The Stratopause Semiannual Oscillation in the Berlin Troposphere Stratosphere Mesosphere GCM

2749 The Stratopause Semiannual Oscillation in the Berlin Troposphere Stratosphere Mesosphere GCM KATRIN M. MÜLLER, ULRIKE LANGEMATZ, AND STEVEN PAWSON Institut für Meteorologie, Freie Universität Berlin, Berlin, Germany (Manuscript received 23 August 1996, in final form 29 April 1997) ABSTRACT The tropical stratopause semiannual oscillation (SAO) in the Berlin troposphere stratosphere mesosphere general circulation model (TSM GCM) is investigated. The model is able to produce a semiannual oscillation that is properly located in time and space in comparison with observations; however, the westerly phase is 10 15ms 1 too weak while the second easterly phase of the year is about the same amount too strong. A case study is performed to examine the westerly forcing of the SAO in detail. At 1 hpa in one particular March, when the strongest westerly acceleration of the year takes place, only 18% of the forcing is due to the dissipation of Kelvin waves, whereas 72% of the forcing is due to the dissipation of other slow eastward propagating planetary-scale waves and 10% is due to the dissipation of eastward propagating inertio gravity waves. Throughout the year the Kelvin wave contribution to the total body force is below 50%. The modeled Kelvin waves are dissipated at higher altitudes than observed Kelvin waves with the same phase speeds. To examine the effect of the QBO on the wave spectrum a relaxation of the zonal-mean wind to an idealized QBO has been implemented into the model. During the westerly phase of the QBO, slow eastward propagating waves with wavenumbers greater than 1 can no longer reach the upper stratosphere. This leads to a reduction of the westerly momentum available to generate the westerly phase of the SAO, and the westerly winds do not descend below 1 hpa as in the control experiment. This reduction in the descent is also present in observations, but there it is less pronounced. As the upper-stratospheric Kelvin waves in the model are partly too slow, they are too strongly affected by the changes in the propagation properties due to the QBO. 1. Introduction The tropical stratopause semiannual oscillation (SAO) can be observed in temperature and the zonal wind. It was discovered by Reed (1962, 1966) using radiosonde and rocketsonde observations. His work was followed by numerous statistical analyses of rocket and balloon observations as well as satellite data (e.g., Quiroz and Miller 1967; Angell and Korshover 1970; van Loon et al. 1972; Belmont et al. 1974, 1975; Hopkins 1975; Garcia et al. 1997; and others). Hirota (1980) reviewed the features of the semiannual oscillation. The mean annual evolution of the stratopause SAO can be seen in Fig. 1, which shows a time height series of the zonal wind between 20 and 60 km derived from nearly 20 years of rocketsonde observations at Ascension Island (8 S, 14 W) and Kwajalein (8 N, 167 E). The westerlies first appear in the lower mesosphere shortly after the solstices and propagate downward with a speed of 6 7 km mo 1. They reach maximum values during the equinoxes with average values of 25 m s 1 Corresponding author address: Katrin M. Müller, Institut für Meteorologie, Freie Universität Berlin, Carl-Heinrich-Becker-Weg 6 10, 12165 Berlin, Germany. E-mail: mueller@strat01.met.fu-berlin.de in April and 20 m s 1 in October. The downward propagation of the westerly phase indicates that the dissipation of vertically propagating waves near critical layers causes the westerly phase of the SAO. Observations (Hirota 1978, 1979; Salby et al. 1984) revealed the existence of short-period, equatorially trapped Kelvin waves that propagate into the stratosphere and might at least partly supply the forcing required. In addition to this the absorption of eastward traveling gravity waves can contribute to the generation of the westerly phase of the SAO. The maximum easterlies have a magnitude of more than 40 m s 1 in January and of about 20 m s 1 in July. In contrast to the onset of the westerly phase the transition from westerlies to easterlies occurs rather suddenly throughout a deep layer. That is because the easterly phase of the SAO is forced by the dissipation of horizontally traveling planetary waves (Hirota 1980) and cross-equatorial advection of easterly winds by the residual mean meridional circulation (Reed 1966; Meyer 1970; Holton and Wehrbein 1980; Mahlman and Sinclair 1980). Planetary wave activity is stronger during Northern than during Southern Hemisphere winter, causing the stronger easterly phase during the first SAO cycle (Delisi and Dunkerton 1988). There are several general circulation models (GCMs) that simulate a semiannual oscillation near the strato- 1997 AMERICAN METEOROLOGICAL SOCIETY

