A linear CO chemistry parameterization in a chemistry-transport model: evaluation and application to data assimilation

. This paper presents an evaluation of a new linear parameterization valid for the troposphere and the stratosphere, based on a ﬁrst order approximation of the carbon monoxide (CO) continuity equation. This linear scheme (hereinafter noted LINCO) has been implemented in the 3-D Chemical Transport Model (CTM) MOCAGE (MOd ` ele de Chimie Atmospherique Grande Echelle). First, a one and a half years of LINCO simulation has been compared to output

±10 ppbv or 100% in the stratosphere. Second, LINCO has been compared to diverse observations from satellite instruments covering the troposphere (Measurements Of Pollution In The Troposphere: MOPITT) and the stratosphere (Microwave Limb Sounder: MLS) and also from aircraft (Measurements of ozone and water vapour by Airbus in-service aircraft: MOZAIC programme) mostly flying in the upper troposphere and lower stratosphere (UTLS). In the troposphere, the LINCO seasonal variations as well as the vertical and horizontal distributions are quite close to MOPITT CO observations. However, a bias of ∼ −40 ppbv is observed at 700 hPa between LINCO and MOPITT. In the stratosphere, MLS and LINCO present similar large-scale patterns, except over the poles where the CO concentration is underestimated by the model. In the UTLS, LINCO presents small biases Correspondence to: M. Claeyman (marine.claeyman@aero.obs-mip.fr) less than 2% compared to independent MOZAIC profiles. Third, we assimilated MOPITT CO using a variational 3D-FGAT (First Guess at Appropriate Time) method in conjunction with MOCAGE for a long run of one and a half years. The data assimilation greatly improves the vertical CO distribution in the troposphere from 700 to 350 hPa compared to independent MOZAIC profiles. At 146 hPa, the assimilated CO distribution is also improved compared to MLS observations by reducing the bias up to a factor of 2 in the tropics. This study confirms that the linear scheme is able to simulate reasonably well the CO distribution in the troposphere and in the lower stratosphere. Therefore, the low computing cost of the linear scheme opens new perspectives to make free runs and CO data assimilation runs at high resolution and over periods of several years. emissions (industries, transport, biomass burning) make CO a good tracer of pollution which is indicative of incomplete combustion. It also enables the tracking of long-distance airmass transport (Stohl et al., 2002;Staudt et al., 2001). Various studies have been carried out to characterize transport over polluted continents such as South America (e.g., Pickering et al., 1996;Freitas et al., 2005), Asia (e.g., Li et al., 2005) or Africa (e.g., Sinha et al., 2004;Guan et al., 2008).
Chemistry Transport Models (CTMs) at global scale are used for a better understanding of global atmospheric chemistry since they provide 4-D fields of chemical species. Several tens of species and hundreds of reactions are required to adequately model the chemical production and loss rates of the major active species. For example, O 3 encounters different regimes in the troposphere and in the stratosphere. In the troposphere, O 3 production consists of oxidation reactions between OH and some trace gas constituents in the presence of nitrogen oxides; whereas in the stratosphere, it is produced by a cycle initiated by photolysis of oxygen and destroyed by reactions involving nitrogen oxides, chlorine and bromine species.
Such complete schemes require a large amount of computing time which can put limitations on the model resolutions or on the duration of the feasible simulations. That is why linear ozone parameterizations have been developed for upper tropospheric and stratospheric studies, where only major ingredients of the atmospheric chemistry are taken into account (temperature and ozone amount). For example, the scheme developed by Cariolle and Déqué (1986) computes the ozone chemistry trend around a long state equilibrum defined by O 3 and temperature. This parameterization has been recently updated by Cariolle and Teyssèdre (2007) and is widely used in many models, such as the ARPEGE-Climat (Action de Recherche Petite Echelle Grande Echelle) general circulation model (Déqué et al., 1994), and the European Centre for Medium-Range Weather Forecasting (ECMWF) model (Andersson et al., 2003) for operational forecasts and the ERA40 reanalysis project (Oikonomou and O'Neill, 2006). Several linear ozone parameterizations (e.g., McLinden et al., 2000;McCormack et al., 2004McCormack et al., , 2006 were validated by Geer et al. (2007) using data assimilation in a stratosphere-troposphere model. Even if the computing capabilities have increased, linear parameterizations are useful. These parameterizations may avoid the impact of misspecified or poorly-known chemical species. By construction, such schemes have no intrinsic trend and then are useful for simulations of several years (e.g., Hadjinicolaou et al., 2005) and data assimilation (e.g., Semane et al., 2007;Massart et al., 2009).
In addition to their representation of chemical processes, CTMs may present deficiencies due to approximations in dynamic processes and in emission inventory. Chemical data assimilation can be used to overcome these deficiencies. It consists of providing consistent chemical species 4-D fields by combining in an optimal way observations and model fields (e.g., Lahoz et al., 2007;El Amraoui et al., 2004;Semane et al., 2009). These fields are well suited for the study of transport processes and budget analyses in the troposphere (Pradier et al., 2006), in the stratosphere (El Amraoui et al., 2008b) or in the Upper Troposphere-Lower Stratosphere (UTLS) (Barret et al., 2008). Because chemical linear schemes produce minimal computing cost and relative good quality of simulated fields, it is then possible to perform data assimilation over periods of several years.
The purpose of this paper is to present a new linear parameterization of the CO chemical distribution for the troposphere and the stratosphere, which makes possible long model runs and data assimilation. The parameterization is based on a linearization of the CO tendencies around an equilibrium state, which has been derived from a 2-D photochemical model similarly to the approach used for ozone (Cariolle and Déqué, 1986). This parameterization is well suited for CO which has a relatively simple chemistry. The CO linear scheme has been implemented into the Météo-France transport chemical model MOCAGE (MOdèle de Chimie Atmospherique Grande Echelle), (Peuch et al., 1999). A free model simulation forced by the ARPEGE meteorological analyses has been performed. A comparison of the model CO outputs with various observational datasets is done for a one and half year period from December 2003 to July 2005. In the stratosphere, the model results are compared to the space-borne Microwave Limb Sounder (MLS) observations. In the troposphere, comparisons are made using the spaceborne MOPITT (Measurements Of Pollution In The Troposphere) observations and the in situ measurements from MOZAIC (Measurements of ozone and water vapour by Airbus in-service aircraft) programme. We also compare the performances of the linear scheme to a detailed chemical scheme, RACMOBUS (Dufour et al., 2004). Besides, the CO linear scheme is used within the MOCAGE-PALM assimilation system (Massart et al., 2005) in order to assimilate the MOPITT CO data during the same period of study (from December 2003to July 2005. Detailed comparisons of the CO analyses with independent MOZAIC and MLS CO observations are reported in order to validate the experiment. This paper is organized as follows. In Sect. 2, we describe the CO linear parameterization, the CTM model, the data assimilation system employed as well as the different datasets used in this study. In Sect. 3, we discuss the results obtained for the validation of the free run with the linear CO chemical scheme. Section 4 presents and validates the analyses of one year of MOPITT CO data assimilation. Lastly, summary and conclusions are presented in Sect. 5.

