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
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.
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
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
Distributions of
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
Time series of zonal-mean
Citation: Monthly Weather Review 151, 12; 10.1175/MWR-D-22-0169.1
From Fig. 3a, the precursory amplification emerges in the
Regarding the SH-SSW, a stratospheric signal is found as a more gradual (slower) peak in
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
Time evolution of the
Citation: Monthly Weather Review 151, 12; 10.1175/MWR-D-22-0169.1
We investigate the time evolution of the vertical structure of
Longitude–height cross sections (60°–80°N meridional mean) of
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
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
Citation: Monthly Weather Review 151, 12; 10.1175/MWR-D-22-0169.1
As in Fig. 5, but for the SH-SSW event. The
Citation: Monthly Weather Review 151, 12; 10.1175/MWR-D-22-0169.1
Regarding the vertical structure,
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
Subsequently, we examined the atmospheric condition of
As in Fig. 3, but for zonal-mean
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
5. Possible contributions of the spread signals on analysis updates
The NH-SSW event is examined. The spatial patterns of the forecast update as
Snapshots of the forecast update
Citation: Monthly Weather Review 151, 12; 10.1175/MWR-D-22-0169.1
The horizontal distributions of the analysis increment as
As in Fig. 9, but for the analysis increment
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
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
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)
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
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
As we presumed that Eliassen–Palm flux pulses in
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
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
EOF first modes for
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
Time series of EOF first-mode contribution rates (%) (red lines) for (a) December 2018–January 2019 and (b) August–September 2019. EOF modes for
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
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
Citation: Monthly Weather Review 151, 12; 10.1175/MWR-D-22-0169.1
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
We then examined whether the barotropic instability could actually occur in the analysis ensemble mean [
Snapshots in
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.
Time series of the area fractions (%) where meridional gradients of absolute vorticity (m−1 s−1) become negative in
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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