QBO and QBO-annual Beat in the Tropical Total Column Ozone: A Twodimensional Model Simulation
X. Jiang, C. D. Camp, R. L. Shia, D. Noone, C. Walker, T. Schneider, and
Yuk L. Yunga
Division of Geological and Planetary Sciences
California Institute of Technology
Mail Stop 150-21
Pasadena, CA 91125
Tel: (626) 395-6940
Fax: (626) 585-1917
yly@ gps.caltech.edu
a
To whom all correspondence should be addressed
Submitted to J. Geophys. Res. Sep. 21, 2003
1
Abstract
The NCEP/NCAR Reanalysis II data are used to calculate the monthly mean
meridional circulation from 1979 to 2002 by zonally averaging the three-dimensional
mass flux on isentropic surfaces. The isentropic stream function is interpolated back to
the pressure surfaces to drive the Caltech/JPL two-dimensional (2-D) chemistry and
transport model. The first two empirical orthogonal functions (EOFs) of the
deseasonalized and detrended stratospheric stream function capture 88% of the total
variance. The first EOF accounts for over 70% of the variance and is related to the quasibiennial oscillation (QBO) and QBO-annual beat signal in the meridional circulation. The
2-D model provides realistic simulations of the seasonal and interannual variability of
ozone in the tropics. The equatorial ozone anomaly from the 2-D model is close to that
derived from the Total Ozone Mapping Spectrometer (TOMS) and the Solar Backscatter
Ultraviolet (SBUV and SBUV/2) merged total ozone data sets. The phase and amplitude
of the QBO signal are well captured by the model. The QBO-annual beat signal found in
the simulated ozone agrees well with that in the observed data. Sensitivity tests are
conducted to test the mechanism that produces the QBO and QBO-annual beat signals in
the ozone data.
2
1. Introduction
The equatorial quasi-biennial oscillation (QBO) is known as the quasi-regular
alternation of the zonally symmetric easterly and westerly wind regimes with period
about 28 months (Veryand and Ebdon, 1961; Reed et al., 1961; Baldwin et al., 2001).
The meridional and seasonal distributions of stratospheric tracers imply that tropospheric
air ascends into the tropical stratosphere, and spreads poleward and downward from there
into the winter hemisphere (Brewer, 1949; Dobson, 1956). Although it has in the past
been common to regard this circulation as being ‘‘driven’’ by diabatic heating in the
tropics and diabatic cooling in middle and high winter latitudes, it has been recognized
that global-scale, axisymmetric circulations of this kind cannot exist without some kind
of drag acting on the flow. By reducing the angular momentum of the zonal flow, the
wave drag drives air poleward, a process described by Holton et al. (1995) as the
‘‘extratropical pump.’’
Superimposed on the mean motion is a circulation induced by the QBO. When the
QBO is in the westerly (easterly) phase, there is descending (upwelling) motion in the
equator stratosphere and upwelling (descending) motion in the subtropics stratosphere
(Plumb and Bell, 1982). There will be more (less) ozone in the equator in the westerly
(easterly) QBO phase (Tung and Yang, 1994a; Randel and Cobb, 1994).
The QBO-annual beat is the result of an interaction between QBO and annual
cycles. It is the difference and sum combination of the QBO frequency and the annual
cycle frequency. The periods of the QBO-annual beat are 20 months and 8.6 months.
These periods are found in the total column ozone data obtained by the Total Ozone
Mapping Spectrometer (TOMS) (Tung and Yang, 1994a). The QBO signal in the total
column ozone is obvious in both the tropics and extra-tropics (Tung and Yang, 1994b).
Using the equatorial wave forcing parameterization, Jones et al. (1998)
successfully generate a QBO with a period of about 28 months. The induced circulation
3
is stronger in the winter hemisphere. The modeled QBO induces a meridional circulation
that produces a QBO signal in ozone in the subtropics by advection of ozone out of the
topics. Further analysis of the Jones et al. (1998) model (Jones et al., 2003, manuscript in
preparation) reveals the existence of a QBO-annual beat signal at about 20 months.
However, the interannual variability of QBO and QBO-annual beat signals cannot be
simulated well by Jones model.
