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  • View in gallery

    (a) Time series of actual (solid) and detrended standardized (dashed) September Arctic SIA (106 km2). Filled (empty) circles denote the selected sea ice increase (reduction) cases. (b) Scatterplot of detrended Arctic SIA index vs Niño-3.4 index.

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    (a)–(c) Regressions of detrended SAT, SLP, and Z500 against sign-reversed September SIA index. (d)–(f) As in (a)–(c), but with the ENSO-related signals removed. (Because La Niña is concerned, the Niño-3.4 index has its sign reversed.) (g)–(i) The difference of the left minus center panels. Contour intervals are 0.5°C, 10 hPa, and 10 gpm in (a)–(c) and (d)–(f) but 0.1°C, 2 hPa, and 2 gpm in (g)–(i), respectively.

  • View in gallery

    (a)–(c) Detrended SAT, SLP, and Z500 regressed against sign-reversed Niño-3.4 index. (d)–(f) As in (a)–(c), but with September Arctic SIC-related signals removed. (g)–(i) The difference of the left minus center panels. Contour intervals are 0.5°C, 10 hPa, and 10 gpm in (a)–(c) and (d)–(f) but 0.1°C, 2 hPa, and 2 gpm in (g)–(i), respectively.

  • View in gallery

    Composite SST (contour) and sea ice reduction (shading around the Arctic, percentage), for (a)–(c) Case-noEN and (d)–(f) Case-EN. Shading over open oceans denotes significance of SSTA exceeding 90%. The contour interval for SST is 0.3°C, the zero contours are omitted, and dashed contours are negative.

  • View in gallery

    Composite winter mean (a),(e) SAT, (b),(f) SLP, (c),(g) Z500, and (d),(h) precipitation anomalies, for (left) Case-noEN and (right) Case-EN. The contour intervals from top to bottom are 0.5°C, 10 hPa, 10 gpm, and 1 mm day−1 and dashed contours are negative values. The zero contours in (a)–(c) and (e)–(g) are indicated by black contours, and those in (d) and (h) are omitted; the thick black lines in (c) and (g) indicate propagation of wave trains. Shading denotes significance exceeding the 90% level.

  • View in gallery

    (a)–(d) Composite differences in SAT, SLP, Z500, and precipitation of Case-EN minus Case-noEN, (e)–(h) observational composite in SAT, SLP, Z500, and precipitation for La Niña years, and (i)–(l) left minus center panels. The contour intervals and shading are as in Fig. 5, but in (i)–(k) the contour intervals are 0.25°C, 5 hPa, and 5 gpm, respectively. The zero contours in (a)–(c), (e)–(g), and (i)–(k) are indicated by black contours, and those in (d), (h), and (l) are omitted; the thick black lines in (c) and (g) indicate propagation of wave trains.

  • View in gallery

    As in Fig. 4, but for the composite November SST anomalies (contours) and sea ice anomalies (shading) corresponding to two kinds of sea ice events in MPI-ESM-LR.

  • View in gallery

    As in Fig. 5, but for the composites of the cases derived from the historical runs in MPI-ESM-LR. The contour intervals are 0.5°C in (a),(e); 5 hPa in (b),(f); 5 gpm in (c),(g); 0.5 mm day−1 in (d); and 1 mm day−1 in (h).

  • View in gallery

    As in Fig. 6, but derived from the cases in the historical simulation datasets in MPI-ESM-LR. The contour intervals from top to bottom are 1.0°C, 5 hPa, 5 gpm, and 1 mm day−1.

  • View in gallery

    AGCM modeled responses to Arctic sea ice reduction and the accompanied SST anomalies (60°S–60°N), for (a)–(d) just the isolated sea ice and (e)–(h) sea ice and SST. Shading denotes significance exceeding the 90% level. Contour intervals from top to bottom are 0.5°C, 5 hPa, 5 gpm, and 2 mm day−1, respectively. The zero contours in (a)–(c) and (e)–(g) are indicated by black contours, and those in (d) and (h) are omitted; the thick black lines in (c) and (g) indicate propagation of wave trains.

  • View in gallery

    (a)–(d) Differences of the modeled responses to both Arctic sea ice reduction and the associated SST anomalies (60°S–60°N) minus the response to the sea ice, (e)–(h) AGCM responses to the isolated SST anomalies, and (i)–(l) left minus center panels (i.e., the differences of responses to sea ice and SST minus the combination of responses to separated sea ice and SST). The contour intervals are 0.5°C in (a),(e),(i); 5 hPa in (b),(f),(j); 5gpm in (c),(g),(k); 2 mm day−1 in (d),(h); and 0.5 mm day−1 in (l). The zero contours in (a)–(c), (e)–(g), and (i)–(k) are indicated by black contours, and those in (d), (h), and (l) are omitted; the thick black lines in (c) and (g) indicate propagation of wave trains.

  • View in gallery

    The 5-day mean responses of Z500 in the transient runs: the response to (a)–(d) sea ice loss, (e)–(h) La Niña, and (i)–(l) combined sea ice loss and La Niña forcing. The contour intervals from left to right are 1, 2, 5, and 10 gpm, dashed contours are negative, and zero contours are omitted. The arrows in (d), (h), and (l) are the wave activity flux (m2 s−2) based on Takaya and Nakamura (2001).

  • View in gallery

    As in Fig. 12, but for (a)–(d) the combination of the responses to sea ice loss and La Niña and (e)–(h) the nonlinearity of the response expressed as the difference the response to the simultaneous two forcing minus the combination of the responses to the two individual forcings.

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Linear Additive Impacts of Arctic Sea Ice Reduction and La Niña on the Northern Hemisphere Winter Climate

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  • 1 China University of Geosciences, Wuhan, and Institute of Atmospheric Physics/RCE-TEA, Chinese Academy of Sciences, Beijing, China
  • | 2 Department of Atmospheric and Environmental Sciences, University at Albany, State University of New York, Albany, New York
  • | 3 Institute of Atmospheric Physics/RCE-TEA, Chinese Academy of Sciences, Beijing, China, and Nansen Environmental and Remote Sensing Center/Bjerknes Center for Climate Research, Bergen, Norway
  • | 4 State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing, China
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Abstract

Both Arctic sea ice loss and La Niña events can result in cold conditions in midlatitude Eurasia in winter. Since the two forcings sometimes occur simultaneously, determining whether they are independent of each other is undertaken first. The result suggests an overall independence. Considering possible interactions between them, their coordinated impacts on the Northern Hemisphere winter climate are then investigated based on observational data analyses, historical simulation analyses from one coupled model (MPI-ESM-LR) contributing to CMIP5, and atmospheric general circulation model sensitive experiments in ECHAM5. The results show that the impacts of the two forcings are overall linearly accumulated. In comparison with one single forcing, there is intensified cooling response in midlatitude Eurasia along with northern warmer–southern cooler dipolar temperature responses over North America. Despite the additive linearity, additive nonlinearity between the two forcings is identifiable. The nonlinearity causes midlatitude Eurasian cooling weakened by one-tenth to one-fifth as much as their individual impacts in combination. The underlying mechanisms for the weak additive nonlinearity are finally explored by transient adjustment AGCM runs with one single forcing or both the forcings switched on suddenly. The day-to-day evolution of responses suggests that the additive nonlinearity may arise initially from the forced wave dynamics and then be amplified because of the involvement of transient eddy feedbacks.

