Sequential assimilation of stratospheric chemical observations in a
three-dimensional model
M. P. Chipperfield
School of the Environment, University of Leeds, Leeds, UK
B. V. Khattatov
National Center for Atmospheric Research, Boulder, Colorado, USA
D. J. Lary
Department of Chemistry, University of Cambridge, Cambridge, UK
Received 18 January 2002; revised 14 June 2002; accepted 18 June 2002; published 12 November 2002.
[1] We describe a technique to assimilate chemical observations in a three-dimensional
(3-D) chemical transport model (CTM). The method uses the established sequential
technique of Khattatov et al. [2000], but here, it is applied simultaneously to many
observed species. Following the assimilation, care is taken to preserve compact
correlations between all modeled long-lived tracers and the total abundance of reactive
families (e.g., inorganic chlorine). This way, the observations of long-lived tracers and
family members constrain many other species in the model. In this paper, we apply the
technique to the assimilation of O3, CH4, H2O, and HCl from the Halogen Occultation
Experiment (HALOE) in 1992. Despite the poor coverage of HALOE, the assimilation of
species with long photochemical lifetimes is a useful global constraint on the model.
Results of the assimilation model have been tested by comparison with Atmospheric Trace
Molecule Spectroscopy Experiment (ATMOS) profiles of O3, CH4, H2O, HCl, and N2O.
Direct comparison of the assimilated species shows that the assimilation model performs
better in reproducing the independent observations. Comparison of the nonassimilated
species (N2O) shows that assimilation has generally improved the comparison, especially
in the midlatitude lower stratosphere. INDEX TERMS: 0340 Atmospheric Composition and
Structure: Middle atmosphere—composition and chemistry; 0341 Atmospheric Composition and Structure:
Middle atmosphere—constituent transport and chemistry (3334); 3334 Meteorology and Atmospheric
Dynamics: Middle atmosphere dynamics (0341, 0342); 3337 Meteorology and Atmospheric Dynamics:
Numerical modeling and data assimilation; KEYWORDS: data assimilation, atmospheric chemistry, modeling,
3-D CTM
Citation: Chipperfield, M. P., B. V. Khattatov, and D. J. Lary, Sequential assimilation of stratospheric chemical observations in a
three-dimensional model, J. Geophys. Res., 107(D21), 4585, doi:10.1029/2002JD002110, 2002.
1. Introduction
[2] The technique of data assimilation is used routinely in
numerical weather prediction to create meteorological anal-
yses. Over the past 5 years or so, there has been increasing
interest in applying similar techniques to observations of
chemical species in the atmosphere. The assimilation of
such observations, and the creation of ‘‘chemical analyses’’
is expected to lead to better use of observations and to
improvements in chemical models. The methods used for
the assimilation of chemical observations can be divided
into variational and sequential [e.g., Khattatov et al., 1999].
[3] Variational chemical data assimilation was pioneered
by Fisher and Lary [1995] who used a box model with a
simplified photochemical scheme and assimilated observa-
tions along trajectories. Variational assimilation in a full
chemistry model is computationally expensive, although it
has now been applied in three dimensions for short simu-
lations. Errera and Fonteyn [2001] used a variational
method with a 3-D chemical transport model (CTM) to
assimilate CRISTA data over 12 hour time windows during
the course of a 6-day mission during 5–11 November 1994.
They compared the assimilated fields with independent
observations and so were able to comment on the systematic
agreement between different instruments.
[4] Khattatov et al. [2000] gave a comprehensive dis-
cussion of the use of optimal interpolation and the Kalman
filter in global chemical models. Lyster et al. [1997]
described the first application of the (full) Kalman filter in
global atmospheric chemistry. They assimilated Upper
Atmosphere Research Satellite (UARS) observations of
CH4 (treated as an inert tracer) at a single potential temper-
ature (q) level. The simplicity of the problem considered
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. D21, 4585, doi:10.1029/2002JD002110, 2002
Copyright 2002 by the American Geophysical Union.
0148-0227/02/2002JD002110$09.00
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permitted the use of the full Kalman filter though it
appeared too computationally expensive for 3-D multispe-
cies models. Menard et al. [2000] and Menard and Chang
[2000] studied various approaches for the application of the
Kalman filter for assimilating UARS data in a two-dimen-
sional (2-D) model. In particular, they described a diagnos-
tic process based on the c-square method for adjusting free
parameters. Khattatov et al. [2000] extended the method-
ology of Menard et al. [2000] and Menard and Chang
[2000] to develop a sequential system based on the sub-
optimal Kalman filter.
