Precursory Analysis Ensemble Spread Signals That Foreshadow Stratospheric Sudden Warmings

Akira Yamazaki aApplication Laboratory, JAMSTEC, Yokohama, Japan

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Shunsuke Noguchi bDepartment of Earth and Planetary Sciences, Kyushu University, Fukuoka, Japan
cResearch Center for Environmental Modeling and Application, JAMSTEC, Yokohama, Japan

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Abstract

This study conducts a thorough investigation into the behaviors of analysis ensemble spreads linked to stratospheric sudden warming (SSW) events. A stratosphere-resolving ensemble data assimilation system is used here to document the evolution of analysis spread leading up to a pair of warming events. Precursory signals of the increased ensemble spreads were found a few days prior to two SSW events that occurred during December 2018 and August–September 2019 in the Northern and Southern Hemispheres, respectively. The signals appeared in the upper and middle stratosphere and did not appear at lower heights. When the signals appeared, it was found that both tendency by forecast and analysis increment in a forecast-analysis (data assimilation) cycle simultaneously became large. An empirical orthogonal function analysis showed that the dominant structures of the precursory signals were equivalent barotropic and were 90° out-of-phase with the analysis ensemble-mean field. Over the same period, the upper and middle stratosphere became more susceptible to barotropic instability than in their previous states. We conclude that the differing growth of barotropically unstable modes across ensemble members can amplify spread during the lead-up to SSW events.

Significance Statement

Winds in the winter stratospheric polar vortex are typically westerly. Occasionally, however, warming over the pole leads to a reversal of the flow through a process known as stratospheric sudden warming. These events are difficult to predict even in state-of-the-art analysis and forecasting systems. In this study, we identify a precursor signal in the form of increased ensemble spread that appears to originate from differing realizations of growing barotropic modes across the ensemble. This signal could serve as a useful forecasting tool by enhancing situational awareness in the lead-up to potential stratospheric sudden warming events.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Akira Yamazaki, yzaki@jamstec.go.jp

Abstract

This study conducts a thorough investigation into the behaviors of analysis ensemble spreads linked to stratospheric sudden warming (SSW) events. A stratosphere-resolving ensemble data assimilation system is used here to document the evolution of analysis spread leading up to a pair of warming events. Precursory signals of the increased ensemble spreads were found a few days prior to two SSW events that occurred during December 2018 and August–September 2019 in the Northern and Southern Hemispheres, respectively. The signals appeared in the upper and middle stratosphere and did not appear at lower heights. When the signals appeared, it was found that both tendency by forecast and analysis increment in a forecast-analysis (data assimilation) cycle simultaneously became large. An empirical orthogonal function analysis showed that the dominant structures of the precursory signals were equivalent barotropic and were 90° out-of-phase with the analysis ensemble-mean field. Over the same period, the upper and middle stratosphere became more susceptible to barotropic instability than in their previous states. We conclude that the differing growth of barotropically unstable modes across ensemble members can amplify spread during the lead-up to SSW events.

Significance Statement

Winds in the winter stratospheric polar vortex are typically westerly. Occasionally, however, warming over the pole leads to a reversal of the flow through a process known as stratospheric sudden warming. These events are difficult to predict even in state-of-the-art analysis and forecasting systems. In this study, we identify a precursor signal in the form of increased ensemble spread that appears to originate from differing realizations of growing barotropic modes across the ensemble. This signal could serve as a useful forecasting tool by enhancing situational awareness in the lead-up to potential stratospheric sudden warming events.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Akira Yamazaki, yzaki@jamstec.go.jp

1. Introduction

Stratospheric sudden warming (SSW) is a phenomenon characterized by occasional reversals of westerly winds within the winter stratospheric polar vortex, accompanied by temperature warming over the pole (Baldwin et al. 2021). In the polar cap region, the appearance of easterlies in the upper to middle stratosphere prevents the propagation of planetary waves originating from the midlatitude troposphere. Consequently, this nonpropagation results in the absorption and/or reflection of incoming planetary waves (e.g., Kodera et al. 2008; Mukougawa et al. 2017), which often exert influences on tropospheric circulations. Therefore, SSW events can substantially impact the general circulation in both the stratosphere and the troposphere (e.g., Baldwin and Dunkerton 2001).

Predicting SSWs remains a challenge even in state-of-the-art forecasting systems. Recent advancements in modeling techniques have significantly contributed to reducing forecast errors that hinder accurate SSW prediction (e.g., Domeisen et al. 2020). However, relatively less attention has been devoted to errors in the forecast initial values. These errors can be effectively represented through ensembles of the analysis fields.

The ensemble Kalman filter (EnKF) enables easy generation of ensemble perturbations without necessitating additional procedures such as the breeding of growing modes or singular vector methods (Houtekamer and Zhang 2016; Saito et al. 2022). Understanding the characteristics of these generated perturbations holds paramount importance in improving the accuracy of the analysis fields, which are subsequently updated in forecast and data assimilation cycles. Furthermore, EnKF systems facilitate the straightforward acquisition of time series of the analysis errors, as the magnitudes of ensemble perturbations, i.e., the analysis ensemble spread, directly reflect the magnitude of the analysis error (e.g., Saito et al. 2022). Consequently, in addition to the analysis ensemble mean, the analysis ensemble spread can also be standard outputs in the EnKF system. As explained in section 2, an experimental ensemble reanalysis, ALERA, has been generated using a local ensemble transform Kalman filter–based data assimilation system called ALEDAS.

Accompanied by the uncertainty fluctuations of weather phenomena, the ensemble spread analysis varies with time. In such cases, a temporal amplification of the spread corresponds to an initial stage of the possible occurrence of a phenomenon, which facilitates the divergence of the ensemble forecasts subsequently. The temporal amplification and subsequent divergence can arise even if a numerical forecast model captures the occurrence. Therefore, detecting temporal spread amplifications before the occurrence of a phenomenon could be useful as an early warning signal of its occurrence.

In the time sequences of the analysis error, precursory signals for critical transitions exist, in which the system shifts abruptly from one state to another. Scheffer et al. (2009) introduced precursory (early warning) signals for the critical transitions occurring in complex dynamical systems, ranging from ecosystems to financial markets and climate. Then, they reviewed several dynamical system theories and showed examples of precursory critical transition signals. Consequently, they concluded that generic signals exist as an increase in error variance before the transition (Ives 1995); the variance should correspond to the ensemble spread. An example of a precursory signal in the Earth system is demonstrated by an increase in variance prior to the “greenhouse–icehouse transition” in the past climate (Dakos et al. 2008). Similarly, in the Lorenz (1963) system, Evans et al. (2004) and Lynch et al. (2016) identified a precursory signal in the form of high growth rates of bred vectors, indicating a potential regime transition upon the completion of the current orbit. These findings encourage us to explore precursory spread signals for various weather phenomena.

Since the SSW phenomenon is a notable candidate that occurs via critical transitions and can have precursory signals, previous studies have often interpreted SSW events as equilibrium states following rapid transitions from the climatological winter stratospheric conditions (e.g., Chao 1985; Yoden et al. 2002). In a study by Enomoto et al. (2010), the time evolution of the analysis ensemble spread associated with various tropospheric and stratospheric phenomena was investigated using the previous version of ALERA (Miyoshi et al. 2007). Specifically, for the Northern Hemisphere (NH)-SSW event of January 2006, the temporal variation of the analysis ensemble spread in the temperature field at 10 hPa (middle stratosphere) was examined. A precursory signal was identified in the analysis ensemble spread, wherein the stratospheric ensemble spread over the NH polar cap region amplified approximately 5 days before the SSW onset, subsiding after the occurrence of the SSW. This increase in analysis ensemble spread was found in the Eliassen–Palm flux field as well, with the analysis spread distribution of the Eliassen–Palm flux displaying a maximum distribution over the Arctic region around 10 hPa at the same timing. Enomoto et al. (2010) is a novel study, which discovered how the analysis spread field responds to atmospheric general circulation variability in the real analysis ensemble-mean field, such as during an SSW event.

Nonetheless, Enomoto et al. (2010) utilized the previous version of ALEDAS, which had a model top of ∼3 hPa and did not sufficiently resolve the upper stratosphere. Moreover, the study focused solely on a single SSW event in the NH, without providing a detailed distribution of the analysis ensemble spread other than at 10 hPa especially in the upper stratosphere, or examining the time evolution of horizontal and vertical distributions of the analysis ensemble spread, and the relationship between the analysis and background ensemble spreads. Thus, this study aims to conduct two additional case studies of SSWs using the updated version of ALEDAS, which can adequately resolve the upper stratosphere. Furthermore, we will explore additional characteristics of the analysis ensemble spread fields, such as the vertical structure and horizontal distribution.

