IASI flies on board the series of polar-orbiting satellites MetOp operated by the EUropean organization for the exploitation of METeorological SATellites (EUMETSAT). It provides hyper-spectral measurements of the Earth's thermal radiation in the 3.62–15.5 µm (2760–645 cm-1) window and serves meteorological and atmospheric chemistry applications . IASI is an operational mission meant to provide long-term (>20 years) time series of accurate TIR spectra at high spatial resolution. A total of three IASI instruments will be flying simultaneously at the end of 2019, providing nearly global coverage six times per day (morning and evening overpasses). Hence, they represent a great opportunity for both NWP and climate–chemistry reanalyses. Only MetOp-A data, available from 2008 to present, have been employed for this study.

Since 2004 the Microwave Limb Sounder (MLS) has been flying on board the research mission AURA and measures thermal emission at the atmospheric limb . It provides about 3500 stratospheric profiles of multiple atmospheric constituents each day, including O3 . Since version 3 of MLS products has been in operation, O3 profiles have been retrieved on 55 pressure levels, with a recommended range for scientific usage between 0.02 and 261 hPa for version 4.2 . The biases of MLS O3 profiles are typically within 5 % with respect to ozonesondes and lidar measurements , with slightly higher values below 200 hPa. Given its good accuracy, MLS O3 has been widely used both for trend analysis and assimilation experiments . Similarly to previous studies , we retain only the most accurate data using MLS, i.e. above 170 hPa. The MLS V4.2 product used in this study has been downloaded from the Goddard Earth Sciences Data and Information Services Center (GES DISC) web portal (https://disc.gsfc.nasa.gov, last access: 16 July 2019).

Ozonesondes are launched on a weekly basis by meteorological services and provide accurate profiles of O3 up to 10 hPa with a vertical resolution of 150–200 m. Electrochemical concentration cell (ECC) sondes, which represent the largest percentage of the global network, have a precision of about 5 % . Radiosoundings are relatively sparse, and their geographical distribution is much more representative of the northern mid-latitudes. However, for several decades they have provided the most precise information on vertical ozone distribution in the troposphere. Therefore, they have been used to derive widely used tropospheric O3 climatologies and validate both satellite products or models . They will be used in this study to validate all model simulations. Data are collected and distributed by the World Ozone and Ultraviolet Radiation Data Center (WOUDC; http://www.woudc.org, last access: 16 July 2019).

Some further preprocessing has been applied to the original L1c and SOFRID datasets to ease the interpretation of the assimilation experiments presented later in Sect. . The objective was to ensure that exactly the same spectra are used for both L1 and L2 assimilation.

Only the spectral channels that are used in SOFRID are extracted from IASI L1c granules, i.e. channel no. 1350 (980 cm-1) to 1818 (1100 cm-1). Some further screening is applied to remove channels that are affected by strong H2O absorption, as also done in SOFRID.

The spatial resolution of the CTM (2∘×2∘; Sect. ) is much coarser than IASI pixel size. Since it is preferable to avoid all kind of spatial averaging of the observations, a significant reduction of ground pixels is needed. In return, we employ strict selection criteria to avoid contamination from clouds and bright surfaces as much as possible, which reduces the RT accuracy and increases retrieval or assimilation errors. The data selection is performed as follows.

First, only L1 pixels with both IASI and AVHRR highest-quality flags are kept.

Then, ground pixels from IASI L1 and SOFRID products are filtered using their respective cloud masks (Sect.  and ) and only keeping pixels with a cloud fraction less than or equal to 1 %.

SOFRID pixels with a sand signature greater than 0.5 and with a number of retrieved levels lower than 35 (mountains) are also filtered out.

Resulting datasets are then matched; i.e. only common ground pixels that remained available after the previous L1 and SOFRID independent selections are kept. Finally, data thinning is performed using a regular grid of 1∘×1∘ resolution and only keeping the first pixel that falls in every two grid boxes. This ensures a minimum distance of 1∘ among assimilated observations. After the completion of the data selection procedure the final number of retained ground pixels for L1 and SOFRID is about 5000 per day, compared to about 105 when only the cloud screening is applied. The total number of L1 and L2 observations resulting from the above selection and further assimilated in this study is displayed in Fig. .

