1. Introduction
The stratospheric polar vortex (SPV) is a unique circulation system in the extratropical stratosphere of both hemispheres that forms due to seasonal radiative cooling in winter (Andrews et al. 1987). The variation of SPV is dynamically coupled to the troposphere from winter to spring via atmospheric waves (Baldwin and Dunkerton 1999, 2001; Waugh and Polvani 2010), among which the planetary-scale Rossby wave is essential (Andrews et al. 1987). The variability of the Northern Hemispheric SPV is larger than that of the Southern Hemisphere because the large orography and land–sea thermal contrasts in the Northern Hemisphere generate stronger upward-propagating Rossby waves (Plumb 1989; Scaife and James 2000; Waugh et al. 2017). Since the SPV in the lower stratosphere has longer time scales than tropospheric circulations, it can potentially be used to improve the prediction skill of the troposphere (Baldwin et al. 2003; Scaife et al. 2016; Domeisen et al. 2020a,b). Many efforts have therefore been devoted to revealing the role of the SPV variations in influencing the tropospheric weather and climate conditions and to understanding the underlying mechanisms (e.g., Baldwin and Dunkerton 1999, 2001; Wang and Chen 2010; Chen et al. 2013; Mitchell et al. 2013; Zhang et al. 2016; Huang et al. 2018).
The most prominent variation of Northern Hemispheric SPV is the change in strength. It is mainly characterized by hemispheric-scale geopotential height anomalies, presenting a dipole between the polar region and the midlatitudes, known as the Northern Annular Mode (NAM; Thompson and Wallace 1998; Baldwin and Dunkerton 1999). The stratospheric NAM explains the variations of the SPV on multiple time scales ranging from day to day (Charlton and Polvani 2007; Mitchell et al. 2013), from month to month (Thompson and Wallace 1998, 2000), and from interannual to interdecadal (Chen et al. 2002, 2003; Hu and Guan 2018), to the long-term trends (Thompson et al. 2000; Hu et al. 2018). The prominence of the stratospheric NAM is further reinforced as it strongly couples with the tropospheric circulation (Thompson and Wallace 1998; Baldwin and Dunkerton 1999; Kidston et al. 2015). On the one hand, the changes in the stratospheric NAM can be driven by the anomalous vertical propagation of planetary waves (Matsuno 1971; Chen et al. 2002, 2003), which are primarily rooted in tropospheric circulations (Polvani and Waugh 2004; Castanheira and Barriopedro 2010; Garfinkel et al. 2010; Woollings et al. 2010; Nishii et al. 2011). On the other hand, the changes in the stratospheric NAM and the associated westerly acceleration or deceleration could modulate the vertical propagation of the planetary waves by altering the background flow (Charney and Drazin 1961; Chen and Robinson 1992). As a result, the NAM-associated stratospheric circulation anomalies can descend through this wave–mean flow interaction and are sometimes followed by anomalies in the troposphere for months (Baldwin and Dunkerton 2001), exerting impacts on the tropospheric weather and climate (Kodera et al. 1990; Thompson and Wallace 2001; Kolstad et al. 2010; Kidston et al. 2015; Nakamura et al. 2016).
In addition to the strength, the location and geometry of the SPV also vary remarkably. For example, the SPV may shift toward Eurasia or North America without apparent changes in its strength (e.g., Huang et al. 2018; Lu et al. 2021; Cohen et al. 2021). Such changes in the SPV are also accompanied by significant changes in regional tropospheric circulation (Kretschmer et al. 2018; Song and Wu 2019; Zhang et al. 2022). The underlying mechanism appears to involve Rossby wave propagation and reflection and the fast response to stratospheric potential vorticity anomalies, both of which can alter the tropospheric circulation within a few days (Ambaum and Hoskins 2002; Perlwitz and Harnik 2003; Itoh and Harada 2004; Huang et al. 2018; Kretschmer et al. 2018). As such, the variations in the location and geometry of the SPV may cause rapid changes in the tropospheric weather and climate on the intraseasonal time scale (White et al. 2021). Moreover, the above variations of the SPV can occur together with the variations in the SPV’s strength. For example, the SPV either splits into two small cyclonic vortices or displaces off the pole during sudden stratospheric warmings (SSWs), the extreme case of weak SPV (Charlton and Polvani 2007; Mitchell et al. 2013; Seviour et al. 2013). These studies suggest the complexity of the SPV-associated stratosphere–troposphere coupling and highlight the importance of variation in location and geometry in addition to the strength of SPV.
The complexity of time scales and spatial characteristics in stratosphere–troposphere dynamical coupling (Perlwitz and Harnik 2003; Dunn-Sigouin and Shaw 2018; Kretschmer et al. 2018) further suggests the necessity to understand the stratosphere–troposphere coupling processes. This necessity is especially crucial for the subseasonal-to-seasonal time scale (Gerber et al. 2012; Domeisen et al. 2020b, Scaife et al. 2022), considering the nature of the stratosphere–troposphere dynamical coupling and the knowledge gap in the current capacity for skillful prediction (Brunet et al. 2010; Pegion et al. 2019). As such, the leading modes of the intraseasonal stratospheric variability, their coupling with the troposphere, and the underlying mechanism will be addressed in this study. Section 2 describes the datasets and methods. Section 3 clarifies the time scales of the leading extratropical stratospheric modes and the dominance of the shift of the SPV on the intraseasonal time scale. Section 4 shows that the intraseasonal shift of the SPV has an oscillating nature and involves both stratospheric and tropospheric circulations. Section 5 diagnoses the underlying mechanism of the oscillation. Section 6 highlights the implications of the STO for the stratosphere–troposphere dynamic coupling. Finally, section 7 summarizes the main findings and discusses some remaining issues. The appendixes provide details of diagnostic tools.