2750 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 54 the QBO on the SAO in the model was therefore examined by performing GCM experiments in which the wind in the lower stratosphere is relaxed toward idealized wind fields, representative of each phase of the QBO. The results are compared with observations. The remainder of the paper is structured as follows. First a brief description of the GCM used for this study is given. In section 3 the modeled semiannual oscillation is presented. It is followed by an analysis of the forcing of the westerly phase of the stratopause SAO in the model in section 4. The interannual variability of the modeled SAO is discussed in section 5. Finally, the modulation of the SAO by the QBO is examined (section 6). Conclusions are presented in section 7. FIG. 1. Zonal-mean zonal wind at the equator from 10 years of rocketsonde observations at Ascension Island (7.6 S, 14.4 W) and Kwajalein (8.7 N, 167.7 W). Contour interval 5 m s 1. pause. However, this oscillation often shows only in the strength of the easterly winds in the Tropics as many models fail to produce the westerly phase of the SAO without a gravity wave drag parameterization. For example, the UGAMP GCM needs a parameterization for traveling gravity waves in order to simulate the westerly phase of the SAO (Jackson and Gray 1994). In the NCAR CCM2, westerly winds do not reach the stratopause region and the easterly winds are much too strong (Sassi et al. 1993). The stratopause equatorial winds in the GISS GCM version without a gravity wave parameterization are easterly throughout the year and only vary in strength (Rind et al. 1984), whereas in the version with gravity wave drag parameterization the SAO becomes more realistic (Rind et al. 1988). The SKYHI GCM version analyzed in Hamilton and Mahlman (1988) simulates a rather realistic SAO; however, in a more recent simulation with the model the westerly phase of the SAO became weaker and less realistic (Hamilton et al. 1995). According to Hamilton et al. this change is probably due to a correction in the convective adjustment scheme of the previous simulation and an improved diurnal averaging procedure that led to changes in the stratospheric heating rates. In this paper it will be shown that the Berlin tropo strato mesosphere (TSM) GCM is able to produce a fairly realistic stratopause SAO, with westerly winds during the equinoxes, without a gravity wave drag parameterization. The contributions of all resolved waves to the forcing of the westerly phase of the SAO will be investigated in a case study. Observations (Hirota 1980; Garcia et al. 1997) suggest that the stratopause SAO is modulated by the quasibiennial oscillation (QBO). The westerly phase of the QBO alters the spectrum of the eastward propagating waves by selective absorption below critical levels. This leads to changes in the westerly forcing of the SAO. So far the Berlin TSM GCM, like most GCMs, does not produce a realistic QBO (Pawson 1992). The effect of 2. Description of the GCM The Berlin TSM GCM (Langematz and Pawson 1997) is a global climate model with an upper level at 0.0068 hpa (close to 84 km). The model has 34 levels, with a vertical resolution of 3.5 km throughout most of the middle atmosphere. Horizontally, the spectral model is truncated at T21 resolution. In the GCM the primitive equations are solved. Most of the tropospheric parameterizations from ECHAM1 (Roeckner et al. 1992) are used. These include a five-level soil model for moisture, snow cover and surface temperature, vertical diffusion of momentum, heat, and moisture, as well as convective and large-scale condensation and precipitation. The tropospheric radiation scheme is that of Morcrette (1991). Solar heating at visible and ultraviolet wavelengths in the middle atmosphere is calculated using the models of Shine and Rickaby (1989) for O 3 and O 2 as well as Strobel (1978) for O 2. Morcrette s scheme is retained for the near-infrared solar radiation and for the terrestrial infrared radiation up to 10 hpa. Longwave cooling above 10 hpa is treated by a cooling-to-space approximation. A weak linear Rayleigh friction was introduced in the mesosphere to close the jets, simulating the effect of gravity wave drag in a crude manner. Additionally, the horizontal diffusion was increased systematically in the five model levels below the top, the value at each of these levels being twice as strong as at the level immediately below. Deep convective clouds are calculated using a modified version of the Kuo (1974) scheme, the model of Tiedke et al. (1988) is used for shallow convection, and stratiform clouds are determined using the technique of Roeckner and Schlese (1985). Most results in the present study are from a 28-yr control run with annual and diurnal cycles. No gravity wave parameterization was used in the troposphere and stratosphere. Climatological sea surface temperatures (SSTs) were prescribed so that there is no interannual variability in the boundary conditions. The model variables were saved every 4 hours. A more detailed description of the model and the climatological structure

