A Robust Arctic Amplication Factor Throughout the Last 21,000 Years

Arctic amplification (AA), a phenomenon that a larger change in temperature near the Arctic areas 3 than the Northern Hemisphere average in the past 100+ years, has significant impacts on mid- 4 latitude weather and climate, and therefore is of great concern in current climate projections. 5 Previous studies suggest a wide range of AA factors from 1.0 to 12.5 using either the 20th century 6 observations or climate model hindcasts. In the present paper, we explore the diversity of AA factor 7 in a long-term transient simulation covering the past glacial-to-interglacial years. It is shown that 8 the natural AA phenomenon is essentially linked with North Atlantic sea ice changes through ice- 9 albedo feedback with a narrowed and robust AA factor of 2.5±0.8 throughout the last 21,000 years. 10 Current observed AA phenomenon is a mixed result combining sea ice melting induced AA mode 11 with GHGs induced global uniform warming, and thus has an AA factor slightly less than 2.5. In the 12 future, as Arctic sea ice gradually melts off, we speculate that AA phenomenon might fade off 13 accordingly and the AA factor will decline close to 1.0 in 1-2 centuries. Our findings provide new evidence for better understanding the range of AA factor and associated key physical processes, 15 and provide new insights for AA’s projection in current anthropogenic warming climate.


