Major sudden stratospheric warmings (SSWs) are extreme wintertime circulation events of the Arctic stratosphere that are accompanied by a breakdown of the polar vortex and are considered an important source of predictability of tropospheric weather on subseasonal to seasonal timescales over the Northern Hemisphere midlatitudes and high latitudes. However, SSWs themselves are difficult to predict, with a predictability limit of around 1 to 2 weeks. The predictability limit for determining the type of event, i.e., wave-1 or wave-2 events, is even shorter. Here we analyze the dynamics of the vortex breakdown and look for early signs of the vortex deceleration process at lead times beyond the current predictability limit of SSWs. To this end, we employ a mode decomposition analysis to study the potential vorticity (PV) equation on the 850 K isentropic surface by decomposing each term in the PV equation using the empirical orthogonal functions of the PV. The first principal component (PC) is an indicator of the strength of the polar vortex and starts to increase from around 25 d before the onset of SSWs, indicating a deceleration of the polar vortex. A budget analysis based on the mode decomposition is then used to characterize the contribution of the linear and nonlinear PV advection terms to the rate of change (tendency) of the first PC. The linear PV advection term is the main contributor to the PC tendency at 25 to 15 d before the onset of SSW events for both wave-1 and wave-2 events. The nonlinear PV advection term becomes important between 15 and 1 d before the onset of wave-2 events, while the linear PV advection term continues to be the main contributor for wave-1 events. By linking the PV advection to the PV flux, we find that the linear PV flux is important for both types of SSWs from 25 to 15 d prior to the events but with different wave-2 spatial patterns, while the nonlinear PV flux displays a wave-3 wave pattern, which finally leads to a split of the polar vortex. Early signs of SSW events arise before the 1- to 2-week prediction limit currently observed in state-of-the-art prediction systems, while signs for the type of event arise at least 1 week before the event onset.

Major sudden stratospheric warmings (SSWs)

Even though the polar vortex undergoes deceleration and disruption during all major SSW events, there are large differences amongst SSW events in terms of their dynamical evolution, vortex structure, and downward impact on the troposphere. Based on the geometry of the polar vortex at the onset of the event, SSWs can be classified into two types: (1) vortex displacement events, when the vortex is shifted off the pole, and (2) vortex split events, when the vortex is split into two parts

Since the stratospheric circulation is well described by Ertel's potential vorticity (PV)

The onset of SSW events is associated not only with the anomalously large excitation of wave activity in the troposphere

The paper is organized as follows. Section 2 describes the data used in the analyses and the methodology behind the mode decomposition analysis. Section 3 shows the results of the analysis and their implications. Section 4 further provides the physical interpretation of the signals found in the mode equation budget by linking them with wave-mean flow interactions. Conclusions are given in Sect. 5.

We use two datasets for analysis in this paper: (1) the ERA-Interim reanalysis

For ERA-Interim, we use daily mean fields of potential vorticity (PV)

The first 10 EOF spatial patterns of PV at 850 K (

The PV data (for both the ERA-Interim reanalysis and the Isca model) are further decomposed into (1) the daily climatology, obtained by computing the daily mean values of PV over all available years, and (2) daily anomalies with respect to the climatological seasonal cycle. Given the limited number of years in the reanalysis, we also applied a 30 d running mean to the daily climatology to remove the high-frequency variability and repeat the analysis performed in the study. The results are almost identical to the ones using climatologies without low-pass filtering, which is mainly due to the fact that applying principal component analysis (PCA) acts as a filter and indicates the importance of the low-frequency components in the evolution of the polar vortex. In the following figures, we show the results using climatologies without low-pass filtering. The EOF modes of the PV and their corresponding PC time series (later used in the mode decomposition analysis) are obtained by employing PCA on the daily PV anomalies at 850 K. The procedure consists of applying PCA twice, as described in the following. We apply a first PCA only to the PV data around the onset date of all SSWs (from

The PC time series (

Following the methodology from

For the mode decomposition analysis of the PV equation, we focus only on the time frame between 50 and 1 d prior to the onset day of SSW events as the goal of this study is to identify signals that precede SSWs. We project the PV field (obtained by concatenating the data from

From the power spectrum of each PC time series

The major SSW definition follows the criterion of

Up to this point, our mode decomposition analysis does not employ any explicit approximation. In this section, we will demonstrate how

In order to provide a physical interpretation for each term in Eq. (

Using the concepts of PV flux and EP flux pseudo-divergence, we rewrite Eq. (

As shown in Fig.

