Abstract

The longitudinal dependence of interannual variations of tropical stratospheric wind is examined in a detailed general circulation model simulation and in the limited observations available. A version of the SKYHI model is run with an imposed zonally symmetric zonal momentum source that forces the zonal-mean zonal wind evolution in the tropical stratosphere to be close to an estimate of the observed zonal wind based on radiosonde observations at Singapore during the period 1978–99. This amounts to a kind of simple assimilation model in which only the zonal-mean wind field in the tropical stratosphere is assimilated, and other quantities are allowed to vary freely. A total of five experiments were run, one covering the full 1978–99 period and four for 1989–99.

The results at and above about 30 hPa are fairly simple to characterize. When the zonal-mean wind near the equator at a particular level is easterly, the monthly mean wind has only very small zonal contrasts. When mean westerlies are present near the equator, significant zonal asymmetries occur at low latitudes, most notably easterly anomalies over South America and westerly anomalies in the eastern Pacific region. These anomalies generally display a continuous meridional phase propagation with the extratropical quasi-stationary eddy field in the winter hemisphere. The net result is a significantly weaker peak-to-peak amplitude of the quasi-biennial oscillation (QBO) in zonal wind over the South American sector than over the rest of the equatorial band. The zonal contrast in QBO amplitude near 10 hPa exceeds 10%.

In the lower stratosphere the zonal asymmetries in the prevailing wind are fairly small. Asymmetries seem to reflect the upward extension of the tropospheric Walker circulation, and are less strongly modulated by the quasi-biennial oscillation in zonal-mean circulation.

The model results were checked against limited station observations at Nairobi (1.3°S, 36.7°E), Singapore (1.4°N, 103.9°E), Rochambeau (4.8°N, 52.4°W), and Bogota (4.7°N, 74.1°W). Overall reasonable agreement was found between the monthly mean zonal winds in the model simulation and these station data. The low-latitude wind field in monthly mean NCEP gridded analyses was also examined. These analyses have some obviously unrealistic features in the tropical stratosphere, but some of the behavior seen in the SKYHI model simulations can be identified as well in the NCEP analyses.

1. Introduction

The quasi-biennial oscillation (QBO) accounts for a major fraction of the interannual variability of the circulation of the tropical stratosphere and has significant effects on aspects of extratropical circulation as well (see Baldwin et al. 2001 for a review). Almost all observational studies of the QBO have been based on the assumption that the oscillation in prevailing wind (as represented by the monthly mean) is nearly zonally symmetric. The circulation in the near-equatorial region of the stratosphere is rather poorly observed due to the scarcity of balloon radiosonde stations near the equator regularly reporting winds in the stratosphere and the limited usefulness of satellite temperature retrievals in deriving winds near the equator. In an early study, Belmont and Dartt (1968) attempted to use available radiosonde data at 50 hPa (and lower levels) to examine the longitudinal variations in the QBO. They mostly focussed on trying to characterize longitudinal variations in the phase of the QBO, with the conclusion that near the equator the phase propagation is very rapid, i.e. the QBO wind variations are nearly simultaneous at all latitudes. Oddly, they reported finding that there was almost no QBO in their 50-hPa wind observations at Nairobi (1.3°S, 36.8°E). These results at Nairobi were based on a very short record, during which only a small number of soundings there reached 50 hPa, and so this is unlikely to be representative of the real situation. However, this does serve as a reminder that much of what has been published about the near-equatorial behavior of the QBO is based on observations in a rather limited sector of longitude, mostly in the western Pacific and Indian Ocean regions (e.g., Wallace 1973). The QBO in the zonal wind at 50 and 30 hPa was studied using balloon data from a large number of single stations by Hamilton (1984) and Dunkerton and Delisi (1985). The results of these studies were consistent with the zeroth-order picture of a zonally symmetric QBO in prevailing wind. However, these studies did not focus on determining the deviations from zonal symmetry, and they also had limited longitudinal coverage in the stations close to the equator that were included.

Most recent work on the QBO wind variations has used the single time series of monthly mean “near equatorial” observations up to the 10-hPa level that has been compiled at the Free University of Berlin (Naujokat 1986). This has been based on data at Canton Island (2.8°S, 171.8°W; January 1953–August 1967), Gan (0.7°S, 73.2°E; September 1967–December 1975), and Singapore (1.4°N, 103.9°E; since January 1976). The Canton Island and Gan stations were closed in the 1960s and 1970s, respectively, and coverage in the equatorial stratosphere was severely limited. The Gan and Canton Island upper-air radiosonde stations were later reopened as part of the Tropical Ocean Global Atmosphere (TOGA) project program, but the Singapore data now appear to be clearly the most reliable of those available for long periods near the equator. The data records at these stations do overlap somewhat, and they match closely enough that there are no obvious discontinuities in the Free University of Berlin time series when the data source changes. This is consistent with the view that the QBO is nearly symmetric, but the stations in this Free University of Berlin standard time series span only a limited longitudinal extent (73.2°E–171.8°W).

In the 1990s the in situ wind observations near the equator were supplemented by the availability of the high-resolution Doppler interferometer (HRDI) observations from the Upper Atmosphere Research Satellite (UARS). Much of the research performed with the HRDI winds has emphasized either zonal means or the mean diurnal cycle, both of which allow considerable averaging to reduce the signal-to-noise ratio below that of the raw wind values. However, Ortland (1997) has examined the zonal asymmetries in 2-week averages of the wind as measured by HRDI during several years, but concentrating on the 30–35-km altitude level (about 10–5 hPa) in the 1994–95 boreal winter period. He showed that the quasi-stationary wave field in the midlatitudes propagated from the Northern Hemisphere extratropics into the equatorial region, leading to large-scale zonal asymmetries in the equatorial prevailing wind. O'Sullivan (1997a) has examined the nitrous oxide concentrations along the 10-hPa surface in boreal winter as measured by the Cryogenic Limb Array Etalon Spectrometer (CLAES) instrument on UARS. He showed that, when mean westerlies are present on the equator at this level, the nitrous oxide concentrations show significant deviations from zonal symmetry even on the equator and in the summer hemisphere Tropics. The patterns of nitrous oxide appear consistent with large-scale quasi-stationary waves propagating from the winter hemisphere and breaking on the summer side of the equator.

