GMDGeoscientific Model DevelopmentGMDGeosci. Model Dev.1991-9603Copernicus PublicationsGöttingen, Germany10.5194/gmd-9-2893-2016EnKF and 4D-Var data assimilation with chemical transport model BASCOE (version 05.06)SkachkoSergeysergey.skachko@aeronomie.behttps://orcid.org/0000-0003-4168-4499MénardRichardErreraQuentinChristopheYveshttps://orcid.org/0000-0003-3243-5036ChabrillatSimonhttps://orcid.org/0000-0003-4378-1567Royal Belgian Institute for Space Aeronomy, BIRA-IASB, Brussels, BelgiumAir Quality Research Division, Environment Canada, Dorval, CanadaSergey Skachko (sergey.skachko@aeronomie.be)26August2016982893290820April201613May201611July201628July2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://gmd.copernicus.org/articles/9/2893/2016/gmd-9-2893-2016.htmlThe full text article is available as a PDF file from https://gmd.copernicus.org/articles/9/2893/2016/gmd-9-2893-2016.pdf
We compare two optimized chemical data assimilation systems, one based on the
ensemble Kalman filter (EnKF) and the other based on four-dimensional
variational (4D-Var) data assimilation, using a comprehensive stratospheric
chemistry transport model (CTM). This work is an extension of the Belgian
Assimilation System for Chemical ObsErvations (BASCOE), initially designed to
work with a 4D-Var data assimilation. A strict comparison of both methods in
the case of chemical tracer transport was done in a previous study and
indicated that both methods provide essentially similar results. In the
present work, we assimilate observations of ozone, HCl, HNO3, H2O and
N2O from EOS Aura-MLS data into the BASCOE CTM with a full description of
stratospheric chemistry. Two new issues related to the use of the full
chemistry model with EnKF are taken into account. One issue is a large number
of error variance parameters that need to be optimized. We estimate an
observation error variance parameter as a function of pressure level for each
observed species using the Desroziers method. For comparison purposes, we
apply the same estimate procedure in the 4D-Var data assimilation, where both
scale factors of the background and observation error covariance matrices are
estimated using the Desroziers method. However, in EnKF the background error
covariance is modelled using the full chemistry model and a model error term
which is tuned using an adjustable parameter. We found that it is adequate to
have the same value of this parameter based on the chemical tracer
formulation that is applied for all observed species. This is an indication
that the main source of model error in chemical transport model is due to the
transport. The second issue in EnKF with comprehensive atmospheric chemistry
models is the noise in the cross-covariance between species that occurs when
species are weakly chemically related at the same location. These errors need
to be filtered out in addition to a localization based on distance. The
performance of two data assimilation methods was assessed through an 8-month
long assimilation of limb sounding observations from EOS Aura MLS. This paper
discusses the differences in results and their relation to stratospheric
chemical processes. Generally speaking, EnKF and 4D-Var provide results of
comparable quality but differ substantially in the presence of model error or
observation biases. If the erroneous chemical modelling is associated with
moderately fast chemical processes, but whose lifetimes are longer than the
model time step, then EnKF performs better, while 4D-Var develops spurious
increments in the chemically related species. If, however, the observation
biases are significant, then 4D-Var is more robust and is able to reject
erroneous observations while EnKF does not.
Introduction
The ensemble Kalman filter (EnKF) and the four-dimensional variational
algorithm (4D-Var) are widely used data assimilation methods that utilize the
model to propagate observational information in time and space into an
estimate of the state. Each method is built around different assumptions and
has its own merits. However, to some extent, the relative merits are
application dependent. In the context of meteorological data assimilation,
the relative advantages of these two methods have been discussed by
, and ,
to name a few, and it has promoted the development of new hybrid methods such
as 4DEnVar and En4DVar . In
atmospheric chemistry, however, there are very few comparison studies. The
purpose of this paper is to compare carefully optimized EnKF and 4D-Var
chemical data assimilation (CDA) systems for an extended time period using
the same chemical transport model (CTM) and same observations.
A short literature review discussing the CDA
problems related to EnKF and 4D-Var their intercomparison and application
to the atmospheric chemistry modelling is already given in hereafter
denoted S14. A more recent review including future
prospects for coupled chemistry–meteorology models is given by
.
As in S14, here we use the BASCOE (Belgian Assimilation System for Chemical
ObsErvations) environment. BASCOE was designed to assimilate satellite
observations of chemical composition into a stratospheric CTM originally
using the 4D-Var assimilation method .
S14 described the implementation of the EnKF as an alternative assimilation
method in BASCOE and compared it with the original 4D-Var approach, using
carefully calibrated error variances for both methods and applying them to
observations of ozone, which was considered as a passive tracer. Indeed, this
preliminary paper performed the comparison in a chemical tracer transport
framework, i.e. taking only transport into account while neglecting chemical
reactions. Our results showed that in this framework the two methods give
nearly identical performance. This outcome can be interpreted as a
consequence of the dynamics of tracer error covariances: as noted early on by
and , such error covariances follow
the characteristics of the flow. Hence in the absence of model error, there
is no distinction between a filtering (EnKF) and a smoothing (4D-Var)
algorithm.
How, then, do the EnKF and the 4DVar methods compare when photochemical
reactions are taken into account? Do the results depend on the assimilated
chemical species? Using actual satellite data sets and operational
configurations, what are their respective performances in terms of precision,
accuracy and computational efficiency? What is the role of the practical
implementation of each method, when the full description of the stratospheric
chemistry is taken into account in the CTM? These are the main questions
addressed in this paper.
The application of the multi-variate EnKF method to an assimilation system with
full chemistry should in principle address two important issues:
the estimation of a large number of input error statistics and
the problem of localization between chemical species.
The first issue is the large number of input error statistics that is needed
(e.g. the observation error variances for each species at each vertical
levels). Clearly, an online estimation of error statistics is desirable to
accomplish this task. In an idealized framework,
proposed an adaptive EnKF in which the model error parameters were estimated
using innovation statistics within a maximum likelihood method. In the same
line of thought, the Desroziers method was also used
to simultaneously estimate the covariance inflation factor and the
observation error variance .
also showed that the Desroziers observation variance
estimates converge to the truth if the background error covariance is close
to the truth, which seems to be a reasonable assumption for EnKF background
error covariances, when the χ2 condition is
respected. Contrary to the EnKF, the 4D-Var is much more tolerant to the
parametrization of the error statistics, as was shown in S14. Hence, the
online estimation of the error statistics is of great importance only for
EnKF.
The second issue related to the implementation of a multi-species EnKF is the
localization between species. It is well known in EnKF applications that a
tapering of the sampling error correlations is needed when the true error
correlation is not close to +1 or -1 e.g.. For
correlations that depend on distance, a widely used sampling error correction
is provided by the Schur product of a compact support correlation function
to the sample covariance. However, in comprehensive
atmospheric chemistry models that have many prognostic chemical species,
sampling errors between species at the same location are also expected to
occur. Long-lived species for instance, which are the best candidates for such
correlations, show in some cases complicated correlations patterns that depend
on latitude and height and vary in time e.g..
Besides, preliminary experiments with BASCOE 4D-Var system showed that the
cross-covariance between innovations of long-lived species is rather noisy
and assimilation experiments that account for cross-covariance between
long-lived species in the background error term do not show
significant improvements in the analysis quality in practice. The approach to the
cross-species sampling correlation noise within a sequential data
assimilation has not been fully explored yet. Several studies in EnKF
chemical data assimilation use a brute force species localization that
consists in zeroing-out cross-species covariances. This is the case for
example for and , where only
O3 is observed and where all cross-covariances between ozone and other
species are zeroed-out in order to reduce the noise in the analysis. In an
ozone assimilation study, kept the cross-covariances
between O3 and some other strongly coupled species, in particular NO,
NO2 and VOCs, as well as the error covariances with the boundary
conditions (O3 dry deposition and model top boundary condition). They
showed that each of these kept cross-covariances give rather similar impact
on the ozone analysis. In a multi-species air-quality EnKF assimilation of surface O3, NO and NO2 measurements,
indicated that in order to reduce the sampling noise they kept the
cross-covariances between these species only at the surface. In another
study, assimilated simultaneously NO2, O3, CO and
HNO3 tropospheric chemical species along with the estimation of surface
emissions. Using verification against satellite observations, such as
innovation variance, they found that cross-covariance between chemical
species needs to be set to 0 unless they are strongly chemically related.
