6, Eyring et al., 2016).Using CMIP6, this research will first investigate historical Arctic winter stratospheric temperature trends and compare this to reanalysis data.We will then extrapolate to the future using Note.Summary of the CMIP6 models used in this evaluation.Included here are the names of the models, variants used, model top level, number of atmospheric levels, and reference to the model documentation.Bolded names indicate models with data available for the SSP2-4.5 and SSP5-8.5 experiments (in addition to the historical output).Models with an asterisk indicate those chosen to be part of a subsample of models for the historical results (see Section 3.4 for details) while circles represent a subsample of models used in the SSP2-4.5 and SSP5-8.5 analysis.

Table 1 List of CMIP6 Models Used in This Analysis
Since SSWs appear to be driving the historical temperature trends, at least in reanalysis data, this research is also motivated by determining which properties of SSWs are the most important.For instance, much work has been dedicated toward determining how the frequency of SSWs has changed in the past, in part due to climate change, and how the frequency will change in the future (e.g., see Ayarzagüena et al., 2020;Rao & Garfinkel, 2021;Wu & Reichler, 2020).But is the frequency of these events the most important when it comes to driving temperature change?As such, we will provide a regression analysis comparing temperature trends with a variety of metrics to establish which SSW properties impact temperature trends the most.

Reanalysis Data
The reanalysis data used to represent the true state of the atmosphere is provided by the European Centre for Medium-Range Weather Forecasts' (ECMWF) fifth generation reanalysis (ERA5) (Hersbach et al., 2020).The variables provided by ERA5 include meridional wind, zonal wind, and temperature.The wind data is taken twice daily (00:00 and 12:00) while monthly averaged and twice daily temperature data are also used.All variables have a 1° × 1° spatial resolution spanning the 1980-2019 period.Note that because this study is focused on temperature trends during the DJF period, the December data will correspond to the previous year.For example, the DJF period of 1980 uses the December data from 1979 while January and February data correspond to 1980.

CMIP6 Data
The CMIP6 models were chosen based on data availability and if the model has a well-resolved stratosphere.
Only high-top models (model top of at least 1 hPa or 50 km in height) are considered here as it has been well documented that high-top models are better at capturing more realistic stratospheric variability and SSW characteristics than low-top models (e.g., see Charlton-Perez et al., 2013;Osprey et al., 2013;Palmeiro et al., 2020;Rao et al., 2022).The CMIP6 models must have daily averaged temperature, zonal, and meridional wind, along with monthly averaged temperature for the historical simulations and the SSP2-4.5 and SSP5-8.5 experiments.Though CMIP6 historical output often extends back to 1850, we use the 1975-2014 period instead since we want to replicate ERA5 as closely as possible.Furthermore, as Eyring et al. (2016) mention, the CMIP6 historical forcings are predominately based on observations and since stratospheric observations prior to the 1980s are generally sparse, we limit the number of years included in this analysis before that time.The SSP2-4.5 and SSP5-8.5 future climate scenarios represent different Shared Socioeconomic Pathways (SSP) of human development.For more information on the scenario types and their differences see O'Neill et al. (2016).A complete list of all 24 CMIP6 models investigated in this analysis can be found in Table 1.Note that in our analysis of CMIP6 temperature trends, we only use one ensemble member from each climate model due to computational considerations.

Detecting a Sudden Stratospheric Warming
The most well-known definition of an SSW states that a major SSW has occurred when there is a reversal of the zonal-mean zonal winds at 10 hPa and 60°N during the extended winter period (see Charlton & Polvani, 2007).
In this work, we instead use the cosine-weighted average of the daily mean zonal-mean zonal winds between 55° and 70°N  ( 55−70 ) .This latitudinal range to check for zonal wind reversals is based on Butler and Gerber (2018), who demonstrate that key properties of SSWs are maximized when reversals of the zonal wind are situated between 55° and 70°N.Moreover, as Palmeiro et al. (2015) point out, when using 55°-70°N this assures that the polar vortex edge is captured even in the cases where climate models have vortex biases.We also stipulate that there must be a reversal of the temperature gradient within 10 days of the initial wind reversal (e.g., see Butler et al., 2015).As in Butler and Gerber (2018), we extend the period for detecting SSWs such that they can be detected at any point after the polar vortex has formed.The polar vortex formation date is based on when  55−70 turns westerly after 1 July and stays westerly for at least 10 days (Ayarzagüena et al., 2020).Conversely, the vortex break-up date is the last day when  55−70 becomes easterly and does not return to a westerly configuration for more than 10 consecutive days (see Butler & Gerber, 2018).We maintain from the original definition that SSWs BLOXAM AND HUANG 10.1029/2023JD039866 5 of 17 must be separated by at least 20 days to ensure the radiative relaxation of the stratosphere.Also, to ensure that any SSW isn't associated with the final warming of the season we exclude any events whereby the zonal winds become easterly but do not return to a westerly configuration for more than 10 consecutive days before the polar vortex break-up date.Note that our definition does not require a 20-day separation between the last SSW of the season and the vortex break-up.The extended period of analysis is used to measure how well the climate models are at capturing a realistic monthly distribution of the events.

