The warm Arctic-cold North American pattern in CanESM5 large ensemble simulations: Eurasian in�uence and uncertainty due to internal variability

10 This study examines the warm Arctic-cold North American pattern (WACNA) and its 11 connection with the warm Arctic-cold Eurasia pattern (WACE) using ERA5 reanalysis and a 50-12 member ensemble of historical climate simulations produced by CanESM5, the Canadian model 13 participated in CMIP6. The results indicate that a negative WACE-like pattern usually precedes a 14 positive WACNA pattern by one month, and that negative Asian-Bering-North American (ABNA) 15 and Pacific-North American (PNA) like circulation patterns appear upstream and precede a 16 positive WACNA. The negative ABNA-like pattern can be attributed to anomalous heating in 17 southern Siberia, which is associated with the negative WACE pattern and its featured Eurasian 18 warming. The negative PNA-like pattern is influenced by negative SST anomalies in the tropical 19 Pacific, resembling tropical ENSO variability. Anomalous temperature advection in the lower 20 troposphere follows the circulation anomaly, which supports the formation of WACNA. 21 Conversely, processes with circulation anomalies of opposite sign result in a negative WACNA 22 pattern. The tropical ENSO variability does not significantly impact the WACNA pattern and its 23 linkage with WACE. CanESM5 simulates the WACNA pattern and WACE-WACNA connection 24 well, with differences mainly in the anomalous magnitude between model simulations and ERA5. 25 The uncertainty in the simulated WACNA pattern due to internal climate variability is dominated 26 by two modes of inter-member variability: a southeast-northwest phase shift and a local variation

On interannual timescales, a negative phase of WACE tends to precede a positive phase of WACNA by approximately 25 days (Yu and Lin, 2022).The WACNA pattern is driven by two primary sources: the decline in Siberian snow, which results in diabatic heating in the lower troposphere, and SST anomalies over the tropical central-eastern Pacific Ocean that resemble tropical El Niño-Southern Oscillation (ENSO) variability.The former drives a zonally oriented atmospheric teleconnection like the Asian-Bering-North American pattern (ABNA, Yu et al., 2016Yu et al., , 2018)), while the latter drives a tropical-extratropical teleconnection similar to the Pacific-North American pattern (PNA, Wallace and Gutzler, 1981).Both teleconnections contribute to the formation of the WACNA pattern.The WACE-WACNA linkage enhances our understanding of the evolution and formation of the WACNA pattern.However, the stability of this linkage over different periods and the potential impact of tropical ENSO variability on WACNA and the WACE-WACNA connection remain unclear.These are the questions to be addressed in this study using observational and reanalysis data, which will also serve as observational evidence for subsequent model verification.
Exploring simulations of the WACNA pattern and the WACE-WACNA connection in climate models, as well as the uncertainty of outcomes resulting from internal climate variability, is another intriguing topic.The single model initial-condition large ensemble (SMILE) simulation method has been widely used to address such issues in recent years.SMILE involves a suite of climate simulations driven by identical external forcings but with slightly different initial conditions within a given climate model (e.g., Deser et al. 2012;Wallace et al. 2014;Kay et al. 2015).Owing to the design, differences between individual SMILE realizations are solely attributed to internally generated climate variability.In this study, we examine the WACNA pattern in outputs from historical SMILE simulations conducted using the Canadian Earth System Model, version 5 (CanESM5).CanESM5 is a fully coupled ocean-atmosphere-land-sea ice climate model (Swart et al., 2019, and references therein) that was developed at the Canadian Centre for Climate Modelling and Analysis (CCCma) and participated in the Coupled Model Intercomparison Project Phase 6 (CMIP6).Specifically, we employ CanESM5 historical simulations to examine whether the model can reasonably capture the WACNA pattern and WACE-WACNA connection.Additionally, we explore the diversity of these results in the large ensemble simulation due to internal climate variability.These are important aspects of model verification and will support our further study on projected changes of WACNA using CanESM5 scenario simulations.
The rest of the paper is organized as follows.Section 2 describes the reanalysis and observational data, CanESM5 historical simulations, and analysis methods employed in this study.
In Section 3, we analyze the WACNA pattern using observational and reanalysis data, including its formation, the connection between WACE and WACNA, and the impact of ENSO on the results.In Section 4, we examine the WACNA pattern and the Eurasian influence on the pattern in CanESM5 historical simulations and assess the uncertainty of the results due to internal climate variability.
Finally, a summary is given in Section 5.