The linear carbon monoxide chemical scheme
The new linear scheme for the computation of the CO chemical tendencies relies on a methodology similar to the approach developed by Cariolle and Déqué (1986) and updated by Cariolle and Teyssèdre (2007) for stratospheric ozone. The CO continuity equation is expanded into a Taylor series up to the first order around the local value of the CO mixing ratio r CO and the temperature T: where the A i terms are monthly averages calculated using the 2-D photochemical model MOBIDIC (MOdèle BIDImensionnel de Chimie) (Cariolle et al., 2008): : production minus loss rate of CO A 2 = ∂(P − L)/∂r CO : zonal net variation of (P−L) due to r CO variations A 3 = r CO : CO zonal mixing ratio A 4 = ∂(P − L)/∂T : zonal net variation of (P−L) due to T variations A 5 = T : zonal mean temperature with P and L being the CO production and loss terms, respectively. The partial derivatives A 2 and A 4 in Eq.
(1) are obtained by perturbing the 2-D model fields by ±10% for the CO mixing ratio and by ±10 K for temperature, respectively. For each month, a set of zonal mean coefficients is obtained. To test the accuracy of the linearity of the system, we have applied perturbations (up to ±30% for CO and ±20 K for temperature), and have found very small deviations in the calculated A i . Figure 1a shows the A 3 term for the month of January. It represents the zonal mean distribution of CO from the MO-BIDIC model. This CO distribution is characterized by larger mixing ratios within the range of 100-130 ppbv (part per billion by volume) in the troposphere of Northern Hemisphere (NH) and in the lower tropical troposphere. Large vertical gradients are observed near the UTLS region with mixing ratios below 30 ppbv in the lower stratosphere. This CO distribution is comparable to current measurements (e.g., Edwards et al., 2003).
The A 1 term in Fig. 1b gives the chemical tendencies needed to balance those due to transport and surface emissions of CO. As expected, this term is negative and large at the equator in the lower troposphere in the presence of large biomass burning and anthropogenic emissions, and rapid vertical transport by the rising branch of the mean meridional circulation and by convection.
The photochemical relaxation time of CO, is given by τ = −1/A 2 (Fig. 1c). Since the CO lifetime is mainly controlled by its reaction with OH, the distribution of τ is closely linked to the OH concentrations. The lowest values of τ , less than 30 days, are found in the equatorial lower troposphere, and in the middle stratosphere outside of the polar vortex (90 S-60 N). From the surface up to the tropopause, the CO relaxation time increases to reach a relative maximum of about 100 days at the equator. At summertime in southern latitudes (90 S-50 S) τ increases to values up to one year in the UTLS. At high latitudes in the NH from 0 to 30 km, τ tends to infinity and CO becomes an inert tracer. Note that for implementation within global models, the CO parameterization is complemented with surface emissions and deposition in a similar way to what is done when a detailed chemical scheme is used (see Sect. 2.2).