Examples of strongly chemically related species are members of the NOy
family, or CO with VOCs. also allowed the coupling
between NO2 and emissions of NO2 or CO with the emissions of CO
but set the cross-covariance between emissions of NOx and CO to 0.
Keeping the cross-covariance with the boundary conditions (surface emissions
and lateral boundary conditions) was also argued in
. Overall, these studies indicate that when a strong correlation is believed to exist between observed and modelled species (or
boundary condition) then these can be kept in the EnKF, but otherwise, to
reduce noise, all other cross-covariances should be zeroed-out.
In this paper we perform an assimilation with EnKF and 4D-Var of several
species in the stratosphere that are not necessarily directly chemically
linked and with real-life constraints. The lifetimes of the assimilated
species are quite diversified and vary with altitude. We use a
state-of-the-art CTM that is in fact in constant improvement but also has
some deficiencies. We use limb sounding observations that give vertically
resolved measurements, and thus there is a need to have vertically resolved
error statistics. As it was shown in S14, the EnKF is more sensitive to the
observation error statistics than 4D-Var assimilation. Yet, to provide a
consistency between the two assimilation systems, the observation error
statistics of 4D-Var will be subject to the same Desroziers estimation
procedure. Localization between species, which is needed in EnKF, is in fact
not applied to 4D-Var because the cross-covariance between species is taken
into account automatically using the 4D-Var adjoint model.
The paper is organized as follows. The next section describes the main
components of the BASCOE Data Assimilation System (version 5.8): the common
CTM, the 4D-Var system and the EnKF system. It also describes the
implementation of Desroziers' method and the tuning of the error covariances
in each system. The assimilated observations and independent data used to
validate the results are given in Sect. . Section
describes the results of our assimilation and model experiments. Section discusses a separate EnKF experiment where the
cross-species correlations are taken into account. Finally, some conclusions
are given in Sect. .
The BASCOE data assimilation systemThe chemical transport model
In this study, all numerical experiments are performed with the Belgian
Assimilation System for Chemical ObsErvations (BASCOE) and its underlying
CTM. The BASCOE CTM computes the temporal
evolution of 58 stratospheric chemical species accounting for the advection,
photochemical reactions and a parametrization of PSC (polar stratospheric
clouds) microphysics. We used a CTM configuration nearly identical to the one
described by for near-real-time production of
4D-Var analyses as part of the MACC (Monitoring Atmospheric Composition and
Climate) project. Here we provide a brief reminder of its most salient
features.
All species are advected by the flux-form semi-Lagrangian scheme
, here driven by ERA-Interim wind fields . The
horizontal resolution is set at 3.75∘ longitude by 2.5∘
latitude. The model considers 37 levels from the surface to 0.1 hPa, which
is a subset of the 60 levels of ERA-Interim that excludes most tropospheric
levels. Hence the CTM state is described by the vector x∈Rn of length n=96×73×37×58≈1.5×107. The model time step is set to 30 min.
The photochemical scheme of BASCOE account for 208 stratospheric chemical
reactions: 146 gas-phase, 53 photolysis and 9 heterogeneous. Photolysis rates
are provided by the Jet Propulsion Laboratory (JPL) recommendations
. The computation of the photolysis rates is based
on the Tropospheric Ultraviolet and Visible (TUV) radiative transfer package
.
Setting up the time windows
Schematic representation of the practical implementation of the
4D-VAR (top) and EnKF (bottom) assimilation methods in BASCOE. Black dots
represent model state and observational information is depicted in blue. The
black arrows represent model integrations by one time step, vertical red
arrows represent model state optimization (4D-VAR) or Kalman filter (EnKF).
Green dots represent the analyses at 0 h which are used as initial conditions
for the diagnostic 24 h forecasts (green arrows). For clarity, the number of
4D-VAR iterations has been limited to two and the number of EnKF members has
been limited to three.
In order to describe the practical implementations of the 4D-Var and EnKF
algorithms in BASCOE, we must first explain the different set-up of their
assimilation windows with respect to time. This is schematically shown by
Fig. . The 4D-Var assimilation window is set to 24 h, i.e.
this is the duration of the forward and backward integrations of the CTM and
its adjoint. Each 4D-Var iteration is followed by a minimizing procedure (see
Sect. for more details). In this 4D-Var implementation, the 24 h
forecast is defined as the first forward model simulation starting from the
analysis of the previous assimilation window. All 4D-Var assimilation cycles
save the model state in observation space during these forecasts, in order to
compute observation-minus-forecast (OmF) statistics discussed below.
The EnKF initializes its ensemble of model states from one given state using
a procedure described in Sect. . The EnKF assimilation is then
based on ensembles of short model forecasts which have the same duration as
the CTM time step, i.e. 30 min, followed by the observational update of each
ensemble member. The updated ensemble states (analyses) are used then as
initial states for the next ensemble forecast. Hence, there is no practical
need to compute the 24 h forecast (green line) as in the 4D-Var approach.
However, we have introduced this option in the EnKF in order to allow a
consistent comparison with the 4D-Var forecasts. Hence in the EnKF approach,
the 24 h forecast is defined as a model simulation started from the ensemble
mean analysis at 0 h UTC. As in the 4D-Var system, the 24 h forecast of
the EnKF stores the OmF statistics.
The 4D-Var system
The BASCOE 4D-Var of this study was already used by S14 and is described in detail by .
The 4D-Var data assimilation is carried out by minimizing the so-called cost
function,
which measures the discrepancy between the model state and observations .
Here, the model state vector contains 58 prognostic variables,
where only 7 chemical species are observed among them (see Sect. ).
The background error covariance matrix B0 is parametrized using a control variable
transform:
Lξ=x0-x0b≡δx0,
where
ξ is a new control variable, x0 the first-guess
field, δx0 is the analysis increment and L is the
square root of B0:
B0=LTL.
As in S14, the error covariance of the first-guess field expresses
spatial correlations on a spherical harmonic basis ,
allowing a representation of homogeneous and isotropic horizontal correlations by
a diagonal matrix with diagonal values repeated for the same zonal wave number.
The operator L is defined by
L=ΣSΛ1/2,
where Σ is the (diagonal) background error standard
deviation matrix with
sb(l)σb(l) values on its diagonal,
sb(l) is an adjustable background error scaling factor
on the level l; Λ1/2 is the spatial correlation
matrix, identical for each chemical species, defined on a spherical harmonic
basis hence diagonal; and S is the spectral transform operator
from the spectral space to the model space. The spatial correlation matrix
considers Gaussian correlations in the horizontal and in the vertical
directions with length scales L0h and L0v in
horizontal and vertical directions, respectively. The between-species
covariances are assumed to be 0 in the background error covariance matrix
B0.
The observation errors are assumed to be uncorrelated both horizontally and
vertically. The observation error covariance matrix Rk is thus
defined as diagonal:
Rk(i,j)=(so(i)σy(i)tk)2,ifi=j0,ifi≠j,
where so(i) is an adjustable observation error variance
scaling factor and σy(i)tk is the
measurement error at level i and time tk. The observations and their
errors are described in Sect. . The adjustment of sb and
so scaling factors is performed in observation space for every
observed species separately, where they are functions of vertical pressure
level (see Sect. ).
Finally, the BASCOE 4D-Var implementation includes the background quality
control procedure BgQC;. This procedure rejects
observations when
(yi,l-Hi,l(xb))2>γ2(diag(R)i,l+Hi,l(diag(B))),
where the operator diag(A) is a diagonal matrix of A
and i,l are the data indices of profile and level, respectively.
The value of γ is set to 5 in BASCOE, so that BgQC rejects only obviously wrong observations.
The EnKF system
The BASCOE EnKF of this study is similar to the system used in S14. An
ensemble of initial states x̃i(t0) is generated by adding to
the model state x0 a set of spatially correlated perturbations
according to the prescribed initial error covariance. This procedure is
schematically represented on Fig. on the left-hand side. The
ensemble of model states is propagated forward in time using the same CTM as
used in the 4D-Var (see Sect. ). The background error covariance is
represented by the addition of a stochastic noise ηi to each
ensemble member at each model time step. In the current implementation, the
model error term is added to observed species only. The non-observed model
species evolve with ensemble and are influenced by the analysis increments
only implicitly through the chemistry scheme of BASCOE CTM.
