As the spatial extent of heat waves in the Arctic increases many-fold, are they causing the melting of Arctic glaciers? Why has climate change become more pronounced in recent years? Is the rate of climate change accelerating?

It is widely accepted that the intensity, frequency, and duration of heat waves are increasing worldwide, including in the Arctic. However, less attention has been paid to the area of land affected by heat waves. Here, using atmospheric reanalysis and global climate models, we show that the area affected by heat waves in the Arctic is expanding significantly. Compared with the mid-20th century, the total land area affected by extreme heat waves in the Arctic has doubled, the area of extreme heat waves has tripled, and the area of very extreme heat waves has quadrupled. Furthermore, climate model projections suggest that the frequency of heat waves will continue to increase in the 21st century, but with large regional differences in the magnitude of heat waves due to intraseasonal summer temperature variability. Our findings highlight the increasing vulnerability of the Arctic region to extreme heat, potentially leading to severe impacts on ecosystems and societies.Among all extreme weather events, the increase in frequency and intensity of heatwaves stands out as the most prominent effect of climate change. Heatwaves have become longer, more intense and more frequent worldwide in recent decades, and this has been shown to be caused by human activity with a high degree of certainty1 . Consequently, it is unsurprising that the occurrence of heatwaves has increased in the Arctic in recent decades2 . One indication of this is that a new Arctic heat record was set recently, in the summer of 2020, when the temperature in Verkhoyansk, Siberia reached 38.0 °C3,4 . Heatwaves, like any extreme weather events, can trigger ecosystemlevel disturbances, which may affect the organisation and functional attributes of the entire ecosystem5 . One notable example is the recent surge in wildfire activity across the Arctic region driven by increasingly warm and dry summers that promote surface flammability and increased vegetation fuel load as a result of higher productivity6–10. Thus, more frequent occurrence of fire weather increases the probability of ignitions11 and further causes ecosystem and societal disruption. Noteworthy, the Arctic region is widely underlain by permafrost (i.e. soils that are frozen at least two consecutive years) storing vast amounts of organic carbon12. Increasing spatial coverage of heatwaves can promote widespread thaw of frozen soils, allowing carbon dioxide and methane to be released into the atmosphere, further amplifying climate change13,14. Early snowmelt and earlier vegetation greening, combined with summer heatwaves, can cause a feedback effect that intensifies the heatwave through reduced soil moisture and summer browning, as in the summer of 202015,16. In addition, heatwaves are a major public health concern leading to a high number of fatalities annually17. Due to the high latitude amplification of climate change and consequent rise in summer temperatures, this particular health risk can become increasingly considerable also among Arctic societies in the future. Three metrics often used tomeasure heatwaves arefrequency, intensity and duration18–20. Perkins-Kirkpatrick and Gibson21 showed that for each degree of global warming, the number of heatwave days increase by about 10–15 days, the duration increase by about 1–3 days, and the intensity increase by about 1–1.5 °C in the mid to high latitudes of the Northern Hemisphere. A comprehensive analysis of observed heatwave trends globally was carried out by Perkins-Kirkpatrick and Lewis19. They highlighted that not only are the number of heatwaves increasing, but their change has recently been accelerating. Although the effects of heatwaves have often been studied using the above-mentioned indicators, a recent study suggests that cumulative indices are more appropriate than indices based on temporal averages because they allow a more robust comparison between events of different lengths20. Cumulative metrics depend both on the duration and the temperature anomalies of the heatwave event, and thus are expected to better capture the overall impact of the heatwave19. A number of cumulative indices have been developed in literature22, one of the most widely used being the heatwave magnitude index daily (HWMId)2,23–25. HWMId is a percentile-based index that aggregates excess temperatures above a certain normalised threshold, combining the duration and temperature anomaly of heatwaves into a single number (Methods).Fig. 1 | The last four decades show an increasing