MOCAGE-PALM
MOCAGE is a three-dimensional chemistry transport model for the troposphere and stratosphere (Peuch et al., 1999) which simulates interactions between dynamical, physical and chemical processes. MOCAGE uses hybrid vertical levels from the surface up to 5 hPa with a resolution of about 150 m in the lower troposphere (40 m near the surface) and up to 800 m in the lower stratosphere. Hybrid vertical levels are designed so that lowermost levels follow the terrain while upper levels are isobaric. The version of MOCAGE used in this study has an horizontal resolution of 2 • ×2 • over the globe and uses a semi-Lagrangian advection scheme (e.g., Josse et al., 2004) to transport the chemical species. Turbulent diffusion is calculated with the scheme of Louis (1979) and convective processes with the scheme of Bechtold et al. (2001). The meteorological analyses of Météo-France, ARPEGE (Courtier et al., 1991) were used to force the dynamics of the model every 6 hours.
The linear scheme is compared to the detailed scheme of MOCAGE, RACMOBUS which is a combination of the stratospheric scheme REPROBUS (Lefèvre et al., 1994) and of the tropospheric scheme RACM (Stockwell et al., 1997). It includes 119 individual species with 89 prognostic variables and 372 chemical reactions. The simulations presented here use the emissions inventory from Dentener et al. (2005). For CO, emissions are given as a monthly mean for biomass burning and a yearly mean for others. Emission rates and deposition velocities are computed externally (Michou and Peuch, 2002) and taken into account in MOCAGE. The dry deposition scheme is based upon the Wesley (1989) scheme. The wet deposition is parameterized for stratiform and convective clouds (Giorgi and Chameides, 1986;Mari et al., 2000) and validated in Michou et al. (2004). MOCAGE is used for several applications: operational chemical weather forecasting in Météo-France (Dufour et al., 2004) and data assimilation research (e.g., El Amraoui et al., 2008b;Semane et al., 2009). A detailed validation of the model has been done using a large number of measurements during the Intercontinental Transport of Ozone and Precursors (ICARTT/ITOP) campaign (Bousserez et al., 2007). Its climate version has also been validated over several years by Teyssèdre et al. (2007).
In addition, we used the assimilation system MOCAGE-PALM (Massart et al., 2005). The assimilation module is PALM (Buis et al., 2006) within which is implemented the 3D-FGAT (First Guess at Appropriate Time) assimilation technique (Fisher and Andersson, 2001). This technique is a compromise between the 3D-Var and the 4D-Var. It has been validated during the assimilation of ENVISAT data project (ASSET) and has producted good quality results compared to independent data and many other assimilation systems (Geer et al., 2006). Details on the method and on the assimilation system can be found in Massart et al. (2005), Massart et al. (2007) and El Amraoui et al. (2010).

MOPITT
The MOPITT (Measurements Of Pollution In The Troposphere) instrument is a nadir infrared correlation radiometer onboard the NASA Terra Satellite (Drummond and Mand, 1996). It has been monitoring CO from March 2000 to date. It provides global coverage in about 3 days. The pixel size is 22 km×22 km and the vertical profiles are retrieved on 7 pressure levels (surface, 850, 700, 500, 350, 250 and 150 hPa). The maximum a posteriori algorithm  is used to retrieve CO from MOPITT measured radiances. It is a statistical combination of the measurement and the a priori information based on an optimal estimation method (Rodgers, 2000). The retrieved profiles are characterized by their averaging kernel matrix, which indicates the sensivity of the MOPITT measurements to the true CO profile. In this study, we select MOPITT CO (Version 3) retrieved profiles with less than 40% a priori contamination to ensure good quality of dataset validation (Emmons et al., 2009). The accuracy of MOPITT CO retrieved profiles is assumed to be less than 20 ppbv for all of the 7 levels according to Emmons et al. (2004).