a. ERA5 reanalysis and observational data
The observation-based analysis is mainly based on monthly atmospheric variables extracted from the fifth generation of atmospheric reanalysis (ERA5, Hersbach et al., 2020) developed by the European Centre for Medium-Range Weather Forecasts (ECMWF).The ERA5 reanalysis fields we employed include surface air temperature (SAT), as well as geopotential, temperature, and wind velocities in the troposphere.These variables are analyzed on 2.5 o × 2.5 o grids over the period from 1960 to 2010, consistent with the later period of historical climate simulations described below.Years refer to the January dates throughout this study.In addition, we use monthly sea surface temperature (SST) data from the Extended Reconstructed Sea Surface Temperature version 5 (ERSSTv5) dataset (Huang et al., 2017), with a resolution of 2.0 o × 2.0 o over 1960-2010.The monthly Niño3.4 index over the same period from the Climate Prediction Center (CPC, http://www.cpc.ncep.noaa.gov/data/indices) is used to characterize the tropical ENSO variability.For simplicity, we will refer to these reanalysis and observation-based data as "observations" in the remainder of this paper.

b. CanESM5 historical simulations
Outputs from historical climate simulations conducted with CanESM5 are employed.
CanESM5 has a horizontal T63 spectral resolution of approximately 2.8 o in the atmosphere and roughly 1 o in the ocean.A detailed description of the model can be found on the website CanESM5 -The Canadian Earth System Model version 5 -Open by Default Portal (canada.ca).We analyze its single model initial-condition large ensemble historical simulations, consisting of 50 ensemble members of 165-yr integrations over the period 1850-2014.Each simulation is forced by identical historical greenhouse gas concentration, sulfate aerosols, and other observation based radiative forcings over 1850-2014 (Eyring et al., 2016;Swart et al., 2019), with slightly different initial conditions for each run in 1850.The modelled variables we considered are interpolated to 2.5° × 2.5° grids using bilinear interpolation.We examine 50 historical simulations over 1960-2010 and compare the results with those obtained from observations.

