The use of O 2 1 . 27 μ m absorption band revisited for GHG monitoring from space and application to MicroCarb ”

Monitoring CO2 from space is essential to characterize the spatio/temporal distribution of this major greenhouse 15 gas, and quantify its sources and sinks. The mixing ratio of CO2 to dry air can be derived from the CO2/O2 column ratio. The O2 column is usually derived form its absorption signature on the solar reflected spectra over the O2 A-band (e.g. OCO-2, Tanso/Gosat, Tansat). As a result of atmospheric scattering, the atmospheric path length varies with the aerosols load, their vertical distribution, and their optical properties. The spectral distance between the O2 A-band (0.76 μm) and the CO2 absorption band (1.6 μm) results in significant uncertainties due 20 to the varying spectral properties of the aerosols over the globe. There is another O2 absorption band at 1.27 μm with weaker lines than in the A-band. As the wavelength is much nearer to the CO2 and CH4 bands, there is less uncertainty when using it as a proxy of the atmospheric path length to the CO2 and CH4 bands. This O2 band is used by the TCCON network implemented for the validation of space-based GHG (Green House Gases) observations. However, this absorption band is contaminated by the 25 spontaneous emission of the excited molecule O2*, which is produced by the photo-dissociation of O3 molecules in the stratosphere and mesosphere. From a satellite looking nadir, this emission has a similar shape as the absorption signal that is used. In the frame of the CNES MicroCarb project, scientific studies have been performed in 2016-2018 to explore the problems associated to this O2* airglow contamination and methods to correct it. A theoretical synthetic 30 spectrum of the emission was derived from an approach based on A21 Einstein coefficients information contained in the line-by-line HITRAN 2016 database. The shape of our synthetic spectrum is fully validated when compared to O2* airglow spectra observed by SCIAMACHY/ENVISAT in limb viewing. We have designed an inversion scheme of SCIAMACHY limb viewing spectra, allowing to determine the vertical distribution of the Volume Emision Rate (VER) of the O2* airglow. The VER profiles and 35 corresponding integrated nadir intensities were both compared to a model of the emission based on the chemicaltransport model REPROBUS. The airglow intensities depend mostly on the Solar Zenith Angle (both in model and data) and the model underestimates the observed emission by ∼15%. This is fully confirmed with SCIAMACHY nadir viewing measurements over the oceans: in such conditions, we have disentangled and retrieved the nadir O2* emission in spite of the moderate spectral resolving power (∼860), and found that the 40

In response to your request to implement "Major Revisions" in our manuscript, we are re-submitting a new version Rev6 of our manuscript taking into account your remarks listed in your letter dated October 22. We have cut the main text from 60 pages (before References) to 37 pages only, a cut of 38 %. The deleted material contains essential information for the reader that would wish to reproduce our results, but possibly not essential for all readers. We have therefore re-organized the text with material now put in several Appendices, which should streamline the narrative.
We have also made some modifications relevant to some detailed remarks that you did, in particular in the Spectroscopy Section and now Appendix B.
1.As you suggested we have added in the main text the following sentence: "We should mention that one reviewer was able to show with some manipulations of equations that the same relationship (4) could be obtained from the equations contained in Sun et al. (2018). It clearly stands as a validation of our present work and shows that the two approaches are consistent." 2.You criticize the fact that we jump from energy levels to transitions back and forth. We admit that it seems not so logical, but it has a deep-rooted reason. Since we are not professional spectroscopists as you seem to be, we have conducted our calculations from the informations contained in the HITRAN database, which consists of all transitions of the O 2 molecules between two wavelength limits, one line per transition containing some informations about the upper energy level (necessary to compute exp(-E/kT) ) and the allowed values of J', as described in Simeckova et al. (2006) Therefore, we had to be careful to extract the relevant informations allowing to compute Q tot (T) for example, for any temperature. It is not trivial (not very complicated either) to extract the informations for all energy levels from the HITRAN list of transitions, and we wanted to caution the reader. We have deleted the sentence: "because from a given energy level having a certain population N 2i , there are several transitions going down to the lower level with different A 21 ." and replace the whole sentence by: "Since the HITRAN database consists in a list of transitions, some caution must be used when using the HITRAN database, in order to extract a list of energy levels." and in the caption of Figure now B2, we have deleted the sentence: "There are 5, 7, or 8 values (and transitions) for each black circle in the figure, present in the HITRAN list, because of transitions selection rules and weak lines (below a certain threshold) are not in HITRAN. The V''=1, V'=1 transitions (1,1) are column ratio. The O 2 column is usually derived form its absorption signature on the solar reflected spectra over the O 2 A-band (e.g. OCO-2, Tanso/Gosat, Tansat). As a result of atmospheric scattering, the atmospheric path length varies with the aerosols load, their vertical distribution, and their optical properties. The spectral distance between the O 2 A-band (0.76 µm) and the CO 2 absorption band (1.6 µm) results in significant uncertainties due 20 to the varying spectral properties of the aerosols over the globe.
There is another O 2 absorption band at 1.27 µm with weaker lines than in the A-band. As the wavelength is much nearer to the CO 2 and CH 4 bands, there is less uncertainty when using it as a proxy of the atmospheric path length to the CO 2 and CH 4 bands. This O 2 band is used by the TCCON network implemented for the validation of space-based GHG (Green House Gases) observations. However, this absorption band is contaminated by the 25 spontaneous emission of the excited molecule O 2 *, which is produced by the photo-dissociation of O 3 molecules in the stratosphere and mesosphere. From a satellite looking nadir, this emission has a similar shape as the absorption signal that is used.
In the frame of the CNES MicroCarb project, scientific studies have been performed in 2016-2018 to explore the problems associated to this O 2 * airglow contamination and methods to correct it. A theoretical synthetic 30 spectrum of the emission was derived from an approach based on A 21 Einstein coefficients information contained in the line-by-line HITRAN 2016 database. The shape of our synthetic spectrum is fully validated when compared to O 2 * airglow spectra observed by SCIAMACHY/ENVISAT in limb viewing.
We have designed an inversion scheme of SCIAMACHY limb viewing spectra, allowing to determine the vertical distribution of the Volume Emision Rate (VER) of the O 2 * airglow. The VER profiles and 35 corresponding integrated nadir intensities were both compared to a model of the emission based on the chemicaltransport model REPROBUS. The airglow intensities depend mostly on the Solar Zenith Angle (both in model and data) and the model underestimates the observed emission by ∼15%. This is fully confirmed with SCIAMACHY nadir viewing measurements over the oceans: in such conditions, we have disentangled and retrieved the nadir O 2 * emission in spite of the moderate spectral resolving power (∼860), and found that the 40 2 nadir SCIAMACHY intensities are mostly dictated by SZA and larger than the model intensities by a factor ∼1.13.
It is shown that with the MicroCarb spectral resolution power (25,000) and SNR, the contribution of the O 2 * emission at 1.27 µm to the observed spectral radiance in nadir viewing may be disentangled from the lower atmosphere/ground absorption signature with a great accuracy. Simulations with 4ARCTIC radiative transfer 5 inversion tool have shown that the CO 2 mixing ratio may be retrieved with the accuracy required for quantifying the CO 2 natural sources and sinks (pressure level error ≤ 1 hPa, X CO2 accuracy better than 0.4 ppmv) with only the O 2 1.27 µm band. As a result of these studies (at an intermediate phase), it was decided to include this band (B4) in the MicroCarb design, while keeping the O 2 A band for reference (B1). Our approach is very similar (likely identical) to the approach of Sun et al. (2018) who also analysed the potential of the O 2 1.27 µm band and 10 concluded favourably for GHG monitoring from space. We advocate for the inclusion of this O 2 band on other GHG monitoring future space missions, such as GOSAT-3 and EU/ESA CO 2 -M missions, for a better GHG retrieval.

Introduction
Carbon dioxide (CO 2 ) is recognized as the main driver of climate change. Its evolution in time is therefore 15 scrutinized with attention. The atmospheric fraction is the ratio of the atmospheric increase of CO 2 mass to the mass of CO 2 anthropogenic emission. On decadal time scales, this ratio has been close to 0.5 since the beginning of continuous measurements of atmospheric concentration in the late 50s, despite an increase of the anthropogenic emissions by a factor of 5 (Le Quéré et al., 2018). An atmospheric fraction lower than 1 is explained by the existence of natural sinks that are fuelled by the increasing amount of CO 2 in the atmosphere. 20 The current global carbon budget indicates that the ocean and land surface contribute roughly equally to the sink.
There is little doubt that the oceanic sink will continue in the future despite a solubility decrease induced by raising temperature, while the fate of the land sink is more uncertain (Ciais et al., 2014). There is a lack of understanding of the vegetation dynamic, and its response to increasing CO 2 and changing climate. In fact, there is no consensus whether the land sink is mostly in the tropics, mid-latitudes or boreal regions. This lack of 25 understanding of the vegetation processes limits our ability to anticipate the carbon budget and thus the rate of climate change.
There is therefore a strong need for a better understanding of the carbon cycle and the processes that control the exchanges of carbon between the atmosphere, the vegetation and the soil. This understanding can be obtained through a continuous monitoring of the CO 2 fluxes at the land-atmosphere interface and the analysis of its 30 response to inter-annual climate anomalies. This objective suggests the development of a satellite monitoring system as recognized by the scientific community and several space agencies (CEOS, 2018).
The first satellites to be launched with the aim of monitoring the CO 2 cycle were ENVISAT (ESA) with SCIAMACHY instrument, GOSAT (JAXA) and OCO (NASA). The latter was unfortunately lost at launched, and a very similar satellite, OCO-2, was build and launched. These have been followed by TANSAT (China), 35 GOSAT-2 and OCO-3 on International Space Station. All instruments rely on a similar method to estimate the CO 2 concentration from space: High resolution spectra of the reflected sunlight are acquired over several bands centred on clusters of CO 2 and O 2 absorption lines. The depths of the lines are sensitive to the number of molecules along the sunlight atmospheric path. The so-called differential absorption method makes it possible 3 to infer the amount of absorbing gas along the line of sight, using some ancillary information on the temperature profile. CO 2 is the target component of the atmosphere and O 2 is used as a normalization component to link the CO 2 estimated number of molecule to a mixing ratio. Note that the sunlight atmospheric path length is linked to the surface pressure, but also to the presence of light-scattering particles (aerosols and clouds) in the atmosphere.
Because oxygen is well mixed in the atmosphere, it is adequate for the normalization of the measurement to 5 estimate a mixing ratio.
The instruments currently in orbit focus on the CO 2 absorption bands at 1.6 and 2.0 µm, and the O 2 absorption band at 0.76 µm. The use of the oxygen band poses several challenges: (i) there is still significant uncertainty on the radiative transfer modelling within this band; and (ii) its central wavelength is notably different from that of the CO 2 bands so that the spectral variations of the atmospheric scatterer optical properties may lead to different 10 optical paths.
An alternative could be the use of the O 2 absorption band around 1.27 µm. It is much closer in wavelength to the CO 2 absorption bands which reduces the uncertainties linked to the spectral variations of the atmospheric path. In addition, the absorption lines are weaker than those in the 0.76 µm band so that the radiative transfer modelling may be more accurate. In fact, the 1.27 µm band is the one used for the processing of TCCON 15 spectra for the estimate of column mixing ratio. This band was not selected for current flying CO 2 monitoring missions because it is affected by airglow, a light emitted by oxygen molecules in the high atmosphere. Oxygen airglow at 1.27 µm has a spectrum that is very similar to the oxygen absorption spectrum used to estimate the sunlight atmospheric path. Previous studies (Kuang et al., 2002) conducted during the preparation phase of the OCO mission (Crisp et al. 2004) indicated that the contribution of airglow could not be corrected with the desired accuracy. Conversely, 5 similar studies performed during the design phase of the CNES-MicroCarb mission indicated that the airglow could be distinguished from the oxygen absorption spectrum, provided that the instrument achieve a high spectral resolution. These unpublished studies led to the addition of a fourth band, centred at 1.27 µm, in the MicroCarb optical concept. The MicroCarb mission shall then be the first CO 2 monitoring mission to test the potential of the 1.27 µm band, rather than the 0.76 µm band, for the estimate of CO 2 column concentrations from 10 space. Note that the instrument does carry the classical O 2 band at 0.76 µm both for safety and for comparison purposes. Recently, an independent study (Sun et al., 2018) confirmed the MicroCarb analysis. This paper shows that, indeed, airglow has a spectral signature that is different from that of the oxygen absorption and can therefore be distinguished from the signature of oxygen absorption. It argues for the inclusion of the 1.27 µm band in the design of future CO 2 monitoring missions . 15 In this paper, we describe the analysis of the airglow signature that has been conducted in the context of the MicroCarb preparation.
When describing the choices made to define the OCO investigation to determine CO 2 vertical columns and mixing ratios from nadir viewing observations (which needs associated O 2 columns), Kuang et al. (2002) recognized the virtues of the O 2 band at 1.27 µm (nearest to the CO 2 bands), but discarded its use because it is 20 contaminated by the intense O 2 airglow day side emission when looking nadir from an orbiter ( Figure 1). They quoted Noxon (1982) as having shown that the emission is not only intense, but variable. In fact, Noxon (1982) analysed spectra of this emission collected from 60 flights of a KC-135 aircraft over 10 years and a variety (latitude and seasons) of observing conditions, including two solar eclipses. He reported that there were no secular variations (within 30%), and also that the variations with latitude (obtained along a single flight) were 25 very smooth. This smoothness is comforted by the present study of both the SCIAMACHY data set and the airglow model that we made, combined with a CTM model of ozone (not a climatology).
We have mentioned before that the TCCON ground-based spectrometer array, observing the sun, uses this 1.27 µm band to derive the CO 2 /dry air mixing ratio (because the O 2 /dry air mixing ratio is fixed = 0.2095) rather than the A band, which can also be measured by some TCCON spectrometers. Why? The argument is that the 30 depth of the O 2 lines at 1.27 µm has the same order of magnitude as those of CO 2 , while the A band (760 nm) absorption lines are much stronger. The use of spectral bands with similar absorption depth may reduce small systematic errors (e. g. detector linearity failure) for atmospheric quantities that are based on measurement ratios.
We argue that the same argument can be used for observations from space, although other problems are added (Ring effect of filling the line bottoms, polarization...). 35 Given the level of accuracy which is needed for a useful retrieval of CO 2 , it may not be possible to rely only on an a priori model of the O 2 airglow to subtract it from a nadir-viewing spectrum which contains both the absorption spectrum of O 2 and the emission spectrum at 1.27 µm, closely blended. An exception may be for high surface reflectance scenes, such as glint viewing, when the transmitted-reflected signal gets much larger than the airglow emission. Indeed, for typical scenes, the amplitude of the reflected and airglow spectra are 40 similar, with nearly identical spectral variations. There are nonetheless some differences that make it possible to 5 disentangle one from the other. First, there is the Collision Induced Absorption (CIA) which is present in absorption, but not in emission, since it is proportional to the square of the O 2 density, and therefore confined to lowest altitudes. Second, the emission at 1.27 µm increases linearly with the column of O 2 * at all wavelengths (re-absorption by O 2 is negligible at emission altitude), resulting in a constant relative shape of the emission spectrum, while the absorption spectrum is not linear: the transmittance Tr=exp(-τ) saturates at high optical 5 thicknesses of O 2 τ>1,and the absorption spectral shape is not constant but depends on the air-mass factor. Third, individual rotational lines are subjected to pressure broadening, also proportional to the air density. Therefore, the emission lines occurring at high altitudes are much thinner than the same absorption lines built in the lower atmosphere. These effects are illustrated in Fig. 2. O'Brien and Rayner (2002) have proposed to discriminate the emission from the absorption by recording one single line at very high spectral resolution (resolving power of 10 400,000), with an imager and three very narrow filters, whose positions are indicated on Fig. 2. One difficulty with this scheme is that the photon flux collected in those three narrow bands is very small and corresponding SNR strongly reduced, rendering this proposal unpractical. By contrast, the size of a pixel element of MicroCarb (corresponding to a resolving power 25,000) is also indicated for comparison. The whole spectrum is recorded, and the shoulders of the absorption line contribute to the disentangling of emission and absorption in a retrieval 15 exercise, with 1024 pixels distributed along the O 2 band. This paper is organized as follows. We have made use of several Appendices in order to ease the reading of the most important results. In Section 2 a brief review of previous observations of the O 2 (0,0) airglow emission at 1.27 µm is presented first. Then the details of the spectral structure of this band are described in Appendix B, together with a method to compute accurately the shape of the airglow spectrum. In Section 3 we describe how the SCIAMACHY observations of this airglow at the limb have been processed in order to derive VER (Volume 5 Emission Rate) vertical profiles, and how a synthetic spectrum may be derived from combining the VER profile and our spectroscopic studies. Our model spectral shapes are validated by a comparison with SCIAMACHY observed shapes. The method of vertical inversion of the limb observations to retrieve a vertical profile of the airglow emissivity is described in Appendix C (onion-peeling accounting for O 2 absorption). In Section 4 we compare the airglow total nadir intensities and VER profiles derived from SCIAMACHY limb observations with 10 our REPROBUS airglow model (described in details in Appendix A). A deficit of airglow from the model is found. Another comparison (Appendix D) of the ozone predicted by REPROBUS with GOMOS/ENVISAT observations indicates a deficit in ozone which, when accounted for, would narrow the discrepancy between SCIAMACHY and the airglow model. The Microcarb space mission with its instrument is briefly described in Section 5, while in Appendix E the accuracy and bias results of the O 2 column retrievals (surface pressure) and 15 O 2 airglow intensity disentangling from nadir MicroCarb simulated spectra are detailed in some typical situations. It is shown in Section 6 that the O 2 airglow emission may be extracted form nadir viewing SCIAMACHY observations over the oceans, where the reflectance is minimal, in spite of its moderate spectral resolution. In Appendix F some other cases where absorption measurements could be contaminated by airglow emission are examined. In Appendix G is illustrated some corrections made to SCIAMACHY Level1c spectra to 20 extract the absolute spectral radiance. Finally some conclusions are drawn, with a prospective on future GHG monitoring space missions. The aeronomical emission at 1.27 µm was first observed in 1956, in the "dayglow" (daytime aeronomical emissions) from instruments on board soviet stratospheric balloons (up to 30 km altitude) (Gopshtein and Kushpil, 1964), but its origin was not understood at that time. Noxon and Vallance Jones (1962) recorded spectra from a KC-135 plane flying at 13 km of altitude and described the origin of the emission in the form of 30 the electronic transition of the oxygen molecule from an excited state to the fundamental, with the emission of a photon in one of the rotating branches of the (0,0) transition that form the entire "1.27 µm atmospheric IR band":

