Atmospheric Response to Arctic and Antarctic Sea Ice: The Importance of Ocean–Atmosphere Coupling and the Background State

The atmospheric response to Arctic and Antarctic sea ice changes typical of the present day and coming decades is investigated using the Hadley Centre global climate model (HadGEM3). The response is diagnosed from ensemble simulations of the period 1979 to 2009 with observed and perturbed sea ice con- centrations. The experimental design allows the impacts of ocean–atmosphere coupling and the background atmospheric state to be assessed. The modeled response can be very different to that inferred from statistical relationships, showing that the response cannot be easily diagnosed from observations. Reduced Arctic sea ice drives a local low pressure response in boreal summer and autumn. Increased Antarctic sea ice drives a poleward shift of the Southern Hemisphere midlatitude jet, especially in the cold season. Coupling enables surface temperature responses to spread to the ocean, amplifying the atmospheric response and revealing additional impacts including warming of the North Atlantic in response to reduced Arctic sea ice, with a northward shift of the Atlantic intertropical convergence zone and increased Sahel rainfall. The background statecontrolsthesign oftheNorthAtlanticOscillation(NAO)responseviatherefractionof planetarywaves. This could help to resolve differences in previous studies, and potentially provides an ‘‘emergent constraint’’ to narrow the uncertainties in the NAO response, highlighting the need for future multimodel coordinated experiments.


Introduction
Over the last three and a half decades Arctic sea ice extent has declined substantially, at an average rate of around 4% per decade annually and more than 10% per decade during the summer (e.g., Vaughan et al. 2013). Further reductions are expected as the climate continues to warm, with model projections suggesting that perennial Arctic sea ice could disappear within the next few decades (e.g., Collins et al. 2013). In contrast, Antarctic sea ice extent has increased slightly, at a rate of about 1.5% decade 21 , but is projected to decrease in future (Vaughan et al. 2013;Collins et al. 2013). Sea ice plays a key role in modulating the flow of energy in the climate system, with potentially important impacts on the global atmospheric circulation. Quantifying and understanding the influence of sea ice changes on the atmospheric circulation is therefore crucial for predicting how climate will change in the coming decades.
Many studies have investigated the potential influence of sea ice on the atmospheric circulation, and are summarized in recent review papers (Cohen et al. 2014;Vihma 2014;Walsh 2014; Barnes and Screen 2015;Overland et al. 2015). Of particular interest is whether Arctic sea ice reductions could affect the North Atlantic Oscillation (NAO), and hence the winter climate in Europe, North America, and parts of Asia. However, there is no consensus even on the sign of the NAO response: previous modeling studies simulate a full spectrum of responses including negative NAO (Honda et al. 2009;Seierstad and Bader 2009;Mori et al. 2014;Kim et al. 2014;Deser et al. 2015;Nakamura et al. 2015), positive NAO (Singarayer et al. 2006;Strey et al. 2010;Orsolini et al. 2012;Rinke et al. 2013;Cassano et al. 2014;Screen et al. 2014), little response (Screen et al. 2013;Petrie et al. 2015;Blackport and Kushner 2016), and a response that depends on the details of the forcing (Alexander et al. 2004;Petoukhov and Semenov 2010;Peings and Magnusdottir 2014;Sun et al. 2015;Pedersen et al. 2016). In contrast, the atmospheric response to Antarctic sea ice has received less attention (Simmonds and Budd 1991;Simmonds and Wu 1993;Menéndez et al. 1999;Kidston et al. 2011;Bader et al. 2013).
Recent studies have highlighted the importance of ocean-atmosphere coupling for simulating the response to sea ice Tomas et al. 2016). However, the response to other forcings, including greenhouse gases, ozone, changes in the polar vortex, and Atlantic sea surface temperatures, is known to depend on the climatological background state (Son et al. 2010;Kidston and Gerber 2010;Sigmond and Scinocca 2010;Garfinkel et al. 2013;Omrani et al. 2014), but this has not previously been investigated in relation to sea ice. Here we report on a comprehensive set of modeling experiments that are designed to assess the influences of both coupling and background state on the response to sea ice. We find that both are important. Coupling generally amplifies the atmospheric response because sea surface temperature (SST) changes driven by sea ice can spread to the surrounding ocean and are consequently larger. The coupled SST response reaches the tropics, and influences Sahel rainfall. The background state plays a key role in the NAO response to reduced Arctic sea ice in our model, to the extent that the sign of the NAO response is controlled by the refraction of planetary waves by the climatological flow. This provides a potential ''emergent constraint'' to narrow the uncertainties in the NAO response, highlighting the need for multimodel coordinated experiments.