Corresponding author address: Dr. Shuanglin Li, CCRC/IAP/CAS, P.O. Box 9804, Beijing 100029, China. E-mail: shuanglin.li@mail.iap.ac.cn

Abstract

Both Arctic sea ice loss and La Niña events can result in cold conditions in midlatitude Eurasia in winter. Since the two forcings sometimes occur simultaneously, determining whether they are independent of each other is undertaken first. The result suggests an overall independence. Considering possible interactions between them, their coordinated impacts on the Northern Hemisphere winter climate are then investigated based on observational data analyses, historical simulation analyses from one coupled model (MPI-ESM-LR) contributing to CMIP5, and atmospheric general circulation model sensitive experiments in ECHAM5. The results show that the impacts of the two forcings are overall linearly accumulated. In comparison with one single forcing, there is intensified cooling response in midlatitude Eurasia along with northern warmer–southern cooler dipolar temperature responses over North America. Despite the additive linearity, additive nonlinearity between the two forcings is identifiable. The nonlinearity causes midlatitude Eurasian cooling weakened by one-tenth to one-fifth as much as their individual impacts in combination. The underlying mechanisms for the weak additive nonlinearity are finally explored by transient adjustment AGCM runs with one single forcing or both the forcings switched on suddenly. The day-to-day evolution of responses suggests that the additive nonlinearity may arise initially from the forced wave dynamics and then be amplified because of the involvement of transient eddy feedbacks.

Corresponding author address: Dr. Shuanglin Li, CCRC/IAP/CAS, P.O. Box 9804, Beijing 100029, China. E-mail: shuanglin.li@mail.iap.ac.cn

1. Introduction

In recent decades, low sea ice extents in the Arctic have occurred frequently. The influence of this on weather and climate has attracted much attention (e.g., Honda et al. 2009; Guo et al. 2014; Yang and Yuan 2014; Cohen et al. 2014). Previous studies documented that a fall Arctic sea ice reduction causes colder conditions in mid-to-high-latitude Eurasia in the following winter (e.g., Francis et al. 2009; B. Wu et al. 2011; Z. Wu et al. 2011; Liu et al. 2012; Cohen et al. 2012; Screen et al. 2014; Mori et al. 2014).

Although Arctic sea ice anomaly can occur independently, it sometimes co-occurs with ENSO. For example, substantially less sea ice occurred in the 2007 fall and was followed by a strong La Niña event in the subsequent winter (December–February). Also, more sea ice appeared in the 1997 fall and was accompanied with a century-record strong El Niño in the subsequent winter. It is well known that ENSO has significant influences on boreal winter climate, and a cold phase of ENSO often corresponds to a colder winter in Eurasia (e.g., Li 1988; Trenberth et al. 1998; Dong et al. 2000; Wang et al. 2000; Greatbatch et al. 2004; Li and Lau 2012; He et al. 2013). Given a possibility of their co-occurrence, the following issues arise naturally. Are the two forcings independent of each other? If yes, are their influences linearly additive? Are there nonlinear interactions between their effects? Particularly, do the atmospheric responses to the combined two forcings equal the sum of the responses to the two individual forcings? In other words, does an interactive modulation exist between the impacts of the two forcings?

The answers to the above issues are associated with the so-called atmospheric additive linearity or nonlinearity. Additive linearity (nonlinearity) is the property that when there are two independent forcings simultaneously, the sum of the responses to the two individual forcings equals (does not equal) the response to the combined forcings (Robinson et al. 2003). Li et al. (2007) suggested that additive nonlinearity might happen more easily when the strengths of forcings are sufficient.

In the present study, whether the occurrence of Arctic sea ice reduction is independent of ENSO is first analyzed, and the result illustrates an overall independence. Because La Niña’s cooling influence on Eurasia winter climate is somewhat similar to Arctic sea ice loss, their collaborative impact is thus studied in depth. Observational data analyses, historical simulations analyses from one coupled model (MPI-ESM-LR) from phase 5 of the Coupled Model Intercomparison Project (CMIP5), and sensitivity experiments from ECHAM5, an atmospheric general circulation model (AGCM), are utilized for this purpose. Additionally, one set of diagnostic ECHAM5 transient adjustment experiments with forcings switched on suddenly is performed to understand the underlying mechanisms.

The rest of this paper is organized as follows. Section 2 describes the observational and simulation datasets, methods, the AGCM, and the experiment design. Section 3 is an observational analysis. Section 4 is the analyses of the long-term historical simulations from MPI-ESM-LR. In section 5 AGCM sensitivity experiments are examined. Section 6 is a brief analysis of the mechanisms using the AGCM transient adjustment runs. Finally, conclusions and a discussion are provided in section 7.

2. Data, method, model, and experiment design

a. Data

Monthly sea ice concentration (SIC) and sea surface temperature (SST) are from the Met Office Hadley Centre (Rayner et al. 2003). Monthly sea level pressure (SLP), 500-hPa geopotential height (Z500), and surface air temperature (SAT) are from the European Centre for Medium-Range Weather Forecasts (ECMWF) interim reanalysis (ERA-Interim; Dee et al. 2011). The period of 1979–2013 is used since better quality sea ice data is available from satellites during that period. This work focuses on interannual variability, so linear trends and decadal components are removed from all the variables. The Niño-3.4 index is used to detect La Niña (or El Niño) conditions that is defined as the monthly average SST anomaly during winter in the Niño-3.4 region (5°S–5°N, 170°–120°W).

