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1Oceanography Department, US Naval Academy, Anapolis, MD, USA. 2Department of Earth System Science, University of California, Irvine, Irvine, CA, USA. 3School of Meteorology, University of Oklahoma, Norman, OK, USA. 4Department of Physics, University of Toronto, Toronto, Ontario, Canada. *e-mail: ghenders@usna.edu

Snow cover has been identified as the most variable land surface condition in both time and space1,2, influencing the climate of a region locally via surface energy balance modulation, or

remotely via snow–atmosphere coupling and the subsequent impli-cations for circulation. Factors that contribute to the local impact of snow include its high surface albedo, thermal emissivity and ground-insulating properties, and the energy required to melt the pack itself during the snowmelt season. Trends and variability in snow cover are of key importance for cold regions facing substan-tially lower spring snow cover than the present day throughout the Northern Hemisphere by the end of the twenty-first century under higher RCP scenarios3, and the degree of global warming is inextri-cably linked to the retreat of seasonal snow cover4.

Trends in Northern Hemisphere early season (boreal fall) snow cover are less monotonic and less confidently projected than those for spring. However, interest in Northern Hemisphere fall snow cover extends beyond understanding its local impacts or the prob-lem of global climate change. More than three decades of scientific literature document how regional snow-cover anomalies, particu-larly during the boreal autumn, might modulate the hemispheric atmospheric circulation during the late autumn and into the boreal winter. Such studies have employed both observed/reanalysis data and climate models to quantify and understand the relationship. The proposed impacts of snow–atmosphere coupling operate on sub-seasonal, seasonal, interannual and multidecadal timescales. Earlier empirical studies often encountered challenges associated with separating cause from effect5,6, leading to subsequent focus on modelling the relationship7–12. Observational and modelling efforts have so far concentrated on Eurasian or Siberian autumn snow-cover variability and its impact on Northern Hemisphere atmo-spheric circulation. This focus is due, as we will review below, to the magnitude and variability of ephemeral snow-cover extent through-out this region, geographic specificities (orography, land–sea ther-mal contrast) that make Siberia a source of upward wave activity and the ability of Eurasian snow-cover extent to produce a mod-elled response when prescribed as a forced boundary condition. However, North American snow cover and depth may also have a detectable, albeit weaker, relationship with downstream climate13–16.

Despite recent advances in the ability of climate models to emu-late complex atmospheric dynamics — including improvements in model resolution and ensemble size — reproducing the sequence of

processes by which snow cover can influence the atmosphere and subsequent atmospheric circulation (see Box 1 and Table 1) remains challenging. Such difficulties have led to a growing body of recent research calling into question the robustness of the atmospheric response to snow forcing. Another key issue identified in this research is non-stationarity: namely, that the connection between Eurasian snow-cover variability and extratropical circulation in previous stud-ies might change17–20. A further complication in efforts to advance our understanding of snow–atmosphere coupling is the need to consider how projected climate change throughout the twenty-first century will impact Northern Hemisphere atmospheric teleconnections3. However, the confidence in projected changes to teleconnections are medium in the near term (up to 2050) and low in the long term (up to 2100), due to large response uncertainty and internal variability21.

Owing to such issues, the scientific community has encountered a roadblock in advancing our understanding of the coupling of snow anomalies to extratropical atmospheric circulation, prompting both the timeliness and motivation for this Review. We seek to appraise this important area of snow–atmosphere coupling, summarize the community’s current level of understanding of the dynamical pro-cesses involved and offer our perspective on the implications of this interaction under future climate change. To aid in a transparent and accessible review of previous findings, unresolved questions and potential future directions, we adapt the ‘Can it?/Has it?/Will it?’ analysis framework of Barnes and Screen22. In particular we ask:

• Can it? What are the dynamical ideas, inferred primarily from model analysis, about how snow cover can influence atmos-pheric circulation?

• Has it? What is the observational evidence for the snow-cover/atmospheric circulation coupling in recent climate variability and change?

• Will it? How will the coupling identified in the preceding sec-tions be manifested with anthropogenic global warming, and how will climate change impact these couplings?

Can it?Early modelling work on snow–atmosphere coupling focused on the local cooling from snow anomalies and its influence on synoptic scales23,24, as well as the boreal winter influences of

Snow–atmosphere coupling in the Northern HemisphereGina R. Henderson   1*, Yannick Peings2, Jason C. Furtado3 and Paul J. Kushner   4

Local and remote impacts of seasonal snow cover on atmospheric circulation have been explored extensively, with observa-tional and modelling efforts focusing on how Eurasian autumn snow-cover variability potentially drives Northern Hemisphere atmospheric circulation via the generation of deep, planetary-scale atmospheric waves. Despite climate modelling advances, models remain challenged to reproduce the proposed sequence of processes by which snow cover can influence the atmo-sphere, calling into question the robustness of this coupling. Here, we summarize the current level of understanding of snow–atmosphere coupling, and the implications of this interaction under future climate change. Projected patterns of snow-cover variability and altered stratospheric conditions suggest a need for new model experiments to isolate the effect of projected changes in snow on the atmosphere.

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Northern Hemisphere snow cover on climate patterns and storm tracks25–29. Although these studies paved the way for a deeper under-standing, they generally prescribed idealized forcing and were susceptible to the impacts of atmospheric noise owing to limited computational resources.

Further progress was motivated by observational evidence of snow influence on Northern Hemisphere winter climate variabil-ity30,31, and by the identification of a stratospheric pathway for this influence32. In particular, the wave-mean flow mechanism of Saito and co-authors32 associated an increased extent of snow over Siberia in fall with the negative phase of the Arctic Oscillation33,34 (AO), or the tropospheric Northern Annular Mode (NAM), the subsequent winter (see Fig. 1 and Box 1). Because of the coherence between the AO, the NAM, and the North Atlantic Oscillation (NAO), we

refer to this as the ‘snow–(N)AO/NAM’ linkage. Subsequent gen-eral circulation model (GCM) literature generally supported the proposed stratospheric pathway mechanism7–9,11,12,35–37. These stud-ies revealed that: (1) snow-driven planetary waves in Siberia are key to force a stratospheric response and associated (N)AO/NAM response at the surface (Fig. 1 and Box 1); (2) Siberian snow anoma-lies are more efficient at driving a large-scale response than North American snow anomalies due to orography and other geographi-cal factors35,36; (3) the response is sensitive to the initial and mean state of the stratosphere8,9,12; and (4) although generally an empha-sis has been placed on the role of snow extent in reflecting short-wave radiation (the albedo effect)9,11, some studies suggest that the influence of snow depth on the surface energy budget and land–atmosphere coupling is equally important37,38. More realistic studies

Box 1 | Challenges of modelling the snow–(N)aO/Nam linkage

The snow–(N)AO/NAM linkage (see Fig. 1 adapted from Cohen and co-authors49 and Furtado and co-authors18) features differ-ent levels of scientific understanding and potential for capture in climate models (see the Table below).