2751 FIG. 3. Zonal-mean zonal wind averaged between 8 S and 8 N from 28 years of model integration. Contour interval 5 m s 1. FIG. 2. Latitude height section of the amplitude of the SAO between 30 S and 30 N (a) from CIRA-86 observations (Fleming et al. 1990), (b) from 28 years of model simulation. Contour interval 2 m s 1. of the control experiment is given in Langematz and Pawson (1997) and Pawson et al. (1997). 3. The stratopause SAO Harmonic analysis of the zonally averaged zonal wind component reveals that the semiannual zonal wind oscillation is strongest in the Southern Hemisphere Tropics. This is illustrated in Fig. 2a using the data of the CIRA-86 (COSPAR International Reference Atmosphere) climatology (Fleming et al. 1990). In the vertical two maxima can be found close to the equator. The first one is located just above the stratopause level at 52 km and the second one below the mesopause level at 75 km. The amplitude of the stratopause SAO reaches 24 ms 1, whereas the mesopause SAO is slightly weaker reaching about 20 m s 1. The mesopause SAO is roughly 180 out of phase with the stratopause oscillation (not shown). In the CIRA compilation the amplitude of the SAO reaches a relative minimum directly over the equator. This minimum cannot be seen in other observations (e.g., Belmont et al. 1974) and is probably caused by the approximations used to determine the wind field in the CIRA climatology near the equator (Fleming et al. 1990). The GCM simulation (Fig. 2b) shows an amplitude of the same magnitude as in the observations near the stratopause. The maximum is, however, located 3 km (one model level) below that observed. As in the CIRA observations the maximum amplitude is slightly shifted toward the Southern Hemisphere. The stratopause SAO in the model is narrower than in the observations: the 20 m s 1 contour line spreads as far as 20 north and south of the equator in the CIRA climatology, whereas it reaches only 7 N and 17 S in the model. The GCM does not reproduce the mesopause SAO, which is believed to be forced by the absorption of gravity waves. Mesospheric gravity wave drag is very crudely parameterized in the GCM using a linear Rayleigh friction, which can only weaken the mean flow but is not able to reverse its direction and produce the observed out-of-phase oscillation at the mesopause. The evolution of the zonal-mean wind averaged over 28 years of the model simulation shows a well-developed SAO in the tropical stratopause region (Fig. 3). To allow comparison with the rocketsonde observations, the winds were averaged over 8 S to8 N. Averaging over the two latitudes closest to the equator (2.8 S and 2.8 N) gives an almost identical picture (see section 5). As observed, the westerly phase of the SAO propagates downward with height and the easterly phase shows almost no phase propagation. The easterly maxima appear during the solstices and the westerly maxima during the equinoxes. In comparison with the observations in Fig. 1 both westerly wind maxima are too weak (10 15ms 1 ), whereas the second easterly maximum is about 10 m s 1 too strong. These two effects cancel each other in the harmonic analysis, which explains the good agreement of the amplitudes of the half-yearly oscillations in observed and simulated data in Fig. 2. By averaging over latitudes north and south of the

2752 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 54 FIG. 4. Zonal wind for (a) Ascension Island (7.6 S, 14.4 W), (b) 28 yr of model integration zonally averaged at 8 S, (c) Kwajalein (8.7 N, 167.7 W), (d) 28 years of model integration zonally averaged at 8 N. Contour interval 5 m s 1. equator, signals caused by the annual cycle on each hemisphere are partly filtered out. Comparing the evolution of the zonal wind north and south of the equator gives some insight into the forcing of the stratopause SAO. Figure 4 shows the evolution of the zonal-mean wind at 8 lat north and south of the equator for rocketsonde observations (Figs. 4a,c) and the GCM simulation (Figs. 4b,d). In both observations and the GCM the easterly winds in the upper stratosphere are strongest during local summer. The easterly phase during January at 8 S is the strongest of all in the observations (Fig. 4a) as well as in the GCM (Fig. 4b), although the modeled winds are 10 m s 1 weaker than the observed ones. Additionally, in