[5] The scheme of Khattatov et al. [2000] has already
been applied in several studies of atmospheric chemistry.
An early variant of the scheme was used by Levelt et al.
[1998] to assimilate UARS Microwave Limb Sounder
(MLS) O3 observations into a 3-D model with full strato-
spheric chemistry. After a 60-day simulation the model with
ozone assimilation gave a better comparison with independ-
ent observations than the model without assimilation.
Lamarque et al. [1999] assimilated satellite observations
of CO into a global 3-D model with detailed tropospheric
chemistry. Over the 10-day run the memory of the assim-
ilation was limited to a few days (due to transport-induced
drift) but other model species were significantly influenced.
Clerbaux et al. [2001] also assimilated satellite CO obser-
vations (from the Interferometric Monitor for Greenhouse
Gases (IMG)). They argued that data assimilation helped to
highlight the difference between the model and observations
and again showed that assimilated fields from the model
gave good agreement with independent CO observations.
[6] In this study we combine a data assimilation scheme
into our 3-D chemical transport model (CTM), SLIMCAT.
This model has already been used extensively for studies of
stratospheric chemistry over multiannual timescales [e.g.,
Chipperfield, 1999]. Therefore, we require an assimilation
scheme which is efficient enough to allow multiannual
integrations but will improve on the basic model by keeping
the model constrained by observed chemical species.
[7] In this paper we have also used the sequential
assimilation scheme of Khattatov et al. [2000]. We have
extended on previous studies by using it to assimilate many
(in this case 4) different chemical species simultaneously.
Although the assimilation itself of each species is done
independently, the nature of the species treated (e.g., long-
lived tracers and members of chemical families) means that
it is necessary to impose constraints on the assimilation to
ensure self-consistency (and to ensure consistency with the
nonassimilated fields). Also, by assimilating the observa-
tions into an established 3-D model, our aim is not to
produce daily, global fields of assimilated species with as
little model content as possible, but to use the observations
to continually ‘‘nudge’’ the 3-D model toward reality.
[8] These consistency constraints raise the question of the
philosophy of data assimilation. On one side, one could
argue that observations should be assimilated into a model
without any other constraint. In terms of chemical species
one would then rely on the coupling of species though
chemical reactions to ensure the nonassimilated species
have realistic values. On the other hand, one could say that
the assimilated fields from the model should not be allowed
to violate some basic constraints which are well established
in atmospheric chemistry. Some such constraints are easy to
envisage, but the point at which one decides to limit these
constraints is probably arbitrary. In general one can imagine
that the 4D-Var assimilation of many simultaneous obser-
vations could be done in a model with no external con-
straints—there may be enough information in the
observations to keep the important species limited to rea-
sonable values. This is the procedure adopted in the 4D-Var
work of Fonteyn and coworkers (D. Fonteyn, personal
communication, 2001). In contrast, the long-term sequential
assimilation of few species (as done here) imposes a greater
need to apply certain constraints.
[9] It is worth noting here that the assimilation of ozone,
which is often used as a test case because of abundant
observations, is the most straightforward. As ozone contains
only O atoms and is formed from O2, which is present in a
huge abundance, the atmospheric concentration of ozone
can vary without any physical constraint. During assimila-
tion there is no concern about conservation of O atoms or of
limits imposed by the abundance of other species.
[10] Section 2 describes our 3-D model, the assimilation
scheme and the experiments performed. Section 3 summa-
rizes the HALOE data used in the assimilation. In section 4
we discuss our method for assimilating the observations
and, in particular, how we impose constraints on nonassi-
milated species. In section 5 we discuss how the assimila-
tion has improved the performance of the 3-D model for
selected test cases. Our discussion and conclusions are
given in section 6.
2. Model and Experiments
2.1. SLIMCAT 3-D CTM
[11] We have used the SLIMCAToff-line 3-D CTM which
is described in detail by Chipperfield [1999]. Horizontal
winds and temperatures are specified using meteorological
analyses. Vertical advection is calculated from heating rates
using the MIDRAD radiation scheme [Shine, 1987] and
chemical tracers are advected by conservation of second-
order moments [Prather, 1986]. The model has the most
important species in the Ox, NOy, Cly, Bry, HOx families
along with a CH4 oxidation scheme and long-lived tracers.