The operator L described in Sect. is used to generate
the initial deviation x̃i(t0) and the model error
ηi(tk) of the EnKF system. This ensures that, at the initial
time, both EnKF and 4D-Var systems have identical error statistics. Initial
deviation is defined as
x̃i(t0)=Lζi(t0),i∈[1,N],
whereas the model error term is written as
ηi(tk)=αLψi(tk),i∈[1,N],
where ζi(t0) and ψi(tk) are vectors
of independent normally distributed random numbers with zero mean and
variance equal to 1 defined in the spectral space, N is the ensemble
size and α is an empirical model error parameter. The
definition of this parameter is explained in Sect. .
The observation error covariance matrix R is defined by
Eq. , where the adjustable scaling factor so(i)
is estimated using the method described in Sect. . The
fact that the matrix R is calibrated automatically without using a
trial and error procedure for every observed species makes EnKF essentially
easier to parametrize than in our previous study. Besides, the current
version of EnKF allows for more accurate observation error variance
estimation with respect to S14 because it computes so(i) as a
function of observation vertical pressure level. It should be noted that EnKF
uses the same background quality control procedure described in
Sect. .
As in our previous study with a chemical tracer model, BASCOE EnKF uses the
Schur (element-wise) product of the ensemble covariance matrix with a compact
support correlation function. This function is the fifth-order piecewise
rational function of , which is isotropic and decreases
monotonically with distance depending on the correlation length scale
Lloc. The function is positive only for distances that are less
than 2Lloc and 0 otherwise. We applied this procedure to both
horizontal and vertical correlations, using the compact support correlation
functions with correlation length scales Lloch and
Llocv, respectively. The choice of these parameters is
discussed in Sect. . In order to make feasible the
computation of much more expensive EnKF in the framework of a full chemistry
model, the analyses are computed locally, around the area where current
satellite observations are situated. To this end, the EnKF algorithm accounts
now for a procedure to find a current local sub domain in the model space
using the K-D tree, which is a binary search tree where the comparison key
is cycled between K components (K=3 in our case, because the
observation location is a three-dimensional vector). More information on the
method can be found on the Web or in any textbook on data structures
e.g..
The EnKF analyses of this study are performed in parallel for every observed species in its own space.
Thus, such analysis increments of every species do not account for cross-correlations
between different chemical observations, which is not the case for the 4D-Var system.
However, it is technically possible to keep all observations from multiple species
in one observation space, thus introducing the cross-correlations between species.
An example of such EnKF data assimilation is discussed in Sect. .
The Desroziers method
We use the method to estimate error variance scaling
factors for each observed species and each vertical level. The diagnosis
relies on linear estimation theory where the statistics is computed using
observation-minus-background, observations-minus-analysis and
analysis-minus-background differences. The estimation of the background error
variance is written as
sb(l)2σb(l)2=〈(dba)Tdbo〉,
and the observation error variance is then
so(l)2σo(l)2=〈(dao)Tdbo〉,
where the vector dba is the difference between
analysis and background, dbo is the difference
between observations and background, dao is the
difference between observations and analysis in observation space and
〈〉 denotes the mathematical expectation. Note that in practical
implementation, the expectation is replaced by a horizontal mean and time
mean of a day.
The BASCOE data assimilation is initialized using sb(l)=1 and
sb(l)=1 for both EnKF and 4D-Var. These initial values are kept
in the system for the first 24 h of system integration. The analysis
increment and model innovation statistics are accumulated during this time.
Then the estimation of the scaling factors is performed using
expressions () and (). In the following 24 h analyses (on
day 2), both EnKF and 4D-Var use the day 1 estimated error variance scaling
factors. The procedure is sequentially updated after every 24 h assimilation cycle
using the statistics accumulated during the previous cycle. Note that we
could have used an estimated sb(l) in EnKF to tune the model
error, but we decided not to apply it and use the χ2 tendency to this
end (see next section, Sect. ).
Initial (INI) observation error covariance matrix of experiment A
(dashed red), starting with R=(σo)2, and B (dashed
blue), starting with R=(1.5σo)2 and their
Desroziers (DRS) estimations (solid red and blue lines, respectively), using
statistics of the first 24 h. The statistics is shown for O3, H2O and
HCl.
The Desroziers estimates appear to be asymptotically stable after only 1
day. That means that changing the initial parameter value has little to no
effect on the resulting time series of estimated parameter values.
Figure shows examples of the observation error standard
deviation for O3, H2O and HCl (at each vertical levels) when we perturb
the initial parameter value by a factor 1.5. The dashed curves represent the
initial values and the solid curves the values estimated after 1 day using
the Desroziers method.
Tuning of error covariances in the two systems
Each assimilation system (i.e. EnKF and 4D-Var) has its own optimized error
variances but shares a common error correlation for the prescribed
B0 in 4D-Var and the prescribed model and initial condition error
correlations in EnKF. As in S14, our starting point is the calibration of the
error covariance matrix B0 used by the 4D-Var system. This is
realized through a calibration of the spatial correlation associated with the
operator L described in Sect. . The operator
L has similar parameters as in S14: L0h=800 km and
L0v=1 model level, and σb(l)=0.2 (with scaling
factor sb(l)=1) at all levels. Then, we take into account the
fact that the use of the Schur product results in shorter correlation length
scales (see S14 for more details). Similarly to our previous work, EnKF uses
an effective correlation length scales of Leh=872 km
and Lev=1.3 in model level coordinates, given that
Lloch=2000 km and Llocv=1.5 are
chosen a priori. The calibrated operator L is then used in the
EnKF system.
The observation error variance scaling factor so (see
Sect. ) is estimated for both systems using the Desroziers method
described in Sect. . The background error covariance
scaling factor sb used in 4D-Var is also estimated using the
Desroziers method. In EnKF, the background error covariance is evolved using
CTM, where we add a model error term that uses a calibration parameter
α. The value of α equal to 0.025 was found in S14 in the case
study of O3 tracer. This value is based on the property that the time
tendency (over periods of weeks and months) of the χ2 diagnostic should
be nearly 0, as argued in . In general, we have found
(in S14) that the value of α changes the slope of the O3χ2
distribution, whereas the observation error variance scaling factor
so is responsible for the mean value of it. In the absence of
better knowledge, we use the value α=0.025 for all observed species
described in Sect. .
Estimated error scale factors within 4D-Var (left) and EnKF (right)
for the period April–November 2008.
The performance of each data assimilation system of BASCOE can be monitored
by the χ2 diagnostic. During the whole period of our experiments,
〈χk2〉/mk values remain close to 1 (result not shown).
This is achieved by using the error variances estimated by the Desroziers
method. In the case of 4D-Var where both observation and the background error
variances are estimated, the Desroziers method gives estimates that achieve
the innovation variance consistency . For EnKF, where only
the observation error variance is estimated, the fact that 〈χk2〉/mk values remain close to 1 is an indirect confirmation that the
model error is tuned appropriately. Figure shows the
evolution of the adjustable parameters for both systems. The solid lines show
the vertically mean values of the observation variance parameter
so, and the dashed lines show the vertically mean values of the 4D-Var
background error variances. The time evolution of the error variance scaling
factors at individual levels is, as in Fig. (result
not shown), generally consistent over time, especially for the EnKF estimates.
Furthermore, we note that for the EnKF results the scaling factors of any
species show no drift in time. We argue from this result that there is
apparently no need to have a different model error α for different
species. Thus we conclude that for a chemical transport models, the main
source of model error can be attributed to transport errors primarily.
Finally, we wish to remark that to keep comparable CPU costs in both data
assimilation systems that can be carried out in a reasonable time,
4D-Var is run with 10 iterations (including 10 adjoint iterations) and the
EnKF uses 20 ensemble members. As in S14, the computation of the EnKF Kalman
gain is performed using Cholesky decomposition in which the full observation
vector is considered at a given time step for a given species. No
simplification is used to compute the inversion of the innovation matrix
[HBeHT+R] or the matrix
BeHT (see S14 for more details). The actual
use of local domain decomposition and integration of the ensemble members on
different processors in parallel decreases essentially the CPU costs as
compared to the previous version of BASCOE EnKF.
Observations
The data set assimilated in this study is the version 4.2 of the retrievals
from the Microwave Limb Sounder (MLS) on board the EOS (Earth Observing
System) Aura satellite . The EOS Aura-MLS
data cover the latitude range between 82∘ S and 82∘ N with
an along-track separation of around 165 km between consecutive scans. Around
3500 vertical scans are performed every day. The vertical resolution varies
for different species. Here we assimilate the retrievals of five species
which are listed in Table along with some key parameters of the
data set and the validation reference for each species.
