15 FEBRUARY 1999 563A L L E N E T A L .
q 1999 American Meteorological Society
Observations of Middle Atmosphere CO from the UARS ISAMS during the Early
Northern Winter 1991/92
D. R. ALLEN,*,## J. L. STANFORD,* M. A. LO´ PEZ-VALVERDE,1 N. NAKAMURA,# D. J. LARY,@
A. R. DOUGLASS,& M. C. CERNIGLIA,** J. J. REMEDIOS,11 AND F. W. TAYLOR11
* Department of Physics and Astronomy, Iowa State University, Ames, Iowa
1 Instituto de Astrofı´sica de Andalucı´a, Granada, Spain
# Department of Geophysical Sciences, University of Chicago, Chicago, Illinois
@ Department of Chemistry, Centre for Atmospheric Science, Cambridge University, United Kingdom
& NASA/Goddard Space Flight Center, Greenbelt, Maryland
** Applied Research Corporation, Landover, Maryland
11 Department of Physics, Oxford University, Oxford, United Kingdom
(Manuscript received 28 July 1997, in final form 28 April 1998)
ABSTRACT
Structure and kinematics of carbon monoxide in the upper stratosphere and lower mesosphere (10–0.03 hPa)
are studied for the early northern winter 1991/92 using the Upper Atmosphere Research Satellite Improved
Stratospheric and Mesospheric Sounder (ISAMS) measurements. The study is aided by data from a 6-week
parameterized-chemistry run of the Goddard Space Flight Center 3D Chemistry and Transport Model (CTM),
initialized on 8 December 1991.
Generally, CO mixing ratios increase with height due to the increasing source contribution from CO2 photolysis.
In the tropical upper stratosphere, however, a local maximum in CO mixing ratio occurs. A simple photochemical
model is used to show that this feature results largely from methane oxidation.
In the extratropics the photochemical lifetime of CO is long, and therefore its evolution is dictated by large-
scale motion of air, evidenced by strong correlation with Ertel potential vorticity. This makes CO one of the
few useful observable tracers at the stratopause level and above. Thus CO maps are used to study the synoptic
evolution of the polar vortex in early January 1992.
Modified Lagrangian mean mixing diagnostics are applied to ISAMS and CTM data to examine the strength
of the mixing barrier at the polar vortex edge. It is demonstrated that planetary wave activity weakens the barrier,
promoting vortex erosion. The vortex erosion first appears in the lower mesosphere and subsequently descends
through the upper stratosphere, and is attributed to effects of planetary wave dissipation.
Agreement between ISAMS and CTM is good in the horizontal distribution of CO throughout the examined
period, but vertical CO gradients in the CTM weaken with time relative to the ISAMS observations.
1. Introduction
The major source of CO in the upper middle atmo-
sphere (mesosphere and lower thermosphere) comes
from CO2 photolysis (see Fig. 1):
CO2 1 hv → CO 1 O. (1)
Generally, CO mixing ratios increase with height
throughout the middle atmosphere due to the high al-
titude source and downward advective and diffusive flux
## Current affiliation: Department of Geophysical Sciences, Uni-
versity of Chicago, Chicago, Illinois.
Corresponding author address: Dr. Douglas Allen, Department of
Geophysical Sciences, University of Chicago, 5734 S. Ellis Ave.,
Chicago, IL 60637.
E-mail: drallen@bethel.uchicago.edu
into the mesosphere and stratosphere. Methane oxida-
tion plays a large role in the stratospheric budget, pro-
viding a CO source that maximizes near 30 km; although
some CO molecules produced from combustion and nat-
ural sources near the surface reach the stratosphere, most
are destroyed in the troposphere (Brasseur and Solomon
1986). The only major CO chemical loss mechanism in
the middle atmosphere is oxidation by the hydroxyl rad-
ical (OH) to CO2:
CO 1 OH → CO2 1 H, (2)
which occurs during the sunlit hours, since OH is pro-
duced from photolysis reactions (e.g., with H2O). In the
thermosphere chemical loss is negligible resulting in a
downward flux of CO into the mesosphere (Allen et al.
1981).
In the upper stratosphere and mesosphere, the pho-
tochemical lifetime of CO is on the same order (weeks
to months) as vertical transport timescales and is gen-

564 VOLUME 56J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S
FIG. 1. Schematic diagram of CO chemistry and transport processes in the meridional plane
under solstice conditions, adapted from Solomon et al. (1985).
erally larger than horizontal transport timescales (days
to weeks), making it a useful tracer of the atmospheric
transport (Hays and Olivero 1970; Wofsy et al. 1972;
Allen et al. 1981; Solomon et al. 1985). In the polar
night, stratospheric and mesospheric CO is conserved
due to the lack of OH, so it should be a particularly
good tracer of winter polar vortex dynamics.
Early predictions of the CO mixing ratio in the middle
atmosphere were made by Hays and Olivero (1970),
who incorporated CO and CO2 photochemistry and ver-
tical transport in a 1D model to calculate mixing ratio
profiles from 0 to 200 km for two recombination regimes
and three eddy diffusion formulations. They found that
CO mixing ratios increase with height throughout the
middle atmosphere due to CO2 photolysis reaching at
least 30 ppmv in the thermosphere. Wofsy et al. (1972)
and Wofsy (1976) furthered this work by including more
complex photochemistry and quantified the importance
of CO2 photolysis, CH4 oxidation, and loss from OH
for the CO distribution.
A pioneering study of CO in the middle atmosphere
by Solomon et al. (1985) used a 2D chemistry and trans-
port model from 10 to 116 km to examine the distri-
bution and seasonal evolution of CO. Salient points from
the study include: 1) CO mixing ratios increase with
height throughout most of the middle atmosphere; 2)
mesospheric CO abundances are larger in winter than
in summer due to vertical advective transport; 3) ex-
tremely large CO mixing ratios are found in the polar
night mesosphere–upper stratosphere due to diabatic de-
scent and lack of OH, with especially sharp CO gra-
dients occurring at the polar night terminator; 4) mid-
latitudes may exhibit significant CO variability during
periods of large-amplitude planetary waves.
Carbon monoxide mixing ratios in the middle at-
mosphere have been previously measured mainly by
ground-based microwave techniques (Waters et al. 1976;
Goldsmith et al. 1979; Kunzi and Carlson 1982; Clancy
et al. 1982, 1984; Bevilacqua et al. 1985; Aellig et al.
1995). These studies have shown the general tendency
of CO mixing ratios to increase with altitude and be-
come larger in the winter hemisphere and propose that
chemical as well as dynamical processes such as plan-
etary wave activity (Bevilacqua et al. 1985), gravity
wave activity (Aellig et al. 1995), vertical and horizontal
mixing, and interhemispheric circulations in the middle
atmosphere, contribute to large CO variability on time-
scales of days to years.
Satellite observations of infrared CO emission by the
Stratospheric and Mesospheric Sounder (SAMS) instru-
ment onboard NIMBUS-7 were obtained from the fun-
damental vibrational–rotational band at 4.6 mm (Mur-
phy 1985). The SAMS CO indicated large variability
with altitude, latitude, and time in the middle atmo-
sphere, as expected from model predictions (Solomon
et al. 1985). Carbon monoxide measurements in the
middle atmosphere have also been made by infrared
occultation instruments on various shuttle missions (Gi-
rard et al. 1988; Gunson et al. 1990; Rinsland et al.
1992; Gunson et al. 1996; Chang et al. 1996).
Carbon monoxide observations have also been ob-
tained from the Improved Stratospheric and Mesospher-
ic Sounder (ISAMS) onboard the Upper Atmosphere
Research Satellite (UARS). This instrument provides
nearly global coverage with good vertical resolution to
examine the CO distribution from approximately 10 to
0.03 hPa (roughly 30–70 km). Preliminary zonal-mean
maps of ISAMS CO were presented in Lo´pez-Valverde