The model has a detailed gas-phase stratospheric chemistry
scheme as well as a treatment of heterogeneous chemistry of
liquid and solid aerosols (for more information see Chipper-
field [1999]). The version used here uses photochemical data
from DeMore et al. [1997]. The model has been widely used
in previous studies of stratospheric chemistry [e.g., Chipper-
field et al., 1996; Chipperfield and Jones, 1999].
2.2. Assimilation Scheme
[12] The sequential assimilation scheme used in this study
is that of Khattatov et al. [2000]. Details of the scheme are
described in Appendix A. For each of the assimilated
species (in this case the 4 HALOE species O3, CH4, H2O
and HCl) an extra tracer was added to the model to advect
the forecast error. The values of the scheme’s tunable
parameters used in this study are given in section 4.2.
2.3. Model Runs
[13] In the experiments discussed here the CTM was run
with a horizontal resolution of 7.5! ! 7.5! (T15 Gaussian
grid) and 18 isentropic levels from 330 K to 3000 K
ACH 8 - 2 CHIPPERFIELD ET AL.: SEQUENTIAL ASSIMILATION IN 3-D CTM

(approximately 10 to 55 km). We have used 24-hourly
United Kingdom Meteorological Office (UKMO) analyses
[Swinbank and O’Neill, 1994] to force the model. A basic
model run was initialized in October 1991 from a 2-D model
and integrated until 31 December 1991. This output was then
used to initialize a series of 3 assimilation runs which are
summarized in Table 1. Run CON is a control run without
assimilation. Run HAL is like CON but includes assimila-
tion of HALOE O3, CH4, H2O, and HCl. Run HALC also
assimilates these species but includes constraints on non-
assimilated species as discussed in section 4.1.
3. HALOE Data
[14] The Halogen Occultation Experiment (HALOE)
[Russell et al., 1993] provides solar occultation observations
of a range of trace gases including O3, CH4, H2O and HCl
which are used in this study. Although this technique gives
relatively poor coverage on any day (only measurements at
a sunrise and at a sunset latitude—see Figure 1) these data
are still useful for our assimilation purpose. This is because
the species assimilated have long photochemical lifetimes,
at least in some regions of the stratosphere. HALOE also
measures NO and NO2. However, the short photochemical
lifetime of these species makes their assimilation in a
sequential system meaningless.
[15] In this paper we have used version 19 data for O3
[Bruehl et al., 1996], HCl, [Russell et al., 1996], H2O,
[Harries et al., 1996], and CH4 [Park et al., 1996]. The
estimated accuracies for these species for different altitudes
were taken from these validation papers and are listed in
Table 2.
4. Assimilation Methodology
[16] In this section we describe how we have imple-
mented the sequential assimilation scheme in our 3-D
CTM.
4.1. Assimilation Constraints
[17] Our first attempts to assimilate HALOE HCl directly
into the 3-D CTM resulted in the modeled total inorganic
chlorine (Cly) rapidly becoming unrealistic. The modeled
values of Cly exceeded 4 ppbv, when we know from
atmospheric chlorofluorocarbon (CFC) abundances that
there is a limit of Cly of about 3.6 ppbv for 1990s
conditions. Indeed, it is relatively straightforward for an
atmospheric model to predict Cly based on known CFC
abundances. In our model (which is used for long trend
simulations, for example) the incorrect Cly would be very
undesirable. Therefore, we need to impose a limit on the
model Cly (and other inorganic chlorine species) when we
assimilate HCl (see below for details).
[18] Another relationship between certain atmospheric
species concerns the correlations that are observed between
pairs of long-lived tracers [Fahey et al., 1989; Plumb and
Figure 1. Coverage of HALOE sunrise and sunset observations for 1992. (Figure adapted from
HALOE home webpage.)
Table 1. 3-D Model Assimilation Runs
Model run Dates Species Assimilated Notes
CON 1 January 1992–30 June 1992 None
HAL 1 January 1992–31 January 1992 O3, CH4, H2O, HCl
HALC 1 January 1992–30 June 1992 O3, CH4, H2O, HCl Constraints
CHIPPERFIELD ET AL.: SEQUENTIAL ASSIMILATION IN 3-D CTM ACH 8 - 3

Ko, 1992]. Measurements of one long-lived tracer can
therefore be used to derive other long-lived tracers.