Some results of the data assimilation will be validated against independent
observations. This will be the case for N2O because the Aura-MLS N2O
precision is 24–14 ppbv (9–38 %, relative to the observation mean at
given altitude) and its accuracy is 70–3 ppbv (9–25 %) in the pressure
range 100–4.6 hPa, but its precision drops to 14 ppbv (250 %) at 1 hPa,
where the accuracy is estimated to 16 % .
Hence we will validate the BASCOE N2O with observations retrieved from the Atmospheric Chemistry Experiment
Fourier transform spectrometer (ACE-FTS) satellite instrument
, which uses solar occultation to provide around 28
profiles per day. validated N2O retrievals from ACE-FTS
(version 2.2) and found a bias of ±15 % between 6 and 30 km and a bias of
±4 ppbv between 30 and 60 km. Here we use the retrieval version 3.5.
We will also use the Michelson Interferometer for Passive Atmospheric
Sounding (MIPAS) retrievals by the IMK/IAA (Institut für Meteorologie und
Klimaforschung, Karlsruhe/Instituto de Astrofisica de Andalucia, Grenada) to
validate the unconstrained distributions of CH4 and NOx (NOx= NO
+ NO2). The MIPAS IMK/IAA retrievals of CH4 were validated by
and the retrievals of NOx were described by
.
List of species retrieved in Aura MLS v4.2 and assimilated for this paper.
This section reports the numerical experiments performed in this study: the
control run, i.e. an unconstrained simulation by the BASCOE CTM including
photochemistry; the “EnKF” and “EnKF tracer” experiments, the former
including photochemistry and the latter neglecting it (i.e. assimilation
in chemical tracer mode as done in S14); and the two corresponding “4D-Var”
and “4D-Var tracer” experiments. All experiments start on 1 April 2008 from
the same initial condition, i.e. a 4D-Var analysis of Aura-MLS retrievals
, and end on 1 November 2008 i.e. after 7 months.
The results of our model and data assimilation experiments will be assessed
using OmF statistics, relative bias and
standard deviation, computed in the observation space. In the case of N2O
the relative bias and standard deviation are not good diagnostics because its
volume mixing ratio decreases by 2 orders of magnitude between 100 and
1 hPa. Hence we will simply compare the mean profiles of N2O by the five
numerical experiments with assimilated and independent measurements. The
statistics are computed in three different latitude bands covering the globe:
South Pole (90–60∘ S), middle latitudes and tropics
(60∘ S-60∘ N) and North Pole (60–90∘ N). The
analyses of the assimilated species are verified by comparison with the
assimilated observations (Sects. –).
Section evaluates the results for methane and nitrogen
oxides which are not assimilated.
O3 OmF bias (top) and standard deviation (bottom) computed for
the full chemistry CTM (green), EnKF (red) and 4D-Var (blue) based on the same
model. The chemical tracer EnKF (dashed yellow) and 4D-Var (cyan) are also
shown. OmF statistics are computed in percent with respect to the assimilated
EOS Aura-MLS data for the period September–October 2008 and for three
latitude bands (from left to right: South Pole, tropics–middle latitudes
and North Pole).
Verification of ozone
Figure shows the OmF statistics for ozone
over the period September–October 2008, i.e. during the period of the
Antarctic ozone hole. The results of the tracer experiments are not shown
above 1 hPa because the tracer approximation is not valid in this region.
The CTM experiment delivers rather large biases (10 to 30 %) in the lower
and upper stratosphere and at all levels above the South Pole region.
All data assimilation experiments succeed in eliminating these biases nearly
completely in the lower and middle stratosphere. The resulting biases are
smaller than 2 % except for the 4D-Var experiment, which overestimates
ozone depletion in the Antarctic ozone hole region (around 50 hPa) by up to
5 %. Compared with the CTM results, the 4D-Var and EnKF experiments also
reduce significantly the OmF standard deviation in the lowest levels. The
smallest OmF standard deviations are delivered by the 4D-Var experiment, with
results about 1 % smaller than those delivered by the EnKF in pressure
range 30–2 hPa.
The experiments 4D-Var tracer and EnKF tracer allow us to assess the impact
of stratospheric chemistry. Neglecting this process results in larger biases
and OmF standard deviations above the South Pole in the region 10–2 hPa,
where both tracer data assimilation systems overestimate ozone by
∼ 5 % and deliver OmF standard deviations reaching 10 %.
The photochemical lifetime of ozone decreases rapidly in the upper
stratosphere and reaches values as short as a few minutes
in the lower mesosphere. In these regions, our CTM
experiment has a significant ozone deficit reaching about 20 % at the
stratopause (1 hPa). The sources of this model bias are out of the scope of the
present paper. However, its presence helps to assess the behaviour of our
assimilation algorithms. It is found that both data assimilation algorithms
fail to correct this model bias: ozone is still underestimated by
∼15 % at the stratopause. In the upper stratosphere and mesosphere,
data assimilation does not improve OmF standard deviations either; these
remain nearly identical to those obtained by the CTM. These results indicate
that when the photochemical lifetime is short (e.g. smaller than the time
step of the model) and the model error is important, both data assimilation
systems fail to improve the representation of the model state. Since this
issue also involves species that have strong chemical interactions with
ozone, it will be further discussed in
Sects. , and .
Verification of HCl
HCl OmF bias (top) and standard deviation (bottom) computed for the
full chemistry CTM (green), EnKF (red) and 4D-Var (blue). OmF statistics are
computed in percent with respect to the assimilated EOS Aura-MLS data for the
period May–June 2008 and for three latitude bands (from left to right: South
Pole, tropics–middle latitudes and North Pole).
During the largest part of the CTM simulation, the HCl distribution is in
agreement with the Aura-MLS observations. Additionally, the EnKF and 4D-Var experiments
deliver nearly identical results where the small CTM biases are completely
corrected (not shown). The only exception is in the South Pole latitude band
during the period May–June 2008, which is shown on Fig. .
During this period the chemical lifetime of HCl is much shorter than at other
latitudes because the heterogeneous removal due to the formation of polar
stratospheric clouds has already started. This loss process is currently
overestimated in the BASCOE CTM due to a crude cold-point temperature
parametrization Sect. 2.2.2 in. As a result,
the CTM experiment underestimates HCl by up to 45 % at 30 hPa in the
Antarctic polar vortex region and its OmF standard deviation also reaches
∼ 45 %. While the 4D-Var approach essentially fails to correct this
large disagreement, the bias is nearly halved in the EnKF experiment and the
OmF standard deviation is significantly reduced as well.
Staying in the lower stratosphere (100–10 hPa), the outcome of the
experiments is different than above the South Pole. Northward of
60∘ S, the CTM biases do not exceed 15 % and they are nearly
eliminated by both data assimilation experiments. The OmF standard deviations
of both data assimilations are also quite similar in these regions.
In the middle stratosphere, the chemical lifetime of HCl decreases from about
1 week at 10 hPa to about 1 day at 1 hPa . The CTM
experiment delivers quite accurate results in this region: the OmF biases do
not exceed 3 % and the standard deviations are less than 10 %, in every
latitude band for the pressure range 10–0.46 hPa. The EnKF and 4D-Var
experiments both succeed in correcting these small CTM biases and reducing
the OmF standard deviations, except at the 1 hPa level where the 4D-Var does
not correct the CTM deficit of 3 % for HCl.
Verification of HNO3
HNO3 OmF bias (top) and standard deviation (bottom) computed for
CTM (green), EnKF (red) and 4D-Var (blue). OmF statistics are computed in
percent with respect to the assimilated EOS Aura-MLS data for the period
September–October 2008 and for three latitude bands (from left to right:
South Pole, tropics–middle latitudes and North Pole).
Figure shows the HNO3 OmF statistics between the assimilated Aura-MLS data and the CTM, EnKF and
4D-Var experiments for the period September–October 2008. For all three
latitude bands, the CTM shows a significant underestimation reaching
20–25 % around 30 hPa. This model bias nearly disappears at 10 hPa but
grows again above this level. In the lower stratosphere, the OmF standard
deviations of the CTM experiment reach minimum values of 10–15 % but at
the lowermost levels the standard deviation is much larger in the Antarctic
polar vortex region than at other latitudes.
Both data assimilation experiments correct the OmF model bias at all
latitudes and at all pressure levels between 100 and 10 hPa. Above that
level, the quickly increasing model OmF bias is not corrected by either
assimilation algorithm. The explanation for this different behaviour in the
upper stratosphere is twofold. First, the observation error grows quickly
with altitude, reducing the weight of observations in the assimilation
experiments. Second, a large discrepancy between the model and the observed
data leads to rejection of most measurements above 10 hPa by the background
quality control procedure (see Sect. for more details).