The chemical transport model (CTM) MOCAGE is used in this study. A global configuration with a horizontal resolution of 2∘×2∘ and 60 hybrid sigma-pressure levels up to 0.1 hPa has been used. The vertical resolution varies from about 100 m in the planetary boundary layer to about 700 m in the upper troposphere, decreasing further to approximately 2 km in the upper stratosphere. Chemical mechanism, emissions and physical parameterizations follow the setup used for operational air-quality forecasts , which includes about 100 species and 300 chemical reactions. A similar configuration has been employed by to assimilate IASI O3 columns over Europe but with a lower model top at 5 hPa. Other authors favoured a simplified chemistry scheme but with a model top at 0.1 hPa to assimilate satellite O3 products globally .

For this study we considered the highest available model top because we need to simulate the full atmosphere to compute radiances. In addition, the 0.1 hPa top matches with the vertical grid used for SOFRID retrievals (Sect. ), making the comparison of the two assimilation approaches (radiances versus L2) stricter. The full chemical scheme is chosen instead of a simplified chemistry to reduce biases of the modelled O3 in the troposphere as much as possible. The main intent of this study is in fact to evaluate the impact of dynamical and accurate O3 prior information on assimilation results.

The meteorological forcing comes from the ECMWF IFS, from which we retrieved the forecast (type “fc”) initialized with the analysis at 00:00 UTC each day. The NWP fields are interpolated on the horizontal grid of MOCAGE (2∘×2∘) during the retrieval process and stored with a time step of 3 h. During the integration of MOCAGE, the meteorological forcing is linearly interpolated at the advection time step of MOCAGE (hourly) and on the CTM's vertical grid.

RTTOV is a community RTM developed for operational NWP models. One of its main advantages is computational efficiency, which is achieved by running accurate but costly line-by-line RT simulations for a large number of satellite sensors, observation geometries and atmospheres and storing the corresponding coefficients in large lookup tables. RTTOV provides application programming interfaces (APIs) for the direct RT computations plus the tangent linear and adjoint model, which are needed in variational assimilation systems.

Version 11.3 of RTTOV has been used in this study for the L1 assimilation. This version includes coefficients for the IASI TIR channels computed using a fine atmospheric grid (101 vertical levels). The SST, 2 m temperature, 2 m pressure and 2 m wind vector are taken from high-resolution (0.125∘×0.125∘) global IFS forecasts initialized with the analysis at 00:00 UTC each day and co-located (nearest neighbour) with satellite ground pixels prior to data assimilation. A linear interpolation from the 3 h forecast steps to the closest hour of the IASI observations is also performed for these fields. The surface emissivity is based on the RTTOV monthly TIR emissivity atlas . Only clear-sky RT computations are performed for this study, and no aerosols have been prescribed. The RTM configuration is summarized in Table . Due to the different processing chains, the auxiliary inputs of RTTOV could not be set exactly equal for L1 assimilation and L2 retrievals (Table ). The potential impact of these residual differences is discussed in Sect. .

The assimilation suite for MOCAGE is based on a variational algorithm and was developed initially within the ASSET (Assimilation of Envisat data) project . The objective was to assimilate satellite products at a global scale, and a 3-D-FGAT implementation was chosen. It evolved later to provide air-quality reanalyses at the surface based on a 3D-Var implementation and was extended to 4D-Var when employing linearized chemistry schemes . In all cases the minimization of the variational cost function is performed using the limited-memory Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm . In this study we used a 3D-Var algorithm with hourly assimilation windows and with O3 as the control variable.

The 3-D background error covariance is modelled through a diffusion operator and allows the specification of heterogeneous correlation length scales. Compared to previous studies using the MOCAGE assimilation suite, a new vertical correlation operator has been employed here: the vertical error correlation is now assigned by explicitly filling a positive definite matrix using the Gaussian formulation of and by numerically computing its square root. This avoids difficulties encountered with diffusion-based operators concerning the normalization in the presence of boundaries (e.g. the surface) and heterogeneity . Since the vertical dimension of the model grid is relatively small, this choice does not impact the numerical cost and the memory requirements significantly with respect to the previous implementation based on diffusion.

