Stratospheric sudden warming (SSW) events exhibit pronounced interannual variability. Based on zonal wind reversals at 60°N and 10 hPa, it has been suggested that SSW events occur more preferentially during El Niño–Southern Oscillation (ENSO) winters (both El Niño and La Niña winters) than during ENSO-neutral winters. This relationship is reevaluated here by considering seven different SSW definitions. For all definitions, SSW events are detected more frequently during El Niño winters than during ENSO-neutral winters, in agreement with a strengthened planetary-scale wave activity. However, such a systematic relationship is not found during La Niña winters. While three SSW definitions, including the wind-reversal definition, show a higher SSW frequency during La Niña winters than during ENSO-neutral winters, other definitions show no difference or even lower SSW frequency during La Niña winters. This result, which is qualitatively insensitive to the choice of reanalysis datasets, ENSO indices, and SST datasets, indicates that the reported ENSO–SSW relationship is dependent on the details of the SSW definition. This result is interpreted in terms of different background wind, latitudinal extent of wind reversal, and planetary-scale wave activity during El Niño and La Niña winter SSW events.
El Niño–Southern Oscillation (ENSO) affects not only the tropospheric circulation but also the stratospheric circulation in the Northern Hemisphere extratropics (Horel and Wallace 1981; van Loon and Labitzke 1987). Although the stratospheric impact is relatively minor, ENSO-induced stratospheric circulation changes are well observed in the seasonal-mean polar vortex. In general, the polar vortex becomes anomalously warm and weak during El Niño winters but cold and strong during La Niña winters (Fig. 1a; van Loon and Labitzke 1987; Manzini et al. 2006; Calvo et al. 2008; Iza et al. 2016). For instance, the Arctic stratospheric temperature difference between El Niño and La Niña winters is over 4 K in the long-term radiosonde observations (Free and Seidel 2009). These ENSO-related polar vortex changes are essentially driven by vertically propagating waves from the troposphere to the stratosphere. However, they can affect the underlying troposphere as well through downward coupling, providing an important source of boreal winter seasonal prediction in the Northern Hemisphere extratropics (Cagnazzo and Manzini 2009; Ineson and Scaife 2009; Butler et al. 2014).
Recent studies have shown that the above relationship may not hold for the subseasonal variability of the polar vortex (Fig. 1b). It is well documented that stratospheric sudden warming (SSW) events occur more frequently during El Niño winters than during ENSO-neutral winters (Taguchi and Hartmann 2006). This is consistent with the anomalously weak polar vortex and enhanced planetary-scale wave activity during El Niño winters. However, Butler and Polvani (2011, hereafter BP11) and Butler et al. (2014, hereafter BPD14) reported that such an increase of SSW frequency is also found during La Niña winters. In other words, SSW events tend to occur more preferentially during both El Niño and La Niña winters (ENSO winters) than during ENSO-neutral winters. Supporting their finding, the polar vortex exhibits enhanced variability during both El Niño and La Niña winters in comparison to during ENSO-neutral winters (Fig. 1b). This is in stark contrast to a linear relationship between ENSO and the seasonal-mean polar vortex strength (Fig. 1a).
More frequent SSW events during ENSO winters than ENSO-neutral winters have been explained by different planetary-scale wave responses to ENSO (Garfinkel et al. 2012; Li and Lau 2013). During El Niño winters, zonal wavenumber 1 (k = 1) waves are strengthened in the lower stratosphere, increasing the probability of polar vortex breakdown. Although k = 1 waves are rather weak during La Niña winters, zonal wavenumber 2 (k = 2) waves often become anomalously strong during La Niña winters, distorting the polar vortex (Garfinkel et al. 2012; Li and Lau 2013; Barriopedro and Calvo 2014).
The ENSO–SSW relationship documented in BP11 and BPD14, however, is somewhat questionable. Polvani et al. (2017) recently reported that whereas enhanced SSW events during El Niño winters are robust, relative changes of SSW events during La Niña winters are somewhat dependent on the choice of sea surface temperature (SST) data. Modeling studies also do not show a systematic increase of SSW frequency during La Niña winters. Taguchi and Hartmann (2006) reported that SSW events occur twice as frequently during El Niño winters than during La Niña winters in their model simulation, which underestimated stratospheric variability. A qualitatively similar result is also found in Polvani et al. (2017).
