a. HALOE data and equivalent latitude mapping

The primary data analyzed here are HALOE V18 vertical profile measurements of CH₄ and H₂O. The HALOE instrument is described in Russell et al.(1993b), and the CH₄ and H₂O data are discussed in detail in Park et al. (1996) and Harries et al. (1996b), respectively. We use HALOE level 3a data, which are available on 16 standard UARS pressure levels spanning 100–0.32 mb (approximately 16–56 km), with a vertical spacing of about 2.5 km. The time period analyzed here covers November 1991–March 1997.

HALOE is a solar occultation instrument that obtains 15 sunrise and 15 sunset measurements per day, each near the same latitude but spaced ∼24° apart in longitude. The latitudinal sampling progresses in time, so that much of the latitude range 60°N–S is sampled in 1 month. One method to analyze the latitude–height structure of these data is to construct zonal means by simple longitudinal averaging. However, this has the disadvantage of averaging airmasses that may be physically distinct, in particular those inside versus outside the polar vortex [for cases when the vortex is elongated or not centered over the pole; see the example Plate 1 of Schoeberl et al. (1995)].

An alternative method is to average data along potential vorticity (PV) contours, which acts as an approximate vortex-following coordinate (McIntyre and Palmer 1983; Buchart and Remsberg 1986; Schoeberl et al. 1989, 1992, 1995; Norton 1994; Manney et al. 1995). For the analyses presented here we have derived PV from daily wind and temperature fields output from the United Kingdom Meteorological Office (UKMO) stratospheric data assimilation system (Swinbank and O’Neill 1994). The utility of PV versus zonal averaging is illustrated in Fig. 1, showing HALOE CH₄ measurements at 10 mb during September–October 1993 plotted versus latitude and versus PV. (Here and throughout the rest of this work the PV coordinate is expressed in terms of “equivalent latitude,” i.e., the latitude of an equivalent PV distribution arranged symmetrically about the pole.) The distribution of CH₄ versus latitude in Fig. 1 shows a wide scatter over high southern latitudes, due to sampling inside (low CH₄) and outside (high CH₄) of the polar vortex. Conversely, the CH₄ shows strong correlation with PV, with pronounced separation of vortex interior data (see also Bithell et al. 1994; Schoeberl et al. 1995). In a similar manner, HALOE H₂O data are found to be correlated with the polar vortex (Pierce et al. 1994; RO97) and associated PV fields.

Figure 2 shows an example of the PV mapping of HALOE CH₄ for data during January 1994. The PV mapping is done on each UARS pressure level separately (one can choose to perform the PV mapping using potential temperature as a vertical coordinate, but this involves vertical interpolations before and after mapping, and gives nearly identical results to mapping on pressure levels used here). Data are analyzed between 80°N and 80°S (as available for each month) on a 4° equivalent latitude grid. There are two advantages to the PV mapping: 1) data that are physically distinct remain separated; and 2) there is an increase in the effective latitude range of the data, as measurements inside the vortexcorrespond to high equivalent latitude (note the NH data shown in Fig. 2). The equivalent latitude data (over 80°N–S) are binned into monthly samples prior to further analyses; we note these are not true monthly means, as data at different latitudes are observed at different times during each month. We require at least three data points at a particular altitude and equivalent latitude or else the corresponding monthly sample is left blank.

b. Seasonal cycle fits

Seasonal cycles are estimated from the monthly binned data by the fitting of seasonal harmonics at each (equivalent) latitude and pressure altitude. This method works well for the irregularly sampled HALOE measurements [similar analyses are used by McCormick et al. (1993)]. Examples are shown in Fig. 3 for CH₄ and H₂O data at 10 mb and 28°S. These show the monthly sampled equivalent latitude data (as “plus” signs), together with the harmonically varying seasonal cycles (the repeating smooth curves). The seasonal cycle at each location is determined using a time mean, plus annual and semiannual harmonics fit by least squares regression. The linear trend (determined over January 1993–December 1996) is removed prior to these seasonal fits, and it is also omitted from the interannual analyses discussed below. Note the opposing seasonality (and interannual variations) in the H₂O and CH₄ data in Fig. 3; this is a feature observed throughout the stratosphere in general, due to conservation of the quantity D = H₂O + 2 × CH₄ (as discussed above).

