Recent Increase in a Recurrent Pan-Atlantic Wave Pattern Driving Concurrent Wintertime Extremes

Kai Kornhuber Earth Institute, Lamont-Doherty Earth Observatory, Columbia University, New York, New York, and Climate Analytics, and German Council on Foreign Relations, Berlin, Germany;

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Gabriele Messori Department of Earth Sciences, and Centre of Natural Hazards and Disaster Science, Uppsala University, Uppsala, and Department of Meteorology, and Bolin Centre for Climate Research, Stockholm University, Stockholm, Sweden

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Abstract

Wintertime extremes such as cold spells and heavy precipitation can have severe socioeconomic impacts, disrupting critical infrastructures and affecting human well-being. Here, we relate the occurrence of local and concurrent cold or wet wintertime extremes in North America and Europe to a recurrent, quasi-hemispheric wave-4 Rossby wave pattern. We identify this pattern as a fundamental mode of the Northern Hemisphere (NH) winter circulation, since wave 4 exhibits phase-locking behavior. Thus, the associated atmospheric circulation and surface anomalies reoccur over the same locations when the pattern’s wave amplitude is high. The wave pattern is most pronounced over the pan-Atlantic region, and increases the probability of extreme cold or wet events by up to 300% in certain areas of North America and Europe, as well as favoring their concurrence at different locations. High-amplitude wave-4 events have increased significantly in frequency over the past four decades (1979–2021), although no clear evidence is found relating this to modes or patterns of climate variability. The identified wave pattern may provide pathways for early prediction of local and concurrent cold or wet wintertime extremes in North America and Europe.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Kai Kornhuber, kk3397@columbia.edu

Kai Kornhuber and Gabriele Messori contributed equally to this work.

Abstract

Wintertime extremes such as cold spells and heavy precipitation can have severe socioeconomic impacts, disrupting critical infrastructures and affecting human well-being. Here, we relate the occurrence of local and concurrent cold or wet wintertime extremes in North America and Europe to a recurrent, quasi-hemispheric wave-4 Rossby wave pattern. We identify this pattern as a fundamental mode of the Northern Hemisphere (NH) winter circulation, since wave 4 exhibits phase-locking behavior. Thus, the associated atmospheric circulation and surface anomalies reoccur over the same locations when the pattern’s wave amplitude is high. The wave pattern is most pronounced over the pan-Atlantic region, and increases the probability of extreme cold or wet events by up to 300% in certain areas of North America and Europe, as well as favoring their concurrence at different locations. High-amplitude wave-4 events have increased significantly in frequency over the past four decades (1979–2021), although no clear evidence is found relating this to modes or patterns of climate variability. The identified wave pattern may provide pathways for early prediction of local and concurrent cold or wet wintertime extremes in North America and Europe.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Kai Kornhuber, kk3397@columbia.edu

Kai Kornhuber and Gabriele Messori contributed equally to this work.

Extreme weather events can have major socioeconomic impacts, causing substantial damage to infrastructure and property and negatively affect human well-being (e.g., Hales et al. 2003; Forzieri et al. 2018; Smith and Sheridan 2019; Munich Re 2020). Wintertime high-impact events include cold spells and rain-driven floods, which may disrupt traffic and supply chains (e.g., Vajda et al. 2014), the energy sector (e.g., Doss-Gollin et al. 2021; Busby et al. 2021), and pose a high risk for lower-income communities and the homeless (e.g., López-Bueno et al. 2020). Recent examples of the former include the 2021 Texas cold spell (Cohen et al. 2021; Doss-Gollin et al. 2021) or the 2019 North American (NA) East Coast cold spell (NOAA 2019). The severity of cold spells is projected to decrease under continued global warming (Screen 2014; Van Oldenborgh et al. 2019). However, atmospheric dynamical changes associated with climate change have been suggested to modulate the risk of cold-air outbreaks in the midlatitudes, with some studies suggesting that they may partly offset the thermodynamic forcing. A commonly invoked cause is Arctic warming and associated changes in the polar vortex (e.g., Cohen et al. 2020, and references therein), possibly coupled with oceanic modes of variability (e.g., Zhang et al. 2022). Others have argued for a role of internal variability of the atmospheric dynamics in favoring midlatitude cooling on local to regional scales (e.g., Deser et al. 2016; Ye and Messori 2020), or that interactions between atmospheric dynamics and altered thermodynamics due to a warmer climate may modify the characteristics of cold spells (e.g., Gao et al. 2015; d’Errico et al. 2022). Regardless of the exact mechanisms, cold spells will likely continue to be a major climate hazard for the coming years (Gao et al. 2015), for instance, through false spring events that can have severe impacts on ecosystems and agriculture (Allstadt et al. 2015). Next to cold spells, heavy rainfall and the associated flooding has caused widespread damage in recent winters. Examples include the severe 2019/20 U.K. floods, and the 2020 floods in Spain and France associated with the winter Storm Gloria (Sefton et al. 2021; Amores et al. 2020). Although recent trends in flood hazards display considerable regional variability (Blöschl et al. 2017), climate projections suggest widespread increases in heavy winter rainfall over large parts of Europe (Scoccimarro et al. 2013; Rajczak and Schär 2017), coupled with an increase in compound hazards such as rain-on-snow flooding events (Musselman et al. 2018).