2. Data and methods
a. Data
The daily mean reanalysis data used in this study are averaged from the 6-hourly data from the European Centre for Medium-Range Weather Forecasts interim reanalysis (ERA-Interim) dataset (Dee et al. 2011), which extends from 1000 to 1 hPa with 37 layers and is used at a 2.5° horizontal resolution. The daily climatology of a particular calendar day is defined as the value of this calendar day averaged over the 39 years from 1979 to 2017, and the daily anomaly is defined as the departure from this daily climatology. The extended winter covers months from November to March (NDJFM), where the 1979 winter denotes 1979/80 winter. A Lanczos filter is applied to obtain low-pass-, bandpass-, and high-pass-filtered data. First, the filtering is applied to the continuous data for the whole period. Second, the filtered NDJFM data are extracted for analysis.
b. Diagnostic tools
The three-dimensional wave activity flux is used to diagnose the propagation of Rossby waves (Takaya and Nakamura 2001). The associated wave activity density tendency equation is used to quantify the relative role of the horizontal and vertical incoming Rossby waves in inducing regional circulation anomaly (Holton 2004; Takaya and Nakamura 2001; Song et al. 2016). See appendix A for details of the wave activity diagnosis. The decomposed streamfunction equation is used to quantify the contribution of different tropospheric processes in inducing the observed tropospheric circulation (Cai and Vandendool 1994; Feldstein 2002, 2003; Xu et al. 2020). See appendix B for details of streamfunction diagnosis.
c. Monte Carlo method
The bootstrap technique test is used to estimate the probability density functions (PDFs) of a finite sample (Efron and Tibshirani 1994). For a group with a sample size of n, we apply the sampling with replacement to obtain a new group with the same sample size of n. This process is repeated 10 000 times to yield 10 000 new groups. Then the PDF of the original finite sample is obtained based on the mean of each new group. Thus, the observed sample mean is statistically significant at the two-tailed 95% confidence level if it lies outside 2.5%–97.5% of the PDF.
3. Time scales of the leading extratropical stratospheric modes
The empirical orthogonal function (EOF) analysis is applied to the daily geopotential height anomaly northward of 20°N at 10 hPa to extract the leading extratropical stratospheric modes (Fig. 1). The first EOF (EOF1) shows a seesaw between the polar region and midlatitudes (Fig. 1a). It reflects the changes in the SPV strength and resembles the NAM, confirming the dominance of the NAM in the extratropical Northern Hemisphere (Thompson and Wallace 1998). The second EOF (EOF2) shows a wavenumber (WN) 1 pattern, with two centers of opposite signs over North America and Eurasia, respectively (Fig. 1b). It reflects the alternating shift of the SPV between the two continents (Itoh and Harada 2004). The third EOF (EOF3) also shows a WN1 pattern but has an approximately π/2 phase difference compared with EOF2. It indicates the alternating shift of the SPV between the Pacific and Atlantic Oceans.
Stratospheric modes of variability. Spatial pattern of (a) EOF1, (b) EOF2, and (c) EOF3 based on the daily geopotential height anomaly northward of 20°N at 10 hPa during NDJFM. Power spectra of (d) PC1, (e) PC2, and (f) PC3. Red, blue, and green lines in (d)–(f) indicate red noise and the 95% and 99% confidence levels, respectively. The vertical gray line in (d)–(f) shows the period of 60 days.
Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0238.1
EOF1 explains 32.6% of the total daily variance within the domain. Its corresponding principal component (PC) time series has strong and significant peaks longer than two months and relatively weak peaks shorter than two months (Fig. 1d). This feature is consistent with previous studies that the NAM at 10 hPa has a long decorrelation time scale (e-folding time) of about 20 days (Baldwin et al. 2003). The EOF2 and EOF3 explain 23.4% and 15.8% of the total variance, respectively. Although their respective values are smaller than that of EOF1, they together explain 39.2% of the total variance, which is larger than that of EOF1 (32.6%). This result indicates that the location shift is as significant as the strength change in the SPV’s variability. The PC time series of EOF2 and EOF3, that is, PC2 and PC3, both show strong and significant peaks on the intraseasonal time scale that spans from 10 to 60 days (Figs. 1e,f). This result is consistent with an 8-day e-folding time for PC2 and PC3, which roughly indicates a life cycle of 32 days (4 times the e-folding time). It is in sharp contrast to the long time scale of PC1 and implies different dynamic processes underlying the changes in the SPV’s strength and location.
