The largest amplitudes of the observed Quasi Biennial Oscillation (QBO) in column ozone are found in high latitudes and this must be taken into account in any explanation of the increased depletion of ozone in the southern polar spring during the 1980's. A QBO in zonal wind, temperature and column ozone has been successfully modelled in a two-dimensional dynamical/chemical model by the introduction of a parameterization scheme to model the transfer of momentum to the zonal flow associated with the damping of vertically propagating Kelvin and Rossby-Gravity waves. The largest anomalies in column ozone of approximately 20 DU are present at high latitudes. The equatorial ozone QBO is out of phase with the mid- and high-latitude ozone QBO, in good agreement with observations

Gray, L. J.

Pyle, J. A.

English

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A Two Dimensional Model of the Quasi Biennial
Oscillation of Ozone
L.J.Gray, Rutherford Appleton Laborat.:_ry, Chilton, Didcot, Oxon., U.K.,
J.A.Pyle, Physical Chemistry Department, Cambridge University, Cambridge U.K.
ABSTRACT. The largest amplitudes of the observed Q_lasi Biennial Oscillation (QBO) in column ozone are
found in high latitudes and this must be taken into account in any explanation of the increased depletion of ozone
in the southern polar spring during the 1980's. A QBO in a:onal wind, temperature and column ozone has been
successfully modelled in a two dimensional dynamical/chemical model by the introduction of a parametrization
scheme to model the transfer of momentum to the zonal flow associated with the damping of vertically propagating
Kelvin and Rossby-Gravity waves. The largest anomalies in column ozone of approximately 20 DU are present at
high latitudes. The equatorial ozone QBO is out of phase _ith the mid- and high latitude ozone QBO, in good
agreement with observations.
1 Introduction
The presence of a quasi-biennial oscillation (QBO) in zonal winds, temperature and column
ozone in the equatorial stratosphere is well known ([_eed 1960, Veryand and Ebdon 1961, WaLlace
1973, Angel] and Korshover 1978, Coy 1979, Tolson 1981, Hasebe 1983, Naujokat 1986). The
largest amplitudes of the ozone QBO, however, are found in high latitudes and this must be
allowed for in any explanation of the increasing d_:,pletion of ozone in the southern polar spring
during the 1980's (Bojkov 1986, Gazcia and Solomon 1987). We describe a simulation of the
QBO in a two-dimensional model which extends from pole to pole and includes a comprehensive
photochemical scheme. We are therefore able to investigate the effects of the equatorial QBO
on the extra-tropical dynamics of the model and _he relationship between the dynamical QBO
and the distribution of ozone.
2 The Model
The two-dimensional model of ttarwood and Pyle (1975,1977,1980) was employed in the study.
The model configuration is essentially the same as that employed by Gray and Pyle (1987a),
hereafter referred to as GP, except that the improved 'wide-band' radiation scheme developed by
Haigh (1984) has been used. This has resulted in ;_much deeper and stronger Hadley circulation
in the equatorial lower stratosphere. (Note that, in this respect the present model differs from
that described by Gray and Pyle 1987b). The parametrization scheme to model the Semi-
Annual Oscillation (SAO) developed in GP was retained in the present runs but the gravity
wave breaking parametrization was omitted.
The zonal wind QBO has been modelled by including the momentum deposition associated
with thermally dissipating Kelvin and Rossby-Gravity waves. A WKB approximation is used
to derive an expression for the mean flow acceler;_tion: _ = Aexp(_=_)R(z)ezp(-P(z)) where
R(z) = _ and P(z) = f_zo R(z')dz' (Lindzen _md Holton 1968). A is the vertical momentum
flux at zo (=16 km), a(z) is the thermal damping rate, N is the Brunt-Vaisala frequency and
k is the zonal wavenumber. The equation was solved with parameter values appropriate to the
Kelvin and Rossby-Gravity waves shown in the _.able below. Note that two Kelvin waves were
forced which were identical apart from their phas,_ speeds. The mean flow acceleration associated
with the faster phase speed c=60 ms -1 occurs a_: higher levels in the modelled atmosphere and
gives rise to the westerly phase of the SAO. The damping of the waves has been restricted to
thermal damping, as in the SAO parametrizati_,n of GP; above 30 km the damping rate a(z)
was chosen to be the 'slow' damping rate of D_mkerton (1979) which peaks at approx_imately
