Model study of the influence of the solar cycle on the Quasi-Biennial Oscillation
period
Le Kuai1, Runlie Shia1, Xun Jiang2, Ka-Kit Tung3, Yuk L. Yung1
1 Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125
2 Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109
3 Department of Applied Mathematics, University of Washington, Seattle, WA 98195
* To whom all correspondence should be addressed. E-mail:
kl@gps.caltech.edu
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Abstract
During the 1960s to early 90s, the westerly phase of the Quasi-Biennial Oscillation (QBO) has
been observed to have longer periods during the solar-minima. This is also the time when the
stratosphere is contaminated by aerosols from major volcanic eruptions. For the two solar cycles
before and after this interval, the QBO period exhibits opposite behavior. To determine the true
dependence of the QBO period on the solar cycle in the absence of volcanic aerosols, we
performed an 82-year model simulation of the QBO using a two-and-a-half dimensional model.
Analysis of the model simulation indicates a positive correlation between the length of QBO
period and the solar flux. The easterly phase QBO duration increases more rapidly with solar
flux than that of the westerly phase above 30 hPa. Below 50 hPa the westerly QBO duration
increases faster than that of easterly QBO. The mechanism for these changes is discussed.
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1. Introduction:
The Quasi-Biennial Oscillation (QBO) is now understood to be an internal oscillation of the
equatorial stratosphere involving wave-mean flow interactions [e.g. Baldwin et al., 1999]. Its period
averages to about 28 months, but is known to have interannual variations of a few months about the
mean. The equatorial QBO is known to significantly affect the polar stratosphere during winter,
with the easterly phase QBO (e-QBO) creating the condition for a more perturbed and warmer polar
vortex [Holton and Tan, 1980, 1982].
Therefore, the variation of the QBO period takes on
additional significance, especially with respect to the timing of its phase relative to the northern
winter [Camp and Tung, 2007].
Using the radiosonde data from Free University of Berlin (FUB) near the equator at 45 hPa from
1956-1996, Salby and Callaghan [2000] found that the duration of the equatorial westerly phase
QBO (w-QBO) appeared to vary with the solar cycle (SC) and tended to be longer during the solar
minima (SC-min; SC-max correspond to solar maxima). By comparison, the e-QBO duration has
little variability. Soukharev and Hood [2001] extended the work of Salby and Callaghan [2000] by
using composite mean analysis on the FUB data at 50 to 10 hPa from 1957 to 1999. Their analysis
indicated that the duration of both QBO phases was longer during SC-min. Pascoe et al [2005]
examined the ERA-40 data set from 1958 to 2001 to study the solar modulation of the mean descent
rate of the shear zone. On average, it requires two more months for the easterly shear zone to
descend from 20 to 44 hPa under SC-min conditions. The w-QBO duration is increased (decreased)
under SC-min (SC-max) conditions. This relation broke down during the 1990s. On the other hand,
Hamilton [2002] and Fischer and Tung [2007] employed an even longer FUB dataset and both
found the opposite behavior in the 1950s, the late 1990s and 2000s.
Although there is anti-
correlation (correlation coefficient is -0.46) between the w-QBO duration at 50 hPa and the solar
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flux for the period 1956-96, Hamilton [2002] showed that the correlation coefficient is only -0.1
during the extended period 1950-2001.
Additionally, Fischer and Tung [2007] applied the
Continuous Wavelet Transform (CWT) to determine the QBO period at 50 hPa for the even longer
record of 1953-2005, and found that the correlation coefficient between the period of the QBO and a
solar cycle was zero. They showed the anti-correlation during the three cycles with SC-min at 1965,
1976 and 1986, confirming Salby and Callaghan [2000]. However, an in-phase relationship was
found starting around 1991 and prior to 1957. It should be mentioned that these later work did not
contradict the findings of the earlier authors. They merely pointed out that the behavior of the 60s,
70s, 80s and early 90s were the opposite to that of the other decades before and after this period.
