In order to achieve optimal channel selection, we used an experimental configuration of the ARPEGE NWP system. This experiment provides access, in addition to other meteorological fields, to variable ozone fields at the horizontal and vertical resolution of the global ARPEGE model. Ozone is not yet a prognostic variable of the model, so the ozone background comes from the chemistry transport model (CTM) MOdèle de Chimie Atmosphérique à Grande Échelle (MOCAGE). The MOCAGE ozone background fields are provided at the beginning of each 6 h assimilation window, unlike the other meteorological variables for which the backgrounds are provided by ARPEGE 3 h forecast run. The fields from MOCAGE were interpolated onto the geometry of the ARPEGE model both horizontally on a varying mesh (from about 7.5 km over France to 36 km at the antipodes) and vertically on 105 hybrid vertical levels from the surface (10 m) to 0.1 hPa.

Then, from this setup, we selected 6123 IASI pixels at near-nadir views (Metop-A and -B), in clear sky conditions (daytime and night-time) on land, sea and sea ice, over the entire globe on 14 and 15 August and November 2016. The IASI instrument also includes an integrated imaging subsystem (IIS) that allows users to co-register interferometric measurements with the high-resolution imager AVHRR (Advanced Very High Resolution Radiometer) . AVHRR provides cloud and heterogeneity information in each IASI pixel. Therefore, to ensure that our pixels are clear, we have eliminated all pixels with an AVHRR cloud cover value greater than 0 %.

Atmospheric background profiles (temperature, humidity and ozone) and surface parameters were extracted at the same coordinates and times as the IASI pixels (also 6123 atmospheric profiles). Noteworthy in this study is that a realistic temperature for all surfaces considered was used. Thus, the skin temperature was retrieved for each atmospheric profile (and pixels) from the inversion of the radiative transfer equation using the IASI window channel 1194 (943.25 cm-1) from the radiative transfer model (RTM) RTTOV version 12 . This retrieval relies on the specification of emissivity values over land from the Combined ASTER MODIS Emissivity over Land (CAMEL) and from a surface emissivity model (IREMIS) over the open sea and sea ice. The IASI 1194 channel will therefore be fixed in the remainder of the study and will not be used for channel selection or assimilated in the evaluation.

In summary, the 6123 profiles are used in the following study for the estimation of the observation-error covariance matrix and at the end to evaluate the channel selections in the 1D-Var data assimilation system. Channel selection was performed from a subset of 60 profiles (and pixels) empirically selected from the 6123 profiles. These 60 profiles were chosen to have a variability close to the set of 6123 profiles. The location of these profiles is shown in Fig. .

To ensure sufficient variability in our set of 60 profiles, we have calculated, and illustrated in Fig. , the mean (black solid line) plus and minus standard deviation (shaded area) and the minimum and maximum values (black dashed line) of the temperature (a), humidity (b) and ozone (c) profiles. There is significant variability that is similar to that obtained with the profiles in the database available in the RTTOV RTM .

The selection of IASI channels made in this study is intended to benefit NWP. Thus, we aim to extract from this selection a maximum amount of information in temperature, humidity, ozone and surface temperature. In order to evaluate the ability of the IASI channels to provide information on these parameters, we have chosen the selection method from the degrees of freedom for signal (DFS), which is used to select a set of optimal channels having the largest information content for each atmospheric profile as described by . The DFS is based on information theory and provides a measure of the gain in information gathered by the observations according to the following formula: 1DFS=Tr(I-AB-1), where Tr denotes the trace, I the identity matrix, B∈Rnxn (n parameters to be retrieved) is the background-error covariance matrix and A∈Rnxn is the analysis-error covariance matrix which is calculated as follow: 2A=(B-1+HTR-1H)-1=(I+BHTR-1H)-1B, where R∈Rmxm (m channels considered) is the observation-error covariance matrix and H∈Rmxn (the derivatives of each channel with respect to each parameter) represents the Jacobian matrix for all IASI channels.