Step 1As snow cover expands it can drive cooling beyond the cold conditions required for snowfall to persist on the ground92 due to the albedo, long-wave emissivity and insulation properties of snow, as well as its latent heat content23,93. However, Fig. 4 shows that it can be challenging to assess causality in the presence of other drivers such as large-scale temperature advection.

Steps 2–4Snow-forced cooling raises isentropic surfaces in the stably stratified lower troposphere (simple scaling suggests displacement of 50–300 m °C−1 of surface cooling, depending on the strength

of the surface inversion), which generates a dome of cold air over which quasi-adiabatic flow must pass and disturb the isentropic layers above9 (Step 2). This regional form stress provides a local source of Rossby wave activity (Step 3). For example, over Eurasia, greater snowfall is associated with the regional enhancement of upward-propagating Rossby wave activity18,48. When the pulse of Rossby wave activity reaches the stratosphere, its interaction and dissipation within the stratospheric polar vortex induces an anomalous westward torque that weakens (or even breaks down) the vortex and drives dynamical warming (Step 4).

Steps 5–6The circulation anomaly associated with a weakened stratospheric polar vortex projects onto the negative phase of the stratospheric NAM. This NAM signal then propagates downwards into the troposphere in subsequent weeks94 (Step 5), yielding an equatorward intensification/shift of the tropospheric jet stream and persistent cold winter extremes95 (Step 6).

Table 1 | Scientific understanding and current model capability for the snow–(N)aO/Nam linkage, for the steps shown above and in Fig. 1

Step Description level of scientific understanding model capability

1 Expansion of snow-cover and cooling

moderate to highSnow cover anomalies enhance surface cooling in fall, but how sensitive surface temperature is to autumn snow cover is uncertain.

moderateModels underestimate variability in boreal fall continental snow-cover expansion, especially over Eurasia18,42,76(Fig. 4).Circulation anomalies are better captured when realistic snow cover is initialized or prescribed.10–12

2–4 Planetary wave generation, propagation and breaking in the stratosphere

Poor to moderateWhat controls stationary waves and the response to surface cooling are only moderately understood.Why specific tropospheric circulation patterns (i.e., precursors to stratospheric circulation changes44,77–79 and anomalous snow cover need to exist for robust statistical predictions of wintertime circulation80 remains poorly understood. Persistence of the Rossby wave signal into the early winter is poorly understood.

Poor to moderateModels poorly simulate the background stationary wave, as well as the phasing of the circulation anomalies and cooling response to Eurasian snow18,40,81.Model atmospheres may be too insensitive to boundary forcing70.

5–6 Stratosphere–troposphere propagation of zonal-mean anomaly

moderate to highHow increased upward Rossby wave-activity flux anomalies into the stratosphere drive negative stratospheric NAM is well understood77,82,83, and downward coupling of NAM circulation anomalies is well-characterized (regardless of snow-cover anomalies18,84,85).However, stratosphere–troposphere dynamical coupling (lower stratospheric dynamical heating, wave reflection and tropospheric wave-mean-flow interactions86–88) is only moderately understood.

Poor to moderateModels simulate observed amplitude of tropospheric (N)AO/NAM reasonably well.Realistic stratospheric representation89,90, tropospheric jet stream structure and synoptic wave variability are required to simulate observed downward coupling as well as the tropospheric (N)AO/NAM state and its variability. GCMs are challenged in these areas, especially as stratospheric NAM anomalies descend into and influence the NAO/NAM in the troposphere18,91.

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also illustrated that interannual variability in Siberian snow modu-lates the phase and amplitude of the NAM, as well as the strength of the Aleutian and Icelandic lows10,39. When coupled to a slab ocean model, the atmosphere exhibits a larger response to snow due to sea surface temperature (SST) cooling upstream and downstream of Eurasian or North American snow anomalies16. The lag between the snow forcing in fall and the following winter has been attributed to the timing of constructive linear interference (that is, phasing) between anomalous and climatological wave flux activity40.

In contrast with the aforementioned work, a recent study by Peings and co-authors19 did not find a significant response to fall Siberian snow anomalies in two recent-generation atmospheric GCMs. One explanation may be their use of more realistic anoma-lies derived from observations. We note that although Gong and colleagues7 also prescribed realistic snow anomalies and recov-ered the snow–(N)AO/NAM link, their simulations included only 20 ensemble members, and as suggested in Fig. 2, this might not be enough to isolate the response from internal atmospheric vari-ability. Indeed, in Fig. 2 very different conclusions are drawn when analysing different 25-year subperiods of the 200-year simulations of Peings and co-authors 19. A small signal-to-noise ratio clearly requires a large ensemble of realizations when exploring the remote extratropical atmospheric response to a boundary forcing41.

The snow–(N)AO/NAM teleconnection is also absent in cou-pled ocean–atmosphere simulations from the Coupled Model Intercomparison Project (CMIP)18,42 (that is, the models assessed in the IPCC Assessment Reports). This absence has been attributed to the lack of constructive planetary wave interference in the GCMs40, as well as to weak vertically propagating waves and the subsequent downward propagation signal from the stratosphere into the tro-posphere18. Of course, models may also simply lack sensitivity to surface forcing associated with snow cover. Eurasian snow-cover variability is also smaller in the CMIP GCMs than in observa-tions18,42 (Fig. 3b), a clear limitation on a robust representation of snow-driven teleconnections. However, the discrepancies among GCM sensitivity studies need to be clarified, as well as the robust-ness of the observed relationship (see Has it? section) to confirm whether these findings point to real deficiencies of coupled GCMs.

Since it is key for the upward propagation of planetary waves and the associated stratospheric response, the constructive linear interference mechanism43,44 needs to be explored more thoroughly in future studies. If only certain configurations of the atmosphere allow for a large-scale effect of snow anomalies, it may explain discrepancies in GCM sensitivity studies and the non-stationarity in the observed teleconnection17.

Has it?Observational evidence linking snow cover, surface temperature and atmospheric circulation has been discussed alongside the mod-elling work cited in the Can it? section for over three decades. Foster and co-authors45 found statistically significant negative correlations between autumnal (October–November) Eurasian snow cover and mean wintertime temperatures over Eurasia, whereas the lagged relationship for North American autumnal snow cover and win-tertime temperatures was far more muted. However, when North American snow depth variability was considered by Ge and Gong14, robust concurrent lead and lag correlations were observed for both the Pacific North American and the Pacific Decadal Oscillation tele-connection patterns, suggesting that there may be climatic causes and consequences associated with snow depth variability. Clark and Serreze5 found that positive snow extremes over East Asia in mid-winter were associated with decreased surface air temperatures over the transient snow zone, influencing geopotential height over the North Pacific and the strength of the East Asia jet. However, even in this early work, the challenge of separating cause and effect was highlighted by the authors, who suggested the need for model stud-ies to address causality.

