QBO and annual cycle variations in tropical lower stratosphere trace
gases from HALOE and Aura MLS observations
M. R. Schoeberl,1 A. R. Douglass,1 P. A. Newman,1 L. R. Lait,2 D. Lary,2 J. Waters,3
N. Livesey,3 L. Froidevaux,3 A. Lambert,3 W. Read,3 M. J. Filipiak,4 and H. C. Pumphrey4
Received 20 March 2007; revised 26 June 2007; accepted 6 December 2007; published 1 March 2008.
[1] We have analyzed thirteen years (1993 to 2005) of HALOE and over two years of
EOS MLS observations (September 2004 to December 2006) for QBO and annual
cycle trace variations in tropical H2O, HCl, ozone, N2O, CO, HF, and CH4. We use these
results to develop the theory explaining both Brewer-Dobson circulation (BDC) and QBO
driven fluctuations in tropical trace gases. For H2O, BDC variations drive part of the
tropopause annual forcing through annual variations in the temperature as has been shown
previously. For CO, the annual variations in the BDC amplify the annual fluctuations in
CO at the tropopause as has recently been shown by Randel et al (2007). In both cases, the
tropopause signal is carried upward by the mean BDC. For ozone, N2O, HCl and
other gases, photochemical processes force fluctuations in the trace gases to be
synchronized with annual and QBO variations in the zonal mean residual vertical velocity
as is shown using lag correlations.
Citation: Schoeberl, M. R., et al. (2008), QBO and annual cycle variations in tropical lower stratosphere trace gases from HALOE
and Aura MLS observations, J. Geophys. Res., 113, D05301, doi:10.1029/2007JD008678.
1. Introduction
[2] Annual cycle variations exhibited by lower strato-
spheric water vapor (i.e., the tape recorder) are a result of
tropical isolation, the mean Brewer-Dobson circulation
(BDC) upwelling and tropopause variations in temperature
during the annual cycle [Mote et al., 1996, 1998]. The
isolation and upwelling of the tropical lower stratosphere
are also evident in higher tropical mixing ratios of N2O and
CH4, and lower tropical amounts of inorganic chlorine,
compared to extratropical latitudes. Measurements of SF6
and CO2 show that tropical lower stratospheric air is
significantly younger than extra-tropical air [Waugh and
Hall, 2002], which also indicates the isolation of that
region.
[3] In the water vapor tape recorder, seasonal changes in
tropical tropopause water vapor mixing ratio rise nearly
unperturbed through the lower stratosphere to from 20–
30 km. Any trace gas that has seasonal variations in its
mixing ratio at the tropical tropopause and has a lifetime
greater than months in the lower stratosphere should pro-
duce a tape recorder signal as the variations are carried
upward by the tropical upwelling. For example, CO, which
seasonally varies at the tropical tropopause due to biomass
burning, also produces a tape recorder signal [Schoeberl et
al., 2006]. A tape recorder signal is also evident in HCN,
which is occasionally enhanced by biomass burning
[H. Pumphrey, personal communication, 2006] and CO2
[Andrews et al., 1999]. The tropical upwelling of the BDC
is driven by the dissipation of extratropical planetary waves
in the mid-stratosphere through the downward control
principal [Haynes et al., 1991] and may vary in magnitude
during the season and from year to year.
[4] The dynamical isolation of the tropics also makes the
tropical quasi-biennial oscillation (QBO) possible [e.g.,
Dunkerton, 1991]. The QBO consists of alternate East-West
direction stratospheric winds descending from about 30 km
to the tropopause with a period of about 26–27 months [see
review by Baldwin et al., 2001]. The QBO is confined to the
tropics although the oscillation induces secondary circula-
tions in the extratropics and affects the extra-tropical lat-
itudes through changes in planetary wave ducting. A
description of the QBO, its tropical and extratropical effects,
and the theory of the QBO are reviewed by Baldwin et al.
op. cit. The secondary circulation associated with the QBO
is superimposed upon the BDC. The QBO secondary
circulation consists of an increase in the upwelling during
the easterly shear phase and a suppression of the upwelling
during the westerly phase [Plumb and Bell, 1982]. At the
peak of the easterly circulation, the QBO secondary circu-
lation is divergent with air flowing away from the equator.
This flow reverses at the peak of the westerly circulation.
[5] The QBO and Brewer-Dobson circulations modified
the constituent distributions in the tropical stratosphere. The
QBO, for instance, is clearly evident in tropical ozonesonde
data [Logan et al., 2003 and references therein] as well as
satellite aerosol data [Trepte and Hitchman, 1992; Grant et
al., 1996] and satellite trace gas data [Hasebe, 1994;
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113, D05301, doi:10.1029/2007JD008678, 2008
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1NASA Goddard Space Flight Center, Greenbelt, Maryland, USA.