To better understand the ENSO–SSW relationship, the present study revisits the SSW statistics in long-term reanalysis datasets. Specifically, seven different definitions of SSW, which have been used in the literature, are applied to two different reanalysis and SST datasets. It is found that the ENSO–SSW relationship is highly sensitive to the SSW definition, and this is partly caused by different background flow and planetary-scale wave activity during El Niño and La Niña winter SSW events.
2. Data and methods
The National Centers for Environmental Prediction (NCEP)–National Center for Atmospheric Research (NCAR) Reanalysis (NNR; Kalnay et al. 1996) and Japanese 55-Year Reanalysis (JRA-55; Kobayashi et al. 2015) are examined from 1958 to 2014. These datasets are chosen simply because they provide longer records than other reanalysis datasets. For a fair comparison, a common resolution of 2.5° × 2.5° is used for both datasets. To be compared with BP11 and BPD14, NNR is set as reference data, and a sensitivity test to the choice of reanalysis data is conducted with JRA-55.
For ENSO, the Extended Reconstructed Sea Surface Temperature version 3b (ERSST) data (Smith et al. 2008) from the National Oceanic and Atmospheric Administration’s (NOAA’s) Climate Prediction Center (CPC) is used. To test the sensitivity to SST, the most updated version of ERSST (Huang et al. 2017; ERSST version 5) is also used.
a. SSW definitions
Various definitions of SSW have been used in the literature (Butler et al. 2015; Martineau and Son 2015; Palmeiro et al. 2015). As summarized in Table 1, SSW has been identified by using the zonal-mean zonal wind at a selected latitude, the area-averaged zonal wind or geopotential height, the leading mode of variability, or a combination of multiple variables. Although 10 hPa is the most common level, 50 or even 100 hPa has been also used to quantify polar vortex variability. The most widely used definitions, the so-called World Meteorological Organization (WMO) definition and its simplified version (Charlton and Polvani 2007), are based on 10-hPa zonal-mean zonal wind reversal at 60°N. Since 60°N does not necessarily represent the edge of the polar vortex, zonal-mean zonal wind at 65°N (Butler et al. 2015) or at any latitude from 55° to 70°N has been also used (Palmeiro et al. 2015).
Following Butler et al. (2015), seven different SSW definitions, which include the one used in BP11 and BPD14 (i.e., the U60 definition), are considered in this study (see Table 1). They are the WMO, U60, U65, U6090, Z6090, EOFU, and 2DM definitions. Here the WMO, U60, Z6090, and 2DM definitions are identical to the U&T, CP07, ZPOL, and MOM definitions in Butler et al. (2015), respectively. The detected SSW events for each definition are listed in Table ES2 of Butler et al. (2015). An exception is the U60 SSW event on 7 January 1968. This event is excluded in this study because it is not detected as an SSW event in the latest version of NNR (A. H. Butler 2017, personal communication; see also the footnote posted on page 3 of BPD14).
Both the WMO and U60 definitions consider the reversal of zonal-mean zonal wind at 60°N and 10 hPa. Although the former has an additional constraint of the meridional temperature gradient change, these two definitions exhibit a similar frequency and onset date of SSW events (Table 1). The U65 and U6090 definitions are similar to the U60 definition but use zonal-mean zonal wind at 65°N and area-averaged zonal wind over 60°–90°N, respectively. The Z6090 definition utilizes the polar-cap geopotential height anomaly. Unlike other definitions, the EOFU definition employs a statistical method. In this definition, the onset of SSW is detected by using the leading mode of extratropical variability of zonal-mean zonal wind at 50 hPa. The last definition, 2DM, is based on two-dimensional moment diagnostics. Specifically, it detects SSW events by computing an aspect ratio and centroid latitude of the polar vortex in 10-hPa geopotential height fields. Since this definition focuses on the morphology of the polar vortex, it may not be directly compared with other definitions that are based on zonal-mean diagnostics.