15 FEBRUARY 1999 565A L L E N E T A L .
et al. (1993) and a more detailed discussion of the sea-
sonal zonal-mean evolution was described in Lo´pez-
Valverde et al. (1996). A detailed comparison with at-
mospheric tracer molecular spectroscopy CO data is pre-
sented in Lo´pez-Valverde et al. (1998).
The present study examines ISAMS CO (data de-
scription provided in section 2) during the early northern
winter 1991/92. ISAMS CO data are compared with
output from a parameterized-chemistry run of the God-
dard Space Flight Center (GSFC) 3D Chemistry and
Transport Model (CTM). The CTM is described in sec-
tion 3 of this paper. Section 4 introduces two Lagrangian
diagnostic schemes that are applied to ISAMS and CTM
data. Section 5 contains the data analysis. First, the me-
ridional distribution of ISAMS CO is discussed, fol-
lowed by an explanation of the local maximum in the
tropical upper stratosphere. Next, the synoptic evolution
of the polar vortex in early January 1992 is presented,
using CO as a dynamical tracer. A comparison of IS-
AMS and CTM CO is made by examining the synoptic
evolution and zonal-mean meridional structure. Finally,
modified Lagrangian mean diagnostics are used to study
horizontal mixing processes during the vortex dissipa-
tion occurring in January 1992. Section 6 contains a
summary of significant points.
2. Data description
This study examines version 12 CO data from the
ISAMS, one of the 10 UARS instruments. ISAMS mea-
sures the CO concentration in the upper stratosphere
and mesosphere by detecting infrared limb emission
from the vibrational–rotational band near 4.6 mm. The
CO signal is contaminated by emissions from other con-
stituents, mainly N2O, CO2, and O3. Although pressure
modulation techniques (see Taylor et al. 1993) help to
discriminate between closely spaced or overlapping
emission lines, contamination is still a major concern
in the CO retrieval (Lo´pez-Valverde et al. 1996).
Another difficulty in the retrieval is that CO is not
in local thermodynamic equilibrium (non-LTE) in most
of the middle atmosphere (Lo´pez-Valverde et al. 1991;
Lo´pez-Puertas et al. 1993). In non-LTE conditions ther-
modynamic equilibrium is not met and therefore the
population of the emitting level does not follow the
Boltzmann distribution. In this case the source function
for the given transition must be used in the retrieval
rather than the Planck function. The non-LTE model
used in the ISAMS retrieval is described by Lo´pez-
Puertas et al. (1993) and Lo´pez-Valverde et al. (1996).
ISAMS CO retrievals are performed from approxi-
mately 10 to 0.03 hPa. At pressures higher than 10 hPa
the signal is significantly contaminated by Pinatubo
aerosols. One criterion used for judging the quality of
the retrieved measurements is the ratio of the retrieved
variance to a priori variance. When this ratio exceeds
2 the data quality (denoted Q here) is flagged by setting
it negative. At this point, the data contain equal infor-
mation from the measurements and a priori climatology,
which for version 12 ISAMS CO is a seasonally varying
zonal-mean field, derived from a blended dataset of
GSFC 2D model output and version 10 ISAMS CO.
This study uses level 2 and level 3AT (described be-
low) CO from ISAMS processing version 12, the most
recent processing version, which has not yet been fully
validated (preliminary error estimates are on the order
of 30% for individual measurements). Version 12 CO
has several improvements over the previously validated
version 10 (see Lo´pez-Valverde et al. 1996), including
inline non-LTE source function calculation rather than
tabulated source function and use of ISAMS N2O to
remove contamination rather than a 2D climatology.
Level 2 refers to the first retrieved data product arranged
as consecutive vertical profiles, which are positioned
along the satellite limb track at regular time intervals,
but irregularly spaced in the vertical. Level 3AT is a
standard UARS format produced by interpolating level
2 data horizontally along the limb track to equally
spaced times (;65 s) and vertically to standard UARS
pressure surfaces. ISAMS measures with twice the hor-
izontal sampling rate of the level 3AT output, so the
interpolation from level 2 to level 3AT involves a rough-
ly 50% decrease in the horizontal resolution.
Figure 2 provides the distribution of good quality (Q
. 0) CO measurements for 12 January 1992, along with
Ertel potential vorticity derived from National Centers
for Environmental Prediction (NCEP) meteorological
analyses at eight nearby potential temperature surfaces
(data provided by G. Manney). Here level 3AT data in
the Northern Hemisphere are plotted at 16 pressure lev-
els from 10 to 0.032 hPa. Each colored circle marks one
level 3AT measurement with the color representing the
log10 of the CO mixing ratio in ppmv. Data flagged with
negative Q are not plotted, resulting in gaps in Fig. 2.
For example, in part of the displaced polar vortex (as
identified by the PV contours) at 4.642 hPa the CO data
are flagged as ‘‘poor,’’ even though CO mixing ratios
in the polar vortex are expected to be large (as will be
explained later) and therefore may be expected to pro-
vide sufficient radiance to make a reliable measurement.
However, by comparing these plots with ISAMS tem-
perature distributions (not shown here) it was found that
a strong zonally asymmetric (wave 1) temperature pat-
tern is present with a maximum displaced slightly west
(clockwise) of the PV maximum. It is likely that the
low temperatures offset the high CO mixing ratios, mak-
ing the radiance measured in this region by ISAMS too
small to make an accurate retrieval. Large regions of
poor data are found above 0.1 hPa due to excessive
noise in the measured radiances. Only limited nighttime
data are available in the mesosphere, whereas solar non-
LTE pumping allows for reliable daytime mesospheric
retrievals (Lo´pez-Valverde et al. 1996).
Gridded ISAMS CO used in this study were produced
from level 2 data by first interpolating vertically in log
pressure coordinates at each lat–long point to a given

566 VOLUME 56J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S
FIG. 2. Version 12 ISAMS CO at 16 pressure levels on 12 January 1992. Each colored circle represents one observation
on the UARS level 3AT grid. The color bar for each level is the log10 of the CO mixing ratio in ppmv. Data flagged as
‘‘poor’’ by the retrieval are not included in the plot. The lowest eight levels are overlaid by contours of NCEP-derived PV
on the potential temperature surfaces indicated. Nominal altitudes are provided for each pressure level. Projection is
orthographic with 08 (1808) long on the right (left) side.
pressure grid (the same grid used by the CTM discussed
below). At each pressure level the data were interpolated
horizontally to a 28 lat 3 58 long grid using a triangular
interpolation routine. To ensure nearly hemispheric cov-
erage of gridded CO, all data were used in the gridding,
even data flagged as ‘‘poor.’’ A comparison of zonal-
mean maps made with and without data flagged by neg-
ative Q show only small differences, none of which
affect any of the conclusions made in this paper. This
procedure also does not adversely affect the horizontal
maps at 1 hPa presented in this paper, since most of the
level 2 data points at that pressure have positive Q (see
Fig. 2). Regions of missing data (largely 808–908N, be-
yond the viewing geometry of UARS) were filled with
CTM CO scaled by the ratio of the zonal-mean ISAMS
CO to CTM CO at 788N. A nine-point (three lat points
3 three long points) average was applied to the sub-
sequent data both to ease the transition from ISAMS to
CTM CO at 808N and to reduce random variability from
instrument noise. No effort was made in this gridding
to account for the asynoptic sampling of the ISAMS
data.

