A sudden stratospheric warming (SSW) was first observed by Richard Scherhag using radiosonde measurements in Berlin, Germany, in January–February 1952 (Scherhag, 1952), when he found an abrupt temperature increase in the stratosphere. After about a decade, the World Meteorological Organization (WMO) Commission for Atmospheric Sciences (CAS) developed an international SSW monitoring program called STRATALERT based on available radiosonde and rocketsonde observations (WMO/IQSY, 1964). The WMO CAS suggested that an SSW warning be provided when a sudden and unusual increase in temperature at 30 km or above is detected.

With time ongoing and after more events were observed, it was well recognized that many SSWs occurred along with wind reversals and/or polar-vortex displacement or splits (Johnson et al., 1969; Charlton and Polvani, 2007). Since the 1970s, many studies combined temperature increases and wind reversals to detect SSWs, though detailed implementation and thresholds used are different (e.g., Schoeberl, 1978; Labitzke, 1981). An often-used definition at this stage was suggested by McInturff (1978). He defined that an SSW event occurred if temperature increased by more than 25 K, and the event was defined as a major one if a stronger temperature increase was jointly observed with a wind reversal.

Since wind reversal is one of the most important features of SSWs, many studies suggest using wind reversal for detecting major SSW events (e.g., Charlton and Polvani, 2007; Hu et al., 2015; Butler et al., 2015, 2017; Butler and Gerber, 2018). One of the most-often-used definitions is the one from Charlton and Polvani (2007) (denoted as CP07 hereafter): a major SSW occurs when the zonal-mean zonal winds at 60∘ N at the 10 hPa level become easterly during wintertime. Wind reversal is a simple and robust definition and is useful in studying many influences triggered by SSW. In addition to wind reversal definitions, there are also studies that used vortex moment, which is another important characteristic of the warmings, to detect SSW events (Seviour et al., 2013; Mitchell et al., 2013). Furthermore, polar-cap or zonal-mean stratospheric geopotential height anomalies at 10 hPa were used to detect SSW events (Baldwin and Thompson, 2009; Gerber et al., 2010).

Butler et al. (2015) tested the sensitivity of SSW detection results to nine definitions and found that SSW frequencies obtained under these different definitions varied from 0.35 to 0.91 events per year and that the onset dates also varied substantially. There are several reasons for these discrepancies. First of all, while SSWs usually occur along with wind reversal or polar-vortex change, this is not always the case. Several studies detected significant stratospheric warming but did not simultaneously detect wind reversals at the commonly used 60 or 65∘ N latitude. For example, Mitchell et al. (2013), who used vortex geometry for diagnosing SSW, found half of their events to be inconsistent with those obtained by CP07. Therefore, definitions based on different parameters can make detection results different. Secondly, single-latitude and/or single-altitude definitions, such as for wind reversal, may miss some important SSWs that occurred primarily in other latitude–altitude domains (e.g., Manney et al., 2015; Singh and Pallamraju, 2015). Thirdly, definitions can be sensitive to background climatology and specific thresholds used, especially if based on broad polar-cap-mean anomalies. Finally, current definitions either use zonal-mean or polar-cap-mean results, which do not enable dynamical 3D tracking of such events, and therefore can only provide information of onset date. However, the dynamic location and strength information is rather important for studies on SSWs' interactions with other phenomena, both regarding causes and impacts. Furthermore, SSW is also not a one-level phenomenon; its occurrence and impacts are related to almost the whole stratosphere.

In view of the studies we surveyed and from our own initial study (Li et al., 2021), we suggest that a new SSW monitoring method should build upon the temperature field that directly expresses the sudden stratospheric warming for quantifying this anomalous thermal behavior as the primary SSW fingerprint. It should robustly detect and characterize SSW events, from minor to extreme ones, as a whole phenomenon without being unduly sensitive to details. The method should also be readily applicable to both observational and model data (as long as they are sampled sufficiently densely, preferably grid based) and should not need adjustment to any specific suitable dataset (e.g., a particular reanalysis, atmospheric forecast, climate model simulation, or observational data record). Finally, upon detection, the SSW monitoring metrics should be informative regarding the duration, strength, and dynamic location of each SSW in order to facilitate long-term change monitoring and effective use in cause-and-impact studies. Implementing these suggestions, we propose our new method and definitions in Sect. 2.2.