The observation operator of MOCAGE allows a large number of measurements to be assimilated, spanning from columns of gases to aerosol optical depth . Next, we give some details of the implementation used in this study to assimilate vertical profiles and radiances.

After the horizontal and temporal interpolation of the model fields at the satellite ground-pixel position, modelled profiles are linearly interpolated to the retrieval's vertical grid. When the averaging kernels are used (i.e. for SOFRID assimilation), the linear estimation equation is used to remove the impact of the prior information from the innovation vector. The ensemble of these operations is stored as coefficients of a large sparse matrix and done through its multiplication by the model 3-D field. This approach is practical since numerous applications of the linearized and adjoint operator are needed during the minimization of the variational cost function. Differently from all previous studies involving IASI O3 assimilation , in which L2 profiles were first reduced to total or partial columns prior to assimilation, here we assimilate the full L2 profiles directly (43 levels). This avoids any loss of information and allows a fairer comparison between L2 and radiance assimilation. The error covariance matrix of the profile-type observations is diagonal in the latitude–longitude dimensions, but off-diagonal terms are allowed along the vertical dimension. Alternative approaches exist to optimally reduce the dimension of the L2 observation space based on the DOF of the retrievals , which are of interest to further reduce the numerical cost of SOFRID assimilation without loss of accuracy. However, this is left for future work.

To compute modelled radiances we employ the same horizontal and temporal interpolation as in the case of profile observations, except for the vertical interpolation. In fact, the RTTOV vertical interpolator is used for radiance computations instead of the MOCAGE one. All model levels (60) and corresponding pressure levels are given as input to RTTOV, which performs the vertical interpolation to the IASI coefficient levels internally. Since the model vertical resolution is lower than the one available in RTTOV for IASI coefficients (101 levels), we used the default option based on . Also, O3 profiles above the CTM top (0.1 hPa) are completed using RTTOV climatological profiles. Auxiliary inputs for the radiance computation include the pressure, temperature and water vapour profiles, which are interpolated from the corresponding MOCAGE fields.

The MOCAGE control vector has been extended to include the SST, as in the SOFRID retrieval scheme. This proved to be important since small errors in the SST translate in significant differences between modelled and measured radiances. Not accounting for this would produce incorrect O3 analyses. The SST does not belong to the MOCAGE prognostic fields, nor is it prescribed on the MOCAGE grid. Hence, the SST analysis is not propagated in time, and no spatial covariance model has been implemented so far. In this regard the treatment of the SST is equivalent to that done in L2 retrievals. In the context of MOCAGE 3D-Var, it can be interpreted as a variational bias correction term in the observation space , with prior values given by the NWP model (IFS; see Sect. ).

We performed numerical experiments for the month of July 2010, which corresponds to the typical presence of summer O3 maxima in the Northern Hemisphere linked to photochemical pollution. July 2010 is also interesting due to the development of a strong La Niña episode . The main difference between assimilating L2 and L1 data consists in using a climatological (L2 assimilation) versus a dynamical a priori profile (L1 assimilation) for the inversion of the radiative transfer problem. The chosen period presents large local deviations of the O3 field from climatological values. Therefore, it provides an interesting benchmark period with respect to the objective of this study.

The CTM was initialized on 1 June 2010 with a zonal climatology and run for a 1-month period (spin-up) to provide chemically balanced initial conditions on 1 July 2010 for all simulations.

The observation error covariance matrix (R) is prescribed according to the choices adopted in SOFRID V3.0. When the radiances are assimilated, a diagonal matrix (i.e. with no inter-channel correlation) is used, with a constant standard deviation of to 0.7 mW m-2 sr-1 cm for all channels. This is a simplified although common setting for most IASI O3 retrievals . The SST, which is controlled as well within radiance assimilation, has a prescribed standard deviation of 4 ∘C for all ground pixels. When L2 profiles are assimilated we used the full non-diagonal error covariance matrix provided by SOFRID or MLS retrievals.

