Multispectral information from TANSO-FTS instrument – Part 1 : Application to greenhouse gases ( CO 2 and CH 4 ) in clear sky conditions

Abstract. The Greenhouse gases Observing SATellite (GOSAT) mission, and in particular the Thermal And Near infrared Sensor for carbon Observations–Fourier Transform Spectrometer (TANSO-FTS) instrument, has the advantage of being able to measure simultaneously the same field of view in different spectral ranges with a high spectral resolution. These features allow studying the benefits of using multispectral measurements to improve the CO2 and CH4 retrievals. In order to quantify the impact of the spectral synergy on the retrieval accuracy, we performed an information content (IC) analysis from simulated spectra corresponding to the three infrared bands of TANSO-FTS. The advantages and limitations of using thermal and shortwave infrared simultaneously are discussed according to surface type and state vector composition. The IC is then used to determine the most informative spectral channels for the simultaneous retrieval of CO2 and CH4. The results show that a channel selection spanning the three infrared bands can improve the computation time and retrieval accuracy. Therefore, a selection of less than 700 channels from the thermal infrared (TIR) and shortwave infrared (SWIR) bands allows retrieving CO2 and CH4 simultaneously with a similar accuracy to using all channels together to retrieve each gas separately.


Introduction
The survey at global scale of greenhouse gases, in particular CO 2 and CH 4 , takes advantage of the numerous space-borne infrared instruments.Work performed from high spectral measurements in the thermal infrared (TIR), such as AIRS (Crevoisier et al., 2003;Engelen and Stephens, 2004;Divakarla et al., 2006;Chahine et al., 2008;Maddy et al., 2008;Xiong et al., 2008), TES (Shepard et al., 2008;Kulawik et al., 2010;Worden et al., 2012) and IASI (Crevoisier et al., 2009;Herbin et al., 2009;Razavi et al.;2009), has demonstrated the sensitivity of these observations to the midtroposphere.Moreover, the OCO's pre-launch studies (Connor et al., 2008;Butz et al., 2009) as well as those from the shortwave infrared (SWIR) instrument SCIAMACHY (Buchwitz et al., 2005;Noël et al., 2005) have illustrated the ability of such measurements to get information on gaseous concentrations near the surface.Therefore, a retrieval exploiting the synergy between TIR and SWIR observations looks promising to reproduce the whole tropospheric gas profile distribution better.
Previous studies from Christi and Stephens (2004), Li et al. (2004), Cho and Staelin (2006), and Aires et al. (2011) have demonstrated that the use of simultaneous, but different, observations can improve the accuracy of the retrieved parameters.Nevertheless, the applications remain particularly sparse because using information from different instruments is notoriously difficult (collocation, field of view size and homogeneity).Moreover, measurements obtained by the same instrument at different spectral ranges have not yet been exploited, because such methodologies need to take into account other parameters such as spectral and radiometric band-to-band calibration and also the development of more complex algorithms, which are highly time-consuming.
Published by Copernicus Publications on behalf of the European Geosciences Union.
The TANSO-FTS (Thermal And Near infrared Sensor for carbon Observations-Fourier Transform Spectrometer) instrument, which measures simultaneously one TIR and two SWIR spectral bands with the same field of view, represents a unique resource for testing the high-resolution multispectral approach suitability.Although the SWIR domain has been extensively used for greenhouse gas measurements (Morino et al., 2011;Yoshida et al., 2011Yoshida et al., , 2013;;Crisp et al., 2012), the TIR has been less often employed (Saitoh et al., 2009), and to our knowledge, there is no study that exploits both spectral ranges.
In this study, we present for the first time the contribution of high-resolution multispectral measurements for an optimal retrieval of the greenhouse gases CO 2 and CH 4 in clear sky conditions.In particular, we discuss the interest of using two or three spectral bands simultaneously according to the surface type and state vector composition.This synergetic approach is evaluated from the three infrared bands of the TANSO-FTS instrument thanks to a new radiative transfer algorithm developed at the Laboratoire d'Optique Atmosphérique (LOA).
The structure of the paper is as follows: GOSAT mission and its two instruments are briefly described in Sect. 2. The forward model, state vector and error description are detailed in Sect.3. Section 4 is dedicated to an information content analysis of the gaseous profiles in clear sky conditions.Section 5 demonstrates the interest of a channel selection spanning the three infrared bands.Finally, Sect.6 summarizes our results and presents perspectives for future applications.