observations and the simulation, the weaker easterly phase during local winter is also strongest in January (e.g., in the Northern Hemisphere). The additional easterly forcing during January is believed to be caused by the absorption of horizontally traveling planetary waves, which are especially strong during Northern Hemispheric winter. Sassi et al. (1993) showed that in the NCAR GCM, the influence of the planetary waves on the zonal-mean wind occurred through local zonally asymmetric inertial instabilities. In the current model there was, however, no indication that the planetary wave contribution to the forcing of the easterly phase occurs because of zonally asymmetric inertial instabilities, as the zonally asymmetric inertial instabilities that can be found in the TSM GCM are present throughout the year and not linked to strong planetary wave activity (not shown). In each hemisphere the stronger easterly phase reaches the mesosphere and suppresses the westerly winds at these altitudes. This can be seen in the observations as well as in the model. The westerly phase that precedes a strong easterly phase does not descend as low as the other westerly phase. Although there are some discrepancies in the absolute values between the GCM and observations, the main features, especially the modulation of the easterly phase by the annual cycle, are in good agreement. This suggests that the forcing mechanisms for the easterly phase in the model are the same as those for the real atmosphere.

2753 4. The forcing of the westerly phase of the SAO It is clear that the absorption of eastward propagating waves is required to force the westerly phase of the SAO. In the tropical stratosphere both planetary-scale Kelvin waves and eastward propagating gravity waves are observed and could contribute to the forcing. The possible effect of Kelvin waves on the mean flow has been examined by Hitchman and Leovy (1988) using LIMS observations. They concluded that Kelvin waves do not provide enough momentum to drive the westerly phase of the SAO. In addition, gravity waves may contribute significantly to the SAO. Hamilton and Mahlmann (1988) came to the same result for Kelvin waves in the older version of the SKYHI GCM. The Kelvin waves in their model were in good agreement with observations but could not provide sufficient momentum to force the SAO. They showed that the resolved gravity waves in the model were largely responsible for the forcing of the SAO. On the other hand, Boville and Randel (1992) showed that in the NCAR CCM1 Kelvin waves alone provide the forcing of the westerly phase of the SAO. This seems to hold for the NCAR CCM2 also (Sassi et al. 1993), but the westerly phase in this model failed to descend below the stratopause. In the UGAMP GCM a parameterization of traveling subgridscale gravity waves had to be included before the model was able to simulate the westerly phase of the SAO (Jackson and Gray 1994). The Berlin TSM GCM is able to simulate the westerly phase of the SAO without a subgrid-scale gravity wave parameterization. To determine the forcing of the westerly phase for the current GCM, a detailed case study is performed. As the strongest westerly acceleration in the model on average takes place in March at 1 hpa, this month and location was chosen for the examination. The study is performed for model year 7. In the upper stratosphere and mesosphere of the GCM the meridional and vertical advection of winds together provide an easterly forcing throughout the year (not shown). The westerly accelerations must therefore be due to eddy forcing. The TSM GCM is able to simulate a variety of tropical stratospheric waves. Figure 5 shows the frequency distribution at 1 hpa of waves with zonal wavenumber 1 using space time spectral analysis according to Hayashi (1982). The spectrum is calculated for February, March, and April for temperature (Fig. 5a) and the meridional wind component (Fig. 5b). Negative frequencies correspond to eastward moving waves and positive frequencies to westward moving waves. The power spectrum for temperature shows two signals for eastward propagating waves centered over the equator. One has a period of 7 days and the other of 15 days. As there is no corresponding signal for the meridional wind component, this signal belongs to Kelvin waves, as further examination confirms. Kelvin waves with a period of 7 days (fast Kelvin waves) have been observed in FIG. 5. Power spectrum for zonal wavenumber 1 in February, March, and April of year 7 of the model integration at 1 hpa between 25 S and 25 N (a) temperature; (b) meridional wind component. Contour interval 1K 2. The thick lines correspond to filtering intervals (see text). the upper stratosphere (e.g., Salby et al. 