Editorial Type:
Article
Article Type:
Research Article

Diverse Eurasian Temperature Responses to Arctic Sea Ice Loss in Models due to Varying Balance between Dynamic Cooling and Thermodynamic Warming

Cheng Zheng aLamont-Doherty Earth Observatory of Columbia University, Palisades, New York

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https://orcid.org/0000-0002-8039-346X
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Yutian Wu aLamont-Doherty Earth Observatory of Columbia University, Palisades, New York

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Mingfang Ting aLamont-Doherty Earth Observatory of Columbia University, Palisades, New York

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James A. Screen bDepartment of Mathematics and Statistics, University of Exeter, Exeter, United Kingdom

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Pengfei Zhang cDepartment of Meteorology and Atmospheric Sciences, The Pennsylvania State University, University Park, Pennsylvania

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Online Publication:
22 Nov 2023
Print Publication:
15 Dec 2023
DOI:
https://doi.org/10.1175/JCLI-D-22-0937.1
Page(s):
8347–8364
Free access

Abstract

Cold winters over Eurasia often coincide with warm winters in the Arctic, which has become known as the “warm Arctic–cold Eurasia” pattern. The extent to which this observed correlation is indicative of a causal response to sea ice loss is debated. Here, using large multimodel ensembles of coordinated experiments, we find that the Eurasian temperature response to Arctic sea ice loss is weak compared to internal variability and is not robust across climate models. We show that Eurasian cooling is driven by tropospheric and stratospheric circulation changes in response to sea ice loss but is counteracted by tropospheric thermodynamical warming, as the local warming induced by sea ice loss spreads into the midlatitudes by eddy advection. Although opposing effects of thermodynamical warming and dynamical cooling are found robustly across different models or different sea ice perturbations, their net effect varies in sign and magnitude across the models, resulting in diverse model temperature responses over Eurasia. The contributions from both tropospheric dynamics and thermodynamics show substantial intermodel spread. Although some of this spread in the Eurasian winter temperature response to sea ice loss may stem from model uncertainty, even with several hundred ensemble members, it is challenging to isolate model differences in the forced response from internal variability.

© 2023 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 author: Cheng Zheng, czheng@ldeo.columbia.edu

Abstract

Cold winters over Eurasia often coincide with warm winters in the Arctic, which has become known as the “warm Arctic–cold Eurasia” pattern. The extent to which this observed correlation is indicative of a causal response to sea ice loss is debated. Here, using large multimodel ensembles of coordinated experiments, we find that the Eurasian temperature response to Arctic sea ice loss is weak compared to internal variability and is not robust across climate models. We show that Eurasian cooling is driven by tropospheric and stratospheric circulation changes in response to sea ice loss but is counteracted by tropospheric thermodynamical warming, as the local warming induced by sea ice loss spreads into the midlatitudes by eddy advection. Although opposing effects of thermodynamical warming and dynamical cooling are found robustly across different models or different sea ice perturbations, their net effect varies in sign and magnitude across the models, resulting in diverse model temperature responses over Eurasia. The contributions from both tropospheric dynamics and thermodynamics show substantial intermodel spread. Although some of this spread in the Eurasian winter temperature response to sea ice loss may stem from model uncertainty, even with several hundred ensemble members, it is challenging to isolate model differences in the forced response from internal variability.

© 2023 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 author: Cheng Zheng, czheng@ldeo.columbia.edu
Keywords: Sea ice; Atmospheric circulation; Climate change; Surface temperature; Climate models; Internal variability

1. Introduction

Rapid Arctic warming has been observed in recent decades, accompanied by sea ice loss (e.g., Screen and Simmonds 2010; Stroeve et al. 2012; Deser et al. 2010). The warm Arctic–cold Eurasia pattern corresponds to the co-occurrence of severe cold winters over Eurasia with warmer than average winters in the Arctic warming, on interannual time scales (Walsh 2014; Cohen et al. 2014; Overland et al. 2011). However, recent studies suggest that the observed connection between the warm Arctic and cold Eurasia may not be primarily driven by Arctic sea ice loss, but rather by internal atmospheric variability or tropical forcing (Matsumura and Kosaka 2019; Warner et al. 2020; Blackport et al. 2019; McCusker et al. 2016; Sun et al. 2016). Many studies use climate models, particularly atmosphere–land general circulation models (AGCMs) in which sea ice concentration (SIC) and sea surface temperature (SST) are prescribed, to isolate and understand the forced response by sea ice loss.

However, no consensus has been reached on the connection between warm Arctic and cold Eurasia or the mechanisms involved [see recent review papers by Screen et al. (2018) and Cohen et al. (2020)], particularly due to the sea ice loss over the Barents–Kara Sea (BKS) region with the largest sea ice trend (e.g., Screen and Simmonds 2010) and winter sea ice variability (e.g., Kim et al. 2017; Zhong et al. 2018). It is possible that with sea ice loss over the BKS region, an anticyclonic circulation in the mid-to-upper troposphere centered over the BKS is induced, which results in anomalous cold air advection to the east of the circulation center and thus colder temperatures over Eurasia (e.g., Zhang et al. 2018a). The mechanism could work via the stratospheric pathway (Kim et al. 2014; Nakamura et al. 2016; Zhang et al. 2018a), as regional sea ice loss such as over the BKS region creates a zonally asymmetric forcing, which induces planetary-scale waves that modulate the upward wave propagation from the troposphere to the stratosphere (e.g., Sun et al. 2015; McKenna et al. 2018). This perturbs the stratospheric circulation, and the slowdown of the stratospheric circulation due to the BKS forcing leads to an anomalous tropospheric anticyclonic circulation centered over the Ural region via downward influences, which gives rise to colder Eurasian winters as discussed above. The role of the tropospheric pathway has also been explored (Xu et al. 2019; He et al. 2020), as the local heating due to sea ice loss directly forces an anticyclonic circulation in the troposphere, and it could be of equal importance to the stratospheric pathway (e.g., Xu et al. 2021). Methods to separate the contribution from the stratospheric and tropospheric pathways include 1) nudging techniques in GCM simulations, particularly nudging the stratospheric circulation toward a target state to isolate the stratospheric influences (Wu and Smith 2016; Zhang et al. 2018a,b; Xu et al. 2021), and 2) regression between surface air temperature and troposphere/stratosphere circulation indices (Xu et al. 2021). Apart from the cooling driven dynamically by atmospheric circulation response due to sea ice loss, local warming induced by sea ice loss could also extend into Eurasia via eddy advection (so-called thermodynamical warming), which counteracts the dynamical cooling (Deser et al. 2010; Screen 2017b; Chripko et al. 2021).

Modeling studies also suggest that the cooling response in Eurasia can be highly sensitive to the magnitude and location of sea ice forcing (Zhang and Screen 2021; Chen et al. 2021; Semenov and Latif 2015; Petoukhov and Semenov 2010; Screen 2017a), which makes it difficult to compare past studies with different sea ice perturbations. In AGCM simulations (Zhang and Screen 2021; Semenov and Latif 2015; Petoukhov and Semenov 2010), the Eurasian temperature response does not scale linearly with the magnitude of sea ice forcing (i.e., stronger sea ice forcing does not necessarily lead to larger cooling or warming response over Eurasia). The atmospheric circulation response to sea ice loss, such as the wintertime Ural blocking, which has been shown to play an important role in cold extremes over Eurasia, also does not respond linearly to different magnitudes of sea ice forcing in idealized GCM simulations (Chen et al. 2021). The atmospheric response is also sensitive to the location of sea ice forcing in AGCM simulations (e.g., Screen 2017a; Sun et al. 2015; McKenna et al. 2018). The atmosphere response is very different when sea ice is decreased in different geographical regions, or when the sea ice loss is regionally confined compared to the pan-Arctic area. Also, the cumulative effects of regional sea ice losses appear nonadditive; that is, the sum of atmospheric response in simulations with sea ice forcing in individual regions is not consistent with the simulated atmospheric response with pan-Arctic sea ice forcing (Screen 2017a).

Moreover, recent studies (e.g., Peings et al. 2021; Streffing et al. 2021; Sun et al. 2022) suggest that a large ensemble size (more than 100 years or seasons) is required to distinguish the remote response to sea ice loss from internal variability, such as the response in stratospheric polar vortex, as well as the spatial structure of tropospheric circulation response and surface air temperature response. Larger ensemble sizes reduce the noise due to internal variability, which enables the detection of a robust remote response forced by sea ice loss (signal), which is usually not large in magnitude. Thus, the forced response by sea ice loss in previous studies with a small ensemble size may be contaminated by internal variability. Previous studies have introduced methods to estimate the ensemble size required to robustly detect the sea ice forced response from the signal-to-noise perspective (Screen et al. 2014; Labe 2020).

Given these apparent sensitivities to both the model and forcing used, here we provide a comprehensive evaluation and synthesis of the Eurasian response to sea ice loss across a wide range of models and experimental designs. In this study, we aim to address the following three questions:

  1. Is the Eurasian temperature response robust across different climate models with the same Arctic sea ice forcing?

  2. Is the Eurasian temperature response robust across different magnitudes of sea ice forcing with the same model?

  3. What physical mechanisms control the diverse Eurasian temperature response and its spread across models and forcings?

As previous studies suggest that models display an inconsistent Eurasian temperature response to sea ice forcing (Ogawa et al. 2018; Screen and Blackport 2019; Smith et al. 2022), we are particularly interested in question 3. Specifically, we aim to address why the Eurasian temperature response has different signs and magnitudes across different models. In terms of the physical mechanisms, we will show what is consistent across the models, and what is leading to the diverse responses.

Details of the model simulations will be introduced in section 2. Results from WACCM simulations, and a regression method to decompose the Eurasian temperature response, will be discussed in section 3. The comparison between different models or between different forcings in PAMIP models will be explored in section 4. Discussions and conclusions will be presented in section 5.