SSWs, as reflected by their name, were originally determined by their strong and rapid temperature increase. Therefore, in the method proposed here, we use temperature as the key variable for the diagnostics. Compared to wind- and polar-vortex-based definitions, temperature is a more accessible parameter that can be obtained from various observations. In addition, temperature is a well-related parameter when analyzing SSW relations to other phenomena in the troposphere, as well as in the mesosphere, thermosphere, and ionosphere. Many studies chose to use temperature solely or combined it with wind field changes in studying the impacts of SSWs (e.g., Zhou et al., 2002; Siskind et al., 2010; Manney et al., 2015; Jonah et al., 2014; Kakoti et al., 2020; Singh and Pallamraju, 2015; Vignon and Mitchell, 2015). Also, further thermodynamic variables, particularly air density and pressure, are often readily available for auxiliary co-information (Li et al., 2021).

Based on temperature changes, we designed the method to be fairly insensitive to temperature field details. Firstly, we use robust stratospheric temperature anomaly profiles or pressure level data at any data location (such as a grid point) as the basis for expressing the local warming, using an anomaly technique that has been proven to be useful and robust in diagnosing many other climate and atmospheric change phenomena, such as those related to tropical cyclones (Biondi et al., 2015), atmospheric blocking (Brunner et al., 2016), or thermal imprints of wildfires (Stocker et al., 2021). As described in detail by Li et al. (2021) and as summarized in Sect. 3 below, we then calculate vertical mean anomalies in selected stratospheric layers or at selected levels and categorize them into large-scale grid cells covering the polar region, based on which we compute, on a daily basis throughout wintertime, temperature threshold exceedance areas and related metrics, which serve as the basis for SSW detection and monitoring.

In establishing SSW climatologies (i.e., cataloguing SSW events over a multi-decadal period), previous studies generally only provide information about onset dates and vortex splits or displacement. In the climatology we build based on the new method, we can provide SSW event onset date (of maximum middle-stratosphere warming), duration, exceedance area, and strength, as well as complementary day-by-day dynamic tracking of the center location, associated maximum warming, and areal extent of the exceedance area. Furthermore, most previously published climatologies do not yet reach beyond 2013 and miss some events over the 1990s decade, while we provide a climatology continuously extending from 1980 to 2021 and hence filling these gaps.

Compared to our initial method introduction and its careful evaluation in Li et al. (2021), which was based on the strong 2009 SSW event only, we focused on and refined the diagnostics for the metrics so that they now fully deploy for multi-decadal detection, classification, and monitoring. The details on data and methodology are described next in Sect. 3.

Since 2001, a continuous record of RO data is provided by GNSS RO missions, including the Challenging Mini-satellite Payload mission (CHAMP; Wickert et al., 2001), followed by the Gravity Recovery and Climate Experiment (GRACE, Wickert et al., 2005), and the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC; Schreiner et al., 2007), the European Meteorological Operational satellites (MetOp; Luntama et al., 2008), the Chinese FengYun-3C operational satellite (Sun et al., 2018), and others. Since the launch of COSMIC, which was a constellation of six satellites, around mid-2006, there has been sufficient coverage with RO event observations for regional-scale studies such as those on SSWs. Therefore, in this study, we use the RO data record from the wintertime of 2006–2007 onwards.

We use the atmospheric profiles from the Wegener Center for Climate and Global Change (WEGC), processed by its Occultation Processing System version 5.6 (denoted as OPSv5.6 hereafter). Several studies that introduced, validated, and evaluated the OPSv5.6 data record showed that these data are of high quality (e.g., Ladstädter et al., 2015; Angerer et al., 2017; Scherllin-Pirscher et al., 2017; Steiner et al., 2020a; Schwärz et al., 2016). A detailed discussion of quality aspects is provided by Angerer et al. (2017). Based on the record available to end 2020, we use RO data from the winter seasons W06–07 until W19–20, which are 14 winters (“W”) in total, which we define to comprise the extended-winter season from November to March (hence, for example, “W06–07” contains the November 2006 to March 2007 timeframe). We use the OPSv5.6 multi-satellite data from COSMIC, CHAMP, GRACE, MetOp, and SAC-C, in the form as available from the WEGC dataset (Schwärz et al., 2016).

