Introduction

Short-term variability of the extratropical stratosphere in winter is predominantly determined by the dynamical forcing from large scale quasi-stationary planetary/Rossby waves originating from the troposphere1,2. Occasionally, this forcing becomes sufficiently strong enough to retard or reverse the pre-existing eastward wind flow in the stratosphere called the Polar Vortex3,4. Such episodes of deceleration of the mean flow are accompanied by a sudden increase in temperature, creating summer-like conditions in the winter stratosphere5,6. Sudden Stratospheric Warming (SSW) events as they are commonly called, have been found to significantly affect near-surface weather over polar and middle latitudes in weeks or months to follow7,8,9,10. Owing to this strong stratosphere-troposphere coupling, SSW events are regarded as a source of improved predictability at sub-seasonal to seasonal (S2S) scales11,12. Recent studies have indicated that the downward propagation of SSW events into the troposphere could be forecasted reasonably well in S2S models13 and that the strength of the warming is more important for the prediction of surface impacts14.

The dynamical forcing necessary to drive SSWs has been identified to be provided mainly by two mechanisms: (1) anomalously strong planetary wave (PW) forcing from the troposphere15,16 and (2) resonance excitation of planetary waves, wherein the stratospheric vortex undergoes preconditioning so as to modulate upward wave flux17,18. In addition, several external drivers such as tropical stratospheric Quasi Biennial Oscillation (QBO)19,20, El-Nino Southern Oscillation (ENSO)20,21, Madden–Julian Oscillation (MJO)20,22, the 11-year solar cycle20,23,24 and arctic snow25,26 have been identified to influence the occurrence of SSWs by modifying planetary wave forcing.

The Holton-Tan27 mechanism has been widely invoked to explain the control of the polar vortex by the tropical stratospheric QBO28,29. As per this classical mechanism, weak vortex states during the easterly phase of the QBO are attributed to the presence of the zero-wind line in the subtropics of the winter hemisphere, which facilitates the focusing of planetary waves into the polar vortex19,24,30. While the Holton-Tan relationship is robustly seen in many observations and model simulations, it is not clear as to what level of the QBO exerts the maximum influence on the polar vortex. More generally, it is unclear whether the location of the zero wind line plays a major role and if so at what levels19. Earlier studies have also demonstrated the QBO-vortex coupling using mechanisms different from the original Holton-Tan mechanism30,31 Many studies have suggested that the control of the polar vortex is not just limited to a particular level of the QBO, rather winds in an extended layer of the tropical stratosphere have a major role to play32,33. Specifically, winds around the tropical stratopause region, where the Semiannual Oscillation (SAO) is dominant, is found to significantly affect the strength of the vortex in the mid-late winter period34,35,36. In a very recent study, constraining winds in the tropical upper stratosphere in addition to the QBO region was found to significantly improve the prediction of SSW events, including its vertical structure and temporal evolution37.

Thus the influence of the tropical upper stratosphere on the strength of the polar vortex is increasingly being recognized. However, the physical mechanism through which the tropical upper stratospheric winds influence the polar vortex is still an open question. In the present study, we provide a plausible physical explanation for this influence, at least for a limited set of background conditions. We focus on the temporal evolution of the subtropical zero wind line before the SSW period to investigate its role in triggering the SSW. Further, we examine wave driving in the tropical stratopause to identify possible precursors for SSW events.

Evolution of the subtropical zero-wind line

Using the SSW event of 2000–2001 boreal winter period as a case study, we examine the evolution of the subtropical zero wind line prior to the SSW. This is important because of the fact that the zero-wind line can act as the critical line for quasi stationary planetary waves which are largely responsible for the generation of SSW events. That is to say, these planetary waves deposit their momentum to the background winds as they encounter the zero-wind line. Zonal mean zonal winds in the 20–60 km region over the Northern Hemisphere on alternate days from day 48 to day 64 are depicted in Fig. 1 (Results for the whole Dec-Feb period are given in Supplementary Fig. S1). During the initial period, the subtropical zero wind line in the upper stratosphere is found around 20° N. As time progresses, the zero-wind line undergoes a poleward and upward excursion. The poleward excursion of the zero-wind line is driven by the deposition of easterly momentum by the interaction of planetary waves with the mean flow. Maximum poleward excursion of the zero-wind line is found on day 58, after which winds in the lower mesospheric altitudes over the Polar Regions reverse from eastward to westward. The westward wind regime further propagates downward with time, reaching stratospheric altitudes, signaling the onset of SSW. After the onset of SSW, the subtropical zero wind line retracts back to the initial position around 20° N.