Over high latitudes of both hemispheres, HALOE data are not available during several months in winter (the equivalent latitude PV mapping helps fill in this void in the NH, but less so during SH winter when the vortex is typically centered over the pole). For such high (equivalent) latitudes where data are unavailable each year, the seasonal cycle is only fit over months that data are available, and the remaining months are left blank [specifically, we require at least two years of data (out of five) for each individual month]. An example is shown in Fig. 4 for CH₄ data at 72°S, where no seasonal cycle is fit during April–August.

c. Addition of CLAES CH₄ and MLS H₂O data

In order to fill in the high latitude voids in the seasonal cycle estimates of CH₄, we include CH₄ observations from the CLAES instrument on UARS (Kumer et al. 1993; Roche et al. 1996). These data span a little more than one year (January 1992–April 1993), but offer more continuous sampling than the HALOE data, in particular observing the polar winter regions. The data used here are from the version 7 (V7) retrieval. The CLAES CH₄ data are mapped into equivalent latitude space and monthly averaged. Direct comparison of the CLAES and HALOE data shows reasonable agreement in the latitudinal structures, although there is an offset (bias), with CLAES approximately 20% higher than HALOE (as discussed in Roche et al. 1996). We remove this bias for the analyses here by simply adjusting the CLAES data (using a latitude-independent multiplicative factor) to match the HALOE measurements over a region adjacent to the missing HALOE data. This matching is done using a seasonal cycle fit of the CLAES data (over 1992–93) together with the seasonal cycle HALOE data (1991–97), in order to obtain smooth transitions. The adjusted CLAES data and fit seasonal cycle are included in the time series at 72°S shown in Fig. 4. Note the CLAES data are used only in the seasonal cycle estimates, since the short CLAES record precludes interannual analyses.

In a similar manner, we augment the HALOE seasonal cycle H₂O results using MLS data in polar regions. Stratospheric H₂O data are derived from MLS 183-GHz measurements, as described in Lahoz et al. (1996b). We use the version 4 (V4) retrieval for the analyses here, with time period spanning November 1991–April 1993. The seasonal cycle fit of the equivalent latitude MLS data are adjusted (by a small amount, ∼5%) to smoothly match the HALOE seasonal cycle fit.

d. Calculation of residual mean circulation

Part of the results here include comparisons of the constituent seasonal cycles with estimates of the mean meridional circulation derived from United Kingdom Meteorological Office stratospheric analyses (Swinbank and O’Neill 1994). Specifically, we calculate monthly average components of the residual mean meridional circulation (υ*, w*) using the coupled transformed Eulerian-mean (TEM) thermodynamic and continuity equations (as in Solomon et al. 1986; Rosenlof 1995). Radiative heating rates were calculated from an accurate radiative transfer code (Olaguer et al. 1992), incorporating UKMO temperatures, HALOE ozone, water vapor and methane, and climatological distributions of other trace gases. The overall circulation features are very similar to previous calculations (e.g., Gille et al. 1987; Eluszkiewcz et al. 1996). Aspects of constituent transport are studied based on the TEM constituent continuity equation [Andrews et al. 1987, their Eq. (9.4.13)]:

View Expanded

Here χ is the zonal-mean constituent mixing ratio, υ* and w* are components of the TEM residual mean circulation (discussed above), ∇·M is an eddy transport term, and S is a chemical source or sink term. This formalism has been used to study constituent transport in three-dimensional model simulations by Randel et al. (1994) and Strahan et al. (1996).

a. Global seasonality

Figure 6 shows the global structure of CH₄ in January, April, July, and October, derived from the seasonal cycle fits. The overall structures are similar to those shown previously (e.g., Luo et al. 1995; Park et al. 1996), but the synthesis of many years of data here allows the seasonality to be studied in some detail. Contours bulge upward in the Tropics and move latitudinally with season in the upper stratosphere, reflecting variations in the upward transport circulation in the Tropics (as shown below). There is a double-peaked pattern in the upper stratosphere in April related to the seasonal subtropical upwelling and thetropical semiannual oscillation (SAO); a similar double-peaked structure is not seen in October (the SAO is discussed in more detail below). Relatively strong horizontal gradients are seen in the subtropical lower stratosphere near 20°–30° N–S throughout much of the year, and strong gradients are also associated with the polar vortex in both hemispheres during winter–spring. These regions of enhanced gradients are associated with differential vertical advection (upward in the Tropics and downward in polar winter) and relative minima in horizontal mixing (so-called mixing barriers). The SH winter–spring polar vortex is particularly robust in these data, due to strong downward flow inside the vortex and small transport across the vortex edge (Russell et al. 1993a; Schoeberl et al. 1995; Fisher and O’Neill 1993; Manney et al. 1994; Sutton 1994). In contrast, the CH₄ contours are relatively flat over midlatitudes during winter–spring, showing evidence of more rapid mixing associated with the planetary waves (McIntyre and Palmer 1983, 1984; Leovy et al. 1985). There are relatively weak vertical gradients in high latitudes over 20–30 km during SH summer (January), possibly a remnant of very low (vortex) CH₄ following the SH final warming.

