Metrics analyzed

We employ three metrics to diagnose the relationship between Arctic temperatures and severe winter weather. The first two are called the polar cap geopotential height anomaly (PCH) index and the polar cap air temperature anomaly (PCT) index. The PCH and PCT indices measure the area-averaged geopotential height and temperature anomalies poleward of 65° N and from 1000 to 10 hPa. Both PCH (units in meters) and temperature (units in °C) are normalized by their standard deviation. The PCH values incorporate air temperature and surface pressure, thus combining both thermodynamic and dynamic influences28. PCT reflects only thermodynamic effects.

The third metric is the Accumulated Winter Season Severity Index (AWSSI)29. We analyzed changes in daily and cumulative AWSSI in relation to changes in PCH/PCT at diverse geographic locations in order to explore the relationship between Arctic variability and severe winter weather (Methods section). The AWSSI diagnoses severe weather owing to extreme snowfall and temperatures at individual stations across the US. It is reported as an accumulated value throughout the winter season, which informs comparisons of weather severity between years. Daily accumulated changes in AWSSI provide insight into episodic severe winter weather. For our study, the AWSSI is advantageous because it integrates both intensity and duration of temperature, snowfall, and snowcover into one index to measure weather severity across seasons and stations. However, the thresholds used to create the index are somewhat subjective. The AWSSI index is incremented based on thresholds of maximum and minimum temperature, snowfall and snow depth. Because the AWSSI index is not increased unless temperatures fall below freezing and snowfall or snowcover exists, the index better represents winter weather variability in cities that experience colder temperatures and/or heavy snowfall, such as those in the mid-west relative to those in the southern US or the west coast.

Arctic variability and mid-latitude weather

The daily change in seasonal AWSSI (or the daily accumulation for that day) is composited for all standardized PCHs at 12 representative cities across the US (see Fig. 1 for the geographic distribution of the chosen stations) by computing the mean change in AWSSI associated with daily PCH values at each isobaric level during winter (DJF) from 1950 to 2016 (Fig. 2). A strong relationship between a warmer Arctic and increased frequency of severe winter weather is apparent for all stations east of the Rockies, with the strongest association in the eastern third of the US, where we find a statistically significant (p < 0.01) and nearly linear relationship between Arctic height changes throughout the troposphere and AWSSI. When Arctic heights are at their lowest (PCH < ~ −1), severe winter weather is unlikely. For larger values of PCH (PCH > +1), the likelihood of severe weather increases, with correlations peaking when the PCH is greater than +1.5. This relationship is fairly consistent throughout the troposphere over the full range of Arctic height anomalies. The correlation generally holds in the stratosphere (below the 30 hPa surface) as well. In the Rockies and along the west coast, however, the relationship is weak, and some stations even exhibit the opposite relationship, i.e., a relatively warm Arctic favors milder winter weather. This result is consistent with the predominance of an anomalous western ridge during the recent period of pronounced Arctic warming.

Fig. 1 Geographic locations of cites analyzed. We chose a geographically diverse set of 12 cities to analyze Arctic variability and severe winter weather, though we chose more cities in the northeastern and mid-western US where severe winter weather is more common than in other regions of the US Full size image

Fig. 2 Warm Arctic related to increased severe winter weather. The departure from the winter average in daily change in the AWSSI (Accumulated Winter Season Severity Index) at several weather stations across the US during December–February shown at all levels between 1000 and 10 hPa. AWSSI is plotted with composited values of the polar cap geopotential height (PCH, a) and air temperature (PCT, b) standardized anomalies from the surface to the mid-stratosphere (10 hPa), north of 65° N, from 1950 to 2016. Anomalies computed relative to climatology from 1981–2010. Results for all stations are consistently statistically significant at p < 0.01. Statistical significance for both PCH and PCT at selected levels for all cities shown in Supplementary Table 1 Full size image

We also investigate the separate association between PCH variability and extreme cold temperatures or heavy snowfall (Figs. 3 and 4). Positive values of PCH exhibit a stronger and more extensive relationship with temperature than with snowfall. The most robust relationship between PCH and snowfall is in the northeastern US, thus it is likely that snowfall in this region is most sensitive to Arctic variability, with higher Arctic geopotential heights and relatively warmer temperatures favoring heavier snowfalls30.