Observations and spectroscopy of O
(1)

35
The recorded intensity was very large (more than 10 MegaRayleigh, one Rayleigh = 10 6 /4π photons cm -2 s -1 sr -1 ), but atmospheric absorption in the very same band absorbs most of it before reaching the ground. There are various ways to produce an O 2 molecule in its excited state a 1 Δ g , which are detailed in Appendix A.
Once it is produced, it remains there with a long lifetime, about 75 minutes, and is spontaneously de-excited by emitting a photon, or also by a collision without a photon ("quenching"). The most important mechanism of production of these excited molecules is the photolysis of ozone by solar UV: which therefore occurs during the day, but can be observed more easily from the ground at dusk with a high intensity of 30 MegaRayleigh.
At night, the emission falls to 100 KiloRayleigh, but this time the origin of the molecules a 1 Δ g is mainly due to 10 the recombination of oxygen atoms O in their fundamental state O( 3 P):

Space Observations of the 1.27 µm 15
With a sounding rocket Evans et al. (1968) were able to reconstruct for the first time the vertical distribution of the emission at 1.27 µm, by inverting the brightness integral. Their VER (Volume Emission Rate) profile showed that emissivity is highest at about 50 km (∼ 10 7 photons cm -3 s -1 ), and zero or low below 30 km (due to quenching and screening of solar UV by ozone). A secondary maximum at about 85 km is due to the presence of 20 a layer of mesospheric ozone well documented by GOMOS/ENVISAT in star occultation mode of observation (Kyrölä et al., 2018).
From space, the following observations at the limb should be noted: -the SME satellite (Solar Mesospheric Explorer), Thomas et al. (1984).
-the IR SABER photometer on board the NASA TIMED aeronomy mission, (Mlynczak et al., 2007). 25 -the OSIRIS spectrometer (Optical Spectrograph and InfraRed Imager System) on the ODIN satellite (Llewellyn et al. 2004).
The objective of observations is generally to derive the concentration of O and O 3 in the upper atmosphere. 30

Spectroscopy and modelling of a synthetic spectrum of the O 2 * airglow.
The spectroscopy of the O 2 molecule and the modelling of a synthetic spectrum of the O 2 * airglow are described with some details in Appendix B. We relied on the HITRAN spectroscopic database, both to illustrate the 35 structure of P, Q, R branches of the 1.27 µm electronic transition, and to verify a theoretical relationship between the absorption and the emission in this band. By using some equations form the paper of Simeckova et al. (2006) which describes how was obtained the parameters contained in HITRAN data base, we obtained a very simple result on the ratio of emission ε(k) to absorption line strength S ν (k,T) for each line: This equation is the same as equation (B13) of the Appendix B, where the various constants are described, and T is the temperature of the atmosphere in which is produced the airglow.
We have used this formulation to transform an absorption spectrum by O 2 that can be easily computed with LBLRTM software (see details in the Appendix B) into a synthetic absorption emission spectrum. This method 5 of construction of a synthetic emission spectrum was the basis of our work on three topics: a satisfactory comparison with the observed spectra of SCIAMACHY (see below); retrieving the airglow intensity from SCIAMACHY nadir data over low albedo regions; retrieving the surface pressure from simulations at high spectral resolution.
We should mention that one reviewer was able to show with some manipulations of equations that the same 10 relationship (4) could be obtained from the equations contained in Sun et al. (2018). It clearly stands as a validation of our present work and shows that the two approaches are consistent.
3. The use of SCIAMACHY data for the study of the O 2 ( 1 Δ) emission 15 Several space instruments have been used in the past for the study of the O 2 ( 1 Δ) emission, mainly to retrieve the O 3 concentration: the Solar Mesosphere Explorer satellite (SME, Thomas et al., 1984); one infra-red radiometer aboard the satellite OHZORA, (Yamamoto et al., 1988); one infra-red imager a part of OSIRIS instrument on board ODIN (Llewellyn et al., 2004); the SABER broad band photometer on board TIMED NASA mission (Russell et al., 1999;Gao et al., 2011) and SCIAMACHY spectrometer on board ESA ENVISAT 20 mission (Burrows et al., 1995) . We have used the SCIAMACHY data because of the spectral capability (resolution λ/dλ∼850) and extensive produced data set during the ESA/ENVISAT mission.

25
SCIAMACHY is a multi-channel spectrometer dedicated to the study of Earth's atmosphere on board the European Space Agency Envisat satellite. The name is the acronym of SCanning Imaging Absorption SpectroMeter for Atmospheric CHartographY (Burrows et al., 1995, Bovensmann et al., 1999. It is an eightchannel grating spectrometer that measures scattered sunlight in limb and nadir geometries from 240 to 2,380 nm. In addition it was operated also in solar and lunar occultation. In this study, we have used both limb and 30 nadir measurements covering the O 2 ( 1 Δ) band (1,230-1,320 nm) in the spectral channel 6 (1,050-1,700 nm).
In a recent study to retrieve the volume emission rates of O 2 ( 1 Δ) and O 2 ( 1 Σ) in the mesosphere and lower thermosphere, Zarboo et al. (2018) have used a special mode of SCIAMACHY: the MLT limb scan mode, dedicated to the study of the mesosphere and lower thermosphere in the region 50-150 km. This mode was used only twice a month from July 2008 until April 2012. In contrast, we have used the normal limb mode viewing 35 geometry, where SCIAMACHY tangentially observes the atmosphere from the surface up to about 100 km with a vertical step of 3.3 km. At each tangent point, the FWHM of the FOV is 2.6 km (with a somewhat coarser vertical resolution), the horizontal along-track resolution is about 400 km, and the horizontal cross-track bertaux 1 nov. 19 15:29 Mis en forme: Police :10 pt bertaux 1 nov. 19 15:29 Mis en forme: Police :10 pt 9 resolution is 240 km. To improve the signal-to-noise ratio, the four cross-track spectra at the same elevation step are co-added, reducing cross-track resolution to 960 km (the swath width).
To generate data for our study, we used the SCIAMACHY dataset level 1b version 8.02 that we converted into level 1c radiometrically calibrated radiances (in physical unit) by using the SCIAMACHY command line tool SciaL1c version 3.2. Before deriving the O 2 ( 1 Δ) VER profiles, we had to perform a few corrections on the level 5 1c radiance spectra, as illustrated in Appendix G. First we subtracted the average of the 4 spectra measured above 105 km tangent height (generally around 150 km or 250 km) as a dark spectrum from the measured spectra at all of the other tangent heights. This high altitude spectrum contains some residual spectral (readout) patterns left from the calibration step. All spectra contain two bad pixels at wavelength 1262.267 nm and 1282.128 nm. In order to correct these two pixels we replaced their value by the average of their two 10 surrounding pixels. When the tangent altitude of the LOS decreases, there is an increasing background signal due to the Rayleigh and/or aerosol scattering outside the O 2 band. We corrected the spectra from this signal by removing a straight line computed as a linear interpolation between the two "surrounding" average backgrounds (estimated from the median value of all points to avoid outliers) in the [1235][1236][1237][1238][1239][1240][1241][1242][1243][1244][1245] nm domain and in the [1295-1305] nm domain. The spectra after correction are ready to be used for the retrieval of the SCIAMACHY O 2 ( 1 Δ) 15 volume emission rate (VER), as described in Appendix C. An onion-peeling method, modified to account ofr the re-absoprtion of O 2 , allows to retreive the VER vertical distribution from any limb scan. Then the VER is integrated vertically, yielding the O 2 ( 1 Δ) intensity that would be observed at nadir for an observer located at the tangent point of the limb scan.
In Fig. 3 the nadir radiances (equivalent to intensities or brightnesses) derived from a series of SCIAMACHY 20 limb scans along one particular orbit are plotted as a function of Solar Zenith Angle (SZA), when different atmospheric models are used. For each model, there are two branches, corresponding to North and South along the dayside polar orbit of ENVISAT (the North branch is in winter, while the South branch is in summer for this orbit). We see that the choice of the atmospheric model in the computation of the O 2 absorption has a small (∼3%) but noticeable impact (on the brightness seen at nadir). We have also plotted the prediction of the 25 REPROBUS model, as described in Section 4 and subsection 4.2.1. It should be noted that the choice of the "adapted climatology" makes it possible to reduce the separation between the two branches and thus to be closer to the separation between the two branches obtained with the REPROBUS model.

Computation of synthetic spectra and comparison with SCHIAMACHY observed spectra
Once we have the vertical profile of VER corresponding to a given SCIAMACHY limb scan, we can compute 10 the spectrum of the local emissivity (in absolute units of photons/ (cm 3 s 1 sr nm)) with the theoretical approach developed in Appendix B. Then we may integrate the spectra with Abel's integral along horizontal LOS tangent at the limb, for a direct comparison with the actually observed SCIAMACHY spectra. In this particular exercise, we did not account for the O 2 absorption for simplicity, and for this reason we restricted our comparison to altitudes >60 km. The spectral resolution of SCIAMACHY was used to smooth the high resolution spectra (line 15 by line) obtained from the approach described in Appendix B.
In Fig. 4 are represented the locations of the tangent points of SCIAMACHY limb scans for a particular orbit of ENVISAT. In Fig.5a are represented the observed spectra, binned by altitudes (60-70 km, 70-80 km, and 80-90 km), along with our model spectra computed for the same scans and binned in the same way, for a particular limb scan (points in green in Fig. 4). The agreement is basically very good, both in shape and intensity. We note 20 that the model is slightly brighter than the data, and the relative difference is larger for the bin 60-70 km than for the other bins. We tentatively assign this behaviour to the fact that we have not accounted for the O 2 absorption along the LOS in the model, more important at 60-70 km than higher.  to the O 2 absorption. In this case, the R branch is systematically overestimated by this crude model.   The ratio of measured spectra /model spectra, Sobs/ Smod were averaged together for all scans of that particular 5 orbit within the same three altitude bins. They are represented on Fig. 6, both for the crude model (absorption = emission, left), and for our "true" model of emission (right). It is clear that the crude model does not represent well the observed spectra, while the model with the true emission agrees quite well with the data. This comparison validates completely the approach that we developed in Section 2 and Appendix B, except that the overall level of the ratio is slightly below 1 (right panel). Again we assign this behaviour to the fact that we have 10 not accounted for the O 2 absorption along the LOS in the model, and it can be seen that the ratios are nearer 1 for larger altitudes. Below 1255 nm and above 1285 nm, the intensity of the spectra is very small and thus we attribute the noisy shape of the ratio spectra to low SNR.

