Asymmetric warming rates between warm and cold weather regimes in Europe

In Europe, the increase in temperatures caused by climate change has been particularly fast in the cold season. Although the magnitude of this change is relatively well known, less research has been done on how the increase of temperatures is manifested in different large‐scale weather types, called weather regimes. For example, one could expect that the weather patterns in which air is flowing from the rapidly‐warming Arctic would have warmed faster than other weather patterns in recent decades. Here we show that such an asymmetric warming actually occurs in the four Euro‐Atlantic weather regimes. In northern Europe, the weather regime which is typically associated with cold airmasses from the Arctic (NAO–) has warmed about 25% faster than the cold‐season days on average, and about 60% faster than the regime where the air flows from the North Atlantic (NAO+). Consequently, the weather regime that on average brings the coldest weather is warming the fastest in a large part of northern Europe. In contrast, the weather regime that typically brings the warmest weather has warmed the slowest, especially in the continental Europe. Our results provide a new perspective on the reported decrease of sub‐seasonal temperature variability.


| INTRODUCTION
In northern Europe, wintertime temperature variability on sub-seasonal-to-seasonal timescales is strongly influenced by large-scale tropospheric circulation patterns.For example, it is well known that the positive phase of North Atlantic Oscillation (NAO) leads to overall warmer and wetter than normal winters in northern Europe (e.g., Hurrell et al., 2003).A notable recent example of this was the winter of 2019/2020, which was anomalously warm and wet in the United Kingdom and Fennoscandia due to the positive phase of the NAO and the closely-related Arctic Oscillation (AO) (Davies et al., 2021;Hardiman et al., 2020;Lawrence et al., 2020;Lehtonen, 2021).In contrast, the negative phase of NAO is associated with colder and drier than normal winter conditions in northern Europe on both seasonal (Cattiaux et al., 2010;Jung et al., 2011) and sub-seasonal timescales (Overland et al., 2020).The second-leading pattern of mid-tropospheric geopotential height variability in the North Atlantic, known as Scandinavian Blocking in its positive phase, is also particularly important for modulating severe wintertime cold in northwestern Europe (Ferranti et al., 2018).
Changes in atmospheric circulation can also modulate regional temperature trends.Vihma et al. (2020) studied how the winter mean temperatures have changed in Europe depending on the direction of the airmass origin.They found that in northeastern Europe (Helsinki, Moscow) airmasses originating from the southeast have experienced weak cooling while airmasses arriving from other directions have warmed.They attribute this finding to increased occurrence of negative NAO (NAO-) patterns.According to Räisänen (2019), changes in atmospheric circulation have enhanced the 1979-2018 warming trend in southern Finland during November and December but slowed the warming in the months of January-March.
A common approach to characterise the large-scale circulation variability in the European-North Atlantic region is to use cluster-based weather regimes (Cassou, 2008;Vautard, 1990).Such an approach aims to capture recurrent and persistent states in the circulation (Michelangeli et al., 1995), which more closely resemble true, full flow patterns than individual empirical orthogonal functions (EOFs).Numerous studies have identified four weather regimes for use in winter over the North Atlantic-European region based on cluster analysis of 500 hPa geopotential height anomalies (Cassou, 2008;Fabiano et al., 2020;Ferranti et al., 2015).These four regimes are robust to reasonable differences in dataset, method, domain or time period (Hannachi et al., 2017) and also appear as a subset of the year-round seven regime classification in Grams et al. (2017).In addition to geopotential height or sea level pressure, similar regimes can be also calculated by clustering the jet streams (Madonna et al., 2017(Madonna et al., , 2021)).Although weather regimes have been well-adopted as weather forecasting tools (e.g., Grams et al., 2020), their use in understanding observed climate variability and change is comparatively limited (Fabiano et al., 2021).
The general wintertime warming trend in Europe is well established (e.g., Sippel et al., 2020).However, less attention has been paid on warming trends in specific weather patterns.For instance, the Arctic region has warmed several times faster in recent decades than the global mean (Rantanen et al., 2022), which could lead to a faster rate of warming during weather patterns in which air is coming from the Arctic than other weather patterns.The opposite could be true for weather patterns when air is advected from the more slowly warming ocean, especially over the North Atlantic warming hole (Keil et al., 2020).It follows that the weather patterns which bring the coldest air during winter (i.e., from the Arctic) are likely to be warming faster than the patterns which bring the warmest air (i.e., from the oceans), possibly yielding an asymmetric warming rate between warm and cold extremes.Such an asymmetry has been previously studied and attributed to human influence (Blackport et al., 2021;Dai & Deng, 2021;Screen, 2014), but not from the standpoint of weather regimes.
Motivated by these hypotheses, this letter aims to quantify the circulation-specific temperature trends in Europe by exploring two main research questions: (1) how have the temperatures during the four wintertime weather regimes changed in the past four decades, and (2) are weather regimes associated with the coldest airmass on average (i.e., NAO-) warming the fastest?Our results help bridge the gap between climate science and weather forecasting.