trend of the HWMId and the summer mean temperature in the Arctic. a Time series of area-averaged HWMId (green) and summer mean temperature anomaly (purple) in the terrestrial Arctic. Dashed lines show the linear trends over 1979–2022, with values annotated. b HWMId trends for the period 1979–2022. Areas without a statistically significant change are masked out (shown with white). The anomalies in a are expressed relative to the 1981–2010 period. The values are based on ERA5-Land. The use of a percentile-based index is particularly important in the Arctic, where summer climate varies greatly from continents to high Arctic islands. Based on ERA-Interim reanalysis, Dobricic et al.2 showed an increasing trend in HWMId during 1979–2015 in the Arctic regions, especially in northeastern Canada and Greenland. In this study, we build our analyses on the state-ofthe-art atmospheric reanalysis ERA5-Land and a suite of global climate models from the Coupled Model Intercomparison Project phase 6 (CMIP6) archives. ERA5-Land has a much higher spatial resolution than ERA-Interim (0.1° vs. 0.75°), and our observational analysis covers the 73-year period 1950–2022, providing new perspectives into the long-term variability of HWMId. Moreover, we use HWMId to investigate the spatial extent of heatwaves, which was not done in the Dobricic et al.2 analysis. The main objective of this study is to quantify the observed (1950–2022) and projected (up to 2099) changes in the spatial coverage of the heatwaves in the terrestrial Arctic. We anticipate that our results will offer novel insights into how climate change manifests in the Arctic region, highlighting the increasing exposure of terrestrial life to intensifying extreme heat. Results Observed increase in HWMId and the spatial extent of heatwaves In this section, we focus on the observed trends of HWMId and the spatial expansion of the heatwave area from 1950 to 2022 in the Arctic, based on ERA5-Land reanalysis. HWMId exhibits a large inter-annual variability with high HWMId values occurring generally during warm summers and vice versa (Fig. 1a). On average, the strongest heatwaves in the Arctic occurred recently, in 2019 and 2021, which are also in the top five for the summer mean temperature. Both HWMId and the summer mean temperature shows a clearly increasing trend since 1979, the period of rapid Arctic warming26. The year 1979 also roughly corresponds to the onset of an increasing trend in HWMId derived from the multi-model median of climate models (Supplementary Fig. 1). Over 1979–2022, HWMId has increased the most in Greenland and high Canadian archipelago, and to some extent also in Siberia (Fig. 1b). The year 1979 marks the advent of satellite observations, which may question the homogeneity of the time series. Yet, it is important to note that our analysis is focused on the terrestrial Arctic, for which in-situ observations have been available well before 1979, thereby enhancing the confidence in the accuracy of the data. ERA5-Land is constrained by the ERA5 reanalysis, which has been shown to be consistent with other datasets for long-term temperature variability in the Northern Hemisphere since the 1940s27. Next, we analyse the observed spatial extent of Arctic heatwaves, focusing on the heatwave extent aggregated over the first and last 30-year periods of our dataset, spanning the years 1950–2022. (Fig. 2a, b). Hereafter, we refer to a heatwave with HWMId ≥3 as a severe heatwave, a heatwave with HWMId ≥6 as an extreme heatwave, and a heatwave with HWMId ≥9 as a very extreme heatwave (see Methods). Averaged over the entire terrestrial Arctic domain in 1981–2010, these levels correspond to a heatwave occurring at a single grid point approximately once every 6, 20, and 60 years, respectively. Over the period 1950–1979, severe heatwaves were detected over 92% of the land area within the Arctic (Fig. 2a). There are localised areas in Greenland, Canada and Siberia that did not experience severe heatwaves throughout the entirety of the 30-year period. While extreme heatwaves were naturally not as widespread as the severe ones, they still encompassed roughly half of the Arctic region (53%) during 1950–1979. Very extreme heatwaves occurred mainly in western Siberia, Fennoscandia and Canada, covering a total of 22% of the region during the 1950–1979 period (Fig. 2a). In particular, high HWMId values were observed in northern Fennoscandia and the Kola Peninsula, largely due to the summer 1972 heatwave, which was ranked as one of the most intense heatwaves in Europe23. Comparing the extent of heatwaves between the first and last 30-year period, the difference is striking (Fig. 2b). In 1993–2022, virtually every