1984), whereas Kelvin waves with periods of more than 10 days have been observed only in the lower stratosphere (Wallace and Kousky 1968). As the Berlin TSM GCM does not simulate the QBO, the lower stratospheric Kelvin waves are able to propagate into the upper stratosphere instead of being dissipated in the lower stratosphere where they should contribute to the forcing of the westerly phase of the QBO. Moreover, in the Berlin TSM GCM longwave radiative transfer is parameterized by Newtonian cooling above 10 hpa. This approach underestimates thermal damping of disturbances with finite vertical structures, such as equatorial Kelvin waves (Fels 1982; Bresser et al. 1995). Also present in the model are mixed Rossby gravity waves propagating both eastward and westward. There is a signal in the meridional wind component in both directions near 2.8 days centered over the equator, which corresponds with a signal in temperature wavenumber 1 at approximately 10 north and south of the equator. In the month analyzed, mixed Rossby gravity waves can be detected only for zonal wavenumbers 1 and 2, whereas in observations these waves have been found for zonal wavenumbers 3 and 4 (Yanai and Maruyama

2754 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 54 1966). Signals for resolved fast inertio gravity waves and slow eastward propagating planetary waves with a meridional wind component can be found only for wavenumbers greater than 1 (not shown). The wave forcing can be examined using the Eliassen Palm flux (F) and its divergence (e.g., Andrews et al. 1987). To separate the contributions of the different types of waves to the total body force D [D F/ ( 0 a cos ), where a is earth radius, is latitude, and 0 is density], a bandpass filter was applied to the data. Then D was calculated for slow eastward propagating waves (periods 3.3 30 days), fast eastward propagating waves (periods less than 3.3 days), slow westward propagating waves (periods 5 30 days), and for fast westward propagating waves (periods less than 5 days). These filtering intervals are indicated by the thick lines in Fig. 5. This was done individually for all 21 zonal wavenumbers. In addition to this, the time series of the contribution of the slow eastward propagating waves was carefully examined and the forcing due to Kelvin waves was separated. The dissipated wave was identified as a Kelvin wave if it was trapped over the equator and had a vertical and zonal wind component as well as a temperature signal but no meridional wind component. Also the zonal and vertical wind components had to be in phase while a phase shift of a quarter wavelength was necessary for the temperature signal. Figure 6 shows the result of this analysis in March: The major contribution to the total forcing is due to waves with zonal wavenumbers 1 8. The forcing is dominated by the westerly forcing due to the dissipation of slow eastward propagating planetary waves. Even though Kelvin waves of zonal wavenumber 1 could be clearly identified in Fig. 5, they are not dissipated at 1 hpa and therefore do not contribute to the forcing. Kelvin waves of wavenumber 2 and 3, however, significantly contribute to the westerly forcing. Their influence decreases rapidly with further increasing wavenumber. For wavenumber 6 the Kelvin wave contribution has entirely vanished. In the current model, which has a vertical resolution of 3.5 km in the upper stratosphere, the dispersion relation allows the existence of stratospheric Kelvin waves up to wavenumber 6. The eastward propagating mixed Rossby gravity waves of wavenumber 1, evident in Fig. 5, are also not dissipated at 1 hpa. Instead, fast eastward propagating waves with zonal wavenumbers 1 and 2 are amplified and reduce the total westerly momentum available for the acceleration of the mean flow. The dissipation of the fast eastward propagating waves becomes more important for higher wavenumbers: Strong absorption occurs for wavenumbers 7 and 8 (Fig. 6). For zonal wavenumbers greater than two eastward propagating mixed Rossby gravity waves do not exist in the model (not shown); therefore the westerly forcing in this spectral interval is entirely due to inertio gravity waves. Slow westward propagating waves of wavenumbers 1 5 are dissipated, while waves of wavenumbers 6 11 FIG. 6. Plot of D (m s 1 day 1 ) according to wavenumber calculated for (a) Kelvin waves (solid line); (b) eastward propagating waves with periods 3.3 30 days not including Kelvin waves (long-dashed line); (c) eastward propagating waves with periods less than 3.3 days (dash dotted line); (d) westward propagating waves with periods 5 30 days (long dash, short dash); (e) westward propagating waves with periods less than 5 days (dash dot dot). Thin lines denote westward