The equatorial QBO affects the polar stratosphere during winter

1
Solar-cycle Induced Jumps of the Quasi-Biennial
Oscillation Period in Perpetual Solar Forcing
Modeling ExperimentsLe Kuai1, Runlie Shia1, Xun
Jiang2, Ka-Kit Tung3, Yuk L. Yung1 1 Division of
Geological and Planetary Sciences, California
Institute of Technology, Pasadena, CA 911252 Jet
Propulsion Laboratory, California Institute of
Technology, 4800 Oak Grove Drive, Pasadena, CA
911093 Department of Applied Mathematics,
University of Washington, Seattle, WA 98195
Abstract Using THINAIR model, we examine the
mechanism of solar-cycle modulation on the
Quasi-biennial Oscillation (QBO) period.
Observational evidence for the existence of such
a modulation--an anti-correlation between the
westerly QBO duration and the solar flux--is
controversial because it is found only during a
period (1960s to early 1990s) contaminated by
volcano aerosols. However, this correlation in
the longest available record was found to be near
zero. In modeling, longer period runs without
volcano influence can be obtained. The
solar-cycle effect on the QBO period is rather
subtle and complicated, with phase locking,
beating and non-stationary behaviors. The
experiments are run with perpetual solar
minimum/maximum conditions, which help us capture
the features in the realistic case of periodic
forcing. Both in our model and observed data, the
QBO period is constant with height. Under low
solar forcing, the QBO period is phase-locked to
a multiple (4) of Semi-Annual Oscillation (SAO)
period. As solar forcing increases, the QBO
period jumps with quantized multiple of the SAO
periods, from 24 to 30 or 36 months. Because of
this non-stationarity even under constant
solar-cycle forcing, QBO periods do not respond
one-to-one to changing solar flux in the
realistic case of periodic solar-cycle forcing.
Therefore the statistical significant QBO-solar
relationship cannot be established without a much
longer observational record. The mechanisms for
solar modulation of QBO period are also discussed.
JAN
JAN
Figure 5. (a) Mass stream function on isentropic
surfaces in units of 109 kg s-1 under 1SC-min
condition. (b) The difference between the
composites of the 1SC-max and 1SC-min. Both
figures are for Jan.

• The equatorial QBO affects the polar stratosphere
  during winter
• with the easterly phase of the QBO (e-QBO)
  creating the
• condition for a more perturbed and warmer polar
  vortex Holton
• and Tan, 1980, 1982 Baldwin and Dunkerton, 1999,
  Ruzmaikin
• et al., 2005. Therefore, the variation of the
  QBO period has
• additional significance, especially with respect
  to the timing of its
• phase relative to the northern winter Baldwin et
  al. 2001.
• Model QBO and Comparison with NCEP
• The THINAIR (Two and a Half dimensional
  INterActive
• Isentropic Research) is a chemical-radiative-dynam
  ical
• model. The model has zonally averaged dynamics
  and
• includes the three longest planetary waves, which
  are
• prescribed by observations at the tropopause
  level
• Kinnersley and Harwood, 1993. The QBO-source
  term in
• the momentum equation uses parameterization of
  wave
• momentum fluxes from Kelvin, Rossby-gravity and
  gravity
• waves Kinnersley and Pawson, 1996. These
  momentum
• sources also force the SAO above the QBO.
  UARS/SOLSTICE
• spectral irradiance observation is used as the
  11-year solar cycle.

In Figure 3 we plot the QBO period as a function
of the solar index in units of solar flux (one
unit represents one half of the difference of
solar flux between the SC-max and SC-min). This
establishes that the period of the QBO generally
increases as the solar flux increases, contrary
to the finding of previous authors that the
period reaches a maximum during SC-min. An
interesting feature revealed in Figure 3 (a) is
the tendency of the QBO period to phase-lock with
the 4 SAO periods (so that it is also
phase-locked with the annual cycle). Once the QBO
period was locked in a 24 months at 2SC-min,
further reduction of the solar flux to 3SC-min
does not seem to be able to change its period,
thus forming a flat ledge in Figure 3 (a). In the
other cases, the averaged QBO period
increases when perturbed by increasing solar
fluxes. Above 30 hPa, it is the easterly duration
which varies with solar flux (Figure 3 (b) and
(c)), while below 30 hPa it is the westerly
duration that varies with solar flux (Figure 3
(d)), consistent with the observational result
of Fischer and Tung 2007.