Instrument description
The Greenhouse gases Observing SATellite (GOSAT), launched on 23 January 2009 by JAXA, is designed to monitor the global CO 2 and CH 4 distributions from space.GOSAT is in a sun-synchronous orbit at 666 km altitude with three-day recurrence, and measures at around 13:00 local time.It is equipped with two instruments: the Thermal And Near infrared Sensor for carbon Observations-Fourier Transform Spectrometer (TANSO-FTS) and the Cloud and Aerosol Imager (TANSO-CAI).The TANSO-FTS performs high-spectral-resolution measurements (0.2 cm −1 , non-apodized) in the thermal infrared (TIR) (Band 4: 700-1800 cm −1 ), shortwave infrared (SWIR) (Band 3: 4800-5200 and Band 2: 5800-6400 cm −1 ) and visible (Band 1: 12 900-13 200 cm −1 ) with an instantaneous field of view of 15.8 mrad, corresponding to a nadir circular footprint of about 10.5 km at ground level.For the SWIR and visible bands, the incident light is recorded as two (P and S) orthogonal polarization components.TANSO-CAI has four narrow bands from the near ultraviolet to near-infrared regions at 0.38, 0.674, 0.87, and 1.6 µm, with spatial resolutions of 0.5, 0.5, 0.5, and 1.5 km, respectively, for nadir pixels.

The forward model
Accurate calculations of the radiances observed by TANSO-FTS are achieved with the high spectral resolution (up to 0.0001 cm −1 ) code LBLDOM (Dubuisson et al., 1996(Dubuisson et al., , 2005) ) over the thermal and solar spectral regions (0.2-16 µm).Radiances at the top of the atmosphere are calculated by solving the radiative transfer equation (RTE) in a horizontally homogeneous scattering atmosphere, using the discrete ordinate method (DOM) (Stamnes et al., 1988).Gaseous absorption is calculated with a line-by-line code based on STRANSAC (Scott, 1974) and the HITRAN 2008 database (Rothman et al., 2009).In this study, we assume a perfect filtering of the spectra containing cloud and aerosol observations.In the absence of atmospheric scattering, it is not necessary to use the O 2 A-Band (Band 1).Indeed, this band is mainly used to obtain an accurate optical path length when significant amount of scattering particles remains in the atmosphere.In this study the term "all bands" refers then to the use of Bands 2, 3 and 4 simultaneously.The absorption lines are computed at 0.01 cm −1 spectral resolution assuming a Voigt line shape.Absorption continua (H 2 O, CO 2 , and N 2 ) are also included from the MT-CKD parameterization (Clough et al., 2005).The solar irradiance database reported by Kurucz (http:// kurucz.harvard.edu/sun/irradiance2008/) is used as the incident solar spectrum.Lambertian surface is assumed; thus the effect of surface polarization is disregarded.The albedo in the two SWIR bands is estimated from MODIS Terra product (Moody et al., 2008) and chosen as follows: desert and seawater in order to cover high and weak surface reflectivities, respectively.The corresponding surface emissivity for the TIR band is estimated from the MODIS UCSB library (http://www.icess.ucsb.edu/modis/EMIS/html/em.html).The only use of a nadir viewing angle, with a solar zenith angle of 30 • , does not alter results or the discussion of the study, even if the sensitivity is correlated to viewing geometry.
Finally, the total intensity of TANSO-FTS spectra is simulated using the instrumental line shapes provided for each band by the GOSAT user interface gateway (https://data.gosat.nies.go.jp/gateway/gateway/MenuPage/open.do), and no post-apodization is applied, which allows the exploitation of the full spectral resolution.
Figure 1 illustrates the forward model capabilities to simulate the three infrared bands of TANSO-FTS in clear sky conditions.It shows an example of observed spectrum and the simulated individual contributions of major molecular absorbers on US standard profiles.Even if this instrument is mainly dedicated to CO 2 and CH 4 measurement, its instrumental qualities (spectral range, spectral resolution and signal-to-noise ratio) could enable detection of number of other species such as water vapor isotopologues HDO, H 2 18 O or H 2 17 O (see Fig. 1 and Frankenberg et al., 2013).