Fig. 3 Warm Arctic related to colder winter temperatures. Temperature contribution to the average daily change in the AWSSI (Accumulated Winter Season Severity Index) at selected weather stations across the US associated with polar cap geopotential height anomalies (PCH) from the surface to the mid-stratosphere (10 hPa) 1950–2016. Anomalies computed relative to climatology from 1981 to 2010 Full size image

Fig. 4 Warm Arctic related to increased snowfall. Snowfall contribution to the average daily change in the AWSSI at selected weather stations across the US associated with polar cap geopotential height anomalies (PCH) from the surface to the mid-stratosphere (10 hPa) 1950–2016. Anomalies computed relative to climatology from 1981 to 2010 Full size image

As discussed earlier, the PCH combines both thermodynamic and dynamic influences. To determine whether a direct relationship exists between Arctic temperatures alone and mid-latitude weather, we have repeated the prior analysis substituting PCT for PCH (Fig. 2), demonstrating that a significant fraction of the relationship between Arctic variability and severe winter weather across the mid-latitudes is related to variability in Arctic tropospheric temperature.

The relationship between PCH and AWSSI is stronger than the relationship between PCT and AWSSI. Given that PCT represents only thermodynamic influences, it is not surprising that PCH is more strongly correlated with severe winter weather than is PCT. As we show in Supplementary Tables 1 and 2, however, the statistical significance of the correlations between AWSSI and either PCH or PCT are extremely high throughout the troposphere. A notable distinction is in the stratosphere, where PCH/AWSSI correlations are strong and PCT/AWSSI correlations are weak, consistent with another recent study27. This finding suggests that the tropospheric Arctic warming contributes most to higher PCH in the stratosphere, which is associated with increased severe winter weather in the eastern US. Previous work suggested that a weakened stratospheric polar vortex (SPV) is related to colder temperatures across mid-latitude continents, including the eastern US25,26,31,32,33. Our analysis refines this notion, suggesting that high geopotential surfaces in the Arctic stratosphere are more important than warm stratospheric temperatures in forcing mid-latitude severe winter weather. Further analysis is needed to confirm this relationship.

Because this is an observational study, cause and effect cannot be determined, and it is possible that the conditions favoring severe winter weather and amplified flow (or larger Rossby waves) also favor Arctic warming. To address this issue, we calculated the lag correlation between PCH at 500 hPa and AWSSI from −30 to +30 days (Fig. 5). We find that correlations peak when the PCH leads AWSSI by five days, then quickly decrease after zero lag and even become slightly negative when the AWSSI leads. These results imply that positive PCHs precede the occurrence of severe winter weather, rather than circulation patterns associated with severe winter weather being the main driver of positive PCH anomalies.

Fig. 5 Arctic variability leads occurrence of severe winter weather. The correlation between average daily change in the AWSSI at selected weather stations across the US associated with polar cap geopotential height anomalies (PCH) for all days between ±30 days. The peak value is reached when the PCH leads the AWSSI by 5 days Full size image

We further analyzed AWSSI variability during the 2-week period 5 to 19 days following high PCH values. We find that severe winter weather is more likely in the eastern US during multiple weeks after positive PCH values occur in the upper troposphere and lower stratosphere (Fig. 6). One interesting difference between the contemporaneous PCH/AWSSI versus the PCH values that lead AWSSI by 2 weeks or more is that significant correlations extend well into the mid-stratosphere when PCH leads. This is consistent with previous results showing that the occurrence of severe winter weather is more likely over multiple weeks following a weak SPV24,25, demonstrating the potential for using Arctic variability to predict the likelihood of extreme winter weather with leads greater than the synoptic time scale (on the order of days).

Fig. 6 Polar cap variability leads increased severe weather up to 19 days. The average daily change in the AWSSI at selected weather stations across the US associated with polar cap geopotential height anomalies (PCH) from the surface to the mid-stratosphere (10 hPa) during 5–19 days preceding the AWSSI values, 1950–2016 Full size image

To compare Arctic versus tropical influences on severe winter weather events, the analysis was repeated but with the PCH index replaced with the El Niño/Southern Oscillation (ENSO) index, as the tropics are generally thought to be the most important remote driver of mid-latitude weather34. In Supplementary Figure 1 we plot the composite AWSSI relative to the standardized Niño 3.4. For all stations across the country, there is no preferential value of AWSSI with ENSO variability, though there does seem to be a decline in severe winter weather for the most extreme El Niño values. This finding suggests that Arctic variability has a stronger influence on severe winter weather events than does ENSO variability.