Camp et al. (2002) apply a principal component analysis to the TOMS/SBUV
merged ozone data set. The first four EOFs of their study capture over 94% of the
variance of the deseasonalized data. The leading two EOFs of their study display
structures attributable to the QBO, with influence from a decadal oscillation. The third
EOF (11% of the variance) represents the QBO-annual beat. The fourth EOF (4% of the
variance) is related to El Nino- Southern Oscillation.
Fleming et al. (2002) use the meteorological data from the United Kingdom
Meteorological Office (UKMO) and constituent data from the Upper Atmospheric
Research Satellite (UARS) to calculate yearly zonal mean dynamical fields to drive the
NASA/Goddard Space Flight Center (GSFC) two-dimensional (2-D) chemistry and
transport model. The model provides a good simulation of the interannual variability of
total column ozone. However, their model underestimates the QBO amplitudes at
equator.
In this study we use the NCEP/NCAR Reanalysis II 4-times daily spectral
coefficients data provided by the NOAA-CIRES Climate Diagnostics Center to calculate
the monthly mean meriodional circulations from 1979 to 2002 for use in the Caltech/JPL
two-dimensional (2-D) chemistry and transport model. The model results for total column
ozone agree well with the observations in the tropics. We apply the principal component
analysis to the ozone calculated from 2-D model. The model ozone result has significant
QBO and QBO-annual beat signals in it, which is consistent with those in TOMS/SBUV
merged total ozone data.
4
2. NCEP-derived transport fields
Stream function
NCEP Reanalysis II 4-times daily spectral coefficients are used to calculate the
monthly mean meridional circulations from 1979 to 2002, using the method of Johnson
(1989). Recently, the same method was used by Bartels (1998) to study the Ertel potential
vorticity flux in the upper troposphere and lower stratosphere. The spectral coefficients
are available on 28 sigma levels and with T62 (triangular wavenumber truncation at 62)
resolution in the horizontal (Kalnay et al., 1996; Kistler et al., 2001). On the pressure
surface, the three-dimensional (3-D) Eulerian mean mass flux, (i, j,k) , is determined by
 (i, j,k) 

P0
0
2 acos (i, j)
V (i, j,k)dp .
g
(1)
where a is the earth radius,  is the latitude, V is the meridional velocity, p is the
pressure, g is the gravitational acceleration rate, P0 is the surface pressure. Then we
interpolate the 3-D Eulerian mean mass flux to isentropic surfaces. The 2-D isentropic
mass stream function   ( j, k ) is calculated by zonal averaging of 3-D isentropic mass
flux,  (i, j,k) , along isentropes. Finally, we interpolate the 2-D isentropic mass stream
function   ( j, k ) to the pressure surface stream function, P ( j,k) , which is used to drive
the 2-D chemistry and transport model.
Figure 1 shows the 2-D isentropic mass stream function   ( j, k ) in the
stratosphere in January, April, July and October of 1985. Because there is net radiative
heating in low-latitudes and net radiative cooling in the high-latitudes of the winter
hemisphere in the lower stratosphere, there is upwelling mass flux in the tropical and
subtropical regions and down-welling mass flux in the high latitudes of the winter
hemisphere (Andrews et al., 1987). This circulation is important for the transportation of
ozone in the stratosphere. The seasonal variation is also captured well by this stream

function. The stream function is strong in the Northern Hemisphere (NH) in January,
when the temperature gradient and wave activity are strong. As a result more ozone can
be transported to the northern pole. The stream function becomes weak in the spring and

5
summer in the NH, when the temperature gradient and wave activity are weak. Less
ozone is transported to the northern pole in these seasons. In the fall the stream function
becomes strong again, and more there is more poleward transport of ozone. The
axisymmetric circulation verifies that the wave activity in the NH is stronger than that in
the Southern Hemisphere (SH).
No previous results for the isentropic mass stream function in the stratosphere
have been published. We can compare these results approximately with the mass stream
functions computed in the pressure coordinates (see, e.g., Fig. 2 in Shia et al., 1989).
There is general agreement in the shape of these stream functions. The annual mean flux
through the tropopause in the Shia et al. (1989) model is 9.3109 kg/s. The analogous
flux through the 400 K isentropic surface, which is close to the tropical tropopause, is
14109 kg/s. This value is in good agreement with the strength of the circulation that is
consistent with the 14C data.
