The nature of Arctic polar vortices in chemistry–climate models



The structure of the Arctic stratospheric polar vortex in three chemistry–climate models (CCMs) taken from the CCMVal-2 intercomparison is examined using zonal mean and geometric-based methods. The geometric methods are employed by taking 2D moments of potential vorticity fields that are representative of the polar vortices in each of the models. This allows the vortex area, centroid location and ellipticity to be determined, as well as a measure of vortex filamentation. The first part of the study uses these diagnostics to examine how well the mean state, variability and extreme variability of the polar vortices are represented in CCMs compared to ERA-40 reanalysis data, and in particular for the UMUKCA-METO, NIWA-SOCOL and CCSR/NIES models. The second part of the study assesses how the vortices are predicted to change in terms of the frequency of sudden stratospheric warmings and their general structure over the period 1960–2100.

In general, it is found that the vortices are climatologically too far poleward in the CCMs and produce too few large-scale filamentation events. Only a small increase is observed in the frequency of sudden stratospheric warming events from the mean of the CCMVal-2 models, but the distribution of extreme variability throughout the winter period is shown to change towards the end of the twentyfirst century. Copyright © 2012 Royal Meteorological Society and British Crown Copyright, the Met Office

1. Introduction

The evolution of the NH* stratospheric polar vortex over the twentyfirst century is still a topic of much debate in the scientific community. Studies over the last decade have shown that anomalies caused by extreme vortex variability can influence the tropospheric climate, and imply a measure of tropospheric predictability from such events (e.g. Baldwin and Dunkerton, 1999, 2001; Thompson et al., 2002). In what is termed an SSW, the polar vortex of westerlies can be slowed and reversed to become easterly by the transfer of momentum from vertically propagating planetary waves. However the detailed mechanism by which this phenomenon occurs is still unknown (e.g. Matsuno, 1971; Esler and Scott, 2005; Scott and Dritschel, 2006).

Due to the tropospheric impact of SSW events, robust predictions of vortex variability under various ozone and GHG conditions are highly sought after. For instance, Bell et al. (2010) showed, using the Hadley Centre HadSM3-L64 model, that under four times pre-industrial CO2 concentrations, the vortex would become more highly disturbed with an increased frequency of SSW events. In contrast, Rind et al. (1998) reported a decrease in SSW frequency using the GISS global climate/middle atmosphere model with two times pre-industrial CO2 concentrations. In addition, Charlton-Perez et al. (2008) showed, using the AMTRAC with the IPCC SRES A1b climate forcings, that an increase of 1 SSW event per decade was predicted over the twentyfirst century. They also noted that the ratio of wave 1 and wave 2 SSW events would remain unchanged for this period, in contrast to Bell et al. (2010) who found that wave 1 events would dominate over wave 2 at a ratio of 4:1, a doubling of the current-day ratio found in the ECMWF ERA-40 and NCEP reanalyses over the 1958–2001 period (Charlton and Polvani, 2007). However, results from these studies are by no means robust, and with competing impacts from changes in the stratospheric ozone and increased GHGs, global climate models give no clear consensus as to whether the polar vortex will become more or less stable in the future. One reason for this is the initial representation of the vortex in models; if indeed the vortex is poorly characterised in past runs can predictions into the future really be trusted? Another reason comes from the typical definitions of extreme vortex variability. Commonly, a so-called ‘major’ SSW is defined as occuring when ‘the ZMZW at 60°N and 10 hPa reverses from westerly to easterly’. Such a definition may be misleading, as the climatological zonal mean state of the stratospheric circulation is likely to change under future climate forcings, hence the SSW frequency may increase simply because the climatology of ZMZW is closer to zero, and vice versa. A future change in SSW frequency could therefore be interpreted as a change in the variability of the vortex, or a change in the basic state of the vortex, both resulting in the same outcome but for fundamentally different reasons. Conversely, if it is the reversal from westerlies to easterlies that has the biggest impact on tropospheric climate, then the ease of fulfilling the SSW criterion becomes less of an issue. Such problems have been addressed in both McLandress and Shepherd (2009), who argue that use of the NAM is needed to measure vortex variability, and Bell et al. (2010), who argue that the zonal mean wind approach is most suitable as it controls wave activity entering the stratosphere.