2x10 -6 s-1 at 50 km; below this level a constant value of 0.35x10 -6 s-1 was specified. Although
no mechanical damping was explicitly employed in the QBO parametrization scheme, the model
includes a vertical diffusion operating on the model wind fields with a constant value of kzz = 1.0
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m_s -1 at all latitudes and heights. A gaussian distribution about the equator was applied to the
forcing associated with the two types of waves, with _n e-folding width YL = (k2_) ½ for the Kelvin
waves and YL = (_),x for the Rossby-Gravity waves where _ = e (Holton 1975). All other
symbols have their usual meaning and an overbar denotes a zonal average. The parametrized
forcing associated with the Kelvin and the Rossy-Gravity waves were both present at all times
of the modelled year.
Kelvin Wave Rossby-Gravity Wave
Zonal wavenumber 1 4
phase speed (ms -1 )
A, amplitude of vertical momentum flux at zo (m_s -l)
-t-25 +60 -25
t2.5 x 10 -a 3.5 x 10 -a 15.0 x 10 -3
3 The QBO in Zonal Wind
The time-height section of the zonal wind at the equator from a model run that included both tile
QBO and SAO parametrizations is shown in figure 1. Four periods of the QBO are evident. The
semi-annual oscillation is dominant above 35 km a_d the QBO is the dominant signal between
10 and 30 kin, in good agreement with observational data. Both phases of the QBO exhibit a
gradual descent with time (at an average rate of just over 1 km per month); the amplitude of
the modelled QBO is a maximum at approximately, 25 km where the winds vary between 20
ms -1 and -18 ms -1. Thermal wind balance is maintained against thermal dissipation in the
model by the development of a meridional circulation with adiabatic heating (cooling) in the
cold (warm) region associated with upward (dowm_'ard) motion (Reed 1964, Plumb and Bell
1982). Therefore, the direction of the induced circuiation depends upon the phase of the QBO.
During a westerly (easterly) phase descending (asce_ding) motion is present at the equator, just
below the level of maximum wind shear, with risi_lg (sinking) motion at mid-latitudes. The
direct forcing of the zonal wind in the model din' to the damping of vertically propagating
equatorial waves is restricted to latitudes less than :Lbout 20 degrees from the equator; however,
changes to the modelled atmosphere, particularly in the amount of the ozone column, occur
further poleward of this as a result of the induced r, mridional circulation.
4 The QBO in Ozone
Observations of large ozone reductions in high so_thern latitudes during Spring (Farman et
al., 1985) make the understanding of the latitudinal variation of the ozone QBO particularly
important. Garcia and Solomon (1987), for exampl_, have speculated that the QBO is relevant
to the understanding of the temporal variation of th_ springtime column ozone in southern polar
latitudes during the 1980's.
The photochemical time consta,t of ozone deer 'ases with increasing altitude and generally,
at any given height, with decreasing latitude. With a lifetime of hours in the upper stratosphere
ozone is expected to be close to its steady state value On the other hand, the ozone concentration
in the polar lower stratosphere can be far from its equilibrium value since the photochemical
time scale is long in that region and dynamics ex_!rts a major influence. Between these two
regions is a portion of the atmosphere where dyr_amieal and photochemical time scales arc
roughly comparable. It is the morphology of this tr_nsition region that defines the ozone budget
and distribution. The strength of the lower stratos]_here circulation is a crucial parameter in a
successful model simulation of the ozone distributiem.
Figure 2 shows the time-series of ozone anomaiy from the model run (the monthly mean
has been subtracted from each point). A prominent QBO signal is present at all latitudes. The
largest anomaly is in high latitudes, reaching 20 D_,bson Units in some cases. A phase reversal
is present at approximately 20 degrees latitude so that high latitude anomalies are out of phase
with the equatorial anomalies. There is no evidence for in-situ photochemical control of the high
latitude ozone anomaly. This is not suprising given that the photochemical constant of ozone is
long there. None of the radicals involved in ozone photochemistry, including OH, HO_, NO and
NO2, show significant biennial variations in high la'itudes.
241
The overall behaviour of the modelled ozone QBO compares favourably with the zonally