Recurrent, persistent patterns that favor the occurrence of wintertime extremes in specific regions are of particular interest in the context of timely prediction and for understanding the physical mechanisms underlying the extremes. Large meridional meanders of the tropospheric jet stream, diagnosed as blocking patterns (Woollings et al. 2018) or amplified Rossby waves (in case of more zonally elongated ridge–trough patterns; White et al. 2022; Kornhuber et al. 2020; Screen and Simmonds 2014) are key atmospheric dynamical drivers of weather extremes in the midlatitudes. Some wave patterns exhibit preferred phases, leading to recurrent ridges and troughs and associated surface anomalies at specific locations (Branstator 2002; Harnik et al. 2016; Kornhuber et al. 2019, 2020). Such recurrence is favored by stationary forcing patterns such as zonal asymmetries of Earth’s surface imposed by mountain ridges, land–ocean boundaries, and sea surface temperature anomalies (e.g., Lin 1982; White et al. 2021) and can provide opportunities for predicting associated extreme weather events (Teng et al. 2013; Harnik et al. 2016).

Due to their zonal extent, amplified Rossby waves are often associated with concurrent weather extremes at geographically remote locations (e.g., Teng et al. 2013; Harnik et al. 2016; Kornhuber et al. 2019, 2020). Such spatially compounding extremes are of particular interest due to their potentially enhanced impacts compared to extremes occurring in isolation (Messori et al. 2016, 2021; Zscheischler et al. 2020; Raymond et al. 2020; Kornhuber et al. 2020). Here, we investigate recurrent Rossby waves in the extended Northern Hemisphere (NH) winter season. This follows the approach outlined in Kornhuber et al. (2020), who identified two recurrent wave patterns in the NH summer season. We analyze the large-scale circulation during the recent January–February 2019 cold and wet spell in Europe and NA (“Anomalous circulation contributing to the 2019 North American and European cold spells and heavy precipitation” section) and the associated wave pattern. We next identify wave 4 as a recurrent, phase-locked wave pattern (“A recurrent wave-4 pattern in the Northern Hemisphere winter circulation” section) associated with significant anomalies in meridional winds, geopotential heights, temperature, and precipitation fields across the NH. We quantify this pattern’s role in driving local cold or wet extremes and their concurrence in NA and Europe with a newly developed concurrence index (“Local and concurrent weather extremes in North America and Europe amplified by a recurrent wave-4 pattern” section). We follow with an analysis of recent trends in the wave pattern and its association with indices representing dominant modes or patterns of climate variability (“Remote forcing and recent trends” section), and conclude by discussing implications of recurrent wave patterns for understanding the predictability of and trends in concurrent extremes.

Data and methods

Data.

The analysis is based on 1979–2020 ERA5 data (Hersbach et al. 2020), with a horizontal spatial resolution of 0.5°. Meridional winds with a horizontal resolution of 1° were used to define the wave-4 pattern, due to its hemispheric scale. The analysis focuses on the extended NH winter season [November–March (NDJFM)]. The data are aggregated from hourly (6-hourly) surface (pressure-level) values to daily values prior to analysis. Long-term trends in wave amplitude, wave events, and phase velocity are analyzed based meridional wind fields on the 250 hPa level using the back-extended ERA5 1950–2020. Temperature and precipitation anomalies are defined relative to a daily climatology, which is smoothed with a 15-day running mean. Precipitation anomalies are further averaged over a 9-day window. Anomaly distributions for temperature and precipitation are constructed from this preprocessed data, and extreme events for each variable are defined as values in the top or bottom 5th percentile of the respective anomaly distributions. Statistical significance is computed as specified in the figure captions.

Time series of monthly values of climate indices such as the North Atlantic Oscillation (NAO), the Arctic Oscillation (AO), El Niño–Southern Oscillation 3.4 (ENSO), the Pacific–North American pattern (PNA), and the Pacific decadal oscillation (PDO) were retrieved from NOAA (NOAA 2021).

Methods.

Definition of wave amplitude and wave phase events.

Wave amplitudes and phases are based on a fast Fourier decomposition, by applying the function “fft” from the R package “stats” (R Core Team 2021) to weekly means of the 250 hPa meridional wind averaged over latitudes 37.5°–57.5°N, following the approach of Kornhuber et al. (2020).

