Chemical data assimilation: A case study of
solar occultation data from the ATLAS 1
mission of the Atmospheric Trace Molecule
Spectroscopy Experiment (ATMOS)
D. J. Lary1,2
Data Assimilation Office, NASA Goddard Space Flight Center, Greenbelt, Maryland, USA
B. Khattatov
National Center for Atmospheric Research, Boulder, Colorado, USA
H. Y. Mussa
Unilever Cambridge Centre/Atmospheric Research Centre, University of Cambridge, Cambridge, UK
Received 12 February 2003; revised 3 April 2003; accepted 18 April 2003; published 7 August 2003.
[1] A key advantage of using data assimilation is the propagation of information from
data-rich regions to data-poor regions, which is particularly relevant to the use of solar
occultation data such as from the Atmospheric Trace Molecule Spectroscopy Experiment
(ATMOS). For the first time, an in-depth uncertainty analysis is included in a
photochemical model-data intercomparison including observation, representativeness, and
theoretical uncertainty. Chemical data assimilation of solar occultation measurements
can be used to reconstruct full diurnal cycles and to evaluate their chemical self-
consistency. This paper considers as an example the measurements made by the ATMOS
instrument ATLAS 1 during March 1992 for a vertical profile in flow-tracking coordinates
at an equivalent potential vorticity (PV) latitude of 38
S. ATMOS was chosen because
it simultaneously observes several species. This equivalent PV latitude was chosen as it
was where ATMOS observed the atmosphere’s composition over the largest range of
altitudes. A single vertical profile was used so that the detailed diurnal information that the
assimilation utilizes could be highlighted. There is generally good self-consistency
between the ATMOS ATLAS 1 observations of O3, NO, NO2, N2O5, HNO3, HO2NO2,
HCN, ClONO2, HCl, H2O, CO, CO2, CH4, and N2O and between the observations and
photochemical theory. INDEX TERMS: 0340 Atmospheric Composition and Structure: Middle
atmosphere—composition and chemistry; 0394 Atmospheric Composition and Structure: Instruments and
techniques; 3337 Meteorology and Atmospheric Dynamics: Numerical modeling and data assimilation;
KEYWORDS: data assimilation, chemical Kalman filter, skill scores, ATMOS, ozone assimilation
Citation: Lary, D. J., B. Khattatov, and H. Y. Mussa, Chemical data assimilation: A case study of solar occultation data from the
ATLAS 1 mission of the Atmospheric Trace Molecule Spectroscopy Experiment (ATMOS), J. Geophys. Res., 108(D15), 4456,
doi:10.1029/2003JD003500, 2003.
1. Introduction
[2] For more than two decades, vertical profile measure-
ments of trace gases have been made by solar occultation
(e.g., from the Stratospheric Aerosol and Gas Experiment
(SAGE), the Halogen Occultation Experiment (HALOE),
Polar Ozone and Aerosol Measurement (POAM), the Atmo-
spheric TraceMolecule Spectroscopy Experiment (ATMOS),
and the Improved Limb Atmospheric Sounder (ILAS)). The
observations are self-calibrating and are therefore useful for
the analysis of temporal trends. However, by definition, the
use of solar occultation limits the measurement opportunities
to satellite sunrise and sunset. It is therefore useful to use
chemical data assimilation cast in flow-tracking coordinates
to reconstruct full diurnal cycles and to check the chemical
self-consistency of the solar occultation measurements. The
use of flow-tracking coordinates allows a more complete
global view to be obtained from the sparse latitudinal
coverage of the solar occultation measurements.
2. Why Use Assimilation?
[3] The question could be asked, How does using chem-
ical data assimilation differ from using reverse domain
filling (RDF) isentropic trajectories, where ozone depletion
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. D15, 4456, doi:10.1029/2003JD003500, 2003
1Also at Goddard Earth Sciences and Technology Center, University of
Maryland, Baltimore County, Baltimore, Maryland, USA.
2Also at Department of Chemistry, University of Cambridge, Cam-
bridge, UK.
Copyright 2003 by the American Geophysical Union.
0148-0227/03/2003JD003500$09.00
ACH 10 - 1

is computed along trajectories using aircraft and satellite
data or other two-dimensional (2D) and 3D photochemical
models? Chemical data assimilation combines the observa-
tional information available from measurements with the
theoretical information encapsulated into a deterministic
model of atmospheric chemistry, together with the associ-
ated uncertainties of each. Specifically, assimilation uses
(1) constituent observations (in this case, observations of
14 constituents simultaneously); (2) observational uncertain-
ty; (3) theoretical knowledge to propagate information from
the observations available to other species and locations;
(4) evaluations of chemical self-consistency; and (5) the
provision of an uncertainty on the analysis produced that
accounts for observational uncertainty, temporal and spatial
representativeness uncertainty, and theoretical (model) un-
certainty; that is, assimilation requires a specification of the
error statistics of the observations and the underlying model.
