Does the Solar Cycle Increase or Decrease the Period of the Quasi-Biennial
Oscillation? A Modeling Study
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
1
Le Kuai, Division of Geological and Planetary Sciences, California Institute of Technology, MC150-21, 1200 E.
California Blvd., Pasadena, CA 91125, USA. (kl@gps.caltech.edu)
Runlie Shia, Division of Geological and Planetary Sciences, California Institute of Technology, MC150-21, 1200 E.
California Blvd., Pasadena, CA 91125, USA. (rls@gps.caltech.edu)
Xun Jiang, Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109,
USA. (Xun.Jiang@jpl.nasa.gov)
Ka-Kit Tung, Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA.
(tung@amath.washington.edu)
Yuk L. Yung, Division of Geological and Planetary Sciences, California Institute of Technology, MC150-21, 1200 E.
California Blvd., Pasadena, CA 91125, USA. (yly@gps.caltech.edu)
2
Abstract
During the period of 1960s, 70s, 80s and early 90s, the westerly phase of the Quasi-Biennial
Oscillation has been observed by a number of authors to have extended periods during the solar
minimum. This is also the time when the stratosphere is contaminated by the aerosols from major
volcanic eruptions. For the one solar cycles prior and one after this period, the QBO period appears
to increase during solar maximum and decrease during solar minimum. The true dependence of
QBO period on the solar cycle in the absence of volcanic aerosol heating cannot be determined
statistically due to the short observational data record. We perform a long model simulation of the
QBO without volcanoes using the THINAIR model. The analysis of the model simulation indicates a
positive correlation between the length of QBO period and the solar cycle flux.
1. Introduction
Quasi-Biennial Oscillation (QBO) is now understood to be an internal oscillation of the equatorial
stratosphere involving wave-mean flow interactions. It period averages to about 28 months, but is
known to have interannual variations of about the mean. The equatorial QBO is known to affect
significantly the polar stratosphere during winter, with the easterly phase creating the condition for a
3
more perturbed and warmer polar vortex. Therefore, the variation of QBO’s period takes on an
added importance (especially with respect to the timing of its phase relative to northern winter.)
Recently, Salby and Callaghan [2000], using the radiosonde data from Free University of Berlin
(FUB) near the equator at 45 hPa from 1956-1996, and found that the duration of the QBO’s
westerly phase tends to be longer during solar minimum. This result is confirmed by Soukharev and
Hood [2001] using composite mean analysis, and Pascoe et al [2005] on the mean descent rate of the
easterly shear zone prior to 1990s. On the other hand, Hamilton [2002] and Fischer and Tung [2007]
studied a longer period of FUB data and found the opposite behavior in the late 1990s and 2000s and
also the 1950s. For the longer period of 1953-2005, Fischer and Tung [2007] found that the
correlation coefficient between the period of the QBO and a solar cycle index to be zero. It should
be mentioned that these later publications 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 reversed in other
decades not included in the period studied by Salby and Callaghan [2000].
The descent rate of QBO shear zones is affected by a number of external factors, some local and
some remote. Local heating due to volcanic aerosols at 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. There
were three major volcanic eruptions whose aerosols reached 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 aerosols, the effect on the QBO period may be different after each eruption.
4
Angel [1986] argued that the increase in westerly period after 1963 was due to the Agung eruption,
and pointed out that the temperature increasing due to aerosol heating was seen at 50 hPa dnd 30 hPa
at the Balboa station. The possibility exists that the inverse relationship between the westerly QBO
period in the lower stratosphere and the solar cycle flux found by Salby and Callaghan [2000] and
others may be anomalous; although the behavior was attributed to solar influence, the volcanic
aerosols during the period studies may have masked the true solar influence. During the solar
minimum of 1997, when the volcanic aerosols from the 1991 eruption of Pinatubo has cleared, the
QBO period reached a low of 25 months. Since then, the period increased as the solar cycle
advanced from minimum to maximum, with positive correlation [Fischer and Tung, 2007]. A few
more decades without major volcanoes 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 above
controversy. We present a study on how the solar cycle influences QBO using a long model
simulation without volcanoes.
2. Model description
The THINAIR model is a two-and-a-half-dimensional dynamics model. It has zonally averaged
dynamics plus three longest planetary waves, which are prescribed from observations at the
tropopause level. It 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.