The manuscript is organized as follows. Section 2 describes the model and experimental design, with results presented in section 3. Sections 4 and 5 explore the boreal winter NAO response and in particular why it depends on the background state. In section 6 we investigate a potential emergent constraint to reduce the uncertainties in the NAO response, and in section 7 we show that the response cannot be inferred from statistical relationships, highlighting the need for model experiments. We summarize and present conclusions in section 8.

Model and experimental design
We assess the impact of Arctic and Antarctic sea ice variations on the climate system by performing numerical experiments using the Met Office Hadley Centre global climate model HadGEM3, at the global configuration GA3 (Walters et al. 2011). The atmosphere resolution is 1.8758 longitude by 1.258 latitude (approximately 130 km in midlatitudes), with 85 vertical levels and an upper boundary at 85 km providing a realistic simulation of the stratosphere (Hardiman et al. 2012). We perform experiments with both an atmosphere only model forced by sea surface temperatures and sea ice concentrations at the lower boundary (following the Atmosphere Model Intercomparison Project protocol, hereafter AMIP), and a fully coupled atmosphere ocean model (hereafter CPLD) but with constrained sea ice concentrations (described below). The ocean component of the coupled model is NEMO3.2 with 75 vertical levels (1 m thick at the surface increasing to approximately 200 m at a depth of 6000 m) and a horizontal resolution of 18 longitude by 18 latitude increasing to 0.38 latitude in the tropics. Note that because CPLD SSTs are unconstrained we use time-varying SSTs in AMIP rather than climatological monthly averages to avoid suppressing the interannual SST variability in AMIP relative to CPLD.
To assess the impact of sea ice changes we perform two sets of simulations of the 30-yr period from December 1979to November 2009. In the first (control) set the model is provided with the observed monthly mean fields of Arctic and Antarctic sea ice concentration (Hurrell et al. 2008). In the second (perturbed sea ice) set, the model is constrained by perturbed monthly mean fields of sea ice concentration, where the perturbations are designed to investigate changes typical of the present day and coming decades rather than the much larger changes expected toward the end of the century. Over the Arctic the perturbed sea ice concentrations for each month are obtained by eroding the ice edge until the Northern Hemisphere total sea ice area is consistent with that expected by projecting the observed monthly trends in Northern Hemisphere total sea ice area forwards. The observed trends are computed over the final 15 years of our period (1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009). Specifically, we require a continuous 30-yr time series of perturbed monthly mean sea ice concentration fields in order to repeat the simulations of the period 1979-2009. This is created by starting from the 5-yr averaged monthly fields from the end of our period (2005-09) and then gradually eroding the sea ice edge at all longitudes until the total area is consistent with the projected trend of total area at the required time. This approach attempts to simulate the gradual melting of the ice pack expected over the coming 30 years, and avoids holes in the ice pack that could appear if we simply projected the trends forwards at each grid point. We originally did not intend to perturb Antarctic sea ice, but we inadvertently created perturbed ice fields equal to the 5-yr averaged monthly fields from the end of our period . Although this was unintentional, it does provide an opportunity to investigate the influence of Antarctic sea ice anomalies typical of the present day.
For the AMIP experiments the observed or perturbed sea ice concentrations are supplied at the lower boundary along with observed monthly mean fields of SST (Hurrell et al. 2008). The SSTs are identical in the control and perturbed sea ice experiments except where the sea ice has disappeared. In these regions the SST for the perturbed experiments is set to 273.14 K (linearly interpolating from 271.36 K based on the sea ice fraction). These values were chosen by analyzing observed SSTs at the sea ice edge. Specifically, grid points close to the ice edge were found to have an average temperature of 273.14 K, becoming progressively colder toward the freezing point of seawater (271.36 K) as the sea ice fraction increased. For the CPLD experiments the observed or perturbed sea ice conditions are imposed during the coupled model integration by relaxing to the required sea ice concentrations (interpolated to the appropriate time from the adjacent monthly mean values), using a 6-h relaxation time scale. This technique is the same as that used to create sea ice initial conditions for the Met Office decadal prediction system (DePreSys; Smith et al. 2013). To avoid undesired responses in deep ocean currents including the Atlantic meridional overturning circulation that might be driven by persistent relaxation increments (Dunstone and Smith 2010), we constrain ocean temperature and salinity below 200 m by relaxing to monthly mean values from the Met Office Statistical Ocean Reanalysis (MOSORA; Smith et al. 2015). Our experiments are therefore similar to slab ocean experiments  but potentially simulate dynamical responses in the upper ocean. However, our experiments are unsuitable for studying potential influences of sea ice on deep ocean circulation that could be important on decadal or longer time scales.