The issue of zonal asymmetries in the prevailing stratospheric equatorial wind has been studied in models of various levels of sophistication. Matsuno (1970) constructed a linear model of the three-dimensional winter stationary wave field in the Northern Hemisphere stratosphere employing a specified zonal-mean state with easterlies on the equator and hence a critical surface for the stationary waves off the equator. He found that the critical surface effectively shut off any propagation of the stationary waves to the equator. The issue of how the presence of a low-latitude critical surface affects planetary wave propagation has been addressed since in barotropic (or shallow water) systems through studies employing nonlinear numerical models (e.g., Waugh et al. 1994; Polvani et al. 1995; O'Sullivan 1997b). These studies suggest that stationary waves forced in the winter extratropics can propagate to the equator and indeed into the summer hemisphere when the equatorial mean winds are westerly, but will be excluded from propagating to low latitudes by equatorial easterlies.

The effect of tropical stratospheric mean winds on the stationary wave field has also been studied in experiments conducted with 3D comprehensive general circulation models (GCMs). Hamilton and Yuan (1992) performed seasonal integrations with initial conditions at the beginning of boreal winter with either strong westerly or easterly mean jets imposed in the tropical stratosphere. The subsequent evolution of the quasi-stationary eddy field over the winter depended strongly on the sign of the initial tropical jet, with waves reaching the equator when the tropical mean winds were westerly, at least above about the 30-hPa level. Similar results are apparent in GCM experiments reported by Balachandran and Rind (1995, see their Fig. 7). Hamilton (1998, hereafter H98) performed a multidecadal integration of a GCM with an imposed, somewhat idealized, QBO cycle in the tropical stratospheric mean wind. The main focus of H98 was on other aspects of the QBO, but H98 did show results for the equatorial stationary wave field near 10 hPa, and once again found evidence for a mean flow modulation of the near-equatorial stationary wave field.

The present paper reports on a project that has extended the earlier GCM studies to a series of integrations incorporating the most realistic possible mean flow QBO, and then considers how well the model results for the eddies are supported in the available limited observational record. The aim is to use models and observations to arrive at as complete as possible picture of the behavior of the deviations from zonal symmetry in the prevailing stratospheric circulation near the equator.

An understanding of the issue of zonal asymmetries in the equatorial wind is of interest for a number of reasons. Monitoring the phase of the QBO now relies almost exclusively on the balloon observations at Singapore, raising the issue of how representative the single station data is for the whole equatorial band.

The equatorial middle atmosphere poses particular challenges for data assimilation efforts, due to the very limited in situ wind observations and to the difficulty of using dynamical balance to relate satellite radiometer observations of temperature and the wind field. There are indications that even the QBO in zonal-mean monthly mean quantities is somewhat misrepresented in current state-of-the-art meteorological analyses, with a tendency for the analyses to underestimate peak QBO extremes when judged against the available station observations (Pawson and Fiorino 1998, 1999; Huesmann and Hitchman 2001). Recent comparisons of analyzed winds [from the European Centre for Medium-Range Weather Forecasts (ECMWF)] with observations from long-lived superpressure balloons (floating at a level of constant density) suggest that instantaneous fields of horizontal wind may be very poorly represented by the analyses in the equatorial lower stratosphere (Vial et al. 2001). An understanding of the behavior of the quasi-stationary eddy field would be useful in evaluating current analyses in the equatorial stratosphere.

The role that mean momentum transports by quasi-stationary eddies may play in the dynamics of the equatorial QBO itself has been considered in earlier modeling studies (Dunkerton 1983, 1997; Hamilton and Yuan 1992; H98). In particular, Dunkerton (1983) suggested that the effects of quasi-stationary eddies propagating from the winter hemisphere to the Tropics could account for the observed tendency of the QBO mean wind accelerations to have a weak phase locking with the annual cycle.

The present paper will report on results from a GCM study in which the zonal-mean wind structure in the tropical stratosphere was constrained to vary in a manner close to that observed in a 22-yr period (1978–99). The result is a kind of assimilation model, but one in which only observations of the zonal-mean wind in the tropical stratosphere are assimilated while the rest of the circulation evolves freely. The results for the quasi-stationary eddy field near the equator are examined and compared with available station observations, as well as gridded meteorological analyses.

The paper is organized as follows. The model employed and the experimental design are described in section 2. The model results for QBO modulation of eddy fields near the equator are reviewed in section 3. Section 4 considers the available station observations of stratospheric wind near the equator and compares the station observations to the present model simulations. Section 5 briefly reviews the low-latitude eddy field in gridded meteorological analyses and its relation to the present model simulations. Section 6 discusses the role the QBO modulation of the of the eddy transports may play the forcing of the QBO itself. Conclusions are summarized in section 7.

2. Model and experiments

The present study uses a version of the Geophysical Fluid Dynamics Laboratory (GFDL) GCM called SKYHI (Fels et al. 1980; Hamilton et al. 1995; H98). This version is updated from that used in Hamilton et al. (1995) and H98 by the inclusion of a prognostic cloud scheme and improved radiative transfer algorithms (see Schwarzkopf and Ramaswamy 1999). The inconsistency in zonal filtering of the surface pressure and wind fields at high latitudes described in H98 has also been corrected in the present SKYHI version. The version used here is discretized on a 3°–3.6° latitude–longitude grid and on the standard 40 SKYHI levels (e.g., Fels et al. 1980) from the ground to 0.0096 hPa (about 80-km altitude). As in H98, the basic model is modified by including an additional zonally symmetric zonal momentum source. In the present project this source is designed to force a QBO in the zonal-mean wind in the tropical middle atmosphere close that actually observed during the 22-yr period 1978–99.

The zonal momentum equation in the model is modified by including a relaxation term as follows:

 
formula

where u is the zonal-mean zonal wind in the model; upre is a prescribed function depending on time, latitude, and pressure that represents the “target” wind distribution toward which the model is being forced. The time scale for relaxation τ is taken from H98 and is a function of height and latitude; τ is 5 days at the equator and 30 hPa, and the relaxation becomes weaker (and hence, τ becomes longer) at higher latitudes and at higher and lower altitudes. The relaxation is not applied below 103 hPa or poleward of 30° latitude.