Information content theory
In the case of an atmosphere divided in discrete layers, the forward radiative transfer equation gives an analytical relationship between the set of observations y (here, the radiances) and the vector of true atmospheric parameters x and is written as where F represents the model that allows mapping the state space to the measurement space, and ε the measurements and/or forward model error vector.
In the case of information content (IC) analysis, we do not need to introduce the whole optimal estimation theory formulation used for the retrieval described by Rodgers (2000).In this study, two matrices (A and S x ) fully characterize the information provided by the observing system.
The first one is the averaging kernel matrix, A, which gives a measure of the sensitivity of the retrieved state to the true state, defined by where K is the Jacobian matrix (or weighting function), the ith row of which is the partial derivatives of the ith measurement with respect to each (j ) element of the state vector: , and K T is its transpose.G is the gain matrix, whose rows are the derivatives of the retrieved state with respect to the spectral points, defined by where S a is the error covariance matrix describing our knowledge of the state space prior to the measurement and S ε represents the forward model and the measured signal error covariance matrix.At a given level, the peak of the averaging kernel row gives the altitude of maximum sensitivity, whereas its full width at half maximum is an estimate of the vertical resolution.Rodgers (2000) demonstrated that the trace of A represents the total degrees of freedom for signal (DOFSs), which indicates the amount of independent pieces of information provided by the observing system as regards as the state vector.In an ideal inverse method, the averaging kernel A would be the identity matrix representing a perfect retrieval with a DOFS equal to the size of the state vector.Consequently, each diagonal element of A is equivalent to partial degree of freedom attached to each element of the state vector (or attached to each parameter we want to retrieve).
The second essential matrix is the error covariance matrix S x , which describes our knowledge of the state space posterior to the measurement.Rodgers (2000) demonstrated that this error covariance matrix can be written as In this expression the matrix S ε can be written as follows: with S b representing the error covariance matrix formed by the errors attached to non-retrieved model parameters, S f the forward model error covariance matrix, and S m the measured signal error covariance matrix.Therefore, we can estimate the contribution of the prior measurement and forward model error to the posterior error S x as follows: The smoothing error covariance matrix S smoothing represents the vertical sensitivity of the measurements to the retrieved profile.
The contribution of the measurement error covariance matrix S m to the posterior error covariance matrix S x is given by S meas .S m is computed from the spectral noise.
The forward model error covariance matrix S f illustrates the imperfect knowledge of the non-retrieved model parameters, and its contribution to the posterior error covariance matrix is given by S fwd.mod. .
The total error covariance matrix can then be regarded as the sum of these individual contributions, and Eq. ( 4) can be rewritten as S x = S smoothing + S meas + S fwd.mod. . (9)

A priori information
The IC analysis uses simulated unpolarized intensity spectra of TANSO-FTS SWIR Bands 2 and 3, and TIR Band 4. The CO 2 and CH 4 vertical concentrations of the a priori state vector x a are based on US standard profile discretized on 21 vertical levels, extending from the ground to 20 km height with 1 km step.In addition, the humidity and temperature profile, surface reflectivity, and the TIR surface emissivity are included in the non-retrieved parameters and will be discussed in detail in Sect.3.4.The a priori values and their a priori variabilities are summarized in Table 1 and described subsequently hereafter.

A priori error covariance matrix
The a priori error covariance matrix S a can be evaluated from climatology or in situ data.Nevertheless, the off-diagonal matrix elements increase the correlation of the vertical layers.Since this study is dedicated to information coming from the measurement rather than climatological or in situ observations, we will always assume S a as a diagonal matrix with the ith diagonal element (S a,ii ) defined as where σ a,i stands for the standard deviation in the Gaussian statistics formalism.The subscript i represents the ith parameter of the state vector.
The CO 2 profile a priori error (red line of Fig. 2) is estimated from Schmidt and Khedim (1991) and is very similar to the one used by Christi and Stephens (2004).The CH 4 a priori error is fixed to P error = 5 %, which corresponds to an under-constrained version of the error covariance matrix used by Razavi et al. (2009) and Frankenberg et al. (2012).