Since reliable sea ice observational data only begin after 1979, cases of extreme sea ice loss or increase on interannual time scales are very limited. As a supplement, the 1860–2005 historical simulations of the MPI-ESM-LR coupled model participating in CMIP5 are used. These data constitute three members beginning from different initial fields, each having an integration period of 145 yr. A total of a 405-yr time series is thus derived for analyses, because each integration loses a 10-yr period when removing decadal components.

b. Method

Additive linearity or nonlinearity is understood as follows. When there are two forcings and the forcing-induced noises can be neglected, the association of responses to the combined two forcings with those to the two separated forcings can be assumed as the following formula:
e1
where f1 and f2 represent two forcings, respectively; R indicates response; and nonR represents additive nonlinearity. The formula can be transformed into
e2

Thus, additive linearity or nonlinearity can be analyzed through comparing the composite difference between R(f1 + f2) − R(f1) − R(f2) and R(f1) + R(f2). The primary methods include regression and composite. A Student’s t test is used to check the results’ significance.

c. AGCM and experiment design

The AGCM used here is ECHAM5, an earlier version of the atmospheric component model constituting the MPI-ESM-LR coupled model. It was developed by the Max Plank Institute for Meteorology (Roeckner et al. 2003, 2006). This model has a horizontal resolution of triangular spectral truncation T42 (approximately 2.8° × 2.8°), with 31 vertical sigma levels up to 10 hPa. Four sets of sensitive ensemble experiments are conducted as follows.

  1. The first is an unforced control experiment, referred to as CTRL_Exp, in which the AGCM is forced with the climatological monthly SST and sea ice. The climatology is calculated as the mean of 1979–2010.

  2. The second is a sea ice alone experiment, referred to as SIC_Exp, in which the AGCM is forced with perturbed Arctic sea ice. The perturbed sea ice is the combination of climatological sea ice plus the composite monthly anomaly in September sea ice reduction cases with La Niña following (i.e., Case-EN in the next subsection).

  3. The third is the combined sea ice and SST forced experiment, referred to as SST_SIC_Exp. It is the same as SIC_Exp except that the composite monthly tropical Pacific SST anomalies are also overlaid onto the climatological SST. The SST anomalies (SSTAs) are derived from the same cases as in the second experiment.

  4. The last one is the SST alone experiment, referred to as SST_Exp. It is the same as SIC_Exp, but only SSTs are perturbed. The SSTA is the same as in the third experiment.

Each experiment contains 60 members and is integrated for nine months beginning from 1 September. The initial conditions are randomly selected from previous model runs. The first three months (September–November) are discarded as model’s spin up. The experiments are summarized in Table 1. The monthly output from December to February of the next year are used for analyses.

Table 1.

Equilibrium experiments conducted in the study.

Table 1.

In addition to the above equilibrium experiments, three sets of diagnostic transient adjustment experiments are carried out to understand physical processes for the additive nonlinearity with a sudden switching on (“switch on” runs) of SIC loss or La Niña SSTA or both, respectively. For each ensemble we carried out 60-member runs starting from 1 December randomly selected initial conditions and integrated the model for 45 days when the atmosphere may reach equilibrium. The SIC anomaly used is derived from the winter sea ice regression against the autumn SIC index. This SIC anomaly is primarily located in the Barents and Kara Seas, and it represents the part of autumn SIC anomaly persisting into winter to some extent. In view of the substantial importance of SIC in the Barents and Kara Seas (Overland et al. 2015), the modeled response with such an SIC anomaly should be able to reflect the across-seasonal impact of autumn SIC due to its persistence to a considerable extent. The 60-member ensemble is compared with a control ensemble with the same size and climatological SIC and SST. All these three ensembles are summarized in Table 2. The daily evolutions of differences in atmospheric states between these parallel ensembles are analyzed based on 5-day means, and their statistical significances are estimated using a Student’s t test. A similar experimental design was used by Hoerling et al. (2004) and Li et al. (2010).

Table 2.

Transient experiments with forcing suddenly switched on.

Table 2.

3. Observational analyses

a. Occurrence’s independence of two forcings

To measure sea ice anomaly in autumn, an Arctic sea ice index is defined as the September detrended normalized sea ice area (SIA) over the Arctic (north of 60°N), which is displayed in Fig. 1a (dashed line). The linear trend is calculated with a least-squared fit for the period of 1979–2012. As expected, the index has no evident trend in comparison with the actual one (solid line in Fig. 1a). Figure 1b shows the scatterplot of the sea ice index versus the winter Niño-3.4 index. Since the negative-phase ENSO (La Niña) is concerned here, the sign of the Niño-3.4 index is reversed. From Fig. 1b, no evident linear relationship is seen between the two indices (with correlation coefficient of 0.1). This suggests that the two forcings are generally independent.

Fig. 1.
Fig. 1.

(a) Time series of actual (solid) and detrended standardized (dashed) September Arctic SIA (106 km2). Filled (empty) circles denote the selected sea ice increase (reduction) cases. (b) Scatterplot of detrended Arctic SIA index vs Niño-3.4 index.

Citation: Journal of Climate 29, 15; 10.1175/JCLI-D-15-0416.1

The occurrence’s independence of Arctic sea ice and ENSO does not necessarily mean independence between their effects, since there are complicated nonlinear dynamic and thermodynamic interactions in the atmosphere. The nonlinear interactions between the atmospheric responses to several different forcings are possible when the forcings are strong (Li et al. 2007). Considering a similar cooling impact on midlatitude Eurasia, the additive linearity or nonlinearity between Arctic sea ice reduction (reduced SIC) and La Niña is analyzed below.

b. Comparison of regressions against sea ice index and Niño-3.4 index

Figure 2 displays a comparison of the regressions of winter SAT, SLP, and Z500 against the Arctic sea ice area index when the La Niña (El Niño)–related signals are included or excluded. The procedure to exclude the La Niña (El Niño)–related signals is as in Li and Li (2014). First, the La Niña (El Niño)–induced anomaly is determined by regressing the time series of the variables at each grid against the Niño-3.4 index time series. Then, the La Niña (El Niño) signal in variables for a particular month is a product of the La Niña (El Niño)–associated anomaly pattern and the La Niña (El Niño) index for that month. Last, the original variables minus the La Niña (El Niño) signals yields the La Niña (El Niño) excluded anomalies.

Fig. 2.
Fig. 2.

(a)–(c) Regressions of detrended SAT, SLP, and Z500 against sign-reversed September SIA index. (d)–(f) As in (a)–(c), but with the ENSO-related signals removed. (Because La Niña is concerned, the Niño-3.4 index has its sign reversed.) (g)–(i) The difference of the left minus center panels. Contour intervals are 0.5°C, 10 hPa, and 10 gpm in (a)–(c) and (d)–(f) but 0.1°C, 2 hPa, and 2 gpm in (g)–(i), respectively.