We considered a dynamical rejection of observations based on the relative differences between simulated and measured values with respect to simulated values. It avoids assimilating observations with departures from the corresponding model background that are too large. The threshold values are set to 12 % for L1 radiances and 2000 % for L2 profiles, and trespassing the threshold for any particular channel or profile level rejects the entire spectrum or profile. The strong difference between the two thresholds is a consequence of the very different nature of assimilated observations: the exponential shape of O3 profiles can produce very large departures when the gradient is the steepest (tropopause), and a small rejection threshold would filter out most of the profile observations. This is not the case for radiances, which vary on a linear scale. Threshold values have been chosen based on misfit histograms in order to remove abnormal tails. As a consequence, L1 and L2 pixels that pass the selection and are further assimilated could differ. However, the relative number of rejected observations for the entire month of July is quite limited in both cases (3 % for L1, 6 % for L2), thus not affecting the results statistically.

The setup of the background error covariance (B) is a critical step both for L2 retrievals and data assimilation. We did benefit from past experiences using MOCAGE, IASI and MLS O3 to define a first guess of B, and we tried to further derive an optimal parameterization for this study. Note that the B matrix (3-D) used in data assimilation is by definition different with respect to the one specified within SOFRID (1-D), but the same 3-D B is used for all data assimilation experiments (L1 and L2).

Concerning the standard deviation, and employed vertically varying errors expressed as percentages of the background O3 profile, with larger relative errors in the troposphere and smaller in the stratosphere. Since we use a more detailed chemistry model here (Sect. ), we evaluated the root mean square error (RMSE) of the free model simulation (control) against ozonesondes and MLS profiles (Fig. ). We remark that the model's RMSE reproduces the vertical features observed in previous studies, with smaller errors in the stratosphere (between 20 and 50 hPa), larger errors in the free troposphere and highest errors close to the tropopause and within the planetary boundary layer. Note also the zonal variability of the maxima, which appear to be linked to the variability of the tropopause height. Thanks to the detailed chemical mechanism, biases (Fig. ) are generally smaller than in the studies cited previously but remain significant compared to standard deviation values (Fig. ), especially around the tropopause. Interestingly, RMSE and standard deviation values computed against MLS are generally smaller than those evaluated against ozonesondes, whereas biases are more consistent between the two datasets. We attribute this effect to the larger number of MLS observations (Table ), which provides more robust standard deviation statistics.

The background standard deviation is prescribed through a smooth step function that takes values of 2 % above 50 hPa and 10 % below to reproduce roughly the patterns observed in Fig. . Values are smaller than those in Fig.  to account for the error reduction during the assimilation, which is particularly strong when MLS observations are used (see Sect. ). Also, neglecting error correlations between IASI channels within R leads to a strong weight towards the observations: reducing the background standard deviation compensates in part for this effect. All the choices made to define B are a result of a large number of assimilation evaluations, in which different options were considered. For example, setting values of 5 % and 25 % leads to less accurate results for both L1 and L2 assimilation (not reported). The percent profile is multiplied by the hourly O3 field of the control simulation once for the entire period and not at every forecast time step. Therefore, all assimilation experiments presented in this study are based on the same B matrix. This choice was made to permit a stricter comparison between L1 and L2 assimilation experiments.

The vertical error correlation diffuses the assimilation increments between model levels and has been found to significantly impact the quality of O3 analyses with current model vertical resolutions (not shown). In general, small values of vertical correlation are favoured in the stratosphere due to the stratification and to avoid injection of large stratospheric O3 increments in the troposphere, whereas larger values are expected within the troposphere due to vertical mixing. In this study a constant value of one model level defines the length scale of the Gaussian correlation (Sect. ). Different choices for the stratosphere and troposphere did not lead to particular improvements (not shown).

Finally, the exponential scale of the horizontal error correlation is set to be equal to 200 km, with the zonal component that is reduced towards the poles to account for the increasing resolution of the model's grid .