In the present project the aim is to force the model mean state as near as possible to the actual mean winds during the 22-yr period 1978–99. A difficulty, of course, is that reliable observations in the low-latitude stratosphere that are obviously representative of the zonal mean are not available. The present approach was to base the upre on the monthly mean of the radiosonde wind at Singapore. Despite the limited sampling, this still seems preferable to using the available gridded analyses which typically underestimate the peak amplitudes of the QBO at low latitudes (e.g., Pawson and Fiorino 1998, 1999).

Specifically the upre was written as uclim + uqbo where uclim represents the long-term mean and mean annual cycle, and uqbo is the interannual QBO variation; uclim was computed for each model level and latitude from a long control run, then uqbo was taken to be equatorially trapped so that

 
u
qbo(θ, p) = Ue(p) exp(−θ22),
(2)

where p is pressure, θ is latitude, and Δ was taken to be 13°. Between 100 and 10 hPa, Ue(p) was computed as the deseasonalized Singapore wind observations low-passed to include only periods longer than 6 months. At pressures less than 10 hPa, the values of Ue(p) were extrapolated upward and backward in time, assuming a constant downward phase progression of about 2 km month−1 and assuming that the amplitude drops off with height above 10 hPa to zero around 40 km.

The separation of upre into the climatological component and the QBO component is designed to allow a smooth transition in the mean wind between the low-latitude region with the imposed relaxation and the higher-latitude region in which the model is completely free to produce its own circulation. The downside of this approach is that biases in the control model climatology will be present in the QBO experiments as well.

Five QBO-perturbed experiments were performed. Four of these were 11-yr integrations in which the QBO forcing was based on the Singapore observations from January 1989 through December 1999. These experiments (labelled “A,” “B,” “C,” and “D”) differed from each other only by the initial conditions, which were taken from 1 January snapshots from four different years of a control run of the model. The fifth experiment (“E”) was a 22-yr integration with forcing based on data from 1978–99. In this paper attention will be focused mainly on the 1989–99 period, and many results will be presented in terms of the mean of all five experiments.

Figure 1 shows the time series of monthly mean zonal wind from the Singapore radiosonde observations (red) and from the average of the five simulations at the nearest model gridpoint (1.5°N, 102.6°E). Results are shown for observations at 10, 30, and 50 hPa and the closest model levels (9, 27, and 47 hPa). Overall the agreement is good, with the model results showing somewhat smoother variations. There is a notable bias however with the model being consistently 5–10 m s−1 easterly relative to the Singapore wind observations near 50 hPa. There is a westerly bias in the model results near 10 hPa, and very close agreement near 30 hPa.

Fig. 1.

Comparison of the time series of monthly mean zonal wind measured at Singapore (1.4°N, 103.9°E) during 1989–99 and the results from an average of the five SKYHI experiments of the model grid point at 1.5°N, 102.6°E. Results for (top) observations at 10 hPa and model level 9 hPa, (middle) observations at 30 hPa and model level 27 hPa, and (bottom) observations at 50 hPa and model level 47 hPa

Fig. 1.

Comparison of the time series of monthly mean zonal wind measured at Singapore (1.4°N, 103.9°E) during 1989–99 and the results from an average of the five SKYHI experiments of the model grid point at 1.5°N, 102.6°E. Results for (top) observations at 10 hPa and model level 9 hPa, (middle) observations at 30 hPa and model level 27 hPa, and (bottom) observations at 50 hPa and model level 47 hPa

The height–time evolution of the equatorial zonal-mean wind in the model simulations have been compared with the UARS Reference Atmosphere Project (URAP) observational estimates for 1992–99 produced by R. Swinbank and D. Ortland (see Randel et al. 2002). The URAP dataset is based on Met Office global meteorological analyses and the HRDI observations from UARS. There is very general agreement between the equatorial mean winds in the SKYHI model experiment and the URAP winds, although there is a clear tendency for the URAP equatorial winds to be weaker than the model results in both the easterly and westerly phases. This underestimation of QBO amplitude is shared by other objective meteorological analyses (Pawson and Fiorino 1998, 1999). Comparison of the model and URAP results above 10 hPa suggests that the simple upward extrapolation for uqbo adopted here works reasonably well.

Figure 2 shows the monthly mean cross section of the zonal wind for November 1994 in the model (average of five experiments) and in the URAP observational analysis. The overall pattern of the wind in the Tropics is similar in the model and the URAP analysis, but the peak near-equatorial winds in both the easterly phase centered near 70 hPa and the westerly phase centered near 15 hPa are larger in the model than in URAP. This degree of disagreement is fairly typical of the comparison of the zonal-mean cross sections between the model and URAP.

Fig. 2.

Cross section of zonal-mean zonal wind averaged over Nov 1994. (top) An average of results from the five SKYHI experiments; (bottom) from the URAP dataset. Contour interval is 10 m s−1, dashed contours denote negative (easterly) winds, and the zero contour is emphasized

Fig. 2.

Cross section of zonal-mean zonal wind averaged over Nov 1994. (top) An average of results from the five SKYHI experiments; (bottom) from the URAP dataset. Contour interval is 10 m s−1, dashed contours denote negative (easterly) winds, and the zero contour is emphasized

3. Zonal variations

a. Midstratosphere

Figure 3 shows the January–February–March (JFM) averaged zonal wind at 9 hPa at each grid point along the 1.5°N grid row in each of the 11 yr 1989–99. Results are shown for just experiment E. The equatorial wind at this level-in this season is strongly easterly in the years 1989, 1991, 1994, 1996, and 1998. In these periods, there seems to be almost no zonal contrast in the prevailing wind. In the other six JFM periods the mean wind is westerly and significant zonal asymmetries are apparent. The exact structure of the asymmetry differs from year to year, but the weakest westerly appears almost always in the 300°–330°E (30°–60°W) sector. In the 1997 results the contrast between strongest and weakest JFM westerlies is about 13 m s−1, but this contrast is at least 8.6 m s−1 in each of the six JFM periods when the mean wind is westerly.