Anomalies, Climatologies, and Trend Analysis
We note here that when determining any anomaly, we use the methodology outlined by Hitchcock, Shepherd, and Manney (2013) whereby deseasonalized and detrended anomalies are computed by fitting a linear trend through the data for each calendar day.See Text S3 in Supporting Information S1 for more details.Climatologies are determined daily and smoothed using a Fourier transform.All trends reported in this analysis use a linear least squares fit of the data.

Historical SSW Frequency and Monthly Distribution
To begin, we present the monthly distribution of SSWs (based on initial zonal wind reversal) in Figure 2a.According to ERA5, ∼80% of SSWs occur during the mid-winter (DJF) period and no events occur prior to December or later than March.In comparing CMIP6 to ERA5 we find most models have an early and late season bias in the time of occurrence.This bias is well known and has also been reported in other works (e.g., see Rao & Garfinkel, 2021;Rao et al., 2021Rao et al., , 2022)).This bias in the timing of SSWs could be linked to an overestimation of the background wave injection into the stratosphere at these times (Palmeiro et al., 2022).However, as Rao and Garfinkel (2021) mention, this bias could also be created due to the limited data record of reanalysis and in this case the limited number of years included in the historical analysis of the CMIP6 models.
The frequency of DJF-occurring SSWs is depicted in Figure 2b.We find that the majority of CMIP6 models produce fewer DJF-occurring SSWs than ERA5 (0.65 SSWs/year), though the confidence interval of all models falls within that of ERA5.Other works that have investigated SSW frequencies such as Ayarzagüena et al. (2020) and Rao and Garfinkel (2021) report a historical frequency of SSWs between 0.55 and 0.65 SSWs/year based on the NCEP/NCAR and JRA-55 reanalysis data.Although we use ERA5 in our work, Rao and Garfinkel (2021) mention that NCEP/NCAR and JRA-55 produce similar results to ERA5.We note, however, that these other works calculate a frequency of SSWs that extends over more months of analysis, instead of just DJF.As such, the high frequency of SSWs reported here is related to our detection algorithm which includes more latitudes (55°-70°N) and thus captures more variability of the polar vortex than the stringent 60°N definition.Like Ayarzagüena et al. (2020) and Rao and Garfinkel (2021) we find a large degree of variability among the CMIP6 models.Wu and Reichler (2020) mention that this variability in the frequency of SSWs is likely associated with the strength of the polar vortex in the CMIP6 models and the associated upward wave activity to the stratosphere.Too strong of a polar vortex will inhibit wave activity while too weak of a vortex will allow more upward propagating waves into the stratosphere which can initiate an SSW.

Arctic Winter Stratospheric Climatology
Before discussing CMIP6 historical temperature trends, it is advantageous to investigate how well the GCMs replicate ERA5's Arctic winter stratospheric seasonal climatology.In Figure 3a, we plot the climatological evolution of  55−70 at 10 hPa over the October-April period.We find that the standard deviation of  55−70 of most CMIP6 models (not shown), falls within ± 1σ of ERA5 during the DJF period.However, it is noticeable that, aside from the magnitude of  55−70 , the seasonality of the polar vortex is quite variable among the models with some of the models showing a peak in the strength of the vortex occurring later in the winter rather than mid-winter, as indicated by ERA5.Again, this variability in timing and strength of the polar vortex which Rao et al. (2015Rao et al. ( , 2021) also find in their work is likely related to wave activity differences among the models as Wu and Reichler (2020) mention and could impact the temperature structure and trends of the stratosphere.
Another important consideration is how well CMIP6 models replicate the seasonality of the temperature structure of the mid-lower Arctic winter stratosphere.In Figures 3b and 3c  at 10 and 100 hPa.In comparing   75−90 at 10 hPa of the CMIP6 models to ERA5, we find that many of the models struggle to reproduce a winter seasonal cycle that falls within ± 1σ of ERA5, having a mid-stratosphere that runs too warm in the early winter.At 100 hPa, on the other hand, most of the models are within ± 1σ of ERA5 with only a few models that are too warm during the DJF period.
In comparing the CMIP6 zonal wind and temperature climatological seasonal cycles to ERA5, 14 of the models are within ± 1σ of ERA5 throughout the entire DJF period and are indicated by an asterisk in Figure 3.

