The Arctic has warmed four times faster than the globe since 1980

In recent decades, the warming in the Arctic has been much faster than in the rest of the world, a phenomenon known as Arctic ampliﬁcation (AA). Numerous studies report that Arctic is warming either twice, more than twice, or even three times as fast as the globe on average. However, the lack of consensus of AA deﬁnition precludes its precise quantiﬁcation. Here we show, by using several observational datasets which cover the Arctic region and adopting a simple deﬁnition of AA, that during the last 40 years the Arctic has been warming almost four times faster than the globe as a whole, which is a higher ratio than generally reported in literature. Furthermore, we compared the observed AA ratio to the ratio simulated by state-of-the-art climate models, and show that the models largely underestimate the present AA, a ﬁnding that is not very sensitive to the exact deﬁnition of AA. The underestimation of AA by climate models most likely results from their inability to realistically simulate feedback mechanisms between sea ice melt and atmospheric temperatures. Our results imply that the

underestimated AA leads to biased projections of climate change both in the Arctic and midlatitudes.

Main
The faster warming rate in the Arctic compared to the globe as a whole is considered nowadays a robust fact. The phenomenon, called Arctic or polar amplification (AA), can be seen in both observations and models (e.g. Holland and Bitz, 2003;Serreze and Francis, 2006;Serreze et al., 2009;Huang et al., 2017).
Arctic amplification is acting to reduce the meridional temperature gradient in mid-latitudes and thus can have implications for mid-latitude weather and climate, in particular via the Polar front jet stream (e.g. Francis and Vavrus, 2012;Cohen et al., 2014;Francis and Vavrus, 2015) and blocking highs (Luo et al., 2018). However it remains debatable whether or not the effects of AA have had discernible influence on recent mid-latitude climate trends (Francis, 2017;Vavrus, 2018;Cohen et al., 2020;Dai and Song, 2020;Screen, 2020, 2021) and occurrence of extreme events .
While there is no doubt on the enhanced warming in the Arctic with increasing greenhouse gases, there seems to be no clear consensus on the relative importance of the feedback mechanisms leading to AA (Richter-Menge and Druckenmiller, 2020). During the last decade, multiple factors have been proposed to explain AA: reduced surface albedo due to sea-ice loss and snow retreat (Screen and Simmonds, 2010;Taylor et al., 2013;Dai et al., 2019), Planck feedback (Pithan and Mauritsen, 2014), lapse-rate feedback (Stuecker et al., 2018), surface thermal inversion (Bintanja et al., 2011), cloud feedback (Taylor et al., 2013), ocean heat transport (Beer et al., 2020) and meridional atmospheric moisture transport (Graversen and Burtu, 2016;Woods and Caballero, 2016;Kim et al., 2017). Furthermore, the reduced pollution in Europe may have contributed to the Arctic warming during the last decades (Navarro et al., 2016;Krishnan et al., 2020), and possible reductions of Asian aerosols under a strong mitigation policy may increase the future AA (Merikanto et al., 2021).
Also, there is little consensus on the magnitude of AA. Numerous recent studies on AA report that the Arctic warms either nearly twice (e.g. Yu et al., 2021), about twice (e.g. Walsh, 2014), or more than twice (e.g. Richter-Menge and Druckenmiller, 2020;Jansen et al., 2020)  The difficulty in defining AA is that both the period of interest and the area of Arctic can be defined in multiple ways. The warming can be calculated using linear trends for the last 30-50 or even longer periods of years. Moreover, the area of Arctic can be defined using the area poleward of 60 • N, 65 • N or 70 • N latitude thresholds, or definitions not based on latitude (Davy et al., 2018). Uncertainties arising when calculating AA in observations and models have also been emphasized (Hind et al., 2016;Davy et al., 2018;Smith et al., 2019).
While there have been improvements in climate models to realistically represent the evolution of Arctic climate (Davy and Outten, 2020) and sea ice (Stroeve et al., 2012) under global warming, most models in the latest generation of Coupled Model Intercomparison Project phase 6 (CMIP6) still fail to simulate plausible sensitivity of sea-ice loss to the rise of global temperatures (Notz and Community, 2020). Because the sea ice loss is one of main mechanisms causing AA, natural follow-up question arising is whether climate models are able to reproduce the magnitude of the observed AA.
The primary motivation of this study comes from the lack of consistent definition and thus consensus on the magnitude of AA in the literature. Also, as AA is not constant in time, the estimates referred to in previous studies are potentially outdated. Our objective is to move towards a more consistent definition of AA, quantify its magnitude by utilizing most recent observational datasets covering the Arctic region, and assess the ability of climate models to reproduce AA.