Figure 2 shows the model correlations of certain tracers
from the model run without assimilation (run CON). In
general the model displays the expected compact correla-
tions for the long-lived tracers. In the case of CH4 versus
N2O the model agrees well with the canonical straight-line
fit estimated from ER-2 aircraft data [see Kawa et al., 1993;
Waugh et al., 1997]. For NOy versus N2O, although the
model displays a relatively compact correlation this version
overestimates the observed NOy abundance (dashed line in
Figure 2c). For CFCl3 versus N2O the model curve is
compact for each q level, although the model produces a
correlation which varies with altitude. This separation with q
in the model is probably related to a too slow vertical
motion in the model. Throughout most of the stratosphere
O3 is not long-lived and overall the correlation plot with
N2O is not compact—it is included here for comparison.
[19] If HALOE CH4 observations, for example, are
assimilated into the model then we would expect compact
correlations involving this tracer to break down. The dra-
matic extent to which this occurs is shown in Figure 3. The
expected compact correlation has been replaced by one
where the value of CH4 for, say, 150 ppbv N2O varies from
0.5 to 1.4 ppmv. Similar results are obtained for other
correlations between CH4 and nonassimilated long-lived
tracers (e.g., CFCs, Cly, etc., not shown). Although, the
Figure 2. Correlation plots of tracers on 31 January 1992 from model run CON (without assimilation)
for (a) O3 versus N2O, (b) CFCl3 versus N2O, (c) NOy versus N2O, and (d) CH4 versus N2O. The dashed
line in panel (c) shows the fit NOy(ppbv) = 20.0 " 0.0625*N2O(ppbv) based on midlatitude balloon
profiles and ER-2 data [see Kondo et al., 1996]. The dashed line in panel (d) shows the fit N2O(ppbv) =
262*CH4(ppmv) " 131 from ER-2 data [see Kawa et al., 1993].
Table 2. Accuracies (Fractional) for HALOE Data
Pressure, hPa O3 CH4 H2O HCl
0.464 0.06 0.06 0.18 0.31
0.681 0.07 0.06 0.16 0.23
1.00 0.08 0.06 0.14 0.15
1.47 0.08 0.07 0.14 0.15
2.15 0.09 0.08 0.14 0.14
3.16 0.09 0.08 0.14 0.14
4.64 0.09 0.09 0.14 0.12
6.81 0.11 0.10 0.16 0.13
10.0 0.12 0.11 0.17 0.14
14.7 0.14 0.12 0.19 0.15
21.5 0.15 0.13 0.21 0.16
31.6 0.17 0.14 0.23 0.17
46.4 0.20 0.16 0.24 0.20
68.1 0.25 0.17 0.26 0.22
100 0.30 0.19 0.27 0.24
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assimilation of CH4 will have resulted in a better modeled
distribution of CH4 (see section 5) the overall model per-
formance will have degraded.
[20] Within the philosophy of data assimilation in this
study (i.e., to constrain multiannual simulations of an
established 3-D model), it is desirable both to assimilate
observations and to maintain the correlations with non-
assimilated long-lived tracers. One method would be to
use a fit to the CH4 versus N2O correlation based on
atmospheric observations (e.g., dashed line in Figure 2d)
to infer a pseudo-observed N2O. This would, in effect, be
mixing the HALOE data with other (e.g., ER-2) observa-
tions. An alternative approach would be to use the model-
predicted correlations to derive a new N2O value for each
assimilated CH4 point. We have chosen this latter
approach so that tracer correlations remain determined by
the model chemistry (i.e., so that other observations can
still be used to test the model’s N2O distribution).
[21] In run HALC we have added the following proce-
dure to adjust the model long-lived species following the
assimilation of HALOE CH4 and HCl. (The assimilation of
O3 and H2O are not used in the following correction,
although if H2O was not available from HALOE, the
modeled field would also need to be corrected).
1. Determine the model gridboxes in which assimilation
has changed the concentration of CH4 by more than 0.1%.
For these gridboxes steps 2–6 are then applied.
2. Average the global model fields of long-lived tracers
(CFCl3, CF2Cl2, N2O and NOy) before assimilation into
bins of different CH4 values. This averaging is done for
each q level i by using the levels i " 1, i and i + 1.
3. Use postassimilation value of CH4, and the average
model correlations deduced in (2), to find a new value for
the nonassimilated long-lived tracers.
4. Based on the postassimilation values of CFCl3 and
CF2Cl2 (the two Cl-containing source gases in the model)
derive a new distribution of Cly.
5. Repartition Cly species based on postassimilation
values of Cly and HCl and preassimilation ratios of other
species.