A further problem with assessing SSWs in climate runs is the large decadal variability associated with them. This was addressed to some extent in Schimanke et al. (2011), who used the EGMAM with different climate forcings taken from IPCC SRES and the zonal wind definition of a SSW. They found that, despite the high variability in the timings of SSW events in the model, statistically significant increases in the frequency of SSW events in the future were still observed but large numbers of model integrations were needed.

An alternative approach to this problem is to use the vortex benchmark developed in Mitchell et al. (2011) (hereafter M11), which itself is an extension of previous studies (Butchart and Remsberg, 1986; Waugh, 1997; Waugh and Rendel, 1999; Matthewman et al., 2009). M11 used the application of 2D moments to measure the area, centroid, aspect ratio and kurtosis of the vortex throughout the ERA-40 dataset (1958–2001) over the winter (DJFM) period. The validity of these data was found to be sound in a companion study undertaken by Hannachi et al. (2011). For a full description of these vortex diagnostics, the reader is referred in the first case to M11, but also to Matthewman et al. (2009). However, in brief, the objective area gives a measure of the vortex's area and strength, the centroid latitude gives a measure of the displacement of the centroid of the vortex, the aspect ratio is a ratio between the major and minor axes of the vortex and the kurtosis gives a measure of vortex variability, where negative kurtosis values indicate a vortex split, values between 0 and 0.5 indicate a stable vortex, and high positive values indicate strong filamentation.

In M11 these diagnostics were modelled using parametric distributions to develop benchmarks for the structure of the vortex in reanalysis data. Here, we calculate and compare the same distributions using three models taken from the CCMVal-2, UMUKCA-METO (hereafter METO), NIWA-SOCOL (hereafter NIWA) and CCSR/NIES models, to build a complete picture of the vortex variability in both past and future simulations. The remaining models from CCMVal-2 are not used for the 2D moment analysis as they do not output daily PV in the mid-stratosphere, a pre-requisite for this type of analysis (Waugh, 1997). However a brief analysis using the more traditional definitions of SSW events developed in Charlton and Polvani (2007) is employed.

By performing the analysis in this way we aim to:

  • 1.Demonstrate the power of using the 2D moments as a geometric method of characterising the vortex, and show how it provides more detailed information regarding all aspects of the vortex variability than the standard SSW definition.
  • 2.Assess the structure of the vortex in past runs of the METO, NIWA and CCSR/NIES models.
  • 3.Determine how vortex variability will evolve under future climatic forcings as a comparison and extension of the studies discussed previously.

The structure of this article is as follows. Section 2 describes the CCMVal-2 model set-up. Section 3 gives an overview of the analysis techniques used throughout this study. In section 4, a review is given of the key results from a similar study (Butchart et al., 2010), which only uses traditional SSW definitions to assess past SSW frequency, with an emphasis on the three CCMVal-2 models used in this study. This is then expanded by using the benchmark technique developed in M11 to build a comprehensive picture of how the structure of the vortex in the three CCMVal-2 models is represented. The structure of the vortex over the twentyfirst century is then assessed in section 5 using a combination of the techniques laid out in Butchart et al. (2010) and M11 with a summary of key results/conclusions given in section 6.

2. Model set-up

The horizontal and vertical resolution, height of the model tops and relevant references are detailed in Table 1 for the three models that are used for the majority of this analysis. A more extensive review is given in Morgenstern et al. (2010) which includes the remaining CCMVal-2 models, many of which are briefly analysed in this study.

Table 1. A summary of specifications for ERA-40 reanalysis and the three CCMVal-2 models used for the majority of this analysis.
ModelVertical resolutionHorizontal resolutionModel topReferences
ERA-40L60T1591 hPaUppala et al. (2005)
UMUKCA-METOL602.5° × 3.75°84 kmHardiman et al. (2010), Osprey et al. (2010)
CCSR/NIESL34T420.012 hPaAkiyoshi et al. (2009)
NIWA-SOCOLL39T300.01 hPaEgorova et al. (2005), Schraner et al. (2008)

The METO, NIWA and CCSR/NIES models all provide daily PV on the 460 K and 840 K isentropic surfaces, and daily zonal winds on surfaces between 1000 and 0.1 hPa. The CCSR/NIES model also has three ensemble members over the historical period, all of which are used in the analysis presented here. M11 showed that the vortex was far more disturbed, and hard to characterise on the 450 K surface due to vigorous stirring of the vortex air at this height. Therefore the 840 K PV surface is used for the 2D moment analysis, and the approximately equivalent pressure surface of 10 hPa is used for the zonal wind analysis so that a direct comparison between ERA-40 and the CCMs can be made. Note that, instead of ERA-40, the NCEP/NCAR dataset could also be used for this study and has been shown to work with the moment-based method (Waugh and Rendel 1999).