One of the motivations for this study stems from the scarcity of reports addressing the reproducibility of SSWs in EnKF systems. Butler et al. (2017) conducted a comparison of the reproducibility of SSWs across representative atmospheric reanalyses, including ERA-Interim (Dee et al. 2011), JRA-55 (Kobayashi et al. 2015), NCEP–NCAR (Kalnay et al. 1996), and NOAA20CR (Compo et al. 2011). The findings revealed that NOAA20CR inadequately reproduces SSWs because that reanalysis system only assimilates ground-level observations (i.e., surface input). Fujiwara et al. (2022, chapter 6) recommend that the most recent reanalyses are utilized for the SSW studies and to avoid older data assimilation systems and lower model tops, as these tend to be less effective in reproducing SSWs compared to modern reanalyses. Existing comparisons of SSW reanalyses are based on their model tops and whether the systems assimilate observations in the free atmosphere (i.e., full input) or are based on surface-level data (surface input). However, no comparisons have been performed regarding the data assimilation methods, whether they are EnKF or variational. Among the compared reanalyses, the only EnKF system was NOAA20CR, leaving the reproducibility of SSWs in the EnKF system with full input largely unexplored in the literature. In the present study, we employ ALEDAS, which utilizes the local ensemble transform Kalman filter (an EnKF) as a full input technique. The local ensemble transform Kalman filter has gained increasing popularity among operational centers for generating ensembles (e.g., Houtekamer and Zhang 2016). As such, the research described in this study offers novel insights into the application of the local ensemble transform Kalman filter in ensemble weather and seasonal forecasting.

This paper is structured as follows. In sections 2 and 3, we provide an overview of ALEDAS and ALERA, along with an assessment of the reproducibility of NH- and Southern Hemisphere (SH)-SSWs in the system. The examination of the time evolution of the analysis ensemble spread fields is presented in section 4. Section 5 delves into whether the time evolution of the analysis ensemble spread can effectively contribute to updating the analysis ensemble-mean fields for the SSWs. Last, in section 6, we discuss the dynamical basis of the analysis ensemble spread. The present findings and conclusions are summarized in section 7.

2. Data

An experimental ensemble reanalysis, ALERA, is generated by the Atmospheric General Circulation Model for the Earth Simulator and the local ensemble transform Kalman filter data assimilation system (ALEDAS). The ALEDAS consists of an atmospheric general circulation model and an EnKF. The ALEDAS, fed by the Atmospheric General Circulation Model for the Earth Simulator, features a horizontal resolution of approximately 100 km (T119), 56 vertical layers (L56), and a model top located at approximately 0.1 hPa. The ocean boundary conditions are supplied using the 1/4° Daily Optimum Interpolation Sea Surface Temperature (Reynolds et al. 2007). To account for gravity wave drag, we have implemented a nonorographic gravity wave drag scheme (Scinocca 2003; Orr et al. 2010; Baba 2019), in addition to an orographic one (McFarlane 1987). Other parameterization schemes such as convective or radiation processes remain consistent with the previous ALEDAS (Enomoto et al. 2013). Although Enomoto et al. (2010) reported that the previous version of ALEDAS successfully reproduced an SSW event in the NH, it remains unclear whether the updated ALEDAS can replicate an SSW in the upper stratosphere (∼1 hPa) and an SSW occurrence in the SH. The number of ensemble members is set at 63. Observations are localized horizontally at 400 km and vertically at 0.4 lnp (same as Yamazaki et al. 2017). A spatially uniform 10% multiplicative inflation method is employed for the covariance inflation (Enomoto et al. 2013; Yamazaki et al. 2021). The observations to be assimilated are PrepBUFR conventional observations, satellite wind observations, and 6–8 channels of the Advanced Microwave Sounding Unit-A (AMSU-A) satellite radiances. For the AMSU-A assimilation, we have implemented the satellite radiance assimilation scheme (Yamazaki et al. 2023). In summary, ALEDAS demonstrates the capability to resolve the stratosphere and moderately observe the lower stratosphere. However, only radiosondes can directly observe the middle stratosphere where an SSW occurs [not discussed, but based on the ensemble-based forecast sensitivity observations results from Yamazaki et al. (2023)]. The differences between the current and previous versions of ALEDAS lie in three aspects: 1) an increase in the model top height, 2) the implementation of a nonorographic gravity wave drag scheme, and 3) the assimilation of AMSU-A satellite radiances (Yamazaki et al. 2023). Utilizing this updated system, we have generated ALERA datasets since November 2018.

Here, the analysis and background ensemble spreads at analysis time t are denoted as σa(t) and σb(t), respectively, and the analysis and background ensemble means are denoted as x¯a(t) and x¯b(t), respectively. Note that the behavior of σb(t) was not discussed in Enomoto et al. (2010). The analysis and background ensemble perturbations are denoted as δXa(t) and δXb(t), with their magnitudes corresponding to σa(t) and σb(t), respectively. Furthermore, the subscripts in σa(t), σb(t), x¯a(t),x¯b(t),δXa(t), and δXb(t) indicate the variables of these values: temperature is T, geopotential height is Z, and the upward Eliassen–Palm flux is Fz. For example, σTa(t) indicates the analysis ensemble spread of temperature.

3. Two SSW events in ALERA

During the period of ALERA monitoring, two SSW events occurred, one in the NH and another in the SH. The NH-SSW event occurred from late November 2018 to January 2019 (Butler et al. 2020), while the SH-SSW occurred in early September 2019 (Noguchi et al. 2020; Lim et al. 2021). SSW events have been rare in the SH, although the SH-SSW was a minor warming. We use the ALERA periods from 1 December 2018 to 31 January 2019 and from 1 August 2019 to 30 September 2019.

The reproducibilities of the NH-SSW and SH-SSW events are depicted in Fig. 1. ALERA reproduced the SSW onsets, which were consistent with other global reanalyses. In addition, the temporal variations in the zonal and easterly winds in the middle stratosphere (Figs. 1a,c) were in good agreement with other reanalyses, capturing well formation of easterly winds during the NH-SSW and the weakening of westerly winds during the SH-SSW. Similarly, temporal variations in temperature (Figs. 1b,d) are well reproduced concerning the timing of temperature increase and subsequent evolution, although the onsets in ALERA are slightly delayed by 1 or 2 days compared to other reanalyses; this holds true for the wind field, reflecting dynamical balance. Notably, certain differences existed between ALERA and other reanalyses regarding warm temperature biases in the stratosphere before the onset of the SSWs. Despite these temperature biases and slight delays in the SSW onsets, ALERA adequately reproduced the NH-SSW and SH-SSW events, enabling a discussion of the precursory signals of ensemble spreads.

Fig. 1.
Fig. 1.

Time series of 10-hPa (a),(b) NH (65°–90°N) and (c),(d) SH (65°–90°S) polar cap (top) zonal wind (m s−1) and (bottom) temperature (K) for the NH-SSW event in (a) and (b) and SH-SSW event in (c) and (d) in ALERA (black solid lines), NCEP–NCAR (magenta, long dashed), ERA5 (cyan, short dashed; Hersbach et al. 2020), and JRA-55 (gray solid).

Citation: Monthly Weather Review 151, 12; 10.1175/MWR-D-22-0169.1

4. Time evolution and distribution of the analysis ensemble spread

The present study focused on identifying the altitudes from which the spread signals for the NH-SSW and SH-SSW originate. Enomoto et al. (2010) previously showed that the precursory amplification signal of σTa(t) at 10 hPa (in the middle stratosphere) was attributed to the spread signal of Eliassen–Palm flux convergence originating from the tropopause. Further investigation by Nishii and Nakamura (2010) regarding the same SSW event concluded that the spread signal can stem from tropospheric blocking over the Atlantic and, subsequently, from an extratropical cyclone upstream of the block.

To investigate these origins, we initially define the latitudinal bands over which the spread is calculated (later in Fig. 3), based on the latitudes of the maximum upward Eliassen–Palm flux (in Fig. 2) at each altitude, excluding 10 hPa, during the occurrence of the NH-SSW and the SH-SSW. Figure 2 illustrates the distribution of x¯Fza(t), which represents the “real” atmospheric condition of upward Eliassen–Palm fluxes Fz [mass-weighted isentropic zonal-mean formulation (MIM); e.g., Iwasaki and Mochizuki 2012] from the upper troposphere (300 hPa) to the middle stratosphere (10 hPa). Generally, Eliassen–Palm fluxes originate in the storm-track region of the upper troposphere and propagate upward and equatorward toward the upper stratosphere. However, during the SSW occurrence, the fluxes exhibit a poleward direction, as shown in Fig. 2. Consequently, above 30 hPa, the flux convergences increased substantially (not shown), a phenomenon associated with the westerly wind deceleration resulting from incoming planetary waves associated with the SSWs.