The choice of the background and observation errors is relatively simplistic in this study. Further improvements of the B parameterization could be achieved by diagnosing the forecast errors hourly or using ensembles of model forecasts. However, more complex and costly estimations do not always improve the results of chemical assimilation systematically and significantly . Moreover, a good estimation of B cannot be done independently of that of R, which is kept fixed here on purpose. Additional research is needed in this regard, which is beyond the scope of this study.

The average O3 values of the control simulation are displayed in Fig. . O3 fields have been first interpolated vertically from the model grid to a selection of pressure levels, covering both the stratosphere and the troposphere, and averaged afterwards. The maps show well known properties of the O3 distribution such as the strong zonal gradients in the stratosphere and the presence of local minima in the tropical free troposphere due to deep convection. The average difference between the control simulation and the fixed a priori profile used in SOFRID retrievals (Sect. ) is displayed in Fig. . Large differences (>100 %) are found at low latitudes both in the lower stratosphere and in the troposphere, with largest values close to the tropical tropopause (150 hPa). This is expected since the SOFRID a priori profile is based on a global ozonesonde climatology that is more representative of mid-latitude O3 profiles (Sect. ).

We discuss the geographical differences between L1a and L2a analyses by looking at the monthly bias between the two experiments, divided by the average O3 of the control simulation (Fig. ). Relative differences are displayed in Fig. . First, we remark that differences are generally significant both in the stratosphere and in the troposphere, with absolute values that can exceed 50 % of the O3 field locally and global averages as high as to 20 %. Largest differences in the stratosphere are found at tropical latitudes, L1a showing larger O3 values than L2a at 20 hPa and lower at 70 hPa. In the troposphere the strongest positive differences are still found in the tropics, especially over central Africa, eastern Asia, South America and Middle East regions. Differences become smaller when moving down to 750 hPa and tend to disappear at lower altitudes (not shown), which is normal considering the vertical sensitivity of IASI. At mid-latitudes and high latitudes, relative differences are smaller than at the tropics. This behaviour is consistent with the fact that the SOFRID prior information is much less accurate for tropical latitudes than for mid-latitudes and high latitudes (Fig. ). Overall, these plots suggest that when the L2 a priori profile is strongly biased (>100 %), the equivalence between L1 and L2 assimilation in the thermal infrared is not verified for O3, even when the averaging kernels are employed.

To confirm that the observed differences are not a consequence of the slightly different NWP inputs used in L1 assimilation and L2 retrievals (Table ) we rerun the L1a simulation using exactly the same SST a priori values used in SOFRID retrievals. Since we cannot use the same water vapour and temperature profiles of SOFRID within L1a due to the different vertical grids, a different approach has been used: we repeated all assimilation experiments but using ERA Interim instead of the NWP forecasts as meteorological forcing for the CTM. This increases potential differences between the L1 and L2 assimilation, due to the different configurations of operational NWP and ERA Interim (model resolution, assimilated instruments, etc.). In all the above cases we obtained very similar results to those presented in Fig.  (not shown), which suggests that differences between L1a and L2a discussed previously do not depend on the auxiliary RTM inputs.

To further verify which one out of the L1a and L2a experiments reproduces the measured O3 profiles better, we validated the three simulations against radiosoundings. Figure  reports the RMSE differences computed globally and for five different latitude bands. The displayed values are the differences between the RMSE of the assimilation experiment and the corresponding value for the control simulation (Fig. ). Negative values in Fig.  indicate that the assimilation improved the O3 field and decreased the relative RMSE with respect to ozonesondes by the amount displayed on the plot. Looking at the global averages we remark that below 70 hPa the gain is similar for both L1a and L2a experiments and quite significant at 200 hPa (20 %). Note, however, the strong similarity between the global and 30–60∘ N statistics, due to the over-representation of ozonesondes for the Northern Hemisphere (NH) mid-latitudes (63 % of the total).