Focus shifted in the late 1990s to examining how Eurasian snow cover could impact not only local weather regimes but hemi-spheric scales. Pioneering work by Cohen and Entekhabi30, as well as Cohen and co-authors46,47, demonstrated that autumnal Eurasian snow cover, particularly during the month of October, skilfully predicted the winter-mean phase of the AO. As discussed in the Can it? section, Fig. 1 and Box 1, Eurasian snow-cover influences can be delayed by 1–3 months through the set-up of an amplified vertically propagating Rossby wave from the troposphere into the

L L

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Polar vortex weakensor breaks down

Snow lineexpands south

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Fig. 1 | Schematic representing the sequence of processes by which snow cover can influence the atmosphere and subsequent atmospheric circulation. Wavy red arrows indicate interaction between surface snow cover and regional enhancement of upward-propagating Rossby wave activity, with the stratospheric polar vortex represented by ‘L’ with anticlockwise flow. Resultant enhanced Rossby wave activity and troughing is indicated by the orange line.

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stratosphere, the subsequent weakening of the stratospheric polar vortex, and the downward influence of this weakened vortex on the troposphere48,49. The stratospheric polar vortex has weakened in recent decades50–52, although the degree to which this weakening is externally forced is unclear50,52. Thus, from the empirical perspec-tive, the snow–(N)AO/NAM teleconnection may not be directly linked to the weakening of the stratospheric polar vortex.

More recently, the issue of non-stationarity in the statistical relationships between snow-cover extent and various atmospheric wintertime variables has emerged. Peings and co-authors17, who used reanalysis data to compute coherence between Eurasian snow cover and the near-surface AO for over 100 years, showed that the snow–(N)AO/NAM connection was episodic and thus not reproducible throughout the twentieth century. However, we also note that assessing longer-term trends in Eurasian snow cover remains challenging due to scarce observations, necessitating a reliance on modelling/reanalysis. Moreover, the snow–(N)AO/NAM teleconnection may also be circumstantial even in the most

recent past. This changing relationship is illustrated when using observations from 1979 to the present day, as for the entire 39-year record (1979–2017), the correlation between October Eurasian snow cover and the subsequent December–February (DJF) near-surface AO index (with linear trends removed) stands at r = − 0.28 (P < 0.1), meaning less than 10% of the total variance in the DJF AO is linearly explained by October Eurasian snow cover (Supplementary Fig. 1). However, when the observational record is subdivided, the correlations in each half are markedly different, with correlations of r = –0.60 (P < 0.01) from 1979–1997, while those after 1998 collapse to nearly zero (r = 0.02 for 1998–2017).

Non-stationarity in the snow–(N)AO/NAM linkage suggests a relationship that relies on intermediary variables such as the phase of the Quasi-Biennial Oscillation19, or other oceanic modes of decadal variability such as the El Niño/Southern Oscillation (ENSO), the Atlantic Multi-Decadal Oscillation or the Pacific Decadal Oscillation. The possible influence of concurrent, but un -related, trends from global climate change and Arctic amplification

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Fig. 2 | Non-stationarity of the response to fall Siberian snow anomalies in sensitivity studies. The anomalies from a control run of the winter (December–March) sea-level pressure (colour shading and contours) in the presence of increased October–November Siberian snow are shown, for experiments with the WACCM model. a–h, Sequential series of 25-year subperiods extracted from 200 years of simulations. i, The mean of the periods shown in a–h, which approximates the climate response to the snow perturbation. Solid (dashed) contours represent positive (negative) sea-level pressure anomalies. Shaded regions indicate significance at the 95% confidence level. See Methods and Peings et al.19 for details of the experimental design. The October-November snow-cover anomalies of the perturbation run are shown in Fig. 4d.

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should also be noted53. Given the low level of correlations involved, internal variability and/or associated noise could easily be contami-nated by atmospheric internal variability, as is the case with ENSO-related impacts54. Ultimately, we must also recognize the possibility that the diagnosed snow–(N)AO/NAM teleconnection reflects a sampling artefact and not a dynamical linkage20. Future analysis of this problem should consider lessons learned when analysing the climatic impacts of ENSO variability54,55. Although assessing snow-cover variability along with circulation variability remains important for climate model evaluation, it is unclear whether this

particular teleconnection should be considered as a benchmark for climate model performance.

Will it?When considering whether future changes in terrestrial snow cover and depth will impact Northern Hemisphere atmospheric circulation and teleconnections, given the complex dynami-cal mechanisms and statistical issues summarized so far, it is no surprise that the answer is inconclusive. To provide insight into the possibility of future snow–atmosphere coupling, let us consider

∆TGLO (°C) ∆TGLO (°C)

Fig. 3 | Future changes in mean and variance of October snow-cover extent projected by 22 CmiP5 models. a, Distribution of the mean October Eurasian snow cover (35° E to 180° and 30–80° N) in the CMIP5 ensemble, for different increases in the global mean temperature (Δ TGLO, + 1 to + 4 °C, relative to the pre-industrial). b, Same as a but for Eurasian snow-cover s.d. Boxplots indicate the maximum, upper-quartile, median, lower-quartile and minimum of the distribution. The mean of the distribution is shown by red diamonds, the blue diamond corresponds to the 1972–2016 observed value (NSIDC satellite data). The average 30-year period corresponding to each global mean temperature increase is given on the x axis. c, Ensemble mean of the change in October snow-cover extent at + 4 °C. d, Same as c but for the snow-cover s.d. Contours indicate the climatology from the pre-industrial period (10% to 90%, contour interval 20%).

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what anthropogenic climate change might imply for the sequence of processes laid out in Box 1 (bearing in mind that the causal chain itself might also be altered by climate change).

Future changes in Northern Hemisphere snow-cover extent is the primary driver of change to consider (impacting Step 1 in our sequence). Based on CMIP Phase 5 (CMIP5) models, Krasting and co-authors56 found that overall annual snowfall is projected to decrease across much of the Northern Hemisphere during the twenty-first century, with trends varying by season and in sign across a transition zone that corresponds to the approximate geographical location of the –10 °C isotherm. This decrease in annual snowfall results in a decrease in snow-cover extent under the RCP8.5 sce-nario that is most pronounced at the southern edge of the snowpack across Northern Hemisphere continents4. Although observed twen-tieth century snow-cover extent records indicate significant trends towards a shortening of the snowmelt season due to earlier spring melt over much of Eurasia57, assessing trends in fall (which is key to the snow–atmosphere coupling sequence in Box 1) is more compli-cated. Fall trends have not echoed the spring decline and observed trends in October snow-cover extent have been found to be particu-larly sensitive to dataset discrepancies58–60, further complicating the non-stationarity issue of the snow–(N)AO/NAM teleconnection.

Conversely, the potential impacts of Arctic amplification on Northern Hemisphere terrestrial snow suggest increases in the Arctic/Siberian snowpack concurrent with sea-ice loss61. Although initial evidence indicates that this inverse sea ice–snow signal is weak, it could strengthen in future decades with continued climate change and global warming.

