Sudden stratospheric warmings (SSWs) are an extreme weather event with impacts on the ionosphere and on tropospheric weather and predictability. The mechanisms governing their formation remain elusive, despite their deterministic predictability at nearly 2 weeks. This study uses high resolution CESM2 (WACCM6) subseasonal reforecasts to examine the dynamics that differentiate successful and unsuccessful SSW predictions. Successful reforecasts are generally initialized with a weaker stratospheric jet. However, the basic relationships between jet deceleration, wave drag, and the residual mean angular momentum flux do not fundamentally differ between successful and unsuccessful reforecasts. Instead, the projection of the residual circulation onto a weakened jet produces a weaker angular momentum flux, which leads to a more rapid erosion of the jet as the residual circulation cannot effectively balance the sustained wave drag. This information could be used to develop forecasting practices that could probe the likelihood of SSWs at longer timescales.

Key Points

In WACCM6, sudden stratospheric warming (SSW) prediction is improved when reforecasts are initialized with a weak stratospheric jet
A weaker jet reduces the angular momentum transport by the residual circulation, maintaining the dynamical cascade to a sudden warming
Simple forecasting practices could better initiate this feedback in WACCM6 and potentially improve SSW prediction

Plain Language Summary

Sudden stratospheric warmings (SSWs) are rapid breakdowns of the stratospheric polar vortex. The sudden change in winds eventually reaches the surface and creates predictable weather patterns, leading to improved weather forecasts. SSWs are driven by turbulently breaking atmospheric waves, sort of like waves breaking on a beach. By looking at forecasts of different SSWs over the past 20 years, this study shows that there is an important feedback that helps these breaking waves destroy the vortex. When the vortex weakens slightly due to breaking waves, the vortex becomes less efficient at rebuilding itself. If this happens frequently enough, it amplifies the effect of the waves and helps them destroy the vortex. It may be possible to encourage this feedback in weather forecasts to better determine the likelihood of a sudden warming occurring.

1 Introduction

A sudden stratospheric warming (SSW) is one of the most extreme weather events in the neutral atmosphere, with rapid increases in polar stratospheric temperatures in excess of 40 K (Schoeberl, 1978). This rapid warming is driven by a surge of poleward heat fluxes associated with upward-propagating planetary-scale Rossby waves which, in the case of a major SSW, destroy the westerly stratospheric vortex. SSW’s can have long-lasting impacts on tropospheric weather through downward coupling, which can lead to increased forecast accuracy and lead times (Domeisen et al., 2020; Hardiman et al., 2011; Karpechko et al., 2017). SSW impacts also extend upward into the mesosphere-lower thermosphere, impacting tides and ionospheric weather (Chau et al., 2012; Pedatella et al., 2012).

By virtue of their extreme nature they are rare, occurring approximately once every 2 years in the Northern Hemisphere and only once in the Southern Hemisphere over the observational record (Butler et al., 2017; Charlton & Polvani, 2007; Manney et al., 2005). In spite of this, they are deterministically predictable at nearly 2 weeks in models with a well-resolved stratosphere (Domeisen et al., 2019; Karpechko, 2018; Marshall & Scaife, 2010). However, the state of the troposphere does have substantial impacts on the development and timing of an SSW (Domeisen et al., 2019; Sun et al., 2012). Blocking episodes, in which the tropospheric zonal flow becomes locked into a high-amplitude ridging pattern, may generate the planetary-scale waves that drive some SSW’s (Martius et al., 2009).

For displacement-type SSW’s, Sun et al. (2012) show evidence of an eddy-mean flow feedback in the week before an SSW when the vortex is initialized to be weaker. As the vortex weakens it refocuses wave drag poleward and amplifies it through spherical geometry (Kanzawa, 1982; Sun et al., 2012). Coaxing the vortex to be weaker (or stronger) may impact the timing of this feedback. On the other hand, vortex preconditioning into a peanut shape may support the development of split-type events through resonance with otherwise unremarkable planetary wave activity (Albers & Birner, 2014).

Our conception of the mean flow contribution to SSW formation is therefore pared down to its impacts on wave propagation. While clearly important, it leaves out the role of the residual circulation in balancing nearly all of the wave drag associated with these events (Martineau et al., 2018). In this study we examine how the mean flow shapes the formation of SSW’s in subseasonal reforecasts in terms of the angular momentum flux by the residual circulation – analogous to the Eliassen-Palm (EP) psuedomomentum flux by Rossby waves. Our results reveal a more comprehensive role for the zonal wind in dictating both wave propagation and the efficiency with which the residual circulation can balance anomalous wave drag.