15 FEBRUARY 1999 567A L L E N E T A L .
FIG. 3. The CO P (production) (a), (b) and L (loss) (c), (d) terms used for the GSFC 3D CTM run analyzed in this study.
These terms [taken from model described in Fleming et al. (1995)] are monthly and zonal means for December 1991 and
January 1992. Also plotted (e), (f ) are the photochemical timescales (in days) computed by 1/L.
3. Model description
This study compares ISAMS CO with CO distribu-
tions simulated by the GSFC 3D CTM [see Douglass
et al. (1996) for a complete model description]. For the
model run presented here, the full-chemistry was not
used, but was substituted with monthly mean parame-
terized photochemical production (P) and loss (L) for
CO, CH4, and N2O (the chemical source in the tracer
continuity equation is given by P 2 xL, where x is the
mixing ratio of the given tracer).
The wind fields used to drive the CTM are taken from
an advanced version of the Goddard Earth Observing
System (GEOS-1) assimilation (Schubert et al. 1993),
which incorporates changes in the modeling component
of the GEOS-1 assimilation system. These changes in-
clude a new radiation scheme, orographic gravity wave
drag, a rotated pole to remove the pole singularity, and
70 sigma levels from the surface to 0.01 hPa. The al-
gorithms are described in DAO (1996). This is the model
that will be part of the new GEOS system scheduled to
start production in 1998. Horizontal winds are taken
from this offline assimilation and vertical winds are cal-
culated internally in the CTM; numerical transport with-
in the CTM is calculated using the piecewise parabolic
scheme of Lin and Rood (1996). The CTM does not
parameterize unresolved (subgrid-scale) turbulence. The
model top (0.01 hPa) and surface (1000 hPa) are con-
strained by zero vertical velocity.
The monthly mean photochemical production and
loss terms are taken from an older version of the the
GSFC 2D model (Fleming et al. 1995). Figure 3 shows
the December and January CO P and L terms used by
the model. The large production rates above 0.1 hPa are
due to CO2 photolysis, whereas small production and
loss rates occur in the polar night (P and L are set to
zero poleward of 768N). The loss rates decrease with
latitude from the summer to winter pole and maximize
near the stratopause (;1 hPa). Also shown in Fig. 3 is
the chemical timescale (in days) calculated from the loss
rates (timescale 5 1/L) for December and January. The
timescale varies from several days near the summer po-
lar stratopause to several years in the high northern lat-
itudes, where the CO mixing ratio should behave as a
conserved tracer.
The CTM was initialized with CO, CH4, and N2O on
8 December 1991 using a potential vorticity (PV)/po-
tential temperature mapping scheme (Lary et al. 1995)
incorporating meteorological data from the GSFC DAO

568 VOLUME 56J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S
along with ISAMS CO and cryogenic limb array etalon
spectrometer N2O and CH4. Regions of missing data
were filled with output from the GSFC 2D model. In
addition, a completely passive tracer (P 5 0; L 5 0)
was introduced that was initialized identically to CO.
The model run was from 8 December 1991 to 18 January
1992, with output once per day at 0000 UTC on a 28
lat 3 2.58 long grid.
4. Analysis techniques: PV mapping and MLM
diagnostics
A fundamental shift in descriptions of atmospheric
dynamics is occurring as Lagrangian analyses are re-
placing conventional Eulerian analyses. This shift has
been facilitated by the production of relatively high-
resolution isentropic PV maps. A technique, denoted
here as ‘‘PV-mapping,’’ is becoming an increasingly
popular diagnostic tool for analyzing atmospheric chem-
ical transport. PV-mapping involves averaging constit-
uent mixing ratios along PV contours on isentropic sur-
faces (i.e., surfaces of constant potential temperature,
u) to produce 2D maps in PV and u coordinates. This
procedure effectively accounts for reversible (and re-
solvable) wave motions that can cause confusion in zon-
al-mean analyses. PV-mapping has proved to be quite
useful for analyzing constituent transport, especially in
the polar stratosphere, and for constructing constituent
distributions from limited observations (e.g., Schoeberl
et al. 1989).
PV-mapping basically involves a transformation of
the tracer continuity equation to conservative coordi-
nates (Schoeberl and Lait 1991). Potential temperature
is chosen as the vertical coordinate, and PV, which is
conserved for adiabatic, frictionless motion, is used in
the horizontal. To the extent that both the constituent
mixing ratio and PV are conserved, the two quantities
will maintain a close correlation. As nonconservative
processes (diabatic heating, friction, mixing, or photo-
chemical effects) become important, the close correla-
tion will be lost. For the PV-mapping in this study, PV
on isentropic surfaces, derived from U.K. Meteorolog-
ical Office (UKMO) meteorological analyses, is first
converted to equivalent latitude, the latitude of a zonal
circle centered at the pole that encompasses the same
area as a given PV contour (see Lary et al. 1995). This
equivalent latitude is then interpolated to the (lat–long
pressure) locations of the ISAMS level 2 measurements
thereby associating each ISAMS observation with a PV-
derived equivalent latitude. Similarly, potential temper-
ature is calculated from UKMO data and interpolated
to the ISAMS level 2 measurement locations. This re-
sults in a series of points with coordinates (equivalent
latitude, potential temperature, CO mixing ratio). The
mixing ratios are then binned every 58 in equivalent
latitude and 50 K in potential temperature, averaged,
and smoothed with a nine-point (three equivalent lati-
tude points by three potential temperature points) av-
erage to further remove instrument noise. To avoid er-
rors from climatological bias and day/night differences
in the retrieval, only daytime data with Q . 0 were used
in the PV-mapping. The resulting map for 12 January
1992 is examined in section 5a.
As we shall see, one of the most dramatic aspects of
the CO during the observed period is rapid horizontal
distortion of isopleths and subsequent mixing. Here we
diagnose horizontal mixing using the modified Lagrang-
ian mean (MLM) technique. The theoretical basis of the
method, which originated with McIntyre (1980), has
recently been developed further by Nakamura (1995,
1996, 1998). In MLM, the tracer transport is measured
with respect to a moving air mass instead of geograph-
ically fixed coordinates. Here the air mass is defined by
the isosurfaces of tracer rather than PV. To the extent
the tracer is conservative, the tracer isosurfaces are ma-
terial surfaces so there is no ‘‘leakage’’ of substance,
or there is no transport. As such, all transport in the
MLM formalism comes from nonconservative processes
including mixing, diabatic heating, and photochemistry.
Although the full formulation (Nakamura 1995, 1998)
encompasses all these effects, in the present paper we
concentrate on isentropic mixing.
The key diagnostic is Le, or the equivalent length of
the tracer contour on the isentropic surface (Nakamura
1996). Suppose the short-term isentropic kinematics of
tracer mixing ratio x is well approximated by the simple
advection–diffusion equation:
]x
2
1 J(C, x) 5 D¹ x (3)
]t
where C is the streamfunction, J is the Jacobian, and
¹
2 is the Laplacian. Here D is assumed constant and
parameterizes all subgrid-scale mixing. Nakamura
(1996, 1998) shows that Eq. (3) can be transformed to
a one-dimensional diffusion equation
] ] ]x
2
x(A, t) 5 DL (4)e
1 2
]t ]A ]A
using A, the area enclosed by the tracer contour, as the
horizontal coordinate. Here
]
2 22 2L (A, t) 5 (]x/]A) A(|=x | )e
]A
22 2
5 (]x/]A) ^|=x | & (5)
defines the square of the equivalent length, where the
operator A( · ) 5 ∫ ∫ ( · ) dA denotes the integral of a
scalar over the area bounded by a x contour; for ex-
ample, A 5 A(1), and the operator ^ · & 5 ]A( · )/]A
represents the contour average (Nakamura 1998). The
quantity Le is, to a good approximation, the perimeter
length of the tracer contour enclosing area A [it reduces
to the actual contour length when |=x| is constant around
the contour], and hence measures the degree of scram-
bling by the flow (Nakamura 1998). It is clear from