Mechanisms for solar modulation of QBO
period. The partition of the whole QBO period
into its easterly and its westerly parts in the
lower stratosphere depends on the equatorial
upwelling rate of the global Brewer-Dobson
circulation. The isentropic stream-function for
the Brewer-Dobson circulation in the stratosphere
in January shows a strengthened Brewer-Dobson
circulation during SC-max conditions as compared
to SC-min conditions (figure 5). Under the SC-max
conditions the planetary waves are more focused
to mid and high latitudes, and 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 mid to high latitudes
Figure 4. Time-height section of the equatorial
monthly-mean zonal wind component (in m s-1) from
the THINAIR model simulation. The individual QBO
period is synchronized with SAO near stratopause.
The black line is the zero-wind line. (a)
2SC-min perpetual condition (b) 1SC-min
perpetual condition (c) SC-mean perpetual
condition (d) 1SC-max perpetual condition (e)
2SC-min perpetual condition. (f) under realistic
periodic solar-cycle forcing from 1SC-min to
1SC-max.
Cordero and Nathan, 2005. This 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 and
extends the QBO period. Because the QBO-induced
secondary circulation is also upward for the
easterly phase at the equator, the e-QBO is more
vulnerable to slowing and eventual stalling,
which usually occurs near 30 hPa Plumb and Bell,
1982 (a), 1982 (b). Below the stalling level,
the westerly phase persists without being
replaced by the descending easterlies, leading to
a longer westerly duration. This explains why the
descent of the easterly shear zone is more
vulnerable to stalling. In this model there is no
local heating due to volcanic aerosols, and so
the anomalous upwelling over the equator shown
here is remotely forced by the breaking of
planetary waves in the extra-tropics. The
prolongation of the westerly phase of the QBO in
the lower stratosphere is an important feature of
the observed decadal variation of the QBO period
because it delays the onset of the next westerly
descent into the stratosphere by filtering out
the westerly waves. In the absence of the
westerly wave momentum deposition, the easterly
duration is lengthened in the upper stratosphere.
In the observational result of Fischer and Tung
2007, the decadal variation of the easterly
duration at 15 hPa is tied to that of the
westerly duration at 50 hPa. This feature is also
seen in this model. A second mechanism is local
radiative heating by the increased solar flux in
SC-max as compared to the SC-min. In this model
the UV radiation of the solar cycle forcing
interacts with ozone most strongly in the
stratopause region, and the resulting diabatic
heating affects the seeding of the QBO by the
SAO. This solar perturbation serves to kick the
QBO period from one SAO multiple into another,
higher (on average) multiple. To test this
hypothesis, we make another run by switching off
the solar cycle-ozone feedback. Ozone in the
model is then not allowed to change as solar
cycle changes, but other interaction with
dynamics are still allowed. In the
non-interactive case, ozone is fixed at the
SC-mean case, but the solar flux is increased to
1SC-max. The average period is 29.80 months
without ozone feedback. The behavior is
non-stationary, and lie between the SC-mean (with
an average period of 28.59 months) and 1SC-max
(with an average period of 31.84 months) case
with ozone feedback.
Figure 3. (a) QBO period as a function of
solar-cycle forcing obtained using the THINAIR
model for five levels from 7-80 hPa. Lines
overlap, showing that the period does not change
with height. Composite mean of e-QBO duration ()
and w-QBO duration () versus solar forcing (b)
10 hPa, (c) 20 hPa, (d) 50 hPa.