2University of Maryland Baltimore County, Baltimore, Maryland, USA.
3NASA Jet Propulsion Laboratory, Pasadena, California, USA.
4School of GeoSciences, The University of Edinburgh, Edinburgh, UK.
Copyright 2008 by the American Geophysical Union.
0148-0227/08/2007JD008678$09.00
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Hollandsworth et al., 1995; Randel and Wu, 1996; Schoeberl
et al., 1997; Randel et al., 1998].
[6] A good portion of the Halogen Occultation Experiment
(HALOE) trace gas data record has been analyzed for trace
gas fluctuations by Dunkerton [2001] (hereafter D2001).
D2001 used rotated principal component analysis to extract
QBO, semi-annual, annual and subbiennial components for
ozone, CH4, and H2O. The subbiennial components are
evidently due to non-linear interactions between the annual
cycle and the QBO. D2001 showed that the subtropical
anomalies were larger in the Northern Hemisphere, and he
was also able to reproduce the trace gas variations using
standard harmonics combined with a decadal variation.
D2001 was also able to identify the seasonal synchronization
of the annual cycle with the QBO in the trace gas data.
[7] In this paper we analyze 11 years of tropical HALOE
trace gas distributions from 1994–2005) of observations
from the aboard the UARS satellite and two years of Earth
Observing System Microwave Limb Sounder (MLS) data
aboard the Aura satellite. We extend the analysis of D2001
to include HCl and HF, and add CO and N2O from MLS.
[8] The MLS and HALOE instruments make measure-
ments in quite different ways: HALOE is an infrared solar
occultation instrument and MLS is a microwave limb
sounder. MLS makes measurements about every 1.5
in
latitude with fourteen passes across the equator each day.
HALOE made tropical measurements only a few times a
month. Between the two instruments, O3, H2O and HCl
were common measurements. HALOE also measured CH4
and HF as well as nitrogen radicals and aerosols. MLS also
measures N2O, CO and other trace gases.
[9] Our goal is to quantify and explain the annual and
QBO variations in the satellite trace gas measurements. We
are extending the D2001 analysis over a longer record using
a single value decomposition analysis employing standard
harmonics.
2. Analysis of the Trace Gas Data
[10] First, zonal monthly mean v19 HALOE [Russell et
al., 1993] and v1.5 MLS [Waters et al., 2006] data sets are
constructed. In the case of HALOE, the data are binned into
5
latitude zones; 2
latitude zones are used for MLS.
Where occasional missing data occurs in the monthly mean
time series, temporal linear interpolation from earlier and
subsequent data is used to fill the gap. We avoid the pre-
1993 HALOE data because of retrieval problems associated
with the dense Pinatubo stratospheric aerosols. The MLS
data sequence is from September 2004–December 2006,
barely encompassing a single QBO cycle.
[11] To perform the analysis, the data is reformed into a
time series for each latitude and altitude grid point. A least
squares fit is performed to a linear trend combined with
annual, semi-annual, and QBO harmonics. Following
D2001 and Randel and Wu [1996], the data are least squares
fit to a set of functions that includes a linear trend and
annual, semi-annual and QBO harmonics. Singular value
decomposition (SVD) is used derive coefficients. This
approach allows us to explain nearly all the variance in
the tropical trace gas data. Although the QBO can vary in
frequency, we assume a fixed frequency of 25.2 months for
HALOE and 28 months for MLS (due to the shorter data
record). The period is determined from a Fourier transform
power spectral analysis of the QBO wind field over the
period. For the HALOE data set, the discrete Fourier
transform periods near the standard QBO period of 26–
Figure 1. The equatorial water vapor anomalies from HALOE data (top). Water vapor field from the
SVD fit (bottom). Singapore winds (m/s) are over-plotted on the figure.
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27 months are 30, 25.2 and 21 months. Nearly all the
spectral power shows up in the 25.2 month period.
[12] The components of the SVD fit are checked for
statistical significance. As each new function (annual,
QBO, etc.) was added to the fit, an F test was used to
determine whether the new fit was a statistically significant
improvement over the previous fit in terms of reducing the
residual variance [see, for example, Mandel, 1964]. Using
the null hypothesis that the new fit made no difference, and
assuming that the grid points are mutually independent, the
95% significance level was used in determining the thresh-
old value for the F statistic above which the null hypothesis
was rejected. Although the grid points are not actually
independent of each other, the results may be taken as a
rough indication of where the signals are likely to be
meaningful.
[13] Because of the short time record of the MLS data,
some of the biennial inter-annual variation will show up as a
QBO signal. This is most evident at midlatitudes so we will
concentrate most of our discussion on the annual and QBO
signal in the tropics.