Citation: Journal of Climate 29, 15; 10.1175/JCLI-D-15-0416.1

From Figs. 2a–c, Arctic sea ice reduction corresponds to colder SAT in midlatitude Eurasia and North America and to warmer SAT over the Arctic, along with negative Arctic Oscillation (AO)-like atmospheric circulation anomalies in SLP and Z500. This is in agreement with previous studies (e.g., Liu et al. 2012; Mori et al. 2014). When the La Niña–related linear signals are removed, the regression maps (Figs. 2d–f) look like those in Figs. 2a–c, suggesting an overall additive linearity between the two forcings. Their difference (left minus center panels in Fig. 2) validates the impact signals from La Niña (negative-phased ENSO), including the cooler SAT and the PNA pattern in SLP and Z500.

A similar comparison is performed for the regressions against the sign-reversed Niño-3.4 index (Fig. 3). When the SIC-related signals are removed, the La Niña–related signals remain there (cf. Figs. 3a–c and Figs. 3d–f). Their difference (Figs. 3g–i) is similar to that seen in Figs. 2a–c, verifying the removal of SIC signals.

Fig. 3.
Fig. 3.

(a)–(c) Detrended SAT, SLP, and Z500 regressed against sign-reversed Niño-3.4 index. (d)–(f) As in (a)–(c), but with September Arctic SIC-related signals removed. (g)–(i) The difference of the left minus center panels. Contour intervals are 0.5°C, 10 hPa, and 10 gpm in (a)–(c) and (d)–(f) but 0.1°C, 2 hPa, and 2 gpm in (g)–(i), respectively.

Citation: Journal of Climate 29, 15; 10.1175/JCLI-D-15-0416.1

The similarity of the derived La Niña signal based on the SIC regression residual (Figs. 2g–i) to the direct regression (Figs. 3a–c), together with the similarity of the derived SIC signals based on the Niño-3.4 regression residual (Figs. 3g–i) to the direct SIC regression (Fig. 2a–c), suggests overall additive linearity. The small difference of the residual derived signal minus the direct regression represents the La Niña– or SIC-related nonlinear signals contained in the SIC or Niño-3.4 regressions. The values are small, just one-tenth to one-fifth as much as the direct signal, which indicates that the La Niña– or SIC-related nonlinear SIC or ENSO signals are very weak.

c. Composite analyses: Two groups of sea ice reduction cases with or without La Niña

Li et al. (2007) illustrated that additive nonlinearity occurs more possibly when forcings are strong. Whether it is the same case for the present study is analyzed through comparing the composite anomalies in extreme sea ice reduction cases and strong La Niña events. Here an extreme sea ice reduction (increase) case is defined as the detrended monthly anomaly of September Arctic sea ice area index is less than −0.8 (greater than 0.8) times its standard deviation. To identify strong La Niña (El Niño) events, an additive threshold, Niño-3.4 index in December less than −0.8 (greater than 0.8) is overlapped with the typical ENSO definition. The latter defines one La Niña (El Niño) event with Niño-3.4 index less than −0.5 (greater than 0.5) and persisting for at least five consecutive winter months.

As such, a total of eight sea ice reduction cases (including 1979, 1981, 1984, 1985, 1990, 2007, 2008, and 2012) and five sea ice increase cases (including 1992, 1994, 1996, 1997, and 2001) are obtained (Fig. 1a). Some sea ice reduction (increase) cases are accompanied by La Niña or El Niño events, but others are not. Since additive linearity or nonlinearity of sea ice reduction and La Niña is the focus of this study, all these cases are separated into two groups based on whether a La Niña or El Niño event follows, regardless of its phase. In other words, El Niño is treated as the phase-reversed La Niña with their asymmetry ignored. The first group is referred to as Case-EN including four cases (two El Niño cases: 1994 and 1997 corresponding to sea ice increase, and two La Niña cases: 1984 and 2007 corresponding to sea ice reduction), while the other is referred to as Case-noEN including nine cases (1979, 1981, 1985, 1990, 1992, 1996, 2001, 2008, and 2012). In the next subsection, the composite difference of sea ice reduction (La Niña) cases minus sea ice increase cases (El Niño) is analyzed because sea ice reduction and La Niña are concerned.

1) The evolution of composite sea ice and SST

Figure 4 displays a comparison of composite sea ice concentration anomalies and SSTA between Case-noEN and Case-EN. The former (Figs. 4a–c) is calculated as the mean of the six cases with less sea ice (1979, 1981, 1985, 1990, 2008, and 2012) minus that of the three cases with more sea ice (1992, 1996, and 2001), where all the nine cases have no ENSO following. The latter (Figs. 4d–f) is the mean of two ice reduction cases followed with La Niña (1984 and 2007) minus that of two ice increase cases followed with El Niño (1994 and 1997). For both groups, sea ice reduction is mainly situated in the Kara, Laptev, East Siberian, Chukchi, and western Beaufort Seas. A similar sea ice anomaly was also seen in Liu et al. (2012). As expected, in the tropics no La Niña SSTA is seen in Case-noEN. By contrast, in Case-EN substantial cold anomalies are seen in the central-eastern tropical Pacific (as well as in the Indian Ocean, but not statistically significant) and warm anomalies in the western tropical Pacific, reminiscent of La Niña SSTA. The substantial difference in SSTA between the two groups verifies the application of the classification.

Fig. 4.
Fig. 4.

Composite SST (contour) and sea ice reduction (shading around the Arctic, percentage), for (a)–(c) Case-noEN and (d)–(f) Case-EN. Shading over open oceans denotes significance of SSTA exceeding 90%. The contour interval for SST is 0.3°C, the zero contours are omitted, and dashed contours are negative.

Citation: Journal of Climate 29, 15; 10.1175/JCLI-D-15-0416.1

2) Comparison of winter climate anomaly

For Case-noEN (Fig. 5a), colder SAT is seen in midlatitude Eurasia, along with warmer SAT in much of the Arctic, the Tibetan Plateau, and North Africa. A western warmer–eastern cooler dipolar pattern is found in North America. There is increased precipitation in the western Pacific warm pool and the tropical Atlantic along with decreased precipitation in the equatorial central-eastern Pacific (Fig. 5d). Positive SLP anomalies are seen over high-latitude Eurasia and the Arctic, along with negative SLP anomalies over subtropical to midlatitude Eurasia, the subtropical and midlatitude North Atlantic, and eastern North America. They in combination project onto a negative-phase AO pattern, as illustrated by previous studies (Francis et al. 2009; Cohen et al. 2012; Liu et al. 2012; Li and Wang 2013). This is more evident at Z500. The overall correspondence in anomaly sign between the lower and middle tropospheric levels indicates a quasi-barotropic structure. These circulation anomalies explain the above SAT anomalies. The positive SLP anomalies over mid-to-high-latitude Eurasia consisting of the negative AO pattern favor intensified cold air activities, causing cold conditions. The negative Z500 anomalies over northeastern Asia indicate an enhanced climatological East Asian trough, resulting in the enhanced East Asian winter monsoon and colder SAT.