Fig. 2.
Fig. 2.

Distributions of x¯Fza(t) (upward Eliassen–Palm flux in the analysis ensemble-mean fields; black line; 105 kg s−2) from 300 to 10 hPa (from the bottom, shown are 300, 100, 50, 30, and 10 hPa). (a) December 2018–January 2019 and (b) August–September 2019 averages. The red dotted boxes indicate the latitudinal bands for the calculation of the time series of σa(t) and σb(t) at each pressure level for the NH-SSW event in (a) and SH-SSW event in (b) in Fig. 3.

Citation: Monthly Weather Review 151, 12; 10.1175/MWR-D-22-0169.1

To investigate the altitude at which the amplification of σa(t) commences, we define latitudinal bands based on the dominant upward Eliassen–Palm fluxes at each altitude, using 20° intervals below 30 hPa. At 10 hPa, the latitudinal bands are broadly defined as 50°–90°N for the NH-SSW and 50°–90°S for the SH-SSW, respectively, to encompass the polar cap regions. Subsequently, we examine the time series of σa(t) and σb(t) averaged over these latitudinal bands.

Initially, we review the time series of the NH-SSW event. Figure 3 presents the time series of σFza(t) from the upper troposphere to the middle stratosphere and σTb(t) at 10 hPa.

Fig. 3.
Fig. 3.

Time series of zonal-mean σTa(t) and σFza(t) (black solid line) and σTb(t) and σFzb(t) (gray line) averaged over the latitudinal bands defined in Fig. 2 (dotted boxes) from 300 to 10 hPa (from the bottom to the second row: 300, 100, 50, 30, and 10 hPa, respectively) for the (a) NH-SSW and (b) SH-SSW. The second row displays the time series of σTa(t) and σTb(t) (K) at 10 hPa and the third row to the bottom portray those of σFza(t) and σFzb(t) (105 kg s−2) below 30 hPa. Only the uppermost panels illustrate the time series of zonal-mean x¯Ta(t) (K) at 10 hPa averaged over the 65°–90°N latitudinal band in (a) and 65°–90°S latitudinal band in (b). Vertical dotted lines are drawn at the dates when the 10-hPa σTa(t) signal peaks on 27 Dec in (a) and 31 Aug in (b).

Citation: Monthly Weather Review 151, 12; 10.1175/MWR-D-22-0169.1

From Fig. 3a, the precursory amplification emerges in the σTa(t) time series at 10 hPa as previously found in Enomoto et al. (2010). This amplification reaches its peak around 27 December and is notably larger over the 2-month time frame. In x¯Ta(t), the 10-hPa analysis temperature increase occurs on 30 December, indicating that the precursory amplification appears approximately 3 days ahead of this date. A similar peak is seen for σFza(t) at 30 hPa, occurring around 24 December. Note that the peak of σTa(t) at 10 hPa shifted to around 24 December when the averaged latitudinal band of the box in Fig. 2 is shifted toward midlatitudes (supplemental material). This suggests that the peak of σTa(t) at 10 hPa and that of σFza(t) at 30 hPa are indicative of the same amplification process. However, these peaks just before the NH-SSW onset are not evident at lower altitudes below 50 hPa. Figure 3a and Fig. S1a (in the online supplemental material) demonstrate that the time series of σa(t) and σb(t) are almost identical, particularly in the stratosphere, with the precursory signal appearing in both σa(t) and σb(t). Moreover, the spread signal at the middle stratosphere appears irrespective of the variables focused on (supplemental material).

Regarding the SH-SSW, a stratospheric signal is found as a more gradual (slower) peak in σTa(t) at 10 hPa and σFza(t) at 30 hPa, spanning about 2 weeks around 31 August, in contrast to the NH-SSW event. The initial warming (onset) of the SH-SSW occurred on 2 September (Fig. 3), approximately 2 days after the spread peak on 31 August. Similar to the NH-SSW event, the stratospheric peak of the SH-SSW became less distinct at lower altitudes and was nearly absent at 300 hPa (upper troposphere) on 31 August. Another spread signal (peak) was identified around the upper troposphere on 26 August. This tropospheric signal extends up to around 30 hPa and appears at 10 hPa only in the midlatitudes (Figs. S2g,h), but it does not correspond to the stratospheric peak around 31 August. Thus, the stratospheric signal, just before the initial temperature increase (the SH-SSW onset), is inherent to the stratosphere, similar to the NH-SSW signal. Interestingly, following the discovery of the tropospheric signal was found, a blocking anticyclone occurred over the southeastern Pacific during the period from 1 to 5 September. As with the NH-SSW, the time series of σa(t) and σb(t) exhibited almost identical behavior in the stratospheric interior (Fig. S1b).

In summary, the precursory amplification spread signals preceding the SSWs were found in both hemispheres. These signals are prominent in the middle stratosphere but not below the lower stratosphere, suggesting that the precursory signals are associated with stratospheric interior dynamics.

Figure 4 displays daily snapshots of the σZa(t) patterns at 10 hPa for the NH-SSW before and after the peak time of the σTa(t) spread signal. During the NH-SSW onset, the Aleutian high pushes and displaces the polar vortex, resulting in local amplification of σZa(t) between the polar vortex and the high (Figs. 4d–h). This amplification occurs where the geopotential height gradient and tendency of x¯Za(t) are large. As the large σZa(t) is distributed between the Aleutian high and the displaced polar vortex, the signal peaks in Fig. 3a and Figs. S2ad move from lower to higher latitudes. The local σZa(t) distribution reaches its maximum amplitude on 27 December (Fig. 4f), that is, the peak date of the spread signal; thus, this distribution is an aspect of the precursory spread signal.

Fig. 4.
Fig. 4.

Time evolution of the σZa(t) (shading) and x¯Za(t) (contours; contour interval 200 m) at 10 hPa (m) for the NH-SSW onset period. In alphabetical order, snapshot fields are displayed (a)–(j) every day, from 0000 UTC 22 Dec 2018 in (a) to 0000 UTC 31 Dec 2018 in (j). The snapshot in (f) at the σTa(t) peak time (Fig. 3a) is framed in red. The polar vortex and Aleutian high are denoted by “L” and “H,” respectively.

Citation: Monthly Weather Review 151, 12; 10.1175/MWR-D-22-0169.1

We investigate the time evolution of the vertical structure of σZa(t) snapshots of longitude–height cross sections averaged at latitudes 60°–80°N (Fig. 5). Until 24 December (Fig. 5c), the geopotential height field of x¯Za(t) demonstrated a westward tilted structure up to the upper stratosphere (1 hPa), revealing an upward propagation of planetary waves. σZa(t) was large between the stratospheric trough (low pressure anomaly) and the ridge (high pressure anomaly) and was dominant in the upper stratosphere (1–5 hPa). σZa(t) was amplified inside the ridge in the upper stratosphere after 25 December (Fig. 5d). The σZa(t) distribution and the ridge demonstrated a barotropic structure in the upper stratosphere. The subsequent σZa(t) distribution became dominant at the eastern and western fringes of the ridge (Figs. 5e,f). The σZa(t) then gradually decreased (Figs. 5g,h); however, the structure was quasi-stationary and was maintained until 30 December (Fig. 5i). Moreover, the ridge in x¯Za(t) was quasi-stationary and almost maintained a barotropic structure during the NH-SSW onset (Figs. 5d–i), with the amplitude maximum moving downward. The time evolution of the vertical σZa(t) structure indicates that the precursory signal originates in the upper stratosphere.

Fig. 5.
Fig. 5.

Longitude–height cross sections (60°–80°N meridional mean) of σZa(t) (m) (shaded) and the deviation of x¯Za(t) (m) from the zonal-mean x¯Za(t) (contours) at the same time as in Fig. 4. The panel framed in red is the same as that in Fig. 4.

Citation: Monthly Weather Review 151, 12; 10.1175/MWR-D-22-0169.1

Similar data for the SH-SSW are shown in Figs. 6 and 7. For the SH-SSW event, the snapshot interval was set to every 2 days because the spread signal amplifies more slowly than in the NH (Fig. 3 and Fig. S2). At 10 hPa, a region of large σZa(t) appeared at the fringe of the polar vortex where the midlatitude high pressure system south of Australia was adjacent, and σZa(t) amplified from a date about 10 days before the spread signal reached its maximum (Figs. 6a–f). As a broader σZa(t) was distributed in the fringe of the polar vortex than that in the NH-SSW, a shift of the signal peak from the lower to the higher latitudes was not found (Fig. 3b and Figs. S2eh).

Fig. 6.
Fig. 6.