2. Model simulations

To explore the above questions in section 1, we use AGCM simulations from two versions of the Whole Atmosphere Community Climate Model (WACCM) with specified chemistry, WACCM4 (Smith et al. 2014) and WACCM6 (Gettelman et al. 2019), plus 11 models from the Polar Amplification Model Intercomparison Project (PAMIP; Smith et al. 2019). More specifically, we use the WACCM simulations to test the sensitivity of modeled response to the magnitude of forcing (question 2) and the PAMIP simulations to examine the sensitivity to different models with the same forcing, as well as sensitivity to the location (regional versus pan-Arctic forcing) and the magnitude (future vs preindustrial) of sea ice forcing (questions 1 and 3). Model simulations used in the study are summarized in Tables 1–3. All analyses are performed for the winter season [December–February (DJF)] by comparing two sets of simulations with different Arctic sea ice conditions.

Table 1.

Summary of WACCM model experiments.
Table 1.
Table 2.

Summary of PAMIP AGCM experiments.
Table 2.
Table 3.

Summary of PAMIP coupled experiments.
Table 3.

The WACCM simulations focus on BKS sea ice forcing, as Eurasian temperature is more sensitive to sea ice loss in this region than in other regions (Screen 2017a). For the 225-yr WACCM4 experiments, which were performed in Zhang et al. (2020), in the control run (WACCM4_control), the SST and SIC boundary conditions are the ensemble average of the CESM1-WACCM4 historical run during 1980–99. The perturbation run (WACCM4_BKS_FU) has the identical setup except that the SST and SIC over the BKS (70°–82°N, 15°–100°E) are replaced by Coupled Model Intercomparison Project (CMIP) phase 5 representative concentration pathway (RCP) 8.5 outputs averaged over 2080–99. More details of the WACCM4 experiment setups are discussed in Zhang et al. (2018a, 2020).

In this study, we perform similar experiments in WACCM6 with sea ice forcing in the BKS (65°–80°N, 30°–90°E). One set of WACCM6 experiments (WACCM6_CEMS1_control and WACCM6_CESM1_BKS_FU) has similar boundary conditions to those in WACCM4, as described above. In another similar set of WACCM6 experiments (WACCM6_CEMS2_control and WACCM6_CESM2_BKS_FU), the boundary conditions are obtained from CESM2-WACCM6 coupled runs with CMIP6 forcing [control SST and SIC from historical run during 1995–2014; future BKS forcing from Shared Socioeconomic Pathway (SSP) 585 during 2080–99]. In the idealized SIC experiments (WACCM6_CESM2_BKS_1%), which are designed to test the sensitivity of model response to the magnitude of sea ice forcing (question 2), the setup is the same as WACCM6_CESM2_control except that the SIC at any grid point in the BKS region is set to 1% of its WACCM6_CESM2_control value. Idealized SIC experiments are also performed with SIC set to different percentages (from 20% to 90%) of the control value, to represent different magnitudes of sea ice forcing. We run each of the WACCM6 experiments mentioned above for 215 years with the first 15 years of spinup excluded from the analysis. Note in WACCM6 simulations that sea ice forcing is only imposed during extended boreal winter (November to April). From May to October, SST and SIC over the BKS are the same as in the control run. Since simulations with all-year-round forcing provide very similar results, we only show the model results with extended boreal winter forcing.

The PAMIP experiments, in which different modeling centers use identical sea ice forcing to perform simulations, are designed to isolate the influence of sea ice loss. These coordinated experiments are well suited for examining the robustness and spread of simulated response across different models with the same forcing (questions 1 and 3). Four different AGCM experiments from PAMIP are selected for the purpose of this study (Table 2). The present-day simulation employing the present-day SST and SIC condition (pdSST_pdSIC) will be referred to as PD. The other three experiments utilize present-day SST everywhere except the Arctic and different Arctic SIC and SST, including future BKS SIC (pdSST_futBKSeasSIC), future Arctic SIC (pdSST_futArcSIC), and preindustrial Arctic SIC (pdSST_piArcSIC). These three experiments will be referred to as FU_BKS, FU_ARC, and PI_ARC. The comparison between FU_BKS and FU_ARC reveals whether the results are sensitive to forcing location, while the comparison between FU_ARC and PI_ARC is helpful to understand the sensitivity to forcing magnitude and spatial patterns. According to the PAMIP protocol, all four experiments are atmospheric time slices with at least 100 members (years), and the only difference across all experiments is the boundary conditions in the Arctic. We include all the PAMIP models that are currently available in the CMIP6 data archive and have at least 2 of the 3 perturbation experiments (FU_BKS, FU_ARC, and PI_ARC) with at least 100 members. In total, 11 PAMIP models are analyzed in the study. Details of these AGCM simulations are summarized in Table 2. To verify whether ocean coupling will change our conclusions derived from AGCM simulations, three coupled ocean PAMIP experiments are analyzed as well, including present-day sea ice (pa_pdSIC), future Arctic sea ice (pa_futArcSIC), and preindustrial Arctic SIC (pa_piArcSIC). These coupled experiments are performed in four PAMIP models, which are summarized in Table 3.

Note that the definition of the BKS region is different across WACCM4 (70°–82°N, 15°–100°E), WACCM6 (65°–80°N, 30°–90°E), and PAMIP (65°–85°N, 10°–110°E) simulations, which may impact the midlatitude response. The magnitudes of the BKS forcing are also different. The forcing in the WACCM experiments is obtained from the simulated end-of-twenty-first-century SIC and SST under high emission scenarios minus the present-day values in historical simulations, while the forcing in PAMIP is simulated 2°C warming from the preindustrial level minus present-day observations. As the warming under high emission scenarios at the end of the twenty-first century is larger than 2°C from the preindustrial level, the BKS forcing (sea ice loss) in the WACCM simulations is stronger than that in the PAMIP simulations. Besides, the coupled WACCM historical simulations have positive sea ice biases over the BKS, meaning higher SIC and colder SST over the BKS region in the WACCM control simulations than that in PAMIP PD simulations. In addition, outside the BKS region, background SST and SIC are also different between the WACCM (from coupled historical CMIP simulations) and the PAMIP (from observations) simulations. Differences in the background SST could lead to different atmospheric basic states, which modulate the response to identical sea ice forcings (Smith et al. 2017; Chen et al. 2016). Thus, the BKS simulations across WACCM4, WACCM6, and PAMIP cannot be directly compared.

To test the statistical significance of the response to Arctic sea ice loss, for an area-averaged quantity (e.g., area-averaged Eurasian temperature response), we use a two-tailed Student’s t test. The response is considered significant when the p value is smaller than or equal to 0.1 (90% significant). Since the rejection of the global null hypothesis is overestimated when applying the Student’s t test on a map consisting of multiple grid points (Wilks 2016), we apply the false discovery rate (FDR; Wilks 2016) when testing the significance of a variable at each grid point on a map. As recommended by Wilks (2016), we apply αFDR = 0.2 in the FDR method, which is twice the value of the threshold in the Student’s t test.

3. Response to BKS SIC decrease in WACCM simulations

a. WACCM4

The surface air temperature (T2m) response over Eurasia in the 225-yr simulation in WACCM4 (Fig. 1a) shows a robust but weak cooling (<0.5 K). Note that T2m is only archived in the land model output in the WACCM4 simulations; thus, data are only available over land. Skin temperature (not shown), which is available over the ocean, displays a very similar response as T2m. To explore the contribution to T2m response by the tropospheric and stratospheric pathways, we apply linear regression between T2m response and atmospheric circulation response among randomly selected 100-yr (same as the smallest PAMIP ensemble sizes) subsamples from the 225-yr simulation with a total of 10 000 such subsamples (the results are not sensitive to the subsample size; see discussion below). The Arctic stratospheric response (60°–90°N; 50-hPa geopotential height; H50) and Eurasian T2m response (40°–60°N, 60°–135°E; green box in Fig. 1a) of each subsample are shown in Fig. 2a. Each red dot represents one 100-yr subsample. There is a weak but robust negative linear relationship between the stratospheric signal and Eurasian T2m response, the so-called stratospheric pathway of the influence of sea ice decline on midlatitudes (Nakamura et al. 2016; Wu and Smith 2016). Meanwhile, there is a much higher correlation between the 500-hPa geopotential height (H500) response in the BKS region (60°–90°N, 30°–150°E; dashed yellow box in Fig. 1a) and the Eurasian T2m response (Fig. 2b), indicating that the Eurasian T2m variability and/or its response to sea ice loss is strongly linked to the tropospheric circulation variability and/or response. As discussed in section 1, the Eurasian cooling is driven by the anticyclonic tropospheric circulation (positive geopotential height) over the BKS and Ural region, which leads to cold advection over the Eurasian region. The high correlation between BKS H500 and Eurasian T2m is consistent with the mechanism, as stronger anticyclonic circulation corresponds to stronger cold advection, leading to colder temperature over the Eurasian region. Both correlations in Fig. 2 are statistically significant at 95%, considering the actual degrees of freedom are 225 (ensemble size).

Fig. 1.
Fig. 1.

(a) T2m response (shading; K) in WACCM4_BKS_FU minus WACCM4_control. The hashed grid points reach statistical significance (FDR threshold). The contours show the H500 response. Contour interval is 5 gpm. Positive contours are represented by solid lines, and negative contours are represented by dashed lines. The zero contour is omitted. The green box (40°–60°N, 60°–135°E) shows the averaging region for the Eurasian T2m response. The yellow box (60°–90°N, 30°–150°E) shows the averaging region for the H500 response. (b) aΔH50Arctic¯ (K), the first term on the right-hand side of Eq. (1). (c),(d) As in (b), but for b(ΔH500BKS¯−dΔH50Arctic¯) and intercept c, the second and third terms on the right-hand side of Eq. (1), respectively. (e) The sum of (b)–(d). (f) The sum of (c) and (d).

