Unnatural Trend Detection of Arctic Amplification

The driving mechanism of Arctic amplification (AA) is so complex that no consistent and definitive conclusion has been formed yet. In particular, the natural or unnatural cause of AA has not yet been investigated and distinguished in clarity and depth. Given that the Arctic is more sensitive than other regions to greenhouse gases and other unnatural forcing, especially human activity, we are focusing on separating unnatural trend (caused by unnatural forcing) from the Arctic surface air temperature (SAT) changes during 1979-2017 to quantify the contribution of unnatural forcing on AA, with converting detection and attribution to probability statistics model. Compared to earlier studies, we find that the Arctic coast of the Siberian Great Plains, from the Barents Sea to the Kara Sea and eastward to the Bering Strait, has been warming most significantly, which is mainly dominated by unnatural trends. From 1979 to 2017, the minimum unnatural warming in most parts of the Arctic Ocean reached above 1.5℃, especi ally in the Kara Sea area, where the unnatural warming was significant, reaching 4℃. The Kara Sea is sensitive to unnatural forcing. In addition, the minimum unnatural contributions exceed 60% in most parts of the Arctic Circle, and was more than 80% in (75-90°N, 150-180°W). In 140 ° W-140 ° E Arctic region, the unnatural trend is the most remarkable with 0.82℃ per decade, accounting for 84.5% of the measured warming trend. Meanwhile, the unnatural trend changes most rapidly for the temporal evolution in this area (0-140°W, 60-90°N).


Introduction
In the past decades, the Arctic air temperature has been dramatically increasing with a rate of 1.2 ℃ /10a . It is faster than 2 times of the global mean warming in observation records (Serreze & Francis, 2006;Serreze et al., 2009;Polyakovand et al., 2012;Cohen et al., 2014) and model simulations (Holland & Bitz, 2003;Stroeve et al., 2012;Wang & Overland, 2012;Barnes & Polvani, 2015), which is known as Arctic amplification (AA). The Arctic amplification manifests itself as the rapid and even accelerated temperature changes in the cryosphere and ocean, and may inevitably affect the global climate and ecosystem through the multispheres' interactions (IPCC, 2019).
To harvest our understandings and knowledge on why Arctic warming is so dramatic, many scientific researches focus on the mechanism of AA, mainly including Arctic local climate feedback and poleward heat transport, such as a key impact of seaice loss (Serreze et al., 2009;Crook et al., 2011;Taylor et al., 2013;Graversen et al., 2014;Yim et al., 2016;Dai et al., 2019), enhanced downward longwave heating triggered by more water vapor and clouds (Taylor et al., 2013;Burt et al., 2016;Gong et al., 2017), decreased outgoing longwave radiation caused by a stable polar temperature profile (Bintanja et al., 2011;Pithan & Mauritsen, 2014), and increased poleward energy transport by changing ocean currents and atmospheric circulation (Gong et al., 2017;Cai, 2005), and other processes (Lu & Cai, 2009;Franzke et al., 2016). The impact of atmospheric circulation transport on Arctic temperature is mainly divided into two aspects: one is to transport water vapor and heat from lower latitudes to the Arctic (Feng & Wu, 2015), and the other is to regulate the movement and output of sea ice (Ding et al., 2017;Zhao et al., 2017).
In the northern hemisphere and the North Atlantic region, the most significant modes of atmospheric circulation are the Arctic Oscillation (AO) and North Atlantic Oscillation (NAO) (Gong et al., 2001;Thompson & Wallace, 1998). Some results indicate that NAO has a significant effect on the warming of Northeast Canada and Greenland and the transport of Arctic sea ice to the Atlantic (Gong et al., 2001). While the contribution of AO to the interannual variability of sea ice in September accounts for about 22% (Park et al., 2017), the connection between AO and Arctic temperatures may be weakening (Ogi et al., 2016). Both AO and NAO contribute to the movement and output of sea ice (Ding et al., 2014;Park et al., 2017), but the most significant atmospheric circulation forcing is the Arctic Dipole (AD) (Wu et al., 2006;Ikeda, 2012). When the AD phase is positive, the Beaufort vortex weakens, and there is more sea ice in Greenland and the Barents Sea.