The 4D-Var OmF bias is generally less than 3 % in the pressure range
100–7 hPa, except for an 8 % OmF bias at 70 hPa in the tropics. The EnKF
delivers even smaller OmF biases in the whole pressure range and at all
latitudes. Both data assimilations result in almost identical OmF standard
deviations, except in the Antarctic polar vortex region where the EnKF errors
are slightly larger below 20 hPa.
Verification of water vapour
Water vapour is a long-lived tracer in the whole stratosphere, with a
photochemical lifetime still longer than 1 month at the stratopause
. The OmF statistics for H2O are shown on
Fig. . The CTM provides OmF biases smaller than 10 % in
the whole pressure range and at all latitudes, except in the Antarctic polar
vortex between 100 and 10 hPa, where H2O underestimation reaches 30 %.
The OmF standard deviation by the CTM is also largest in this region,
reaching 23 %, while it does not exceed 15 % elsewhere.
H2O OmF bias (top) and standard deviation (bottom) computed for
the full chemistry CTM (green), EnKF (red) and 4D-Var (blue). OmF statistics
are computed in percent with respect to the assimilated EOS Aura-MLS data for
the period September–October 2008 and for three latitude bands (from left to
right: South Pole, tropics–middle latitudes and North Pole).
Both data assimilations mostly correct the OmF bias and standard deviation
errors with respect to the CTM. Their OmF biases do not exceed 2% except
for the OmF bias by the 4D-Var, which reaches 3 % at 1 hPa, i.e. the level
where the ozone deficit described in Sect. is maximum. The
OmF standard deviation errors resulting from the two assimilation experiments
are also quite similar, with slightly larger EnKF errors in the Antarctic
polar vortex below 10 hPa.
Verification of N2O
The relative error statistics shown for other species are difficult to
interpret in the case of N2O because its volume mixing ratio decreases by
2 orders of magnitude between 100 and 1 hPa. Hence Fig.
simply compares mean profiles of forecasts and observations. We display the
assimilated Aura-MLS observations along with their validation uncertainties
grey filled region as reported by. Since these
uncertainties are very large in the upper stratosphere, we also compare with
independent observations by the ACE-FTS solar occultation instrument (see
Sect. ).
In the lower stratosphere the two satellite data sets and the CTM experiment
are in good agreement. Above 10 hPa the mixing ratios retrieved from Aura
MLS are much larger than those from ACE-FTS, and above 5 hPa they become
pressure independent, which is not realistic. As expected, the CTM experiment
agrees much better with the ACE-FTS N2O retrievals since they are much
more precise in the upper stratosphere. How do the 4D-Var and
EnKF treat the Aura-MLS N2O data set containing a bias? To answer this
question we inhibited any a priori filtering of the Aura-MLS observations of
N2O above 5 hPa, and we used both the full-chemistry CTM and its
transport-only version. Figure shows that both EnKF
experiments follow the assimilated Aura-MLS data in the upper stratosphere,
whereas the mean profile delivered by the 4D-Var experiment remains closer to
the CTM. This is due to the automatic rejection by the 4D-Var of most
Aura-MLS observations of N2O above 5 hPa. However, 4D-Var assimilation
with a chemical tracer transport model (cyan dashed curve) assimilates more
Aura-MLS data, keeping the model closer to the assimilated observations. This
episode reveals the role of chemistry in the multivariate assimilation: it
acts as a strong constraint within 4D-Var, preventing it from assimilating
erroneous observations.
Evaluation of non-observed species
Mean N2O from the full chemistry CTM (green), 24 h forecasts
from EnKF (red) and 4D-Var (blue), based on the same model, and Aura-MLS
(black dots) and ACE-FTS data (triangles); 24 forecasts from chemical tracer
EnKF (dashed yellow) and 4D-Var (cyan) assimilation are also shown. The grey
area shows the precision of Aura-MLS data. The statistics are computed for
September–October 2008 and for three latitude bands (from left to right:
South Pole, tropics–middle latitudes and North Pole).
Verification of non-observed species from CTM (green), 24 h
forecasts from EnKF (red) and 4D-Var (blue) assimilation against MIPAS IMK
data (black dots): mean CH4 (top) and mean NOx (bottom) profiles. The
statistics are computed for September–October 2008 and for three latitude
bands (from left to right: South Pole, tropics–middle latitudes and North
Pole).
Finally, the forecasts of two non-observed species issued from both data
assimilation systems will be validated: CH4 and NOx, the sum of NO2
and NO (Fig. ). CH4 CTM forecasts agree well with the
MIPAS IMK/IAA data. Additionally, both data assimilation systems generally
keep this agreement, except the region around 2–1 hPa where 4D-Var develops
an artificial bias related to the presence of O3 model bias and the fact
that O3 data were assimilated in the upper stratosphere. As we saw before,
4D-Var tends to develop such biases in many assimilated and non-assimilated
species to compensate the O3 bias. The problem of model O3 bias is out
of the scope of the present article. We should only note that it can not be
solved directly by data assimilation without an improved version of CTM.
NOx CTM forecasts are essentially different with data due to absent NOx
sources in the model. As for CH4, both data assimilations keep the model
state unperturbed, except the region around 2–1 hPa where 4D-Var develops a
bias for the same reason as stated above. Incidentally, this bias provides
better agreement between the model and data in this region.
EnKF with cross-correlations between species
All the EnKF experiments done so far used a brute force species localization;
in other words, the sample covariance between species is set to 0. This
type of localization should not be confused with the localization based on
distance for the same species, which we keep. Now we examine what happens
when we keep the sample cross-covariance intact.
To this end, we conducted an experiment in which we assimilate O3 and
N2O, two species that are not strongly related via the chemistry system.
We will call this experiment the EnKF-CC, standing for EnKF with
cross-covariances. In principle, we would expect that an observation of O3
does not change significantly N2O and vice versa. In EnKF-CC, O3 and
N2O are put into a common observation space, defined by the observation
vector y and the observation error covariance matrix R.
The ensemble of model vectors in observation space Hxi thus contains
two blocks of O3 and N2O. This provides the cross-correlation terms in
the background error covariance matrix in observation space HBHT
computed as
HBHT=∑iNH(xi-x¯)H(xi-x¯)T,
where i∈[1,N] is the number of ensemble member, N is the ensemble
size and
x¯ is the ensemble mean (see S14 for more details).
The cross-correlation terms between species remain after the localization of the error covariance via the Schur product
because it filters out only the spurious spatial correlations.
OmF bias (top) and standard deviation (bottom) between Aura-MLS data
and O3 analyses of EnKF (red), EnKF-CC (yellow) and CTM (green); see text
for acronym definition. The statistics are computed during 24 h on
15 September 2008.
Figure shows an example of such EnKF-CC data
assimilation,
comparing its results with EnKF discussed in the previous sections where the
sample covariance between species was set to 0. The figure shows the O3
OmF bias and standard deviation for EnKF (red) and EnKF-CC (yellow) analyses
during 24 h of 15 September 2008. We observe that the EnKF-CC has noisy bias
and increased and noisy error standard deviations in the OmF correlations
compared with the EnKF experiment. A similar kind of impact is also obtained
when we assimilate only one species and examine the OmF of the other
non-observed species (results not shown). We thus conclude, as other studies
have indicated, that the sample cross-covariance between weakly chemically
related species gives rise to spurious analysis increments with a
deterioration of the overall performance of the assimilation system.
Conclusions
We have conducted a comparison of an EnKF and 4DVar data assimilation system
using a comprehensive stratospheric chemical transport model. We considered
4D-Var and EnKF configurations that are normally used for chemical data
assimilation applications. Both data assimilation systems have online
estimation of error variances based on the Desroziers method and share the
same correlation model for all prescribed error correlations (i.e. the
background error covariance for 4D-Var, initial error and model error for
EnKF) so that each data assimilation system is nearly optimal and can also be
compared to each other. A previous comparison study by
showed that for chemical tracer transport only
both assimilation systems provide results of essentially similar quality
despite the difference in practical implementation of each method: the 4D-Var
was applied in its strong constraint formulation with a 24 h assimilation
window with the assumption of no model error over this period, whereas the
EnKF was used to sequentially assimilate observations every 30 min with
model error perturbations added every 30 min. This study examines in what
way the inclusion of chemistry changes the performance of the assimilation
systems, but perhaps more importantly how an EnKF and a 4D-Var chemical data
assimilation can be implemented in a real-life situation with several
modelled and assimilated species. In this study we assimilate ozone, HCl,
HNO3, H2O and N2O observations from EOS Aura MLS.