Citation: Journal of Climate 36, 24; 10.1175/JCLI-D-22-0937.1

Fig. 2.
Fig. 2.

(a) Scatterplot of 100-yr subsamples in WACCM4_BKS_FU minus WACCM4_control. Each red dot represents one subsample. The horizontal axis is the Arctic (60°–90°N) H50 response, and the vertical axis is Eurasian T2m response (green box in Fig. 1). The black cross represents the 225-yr average. The black line is the regression line of the subsamples, and the correlation coefficient is displayed in the top right corner. (b) As in (a), but the horizontal axis represents the H500 response over the BKS (60°–90°N, 30°–150°E; yellow box in Fig. 1a).

Citation: Journal of Climate 36, 24; 10.1175/JCLI-D-22-0937.1

The correlation in Fig. 2 represents the covariability of T2m and atmospheric circulation across the subsamples. The spread of subsamples is due to internal variability. We find that the linear relationship is not sensitive to the subsample size (see discussion below), suggesting that T2m and tropospheric circulation are correlated in both the forced response and internal variability. We use the 225-yr mean circulation response (in which internal variability is largely removed by averaging) and apply the linear relationship to estimate the sea ice–forced T2m response associated with the tropospheric and stratospheric circulation. A two-step linear regression method is applied: we first regress the T2m response and tropospheric geopotential height response onto stratospheric geopotential height response using the 10 000 100-yr subsamples:
ΔT2m̂=aΔH50Arctic+g,
ΔH500BKŜ=dΔH50Arctic+h,
where ΔT2m is the T2m response at any grid point, ΔH50Arctic is the Arctic H50 response, and ΔH500BKS is the BKS H500 response. The hat symbol means regression. Then, after removing the stratospheric influence, we regress the T2m onto the tropospheric geopotential height response,
(ΔT2m−aΔH50Arctic)̂=b(ΔH500BKS−dΔH50Arctic)+c.
Thus, T2m response to sea ice loss at any grid point could be estimated by
ΔT2m¯=aΔH50Arctic¯+b(ΔH500BKS¯−dΔH50Arctic¯)+c+ϵ.
Here, the overbars mean averaging over 225 years. The coefficient a is the regression coefficient between ΔT2m and ΔH50Arctic, while d is the regression coefficient between ΔH500BKS and ΔH50Arctic. Coefficients b and c are the regression coefficient and intercept obtained from the second step of the regression. Thus, a represents the contribution due to stratospheric dynamics; b represents the contribution due to tropospheric dynamics that is uncoupled with stratospheric dynamics; c represents the T2m response in the absence of tropospheric and stratospheric dynamics. The error term ϵ is very small and can be ignored.

The linear regression estimates of T2m response due to (aΔH50Arctic¯) and tropospheric b(ΔH500BKS¯−dΔH50Arctic¯) dynamics, and the intercept c are shown in Figs. 1b–d. The combination of the three terms (Fig. 1e) is almost identical to the total T2m response (Fig. 1a), confirming that the error term ϵ is relatively small. Most of the cooling signal over the Eurasian region (green box in Fig. 1a) comes from the tropospheric dynamics (Fig. 1c). The stratosphere-related cooling signal (Fig. 1b) is over Siberia, to the north of the significant cooling signal in Fig. 1a. The stratospheric induced cooling signal is overwhelmed by the warming related to the intercept term c (Fig. 1d), which is interpreted as the tropospheric thermodynamics term, representing the local warming induced by sea ice loss, in the absence of circulation responses, that spreads into the subarctic latitudes by advection of transient eddies, primarily in the meridional direction [see appendix A; similar interpretation as in Screen (2017b)]. This is consistent with Deser et al. (2010), who performed a similar heat budget analysis and found the warming over the high-latitude continents due to Arctic sea ice loss is mostly driven by advection of submonthly transient atmospheric motions. The cancellation of dynamical cooling and thermodynamical warming has been revealed by Screen (2017b), as dynamical cooling over Europe related to negative North Atlantic Oscillation (NAO) promoted by reduction of Arctic sea ice is balanced by thermodynamical warming. Chripko et al. (2021), who implemented the dynamical adjustment method to separate T2m response due to Arctic sea ice loss into dynamical and residual components, also showed that there is a cancellation between dynamical cooling and thermodynamical warming over Eurasia.

The large spread of Eurasian T2m response for 100-member subsamples (Fig. 2a), which ranges from −0.9 to 0.5 K, is consistent with previous studies (section 1) that 100 members are insufficient to robustly detect remote responses to sea ice forcing. We show in appendix B that 225 members should be sufficient to detect a robust signal (at least for the sign). The regression method shows the cooling is driven by the tropospheric and stratospheric dynamics, while tropospheric thermodynamics leads to warming. By combining the tropospheric dynamics and thermodynamics, as the thermodynamic warming cancels much of the cooling, the net contribution to the cooling of the two tropospheric processes is 30% (Fig. 1f; averaged over the box), weaker than that from stratospheric processes (70%). This is broadly consistent with Zhang et al. (2018a) and Xu et al. (2021), who found that stratospheric processes contribute more to the cooling than tropospheric processes from nudging experiments with BKS SIC forcing in WACCM4.

We estimate the uncertainty of the regression coefficients in the subsample method (Fig. 3) for different sizes (number of years) of each subsample (x axis) and different total counts of subsamples (different colors). The uncertainty is obtained by repeating the random selection of the subsamples (for a certain size and a certain total count) 1000 times. When the subsample size equals 1 and the total subsample count is 225, the regression is across the year-to-year response (perturb run minus control run) among the ensemble members. For regression between Arctic H50 and Eurasian T2m (Fig. 3a), as well as between BKS H500 and Eurasian T2m (Fig. 3b), it is clear that when the subsample count is larger (darker color), the uncertainty greatly reduces, while the uncertainty is not sensitive to the size of each subsample (x axis; from 1 to 100). Thus, we obtain the regression coefficient by selecting 10 000 100-yr subsamples, as it shows smaller uncertainty. We also repeat the analysis by using H500 over the entire Arctic (60°–90°N) instead of over the BKS (not shown), and the two-step regression results are not sensitive to whether the tropospheric circulation response is averaged over the BKS or the entire Arctic. Using H100 (100-hPa geopotential height) instead of H50 to represent the stratospheric response in the regression method also displays similar results (not shown).

Fig. 3.
Fig. 3.

(a) Regression coefficient between Eurasian T2m and Arctic H50. The horizontal axis represents the size of each subsample. The box plots represent the uncertainty of the regression coefficient for different sizes of each subsample and different counts of subsamples. Different colors represent different total counts of subsamples. When the subsample size equals 1 and the total subsample count is 225, the regression is across the year-to-year response between the control run and the perturb run ensemble members (nonrepetitive selection of the 225 years). (b) As in (a), but for the regression coefficient between Eurasian T2m and BKS H500. The scale of the vertical axis is different between (a) and (b).

Citation: Journal of Climate 36, 24; 10.1175/JCLI-D-22-0937.1

b. WACCM6

Similar experiments with BKS forcing using the latest version of WACCM6 are performed. The T2m response from the 200-yr WACCM6 experiments using the SIC and SST forcing taken from CESM1-WACCM4 (CMIP5 forcing), which has very similar forcing as the WACCM4 experiments in section 3a, is shown in Fig. 4a. There is no cooling signal over Eurasia. All other WACCM6 experiments show little or no cooling signals over Eurasia, including WACCM6 experiments with CESM2-WACCM6 (CMIP6) forcing (Fig. S1a in the online supplemental material), as well as idealized SIC experiments from 1% to 90% (Figs. S1b–g). We apply the two-step linear regression method to understand the WACCM6 results. The decomposition of WACCM6_CESM1_BKS_FU minus WACCM6_CESM1_control (Fig. 4a) is shown in Figs. 4b–d. Similar to WACCM4, the stratospheric and tropospheric dynamics (Figs. 4b,c) generate cooling signals. However, the eddy advection term (Fig. 4d) displays warming which extends more equatorward than that in WACCM4 (Fig. 1d), which cancels the cooling induced by the tropospheric circulation, resulting in very little cooling over Eurasia (Fig. 4e). Similar strong warming driven by tropospheric thermodynamics is also found in other WACCM6 experiments. This discrepancy in WACCM4 and WACCM6 (even with very similar forcing) highlights that the Eurasian cooling signal could be sensitive to internal variability and/or model physics, which will be further explored in section 4 using the PAMIP models. One possible reason leading to this discrepancy in model physics is that high-latitude temperature biases are much improved (Simpson et al. 2022) due to better representation of high-latitude snow cover in CESM2 (WACCM6) than CESM1 (WACCM4). However, more experiments are required to test this, and pinpointing the exact mechanism in model physics for the discrepancy is beyond the scope of this study. Despite different net T2m responses in WACCM4 and WACCM6 with similar forcing, each term from the decomposition shows consistent sign over the Eurasian region; that is, the stratospheric dynamics and tropospheric dynamics terms show cooling in both WACCM4 and WACCM6, and the tropospheric thermodynamics term shows warming in both models. We will explore whether the sign of each term is still consistent in the PAMIP models.

Fig. 4.
Fig. 4.

(a) As in Fig. 1a, but for WACCM6_CESM1_BKS_FU minus WACCM6_CESM1_control. (b)–(e) As in Figs. 1b–e, but for WACCM6_CESM1_BKS_FU minus WACCM6_CESM1_control.