and thick lines eastward propagating waves. are amplified or generated. The slow westward propagating waves of all wavenumbers together result in a small easterly forcing. Fast westward propagating waves of wavenumber 2 4 and 6 9 (inertio gravity waves and mixed Rossby gravity waves of wavenumber 2) are dissipated at 1 hpa and significantly reduce the total westerly forcing. A small amount of the easterly momentum is used to generate or amplify fast westward propagating waves of wavenumbers 1 and 5. The total westerly forcing is due to a combination of the dissipation of slow eastward propagating waves of planetary scale, Kelvin waves, and eastward propagating inertio gravity waves. The most important contribution is, however, due to the dissipation of slow eastward propagating waves of planetary scale with periods between 3.3 and 30 days (0.94 m s 1 day 1 or 63%). The Kelvin wave contribution is 0.27 m s 1 day 1 (18%). Approximately 10% of the forcing is provided by the dissipation of fast eastward propagating inertio gravity waves. The remaining 9% of the forcing is due to the dissipation of eastward propagating waves slower than 30 days. These values were derived by analyzing only one particular month. A more general but less detailed conclusion can be drawn by comparing the body force due

2755 and Fig. 3). However, in general more than 50% of the total forcing is due to waves with zonal wavenumbers greater than 6 or with a meridional wind component. The dissipation of Kelvin waves alone is clearly not sufficient to generate the westerly phase of the SAO in the Berlin TSM GCM. The forcing in the model is in some respects different from the forcing in the real atmosphere. As already mentioned, Kelvin wave dissipation takes place too high: The lower stratospheric Kelvin waves reach the upper stratosphere and the fast Kelvin waves propagate well into the mesosphere (70 km) for wavenumbers 1 and 2. As the westerly phase of the SAO is too weak in the mesosphere compared with observations, including a gravity wave drag parameterization for small-scale gravity waves with high phase speed would probably improve the simulation of the SAO. But taking into account that the model was run with a horizontal resolution of T21, has a vertical resolution of 3.5 km and no gravity wave drag parameterization, those waves that are resolved generate a stratopause SAO that is in remarkably good agreement with observations. FIG. 7. Plot of D (m s 1 day 1 ) (a) for all 21 wavenumbers and (b) for the first 6 zonal wavenumbers calculated for eastward propagating waves setting 0. Contour interval 0.5 m s 1 day 1. to all 21 resolved wavenumbers to that of the largescale (wavenumbers 1 6) eastward propagating waves, where the influence of waves with a meridional wind component has been partly suppressed (Fig. 7). The latter was derived by applying a bandpass filter to the data to remove westward propagating waves and then calculating the body force as before but neglecting ( : deviation of the meridional wind component from its zonal mean). The E P flux divergence then takes the following form: FKW ( 0a cos w u ), (1) z where 0 is density, is latitude, a the radius of the earth, and u and w represent the zonal and vertical velocity perturbations. This estimate includes Kelvin waves but also a contribution of the vertical and zonal velocity disturbances of large-scale eastward propagating waves that have a meridional wind component. Comparing Figs. 7a and 7b can therefore only give an idea of which part of the forcing is definitely not due to Kelvin waves. The strongest D coincides with the acceleration of the westerly phase of the SAO (Fig. 7a 5. The interannual variability of the modeled SAO In section 3 only the long-term mean features of the SAO have been described. There is, however, also some interannual variability in the modeled SAO. Figure 8 displays 10 years of zonal-mean zonal wind from the GCM averaged over 2.8 S and 2.8 N. The stratopause SAO is present in all years. The westerly phase descends to different altitudes in different years. The lowest altitude reached by the westerly phase is 36 km during the second cycle of year 5. During the first cycle of year 6 it reaches an altitude of only 42 km. The maximum strength of the westerly phase also varies from year to year. In year 8 of the control run more than 15 m s 1 are simulated during the first cycle. In the long-term mean the westerly phase has a strength of only 10 m s 1. The height of the westerly maximum is also variable. On average it is located at 60 km. During the first cycle of year 12 it is, however, located at 65 km while it can also be found at 58 km (e.g., November of year 10). The time of the occurrence of the maximum westerlies shows little variability. In all years the westerly phase has its maximum in April and October. It can be seen that the westerly phase during year 7 of the control run, which was chosen for the studies in the previous section, is representative of the climatology. There is also considerable variability of the easterly phase of the SAO. In the long-term mean the first easterly maximum occurs in January and has a strength of 35ms 1. However, in individual years often values of 40ms 1 and more can be found, for example, the first easterly maximum in year 9. In addition to this there are years when the maximum is first reached in February (e.g., year 7). During the second cycle of the SAO the

