The Climatology of the Middle Atmosphere in a Vertically Extended Version of the Met Office’s Climate Model. Part II: Variability

1) QBO

Figure 1 shows the height–time development of monthly-mean, zonal-mean zonal wind between 5°S and 5°N from a single member of each of the N48 and N96 ensembles. These runs illustrate typical ensemble behavior and exhibit a spontaneously generated QBO in the stratosphere, with ensemble-averaged periods of 34.0 ± 3.5 months and 36.8 ± 3.3 months at 10 hPa in the N48 and N96 simulations, respectively. The differences between the two periods are statistically significant at some but not all heights. Peak westerlies occur above 32 km (10 hPa), reaching 25 m s⁻¹ in places. QBO easterlies peak more strongly and occur at lower levels, reaching amplitudes of at least −25 m s⁻¹ regularly. However, neither set of ensembles exhibits a QBO signal that penetrates right down to 100 hPa, as seen by the observed downward propagation of westerlies, described by Naujokat (1986). On the other hand, Fig. 2 shows a clearer comparison at 90 hPa with a prominent QBO signal present as far down as 90 hPa in the N96 ensemble that is less evident in the N48 resolution run. Both ensembles show a strong and regular SAO in the mid–upper stratosphere, which extends into the upper mesosphere (not shown).

Figure 3 shows, as a function of height, the time-spectral amplitude of tropical winds and the total wind amplitude, displaying the annual, QBO, and SAO cycles, in each of N48, N96, and ERA-40 ensembles, using monthly data. The methods for constructing the total wind amplitudes are outlined in Pascoe et al. (2005) and represent the amplitude associated with the ratio of an integrated range of Fourier harmonics to the total wind variance. The spectral amplitudes for both the N48 and N96 ensemble averages compare well with the ERA-40 data. The height and magnitude of the peak QBO amplitude are in good agreement. The period for the QBO is slightly longer than ERA-40 (28 months) and is directly related to the magnitude of the prescribed source of gravity waves in the model. No explicit tuning of the tropical variability was made and the same spectral gravity wave parameter values were employed for both N48 and N96.

Little annual tropical variability is displayed by the high-top MetUM in Fig. 3. In ERA-40, the annual cycle appears linked with the SAO near the stratopause: seasonal modulation of the SAO is manifested by a strengthened annual cycle, with stronger SAO amplitudes in NH winter and spring periods (Gray 2010, see also next section); however, little of this is seen in the model and the SAO amplitude is overestimated, especially at N48. The relative strengths of the SAO and QBO appear linked between the two model resolutions: a weaker SAO at N96 is linked with a stronger QBO, compared with N48, and is consistent with systematic differences in wave filtering. At both resolutions, a notable residual in tropospheric wind variance is seen in the troposphere, which is not explained by annual, semiannual, or QBO variability. This variability is spread across a broad range of frequencies and so does not appear to be associated with narrowband processes (not shown).

Figure 4 shows the various components of the transformed Eulerian mean (TEM) zonal-mean zonal momentum budget acting on the mean flow at 30 hPa in the tropics during the QBO cycle, split into planetary (resolved) wave forcing (DIVF), nonorographic gravity wave forcing (NOGWD), and vertical advection (Andrews et al. 1987). Horizontal advection [see Eq. (1) of Part I] and orographic gravity wave forcing were found to be negligible and are not shown. Superimposed is the value of zonal-mean zonal wind U. Diagnostics are averaged from 5°S to 5°N over all complete QBO periods, with each period scaled to a unit time length. The magnitude of the climatological cycles shown is smaller than that of the individual cycles since they are not perfect sinusoids and so some cancellation will occur at each point within the period.

Under both resolutions NOGWD dominates over DIVF. NOGWD leads U so it can be assumed that it drives the changes in U. Compared with a similar figure in Scaife et al. (2000) that employed an earlier version of the MetUM, there is larger parameterized wave forcing (NOGWD) in the current model in the tropics. The time evolution of U is dominated by two terms: the NOGWD drives the wind evolution while the vertical advection opposes it. The vertical advection term consists of the background upwelling associated with the upwelling branch of the Brewer–Dobson circulation, and this is expected to oppose the descent of the QBO phases. In addition, there is a local induced meridional circulation that arises in order to maintain thermal wind balance. In the case of the descending easterly phase, this local circulation consists of equatorial upwelling and thus also opposes the descent of the QBO, while in a descending westerly phase the local induced circulation consists of descent at the equator, thus reducing the opposition to the descending QBO. This asymmetry can clearly be seen in Fig. 4, where the (vertical) advection is 3 times as large during the period of easterly acceleration (from π/2 to π) compared with the westerly acceleration period (3π/2–2π). Also noticeable, at both resolutions, is that the resolved waves (DIVF) contribute primarily to the westerly phase of the QBO and reinforce the forcing due to NOGWD.

