Reconciling Roles of External Forcing and Internal Variability in Arctic Sea Ice Change on Different Time Scales

Zili Shen aKey Laboratory of Polar Atmosphere-Ocean-Ice System for Weather and Climate of the MOE, Department of Atmospheric and Oceanic Science and Institute of Atmospheric Science, Fudan University, Shanghai, China

Search for other papers by Zili Shen in
Current site
Google Scholar
PubMed
Close
,
Anmin Duan cState Key Laboratory of Marine Environmental Science, College of Ocean and Earth Sciences, Xiamen University, Xiamen, China

Search for other papers by Anmin Duan in
Current site
Google Scholar
PubMed
Close
https://orcid.org/0000-0002-3022-2582
,
Wen Zhou aKey Laboratory of Polar Atmosphere-Ocean-Ice System for Weather and Climate of the MOE, Department of Atmospheric and Oceanic Science and Institute of Atmospheric Science, Fudan University, Shanghai, China
bKey Laboratory for Polar Science of the MNR, Polar Research Institute of China, Shanghai, China

Search for other papers by Wen Zhou in
Current site
Google Scholar
PubMed
Close
https://orcid.org/0000-0002-3297-4841
,
Yuzhuo Peng cState Key Laboratory of Marine Environmental Science, College of Ocean and Earth Sciences, Xiamen University, Xiamen, China

Search for other papers by Yuzhuo Peng in
Current site
Google Scholar
PubMed
Close
, and
Jinxiao Li dShanghai Investigation, Design and Research Institute Co., Ltd., Shanghai, China

Search for other papers by Jinxiao Li in
Current site
Google Scholar
PubMed
Close
Open access

Abstract

Two large ensemble simulations are adopted to investigate the relative contribution of external forcing and internal variability to Arctic sea ice variability on different time scales since 1960 by correcting the response error of models to external forcing using observational datasets. Our study suggests that previous approaches might overestimate the real impact of internal variability on Arctic sea ice change especially on long time scales. Our results indicate that in both March and September, internal variability plays a dominant role on all time scales over the twentieth century, while the anthropogenic signal on sea ice change can be steadily and consistently detected on a time scale of more than 20 years after the 2000s. We also reveal that the dominant mode of internal variability in March shows consistency across different time scales. On the contrary, the pattern of internal variability in September is highly nonuniform over the Arctic and varies across different time scales, indicating that sea ice internal variability in September at different time scales is driven by different factors.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding authors: Anmin Duan, amduan@lasg.iap.ac.cn; Wen Zhou, wen_zhou@fudan.edu.cn

Abstract

Two large ensemble simulations are adopted to investigate the relative contribution of external forcing and internal variability to Arctic sea ice variability on different time scales since 1960 by correcting the response error of models to external forcing using observational datasets. Our study suggests that previous approaches might overestimate the real impact of internal variability on Arctic sea ice change especially on long time scales. Our results indicate that in both March and September, internal variability plays a dominant role on all time scales over the twentieth century, while the anthropogenic signal on sea ice change can be steadily and consistently detected on a time scale of more than 20 years after the 2000s. We also reveal that the dominant mode of internal variability in March shows consistency across different time scales. On the contrary, the pattern of internal variability in September is highly nonuniform over the Arctic and varies across different time scales, indicating that sea ice internal variability in September at different time scales is driven by different factors.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding authors: Anmin Duan, amduan@lasg.iap.ac.cn; Wen Zhou, wen_zhou@fudan.edu.cn

1. Introduction

With the increasing intensity and frequency of human disturbance to nature, the influence of human activities on the climate system is becoming more and more significant (Overland and Wang 2007; Fyfe et al. 2013; Notz and Stroeve 2016; Screen 2018; Haustein et al. 2019; Polvani et al. 2020). The external forcing, which mainly refers to human activities such as greenhouse gas emissions, is very likely the main driver of the Arctic sea ice loss between 1979–88 and 2010–19 in September as stated in the Intergovernmental Panel on Climate Change (IPCC) Assessment Report 6 (AR6) (Gulev et al. 2021). However, most of the models participating in phases 5 and 6 of the Coupled Model Intercomparison Project (CMIP5 and CMIP6) underestimate the declining trend in sea ice over recent decades (Stroeve et al. 2012; Notz and SIMIP Community 2020; Shen et al. 2021). Biases in the models’ internal variability and their forced response are usually interpreted as potential drivers for the discrepancy between models and observational records. Internal variability, which arises from random fluctuations inherent to the climate system, can mitigate or strengthen externally forced climate change on annual to multidecadal time scales (Maslanik et al. 2007; Serreze et al. 2007; Kay et al. 2011; Stroeve et al. 2012; Screen and Francis 2016; Ding et al. 2017, 2019; England et al. 2019). On interannual time scales, the internal variability of sea ice is most related to atmospheric circulation, such as cyclonic activity (Wernli and Papritz 2018; Olonscheck et al. 2019), while the multidecadal change in internal variability mainly corresponds to the ocean heat transport (Zhang 2015; Årthun et al. 2019; Halloran et al. 2020). Previous studies have suggested that internal variability can contribute to 30%–50% of the observed September Arctic sea ice extent (SIE) decline since 1979 (Kay et al. 2011; Stroeve et al. 2007, 2012; Zhang 2015; Ding et al. 2014, 2019; England et al. 2019). However, the model uncertainty could potentially lead to bias in the estimation of internal variability. For example, the magnitudes of Arctic sea ice internal variability simulated by CMIP5 and CMIP6 models [0.5 × 106 km2 for multimodel ensemble mean (MMEM) estimated through regressing internal variability from preindustrial control run on the variability from model’s ensemble simulations; Olonscheck and Notz 2017] are higher than that estimated through detrended standard deviation from the satellite observations and observation-reconstructed data (0.2 × 106 and 0.3 × 106 km2, respectively; Brennan et al. 2020).

Methods previously used to distinguish between externally forced component and naturally occurring variability include (i) estimating the externally forced portion from a simple linear trend of the time series (Wyatt et al. 2012; Wyatt and Curry 2014; Zhang and Delworth 2007), (ii) using the MMEM of different climate models as the forced signal (Shen et al. 2021; Steinman et al. 2015; Stroeve et al. 2012), and (iii) defining the forced component as the ensemble mean of a large ensemble from a single model and defining the internal variability component as the difference between the observed sea ice and the large ensemble mean (England et al. 2019; Kay et al. 2011). However, these methods have their own drawbacks: First, a linear trend will underestimate the forced signal because it neglects the nonlinear forced response produced by different forcing agents (England 2021). Second, different climate models may differ in their dynamical cores and physical parameterization schemes, which can confuse the models’ structural differences with the internal variability. Third, though a large ensemble from a single model can efficiently quantify the forced component by averaging across all ensemble members, Wyburn-Powell et al. (2022) found that most models tend to underestimate interannual variability in March and overestimate it in September. Therefore, given the potential bias of internal variability and the underestimation of Arctic sea ice sensitivity (defined as the amount of sea ice change when global temperature increases by a certain value) in climate models (Mahlstein and Knutti 2012; Notz and Stroeve 2016; Rosenblum and Eisenman 2017), unrealistic values might be introduced when raw model values are directly employed to quantify the relative contribution of external and internal variability to Arctic sea ice change.

Taking into account the limitations of the above methods, in this study, we estimate the externally forced and internally generated parts of Arctic sea ice change based on a large ensemble from a single model in combination with the method proposed by Steinman et al. (2015), in which they regressed the mean of the CMIP5 ensemble (estimated as the forced components) against the observed time series to account for the potential mismatch between the observed and modeled climate sensitivity. The difference in the method used in our study from that used by Steinman et al. (2015) is that we use the mean of the large ensemble from a single model as an initial estimate of the forced component rather than the MMEM to avoid confusing the models’ structural differences with the internal variability. Our study aims to address the following questions: (i) Is there any difference between the previously identified contribution of internal variability to Arctic sea ice and our estimation based on this new method? (ii) At which time scale can external forcing be consistently detected? (iii) Will the time scales at which external forcing can be detected change with global warming?

2. Data and methods

a. Observational data

The observed SIE for March and September from 1960 to 2020 is calculated based on sea ice concentration (SIC) data from the Met Office Hadley Center Sea Ice and Sea Surface Temperature and Sea Surface Temperature dataset, version 2.1 (HadISST2.1.0.0) (Titchner and Rayner 2014). We only use one sea ice observational product because we intend to utilize sea ice data before 1979, which is prior to satellite. As previous studies have pointed out, the observational uncertainty in the sea ice observation product is significantly smaller in magnitude than the internal variability (Shen et al. 2021); therefore, the observational dataset will not fundamentally alter the results. However, it is important to note that the reliability of HadISST sea ice data before 1979 can be subject to certain limitations, such as accuracy and consistency of different data sources, limited spatial coverage of sea ice observations, and seasonally biased availability of sea ice observations. Caution should be paid to the results before the satellite era. Despite these limitations, HadISST sea ice data are valuable for climate research and the study of long-term trend in sea ice conditions because HadISST is one of the few sources of sea ice observational data available with temporal and spatial continuity up to the present. SIE is defined as the total area of all grid cells with SIC greater than 15%. We choose SIE over sea ice area (SIA) to minimize the observation uncertainty. Because SIA is more dependent on sea ice concentration value than SIE, the accuracy of the sea ice concentration might be less certain before the satellite era due to the combined use of reconnaissance flights and ship observations in the HadISST dataset. In addition, most of the previous studies have estimated the contribution of internal variability based on SIE (Ding et al. 2017; England et al. 2019; Kay et al. 2011; Stroeve et al. 2007, 2012), and the choice of SIE in this study allows for better comparison with prior results. Our study focuses on the period of 1960–2020 because climatological values are mostly used prior to 1953, and the reliability of Arctic sea ice is higher after this (Titchner and Rayner 2014).