Fig. 5.
Fig. 5.

Composite winter mean (a),(e) SAT, (b),(f) SLP, (c),(g) Z500, and (d),(h) precipitation anomalies, for (left) Case-noEN and (right) Case-EN. The contour intervals from top to bottom are 0.5°C, 10 hPa, 10 gpm, and 1 mm day−1 and dashed contours are negative values. The zero contours in (a)–(c) and (e)–(g) are indicated by black contours, and those in (d) and (h) are omitted; the thick black lines in (c) and (g) indicate propagation of wave trains. Shading denotes significance exceeding the 90% level.

Citation: Journal of Climate 29, 15; 10.1175/JCLI-D-15-0416.1

Such an across-seasonal impact of autumn Arctic sea ice loss on winter climate may be related to the persistence of sea ice anomaly. A considerable fraction of autumn sea ice reduction is located in the Barents and Kara Seas, and can persist into winter and influence winter climate. Besides, other processes may also play roles (Walsh 2014). For example, sea ice reduction can influence snow cover over the Eurasian continent, which can “memorize” the autumn sea ice’s signals and extend its impact into winter.

For Case-EN (Fig. 5e), we also see colder SAT over the Eurasian continent, which is similar to Case-noEN. However, the region with cold anomalies is much broader, and the warm anomalies over North Africa disappear as compared to those of Case-noEN. This is also the case for North America. Colder SAT covers entire North America with the minimum below −3°C. This is consistent with the documented impacts in earlier studies (e.g., Greatbatch et al. 2004). The spatial pattern of tropical precipitation anomalies is similar to that of Case-noEN, but the magnitude of anomalies is substantially intensified (Fig. 5h). As for SLP, in comparison with Case-NoEN, negative anomalies appear in part of the central Arctic Ocean, and the center of positive SLP anomalies over the northern North Atlantic shifts more toward northern Europe (Fig. 5f). The anomalies do not project onto the AO pattern so well as in Case-noEN. Besides, a Pacific–North American (PNA) pattern (Wallace and Gutzler 1981) is seen with positive SLP anomalies over the eastern North Pacific and the Gulf of Mexico and negative SLP anomalies over northeastern Canada. Similar anomalies are also seen at Z500, suggesting a barotropic vertical structure. The overall similar but weakened circulation anomalies over Eurasia in Case-EN relative to Case-noEN are in agreement with the weakened SAT anomaly at high latitudes (cf. Figs. 5a and 5e). The different circulation anomaly over the Western Hemisphere (the PNA pattern) in Case-EN accounts for the difference in SAT there. The tropical precipitation anomalies in Case-EN have a similar spatial pattern but are much stronger than that of Case-noEN. This implies that the precipitation is forced by the sea ice reduction and SSTA.

3) A comparison with composite anomaly in La Niña years

Figure 6 displays the composite difference between the Case-EN and Case-noEN (Figs. 6a–d), the composite of La Niña cases (Figs. 6e–h, represented by La Niña minus El Niño), and their residual (Figs. 6i–l, left minus center panels of Fig. 6). The left, center, and right panels of Fig. 6 correspond to R(f1 + f2) − R(f1), R(f2), and [R(f1 + f2) − R(f1)] − R(f2), respectively, from Eq. (1). Here La Niña and El Niño cases are identified based on the typical definition. A total of seven La Niña (eight El Niño) cases are found during 1979–2013. As shown in Fig. 6, the difference of Case-EN minus Case-noEN resembles the composite of La Niña cases (Figs. 6a–d vs Figs. 6e–h). They all show cooler SAT anomalies in Eurasia and over northern and western North America along with warmer SAT over the Arctic. The PNA pattern is evident in SLP and Z500. This suggests an overall additive linearity. However, additive nonlinearity is also identifiable. The additive nonlinearity causes reduced coldness in East Asia (Fig. 6i), along with negative SLP anomalies over Eurasia (the weakened Siberian and Mongolian high; Fig. 6j), and positive Z500 anomalies over coastal East Asia (the weakening climatological East Asian trough; Fig. 6k). These correspond to the weakened East Asian winter monsoon. The nonlinearity tends to cancel the SIC-induced or SIC- and SST-induced precipitation anomalies with a ratio of one-tenth to one-fifth, which is seen from the opposite sign of precipitation anomalies (cf. Fig. 6i and Figs. 6d,h). These results are consistent with the additive linearity and nonlinearity found in the regression analyses.

Fig. 6.
Fig. 6.

(a)–(d) Composite differences in SAT, SLP, Z500, and precipitation of Case-EN minus Case-noEN, (e)–(h) observational composite in SAT, SLP, Z500, and precipitation for La Niña years, and (i)–(l) left minus center panels. The contour intervals and shading are as in Fig. 5, but in (i)–(k) the contour intervals are 0.25°C, 5 hPa, and 5 gpm, respectively. The zero contours in (a)–(c), (e)–(g), and (i)–(k) are indicated by black contours, and those in (d), (h), and (l) are omitted; the thick black lines in (c) and (g) indicate propagation of wave trains.

Citation: Journal of Climate 29, 15; 10.1175/JCLI-D-15-0416.1

4. An analysis based on the CMIP5 coupled historical simulations

Because of the limited size of sea ice anomaly cases in the observations, the above results have a considerable uncertainty. Analyses of longer model data may provide insights to the issue. Thus, we identify the anomalous cases of Arctic sea ice in the 405-yr historical simulations of the coupled model, MPI-ESM-LR, and conduct similar analyses to the above.

Similar to the observations, an extreme sea ice reduction (increase) case is defined as the sea ice area index is less than −1.0 (greater than 1.0) of its standard deviation. Here the threshold value of ±1.0 standard deviation is slightly higher than that used in the above observational analysis because the atmospheric signals linked to sea ice loss in the model is weaker. As such, a total of 126 extreme sea ice anomaly cases are identified (59 cases with ice increase and 67 cases with ice decrease). As for whether ENSO co-occurs, 86 cases (45 with ice increase and 41 with ice reduction) are not accompanied by La Niña or El Niño (Case-noEN). The remaining 40 cases are accompanied by La Niña or El Niño, among them are 23 cases (Case-EN) with La Niña (El Niño) corresponding to ice reduction (increase) (12 vs 11 cases) and 17 cases with La Niña (El Niño) corresponding to ice increase (reduction) (11 vs 6 cases). That most of ice anomaly cases are not accompanied with ENSO, together with a nearly same occurrence probability of opposite-phase ENSO when sea ice increases or reduces, confirms an overall independence between the two forcings.