| DATA AND METHODS
This study relies purely on ERA5 reanalysis (Hersbach et al., 2020), which is the state-of-the-art reanalysis product from European Centre for Medium-Range Weather Forecasts.Our study covers the cold season, that is, November-March (NDJFM) period from 1979/1980 to 2021/2022.

| Calculation of the weather regimes
The weather regime classification is based on once-daily 00 UTC fields of 500 hPa geopotential height (hereafter Z500) anomalies at 1 horizontal resolution from the ERA5 dataset.In line with Cassou (2008), the regime calculation is performed in the region 20 -80 N, 90 W-30 E. The anomalies of Z500 were calculated by subtracting the seasonal cycle from the full fields, computed for each day by averaging 1979-2022 fields with a 15-day running window.
The weather regime calculation follows the method from Cassou (2008): the k-means clustering algorithm with k = 4 (four regimes) was applied to the leading 14 EOFs (explaining 86% of the total daily variance) of the daily Z500 anomalies over the cold-seasons 1980-2022.At each grid point, the Z500 fields were linearly detrended and weighted by the square root of cosine latitude before the analysis (to give data points equal weighting in the covariance matrix).After the clustering, each day in the time series was assigned to a regime, based on the Euclidean distance to the closest cluster centroid in the space spanned by the 14 principal components.For consistency with Cassou (2008), the resulting four regimes are named NAO-, NAO+, Scandinavian Blocking (SB), and Atlantic Ridge (AR), and we did not apply a 'no regime' classification.Out of all cold-season days in 1980-2022, about 31% belong to the NAO+ regime, 19% to the NAO-regime, 27% to the SB regime and 22% to the AR regime (Table 1 and Figure S1).

| Temperature and wind anomalies during the weather regimes
We used daily mean, maximum and minimum 2-metre temperature (T2m) anomalies at 0.5 horizontal resolution from ERA5 over the cold seasons 1980-2022.The daily mean, maximum and minimum T2m fields were calculated from hourly data.To obtain daily T2m anomalies, the seasonal cycle, as computed using the 1981-2010 normal period and 15-day moving window, was subtracted from the full T2m fields.The same procedure was applied to 925-hPa wind speeds.
For each cold season (NDJFM) in 1980-2022, we calculated the average temperatures for the days which belong to each weather regime.These average temperatures represent the average of all regime days within the season, regardless of how many regime days there are or in how many periods they occurred.
The temperature trends were computed using Theil-Sen's slope estimator (Hussain & Mahmud, 2019;Sen, 1968;Theil, 1950).For the difference between trends across the regimes, a bootstrapping test with replacement is run against the null hypothesis of equal trends.We bootstrapped the annual NDJFM temperature anomalies 10,000 times and each time calculated Theil-Sen's slopes depicting the temperature trend.The difference between the two Theil-Sen's slopes constructs a distribution from which the 5th and 95th percentiles are determined.If the 5th and 95th percentiles of the resampled slope distribution have the same sign, the trends are deemed significantly different at the 90% confidence level.