Affected by AD, the surface air temperature changes of the Laptev Sea and the Barents Sea both show a seesaw distribution (Wu et al., 2006).
In addition to the effect of atmospheric circulation, the poleward heat transfer of ocean current also contributes to the AA. The connection of the Arctic Ocean with the North Atlantic through Fram Strait and Barents Sea is dominant in the heat exchange between the Arctic and the outside (Zhang, 2015). The Atlantic seawater entering the Arctic through the Fram Strait in recent decades has become obviously more and warmer (Spielhagen et al., 2011). A large amount of heat carried by the Atlantic seawater is released in the Arctic Ocean, resulting in Arctic warming and sea ice melting.
Furthermore, the inflow of Atlantic water and the melting of sea ice will lead to changes in the structure of the mixed layer and halocline of the Arctic Ocean, which will increase the mixing inside seawater and increase the heat release from ocean to atmosphere, and will further lead to the Arctic warming (Polyakov et al., 2017).
Although much progress has been made, there are still some key issues that are controversial or unresolved, mainly in two aspects: (1) Most of the current results are qualitative studies, and there are relatively few quantitative researches on the relative contribution of different driving mechanisms. The existing research results are also very inconsistent. Because the climate system is a highly coupled whole, there are complex interactions between different factors, and it is very difficult to assess the relative importance of different factors and quantify the contribution of a certain factor. For example, the poleward heat transport could also stimulate a series of Arctic local responses such as sea ice melting and enhanced air-sea interaction. Sea ice and temperature changes will in turn affect atmospheric and ocean circulation. (2) In different time scales, seasons, areas and heights, the mechanisms driving the AA may be different.
The driving mechanism of AA is so complex that no definitive conclusion has been formed yet.
The Fifth Assessment Report of the Intergovernmental Panel on Climate Change anticipates that the AA will continue accompanying future anthropogenic emissions of greenhouse gases and aerosols. Given that the Arctic is more sensitive to greenhouse gases and other unnatural forces, we are focusing on separating natural variability and unnatural trend (caused by unnatural forcing) from AA to quantify the contribution of unnatural forcing on AA, with converting detection and attribution to probability statistics method (Lennartz and Bunde, 2009, 2011. The confidence interval of natural variability, the effect degree of unnatural forcing and corresponding minimum unnatural contributions to AA in different regions could be quantitatively and simply determined with a certain confidence by the method. We first calculate the long-term correlation, and separate the statistically significant unnatural trend from the Arctic warming by applying the statistical model based on Lennartz and Bunde (2009, 2011 and Tamazian et al. (2015). Then, the range of SAT change resulted from unnatural forcing, the minimum contributions of unnatural effect to warming and the temporal evolutions of regional unnatural trends are further explored. We hope, through this quantitative research, to summarize and enhance our understanding on AA, to provide a reference for adapting and mitigating AA effectively and in a sustainable way.
The rest of this paper is structured as follows. The data and a discussion of the methodology used in this research are given in Sect. 2. In Sect. 3, we present detailed detection results for unnatural effects of Arctic long-term SAT change. The main conclusions and discussions are shown in Sect. 4.

Data
The National Centers for Environmental Prediction/Department of Energy Atmospheric Model Inter-comparison Project reanalysis (NCEP-2, Kanamitsu et al., 2002) 2m month air temperature data from January 1979 to December 2017 are used in this paper. The spatial resolution of NCEP-2 reanalysis data is about 1.915 • ×1.875 • . To make a compare, we also use the ERA-Interim reanalysis 2m month air temperature data during1979-2017 from the European Center for Medium-Range Weather Forecasts (Dee et al. 2011), with a horizontal resolution of 0.5 • ×0.5 • . The ERA-I data have been used for Arctic climate studies (Serreze et al., 2007;Gong et al., 2017), which arguably represent one of the best datasets available for the Arctic region.

