Calculations of the Northward eddy fluxes of stratospheric ozone in a three-dimensional chemical-dynamical model are discussed. It is shown that, although approximately 50 percent of the zonal mean flux is produced by stationary planetary wavenumbers 1 and 2, the wintertime flux due to the chemical eddies is substantially underestimated when a quasi-linear representation is used

Cunnold, D. M.

Hsu, N. C.

English

NASA Technical Reports Server

N95- 10665
A 3-D MODEL STUDY OF OZONE EDDY TRANSPORT
IN THE WINTER STRATOSPHERE
N. C. Hsu 1 and D. M. Cunnold 2
1 Science Application International Corp., Hampton, VA 23666
2School of Earth and Atmospheric Sciences,Georgia Institute of Technology, Atlanta, Ga 30332
Abtntract
Calculations of the Northward eddy fluxes of stratospheric
ozone in a three-dimensional chemical-dynamical model are
discussed. It is shown that, although approximately 50% of
the zonal mean flux is produced by stationary planetary
wavenumbers 1 and 2, the wintertime flux due to the chemical
eddies is substantially underestimated when a quasi-linear
representation is used.
Introduction
The problem of modeling ozone of the middle atmosphere
has been considered to be complex because of the coupling
between radiation, dynamics and photochemistry. The eddy
transport of ozone plays an important role in determining the
stratospheric ozone distribution, especially in the winter.
Based upon the linear wave theory, Hartmann and Garcia
(1979) and Garcia and Solomon (1983) argued that the net
eddy transport is significant only in the region where advective
and photochemical time scales are comparable and that the
zonal mean eddy flux might be approximated by including just
the contribution by stationary wavenumber 1 based upon
quasi-linear mathematics. On the other hand, using the LIMS
satellite data, Leovy et al. (1985) showed that the ozone
distribution is strongly influenced by irreversible deformation
associated with planetary wave breaking, which is a highly
nonlinear process. The purpose of this work is to study the
effect of the nonlinear wave-wave interactions on ozone eddy
fluxes using the results of a spectral global 3-D model.
Model Description
The model used in this study is an improved version of the
3-D GCM model by Cunnold et al. (1975). This model utilizes
quasi-geostrophic governing equations (see Cunnold et al.,
1975 for details). The vertical domain of integration extends
from the ground to approximately 85 km in log-pressure
altitude. In the horizontal plane, truncated series of spherical
harmonics are used to represent the zonal and meridional
structures up to wavenumber 18. This self-consistent 3-D
model allows for full interaction between radiative heating,
dynamics and photochemistry without much ad-hoc
parameterization in either the dynamical or the chemical
schemes.
Results
The model has been integrated for 18 months starting from
December 1. The results discussed in this section are based
upon the model output of the second January.
Figure 1 shows the calculated January monthly mean ozone
map at 10 mb. A distinct region of strong ozone gradient
spiraled westward and outward from the vortex between 50 °
wld 60 ° N to the tropical regi_m. Between the edge of the
vortex and the tropical branch of the spiral a prominent tongne
of high ozone stretches inward toward the polar region near
60 ° N, 210 ° E. These features are consistent with the
data analyzed by Leovy et al. (1985).
Figure 2 shows the model-generated amplitude and phue of
the geopotential height of wavenumber one in January.
Compared to the satellite observations analyzed by Labitzke et
al. (1985), the location of the maximum amplitude of the
model geopotential height disturbance is at a slightly lower
altitude than the observed which is at about 65 degree north
and 7 mb, and the measured magnitudes are underestimated by
approximately 10% in the stratosphere and the polar night
region. The phases of the model geopotential heights are
generally in good agreement with the satellite data, which
exhibit decreasing phase with increasing altitude and
increasing phase with increase of latitude toward the north
pole.
The comparison of the model temperature disturbances of
wavenumb_i" one with the satellite measurements by Labitzke
et al. (not shown here) also indicates that the observed
amplitude of temperature disturbance is characterized by a
major maximum located at 62 ° N and 40 mb, which is about
the same amplitude and location as the model predicted, and a
minor maximum at 58 ° N and 2 mb, which is overestimated
by approximately 40% in the model. The constant phase lines
in both the model and the observations tilt equatorward and
downward with magnitudes decreasing with height.
