Preconditioned Stratospheric Modulation on the Occurrence of Stratospheric Final Warmings

Stratospheric Final Warmings (SFWs) are considered to have a distinct impact on the surface weather and stratospheric ozone. Most SFWs are predominantly wave‐driven, while previous studies generally focused on the effects of tropospheric anomalous wave forcing on stratospheric wave amplification. This study demonstrates the crucial role of preconditioned stratospheric modulation on the occurrence of wave‐driven SFWs in the Northern Hemisphere, using ERA5 reanalysis. In most cases, the preconditioned stratospheric state is the key factor in determining the occurrence of both early and late SFWs. The tropospheric anomalous wave forcing cannot independently trigger most SFWs without stratospheric modulation. The proportion of anomalous stratospheric signals followed by SFWs is much higher than that of anomalous tropospheric forcing, even if the proportions of SFWs preceded by anomalous stratospheric signals and tropospheric wave forcing are similar. Additionally, about 25% of SFWs are only preceded by stratospheric modulation without anomalously strong tropospheric wave amplification.

The earliest onset date of SFW was as early as in early March, while the latest date was in mid-May (Ayarzagüena & Serrano, 2009;Hu et al., 2014).Such a large interannual variability can be attributed to the effects of stratospheric planetary waves (Waugh et al., 1999).In the absence of wave forcing, the formation timing of the polar vortex dominated by radiative process only varies by 9 days during the period 1979-2017 (Butler et al., 2019).Obviously, SFWs with large interannual variability are driven by a combination of stratospheric planetary wave forcing and radiative cycle (Black & McDaniel, 2007;Butler & Domeisen, 2021;Hauchecorne et al., 2022;Salby & Callaghan, 2007).Most early SFWs and many late SFWs are significantly affected by anomalous wave forcing in the stratosphere.Similar to these SFWs, SSWs are also predominantly wave-driven (Limpasuvan et al., 2004;Matsuno, 1971;Polvani & Waugh, 2004).The wave-driven SSWs are generally caused by a combination of anomalous upward wave activity from the troposphere and self-modulation of the stratosphere (Polvani & Waugh, 2004;Scott & Polvani, 2004, 2006;Sjoberg & Birner, 2012, 2014;Yang et al., 2023b).The latter, manifested as the vortex resonance or favoring more planetary waves to focus in the stratosphere, may even play a more important role in the occurrence of many SSWs than the former (Albers & Birner, 2014;Birner & Albers, 2017;Esler & Matthewman, 2011;Matthewman & Esler, 2011;Yang et al., 2023aYang et al., , 2023b)).As for the wave-driven processes of SFWs, however, only the effects of tropospheric anomalous wave sources have been generally considered (Black & McDaniel, 2007;Hu et al., 2014;Salby & Callaghan, 2007).The effects of stratospheric modulation on the wave forcing are rarely investigated so far.
This paper seeks to determine whether stratospheric modulation can play a crucial role in the formation of SFWs, using ERA5 reanalysis data.The specific contribution of stratospheric processes in the occurrence of early and late SFWs is investigated, respectively.Section 2 describes the data and methods.Section 3 shows the effects of stratospheric processes on SFWs.Conclusions and discussion are given in Section 4.

Data
We use the European Centre for Medium-Range Weather Forecasts Reanalysis, the fifth generation (ERA5) data set (Hersbach et al., 2023) to obtain daily reanalysis data on a 1.25° × 1.25° grid from 1950 to 2020, including the geopotential, temperature, and winds.The standardized variables used in this study are calculated for each calendar day by first removing the daily climatological mean and then dividing by the daily standard deviation at each level (Birner & Albers, 2017;de la Cámara et al., 2019).

Definitions of Early and Late SFWs
Following the widely used method of previous literature (Butler et al., 2019;Hu et al., 2014Hu et al., , 2023;;Kelleher et al., 2020), an SFW occurs when the zonal-mean zonal wind at 60°N and 10 hPa reverses and does not return to 5 m s −1 until the subsequent autumn.The recovered westerly winds cannot last more than 5 days.The first day when the wind turns to easterly is defined as day 0.Among 71 SFWs, there are 37 events that occur before the mean SFW date (15 April in ERA5), defined as early SFWs, and 34 events that occur on or after 15 April, defined as late SFWs (Table S1 in Supporting Information S1, Butler et al., 2019;Hu et al., 2014;Rao & Garfinkel, 2021a, 2021b).Our results are insensitive to use one standard deviation before and after the mean date as a distinguishing criterion.