6. Repartition NOy species based on postassimilation
values of NOy and preassimilation ratios of other species.
[22] An important consideration in these constraints (step
(1)) is that in the absence of observations they do not modify
the model fields. This is a desirable property of any assim-
ilation scheme. Note that we apply the correlations with CH4
as a strong constraint. In our case, as CH4 is the only observed
tracer used, this is reasonable. However, if two (or more)
long-lived tracers were available we would not necessarily
expect the inferred values of a nonobserved species from
each of these observations to be consistent. In this case it
would be more appropriate to apply a weak constraint.
[23] The result of including these constraints is shown in
Figure 4. The CH4 versus N2O correlations is now more
compact than Figure 3 and similar to the basic model in
Figure 2; evidently for any gridbox in which CH4 is changed
by assimilation, the scheme adjusts N2O to maintain the
model-predicted correlation. The NOy versus N2O and
CFCl3 versus N2O correlations are also similar to the basic
model. However, these correlations show more curvature
which has been slightly smoothed by the assimilation/
correction procedure. Overall, the corrections applied to
the long-lived tracers has resulted in a much better behaved
model.
4.2. Assimilation Parameters
[24] The assimilation scheme contains a number of tun-
able parameters. The values for these were chosen using c2
Figure 3. As Figure 2d but for run HAL.
CHIPPERFIELD ET AL.: SEQUENTIAL ASSIMILATION IN 3-D CTM ACH 8 - 5

diagnostics and OmF (observations " forecast) differences
(as described by Khattatov et al. [2000]) in a series of 1-
month test runs. The values chosen are given in Table 3,
along with the values used by Khattatov et al. [2000] for
assimilation of MLS O3 data for comparison. The values
of the normalized c2 diagnostics are shown in Figure 5 for
the first 3 months of run HALC. As discussed by
Khattatov et al. [2000], this diagnostic should ideally
produce values near 1 and we have adjusted the parame-
ters in Table 3 to achieve this. In run HALC we have used
the published HALOE accuracies (given in Table 2) except
for H2O. When we used the published errors the c2
diagnostic (Figure 5b) gave values much smaller than
0.5. Therefore, we have reduced the H2O errors used in
the model to 30% of the published values to increase c2/N
following the discussion given by Khattatov et al. [2000].
Even with this reduction in the error, the c2 diagnostic for
H2O is only around 0.6.
[25] For chemically inert tracers (no production or loss)
the error growth rates (!) should be identical for all species.
In this case ! is simply an indicator of how good are the
dynamical field and model numerics. These rates should be
numerically different at different latitudes and altitudes. In
our approach, we are trying to find a single number for !
that fits all geographical regions, which is an approxima-
tion. Therefore, for species which are not chemically inert
and which depend on different chemistry in different
regions the values of ! can differ, which is the case for
the species given in Table 2. The value of ! for O3 derived
in this study is different from that derived by Khattatov et
al. [2000], which could be due to different model dynam-
ics and numerics.
4.3. Error Tracers
[26] Figure 6 shows the zonal mean cross-section of the
normalized model error tracers for the 4 assimilated
species on 31 January 1992. At this time the HALOE
observations occur at latitudes around 20!N (see Figure 1).
Consequently, this latitude corresponds to a minimum in
the species errors. Ideally, for chemically inert tracers with
the same observational errors these plots should show a
similar pattern for all species. The differences between the
Figure 4. As Figure 2 but for run HALC.
Table 3. Adjustable Parameters for Assimilation Scheme
For MLSa For HALOE
Parameter O3 O3 H2O CH4 HCl
Error growth !/hour 0.0135 0.005 0.001 0.01 0.005
Rel. Rep. error r 0.1 0.1 0.1 0.1 0.1
Lxy = 1000 km, Lz = 0.4 scale height. See Appendix A.
aKhattatov et al. [2000].
ACH 8 - 6 CHIPPERFIELD ET AL.: SEQUENTIAL ASSIMILATION IN 3-D CTM

species plots are due to the different photochemical life-
times of the species in different regions and to the different
instrumental errors for different species at different alti-
tudes (see Table 2).
5. Results
[27] We now compare results from the model runs with
and without assimilation to examine the benefit of assim-
ilation on some aspects of the 3-D model performance.