In the context of atmospheric chemistry, EnKF and 4D-Var differ in a number
of ways. While 4D-Var, built on the assumption of a perfect model, tries to
find a strong constraint solution that fits observations over a 24 h window,
EnKF provides estimates at each model time step but allows
for modelling error (mainly as a background error covariance). Furthermore,
while 4D-Var infers information based on error correlation between observed
and non-observed species, EnKF introduces noise between
weakly chemically related species; so far in practice, these
cross-species error covariances are set to 0. So the question is: to what
extent is the chemical modelling an important component of the analysis? The
implementation of a multi-species sequential chemical data assimilation is
challenged by the need to properly tune and automate the estimation of a
large number of input error parameters.
The comparison done in this paper shows that, in general, there is not a
significant improvement in the OmF statistics of the system when the
cross-correlation between species is kept (4D-Var) versus the EnKF system
where the cross-species error correlation has been filtered out. Differences
do occur, however, when there is an important chemical modelling error or
when there are large biases between model and observed values.
For example, the BASCOE CTM has an important model O3 deficit near or
above 1 hPa. The source of this model bias is unclear and is not discussed
in this paper. The experiments show, however, that assimilating O3 at these
altitudes gives a poor agreement with observations. At these altitudes the
chemical lifetime of O3 is smaller than the time step of the model and,
consequently, any correction on the O3 concentrations by the assimilation
of O3 measurements simply cannot correct for the model error. For the
other species, such as HCl and HNO3, the OmF statistics for EnKF are
always better than for the 4D-Var. Two main reasons are responsible for this
better performance. First, EnKF has a short time forecast followed by
frequent observational updates that is possibly more adequate for moderately
fast chemical processes (but not for processes of lifetime smaller than the
model time step). Second, the ensemble of CTMs provides better
representation of the model variance. However, the cross-species
covariances, implicit to a 4D-Var assimilation system, have a negative effect
in the presence of strong model O3 bias. The 4D-Var system tries to
compensate the bias and thus develops small artificial biases in many
chemically related O3 species, observed and non-observed. This is
shown using OmF statistics for two observed species, HCl and H2O, and two
non-observed, CH4 and the NOx family.
The effect of large observation biases has a very different impact. For
example, the EOS Aura-MLS N2O has significant biases above 4 hPa. In this
case, EnKF reaches the state close to observations from the first observation
updates during the spin-up phase and keeps model close to observations
afterwards because of short ensemble model forecasts and frequent
observational updates. In contrast, 4D-Var appears to be robust to
erroneous observations. A significant number of observations are rejected by
the quality control and 4D-Var provides analyses with more
weight given to the model forecast rather than to the observations in the end.
We have also examined the need to have cross-species localization in an EnKF.
Our study shows that the simultaneous assimilation of O3 and N2O, two
species that are only weakly chemically related, gives rise to spurious
cross-species error correlations, which deteriorates the performance of EnKF,
and it is thus better to simply ignore those error correlations. To have a
more sensible approach to species localization could be the object of future
work.
An important aspect of this study is the implementation of an online
estimation of error variance parameters. The estimation of observation error
variance and, in addition, the background error variance for 4D-Var is done at
each observation vertical level, using the Desroziers method. The variance
parameters being estimated are in fact very robust over time, showing little
variability one day to the next. Finally all the experiments were done with
comparable wall clock time for EnKF and 4D-Var settings.
The study has also some limitations. An acknowledged difficulty often
encountered in chemical data assimilation is the situation in which both the
model and the observations suffer from significant biases. This is the case,
for example, with the BASCOE CTM CO and ClO when using the Aura-MLS data
sets. Solving this problem represents a challenging task that we have not
conducted here and would necessitate a dedicated study. Another limiting
factor is the correlation length used in this study. We have not attempted to
estimate it but rather have used what appears to be a reasonable value from
past 4D-Var experiments. The estimated error variances and thus the weight
given to the observations are also linked to the correctness of the error
correlation, and this issue could also be investigated further. A future
development of the BASCOE chemical data assimilation system would be a hybrid
4D-EnKF approach using the ensemble of models to construct a 4-D background
error covariance matrix.
Other possibilities may be considered to properly compare two essentially
different data assimilation systems. For example, the 4DEnKF
approach could be used that computes 4-D error covariances from the ensemble
of forecasts at several times within the assimilation window. This would
allow a longer assimilation window to be used in the EnKF experiment, making
it more comparable to the configuration of 4D-Var. In this case, the EnKF
analysis would be forced to simultaneously fit all of the observations
distributed over a longer window, while still satisfying the model equations,
as in 4D-Var. Applying the model error in this 4DEnKF only at the beginning
of each assimilation window would make it similar to the strong constraint
version of the 4D-Var that was used.
Code availability
Readers interested in the BASCOE code can contact the developers through
http://bascoe.oma.be.
S. Skachko and R. Ménard designed the experiments and S. Skachko carried them out.
Q. Errera developed the codes of 4D-Var and the Desroziers method. S. Skachko
and Y. Christophe developed the EnKF code. S. Chabrillat and Y. Christophe
worked on the CTM code. S. Skachko prepared the manuscript with contributions
from all co-authors.
Acknowledgements
This research was financially supported at BIRA-IASB by the Belspo/ESA/PRODEX
programme. The authors thank the ISSI (International Space Science Institute)
for the funding of two work meetings in Bern to prepare the present article
within the international “Study group on the added-value of chemical data
assimilation in the stratosphere and upper-troposphere”. The authors thank
three anonymous referees for their useful comments that have essentially
improved the article and Samuel Remy for editing the
paper.Edited by: S. Remy
Reviewed by: three anonymous referees
ReferencesAnderson, E. and Järvinen, H.: Variational quality control, Q. J.
Roy.
Meteor. Soc., 125, 697–722, 10.1002/qj.49712555416, 1999.Anderson, J. L.: Localization and Sampling Error Correction in Ensemble
Kalman
Filter Data Assimilation, Mon. Weather Rev., 140, 2359–2371,
10.1175/MWR-D-11-00013.1, 2012.Bernath, P. F., McElroy, C. T., Abrams, M. C., Boone, C. D., Butler, M.,
Camy-Peyret, C., Carleer, M., Clerbaux, C., Coheur, P.-F., Colin, R., DeCola,
P., DeMazière, M., Drummond, J. R., Dufour, D., Evans, W. F. J., Fast, H.,
Fussen, D., Gilbert, K., Jennings, D. E., Llewellyn, E. J., Lowe, R. P.,
Mahieu, E., McConnell, J. C., McHugh, M., McLeod, S. D., Michaud, R.,
Midwinter, C., Nassar, R., Nichitiu, F., Nowlan, C., Rinsland, C. P., Rochon,
Y. J., Rowlands, N., Semeniuk, K., Simon, P., Skelton, R., Sloan, J. J.,
Soucy, M.-A., Strong, K., Tremblay, P., Turnbull, D., Walker, K. A., Walkty,
I., Wardle, D. A., Wehrle, V., Zander, R., and Zou, J.: Atmospheric Chemistry
Experiment (ACE): Mission overview, Geophys. Res. Lett., 32,
l15S01, 10.1029/2005GL022386,
2005.Bocquet, M., Elbern, H., Eskes, H., Hirtl, M., vZabkar, R., Carmichael, G.
R., Flemming, J., Inness, A., Pagowski, M., Pérez Camaño, J. L., Saide,
P. E., San Jose, R., Sofiev, M., Vira, J., Baklanov, A., Carnevale, C.,
Grell, G., and Seigneur, C.: Data assimilation in atmospheric chemistry
models: current status and future prospects for coupled chemistry meteorology
models, Atmos. Chem. Phys., 15, 5325–5358, 10.5194/acp-15-5325-2015,
2015.Brasseur, G. and Solomon, S.: Aeronomy of the middle atmosphere: chemistry
and physics of the stratosphere and mesosphere, Springer Netherlands,
Dordrecht, Reidel, 10.1007/1-4020-3824-0, 1986, 2005.
Buehner, M., Houtekamer, P. L., Charette, C., Mitchell, H. L., and
He, B.: Intercomparison of Variational Data Assimilation and the Ensemble
Kalman Filter for Global Deterministic NWP. Part I: Description and
Single-Observation Experiments, Mon. Weather Rev., 138, 1550–1566,
2010a.