Climatology of O 2 * VER derived from SCIAMACHY limb radiances
To build up a climatology of the O 2 * emission at 1.27 µm, we have applied our inversion scheme to get VER 5 vertical distributions (Appendix C) to all SCIAMACHY limb data collected during the first 3 days of each month of year 2007. Note that in the normal mode, the limb scans extend down to 0 km (our inversion is made >30 km), while in the special SCIAMACHY MLT mode, only altitudes >50 km are observed. Our data base contains the analysis of 448 orbits, containing 12,400 limb scans in the normal mode which go down sufficiently for our purpose (some limb scans do not reach low enough altitudes to allow retrieval of the full VER profile 10 above 30 km).
The vertical inversion of SCIAMACHY limb radiances to get a VER vertical profile is done below 90 km, down to 0 km; but only results>30 km are significant, because at the limb and low altitudes, there is Rayleigh and aerosol solar radiation scattering (the useful signal for SCIAMACHY limb mode ozone retrieval) which dominates over the O 2 * radiance. Once a VER profile is obtained, it can be integrated vertically, taking into 15 account the absorption by O 2 . Therefore, a "SCIAMACHY" nadir radiance is obtained, which corresponds to the O 2 * radiance that would be observed by SCIAMACHY if it were observing nadir at the position of tangent points where the limb radiances were obtained. In fact, the nominal operation mode of SCIAMACHY does indeed alternate limb-viewing and nadir-viewing observations to discriminate tropospheric ozone from stratospheric ozone (Ebojie et al., 2014). 20 When this VER is integrated vertically to get a nadir radiance, the integration stops at the upper limit of 80 km in order to have a better comparison with the REPROBUS model which stops also at 80 km. The air atmospheric model selected to compute the re-absorption by O 2 is our so-called "adapted climatology" (see Appendix C). In Fig. 7 about one third of all VER profiles collected for the first three days of January 2007 are displayed (other months are quite similar). The colour code corresponds to the SZA of the limb scan. We kept also scans near the 25 terminator, where the VER is significant only above 80 km. Clearly the SZA is the factor dominating the shape, the peak altitude and the intensity of the airglow VER profiles between 30 and 80 km. This is due to UV photodissociation of ozone (the main process of O 2 * production) penetrating more deeply when the SZA is small (because of ozone UV screening). The lower the SZA, the brighter is the airglow emissivity. Above 80 km, other processes come into play and a second airglow peak is observed which seems less correlated with the SZA than 30 is the main peak at 45-50 km. The altitude of the main airglow emissivity peak varies between 43-45 km for values of SZA below 50° and increases for higher values of SZA up to about 60 km. brightness is displaced with season, following the latitude of the sub-solar point, again an effect of the SZA dependence of the O 2 * radiance. This is illustrated in Fig. 9 where all the nadir radiances are plotted as a function of SZA, with a colour code on latitude. The lower SZA, the brighter is the nadir emission. Still, there is a separation of the curves in two branches that are relevant to northern and southern hemispheres. The separation between the two branches depends on the season. As we will see later on, the overall pattern of the O 2 * radiance 15 is directly linked to the climatology of upper stratosphere/ lower mesosphere ozone.

16
In this section we compare the predictions of a dedicated 3D model of the airglow emission of O 2 (a 1 Δ g ) at 1.27 µm to the airglow observations of SCIAMACHY. The comparison makes use exclusively of the SCIAMACHY limb observations, but is made in two different ways. One way is to compare the SCIAMACHY VER vertical profile retrieved from limb measurements through vertical inversion as described in Appendix C. The second way is to compare the nadir integrated emission I ag (brightness) of the airglow. Both model and data nadir 5 emissions are obtained by vertical integration of the VER, respectively in the airglow model and in the SCIAMACHY-derived VER vertical profile. This nadir emission is directly relevant to the GHG observations since, from an orbiter and nadir viewing, this signal is superimposed on the solar back-scattered emission from which the columns of GHG gases and O 2 must be retrieved. This is why it is not practical to use the nadir observations of SCIAMACHY to study the O 2 * airglow, since the nadir signal is dominated by surface back-10 scattered solar radiation (except in special conditions, over the seas, as we shall see in Sub-section 6.2.2).
Since the photolysis of ozone is the major source of the O 2 (a 1 Δ g ) airglow, it was also felt necessary to compare the ozone density predicted by our airglow model and GOMOS (Global Ozone Monitoring by Occultation of Stars) ozone measurements also on ENVISAT, simultaneous with SCIAMACHY observations (but not with the same geometry), as described in Appendix D.

REPROBUS 3D simulations 25
REPROBUS is a global CTM (Chemical Transport Model) developed for the stratosphere (Lefèvre et al., 1994). well as the integrated O 2 (a 1 Δ) emission in coincidence with the GOMOS and SCIAMACHY measurements performed the same year. This dataset represents 4,026 profiles modelled in coincidence with GOMOS and 12,800 in coincidence with SCIAMACHY. The statistical analysis of the comparison between the model and observations is presented in sub-section 4.2 for SCIAMACHY observations and in Appendix D for GOMOS observations. It should be noted that, as a result of some discrepancies revealed by this comparison, the 5 REPROBUS model will be modified in the future for a better representation of mesospheric ozone. Although the retrieval of O 2 column does not need a model, it is likely that the output of the improved REPROBUS model (O 2 * intensity) will be used as a prior information in the retrieval process.

Simulation of airglow emission of O 2 (a 1 Δ g ) at 1.27 µm 10
Here we do not care about the details of the spectral shape of the emission, but rather we compute the local emissivity (VER) and the vertically integrated emission, in order to compare with SCIAMACHY observations. The airglow at 1.27 µm is calculated off-line from the 3D outputs of the REPROBUS model. It takes into account all the mechanisms of production and loss of O 2 (a 1 Δ), as detailed in Appendix A and shown in Fig. 10. 15 In practice, the O 2 (a 1 Δ) emission model uses as input the ECMWF temperature and pressure profiles as well as the O 3 and O( 3 P) profiles calculated by REPROBUS for the selected date and location. From the pressure and temperature are also calculated the total density and density profiles of N 2 , O 2 , and CO 2 . The airglow model then provides the vertical profiles of the mixing ratios of O( 1 D), O 2 (b 1 Σ), O 2 (a 1 Δ), the vertical profile of the volume emission rate (VER) at 1.27 µm expressed in photon.cm -3 .s -1 , and the vertically integrated intensity expressed in 20 photon.cm -2 .s -1 .sr -1 (brightness or intensity, directly comparable to the radiance signal of the solar radiation backscattered by the gaseous atmosphere, aerosols and the surface).
Two versions of the airglow model were used. One early version of the model (v01) was later modified to a version v02 which yielded better agreement with SCIAMACHY observations. They differ only by the value of the quenching rate of the O 2 ( 1 Δ). The early version v01 contained a quenching constant k: 25 At stratospheric temperatures, the value of k Δ,Ο2 is decreased with v02 by about 10%, enhancing the emission 30 rate of O 2 ( 1 Δ). This gives a better fit (but not perfect) between SCIAMACHY observations and the airglow model. According to Wiensz (2005), this IUPAC recommended value gives a better agreement between OSIRIS/ODIN direct and indirect measurements of ozone. Unless otherwise specified, we are presenting in this paper the v02 results.

Some examples of model results
As an example, Figs

Comparison of SCIAMACHY data with REPROBUS derived airglow model
For each observation of our SCIAMACHY 2007 data set in limb viewing we have a co-located VER profile of O 2 (a 1 Δ) calculated by the REPROBUS-based airglow model. We were therefore able to make comparisons 10 between the airglow of SCIAMACHY and that of REPROBUS in two different ways: i) The brightness of the airglow as it would be seen by a TOA (Top Of Atmosphere) observer in nadir viewing. ii) the VER (Volume Emission Rate) airglow vertical profiles.

Comparison of O 2 (a 1 Δ) airglow brightness as seen by a TOA observer in nadir view 15
The airglow model brightness is obtained by a vertical integration of the VER produced by the airglow model.
Re-absorption by O 2 in nadir geometry is small and has been neglected. However, this nadir model intensity cannot be directly compared with a nadir observation of SCIAMACHY, as it is most of the time completely dominated by terrestrial albedo. Therefore, to evaluate the nadir intensity corresponding to the SCIAMACHY 20 data in limb viewing we proceeded as follows: -for each vertical scan at the limb with SCIAMACHY, the total brightness of the airglow was first estimated by integrating spectrally the SCIAMACHY spectra at each altitude, and then the VER profile was determined with an onion-peeling method (taking into account horizontal re-absorption), as described in Appendix C.
-then the VER was vertically integrated to yield the intensity (or brightness) that an observer placed above the 25 tangent points of the SCIAMACHY scan would see looking to nadir. Figure 12 compares the nadir intensities as a function of SZA co-located for SCIAMACHY and REPROBUS for the first three days of January, April, July and October 2007. This represents the data collected over ∼ 50 orbits of ENVISAT for each considered month. The ENVISAT orbit is almost polar and descending in latitude on the day side (equator crossing around 10:30 Local Time, descending node). In both data and model the SZA is the 30 dominating factor for the intensity. The latitude (which is colour coded in the plot) plays also a small role (through the ozone field), more important in July. The repeatability of the SCIAMACHY derived nadir intensities is obvious, with very little dispersion. The main difference between data and model is that at SZA < ~70° the REPROBUS/airglow model systematically underestimates by 10-20 % the airglow intensity compared to that seen in the SCIAMACHY data. 35 Note regarding the SZA of the SCIAMACHY data: We noted that the SZA value provided in the SCIAMACHY ESA products in limb viewing, as defined in the data product, is the SZA value of one of the two points (the nearest to ENVISAT) corresponding to the intersection between the LOS and TOA (Top of Atmosphere defined at 100 km altitude). But what we need is the SZA of the tangent point of the line of sight (LOS), which is different. Therefore, we systematically calculated the SZA at the tangent point of the 40 SCIAMACHY LOS using an external tool (IDL routine). All results presented in this report are obtained using  Note that in Fig. 12 there is a remaining difference between the minimum SZA of the SCIAMACHY data and the minimum SZA of the model of up to about 8°. This difference may be explained due to the UT time difference between the model and the data since, unlike the data, the model was calculated on a fixed UT time 10 grid with a round hour (e.g. 10:00, 11:00, etc.). There is therefore a time difference between model and data of up to 30 minutes, which can be both ways in difference of SZA, SZA(model)-SZA(data). The true SZA is the data one; and the model SZA may be the same as the data ± 8°, but only the negative differences SZA(model)-SZA(data) are obviously visible on the plot, when SZA(data) is at its minimum value, and SZA(model) is below SZA(data). Points with positive differences are just mixed with all other points. 15

Comparison of VER vertical profiles
We have seen systematic differences between the nadir intensities (vertically integrated VER) of SCIAMACHY and REPROBUS. It is therefore interesting to pinpoint at which altitude the differences are essentially located, 20 by directly comparing the vertical VER profiles produced by the REPROBUS model and those that could be derived from the SCIAMACHY limbs by onion-peel inversion. The comparison of some typical VER profiles of SCIAMACHY and REPROBUS is illustrated in Fig. 13  One obvious possible reason for this discrepancy would be the radiometric calibration of SCIAMACHY in this airglow band. For the time being, we reject this hypothesis for two reasons. The first is that the radiometry of SCIAMACHY must have been verified with nadir viewing observations when the surface albedo is dominating, and comparing to MODIS results for instance. The observation of Deep Convective Clouds (DCC) found in the 5 tropics, which begin to become a standard in Earth Observations radiometric calibration, might be an additional source of comparison. The second reason is that the onion-peel inversion scheme that we have designed to derive VER vertical profiles is a linear one. Therefore, changing the calibration of SCIAMACHY by a scaling factor would also change the VER profile by the same factor, while we see that the VER discrepancies are changing with altitude. Other sources of discrepancies might come from the ozone distribution (as examined in Appendix 10 D), or in some details of the airglow model. Focusing our attention to the altitude range 40-70 km where most of the emission occurs, it seems that the relative difference behaviours with altitude are identical for SZA= 80° and 60° (green and blue curves) with a peak of discrepancy at 67 km, while for SZA around 30° the peak of discrepancy is at a lower altitude ∼ 58 km. 25 In Appendix D we compare the ozone profile calculated by REPROBUS with ozone measurements taken by

