1. Introduction
The important contribution that breaking gravity waves can make to the atmospheric momentum budget has long been known. Leovy (1964) and Wehrbein and Leovy (1982) showed that a qualitatively reasonable mesospheric circulation can be obtained in simple models with vertical eddy viscosity and Newtonian cooling, provided that additional momentum forcing from Rayleigh friction is included. Using Lindzen's (1981) saturation threshold, Holton (1982) subsequently showed that forcing from gravity waves could provide this missing component of the mesospheric momentum budget. The additional gravity wave forcing in the mesosphere drives ascent in summer and descent in winter. The associated warming is large enough to outweigh the seasonal cycle in solar heating so that minimum temperatures are observed in summer (Nordberg et al. 1965).
Parameterizations of orographic gravity waves with zero phase speed were subsequently developed (Palmer et al. 1986; McFarlane 1987). Recently, parameterization has been extended to represent a wide spectrum of gravity waves. These can be divided into discrete schemes, which include a finite number of phase speeds (e.g., Medvedev and Klaassen 1995, 2000; Norton and Thuburn 1997; Alexander and Dunkerton 1999), and continuous schemes (e.g., Fritts and Lu 1993; Hines 1997a,b; Warner and McIntyre 1999). Several have now been tested in comprehensive general circulation models (GCMs; e.g., McFarlane et al. 1997; Manzini et al. 1997; Medvedev et al. 1998; Scaife et al. 2000). A wide spectrum of phase velocities is important in the middle atmosphere since winds vary rapidly enough with height to present critical lines to a significant part of the upward propagating gravity wave spectrum. In the extratropical stratosphere this leads to the summer and high-latitude winter jets being accelerated by gravity wave forcing due to dissipation just below critical levels (Alexander and Rosenlof 1996).
Lindzen and Holton (1968) highlighted the importance of forcing from gravity waves in the Tropics by showing how these waves could force the quasi-biennial oscillation (QBO). It has also become apparent that observed planetary-scale waves in the lower tropical stratosphere carry insufficient momentum flux to drive the observed oscillation (e.g., Takahashi and Boville 1992; Dunkerton 1997). In light of estimates of vertical momentum flux from mesoscale models of tropical storms (Alexander and Holton 1997) and recent evidence from analysis of observational data (e.g., Bergman and Salby 1994; Sato and Dunkerton 1997; Ricciardulli and Garcia 2000; Vincent and Alexander 2000), it now seems likely that small-scale gravity waves provide a significant component of the forcing that drives the QBO (e.g., Dunkerton 1997).
In a separate paper (Warner et al. 2001, unpublished manuscript) the global climatology of gravity waves from the parameterization of Warner and McIntyre (1999) is examined in the Met Office Unified Model (Cullen 1993). Here we show its importance for simulating the large-scale stratospheric circulation. Section 2 describes the GCM and gravity wave parameterization. In section 3, changes in the structure of the extratropical summer and winter jets show how the cold bias over the winter pole that is common to many middle-atmosphere GCMs (Pawson et al. 2000) can be alleviated. We also describe the effect on the seasonal descent of the southern winter jet, which is improved by including the gravity wave forcing. In section 4 we examine the modeled tropical oscillations in detail, including the QBO that appears when the parameterized gravity wave spectrum is included. We also examine the sensitivity of the QBO to artificial model diffusion and dissipation.
2. Model formulation and validating data
The troposphere–stratosphere configuration of the Met Office Unified Model uses the physical parameterizations documented by Pope et al. (2000) in tropospheric climate prediction experiments. They were implemented in the troposphere–stratosphere configuration by Butchart et al. (2000) and an updated climatology is given in Jackson et al. (2001). We use 55 quasi-horizontal levels to model the atmosphere from the surface up to 0.01 hPa on a 2.5° × 3.75° latitude–longitude grid. No Rayleigh drag is applied in the model and the orographic gravity wave parameterization of Gregory et al. (1998) is run simultaneously with, but uncoupled to, the spectral gravity wave parameterization of Warner and McIntyre (1999). The orographic scheme is only applied up to the lower stratosphere (40 hPa). Convection is parameterized using the penetrative mass flux scheme of Gregory and Rowntree (1990). The choice of convection scheme is important in this study since model resolved gravity wave fluxes are sensitive to the choice of convective parameterization (Takahashi 1999; Ricciardulli and Garcia 2000). Note that our model has a momentum flux that is within, but near the lower end of, the range of momentum flux in GCMs with similar convective parameterizations (T. Horinouchi 2000, personal communication).
Above 50 hPa the stratospheric water vapor mass mixing ratio is set to 2.5 × 10−6 for the purpose of radiation calculations since no methane oxidation scheme is included here and advection alone results in unrealistically low concentrations. Climatological sea surface temperatures and atmospheric trace gases used in calculating heating rates are annually periodic and specified for each month. The model has no external source of interannual variability.