15 FEBRUARY 1999 569A L L E N E T A L .
FIG. 4. (a) Potential vorticity (converted to equivalent latitude)–
potential temperature map of ISAMS CO for 12 January 1992, made
with UKMO temperatures and UKMO-derived PV. Only daytime data
with good quality (as identified by the quality factor in the retrieval)
were used in this analysis. Units are log (base 10) of the mixing ratio
in ppmv. (b) Same as (a) but for ISAMS N2O [note the difference
in extent of the vertical scales in (a) and (b)].
Eq.(4) that serves as an ‘‘effective horizontal dif-2DLe
fusivity’’ (a Lagrangian equivalent of Kyy) and hence
the drive for the tracer distribution in the area coordi-
nate. Notice that although microscale mixing D is cru-
cial, its effect is magnified by so the effective dif-2Le
fusivity is large when the tracer is well scrambled. Aside
from the uncertainty in D at a given resolution, the
effective diffusivity is precise and in principle com-
putable from the instantaneous tracer distribution alone
without resorting to particle advection. This is an ad-
vantage for tracer transport diagnosis in the middle at-
mosphere where wind observation is not readily avail-
able. Nakamura (1996) and Nakamura and Ma (1997)
show that the diagnostic is resolution-sensitive quanti-
tatively but not qualitatively.
In this paper we calculate by evaluating Eq. (5)2Le
literally using area averaging rather than contour av-
eraging [the first equality in Eq. (5), see Nakamura and
Ma (1997) for more details] and display it in a nor-
malized form j 5 ln( / ) where Lo 5 2pa cosf e is2 2L Le o
the circumference of the zonal circle at latitude f e, the
equivalent latitude defined by A(x, t) 5 2pa2(1 2
sinf e), where a is the earth’s radius. Thus j measures
how much the tracer contour is stretched from a zonal
circle, and vanishes when the tracer is perfectly zonal.
Here is calculated on pressure surfaces here for con-2Le
venience, rather than isentropic surfaces; the difference
is small in the regions of interest.
5. Results
a. Meridional structure
The map of ISAMS CO for 12 January 1992 (Fig.
4a), constructed using the PV-mapping technique de-
scribed in the previous section, provides a wealth of
information about the transport and chemistry of CO in
the middle atmosphere. Mixing ratios generally increase
with potential temperature except from 308N to 408S
equivalent latitude, below 1800 K (note: the log10 of the
mixing ratio in ppmv is plotted in Fig. 4). Winter polar
descent, bringing CO-rich air downward, is suggested
by the high CO mixing ratios poleward of 508N equiv-
alent latitude [CO in the winter polar region is also
enhanced due to lack of OH, which provides the main
CO sink (Solomon et al. 1985)]. The CO mixing ratio
increases by an order of magnitude between 308 and
808N equivalent latitude over the potential temperature
range 1200–1800 K. The large mesospheric CO mixing
ratios appear to reach 1000 K (;35 km). There are few
ISAMS observations with Q . 0 below 1000 K, and
therefore the sharp vertical gradient at high equivalent
latitudes between 800 and 1000 K does not necessarily
denote the lower boundary of diabatic descent.
CO mixing ratios decrease from high to low northern
equivalent latitudes in the mesosphere (above ;1900
K), whereas in the stratosphere near 1500 K minima are
found near 208N and 308S equivalent latitude with a
local maximum near 58S. This feature persists without
much change throughout November and December 1991
and January 1992. A similar map of N2O (Fig. 4b) dis-
plays monotonically increasing mixing ratios from high
to low equivalent latitudes as expected for a long-lived
tracer with tropospheric source advected by the mean
meridional circulation. The contrast between the CO and
N2O contours in the Tropics suggests that photochem-
istry is likely causing the tropical CO maximum. Section
5b examines this feature in detail, arguing that the low
latitude CO maximum is due largely to methane oxi-
dation.
b. Evidence of CH4 oxidation in the upper
stratosphere
The amount of CO produced from CH4 oxidation in
the upper stratosphere can be estimated by assuming a
first-order balance between the following two reactions:
OH 1 CH → CH 1 H O (k ) ⇒ CO, (6)4 3 2 1
OH 1 CO → CO 1 H (k ). (7)2 2

570 VOLUME 56J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S
FIG. 5. (a) Zonal-mean [CH4]/[CO] ratio as observed from ISAMS V12 data for 1 January
1992. (b) The predicted [CH4]/[CO] ratio for 1 January 1992 as calculated from Eq. (9) using
reaction rates from DeMore et al. (1997) and temperatures from the GSFC DAO assimilation.
Here we assume efficient (100%) conversion from CH4
to CO in the upper stratosphere through the reaction
given in Eq. (6) and neglect CH4 loss from O1D and
Cl. As will be shown below, this provides a fairly good
(within a factor of 2) approximation of the CO produced
from CH4 loss processes. Equations (6) and (7) represent
one source and one sink of CO, which if balanced, pro-
vide the [CH4]/[CO] ratio:
[CH ] k4 2
5 . (8)[CO] k1
Figure 5a shows the observed zonal mean [CH4]/
[CO] in the upper stratosphere from 308S to 308N for
1 January 1992 as calculated from ISAMS version 12
data, whereas Fig. 5b shows the predicted ratio from
Eq. (8) using reaction rates from DeMore et al. (1997)
and temperatures from the DAO assimilation. The ob-
served and predicted ratio isopleths show similar slopes
from 5 to 2 hPa for the region 308S to the equator. North
of 108N, the observed ratio decreases rapidly with lat-
itude, whereas the predicted ratio remains nearly con-
stant with latitude from 108S to 308N. The Northern
Hemisphere discrepancy is likely due to large meridi-
onal excursions of vortex air to low latitudes observed
on this day (see Fig. 12a). Since the CO mixing ratio
varies by an order of magnitude inside and outside the
vortex, even localized regions of vortex air can cause
large perturbations in the zonal-mean CO.
To estimate the relative contributions from chemistry
and transport, we obtained chemical loss and transport
timescales for CO from the GSFC 2D CTM (Jackman
et al. 1996) for the month of January. Figure 6 shows
the timescales at 158S and 358N for the following pro-
cesses: chemical loss T(CO), advection by the trans-
formed Eulerian mean [TEM, see Andrews et al. (1987)]
meridional circulation T(y*) and T(w*), and diffusive
processes T(Kyy) and T(Kzz). At 158S the photochemical
lifetime is much shorter than the dynamical timescales
from 10 to 1 hPa, so the upper stratosphere southern
tropical CO is controlled mainly by photochemistry. At
358N, however (Fig. 6b), the timescale for meridional
diffusion T(Kyy) is comparable to the photochemical
timescale T(CO) in the upper stratosphere therefore mix-
ing processes (largely from winter planetary wave ac-
tivity) are expected to significantly affect the CO profile,
as evidenced by the sharp drop off of [CH4]/[CO] north-
ward of 108N in Fig. 5a.
Above 2 hPa the observed [CH4]/[CO] decreases
more rapidly with altitude than the predicted ratio (cf.
Figs. 5a and 5b). This is likely due both to the increased
dynamical contribution at higher altitudes and the in-
creasing effect of CO2 photolysis on the CO budget, as
described below. The very large ISAMS CH4/CO ratios
observed near 10 hPa may be influenced significantly
by aerosol contamination of both the CO and CH4 IS-
AMS channels (Lo´pez-Valverde et al. 1996; Remedios
et al. 1996).
Equation (8) can be rearranged to calculate the ex-
pected CO contribution from CH4 oxidation by OH:
k1[CO] 5 [CH ]. (9)4k2
The zonal-mean ISAMS CO mixing ratio (black solid
line) and that calculated from Eq. (9) (dashed line) using
version 12 ISAMS CH4 are shown in Fig. 7 for 16
pressure levels on 1 January 1992. Also provided are
the CO mixing ratios calculated with the GSFC 2D CTM
(Jackman et al. 1996) production and loss terms for
January assuming photochemical equilibrium. First we
set the total CO production from the model (which in-
cludes CO2 photolysis) equal to the loss of CO by re-
action with OH (P 5 k2[CO][OH]). Then we solve for
[CO] using the January [OH] from the 2D model along
with the rate constant k2 from Eq. (7) and plot it with
a blue line in Fig. 7. This calculation is performed again
after subtracting the model’s CO2 photolysis rate from
the total production. This line (red in Fig. 7) estimates
the CO produced from loss of CH4. It is close to the
estimated value from Eq. (9) (dashed line), being some-
what larger (smaller) at altitudes above (below) ;2 hPa,
but always remaining within a factor of 2.
In the southern tropical latitudes at 8.54 and 6.99 hPa
the predicted CO mixing ratio from Eq. (9) is larger
than that observed by ISAMS (cf. dashed and solid
lines). From 6.99 to 1.27 hPa there is fairly good (better
than 50%) agreement in magnitude between the ob-