Fig. 3.

The zonal wind at 9 hPa and 1.5°N averaged over JFM periods of 11 individual years (1989–99) in SKYHI experiment E

Fig. 3.

The zonal wind at 9 hPa and 1.5°N averaged over JFM periods of 11 individual years (1989–99) in SKYHI experiment E

Figure 4 shows the same quantity as Fig. 3 but for only the westerly cases, and now plotted for each individual model run. There are some variations from run to run, but the overall pattern is reasonably consistent. This occurs despite the fact that the extratropical stratospheric circulation in individual boreal winters can differ widely among the separate realizations. As an example, the 28-hPa zonal-mean zonal wind averaged poleward of 60°N and over JFM 1997 varies from 12.8 to 25.7 m s−1 among the five SKYHI realizations.

Fig. 4.

The zonal wind at 9 hPa and 1.5°N averaged over JFM periods of those individual years in which the zonal mean was westerly. Results shown for each of the five SKYHI experiments

Fig. 4.

The zonal wind at 9 hPa and 1.5°N averaged over JFM periods of those individual years in which the zonal mean was westerly. Results shown for each of the five SKYHI experiments

To the extent that the dynamics of the eddies in the SKYHI model is realistic, this implies that the zonal asymmetry in the prevailing wind at the equator is largely a predictable function of the low-latitude zonal-mean wind. This is an important simplification and suggests that the full three-dimensional structure of the low-latitude QBO could be captured by an assimilation model that had realistic zonal-mean tropical stratospheric winds imposed.

Figures 5 and 6 show the 9-hPa zonal wind averaged over April–May–June (AMJ) and July–August–September (JAS) in individual years for which the mean wind is westerly. In each season there is a clear pattern of zonal asymmetry in the years with westerly mean winds. A similar pattern is seen in October–November–December (OND) means (not shown). The zonal contrasts along the latitude row are weaker in AMJ, JAS, and OND than in JFM, but only slightly weaker. There are some systematic seasonal changes in the shape of the eddy field, but the general pattern of minimum westerlies winds in the 240°–330°E sector is consistent from year to year and in different seasons.

Fig. 5.

The zonal wind at 9 hPa and 1.5°N averaged over AMJ periods of those individual years in which the zonal mean was westerly. Results shown for the mean of the five SKYHI experiments

Fig. 5.

The zonal wind at 9 hPa and 1.5°N averaged over AMJ periods of those individual years in which the zonal mean was westerly. Results shown for the mean of the five SKYHI experiments

Fig. 6.

As in Fig. 5, but for the JAS period

Fig. 6.

As in Fig. 5, but for the JAS period

Figure 7 is a plot of the 9-hPa zonal wind averaged over the five runs for January 1997 (top) and the eddy component of the zonal wind (bottom). The near-equatorial asymmetries can be seen to result from the southward propagation of the extratropical NH stratospheric stationary wave field. There is an apparent continuous phase propagation from the well-developed Aleutian high in midlatitudes all the way to the easterly anomaly at the equator that stretches from about 110°W to 30°E.

Fig. 7.

Zonal wind at the 9-hPa level averaged over Jan 1997 and over the five SKYHI experiments. (top) The zonal wind with contour interval of 10 m s−1 and dashed contours denote negative (easterly) winds. (bottom) The deviation of the wind values from the zonal mean. Contour interval is 3 m s−1 and dashed contours denote negative (easterly) anomalies

Fig. 7.

Zonal wind at the 9-hPa level averaged over Jan 1997 and over the five SKYHI experiments. (top) The zonal wind with contour interval of 10 m s−1 and dashed contours denote negative (easterly) winds. (bottom) The deviation of the wind values from the zonal mean. Contour interval is 3 m s−1 and dashed contours denote negative (easterly) anomalies

Figure 8 shows the monthly mean horizontal wind vectors at 5 hPa for November 1994. The present Fig. 8 [top (total) and bottom (eddy components)] can be compared with Figs. 1a and 1b of Ortland (1997), which show the same quantities at 35 km averaged for 16–30 November, determined from the HRDI satellite observations. The zonal-mean winds near the equator in both the model and HRDI observations are westerly, but the equatorial mean westerlies are somewhat stronger in the model.

Fig. 8.

Horizontal wind vectors at 5 hPa for Nov 1994 mean of the five SKYHI experiments: (top) raw values and (bottom) deviations from zonal mean. The arrow near the lower right of each gives the scale in meters per second

Fig. 8.

Horizontal wind vectors at 5 hPa for Nov 1994 mean of the five SKYHI experiments: (top) raw values and (bottom) deviations from zonal mean. The arrow near the lower right of each gives the scale in meters per second

The eddy component of the wind near the equator in the model results display similarities to that in Ortland's observations. In both cases the most striking feature in the eddy field is the jetlike core of west-southwesterlies starting south of Hawaii and stretching eastward across Mexico and the Caribbean. In the model, this feature also can be identified as an extension of a weaker westerly jet in the eddy wind field that extends westward back across the Pacific and Indian Oceans and Africa to the east coast of South America at the equator. Also evident in both model and observations are eddy easterlies over south Asia, although the extension of this feature over Africa is more pronounced in the model results than in the HRDI observations.

Figure 9 shows the geographical distribution of the simulated 9-hPa zonal wind averaged over July 1997, during a westerly QBO phase at this level. This shows a large-scale wave in the extratropics that seems to propagate equatorward in something like a mirror image of the results for boreal winter (e.g., Fig. 7). The main difference is that the amplitude of the wave in the extratropics is smaller than in the NH winter case, consistent with the weaker topographic forcing in the SH. As noted in the discussion of Figs. 46, there is a striking consistency of the phase of the stationary wave on the equator during westerly mean periods, regardless of season. Comparison of Figs. 7 and 9 suggests that the consistency of phase between boreal summer and winter may be a coincidence—the zonal asymmetries result from equatorward propagation of quasi-stationary waves forced by topography and land–sea contrast in the winter hemisphere. There would seem to be no fundamental reason for the quasi-stationary waves in the two hemispheres to have the same longitudinal phasing on the equator, but in practice they do, at least in these model simulations. Figure 10 shows the zonal wind at 9 hPa for an individual April when the equatorial mean wind was westerly. In this month, quasi-stationary waves appear to propagate from both hemispheres and overlap at the equator. Once again, there is a tendency for the resulting stationary wave at the equator to have a phase such that the minimum westerlies occurs in the South American–eastern Pacific sector. Similar results are obtained in the boreal autumn period as well.