The MicroCarb mission dedicated to CO 2 investigations
In the domain of Earth Observations and GHG monitoring, CNES (Centre National d'Etudes Spatiales) has developed the MicroCarb mission, a space observatory dedicated to CO 2 monitoring. As a result of the studies conducted since 2016 by CNES concerning the use of the 1.27 µm O 2 band reported in the present paper, it was 15 decided to incorporate in the instrument the 1.27 µm O 2 band as band B4.
The MicroCarb mission builds on a high spectral resolution infrared grating spectrometer onboard a microsatellite. The satellite platform is an enhanced version of the Myriade family. The total mass of the satellite including payload is 170 kg for a power of 100 W. MicroCarb will be launched in 2021 on an 11h30 ascending node or alternately13h30 descending node helio-synchronous orbit (to be decided later). 20 The MicroCarb data consists of the measurement in four spectral bands of the solar irradiance reflected by the surface and partially absorbed by atmospheric gases. Two bands are dedicated to the measurement of CO 2 24 around 1.60 µm (weak CO 2 B2) and 2.04 µm (strong CO 2 B3). Two spectral bands are dedicated to O 2 around 0.76 µm (strong O 2 B1) and 1.27 µm (weak O 2 B4). Figure 15 illustrates typical radiances in the four MicroCarb bands and Table 1 gives the main properties of the MicroCarb bands. The mechanical implementation on a micro-satellite is enabled by a very compact design of the instrument, having a unique telescope, one slit per band, a unique grating and a unique Sofradir Next Generation Panchromatic 1024 x 1024 pixels detector for the 5 four bands [Pasternak et al. 2016].  look at sunglint over seas and lakes. Specific observations will be dedicated to calibration (target, sun, internal lamp, internal shutter, cold space, Moon) or probatory experiments (local mapping).
The MicroCarb ground segment will produce five levels of products: level 0 (L0) corresponding to raw telemetry, L1 to spectra calibrated for radiometry, spectrometry and geometry, L2 to dry air column-averaged 5 CO 2 volume mixing ratios, L3 to space and time averages of the L2, and L4 to surface carbon fluxes.
The computation of L2 products from L1 data is a very active research field (see e.g. Boesch et al. (2011), Crisp et al. (2017), Hasekamp et al. (2015), Heymann et al. (2015), Yoshida et al. (2011). The MicroCarb is developing its own inversion tool named 4ARTIC (4AOP Radiative Transfer Inversion Tool). This tool is based on the optimal estimation described in Rodgers (2000). 4ARTIC retrieves CO 2 and H 2 O on 19 vertical layers, 10 mean and wavelength slope of albedo for each band, surface pressure, aerosol properties, 0.76 µm fluorescence, potential instrumental parameters, and the 1.27 µm airglow emission as described hereafter.
The prior information will be provided by the ECMWF analysis for pressure, temperature and humidity, CAMS (Copernicus Atmosphere Monitoring Service) for CO 2 and aerosols, PlanetObserver for the digital elevation model (https://www.planetobserver.com/products/planetdem/planetdem-30/) and Sentinel 2 images for albedo 15 (from the Multi Spectral Instrument MSI, the unique instrument on-board Sentinel-2). The jacobians (partial derivatives of the spectrum with respect to geophysical variables) will be computed by the 4AOP radiative transfer code (Scott and Chedin, 1981). The scattering by molecules and aerosols will be computed by a discrete ordinated scheme using LIDORT (Spurr, 2012).
A major difficulty for passive spectrometry space missions dedicated to trace gases is to handle the perturbation 20 of the light path by the aerosol scattering. Aerosols may increase or decrease the optical length, depending on conditions. The available prior information about aerosols (type, density, vertical distribution, optical properties) is poor, as well as the aerosol information content in the spectrum. A specific retrieval scheme was therefore developed for 4ARTIC to handle aerosols as an equivalent distribution with a limited number of free parameters.
The vertical distribution of aerosols is described as a Gaussian: 25 where A' is a normalization coefficient, and the width of the Gaussian w aer is linked to the height Z aero of peak aerosol concentration by: 30 where w 0 equals to 4 km. This scheme is inspired from Butz et al. (2009). The spectral dependence of Aerosol Optical Depth (AOD) is described by the Angström coefficient kaero: where σ is the wavenumber and σ 0 a wavenumber reference. 4ARTIC then retrieves three aerosol parameters at the same time as CO 2 : the AOD at σ 0 =0.76 µm, the altitude of the maximum of the gaussian (Z aero ) and the Angström coefficient (kaero). The Single Scattering Albedo (SSA) of one aerosol particle is currently fixed to 1 and the phase function is described by the Henyey Greenstein function with g currently fixed to 0.8, a value used frequently in the literature to describe preferential forward scattering, but could be adapted if necessary.
One of the main purposes of the O 2 bands is to provide information about aerosols. Contrary to MicroCarb, most 5 of the current CO 2 missions (e.g. GOSAT (Yokota et al., 2009) or OCO-2 (Crisp et al., 2017)) acquire only one O 2 band, at 0.76 µm. As this band is spectrally far from the CO 2 bands, any spectral dependence of the aerosols will disturb the evaluation of aerosol impact in the CO 2 bands. As an example the OCO-2 products are known to be sensitive to aerosols, making a bias correction post-processing mandatory (O'Dell, 2018).
The instrumental concept of MicroCarb gave the possibility to carry four spectral bands. The MicroCarb Mission 10 Group chose the same 0.76, 1.60 and 2.04 µm bands as OCO-2 or GOSAT, and chose the additional 1.27 µm O 2 band in order to get aerosol information spectrally closer to the CO 2 bands, and therefore to better constrain the kaero Angström coefficient.
6. Using a synthetic spectrum of O 2 *airglow emission to disentangle it from O 2 absorption in nadir 15 viewing

Overview
With the theoretical shape of the O 2 * dayglow emission spectrum (Appendix B) and a selected VER vertical 20 profile (e.g., Fig. E1), it is possible to construct a synthetic spectrum of the dayglow in absolute radiance units at the native spectral resolution of LBLRTM (several 10 5 ), which may be degraded to any spectral resolution to simulate various instruments. For a given surface albedo and SZA, the radiance of solar radiation scattered by the surface modified by O 2 absorption may also be computed, using LBLRTM. Adding both spectra is a simulation of what will be seen by a nadir-viewing instrument (in the case of no aerosols) in the region around 25 1.27 µm, as shown on Fig. 16 for two cases with different albedos and SZA, where the two spectra are separated.
The contribution of atmospheric Rayleigh scattering is small at this wavelength and ignored in this exercise.  -airglow lines are narrower than absorption lines (no pressure broadening at high altitude).
-the CIA (Collision Induced Absorption) affects only the O 2 absorption spectrum.
-as shown in Section 2 and Appendix B the ratio of O 2 * emission to O 2 absorption is not a constant, but a 15 changing continuous function of the wavenumber ν (in cm -1 ). 28 Basically a retrieval software tool allowing to determine from an observed spectrum simultaneously the albedo, the O 2 vertical column (or surface pressure P surf , when the water vapour is ignored), and the O 2 * airglow intensity consists of two parts: a forward model to simulate what would be observed (depending on the parameters to be retrieved), and a scheme to minimize the chi 2 of the fit of the observed spectrum by the simulated spectrum (Levenberg-Marquardt). 5 For the present study we have developed the LATMOS breadboard, a software (in IGOR language) dedicated first to proof of concept for the use of the O 2 band at 1.27 µm in presence of O 2 * airglow contamination, and then applied it to SCIAMACHY nadir observations, showing that when the albedo is weak, the O 2 *airglow intensity may be identified and its intensity actually measured, as a scaling factor of a synthetic airglow spectrum ( see below Sub-section 6.2). We have also used the 4ARCTIC software to evaluate the performances 10 of the particular Microcarb instrument configuration (wavelength coverage and spectral resolution) and specified SNR as a function of spectral radiance of the nadir-viewing scenery (Sub-section 6.3).

15
The possibility to extract 1.27 µm airglow information from nadir SCIAMACHY spectra is limited by the relatively low resolving power of this instrument (about 860). The intensity of the sunlight reflected by the surface and the atmosphere is in general much larger than the airglow in this spectral band. This is true above continents but above ocean, where the near infrared albedo is very low, it should be possible to extract the airglow when the sky is clear. We tested this possibility using the spectral inversion LATMOS breadboard, 20 originally developed to test the possibility to determine the airglow intensity in the 1.27 µm O 2 band in the MicroCarb CO 2 mission.

25
As said above, the spectrum observed by SCIAMACHY in the 1.27 µm band at nadir is the sum of the nadir solar flux reflected by the ground and the atmosphere, partly re-absorbed by atmospheric O 2 , and the airglow O 2 * emission spectrum. For clear sky conditions if we neglect the reflection by the atmosphere, the reflected solar spectrum may be expressed as: where: • A: albedo (assuming a Lambert law (isotropic) reflectance) • λ: wavelength • F(λ): Solar spectrum outside atmosphere 35 • SZA: solar zenith angle • T atm : one way vertical atmospheric transmission The airglow spectrum is assumed to be proportional to the logarithm of the atmospheric O 2 transmission at high altitude multiplied by the emission to absorption ratio ε(λ)/SS(λ) as explained in Appendix B. The relative intensity of the lines depends mainly on temperature. To take into account this dependency, we represent the 40 29 airglow spectrum Ag(λ) as a linear combination of a warm spectrum Ag warm (λ) and a cold spectrum Ag cold (λ).
These warm and cold spectra are computed using US standard atmosphere transmission tables from LBLRTM for nadir viewing around 50 km where the temperature is higher (270 K) and 70 km where the temperature is lower (217 K):

Ag warm (λ) ≈C norm .[Ln(T 51km (λ))-Ln(T 49 km (λ)].[ε(λ)/SS(λ)]
(9) 5 (10) where T z (λ) is the transmission at wavelength λ from altitude z to the top of the atmosphere and C norm a normalisation constant determined in order that the integral of the spectrum is equal to the integral of a reference 10 spectrum, and using equations (B15) and (4).

Ag cold (λ) ≈C norm .[Ln(T 71km (λ))-Ln(T 69 km (λ)].[ε(λ)/SS(λ)]
A Levenberg-Marquardt (L-M) method is used to determine the parameters giving the best fit to SCIAMACHY spectra. The total column of O 2 , assimilated to surface pressure, the airglow, the H 2 O column and the albedo are inverted using the L-M converging scheme. As atmospheric transmission depends non-linearly on the O 2 column, its Jacobian is calculated at ground level from the difference in transmission between the ground and 1 15 km altitude.
The measured spectrum will therefore be expressed as: where K 1 is the intensity of the reflected spectrum (albedo); K 2 : is the sensitivity of the reflected spectrum to surface pressure; K 3 is the warm component of the airglow spectrum; K 4 is the cold component of the airglow spectrum and K 5 is the ratio H 2 O column / reference column. The coefficients K 1 , K 2 , K 3 , K 4 , K 5 can be imposed or left free in the L-M inversion. The measurement uncertainty in each spectel (spectral element) is assumed to 25 be proportional to the square root of the signal. • SNR 1500 @ 25 W m -2 sr -1 µm -1 The SNR is probably optimistic but it does not matter for the present study. The uncertainty is not calculated from the SNR but evaluated from the dispersion of the results. Figure 17 shows two examples of similar SZA spectra (35 ° -36 °), one with a high radiance over a thick cloud cover and one with a low radiance on a clear day. In the case of high-reflected radiance (Fig. 17, top) (Fig. 17, bottom), the band is dominated by the airglow.

5
SCIAMACHY spectrum is in blue, fitted spectrum in thick black, determined airglow spectrum in red, fitted reflected spectrum in light black, reflected spectrum without absorption in dotted black. The word "radiance" in the label axis means the spectral radiance or intensity.
In Fig. 18, it can be seen that when the reflected solar radiance is small, the values of the inverted airglow 10 intensity are little dispersed. On the contrary, a very high dispersion is observed with a high-reflected radiance. It is concluded that airglow inversion is only possible at low reflected solar radiance, corresponding to situations above the ocean on a clear day or at a high SZA. For the rest of this study of SCIAMACHY nadir observations, we will limit the analysis to spectra with a reflected radiance lower than 5 W.m -2 .sr -1 µm -1 .  In order to validate the airglow values inverted using nadir observations, we compare them to the values inverted 5 using limb observations (Fig. 19). The latter are obtained by vertical inversion of the airglow profile observed at limb and integrated over the vertical column as described in Appendix C. The good agreement observed between the two methods gives us confidence in the results obtained with nadir observations. On the other hand, when the data are compared to our model there is an underestimation of the nadir intensity of the airglow simulated by REPROBUS v02 of about 10-15%. This underestimation had already been found for limb comparisons. The 10 inverted airglow follows the same SZA dependence as that simulated by REPROBUS. It can be noticed that for SZA> 90 °, the airglow values at nadir are divided into two families of different intensity. Figure 20 shows these values with distinction between morning and evening data. The values higher in the evening than in the morning are due to the long lifetime of O 2 (a 1 Δg), greater than 1 hour in the absence of quenching in the high mesosphere.
REPROBUS cannot reproduce this morning-evening difference, the concentration of O 2 (a 1 Δ) being calculated 15 by assuming the photochemical equilibrium.

5
In order to evaluate the underestimation of the airglow by REPROBUS, a linear regression is performed between the SCIAMACHY measurements with nadir and the nearest REPROBUS values in time and position (Fig. 21).
The slope of the regression is 1.13. SCIAMACHY therefore sees on average 13% more airglow than estimated with REPROBUS. The regression line does not go through the origin but to 2x10 11 photon cm -2 s -1 sr -1 . This can be attributed to not taking into account in REPROBUS the airglow above 80 km that is present both day and 10 night.

5
We have demonstrated that, despite the moderate resolving power of SCIAMACHY (∼860 against 25,000 for the future MicroCarb mission), it is possible to extract the O 2 airglow at 1.27 μm in nadir spectra provided that the spectra are selected above the sea with a low reflected solar flux (clear sky conditions). The inverted airglow is on average 13% higher than that simulated by REPROBUS v02, in agreement with REPROBUS -SCIAMACHY comparisons at limb (section 4.2.1). The inverted airglow follows the same SZA dependency as 10 that simulated by REPROBUS except at twilight where the morning-evening difference is not reproduced by REPROBUS which assumes photochemical equilibrium. Sun et al. (2018) had concluded that it is not possible to extract nadir airglow from SCIAMACHY measurements. We have shown on the contrary that this is possible if we select the low flux spectra reflected over the ocean in clear weather.
With MicroCarb data and its higher resolving power, one will be able around coastal zones to compare the O 2 * 15 airglow intensity measured above the sea and above the ground, just nearby. They should be very similar, if the characteristics of spatial lengths of intensity variations are as large as found by REPROBUS model, larger than the 2x2° REPROBUS resolution. This comparison would provide an important "sanity check" of the retrieval of Psurf (or O 2 column).
Following an interesting suggestion of anonymous Referee#1, we have tried to estimate from nadir viewing 20 SCIAMACHY data the small-scale horizontal variations of O 2 * airglow that could be due to gravity waves and are not represented in REPROBUS CTM. This is not an easy task using the relatively low spectral resolution of SCIAMACHY data. At this resolution spectral features in airglow and O 2 absorption spectra are highly correlated and the estimation of airglow is accurate only for very low values of reflected solar flux as illustrated on Figure 18, where a large dispersion of airglow is observed for high values of reflected solar radiance. There are not enough observations reaching a low level of solar flux to plot maps of airglow. In spite of these limitations, we made an attempt to estimate at least an upper limit for the small-scale variations of airglow. We selected all pairs of nadir observations with reflected solar flux < 2 mW/m 2 /nm/sr, solar zenith angle < 60° and distance < 110 km. With these strong criteria only 1% of the observations were selected. The average relative 5 difference in airglow intensity between the pairs of observations was equal to 1.0%. We consider this value as an upper limit of the impact of gravity wave perturbation in airglow intensity. At this level the impact on the retrieval of P surf and X CO2 will be very limited.