The analysis makes use of two of the CCMVal-2 scenarios. The first, termed REF-B1, is a transient run from 1960 to 2006 with all known climate forcings (Morgenstern et al., 2010). This scenario is used to study how well the vortex is represented compared to ERA-40 reanalysis data. The second, termed REF-B2, runs from 1960 to 2100 following the middle-of-the-road SRES A1b (IPCC 2008) and is used to examine future vortex variability and the possibility of a change in the frequency of SSW events.

3. Techniques

3.1. Defining moments

The analysis employed throughout this study compares the zonal mean diagnostics, of which there are numerous examples in the literature (e.g. Andrews et al., 1987; O'Neill, 2003; Charlton and Polvani, 2007), with the geometric-based moments. A brief summary of the moment diagnostics is presented here, but for technical details readers are referred to Matthewman et al. (2009) and M11.

The moment diagnostics are based on manipulation of the 2D moment equation, which in Cartesian form, is

equation image(1)

where a and b give the order of the moment in the x and y directions respectively, and q(x,y) represents the PV inside the vortex region.

The application of 2D moments to the vortex PV field essentially expresses a complex vortex structure as a set of vortex centric parameters, such that setting a + b = 0 gives the vortex objective area, a measure of the vortex strength and size. Setting a + b = 1 gives the vortex centroid location, setting a + b = 2 gives the vortex aspect ratio, and setting a + b = 4 gives the vortex kurtosis. The kurtosis provides a measure of how split the vortex is (negative kurtosis) or of the presence of large filamentation events (high positive kurtosis).

3.2. Parametric distributions

Analysis of all the vortex diagnostics is undertaken using parametric distributions. Following M11, we use Gaussian and GEV distributions to model whole timeseries of the vortex diagnostics, and GP distributions to provide a more in-depth analysis of the extremes of these datasets. Mathematically, the Gaussian, GEV and GP distributions are defined respectively in Eqs (2), (3) and (5).

equation image(2)

where σ is the standard deviation and μ is the mean of the data,

equation image(3)


equation image(4)

where μ is the location parameter, σ is the scale parameter and ξ is the shape parameter, and

equation image(5)

The application of extreme value statistics to the vortex data allows for a more involved analysis than using the standard distributions. It is often more meaningful to interpret extreme values in terms of return levels instead of the GP parameters. In this case, the return level is the level expected to be exceeded in a given unit of time, N. For example, it can be used to show the predicted number of years until an event where the vortex would have an aspect ratio of 4 or above. Mathematically the return level can be expressed as

equation image(6)

where u is the threshold value, ny is the number of observations, ζu = Pr{X > u} and X is the dataset being considered (Cole, 2001, pp 81–82 provides a complete derivation of Eq. (6)).

4. The representation of the vortex in CCMs

4.1. Using the traditional diagnostics

We begin the analysis of vortex variability with a brief overview of the findings from Butchart et al. (2010), who used the methodology developed in Charlton and Polvani (2007) based on the ZMZW at 60°N and 10 hPa to compare the SSW frequency (their Figure 12) of models in the CCMVal-2 intercomparison REF-B1 runs (1960–2000). They show that the multi-model mean of 13 of the CCMs gave a SSW frequency of ∼0.55 events/yr compared to an average of ∼0.6 events/yr in ERA-40. Of particular interest for this study, NIWA had ∼0.35 events/yr, CCSR/NIES had ∼0.4 events/yr and METO had a value approximately the same as ERA-40.

To expand on Butchart et al. (2010), we model the daily ZMZW anomaly at 60°N and 10 hPa over the period DJFM from 1960 to 2000 with a Gaussian distribution, and this is presented in Figure 1. The black line shows data from ERA-40, and is the same as the distribution shown in M11. Figure 1 (b) is a Q–Q plot which compares quantiles from ERA-40 (x-axis) with quantiles from each of the CCMs (y-axis). Models which agree well with ERA-40 lie on the 1:1 line (e.g. Wilks, 1995).