The QBO period is influenced by the descent rate of the shear zone. Local heating due to
volcanic aerosols at the equator can temporarily induce an upwelling in the lower stratosphere that
can affect the descent rate of the easterly shear zone. At equilibrium the increase in temperature may
introduce a horizontal temperature gradient anomaly. By the thermal wind relationship, different
vertical shears in the zonal wind may be introduced above and below the region of heating, which
may affect the apparent descent of the QBO shear zone. In the decades of interest to the above QBO
studies, there were three major volcanic eruptions with aerosols forming in the equatorial
stratosphere, Agung in 1963, El Chichon in 1982 and Pinatubo in 1991. Due to the difference in
timing, location and height of the injection of the SO2, the effect on the QBO period may be different
after each eruption. Angell [1986] argued that the increase in westerly period after 1963 was due to
the Agung eruption, and pointed out that the temperature increase due to aerosol heating was seen at
50 and 30 hPa at the Balboa station (9.0N, 79.6W). The possibility exists that the inverse
relationship between the westerly QBO period in the lower stratosphere and the solar cycle flux from
1957 to 1991 may be compromised by volcanic aerosols. During the SC-min of 1997, when the
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volcanic aerosols from the eruption of Pinatubo had cleared, the QBO period reached a low value of
25 months. Since then, the period has increased as the solar cycle advanced from SC-min to SCmax [Fischer and Tung, 2007]. A few more decades without major volcanic interference are needed
to obtain a statistical significant correlation with the solar cycle.
We take another approach in this paper in an attempt to resolve the aforementioned conflicting
conclusions regarding the solar cycle modulation of the QBO. The next section described the model
and the sources of QBO and solar forcing used in the simulations. Section 3 presents the results on
how the QBO period and its easterly and westerly phase duration are modulated by solar forcing.
The conclusions and detailed discussion of the mechanism follows in the last section.
2. Model QBO and comparison with NCEP:
The THINAIR (Two and a Half dimensional INterActive Isentropic Research) model is a twoand-a-half-dimensional dynamics model.
It has zonally averaged dynamics plus three longest
planetary waves, which are prescribed from observations at the tropopause level. For this study, the
planetary wave forcing at the tropopause is fixed at 1.1 times of the 1979 year level, annually
periodic and repeated for all the years. The model uses isentropic vertical coordinate above 350 K.
Below 350 K a hybrid coordinate is used to avoid intersection of the coordinate layers with the
ground. The model version used in this study has 29 layers from the ground up to ~100 km for
dynamics and 17 layers from ground up to ~60 km for chemistry. The model has 19 horizontal grid
points evenly distributed from pole to pole. The QBO-source term in the momentum equation uses
parameterization of wave momentum fluxes from Kevin, Rossby-gravity and gravity waves
[Kinnersley and Pawson, 1996]. The model was run with perpetual solar minima or solar maxima.
Sensitivity studies are also carried out with many times the solar cycle forcing.
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The climatological behavior of the QBO in the THINAIR model at the equator for various
elevations in the lower stratosphere are showed in Supplemental Material Figure A1 and has
reported in other’s paper [Kinnersley and Pawson, 1996]. Figure 1a shows the e-QBO and the wQBO duration versus pressure from 10 to 50 hPa from the THINAIR model for SC-min condition. It
shows that higher up, near 10 hPa, the QBO period is dominated by its easterly phase. The e-QBO
duration decreases and the w-QBO duration increases until they are about equal near 50 hPa. The
QBO period changes little with height, as noted by Fischer and Tung [2007]. Figure 1 (b) shows the
corresponding behavior in the NCEP reanalysis and demonstrates that the model has the correct
behavior as compared to the observation. Similar behavior was reported by Fischer and Tung
[2007] using the FUB data. Not shown in this composite average is the behavior that during certain
years, the westerly phase of the QBO stalls below 30 hPa [Kinnersley and Pawson, 1996]. During
these years, the w-QBO duration can be twice as long as that of the e-QBO duration near 50 hPa
[Salby and Callaghan, 2000].
3. Solar cycle influence on QBO:
With the time dependent oscillatory solar forcing, measuring the QBO period is not
straightforward, since the period itself is changing with the solar cycle. A number of subjective and
objective methods have previously been used in the literature. However, with constant solar forcing,
the QBO period can be unambiguously determined using its Fourier spectrum. Therefore in this
paper we present the model result with constant solar forcing. We performed the run with the SCmin condition (the minimum value of the realistic solar oscillatory forcing is used for all the time
period), the SC-max condition (the maximum value of the realistic solar oscillatory forcing is used
for all the time period) and 2x, 3x the SC-max conditions.