To highlight the robustness of the link between the wave-4 pattern and surface anomalies, we test complementary wave event definitions. Wave phase events are directly linked to the wave-4 pattern’s preferred phase, following Drouard et al. (2019). We compute the spatial correlation of 7-day running mean meridional wind fields over the pan-Atlantic sector, which covers 30°–72.5°N, 160°W–40°E, with the meridional wind field in the same domain, averaged over all wave amplitude events (see below). We then identify days on which the correlation exceeds the 90th percentile of the full distribution, select local maxima in the case of exceedance on consecutive days, and finally impose a minimum 10-day separation between successive local maxima. This minimizes event aliasing and confounding influences from autocorrelation, and yields a total of 102 wave phase events.

To complement the wave phase perspective, we further define wave amplitude events as weeks when the amplitude of wave 4 is at least 1.5 standard deviations above the mean climatological value within NDJFM. This definition yields 82 events. Note that wave amplitude does not refer to the north–south extension of the jet meander, but rather to the meridional wind velocity within the midlatitude belt. Wave amplitude events make no a priori assumption about the waves’ longitudinal location (i.e., the location of ridges and troughs). To study extreme events, we also define daily wave amplitude events, in keeping with the definition adopted for the daily wave phase events. We construct a daily wave-4 amplitude time series by applying the aforementioned fft decomposition to meridional wind fields averaged with a 7-day running mean. We then identify days on which the amplitude exceeds the 90th percentile of the full distribution, select local maxima in the case of exceedance on consecutive days, and finally impose a minimum 10-day separation between successive local maxima. This yields a total of 103 daily wave amplitude events.

The key point of these different definitions is to highlight that our qualitative results are independent of arbitrary choices in defining the wave-4 events. Many of the weekly wave amplitude events correspond to either wave phase events or very high spatial correlation values (Fig. S1 in the online supplement; https://doi.org/10.1175/BAMS-D-21-0295.2). Even if there is not a one-to-one match between the two sets of events, the composite anomalies they are associated with are qualitatively similar (see “A recurrent wave-4 pattern in the Northern Hemisphere winter circulation” section). The same holds for the anomalies in extreme event occurrences for the wave phase and daily wave amplitude events (see “Local and concurrent weather extremes in North America and Europe amplified by a recurrent wave-4 pattern” section).

Analysis of extreme weather and its concurrence.

To quantify whether wave-4 events favor extreme events, we compute an extreme event ratio. This is the extreme event frequency at each grid point during wave-4 events, normalized by the climatological frequency of extreme events at a particular location (e.g., Messori et al. 2017). A value of 1 at a given location indicates no effect of the wave-4 events on extreme event frequency, while a value below 1 indicates fewer extremes and a value above 1 indicates an increased frequency of extremes. Here, we define extreme events as those in the top or bottom 5% of the local distribution, meaning that the extreme event ratio is computed relative to a climatological frequency of 5%. To quantify the cooccurrence of extreme events in NA and Europe, we introduce the extremes concurrence index (ECI). For every wave event (first section) and grid point in NA (30°–72.5°N, 160°–40°W), we identify surface extreme events and we count how many grid points in Europe (30°–72.5°N, 40°W–40°E) display a concurrent extreme event during each of the 5 days centered on the peak of the wave event. We then weigh by gridpoint area and normalize over [0, 1] to obtain a spatial compounding index. The same process is repeated for every grid point in Europe, while considering extreme events in NA. The value assigned to each grid point is the ECI value composited across all wave events. Thus, high values of ECI at a given gridpoint in Europe (NA) indicate cooccurrence of extreme events between that location and grid points in NA (Europe). Greenland and Iceland are not included in the calculation. ECI values are computed only for the locations that experience an increased frequency of extremes during wave-4 events (i.e., with an extreme event ratio > 1).

Results

Anomalous circulation contributing to the 2019 North American and European cold spells and heavy precipitation.

A severe cold spell affected the central United States and Canada in late January–early February 2019, with record low temperatures approaching −40°C measured at a local station on Mount Carrol, Illinois (NOAA 2019). The cold spell affected supply chains and traffic by blocking roads and disrupting train lines and airports. A total of 21 fatalities were reported, several of which were from hypothermia (BBC 2019). Within the same weeks, southern France recorded lows of −6°C and snowfall occurred across the country (Meteo France 2019; France 24 2019) while Sweden recorded a temperature of −36°C in Northern Lapland (SMHI 2019). Investigating the large-scale circulation, we find that the cold spell in NA and cold and snowy spell in Europe were connected by a wave pattern in the upper-tropospheric midlatitude circulation. This pattern arches over the Atlantic (Fig. 1a) and corresponds to an amplified, phase-locked wave-4 pattern (Figs. 1b,c). The wave phase remained stationary and close to its preferred phase (cf. Fig. 2b) for several weeks, resulting in a high meridional wind correlation (Figs. 1c,d). The 2019 concurrent cold and wet spells were not unique in being associated with an amplified, phase-locked wave-4 pattern. Examples of other past concurrent cold and wet events that may be linked to such pattern include the severe 2013 and 2018 wintertime episodes (see Figs. S2 and S3).

