Introduction

In late December 2015, an intense windstorm named Frank attacked the hinterland of the Arctic from the Atlantic, with the consequences of the North Pole temperature rising above 0 °C1,2. This Arctic daily warming event aroused interest from all walks of life, including the scientist, press and general public. It is not a unique instance but its counterpart; similar Arctic daily warming events have occurred from time to time in Arctic history. Specifically, as early as 1956, the North Pole experienced winter near-surface temperatures exceeding –1 °C, and near-surface temperatures above –5 °C (–10 °C) were recorded once every 3 years (ten times per winter)3. Previous research has shown that these Arctic daily warming events are triggered by storms with large warm and humid air masses, which are synoptic processes and different from Arctic Amplification (AA)1,3,4,5. The Atlantic Ocean is the main source of storms which often cross the North Pole3,6,7. Compared with the AA, these Arctic winter daily warming events have received less attention. Therefore, in the present study, we focus on the Arctic winter daily warming event triggered by Atlantic storms, shortened as A-RTDW, which refers to the increase in temperature from the prior day to the day of interest8,9,10 (see METHODS for details). Since Atlantic storm movement is steered by 500- or 700-hPa low-frequency mean winds over the North Atlantic (NA)11,12,13, the low-frequency atmospheric circulation over the NA could influence the occurrence of A-RTDW events by steering the storms into the Arctic. Moreover, previous modeling and reanalysis studies both confirmed that the El Niño-Southern Oscillation (ENSO), which is a major driver of global interannual variability14,15,16, could have a significant impact on the low-frequency mean winds over the NA and Arctic regions by the ENSO/North Atlantic oscillation (NAO) teleconnection17,18,19. Thus, we speculate that ENSO may exert an influence on the occurrence frequency of A-RTDW events.

In the recent decade, increasing attention has been paid to the Central Pacific ENSO (CP ENSO) which is characterized by mostly positive sea surface temperature (SST) anomalies located in the central equatorial Pacific20,21,22. The CP ENSO/NAO teleconnection in boreal winter has also been demonstrated by some research23,24 and explained as the weaker El Niño-related polar vortex being a favorable condition for the formation of NAO’s negative phase25. Thus, the CP ENSO could have a significant impact on Arctic warming by acting on the polar vortex and NAO. Specifically, Li et al.26 found that the warm (cold) phase of CP ENSO contributes to anomalously warm (cold) conditions over Greenland and northeastern Canada in February by inducing a negative (positive) NAO-like pattern. Hu et al.27 proposed that by analyzing observation and model data, CP El Niño events inhibit summer Arctic warming by influencing the polar vortex. However, Garfinkel et al.28 suggested that in the limited observational record, the stratospheric response to CP ENSO is very sensitive to the CP-El Niño index used, the composite size and the month or seasonal average examined. Moreover, Yin and Zhou24 found that the CP ENSO-NAO connection is unstable; before the mid-1980s, the CP ENSO is closely related to the NAO, while the connection has been interrupted since the mid-1980s. Taking these factors into account, the present study seeks to assess the relationship between CP ENSO and the occurrence frequency of A-RTDW events.

Results

Synoptic-scale atmospheric conditions of the A-RTDW event

Figure 1a shows the synoptic meteorological conditions of the A-RTDW events from 3 days to 0 day before the A-RTDW event occurrence. At the surface, there is a storm located southeast of Greenland 3 days before the A-RTDW event occurrence (A-RTDW day −3 in Fig. 1a). At the mid-troposphere, a ridge and a trough can be clearly seen at east and west of Greenland, respectively. Situated between the ridge and trough, the southerly anomaly, which is averaged from 3 to 0 days before the A-RTDW event occurrence, blows to the North Pole from the NA. Then, the storm with humid and warm air masses moves northwards along the southerly, which is consistent with previous studies11,12,13. On the peak date of A-RTDW event (the day when the A-RTDW event occurs), the most pronounced feature is that the storm arrives at the North Pole with a maximum local increase in temperature above 5 °C within a day. Thus, the mean wind at the mid-troposphere over the NA is key to the A-RTDW event occurrence by determining whether storms can enter the Arctic to trigger warming. In the following, we will explore the large-scale atmospheric conditions associated with the occurrence frequency of A-RTDW events during 1950–2018.