We perform both AMIP and CPLD experiments in order to investigate the role of ocean-atmosphere coupling, which has been found to be important in simulating the response to sea ice Tomas et al. 2016). However, differences between CPLD and AMIP could also be caused by differences in the climatological background state of the model, because SSTs in the AMIP simulations are close to reality whereas the CPLD experiments are only constrained below 200 m so that SSTs may drift toward the coupled model biases. To isolate the impact of the background state we perform an additional set of experiments (hereafter AMIP_CPLD) by repeating the AMIP simulations (both control and perturbed) but imposing the SST biases from the CPLD simulations. This is achieved by removing at each grid point and month the observed climatological average SST and replacing it with the climatological average from the ensemble mean of the CPLD experiments, thereby superimposing the observed variability onto the CPLD background state.
The changes in sea ice concentration and SST where the sea ice has disappeared are the same as in the AMIP experiment.
Both control and perturbed sea ice simulations consist of multiple ensemble members in order to isolate the impact of sea ice changes that appears to be small relative to intrinsic variability in models (e.g., Screen et al. 2013;Mori et al. 2014). However, we note that the signal-tonoise ratio may be too small in models (Eade et al. 2014;Scaife et al. 2014;Dunstone et al. 2016) so that the magnitude of any response could be underestimated. Hence we focus on diagnosing, and understanding, the robust response in our model. The AMIP and CPLD simulations contain 10 ensemble members (a total of 300 simulated years) and the AMIP_CPLD simulation contains 5 ensemble members. Ensemble members were generated by very small perturbations to the SST initial conditions. We diagnose the impact of sea ice as the difference between the perturbed sea ice and control experiments, and compute the average difference over all 30 years and all ensemble members to obtain the most robust results. Results are presented for the different seasons: June-August (JJA), September-November (SON), December-February (DJF), and March-May (MAM). We test for statistical significance using a twotailed Student's t test of the difference between two means.

Results
The imposed sea ice concentration perturbations averaged over the whole 30-yr period are shown in Fig. 1. Arctic sea ice is reduced in all seasons, with the largest reductions, especially in the interior of the ice pack, in boreal summer and autumn, and reductions mainly confined to the marginal ice regions in winter and spring. Antarctic sea ice is mainly increased, especially in June to November when the seasonal extent is largest, reflecting an increasing trend over the last few decades (e.g., Vaughan et al. 2013). However, there is some reduction around the Antarctic Peninsula. Near-surface temperatures ( Fig. 2) warm (cool) in the cold seasons where sea ice is reduced (increased), consistent with reduced ocean to atmosphere heat fluxes in the presence of sea ice (e.g., Screen et al. 2013;Peings and Magnusdottir 2014;Deser et al. 2015). There is little temperature change in the summer months in AMIP (Figs. 2a,c) since the imposed SST where the ice has been removed is similar to the control run surface temperature over sea ice, which is governed by temperatures near the melting point at this time of year. Temperature changes are larger in CPLD than AMIP, consistent with other studies , because areas of sea ice loss warm in summer, potentially leading to surface warming into the colder seasons, and also because changes over the sea ice are able to spread to the surrounding ocean in CPLD. The active ocean in CPLD also enables remote changes in SST Chiang and Bitz 2005). In particular, we find a warming in the tropical Atlantic in JJA, which will be discussed further below.
Both AMIP and CPLD show a significant increase in precipitation over the Arctic in SON (Fig. 3), consistent with increased evaporation in the absence of sea ice (not shown). However, precipitation changes over midlatitude land regions are insignificant and hypothesized increases in Eurasian snow cover (Cohen et al. 2012) are not simulated by our model (not shown).