Introduction 17
Arctic amplification (AA) is a prominent mode of modern climate change showing that the near-18 surface temperature at high latitudes has a much larger warming rate than the Northern Hemisphere 19 (NH) average during the last 100+ years in both observations and model simulations [1][2] [3] . 20 Although AA's impact on mid-latitude weather and climate extremes has been recognized widely 21 , its dynamics are complex and still remain controversial [1][8] [9] . Traditionally, Arctic ice-22 albedo feedback is considered as the basic cause in forming AA [10][11] [12] . Recently, some researchers 23 argued that the remote processes, such as atmospheric and oceanic meridional heat transport, play 24 an important role in shaping a detectable or considerable AA on Earth-like planets 25  [19] or even on an ice-free planet [20] . Besides, it is also found that some local 26 processes, including water vapor and low-cloud increment, can also perform additional warming 27 over Arctic area [21] [22] . In addition, the lapse-rate constrain, affecting the atmospheric heating 28 profiles through both the local and remote (tropical) processes, is also considered as an important 29 mechanism in intensifying near-surface AA [23] [24] [25] . At the current stage, the community still have 30 no consensus on the relative importance among the above candidates, which results in the diverse 31 modeling projections of AA for the next centuries [1][26] [27] . 32 AA factor (i.e. AA index), generally defined as the Arctic-to-NH surface warming/cooling ratio 33 to quantify AA's amplitude, is estimated to be in a wide range of 1.3-12.5 in the past 100+ years. 34 Davy et al. [28] did a comprehensive work by investigating 2 sets of observed data and 6 sets of 35 reanalysis data, and suggested that the AA factor could be in 2.5-8.0. With the similar approaches, 36 Bekryaev et al. [29] and Chylek et al. [30] found the AA factor could be in 1.3-2.0 and 2.0-12.5 37 respectively using weather station records. It should be noted that the calculation of AA factor is 38 sensible to the selection of temporal windows. A shorter temporal window, such as a 30-year or even 39 shorter window, usually brings about the greater variability of AA factor. 40 The AA factor in modern modeling studies is estimated to be in 1.0-4.5, a wide range still but 41 relatively smaller than those estimates based on the observations. Dai et al. [10] suggested the AA 42 factor can be in the range of 1. scenarios. He also emphasized the importance of sea-ice loss in forming AA and pointed out that 45 the AA phenomenon might be vanished once Arctic sea ice melt off. In a similar study, Barnes et al. 46 [31] argued the AA factor could be in the range of 1.0-2.0 by visiting 5 CMIP5 models. In addition 47 used datasets show diverse AA patterns with large uncertainty ( Supplementary Fig. 1), mainly due 86 to their sparse records over Arctic and oceans in the early 20th century. Instead, the multi-model 87 means of historical and future simulations from the Coupled Model Inter-comparison Project, Phase 88 6 (CMIP6) can present a distinct zonal AA pattern for the past 100+ years (Fig. 1a) and the near 89 future (Fig. 1b). The current AA pattern, as a result of anthropogenic forcing plus natural variabilities, 90 comprises simultaneously the uniformly global warming and polar amplification signal. We can see 91 this pattern clearly in the CMIP6 estimates for the 20th century (Fig. 1a) and the 21th century (Fig.  92 1b). But in the much longer future, say 2151-2250 in CMIP6 extension scenarios (Fig. 1c), AA tends 93 to disappear largely even when the CO2 concentration keeps increasing from 1751 ppm to 2206 94 ppm, reminding us that AA might not be linked with CO2 forcing as tightly as in the observations. 95 Hence, it is much helpful to separate the AA pattern related to sea ice melting as an independent 96 internal mode of climate system from current human-induced global warming framework. 97 The paleoclimate simulation TraCE-21ka can reproduce as similar spatial pattern of AA as the 98 CMIP6 estimates for a series of abrupt climate change (ACC) intervals in the last 21,000 years. 99 Here, we show the SAT trend during a 100-year window in Bølling-Allerød (BA) warming period 100 as an example (Fig. 1d). It shows that paleo-AA pattern is also featured with a major warming center 101 around Arctic but very small warming at low-to mid-latitudes (Fig. 1d). In addition, the AA patterns 102 in CMIP6 and TraCE-21ka share another common feature that the significant SAT warming 103 normally occurs at the areas where sea ice melts rapidly (white dotted areas in Fig. 1a,b,d), 104 suggesting that sea ice changes play an important role in shaping AA pattern, which will be 105 discussed in-depth in the following sections. 106 What is the range of AA factor across the last 21,000 years? Here we examine this value in 107 three datasets, including TraCE-21ka covering the last 20,000+ years, NOAA-NCEI/LMR covering 108 the last 2000+ years, and NOAA-CIRES/20CR covering the last 100+ years. The results are shown 109 in Fig. 2 with 1972 samples from TraCE-21ka (Fig. 2a, navy blue, green, steel blue dots), 1901 110 samples from NOAA-NCEI/LMR (Fig. 2a, orange dots), and 1 single sample from NOAA-111 CIRES/20CR (Fig. 2a, red cross). Each sample refers to one AA factor (see Method, for the detailed 112 definition) within a 100-year window. We can see those TraCE-21ka dots scattering in a diamond 113 shape that reflect two distinguished climatic states. The first state features 1654 samples in total 114 close to the y-axis, referring to those samples having relatively stable 100-year climate with NH 115 averaged temperature changing less than 0.2 °C/100a, which acts as a small denominator and makes 116 the AA factors vary largely from -15 to +20. The second state includes 318 samples in total at 3 117 o'clock and 9 o'clock directions, representing those intervals, mostly in deglaciation years, having 118 significant warming or cooling trends with NH SAT trend greater than 0.2 °C/100a. In such cases, 119 AA factors almost stabilize around the level of 2.5 (see Method and Supplementary Fig. 2). Similarly, 120 the NOAA-CIRES/20CR sample (Fig. 2a, red cross) also presents an estimate of AA factor at 2.43 121 for the 20th century, a value slightly less than the estimate from TraCE-21ka. The NOAA-122 NCEI/LMR samples (Fig. 2a, orange dots), however, give an estimate of AA factor in a wide range 123 of 0-5, since Earths' climate was quite stable in the last 2,000 years with NH averaged temperature 124 varying almost no more than 0.4 °C/100a even in either the Medieval Warm Period (MWP) or the 125 Little Ice Age (LIA), which can be compared to the first climatic state in TraCE-21ka. Overall, the 126 majority of AA factors in both state 1 and state 2 fall in a narrow spread around 2.5 (Fig. 2a). 127 We further precisely examine the uncertainty of AA factors in TraCE-21ka data by 128 investigating the weighted probability density functions (Fig. 2b,c). It is shown that all the 1972 129 samples of AA factors follow a gaussian distribution with 2.5 as the median and ±0.8 as two wings 130 accounting for 50% total variance, i.e. the range from 25th to 75th percentiles. This narrowed factor, 131 2.5±0.8, implies a robust AA phenomenon is one of the internal modes of Earth's fluctuated climate 132 in the last 21,000 years, suggesting that the natural processes within climate system may play a more 133 important and robust role in shaping AA rather than modern anthropogenic forcing. 134