Finally, when comparing the two different resolutions, the relative length of time of the westerly phase compared with the easterly phase is clearly longer at N96, consistent with Fig. 1. This is linked to a 10% increase at N96 of the integrated vertical component of horizontal momentum flux density of the eastward NOGWD spectrum at 100 hPa, leading to a reduced easterly phase and longer westerly phase in the lower stratosphere. This increased vertical flux leads to a slightly stronger westerly phase-induced meridional circulation, which can then further aid the vertical descent of the QBO deeper into the lower stratosphere, thus leading to the differences seen at 90 hPa in Fig. 2. These differences in NOGWD fluxes must originate from changes in the tropospheric winds that filter the propagation of the specified nonorographic gravity waves, but investigation of these tropospheric differences is outside the scope of this paper.

These results can be compared to those from the MAECHAM5 model reported by Giorgetta et al. (2006), who showed an insensitivity of the QBO period in MAECHAM5 to modest changes in horizontal resolution but an increase in the strength and duration of the westerly phase. However, they propose that the latter is due to an increase in resolved wave driving. They also report that the QBO in MAECHAM5 is principally driven by resolved waves during the westerly phase and parameterized gravity waves during the easterly phase. While we find that the contribution to the easterly QBO phase is increased at N96 (see Fig. 4), it is still small when compared with the NOGWD term.

2) SAO

Figure 5 shows the annual cycle of equatorial zonal-mean zonal wind in ERA-40 and the MetUM ensembles. The SAO is conspicuous in both model and observations, with its easterly phase peaking near 1 hPa. Apparent in the ERA-40 data and other observations (Garcia et al. 1997; Gray 2010) is a strong annual cycle modulation, noticeable as a reduction in peak easterlies at 1 hPa during July compared with December. This feature is less prominent in the model, although the N96 ensemble does show a reduced easterly phase compared to the N48 ensemble during these times. In the observations, it is thought that a weakened Brewer–Dobson circulation during this period (i.e., weakened meridional advection of easterly zonal winds from the summer hemisphere) gives rise to the observed annual cycle at these heights (Hitchman and Leovy 1986; Delisi and Dunkerton 1988; Gray 2010). In addition, the observations also show an annual cycle modulation in the amplitude and descent in time below 1 hPa (see bottom panel of Fig. 5). This is linked with momentum forcing from gravity waves, which are sensitive to the background flow through which they propagate. The peak SAO westerlies in ERA-40 are near 1 hPa, contrasting with both sets of model ensembles, which display peak westerlies nearer 0.1 hPa, one month earlier. This suggests differences in gravity wave forcing in the lower mesosphere, although the reliability of the ERA-40 winds above 1 hPa is questionable, since observational constraints are substantially reduced there (Baldwin and Gray 2005).

To better understand the origin in forcing of the modeled easterly phase of the SAO, Fig. 6 shows the annual cycle of the zonal momentum budget at 2 hPa and 5°S–5°N. At N48 the easterly phase of the SAO peaks in February and August. Driving this is the meridional advection of easterlies from the summer hemisphere, peaking one month earlier, although no annual cycle is evident in this forcing. Secondary to this is forcing from DIVF and NOGWD, peaking early during the easterly phase (April and November). The vertical advection term is associated with the locally induced meridional circulation required to maintain thermal wind balance. The term appears in quadrature and is upward (to achieve cooling) and therefore opposes the forcing. The westerly SAO phase occurs at the equinox and coincides with a reduced magnitude of horizontal zonal wind advection associated with the reversal of the Brewer–Dobson circulation. This phase is primarily driven by NOGWD, peaking in strength in March with a second peak in forcing during September. Its descent is also aided by suppressed vertical upwelling and hence reduced vertical advection during this period. The driving and timing of the easterly–westerly SAO phases by horizontal advection/NOGWD is consistent with a study by Richter and Garcia (2006) using the Whole Atmosphere Community Climate Model, version 2 (WACCM2). Resolved wave driving is also strongest in March and September and peaks less strongly during the early Southern Hemisphere winter as expected. At N96, there is a similar momentum forcing of the easterly phase SAO and the strength and seasonality of the resolved wave driving (see Fig. 6). However, driving of the westerly SAO phase is significantly different during the NH spring, with NOGWD reduced in strength. This is partly offset by marginally stronger westerly driving by vertical advection during these times. The presence of additional parameterized wave forcing at N48 is consistent with changes in wave filtering due to reduced wind shear associated with a weaker QBO at N48.