The CPLD experiments simulate warming in the North Atlantic in response to reduced Arctic sea ice in all seasons, projecting onto the positive phase of Atlantic multidecadal variability (e.g., Knight et al. 2005). Although the changes in zonal wind are small and generally not significant for individual grid points, there is a reduction in zonal wind shear averaged over the hurricane main development region (MDR; 108-208N, 808-208W) of 0.6 m s 21 ( p , 0.07), amounting to 15% of the interannual variability. Reduced zonal wind shear and increased ascent in the MDR (Fig. 4) would be expected to promote hurricanes (e.g., Goldenberg et al. 2001;Smith et al. 2010;Dunstone et al. 2011), but the magnitude of this response is difficult to quantify in a model that does not have sufficiently high resolution to simulate realistic hurricanes. An anomalous Hadley circulation is also associated with Sahel rainfall (Sheen et al. 2017), which significantly increases in CPLD (0.09 mm day 21 , p , 0.025, computed over the region 108-208N, 208W-358E for the peak rainfall period July-September), comparable in magnitude to long-term projections (Biasutti 2013). These responses in the tropical Atlantic are not simulated by AMIP, showing the need for coupled models to simulate the full response to sea ice changes in agreement with previous studies Tomas et al. 2016). However, we note that our experiments inhibit changes in deep ocean circulation that could also play a role, especially on decadal time scales.
Changes in mean sea level pressure (MSLP) are shown in Figs. 5 and 6 for the Arctic and Antarctic regions. The AMIP simulations show a weak low pressure over reduced Arctic sea ice in all seasons consistent with a ''heat low'' (e.g., Rácz and Smith 1999)  than AMIP since the surface warms more (Fig. 2) and is significant for the area average north of 608N in both seasons. In boreal winter the AMIP response projects onto a significant positive North Atlantic Oscillation [NAO; computed here as the difference between normalized pressure indices for Lisbon (38. 78N, 9.18W) and Iceland (65.18N, 22.78W)] (Hurrell 1995). However, the NAO response is baroclinic, with no significant response in 500-hPa geopotential height (z500) over the Arctic (not shown). In contrast, the CPLD simulations are very different in boreal winter and spring, showing a barotropic response with significantly high z500 over the Arctic (not shown), high pressure over the Nordic Seas, and low pressure farther south, and hence a significant negative NAO. We focus on the DJF NAO and investigate the reason for the different responses in CPLD and AMIP in sections 4 and 5. Over the Antarctic the response broadly resembles a positive southern annular mode (SAM; the difference in normalized zonal mean pressure between 408 and 658S; Gong and Wang 1999), with low pressure near the pole surrounded by a ring of high pressure. However, the SAM response is only significant in MAM in CPLD and JJA in AMIP.
Zonal mean changes as a function of latitude and height are shown in Figs. 7 and 8 for temperature and zonal wind. In AMIP, DJF warming over the Arctic is confined to the boundary layer, due to the surface-based warming and the stable lower atmosphere during winter. Consequently there is very little response in zonal wind (Figs. 7c and 8c) consistent with little change in MSLP (Fig. 5c). In contrast, CPLD shows a barotropic response with a weakening of the stratospheric polar vortex and weaker zonal winds extending down to the surface (Fig. 8g). Furthermore, the upper troposphere and stratosphere warm (Fig. 7g), consistent with adiabatic warming due to descent and compression of air over the pole leading to high pressure and hence a negative NAO (Fig. 5g).
Both AMIP and CPLD simulate a poleward shift of Southern Hemisphere midlatitude tropospheric jet in the cold seasons (JJA and SON) in response to increased Antarctic sea ice extent consistent with previous studies (Simmonds and Budd 1991;Simmonds and Wu 1993;Menéndez et al. 1999;Kidston et al. 2011;Bader et al. 2013). The mechanism involves changes in planetary waves (not shown), in agreement with Kidston et al. 2011, and is the same as for the CPLD NAO response that is discussed in section 5. Strengthened Southern Hemisphere winds in MAM are simulated by CPLD but not AMIP (Figs. 8d,h). This is discussed further in the next section.

Why is the NAO response different in CPLD and AMIP?
We now investigate the reasons for the different DJFmean NAO response in AMIP and CPLD. Whether reduced Arctic sea ice induces a positive or negative NAO has important implications for wintertime weather and climate over Europe, the United States, and Asia. However, there is no consensus in previous studies even on the sign of the NAO response, as summarized in section 1. In our experiments the NAO response depends on whether the model was run in AMIP or CPLD mode (cf. Figs. 5c,g). Understanding the reason for this may help to resolve the lack of agreement in previous studies.