Fig. 1: Atmospheric conditions of A-RTDW events.
figure 1

a Synoptic anomalous atmospheric conditions from the initial day (A-RTDW day −3, i.e., 3 days before the A-RTDW event occurs) to the peak date (A-RTDW day 0, i.e., the day when the A-RTDW event occurs) of A-RTDW events, including 1000 hPa temperature increment anomalies from the prior day to the peak date (colored, interval: 1, units: °C; positive in red and negative in blue), 500 hPa horizontal wind anomaly (blue vector, units: m·s−1) and geopotential height (black contours, interval: 100, units: m) averaged from A-RTDW day −3 to A-RTDW day 0. The purple line, purple solid dots and purple numbers −3, −2, −1, 0 in (a) represent the storm trajectory, centers of the storm and 3, 2, 1, 0 days before the A-RTDW event occurs, respectively. Anomalies of 500 hPa geopotential height (colored, interval: 3, units: m) and horizontal wind (black vector, units: m s−1) in DJF obtained by regression on the (b) A-RTDW index and (c) DJF EMI index during 1950–2018, respectively. In (b) and (c), only vectors with meridional component anomalies at the significance level of p < 0.1 are shown. The EMI index in (c) has been multiplied by –1 for display purposes. The dashed purple boxes in (b) and (c) mark the region (60°–90°N, 30°W–20°E). d Anomalies of 850 hPa eddy kinetic energy (EKE; colored, interval: 0.3, units: m2 s−2) in DJF obtained by regression on the DJF V index during 1950–2018. The dots indicate significance at p < 0.1.

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Large-scale atmospheric conditions associated with the occurrence frequency of A-RTDW events during 1950–2018

To explore the relationship between the occurrence frequency of A-RTDW events (denoted as the A-RTDW index) and large-scale atmospheric conditions, as well as the CP ENSO, the anomalies of 500 hPa geopotential height and horizontal wind in DJF are regressed onto the A-RTDW index and EMI index from 1950 to 2018, respectively, as shown in Fig. 1b, c. Corresponding to the winter when A-RTDW events are more than normal, there are two anomalous anticyclonic centers at east of the United States and Iceland, respectively, as well as an anomalous IL (Fig. 1b). Furthermore, there are significant southerly anomalies at east of IL (60°–90°N and 30°W–20°E). In contrast, there is an anomalous anticyclonic center at east of the United States and an anomalous IL in the cold phase of the CP ENSO, respectively, showing a positive NAO-like pattern, but there is almost no significant southerly anomaly over the NA (Fig. 1c). To analyze the relationship between the southerly over the NA (denoted as the V index; see METHODS for details) and storm tracks (denoted as the EKE; see METHODS for details), Fig. 1d shows EKE anomalies associated with the V index. Corresponding to the winter when winter-mean meridional wind anomalies are positive, i.e., southerly anomalies, there are significant positive EKE anomalies from the NA to the Arctic region, suggesting that storm track is tilted poleward. Thus, the mean wind over the NA is important for the A-RTDW event by steering storms into or away from the Arctic, which is consistent with previous research11,12,13.

Overall, the CP ENSO-related interannual atmospheric conditions are partially similar to the interannual atmospheric conditions associated with the A-RTDW index (Fig. 1b, c), implying that CP ENSO may impact the frequency of A-RTDW occurrences, but the impact may be weak during 1950–2018. Meanwhile, considering that the CP ENSO/NAO connection is unstable24, we suspect that there may be an interdecadal change in the CP ENSO’s role in the occurrence frequency of A-RTDW events. In the next subsection, we will investigate their specific relationships.

The interdecadal change in the relationship between the A-RTDW index and CP ENSO

As shown in Fig. 2a, the A-RTDW index and EMI index in December–January-February (DJF) are frequently of opposite signs before the mid-1980s, while they are sometimes of opposite signs and sometimes of the same signs after the mid-1980s. These results imply that there may be a decadal change in the relationship between the two indices. Figure 2b shows their 21-year moving correlation coefficient; specifically, the 21-year moving correlation coefficients from 1967 to 1975, representing the central years of 1957–1985, are stably significantly negative (p < 0.05), while they become insignificant afterward. Thus, we obtain one significant correlation period from 1957 to 1985 (P1) and one insignificant correlation period during 1986–2018 (P2).

