In atmospheric chemistry retrievals and data assimilation systems, observation errors associated with satellite radiances are chosen empirically and generally treated as uncorrelated. In this work, we estimate inter-channel error covariances for the Infrared Atmospheric Sounding Interferometer (IASI) and evaluate their impact on ozone assimilation with the chemistry transport model MOCAGE (Modèle de Chimie Atmosphérique à Grande Echelle). The method used to calculate observation errors is a diagnostic based on the observation and analysis residual statistics already adopted in many numerical weather prediction centres. We used a subset of 280 channels covering the spectral range between 980 and 1100 cm

The results show significant differences between using the estimated error covariance matrix with respect to the empirical diagonal matrix employed in previous studies. The validation of the analyses against independent data reports a significant improvement, especially in the tropical stratosphere. The computational cost has also been reduced when the estimated covariance matrix is employed in the assimilation system, by reducing the number of iterations needed for the minimizer to converge.

Ozone is an important trace gas that plays a key role in the Earth’s radiative budget

Remote soundings from satellites are an essential component of an observational network

Data assimilation has been introduced relatively recently in atmospheric chemistry, in the stratosphere

The weight given to the observation in the assimilation process is determined by its error covariance matrix

The estimation of

In the present work, we estimate observation errors and their inter-channel correlations for IASI using the Desroziers method. We evaluate, then, their impact on ozone assimilation in a CTM (MOCAGE). The paper is organized as follows. The CTM, the radiative transfer model, the assimilation algorithm, the data, and the experimental framework are described in Sect. 2. The estimation of

MOCAGE (Modèle de Chimie Atmosphérique à Grande Echelle) is the CTM used in this study. It is a three-dimensional CTM providing the space and time evolution of the chemical composition of the troposphere and the stratosphere. Developed by Centre National de Recherches Météorologiques (CNRM) at Météo France

A global configuration with a horizontal resolution of 2

Remote sensing instruments measure, within a certain wavelength range, the intensity of electromagnetic radiation passing through the atmosphere (radiances). Radiative transfer models are used to simulate the radiation measured by the satellite as a function of atmospheric state, to be able to compare the model state to the observed radiances.

In our study, IASI radiances are simulated using the radiative transfer model RTTOV (Radiative Transfer for TOVS), which was initially developed for TOVS instruments

The variational data assimilation system of MOCAGE was developed jointly by CERFACS and Météo France in the framework of the European project ASSET (Assimilation for Envisat data)

The background-error covariance matrix is divided into two distinct parts, the diagonal matrix of the standard deviations and the correlation matrix. The latter, allowing the spatial smoothing of the assimilation increments, is modelled through a diffusion operator

The 3D-Var implementation has been used with hourly assimilation windows. The variational cost function is minimized using the BFGS (Broyden–Fletcher–Goldfarb–Shanno) algorithm

As we mentioned before, the aim of this work is to evaluate the impact of the estimated observation-error covariances on the ozone analysis. Hence, in order to be able to compare our results to those that have already been discussed and validated, we kept exactly the same configurations as those used in

IASI is one of the instruments operating on board the polar-orbiting satellite Metop-A, B, and C launched by the European organization for the Exploitation of Meteorological Satellites (EUMETSAT). It is based on a Fourier transform spectrometer (FTS) and measures the spectrum emitted by the Earth atmosphere system in the spectral range between 645 and 2760 cm

For this study, a subset of 280 channels covering the spectral range between 980 and 1100 cm

The Microwave Limb Sounder (MLS) provides vertical profiles of several chemical components, by measuring the microwave thermal emission from the limb of Earth's atmosphere

In our study, we use the ozone profiles retrieved from MLS (V4.2 Products) as independent data to validate our results. The data have been downloaded from the Goddard Earth Sciences Data and Information Services Center (GES DISC) web portal (

The Ozone Monitoring Instrument (OMI) is a nadir-viewing, ultraviolet–visible (UV-VIS) spectrometer

Ozonesondes are in situ instruments carried by a radiosonde continuously transmitting the measurements as it ascends. The profiles of O

The main purpose of this study is to estimate the IASI observation-error covariances and verify their impact on the quality of the ozone assimilation results. The setup of the experiment in terms of the period of the study, the model configuration, the choice of assimilated observations, and the background-error covariance matrix is reported in Table 1. The observation-error covariance matrix will be discussed in the results section (Sect. 3).

The model was initialized with a zonal climatology, and the spin-up time used is 1 month (June 2010). Then, our simulations were performed for the month of July 2010.
The ozone forecast-error standard deviation was assumed to be proportional to the ozone concentration. In fact,

The ozone background-error covariance matrix is split into a diagonal matrix filled with the standard deviation and a correlation matrix modelled using a diffusion operator. The correlation, characterized by the length scale, spreads the assimilation increments in space. The configurations of horizontal and vertical length scales are described in Table 1.