Three AA modes in the last 21,000 years 135
What do the scattering points imply in difference regimes in Fig. 2a? To address this question, we 136 perform composite analysis on those points over various regimes and name them in 3 modes (Fig.  137 3): the Arctic Mode with two phases AM+ and AM- (Fig. 3h, purple areas) standing for samples at 138 Mode implies that the SAT changes mostly occur at extra-tropics and even high-latitudes, especially 150 surrounding the North Atlantic regions (Fig. 3a,b). In contrast, the temperature changes in the tropics 151 are secondary and subtle. That is why we name these cases as the Arctic Mode by emphasizing the 152 essential role of Arctic temperature changes in dominating the NH averaged climate changes, 153 whereas the tropical temperature remains unchanged or slightly changed (Fig. 3g). Here, we develop 154 a simplified model to depict this pattern by defining a critical latitude separating high-latitude major 155 warming/cooling from low-latitude minor warming/cooling, which could be valid ranging from Arctic warming/cooling pattern (Fig. 3a, b) with an AA factor at 2.5±0.8 (Fig. 2c). 166 The samples in Warm-arctic-Cold-tropics Mode (WCM+ and WCM-), as well as Cold-arctic-167 Warm-tropics Mode (CWM+ and CWM-), represent the snapshots of Earth experiencing stable 168 climate when NH temperature has small centennial trend (Fig. 3h, green for WCM and yellow for 169 CWM) since high-and low-latitudes have comparable but opposite temperature trends (Fig. 3 c,d  170 for WCM, e,f for CWM). The differences between WCM+ and WCM-(CWM+ and CWM-) are the 7 warming (cooling) at high-latitudes is slightly overwhelming, so that the NH average also appears 172 a faintly warming (cooling), and vise versa. 173 What about the zonal-mean structure of the three modes? We perform composite analysis on 174 temperature trends at multiple pressure levels, and obtain the zonal mean features of the three modes, 175 as shown in Fig. 4. In Arctic Mode (Fig. 4a, b), there is significant warming/cooling in extra-tropics 176 extending from the surface to 500 hPa, whereas in tropics there is also considerable 177 warming/cooling in the upper-troposphere from 500 hPa to 150 hPa, the so-called "mini global 178 warming" or "tropical amplification" in the literatures [42] , but in apparently weaker amplitude than 179 that in the Arctic surface. In the plots for WCM and CWM modes (Fig. 4, c-f), no significant 180 temperature trends (dotted areas in Fig. 4) can be found in the troposphere except for the slight near-181 surface warming/cooling at high latitudes, but with very low statistical significance. In general, the 182 WCM and CWM modes have no statistically significant features on either spatial maps ( Fig. 3c-f) 183 or cross-section views (Fig. 4c-f), indicating that they can be seen as climatic noises rather than a 184 typical AA mode. 185 The spatial pattern and vertical structure of the three modes hint us that the Arctic Amplification 186 phenomenon, in nature, might be closely linked to sea-ice-air coupling processes happening over 187 the North Atlantic sector. The AM mode composite represents a typical changing climate (Fig. 3a,b) 188 that some sea-ice related large-scale low-frequency (close to or even longer than centennial 189 timescale) forcing, such as the Atlantic Multi-decadal Oscillation (AMO) or the Atlantic Meridional 190 Overturning Circulation (AMOC), trigger ice-albedo positive feedbacks, which further causes 191 abundant sensible heat released from the upper ocean to the lower atmosphere. Fig. 1d, for instance, 192 gives a 100-year example in Bølling-Allerød period showing that the fast warming (Fig. 1d, red  193 shadings) area over the North Atlantic is essentially caused by the ocean's heat release due to sea 194 ice melting (Fig. 1d, white dots). The cases in the other 2 modes imply that the NH climate is overall 195 stable with minor internal high-frequency climatic oscillation or disturbance, such as the Arctic 196 Oscillation (AO) and/or the Pacific Decadal Oscillation (PDO), but without ice-albedo feedback 197 triggered ( Fig. 3c-f, no dots over North Atlantic or North Pacific). In the next section we would 198 discuss the contribution of sea-ice melt (or freeze) to AA's formation. 199