ERA5 is the fifth-generation ECMWF atmospheric reanalysis of the global weather and climate (Hersbach et al., 2019, 2020; Simmons et al., 2020). It was produced for the European Copernicus Climate Change Service (C3S) by ECMWF and replaces the ERA-Interim reanalysis (Dee et al., 2011), which stopped being produced by August 2019. ERA5 combines vast amounts of historical observations into global atmospheric gridded field estimates using ECMWF's modeling and data assimilation system. The basic resolution of ERA5 is about 30 km horizontal resolution and 137 vertical levels from the surface up to an altitude of about 80 km (basic case with full resolution, also termed “full-res ERA5”). We use the ERA5 datasets from 1979 onwards over the 42 winters from 1979–1980 (W79–80) to 2020–2021 (W20–21), also fully encompassing the RO data period.

For cross-check of the dependence of detection and monitoring results on the vertical resolution of the input temperature fields, we alternatively also used the data at coarser standard pressure levels (using the C3S 37 pressure levels dataset, also termed “37-plevels ERA5”) or, as a minimum-input case, at the 10 and 50 hPa pressure levels only (termed “10 hPa & 50 hPa level ERA5”). These cross-checks are reported as part of the long-term monitoring results in Sect. 5 below; otherwise, the basic-case resolution was used throughout for introducing, illustrating, and describing the method. For the stratospheric focus of this study, we note that the basic-case full-resolution data cover the stratosphere with roughly 1 km vertical resolution (i.e., they are well altitude resolved), while the 37 pressure levels include no more than 10 levels from 70 hPa (∼19 km) to 1 hPa (∼48 km) (70, 50, 30, 20, 10, 7, 5, 3, 2, 1 hPa). The latter hence correspond to a quite coarser resolution but still easily allow one to compute reasonable finer-sampled vertical temperature profiles for our method's input, which we constructed by simple and robust vertical linear interpolation between the pressure level temperatures.

ERA5 data are used jointly with RO data for two purposes. On the one hand, they are used as part of cross-checking the new method to make sure that the method can be applied to both RO and reanalysis data. On the other hand (and even more relevant), since dense RO observations are only available from the year of 2006 onwards, we need to have reanalysis data, which provide much longer data records, to fully explore our method and to develop a long-term SSW climatological record. In terms of horizontal resolution, we use them on a 2.5∘ latitude × 2.5∘ longitude grid to provide an adequate resolution that also roughly matches the RO horizontal resolution of about 300 km (e.g., Kursinski et al., 1997; Anthes et al., 2008). The temporal resolution used is 6 h (four time layers per day at 00:00, 06:00, 12:00, and 18:00 UTC), following the experience of many previous studies that intercompared and/or jointly used atmospheric (re)analysis and RO data (e.g., Gobiet et al., 2007; Scherllin-Pirscher et al., 2011a, b; Angerer et al., 2017; Steiner et al., 2020a; Li et al., 2021).

Figure 1 illustrates characteristics of the RO and ERA5 profile datasets as relevant for the present SSW study, including the daily number of events available (Fig. 1a) and for exemplary days during SSW events (Fig. 1b–d, see caption for details). Evidently, RO observational atmospheric profile data are comparatively sparse over the (northern high-latitude) region of interest, while ERA5 as a gridded dataset regularly provides its profiles at each and every one of its grid cells without sparsity. Hence, while the number of RO profiles is of the order of several hundred per day, the ones of ERA5 amount to near 10 000 per day. Furthermore, as Fig. 1b–d shows, the spatial distribution of ERA5 data is regular on grid, while RO events occur with reasonable overall coverage but irregular sampling in detail. A few exemplary events (“Event1” to “Event3”) are highlighted, against the back-plot of illustrated SSW temperature anomalies over the polar region, in order to use them next to explain the methodology.

Since we recently provided a detailed basic introduction of the new SSW monitoring approach in Li et al. (2021) and already discussed the main overall features in Sect. 2.2 above, we restrict ourselves to a brief summary here, supported by a schematic overview and concise tabular information and focusing on updates and refinements since that introduction, which provides further technical details.