c. Data processing and analysis methods
To analyze monthly anomalies of variables, we first calculate their differences from the 50year monthly mean climatology over 1961-2010 after removing the secular linear trend.Empirical orthogonal function (EOF) analyses are then employed to identify dominant modes of SAT anomalies over different domains of interest.Previous studies have shown that the leading mode (EOF1) of SAT anomalies over the NA sector features the WACNA pattern (e.g., Guan et al., 2020;Yu and Lin, 2022), while the second mode (EOF2) of SAT anomalies over the Eurasian sector features the WACE pattern (e.g., Mori et al., 2019).These modes are well separated from other corresponding EOFs based on the criterion of North et al. (1982).We use the first principal component (PC1) over North America as an index of the WACNA pattern and the second principal component (PC2) over Eurasia as a WACE index.An EOF analysis is also performed to capture the WACNA pattern simulated by CanESM5.In addition, another EOF analysis is conducted to characterize the inter-member variability of the WACNA patterns in the ensemble simulation.
To quantify relationships between an index and variables of interest, correlation and regression analyses are used.The statistical significance of a correlation is determined by a Student-t test, with the effective degree of freedom estimated by considering the autocorrelation of the time series (Bretherton et al., 1999).To avoid potential over-interpretation of multiple testing results for grid points over a domain of interest, we apply the false detection rate (FDR) approach as demonstrated in Wilks (2016).For most variables, we consider the Northern Hemisphere (0-90 o N) domain, which consists of 5328 local tests at 2.5° × 2.5° grids (as shown in Figs. 1 and 2 below) with a significance level of 5% (αFDR = 0.05).For SST, we examine the 30 o S-60 o N band, which covers both tropical and northern mid-latitude regions.We use 5670 ocean grids at 2.0° × 2.0° for ERSSTv5 and 3521 ocean grids at 2.5° × 2.5° for CanESM5 model simulations to perform local tests.In addition, the power spectrum of a time series is estimated using the Parzen estimator (e.g., von Storch and Zwiers, 1999).
To explore the driving mechanism of the circulation anomalies in association with the WACNA variability, we examine the PC1 associated wave activity flux anomalies in the upper troposphere.The horizontal wave activity flux ( WAF ) is computed following Takaya and Nakamura (2001) as follows: where   = (  ,   ) and  are horizontal geostrophic winds and stream function, respectively, which are calculated from the geopotential field.The overline and prime denote the 50-DJF (December-January-February) climatological mean over 1961-2010 and its anomaly, respectively.
The subscripts represent partial derivatives.WAF tends to be parallel to the local group velocity of stationary Rossby wave, which indicates sources and sinks of wave activity and reveals the atmospheric wave dispersion (Takaya and Nakamura, 2001).
The PC1 associated temperature advection anomalies are examined to aid in understanding the formation of surface temperature anomalies.The anomalous horizontal temperature advection (Fadv) in the lower troposphere, which is dominated by wind variations, can be written as, where  * = ( * ,  * ) is the PC1 associated horizontal wind velocity anomaly and  ̅ is the 50-DJF climatological mean temperature.EOF1 over the Eurasian sector accounts for 34.5 % of total variance and reveals a North Atlantic Oscillation (NAO, e.g., Hurrell et al., 2003) or Arctic Oscillation (AO, Thompson and Wallace, 1998) like pattern in the Northern Hemisphere (not shown), consistent with Mori et al. (2014).EOF2, which accounts for 15.3% of the total variance, is identified as the WACE pattern (Fig. 1, top-left).WACE also shows a dipole structure, one centered on the Barents-Kara Sea (BKS) and the opposite sign in southern Siberia.These patterns resemble relevant WACC patterns over the NA and Eurasian sectors, respectively, that were previously identified in observational and climate simulation studies on intraseasonal and interannual timescales (e.g., Kug et al., 2015;Lin, 2015;Blackport et al., 2019;Guan et al., 2020;Yu and Lin, 2022;Lin et al., 2022) and in long-term SAT trends (e.g., Kug et al., 2015;Sigmond and Fyfe, 2016;Sun et al., 2016), indicating the robustness of the two patterns.WACNA pattern.The ABNA-like atmospheric teleconnection connects WACE and WACNA across continents, as documented in previous studies (Yu and Lin, 2022;Lin et al., 2022).

WACNA in
Consistent with the circulation anomaly, two meridional tripole structures in the 200-hPa zonal wind anomalies are observed around the dateline and NA (U200, Fig. 2, top-right).
Specifically, in association with a positive WACNA, U200 reveals a strong easterly anomaly in the central North Pacific, located to the north of the exit of the strongest subtropical jet in the western Pacific.This easterly anomaly is surrounded by westerly anomalies on its south and north sides.
Relatively weak U200 anomalies are also seen over NA, with two centers around the NA subtropical jet and a third centered over the Canadian Arctic Archipelago.In the lower troposphere, the anomalous temperature advection follows the circulation anomaly (Fadv and V at 850-hPa, Fig. 2, bottom-right).This results in warming in the mid-high latitude North Pacific and central-eastern Arctic with an action center over CBS, as well as cooling in the NA northwest, which contributes to the WACNA pattern.WACNA and the relationship between WACE and WACNA, we remove the ENSO contribution from the field of interest by using linear regression to isolate the non-ENSO related variability.
We construct monthly residual SAT anomalies and conduct an EOF analysis of monthly SAT residuals over the NA sector.This EOF1 explains 31.6% of total variance and is still dominated by a dipole pattern over the NA sector (Fig. 5, top-left), similar to the original EOF1 (Fig. 1, topright).The pattern correlation between the two is high at 0.99 over the NA sector.The corresponding principal component, denoted as PC1-rENSO, is highly like PC1 (Fig. 4), with a correlation of 0.98 between the two indices.Additionally, PC1-rENSO associated temperature and circulation anomalies closely resemble corresponding anomalies associated with PC1, as shown in Fig. 5, which displays the PC1-rENSO associated Ф500(0), SAT(-1) and Φ500-1000(-1) anomalies.
The correlation between anomaly patterns for both indices is above 0.96 across all three fields in the Northern Hemisphere.This suggests that the WACNA pattern and the linkage between WACE and WACNA are not significantly influenced by ENSO.