2.1. Annual and QBO Cycles in the HALOE and
MLS Constituent Data
[14] Trace gas variations in the stratosphere between the
tropopause and
35 km fall into two types: those strongly
synchronized with the zonal mean circulation at the altitude
of the fluctuation (whether that zonal mean circulation is
driven by the BDC or by the QBO) and those whose
fluctuations can be traced back to BDC changes at the
tropopause. Ozone, for example, falls into the first category
and H2O, the second. CO appears to be a mixed type.
[15] We begin our analysis by examining the trace gas
fluctuations themselves. In the section below, we restrict our
analysis to the trace gases H2O, O3, HCl and CO. The first
three are common to both HALOE and MLS. Other tracers,
HF and CH4 for HALOE, and N2O for MLS are discussed
in Appendix A.
[16] In our analysis, we report the amplitude and phase of
the annual oscillation (AnO) and the QBO. The phases are
reported relative to the beginning of the analysis. For
HALOE this is January 1993; for MLS this is September
2004.
2.2. Water Vapor
[17] Figure 1 shows the HALOE water vapor anomalies
(top) data and the SVD fit reconstruction (bottom). Upward-
progressing annual variations in water vapor are clearly
evident. This is the water vapor ‘‘tape recorder.’’ The tape
recorder signal was first identified in UARS MLS and
HALOE water vapor data by Mote et al. [1996]. Also
evident in the figure is the decrease in water vapor in the
later years [Randel et al., 2006]. The fit shown in the bottom
panel of the figure reasonably captures the interannual and
long-term variability of water vapor. Simulation of the
secular decrease in tropical water vapor required additional
long-term components to the SVD fit in addition to the
linear trend in order to reduce the variance.
[18] Figure 2 shows the mean HALOE H2O field along
with the annual and QBO component amplitudes and
Figure 2. Top, zonal mean, time mean water vapor from 13 years of HALOE data. Bottom left,
amplitude and phase of the annual oscillation (AnO). Bottom right, amplitude and phase of the QBO
oscillation. Phase measured from the beginning of the analysis period, January 1993 so decreasing phase
with altitude indicate upward propagating signals. Cross hatching indicates regions where the 95%
confidence limit is not met.
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phases. The mean field shows a drier zone near the top of
the tropical tropopause that extends southward and down-
ward as noted by Rosenlof et al. [1997]. The annual
oscillation (AnO) shows the coherent regular phase varia-
tion with altitude characteristic of the tape recorder. In this
convention, the upward propagating signal will show a
phase decrease with altitude.
[19] At low altitudes, the amplitude of the annual signal is
stronger north of the equator, which is not surprising since
the wet phase of the tape recorder is strongly forced by the
Figure 3. Equatorial EOS MLS water vapor anomalies as in Figure 1.
Figure 4. Same as Figure 2 for MLS H2O.
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Himalayan monsoon [Dunkerton, 1995; Randel et al., 2001;
Gettelman et al., 2004]. Figure 2 also shows that there is a
weak QBO water vapor signal mostly at upper levels. The
QBO signal is also evident in Figure 1 where a modulation
in the tape recorder occurs when the QBO shear zones
descend across the water vapor anomalies in 2000 and 2003
near 20 km. As found by D2001, the amplitude of the signal
is higher in the Northern Hemisphere. Note that the phase
also decreases with altitude although the QBO descends. As
will be shown below, the phase of tracers anomalies is also
determined by the mean gradient of the anomaly field.
[20] Figure 3 shows the water vapor anomalies from EOS
MLS for the period September 2004–December 2006. As
with the HALOE data, the fitting procedure does a good job
reproducing the data. Figure 4 shows the results for the
analysis of 28 months of MLS observations. The mean field
is generally similar although MLS water vapor mixing
ratios are slightly higher; preliminary validation shows that
MLS water vapor is about 10–15% higher than HALOE
[Froidevaux et al., 2006]. We also note that the low tropical
MLS water vapor field is significantly narrower in latitude
than the HALOE field. By selecting shorter periods of
HALOE data analysis, we can reproduce the narrower field
in the MLS data (not shown). Thus it is the 13 years of inter-
annual variation in the location of the tropical stratospheric
dry zone that produces the wider tropical average in
HALOE.
[21] The MLS annual amplitude and phase (Figure 4) are
similar to HALOE results (Figure 2) including a slight shift
in amplitude toward the Northern Hemisphere (NH) in the
lower stratosphere and a bend in the amplitude toward the
south near 26 km. The QBO amplitude and phase are also
similar, although the magnitude is larger consistent with a
sharper vertical and horizontal gradient in the MLS H2O
mixing ratio.
2.3. Ozone
[22] The ozone QBO has been previously identified in the
column measurements [Bowman, 1989; Hollandsworth et
al., 1995; Randel and Wu, 1996] and in profile measure-
ments from Stratospheric Aerosol and Gas Experiment II
(SAGE II) data [Zawodny and McCormick,1991; Hasebe,
1994; Randel and Wu, 1996], HALOE data (D2001) and
ozonesonde data [Logan et al., 2003].