Stratospheric Indicators
The zonal-mean quasigeostrophic potential vorticity (QGPV) gradient and refractive index are used to diagnose the distribution of stratospheric signals that affect the upward propagation of planetary waves.The zonal-mean QGPV gradient is calculated according to the following form (Andrews et al., 1987): where   is the zonal-mean QGPV gradient; Ω,  denote Earth-rotation frequency and buoyancy frequency, respectively. = 0 exp is the standard density in log-pressure coordinates; z is height;  0 is the sea level reference density; and H is the height scale (7,000 m).
The refractive index form is referred to Weinberger et al. (2021): where s is the zonal wavenumber.Based on the method of Q. Li et al. (2007), we further use the frequency of negative refractive index (Fn) to visualize it more effectively.Namely, a smaller Fn favors more planetary waves into the region.
Moreover, the meridional PV gradient index (   ) is used to represent the temporal evolution of stratospheric state, which is useful for the statistical prediction of vortex disruption (Jucker & Reichler, 2018).The   is obtained by computing the meridional mean value of   at 30 hPa between 55° and 75°N.The more detailed descriptions of   are seen in Jucker and Reichler (2018).

Tropospheric Wave Event and Stratospheric Meridional PV Gradient Event
The vertical component of quasi-geostrophic Eliassen-Palm flux ( z , Andrews et al., 1987) is used to diagnose upward wave activity.The  z is averaged over 45°-75°N and filtered for planetary wave 1 + 2, wave 1, and wave 2, respectively.Then, tropospheric wave events (TWEs) are introduced to visually analyze the effects of tropospheric wave forcing processes (Birner & Albers, 2017;de la Cámara et al., 2019;Yang et al., 2023b).Since the earliest onset date of SFW is 5 March, and the latest is 12 May (Table S1 in Supporting Information S1).A TWE is identified when the 11-day running-mean standardized  z anomaly exceeds one standard deviation from 1 March to 20 May.We use one standard deviation here to represent the anomalously strong wave forcing in the troposphere.Using 0.5 standard deviation or higher thresholds will not significantly affect our main results (Figures S1 and S2 in Supporting Information S1).Changing the time scale of  z will also not affect our main conclusions (e.g., from 10 to 40 days, not shown).The day with the maximum value of  z anomaly is defined as day 0 of a TWE.Perform the above steps separately for waves 1 and 2. If the wave-1 and wave-2 TWEs are less than 20 days apart, the event with the largest  z value is selected.We use a mixed set of the TWEs across 700, 500, and 350 hPa to indicate the anomalous tropospheric wave forcing (The results are insensitive to select other levels or only use single tropospheric level, not shown).Consecutive events must be at least 20 days apart to avoid double counting.A total of TWEs 133 are identified.
To diagnose the effects of stratospheric anomalous processes, the stratospheric meridional PV gradient event (SPVE) is introduced in this paper (Yang et al., 2023a(Yang et al., , 2023b)).SPVEs can effectively modulate the upward wave activity into the stratosphere and somewhat represent the preconditioned stratospheric process that favors the occurrence of subsequent vortex disruption.An SPVE occurs when the   exceeds one standard deviation.The day with the maximum value of   is recorded as day 0 of an SPVE.Consecutive events must be at least 30 days apart due to the slower evolution of stratospheric circulation compared to the troposphere.Fifty Seven SPVEs have been identified from 1 March to 20 May.Moreover, the SFW in 2016 occurred as early as 5 March, and an SPVE is identified on 17 February 2016.Thus, a total of 58 SPVEs are included in our statistics.This SPVE in February 2016 does not significantly change our results.