As a general overview, Fig. 2 provides a schematic summary of the method's workflow. It highlights the computation sequence, starting with the temperature field input data via anomalies construction and gridded maps generation in stratospheric layers or at pressure levels to extract the threshold exceedance areas (TEAs) of different SSW phases and finally deriving the SSW metrics then used for detection, classification, and characterization. Table 1, which is a condensed and refined update of Table 1 in Li et al. (2021), complements this schematic overview by summarizing the basic parameters and features of the method in more detail along with respective explanations (rightmost column). This ranges from the definition of the temperature anomalies and the related daily TEAs in three characteristic stratospheric layers – lines (1)–(4) – via the anomaly-maximum value and location – lines (5) and (6) – to the four derived TEA key variables during SSW events – lines (7)–(10) – that monitor and characterize the different SSW phases. We note that the daily TEAs for the three layers – lines (2)–(4) – are computed for a range of threshold values for convenient closer insight to the depth of the anomalies (as illustrated in Sect. 4), while only one basic threshold value – boldfaced in lines (2)–(4), middle column – is subsequently used for defining the TEA key variables – lines (7)–(10). All selections and settings summarized and explained in Table 1, including those in the footnotes a–c related to the vertical-resolution options, are based on very extensive sensitivity tests of all the choices, using the ERA5 and RO data as the testing input datasets.

For aiding the understanding on how the profile and layer-mean anomalies typically look, Fig. 3 graphically illustrates the construction of the anomalies and variables by way of the three example RO events indicated in Fig. 1 and, correspondingly, for three ERA5 profiles from adjacent grid points. It can be seen that RO and ERA5 profiles are overall consistent, with the latter profiles being somewhat smoother in their resolution of vertical variability. Deviations of temperature and corresponding climatological profiles are smallest for Event1 that is located in a non-warming area (see Fig. 1b). Event2 and Event3, which are most affected, show larger deviations and anomalies than Event1, since these are located in the warming area of the SSW (see Fig. 1b and d). The largest anomalies for the latter two events are found in the mid-stratosphere layer (30–35 km), with values of about 45 and 60 K, respectively. Maximum values in the other altitude layers are smaller. In this way, these few examples are consistent with the broader and long-term picture over many SSW events (see Sect. 4 below), which show the SSW warming to be strongest in the middle stratosphere (about 30 to 40 km).

While Li et al. (2021) introduced and initially tested the approach based on the single 2009 SSW event, here we made sure for the long-term application that the four TEA key variables are captured and exploited in such a way that they reliably detect and quantify actual SSW warmings and cooling in the trailing phase, if it occurs, among the ongoing weaker and more “random” polar variability due to other driving factors. The rightmost column of Table 1 – lines (7)–(10) therein – summarizes the criteria that we chose for them after comprehensive testing and sensitivity studies with both the RO and ERA5 data, including on the different options of vertical resolution of the ERA5 temperature input fields. Based on these well-selected TEA key variables and the auxiliary variables on maximum values and locations, all prepared at daily sampling, we could finally define the fundamental metrics and criteria that we use for the detection, classification, and further characterization of SSWs. These definitions were accompanied by another comprehensive portfolio of sensitivity tests, and the choices distilled are summarized in Table 2, including brief explanations (rightmost column therein and footnote *).

Overall, the extensive robustness and sensitivity testing provided us with due evidence and confidence that the new method, effectively constructed from the dynamic temperature anomaly field as perturbed by the SSW, should enable a new level of quality and quantitative insight into SSWs in the long-term, maturing the methodology from our initial Li et al. (2021) single-event study. Hence, as a next step, we applied the method with the parameters and definitions summarized in Table 2 to the complete RO and ERA5 datasets and discuss the results below.

Polar cap daily mean temperature anomalies over the 15 winters period from W06–07 to W20–21 are presented in Fig. 4, where both the RO and ERA5 datasets overlap for 14 winters. The RO and ERA5 polar cap results are closely consistent, with anomalies from ERA5 typically about 5 K (occasionally up to 10 K) larger than RO data above 35 km. These differences can mainly be attributed to the denser sampling of ERA5, leading to less spatial smoothing. In general, the overall close results of these independently produced and quite differently sampled datasets (for detailed discussion, see Li et al., 2021) lend confidence that we may use ERA5 data for the inspection of the multi-decadal time period from 1980 onwards.