Citation: Journal of Climate 36, 24; 10.1175/JCLI-D-22-0937.1

Although the BKS region is defined differently in WACCM4 and WACCM6, it is very unlikely that this influences the conclusions we draw from WACCM4 and WACCM6. Comparing the definitions of the BKS region in WACCM4 (70°–82°N, 15°–100°E) and WACCM6 (65°–80°N; 30°–90°E), since there is little sea ice between 65° and 70°N within the BKS region, the WACCM4 definition corresponds to more sea ice loss, as it covers a larger area than in WACCM6. Thus, if the WACCM4 BKS region were used in WACCM6, the sea ice forcing would be larger than that in WACCM6. Larger sea ice forcing would result in larger thermodynamic warming and warmer Eurasian temperature response in WACCM6 (see discussion below related to Fig. 5). Therefore, the conclusions will not change if the BKS region were defined differently in WACCM6.

Now we explore the robustness of circulation and T2m response (Fig. 5) to different magnitudes of forcing (from 1% to 90%) using the idealized SIC experiments with WACCM6. In appendix B, we show that in these experiments with large sea ice forcing, 200 members in WACCM6 are sufficient to detect a robust signal. To understand different contributions to Eurasian T2m response, we also decompose the response using the two-step regression method. For tropospheric circulation response ΔH500BKS¯ (Fig. 5a), stronger forcing leads to a larger response; however, this is not always true for stratospheric circulation response ΔH50Arctic¯, as the idealized 60% SIC experiment shows the weakest stratospheric response. All the experiments show weak but robust warming signals over Eurasia (Fig. 5b), with a small spread (about 0.2 K) across the experiments. The cooling driven by stratospheric dynamics is weak. As the stratospheric-driven cooling signal scales with ΔH50Arctic¯, it is not surprising that stronger forcing does not always lead to stronger cooling driven by stratospheric dynamics. The cooling driven by tropospheric dynamics is well correlated with the magnitude of forcing (statistically significant at 99%). However, the cooling is overwhelmed by the warming driven by tropospheric thermodynamics, which in general is stronger when the forcing is larger. Although both tropospheric dynamics and tropospheric thermodynamics terms are highly correlated with the magnitude of forcing, the correlated component largely cancels when the two terms are combined together. Thus, the total T2m response is less correlated with the magnitude of forcing than either of the tropospheric terms (i.e., stronger forcing does not always lead to stronger net T2m response). Currently, it is unclear whether the true net T2m response does not entirely scale with the magnitude of forcing linearly, or the signal is conflated with internal variability due to limited ensemble members.

Fig. 5.
Fig. 5.

(a) Arctic (60°–90°N) H50 response and BKS (60°–90°N, 30°–150°E) H500 response for different magnitudes of idealized SIC forcing. The vertical axis represents the magnitude of SIC forcing. The horizontal axis represents the geopotential height response. (b) As in (a), but for Eurasian T2m response for different magnitudes of idealized SIC forcing. Each row represents the contribution from different terms in Eq. (1).

Citation: Journal of Climate 36, 24; 10.1175/JCLI-D-22-0937.1

4. Response to Arctic SIC decrease in PAMIP simulations

a. Response in Eurasian T2m and tropospheric and stratospheric circulations

The Eurasian T2m responses in the uncoupled PAMIP experiments, specifically FU_BKS versus PD (only differs in BKS SIC and SST), FU_ARC versus PD (only differs in Arctic SIC and SST, future versus present day), and PD versus PI_ARC (only differs in Arctic SIC and SST, present day versus preindustrial), are analyzed in this section. Given the inconsistency in Eurasian T2m responses between WACCM4 and WACCM6 (section 3), it can be better tested in PAMIP models as different models share the same sea ice forcings. The multimodel mean of T2m responses is displayed in Fig. 6. There is little cooling signal over Eurasia, apart from a very small patch of cooling in FU-ARC minus PD (Fig. 6b). The sign agreement (hashed; representing at least 80% of models agree on the sign) shows that models only agree with the high-latitude warming forced by sea ice loss. The low sign agreement for T2m response over the midlatitude continents shows that the midlatitude T2m response is not robust across models. The T2m responses of each individual model are shown in Figs. S2–S4.

Fig. 6.
Fig. 6.

(a) Multimodel mean of T2m response for FU_BKS minus PD. The hashed regions represent where 80% of the models have the same sign. (b),(c) As in (a), but for FU_ARC minus PD, and PD minus PI_ARC, respectively.

Citation: Journal of Climate 36, 24; 10.1175/JCLI-D-22-0937.1

We averaged the Eurasian T2m response (Fig. 7a) over the same area (boxes in Fig. 6) as in section 3. Note that this region captures the cooling driven by tropospheric dynamics using the two-step regression method (the same method as in section 3a but with 10 000 50-yr subsamples; not shown). For all models and experiments, the Eurasian T2m response is weak as the amplitude is generally less than 0.5 K, with only 5 out of 29 cases reaching the 90% statistical confidence level (Student’s t test; filled). Within each set of scenarios, there is no sign agreement across the models. Moreover, when comparing FU_ARC minus PD and PD minus PI_ARC within the same model, 6 of 10 models have the opposite sign. The disparity in the amplitude and sign of the Eurasian T2m response within the same model is likely due to internal atmospheric variability (as some model experiments only have 100 members), as well as the potential sensitivity to forcing amplitudes and spatial patterns.

Fig. 7.
Fig. 7.

(a) Eurasian T2m response averaged over the green box in Fig. 6 in PAMIP model simulations. Each marker represents one model. Filled markers represent the response is statistically significant at 90% level from the results of the Student’s t test. Each row represents one boundary forcing setup. The triangles, squares, and circles represent that for the two experiments being compared in one model, at least one of the experiments has only 100, 200, or 300 members, respectively. (b),(c) As in (a), but for the H50 response in the Arctic and H500 response over the BKS region.

Citation: Journal of Climate 36, 24; 10.1175/JCLI-D-22-0937.1

The stratospheric polar vortex response in these PAMIP simulations (Fig. 7b), though mostly positive, is only statistically significant in 7 of the 29 cases. The tropospheric circulation response in BKS (Fig. 7c) is positive and statistically significant in most cases. Within each set of scenarios, the response in tropospheric and stratospheric circulation has a substantial spread across the models. The results are consistent with Smith et al. (2022) that there is a weak but robust tropospheric circulation response in PAMIP simulations to Arctic sea ice loss, while the stratospheric response is more divergent. Due to the limited number of models, it is difficult to conclude whether different ensemble sizes influence the distribution of the model response in Fig. 7.

For BKS SIC loss, no model has a significant cooling signal in Eurasia (Fig. 7a. In addition, although at least 7 of 8 PAMIP models are “high-top” models with a well-resolved stratosphere (with the exception of CanESM5; Table 2), only 2 of 8 models have a significant stratospheric response (Fig. 7b), showing that the stratospheric pathway is likely not robust across different models. As discussed in section 2, the FU_BKS versus PD experiments in PAMIP (2°C warming above the preindustrial climate) have a weaker sea ice forcing than our WACCM BKS perturbation experiments in section 3 (differences between the end of twenty-first century in the high emission scenario and the end of twentieth century) and the BKS region boundaries are also different between WACCM and PAMIP; thus, these experiments might not be compared directly. In addition, CESM1-WACCM-SC in PAMIP is the same model as WACCM4 in section 3; however, this model does not have a significant Eurasian T2m response (Fig. 7a). Possible reasons for the discrepancy between the two WACCM4 model responses include 1) the fact that the BKS SIC forcing and background SST are different in CESM1-WACCM-SC and our own WACCM simulations (see section 2) and 2) the relatively small ensemble size of the FU_BKS in CESM1-WACCM-SC (100 members). Comparing the regional BKS forcing to the future pan-Arctic forcing, the stratospheric response (Fig. 7b) is not significantly different between the two, although previous studies suggested that pan-Arctic forcing could induce a weaker stratospheric response than regional forcing due to destructive wave interference (Sun et al. 2015; McKenna et al. 2018).

Out of the 40 uncoupled PAMIP model simulations, 18 simulations only have 100 winters (Table 2), which are insufficient for a robust midlatitude response due to internal variability (sections 1, 3a, and 5). Therefore, the intermodel and interexperiment differences discussed above could be largely due to internal variability rather than just differences in model physics or forcing. This will be further explored in section 4b.

b. What contributes to the T2m response over Eurasia?

In section 3, we show that the inconsistent Eurasian temperature response due to sea ice loss across WACCM4 and WACCM6 likely rises from different magnitudes of eddy advection of warming, with the two-step linear regression method. To better understand the spread of Eurasian temperature response in PAMIP models, we apply the same method with 10 000 50-yr subsamples for each PAMIP simulation and quantitatively estimate the contribution to Eurasian T2m response from the stratospheric dynamics, the tropospheric dynamics, and thermodynamics (Figs. 8a–c). The cooling signal from the stratospheric dynamics (aΔH50Arctic¯) is relatively small compared to the contribution from the tropospheric dynamics (bΔH500BKS¯), showing that most of the cooling signal is driven by the tropospheric circulation response, consistent with section 3. Similarly, the thermodynamic term leads to strong warming over Eurasia. All three terms (stratospheric dynamics, tropospheric dynamics, and tropospheric thermodynamics) show good sign agreement across models, suggesting a qualitative robustness in the three mechanisms. The intermodel spread of the stratospheric dynamics is small, likely due to weak stratospheric response (ΔH50Arctic¯), while much of the T2m spread comes from the tropospheric terms. The spread of tropospheric thermodynamics is slightly larger than that of the tropospheric dynamics except for PD minus PI_ARC (Fig. 8c). The intermodel correlation between tropospheric thermodynamics and Eurasian T2m response is higher than that between tropospheric dynamics and Eurasian T2m response in all different PAMIP sea ice forcing experiments (not shown), suggesting the dominant role of the spread of tropospheric thermodynamics.

Fig. 8.
Fig. 8.