If we consider future changes during October only (that is, the most relevant month for the snow–(N)AO-NAM linkage), as pro-jected by an ensemble of 22 CMIP5 models under the RCP8.5 sce-nario, it is not surprising that the mean Northern Hemisphere snow cover decreases with increasing global mean temperature (Fig. 3a).

Indeed, with a projected 4 °C global mean temperature increase (centred on the 2063–2092 period in the 22 model ensemble), mean Northern Hemisphere snow cover decreases from 19% to 11%, with snow-cover reductions most prominent across much of high-lati-tude North America and to the west of 60° E in Eurasia (based on the ensemble mean; see Fig. 3c). When considering the projected change to the interannual variability of snow-cover, a source of vari-ability of Rossby waves in the proposed snow–(N)AO/NAM link-age, the standard deviation of October Eurasian snow cover displays little sensitivity to the magnitude of global temperature increase (Fig. 3b). However, the spatial average masks regional disparities, with the variance decreasing at the southern edge of the snowpack and increasing in high-latitude continents surrounding the Arctic Ocean (Fig. 3d). Whether the poleward shift in maximum snow variability, which could lead to weaker shortwave forcing, will have any influence on the lower atmosphere or the generation of wave forcings in the future remains to be explored. Testing for this effect in relation to other snow-related effects requires model studies in which projected snow changes are prescribed in isolation. Notably, the sole such study that has been carried out62 found that local dia-batic responses to this forcing do not extend to teleconnected (N)AO/NAM type responses in the presence of noise and feedbacks with other components of the climate system.

In addition to modelled changes in the cryosphere and associ-ated impacts on extratropical circulation, responses of the other components of the linkage to climate change are also likely to take place, quite apart from the influence of snow cover. Decades of stud-ies considering predicted trends in the near-surface (N)AO/NAM under future climate change reveal inconclusive results. Although early-generation coupled climate models simulated robust positive trends in the (N)AO/NAM in the future63–65, later generations of the models — particularly those with atmospheric chemistry and bet-ter representation of the stratosphere — produce neutral or even

Box 2 | ideas for future snow-constrained experiments

We suggest several potential approaches for future modelling studies, using atmospheric GCMs (AGCMs) or fully coupled ocean–atmosphere GCMs. Such experiments should be carried out with large numbers of ensemble members and various GCMs to characterize internal variability and model uncertainty. GCMs with enhanced stratospheric representation (or 'high-top models') should be used to improve simulations of stratosphere–tropo-sphere coupling processes.

Imposing regional rather than continental-scale snow anomalies. Regional snow anomalies, for example over eastern versus western Siberia, may very well be more efficient in driving upward-prop-agating planetary waves than a uniform anomaly over the whole of Siberia. Destructive interference leading to a cancellation of the remote atmospheric response has been shown to occur in the case of regional Arctic sea-ice anomalies96,97. Whether such can-cellation mechanisms may occur between regional snow anoma-lies has yet to be addressed using GCM numerical experiments, but these mechanisms may explain some of the nonlinearity in the snow–(N)AO teleconnection17, and inconsistencies between GCM sensitivity studies.

Combining Siberian snow and Arctic sea-ice/SST anomalies. How snow anomalies combine with Arctic sea-ice and SST anomalies is an open question. In observations, combining snow and sea-ice indices together increases the skill in predicting the (N)AO/NAM with a linear statistical model98. Large Siberian snow-cover

and Arctic sea-ice anomalies have coincided in recent years with the emergence of the Warm Arctic Cold Siberia (WACS) pat-tern, which has been suggested to be forced by a warmer Arctic99. Although Karpechko and coauthors91 found a large role for atmo-spheric internal variability in the WACS trend, the combined influence of Siberian snow and Arctic sea ice on such atmospheric patterns remains to be examined.

Imposing intraseasonal snow variability rather than constant sea-sonal averages or smooth rates of snow increase. GCM studies might address the suggestion of Cohen and Jones100 that the rate of advance in snow extent in October is a better predictor of the wintertime (N)AO/NAM than its seasonal mean amplitude. It is possible that snow-driven atmospheric perturbations mainly occur after large snowfall events and abrupt changes in the surface conditions that induce pulses of upward-propagating wave activ-ity. To verify this, time-evolving Siberian snow anomalies could be prescribed in GCMs in fall with various rates and characteristics of increase.

Impact of projected retreat of snow cover in future. Compared to Arctic sea-ice decline, the impact of projected decreasing snow cover in future has received little attention as a driver of circula-tion change. GCM simulations forced with present versus future snow-cover extent similar to Alexander and coauthors62 (possibly with regional forcings only, for Siberia for example) are needed to improve our knowledge on the future consequences of snow retreat.

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negative trends in the (N)AO/NAM in the future66,67. A growing number of studies also indicated that the Northern Hemisphere stratospheric polar vortex is projected to weaken and become more variable68,69, which could result in more variability in the wintertime tropospheric circulation. This change in the polar stratosphere is projected to occur at the same time, but independently of projected autumnal snow retreat. This underlines how the teleconnection may not be a constant dynamical mechanism in the climate system.

Discussion and conclusionIn light of limited recent progress in advancing our understanding of the coupling between snow and extratropical atmospheric circu-lation, and the uncertainty on the implications of climate change for this coupling, we have been motivated to summarize and take stock of this line of research. Based on the community’s thirty-year focus on Eurasian snow–(N)AO/NAM teleconnection linkages, and recent diverging views resulting from model-driven studies in par-ticular, we now offer our perspective on possible ways forward.

Future research will have to clarify causality between snow anomalies and atmospheric patterns on seasonal to sub-seasonal, interannual and multidecadal timescales. Clarifying issues such as the mechanisms for generating planetary waves from surface dia-batic heating anomalies arising from snow is important for climate prediction and climate change projection on these timescales, as well as for our mechanistic understanding of extratropical climate dynamics. Limitations to our understanding are exemplified in Fig.

4. In observations and control experiments of land–atmosphere GCMs19, extended snow cover over Siberia during fall is associated with a contemporaneous anticyclonic circulation pattern over north-western Siberia (Fig. 4a–c). On the other hand, when anomalous snow cover is imposed as a forcing, as is the case in most of the modelling studies reviewed here, that anticyclonic pattern is absent (Fig. 4d–e). The analysis suggests that variability in snow-cover extent is driven by anomalous temperature advection — that is, the atmosphere — rather than snow cover forcing the atmosphere. Of course, model and forcing protocol limitations in reproducing the correct snow–atmo-sphere coupling cannot be disregarded. Further studies are certainly needed to clarify causality, not only between autumn snow and the winter (N)AO/NAM, but also with synchronous atmospheric pat-terns that are outlined in Box 1. It is important to rectify this causal-ity chain for benchmarking and understanding the impact that the diminishing autumnal snow cover projected by the climate models may have on future winters. Targeted climate experiments run with future warming scenarios and prescribed continental snow-cover anomalies62 may be warranted to deduce these contradictory ele-ments. For this, new protocols may be applied in future GCM studies; for instance, considering the role of regional versus continental snow-cover anomalies, or the importance of individual snowfall events (see Box 2 for ideas on novel snow–atmosphere GCM experiments).