There are large interannual fluctuations of planetary wave
activities from year to year. Although the model-predicted
amplitudes of geopotential height and temperature of
wavenumber 1 and 2 do not agree exactly with the multi-year
averaged satellite measurements reported by Labitzke et al.,
they are within the range of the interannual variations given in
the four-year NOAA/NMC observations (Geller et al., 1984).
Therefore the perturbations of the winter middle atmosphere
generated by the model are representative of the real
atmosphere and can be used to study the ozone eddy tranport
in the stratosphere.
The Importance of The Nonlinear Terms In The
Mass Continuity Equation
The complete Eulerian ozone eddy continuity equation can be
written as follow:
_-+(u+u')-_-x+V'(v_ v_+ )+w-_-z=S (1)
where X is the ozone mixing ratio; S denotes the ozone
production/loss rate; (u,v,w) are zonal, meridional and vertical
velocities, respectively; overbars represent the zonal means of
quantities and primes denote the departures from zonal
averages.
314
https://ntrs.nasa.gov/search.jsp?R=19950004253 2020-06-16T11:26:00+00:00Z
90E
180 0E
270 E
Figurel January monthly mean ozone (in ppmv) map at I0 mb
observationally by Wu et al. (1987). In this section, we will
discuss the significance of the transient and nonlinear effects in
calculating the net ozone eddy transport due to stationary
wavenumber 1 and 2 using the output of the 3-D model
Time averaging equation (1) and following Garcia and
Solomon's procedures (1983), the net ozone eddy fluxes due
to stationary waves can he represented as
The nonlinear terms in equation (1) have been neglected in a
number of studies concerning ozone eddy transport. The
rationale for the neglect of the nonlinear transport depends on
the validity of the linear wave theory which assumes that the
wave amplitudes are small and thus the linear terms would he
much larger than the nonlinear terms in the tracer eddy
continuity equation. Using the satellite measurements,
Douglass et al. (1985), however, pointed out that the nonlinear
terms could he an important part of the net dynamical forcing
in the winter stratosphere and the inclusion of these terms
improved the agreement between the calculated ozone mixing
ratios and the observations. To investigate the importance of
the nonlinear terms in the net dynamical forcing, the nonlinear
terms have been calculated at each timestep of the 3-D model
and averaged over the simulated month of January.
Figure 3 (a) and (b) show the comparisons of the nonlinear
terms against the linear terms at the Gaussian longitudes at 60 °
N and 42 ° N for wavenumber 1. For both wavenumber 1 and
2 (not shown) the nonlinear terms are small compared to the
linear terms between 1 and 10 mb at 60 ° N, while at 42 ° N the
nonlinear terms are comparable to or even larger than the linear
terms in the altitudes between 1 and 10 mb.
Generally speaking, the region where the nonlinear terms are
significant in the eddy ozone budget takes place at a lower
latitude for wavenumber 2 than for wavenumber 1. The
nonlinear terms are more important to the net dynamical
forcing at midlatitudes than at high latitudes, implying that the
ozone distribution is greatly influenced by the nonlinear wave
interaction at some distance from the core of the polar night jet
stream. This is consistent with the idea that wave breaking
(i.e. strong nonlinear interaction) occurs in winter outside the
polar vortex (e.g. Mclntyre and Palmer, 1984).
The Roles of The Transient and The Nonlinear
Terms on The Net Ozone Eddy Fluxes Due To
Stationary Rossby Waves
Model calculation indicates that in the winter stratosphere
about 50% of the model net ozone eddy fluxes are attributed to
the contributions of stationary waves, while the contributions
of planetary wavenumber 1 and 2 account for 90% of the
model net ozone transport due to stationary waves. Therefore
approximately half of the net ozone eddy transports result from
the transports by stationary planetary wavenumber 1 and 2.
The importance of wavenumber 1 has been noted
where
_ (c, A+B/SI= A-B C 2 )
-- [ T02[n'] 2 _.'(02[h-qlV] - (hi i-[V][_'
s2 = _ v (02[_ + 0_ i"[glg']) v*2 [;,]2
' )
,,o(,t 02i{w  )
"- <02 +0,
'° iM-- 
A = ,D ; B = ,C-'-'-_i"[-_-'-_- ;
((c/,_D) ( _-c/,{D)2
01-- l + (_'-c/'{D)2 ; 02---- I +(_-c/'{D)2 ;
D_= 'OX' ,o-_' -._'" _-" + w"--u +v +v'"  ooz
DT = q, _ u, OT' v, OT' 3T" 3T'
bracket [ ] denotes the time average, star * represents the
deviation from the time average, Xc is the chemical time
315
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0.1
E
v
In
Q.