(a) Eurasian T2m response (K) in FU_BKS minus PD and the contribution from different terms in Eq. (1). Each marker represents one model in PAMIP. Similar to Fig. 7, the triangles, squares, and circles represent that for the two experiments being compared in one model, at least one of the experiments has only 100, 200, or 300 members, respectively. Filled markers represent the total T2m response is statistically significant at 90% level from the results of Student’s t test. (b),(c) As in (a), but for FU_ARC minus PD, and PD minus PI_ARC, respectively. (d),(e) As in (a), but for coupled experiments pa_ArcSIC minus pa_pdSIC, and pa_pdSIC minus pa_piArcSIC, respectively. (f) Box plots of Eurasian T2m response and contribution from different terms for the models with at least 200 ensemble members in FU_ARC minus PD. The boxplot represents the distribution of the 10 000 200-yr subsamples randomly selected from each model ensemble. Note the scale of the x axis is different in different panels.

Citation: Journal of Climate 36, 24; 10.1175/JCLI-D-22-0937.1

To verify whether ocean coupling will change our conclusions derived above from AGCM simulations, four coupled models in PAMIP that perform Arctic-wide sea ice loss experiments from present-day to future (Fig. 8d, pa_pdSIC minus pa_futArcSIC) and from preindustrial sea ice to present-day sea ice (Fig. 8e, pa_piArcSIC minus pa_pdSIC) are analyzed by using similar methods. Similar to AGCM simulations, coupled experiments also show diverse and weak temperature responses over Eurasia, as models disagree on the sign of T2m response in Figs. 8d and 8e. Spatial patterns of T2m response are shown in Figs. S5 and S6. Consistent with AGCM simulations, all three terms (stratospheric dynamics, tropospheric dynamics, and tropospheric thermodynamics) show good sign agreement across models; both tropospheric (dynamics and thermodynamics) terms show large intermodel spread, especially in Fig. 8d. Thus, these results above are robust in both uncoupled and coupled simulations.

Is the intermodel spread due to internal variability or model physics? There are significant intermodel differences as the Eurasian T2m response in any model is significantly different from about half of the other models with the same forcing (Fig. S7). As discussed previously, for the remote response to sea ice loss, 100 ensemble members are found to be insufficient to provide robust results as internal variability is conflated with the forced signal. Thus, in Figs. 8a–c, for models with 100 ensemble members (crosses), we cannot determine whether the signal is due to forced response or internal variability. We focus on FUT_ARC minus PD (Fig. 8b), in which most of the models have at least 200 members (squares), and internal variability is expected to largely be averaged out. To further separate internal variability and model physics, we randomly select 10 000 200-yr subsamples from each model with more than 200 members (squares) in Fig. 8b and perform the two-step linear regression within each 200-yr subsample. The box plots in Fig. 8f show the distribution of the 10 000 200-yr subsamples, representing the uncertainty of T2m response due to internal variability for a 200-yr simulation. For the four models with more than 200 members (CESM1-WACCM-SC, CNRM-CM6-1, CanESM5, and HadGEM3-GC31-MM), the uncertainty boxes largely overlap, indicating it is difficult to separate differences due to model physics from internal variability. The Eurasian T2m responses in E3SM-1-0, IPSL-CM6A-LR, and NorESM2-LM are outside of the range of internal variability of other models in the tropospheric component (combining dynamics and thermodynamics). However, assuming the uncertainty ranges (box plot) for a 200-member ensemble of these three models (E3SM-1-0, IPSL-CM6A-LR, and NorESM2-LM, with only 200 members) are similar to the models with more than 200 members, if these three models also have 300 members, then the average of the 300 members could be 1) colder than the current 200-member average in Fig. 8d, meaning uncertainty boxes of these three models will likely overlap with other models, or 2) similar to or warmer than the current 200-member average, meaning the uncertainty range of these three models would have little overlap with other models. In scenario 2, we could conclude that internal variability is insufficient to explain the differences across the models, meaning differences in model physics must play an important role; however, in scenario 1, we still could not separate the role of model physics from internal variability. Currently, there are insufficient data to determine which scenario is true, meaning it is challenging to isolate differences due to model physics from internal variability.

5. Discussion and conclusions

We conclude by addressing the questions raised in section 1:

1) Is the Eurasian temperature response a robust signal across different models with the same Arctic sea ice forcing? Our results indicate that Eurasian cooling is not a robust signal across different models with the same Arctic sea ice forcing. The PAMIP models do not show consistent Eurasian temperature response to the same sea ice forcing; different versions of WACCM also show inconsistent Eurasian temperature response to BKS sea ice forcing, although the BKS forcing region is slightly different. The temperature response over Eurasia is weak and generally less than 0.5 K across different sea ice forcings and different models.

2) Is the Eurasian temperature response robust across different magnitudes of sea ice forcing with the same model? This is true in WACCM6, as different magnitudes of forcing lead to robust but weak warming signals with a small spread. Tropospheric dynamics and thermodynamics drive robust cooling and warming, respectively, which are highly correlated with the magnitude of the forcing. However, much of the signal that is correlated with the magnitude of the forcing in these two terms is canceled, accompanied by the low correlation between the stratospheric driven cooling and the magnitude of forcing, resulting in weak correlation between the magnitude of T2m response and the magnitude of forcing.

3) What physical mechanisms control the diverse Eurasian temperature response and its spread across models and forcings? Stratospheric dynamics contributes a robust but weak cooling signal. Tropospheric dynamics drives a robust and relatively larger cooling response over Eurasia across different models, while strong and robust warming driven by tropospheric thermodynamics (eddy advection of warming) largely cancels or overwhelms the cooling driven by stratospheric and tropospheric dynamics. Both tropospheric dynamics and thermodynamics show substantial spread across models, and the spread of these two terms does not cancel among the models, leading to large intermodel spread in Eurasian T2m response.

The model discrepancy in sea ice forced response could arise from differences in model physics (Screen and Blackport 2019) or internal variability (Chen et al. 2016). Even with 200 or 300 ensemble members in some PAMIP simulations, internal variability is still large in magnitude and likely obscures the response due to differences in model physics.

As discussed in previous studies (e.g., Peings et al. 2021; Streffing et al. 2021; Sun et al. 2022), 100 ensemble members are insufficient to detect a robust remote signal forced by sea ice loss within one single model. Here, we introduce a simple method (appendix B) from the signal-to-noise perspective to estimate the ensemble size required to detect a robust response in a single model. The method shows that the 225 members in WACCM4 and 200 members in WACCM6 are sufficient to detect a robust signal (at least in sign). In PAMIP, for models with a relatively large response (e.g., 0.2 K), 200–300 members are sufficient to detect a robust signal. If the forced response becomes smaller (e.g., around 0.1 K), a much larger ensemble size (more than 500) is required to robustly detect the signal, which is beyond the size of most PAMIP simulations currently.

Although the Eurasian T2m response in PAMIP models has little sign agreement (Figs. 5 and 6), the contribution from each individual term (stratospheric dynamics, tropospheric dynamics, and tropospheric thermodynamics) has good sign agreement across the models (Fig. 8). It is not surprising that the tropospheric thermodynamics term consistently drives warming across different models, as it is a direct response to the warming induced by sea ice loss. The sign and amplitude of the dynamics terms depend on the circulation response, as well as how Eurasian T2m responds to circulation changes in different models. The circulation response (H500 and H50) is positive in almost all model simulations (Figs. 7b,c), as has been discussed in Smith et al. (2022). The coefficients a and b in Eq. (1), which measure the covariability between Eurasian T2m and stratospheric or tropospheric circulation, both have good sign agreement over the Eurasian region across different models and forcings (not shown). This suggests similar dynamical T2m responses (at least in sign) across the models if the circulation response is the same. Thus, the good sign agreement in the tropospheric dynamics and stratospheric dynamics terms across different models results from the high sign agreement in circulation response, as well as the robustness in simulating the covariability between T2m and atmospheric circulation across different models.

Therefore, the uncertainty in the sign of Eurasian T2m response across different models does not come from the uncertainty in the sign of any individual term but rises from the competition/balance between thermodynamic warming and dynamical driven cooling. Both tropospheric dynamics and thermodynamics show large intermodel spread, and the spread of these two terms does not cancel across the models, resulting in diverse model responses in Eurasian temperature. For example, in Fig. 8a, models with strong thermodynamic warming may have weak dynamic cooling (IPSL-CM6A-LR), while models with weak thermodynamic warming may have strong dynamic cooling (HadGEM3-GC31-MM), resulting in large uncertainty in the sign of Eurasian T2m response. These conclusions are robust in both uncoupled AGCM simulations and coupled simulations. How differences in model physics cause the different magnitude of thermodynamic warming, circulation response, and associated dynamical cooling across different models can be explored in future studies if the model ensemble size becomes large enough to isolate the role of model physics from internal variability.

In terms of the nonlinear T2m response to the different magnitudes of sea ice forcing reported by previous studies (Semenov and Latif 2015; Petoukhov and Semenov 2010; Chen et al. 2021; Zhang and Screen 2021), we do not find strong nonlinearity in our idealized sea ice forcing experiments in WACCM6. Possible reasons include the following. 1) As different models respond differently to the sea ice loss, some models may present a nonlinear response to different magnitudes of sea ice forcing. 2) The nonlinear response concluded in some studies (Semenov and Latif 2015; Petoukhov and Semenov 2010) is from simulations with limited ensemble size (50 or 100 members), meaning internal variability could be conflated with the true forced signal. In Zhang and Screen (2021), the nonlinear response comes from the autumn sea ice loss which modulates winter Eurasian temperature through the stratospheric pathway. This is consistent with our results in WACCM6 that the stratospheric dynamics term suggests a possible nonlinear response despite its small magnitude. Whether the linearity of the response depends on the models can be explored in future studies.