In addition, future work will need to address snow–atmos phere coupling in the broader context of statistical and dynamical cli-mate prediction. Recent research in seasonal and longer-timescale

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ARPEGE180°

Fig. 4 | Causality between the atmosphere and snow-cover anomalies over Siberia. a, Composite of sea-level pressure (contours, 0.5 hPa) and snow-cover extent colour scale) based on high minus low extent of October–November Siberian snow cover for the period 1972–2016 in NCEP. b, Same composite in a 200-year control simulation of WACCM. c, Same composite in a 200-year control simulation of ARPEGE-Climat. d, Response of the October–November sea-level pressure (contours, 0.5 hPa) to increased October–November Siberian snow in WACCM (200-year average). e, Same as d but for ARPEGE-Climat. Solid (dashed) contours represent positive (negative) sea-level pressure anomalies, whereas positive (negative) sea-level pressure anomalies that are significant at the 95% confidence level are red (blue). Only snow-cover anomalies that are significant at the 95% confidence level are shown. See Methods and Peings et al.19 for details of the experimental design. The following winter (December-March average) snow-cover and sea-level pressure anomalies are shown in Supplementary Fig. 2.

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prediction suggests that coupled dynamical seasonal prediction systems seem to be insufficiently constrained by surface and strato-spheric boundary conditions70–72. As such systems feature improved resolution and improved representation of the processes relevant to planetary wave generation and wave mean-flow interactions com-pared to the climate models that have been the primary focus of this review, the boundary control problem presumably applies to these climate models as well. In such systems, October Eurasian snow cover can play an important role in the processes relevant to planetary wave generation73. However, we also note that October Eurasian snow cover provides comparable predictability if replaced by an indicator of October stratospheric variability in an empiri-cal (N)AO/NAM prediction scheme74, rendering it uncertain what the most dynamically relevant independent predictors of long-lead wintertime predictions are. All aspects of empirical and dynamical prediction will need to be explored carefully given non-stationary relationships noted here for the snow–(N)AO/NAM teleconnec-tion, which is an example of the broader tendency towards multi-decadal variability of predictive skill in (N)AO/NAM forecasting75.

A central question remains the extent to which extratropical modes of variability, which strongly control variability in jet stream and regional temperature extremes, are sensitive to climate change. It is thus still urgent to deepen our understanding of the enigmatic snow–(N)AO/NAM linkage, which operates on timescales of weeks to months, but could be highly sensitive to the coming decades of projected climate change.

Online contentAny methods, additional references, Nature Research reporting summaries, source data, statements of data availability and asso-ciated accession codes are available at https://doi.org/10.1038/s41558-018-0295-6.

Received: 18 June 2018; Accepted: 6 September 2018; Published online: 29 October 2018

References 1. Cohen, J. Snow cover and climate. Weather 49, 150–156 (1994). 2. Gutzler, D. S. & Rosen, R. D. Interannual variability of wintertime snow

cover across the Northern Hemisphere. J. Clim. 5, 1441–1448 (1992). 3. IPCC Climate Change 2013: The Physical Science Basis (eds Stocker, T. F. et

al.) (Cambridge Univ. Press, 2013). 4. Brutel-Vuilmet, C., Ménégoz, M. & Krinner, G. An analysis of present and

future seasonal Northern Hemisphere land snow cover simulated by CMIP5 coupled climate models. Cryosphere 7, 67–80 (2013).

5. Clark, M. P. & Serreze, M. C. Effects of variations in East Asian snow cover on modulating atmospheric circulation over the North Pacific Ocean. J. Clim. 13, 3700–3710 (2000).

6. Cohen, J. & Entekhabi, D. The influence of snow cover on Northern Hemisphere climate variability. Atmos. Ocean 39, 35–53 (2001).

7. Gong, G., Entekhabi, D. & Cohen, J. Modeled Northern Hemisphere winter climate response to realistic Siberian snow anomalies. J. Clim. 16, 3917–3931 (2003).

Modelling study that reproduces the snow–(N)AO teleconnection and the stratospheric pathway in an AGCM, using observed snow anomalies.

8. Fletcher, C. G., Kushner, P. J. & Cohen, J. Stratospheric control of the extratropical circulation response to surface forcing. Geophys. Res. Lett. 34, L21802 (2007).

9. Fletcher, C. G., Hardiman, S. C., Kushner, P. J. & Cohen, J. The dynamical response to snow cover perturbations in a large ensemble of atmospheric GCM integrations. J. Clim. 22, 1208–1222 (2009).

10. Orsolini, J. Y. & Kvamstø, N. G. Role of Eurasian snow cover in wintertime circulation: decadal simulations forced with satellite observations. J. Geophys. Res. 114, 19108 (2009).

11. Allen, R. J. & Zender, C. S. Forcing of the Arctic Oscillation by Eurasian snow cover. J. Clim. 24, 6528–6539 (2011).

12. Peings, Y., Saint-Martin, D. & Douville, H. A numerical sensitivity study of the Siberian snow influence on the northern annular mode. J. Clim. 25, 592–607 (2012).

13. Klingaman, N. P., Hanson, B. & Leathers, D. J. A teleconnection between forced Great Plains snow cover and European winter climate. J. Clim. 21, 2466–2483 (2008).

14. Ge, Y. & Gong, G. North American snow depth and climate teleconnection patterns. J. Clim. 22, 217–233 (2009).

15. Sobolowski, S., Gong, G. & Ting, M. Modeled climate state and dynamic responses to anomalous North American snow cover. J. Clim. 23, 785–799 (2010).

16. Henderson, G. R., Leathers, D. J. & Hanson, B. Circulation response to Eurasian versus North American anomalous snow scenarios in the Northern Hemisphere with an AGCM coupled to a slab ocean model. J. Clim. 26, 1502–1515 (2013).

17. Peings, Y., Brun, E., Mauvais, V. & Douville, H. How stationary is the relationship between Siberian snow and Arctic Oscillation over the 20th century? Geophys. Res. Lett. 40, 183–188 (2013).

18. Furtado, J. C., Cohen, J. L., Butler, A. H., Riddle, E. E. & Kumar, A. Eurasian snow cover variability and links to winter climate in the CMIP5 models. Clim. Dynam. 45, 2591–2605 (2015).

Investigates the snow–(N)AO teleconnection in CMIP5 GCMs and shows the lack of linkage in the models.

19. Peings, Y., Douville, H., Colin, J., Saint Martin, D. & Magnusdottir, G. Snow–(N)AO teleconnection and its modulation by the Quasi-Biennial Oscillation. J. Clim. 30, 10211–10235 (2017). Explores the possible role of the QBO in modulating the snow–(N)AO teleconnection and explaining its non-stationarity.

20. Douville, H., Peings, Y. & Saint-Martin, D. Snow-(N)AO relationship revisited over the whole twentieth century. Geophys. Res. Lett. 43, 569–577 (2017).