[4] For example, Figure 1 shows the time evolution of the
NO and NO2 analyses and the analyses’ uncertainties.
Conventional modeling studies do not present the time
evolution of uncertainty associated with their predictions.
Very useful as they are, techniques such as using RDF
isentropic trajectories or 2D and 3D chemical models are
not able to do this.
[5] Assimilation should not be seen as competing with
other modeling tools; rather, its purpose is objective im-
provement by combining observational, theoretical, and
uncertainty information formally and statistically in a mathe-
matical framework. The key aim in developing such a
powerful method is to look at scientific issues. However,
Figure 1. Diurnal cycles of (a and c) NO and (b and d) NO2 vertical profiles for the 30 March 1992
assimilation of ATMOS ATLAS 1 data at 38
S. (top) The chemical analyses produced by assimilation
overlaid with the observations (colored circles). (bottom) The analyses’ uncertainties overlaid with
the observation uncertainties (colored circles). The reduction in analysis uncertainty can be seen in the
bottom plots when new observational information comes in. The dots indicate the locations of the
assimilation analysis grid. A single vertical profile was used so that the detailed diurnal information that
assimilation utilizes could be highlighted.
ACH 10 - 2 LARY ET AL.: CHEMICAL DATA ASSIMILATION OF SOLAR OCCULTATION DATA

the credentials of the method must first be rigorously estab-
lished. The purpose of this paper is to evaluate critically the
analyses produced by chemical data assimilation and evalu-
ate this method’s skill with objective measures. Subsequent
papers will use the method to look at a variety of scientific
issues, for example, the role of halogens in the initiation and
catalysis of methane oxidation in the upper troposphere/
lower stratosphere region and the time evolution and parti-
tioning of nitrogen, chlorine, bromine, and hydrogen species
as well as the relative importance of ozone loss catalytic
cycles from the start of the UARS period to the present.
3. Flow-Tracking Coordinates
[6] Under adiabatic conditions, air parcels move along
isentropic surfaces (surfaces of constant potential tempera-
ture, q). So, when considering tracer fields, q is a suitable
vertical coordinate. McIntyre and Palmer [1983, 1984],
Hoskins et al. [1985], and Hoskins [1991] have shown the
value of isentropic maps of Ertel’s potential vorticity (PV)
for visualizing large-scale dynamical processes. PV plays a
central role in large-scale dynamics, where it behaves as an
approximate material tracer [Hoskins et al., 1985].
[7] As a result, PV can be used as the horizontal spatial
coordinate instead of latitude and longitude [Norton, 1994;
Lary et al., 1995a]. PV is sufficiently monotonic in latitude
on an isentropic surface to act as a useful replacement
coordinate for both latitude and longitude, reducing the
tracer field from three dimensions to two. These ideas have
already led to interesting studies correlating PV and chem-
ical tracers such as N2O and O3 [Schoeberl et al., 1989;
Proffitt et al., 1989; Lait et al., 1990; Douglass et al., 1990;
Proffitt et al., 1989, 1993; Atkinson, 1993]. A key result of
these studies is that PV and ozone mixing ratios are
correlated on isentropic surfaces in the lower stratosphere,
as was first pointed out by Danielsen [1968].
[8] Since the absolute values of PV depend strongly upon
height and the meteorological condition, it is useful to
normalize PV and use PV-equivalent latitude, fe, as the
horizontal coordinate instead of PV itself. fe is calculated
by considering the area enclosed within a given PV contour
on a given q surface. The fe assigned to every point on this
PV contour is the latitude of a latitude circle which encloses
the same area as that PV contour. Therefore for every level
in the atmosphere, fe has the same range of values,
90
–
90
. This provides a vortex-tracking and, indeed, a flow-
tracking stratospheric coordinate system.
[9] We have taken these now well-established ideas and
used them as a framework for our chemical data assimila-
tion. This approach is valid for our analysis interval of 1 day
and often for up to 10 days or longer in the stratosphere.
Because a major component of the variability of trace gases
is due to atmospheric transport, it makes sense to use a
coordinate system that ‘‘follows’’ the large-scale flow
pattern to perform our data assimilation.