5.1. Long-Lived Tracers
[28] Figure 7 shows the zonal mean cross-section of
CH4, H2O and 2CH4 + H2O on 31 January 1992 from
runs CON and HALC. The most evident effect of the
assimilation on CH4 is an increase in the tracer gradient in
the subtropics, driven mainly by an increased descent in
the midlatitudes and also more ascent in the tropics above
about 5 hPa. A similar change is seen in the H2O
distribution. In the basic model CH4 and H2O are related
by the bottom boundary condition 2CH4 + H2O = 7 ppmv
and the model CH4 oxidation chemistry which is assumed
to yield 2H2O per CH4 oxidized. This conservation can be
seen in Figure 7e except in the lower stratosphere due to
remnants of Antarctic dehydration. The sum from the
HALOE data shows more fine structure and it varies
between 6 and 7 ppmv. (Note that the contour interval
in Figure 7f is only 0.1 ppmv, while a 10% error in a 7
ppmv quantity in can lead to a 1 ppmv variation).
5.2. Chlorine Species
[29] Figure 8 shows the zonal mean cross-section of HCl
and total inorganic chlorine (Cly) on 31 January 1992 from
runs CON and HALC. The constraints imposed on the
modeled long-lived chlorine source gases CFCl3 and
CF2Cl2 (via their correlation with methane), and the
subsequent balance of total chlorine between organic and
inorganic forms, has produced a Cly distribution in run
HALC which resembles the assimilated CH4 (i.e., stronger
descent at midlatitudes and stronger subtropical gradients).
This additional Cly in the mid–high latitude lower strato-
sphere is mostly partitioned into HCl.
5.3. Ozone
[30] Figure 9 shows the zonal mean cross-section of O3
on 31 January 1992 from runs CON and HALC. The
assimilated model shows less elongated tracer isopleths in
the mid stratosphere.
5.4. Comparison With ATMOS Data
[31] Figure 10 compares modeled profiles from runs
CON and HALC with observations from the Atmospheric
Figure 5. Plot of c2/N as a function of day for 1 January 1992 to 31 March 1992 from run HALC for
(a) O3, (b) H2O, (c) CH4 and (d) HCl. The plots show hourly output smoothed with a 100-hour running
mean. The gap in early March indicates a 6-day period when no HALOE data was available.
CHIPPERFIELD ET AL.: SEQUENTIAL ASSIMILATION IN 3-D CTM ACH 8 - 7

Trace Molecule Spectroscopy Experiment (ATMOS) [Gun-
son et al., 1996] during late March 1992. These observa-
tions cover the latitude range 17.5!N to 51.6!S and the
model profiles from the nearest output time have been
interpolated to the same location. For CH4 in the southern
midlatitudes (38.8!S to 51.6!S) the assimilated run
(HALC) is more realistic, especially in the lower strato-
sphere. In HALC the isopleths of CH4 show more descent
(see Figure 7), in better agreement with the ATMOS
observations. In the tropics and subtropics (7.8!S to
17.5!N) there is less difference between the two model
runs and both simulations give a similar comparison with
the observations.
[32] The assimilation procedure has modified the mod-
eled N2O distribution which is compared with ATMOS
measurements in Figure 10. Again, in the southern hemi-
sphere lower stratosphere the increased descent in the N2O
profiles gives better agreement with the ATMOS data. In
the upper stratosphere, however, the assimilation run
HALC sometimes does not simulate ATMOS N2O well,
although the CH4 agreement is very good. Evidently in
model run HALC the CH4:N2O correlation deviates from
the ATMOS observations. This is illustrated in Figure 11a
which shows ATMOS observations with relatively large
values of N2O (for 1 ppmv CH4) compared to the model
runs and the canonical fit from ER-2 data.
[33] The assimilation model shows less H2O throughout
the profile than model run. Based on the profile compar-
isons it is not possible to state that either model gives
better agreement with the ATMOS data. It is clear that the
ATMOS profiles show a lot of vertical structure which is
not captured by the model. (The vertical resolution of the
Figure 6. Zonal mean distributions of error tracers (normalized by the respective chemical tracers) for
(a) O3, (b) CH4, (c) H2O and (d) HCl. See color version of this figure at back of this issue.
ACH 8 - 8 CHIPPERFIELD ET AL.: SEQUENTIAL ASSIMILATION IN 3-D CTM

Figure 7. Zonal mean distributions of CH4, H2O, and 2CH4 + H2O (ppmv) on 31 January 1992 for run
CON (left, no assimilation) and run HALC (right, with HALOE assimilation). See color version of this
figure at back of this issue.