Fig. 1.
Fig. 1.

The January–February 2019 cold and wet spell. (a) Temperature anomalies (K) and 250 hPa meridional wind fields (m s−1; contours; red: northerly; blue: southerly) and areas of amplified precipitation (green dots) averaged over the 7 days centered around the 28 Jan 2019 [gray dashed vertical lines in (b)–(d)]. Precipitation is shown for grid points above 36°N at which the 7-day average anomalies exceed the 85th percentile of the daily distribution. (b) Wave-4 amplitude (m s−1) from 8 Jan to 20 Feb 2019; the dashed red line shows 1.5 standard deviation above the mean, while the dashed black line shows the mean amplitude. (c) Wave-4 phase (rad) over the same time period; the dashed red line shows the preferred phase position of wave 4 (also see Fig. 2b). (d) Meridional wind correlation as used to compute wave phase events (see text). The dashed black line shows 0 correlation.

Citation: Bulletin of the American Meteorological Society 104, 9; 10.1175/BAMS-D-21-0295.1

Fig. 2.
Fig. 2.

Density distributions of waves 3–7 phase during weeks of high-amplitude (wave amplitude events; red) and all other weeks (black) detected in NH NDJFM 1979–2020. Gray hatching shows the area within the 25th–75th percentiles of phase for wave amplitude events (width in rad provided in upper-right corner), while the dashed black lines denote the corresponding median phase position. The p value from a Kolmogorov–Smirnov test for the difference between the distribution of wave amplitude events and of all remaining weeks is provided in the upper-left corner above the sample size of each distribution. Note that the x axes are extended beyond π to provide a continuous depiction of the distributions.

Citation: Bulletin of the American Meteorological Society 104, 9; 10.1175/BAMS-D-21-0295.1

A recurrent wave-4 pattern in the Northern Hemisphere winter circulation.

Wave 4 constitutes a recurrent pattern in the Northern Hemisphere winter circulation. The recurrence of the pattern is defined by a close relationship between the wave’s amplitude and phase (Fig. 2b), i.e., the phase position of the wave converges toward a preferred value with increasing amplitude. Such phase-locking behavior was found for waves 5 and 7 in summer (June–August; Teng et al. 2013; Kornhuber et al. 2020, 2019), but for winter (NDJFM) this behavior is most pronounced for waves 3 and 4 in the NH midlatitudes. However, while wave 4 displays a clear separation between wave amplitude events and all other weeks (red and black lines in Fig. 2, respectively), for wave 3 the two overlap closely. This may reflect the fact that wave 3 is a mostly stationary wave reflecting zonal asymmetries in the Northern Hemisphere. Waves 5 and 6 do exhibit a single peak in their probability densities, yet the range of the 25th–75th percentiles around the median phase is wide (gray hatched area in Fig. 2) during wave amplitude events, and exceeds π/2 [the threshold for phase locking defined in Kornhuber et al. (2020)]. This phase locking criterion is intended to identify waves with minimal aliasing between different wave amplitude events, which thus have the potential to lead to large and recurrent surface anomalies in specific regions. Finally, wave 7 only displays a broad and low phase peak during wave amplitude events (red line in Fig. 2e), and will not be analyzed further.

As a direct consequence of its phase-locking behavior, the composite fields of the 82 identified wave-4 amplitude events shows a well-organized pan-Atlantic pattern in the 250 hPa meridional wind and 500 hPa geopotential height fields (Figs. 3a,b, first section). This is in spite of the fact that the meridional wind and geopotential height composites in Figs. 3a and 3b are conditioned on amplitude alone and not filtered by a specific phase. Wave phase events display a very similar picture (Fig. S4). The wave pattern is strongest over NA and Europe, and seemingly emanates from the tropical Pacific. The geopotential height ridge over NA is collocated with the Rocky Mountains, forming a dipole of high and low geopotential height anomalies over the continent. This is followed farther downstream by a ridge that spans across the North Atlantic. A weaker pattern of ridges and troughs is visible across Eurasia. Wave 3 also shows a clear circumglobal structure in 250 hPa meridional wind and 500 hPa geopotential height fields during wave amplitude events (Figs. S5a,b). In keeping with the wider, lower peaks in their phase probability distributions, wave-5 and -6 amplitude events do not display a complete circumhemispheric circulation anomaly structure (Figs. S6a,b and S7a,b). Indeed, a broader peak in the phase of wave amplitude events suggests that wave patterns from separate events in these wavenumbers align to a lesser degree than for waves 3 and 4.