Key sea-ice process in shaping AA 200
In order to identify the physics associated with AA phenomenon, we explore the variations of Arctic 201 sea ice areas and CO2 concentrations for all the ACC snapshots, which is defined here as a 100-year 202 sample having SAT trend larger than±0.5°C/100a (Fig. 5a). Most of these cases, which belong to 203 AM+ and AM-modes for sure, are in the Bølling-Allerød (BA) interstadial, while the rests are in 204 the recovery phase of Younger Dryas (YD), the 8.2ka event, and other ACC events in the Holocene 205 (Fig. 5a, purple circles). Fig. 5b and 5c show the AA factor with respect to the 100a-window trend 206 of NH sea-ice and CO2 respectively. The purple points scatter in the regimes at 3 o'clock and 9 207 o'clock directions, in Fig. 5b, suggesting a robust bond between sea ice expansion/retreat and AA 208 formation in those ACC epochs. However, the purple points scatter randomly around the zero point 209 in x-axis (Fig. 5c), suggesting that a typical AA event can even happen without significant CO2 210 increase/decrease. Alternatively, it is implied that the rapid change of sea ice, rather than CO2 211 concentration, might be the direct and solid reason for AA's formation. 212 The sea ice changes on centennial timescale induce Arctic temperature response, i.e. AA pattern, 213 through a series of thermodynamic processes. By taking a NH warming case as an example, sea ice 214 melting exposes more low-albedo sea surface water absorbing more downward solar radiation [10] [12] , 215 which further results in more heat release from oceanic mixed layer to the lower troposphere in 216 autumn that delays the ice freeze [43] [44] . In this situation, newly frozen ice is relatively thin, and is 217 quite easy to melt further in the next summer. This ice-albedo positive feedback process leads to a 218 rapid increase of surface temperature surrounding the sea ice melting areas, i.e. the Arctic 219 Amplification pattern shown in Fig. 1a,b,d. It should be noted that the entire processes are natural 220 within the sea-ice-air system, triggered by a variety of low-frequency sea-ice-air coupling process 221 (in paleoclimate) or anthropogenic GHGs forcing (in modern climate). Hence, it could be more 222 accurate to attribute current AA phenomenon to sea ice melting near North Atlantic and 223 Barents/Kara seas rather than the human-induced GHGs increasing. Jekins and Dai [45] also 224 confirmed the importance of sea ice loss rather than other causes in forming AA in a cutting-edge 225 climate model. Ideally, we can speculate that a very weak or even no AA pattern can be expected 226 before sea-ice starting melting or after its melting off, even if anthropogenic emission of CO2 227 continued (Fig. 1c, Fig. 5c). 228 Let us go back to Fig. 1 again to discuss the diversity of AA patterns in the past, present, and 229 the future. In the last and the future 100 years (Fig. 1a,b), anthropogenic CO2 is persistently 230 warming Earth's surface, resulting in subsequent sea ice melting that further amplifies the near 231 surface warming in Arctic. Thus, the current observed warming pattern accounts for not only the 232 CO2-induced global warming ( Supplementary Fig. 3b, grey shadings) but also the AA outcome 233 ( Supplementary Fig. 3b, blue line). Thus, the AA factor tends to be less than 2.5 but greater than 1 234 ( Supplementary Fig. 3b), e.g. they are 2.36 and 1.76 for Fig. 1a and 1b respectively. In the 235 paleoclimate context, there was not such massive and rapid CO2 increase/decrease due to 236 anthropogenic activities. But sea ice melt/freeze still happened naturally, which also introduced a 237 clear and distinct AA mode, i.e. Arctic Mode, by a AA factor of 2.5±0.8 approximately (Fig. 1d, Fig.  238 2c, Fig. 3a,b, Supplementary Fig. 3a). In the long-term future, by taking the years of 2151-2250 239 from CMIP6 extended projections as an example, the AA factor is reduced down to 1.14 ( Fig. 1c), 240 implying that the AA phenomenon will be weakened dramatically or even disappear, since the 241 summertime sea ice already melts off and ice-albedo positive feedback accordingly shuts down. In 242 other words, even anthropogenic GHGs still keep rising, the surface warming pattern simply appears 243 to be globally uniform, partly plus land amplification through vegetation feedbacks (Fig. 1c). We 244 cannot expect to find a clear Arctic amplification phenomenon anymore and the AA factor should 245 be reduced down to 1.x approximately. 246