4. ATMOS Observations
[10] As an example of how chemical data assimilation
cast in flow-tracking coordinates can be used to extend the
value of solar occultation data sets, we consider the ATLAS
1 data from the ATMOS instrument. The ATMOS instru-
ment is an infrared spectrometer (a Fourier transform
interferometer) that was designed to study the chemical
composition of the atmosphere. The ATMOS instrument has
flown four times on the space shuttle, on Spacelab-3 in
April 1985, and on ATLAS 1, ATLAS 2, and ATLAS 3 in
March 1992, April 1993, and November 1994, respectively.
In this study we use all the data from ATLAS 1 for a
vertical profile in our flow-tracking coordinates at an
equivalent PV latitude, fe, of 38
S. This equivalent PV
latitude was chosen as it was where ATMOS observed
the atmosphere’s composition over the largest range of
altitudes. We wanted to study a single vertical profile so
that the detailed diurnal information that assimilation
provides could be highlighted. We assimilated ATMOS
ATLAS 1 observations of 14 species, namely O3, NO,
NO2, N2O5, HNO3, HO2NO2, HCN, ClONO2, HCl, H2O,
CO, CO2, CH4, and N2O.
[11] The relative role played by the observations of
different species in the assimilation is an interesting issue.
The top 10 ranking of chemical information content for this
vertical situation over an entire diurnal cycle is O3, CO, HO2,
NO2, ClO, CH3OO, HCHO, NO, BrO, and H2O. It is not at
all surprising (in fact, it is rather reassuring) that O3 comes
out as number one. We also see key representatives of
carbon, nitrogen, hydrogen, and bromine species, reminding
us how coupled atmospheric chemistry is. It is interesting
that two of the top 10 are peroxy radicals: number three is
HO2 and number six is CH3OO. It is also noteworthy that the
methyl species are rarely considered in stratospheric studies
yet have significant information content.
5. Chemical Assimilation Scheme
[12] Data assimilation enables better use of observations
of atmospheric chemistry. An example of the way assimi-
lation can reconstruct a full diurnal cycle from occultation
observations is shown in Figure 1. This example will be
discussed more later.
[13] The first use of chemical data assimilation was by
Fisher and Lary [1995]. Khattatov et al. [1999] have de-
scribed the chemical Kalman filter used in this study. Other
studies using assimilation include those by Elbern [1997],
Elbern et al. [1997], Eskes et al. [1998, 1999], Khattatov et
al. [1999], Lary [1999], Elbern et al. [2000], Khattatov et al.
[2000, 2001], Wang et al. [2001], Smyshlyaev and Geller
[2001], Clerbaux et al. [2001], Errera and Fonteyn [2001],
Chipperfield et al. [2002], and Daescu and Carmichael
[2003]. The photochemical mode used is the extensively
validated AutoChem model [Fisher and Lary, 1995; Lary et
al., 1995b; Lary, 1996]. The model is explicit and uses an
adaptive-time step, error-monitoring time integration
scheme for stiff systems of equations [Press et al., 1992;
Stoer and Bulirsch, 1980]. AutoChem was the first model to
perform 4D variational data assimilation (4D-Var) [Fisher
and Lary, 1995] and now also includes a Kalman filter
[Khattatov et al., 1999]. AutoChem uses kinetic data largely
based on the work of Atkinson et al. [1997] and DeMore et
al. [1997], with updates for nitrogen chemistry based on the
work of Brown et al. [1999a], Portmann et al. [1999], and
Brown et al. [1999b].
[14] A key part of the chemical model is the calculation of
photolysis rates. In this study they are calculated using full
LARY ET AL.: CHEMICAL DATA ASSIMILATION OF SOLAR OCCULTATION DATA ACH 10 - 3

spherical geometry and multiple scattering [Anderson,
1983; Lary and Pyle, 1991a, 1991b; Meier et al., 1982;
Nicolet et al., 1982], corrected after Becker et al. [2000].
The photolysis rate used for each time step is obtained by
10-point Gaussian-Legendre integration [Press et al., 1992].
These calculations are updated on every assimilation itera-
tion to ensure that the improved ozone profile at a given
equivalent latitude is used to calculate the photolysis rates.