Conclusions 10
In this paper we have reported the results of a three years (2016-2018) scientific research effort to revisit the use of the O 2 absorption band at 1.27 µm in the problem of GHG retrieval from space observations of the detailed spectrum of the solar radiation scattered by aerosols, atmosphere and surface. It is widely recognized that this 1.27 µm band being nearer in wavelength to the CO 2 bands at 1.6 µm and 2.0 µm, it would be less uncertain to 15 "transport" aerosols optical properties (wavelength dependent) from this O 2 band to the CO 2 bands, than from the O 2 A band at 0.76 µm. However, the O 2 absorption band at 1.27 µm is contaminated by a strong airglow emission, presenting a similar spectral structure. This airglow is mainly due to photolysis of ozone in the mesosphere, letting an O 2 molecule in an excited state O 2 * which spontaneously de-excite. 20

Nadir O 2 * airglow Intensity
As a first approach, we needed to have an idea of the absolute amount of O 2 * airglow contamination, in order to compare to the expected radiances in nadir viewing which are well documented. We could not use the SCIAMACHY nadir observations around 1.27 µm for this purpose, since they are contaminated by solar 25 scattered radiation from the surface. Therefore, we used the limb-viewing observations of SCIAMACHY in this band, which are not contaminated when looking above ~30 km of altitude. We have designed a method to retrieve the vertical profile of the O 2 * VER from a limb scan of SCIAMACHY, taking into account the reabsorption of O 2 along each LOS. A "fictitious" nadir-viewing intensity from SCIAMACHY could therefore be derived by vertical integration of the VER. When extracting the data for various periods of the year, it was found 30 that the major factor governing this O 2 * airglow intensity was the Solar Zenith Angle, with little variability otherwise.
In parallel, we have conducted a major effort to model the intensity of the O 2 * airglow emission, as an off-line extension of the CTM REPROBUS model providing the ozone field within the ECMWF meteorological field.
We found the same overall behaviour with SZA and some weak seasonal dependence. A systematic comparison 35 of 12,833 limb-scans acquired by SCIAMACHY in 2007 and corresponding fictitious nadir-viewing intensities with the prediction of our model (and also VER vertical profiles) indicates an overall good agreement, although with a deficit of about 15% in the modelled intensity w.r.t. the SCIAMACHY intensity. For the time being, we assign this deficit to be due at least partially (but possibly not totally) to an ozone deficit in the REPROBUS In summary, we have found that the intensity of the O 2 * airglow is well organized (with a weak horizontal variability), and quite predictable, with a dispersion of probably only a few per cent around a climatological average. Also, it should be almost as good as the ozone field in CTM models which are run with the actual meteo fields like ECMWF. Therefore, one could imagine that a GHG nadir viewing observation in the O 2 band 5 could be corrected by subtraction of a model of the O 2 * airglow to get the pure nadir solar scattered intensity (on which is imprinted the O 2 absorption that we are analysing to get the O 2 column). However, the degree of accuracy that is needed for the determination of Psurf for useful measurements of GHG gases is very large, about ~ 0.1 hPa for the bias and 1 hPa for random error. According to our simulations, and if the airglow is ignored in the inversion but subtracted from a model, this airglow intensity model would have to be accurate to 10 ~1.5% (for a mean radiance with albedo= 0.2) to achieve the 1 hPa random error. Therefore, in most cases it is insufficient to rely entirely on a model to predict the actual airglow intensity to be subtracted from an observation. We need to disentangle in the observed spectrum itself the contribution of the airglow and the contribution of the solar scattered radiation. For this, we will rely on the fact that the spectrum shape of the O 2 * airglow is different from the O 2 absorption spectrum. 15

Spectral shape of the O 2 * airglow
It is clear that if the dayglow spectrum of O 2 * were strictly identical to the O 2 absorption spectrum, it would be impossible to disentangle one from the other, and one would have to subtract blindly a model of the airglow 20 emission from the observed spectrum, with an associated uncertainty.
While all the transitions of the O 2 1.27 µm do exist in both the absorption spectrum and in the O 2 * airglow emission spectrum, the resulting spectra in a nadir viewing geometry are different for two reasons and under three aspects.
First, the emission happens at high altitude and low air densities, while the absorption happens in the dense, 25 lower atmosphere. Therefore, each absorption line is broadened by collisions, as shown in Fig. 2. Also, while for the shape of the airglow emission, all the spectral lines are proportional to each other, on the contrary the radiance factor (=π B/solar flux cos(SZA), B brightness) is modulated by the O 2 transmittance spectrum (Tr(τ)=exp(-τ)) which is not linear for the strong lines with large τ. Finally, there is the CIA effect producing a broad band absorption (Fig. 16), which is totally negligible in the upper atmosphere where emission takes place. 30 Second, for the same line, the rotational states J', J'' of the upper and lower states are inverted between absorption and emission, and since the rotational levels are populated differently, the P and R branches (ΔJ=± 1) of the electronic transition have a different intensity distribution populated differently.
We have computed the theoretical shape of the dayglow spectrum from the Einstein coefficients A 21 of spontaneous emission from data contained in the HITRAN database. It depends on the temperature of the 35 atmosphere at the place of emission (rotational relative populations). We have compared our theoretical spectra degraded to the resolving power of SCIAMACHY (∼860) with limb observations of SCIAMACHY and found an overall excellent agreement, validating our theoretical approach of the airglow spectrum. This allowed performing some simulation exercises with good confidence about their ability to represent reality, showing that with the resolving power of 25,000 of the MicroCarb instrument, it is indeed possible to disentangle the airglow 40 37 emission from the O 2 absorption in the O 2 band at 1.27 µm. We note that the broad CIA band would not require such a high spectral resolution to be useful for the disentangling.

5
Simulation exercises performed with the 4ARCTIC software (Appendix E) have demonstrated that with the resolving power of Microcarb (25,000), and only using the O 2 IR band B4 at 1.27 µm, we may retrieve Psurf (or similarly the O 2 vertical column of dry air) with an accuracy almost compliant with the strong MicroCarb requirements. The use of the B1 band (0.76 µm), in addition to the B4 band, will most likely yield a better understanding of the behaviour of this band B1 which at present is not fully understood. Once better understood, 10 it will certainly improve the accuracy of the Psurf MicroCarb retrieval by constraining further the aerosols optical properties. One may even hope that such a new knowledge could be used for an improved retrieval of other GHG missions. for an SNR of ∼500 and a spectral resolving power of 5,700, which would result on an error of 1.4 ppm for X CO2 , marginally insufficient. Their whole analysis was done with already accounting for the CIA O 2 absorption, whose broad size and smooth pattern is insensitive to spectral resolving power (Fig. 16). On the other hand, as can be seen in Fig. 16 with the same number of spectels as MicroCarb and a coarser spectral resolution (and 20 sampling), the whole O 2 band would be measured and would possibly allow to better constrain the CIA absorption and O 2 column retrieval. The larger spectral sampling gives additional photons per spectel, which may be traded-off for an increased spatial resolution. However, the high resolving power of MicroCarb is an asset for the exact knowledge of the instrumental spectral function which is important for the retrieval accuracy.
On the other hand, with our Igor-software breadboard tool, we have shown that with the SCIAMACHY 25 spectral resolving power (∼ 860), it was possible to determine the intensity of the O 2 * airglow over oceans (low albedo), but not to disentangle it and retrieve the CO 2 column, whatever the albedo, with a useful enough accuracy. We suggest though, on the basis of our analysis and the results of Sun et al. (2018), that when CIA is taken into account, a spectral resolving power of about 5,000 and a high SNR could possibly yield a sufficiently good accuracy on the Psurf retrieval in the O 2 band at 1.27 µm, and could improve the treatment of aerosols and 30 their wavelength dependent optical properties, being nearer the CO 2 bands, for a better X CO2 retrieval. The CO 2 Mission (space mission CO 2 -M) is sponsored by European Community, and developed and operated by ESA, as a space segment for the monitoring of CO 2 anthropogenic emissions, with potentially a series of three operational spacecraft on sun-synchronous orbits. The present typical baseline optical design of the CO 2 -M has a spectral resolving power of about 6,300 at 0.76 µm, and 5,400 for the weak CO 2 channel at 1.60 µm. There is no 35 channel for the O 2 band at 1.27 µm but it can be imagined by interpolation that a new channel for this band derived from the baseline design would have a resolving power of about 5,750. Based on the discussion in the previous paragraph and on the whole present study, we advocate for the inclusion in the design of CO 2 -M instrument of a channel at 1.27 µm.
The Tanso 45 38 space platform. The Tanso-Gosat 2 was launched in October 2018 and use bands at 0.76 (for O 2 ), 1.60 µm weak CO 2 band and 2.0 µm (strong CO 2 band). We advocate for the inclusion of an additional channel dedicated to the measurement of the O 2 band at 1.27 µm in the design of future Tanso instruments, as well as for the chinese family of TANSAT following the TANSAT-1 already collecting data.

5
Competing interests. The authors declare that they have no conflict of interest.
Author contribution: JLB conceptualized revisiting the use of the 1.27 µm O 2 band for GHG retrieval and prepared the manuscript with contributions from all co-authors. JLB and PA developed the theory of airglow emission spectrum and the building of a synthetic spectrum. FMB is the principal investigator of the MicroCarb 10 mission, in the frame of which this study was performed. This study was organized by DJ and technically managed by LB at ACRI and scientifically by JLB at LATMOS. JLB and AH developed the algorithms for the analysis of SCIAMACHY data. FL developed the REPROBUS model and the O 2 * airglow model and participated to comparisons with GOMOS and SCIAMACHY data. PL maintained the 4ARCTIC software. LB performed the SCIAMACHY data analysis for VER retrieval from limb measurements, and comparison with 15 REPROBUS model and ozone GOMOS data. LB computed also the airglow synthetic spectra and made comparisons with SCIAMACHY limb spectra. AH developed the LATMOS breadboard inversion tool and conducted the retrieval of airglow intensity from nadir observations of SCHIAMACHY.

A.1: Physics of O 2 (a 1 Δ) emission in the Earth's atmosphere
The emission in the near infrared of a photon at 1.27 µm occurs when molecular oxygen in its first excited electronic state O 2 (a 1 Δ) spontaneously relaxes to its fundamental state O 2 (X 3 Σ). It is one of the most intense lines 5 measured in the atmosphere of telluric planets. This first part describes the mechanisms of production and relaxation of O 2 (a 1 Δ) in the Earth's atmosphere, shown in Fig. 10. They form the theoretical basis of the O 2 (a 1 Δ) emission model that we have developed for the present study.

A.1.1.1 Direct Production
The main direct process leading to the formation of O 2 (a 1 Δ) in the Earth's middle atmosphere is the photodissociation of ozone at wavelengths shorter than 310 nm. This produces an O 2 molecule in the electronic state contribution to the vertically integrated emissivity of O 2 (a 1 Δ) being in the range of 10 -4 (Wiensz, 2005), it will be neglected here.

A.1.1.2 Indirect Production by O( 1 D)
A minor but not negligible contribution to the production of O 2 (a 1 Δ) is of an indirect character since it occurs through the excited oxygen O( 1 D) and the subsequent energy cascade to O 2 (a 1 Δ). As shown in Fig. 17 The last process k D,O2 indicated above produces an O 2 molecule in its second excited state O 2 (b 1 Σ). This unstable molecule in turn transmits its energy either radiatively or collisionally. Radiative relaxation to the fundamental state O 2 (X 3 Σ) occurs with a time constant 1/A Σ of 13 s (Mlynczak and Solomon, 1993) and is accompanied by 5 the emission of a photon at 762 nm: The collisional relaxation (quenching) of O 2 (b 1 Σ) is carried out with O, O 2 , O 3 , N 2 , and CO 2 , and results in the lower energy state O 2 (a 1 Δ) : Taking into account the contribution of O( 1 D) to the emission of O 2 (a 1 Δ) therefore requires a calculation of the concentration of O 2 (b 1 Σ) which involves its radiative relaxation and its collisional relaxation rates with the 5 molecules above.

A.1.1.3 Indirect production by solar excitation of O 2 (b 1 Σ)
For an accurate calculation of the O 2 (a 1 Δ) emission profile, it is also necessary to take into account the solar 20 excitation (or optical resonance) of O 2 (b 1 Σ) at 762 nm, whose indirect contribution to the O 2 (a 1 Δ) emission becomes significant above 60 km. Indeed, the absorption by O 2 of a solar photon in the O 2 A-band at 762 nm raises it directly to the energy level O 2 (b 1 Σ): The photo-excited O 2 (b 1 Σ) molecule is then affected by the same processes as those mentioned in the previous 25 paragraph, which in case of quenching lead to the O 2 (a 1 Δ) state.

A.1.2 Relaxation of O 2 (a 1 Δ)
Once produced in its excited state O 2 (a 1 Δ), molecular oxygen transmits its energy either by radiative relaxation or by quenching with surrounding molecules. Radiative relaxation operates by emitting a photon in the near infrared at 1.27 µm, which lowers O 2 to its fundamental level O 2 (X 3 Σ): This transition is carried out with a fairly long time constant. The current consensus supported by the laboratory 5 measurements of Lafferty et al. (1998) is 1/A Δ = 75 mn for the radiative lifetime of O 2 (a 1 Δ). The collision relaxation of O 2 (a 1 Δ) can be performed with O 2 , N 2 , O, O 3 , or CO 2 . According to current kinetics data (Burkholder et al., 2015;Atkinson et al., 2005), collisions with O 2 are very largely dominant in the Earth's middle atmosphere: The frequency of collisions between O 2 (a 1 Δ) and O 2 obviously increases with density and therefore when descending in altitude. Thus the collision relaxation of O 2 (a 1 Δ) dominates the radiative relaxation of O 2 (a 1 Δ) at all altitudes below 75 km. It is 10 times larger at 60 km, and 50-100 larger at 50 km (Wiensz, 2005).