Figure 1.

A comparison of the zonal mean zonal wind at 60°N and 10 hPa for (a) the distributions of ERA-40, METO, CCSRNIES and NIWA throughout the winter period (DJFM) and (b) the corresponding two-sampled Q–Q plots. The Q–Q plots are relative to the ERA-40 diagnostics which lie on the 1:1 line. Each model contains daily data from 1960 to 2000 and is plotted using a Gaussian distribution.

Figure 1 shows that all the models, in particular the METO model, reproduce the variability of the ZMZW well with the average standard deviation of the models and ERA-40 being close to 15ms−1. The NIWA and CCSR/NIES models both slightly underestimate the extremes in ZMZW. However, in general, it is hard to distinguish between models based on this diagnostic.

4.2. Using the geometric diagnostics

Figure 2 shows the same analysis for the moment diagnostics of objective area, centroid latitude, aspect ratio and kurtosis on the 840 K isentropic surface. Note that a cubic axis is used in modelling the centroid latitude to provide an optimal fit for the Gaussian distribution to the data (M11 gives more details regarding this). The diagnostics from Figure 2 are compared on a model by model basis against ERA-40 (black line) in the analysis presented below.

Figure 2.

A comparison of the moment diagnostics on the 840 K surface for (a, c, e, g) the distributions of ERA-40, METO, CCSRNIES and NIWA throughout the winter period (DJFM) and (b, d, f, h) the corresponding two-sampled Q–Q plots. The Q–Q plots are relative to the ERA-40 diagnostics which lie on the 1:1 line. (a) shows the vortex objective area modelled using a GEV distribution, (c) shows the vortex centroid latitude using a Gaussian distribution, (e) and (g) show the vortex aspect ratio and kurtosis respectively using GEV distributions.

The CCSR/NIES model (light grey line) shows a different representation in all four of the moment diagnostics compared with ERA-40. The variability in terms of PV filamentation and destruction of the vortex is too low, as seen from the narrow, tall peaked distributions of the objective area (a) and kurtosis (g) diagnostics. This suggestion of a more stable vortex is also apparent in the centroid latitude diagnostics (c), which shows the vortex centroid on average too far poleward, with a mean latitude of ∼80.5°N as opposed to ∼77°N in ERA-40. The Q–Q plot of the centroid latitude (Figure 2(d), light grey line) shows that the extremes in this diagnostic are also too far poleward, indicating that vortex displacement events are under-represented in CCSR/NIES. One reason for the vortex to be displaced too far poleward is a lack of planetary wave disturbances from the troposphere. To expand on this, Figure 3 shows composites of heat fluxes at 100 hPa for the three CCMs (a, b, c), and differences between each CCM and ERA-40 (d, e, f). In this analysis, the eddy heat fluxes are used as a proxy for wave activity entering into the stratosphere from the troposphere (e.g. Andrews et al., 1987). Figure 3 shows that the heat fluxes in the CCSR/NIES model (c, f) are too far poleward and when compared with the same plot using ERA-40 (not shown) they are also too weak. The stippled areas in this plot, which show that the CCMs and ERA-40 are statistically different at the 95% level according to a standard t-test, indicate that wave activity is significantly too low between 40 and 60°N throughout the winter. This suggests that there is not enough dynamical forcing of the vortex, and hence the vortex remains too far poleward.

Figure 3.

Eddy meridional heat flux (vT′) climatologies at 100 hPa as a function of latitude for (a, d) METO, (b, e) NIWA and (c, f) CCSR/NIES using winters (DJFM) from 1980 to 2000. (a, b, c) show the heat flux climatology from each CCM, and (d, e, f) the difference between the CCM and ERA-40 heat flux climatologies. Stippled areas show significance at the 95% level using a standard two-sided t-test.

In contrast, distribution plots for the METO model show good agreement for the objective area and kurtosis diagnostics compared with ERA-40 (Figure 2, dashed grey line). This indicates that the variability of the vortex area, and hence periodic breakdown of the vortex, is represented well and this is confirmed by the kurtosis Q–Q plot (h) which shows a good model–data fit. Especially notable is the extreme value fit in the kurtosis, an indication that vortex filamentation is adequately reproduced and, when compared with the other CCMs, begins to demonstrate the range in variability across models.