Historical DJF Temperature Trends
Illustrated in Figure 1d is the multi-model mean of all 24 CMIP6 temperature trends along with the standard deviation.Though we find a small positive temperature trend in the lower polar stratosphere, the signal is much weaker and less widespread than ERA5 (see Figure 1a).When we filter the trends according to years with and without SSWs (Figures 1e and 1f) we find a slightly stronger warming trend in the SSW years, though still much weaker than ERA5 (Figure 1b), while the warming trend in the non-SSW-occurring years has disappeared, similar to ERA5 BLOXAM AND HUANG 10.1029/2023JD039866 7 of 17 (Figure 1c) (see Text S2 in Supporting Information S1 for the justification of filtering the years with and without SSWs).Also noticeable is the large degree of variability between the models.Aside from the sign, some of this variability can be attributed to the spatial distribution of the trends.For instance, in the EC-Earth3-Veg model the stratospheric warming trend is much narrower, confined around 100 hPa (not shown), while the warming trend in MRI-ESM2-0 is much larger spatially, extending from ∼10 to 250 hPa (not shown).This may be the result of inherent biases in the models.For example, Palmeiro et al. (2022) mention that the EC-Earth3 model simulates too strong of a polar vortex in the upper stratosphere which could inhibit wave activity and ultimately reduce the amount of dynamical heating there.
If instead of using all 24 GCMs we select the ones which capture a similar DJF zonal wind and temperature seasonal cycle compared to ERA5 (see Section 3.2) and we remove the two outliers along with EC-Earth3 (see Section 3.4 for details), the resulting temperature trends of those 11 models are found in Figures 1g-1i.We find a slightly warmer trend in the all years, a more robust positive temperature trend during the SSW-only years, and a stronger cooling trend in the non-SSW-occurring years.However, despite using this subsample of CMIP6 models, there remains some uncertainty over the sign of the temperature trends.
Altogether, Figure 1 indicates that GCMs can replicate the sign of the temperature trend but with a noticeably weaker magnitude, possibly due to inherent biases of the models (see Section 4).Nevertheless, given that CMIP6 models can qualitatively capture the cooling hole, it is worth examining the future projection in Section 3.5.

Regression Analysis of Historical SSW Properties and Temperature Trends
In this section we provide an overview of the trends of a variety of SSW properties in terms of their relationship to the temperature trends and in doing so provide an investigation of inter-model differences.A complete list of all SSW properties investigated and how well they correlate with the historical 10-250 hPa pressure weighted and 75°-90°N cosine weighted average DJF temperature trends  (  10−250ℎ  75−90 ) during SSW-occurring years can be found in Table 2.Note that the initial 14 CMIP6 models used in this regression analysis were chosen based on their ability to capture a similar DJF seasonal climatology of stratospheric zonal wind and temperature to ERA5 (see Section 3.2).

When the trend in 𝐴𝐴 𝑇𝑇
10−250ℎ  75−90 is regressed against the trend in the starting date of the DJF-occurring SSWs we find a small degree of anticorrelation between the two, suggesting that SSWs occurring earlier in the DJF period are more associated with a positive temperature trend while events that occur later in the DJF period show more negative temperature trends.Gómez-Escolar et al. (2012) mention that variations in the seasonal distribution of SSWs can result in discrepancies to the climatological state of stratospheric temperatures, which in our case may be impacting the temperature trends.
Given how much effort has been dedicated to investigating how SSW frequencies have changed and will change in the future, a surprising result of this regression analysis is that there is only a weak relationship (R 2 value of 0.21) between temperature trends and SSW frequency trends.
The strength of the zonal wind reversals during SSWs and their relationship to temperature trends is also explored  Note.Summary of the correlation coefficients (R), coefficients of determination (R 2 ), and p-values describing the relationships between the DJF-averaged temperature trends during sudden stratospheric warming (SSW)-occurring years and various SSW properties.The first number in each column relates to the 14 CMIP6 models with an asterisk in Figure 2 while the second number relates to the same models excluding ACCESS-CM2, EC-Earth3, and MIROC6 which were deemed as outliers or have known biases.Bolded names and values indicate the SSW properties with the highest correlation.