2756 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 54 FIG. 8. Time series from year 5 to year 14 of the zonal-mean zonal wind of the control simulation. Contour interval 5ms 1. easterly maximum normally occurs in July but can be delayed until August, as in year 9. The height of the easterly maxima shows only small variability. They are usually located at 48 km but can be also found at the next higher model level at 52 km. The GCM was run with boundary conditions that stayed constant from year to year. The interannual variability of the modeled SAO is therefore caused exclusively by internal processes. The magnitude of the simulated variability is of the same order to that in the GFDL SKYHI model (Hamilton et al. 1995). 6. The role of the QBO on the stratopause SAO Figure 8 clearly shows that the Berlin TSM GCM does not simulate the QBO. In the tropical lower stratosphere easterly winds are present throughout the whole period. There is, however, some evidence that the QBO modulates the SAO in the real atmosphere (e.g., Garcia et al. 1997). To examine the effect of the QBO on the SAO in the model, an idealized QBO was implemented into the GCM following the approach of Balachandran and Rind (1995). The zonal-mean zonal wind at the equator was forced to 25 m s 1 to crudely represent the westerly phase of the QBO using a time constant of 30 days. The maximum forcing took place at the 19.8 and the 32.7 hpa levels. The forcing decays exponentially away from these levels and away from the equator. It vanishes at 30.4 N and 30.4 S. To avoid damping of the waves, only the zonal-mean zonal winds have been relaxed, leaving deviations from the zonal-mean state unaffected. The experiments started with an initial field from the control run. The model was given half a year to adjust to the additional forcing and was then run for 2 years. Figure 9 shows a time height series of the zonal-mean zonal wind at the equator for the QBO westerly phase for the second year of the integration (the first year looks very similar). In the lower stratosphere between 20 and 30 km westerly winds representing the westerly phase of the QBO with values up to more than 20 m s 1 can be found where easterly winds of 15ms 1 were present in the control run (Fig. 3). Between 30 and 50 km the zonal-mean zonal flow is easterly. The easterly winds show almost the same time evolution as in the control run and observations with maxima during the solstices. The second easterly maximum occurs in August instead of July as in the long-term mean of the control integration. In the previous section, however, it was shown that this delay can be found in individual years of the control run and is therefore not significant. The maximum winds are, however, 20 m s 1 stronger than in the control run. Westerly winds are still present in the mesosphere with maximum values during the

2757 FIG. 9. Zonal-mean zonal wind averaged over the latitudes 2.8 S and 2.8 N in year 2 of the QBO-West model experiment. Contour interval 5 m s 1. equinoxes. At 60-km altitude the westerly winds reach maxima of 15 m s 1, which is 5 m s 1 stronger than in the long-term mean of the control run, though westerly maxima of this magnitude can be found in some years of the control integration. The westerly phase in the QBO-West experiment does not propagate downward as far as in the control run. This is in good agreement with the observations analyzed by Garcia et al. (1997) showing that the QBO modulates the altitude of the maximum descent of the westerly winds of the stratopause SAO. In the observations, however, the westerly phase of the SAO still reaches the 1-hPa level during the westerly phase of the QBO, whereas this is not the case in the QBO-West experiment. In idealized theory tropical waves are dissipated just below their critical levels, where u c 0(c: phase speed of the wave). A zonal wind value of 25ms 1 still allows penetration of eastward propagating waves with periods of 18 days and less for wavenumber 1, 9 days and less for wavenumber 2, 6 days and less for wavenumber 3, and 4.6 days and