Complementary back-extended polar cap temperature anomalies of ERA5 for the 27 winter periods W79–80 to W05–06 are shown in Fig. 5. The results provide a neat first overview on which winter seasons hosted potentially strong SSWs (e.g., W84–85, W03–04, W18–19) and which were comparatively quiet, including having little evidence of SSWs (e.g., W81–82, W93–94, W10–12). It is also revealed to be a very salient feature already in this polar-cap-mean inspection that strong SSW events often are entailed by a distinct upper-stratospheric cooling, which is hence reflected in our metric definitions – see Table 2, lines (6)–(8). Another interesting feature hinted at here already is that, in the 1990s, where existing SSW climatologies detect very few events (e.g., Charlton and Polvani, 2007; Hu et al., 2015; Butler and Gerber, 2018), we do detect several reasonably strong SSWs that can be classified as major events (more details in Sect. 4.4).

Some distinct temperature anomalies are found in almost every winter in one or another form, which underlines the fact that the polar stratosphere is quite variable in winter. Regarding SSWs, some winters signal one strong warming, while some others show multiple moderately strong or minor warmings. Strong warmings propagate to lower altitude levels and also cause longer-lasting warmings and, as noted above, may be accompanied by distinct cooling (such as in the most recent decade W12–13 and W18–19). A final observation from this basic synoptic view is that the altitude range of maximum warming varies somewhat from event to event. For example, the W11–12 warming is largest at about 35 to 40 km, while the W17–18 warming exhibits its largest anomalies at about 25 to 30 km. Our definition of main phase, combining middle- and lower-stratospheric TEA diagnostics – see Table 1, line (9) – robustly captures such different specific event dynamics.

Figure 6 illustrates TEA spatial contour map results for typical daily temperature anomalies across the temporal evolution (top to bottom) of three representative SSW events of increasing strength (left to right; those already used for back-plot in Fig. 1). Evidently, both the temperature anomalies' magnitude and warming area increase from minor to extreme events, as expected based on our classification, which is particularly visible in the mid-stratosphere temperature anomaly on the event onset date (second row). Complementary to this, the snapshot day shown from the trailing phase (four weeks after onset date, bottom row) highlights that the extreme event (right) exhibits a very distinct upper-stratosphere cooling anomaly, exceeding -40 K in a TEA of about 10 million km2 size.

Following this representative spatial view on individual daily TEAs, Fig. 7 depicts, for the same events as shown in Fig. 6, how our method leads from TEA time series in the three stratospheric layers (first three rows of Fig. 7) to the TEA key variables (fourth row) from which the SSW metrics for the event characterization according to Table 2 are finally derived.

Daily TEA values over positive thresholds quantify the size of exceedance areas of warming, while those over negative thresholds diagnose the exceedance areas of cooling. It can be seen, for example, that middle-stratosphere temperature anomaly TEAs (MSTA-TEAs) over positive thresholds of all events increase rapidly to maximum and then quickly decrease, indicating the typical sudden warming of the primary phase. Lower-stratosphere temperature anomaly TEAs (LSTA-TEAs) over positive thresholds are overall of smaller magnitude but longer duration, and with maxima delayed against MSTA-TEAs, from the SSW downward propagation. Regarding event strength, while MSTA-TEAs > 30 K of major and extreme events are of small discrepancy within 2×106 km2, the duration of the extreme event is longer than for the major event. The upper-stratosphere temperature anomaly TEA (USTA-TEA) time series of the extreme event shows the distinct several-weeks-long cooling behavior in the trailing phase.