Full details of the ultrasimple spectral parameterization (USSP) for gravity waves are given by Warner and McIntyre (1999) and detailed analysis of the gravity wave climatology in the model are to be reported in a separate paper (Warner et al. 2001, unpublished manuscript). Nevertheless, we give an outline of the scheme since some features are different from the original formulation and details of the sources, for example, may be of use for comparison with other schemes and models. The USSP models the evolution of, and forcing from, a continuous spectrum of upward propagating gravity waves. The original formulation of the scheme launched a constant amount of wave energy from each location, but this produced large pseudomomentum fluxes at polar latitudes since the integrated total flux at the source was dependent on the local value of the inertial frequency and these gave unrealistically slack zonal winds over the poles. Instead we use a source spectrum that launches waves with a homogeneous total wave stress. The wave source is assumed isotropic relative to the surface and is launched from model level 3 near the surface, in each of four horizontal wave vector directions: north, south, east, and west. This launch spectrum is unsaturated at the surface since the semiempirical breaking criterion used in the scheme is set to the same level as in Warner and McIntyre (1999). The momentum flux spectrum at source peaks at a vertical wavelength of 4.3 km. In the absence of orography, the launch spectrum contains a total vertical flux of horizontal momentum of 6.6 × 10−3 kg m−1 s−2, which is the equatorial value used by Scaife et al. (2000). In the absence of tropospheric filtering, the total wave flux |u′w′| at about 100 hPa is then 5.5 × 10−2 m2 s−2. This corresponds to 1.4 × 10−2 m2 s−2 in each of the 4 wave vector directions. This is within current observational estimates of gravity wave flux for east or west propagating waves. For example, Sato and Dunkerton (1997) used radiosonde data to estimate lower-stratospheric fluxes in the range 0.2–4.0 × 10−2 m2 s−2, while Ricciardulli and Garcia (2000) used measurements of outgoing longwave radiation to infer fluxes of 1.35 × 10−2 m2 s−2 in each direction. Finally, Alexander and Vincent (2000) used a gravity wave model to fit radiosonde observations of waves and derived a value equivalent to 1.2 × 10−2 m2 s−2. Other studies have provided estimates of net fluxes. These are zero at launch in our model but after tropospheric filtering the net fluxes are no longer zero and these are considered in a separate paper (Warner et al. 2001, unpublished manuscript).
In the USSP, the wave spectrum in each wave vector direction is Doppler-shifted by the vertical shear in the horizontal wind parallel to the wave vector, neglecting Coriolis and hydrostatic effects in the dispersion relation (ω/k = N/m, where ω is the intrinsic frequency, k and m are horizontal and vertical wavenumbers, and N is the buoyancy frequency). Although this is a parameterization of gravity waves, the same dispersion relation applies to Kelvin waves so it could be considered that we are including some of the smaller-scale Kelvin wave forcing at and near the equator. If severe enough, Doppler shifting leads to part of the wave spectrum exceeding a built-in empirical saturation spectrum proportional to m−3. The momentum flux associated with this part of the spectrum is then removed, and a corresponding local wave induced horizontal force is applied in the wave vector direction. The remaining spectrum is then propagated to the next higher model level. The isotropic source spectrum used here launches net zero momentum flux and so the model still conserves momentum apart from the very small amount due to the net remaining gravity wave flux that exits from the top of the model.1 This is a more physically based alternative to the Rayleigh drag used previously in this and some other models since Rayleigh drag can act as an unrealistic source of momentum when applied to the zonal mean wind (Shepherd et al. 1996). Also Rayleigh drag cannot accelerate the flow, as can gravity wave forcing.
We validate the large-scale features of the model by comparison with Met Office assimilated stratospheric analyses (Swinbank and O'Neill 1994) for the period November 1991 to January 2000. The tropical winds are also compared to radiosonde data (updated from Naujokat 1986) to obtain a long enough time series to examine low-frequency variability.
3. Effects on the extratropics
a. The stratosphere in summer and winter
With the USSP included, the model has peak winter westerlies and summer easterlies close to the observed maxima (cf. Figs. 1a and 1b with Figs. 1e and 1f). The net effect on the winds of including the USSP (Figs. 1c and 1d) peaks at high latitudes and over the equator and is largest in the upper stratosphere.
Maxima in the winter westerly jets are halved by the effect of the USSP. In January, the deceleration of winter westerlies around 70°N is mirrored by an almost identical weakening of the easterly jet at 70°S, whereas in July, the effect on the southern winter jet is much greater and far outweighs the weakening of summer easterlies over the Arctic.
Compared to the no drag case, the USSP also produces greater equatorward tilt of the westerly jets with height. Enhanced equatorward tilt can be seen as a meridional dipole at upper levels in the difference plots (Figs. 1c and 1d), although compared to observations, the southern winter jet is still close to vertical (Fig. 1f). Improved equatorward tilt of the winter jet has also been reported in GCMs with discrete gravity wave spectra (e.g., Norton and Thuburn 1997; Medvedev et al. 1998). Details of the gravity wave spectrum are therefore not essential to obtain the tilt. This is confirmed by an experiment where Rayleigh drag is applied to the full model wind (Fig. 2) in place of the spectral gravity wave parameterization (the Rayleigh drag e-folding time decreases as the 4th power of log-pressure height above 36 km, and by 64 km the timescale is just 1.5 days). The winter westerly jets obtained with this friction are very similar to those obtained with the USSP (cf. Figs. 1a,b and 2).