2 Model, Reanalysis, and Methods

All reforecasts are sourced from the CESM2 (WACCM6) subseasonal reforecast system. WACCM6 is run at 1° horizontal resolution with 70 vertical levels from the surface to approximately 140 km and includes comprehensive troposphere-stratosphere-mesosphere-lower-thermosphere chemistry (Gettelman et al., 2019), an interactive land model, and prescribed sea surface temperatures. Five-member reforecast ensembles are initialized every Monday from 1999 to 2019 and run for 45 days. Atmospheric initial conditions are seeded from 1980 to 2019 WACCM6 simulation with horizontal winds and temperatures nudged to the Modern-Era Retrospective Analysis 2 (MERRA2) reanalysis at a 1 h timescale. Prescribed sea surface temperatures are drawn from this simulation, which has an interactive ocean model reinitialized to JRA-55 (Kobayashi et al., 2015) every 5 years. A stand-alone land model forced by NCEP CFSv2 (Saha et al., 2014) is used to generate land initial conditions. The random field perturbation method is used to produce substantial but dynamically consistent variations in the initial state across ensemble members (Magnusson et al., 2009).

SSW’s are defined as in Charlton and Polvani (2007) as dates when the zonal mean westerly winds at 60°N and 10 hPa become easterly any time from November to March. For any subsequent warmings, we require that the zonal mean zonal wind recover to a westerly value at least as large as its most easterly value after the SSW.

Our analysis spans only the WACCM6 reforecasts initialized at any time in the 35 days before each SSW. We divide the reforecasts into two categories: successful reforecasts that predict an SSW within 7 days before or after its actual date (with an average 2.1 day offset), and unsuccessful reforecasts that do not. Composites for successful WACCM6 SSW reforecasts are assessed relative to the forecasted SSW date, while composites for unsuccessful WACCM6 SSW reforecasts are assessed relative to the actual SSW date in MERRA2.

All statistical significance is assessed at the 95% confidence level using two-sided Student’s t-tests. In figures displaying flux and divergence quantities, vectors are scaled as in Edmon et al. (1980), but are then scaled to be unit vectors or multiples of the unit vector. See individual figures for details.

3 Results

Throughout the analysis period the stratospheric jet is weaker in the successful reforecasts than it is in the unsuccessful reforecasts (Figures 1a–1e vs. 1f–1j). Twenty-four days before the SSW these differences are limited to the upper stratosphere/lower mesosphere (Figures 1a and 1f), but by 16 days before the SSW they shift down toward the tropopause (Figures 1b and 1g). In the successful reforecasts the winds at 60°N and 10 hPa are initialized statistically significantly weaker than in the unsuccessful reforecasts by 1, 2.5, and 1 m/s 21, 14, and 7 days before the SSW, respectively.

Details are in the caption following the image — **Figure 1**
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Composites of (shading, every 5 m/s) zonal mean zonal wind in the days preceding a sudden stratospheric warming (SSW), in WACCM6 reforecasts that are (top row) unsuccessful and (middle row) successful in producing an SSW, and (bottom row) in MERRA2. Hatching shows where differences between successful and unsuccessful WACCM6 composites are not statistically significantly different. The number of samples, N, is indicated in the titles.

There is a progressive deceleration of the stratospheric jet in both composites, but the jet stabilizes at 20 m/s up to the SSW date in the unsuccessful reforecasts. In MERRA2 the jet deceleration is consistently more rapid than in the successful WACCM6 reforecasts (Figures 1k–1o).

The momentum budget may shed some light on why there is disparate behavior among the reforecasts and between WACCM6 and MERRA2. We will examine the transformed Eulerian mean zonal momentum budget in flux-divergence form,

$urn:x-wiley:00948276:media:grl61927:grl61927-math-0001$ (1)

where u is the zonal wind, $urn:x-wiley:00948276:media:grl61927:grl61927-math-0002$ is the EP flux vector, $urn:x-wiley:00948276:media:grl61927:grl61927-math-0003$ is the transformed Eulerian mean residual circulation vector where [v*] and [ω*] are the residual meridional and vertical pressure velocities, here calculated in the conventional way via the streamfunction, M is the angular momentum per unit mass, a is the radius of the earth, ϕ is latitude, X includes nonconservative forces like friction, brackets indicate the zonal mean, and [N] is the net momentum flux vector given by