As in Fig. 4, but for the SH-SSW event. (a)–(j) Snapshots for every 2 days from 0000 UTC 21 Aug 2019 in (a) to 0000 UTC 8 Sep 2019 in (j) in alphabetical order. The contour interval of x¯Za(t) is 200 m. The snapshot in (f) at the σTa(t) peak time (Fig. 3b) is framed in red. The polar vortex and midlatitude high are denoted by an “L” and “H,” respectively.

Citation: Monthly Weather Review 151, 12; 10.1175/MWR-D-22-0169.1

Fig. 7.
Fig. 7.

As in Fig. 5, but for the SH-SSW event. The σZa(t) and x¯Za(t) fields are meridionally averaged within 50°–80°S. The displayed dates and the panel framed in red are as in Fig. 6.

Citation: Monthly Weather Review 151, 12; 10.1175/MWR-D-22-0169.1

Regarding the vertical structure, σZa(t) and the ridge in the SH-SSW exhibited similar behavior to the NH-SSW before reaching the maximum of the spread signal (Figs. 7a–f). An initial amplification of σZa(t) occurred in the upper stratosphere between the ridge and the trough (Figs. 7a–c). On 27 August, σZa(t) increased inside the ridge (Fig. 7d), which occurred 4 days before the date of the maximum spread signal. Subsequently, the increased σZa(t) shifted its local maximum to the fringes of the ridge in x¯Za(t), and both σZa(t) and the ridge began to exhibit a barotropic structure below the middle stratosphere (10 hPa, Fig. 7e). Around the peak date (31 August, Fig. 7f), both σZa(t) and the ridge remained quasi-stationary. By around 6 September (Fig. 7i), when the SH-SSW began to develop, the ridge again transformed into a westward tilted structure, and the σZa(t) structure gradually began to decay.

In conclusion, the precursory analysis ensemble spread signals before the NH-SSW and SH-SSW onsets have been detected. Furthermore, the time evolution of the σZa(t) structures indicates that the precursory spread signals are generated by processes in the stratosphere rather than originating in the troposphere.

Subsequently, we examined the atmospheric condition of x¯a(t) when the precursory signals appeared. Figure 8 illustrates the time series of zonal-mean x¯Fza(t) fields from the upper troposphere to the middle stratosphere, averaged over the same latitudinal bands for the spreads (Fig. 3), where the “real” atmospheric condition is depicted by x¯a(t).

Fig. 8.
Fig. 8.

As in Fig. 3, but for zonal-mean x¯Fza(t) averaged over the latitudinal bands defined in Fig. 2 (dotted boxes) from 300 to 10 hPa (from the bottom to the top: 300, 100, 50, 30, and 10 hPa, respectively). Vertical dotted lines are drawn at the spread signal peak dates in Fig. 3.

Citation: Monthly Weather Review 151, 12; 10.1175/MWR-D-22-0169.1

For the NH-SSW, a clear pulse of upward Eliassen–Palm flux from the lower stratosphere (around 24 December) to the middle stratosphere (around 27 December) was found. This enhanced upward propagation of the Eliassen–Palm flux before the SSW onset is consistent with well-known SSW mechanisms (Matsuno 1971; Andrews and McIntyre 1976). The spread signal in the middle stratosphere was accompanied by this Eliassen–Palm flux pulse (Fig. 3a). For the SH-SSW, we found a similar but more gradual evolution of an enhanced upward Eliassen–Palm flux, characterized by three distinct flux pulses, except for the one around 19 September (Fig. 3b). Thus, the precursory spread signals emerged when the enhanced upward x¯Fza(t) Eliassen–Palm flux entered the stratosphere, originating from the troposphere. However, these spread signals were detected in the stratospheric interior. Furthermore, Fig. 8 demonstrates that as the upward Eliassen–Palm flux for the SH-SSW evolved more gradually than that for the NH-SSW, the precursory spread signal for the SH-SSW became longer than that for the NH-SSW, and the rise in the SH-SSW temperature progressed more gradually (Fig. 3b).

5. Possible contributions of the spread signals on analysis updates

We begin to discuss how the ensemble spread fields σa(t) and σb(t) can contribute to the update of x¯a(t). The update of the analysis field at time t − 6 → t (1 cycle) is
x¯a(t)x¯a(t6),
where the assimilation window is 6 h. This update can be decomposed as follows: one is the update or tendency owing to the forecast:
x¯b(t)x¯a(t6),
and the other is the update by the analysis (analysis increment):
x¯a(t)x¯b(t).

The NH-SSW event is examined. The spatial patterns of the forecast update as x¯Zb(t)x¯Za(t6) [Eq. (2)] and σZa(t6) are displayed in Fig. 9. Comparison with Fig. 4 indicates that σZa(t6) (the contours in Fig. 9), one data assimilation cycle prior, has almost the same pattern as σZa(t) (shades in Fig. 4). Locally large σZa(t6) or σZa(t) around the date of the spread signal corresponds to the local maximum of the positive forecast update (Figs. 9c–h): this is because of the large positive geopotential height tendency where the polar vortex is displaced by the Aleutian high.

Fig. 9.
Fig. 9.

Snapshots of the forecast update x¯Zb(t)x¯Za(t6) (m; shading) and σZa(t6) (m; contours; contour interval 30 m) at 10 hPa during the NH-SSW onset for the same dates in Fig. 4. The panel framed in red is the same as in Fig. 4.

Citation: Monthly Weather Review 151, 12; 10.1175/MWR-D-22-0169.1

The horizontal distributions of the analysis increment as x¯Za(t)x¯Zb(t) [Eq. (3)] and σZb(t) are exhibited in Fig. 10. Comparison with Figs. 9 and 10 displays that the spread distributions [σZa(t6) and σZb(t)] correspond well before and after the forecast update; the spread fields apparently intensified while maintaining their distributions during each forecast of the data assimilation cycles. From Figs. 3, 4, and 10, σZa(t6),σZb(t), and σZa(t) behaved almost identically in the daily time scale during the SSW onsets, indicating that the precursory signals do not change within the short time scale of the forecast update and analysis increment (6 h). Moreover, we found that the analysis increment becomes locally large, where the σZb(t) distribution presides over a local maximum.

Fig. 10.
Fig. 10.

As in Fig. 9, but for the analysis increment x¯Za(t)x¯Zb(t) (m; shading) and σZa(t) (m; contours; the contour interval is 30 m).

Citation: Monthly Weather Review 151, 12; 10.1175/MWR-D-22-0169.1

For this SH-SSW event (Figs. S3 and S4), we found features similar to the NH-SSW: local maximum distributions in σZa(t6),σZb(t), and σZa(t), corresponding to regions and timings where a large positive geopotential height tendency appears due to the forecast update (Fig. S3). At the same locations and times, the analysis increment becomes substantial (Fig. S4). Owing to the more gradual decay of the spread signal in the SH-SSW event than in the NH-SSW event (Fig. 3), the forecast and analysis updates persisted for a longer time after the peak date.

As depicted in Figs. 9 and 10 and Figs. S3 and S4, the forecast update and the analysis increment coincide with the precursory spread signals, contributing to the onsets of the SSWs. Here, we examine which update is associated with the spread signals. For the NH-SSW event, Figs. 11a–c illustrate the time series of zonal-mean σTa(t) and σTb(t), the forecast update x¯Tb(t)x¯Ta(t6), and the analysis increment x¯Ta(t)x¯Tb(t) averaged over the NH polar cap region (65°–90°N). As σTa(t) and σTb(t) start to increase toward the spread peak signal, the forecast update simultaneously rises, contributing to the NH-SSW onset. Although the analysis increment increased along with the spread peak signal, this increment was delayed compared to the spread peak. Additionally, the forecast update exhibited a higher rise in temperature than the analysis increment. For the SH-SSW (Figs. 11e–g), the forecast update started to increase with the initiation of the spread signal (around 25 August 2019), while the analysis increment delayed increasing weakly, similar to the NH-SSW. Thus, the precursory signals are more closely related to the forecast update or the forecast model component in ALERA than to the data assimilation component (analysis increment). These results would encourage us to observe adaptively the locations where precursory spread signals appear; moreover, this could considerably contribute to the beneficial observation impacts for reproducing and possibly forecasting SSWs.

Fig. 11.
Fig. 11.

Time series of various zonal-mean temperature properties at 10 hPa for the (left) NH-SSW (averaged over 65°–90°N) and (right) SH-SSW (65°–90°S) events. Time series of (a),(e) σZa(t) (black solid) and σTb(t) (gray dashed) (K); (b),(f) the forecast update x¯Tb(t)x¯Ta(t6) (black lines) with its ±1.0 absolute values (gray bars) (K); (c),(g) the analysis increment x¯Ta(t)x¯Tb(t) (black) with its ±1.0 absolute values (gray) (K); and (d),(h) skewness of δXTa(t) at 10 hPa are displayed. Vertical dotted lines are drawn at the spread signal peak dates in Fig. 3.