Table 2 Regression Analysis of Sudden Stratospheric Warming-Driven Temperature Trends
BLOXAM AND HUANG 10.1029/2023JD039866 9 of 17 relationship such that when the winds are weakened (i.e., more negative), this correlates with a stronger temperature trend.
In addition to using the minimum of the zonal wind as an indicator of the strength of SSWs, we also use the anomaly.Note that in determining the maximum temperature and anomaly we look at the −10 to +20 day period surrounding the initial reversal of the zonal winds.We find a positive relationship between the temperature trends and the trend in the maximum temperature reached during SSWs and the associated temperature anomaly.This implies that the strength of SSWs has an impact on the temperature trends.We also explore the relationship between the temperature trend and the duration of the temperature anomaly (measured as the number of days the temperature anomaly is greater than 1°K following the time when the maximum temperature anomaly is reached).Given the positive correlation, it appears that longer lasting temperature anomalies are impacting the temperature trends.
Since SSWs are largely the result of upward propagating planetary waves (primarily wavenumbers 1-2) (Baldwin et al., 2021), a commonly used metric to measure wave activity is the meridional eddy heat flux,   ′  ′ , where v is the meridional wind, T is the temperature, primes indicate the deviation from the zonal average, and the overbar implies the zonal average has been taken.Most commonly, the eddy heat flux is investigated at 100 hPa over a range of latitudes (e.g., see Hall et al., 2021;Palmeiro et al., 2020Palmeiro et al., , 2022)).However, for our regression analysis we use a cosine weighted average over the 45°-75°N region and a pressure weighted average over the 10-250 hPa layer of the atmosphere  (  ′  ′ 10−250ℎ

45−75𝑁𝑁
) . We choose to incorporate multiple levels of the atmosphere, instead of the typical 100 hPa, to capture more variability among the CMIP6 models.To gain a sense of the wave activity to the stratosphere prior to and after the onset of SSWs, we determine the 0-20-day average of before and after the initial reversal of the zonal winds and the associated anomalies (see Figure S6d in Supporting Information S1 for typical meridional eddy heat flux anomaly values during SSWs).Another surprising result of this regression analysis is the negative and very weak correlation among the trends of these four properties which suggests that wave forcing of the models cannot explain the observed temperature trends.
Based on their R 2 value, the five SSW property trends with the highest correlation are: the maximum  In examining Figure 4, it also becomes apparent that there are some potential outliers among this sample of 14 CMIP6 models, the most obvious being MIROC6.To help elucidate the impact MIROC6 and other outliers have on the temperature trends we create another subsample of CMIP6 models whereby only the models in which the 95% confidence interval of their temperature trend is also within the 95% confidence interval of ERA5.In doing so, this eliminates ACCESS-CM2 and MIROC6 from the 14-model sample.However, as we have mentioned throughout this work, there are known biases in the EC-Earth3 model and so we have also removed it from this new subsample of CMIP6 models.In revisiting Table 2 we can see the impact these three models were having on the regression analysis (see the second number listed in each column) whereby over half of the correlation coefficients have changed sign.Furthermore, among the reported SSW properties with the highest correlation, except for the average of ) reached during the events and the trend in the minimum anomaly of   10ℎ  55−70 have become significant (though weak).In reviewing the regression analysis using this subsample, the connection between temperature trends and trends in zonal wind strength (based on R 2 values) becomes apparent.

Future Temperature Trends Under the SSP2-4.5 and SSP5-8.5 Scenarios
The 17-model (see Table 1) averaged temperature trends under the SSP2-4.5 climate scenario are presented in Figure 5a.Also depicted in Figures 5b and 5c are the SSW-driven temperature trends and the non-SSW-driven temperature trends.Together these figures indicate that SSWs are projected to have a minimal impact on future temperature trends and instead there is more widespread cooling throughout the stratosphere.However, there is some uncertainty as to the sign of the trend in the mid-lower stratosphere based on the standard deviation.We also determine the temperature trend using the same subsample as those used in Figures 1g-1i (excluding the BLOXAM AND HUANG 10.1029/2023JD039866 10 of 17 models that do not have SSP2-4.5 data available-see Table 1).Unlike the historical results, choosing models that can well replicate ERA5's winter stratospheric climatology did not produce a more robust signal.Instead, the temperature trends continue to show a considerable amount of uncertainty in the mid-lower stratosphere.
The predicted temperature trends under the SSP5-8.5 scenario can be found in Figure 6.Here the cooling trend is more robust which aligns with the amount of CO 2 injected into the atmosphere in this scenario, inducing strong radiative cooling rates in the stratosphere.As such, regardless of filtering the years according to with or without SSWs, the powerful longwave radiative cooling rates dominate and any changes associated with dynamical heating are likely being masked.
Given the amount of uncertainty that remains in the predicted temperature trends, is it possible to determine when a significant trend will emerge?To answer this question, we have determined the ToE using two CMIP6 models, EC-Earth3-Veg and MRI-ESM2-0 (see Supporting Information S1).Under the SSP2-4.5 scenario, there is a considerable amount of uncertainty in both EC-Earth3-Veg and MRI-ESM2-0, indicating that a significant temperature trend will not appear for hundreds of years.Though the ToE under the SSP5-8.5 scenario for both climate models decreases, there remains a large amount of uncertainty in the mid-lower stratosphere over the timing of a significant trend to appear.Based on the analysis presented here, it is likely that the temperature trends will decrease in the future.However, as the ToE suggests, there remains a significant amount of uncertainty.Depending on how well CMIP6 models produce realistic SSWs, this could impact the temperature structure and trends of the stratosphere.As it stands, the current temperature trends exhibited by ERA5 over the past 40 years have the strongest signal and lowest ToE value.As such, more years of data are required before we can concretely determine Arctic winter stratospheric temperature trends and if SSWs are in fact impacting these trends.