less for wavenumber 4. Therefore the westerly phase of the QBO mostly affects waves with zonal wavenumbers greater or equal to 2. This is confirmed by comparing the power spectrum of the control run with the power spectrum of the QBO-West experiment (Figs. 10a and 10b). For zonal wavenumber 1 the strength of the signal is nearly unchanged, but with increasing wavenumber the signals of the slower waves disappear. It has been shown in section 4 that eastward propagating planetary waves with zonal wavenumbers greater than 2 are essential for the westerly forcing at 1 hpa. In addition to this, the slower Kelvin waves of wavenumber 2 that contributed to the forcing at 1 hpa can no longer reach the stratopause. This explains why the westerly phase of the stratopause SAO does not descend to 1 hpa in the QBO- West experiment. The change of forcing in the upper stratosphere due to the changes in the wave spectrum is illustrated in Fig. 11. The body force D due to the FIG. 10. Power spectrum according to the zonal wavenumber for temperature in January, February, and March at 1 hpa averaged over the latitudes 2.8 S and 2.8 N for (a) year 7 of the control experiment (b) year 2 of the QBO-West model experiment. Contour interval 2K 2. vertical component of the E P flux for the control run and the QBO-West experiment were averaged over the height interval between 40 and 55 km. The horizontal component of the E P flux is dominated by the signal of westward propagating planetary waves and was therefore ignored. It is clearly visible that there is considerably less westerly forcing in the QBO-West experiment due to the absence of the important shorter waves, leading to stronger easterly winds in this region in comparison with the control integration. A similar experiment, where the winds were relaxed FIG. 11. Plot of D for the vertical component of the E P flux averaged between 40 km and 55 km. Solid line control experiment. Dashed line QBO-West experiment.

2758 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 54 to 25ms 1 to represent the easterly phase of the QBO, showed no effect on the eastward propagating waves. As expected, the SAO in this experiment hardly changed in comparison with the control run (not shown). 7. Conclusions In this paper the stratopause semiannual oscillation of the Berlin TSM GCM was examined in some detail. It was found that the model produces a SAO that is in reasonably good agreement with observations in relation to its location and evolution. The westerly phase of the modeled SAO, however, is too weak and the second easterly phase is too strong. A case study was performed to determine the contribution of the resolved waves to the forcing of the westerly phase of the stratopause SAO. This was done at 1 hpa in March when the strongest westerly acceleration of the SAO during the year takes place. The strongest contribution is due to waves with zonal wavenumbers less than or equal to 8. Eastward propagating waves with phase speeds of more than 3.3 days, which are not equatorially trapped or do not have a meridional wind component, account for 72% of the total forcing at this altitude. The Kelvin wave contribution is 18%. However, these Kelvin waves are partly too slow compared with observations. The contribution of fast eastward propagating inertio gravity waves is 10%. Eastward propagating mixed Rossby gravity waves have also been found in the model but do not contribute to the forcing. Thermal damping of the waves is underestimated in the model, which allows the slow waves to propagate too high in the atmosphere. A more realistic damping, however, reduces the momentum available in the stratopause region and weakens the SAO, as preliminary results with a modified model version confirm. Then a parameterization of fast eastward propagating small-scale gravity waves would become necessary in order to simulate a realistic stratopause SAO, when the model is run with the same vertical and horizontal resolution as in this study. In the model run analyzed here no parameterization for subgrid-scale waves is included. Instead their effect in the mesosphere is simulated by including Rayleigh friction at the top model levels (Pawson et al. 1997). The effect of the QBO on the SAO was examined by performing two model experiments in which the zonal wind component was relaxed toward an idealized QBO easterly or westerly phase. As expected, the easterly phase of the QBO does not influence the SAO as the propagation of easterly waves is not affected. During the westerly phase of the QBO the SAO is modulated. The westerly winds in the lower stratosphere prevent the propagation of slow eastward-traveling waves with zonal wavenumbers greater than 1. 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