The corresponding seasonal cycle patterns in H₂O are shown in Fig. 7. The overall patterns are approximate mirror images of the CH₄ data in Fig. 6, including the seasonal movement of the upper-stratospheric maxima and appearance of a double peak in April. These similar patterns reflect the fact that the H₂O increase with altitude is due to CH₄ oxidation, so that total hydrogen is conserved (see references in introduction). This is demonstrated with the data here by calculation of the quantity 2CH₄ + H₂O, shown for the October distribution in Fig. 8. Note the contour interval is identical between Figs. 7 and 8, so that the relative lack of spatial structure in 2CH₄ + H₂O (cf. H₂O or CH₄ alone) demonstrates that to first order 2CH₄ + H₂O ≈ constant for these seasonal cycles. Two locations where this approximation does not holdare 1) in the tropical lower stratosphere, and 2) over Antarctica in winter–spring, as discussed in the introduction.

The latitude–time evolution of CH₄ at 68, 10, and 2.2 mb is shown in Fig. 9. There is a slight latitudinal shifting of the tropical maximum region in the lower stratosphere (68 mb) toward the respective summer hemisphere. Low CH₄ is observed in the springtime high latitudes of both hemispheres; these low polar values in the NH have received less attention than those in the SH (e.g., Russell et al. 1993a; Schoeberl et al. 1995), but appear very similar in these equivalent latitude data. These overall variations of CH₄ are in reasonable agreement with seasonality in the mean vertical circulation at 68 mb shown in Fig. 10 (calculated as discussed in section 2d). The patterns of high tropical CH₄ follow the upward velocity variations over low latitudes; note the weak tropical maximum during NH winter and the similar latitudinal movement of the contours (the w* = 0 contour isincluded in the lower panel in Fig. 9). Furthermore, there are springtime maxima in downward motion over both poles, in agreement with the corresponding minima in CH₄.

The CH₄ seasonal cycle in the middle stratosphere (10 mb) shows weakening of the midlatitude gradients during winter–spring in both hemispheres; this effect is more obvious in the SH. Similar midlatitude evolution at 10 mb is seen in the seasonal variation of nitrous oxide (N₂O) measured by CLAES (Randel et al. 1994). At 10 mb strong CH₄ gradients are seen across both polar vortices beginning in autumn, and the larger and stronger SH vortex is echoed in these CH₄ measurements.

Seasonality in the upper stratosphere (2.2 mb) is very different from the lower levels, showing a strong semiannual oscillation (SAO) with distinct maxima in the respective summer subtropics. These maxima are very similar to the patterns of vertical velocity at 2.2 mb (shown in Fig. 10), with the CH₄ maxima lagging theupward motion by approximately 1 month. A double- peaked latitudinal structure in CH₄ is seen over April–June.

Figure 11 shows the altitude–time variation of CH₄ at 76°N and S; note the time axes have been shifted in order to directly compare midwinter variations over both poles. The overall evolution is similar between hemispheres, with regular downward movement of the isolines during autumn and winter, followed by rapid elevation of the contours in spring (associated with breakup of the polar vortices and mixing in of midlatitude air). Somewhat lower CH₄ values are observed in the SH middle and upper stratosphere in winter, and the springtime transition is more dramatic and somewhat later in the SH; these aspects are due to the larger and more isolated SH polar vortex. The 0.3–0.8 isolines show consistent downward movement in the SH middle stratosphere during autumn and winter with a rate of −1.0 to −1.5 km month⁻¹; there is little downwardmovement in the lower stratosphere until spring (September–October), when values near −1.5 km month⁻¹ (−0.6 mm s⁻¹) are inferred. These latter values are in excellent agreement with the downward velocities derived from the HALOE CH₄ data by Schoeberl et al. (1995), and with the TEM vertical velocities shown in Fig. 10 (see also Rosenfield et al. 1994). The NH middle stratosphere data (e.g., the 0.5 contour) yields descent rates near −1.5 km month⁻¹, similar to the SH. In the NH lower stratosphere the data in Fig. 11 shows a relative maximum in November–December (see also the lower panel of Fig. 9) that is inconsistent with the downward circulation in Fig. 10. This isolated feature is entirely due to the use of CLAES data during one year (1992), and its reality is suspect.