Explores the snow–(NAO) teleconnection in various reanalysis datasets, and discusses potential causes for its non-stationarity.

21. Deser, C., Phillips, A., Bourdette, V. & Teng, H. Uncertainty in climate change projections: the role of internal variability. Clim. Dynam. 38, 527–546 (2012).

22. Barnes, E. A. & Screen, J. A. The impact of Arctic warming on the midlatitude jet-stream: Can it? Has it? Will it? WIREs Clim. Change 6, 277–286 (2015).

23. Cohen, J. & Rind, D. The effect of snow cover on climate. J. Clim. 4, 689–706 (1991).

24. Ross, B. & Walsh, J. Synoptic-scale influences of snow-cover and sea ice. Mon. Weath. Rev 114, 1795–1810 (1986).

25. Barnett, T., Dumenil, L., Schlese, U., Roeckner, E. & Latif, M. The effect of Eurasian snow cover on regional and global climate variations. J. Atmos. Sci. 46, 661–685 (1989).

26. Walland, D. J. & Simmonds, I. Modelled atmospheric response to changes in Northern Hemisphere snow cover. Clim. Dynam. 13, 25–34 (1996).

27. Watanabe, M. & Nitta, T. Relative impacts of snow and sea surface temperature anomalies on an extreme phase in the winter atmospheric circulation. J. Clim. 11, 2837–2857 (1998).

28. Watanabe, M. & Nitta, T. Decadal changes in the atmospheric circulation and associated surface climate variations in the Northern Hemisphere winter. J. Clim. 12, 494–509 (1999).

29. Cohen, J., Saito, K. & Entekhabi, D. The role of the Siberian high in Northern Hemisphere climate variability. Geophys. Res. Lett. 28, 299–302 (2001).

30. Cohen, J. & Entekhabi, D. Eurasian snow cover variability and Northern Hemisphere climate predictability. Geophys. Res. Lett. 26, 345–348 (1999). Identifies a statistical link between the extent of snow in fall over Siberia and the following winter (N)AO.

31. Bojariu, R. & Gimeno, L. The role of snow cover fluctuations in multiannual NAO persistence. Geophys. Res. Lett. 30, 1156 (2003).

32. Saito, K., Cohen, J. & Entekhabi, D. Evolution of atmospheric response to early-season Eurasian snow cover anomalies. Mon. Weath. Rev. 129, 2746–2760 (2001).

Proposes a physical mechanism for the observed snow–(N)AO linkage, involving upward wave-activity anomalies and a stratospheric pathway.

33. Thompson, D. W. J. & Wallace, J. M. The Arctic Oscillation signature in the wintertime geopotential height and temperature fields. Geophys. Res. Lett. 25, 1297–1300 (1998).

34. Thompson, D. W. J. & Wallace, J. M. Annular modes in the extratropical circulation. Part I: month-to-month variability. J. Clim 13, 1000–1016 (2000).

35. Gong, G., Entekhabi, D. & Cohen, J. Relative impacts of Siberian and North American snow anomalies on the winter Arctic Oscillation. Geophys. Res. Lett. 30, 1848 (2003).

36. Gong, G., Entekhabi, D. & Cohen, J. Orographic constraints on a modeled Siberian snow-tropospheric-stratospheric teleconnection pathway. J. Clim. 17, 1176–1189 (2004).

37. Gong, G., Entekhabi, D. & Cohen, J. Sensitivity of atmospheric response to modeled snow anomaly characteristics. J. Geophys. Res. 109, D06107 (2004).

38. Dutra, E., Schär, C., Viterbo, P. & Miranda, P. M. A. Land atmosphere coupling associated with snow cover. Geophys. Res. Lett. 38, L15707 (2011).

FOCUS | Review ARticlehttps://doi.org/10.1038/s41558-018-0295-6FOCUS | Review ARticleNaTurE CLimaTE CHaNgE

NatuRe Climate CHaNGe | VOL 8 | NOVEMBER 2018 | 954–963 | www.nature.com/natureclimatechange 961

Review ARticle | FOCUS NaTurE CLimaTE CHaNgE

39. Gong, G., Entekhabi, D. & Cohen, J. A large-ensemble model study of the wintertime AO–NAO and the role of interannual snow perturbations. J. Clim. 15, 3488–3499 (2002).

40. Smith, K. L., Kushner, P. J. & Cohen, J. The role of linear interference in Northern Annular Mode variability associated with Eurasian snow cover extent. J. Clim. 24, 6185–6202 (2011).

Reveals the importance of the linear interference mechanism in the snow–(N)AO teleconnection.

41. Screen, J. A., Deser, C., Simmonds, I. & Tomas, R. Atmospheric impacts of Arctic sea-ice loss, 1979–2009: separating forced change from atmospheric internal variability. Clim. Dynam. 43, 333–344 (2014).

42. Hardiman, S. C., Kushner, P. J. & Cohen, J. Investigating the ability of general circulation models to capture the effects of Eurasian snow cover on winter climate. J. Geophys. Res. 113, D21123 (2008).

43. Nishii, K., Nakamura, H. & Orsolini, Y. J. Cooling of the wintertime Arctic stratosphere induced by the western Pacific teleconnection pattern. Geophys. Res. Lett. 37, L13805 (2010).

44. Smith, K. L. & Kushner, P. J. Linear interference and the initiation of extratropical stratosphere-troposphere interactions. J. Geophys Res. 117, D13107 (2012).

45. Foster, J., Owe, M. & Rango, A. Snow cover and temperature relationships in North America and Eurasia. J. Clim. Appl. Meteor. 22, 460–469 (1983).

46. Cohen, J. L. & Saito K. Eurasian snow cover, more skillful in predicting U.S. winter climate than the NAO/AO? Geophys. Res. Lett. 30, 2190 (2003).

47. Cohen, J., Salstein, D. & Saito, K. A dynamical framework to understand and predict the major Northern Hemisphere mode. Geophys. Res. Lett. 29, 1412 (2002).

48. Cohen, J., Barlow, M., Kushner, P. J. & Saito, K. Stratosphere-troposphere coupling and links with Eurasian land surface variability. J. Clim. 20, 5335–5343 (2007).

49. Cohen, J. et al. Linking Siberian snow cover to precursors of stratospheric variability. J. Clim. 27, 5422–5432 (2014).

50. Zhang, J., Tian, W., Chipperfield, M., Xie, F. & Huang, J. Persistent shift of the Arctic polar vortex towards the Eurasian continent in recent decades. Nat. Clim. Change 6, 1094–1099 (2016).

51. Kretschmer, M. et al. More-persistent weak stratospheric polar vortex states linked to cold extremes. Bull. Am. Meteorol. Soc. 99, 49–60 (2017).

52. Seviour, W. J. M. Weakening and shift of the Arctic stratospheric polar vortex: internal variability or forced response? Geophys. Res. Lett. 44, 3365–3373 (2017).

53. Serreze, M. C., Barrett, A. P., Stroeve, J. C., Kindig, D. N. & Holland, M. M. The emergence of surface-based Arctic amplification. Cryosphere 3, 11–19 (2009).

