CO2 retrievals in the Mars daylight thermosphere from 4.3 μM limb emissions

• Autores: Sergio Jiménez Monferrer
• Directores de la Tesis: Bernd Funke (dir. tes.) , Miguel Angel López Valverde (dir. tes.)
• Lectura: En la Universidad de Granada ( España ) en 2019
• Idioma: inglés
• ISBN: 9788413063379
• Número de páginas: 224
• Tribunal Calificador de la Tesis: Manuel López Puertas (presid.) , Francisco José Olmo Reyes (secret.) , Maia García Comas (voc.) , Anni Elisa Määttänen (voc.) , Denis Belyaev (voc.)
• Enlaces
  • Tesis en acceso abierto en: DIGIBUG
• Resumen

  • * Introduction * Despite the importance of the thermosphere, for instance, to the atmospheric escape to space, this is maybe the less known region of the Martian atmosphere. Most of the information we have of these altitudes comes from very disperse and unconnected sources. Among them,a few in situ profiles taken during the descent of some missions, like Viking 1 and 2, the aerobraking manoeuvres by the Mars Global Surveyor and Mars Reconnaissance Orbiter spacecrafts, the SPICAM instrument on board Mars Express, and the instruments on board the MAVEN mission. These measurements allowed to obtain density and temperature profiles, and to study the seasonal and geographical variabilities of the thermosphere. According to these observations and their numerical simulations, the thermosphere of Mars is a complex and dynamic region, strongly coupled to lower layers. Concretely, the effects caused by the dust storms and the temperature variability in the low atmosphere are propagated upwards up to the thermosphere. To understand this region, it is therefore necessary a global view of the atmosphere, from its interactions with the surface, to the exchanges of species with the exosphere.

    The thermospheric data previously described have a limited temporal and geographical coverage. Some important issues, like the influence of solar activity, are difficult to understand from the available data. Most of them, except aerobraking measurements, concentrate in the night side of the planet, leaving the diurnal thermosphere almost unexplored. It is in the dayside thermosphere where the strongest infrared atmospheric non-thermal emissions are produced. These infrared emissions offer an interesting possibility for remote sounding at these heights in all terrestrial planets.

    There are indeed thermospheric observations of Mars in the infrared, but they have not been sufficiently exploited so far, due to the complexity of the physical interpretation and the numeric difficulty of the required mathematical inversion. These observations were acquired by two instruments on board Mars Express, OMEGA and PFS. Their analysis is expected to provide a wider and deeper understanding of the dayside thermosphere at the maximum sensitivity altitudes.

    In the Group of Terrestrial Planetary Atmospheres (GAPT, for its Spanish acronym) at the Instituto de Astrofı́sica de Andalucı́a (IAA), a large experience on non-thermal atmospheric emissions, physical models for the Mars atmosphere, and tools for the inversion of such emissions are available. Molecular species, like CO2 , produce strong non-thermal emissions in the infrared in the higher layers of the atmosphere. At those altitudes, the density is so low and molecular collisions are so rare that local thermodynamic equilibrium (LTE) conditions no longer apply. The departure from LTE typically occurs in the diurnal hemisphere when such species are excited by solar radiation in the rotational-vibrational bands in the near and medium infrared (between 1 and 10 um). The emissions produced contain information on the densities of the emitting species, and therefore contribute to the extraction of density and temperature profiles in the higher atmosphere. Some difficulties arise with this type of observations. First, the emission of these tenuous layers is low, so the observation in limb geometry, where the emission of a large atmospheric path is integrated on the detector, is extremely helpful. Besides, inherent difficulties arise when dealing with non-LTE conditions, as this approximation is not valid. This issue is solved by the use of inversion codes including a non-LTE model in the forward calculation (fundamental tool of the inverse problem). Finally, the lack of local measurements of the atmospheric magnitudes involved, needed to start and guide the retrieval, is overcame by the assumption of a priori conditions predicted by 3-D numerical simulations by state-of-the-art General Circulation Models of Mars.