Although the kurtosis is a useful diagnostic for indicating displacement events (high positive values) and splitting events (negative values), the most useful diagnostics to distinguish SSW type are centroid latitude, a measure of the vortex displacement, and aspect ratio, a measure of how elongated the vortex is. Both the density plots of centroid latitude (Figure 2(c)) and aspect ratio (e) show good fits between the METO model and ERA-40. However, closer examination using the Q–Q plots indicates that the METO model produces events that are too extreme in both these diagnostics, i.e. the vortex is displaced too far equatorward in some cases, as well as producing a vortex with too large an aspect ratio compared with ERA-40. However, the analysis here breaks down in part because these poorly fitted extreme values could all originate from one single event. Due to this information being unobtainable from the current plots, a further analysis must be performed. This is addressed using extreme value theory in the following section. However, one contribution to these large-magnitude events can be seen in the heat fluxes (Figure 3(a, d)). Here the METO model predicts the location of the maximum heat flux correctly but overpredicts its magnitude. Therefore excessive wave activity is observed, and hence large variability in the vortex diagnostics, as shown in the distributions.

In contrast, Figure 2 shows the mean location of the vortex centroid in the NIWA model to be slightly poleward of the ERA-40 distribution, although the extreme events appear to be better modelled. However the remaining diagnostics for NIWA do not perform so well. The Q–Q plot of kurtosis (h) shows that the extreme positive values, associated with vortex filamentation, have a higher magnitude than those corresponding to the ERA-40 data, although, as before, these could be from one large event and declustering of the data must be employed to further test this hypothesis. This result is in contradiction to what might be expected from studying the density plot of objective area (a), which shows that the vortex has less variation in the NIWA model than in ERA-40.

Finally the distribution of aspect ratio (e) shows that the NIWA model is on average too circular compared to ERA-40, although the corresponding Q–Q plot (f) shows that the extreme aspect ratios are larger in magnitude than those of ERA-40, indicating higher magnitude displacement events for the NIWA model over ERA-40.

It should be noted that both the NIWA and CCSR/NIES models are spectral models, as opposed to the grid-point METO model. The nature of spectral models is such that they are often less effective at preserving gradients, such as the strong PV gradient of the vortex edge. Indeed Chapter 5 of SPARC (2010) indicates that both the CCSR/NIES and NIWA models have a weak vortex edge in the lower stratosphere region, whereas the METO model has a stronger, more well-defined barrier that more closely resembles observations. The weak edge probably means that filaments of PV are less likely to be stripped away from the main vortex. This is confirmed by the distribution of kurtosis for the CCSR/NIES model. It is therefore hypothesised that vortex filamentation is both a function of resolution and model type.

4.3. Extreme variability of the vortex

Much of the analysis presented thus far has hinted at poorly represented extreme events which are often hard to interpret. We therefore examine these more closely following the same methodology as M11.

Two principal differences arise in the study of extreme data over that of modelled data as a whole.

  • 1.In the first instance, consecutive days over a chosen threshold are considered as one event rather than multiple events (the largest magnitude event in the group is chosen to ‘represent’ the group). The advantage here is that if more than one point does not fit the extreme value statistical model well, it is probably due to the model being badly defined, rather than one random event skewing the results. The disadvantage is that there are far fewer points available to estimate the parameters of the distributions, so the model to data fit may not be as accurate.
  • 2.A different set of distributions are employed collectively known as extreme value distributions. For this study the GP distribution is chosen as it has been shown to fit meteorological data well (e.g. M11, also Coelho et al., 2008).

The first step in this analysis is to calculate the threshold over which data points are classed as extreme and, where possible, the same thresholds are used for each of the models (Cole, 2001). These are summarised in Table 2. In addition, the percentage of data above the threshold is indicated in brackets.

Table 2. The upper and lower tail thresholds for the vortex diagnostics of objective area, centroid latitude, aspect ratio and kurtosis on the 850 K isentropic surface.
  1. U=upper tail threshold, L=lower tail threshold.