It should be noted that the number of SSW events differs substantially among the definitions (Table 1). While the U6090 definition detects the largest number of SSW events (37), the EOFU definition detects the smallest number of SSW events (26). When only 10-hPa definitions are considered (i.e., the first five definitions in Table 1), the WMO definition shows a minimum SSW frequency.
b. ENSO definitions
ENSO is determined by the Niño-3.4 index (i.e., SST anomaly averaged over 5°N–5°S and 170°–120°W). To objectively define its phase, two thresholds are adopted (Table 2). First, the NCEP–CPC convention, referred to as the CPC definition, is used as in BPD14. Specifically, El Niño and La Niña winters are defined as the winters when the seasonal running mean Niño-3.4 index consecutively surpasses ±0.5 K for at least five seasons. Other winters are simply set to be ENSO-neutral winters. A total of 19 and 18 winters are identified as El Niño and La Niña winters, respectively. If ERSSTv5 is used (CPCv5), 20 El Niño and 18 La Niña winters are identified. Second, ENSO is also simply defined by the seasonal-mean Niño-3.4 index from November to March (NDJFM). In this definition, referred to as the SIMPLE definition, El Niño and La Niña winters are defined when the NDJFM-averaged Niño-3.4 index surpasses ±0.5 K as in BP11. This definition results in somewhat different ENSO winters from the CPC definition. A total of 16 and 20 winters are identified as El Niño and La Niña winters, respectively.
The CPC definition for the ERSSTv3b data is set as the reference in this study. The SIMPLE definition is used to test the sensitivity of SSW statistics to the ENSO definition. Although not shown, different threshold values (e.g., ±0.6 and ±0.7 K) were also tested for both the CPC and SIMPLE definitions. It turns out that the overall results are not sensitive to the threshold values [BP11; see also Taguchi (2015)].
The two different types of El Niño [i.e., central Pacific (CP) and eastern Pacific (EP)] are also briefly considered (e.g., Yeh et al. 2014). They are classified by comparing NDJFM-mean Niño-3 and Niño-4 indices. If the former is larger than the latter for the selected El Niño winter, it is classified as EP El Niño. Likewise, if the latter is larger than the former, it is set to CP El Niño. Note that this is one of the simplest approaches. Various definitions have been used to determine CP El Niño in the literature (e.g., Garfinkel et al. 2013). As such, the comparison of CP and EP El Niño winters in this study should be taken only qualitatively.
c. Significance test
The statistical significance of the ENSO–SSW relationship is tested with the bootstrap method. The detected SSW events are randomly redistributed over 57 winters from 1958 to 2014. This random sampling is repeated 1000 times to generate the probability density function (PDF) of the ENSO–SSW relationship. Using this PDF, it is tested whether El Niño winter or La Niña winter SSW frequency is statistically different from ENSO-neutral winter SSW frequency. This approach is essentially same as BP11. The statistical significance of composite fields is simply determined by using two-sided Student’s t test.
Figure 2 presents SSW statistics for seven SSW definitions. The NNR dataset along with the CPC ENSO index is used. In this figure, both the number of SSW events and their relative frequency are shown as in Taguchi (2015). The frequency is defined by dividing the number of SSW events by the number of selected winters for a given ENSO phase. Since multiple SSW events could occur in one winter, SSW frequency could be greater than 100%.
The WMO and U60 definitions show similar SSW statistics. As described in BP11 and BPD14, SSW events occur more frequently not only during El Niño winters but also during La Niña winters, with a slightly higher frequency during El Niño winters. More quantitatively, SSW frequency is about 70%–80% during ENSO winters, but only 35% during ENSO-neutral winters (Fig. 2b). This result, which is essentially an incremental extension of BP11 and BPD14 to the 2013/14 winter, reaffirms the nonmonotonic relationship between ENSO and SSW frequency in the U60 definition (BP11; BPD14).
More frequent SSW events during El Niño winters are also found in other definitions. In fact, although not always statistically significant, all seven definitions consistently show a higher SSW frequency during El Niño winters than ENSO-neutral winters. However, La Niña winters do not show any systematic relationship. While La Niña winter SSW frequency is higher than normal in some definitions (i.e., WMO and U60), it is comparable (i.e., U65 and U6090) or slightly lower than normal in other definitions (i.e., Z6090 or EOFU). The 2DM definition even shows more frequent SSW events during La Niña winters than during other winters.
The above results clearly suggest that the ENSO–SSW relationship, especially the ratio of La Niña winter SSW frequency to ENSO-neutral winter SSW frequency, is dependent on the details of the SSW definition. Their relationship can be roughly grouped into two groups. The first group, consisting of the WMO, U60, and 2DM definitions, shows more frequent SSW events during ENSO winters than during ENSO-neutral winters, whereas the second group, which includes the U65, U6090, Z6090, and EOFU definitions, shows more frequent SSW events only during El Niño winters. In the latter group, La Niña winter SSW frequency is not statistically separable from ENSO-neutral winter SSW frequency even at the 90% confidence level. A direct comparison between these two groups is not straightforward because each definition utilizes different variables and methodology. The physical and dynamical explanations of the detected ENSO–SSW relationship are also not easy.