In the NH the RMSE of the control simulation is effectively reduced between 70 and 300 hPa (up to 20 %). L1a shows a slightly better gain than L2a between 150 and 300 hPa. Interestingly, both L1a and L2a display increased RMSE between 300 and 400 hPa. This behaviour is also confirmed when the vertical error correlation is switched off in the 3D-Var B and with different choices for the vertical interpolation of O3 optical coefficients within RTTOV (log-linear or Rochon, not shown). Since large negative biases were present in the control simulation (as low as -30 %; see Fig. ), a possible explanation is that part of the strong positive correction of O3 between 100 and 300 hPa is propagated downwards, where both absolute O3 concentrations and relative biases are much lower. This can degrade the analysis accuracy below 300 hPa. Whether this propagation is carried out by the Jacobian matrix of the observation operator (either through the RTM or the retrieval's AK) or by vertical O3 transport is not yet elucidated and would need further investigation. Also, other possible factors affecting the accuracy of the RTM exist, like inadequate vertical resolution close to the tropopause or uncertainties in meteorological profiles or in the impact of aerosols. Nonetheless, these errors impact both L1a and L2a in our study: further optimization of the L1 assimilation configuration with respect to the L2 retrievals is left for a future study. The RMSE is reduced again at about 500 hPa between 30 and 60∘ N, although not very significantly. The assimilation increases the RMSE of the tropospheric profile (350–1000 hPa) at northern latitudes (60–90∘ N). In general, the validation confirms that L1a and L2a have a very similar accuracy in NH at mid-latitudes and high latitudes, as also suggested previously by Fig. . However, the strongest positive corrections are confined to the UTLS.

At the tropics (30∘ S–30∘ N) the results differ more significantly. In the troposphere (below 100 hPa), both L1a and L2a reduced the RMSE of the control simulation, although by a smaller amount than in the NH (5 %). Note also that L1a RMSE reduction is larger than L2a between 400 and 600 hPa, whereas it is the other way around at about 250 and 800 hPa. Above 100 hPa we observe an increase of RMSE that peaks at 60 hPa with L2a and at 30 hPa with L1a but smaller in magnitude for L1a. This behaviour might be linked to the strong differences that exist between the SOFRID prior information and the modelled O3 at the tropical tropopause, to some other factor affecting the RT computations, to overestimation of the background error covariances or to a complex combination of all previous causes. A full satisfactory explanation has not been found yet.

Results in the Southern Hemisphere (SH) (30–90∘ S) are again similar: a lower RMSE than for the control simulation is found for both L1a and L2a in the upper and lower stratosphere (between 30 and 100 hPa and between 150 and 300 hPa). An improvement is also found in the troposphere (400–600 hPa) at mid-latitudes (30–60∘ S), but the low number of ozonesondes available in this band (Table ) requires a more careful interpretation.

Since radiosoundings do not provide a uniform global coverage, and vertical coverage is also lacking in the vicinity of the O3 maximum, we validated the three simulations against MLS measurements. The RMSE differences for stratospheric profiles can be found in Fig. . These statistics are based on more than 105 profiles for the global average and between 15 000 and 30 000 for zonal averages, depending on the latitude band (Table ). The patterns observed in the stratosphere with respect to ozonesondes are also confirmed with MLS. The only exceptions are a smaller RMSE degradation at 50 hPa for L2a in the tropics and for both L1a and L2a at 150 hPa in the 30–60∘ S band. Higher confidence should be given to the RMSE values provided by MLS than those obtained with radiosoundings (see also Fig.  and the relative discussion in Sect. ). However, a similar RMSE behaviour is observed overall, and this bolsters the robustness of the conclusions derived with the radiosoundings in the troposphere.