WACNA in CanESM5 SMILE simulations
To examine the simulation of the WACNA pattern and its connection with WACE in CanESM5, we perform an EOF analysis on monthly SAT anomalies over the NA sector during DJF from 1961-2010, using data from all 50 historical simulations.We analyze the temperature and circulation anomalies associated with the corresponding PC1, and then explore the diversity of results by analyzing the inter-member variability among the 50 ensemble members.By examining the inter-member variability, we can assess the uncertainty of outcomes due to internal variability.
a. WACNA in historical simulations The circulation anomalies associated with WACNA in CanESM5 (Fig. 7) are generally similar to those in ERA5 (Fig. 2), with differences mainly in the anomalous magnitude.In  Preceding the positive WACNA pattern, Φ500-1000(-1) shows a significant positive (negative) anomaly in southern (northern) Siberia, consistent with the ERA5 result over Eurasia.The simulated SST(-1) pattern also bears resemblance to the observed pattern, with a negative SST anomaly in the tropical central-eastern Pacific.However, the Φ500-1000(-1) anomalies are weaker in CanESM5 than in ERA5, as indicated by the different contour intervals used in Figs. 8 and 3.This weakness is similar to the weak SAT(-1) anomalies described above.Meanwhile, the SST(-1) anomalies are much weaker in CanESM5 than in ERA5.The small SST(-1) anomalies seen here may be associated with the weak ENSO variability observed in CanESM5 (Swart et al., 2019).
The relatively weak anomalies can also be attributed in part to the application of large ensemble data in the CanESM5 calculation, as previously discussed.In addition, the similarity of the WACNA and anomalous circulation patterns in ERA5 and CanESM5, along with the weak ENSO variability in CanESM5, strengthens the argument that the WACNA pattern and its connection to WACE are not significantly impacted by ENSO.
The variability of WACNA in ERA5 and CanESM5 historical simulations has been further compared.The PC1 time series from ERA5 exhibits interannual variances dominated by frequencies ranging from 3 to 7 years, with one power peak of 3.6 years that is statistically significant at the 5% level and another at 6.2 years that is insignificant at the 5% level (Fig. 9, red curves).To calculate the spectra of the CanESM5 simulations, the corresponding PC1 series from the 50 ensemble members are used.The ensemble mean spectrum shows reasonable reproducibility of the ERA5 result, with variances also weighing toward frequencies from 3 to 7 years.However, CanESM5 reveals two power peaks of 3.1 and 5.6 years that are not significant at the 5% level (Fig. 9, blue curves).Additionally, the CanESM5 simulations display a considerable spread of spectra across the ensemble members, as indicated by the spectrum between the ensemble mean plus and minus one inter-member standard deviation of the 50 spectra (Fig. 9, grey shading).Nevertheless, the inter-member spread covers most of the observed variability, especially the 6.2-year power peak in ERA5 but not the 3.6-year peak in ERA5.Overall, the uncertainty in WACNA patterns due to internal climate variability is dominated by two modes of inter-member variability: a phase shift of WACNA and a local variation of WACNA.