MLS
The Microwave Limb Sounder (MLS) (Waters et al., 2006) onboard the Aura spacecraft was launched on 15 July 2004 and placed into a near-polar Earth orbit at ∼705 km with an inclination of 98 • and an ascending mode at 13:45 h. It orbits the Earth around 14 times per day and provides dense spatial coverage for a limb sounder with daily 3500 profiles, between 82 • N and 82 • S. MLS observes thermal microwave emission from Earth's limb in five spectral regions from 118 GHz to 2.5 THz. The MLS CO measurements are made in the 240 GHz region. The optimal estimation method is used to retrieve CO profiles (Rodgers, 2000). The retrieval grid has 6 levels per pressure decade for altitudes below 0.1 hPa and 3 levels per pressure decade above this. The MLS CO level 2 products used in this paper are produced by version 2.2 of the data processing algorithms. The vertical resolution of MLS CO retrieved profiles is about 3-4 km in the stratosphere and the horizontal resolution is between 500 km for lower stratospheric levels and 300 km for upper stratospheric levels. Data are selected according to quality flag criteria presented in Livesey et al. (2007). In the version used in this study, the impact of extra terrestrial signals generated by the Milky Way and affecting the terrestrial CO retrieval mainly at 22 hPa for some specific days of year and latitudes has been eliminated according to Pumphrey et al. (2009). The MLS CO data set was validated by Livesey et al. (2008) for the upper troposphere and lower stratosphere and by Pumphrey et al. (2007) for the stratosphere and the mesosphere where the accuracy was estimated to be 30 ppbv for pressures of 147 hPa and less.

MOZAIC
The MOZAIC (Measurements of ozone and water vapour by Airbus in-service aircraft) programme (Marenco et al., 1998) was launched in January 1993. The project results from the collaboration of the aeronautics industry, airline carriers, and research laboratories. Measurements started in August 1994, with the installation of ozone and water vapor sensors aboard five commercial aircrafts. In 2001, the in-strumentation was upgraded by installing CO sensors on all aircrafts. For the measurement of CO, the IR gas filter correlation technique is employed (Thermo Environmental Instruments, Model 48CTL). This IR instrument provides excellent stability, which is important for continuous operation without frequent maintenance. The sensitivity of the instrument was improved by several modifications (Nédélec et al., 2003), achieving a precision of 5 ppbv or 5% for a 30 s response time. The majority of these flights are in the NH and connect Europe, North America and eastern Asia, but also include flights to South America and Africa. About 90% of the MOZAIC measurements are made at cruise altitude, between 9 and 12 km. The remaining measurements are performed during ascent and descent phases. A complete description of the MOZAIC programme may be found at http: //mozaic.aero.obs-mip.fr/web/ and in the IGAC Newsletters (Cammas and Volz-Thomas, 2007). We selected MOZAIC data from flights over Europe, North America and Eastern Asia.

Evaluation of the linear CO chemical scheme
In order to evaluate the linear CO chemical scheme, two MOCAGE simulations have been made in the period between 1 December 2003 and 1 July 2005. The first one (hereinafter referred to as LINCO) used the linear CO parameterization and the second one used the detailed chemical scheme RACMOBUS. All the other model components are kept the same: in particular, they both used the same atmospheric forcing from ARPEGE analysis and the same emission inventory. The simulated field for 1 December 2003 has been obtained from a free run with RACMOBUS started from the October climatological initial field. Independent observations are used to evaluate LINCO: measurements from MOPITT in the troposphere, MLS in the stratosphere and MOZAIC in the UTLS.