Two possible causes of differences between AMIP and CPLD are 1) ocean-atmosphere coupling, which allows sea ice changes to influence the surrounding ocean in CPLD and enables feedbacks between the atmosphere and the active upper ocean, and 2) differences in the climatological background state, which arise because AMIP SSTs are constrained to be close to reality whereas the upper 200 m of our CPLD simulations are free to drift toward the coupled model's preferred state. Differences in the background state are illustrated in Fig. 9 for DJF. The CPLD simulations are cooler than AMIP in most regions but warmer in the Southern Ocean. The tropospheric jets (at around 200 hPa) are weakened and shifted poleward in both hemispheres, and the northern stratospheric polar vortex is strengthened and shifted poleward.
We isolate the impact of background state using the AMIP_CPLD simulations. These repeat AMIP with the same SST and sea ice perturbations, but imposing the climatological background ocean state from CPLD (as described in section 2). This successfully reproduces the CPLD biases in zonal wind (cf. Figs. 9b,c). The AMIP_CPLD simulations closely reproduce the CPLD DJF Northern Hemisphere MSLP response (cf. Figs. 10a and 5g), together with the weakened zonal winds throughout the troposphere and stratosphere (cf. Figs. 10c and 8g). This shows that background state rather than other effects of coupling is the main reason for differences in the NAO response between AMIP and CPLD. However, the AMIP_CPLD simulations do not reproduce the CPLD MAM MSLP response over the Antarctic (cf. Figs. 10b and 6h) or the strengthened Southern Hemisphere winds (cf. Figs. 10d and 8h), showing that coupling (such as the stronger cooling shown in Fig. 2h) is important here.
How can the NAO response to the same sea ice changes be opposite in the AMIP and CPLD experiments? A possible explanation is that the total response FIG. 6. As in Fig. 2, but for Southern Hemisphere mean sea level pressure (hPa). is a combination of thermodynamic and dynamic responses (e.g., Deser et al. 2004). The thermodynamic response consists of low pressure (a heat low) over the warmer surface temperatures where the sea ice has been reduced, and hence a positive NAO. In contrast, the dynamic response consists of a weakening of the midlatitude westerly winds, with a weaker meridional pressure gradient to maintain geostrophic balance and higher pressure over polar regions as seen in a negative NAO. We suggest that the thermodynamic response is dominant in AMIP, whereas the dynamic response is dominant in CPLD, leading to opposite responses in the NAO. However, the AMIP simulations do show a weakening of the midlatitude westerly winds in MAM (Fig. 8d), suggesting that a dynamic response is occurring but is delayed relative to CPLD and AMIP_CPLD.

Why does the NAO response depend on the background state?
Although AMIP_CPLD successfully reproduces the large scale patterns of bias in the CPLD background state (Figs. 9b,c), the magnitudes of the biases are slightly smaller. This provides an opportunity to investigate the response across the three sets of simulations with different background states (AMIP, CPLD, and AMIP_CPLD) in order to understand the physical reasons for their differences. We present results focusing on the DJF Atlantic eddy-driven jet (diagnosed from zonal velocity at 200 hPa, 508-608N, 608-08W), but results for the polar vortex (at 10 hPa, 608N) provide similar conclusions.
Model responses to changes in ozone (Son et al. 2010), greenhouse gases (Kidston and Gerber 2010), and the stratospheric polar vortex (Garfinkel et al. 2013) depend on the climatological position of the jet. We find a similar dependence for the response of the Atlantic jet to Arctic sea ice (Fig. 11a). One possibility is that the influence of the sea ice depends on the distance to the jet, as argued by Kidston et al. (2011) for the Southern Hemisphere. However, the physical mechanism for this is unclear, especially since differences in jet latitude FIG. 9. Climatological difference between CPLD and AMIP (a) near-surface temperature and (b) zonal mean zonal wind as a function of latitude and height (hPa). (c) As in (b), but for the difference between AMIP_CPLD and AMIP. Differences are shown for DJF averaged over all 30 years of the control experiments. Contours show the AMIP climatological winds (contour interval 5 m s 21 ; negative contours are dashed).
between simulations are small compared to the distance between the jet and the sea ice edge. Furthermore, the response also appears to depend on the strength of the jet (Fig. 11b), suggesting that other properties of the background state rather than simply the proximity to the ice edge could be the underlying reason the different responses.