[23] Figure 5 shows our results for HALOE ozone, we
now also show the percent amplitude relative the mean
value to bring out the structure in the UTLS. The QBO
signal peaks near 24–26 km as noted by D2001 and is
remarkably symmetric about the equator. This symmetry
can be explained as follows: the QBO secondary circulation
vertical motion field has its peak amplitude at the equator,
and this vertical motion field acting on the mean gradient
produces the structure in Figure 5 bottom right. The lack of
a meridional gradient in the mean ozone field suppresses
any contribution by off-equatorial QBO that result from
QBO meridional secondary circulation.
[24] The tropical annual oscillation in ozone is only
statistically significant below 20 km and above 30 km and
the amplitude is quite high relative to the mean in the lower
tropical stratosphere (see percentage plot, Figure 5 lower
left). As noted by Randel et al. [2007], the annual oscilla-
tion in lower stratospheric ozone is due to the annual
variation of the BDC acting on the mean ozone vertical
gradient. Outside of the tropics near 30 km, the annual
oscillation is strong and is probably driven by annual
variations in the residual circulation (the meridional and
Figure 5. Same as Figure 2 for HALOE O3. except lower figure s show changes in % rather than
mixing ratio.
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vertical advective components of the BDC) as indicated by
weak phase shift between the tropical lower stratosphere
region and the northern midlatitude region.
[25] Figure 6 shows the analysis for MLS ozone which
should be compared to Figure 5. The picture from MLS
generally confirms the picture from HALOE, but there are
several differences worth noting. The peak in the MLS
QBO signal is stronger and is near 27 km, about two km
higher than HALOE. We also see clear secondary peaks in
the QBO in the subtropics above 30 km where the merid-
ional ozone gradient is larger (see D2001).
[26] In the MLS AnO field a signature from 5
N near
24 km connects to a stronger feature at 30 km and 30
N also
seen in the HALOE data. Again, the lack of phase differ-
ence with the tropopause region suggests that this AnO
feature is connected to the extratropical BDC. The increase
in AnO amplitude with altitude at the equator is consistent
with the increase in the ozone vertical gradient with
increasing altitude. Both HALOE and MLS show (in the
percentage plots) strong annual amplitude structure in the
tropical upper troposphere peaking at about 8–12
N, roughly
the mean position of the ITCZ.
2.4. HCl
[27] HCl forms from the reaction of Cl with CH4 follow-
ing photolysis of chlorine-containing halogens (e.g., chlor-
ofluorocarbons) rising in the tropical stratosphere. Surface
observations of the dominant long-lived chlorine species
show very weak annual variations (e.g., WMO, 2007).
Because production of HCl increases slowly with height,
HCl has a weak vertical gradient and will have very small
annual variations at the tropical tropopause.
[28] Figure 7 shows our analysis of the HALOE HCl data.
The AnO signal is very weak but detectable in the lower
tropical stratosphere where the HCl mixing ratio is low. The
tropical stratospheric AnO signal can only form because of
annual variations in the vertical velocity in the lower
stratosphere. This kind of variation will not produce a phase
shift with altitude, in contrast to the water vapor case.
[29] Stronger extratropical AnO signals exist where the
meridional gradient in HCl is large and these signals
presumably arise due to the effect of the BDC acting on
the horizontal gradient. The low HCl zonal mean tropical
upward bulge moves from side to side with the seasonal
cycle. This would produce the two peaks in the AnO
amplitude, one on either side of the equator.
[30] The QBO signal in HCl has a peak at the equator just
above 30 km with an extension into the NH and a smaller
secondary peak in the SH. The off-equator signals may be
due to the meridional circulation associated with the QBO
acting on the time mean meridional gradient of HCl or it
may be the effect of the QBO on midlatitude planetary wave
breaking and meridional mixing of HCl.
[31] Figure 8 shows the MLS HCl results. MLS HCl is
10–15% higher than HALOE HCl [Froidevaux et al., 2006]
on average. In addition to this offset, MLS HCl shows a
narrower tropical bulge compared to HALOE (also see
Figures 2 and 4 for H2O). This means the meridional
gradients in HCl are larger and the subsequent AnO and
QBO signals driven by meridional advection and mixing
will be larger. The best example of this effect is the peak in
the HCl QBO signal near 20
N at 25 km that is clearly seen
in the MLS data (Figure 8) but is nearly absent in the
HALOE data (Figure 7). Looking at the mean fields in both
figures, there a sharp meridional gradient in HCl in the
MLS data at this altitude and latitude that, in the HALOE
data, is much weaker. A similar feature is seen in the
Figure 6. Same as Figure 5 except for MLS O3.