Measurement error covariance matrix
In order to compute the measurement error covariance matrix, one needs to know the instrument performance or accuracy.The instrument performance corresponds to the radiometric calibration (which could be a bias) and radiometric noise, usually given as signal-to-noise ratio (SNR).This error covariance matrix is assumed to be diagonal, and the ith diagonal element can be computed as follows: where σ m,i is the standard deviation of the ith measurement (y i ) of the measurement vector y, representing the noise equivalent spectral radiance.For the TIR Band 4, the SNR is estimated as 300 for a 280 K blackbody light input (Kuze et al., 2009).For the SWIR bands, there are two main noise sources: (1) the detector and electronics noise, which is independent of the signal intensity and (2) the shot noise, which is proportional to the square root of the total amount of input light.Because of the wide spectral range of Band 2, the main contribution to the total noise comes therefore from the shot noise.However, we have applied an identical SNR for Bands 2 and 3.The latter is estimated from the Band 2 SNR values given by Yoshida et al. (2011).According to the different surface types, the SNR was set to 500, and 150 representative of our high (desert-like), and low (seawater-like) surface reflectivity cases.

Non-retrieved parameter characterization and accuracy
Evaluation of the forward model accuracy is the most difficult part of the error description.Indeed, it consists in both the model precision (for example 1-D approximation, Lambertian surface, accuracy of the computation) as well as the error due to the non-retrieved parameters (x b ) used in the forward model (e.g., temperature profile, ground emissivity, gas profile when they are not retrieved).As horizontal variability of gas and aerosol are small enough on a GOSAT pixel size, and as it is beyond the scope of this paper to explore 3-D effects due to horizontal sub-pixel heterogeneity, we choose to neglect it in this study.Thus, only effects of non-retrieved parameters uncertainties are explored here.Moreover, a vertically uniform uncertainty is assumed.
The most important variables when dealing with infrared measurements such as TANSO-FTS Band 4 are the temperature profile and surface temperature.We assume a realistic uncertainty, compatible with the typical values used for the ECMWF assimilation, of 1 K ( T = 1 K) on each layer of the temperature profile as well as on surface temperature.The contribution to the ith diagonal element of the forward model error covariance matrix can be computed as where j stands for the j th level and i for the ith measurement.
The surface emissivity (ε m ) uncertainty is set to P ε m = 2 %, which corresponds to an average value of the albedo absolute accuracy from MODIS and IASI (Capelle et al., 2012), and its contribution to the ith diagonal element of the forward model error covariance matrix is We assumed a very poor knowledge on the interfering molecule concentration with an uncertainty (P Cmol ) of 100 %, and as before their contribution to the ith diagonal element of the forward model error covariance matrix can be computed as where C mol k represents the concentration of the kth interfering molecule.
If H 2 O is treated as a non-retrieved molecule and is assumed to be known from ancillary data, its a priori error profile is set to P CH 2 O = 10 %.This error value is compatible with typical a posteriori uncertainties from operational Level 2 products of a dedicated instrument such as IASI (Clerbaux et al., 2007).
Finally, the total forward model error covariance matrix (S f ), assumed diagonal in the present study, is given by summing all the previous contributions for each diagonal element, and the ith diagonal element (S f,ii ) is given by Here, we did not consider the spectroscopic line parameter, line-mixing, continua or calibration errors.