For a direct comparison, two representative definitions are chosen in this study. They are the U60 and U65 definitions. These two definitions differ only in the reference latitude. By shifting the reference latitude only 5° poleward, the U65 definition detects four and six more SSW events during El Niño and ENSO-neutral winters, respectively, but essentially the same (one fewer SSW event) during La Niña winters (Fig. 2). The net result is a comparable SSW frequency between ENSO-neutral and La Niña winters in the U65 definition. This contrasts with more frequent SSW events during La Niña than ENSO-neutral winters in the U60 definition.
What causes the different ENSO–SSW relationship between the U60 and U65 definitions? Figure 3 presents the temporal evolution of 10-hPa zonal-mean zonal wind at 60°N (Fig. 3a) and 65°N (Fig. 3b) during the four El Niño winters when SSW events are detected by the U65 definition but not by the U60 definition. The two common SSW events (blue and red Xs in Fig. 3a) appear at almost the same dates. However, in the U65 definition, four additional SSW events are further detected (Xs in Fig. 3b). These events exhibit near-zero zonal-mean zonal wind at 60°N, but not easterly winds. For instance, the U65 SSW event in February 1958 (second red X in Fig. 3b) results from zonal wind deceleration at 65°N from 16 to −2 m s−1 over two weeks. A similar deceleration is also found at 60°N. However, the deceleration is weaker (from 13 to 1 m s−1) and does not end up with a wind reversal (Fig. 3a). A similar result is also found in January 1977 and February 1995 (yellow and green Xs in Fig. 3b). Although the zonal wind deceleration is strong at 60°N, the zonal wind does not cross the zero line. In these two cases, minimum zonal winds at 60°N are 0.02 and 0.3 m s−1, respectively. These results clearly indicate that different El Niño winter SSW events between the U60 and U65 definitions are simply caused by the threshold problem. If the U60 definition uses a threshold wind speed of a few meters per second rather than 0 m s−1 (wind reversal), its SSW statistics becomes quantitatively similar to that of the U65 definition. This result implies that a minor warming event in one definition can be a major warming event in another definition by slightly changing the reference latitude or threshold value. Although not shown, essentially the same results are found during ENSO-neutral winters.
The above threshold behavior does not exist in La Niña winter SSW events at least in the U60 and U65 definitions (Fig. 2). This difference is partly caused by the different latitudinal extent of the wind reversal during El Niño and La Niña winter SSW events (cf. red lines in Figs. 4a,c). The lowest latitude of the wind reversal, within 20 days after the onset of U65 SSW events, is 46.0°N ± 7.4° during La Niña winters but 53.5°N ± 8.5° during El Niño winters (55.6°N ± 7.8° for ENSO-neutral winters). When computing these latitudes, the SSW events where the wind-reversal latitude is extended to the subtropics and influenced by the quasi-biennial oscillation are discarded. Two cases for La Niña winters and five cases for both El Niño and ENSO-neutral winters are excluded.
This result indicates that the wind reversal during La Niña winters is wider in latitude (from ~46°N to the pole) than that during El Niño winters (from ~54°N to the pole). Given the fact that the wind-reversal latitude varies widely among the events, the detection of El Niño winter (and ENSO-neutral winter) SSW events can be sensitive to the choice of the reference latitude of 60° or 65°N. However, La Niña winter SSW events, which are associated with a wider latitudinal wind reversal, can be well detected by both the U60 and U65 definitions.
Figure 4 illustrates the temporal evolution of 10-hPa zonal-mean zonal wind and 100-hPa zonal-mean eddy heat flux as a function of time lag with respect to U65 SSW onset dates. Here, eddy heat flux is used to quantify a vertically propagating wave energy that can lead to the SSW event (e.g., Polvani and Waugh 2004). The background wind (earlier than lag −10 days) in El Niño winters is weaker than that in La Niña winters (Fig. 4e; see also Fig. 1a). Such a difference, which is statistically significant at the 95% confidence level, is consistent with a stronger planetary-scale wave activity during El Niño winters than during La Niña winters from lag −40 to −20 days [right column of Fig. 4; see also Taguchi and Hartmann (2006) and Calvo et al. (2008)]. The relatively weak polar vortex then may allow an easy wind reversal by moderate wave forcing. In fact, maximum wave activity associated with El Niño winter SSW events is relatively weaker than that of La Niña winter SSW events from lag −15 to 0 days (cf. Figs. 4b and 4d; see also Fig. 5).