Fig. 2: Interdecadal change in the relationship between the A-RTDW and EMI indices.
figure 2

a The standardized A-RTDW index (solid red line) and EMI index in DJF (solid blue line) from 1950 to 2018; (b) the 21-year moving correlation coefficient between the A-RTDW index and DJF EMI index. Relationships between the standardized A-RTDW and DJF EMI indices during (c) 1957–1985 (P1) and (d) 1986–2018 (P2), respectively. In b, the dashed red line represents the significance level of p < 0.05 and the red dots represent the central years with significant 21-year moving correlation coefficients. The red line and p in (c), as well as r in (c) and (d), represent the linear fit, significance level and correlation coefficient between the standardized A-RTDW and DJF EMI indices, respectively.

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To further confirm the interdecadal change in the relationship between the A-RTDW index and the DJF EMI index, the scatter plots between the two indices over P1 and P2 are shown in Fig. 2c, d. The correlation coefficient between the A-RTDW and winter EMI is –0.47 (p < 0.01; significant) in P1 (Fig. 2c), while it is only –0.07 (insignificant) in P2 (Fig. 2d). The scatter plots between the A-RTDW_new (another index reflecting occurrence frequency of A-RTDW events; see METHODS for details) and winter EMI in P1 and P2 support the results obtained by the A-RTDW index (Supplementary Fig. 1). Additionally, to evaluate whether the relationships between the occurrence frequency of A-RTDW events and CP ENSO are affected by the selection of CP ENSO index, we recalculate their correlation coefficient by using the IEMI index, another index reflecting CP ENSO (see METHODS for details). In P1, the correlation coefficient between the A-RTDW and DJF IEMI is –0.5 (p < 0.01; significant), while in P2, it is only –0.07 (insignificant). The results obtained with IEMI are consistent with those obtained with EMI; the EMI index is used in the following analysis.

Furthermore, the A-RTDW and A-RTDW_new exhibit significant correlations with the central equatorial Pacific SST anomalies in P1, while there is no significant correlation region of the SST anomaly associated with the A-RTDW and A-RTDW_new indices in the central equatorial Pacific in P2 (Supplementary Fig. 2). Therefore, the 21-year moving correlation coefficient between these two indices (Fig. 2) and the relationships between the A-RTDW and SST (Supplementary Fig. 2) confirm the interdecadal change in the relationship between the occurrence frequency of A-RTDW events and CP ENSO around the mid-1980s.

Large-scale atmospheric conditions associated with the occurrence frequency of A-RTDW events in P1 and P2

To explore what the large-scale atmospheric conditions affect the occurrence frequency of A-RTDW events in P1 and P2, the anomalies of geopotential height and horizontal wind speed in DJF are regressed onto the A-RTDW index in two periods (Fig. 3). Corresponding to the winter when A-RTDW events are more than normal, the IL was strengthened in P1 (Fig. 3a); in contrast, there are anticyclonic anomalies at east of Iceland in P2 (Fig. 3b). The anomalies of geopotential height associated with the A-RTDW are different between P1 and P2; however, the significant southerly anomalies at east of IL in P1 and west of the anticyclone in P2 exist over the NA (purple box in Fig. 3), which steer the Atlantic cyclone into the Arctic to induce the A-RTDW occurrence, as in the above results and previous studies11,12,13. Given that the meridional wind anomaly over the NA determines the occurrence frequency of A-RTDW events, it could be a key connecting the CP ENSO and A-RTDW. Specifically, if the CP ENSO could induce such meridional wind anomalies over the NA, it could have an impact on the occurrence frequency of A-RTDW events, and vice versa.

Fig. 3: Large-scale atmospheric conditions associated with the A-RTDW index.
figure 3

Anomalies of 500 hPa geopotential height (colored, interval: 6, units: m) and horizontal wind (vector, units: m s−1) in DJF obtained by regression on the A-RTDW index during 1957–1985 (P1; a) and 1986–2018 (P2; b), respectively. Only vectors with meridional component anomalies at the significance level of p < 0.05 are shown; the dots indicate significance at p < 0.05. The dashed purple boxes mark the region (60°–90°N, 30°W–20°E).