A.2.1 Input data 15
The input data used to calculate the volume emission rate of O 2 (a 1 Δ) (VER) are the vertical profiles of temperature, ozone O 3 , and atomic oxygen O( 3 P). These profiles are provided by the REPROBUS threedimensional chemistry-transport model (Lefèvre et al., 1994). REPROBUS is a global model with a horizontal resolution of 2°x2°. It includes a complete description of stratospheric chemistry using 58 species and about 100 chemical reactions. The winds and temperatures used by REPROBUS are forced by ECMWF operational 20 analyses. Since 2013, REPROBUS has been integrated in near-real time on the IPSL servers in a vertical configuration identical to those of the ECMWF analyses: chemistry and transport are calculated on 137 pressure levels distributed from the ground to 0.01 hPa, or about 80 km altitude. The chemical species distributions calculated by REPROBUS are stored and available every day at 12 UT on the whole Earth.
In practice, the user of the O 2 (a 1 Δ) emission model developed here enters the latitude-longitude coordinates and 25 the date he wishes to process. The model then extracts the ECMWF temperature profile as well as the O 3 and O( 3 P) profiles calculated by REPROBUS for the selected date and location. From the pressure and temperature the total density and density profiles of N 2 , O 2 , and CO 2 are also calculated, adopting uniform mixing ratios of 0.78, 0.21, and 380×10 -6 for the latter species respectively.

A.2.2.1 Photo-dissociation of ozone
The calculation of the J H photo-dissociation rate of ozone is performed in the same way as in the 3D REPROBUS model. It uses an ultraviolet radiative transfer model inherited from the TUV model developed at 47 NCAR (Madronich and Flocke, 1998). It uses both spherical harmonics and discrete ordinates to represent the radiation field, resolved with a spectral interval of 0.5 nm in the Hartley band of ozone. The effective ozone absorption cross-section and the quantum efficiency of O( 1 D) production are derived from the latest JPL recommendation (Burkholder et al., 2015). To save computation time, J H is pre-calculated for the entire range of zenithal angles (0-90°) that can be used in the 1D model. It is then stored in a "look-up table" (LUT) which is a 5 function of the total air and ozone columns above the considered point, as well as the zenith angle. A simple three-dimensional interpolation in the look-up table allows to determine the vertical photo-dissociation profile J H for a given ozone profile and zenith angle.
Spontaneous probability of transition (Baluja and Zeippen, 1988)  Once the concentration [O( 1 D)] has been determined, the density of O 2 (b 1 Σ) can be calculated, which is obtained by making the justified hypothesis of photochemical equilibrium by equalizing the terms of production and loss: 5 In the above expression g O2 is the solar excitation rate of O 2 (b 1 Σ) at 762 nm, detailed in the following paragraph.

A.2.2.3 Solar excitation of O 2 (b 1 Σ)
The calculation of the solar excitation rate g O2 of O 2 (b 1 Σ) in the A-band at 762 nm is parameterized from the line-by-line calculations of Wiensz (2005). The expression of g O2 used here is the form: 20 where N O2 is the oblique column of O 2 above the considered point and g ∞ = 6.1×10 -9 s -1 the solar excitation rate at the top of the atmosphere. The coefficients b and c (power law) are determined by a fit log/log of the data from Wiensz (2005). As an example, Fig. A2 illustrates the g O2 values calculated at the Equator for several zenith angles. We verified that these results were in good quantitative agreement with the complete calculation of Wiensz (2005). 5

A.2.2.4 Emission of O 2 (a 1 Δ)
The final step is to calculate the O 2 (a 1 Δ) emission rate. Its number density (molecule.cm -3 ) is obtained using the 10 source terms J H and S Σ calculated previously, assuming photochemical equilibrium: The volume emission rate (or emissivity) εΔ at 1.27 µm expressed in photons.cm -3 .s -1 is simply obtained by 15 multiplying the concentration of O 2 (a 1 Δ) by AΔ :  (Fig. 20).

A.2.3 Processes neglected in the model
In addition to the direct production of O 2 (a 1 Δ) by recombining atomic oxygen, three other physical 5 mechanisms have been neglected in our model, based on the following reasons: -The production of O( 1 D) from the photo-dissociation of O 2 in the Schumann-Runge continuum (SRC) and at Lyman-α. These processes noted respectively J SRC and J Ly-α in Fig. 10 become important only in the thermosphere above 90 km. Their contribution to the emission of vertically integrated O 2 (a 1 Δ) from the ground is between 0.1 and 1% (Wiensz, 2005). 10 -The photo-excitation (or optical resonance) of O 2 (a 1 Δ) at 1.27 µm. This process occurs throughout the stratosphere and mesosphere. It contributes less than 1% of the integrated O 2 (a 1 Δ) emission (Wiensz, 2005).

A.3. Airglow Model Results
Our model provides the vertical profiles of the mixing ratios of O( 1 D), O 2 (b 1 Σ), O 2 (a 1 Δ), the emissivity (same as VER) profile at 1.27 µm expressed in photon.cm -3 .s -1 , and the vertically integrated emissivity I ag expressed in 15 photon.cm -2 .s -1 .sr -1 .  represents about 80% of the total O 2 (a 1 Δ) emission and the energy transfer of O( 1 D) about 20%. The solar excitation of O 2 (b 1 Σ) becomes important in the mesosphere. It contributes 20% to O 2 (a 1 Δ) at 60 km and 50% at 80 km. These results are consistent with the literature (Mlynczak and Olander, 1995;Wiensz, 2005) but an 5 accurate comparison would require the use of identical input profiles (especially ozone).

A.3.4 Integrated vertical intensity I ag
The model also provides the output emissivity of O 2 (a 1 Δg) vertically integrated between the ground and 80 km altitude, or integrated vertical intensity I ag (index ag for airglow), which is observed in nadir viewing expressed in photon.cm -2 .s -1 .sr -1 . On Fig. A6 (left) the values of I ag are represented for equinoxes and solstices (Mars, June, September, December) at various latitudes (labelled 60S, 40 S, 40N, and 60 N) as a function of solar zenith angle 5 (SZA). The main factor dictating the emerging vertical intensity I ag is the value of SZA. Figure A6 (right) represents the variation of the I ag intensity calculated at 12:00 UT during a complete year, from a 3D simulation of REPROBUS forced by the 2015 ECMWF analyses. For a given date, the latitude distribution of the intensity reflects the slow seasonal/latitude evolution of the ozone field.    Khomich et al., 2008) presents the various electronic states of the di-oxygen molecule O 2 and the 5 names of the transitions between them. The O 2 molecule, being composed of two identical atoms, is said to be homopolar. The fundamental state X 3 Σ g is put at a reference energy level=0. The number 3 indicates a triplet state, which may be decomposed in 3 sub-states with very nearby energies. The descending arrows in Fig. B1 indicate transitions to a lower level, corresponding to the emission of one photon. The reverse process corresponds to the absorption of one photon. We describe briefly below three of the transitions indicated in Fig.  10 B1 which are the most relevant to GHG gases, since O 2 is used as a reference to determine the mixing ratio of CO 2 . We can make use of the energy/wavelength conversion: 2. The « atmospheric » band is the transition (b 1 Σ g + à X 3 Σ g -), around 760 nm also called A-band from Fraunhofer' early nomenclature, or "atmospheric band", heavily used in GHG studies. 10 3. The « infra-red atmospheric » band is the transition (a 1 Δ g à X 3 Σ g -), around 1270 nm or 1.27 µm in the near infra-red, sometimes called O 2 IR band, or ( 1 Delta band) (according to Gordon et al., 2010). This band is the subject of the present study.
Because the O 2 molecule is homopolar, it has no electric dipolar moment and in principle electronic transitions are forbidden. The electronic transitions can only happen thanks to the existence of a magnetic dipole moment 15 (M1) and/or a quadrupolar electric moment (E2). As a consequence, spontaneous transitions from a given electronic state down to the fundamental state X 3 Σ g are unlikely, therefore the lifetime of such a state is rather long: 13 s for the atmospheric A-band at 760 nm, transition (b 1 Σ g + à X 3 Σ g -) (Mlynczak and Solomon, 1993) and 75 minutes for the O 2 IR band at 1.27 µm, transition (a 1 Δ g à X 3 Σ g -) (Lafferty et al. 1998). Therefore, the O 2 molecule excited at level a 1 Δ g (often represented by O 2 * or 1 Δ O 2 in the following) which results from ozone 20 photo-dissociation has plenty of time to reach thermal equilibrium with ambient gas, and the various states of vibration-rotation will be populated according to a Boltzmann law (therefore, depending on the local temperature T) modulated by the rotation quantum number J, with a statistical weight 2J+1 as described later below.
For the O 2 IR band at 1.27 µm, the transition (a 1 Δ g à X 3 Σ g -) is mainly due to a magnetic dipole (M1). There is, however, also a system of absorption lines due to the electric quadrupo: (E2), identified for the first time both in 25 atmospheric absorption spectra (looking at the sun) and in laboratory experiment (Gordon et al., 2010). The overall absolute strength of this (E2) system is about 215 times weaker than the (M1) system (Gordon et al., 2010).

B.2. Observations of the 1.27 µm in the atmosphere of the Earth from the ground 30 57
One difficulty for ground-based observations of the 1.27 µm emission is that most of the emission is absorbed by O 2 before reaching the ground, letting 4-10 % coming down to the ground. The second difficulty is that there is a strong contribution of scattered solar radiation by the atmosphere/dust. It is (now) clear what should be the optimal observing conditions: 5 -look near the zenith to minimize O 2 absorption in the lower atmosphere. From a ground based observing station located at high altitude the O 2 absorption will be a little bit reduced.
-look just after the sunset, when the sun is still illuminating the ozone layer producing this emission, between 30 and 80-90 km, but not illuminating the lower atmosphere, to avoid Rayleigh/Mie scattering which produces a strong sky background signal. 10 The first observation form the ground was reported by Lowe et al. (1969), followed by Baker et al. (1975) and Pendleton et al. (1996), all fulfilling the above-mentioned optimal conditions.

15
The emission of Venus at 1.27 µm was discovered by Pierre Connes (Connes et al., 1979), then studied in particular by Crisp et al. (1996). It is due to the recombination reaction (3) O+O+M. On Mars, both types of emissions (2) and (3) exist. The ozone emission was discovered by Pierre Connes (Noxon et al., 1976), and recombination emission (3)

B.4 Computation of a synthetic spectrum of O 2 * emission from HITRAN 2016
The aim of this section is to describe a way to compute what could be the emission spectrum of the emission of O 2 * in the dayglow, relevant to nadir GHG daylight observations. In an early phase of the present studies in 2016, we made the following crude approximation. We computed, from HITRAN 2016 (Gordon et al., 2017) the 25 local high resolution spectrum of absorption by O 2 molecule at a variety of altitudes. Then we assumed that the emission spectrum shape (but not magnitude) was identical to the absorption spectrum. In the following, we detail how we can compute more accurately a theoretical spectrum of the local emission of O 2 * molecule, from the data that are present in HITRAN 2016 line-by-line informations and some additional considerations.

B.4.1 Computation of the total emission rate of O 2 * molecule coming from ozone dissociation
As described in the main text with more details in Appendix A, the Reprobus CTM model is used to compute the 3D distribution of ozone as a function of space and time, based on a set of chemical reactions, solar photolysis of 5 various species, and the actual meteorological fields of winds, temperature and pressure procured by ECMWF.
Then an additional model computes the photo-dissociation of ozone with the UV solar spectrum of the day, yielding to a 3D distribution of the concentration [O 2 *] of species O 2 * (electronic state 1 Δ g ), in units of cm -3 . As said above, the lifetime of this electronic state is about 75 minutes, corresponding to a spontaneous emission rate A global of 1/75*60= 2.22x10 -4 s -1 . For low altitudes, one must take into account the quenching of this excited state 10 by collisions with all other gases (including O 2 ), mainly at the lowest altitudes (<50 km). Ignoring the quenching, the rate of emitted photons, the Volume Emission Rate VER in units of photons/ (cm 3 s) may be computed from:

B.4.2 Computation of the airglow detailed line-by-line intensity
The same principle may be applied to the detailed emission spectrum, by computing a VER for each transition In their 2006 paper, Simeckova et al. (2006) describe « the calculation of the statistical weights and the Einstein A -coefficients for the 39 molecules and their associated isotopologues/isotopomers currently present in the lineby-line portion of the HITRAN database ». This is all that is needed to calculate second members of equation (6) for all allowed transitions L i , giving the rate of emission of the corresponding spectral line VER(L i ).
In an approximation of a two level system (upper m and lower n levels are denoted as 2 and 1 respectively) at 10 LTE (Local Thermodynamic Equilibrium), we have the well-known equations linking the Einstein Acoefficients and B-coefficients where A 21 (spontaneous emission) is in s -1 , and B 12 (absorption) and B 21 (stimulated emission) are in cm 3 (J s 2 ) -1 , and g 1 and g 2 are the statistical weights of the levels 1 and 2, respectively.
We start from equation (17) of Simeckova et al. (2006) with molecules in the lower level 1 and the upper level 2 (much less numerous at atmospheric temperatures), to describe their relative distribution according to their 20 energy level E 1i or E 2i and temperature T, the index i indicating a particular rovibrational level defined by J' and V'. If N is the total number of molecules per unit volume at the temperature T, the population N 2i of one of the energy level E 2i of the upper level 2 is equal to: and a similar equation for N 1i and the energies E 1i of the lower level (equation (17) of Simeckova et al. 2006).
Here, Q tot (T) is the total internal partition sum of the absorbing gas at the temperature T, g 2i =2J'+1, and E 2i is the 60 energy of the upper state in units of wavenumber (cm -1 ) . c 2 is the second radiation constant, c 2= hc/k B , where c is the speed of light, h is the Planck constant, and k B =1.38065 x10 -23 joule K -1 is the Boltzmann constant.
The total number of molecules per unit volume N= ΣN 1i + ΣN 2i , and Q tot (T) is the sum of Q tot lo (T) and Q tot up (T), respectively the internal partition sum of the lower level and the upper level. The index i refers to all possible values of J', starting at J'=2 (J'=0 and J'=1 do not exist). We have by definition: 5 We may find the value of Q tot (T) in Table 1 of the paper of Simeckova et al. (2006). For instance, Q tot (T=296 K)=215.77 for the main oxygen isotopologue 16 O 16 O. The temperature 296 K is a reference temperature for the HITRAN database. For our purpose, we have to find Q tot up (T) for the upper level of the transition, from a 10 summation described in equation (B7). The summation must be not over all the transitions, but over all energy levels. Since the HITRAN database consists in a list of transitions, some caution must be used when using the HITRAN database, in order to extract a list of energy levels. Once we have Q tot (T), the total internal partition sum, then we may compute all values of N 2i , for the required temperature, from the distribution of the excited molecules between the various energy levels from equation (B6).  At LTE and atmospheric temperatures, !"! !" ≪ !"! !" ≈ !"! with a factor is approximately between 0.1 and 1.
The partition functions described above, as well as the connection between the A 21 and the strength of the transition S HIT were established with considering a gas at LTE conditions. But then the value of A 21 does not depend if there is LTE or not. In particular, when a population of excited O 2 * molecules are produced from ozone photolysis, the ratio ΣN 2i /N may be much larger than with LTE conditions. Whatever rotational level in 10 which they will be produced by photolysis, they will soon re-equilibrate among the various rotational upper levels because the radiative lifetime is quite long versus the collision time with ambient molecules which tend to relax to the collisional equilibrium of the various rovibrationnal levels, without changing ΣN 2i /N (in the absence of quenching). Each particular rotational level may decay through several transitions, each transition with its own decay rate, or Einstein probability of spontaneous emission, called A 21 , which is given in HITRAN tables of line-by-line lists.
The total (average) decay rate from the upper level is obtained by summing all A 21 on all transitions weighted by 5 the relative population of each rotational level: Since there is the emission of one photon around 1.27 µm for each decay of one excited O 2 * molecule, A 21tot is 10 the weighted sum of all rates of all transitions going down, which is the total emission rate, the total number of photons emitted in the whole band per second by one single molecule of O 2 *.
Then we must multiply by the number density of O 2 * to get the volume emission rate in photons per (cm 3 s). We found from the HITRAN data that the total decay rate is A 21tot =2.29 10 -4 s -1 , slightly different from 2.22 10 -4 s -1 derived from the rounded value 75 mn of the lifetime quoted by Lafferty et al. (1998). We may compute the 15 lifetime 1/ A 21tot =4367 s∼ 73 mn. The excited molecule O 2 * will, in average, stay excited for more than one hour (in the absence of quenching, de-excitation by collisions without the emission of one photon, not addressed here).
It must be realized that it is experimentally very difficult to measure directly such a long lifetime. Instead, because the values of A 21 are connected to the values of absorption coefficients B 21 , it is easier to measure the 20 absorption of O 2 molecules, and then make the appropriate calculations to derive the A 21 values, according to principles explained in Simeckova et al. (2006), which have been used to fill the HITRAN line-by-line lists with A 21 rates for each transition.

B.4.5 Computing the emission spectrum of the excited molecule O 2 * 25
The emission rate per O 2 * molecule ε(k) of a transition k is obtained by multiplying the Einstein Coefficient A 21 (k) by the relative population of the upper level:   O 2 * emission rate @296 K (right scale) R Q P Therefore, a spectrum of the local emission in the band could be computed, by describing each emission transition by a gaussian with an appropriate width (associated to the temperature), adding all transitions to form a full spectrum, and multiplying by the actual density of O 2 * molecules.
However, we have implemented another method, to take advantage of LBLRTM software (Line By Line Radiative Transfer Model, Clough and Iacono, 1995) which computes for the terrestrial atmosphere absorption 5 spectra (either local, or integrated over one LOS, line-of-sight) from HITRAN database. Indeed, with the adequate scaling of both right and left scale of Fig. B4, it is noted that the strength of absorption lines are just above the emission rates on the left side of the graph (short wavelength), while it is the reverse on the right side.
As we shall see below, there is a theoretical reason for this progressive change of the ratio of emission to absorption strength. 10

B.4.6 Theoretical computation of the ratio emission/absorption
We first repeat here the equation (19) from Simeckova et al. (2006) which links A 21 to the line strength SS (below, S ν (k,T)) in which k designates one transition from energy level E 1k with a wave number ν 0 : 15 We may extract the expression of A 21 (k) from equation (14) and put it in equation (13). Taking into account that E 2k -E 1k = ν 0 and that the statistical weight of energy level E 2k is: we could find a very simple result on the ratio of emission ε(k) to absorption line strength S ν (k,T) for each line: In Fig. B5   In order to simulate a local emission spectrum, we could use the method exposed in B.2.4, giving the emissivity per molecule O 2 * for each line, and then distribute this emissivity over a gaussian attached to each line, and add spectrally all line contributions. We have developed another method, capitalizing on the capabilities of 5 LBLRTM software (Clough and Iacono 1995). With LBLRTM, we may compute a local absorption spectrum of O 2 (for instance, computing the vertical atmospheric transmission between 67 and 68 km of altitude, Tr(λ)). This transmission is linked to the local absorption a(λ) by : The shape of the local emission spectrum E m (λ) of O 2 * molecules is then obtained by multiplying a(λ) by the expression (B13) of the ratio emission/absorption ε/SS, which depends only of the wave number ν and temperature T, according to a continuous function. The wave number ν in cm -1 is equal to 10000/ λ (in µm). 15 Then the obtained local emission spectrum E m (λ) has to be normalized (by integration over wavelength) to the actual VER for which we wish to compute the local emission rate spectrum, yielding E mn (λ) where the letter n stands for "normalized" .
The advantage of this approach is that LBLRTM computes the local absorption spectrum with a number of effects (line broadening, pressure shifts, gaussian profiles,…) that may become non-negligible at low altitudes. 20 Applying equation (B13) on the continuous spectrum, instead of applying it to the discrete set of wavelengths of each transition is justified by the fact that ν and expression (B13) varies very little over the spectral extent of one individual line.
In order to compute the brightness spectrum of the O 2 * emission along any LOS, one has to integrate E mn (λ) over length through the atmosphere. The "self-absorption" by O 2 molecules along the LOS must be accounted 25 for, except in regions where it is negligible (high altitudes, say >80 km).

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Appendix C: Retrieval of O 2 ( 1 Δ) volume emission rate (VER) from SCIAMACHY limb radiances We have developed a numerical scheme to retrieve the vertical distribution of the O 2 ( 1 Δ) volume emission rate (VER) from a series of limb radiances obtained during a SCIAMACHY limb scan, taking into account the absorption along the LOS by background O 2 of the O 2 ( 1 Δ) emission between the location of the emission and the 5 spacecraft (sometimes this O 2 absorption is called self-absorption, improperly in our opinion, because the O 2 ( 1 Δ) molecule is different from the background O 2 , as long it is in the excited state ( 1 Δ)).

10
When there is no absorption, the radiance B is related to the integral along the LOS of the VER (or emissivity) ε(s), s being an abscissa along the LOS.
B is the wavelength-integrated spectral radiance, expressed in photons/(cm 2 s sr), while ε(s) is here spectrally 15 integrated and expressed in photons/(cm 3 s).
A classical way to retrieve a vertical distribution of ε from a series of radiance measurements at the limb is the onion-peeling method (Fig. C1), which assumes that the emissivity (or VER) is locally spherically symmetric, depending only on the altitude. Furthermore, the problem is discretized by dividing the atmosphere in spherical layers, in which the VER is constant. 20

5
Let p 0 ,..p j be the series of impact parameters of viewing LOS with p= tangent altitude z + R earth , p 0 the largest.
We define a series of spheres with r 0 > p 0 and decreasing radii. Let L j,n =length of one of the two equal segments (j,n) between spheres of radius r n and r n+1 along the LOS with impact parameter p j .
We have the expressions (C2): 10 For the last segments when j=n, the formula is slightly different because the sphere of radius r j+1 is irrelevant: The radiances B(p) may then be expressed (20) as a function of ε(z): This is a linear system of n equations with the n unknowns ε(z j ). This system may be written under a matrix form 5 4πB=M ε, M being a triangular matrix of order n, the number of atmospheric layers. Elements of the matrix are the lengths of LOS segments within a layer between two spherical shells. Therefore the matrix may be simply inverted to yield the vector ε from the vector of measurements B:

C.2 The case with absorption: a modified onion-peeling technique
When absorption by O 2 is considered, the equation (18) is modified into: where τ(s) is the optical thickness between the emission point and the observer (here, assumed to be outside of the atmosphere). The corresponding attenuation factor is: In reality, ε, τ(s), Tr(s) and B all depend on wavelength λ. However, the quantities τ(s, λ), Tr(s, λ) may be computed for a given atmospheric model defined by a vertical profile of temperature T(z) and pressure p(z), with the dry air density n(z)= p(z)/k T(z), and O 2 density= 0.2095 n(z). We made use of the LBLRTM code and 5 HITRAN2016 data base to conduct such computations.
The detailed spectral shape of the local emission of the O 2 * molecule ε(z, λ) may be computed from the analysis of Section 2. Therefore, we can compute a wavelength-integrated attenuation factor between the emission location and the external observer, independent of the actual value of the local VER(z)= ∫ε(z,λ) dλ for every cell of the onion-peeling scheme described above. We keep the matrix approach, but now each element of the matrix 10 is a length of a segment multiplied by the pre-calculated attenuation factor. While in the standard onion-peeling scheme, there are two identical segments, symmetric w.r.t. the tangent point, giving equal contributions to the observed intensity, the attenuation factor is different for the two segments (one in the foreground, the other in the background).
For a given limb observation, each SCIAMACHY spectrum is integrated in wavelength to yield the total limb 15 radiance measurements B(z), and equation (C4), where M matrix is modified to include the attenuation factor, is used to derive the vertical profile of the volume emission rate ε(z). It may be shown that the attenuation factor FAS j,n affecting both foreground and background segments on one LOS may be written as: absorption from the segment to the observer, along the LOS. 25 Zarboo et al. (2018) have also used the SCIAMACHY limb scans in order to retrieve the vertical profile of the O 2 * emissivity. However, their technique is quite different. They find a best fit to the whole series of observed 72 spectra with a model of the vertical distribution of spectral emissivity, but they do not account for attenuation by O 2 . Therefore, they must underestimate their emissivities more and more with lower altitudes. Their method does not need to know the state of the atmosphere nor the theoretical shape of the emissivity; in principle, if their SNR would be large enough, they could interpret the spectral shape of their retrieved emissivities in terms of local temperature, by comparing with model predictions built on our approach developed in Section 2. Because they 5 have used a special SCIAMACHY mode of observation dedicated to the mesosphere and lower thermosphere (MLT), in which the scanning at the limb is in the range 50-150 km, the fact that they did not account for O 2 reabsorption along the LOS is probably not very important. They have limited their study to altitudes >50 km. Sun et al. (2018) have studied also the SCIAMACHY spectra in the O 2 * band for the same purpose as us: for a better retrieval of the X CO2 mixing ratio. In order to retrieve the spectral emissivities at each altitude, they have 10 developed two methods. The first one (they call it "linear inversion") is identical to the method of Zarboo et al. 2018, and does not account for O 2 absorption. In their second method (they call it "onion-peeling"), they account for O 2 absorption, except for the two tangent heights where absorption is negligible, from which they can derive SUBARCTIC_WINTER, and MIDLAT_SUMMER (this last one should correspond best to the conditions of this particular observation). The relative differences may reach ± 10% between 40 and 60 km, with smaller differences above 60 km (less absorption) and larger differences below 35 km (more absorption, but anyway the VER is small). Therefore, for our following studies of many SCIAMACHY limb scans we have systematically used the most relevant standard profile, according to the latitude and season: a so-called CLIMATO_ADAPTED 30 73 atmospheric profile ("adapted climatology").

C.3 Comparison of methods used by others
In particular, for each studied limb scan we have first inverted the SCIAMACHY limb total radiances to retrieve a VER vertical distribution. Then we could compute what would be the nadir radiance in the O 2 band that should have been observed with such a profile, to simulate the MicroCarb geometry of observation or any other GHG monitoring system. The vertical integration was done above 30 km up to 80 km to be consistent with 5 REPROBUS model which stops at 80 km. Absorption by O 2 may be computed in the nadir viewing geometry, though attenuation in this geometry (altitude z>30 km) is small (2% for the Q branch, less outside of the Q branch).