Figures 1a and 1b
show the composite time-height cross sections of 11-day running-mean standardized  z anomalies with wavenumber 1 + 2 for early and late SFWs.For early SFWs (Figure 1a), the strong  z anomalies appear in the troposphere around lag −20 days before the onset, while the anomalous center is located in the lower stratosphere.For late SFWs (Figure 1b), the anomalous wave forcing in the troposphere is weaker compared to early composites before day 0. The  z anomalies are mainly focused on the stratosphere.The timing of  z anomaly in the stratosphere appears earlier than that in the troposphere.
We next divide these SFWs into two groups based on whether they are preceded by TWEs to further investigate the effects of tropospheric anomalous wave forcing (Figures 1c-1f).An SFW preceded by a TWE is identified when a TWE occurs within −20 to 0 days before the SFW onset.This time interval is selected according to the period of significant  z anomalies shown in Figure 1a.The results are insensitive to slight changes in this interval.For both early and late SFWs, about 56% of events are preceded by strong wave forcing anomaly in the troposphere (Figures 1c and 1d).Many SFWs are not preceded by an anomalously strong wave source in the troposphere (Figures 1e and 1f), while the robustly strong wave forcing is still seen within the stratosphere for these SFWs not preceded by TWEs.The above results indicate that the stratosphere itself may play an important role in the occurrence of both early and late SFWs in addition to the tropospheric anomalous wave forcing.Another distinct difference between early and late SFWs is that there is a period of anomalous  z around lag −100 days before the onset of late SFWs (Figure S3 in Supporting Information S1).It is consistent with Hu et al. (2014) that late SFWs are more likely to occur after the winter with an SSW.
Figures 2a-2f depict the composite height-latitude sections of standardized anomalies of the QGPV gradient and wave-1 Fn for TWEs followed and not followed by SFWs.For both TWEs followed by early (Figures 2a and 2d) or late SFWs (Figures 2b and 2e), the significantly positive QGPV gradient anomalies and negative Fn anomalies appear in the stratosphere around 65°N.Such an anomalous structure along the vortex edge favors more planetary waves propagating upward toward the polar vortex (Albers & Birner, 2014;Jucker, 2016;Yang et al., 2023b).In contrast, no distinct QGPV gradient anomaly appears along the vortex edge for TWEs not followed by any SFW (Figure 2c).The robustly positive anomalies of Fn appear in the stratosphere at middle-high latitudes (Figure 2f).It is not favorable for the upward propagation of planetary waves into this area.(c, e) Show the composites of early SFWs preceded and not preceded by tropospheric wave events, respectively.(d, f) Are as in (c, e), but for late SFWs.Lag = 0 denotes the onset date of SFWs.Thick and black lines highlight the area with a 95% confidence level according to the Student's t test.A horizontal gray line represents the approximate tropopause level (∼270 hPa; the same below).
According to the evolutions of   for TWEs (Figure 2g), it is further suggested that only those TWEs preceded by robust stratospheric signals can generally trigger subsequent SFWs, even for anomalous wave forcing in the middle-upper troposphere.The results of early and late SFWs are similar to all SFW composites (Figure S4 in Supporting Information S1).That is, the anomalously strong wave forcing in the troposphere cannot independently determine the occurrence of most SFWs without the modulation of preconditioned stratospheric signals.
We next use SPVEs mentioned in Section 2.4 to directly investigate the effects of stratospheric anomalous processes on the occurrence of early and late SFWs. Figure 3 shows the height-time composites of standardized  z anomalies with wavenumber 1 and wavenumber 2 for SFWs preceded and not preceded by SPVEs.An SFW  (d-f) Are as (a-c), but for the frequency of negative refractive index (Fn).Composites are taken averaged over −30 to 0 days.Thick and black lines in panels (a-f) highlight the area with a 95% confidence level according to the Student's t test.(g) Presents the composite evolutions of meridional PV index (   , the meridional mean value of   at 30 hPa between 55° and 75°N) for TWEs.Black and red lines in (g)-(i) denote those TWEs followed and not followed by SFWs, respectively.Lag = 0 denotes the onset date of TWEs.Thick lines highlight the stage with a 95% confidence level.Vertical gray lines in panel (g) denote the difference in the two series is significant at the 95% level.
preceded by an SPVE is identified when an SPVE occurs within −30 to 0 days before the SFW onset.This period corresponds to the robustly anomalous stage of   (Figure S5 in Supporting Information S1) and radiative timescales in the lower stratosphere (Newman & Rosenfield, 1997).More than half (40/71) of SFWs have significant stratospheric signals before the onset.For early SFWs, the anomalous wave-1 forcing in the troposphere for those preceded by SPVEs is weaker and shorter in duration than those without SPVEs, while the wave-1 forcing in the stratosphere is stronger (Figures 3a and 3c).Moreover, the strong wave-2  z anomalies in the stratosphere only appear for those early SFWs preceded by SPVEs (Figure 3b).The stratospheric wave-2 forcing is absent for those SFWs without SPVEs (Figure 3d).
For late SFWs preceded by SPVEs (Figures 3e and 3f), the robust  z anomalies are still seen in the stratosphere, exhibiting wave-driven characteristics.The  z anomalies in the troposphere are weak for these events.The above results further demonstrate the important role of stratospheric modulation in the occurrence of wave-driven early and late SFWs.Compared to late SFWs, we note that the occurrence of some early SFWs with stratospheric  (c, d) not preceded by SPVEs.(e-h) Are as (a-d), but for late SFW composites.Thick and black lines in panels (a-f) highlight the area with a 95% confidence level according to the Student's t test.Lag = 0 denotes the onset date of SFWs.modulation also requires stronger wave forcing from the troposphere (Figures 3a and 3e; The strength of 700-hPa wave-1 forcing anomalies averaged over lag −20 to −1 days for early SFWs is almost twice as large as that for late SFWs).The stratospheric wave amplification is thus stronger than that for late SFWs preceded by SPVEs (Figure 3e).
On the other hand, the anomalous wave forcing is absent in both the stratosphere and troposphere for those late SFWs without SPVEs (Figures 3g and 3h).Based on the Figure S6 in Supporting Information S1, these late SFWs without SPVEs are preceded by a dramatic vortex disruption during winter.The background circulation weakens and does not recover.As the season changes, the weak zonal wind slowly transitions to the easterly.Namely, these late SFWs without SPVEs are predominantly driven by the radiative forcing.
Table 1 summarizes the statistics for early and late SFWs associated with TWEs and SPVE.About 56% of SFWs are preceded by SPVEs.Although about 56% of SFWs are also preceded by TWEs, which is higher to the proportion of 700-hPa TWEs associated with SSWs (about 1/3, Birner & Albers, 2017;de la Cámara et al., 2019;White et al., 2019), only about 30% (40/133) of TWEs are followed by an SFW.This proportion is much lower than the statistics for SPVEs followed by an SFW (about 69%, 40/58).Obviously, the stratospheric modulation plays at least as important a role in the occurrence of SFW as tropospheric anomalous wave forcing.Besides, about 25.4% of SFWs (24.3% of early events and 26.5% of late events) are only preceded by SPVEs and without TWEs.It highlights the major role of stratospheric modulation in the occurrence of these SFWs.