To concentrate on the intraseasonal variability of the extratropical stratosphere, the EOF analysis was repeated using 10–60-day bandpass-filtered data. On the intraseasonal time scale, the first two EOF modes show a WN1 structure resembling the unfiltered EOF2 and EOF3, respectively (Figs. 2a,b). They explain over 50% of the intraseasonal variance. This result suggests that the shift of the SPV dominates the intraseasonal variability of the extratropical northern stratosphere. In contrast, only EOF6 bears some similarity to the NAM in the filtered data, and its explained variance is only 3.2% (not shown). The EOF analysis was also repeated with the 60-day low-pass-filtered data, and the EOF1 shows a NAM-like pattern and explains 49.6% of the variance (not shown). This result confirms the dominance of the NAM on time scales longer than 60 days, consistent with Fig. 1d.
Intraseasonal modes of stratospheric variability. Spatial pattern of (a) EOF1 and (b) EOF2 based on the 10–60-day bandpass-filtered geopotential height anomaly northward of 20°N at 10 hPa during NDJFM. (c) Lead–lag correlation coefficients between PC1 and PC2 that correspond to (a) and (b). The red dash lines in (c) denote the 95% confidence level. Negative (positive) days in (c) mean PC1 leads (lags) PC2.
Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0238.1
In the following, we focus on the intraseasonal, 10–60-day-filtered variability unless otherwise stated. The lead–lag correlation between PC1 and PC2, which correspond to Figs. 2a and 2b shows two peaks when PC1 leads or lags PC2 by 6 days (Fig. 2c). Though the correlation is modest, it is significant at the 95% confidence level given the large sample size of the daily data. This result, together with the π/2 phase difference between EOF1 and EOF2 (Figs. 2a,b), suggests that the shift of the SPV is a propagating mode. As such, the phase corresponding to EOF1 (Fig. 2a) is selected as the reference point for subsequent analyses.
4. Stratosphere–troposphere oscillation as the leading intraseasonal mode
Figure 3a presents the autocorrelation coefficient of PC1 corresponding to Fig. 2a. The point at which the autocorrelation function falls below 1/e indicates a decorrelation time of approximately 5 days and suggests the involvement of dynamic processes on the intraseasonal time scale. Besides, the autocorrelation coefficient reaches its maximum negative value on day 15, and the correlation gradually weakens afterward. This result indicates a possible periodic oscillation for the intraseasonal shift of the SPV.
The time scale of the SPV shift events. (a) Autocorrelation coefficients of PC1 with a lag from 0 to 30 days. The red horizontal line indicates 1/e. The blue vertical line represents the decorrelation time, measured by the time taken for the autocorrelation coefficient to drop to 1/e. (b) Evolution of the composited PC1 for positive and negative events. Dots indicate values significant at the 95% confidence level. Shading shows the boundary of 0.5 standard deviations.
Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0238.1
To illustrate the evolution of the intraseasonal shift of the SPV, composite analysis is employed based on the PC1 time series. First, the PC1 time series is normalized. Second, the positive SPV shift events are selected if the maximum value of the normalized PC1 in an 11-day window exceeds the threshold of +1.5, and the negative SPV shift events are identified if the minimum value is smaller than −1.5. The day that the maximum absolute value appears is referred to as peak day or day 0. Third, the above process is repeated to find the next event. In this process, day 0 of the next event and that of the previous one will be separated by at least 10 days. This procedure yields 68 positive and 69 negative events (Table S1 in the online supplemental material). The composite of the PC1 time series shows that the positive and negative phases both persist for about two weeks (Fig. 3b). Moreover, a periodic phase transition is observed between negative and positive with a period of about four weeks (Fig. 3b). This is consistent with the decorrelation time scale (Fig. 3a), as the estimated life cycle from 4 times the decorrelation time scale is approximately 20 days. Although there exists diversity among cases (shading in Fig. 3b), the overall phase transition feature is robust. Since the composite results of negative and positive events are almost symmetric, we mainly consider the positive events in the following analyses. It is also worth mentioning that the results here are not significantly sensitive to the threshold value used in selecting typical events.
Figure 4 shows the evolution of geopotential height and its anomalies at 10 hPa during the life cycle of the positive SPV shift events to reveal their spatial characteristics. On day −10, an anomalous anticyclonic and cyclonic center is located above North America and Eurasia, respectively (Fig. 4a). This pattern projects onto the negative phase of the EOF1 pattern (Fig. 2a) and indicates a shift of the SPV off North America and toward Eurasia (Fig. 4b). It decays and propagates westward in the following days. On day −5, the anomalous anticyclonic and cyclonic centers occupy northeast Asia and North America, respectively, indicating the pronounced shift of the SPV toward North America. This pattern develops from day −5 to day 0, with the center over North America being quasi-stationary and the center over Eurasia moving westward. Meanwhile, the magnitude of the pattern intensifies significantly and peaks on day 0. It projects onto the positive phase of the EOF1 pattern and indicates an apparent shift of the SPV off Eurasia and toward North America (Fig. 4b). From day 0 to day 10, the pattern decays and propagates westward, with the structure on day 10 resembling that on day −10. The spatial characteristics during the evolution confirm the periodic characteristics shown in the temporal analysis (Fig. 3b). These results suggest that the intraseasonal shift of the SPV has an oscillating feature with westward propagation and a period of about four weeks. Also, note that the corresponding PC2 values exhibit the same oscillating characteristics as PC1 during the life cycle of SPV shift events (shown in the brackets in Fig. 4), with the PC1’s peak (e.g., day −10) leading the PC2’s peak (e.g., day −5), and then followed by the PC1’s peak of the opposite sign (e.g., day 0). This feature confirms the statistical lead–lag correlation relationship suggested in Fig. 2c and validates the representativeness of the PC1 in selecting the SPV shift event.
