Cluster analysis

We perform hierarchical clustering on the daily geopotential height anomaly field at 100 hPa (Z100) poleward of 60°N in winter (January and February) from 1979 to 2018 (Methods). We chose such a lower stratospheric level as those are especially crucial for troposphere-stratosphere coupling,11,12,14 and we focus on January and February because these months show the largest vortex variability. The choice of the number of clusters is usually somewhat subjective and metric dependent. However, here the goal of our clustering approach is to identify specific events of interest and use those as a starting point for a more detailed statistical analysis. We discuss the robustness of the clustering in the SI.

We detect five clusters capturing lower stratospheric variability, presented by their composites calculated over all days that were assigned to the cluster and ordered by mean polar cap height in Fig. 1. Cluster 1 represents extremely strong polar vortex states, with negative geopotential height anomalies over the entire polar cap. Clusters 2 and 3 show subsequently weaker and displaced vortex patterns. In the remainder of the manuscript, we restrict ourselves to discussing only the two weakest vortex clusters 4 and 5.

Fig. 1 Cluster representatives. Composites of geopotential height anomalies at 100 hPa in winter (JF) from 1979 to 2018 for days assigned to the same cluster. The number in brackets gives the total occurrence (in percent) over all winter days. The bar plots below the clusters shows the seasonal-mean occurrence frequency for each winter Full size image

Cluster 4 is characterized by zonally asymmetric Z100 anomalies with strong positive anomalies over Siberia, but negative anomalies over Canada and the North Atlantic. It is detected on approximately 14% of all winter days with a total of 48 events (defined as consecutive days of the same cluster), giving an average duration of 7 days. Though cluster 4 events are characterized by a disturbed polar vortex (in terms of a high polar cap height anomaly), only 4 out of 48 cluster 4 events are associated with major SSWs (see SI for a discussion on the robustness of the clustering and a detailed comparison with other metrics). In contrast, cluster 5 represents a completely disturbed polar vortex with positive zonally symmetric Z100 anomalies over the entire polar cap. Approximately 16% of all winter days are assigned to the weakest polar vortex events described by cluster 5, coming from only 32 events with a mean-duration of nearly 12 days. Most of the observed extremely weak vortex states, defined as major SSWs, coincide with cluster 5 events (see SI).

Reflective and absorbing stratospheric pathways

To test for the dynamical coupling mechanisms, we first compute the absolute and anomalous vertical wave-activity flux (WAF), here calculated as the vertical component of the Plumb fluxes27 at 100 hPa, averaged over all cluster 4 (Fig. 2a, c) and cluster 5 events (Fig. 2b, d). During cluster 4 events, waves propagate upward over eastern Siberia with simultaneous downward propagation over Canada (Fig. 2a), which is also characterized by significant (p < 0.05, see Methods) positive and negative wave flux anomalies respectively in these regions (Fig. 2c). The enhanced upward wave activity over eastern Siberia is consistent with the associated Z100 dipole pattern of cluster 4 days, showing a shifted polar vortex towards eastern Canada (Fig. 1). During cluster 5 events, we find upward wave propagation across the hemisphere (Fig. 2b) with strongest positive anomalies over Canada and the North Atlantic (Fig. 2d).

Fig. 2 Composites of the vertical component of the Plumb flux at 100 hPa for clusters 4 and 5. a Color shading shows the absolute values during cluster 4 events and the contours represent the winter climatology. b Same as in a but during cluster 5 events and with contours indicating regions over Siberia (pink), Canada (brown) and the Euro-Atlantic sector (red), which are used to calculate regional indices. c Color shading shows the anomalous values during cluster 4 events and the stippling shows significant values (p < 0.05, see Methods). d Same as c but for cluster 5 events Full size image