The same preprocessing described in

Summary of the configuration of the MOCAGE assimilation system.

The observations used in the assimilation system could have a margin of error. We can identify two types of errors, systematic and random errors. The systematic error is ordinarily corrected before the data assimilation process. In NWP, these types of errors in satellite observations are in general corrected before assimilating the observations or within the data assimilation process by the VarBC scheme

In atmospheric chemistry, we used to assimilate level 2 products of ozone

Random errors can arise from the measurements (e.g. instrumental error), forward model, representativeness error (e.g. difference between point measurements and model representation), or quality control error (e.g. error due to the cloud detection scheme missing some clouds within clear-sky-only assimilation). These types of errors should be accounted for by the observation-error covariance matrix

In this paper, we estimate the total error using the statistical approach introduced by

This method has been used to estimate observation errors and inter-channel error correlations

The Desroziers method was computed on the output of a 3D-Var experiment using a diagonal matrix

Using outputs (analyses and forecasts) derived from a 3D-Var experiment that used a diagonal

Figure 1 presents the standard deviation diagnosed using the Desroziers approach (solid black line) and that used in

Standard deviation estimated using the Desroziers method (solid black line) and that used in the previous studies (blue dotted line)

The IASI instrumental error is provided by the CNES (Centre National d'Etudes Spatiales), taking into account different known effects such as flight homogeneity and apodization effect (Le Barbier Laura, personal communication). The instrumental error covariance matrix is computed as described in

To investigate the off-diagonal part of

Correlation matrix estimated using the Desroziers method.

The high correlation found here was expected since previous studies have highlighted the same behaviour in this spectral region

The diagnostic discussed above is based on a global estimation, without any distinction between the type of the surface (land or sea) or the time of the observation (day or night). Since the emissivity varies according to the type of the surface, and the skin temperature is strongly driven by the sun radiation, we evaluated

The separate treatment of land–sea covariance matrices did not yield significant differences in terms of assimilation results compared with the use of global estimation. Hence, we have adopted the global estimation in our study. The rationale for this choice will be given during the discussion of the validation results (Sect. 5.2).

In this section, we discuss the impact of the observation-error covariances estimated previously on the ozone analysis. To this end, three experiments for the month of July 2010 were carried out:

(i.) model run without data assimilation hereafter called the free run (or Control), and denoted in the rest of this paper as ControlExp;

(ii.) 3D-Var assimilation of IASI radiances using a diagonal observation-error covariance
matrix (as in

(iii.) 3D-Var assimilation of IASI radiances using a full matrix estimated with the Desroziers diagnostic denoted hereafter as RfullExp.

Figure 3 shows the difference between the zonal average of the ozone analysis from the two assimilation experiments in units of parts per billion volume (ppbv). The zonal values were averaged over the month of the study before performing the difference. The impact of the estimated

The difference between the zonal average of the analysis (ppbv) from the two assimilation experiments, averaged over the month of the study (nonlinear colour map).

The assimilated spectra include channels sensitive to both ozone and surface skin temperature. The IFS skin temperature was taken as a background in the assimilation process. We have computed the difference between the SST analysis and the background at the end of each assimilation experiment (RdiagExp and RfullExp). The skin temperature is physically linked to the ozone measured. In fact, the skin temperature interacts with the ambient atmosphere. An increase in SST can for example create a convective movement impacting the transport of the ozone. However, the skin temperature is given only at the observation location in this study, and it is specified with values interpolated from NWP forecasts (IFS), whereas ozone is a 3D field issued from the chemistry transport model. Hence, the estimation and potential account of error correlations between the two variables seem challenging in our system. In this work, we did not consider the background-error correlation that might exist between O

Figure 4a shows the difference between the analysis of the SST given by RdiagExp and the IFS SST forecast, whereas Fig. 4b shows the difference between the analysis of the SST given by RfullExp and the IFS SST forecast. In terms of geographical distribution, we notice that the differences are smaller through the tropics and mid-latitudes, especially over sea, when the estimated

Difference (

In our assimilation setup, the cost function is minimized hourly. For each window, the minimizer needs to converge after a certain number of iterations. The cost of each iteration is dominated by the cost of the radiative transfer operators (tangent linear, the adjoint model) and of the background-error covariance operators. When the observation error was assumed to be uncorrelated (RdiagExp), the number of iterations needed for each hourly cycle is significantly higher than when the estimated observation-error covariance matrix is used. In fact, the introduction of the estimated

In an attempt to distinguish the impact of the variance on the convergence speed from that of the correlations, we have performed three assimilation experiments using different