Life cycle of the positive SPV shift events. (a) Composite of geopotential height anomalies at 10 hPa [contour interval (CI) = 100 gpm] during the life cycle of the STO from day −10 to day 10. Shading indicates values exceeding the 95% confidence level. The corresponding values of PC1 and PC2 are shown in parentheses. (b) As in (a), but for absolute geopotential height (red contours; CI = 500 gpm) overlaid by the climatology (black contours; CI = 500 gpm).
Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0238.1
A stratospheric oscillation resembling the SPV shift events with similar amplitude and shorter time scale has previously been found in a mechanistic model where the troposphere is steady (Scaife and James 2000). So, a question is whether the observed SPV shift couples with a periodically varying tropospheric circulation, or whether it is a self-contained stratospheric phenomenon. To address this question, Fig. 5 shows the vertical profile of geopotential height anomalies along 65°N, at which latitude the anomalous cyclonic and anticyclonic centers maximize at 10 hPa (Fig. 4a). Two remarkable features emerge. First, this stratospheric pattern has a deep vertical structure that extends between the stratosphere and the lower troposphere. Despite some vertical tilting features, it is overall characterized by a quasi-equivalent barotropic structure. Second, strong wave energy propagates persistently between the troposphere and the stratosphere as the stratospheric circulation evolves. These two features indicate that the intraseasonal shift of the SPV is very likely coupled with variations in the tropospheric circulation.
Coherent intraseasonal stratosphere–troposphere variations. Composite of geopotential height anomalies (contour; CI = ±25, ±100, ±200, ±400, ±800 gpm) and associated wave activity flux (vector; m2 s−2) along 65°N on (a) day −10, (b) day −5, (c) day 0, (d) day 5, and (e) day 10. Negative values are dashed, and zero contours are omitted. Shadings denote values exceeding the 95% confidence level. The gray horizontal line shows the approximate level of the tropopause.
Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0238.1
The stratospheric circulation associated with the shift of the SPV shows a periodic phase transition (Figs. 3 and 4) and is coupled to the troposphere (Fig. 5), so we infer that the associated tropospheric circulation also evolves periodically. To verify this conjecture, Fig. 6 shows the geopotential height anomalies at 300 hPa. On day −10, the subpolar region is characterized by a zonal WN2 structure, whose anticyclonic centers are located south of Alaska and western Europe and cyclonic centers over North America and Eurasia (Fig. 6a). This WN2 pattern rotates westward from day −10 to day −5. Meanwhile, it intensifies and evolves into a WN1 pattern on day −5 (Fig. 6b), with the anticyclonic and cyclonic centers being located over the Bering Strait and North America, respectively. From day −5 to day 10, it continues to rotate westward. The tropospheric circulation on day 5 and 10 projects well onto that on day −5 and −10 with opposite signs (Figs. 6a,b,d,e). This feature is also visible in the vertical profile along 65°N (Fig. 5). Hence, these results suggest that the tropospheric circulation associated with the SPV shift shows evident quasi-oscillating features and that the associated tropospheric and stratospheric circulations are tightly coupled. To highlight the quasi-oscillating nature of the SPV shift and the associated troposphere–stratosphere coupling, the intraseasonal leading mode of the SPV, which represents the shift of the SPV, is named the stratosphere–troposphere oscillation (STO).
Tropospheric signature of the SPV shift events. Composite of geopotential height anomalies at 300 hPa (contour; CI = 40 gpm), the associated horizontal component of wave activity flux at 300 hPa (vector; m2 s−2), and vertical component of wave activity flux (Fz) at 150 hPa [shading; shading interval (SI) = ±0.4, ±1.2, ±2.4, ±4.8; ×10−2 m2 s−2]. Red and blue contours indicate positive and negative values, respectively. The zero contours are omitted.
Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0238.1
The STO-associated tropospheric circulations on certain days (e.g., day −5) resemble those that facilitate cold events (e.g., Tan et al. 2017; Kretschmer et al. 2018) and the intraseasonal oscillation of surface temperature over North America (e.g., Guan et al. 2020), implying the influences of the STO on tropospheric weather and climate. To confirm this inference, Fig. 7 shows the composited surface air temperature anomalies during the life cycle of the STO. Significant cooling is observed over North America from day −10 to day 0, accompanied by significant warming near the Bering Strait (Figs. 7a–c). This temperature pattern propagates westward with time and reverses in sign from day 5 to day 10 (Figs. 7d,e), consistent with the circulation (Figs. 5 and 6). The temperature signatures over the Bering Strait and North America are symmetric in this process, with peaks occurring on day −5 and day 5. In contrast, those over East Asia are less symmetric, with warming on day −10 and cooling on day 5 and day 10.
Near-surface temperature signature of the stratosphere–troposphere oscillation. As in Fig. 6, but for surface air temperature anomalies (shading; SI = 0.5 K). Dots indicate values exceeding the 95% confidence level.
Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0238.1
The westward propagation of the STO’s tropospheric anomalies at 300 hPa has a phase speed of about −4.5 m s−1. This value lies between the phase speed of free Rossby waves with zonal WN1 and WN2, for instance, the values of which are −9.38 and −1.71 m s−1 at 50°N, respectively. This observed propagation is, therefore, generally in accordance with the theoretical results. Besides, similar westward retrograding disturbances with a life cycle of about three weeks near Alaska were also reported in previous studies (e.g., Branstator 1987; Kushnir 1987; Feldstein 2002). For example, Branstator (1987) found a midtropospheric mode that resembles the STO’s tropospheric signature, and he noticed its extension into the stratosphere but did not explore this feature further. As will be shown later, in contrast, this study emphasizes the oscillating feature and essence of the stratosphere–troposphere coupling in the STO.
5. Mechanism of the stratosphere–troposphere oscillation
a. Reflection of the intraseasonal Rossby waves
Large-scale atmospheric waves play a critical role in the stratosphere–troposphere dynamical coupling (e.g., Andrews et al. 1987), so the propagation of Rossby waves is examined to understand the coupling between the stratospheric and the tropospheric circulations of the STO. Figures 5 and 6 show the STO-associated wave activity flux [Eq. (A1) in appendix A; Takaya and Nakamura 2001] in the vertical profile along 65°N (Fig. 5) and at a pressure level near the tropopause (150 hPa, Fig. 6). On day −10 when the STO is in its negative phase, a wave train emanates from Asia and propagates upward into the stratosphere (Fig. 5a). It propagates eastward in the lower stratosphere and then reflects downward into the troposphere over North America (near 120°W), indicating a wave reflection process (Harnik and Lindzen 2001; Perlwitz and Harnik 2003; Kodera et al. 2008). Meanwhile, a tropospheric wave train emanates from the subtropical central Pacific and propagates toward North America (Fig. 6a). The two wave trains lead to the anticyclonic center near Alaska (around 150°W) and the cyclonic center over North America (around 90°W, Fig. 6a). This dipole pattern, together with the cyclonic center over the North Pacific and the anticyclone center over the North Atlantic, resembles the negative phase of the Western Hemisphere (WH) pattern (Bao and Wallace 2015).
On day −5, the upward and eastward wave propagation from northeast Asia intensifies (Figs. 5b and 6b) and increases the amplitude of the stratospheric circulation from day −5 to day 0 (Figs. 5b,c). Meanwhile, the cyclonic anomaly near 90°W, which was confined in the troposphere on day −10, extends into the stratosphere and becomes equivalent barotropic. In this process, the downward wave reflection from the stratosphere toward North America weakens and is further replaced by widespread upward propagation on day −5 (Fig. 6b). It reemerges from day 0 to day 5 (Figs. 5c,d and 6c,d), in association with the westward shift of the entire circulation pattern and leads to the cyclonic center near Alaska (around 150°W) and tropospheric-confined anticyclonic center over North America (around 90°W) on day 5. On day 10, the tropospheric anticyclonic center over North America then extends into the stratosphere (Fig. 5e). The overall patterns (Figs. 5e and 6e) project well onto those on day −10 (Figs. 5a and 6a) and indicate the ending of one STO life cycle. From day 0 to day 5, the wave reflection from the stratosphere is already apparent before the emergence of the tropospheric wave train propagating northward from the subtropical central Pacific toward North America (Figs. 6c,d). These results suggest that the large-scale Rossby wave propagating upward into the stratosphere contributes essentially to the stratospheric component of the STO and that the wave reflection from the stratosphere contributes constructively to the tropospheric component of the STO.
To further illustrate the wave propagations across the tropopause during the life cycle of the STO, Fig. 8a shows the time evolution of the regional mean vertical component of the wave activity flux (i.e., Fz) at 150 hPa over northeast Asia (45°–75°N, 140°E–180°) and North America (45°–75°N, 100°–140°W). Persistent positive Fz (i.e., upward wave propagation) is visible from day −10 to day 10 over northeast Asia and peaks on day −4. It is consistent with the amplification of the STO-associated stratospheric circulations. In contrast, strong negative Fz (i.e., downward wave propagation) is observed around day −10 and day 2 (Fig. 8a), right before the amplification of the North American circulation. A comparison of the above Fz with the 60°–70°N averaged 300-hPa geopotential height anomalies confirms that the reflection of Rossby waves from the stratosphere precedes the amplification of cyclonic/anticyclonic center over North America (Fig. 9). Meanwhile, strong positive Fz is observed around day −3 during the transition of the cyclonic to anticyclonic center over North America (Figs. 8a and 9). The oscillating nature of Fz (Fig. 8a) and its good correspondence to the tropospheric North American geopotential height centers (Figs. 5 and 6) further indicate the essential role of the Rossby wave reflection from the stratosphere in forming the tropospheric component of the STO.
Evolution of wave activity during the stratosphere–troposphere oscillation. (a) Temporal evolution of the regional mean vertical wave activity flux (Fz) at 150 hPa over North America (45°–75°N, 100°–140°W, red line) and northeast Asia (45°–75°N, 140°E–180°, blue line) during the life cycle of the STO. (b) Temporal evolution of the 300 hPa wave activity density tendency (∂A/∂t) and the divergence of wave activity flux over North America (40°–70°N, 30°–120°W) during the life cycle of the STO. The black, red, green, and blue lines show the observed ∂A/∂t, the three-dimensional divergence of wave activity flux (−∇3 ⋅ F), and the divergence arising from the horizontal and vertical components of the wave activity flux, respectively. Note that the region of North America in (b) is slightly different from that in (a) to better include the cyclonic/anticyclonic centers in the troposphere.
Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0238.1
Westward propagation of the stratosphere–troposphere oscillation. Time–longitude plot of the geopotential height anomalies averaged between 60° and 70°N at 300 hPa (shading; SI = 30 gpm) and 30 hPa (contour; CI = ±50, ±100, ±200, ±400, ±800; gpm). The regional mean Fz over North America, which is the same as in Fig. 8a, is shown on the right side for easy comparison. Negative contours are dashed, and zero contours are bolded.
Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0238.1
The downward wave reflection may not inherently indicate a good coupling between the stratosphere and the troposphere (Plumb 2010; Dunn-Sigouin and Shaw 2018; Davis et al. 2022). In addition, there exists an apparent tropospheric wave train from the subtropical Pacific (Fig. 6), which may also contribute dramatically to the evolution of the tropospheric circulation. Therefore, it is critical to reveal to what extent the downward wave reflection from the stratosphere contributes to the anomalous geopotential height center in the troposphere over North America. When the wave and the basic flow are both conservative in the Wentzel–Kramers–Brillouin approximation, the development of the circulation could be interpreted as a result of the incoming Rossby wave (Holton 2004; Takaya and Nakamura 2001). Thus, the relative role of vertical and horizontal incoming Rossby waves in inducing a circulation anomaly can be quantified by diagnosing the wave activity density equation [Eq. (A2) in appendix A; Song et al. 2016]. Figure 8b shows the temporal evolution of the 300 hPa wave activity density tendency (∂A/∂t) and the divergence of wave activity flux over North America ([40°–50°N, 30°–120°W]). Note that a positive ∂A/∂t can be associated with both the amplified cyclonic and anticyclonic anomalies because the wave activity density (A) is proportional to the squared eddy potential vorticity. Positive peaks of ∂A/∂t (black line) around day −7 and day 4 correspond well with the amplification of the cyclonic and anticyclonic anomaly over North America (Figs. 8b and 9). Meanwhile, the evolution of ∂A/∂t generally coincides with that of the three-dimensional divergence of the wave activity flux (−∇3 ⋅ F, red line), although their magnitudes have some differences. These results confirm the validity of this diagnosis in explaining the circulation evolvement. It is apparent that the −∇3 ⋅ F primarily arises from its vertical component, with a weak contribution from its horizontal component. This result reinforces the idea that wave reflections from the stratosphere play a critical role in causing the STO’s tropospheric center over North America.
A remaining question is why wave reflection is observed in the lower stratosphere. On the one hand, the mean flow can constrain the vertical propagation of Rossby waves (Charney and Drazin 1961). Throughout the life cycle of STO, the refractive index of both WN1 and WN2 show negative values near the troposphere at mid–high latitudes (Fig. S1; Matsuno 1970; Hu and Tung 2002). It indicates that the mean flow sets a favorable background for wave reflection. On the other hand, other factors should account for the oscillating feature of vertical wave propagation. As the vertical wave propagation is related to the vertical structure of the circulation system, the daily evolution of the vertical structure is examined further (Fig. 9). The circulation anomalies always tilt westward with height over the Asia region, with the stratospheric action center lying to the west of the tropospheric one, consistent with the persistent upward wave propagation (Figs. 5 and 8a). In contrast, the vertical structure presents a periodical change of westward and eastward tilting with height over North America, in agreement with the oscillating feature of Fz (Figs. 5, 8a, and 9). A close inspection suggests that the changes in vertical structure are featured by rapid development and westward propagation in the troposphere, while the evolution of the stratospheric circulation is much slower (Fig. 9). These results suggest that the evolution of the tropospheric circulation partly facilitates the oscillation of the vertical wave propagation.
b. Linear and nonlinear processes in the troposphere
Section 5a demonstrates the critical role of the Rossby wave reflection from the stratosphere in the formation of the STO and suggests that the tropospheric circulation may have a substantial contribution. Meanwhile, the reflection of Rossby waves alone cannot fully explain the changes in the STO-associated tropospheric circulation (e.g., Fig. 8b). Hence, it is essential to understand what drives the evolution of tropospheric circulation during the STO.
To address the above issue, the streamfunction tendency equation [Eq. (B1) in appendix B, Cai and Vandendool 1994] is diagnosed. The terms on the right-hand side (rhs) of the decomposed streamfunction equation are projected onto the 300 hPa streamfunction anomaly of the target date [Eq. (B9) in appendix B] to quantify the respective role of different processes in the STO (Feldstein 2002, 2003; Xu et al. 2020). Here, day 5 is chosen as the target date because it is the time with clear wave reflection from the stratosphere (Fig. 5d) and the northward-propagating wave train over the Pacific (Fig. 6d) and at the early stage of the North American anticyclone (Figs. 5d and 6d). The domain 20°–80°N and 60°E–60°W is chosen for the projection because it is where the STO’s tropospheric signal is located, and the results do not change if a relatively smaller range is chosen. The diagnosis considers the role of synoptic eddies, which have periods shorter than 10 days and are denoted with superscript H, and low-frequency eddies, which have periods longer than 10 days and are denoted with superscript L.
