Midtropospheric carbon dioxide (CO2) concentration is retrieved in the tropics [20S:20N], over sea, at night, for the period April to October 2003 from the Atmospheric Infrared Sounder (AIRS) observations. The method relies on a non-linear regression inference scheme using neural networks. A rough estimate of the mean precision of the method is about 2.5 ppmv (0.7%). The retrieved seasonal cycle and its latitudinal dependence agree well with aircraft CO2 in situ measurements made at the same altitude range. Maps produced on a monthly basis at a resolution of 15° × 15°, although not yet fully understood, show good agreement with known characteristics of CO2 distribution reflecting both atmospheric transport and surface fluxes (fossil fuel emissions, biomass burning, air-surface gas exchanges).
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 Knowledge of today's carbon sources and sinks, their spatial distribution and their variability in time is essential for predicting the future carbon dioxide (CO2) atmospheric concentration levels. The distribution of atmospheric CO2 reflects both spatial and temporal evolutions as well as the magnitude of surface fluxes [Tans et al., 1990]. In principle, it is thus possible to estimate these fluxes from atmospheric CO2 concentration, provided that atmospheric transport can be accurately modelled. However, this approach is currently limited by the sparse and uneven distribution of the global flask sampling programs. Densely sampling the atmosphere in time and space, satellite measurements of the distribution of global atmospheric CO2 concentration would in principle fill this gap in scale [Rayner and O'Brien, 2001].
 The feasibility of retrieving CO2 and other trace-gas concentrations from space observations in the infrared has been demonstrated by Chédin et al. [2002, 2003] using the NOAA TOVS instruments. For the first time, 4 years of monthly mean midtropospheric CO2 concentration were retrieved from TOVS infrared and microwave observations over the tropics [20S:20N] for the period July 1987–June 1991. A rough estimate of the method-induced standard deviation of these retrievals was of the order of 3 ppmv (less than 1%).
 With its 2378 channels covering most of the infrared spectrum at a very high spectral resolution, the Atmospheric Infrared Sounder (AIRS), launched onboard the NASA's Aqua platform in May 2002, gives the opportunity to use channels specifically sensitive to CO2 and well covering the mid-to-high troposphere. Also flying onboard Aqua, the Advanced Microwave Sounding Unit (AMSU), with its 15 channels, provides microwave observations coupled with those of AIRS.
 Infrared CO2 sensitive channels are also and much more sensitive to temperature. Hence, the simultaneous use of infrared measurements, sensitive to both temperature and CO2 variations, and of microwave measurements, only sensitive to temperature, allows separating these two effects.
 As compared to other regions, the tropics present a greater tropospheric temperature stability. Therefore, the separation between CO2 and temperature variations is easier. The study is thus limited to the latitudinal band [20S:20N]. Retrieving CO2 concentrations in the tropical zone is important for two reasons: the flask network is the least efficient in this part of the globe [Rayner and O'Brien, 2001] and the strong convective vertical mixing existing in the tropics rapidly transmits surface carbon flux variations to that part of the atmosphere seen by AIRS.
2. Data and Method
 A set of 43 AIRS channels, located in the two spectral bands where CO2 is an absorber, near 15 μm and 4.3 μm, and presenting optimal properties to retrieve CO2, has been selected with the Optimum Sensitivity Profile (OSP) method [Crevoisier et al., 2003a]. These channels are characterized by a strong sensitivity to CO2 variations and a low sensitivity to other atmospheric components such as water vapour (H2O), ozone (O3), nitrous oxide (N2O), carbon monoxide (CO), and surface characteristics. They are part of the 324 AIRS channels distributed by NOAA/NESDIS [Goldberg et al., 2003]. To design a method that may be used to process night-time as well as daytime observations, the channels located in the 4.3 μm band, potentially contaminated by solar radiation, have not been selected for this study. Use is made of the eight AIRS channels 173, 175, 180, 185, 193, 213, 218 and 250. They are sensitive to CO2 variations in the range 100–500 hPa (5–15 km), as shown by the corresponding 8-channel mean CO2 Jacobian (partial derivative of the channel brightness temperature (BT) to a layer CO2 concentration) plotted on Figure 1 for a representative tropical situation.
 The weakness of the signal induced on AIRS BT by CO2 variations, associated with the complexity and non-linearity of the relationship between CO2 concentration and observed BT, makes it difficult to solve this inverse problem. Therefore, as in the work of Chédin et al. , a non-linear inference method, based on the Multilayer Perceptron (MLP) neural network [Rumelhart et al., 1986] with two hidden layers, has been preferred to a more classical one. A detailed description of the method, already used for TOVS observations, can be found in this reference.
