Arctic amplification has already peaked

It has been demonstrated that the Arctic has warmed at almost four times the global average rate since 1979, a phenomenon known as Arctic amplification. However, this rapid Arctic warming is tightly linked to the retreat and thinning of summer sea ice, and so may be expected to weaken as the Arctic transitions to seasonal ice cover. Here we show evidence from gridded observations and climate reanalysis that Arctic amplification peaked sometime in the early 2000s. This occurred concurrently with a maximum in the rate of loss of sea ice area, thickness, and volume. From CMIP6 projections and the CESM2 large ensemble we see that Arctic amplification is unlikely to be so high again at any future point in the 21st century except in the lowest emissions scenarios in which global temperatures stabilize while the Arctic continues to warm.


Introduction
During periods of global warming the Arctic tends to warm much faster than the global average [1][2][3][4][5]. This is known as Arctic amplification and since 1979 the Arctic has been observed to warm at almost four times the global-mean rate [6]. This rapid warming in the Arctic in recent decades has led to physical, ecological, social, and economic changes in the region [7,8]. Arctic amplification has profound consequences for the region that are further enhanced by a positive feedback between warming and the retreat and thinning of Arctic sea ice [9]. A shift to seasonal ice-cover in the Arctic is expected to occur by the 2040s under almost all emissions scenarios for the 21st century [10].
There are many processes that drive Arctic amplification including the sea-ice albedo feedback [9,11], snow-albedo feedback [12], lapse-rate feedback [13], Planck feedback [14], near-surface inversions [15,16], and Atmospheric and Oceanic heat transfer [17]. It can be difficult to quantify the relative contributions of these processes as they are tightly coupled [14,18]. Multi-decadal variability in forcings, such as aerosol forcing due to biomass burning, can also induce variability in sea ice loss and hence Arctic amplification on these timescales. Climate models have been shown to underestimate the recent Arctic amplification in the multi-model mean (MMM) [6], but natural variability definitely plays a large role in variability of Arctic amplification [3]. Hence it is uncertain whether this underestimation of the recent warming is due to biases in climate models response to forcing or if large internal variability on regional scales is the reason the MMM does not reproduce the observed Arctic amplification [19,20].
There is also a strong seasonality to Arctic amplification with the largest amplification occurring in the winter months due to the combination of a more stably-stratified atmosphere [15], the effective heat capacity of sea ice [21], and ocean-mediated seasonal transfer of energy between ocean, sea ice, and atmosphere [22]. This seasonality is expected to change under increased CO 2 forcing with the peak moving later in the season [23,24]. While there is not a consensus on the relative importance of the processes behind Arctic amplification, many approaches including the evaluation of climate models using radiative kernels have shown that the sea-ice albedo feedback and atmospheric stability are two of the most important processes [25]. Several of the processes that cause Arctic amplification are expected to weaken as sea ice retreats [26], thins, and becomes more broken i.e. there is a larger fraction of open water within the sea ice cover. This is expected to lead to a reduced influence of sea ice on air temperatures in the Arctic as seen from analysis of information transfer using the EC-Earth large ensemble [27]. However, the timeline for when Arctic amplification might be expected to peak has not been established in the literature. A research synthesis of the processes behind Arctic amplification published in 2011 stated that it was expected to increase in the 2010s and beyond [28].
While there are several different ways to measure Arctic amplification [29], one of the most widely used is the ratio of the warming trend in the Arctic to the global-mean [6,17]. This metric has the advantage of being easy to interpret and being local in time and so not dependent on a given reference climate. Here we make use of this metric to assess recent changes in Arctic amplification in observations, reanalysis and CMIP6 climate model simulations and relate these to the corresponding changes in sea ice cover. We use this to identify a recent peak in Arctic amplification within observational datasets that coincides with a peak in the rate of loss of sea ice cover, thickness, and volume. We compare this result to the CMIP6 MMM historical and scenario projections for the 21st century to determine if such a peak in Arctic amplification is found in model simulations as a response to changes in external forcing and loss of sea ice. We investigated how the peak in Arctic amplification changes with time-window used to establish the transient nature of recent changes in the magnitude of Arctic amplification. And finally, we look at the seasonality to determine the season in which Arctic amplification has peaked and whether this seasonal signature is captured in the CMIP6 simulations.
We then created two timeseries of Arctic and global monthly-mean temperatures by taking areaweighted means of the gridded data for the two domains e.g.
where T i is the surface air temperatures of each gridcell within the Arctic, w i is the area of each gridcell, and n is the number of gridcells. The Arctic was defined as all regions north of 66 • N by default, but we also computed Arctic timeseries using thresholds in 5 • bands from 60 • N to 80 • N. Trends were calculated using least-squares linear regression over time windows in the range of 9-41 years in steps of 4 years. Trends were considered non-significant if they were not significantly different from zero at the 90% confidence interval. Arctic amplification was then calculated as the ratio of the Arctic trend to the global trend: whereṪ Arctic andṪ Global are the Arctic and global temperature trends respectively. Arctic amplification may therefore have a positive or negative value depending upon the sign of the trends, although no period in either the models or the observations had negative values for the Arctic amplification. The uncertainty in the value of the Arctic amplification was calculated using a bootstrap method with 1000 random samples of the normally distributed probability density function of the trends in the Arctic-and global-mean temperature trends. The uncertainty in AA is then given by the 5th and 95th percentiles of the bootstrapped uncertainty. To calculate the MMM of the Arctic amplification in the CMIP6 simulations we first calculated the mean of the temperature trends across all models and then took the ratio.
We acquired the monthly mean sea ice concentration for ERA5 from the ECMWF website, for the CMIP6 models from the ESGF website, and for the CESM2 large ensemble from the climate data archive listed above. Supplementary figure 1 lists all the CMIP6 models used. We then calculated the total sea ice area for the Arctic by multiplying the sea ice concentration by the area of each gridcell, and then summing this for the Arctic domain. The trends in the sea ice area were calculated using a least-squares regression for each of the time periods and windows used.
To calculate the average height of peaks in Arctic amplification from the CESM2 large ensemble (figure 4) we first calculated the timeseries of Arctic amplification in each of the 100 ensemble members. We then ran a peak-detection algorithm on each time series which identified when a peak had occurred according to the condition that the Arctic amplification in a given year was the highest value for the decade centred around that year, and that there was a real value for the Arctic amplification in every year of that decade. We then extracted the values of the Arctic amplification in each of those years where a peak was identified to create a timeseries of Arctic amplification that tells us how strong Arctic amplification would be if it happened to peak in that particular year. We tested the sensitivity of this result to the window length over which a peak is defined but a wide range of windows, 5-20 years, did not change the result that the peak value decreases over time, it only changed how many peaks were found.