Figure 10a shows the projected time series for the observed STO-associated streamfunction tendency (∂ψSTO/∂t, yellow line), the low-frequency streamfunction tendency (∂ψL/∂t, gray line), and the seven forcing terms (
Projections of various combinations of terms in the streamfunction tendency equation [Eq. (B1) in appendix B] onto the STO-composited 300 hPa streamfunction anomalies on day 5 over a large domain surrounding North America [20°–80°N, 60°E–60°W]. (a) ∂ψSTO/∂t (yellow), ∂ψL/∂t (gray), and the sum of the first seven rhs terms (black). (b) Sum of the rhs terms (black), linear terms (blue), and nonlinear terms (red). (c) Each term of the linear process, including the beta term (ξ1, green), advection of relative vorticity (ξ2, purple), interaction with climatological stationary wave (ξ3, orange), and divergence term (ξ4, brown).
Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0238.1
The above analysis identifies the essential role of the divergence term in the STO’s tropospheric evolution. However, this projection result only explains the development of the tropospheric circulation but does not clarify why it propagates westward. Hence, Fig. 11 further shows the spatial distribution of selected terms on several key days. On day −5, a negative streamfunction tendency is located to the west of the cyclonic center over North America (red box in Fig. 11a). This tendency arises primarily from the linear process (Fig. 11b) and tends to drive the circulation system westward. The beta effect greatly contributes to the linear term (Fig. 11d), but it is canceled by the advection of the relative vorticity (Fig. 11e). In contrast, the divergence term induces a large cyclonic tendency over Alaska and explains a large proportion of the observed tendency (Fig. 11f). This result suggests that the secondary circulation-induced divergence plays a vital role in driving the STO westward in addition to causing its development (Fig. 10). This conclusion also holds for the following days, such as day 0 and day 5.
Spatial distribution of components of the streamfunction tendency. The rhs terms of Eq. (B1) in appendix B at 300 hPa on day −5, day 0, and day 5 (shading; SI = 106 m2s−2). (a) Sum of the seven terms. (b) Sum of linear terms (
Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0238.1
Although the effects of nonlinear processes are overall weak during the STO (Fig. 10b), they can be important on the local scale. For example, the cyclonic tendency near the Aleutian Islands on day −5 (Fig. 11a) cannot be fully explained by the linear processes, and the nonlinear processes are essential (Figs. 11b,c). This feature is more evident on day 0 when the nonlinear processes explain a large proportion of the cyclonic tendency (Figs. 11a,c). To quantify the role of the nonlinear processes on the local scale, the projection procedure is repeated like in Fig. 10 using a small domain near the Aleutian Islands (35°–70°N, 180°–140°W, red box in Fig. 11a).
The time series of ∂ψSTO/∂t for this small domain (Fig. 12a) resembles that shown in Fig. 10a and agrees well with ∂ψL/∂t and
Projections of various combinations of terms in the streamfunction tendency equation [Eq. (B1) in appendix B] onto the STO composited 300-hPa streamfunction anomalies on day 5 over a small domain near the Aleutian Islands (35°–70°N, 180°–140°W, red box in Fig. 11a). (a) ∂ψSTO/∂t (yellow), ∂ψL/∂t (gray) and the sum of the first seven rhs terms (black). (b) Sum of the rhs terms (black), linear terms (blue), and nonlinear terms (red). (c) Each term of the nonlinear process, including the self-interaction among the low-frequency anomalies (ξ5, green), the self-interaction among the high-frequency anomalies (ξ6, purple), and the cross-frequency interaction between high- and low-frequency anomalies (ξ7, orange).
Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0238.1
6. Implications for the stratosphere–troposphere dynamic coupling
The STO is defined in this study, but STO-like circulations have been reported by several previous studies. In the stratosphere, a disruption of the polar vortex resembling the STO is suggested to be responsible for the widespread cold spell in North America through wave reflection processes (Kretschmer et al. 2018; Matthias and Kretschmer 2020; Cohen et al. 2021, 2022; Ding et al. 2022; Messori et al. 2022). In the troposphere, a westward-propagating tropospheric circulation resembling the STO was identified as the dominant intraseasonal variability over the North Pacific region (Branstator 1987; Kushnir 1987), and a Western Hemisphere teleconnection resembling the STO was found to precede the SPV shift (Tan and Bao 2020). Nevertheless, it was unclear how the tropospheric and stratospheric signals interact with each other and on what time scale this mechanism is dominant. In most studies, the NAM is regarded as the dominant mode when the stratosphere–troposphere coupling is investigated. Here, we reveal that the STO excels if the intraseasonal time scale is considered. This result highlights the importance of taking the time scale into account when the stratosphere–troposphere coupling is considered. Moreover, the concept of the STO may put all the abovementioned studies into one framework and explain the physical linkages among them. As such, the STO may provide a holistic view to better understand the intraseasonal variation in the extratropical stratosphere and the mid–high-latitude troposphere and their interactions.
Meanwhile, the dominance of the STO on the intraseasonal time scale is consistent with the knowledge that the time scale of planetary wave coupling is much shorter than the downward migration of zonal mean anomalies (Perlwitz and Harnik 2004; Shaw et al. 2014; Dunn-Sigouin and Shaw 2018). It also suggests the importance of wave reflection in coupling the stratosphere and troposphere on the intraseasonal time scale. The distribution of the STO events among months shows that the STO tends to occur more frequently between December and March and less in November (Fig. 13), regardless of the criterion to define the STO. This result is consistent with the period when the stratosphere–troposphere planetary wave coupling is most active (Shaw and Perlwitz 2013; Dunn-Sigouin and Shaw 2015).