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The possible mechanism of the change in CP ENSO’s role in the occurrence frequency of A-RTDW events

Figure 4a shows that in the warm (cold) phase of CP ENSO, the IL was weakened (strengthened) in P1, called the CP ENSO/IL teleconnection. The resulting significant northerly (southerly) anomalies at the east of IL are clearly seen over NA (purple box in Fig. 4a); thus, CP El Niño (La Niña) could decrease (increase) the occurrence frequency of A-RTDW events. In contrast, in P2, the CP ENSO/IL teleconnection disappears, and there is almost no significant meridional anomaly over NA (purple box in Fig. 4b), implying a weak relationship between the occurrence frequency of A-RTDW events and CP ENSO.

Fig. 4: Large-scale atmospheric conditions associated with the CP ENSO.
figure 4

Anomalies of 500 hPa geopotential height (colored, interval: 6, units: m; a, b) and horizontal wind (vector, units: m s−1; a, b) in DJF obtained by regression on the DJF EMI index, as well as wave activity flux (horizontal component units: m2 s−2; vertical component units: Pa m s−2; vectors; c, d) and its divergence (contour, interval: 4, units: m s−1 d−1; c, d) and 50 hPa geopotential height (colored, interval: 10, units: m; e f) in NDJ obtained by regression on the NDJ EMI index during 1957–1985 (P1; a, c and e) and 1986–2018 (P2; b, d and f), respectively. In a, b, only vectors with meridional component anomalies at the significance level of p < 0.05 are shown, and the dashed purple boxes mark the region (60°–90°N, 30°W–20°E). In c, d, red (blue) contours denote positive (negative) values, and only vectors exceeding 0.1 are shown. The dots in (a), (b), (e) and (f) represent geopotential height anomalies at the significance level of p < 0.05; the gray areas in (c) and (d) represent wave activity flux with vertical component anomalies at the significance level of p < 0.05.

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The CP ENSO is related to the occurrence frequency of A-RTDW events by the CP ENSO/IL teleconnection in P1; however, this connection is interrupted in P2 due to the disappearance of the CP ENSO/IL teleconnection. Why does the CP ENSO/IL teleconnection disappear in P2? In the following, the changes in the CP ENSO effect on the IL and meridional wind over NA are investigated first; then, we explore the possible factors that change the relationship.

The CP ENSO-related geophysical fields in November–December–January (NDJ; 1 month ahead of A-RTDW event occurrence) are used to reflect the effect processes of CP ENSO on the occurrence frequency of A-RTDW events. The wave activity flux and its divergence in NDJ are regressed onto the NDJ EMI index, as shown in Fig. 4c, d. In P1, the wave activity flux propagates poleward and upwards significantly into the stratosphere in the polar region in the warm phase of CP ENSO (gray areas in Fig. 4c). By wave-mean flow interaction, the convergence of the wave activity flux could decrease the zonal wind in the stratosphere, implying a weak polar vortex29,30,31. In contrast, there is almost no significant wave activity flux associated with CP ENSO propagating upwards into the stratosphere in P2 (Fig. 4d), implying that CP ENSO has no effect on the polar vortex. To further show the changes in upwards propagating wave activity flux excited by CP ENSO between P1 and P2, the vertical component of wave activity flux at 100 hPa over the Arctic region (66.5°–90°N) is averaged, which is denoted as the Fp index. The correlation coefficient of –0.55 between the Fp and EMI indices is at a statistical significance level of p < 0.01 in P1, while the correlation coefficient in P2 is –0.3 and insignificant (Supplementary Fig. 3), which suggests a weakening of the upwards propagating wave activity flux excited by CP ENSO from P1 to P2.

To further confirm the relationship between the CP ENSO and polar vortex, the 50 hPa geopotential height anomalies in NDJ are regressed onto the NDJ EMI index, as shown in Fig. 4e, f. In the warm phase of CP ENSO, the polar vortex is significantly weakened in P1 (Fig. 4e), whereas in P2, it changes little (Fig. 4f). Furthermore, a previous study found that the weakened polar vortex would reinforce a negative NAO pattern with the stratospheric and tropospheric cooperation25,32. A negative NAO means a weakened IL. Thus, in P1, the CP ENSO-related wave activity flux propagates upwards into the stratosphere to weaken the polar vortex to induce a weakened IL; then, the CP ENSO/IL teleconnection is established. In contrast, there is no significant wave activity flux propagation upwards into the stratosphere associated with CP ENSO in P2; therefore, the CP ENSO/IL teleconnection disappears. Whether the wave activity flux could propagate upwards into the stratosphere is the key to the existence of the CP ENSO/IL teleconnection; namely, it could partly determine the connection between the CP ENSO and the occurrence frequency of A-RTDW events.