5
The QBO-source term in the momentum equation uses parameterization of wave momentume fluxes
from Kevin, Rossby-gravity and gravity waves [Kinnersley, 1996]. UARS/SOLSTICE spectral
irradiance observation (Figure 1) has been used as the 11-year solar cycle input. It consists of the
solar spectrum in UV 119-400 nm during 1991-2002, with 1-nm resolution. The monthly data has
been extended to 1947-2005 using F10.7-cm as a proxy [Jackman et al., 1996]. For the longer runs
beyond 2005, the solar cycle is simply repeated using the previous period.
3. Solar cycle influence on the length of QBO period:
The composite analysis of Soukhrarew and Hood [2001, Figure 12] is here reproduced using 82
years of THINAIR model results. Figure 2 shows the mean vertical-time cross section of the
westerly QBO of the lowpass filtered equatorial zonal wind for solar maximum conditions (Figure 2
a), solar minimum conditions (Figure 2 b) and the difference of them (Figure 2 c). The duration of
the westerly QBO phase is found to be longer in solar maximum conditions than in solar minimum
conditions, in contrast to Soukhrarew and Hood’s conclusion. Fischer and Tung [2007] showed that
the anti-correlation with the solar cycle mentioned by Salby and Calleghan [2000] breaks down in
the solar minimum in 1997 with QBO period being as low as about 25 months when there were no
major volcanic perturbations. Our model, exclusive of the volcanic influence, supports Fischer and
Tung’s prediction that the in-phase relationship will be found during the solar cycle without the
volcanic eruptions.
We have also performed a set of calculations where the solar radiation is held either in perpetual
solar minimum or solar maximum conditions. This allows the use of the Fourier analysis to
determine the QBO period unambiguously. Figure 3a is the 82 year run under perpetual solar
minimum conditions, and Figure 3b shows the corresponding run under perpetual solar maximum
6
conditions. In Figure 3c we show the case with 5 times solar maximum condition. Their Fourier
frequency spectra are shown in Figure 3d. It shows unambiguously that as the solar radiation is
increased, the period of the QBO lengthens.
In Figure 4, we show the zonal mean streamfunction in isentropic coordinates, which theoretically is
closest to the Lagrangian mean circulation. It is seen that during solar maximum conditions, there is
a stronger Brewer-Dobson circulation with stronger downwelling in polar stratosphere and
upwelling in the equatorial lower stratosphere. The latter slows the descent of both the easterly and
westerly shear zones and thus lengthens the QBO period.
4. Conclusion and discussion
Camp and Tung [2007] found in NCEP data that during solar maximum conditions there are more
Stratospheric Sudden Warmings in the polar stratosphere during late winter. Consequently the polar
stratosphere is warmer and the Brewer-Dobson circulation is more downward. This then could
remotely force a stronger upwelling branch of the Brewer-Dobson circulation over the equator,
which then slows the descent of the QBO shear zone. Fischer and Tung [2007] found that above 30
hPa it is the easterly phase of the QBO which is lengthened while below 30 hPa it is the westerly
phase. Both follow the variation of the whole period of the QBO. Because of the self induced
secondary circulation of the QBO itself is upward for the easterly phase, the easterly phase 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
7
Warming over the polar stratosphere. This mechanism then argues for a lengthening of the QBO
period during solar maximum in the absence of volcanoes.
Acknowledgements. We would like to thank Alexander Ruzmaikin and John Lawrence for their
contribution in the useful discussions about these works. We also thank graduate student King-Fai Li
of Caltech for his solar cycle input and helpful suggestions. This work was supported by …..
References
Andrews, D. G., F. W. Taylor, and M. E. Mcintyre, (1987), The influence of atmospheric waves on
the general-circulation of the middle atmosphere, Philos. Trans. R. Soc. London, Ser. A, 323, 693-705.
Alexander Ruzmaikin, John Lawrence and Cristina Cadavid, (2003), A simple Model of stratospheric
dynamics including solar variability, J of climate, 16, 1593-1600.
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., M. S. Roulston MS, and Y. L. Yung, (2003), Temporal and spatial patterns of the
interannual variability of total ozone in the tropics, J. Geophys. Res., 108 (D20): Art. No. 4643.
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.
Charlotte L. Pascoe, et al., The quasi-biennial oscillation, (2005), Analysis using ERA-40 data,
Journal of Geophysical Research, vol. 110, D08105, doi:10.1029/2004JD004941.
Charney, J. G., and P. G. Drazin (1961), Propagation of planetary-scale disturbances from lower into
upper atmosphere, J. Geophys. Res., 66(1), 83.
8
Coughlin, K., K. K. Tung, (2004), Eleven-year solar cycle signal throughout the lower atmosphere, J.