Results
Arctic temperatures have been rapidly increasing since the late 1970s ( figure 1(a)). Whereas global temperatures have been increasing more steadily since the 1950s. There is very good agreement between the reference datasets as to the global-mean and the Arctic-mean temperatures after the beginning of the satellite era in 1979. However, we see some discrepancy between the gridded observations and the ERA5 reanalysis before this time with the reanalysis being consistently cooler in the Arctic. This is likely due to the limited number of regular observations in the Arctic prior to the use of satellite remote sensing, which means that Arctic temperatures in the ERA5 dataset are poorly constrained by observations. We also see this difference between ERA5 and the observational datasets in the timeseries of Arctic amplification calculated using a 29 year window ( figure 1(b)). For this reason we choose to focus our analysis on the period after 1980 as others have recommended [6]. Since the reference datasets are so similar for this post-1980 period we use a multi-observational mean (MOM) for the remainder of our analysis. This is a mean of the ERA5, BEST, GISTEMP, and HadCRUT5 timeseries. We can see that Arctic amplification in the observation datasets starts with values close to 1 in the late 1970s, steadily increases to a peak value of around 4 at the turn of the century, before decreasing in the 2000s. In the last year of each timeseries the expectation value of the Arctic amplification is below the 5th percentile of the peak value in the timeseries, giving high confidence that Arctic amplification has peaked.
By using the definition of Arctic amplification as the ratio of the trend in the Arctic to the trend in the global-mean temperatures one must choose a window over which to calculate the temperature trends. Figure 2 shows the Arctic amplification as a function of time for window lengths ranging from 9 to 41 years, together with the corresponding trend in sea ice area. There is a clear peak in both the Arctic amplification and the rate of loss of sea ice in the early 2000s, centred around 2005. For example, Arctic amplification calculated using a 17 year window reaches a peak of 8 in 2004 before dropping to 2.5 in 2011. There is no indication of any other peak in Arctic amplification in the period since 1970, and the values of Arctic amplification found in the early 2000s of around 8 for the shorter time windows of 13 and 17 years are unprecedented. This peak in Arctic amplification is concurrent with an unprecedented rate of loss of sea ice area, as may be expected given the dominant role of the sea ice feedback in Arctic amplification at this time.
That this peak in Arctic amplification is coupled to the rate of loss of sea ice area is clear when we adjust the latitude threshold we use to define the Arctic (see supplementary figure 2). We find that across all latitude thresholds considered and a wide range of time windows, from 13 to 29 years, we see a clear peak in Arctic amplification. The magnitude of Arctic amplification increases as we move the threshold to higher latitudes, confirming the expectation that Arctic amplification is most pronounced over the Arctic Ocean. It is the values close to the peak Arctic amplification which increases the most as we move towards higher latitudes, meaning that the peak becomes even more pronounced the further north we set the definition of the Arctic.
If this peak in Arctic amplification was purely due to the forced response from increasing atmospheric CO 2 then we would expect to find a peak in the CMIP6 MMM. The MMM of 32 global climate models shows that Arctic amplification tends to decrease from the 1980s through to the end of the 21st century where it remains stable with values of 2.4 ± 0.2 under emissions scenarios where global temperatures continue to rise throughout the 21st century ( figure 3). In the SSP126 scenario global temperatures stabilize sometime in the second half of the 21st century, but the Arctic continues to warm [31], and so Arctic amplification once again increases in the mid-to-late 21st century. However, there is no strong evidence of a peak in Arctic amplification occurring in the MMM. Individual models show a wide range of behaviours, but they all have the highest values of Arctic amplification occurring at some time in the 20th century in all scenarios except for the SSP126 (supplementary figure 1). This suggests that internal variability is key to creating a peak in Arctic amplification, but the MMM plot suggests that the magnitude of that peak is controlled by the mean state, and so peaks in Arctic amplification that occur in a climate with less sea ice will have lower values. This is confirmed by analysis of the CESM2 large ensemble. We calculated how large a peak in the Arctic amplification would be if it occurred in each year from 1850 to 2100 (figure 4). We found that peaks in Arctic amplification never occurred in the CESM2-LE before the 1980s and that the magnitude of the peaks decreased in time from the 1980s until the end of the 21st century.
This pattern in the observations of a peak in Arctic amplification occurring around the turn of the century is even clearer when we look at the seasonal cycle ( figure 5). There is a large seasonal variation in Arctic amplification with the highest values found in the winter months (October-April). For the MOM we see a clear peak in Arctic amplification occurs around 1998-2002 and that within the seasonal cycle the peak is centred on January. Whereas during the summer (June-July) Arctic amplification is relatively weak (1-3) and does not change much over time.
The MMM does capture the essential element of the seasonal cycle in Arctic amplification: that    the highest Arctic amplification occurs in the winter months. However, there is not such a clear peak in Arctic amplification during the 20th century as seen in the observations. However, there is a clear shift in the seasonality of Arctic amplification in the high emissions scenario ssp585 during the 21st century. As there is a shift towards seasonal ice cover in the Arctic in SSP585 around the 2040s we see a corresponding reduction in Arctic amplification in the autumn months of September, October, and November.