In previous work, the diabatic meridional circulation is usually computed from the
net radiative heating rates using a diagnostic stream function model (see, e.g., Ko et al.,
1985). However, this method will underestimate the tropical total column ozone and
overestimate the column ozone in the extra-tropics (see, e.g., Fleming et al., 2002). In our
model, we adopt the isentropic stream function, which is a closer approximation to the
diabatic circulation than the residual mean meridional circulation.
Isentropic mixing coefficient K yy
It is known that in the lower stratosphere zonal mean transport mainly takes the
form of advection by the mean diabatic circulation in the meridional plane and eddy
mixing approximately along isentropic surfaces (Mahlman et al., 1984; Tung, 1984). The
isentropic mixing coefficient, K yy , can be related to the Eliassen-Palm flux divergence.
We calculate the K yy in the stratosphere from 1979 to 2002 using NCEP Reanalysis II
data. The isentropic mixing coefficient K yy is defined by (Yang and Tung, 1990)
6
K yy    P *V1* ( cos
Pˆ
).
y
(2)
where P 
f
is the Ertel potential vorticity, V1   V cos is the meridional mass flow

rate.   
1 p
denotes the density in the isentropic coordinates, where p and z are the
g z
pressure and height on the isentropic surfaces. y  a  sin  , where a is the earth radius, 
is the latitude. The over bar means zonal average, e.g., h 
1
2

2
0
hd and deviation
from the zonal mean is given by h*  h  hˆ , hˆ   h /  .
Figure 2 shows the K yy field in January, April, July and October of 1985. The K yy
values calculated from NCEP/NCAR reanalysis II data set are only from 15km to 35km.
All the K yy values above 35km and in the troposphere are from Fleming et al. (2002), and
do not change in different years. The values of K yy are large in the mid-latitude and on
the order of 1010 cm2 s-1. They are small in high latitudes and tropical regions and on the
order of 109 cm2 s-1. K yy is larger in the NH than in the SH, as a result of more wave
activity in the NH. There are negative K yy calculated from NCEP/NCAR Reanalysis II
data sets. This is due to the assumption that turbulence appears in the regions where the
zonally averaged PV gradient is negative (Kinnersley, 1996). All negative values of K yy
are set to zero.
3. Interannual Variability of the Stream function

In order to study the interannual variability of the pressure surface stream function

used to drive the 2-D model, we define a stream function anomaly in the following
manner. First the time series for each grid point is decomposed
 p (t)  A 0p  A1p t   ap (t)   'p (t) .
(3)
Where the first two terms constitute a linear trend, determined by a least squares fit. The

a
mean annual cycle,  p (t) , is determined by evaluating the mean value for each month
7
independently. To isolate the interannual variability from higher frequency oscillations, a
spectral filter is applied to the anomaly,  'p (t) . The filter is constructed as the
convolution of a step function with a Hanning window and chosen to obtain a full signal
from periods above 15 months and no signal from periods below 12.5 months. A
principal components analysis is then performed on the filtered stream function anomaly,
 (x ,t) . The details of the methodology are referred to Camp et al. (2003). The first three
empirical orthogonal functions (EOF) from this analysis, along with the associated
principal component (PC) time series and their power spectra, are shown in Figure 3 and
Figure 4. These three EOFs account for 95% of the total variance of the filtered stream
function anomaly.
The first EOF captures over 70% of the variance and represents an oscillation in
the strength of Brewer-Dobson circulation caused by the quasi-biennial oscillation
(QBO). During the westerly (easterly) phase of the QBO, the Brewer-Dobson circulation
is weakened (strengthened). The associated principal component time series, PC1, is
plotted against the inverted 30 mb QBO index (the zonal average of the 30mb zonal wind
at the equator as computed from the NCEP/NCAR Reanalysis) in Figure 4a. The power
spectrum of PC1, Figure 4b, shows the 28-month period characteristic of the QBO. A
secondary 20-month period oscillation is also evident. The modulation of the annual
cycle of the Brewer-Dobson circulation by the QBO results in the creation of two beat
oscillations with frequencies equal to the difference and sum of the QBO and annual
frequencies; i.e., at periods of 20 and 8.6 months. The spectral filtering destroys the
signal from the faster beat frequency. The QBO effect is distinctly asymmetric about the
equator; the amplitude of the oscillation in the north is stronger than that in the south by
more than a factor of three.