54. Deser, C., Simpson, I. R., McKinnon, K. A. & Phillips, A. S. The Northern Hemisphere extra-tropical atmospheric circulation response to ENSO: how well do we know it and how do we evaluate models accordingly? J. Clim. 30, 5059–5082 (2017).

55. Gershunov, A., Schneider, A. N. & Barnett, T. Low-frequency modulation of the ENSO–Indian monsoon rainfall relationship: signal or noise? J. Clim. 14, 2486–2492 (2001).

56. Krasting, J. P., Broccoli, A. J., Dixon, K. W. & Lanzante, J. R. Future changes in Northern Hemisphere snowfall. J. Clim. 26, 7813–7828 (2013).

57. Takala, M., Pulliainen, J., Metsamaki, S. J. & Koskinen, J. T. Detection of snowmelt using spaceborne microwave radiometer data in Eurasia from 1979 to 2007. IEEE Trans. Geosci. Remote Sens. 47, 2996–3007 (2009).

58. Brown, R. D. & Derksen, C. Is Eurasian October snow cover extent increasing? Environ. Res. Lett. 8, 024006 (2013).

59. Mudryk, L. R., Kushner, P. J., Derksen, C. & Thackeray, C. Snow cover response to temperature in observational and climate model ensembles. Geophys. Res. Lett. 44, 919–926 (2017).

60. Hori, M. et al. A 38-year (1978–2015) Northern Hemisphere daily snow cover extent product derived using consistent objective criteria from satellite-borne optical sensors. Remote Sens. Environ. 191, 402–418 (2017).

61. Ghatak, D., Frei, A., Gong, G., Stroeve, J. & Robinson, D. On the emergence of an Arctic amplification signal in terrestrial Arctic snow extent. J. Geophys. Res. 115, D24105 (2010).

62. Alexander, M. A., Tomas, R., Deser, C. & Lawrence, D. M. The atmospheric response to projected terrestrial snow changes in the late twenty-first century. J. Clim. 23, 6430–6437 (2010).

Explores how projected future changes in snow cover may affect the Northern Hemisphere climate at the end of the twenty-first century.

63. Fyfe, J. C., Boer, G. J. & Flato, G. M. The Arctic and Antarctic Oscillations and their projected changes under global warming. Geophys. Res. Lett. 26, 1601–1604 (1999).

64. Gillett, N. P. et al. How linear is the Arctic Oscillation response to greenhouse gases? J. Geophys. Res. Atmos. 107(D3), 4022 (2002).

65. Miller, R. L., Schmidt, G. A. & Shindel, D. T. Forced annular changes in the 20th century Intergovernmental Panel on Climate Change Fourth Assessment Report models. J. Geophys. Res. 111, D18101 (2006).

66. Gillett, N. P. & Fyfe, J. C. Annular mode changes in the CMIP5 simulations. Geophys. Res. Lett. 40, 1189–1193 (2013).

67. Cattiaux, J. & Cassou, C. Opposite CMIP3/CMIP5 trends in the wintertime Northern Annular Mode explained by combined local sea ice and remote tropical influences. Geophys. Res. Lett. 40, 3682–3687 (2013).

68. Mitchell, D. M. et al. The effect of climate change on the variability of the Northern Hemisphere stratospheric polar vortex. J. Atmos. Sci. 69, 2608–2618 (2012).

69. Kang, W. & Tziperman, E. More frequent sudden stratospheric warming events due to enhanced MJO forcing expected in a warmer climate. J. Clim. 30, 8727–8743 (2017).

70. Scaife, A. A. et al. Skillful long-range prediction of European and North American winters. Geophys. Res. Lett. 41, 2514–2519 (2014).

71. Eade, R. et al. Do seasonal-to-decadal climate predictions underestimate the predictability of the real world? Geophys. Res. Lett. 41, 5620–5628 (2014).

72. Dunstone, N. et al. Skillful predictions of the winter North Atlantic Oscillation one year ahead. Nat. Geosci. 9, 809–814 (2016).

73. Orsolini, Y. J. et al. Influence of the Eurasian snow on the negative North Atlantic Oscillation in subseasonal forecasts of the cold winter 2009/2010. Clim. Dynam. 47, 1325–1334 (2016).

74. Wang, L., Ting, M. & Kushner, P. J. A robust empirical seasonal prediction of winter NAO and surface climate. Sci. Rep. 7, 279 (2017).

75. Weisheimer, A., Schaller, N., O’Reilly, C., MacLeod, D. A. & Palmer, T. Atmospheric seasonal forecasts of the twentieth century: multi-decadal variability in predictive skill of the winter North Atlantic Oscillation and their potential value for extreme event attribution. Q. J. R. Meteorol. Soc. 143, 917–926 (2016).

76. Riddle, E. E., Butler, A. H., Furtado, J. C., Cohen, J. L. & Kumar, A. CFSv2 ensemble prediction of the wintertime Arctic Oscillation. Clim. Dynam. 41, 1099–1116 (2013).

77. Limpasuvan, V., Thompson, D. W. J. & Hartmann, D. L. The life cycle of the Northern Hemisphere sudden stratospheric warmings. J. Clim. 17, 2584–2596 (2004).

78. Kolstad, E. W. & Charlton-Perez, A. J. Observed and simulated precursors of stratospheric polar vortex anomalies in the Northern Hemisphere. Clim. Dynam. 37, 1443 (2011).

79. Watt-Meyer, O. & Kushner, P. J. Why are temperature and upward wave activity flux positively skewed in the polar stratosphere? J. Clim. 31, 115–130 (2018).

80. Cohen, J. L. & Fletcher, C. G. Improved skill of Northern Hemisphere winter surface temperature predictions based on land-atmosphere fall anomalies. J. Clim. 20, 4118–4132 (2007).

81. Lee, Y. Y. & Black, R. X. Boreal winter low frequency variability in CMIP5 models. J. Geophys. Res. Atmos 118, 6891–6904 (2013).

82. Newman, P. A., Nash, E. R. & Rosenfield, J. E. What controls the temperature of the Arctic stratosphere during the spring? J. Geophys. Res. 106, 19 999–20 010 (2001).

83. Polvani, L. M. & Waugh, D. W. Upward wave activity flux as a precursor to extreme stratospheric events and subsequent anomalous surface weather regimes. J. Clim. 17, 3548–3554 (2004).

84. Charlton-Perez, A. et al. On the lack of stratospheric dynamical variability in low-top version of the CMIP5 models. J. Geophys. Res. Atmos. 118, 2494–2505 (2013).

85. Lehtonen, I. & Karpechko, A. Y. Observed and modeled tropospheric cold anomalies associated with sudden stratospheric warmings. J. Geophys. Res. Atmos. 121, 1591–1610 (2016).

86. Song, Y. & Robinson, W. A. Dynamical mechanisms for stratospheric influences on the troposphere. J. Atmos. Sci. 61, 1711–1725 (2004).