However, a version of the model employing drag with the same dependence on height but a lower model lid produced vertically orientated jets (Swinbank et al. 1998; Butchart and Austin 1998). This suggests that the total mesospheric drag and not the detailed mechanism of deposition is the main factor in obtaining equatorward tilting jets in the upper stratosphere. This might also be expected from “downward control” arguments (Haynes et al. 1991). Note that for a model lid at 0.01 hPa, the Rayleigh drag used to produce Fig. 2 and needed to match the parameterized gravity wave forcing is very large in the mesosphere and is greater than middle-atmosphere models have tended to use (e.g., Boville 1995; Butchart and Austin 1998).
b. Wave forcing of the mean flow
Figure 3 shows the net, wave induced acceleration provided by the USSP. The net acceleration from resolved waves in the model is also plotted to show the relative importance of the two sources of wave driving [resolved wave drag is the divergence of the Eliassen–Palm (EP) flux divided by density and the cosine of latitude (see e.g., Andrews et al. 1987)].
In the troposphere, the resolved wave forcing dominates that from the USSP. The flux of resolved wave activity shows peak convergence in upper levels of the extratropics and divergence at lower levels. This is similar to a signature seen in baroclinic eddy life cycles in the troposphere (Edmon et al. 1980; Thorncroft et al. 1993). Orographic drag (not shown) is the largest wave forcing near 100 hPa where it peaks at 2–3 m s−1 day−1 in winter. It decreases rapidly with height in the lower stratosphere and is not applied above 40 hPa.
Zonal forcing from resolved waves in the stratosphere (Fig. 3, top) has negative sign and a large spatial scale over most of the stratosphere, consistent with convergence of Rossby wave activity. Decelerations of up to 10 m s−1 day−1 occur near the stratopause in winter. Interestingly, there are also areas of EP flux divergence, such as in the subtropical lower mesosphere in summer, indicating a possible wave source in this region. Norton and Thuburn (1996, 1999) found a similar source in a middle-atmosphere GCM and showed how it was responsible for the 2-day wave in the mesosphere. They attributed it to instability of the zonal mean flow. Comparison with Fig. 1 shows that the divergent EP fluxes in Fig. 3 are closely aligned with the regions of strong wind curvature. As found by Norton and Thuburn, the meridional gradient of potential vorticity (not shown) also changes sign in the region of divergence, as required for instability. This at least partly explains why the region of EP flux divergence in the Southern Hemisphere is stronger than that in the north since there is much stronger curvature in the southern hemisphere easterly jet (see upper panels of Fig. 1). Norton and Thuburn also concluded that gravity wave drag was important for generating these signals, since when the wave drag was weakened in their model, the region of EP flux divergence was greatly reduced. In contrast, after removing the USSP from the Unified Model a similar area of EP flux divergence remains but at slightly lower latitudes (10°–20° latitude). Although it is undoubtedly important, it seems that an unstable zonal mean state can also occur without parameterized gravity wave forcing in our model.
The forcing due to the USSP of gravity waves (lower panels in Fig. 3) is generally much less than that from resolved waves in the stratosphere but the USSP does provide an easterly force of up to 0.5 m s−1 day−1 throughout the summer stratosphere that helps to maintain the summer easterly jets (Figs. 1a and 1b). Easterly forcing is also found between the equator and midlatitudes in the winter hemisphere but this reverses to westerly forcing at high latitudes where it helps to maintain the mean westerly flow (cf. Figs. 1a and 1b). A similar pattern of forcing has been inferred from observational analyses where it was attributed to acceleration of stratospheric winds by unresolved gravity waves (Alexander and Rosenlof 1996). For the amplitude of the source used here, linear Doppler shifting followed by the empirical wave breaking criterion applied in the USSP appears to be sufficient to capture this transfer from accelerative forcing of stratospheric winds to decelerative forcing in the mesosphere.
In the upper stratosphere and lower mesosphere the parameterized forcing gives a drag on both the winter westerly jet (30 m s−1 day−1 in January and 50 m s−1 day−1 in July) and the summer easterly jet (5–10 m s−1 day−1). The response generally has the same sign as the forcing (Figs. 1c and 1d). Despite this, the direct effect on the zonal flow may not be the dominant term in the momentum budget. For example, in the lower mesosphere in January, the parameterization provides a much larger force at 60°N than 60°S yet the response of the modeled winds has a similar magnitude at these locations. This suggests that secondary effects such as those due to advection by altered residual meridional circulation are also important.
c. Meridional circulation and temperature
The weakening of high-latitude upper-stratospheric winds in both hemispheres is consistent with increased meridional circulation. Without the USSP, the 2-cell Brewer–Dobson circulation extends all the way through the stratosphere and into the mesosphere (not shown), whereas when the USSP forcing is added, the mesospheric branch becomes a more realistic single summer to winter cell.