[15] The chemical system under study here contains a total
of 60 species. Fifty-five species are time integrated, namely
O(1D), O(3P), O3, N, NO, NO2, NO3, N2O5, HONO, HNO3,
HO2NO2, CN, NCO, HCN, Cl, Cl2, ClO, ClOO, OClO,
Cl2O2, ClNO2, ClONO, ClONO2, HCl, HOCl, CH3OCl, Br,
Br2, BrO, BrONO2, BrONO, HBr, HOBr, BrCl, H2, H, OH,
HO2, H2O2, CH3, CH3O, CH3O2, CH3OH, CH3OOH,
CH3ONO2, CH3O2NO2, HCO, HCHO, CH4, CH3Br,
CF2Cl2, CO, N2O, CO2, and H2O. The remaining five
species are not integrated and are not in photochemical
equilibrium, namely O2, N2, HCl(S), H2O(S), and HNO3(S).
The model contains a total of 420 reactions, 278 bimolecular
reactions, 32 trimolecular reactions, 60 photolysis reactions,
4 cosmic ray processes, and 46 heterogeneous reactions.
[16] The first guess used came from a January simulation
of the Cambridge 2D chemical model [Law and Pyle, 1991,
1993a, 1993b]. As these are not particularly well suited to
the conditions observed by ATMOS during March 1992,
our chemical assimilation was cycled three times. The
results presented are from the third cycle. This allowed
for quite rapid convergence to the conditions observed by
ATMOS. Each cycle involves a first-guess simulation,
followed by two iterations of the chemical Kalman filter,
and then an analysis simulation. The analysis simulation is a
free-running chemical simulation starting from the chemical
state vector at the end of the chemical Kalman filter. This is
done to mimic the way 4D-Var works, with the added
advantage of having the time evolution of the full species
error covariance matrix. This is desirable as it means there
are no steps in the species concentrations with time due to
Kalman filter increments (i.e., no time discontinuities when
new information is used).
5.1. Observations
[17] The key difference between conventional modeling
and data assimilation is the use of observations and infor-
mation on observational and other uncertainties. The uncer-
tainties we consider are the observational uncertainty quoted
by the observation team, the representativeness uncertainty
(i.e., the spatial variability over an analysis grid cell), and
the photochemical theoretical uncertainty.
[18] We obtain information on the representativeness
uncertainty and improve the signal to noise by using all
observations available within a grid cell and by studying the
probability distribution function (PDF) of these observa-
tions. The width of the PDF is used as a measure of the
variability, or representativeness uncertainty, for the grid
cell. When more than one observation is available in a grid
cell, we take the median of the PDF as the observation for
that cell and the median of the observation uncertainty PDF
as the observation uncertainty for that grid cell. So, both
the observation and observation uncertainty are obtained
directly from the data in a way that makes them truly
representative of that grid cell.
[19] The Kalman filter assimilation is a multivariate
technique which can simultaneously process the observa-
tion/uncertainty information pairs of the 55 time-integrated
species whenever and wherever they are available, together
with the theoretical information from our photochemical
model.
5.1.1. Temporal Search Criteria
[20] The criteria used to determine at what time we use
an observation are local solar time and solar zenith angle.
In the case of short-lived species or those with a signif-
icant diurnal cycle, such as NO and NO2, the observation
solar zenith angle needs to be within 2
of the analysis
time step solar zenith angle, and the observation local
solar time needs to be within 1 hour of the analysis local
solar time for the observation to be used. This ensures that
sunrise measurements are used at sunrise and that sunset
measurements are used at sunset. This is also important as
there can be a significant difference between the geo-
graphic latitude and the equivalent PV latitude. As our
analysis grid uses equivalent PV latitude, it is important
that we use the local solar zenith angle as the criteria for
using an observation and not just the local solar time. In
the case of longer-lived species or those without a signif-
icant diurnal cycle, we can use less stringent criteria. For
these longer-lived species we specify that the observation
solar zenith angle needs to be within 6
of the analysis
time step solar zenith angle and that the observation local
solar time needs to be within 1 hour of the analysis local
solar time. These, in fact, are rather strict criteria for the
long-lived species. Sensitivity experiments have shown
that much more lax values work just as well for the
long-lived species.
5.1.2. Spatial Search Criteria
[21] The criteria used to determine at what location we use
an observation are equivalent PV latitude, fe, and potential
temperature, q. An observation is used in the fe-q grid box
where it lies. The grid has 21 potential temperature levels,
spaced equally in log(q) between 400 and 2000 K, and
32 equivalent PV latitudes, spaced evenly between
90

and 90
. That means that no interaction between the boxes
(meridional transport, mixing, diabatic ascent/descent) is
considered.