| Weather patterns of the regimes
The composite fields of Z500 anomalies in the regimes are shown on the upper row of Figure 1, and the composite fields of T2m anomalies and 925-hPa wind speed anomalies on the bottom row.Note that despite their names and similarity with the (EOF or station-based) NAO index patterns, the circulation anomalies in the NAO-and NAO+ regimes are not simply the opposite of each other (Figure 1a vs. b).
The NAO-regime is associated with a blocking high over Greenland (Figure 1a), and consequently cold air advection from the north and below-average temperatures especially in Fennoscandia (Figure 1e).The NAO+ regime represents a cyclonic pattern over the North Atlantic (Figure 1b) which often leads to very mild temperatures across Europe associated with flow off the Atlantic (Figure 1f).The SB regime brings a typically anticyclonic weather pattern to northern Europe (Figure 1c, g), while in the AR regime the anticyclone is located further west over the North Atlantic (Figure 1d) and cold-air advection associated with an anomalous northerly flow affects western Europe (Figure 1h).

| Cold-season temperature trends in Europe
Over the last 43 years, the cold-season temperatures in northern Europe have experienced considerable warming, with a higher warming rate in eastern and northern Europe than in western Europe (Figure 2a).The warming has been strong especially in Fennoscandia where the temperatures have risen at over 0.6 C decade À1 , three times faster than global average (Figure 2a).In contrast to Fennoscandia, the warming in the United Kingdom and Ireland has been weaker, with most of Ireland experiencing statistically insignificant trends of cold-season temperatures since 1980, potentially resulting from the North Atlantic warming hole (Gervais et al., 2020;Hand et al., 2019).
When the temperature trends in the regimes are compared with the overall cold-season temperature trend, we see some notable differences.First, the NAO-regime has warmed faster than average in Finland, Sweden, the British Isles, and over large oceanic regions in the Norwegian Sea (Figures 2b and 3a).Especially over the Norwegian Sea the difference between the NAO-trend and the overall trend is large and statistically significant, which is expected as this area acts as a pathway for cold airmasses T A B L E 1 The average number of days in each weather regime.The values are averages from the 43 cold seasons (NDJFM 1980(NDJFM -2022)).The percentages in the brackets show the statistics from the most recent 30-year climate period  arriving from the rapidly warming Arctic during the NAO-regime.
In contrast to the NAO-regime, the NAO+ regime has warmed slower than average in central and northern Europe (Figure 2c).However, the opposite is true in north-west Russia where the NAO+ regime has warmed faster than the cold-season days on average.We suggest that the weaker warming trend in the NAO+ regime in large parts of Europe can be explained by the fact that the near-surface air in this weather pattern is advected from the slowly warming ocean, unlike in northwest Russia where the fetch of the air over land is much greater (Figure 1).
An interesting finding is the high warming rate in the SB regime in western and central Europe where the difference to the overall trend is also statistically significant (Figure 2d).For example, in the Czech Republic and Germany, the SB regime has warmed locally >0.4 C decade À1 faster than the cold-season days on average.The high warming rate in central Europe and low warming rate in north-west Russia in the SB regime (Figure 2d) appears almost as the opposite pattern to the warming dipole in the NAO+ regime (Figure 2c).These contrasting warming dipoles in these regimes are likely due to their opposing circulation fields over central and eastern Europe and the fact that both locations have a long fetch over land in these regimes (central Europe in the SB regime and north-west Russia in the NAO+ regime).The combination of a slower-warming ocean relative to the land surface leads to a reduced zonal temperature gradient between the Atlantic and Europe.As a result, the strength of the warm-air advection in NAO+, and coldair advection in SB, is reduced, which is consistent with their relative temperature trends.
Finally, in the AR regime, the temperature trends are weaker than average in Iberia, United Kingdom, and northeastern Europe, and stronger than average in southeastern Europe (Figure 2e).The weak warming trend in western Europe is broadly consistent with the mix between northerly flow from the Arctic and a clockwise circulating flow from the Atlantic (Figure 1h).
In most of northern Europe, NAO-regime days show notably faster warming trends than days in the NAO+ regime (Figure 3b).This is true especially in Fennoscandia and central Europe where the NAOregime has warmed >0.4 C decade À1 faster than the NAO+ regime.When comparing NAO-with SB, the situation is somewhat twofold: in northern Fennoscandia the NAO-regime shows a higher warming while in central and eastern Europe the NAO-regime exhibits slightly weaker warming than the SB regime (Figure 3c).Finally, relative to the AR regime, the NAO-regime is mostly warming faster (Figure 3d) although in many places the difference is not as pronounced as compared to the NAO+ regime (Figure 3b).An exception to this is the Balkan region where the NAO-regime is warming slower than the AR regime.
Our second research question was whether the coldest weather regimes are warming the fastest.In most of Fennoscandia and the northern North Atlantic, the NAO-regime has warmed the fastest, while in central Europe the fastest warming regime is SB (Figure 4a).The NAO+ regime has warmed the fastest in north-west Russia.In Figure 4c, at each grid point, the colour represents the regime that both warms the fastest and is the coldest.As can be seen, the fastest warming (Figure 4a) and coldest regimes (Figure 4b) have similar spatial extents throughout much of northern Europe, and this regime is NAO-(Figure 4c).The same is true for the SB and AR regimes in smaller areas in southeastern Europe.
The slowest warming regime in most of Europe is NAO+ (Figure 4d).For the British Isles and north-west Russia, the slowest warming regime is AR, and for northern Fennoscandia the SB regime has warmed the slowest.The warmest regime in the majority of Europe is NAO+, excluding parts of British Isles and northern Fennoscandia where the warmest regime is SB (Figure 4e).Therefore, in large parts of Europe the warmest regime (NAO +) is warming the slowest (Figure 4f).Hence, in almost all of Europe, the fastest warming regime is on average associated with colder than average temperatures, whilst the slowest warming regime is associated with warmer than average temperatures (Figure S3).