Distribution of the number of STO events by month. Results for the (a) positive and (b) negative phases. Purple, green, brown, and red indicate the events detected with the threshold of 1.0σ, 1.5σ, 2.0σ, and 2.5σ, respectively.
Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0238.1
7. Summary and discussion
It is well known that the leading mode of variability of the extratropical Northern Hemisphere stratosphere on seasonal time scales is the changes in the strength of the SPV, represented by the NAM. This study shows that the NAM dominates the stratospheric variability in the extratropical Northern Hemisphere on time scales longer than 60 days, but in contrast, the shift of the SPV stands out as the leading mode on the intraseasonal time scale with a 10–60-day period. The shift of the SPV shows a periodic westward-propagating WN1 signature in the geopotential height field, reflecting the alternating shift of the SPV off (toward) the Eurasian (North American) continent or the North Pacific (North Atlantic) Ocean. Moreover, it is found that this mode is dynamically coupled to the troposphere, forming an intraseasonal STO. The STO has an overall quasi-barotropic structure, and its tropospheric signature at certain stages resembles the WH pattern (Bao and Wallace 2015), a circulation that accounts for the widespread extreme cold events over North America (Wallace et al. 2014; Tan et al. 2017; Kretschmer et al. 2018; Lee et al. 2019; Guan et al. 2020). The STO is associated with significant changes in surface air temperature over North America, North Pacific, and East Asia, suggesting its importance in intraseasonal temperature variability. The mechanism of the STO involves the reflection of intraseasonal Rossby waves from the stratosphere and the linear and nonlinear interactions in the troposphere.
The evolution and mechanism of the STO are summarized in a schematic shown in Fig. 14. At stage I, the SPV shifts off North America toward Eurasia during the negative phase of the STO, characterized by a deep cyclonic anomaly in the eastern Hemisphere (blue contours) and an anticyclonic anomaly in the western Hemisphere (red contours). An intraseasonal Rossby wave train propagates upward and eastward from the troposphere near northeast Asia into the stratosphere and amplifies the stratospheric circulation. Then, driven primarily by the divergence-dominated linear process (orange arrow) and partly by nonlinear processes arising from the self- and cross-frequency-interactions of high- and low-frequency waves (black wavy arrow), the tropospheric circulation moves westward, especially over the North Pacific. At stage II, the vertical structure evolves into an eastward tilting phase over North America and facilitates the wave reflection process here. The reflected Rossby wave contributes substantially to the development of a cyclonic center in the upper troposphere over eastern North America. The STO’s tropospheric centers then further intensify and move westward through the divergence-dominated linear processes. At stage III, the circulation gradually turns into a westward tilting structure, consistent with the upward wave propagation. Therefore, the upward-propagating Rossby wave from northeast Asia toward North America maintains the amplitude and westward shift of the stratospheric circulation. Accordingly, the cyclonic center over North America develops and extends from the troposphere to the stratosphere. The circulation anomalies at this stage project onto those at stage I with opposite signs. It indicates a shift of the SPV off Eurasia and toward North America, corresponding to the positive phase of the STO. The subsequent evolvement of the STO from stage III to stage IV and I resembles that from stage I to stage II and III, closing the life cycle of the STO. It should be noted that despite the symmetric temporal evolution of STO’s stratospheric center, the spatial pattern of the circulation before and after the mature period (e.g., stage II and IV) shows a clear asymmetry (e.g., day −5 and day 5 in Fig. 4). This asymmetry is more evident in STO’s tropospheric center (Figs. 5 and 6) and may be attributed to the nonlinear tropospheric processes (Fig. 10b).
Schematic for the life cycle of the STO. Blue and red contours indicate cyclonic and anticyclonic anomalies, respectively. Purple arrows denote the propagation of Rossby waves. The orange arrow and black wavy arrow represent the effect of linear and nonlinear processes that account for the propagation of tropospheric circulations.
Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0238.1
This study shows the evolution of the STO as a periodic oscillation via composite analysis. This periodic feature is apparent in both the stratospheric and the tropospheric circulations, albeit with some differences in amplitude and duration among events (Figs. S2–5). Meanwhile, the signature of the STO can also be found in some case studies, such as that observed in 2013/14, which led to the severe winter in North America (Cohen et al. 2022). This observational evidence strengthens the prominent role of the STO in influencing the wintertime weather condition in North America.
Acknowledgments.
We thank the three anonymous reviewers for their insightful comments and suggestions. X. S. and L. W. were supported by the National Natural Science Foundation of China (41925020, 41721004). A. A. S. and S. C. H. were supported by the U.K.–China Research and Innovation Partnership Fund through the Met Office Climate Science for Service Partnership (CSSP) China as part of the Newton Fund. P. X. was supported by the National Natural Science Foundation of China (42005057) and the China Postdoctoral Science Foundation (2020M670418, 2021T140652).
Data availability statement.
The ERA-Interim reanalysis data were downloaded from https://www.ecmwf.int/en/forecasts/datasets/browse-reanalysis-datasets.
APPENDIX A
Wave Activity Flux
APPENDIX B
Decomposed Streamfunction Tendency Equation
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