[22] We have chosen to deal with an entire vertical profile
of observations at a time as vertical profiles can contain
gaps. These are easy to fill in by eye, but for an algorithm to
deal with the data voids we need to consider an entire
profile at a time in our flow-tracking coordinate space. In a
full 3D assimilation the 3D spatial covariance matrix would
be performing this task. However, in this study we are using
an array of 0D boxes with a full Kalman filter and detailed
chemistry. To make this computationally achievable, we use
multiple 0D box models which are stacked into a series of
profiles, giving us a 2D global assimilation with 21 poten-
tial temperature levels, spaced equally in log(q) between 400
and 2000 K, and 32 equivalent PV latitudes, spaced evenly
between
90
and 90
.
[23] So, to clarify, the actual assimilation is done in a 2D
array of completely independent boxes. However, the ob-
servation reconstructions used for this independent array of
boxes are generated by considering an entire profile at a
time, where the profile is a function of potential temperature
for a given equivalent PV latitude range. The equivalent PV
ACH 10 - 4 LARY ET AL.: CHEMICAL DATA ASSIMILATION OF SOLAR OCCULTATION DATA

latitude range is the width of the grid box. This is not ideal
but is a necessary and good approximation because of the
computer time required to do a full 3D assimilation with a
Kalman filter.
[24] Our observation reconstruction algorithm consists of
the following steps: (1) For each level in the analysis profile
we determine which observations lie between the bottom of
the level below and the top of the level above; (2) if there
are more than nthresh (usually taken to be 25) observations,
we sort them in order of their percentage uncertainty and
just use the nthresh most reliable data points (i.e., those with
the lowest concentration uncertainty to concentration ratio);
(3) for these data points we calculate the median concen-
tration; (4) if there are any levels which have no observa-
tions bracketed above and below by levels which did have
observations, we linearly interpolate using the available
values above and below.
5.2. Observation Uncertainties
[25] The uncertainty of the reconstructed observation has
two components. First, for each (fe,q) grid box we have a
distribution of observed concentrations and a distribution of
observed concentration uncertainties. We take the observa-
tional uncertainty to be the median observed concentration
uncertainty for the current distribution in the given (fe,q) grid
box. Second, we have the representativeness uncertainty.
Information on the representativeness uncertainty is gained
by using all observations available within a grid cell and
studying the PDF of these observations. The width of the
PDF is used as a measure of the variability or representative-
ness uncertainty for the (fe,q) grid cell. So, both the obser-
vation and observation uncertainty used are derived directly
from the data but are selected in a way that we are sure
whether they are truly representative of that grid cell. The
average deviation, or mean absolute deviation, is a robust
estimator of the width of the distribution [Press et al., 1992]:
srep ¼ ADev c1 . . .cNð Þ ¼
1
N
XN
j¼1
cj
c
 ; ð1Þ
where ADev is the average deviation, c is the volume
mixing ratio, c j refers to the individual concentration
observations available in the grid cell, and c is the mean
(i.e., average) mixing ratio. The reconstructed observation
for the (fe, q) grid box is the median of the 25 most accurate
observations available in the grid box. The median is used
so that the reconstructed observations, and hence the
analyses, are not affected by outliers.
[26] The representativeness uncertainty is an interesting
quantity as it clearly picks out mixing barriers such as the
polar vortices, the tropical pipe, and the tropopause. In
addition, for species such as ozone in polar day we see a
large representativeness uncertainty at the summer pole. It is
important to note that this representativeness uncertainty is
fully accounted for, goes into the analysis, and is reflected in
the analysis uncertainty. Whatever coordinate system is used,
such situations will be encountered; it is therefore important
to account for the grid representativeness uncertainty as
accurately as possible and to include them in the analysis.
[27] It is also fair to observe that this level of treatment of
uncertainties is seldom, if ever, performed for atmospheric
chemical modeling. It is suggested that this is a major step
taken in this study.
5.3. Photochemical Theory Uncertainties
[28] Currently, we assume a growth rate in the photo-
chemical theory uncertainty of 5% per time step (that is, the
diagonal of the covariance matrix is increased by 5% at each
time step to crudely account for photochemical theory
uncertainties). The time step used here is 15 min, but we
often use a 1 hour time step, also. This is deliberately
conservative to avoid filter divergence. In the future we
want to explicitly calculate the photochemical theory un-
certainty by using the uncertainty in each rate coefficient
and in the constituent concentrations.
5.4. Analysis Quality Measures
[29] Once the analysis has been performed, we quantify
its quality by generating a set of statistics that compare the
observations used in making the analysis with the analysis
itself.