In contrast to the channel selection made by , we have chosen not to separate the selection by variables. Thus, in this study, all the channels considered have the ability to provide information on temperature, humidity, ozone and surface temperature at each step of the selection process. Indeed, unlike the selection method chosen by Collard, the use of an R matrix accounting for inter-channel error correlations allows us to consider all the channels sensitive to several variables (temperature from the CO2 band and water vapour, ozone and skin temperature in the atmospheric window). Note that the IASI spectrum is also sensitive to the main absorbing gases (CH4, CO and N2O) and weaker absorbers (CCl4, CFC-11, CFC-12, CFC-14, HNO3, NO2, OCS, NO and SO2). The total DFS taking into account all the information content for these parameters is used as a figure of merit such as 3DFSTOT=DFST+DFSq+DFSO3+DFSTskin. Then, only the first 5499 IASI channels (whose specifications are listed in Table ) included in band 1 (645 to 1210 cm-1) and 2 (1210 to 2019.75 cm-1) were retained for selection (5500 minus channel 1194 used to retrieve skin temperature). Thus, the channels in band 3 (2020 to 2760 cm-1), influenced by the non-LTE (local thermodynamic equilibrium) effects and the solar irradiance, were not considered. Inter-channel error correlations are considered in this study using a diagnosed observation-error covariance matrix from the 5499 channels of IASI. Finally, in order to ensure the robustness of the channel selection, we considered different scenarios simultaneously by performing the selection on a sample of 60 previously chosen atmospheric profiles.

For each atmospheric profile, the selection begins by selecting the most informative of the 5499 channels using the total DFS with a matrix R of dimension 1×1. Then the first selected channel is fixed and the combination of the two most informative channels is searched for among the (5499-1) channels with a matrix R of dimension 2×2. This operation is repeated iteratively until the required number of channels, or the target value of the total DFS, is reached. Here, the channel selection process is stopped when the improvement resulting from the addition of new channels is relatively small. This choice is subjective.

In order to calculate the Jacobians and to simulate IASI radiances, we used the RTM RTTOV version 12. RTTOV is developed and maintained by the Satellite Application Facility on Numerical Weather Prediction (NWP SAF) of EUMETSAT. In the RTTOV algorithm, the input atmospheric profiles (temperature, humidity and ozone) are variable and provided by the users, the other constituents, such as CO2, CH4, CO, N2O, etc., can also be provided, but in this case, as in operational NWP, they are assumed to be constant profiles in time and space (depending on the version of the coefficients).

The NWP SAF one-dimensional variational (1D-Var) data assimilation algorithm is based on the optimal estimation method (OEM) . The unidimensionality makes this algorithm fast, flexible and suitable for research purposes close to NWP operational frameworks. Similar to other variational data assimilation algorithms (e.g. 3D-VAR and 4D-Var), the objective of the 1D-Var is to minimize both the observational and background deviation by minimizing a cost function J. Assuming that the background error is not correlated to the observation error and the errors have a Gaussian distribution, we retrieve state x by minimizing the cost function such as 6J(x)=12(x-xb)TB-1(x-xb)+12(y-H(x))TR-1(y-H(x)), where xb is the background profiles, y is the IASI observations, H(x) represents the BTs which are simulated by RTTOV, and B and R are the background- and observation-error covariance matrices, respectively. The retrieved state is called analysis and denoted xa.

In this paper, the 1D-Var algorithm was also used to compute the observation-error covariance matrix from the diagnostic and to evaluate the different channel selections. We modified the code to jointly retrieve temperature, humidity, ozone and surface parameters. The profiles are available on 54 pressure levels from 1050 to 0.005 hPa.

In the same way as the observation-error covariance matrix, it is necessary to estimate accurately the background-error covariance matrix B. Since the ozone background errors are not yet available in the ARPEGE NWP model and the temperature and humidity fields forcing the MOCAGE CTM come from ARPEGE, we have chosen to estimate the background errors of temperature, humidity and ozone together using a statistical method with the MOCAGE model.

The National Meteorological Center (NMC) method by is a technique that defines background errors from the difference between NWP forecasts of various ranges valid at the same time. This method is here applied to ozone forecasts. We consider differences from between 36 and 12 h forecast ranges. The background error covariance matrix B is then constructed using long-term modelling results. Two twin simulations were performed. For each one, the configuration uses 60 hybrid levels, from the ground up to 0.1 hPa, and a global domain with a 1∘ horizontal resolution, and the ARPEGE meteorological fields are provided to MOCAGE every 3 h. The model was run from September 2016 to April 2018, with the first 6 months considered spin-up. The various forecasts used in our application of the NMC method are illustrated in Fig. :

The first simulation uses the operational setup (named here MOC+12H); i.e. every day an ozone forecast up to 24 h is produced by MOCAGE. The initial ozone state of this forecast is the 24 h forecast of the previous day. The meteorological fields used for the forcing of this ozone forecast come from the ARPEGE forecast beginning at the same moment (ARPEGE analysis for 00:00 UTC, then ARPEGE forecasts every 3 h). A 1.5-year simulation has been produced with this cycling mode.