The TEA key variables (Fig. 7j to l) capture the essential daily TEA information per SSW event, in the form summarized in lines (7)–(10) of Table 1, as the basis for the three key metrics per event according to lines (1)–(3) of Table 2, the quantified values of which are shown in the panel legends. As already indicated by the polar-cap-mean view in Figs. 4 and 5, it is well seen here that the ERA5 TEAs (heavy lines) are generally higher than those from the RO data (thin lines), which particularly applies for the trailing-phase cooling of the extreme event (Fig. 7l) in the upper stratosphere, where the sparser sampling by RO events leads to the relatively larger difference. In terms of magnitudes, it is clearly visible from the values that the main-phase strength (MPS), main-phase duration (MPD), and main-phase area (MPA) metrics reach that the event strength grows substantially from minor to extreme – see also the strength class definitions based on the MPS in line (5) of Table 2.

The polar-map plots of Fig. 7 (bottom row) finally illustrate the dynamic event-tracking information of the SSW-PP-TEA, SSW-SP-TEA, and SSW-TP-TEA time series for the three representative events. This view enables one to see the geographic trajectory of the daily anomaly center location – maximum-value location, see line (6) of Table 1 – together with an indication of the anomaly magnitude (color of corresponding TEA thresholds). This type of plot helps the detailed diagnostics and characterization of any specific event, as introduced in Sect. 2 above (for details, see also Li et al., 2021).

Figures 8 and 9 employ the view introduced in Fig. 7j–l to display the TEA diagnostics and MPS, MPD, and MPA metrics results for all SSWs detected over the full multi-decadal period from 1980 to 2021 (Fig. 8 for the recent winters since 2001–2002 and Fig. 9 for those before, up to 2000–2001). In the recent two decades, typically one or two SSWs occurred during almost every winter (except in W04–05 and W10–11), while in the two decades before, there were somewhat more SSW-quiet winters.

The strongest event during the entire period is the one in W08–09, with a main-phase strength (MPS) of over 360 million km2 days for the ERA5 data (330 million based on the cross-verifying RO data). The second strongest event is the one of W18–19, where the MPS from ERA5 exceeded 290 million km2 days. Additionally, the winters W01–02, W12–13, and W17–18, as well as the winters W84–85, W87–88, and W88–89 in the 1980s, hosted extreme events exceeding our classification threshold of 180×106 km2 days. Half of these eight extreme events also are seen to have caused a strong upper-stratospheric cooling during the trailing phase that lasted for more than a month.

In addition, several major events occurred (e.g., W02–03, W03–04, W05–06), with the MPS of such events varying from 90 to 180×106 km2 days, as defined in Table 2. Also, two of the major events caused a long-lasting upper-stratospheric cooling in the trailing phase (in W03–04 and W05–06); however, this is an exception for these events. Together with these major events, a range of minor events were also detected and diagnosed, exhibiting an MPS smaller than 90×106 km2 days. Based on these long-term SSW tracking results, shown in Figs. 8 and 9, we are now prepared to collect and analyze the long-term results in a more climatological, statistical manner, including inspection for possible long-term transient changes in the record under climate change.

Based on the detection results in Sect. 4, a climatological summary of the ERA5-based results for all SSW events detected during the entire 42-year period is provided in Table 3. It lists, for each event, the main characteristics as defined by Table 2 and intercompares the onset dates to the onset dates found by the Butler and Gerber (2018) work (BG18) that extended to the year 2013. The intercomparison reveals that a range of minor and major events was not part of the BG18 list, while several are part of that list and not detected here. In general, the onset dates detected by the new method introduced here are consistent with those in the BG18 climatology, with coincidence of the dates commonly within ±1 d.

As a complement, the corresponding onset dates and key metrics, as obtained from the RO data, are shown in Table 4. Four minor events (in W07–08, W11–12, and W16–17) did not meet the detection criteria for this dataset, though they were detected based on the ERA5 data. One of the two of W07–08, which overlaps with the BG18 data record, was also not detected by RO data.

In terms of count statistics, 43 events in the 42 winters are detected, corresponding to a frequency of 1.02 per year. This is close to the frequency estimate of 0.9 per year by McInturff (1978). The BG18 climatology, which only lists major SSW events, yields a frequency estimate of 0.6 per year, which is close to the 0.50 per-year frequency we find for our major and extreme events (i.e., discounting the minor events). In general, the high consistency of onset dates with the BG18 definition provides evidence that our new temperature-anomalies-based method is robust in detecting SSW events and that the warming anomalies are strongly related to wind reversals during SSWs. For those events detected by the BG18 definition but not by our method (e.g., the W06–07 event in February 2007), we do find minor warmings also signaled in our TEA diagnostics, but they do not exceed thresholds long enough (for at least 6 d) for detection according to Table 2.