Observed and simulated Arctic amplification
We begin by showing the evolution of global mean and Arctic mean temperatures during 1900-2019 ( Fig. 1) by considering the four observational datasets: GISTEMP, BEST, CW and ERA5 (see Methods). Compared to the global temperatures (Fig 1, light colors), the temperature variations in the Arctic (Fig 1, dark colors) have been much more amplified. The multi-decadal variations can be divided into three distinct periods: first, a rise of temperatures in  (often called as early twentieth-century warming, e.g. Hegerl et al., 2018); secondly, a decrease of temperatures in 1940-1980 (referred as mid-twentieth-century cooling, e.g. Haustein et al., 2019); and finally, the recent warming period since around 1980. The warming in the Arctic since the 1980s has been particularly strong, and the different datasets are in a close agreement with each other. The agreement between observational data sets and ERA5 is likewise good when land and ocean areas are considered separately (Figs. S1 and S2), although the differences over the ocean are somewhat larger during the pre-1979 period. Due to the good agreement in the 1980-2019 period, we next consider the average of these four datasets as an observational estimate.
The observations indicate that, during 1980-2019, a large fraction of the Arctic Ocean is warming faster than 0.75 • C decade −1 (Fig. 2a)  Regarding the simulated temperature trends, CMIP5 models ( Fig. 2b) indicate weaker warming over the Arctic Ocean compared to observations (Fig. 2a). For example, the CMIP5simulated warming rate near the Svalbard region is less than 1 • C decade −1 while the observations show more than 1.25 • C warming per decade.
In the multi-model mean of CMIP6 (Fig. 2c), the magnitude of the warming in the Arctic Ocean is slightly higher than in the CMIP5 models and thus closer to the observations, albeit Svalbard, which were locally warming more than seven times as fast as the global average in 1980-2019 . The primary reason for such a high amplification ratio is the loss of sea ice, which has been most pronounced in the Barents Sea (Onarheim andÅrthun, 2017). Furthermore, it has been found that changes in atmospheric circulation have amplified warming in this area (Wickström et al., 2020;Räisänen, 2021). In general, there are no regions within the Arctic Circle where AA 40 is smaller than two, apart from the northern North Atlantic.
As already suggested by the temperature trends shown in Figs  The CMIP5 multi-model mean warming trend for 1980-2019 is 0.61 K decade −1 for the Arctic and 0.24 K decade −1 for the entire globe (Fig. 3a). The CMIP5 multi-model mean AA 40 is 2.5 (Fig. 3b). Thus, while CMIP5 models have underestimated the warming in the Arctic, they have overestimated the global warming rate, resulting in a 36 % underestimation of the ongoing Arctic amplification.
CMIP6 models have simulated the temperature change in the Arctic somewhat more realistically than their predecessors. The multi-model mean warming rate in the Arctic is 0.68 K decade −1 (Fig. 3a), but compared to CMIP5 models, the CMIP6 models exhibit much higher inter-model spread in the trends (Fig. 3a). In line with the higher warming rate in the Arctic, the global mean warming rate in CMIP6 models is slightly higher than in CMIP5 models as well, being 0.25 K decade −1 . Due to higher temperature trends both in the Arctic and globally, the mean AA 40 of 2.6 in the CMIP6 models does not differ much from the CMIP5 ensemble and still underestimates the observed Arctic amplification by 33 % (Fig. 3b). However, due to the considerably larger spread in the warming rates in the Arctic (Fig. 3a), the AA 40 values in the CMIP6 models feature wider 90 % confidence spread ranging from 1.0 to 3.8.
How large portion of this spread is due to internal variability and what is the role of model uncertainty? To assess the role of internal variability in the AA uncertainty, we use the 100member MPI-GE, which is the largest available single-model ensemble known to realistically represent the observed variability (Maher et al., 2019). Individual members of MPI-GE historical simulations are initialized from different years of the long preindustrial control run; thus the spread in this ensemble is solely due to internal variability. Compared to the CMIP5 and CMIP6 multi-model means, MPI-GE simulations show lower warming trend in the Arctic, with the central estimate being 0.52 K decade −1 for the 1980-2019 period (Fig. 3a). Consistently with the lower warming rate in the Arctic, the global warming rate in MPI-GE is likewise weaker and thus closer to observations, being 0.21 K decade −1 . As a result, the ensemble mean AA 40 in MPI-GE for 1980-2019 is 2.5, close to both CMIP5 and CMIP6 ensemble means (Fig.   3b). Looking at MPI-GE spread, we find that it explains majority of the total CMIP5 spread, suggesting that the model uncertainty plays a relatively small role in CMIP5 spread during this period. However, model diversity is much larger in CMIP6, with MPI-GE explaining only half of the CMIP6 spread. In particular, a few CMIP6 models simulate AA 40 values close to those observed, suggesting that these models might be able to capture feedbacks associated with AA well. We analyze the apparently realistic AA values in these models in more detail in the next section.  However, the model capability to simulate a large AA is partly due to the extension of the period until 2040, when there is less sea ice. Nevertheless, in most cases models cannot simulate high AA 40 even if we allow for a time gap, and therefore we do have evidence that the model runs generally underestimate the recent Arctic amplification. Furthermore, Fig. S5 demonstrates that CMIP6 models tend to underestimate AA under a wide range of different Arctic definitions and time windows. The underestimation is the strongest in the high Arctic (> 70 • N, Fig. S5b) and over the ocean (Fig. S7b).
4 The role of Arctic sea ice loss and the hiatus phase in global warming in the modelled Arctic amplification As evidenced previously, the observed Arctic amplification lies outside the uncertainty range of CMIP5, CMIP6 and MPI-GE ensembles, with most models not capturing the presently observed AA value even when a period gap is allowed (Fig. 3b). We next address the question of what are the potential factors behind underestimated AA in climate models. We focus on CMIP6 models since they show much larger spread than that in CMIP5.
In the CMIP6 models, the absolute warming rate in the Arctic is strongly coupled with the SIA trend (Fig. 4a, green dots), with stronger sea ice loss promoting faster warming and vice versa. Most of the models simulate somewhat weaker sea ice loss than what is observed (red dot in Fig. 4a) but, consistently with Notz and Community (2020), the observed SIA trend is not outside of the CMIP6 model spread.
When looking at the sea ice loss during periods of maximum AA normalized by the corresponding global warming trend in the models and plotted against maximum AA values, the picture becomes different (Fig. 4b). Almost all models simulate too weak sea ice loss relative to their global warming rate, and thus their maximum Arctic amplification ratio in  remains smaller than what is observed (Fig. 4b). However, because SIA loss is not the only factor causing AA, the causal relationship can be also other way around: too weak Arctic amplification in the models can lead to smaller SIA loss for a given amount of global warming. The issue is further complicated by potential model biases in oceanic forcing on sea ice. The oceanic heat flux affects SIA but does not have a direct effect on air temperatures over ice-covered parts of the Arctic Ocean (Koenigk et al., 2020). Only in three models (EC-Earth3, MRI-ESM2-0 and NESM3), the sensitivity of SIA trend to their global warming rate is at same level as in observations, and these model also produce the high AA ratios.
Another potential factor inducing differences between the modelled and observational AA ratios is the hiatus phase in global warming that occurred between about 1998 and 2012 (Medhaug et al., 2017), although in statistical terms, the existence of the hiatus is questionable (Mudelsee, 2019). Nevertheless, in these years global mean temperature nearly ceased to increase, which acts to reduce the denominator of Eq. (1) for the entire period 1980-2019.
According to Stolpe et al. (2021), an important contributing factor to the hiatus was the low sea surface temperature in equatorial Pacific Ocean. Nevertheless, the impact of tropical Pacific temperature anomalies did not extend to high northern latitudes where warming continued unabatedly (Fig. 1), keeping the numerator of Eq. (1) large.
According to Box TS.3, Fig. 1a of IPCC AR5 report (Stocker et al., 2013), in the CMIP5 model simulations a hiatus is quite a possible albeit infrequent phenomenon. If the hiatus indeed proves to be an important source for the difference of AA between the model simulations and observations, one can expect that the observed AA will be reduced in the long term, along with the reduction of the ratio of forced to unforced climate change. Indeed, AA calculated using the last 10-15 years is clearly smaller than using longer time windows (Fig. S5).