b. Model simulations

As mentioned above, different climate models may differ in their dynamical cores and physical parameterization schemes, which can confuse the models’ structural differences with the internal variability. The mean of the large ensemble from a single model can efficiently quantify the forced component. Therefore, to quantify the relative role of internal variability and external forcing in sea ice change, we use the 40 members of the Community Earth System Model, version 1, Large Ensemble (CESM1-LE) (Kay et al. 2015). The atmospheric component of the CESM1-LE is the Community Atmosphere Model, version 5.2 (CAM5.2), which has a horizontal resolution of 1° and 60 vertical levels. The ocean component is the Parallel Ocean Program, version 2 (POP2), which has a horizontal resolution of approximately 1° and 60 vertical levels. The horizontal resolution of the sea ice model, CICE4, is consistent with that of the atmosphere and ocean models. All 40 members of the CESM1-LE undergo the same historical forcing from 1920 to 2005 (Lamarque et al. 2010), and future emissions are based on the representative concentration pathway 8.5 (RCP 8.5) scenario for the period 2006–2100 (Meinshausen et al. 2011). The variations among the 40 members are solely due to random fluctuations resulting from small perturbations in the initial conditions of the air temperature field. Therefore, each member represents an independent realization of the climate system, and the differences among members reflect the uncertainty caused by internal variability alone.

We compare results from CESM1-LE with simulations from the Max Planck Institute Earth System Model, version 1.1 (MPI-ESM1.1), which includes 100 ensemble members (Maher et al. 2018, 2019). The atmospheric and oceanic modules have horizontal resolutions of T63/1.9° and 1.5°, respectively, and vertical resolutions of 47 and 40 layers, respectively. The historical simulation experiment covers the period from 1850 to 2005, using the same external forcing as the CMIP5 historical radiative forcing (including greenhouse gas emissions, anthropogenic aerosols, human-induced land-use changes, ozone concentrations, and natural forcing such as volcanic activity). The representative concentration pathway experiments are used for the period from 2006 to 2099 and include three different scenarios: RCP2.6, RCP4.5, and RCP8.5. This study mainly focuses on the high-emission scenario RCP8.5, whose radiative forcing reaches 8.5 W m−2 relative to the preindustrial level by the end of the twenty-first century. For a detailed introduction to the MPI-ESM large ensemble, please refer to http://www.mpimet.mpg.de/en/grand-ensemble.

Monthly mean SIC data from 25 models within CMIP6 (Table S1 in the online supplement material) are used to demonstrate the advantage of the method used in our study. We augmented the CMIP6 historical projections with results from CMIP6 Shared Socioeconomic Pathway 8.5 (SSP8.5) future emission scenario simulations (Eyring et al. 2016) to achieve the same length of time series as the observations. SSP5-8.5 is selected from five available future emission scenarios, and the main difference between these scenarios lies in the assumption about future demographic, economic, social, and technological developments, which lead to differences in energy consumption, land use, and greenhouse gas emissions. The different ensemble members for each model are averaged to avoid weighting toward any model that provides more simulations.

c. Separating forced and internal components in Arctic sea ice

We use a standard optimal detection method where observations [Y(t)] are expressed as the sum of scaled fingerprints [X(t)] and internal variability [ε(t)]: Y(t) = X(t)β + ε(t). The fingerprint X(t) represents the externally forced signal in models, which is derived from the 40-member mean in CESM1-LE or the 100-member mean in MPI-ESM based on the principle that internal variations among different ensemble members are uncorrelated and could be largely averaged out with sufficient ensemble simulations. To account for potential biases in the amplitude of the forced response in the models relative to that in the real world, the forced series estimated by models are rescaled through linear regression against the observed series (regression coefficient β) at each grid point based on the assumption that the external component in observations is linearly dependent on the external component estimated by climate models (Dai et al. 2015; Steinman et al. 2015). The product of X(t) and β can be treated as the response to external forcing derived from the observations. The internal variability in the observations is then calculated as the difference between observations [Y(t)] and rescaled externally forced signal [X(t)β] at each grid box and time step.

To verify the advantage of this method in isolating internal variability in the observations, we use a cross-validation approach (Deser and Phillips 2021). We cannot obtain the true internally generated sea ice variability using observational datasets, but the internal variability of sea ice in each member i at each grid and time step [SICiv(i, t)] in an initial-condition LE can be obtained by subtracting the single-model ensemble mean (SMEM) from each member, and it can be written as
SICiv(i,t)=SIC(i,t)1ni=1nSIC(i,t),
where SIC(i, t) represents the sea ice series in each member i and n is the number of ensemble members. We choose one of the LE members, member e, as the “pseudo reality” [SICpr(t) = SIC(e, t)]. Each member is chosen in turn, and for each turn, the internal component in the pseudo reality member [IVpr(t)] is calculated as SICpr(t) minus the CESM-LE ensemble mean. The MMEM series from CMIP6 is used as the initial estimate of externally forced response in models [EXin(t)]. The rescaled series of forced components [EXre(t)] is calculated through linear regression of EXin(t) against the pseudo reality [SICpr(t)] based on the method mentioned above. Then, the initial [IVin(t)] and rescaled [IVre(t)] internally generated sea ice series are estimated as the SICpr(t) minus the EXin(t) and EXre(t), respectively. Finally, the IVin(t) and IVre(t) are compared with the IVpr(t) to test whether the rescaled internal variability [IVre(t)] is closer to the “true internal variability” [IVpr(t)]. The above procedures are repeated 40 times for each ensemble member.

Figure 1 illustrates the spatial pattern of correlation coefficients and root-mean-square error (rmse) between the true internal variability [IVpr(t)] and the initial [IVin(t)] and rescaled [IVre(t)] internal variability. It is clearly seen that the rescaled MMEM generally leads to a better representation of internal Arctic sea ice change, especially along the summer sea ice edge in the Bering Sea, Sea of Okhotsk, and Greenland Sea (Figs. 1a,b). The magnitudes of internal Arctic sea ice estimated with the MMEM are also closer to the true internal variability over the central Arctic (Figs. 1c,d). Despite the difference in external forcing fields between CMIP6 and CESM1-LE, the ensemble members from CESM1-LE are only used here as pseudo reality to verify whether the method we are employing can bring the estimated internal variability closer to the reality through rescaling the CMIP6 MMEM results. The advantage of the rescaling approach can also be demonstrated through replacing CMIP6 MMEM with the ensemble mean of MPI-ESM as an initial estimate of the forced component (Fig. S1). These results indicate that the rescaled ensemble mean performs better in decomposing the internal and external components of Arctic sea ice at each grid box and time step than the original ensemble mean, which demonstrates that this method can be applied to the LE models in combination with the observations to obtain a more realistic internal variability of sea ice.

Fig. 1.
Fig. 1.

Correlation coefficients between the true internal component of September SIC in CESM-LE and those estimated with (a) the 27-model MMEM and (b) the rescaled MMEM during the time period 1960–2020. (c),(d) As in (a) and (b), but for rmse values between the true and estimated internal components. Note that the results are the average of the 40 cases.

Citation: Journal of Climate 37, 13; 10.1175/JCLI-D-23-0280.1

3. Results

a. Internal versus forced SIE variations

As shown in Fig. 2a, the September SIE (SSIE) time series have exhibited an obvious decreasing trend since 1960. In addition to the linear decline, SSIE also exhibits variability ranging from interannual to multidecadal time scales. At the multidecadal time scale, SSIE has experienced rapid loss during 1960–79 (before the satellite observations) and 2000–12 (time period when sea ice decline accelerated and reached a record low in 2012; Walsh et al. 2017; Chen et al. 2019) (reduction rate of −0.44 × 106 and −2.37 × 106 km2 decade−1, respectively) but slower melting during 1980–99 and 2012–20 (reduction rate of −0.15 × 106 and −0.33 × 106 km2 decade−1, respectively; Baxter et al. 2019). The question then arises whether the multidecadal variability of SSIE is dominated by internal variability or external forcing.

Fig. 2.
Fig. 2.

(a) SSIE evolution during the time period 1960–2020. The gray, green, blue, and red lines represent the observed, original, rescaled externally forced, and rescaled internal components of SIE based on CESM1-LE, respectively. (b) The relative contribution of external forcing and internal variability to the SSIE during the different time periods of 1960–79, 1980–99, 2000–12, 2012–20, and 1960–2020. The gray, red, and blue bars represent the observed, internally generated, and externally forced SIE trends, respectively.

Citation: Journal of Climate 37, 13; 10.1175/JCLI-D-23-0280.1

Following the decomposition method described in section 2c, we find that the externally forced SSIE change during 1960–2020 exhibits a linear downward trend (Fig. 2a). While the internally generated SSIE variability has obvious interdecadal variations, which shows negative trends during 1960–79 (−0.39 × 106 km2 decade−1) and 2000–12 (−1.48 × 106 km2 decade−1), but positive trends during 1980–99 (0.24 × 106 km2 decade−1) and 2012–20 (1.11 × 106 km2 decade−1) (Fig. 2a), the accelerated SSIE melting during 1960–79 and 2000–12 is caused by the in-phase change in external and internal variability (Fig. 2b). Conversely, when internally generated SSIE changes are out of phase with external forcing during 1980–99 and 2012–20, SSIE loss caused by global warming would be counteracted by internally generated sea ice recovery, leading to a slowing down in sea ice melting. A comparison with the decomposition using the raw ensemble mean of CESM1-LE (Fig. S2) suggests that the contribution from external forcing is underestimated without rescaling.