averaged observations of the QBO derived by Ha.,;ebe(1983) using _SBUV data. In agreement
with observations the positive ozone anomalies o_:cur at approximately the same time as the
westerly phase of the equatorial zonal wind QBO _t 50 mb (seefigure 2).
The modelled QBO in column ozone arisesas a result of the interaction of dyna,mics and
photochemistry in the following sequence of events. The equatorial zonal wind QBO giverise
to a rising and sinking motion at the equator as alrea_lydescribed. Hence, during a westerly
phase the strength of the equatorial ascent of the [[a_lleycellis reduced and during an easterly
phase it is enhanced. During an easterly phase tl_eenhanced upward motion lowers the ozone
column by reducing the lower stratosphere mixing ratios,since the mixing ratio profileincreases
with altitude;conversely,during a westerly phase downward motion increases the ozone column
by advecting higher mixing ratiosinto a region where the photochemical lifetime islong. Thus
during a westerly (easterly)phase a positive (neg;_tive)equatorial ozone anomaly will result.
The induced circulation is also responsible for the high latitude QBO in ozone. During a
westerly phase of the QBO the induced downwa_-d motion at the equator implies an upward
motion in the subtropics which opposes the Hadley circulation. The latitudinal extent of the
induced circulation is restricted to the subtropics, however (Plumb 1982), so that it cannot
directlytransfer an ozone anomaly to high latitu.:les.Nevertheless, the descending arm of the
Hadley cell extends to mid-latitudes and crosses the transition region from photochemical to
dynaraical control of the ozone distribution. Henre, for example, a suppression of the strength
of the Hadley circulation during a westerly phase of the QBO results in a negative anomaly
in mid-latitudes (not just in the subtropics). The ozone anomaly is then transferred further
poleward by eddy motions (this is opposed by the mean motion and hence the distribution of
ozone at high latitudes is determined by the balance between eddy and mean motion - see for
example, Harwood and Pyle (1977) and Haigh (1',}84)).
The high latitude column ozone anomaly m_xima in the two hemispheres of the run are
displaced by several months; they tend to occur ia spring/early summer and coincide with the
column ozone maxima. This compares well with observations and arisesin the model because
the phase of the modelled QBO in column ozone tends to reverse during April/May of each year.
Because of the direction of the mean circulationin the following months the ozone enomaly is
immediately evident in the southern hemisphere mid-latitudes and thisis then transferred to
higher latitudes via eddy transfer (which is strongest in winter months). The corresponding
anomaly maximum does not occur in the northern hemisphere untilsix months later when the
directionof the mean circulationhas reversed in direction.
Re_ore_ces
Xngell, J.I. and J. lorshover, 1978. Men. Weathex Rev., 106, 725.
Bojkov, R.D., 1986. Goophye. Roe. Lett., 13, 1236.
Coy, T.. 1979, J. £tmoe. Sci.o 35, 174.
Farman, J.C., B.G. Gaxdiner, and J.D. 3hanklin, 1986. Nature. 315, 207.
Gazcia, R.R. and S.Solomon, 1987. Geophye. Roe. Lett, 14, 848.
Grey, L.J. and 3.A. Pyle, 1987a. Quazt. J. Roy. _et. So¢., I13, 635.
Gray, L.J. and 3.1. Pyle, 1987b. in Transport Processes in the Middle
Atmosphere. eds G. Viscont£ and R.Garcia. p.b. Reidel.
Haigh, J.D., 1984. Quart. J. Roy. Met. Soc.,llO, 167.
Xazwood, R.S. and J.A. Pylo, 1975. Quart. J. Roy. Net. See., 101, 723.
H_rgood, R.S. and J.A. Pyle, 1977. Quart. 3. Roy Her. Soc., 103, 319.
Ha.ruood, R.S. and J.A. Pyle, 1980. Quart. J. Roy Net. See., 106, 395.
I_asebe, F., 1983. J. Geophye. Ree., 88, 6819.
Bolton, J.R. 1972. 1,, Y.utroduction to Dynamic Neteorology. pb academic Press.
Lindzen, R.S. and J.R. Holton 1968. J. Xtmoe. Sc_o, 30, 513.
Raujok&t, B. 1986. J. AthOS. Sci., 43, 1873.
Pluzb0 R.A. 1982..7. Atmoe. S¢i.., 39, 983.
Pl,,-b, R.A. and K.C. Bell, 1982o Quart. J. Roy. _ot. Soc., 108, 313.
Rood, R.J. 1960. Paper presented at the 40th ann:_versary meetJ.u_ of the
luer. Met. _oc. Boston.
Reed, R.J. 1964. quart. J. Roy. Net. See., 90, 4¢1.
Tolson. R.B. 1981. 3. Geophya. ReS.o 86, 7312.
Veryand, R.G. and Elcxlon, R.£. 1931. Meteor. Ha 8. 90, 128.
Nallace, 3.N. 1973. Rev. Geophya. Space Phys., 1!_, 191.
242
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11
243


A two-dimensional model of the quasi biennial oscillation of ozone

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