Finally, the B matrix with temperature, humidity and ozone background errors is computed statistically from MOC+12H and MOC+36H forecast differences, valid at the same time, over a 1-year period (March 2017 to March 2018). It should be noted that the ozone background errors estimated here are the result of differences in meteorological forcing from ARPEGE and not chemical differences. Nevertheless, this is a reasonable approximation since the photochemical lifetime of ozone in the upper troposphere and lower stratosphere (UTLS) region is relatively long . In order to be used in the 1D-Var algorithm, the MOCAGE fields were interpolated on 54 levels from 1050 to 0.005 hPa before calculating the B matrix. As the MOCAGE fields are provided up to 0.1 hPa, the interpolated fields have four levels above 0.1 hPa with similar values. Thus, we have chosen not to use the levels above 0.1 hPa for temperature and ozone background errors. In the same manner, the interpolated fields go up to 1050 hPa, which is in fact rarely reached. We have therefore chosen not to use the first two levels. Finally, as for the B matrix provided by the 1D-Var, we have chosen not to use the levels located in the stratosphere for the humidity background errors.

In conclusion, the 1D-Var experiments and the channel selections will use the temperature (K) and ozone (ppmv) background errors in over 48 levels from 1013 to 0.1 hPa and the humidity background errors (log(kg kg-1)) in over 27 levels from 1013 to 100 hPa. The B matrix was calculated in a multivariate approach, but here we chose to use a univariate B matrix, which means that cross-correlation between temperature, humidity and ozone variables are not taken into account. This assumption prevents feedback effects of ozone on temperature and humidity .

We show in Fig.  the temperature (Fig. a), humidity (Fig. b) and ozone (Fig. c) background-error standard deviations with respect to pressure, and the temperature (Fig. d), humidity (Fig. e) and ozone (Fig. f) background-error vertical correlations with respect to model levels are also shown. We notice that the correlations for the three variables have higher values in the troposphere between 1013 and 100 hPa (model levels 54 and 25, respectively). Correlations are weaker in the stratosphere and increase in the upper stratosphere, probably due to interpolation as mentioned above. These results for temperature and humidity are consistent with the study carried out by and . Finally, ozone background errors have values up to 0.11 ppmv. This maximum is consistent with values obtained in other studies, e.g. the work by and , which were carried out using ozone background-error standard deviations with maximum values up to 0.10 ppmv. In addition, the study for the assimilation of ozone satellite data product (Level 2) into the Composition Integrated Forecasting System (C-IFS) model as part of the Copernicus Atmospheric Monitoring Service (CAMS) programme, used ozone background-error standard deviations with maximum values between 1.4 and 1.6 kg kg-1 or about 0.08 and 0.10 ppmv, respectively. The background errors of skin temperature, surface temperature and surface humidity used in this study are derived from the values available in the reference B matrix of the 1D-Var. The background-error standard deviation value for skin temperature is 2.0 K.

A correct estimation of observation errors is essential in the data assimilation process. Until a few years ago, only the variances of these errors were taken into account (diagonal R matrix). Then innovative techniques to determine these errors and their correlations more accurately by deriving estimates of the real observation error from the departure statistics from assimilation systems emerged to be used for operational NWP (e.g. ; ). Several research works have successfully applied these methods to infrared hyperspectral instruments in order to estimate their total observation errors (instrumental noise, spatial representativeness error, error in the calculation of radiative transfer, etc.). For IASI, many NWP centres are starting to use R matrices that take into account cross-channel error correlations with significant benefits in terms of forecast impact. This is the case at the Met Office (; ), the Environment and Climate Change Canada , Météo-France (Vincent Guidard, personal communication, 2019) and the European Centre for Medium-Range Weather Forecasts (ECMWF) .

However, these observation errors have been estimated for already selected IASI channels. Considering the significance that inter-channel error correlations can have in the data assimilation process, they should also have a particular influence on the selection of the most informative channels. Some works have consequently carried out new selections of IASI channels using R matrices that take into account inter-channel observation-error correlations (e.g. ; ). They constructed their total R matrix using a “bottom-up” approach by estimating separate sources of forward model uncertainty, as opposed to the top-down approach we have chosen to use in this study.

To determine the total R matrix of the 5499 IASI channels for channel selection, we used the following method:

First, we constructed a diagonal R matrix with observation-error variances (σo)2 derived from the standard deviations of the innovations previously computed from the simulated observations in RTTOV.