When we shift our focus to the observed SSIE running trends with the length ranging from 5 to 60 years over 1960–2020, we can see that on time scales of more than 20 years, SSIE all exhibit decreasing trends (Fig. 3a). However, on a time scale of 5–20 years, the observed SSIE shows an increasing trend around the 1990s, and the missing of this increasing trend in externally forced SSIE change indicates a potential role of internal variability in regulating the magnitude of sea ice loss (Fig. 3b). Figure 3c demonstrates that the internal variability has played a vital role in weakening (enhancing) the sea ice loss caused by anthropogenic activity on time scales from 5 to 20 years in the 1900s (2000s). The impact of internal variability versus external forcing on the variability of SSIE is strongly influenced by the length of the trend (Fig. 3d). The signal-to-noise ratio (SNR), which represents the ratio of external forcing to internal variability (Tian et al. 2015; Deser et al. 2014, 2016), increases with longer trend lengths. For time scales exceeding 40 years, the strength of internal variability is insufficient to offset the externally forced loss of SSIE.

Fig. 3.
Fig. 3.

SSIE trends during different periods. The x axis represents the ending year of the trend segment, and the y axis represents the length of the trend segment. (a)–(c) The observed, rescaled externally forced, and internal variability of SIE trends based on CESM1-LE. (d) The SNR, calculated as the forced trend divided by the internal trend. SNR greater than 1 implies that the influence of external forcing is greater than the internal variability.

Citation: Journal of Climate 37, 13; 10.1175/JCLI-D-23-0280.1

Jahn (2018) points out that the internal variability will reach a peak at global temperature anomalies of around 1.4°C. And it can be found that with the cumulative effect of carbon dioxide, the contribution of external forcing to SSIE change increases almost linearly with time (Fig. 2b); however, the magnitude of sea ice change caused by internal variability is also increasing. Although currently it appears that the internal variability has an impact on SSIE at various time scales, it is unlikely to fully counteract the effects of external forcing at all time scales, especially given the continued increase in greenhouse gas emissions. The time scale at which external forcing becomes dominant decreases if we consider the later part (after the 2000s) of the time series (Fig. 5a). Before 2000, external forcing does not take effect on SSIE variability on time scales less than 40 years, but after 2000, external forcing begins to have a significant influence on SSIE on time scales of 20 years or more (Fig. 5a).

For the trends in March SIE (MSIE) over 1960–2020, the observed MSIE variability on time scales ranging from 5 to 15 years is almost entirely controlled by internal variability (Figs. 4a,c). On time scales of more than 40 years, the externally forced MSIE variability becomes similar to the observed MSIE changes, suggesting that external forcing is beginning to take effect (Figs. 4a,b). For the earlier part of the time series (before 2000), the influences of external forcing are not significant, as can be seen from the SNR value of less than 1 at all time scales, but after 2000, external forcing is more important than internal variability on time scales of over 15 years (Fig. 5b). Interannual to decadal-scale MSIE variability is still dominated by internal variability.

Fig. 4.
Fig. 4.

As in Fig. 3, but for March.

Citation: Journal of Climate 37, 13; 10.1175/JCLI-D-23-0280.1

Fig. 5.
Fig. 5.

SNR on different time scales and ending year before (blue) and after (red) 2000 for (a) September and (b) March.

Citation: Journal of Climate 37, 13; 10.1175/JCLI-D-23-0280.1

The magnitudes of SNR in September and March do not differ significantly before the year 2000, but there is a significant difference in their magnitudes after 2000. The median values of September SNR on time scales of more than 30 years after 2000 are greater than 5, even reaching 10 on 40-yr time scales, which means that the contribution of internal variability to the interdecadal changes in Arctic sea ice is no more than 10%, and as global warming continues, this contribution rate will become even lower. The emergence of anthropogenic signal in the amplified Arctic warming has also been found to occur near the transition of the twentieth–twenty-first centuries by Holland and Landrum (2021). However, the median values of March SNR do not exceed 2.5 at all time scales, which suggests that the contribution of internal variability can still reach around 30% or even higher. The conclusions obtained from the MPI models are similar, except that the estimated magnitude of external forcing is slightly larger than that of CESM1-LE (Fig. S3 and Fig. 4).

b. Regional sea ice variations and internal variability

Summer sea ice has experienced accelerated melt since the 2000s, contributing to the record minima in SSIE in 2007 and 2012 (Fig. 2a; Baxter et al. 2019; Swart et al. 2015). The apparent deceleration in the rate of sea ice loss since the 2010s, following a preceding acceleration, is perplexing given the steadily increasing rate of greenhouse gas emissions, which has been at 2 ppm yr−1 in the past decade, providing a consistent climate forcing. The above research has suggested that internal variability contributes to around 62% of the SSIE loss during 2000–12; however, sea ice loss is regionally nonuniform. To enhance our understanding of the change in Arctic sea ice, it is crucial to determine the extent to which the observed sea ice reduction in various Arctic basins can be attributed to the rising anthropogenic emissions and how much of it is a result of internal variability of the climate system.

To address these questions, we now move away from pan-Arctic to regional patterns. The spatial pattern of the September SIC trend from 2000 to 2012 shows a dipole mode, which is characterized by a dramatic decrease in SIC from the Barents Sea eastward to the Beaufort Sea and an increasing trend in SIC in the Greenland Sea (Fig. 6a). Apart from the Greenland Sea, the spatial distribution of September SIC loss caused by external forcing is similar to the observations, but the magnitude is much smaller (Fig. 6b). Internal variability contributes to the increase in SIC in the Greenland Sea and accounts for roughly 70%–80% of the observed sea ice loss across much of the Arctic from 2000 to 2012, especially in the ocean closer to the pole, whereas the forced response dominates along the continental coastlines (Figs. 6c,d). Baxter et al. (2019) proposed that the sea surface temperature (SST) in the east-central tropical Pacific serves as the primary internal component influencing the summer sea ice through generating a Rossby wave train that propagates into the Arctic. However, Meehl et al. (2018) demonstrate that the accelerated Arctic sea ice decline during summer since 2000 is driven by the positive convective heating anomaly in the tropical Atlantic, while the negative convective heating anomaly in the tropical Pacific is mainly responsible for the Arctic sea ice decline in winter. The physical mechanisms responsible for accelerating summertime sea ice decline warrant further investigation, and a more in-depth study is needed to understand the specific impacts of ocean basin interactions and ocean–atmosphere interactions on sea ice.

Fig. 6.
Fig. 6.

September SIC trends during the time period 2000–12. (a)–(c) The observed, rescaled externally forced, and internally generated SIC trends based on CESM1-LE. (d) The SNR, defined as the absolute value of the externally forced trend divided by the internally generated trend. The SNR value greater than 1 implies that the impact of external forcing is stronger than the internal variability.

Citation: Journal of Climate 37, 13; 10.1175/JCLI-D-23-0280.1

In contrast with the results for the period of 2000–12, we find that on a long time scale, the externally forced September SIC change from 1960 to 2020 is very similar to observations in terms of spatial distribution and magnitude (Figs. 7a,b), indicating that the changes in sea ice during this period are almost completely controlled by external forcing, with little contribution from internal variability (Fig. 7c). The SNR of the climate change signal is orders of magnitude higher in 1960–2020 than in 2000–12 (Fig. 7d). Furthermore, without the combined influence of internal variability and external forcing on sea ice, September sea ice loss from 1960 to 2020 is concentrated mainly in the marginal seas and does not extend to the central Arctic Ocean as it does from 2000 to 2012.

Fig. 7.
Fig. 7.

As in Fig. 4, but for the time period 1960–2020.

Citation: Journal of Climate 37, 13; 10.1175/JCLI-D-23-0280.1

The above results indicate that on a multidecadal time scale, both the entire and regional Arctic sea ice changes are directly following cumulative carbon dioxide (CO2) emissions (Notz and Stroeve 2016), but on interannual to decadal time scales, Arctic sea ice can still be modulated by internal variability. Then, what are the main spatial patterns of Arctic sea ice changes caused by internal variability, and are these patterns consistent across different time scales?

Figure 8 shows the two leading EOF modes of internally generated 10- and 20-yr SIC trends in September. Using the latitudinally weighted 10-yr (20-yr) trend in Arctic SIC, we calculate the EOFs across the overlapping 10-yr (20-yr) trends sampled across the observed period (1960–2020). In terms of 10-yr changes, the first two EOF modes explain about 40% of the variance and are well separated from each other (Figs. 8a,b). In September, the first EOF mode shows a consistent change in SIC from the Laptev Sea eastward to the Beaufort Sea (Fig. 8a), and the second EOF mode reflects an opposite and out-of-phase change in the Beaufort Sea, Chukchi Sea, and Laptev Sea areas near the central Arctic Ocean compared with the East Siberian Sea and the Greenland Sea (Fig. 8b). We find that the second EOF mode of the 10-yr changes can well explain the spatial pattern of internal variability during 2000–12 (with the pattern correlation of −0.72) that we just mentioned. The main EOF modes of the 20-yr changes in September are very different from those on the 10-yr time scale (Figs. 8c,d), indicating that the different physical mechanisms are driving the September Arctic sea ice internal variability at different time scales. Overall, the internal variability of September Arctic sea ice varies across different time scales and regions. This implies that when studying the summertime Arctic climate, we should not consider the Arctic as a whole, but instead divide it into specific regions and time scales.