  2. Bracketed values indicate the percentage of data above (or below for the lower tail) the threshold value.

Objective area (PVU m2)L–1.3 (10%)–1.3 (10%)–0.8 (16%)–0.5 (19%)
Centroid latitude (°N)L72 (18%)72 (18%)72 (11%)72 (4%)
Aspect ratioU2.3 (13%)2.3 (17%)2.3 (10%)2.3 (15%)
KurtosisU1.7 (5%)1.7 (2.5%)1.7 (2%)1.7 (1.5%)

Table 2 indicates some anomalous results, the first being the objective area thresholds for the NIWA and CCSR/NIES models. These thresholds show that the models do not reproduce events which are as extreme as those in ERA-40, and hence the same threshold cannot be used. Also the centroid latitude and kurtosis diagnostics for the CCSR/NIES model achieve the same threshold value as ERA-40, but there are far fewer exceedances over this threshold, again indicating a lack of extreme events in this model.

To better understand these thresholds, and indeed the extreme events of the diagnostics, the data are modelled using the GP distribution. In addition, Q–Q plots, as used in the previous analysis, are employed as well as return level plots, which show how often a certain value is exceeded in the dataset (section 3.2 provides more detail regarding these).

The density, Q–Q and return level plots are shown in Figure 4. In general, all the models overestimate the magnitude of kurtosis events. This is most evident from the kurtosis Q–Q plot. However Table 2 shows that all the models have less data available to model the kurtosis using a threshold of 1.7 than the ERA-40 dataset. On average, large-scale filamentation events last for 3–4 days in all of the models, a similar frequency to ERA-40. However, the kurtosis Q–Q plot in Figure 4 suggests that these events are too high in magnitude. Analysis of the PV fields (not shown) suggest that this discrepancy arises because the filaments are more idealised in the models and more noisy in ERA-40. The idealised filaments tend to produce a well-defined PV distribution, whereas the filaments in ERA-40 are disturbed by the noisy PV field and hence the kurtosis is not as large as otherwise.

Figure 4.

A comparison of the vortex diagnostics on the 840 K surface for (top) the distribution tails of each CCM throughout the winter period (DJFM), (middle) the corresponding two-sided Q–Q plots with the solid black line indicating goodness of fit to ERA-40 data, and (bottom) the return level plot as predicted by each of the three CCMs. The solid black line shows the ERA-40 prediction and the dashed lines show the 95% confidence intervals. The rows indicate the diagnostic being used, from top to bottom: objective area, centroid latitude, aspect ratio and kurtosis. Note that the objective area in the NIWA-SOCOL model does not fit a GP distribution, therefore it is omitted for this diagnostic.

The remaining diagnostics of objective area, centroid latitude and aspect ratio do not show consistent evolutions across the three models, therefore each model is considered separately to emphasise the range in variability.

The kurtosis and objective area diagnostics indicate that the METO model reproduces filamentation relatively well. The return level plots show agreement within the 95% confidence intervals for both these diagnostics, and the kurtosis shows particularly good agreement between the METO model and ERA-40, although for reasons outlined above it is an overestimate. Comparisons of the density, Q–Q plot and return level plot show that the METO model reproduces the aspect ratio extremes poorly, a result that is shared with the analysis of the whole distributions (Figure 2(e)). One hypothesis for this overestimate of the aspect ratio extremes is that the extreme aspect ratio events last far longer in the METO model than in ERA-40. With large aspect ratio events lasting longer, extreme event diagnostics are more likely to be larger in magnitude for the METO model than the ERA-40 dataset and this is indeed what is observed.

The NIWA model performs less well than the METO model at modelling the extremes of the diagnostics, although it does surprisingly well at reproducing the centroid latitude of the vortex. This is in agreement with the previous analysis, which showed that, although the mean state of the vortex was poorly reproduced, the distribution tail showed a good model to data correlation. The extreme objective area could not be modelled. This is most likely due to the limited wave mean flow momentum transfer in this model (also observed in the analysis of heat fluxes presented in Figure 3), which means that the vortex does not break down completely and hence the lower threshold of zero area is never reached.

The CCSR/NIES model does not capture the vortex breakdown well, as seen in the objective area. However it does perform well at modelling the aspect ratio. This is consistent with the study of the whole distributions in the previous section. The few extreme kurtosis outliers give rise to too high a return level rate, with values of over 20 for the 100-year return level, which is close to residing outside the bounds for ERA-40 errors. However, most notably, the extremes in the centroid latitude do not reach as far equatorward as in the ERA-40 data, indicating a lack of wave activity interacting with the vortex, and confirming the analysis of the heat fluxes and full probability density functions presented earlier.