Regression Analysis of Future SSW Properties and Temperature Trends
Using the same subsample of models that were included in the SSP2-4.5 and SSP5-8.5 temperature trends (Figures 5 and 6d-6f) we perform the same regression analysis done in Section 3.4 but for the SSP2-4.5 and SSP5-8.5 climate forcing scenarios (see Table S1 in Supporting Information S1).In comparing the historical regression analysis (using the subsample) to the regression analysis of future temperature trends we can gain insight into how SSW properties have changed and how this may be impacting the temperature trends.Among the SSW properties tested in this regression analysis, seven maintained the same sign of the correlation coefficient from the historical to the two future climate forcing scenarios.However, a quick glance at the p-values indicates that most of these metrics are insignificant.In fact, when looking at the SSP2-4.5 scenario almost all the correlation coefficients are insignificant.This could be in part due to the relatively weak temperature trends found in the models included in the SSP2-4.5 analysis (see Figure 5).As a result, for the remainder of this section, we will compare the historical regression analysis to SSP5-8.5.
Among the correlation coefficients, the three SSW properties that not only share the same sign but also have the highest and most significant correlation coefficients shared between the historical and SSP5-8.5 data include: the minimum SSW  | 10ℎ  55−70 , the minimum SSW  | 10ℎ  55−70 anomaly, and the average  | 10ℎ  55−70 over the −20 to 0 day period before SSW.In Figure 7 we provide scatter plots of these three properties for the subsample of CMIP6 models that are available for both the historical (black) and SSP5-8.5 scenario (blue).Aside from demonstrating  1).Black contours represent the multi-model standard deviation while stippling indicates if at least 2/3 of the models agree on the sign of the trend.CMIP6 data has been interpolated to match the latitudinal and pressure range of ERA5.Note that the majority of the CMIP6 temperature trends are significant at 250 hPa and below, however for the 10-100 hPa and 75°-90°N region the trends are mostly insignificant at 95% (not shown).
BLOXAM AND HUANG 10.1029/2023JD039866 12 of 17 the connection between temperature trends and polar vortex strength, these scatter plots also provide a useful means to determine how changes in any of these properties have influenced temperature trends.It stands to reason that if there has been a change in the sign of a given property trend, this should also induce a change in the sign of the temperature trend.However, in analyzing Figure 7, only in the EC-Earth3-CC and KACE-1-0-G models do we find this to be the case for the trend in the minimum  | 10ℎ  55−70 and the minimum SSW  | 10ℎ  55−70 anomaly.While only for EC-Earth3-CC do we also find this to be the case for the average  | 10ℎ  55−70 over the −20 to 0 day period before SSW.Of the 8 models analyzed here only UKESM1-0-LL can be found in the same quadrant for all three scatter plots.Together this implies that despite picking three properties with the strongest correlations, these SSW properties alone cannot explain the observed temperature trends and instead it is likely a combination of factors that are driving the trends, aside from the enhanced radiative cooling rates.