Figure 4 shows the average annual cycle in the tropical component of the residual circulation [as defined by Andrews and McIntyre (1976)]. The mean vertical velocities are systematically upward at all levels in the stratosphere and increase with height from 0.25 mm s−1 in the lower stratosphere to around 1.5 mm s−1 at 1 hPa.
In the upper 2 panels of Fig. 4 there is a strong semiannual component to the upwelling. At 1 hPa, peak vertical velocities occur in May–June and November–December just before peak zonal mean easterly winds occur and when the easterly shear with height is largest (not shown). The northern winter peak in the upwelling is also larger than that in southern winter, consistent with the stronger equatorial easterly phase of the stratopause semiannual oscillation (SAO) in northern than southern winter (Hirota 1980). At 3.2 hPa, the phases of this cycle are retarded by 1–2 months. A semiannual signal in the upwelling can be traced down through 10 hPa and into the lower stratosphere where seasonal variability in the upwelling is dominated by an annual frequency with a minimum in northern summer. This cycle is normally attributed to greater wave driving in northern winter (Yulaeva et al. 1994) and similar vertical velocities were derived from observational analyses by Randel et al. (1999).
Midwinter temperature biases with the USSP included are less than 5 K throughout most of the lower stratosphere and no more than 2 K in the vicinity of the ozone hole over Antarctica (Fig. 5). Biases are now small in winter in the lower and middle stratosphere (especially in northern winter) where most models show a large cold bias. At least this level of accuracy is required for comprehensive chemical modeling since temperature biases of just a few kelvins in the lower polar stratosphere can significantly affect rates of ozone depletion resulting from heterogeneous chemistry (Solomon 1986). This represents a significant improvement on previous model biases but cold biases up to 10 K can still be found at 10 hPa over the southern pole later in winter when cold anomalies descend from aloft. Considering the size of the net effect of gravity waves on the zonal mean temperatures shown in Fig. 5, it seems likely that remaining temperature biases are likely to be within the uncertainties in gravity wave forcing. Related to this increasing temperature bias towards the end of winter is a bias in the timing of peak interannual variability in late winter (Fig. 6). Although the modeled interannual variability has a realistic maximum of 8–10 K, it peaks too early in both northern and southern winter compared to observational analyses (lower panel in Fig. 6). In the Northern Hemisphere, for example, this leads to significantly more interannual variability in the model than in observations between September and November. Nevertheless, modeled sudden warmings, in which the 10-hPa wind at 60°N reverse to easterlies for 2 or more days in midwinter, occur in 12 out of the 20 modeled years and this is in agreement with the 50% or so of observed winters that show major warmings (see, e.g., Table 6.1, Andrews et al. 1987). Errors in the timing of interannual variability also appear to occur in other middle-atmosphere GCMs (e.g., Hamilton 1995; Beagley et al. 1997).
In summer, there is a large cold bias just above the polar tropopause in July (Figs. 5e and 5f). Centered close to 200 hPa, it is almost 10 K over the North Pole in July and shows a similar peak at 70°S in January. A similar bias was found in previous versions of this model (Swinbank et al. 1998; Butchart and Austin 1998; Jackson et al. 2001). It is also clear that this region is sensitive to gravity wave forcing since the response of the modeled temperatures to the USSP helps to counteract this cold bias (Figs. 5c and 5d). This is presumably due to enhanced downwelling in the lower summer stratosphere driven by the parameterized wave forcing. Similarly, Rosenlof (1996) has also suggested that small-scale wave forcing affects summer downwelling in the extratropics, leading to warming effects of several kelvins in the lower stratosphere.
d. Transition to spring
A cold bias in middle-atmosphere models is often accompanied by a delayed transition to spring. Hamilton et al. (1999), for example, found that the spring transition in the Southern Hemisphere was sensitive to horizontal resolution (and hence the amount of resolved wave activity). In the Southern Hemisphere this is important for heterogeneous ozone depletion, which requires both sunlight and cold temperatures to occur (Solomon 1986). We use the reversal of the zonal mean wind to continuous easterlies at 61.25°S to mark the transition to spring in the Southern Hemisphere. This occurs as the jet core descends through the stratosphere and easterly winds descend from aloft. The relatively small year-to-year variability in the southern winter circulation mean that this normally occurs in the narrow range of late October to early November, whereas in the model without parameterized drag it is delayed by about a month. With the USSP included, the spring transition occurs earlier and closer to the observed time (Fig. 7).
At 60°S, the Coriolis acceleration is generally positive (westerly) throughout the depth of the stratosphere, whereas resolved wave driving is generally negative (easterly). Meanwhile, the gravity wave (GW) forcing is positive below the jet core (due to the positive shear of the zonal wind with height) and negative above it (due to density effects). The advection of momentum is also mainly negative above the jet core and positive below, due to the poleward and downward residual circulation and the structure of the jet.