To assess the coupling mechanisms in more detail, we next plot the temporal evolution of different standardized stratospheric indices before, during and after cluster 4 (Fig. 3a, c, e) and cluster 5 events (Fig. 3b, d, f). Composites for the absolute values are shown in the SI. In each panel, lag 0 denotes the start day (i.e., the first day cluster 4 and cluster 5 events were respectively detected). We construct an index P 4 (P 5 ) describing the similarity between the observed polar vortex pattern and cluster 4 (cluster 5) for each day in winter: We project the daily Z100 anomaly field onto the cluster composite (Fig. 1) and normalize the index by its multi-year standard deviation of the respective day. The upper row in Fig. 3 shows this P 4 (P 5 ) index as well as the mean polar cap height index (PCH) at 10 hPa. The difference in event-duration between cluster 4 and cluster 5 becomes evident again by the evolution of the P 4 and P 5 indices, with cluster 4 events only showing a relatively short period (14 days) of significantly high P 4 values (Fig. 3a), while the P 5 index is significantly increased in the 20 days before and after the detection of cluster 5 events (Fig. 3b). The middle row plots the vertical component of the Plumb flux at 100 hPa averaged over the latitudinal belt from 50°N to 75°N (WAF Hem , red shading). Further, regional indices (see boxes in Fig. 2b) of the vertical Plumb wave-activity flux are calculated over the Euro-Atlantic sector (WAF Euro-Atl , red line in middle row), over eastern Siberia (WAF Siberia , pink shading in bottom row) and over Canada (WAF Canada , brown line in bottom row). As expected,15 both cluster 4 and cluster 5 events are preceded by anomalously strong vertical wave-activity fluxes of approximately the same magnitude (red shading in Fig. 3c, d). For cluster 5, however, the positive wave-activity anomalies precede the event start much earlier. Consistently, the PCH is already significantly large before and during the onset of cluster 5 events and the vortex remains weakened afterwards (Fig. 3b). The increased hemispheric vertical wave-activity anomalies preceding cluster 5 events are preconditioned by significantly positive wave fluxes (Fig. 3f, see Fig. S4b for absolute values) over Canada ~2 weeks before the event start and characterized by enhanced wave flux anomalies over the Euro-Atlantic sector with the event onset (Fig. 3d). Wave flux anomalies over Siberia are slightly positive but drop with the event start (Fig. 3f). For cluster 4, in contrast, the hemispheric vertical wave-activity flux anomalies are significantly increased only 5 days before the event start, and become negative shortly after (Fig. 3b). Consistently, the polar vortex is briefly disrupted (i.e. the PCH rises) and recovers quickly thereafter (Fig. 3a). Also the regional Plumb flux indices show a different evolution: Vertical wave-activity flux is significantly enhanced over eastern Siberia for several days (Fig. 3e) but shows only moderate anomalies over the Euro-Atlantic sector (Fig. 3c). Moreover, wave-activity fluxes over Canada become significantly negative with the event start (Fig. 3e, Fig. S4a for absolute values), indicating downward propagation over this region.

Fig. 3 Composites of temporal evolution of different standardized stratospheric indices 20 days prior and after cluster 4 events (left column) and cluster 5 events (right column). a, b The P 4 and P 5 index (light green shading), and the polar cap height mean index PCH at 10 hPa (green line). c, d The hemisphere-averaged vertical wave-activity flux (WAF Hem , red shading) and the regional index of vertical wave-activity flux over the Euro-Atlantic sector (WAF Euro-Atl , red line). e, f Regional indices of vertical wave-activity flux over eastern Siberia (WAF siberia , pink shading) and Canada (WAF Canada , brown line). In all panels, significant values (p < 0.05, see Methods) are indicated with dots Full size image

Overall, these findings are consistent with previous studies and support the notion of a reflecting (cluster 4) and absorbing (cluster 5) coupling mechanisms.8,16,17,18,19 Cluster 5 events, often coinciding with SSWs, are associated with persistent stratospheric disturbances (absorbing-type), preceded by enhanced hemisphere-wide vertical wave activity that is absorbed in the stratosphere leading to increased geopotential heights over the entire stratospheric polar cap. The composites for cluster 4 events, of which only a few are associated with major SSWs, suggest that a strong but short-lasting pulse of vertical wave-activity resulting from enhanced upward propagation over eastern Siberia is reflected by the stratospheric flow and descends over Canada (reflecting-type), in agreement with previous studies.8,17 Also the precondition of the polar vortex (i.e., already weak before cluster 5 and neutral before cluster 4 events) is in agreement with earlier studies16,17,28 and supports the finding of reflected (absorbed) waves if the stratospheric flow is sufficiently strong (weak). We find that 70% of all cluster 4 events occurred during the westerly phase of the Quasi-Biennial-Oscillation (QBO-W), which is linked to a strengthened polar vortex29 and might thus favor the occurrence of cluster 4. Thus, the locations of the upward wave-activity flux and the initial strength of the polar vortex seem to have a central role in whether the stratospheric pattern is of reflective or of absorbing-type.

Note that several cluster 4 (and some cluster 5 events) can occur in the same winter, with the events sometimes only being separated by a few days, leading to overlapping time-ranges for the composites. Composites of all individual cluster 4 and cluster 5 events and of the associated wave flux activity are presented in the SI, partly showing substantial differences, but overall supporting the main findings. Here we decided not to apply further criteria to exclude or merge particular individual events and leave this for subsequent research.