Note that the sign of

The SSW composite of the

Figure

The contributions from each term are different between the composites of wave-1 vs. wave-2 events (Fig.

The relative importance of the linear and nonlinear advection terms for the two types of SSW events is similar to that of the stratospheric wave amplitude of the wavenumber 1 and 2 components for wave-1 and wave-2 SSW events as shown in

The comparison of the

In order to examine the significance in the differences and the robustness of the relative importance of the linear and nonlinear advection terms for the two types of SSW events, we perform bootstrapping on individual wave-1 and wave-2 events with replacement, respectively. We repeat the resampling

Given the limited number of SSW events in the reanalysis data and to further examine the characteristics and robustness of the linear and nonlinear term contributions to the vortex breakdown, we now apply the same analysis as for ERA-Interim to the output of the Isca model experiment. We use the methodology from Sect. 2 to extract the EOF modes (spatial patterns) and apply the mode decomposition analysis to the data concatenating 50 to 1 d prior to the 78 SSWs present in the model data. The EOF spatial patterns derived from the model output are similar to those derived from ERA-Interim, especially the first 10 EOF modes (Fig.

The composite of

Figure

In our analyses above, we found that the persistent positive values of

Composites of zonal-mean poleward PV flux averaged north of 45

As demonstrated in Sect. 2.4, the total linear and nonlinear advection terms in Eq. (

From Fig.

The spatial pattern of the linear PV flux for

The longitude–

Even though the spatial patterns of the linear PV flux in the two types of SSWs show a wave-2 pattern in the period of 20 to 10 d preceding the central day of SSWs, the locations of the maximum and minimum PV flux shift around 30

The spatial pattern of anomalies of PV and meridional wind after removing the daily climatology and zonal mean values

In this paper we employ a mode decomposition analysis to investigate the preconditioning of sudden stratospheric warming events. We study the (linear and nonlinear) terms in the potential vorticity equation by means of a budget analysis in order to identify the components in the first PC time series

Even though the contributions from linear and nonlinear PV advection terms are different in the two types of SSW events, their overall effects on

In both the ERA-Interim reanalysis and the simplified Isca model experiments, the increase in

As suggested by

Even though the increase in

Since the signals shown here indicate that most SSWs may be predictable on subseasonal timescales, it is important to understand which processes lead to the variability of the first EOF pattern and help to improve subseasonal forecast skill. A recent study by

In conclusion, our study finds signals that are representative of SSW events as early as 25 d preceding the events. This lead time is significantly longer than the current predictability limit of SSWs. We furthermore find that mode decomposition analysis can help infer wave-1 and wave-2 events at least 1 week ahead of the event, which is longer than the lead times identified in previous studies

In this appendix, we show the derivation procedure for obtaining the mode decomposition equation budget (Eq.

Given that

Here we show the justification for the choice of truncation at the 1000th EOF mode and the choice of low modes. The first 1000 modes together explain

In this appendix, we show the derivation for obtaining approximations of the linear and nonlinear terms (Eq.

In this appendix, we show the spatial patterns of the first 10 EOF modes of PV anomalies at 850 K and the associated first PC time series in the Isca model as described in Sect. 2.1. The first 10 modes together explain

The first 10 EOF modes of PV at 850 K (

The PC time series (

In this appendix, we show the

The composite of the

The Isca modeling framework was downloaded from the GitHub repository (

ZW performed the derivations and data analysis, made the figures, and wrote the first draft. BJE performed the Isca model computations. ZW and DIVD designed and supervised the study. All authors provided feedback for the manuscript and helped with discussions of the analysis.

The authors declare that they have no conflict of interest.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The work of Zheng Wu and Raphaël de Fondeville was funded by the Swiss Data Science Center within the project EXPECT (C18-08). Funding from the Swiss National Science Foundation to Bernat Jiménez-Esteve and Daniela I. V. Domeisen through project PP00P2_170523 is gratefully acknowledged. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement no. 847456). The authors would like to thank the two anonymous reviewers, John Albers, and the co-editor Thomas Birner for their helpful comments throughout the revision of the manuscript.

This research has been supported by the Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (grant no. PP00P2_170523), the Swiss Data Science Center (project no. C18-08), and the European Research Council (grant no. 847456).

This paper was edited by Thomas Birner and reviewed by two anonymous referees.