We reach similar conclusions in both coupled and uncoupled experiments in terms of Eurasian temperature response and its physical mechanism. This is consistent with Screen and Blackport (2019) pointing out that there is no evidence suggesting coupled simulations with interactive ocean would simulate a stronger Eurasian cooling (Deser et al. 2016; Smith et al. 2017; Collow et al. 2018; Sun et al. 2018). By comparing coupled and uncoupled simulations with identical sea ice forcing in one model, some studies (Deser et al. 2016; Peings et al. 2021) found that coupled simulations display a stronger Arctic warming from the surface to mid-to-upper troposphere, due to local oceanic feedbacks and remote responses (Blackport and Kushner 2018). The stronger and deeper Arctic warming in the coupled simulation could intensify the thermodynamic warming that is transported into the midlatitudes, as well as the dynamical cooling as deeper and stronger warming results in larger circulation response (He et al. 2020; Labe et al. 2020), which drives more cooling over Eurasia. However, it is not clear that dynamical cooling and thermodynamical warming are necessarily stronger in the coupled simulations than in the uncoupled simulations (Fig. 8), possibly due to small ensemble sizes and limited number of models in coupled simulations. Future studies can further explore the balance between thermodynamic warming and dynamical cooling when coupled simulations are available in more models with larger ensemble sizes.

Acknowledgments.

C. Z., Y. W., and M. T. acknowledge the support from NSF Award OPP-1825858 and NASA Award 80NSSC20K1254. C. Z. and Y. W. also acknowledge the support from NSF Award AGS-2220948. Computing and data storage resources, including the Cheyenne supercomputer, were provided by NCAR’s Computational and Information Systems Laboratory, which is sponsored by NSF. We thank four anonymous reviewers for their constructive comments to improve this study. C.Z. is also thankful for the constructive discussions with Dr. Peter Yu Feng Siew.

Data availability statement.

PAMIP model data are available in the CMIP6 data archive (https://esgf-node.llnl.gov/projects/cmip6/). Winter seasonal mean data of selected variables (including H50, H500, and T2m) of the WACCM6 simulations are available in the Columbia University Academic Commons (https://doi.org/10.7916/nygt-mb09). Other variables or higher temporal frequency data will be available upon request.

APPENDIX A

Interpretation of the Intercept Term

To better understand the intercept term c, we apply the potential temperature tendency equation on daily data at the second lowest model level,
∂θ∂t=−u∂θ∂x−υ∂θ∂y−ω∂θ∂p+Res(diabatic),
where θ is potential temperature and u, υ, and ω are zonal, meridional, and vertical velocity on pressure coordinates. The residual term consists of the diabatic and diffusion terms, as well as any errors due to using daily data to estimate the first three terms on the rhs of the equation. For temperature and wind, one can separate them into the time-mean component and daily variations during winter (DJF), for example,
u=u¯+u′
where the overbar represents the time mean (averaged over all days in all winters within one model experiment) and the prime represents the daily deviations from the time mean. Then, the time-mean potential temperature tendency equation can be written as
∂θ∂t¯=−(u¯∂θ∂x¯+υ¯∂θ∂y¯+ω¯∂θ∂p¯)−(u′∂θ′∂x+υ′∂θ′∂y+ω′∂θ′∂p)+Res(diabatic).
Then, on the rhs of the equation, the first term represents the contribution from the time-mean flow and the second term represents the contribution from daily variations (mostly transient eddies). Note that the lhs of the equation is a small term (i.e., climatological temperature difference between 1 December and 1 March divided by 90 days), compared with any of the three terms on the rhs. Thus, ∂θ¯/∂t≈0, and the terms on the rhs of the equation are almost balanced. As an example, if temperature advection drives warming in a region, the enhanced longwave radiative cooling will damp the warming, resulting in very small total temperature tendency in a long-term average.
For the control and perturbation experiment, one can apply the potential temperature equation and calculate the difference in the temperature tendency in the two experiments:
∂θp∂t¯−∂θc∂t¯=−(up¯∂θp∂x¯−uc¯∂θc∂x¯+υp¯∂θp∂y¯−υc¯∂θc∂y¯+ωp¯∂θp∂p¯−ωc¯∂θc∂p¯)−(up′∂θp′∂x−uc′∂θc′∂x+υp′∂θp′∂y−υc′∂θc′∂y+ωp′∂θp′∂p−ωc′∂θc′∂p) +(Resp¯−Resc¯),
where p represents the perturbation experiment and c represents the control experiment. As discussed above, since ∂θ¯/∂t≈0, (∂θp¯/∂t)−(∂θc¯/∂t) will be close to zero and will not resemble the pattern of θp¯−θc¯ (similar to Fig. 1a). Thus, the equation above cannot explain the temperature response due to sea ice forcing in Fig. 1a, since any forcing in one term on the rhs of the equation will be damped by the other terms. However, if any term on the rhs of the equation resembles the spatial pattern of temperature response, it suggests that this term probably is the driver of the temperature response, while other terms would respond to this term and damp the tendency. The three terms on the rhs of the equation for WACCM4_BKS_FU minus WACCM4_control are shown in Figs. A1a–c. The spatial pattern of the transient eddy term (Fig. A1b) resembles the pattern of the intercept term c (Fig. 1d) well. Thus, we interpret the intercept term c as advection of the warming by transient eddies. Note that in Eq. (1), the regression parts aΔH50Arctic¯ and b(ΔH500BKS¯−dΔH50Arctic¯) represent how temperature response is related to time-mean circulation response, while the intercept term c can be considered as the residual of the two-step regression, which is likely unrelated to the time-mean circulation response. Thus, it is not surprising that the intercept term c should be highly connected with the transient eddy term. Most of the warming in the eddy advection term (Fig. A1b) over the Eurasian continent comes from its meridional component (Fig. A1d), which is consistent with Deser et al. (2010).
Fig. A1.
Fig. A1.

Potential temperature tendency equation difference averaged over winter between WACCM4_BKS_FU and WACCM4_control: (a) time-mean term, (b) transient eddy term, (c) residual term, and (d) meridional component of the transient eddy term (all units in K day−1).

Citation: Journal of Climate 36, 24; 10.1175/JCLI-D-22-0937.1

APPENDIX B

A Method to Estimate the Ensemble Size Required to Detect a Robust Response in a Single Model

As discussed above and in previous studies (e.g., Peings et al. 2021), 100 ensemble members are insufficient to detect a robust remote signal forced by sea ice loss within one single model. Here, we introduce a simple method to estimate the ensemble size required to detect a robust response in a single model and discuss whether the ensemble sizes in the WACCM and PAMIP simulations are sufficient to robustly detect the signal.

This problem can be considered as a signal-to-noise ratio problem; that is, to detect a robust response, the magnitude of the true response forced by sea ice (signal) needs to be larger than the magnitude of the climate noise due to internal variability. For a given variable (e.g., temperature, geopotential height), the differences between the forced experiment and the control experiment for one single ensemble member can be written as ΔX = ΔX˜+ΔX′, where ΔX˜ is the true forced response and ΔX′ is the noise due to internal variability. The distribution of ΔX′ has an average of zero, and we write its standard deviation as σX. Then, for an N-member simulation, the ensemble mean difference between the forced experiment and the control experiment is [ΔX]N=ΔX˜+[ΔX]′N, where [ΔX]′N is the noise due to internal variability for an N-member experiment. From the central limit theorem, [ΔX]′N has a normal distribution and its standard deviation is σN=σX/N. To detect a robust signal, one could require the magnitude of the forced signal ΔX˜ to be larger than the magnitude of the noise σN, say |ΔX|˜>kσN, where k is the required signal-to-noise ratio. Since σN=σX/N, the requirement above can be written as
N>(kσX|ΔX˜|)2,
which is the ensemble size (N) required to detect a forced signal which has a magnitude of |ΔX˜|, for a signal-to-noise ratio of k, when the differences between the forced experiment and the control experiment have an intermember standard deviation σX. The equation above is very similar to that used in Screen et al. (2014) and Labe (2020) to estimate the ensemble size required to robustly detect the response force by sea ice, despite different approaches to derive the equation. Compared with the studies mentioned above, we use a slightly different method to estimate the intermember spread due to internal variability, and we will explore the equation above with flexible signal-to-noise ratio k, which is fixed in previous studies.

We can use all the experiments (WACCM and PAMIP) in this study to estimate σX (Table S1) for Eurasian temperature response. For most of the models and experiments, σX is around 2.0–2.5 K, except for FGOALS-f3-L (around 3 K). In Fig. B1, we plot the required ensemble size N (x axis) to detect a forced signal with a magnitude of |ΔX˜| (y axis), when σX = 2.0 K (dashed lines) and σX = 2.5 K (solid lines). We also plot three selected signal-to-noise ratios k = 1 (red), k = 1.5 (orange), and k = 2.0 (blue), which means there is a 15.9%, 6.7%, and 2.3% chance, respectively, that the N-member ensemble mean has an opposite sign of the true forced signal. Due to the quadratic relationship between N and |ΔX˜|, to detect a small, forced signal (e.g., 0.1 K), a very large ensemble size is required (beyond 500 members). For the WACCM4 experiments (σX ∼ 2.0 K; dashed lines), the ensemble mean response is around −0.2 K (Fig. 2a). Assuming the 225-yr ensemble mean is the true forced response (0.2 K), a 225-yr simulation can reach k = 1.5 (meaning about 93% chance that the sign of the ensemble mean is correct); thus, the detected response is likely robust. But for a 100-member simulation, the signal-to-noise ratio k is about 1, resulting in substantial probability that the ensemble mean of a 100-member simulation has an opposite sign to the true forced response. For the 200-member WACCM6 experiments (σX ∼ 2.0 K; dashed lines), the ensemble mean signal is above 0.3 K (Fig. 5b) with large sea ice forcing, which have a signal-to-noise ratio larger than 2 in Fig. B1, suggesting a robust signal with a 200-member simulation. Most of the PAMIP experiments have a Eurasian T2m response less than 0.3 K (Fig. 7a). From Fig. B1, such magnitude of response would result in the signal-to-noise ratio k to be less than 1.5 for a 100-member simulation, meaning 100 members may not be sufficient to obtain a robust response in these simulations. For a 0.2-K response, 200–300 members (e.g., in PAMIP) are sufficient to reach a 1.5 signal-to-noise ratio, meaning the signal detected is likely robust. As discussed above, if the forced response becomes even smaller (e.g., around 0.1 K), a much larger ensemble size is required to robustly detect the signal, which is beyond the size of PAMIP simulations used in this study.