Fig. 9.

As in Fig. 7, but for Jul 1997

Fig. 9.

As in Fig. 7, but for Jul 1997

Fig. 10.

As in Fig. 7, but for Apr 1999

Fig. 10.

As in Fig. 7, but for Apr 1999

The QBO modulation of the stationary wave field near the equator affects the longitudinal modulation of the amplitude of the QBO wind variations. The easterly extremes of the QBO should be similar at all locations along the equatorial band, but the westerly extremes should be weaker over the South American–eastern Pacific sector. Characterizing the amplitude of the somewhat irregular QBO is problematic. The approach adopted by Reed (1965) and Belmont and Dartt (1968), among others, is to just perform a least squares fit of a sinusoid to a portion of a time series, allowing straightforward determination of both an amplitude and phase. A limitation of this approach is that the amplitude determination will not be stable—as longer time series are fit, the determined amplitude will decrease, reflecting the nonmonochromatic nature of the QBO signal. However, amplitude and phase estimates useful for present purposes can be obtained by fitting segments of data spanning a few periods. Figure 11 shows the amplitude estimates obtained this way for the first 11 yr (1978–88) and the last 11 yr (1989–99) of experiment E. For each segment, a least squares fit of a sinusoid was performed varying the amplitude, period, and phase. The best-fit periods of 1978–88 turned out to be 29.3 months, and for 1989–99 it was 26.75 months. The best-fit phase determination was remarkably constant at all longitudes (less than 10 days contrast). The least squares fit amplitude shown in Fig. 11 displays a significant (more than 10%) zonal variation. As expected the minimum amplitude is around 270°–330°E (90°–30°W).

Fig. 11.

The amplitude of the zonal wind QBO at the equator and 9 hPa determined by a least squares fit of the time series of monthly mean zonal wind during 1978–88 (solid) and 1989–99 (dashed). The period used for the sinusoid in 1978–88 was 29.3 months, and for 1989–99 was 26.75 months

Fig. 11.

The amplitude of the zonal wind QBO at the equator and 9 hPa determined by a least squares fit of the time series of monthly mean zonal wind during 1978–88 (solid) and 1989–99 (dashed). The period used for the sinusoid in 1978–88 was 29.3 months, and for 1989–99 was 26.75 months

b. Lower stratosphere

Figure 12 shows the JFM mean wind at 47 hPa and 1.5°N averaged over the five experiments for each of the 11 yr 1989–99. The zonal contrasts are fairly small in each year (less than about 4 m s−1). The zonal variations appear to be less dependent on the phase of the QBO, than in the middle stratosphere. Figure 13 shows the geographical distribution of the 47-hPa zonal wind averaged over January 1999 in the same format as in Fig. 7. Even though this is a time of strong mean equatorial easterlies at this level, zonal contrasts are still present along the equator, with anomalous easterlies of up to 3 m s−1 from 120°–300°E and comparably strong westerly anomalies in the Southern Hemisphere. This pattern seems to have a large component that is unconnected with the stationary wave field in the extratropical winter hemisphere, in strong contrast with the behavior documented earlier at the 9-hPa level.

Fig. 12.

The zonal wind at 47 hPa and 1.5°N averaged over JFM of individual years (1989–99) and averaged over the five SKYHI experiments

Fig. 12.

The zonal wind at 47 hPa and 1.5°N averaged over JFM of individual years (1989–99) and averaged over the five SKYHI experiments

Fig. 13.

As in Fig. 7, but for the 47-hPa level in Jan 1999

Fig. 13.

As in Fig. 7, but for the 47-hPa level in Jan 1999

Figure 14 shows the equatorial height–zonal section of the January 1999 mean zonal wind. The deviations from zonal mean at each level are shown by the thin contours. At and above 30 hPa, there are mean westerlies, and the eddy field is dominated by the easterly anomaly in the 270°–330°E (90°–30°W) sector documented in detail at the 9-hPa level earlier. As shown above, this behavior is consistent with the propagation of extratropical stationary waves from the winter hemisphere to the equator. Below about 60 hPa the eddy field appears to be dominated by an extension of the tropospheric Walker circulation (note the zonal divergence above the western equatorial Pacific/Indonesia region), which is usually regarded as the response to zonal contrasts in tropospheric heating in the Tropics itself. This has little dependence on the phase of the QBO. The 50-hPa level seems to be a kind of transition between the two regimes. Results for boreal summer are similar in the region below 50 hPa.

Fig. 14.

Equatorial zonal wind averaged over the five SKYHI experiments and for Jan 1999. The thin black contours show the eddy component of the wind with a contour interval of 2 m s−1, the thick black contours show the full wind field with a contour interval of 10 m s−1 with westerlies (solid) and easterlies (dashed)

Fig. 14.

Equatorial zonal wind averaged over the five SKYHI experiments and for Jan 1999. The thin black contours show the eddy component of the wind with a contour interval of 2 m s−1, the thick black contours show the full wind field with a contour interval of 10 m s−1 with westerlies (solid) and easterlies (dashed)

4. Station observations

As noted in the introduction, the available in situ wind observations in the near-equatorial stratosphere are very limited, and this limitation becomes particularly severe above 50 hPa. The passage through the very cold tropical tropopause can severely chill the balloons and lead to bursting in the lower stratosphere.