The second EOF, capturing about 18% of the variance, represents a smaller
oscillation in just the southern cell of the circulation. It oscillates with the 20-month
period characteristic of the QBO-annual beat. The pattern of the 20-month signal is a
linear combination of EOF1, containing the entire northern cell variability and some of
8
the southern cell variability, and EOF2, containing the remaining southern variability. In
Figure 4c, PC2 is shown against the constructed index for the QBO-annual beat.
The third EOF, capturing about 6% of the variance, represents an oscillation in
the height of the upwelling branch of the convection at the equator. Similar to PC1, the
time series is dominated by a 28-month period signal with a secondary 20-month period
signal. In Figure 4e, PC3 is shown along with the 30 mb QBO index.
4. Modeling of total column ozone in the tropics
The Caltech/JPL two-dimensional (2-D) chemistry and transport model (CTM) is
a zonally averaged model for trace species in the terrestrial troposphere and middle
atmosphere. See Shia et al. (1989) and Appendix A in Morgan et al. (2003) for details.
The model has 18 latitude boxes, equally spaced from pole to pole, and 40 layers, equally
spaced in log(p) from the surface to the upper boundary at 0.01 mbar. Transport in the
model is by the stream function and K yy calculated from NCEP Reanalysis II data sets.
The values for Kzz are taken from Summers et al. (1997). They are not important except
in the mesosphere. The model includes all the gas phase chemistry in the NASA
recommendations for stratospheric modeling (DeMore et al., 1997). There is no
heterogeneous chemistry. The numerical method used for solving continuity equation in
the model is the Prather scheme (Prather, 1986; Shia et al., 1990).
To understand the interannual variability of ozone, we calculate the total column
ozone from 1979 to 2002. The climatology of total column ozone in these 24 years from
TOMS/SBUV merged total ozone data sets and 2-D chemistry model are compared in
Figure 5. The model simulates the total column ozone well. More ozone is transported to
the polar region by the strong meridional circulation in winter hemisphere. Less ozone is
transported to the pole by the weaker circulation in the summer hemisphere. Because we
do not have the heterogeneous chemistry in the 2-D chemical model, thus there are some
differences in the Southern Hemisphere. In addition, the NCEP Reanalysis II meridional
9
wind field may not be realistic in the high latitudes of the Southern Hemisphere because
there are fewer radiosonde measurements.
The ozone anomaly is calculated by removing the monthly mean data from the
original total column ozone. The latitudinal distribution of the anomaly of the total
column ozone from 1979 to 2002 is plotted in the Figure 6. The 2-D CTM reproduces the
seasonal and interannual variability of TOMS/SBUV merged total ozone data well. There
is an obvious QBO signal of the ozone from 2-D chemistry model at equator, it begins to
transport to the high latitude in the winter and spring seasons
Figure 7 shows the equatorial detrended total column ozone anomaly from 1979
to 2002. The linear trend is removed from the ozone anomaly by a least squares fit. The
solid line is the detrended TOMS/SBUV merged total ozone anomaly. The dot line is the
detrended model ozone anomaly. The model ozone anomaly is close to the TOMS/SBUV
merged total ozone anomaly. The correlation coefficient of this two curve is 0.75; the
corresponding confidence level is 99.6%.
Fleming et al. (2002) first successfully calculated the residual mean meridional
stream function using data from UKMO GCM and UARS observations. Their results for
total column ozone are a good simulation of the TOMS/SBUV data from 1993 to 2000.
Our model can simulate the interannual variability of ozone from 1979 to 2002 better
than previous models. $$$ discuss Fleming/ not enough QBO/ too much/ scale down by
1.6
EOF results of total column ozone from 2-D model
A principle component analysis is applied to the detrended and deseasonalized
total column ozone anomaly from 2-D model. The first four EOFs capture over 96% of
the total variance as shown in Figure 8 and Figure 9. The first EOF captures 74% of the
variance, and displays structure attributable to the QBO. It is asymmetric about the
equator and oscillates about nodes at 15N and 19S. The values show range from a high of
10
11 Dobson units (DU) to a low of –5 DU. The associated principal component time
series, PC1, is plotted against the 30 mb QBO index in Figure 9a. The power spectrum of
PC1, Figure 9b, shows a strong peak at 28 months. Ozone is transported to the polar
region by the Brewer-Dobson circulation. During QBO westerly (easterly) phase, the
meridional circulation is weak (strong). Therefore the tropical total column ozone will
increase (decrease) while the opposite will occur at higher latitudes.