    We analysed limb infrared CO2 emissions, in the region around 4.3 um, obtained by OMEGA in the daylight thermosphere of Mars, in order to infer information on fundamental atmospheric parameters, like density and temperature. These emissions are caused by CO2 fluorescence of solar radiation, and the investigation needs to take into account non-LTE conditions. We performed a radiometric calibration on the data provided by OMEGA, cleaned the available spectra, including the use of clustering techniques, and generated radiance vertical profiles for each orbital dataset. The distribution and geometry of the spectra acquired by OMEGA are highly heterogeneous, leading to very different projections in the limb of the Martian atmosphere. For this reason, a series of geometric criteria was established in order to allow for an easier and consistent comparison among the results of the retrievals.

    Once the radiance vertical profiles were generated, we applied a non-LTE retrieval scheme based on a extensively validated scheme working for Earth, which we adapted to Martian conditions. In this work we present information on the inversion set up, and a discussion on the retrieved CO2 density profiles. A total of 742 profiles were formed from the 47 OMEGA orbits with limb observations previously selected. The convergence rate achieved considering the entire dataset was 94%, which is considered as very satisfactory.

    From the retrieved CO2 densities, we derived temperature profiles, assuming hydrostatic equilibrium. For this, we made use of an algorithm developed for that task. For 60% of the orbits analysed we found a minimum in the temperature profile at 140–150 km, indicating a thermosphere colder than that of the model used, the LMD-MGCM. On the opposite side, a thermosphere warmer than that predicted by the model was obtained in 30% of the orbits.

    An extensive sensitivity study of the retrieval scheme was also carried out. We found that, in general, the uncertainty due to the instrumental Gain calibration and that caused by the retrieval noise error itself are of primary importance, while the influence of the temperatures in the reference atmosphere used as a priori, provided by our General Circulation Model (GCM), is minor. According to our study, CO2 profiles can be derived with a precision of around 20% and a vertical resolution of around 15 km between 120 and 160 km tangent altitude.

    Finally, we compared the density and temperature profiles obtained to the predictions of the LMD-MGCM and to the results recently provided by other instruments studying the Martian thermosphere. In general, no clear correlation of the data-model discrepancies obtained with any temporal or spatial dimension is observed, neither from a global study nor when a more homogeneous subset of OMEGA observations, i.e., at constrained geolocation, is analysed. There is one exception, the solar zenith angle, which affects the atmospheric emission. Most observations from other instruments, like in situ or remote measurements by NGIMS and by IUVS (both on board MAVEN), respectively, have uncertainties of the order of those presented in this work. The results from these experiments also bring to light important differences when compared to the LMD-MGCM or other General Circulation Models. This global comparison with numeric simulations indicates an atmospheric variability in line with that found in our OMEGA data. This result points to the necessity of validation of global models at thermospheric altitudes. The thermosphere of Mars is, indeed, a complex and dynamic region.

    * Motivation * The Martian thermosphere is a complex region, strongly coupled with lower layers, and not observationally explored in a systematic way. Several instruments on board Mars Express have improved their limb-pointing capabilities to perform observations at high altitudes (above 50 km) in the Martian atmosphere. This is the case of the strong emissions, due to solar fluorescence of CO2, observed by OMEGA and PFS, in the spectral range around 4.3 um (Formisano et al., 2006; López-Valverde et al., 2011; Piccialli et al., 2016). These emissions have not been fully exploited so far, i.e., used to derive both temperature and CO2 density. Retrieving these parameters from non-LTE solar fluorescence is a challenging task. However, if non-LTE effects were properly incorporated into an inversion scheme, an entirely new set of observations of the dayside of Mars would be available at thermospheric altitudes. This could improve our understanding of the thermospheric state and its variability, and should help to validate and enhance the performance of global models at these altitudes.