US_STANDARD SUB_ARCTIC_WINTER SUB_ARCTIC_SUMMER CLIMATO_ADAPTED
The photo-dissociation of ozone is the main mechanism for producing O 2 (a 1 Δ) airglow in the atmosphere. It is therefore important that the ozone profile calculated by the REPROBUS model is accurate. In order to verify this condition, comparisons were carried out with the ozone profiles measured by the GOMOS instrument on board 5 ENVISAT. GOMOS (Bertaux et al., 2010) measured ozone profiles by the stellar occultation method under night and day illumination conditions. For daytime occultations, there is a contaminating signal both from the illuminated limb and from the nadir emission scattered by the GOMOS baffles. Though the processing pipelines have been designed to correct for these contaminations, the resulting uncertainties in ozone density retrieval may be larger, depending on the geometrical conditions of the occultation and the altitude, lower altitudes having 10 more stray light. Therefore, we are separating night and day conditions for the comparison.  There is a significant difference above 60 km, where REPROBUS overestimates the amount of ozone relative to GOMOS. At night, GOMOS ozone profiles show a strong ozone minimum around 80 km. This is a true feature, which can be seen directly on the light of the star that increases again when the LOS passes at this altitude during the occultation of the star. This ozone "hole", explained by loss reactions with OH radicals at night, is not reproduced by REPROBUS. The reason for this discrepancy is the assumption in the model that ozone 5 concentration is much larger than atomic oxygen at night and thus can be set as equal to the odd oxygen family . This approximation is justified in the stratosphere and the lower mesosphere but is wrong in the upper mesosphere, where oxygen atoms have a lifetime of the order of a day and a concentration similar to ozone during the night (e.g., Brasseur and Solomon, 2005). This shortcoming of REPROBUS will be corrected in the next version of the model. It must be noted however, that this O 3 overestimation in the upper 10 mesosphere by REPROBUS only occurs in night-time conditions.
Below 20 km the REPROBUS and GOMOS (night) curves are also diverging. Occultation measurements are less accurate below 15-20 km, because of the attenuation of the star signal, so this difference must be considered with caution. In any case, this bias is not relevant to our study since the airglow of O 2 (a 1 Δ) is negligible below 30 km. 15 We then compared all GOMOS ozone profiles in night occultation for 2007 with REPROBUS for 6 different stars, and plotted the relative difference (GOMOS-REPROBUS)/REPROBUS for the four brightest stars in Fig.   D2. Below 60 km, there is an underestimate of ozone in REPROBUS relative to GOMOS with a maximum of about -15% at 55 km which gradually decreases to 0% at 20 km. At the location of the maximum airglow (45-50 km) 10 the bias is about -8 to -10%. This lack of ozone in REPROBUS is a major reason to explain why the airglow emission estimated by model is lower than observed by SCIAMACHY (Fig. 12). However, some exercises done by multiplying arbitrarily the REPROBUS O 3 profiles by a factor 1.2 (not shown here) show a small remaining underestimation of the airglow calculated by the model. This discrepancy certainly warrants future detailed studies that are well beyond the scope of the present paper. 15

D.2 Day time ozone profiles
During the day, one comparison of REPROBUS to GOMOS observations is displayed in Fig.D3 for an SZA angle of 38°. There is a deficit (∼ 20 %) of ozone in REPROBUS versus GOMOS around 60 km. However, high 20 quality day side data are scarce with GOMOS, and definitive conclusions cannot be drawn at this stage.

5
We may summarize the comparisons GOMOS/REPROBUS with the following points: -In principle, only dayside ozone is relevant for the prediction of O 2 * airglow at 1.27 µm.
-GOMOS ozone concentration vertical profiles show quite similar values below 60 km between day and night, and larger values of O 3 at night above 60 km, a feature well understood from mesospheric chemistry.
-there is a known shortcoming of the chemistry of REPROBUS model affecting strongly night side predictions 10 above 60 km, quite apparent with GOMOS ozone night side comparisons (too much ozone in REPROBUS).
-Because the O 3 diurnal variation is small below 60 km (there, we are more confident in the model than in GOMOS dayside data to estimate the small ozone diurnal variation), the comparison GOMOS/REPROBUS on the night side showing a deficit (10-20 %) of the model versus GOMOS ozone below 60 km may be applied also to the dayside. Therefore, the comparison of GOMOS ozone data with REPROBUS ozone suggests that one part 15 of the airglow discrepancy is due to a deficit in the ozone predicted by REPROBUS in the range 40-60 km (figure D3).
Appendix E: Surface pressure retrieval on simulated nadir spectra contaminated by O 2 * airglow We performed the inversion of nadir simulated spectra with the 4ARTIC v4.2 software in order to have an estimation of the performance of the O 2 1.27 µm band on the retrieval of the surface pressure "Psurf" when the spectra are contaminated by the O 2 * airglow signature. 5 In order to build the synthetic spectra simulating the data to be fitted in our inversions we followed the following three steps: 1. Computation of a very high resolution "reflected" spectrum in the B4 Microcarb band (1.27 µm), without noise, by calling the radiative transfer model 4AOP (sampling 0.001cm -1 ). This spectrum is then degraded at the resolution of the Microcarb instrument (resolving power = 25000) and resampled 10 on the Microcarb wavelength grid.
2. Adding an airglow spectrum as seen from TOA with nadir view. This spectrum is assumed to be proportional to the logarithm of the atmospheric O 2 transmission at high altitude multiplied by the emission to absorption ratio ε(λ)/SS(λ) as explained in Appendix B. In the frame of this study, we developed a software tool for building such a spectrum. 15 3. Finally generate 1000 noisy spectra by adding a randomly generated Gaussian noise with amplitude based on the Microcarb SNR.
We tested two inversion methods: -Method #1: Simultaneous inversion of airglow and Psurf. 20 -Method #2: Inversion of only Psurf using a spectel mask, eliminating from the fit the most contaminated spectels (as recommended by Sioris 2003 for the O 2 A band).
For both methods the performance of estimation of Psurf is based on a Monte-Carlo approach with the inversion of 1000 noisy spectra. The two statistical performance estimators are the Psurf random error which is calculated as the standard deviation of the 1000 retrieved Psurf values and the Psurf bias which is calculated as the 25 difference between the Psurf true value (1013 hPa) and the average of the 1000 retrieved Psurf values.
The inversion scheme used by 4ARTIC is based on the Optimal Estimation Method (OEM) described by Rodgers (2000) which uses a Bayesian approach (use of a-priori information to constrain the inversion). The elements of the state vector are: Psurf, mean Albedo, spectral slope of albedo, dry air mixing ratios X CO2 , X H2O and (only for method #1) the airglow scaling factor(s). 30 80 Both methods are described below with their associated results of the Psurf performance estimators. We remind that the MicroCarb requirements on the Psurf retrieval for a median intensity luminance Lmoy scenario are 0.1 hPa in term of bias and 1 hPa in term of random error. This reference luminance value Lmoy corresponds to an observation with SZA=36° and albedo at 1.27µm = 0.2. For both methods, these values have been used for computing the reflected spectrum with 4AOP (see step 1 above). Only a clean atmosphere scenario, i.e. without 5 aerosol, was tested for both methods.
Method #1: In the first method, we try to invert the O 2 * airglow at the same time as Psurf (and the other state vector elements). We tested three different approaches concerning the inversion of the airglow: 10 1. The shape of the airglow spectrum is considered to be perfectly known. In the state vector, we invert an 'airglow scaling factor' whose associated jacobian is the airglow spectrum that we put in the simulated data. The starting value for the scaling factor is equal to 0 and the true value which is expected to be retrieved is 1.
2. The shape of the airglow spectrum is not considered to be perfectly known. We still use a single 15 'airglow scaling factor' but its associated jacobian spectrum has a slightly different shape than the spectrum that we put in the simulated data. We took for the jacobian spectrum the airglow spectrum obtained with the REPROBUS VER profile in colocation with the SCIAMACHY profile used to build the airglow spectrum put in the simulated data. This is illustrated in Fig. E1 and E2.
Thus the error done on the shape of the airglow spectrum is representative of the error that the 20 REPROBUS model does on the computation of an airglow VER profile.
3. The shape of the airglow spectrum is considered not perfectly known. However we try to "approach" it as much as possible by inverting a linear combination of a cold airglow and a warm airglow (different mesospheric temperatures), both having slightly different shapes. A cold airglow spectrum is built with our tool by using a SCIAMACHY VER profile at SZA=85° (whose peak is 25 around 60 km) and a warm spectrum by using a SCIAMACHY VER profile at SZA=36° (peak near 45 km). These two spectra are then normalized to the intensity of the airglow spectrum that is put inside the simulated spectrum which we wish to invert. The model spectrum that we wish to best approximate this simulated spectrum will be a linear combination of these two normalized spectra, with a sum of coefficients near unity, which is more convenient for the description of the 30 81 mesosphere. The cold and warm "normalized" spectra are used in the inverse model as jacobians of two elements of the state vector, respectively a cold and a warm airglow scaling factor.

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The results of the Psurf inversion by method #1 for the three approaches, using only the 1.27 µm band, are presented in Table 2. The results presented in Table 2 show that the Microcarb B4 band allows retrieving Psurf with a random error of 0.88 hPa which is compliant with the Microcarb requirement (1 hPa). Adding a second element of airglow does not seem to increase the Psurf random error. When considering that the shape of the airglow spectrum is perfectly known (test #1), the bias on Psurf is completely negligible. However in true conditions, this will not be 10 the case since the shape of the airglow spectrum is dependant of not perfectly determined variables like the temperature profile or the airglow VER profile. When forcing the shape of the spectrum with an error representative of the error done by REPROBUS model on the determination of the airglow VER profile (Test #2), we obtain a significant bias of 0.26 hPa. However by letting the inversion process adjusting the shape of the airglow spectrum, that is,to say, using a linear combination of a cold and warm airglow (test #3), the Psurf bias is 15 reduced to -0.11 hPa which is very close to the Microcarb requirement (0.1 hPa).

Method #2:
In the second method the airglow is not inverted. Instead, we used a mask of spectel in order to discard the spectels which are the most contaminated by the airglow emission. Indeed, since the emission lines are thinner 20 than the absorption lines and centred on the same wavelength, we can apply a narrow mask on the central part of each absorption line which will remove most of the airglow emission lines while keeping the wings of the bertaux 31 oct. 19 16:15 Supprimé: i.e 84 absorption lines as well as the CIA continuum, both bringing useful information to retrieve Psurf. As we consider that the airglow spectrum can be a-priori estimated (by a model) and corrected with an accuracy of about 90%, the airglow spectrum which is put in the simulated spectrum to be inverted is only 10 % of the intensity of the airglow spectrum used in method #1.
We tested three pixel masks which remove all spectels whose intensity is higher than 10%, 1% and 0.1% 5 respectively of the maximum intensity of the airglow spectrum (located at 7882 cm -1 ). This is illustrated in Fig.   E3. Figure E3: Airglow spectra at 1.27 µm, at Microcarb resolution, used in our tests of inversion of Psurf 10 with method #2 for several values of the spectel mask: no mask (pink), 10% mask (blue), 1% mask (red), 0.1% mask (green). The three masks remove respectively 14%, 31% and 44% of the spectels in the B4 band.
The results of the Psurf inversion with the 3 masks, using only the 1.27 µm band are presented in Table 3  The spectels contaminated by airglow are a source of bias on the Psurf retrieval. The more contaminated spectels we discard with a mask, the more this bias is expected to be reduced. However, at the same time, the more spectel we discard, the more we increase the random error since we lose some useful information on Psurf in the absorption bands. Thus we are looking for a mask which provides a good compromise between bias and random 10 error. Table 3 shows however that the spectel mask method does not allow meeting the Microcarb requirement simultaneously in term of bias and random error using the Microcarb B4 band only. Values are however not that far from Microcarb requirements and mask number #3 for example allows being in spec in term of bias (-0.04 hPa) while keeping a reasonable random error of 1.52 hPa. This method can thus be foreseen as a good alternative to the method #1 and is worth being tested on Microcarb data when available. 15 Therefore, we have demonstrated with the above simulations that with the spectral resolving power of Microcarb (25000), and only using the O 2 IR band B4 at 1.27 µm, we may retrieve Psurf (or similarly the O 2 vertical column of dry air) with an accuracy almost compliant with the Microcarb requirements. Other tests were also made with 4ARCTIC, by using simultaneously both O 2 bands B1 (0.76 µm) and B4 (1.27 µm) of Microcarb. Of course, it improves very much the retrieval accuracy, but since we are investigating the use of the B4 band 20 because band B1 is suspected to present some problems, we do not show the results here. It will be particularly interesting to investigate the improvement of using the B4 band, in addition to the B1, in the presence of aerosols. This is way beyond the scope of the present study. However, the capability to disentangle the spectrum of the O 2 * emission from the O 2 IR absorption with their fine structure should not depend very much on the presence of aerosols, in view of their slowly varying spectral signature with wavelength. 25 87 represented up to 60% of the emission at 70 km. Therefore, this non-LTE emission triggered by solar radiation forms an airglow layer that is intercepted in a nadir viewing geometry. Such a known-to-exist contribution should be subtracted systematically from nadir-viewing measurements (i.e., IASI measurements). This contribution has been ignored by de Wachter et al. (2017), analyzing nadir IASI methane measurements. A rough estimate from figures of Lopez-Puertas et al. (2005) indicates a non-LTE horizontal emission of 100 5 nanowatt/cm 2 /sr, over 4 cm -1 at 50 km altitude. A vertical viewing would reduce this value by a Chapman factor of several tens, probably below the noise of IASI measurements (∼10 nw/(cm 2 sr cm -1 ). However, it should be noted that there is also certainly some non-LTE emission below 50 km (difficult to see for MIPAS), and that this spectrum has a very similar shape as the LTE emission. Therefore, the non-LTE emission should be modelled, scaled to MIPAS determinations at high altitudes, and subtracted blindly form nadir viewing (IASI-type 10 measurements). It is possible that other bands of CH 4 used for GHG retrievals may be similarly affected.
The fluorescence of H 2 O molecule excited by solar radiation has been observed at 2.67 µm in the coma of several comets (i.e., Bockelée-Morvan et al. 2015) and should be present in the atmosphere of the Earth, as well as in the other lines which are present in GHG bands (i.e. at 2.0 µm). These H 2 O airglow emissions superimposed to surface radiation have not been subtracted from nadir observations or their intensity even 15 estimated, to the best of our knowledge.
The fluorescence of CO molecule excited by solar radiation has been observed at 4.53 µm in the upper atmosphere of Venus with high spectral resolving power (R~43,000) by Marcq et al. (2015). The same must happen in the atmosphere of the Earth, introducing a bias of about 1% on the CO column retrieval (rough estimate), may be not so important because well below the currently achieved accuracy of some tens of % on CO 20 columns. Here we show some figures describing our processing of Level-1c SCIAMACHY radiance data, as explained in Section 3.1, in order to get a "pure" radiance spectrum of the O 2 * airglow. 5 Figure G1. This high altitude spectrum recorded above 105 km contains some residual spectral (readout) patterns left from the calibration step and is subtracted from all measurements obtained at lower altitude in the same scan limb. Figure G2. Spectra corrected from high altitude spectrum showing still two bad pixels at wavelength 1262.267 nm and 1282.128 nm. We replaced their value by the average of their two surrounding pixels to obtain spectra of Figure G3.

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The tangent altitude of the LOS is colour coding each spectrum.