Methods
The method used here is based on studies from Lennartz and Bunde (2009, 2011. In order to extract the external trend caused by unnatural factors (hereinafter abbreviated as the unnatural trend), one need to firstly research the internal memory of the temperature records, namely, the long-term correlation. Previous studies indicate that the long-term correlation could be extracted effectively by detrended fluctuation analysis (DFA) (Peng et al. 1994;Kantelhardt et al., 2001). We briefly introduce the DFA algorithm for a record X(i), i=1,2,...N. The cumulated sum Y(k) of the record X(i) is obtained as follows.
After dividing the cumulated sum Y(k) into n=Int(N/s) non-overlapping subsequences of size s, the local trend y(k,v) will be fitted with a polynomial function in each subsequence v, where v=1, 2, 3,..., n. Then the detrended fluctuations can be denoted as the difference between the cumulated sum Y(k,v) and the local trend y(k,v): One can further provide the variance of this integrated and detrended sequence by The fluctuation function is determined with repeating this computation over all time scales: Typically, the power law is present as the linear relationship on a log F(s)-log(s) plot, and correlation could be described by the slope α of the fitline relating log F(s) to log (s).
The sequences is long-term correlated as α>0.5. As the value increases, the correlation is stronger (except α=1). At present, the second-order DFA (DFA2), which systematically removes the influence of local trend by using the quadratic polynomial fitting, is widely used in temperature records (Kantelhardt et al. 2001).
Next, the relative trend is characterised as x=Δ/σ, of which the total temperature increase Δ is calculated through linear regression, and σ is the standard deviation of the record around regression line. It's important to point out that the relative trend x is described by a standardized dimensionless expression as the relative change based on unit fluctuation degree. Therefore, the trend significance and the corresponding differences between regions could be more accurately reflected by the relative trend than traditional linear regression trend Tamazian et al., 2015;Yuan et al., 2015;Wang et al., 2020). Then, one could describe any deseasonalized temperature record by the three physical quantity: long-term correlation index α estimated by DFA2, record length L, and relative trend x=Δ/σ. To separate unnatural trend from the relative trend, we need to calculate the probability density of a relative trend and the confidence interval [-xQ, xQ] belonging to natural variability under a given confidence probability Q. Lennartz and Bunde (2011) applied a scaling approach to provide an estimation of natural variability confidence limit xQ (for more details, see Lennartz and Bunde, 2009, 2011: where erf is the error function. Within the tolerance of error, Therefore, we could determine whether the relative trend is resulted from unnatural forcing by estimating the natural variability critical value xQ with given confidence probability Q. For Q = 0.95, we compare the measured x=Δ/σ with calculated [-x95, x95].
, the change is considered to be beyond the scope of natural variability. In other words, the trend is significantly affected by unnatural forcing, and the trend is significant at 95% confidence. We define x -x95 as the minimum unnatural trend.
For the sake of intuition, this standardized dimensionless expression x could be converted into the traditional linear trend K. Due to Δ=K*L, K=x*σ/L, minimum unnatural linear trend is expressed as Kan=(x -x95)*σ/L.
Furthermore, the minimum warming resulting from unnatural effect could be inferred, and defined to be minimum unnatural warming =σ(x-x95). When the relative trend is measured to be the warming trend (x>0), a positive x-x95 value (x>x95, x95>0) demonstrates that unnatural effect is significant, and as x-x95 increases, the unnatural warming trend is the more significant. Analogously, when the relative trend is a cooling trend (x<0), a negative value of x-x95 (x<x95, x95<0) demonstrates that unnatural effect is significant, and as x-x95 decreases, the unnatural cooling trend becomes more significant.
If x falls in the confidence interval [-x95, x95], we could attribute the relative trend to natural variability, and the unnatural effect is not significant. For detection and attribution research of climate change, this study provides new perspectives and approaches.

Spatiotemporal characteristics of Arctic warming
The global and Arctic mean surface air temperature (SAT) anomalies from 1979- is more dramatic than GMT. Therefore, more attention should be paid to Arctic temperature change. We further detect Arctic temperature change by using ERA-Interim (ERA-I) and NCEP-2 reanalysis data.  Given that the detection method here is based on the long-term memory of climate systems, we estimate the long-term correlation index α through DFA2 to validate the ability of the ERA-I and NCEP-2 data to represent the long-term memory. The fluctuation functions can be both well approximated in two data sets (Fig3), for s above 10, by a power-law dependence, F(s) ∼s α . The fluctuation index α of ERA-I data is 0.579, which is close to that of NCEP-2 (0.556). Both two data sets are basically consistent on the description ability of long-term memory.