    Non-LTE retrievals of CO and CO2 from IR emissions at high altitudes have been commonly undertaken in the case of Earth's atmosphere (Jurado-Navarro et al., 2016; Funke et al., 2009; Kaufmann et al., 2002; Mertens et al., 2009), and have recently been performed also for the Titan (López-Valverde et al., 2005; Adriani et al., 2011; Garcı́a-Comas et al., 2011) and Venus (Gilli et al., 2015; Peralta et al., 2016) atmospheres. The retrievals on Venus were performed for CO from VIRTIS/Venus Express measurements, assuming optically thin conditions, or from a nadir down-looking geometry, with a fixed and broad emission layer, which simplifies the inversions. However, CO2 is a minor species on Earth, unlike the case of Mars. The application of a non-LTE retrieval in a limb geometry which addresses optically thin and thick conditions, from the emission of the dominant species of the atmosphere is an entirely new problem in terrestrial atmospheres.

    Both OMEGA and PFS provide datasets of these emissions, whose full exploitation was a target within the scope of the European project UPWARDS (Understanding Planet Mars With Advanced Remote-sensing Datasets and Synergistic Studies), an integral study of Mars in preparation for Exomars (UPWARDS, 2019). OMEGA provides simultaneous 2-D imaging and spectra of the CO2 emissions with a relatively small field of view, allowing to study the altitude variation of the 4.3 um emission (Piccialli et al., 2016). On the other hand, PFS has a larger field of view, although with a better spectral resolution. This work focuses on the OMEGA dataset.

    * Theoretical Fundamentals * The radiative-transfer equation at point s' can be written as Lv(s,*s*) = Lv(s0,*s*) exp (-tv(s0,s)) + int (Jv(s',*s*) exp (-tv(s',s)) dtv).

    This equation has a simple physical interpretation. The radiance Lν reaching s is composed of two terms. The first term is the contribution at s0, attenuated by an exponential factor due to extinction over the distance s−s0. The second term, the integral, is the sum of emissions from all the elements ds' at different positions, s', along the path, each of them attenuated by extinction over the remaining distance, s−s'.

    The previous equation, which involves macroscopic quantities, solves the RTE and can thus be used to simulate the atmospheric emissions, but only if the source function is known. For example, under LTE conditions the source function is described by the Planck function, which is known if the temperature is so. However, when we need to consider non-local thermodynamic equilibrium (non-LTE) conditions, the source function is unknown and, therefore, needs to be computed before obtaining the radiation field. Its calculation can be more complicated if many microscopic processes become relevant. For that reason, it is necessary to solve the RTE equation together with the equation that describes the source function, the statistical equilibrium equation (SEE).

    We consider that a given state is in local thermodynamic equilibrium (LTE) when its population is provided by Boltzmann's law at this local kinetic temperature (López-Puertas and Taylor, 2001), i.e., when the mean time between collisions for a given molecule is much shorter than the lifetime for radiative decay. It then follows that the source function, Jν, is described by the Planck function, Bν, at the local kinetic temperature. It should be remarked that LTE may prevail for a form of energy and not for all of them at the same time. In particular, rotational levels might be in LTE while vibrational levels are not, and the same situation is usual for different vibrational levels, with LTE conditions applying to some of them, but not all.

    In strict thermodynamic equilibrium, the radiative field is blackbody radiation (Lν = Bν) and the source function is given by the Planck function (Jν = Bν). In LTE the source function is still given by Planck's function, but the radiance, Lν, can differ from Bν. For this reason, LTE, unlike strict TE, is compatible with a net gain or loss of radiative energy by the gas. In other words, it is compatible with a non-zero heating rate. The only requirement is that collisions should be fast enough to transfer the net absorbed or emitted radiative energy into kinetic energy (López-Puertas and Taylor, 2001).

    When thermal collisions are not enough to keep a Boltzmann distribution of populations, i.e., a distribution determined by the local kinetic temperature, non-local thermodynamic equilibrium (non-LTE) considerations need to be taken into account. The concept of non-LTE was introduced in the context of stellar atmospheres by Milne (1930). In atmospheric context, non-LTE conditions typically apply at high altitudes (low pressures) and for the shorter wavelength bands (more energetic).