Fig. 3.
Fig. 3.

The wave-4 pattern in NH NDJFM 1979–2020 and associated surface anomalies. Composites of the (a) 250 hPa meridional wind (m s−1), (b) 500 hPa geopotential height (m), (c) 2 m temperature (K), and (d) precipitation (mm day−1) anomaly fields during wave-4 amplitude events (N = 82). Anomalies significant at the two-sided 5% level determined using 1,000 random sampling iterations are cross-hatched. The black box in (a) illustrates the pan-Atlantic domain (30°–72.5°N, 160°W–40°E) based on which wave phase events are determined (see text).

Citation: Bulletin of the American Meteorological Society 104, 9; 10.1175/BAMS-D-21-0295.1

Surface temperature and precipitation anomalies follow the position of the wave-4 ridges and troughs over NA and Europe (Figs. 3c,d). The strongest temperature anomalies occur over NA, where the presence of a southerly flow anomaly in the western part of the continent and a corresponding northerly flow farther to the east lead to a zonal temperature anomaly dipole with a magnitude of roughly 6 K. This is akin to the intensified NA winter dipole reported by Singh et al. (2016). Western Europe displays weaker, yet regionally significant, cold anomalies associated with an anomalous northerly flow. Cold wintertime spells over Europe are primarily associated with easterly or northeasterly air flows (e.g., Sillmann et al. 2011), explaining the weaker surface temperature footprint of the wave pattern, in particular for central Europe. These anomalies reflect to some extent those observed during the 2019 cold spell discussed in the “Anomalous circulation contributing to the 2019 North American and European cold spells and heavy precipitation” section and the additional case studies outlined in Figs. S2 and S3.

In eastern NA, the cold surface temperature anomalies are roughly aligned with lower-than-average precipitation. Indeed, the northerly flow advects cold, dry air masses across the continent. In southern Europe, we instead find a partial overlap between a region of cold anomalies and a region of positive precipitation anomalies (Figs. 3c,d). The anomalously strong meridional wind component likely reduces zonal advection of moist oceanic air, leading to negative precipitation anomalies in western Iberia and the British Isles. Farther south and east, in areas where the Mediterranean Sea provides an important moisture source for wintertime precipitation (Ciric et al. 2018), the wave pattern displays a southerly flow, which leads to positive precipitation anomalies.

Wave 3 also corresponds to large surface anomalies, comparable in magnitude to those associated with wave-4 events (cf. Figs. 3c,d with Figs. S5c,d). In keeping with their weaker phase locking, waves 5 and 6 instead match weaker regional surface anomalies than those found for wave 4 (Figs. S6c,d and S7c,d).

Local and concurrent weather extremes in North America and Europe amplified by a recurrent wave-4 pattern.

The probability of local and concurrent extremes in Europe and NA is significantly increased during the occurrence of wave-4 events. Here, we consider wave phase events (see first section). These enable a direct connection between daily extremes and wave-4 pattern occurrence, following the arguments in (Drouard et al. 2019). During wave-4 phase events, the NA east coast is heavily affected by extreme cold spells from 30°N to beyond the Arctic circle (Fig. 4a). The frequency of cold extremes is increased by a factor of up to 3 compared to climatology. The probability of cold spells in Europe is amplified chiefly in southwestern Europe and Scandinavia, with up to twofold increases in frequency. Wave-4 phase events also correspond to an increased frequency of precipitation extremes, notably over central and eastern Europe (Fig. 4b), where the likelihood of wet extremes is locally amplified by a factor of more than 3.

Fig. 4.
Fig. 4.

Amplifying effect of wave-4 phase events on regional and concurrent cold and wet extremes over the pan-Atlantic sector. NH NDJFM 1979–2020 ratio of extreme (a) cold and (b) wet events during wave phase events, relative to climatology. Concurrent extremes quantified by ECI for (c) cold extremes over NA and Europe and (d) cold extremes over NA and wet extremes over Europe. Anomalies significant at the one-sided 5% level determined using 1,000 random sampling iterations are cross-hatched. Fields correspond to the 5 days centered around the wave phase event day.