For the linear regression and relative trends of global and Arctic SAT, the probability distributions of the two data sets are both similar, and the relative trends are more consistent than the linear regression trends, as shown in Figure 4. Figure 4a display the linear trend frequencies of the NCEP-2 data and ERA-I data. Both trends are mainly distributed between 0~0.3℃ /10a, and the distribution of trend value of NCEP-2 is more concentrated than that of ERA-I. The peak value of the trend in the ERA-I data is located at 0.10℃ /10a with a frequency of 16%, while the peak value in the NCEP-2 data is located at 0.13℃ /10a with a frequency of 33%. It is noted that the warming trend of ERA-I data is slightly lower than that of NCEP-2. For the Arctic region, the SAT linear trend frequency distribution of the ERA-I data has a bimodal structure, one peak of which is located near 0.57℃ /10a, and the other is located near 1.10℃ /10a. In contrast, the linear trend frequency distribution of the NCEP-2 data has only one peak near 1.13 ℃ /10a. It reveals that there are at least two regions where the warming trends are significantly different in the Arctic for the ERA-I data.
In Figure 4b, the relative trend frequency distributions based on the two reanalysis temperature data sets are almost the same, but there is a slight difference in the peak value position. The peak value position of the relative trend calculated with the ERA-I data is located near 0.4, while the peak value position of the NCEP-2 data is near 0.5, and the corresponding frequency values are both about 11%. Consistent with the traditional linear trend, the relative trend of ERA-I is slightly lower than NCEP-2, but the difference of the relative trend between the two data sets is smaller than that of the linear trend. For the Arctic region, the relative trend frequency distribution of ERA-I data is still a bimodal structure, of which one peak is located at 1.0, and the other is at 1.7. The relative trend frequency distribution of NCEP-2 data presents a multimodal structure as shown in the small figure of Figure 4b. This means that there are regional differences in the warming trend over the Arctic region, so further research will analyze the warming situation in different regions.

Unnatural trend detection
In the Arctic region (north of 60°N), the unnatural trend is detected by the method mentioned in Sect. 2, and the detection results of the two data sets are relatively consistent    For the minimum unnatural warming caused by the minimum unnatural trend in the Arctic region during these 39 years (Fig 6), the amplitudes of minimum unnatural warming have reached 1.5°C or more in most parts of the Arctic Ocean based on NCEP-2 and ERA-I. In particular, the SAT increases 3.0°C or above in the seas close to Eurasia.
The Kara Sea is a highly warming area both in the detection results of the two data sets, where the minimum unnatural temperature increase is about 4°C during 1979-2017.
Meanwhile, combined with the distribution of minimum unnatural trends (Figure 5c, f), the unnatural trend of Kara Sea area is not at the maximum, but the corresponding unnatural warming is at the maximum. So the Kara Sea is sensitive to unnatural forcing.
That is, under the equal unnatural effect, the warming is the most significant, and the corresponding response is the most prominent in this area. For the East Siberian sea near East Russia, the minimum unnatural warming calculated based on NCEP-2 data is more significant, reaching more than 4.5°C, while the result calculated by ERA-I is about 3.5°C.