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Figure 2 shows the 82-year time series of the QBO zonal wind at equator at 31 hPa at perpetual
SC–min condition (a), SC-max condition (b) and 3xSC-max condition (c). The Fourier spectra of
the zonal wind are shown in (d). The results review a QBO period of 25 months for the solar-min,
26 months for the solar-max and 29 months for the 3xSC-max conditions. Thus, the period of the
QBO is lengthened as the solar flux increases. Also seen in the Fourier spectra are the QBO-annual
beats, which result from the interaction of the QBO period with the annual cycle [Tung and Yang,
1994a, 1994b]. These periods also increase as the QBO periods increase.
Figures 3 (a) and (b) show the mean vertical-time cross section of the zonal wind for w-QBO for
3xSC-max and SC-min respective. The results are derived from composite analysis after applying
five-month running average to the data. The duration of the w-QBO phase is found to be longer in
the three-time SC-max conditions than that in the SC-min conditions. Figures 3 (c) and (d) show the
similar results for the e-QBO phase. Again the duration of the e-QBO is longer for the three-time
SC-max conditions than that in the SC-min conditions. This results are opposite of those obtained
by Soukhrarew and Hood [2001] (see their Figure 12).
Our model supports Fischer and Tung’s [2007] prediction that the in-phase relationship will be
found during the solar cycle without the volcanic eruptions. In addition, Figures 3 (a) and 3 (b)
illustrate that it takes on average 9.3 months for the westerly critical line descend from 10 to 70 hPa
in the case of three-time solar maximum, as compared with less than 9 months in the case with SCmin. Thus the difference caused by the solar forcing in this case is less than half month. In contrast,
the descend of the easterly critical line from 10 to 70 hPa is more than 15 month in the three-time
SC-maximum case, which is 1 month more than that in SC-min case (Figures 3 (c) and 3 (d)). The
slowing down of the descent rate of the easterly critical line occurs mostly below 40 hPa. The
physical cause of this is the stalling due to upwelling. These prolongations of easterly descent rate
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are mostly below 40 hPa which cause the stalling. Therefore, the duration of the w-QBO below 40
hPa is longer than that above 40 hPa. The reverse is true for e-QBO.
In Figure 4, we plot separately the e-QBO and w-QBO duration as a function of the solar flux in
units of solar cycle (one unit represents one half of the difference of solar flux between SC-max and
SC-min) over the pressure range from 10 to 50 hPa. This establishes the approximately linear
relationship between the QBO duration and the solar flux. Above 30 hPa, the duration of the e-QBO
is affected more by the solar cycle, as the remotely forced equatorially upwelling retards the descent
rate of the e-QBO more than that of the w-QBO. This is because the self-induced QBO secondary
circulation is upward for the easterly phase [Plumb and Bell, 1982a, 1982b]. Below 30 hPa, the eQBO sometimes stalls, leaving a lengthened w-QBO. Figure 4 (d) shows that the w-QBO duration
increases more with solar flux below 50 hPa.
In the Supplemental Material, we discussed the stream function variation due to solar variation
and QBO phase. The meridional circulation is stronger during SC-max (e-QBO) than SC-min (wQBO) (see Figure A2 and A3).
Cordero and Nathan [2005] employed a model simulation to show that the QBO circulation is
slightly stronger (weaker) during SC-max (SC-min) and this results in the shorter (longer) QBO
period during SC-max (SC-min). They argued that the wave-ozone feedback leads to the required
diabatic heating and provides a pathway for communicating solar cycle signal to the QBO.
Unfortunately, their model can only study the tropical stratosphere and does not include either the
annual cycle in equatorial upwelling or extratropical Rossby wave forcing. It does not account for
the chemical feedbacks and interaction between the QBO and the semiannual oscillation above 30
Km. Consequently, this model may not be realistic enough to model the interaction between the
QBO and solar cycle.
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4. Discussion and conclusions
We have explored modulation of the QBO period by the solar forcing, and in-phase relation was
found. The dominant change of the QBO period occurs mostly in the e-QBO duration above 30 hPa.