Figure 8a shows that the Coriolis acceleration (C) is almost as large as, and opposite in sign to, the total wave driving (E + G). At 1 hPa the net of these terms (C + E + G) is similar in magnitude to the advection of momentum by the residual circulation (Fig. 8b). As the winds decelerate in spring, this advection of momentum provides up to 40% of the net deceleration in the middle to upper stratosphere. To this degree, the jet core is advected poleward and downward by the residual circulation rather than being directly eroded by wave driving. This suggests that the seasonal descent of anomalies in the polar night jet (Kodera 1995) may also be partly driven by the poleward and downward advection of momentum by the residual circulation (as well as the tendency of wave–mean flow interactions to descend), at least in the upper stratosphere.
4. Effects on the Tropics
a. Morphology of the QBO
Including the USSP reduces the tropical easterly bias in the model. It allows a QBO to be generated from forcing by both the resolved and parameterized waves (Scaife et al. 2000). In contrast to Scaife et al. (2000), the integration described here uses a homogeneous gravity wave source. It reproduces a similar QBO but with more variation between individual cycles of the oscillation. Figure 9 shows the vertical structure of the oscillation through approximately 8 periods. It has amplitudes of 20–30 m s−1 with stronger easterly phases than westerly phases by approximately 10 m s−1. The QBO in Fig. 9 is also the dominant variability in equatorial temperatures on timescales greater than a year. Warm anomalies accompany the descent of easterly wind shear with height and cold anomalies accompany westerly wind shear as expected from thermal wind balance. The amplitude of the QBO in temperature increases with height from about 0.5 K at 100 hPa, to 2 K at 30 hPa, to around 5 K in the upper stratosphere and the signal can be traced up to 1 hPa or higher. Unlike the winds, these temperatures were filtered to remove the long-term annual mean and mean annual cycle and so the mean stratopause SAO has also been removed. Even after this, the QBO temperature signal at these upper levels still fluctuates on a roughly semiannual timescale, suggesting that the QBO at this level is better described as a modulation of the SAO. The acceleration provided by the USSP (Fig. 9, bottom) shows strong QBO related variations of up to 0.5 m s−1 day−1 in the stratosphere. There is also some semiannual variability in the forcing from the USSP in the lower stratosphere that has a corresponding signal in the QBO winds and temperatures. This appears to be a filtering effect of the small but significant semiannual variation in the weak band of westerly winds near the top of the Hadley circulation at 100 hPa (although the stratopause SAO could also be responsible). At the stratopause and above, the USSP forcing is net westerly and this helps to remove an easterly bias in the model and reproduce the westerly phase of the SAO.
As well as amplitude, the meridional width of the two QBO phases is also asymmetric: the westerly phase is confined to just 10°–15° of latitude compared to 20° or more for the easterly phase. Dunkerton (1991) showed that this is at least partly due to the meridional circulation associated with the QBO itself, which narrows the westerly phase as it descends. This appears to occur for composite westerly and easterly QBO phases in our model (Fig. 10). When it is a maximum at 4.6 hPa (Fig. 10a), the composite westerly phase is about 30° wide and just over 30 m s−1, yet by the time it has descended to 40 hPa, its amplitude and meridional width are halved (Fig. 10b). This contrasts with the composite easterly phase, which maintains its width and most of its amplitude as it descends from 5 to 40 hPa (Figs. 10c and 10d). Similar asymmetry between phases is seen in observations of the QBO (Hamilton 1984; Dunkerton and Delisi 1985). Throughout their descent, both phases also show a high degree of zonal symmetry. Composite equatorial easterly and westerly winds vary by just a few percent around the globe although more intense easterlies on the summer side of the QBO also give the easterly phase the appearance of oscillating from north to south as it descends.
Figure 11 shows histograms of the QBO periods defined as the time between successive easterly to westerly wind transitions at 40 hPa. The mean period is close to the observed mean at 28 months, and there is more variability between individual periods than with a latitudinally varying gravity wave source (Scaife et al. 2000), which showed little QBO period variability and a mean period closer to 2 yr. The variable period is also clearly seen in the temperature anomalies. At 40 hPa the period ranges from 24 to 36 months. Note that this variability arises mainly from variation in the duration of the westerly QBO phase, as found in observations by Salby and Callaghan (2000).
Comparison with radiosonde observations shows that this range compares well with the variability found in the observed QBO. Although variations in sea surface temperature and tropical wave sources probably lead to modulations of the period of the QBO (Geller et al. 1997) the range of periods in our experiment shows that these factors are not necessary to generate the observed range of periods. Dunkerton (1990) suggested that a longer QBO period could result from larger extratropical wave forcing, since the QBO would have to descend against stronger tropical upwelling. Given that the main difference between the model used here and that used by Scaife et al. (2000) is the reduction of large fluxes of gravity wave activity in the extratropics, it seems plausible that the more variable QBO periods seen here may also be connected to changes in the extratropical stratosphere, perhaps through the meridional circulation.