Citation: Monthly Weather Review 151, 12; 10.1175/MWR-D-22-0169.1

Related to the increases in the forecast updates associated with the precursory spread signals, we subsequently examined bimodality in the inter-ensemble frequency distributions of ALERA, comprising 63 ensemble members. Figures 11d and 11h illustrate the time series of skewness of δXTa(t) at 10 hPa in ALERA. When the spread signals started to increase, δXTa(t) became positively skewed, implying that a few ensemble members represented warming temperature (SSW-like) states. However, no clear signals of the positive skewness synchronized with the ensemble spread signals. When we examined horizontal maps of the δXZa(t) distributions at 10 hPa (Figs. S5 and S6), it was difficult to identify clear positive skewness regions associated with normal and SSW-like bimodal states in the ensemble space, although for the NH-SSW, a positive skewness region appeared over the north of the Bering Strait on 24 December and lasted until 28 December (Fig. S5). Similar results were obtained for the skewness of δXb(t) (not shown). These findings indicate that the bimodality associated with the precursory spread signals remained an open question. To address this, previous studies have suggested that at least O(1000) ensemble members are needed to detect such bimodality (Yoden et al. 2002; Miyoshi et al. 2014).

We finally discuss the reason behind the analysis increments following the spread signals and the forecast updates in ALERA. Equation (3) is written as follows (e.g., Houtekamer and Zhang 2016; Kotsuki et al. 2019):
x¯a(t)=x¯b(t)+δXb(t)P˜a(Yb)TR1d,
where d, Yb, R1, and P˜a denote the innovation of the observation, the background ensemble perturbation δXb(t) in observation space, the observation error covariance matrix, and the analysis error covariance in observation space, respectively. As σb(t) corresponds to the amplitude of δXb(t), where σb(t) is temporary and locally large, the analysis increment is expected to be large as well. Figure 10 and Fig. S4 portray that the analysis increments became large around the peak dates of the spread signals. In other words, the spread amplification signals ahead of the SSW could favor the analysis update as described in Eq. (4). Moreover, as depicted in Fig. 11, the increased analysis increments followed the spread signals.

As illustrated in Fig. 1, the onsets of the NH- and SH-SSWs were slightly delayed compared to the other reanalyses, although the precursory signals appeared earlier than these onsets. This delay can be explained by the time series of the analysis increments (Figs. 11c,g), which increased slightly later and had smaller magnitudes than the forecast updates (Figs. 11b,f) when the precursory signals appeared and the SSWs began. Only the radiosonde observation type was effective for the analysis increments above 10 hPa in ALERA (Yamazaki et al. 2023). Therefore, it was expected that the contribution of the positive temperature analysis increments around the spread peaks would become more substantial if more observations in the upper to middle stratosphere were assimilated.

Note that the stratospheric warm temperature biases found in Fig. 1 could pose an impact on the timing and magnitude of the spread signals, potentially causing slight delays in the SSW onsets. When comparing the upward Eliassen–Palm flux in x¯Fza(t) (ALERA) with that in JRA-55 (as a representative of the other reanalysis datasets), the upward Eliassen–Palm flux in JRA-55 exhibited similar distributions to ALERA (Fig. 2). The Eliassen–Palm flux time sequences were similar below the middle stratosphere (the panels in Fig. 8 except for the uppermost ones). However, the Eliassen–Palm flux pulse for the NH-SSW in ALERA at 10 hPa was slightly delayed by 1 or 2 days compared with the pulse in JRA-55. Moreover, the 10-hPa Eliassen–Palm flux in ALERA had a relatively diminishing tendency (not displayed). Therefore, from Figs. 3 and 8, we speculate that stronger Eliassen–Palm flux pulses could accompany clearer precursory signals and could trigger more abrupt SSW onsets. These Eliassen–Palm flux differences stem from the different wave propagation properties of planetary waves above the middle stratosphere and are related to the warm temperature biases. Polar night jets above the upper stratosphere were weaker in ALERA than those in JRA-55, resulting in weaker upward Rossby wave propagation and warmer polar temperature in the middle stratosphere in ALERA.

As we presumed that Eliassen–Palm flux pulses in x¯Fza(t) could accompany precursory signals, we further hypothesized that the warm temperature biases could induce ambiguity and delay in both the precursory signals and the subsequent SSW onsets. Thus, if we could reduce the biases, the precursory signals could become more useful. However, we should consider the potential risk that the upper-stratospheric difference in the basic state (caused by the model bias) significantly alters the dynamics represented in the data assimilation system from the desired representation. Moreover, the spread signal does not necessarily reflect the right precursory behavior in such situations. The fact that our system has small bias that is enough to reproduce the expected dynamics cannot be proven here, although we found that the forecast updates and the analysis increments yielded reasonable distributions and time evolution. Thus, further detailed comparisons with the other reanalyses, a less biased forecast model in the stratosphere, and more stratospheric observations are required to estimate the possible and quantitative impacts of stratospheric biases on the precursory spread signals and onset delays.

6. Discussion: Dynamical basis of the analysis ensemble spread

The dynamical basis of the precursory spread signals is discussed here. An empirical orthogonal function (EOF) analysis was used to extract the dominant variability mode in the ensemble perturbation fields derived from the spread fields. The EOF analysis was conducted on δXZa(t) and δXZb(t) at each pressure level from the upper stratosphere (1 hPa) to the lower stratosphere (100 hPa) within the polar regions (within the latitudes 20°–90°N for the NH-SSW and 20°–90°S for the SH-SSW). The EOF analysis was applied for every 6-h analysis and background fields, and the number of EOF modes was equal to that of the ensemble size. Here, we examine the patterns and contribution rates of the first EOF modes.

Figure 12 plots the EOF first modes at 10 hPa around the signal peak dates for the NH-SSW and SH-SSW. The patterns are located at 90° out-of-phase from the wavenumber 1 of the geopotential height field pattern composed of the polar vortices and midlatitude anticyclones in x¯Za(t) (the “real” atmospheric field). Note that the first δXZb(t) EOF modes depict almost the same patterns (not shown). The figures also indicate closely and vertically aligned maximum centers of the most dominant ensemble perturbation modes at each altitude in the stratosphere. Thus, the dominant perturbation patterns in δXa(t) or δXb(t) became equivalent barotropic when the precursory signals appeared.

Fig. 12.
Fig. 12.

EOF first modes for δXZa(t) (shaded) and x¯Za(t) (m) (contour; contour interval 200 m) at 10 hPa for the (a) NH-SSW and (b) SH-SSW events. Snapshot fields are displayed at 0000 UTC 27 Dec 2018 in (a) and 0000 UTC 31 Aug 2019 in (b). Maximum amplitude positions (centers) of the EOF first modes for δXZa(t) and δXZb(t) at 5–100 hPa are displayed [filled marks: the EOFs for δXZa(t); opened marks: the EOFs for δXZb(t)]. The symbols , ○, △, ◇, and ∘ indicate the maximum amplitude positions at 5, 10, 30, 50, and 100 hPa, respectively. The polar vortices and Aleutian high in (a) or midlatitude high in (b) are denoted by “L” and “H,” respectively.

Citation: Monthly Weather Review 151, 12; 10.1175/MWR-D-22-0169.1

Figure 13 charts the time evolution of the contribution rates of the first mode for the NH-SSW and SH-SSW events. The time series exhibits similar features to those of σa(t) and σb(t) (Fig. 3). The spread signals prior to the SSWs are well captured in the ensemble perturbation EOF contribution rates, with a contribution rate of up to 50% at 10 and 5 hPa. The time series of the EOF first-mode contribution rates of δXZb(t) were aligned with those of δXZa(t): the most dominant perturbation modes of δXb(t) behave similar to those of δXa(t).

Fig. 13.
Fig. 13.

Time series of EOF first-mode contribution rates (%) (red lines) for (a) December 2018–January 2019 and (b) August–September 2019. EOF modes for δXZa(t) (solid) and δXZb(t) (dashed) at each pressure level of the stratosphere shown from the bottom, at 100, 50, 30, 10, and 5 hPa. The vertical dotted line indicates the dates of the spread signals, as displayed in Fig. 3.

Citation: Monthly Weather Review 151, 12; 10.1175/MWR-D-22-0169.1

The maximum amplitude positions (centers) of the EOF first modes in the stratosphere at each daily or twice daily snapshot are plotted for the NH-SSW and the SH-SSW in Figs. 14 and 15, respectively. As found in Fig. 12, the maximum centers become closely vertically aligned, especially near the dates of the spread signals in both the NH-SSW and SH-SSW events. In addition, the amplitude centers are again located at 90° out-of-phase from the wavenumber 1 of the x¯Za(t) pattern.