Fig. B1.
Fig. B1.

Estimated ensemble size (N; x axis) required to detect a forced response with a specific magnitude of T2m response (y axis) over Eurasia, for the required signal-to-noise ratio k = 2.0, 1.5, and 1.0 (blue, orange, and red), respectively. The solid lines represent the standard deviation of intermember Eurasian T2m response σX = 2.5 K, and the dashed lines represent σX = 2.0 K.

Citation: Journal of Climate 36, 24; 10.1175/JCLI-D-22-0937.1

Therefore, the 225 members in WACCM4 and 200 members in WACCM6 are sufficient to detect a robust signal (at least in sign). In PAMIP, for models with a relatively large response (e.g., 0.2 K), 200–300 members are sufficient to detect a robust signal. The method above could be applied to estimate the ensemble size required to robustly detect signals of different variables in climate model simulations.

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  • Blackport, R., and P. J. Kushner, 2018: The role of extratropical ocean warming in the coupled climate response to Arctic sea ice loss. J. Climate, 31, 9193–9206, https://doi.org/10.1175/JCLI-D-18-0192.1.

    • Search Google Scholar
    • Export Citation

  • Blackport, R., J. A. Screen, K. van der Wiel, and R. Bintanja, 2019: Minimal influence of reduced Arctic sea ice on coincident cold winters in mid-latitudes. Nat. Climate Change, 9, 697–704, https://doi.org/10.1038/s41558-019-0551-4.

    • Search Google Scholar
    • Export Citation

  • Chen, H. W., F. Zhang, and R. B. Alley, 2016: The robustness of midlatitude weather pattern changes due to Arctic sea ice loss. J. Climate, 29, 7831–7849, https://doi.org/10.1175/JCLI-D-16-0167.1.

    • Search Google Scholar
    • Export Citation

  • Chen, X., D. Luo, Y. Wu, E. Dunn-Sigouin, and J. Lu, 2021: Nonlinear response of atmospheric blocking to early winter Barents–Kara Seas warming: An idealized model study. J. Climate, 34, 2367–2383, https://doi.org/10.1175/JCLI-D-19-0720.1.

    • Search Google Scholar
    • Export Citation

  • Chripko, S., R. Msadek, E. Sanchez-Gomez, L. Terray, L. Bessières, and M.-P. Moine, 2021: Impact of reduced Arctic sea ice on Northern Hemisphere climate and weather in autumn and winter. J. Climate, 34, 5847–5867, https://doi.org/10.1175/JCLI-D-20-0515.1.

    • Search Google Scholar
    • Export Citation

  • Cohen, J., and Coauthors, 2014: Recent Arctic amplification and extreme mid-latitude weather. Nat. Geosci., 7, 627–637, https://doi.org/10.1038/ngeo2234.

    • Search Google Scholar
    • Export Citation

  • Cohen, J., and Coauthors, 2020: Divergent consensuses on Arctic amplification influence on midlatitude severe winter weather. Nat. Climate Change, 10, 20–29, https://doi.org/10.1038/s41558-019-0662-y.

    • Search Google Scholar
    • Export Citation

  • Collow, T. W., W. Wang, and A. Kumar, 2018: Simulations of Eurasian winter temperature trends in coupled and uncoupled CFSv2. Adv. Atmos. Sci., 35, 14–26, https://doi.org/10.1007/s00376-017-6294-0.

    • Search Google Scholar
    • Export Citation

  • Deser, C., R. Tomas, M. Alexander, and D. Lawrence, 2010: The seasonal atmospheric response to projected Arctic sea ice loss in the late twenty-first century. J. Climate, 23, 333–351, https://doi.org/10.1175/2009JCLI3053.1.

    • Search Google Scholar
    • Export Citation

  • Deser, C., L. Sun, R. A. Tomas, and J. Screen, 2016: Does ocean coupling matter for the northern extratropical response to projected Arctic sea ice loss? Geophys. Res. Lett., 43, 2149–2157, https://doi.org/10.1002/2016GL067792.

    • Search Google Scholar
    • Export Citation

  • Gettelman, A., and Coauthors, 2019: The Whole Atmosphere Community Climate Model version 6 (WACCM6). J. Geophys. Res. Atmos., 124, 12 380–12 403, https://doi.org/10.1029/2019JD030943.

    • Search Google Scholar
    • Export Citation

  • He, S., X. Xu, T. Furevik, and Y. Gao, 2020: Eurasia cooling linked to the vertical distribution of Arctic warming. Geophys. Res. Lett., 47, e2020GL087212, https://doi.org/10.1029/2020GL087212.

    • Search Google Scholar
    • Export Citation

  • Kim, B.-M., S.-W. Son, S.-K. Min, J.-H. Jeong, S.-J. Kim, X. Zhang, T. Shim, and J.-H. Yoon, 2014: Weakening of the stratospheric polar vortex by Arctic sea-ice loss. Nat. Commun., 5, 4646, https://doi.org/10.1038/ncomms5646.

    • Search Google Scholar
    • Export Citation

  • Kim, B.-M., and Coauthors, 2017: Major cause of unprecedented Arctic warming in January 2016: Critical role of an Atlantic windstorm. Sci. Rep., 7, 40051, https://doi.org/10.1038/srep40051.

    • Search Google Scholar
    • Export Citation

  • Labe, Z., Y. Peings, and G. Magnusdottir, 2020: Warm Arctic, cold Siberia pattern: Role of full Arctic amplification versus sea ice loss alone. Geophys. Res. Lett., 47, e2020GL088583, https://doi.org/10.1029/2020GL088583.

    • Search Google Scholar
    • Export Citation

  • Labe, Z., 2020: The effects of Arctic sea-ice thickness loss and stratospheric variability on mid-latitude cold spells. Ph.D. dissertation, University of California, 158 pp., https://escholarship.org/uc/item/778982rr.

  • Matsumura, S., and Y. Kosaka, 2019: Arctic-Eurasian climate linkage induced by tropical ocean variability. Nat. Commun., 10, 3441, https://doi.org/10.1038/s41467-019-11359-7.

    • Search Google Scholar
    • Export Citation

  • McCusker, K. E., J. C. Fyfe, and M. Sigmond, 2016: Twenty-five winters of unexpected Eurasian cooling unlikely due to Arctic sea-ice loss. Nat. Geosci., 9, 838–842, https://doi.org/10.1038/ngeo2820.

    • Search Google Scholar
    • Export Citation

  • McKenna, C. M., T. J. Bracegirdle, E. F. Shuckburgh, P. H. Haynes, and M. M. Joshi, 2018: Arctic sea ice loss in different regions leads to contrasting Northern Hemisphere impacts. Geophys. Res. Lett., 45, 945–954, https://doi.org/10.1002/2017GL076433.

    • Search Google Scholar
    • Export Citation

  • Nakamura, T., K. Yamazaki, K. Iwamoto, M. Honda, Y. Miyoshi, Y. Ogawa, Y. Tomikawa, and J. Ukita, 2016: The stratospheric pathway for Arctic impacts on midlatitude climate. Geophys. Res. Lett., 43, 3494–3501, https://doi.org/10.1002/2016GL068330.

    • Search Google Scholar
    • Export Citation

  • Ogawa, F., and Coauthors, 2018: Evaluating impacts of recent Arctic sea ice loss on the Northern Hemisphere winter climate change. Geophys. Res. Lett., 45, 3255–3263, https://doi.org/10.1002/2017GL076502.

    • Search Google Scholar
    • Export Citation

  • Overland, J. E., K. R. Wood, and M. Wang, 2011: Warm Arctic–cold continents: Climate impacts of the newly open Arctic sea. Polar Res., 30, 15787, https://doi.org/10.3402/polar.v30i0.15787.

    • Search Google Scholar
    • Export Citation

  • Peings, Y., Z. M. Labe, and G. Magnusdottir, 2021: Are 100 ensemble members enough to capture the remote atmospheric response to +2°C Arctic sea ice loss? J. Climate, 34, 3751–3769, https://doi.org/10.1175/JCLI-D-20-0613.1.

    • Search Google Scholar
    • Export Citation

  • Petoukhov, V., and V. A. Semenov, 2010: A link between reduced Barents-Kara sea ice and cold winter extremes over northern continents. J. Geophys. Res., 115, D21111, https://doi.org/10.1029/2009JD013568.

    • Search Google Scholar
    • Export Citation

  • Screen, J. A., 2017a: Simulated atmospheric response to regional and pan-Arctic sea-ice loss. J. Climate, 30, 3945–3962, https://doi.org/10.1175/JCLI-D-16-0197.1.

    • Search Google Scholar
    • Export Citation

  • Screen, J. A., 2017b: The missing northern European winter cooling response to Arctic sea ice loss. Nat. Commun., 8, 14603, https://doi.org/10.1038/ncomms14603.

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  • <sc>Fig</sc>. 1.
    View in gallery
    Fig. 1.

    (a) T2m response (shading; K) in WACCM4_BKS_FU minus WACCM4_control. The hashed grid points reach statistical significance (FDR threshold). The contours show the H500 response. Contour interval is 5 gpm. Positive contours are represented by solid lines, and negative contours are represented by dashed lines. The zero contour is omitted. The green box (40°–60°N, 60°–135°E) shows the averaging region for the Eurasian T2m response. The yellow box (60°–90°N, 30°–150°E) shows the averaging region for the H500 response. (b) aΔH50Arctic¯ (K), the first term on the right-hand side of Eq. (1). (c),(d) As in (b), but for b(ΔH500BKS¯−dΔH50Arctic¯) and intercept c, the second and third terms on the right-hand side of Eq. (1), respectively. (e) The sum of (b)–(d). (f) The sum of (c) and (d).