Although they have a realistic range, Fig. 11 suggests that the modeled QBO periods may be too close to a discrete distribution of multiples of the period of the stratopause SAO. The link between the QBO and SAO is also clear in Fig. 9, which shows continuous connections between the onset of similar phases of the two oscillations and the westerly phase of the SAO occurring at lower levels at the onset of new westerly QBO phases. Indeed, it seems that the QBO may be coupled to and/or triggered by the SAO or annual cycle (Dunkerton and Delisi 1997; Gruzdev and Bezverkhny 2000) and the observations in Fig. 11 contain signs of clustering around 24 and 30 months with an additional peak close to the mean.
The reason that the period of our modeled QBO in the lower stratosphere follows a more discrete distribution than found in observations may not lie with the apparent triggering by the SAO (seen in Fig. 9) since this appears to be realistic (cf. Dunkerton and Delisi 1997). Rather, it may be that the correlation with the SAO is too well preserved as the oscillation propagates to lower levels, due to lack of variability in the descent rate of the modeled QBO. This should be expected given that the parameterized gravity wave launch stress is held constant in our simulation and the SSTs are annually repeating. In reality, by the time a particular phase of the observed QBO reaches the lower stratosphere, it has been subjected to continuous variations in upward propagating fluxes of wave activity and hence accelerative forcing, so that the descent time and the oscillation period vary continuously in the atmosphere. This perhaps explains the more continuous distribution of periods found in the observations shown in Fig. 11.
The current simulation shows an improved SAO when compared to the model without the USSP of gravity waves. Without the USSP, the SAO is highly regular and shows such a strong easterly bias that there is no westerly SAO phase. The current simulation has a more irregular oscillation and produces westerly phases of the SAO, although these are weaker (5–10 m s−1) and occur slightly lower in the atmosphere than the observed oscillation. Nevertheless, it seems reasonable to approach the problem of simulating the tropical oscillations from the surface upward as the filtering effect of underlying winds appears to be very important and any model simulation of the SAO alone is likely to be strongly affected when a QBO is present in the underlying winds. A similar conclusion was reached by Nissen et al. (2000), who found that increased vertical resolution in their GCM degraded the SAO but was physically justified as an improvement because more realistic dissipation of Kelvin waves occurred, providing westerly acceleration at lower levels.
These equatorial oscillations also have a signal in vertical residual velocity. Eight cycles can be seen in the anomalies of residual circulation shown in Fig. 12, corresponding to the eight cycles of the QBO in this integration. There is also variability in the upwelling due to subannual variability not directly related to the annual cycle (which has been removed here). The amplitude of the quasi-biennial variations in vertical velocity increases with altitude from around 0.1 mm s−1 at 32 hPa to 1 mm s−1 at 1 hPa. Comparing these velocities with the mean annual cycle in upwelling (Fig. 4) shows that, above the midstratosphere, the amplitude of the quasi-biennial variations exceed the mean upwelling for most months of the year. Providing the downward perturbations due to the QBO occur at the right time of year, they are therefore large enough to temporarily reverse the sign of the vertical velocity in the tropical upper stratosphere. Randel et al. (1999) derived some similar amplitude signals from observational analyses but these relied on an artificial scaling of the anomalies and it will be interesting to see if improving the observational analyses will reveal this feature.
b. Direct effects of model diffusion
To test this, we reran the model for 3 yr to ensure at least 1 QBO cycle with the diffusion coefficient (κ) reduced by a factor of 3. The resulting oscillation shows improved descent of the westerly phase (Fig. 13) while the easterly phase remains largely unchanged (it would be desirable to have a longer integration to confirm this). Reducing the diffusion coefficient may also increase the amount of resolved wave activity at small scales in the model (e.g., Takahashi 1999). Since we reduced only the stratospheric diffusion coefficients while keeping the tropospheric coefficients the same, and the effect on the (narrower) westerly phase is evidently stronger than that on the easterly phase in Fig. 13, direct damping of the QBO winds is more likely to be responsible.
5. Conclusions and discussion
Before summarizing our results, we examine some of the assumptions made in this study. For want of a better determined source, we launched a constant, isotropic spectrum of gravity waves from near the surface. Filtering by the background wind in the troposphere then generates anisotropy in the subtropical wave fluxes at the tropopause. This anisotropy is important for reasonable forcing of the stratospheric summer easterlies at higher levels since an integration where isotropic fluxes were launched near the tropopause gave very weak subtropical summer easterlies (not shown). A similar result has also been found with the Hines (1997a,b) GW parameterization (W. Norton 2000, personal communication).