Connection to tropospheric circulation and cold-extremes

To investigate the influence of reflecting and absorbing events on the tropospheric circulation, we next compute the geopotential height anomalies at 500 hPa (Z500) during cluster 4 (reflecting-type) and cluster 5 (absorbing-type) events (Fig. 4a, b). As expected,3,9,10,13 cluster 5 days coincide with a negative NAO-type Z500 pattern with increased geopotential heights over Iceland and the North Atlantic and anomalously low values over the Azores (Fig. 4b). Moreover, during cluster 5 days the NAO index is significantly (p < 0.01, using a two-sample Kolmogorov–Smirnov test) shifted towards more-negative values compared to all other winter days (Fig. 4d). Also the daily P 5 index is significantly (p < 0.01 according to a bootstrapping test) correlated (r = −0.5) with the NAO index. Thus, the absorbing-type cluster 5 events resemble the well-documented case of a zonally symmetric disturbed vortex including downward propagation of a negative NAM pattern.3,9,11,12

Fig. 4 Tropospheric circulation patterns associated with cluster 4 and cluster 5. a Composites of geopotential height anomalies (Z500) during cluster 4 days and b during cluster 5 days. Significant values (p < 0.05) are indicated with dots. c Histogram of the WPO index during cluster 4 days and all other days in winter. d as c but for the NAO index and cluster 5 days Full size image

In contrast, Z500 composites during cluster 4 days show a negative phase of the WPO with lower geopotential heights over the central Pacific and pronounced positive anomalies over the North Pacific (Fig. 4a). Moreover, Z500 anomalies over the Atlantic show a positive NAO-like dipole, but with the centers of maximum anomalies shifted southward. Comparing the WPO during cluster 4 days and all other winter days, we find again a significant negatively shifted distribution during cluster 4 days (Fig. 4c). More generally, the WPO and the daily P 4 index are significantly correlated (r = −0.5) but note that the P4 (P5) index and the NAO (WPO) only show a correlation of 0.09 (−0.02). The negative WPO pattern is consistent with the Siberian/Aleutian high in the stratosphere, descending downward due to suppression of upward wave propagation as was described in detail in Kodera et al.8 Our results thus strongly support the hypothesis that reflecting-type events, here represented by cluster 4, can lead to increased geopotential heights over the North Pacific.

In agreement with the negative phase of the NAO during cluster 5 days, near-surface temperature composites show a pronounced pattern of significant cold anomalies over northern Eurasia (Fig. 5b). To assess the relationship between cold-extremes in this region and cluster 5 events in more detail, we count the frequency of each cluster during the 10% coldest days in northern Eurasia (averaged over 50°N–65°N, 10°E–130°E, see blue box in Fig. 5b) and normalize this number by their overall occurrence frequency (Fig. 1). A value of 1 thus indicates that the cold-extreme frequency is the same as expected by chance, implying no statistical relationship between the stratospheric cluster and cold-extremes. We find that cold-extremes occur twice as often during cluster 5 days than expected by chance (Fig. 5d), indicating a strong statistical relationship between northern Eurasian cold-snaps and cluster 5 events. Yet, over North America there are no significant cold anomalies during cluster 5 events (Fig. 5b). In fact, the 10% coldest winter days in this region (averaged over 40°N–55°N to 100°W–70°W, orange box in Fig. 5a), coincide less often with cluster 5 than expected (Fig. 5c). During cluster 4 events, however, there is a pronounced pattern of negative temperature anomalies over most of Canada, the Great Lakes regions and the eastern US (Fig. 5a). The 10% coldest days in North America (orange box in Fig. 5a) occur more than twice as often during cluster 4 events than statistically expected (Fig. 5c).

Fig. 5 Links to cold-extremes. Composites of near-surface temperature for a cluster 4 and b cluster 5 days. Significant values (p < 0.05) are indicated with dots. Normalized occurrence of each cluster during the 10% coldest days in c North America (yellow box in a and d northern Eurasia (blue box in b). The normalized values were calculated by dividing the occurrence percentage of each cluster during cold days by its occurrence percentage during all winter days. A value of 1 thus refers to the same proportion Full size image

Overall, the analyses thus present a strong statistical relationship between the reflecting (absorbing) cluster 4-type (cluster 5) pattern and the WPO (NAO) and associated cold-extremes over parts of North America (northern Eurasia). Moreover, in agreement with the composites, seasonal-mean cluster 4 frequency can explain a large fraction (up to 45%) of seasonal temperature variability over Canada and the US (Fig. 6a), while cluster 5 accounts for variability over large parts of Eurasia but not over North America (Fig. 6b). Thus, although in particular the reflecting-type events are only of short duration, their seasonal-mean projects strongly onto winter temperature variability. Understanding the precursors of wave-reflection might thus help to improve predictions for this region. For example, Kodera et al.19 proposed that blocking over the North Atlantic can trigger a wave train into the stratosphere, which by suppression of upward-propagating waves can cause blocking over the North Pacific. In subsequent research, we will assess the role of these tropospheric drivers in more detail.