The AWSSI is calculated only for the US, but to provide a sense of applicability of this approach to the whole NH, we composited hemispheric surface temperature anomalies based on cold [−3.0 to −0.5] and warm [0.5 to 3.0] PCH and PCT values (Fig. 7). In the transition from a relatively cold to warm Arctic, the mid-latitude continents transition from warm to cold temperature anomalies. This relationship is especially apparent in central and southeastern North America, northern Europe, northern Asia, and East Asia. The relationships between PCH/PCT and AWSSI exhibited in the US, therefore, appear to be valid across northern Eurasia, consistent with other recent studies35,36.

Fig. 7 As the Arctic warms the continents become colder. Northern Hemisphere surface temperature anomalies plotted for 500 hPa PCH anomalies binned on the intervals a [−3.0, −0.5], b [0.5, 3.0] and 500 hPa PCT c [−3.0, −0.5], and d [0.5, 3.0] for all winters 1950–2016. Climatological averages computed over the period 1981–2010. Where difference was found to be statistically significant above 95% is hatched in light gray (e.g., [−3.0, −0.5] to [0.5, 3.0]). We also tested for field significance in all plots and the differences were found to be highly significant. Ocean mask was applied south of 60° N Full size image

Arctic mid-latitude linkages in era of Arctic amplification

It is well documented that the Arctic is warming at a rate two to three times faster than the global average, a phenomenon known as Arctic amplification (AA)37,38,39. While AA is anticipated to reduce the severity of cold-air outbreaks and heavy snowfalls40,41,42, cooling trends have dominated NH continents since the emergence of rapid Arctic warming around 19906,15,23, contrary to expectations.

One reason offered for this counter-intuitive cooling is the two decades cooling trend in tropical Pacific sea-surface temperatures that resemble a La Niña pattern4. An alternative explanation is that AA is modifying the large-scale circulation where winter cooling over NH continents is favored5,8,13,15,24,25,33. Furthermore, recent climate trends—including mid-latitude temperatures—better match Arctic warming trends than tropical cooling trends4,43. This hypothesis is controversial, however, owing to large internal variability and because pre-AA-era studies of mid-latitude dynamics identify the tropics as the predominant driver of change9,17. Furthermore, global climate model simulations that correctly reproduce AA indicate that cold extremes and seasonal snowfall will continue to decrease as the globe warms40,41,42. Challenges to the idea of Arctic influence are discussed in greater detail below.

In Fig. 8 we plot the trends in daily PCH and PCT throughout the winter from 1990 to 2016. The tendencies are consistent with the observed warming trend in the Arctic and are not limited to the near-surface, but rather extend throughout the troposphere. The stratosphere cools in early winter but warms in mid-winter, consistent with a reported increasing frequency of sudden stratospheric warmings (SSWs)24. Also shown in Fig. 8 are daily trends in AWSSI for selected cities. Despite model projections for decreasing cold extremes as global warming intensifies, the trends in AWSSI during recent decades are more complex. In the western US, where no strong relationship between Arctic warming and AWSSI is apparent (Fig. 2), severe winter weather has generally decreased since 1990. In contrast, in the eastern US during periods when PCH trends are largest and during periods of substantial stratospheric and upper tropospheric warming (15 January–15 February), severe winter weather has increased. This is consistent with the result that severe winter weather is more likely for multiple weeks following SSW events (Fig. 6).

Fig. 8 Warming trend in Arctic coincides with increased severe winter weather. The annual daily trend in the a PCH (shading) and b PCT (shading) from the surface to the mid-stratosphere (10 hPa) and the annual trend in the daily change in the AWSSI for three eastern US cities (near Boston, Chicago, Detroit) and three western US cities (Helena, Salt Lake City, Seattle) for the winters 1990/91–2015/16 multiplied by the total number of winters. Statistical significance above 90% for PCH and PCT trends are hatched in dark gray. In Supplementary Figure 8 we have included the variability in the AWSSI with the daily trend Full size image

Our analysis to this point has been independent of AA, a metric that relates Arctic warming to that of lower latitudes, which may, itself, be caused by sea-ice loss and Arctic-only warming. It is important to note that metrics of PCH and PCT are Arctic-only metrics. While our analysis thus far suggests that a warmer Arctic relative to an Arctic mean temperature is related to colder temperatures across the continents of the NH mid-latitudes, additional analysis is performed to elucidate the degree to which Arctic warming relative to lower latitudes is associated with AWSSI.