Figure 1
figure 1

Zonal mean zonal winds (ms−1) in the 20–60 km altitude region over the Northern Hemisphere for (a) day 48, (b) day 50, (c) day 52, (d) day 54, (e) day 56, (f) day 58, (g) day 60, (h) day 62 and (i) day 64. Day 01 corresponds to 01 Dec 2000 and Day 90 Corresponds to 28 Feb 2001. Black solid lines denote the zero-wind contours. Results for the whole Dec-Feb period is given in supplementary Fig. S1. Winds in the polar cap (60° N–90° N) at 10 hPa level reverse from eastward to westward on Day 63. As per the conventional SSW definition, SSW onset for this event happens on day 73 when winds over 60° N, 10 hPa level reverse. The slow budging of the subtropical easterly wind regime around the stratopause can be noticed. Concomitantly, the region of strong westerly winds associated with the polar vortex is also found to shrink and undergo a poleward confinement. Upon reaching ~ 60° N, the zero wind line undergoes a rapid progression to the Polar Regions. Thus the poleward progression of the zero wind line starts well in advance of the SSW onset; it expands poleward and upward; upon reaching high latitudes this forms the critical line for planetary waves propagating from below. This demonstrates that the poleward propagation of the zero wind line plays a crucial part in the generation of SSW.

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Modification of wave forcing

Eliassen-Palm (EP) diagnostics (see “Methods” section) provide an efficient way to visualize the interactions between waves and the mean-flow38,39,40, especially during extreme events such as SSWs. The effect of poleward propagating zero wind line on the wave-mean flow interaction can be inferred from Fig. 2. Starting from the initial phase, the maximum wind anomaly can be seen on the poleward flank of the subtropical zero wind line in the upper stratosphere. Moving forward in time, the wind anomaly enhances and moves poleward, together with the propagation of the zero-wind line. It can also be seen that during the phase of rapid poleward progression of the zero-wind line (Fig. 2c–e) the EP flux vectors show a prominent upward and poleward tendency. This suggests that the poleward progression of the zero-wind line facilitates the focusing of wave activity towards the polar mesosphere. Once the zero-wind line reaches the maximum poleward extent, the wind anomaly becomes the strongest, resulting from the increased wave focusing. Thereafter, the EP flux arrows point downward (Fig. 2f–h) showing the descent of the critical line and hence of the easterly wind regime. Thus, our results show that the poleward propagation of the zero-wind line helps in better focusing of planetary waves into the polar mesosphere, eventually culminating in the breakdown of the vortex through wave-mean flow interaction. (Readers are referred to Supplementary Fig. S2 for EP Flux vectors corresponding to Fig. 2).

Figure 2
figure 2

Differences in zonal mean zonal wind between alternate days shown in Fig. 1. The zero wind contours for the first day in the pair is also shown. Overlaid are the differences in EP Flux vectors between the respective days. See Supplementary Fig. S2 for the corresponding EP Flux vectors.

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Tropical wave driving as a harbinger for SSW

Having shown that the poleward propagation of the zero-wind line and subsequent focusing of the planetary waves into the polar mesosphere precedes the SSW event in the extratropical stratosphere, we now examine the temporal evolution of the wave driving (Fig. 3) to gain more physical insights. It can be seen that maximum wave driving in the polar stratopause is found around day 56. Interestingly, the maximum wave driving around the tropical stratopause peaks on day 48, approximately one week before their polar counterpart. It should be remembered that the magnitude of wave driving in the tropical stratopause is significantly smaller compared to that in the Polar Regions, as the wave driving varies inversely with the cosine of the latitude. From the long-term mean and standard deviations it can be inferred that for both the tropical as well as Polar Regions, the wave driving prior to the SSW period is significantly higher than the climatological variability. Poleward progression of the zero-wind line around day 47 coincides with the maximum tropical stratopause wave driving. Then, as the zero-wind line propagates poleward, the wave driving in the polar stratopause also increases, which also concurs with enhanced wave 1 amplitude. Finally, maximum wave driving in the polar stratopause nearly coincides with the maximum poleward extension of the zero-wind line. Winds in the polar cap reverse on day 63, which follows the peak wave driving in the polar stratopause on day 56. A minor warming event was observed around day 20 when wave 1 amplified. Prior to this minor warming also enhanced wave driving in tropical and high latitude stratopause regions can be noticed.

Figure 3
figure 3

Magnitudes of wave driving in (a) tropical and (b) polar stratopause regions, (c) latitude of the subtropical zero wind line and (d) the amplitudes of wave number 1 and 2 planetary waves at 60° N, 1 hPa level during the SSW event of 2000–2001. The thin lines and the shadings in (a,b) represent the long term (1979–2021) mean wave driving and its standard deviation, respectively. Vertical blue dashed line represents the day on which winds in the polar cap at 10 hPa level reverses to westward. Red dashed line represents the day of wind reversal at 60° N, 10 hPa level. Wave driving at the stratopause is averaged for the reanalysis pressure levels 2 hPa to 0.7 hPa for tropics from 7.5 to 12.5° N (averaging to 10° N) and for polar regions from 57.5 to 62.5° N (averaging to 60° N). This averaging is done to minimize errors due to considering single latitude and pressure levels.