Figure 12 compares the observed wintertime variation of zonal-mean methane (χ) near the South Pole (76°S) with a transport calculation based solely on the mean vertical velocity w*:

View Expanded

This is derived from Eq. (1), neglecting the υ*χ_y, ∇·M, and S terms. This is a reasonable approximation inside the Antarctic winter vortex, where w* transport dominates υ*, the chemical lifetime is very long (S is small), and eddy mixing with the vortex exterior is small (Bowman 1993; Chen et al. 1994; Strahan et al. 1996). March is chosen for the starting time as this is near the formation of the SH polar vortex, and the idea here is to test how well calculated descent rates in the vortex agree with observations (the comparisons go through October, just prior to vortex breakup). The comparisons in Fig. 12 show quite reasonable agreement at both the 10- and 46-mb levels. There is relatively strong downward motion in autumn (March–May) at 10 mb, followed by a relative minimum in w* and more constant CH₄ in winter. At 46 mb there is relatively little downward motion until late winter–spring (see also Figs. 9 and 10). The approximate agreement in these comparisons provides a confirmation of the heating rates and vertical velocities derived from the meteorological analyses, and also supports the notion of vortex isolation in the SH (e.g., Bowman 1993; Chen et al. 1994; Manney et al. 1994; Bacmeister et al. 1995). Similar calculations in the NH (beginning in September) are shown in Fig. 13; here there is poor agreement, with the observed CH₄ changes much less than those calculated from w*. This is likely due to stronger meridional transport into and less isolation of the NH polar vortex.

Both NH and SH data in Fig. 11 show CH₄ minima (below 0.1 ppmv) near the stratopause during summer (see also the top panel in Fig. 9). These minima are due to rapid photochemical destruction of CH₄ over polar regions during summer (see Fig. 17 below); the calculated photochemical lifetime of CH₄ in this region is near 1 month [see Fig. 1 of Solomon et al. (1986)].

b. Tropical variations

The altitude–time variations of both CH₄ and H₂O over the equator are shown in Fig. 14, which also includes diagrams with the respective time means removed at each altitude to highlight seasonality. There is a strong upward propagating annual variation in H₂O in the lower stratosphere, associated with the seasonal variation of tropical tropopause temperatures and the freezing out of H₂O in the tropical upwelling region [see extensive discussions in Mote et al. (1995) and (1996)]. A nearly identical pattern is seen in the total hydrogen 2CH₄ + H₂O, as illustrated in a different manner in Fig. 15. Here the individual zonal means over 4° N–S are plotted, along with the associated harmonic fits,for pressure levels 100–10 mb (16–32 km). A strong annual cycle that progresses upward with time is observed over 100–32 mb; this cycle can be traced to 22 mb using the harmonic analysis, although there is substantially more interannual variability at this level. At 15 and 10 mb (29–32 km), the annual harmonic is relatively weak, and a semiannual component dominates at these levels (and above). The upward propagation of the annual signal over 100–32 mb (16–24 km) takes approximately 11 months; this corresponds to a vertical velocity of ∼0.7 km month⁻¹ (∼0.25 mm s⁻¹), in reasonable agreement with the tropical TEM vertical velocities in Fig. 10.