The second EOF, capturing 10.8% of the variance, is a tilted plane oscillating
about the node at equator. Values range from 3.5 DU in the north to –3.5 DU in the south.
In Figure 9c, PC2 is shown against the constructed index for the QBO-annual beat. The
power spectrum of the associated PC2 has a dominant peak at 20 months. It is the
interaction between the QBO and the annual cycle.
5. QBO-annual beat mechanism
To understand the mechanism for the QBO-annual beat, we enhance the signal of
the QBO in the stream function by three times. $$$ move to Fig 7b/ First, we use a linear
regression of QBO index on the stream function to calculate the QBO signal part. Then
we time the signal of the QBO by two times. We add it back to the original stream
function to drive our 2-D CTM.
The EOF patterns and PCs of the total column ozone are shown in Figure 10 and
Figure 11.
6. Conclusions
We have used a two-dimensional model to study the signals of QBO and QBOannual beat in ozone. The NCEP Reanalysis II dynamical fields are used to calculate the
monthly mean meridional circulation on isentropic surfaces from 1979 to 2002. The
11
isentropic stream function is interpolated to the pressure surface to drive the Caltech/JPL
two-dimensional (2-D) chemistry and transport model.
The 2-D model successfully simulates the seasonal and interannual variability of
ozone in the tropics. The phase and amplitude of the QBO signal in total column ozone in
the tropics are captured by the model. The model also simulates the QBO-annual beat
well. The first four EOFs of the detrended and deseasonalized total column ozone
anomaly from model capture over 96% of the total variance. The first EOF explains 74%
of the variance, and displays a structure attributable to the asymmetric QBO with a period
of 28 months. The second EOF, capturing 10.8% of the variance, is related to the QBOannual beat at 20 months. It is the interaction between the QBO and annual cycles. All of
these signals found in the model ozone are close to those in TOMS/SBUV merged total
data sets.
12
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Figure Captions
Figure 1: Stratospheric isentropic stream function in 1985. (a) January, (b) April, (c) July,
and (d) October. Units are 109 kg/s.
Figure 2: Isentropic mixing coefficient K yy in January 1985. (a) January, (b) April, (c)
July, and (d) October. Units are 109 cm2/s.
Figure 3: First three spatial EOF patterns of the stream function on the pressure surface.
Units are cm/s.
Figure 4: First three PCs of the stream function on the pressure surface. The first column
contains the associated PC timeseries (solid) along with an appropriate index (dotted);
PC1 and PC3: 30mb QBO index (inverted), PC2: constructed QBO-annual beat index
(see text). The second column contains the power spectra of the PC.
Figure 5: (a) Composite of TOMS/SBUV total column ozone from 1979 to 2002, (b)
Composite of total column ozone from 2-D model from 1979 to 2002.
Figure 6: Latitude distribution of ozone anomaly from (a) TOMS/SBUV merged total
ozone data set, (b) 2-D Caltech/JPL chemical and transport model.
Figure 7: Time series of equatorial detrended ozone anomaly from TOMS/SBUV merged
total data set (Sold line) and 2-D Caltech/JPL chemical and transport model ozone result
(Dot Line).
Figure 8: First two spatial EOF patterns of the total column ozone from 2-D model.
Figure 9: First two PCs of the total column ozone from 2-D model. The first column
contains the associated PC timeseries (solid) along with an appropriate index (dotted);
16
PC1: 30mb QBO index; PC2: constructed QBO-annual beat index. The second column
contains the power spectra of the PC.
Figure 10: First two spatial EOF patterns of the total column ozone from 2-D model.
QBO signal is enhanced by 3 times in the stream function.
Figure 11: First two PCs of the total column ozone from 2-D model. The first column
contains the associated PC timeseries (solid) along with an appropriate index (dotted);
PC1: 30mb QBO index; PC2: constructed QBO-annual beat index. The second column
contains the power spectra of the PC. QBO signal is enhanced by 3 times in the stream
function.
17
Figure 1
18
Figure 2
19
Figure 3
20
Figure 4
21
Figure 5
22
Figure 6
(a)
(b)
23
Figure 7
24
Figure 8
25
Figure 9
26
Figure 10
27
Figure 11
28