15 FEBRUARY 1999 571A L L E N E T A L .
FIG. 6. Chemical and transport timescales from the GSFC 2D CTM (Jackman et al. 1996) for January at 158S and 358N. Timescales are
for chemical loss, T(CO); advection by the transformed Eulerian mean (TEM) meridional circulation T(y*), T(w*); and diffusive processes
T(Kyy), T(Kzz).
served and predicted CO from 308S to the equator with
both showing a clear maximum near 108S from 3.77 to
1.98 hPa. A similar feature can be seen in the zonal-
mean (pressure vs latitude) solstice CO distributions
from the models of Solomon et al. (1985) (see their Fig.
3) and Fleming et al. (1995) (see their Fig. A-14). Both
models show the low-latitude maximum in the upper
stratosphere, although quantification of the strength of
the maximum is difficult in each case due to widely
spaced contours in the tropical stratosphere. The CO
production terms from the GSFC 2D model (see Fig. 3
of this paper and the colored lines on Fig. 7) also show
a low-latitude maximum, again suggesting that the fea-
ture is controlled by photochemical processes. Indeed,
a passive-tracer (P 5 0; L 5 0) initialized in the 3D
CTM with an identical distribution to ISAMS CO on 8
December 1991 shows no distinguishable tropical max-
imum on 1 January 1992.
At altitudes above 1.01 hPa the ISAMS CO (black
line) increases rapidly with height, whereas the pre-
dicted CO from CH4 oxidation (dashed and red lines)
decreases. This is due to the increased influence of CO2
photolysis and decreasing contribution from CH4 oxi-
dation. Reaction rates in Allen et al. (1981) show that
above ;55 km (;0.4 hPa), the primary source of CO
is from CO2 photolysis, whereas at the stratopause (;50

572 VOLUME 56J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S
FI
G
.
7.
O
bs
er
v
ed
z
o
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om
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.(
9)
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ra
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at
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us
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al
eq
ui
lib
riu
m
.

15 FEBRUARY 1999 573A L L E N E T A L .
km or ;1 hPa) and below, methane oxidation domi-
nates. The CO predicted using the total CO source term
from the GSFC 2D CTM (blue line) does show increased
influence of CO2 photolysis with altitude; note that the
difference between the blue and red lines in Fig. 7 is
due solely to CO2 photolysis. However, above 1.01 hPa
the modeled CO mixing ratio underestimates that ob-
served by ISAMS. The difference could be caused by
the increased influence of dynamical processes at higher
altitudes (see Fig. 6), but it is also possible that the
source term from the 2D model underestimates the CO2
photolysis rate.
The influence of vortex excursions and/or horizontal
mixing of CO-rich vortex air to low latitudes is esti-
mated to extend to approximately 108N from 3 to 1 hPa,
where the shape of the ISAMS CO mixing ratio lines
differ from the monotonically decreasing CO mixing
ratio predicted from photochemical processes alone.
Northward of 308N (not shown here) the observed CO
mixing ratio increases rapidly toward the pole, whereas
the predicted values from CH4 oxidation decrease
monotonically.
c. Merger of two anticyclones during strong warming
from 1 to 16 January 1992
The early northern winter stratosphere 1991/92 has
been the subject of several observational and modeling
studies. Rosier et al. (1994) examined the dynamical
evolution of this period using ISAMS temperatures and
derived winds and potential vorticity; O’Neill et al.
(1994) used the UKMO data assimilation to study the
Northern Hemisphere circulation during this winter;
Ruth et al. (1994) examined tracer transport with IS-
AMS N2O data; Sutton et al. (1994) applied Lagrangian
trajectory calculations to study finescale mixing. We
will further scrutinize this period by examining the evo-
lution of ISAMS and CTM data in the upper stratosphere
and lower mesosphere.
December 1991 to mid-January 1992 are marked by
three warming events accompanied by large incursions
of low-latitude air penetrating to high latitudes and
tongues of polar vortex air peeling off, stretching, and
mixing in low latitudes. The most significant event oc-
curred in mid-January when an anticyclonic vortex,
originating near the Greenwich Meridian, was advected
eastward and merged with the persistent Aleutian high,
forming an intense anticyclone that completely pushed
the vortex off the pole and weakened it considerably.
Here we provide a synoptic view of this vortex merger
at 1 hPa (near 50 km) in ISAMS and CTM CO.
Figure 8 shows ISAMS CO at 1 hPa (colored con-
tours) overlaid with NCEP-derived PV data at 1900 K
for 1–12 January 1992, and Fig. 9 shows CTM CO (at
1 hPa) for the same period. On 1 January the vortex
(identified by large values of PV and CO in Fig. 8) is
centered nearly over the pole and slightly elongated on
the 458–2258 long axis. A tongue of vortex air is
stretched along approximately the 308N latitude circle
from 1808 to 908E. This tongue elongates farther over
the next four days while a tongue of low-latitude, low-
CO mixing ratio air encroaches from near 908E (see
blue region marked with arrow near 1008E, 508N on 2
January, Fig. 8). This feature is most prominent on 3
January when the vortex exhibits a ‘‘comma’’ shape
with main cell and extending tail of high PV and CO,
resolved clearly by both ISAMS and the CTM. Con-
currently, the Aleutian high (near 1808) is growing rap-
idly and by 5 January is quite strong. Both ISAMS and
CTM CO on 5 January show this feature as a region of
low CO mixing ratio surrounded by a ring of high CO
vortex air. By this time the vortex ‘‘tail’’ has nearly
reconnected with the main vortex cell near 908E.
O’Neill et al. (1994) explain that on 6 January another
anticyclone, apparent in UKMO wind fields, is begin-
ning to form near 308N, 308E. This feature moves east-
ward (counterclockwise) over the next two days and by
8 January is centered near 708E. The effects of this
anticyclone on CO are observed by ISAMS and the
CTM on 8 January as the counterclockwise winds begin
to pull a tongue of CO-rich air off the main vortex near
308N, 908E (see arrow on Fig. 8). This tongue elongates
from 9 to 11 January as the traveling anticyclone moves
further eastward, advecting CO-rich air to the south,
while the Aleutian high is drawn into a thin tongue.
O’Neill et al. (1994) applied high resolution trajectory
methods to elucidate mixing process accompanying the
vortex merger. They showed that a portion of the air
that constitutes the Aleutian high on 8 January was
drawn into the traveling anticyclone while another por-
tion was drawn eastward along the southern boundary
of the displaced main vortex. The latter effect is clearly
resolved in the CTM CO on 10 January (note the elon-
gated region marked with arrow near 308N, 1808 to 2508
long in Fig. 9), whereas ISAMS (Fig. 8) is not able to
resolve the decaying Aleutian high beyond 8 January.
ISAMS CO shows very good correlation with PV con-
tours during this period; compare the vortex location
and shape for 1–12 January and detached ‘‘blobs’’ of
high CO and PV air on 10–12 January.
The horizontal structure on 12 January resembles that
of 5 January, with a comma-shaped main vortex cell
completely displaced off the pole and a strong Aleutian
anticyclone surrounded by a ring of vortex air. By 12
January the vortex area has diminished significantly
(compare red regions of Figs. 8 and 9 for 1 and 12
January). The trajectory analysis of O’Neill at al. (1994)
revealed that the strong anticyclone on 12 January is
actually composed of air that originated from three dis-
tinct vortices: the Aleutian high, the traveling anticy-
clone, and the polar vortex. The period from 13–16
January (not shown here) involved rapid mixing and
vortex erosion that produced a highly irregular state on
16 January with nearly indistinguishable vortex (shown
in Fig. 13d). A more detailed analysis of mixing pro-
cesses accompanying these events is provided in section