At the stratopause, more ozone heating under the SC-max condition would delay the transition of
QBO phase and then lengthen the QBO period.
The equatorial QBO period and its phase duration is strongly affected by the descent rate of the
critical line for each phase. The mean upwelling over the equator acts to slow down this descent rate,
and consequently extends the QBO period.
The equatorial upwelling could be produced by
planetary wave dissipation, solar insolation and heating by volcanic aerosols. Moreover, the QBOinduced circulation during the easterly (westerly) phase may strengthen (cancel) the upwelling due
to above three forcings. As the w-QBO induces a sinking motion at the equator, which would cancel
the upwelling in the Brewer-Dobson circulation, the westerly critical line is scarcely modulated by
the solar variation, and hence it has a regular descent rate. During the SC-max conditions there are
more Stratospheric Sudden Warmings in the polar stratosphere during late winter [Camp and Tung,
2007]. Consequently the polar stratosphere is warmer and the Brewer-Dobson circulation is more
downward in the polar region. This could remotely force a stronger upwelling branch of the BrewerDobson circulation over the equator, which then slows the descent of the QBO shear zone and
extends the QBO period. This delay of phase transition is much larger in the e-QBO and especially
at levels below 30 hPa. These results agree with the previous studies by Fischer and Tung [2007].
Both follow the variation of the QBO period. Because the self induced secondary circulation of the
QBO itself is also upward for the easterly phase at the equator, the e-QBO is more vulnerable to the
slowing and eventual stalling, which usually occurs near 30 hPa. Below the stalling level, the
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westerly phase persists without being replaced by the descending easterlies, leading to a longer
westerly duration. In this model there is no local heating due to volcanic aerosols, and so the
anomalous upwelling over the equator is probably remotely forced by the Sudden Warming over the
polar stratosphere. We have shown that in the model the Brewer-Dobson circulation is strengthened
during solar max conditions. This mechanism then argues for a lengthening of the QBO period
during solar maximum in the absence of volcanoes. The modeling study has helped us to reveal the
real solar cycle modulation on the QBO period without the disturbance by the local heating due to
the volcanic aerosols.
5. Future work:
The work reported here is a preliminary study of the influence of the solar cycle on the QBO
period using the THINAIR model. Further study is needed on the cases driven by a realistic timedependent solar cycle forcing.
More simulations will be performed to study the influence of
volcanic aerosols on QBO to explain the puzzling results between 1960 and 1995. Ultimately, the
results obtained here must be verified in a three-dimension general circulation model.
6. Acknowledgements:
We would like to thank A. Ruzmaikin and J. Feynman for their contribution in the useful
discussions about these works. We also thank graduate student K. F. Li of Caltech for his solar flux
data and helpful suggestions. This work was supported in part by NASA grants NAG1-1806 and
NNG04GN02G to the California Institute of Technology.
7. References:
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Angell, J. K., (1986), On the variation in period and amplitude of the Quasi-Biennial Oscillation in
the equatorial stratosphere, Mon. Weather Rev., 114 (11): 2272-2278.
Baldwin, M. P., and T. J. Dunkerton (1999), Propagation of the Arctic Oscillation from the
stratosphere to the troposphere, J. Geophys. Res., 104(D24), 30,937-30,946.
Camp, C. D., and K. K. Tung (2007), The influence of the solar cycle and QBO on the late-winter
stratospheric polar vortex, J. Atmos. Sci., 64(4), 1267-1283.
Fischer, P., and K. K. Tung (2007), A reexamination of the QBO-period modulation by the solar
cycle using continuous wavelet transform, Submitted to Geophys. Res. Lett..
Hamilton, K. (2002), On the quasi-decadal modulation of the stratospheric QBO period, J. Climate,
15, 2562-2565
Holton, J. R. and H. C. Tan, (1980), The influence of the equatorial quasi-biennial oscillation on the
global circulation at 50 mb. J. Atmos. Sci.,37, 2200-2208.
Holton, J. R. and H. C. Tan, (1982), The quasi-biennial oscillation in the northern hemisphere lower
stratosphere. J. Meteor. Soc. Japan, 60, 140-148.