Comparison with the detailed chemical scheme RACMOBUS
In this section, we evaluate the effect of CO chemistry representation in the model (detailed or linearized), by comparing two simulations. Both RACMOBUS and LINCO use the same model components (e.g., transport, atmospheric processes and emissions). In Fig. 2, we present the temporal evolution of the CO zonal mean obtained from LINCO and RACMOBUS for the period from December 2003 to June 2005 at the pressure levels 850 and 150 hPa, in the lowermost and uppermost troposphere respectively. Qualitatively, the two schemes behave similarly with differences between schemes of about ±20%, never exceeding ±40%. However, at the beginning of the period, LINCO concentrations tend to be higher than RACMOBUS CO concentrations whereas elsewhere, the opposite behavior is observed at both Figure 3 presents CO zonal means obtained from LINCO and RACMOBUS for two specific months (July 2004 and January 2005) representative of NH summer and winter, respectively. Both chemical schemes have similar patterns with small differences. The distribution of CO from both schemes reproduces the impact of African biomass burning emissions in the tropics. In the same way, the two schemes capture the mesospheric subsidence of CO within the stratospheric polar vortex (latitudes poleward of 60 • ) evidenced by high CO concentrations between 25 and 30 km. For both months, concentrations in LINCO are lower than those in RACMOBUS in the troposphere but the differences do not exceed ∼25 ppbv (∼35%). The maxima of the difference between both schemes in the troposphere, are located in the region with the intense convective activity, namely the intertropical convergence zone.
The negative bias observed in the troposphere between RACMOBUS and LINCO may come from 4 causes. The first hypothesis could be a negative bias between RACMOBUS average values and the A 3 coefficient which would lead LINCO to relax towards too low CO concentrations. Figures 1a and 3 show that the opposite is actually observed: the A 3 coefficient is larger than RACMOBUS and, on the contrary, A 3 tends to increase the concentrations in LINCO.
The second hypothesis is a bias between the A 5 LINCO coefficient and the ARPEGE temperature analyses used in MOCAGE. The comparison of these two terms shows that the differences are of the order of 1 K and the A 4 coefficient values are small in the troposphere, leading to a small contribution of the temperature term A 4 (T − A 5 ) in comparison to the other coefficients. The third hypothesis is an inconsistency between the production minus loss rate (A 1 coefficient) and the transport in MOCAGE since the MOCAGE and MOBIDIC models are different: the first one is a 3-D CTM and the second is a 2-D photochemical model. The fourth hypothesis comes from the different emission representations of MOBIDIC and MOCAGE. MOCAGE uses an emission inventory whereas MOBIDIC is relaxed to a climatology at the surface. This could introduce a too strong destruction of CO in the LINCO scheme. Moreover, the approach developed for the LINCO scheme is slightly different from that of the linear ozone scheme (Cariolle and Déqué, 1986) in the sense that for LINCO, the emissions are taken into account whereas for linear ozone there are no emissions. Consequently, the "production loss" term (A 1 ) should also be balanced with the emissions.
The three first hypotheses have already been studied in the context of linear ozone schemes (e.g. McCormack et al., 2006;Coy et al., 2007;Geer et al., 2007) whereas the emission effect in the LINCO scheme is something entirely new. To confirm an inconsistency in the A 1 coefficient, we made a sensitive test (not shown) by increasing the A 1 coefficient of LINCO. This test shows that by changing arbitrarily the A 1 coefficient, the bias between LINCO and RACMOBUS can be reduced in the troposphere. However, the A 1 LINCO coefficient is not anymore consistent with the chemistry and physics of the other coefficients calculated with MOBIDIC. Furthermore, the CO interannual variability is typically of 10-20% in the free troposphere, and nothing indicates that the tuning for a specific period could improve results for integrations of several years. Therefore, we decided to keep the set of coefficients calculated with MOBIDIC in the next sections.
In the stratosphere, LINCO concentrations are higher than RACMOBUS except between 70 • S and 90 • S in July 2004 and between 60 • N and 90 • N in January 2005. In these regions, LINCO underestimates the CO concentration of the mesospheric descent compared to RACMOBUS. The absolute difference in the stratosphere is about ∼15 ppbv (∼200%). Note that CO concentrations are generally very low in RACMOBUS in the stratosphere compared to LINCO, which explains such high relative differences between both schemes in the stratosphere. The positive bias observed between RACMOBUS and LINCO may be explained by the positive bias between the A 3 LINCO coefficient (Fig. 1a) and RACMOBUS (Fig. 3) in the stratosphere which relax LINCO concentrations to higher values. Moreover, the production minus loss rate in the stratosphere (Fig. 1b, A 1 coefficient) is positive which may also contribute to the positive bias between RACMOBUS and LINCO. In the following sections, we evaluate the LINCO fields in comparison to independent data from satellites and in situ measurements. Figure 4 shows the time evolution of CO from December 2003 to June 2005 as obtained by LINCO, RACMOBUS and MOPITT measurements at 700 and 250 hPa in the NH and SH. Note that modeled CO fields have been smoothed by MOPITT averaging kernels in order to take into account the vertical resolution and the a priori information used in the retrieval process of the V3 MOPITT product. At 700 hPa (Fig, 4c and d), the seasonal CO variations are fairly well represented by both chemical schemes showing a maximum in April in the NH and a maximum in October in the SH.