Figure  shows the observation-error standard deviation from FG departures standard deviation with a red line, diagnosed observation errors with a blue line and instrumental noise of IASI at 280 K with a grey with respect to 5499 IASI channel number (a) and the diagnostic IASI observation error correlation for the same channels (b). The diagnosed observation-error standard deviations are above instrumental noise but below the standard deviations of FG departure. Furthermore, our diagnosed standard deviations of observational error are consistent with those obtained by for a subset of channels, except for the ozone-sensitive channels where the ozone background differed from ours. The higher values observed in the ozone and water vapour band for observation-error standard deviations are probably due to errors in the radiative transfer modelling because of larger biases for these variables. Indeed, the ozone profiles from MOCAGE used as an input variable to RTTOV are more realistic than the single profile, but they have biases that can affect the quality of the simulations. Similarly, the humidity profiles from ARPEGE are more realistic in the troposphere than in the stratosphere, which can lead to poor simulations of sensitive water vapour channels in the stratosphere. Hence, this results in these high and low standard deviations in the water vapour band. The values of the observation-error correlations are also consistent with values obtained in other similar studies (; ; ; ).

Once the matrices R, B and H were determined, we carried out the selection of the most informative channels by solving Eqs. () with () as the figure of merit. As described in Sect. 2.2, for each of the 60 profiles, we looked for the channel with the highest DFS value, then the channel pair with the highest DFS value, and so on. The selection threshold is achieved when the difference in total DFS between the last selected channel and the previous one is less than 0.005, which corresponds to the 397th selected channel on average over the 60 profiles. We decided to stop our selection at 400 channels for each of the 60 profiles. In Fig. , we plotted the evolution of the DFS mean plus and minus standard deviations in temperature (a), humidity (b), ozone (c), skin temperature (d) and total (e) during the IASI channel selection on the subset of 60 atmospheric profiles. A large part of the possible maximum total DFS is reached quickly since 90 % of the maximum total DFS over the 400 channels is achieved with only 172 channels. The maximum skin temperature DFS is obtained very quickly as only three channels are sufficient to provide more than 90 % of the maximum skin temperature DFS over the 400 selected channels. The humidity DFS also increases very quickly. Finally the total DFS with 400 selected channels consists of 50.3 % temperature DFS (7.6), 33.1 % humidity DFS (5.0), 10.1 % ozone DFS (1.5) and 6.5 % skin temperature DFS (1.0).

In order to characterize the channel selection process, a histogram of the percentage of the selected number of channels (up to 400 channels) on the subset of the 60 atmospheric profiles is shown in Fig. . These percentages are separated by the main spectral bands to temperature sounding (in red), atmospheric window (in green), ozone (in purple), humidity sounding (in blue) and total (in black). This means that if a channel is selected for all profiles, it achieves 100 % selection. Conversely, a channel never selected among the 60 profiles reaches 0 % selection. In this selection, out of the 5499 available channels only 44 channels are always selected (41 for the temperature sounding and 3 for the humidity sounding) and 3720 channels are never selected, mainly humidity-sounding channels (2417) and channels of the atmospheric window (1060). The channels which are selected more often (>80 %) are mainly temperature-sounding channels. Then humidity-sounding channels are more diversely selected until the end of the process. From these results we can sort the channels selected at least once (1779) according to their selection frequency. Thus the n most frequently selected channels will form a new selection of n channels.

The objective here is to demonstrate that the use of an R matrix accounting for the inter-channel observation errors during the channel selection process allows for more effective identification of the most informative channels compared to a selection using a diagonal R matrix. Therefore, we compared our selection to the channel selection made by by applying the inter-channel observation errors to it. In this study, we chose not to use the IASI channels in band 3; Collard's selection counts 24 of them. Channel 1194 is excluded for the selection, as it is used for skin temperature retrieval. Which leaves us with 275 channels from the Collard's selection, hereafter named CS275. We have taken the first 275 channels in our new selection, hereafter named NS275.

The first difference between the two selections is that there are less than 30 % of channels in common. Only 60 channels are common in the temperature-sounding spectral group, one in the atmospheric window, 4 in the ozone band and 13 in the humidity-sounding spectral group. This represents a total of 28 % of common channels between CS275 and NS275. It can also be noticed in Table  that our selection has more channels in the temperature-sounding and ozone spectral groups and less in the atmospheric window and humidity-sounding spectral groups.