Previous research has shown that the polar vortex intensity could influence Rossby wave propagation upwards into the stratosphere24,33,34. Namely, the climate state of polar vortex intensity may influence the relationship between CP ENSO and A-RTDW events. Figure 5a shows that the polar vortex in P2 is significantly deeper than that in P1, which confirms that the polar vortex intensity in P2 is truly stronger than that in P1. Thus, in P2, there is almost no CP ENSO-related Rossby wave propagation upwards to the stratosphere, which may be related to the polar vortex with a strong climate state. Then, the CP ENSO/IL teleconnection disappears. These results are consistent with the findings of Jimenez-Esteve and Domeisen32 that the polar vortex intensity has an impact on the ENSO/NAO teleconnection.

Fig. 5: Mechanistic schematic diagram.
figure 5

a The climate mean of 50 hPa geopotential height in NDJ in P1 (contour, intervals: 100, units: m); difference in climate mean of 50 hPa geopotential height in NDJ between P2 and P1 (colored, intervals: 15, units: m). The dots indicate the climate mean of the 50 hPa geopotential height in NDJ significant anomalies with the difference between P2 and P1 at the significance level of p < 0.05. b Mechanistic schematic diagram of CP ENSO’s role in A-RTDW in P1.

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The possible mechanism of the change in CP ENSO’s role in the occurrence frequency of A-RTDW events in the mid-1980s is as follows. As shown in Fig. 5b, before the mid-1980s (P1), the CP El Niño (La Niña) could increase (decrease) planetary wave propagation upwards significantly into the stratosphere to weaken (deepen) the polar vortex; then, the IL is weakened (deepened); the resulting northerly (southerly) anomalies at east of IL would decrease (increase) the occurrence frequency of A-RTDW events. Thus, the CP ENSO could impact the occurrence frequency of A-RTDW events in P1. However, after the mid-1980s (P2), the CP ENSO-related planetary wave is prevented from propagating upwards into the stratosphere, which may be related to the strong climate state of the polar vortex; thus, the connection between the CP ENSO and IL disappears. As a result, the CP ENSO could not influence the occurrence frequency of A-RTDW events. What factors affect the occurrence frequency of A-RTDW events in P2 deserves further study in the future.

Discussion

Arctic warming is always a hot topic. In the present study, Arctic winter daily warming events triggered by Atlantic storms (A-RTDW) are investigated, especially the relationship between their occurrence frequency and CP ENSO. The A-RTDW event is triggered by the warm and humid air mass transported from the Atlantic Ocean by a storm. The meridional wind anomaly over the NA could determine the occurrence frequency of A-RTDW events. Herein, the A-RTDW events emphasize temperature increments from the prior day to the day of interest during synoptic-scale processes, while the other warming events using the daily temperature anomaly focus on the changes in temperature compared to climate states. There are also some connections between these two definitions. Supplementary Fig. 4 shows that the maximum temperature anomaly is above 10 °C, suggesting that there are great positive temperature anomalies over the Arctic region when the A-RTDW events occur.

We find a change in the role of CP ENSO in the occurrence frequency of A-RTDW events. Specifically, before the mid-1980s, the CP ENSO/IL teleconnection could be established by CP ENSO-related planetary wave propagation upwards to the stratosphere; thereby, CP ENSO could induce the meridional wind anomaly over the NA to influence the occurrence frequency of A-RTDW events. However, in P2, the CP ENSO-related Rossby wave could not propagate upwards to the stratosphere, possibly related to the strong climate state of the polar vortex; then, the CP ENSO/IL teleconnection disappears. Thus, CP ENSO could not have an impact on the occurrence frequency of A-RTDW events in P2.