Comparison with satellite data in the troposphere
April maximum in the NH is due to the very weak sunshine during winter and correspondingly less destruction of CO by OH leading to the buildup of CO because of its long lifetime. In addition, in the SH, this period corresponds to an intense biomass burning activity in South Africa and later on in Australia . However, the LINCO scheme presents lower concentrations than RACMOBUS and MO-PITT in both hemispheres. As already explained in the Sect. 3.1, this suggests a larger destruction of CO in LINCO compared to RACMOBUS and MOPITT retrievals. The bias between MOPITT and LINCO is about 30-40 ppbv in the NH and 20-30 ppbv in the SH. However, LINCO follows very well the variations seen in MOPITT CO retrievals with a constant bias. RACMOBUS scheme seems to have a better CO time evolution in the SH than in the NH where emissions patterns and variability as well as photochemistry are more complex. Even if the bias between RACMOBUS and MOPITT is very low in the SH and at 250 hPa in the NH, a negative bias between RACMOBUS and MOPITT is observed in the NH at 700 hPa which can reach 30 ppbv. The bias between measured and modeled CO fields also suggests that CO emissions used in the model are underestimated. LINCO (ppbv) MOPITT MOPITT CO at 700 hPa (Fig. 5) shows generally high concentrations linked to intense emissions in the NH but also in regions of SH mostly affected by biomass burning such as South America, South Africa or Australia in October 2004. LINCO also underestimates the CO retrieved from MOPITT measurements in April 2005 reinforcing the idea of too much destruction of CO in the linear scheme combined with too low emissions used in CTMs as suggested by Shindell et al. (2006) or lately by Pison et al. (2009). Nevertheless, LINCO tends to accumulate CO over the Tibetan plateau especially in October 2004 (Fig. 5), which is located near populated regions with high emissions. Li et al. (2005) suggested that the boundary layer pollution, transported by Asian summer monsoon convection, is trapped by the Tibetan anticyclone. The model appears to overestimate this accumulation compared to MOPITT data. A similar behaviour is observed over the Tibetan plateau using RACMOBUS which confirms that this overestimation is not linked to the LINCO chemistry but rather to transport and dynamics (common to the two simulations). In Fig. 6, similar remarks as in Fig. 5 can be made, but a smaller bias is noticed between LINCO and MOPITT CO concentrations, ∼ −20% instead of ∼ −40% at 750 hPa.

Comparison with satellite data in the stratosphere
In this section, we compare the LINCO simulation with MLS CO data, in order to evaluate the CO linear scheme in the lower stratosphere. CO fields from LINCO simulation are smoothed by a theoretical triangular averaging kernel with the full-width at half-maximum equal to the MLS vertical resolution according to Pumphrey et al. (2007). This is made to represent the contribution of the range of layers of the atmosphere for which the satellite retrieval is sensitive. This contribution is important in the lower stratosphere where CO vertical gradients are strong. Figure 7 presents the CO monthly zonal means for the month of October 2004 and March 2005 calculated for LINCO and MLS CO. The MLS pressure levels are selected from 146 to 14 hPa. For both months, the vertical and latitudinal gradients of CO in the UTLS for pressures larger than 70 hPa are well represented by the model compared to MLS CO with the same range of mixing ratios except over the poles, where the LINCO mixing ratios are underestimated compared to the CO observed by MLS. This may be explained by a too rapid transport of the meridional circulation observed in ARPEGE analysis used in this study. This behaviour has already been reported by (e.g., van Noije et al., 2004;Monge-Sanz et al., 2006) for ECMWF reanalyses. In the same way, Teyssèdre et al. (2007) present similar behaviour with MOCAGE (using other years of ARPEGE analyses) and show that the age of the air is too young which suggest also a too rapid meridional transport. The mid-stratospheric air, where CO is less concentrated, is transported downward into the lower stratosphere too fast. It leads to smaller CO concentrations than the ones actually found by MLS in the lower stratosphere. presents the mesospheric descent observed by MLS, ACE-FTS (Atmospheric Chemistry Experiment Fourier Transform Spectrometer onboard SCISAT-1 satellite), Odin/SMR (Sub-Millimeter Radiometer onboard Odin satellite) and simulated by the Canadian Middle Atmosphere Model at higher altitudes for the same period. Compared to this study, the maximum of CO shown here above 20 hPa only corresponds to the bottom part of the mesospheric descent. The values are underestimated by MOCAGE probably because of the model top, namely located at 5 hPa and constrained by a zonal climatology. Consequently, MOCAGE leads to a misrepresentation of the mesospheric descent. A positive bias is observed between MLS CO and LINCO for pressure levels between 45 and 10 hPa for both months. As explained in Sect. 3.1, the bias may come from the LINCO coefficients (A 1 and A 3 ) which relax to a CO climatology that is higher than measured by MLS at these stratospheric pressure levels.