Information content analysis applied to greenhouse gas profiles in clear atmosphere
In order to quantify the benefit of multispectral synergy, it is essential to perform, first, an information content analysis on CO 2 , and CH 4 profiles separately (Case 1).By separately we mean that the state vector is constituted of only one of the above gas concentrations at each level between 0 and 20 km.This corresponds to the case where we estimated each gas profile alone when all other atmospheric parameters and all other gas profiles are assumed to be known from ancillary data with a specific variability or uncertainty.
Figures 2 and 3 show the averaging kernel A and total posterior error S x for CO 2 and CH 4 , respectively, and for each surface type.A is obtained for each greenhouse gas independently using the variability introduced in the previous section and considering an observing system composed of Band 2, 3 or 4 alone and all the bands together.Each colored line represents the row of A at each vertical grid layer.The blue circles represent the partial degree of freedom of the gas at each level (diagonal element of A).The latter indicates the proportion of information provided by the measurement.Indeed, a value close to unity means that the information mainly comes from the measurement, while a value close to zero indicates that the information is strongly related to the a priori.
For both surface types, Fig. 2 shows that most of the information about CO 2 arises from the ground to 10 km high in the atmosphere, while at upper altitude the error is mainly governed by the a priori uncertainty, due to a smaller sensitivity to CO 2 in the upper troposphere.In the lower part of the atmosphere, the a posteriori total error (black line) is significantly weaker than the a priori error (red line).The vertical distribution of A illustrates the sensitivity to CO 2 in the lower atmosphere (0-3 km) from SWIR bands.Nevertheless, this sensitivity dramatically decreases with the surface albedo to be almost insignificant above seawater.This phenomenon is well known, and the operational Level 2 products from TANSO-FTS (Yoshida et al., 2011(Yoshida et al., , 2013) ) treat only the spectra over ocean where the specular reflection occurs and reflectance is high.The TIR sensitivity in the midtroposphere (3-10 km) is less influenced by the surface characteristics (see panels Band 4 from Fig. 2) and appears to be very suitable to retrieve CO 2 abundances when the surface albedo is weak.The most important result of Fig. 2 is the improvement of the vertical information distribution when we use all the bands simultaneously, in particular, when the reflectivity is significant.For instance, in the case of desert surface, the total DOFSs are 0.75, 1.16, 1.32 and 2.59, for Band 2, 3, 4 and all the bands respectively.The latter show that one might be able to retrieve between 2 and 3 partial tropospheric columns for CO 2 .Nevertheless, the CO 2 error is always dominated by the a priori error, which means that the information is strongly constrained by the a priori profile and little information is introduced from the measurement.Therefore, even with a high a priori constraint on the CO 2 profile, this study shows that using all the TANSO-FTS bands together leads to an improvement of the a posteriori www.atmos-meas-tech.net/6/3301/2013/Fig. 2. Averaging kernels and error budgets of CO 2 vertical profiles for Bands 2, 3, and 4 separately and all the bands together in Case 1. the red and black lines stand for the prior (S a ) and posterior (S x ) errors, respectively; the smoothing (S smoothing ), model parameters (S fwd.mod.), and measurement (S meas. ) errors are dotted, dashed, and dashed/dotted lines, respectively.The averaging kernels of each altitude layer are represented by different colors.
error profile on CO 2 concentration, especially in the lower part of the atmosphere.
These results are close to those from previous studies (Christi and Stephens, 2004;Connor et al., 2008;Saitoh et al., 2009;Yoshida et al., 2011), but it is important to note that the absolute values of averaging kernel and error profile cannot be directly compared, since they depend on several parameters: (1) a priori values x a and x b , (2) the variability of the error covariance matrix S a , S f and S m , as well as (3) the vertical grid.The latter can be circumvented if the tropospheric column error (S XCO 2 ) is derived from the vertical profile error as in Yoshida et al. (2011): where C air is the vector containing the air molecule concentration at each level, and 1 is a column vector with unity elements.The CO 2 total column posterior error is estimated to be less than 1.2 % whatever the surface (see Table 2), which is comparable to the results from previously mentioned studies.
As for CO 2 , Fig. 3 shows that the general conclusion is identical for CH 4 but with a smaller information content.Because it does not contain any methane absorption lines, Band 3 shows no information (see Figs. 1 and 3).For the remaining bands, the A's are broader than those of CO 2 , suggesting a very important correlation between layers and then a degradation of the vertical resolution.Moreover, Band 2 becomes unusable for small surface albedo values (see seawater panel of Fig. 3).For comparison with CO 2 , in the case of desert, the total DOFSs are 0.64, 0.84 and 1.63, for Band 2, 4 and all the bands respectively.These weak values highlight the difficulty in retrieving more than one or two tropospheric columns of methane from such measurements.
As a general trend, the simultaneous use of all the bands together instead of Band 4 alone (TIR) or Band 2 and 3 (SWIR) increases the total DOFS and reduces systematically the total errors of the two gas species.Band 4 has the advantage of providing mid-tropospheric information weakly affected by the surface albedo.The SWIR bands have the advantage of having low measurement and non-retrieved parameter errors (dashed and dotted lines in Figs. 2 and 3).This effect is mainly due to weak temperature dependence and  less interference from other molecules in the SWIR.Moreover, in the case of high reflectance, the sensitivity to CO 2 and CH 4 concentrations is comparable to TIR spectral range, but centered in the lower troposphere, where variability of greenhouse is the most important.
In the operational GOSAT level 2 products, both CO 2 and CH 4 gas concentrations are obtained simultaneously (Yoshida et al., 2011).Therefore, we investigate how the inclusion of CO 2 and CH 4 profiles in the same state vector could improve the information content (this case will be refereed as Case 2 hereafter).All the a priori values and variabilities are the same as in the previous section (see Table 1).
Although the differences with the results from the previous section are rather small, we can observe a significant effect over bright surface (e.g., desert) in the lower atmosphere where the sensitivity is higher.The averaging kernels (not shown here) appear to be narrower with strongest amplitude involving a better vertical resolution, especially from the ground up to 5 km.Table 2 summarizes the CO 2 and CH 4 total DOFS and total column errors for all cases, each gas individually (Case 1) or together (Case 2) in the state vector.
The latter illustrates how a state vector including both gases enhances the total information.However, even if the total information is better, the impact on the total errors seems limited, due to the high constraint on each a priori gas profile.Nevertheless, we can conclude that taking into account CO 2 and CH 4 together in the state vector involves an improvement of their accuracy retrievals.Obviously, this improvement is driven by the relative amount of information coming from the measurement in regard to the a priori and non-retrieved parameter uncertainties.This improvement is weak (cf.Table 2) for CO 2 and CH 4 .Therefore, the benefit of simultaneous retrieval depends on the additional computing time generated (see following section).