Conclusions 247
Our work shows the diversity of AA factor in the last 21,000 year in a transient simulation. From 248 the modeling point of view, we conclude that the AA phenomenon in nature is linked with sea-ice-249 air coupling through ice-albedo feedback process, which could be triggered by either natural 250 climatic variability in ancient times or by anthropogenic forcing, like GHGs, in current global 251 warming centuries. In paleoclimate context, AM mode presents a typical and distinct AA structure 252 with a robust AA factor around 2.5±0.8 when NH climate rapidly changed, whereas WCM and 253 CWM modes present abnormal AA structure with a largely varying AA factor from -15 to 20 when 254 NH climate is relatively stable. In current climate context, the AA factor is slightly less than 2.5 255 since the observed warming pattern includes not only sea-ice-induced AA but also GHGs-induced 256 uniform warming. In future climate context, we estimate that the AA factor will gradually decrease 257 down to 1.x when Arctic sea ice completely melt off, leaving a GHGs-induced warming NH without 258

AA phenomenon. 259
This work has some uncertainties regarding the definition of AA factor, especially in terms of 260 the latitudinal range of Arctic region and the temporal window chosen for computing linear trends 261 of SAT. For the first parameter, we tested various definitions of Arctic region as north of 45N, 50N,  262   55N, 60N, 65N, and 70N (Supplementary Fig. 5a-f) Fig.  265 7a-f). It seems that the distribution of AA factor is quite sensitive to this parameter and changes 266 largely. Considering the stability of AA factor and the convenience of data processing, we choose 267 100-year as the temporal window in this article. For more information regarding the definition of 268 AA factor, the statistical method, and some schematic diagrams, please find in the method section.

The selection of Arctic region 290
Arctic region in the calculation of AA factor is defined as 60°N-90°N, in order to fit in previous 291 Arctic Amplification related literatures. Considering North Atlantic sea ice expanding to lower 292 latitudes in glacial period, and shrinking in deglaciation and interglacial period ( Supplementary Fig.  293 4), we also examine AA factor distribution with other definitions of the Arctic region from 45°N-294 90N to 70°N-90N ( Supplementary Fig. 5). Results show that no significant distinction of AA factor 295 distributions can be found with different Arctic region definitions. In another word, AA factor is not 296 sensitive to the selection of Arctic regions. 297

The selection of temporal window 298
We tested temporal windows with different length of years for AA factor's calculation using NOAA-299 CIRES/20CR data (Supplementary Fig. 7 and 8). The results show that when the length of temporal 300 window is less than 64 years, temperature changes are influenced largely by high frequency internal 301 climate variabilities. When time window is greater than 100 years, AA factors are stabilized around 302 2-6, consistent with previous literatures. In this study, we choose 100-year as the temporal window 12 for AA factor's calculation, which is fairly good length for computing Arctic and NH temperature 304 changes in a typical AA case. 305 The robust AA factor 2.5 306 We investigated the robustness of AA factor with two methods. For the first method, we simply 307 calculate the linear regression coefficients of Arctic temperature change over NH temperature 308 change in TraCE-21ka, and find the best fit of the slope is 2.46 ( Supplementary Fig. 2). For the 309 second method, we calculate the distribution of all AA factors in TraCE-21ka by multiplying their 310 corresponding NH temperature change as weights. In this method, those AA factors with larger NH 311 temperature changes have larger weights, i.e. highlighting the points at 9 o'clock and 3 o' clock 312 directions of the diamond shape (Fig. 2a), since we want to capture the features of typical AA 313 phenomenon under significant climate change. In addition, we test different bins in counting the 314 distributions and finally choose 0.05 as a proper value that can balance systematical and sampling 315 errors ( Supplementary Fig. 6). As the final step, we perform a Gaussian fitting on the weighted 316 distribution of AA factors and find the median is 2.5 with ±0.8 spreads accounting for its 50% total 317 variance (Fig. 2c). 318 We also checked the credibility of our findings by comparing the AA factors in TraCE-21ka 319 with those in PMIP3 snapshots ( Supplementary Fig. 2b). The best fitting slope of eight models' 320 results in PMIP3 is 2.33, which is very close to 2.32 in TraCE-21ka, suggesting that the results of 321 transient simulation TraCE-21ka are reliable. It should be noted that the value 2.33 or 2.32 here is 322 derived from glacial-to-interglacial timescale rather than aforementioned 2.5, which is derived from 323 centennial timescale. A further discussion on the discrepancy of these two figures (Supplementary 324 Fig. 2a and 2b) is beyond the scope of this paper. 325

