Model study of the influence of the solar cycle on the Quasi-Biennial Oscillation
period
Le Kuai1, Run-Lie 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:
[email protected]
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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 zonal wind in the stratosphere involving wave mean flow interactions [e.g. Baldwin et al.,
2001]. 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; Baldwin and Dunkerton, 1999]. 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 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) appears to vary with the solar cycle (SC) and tends to be longer during the solar
minima (SC-min; SC-max corresponds 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 is longer during the 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 the SC-min condition. The w-QBO duration is increased
(decreased) under the SC-min (SC-max) condition. This relation breaks 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 anticorrelation (correlation coefficient = -0.46) between the w-QBO duration at 50 hPa and the solar flux
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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 to determine the QBO period at 50 hPa for the longer record of 1953-2005, and
found that the correlation coefficient between the period of the QBO and a solar cycle is zero. They
did show 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. Why is there a
change in the behavior of SC and QBO interaction?
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). It is possible that the inverse relationship
between the westerly QBO period in the lower stratosphere and the solar flux from 1957 to 1991 is
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obtained under the influence of volcanic aerosols. During the SC-min of 1997, when the 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 SC-max
[Fischer and Tung, 2007]. A few more decades without 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 SC modulation of the QBO. The next section describes the model and the
sources of the QBO and solar forcing used in the simulations, along with comparison with the
assimilated data from the National Centers for Environmental Prediction (NCEP) reanalysis [Kalnay,
et al., 1996; Kistler, et al., 2001]. Section 3 presents results on how the QBO period and its easterly
and westerly phase durations are modulated by the solar forcing. A discussion of the mechanism,
conclusions of this paper and future directions follow in the last section.
2. Model QBO and Comparison with NCEP
The THINAIR (Two and a Half dimensional INterActive Isentropic Research) model is an
isentropic chemical-radiative-dynamical model. It has zonally averaged dynamics plus three longest
planetary waves, which are prescribed from observations at the tropopause level [Kinnersley and
Harwood, 1993]. For this study, the planetary wave forcing at the tropopause is fixed at 1.1 times of
the 1979 year level, annually periodic repeated for all the years. This choice is to reduce interannual
variability of the planetary wave, so that the (weak) influence of the SC on the QBO can be studied.
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
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~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 (the minimum value of the realistic solar oscillatory forcing is used for
all the time period) or solar maxima (the maximum value of the realistic solar oscillatory forcing is
used for all the time period). Sensitivity studies are also carried out with many times of the solar
forcing.
The performance of the model has been reported in the literature [Kinnersley and Pawson, 1996].
The climatological behavior of the QBO in the THINAIR model at the equator for various elevations
in the lower stratosphere is showed in Supplemental Material Figure A1. Figure 1 (a) presents the eQBO and the w-QBO duration versus pressure from 10 to 50 hPa from the THINAIR model for the
SC-min conditions. 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 observations. 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, Baldwin et al., 2001, Pascoe et
al., 2005].
3. Solar Cycle Influence on QBO
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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 SC-max condition and 2×, 3× the SC-max conditions.
Figure 2 shows the 82-year time series of the QBO zonal wind at equator at 31 hPa under the
perpetual SC–min condition (a), SC-max condition (b) and 3×SC-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 3×SC-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 3 (b) show the mean vertical-time cross section of the zonal wind transition
from the e-QBO to w-QBO under the 3×SC-max and SC-min conditions respective. The results are
derived from composite analysis after applying five-month running average to the data. The profiles
were obtained by taking the average of those w-QBO phases which all started from the same “zero”
point at 10 hPa [Soukhrarew and Hood, 2001]. The duration of the w-QBO phase is found to be
longer under the 3×SC-max conditions than that under the SC-min conditions. Figures 3 (c) and 3 (d)
show the similar results for the transition from the w-QBO to e-QBO phase. Again the duration of
the e-QBO is longer for the 3×SC-max condition than that in the SC-min condition. These results
are opposite of those obtained by Soukhrarew and Hood [2001] (see their Figure 12). They showed
the duration of both w-QBO and e-QBO in the lower stratosphere last longer at SC-min than at SC-
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max. Because they only analysis the eight cases of the w-QBO/e-QBO under SC-max and SC-min
conditions, it is difficult to get a statistically robust result.
Our model supports Fischer and Tung’s [2007] prediction that the in-phase relationship will be
found during the solar cycle in the absence of volcanic eruptions. In addition, Figures 3 (a) and 3 (b)
illustrate that it takes on average 8.2 months for the westerly critical line (dot line in Figure 3 (a)) to
descend from 10 to 70 hPa in the case of 3×SC-max, as compared with less than 8 months in the
case with the SC-min (dot line in Figure 3 (b)). Thus the difference in the descent of the westerly
critical line caused by the solar forcing is less than half month. In contrast, the descent of the
easterly critical line from 10 to 70 hPa takes more than 14 month in the 3×SC-max case, which is 1
month more than that in the SC-min case (Figures 3 (c) and 3 (d)). The slowing down of the descent
of the easterly critical line occurs mostly below 40 hPa. This foundings agree with Soukhrarew and
Hood [2001]. They stated that the largest difference in the duration of the e-QBO is observed in the
lower stratosphere at 30 to 50 hPa. The physical cause of this is the stalling due to upwelling. This
prolongation of the easterly descent occurs mostly below 40 hPa, where stalling could become
important. Therefore, the duration of the w-QBO below 40 hPa is longer than that above 40 hPa.