For the present study the Free University of Berlin Singapore data have been supplemented with balloon data at three near-equatorial stations that have been provided by Meteo-France. In particular, daily or twice-daily balloon wind observations from Nairobi, Kenya (1.30°S, 36.75°E); Bogota, Colombia (4.70°N, 74.13°W); and Rochambeau, French Guyana (4.83°N, 52.36°W) for the period 1990–2000 were provided. The Rochambeau data, in particular, are regarded as being very high quality. The Rochambeau station is run by Meteo-France, and wind observations were taken with RS80-15 sondes tracked by radio theodolite (pre-1993), RS80-15N sondes with Omega system tracking (1993–August 1997), and RS80-15G tracked by GPS (after August 1997). The data at these stations are very limited at levels above 30 hPa, and only a fraction of individual soundings reach even to 30 hPa. During the 11 yr considered, the number of months with at least six wind observations at 30 hPa is 54 at Nairobi, 70 at Bogota, and 93 at Rochambeau. In those months with at least six observations at 30 hPa, there are an average of 21.5 observations at Nairobi, 25.1 at Bogota, and 28.3 at Rochambeau.

a. Near 30 hPa

Figure 15 shows averages over the five SKYHI runs for monthly mean zonal winds during 1989–99 at the 28-hPa level from the model grid points nearest the four stations Singapore, Nairobi, Bogota, and Rochambeau. Figure 16 shows the monthly mean observations at the four stations for the slightly different 11-yr period 1990–2000. Points are plotted only when at least six observations are available in a given month.

Fig. 15.

Time series of monthly mean zonal wind at the 28-hPa level for SKYHI grid points near the Singapore (1.5°N, 102.6°E), Nairobi (1.5°S, 37.8°E), Rochambeau (4.5°N, 52.2°W), and Bogota (4.5°N, 73.8°W) stations. Results are an average of the five SKYHI experiments.

Fig. 15.

Time series of monthly mean zonal wind at the 28-hPa level for SKYHI grid points near the Singapore (1.5°N, 102.6°E), Nairobi (1.5°S, 37.8°E), Rochambeau (4.5°N, 52.2°W), and Bogota (4.5°N, 73.8°W) stations. Results are an average of the five SKYHI experiments.

Fig. 16.

Time series of monthly mean zonal wind at the 30-hPa level from radiosonde observations at Singapore (1.36°N, 103.98°E), Nairobi (1.30°S, 36.75°E), Rochambeau (4.83°N, 52.36°W), and Bogota (4.70°N, 74.13°W) for the 28-hPa level.

Fig. 16.

Time series of monthly mean zonal wind at the 30-hPa level from radiosonde observations at Singapore (1.36°N, 103.98°E), Nairobi (1.30°S, 36.75°E), Rochambeau (4.83°N, 52.36°W), and Bogota (4.70°N, 74.13°W) for the 28-hPa level.

The results in Figs. 15 and 16 are displayed so that the data from the South American stations are in red and the Nairobi and Singapore data are in black. In the model results the two South American stations are very similar and the Singapore and Nairobi results are also reasonably close in most months. The systematic contrast between the model results at the South American grid points and the Singapore/Nairobi grid points is consistent with the geographical variation of the prevailing wind documented above. Notably, the westerly phase of the QBO cycle is significantly weaker at the South American grid points, while the easterly extremes are more similar among the grid points. The peak-to-peak amplitude of the QBO at the South American grid points is ∼10%–15% less than at the Singapore location.

The actual observations in Fig. 16 are noisier than the model simulation results, which is understandable since the monthly mean observational values are subject to considerable sampling errors and also any random observational errors in the individual soundings. The overall picture at the four stations is reasonably consistent with the model results, however. The Bogota and Rochambeau results are fairly similar in most months. The South American station observations are mostly close to the Singapore data in the easterly phase of the QBO, but display weaker winds over most of the westerly phase. Interestingly, the major exceptions to this occur in the first few months of 1995 and then again in the last few months of 1999, when the westerly phase in the Singapore data has an unusual weakening. The model simulation data in Fig. 15 shows a similar drop in the contrast between Bogota/Rochambeau and Singapore at precisely the same times.

The data coverage at Nairobi is rather spotty and, in particular, there are only a very few months with sufficient data to define a reasonable monthly mean during easterly QBO phases. However, even these limited data suggest that the QBO in the zonal wind has a similar peak-to-peak amplitude at Nairobi as at Singapore, and certainly these data rule out the suggestion of Belmont and Dartt (1968) that the QBO is particularly weak near Nairobi. In the SKYHI model at 28 hPa (Fig. 15) the Singapore and Nairobi results are quite similar, with a slight tendency for the westerly extremes to be a little stronger at Nairobi. The observations are noisier but the similar tendency can be seen.

b. Near 50 hPa

Figure 17 shows the results for the average of the five SKYHI runs at 47 hPa for the same four “Station” grid points. Again the main contrast is between the South American stations versus Singapore and Nairobi, with the westerly extremes larger at Singapore and Nairobi. However, the contrasts among the stations near the westerly extreme are smaller here than at 28 hPa (Fig. 15). Figure 18 shows the actual 50-hPa observations at the four stations. There is more consistency among the station observations near the easterly extremes and more scatter in the westerly phase. The variations in the westerly phase are hard to characterize simply, with some months having stronger winds at Singapore/Nairobi and others with stronger winds at the South American stations.

Fig. 17.

As in Fig. 15, but for the 47-hPa level

Fig. 17.

As in Fig. 15, but for the 47-hPa level

Fig. 18.

As in Fig. 16, but at the 50-hPa level

Fig. 18.

As in Fig. 16, but at the 50-hPa level

5. NCEP analyses

Some of the problems that current meteorological analyses manifest in representing the circulation in the tropical stratosphere were discussed in the introduction. Despite these limitations, it is of interest to see if the zonal inhomogeneities found in the present SKYHI model results and station observations are also apparent in available gridded analyses. As part of the present study, plots of the monthly mean zonal wind field in the National Centers for Environmental Prediction (NCEP) reanalyses were examined for several stratospheric levels during the 1989–99 period. In the Tropics, the monthly mean maps from the analyses generally displayed a number of implausible features, notably isolated small maxima and minima. Some of these problems may be associated with previously documented deficiencies with the treatment of steep topography in the NCEP reanalyses (Trenberth and Stepaniak 2002), but some also occur away from steep topography.