CHIPPERFIELD ET AL.: SEQUENTIAL ASSIMILATION IN 3-D CTM ACH 8 - 9

assimilation could be increased by decreasing the param-
eter Lz). Figure 11b shows the CH4:H2O correlation plot
for the profiles shown in Figure 10. There is considerable
scatter in the ATMOS data which precludes a critical test
of the two model runs.
[34] For HCl the assimilation model shows increases in
the lower stratosphere (due to increased Cly correlating
with decreased CH4) and some decreases at higher alti-
tudes compared to run CON. This has improved the
comparison slightly in the upper stratosphere. For the
two ATMOS HCl profiles which extend to the lower
stratosphere (38!S, 47!S) the assimilation model shows
better agreement.
[35] For O3 the basic model (run CON) already shows
reasonable agreement with the observations. There is not
much change in the assimilation run HALC. However, at
47!S there is an improvement in the detail of the profile:
there is a small decrease in the maxima around 10 hPa and
an increase in O3 above this altitude.
6. Summary
[36] We have described a technique to assimilate chem-
ical observations in the SLIMCAT three-dimensional (3-D)
chemical transport model (CTM). The model has a
detailed description of stratospheric chemistry and has
been widely used and tested in past studies. We have
used an established sequential assimilation scheme [Khat-
tatov et al., 2000] and extended it to apply it simulta-
neously to many observed species.
[37] A major improvement of our method is that follow-
ing the assimilation step the scheme ensures the consistency
between the assimilated species and between the assimilated
and nonassimilated species. The consistency is imposed by
Figure 8. Zonal mean distributions of HCl and Cly (ppbv) on 31 January 1992 for runs (a) CON
(above), and (b) HALC (below). See color version of this figure at back of this issue.
ACH 8 - 10 CHIPPERFIELD ET AL.: SEQUENTIAL ASSIMILATION IN 3-D CTM

using the compact correlations between long-lived tracers
and the total abundance of chemical families. In this study
we have applied the correlations using a single observed
long-lived tracer (CH4) as a strong constraint.
[38] In this study we have used the CTM to assimilate
HALOE occultation observations of O3, CH4, H2O and
HCl. Even though the coverage of the occultation obser-
vations is limited on any day, where the photochemical
lifetime of any observed species is long, the assimilation
still provides a useful constraint on the model. This is
because we are using the observations to perform slight
adjustments to a realistic model, rather than requiring the
assimilation to change the model fields drastically.
[39] A number of model simulations have been per-
formed for early 1992. The assimilation of HALOE data
has improved the model overall when compared with
independent ATMOS observations for both assimilated
and nonassimilated species. As well as generally better
comparison of absolute magnitudes, the assimilated model
shows more realistic tracer gradients in the subtropical
lower stratosphere.
[40] The assimilation method described here is computa-
tionally cheap. The assimilation of the HALOE data (around
15 profiles per day) adds only a minor overhead to the full
chemistry model. Therefore, it can be used in multiannual
simulations to further improve our ability to model long-
term changes.
Appendix A: Assimilation Scheme
[41] Our assimilation scheme is an efficient sequential
assimilation scheme with estimate of analysis errors, based
on Khattatov et al. [2000], and is described here.
A.1. Method
[42] The integration of model M gives concentrations of
species x at a new time:
xtþ!t ¼ M t; xtð Þ
The observations y are generally available on a different
grid which is related to x by linear operators I (horizontal
interpolation) and A (‘‘averaging kernel’’).
y ¼ A I xð Þð Þ
We can define an ‘‘observational operator’’ H such that:
y ¼ H xð Þð Þ ð1Þ
The solution to (1) is:
xat ¼ xt þK y"Hxtð Þ
The Kalman gain matrix K is given by:
K ¼ BHT HBtHT þOþ R
! ""1
where, Bt is the forecast error covariance, O is the
observation error covariance, and R is representativeness
error covariance (errors of interpolation and discretization).
[43] The analysis error covariance is:
Bat ¼ Bt " BtH
T HBtH
T þOþ R
! ""1
HBt ð2Þ
A.2. Treatment of Errors
[44] In the extended Kalman filter method, the evolution
of error covariance is obtained using a linearization L of the
original model M.
Btþ!t ¼ LBat L
T þQ ð3Þ
where
L ¼
dxtþ!t
dxt
ð4Þ
Figure 9. Zonal mean distributions of O3 (ppmv) on 31 January 1992 for runs (a) CON (left), and (b)
HALC (right). See color version of this figure at back of this issue.