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Southern hemisphere near 30 km and 20
S. In general,
however, most of the features seen in the HALOE HCL
have corresponding features in the MLS HCL.
2.5. MLS CO
[32] CO has a chemical lifetime of only a few months in
the stratosphere due to reaction with OH [Schoeberl et al.,
2006]. The tropospheric source is primarily biomass and
fossil fuel burning. Figure 9 shows the analysis of MLS CO.
MLS CO has a positive bias in the lower stratosphere
compared to other CO measurements [Froidevaux, L. et
al., 2006]. Because of the weak horizontal and vertical
gradients above 20 km, the tropical QBO signal is not
Figure 7. Same as Figure 5 for HALOE HCl.
Figure 8. Same as Figure 7 for MLS HCl.
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present. More interesting is the annual cycle. The increase
in amplitude of the AnO between 18 and 20 km is due to the
annual variation in the strength of the Brewer-Dobson
circulation acting on the strong vertical gradient in CO in
the UTLS [Randel et al., 2007]. However, the tape recorder
signal is still evident as the regular phase shift in the CO
AnO with altitude between 18 and 22 km [Schoeberl et al.,
2006].
[33] Comparing Figure 6 with Figure 9 we note that the
ozone and CO signals at 18 km are
180
out of phase.
Folkins et al. [2006] argued that the anti-correlation of
UTLS CO and ozone was due to convection. In their model,
convection brings up high CO amounts and low boundary
layer ozone so the two are anti-correlated. Randel et al.
[2007] pointed out that annual variation in the strength of
the BDC produces the same effect because the vertical
gradients in ozone and CO are opposite. They were able
to reproduce the observed variations using the residual
vertical velocity acting on the mean gradient. The existence
of the AnO maximum in CO between 18 and 20 km argues
for the Randel et al. [2007] mechanism. The Folkins et al.
[2006] mechanism should produce a CO peak at lower
altitudes than is seen and an amplitude that decreases with
height following decreasing convective detrainment with
altitude.
3. The Dynamics of Tape Recorder and the QBO
Trace Gas Perturbations
[34] In this section we lay out the dynamical mechanisms
behind the variations in trace gases due to the QBO and
Brewer Dobson circulation. If m is the volume mixing ratio
of a trace gas then to first order [Mote et al., 1998],
@m
@t
þ w* @m
@z
þ v* @m
@y
¼ S  Lþ K @
2m
@y2
ð1Þ
where K parameterizes the meridional eddy mixing from the
extratropics and v* and w* are the zonal residual meridional
and vertical velocities, respectively. The overbar represents
zonal mean, t is time, z is the log-pressure height, y is the
meridional distance, S is the chemical source and L is the
chemical loss rate. The vertical residual velocity is
approximated as w* = Q/Qz, where Q is the isentropic
diabatic heating rate and Qz is the potential temperature
vertical gradient. We neglect vertical diffusion by breaking
gravity waves as this is not very important in the lower
stratosphere.
[35] Now we consider a periodic trace gas variation
driven by advection and source terms and linearize around
the QBO or AnO frequency neglecting the eddy mixing
from the tropics to midlatitudes which is small [Mote et al.,
1998]
isjmj þ w*j
@hmi
@z
þ hw*i
@mj
@z
þ v*j
@hmi
@y
þ hv*i
@mj
@y
¼ Sj  amj þ Kj
@2hmi
@y2
þ hKi
@2mj
@y2
ð2Þ
where the subscript j indicates a periodic variation such as
the QBO (Q) or AnO (A). The j subscripted variables are

exp(isjt) and the other variables with h i are time
Figure 9. Same as Figure 4 for MLS CO.
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averaged. We have assumed that chemical production and
loss can be linearized around a mean state. Chemical loss
rate perturbations relax to the mean state with a time
constant 1/a where a is the chemical loss rate, s is the
frequency.
[36] In the simplest AnO case, we assume that the sources
and sinks are zero, the mean vertical gradients and all the
meridional gradients are zero. In this case, the 1st and 3rd
terms on the LHS of (2) are in balance. If hw*i is constant
with altitude, the dispersion equation is lz = 2p hw*i/sA
where lz is the vertical wavelength and is sA is the
frequency. This is the tape recorder case and the mixing
ratio mA = mT exp (isAt + i2pz/lz) is determined by the
tropopause forcing (mT). The phase (2pz/lz) changes with
altitude as is seen in the tape recorder. Mote et al. [1998]
included the extra-tropical mixing term in (2) (hKi @
2mj
@y2 ) and
used the amplitude of the tape recorder signal to diagnose
K. Consistent with earlier studies of the QBO [e.g., Schoeberl
et al., 1997] they found that K was very small in the lower
stratosphere. At 22 km the mixing timescale was 80 months.