Fig. 14.
Fig. 14.

As in Fig. 12a, but does not display the EOF first-mode patterns at 10 hPa. Maximum amplitude positions of EOF first modes (centers) and x¯Za(t) at 10 hPa (m) (contour; contour interval 200 m) are presented for the NH-SSW event. The symbols , ○, △, ◇, and ∘ indicate the maximum amplitude positions at 5, 10, 30, 50, and 100 hPa, respectively. (a)–(j) Daily snapshots from 0000 UTC 22 Dec 2018 in (a) to 0000 UTC 31 Dec 2018 in (j) are shown in alphabetical order. A snapshot in (f) at the peak date of the spread signal (Fig. 3) is framed in red.

Citation: Monthly Weather Review 151, 12; 10.1175/MWR-D-22-0169.1

Fig. 15.
Fig. 15.

As in Fig. 14, but for the SH-SSW event. (a)–(j) Snapshots for every 2 days from 0000 UTC 21 Aug 2019 in (a) to 0000 UTC 8 Sep 2019 in (j). The contour interval is 200 m.

Citation: Monthly Weather Review 151, 12; 10.1175/MWR-D-22-0169.1

The dominant perturbation or spread modes of the precursory signals may correspond to the barotropic instability in the upper to middle stratosphere associated with SSWs; the existence of the mode has been pointed out in Mukougawa et al. (2017). Mukougawa et al. (2017) conducted ensemble forecast experiments for the NH-SSW case of March 2007 using a global atmospheric general circulation model at the Meteorological Research Institute of the Japan Meteorological Agency. Mukougawa et al. (2017) found out that the forecast ensemble perturbations (i.e., deviations from the forecast ensemble means) evolved as a mode of the barotropic instability in the stratospheric interior; the unstable mode was found to have a dominant wavenumber 2 structure and be 90° out-of-phase with the ensemble-mean field. The pattern of the δXZa(t) and δXZb(t) EOF first mode for the NH-SSW (Fig. 12) is similar to the unstable mode reported by Mukougawa et al. (2017). This finding indicates that the precursory signals in ALERA may be equivalent to the mode discovered in Mukougawa et al. (2017).

We then examined whether the barotropic instability could actually occur in the analysis ensemble mean [x¯a(t)] field of ALERA, by assessing the meridional gradient of zonal-mean potential vorticity (PV) at 850 K, which corresponds to approximately 7 hPa. Figure 16 reveals that the meridional gradient of PV turns negative near the poles on the peak dates of the spread signals in both the NH-SSW and the SH-SSW events; the x¯a(t) fields marginally satisfy the necessary conditions of barotropic instability at the signal peak dates.

Fig. 16.
Fig. 16.

Snapshots in x¯a(t) of the latitudinal cross sections of the meridional gradient of zonal-mean 850-K PV [10−4 PVU m−1 (1 PVU = 10−6 K kg−1 m2 s−1)] for the (a) NH-SSW and (b) SH-SSW events. Snapshots at 0000 UTC 27 Dec 2018 in (a) and 0000 UTC 31 Aug 2019 in (b) (peak dates of the spread signals).

Citation: Monthly Weather Review 151, 12; 10.1175/MWR-D-22-0169.1

Additionally, we monitored the time series of area fractions of the negative meridional gradient of absolute vorticity within the NH and SH extratropics in the stratosphere during the NH-SSW and SW-SSW events (Fig. 17). The area fractions were calculated as the area ratios where the meridional gradient of absolute vorticity was negative to the entire areas within 35°–90°N for the NH-SSW and 35°–90°S for the SH-SSW events. In both events, the area fractions in the upper to middle stratosphere abruptly increased around the peak dates of the spread signals, and the increased values persisted for 2 or 3 weeks. Greater fraction areas correspond to a more favorable condition for barotropic instability.

Fig. 17.
Fig. 17.

Time series of the area fractions (%) where meridional gradients of absolute vorticity (m−1 s−1) become negative in x¯a(t) within the latitudes (a) 35°–90°N and (b) 35°–90°S at each level of the stratosphere for the NH-SSW in (a) and SH-SSW in (b). Time series at 100, 50, 30, 10, and 5 hPa are displayed from bottom to top, respectively. Vertical dotted lines are drawn at the spread signal peak dates (Fig. 3).

Citation: Monthly Weather Review 151, 12; 10.1175/MWR-D-22-0169.1

An increase in the area fractions was found in the lower stratosphere but occurred later than in the upper and middle stratosphere. This result supports the conclusion that the spread signals in the upper to middle stratosphere correspond to the initiation of the barotropic instability mode dominant in the stratosphere.

We would finally mention an insight to distinguish the mechanism of SSWs from the present study. Our inference is that the precursory spread signals prior to the NH- and SH-SSWs stem from the dynamics in the stratospheric interior associated with SSWs in general. The main general mechanism of the SSW consists of wave–mean flow interactions in the stratosphere, in which planetary waves are excited by tropospheric processes such as blocking (e.g., Matsuno 1971). However, initiation of critical wave behaviors by stratospheric interior dynamics is also important (e.g., Nakamura et al. 2020). For instance, Tung and Lindzen (1979) and Plumb (1981) proposed a resonance process to account for such behaviors. These critical intra-stratospheric behaviors might be associated with the spread signals appearing in the stratosphere. However, it remains unclear the extent to which tropospheric and critical processes mentioned above contribute to the onset of SSWs. The spread signals in the stratosphere can provide additional information quantifying the contribution rate of the critical processes in the stratosphere. Therefore, we anticipate that further examinations for more SSWs using ensemble-based analysis products covering longer periods would be useful in characterizing the mechanisms of SSWs more comprehensively.

Note that the precursory signals detected in this study may be different from that discovered in Enomoto et al. (2010). In that work, it was found that the latter signal originates in the troposphere (Nishii and Nakamura 2010). In contrast, the signals in this study are of stratospheric origins. The signal found in these previous studies could be equivalent to another tropospheric signal found in the SH-SSW event (see section 4). Such difference of origins might stem from the diversity of SSW events, such as the diversity of tropospheric blocking (Woollings et al. 2018). Nonetheless, both the results of Enomoto et al. (2010) and the results here commonly indicate that the spread of signals in the middle stratosphere (at 10 hPa) precedes a few days prior to the SSW onsets.

7. Conclusions and remarks

We investigated the behavior of the analysis ensemble spread when two SSW events occurred in the experimental global ensemble reanalysis ALERA, generated by an updated version of ALEDAS. The NH-SSW event took place during December 2018–January 2019, and the SH-SSW event occurred during August–September 2019. ALEDAS was able to reproduce the timing of temperature increases (warmings) and the weakening of westerly wind or formation of easterly wind in both SSW events, which aligned with results from several other reanalyses.

Precursory spread signals in temperature, originally discovered in a previous study (Enomoto et al. 2010), where the analysis ensemble spread temporally increased and reached a peak a few days prior to an SSW onset, were detected for both the NH-SSW and SH-SSW events. These signals were most pronounced in the upper to middle stratosphere and less evident in the lower stratosphere or the upper troposphere.

Investigation of the precursory spread signals revealed that the amplification of spreads primarily occurred between the polar vortices and midlatitude anticyclones in the stratosphere. During the SSW onsets, the polar vortices were displaced by the anticyclones. Additionally, vertical cross sections of the spreads indicated that the stratospheric signals were dominant and originated primarily in the upper stratosphere.

In our discussion, we explored the contribution of the precursory spread signals to the updating of the analysis ensemble-mean fields. We found that in the regions where the ensemble spreads locally increased, both the tendency by the forecast cycles and the analysis increment by the analysis cycles in ALEDAS became large locally and temporally. These findings implied that the precursory signals could contribute to the analysis (ensemble mean) updates through the analysis increment of each forecast-analysis cycle.

We discussed the dynamical basis of the precursory signals. An EOF analysis of the analysis ensemble perturbation (spread) fields revealed that the EOF first modes dominate at the equivalent timing of the spread amplification signals. During this timing, the modes were equivalent barotropic in the stratosphere and were 90° out-of-phase with the analysis ensemble-mean fields, which represented the wavenumber-1 patterns of the displaced polar vortices and midlatitude anticyclones. These spread EOF modes might correspond to the growing mode resulting from stratospheric barotropic instability, as previously discovered by Mukougawa et al. (2017). Consequently, we concluded that the precursory signals are mechanically generated by the barotropic instability mode in the middle to upper stratosphere.