Figure 16 shows the space–time structure of both H₂O and 2CH₄ + H₂O at 100, 68, and 46 mb. While the annual cycles at 68 and 46 mb are approximately centered over the equator, variations at 100 mb are maximum near 15°–30°N. Lowest values are observed near 15°N in February–March, although the minimum 100- mb temperatures occur near the equator (e.g., Newell and Gould-Stewart 1981; Tuck et al. 1993). The maximum during NH summer (August–September) is even more asymmetrical, with maximum near 20°–30°N; this structure has little relation to zonal-mean temperatures. There is also a seasonal variation in meridional transport at 100 mb inferred in Fig. 16, with relatively little spreading of the low subtropical values into the NH during NH winter (note the strong gradients near 30°N), but stronger propagation of the NH summer maximum into high latitudes (with a time lag of order three months between 30° and 60°N). There is much less spreading of this maximum into SH midlatitudes. Based on analyses of these same HALOE H₂O data, RO97 discuss the asymmetry seen in Fig. 16 and note the meridional propagation of maximum values into NH midlatitudes. The asymmetry of these patterns (particularly the NH summer maximum) contribute to the higher values of H₂O observed in the NH versus SH lower stratosphere, as reported by Kelly et al. (1990). These data suggest the NH–SH asymmetry in the lower stratosphere is notdue to asymmetric transport of equatorially centered maxima, but to dynamical processes in the NH subtropics (such as the Indian monsoon during NH summer). The enhanced meridional speading of the H₂O and 2CH₄ + H₂O at 100 mb compared to levels at and above 68 mb agrees with the results of Trepte et al. (1993), who present evidence for rapid meridional flow between Tropics and midlatitudes below 20 km, but not above this altitude. Similar results were inferred from the aerosol observations in Grant et al. (1994). This behavior is consistent with the tropical vertical velocity profile discussed by RO97: there is a minimum in w* near 50–70 mb, such that only 20% of the upward mass flux at 100 mb continues upward across this level (with the remaining 80% moving laterally to either hemisphere). The data in Fig. 16 also provide convincing evidence that there is not strong mixing of the dehydrated SH polar vortex air into midlatitudes following vortex breakup (as also noted by RO97).

The H₂O data at 68 and 46 mb in Fig. 16 show minimum values in the Tropics and relatively strong horizontal gradients near both 30°N and 30°S, similar (but opposite) to the CH₄ latitudinal structure seen in Fig. 9. The lack of such gradients in the quantity 2CH₄ + H₂O (i.e., the 46-mb plot in Fig. 16) implies that it is the downward transport of photochemically aged air in the extratropics, plus a lack of rapid meridional mixing with the Tropics, that is responsible for these latitudinal H₂O gradients. Seasonal variations in both H₂O and 2CH₄ + H₂O show that the upward propagating tropical annual cycle is confined to ∼30°N–S.

Inspection of Fig. 16 and the time series in Fig. 15 shows an attenuation of the amplitude of this annual cycle over 100–32 mb (in both H₂O and 2CH₄ + H₂O) from approximately 1.5 to 0.7 ppmv; the attenuation is most rapid between 100 and 68 mb. Above 68 mb, where the tropical signal appears isolated from midlatitudes, the annual amplitude decreases from 1.1 to 0.7 ppmv between 68 and 32 mb. Supposing that this attenuation is due entirely to the mixing in of extratropical air (withvery small annual cycle in 2CH₄ + H₂O, of order 0.1–0.2 ppmv; see Fig. 16), an estimate of the mixing time τ may be estimated from

View Expanded

where A is the amplitude of the tropical annual harmonic, A₀ is the midlatitude value, and d/dt is the derivative following the upward propagating signal. This is an approximation to Eq. (1), where the meridional and eddy transport terms are approximated as a mixing process with timescale τ. Using dA/dt = (0.4 ppmv per 10 months) between 68 and 32 mb, and (A − A₀) ∼ (0.6 ppmv) averaged over 68–32 mb, gives an estimate of τ ∼ 15 months. This is a lower limit on the meridional mixing time for air entering the Tropics (30°N–S) frommiddle latitudes above 19 km, in order to maintain the observed tropical annual cycle. The estimate of 15 months is in reasonable agreement with that derived by Volk et al. (1996) from aircraft constituent measurements, and by Schoeberl et al. (1997) using UARS constituent data.