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Prospects/implications for prediction of SSW

From the simultaneous analysis of wave driving in the tropical and polar stratopause regions, it can be suggested that the occurrence of enhanced wave driving in the tropical stratopause prior to that over the Polar Regions can be considered as a predecessor for SSW to occur. In a similar line, we now examine multiple SSW events to confirm this observation. Results from the analysis of 29 SSW events from 1979 to 2021 are listed in Table 1. It can be seen that 20 out of the 29 SSW events considered in the study showed enhanced tropical stratopause wave driving prior to the occurrence of SSW (readers are referred to Supplementary Fig. S3 for more details). It is very interesting to note that after 2000, the number of SSW events with enhanced tropical stratopause wave driving increased significantly. Only two out of 17 SSW events from 2000 did not show enhanced stratopause wave driving prior to SSWs. Further analysis based on the phase of the QBO indicates that, while 14 of the 16 events during QBO-E showed enhanced stratopause wave driving, the same was observed in only 6 of 13 events in the QBO-W phase.

Table 1 Details of SSW events considered in the present study.
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From the foregoing analysis, it can be inferred that wave driving in the tropical stratopause region enhances prior to a significant number of SSW events. This motivates us to suggest that enhanced wave driving in the tropical stratopause can be treated as a ‘symptom’ for SSW to occur.

Discussions

It is well established that SSW events are primarily caused by quasi-stationary planetary waves with zonal wave numbers 1 and 2 (PW1 & PW2)5,15,41. For very few SSW events, zonal wavenumber 3 planetary waves also may be prominent20. Studies have demonstrated that while wavenumber 1 events are preceded by enhanced forcing from PW1 alone, wavenumber 2 events are preceded by either PW2 alone or a combination of PW1 and PW242. According to the Charney-Drazin theorem, smaller wavenumber PWs are capable of propagating to a deeper layer into the atmosphere compared to larger wavenumber PWs43. During the quiet period, strong winds in the mid-latitude westerly jet refract waves from below into two channels: one towards the equator and the other towards the poles44. Here we observe that PWs are focused more towards the equator prior to the onset of SSW. They ultimately undergo interaction with the mean flow at the low latitude stratopause region as they encounter the zero-wind line, which subsequently results in the poleward excursion of the zero-wind line. Using multiple case studies, we observe that the poleward excursion of the zero-wind line is a prominent feature. It is known that the tropical stratopause region is dominated by the semiannual oscillation (SAO) with westerly winds during equinoxes and easterly winds during solstices. The easterly SAO winds in solstices develop as a response to the dissipation of planetary waves in the winter hemisphere. Our results suggest that anomalous planetary wave dissipation prior to SSW events reflects as the poleward excursion of the zero-wind line near the SAO region. We also caution that this mechanism is found to hold true only for events preceded by enhanced planetary wave forcing. Poleward propagation of the zero wind line or enhanced tropical stratopause wave driving may not necessarily be characteristic of SSW events involving resonant amplification internally in the extratropical stratosphere.

Using EP flux diagnostics, we demonstrated that the poleward propagation of the zero-wind line facilitates the focusing of planetary waves into the polar mesosphere. Such a focusing of wave activity is also found to be crucial in establishing the critical layer at polar mesosphere. In many cases, it is found that the subtropical zero wind line itself expands poleward and results in the triggering of SSW. Here we show that the equatorial upper stratosphere plays a major role than previously anticipated in focusing the wave activity towards the polar latitudes. This, according to us, follows from the linear theory wherein wavenumber 1 PWs propagate to a deeper layer, encountering the critical layer only at the subtropical upper stratosphere and culminating in its subsequent poleward expansion. Similar poleward intruding zero wind critical line have been previously noticed in observations45, in numerical simulations46, and it was suggested that such a critical line would reflect waves back to higher latitudes47. Here we show that the poleward propagation of the zero-wind line originates in the upper stratosphere and the exact height of this excursion can vary from event to event depending on the background conditions.

Earlier studies have emphatically shown that the accurate prediction of SSW can aid in improving the seasonal forecasting of tropospheric weather over mid and high latitudes13,14,48,49, and the present study identifies enhanced tropical stratopause wave driving as one of the important precursors, which has implications in predicting SSWs. Though not in all cases, this precursor is found be present in a statistically significant number of SSW events. While there is a preponderance for this precursor to occur during QBO-E, which is in line with the well-established Holton-Tan mechanism, it is not always absent during QBO-W phases. It needs to be examined under what conditions enhanced wave driving occurs at tropical stratopause and what role do the underlying QBO winds play in controlling them. Also, our analysis identified a few cases (not shown) where there was enhanced tropical stratopause wave driving and no following SSW, which indicates that the presence of this feature alone does not imply the occurrence of an SSW. Another very important scientific question worth addressing is the increased rate of occurrence of enhanced tropical stratopause wave driving for SSW events after the year 2000, which probably points towards a shift in the internal dynamics of the system.