The reverse is true for the e-QBO.
In Figure 4, we plot separately the e-QBO and w-QBO durations as a function of the solar flux in
units of solar cycle (one unit represents one half of the difference of solar flux between the 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 forcing, 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
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hPa, the e-QBO sometimes stalls, leaving a lengthened w-QBO. Figure 4 (d) shows that the w-QBO
duration increases more rapidly with the solar flux than the e-QBO below 50 hPa.
In the Supplemental Material, we discussed the stream function variation due to SC variation and
the QBO phase. The meridional circulation is stronger during the e-QBO (SC-max) than the w-QBO
(SC-min) (see Figures A2 and A3).
Cordero and Nathan [2005] employed a model simulation to show that the QBO circulation is
slightly stronger (weaker) during the SC-max (SC-min), resulting in a shorter (longer) QBO period
during the SC-max (SC-min). They argued that the wave-ozone feedback leads to the required
diabatic heating and provides a pathway for communicating the 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 simulate the interaction between the
QBO and the solar cycle and their results are inconsistent with those obtained by our model.
4. Discussion and Conclusions
We have explored the modulation of the QBO period by the solar forcing, and an 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 the QBO phases 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,
and consequently extends the QBO period.
The equatorial upwelling could be produced by
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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
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 in the supplemental material that in the model the BrewerDobson circulation is strengthened during the solar max conditions. This mechanism then argues for
a lengthening of the QBO period during the SC-max 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.
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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 such as the
Whole Atmosphere Community Climate Model (WACCM) [Garcia et al., 2007].
Acknowledgements: We would like to thank A. Ruzmaikin and J. Feynman for useful discussions.
We also thank 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.
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Plumb, R. A., and R. C. Bell (1982b), A model of the quasi-biennial oscillation on an equatorial betaplane, Q. J. R. Meteorol. Soc., 108, 335-352.
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Figure 1. (a) Composite mean of e-QBO duration (*) and w-QBO duration (+) versus pressure from the
THINAIR model. (b) Same as (a) from NCEP reanalysis.
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Figure 2. 82-year time series from the THINAIR model for the equatorial zonal wind at 31 hPa under
perpetual solar forcing condition. (a) 1×SC-min; (b) 1×SC-max; (c) 3×SC-max; (d) Fourier spectra of the
zonal wind time series; black line for 1×SC-min case; red line for 1×SC-max case; blue line for 3×SCmax case.
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Figure 3. Mean vertical cross section of the w-QBO and e-QBO of the 5 month running mean equatorial
zonal wind for (a) 3×SC-max perpetual condition and easterly to westerly; (b) SC-min perpetual condition
and easterly to westerly (c) 3×SC-max perpetual condition and westerly to easterly; (d) SC-min perpetual
conditions and westerly to easterly. The dotted line is the shear zone critical line.
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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”
As shown in Figure A1, the model simulated QBO is comparable with the observations [Baldwin,
et al., 2001, Plate 1] and exhibits the similar features with the observed QBO. The time-height
section of the equatorial zonal wind for the case under the SC-min condition displays a 26 month
oscillation in the lower stratosphere. The downward propagating easterly and westerly wind regimes
are clearly revealed in this figure. The amplitude of the zonal wind is between -30 to +30 m/s. The
maximum wind speeds occur near 33 km, which is slightly higher than observation (26 km). The
westerly shear zone descends quite regularly from high to low, while the easterly shear zone
propagates down more slowly and more irregularly. This is caused by the stalling of the easterly
shear zone due to the QBO induce meridional circulation.
The differences of stream functions between the e-QBO and w-QBO are showed in Figure A2 for
January and February in isentropic coordinates. 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). This demonstrates that, during the eQBO (w-QBO), the self-induced circulation is upward (downward) over equator and strengthens
(weakens) the Brewer-Dobson circulation. Thus, the meridional circulation is stronger during the eQBO than w-QBO.
Figure A3 (a) presents the zonal mean stream function during February for the case with the SCmin condition, which theoretically is closest to the Lagrangian mean circulation. Figure A3 (b)
shows the difference of stream function between the 3×SC-max and SC-min. It is clear that during
3×SC-max conditions, there is a stronger Brewer-
upwelling in the
equatorial lower stratosphere, accompanied by more upwelling in the polar stratosphere. This helps
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to explain why greater stalling occurs under the larger solar forcing, leading to the lengthening of the
w-QBO duration that is larger than that of e-QBO below 50 hPa.
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Figure A1. Time-height section of the equatorial monthly-mean zonal wind component (m s-1)
from the THINAIR model simulation.
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Figure A2. Mass stream function on isentropic surfaces in units of 10 9 kg s-1 under SCmin condition. Difference between the composites of the e-QBO and w-QBO. Contour
spacing: 0.3 (a) January (b) February.
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Figure A3. (a) Mass stream function on isentropic surfaces in units of 10 9 kg s-1 under SCmin condition. (b) The difference between the composites of the 3×SC-max and SC-min. Both
figures are for Feb.
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