    The non-LTE source function depends on the number densities of the populations of the upper and lower energy levels of the transition involved. In addition, the absorption coefficient is given by the parameters introduced at microscopic levels in Einstein's formulation. In non-LTE, the populations of the energetic levels are no longer governed by the kinetic temperature. It is convenient to introduce the concept of vibrational temperature, Tv, to describe them (López-Puertas and Taylor, 2001). These temperatures give the excited populations, in a functional form identical to LTE, playing the role of the kinetic temperature in LTE. It then follows that if the vibrational temperature of a level differs from the local kinetic temperature, the level is in vibrational non-LTE. An equivalent expression can be derived for non-LTE due to rotational transitions.

    Combining the processes contributing to populate and depopulate the vibrational levels described in the full text, we obtain the statistical equilibrium equation for a two-level system as n2/n1 = (B12 Liv + pt + pnt) / (A21 + B21 Liv + lt, lnt), where all the involving terms are explained in the full text.

    We can derive a new expression for the source function, centred at ν0 , for the two-level approximation (Goody and Yung, 1989; López-Puertas and Taylor, 1989; Jurado-Navarro, 2015), Jv0 = (Liv + e1Bv0) / (1 + e2), where values e1 and e2 can be consulted in the full text.

    This equation calculates the non-LTE source function taking into account the contribution of the microscopic processes, including the radiation field. We can now solve the RTE together with the SEE to obtain both the source function and the radiation field (or its divergence, the heating rate).

    When no approximations are valid, we need to solve the RTE, coupled to the SEE, in a general case, considering the exchange of photons between atmospheric layers, the variation of the absorption coefficient with frequency due to vibration-rotation lines, the local thermal and non-thermal processes, and the collisional coupling between some vibrational levels. This generic case is the one solved in this Thesis, and in previous studies in the GAPT team at the Instituto de Astrofı́sica de Andalucı́a (IAA) (López-Valverde and López-Puertas, 1994a; López-Valverde et al., 2008).

    Remote sensing allows to derive fundamental atmospheric parameters, like composition or temperature, via global-coverage observations. The derivation is usually done, however, indirectly, as the actual observations are based on measurements which have some dependence on these fundamental quantities. For example, the target parameters of this study are the CO2 abundance and the temperature in the higher atmosphere of Mars, but they will be inferred from spectral radiances emitted by CO2 molecules, following radiative or collisional interactions.

    The solution of the inverse problem is normally achieved by an iterative process, given the usually high non-linearity of the equations. The iteration, to obtain the solution at step k+1 from step k, can be written as *xi+1* = *xi* + (K' Sy^-1 K + R + LI)^-1 (K' Sy^-1 (*y*-F(*x*)) - R (*xi*-*xa*)), where all the terms are described in the full text. This equation is solved in this work with a tool called Retrieval Control Program (RCP, von Clarmann et al. (2003)).

    The forward model, F(*x*), is an essential piece of every inversion process. It basically consists on a precise line-by-line radiative transfer calculation with a careful handling of geometrical conditions, ray-tracing and instrumental line shape, among others. Under non-LTE conditions, it additionally requires the simulation of the energy state populations of the species responsible for the emissions. This is performed with a dedicated non-LTE model, developed for the species at work, and which is coupled to the line-by-line model.

    At the IAA, our team has been developing and applying non-LTE inversion methods to Earth's atmosphere observations, in collaboration with the Karlsruhe University, during the last two decades. The forward model adopted for the present study combines a generic non-LTE radiative transfer algorithm, the Generic RAdiative traNsfer AnD non-LTE population Algorithm (GRANADA) (Funke et al., 2012), with a well tested line-by-line radiative transfer model, the Karlsruhe Optimized and Precise Radiative transfer Algorithm (KOPRA) (Stiller, 2002).

    We used the Mars GCM developed at the Laboratorie de Météorologie Dynamique, LMD-MGCM (Forget et al., 1999; González-Galindo et al., 2015) in two different ways. First, for characterising the atmospheric conditions (temperature, pressure and abundance profiles) of the geolocations corresponding to measurements. In other words, to build an a priori climatology and a first guess input for the inversion problem. Secondly, when comparing the results of our inversions with model predictions, with the goal of validating the model on one hand and guiding the physical interpretation of our results on the other.