An examination of the meridional advection of zonal wind in ERA-40 (not shown) exhibits strong horizontal advection of easterlies at 2 hPa during the NH winter but vanishing horizontal advection during the SH winter. This gives rise to the strong annual-cycle modulation in the ERA-40 SAO in Fig. 5, which is absent in the model. Examination of the structure of the zonal wind jets in June–August (JJA) (see Fig. 1 of Part I) shows substantial differences in the equatorial meridional gradient in zonal-mean zonal wind between the high-top MetUM and ERA-40 during JJA in the upper stratosphere, with a peak wind difference of 20 m s⁻¹ near 1 hPa. This is likely to account for the differences in horizontal zonal wind advection in Fig. 5 and thus for the absence of an annual cycle in the upper stratosphere in the MetUM.

1) Sudden stratospheric warmings

The left panel of Fig. 7 shows histograms of daily September–October temperature averaged between 60° and 90°S at 50 hPa for the two model resolutions and ERA-40. The MetUM exhibits a warm bias of up to 5 K compared to ERA-40 at both resolutions. The shapes of the temperature distributions are similar between the two ensemble sets and exhibit less spread compared with observations.

The right panel of Fig. 7 shows a histogram of daily December–February (DJF) temperature averaged between 60° and 90°N, at 50 hPa. The model distributions again show slightly higher mean temperatures but are in much better agreement. Both model and observational distributions are skewed, weighted slightly to higher temperatures (Pascoe et al. 2006), although at both resolutions the model shows a greater proportion of days having temperatures above 215 K, compared against ERA-40. This skewness is associated with the occurrence of SSWs and suggests an overestimation of these in the high-top MetUM, compared with the observations. Also, minimum temperatures do not fall much lower than 200 K. Temperatures below 196 K are required for the formation of type-1 polar stratospheric clouds and are a necessary condition for heterogeneous ozone-destroying processes (Solomon 1999). It should, however, be emphasized that the model runs were forced by climatological ozone fields and cannot be directly compared with observations and these polar average temperatures do not preclude the presence of cooler, localized regions.

The top panel of Fig. 8 shows the daily evolution of 10-hPa climatological temperatures, averaged between 60° and 90°N, during the extended NH winter (October–June) and the ensemble spread (i.e., ensemble mean ± one standard deviation). The temperatures show reduced variability during times when radiative forcing is controlling seasonal evolution (i.e., during summertime and early autumn), as expected. Significantly greater variability is seen from late December through mid-March. During this time, the NH winter stratospheric vortex undergoes rapid changes due to vertically propagating (and dissipating) Rossby waves. The bottom panel of Fig. 8 corroborates this fact. Here is shown the relative frequency of SSW events, as defined by Charlton and Polvani (2007). The relative frequency of SSWs is greater in the N48 ensemble than in N96 or ERA-40 during mid- to late winter (January–March), corresponding to a SSW frequency of 8.5 decade⁻¹. The frequency of SSWs in the N96 ensemble is reduced during mid–late winter (6.7 decade⁻¹) and is comparable to ERA-40 (6.6 decade⁻¹). Confidence interval estimates were calculated for the N48 and N96 ensembles employing the methodology set out in Charlton et al. (2007). The incidence of SSWs in N96 (but not N48) was found to be indistinguishable from those in ERA-40, at the 95% confidence level. These results suggest that the higher resolution improves the representation of SSW variability in this model.

The reduced incidence of SSW at N96 is most likely associated with subtle changes in circulation impacting the propagation of Rossby waves into the stratosphere. Support for this hypothesis comes from the analysis of the climatology of resolved waves and parameterized gravity waves performed in Part I (see Fig. 8), which showed a relative drop in DIVF in the mid–upper stratosphere between N48 and N96. Differences in the gradient of wave refractive index were also found at ∼35°N and 100 hPa, linking upper-troposphere circulation with resolved waves entering the stratosphere. Consequently, it was concluded that more resolved waves are directed toward the equator at N96 than at N48.