| Regime temperature trends in northern Europe
Because the differences in the temperature trends of the regimes appeared to be the most pronounced in northern Europe (Figure 3), we investigated this region in more detail (Figure 5).The area of northern Europe is shown in Figure 2a and follows the Intergovernmental Panel on Climate Change definition (Iturbide et al., 2020).We found that the warming trend in the NAO-regime is the highest (Figure 5b, 0.69 C decade À1 ), about 25% higher than the overall NDJFM temperature trend (Figure 5a) and about 60% higher than the NAO+ trend (Figure 5c).The linear trend equates to NAO-regime days being on average around 3 C warmer in the present climate than at the start of the record in northern Europe, and the magnitude of the trend is close to the Arctic warming trend of 0.73 C decade À1 found in Rantanen et al. (2022).
The slowest warming trend in northern Europe is in the NAO+ regime (Figure 5c regimes (Figure S4) consistent with the expected influence of greenhouse warming (Davy et al., 2017;Vose et al., 2005).Although the differences between the trends in different regimes are not significant, their relative behaviour is consistent with both our prior expectation and the other results presented here.The highest trend (0.74 C decade À1 ) is for minimum temperatures in the NAO-regime, and the lowest (0.40 C decade À1 ) for maximum temperatures in the NAO+ regime.
The number of cold-season days in each regime exhibits substantial interannual variability (Figure S1), ranging from 1 (NAO-days in 1993) to 94 (NAO-days in 2010).Thus, the comparison of average temperatures is not completely fair due to the varying sample size between different years.However, for northern Europe, there is only a very marginal relationship between the number of regime days and the average temperatures (R 2 = 0.01-0.14, Figure S5).Therefore, and taking into account that there were no trends in the regime days (Figure S1), we estimate that the trends are unlikely to have arisen due to the effect of the number of days in each regime.In fact, such interannual variability may preclude a more robust quantification of the trends.