Buehner, M., Houtekamer, P. L., Charette, C., Mitchell, H. L., and
He, B.: Intercomparison of Variational Data Assimilation and the Ensemble
Kalman Filter for Global Deterministic NWP. Part II: One-Month Experiments
with Real Observations, Mon. Weather Rev., 138, 1567–1586,
2010b.
Cohn, S. E.: Dynamics of Short-Term Univariate Forecast Error
Covariances, Mon. Weather Rev., 121, 3123–3148, 1993.Constantinescu, E. M., Chai, T., Sandu, A., and Carmichael, G. R.:
Autoregressive models of background errors for chemical data assimilation,
J. Geophys. Res.-Atmos., 112, d12309,
10.1029/2006JD008103,
2007.
Courtier, P., Andersson, E., Heckley, W., Pailleux, J., Vasiljevic,
D., Hamrud, M., Hollingsworth, A., Rabier, F., and Fisher, M.: The
ECMWF implementation of three-dimensional variational assimilation (3D-Var).
I: Formulation, Q. J. Roy. Meteor. Soc., 124, 1783–1807, 1998.Curier, R., Timmermans, R., Calabretta-Jongen, S., Eskes, H., Segers, A.,
Swart, D., and Schaap, M.: Improving ozone forecasts over Europe by
synergistic use of the LOTOS-EUROS chemical transport model and in-situ
measurements, Atmos. Environ., 60, 217–226,
10.1016/j.atmosenv.2012.06.017,
2012.
Dee, D. P., Uppala, S. M., Simmons, A. J., Berrisford, P., Poli,
P.,
Kobayashi, S., Andrae, U., Balmaseda, M. A., Balsamo, G., Bauer,
P., Bechtold, P., Beljaars, A. C. M., van de Berg, L., Bidlot, J.,
Bormann, N., Delsol, C., Dragani, R., Fuentes, M., Geer, A. J.,
Haimberger, L., Healy, S. B., Hersbach, H., Hólm, E. V.,
Isaksen, L., Kållberg, P., Köhler, M., Matricardi, M.,
McNally, A. P., Monge-Sanz, B. M., Morcrette, J.-J., Park, B.-K.,
Peubey, C., de Rosnay, P., Tavolato, C., Thépaut, J.-N., and
Vitart, F.: The ERA-Interim reanalysis: configuration and performance of
the data assimilation system, Q. J. Roy. Meteor. Soc., 137, 553–597, 2011.Desroziers, G., Berre, L., Chapnik, B., and Poli, P.: Diagnosis of
observation,
background and analysis-error statistics in observation space, Q. J. Roy.
Meteor. Soc., 131, 3385–3396, 10.1256/qj.05.108, 2005.Eben, K., Juruş, P., Resler, J., Belda, M., Pelikán, E., Krüger,
B. C., and Keder, J.: An ensemble Kalman filter for short-term forecasting of
tropospheric ozone concentrations, Q. J. Roy.
Meteor. Soc., 131, 3313–3322, 10.1256/qj.05.110,
2005.Errera, Q. and Ménard, R.: Technical Note: Spectral representation of spatial correlations in variational assimilation with grid point models and
application to the Belgian Assimilation System for Chemical Observations (BASCOE), Atmos. Chem. Phys., 12, 10015–10031, 10.5194/acp-12-10015-2012, 2012.Errera, Q., Daerden, F., Chabrillat, S., Lambert, J. C., Lahoz, W. A.,
Viscardy, S., Bonjean, S., and Fonteyn, D.: 4D-Var assimilation of MIPAS
chemical observations: ozone and nitrogen dioxide analyses, Atmos. Chem.
Phys., 8, 6169–6187, 10.5194/acp-8-6169-2008, 2008.Froidevaux, L., Jiang, Y. B., Lambert, A., Livesey, N. J., Read, W. G.,
Waters,
J. W., Browell, E. V., Hair, J. W., Avery, M. A., McGee, T. J., Twigg, L. W.,
Sumnicht, G. K., Jucks, K. W., Margitan, J. J., Sen, B., Stachnik, R. A.,
Toon, G. C., Bernath, P. F., Boone, C. D., Walker, K. A., Filipiak, M. J.,
Harwood, R. S., Fuller, R. A., Manney, G. L., Schwartz, M. J., Daffer, W. H.,
Drouin, B. J., Cofield, R. E., Cuddy, D. T., Jarnot, R. F., Knosp, B. W.,
Perun, V. S., Snyder, W. V., Stek, P. C., Thurstans, R. P., and Wagner,
P. A.: Validation of Aura Microwave Limb Sounder stratospheric ozone
measurements, J. Geophys. Res.-Atmos., 113, D15S20,
10.1029/2007JD008771, 2008a.Froidevaux, L., Jiang, Y. B., Lambert, A., Livesey, N. J., Read, W. G.,
Waters,
J. W., Fuller, R. A., Marcy, T. P., Popp, P. J., Gao, R. S., Fahey, D. W.,
Jucks, K. W., Stachnik, R. A., Toon, G. C., Christensen, L. E., Webster,
C. R., Bernath, P. F., Boone, C. D., Walker, K. A., Pumphrey, H. C., Harwood,
R. S., Manney, G. L., Schwartz, M. J., Daffer, W. H., Drouin, B. J., Cofield,
R. E., Cuddy, D. T., Jarnot, R. F., Knosp, B. W., Perun, V. S., Snyder,
W. V., Stek, P. C., Thurstans, R. P., and Wagner, P. A.: Validation of Aura
Microwave Limb Sounder HCl measurements, J. Geophys. Res.-Atmos., 113, d15S25, 10.1029/2007JD009025,
2008b.Funke, B., López-Puertas, M., von Clarmann, T., Stiller, G. P., Fischer,
H.,
Glatthor, N., Grabowski, U., Höpfner, M., Kellmann, S., Kiefer, M., Linden,
A., Mengistu Tsidu, G., Milz, M., Steck, T., and Wang, D. Y.: Retrieval of
stratospheric NOx from 5.3 and 6.2 nm nonlocal thermodynamic equilibrium
emissions measured by Michelson Interferometer for Passive Atmospheric
Sounding (MIPAS) on Envisat, J. Geophys. Res.-Atmos.,
110, d09302, 10.1029/2004JD005225,
2005.
Gaspari, G. and Cohn, S. E.: Construction of correlation functions in two
and three dimensions, Q. J. Roy. Meteor. Soc., 125, 723–757, 1999.Gaubert, B., Coman, A., Foret, G., Meleux, F., Ung, A., Rouil, L., Ionescu,
A., Candau, Y., and Beekmann, M.: Regional scale ozone data assimilation
using an ensemble Kalman filter and the CHIMERE chemical transport model,
Geosci. Model Dev., 7, 283–302, 10.5194/gmd-7-283-2014, 2014.
Gonnet, G. H. and Baeza-Yates, R.: Handbook of Algorithms and Data
Structures:
In Pascal and C, 2nd Edn., Addison-Wesley Longman Publishing Co., Inc.,
Boston, MA, USA, 1991.Hunt, B. R., Kalnay, E., Kostelich, E. J., Ott, E., Patil, D. J., Sauer, T.,
Szunyogh, I., Yorke, J. A., and Zimin, A. V.: Four-dimensional ensemble
Kalman filtering, Tellus A, 56, 273–277,
10.1111/j.1600-0870.2004.00066.x,
2004.