574 VOLUME 56J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S
FI
G
.
8.
La
m
be
rt
eq
ua
la
re
a
pr
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cti
on
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A
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at
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12
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co
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de
s
ar
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.

15 FEBRUARY 1999 575A L L E N E T A L .
FI
G
.
9.
Sy
no
pt
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m
ap
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o
f
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SF
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3D
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at
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8.
N
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lo
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ar
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se
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fo
r
Fi
gs
.8
an
d
9.

576 VOLUME 56J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S
FIG. 10. (a), (d) ISAMS CO for 8, 12 January 1992 at 1 hPa. (b), (e) CTM CO for 8, 12 January at 1 hPa. (c), (f ) CTM CO gridded
equivalently to the ISAMS data (see text) for 8,12 January at 1 hPa. Projections are Lambert equal area with latitude circles at 08, 308, and
608N.
5e, where a modified Lagrangian mean mixing diag-
nostic is applied to ISAMS and CTM data.
d. Comparison of ISAMS and CTM CO
A cursory comparison between ISAMS and CTM CO
was made in the previous section by examining the Jan-
uary vortex merger at 1 hPa in ISAMS (Fig. 8) and
CTM (Fig. 9) CO. A qualitative analysis of the two
figures reveals the ability of both model and observa-
tions to resolve the large-scale features involved in the
vortex evolution. This section compares in more detail
distributions of ISAMS and CTM CO several weeks
into the model run. As will be shown, the model and
observations show similar horizontal morphology of the
CO contours, but certain differences occur in the mean
meridional distribution.
Figure 10 compares ISAMS and CTM CO for 8 and
12 January at 1 hPa along with CTM CO sampled and
gridded identically to the ISAMS data (see below). On
8 January the distorted vortex with extending ‘‘hook’’
near 908E produced from the traveling anticyclone is
evident in ISAMS (Fig. 10a) and CTM (Fig. 10b) CO.
The model reveals a very distinct region of low CO near
2208 long associated with the strong Aleutian high,
whereas in ISAMS the Aleutian high appears to be
stretched into a thin tongue of low CO. This discrepancy
could partly be due to the fact that whereas the CTM
data are synoptic (at 0000 UTC), the ISAMS data are
taken over a period of 24 h (0000–2400 UTC); as men-
tioned in section 2 no effort was made in the gridding
of ISAMS data to correct for the asynoptic sampling.
To analyze this more closely we ‘‘flew’’ UARS
through the CTM by linearly interpolating the synoptic
CTM data in space and time to the ISAMS level 2 grid
and subsequently mapped the data with the identical

15 FEBRUARY 1999 577A L L E N E T A L .
FIG. 11. Zonal-mean (a) ISAMS CO, (b) CTM CO, and (c) ISAMS/CTM ratio for 1 and January 1992. (d)–(f ) Same as (a)–(c) but for 13
January 1992. The contour for ISAMS/CTM ratio of 1 is emphasized by the black line in (c) and (f ).
gridding procedure used for ISAMS CO (see section 2).
The resulting map for 8 January (Fig. 10c) shows a
slight improvement over the synoptic CTM map in the
orientation of the main vortex cell and elongated shape
of the decaying Aleutian high.
On 12 January, as the vortex becomes completely
displaced off the pole, both ISAMS and CTM CO show
good spatial agreement of large-scale features, although
the CTM CO is nearly everywhere larger than ISAMS
CO. The comma-shaped vortex structure is well defined,
and a region of high CO mixing ratio has been pulled
from the vortex tail and has nearly reconnected with the
main vortex. The model reveals finescale structure that
is not resolvable by ISAMS. The ISAMS-equivalent
map of CTM CO for 12 January (Fig. 10f) also shows
relatively good agreement with ISAMS CO (Fig. 10d)
in the shape of the polar vortex and strong Aleutian
high. We conclude that both ISAMS and CTM CO cap-
ture the large-scale variability of the upper stratospheric
vortex during this period.
Although the CTM is used for this study primarily
to examine the horizontal distributions of CO, we also
present a zonal-mean comparison in the meridional
plane as an example of how ISAMS CO can be used
to diagnose model deficiencies and vice versa. Zonal-
mean plots of ISAMS and CTM CO from 10 to 0.1 hPa
on 1 and 13 January 1992 (24 and 36 days after ini-
tialization) are provided in Fig. 11 along with the IS-
AMS/CTM ratio. On 1 January both ISAMS and CTM
CO show strong meridional gradients near 608N from
5 to 1.0 hPa, signifying the ‘‘edge’’ of the polar vortex.
The low-latitude double-lobed minima in the upper
stratosphere are evident in ISAMS at 308S and 158N
(see Fig. 11a); minima are also present in the CTM near
608S and 158N (see Fig. 11b), but are not as distinct.
By 13 January this feature becomes more obscured in
the model as a broad upper-stratospheric maximum sets
in from 608S to 158N (Fig. 11e), whereas ISAMS con-
tinues to display a compact double-lobed structure (Fig.
11d).
Vertical gradients in ISAMS tend to be larger than in
the model from 1 to 0.1 hPa on both 1 and 13 January.
The ISAMS/CTM ratios provided in Fig. 11c,f show
that the ISAMS CO mixing ratios are larger than the
CTM CO by about a factor of 2–3 near 0.1 hPa and
smaller throughout most of the upper stratosphere (10–
1.0 hPa). The contour of ISAMS/CTM 5 1 is high-
lighted in black. On 13 January both ISAMS and CTM
show strong horizontal gradients near 308N and weak
horizontal gradients poleward of 308N above ;1 hPa.