Despite the clear deficiencies in the analyses, some of the features in the stationary wave field simulated in the present SKYHI experiments can be found in the NCEP analyses, particularly in the middle stratosphere. Figure 19 shows the zonal wind at 10 hPa from the NCEP reanalyses averaged over January 1997 and plotted in the same format as the comparable model results (Fig. 7). There are some significant differences in the near-equatorial zonal-mean winds for this month: in the SKYHI simulation the equatorial mean westerlies are stronger and the region of mean westerlies stretches further into the SH than in the NCEP analyses. Close examination of the NCEP results shows that the strongest westerlies are present only in an isolated “bull's eye” around Singapore. In the rest of the equatorial zone, the NCEP results are presumably more affected by the satellite temperature retrievals, which by themselves lead to an underestimate of wind shears. The present SKYHI simulations more plausibly employ the Singapore observations as the primary determinant of the zonal-mean wind near the equator at this level.

Fig. 19.

(top) The Jan 1997 mean of the 10-hPa zonal wind field computed from the NCEP reanalyses. Contour interval is 10 m s−1 and negative values are denoted by dashed contours. (bottom) The deviation of the zonal wind from the zonal average. Contour interval is 3 m s−1 and negative values are denoted by dashed contours

Fig. 19.

(top) The Jan 1997 mean of the 10-hPa zonal wind field computed from the NCEP reanalyses. Contour interval is 10 m s−1 and negative values are denoted by dashed contours. (bottom) The deviation of the zonal wind from the zonal average. Contour interval is 3 m s−1 and negative values are denoted by dashed contours

The presence of the apparent bull's-eye near Singapore is only one of a number of implausible features in the NCEP analyses for this month. The noisy results in the vicinity of the Andes Mountains is also almost certainly unrealistic at this level and is consistent with the problems in the NCEP reanalyses noted earlier by Trenberth and Stepaniak (2002). It is also possible that the contrast seen between the results over tropical Africa and the adjacent oceans may primarily reflect differences in data coverage.

If one ignores these presumed deficiencies and concentrates on the largest scales, then the NCEP results in Fig. 19 do have some resemblance to the SKYHI simulation results shown in Fig. 7. Notably both pictures show a large-scale stationary wave propagating from the NH to the equator, with rough agreement in amplitudes and phase. A similar pattern of overall agreement in the structure of the large-scale wave field can be seen in Fig. 20, which shows the 10-hPa NCEP result averaged for July 1997 and the comparable SKYHI result in Fig. 9. Once again, the NCEP results also show small spatial scale structures that are not plausible in a monthly mean wind field.

Fig. 20.

As in Fig. 19, but for Jul 1997

Fig. 20.

As in Fig. 19, but for Jul 1997

The monthly mean NCEP analyses of the wind in the equatorial lower stratosphere (e.g., 50 or 70 hPa) tend to be even noisier and it is hard to subjectively determine which features are likely to be real. Paradoxically, the fact that the lower-stratospheric analyses look worse than the upper-stratospheric analyses may reflect the increased station data available at lower levels. If the analysis scheme cannot reconcile the smooth temperature retrieval data from satellites and the station data, then increasing the number of stations may just add to the noise that appears in the final product.

The present results may shed light on the issue of how to improve the current meteorological analyses in the tropical stratosphere. The fact that assimilating only the zonal-mean wind seems to work quite well and leads even to results that are somewhat repeatable among the SKYHI model realizations, suggests that, in the tropical stratosphere at least, it may make sense to assimilate the zonal mean and eddy components separately, with the zonal mean being strongly constrained by the highest-quality station wind observations, and only weakly by the satellite temperature observations. In general, the satellite observations should probably be given small weight in the tropical stratosphere; it may be better to rely on the model dynamics to properly take care of the eddy propagation from midlatitudes and even the upward extension of the Walker circulation that may be an important component of the circulation in the equatorial lower stratosphere.

6. QBO modulation of eddy momentum transports

The possibility that the Reynolds stresses associated with quasi-stationary eddies forced in the extratropical troposphere could affect the zonal-mean QBO near the equator has been raised in earlier studies (e.g., Dunkerton 1983). The southwest–northeast phase tilts evident for the waves in the NH (and northwest–southeast tilts in the SH) show, as expected, that the Reynolds stress associated with these waves effectively transports negative (westward) mean momentum from the extratropics toward the equator. The divergence of the stress will result in forcing of mean easterly (i.e., westward) accelerations at low latitudes.

Figure 21 shows the zonal-mean zonal wind and the zonal mean of the product of the monthly mean eddy zonal and eddy meridional wind components ([u]′[υ]′) for January 1999, averaged over the five SKYHI experiments. Here, [ ] represents a monthly mean and, as before, the overbar represents a zonal mean, and the prime denotes the deviation from the zonal mean. Above about 23 km there are mean westerlies on the equator, and the positive values of [u]′[υ]′ extend from the NH extratropics across the equator. The values of [u]′[υ]′ near the equator are, of course, much smaller than at higher northern latitudes. However, even [u]′[υ]′ of order 1 m2 s−2 can be significant for the momentum budget in the tropical stratosphere.

Fig. 21.

The black contours show the zonal-mean zonal wind averaged over Jan 1999 and over the five SKYHI experiments. The contour interval is 5 m s−1, easterly winds are denoted by dashed contours and the zero contour is emphasized. The green contours show the eddy horizontal momentum transport term uυ computed from the monthly mean wind values. The contour interval is 1 m2 s−2, negative values (i.e., southward transport of westerly mean momentum) are denoted by dashed contours, and the zero contour is emphasized

Fig. 21.

The black contours show the zonal-mean zonal wind averaged over Jan 1999 and over the five SKYHI experiments. The contour interval is 5 m s−1, easterly winds are denoted by dashed contours and the zero contour is emphasized. The green contours show the eddy horizontal momentum transport term uυ computed from the monthly mean wind values. The contour interval is 1 m2 s−2, negative values (i.e., southward transport of westerly mean momentum) are denoted by dashed contours, and the zero contour is emphasized

Figure 22 shows the same quantities for January 1998 when mean easterlies dominated most of the tropical stratosphere. In this case the [u]′[υ]′ is almost zero near the equator. The region of significant [u]′[υ]′ extends somewhat equatorward of the zero wind line near 25°N, but does not even approach the equator. This is very typical of the NH winter cases with mean easterlies on the equator, and is consistent with the earlier indications that quasi-stationary waves are virtually absent from the equator above 30 hPa when the mean winds are easterly.