As pointed out by previous authors (Lindzen and
Holton 1968 Dunkerton and Delisi, 1997), the
SAOs alternating easterly and westerly shear
zones serve to seed the QBO below. In
particular, the onset of the westerly phase of
the QBO is tied to the downward propagation of
the westerly phase of the SAO. A QBO period
starts with the zero-wind line associated with
the westerly shear zone of the SAO descending
into the QBO region below, and ends when next
such westerly descent occurs, to replace the
easterly QBO below, at a multiple of SAO period
later. In this way the QBO period is quantized in
units of SAO period. Panel (a) in Figure 4 shows
the simplest case, a QBO period locked in 4 SAO
periods for 2SC-min. Panel (b) shows the case
for 1SC-min. The QBO period comprises 4 SAO
periods most of the time, and occasionally there
is one or two QBO periods consisting of 5 SAO
periods. As a result, the average QBO period is
25.08 months. Apparently the solar forcing is not
strong enough to force the QBO period into 5 SAO
periods permanently. There is also the
possibility that an odd multiple of SAO periods
is not stable with respect to annual-cycle
perturbation. Panel (d) shows the result with
1SC-max condition. Similar to the 1SC-min case,
the time series is also non-stationary. A QBO
period can comprise of mostly 4 and 6 and
occasional 5 SAO periods, yielding an average
QBO period of 31.85 months. Panel (c) shows the
case of SC-mean (without solar-cycle forcing) and
it appears to behave approximately as the average
of 1SC-min and 1SC-max cases, with an average
period of 28.59 months, which comprises mostly 5
and 4 SAO periods with an occasional 6 SAO
periods. Panel (e) shows the behavior for
2SC-max, where the QBO period time series
becomes stationary again and phase-locked into 6
SAO periods.
Figure 2. Fourier power spectra of the 70-year
zonal wind time series from the THINAIR model
black line for 1SC-min case red line for
1SC-max case blue line for 2SC-max case. (a)
at potential temperature level 712 K (15 hPa)
(b) 595 K ( 26 hPa)
Discussion and Conclusions It is well known that
the polar stratosphere in winter is significantly
more perturbed when the equatorial QBO is
easterly than when it is westerly Holton and
Tan, 1980, 1982 Baldwin et al, 2001. A
mechanism that can affect the period of the
equatorial QBO, by altering the timing of the
phase of the QBO relative to the polar winter
will therefore have a significant impact on the
circulation of the entire stratosphere. The
11-year solar cycle has often been cited as able
to modulate the equatorial QBO period, especially
its westerly duration in the lower stratosphere.
In the present model where there is no volcanic
influence and long runs are possible, we have
established that the QBO period is lengthened
during solar maxima. We also find that such an
effect is difficult to establish without a long
time record because of the presence of
non-stationary behavior, whereby the QBO period
can change even if the solar flux is held
constant. To understand the mechanism of
solar-cycle modulation of the QBO period, model
runs with perpetual solar conditions are
performed. We find a tendency of the QBO period
to synchronize with the SAO period. That the
observed mean period (e.g. 28 month) is not
always a multiple of six months can be partially
explained by the fact that the QBO period is
non-stationary even when the solar forcing is
constant. Two exceptions occur at 24 months and
36 months, forced by 2?SC-min forcing and
2?SC-max conditions. These two periods are more
stable because there is also a synchronization
with the annual cycle. In between these two cases
there are temporary (non-stationary) quantum
jumps of the QBO period by a SAO period when the
stratopause region is perturbed by the solar
cycle, yielding non-integer multiples of the SAO
period as the average period of the QBO. In the
model two mechanisms are responsible for the
solar influence of the QBO period a radiative
perturbation of the SAO-QBO transition region
when ozone production is enhanced by the
increased solar flux a dynamical mechanism which
increases the strength of the Brewer-Dobson
circulation. 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 time-dependent 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.
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.
Solar Cycle Influence on the QBO Period With the
time-dependent oscillatory solar forcing,
determining the QBO period is not
straightforward, since the period itself is
changing with the solar cycle. However, with
fixed solar forcing, the QBO period can be
determined using its Fourier spectrum. We perform
the simulation with the 1 to 3 SC-min/SC-max
conditionand the SC mean conditions. Figure 2
shows the Fourier spectrum of the 70-year time
series of the QBO zonal wind at equator at
various altitudes. The period of the QBO was
showed to be independent on height. The results
reveal a QBO Period of 25.08 months for 1SC-min
(black line), 31.85 months for the 1SC-max (red
line) and 36.01 months for the 2SC-max (blue
line) conditions. Thus, the period of the QBO is
unambiguously lengthened as the solar
fluxincreases.