Summary
This study analyzes the WACNA pattern and WACE-WACNA linkage over the period from The WACNA patterns in both ERA5 and CanESM5 simulations reveal interannual variances with dominant frequencies ranging from 3 to 7 years.ERA5 exhibits a significant power peak at 3.6 years and another insignificant peak at 6.2 years.The ensemble mean spectrum from the CanESM5 simulations shows two power peaks at 3.1 and 5.6 years, although they are not significant at the 5% level.CanESM5 also displays a considerable spread of spectra across the 50 ensemble members.The inter-member spread covers most of the observed variability, especially the 6.2-year power peak in ERA5.The impact of internal climate variability on WACNA is also assessed by examining the inter-member variance in WACNA patterns across the ensemble members.The uncertainty in the WACNA pattern is dominated by two modes of inter-member variability: a southeast-northwest phase shift and a local variation of its amplitude.
the ERA5 reanalysis a. WACNA and Eurasian influence WACNA is identified as the leading EOF mode of monthly SAT anomalies over the NA sector (20-90 o N, 150 o E-40 o W) for the 50 DJFs over 1961-2010 (e.g., Yu and Lin, 2022).EOF1 accounts for 32.2% of total variance and is dominated by a dipole structure over the NA sector (Fig.1, top-right).Specifically, it features a large SAT anomaly centered over the Great Plains and another anomaly of opposite sign spreading over the central-eastern Arctic and mid-high latitude North Pacific, centered over the Chukchi-Bering Seas (CBS).The variability of the WACNA pattern is characterized using the PC1 series corresponding to this EOF1.Similarly, an EOF analysis of DJF monthly SAT anomalies over the Eurasian sector (20-90 o N, 0-150 o E) is conducted.

Fig. 1 (
Fig. 1 (top panels) Regressions of SAT anomalies onto the WACE (left) and WACNA (right) indices.The green boxes indicate the regions of (20-90 o N, 0-150 o E) and (20-90 o N, 150 o E-40 o W) used for the EOF analysis to define the WACE and WACNA patterns, respectively.Contour interval is 0.5 o C. (bottom panels) Lead regressions of SAT anomalies onto the WACNA index, with the temperature anomaly leads WACNA by 2 months (left) and 1 month (right).Contour interval is 0.2 o C. Black dots indicate the regression is statistically significant with p values small enough to satisfy the FDR criterion of   = 0.05.Results are based on the ERA5 reanalysis over 1961-2010.

Fig. 2
Fig. 2 (top-left) Regression of Φ250 anomalies (shading in m 2 s -2 ) onto PC1 and the corresponding wave activity fluxes poleward of 20 o N (vectors in m 2 s -2 , flux values less than 0.5 m 2 s -2 are omitted).The vector scale is shown at the lower middle.(top-right) Regression of U200 anomalies (contour, interval 1.0 ms -1 ) onto PC1 superimposed on the DJF climatological mean U200 (shading in ms -1 ).(bottom-left) Regression of Φ500 anomalies (interval 60 m 2 s -2 ) onto PC1.(bottom-right) Anomalies of horizontal temperature advection (Favd, shading in o C day -1 ) and winds (arrows in ms -1 with the scale shown at the lower middle, anomalies less than 0.1 ms -1 in both directions are omitted) at 850-hPa regressed upon PC1.Black dots indicate the regression is statistically significant with p values small enough to satisfy the FDR criterion of   = 0.05.Results are based on the ERA5 reanalysis over 1961-2010.

Fig. 3
Fig. 3 Lead regressions of thickness Φ500-1000 (top, interval 60 m 2 s -2 ) and SST (bottom, interval 0.1 o C) anomalies onto PC1, with the anomaly leads PC1 by one month.Black dots indicate the regression is statistically significant with p values small enough to satisfy the FDR criterion of   = 0.05.The WAF analysis above indicates that the primary source of wave activity associated with

Fig. 5 (
Fig. 5 (left panels) Regressions of SAT anomalies onto PC1-rENSO, with the temperature anomaly leads PC1-rENSO by 0 (top) and 1 (bottom) month.The green box indicates the region for the EOF analysis.Contour interval is 0.5 (0.2) o C in the top-left (bottom-left) panel.(top-right) Regression of Φ500 anomalies (interval 60 m 2 s -2 ) onto PC1-rENSO.(bottom-right) Lead regression of Φ500-1000 anomalies (interval 60 m 2 s -2 ) onto PC1-rENSO, with the thickness anomaly leads PC1-rENSO by one month.Black dots indicate the regression is statistically significant with p values small enough to satisfy the FDR criterion of   = 0.05 .Results are based on the ERA5 reanalysis over 1961-2010.