    * Measurements * In this work, we created a large dataset of vertical Level 2 radiance profiles and performed retrievals for them. They were created from Level 1 calibrated radiances pertaining to a total of 47 OMEGA qubes. The generation of these Level 2 profiles is described in Chapter 4. Most of the datasets used in this Thesis correspond to nadir orbits, with a strip acquired in limb geometry (target of opportunity), selected from a larger sample of 98 qubes containing limb observations, provided by the OMEGA team. They are listed next, sorted according to their acquisition date.

    The coverage of the planet atmosphere is not rich enough to allow for a global atmospheric study. There are, however, some interesting regions, where the population of available observations is denser and variability studies are possible (longitudinal variations for a fixed latitude, seasonal variations for a fixed latitud, or latitudinal variations within specific seasons, i.e., with a fixed solar longitude). These scenarios are studied in Chapter 8, where the retrievals are compared with General Circulation Models and other instruments observations.

    * Conclusions * 1. This research successfully tackled and completed two ambitious tasks of the UPWARDS H2020 project: Task T1.3, related to the development of innovative data analysis tools, concretely, the development of a non-LTE inversion scheme for Mars limb infrared emissions; and Task 7.1, related to the scientific exploitation of a unique dataset from OMEGA/Mars Express (its observations of infrared emissions in a limb geometry at thermospheric altitudes), in order to derive for the first time CO2 density profiles from such a complex dataset.

    2. A total of 47 OMEGA SWIR L limb qubes were analysed in detail, including corrections in the calibration pipeline of the OMEGA Team. Radiance vertical profiles, or Level 1 OMEGA limb spectra, were built from the unevenly spaced projection of the instrument's 2-D detector on the limb. These profiles exploited the excellent vertical resolution of OMEGA and incorporated the calibration improvements. The 1-D profiles are the basic input of our inversion scheme and can also be useful for other future studies. They were released to the ESA Planetary Science Archive, where they are open to the scientific community, as a data-product of the UPWARDS project.

    3. The non-LTE scheme for Mars is entirely based on the KOPRA-GRANADA-RCP scheme used for inversion of limb infrared emissions of Earth's upper atmosphere with MIPAS/Envisat, although some adaptation was needed for Martian conditions. One of the key ingredients of the foward model is the non-LTE model for CO2 vibrational populations. We used the GRANADA code, after its comparison and fine-tuning with a specific non-LTE model for Mars and Venus, also developed by our team and applied to Mars in numerous previous studies. Comparisons of the best fit spectra with the data indicate no biases (within measurement noise), which gives us confidence on this code's adaptation to OMEGA and Mars' atmosphere. This non-LTE model is now ready for further application to remote sounding of any CO2 atmosphere, like Mars' or Venus'.

    4. The application of the non-LTE retrieval scheme to the 47 OMEGA data qubes was successful, after tuning and experimenting with numerous internal parameters. The altitude range of the inversion was fixed at 120–180 km, where a high degree of convergence with a small number of iteration steps was achieved. The iteration started from a first guess profile extracted from simulations of the LMD-MGCM for the locations and Mars Year (dust and solar flux conditions) corresponding to every data profile. This was also used as a priori. The vertical resolution of the inverted profile was typically about 15 km, as calculated from the full width at half maximum of the averaging kernels, which critically depends on the spectral resolution and on the sensitivity of the instrument. The retrieval code is now ready for direct application to similar datasets, like measurements by the instrument PFS on board Mars Express, the recent limb emission measurements by NOMAD-LNO on board ExoMars, or an entirely similar set of limb measurements also at 4.3 um of Venus' upper atmosphere taken by the instrument VIRTIS/Venus Express.

    5. The extensive error analysis performed, including sensitivity to non-LTE parameters, indicates that the total uncertainty in the retrieved CO2 densities varies between 20% and 35%, at 120 and 180 km, respectively. The principal contributions to this uncertainty come from the instrumental Gain calibration and from the propagation of the measurement noise error. The individual sensitivities to other parameters uncertainties are significantly smaller. In particular, the sensitivity to the thermal structure extracted from the LMD-MGCM is about a third of the total error in density. This study, together with the description of the non-LTE retrieval scheme, was included in a manuscript led by the author of this Thesis and submitted to a special issue of Icarus, and is currently under revision by the authors once the reviewers submitted their comments.