Discussion & conclusions
We present evidence that during the last 40 years the Arctic has been warming nearly 4 times as fast as the entire globe and caution that referring to Arctic warming as to being twice or even three times faster than the global warming is a clear underestimation of the situation during 1980-2019. Our results likewise demonstrate that climate models on average underestimate the Arctic amplification by 33-36 % (Fig. 3b). This is also true for the latest CMIP6 models despite the fact that some of these models better reproduce the absolute warming rate in the Arctic. However, those models which show plausible Arctic warming trend simultaneously have too much global warming. In contrast, those models which simulate reasonable global warming, generally have too weak Arctic warming. Thus, our results show that most climate models are unable to simulate a fast-warming Arctic simultaneously with weaker global warming similar to the observed "global warming hiatus" (e.g. Medhaug et al., 2017).
The reasons for the underestimation of AA in the climate models are not clear. It is likely that internal climate variability, e.g. the early 21th century hiatus in global warming contributes to the observed large AA; however, we show evidence of underestimated AA by models also when we compare observations with a large ensemble that faithfully accounts for the internal variability. Our analysis suggest that one potential cause of the underestimated AA is too weak feedback mechanisms between sea ice melt and atmospheric warming in climate models, which is reflected in their inability to reproduce the vertical structure of observed Arctic warming (Cohen et al., 2020). However, it remains unknown which mechanisms are underestimated in models. Model uncertainties and deficiencies as well as contrasting results between models have been reported related to numerous subgrid-scale processes acting in the Arctic (Vihma et al., 2014) and in large-scale transports affecting AA (Burgard and Notz, 2017).
Further, we suggest that the inability of climate models to simulate realistic AA may have implications for future climate projections. Specifically, the tug of war between AA and tropical warming over the future changes in storm tracks (Shaw et al., 2016;Peings et al., 2019) projected by climate models may be biased towards the forcing by tropical warming, implicating that both projected storm track changes and associated regional climate changes may be biased. Our results call for more detailed investigation of mechanisms behind AA and their representation in climate models.