Channel selection
Using all channels, measured by TANSO-FTS, in the retrieval scheme has two disadvantages.Firstly, it requires a very large computational time.This problem could be circumvented with optimized parallel programming and exploitation of the latest computer technologies such as GPU (Huang et al., 2011).Secondly, it increases the systematic error from correlation of the interfering species.In this case, a good evaluation of the a priori state vector x a and error covariance matrix S a is very challenging.As emphasized by Rodgers (2000), the IC framework is very well suited to optimize the selection of channels that carry the greatest amount of information.This procedure is well described in L' Ecuyer et al. (2006) and will not be developed in this paper.Previous studies already used channel selection to optimize the greenhouse gas retrievals from high-resolution infrared sounders.We can cite, for instance, the study of Dudhia et al. (2002) from the MIPAS spectra, or the works of Crevoisier et al. (2003) and Worden et al. (2004) from AIRS and TES respectively.Specifically applied to TANSO-FTS, Saitoh et al. (2009) developed a retrieval algorithm to retrieve CO 2 vertical profiles using the TIR (Band 4), and Kuai et al. (2010) discussed the practical advantages of channel selection in the SWIR bands (Band 2 and 3).The goal of this section is therefore to present results of a channel selection in order to reach a reasonable amount of information on both CO 2 and CH 4 columns using measurements from the TIR and SWIR spectral range simultaneously (Bands 4, 3 and 2). Figure 4 presents the CO 2 and CH 4 total DOFS evolutions as a function of the number of selected channels from all spectral bands and for each surface type.The maximum number of selected channels has been fixed to 2032, which corresponds to all the channels from both 1.61 and 2.06 µm CO 2 bands used by Kuai et al. (2010).The first highlight coming from Fig. 4 is that the DOFS magnitude and evolution are strongly correlated to the surface type.Moreover, for each gas, the DOFS increases sharply with the first selected channels and then more steadily.This is perfectly illustrated in Table 3, which gives the number of channels required to reach 75 % and 90 % of the total information provided by using all the channels, for each gas and surface type.The distributions (in %) by spectral band of the previous selected channels are reported in Table 4.The TIR band (Band 4) appears predominant when the surface reflectivity is weak, whereas over bright surface SWIR bands (Band 2 and 3) become more important for CH 4 and preponderant for CO 2 (Table 4).Finally, the results from Table 4 demonstrate the usefulness of the multispectral information to retrieve the greenhouse gas concentrations with good accuracy for all the surface types.
Table 5 shows DOFSs and total errors, for different amounts of selected channels.As previously stated, Case 1 is related to the treatment of each gas separately and Case 2 when both gases are treated simultaneously.The different values of DOFSs and column errors confirm the retrieval improvement for each gas when they are treated simultaneously (see previous section).Obviously, the best information is provided by the use of all the available channels in Case 2 (see Table 2).However, the reduction to 2032 selected channels (Yoshida et al., 2011) does not affect the accuracy of the retrieved CO 2 and CH 4 columns.Moreover, a retrieval scheme that uses selected channels corresponding to 75 % or 90 % of the total information content would give comparable errors to a retrieval scheme using the entire set of channels.These results point out the interest of determining an optimal set of channels for each gas separately, and using this selection to retrieve these two gases simultaneously (see lines 355 and 694 of Table 5).