    6. The total number of 742 individual CO2 profiles in the Mars thermosphere were retrieved and are presented. They correspond to an average of 16 profiles per OMEGA orbit. All of them have a physically meaningful shape, not far from the a priori, although on average the retrieved densities are larger than the model climatology, between 125 and 150 km, with largest differences of 75% around 135 km tangent altitude.

    7. The distribution of the retrieved densities follows that of the instrument limb orbits, which is very patchy and irregular in a latitude/solar longitude/Mars Year frame. Within each orbit, the profiles obtained present a small dispersion, as expected given their close location and the same acquisition time. This dispersion increases with altitude as the measurement noise component dominates. On a larger scale, the variations in the CO2 density coincide with those in the LMD-MGCM. The study of the data-model biases does not show any global trend, nor seem to be correlated with any of the temporal or spatial dimensions, except for the solar zenith angle, as expected, since the weaker the solar irradiation the noisier are the retrieved profiles.

    8. An algorithm was developed in this Thesis to derive temperature profiles from the retrieved densities, by assuming hydrostatic equilibrium, and it was presented and validated using densities and temperatures from the LMD-MGCM. The temperature profiles cover the same altitude range than the CO2 retrievals and include an error calculation based on the CO2 retrieved errors. The temperatures obtained from the OMEGA CO2 retrievals present a larger dispersion than the densities above 130 km, and much larger than the LMD-MGCM collocated temperatures. This dispersion is particularly large around 150 km. A significant number of OMEGA orbits (60%) show a local minimum between 140 and 150 km, with very cold temperatures, which are not reproducible under usual climatic scenarios by the LMD-MGCM. On the opposite side, about 30% of the orbits exhibit a larger value of the temperature around 150 km. No correlation with location or time was found in these variations. Potential candidates to explain these differences include propagation of gravity waves from below, variations in dust content from the climatological values, deviations from hydrostatics due to wave activity, and model deficiencies in the local absorption of solar EUV radiation.

    9. The hydrostatic algorithm developed in this Thesis is being currently applied to determine thermospheric temperatures from UV dayglow measurements by SPICAM/Mars Express, as part of an ongoing research by our team at IAA. The fist part of such project is the application to those dayglow emissions as simulated by the LMD-MGCM. This application demonstrated that the traditional derivation of temperatures from the scale height of the UV emissions is incorrect in the case of the CO Cameron bands, producing too warm values. A similar warning applies to the temperatures derived from the CO2+ UV doublet, affected by a small positive bias in the 175–225 km range, but larger errors outside these altitudes. This result may require a revision of results from diverse previous experiments.

    10. Very recent and precise determinations of densities and temperatures from the MAVEN suite of instruments (NGIMS, EUVM and IUVS) are starting to be available. The different geometries, mode of sounding and altitude explored do not permit a proper collocation of observations with our OMEGA limb data though. However, some variations of the IUVS CO2 densities with latitude at a fixed local time show similar trends than those in our dataset. A very indirect evaluation is also possible via their reported comparison with the LMD-MGCM, which they also used as first guess and ultimate theoretical source for comparison. All these experiments presented a larger variability than the model, which is consistent with our results. Their tentative explanations also coincide with our potential candidates, as they include gravity wave propagation (or deficiencies in their implementation into the LMD-MGCM), and unknown thermal structure of the Martian lower atmosphere. Another aspect of agreement is their reported total error. All those experiments reported uncertainties entirely similar to our more complex inversion technique, around 30% errors in the CO2 density. These comparisons, together with the complete dataset of CO2 and temperatures from OMEGA is part of a second manuscript led by the author of this Thesis, currently in preparation.