Figure 9 shows the relationship between early season (January–February) planetary wave activity, as diagnosed by meridional heat-flux anomalies υ′T ′ at 100 hPa, 40°–80°N, and late winter (February–March) polar temperatures at 50 hPa, averaged poleward of 60°N (Newman et al. 2001). For both N48 and N96 ensembles, a clear correlation is seen, comparing well with ERA-40. During the NH winter, both N48 and N96 are found to be statistically indistinguishable from ERA-40 (95%). However, significant temperature and meridional heat-flux biases are seen between the model ensembles and ERA-40 during the SH winter (>99%). These figures are useful for inferring mean polar temperature in the absence of dynamical heating from the resolved circulation (Steil et al. 2003; Manzini et al. 2003). That is, they show up possible differences in diabatic heating or circulation due to nonresolved wave forcing. In the present context we find mean polar temperatures of: 191.5 ± 0.6 K (N48), 191.0 ± 0.8 K (N96), and 189.0 ± 1.1 K (ERA-40). These differences are not statistically significant. Both N48 and N96 values for heat-flux anomalies are consistent with CCMVal model intercomparisons and ERA-40 data (Eyring et al. 2006).

The strength of the wintertime stratospheric vortex is known to be related to the phase of equatorial winds (Holton and Tan 1980, 1982; Lu et al. 2008; Gray 2010). Figure 10 shows the composite differences at N48 of zonal-mean zonal wind during times when the lower tropical stratosphere winds are easterly (<−10 m s⁻¹) at 30 hPa compared to when they are westerly (>10 m s⁻¹). The methodology follows that of Calvo et al. (2007, 2009) and calculates bimonthly averages for early winter (November–December) through to late winter (February–March). The zonal wind threshold separating QBO westerly-phase and easterly-phase composites is applied to mean November–December only and defines those years used for the subsequent bimonthly composites. It is evident from the N48 ensemble that the polar night jet (70°N, 5 hPa) is significantly stronger (>9 m s⁻¹, 95%) during times when the tropical lower stratosphere is in a westerly QBO phase (cf. 30 hPa). The positive vortex wind anomaly descends and intensifies throughout the winter. A threefold statistically significant structure is seen at equatorial latitudes, in good agreement with ERA-40 analysis (Pascoe et al. 2005). A region of statistically significant differences observed between 1.0 and 0.1 hPa between 30°S and 30°N is linked with the possible QBO modulation of the SAO and is most evident during the early winter (November–January) when the stratospheric SAO is in an easterly phase.

In the corresponding diagnostic at N96 (Fig. 11) similar behavior is seen, but with notable differences. The positive anomaly showing a strengthened polar night is evident and descends throughout the winter. However, it is significantly stronger in the upper stratosphere during early winter, showing a nonlinear change in strength throughout winter with less statistical significance in late winter, possibly because there are only two ensemble members.

The relative strength and timing of the extratropical stratospheric zonal wind anomaly seen during different phases of the QBO is consistent with the relative number and timing of SSWs observed at N48 and N96. There are more mid–late winter SSWs observed at N48 than at N96, coinciding with a larger extratropical stratospheric wind anomaly in late winter seen in Fig. 10 than in Fig. 11.

Further insight into the significance of the composite differences shown in Figs. 10 and 11 can be achieved by comparing mean January–February time series of equatorial zonal wind u_eq and polar-cap temperature T_np at 30 hPa (Fig. 12). The top and middle panels show four combined time series of the N48 ensemble while the bottom panel shows the two at N96. Also shown are the correlations between u_eq and T_np, for each ensemble member. Nondirectional significances are determined using

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where r represents correlation and N is the number of years in each run (Clarke and Cooke 1992, 343–344). The confidence level is taken to be 100(1 − t). No allowance is made for possible degrees-of-freedom issues relating to autocorrelation in the equatorial zonal wind. The validity of this was tested using data contained in Figs. 3 and 4 of Lu et al. (2008). Similar levels of confidence were obtained for the higher absolute levels of correlation.