 For this study, the Thermodynamic Initial Guess Retrieval (TIGR) database [Chédin et al., 1985; Chevallier et al., 1998] is used as the training set. Each situation is described by its profiles of temperature, water vapour and ozone. Trace gas concentrations are assumed constant along the vertical. CO2, N2O and CO reference concentrations are 372 ppmv, 324 ppbv and 100 ppbv, respectively. These are the predicted concentration values for the year 2003 [IPCC, 2001]. Clear-sky AIRS BT, transmittances and Jacobians are then computed for all the profiles using the fast line-by-line 4A model in its latest version [Scott and Chédin, 1981] (http://ara.lmd.polytechnique.fr). AMSU BT are computed using the in house STRANSAC model. The computation is performed for all scan angles.
 The chosen neural architecture is the following. The input layer is composed of: (1) the 8 AIRS BT of the tropospheric channels given above, (2) 3 AMSU-A BT of channels 6, 8, and 9, and (3) 6 differences between AIRS and AMSU BT, to help constraining the convergence process. Very unfortunately, the high noise observed on AMSU channel 7 precluded using this tropospheric channel although presenting the best coincidence with the mean CO2 Jacobian. All together, there are 17 predictors. Network input BT correspond to randomly drawn values of CO2 concentration in the range 362–392 ppmv and are computed from the reference value in TIGR using the CO2 Jacobians. The output layer of the network is composed of: (1) the difference between the true value of CO2 concentration (associated with inputs) and the reference one (372 ppmv), and (2) 8 differences between the “true” AIRS BT (associated with the true CO2 concentration value) and the “reference” one (associated with the reference CO2 concentration value), once again to constrain the solution. All together, there are 9 predictands. Our past experience and several trials have led us to chose 60 neurons for the first hidden layer and 40 for the second one.
 Use is made of the Error Back-Propagation learning algorithm [Rumelhart et al., 1986], with stochastic steepest descent. At each step of the learning phase, the instrument noise is taken into account by adding to the BT of each channel a random Gaussian noise characterized by the equivalent noise temperature (NeΔT) computed at the BT of the channel. Use is made of the January-2003-in-flight NeΔT.
 A total of 10 MLPs have been trained, one for each local zenithal angle, ranging from nadir to an upper limit of 40° to avoid the edges of the orbits.
 The MLPs are trained with simulated data. Therefore, before presenting observations to the networks, eventual BT systematic biases existing between simulations and observations must be removed. For each channel, the bias is obtained by averaging, over the whole time period and the whole tropics [20S:20N], the differences between collocated (in time and space) satellite observations and simulations based on the forward model used and radiosonde measurements from the ECMWF database. It has been previously verified that these differences show negligible latitudinal and time variations (not shown).
3. Results and Discussion
 In the absence of AMSU channel 7, most of the information on midtropospheric temperature comes from AMSU channel 6, which is modestly, though significantly, sensitive to surface, and particularly to relief. Hence, performing the retrievals over land would require a more detailed study of the influence of surface elevation: so far, the present application is limited to sea cases.
 CO2 midtropospheric concentration was retrieved for seven months of AIRS observations from April to October 2003. Use is made of AIRS observations at 1:30 am local time, and of the best spatial resolution available from NOAA/NESDIS (nine AIRS fields of view (FOV) for every other AMSU FOV). Retrievals are only performed for FOV detected clear by a cloud detection procedure based on threshold tests [Crevoisier et al., 2003b].
3.1. Comparison With In Situ Aircraft Measurements
 An important part of our present knowledge on CO2 distribution in the mid-to-high troposphere comes from in situ observations made by commercial airliners from April 1993 to March 2003 between Japan and Australia (data available at http://gaw.kishou.go.jp/wdcgg.html). These observations, partly analysed by Matsueda et al. , cover the altitude range 9–13 km.
 Monthly mean CO2 variations measured in situ in the northern [0:20N] and southern [20S:0] tropics are shown on Figure 2 (crosses) from January 1999 to March 2003. Both the positive trend and the seasonal cycle are approximated by fitting the sum of a linear function and four harmonics to the data and extrapolated to the next seven months (dashed lines). A first comparison has shown a systematic difference of about 0.9 ppmv between the mean value expected by the fit and the AIRS retrieved CO2 concentration. This modest shift has three potential causes: first, the radiative model bias removal procedure described in Section 2 that is not optimal because of the low number of radiosonde measurements available for the period considered; second, the different geographical regions considered; third, remaining undesirable instrumental effects (such as the sidelobes effect observed on AMSU channels which is still investigated by the AIRS team (B. H. Lambrigtsen, personal communication, 2003)).