Observational data
For the near-surface temperature, we used the following datasets: NASA's Goddard Institute for Space Studies Surface Temperature version 4 (GISTEMP; Lenssen et al., 2019), Berkeley Earth temperature dataset (BEST; Rohde and Hausfather, 2020), and Cowtan & Way temperature dataset version 2.0 (CW; Cowtan and Way, 2014). In these datasets, near-surface temperature is based on a combination of 2-m temperature observations over land and sea surface temperature (SST) observations over the ocean.
GISTEMP, BEST and CW were chosen for this study because they interpolate the temperatures into data-sparse regions, which are especially abundant in the Arctic. GISTEMP spatially extrapolates temperatures into unmeasured regions using a 1200-km radius of influence for the stations, while BEST and CW employ kriging-based spatial interpolation. In all these datasets, areas of sea ice are treated as if they were land, and SST observations are used only in the grid points which are ice free all year. Thus, temperatures in both terrestrial and marine Arctic are mostly based on terrestrial station observations.
In addition to the three observational datasets, we used ERA5 reanalysis (Hersbach et al., 2020), which has been produced by the European Centre for Medium-Range Weather Forecasts.
We used monthly mean 2-m temperature fields in the native, 0.25 • (31 km) horizontal resolution.
The first release of ERA5 covers the years from 1979 to present, but a preliminary extension for 1950-1978 was recently released. We used the whole time series, from 1950 to 2019. All the observational temperature datasets used are listed in Table S1.
For Arctic sea ice area (SIA), we used the University of Hamburg Sea Ice Area product (Doerr et al., 2021), which contains time series of the monthly SIA in the Northern Hemisphere by several producers. To get a robust observational estimate, we used the average of the following five products: OSI SAF (Lavergne et al., 2019), NASA-Team , Comiso-Bootstrap (Comiso et al., 1997), HadISST2 (Titchner and Rayner, 2014) and Walsh dataset version 2 (Walsh et al., 2017).