Summary and conclusion
To summarize, this study investigates the interest of retrieving greenhouse gas profiles from multispectral measurement.First, we performed an information content analysis on CO 2 and CH 4 separately in clear sky conditions from the TIR and SWIR bands of the TANSO-FTS instrument.We showed that by using all the available channels, one might be able to retrieve between 1 and 2 partial columns for CH 4 , and 2 or 3 for CO 2 from the ground to 20 km, demonstrating the interest of the spectral synergy.Assuming one single column leads to posterior errors better than 1.4 % and 1.2 %, for CH 4 and CO 2 respectively.Moreover, merging the CO 2 and CH 4 profiles in the same state vector implies a small improvement of a posteriori uncertainties and DOFSs.However, the impact on the tropospheric column errors of CO 2 and CH 4 appears rather weak because of the high constraint assumed on the a priori gas profile.
Finally, we showed that a selection of less than 700 channels from the three spectral bands allows retrieving CO 2 and CH 4 simultaneously with a comparable accuracy than using all channels to retrieve each gas separately.
Therefore, this study demonstrates that the most efficient way to retrieve CO 2 and CH 4 is to perform a channel selection across all the spectral bands for CO 2 and CH 4 separately for different surface types and to use all selected channels to retrieve both gases simultaneously.
This first paper is dedicated to an information content analysis on greenhouse gases (CO 2 and CH 4 ) from multispectral infrared measurements in clear sky conditions.Nevertheless, it is well known that the main source of errors is related to the presence of scattering particles.The second paper will therefore address this problem by studying (1) the aerosol information content using the four bands (from TIR to visible) of TANSO-FTS instrument and (2) their impact on the greenhouse gas retrievals.

Fig. 1 .
Fig. 1.Example of observed TANSO-FTS spectrum in normalized radiances, simulated solar contribution and individual major molecular absorbers.Each band is calculated from our line-by-line forward model on US standard profiles with nadir viewing angle and solar zenith angle of 30 • .

Fig. 4 .
Fig. 4. Evolution of the DOFSs with number of selected channels for CO 2 (solid black line) and CH 4 (black dashed line) separately, and all together (blue line).The red crosses and circles symbolize the number of channels (355 and 694) corresponding to 75 % and 90 % of the total IC.

Table 2 .
Total DOFSs and column errors of CO 2 and CH 4 for each surface using all spectral channels.

Table 3 .
Number of selected channels.

Table 4 .
Band-by-band distribution (in %) of the selected channels in Case 2.

Table 5 .
Total DOFSs and column errors (%) of CO 2 and CH 4 for each surface from different amounts of selected channels.