Tropospheric filtering may have a similar effect to wave generation in the westerly tropospheric jets well above the surface, since increasing wind with height might also tend to generate a wave spectrum with phase velocities mainly opposite to the mean flow at that level (e.g., Kershaw 1995). In contrast, Medvedev et al. (1998) found that launching waves near the tropopause with phase speeds in the direction of the local wind gave some improvement in their model. There is still much uncertainty over even these basic parameters for gravity wave sources. Improved observations should help to isolate the mechanisms for producing the required anisotropic spectrum entering the lower stratosphere. Alexander and Vincent (2000) recently suggested that much of the observed seasonal variability in tropical wave fluxes can be explained by variations in the background conditions so the assumption of a constant source strength may be reasonable. However, they also suggest that tropical convective sources are strongest in the upper troposphere and other studies have suggested that larger fluxes are found in the Tropics than the extratropics in the lower stratosphere (e.g., Allen and Vincent 1995). The source of these waves in the atmosphere may be stronger and at higher altitudes in the Tropics than at high latitudes, representing the local intensity and depth of convection (e.g., Piani et al. 2000).
We also assumed that Met Office stratospheric analyses are the best estimate of the actual stratospheric state. However, the analyses were constructed using data assimilation and therefore depend on the numerical model used. This mixing of observations and model raises the possibility of circular arguments when validating the model. Nevertheless, there is added confidence in the improvements shown here because despite introducing an additional difference (the USSP) from the model used in the assimilation, we have shown that the model simulation is now in better agreement with the assimilated analyses.
One of the primary reasons to include spectral parameterizations such as the USSP is to alleviate the “cold pole” problem. Overall we conclude that significant improvements in the cold pole and extratropical jets can be achieved even with an isotropic, homogeneous spectrum of gravity waves. Both the intensity and structure of the stratospheric jets are very sensitive to the gravity wave forcing and in the upper stratosphere and lower mesosphere the strength of the jets is halved when the USSP is included. As well as the cold pole problem, the delayed breakdown of the southern winter jet is alleviated. This sensitivity highlights the importance of gravity wave forcing for the stratospheric winds. In agreement with previous studies, we found that the USSP has an accelerative effect on lower-stratospheric winds. As noted by Alexander and Rosenlof (1996), this is another reason why Rayleigh friction, which damps the winds everywhere, should be replaced by a more realistic parameterization.
Another reason for including a parameterized spectrum of gravity waves is its importance for the QBO, as originally envisaged by Lindzen and Holton (1968). At the resolution considered here, extra parameterized forcing is necessary to generate a QBO in our model. In contrast, Takahashi (1999) demonstrated that moist convective adjustment (MCA) parameterizations can generate enough wave activity to force a QBO without additional parameterized gravity wave forcing. However, many current convective parameterizations generate smaller wave fluxes than MCA (T. Horinouchi 2000, personal communication) and it seems likely that spectral gravity wave parameterizations will be needed to generate the QBO in other models at similar resolution. It also appears that horizontal diffusion coefficients need to be scale selective enough not to have a direct effect on the QBO. Although the QBO width is much larger than the minimum resolvable scale in GCMs, its very long timescale implies an upper limit to the level of horizontal diffusion that can be realistically applied in the lower stratosphere in models.
A number of features of the observed QBO have been reproduced in our experiment. Despite the annual repetition of trace gas concentrations and other forcing such as sea surface temperatures, and the assumption of constant gravity wave stress at launch, the simulated QBO shown here has a range of periods similar to that found in observations. This suggests that much of the variability of the observed QBO period could be produced internally by the atmosphere.
The meridional structure of the modeled oscillation shown here is also similar to that seen in observations. Since the parameterized gravity wave source is uniform in latitude but the QBO has realistic width, this supports the conclusion that this aspect of the oscillation is also determined internally by the dynamics (Haynes 1998) (although the amplitude of model-resolved waves inevitably varies with latitude and may contribute).
The observed asymmetry between the easterly and westerly phases is reproduced without introducing asymmetries between easterly and westerly phase speed waves in the parameterized gravity wave source. This supports the conclusion that many features of the phase asymmetry arise internally from nonlinear self-advection of the QBO by its associated meridional circulation (Dunkerton 1991; although again, model resolved waves may not be symmetric between east and west phase speeds and may also contribute to the modeled phase asymmetry).
Most vertically extended GCMs have errors in common with our GCM such as a cold pole and absence of a tropical QBO. Here we have shown that these errors can be alleviated by the effects of a parameterized spectrum of gravity waves. Remaining errors are generally smaller than these effects.
Acknowledgments
This work was supported by the Research Program of the Met Office, United Kingdom, and by the Natural Environmental Research Council. We thank Dr. B. Naujokat for the radiosonde data used to compile the observed QBO periods and Dr. T. Horinouchi for suggesting the possibility of a direct effect of model diffusion on the QBO winds.