Discussion
Recent work has demonstrated that on average the Arctic has been warming at almost four times the global-mean rate since satellite records began in 1979 [6]. This rapid Arctic warming has already had profound consequences for the region, particularly in the thinning and retreat of sea ice. Since the emergence of recent Arctic amplification in the late 1990s and early 2000s it has been proposed that the retreat of sea ice is critical to the establishment of strong Arctic amplification [9]. This is supported by the identification of a strong positive feedback between summer sea ice area and Arctic warming. The observation that Arctic amplification already peaked around 2000 is consistent with a peak in the rate of loss of sea ice area, volume, and thickness around that time. While a lot of focus has been on the retreating sea ice edge, the loss of sea ice volume is more dramatic with around twothirds of sea ice volume observed during the 1980s already having melted [10].
In addition to the slowed reduction of sea ice, and so reduced albedo-feedback effect, another cause for the recent peak in Arctic amplification may be that as sea ice thins and becomes more broken there is less frequent occurrence of shallow, stably-stratified atmospheric boundary layers over ice. It is the presence of these shallow boundary layers which can strongly influence surface air temperature responses to changes in radiative forcing [15] and these surface inversions have been demonstrated to be an important component of Arctic amplification [25]. However, this is complicated by the small-scale processes that occur over leads in ice during winter. The large air-sea temperature difference can cause plumes to form in the atmosphere over leads that, when advected over sea ice, act to increase the near-surface atmospheric stability. However, the net effect of leads on the surface air temperatures is unclear, and further complicated by the effect surface moisture fluxes from leads have on cloud formation.
Another possibility is that the peak in Arctic amplification is due to natural variability in the climate system. This could be due to Bjerknes compensation: the slow change in advection in the atmosphere and ocean on multi-decadal timescales [32]. This has been widely debated in the context of the early 20th century Arctic warming which was a period of significant Arctic warming not driven by changes in external forcing [33].
The CMIP6 and CESM2 large ensemble simulations show us that the Arctic will continue to warm at more than twice the rate of the global average, even if the Arctic transitions to seasonal ice cover. This is supported by paleo records of Arctic amplification [34]. But so long as the world continues to warm, we are unlikely to see as strong Arctic amplification as has been observed in recent decades. This is conditioned on the assumption that the climate model biases in representing the processes and coupling of processes that cause Arctic amplification do not substantially change in the 21st century. If global temperatures do stabilize in the 21st century, Arctic amplification may increase again, but in this case the absolute rate of Arctic warming will be much less than observed over the last 40 years.

Data availability statement
No new data were created or analysed in this study.