Citation: Bulletin of the American Meteorological Society 104, 9; 10.1175/BAMS-D-21-0295.1

We further analyze the effect of the wave-4 pattern on the cooccurrence of extremes in both Europe and NA, using the ECI diagnostic (“Data and methods” section). We consider both concurrent cold NA–cold European extremes (Fig. 4c) and concurrent cold NA–wet European extremes (Fig. 4d). The cooccurrence of cold extremes increases significantly across eastern NA and southern Europe and Scandinavia. Similar results are found for extreme cold events in NA and wet events in Europe. However, the affected regions in Europe are located chiefly in the central and eastern parts of the continent, mirroring the pattern identified for local precipitation extremes (Fig. 4b). The amplified concurrence in both continents provides further evidence that the wave-4 pattern identified in the upper level circulation (Figs. 3a,b) is not a product of separate local ridges that occur independently, owing their coherent pattern to the applied averaging. Rather, the pattern is a true pan-Atlantic feature favoring the cooccurrence of surface extremes on synoptic time scales.

Wave-3 phase events also correspond to regionally heightened extreme event frequencies in Europe and North America. However, the footprint of these events on concurrent surface extremes in Europe and North America is weaker than what is observed for wave 4, especially over Europe (cf. Fig. 4 with Fig. S8). This is partly due to the alignment of the wave’s peaks and troughs, which are less conducive to extreme events over Europe. We also hypothesize a link to the above-discussed similarity in wave 3 during wave events relative to its climatological behavior. Due to this, we focus the remaining analysis on wave 4.

The patterns based on daily wave amplitude events for wave 4 show qualitatively similar results (Fig. S9). However, the bands of enhanced occurrence or concurrence of cold and precipitation extremes are less sharp, with lower extreme event ratio and ECI values. This is particularly evident for heavy precipitation over central Europe (Figs. S9b,d). We ascribe these quantitative differences to the fact that wave amplitude events may combine episodes with slightly different phases, thus introducing some aliasing in the composites.

Remote forcing and recent trends.

We next investigate long-term trends (1950–2020) in wave-4 activity. We find that there is a positive, statistically significant trend (p < 0.05) in wave amplitude if the trend calculation is started from 1963 and until the 1990s (Fig. 5a), while for earlier starting years some of the trends are statistically significant at the 90% confidence level only (p < 0.1, see, e.g., dark green dot for years 1950 and 1959). For wave amplitude events, we similarly find statistically significant trends (p < 0.05) for most years in the 1960s–1990s when selecting them as starting year (Fig. 5b). In both wave amplitude events and wave amplitude, the trend slopes increase for later starting years. As expected, there is no significant trend for starting years from the 1990s onward due to the brevity of the remaining time series. Mostly decreasing and not statistically significant trends are identified for amplitudes and wave events for other wavenumbers (Figs. S10–S12), suggesting that the increase in wave-4 amplitude might have occurred at the expense of the remaining wavenumbers.

Fig. 5.
Fig. 5.

Linear trends in (a) wave-4 amplitude, (b) wave-4 amplitude events, and (c) wave-4 phase velocity in NH NDJFM 1950–2020 (red line). Each cold season is analyzed as one data point; the months of January–March 1951 are thus merged with November and December 1950 and similarly for all other years. The red line shows the linear regression over 1950–2020; the vertical stripes indicate the slope over a 10-yr period from linear regressions when using the respective year as a starting point. Consequently, the last 10 years are exempt from this analysis. The level of statistical significance of these trends are given by the colored dots (see legend).

Citation: Bulletin of the American Meteorological Society 104, 9; 10.1175/BAMS-D-21-0295.1

Considering the entire time period analyzed (1950–2020), we find that the number of wave-4 amplitude events within the extended winter season doubles from approximately one event per season at the beginning to more than two events per season at the end, while the seasonal-mean wave-4 amplitude increases from 5.3 to 6 m s−1, which corresponds to a gain of approximately 13%. We acknowledge that the time series exhibit considerable temporal variability and indications of multidecadal oscillations with stronger signals toward the end of the 1950s. No notable trends in meridional wind spatial correlation nor in the frequency of wave phase events (Fig. S13) are found. This is consistent with the fact that the phase of wave 4 overall shows no significant trends over the past decades (not shown). No significant trend is found in phase velocity throughout NDJFM 1950–2020 (Fig. 5c). The positive trends in wave-4 amplitude and amplitude event frequency are consistent with Singh et al. (2016), and could serve as an explanation for the increasing occurrence of a winter temperature dipole over NA, which regionally matches patterns associated with a high-amplitude wave 4.