A wide spread in correlation values is found for u_eq and T_np within the N48 ensemble. The first (0–25 yr) shows little correlation during the period [−0.01 (5%)] whereas the third (50–75 yr) shows a noticeable degree of anticorrelation [−0.52 (99%)]. During periods showing strong anticorrelation between equatorial 30-hPa zonal wind and polar temperature, the composite analysis used in Figs. 10 and 11 reveals a strong positive extratropical anomaly, as discussed previously. Superficially, the two N96 integrations show little correlation: −0.06 (20%) and 0.09 (29%), respectively. However, within the first member a noticeable anticorrelation is seen during the latter half of the time series: −0.61 (96%). Similar sporadic behavior was discussed in Lu et al. (2008). Using the ECMWF ERA-40 and operational analyses, they noted a drop in correlation between tropical stratosphere u and high-latitude stratosphere u and T between 1977 and 1997, with significantly larger (anti)correlations outside this period. Sporadically changing variability such as this complicates the significance and interpretation of composite analyses such as shown in Figs. 10 and 11 and studies such as those of Calvo et al. (2007, 2009). Further exploration of the nature of this variability (e.g., the role of interannual variations of SST) is outside the scope of this study.

2) Annular modes

The behavior of the annular modes has also been examined, with emphasis on the persistence times of annular mode anomalies. The annular modes were identified as the leading empirical orthogonal functions (EOFs) of daily zonal-mean wintertime geopotential height on individual model levels. Two sets of EOF patterns were constructed from height anomalies poleward of 20°, thus obtaining separate patterns for the southern annular mode (SAM) and northern annular mode (NAM). The EOFs were constructed from deseasonalized and linearly detrended data, which were then smoothed using a 90-day filter. The full daily time series of the original model height anomalies were then projected onto the leading EOF pattern of filtered data, retrieving a principal component time series. An autocorrelation analysis was then performed, employing a Gaussian filter to recover time-of-year decorrelation time scales. These were inferred after fitting the autocorrelation function to an exponential. For this study the methodology is taken from Baldwin and Dunkerton (2001), and for comparison, ECMWF ERA-40 and operational analysis daily zonal-mean geopotential height data were used. Significance tests have been applied to assess differences between the MetUM and ECMWF reanalysis time scales (see the appendix).

Figure 13 shows the time evolution of persistence times of the NAM calculated from the N48 and N96 ensembles and ECMWF. Common features appear in the three sets of data, most conspicuous being the elevated residence times in the wintertime troposphere–lower stratosphere and summertime midstratosphere. Significant differences are seen during late summer between the MetUM and ECMWF, where the former show reduced time scales. Previously, these have been interpreted as being linked with either longer radiative damping times in the stratosphere (Baldwin and Dunkerton 2001) or ozone anomalies persisting from the previous winter (Fioletov and Shepherd 2003). However, elevated time scales peak well into the mid–upper stratosphere (not shown), so it is not evident that radiative relaxation helps to explain these features at upper levels, as these are on the order of days only. MetUM wintertime tropospheric time scales are in broad agreement with the ECMWF data, although dates showing peak persistence extend out to April at N48 (although they are not statistically significant). These features coincide with similarly elevated tropospheric persistence time scales reported by Baldwin et al. (2003). The coverage and distribution of regions showing significance difference with the ECMWF data suggests little difference between N48 and N96.

Figure 14 shows the corresponding height–time evolution of SAM persistence time scales. Long persistence times occur in the stratosphere during midsummer and midwinter at N48 and are longest during late spring early summer at N96. This behavior is distinct from the NH variability in that the extrema do not occur with a 6-month lag. Furthermore, the peak in tropospheric persistence time scales coincides with the summertime peak in the stratosphere. These tropospheric features are also seen in the ECMWF data but show less persistence. The only significant differences occur in the troposphere during September–June at N48, and during spring and February at N96. This is linked with peak elevated time scales occurring over a longer time at N48 and represents a significant improvement at N96.

These results are consistent with those of Gerber et al. (2008a), who examined persistence time scales in the models of the Intergovernmental Panel on Climate Change Fourth Assessment Report (IPCC AR4). They report similarly timed peaks in persistence time scales in these models, with reduced (inflated) tropospheric time scales during the NH (SH) winter (summer). In this study, the reduction in persistences seen between the N48 and N96 ensembles in the stratosphere is consistent with the conclusions of Gerber et al. (2008b). Using a simplified model, they suggest a reduction in persistence time scales with improved horizontal resolution.