Fig. 6 Explained variance of winter temperature by cluster 4 and cluster 5. a R2 values for regression of winter (JF) mean temperature at each grid-point on seasonal-mean cluster 4 frequency and, b on seasonal-mean cluster 5 frequency. Before calculation the regression models, the linear trends of the regressors and the temperature were removed. Significant (p < 0.05) models according to two-sided Student’s t-test are indicated in hatches Full size image

Causal effect network analysis

The composite analysis based on the detected cluster 4 events suggest that a stratospheric pathway contributes to the formation of North Pacific blocking, consistent with previous studies on wave-reflection.18,19 However, clustering includes some subjective criteria which might lead to selection bias, potentially producing non-robust results when studying continuous time series. Therefore, to test the involved hypotheses and to assess the causal relationship between the considered indices in more detail, we apply causal effect network (CEN) analysis (Methods). CEN is a multi-variate statistical framework based on a causal discovery algorithm, introduced to climate science for hypothesis testing of teleconnection processes.26 CEN detects spurious correlations (e.g., due to common drivers, indirect links or auto-correlation effects30) by iteratively calculating partial correlations between different combinations of variables and at different lags. Those relationships that are found to be conditionally dependent (i.e., for which the linear relationship is significantly different from zero even when the influence of a combination of other drivers or auto-correlation effects is excluded) form the links in the CEN. These links can be interpreted as potentially causal for the set of considered processes and time-lags. Thus, CEN-analysis allows for much stronger statements towards a causal interpretation beyond simple cross-correlation analysis or the bivariate concept of Granger-causality.30,31,32

Here we particularly want to test the hypothesis that enhanced vertical wave activity over eastern Siberia (WAF S ) leads to increased geopotential heights over the North Pacific (Pac). We also include the PCH index at 10 hPa to describe stratospheric polar vortex variability (PCH). Moreover, we include the regional WAF index over Canada (WAF C ). The regions over which the time-series indices are calculated are displayed in Fig. 7.

Fig. 7 Regions and variables over which indices for CEN-analysis are calculated. a PCH: polar cap heights at 10 hPa northward of 60°N. b WAF S : eastern Siberian vertical wave-activity flux at 100 hPa calculated over the sector 50°N–75°N and 120°E–185°E. WAF C : same as WAF S but calculated over the Canadian longitudes 225°E–300°E. c Pac: geopotential heights at 500 hPa in the north Pacific calculated over the domain 50°N–70°N and 200°E–235°E (northern component of the WPO index) Full size image

Since we are interested in low-frequency sub-seasonal variability, we remove synoptic variability by calculating centered 5-day mean time-series (i.e., by calculating means over bins of 5 days) before accessing their causal links. Thus, a lag-1 relationship refers to a lag of 6–10 days which covers the timescales at which links are approximately expected based on the composites (Fig. 3) and previous studies on wave-reflection.8,16,19 We perform CEN-analysis for the winter months of January and February (JF) only. When performing conditional independence tests, we allow time-lags of up to one month (lag-6). The detected causal links (i.e., the conditionally dependent relationships) are shown in Fig. 8, whereby red arrows correspond to significant (p < 0.01) positive linear relationships and blue arrows represent negative relationships. The node-color denotes the strength of the strongest auto-correlation coefficient (at lag-1). The exact values are given in Table 3 of the SI.

Fig. 8 Causal effect network (CEN) constructed for winter 5-days-mean indices of the polar cap height mean index at 10 mb (PCH), regional indices of vertical wave activity over eastern Siberia (WAF s ) and Canada (WAF C ), and Z500 over the North Pacific (Pac). The node-color denotes the strength of the auto-correlation coefficient at lag-1. Red (blue) arrows correspond to significant (p < 0.01) positive (negative) causal (i.e., conditionally dependent) relationship and the lag is 6–10 days (i.e., lag-1). Exact values of the links are given in the SI Full size image