Another important difference in wave activity shown in Figs. 4b and 4d is the central latitude of wave activity. The maximum wave activity is found at somewhat higher latitudes during El Niño winter SSW events (Fig. 4b) than during La Niña winter SSW events (Fig. 4d). Although not statistically significant, their difference clearly exhibits a dipole pattern at about ~70°N before the onset of the SSW events (Fig. 4f). More quantitatively, the maximum eddy heat flux, integrated over 40 days before the wind reversal at the lowest latitude, is found at ~70.1°N during El Niño SSW events but at ~61.0°N during La Niña SSW events. Here, only SSW events that are used in computing wind-reversal latitudes are considered.
This result, which is further summarized in Fig. 5 from lag −15 to 0 days, is consistent with the different extent of the wind reversal during El Niño and La Niña winters. In other words, a rather weak wave forcing at higher latitudes likely leads to a narrow wind reversal during El Niño winter (and ENSO-neutral winter) SSW events. This contrasts to a broad wind reversal by strong wave forcing at relatively lower latitudes during La Niña winter SSW events. Although the linear relationship between the minimum wind-reversal latitude and the maximum heat-flux latitude is rather weak (correlation coefficient of 0.25), this result suggests that the wave-driving latitude is one of the factors that determines the latitudinal width of the wind reversal.
The different wave activity, shown in Figs. 4b and 4d, results from different contributions of k = 1 and k = 2 waves. Figure 5 shows that El Niño winter SSW events are largely driven by k = 1 waves, whereas La Niña winter SSW events are led by both k = 1 and k = 2 waves. This difference, which could explain the different latitudinal extent of the wind reversal between El Niño and La Niña winter SSW events, is consistent with previous studies. Garfinkel et al. (2012) showed that k = 1 waves are enhanced at high latitudes during El Niño winters (see their Fig. 3). During La Niña winters, k = 2 waves are strengthened at low latitudes. By integrating the stratosphere-resolving model with prescribed SST anomalies, Taguchi and Hartmann (2006) showed that k = 1 waves are enhanced around 65°N in response to El Niño–like SST forcing. In contrast, during La Niña winters, k = 2 wave amplitude becomes stronger around 55°N. Calvo et al. (2008) also documented a stronger planetary-scale wave activity during El Niño winters than during La Niña winters, particularly in high latitudes.
4. Sensitivity tests
The sensitivity of the above results to the choice of reanalysis datasets, ENSO indices, and SST datasets is examined in this section. Overall results are summarized in Fig. 6 for both the U60 and U65 definitions. It is evident from Fig. 6a that the relative ratio of ENSO winter to ENSO-neutral winter SSW frequency does not change much when different ENSO indices are used (CPC vs SIMPLE definitions). Its sensitivity to the choice of SST data (CPC vs CPCv5) is also relatively minor.
Here, it is important to note that statistical significance is somewhat sensitive to the datasets. La Niña winter SSW frequency slightly decreases when the SIMPLE ENSO index is used, whereas ENSO-neutral winter SSW frequency slightly increases (middle box in Fig. 6a). This leads to a statistically indistinguishable SSW frequency between La Niña and ENSO neutral winters.
The ENSO–SSW relationship is also only weakly sensitive to the choice of reanalysis datasets (cf. Figs. 6a,b). However, the statistical significance becomes lower in JRA-55 than in NNR. The significant values, obtained in the SIMPLE ENSO index, also become statistically insignificant if the analysis period is shortened or only one SSW event is counted for a given winter. These results indicate that the ENSO–SSW relationship, reported in this study, is only marginally significant.
The El Niño–SSW relationship is further explored by considering two different types of El Niño, CP El Niño and EP El Niño (Yeh et al. 2014). Iza and Calvo (2015) reported no significant modulation of SSW frequency by the two types of El Niño. In agreement with their finding, El Niño winter SSW events are not biased toward either Niño-3 or Niño-4 SST anomalies in both the U60 and U65 definitions (not shown). This result, however, needs to be interpreted with caution as it could be sensitive to the datasets and the definitions of CP and EP El Niño. Hegyi et al. (2014), for example, showed no distinct relationship between polar stratospheric warming and El Niño types in their model simulation. This result contrasts to the modeling studies of Garfinkel et al. (2013) and Calvo et al. (2017), who reported more frequent SSW events during EP El Niño winters than during CP El Niño winters. To better understand these results, further analyses with a long-term climate model simulation would be needed.