part of the Arctic experienced at least one severe heatwave, with 99.8% of total coverage. Extreme heatwaves became more widespread too, being 86% in the 1993–2022 period. Furthermore, the largest relative increase is seen in very extreme heatwaves, which have more than doubled in extent, being 54% in 1993–2022. The most extreme heatwaves for the period 1993–2022 stand out in Alaska28, and the northern part of Greenland and the Canadian archipelago where HWMId reaches locally up to 138. The maximum HWMId in the periods 1950–1979 and 1993–2022 exhibit large spatial non-uniformity (Fig. 2a, b). One reason for the heterogeneity comes from the non-linear nature of HWMId. It is possible that over a 30-year period, some areas may not experience a particularly intense heatwave at any time, while others may coincidentally experience a heatwave that is clearly more intense than its surroundings. The non-linearity of HWMId means that even slight increases in temperature or duration can lead to disproportionately higher cumulative values.Time series of heatwaves’ annual coveragesillustrate theincreasing spatial extent of heatwaves (Fig. 2c). Severe heatwaves reached almost 50% extent in summer 2021.While the annual extent of severe heatwaves never reached 30% before 1990, it has exceeded 30% in four years since 2010. Extreme heatwaves now cover about 10% of the terrestrial Arctic, compared to about 3% at the beginning of the time series. Very extreme heatwaves are rare by definition. According to ERA5-Land, in some years (1970, 1978 and 1992) there were no such heatwaves at all in the terrestrial Arctic. In recent years, however, their coverage has been about 4%, and the most widespread summer was in 2012, when almost 10% of the land area experienced a very extreme heatwave.Fig. 2 | Increased spatial extent of heatwaves in the terrestrial Arctic. Maximum value of HWMId during the first 30-year period of the time series (a) 1950–1979 and the last 30-year period (b) 1993–2022. Annotated are the proportional spatial extents of severe, extreme and very extreme heatwaves, respectively. Dashed line depicts the Arctic Circle, 66.5°N. c Time series of the spatial extent of three different heatwave magnitude indices (severe, extreme and very extreme), expressed as a percentage of the total terrestrial area of the Arctic. d Same as c, but expressed as a ratio of land area relative to the reference period 1950–1979. Here, a ratio of 2 represents a doubling of the affected area relative to the reference period. The thick lines in c and d show 10- year moving averages.The mean area covered by all heatwave definitions over the last 10 years is now higher than in any single summer between 1950 and 1979 (Fig. 2c). The only exception is the summer 1972, when the spatial extent of very extreme heatwaves was 5.9%, a slightly higher value than the 2013–2022 average (orange line in Fig. 2c). It is evident that the heatwave coverage in the terrestrial Arctic in the current climate is now well outside the historical climate. The land area ratio shown in Fig. 2d indicates how much more widespread these heat extremes have become compared to the reference period 1950–1979. The more severe heatwave by definition, the greater the relative increase, as strong heatwaves were less widespread during the reference period. The results suggest that the spatial extent of severe heatwaves has increased by a factor of two, extreme heatwaves by a factor of three, and very extreme heatwaves by a factor of four (Fig. 2d). Very extreme heatwaves in 2012 and 2019 were up to 10 times more widespread than the average extent in 1950–1979. Model-simulated changes in heatwave magnitude index To shed light on the potential future changes in the heatwaves, Fig. 3a, b show the simulated ensemble-mean maximum HWMId values in theArctic for 2040–2069 and 2070–2099, respectively, using the middle-of-line SSP2- 4.5 emission scenario. From each CMIP6 simulation (n = 43), we calculated maximum HWMId for the two 30-year periods, and then took the average across the simulations. The model simulations for the Arctic-average HWMId are in agreement with the observations (Supplementary Fig. 1). By mid-century, virtually all Arctic regions are projected to experience temperatures exceeding the threshold for very extreme heatwaves (Fig. 3a). This suggests that very extreme heatwaves are projected to occur everywhere in the Arctic at least once during the 30-year period of 2040–2069. In the end of the century, very extreme heatwaves become increasingly common as the multi-model mean HWMId values exceed 15 in large areas of the Arctic (Fig. 3b). Based on the estimated pixel-wise linear trends of HWMId over 2000–2099, the