5. Predictions of future vortex variability

As with the previous section, we begin the analysis with a study using the traditional measures of vortex variability, which means that far more models can be analysed. To calculate SSWs, we used the methodology employed by Charlton and Polvani (2007) based on the zonal mean wind reversal at 60°N and 10 hPa. Figure 5 shows the trend§ in SSW frequency for 1960–2100 (squares) and 2000–2100 (circles).

Figure 5.

The linear trend in SSW frequency (events per decade) for periods 1960–2100 (squares) and 2000–2100 (circles) for ten models taken from the CCMVal-2 intercomparison. The multi-model mean is also given in the final column. Whiskers show 95% confidence intervals. The number of ensemble members used in the prediction is displayed after the model name. Highlighted model names denote those used throughout this article. GEOSCCM does not output data for the 1960–2000 period in the REF-B2 runs, therefore only one analysis is included for this model. The trend in METO is fitted only up to 2087, which is when this simulation ends.

Overall, the trend is small and the multi-model mean predicts an increase of ∼1 SSW event per century, consistent with Charlton-Perez et al. (2008). However, this is not the case for CMAM and the 1960–2100 period of SOCOL, both of which have three ensemble members, increasing the confidence in the prediction and underlining the need for multiple ensemble members. Importantly for this study, the CCSR/NIES, METO and NIWA models show no significant change in the SSW frequency over the twentyfirst century. One reason for this, particularly for the METO model, is the large decadal variability within the runs, again demonstrating the need for multiple ensemble members.

As a further test of future SSW frequency, Figure 6 shows the change in SSW frequency between the 1960–2000 period and the 2040–2080 period. Lending further support to the results obtained in Figure 5, the SOCOL model indicates an increase in SSW frequency of ∼3 events per decade over the twentyfirst century, and this is significant at the 95% confidence level. However, the models as a whole indicate a slight increase in the frequency of SSW events as seen in the multi-model mean (final column). One interesting result comes from the CCSR/NIES model which shows a reasonably strong negative change in SSW frequency, which appears to be in contrast to the approximately zero trend in SSW frequency observed in Figure 5. However, closer inspection of the timeseries of SSWs per decade (not shown) reveals that the period 1960–2000 in the model has a higher frequency of events than the 2000–2100 period. Hence in Figure 5 the trend is diluted, but in Figure 6 the change in SSW frequency coincidently uses high contrasting periods (1960–2000 and 2060–2100) and is therefore amplified. This particular result, although exclusive to the CCSR/NIES model, indicates the need for caution when interpreting results from analysis of SSW events.

Figure 6.

The change in SSW frequency (events per decade) from the 1960–2000 period to the 2040–2080 period for models which output daily zonal wind data. The multi-model mean is given in the final column. Highlighted model names indicate those used throughout this article. Filled boxes indicate that the change is statistically significant at the 95% level. The GEOSCCM model is not included in this analysis as it does not output data for the 1960–2000 period.

Analysis using the moment-based diagnostics confirms these findings, although adds little to the overall conclusions and is therefore omitted. However, one interesting result comes from the evolution of the objective area climatology in the METO model, shown in Figure 7. The evolution of the climatology over winter changes since a dip in late January–early February begins to emerge towards the end of the twentyfirst century (note the analysis has been extended to include October and November), although a similar response is not observed in the NIWA and CCSR/NIES models. This change indicates that the vortex becomes consistently weak in this mid-winter region and is likely caused by an increased concentration of extreme variability at this time. Significance in Figure 7, indicated by grey shading, is also observed at the beginning of winter, indicating that the vortex is often more dynamically active during this time, and hints at the possibility of an increase in the number of SSW-like events in November, of which presently only one has been recorded in ERA-40 for the 1958–2001 period (Charlton and Polvani, 2007).

Figure 7.

A climatology of the objective area diagnostic on the 840 K surface over the extended winter period (ONDJFM) for the UMUKCA-METO model. The climatology contains 40 years of data that are shifted by 20 years starting from 1960. Lighter grey lines represent predictions further into the future. Grey shading indicates that the 1960–2000 and 2040–2080 periods are significantly different at the 95% confidence level according to a standard t-test. The model was terminated in 2087, so the 2060–2100 period is omitted.