Fig. 8.
Fig. 8.

EOF analysis of estimated observed (top) 10-yr and (bottom) 20-yr internally generated SIC trends based on CESM1-LE.

Citation: Journal of Climate 37, 13; 10.1175/JCLI-D-23-0280.1

When we shift our focus to the sea ice change in March, we find significant differences compared with the counterpart in September. The first and second EOFs of 10-yr changes are regionally focused on the Greenland Sea and the Barents Sea; these two dominant modes also exist in the EOFs of 20-yr time scale, but the dominant mode order has been exchanged (Fig. 9). This suggests that March sea ice change at different time scales might be driven by the same physical mechanism. In the MPI-ESM, although the spatial distribution and magnitude of the simulated historical sea ice trends differ greatly from those of CESM1-LE (Shen et al. 2021), the EOF modes obtained using the rescaled ensemble mean (EM) method are almost identical (Fig. S5 and Fig. 6). This means that the above results are not dependent on the choice of the model. When the sample size of ensemble members is large enough to eliminate the effect of internal variability, the rescaled EM method can effectively distinguish between externally forced and internally generated sea ice changes in the observations.

Fig. 9.
Fig. 9.

As in Fig. 8, but for March.

Citation: Journal of Climate 37, 13; 10.1175/JCLI-D-23-0280.1

4. Summary and discussion

Using two large ensemble simulations from CESM1-LE and MPI-ESM in combination with the rescaled EM method, we calculate the relative contribution of internal variability and external forcing to observed Arctic sea ice loss on different time scales. Our results indicate that the relative importance of internal variability and external forcing on SSIE variability depends not only on the trend length but also on the amount of carbon dioxide emissions. In terms of September sea ice variability, the SNR increases with trend length, and external forcing dominates on time scales of 40 years or more. However, the time scale at which external forcing becomes dominant will decrease with time as the carbon dioxide accumulates, and whether the internally generated temporary recovery of SSIE might eventually be unable to reverse the externally forced melting at all time scales needs to be further discussed. For March, the observed sea ice variability on time scales below 20 years is almost entirely controlled by internal variability even by the end of the twenty-first century, complicating and delaying the detection of forced signals. Focusing on the spatial pattern of internal variability, we find that the dominant mode of internal variability in September is regionally nonuniform and varies across different time scales, indicating the complex nature of the summertime Arctic system. In contrast with September, the dominant mode of internal variability in March shows consistency across different time scales. Further work will be needed to decompose the internal and forced factors of observed sea ice change into dynamic and thermodynamic components (Deser et al. 2016), which could help us gain a more comprehensive and in-depth understanding of the physical mechanisms behind sea ice changes. The robustness of the above results is verified by a large ensemble of 100 members from MPI-ESM. Although the distribution and magnitudes of the forced response of the two large ensembles are different, based on the rescaled EM method, the relative contribution of internal variability and external forcing obtained by these two models is almost consistent, and the spatial pattern of internal variability is highly similar.

There have been numerous studies focusing on the contribution of internal variability to Arctic sea ice. For example, Kay et al. (2011) used six ensemble members of CCSM4 and estimated that the external forcing contributes to 56% for the observed SSIE trend from 1979 to 2005 [the ratio of the ensemble mean trend (−0.49% yr−1) to the observation trend (−0.87% yr−1)]. Stroeve et al. (2007) estimated that the external forcing contributes to approximately 47%–57% for the SSIE trend from 1979 to 2006 based on CMIP3 models. However, they both used the ensemble mean results directly without considering the biases in the models’ response to external forcing. Based on the rescaled EM method, we find that external forcing can explain about 60.3% of the observed SSIE trend from 1979 to 2005, slightly higher than the previous results. However, if we extend the ending year to recent years, that is to say, from 1979 to 2014 when the impact of external forcing is stronger, it can be found that the difference in the estimated contribution of external forcing using the rescaled EM method and those estimated without the rescaled EM method will be more pronounced. For example, Ding et al. (2019) used a pattern matching method based on CESM1-LE to calculate the impact of internal variability on the SSIE trend from 1979 to 2014 and found that internal variability could account for around 50% of the sea ice change. But our results suggest that the contribution of internal variability to SSIE change from 1979 to 2014 might be only 17.8%, which is much lower than their estimates. The potential reason for this large difference in the estimated contribution of internal variability might be that Ding et al. (2019) used coefficients obtained from a linear combination of forced and internal atmospheric circulation patterns in CESM1-LE to reconstruct the sea ice decline in observations, which implies that they consider the magnitude of bias in the atmospheric circulation and sea ice response to external forcing is the same in models. Uncertainty would arise due to disparities in the representation of physical mechanism driving the sensitivity of atmosphere and sea ice to external forcing and different models would obtain different estimations of internal contribution to sea ice change. England et al. (2019) proposed that internal variability contributed around 24% to the observed SSIE change during 1958–2017, but our results suggest that the contribution of internal variability is only around 8%. The above results mean that the contribution of internal variability to sea ice change estimated by directly considering the ensemble mean of a large ensemble from a single model as an externally forced component in observations might be larger than that estimated using the rescaled EM method, especially when the time scale is extended. It has also been suggested that the simulated sea ice response to external forcing in CMIP models and CESM1-LE might be too low (Notz and Stroeve 2016; Rosenblum and Eisenman 2017). Therefore, the role of internal variability might be overestimated when treating the externally forced component estimated by climate models as the response to external forcing in observations, and different results will be obtained when using different models, which can lead to a large spread in the estimation of internal variability due to model uncertainty. However, the rescaled EM method used here can effectively avoid this issue, and the consistency between the results of MPI-ESM and CESM1-LE demonstrates that this method is model independent.

To conclude, our analysis based on the rescaled EM method revises the previous estimates of the relative contributions of internal variability and external forcing to Arctic sea ice change. Several previous studies have shown a large contribution of internal variability to Arctic sea ice loss (Kay et al. 2011; Stroeve et al. 2007, 2012; Zhang 2015; Ding et al. 2017, 2019; England et al. 2019), but our study suggests that their estimations might overestimate the real impact of internal variability. Rosenblum and Eisenman (2017) have pointed out that the climate models have systematic errors in simulating sea ice changes due to the lower sensitivity of sea ice to global warming compared with the real world. Bitz (2008) has suggested that the model may potentially overlook crucial processes or encounter negative feedback mechanisms, like the negative growth-thickness feedback, when combined with a favorable period due to internal variability, could transiently facilitate recovery of sea ice, even in the face of rising anthropogenic emissions. Considering these factors, the estimated forced signal from climate models needs to be adjusted. A recent study by Kim et al. (2023) also uses the optimal detection method to scale models’ response to external forcing and finds that climate models underestimated human influence on Arctic sea ice. These results have important implications for policymakers as the improved SNR estimated here implies that the role of external forcing on sea ice is larger than previously expected. However, the contribution of internal variability estimated based solely on observations will be lower than our results obtained through a combination of climate models and observations; for example, Dörr et al. (2023) used low-frequency component analysis to separate the forced component from sea ice trends and they estimated that internal variability contributes approximately 40%–50% to the accelerated sea ice loss from 2000 to 2012, but our estimation suggests that the contribution of internal variability can be as high as 76%. It is worth noting that for simple linear regression, regression analysis is typically more reliable and stable with a large number of data points, as it can better capture trends and relationships in data. More data points can provide more accurate estimates of regression coefficients, reducing errors due to random noise. For example, if we reduce the time length, using the time period 1980–2020 to calculate the scaling factor β, it could be found that the rescaled external forcing during 1980–2020 is slightly smaller than that estimated using the time period 1960–2020 (Fig. S7). The possible reason for this phenomenon is that the ensemble mean reflects the models’ response to external forcing, while the observations are a combination of external forcing and internal variability. Due to the influence of internal variability, the regression between the ensemble mean and the observations during short time periods is more susceptible to the influence of outliers or uneven data distribution, making the results unstable and inconsistent. Therefore, when we focus on the external forcing, the longer time regression results might be more reliable because they encompass a greater amount of historical data, allowing them to capture more extensive trends and changes. Some previous studies use the dynamical adjustment method to distinguish between the forced and internally generated components based on the assumption that the response of atmospheric circulation to external forcing is much weaker than internally generated variability (Allen and Tett 1999; Lehner et al. 2017; Smoliak et al. 2015). This might lead to an inconsistency between the results estimated from the observations and climate model; in addition, the forced variability might also be left in the atmospheric circulation. Our method can eliminate the internal variability to a large extent by averaging across all ensemble members, but the potential issue is that our method is based on the assumption that the observed and modeled sea ice response to external forcing exists in a linear relationship. However, due to the inaccuracies in the magnitudes of different radiative forcing specifications (for instance, most of the CMIP5 simulations do not factor in the cumulative impact of small volcanic eruptions over the past decades), it could also lead to an imperfect estimate of the externally forced sea ice change and it may seep into a residual estimate of internal variability. Mann et al. (2022) have pointed out that this rescaled EM method performs well in estimating the forced variability when the forcings and observational data are all certain and reliable. Further research toward rescaling the forced response based on CESM2 Large Ensemble, in which the external forcing is changed to be consistent with CMIP6 generation and is different from that used in CESM1-LE (e.g., prescribed biomass burning emissions and volcanic aerosol forcing), is needed. But no matter what, our results suggest that the influence of greenhouse gas emissions on Arctic sea ice is larger than previously estimated, which indicates that we will likely witness a frequent ice-free Arctic earlier than the results predicted by climate models.

Acknowledgments.