87. Shaw, T. A., Perlwitz, J. & Harnik, N. Downward wave coupling between the stratosphere and troposphere: the importance of meridional wave guiding and comparison with zonal-mean coupling. J. Clim. 23, 6365–6381 (2010).

88. Thompson, D. W. J., Furtado, J. C. & Shepherd, T. G. On the tropospheric response to anomalous stratospheric wave drag and radiative heating. J. Atmos. Sci. 63, 2616–2629 (2006).

89. Roff, G., Thompson, D. W. J. & Hendon, H. Does increasing model stratospheric resolution improve extended range forecast skill? Geophys. Res. Lett. 38, L05809 (2011).

90. Richter, J. H., Solomon, A. & Bacmeister, J. T. Effects of vertical resolution and non-orographic gravity wave drag on the simulated climate in the community atmosphere model, version 5. J. Adv. Model. Earth Syst. 6, 357–383 (2014).

91. Karpechko, A. Y., Hitchcock, P., Peters, D. H. & Schneidereit, A. Predictability of downward propagation of major sudden stratospheric warmings. Q. J. R. Meteorol. Soc. 143, 1459–1470 (2017).

92. Mote, T. L. On the role of snow cover in depressing air temperature. J. Appl. Meteorol. Climatol. 47, 2008–2022 (2008).

93. Vavrus, S. The role of terrestrial snow cover in the climate system. Clim. Dynam. 29, 73–88 (2007).

Review ARticle | FOCUShttps://doi.org/10.1038/s41558-018-0295-6Review ARticle | FOCUS NaTurE CLimaTE CHaNgE

NatuRe Climate CHaNGe | VOL 8 | NOVEMBER 2018 | 954–963 | www.nature.com/natureclimatechange962

FOCUS | Review ARticleNaTurE CLimaTE CHaNgE

94. Baldwin, M. P. & Dunkerton, T. J. Stratospheric harbingers of anomalous weather regimes. Science 294, 581–584 (2001).

95. Baldwin, M. P. et al. Stratospheric memory and skill of extended-range weather forecasts. Science 301, 636–640 (2003).

96. Sun, L., Deser, C. & Tomas, R. A. Mechanisms of stratospheric and tropospheric circulation response to projected Arctic sea ice loss. J. Clim. 28, 7824–7845 (2015).

97. Screen, J. A. Simulated atmospheric response to regional and pan-Arctic sea ice loss. J. Clim. 30, 3945–3962 (2017).

98. Furtado, J. C., Cohen, J. L. & Tziperman, E. The combined influences of autumnal snow and sea ice on Northern Hemisphere winters. Geophys. Res. Lett. 43, 3478–3485 (2016).

99. Mori, M., Wanatabe, M., Shiogama, H., Inoue, J. & Kimoto, M. Robust Arctic sea-ice influence on the frequent Eurasian cold winters in past decades. Nat. Geosci. 7, 869–873 (2014).

100. Cohen, J. & Jones J. A new index for more accurate winter predictions. Geophys. Res. Lett. 38, L21701 (2011).

acknowledgementsThis work was partially supported by the Natural Science and Engineering Research Council of Canada under CanSISE and by the National Science Foundation under grant no. NSF PHY-1748958. Y.P. is supported by the National Science Foundation under grant no. NSF AGS-1624038. G.R.H. is supported by SERDP and ESTCP under grant no.

RC18-Z1-1658. The authors also thank E. A. Barnes and J. A. Screen for encouraging us to use their Can it? /Has it? /Will it? analysis framework.

author contributionsG.R.H. outlined the study scope, which was then further developed by all authors. Y.P. led the Can it? section and produced Figs. 2–4, Supplementary Fig. 2 and Box 2. J.C.F. and G.R.H. led the Has it? section, and developed Fig. 1. J.C.F. performed the analysis for Supp. Figure 1. P.J.K. helped frame the paper, and led the Box 1 discussion along with J.C.F. All authors contributed to writing the manuscript.

Competing interestsThe authors declare no competing interests.

additional informationSupplementary information is available for this paper at https://doi.org/10.1038/s41558-018-0295-6.

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(for example 14.67 °C for + 1°C), and we compute the 30-year average and standard deviation of snow cover for Siberia.

Supplementary Fig. 1 uses monthly mean October Eurasian snow-cover extent data provided by the Rutgers Global Snow Laboratory102. The monthly snow-cover mean standardized AO index is taken from the NOAA Climate Prediction Center103. The base period for the standardized anomalies for both indices is 1981–2010. Both indices were detrended before correlations were computed. A two-tailed Student’s t-test with N − 1 = 38 degrees of freedom (with N representing the sample size/number of years from 1979–2017) was used to calculate significance.

References 101. Haustein, K. et al. Frame: a real-time global warming index. Sci. Rep. 7,

15417 (2017). 102. Robinson, D. A. et al. NOAA Climate Data Record (CDR) of Northern

Hemisphere (NH) Snow Cover Extent (SCE): Monthly Eurasian Snow Cover Version 1 (NOAA National Centers for Environmental Information, accessed 10 May 2018).

103. Monthly Mean AO Index (NOAA Climate Prediction Center, accessed xx month year); http://www.cpc.ncep.noaa.gov/products/precip/CWlink/daily_ao_index/monthly.ao.index.b50.current.ascii.table

methodsFigures 2 and 4 and Supplementary Fig. 2 use two AGCM experiments carried out with the Whole Atmosphere Community Climate Model version 4 (WACCM4) and ARPEGE-Climat version 6, as described in Peings and co-authors19. Two hundred seasonal runs perturbed with a Siberian snow anomaly are branched on each 1 October of a 200-year control run with climatological SST and sea ice and run until 31 March. Daily snow water equivalent, which corresponds to two daily standard deviations over the 1979–2014 period from the ERA-Interim Land Surface reanalysis, are imposed from 1 October to 30 November over Siberia (35° E–180°, 40–80° N domain). After 30 November, the snow constraint is removed and the snow pack evolves freely.

Monthly snow cover from historical and RCP8.5 simulations of 22 CMIP5 models that provide this variable (BNU-ESM, bcc-csm1-1, bcc-csm1-1-m, CanESM2, CCSM4, CESM1-BGC, CESM1-CAM5, CNRM-CM5, CSIRO-Mk3-6-0, FGOALS-g2, FIO-ESM, GISS-E2-H GISS-E2-R, inmcm4, MIROC5, MIROC-ESM-CHEM, MIROC-ESM, MPI-ESM-LR, MPI-ESM-MR, MRI-CGCM3, NorESM1-M, NorESM1-ME) is used to construct Fig. 3. The global warming thresholds + 1 to + 4 °C are defined relative to the pre-industrial global mean temperature (13.67 °C)101, which was obtained by removing an estimate of the global warming index for the period 1979-2008 (0.57°C) from the present-day value (1979-2008, 14.24°C). For each model, we find the period when the 30-year mean global temperature equals the pre-industrial (13.67 °C) or warming threshold

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