$urn:x-wiley:00948276:media:grl61927:grl61927-math-0004$ (2)

The angular momentum per unit mass is defined as

$urn:x-wiley:00948276:media:grl61927:grl61927-math-0005$ (3)

where Ω is the rotation rate of the earth. The EP flux is

$urn:x-wiley:00948276:media:grl61927:grl61927-math-0006$ (4)

where θ is the potential temperature, v is the meridional wind, ω is the vertical pressure velocity, primes denote deviations from the zonal mean, and subscripts denote derivatives. For steady linear solutions the EP flux corresponds to the Rossby wave group velocity, such that EP flux convergence corresponds to Rossby wave dissipation and drag on the mean flow by virtue of their intrinsic easterly phase speeds.

In this form of the momentum equation the Coriolis torque and the residual mean zonal momentum fluxes are absorbed into a single residual mean angular momentum flux. If we consider the transient case of Equation 1 in the absence of nonconservative forces, the residual mean angular momentum flux and the negative of the EP flux must form a seamless, nondivergent momentum flux to maintain the zonal mean zonal wind.

Sixteen days before the SSW there is significantly elevated wave drag (negative EP flux divergence) in the successful reforecasts between 10 and 50 hPa in the midlatitudes (Figures 2a and 2d; note the logarithmic scale). In MERRA2 the wave drag shifts from the upper to middle stratosphere in the final week before the SSW (Figures 2g–2i), with enhanced upward wave propagation from below. A poleward concentration of upward wave propagation between 100 and 0.1 hPa can be seen in the successful reforecasts (Figures 2e and 2f), but in the unsuccessful reforecasts the upward wave propagation weakens (Figures 2b and 2c).

There is also a significant increase in wave drag in a narrow band at 60°N in the mesosphere and upper stratosphere 8 days before the SSW in the successful reforecasts that presages the erosion of the upper edge of the jet (Figures 2e and 2f). Over the final week before the SSW the eroding poleward jet edge converges on the peak wave drag at 1 hPa (Figures 2e, 2f, 2h, and 2i), but in the unsuccessful reforecasts the wave drag and jet core remained locked (Figures 2b and 2c). Additionally, as the jet erodes from above the wave drag descends downward as vertically propagating waves become trapped at progressively lower altitudes (Figures 2d–2f).

In the successful reforecasts there is a significantly stronger residual mean angular momentum flux convergence between 10 and 50 hPa throughout the entire reforecast period, which opposes the enhanced wave drag (Figures 3d–3f). By Equation 1, the only way to balance the enhanced upward EP flux and divergence between 100 and 0.1 hPa (Figures 2e and 2f) without decelerating the jet is through an enhanced residual mean angular momentum flux and convergence over the entire layer. However, the increase in the residual mean angular momentum flux convergence is accomplished through stronger poleward transport in a narrow band at 1 hPa (Figures 3e and 3f). Aloft the residual mean angular momentum flux completely disappears and below it does not increase (Figure 3f), which necessarily leads to a deceleration of the jet (Figure 1j).

As the residual circulation is driven by waves, one has to ask why the residual circulation is unable to balance wave drag and prevent an SSW when the jet is weak, but able to balance wave drag and stave off an SSW when the jet is strong? The other component of the residual mean angular momentum flux is the angular momentum itself, which also differs substantially between the successful and unsuccessful forecasts (Figure 1).

To assess the particular dynamical structures associated with the deceleration of the jet we will regress the terms in the momentum equation onto the zonal mean zonal wind tendency at 60°N and 10 hPa. All regressions are performed using only the 7 days before the SSW to increase the signal-to-noise ratio and are multiplied by −86,400 to display patterns for a 1 m/s/day deceleration of the zonal mean zonal wind.

The EP flux divergence, residual mean angular momentum flux convergence, and net momentum tendency patterns are essentially the same in the successful and unsuccessful reforecasts (Figure 4). However, the magnitudes of the regression patterns are slightly larger in the successful reforecasts, which indicates that the wave drag is less efficient. For a given deceleration of the zonal mean zonal wind at 60°N and 10 hPa, then, there is not anything particularly unique about the momentum budget in the week before an SSW in either the successful or unsuccessful reforecasts. The response patterns are similar between WACCM6 and MERRA2, as well, so while the deceleration is more rapid in MERRA2, there is not any obvious pathology in WACCM6’s dynamics.