6. Summary

Prompted by the lack of coherence between studies of the trend in SSW frequency over the twentyfirst century, we have employed a novel technique developed in M11 to study the structure and evolution of the NH polar vortices in three CCMs taken from the intercomparison CCMVal-2. This method allows a complete and comprehensive comparison of the vortex between datasets which greatly expands on the traditional zonal wind definition of a SSW. Key conclusions from this study are:

  • 1.CCMs often reproduce the zonal mean diagnostics well but do less well at reproducing the moment-based diagnostics, especially the more nonlinear diagnostics such as kurtosis which indicate large filamentation events.
  • 2.In general, the vortex is climatologically located too far poleward in CCMs compared to ERA-40 and this can be attributed to an underestimate of vertically propagating planetary waves.
  • 3.All three of the CCMs examined failed to capture the frequency of large-scale filamentation events observed in ERA-40, although they did capture the persistence of such events well. The analysis suggested that this defect may well be related to model resolution and type of model grid.
  • 4.The multi-model mean predicts no significant change in vortex variability over the twentyfirst century, although the distribution of extreme variability within the winter period may well change, i.e. become more concentrated in midwinter.

A consistent theme throughout the analysis was the large range of inter-model variability. This explains the contradictory results regarding future vortex variability in the literature and raises questions of reliability in vortex projections from single-model studies (e.g. Rind et al., 1998; Charlton-Perez et al., 2008; McLandress and Shepherd, 2009; Bell et al., 2010). For example, our results showed that the METO model predicts a shift in vortex variability towards midwinter. While this result was not reproduced in the other two models, these same models performed less well than METO in capturing the structure of the historical vortex variability.

We also show that the impact on the vortex from anthropogenic gas emissions under the middle-of-the-road SRES A1b scenario may not produce a sufficiently large signal to detect a statistically significant trend. This is consistent with Bell et al. (2010), who found no statistically significant changes in SSW under 2×CO2 experiments, a comparable scenario to the one used here. It was not until the forcing was increased to 4×CO2 that a statistically significant increase in SSWs was obtained. If such runs could be undertaken in future CCM simulations, a more extreme scenario could be developed which may well dictate how stratosphere–troposphere connections are viewed in future climate projections.


DMM is funded by the National Environmental Research Council (NERC), LJG is funded by the NERC National Centre for Atmospheric Science, and the work of NB and SCH was supported by the Joint DECC and Defra Integrated Climate Program – DECC/Defra (GA01101). CCSR/NIES research was supported by the Global Environmental Research Fund of the Ministry of the Environment of Japan (A-071 and A-0903) and the simulations were completed with the supercomputer at CGER of the NIES. We would also like to thank the CCMVal-2 project for the organisation and coordination of the models, and to the British Atmospheric Data Centre for archiving the model output.


Table A.1.. Abbreviations and acronyms.
AMTRACAtmospheric Model with Transport and Chemistry
CCMValChemistry–Climate Model Validation
CCSRCenter for Climate Systems Research (USA)
CMAMCanadian Middle Atmosphere Model
ECMWFEuropean Centre for Medium-range Weather Forecasts
EGMAMEcho-G Middle Atmosphere Model
ERA-40ECMWF 40-year reanalysis
GEVGeneralised extreme value (distribution)
GHGGreenhouse gases
GISSGoddard Institute for Space Studies (USA)
GPGeneralised Pareto (distribution)
IPCCIntergovernmental Panel on Climate Change
NAMNorthern Annular Mode
NCARNational Center for Atmospheric Research (USA)
NCEPNational Centres for Environmental Prediction (USA)
NHNorthern Hemisphere
NIESNational Institute for Environmental Studies (Japan)
NIWANational Institute for Water and Atmospheric Research
 (New Zealand)
PVPotential vorticity
SOCOLSolar–Climate–Ozone Links
SRESSpecial report on Emission Scenarios
SSWSudden stratospheric warming
UMUKCAUnified Model (Met Office) version of UK
 Chemistry–Aerosol model
ZMZWZonal mean zonal wind
  • *

    All abbreviations and acronyms are given in Table A1.

  • In M11 the 850 K surface was used instead of the 840 K surface, however sensitivity tests have shown that the structure of the vortex on both levels is very similar in ERA-40.

  • If the datasets were the same length, the Q–Q plot would essentially show the ordered data from ERA-40 plotted against the ordered data from each of the CCMs.

  • §

    The trend is calculated by finding the gradient of the best fit line through the time series of decadal SSW frequency. Where multiple ensemble members for a model are available, the trend is calculated for the ensemble mean.