The contributions of the minimum unnatural effect on observed warming for NCEP-2 and ERA-I data are displayed in Figure 7. 3.3 The detection of regional mean unnatural trend According to the distribution of the minimum unnatural contribution, the Arctic could be divided into four regions with blue lines in Figure 7-Zone I (0-60°E), Zone II (60-140°E), Zone III (140°E-135°W) and Zone IV (135°W-0). The regional mean temperature anomaly sequences are detected respectively. The detection results for the four regions are shown in Figure 8. All the warming relative trends exceed the range of the corresponding natural variability, which means unnatural influences are all significant in these regions. It is found that the unnatural effect (difference between the measured relative trend and the maximum natural variability) in Zone III is the largest, and that of Zone I is the smallest. Among the four regions, the linear trend of Zone III is the greatest (0.97°C/10a), and the unnatural trend is also the most remarkable (0.82°C/10a, Fig 9), accounting for 85% of the observed temperature increase in this region (Fig10). The linear trend in Zone I takes the second place (0.91°C/10a). Although its temperature increases fast, the unnatural trend is relatively small (0.48°C/10a), accounting for 53% of the observed warming. The temperature increases relatively slowly in Zone II (0.76°C/10a), but the unnatural trend reaches 0.57°C/10a, accounting for 74%. The linear trend of Zone IV is the smallest (0.69°C/10a), and its unnatural trend is also the smallest (0.41°C/10a), accounting for 59%.
From the box plots of the four regions (Fig 10), the data distribution characteristics are basically similar, but the total warming, unnatural warming and contributions in the four regions are different. In addition, it can be intuitively seen that the unnatural warming in the region with a larger total warming is not necessarily more obvious, and this is also    In this study, we detect the effects of natural variability and unnatural forcing in the rapidly warming Arctic region, and reveal the quantitative contributions of unnatural effects and the temporal evolutions of regional unnatural trends. For the Arctic region, unnatural influences are all significant in four zones. In 140°E-135°W region of the Arctic, the linear trend is the greatest, and the unnatural trend is the most remarkable with 0.82℃ /10a, accounting for 85% of the measured linear trend.
However, the linear trend of 0-135°W is the smallest and the unnatural trend is also the smallest (0.41℃ /10a), accounting for 59%. At the same time, with the temporal evolution, the unnatural trend changes most rapidly in this area (0-135°W, 60-90°N).
Why unnatural contributions are so remarkable in the untraversed Arctic? It is considered that unnatural effects in the Arctic result from poleward energy and material transport of mid-to high latitudes. The long-term warming trend of the oceans is mainly caused by greenhouse gases such as carbon dioxide emitted by human activities (Bindoff et al., 2013). About 93% of the energy imbalance caused by human activities accumulates in the ocean (Hansen et al., 2011).  (Polyakov et al., 2017). This is likely to be one of the main reasons for the rapid warming and obvious unnatural contribution in the region. In addition, as a key process on the sea-atmosphere interface, the ocean wave process affects the heat flux, momentum flux and material flux between the ocean and the atmosphere (Hemer et al., 2012), which may further transport unnatural forcing to the Arctic. The research based on satellite observation data shows that the effective wave height of the Chukchi Sea, Beaufort Sea (near northern Alaska) and Laptev Sea increased at a rate of 0.01-0.03m/a from 1996 to 2015, and the Bering sea wave height also increased significantly (Young et al., 2019).
Meanwhile, black carbon aerosol (BC) is the main component of anthropogenic pollutants in the Arctic, and plays a key role in regional climate change. The climate effects of BC in atmosphere are complex. Generally, BC is thought to make the climate warmer because of its light absorption (Ramanathan and Carmichael, 2008). Over the Arctic, atmospheric light absorption is enhanced above the reflecting snow and ice surfaces (AMAP, 2015). Combined with the results of Cheng et al. (2019), BC mean concentrations are high in Arctic region with remarkable unnatural contributions that we have detected. In addition, the BC over the Arctic is mainly transported from mid-to high-latitudes (Stohl, 2006;Law and Stohl, 2007;Bond et al., 2013;Shindell et al., 2008;Yang et al., 2014;Sand et al., 2016).
The quantitative results of unnatural influences have been obtained in this paper, which provide a certain reference for the attribution study of rapid warming in the Arctic.
However, there are still more urgent questions to be further explored in the future study, such as, the reason for the different unnatural contributions in various regions of the Arctic, and the mechanisms of temporal evolutions of the unnatural trends in the various Arctic regions. Figure 12. Mechanism Schematic of possible causes for non-uniform unnatural warming and contribution distribution in the Arctic. The small picture at the top is minimum unnatural warming of the Arctic, and the big picture at the bottom is minimum unnatural contribution of the Northern Hemisphere.