strongest increase in HWMId is projected to occur in the High Arctic, namely the Canadian archipelago, the coasts of Greenland, Svalbard, and some Russian islands such as Novaja Zemlja (Fig. 3c). In these regions, HWMId may increase more than 3 units per decade over the 21st century. Notably, the observed trend of HWMId over 1979–2022 already shows an emerging increase of HWMId in these areas (Fig. 1b).Fig. 3 | Projected changes in heatwaves during the 21st century. Multi-model mean values of CMIP6-simulated maximum HWMId in a 2040–2069 and b 2070–2099 under SSP2-4.5 emission scenario. c Linear trend of CMIP6-simulated HWMId calculated over 2000–2099, expressed as change in index per decade. d Time series of CMIP6-simulated spatial extent of heatwaves, expressed as a percentage of the total land area of the Arctic. Thick lines represent the ensemble mean and the shading shows the 5-95th percentile range of the model simulations. The ensemble mean describes the average of the individual model simulations, and not the extent of the ensemble mean. e Boxplots of the distributions of heatwave area by CMIP6 models for 1950–1979 and 2070–2099. The black lines indicate the medians of the CMIP6 simulations, the boxes show the first and third quartiles, and the whiskers extend to the 5-95th percentiles of the simulations. In contrast, the continental parts of Eurasia, North America and the Greenland ice sheet show spatially more uniform trends in HWMId (Fig. 3c). In Section 3.4 we discuss in more detail the asymmetry in the HWMId trend between the continents and the Canadian archipelago. Projected changes in the spatial extent of heatwaves The CMIP6-based projections for the spatial extent of severe, extreme and very extreme heatwaves using the SSP2-4.5 emission scenario are shown in Fig. 3d. All these simulated heatwave extents show a relatively stable evolution until the 1990s, after which the extents start to increase. By the end of the century about 75% of the terrestrial Arctic are projected to experience severe heatwaves annually (Fig. 3d). The median peak coverage of individual models by 2099 is 91% (not shown), so it is plausible that by the end of the century the Arctic will experience a summer in which virtually the entire land areais affected by a severe heatwave. The projections for the end of century have relatively high uncertainty intervals, with 5–95 percentiles rangingfrom 41% to 93%for the 2070–2099 period (Fig. 3e). The uncertainties are due to both (1) interannual variability inherent for Arctic climate and (2) inter-model differences, e.g. in the pace of global warming in the model simulations. Extreme heatwaves are projected to affect about a third of the Arctic by 2050, and about half of the Arctic by the end of the 21st century, with a multi-model mean projection of 49% (20–79%) for the 2070–2099 period (Fig. 3e). Finally, very extreme heatwaves, comparable or stronger than those observed in Verkhoyansk in 2020 (Supplementary Fig. 2a), could affect 20 % in 2050 and 32 % (10–64%) of the terrestrial Arctic in 2070–2099 (Fig. 3e). This constitutes a major increase from the 1–2% range seen during the 20th century (Fig. 2c). In summary, our findings show a substantial spatial expansion of heatwaves even under a medium emission scenario. Longer heatwaves explain higher HWMId trend in the Canadian archipelago than in Siberia In Section 2.2, we showed that CMIP6 models project a stronger trend in HWMId in the Canadian archipelago (CA) than in the continental areas of the Arctic. This raises the question of why the HWMId is predicted to increase disproportionately in CA compared to the continental areas of the Arctic. Analysis of the projected summer mean temperature (Fig. 4a) and HWMId (Fig. 4b)from CA and Siberia illustrates the divergent behaviour of HWMId with the warming between these two locations. While both domains show approximately the same amount of warming in the SSP2-4.5 scenario, heatwaves are projected to become stronger in CA compared to Siberia. Regression of HWMId onto T2m anomaly (Methods) across the whole Arctic provides further evidence about the finding (Fig. 4c). The ensemble mean regional average of the linear regression slope SHWMId Fig. 4 | HWMId is more sensitive to summer warming in the Canadian archipelago than in Siberia. CMIP6-simulated a summer mean temperature anomaly and b HWMId in the Canadian archipelago and Siberia. The lines show multi-model mean regional averages. Regression of c HWMId, d heatwave length, and e heatwave intensity onto summer mean temperature anomaly in the CMIP6 models. The polygons in panels c–e depict the domains of Canadian archipelago and Siberia used in a and b. The anomalies in