    * Bibliography * A. Adriani, B. M. Dinelli, M. López-Puertas, M. Garcı́a-Comas, M. L. Moriconi, and B. Funke. Distribution of HCN in Titan's atmosphere from non-LTE emission from CASSINI/VIMS observations at 3 um. Icarus, 214:584–595, 2011. doi:10.1016/j.icarus.2011.04.016. URL http://dx.doi.org/10.1016/j.icarus.2011.04.016.

    F. Forget, F. Hourdin, R. Fournier, C. Hourdin, O. Talagrand, M. Collins, S. R. Lewis, P. L. Read, and J.-P. Huot. Improved general circulation models of the Martian atmosphere from the surface to above 80 km. JGR, 104(E10):24155–24176, Oct 1999. doi:10.1029/1999JE001025.

    V. Formisano, A. Maturilli, M. Giuranna, E. D'Aversa, and M. A. López-Valverde. Observations of non-LTE emission at 4 5 microns with the planetary Fourier spectrometer abord the Mars Express mission. Icarus, 182:51–67, May 2006. doi:10.1016/j.icarus.2005.12.022.

    B. Funke, M. López-Puertas, M. Garcı́a-Comas, G. P. Stiller, T. von Clarmann, M. Höpfner, N. Glatthor, U. Grabowski, S. Kellmann, and A. Linden. Carbon monoxide distributions from the upper troposphere to the mesosphere inferred from 4.7 um non-local thermal equilibrium emissions measured by MIPAS on Envisat. 9(7):2387–2411, 2009.

    B. Funke, M. López-Puertas, M. Garcı́a-Comas, M. Kaufmann, M. Höpfner, and G. P. Stiller. GRANADA: A Generic RAdiative traNsfer AnD non-LTE population algorithm. Journal of Quantitative Spectroscopy and Radiative Transfer, 113:1771–1817, Sept. 2012. doi:10.1016/j.jqsrt.2012.05.001.

    M. Garcı́a-Comas, M. López-Puertas, B. Funke, B. Dinelli, M. L. Moriconi, A. Adriani, A. Molina, and A. Coradini. Analysis of Titan CH4 3.3 um upper atmospheric emission as measured by Cassini/VIMS. Icarus, 214:571–583, 2011. doi:10.1016/j.icarus.2011.03.020. URL http://dx.doi.org/10.1016/j.icarus.2011.03.020.

    G. Gilli, M. A. López-Valverde, J. Peralta, S. Bougher, A. Brecht, P. Drossart, and G. Piccioni. Carbon monoxide and temperature in the upper atmosphere of Venus from VIRTIS/Venus Express non-LTE limb measurements. Icarus, 248:478–498, Mar. 2015. doi:10.1016/j.icarus.2014.10.047.

    F. González-Galindo, M. A. López-Valverde, F. Forget, M. Garcı́a-Comas, E. Millour, and L. Montabone. Variability of the Martian thermosphere during eight Martian years as simulated by a ground-to-exosphere global circulation model. Journal of Geophysical Research (Planets), 120:2020–2035, Nov. 2015. doi:10.1002/2015JE004925.

    R. M. Goody and Y. L. Yung. Atmospheric radiation : theoretical basis. 1989.

    A. A. Jurado-Navarro. Retrieval of CO2 and collisional parameters from the MIPAS spectra in the Earth atmosphere. PhD thesis, Universidad de Granada, 2015.

    A. A. Jurado-Navarro, M. López-Puertas, B. Funke, M. Garcı́a-Comas, A. Gardini, F. González-Galindo, G. P. Stiller, T. von Clarmann, U. Grabowski, and A. Linden. Global distribution of CO2 volume mixing ratio in the middle and upper atmosphere from MIPAS high resolution spectra. Atmospheric Measurements Techniques, Discuss., 2016, 2016.

    M. Kaufmann, O. A. Gusev, K. U. Grossmann, R. G. Roble, M. E. Hagan, C. Hartsough, and A. A. Kutepov. The vertical and horizontal distribution of CO2 densities in the upper mesosphere and lower thermosphere as measured by CRISTA. J. Geophys. Res., 107(D23):8182, 2002. doi:10.1029/2001JD000704.