5.4.1. Observation Increment, (O
F )
[30] This is typically the best measure of forecast skill:
the difference between the first guess and the observations,
also known as the observed-minus-background difference
or as the innovation vector [Daley, 1991]:
O
Fð Þ ¼ 1
n
Xn
k¼1
ok
fkð Þ; ð2Þ
where ok denotes the kth observation and fk denotes the
corresponding value from the first-guess forecast. The lower
the absolute value of (O
F ), the better.
5.4.2. Analysis Increment, (A
F )
[31] This is a good measure of model bias: the difference
between the first guess and the final analysis, also known as
the analysis-minus-background difference or as the correc-
tion vector [Daley, 1991]:
A
Fð Þ ¼ 1
n
Xn
k¼1
ak
fkð Þ; ð3Þ
where ak denotes the analysis and fk denotes the
corresponding value from the first-guess forecast. The
lower the absolute value of (A
F ), the better.
5.4.3. Analysis-Observations, (A
O)
[32] This is typically the best measure of the analysis
bias: the difference between the analysis and the observa-
tions, also known as the analysis-minus-observed difference
or as the innovation vector [Daley, 1991]:
A
Oð Þ ¼ 1
n
Xn
k¼1
ak
okð Þ; ð4Þ
where ok denotes the kth observation and ak denotes the
corresponding value from the analysis. The lower the
absolute value of (A
O), the better.
6. Assessment of the Assimilation
[33] ATMOS ATLAS 1 observed 14 of the 55 species
which our assimilation scheme can simultaneously analyze.
These 14 observed species include key species in reactive
LARY ET AL.: CHEMICAL DATA ASSIMILATION OF SOLAR OCCULTATION DATA ACH 10 - 5

nitrogen and chlorine chemistry as well as several long-lived
source gases. The ATLAS 1 observations are only available
at satellite sunrise and sunset. In this case study for 30 March
1992 the measurements are mainly available at sunset.
6.1. O3
[34] Figure 2a displays vertical profiles for the 30 March
1992 assimilation (ATMOS ATLAS 1) of the O3 analysis
concentrations, uncertainties, and skill measures. The left-
most panel shows that there is excellent agreement between
the ATMOS observations (diamonds with error bars) and
the analysis (line with error bars).
[35] The total observational uncertainty has two compo-
nents, the measurement uncertainty (solid line in the right-
most panel) and the representativeness uncertainty (dashed
line). The representativeness uncertainty attempts to quan-
tify the spatial variability of ozone over the grid box. This
has been quantified by using the average deviation observed
in each grid box. The analysis uncertainty is the diagonal
element of the time-integrated Kalman filter error covari-
ance matrix (solid line with overlaid circles). It can be seen
that these uncertainties are of the order of 0.1 ppmv, or a
few percent.
[36] The analysis bias, (O–A), is small and well within
the observational uncertainties. The forecast skill, (O–F ),
and model bias, (A–F ), are a little larger. This is because
the a priori first guess was not entirely suitable for the
situation that ATMOS observed. As was mentioned in the
introduction, it came from a 2D model of the atmosphere.
6.2. NO and NO2
[37] Full diurnal cycles produced by the assimilation for
NO and NO2 from the occultation measurements are shown
in Figure 1. The left plots show the analyses overlaid with
the observations (colored triangles). The right plots show
the analyses’ uncertainties overlaid with the observation
uncertainties (colored triangles). The reduction in analysis
uncertainty can be seen in the right plots when new
observational information comes in. The dots indicate the
locations of the assimilation analysis grid.
[38] Figures 2b and 2c display vertical slices through the
NO and NO2 diurnal cycles at sunset. The leftmost panels of
Figures 2b and 2c show that there is good agreement
between the ATMOS observations (diamonds with error
bars) and the analyses (lines with error bars).
6.3. N2O5, HONO2, and HO2NO2
[39] Figures 3a–3c display vertical slices through the
N2O5, HNO3, and HO2NO2 diurnal cycles at sunset, re-
spectively. For each of these species the analyses and
observations agree to within the analyses’ uncertainties.
6.4. Other Species
[40] Figure 4 displays vertical slices through the ClONO2,
HCl, HCN, H2O, CH4, N2O, CO, and CO2 diurnal cycles at
sunset. For each of these species the analyses and observa-
tions agree to within the analyses’ uncertainties. It is
noteworthy that in some cases (for example, ClONO2) the
assimilation gives a larger uncertainty than was specified by
the measurement team. This occurs for at least two reasons:
[41] (1) The assimilation also accounts for the represen-
tativeness uncertainty. In some cases where there are large
spatial gradients, this uncertainty can be larger, even con-
siderably larger, than the observational uncertainty. The
analysis uncertainty as well as the photochemical model
uncertainty reflects this.