a are expressed relative to the 1981–2010 period.10.3 °C⁻¹ in CA and 1.9 °C⁻¹ in Siberia. Hence, it is clear that heatwaves over continental areas of theArctic are less sensitive to the summer warming than the coasts of CA. HWMId is a cumulative index that considers both the length (HWL) and intensity (HWI) of the strongest heatwave of the summer. Therefore, changes in either parameter could result in higher HWMId values. Further investigation into the sensitivity of HWL and HWI (Fig. 4d, e) to the summer mean temperature anomaly reveals that the stronger trend in HWMId in CA, compared to continental areas, is mainly due to longer heatwaves rather than more intense ones. The ensemble-mean regional average of SHWL is 5.0 days °C⁻¹ in CA and 1.6 days °C⁻¹ in Siberia (Fig. 4d). In other words, for one degree of summer warming, the most intense summer heatwave will lengthen three times faster in CA than in Siberia. In contrast, there are no marked differences in the sensitivity of HWI between the two regions as in CA the ensemble-mean regional average of SHWI is 1.2 °C °C⁻¹ while in Siberia it is 0.9 °C °C⁻¹ (Fig. 4e). Thus, in both regions, the sensitivity is close to unity, meaning that the strongest summer heatwaves are projected to warm close to the same rate as the summer mean temperature in the region. Discussion This study has improved our understanding of how climate change is increasing the area of theArctic exposed to heatwaves.An importantfinding of our study is that heatwaves in CA and northern Greenland are more sensitive to summer warming than heatwaves on the mainland Arctic. We attribute these dynamics mainly to prolonged heatwaves rather than more intense heatwaves (Fig. 4). In CA, the day-to-day temperature variation during the summer months is suppressed compared to Siberia (Supplementary Fig. 3). Therefore, a certain degree of climate warming during summer results in more days with temperatures above the 90th percentile in CA compared to Siberia (Supplementary Fig. 2). As a result, even though the average intensity of the heatwaves would remain approximately the same in both regions as the climate warms, the less pronounced temperature variability in CA leads to longer heatwaves and thus higher HWMId values. This further implies that the ecosystems in CA are likely to be particularly exposed to increasing thermal stress due to climate change. The underlying reason that heatwaves are projected to intensify in the Canadian Archipelago and northern Greenland may be due to a feedback effect from the loss of ice cover. In the present climate, the Siberian coasts are typically ice-free in late summer, but ice cover persists throughout the summer in CA and northern Greenland. During this century, however, the decline in summer ice is projected to be most pronounced in CA and northern Greenland29, which could be one reason for the rapid increase in heatwave intensity in these regions as less heat is spent melting snow and ice. This hypothesis isfurther supported by thefact that the projected increase of heatwaves specifically in CA, Greenland and Svalbard is broadly consistent with Delhaye et al. 30. After a simulated sudden retreat of sea ice, they found an increase in summer maximum temperatures in regions consisting of islands previously surrounded by sea ice, such as Svalbard or CA. The increase in HWMId over CA and Greenland was also noted and linked to sea ice melt in previous research2 . However, a more detailed energy budget analysis would be required for a mechanistic understanding of the role of snow and ice in the occurrence of local Arctic heatwaves. In addition to the recent upward trend, the time series in Fig. 2c indicates a local maximum in the spatial extent of heatwaves around 1990, suggesting decadal variability in Arctic heatwaves. Previous studies have established a link between a positive Arctic Oscillation (AO) and the occurrence of wildfires in Siberia, Canada, and Alaska31–33. Noteworthy, at the turn of the 1990s, the AO shifted to a positive phase34, which coincides with the local maximum of heatwave spatial extent (Fig. 2c). Further research is needed to elucidate the role of large-scale atmospheric conditions in the interannual and decadal variability of heatwave area in the Arctic. In ERA5-Land and CMIP6 simulations, the spatial extent of heatwaves is highly correlated with the summer mean temperature (Supplementary Fig. 4). The Pearson correlation coefficient (R) in CMIP6 models is >0.85for all heatwave definitions. This strong relationship implies that rising mean temperatures across the Arctic favours increasingly widespread heatwaves. The relationship between summer mean temperature and heatwave area