To explore whether the change in the CP ENSO’s role in the occurrence frequency of A-RTDW events is sensitive to warming thresholds in definition of A-RTDW event, the A-RTDW index is recalculated by using warming thresholds of 0.8 and 1.2 standard deviations. The results obtained by using different new warming thresholds support the above conclusions (Supplementary Fig. 5). Furthermore, the correlation coefficients between the A-RTDW and EMI indices are recalculated in P1 and P2 by using the ERA5 dataset (Supplementary Fig. 6). The correlation coefficients of P1 and P2 are –0.46 (significant) and 0.13 (insignificant), respectively, suggesting that the interdecadal change in the CP ENSO’s role in the occurrence frequency of A-RTDW events is robust.

Many previous studies have also suggested that since the early 1990s, the CP ENSO emerges more frequently and becomes stronger20,35,36,37. Supplementary Fig. 7 shows that the spatial distributions of CP ENSO-related SST anomalies are consistent in P1 and P2; however, the CP ENSO-related SST anomalies in the central equatorial Pacific in P2 are stronger than those in P1, suggesting that the CP ENSO becomes stronger in P2. These results seem to conflict with the weakened role of CP ENSO in the occurrence frequency of A-RTDW events. Indeed, the planetary wave induced by stronger CP ENSO may be prevented by the strengthened climate state of the polar vortex in P2, which is consistent with previous findings24,32. Thus, the CP ENSO’s role in the occurrence frequency of A-RTDW events disappears in P2, although the CP ENSO emerges more frequently and becomes stronger.

Additionally, by analyzing observational and modeling data, both sea ice and SST over the NA are related to the IL38,39,40,41. Therefore, the sea ice and SST over the NA may play roles in A-RTDW events by influencing IL, which deserves further study.

Methods

Data

For this study, the daily and monthly temperature, geopotential height and horizontal winds from 1000 hPa to 10 hPa are obtained from the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) Reanalysis42 (available at the website https://psl.noaa.gov/data/gridded/reanalysis/). These reanalysis atmospheric data are on 2.5° × 2.5° latitude-longitude grids and cover the period from 1950 to 2019. Those reanalysis atmospheric data on 0.25° × 0.25° latitude-longitude grids and covering the same period are also obtained by using the ERA5 reanalysis dataset from the European Center for Medium-Range Weather Forecasts (ECMWF)43. The monthly SST is from the Hadley Center Sea Ice and Sea Surface Temperature (HadISST) dataset, with a horizontal resolution of 1°×1° latitude-longitude, covering the same period as the atmospheric data.

The CP ENSO index, hereafter El Niño Modoki index (EMI), is defined as follows20:

$${\rm{EMI}}={[{\rm{SSTA}}]}_{{\rm{A}}}-{0.5[{\rm{SSTA}}]}_{{\rm{B}}}-{0.5[{\rm{SSTA}}]}_{{\rm{C}}}$$

where the [SSTA] with subscripts A, B and C represents the SST anomaly (SSTA) averaged over region A (central Pacific region: 10°S–10°N, 165°E–140°W), region B (eastern Pacific region: 15°S–5°N, 110°–70°W) and region C (western Pacific region: 10°S–20°N, 125°–145°E), respectively. Li et al.44 modified the EMI index by adjusting the weight coefficient of the SSTA in regions A, B and C, named the Improved El Niño Modoki Index (IEMI). And the definition of IEMI is as follows:

$${\rm{IEMI}}={3.0[{\rm{SSTA}}]}_{{\rm{A}}}-{2.0[{\rm{SSTA}}]}_{{\rm{B}}}-{1.0[{\rm{SSTA}}]}_{{\rm{C}}}.$$

For convenience, November–December–January and December–January–February are shortened to NDJ and DJF, respectively.

Definition of the A-RTDW event

The A-RTDW event is any day in the winter (DJF) of 1950–2018 satisfying the two conditions as follows8,9,10.

  1. 1.

    Over the region north of 66.5°N, the 1000 hPa “daily temperature increment anomaly” is greater than a standard deviation (\({\boldsymbol{\sigma }}\)).

  2. 2.

    The 1000 hPa southerly anomaly, which triggers the daily warming, originates from the Atlantic Ocean.