It was found that the precursory signals prior to the SSWs in the analysis ensemble spread are flow-dependent. As already reported in Enomoto et al. (2010), other precursory signals may be detected before various weather phenomena. Therefore, the specific weather events exhibiting such spread amplifications should be investigated, which can be extended to ocean and other geophysical phenomena as well.

Furthermore, future discussion should focus on the general occurrence of precursory signals before SSWs. In this study, we identified precursory signals for only two SSW events. Possibly, certain events may exhibit spread amplification without influencing an SSW, and in a few cases, no spread amplification is detected before the occurrence of an SSW. By extending the dataset period of ALERA, we can examine the frequency of these signals before SSWs and explore whether they differ across the types of SSW, such as the vortex-displacement and vortex-splitting types.

In this study, we discovered precursory signals that presage the formation of SSWs in an EnKF-based data assimilation system. In the future, we aim to further investigate that the use of a forecast model with less temperature bias in the stratosphere, more observations above the middle atmosphere, and a larger size of ensemble members in the data assimilation system can yield better detection of precursory signals and then can improve analysis and prediction of SSWs.

Acknowledgments.

The Earth Simulator at JAMSTEC was used to create ALERA. Dr. Yuya Baba implemented the nonorographic gravity wave drag scheme in the Atmospheric General Circulation Model for the Earth Simulator (AFES). The authors are grateful to three anonymous reviewers for their careful review, Dr. Daniel Hodyss for careful editing, and Dr. Patrick Martineau, Prof. Norihiko Sugimoto, Prof. Takeshi Enomoto, Prof. Hitoshi Mukougawa, Dr. Shiori Sugimoto, Dr. Yohei Yamada, and Editor-in-Chief Dr. Ron McTaggart-Cowan for their advice. This work was supported by JSPS KAKENHI (20H01976, 18K13617, and 19H05702) and Arctic Challenge for Sustainability II (ArCS II).

Data availability statement.

Datasets of the analysis and background ensemble mean and spread fields of ALERA are available from https://www.jamstec.go.jp/esc/fes/dods/alera3/plev. NCEP PrepBUFR and AMSU-A brightness temperature data are available online (https://doi.org/10.5065/Z83F-N512 and https://doi.org/10.5065/DWYZ-Q852). The Eliassen–Palm flux was calculated using the mass-weighted isentropic zonal-mean formulation (MIM) analysis package developed by Prof. Toshiki Iwasaki and contributors (distributed from http://wind.gp.tohoku.ac.jp/mim/).

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  • Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77, 437472, https://doi.org/10.1175/1520-0477(1996)077%3C0437:TNYRP%3E2.0.CO;2.

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    • Export Citation
  • Kobayashi, S., and Coauthors, 2015: The JRA-55 reanalysis: General specifications and basic characteristics. J. Meteor. Soc. Japan, 93, 548, https://doi.org/10.2151/jmsj.2015-001.

    • Search Google Scholar
    • Export Citation
  • Kodera, K., H. Mukougawa, and S. Itoh, 2008: Tropospheric impact of reflected planetary waves from the stratosphere. Geophys. Res. Lett., 35, L16806, https://doi.org/10.1029/2008GL034575.

    • Search Google Scholar
    • Export Citation
  • Kotsuki, S., K. Kurosawa, and T. Miyoshi, 2019: On the properties of ensemble forecast sensitivity to observations. Quart. J. Roy. Meteor. Soc., 145, 18971914, https://doi.org/10.1002/qj.3534.

    • Search Google Scholar
    • Export Citation
  • Lim, E.-P., and Coauthors, 2021: The 2019 Southern Hemisphere stratospheric polar vortex weakening and its impacts. Bull. Amer. Meteor. Soc., 102, E1150E1171, https://doi.org/10.1175/BAMS-D-20-0112.1.

    • Search Google Scholar
    • Export Citation
  • Lorenz, E. N., 1963: Deterministic nonperiodic flow. J. Atmos. Sci., 20, 130141, https://doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Lynch, E., D. Kaufman, A. S. Sharma, E. Kalnay, and K. Ide, 2016: Brief communication: Breeding vectors in the phase space reconstructed from time series data. Nonlinear Processes Geophys., 23, 137141, https://doi.org/10.5194/npg-23-137-2016.

    • Search Google Scholar
    • Export Citation
  • Matsuno, T., 1971: A dynamical model of the stratospheric sudden warming. J. Atmos. Sci., 28, 14791494, https://doi.org/10.1175/1520-0469(1971)028%3C1479:ADMOTS%3E2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • McFarlane, N. A., 1987: The effect of orographically excited gravity wave drag on the general circulation of the lower stratosphere and troposphere. J. Atmos. Sci., 44, 17751800, https://doi.org/10.1175/1520-0469(1987)044%3C1775:TEOOEG%3E2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Miyoshi, T., S. Yamane, and T. Enomoto, 2007: The AFES-LETKF experimental ensemble reanalysis: ALERA. SOLA, 3, 4548, https://doi.org/10.2151/sola.2007-012.

    • Search Google Scholar
    • Export Citation
  • Miyoshi, T., K. Kondo, and T. Imamura, 2014: The 10,240-member ensemble Kalman filtering with an intermediate AGCM. Geophys. Res. Lett., 41, 52645271, https://doi.org/10.1002/2014GL060863.

    • Search Google Scholar
    • Export Citation
  • Mukougawa, H., S. Noguchi, Y. Kuroda, R. Mizuta, and K. Kodera, 2017: Dynamics and predictability of downward-propagating stratospheric planetary waves observed in March 2007. J. Atmos. Sci., 74, 35333550, https://doi.org/10.1175/JAS-D-16-0330.1.

    • Search Google Scholar
    • Export Citation
  • Nakamura, N., J. Falk, and S. W. Lubis, 2020: Why are stratospheric sudden warmings sudden (and intermittent)? J. Atmos. Sci., 77, 943964, https://doi.org/10.1175/JAS-D-19-0249.1.

    • Search Google Scholar
    • Export Citation
  • Nishii, K., and H. Nakamura, 2010: Three-dimensional evolution of ensemble forecast spread during the onset of a stratospheric sudden warming event in January 2006. Quart. J. Roy. Meteor. Soc., 136, 894905, https://doi.org/10.1002/qj.607.

    • Search Google Scholar
    • Export Citation
  • Noguchi, S., Y. Kuroda, K. Kodera, and S. Watanabe, 2020: Robust enhancement of tropical convective activity by the 2019 Antarctic sudden stratospheric warming. Geophys. Res. Lett., 47, e2020GL088743, https://doi.org/10.1029/2020GL088743.

    • Search Google Scholar
    • Export Citation
  • Orr, A., P. Bechtold, J. Scinocca, M. Ern, and M. Janisková, 2010: Improved middle atmosphere climate and forecasts in the ECMWF model through a nonorographic gravity wave drag parameterization. J. Climate, 23, 59055926, https://doi.org/10.1175/2010JCLI3490.1.

    • Search Google Scholar
    • Export Citation
  • Plumb, R. A., 1981: Instability of the distorted polar night vortex: A theory of stratospheric warmings. J. Atmos. Sci., 38, 25142531, https://doi.org/10.1175/1520-0469(1981)038<2514:IOTDPN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Reynolds, R. W., T. M. Smith, C. Liu, D. B. Chelton, K. S. Casey, and M. G. Schlax, 2007: Daily high-resolution-blended analyses for sea surface temperature. J. Climate, 20, 54735496, https://doi.org/10.1175/2007JCLI1824.1.

    • Search Google Scholar
    • Export Citation
  • Saito, K., L. Duc, T. Matsunobu, and T. Kurihana, 2022: Perturbations by the ensemble transform. Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications, S. Park and L. Xu, Eds., Vol. IV, Springer, 115–141, https://doi.org/10.1007/978-3-030-77722-7_5.

  • Scheffer, M., and Coauthors, 2009: Early-warning signals for critical transitions. Nature, 461, 5359, https://doi.org/10.1038/nature08227.

    • Search Google Scholar
    • Export Citation
  • Scinocca, J. F., 2003: An accurate spectral nonorographic gravity wave drag parameterization for general circulation models. J. Atmos. Sci., 60, 667682, https://doi.org/10.1175/1520-0469(2003)060<0667:AASNGW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Tung, K. K., and R. S. Lindzen, 1979: A theory of stationary long waves. Part I: Simple theory of blocking. Mon. Wea. Rev., 107, 714734, https://doi.org/10.1175/1520-0493(1979)107<0714:ATOSLW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Woollings, T., and Coauthors, 2018: Blocking and its response to climate change. Curr. Climate Change Rep., 4, 287300, https://doi.org/10.1007/s40641-018-0108-z.

    • Search Google Scholar
    • Export Citation
  • Yamazaki, A., T. Enomoto, T. Miyoshi, A. Kuwano-Yoshida, and N. Komori, 2017: Using observations near the poles in the AFES-LETKF data assimilation system. SOLA, 13, 4146, https://doi.org/10.2151/sola.2017-008.