To identify potential remote drivers of the identified wave-4 pattern and trends, we investigate the relationship of monthly mean wave amplitude and meridional wind spatial correlation with monthly mean values of indices of climate variability. We consider indices representing the NAO, the AO, ENSO, the PNA, and the PDO. We further investigate the relationship of the wave-4 pattern with the meridional temperature gradient as defined by the difference between temperatures averages in the high (70°–90°N) and middle latitudes (50°–30°N), following the definition in Blackport and Screen (2020) and Kornhuber and Tamarin-Brodsky (2021). The strongest correlations are found for the indices that relate to Pacific variability (ENSO, PNA, PDO), whose significance depends on the month considered (Fig. S14). For wave amplitude, we find significant relationships for PNA in November and for ENSO and PDO in December. For meridional wind spatial correlation in the pan-Atlantic sector, significant relationships are found for January, February, and NDJFM for the PDO and for NDJFM and all months expect March for the PNA. The PNA has a marked meridional structure and has long since been related to a zonal temperature dipole over North America and precipitation anomalies in the central portions of the continent (Leathers et al. 1991). It has also been related to extreme wintertime temperatures, albeit with the strongest footprint in the northwestern portion of North America (Loikith and Broccoli 2014), in contrast to the wave-4 pattern analyzed here. The PDO has a relatively strong lag-0 correlation with the PNA during the winter months (Newman et al. 2016). Patterns associated with the Atlantic circulation show weak and mostly nonsignificant correlations, except for the AO and NAO in January. The meridional temperature gradient exhibits no notable correlation with either wave-4 metric. This analysis, while not providing any causal evidence, supports the plausibility of a weak but detectable role of Pacific signals in modulating wave-4 activity.

Discussion and conclusions

We identified a quasi-hemispheric wavenumber-4 pattern, which modulates the occurrence and concurrence of wintertime cold or wet extremes in NA and Europe. Due to its phase-locked behavior and recurrence, the extremes associated with the wave-4 pattern occur repeatedly in the same geographical regions, similar to the wavenumber-5 and -7 patterns identified in summer (Kornhuber et al. 2020). The wave-4 pattern’s large zonal extent implies that the cold or wet extreme events on the two sides of the North Atlantic occur in a largely synchronized fashion. Higher wavenumbers also display high-amplitude events, yet they lack the phase-locked behavior and complete circumhemispheric structure of wave 4 and the surface anomalies they engender are weaker and spatially less extended. Wave 3 is phase locked during high-amplitude events, but nonetheless shows a weaker link to concurrent NA and European surface extremes than wave 4.

The synchronized occurrence of pan-Atlantic extremes echoes earlier results from Messori et al. (2016) and De Luca et al. (2020). Motivated by the ostensibly frequent cooccurrence of cold wintertime extremes in NA and stormy weather in Europe, the authors had proposed a systematic relationship between the two. Messori et al. (2016) highlighted the role of a zonalized jet stream in favoring the concurrent extremes, and indeed the European precipitation events identified there were located in the westernmost reaches of the continent. This is very different from the wave perspective taken here, and indeed both the location of the heavy precipitation and the occurrence of anomalously cold temperatures in Europe do not match the results of Messori et al. (2016). This indicates that the physical mechanisms driving concurrent pan-Atlantic extremes may be strongly region dependent, or alternatively that different mechanisms may contribute to concurrent extremes that at first glance look similar.

The upper-level and surface anomaly patterns over North America associated with wave 4 resemble those previously found for the so-called NA winter dipole (Wang et al. 2015; Singh et al. 2016). The similarity in the patterns suggests that the winter dipole and wave-4 approaches share a set of detected events. However, there are notable differences in the temporal and spatial scales over which the events are defined [weekly and circumhemispheric here versus seasonal in Wang et al. (2015) and continental scale in Singh et al. (2016)]. Moreover, there is no evidence that the NA winter dipole leads to surface impacts beyond North America. It may be of interest in future work to verify whether the NA winter dipole may be interpreted as a climatological manifestation of high-amplitude wave-4 events.

The phase-locked and recurrent nature of the wave-4 pattern driving regional extreme events may be exploited in the context of predictability. Harnik et al. (2016) defined a circumglobal North American pattern based on Branstator’s (2002) circumglobal teleconnection pattern, and showed that it could provide medium-range predictability for NA cold spells. The broader role of wave patterns or packets as drivers of concurrent extreme events and predictability tools has been discussed in a number of studies (e.g., White et al. 2022; Wirth et al. 2018; Kornhuber et al. 2020; Fragkoulidis and Wirth 2020, and references therein). In the specific case analyzed here, we identify typically two to three wave-4 events per season. From an extreme events perspective, the wave-4 pattern is therefore a relatively frequent occurrence, and not a sporadic feature that is only relevant for a handful of days in the observational record. In this respect, the wave-4 pattern may be likened to the concept of large-scale meteorological patterns, namely, specific patterns whose frequency and time scale match those of the associated extreme events (Grotjahn et al. 2016; Barlow et al. 2019). Much like the large-scale meteorological patterns, the pattern we discuss here is distinct from the conventional modes of variability or weather regimes, although it may partly project or be correlated with specific modes. The wave-4 pattern also has the properties of a teleconnection, since it systematically relates geographically remote climate anomalies. The wave-4 pattern could therefore be used to build a statistical predictor for cooccurring regional wintertime extremes, or to better understand the performance of numerical weather forecasts for some extreme event case studies.