We investigate further by examining the planetary wave response, diagnosed from Eliassen-Palm (EP) fluxes (e.g., Edmon et al. 1980). The zonal-mean zonal flow is accelerated (decelerated) where there is divergence (convergence) of the EP flux. On average, planetary waves originate near the surface in the storm tracks between latitudes 308 and 708N (red shading in Fig. 12a). They propagate vertically into the stratosphere and are refracted equatorward, especially in the troposphere (e.g., Li et al. 2007). At midlatitudes, zonal winds are on average accelerated by a divergence of EP flux near the surface and decelerated by a convergence of EP flux in the midtroposphere (shading in Fig. 12e).
In response to reduced Arctic sea ice all three experiments exhibit a reduction in DJF vertical EP flux near the surface, especially between 508 and 608N, (blue shading near the surface in Figs. 12b-d). This is consistent with reduced Eady growth rates (Eady 1949) in the Gulf Stream and Kuroshio regions (not shown) and can be understood as a weakening of the baroclinic eddy wave source in response to a weaker equator-to-pole surface temperature gradient with reduced ice. Other studies show a similar reduction in wave fluxes FIG. 10. As in Figs. 5 and 8, but for AMIP_CPLD simulations of (a),(b) mean sea level pressure (hPa) in DJF and MAM and (c),(d) zonal mean zonal wind (m s 21 ) as a function of latitude and height (in pressure coordinates) for DJF and MAM, respectively. Contours show the AMIP climatological zonal winds (contour interval 5 m s 21 ; negative contours are dashed). (Seierstad and Bader 2009;Smith and Scott 2016). However, some studies (Jaiser et al. 2013;Kim et al. 2014;Peings and Magnusdottir 2014;Feldstein and Lee 2014;Sun et al. 2015;Nakamura et al. 2015;Overland et al. 2016) argue that increased vertical EP fluxes, particularly in individual months or in certain regions, are important for driving a negative NAO. While we do find increased vertical EP fluxes in individual months (not shown), and in the high-latitude (708-808N) upper troposphere and stratosphere in AMIP and CPLD for DJF (Figs. 12b,c), they are not consistent with the differences in NAO response in the three sets of simulations: for example, the increases at high latitudes occur in both CPLD and AMIP but the NAO response is opposite. Increased vertical EP fluxes are therefore likely to be secondary effects in our simulations.
Although the vertical EP flux source near the surface is reduced in all experiments, the response at higher levels in the atmosphere is different. In particular, there is a convergence (divergence) of EP flux on the poleward (equatorward) flank of the tropospheric jet in both CPLD and AMIP_CPLD, whereas AMIP shows broadly the opposite though the convergence on the equatorward side of the jet is not significant (shading in Figs. 12f-h). Hence, wave forcing acts to shift the tropospheric jet equatorward (poleward) in CPLD and AMIP_CPLD (AMIP), consistent with a negative (positive) NAO response. A possible explanation for the different behavior is therefore that the different background states cause waves to propagate differently.
We investigate further by considering the dependence of the jet response on the climatological refractive index n 2 k (e.g., Li et al. 2007): is the meridional gradient of the zonal mean potential vorticity, and k, N, H, f, a, V, and u denote the zonal wavenumber, buoyancy frequency, scale height, Coriolis parameter, Earth radius, Earth rotation frequency, and latitude, respectively. Note that waves are refracted toward high values of n 2 k (e.g., Matsuno 1970;Li et al. 2007).
The reason for the different responses in our simulations is easiest to illustrate by considering the propagation of waves away from an anomalous source. This would be the case for increased Arctic sea ice, which drives an increase in the Atlantic eddy-driven jet in CPLD and AMIP_CPLD but not in AMIP (as shown in Fig. 11 but with the sign of the response reversed). To understand these differences we compare the response in the jet across the three sets of simulations with the corresponding climatological refractive index and with the response in EP fluxes and divergence. Although there are just three sets of simulations, the large-scale patterns (Fig. 13) suggest that differences in the climatological refractive index potentially explain the different responses. Specifically, a strengthening of the Atlantic jet is associated with an increased equatorward wave flux in the troposphere (Fig. 13, arrows), which interacts with the mean flow associated with the tropospheric jet, resulting in increased EP flux divergence (convergence) on the poleward (equatorward) side of the jet (Fig. 13a). Since EP flux divergence (convergence) accelerates (decelerates) the flow, this is consistent with a poleward shift of the jet and a positive NAO. The role of the background climatological state can now be understood by considering the relation between the jet response and the climatological refractive index (Fig. 13b): since waves tend to be refracted toward higher values of the refractive index (e.g., Matsuno 1970;Li et al. 2007), increased equatorward wave flux in the troposphere is consistent with stronger refraction of waves toward a climatological refractive index that is higher in midlatitudes (positive correlations shown by red shading) and lower at high latitudes (negative correlations shown by blue shading).