I//,,7 o.o,
16 2
32 _ 0.1
I o I
10 o_ 10
100 IO0
80 60 40 20 0
N
Lotitute (degree)
JD
E
v
t@
O.
0.01
0.1
I
10
100
80
'18f/J/l\ :
4so/(o, \ i
120_ 6030 \ I
 o\1'o:
_ _..__ ',
60 40 20
N
Lotltute (degree)
0
0.01
.-. 0.1'
E
v
10'
n
100
ii
8b ';0' 2'0"o
N
Lotitute (degree)
..90 \_
8o6'0'2o'2oo
N
Lotltute (degree)
Figure2 The monthly mean amplitude and phase of the model
geopotential height of wavenumber one ( on the right)
for January with the observations analyzed by
Labitzke et al. (1985) (on the left).
constant of ozone, xo is the advective time constant [kl;]-t, k is
the wavenumber, o denotes the static stabifity parameter and q'
is the heating rateperturbation.
The fast two terms on the right hand side of (2) are similar
to those derived based on a quasi-linear theory by Garcia and
Solomon and many others, except that an extra term appears in
the anti-symmetric components of the first term, which results
from the effect of Dr' on the ozone eddy transport. This is
compensated by the transports by the Eulerian mean motion.
The last two terms are caused by the inclusion of Dx' and Dr'
which represents the transient and nonlinear terms in the
ozone continuity equation and the thermodynamic equation,
repectively.
As depicted in figure 4, the chemically induced ozone eddy
fluxes predicted by the quasi-linear theory (i.e. Dx' = 0 and Dr'
-- 0) substantially underestimate the model net ozone eddy
fluxes for wavenumber 1 as well as wavenumber 2. Neither
the magnitudes of the net ozone eddy fluxes nor their
structures have been reproduced.
When the nonlinear terms and the linear transient terms in the
ozone eddy continuity equation and the thermodynamic
equation are included in the calculation of the net ozone eddy
transport, the resulting net ozone eddy fluxes of wavenumber
1 and 2 calculated from (2), shown in Figure 5, are in
remarkable agreement with those from the model except in the
region south of 40 ° N, where the model mean zonal wind is
4
At 2 mb I I I2 (a)
-2
-4 I I I
4
-2 -
i -4 I I I
4
-2
-4 __ I I
0 90 IRO 270 360
LONGITUDE (DEGREE)
i
O@ [At2mb I I ' _)1
-0.5
-: I I I
I
-0.5
-' I I Io
At I1 mb . -- I
,05
-I _t .... t I
0 go HqO 2.70 360
I OLIGITI)i)[ {[)IF(;R[ F)
Figure3(a) The comparison of the linear advection terms with
the nonlinear advection terms for wavenumber 1 at
60 ° N for January. The solid line denotes the linear
--_ , the short-dashed line the nonlinearterm term
u'-_ , the long-dashed line the linear term v _- ,
the dot-dashed line the nonlinear term v oz'
3y"
Figure 3 (b) As in Figure 3 (a) except for 42 ° latitude.
weak and the particle trajectories are quite variable. Obviously,
the discrepancies between the net model ozone eddy fluxes and
those calculated By the linearized formulation of Garri¢_ and
Solomon (1983) are caused by the neglect of the nonlinear
terms and the linear transient terms.
The relative importance of the transient linear terms and the
nonlinear terms was also investigated by comparing the net
ozone eddy fluxes resulting from the nonlinear terms against
those arising from the linear transient terms for wavenumber 1
and 2. For wavenumber 1, the linear transient forcings are
prominent in the the upper stratosphere, while the effccls of
the nonlinear terms are dominant in the middle and lower
stratosphere• For wavenumber 2, the net ozone eddy
316
t ........ ,,
o.ol (a)
"_'E 0"I I
1J0'90 tL'-o 951
1.21
I010.
13..