5. Summary and discussion
It is found that the ENSO–SSW relationship is dependent on the SSW definition. Regardless of the definitions, SSW events tend to occur more frequently during El Niño winters than ENSO-neutral winters. The same is also true for La Niña winters in some definitions (e.g., U60 definition), resulting in a comparable SSW frequency between El Niño and La Niña winters (BP11; BPD14). However, this relationship does not hold in other definitions. For example, by shifting the reference latitude of SSW detection from 60° to 65°N (e.g., U65 definition), El Niño winter SSW frequency becomes much larger than La Niña winter SSW frequency.
A comparison of U60-based and U65-based SSW events reveals that the definition-dependent ENSO–SSW relationship is partly caused by the different latitudinal extent of the wind reversal during El Niño and La Niña winter SSW events. The El Niño winter (and ENSO-neutral winter) SSW events are typically accompanied by a narrow wind reversal from ~54°N to the pole. This may result in a misdetection of some U65 SSW events by the U60 definition. In contrast, La Niña winter SSW events are associated with a broad wind reversal from ~46°N to the pole. Both the U60 and U65 definition detect the same events.
The latitudinal extent of the wind reversal is largely determined by the latitudinal structure of planetary-scale waves in the lower stratosphere. During El Niño winters when the polar vortex is anomalously weak, SSW events are primarily driven by k = 1 waves, which are centered at ~70°N. On the other hand, La Niña winter SSW events are driven by both k = 1 and k = 2 waves. The enhanced k = 2 waves during La Niña winter SSW events are centered at ~60°N, likely resulting in a wider wind reversal than El Niño winter SSW events.
While reanalysis datasets are useful to identify the observed ENSO–SSW relationship, they suffer from relatively short records. For example, the EOFU definition, shown in Fig. 2, detects only 26 SSW events. With this small sample size, separate statistics of El Niño and La Niña winter SSW could be ill posed. In this regard, climate model datasets could be useful to establish more objective ENSO–SSW relationships.
Figure 7 presents the ENSO–SSW relationship in 12 high-top models archived for phase 5 of the Coupled Model Intercomparison Project (CMIP5). Details of the selected models are described in Calvo et al. (2017) and Kim et al. (2017). It is evident from Fig. 7a that the ENSO–SSW relationship in these models widely varies. Only two models (HadGEM2-CC and MIROC-ESM-CHEM) show the SSW statistics that are comparable to reanalysis datasets. Whereas three models, including these two models and GFDM-CM3, exhibit more frequent SSW events during El Niño winters than during ENSO-neutral winters, three other models (IPSL-CM5A-MR, MPI-ESM-MR, and MRI-CGCM3) show more frequent SSW events during La Niña winters than during El Niño winters. All in all, the multimodel mean SSW frequency shows no systematic relationship with the ENSO phase (right column). The enhanced SSW frequency during El Niño winters, highlighted in this study (Fig. 2) and the previous modeling studies (Taguchi and Hartmann 2006; Polvani et al. 2017), does not appear in most models in both the U60 and U65 definitions (cf. Figs. 7a and 7b). It is unclear why the CMIP5 models do not show an enhanced SSW frequency during El Niño winters. Although further studies are needed, it might be partly related to model mean biases. Kim et al. (2017) reported that SSW statistics can substantially change when the relative definition such as a wind tendency definition is used instead of an absolute wind-reversal definition.
Here, it should be stated that the present study is not aiming to identify or propose the best SSW definition. As noted earlier, there are many other SSW definitions that are not discussed in this study (Butler et al. 2015; Martineau and Son 2015; Palmeiro et al. 2015), and each definition results in somewhat different long-term variability of SSW frequency (Butler et al. 2015). More detailed analyses on other SSW events, such as those based on EOF, 2D vortex moments, and tendency (Limpasuvan et al. 2004; Seviour et al. 2013; Martineau and Son 2013), certainly deserve further analyses. These additional analyses would be helpful to better understand not only the interannual variability but also decadal variability of SSW events (Woo et al. 2015). In this regard, it would be useful to employ multiple SSW definitions to explore any statistical relationship between SSW frequency and climate variability.
This work is supported by the Korea Meteorological Administration Research and Development Program under Grant KMIPA 2015-2094