The two selections can also be compared in terms of location on the IASI spectrum. In Fig. , we have located the selected channels on a typical IASI spectrum in brightness temperature. The red, green, purple and blue circles represent the channels of the temperature-sounding, atmospheric window, ozone and humidity-sounding spectral groups, respectively. Note that NS275 mainly selects channels at the beginning of the spectral bands. Indeed, the channels selected in the atmospheric window are mainly located at the beginning of the first window band. The same is observed with the channels selected for the humidity sounding. More ozone channels are selected and distributed over the entire ozone-sensitive spectral band.

Finally, we compared the Jacobians in the channels of the two selections. We have represented in Fig.  mean Jacobians of CS275 for temperature (a), water vapour (b), ozone (c) and mean Jacobians of NS275 for temperature (d), water vapour (e) and ozone (f). The red, green, purple and blue lines represent the channels to temperature sounding, window, ozone and humidity sounding, respectively. The visualization of the Jacobians of the newly selected channels confirms this assumption of channel homogeneity. Indeed, we observe that the temperature Jacobians (d) for the temperature-sounding channels (in red) are relatively evenly distributed especially in the stratosphere for the NS275. We also notice that the temperature Jacobians of the channels selected in the atmospheric window (in green) are higher in the lower troposphere than in CS275. The water vapour Jacobians (e) also show a more homogeneous distribution with the new channels selected mainly there also for the channels in the atmospheric window (in green). The water vapour Jacobians of the ozone (purple) and temperature-sounding channels (red) are also stronger than those of Collard. Finally, as before, the ozone Jacobians (f) have a more homogeneous distribution with the new selection and smaller Jacobian values carried by the temperature-sounding channels (in red). Globally, it is conceivable that this homogeneous distribution of the Jacobians is due to the precise taking into account of inter-channel observation errors during the channel selection process. This allows for the selection of the most informative channels to cover the full range of the atmosphere. Furthermore, we have seen earlier that 90 % of the maximum skin temperature DFS is obtained with only three channels. In addition, Jacobians of the Fig.  shows that channels in the first atmospheric window are also sensitive to temperature and water vapour in the lower troposphere. Using these channels could be beneficial to provide additional information for NWP.

We evaluated CS275, NS275 and a selection of 400 channels (named NS400) by assimilating them into the 1D-Var (Eq. ). We used the diagnosed observation error covariance matrices with the appropriate number of channels for each selection. Data assimilation experiments were performed on the 6123 profiles in order to closely approximate the variability of the operational NWP models. In a first step, the DFS mean values of the 6123 profiles for the three selections were calculated. The mean vertical profiles of the DFS for the three selections (Collard in black, the new selection with 275 channels in blue and with 400 channels in red) are shown in Fig.  for temperature (a), humidity (b) and ozone (c), and results of DFS values are summarized in Table . Compared to CS275 and the equivalent number of channels the NS275 increases the information content since the DFS for temperature is increased by 0.62, for humidity by 0.23 and for ozone by 0.33. It is observed that for temperature, the new selections increase the information content mainly in the stratosphere between 100 and 1.0 hPa and in the lower troposphere between 900 and 300 hPa. For humidity, the information content is increased mainly between 950 and 300 hPa, while for ozone the information content is increased, especially at UTLS. It can be noted that the assimilation of NS400 provides additional information compared to NS275 especially in the troposphere for temperature and humidity and UTLS for ozone.

Finally, we evaluated the impact of the different selections by comparing the analysis-error standard deviations (σa) to the background-error standard deviations (σb). Figure  shows the mean vertical profiles of the relative differences between σa and σb with respect to the pressure for CS275 in black  (d), NS275 in blue (e) and NS400 in red (f). Interestingly, the profiles of DFS and the relative differences between σa and σb are consistent. In addition, NS400 improves everywhere on top of NS275 with additional contribution in the troposphere for temperature and humidity and at the UTLS for ozone.

As expected, the new channel selections further reduce the σa compared to the σb at the same atmospheric levels as previously identified where the information content has been increased. The mean results are summarized in Table 4. We provide a more detailed description of the benefit of the new selections compared to the results with CS275:

Compared to CS275, NS275 allows us to reduce on average the temperature analysis error by 3.0 % (3.9 % in troposphere and 1.8 % in stratosphere) with a maximum reduction up to 8.6 % at 700 hPa. Humidity analysis error is reduced by an average of 1.8 % with a maximum reduction of 4.1 % at 745 hPa. Finally, the ozone analysis error is reduced by an average of 0.9 % with a maximum reduction of 3.6 % at 70 hPa.