| SUMMARY AND CONCLUDING REMARKS
In this study, we quantified temperature trends in Europe during the four canonical Euro-Atlantic weather regimes: NAO-, NAO+, Scandinavian Blocking and Atlantic Ridge.Although many previous studies have estimated the effect of atmospheric circulation changes on observed temperature changes in Europe (e.g., Räisänen, 2021;Saffioti et al., 2016), this study is, to the best knowledge of the authors, the first comparison of temperature trends within the different weather regimes.
Our primary result is the observed asymmetric warming rates in the NAO-and NAO+ regimes, with NAO-regime days showing generally faster warming and NAO+ regime days slower warming than the coldseason days on average in Europe (Figures 3 and 5).The NAO-regime is associated with a blocking high over Greenland and consequently northerly flow in northern Europe.Thus, our results suggest that these cold air outbreaks have warmed, on average, faster than other weather situations in northern Europe.Despite the large interannual variability of the temperatures (Figure S6), the temperature trend in the NAO-regime is statistically significant in most parts of continental Europe.In addition to the asymmetry between NAO+ and NAOwarming trends, we found that the SB regime has warmed particularly strongly in central Europe.
The higher warming trend for NAO-days is supported by a sound physical basis, as the NAO-regime in northern Europe is typically associated with cold air advection from the Arctic.The Arctic, in turn, has warmed much faster than the mid-latitudes in recent decades (Rantanen et al., 2022).Thus, in northern Europe, the source regions of the air during the NAOregime have warmed considerably faster than the source regions of the other regimes.It has been suggested that the future sea-ice loss in the Arctic would drive more intense NAO-events (e.g., Nakamura et al., 2015;Seierstad & Bader, 2009) which would in turn lead to winter cooling (or lack of warming) over northern Europe.However, our results show, consistent with Screen (2017), that the advection of warmer airmasses effect is likely to offset the potential NAOrelated dynamical cooling.Finally, we would like to emphasise that our study only addresses the seasonally averaged temperatures of the regimes, and thus, we did not investigate how Arctic warming is affecting the severity of short-term winter weather that have been the subject of active research recently (Cohen et al., 2020).
In summary, our results demonstrate that in large parts of Europe, the regime that typically brings colder than normal weather is warming the fastest, and the regime that typically brings the warmest weather is warming the slowest.This is consistent with the reported decreasing sub-seasonal temperature variability in northern extratropics (Dai & Deng, 2021;Screen, 2014) which has been attributed to human influence (Blackport et al., 2021).Thus, our results serve as an example of the notion 'the coldest things are warming the fastest'.

AUTHOR CONTRIBUTIONS
Mika Rantanen calculated the main results and led the manuscript writing.Simon H. Lee helped in the calculation of the regimes.Juha Aalto assisted with the statistical analyses.All authors discussed the results at all stages and contributed to writing the manuscript.

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I G U R E 2 (a) Temperature trends ( C per decade) over all days in the cold seasons 1980-2022.(b-e) trend differences to the overall trend (panel a) in the regimes.In (b-e), the stippling indicates regions where the temperature trend in the regime is significantly different from the overall trend (a) as calculated with the bootstrapping method.The polygon in (a) depicts the domain of northern Europe used in Figure 5. See Figure S2 for the absolute values of the regime trends.F I G U R E 1 Composite fields of 500 hPa geopotential height anomalies (a-d) and 2-m temperature and 925-hPa wind speed anomalies (e-h) of the regimes.The anomalies are calculated relative to the 1981-2010 period.
, 0.43 C decade À1 ).The temperature trends in the SB (Figure 5d, 0.53 C decade À1 ) and AR (Figure 5e, 0.48 C decade À1 ) regimes lie between the NAO-and NAO+ regimes and close to the overall NDJFM temperature trend (Figure 5a, 0.56 C decade À1 ).When considering the daily mean, maximum and minimum temperatures in northern Europe, the minimum temperatures have warmed the fastest in all four F I G U R E 4 Top row: (a) the fastest warming regime, (b) the coldest regime and (c) areas where the coldest regime is also warming the fastest.Bottom row: (d) the slowest warming regime, (e) the warmest regime and (f) areas where the warmest regime is also warming the slowest.The stippling in (a) and (d) indicate regions where the fastest warming regime is warming significantly faster than the slowest warming regime.

F
I G U R E 5 Area-averaged cold-season (NDJFM) temperature anomalies in northern Europe in (a) all cold season days and (b-e) during each Euro-Atlantic weather regime.Shown are also the linear trends in 1980-2022 and their 90% confidence intervals (shading).The trends are statistically significant at the 1% level.The area of northern Europe is shown in Figure 2a. .