Discussion
While the historical regression analysis in this study (see Section 3.4) provides valuable insights into the most important SSWs properties in terms of their relationship with temperature trends, we can also gain some crucial information on the performance of CMIP6 by comparing these models to ERA5.In looking at the 40-year temperature trends of ERA5 and CMIP6 (see Figure 4) we find that apart from HadGEM3-GC31-LL, none of the other 13 GCMs included in this regression analysis have a temperature trend as strong or stronger than ERA5, which may suggest an inherent bias among these models.One source of bias may be traced to the definition of an SSW.For instance, Palmeiro et al. (2015) mention that the decadal variability of SSWs is sensitive to the SSW definition.The authors stipulate that only definitions that include a wind reversal should be included as to remove any impact minor warming events (no wind reversal) may have on the analysis.On the other hand, Kim et al. (2017) suggest that the frequency of SSWs using the standard wind reversal definition is quite sensitive to model mean biases associated with, in their case, CMIP5.Associated with the definition of an SSW is a reflection on the state of the polar vortex.Depending on how well climate models can reproduce a realistic vortex and capture its seasonal morphology, this can lead to biases among the climate models.For example, Palmeiro et al. ( 2022) BLOXAM AND HUANG 10.1029/2023JD039866 13 of 17 demonstrate that EC-Earth3 simulates too strong of polar vortex in the upper stratosphere.As such, this could also explain why the positive temperature trend in EC-Earth3-Veg (not shown) is concentrated in the lower stratosphere, compared to reanalysis where the trend is more widespread throughout the Arctic winter stratosphere.
In fact, as Wu and Reichler (2020) reveal, the most reliable indicator for SSW frequency in CMIP5 and CMIP6 is the climatological mean strength of the polar vortex, followed by wave activity in the lower stratosphere.The inability of models to capture a realistic polar vortex strength, particularly in the upper stratosphere, could also explain, in part, why in Figure 3 we find that 10 of the 24 models do not reproduce the climatological temperature evolution at 10 hPa well when compared to ERA5.Furthermore, according to Kim et al. (2017), SSWs appear more frequently in models that have a weaker climatological polar vortex.They demonstrated that if a tendency-based definition (i.e., polar vortex deceleration) is used instead of the standard wind reversal definition, only strong vortex decelerations are detected and the SSW frequency becomes correlated with climatological upward wave activity situated at 100 hPa.
This prompts a discussion of what type of SSWs should be used in our analysis of temperature trends.For instance, in selecting only stronger vortex decelerations, this may improve our detection of SSW-induced temperature trends.For example, as Butler and Gerber (2018) demonstrate, by selecting events that are subject to a more negative zonal wind reversal threshold this will filter out weaker vortex reversal events and will generally lead to larger temperature increases among the selected events.Aside from selecting SSWs based on the strength of the polar vortex deceleration, another way to filter out the weaker SSWs is to focus on a type of SSW known as a BLOXAM AND HUANG 10.1029/2023JD039866 14 of 17 polar-night jet oscillation (PJO).This form of stratospheric variability is characterized by a downward propagation of anomalous polar temperatures and zonal-mean zonal wind anomalies (Kuroda & Kodera, 2001).In addition, PJOs are also associated with extended stratospheric recovery times, meaning that temperature anomalies in the lower polar stratosphere can persist for months.As Hitchcock, Shepherd, and Manney (2013) mention, this long recovery phase of the stratosphere is strongly related to the depth of the initial warming and to the radiative dampening time scales in the lowermost stratosphere.Furthermore, PJOs are also associated with a strong suppression of upward fluxes of wave activity and that this suppression lasts much longer than non-PJO events.Hitchcock, Shepherd, and Manney (2013) also mention that PJO events account for approximately half of all SSWs and that they are associated more so with vortex splitting events rather than displacement type events.However, as Hall et al. (2021) report, there is a persistent bias among CMIP6 models in the underrepresentation of vortex splitting events due to a large positive bias in the strength of the stratospheric zonal winds which inhibits the propagation of wavenumber 2 planetary waves, which are typically associated with split events.With an underrepresentation of split events in CMIP6, this could implicate the number of PJO-type events produced by CMIP6 models, and in turn impact the resulting temperature trends.
Another possible way to filter SSWs to test for their impact on temperature trends is to separate them according to whether they are an absorbing or reflecting type event.As Kodera et al. (2016) discuss, absorbing events are similar to PJOs in that they are characterized with a longer timescale and there is a downward propagation of the zonal wind deceleration and positive temperature anomalies.Unlike PJOs, however, absorbing type events are the result of persistent incoming planetary waves from the troposphere.Reflection type events, on the other hand, represent SSWs whereby there is an abrupt halt to the warming due to the reflection of planetary waves.Reflected waves from the stratosphere, marked by periods of negative eddy heat flux, act to cool and strengthen the polar vortex by weakening or reversing the residual circulation (e.g., see Lawrence et al., 2020;Shaw & Perlwitz, 2014).In the case of the research presented here, there is a potential for biases to occur depending on how frequently CMIP6 models generate either absorbing or reflecting type SSWs, as this will impact both the duration and the depth to which temperature anomalies penetrate in the stratosphere and in turn the resulting temperature trends.
The amount and timing of wave activity to the stratosphere is another potential source of bias among the CMIP6 models.For instance, as Palmeiro et al. (2020) suggest, the background climatological eddy heat flux has a major impact on the seasonality of SSWs.Palmeiro et al. (2022) speculate that an overestimated background wave injection in the EC-Earth model could be linked to an overestimated number of SSWs occurring in early winter and that this overestimated wave activity is related to a weaker lower-stratospheric polar vortex and less effective wave filtering.Palmeiro et al. (2022) also mention that another contributor to the bias is the parameterized non-orographic gravity wave driving, which for EC-Earth may be excessive.As such, if the timing and strength of the wave activity is not realistic among the CMIP6 models this can lead to late/early season biases in the occurrence of SSWs which in turn may again impact temperature trends.
There are several other potential sources of bias that could impact the results of this study.For instance, in our analysis of CMIP6 temperature trends, we only use one ensemble member from each GCM.In doing so, we may have inadvertently excluded some models that demonstrate SSW-induced temperature trends among the variants not used in this study.Another potential source of bias is related to the time periods of this study.It is entirely possible that if we had chosen a longer historical time scale, that the temperature trends would not show as much variability among the CMIP6 models.It is also possible that if we used the back extension of ERA5 data, the temperature trends would look different.Finally, the relationship (or lack thereof) between the meridional eddy heat flux and temperature trends could change if different latitudes, pressure levels, and periods of time are chosen.