[42] (2) Information on this species is propagating
through the assimilation system from observations of other
chemically coupled species. This other information, with its
associated weight(uncertainty), is not entirely consistent
with the observations, and so the analysis acquires a higher
uncertainty, for example, due to the presence of observation
or model biases.
7. Data-Theory Intercomparison
[43] A key advantage of using data assimilation is the
propagation of information from data-rich regions to data-
poor regions, which is very relevant to the assimilation of
solar occultation data such as from ATMOS.
7.1. Mathematical Framework for Intercomparison
[44] Previous studies, such as that by Chang et al. [1996],
have shown good agreement of volume mixing ratio profiles
measured by ATMOS with in situ measurements acquired
from platforms on the NASA ER-2. Sen et al. [1998]
presented volume mixing ratio profiles of NO, NO2,
HONO, HO2NO2, N2O5, and ClONO2 and their composite
budget (NOy) from 20 to 39 km, measured remotely in solar
occultation by the Jet Propulsion Laboratory MkIV Inter-
ferometer during a balloon flight from Fort Sumner, New
Mexico (35
N), on 25 September 1993. In general, the
observed profiles agree well with values calculated using a
photochemical steady state model constrained by simulta-
neous MkIV observations of long-lived precursors and
aerosol surface area from SAGE II.
[45] What is new in this study is that the comparison
between observations and photochemical theory and the
constraint of photochemical theory by observations is done
within an objective mathematical framework, where full
account is taken of information uncertainty both in the
observations and in photochemical theory. Previous ATMOS
intercomparisons have not done this.
[46] After examining Figures 1–4 in this paper, it may
be asked, How much information is ATMOS providing,
and how is this any different from what we would obtain
from using a free-running model? ATMOS has provided a
great deal of information for Figures 1–4. If it was not for
the constraint of ATMOS ATLAS 1 observations, the
sunset observations would not have agreed with the
photochemical model and would not have simultaneously
agreed with the O3, NO, NO2, N2O5, HNO3, HO2NO2,
HCN, ClONO2, HCl, H2O, CO, CO2, CH4, and N2O
photochemical models.
7.2. Quantifying Uncertainty
[47] If the primary interest is the likely magnitude of
diurnal variation, then one does not need assimilation. The
reason for using the assimilation is to simultaneously use as
much information as we have and to provide an estimate of
the uncertainty associated with this information, which
includes a treatment of observational uncertainty, spatial
and temporal representativeness uncertainty, and photo-
chemical theory uncertainty. Assimilation also allows ob-
ACH 10 - 6 LARY ET AL.: CHEMICAL DATA ASSIMILATION OF SOLAR OCCULTATION DATA

Figure 2. (left) Vertical profiles of analyses and observations: (a) O3, (b) NO, and (c) NO2. (middle)
Skill measures described in section 4.4, namely the observation increment, (O–F ), which is a measure of
forecast skill, the analysis increment, (A–F ), which is a measure of model bias, and the analysis-
observations, (A–O), which is a measure of the analysis bias. (right) The uncertainties: observational,
representativeness, and analysis. All data are from the 30 March 1992 assimilation of ATMOS ATLAS 1
data at 38
S. Observations and observation error bars are in blue.
LARY ET AL.: CHEMICAL DATA ASSIMILATION OF SOLAR OCCULTATION DATA ACH 10 - 7

Figure 3. Same as Figure 2, except for (a) N2O5, (b) HNO3, and (c) HO2NO2.
ACH 10 - 8 LARY ET AL.: CHEMICAL DATA ASSIMILATION OF SOLAR OCCULTATION DATA

jective self-consistency tests such as those described in
section 4.4 and by the c2 test of (O–F ) proposed by Dee
[1995] and applied by Menard et al. [2000], Menard and
Chang [2000], and Khattatov et al. [2000]. The currently
available techniques, other than assimilation, do not provide
this capability.
7.3. Inferring Information on Unobserved Quantities
[48] In the case of a quality data set such as ATMOS, the
assimilation can reliably produce full diurnal cycles from
just occultation observations and relatively reliably infer
analyses for unobserved species. In this case study, full
diurnal analyses and uncertainties of 55 species were
produced from observations of just 14 of these species. In
addition, the assimilation has provided a useful check for
photochemical self-consistency between the ATMOS obser-
vations and between the observations and photochemical
theory. Self-consistency is not always present between the
multiconstituent observations made from a given platform;
for example, UARS observed NO2 from three instruments
which were not self-consistent with each other. This will be
the subject of further papers.