    • Search Google Scholar
    • Export Citation
  • Yamazaki, A., T. Miyoshi, J. Inoue, T. Enomoto, and N. Komori, 2021: EFSO at different geographical locations verified with observing system experiments. Wea. Forecasting, 36, 12191236, https://doi.org/10.1175/WAF-D-20-0152.1.

    • Search Google Scholar
    • Export Citation
  • Yamazaki, A., K. Terasaki, T. Miyoshi, and S. Noguchi, 2023: Estimation of AMSU-A radiance observation impacts in an LETKF-based atmospheric global data assimilation system: Comparison with EFSO and observing system experiments. Wea. Forecasting, 38, 953970, https://doi.org/10.1175/WAF-D-22-0159.1.

    • Search Google Scholar
    • Export Citation
  • Yoden, S., M. Taguchi, and Y. Naito, 2002: Numerical studies on time variations of the troposphere-stratosphere coupled system. J. Meteor. Soc. Japan, 80, 811830, https://doi.org/10.2151/jmsj.80.811.

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    • Export Citation

Supplementary Materials

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    • Search Google Scholar
    • Export Citation
  • Kobayashi, S., and Coauthors, 2015: The JRA-55 reanalysis: General specifications and basic characteristics. J. Meteor. Soc. Japan, 93, 548, https://doi.org/10.2151/jmsj.2015-001.

    • Search Google Scholar
    • Export Citation
  • Kodera, K., H. Mukougawa, and S. Itoh, 2008: Tropospheric impact of reflected planetary waves from the stratosphere. Geophys. Res. Lett., 35, L16806, https://doi.org/10.1029/2008GL034575.

    • Search Google Scholar
    • Export Citation
  • Kotsuki, S., K. Kurosawa, and T. Miyoshi, 2019: On the properties of ensemble forecast sensitivity to observations. Quart. J. Roy. Meteor. Soc., 145, 18971914, https://doi.org/10.1002/qj.3534.

    • Search Google Scholar
    • Export Citation
  • Lim, E.-P., and Coauthors, 2021: The 2019 Southern Hemisphere stratospheric polar vortex weakening and its impacts. Bull. Amer. Meteor. Soc., 102, E1150E1171, https://doi.org/10.1175/BAMS-D-20-0112.1.

    • Search Google Scholar
    • Export Citation
  • Lorenz, E. N., 1963: Deterministic nonperiodic flow. J. Atmos. Sci., 20, 130141, https://doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Lynch, E., D. Kaufman, A. S. Sharma, E. Kalnay, and K. Ide, 2016: Brief communication: Breeding vectors in the phase space reconstructed from time series data. Nonlinear Processes Geophys., 23, 137141, https://doi.org/10.5194/npg-23-137-2016.

    • Search Google Scholar
    • Export Citation
  • Matsuno, T., 1971: A dynamical model of the stratospheric sudden warming. J. Atmos. Sci., 28, 14791494, https://doi.org/10.1175/1520-0469(1971)028%3C1479:ADMOTS%3E2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • McFarlane, N. A., 1987: The effect of orographically excited gravity wave drag on the general circulation of the lower stratosphere and troposphere. J. Atmos. Sci., 44, 17751800, https://doi.org/10.1175/1520-0469(1987)044%3C1775:TEOOEG%3E2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Miyoshi, T., S. Yamane, and T. Enomoto, 2007: The AFES-LETKF experimental ensemble reanalysis: ALERA. SOLA, 3, 4548, https://doi.org/10.2151/sola.2007-012.

    • Search Google Scholar
    • Export Citation
  • Miyoshi, T., K. Kondo, and T. Imamura, 2014: The 10,240-member ensemble Kalman filtering with an intermediate AGCM. Geophys. Res. Lett., 41, 52645271, https://doi.org/10.1002/2014GL060863.

    • Search Google Scholar
    • Export Citation
  • Mukougawa, H., S. Noguchi, Y. Kuroda, R. Mizuta, and K. Kodera, 2017: Dynamics and predictability of downward-propagating stratospheric planetary waves observed in March 2007. J. Atmos. Sci., 74, 35333550, https://doi.org/10.1175/JAS-D-16-0330.1.

    • Search Google Scholar
    • Export Citation
  • Nakamura, N., J. Falk, and S. W. Lubis, 2020: Why are stratospheric sudden warmings sudden (and intermittent)? J. Atmos. Sci., 77, 943964, https://doi.org/10.1175/JAS-D-19-0249.1.

    • Search Google Scholar
    • Export Citation
  • Nishii, K., and H. Nakamura, 2010: Three-dimensional evolution of ensemble forecast spread during the onset of a stratospheric sudden warming event in January 2006. Quart. J. Roy. Meteor. Soc., 136, 894905, https://doi.org/10.1002/qj.607.

    • Search Google Scholar
    • Export Citation
  • Noguchi, S., Y. Kuroda, K. Kodera, and S. Watanabe, 2020: Robust enhancement of tropical convective activity by the 2019 Antarctic sudden stratospheric warming. Geophys. Res. Lett., 47, e2020GL088743, https://doi.org/10.1029/2020GL088743.

    • Search Google Scholar
    • Export Citation
  • Orr, A., P. Bechtold, J. Scinocca, M. Ern, and M. Janisková, 2010: Improved middle atmosphere climate and forecasts in the ECMWF model through a nonorographic gravity wave drag parameterization. J. Climate, 23, 59055926, https://doi.org/10.1175/2010JCLI3490.1.

    • Search Google Scholar
    • Export Citation
  • Plumb, R. A., 1981: Instability of the distorted polar night vortex: A theory of stratospheric warmings. J. Atmos. Sci., 38, 25142531, https://doi.org/10.1175/1520-0469(1981)038<2514:IOTDPN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Reynolds, R. W., T. M. Smith, C. Liu, D. B. Chelton, K. S. Casey, and M. G. Schlax, 2007: Daily high-resolution-blended analyses for sea surface temperature. J. Climate, 20, 54735496, https://doi.org/10.1175/2007JCLI1824.1.

    • Search Google Scholar
    • Export Citation
  • Saito, K., L. Duc, T. Matsunobu, and T. Kurihana, 2022: Perturbations by the ensemble transform. Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications, S. Park and L. Xu, Eds., Vol. IV, Springer, 115–141, https://doi.org/10.1007/978-3-030-77722-7_5.

  • Scheffer, M., and Coauthors, 2009: Early-warning signals for critical transitions. Nature, 461, 5359, https://doi.org/10.1038/nature08227.

    • Search Google Scholar
    • Export Citation
  • Scinocca, J. F., 2003: An accurate spectral nonorographic gravity wave drag parameterization for general circulation models. J. Atmos. Sci., 60, 667682, https://doi.org/10.1175/1520-0469(2003)060<0667:AASNGW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Tung, K. K., and R. S. Lindzen, 1979: A theory of stationary long waves. Part I: Simple theory of blocking. Mon. Wea. Rev., 107, 714734, https://doi.org/10.1175/1520-0493(1979)107<0714:ATOSLW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Woollings, T., and Coauthors, 2018: Blocking and its response to climate change. Curr. Climate Change Rep., 4, 287300, https://doi.org/10.1007/s40641-018-0108-z.

    • Search Google Scholar
    • Export Citation
  • Yamazaki, A., T. Enomoto, T. Miyoshi, A. Kuwano-Yoshida, and N. Komori, 2017: Using observations near the poles in the AFES-LETKF data assimilation system. SOLA, 13, 4146, https://doi.org/10.2151/sola.2017-008.

    • Search Google Scholar
    • Export Citation
  • Yamazaki, A., T. Miyoshi, J. Inoue, T. Enomoto, and N. Komori, 2021: EFSO at different geographical locations verified with observing system experiments. Wea. Forecasting, 36, 12191236, https://doi.org/10.1175/WAF-D-20-0152.1.

    • Search Google Scholar
    • Export Citation
  • Yamazaki, A., K. Terasaki, T. Miyoshi, and S. Noguchi, 2023: Estimation of AMSU-A radiance observation impacts in an LETKF-based atmospheric global data assimilation system: Comparison with EFSO and observing system experiments. Wea. Forecasting, 38, 953970, https://doi.org/10.1175/WAF-D-22-0159.1.

    • Search Google Scholar
    • Export Citation
  • Yoden, S., M. Taguchi, and Y. Naito, 2002: Numerical studies on time variations of the troposphere-stratosphere coupled system. J. Meteor. Soc. Japan, 80, 811830, https://doi.org/10.2151/jmsj.80.811.

    • Search Google Scholar
    • Export Citation