Climate model data
We compared the observed temperatures to three different climate model ensembles, which are listed in Table S2. These ensembles are 35 CMIP5 models (Taylor et al., 2012), 32 CMIP6 models (Eyring et al., 2016) and the 100-member Max-Planck Institute Grand Ensemble (MPI-GE) (Maher et al., 2019). All three climate model datasets contained historical simulations (1850-2005for CMIP5 and MPI-GE, and 1850-2014 for CMIP6) and future projections forced by the RCP8.5 scenario for CMIP5 and MPI-GE, and SSP2-4.5 and SSP5-8.5 scenarios for CMIP6 (Table S2). For CMIP6, the monthly averaged data for 2-meter temperature and sea ice concentration were used; for CMIP5 and MPI-GE, only 2-meter temperatures were considered. Sea ice concentration data were only available from 25 CMIP6 models. Also, there is no data from SSP2-4.5 scenario data for CMIP6 TaiESM1 model. The list of all the used CMIP5 and CMIP6 models can be found from the supplement tables S3 and S4.

Defining the Arctic amplification
We follow the recommendation of Smith et al. (2019), and define Arctic amplification (AA) as the ratio of Arctic warming to global-mean warming: where dT /dt A and dT /dt G are the slopes of linear trends of near-surface temperature, calculated using a least-squares fitting for the annual mean values for the Arctic and global domain.
The trends were calculated for different time periods (see Fig. S5a), but the last 40 years  et al., 2007), and AR5 used 67.5 • N (Collins et al., 2013). For a sensitivity assessment, dT /dt A was also calculated using different definitions for the southern boundary of the Arctic, ranging from 55 • N to 80 • N (Fig. S5).

Statistical analysis
For observations, we give the uncertainty ranges in dT /dt A and dT /dt G as the 90 % statistical uncertainty range. For CMIP5 and CMIP6 simulations, the uncertainty ranges reflect the 90 % confidence interval (5th-95th percentile range) derived from multi-model ensemble. For MPI-GE simulations, we use the 90 % confidence interval (5th-95th percentile range) derived from the ensemble members. The statistical significance of the observed trends was estimated at 95 % level (P<0.05) using nonparametric Mann-Kendall test (Kendall, 1948;Mann, 1945) with pyMannKendall python package (Hussain and Mahmud, 2019).
The uncertainty range in observed AA 40 ratios reflects 90 % confidence intervals which were estimated using the bootstrap method (Efron, 1992). For CMIP5 and CMIP6 simulations, the corresponding uncertainty range is the 90 % confidence interval derived from the multi-model ensemble, and for MPI-GE, derived from the ensemble members. The AA 40 ratios in climate models were first calculated separately for each model/member and then averaged across them (i.e. as mean ratios, not a ratio of means), thus following the recommendation by Smith et al.

Author contributions
The study was initialized together by ALi, ALa, MR, and KN. MR prepared the initial draft of the manuscript with the help of AK. MR conducted most of the data analysis and created part of the figures. AK produced the MPI-GE results and contributed to the initial preparation of the manuscript with MR. ALi created half of the figures. KN and KR contributed to the downloading of CMIP model data, and OH calculated the uncertainty estimates of the results.
TV and ALa contributed to the commenting of the results and revising of the manuscript. All authors commented the manuscript and discussed the results at all stages.