Figure 5 shows the difference of the ozone total column (in Dobson units (DU)) provided by OMI and that of RdiagExp (a) and that of RfullExp (b). At first sight, we note smaller differences over the tropics between the OMI total column and the total column given by RfullExp in comparison with that given by RdiagExp. This behaviour was expected since a large reduction of the amount of ozone was observed in these regions (see Fig. 3). In the high northern latitudes, the differences were slightly increased when the estimated matrix was adopted. This is a consequence of the increase in the amount of ozone encountered in these regions in the stratosphere, compared to the amount reduced in the same region in the troposphere (Fig. 3). On the other hand, the global mean and the standard deviation of these differences are lower in the case of using the new estimated matrix (10.1 DU as a mean and 6.3 as a standard deviation when the new estimated matrix was used instead of 10.6 DU as a mean and 7.3 as a standard deviation when a diagonal matrix was used). Hence, we conclude that the estimated matrix

In this section, we validate the two simulations against radiosoundings and MLS data. We use the root-mean-square error (RMSE) as the main statistical indicator to quantify the accuracy of the experiments.

Normalized difference of the RMSE with respect to the ozonesondes for the

We compute the relative (to the control simulation) difference of RMSE with respect to radiosoundings and MLS averages globally and for five different latitude bands. The difference is computed by subtracting the RMSE of each experiment from that of the control simulation. Negative values indicate an improvement of the O

Figure 6 reports the RMSE differences with respect to the radiosoundings. Considering the global RMSE (ALL), we notice that the experiment with the estimated matrix improves the results above 150 hPa, around 400 hPa, and near the surface. However, it also reduces the improvement from 30 % (the case of using a diagonal matrix) to 15 % in the vicinity of the upper troposphere–lower stratosphere (UTLS, 100–300 hPa).

The issue of increasing the ozone analysis errors compared to the control simulation encountered in

The MLS validation in Fig. 7 shows almost the same behaviour reported by radiosounding validation in the tropical stratosphere, where the reduction of error is remarkable. In the other latitude bands, MLS reports a similar behaviour of the two experiments, with some small differences in the Northern Hemisphere.

Normalized difference of the RMSE with respect to the MLS for the

To evaluate the significance of the differences between the analyses of the two experiments with respect to MLS and ozonesounding measurements, we have performed the

All things considered, the introduction of the estimated

The matrix used for this study (see Sect. 3.2) will now be discussed in this section since the decision was also based on the outcome of the assimilation experiments presented in this section. We sequentially performed three assimilation experiments using the first, second, and third estimations of

We have also discussed the type (sea or land) and the time (day or night) of the observations while estimating the matrices. To check the impact of these differences on the assimilation results, we ran an additional assimilation experiment using the matrix estimated considering the type of the surface of each observation (since the differences were more important than if the time of the observation was considered). Only slight differences among the results have been noticed (not shown). This behaviour might be explained by the number of observations over the sea and over the land. In fact, the observations over the sea represent more than 70 % of the total observations. The differences, in terms of standard deviation, of the global estimation and that using pixels over the sea is very small in comparison with that using pixels over the land (not shown). The differences are also small in terms of correlations in the case of the sea surface in comparison with the land surface (not shown). Hence, we consider that the predominance of observations over sea averages out the potential differences caused by a separate land–sea specification of

The correct specification of the observation error becomes a critical issue to efficiently assimilate the increasing amount of satellite data available in recent years. We have estimated the observation errors and their inter-channel correlations for clear-sky radiances from IASI ozone-sensitive channels. We have evaluated, then, the impact of the estimated

The Desroziers diagnostics were adopted here to estimate

Significant differences between the results of the experiments were encountered. The introduction of the estimated

The validation against MLS and ozonesondes showed that the introduction of the estimated

In summary, accounting for an estimated

In this study, the estimation was computed without taking into account any distinction of the error sources and assuming that the observation error was unbiased. More efforts will be needed to tackle these points. It should also be noted that we kept the same experiment setup of

The code used to generate the analysis (MOCAGE and its variational assimilation suite) is a research-operational code property of Météo France and CERFACS and is not publicly available. The readers interested in obtaining parts of the code for research purposes can contact the authors of this study directly.

The input data used in this study are freely accessible through the web pages reported in the paper. All results are available upon request to the author.

MEA developed the code to compute the IASI error covariance matrix, carried out the experiments, analysed the results, and wrote the manuscript. EE provided the data needed to run the experiments and revised the paper. VG revised the paper.

The authors declare that they have no conflict of interest.

We acknowledge EUMETSAT for providing IASI L1C data, WOUDC for providing ozonesonde data, and the NASA Jet Propulsion Laboratory for the availability of Aura MLS Level 2 O

This research has been supported by the Région Occitanie and CNES (Centre National d’Etudes Spatiales), through the IASI program.

This paper was edited by Alyn Lambert and reviewed by two anonymous referees.