The computational cost of L1 assimilation is necessarily higher than for L2 assimilation. Additional CPU time is due not only to online RTM computations but also to a higher number of iterations needed by the minimizer to converge. For a typical 24 h long simulation performed on Intel Xeon E5-2680 V3 CPU, the total CPU time is 3.9 CPU hours for L2a and 13.2 CPU hours for L1a. Note that the L2a time does not include the cost of the L1 to L2 processor but only the cost of the 3D-Var assimilation plus the model forecasts. Most of the CPU time for L1a is spent on the linearized and adjoint calls of the RTM (50 % of the total CPU time), whereas the corresponding time spent for the observation operator within the L2a experiment is about 1 %. However, the total CPU time can be significantly decreased by reducing the maximum number of iterations of the minimizer. A simulation with a halved number of iterations (75) showed very similar results to the ones that have been reported (150 iterations) and could be considered if computation time is a critical factor. Moreover, with standard high-performance computers, and thanks to the parallel nature of the observation operator and the RTM, we could obtain a speed-up of about 24 on the 24 CPU cores. This reduces the runtime of L1a to about 36 min for the 24 h long simulation versus 13 min for L2a. The extra cost of L1 assimilation therefore also seems acceptable for operational applications.

Some issues were identified in the previous section in the stratosphere, especially at tropical latitudes. Among possible reasons, one is that inversion of TIR measurements might be particularly sensitive to the vertical distribution of O3 in the tropical stratosphere. We consider assimilating MLS L2 profiles in combination with IASI here to correct the model stratosphere and troposphere simultaneously, as also done in previous studies . When the radiances are assimilated, the RT problem is solved for the entire atmospheric column within the iterations of the variational algorithm. Therefore, enhanced and better synergies could be observed than when only L2 products are assimilated.

We report in Fig.  the impact of assimilating MLS in combination with IASI L1 and L2 by computing the average differences between MLS + L1a and MLS + L2a. We remark that the differences in the stratosphere are highly reduced with respect to Fig. , which is expected due to the direct constraint of MLS observations. Significant differences (>10 %) remain below 150 hPa, with patterns and sign similar to those in Fig. . The amplitude of the differences is, however, also slightly reduced at 300 and 500 hPa.

We compared the RMSE of MLSa, MLS + L1a and MLS + L2a computed against ozonesondes (Fig. ) to evaluate if the joint assimilation improves the overall O3 distribution. MLSa provides particularly accurate results down to 200 or 300 hPa, depending on the latitude, with a robust reduction of the RMSE with respect to the control simulation. The only exception is in the SH mid-latitudes below 250 hPa, where the MLSa RMSE increases. We suspect that this might be linked again to the combination of strong O3 gradients at the tropopause height and the negative bias of the control simulation above the tropopause (see Sect. ). Overall MLSa confirms results found in past studies and represents much better prior information for assimilation of radiances or retrievals.

We remark that MLS + L1a and MLS + L2a now provide closer results in the NH and in the tropics compared to Fig. . The stratospheric O3 gain is much more significant with MLS + L1a and MLS + L2a than with L1a and L2a and remains very close to MLSa, demonstrating that assimilating accurate stratospheric profiles remains essential for O3 reanalyses. The only region where IASI further improves the UTLS profile with respect to MLSa is in the NH: a positive, albeit small, effect of assimilating IASI in combination with MLS is found between 150 and 300 hPa. On the other hand, below 300 hPa, the addition of MLS (Fig. ) does not bring further improvements with respect to IASI alone (Fig. ). We can conclude that MLS corrects most of the errors introduced by IASI assimilation in the stratosphere (Fig. ), but no particular synergy is observed in the case of MLS and L1 assimilation in the troposphere.

In Fig.  we report the Taylor plots concerning the free troposphere O3 column (340–750 hPa), to further evaluate the skills of the assimilation experiments in terms of variability. We examine the free troposphere here since it is where the direct impact of IASI assimilation is the largest and the impact of MLS the smallest (except for the 30–60∘ S band). IASI assimilation improves the variability of the modelled O3 field when looking at global averages, but this conclusion varies as a function of the latitude band. Robust and significant improvements are only found at the tropics and in the SH polar region; mixed results are obtained elsewhere. This confirms previous findings obtained with L2 assimilation and adds the conclusion that better prior information does not necessarily solve all issues related to the assimilation of TIR measurements at mid-latitudes and high latitudes. Nevertheless, the assimilation of radiances provides slightly better results at all latitudes in general and permits more variability to be extracted from IASI spectra, especially at tropical latitudes.