Conclusions and Discussions
This study has classified the crucial role of stratospheric modulation in the occurrence of both early and late SFWs, using ERA5 reanalysis data.We use TWEs and stratospheric meridional PV gradient events (SPVEs) to diagnose the effects of tropospheric anomalous wave forcing and the modulation of stratospheric anomalous signal on the stratospheric wave amplification in SFWs, respectively.
Our results suggest that the stratospheric modulation is not less important for the occurrence of both early and late SFWs than the anomalously strong wave forcing in the troposphere.Those TWEs followed by early or late SFWs are both accompanied by robust stratospheric signals.This stratospheric anomalous structure favors more upward planetary waves into the polar vortex.By contrast, the preconditioned stratospheric processes are absent for those TWEs not followed by SFWs.Obviously, the preconditioned stratospheric signals are generally the key factor to trigger SFWs.The anomalously strong wave forcing in the troposphere cannot independently control the occurrence of SFWs in most cases without stratospheric modulation.Quantitatively, about 69% of SPVEs are followed by an SFW, this proportion is much higher than that of TWEs (about 30%), even if the proportions of SFWs preceded by anomalous strong stratospheric signals and tropospheric wave forcing are similar (about 56%).Furthermore, about 25% of SFWs are only preceded by robust stratospheric signals and no anomalously strong wave source in the troposphere.It highlights the major role of stratospheric modulation in triggering these SFWs.The statistics of early and late SFWs are similar.Note that our work mainly shows the results of anomalously strong wave forcing.Although a long-term accumulation of the weak wave forcing may be more effective to the occurrence of vortex disruption than the effect of short and strong wave forcing (e.g., Polvani & Waugh, 2004), it is independent to the important role of stratospheric modulation in triggering SFWs.We also note that those SFWs not preceded by TWE and SPVE are not unaffected by the stratospheric modulation and tropospheric anomalous wave forcing.Since we define events in terms of specific thresholds, it is just representative that the forcing on these events is not very strong.
These results have demonstrated the crucial role of preconditioned stratospheric state in the occurrence of wave-driven SFWs.It provides a possible help to further understand the nature of SFWs.Additionally, the predictability of SFWs and SSWs is limited to 3-4 weeks ahead due to factors such as the rapidity and uncertainty of upward wave activity from the troposphere (e.g., Butler et al., 2019;Rao et al., 2018Rao et al., , 2019)).The time scale of changes in stratospheric circulation is generally longer than that in the troposphere.The preconditioned stratospheric signal favoring the occurrence of SFWs often appears 30 days before the onset and can persist for more than 20 days.Such a long time-scale may effectively improve the prediction skill of SFWs.Thus, future studies on the predictability of SFWs and climate impacts could focus more on the role played by the preconditioned stratospheric signals.