The daily increment to the seasonal value of the AWSSI is composited for all standardized PCH for the sub-periods before (1950–1989) and during (1990–2016) the accelerated period of AA (Supplementary Figure 2). The analysis was repeated for the standardized PCT for both before and after the period of AA (Supplementary Figure 3). The relationship is fairly consistent throughout the troposphere. During both periods, the relationship is qualitatively the same: severe winter weather is more common when PCHs/PCTs are elevated throughout the Arctic troposphere. Dividing the winters into early and late winter produced a stronger relationship between PCT and severe winter weather during late winter (Supplementary Figure 4). In our analysis, however, the relationship between a warm Arctic and severe winter weather is stronger in the era prior to AA. Therefore, the analysis presented in Supplementary Figures 2 and 3 indicates that a warm Arctic is related to increased severe winter weather but only suggestive that AA is contributing to increased severe winter weather. One possible exception is in the stratosphere where the relationship between a warm polar stratosphere and increased severe winter weather has become more robust in the period of AA. These findings suggest a growing dependence of severe winter weather in mid-latitudes on weakening of the SPV or SSW (which are defined at 10 hPa) events during the AA era.

Snowfall before and during era of Arctic amplification.

Northeastern US cities have experienced a streak of winters with heavy snowfalls over the past two decades, with some famously nicknamed as Snowpocalypse44, Snowmaggedon45, and Snowzilla46. Modeling studies have reported divergent conclusions as to whether AA contributes to less42 or more snowfall30. We computed the return period of varying thresholds of snowfall across the US before (1950–1989) and after (1990–2016) the emergence of AA (Fig. 9). Consistent with our earlier results that a warmer Arctic favors heavier snowfalls, we find that across the northeastern US, heavy snowfalls are generally more frequent since 1990, and in many cities the most extreme snowfalls have occurred primarily during recent decades. In contrast, severe snowfalls in the western US have in general decreased during the AA period. For most cities shown in Fig. 9, the snowfall return periods were found to differ between the two periods with a confidence level greater than 95%.

Fig. 9 Major snowfalls in eastern US are becoming more frequent. The return period (y axis; 0 to 15 years) of varying snowfall events (x axis; 0 to 18 inches) for weather stations during two periods: cold Arctic (1950–1989; blue) and warm Arctic (1990–2016; green). Lower values indicate more frequent snowfalls (shorter return period). The time series that were found to be significantly different at the 95% confidence level are shown in bold lines and include Atlanta, Boston (Blue Hill), Des Moines, Detroit, Helena, New York, Salt Lake City, Seattle, and Washington Full size image

These findings suggest that recent observed heavy snowfalls, in particular in the northeastern US, may be linked to AA, though further research is required to confirm the linkage. This result is consistent with evidence that extreme rainfall in the northeastern US has also increased over the same period47.

Study limitations

There are important limitations to this study. The most obvious is common to all observational analysis, i.e., correlation does not mean causation. Thus, even though elevated heights and warmer temperatures in the Arctic are positively correlated with more frequent severe winter weather in the mid-latitudes, we cannot conclude that the warmer Arctic is responsible. That said, the highest correlations occur when Arctic variability leads AWSSI by five days, implying it is more likely that Arctic variability is contributing to mid-latitude winter extremes. Another challenge is that the observational record during rapid Arctic change is short, which makes the demonstration of statistical significance difficult6,8. We have partially compensated for the short record by computing daily rather than seasonal correlations. This has allowed us to greatly expand the degrees of freedom in analyses of relationships between PCH/PCT and severe winter weather, resulting in highly significant correlations. Based on observations and correlations alone, we also cannot offer physical mechanisms for the relationships we demonstrate, though our analysis is consistent with previously studied mechanisms on how a warmer Arctic can influence mid-latitude weather5,6,15. We hope to continue this work with model simulations to identify mechanisms behind the correlations.

Comparing polar cap with the annular mode

The PCH has been shown to be highly correlated with the first empirical orthogonal function of geopotential height (sea-level pressure) poleward of 20° N, referred to as the Northern Annular Mode: NAM31,48 (Arctic Oscillation: AO). We now explore the similarities and differences in relationships between the PCH/PCT, the NAM, and severe winter weather.