In the context of longer-term climate change, associating sets of extreme events with specific dynamical mechanisms can help to understand ongoing and future trends. In the case of midlatitude cold spells, recent studies have argued for the importance of Arctic amplification, the polar vortex (Cohen et al. 2014, 2021), and changes in jet stream sinuosity or wave activity (e.g., Screen and Simmonds 2014; Francis and Vavrus 2015; Martin 2021) in driving cold spell trends, sparking a lively discourse in the scientific community (Barnes and Screen 2015; Cattiaux et al. 2016; Cohen et al. 2020). Here, we find statistically significant long-term trends in wave-4 amplitude and wave-4 event occurrence during the observational period from the early 1960s onward. There are no noteworthy trends in wave-4 phase itself nor in the number of wave-4 phase events, suggesting that increased amplitude has occurred on the background of a roughly constant phase, and may potentially aggravate the concurrent surface impacts of wave-4 phase events.

The wave-4 amplitude shows no direct relation to annual changes in the meridional temperature gradient, but shows moderate correlations with some variability indices in the Pacific, including the PDO index. One may thus hypothesize that the positive trends are the result of a remote forcing located in the Pacific. Indeed, several arguments have been made for the role of tropical Pacific sea surface temperatures (SSTs) and convection in modulating midlatitude wave trains and winter weather over both NA and Europe (e.g., Watson et al. 2016; Scaife et al. 2017). Similarly, the PDO may be understood as a pattern integrating tropical and extratropical signals (Newman et al. 2016). Moreover, (Wang et al. 2015) linked the occurrence of the North American winter dipole, which resembles the North American footprint of the hemispheric wave-4 pattern on seasonal time scales, to El Niño precursor SST anomalies. Finally, tropical forcings can also lead to decadal or longer trends in the midlatitude weather and climate (Li et al. 2010; Sigmond and Fyfe 2016). In a preliminary analysis of tropical SST and OLR anomalies, we nonetheless found no clear signal of a tropical forcing preceding wave-4 amplitude events (not shown). A systematic analysis of the origin of the atmospheric dynamical mechanisms that lead to wave-4 events and recently observed trends are necessary to conclusively evaluate the role of tropical forcing.

When looking at wintertime wave patterns, other studies have not highlighted a clear trend in wave-4 amplitude under climate change, with positive trends emerging only at specific latitudes (Simpson et al. 2016; Wills et al. 2019). The difference with the clear upward amplitude trend observed here may be partly due to the fact that we have focused on trends within the observational period. We also underscore that some of the strongest positive trends are observed in the frequency of high-amplitude wave-4 events, whose trends may not follow those of the overall wave activity. If true, this would imply that hydroclimatic changes associated with the mean change in wave-4 amplitude would not match the changes in surface extremes associated with high-amplitude wave-4 events. Future work will investigate if identified trends in the wave-4 pattern are reproduced by historical climate model simulations, if they are an expression of multiannual oscillations, if they are projected to continue in simulations based on future emission scenarios and whether they may be attributed to anthropogenic forcing.

We conclude that the identified wave-4 pattern could provide a complementary perspective for both statistical forecasting of regional and concurrent pan-Atlantic wintertime extremes and for an improved understanding of their future changes.

Acknowledgments.

KK was partially supported by the NSF Project NSF AGS-1934358 and by the NOAA RISA Program Award NA20OAR4310147A. GM has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement 948309, CENÆProject).

Data availability statement.

The ERA5 data used here are freely available from the Copernicus Climate Change Service.

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Supplementary Materials

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  • Allstadt, A. J., S. J. Vavrus, P. J. Heglund, A. M. Pidgeon, W. E. Thogmartin, and V. C. Radeloff, 2015: Spring plant phenology and false springs in the conterminous US during the 21st century. Environ. Res. Lett., 10, 104008, https://doi.org/10.1088/1748-9326/10/10/104008.

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  • Amores, A., M. Marcos, D. S. Carrió, and L. Gómez-Pujol, 2020: Coastal impacts of Storm Gloria (January 2020) over the north-western Mediterranean. Nat. Hazards Earth Syst. Sci., 20, 19551968, https://doi.org/10.5194/nhess-20-1955-2020.

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  • Barlow, M., and Coauthors, 2019: North American extreme precipitation events and related large-scale meteorological patterns: A review of statistical methods, dynamics, modeling, and trends. Climate Dyn., 53, 68356875, https://doi.org/10.1007/s00382-019-04958-z.

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