 After the addition of a scalar offset of −0.9 ppmv, monthly mean CO2 concentration, as retrieved from AIRS observations for the northern and southern tropics, is shown on the same figure for the period April–October 2003 (stars). AIRS retrieved CO2 variations agree with the aircraft measurements. In the northern tropics, a clear seasonal cycle is seen, with a maximum in April, a minimum in September, and a peak-to-peak variation of 3.1 ppmv. In the southern tropics, a relatively more complicated variation appears, in agreement with [Matsueda et al., 2002]. Also, the latitudinal variation of the mean AIRS retrieved seasonal cycle, as seen in 8 latitude bands of 5° each, from 20S to 20N, is in good agreement with aircraft observations (not shown).
3.2. Maps of Retrieved Midtropospheric CO2 Concentration
 Maps of monthly mean CO2 concentration are shown on Figure 3 for the four months April, June, August and October 2003, at a spatial resolution of 15° × 15° (1° × 1° moving average). This resolution was chosen to average enough individual retrievals to make robust statistics. After the removal of not-clear observations, the number of individual retrievals, per month and per 15° × 15° grid-box, is about 2000 in regions where clear-sky is prevailing but can be as low as 100 in more cloudy areas. To eliminate possible undetected clouds, boxes having less than 300 individual retrievals are not considered (blank areas on Figure 3). They mostly correspond to the regions of deep convection.
 The decrease of CO2 concentration from April (maximum) to October (minimum), especially in the northern hemisphere, is well seen. As expected, the maximum of variability is found in Spring (April and May), whereas autumnal months (September, October) show a relatively low variability of CO2. In Spring, higher concentrations are found in northern tropics, with a latitudinal 20N to 20S gradient of about 6 ppmv. A decrease of these high concentrations is observed at the beginning of summer, probably due to the increase of photosynthesis activities of the northern biomass. The retrieved latitudinal gradient then decreases and reaches about −1.5 ppmv in September. These values are coherent with several studies made on latitudinal variation of CO2 [Machida et al., 2003; Vay et al., 1999]. In October, the concentration is minimal in the Pacific, particularly in its Eastern part. From July to September, a maximum of CO2 concentration is found east of Africa in the equatorial region. This strong signature, already found with TOVS observations in the years 1987–1991, might be due to pollution in Asia migrating to this region. The obtained variabilities are partly yet not fully understood. A more detailed study of both the transport phenomena and the sources (location and amplitude) is needed to study to what extent the patterns are relevant or not.
 A first estimate of the precision of the retrievals is provided by the monthly standard deviation (std) on the 15° × 15° (1° × 1° moving average) basis [Chédin et al., 2003]. A global dispersion around 3 ppmv (0.8% of the mean CO2 concentration) is observed, the maximum std being found in the months of April–May (3.2 ppmv), when the natural variability of CO2 is high, and the minimum std being found in the months of July–September (2.7 ppmw), when the natural variability of CO2 is low. These values may be seen as the combination of the std of the method (σM) and of the std of the natural variability (σV) [Chédin et al., 2003]. Doing so, σM comes to 2.5 ppmv (0.7% of the mean CO2 concentration) and σV comes to 2.1 ppmv for April and to 1 ppmv for July–September. These values look reasonable as the retrievals are only performed over sea and therefore do not take full account of the variability of CO2 over land.
 Midtropospheric CO2 concentration has been retrieved in the tropics [20S:20N] from the new high spectral resolution sounder AIRS, using a non linear regression inference scheme similar to the one developed for the lower spectral resolution TOVS sounder onboard the polar NOAA platforms [Chédin et al., 2003]. For the time period covered (April to October 2003), the retrieved seasonal cycle, as well as its latitudinal dependence, agree well with in situ aircraft observations made approximately at the same altitude range. Monthly maps of CO2 concentration, produced at a resolution of 15° × 15°, display features in agreement with the known characteristics of the distribution of this gas, influenced by both the transport and the pollution. These features were already observed with TOVS but two differences can be noted: the dynamic of AIRS retrievals is lower and the mean AIRS retrieval precision that has been estimated of the order of 2.5 ppmv (0.7%) is significantly better than the one obtained with TOVS (about 0.9%). Presently limited to night-time and over sea observations, an extension of the method to land and to extratropical regions, as well as to daytime observations, is in progress.
 We are very happy to thank Walter Wolf for his constant help while providing us with AIRS data. We also thank Richard Engelen and Claudia Stubenrauch for fruitful discussions, and the anonymous reviewer for his constructive comments. Calculations were performed at IDRIS, the computer centre of CNRS. This work was supported by the European Community, under contract EVG1-CT-2001-00056 (COCO project).