becomes saturated at high mean temperatures, as the entire Arctic becomes covered by heatwaves. For some models such saturation (>95% land area) for severe heatwaves already occurs during this century in the SSP2- 4.5 scenario (Supplementary Fig. 4). In these models, global warming reaches more than 3 °C compared to pre-industrial times (not shown).The model projections presented in our study are based on a selection of 21 CMIP6 models with varying degrees of equilibrium climate sensitivity (Supplementary Table 1). We found that the future extent of heatwaves increases the most substantially in the high-sensitivity models (Supplementary Fig. 5), where global warming is also the fastest35. The effect of overly rapid or slow rates of global warming simulated by some models for the spatial extents of heatwaves can be eliminated by using fixed levels of global warming35. At 2.0 °C global warming compared with the 0.5 °C climate, the CMIP6 multi-model mean number of severe heatwave area is threefold, the extreme heatwave area is fivefold, and the very extreme heatwave is eightfold (Supplementary Fig. 6). However, there is variability between model simulations, suggesting that the relationship between the spatial extent of heatwaves and global warming is to some extent model dependent. Here, using state-of-the-art atmospheric reanalysis and the latest global climate models we have quantified the observed and projected long-term changes in heatwaves over the terrestrial Arctic. In particular, we showed evidence of a manifold increase in the area covered by heatwaves in recent decades compared to the mid-20th century, indicating a departure from historical climate norms. In addition, we found robust signals of increasing extent of heatwaves at various intensities across the domain, whilst highlighting the region-specific dynamics likely driven by sea ice loss. We conclude that heatwaves are escalating in severity and geographical extent, even in the near future and under a medium emission scenario. These changes are anticipated to exert profound impacts on Arctic ecosystems and communities. Methods Analysis period and domain Our analysis is restricted to boreal summer (June-August) in 1950–2022 in observations, and 1950–2099 in models. We focus on the terrestrial Arctic, that is, land areas poleward of 60°N latitude. Observational data We use the heatwave magnitude index daily (HWMId) from the ARCLIM dataset36. Note that HWMId is named HWMI in ARCLIM. The original ARCLIM covers the years 1950–2021, but we use HWMId which is extended by one year, to cover 1950–2022. ARCLIM is derived from the ERA5-Land reanalysis37. The ERA5-Land reanalysis, developed by the European Centre for Medium-Range Weather Forecasts, is an advanced meteorological dataset providing 0.1° resolution global climate information from 1950 to the present. ERA5-Land provides hourly data on meteorological variables at the land surface, allowing for a temporally and spatially consistent analysis of climate patterns, extreme weather events and regional climate change. Model data We employ global climate model simulations from the CMIP6 models38, listed in Supplementary Table 1. For 1850–2014 we use the historical simulations of the models. These are concatenated with medium-emission shared socioeconomic pathway (SSP2-4.5) scenario simulations for 2015-2099. Daily maximum temperatures (variable “tasmax”) from a total of 21 models are used. The native model grids are remapped to the same 1° latitude-longitude grid. A land-sea mask is used to extract information on land areas only. For each model, 1–4 realisations per model are included, resulting in a total of 43 climate model simulations. No more than 4 realisations were selected from each model to avoid overweighting the results for a particular model. See the number of realisations per model in Supplementary Table 1. Heatwave magnitude index Our analysis relies on heatwave magnitude index daily (HWMId), originally derived by Russo et al. 23,39. but which has been later on used in multiple studies2,20,24,40. Heatwaves are defined as days when the daily maximum temperature exceeds the 90th percentile (P90) threshold for at least three consecutive days. P90 is a typical threshold for defining a heatwave19,20. P90 threshold is calculated using the period 1981–2010 and a window of 31 days. Thus, for each day there is a sample of 30 × 31 = 930 days from which the 90th percentile is calculated. We chose 1981–2010 as the baseline because previous studies have used the same baseline. Then, the daily magnitude of heatwave is calculated as MdðT maxÞ -T max T25 T75 T25 where Tmax is the daily maximum temperature and T25 and T75 are the 25th and 75th