The upper stratosphere signal in Fig. 14 is dominated by a semiannual oscillation (SAO), with a much stronger amplitude during the first half of the year. This is a well- known aspect of the SAO (e.g., Dunkerton and Delisi 1988), related to stronger extratropical wave driving in the NH winter (as compared to the SH winter). Variations in H₂O echo those in CH₄, such that the total hydrogen 2CH₄ + H₂O is nearly constant throughout the seasonal cycle. Dynamics of the SAO is discussed further in the next section.

c. Global budgets and estimates of eddy transport

In this section we examine details of the constituent continuity equation [Eq. (1)] applied to the observed seasonal cycle variations in global CH₄. For these calculations we use the monthly average residual mean circulation (υ*, w*) derived from UKMO data (e.g., Fig. 10), and the chemical sink term S is approximated by a linear relaxation expression

View Expanded

with CH₄ lifetimes (τ) taken from the model results of Garcia and Solomon (1983). The ∇·M term in Eq. (1) is a complicated quantity involving eddy covariances, and not derivable from the data here. We calculate thisterm as a residual to the balance in Eq. (1); it thus contains the actual eddy transports plus any errors in the explicitly calculated terms.

Figure 17 shows the structure of the individual terms ∂χ/∂t, − υ*χ_y − w*χ_z, S, and ∇·M (calculated as a residual) for the seasonal CH₄ budget, for statistics averaged over January–February. Transport by the residual mean circulation is associated with large positive tendencies in the tropical upper stratosphere (due to upward and northward transport of relatively high CH₄) and negative tendencies over winter polar regions (due to downward transport of low CH₄). The parameterized chemical sink S is an important component of the budget in the tropical upper stratosphere, with relatively large values also over the summer (SH) high latitudes (this photochemical destruction leads to the very low CH₄ summer pole amounts observed in Fig. 11). The calculated residual (∇·M term) shows a north–south dipole pattern over the Tropics and NH, with opposite sign to the mean meridional circulation transport. Although this is a residual calculation, the structure of this field shows characteristics very similar to ∇·M calculated explicitly using general circulation model output in Randel et al. (1994) (see their Fig. 8). An important point is that these eddy transport effects extend well into the Tropics in both model calculations and the residual estimate here. Note also that the tendency term ∂χ/∂t is a relatively small part of the overall budget, so that accurate simulation of ∂χ/∂t will be sensitive to small uncertainties in calculation of the other budget terms.

Figure 18 shows altitude–time plots of several CH₄ seasonal budget terms over the equator [−υ*χ_y, −w*χ_z and ∇·M (residual)]. The chemical sink S (not shown) is nearly constant over the equator throughout the year, and the observed tendency ∂χ/∂t (not shown) is a relatively small component. Transport by the mean meridional circulation (υ*, w*) exhibits a pronounced semiannual variation in the upper stratosphere, with maxima near the solstices. Transport by both mean circulation components is important in this variation: the w* transport is a maximum during NH winter, while the υ* component exhibits a dominant maximum during SH winter (along with a weaker NH winter peak). These enhanced υ* transports during both solstices are due to strong flow toward the winter hemisphere (see Fig. 17) combined with enhanced meridional constituent gradients near the equator (see Fig. 6). The budget residual (∇·M in Fig. 18) also shows a strong semiannual variation at the equator for altitudes above approximately 30 km. Although some component of this may be due to budget uncertainties, this semiannual seasonality is consistent with enhanced planetary wave transport in the respective winter hemispheres reaching into the Tropics (as discussed above). The strong semiannual forcing (by both mean flow and eddy components) is likely responsible for the dominance of semiannual behavior for the tropical constituent fields above ∼30 km (see Figs. 14 and 15).

a. Observations

This section focuses on interannual variations in CH₄ and H₂O over 1991–97, defined as deviations from the seasonal cycles defined above (with linear trends also removed). Figure 19 shows altitude–time sections of CH₄ anomalies over the equator (average over 10°N–10°S); here data gaps have been interpolated and the monthly anomalies smoothed slightly in time. Largest CH₄ anomalies are observed in the upper stratosphere, over 35–45 km, with an approximate 2-yr periodicity; these values represent approximately ±10% deviations from the time mean. The approximate 2-yr periodicity in CH₄ anomalies suggests a link with the equatorial quasibiennial oscillation (QBO), and this is confirmed by comparison with the UKMO equatorial zonal wind anomalies shown in Fig. 20a (with the CH₄ anomalies superimposed). Specifically, the CH₄ anomalies over 35–45 km are approximately in phase with the zonal wind anomalies near 30 km.