This work was supported by the National Natural Science Foundation of China (Grants 42030602 and 42120104001).

Data availability statement.

The observed sea ice concentration data from the Met Office Hadley Center are available at https://www.metoffice.gov.uk/hadobs/hadisst/. The CESM1-LE simulations can be found at https://www.cesm.ucar.edu/projects/community-projects/LENS/. The MPI-ESM grand ensemble data can be assessed at https://esgf-data.dkrz.de/search/mpi-ge/. The CMIP6 data can be obtained from the ESGF nodes (https://esgf-data.dkrz.de/projects/esgf-dkrz/).

REFERENCES

  • Allen, M. R., and S. F. B. Tett, 1999: Checking for model consistency in optimal fingerprinting. Climate Dyn., 15, 419434, https://doi.org/10.1007/s003820050291.

    • Search Google Scholar
    • Export Citation
  • Årthun, M., T. Eldevik, and L. H. Smedsrud, 2019: The role of Atlantic heat transport in future Arctic winter sea ice loss. J. Climate, 32, 33273341, https://doi.org/10.1175/JCLI-D-18-0750.1.

    • Search Google Scholar
    • Export Citation
  • Baxter, I., and Coauthors, 2019: How tropical Pacific surface cooling contributed to accelerated sea ice melt from 2007 to 2012 as ice is thinned by anthropogenic forcing. J. Climate, 32, 85838602, https://doi.org/10.1175/JCLI-D-18-0783.1.

    • Search Google Scholar
    • Export Citation
  • Bitz, C. M., 2008: Some aspects of uncertainty in predicting sea ice thinning. Arctic Sea Ice Decline: Observations, Projections, Mechanisms, and Implications, Geophys. Monogr., Vol. 180, Amer. Geophys. Union, 63–76, https://doi.org/10.1029/180GM06.

  • Brennan, M. K., G. J. Hakim, and E. Blanchard‐Wrigglesworth, 2020: Arctic sea‐ice variability during the instrumental era. Geophys. Res. Lett., 47, e2019GL086843, https://doi.org/10.1029/2019GL086843.

    • Search Google Scholar
    • Export Citation
  • Chen, J.-L., S.-C. Kang, X.-H. Meng, and Q.-L. You, 2019: Assessments of the Arctic amplification and the changes in the Arctic sea surface. Adv. Climate Change Res., 10, 193202, https://doi.org/10.1016/j.accre.2020.03.002.

    • Search Google Scholar
    • Export Citation
  • Dai, A., J. C. Fyfe, S.-P. Xie, and X. Dai, 2015: Decadal modulation of global surface temperature by internal climate variability. Nat. Climate Change, 5, 555559, https://doi.org/10.1038/nclimate2605.

    • Search Google Scholar
    • Export Citation
  • Deser, C., and A. S. Phillips, 2021: Defining the internal component of Atlantic multidecadal variability in a changing climate. Geophys. Res. Lett., 48, e2021GL095023, https://doi.org/10.1029/2021GL095023.

    • Search Google Scholar
    • Export Citation
  • Deser, C., A. S. Phillips, M. A. Alexander, and B. V. Smoliak, 2014: Projecting North American climate over the next 50 years: Uncertainty due to internal variability. J. Climate, 27, 22712296, https://doi.org/10.1175/JCLI-D-13-00451.1.

    • Search Google Scholar
    • Export Citation
  • Deser, C., L. Terray, and A. S. Phillips, 2016: Forced and internal components of winter air temperature trends over North America during the past 50 years: Mechanisms and implications. J. Climate, 29, 22372258, https://doi.org/10.1175/JCLI-D-15-0304.1.

    • Search Google Scholar
    • Export Citation
  • Ding, Q., J. M. Wallace, D. S. Battisti, E. J. Steig, A. J. E. Gallant, H.-J. Kim, and L. Geng, 2014: Tropical forcing of the recent rapid Arctic warming in northeastern Canada and Greenland. Nature, 509, 209212, https://doi.org/10.1038/nature13260.

    • Search Google Scholar
    • Export Citation
  • Ding, Q., and Coauthors, 2017: Influence of high-latitude atmospheric circulation changes on summertime Arctic sea ice. Nat. Climate Change, 7, 289295, https://doi.org/10.1038/nclimate3241.

    • Search Google Scholar
    • Export Citation
  • Ding, Q., and Coauthors, 2019: Fingerprints of internal drivers of Arctic sea ice loss in observations and model simulations. Nat. Geosci., 12, 2833, https://doi.org/10.1038/s41561-018-0256-8.

    • Search Google Scholar
    • Export Citation
  • Dörr, J. S., D. B. Bonan, M. Årthun, L. Svendsen, and R. C. J. Wills, 2023: Forced and internal components of observed Arctic sea-ice changes. Cryosphere, 17, 41334153, https://doi.org/10.5194/tc-17-4133-2023.

    • Search Google Scholar
    • Export Citation
  • England, M., A. Jahn, and L. Polvani, 2019: Nonuniform contribution of internal variability to recent Arctic sea ice loss. J. Climate, 32, 40394053, https://doi.org/10.1175/JCLI-D-18-0864.1.

    • Search Google Scholar
    • Export Citation
  • England, M. R., 2021: Are multi‐decadal fluctuations in Arctic and Antarctic surface temperatures a forced response to anthropogenic emissions or part of internal climate variability? Geophys. Res. Lett., 48, e2020GL090631, https://doi.org/10.1029/2020GL090631.

    • Search Google Scholar
    • Export Citation
  • Eyring, V., S. Bony, G. A. Meehl, C. A. Senior, B. Stevens, R. J. Stouffer, and K. E. Taylor, 2016: Overview of the Coupled Model Intercomparison Project Phase 6 (CMIP6) experimental design and organization. Geosci. Model Dev., 9, 19371958, https://doi.org/10.5194/gmd-9-1937-2016.

    • Search Google Scholar
    • Export Citation
  • Fyfe, J. C., K. von Salzen, N. P. Gillett, V. K. Arora, G. M. Flato, and J. R. McConnell, 2013: One hundred years of Arctic surface temperature variation due to anthropogenic influence. Sci. Rep., 3, 2645, https://doi.org/10.1038/srep02645.

    • Search Google Scholar
    • Export Citation
  • Gulev, S. K., and Coauthors, 2021: Changing state of the climate system. Climate Change 2021: The Physical Science Basis, V. Masson-Delmotte et al., Eds., Cambridge University Press, 287–422.

  • Halloran, P. R., and Coauthors, 2020: Natural drivers of multidecadal Arctic sea ice variability over the last millennium. Sci. Rep., 10, 688, https://doi.org/10.1038/s41598-020-57472-2.

    • Search Google Scholar
    • Export Citation
  • Haustein, K., and Coauthors, 2019: A limited role for unforced internal variability in twentieth-century warming. J. Climate, 32, 48934917, https://doi.org/10.1175/JCLI-D-18-0555.1.

    • Search Google Scholar
    • Export Citation
  • Holland, M. M., and L. Landrum, 2021: The emergence and transient nature of Arctic amplification in coupled climate models. Front. Earth Sci., 9, 719024, https://doi.org/10.3389/feart.2021.719024.

    • Search Google Scholar
    • Export Citation
  • Jahn, A., 2018: Reduced probability of ice-free summers for 1.5 °C compared to 2 °C warming. Nat. Climate Change, 8, 409413, https://doi.org/10.1038/s41558-018-0127-8.

    • Search Google Scholar
    • Export Citation
  • Kay, J. E., M. M. Holland, and A. Jahn, 2011: Inter-annual to multi-decadal Arctic sea ice extent trends in a warming world. Geophys. Res. Lett., 38, L15708, https://doi.org/10.1029/2011GL048008.

    • Search Google Scholar
    • Export Citation
  • Kay, J. E., and Coauthors, 2015: The Community Earth System Model (CESM) large ensemble project: A community resource for studying climate change in the presence of internal climate variability. Bull. Amer. Meteor. Soc., 96, 13331349, https://doi.org/10.1175/BAMS-D-13-00255.1.

    • Search Google Scholar
    • Export Citation
  • Kim, Y.-H., S.-K. Min, N. P. Gillett, D. Notz, and E. Malinina, 2023: Observationally-constrained projections of an ice-free Arctic even under a low emission scenario. Nat. Commun., 14, 3139, https://doi.org/10.1038/s41467-023-38511-8.

    • Search Google Scholar
    • Export Citation
  • Lamarque, J.-F., and Coauthors, 2010: Historical (1850–2000) gridded anthropogenic and biomass burning emissions of reactive gases and aerosols: Methodology and application. Atmos. Chem. Phys., 10, 70177039, https://doi.org/10.5194/acp-10-7017-2010.

    • Search Google Scholar
    • Export Citation
  • Lehner, F., C. Deser, and L. Terray, 2017: Toward a new estimate of “time of emergence” of anthropogenic warming: Insights from dynamical adjustment and a large initial-condition model ensemble. J. Climate, 30, 77397756, https://doi.org/10.1175/JCLI-D-16-0792.1.

    • Search Google Scholar
    • Export Citation
  • Maher, N., D. Matei, S. Milinski, and J. Marotzke, 2018: ENSO change in climate projections: Forced response or internal variability? Geophys. Res. Lett., 45, 11 39011 398, https://doi.org/10.1029/2018GL079764.

    • Search Google Scholar
    • Export Citation
  • Maher, N., and Coauthors, 2019: The Max Planck institute grand ensemble: Enabling the exploration of climate system variability. J. Adv. Model. Earth Syst., 11, 20502069, https://doi.org/10.1029/2019MS001639.