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Climatological zonal mean zonal winds for (left) Jan and (right) Jul: (a) and (b) show the model with the USSP; (c) and (d) show differences from the model without the USSP; and (e) and (f) show differences from assimilated observational analyses (to 0.32 hPa only). Winds are averaged over 20 yr for the model with the USSP, 10 yr for the model without the USSP, and 8 yr for the assimilated analyses. The contour interval is 10 m s−1
Citation: Journal of the Atmospheric Sciences 59, 9; 10.1175/1520-0469(2002)059<1473:IOASGW>2.0.CO;2
Climatological zonal mean zonal winds for (left) Jan and (right) Jul for the model with Rayleigh friction. Winds are averaged over 10 yr and the contour interval is 10 m s−1
Citation: Journal of the Atmospheric Sciences 59, 9; 10.1175/1520-0469(2002)059<1473:IOASGW>2.0.CO;2
Net westerly acceleration (m s−1 day−1) from (top) the model resolved waves and (bottom) parameterized gravity wave spectrum for (left) Jan and (right) Jul. Averages over 20 yr are plotted with contour values [0, ±0.5, ±1, ±2, ±4, ±8 …]
Citation: Journal of the Atmospheric Sciences 59, 9; 10.1175/1520-0469(2002)059<1473:IOASGW>2.0.CO;2
Mean annual cycle in upwelling residual velocity (mm s−1) as a function of time at several pressure levels in the stratosphere. Vertical velocities are shown after area averaging over (20°N–20°S) and 1 month
Citation: Journal of the Atmospheric Sciences 59, 9; 10.1175/1520-0469(2002)059<1473:IOASGW>2.0.CO;2
Climatological zonal mean temperatures for (left) Jan and (right) Jul: (a) and (b) show the model with the USSP; (c) and (d) show differences between the model with USSP and no parameterized drag and (e) and (f) show differences from assimilated observational analyses (to 0.32 hPa only). Temperatures are averaged over 20 yr for the model with USSP, 10 yr for the model without parameterized drag, and 8 yr for the assimilated analyses
Citation: Journal of the Atmospheric Sciences 59, 9; 10.1175/1520-0469(2002)059<1473:IOASGW>2.0.CO;2
Interannual std dev of monthly mean temperatures (K) as a function of time of year at 10 hPa (top) for the model and (bottom) observational analyses
Citation: Journal of the Atmospheric Sciences 59, 9; 10.1175/1520-0469(2002)059<1473:IOASGW>2.0.CO;2
Seasonal descent of the zero zonal mean wind line at 61.25°S starting from Sep. The dashed curve shows the 20-yr mean from the model with the USSP. The dot–dashed curve shows a 10-yr mean from the model with no parameterized drag and the solid line shows an 8-yr mean of assimilated observational data
Citation: Journal of the Atmospheric Sciences 59, 9; 10.1175/1520-0469(2002)059<1473:IOASGW>2.0.CO;2
Transformed Eulerian mean budget at 1 hPa and 61.25°S. (left) The near cancellation of the Coriolis term (C), resolved wave driving (E), and parameterized gravity wave driving (G). (right) The sum of these three terms (C + E + G) and advection by the residual circulation (A). An approximate value of the zonal wind acceleration estimated from monthly mean data is also shown (Ut)
Citation: Journal of the Atmospheric Sciences 59, 9; 10.1175/1520-0469(2002)059<1473:IOASGW>2.0.CO;2
(top) Time series of the equatorial zonal mean zonal wind (m s−1), (middle) anomalous zonal mean temperature (K) and (bottom) zonally averaged gravity wave forcing (m s−1 day−1). The climatological mean and annual cycle have been removed from the temperature series in the middle panel
Citation: Journal of the Atmospheric Sciences 59, 9; 10.1175/1520-0469(2002)059<1473:IOASGW>2.0.CO;2
Composite peak phases of the modeled QBO in the upper and lower stratosphere: (a) maximum westerlies at 4.6 hPa, (b) maximum easterlies at 4.6 hPa, (c) maximum westerlies at 40 hPa, (d) maximum easterlies at 40 hPa. The contour interval is 5 m s−1
Citation: Journal of the Atmospheric Sciences 59, 9; 10.1175/1520-0469(2002)059<1473:IOASGW>2.0.CO;2
Histograms of the (top) observed QBO period from radiosonde data and (bottom) modeled QBO period, both at 40 hPa. The period is taken as the time between easterly to westerly wind transitions and thin vertical lines are used to show the mean periods
Citation: Journal of the Atmospheric Sciences 59, 9; 10.1175/1520-0469(2002)059<1473:IOASGW>2.0.CO;2
Anomalies in the residual vertical velocity as a function of time at several pressure levels in the stratosphere. Vertical velocities (mm s−1) are shown after area averaging over (20°N–20°S) and monthly intervals. The mean annual cycle has been removed and is shown in Fig. 4
Citation: Journal of the Atmospheric Sciences 59, 9; 10.1175/1520-0469(2002)059<1473:IOASGW>2.0.CO;2
The first 3 yr of the modeled QBO winds at 1.25°N for (top) standard horizontal diffusion and (bottom) reduced horizontal diffusion. The contour interval is 5 m s−1. Only the region between 100 and 1 hPa is plotted for detailed examination of the descent of the QBO
Citation: Journal of the Atmospheric Sciences 59, 9; 10.1175/1520-0469(2002)059<1473:IOASGW>2.0.CO;2
To the extent that downward control applies (Haynes et al. 1991), it would be physically justifiable to deposit any remaining flux in the top model layer, as done by Lawrence (1997), for example. Unfortunately this led to numerical instability in our model and so was not adopted.