However, there is a weaker residual angular momentum flux across the poleward edge of the jet between 10 and 0.1 hPa in the successful reforecasts (Figure 4e). This is in spite of an enhanced residual mean and net momentum flux upstream from 10°N-30°N at 1 and 100 hPa (Figure 4f), characteristic of the hemispheric momentum adjustment to localized forcings (Abalos et al., 2014; de la Cámara et al., 2018; Dunkerton et al., 1981; Gómez-Escolar et al., 2014; Randel, 1993; Smith et al., 2020). The weaker residual mean angular momentum flux across the jet – and not a stronger EP flux – results in a broader region of net momentum divergence (Figures 4c and 4f).

In the unsuccessful reforecasts the wave drag, residual mean angular momentum flux, and net momentum tendency are locked on a strong jet core (Figures 4a–4c). However, in the successful reforecasts and in MERRA2 they occur on the poleward edge of a weakened and southward-shifted jet, from which there is less angular momentum to flux (Figures 4d–4i). How the residual circulation and wave dynamics project onto the jet may be the distinguishing factor governing SSW formation in these reforecasts, and not the actual residual circulation and wave dynamics themselves.

To demonstrate the kinematic effect of the difference in the jet strength, we will swap the zonal mean terms in the momentum budget between the successful and unsuccessful composites. For ease of analysis, we will focus on a polar cap average outlined by the box in Figure 4. For the “swapped mean” composites, we swap all incidences of the zonal mean angular momentum, [M], and potential temperature, [θ], from the opposing composite and recalculate the residual circulation, EP flux divergence, and residual mean angular momentum flux convergence. It is important to note that this kinematic analysis neglects feedbacks between wave propagation and the zonal mean zonal wind, and we emphasize this analysis uses the full composite fields – not the regressions.

In the unsuccessful reforecasts both the wave drag and residual mean angular momentum flux convergence remain low and in balance throughout the forecast period (Figure 5a). However, in the successful reforecasts they are elevated from 25 to 10 days before the SSW, with a slightly negative net tendency (Figure 5b). Ten days before the SSW the wave drag rapidly increases. The residual mean angular momentum flux convergence increases, but not as rapidly, resulting in a negative zonal wind tendency that amplifies with time. This mirrors the behavior seen in MERRA2, but at a much weaker magnitude (Figure 5c).

Using the zonal circulation from the unsuccessful reforecasts – equivalently, substituting a stronger jet – results in a much stronger residual mean angular momentum flux convergence in the successful reforecasts that more than offsets the ramp-up in the wave drag (Figure 5b), which also increases via the projection of the eddy heat flux onto the stronger angular momentum gradient. Swapping the zonal circulation from the successful forecasts into the unsuccessful forecasts leads to unremarkable changes (Figure 5a).

As an aside, quasigeostrophic scaling will not be sufficient to develop a comprehensive understanding of SSW dynamics as it neglects the critical importance of the zonal momentum component of the residual mean angular momentum flux (Figure 5b).

4 Discussion

For a given residual circulation, a weaker stratospheric jet reduces the residual mean angular momentum flux convergence through reduced stratospheric zonal momentum (Figure 3). As the jet weakens and the gradients in angular momentum erode, the efficiency with which the residual circulation can balance wave drag decreases – instantaneously. The resulting downward net momentum flux divergence out of the jet by Rossby waves is a consequence of insufficient poleward momentum transport by the residual circulation (Figures 4c, 4f, and 4i). Further, as the jet weakens, vertically propagating planetary waves become trapped at progressively lower altitudes, concentrating the wave drag (Figure 2). Reforecasts initialized with a weaker jet nudge the stratosphere toward this positive feedback cycle and erode the jet, while reforecasts initialized with a stronger jet delay the feedback cycle indefinitely (Figures 1 and 5).

There are a few issues that need to be addressed regarding the compositing of reforecasts initialized at different times relative to the SSW date. Most reforecasts are initialized during the compositing period, as can be inferred from the increasing N as forecasts approach the date of an SSW (Figure 1). By construction these initializations will pull the composites toward an SSW in the days before the event, but because the composite differences are so large and statistically significant, the initializations themselves apparently do not deviate much from the rest of the composite members. However, two out of three of the reforecasts initialized within a few days of an SSW remain unsuccessful in predicting an SSW (compare the N’s from Figures 1e and 1j). What seems most likely is that the random field perturbation method initializes most of the reforecasts with a jet stronger than can be decelerated by WACCM6 (compare the successful and MERRA2 rows in Figure 1), which shuts down the positive feedback cycle (Figure 5b).