    • Search Google Scholar
    • Export Citation
  • Mahlstein, I., and R. Knutti, 2012: September Arctic sea ice predicted to disappear near 2°C global warming above present. J. Geophys. Res., 117, D06104, https://doi.org/10.1029/2011JD016709.

    • Search Google Scholar
    • Export Citation
  • Mann, M. E., B. A. Steinman, D. J. Brouillette, A. Fernandez, and S. K. Miller, 2022: On the estimation of internal climate variability during the preindustrial past millennium. Geophys. Res. Lett., 49, e2021GL096596, https://doi.org/10.1029/2021GL096596.

    • Search Google Scholar
    • Export Citation
  • Maslanik, J., S. Drobot, C. Fowler, W. Emery, and R. Barry, 2007: On the Arctic climate paradox and the continuing role of atmospheric circulation in affecting sea ice conditions. Geophys. Res. Lett., 34, L03711, https://doi.org/10.1029/2006GL028269.

    • Search Google Scholar
    • Export Citation
  • Meehl, G. A., C. T. Y. Chung, J. M. Arblaster, M. M. Holland, and C. M. Bitz, 2018: Tropical decadal variability and the rate of Arctic sea ice decrease. Geophys. Res. Lett., 45, 11 32611 333, https://doi.org/10.1029/2018GL079989.

    • Search Google Scholar
    • Export Citation
  • Meinshausen, M., and Coauthors, 2011: The RCP greenhouse gas concentrations and their extensions from 1765 to 2300. Climatic Change, 109, 213241, https://doi.org/10.1007/s10584-011-0156-z.

    • Search Google Scholar
    • Export Citation
  • Notz, D., and J. Stroeve, 2016: Observed Arctic sea-ice loss directly follows anthropogenic CO2 emission. Science, 354, 747750, https://doi.org/10.1126/science.aag2345.

    • Search Google Scholar
    • Export Citation
  • Notz, D., and SIMIP Community, 2020: Arctic sea ice in CMIP6. Geophys. Res. Lett., 47, e2019GL086749, https://doi.org/10.1029/2019GL086749.

    • Search Google Scholar
    • Export Citation
  • Olonscheck, D., and D. Notz, 2017: Consistently estimating internal climate variability from climate model simulations. J. Climate, 30, 95559573, https://doi.org/10.1175/JCLI-D-16-0428.1.

    • Search Google Scholar
    • Export Citation
  • Olonscheck, D., T. Mauritsen, and D. Notz, 2019: Arctic sea-ice variability is primarily driven by atmospheric temperature fluctuations. Nat. Geosci., 12, 430434, https://doi.org/10.1038/s41561-019-0363-1.

    • Search Google Scholar
    • Export Citation
  • Overland, J. E., and M. Wang, 2007: Future regional Arctic sea ice declines. Geophys. Res. Lett., 34, L17705, https://doi.org/10.1029/2007GL030808.

    • Search Google Scholar
    • Export Citation
  • Polvani, L. M., M. Previdi, M. R. England, G. Chiodo, and K. L. Smith, 2020: Substantial twentieth-century Arctic warming caused be ozone-depleting substances. Nat. Climate Change, 10, 130133, https://doi.org/10.1038/s41558-019-0677-4.

    • Search Google Scholar
    • Export Citation
  • Rosenblum, E., and I. Eisenman, 2017: Sea ice trends in climate models only accurate in runs with biased global warming. J. Climate, 30, 62656278, https://doi.org/10.1175/JCLI-D-16-0455.1.

    • Search Google Scholar
    • Export Citation
  • Screen, J. A., 2018: Arctic sea ice at 1.5 and 2°C. Nat. Climate Change, 8, 362363, https://doi.org/10.1038/s41558-018-0137-6.

  • Screen, J. A., and J. A. Francis, 2016: Contribution of sea-ice loss to Arctic amplification is regulated by Pacific Ocean decadal variability. Nat. Climate Change, 6, 856860, https://doi.org/10.1038/nclimate3011.

    • Search Google Scholar
    • Export Citation
  • Serreze, M. C., M. M. Holland, and J. Stroeve, 2007: Perspectives on the Arctic’s shrinking sea-ice cover. Science, 315, 15331536, https://doi.org/10.1126/science.1139426.

    • Search Google Scholar
    • Export Citation
  • Shen, Z., A. Duan, D. Li, and J. Li, 2021: Assessment and ranking of climate models in Arctic sea ice cover simulation: From CMIP5 to CMIP6. J. Climate, 34, 36093627, https://doi.org/10.1175/JCLI-D-20-0294.1.

    • Search Google Scholar
    • Export Citation
  • Smoliak, B. V., J. M. Wallace, P. Lin, and Q. Fu, 2015: Dynamical adjustment of the Northern Hemisphere surface air temperature field: Methodology and application to observations. J. Climate, 28, 16131629, https://doi.org/10.1175/JCLI-D-14-00111.1.

    • Search Google Scholar
    • Export Citation
  • Steinman, B. A., M. E. Mann, and S. K. Miller, 2015: Atlantic and Pacific multidecadal oscillations and Northern Hemisphere temperatures. Science, 347, 988991, https://doi.org/10.1126/science.1257856.

    • Search Google Scholar
    • Export Citation
  • Stroeve, J., M. M. Holland, W. Meier, T. Scambos, and M. Serreze, 2007: Arctic sea ice decline: Faster than forecast. Geophys. Res. Lett., 34, L09501, https://doi.org/10.1029/2007GL029703.

    • Search Google Scholar
    • Export Citation
  • Stroeve, J. C., V. Kattsov, A. Barrett, M. Serreze, T. Pavlova, M. Holland, and W. N. Meier, 2012: Trends in Arctic sea ice extent from CMIP5, CMIP3 and observations. Geophys. Res. Lett., 39, L16502, https://doi.org/10.1029/2012GL052676.

    • Search Google Scholar
    • Export Citation
  • Swart, N. C., J. C. Fyfe, E. Hawkins, J. E. Kay, and A. Jahn, 2015: Influence of internal variability on Arctic sea-ice trends. Nat. Climate Change, 5, 8689, https://doi.org/10.1038/nclimate2483.

    • Search Google Scholar
    • Export Citation
  • Tian, D., Y. Guo, and W. Dong, 2015: Future changes and uncertainties in temperature and precipitation over China based on CMIP5 models. Adv. Atmos. Sci., 32, 487496, https://doi.org/10.1007/s00376-014-4102-7.

    • Search Google Scholar
    • Export Citation
  • Titchner, H. A., and N. A. Rayner, 2014: The Met Office Hadley Centre sea ice and sea surface temperature data set, version 2.1: Sea ice concentrations. J. Geophys. Res. Atmos., 119, 28642889, https://doi.org/10.1002/2013JD020316.

    • Search Google Scholar
    • Export Citation
  • Walsh, J. E., F. Fetterer, J. S. Stewart, and W. L. Chapman, 2017: A database for depicting Arctic sea ice variations back to 1850. Geogr. Rev., 107, 89107, https://doi.org/10.1111/j.1931-0846.2016.12195.x.

    • Search Google Scholar
    • Export Citation
  • Wernli, H., and L. Papritz, 2018: Role of polar anticyclones and mid-latitude cyclones for Arctic summertime sea-ice melting. Nat. Geosci., 11, 108113, https://doi.org/10.1038/s41561-017-0041-0.

    • Search Google Scholar
    • Export Citation
  • Wyatt, M. G., and J. A. Curry, 2014: Role for Eurasian Arctic shelf sea ice in a secularly varying hemispheric climate signal during the 20th century. Climate Dyn., 42, 27632782, https://doi.org/10.1007/s00382-013-1950-2.

    • Search Google Scholar
    • Export Citation
  • Wyatt, M. G., S. Kravtsov, and A. A. Tsonis, 2012: Atlantic multidecadal oscillation and Northern Hemisphere’s climate variability. Climate Dyn., 38, 929949, https://doi.org/10.1007/s00382-011-1071-8.

    • Search Google Scholar
    • Export Citation
  • Wyburn-Powell, C., A. Jahn, and M. R. England, 2022: Modeled interannual variability of Arctic sea ice cover is within observational uncertainty. J. Climate, 35, 68276842, https://doi.org/10.1175/JCLI-D-21-0958.1.

    • Search Google Scholar
    • Export Citation
  • Zhang, R., 2015: Mechanisms for low-frequency variability of summer Arctic sea ice extent. Proc. Natl. Acad. Sci. USA, 112, 45704575, https://doi.org/10.1073/pnas.1422296112.

    • Search Google Scholar
    • Export Citation
  • Zhang, R., and T. L. Delworth, 2007: Impact of the Atlantic multidecadal oscillation on North Pacific climate variability. Geophys. Res. Lett., 34, L23708, https://doi.org/10.1029/2007GL031601.

    • Search Google Scholar
    • Export Citation

Supplementary Materials

Save
  • Allen, M. R., and S. F. B. Tett, 1999: Checking for model consistency in optimal fingerprinting. Climate Dyn., 15, 419434, https://doi.org/10.1007/s003820050291.

    • Search Google Scholar
    • Export Citation
  • Årthun, M., T. Eldevik, and L. H. Smedsrud, 2019: The role of Atlantic heat transport in future Arctic winter sea ice loss. J. Climate, 32, 33273341, https://doi.org/10.1175/JCLI-D-18-0750.1.

    • Search Google Scholar
    • Export Citation
  • Baxter, I., and Coauthors, 2019: How tropical Pacific surface cooling contributed to accelerated sea ice melt from 2007 to 2012 as ice is thinned by anthropogenic forcing. J. Climate, 32, 85838602, https://doi.org/10.1175/JCLI-D-18-0783.1.