Conclusions
Sudden stratospheric warmings have played an integral role in the recent temperature trends of the Arctic winter stratosphere.It has been found that when the 1980-2019 period is filtered according to years with and without SSWs, it is the SSW-occurring years that are dictating the midwinter (December-February) temperature trends in the Arctic stratosphere (Figure 1).Motivated by this finding, this work uses CMIP6 to explore what future temperature trends may look like and if SSWs will continue to drive the positive temperature trends found in the Arctic winter stratosphere.This work first establishes which CMIP6 models capture a realistic monthly distribution and DJF frequency of SSWs over a historical period (Figure 2).In total 24 high-top CMIP6 models are explored.We find a systematic early and late bias in the occurrence of SSWs among the majority of the CMIP6 models, compared to ERA5 reanalysis data.We also find a large degree of variability in the frequency of SSWs with most of the models producing too few DJF-occurring SSWs, though all models are within the 95% confidence interval of ERA5.
The seasonal climatology of the Arctic winter stratosphere among CMIP6 models is also explored and compared to ERA5 (Figure 3).We find that  55−70 at 10 hPa is well represented by the models, though there are some clear biases regarding the strength and timing of the polar vortex.Compared to ERA5,  55−70 in some models peaks too soon during the DJF period while for others it is too late.We also find that while the   75−90 at 100 hPa is in general well captured by CMIP6, the same cannot be said for 10 hPa, whereby 10 out of the 24 CMIP6 models do not always fall within ± 1σ of ERA5 during the DJF period.
The mutli-model mean of the historical  temperature trends of CMIP6 are determined (Figure 1) and though the CMIP6 models capture a positive SSW-driven temperature trend in the mid-lower stratosphere it is much weaker and less widespread than ERA5.Moreover, when choosing a subsample of CMIP6 models that are best able to capture a realistic Arctic winter climatology, compared to ERA5, we find similar results to when all 24 GCMs are included.
A 17 multi-model mean of future (2015-2100) CMIP6 Arctic winter temperature trends under both the SSP2-4.5 and SSP5-8.5 climate forcing scenarios (Figures 5 and 6) are also determined.We find that regardless of the climate forcing scenario, the models project widespread cooling throughout the winter Arctic stratosphere regardless of the occurrence of SSWs.However, particularly in the case of SSP2-4.5, there remains a considerable amount of uncertainty over the sign of the temperature trend in the mid-lower stratosphere.
A regression analysis is also performed among a subsample of CMIP6 to examine a variety of SSW properties and determine how well they correlate with the temperature trends.Among the metrics tested, the three most important properties that were shared between the historical and SSP5-8.5 scenario include the trends in: the minimum zonal wind reached during an SSW, the minimum zonal wind anomaly, and the zonal wind averaged over the −20 to 0 days before the onset of an SSW.Together these SSW properties indicate that the strength of the polar vortex has an important role over temperature trends.However, these properties alone cannot account for the observed temperature trends among the CMIP6 models.
In comparing the models used in the historical regression analysis to ERA5, we find that aside from one model, none of the other models exhibit a DJF SSW-induced temperature trend as strong or stronger than ERA5.This result highlights how inherent CMIP6 model biases could be impacting the temperature trends.
It is evident that more research is required to explain the variability among the CMIP6 temperature trends, both historical and predicted.Future work on temperature trends in the Arctic winter stratosphere should also focus on the type of SSW that is being produced as this may have a substantial impact on projected temperature trends.