Fig. 22.

As in Fig. 21, but for Jan 1998

Fig. 22.

As in Fig. 21, but for Jan 1998

Figure 23 shows the same quantities for April 1999, when there was strong equatorial mean westerlies. As seen earlier in Fig. 10, there is penetration of quasi-stationary eddies to the equator in this month, but, near the equator, the tilt of the wave phase with latitude is small. This is reflected in the very small values of [u]′[υ]′ in Fig. 23.

Fig. 23.

As in Fig. 21, but for Apr 1999

Fig. 23.

As in Fig. 21, but for Apr 1999

Figure 24 shows the same quantities for July 1999, when there were still strong mean westerlies over much of the low-latitude stratosphere. Now the dominant [u]′[υ]′ is negative and is associated with eddies propagating from the SH.

Fig. 24.

As in Fig. 21, but for Jul 1999

Fig. 24.

As in Fig. 21, but for Jul 1999

The net result of these fluxes is to produce a forcing of the mean flow near the equator with strong modulation by the QBO and by the annual and semiannual signals. Figure 25 shows time series of the 9-hPa monthly mean values of 1) the equatorial mean wind (middle), 2) the flux [u]′[υ]′ at the equator associated with the monthly mean eddy field (top), and 3) the zonal force per unit mass F associated with the divergence of the flux at the equator (bottom). Here, F is defined as

 
formula
Fig. 25.

Time series of monthly mean quantities for the equator and 9 hPa, for each of the five SKYHI experiments. (top) The northward eddy flux of zonal momentum associated with the monthly mean fields. (middle) The zonal-mean zonal wind. (bottom) The forcing of the zonal mean flow acceleration from the divergence of the horizontal eddy momentum flux associated with monthly mean fields

Fig. 25.

Time series of monthly mean quantities for the equator and 9 hPa, for each of the five SKYHI experiments. (top) The northward eddy flux of zonal momentum associated with the monthly mean fields. (middle) The zonal-mean zonal wind. (bottom) The forcing of the zonal mean flow acceleration from the divergence of the horizontal eddy momentum flux associated with monthly mean fields

In Fig. 25 results are plotted individually for each of the five SKYHI experiments. The mean winds among the experiments are almost identical, of course, but also the flux and even flux divergence are fairly consistent among the five cases. The fluxes show the expected annual and QBO modulations: they are nearly zero during times of mean easterlies, and during the westerly QBO phases the fluxes are positive (negative) in boreal (austral) winter as the waves propagate from the winter hemisphere. The eddy forcing of the mean flow F is almost always negative, corresponding to a forcing of mean easterly (westward) accelerations. The magnitude of F reaches as much as 0.5 m s−1 day−1 in some months, which is quite significant relative to the actual mean flow accelerations in the QBO. This forcing is modulated by the QBO and is only significant during periods of mean westerlies. It also has a strong semiannual dependence corresponding the the annual cycle seen in the fluxes themselves.

7. Conclusions

This project has aimed at understanding the standing eddy patterns near the equator in the stratosphere and how these patterns are modulated by the seasonal and quasi-biennial cycles. In order to do this, three rather imperfect tools were used: 1) a GCM that must have some significant deficiencies in the tropical stratosphere since it does not spontaneously simulate a QBO, 2) station wind observations that are likely reasonably accurate but suffer from severe spatial sampling limitations, and 3) gridded analyses that have some obvious deficiencies in the tropical stratosphere. Despite the limitations of the model and data employed, a fairly consistent picture of the zonal asymmetries in the prevailing wind near the equator has emerged. The model results show that, near the equator the zonal asymmetry in prevailing winds above about 30 hPa is controlled by the propagation of quasi-stationary waves from midlatitudes. When there are mean westerlies over the equator at some level, the quasi-stationary waves from the winter hemisphere (or from both hemispheres in fall/spring) can propagate to the equator. The phase of these quasi-stationary waves is such that the weakest prevailing westerlies over the equator occur over South America and the ocean areas to the west. When there are mean easterlies at low latitudes, the quasi-stationary waves are excluded from the equatorial band and there is almost no zonal asymmetry in the prevailing wind.

The net result is a significantly weaker peak-to-peak amplitude of the QBO in zonal wind over the South American–eastern Pacific sector than over the rest of the equatorial band. Near 10 hPa, this contrast exceeds 10%. The phase of the QBO in the simulations has almost no zonal variation at all.

Below about 30 hPa, the stationary eddies in the prevailing wind are fairly small. Zonal asymmetries seem to reflect the upward extension of the tropospheric Walker circulation, and are not strongly modulated by the QBO in zonal-mean circulation.

The model simulations confirm the suggestion that the Reynolds stress divergences associated with the quasi-stationary eddies may play a significant role in the dynamics of the QBO, at least above about 30 hPa. This component of the eddy forcing acts to reduce the strength of the mean westerlies and could play a role in at least the initial easterly-to-westerly transitions in the QBO. This forcing also has a strong semiannual modulation, and thus it could be responsible for the coupling seen in observations between the QBO transitions and the seasonal cycle.

Acknowledgments

The authors thank Barbara Naujokat for providing the Singapore wind data. V. Ramaswamy and M. Daniel Schwarzkopf of GFDL provided important support and practical assistance. The IPRC is supported in part by the Frontier Research System for Global Change. K. Hamilton's work was supported by NASA Grant NAG 5-12214. G. Stenchikov's work was supported by NASA Grant NAG 5-9792 and NSF Grant ATM-9988419.

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Footnotes

Corresponding author address: Kevin Hamilton, International Pacific Research Center, University of Hawaii at Manoa, Honolulu, HI 96822. Email: kph@hawaii.edu