    • Search Google Scholar
    • Export Citation
  • Bitz, C. M., 2008: Some aspects of uncertainty in predicting sea ice thinning. Arctic Sea Ice Decline: Observations, Projections, Mechanisms, and Implications, Geophys. Monogr., Vol. 180, Amer. Geophys. Union, 63–76, https://doi.org/10.1029/180GM06.

  • Brennan, M. K., G. J. Hakim, and E. Blanchard‐Wrigglesworth, 2020: Arctic sea‐ice variability during the instrumental era. Geophys. Res. Lett., 47, e2019GL086843, https://doi.org/10.1029/2019GL086843.

    • Search Google Scholar
    • Export Citation
  • Chen, J.-L., S.-C. Kang, X.-H. Meng, and Q.-L. You, 2019: Assessments of the Arctic amplification and the changes in the Arctic sea surface. Adv. Climate Change Res., 10, 193202, https://doi.org/10.1016/j.accre.2020.03.002.

    • Search Google Scholar
    • Export Citation
  • Dai, A., J. C. Fyfe, S.-P. Xie, and X. Dai, 2015: Decadal modulation of global surface temperature by internal climate variability. Nat. Climate Change, 5, 555559, https://doi.org/10.1038/nclimate2605.

    • Search Google Scholar
    • Export Citation
  • Deser, C., and A. S. Phillips, 2021: Defining the internal component of Atlantic multidecadal variability in a changing climate. Geophys. Res. Lett., 48, e2021GL095023, https://doi.org/10.1029/2021GL095023.

    • Search Google Scholar
    • Export Citation
  • Deser, C., A. S. Phillips, M. A. Alexander, and B. V. Smoliak, 2014: Projecting North American climate over the next 50 years: Uncertainty due to internal variability. J. Climate, 27, 22712296, https://doi.org/10.1175/JCLI-D-13-00451.1.

    • Search Google Scholar
    • Export Citation
  • Deser, C., L. Terray, and A. S. Phillips, 2016: Forced and internal components of winter air temperature trends over North America during the past 50 years: Mechanisms and implications. J. Climate, 29, 22372258, https://doi.org/10.1175/JCLI-D-15-0304.1.

    • Search Google Scholar
    • Export Citation
  • Ding, Q., J. M. Wallace, D. S. Battisti, E. J. Steig, A. J. E. Gallant, H.-J. Kim, and L. Geng, 2014: Tropical forcing of the recent rapid Arctic warming in northeastern Canada and Greenland. Nature, 509, 209212, https://doi.org/10.1038/nature13260.

    • Search Google Scholar
    • Export Citation
  • Ding, Q., and Coauthors, 2017: Influence of high-latitude atmospheric circulation changes on summertime Arctic sea ice. Nat. Climate Change, 7, 289295, https://doi.org/10.1038/nclimate3241.

    • Search Google Scholar
    • Export Citation
  • Ding, Q., and Coauthors, 2019: Fingerprints of internal drivers of Arctic sea ice loss in observations and model simulations. Nat. Geosci., 12, 2833, https://doi.org/10.1038/s41561-018-0256-8.

    • Search Google Scholar
    • Export Citation
  • Dörr, J. S., D. B. Bonan, M. Årthun, L. Svendsen, and R. C. J. Wills, 2023: Forced and internal components of observed Arctic sea-ice changes. Cryosphere, 17, 41334153, https://doi.org/10.5194/tc-17-4133-2023.

    • Search Google Scholar
    • Export Citation
  • England, M., A. Jahn, and L. Polvani, 2019: Nonuniform contribution of internal variability to recent Arctic sea ice loss. J. Climate, 32, 40394053, https://doi.org/10.1175/JCLI-D-18-0864.1.

    • Search Google Scholar
    • Export Citation
  • England, M. R., 2021: Are multi‐decadal fluctuations in Arctic and Antarctic surface temperatures a forced response to anthropogenic emissions or part of internal climate variability? Geophys. Res. Lett., 48, e2020GL090631, https://doi.org/10.1029/2020GL090631.

    • Search Google Scholar
    • Export Citation
  • Eyring, V., S. Bony, G. A. Meehl, C. A. Senior, B. Stevens, R. J. Stouffer, and K. E. Taylor, 2016: Overview of the Coupled Model Intercomparison Project Phase 6 (CMIP6) experimental design and organization. Geosci. Model Dev., 9, 19371958, https://doi.org/10.5194/gmd-9-1937-2016.

    • Search Google Scholar
    • Export Citation
  • Fyfe, J. C., K. von Salzen, N. P. Gillett, V. K. Arora, G. M. Flato, and J. R. McConnell, 2013: One hundred years of Arctic surface temperature variation due to anthropogenic influence. Sci. Rep., 3, 2645, https://doi.org/10.1038/srep02645.

    • Search Google Scholar
    • Export Citation
  • Gulev, S. K., and Coauthors, 2021: Changing state of the climate system. Climate Change 2021: The Physical Science Basis, V. Masson-Delmotte et al., Eds., Cambridge University Press, 287–422.

  • Halloran, P. R., and Coauthors, 2020: Natural drivers of multidecadal Arctic sea ice variability over the last millennium. Sci. Rep., 10, 688, https://doi.org/10.1038/s41598-020-57472-2.

    • Search Google Scholar
    • Export Citation
  • Haustein, K., and Coauthors, 2019: A limited role for unforced internal variability in twentieth-century warming. J. Climate, 32, 48934917, https://doi.org/10.1175/JCLI-D-18-0555.1.

    • Search Google Scholar
    • Export Citation
  • Holland, M. M., and L. Landrum, 2021: The emergence and transient nature of Arctic amplification in coupled climate models. Front. Earth Sci., 9, 719024, https://doi.org/10.3389/feart.2021.719024.

    • Search Google Scholar
    • Export Citation
  • Jahn, A., 2018: Reduced probability of ice-free summers for 1.5 °C compared to 2 °C warming. Nat. Climate Change, 8, 409413, https://doi.org/10.1038/s41558-018-0127-8.

    • Search Google Scholar
    • Export Citation
  • Kay, J. E., M. M. Holland, and A. Jahn, 2011: Inter-annual to multi-decadal Arctic sea ice extent trends in a warming world. Geophys. Res. Lett., 38, L15708, https://doi.org/10.1029/2011GL048008.

    • Search Google Scholar
    • Export Citation
  • Kay, J. E., and Coauthors, 2015: The Community Earth System Model (CESM) large ensemble project: A community resource for studying climate change in the presence of internal climate variability. Bull. Amer. Meteor. Soc., 96, 13331349, https://doi.org/10.1175/BAMS-D-13-00255.1.

    • Search Google Scholar
    • Export Citation
  • Kim, Y.-H., S.-K. Min, N. P. Gillett, D. Notz, and E. Malinina, 2023: Observationally-constrained projections of an ice-free Arctic even under a low emission scenario. Nat. Commun., 14, 3139, https://doi.org/10.1038/s41467-023-38511-8.

    • Search Google Scholar
    • Export Citation
  • Lamarque, J.-F., and Coauthors, 2010: Historical (1850–2000) gridded anthropogenic and biomass burning emissions of reactive gases and aerosols: Methodology and application. Atmos. Chem. Phys., 10, 70177039, https://doi.org/10.5194/acp-10-7017-2010.

    • Search Google Scholar
    • Export Citation
  • Lehner, F., C. Deser, and L. Terray, 2017: Toward a new estimate of “time of emergence” of anthropogenic warming: Insights from dynamical adjustment and a large initial-condition model ensemble. J. Climate, 30, 77397756, https://doi.org/10.1175/JCLI-D-16-0792.1.

    • Search Google Scholar
    • Export Citation
  • Maher, N., D. Matei, S. Milinski, and J. Marotzke, 2018: ENSO change in climate projections: Forced response or internal variability? Geophys. Res. Lett., 45, 11 39011 398, https://doi.org/10.1029/2018GL079764.

    • Search Google Scholar
    • Export Citation
  • Maher, N., and Coauthors, 2019: The Max Planck institute grand ensemble: Enabling the exploration of climate system variability. J. Adv. Model. Earth Syst., 11, 20502069, https://doi.org/10.1029/2019MS001639.

    • Search Google Scholar
    • Export Citation
  • Mahlstein, I., and R. Knutti, 2012: September Arctic sea ice predicted to disappear near 2°C global warming above present. J. Geophys. Res., 117, D06104, https://doi.org/10.1029/2011JD016709.

    • Search Google Scholar
    • Export Citation
  • Mann, M. E., B. A. Steinman, D. J. Brouillette, A. Fernandez, and S. K. Miller, 2022: On the estimation of internal climate variability during the preindustrial past millennium. Geophys. Res. Lett., 49, e2021GL096596, https://doi.org/10.1029/2021GL096596.

    • Search Google Scholar
    • Export Citation
  • Maslanik, J., S. Drobot, C. Fowler, W. Emery, and R. Barry, 2007: On the Arctic climate paradox and the continuing role of atmospheric circulation in affecting sea ice conditions. Geophys. Res. Lett., 34, L03711, https://doi.org/10.1029/2006GL028269.

    • Search Google Scholar
    • Export Citation
  • Meehl, G. A., C. T. Y. Chung, J. M. Arblaster, M. M. Holland, and C. M. Bitz, 2018: Tropical decadal variability and the rate of Arctic sea ice decrease. Geophys. Res. Lett., 45, 11 32611 333, https://doi.org/10.1029/2018GL079989.