For the higher number of events detected by us but not detected by the BG18 definition, there are several reasons. The main reason is that a detection based on single altitudes and latitudes misses events occurring in other domains. Related to altitude, we found that a number of events occurred at levels higher than 10 hPa; therefore, such events were not detected by the BG18 definition (e.g., in W92–93 and W00–01). In W07-08, we basically found four warmings (as can be seen in Fig. 4), of which three satisfied our detection criterion. This is in line with Singh and Pallamraju (2015), who also found four warmings based on a temperature increase definition. Related to latitude, Hu et al. (2015) used a wind reversal definition at 65∘ N, detecting an event on 26 January 2010, which is close to our onset date of 29 January 2010 rather than the BG18 date of 9 February 2010. This indicates that selection of a specific latitude for detection also can hinder reliable detection. Finally, some temperature increase events may not be associated with wind reversals at 10 hPa.

Furthermore, we detected a number of events in the 1990s, while BG18 detected only one in W98–99. This can be attributed to three reasons. Firstly, the largest warmings occur at higher altitudes than at the 10 hPa level and therefore may not be detected by data using such a single level. Secondly, a significant amount of radiosonde stations ceased operations in the 1990s, and the availability of wind measurements to the BG18 study for SSW detection was degraded. Thirdly, several warming events are not highly related with wind reversal. Our method, based on temperature data records (here primarily from ERA5, verified by RO data), is robust against such observation network changes, and in addition, temperature is an easily available variable, including in the form of multi-decadal records with reasonable long-term stability.

Figure 10 finally depicts summary statistics on the long-term results along various perspectives of interest, both for the full vertical-resolution (basic case) and coarser-resolution data (see the caption and the respective panel titles for an explanation of the various panels). Regarding the upper half (Fig. 10a–d), it is seen that the results from using the standard pressure level input data (“37-plevels ERA5”) are very similar to those from the basic case (“full-res ERA5”), with the coarser-resolution case detecting only one event less and two events differently. In addition, from simply using linear interpolation between the pressure level temperatures before computing layer-mean temperatures (cf. Fig. 3) from the interpolated coarser-resolution profiles, the SSW strength (MPS) is found to be overall slightly smaller than for the basic case (see the difference of adjacent color and gray symbols in Fig. 10a). However, the size of these differences relative to the basic case is typically smaller than 3 %.

Furthermore, while the MPS appears widely variable as a time series (Fig. 10a), the inspection of its component metrics MPD and MPA reveals that the former (the duration) most clearly drives the strength (Fig. 10b, upper left subpanel) and that a salient trail-cooling phase, indicated by the TPD and TPA auxiliary metrics, is dominated by some of the strongest events (Fig. 10b, lower subpanels). Inspecting the SSW onsets, almost all of them (over 95 %) are found within the deep winter (i.e., the December–January–February timeframe, with about half in January; Fig. 10c) and more than three-quarters are found to have their onset location over northern Eurasia and the adjacent polar ocean (Fig. 10d).

The cross-check of using simple two-pressure-levels input data only (“10 hPa & 50 hPa level ERA5”), depicted in the bottom half of Fig. 10e–h, shows that the results are overall similar to the basic case but are notably diluted in the number of detected events (32 instead of 43) and provide systematically smaller MPS estimates by about 20 %–30 % (cf. Fig. 10a and e). The main reason for this is that the downward-propagating warmings are captured at less strength at the 10 hPa (∼32 km) and 50 hPa (∼21 km) levels than by the layer means taken over 30–35 and 20–25 km, respectively. The respective minimum-threshold and MPS classification parameter adjustments for this simple two-levels approach (see Table 1 and 2 footnotes; TEAMin reduced from 3 to 2×106 km2 and classification boundaries lowered from 90–180 to 70–140×106 km2 days) help to compensate for this “low bias” relative to the basic case. The overall detection frequency is nevertheless reduced to 0.76 per year (Fig. 10g), while we find the frequency of the major and extreme events of 0.48 per year to be closely similar to the one for the basic case (0.50 per year). The relative under-detection of events is hence mainly attributable to minor events.