What is the NAO response in reality?
Our results imply a central role for the refractive index in determining the Northern Hemisphere winter response to Arctic sea ice. This is consistent with modeled sensitivity to climate change (Sigmond and Scinocca 2010) and with the mechanism proposed by Simpson et al. (2012) to explain the dependence of jet response on its climatological latitude (Son et al. 2010, Kidston andGerber 2010). A key challenge now is to quantify the response of the real world.
One approach is to use ''emergent constraints'' (e.g., Collins et al. 2012) in which modeled uncertainties may be reduced by using observations of a quantity that is correlated across the range of model responses. Observations of the latitude and strength of the Atlantic eddy-driven jet would suggest little response in reality, in closer agreement with AMIP than CPLD (Fig. 11). However, this approach can lead to spurious conclusions (Bracegirdle and Stephenson 2013), particularly if the constraint does not capture the underlying physical mechanism responsible for the model spread (Scaife et al. 2009). The underlying mechanism in our simulations is differences in wave propagation caused by differences in tropospheric refractive index between mid and high latitudes (Fig. 13). A constraint based on refractive index difference is therefore likely to be more realistic than one based on the jet position or strength, and provides further evidence for a negative NAO response to reduced Arctic sea ice (Fig. 14). We note that the refractive index differences between the experiments are dominated by the meridional gradient of the zonal mean potential vorticity, and it is the high-latitude refractive index that is inaccurately simulated in AMIP (not shown), leading to the different constraints in Figs. 11 and 14. Understanding the reason for this is left for future work. Furthermore, we caution that the signal-to-noise ratio in seasonal predictions of the NAO appears to be unrealistically small (Eade et al. 2014, Dunstone et al. 2016, so that the magnitude of the response could be larger than simulated by our model.

Regression versus true response
Many studies have attempted to assess the impact of Arctic sea ice on the atmospheric circulation from the observations, using statistical analysis usually based on FIG. 13. Correlation across the AMIP, AMIP_CPLD, and CPLD experiments between the response in the Atlantic eddy-driven jet speed to increased Arctic sea ice (as in Fig. 11 but with the sign reversed) and (a) the response in EP flux divergence, and (b) the climatological refractive index for DJF (color shading). Arrows show the correlations between the response in the Atlantic jet and the response in vertical and meridional EP fluxes, plotted as a vector (arrow length for a meridional EP flux correlation of one is indicated). Black contours show the climatological zonal wind for AMIP. regression or composites (e.g., Overland and Wang 2010;Liu et al. 2012;Tang et al. 2013;Jaiser et al. 2013;Kim et al. 2014;Feldstein and Lee 2014;Francis and Vavrus 2015;Handorf et al. 2015;Kug et al. 2015;Luo et al. 2016;Yang et al. 2016). However, causality cannot be inferred from statistical relationships, and this approach may give misleading results when other factors are important. We illustrate this by computing the linear regression between autumn (SON) Arctic sea ice extent and the following winter (DJF) mean sea level pressure. A lag is required to avoid the contemporaneous impact of the atmospheric circulation on the sea ice, and assumes that sea ice in SON drives a response that propagates through the climate system to influence the DJF sea level pressure. Both observed and AMIP regressions show a negative NAO pattern (Figs. 15a,b), suggesting that reduced Arctic sea ice loss could be driving a negative NAO. However, the actual response to Arctic sea ice in the AMIP simulations is very different from that suggested by the regression analysis, with a very weak positive NAO (Fig. 15c). Similar analysis of the CPLD experiments also shows a different response from that diagnosed from regression (not shown). Hence, although statistical analysis can give some insight in some cases, it can also give misleading results. Statistical analysis must therefore be interpreted with caution, and model experiments are needed to assess causality.