  • <sc>Fig</sc>. 2.
    View in gallery
    Fig. 2.

    (a) Scatterplot of 100-yr subsamples in WACCM4_BKS_FU minus WACCM4_control. Each red dot represents one subsample. The horizontal axis is the Arctic (60°–90°N) H50 response, and the vertical axis is Eurasian T2m response (green box in Fig. 1). The black cross represents the 225-yr average. The black line is the regression line of the subsamples, and the correlation coefficient is displayed in the top right corner. (b) As in (a), but the horizontal axis represents the H500 response over the BKS (60°–90°N, 30°–150°E; yellow box in Fig. 1a).

  • <sc>Fig</sc>. 3.
    View in gallery
    Fig. 3.

    (a) Regression coefficient between Eurasian T2m and Arctic H50. The horizontal axis represents the size of each subsample. The box plots represent the uncertainty of the regression coefficient for different sizes of each subsample and different counts of subsamples. Different colors represent different total counts of subsamples. When the subsample size equals 1 and the total subsample count is 225, the regression is across the year-to-year response between the control run and the perturb run ensemble members (nonrepetitive selection of the 225 years). (b) As in (a), but for the regression coefficient between Eurasian T2m and BKS H500. The scale of the vertical axis is different between (a) and (b).

  • <sc>Fig</sc>. 4.
    View in gallery
    Fig. 4.

    (a) As in Fig. 1a, but for WACCM6_CESM1_BKS_FU minus WACCM6_CESM1_control. (b)–(e) As in Figs. 1b–e, but for WACCM6_CESM1_BKS_FU minus WACCM6_CESM1_control.

  • <sc>Fig</sc>. 5.
    View in gallery
    Fig. 5.

    (a) Arctic (60°–90°N) H50 response and BKS (60°–90°N, 30°–150°E) H500 response for different magnitudes of idealized SIC forcing. The vertical axis represents the magnitude of SIC forcing. The horizontal axis represents the geopotential height response. (b) As in (a), but for Eurasian T2m response for different magnitudes of idealized SIC forcing. Each row represents the contribution from different terms in Eq. (1).

  • <sc>Fig</sc>. 6.
    View in gallery
    Fig. 6.

    (a) Multimodel mean of T2m response for FU_BKS minus PD. The hashed regions represent where 80% of the models have the same sign. (b),(c) As in (a), but for FU_ARC minus PD, and PD minus PI_ARC, respectively.

  • <sc>Fig</sc>. 7.
    View in gallery
    Fig. 7.

    (a) Eurasian T2m response averaged over the green box in Fig. 6 in PAMIP model simulations. Each marker represents one model. Filled markers represent the response is statistically significant at 90% level from the results of the Student’s t test. Each row represents one boundary forcing setup. The triangles, squares, and circles represent that for the two experiments being compared in one model, at least one of the experiments has only 100, 200, or 300 members, respectively. (b),(c) As in (a), but for the H50 response in the Arctic and H500 response over the BKS region.

  • <sc>Fig</sc>. 8.
    View in gallery
    Fig. 8.

    (a) Eurasian T2m response (K) in FU_BKS minus PD and the contribution from different terms in Eq. (1). Each marker represents one model in PAMIP. Similar to Fig. 7, the triangles, squares, and circles represent that for the two experiments being compared in one model, at least one of the experiments has only 100, 200, or 300 members, respectively. Filled markers represent the total T2m response is statistically significant at 90% level from the results of Student’s t test. (b),(c) As in (a), but for FU_ARC minus PD, and PD minus PI_ARC, respectively. (d),(e) As in (a), but for coupled experiments pa_ArcSIC minus pa_pdSIC, and pa_pdSIC minus pa_piArcSIC, respectively. (f) Box plots of Eurasian T2m response and contribution from different terms for the models with at least 200 ensemble members in FU_ARC minus PD. The boxplot represents the distribution of the 10 000 200-yr subsamples randomly selected from each model ensemble. Note the scale of the x axis is different in different panels.

  • <sc>Fig</sc>. A1.
    View in gallery
    Fig. A1.

    Potential temperature tendency equation difference averaged over winter between WACCM4_BKS_FU and WACCM4_control: (a) time-mean term, (b) transient eddy term, (c) residual term, and (d) meridional component of the transient eddy term (all units in K day−1).

  • <sc>Fig</sc>. B1.
    View in gallery
    Fig. B1.

    Estimated ensemble size (N; x axis) required to detect a forced response with a specific magnitude of T2m response (y axis) over Eurasia, for the required signal-to-noise ratio k = 2.0, 1.5, and 1.0 (blue, orange, and red), respectively. The solid lines represent the standard deviation of intermember Eurasian T2m response σX = 2.5 K, and the dashed lines represent σX = 2.0 K.

Fig. 1.

(a) T2m response (shading; K) in WACCM4_BKS_FU minus WACCM4_control. The hashed grid points reach statistical significance (FDR threshold). The contours show the H500 response. Contour interval is 5 gpm. Positive contours are represented by solid lines, and negative contours are represented by dashed lines. The zero contour is omitted. The green box (40°–60°N, 60°–135°E) shows the averaging region for the Eurasian T2m response. The yellow box (60°–90°N, 30°–150°E) shows the averaging region for the H500 response. (b) aΔH50Arctic¯ (K), the first term on the right-hand side of Eq. (1). (c),(d) As in (b), but for b(ΔH500BKS¯−dΔH50Arctic¯) and intercept c, the second and third terms on the right-hand side of Eq. (1), respectively. (e) The sum of (b)–(d). (f) The sum of (c) and (d).
Fig. 2.

(a) Scatterplot of 100-yr subsamples in WACCM4_BKS_FU minus WACCM4_control. Each red dot represents one subsample. The horizontal axis is the Arctic (60°–90°N) H50 response, and the vertical axis is Eurasian T2m response (green box in Fig. 1). The black cross represents the 225-yr average. The black line is the regression line of the subsamples, and the correlation coefficient is displayed in the top right corner. (b) As in (a), but the horizontal axis represents the H500 response over the BKS (60°–90°N, 30°–150°E; yellow box in Fig. 1a).
Fig. 3.

(a) Regression coefficient between Eurasian T2m and Arctic H50. The horizontal axis represents the size of each subsample. The box plots represent the uncertainty of the regression coefficient for different sizes of each subsample and different counts of subsamples. Different colors represent different total counts of subsamples. When the subsample size equals 1 and the total subsample count is 225, the regression is across the year-to-year response between the control run and the perturb run ensemble members (nonrepetitive selection of the 225 years). (b) As in (a), but for the regression coefficient between Eurasian T2m and BKS H500. The scale of the vertical axis is different between (a) and (b).
Fig. 4.

(a) As in Fig. 1a, but for WACCM6_CESM1_BKS_FU minus WACCM6_CESM1_control. (b)–(e) As in Figs. 1b–e, but for WACCM6_CESM1_BKS_FU minus WACCM6_CESM1_control.
Fig. 5.

(a) Arctic (60°–90°N) H50 response and BKS (60°–90°N, 30°–150°E) H500 response for different magnitudes of idealized SIC forcing. The vertical axis represents the magnitude of SIC forcing. The horizontal axis represents the geopotential height response. (b) As in (a), but for Eurasian T2m response for different magnitudes of idealized SIC forcing. Each row represents the contribution from different terms in Eq. (1).
Fig. 6.

(a) Multimodel mean of T2m response for FU_BKS minus PD. The hashed regions represent where 80% of the models have the same sign. (b),(c) As in (a), but for FU_ARC minus PD, and PD minus PI_ARC, respectively.
Fig. 7.

(a) Eurasian T2m response averaged over the green box in Fig. 6 in PAMIP model simulations. Each marker represents one model. Filled markers represent the response is statistically significant at 90% level from the results of the Student’s t test. Each row represents one boundary forcing setup. The triangles, squares, and circles represent that for the two experiments being compared in one model, at least one of the experiments has only 100, 200, or 300 members, respectively. (b),(c) As in (a), but for the H50 response in the Arctic and H500 response over the BKS region.
Fig. 8.

(a) Eurasian T2m response (K) in FU_BKS minus PD and the contribution from different terms in Eq. (1). Each marker represents one model in PAMIP. Similar to Fig. 7, the triangles, squares, and circles represent that for the two experiments being compared in one model, at least one of the experiments has only 100, 200, or 300 members, respectively. Filled markers represent the total T2m response is statistically significant at 90% level from the results of Student’s t test. (b),(c) As in (a), but for FU_ARC minus PD, and PD minus PI_ARC, respectively. (d),(e) As in (a), but for coupled experiments pa_ArcSIC minus pa_pdSIC, and pa_pdSIC minus pa_piArcSIC, respectively. (f) Box plots of Eurasian T2m response and contribution from different terms for the models with at least 200 ensemble members in FU_ARC minus PD. The boxplot represents the distribution of the 10 000 200-yr subsamples randomly selected from each model ensemble. Note the scale of the x axis is different in different panels.
Fig. A1.

Potential temperature tendency equation difference averaged over winter between WACCM4_BKS_FU and WACCM4_control: (a) time-mean term, (b) transient eddy term, (c) residual term, and (d) meridional component of the transient eddy term (all units in K day−1).
Fig. B1.

Estimated ensemble size (N; x axis) required to detect a forced response with a specific magnitude of T2m response (y axis) over Eurasia, for the required signal-to-noise ratio k = 2.0, 1.5, and 1.0 (blue, orange, and red), respectively. The solid lines represent the standard deviation of intermember Eurasian T2m response σX = 2.5 K, and the dashed lines represent σX = 2.0 K.
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