In summary, we thus recommend the use of temperature field data with adequately high vertical resolutions as input to the method. At the same time, the cross-checks demonstrate that the method is also robust and reliable for coarser-resolution data and as a minimum for 10 and 50 hPa level data only, though it is in the latter case somewhat less apt in its detection and monitoring capacity.

Visually spotting a long-term “tendency” of some possible strength intensification in Fig. 10a and b and the numbers of Table 3, the inspection of long-term trends in the SSW metrics during the climate change period from the 1980s to the 2010s is also of particular interest. Hence, we quantitatively inspected for multi-decadal trends in MPS, MPD, and MPA based on the 33 decadal-mean values of these three metrics over the 1984 to 2016 center years. Regarding a robustness cross-check, we performed this not only for the basic case with full-vertical-resolution input but also for the coarser-resolution cases.

In computing the decadal-mean value of a metric from all individual-event values of a decade, events are allocated to a year based on their onset month, and the mean is obtained from the 10-year-aggregated values over the center year -4 years to the center year +5 years divided by 10 (we also cross-checked to a simple averaging over the events in any 10-year window, which led to similar results but with somewhat more variability due to a direct dependence, in this case, on the sometimes small event count per decade). For the trend fits, we used ordinary-least-squares linear fitting and included uncertainty estimation for the trend rate, accounting for reduced degrees of freedom due to autocorrelation and assuming small-sample t-distribution statistics (Santer et al., 2000; Loeb et al., 2022).

Figure 11 shows that we indeed find a statistically significant positive trend in the MPS, with a best-estimate strength intensification for the basic case (top row, “full-res ERA5”) of about 12(±8) million km2 days per decade (95 % significance level, left subpanel), which is driven by a highly significant increase in the MPD of about 1.8(±0.7) d per decade (99 % significance level, middle subpanel). This implies an increase in the duration of SSW main-phase warmings of about 5(±2) d from the 1980s to the 2010s, raising the average duration by nearly 50 %, from about 10 to 15 d, and inducing an SSW strength increase of about 40(±25) million km2 days, from about 100 to 140 million km2 days.

No robustly significant trend was found in the MPA (right subpanel) or in the associated threshold exceedance magnitude (the average warming strength of the main-phase temperature anomaly above threshold, as indicated by the Max ΔT threshold exceedance defined in line 11 of Table 2), for which sensitivity testing confirmed that it is clearly correlated with the MPA. As part of extensive sensitivity testing, we also found an indication of an increasing trend in the number of major and extreme SSW events of about 0.4 events per decade (near 90 % significance level). The time series is still quite short for such an analysis, however, and it somewhat depends for the minor event counts on the threshold definition for their detection.

The coarser-resolution-based results (middle and bottom row of Fig. 11, “37-plevels ERA5” and “10 hPa & 50 hPa ERA5”) confirm that the trends found are robust across using different input data resolutions (i.e., consistent within the co-estimated uncertainties). Though the mean estimates and associated uncertainty bounds are quite varied across the three cases, reflecting the small-sample statistics with fairly few effective degrees of freedom (typically 8 to 12 only for the 33 decadal-mean values) of the rather short and volatile time series, the overall result of a clearly significant MPD increase that drives a corresponding MPS increase is robustly evident.

While a detailed interpretation and further study of the possible causes of this increase in warming duration, including cross-comparison with other temperature field datasets beyond ERA5, are beyond the scope of this study that focuses on introducing the new monitoring method and related SSW climate data record, we speculate that it may be related to changes in the polar-vortex dynamics over the recent decades that have led to transient changes in prevalent vortex patterns, partly induced by anthropogenic climate change in the polar region (e.g., Kretschmer et al., 2018a, b). Since the MPS metric can be interpreted as an anomalous heat energy content contained in the exceedance warming of an SSW event (similar to the threshold exceedance metric of cooling degree days in the analysis of energy demand during hot days or even heat extremes; Forster et al., 2021), the estimated increase of about 40 % since the 1980s corresponds to substantially more energy stored in and released by recent SSW events.