When the PCH was first introduced49, it was argued that the advantage of using the PCH over the NAM is that the PCH (and PCT) represents Arctic-only variability, while the NAM includes variability from the entire NH. This distinction is important because the NAM represents a conflation of variability in the Arctic, mid-latitudes, and sub-tropics, thus by definition will exhibit a relationship with mid-latitude weather. Because PCH and PCT are largely independent of mid-latitude influences, any connection between them will shed light on Arctic/mid-latitude linkages.

Though the PCH and the NAM are correlated48 (Supplementary Figure 5), there are also important differences. By definition, a positive PCH indicates above-normal geopotential heights throughout the Arctic (Supplementary Figure 6). The negative phase of the NAM, in contrast, is characterized by above-normal geopotential heights mostly in the North Atlantic sector, especially near Greenland50.

The PCT is more strongly related to the PCH, particularly in the troposphere, than it is to the NAM (Supplementary Figure 5). The reason for the independence between the PCT and the NAM in the troposphere can be understood by analyzing surface temperatures (T s ) associated with the negative NAM and the positive PCT at 1000 hPa (Fig. 10). We computed the T s variability related to the NAM at 1000 hPa (Fig. 10a). We also computed the surface temperature variability related to the NAM at 500, 300, and 10 hPa, and the results were qualitatively similar. We further assessed the difference in surface temperature anomalies between the positive PCT (PCT+) and the negative phase of the NAM (NAM–; Fig. 10b). The temperature anomalies associated with NAM– are positive only near and to the south of Greenland, along with negative anomalies across the Eurasian sector of the Arctic (Fig. 10a). In contrast, the T s anomalies associated with PCT+ are pan-Arctic and T s are warmer in the Eurasian Arctic relative to the NAM– (Fig. 10b). The PCT+ represents basin-wide warming, while the NAM– represents mainly regional warming in the Arctic. Also, T s are colder in the eastern US for PCT+ relative to NAM–. Consistent with this finding we repeated the analysis in Fig. 2 with the NAM index instead of the PCH/PCT in Supplementary Figure 7. Our analysis shows that in general the PCH/PCT have a more robust signal with extreme weather than the NAM. Another difference is that the NAM signal is stronger in the stratosphere in contrast to the PCH/PCT where the tropospheric signal is stronger.

Fig. 10 Arctic amplification is more closely associated with polar cap temperature than annular mode or warming in the Barents–Kara seas. a Surface temperature anomalies associated with the negative phase of the NAM, b difference in surface temperature anomalies associated with positive PCT at 1000 hPa and the negative NAM, c Northern Hemisphere surface temperatures trends in era of AA (1990–2016), d association between surface temperature anomalies across the NH and in the Barents–Kara seas. Climatological averages computed over the period 1981–2010. Note differences in scales. Hatching in all figures represents those values found to be statistically significant above 95%. We also tested for field significance in plots a, b, and d and the differences were found to be highly significant. Ocean mask was applied south of 60° N Full size image

Observed trends in NH surface temperature during the era of amplified Arctic warming are characterized by general warming across the entire Arctic basin punctuated by two regional maxima near Greenland and the Barents–Kara seas (Fig. 10c). The distinct patterns in the NAM versus the PCT suggest that the basin-wide positive temperature trends observed in the period of AA are more similar to, and thus more closely related to, PCT+ than with the NAM–. This is consistent with findings that the influences of the NAM and AA on the NH circulation are distinct in idealized modeling studies51.

In Fig. 10d we present the 2-m temperature trends associated with temperature anomalies at 850 hPa averaged over the Barents/Kara seas. A broad area of warming extends from the Barents/Kara area eastward through the Eurasian Arctic, while cooling appears elsewhere in the Arctic. Also in contrast to the PCT+ and the NAM− patterns, continental cooling is limited to Asia, along with warming across North America. Temperature trends appear to result from a combination of basin-wide warming, as seen in the positive PCT patterns, and warming in the Barents–Kara region. Thus, constructive interference of these two warming areas may explain the observation of statistically significant continental cooling in Asia only52. Basin-wide Arctic warming favors a cooling response in the eastern US, while Barents/Kara warming favors the opposite35, resulting in destructive interference and partial cancellation (though the temperature trends are still negative). This hypothesis requires further analysis.

In conclusion, from Fig. 10, the PCH and the PCT represent coherent Arctic temperature variability that is basin-wide, while the NAM also varies coherently with these indices but represents regional Arctic temperature variability, which is strongest in and around Greenland. Therefore, the NAM– captures some of the regional warming observed over the past two to three decades (near Greenland), while the PCH+ and PCT+ better capture pan-Arctic warming.