Fig. 6
Fig. 6 Regressions of SAT anomalies onto the simulated WACNA index, with the temperature anomaly leads WACNA by 0 (top, interval 0.5 o C) and 1 (bottom, interval 0.1 o C) month.The green box indicates the region (20-90 o N, 150 o E-40 o W) for the EOF analysis.Black dots indicate the regression is statistically significant with p values small enough to satisfy the FDR criterion of   = 0.05.Results are based on the 50 CanESM5 historical simulations over 1961-2010.The simulated EOF1, which explains 29.5% of the total SAT variances over the NA sector, Fig. 7 As in Fig. 2, but for the variables regressed on the PC1 from the 50 CanESM5 historical simulations over 1961-2010.

Fig. 9
Fig. 9 Power spectra of the PC1 time series for ERA5 (red) and the ensemble mean of the CanESM5 simulations (blue).The dot curve is the red-noise spectrum calculated from the lag 1 autocorrelation.The dash curve is the power spectrum of 95% confidence level.Ensemble spread, indicated by the spectrum between the CanESM5 ensemble mean plus and minus one intermember standard deviation of the 50 spectra, is shown by grey bars.

Fig. 12
Fig. 12 As in Fig. 11, but for the variables regressed onto PC250.
1960 to 2010, using ERA5 reanalysis and CanESM5 large ensemble historical simulations.One main objective is to determine whether WACNA and the WACE-WACNA connection are affected by tropical ENSO variability.The other is to assess simulations of WACNA and the WACE-WACNA relationship in CanESM5, as well as the impact of internal climate variability on these simulations.Based on the ERA5 reanalysis, a negative WACE-like pattern typically precedes a positive WACNA pattern by one month, with an atmospheric teleconnection resembling the ABNA pattern linking Eurasia and North America.Upstream, negative PNA-like and ABNA-like circulation patterns are observed in association with a positive WACNA pattern.Consistent with the circulation anomaly, two meridional tripole structures in the 200-hPa zonal wind anomalies appear around the dateline and NA, which correspond to changes in subtropical jets in the western Pacific and NA.In the lower troposphere, the anomalous temperature advection follows the circulation anomaly and supports the WACNA pattern.The negative ABNA-like pattern may be attributed to heating anomalies in the lower troposphere in southern Siberia, which is associated with a negative WACE pattern and its featured Eurasian warming.The negative PNA-like pattern is influenced by negative SST and deep convection anomalies in the tropical Pacific, resembling tropical ENSO variability.Conversely, processes with circulation anomalies of opposite sign could result in a negative WACNA pattern.These observational results are consistent with those inYu and Lin  (2022)  for a different period over 1980-2019, indicating the robustness of the WACNA pattern and WACE-WACNA connection.In addition, the main results can be reproduced using non-ENSO related variables, suggesting that the WACNA pattern and the link between WACE and WACNA are not significantly influenced by tropical ENSO variability.CanESM5 reasonably well simulates the WACNA pattern, although there are slight differences in the intensity and location of the centers of action of WACNA between ERA5 and CanESM5 results.The model also reproduces the WACE-WACNA connection and anomalous circulation and temperature advection patterns, with some differences mainly in the anomalous magnitude.Consistent with ERA5, the model simulations show that heating in the lower troposphere in southern Siberia and negative SST in the tropical central-eastern Pacific precede the positive WACNA pattern.However, the Φ500-1000(-1) and SST(-1) anomalies are weaker in CanESM5 than in ERA5.This is partly due to the application of large ensemble data in CanESM5, which may dampen the signal.Nevertheless, the similarity of WACNA and its associated circulation patterns in ERA5 and CanESM5, along with the weak ENSO variability in CanESM5, strengthens the argument that the WACNA pattern and its connection to WACE are not significantly influenced by ENSO.