578 VOLUME 56J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S
The weakening of the horizontal gradients from 1 to 13
January is due to the polar vortex breakdown accom-
panied by large horizontal mixing discussed in sections
5c and 5e.
The weaker vertical gradients observed in the CTM
are likely due to several competing factors. Notably,
there are some questionable features in the residual cir-
culation used in this study. Zonal-mean latitude–height
cross sections of CTM CO (not shown here) show an
unexpected decrease in CO in the Northern Hemisphere
high latitudes above ;1 hPa throughout the run. This
is due to unrealistic upward motion in the model, which
dilutes CO mixing ratios. In this region the photochem-
ical lifetime is very long (see Fig. 3f) so discrepancies
are expected to be due to errors in transport rather than
chemistry. In the Tropics, however, the photochemical
lifetime is comparable to or smaller than the dynamical
timescales (see Fig. 6a) so discrepancies there could be
influenced by errors in the model photochemistry. The
analysis presented in section 5b, for example, suggests
that the CTM may be underestimating the CO produc-
tion from CO2 photolysis at higher altitudes. Further
limitations of the model that could factor into the dis-
crepancy with observations include the upper boundary
constraint of zero vertical velocity at 0.01 hPa, which
does not allow downward flux of CO from the upper
mesosphere and the exclusion of explicit horizontal and
vertical subgrid-scale diffusion. A complete diagnosis
of the relative contribution from each of these factors
is planned for future work.
Although further examination of ISAMS version 12
CO is necessary, the comparison of ISAMS CO with
PV and CTM CO presented here provides a useful pre-
liminary validation of ISAMS data quality as well as
constraints on the CTM, which may help to improve the
model’s transport and chemistry in the upper strato-
sphere and lower mesosphere. The good agreement in
horizontal morphology lends confidence to the use of
ISAMS CO as a tracer to identify rapidly varying zon-
ally asymmetric features in the upper stratosphere/lower
mesosphere and provides validation for the horizontal
winds and transport scheme used by the CTM. The dis-
crepancies in the mean meridional structure points to
possible model deficiencies and provides incentive for
a more thorough validation of ISAMS and CTM CO.
e. MLM diagnostics of vortex merger
The equivalent length (Le) described in section 4 can
be used to examine barrier evolution and mixing that
accompany large stratospheric wave events. Here Le
provides both a diagnostic for the instantaneous degree
of scrambling of the tracer isopleths as well as the ‘‘ef-
fective horizontal diffusivity,’’ which drives the tracer
distribution in the MLM coordinates. Local minima in
Le generally indicate barriers to horizontal mixing,
whereas maxima indicate regions where large mixing is
expected (see Nakamura 1996, 1998). Figure 12 pro-
vides synoptic maps of ISAMS CO at 1 hPa for 1 and
6 January 1992 along with normalized equivalent
length, j 5 ln( / ), where Lo 5 2pa cosf e is the2 2L Le o
circumference of the zonal circle at latitude f e, the
equivalent latitude defined by A(x, t) 5 2pa2(1 2
sinf e), where a is the earth’s radius. On 1 January the
circumpolar vortex is slightly elongated on the 458–2258
axis with an emerging tail and intruding tongue of low-
latitude air ; j for this tracer distribution (Fig. 12b) dis-
plays a minimum near 608 equivalent latitude, indicating
a mixing barrier. The location of the 608 equivalent lat-
itude contour, identified by black contour on Fig. 12a,
shows that the mixing barrier is near the vortex ‘‘edge,’’
identified here by strong CO gradients. Five days later
the vortex has been pushed off the pole and is deformed
into a ‘‘comma’’ shape. Here j no longer shows a local
minimum near 608 indicating that the distinct mixing
barrier has weakened considerably; the situation on 6
January is more likely to experience horizontal mixing
across the 608 contour. As explained in section 4, Le
also gives to a good approximation of the perimeter
length of a given contour. As evident from Fig. 12 the
length of the 608 equivalent latitude contour has in-
creased from 1 to 6 January.
To examine the meridional structure of mixing pro-
cesses during January 1992, MLM diagnostics are ap-
plied to CTM output from 10 to 0.1 hPa. MLM assumes
mixing ratios are generally monotonically increasing or
decreasing with latitude in the region of interest. Due
to the tropical upper stratosphere maximum in CO,
MLM cannot be reliably applied to CO in that region.
However, if two tracers are in contour equilibrium (i.e.,
their contours overlap, even if the gradients differ) one
can prove mathematically (see appendix) that their
equivalent lengths will be identical. A comparison of
CTM CO (Figs. 13a–d) with CTM N2O (Figs. 13e–h)
for 1, 6, 11, and 16 January shows that CO and N2O
at 1 hPa have similar contour shapes. Since N2O has
monotonic gradients throughout the Northern Hemi-
sphere stratosphere, we can apply MLM diagnostics to
N2O as a surrogate for CO to obtain a 2D picture of
barrier evolution and horizontal mixing.
The normalized equivalent length j at 1 hPa on 1
January 1992 calculated from CTM N2O is provided in
Fig. 14e. This shows similar structure to j calculated
from ISAMS CO (Fig. 12b), although the mixing barrier
appears relatively stronger and is centered near 708 rath-
er than 608 equivalent latitude. The difference in mag-
nitude of j between the ISAMS and CTM analyses is
due partly to the different horizontal resolution of the
two datasets [see Nakamura and Ma (1997) for discus-
sion of resolution dependence]. Figures 14a–d show the
N2O mixing ratio as a function of equivalent latitude at
1 hPa. The minimum in j on 1 January is colocated
with a strong gradient of N2O with equivalent latitude
near the vortex edge. The mixing barrier appears to
weaken by 6 January as j near 708 equivalent latitude
increases to midlatitude levels (similar to Fig. 12d); it

15 FEBRUARY 1999 579A L L E N E T A L .
FIG. 12. (a) ISAMS CO and (b) normalized equivalent length j (from the MLM formulation, see text) at 1.01 hPa for 1 January 1992.
(c), (d) Same as (a), (b) but for 6 January 1992. Projection for (a), (c) is identical to Fig. 8.
attempts a slight comeback by 11 January, but is com-
pletely eliminated by 16 January, when a broad region
of large j develops from 408 to 708 equivalent latitude.
The rapid mixing occurring during this period is evident
in the synoptic plots of CTM CO (Figs. 13a–d) and
CTM N2O (Figs. 13e–h). The main vortex cell, high-
lighted in Fig. 13 by white/gray regions in CO and deep
blue/purple regions in N2O, which covers a large area
on 1 January, has nearly disappeared by 16 January,
leaving a broad well-mixed region in the upper strato-
sphere. Interestingly, although j responds rapidly to
tracer contour deformation the tracer-area (or tracer-f e)
relation shown in Figs. 14a–d does not change signif-
icantly over this time period. As expected from the def-
inition of Le in Eq. (5) there is a tendency for the mag-
nitude of the slope of the tracer-area curve |]x/]A| to
be smaller in magnitude when Le is large; see, for ex-
ample, the broad region of relatively weak slope in Fig.
14d from 408 to 708 equivalent latitude where j is large
(Fig. 14h). Also note that the steep slope observed on
1 January (Fig. 14a) weakens with the decay of the
mixing barrier.
Maps of j are plotted in Figs. 14i–l as a function of
pressure and equivalent latitude. On 1 January a strong
barrier is evident at 708 from 10 to 1 hPa with minimal
regions of large mixing (here defined arbitrarily by j $
2.8, i.e., Le ; 4Lo). Five days later (Fig. 14j) the barrier
has weakened significantly while a region of large j
develops roughly from 208 to 458 equivalent latitude
and 1 to 0.1 hPa. The polar upper-stratospheric barrier
strengthens slightly by 11 January (Fig. 14k) while the
entire lower mesosphere becomes saturated by large
equivalent lengths. By 16 January the lower mesosphere
is thoroughly mixed as values of j greater than 2.8
extend from 208 to 808 equivalent latitude, and the upper
stratosphere shows a broad well-mixed ‘‘surf zone’’ re-
gion from 508 to 608 near 10 hPa, widening to 408 to
708 near 1 hPa.
These analyses indicate that the well-mixed region
from 1 to 16 January first appears in the mesosphere