A simplified AA model 326
We simplify the typical AA into a conceptual model in order to better understand its essential 327 features ( Supplementary Fig. 3). For the natural AA mode, it is assumed that the NH average 328 warming rate is 1 °C/100a, and there exists a critical latitude, north of which (so-called Arctic region) 329 is uniformly warming at the rate of 2.5 °C/100a, and south of which is uniformly warming at the 13 rate of X °C/100a (Supplementary Fig. 3a). Thus, the AA factor has the unchangeable value 2.5, but 331 the critical latitude can vary with the changing low-latitudes warming rate X. By assuming the above 332 conditions, all valid configurations are illustrated with red (the southernmost critical latitude), black, 333 and blue lines (the northernmost critical latitude). In the paleoclimate context, the composite 334 analysis show that the natural AA pattern is very similar to the red line, where the critical latitude is 335 close to 37N (Fig. 3a, b), partly because of the greater sea ice extent than present. However, for the 336 anthropogenic AA mode, a uniform hemispheric warming is added over the natural AA mode 337 ( Supplementary Fig. 3b) al. [47] for more information and find the data at https://www.atmos.uw.edu/~hakim/LMR/. 360
Black line represents the sum of glacial, deglaciation, and interglacial periods. c, Zoom-in of subplot b between -1 and 6 with a Gaussian tting curve (red line). Red bar is the median of Gaussian tting. Grey shadow refers to the AA's spread accounting for its 50% variance.

Figure 3
Composite spatial patterns of 2m air temperature trends in 3 modes in TraCE-21ka. a-b, Composite of cases with NH temperature trends larger than 0.2/100a (a) or smaller than -0.2/100a (b). c-d, Composite of cases with NH temperature trends are 0-to-0.2 /100a and AA factor greater than 6 (c), or NH temperature trends are -0.2-to-0 /100a and AA factor smaller than -4 (d). e-f, Composite of cases with NH temperature trends are 0-to-0.2 /100a and AA factor smaller than -4 (e), or NH temperature trends are -0.2-to-0 /100a and AA factor greater than 6 (f). Red contours are the NH average. Black dots mark areas with trend passing 95% signi cance test. Boxes right to the maps are zonal mean SAT trends. Vertical lines are the NH average. Red horizontal lines are the critical latitude in the simpli ed AA model with AA factor assuming to be 2.5 (see Method). g, Conceptual illustration of 3 modes. h, Corresponding regimes of 3 modes in the diamond-shape diagram as shown in  Composite cross-sections of zonally-averaged temperature trends in 3 modes in TraCE-21ka. The layout are the same as Fig 3 a-f, but for zonally-averaged temperature trends at multiple pressure levels. Black dots mark the areas with trend passing 95% signi cance test.

Figure 5
Sea ice and CO2 changes with respect to AA factor in abundant abrupt climate change (ACC) events. a, NH (black) and Arctic (red) 2m air temperature evolution in the last 21,000 years in TraCE-21ka. Purple circles highlight the samples having temperature trends larger than ±0.5 /100a. b, AA factor and corresponding NH sea ice area trends. c, AA factor and corresponding NH CO2 concentration trends.
Purple dots are same cases as purple circles in a. Red crosses are the 20th century ensemble mean of CMIP6.

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