Figure 7 displays a comparison of composite sea ice area and SSTA between the two groups of cases. As in the observations, one significant distinction is seen in the SSTA of the tropical central eastern Pacific. This confirms the separation of the two groups of events. In comparison with the observations, the magnitude of La Niña events for Case-EN from the model is weaker (cf. Figs 7b and 4e).

Fig. 7.
Fig. 7.

As in Fig. 4, but for the composite November SST anomalies (contours) and sea ice anomalies (shading) corresponding to two kinds of sea ice events in MPI-ESM-LR.

Citation: Journal of Climate 29, 15; 10.1175/JCLI-D-15-0416.1

Figure 8 displays a comparison of composite SAT, SLP, Z500, and tropical precipitation. Overall the two groups of cases are similar to each other, with cooler SAT in midlatitude Eurasia along with warmer SAT over the Arctic, as well as the increased climatological Siberian-Mongolian high and the deepened East Asian grand trough. In comparison, the anomalies in Case-EN are stronger. This suggests that La Niña intensifies colder SAT in midlatitude Eurasia, as seen in the observational analyses (cf. Figs. 8 and 5). Despite this overall similarity, the Arctic warming and Eurasian cooling for both the cases in the model are visually weaker and less prominent than the observations. One possible reason is the model’s bias, which underestimates atmospheric sensitivity to lower boundary forcing. For Case-EN, the model’s underestimate of the strength of ENSO may also play a role.

Fig. 8.
Fig. 8.

As in Fig. 5, but for the composites of the cases derived from the historical runs in MPI-ESM-LR. The contour intervals are 0.5°C in (a),(e); 5 hPa in (b),(f); 5 gpm in (c),(g); 0.5 mm day−1 in (d); and 1 mm day−1 in (h).

Citation: Journal of Climate 29, 15; 10.1175/JCLI-D-15-0416.1

As with Fig. 6, Fig. 9 displays the composite difference between the two groups (Figs. 9a–d), together with the composite of La Niña cases (Figs. 9e–h, represented by La Niña minus El Niño), as well as their residual (Figs. 9i–l, left minus center panels of Fig. 9). Based on the same threshold used above, a total of 127 ENSO cases (61 La Niña and 66 El Niño events) are identified without sea ice anomaly in preceding autumn. Again, additive linearity is dominant. In contrast, nonlinearity is weak and just identifiable, and tends to cancel a fraction of impacts from ice loss or La Niña (cf. Figs. 9 and 6). This suggests the existence of similar additive linearity and nonlinearity to that in the observations.

Fig. 9.
Fig. 9.

As in Fig. 6, but derived from the cases in the historical simulation datasets in MPI-ESM-LR. The contour intervals from top to bottom are 1.0°C, 5 hPa, 5 gpm, and 1 mm day−1.

Citation: Journal of Climate 29, 15; 10.1175/JCLI-D-15-0416.1

5. AGCM results

a. A comparison of responses to separated SIC reduction and to the combined SIC and La Niña SSTA

Additive linearity and nonlinearity is addressed further by AGCM sensitivity experiments with idealized SIC or SST forcing. Figure 10a–d shows the responses of SAT, SLP, Z500, and precipitation to sea ice reduction alone. There are colder SAT responses in mid-to-high-latitude Asia, along with warmer SAT in the region east to the Mediterranean Sea and the Tibetan Plateau, although the warming over the Arctic and the cooling in Europe seen in the observational analysis (Figs. 5 and 6) are not prominent. The SAT responses in North America feature a weak southwest warmer–northeast colder dipolar pattern. The responses are similar to the observational composite in Case-noEN, with the spatial correlation coefficient (CC) of 0.37 in the Northern Hemisphere (0.68 over the Eurasian region) (cf. Figs. 10a and 5a).

Fig. 10.
Fig. 10.

AGCM modeled responses to Arctic sea ice reduction and the accompanied SST anomalies (60°S–60°N), for (a)–(d) just the isolated sea ice and (e)–(h) sea ice and SST. Shading denotes significance exceeding the 90% level. Contour intervals from top to bottom are 0.5°C, 5 hPa, 5 gpm, and 2 mm day−1, respectively. The zero contours in (a)–(c) and (e)–(g) are indicated by black contours, and those in (d) and (h) are omitted; the thick black lines in (c) and (g) indicate propagation of wave trains.

Citation: Journal of Climate 29, 15; 10.1175/JCLI-D-15-0416.1

As for atmospheric circulation, there are negative SLP responses over most of the midlatitudes (Fig. 10b), along with positive (but less significant) SLP responses over the Arctic. They resemble the observational composite in Case-noEN (cf. Figs. 10b and 5b) well, with a CC of 0.64 over the Northern Hemisphere. Similar responses are also seen at Z500 (Fig. 10c) with a spatial CC of 0.52. They project on a negative-phase AO or North Atlantic Oscillation (NAO) visually.

Figures 10e–h show the AGCM responses to the Arctic sea ice reduction and the La Niña SSTA in combination. There is colder SAT response in the Eurasian region extending toward Lake Baikal, Japan, and southeastern China, along with warmer SAT in the Tibetan Plateau and northeastern Africa (Fig. 10e). These SAT responses bear an overall resemblance to the observational composite for Case-EN (cf. Figs. 10e and 5e), with the spatial CC of 0.44 over the Northern Hemisphere (Table 3), although the area within Eurasia with colder SAT is relatively small. In North America, SAT responses exhibit a northeast cooling–southwest warming dipolar pattern, different from the unanimous cooling in the observational composite. This may be related to the model’s bias in simulating the PNA pattern as seen in Fig. 10g.

Table 3.

Spatial CC between the AGCM modeled response and the observational composite over the Northern Hemisphere (20°–90°N). The two values in parentheses correspond to the CCs over the Eurasian region (20°–90°N, 0°–130°E) and the North American region (20°–90°N, 150°–60°W), respectively.

Table 3.