Specifically, the “daily temperature increment anomaly” (\({\Delta T}^{i}\)) represents the difference in daily temperature between the day of interest and the day before. \({\Delta T}^{i}\) is calculated as \({T}^{i}-{T}^{i-1}\), where T is the daily air temperature, the superscript “i” represents any day in DJF from 1950 to 2018 and “i–1” represents the previous day. \({\boldsymbol{\sigma }}\) is the standard deviation of the “daily temperature increment anomaly” (\({\Delta T}^{i}\)) in the winter of 1950–2018, which indicates the warming threshold. According to the first criterion, we obtain 891 warming events (denoted as RTDW events). By using a classification method, the fuzzy c-means method (FCM)45,46, the 454 A-RTDW events were picked out of all RTDW events based on the second criterion. To verify the accuracy of classification, the k-means method47 is also used as a classification method. Its classification results are almost the same as those obtained by the FCM method.

The A-RTDW event refers to the increase in temperature from the prior day to the day of interest. For example, an occurrence day of an A-RTDW event (j) means that \({\Delta T}^{j}\) is large. Moreover, A-RTDW events are extreme daily warming events on a synoptic scale and are different from Arctic warming based on the winter mean of temperature, such as AA. Specifically, the Arctic warming based on the winter mean of temperature focuses on the average of daily temperature in winter ((T1+T2+T3+T4+….)/N); however, the A-RTDW event focuses on the daily temperature difference between 2 days in winter (T2–T1, T3–T2, T4–T3…).

Definition of the A-RTDW index

The number of A-RTDW events in each winter varies widely; for example, there were 14 A-RTDW events in 1959 but none in 1992. What factors affect the occurrence frequency of A-RTDW events in each winter deserves attention. Thus, the A-RTDW index is defined as the frequency of A-RTDW events (or the number of A-RTDW events) that occurred each winter. The A-RTDW index could be used to investigate the relationship between the occurrence number of A-RTDW events in winter each year and some climatic factors, such as CP ENSO. If the correlation between CP ENSO index and A-RTDW index is significantly positive or negative, it means that CP ENSO might be related to the occurrence frequency of A-RTDW events.

Given that some identified warming days lasted for >1 day (Supplementary Table 1), we redefined the A-RTDW index as the number of A-RTDW events that occurred each winter, while identified warming days lasting for >1 day were only counted 1 time, denoted as the A-RTDW_new index. For example, if the identified warming days lasted for 3 days, the A-RTDW_new index is 1, while the A-RTDW index is 3. Overall, most identified warming days lasted for 1 day, some identified warming days lasted for 2 days, and few identified warming days lasted >2 days. In the present study, the A-RTDW index is mainly used, and the A-RTDW_new index is used to increase the completeness and comprehensiveness of the definition.

Synoptic meteorological conditions of the A-RTDW events

The synoptic meteorological conditions of the A-RTDW events –3, –2, –1 and 0 days are calculated as the geophysical field anomalies averaged over 3, 2, 1 and 0 days prior to the occurrence of all A-RTDW events, respectively.

Schematic diagram of storm motion

The centers of the storm (marked by the purple dots in Fig. 1a) are the locations of the lowest value of the storm at corresponding times. In addition, linking the storm centers at different times forms trajectories (marked by the purple line in Fig. 1a). Significantly, this method only produces a schematic diagram of storm motion.

Definition of the EKE

The regions of strengthened synoptic-scale eddy kinetic energy (EKE) are used to define the storm track48, which is an Eulerian approach, according to Eq. (1):

$${EKE}=\frac{1}{2}({u}^{{\prime} 2}+{v}^{{\prime} 2})$$
(1)

where \({u}^{{\prime} }\) and \({v}^{{\prime} }\) are 2–8 days period band-pass filtered zonal and meridional velocities.

Definition of the V index

Given that significant 500-hPa southerly anomalies are mainly at 60°–90°N and 30°W–20°E (Fig. 1b), the low-frequency mean meridional winds index (denoted as the V index) is defined as 500-hPa winter-mean meridional winds averaged over 60°–90°N and 30°W–20°E from 1950–2018.

Definition of the p-value

The p-value is an estimate of the statistical significance. And p < 0.01, 0.05 and 0.1 denote the results over 99%, 95% and 90% confidence levels, respectively. The significances of the composite, correlation and regression analyses are determined using the two-tailed Student’s t-test.