CHIPPERFIELD ET AL.: SEQUENTIAL ASSIMILATION IN 3-D CTM ACH 8 - 11

Figure 10. Comparison of version 3 ATMOS profiles of (a) N2O, (b) CH4, (c) H2O (d) HCl and (e) O3
with run CON (dashed line) and HALC (dotted line) for 6 profiles in late March 1992 between 17.5!N
and 51.6!S.
ACH 8 - 12 CHIPPERFIELD ET AL.: SEQUENTIAL ASSIMILATION IN 3-D CTM

[45] The sizes of x, B, L can be large which makes a 3-D
analysis impossible. Therefore, in the 3-D scheme some
simplifications are employed. The off-diagonal elements of
B are obtained from:
bij ¼
ffiffiffiffiffiffiffiffiffi
biibjj
p
exp "
!r2xy
2L2xy
!
exp "
!r2z
2L2z
$ %
where !rxy and !rz represent horizontal and vertical
distances between locations i and j.
[46] The time evolution of error covariance is parameter-
ized as:
biiðt þ!tÞ ¼ ~bii t þ!tð Þ þ qii tð Þ ð5Þ
~bii t þ!tð Þ ¼ M bii tð Þð Þ ð6Þ
qii tð Þ ¼ !xi t þ!tð Þ!tð Þ
2 ð7Þ
where ! is a tunable parameter.
[47] The observational error covariance O is assumed to
be diagonal and for our HALOE assimilation the elements
are set equal to the estimated absolute error at each pressure
altitude (see section 4.2).
[48] The representativeness error covariance matrix R is
assumed to be diagonal, with elements computed as:
rii ¼ ryið Þ
2
where r is the relative representativeness error.
[49] The analysis error variance is computed directly from
equation (2). Since clearly it impossible to implement
matrix operations implied by (2) directly, only the diagonal
elements of the covariance matrix (i.e., variances) are
computed. The HBtH
T term represents the background
error covariance interpolated to the locations of observa-
tions as discussed by Menard et al. [2000] and thus can be
computed easily. The matrix inversion is performed directly
since the size of the matrices in observation space is fairly
small. Once this is done, each line of BtH
T is computed and
stored and multiplied by the appropriate column of the
(HBtH
T + O)"1 matrix.
[50] The adjustable parameters (r, !) are chosen using c2
diagnostics and OmF (observations " forecast) differences
(see Table 3).
[51] Acknowledgments. This work was initiated by a European Space
Agency contract. We are grateful to Tobias Wehr for this support. This work
was also supported by the U.K. Natural Environment Research Council. We
thank the HALOE team for the use of the HALOE data which was obtained
via the Cambridge Atmospheric Data Centre (CADC). We thank the
ATMOS team for use of the ATMOS data.
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""""""""""""""""""""""
M. P. Chipperfield, School of the Environment, University of Leeds,
Woodhouse Lane, Leeds, LS2 9JT, UK. (martyn@env.leeds.ac.uk)
B. V. Khattatov, National Center for Atmospheric Research, Boulder, CO,
USA.
D. J. Lary, Department of Chemistry, University of Cambridge,
Cambridge, UK.
ACH 8 - 14 CHIPPERFIELD ET AL.: SEQUENTIAL ASSIMILATION IN 3-D CTM

Figure 6. Zonal mean distributions of error tracers (normalized by the respective chemical tracers) for
(a) O3, (b) CH4, (c) H2O and (d) HCl.
ACH 8 - 8
CHIPPERFIELD ET AL.: SEQUENTIAL ASSIMILATION IN 3-D CTM

Figure 7. Zonal mean distributions of CH4, H2O, and 2CH4 + H2O (ppmv) on 31 January 1992 for run
CON (left, no assimilation) and run HALC (right, with HALOE assimilation).
ACH 8 - 9
CHIPPERFIELD ET AL.: SEQUENTIAL ASSIMILATION IN 3-D CTM

ACH 8 - 10
Figure 8. Zonal mean distributions of HCl and Cly (ppbv) on 31 January 1992 for runs (a) CON
(above), and (b) HALC (below).
CHIPPERFIELD ET AL.: SEQUENTIAL ASSIMILATION IN 3-D CTM

ACH 8 - 11
Figure 9. Zonal mean distributions of O3 (ppmv) on 31 January 1992 for runs (a) CON (left), and (b)
HALC (right).
CHIPPERFIELD ET AL.: SEQUENTIAL ASSIMILATION IN 3-D CTM