Figure 21 shows the H₂O interannual anomalies over the equator. Maxima are observed in the upper stratosphere with very similar (but oppositely signed) patterns to the CH₄ anomalies, reflecting conservation of 2CH₄ + H₂O on interannual (as well as seasonal) timescales. There are also significant H₂O anomalies in the lower and middle stratosphere; there are relative maxima over 27–33 km with an approximate 2-yr periodicity, but these are not observed in the CH₄ data.

Space–time structure of coherent QBO variations in CH₄ may be isolated in an optimal manner using singular value decomposition (SVD) (Randel and Wu 1996). This involves manipulation of the covariance matrix between CH₄ anomalies (as a function of latitude and altitude) and zonal wind anomalies (over 10–70 mb), and yields modal spatial structures that explain optimum fractions of covariance between these fields. Figure 22 shows the spatial structure of the first two modes derived from this analysis (termed SVD1 and SVD2); patterns show the location (and phase) of anomalies in CH₄ that are coherent with the QBO zonal windanomalies. (Two such modes are typical for a propagating oscillation, analogous to a harmonic sine and cosine Fourier decomposition.) The spatial structure of SVD1 shows a maximum in the upper stratosphere over 35–45 km, centered in the Tropics over approximately 30°N–S. This structure corresponds to the equatorial anomalies seen in Fig. 19. The structure of SVD2 shows a narrow maximum over the equator at 40–45 km, and several maxima over ∼10°–40° in both hemispheres [note these modes are spatially (and temporally) orthogonal by construction]. These extratropical patterns are qualitatively similar to QBO variations observed in column and profile ozone and NO₂ data (Bowman 1989;Randel and Wu 1996), and deduced from CLAES N₂O data by O’Sullivan and Dunkerton (1997). The QBO patterns in Fig. 22 are largest near gradients in the background CH₄ structure (included in Fig. 22), as anticipated for anomalies due to transport variations. Note the similarity of these QBO patterns with the total interannual variance map shown in Fig. 5.

Temporal evolution of the QBO patterns in CH₄ is revealed by projection of the full monthly CH₄ anomalies onto the spatial patterns in Fig. 22. Figure 23 shows a phase-space plot of the projections of SVD1 versus SVD2 over the entire time record 1991–97. Nearly regular counterclockwise phase progression is observed as the QBO anomalies project successively onto the patterns in Fig. 22. This nearly regular QBO phase variation in CH₄ data is analogous to the harmonic QBO variations in dynamical quantities discussed by Wallace et al. (1993), and the ozone variations shown in Randel and Wu (1996).

Figure 24 shows CH₄ data observed during April for four years (1993–96); these time periods are indicated in Fig. 23 and correspond to opposing projections of SVD1 and SVD2. These plots demonstrate that there is a strong effect of the QBO in modulating the double- peaked structure in upper-stratospheric CH₄: data during April 1993 and 1995 (westerly QBO winds in Fig. 20a) exhibit a pronounced double peak, whereas April 1994 and 1996 (easterly QBO winds) do not.

Figure 25 shows latitude–time series at 3 mb of the full CH₄ field and the detrended anomalies (which exhibit a clear QBO dependence). Time periods of enhanced double-peak structure are also indicated in Fig. 25. The QBO anomalies show maxima centered near the equator, with a suggestion of propagation into the subtropics, particularly into the NH. This latitudinal propagation near 3 mb is associated with successive projections of SVD1 and SVD2 (Fig. 22). The timing of these anomalies is such that large NH subtropical maxima occur during NH winter–spring; this is the time of seasonal maximum in SH subtropics, and this combination leads to double-peaked structure for the positive QBO anomalies in NH spring 1993 and 1995. The details of this behavior clearly depend on the phase relationship between the QBO and the seasonal cycle, and this is something that will change on a decadal timescale (Gray and Dunkerton 1990). We note that relatively small anomalies are observed over the equator during these times; the double-peak structure (or its absence) in this time sample is mostly due to the presence of subtropical anomalies, particularly in the NH (corresponding to a positive projection of SVD1 + SVD2, i.e., Fig. 23).