Geophys. Res., 109(D21): D21105.
Coughlin, K., K. K. Tung, (2004), 11-year solar cycle in the stratosphere extracted by the empirical
mode decomposition method, ADVANCES IN SPACE RESEARCH, 34(2): 323-239.
Fischer. P and K. K. Tung, A reexamination of the QBO-period modulation by the solar cycle using
continuous wavelet transform, Submitted to Geophys. Res. Lett. 2007.
Haigh, J. D., (1996), The impact of solar variability on climate. Science, 272, 981-984.
Haigh, J. D., (1999), A GCM study of climate change in response to the 11-year solar cycle. Quart. J.
Roy. Meteor. Soc.,125, 871-892.
Holton, J. R. (2004), An Introduction to Dynamic Meterology, 4th Ed., Academic Press.
Hood, L. L., J. L. Jirikowic, and J. P. McCormack (1993), Quasi-decadal variability of the
stratosphere – Influence of long-term solar ultraviolet variations, J. Atmos. Sci., 50(24), 3941-3958.
Hood, L. L., and B. e. Soukharev, (2003), Quasi-decadal variability of the tropical lower stratosphere:
The role of extratropical wave forcing. J. Atmos. Sci., 60, 2389-2403.
Hoyt, D. V., and K. H. Schatten (1998), Group Sunspot Numbers: A new solar activity reconstruction,
Solar Physics, 181(2), 491-512.
Jackman, C. H., E. L. Fleming, S. Chandra et al. ,(1996), Past, present, and future modeled ozone
trends with comparisons to observed trends, J. Geophs.Res., 101(D22): 28753-28767.
Kinnersley, J. S. and R. S. Harwood, (1993), An isentropic 2-dimensional model with an interactive
parameterization of dynamical and chemical planetary-wave fluxes, QUARTERLY JOURNAL OF THE
ROYAL METEOROLOGICAL SOCIETY, 119 (513): 1167-1193.
Kinnersley, J. S., (1996), The climatology of the stratospheric ‘THIN AIR’ model, QUARTERLY
JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, 122 (529): 219-252.
9
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.
Kinnersley, J. S., (1998), Interannual variability of stratospheric zonal wind forced by the northern
lower-stratospheric large-scale waves, J. Atmos. Sci., 55(13), 2270-2283.
Kinnersley, J. S., and K. K. Tung (1999), Mechanisms for the extratropical QBO in circulation and
ozone, J. Atmos. Sci., 56(12), 1942-1962.
Kodera, K. (1993), Quasi-decadal modulation of the influence of the equatorial quasi-biennial
oscillation on the north polar stratospheric temperatures, J. Geophys. Res., 98(D4).
Labitzke, K., (1982), On the interannual variability of the middle stratosphere during the northern
winter, J. Meteor. Soc. of Janpan, 60(1): 124-139
Lean, J., and D. Rind (2001), Earth’s response to a variable sun, Science, 292(5515), 234-236.
Mayr, H. G., J. G. Mengel, C. L. Wolff, and H. S. Porter, QBO as potential amplifier of solar cycle
influence, Geophys. Res. Lett., 33(5), L05812.
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.
Salby, M. L., and P. F. Callaghan (2006), Influence of the solar cycle on the general circulation of the
stratosphere and upper troposphere, Space Science Reviews, 125(1-4), 287-303.
Shindell, D., D. Rind, N. Balachandran, J. Lean, and P. Lonergan, (1999), Solar cycle varibility,
ozone, and climate. Science, 284, 305-308.
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), 14,85-14,868.
Thompson, D. W. J., and J. M. Wallace (1998), The Arctic Oscillation signature in the wintertime
geopotential height and temperature fields (1998), Geophys. Res. Lett., 25(9), 1297-1300.
10
Figure 1. The ratio of change of the photon flux input at the Lyman-alpha line (121.5 nm) of the 96-year input.
The first three cycles (corresponding to 32 years) were repeated three times to give the 96-year data set.
Ratio = 1 corresponds to the original flux input at the Lyman-alpha line in the THINAIR model.
11
Figure 2. Mean vertical cross section of the westly phase of the band-pass-filtered equatorial zonal wind
for (a) solar maximum condition and (b) solar minimum conditions. (c) the difference between (a) and (b).
12
0.46
SC-min/eQBO
1.2 events/yr
SC-max/eQBO
1.17 events/yr
2.81
2.36
SC-min/wQBO
0.33 events/yr
0.36
2.45
SC-max/wQBO
0.33 events/yr
Figure 3
13
Figure 4
14