Comparison with MOZAIC aircraft data in the UTLS
To evaluate the linear scheme in the UTLS region, we compared CO from MOZAIC aircraft data and model output interpolated on-line at flight times and locations. We averaged the observations where pressures are lower than 300 hPa into boxes of 2 • ×2 • in order to match the model resolution. In Fig. 8, the LINCO and the MOZAIC data are compared for the months of October 2004 and April 2005 which cor-respond to CO maxima in the SH and in the NH, respectively. In both cases, LINCO tends to overestimate the aircraft observations, with very low biases, less than 2%, but with a large standard deviation of ∼27%. This indicates that LINCO does not present a systematic bias at the levels between 300 hPa and 180 hPa. However, as expected, LINCO is not able to represent the variability observed by aircraft in situ measurements. In October 2004, the model represents well the spatial distribution of CO as observed by MOZAIC. Both observations and model show a meridional gradient between equator and high latitudes as aircraft fly in the lower stratosphere at mid-latitudes (low CO amounts of ∼50 ppbv) and in the troposphere at low latitudes (high CO amounts of

Assimilation diagnostics
The linear scheme of CO is used here to demonstrate its great interest for data assimilation over long periods of time due to its low computational cost. The assimilation experiment started on 1 December 2003 and ended on 1 July 2005. The initial 3-D field of atmospheric constituents is the same as for twin runs for LINCO and RACMOBUS discussed in Sect. 3. MOPITT data are averaged in boxes of 2 • ×2 • to obtain super-observations directly assimilated into the used version of the MOCAGE-PALM system. Moreover, in order to take into account the vertical resolution of the MOPITT measurements, their averaging kernels as well as their a priori profiles are considered in the assimilation procedure. Note that the variance-covariance error matrices of MOPITT measurements are also taken into account during the assimilation process through the error covariance matrix of the observations. The analysed fields are studied for the period between July 2004 and July 2005. The period prior to 1 July 2004 is assumed to be perturbed by spinup effects, and thus is not considered in our analysis.
We check the consistency of the observations minus analyses (OMA) and observations minus forecast (OMF) in order to evaluate the quality of the CO assimilated fields. Figure 9 shows the two distributions of OMA and OMF for all of the 7 MOPITT levels and for the full period (July 2004-July 2005. Both distributions are nearly Gaussian and therefore are assumed to have a Gaussian error. The mean of OMF values is close to zero (∼0.7 ppbv) with a standard deviation of ∼16.6 ppbv (∼21%), which indicates a small bias between MOPITT observations and model forecast. The standard deviation and the mean value of OMA (with a correlation coefficient of 0.99) are smaller than that of OMF (with a correlation coefficient of 0.94) which shows that the analyses are closer to the observations than the forecast. This again indicates that the assimilation system behaves properly.

Comparison in the troposphere with independent MOZAIC aircraft data
In this section, we use MOZAIC CO as independent data in order to evaluate MOPITT CO assimilated fields (hereinafter referred to MOPan) and the LINCO simulation (reference standard simulation) with the objective to determine the added-value of data assimilation. Table 1 presents correlation, bias and standard deviations between LINCO and MOZAIC CO, and between MOPan and MOZAIC CO. LINCO underestimates CO in the lower troposphere with a negative bias of −25% compared to MOZAIC at 700 hPa whereas MOPan reduces this bias to a positive value of 8.6%. These results are consistent with the bias of +5% obtained by Emmons et al. (2009) directly considering MOPITT and MOZAIC in 2004 over coincident profiles. In this study, we consider all MOZAIC profiles and not only MOPITT coincident profiles as done by Emmons et al. (2009) which may lead to a slightly different bias (+8% instead of +5%). As presented in Sect. 3.4, the model tends to increase the CO concentrations in the UTLS region. This may explain the differences between a ∼16% bias found between MOZAIC data and MOPan at 250 hPa and a ∼2% bias between MOZAIC and MOPITT CO data found by Emmons et al. (2009) for the same period.
In order to go a step further in our analysis, CO averaged profiles are presented over 3 regions of the globe: North America (140-30 W, 15-70 N),  and   In Fig. 10 Emmons et al. (2004). In the lower troposphere and over Asia, LINCO slightly overestimates CO in summer (July-August-September) but widely underestimates CO during the other seasons. This is likely due to a mis-specified fossil fuel burning in the inventory emissions of the model over Asia as suggested by Shindell et al. (2006). The data assimilation corrects this discrepancy by decreasing the CO concentration in summer and increasing CO elsewhere. Moreover, the annual added CO mass in the troposphere by the MOPITT CO assimilation (via the assimilation increment) is estimated to be 680 Tg. This corresponds to ∼68% of the total mass introduced during one year by the emission inventory.