Summary and conclusions
We have performed a comprehensive set of model experiments to assess the atmospheric impact of Arctic and Antarctic sea ice changes typical of the present day and near future. The experiments enable the roles of ocean-atmosphere coupling and the climatological background state of the atmosphere to be assessed. We show that the response inferred from statistical relationships may be opposite to the true response due to confounding factors. Hence, the response cannot easily be inferred from the observations, despite many attempts in the literature.
In boreal summer and autumn sea level pressure reduces over the Arctic consistent with a heat low response to warmer surface temperatures. This response is larger in the coupled simulations, which have greater surface warming. Precipitation increases significantly over the Arctic in SON. However, hypothesized increases in Eurasian snow cover (Cohen et al. 2012) are not simulated by our model, in agreement with Sun et al. (2015). Further studies are needed to assess this potential linkage.
The response to increased Antarctic sea ice shows a poleward shift of the midlatitude tropospheric jet in the cold seasons consistent with previous studies (Simmonds and Budd 1991;Menéndez et al. 1999;Kidston et al. 2011;Bader et al. 2013). However, further work is required to assess the response to projected future decreases in Antarctic sea ice, for which Bader et al. (2013) find an equatorward shift of the jet but Kidston et al. (2011) find little response, arguing that ice edge becomes too far away to influence the jet. However, our results for the Northern Hemisphere jet (summarized below) highlight the importance of the background state rather than the distance to the ice edge, and might help to explain the difference in these two studies. Coupling enables surface temperature responses to spread to the ocean Tomas et al. 2016). In our model, reduced Arctic sea ice drives a warmer North Atlantic especially in boreal summer and autumn, leading to increased Sahel rainfall comparable in magnitude to long-term projections in response to greenhouse gases (Biasutti 2013). This is consistent with Chiang and Bitz (2005) but does not appear to be simulated in some other studies Tomas et al. 2016). Further work is needed to understand the reason for these differences.
Our main focus is on the boreal winter NAO, for which previous results are controversial . The sign of the NAO response to reduced Arctic sea ice depends on the climatological background state in our model. The overall response consists of a thermodynamic heat low projecting onto a positive NAO, together with a dynamical weakening of the westerly flow which projects onto a negative NAO. Whether the dynamical weakening dominates, giving a negative NAO overall, depends on the propagation of planetary waves, which is governed by the climatological refractive index and in particular its difference between the middle and high latitudes.
The mechanism for the NAO response is different from many studies that highlight an increase in planetary wave activity in response to reduced Arctic sea ice (Jaiser et al. 2013;Kim et al. 2014;Peings and Magnusdottir 2014;Feldstein and Lee 2014;Sun et al. 2015;Nakamura et al. 2015;Overland et al. 2016). Instead, we find that reduced Arctic sea ice drives a reduction in upward planetary waves from the surface. This is in agreement with some previous studies (Seierstad andBader 2009, Smith andScott 2016) and can be understood as a weakening of the baroclinic-eddy wave source in response to a weaker equator to pole surface temperature gradient. The impact on the tropospheric jet (and hence the NAO) is easier to illustrate by considering the case of increased Arctic sea ice. This drives an increase in upward planetary waves, which are refracted equatorward in the troposphere. They converge (diverge) on the equatorward (poleward) flank of the jet, leading to poleward shift and a positive NAO (negative for reduced sea ice). The magnitude of this response is governed by the amount of equatorward refraction of planetary waves, and hence depends on the background refractive index.
The importance of the background state for the NAO response could help to resolve some of the differences seen in previous studies, and potentially provides an ''emergent constraint'' to reduce the uncertainties. In our simulations, an emergent constraint based on the observed difference in upper tropospheric refractive index between the middle and high latitudes provides further support for a negative NAO response to reduced Arctic sea ice in reality. However, our results are with a single model and a single experimental design, whereas differences found in previous studies might be caused by different models, forcings, and experimental setups. Hence, multimodel coordinated experiments are required to isolate these different factors, and to provide a more robust constraint on the likely real-world response to Arctic sea ice loss. Finally, we note that although the simulated NAO response is quite weak (less than 80% of its interannual standard deviation), the magnitude could be incorrect given that the signal-to-noise ratio in climate predictions of the NAO is too small (Eade et al. 2014;Scaife et al. 2014). Further work is needed to resolve this issue.