The SLP responses also bear some similarity to the observational composite in Case-EN (cf. Figs. 10f and 5f; also see Table 3), with projections onto the negative-phase PNA-like pattern. There are positive SLP responses over mid-to-high-latitude Eurasia, along with negative SLP responses over the tropical Indian Ocean and the western Pacific. This SLP response difference reflects an enhanced winter land–sea thermodynamic contrast, explaining intensified cold air activities and colder SAT in Eurasia. Similar responses are seen in Z500 over the Eurasian region (Fig. 10g), with a CC of 0.52 with the observational composite in Case-EN. The CC in the PNA region is relatively low, which is related to a nearly 30° westward bias of the positive center over the North Pacific (cf. Figs. 10g and 5g).

One may note that, similar to those in the CMIP5 model, the AGCM simulated Arctic warming and Eurasian cooling responses are weaker than the observational composite (cf. Figs. 10 and 5). This underestimate may arise from the present modeling experiment designs, in addition to the model’s bias in simulating the atmospheric sensitivity to lower boundary forcing. An autumn sea ice anomaly influences the following winter climate primarily through two processes. One is due to the persistence of sea ice anomaly. The other is due to the memory of land surface processes or oceanic thermal inertia. A September sea ice anomaly tends to induce more snowfall over the Eurasian continent (Cohen et al. 2012, 2014) as well as SSTA particularly over the North Atlantic (Guo et al. 2014; also Figs. 4b and 7a herein) in the following months. Although the present AGCM experiment design considers the persistence of autumn sea ice, it includes only a small part of land surface process. One analysis reveals that the present AGCM fails to capture the increased snow cover response in October in the Eurasian continent (not shown). In addition, the AGCM excludes the feedback of SST, since it is uncoupled with any oceanic model. Thus, the present experiments simulate just a fraction of atmospheric response signals to autumn sea ice anomaly.

Nonetheless, these AGCM results suggest that the sea ice reduction alone contributes to the observational composite anomalies in Case-noEN. Consistently, the SIC reduction and La Niña SSTA together account for the observed anomalies in Case-EN. This is a basis on which to separate the additive linearity or nonlinearity.

b. Additive linearity and nonlinearity in AGCM simulations

Similar to the observational analyses, additive linearity and nonlinearity can be understood by comparing the AGCM simulated response to simultaneous two forcings with those to separated two forcings. Referring to Eq. (1), the response to SIC and SSTA here corresponds to R(f1) and R(f2), respectively, while the response to simultaneous SIC and SSTA corresponds to R(f1 + f2).

From Fig. 11, the difference in Eurasian SAT response between the simultaneous two forcings and the only SIC forcing [Figs. 6a–d, calculated from the right minus the left panels of Fig. 10; i.e., R(f1 + f2) − R(f1)] bears some similarity to La Niña [Figs. 11e–h; i.e., R(f2)]. There are cold anomalies in East Asia and western Europe, along with a southern warmer–northern colder dipole in North America. Similar responses are seen in SLP and Z500. There are large positive SLP and Z500 responses over the North Pacific and the North Atlantic, which together encircle the negative values in the Arctic (Figs. 11b,c). This similarity suggests an overall additive linearity.

Fig. 11.
Fig. 11.

(a)–(d) Differences of the modeled responses to both Arctic sea ice reduction and the associated SST anomalies (60°S–60°N) minus the response to the sea ice, (e)–(h) AGCM responses to the isolated SST anomalies, and (i)–(l) left minus center panels (i.e., the differences of responses to sea ice and SST minus the combination of responses to separated sea ice and SST). The contour intervals are 0.5°C in (a),(e),(i); 5 hPa in (b),(f),(j); 5gpm in (c),(g),(k); 2 mm day−1 in (d),(h); and 0.5 mm day−1 in (l). The zero contours in (a)–(c), (e)–(g), and (i)–(k) are indicated by black contours, and those in (d), (h), and (l) are omitted; the thick black lines in (c) and (g) indicate propagation of wave trains.

Citation: Journal of Climate 29, 15; 10.1175/JCLI-D-15-0416.1

Nonetheless, one scrutiny check suggests that the negative SAT response in Asia in Fig. 11e [R(f2)] is stronger than the derived response in Fig. 6a [i.e. R(f1 + f2) − R(f1)]. The values of SLP and Z500 are enhanced in Eurasia (Figs. 11f,g), along with weakened SLP and Z500 responses in the Western Hemisphere and a weakened projection onto the PNA pattern. This suggests the existence of identifiable additive nonlinearity.

This nonlinearity is seen more clearly in the difference—see the left minus center panels in Fig. 8; that is, [R(f1 + f2) − R(f1)] − R(f2). There are positive SAT values in Eurasia extending to southeastern Asia (Fig. 11i), which is about one-tenth to one-fifth of their linear sum, close to the observations (cf. Figs. 11i–k and Figs. 6i–k). Correspondingly there are negative SLP values over the Arctic extending to the Eurasian continent, which tends to weaken the climatological winter Siberian high. There is a “positive–negative–positive” chain-like difference pattern in Z500, where the positive values over coastal East Asia tend to weaken the climatological East Asian grand trough. These circulation differences are in agreement with the warmer SAT, weakened cold air activities, and weakened East Asian winter monsoon. The agreement between the AGCM results and the observational composites suggests the robustness of the obtained additive linearity and nonlinearity.

6. A brief analysis of the underlying mechanism

In this section we will investigate the switch-on transient adjustment runs to diagnose the development of atmospheric responses related to the persistent sea ice anomaly. The suitability of studying these experiments to understand the above equilibrium results is supported by the resemblance of the response at quasi-equilibrium stage (roughly day 35) to the winter response in the sensitive runs (cf. Figs. 12d and 10c, Figs. 12l and 10g, and Figs. 12h and 10g).

Fig. 12.
Fig. 12.

The 5-day mean responses of Z500 in the transient runs: the response to (a)–(d) sea ice loss, (e)–(h) La Niña, and (i)–(l) combined sea ice loss and La Niña forcing. The contour intervals from left to right are 1, 2, 5, and 10 gpm, dashed contours are negative, and zero contours are omitted. The arrows in (d), (h), and (l) are the wave activity flux (m2 s−2) based on Takaya and Nakamura (2001).

Citation: Journal of Climate 29, 15; 10.1175/JCLI-D-15-0416.1

The transient atmospheric adjustment to a thermodynamic forcing (e.g., SSTA) can be broadly viewed as occurring on a 2–4-week time scale before equilibrium (Jin and Hoskins 1995). In the first week, heating anomalies develop and mature while the circulation response is mostly locally confined. Around week 2 linear wave dynamics develop and a global stationary wave response matures. The latter can be viewed as direct linear response to the thermodynamic forcing. It then modifies the basic state, resulting in reorganization of transient eddies and inducing anomalous transient eddy flux. The induced eddy forcing further interacts with the basic flow. This latter feedback process is important in determining the equilibrated solution (e.g., Held et al. 1989), whose ultimate adjustment time scale is on the order of a few weeks for a steady forcing. The different stages of this adjustment can be monitored in output of experiments.