The relevance of this process for the development of SSW’s versus its role in ensemble forecasting is unclear and should be addressed in future work. Idealized modeling experiments and reanalyzes show that a sustained elevation of wave activity is necessary for SSW’s (Newman & Rosenfield, 1997; Polvani & Waugh, 2004; Sjoberg & Birner, 2014), that they may even occur when the tropospheric wave forcing or variability is held constant (Christiansen, 1999; Scott & Polvani, 2006; Sjoberg & Birner, 2012), and that the stratospheric state mediates the resulting evolution of an SSW for given tropospheric variability (Cámara et al., 2017). It is possible that sustained wave forcing fundamentally weakens the hemispheric angular momentum gradient and hence the ability of the residual circulation to balance wave drag. SSW frequency is enhanced during the easterly phase of the quasi-biennial oscillation, when the hemispheric angular momentum gradient is weakened due to the easterly equatorial wind anomaly and strengthened stratospheric jet in the middle and upper stratosphere (Garfinkel et al., 2012; Holton & Tan, 1980; Rao et al., 2019). A reasonable perspective is that preconditioning of wave propagation and resonance (Albers & Birner, 2014), internal stratospheric amplification of wave activity (Birner & Albers, 2017; Cámara et al., 2019), and a weakening of the angular momentum gradient which weakens the efficiency of the residual circulation angular momentum flux could all work to stack the deck in favor of an SSW. A fixed-eddy-forcing framework could be a useful starting point for examining the relative importance of these different feedbacks (Davis & Birner, 2019; Kushner & Polvani, 2004; Sun et al., 2013).

More practically, across all reforecasts – not just those in proximity to an SSW – the WACCM6 member initialized with the weakest jet successfully predicts 44% more SSW’s than all other reforecasts within one week of the actual event, at a cost of 15% more false positives. For WACCM6, and potentially any other forecasting system with a weak jet-deceleration bias, initializing more ensemble members with a decelerated jet or even a particular jet structure could provide extended forecasting lead times for SSW’s and probe whether the stratosphere is conducive to initiating the positive feedbacks that lead to SSW’s.

Acknowledgments

The authors thank two anonymous reviewers for their constructive comments, and thank their colleagues A. K. Smith and W. P. Smith for comments on an earlier version of this manuscript. This work was supported by NOAA’s Weather Program Office/Climate Test Bed program, and by the National Center for Atmospheric Research, which is a major facility sponsored by the National Science Foundation under Cooperative Agreement 1852977. Portions of this study were supported by the Regional and Global Model Analysis (RGMA) component of the Earth and Environmental System Modeling Program of the U.S. Department of Energy’s Office of Biological & Environmental Research (BER) via National Science Foundation IA 1844590.

Open Research

Data Availability Statement

Computing and data storage resources, including the Cheyenne supercomputer (https://doi.org/10.5065/D6RX99HX), were provided by the Computational and Information Systems Laboratory (CISL) at NCAR. Raw model output necessary to repeat this analysis is available at http://doi.org/10.5281/zenodo.4420191. MERRA2 output is available from NASA’s Global Modeling and Assimilation office at https://gmao.gsfc.nasa.gov/reanalysis/MERRA-2/.

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Citing Literature

Volume48, Issue5

16 March 2021

e2020GL090863

A Positive Zonal Wind Feedback on Sudden Stratospheric Warming Development Revealed by CESM2 (WACCM6) Reforecasts

Abstract

Key Points

Plain Language Summary

1 Introduction

2 Model, Reanalysis, and Methods

3 Results

4 Discussion

Acknowledgments

Open Research

Data Availability Statement

References

Citing Literature

Figures

References

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A Positive Zonal Wind Feedback on Sudden Stratospheric Warming Development Revealed by CESM2 (WACCM6) Reforecasts

Abstract

Key Points

Plain Language Summary

1 Introduction

2 Model, Reanalysis, and Methods

3 Results

4 Discussion

Acknowledgments

Open Research

Data Availability Statement

References

Citing Literature

Figures

References

Related

Information

RESOURCES

PUBLICATION INFO