Kinnersley, J. S., and R. S. Harwood (1993), An isentropic 2-dimensional model with an interactive
parameterization of dynamical and chemical planetary-wave fluxes, Q. J. R. Meteorol. Soc., 119(513),
1167-1193.
Kinnersley, J. S., and S. Pawson (1996), The descent rates of the shear zones of the equatorial QBO,
J. Atmos. Sci., 53(14), 1937-1949.
Pascoe, C. L., et al. (2005), The quasi-biennial oscillation: Analysis using ERA-40 data, J. Geophys.
Res., 110(D8), D08105, doi:10.1029/2004JD004941.
Plumb, R. A., and R. C. Bell, (1982a), Equatorial waves in steady zonal shear flow, Q. J. R. Meteorol.
Soc., 108, 313-334.
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Plumb, R. A., and R. C. Bell, (1982b), A model of the quasi-biennial oscillation on an equatorial
beta-plane, Q. J. R. Meteorol. Soc., 108, 335-352
Ruzmainkin, A., et al., (2005), The extratropical signature of the Quasi-Biennial Oscillation. J.
Geophys. Res., 110, doi: 10.1029/2004JD005382.
Salby, M. L., and P. F. Callaghan (2000), Connection between the solar cycle and the QBO: The
missing link, J. Climate, 13(4), 2652-2662.
Soukharev, B. E. and L. L. Hood (2001), Possible solar modulation of the equatorial quasi-biennial
oscillation: Additional statistical evidence, J. Geophys. Res., 106(D14), 14,855-14,868.
Tung, K. K., and H. Yang (1994a), Global QBO in circulation and ozone: 1. Reexamination of
observational evidence, J. Atmos. Sci., 51(22), 2699–2707.
Tung, K. K., and H. Yang (1994b), Global QBO in circulation and ozone: 2. A simple mechanistic
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Figure 1. (a) Composite mean of e-QBO duration (*) and w-QBO duration (+) versus pressure for
THINAIR model (b) the same as (a) from NCEP.
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Figure 2. The 82-year time series of the model simulation for the equatorial zonal wind at 31 hPa under
perpetual solar forcing condition. (a) 1xSC-min; (b) 1xSC-max; (c) 3xSC-max; (d) the Fourier spectrum
of the zonal wind time series.
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Figure 3. Mean vertical cross section of the w-QBO and e-QBO of the 5 months running mean equatorial
zonal wind for (a) 5 times SC-max perpetual condition and easterly to westerly; (b) SC-min perpetual
conditions and easterly to westerly (c) 5 times SC-max perpetual condition and westerly to easterly; (b)
SC-min perpetual conditions and westerly to easterly
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Figure 4. Composite mean of e-QBO duration (*) and w-QBO duration (+) versus solar forcing
obtained using the THINAIR model (a) 10 hPa, (b) 20 hPa, (c) 30 hPa and (d) 50 hPa.
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Supplemental Material for the article, “Model study of the influence of the solar cycle on the
Quasi-Biennial Oscillation period”
The QBO simulated by THINAIR is comparable with the observation data. The time-height
section of the equatorial zonal wind from the run under the SC-min condition display the QBO
signal in stratosphere (Figure A1).
In Figure A2 (a), we show the zonal mean stream function in isentropic coordinates during
Febuary, which theoretically is closest to the Lagrangian mean circulation. Figure A2 (b) shows the
difference of stream function between the 3xSC-max and SC-min. It is clear that during SC-max
conditions, there is a stronger Brewer-Dobson circulation with stronger downwelling in polar
stratosphere and upwelling in the equatorial lower stratosphere. The difference of stream function
between the e-QBO and w-QBO is showed in Figure A3 for February and March. The meridional
circulation in mid-latitude region is stronger during e-QBO than w-QBO, in agreement with the
results based on the NCEP derived products examined by Ruzmaikin et al. [2005] (their Figure 6).
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Figure A1. Time-height section of the equatorial monthly-mean zonal wind component (m s-1)
from the model simulation.
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Figure A2. (a) The mass stream function on isentropic surfaces in units of 10 9 kg s-1 under SCmin condition. (b) Difference between the composites of the 3xSC-max and SC-min
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Figure A3. (a) The same as Figure A2 (b) but difference between e-QBO and w-QBO in
February; (b) the same as (a) but in March.
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