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The modulation of preconditioned stratospheric state on stratospheric wave amplification is a key factor to trigger wave-driven stratospheric final warmings (SFWs) • More than half of SFWs is preceded by anomalously strong stratospheric signals • About 25% of SFWs are only preceded by robust stratospheric signals and without anomalously strong tropospheric wave forcing Supporting Information: Supporting Information may be found in the online version of this article.

Figure 1 .
Figure1.Composite time-height cross sections of 11-day running-mean standardized  z anomalies with wavenumber 1 + 2 for (a) early and (b) late stratospheric final warmings (SFWs).(c, e) Show the composites of early SFWs preceded and not preceded by tropospheric wave events, respectively.(d, f) Are as in (c, e), but for late SFWs.Lag = 0 denotes the onset date of SFWs.Thick and black lines highlight the area with a 95% confidence level according to the Student's t test.A horizontal gray line represents the approximate tropopause level (∼270 hPa; the same below).

Figure 2 .
Figure 2. Composite height-latitude cross sections of standardized anomalies of zonal-mean PV gradient for tropospheric wave events (TWEs) followed by (a) early, (b) late stratospheric final warmings (SFWs), and (c) no SFW.(d-f)Are as (a-c), but for the frequency of negative refractive index (Fn).Composites are taken averaged over −30 to 0 days.Thick and black lines in panels (a-f) highlight the area with a 95% confidence level according to the Student's t test.(g) Presents the composite evolutions of meridional PV index (   , the meridional mean value of   at 30 hPa between 55° and 75°N) for TWEs.Black and red lines in (g)-(i) denote those TWEs followed and not followed by SFWs, respectively.Lag = 0 denotes the onset date of TWEs.Thick lines highlight the stage with a 95% confidence level.Vertical gray lines in panel (g) denote the difference in the two series is significant at the 95% level.

Figure 3 .
Figure 3. Composite height-time cross sections of 11-day running-mean standardized  z anomalies with wavenumber 1 (left column) and wavenumber 2 (right column) for (a, b) early stratospheric final warmings (SFWs) preceded and(c, d) not preceded by SPVEs.(e-h) Are as (a-d), but for late SFW composites.Thick and black lines in panels (a-f) highlight the area with a 95% confidence level according to the Student's t test.Lag = 0 denotes the onset date of SFWs.

Table 1
The Statistics forEarly and Late Stratospheric Final Warmings Associated With Stratospheric Meridional PV Gradient Events and Tropospheric Wave Events