From Fig. 12, the responses at week 1 to SIC loss or La Niña SSTA are weak and locally situated (left panels). Since then the responses develop and propagate upstream and downstream, so that wavelike patterns are seen at week 2 (the two center panels from the left). For the SIC switch-on runs, there is a wavelike response stretching from Greenland downstream toward northern Eurasia and upstream toward the midlatitude North Atlantic, along with another wavelike pattern extending across the North Pacific to North America (Fig. 12c). These response patterns are even clearer in the equilibrium stage (after week 4). They originate respectively from the Barents and Kara Seas and from the North Pacific adjacent to Bering Strait, the two evident ice loss regions (Fig. 4a). This is even clearer from the wave activity flux based on Takaya and Nakamura (2001) (Fig. 12d). For the La Niña runs, there are two branches of wavelike response patterns, one originating from the tropical central-eastern Pacific and propagating toward North America (like the PNA pattern) and the other originating from the tropical western Pacific and Indian Oceans and propagating toward the North Pacific. The former arises directly from the La Niña SSTA while the latter can be explained from the La Niña–induced thermodynamic forcing through the Walker cell (Li et al. 2010). Similar to the SIC switch-on case, the two wave trains become stronger in the equilibrium stage.

The response to the combined SIC loss and La Niña forcings look similar to the sum of the individual responses (cf. Figs. 13a–d and Figs. 12i–l). The resemblance explains the overall linear additivity of impacts of the two forcings. Indeed, in the beginning five days no evident additive nonlinearity {i.e. R(f1 + f2) − [R(f1) + R(f2)]} is seen. But, at week 1 in midlatitude Eurasia one opposite-sign additive nonlinearity pattern tends to cancel a fraction of the combination of the two impacts. Thus the interaction between the forcing-induced direct linear responses may contribute to the additive nonlinearity. This seems physically reasonable, because the linear wavelike response induced by one forcing may modify the basic flow and result in a different atmospheric response. At week 5 (nearly the equilibrium stage), the additive nonlinearity become intensified, suggesting that the eddy feedback processes may amplify the additive nonlinearity.

Fig. 13.
Fig. 13.

As in Fig. 12, but for (a)–(d) the combination of the responses to sea ice loss and La Niña and (e)–(h) the nonlinearity of the response expressed as the difference the response to the simultaneous two forcing minus the combination of the responses to the two individual forcings.

Citation: Journal of Climate 29, 15; 10.1175/JCLI-D-15-0416.1

7. Conclusions and discussion

In this study we first investigated the occurrence’s connection of September Arctic sea ice anomaly with following winter ENSO, and found an overall independence between them. In view of a similar cooling impact on Eurasian winter climate, additive linearity and nonlinearity between the two forcings (Arctic sea ice reduction and La Niña) were explored through observational analyses, historical simulations analysis in the MPI-ESM-LR coupled model, and AGCM (ECHAM5) sensitivity experiments. The results consistently suggest overall additive linearity, in spite of identifiable weak additive nonlinearity. The amplitude of additive nonlinearity is weak, just one-tenth to one-fifth as much as their linear additivity.

The underlying mechanisms responsible for the additive nonlinearity have been explored through comparing the transient adjustment AGCM runs with sea ice loss or La Niña SSTA or both the forcings switched on suddenly. The evolution of day-to-day responses suggests that the nonlinearity may arise initially from the forced wave dynamics around week 2, and be amplified by the involvement of transient eddy at the equilibrium.

This study highlights special attention to the co-occurrence of Arctic sea ice loss and ENSO events when predicting midlatitude Eurasian winter climate. This not only brings an additional supplementary to the role of sea ice reduction (e.g., Honda et al. 2009; Francis et al. 2009) but also accounts for some Eurasian extreme cold events like the January 2008 persistent snowstorm in southern China (Han et al. 2011; Wen et al. 2009; Zhou et al. 2009). One important cause for this extreme event is the co-occurrence of preceding-autumn extreme Arctic sea ice loss and winter strong La Niña.

In addition, we found two groups of Arctic sea ice reduction cases: one having negative-phase ENSO–like (i.e., La Niña) SST in the following winter (denoted as Case-EN) and the other not (denoted as Case-noEN). Substantial differences are seen between them. For Case-noEN the winter circulation anomaly projects onto the AO, but not for Case-EN. This explains the lack of consensus about the existence of the AO anomaly linked to sea ice reduction (e.g., Francis et al. 2009; Liu et al. 2012; Cohen et al. 2012; Screen et al. 2014; Mori et al. 2014; Walsh 2014; Wu et al. 2015).

Because the number of observational sample size with the co-occurrence of sea ice loss and La Niña events is small, the present study should be treated as a case study. There is uncertainty about the occurrence independence between Arctic sea ice anomaly and ENSO, as suggested by recent studies (Ding et al. 2014; Sato et al. 2014). From Fig. 1b, for the whole period the number of years (14) when the two indices have opposite signs is less than the number of years (20) when the two indices have the same signs (20 dots in quadrant 1 or 3 versus 14 dots in quadrant 2 or 4 in Fig. 1b). Also, the simulated Arctic warming and Eurasian cooling in both the CMIP5 model and the AGCM are weaker than the observational composite as analyzed in section 5a above. These suggest a further need to address this uncertainty.

Recent studies (Petoukhov and Semenov 2010; Semenov and Latif 2015) suggest substantial atmospheric nonlinearity with respect to the amplitude of sea ice loss. The weak additive nonlinearity found here may be related to the modest amplitude of Arctic sea ice loss. When the sea ice loss is doubled, nonlinearity indeed intensifies (not shown). Thus, the present results may be not applicable for future extreme sea ice loss cases. Besides, some recent studies have not found consistently robust linkages between Arctic sea ice and large-scale circulation anomalies (Walsh 2014; Overland et al. 2015; Wu et al. 2015). Also, the tropical North Atlantic may play a role in modulating the impact of sea ice loss (Sato et al. 2014). Nevertheless, these issues deserve further studies.

Acknowledgments

The authors are very grateful to the editor and the three anonymous reviewers for their insightful comments and constructive suggestions, which helped improve the manuscript substantially. This work was jointly supported by the National Basic Research Program (Grant 2015CB453202 and 2012CB417403), the Strategic Project of the Chinese Academy of Sciences (Grant XDA11010401), and the Natural Science Foundation of China (41305064 and 41375085).

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