percentiles of the annual maximum temperatures of the grid cell in the period 1981–2010. Thus, the index is normalised by the inter quartile range (IQR) of annual maximum temperature. Negative Md values are considered as zero. We then calculate the heatwave magnitudes of all the heatwaves within a summer by summing the daily magnitudes Md of the consecutive days that make up a heatwave. In each summer, there may be several heatwaves with different cumulative Md values. Finally, themaximum value of cumulativeMd occurring within a given summer is defined as the HWMId at that grid point for that summer. HWMId thus represents the strongest heatwave of the summer. HWMId is calculated for ERA5-Land (in ARCLIM dataset) for 1950–2022 and for CMIP6 models for 1950–2099. Since P90, T25 and T75 are calculated separately for each CMIP6 model, the percentile-based method enables a fair comparison between observations and models that may have systematic biases in absolute daily maximum temperatures, in which case the use of a fixed temperature value would not be advisable. Broadly following previous studies41,42, we define three HWMId thresholds of 3, 6 and 9 and refer to these as ‘severe’, ‘extreme’ and ‘very extreme’ heatwaves, respectively. The average recurrence periods for these heatwave levels are 6, 20, and 60 years, respectively, when calculated over the entire terrestrial Arctic from 1981 to 2010.The key advantage of the HWMId is that it takes into account both the intensity and duration of heatwaves. In addition, the percentile-based approach, normalised by the IQR of the annual maximum temperature, allows a robust comparison of heatwaves between different climatic regions characterised by different interannual variability of the summer maximum temperatures20. Trend analysis Trends of HWMId are calculated pixel-wise, usingMann–Kendall trend test from pyMannKendall Python package43. Sensitivity analysis To investigate the sensitivity of heatwave characteristics to the local summer (JJA) mean temperature (TJJA) in the Arctic, we regressed HWMId, heatwave length (HWL) and heatwave intensity (HWI) against TJJA using the CMIP6 historical and SSP2-4.5 simulations for the years 2000–2099. HWL represents the number of heatwave days during the most intense heatwave of the summer, and HWI describes the maximum temperature anomaly above the heatwave threshold during the most intense heatwave of the summer. Here, the CMIP6 multi-model mean regression coefficient SHWMId indicates how much HWMId increases as a function of summer mean temperature. SHWL and SHWI in turn show how the length and the maximum intensity of the most intense summer heatwave change as a function of summer mean temperature. Note that HWL and HWI in Eqs. (3) and (4) represent the length and maximum intensity of the most intense heatwave of the summer, i.e. the one used to calculate HWMId.While these regression coefficients could, in principle, also be estimated from ERA5-Land, the CMIP6 model simulations provide a much better signal-to-noise ratio because of their larger number and longer time series. Global warming levels The extent of heatwaves at different levels of global warming is studied using climate models. Four different levels are used: 0.5, 1, 1.5, and 2 °C compared to the 1850–1900 average. Higher levels are not studied because some models in the SSP2-4.5 scenario do not reach such levels in the 21st century. To find the years corresponding to each level of global warming, the following method is used for each climate model: 1. Calculate the global mean temperature, weighted by the cosine of latitude. 2. Calculate annual means. 3. Subtract the 1850–1900 mean from the time series (historical data concatenated with SSP2-4.5 scenario runs). 4. Calculate 20-year centred moving average. 5. Find the first year in which the 20-year centred moving average reaches the predefined global warming level (0.5, 1.0, 1.5 or 2.0 °C). A 20-year centred moving average of the simulated heatwave extent is then calculated and the value corresponding to the year found in 5. represents the heatwave extent at that level of global warming. For example, if the 2.0 °C level of warming is reached in 2073, the period considered is 2063–2082. Data availability HWMId data is available from the ARCLIM dataset36. ERA5-Land data are available from Copernicus Climate Data Store at https://cds.climate. copernicus.eu. CMIP6 model data are available from Pangeo Gallery at http://gallery.pangeo.io/repos/pangeo-gallery/cmip6/index.html. The code and datasets needed for reproducing the results are available at https://doi. org/10.5281/zenodo.1359715144.

References :

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