Figure 1 .
Figure 1.The 1980-2019 DJF averaged ERA5 temperature trends broken up according to all years (a), sudden stratospheric warmings (SSWs)-occurring years (b), and non-SSW years (c) with stippling indicating significant trends at 95%.The 1975-2014 DJF averaged Coupled Model Intercomparison Project (CMIP6) composite temperature trends broken up according to all years (d), SSW-occurring years (e), and non-SSW years (f) with black contours representing the multi-model standard deviation and stippling indicates if at least 2/3 of the models agree on the sign of the trend.Similar figures as(d-f) are displayed in (g-i), except using a subsample of CMIP6 models (see Table1).CMIP6 data has been interpolated to match the latitudinal and pressure range of ERA5.Note that for the 10-250 hPa and 75°-90°N region the CMIP6 temperature trends are mostly insignificant at 95% (not shown).

Figure 2 .
Figure 2. The percent of total sudden stratospheric warmings (SSWs) that occurred during the 1975-2014 (CMIP6) and 1980-2019 (ERA5) periods separated into the month of the initial zonal wind reversal (a) and the DJF frequency (# of SSWs/year) of SSWs that occurred during the same periods (b).The black error bars indicate the 95% confidence interval using a Poisson distribution.

Figure 3 .
Figure 3.The 55°-70°N cosine weighted climatological zonal wind at 10 hPa spanning the October-April period (a).The 75°-90°N cosine weighted climatological temperature at 10 hPa (b) and 100 hPa (c).Black lines represent ERA5 with the associated standard deviation indicated by the black shading.CMIP6 models are represented by colored lines (color coding created by Holy (2023)).CMIP6 models with an asterisk indicate those in which their standard deviations (not shown) are within ± 1σ of ERA5 throughout the December-February period for all three panels.
by investigating the trends in the minimum value of u 55−70N at 10 hPa  (  10ℎ  55−70 ) reached during the events and the trend in the minimum anomaly of   10ℎ  55−70 .The results indicate a negative relationship between the temperature trend and the strength of the polar vortex disruption.Models with a stronger zonal wind reversal are associated with a more positive temperature trend while weaker zonal wind reversals are linked with negative temperature trends.We also examine the relationship between the average of   10ℎ  55−70 over the −20 to 0 day period before the onset of DJF-occurring SSWs, and the 0-20 day period following the central date (see FigureS6ain Supporting Information S1 for the typical zonal wind behavior during SSWs).The results again indicate a negative over the −20 to 0 day period before the onset of SSWs, and the frequency of SSWs.The scatter plots associated with these five properties are presented in Figure4.
over the −20 to 0 day period before the onset of SSWs, all other properties are now insignificant.Using this new subsample of CMIP6 models the trend in the minimum value of u 55−70N at 10 hPa  (

Figure 4 .
Figure 4. Scatter plots of the DJF CMIP6   10−250ℎ  75−90 trends for the sudden stratospheric warming (SSW)-occurring years as a function of the trend in the DJF frequency of SSWs (a), the average  55−70 for the −20 to 0 day period before the SSW starting date (b), the maximum   10−250ℎ  75−90 reached (c), the maximum   10−250ℎ  75−90 anomaly reached (d), and the duration of the

Figure 5 .
Figure 5.The 17-model average of the 2015-2100 DJF averaged SSP2-4.5 temperature trends broken up according to all years (a), sudden stratospheric warming (SSW)-occurring years (b), and non-SSW years (c).Similar figures as (a-c) are displayed in (d-f) but use a subsample of CMIP6 models (see Table1).Black contours represent the multi-model standard deviation while stippling indicates if at least 2/3 of the models agree on the sign of the trend.CMIP6 data has been interpolated to match the latitudinal and pressure range of ERA5.Note that the majority of the CMIP6 temperature trends are significant at 250 hPa and below, however for the 10-100 hPa and 75°-90°N region the trends are mostly insignificant at 95% (not shown).

Figure 6 .
Figure6.The same as Figure5except for the SSP5-8.5 climate forcing scenario.Note that the majority of the CMIP6 temperature trends are significant at 250 hPa and below and from 10 hPa and above (not shown).However, for the 10-100 hPa and 75°-90°N region the trends are mostly insignificant at 95% if the model indicates a warming trend while cooling trends tend to be significant.

Figure 7 .
Figure 7. Scatter plots of a subsample of CMIP6 models depicting the DJF   10−250ℎ  75−90 trends for the sudden stratospheric warming (SSW)-occurring years as a function of the trend in the minimum value of  55−70 reached during SSWs (a), the minimum  55−70 anomaly (b), and the average  55−70 for the −20 to 0 day period before the SSW starting date (c).The black data points are historical data while the blue markers are for the SSP5-8.5 scenario.