580 VOLUME 56J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S
FIG. 13. (a)–(d) CTM CO at 1 hPa for 1, 6, 11, and 16 January 1992 with same projection as Figs. 12a,c. (e)–(h) CTM N 2O at 1 hPa.
White (purple) indicates large (small) mixing ratio.
and subsequently descends through the upper strato-
sphere. This descent is consistent with the general the-
ory of stratospheric sudden warming first proposed by
Matsuno (1971) in which vertically propagating, tro-
pospherically forced planetary waves act to decelerate
(or ‘‘break down’’) the westerly polar night vortex. The
wave amplitudes increase with altitude (due to the de-
crease in air density) until they reach a critical layer
where the phase speed equals the zonal wind speed. Near
the critical layer the wave ‘‘breaks,’’ causing an easterly
acceleration that weakens the westerly jet. The altitude
of the critical layer then decreases with time as the
westerly jet turns easterly, so planetary waves break at
progressively lower altitude, consistent with the time
evolution of the Le diagnostic displayed in Figs. 12i–l.
6. Summary and conclusions
This paper presents observations of ISAMS CO from
10 to 0.03 hPa during the dynamically active early
northern winter 1991/92. The mean meridional structure
agrees with previous 2D model predictions; CO mixing
ratio generally increases with height in the upper strato-
sphere and lower mesosphere and increases with latitude
toward the winter pole. A previously unreported max-
imum in CO mixing ratio occurs in the tropical upper
stratosphere. This feature is attributed largely to the CO
source from methane destruction.
Large CO mixing ratios are found in the winter polar
vortex due to diabatic descent and long photochemical
lifetime. Because of the latter, CO is a useful tracer of
polar vortex dynamics. In January 1992, the merger of
the upper-stratospheric Aleutian high with a traveling
anticyclone is well captured by the synoptic evolution
of ISAMS CO data. Carbon monoxide becomes a par-
ticularly important tracer near the stratopause and
above, where the detection of many long-lived tracers
becomes difficult due to their decreasing mixing ratios
with altitude.
The evolution of ISAMS CO is compared with output
from a 6-week run of the GSFC 3D CTM. The synoptic
evolutions of ISAMS and CTM CO compare well at 1
hPa during the highly dynamic period from 1 to 12
January 1992, whereas two obvious differences are ev-
ident in the zonal-mean meridional distributions from
10 to 0.1 hPa. First, a relative weakening in the model
vertical gradients occurs compared with ISAMS. Sec-
ond, the model is not able to capture the persistent trop-
ical upper-stratospheric maximum observed in ISAMS.
Modified Lagrangian mean diagnostics are applied to
ISAMS CO and CTM N2O to examine the evolution of
mixing barriers in early January 1992. Mixing barriers
and regions of significant mixing are identified by min-
ima and maxima in the constituent ‘‘equivalent length,’’
a modified Lagrangian mean diagnostic. This diagnos-
tic, unlike time-averaged ‘‘eddy diffusivity’’ parameters

15 FEBRUARY 1999 581A L L E N E T A L .
FIG. 14 (a)–(d) CTM N2O as function of equivalent latitude at 1 hPa for 1, 6, 11, and 16 January 1992. (e)–(h) Normalized equivalent
length j calculated from CTM N2O at 1 hPa. (i)–(l) Two-dimensional cross section of normalized equivalent length calculated from CTM
N2O. Contour interval is 0.4.
common among two-dimensional models, is defined in-
stantaneously; as a result, it is better suited to describe
the process of a mixing event (Nakamura 1996). For 1
January 1992 a mixing barrier is identified near the
vortex edge in both ISAMS CO and CTM N2O. This
barrier weakens over the next two weeks as planetary
wave activity erodes the polar vortex, leaving a well-
mixed lower mesosphere and broad ‘‘surf zone’’ in the
upper stratosphere. The altitude of strong polar vortex
erosion, as viewed in the MLM framework, appears to
descend from mesosphere into the upper stratosphere.
This is consistent with the idea that vortex dissipation
is caused by the breaking of vertically propagating plan-
etary waves.
In conclusion, we have demonstrated that, used with
care, ISAMS CO data can enhance our understanding
of the dynamics and chemistry of the upper stratosphere
and lower mesosphere. The data are useful for both
observations and model comparisons.
Acknowledgments. We want to thank three anony-
mous reviewers for helpful comments on the manuscript
and R. J. Wells for invaluable assistance with the ISAMS
data. R. Swinbank and A. O’Neill developed the UKMO
data (used in the PV-mapping) from which PV was cal-
culated using code from M. Chipperfield. A. Miller and
M. Gelman developed the NCEP data from which PV
was derived and provided to us by G. Manney. Many
of the IDL and FORTRAN programs used for this study
were modified from programs written by H. Pumphrey.
We also want to thank R. Rood, K. Ekers, and the entire
GSFC (DAO, code 915) Data Assimilation Office for
providing winds from the ‘‘PREFGGEO’’ assimilation
that were used in this study. UARS level 3AT data were
obtained from the Earth Observing System (EOS) Dis-
tributed Active Archive Center (DAAC, code 902.2) at
the GSFC, Greenbelt, MD. The activities of the EOS
DAAC and the UARS Project (code 916) are sponsored
by NASA’s Mission to Planet Earth Program. ISU co-
authors are sponsored in part by National Aeronautics
and Space Administration Grant NAG 5-2787. Part of
this work was done while D. Allen was a Guest Graduate
Student at Argonne National Laboratory, Argonne, IL.

582 VOLUME 56J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S
APPENDIX
Proof that Equivalent Length is the Same for all
Species in Contour Equilibrium
By definition any two tracers in contour equilibrium
hold a compact relationship. That is, the mixing ratio
of one is specified by that of another:
x1(x, y, u, t) 5 x1(x2(x, y, u, t)), (A1)
where x1 and x2 are the mixing ratios of the two species.
The above relationship does not necessarily have to be
monotonic (one-to-one). Equivalent length defined
through x1 is
5 (]x1/]A)22^|=x1|2&,2Le (A2)
where the angle brackets denote the contour average.
However, since
]x dx ]x dx1 1 2 1
5 ; =x 5 =x , (A3)1 2
]A dx ]A dx2 2
Eq. (A3) can be rewritten as
2 22 2L 5 (]x /]A) ^|=x | &e 1 1
22 22 2 2
5 (]x /]A) (dx /dx ) ^(dx /dx ) |=x | & (A4)2 1 2 1 2 2
22 2
5 (]x /]A) ^|=x | &. (A5)2 2
The last identity uses the fact that dx1/dx2 is a constant
on the tracer contour. Hence equivalent length is iden-
tical whether x1 or x2 is used. Notice, however, that the
gradients of the two tracers are not necessarily the same
since in general dx1/dx2 ± 1 in Eq. (A3).
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