Above 26 km, however, the mixing timescale was estimated
to be less than 20 months. We note that the effect of time
mean mixing can be incorporated into a, that is a =
achemistry + hKiL2 where L is the meridional length scale
of the tropical perturbation. We neglect the annual and QBO
variations in K(Kj) which are likely smaller than hKi.
[37] In the case discussed by Randel et al. [2007] the
annual variation of the Brewer-Dobson circulation drives
the annual fluctuations in ozone and CO near the tropo-
pause. For that situation w*A
@hmi
@z


hw*i @mA@z


, so the
LHS 1st and 2nd terms of (2) are dominant. K is assumed
zero. Thus mA = iwA
*
sA
@hmi
@z which is equivalent to equation (4)
in Randel op cit. Note that the phase variation with altitude
is dictated by wA*, and that the mixing ratio response will be
90
degrees out of phase with wA*. This solution suggests
there will be no apparent upward phase propagation as seen
with the tape recorder.
[38] These two extreme cases explain the two different
kinds of equatorial phase variation with altitude associated
with the AnO seen in H2O, CO, O3 and HCl above as well
as N2O, HF shown in the Appendix. In the case of O3, N2O,
HF and HCl we see almost no AnO phase shift with altitude
in the very lowest part of the tropical stratosphere. These
annual variations are thus driven by the BDC’s annual
variations. In the case of H2O, a strong phase propagation
signal with altitude shows that the AnO in the tropopause
forcing is providing a signal that is simply carried upward.
CO is a mixed case with no phase shift below
18–20 km
and a phase shift above suggesting a strong Brewer-Dobson
component of the annual cycle below 18–20 km with a
standard tape-recorder signal above. In the case of CO, it is
the very rapid reduction of the vertical gradient with altitude
that allows CO to shift behavior from BDC forcing to a tape
recorder signal.
Figure 10. Residual circulation, w*, from UKMO analysis. Upper figure, time mean component, lower
left, annual oscillation, lower right, QBO component. White lines show phase.
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[39] An alternative approach to showing the Brewer-
Dobson and advective effects is to reform the equations as
a Lagrangian transport system. Equation (2) can be rewritten
as
d mA
dt
¼ SA  amA  w*A
@hmi
@z
þ v*A
@hmi
@y
 
ð3Þ
where the total derivative dmA/dt is the Lagrangian residual
tendency, it has the mean advection terms (3rd and 5th in
equation (2)) folded together with the partial time
derivative. The Brewer-Dobson forcing can now be seen
as a kind of ‘‘chemical source/sink’’ term.
[40] Parcels move upward since w* > 0. In the case of
CO, CO decreases with altitude so the 3rd term on the RHS
of (3) term will increase mA as seen between 16 and 18 km
in Figure 9. For the case of water vapor near the tropopause,
(3) shows how changes in the mean temperature processes
can affect the tape recorder signal since w*A
TA through
the diabatic heating term and SA
TA through the Clausius-
Clapeyron equation.
4. Mean, Annual and QBO Transport Fields
[41] Using diabatic heating rates and assimilated temper-
atures, we can compute w*. The heating rate is adjusted so
that the global integral of w* is zero at each pressure level
for mass continuity. For the HALOE period we use the
United Kingdom Meteorological Office (UKMO) meteoro-
logical fields [Swinbank and O’Niell, 1994; Randel et al.,
2004]. Heating rates for these fields are computed off-line
as described by Rosenfield et al. [1994]. For the MLS
period we use GEOS-4 assimilated meteorological fields
[Bloom et al., 2005]. The w* mean, annual cycles, and QBO
amplitudes and phases for 1993–2005 (UKMO) and 2003–
2006 (GEOS-4) are calculated using the same SVD analy-
sis. The results are shown in Figures 10 and 11, respectively.
[42] Randel et al. [2004] have analyzed the stratospheric
climatologies of several assimilation systems. Among other
things, they looked at the mean tropical biases and model
representation of the stratospheric QBO and semi-annual
oscillations. The UKMO (called METO in their study) mean
tropical 100 hPa temperatures are systematically
2 K
warmer than ERA-40 temperatures (ERA-40 is comparable
to GEOS-4). This would put ERA-40 further from radiative
equilibrium and increase the tropopause diabatic heating,
which would increase w* in ERA-40 compared to UKMO.
In other words, a colder tropopause will cause increased
diabatic heating and increased diabatic uplift. This is
consistent with the differences in the mean fields shown
in Figures 10 and 11.
[43] Comparison of the UKMO and ERA-40 assimilation
QBO wind fields by Randel et al. [2004] show that UKMO
zonal winds are roughly 20–30% weaker than the observed
Singapore winds. The ERA-40 winds show almost no bias
compared to observations below 30 km. From the equatorial
thermal wind equation, the wind bias between the two
assimilation systems should propagate into the estimate of
Figure 11. Same as Figure 10 except for GEOS-4 assimilation White lines show phase.