    M. López-Puertas and F. W. Taylor. Carbon dioxide 4.3-um emission in the Earth's atmosphere: A comparison between Nimbus 7 SAMS measurements and non-local thermodynamic equilibrium radiative transfer calculations. JGR, 94(D10):13045–13068, Sep 1989. doi:10.1029/JD094iD10p13045.

    M. López-Puertas and F. W. Taylor. Non-LTE radiative transfer in the atmosphere. Singapore: World Scientific, 2001.

    M. A. López-Valverde and M. López-Puertas. A non-local thermodynamic equilibrium radiative transfer model for infrared emissions in the atmosphere of Mars. 1: Theoretical basis and nighttime populations of vibrational levels. Journal of Geophysical Research, 99:13093–13115, June 1994a. doi:10.1029/94JE00635.

    M. A. López-Valverde, E., Lellouch, and A. Coustenis. CO fluorescence from Titan's atmosphere. Icarus, 175:503–521, 2005. doi:10.1016/j.icarus.2004.12.015.

    M. A. López-Valverde, G. Gilli, M. Garcı́a-Comas, F. González-Galindo, P. Drossart, and G. Piccioni. The upper atmosphere of Venus observed by Venus Express, volume 3, pages 13–32. 2008.

    M. A. López-Valverde, M. López-Puertas, B. Funke, G. Gilli, M. Garcı́a-Comas, P. Drossart, G. Piccioni, and V. Formisano. Modeling the atmospheric limb emission of CO2 at 4.3 um in the terrestrial planets. Planetary and Space Science, 59:988–998, Aug. 2011. doi:10.1016/j.pss.2010.02.001.

    C. J. Mertens, J. M. Russell III, M. G. Mlynczak, C.-Y. She, F. J. Schmidlin, R. A. Goldberg, M. López-Puertas, P. P. Wintersteiner, R. H. Picard, J. R. Winick, and X. Xu. Kinetic temperature and carbon dioxide from broadband infrared limb emission measurements taken from the TIMED/SABER instrument. Adv. Space Res., 43(1):15–27, 2009. doi:10.1016/j.asr.2008.04.017.

    E. A. Milne. Thermodynamics of the Stars, pages 65–255. Springer Berlin Heidelberg, Berlin, Heidelberg, 1930. ISBN 978-3-642-90705-0. doi:10.1007/978-3-642-90705-0 2.

    J. Peralta, M. A. López-Valverde, G. Gilli, and A. Piccialli. Dayside temperatures in the Venus upper atmosphere from Venus Express/VIRTIS nadir measurements at 4.3 um. Astronomy and Astrophysics, 585:A53, Jan. 2016. doi:10.1051/0004-6361/201527191.

    A. Piccialli, M. A. López-Valverde, A. Määttänen, F. González-Galindo, J. Audouard, F. Altieri, F. Forget, P. Drossart, B. Gondet, and J. P. Bibring. CO2 non-LTE limb emissions in Mars' atmosphere as observed by OMEGA/Mars Express. Journal of Geophysical Research (Planets), 121:1066–1086, June 2016. doi:10.1002/2015JE004981.

    G. Stiller. Sensitivity of trace gas abundances retrievals from infrared limb emission spectra to simplifying approximations in radiative transfer modelling. Journal of Quantitative Spectroscopy and Radiative Transfer, 72:249–280, Feb. 2002. doi:10.1016/S0022-4073(01)00123-6.

    UPWARDS. Understanding Planet Mars With Advanced Remote-sensing Datasets and Synergistic studies, 2019. URL http://upwards-mars.eu. Online.

    T. von Clarmann, N. Glatthor, U. Grabowski, M. Höpfner, S. Kellmann, M. Kiefer, A. Linden, G. M. Tsidu, M. Milz, T. Steck, G. P. Stiller, D. Y. Wang, H. Fischer, B. Funke, S. Gil-López, and M. López-Puertas. Retrieval of temperature and tangent altitude pointing from limb emission spectra recorded from space by the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS). Journal of Geophysical Research (Atmospheres), 108:4736, Dec. 2003. doi:10.1029/2003JD003602.