Figure 26 shows the latitude–time evolution of CH₄ at 10 mb throughout 1991–97, for both the full-field and interannual anomalies. The anomalies at this altitude are very small at the equator but large over the subtropics of each hemisphere (somewhat larger in the NH), with a strong QBO time dependence. These interannualanomalies are associated with a latitudinal shifting of the tropical maximum region in CH₄, as seen in the upper panel of Fig. 26. The maximum is shifted toward the NH during QBO easterlies (near 30 mb) enhancing NH subtropical gradients, and toward the SH for QBO westerlies (decreasing these gradients). Similar CH₄ patterns are observed over approximately 22–10 mb (27–32 km), but not below 30 mb; these anomalies are associated with strong projection onto SVD2 in Fig. 22. Note the clear effect of these anomalies in the cross sections in Fig. 24, especially on the vertical gradient structure in NH midlatitudes. This is remarkable evidence of QBO modulation of the latitudinal position of the tropical maximum region (Trepte and Hitchman 1992) and the interaction with extratropics.

Figure 27 shows the latitudinal structure of H₂O at 10 mb throughout 1991–97, for both the full field and the interannual anomalies. Large anomalies are observed in the NH subtropics, mirroring the CH₄ patterns in Fig. 26. Unlike the CH₄ data, the H₂O anomalies extend across the equator, giving rise to the equatorial anomalies centered near 10 mb seen in Fig. 21. The overall structure of H₂O at 10 mb shows latitudinal movement of the tropical minimum region and modulation of subtropical gradients on the QBO timescale, very similar to that seen for CH₄ in Fig. 26.

b. QBO budget calculations

The observed QBO anomalies in CH₄ and H₂O likely result from transport variations associated with the QBO. Although a detailed budget analysis of QBO transport is beyond the scope of this work, there are some aspects of coupling with QBO circulation anomalies that deserve mention. Figure 20b shows an altitude–time section of the QBO anomalies in residual mean vertical velocity (w*) over the equator derived from UKMO data (Randelet al. 1997). These data have been filtered to isolate QBO variations, but the QBO patterns are clearly evident in the full interannual anomaly fields (see W. Randel et al. 1998, manuscript submitted to J. Atmos. Sci.). These w* anomalies are maximum near regions of largest vertical shear of the zonal-mean wind (Fig. 20a)—which are also regions of largest QBO temperature anomalies—and exhibit similar downward propagation in time. These QBO anomalies in w* are of order 10%–20% of the time-mean background values; largest w* anomalies are observed in the upper stratosphere (35–45 km), although largest QBO zonal winds are seen in the lower-middle stratosphere. Comparison between the vertical velocity anomalies and the equatorial CH₄ anomalies (also included in Fig. 20b) shows strong correlation in the upper stratosphere, with upward velocities associated with positive CH₄ maxima, and vice versa.

The observed space–time coherence between QBO anomalies in w* and CH₄ in the equatorial upper stratosphere (Fig. 20b) is puzzling in light of Eq. (1). If vertical transport is the dominant effect (a reasonable assumption for equatorial QBO variations), the continuity equation [Eq. (1)] suggests a correlation between w* and ∂χ/∂t, rather than between w* and χ as observed. An estimate of the budget based on Eq. (1) (not shown) results in large residuals with an approximate QBO periodicity, with a phase relationship such that the residual is a (negative) maximum during QBO westerly winds. One possible explanation is that eddy transport effects are modulated by the QBO zonal wind structure. Although this is speculative, based on variations in the residual to Eq. (1), the in-phase coherence between w* and CH₄ (or H₂O) anomalies near 40 km appears to be a robust result (leading to these large residuals).

Figure 28 shows a latitude–time diagram of the QBO anomalies in w* at 10 mb. Together with alternating anomalies over the equator (over 10°N–S), this figure shows large anomalies in the NH subtropics that are approximately out of phase with those at the equator. These coupled patterns are likely a manifestation of the meridional circulation cells anticipated theoretically for the QBO (e.g., Plumb and Bell 1982), although the meridional scale is somewhat wider than in idealized models and there is substantial NH–SH asymmetry in these observations. The subtropical w* maxima at 10 mb bear strong resemblance to the CH₄ and H₂O anomaly patterns shown in Figs. 26 and 27. Comparison of the time evolution shows the circulation anomalies lead the constituent patterns by up to a quarter cycle (as expected for transport variations), although the anomalies in early 1994 are more nearly in phase. The similarity in these patterns suggests that advection by the mean meridional circulation is one important component for forcing the observed subtropical QBO constituent variations. Model calculations furthermore suggest that eddy transport effects are important for modulation of the subtropical mixing barrier (Polvani et al. 1995; O’Sullivan and Chen 1996).