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the QBO thermal field and the residual circulation. The
differences between the assimilation systems would explain
some of the differences in QBO w* fields shown in
Figures 10 and 11.
[44] The time mean hw*i field is the driver for the tape
recorder signal. Figures 10 and 11 show broad regions of
upwelling from roughly 30
N to 30
S. The upwelling
decreases with altitude near 25 km in the UKMO analysis
and 18–20 km in the GEOS-4 analysis. These analyses
suggest that there should be a widening of the tape recorder
phase above 20 km as the BDC weakens. Such widening is
evident in Figure 2 near 24 km.
[45] Figures 10 and 11 also show that the tropical annual
cycle in the residual circulation is strongest near the
tropopause, decreasing with altitude. The QBO residual
circulation is strongest in the GEOS 4 analysis and the
tropical phase structure is clearly visible in Figure 11. Note
that the QBO phase increases with altitude indicating a
descending oscillation.
5. Linkage Between the Mean Fields and the
Trace Gas Oscillations
[46] A simple way to link the changes in trace gases with
the circulation is to plot the correlation between the trace
gas perturbation field lagged with the residual circulation.
[47] It is straightforward to show using the thermal wind
equation that TQBO is correlated with the vertical wind shear
[see Andrews et al., 1987; Baldwin et al., 2001]. Since the
diabatic heating rate will be anticorrelated with TQBO, it
follows from (2) that
mQBO

@uQBO
@z
@hmi
@z
= aþ i sQBO þ hw*ig



ð4Þ
where g is the vertical wave number of the QBO
perturbation. Since the chemical time constant for ozone
(a) in the lower stratosphere is faster than the other terms in
the denominator (
1 month at these altitudes, Brasseur and
Solomon, 1986), the ozone perturbations should be highly
correlated with the QBO vertical wind shear. This is seen in
Figure 12. We also expect that the correlation coefficient
would be slightly out of phase from exact synchronization
with the wind shear due to the inertial terms in the
denominator of (4) and that the correlation would begin to
reverse when ozone mean vertical gradient begins to
weaken (Figure 6) as is also seen in Figure 12.
[48] In the above example, correlation of the trace gas
with the zonal wind shear is essentially a filter that passes
the QBO component of w*; however, using the w* analysis
fields themselves (Figures 10 and 11) we can look at the
correlations in general. Figure 13 shows three correlations,
HALOE O3, H2O, HCl.
[49] Figure 13a shows that ozone is strongly anticorre-
lated with UKMO w* with almost no phase lag. Because
ozone increases with altitude, upward motion fluctuations
will produce lower ozone amounts hence the strong anti-
correlation. It is important to remember that w* includes the
velocity perturbations associated with seasonal BDC and
the QBO. Because of the rapid chemical relaxation time
ozone, the perturbations generated by the vertical motion
field and ozone tend to stay in synchronization, in other
words to first order mj
w*j
@hmi
@z /aj. The slight phase lag is
due to the inertial terms included in (4) that become more
important at lower altitudes where the ozone time constant
becomes longer than a month. (Note that in Figure 12, the
ozone shows a phase lead because w*QBO
 @uQBO@z .)
Ozone shows secondary correlation peaks at ±6 months at
16 km moving to ±12 months peaks near 25 km. The lowest
correlation peak is due to annual cycle synchronization;
ozone fluctuations anticorrelated with the annual cycle will
be correlated with that same cycle 6 months later. Higher up
we are seeing the correlation with the QBO cycle; ozone is
anticorrelated with the QBO w* field but will become
correlated a cycle later,
12 months.
Figure 12. Lag correlation between the vertical wind shear and the ozone perturbation field.
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Figure 13. Part a, lag correlation of equatorial HALOE ozone with UKMO w*, part b with H2O and
part c with HCl.
Figure 14. Part a, lag correlation of equatorial MLS ozone with GEOS-4 w*, part b with CO.
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[50] The correlation plot for water is quite different
(Figure 13b). The synchronization with w* is strong only
near the tropopause where water vapor fluctuations are
controlled by the BDC annual variations. The figure shows
that the correlation shifts with altitude as expected with the
tape recorder signal. The case of HCl shown in Figure 13c is
similar to that of ozone; we see a shift from annual control
near the tropopause, due to the mean vertical gradient in
HCl, to QBO control at 25 km.
[51] Figure 14 shows the correlation plots for MLS and the
w* field from GEOS-4. The ozone correlation (Figure 14a) is
very similar to that produced from the HALOE analysis
(Figure 13a), providing a check on that analysis. Figure 14b
shows the analysis for CO. As discussed above, the figure
Figure A1. Same as Figure 2 except for HALOE HF.