100
L ...... , , , ....... i
80 60 40 20 0 20 40 60 80
O.Oli
•"--" 0.1
E
10
13.
100
Co)
80 60 40 20 0 20 40 60 80
N Lotltude (degree) S
Figure 4 The chemical meridional ozone eddy fluxes, derived
from the linear theory, due to (a) standing
wavenumber 1; (b) standing wavenumber 2.
Contour interval is 0.6 ppmv*m/s.
_'ansports are almost completely controlled by the nonlinear
processes.
Therefore the nonlinear process, such as planetary wave
breaking, plays an important role in determining the net ozone
eddy transport and consequently the mean ozone distribution
in the transition region.
Concluding Remarks
The model results suggest that in the winter stratosphere the
contribution of stationary waves accounts for more than 50%
of the net ozone eddy fluxes and that the net ozone eddy
transport contributed by stationary planetary wavenumber 2
may not be ignored, especially in the sublropical region where
the nonlinear process is dominant in controlling ozone
transport.
Calculations also indicate that the chemical ozone eddy
fluxes of stationary wavenumber 1 and 2 estimated by the
linearized tracer continuity equation, although significant, do
not agree well with the net ozone eddy fluxes evaluated
directly from the model for the month of January. The linear
chemical transport is important only over a limited area near
the edge of the polar vortex and even there it is no larger than
the nonlinear contribution.
Acknowledgments
This work is supported by NASA contract NAS 5-27264 to
Georgia Institute of Technology.
References
Cunnold, D., and F. Alyea, N. Philips, and R. G. Prinn,
1975 : A three-dimensional dynamical-chemical model or
atmosphe¢c ozone, ,.LALm_,_, 32, 170-194.
o.o_:
0.11
t-,
E
10
rl
1001
(a)
80 60 40 20 0 20 40 60 80
t ......
o.o I (b)
"Z' o.1
p
E ' ;,,,- 1.55
,-_' 10' 2.06
Q_
1.29
100 o
8o'6o'42o o'2'o'4 6'o'8o
N Lot_tude (degree) S
Figure 5 The calculated net meridional ozone eddy fluxes
including the effects of the nonlinear terms and the
transient terms, due to (a) standing wavenumber 1;
(b) standing wavenumber 2. Contour interval is 0.6
ppmv*m/s.
Douglass, A. R., R. B. Rood and R. S. Stolarski, 1985:
Interpretation of ozone temperature correlations, 2,
Analysis of SBUV ozone data, J, Geophys. Res., 90,
10,693-10,708.
Garcia, R. R. and S. Solomon, 1983: A numberical model of
zonally averaged dynamical and chemical structure of the
middle atmosphere, J. Geophys. Res.. 88, 1379-1400.
Geller, M. A., M.-F. Wu, and M.E. Geiman, 1984:
Troposphere-stratosphere (surface-55 km) monthly winter
general circulation statistics for the nor'them hemisphere-
interannual variations, J. Atmos. Sci.. 41, 1726-1744.
Hartmann, D. L., and R. R. Garcia, 1979: A mechanistic
model of ozone transport by planetary waves in the
stratosphere, J. Atmos. Sci.. 36, 350-364.
Labitzke, K., J. J. Barnett, and B. Edwards, 1985:
Atmospheric structure and its variation in the region 20 to
120 km, draft of a ncw reference middle atmosphere,
Handbook for MAP. Vol 16 SCOSTEP, Univ. of
Illinois, Urbana-Champaign.
Lcovy, C. B., C-R. Sun, M. H. Hitchman, E. E. Remsberg,
J. M. Russell, III, L. L. Gordley, J. C. Gille and L. V.
Lyjak, 1985: Transport of ozone in the middle
stratosphere: Evidence for planetary wave breaking, J.
Atmos. Sci., 42, 230-244.
Mclntyre, M. E. and T. N. Palmer, 1984: The surf zone in the
stratosphere, J. Atmos. Terr. Phys.,46.825-849.
Wu, M.-F., M. A. Geller. J. G. Olson and E. M. Larson.
!987: A study of global ozone transport and the role _f
planetary waves using sateP.,_: .;4!a. l___Rcm.
92, 31181-31Y-17.
OAIOINAL PAOt I
OF Poor QL,UU,
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A 3-D model study of ozone eddy transport in the winter stratosphere

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