[49] The reason for choosing 38
S for this case study is
that at this latitude, there was the greatest vertical extent of
ATMOS ATLAS 1 observations. The good agreement
obtained between ATMOS observations and photochemical
Figure 4. Vertical profiles for ClONO2, HCl, HCN, H2O, CH4, N2O, CO, and CO2 analyses from the
30 March 1992 assimilation of ATMOS ATLAS 1 data at 38
S. Observations and observation error bars
are in blue.
LARY ET AL.: CHEMICAL DATA ASSIMILATION OF SOLAR OCCULTATION DATA ACH 10 - 9

theory reported here was not the result of a fortuitous choice
of data. Many other studies have been performed with
data from numerous platforms, including other ATMOS
missions, MkIV balloon flights, ER-2 data, and UARS
data. Space does not us allow to present these here; they
will be the subject of other papers.
[50] Observations from other platforms and measurement
campaigns have been considered such as the Stratospheric
Photochemistry Aerosol and Dynamics Experiment
(SPADE) in May 1993 and the Cryogenic Limb Array
Etalon Spectrometer (CLAES), which have much more
diurnal coverage than just sunrise and sunset and which
show the same result. Chemical data assimilation can
reconstruct well an entire diurnal cycle from reliable obser-
vations at one time, whether the observations are at sunrise,
sunset, or spaced throughout the day.
[51] This means that multispecies chemical data assimi-
lation is likely to be useful for data product monitoring and
quality assessment. This is relevant to the use of data
assimilation within a validation campaign of new instru-
ments such as those to be placed on board EOS Aura. Solar
occultation data (such as from the Canadian Atmospheric
Chemistry Experiment, the Aerosol Characterization
Experiment (ACE), and HALOE), aircraft data (such as
from the DC-8 and ER-2), and balloon data (such as the
MkIV) could be used to reconstruct full diurnal cycles
of species such as NO and NO2, thus relaxing the local
solar time/zenith angle coincidence requirements needed to
validate Aura observations.
8. Summary
[52] Multispecies chemical data assimilation is useful for
constituent data product monitoring/validation and quality
assessment. Two key advantages of using data assimilation
are the ability to check the chemical self-consistency of
multispecies observations and information prorogating from
data-rich regions to data-poor regions. This is particularly
relevant to the assimilation of solar occultation data such as
from ATMOS.
[53] Chemical data assimilation has been able to take
solar occultation measurements of 14 species at sunrise and
sunset and produce full diurnal cycles for 55 observed
and unobserved species, together with their associated
uncertainty. The associated uncertainty includes a treatment
of the observation, representativeness, and photochemical
theory uncertainty.
[54] We confirm that there is self-consistency between the
ATMOS ATLAS 1 observations of O3, NO, NO2, N2O5,
HNO3, HO2NO2, HCN, ClONO2, HCl, H2O, CO, CO2,
CH4, and N2O and between ATMOS and photochemical
theory. If there had been inconsistency between the obser-
vations and photochemical theory, the assimilation skill
scores such as (O–F ) and (O–A) would have highlighted
these and quantified their magnitude.
[55] Future studies in preparation using chemical data
assimilation include the halogen-catalyzed oxidation of
hydrocarbons in the upper troposphere and lower strato-
sphere; the partitioning of hydrogen, nitrogen, chlorine,
bromine, and carbon species as a function of temperature,
solar illumination, and aerosol loading; the relative roles of
catalytic ozone loss cycles and how they have changed with
time and location over the UARS period; and satellite
instrument validation including Envisat, ACE, and Aura.
[56] Acknowledgments. It is a pleasure to acknowledge NASA for a
distinguished Goddard Fellowship in Earth Science; the Royal Society for a
Royal Society University Research Fellowship; the government of Israel for
an Alon Fellowship; the NERC, EU, and ESA for research support; and
Simon Hall of Cambridge University, who has provided such excellent
computational support.
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B. Khattatov, National Center for Atmospheric Research, P.O. Box 3000,
Boulder, CO 80307-3000, USA. (boris@ucar.edu)
D. J. Lary, Data Assimilation Office, NASA Goddard Space Flight
Center, Code 910.3, Greenbelt, MD 20771, USA. (dlary@dao.gsfc.nasa.
gov)
H. Y. Mussa, Unilever Cambridge Centre/Atmospheric Research Centre,
University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK.
(hym21@cam.ac.uk)
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