Figure A2. Same as Figure 2 for HALOE CH4.
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shows that CO is strongly synchronized with the annual
variation in the BDC below 20 km (note the maximum with
zero phase lag and two minimum near ±6 months). The
correlation shifts above 20 km and a phase slight lag is
evident; this is the CO tape recorder [Schoeberl et al.,
2006]. Above 26 km CO becomes anticorrelated with w*
which is expected since the vertical gradient reverses at
25 km as seem in Figure 9.
[52] To make a more quantitative analysis of the lag
correlations we would need to use a full chemical transport
model because the chemical time constants are only esti-
mated here. Such an analysis would no doubt give more
insight into model behavior compared to observations.
6. Summary
[53] We have analyzed thirteen years of HALOE O3,
H2O, HF, HCl and CH4 measurements and 30 months of
EOS MLS O3, H2O, HCl, CO and N2O measurements for
QBO and AnO signals using a joint SVD fit to those cycles.
Our HALOE analysis is similar to that performed by D2001
over a shorter data record.
[54] Trace gas data from both instruments show AnO and
QBO signals. These signals are broadly consistent between
the instruments although there are small structural and mag-
nitude differences in the mean, annual and QBO fields. These
differences can probably be attributed to the differences in
the sensors and the different lengths of the time series.
[55] Using the equations of motion we note that when the
chemistry is weak and there is an annual variation in the
tracer field at the tropopause, then a ‘‘tape recorder’’ signal
will emerge. A tape recorder signal is characterized by
progressive phase variation with altitude driven by the time
mean w* field. The tape recorder signal is mostly indepen-
dent of the annual variations or QBO variations in the
vertical motion fields because they are weaker than the time
mean BDC – although the upward phase progression may
be perturbed by those variations. If the chemical time
constants are more rapid then the tracer variations tends to
be phase locked to the circulation (BDC + QBO). We
demonstrate this phase locking using lag correlation plots
between tracer fluctuations and @u/@z (which isolates the
QBO secondary circulation) and lag correlations between
the tracer and the w* field that includes both QBO circu-
lation and the annual BDC variations.
Appendix A
A1. Annual and QBO Cycles in the HALOE
Unique Constituent Data
A1.1. HALOE HF
[56] Like HCl, HF mainly originates from the photolysis
of CFC-11, 12, 113, HCFC-22, Halons 1211 and 1301 and
increases in altitude in the stratosphere.
[57] Figure A1 shows the results for HF. These HF results
show similar features to the HALOE HCl (see Figure 7). As
with HCl two peaks in the QBO signal are seen at 30 km
straddling the equator, and two extra tropical peaks in the
AnO signal are also seen. In the percentage plots, we also
see the tropical annual oscillation peak just north of the
equator that is also visible in the HCl measurements.
A1.2. HALOE CH4
[58] Figure A2 shows the HALOEmethane signal that was
also analyzed by D2001. Methane rises from the tropical
troposphere into the stratosphere where it reacts with OH, Cl,
and O(1D). Methane thus has the opposite meridional
gradient from HCl and HF, so we expect to see the same
pattern in amplitude for QBO and AnO features as HCl but
with opposite phase. Figure A2 shows that this is indeed the
Figure A3. Same as Figure 2 for MLS N2O.
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case – both NH and SH features visible in HF and HCl are
reproduced in CH4 with the phase shifted by
180
.
A1.3. MLS N2O
[59] Nitrous oxide, like methane, rises through the trop-
ical troposphere and is destroyed by a reaction with O(1D)
or photolysis. As with HALOE CH4, we expect that the
features shown will be quite similar to HCl, except the
phase of the AnO and QBO will be 180
off.
[60] Figure A3 displays the N2O signal (compare to MLS
HCl, Figure 8). As expected from the discussion above, the
overall features shown in Figure 8 are reproduced in
Figure A3 with slightly different amplitudes and nearly
180
phase shift. The differences in the amplitudes can be
attributed to the differences in the mean gradient between
HCl andN2O. At these altitudes and latitudes photochemistry
is not significant, with one exception. Note the increase in
amplitude in the HCl AnO in Figure 8 at the southern edge of
the plot. Even though N2O shows a weak feature near that
region, the HCl feature is stronger. The likely explanation is
the influence of the chemistry of the ozone hole on HCl. HCl
is drawn down during the formation of the ozone hole and
then rapidly increases afterward [Douglass et al., 1995;
Santee et al., 2005], which would increase the AnO signal.
[61] Acknowledgments. The first author acknowledges helpful dis-
cussions with W. Randel on the causes of CO variations at the tropopause.
The work was supported by NASA Earth Sciences Program.
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A. R. Douglass, P. A. Newman, and M. R. Schoeberl, NASA Goddard
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