    • Search Google Scholar
    • Export Citation
  • Meinshausen, M., and Coauthors, 2011: The RCP greenhouse gas concentrations and their extensions from 1765 to 2300. Climatic Change, 109, 213241, https://doi.org/10.1007/s10584-011-0156-z.

    • Search Google Scholar
    • Export Citation
  • Notz, D., and J. Stroeve, 2016: Observed Arctic sea-ice loss directly follows anthropogenic CO2 emission. Science, 354, 747750, https://doi.org/10.1126/science.aag2345.

    • Search Google Scholar
    • Export Citation
  • Notz, D., and SIMIP Community, 2020: Arctic sea ice in CMIP6. Geophys. Res. Lett., 47, e2019GL086749, https://doi.org/10.1029/2019GL086749.

    • Search Google Scholar
    • Export Citation
  • Olonscheck, D., and D. Notz, 2017: Consistently estimating internal climate variability from climate model simulations. J. Climate, 30, 95559573, https://doi.org/10.1175/JCLI-D-16-0428.1.

    • Search Google Scholar
    • Export Citation
  • Olonscheck, D., T. Mauritsen, and D. Notz, 2019: Arctic sea-ice variability is primarily driven by atmospheric temperature fluctuations. Nat. Geosci., 12, 430434, https://doi.org/10.1038/s41561-019-0363-1.

    • Search Google Scholar
    • Export Citation
  • Overland, J. E., and M. Wang, 2007: Future regional Arctic sea ice declines. Geophys. Res. Lett., 34, L17705, https://doi.org/10.1029/2007GL030808.

    • Search Google Scholar
    • Export Citation
  • Polvani, L. M., M. Previdi, M. R. England, G. Chiodo, and K. L. Smith, 2020: Substantial twentieth-century Arctic warming caused be ozone-depleting substances. Nat. Climate Change, 10, 130133, https://doi.org/10.1038/s41558-019-0677-4.

    • Search Google Scholar
    • Export Citation
  • Rosenblum, E., and I. Eisenman, 2017: Sea ice trends in climate models only accurate in runs with biased global warming. J. Climate, 30, 62656278, https://doi.org/10.1175/JCLI-D-16-0455.1.

    • Search Google Scholar
    • Export Citation
  • Screen, J. A., 2018: Arctic sea ice at 1.5 and 2°C. Nat. Climate Change, 8, 362363, https://doi.org/10.1038/s41558-018-0137-6.

  • Screen, J. A., and J. A. Francis, 2016: Contribution of sea-ice loss to Arctic amplification is regulated by Pacific Ocean decadal variability. Nat. Climate Change, 6, 856860, https://doi.org/10.1038/nclimate3011.

    • Search Google Scholar
    • Export Citation
  • Serreze, M. C., M. M. Holland, and J. Stroeve, 2007: Perspectives on the Arctic’s shrinking sea-ice cover. Science, 315, 15331536, https://doi.org/10.1126/science.1139426.

    • Search Google Scholar
    • Export Citation
  • Shen, Z., A. Duan, D. Li, and J. Li, 2021: Assessment and ranking of climate models in Arctic sea ice cover simulation: From CMIP5 to CMIP6. J. Climate, 34, 36093627, https://doi.org/10.1175/JCLI-D-20-0294.1.

    • Search Google Scholar
    • Export Citation
  • Smoliak, B. V., J. M. Wallace, P. Lin, and Q. Fu, 2015: Dynamical adjustment of the Northern Hemisphere surface air temperature field: Methodology and application to observations. J. Climate, 28, 16131629, https://doi.org/10.1175/JCLI-D-14-00111.1.

    • Search Google Scholar
    • Export Citation
  • Steinman, B. A., M. E. Mann, and S. K. Miller, 2015: Atlantic and Pacific multidecadal oscillations and Northern Hemisphere temperatures. Science, 347, 988991, https://doi.org/10.1126/science.1257856.

    • Search Google Scholar
    • Export Citation
  • Stroeve, J., M. M. Holland, W. Meier, T. Scambos, and M. Serreze, 2007: Arctic sea ice decline: Faster than forecast. Geophys. Res. Lett., 34, L09501, https://doi.org/10.1029/2007GL029703.

    • Search Google Scholar
    • Export Citation
  • Stroeve, J. C., V. Kattsov, A. Barrett, M. Serreze, T. Pavlova, M. Holland, and W. N. Meier, 2012: Trends in Arctic sea ice extent from CMIP5, CMIP3 and observations. Geophys. Res. Lett., 39, L16502, https://doi.org/10.1029/2012GL052676.

    • Search Google Scholar
    • Export Citation
  • Swart, N. C., J. C. Fyfe, E. Hawkins, J. E. Kay, and A. Jahn, 2015: Influence of internal variability on Arctic sea-ice trends. Nat. Climate Change, 5, 8689, https://doi.org/10.1038/nclimate2483.

    • Search Google Scholar
    • Export Citation
  • Tian, D., Y. Guo, and W. Dong, 2015: Future changes and uncertainties in temperature and precipitation over China based on CMIP5 models. Adv. Atmos. Sci., 32, 487496, https://doi.org/10.1007/s00376-014-4102-7.

    • Search Google Scholar
    • Export Citation
  • Titchner, H. A., and N. A. Rayner, 2014: The Met Office Hadley Centre sea ice and sea surface temperature data set, version 2.1: Sea ice concentrations. J. Geophys. Res. Atmos., 119, 28642889, https://doi.org/10.1002/2013JD020316.

    • Search Google Scholar
    • Export Citation
  • Walsh, J. E., F. Fetterer, J. S. Stewart, and W. L. Chapman, 2017: A database for depicting Arctic sea ice variations back to 1850. Geogr. Rev., 107, 89107, https://doi.org/10.1111/j.1931-0846.2016.12195.x.

    • Search Google Scholar
    • Export Citation
  • Wernli, H., and L. Papritz, 2018: Role of polar anticyclones and mid-latitude cyclones for Arctic summertime sea-ice melting. Nat. Geosci., 11, 108113, https://doi.org/10.1038/s41561-017-0041-0.

    • Search Google Scholar
    • Export Citation
  • Wyatt, M. G., and J. A. Curry, 2014: Role for Eurasian Arctic shelf sea ice in a secularly varying hemispheric climate signal during the 20th century. Climate Dyn., 42, 27632782, https://doi.org/10.1007/s00382-013-1950-2.

    • Search Google Scholar
    • Export Citation
  • Wyatt, M. G., S. Kravtsov, and A. A. Tsonis, 2012: Atlantic multidecadal oscillation and Northern Hemisphere’s climate variability. Climate Dyn., 38, 929949, https://doi.org/10.1007/s00382-011-1071-8.

    • Search Google Scholar
    • Export Citation
  • Wyburn-Powell, C., A. Jahn, and M. R. England, 2022: Modeled interannual variability of Arctic sea ice cover is within observational uncertainty. J. Climate, 35, 68276842, https://doi.org/10.1175/JCLI-D-21-0958.1.

    • Search Google Scholar
    • Export Citation
  • Zhang, R., 2015: Mechanisms for low-frequency variability of summer Arctic sea ice extent. Proc. Natl. Acad. Sci. USA, 112, 45704575, https://doi.org/10.1073/pnas.1422296112.

    • Search Google Scholar
    • Export Citation
  • Zhang, R., and T. L. Delworth, 2007: Impact of the Atlantic multidecadal oscillation on North Pacific climate variability. Geophys. Res. Lett., 34, L23708, https://doi.org/10.1029/2007GL031601.

    • Search Google Scholar
    • Export Citation
  • Fig. 1.

    Correlation coefficients between the true internal component of September SIC in CESM-LE and those estimated with (a) the 27-model MMEM and (b) the rescaled MMEM during the time period 1960–2020. (c),(d) As in (a) and (b), but for rmse values between the true and estimated internal components. Note that the results are the average of the 40 cases.

  • Fig. 2.

    (a) SSIE evolution during the time period 1960–2020. The gray, green, blue, and red lines represent the observed, original, rescaled externally forced, and rescaled internal components of SIE based on CESM1-LE, respectively. (b) The relative contribution of external forcing and internal variability to the SSIE during the different time periods of 1960–79, 1980–99, 2000–12, 2012–20, and 1960–2020. The gray, red, and blue bars represent the observed, internally generated, and externally forced SIE trends, respectively.

  • Fig. 3.

    SSIE trends during different periods. The x axis represents the ending year of the trend segment, and the y axis represents the length of the trend segment. (a)–(c) The observed, rescaled externally forced, and internal variability of SIE trends based on CESM1-LE. (d) The SNR, calculated as the forced trend divided by the internal trend. SNR greater than 1 implies that the influence of external forcing is greater than the internal variability.

  • Fig. 4.

    As in Fig. 3, but for March.

  • Fig. 5.

    SNR on different time scales and ending year before (blue) and after (red) 2000 for (a) September and (b) March.

  • Fig. 6.

    September SIC trends during the time period 2000–12. (a)–(c) The observed, rescaled externally forced, and internally generated SIC trends based on CESM1-LE. (d) The SNR, defined as the absolute value of the externally forced trend divided by the internally generated trend. The SNR value greater than 1 implies that the impact of external forcing is stronger than the internal variability.

  • Fig. 7.

    As in Fig. 4, but for the time period 1960–2020.

  • Fig. 8.

    EOF analysis of estimated observed (top) 10-yr and (bottom) 20-yr internally generated SIC trends based on CESM1-LE.

  • Fig. 9.

    As in Fig. 8, but for March.