Kalnay, E., Li, H., Miyoshi, T., Yang, S.-C., and Ballabrera-Poy,
J.:
4-D-Var or ensemble Kalman filter?, Tellus A, 59, 758–773, 2007.Laeng, A., Plieninger, J., von Clarmann, T., Grabowski, U., Stiller, G.,
Eckert, E., Glatthor, N., Haenel, F., Kellmann, S., Kiefer, M., Linden, A.,
Lossow, S., Deaver, L., Engel, A., Hervig, M., Levin, I., McHugh, M., Noël,
S., Toon, G., and Walker, K.: Validation of MIPAS IMK/IAA methane profiles,
Atmos. Meas. Tech., 8, 5251–5261, 10.5194/amt-8-5251-2015, 2015.Lambert, A., Read, W. G., Livesey, N. J., Santee, M. L., Manney,
G. L., Froidevaux, L., Wu, D. L., Schwartz, M. J., Pumphrey, H. C.,
Jimenez, C., Nedoluha, G. E., Cofield, R. E., Cuddy, D. T., Daffer,
W. H., Drouin, B. J., Fuller, R. A., Jarnot, R. F., Knosp, B. W.,
Pickett, H. M., Perun, V. S., Snyder, W. V., Stek, P. C.,
Thurstans, R. P., Wagner, P. A., Waters, J. W., Jucks, K. W., Toon,
G. C., Stachnik, R. A., Bernath, P. F., Boone, C. D., Walker, K. A.,
Urban, J., Murtagh, D., Elkins, J. W., and Atlas, E.: Validation of
the Aura Microwave Limb Sounder middle atmosphere water vapor and nitrous
oxide measurements, J. Geophys. Res., 112, D24S36,
10.1029/2007JD008724, 2007.Lefever, K., van der A, R., Baier, F., Christophe, Y., Errera, Q., Eskes, H.,
Flemming, J., Inness, A., Jones, L., Lambert, J.-C., Langerock, B., Schultz,
M. G., Stein, O., Wagner, A., and Chabrillat, S.: Copernicus stratospheric
ozone service, 2009–2012: validation, system intercomparison and roles of
input data sets, Atmos. Chem. Phys., 15, 2269–2293,
10.5194/acp-15-2269-2015, 2015.Li, H., Kalnay, E., and Miyoshi, T.: Simultaneous estimation of covariance
inflation and observation errors within an ensemble Kalman filter, Quarterly
J. Roy. Meteor. Soc., 135, 523–533,
10.1002/qj.371, 2009.
Lin, S.-J. and Rood, R. B.: Multidimensional Flux-Form Semi-Lagrangian
Transport Schemes, Mon. Weather Rev., 124, 2046–2070, 1996.Liu, C., Xiao, Q., and Wang, B.: An Ensemble-Based Four-Dimensional
Variational
Data Assimilation Scheme. Part I: Technical Formulation and Preliminary Test,
Mon. Weather Rev., 136, 3363–3373, 10.1175/2008MWR2312.1,
2008.Livesey, N. J., Read, W. G., Wagner, P. A., Froidevaux, L., Lambert, A.,
Manney, G. L., Pumphrey, H. C., Santee, M. L., Schwartz, M. J., Wang, S.,
Fuller, R. A., Jarnot, R. F., Knosp, B. W., and Martinez, E.: Earth
Observing System (EOS) Aura Microwave Limb Sounder (MLS) Version
4.2x Level 2 data quality and description document, Jpl d-33509 rev.a, Jet
Propulsion Laboratory, available at: http://mls.jpl.nasa.gov/data/v4-2_data_quality_document.pdf (last access: 18 August 2016),
2015.
Lorenc, A. C.: The potential of the ensemble Kalman filter for NWP – a
comparison with 4D-Var, Q. J. Roy. Meteor. Soc., 129, 3183–3203, 2003.Lorenc, A. C., Bowler, N. E., Clayton, A. M., Pring, S. R., and Fairbairn,
D.:
Comparison of Hybrid-4DEnVar and Hybrid-4DVar Data Assimilation Methods for
Global NWP, Mon. Weather Rev., 143, 212–229,
10.1175/MWR-D-14-00195.1,
2015.Madronich, S. and Flocke, S.: The Role of Solar Radiation in Atmospheric
Chemistry, in: Environmental Photochemistry, edited by Boule, P., vol. 2/2L
of The Handbook of Environmental Chemistry, Springer
Berlin Heidelberg, 1–26, 10.1007/978-3-540-69044-3_1,
1999.Ménard, R.: Error covariance estimation methods based on analysis
residuals: theoretical foundation and convergence properties derived from
simplified observation networks, Q. J. Roy. Meteor. Soc., 142, 257–273,
10.1002/qj.2650,
2016.Ménard, R. and Chang, L.-P.: Assimilation of Stratospheric Chemical
Tracer Observations Using a Kalman Filter. Part II: χ2-Validated
Results and Analysis of Variance and Correlation Dynamics, Mon. Weather Rev.,
128, 2672–2686, 2000.
Ménard, R. and Daley, R.: The application of Kalman smoother theory
to
the estimation of 4DVAR error statistics, Tellus A, 48, 221–237, 1996.Mitchell, H. L. and Houtekamer, P. L.: An Adaptive Ensemble Kalman Filter,
Mon. Weather Rev., 128, 416–433,
10.1175/1520-0493(2000)128<0416:AAEKF>2.0.CO;2,
2000.Miyazaki, K., Eskes, H. J., Sudo, K., Takigawa, M., van Weele, M., and
Boersma, K. F.: Simultaneous assimilation of satellite NO2, O3, CO, and
HNO3 data for the analysis of tropospheric chemical composition and
emissions, Atmos. Chem. Phys., 12, 9545–9579, 10.5194/acp-12-9545-2012,
2012.Poterjoy, J. and Zhang, F.: Systematic Comparison of Four-Dimensional Data
Assimilation Methods With and Without the Tangent Linear Model Using Hybrid
Background Error Covariance: E4DVar versus 4DEnVar, Mon. Weather Rev.,
143, 1601–1621, 10.1175/MWR-D-14-00224.1,
2015. Sander, S., Friedl, R., Golden, D., Kurylo, M., Moortgat, G., Keller-Rudek,
H.,
Wine, P., Ravishankara, A., Kolb, C., Molina, M., Finlayson-Pitts, B., Huie,
R., and Orkin, V.: Chemical Kinetics and Photochemical Data for Use in
Atmospheric Studies. Evaluation Number 15, JPL Publication 06-2, Jet
Propulsion Laboratory, Pasadena,
available at: http://jpldataeval.jpl.nasa.gov (last access:
18 August 2016), 2006.Sankey, D. and Shepherd, T. G.: Correlations of long-lived chemical species
in
a middle atmosphere general circulation model, J. Geophys.
Res.-Atmos., 108, 4494, 10.1029/2002JD002799,
2003.Santee, M. L., Lambert, A., Read, W. G., Livesey, N. J., Cofield, R. E.,
Cuddy,
D. T., Daffer, W. H., Drouin, B. J., Froidevaux, L., Fuller, R. A., Jarnot,
R. F., Knosp, B. W., Manney, G. L., Perun, V. S., Snyder, W. V., Stek, P. C.,
Thurstans, R. P., Wagner, P. A., Waters, J. W., Muscari, G., de Zafra, R. L.,
Dibb, J. E., Fahey, D. W., Popp, P. J., Marcy, T. P., Jucks, K. W., Toon,
G. C., Stachnik, R. A., Bernath, P. F., Boone, C. D., Walker, K. A., Urban,
J., and Murtagh, D.: Validation of the Aura Microwave Limb Sounder HNO3
measurements, J. Geophys. Res.-Atmos., 112, d24S40,
10.1029/2007JD008721,
2007.Skachko, S., Errera, Q., Ménard, R., Christophe, Y., and Chabrillat, S.:
Comparison of the ensemble Kalman filter and 4D-Var assimilation methods
using a stratospheric tracer transport model, Geosci. Model Dev., 7,
1451–1465, 10.5194/gmd-7-1451-2014, 2014.Strong, K., Wolff, M. A., Kerzenmacher, T. E., Walker, K. A., Bernath, P. F., Blumenstock, T., Boone,
C., Catoire, V., Coffey, M., De Mazière, M., Demoulin, P., Duchatelet, P., Dupuy, E., Hannigan, J., Höpfner, M., Glatthor, N., Griffith, D. W. T.,
Jin, J. J., Jones, N., Jucks, K., Kuellmann, H., Kuttippurath, J., Lambert, A., Mahieu, E., McConnell, J. C., Mellqvist, J., Mikuteit, S., Murtagh, D. P.,
Notholt, J., Piccolo, C., Raspollini, P., Ridolfi, M., Robert, C., Schneider, M., Schrems, O., Semeniuk, K., Senten, C., Stiller, G. P.,
Strandberg, A., Taylor, J., Tétard, C., Toohey, M., Urban, J., Warneke, T., and Wood, S.: Validation of ACE-FTS N2O
measurements, Atmos. Chem. Phys., 8, 4759–4786, 10.5194/acp-8-4759-2008, 2008.
Talagrand, O. and Courtier, P.: Variational assimilation of
meteorological
observations with the adjoint vorticity equation. I: Theory, Q. J. Roy.
Meteor. Soc., 113, 1311–1328, 1987.Tang, X., Zhu, J., Wang, Z. F., and Gbaguidi, A.: Improvement of ozone
forecast over Beijing based on ensemble Kalman filter with simultaneous
adjustment of initial conditions and emissions, Atmos. Chem. Phys., 11,
12901–12916, 10.5194/acp-11-12901-2011, 2011.