To conclude, the present results demonstrate that the tropical stratopause region plays a major role than previously conceived in the generation of SSW events. The background wind conditions at the tropical stratopause region may be crucial for re-focusing the planetary waves towards the polar latitudes. It needs to be verified further if this also reflects in the strength of the SAO winds. Extension of this analysis to higher altitudes is expected to shed light on the formation of the critical layer in the polar upper mesosphere which is crucial for triggering SSW events. Our results support the argument of Gray et al.37 in that improved representation of tropical upper stratosphere can lead to improved prediction of SSW events. We suggest more studies to be oriented in this direction to further delineate the behavior of the zero-wind line for more specific tropical stratospheric wind conditions and dominant wave forcing.

Methods

Data

This study makes use of temperature, zonal and meridional winds from Modern Era Retrospective Reanalysis for Research and Applications -2 (MERRA-2) assimilated meteorological fields50. Reanalysis datasets are found to have a reasonable agreement with satellite-based winds around the stratopause region51. Data from 1000 to 0.1 hPa archived at 0.5° × 0.625° (latitude × longitude) have been used to examine the day-to-day evolution of zonal mean zonal winds and to perform Eliassen-Palm Diagnostics. A pressure scale height of 7 km was used to convert the data from pressure levels to the corresponding height levels. There is no universal definition for characterizing SSW events52. For our discussions, we use the day in which winds in the 60° N, 10 hPa level reverse from eastward to westward as the day of SSW.

Eliassen-Palm diagnostics

We use Eliassen Palm Flux (EP Flux) diagnostics to examine planetary wave propagation and breaking during the SSW period. In the spherical geometry, the meridional and vertical components of EP Flux are defined as53:

$$F_{\left( \phi \right)} = - \rho_{0}\,a\, cos\phi \left( {\overline{u^{\prime}v^{\prime}} } \right)$$
$$F_{\left( z \right)} = f\rho_{0}\, a\, cos\phi \left( {\frac{{\overline{{v^{\prime}\theta^{\prime}}} }}{{\overline{{\theta_{z} }} }}} \right)$$

(See ref39 and ref1 for detailed descriptions on EP Flux. The direction of planetary wave propagation can be inferred from the orientation of EP Flux vectors. Since the meridional and vertical components of the EP Flux differs significantly in magnitude, scaling is applied before the components are plotted in the height-latitude plane. They are scaled as follows:

$$\tilde{F}_{\left( \phi \right)} = \frac{{F_{\left( \phi \right)} *cos\phi }}{a* \pi }$$
$$\tilde{F}_{\left( z \right)} = \frac{{F_{\left( z \right)} *cos\phi }}{{10^{5} }}$$

Finally, to make the EP Flux vectors visible throughout the height domain, an additional scaling factor of \(\sqrt {1000/p\left( z \right)}\) is used.

The divergence of EP Flux is used to infer the interaction of planetary waves with the mean flow. It is estimated as:

$$\nabla \cdot F = \frac{1}{a\, cos\phi }\left( {F_{\left( \phi \right)} cos\phi } \right)_{\phi } + \left( {F_{\left( z \right)} } \right)_{z}$$

Remember that there is no scaling involved in the calculation of EP Flux divergence. The total wave driving is calculated from the divergence of EP Flux as

$$D = \frac{1}{{\rho_{0} a\, cos\phi }} \nabla \cdot F$$

Here u, v and \(\theta\) represent zonal wind, meridional wind and potential temperature. Potential temperature is estimated from temperature \(T\) and pressure \(p\) as \(\theta = T \left( {\frac{{p_{0} }}{p}} \right)^{0.286}\) where \(p_{0}\) is the reference pressure (1000 hPa).

\(\rho_{0}\) is the background density, a is the mean radius of earth and \(f\) is the coriolis parameter defined as \(f = 2{\Omega }sin\phi\), where \({\Omega } = 7.29 \times 10^{ - 5} \;{\text{rad}}\;{\text{s}}^{ - 1}\) is the angular velocity of Earth’s rotation. Primed quantities denote deviations from the zonal mean and subscripts denote derivatives with respect to the subscripted variable. Over-bars represent zonal means.

Phase of equatorial QBO has been identified from the zonal mean zonal winds at 30 hPa level obtained from NOAA-PSL (https://psl.noaa.gov/data/climateindices/list/) as computed from NCEP-NCAR reanalysis.