Comparison in the UTLS with MLS
MOZAIC data are only available up to 190 hPa, therefore we used independent MLS data at 147 hPa which is nearly an overlapped level with MOPITT at 150 hPa to evaluate MOPan at higher altitude. We applied the same theoreti-cal triangular averaging kernel as described in Sect. 3.3. In Fig. 11 Livesey et al. (2008), which may also contribute to this high difference between MOPITT CO analyses and MLS CO at high latitudes.

Summary and conclusions
In this study, we have presented a new linear parameterization for CO (LINCO) which can be used both in the troposphere and in the stratosphere. In order to evaluate this linear chemical scheme, we have implemented the parameterization into the MOCAGE CTM. In a first part, the results of LINCO have been compared to the detailed chemical scheme of MOCAGE, RACMOBUS. LINCO results have also been compared to several CO measurements from satellite instruments (MOPITT in the troposphere and MLS in the stratosphere) and from in situ aircraft data (MOZAIC) in the UTLS. In a second part, we have assimilated MOPITT CO with LINCO over one and a half years and compared analyses to independent observations (MOZAIC and MLS) to evaluate the quality of the results. This evaluation was done to demonstrate the interest of the LINCO low computation cost which allows data assimilation over long periods of time.
The CO distributions of both the linear and the detailed chemical schemes behave qualitatively similarly. The linear scheme has smaller CO concentrations in the troposphere and larger CO concentrations in the stratosphere compared to RACMOBUS. We deduced that these differences are mainly due in the troposphere to a too high destruction of CO concentration by the production minus loss rate LINCO coefficient (A 1 ). Indeed, the emission inventory used with LINCO in MOCAGE is different from the CO climatology at the surface used in MOBIDIC. This naturally leads to tropospheric biases in the LINCO scheme, because the A 1 coefficient remains fixed. In the stratosphere the positive bias between LINCO and RACMOBUS, is partly due to the positive bias between the CO climatological coefficient (A 3 ) and RAC-MOBUS. However differences between the two chemical schemes remain quite small (∼30 ppbv, 20%). The comparisons between model results and MOPITT CO data globally show a good agreement. The model is able to capture the main spatial patterns of CO and to represent the seasonal CO variations with a maximum in the NH in April and a maximum in the SH in October as observed in MOPITT data. A negative bias of LINCO in the troposphere is observed compared to MOPITT CO, predominant in the NH with a maximum near the surface (30-40 ppbv at 850 hPa) and a decrease with altitude (20 ppbv at 250 hPa). One can note that this negative bias is quite similar or a little higher to this encountered between LINCO and RACMOBUS. In the lower and middle stratosphere, LINCO simulates very well the CO concentrations distributions except at the poles where CO concentrations are underestimated. We suggest that this deficiency in LINCO is related to a too rapid downward transport of poor CO air from middle stratosphere to the lower stratosphere at the poles. In the UTLS, we obtained a very good agreement between LINCO results and MOZAIC CO observations with a small bias of +2% but with a large variability of ±27%.
The MOPITT CO analyses generally show a good agreement with the MOZAIC observations and reduce the negative bias in the troposphere compared to the model without assimilation and MOZAIC (from ∼ −20% without assimilation to ∼ +8% with assimilation). At 250 hPa, the bias between MOPITT CO analyses and MOZAIC is larger than the bias between MOPITT CO and MOZAIC CO obtained by Emmons et al. (2009) likely because of the model transport deficiency. We compared MOZAIC CO profiles with LINCO profiles over North America, Europe and Asia for different seasons. In each case, the assimilation greatly improves the CO vertical distribution from 700 to 350 hPa. The annual added CO mass in the troposphere by the MOPITT CO assimilation is estimated to be 680 Tg, which corresponds to ∼68% of the total mass introduced by the emission inventory during one year. MOPITT CO analyses also present a good agreement with MLS data at 146 hPa. However, at extratropical latitudes, MOPITT CO analyses underestimate the CO concentration compared to MLS CO (∼ −50%). This bias may be related to a too rapid downward transport of the meridional circulation.
Finally, we show that the linear parameterization for CO, introduced in a CTM, is able to represent reasonably well the main CO distribution in the troposphere and the lower stratosphere. In the context of data assimilation, we have shown that the bias is corrected by using MOPITT CO observations. The main advantage of such a chemical scheme is its low computing cost (only one tracer) which makes possible simulation and data assimilation for long periods. It is now possible to assimilate data at higher global resolution (for example 0.5 • instead of 2 • actually used) to use the full horizontal resolution of current nadir satellite-borne instruments.