Evidence of a significant rotational non-LTE effect in the CO2 4.3 µm PFS-MEX limb spectra

Abstract

Since January 2004, the planetary Fourier spectrometer (PFS) on board the Mars Express satellite has been recording near-infrared limb spectra of high quality up to the tangent altitudes $\approx$ 150 km, with potential information on density and thermal structure of the upper Martian atmosphere. We present first results of our modeling of the PFS short wavelength channel (SWC) daytime limb spectra for the altitude region above 90 km. We applied a ro-vibrational non-LTE model based on the stellar astrophysics technique of accelerated lambda iteration (ALI) to solve the multi-species and multi-level CO${}_{\mathrm{2}}$ problem in the Martian atmosphere. We show that the long-standing discrepancy between observed and calculated spectra in the cores and wings of 4.3 $\mathrm{\mu }$m region is explained by the non-thermal rotational distribution of molecules in the upper vibrational states 10011 and 10012 of the CO${}_{\mathrm{2}}$ main isotope second hot (SH) bands above 90 km altitude. The redistribution of SH band intensities from band branch cores into their wings is caused (a) by intensive production of the CO${}_{\mathrm{2}}$ molecules in rotational states with $j>30$ due to the absorption of solar radiation in optically thin wings of 2.7 $\mathrm{\mu }$m bands and (b) by a short radiative lifetime of excited molecules, which is insufficient at altitudes above 90 km for collisions to maintain rotation of excited molecules thermalized. Implications for developing operational algorithms for massive processing of PFS and other instrument limb observations are discussed.

Introduction

For more than 6 Martian years the Planetary Fourier Spectrometer (PFS) on board the Mars Express satellite has been measuring the near-infrared radiances in both nadir and limb geometries. For the study of Martian middle and upper (60–130 km) atmosphere, limb measurements of the CO${}_{\mathrm{2}}$ 4.3 $\mathrm{\mu }$m emission are of particular interest as the source of information on density and thermal structure of this layer. These measurements are achieved by the PFS' short wavelength channel (SWC) [1.25–5 $\mathrm{\mu }$m] with the spectral resolution allowing the unambiguous identification of many of the CO${}_{\mathrm{2}}$ emission bands. Details on the instrument description, its calibration and in-flight performance can be found in , , and .

The strong daytime CO${}_{\mathrm{2}}$ 4.3 $\mathrm{\mu }$m emissions measured by PFS SWC are formed in the non-local thermodynamic equilibrium (non-LTE), which requires detailed accounting for the variety of processes influencing the ro-vibrational populations. The excitation of the CO${}_{\mathrm{2}}$(${\mathit{\nu }}_{\mathrm{3}}$) vibrations is facilitated by absorption of solar radiation in the range of 1–2.7 $\mathrm{\mu }$m by the CO${}_{\mathrm{2}}$ molecules. This excitation is followed by the cascade radiative one-quantum 4.3 $\mathrm{\mu }$m transitions. In addition, the collisional quenching of molecular vibrations (V-T processes) and the inter- and intra-molecular exchange of vibrational energy (V-V processes) also strongly influence the populations.

A number of studies (hereafter “previous studies”) were undertaken in recent years aimed at interpretation of the PFS SWC limb spectra. These studies consider only vibrational non-LTE in CO${}_{\mathrm{2}}$ assuming molecular rotations completely thermalized (rotational LTE) and reiterate main features of daytime 4.3 $\mathrm{\mu }$m CO${}_{\mathrm{2}}$ emission formation in the upper atmosphere, which is dominated by the second hot (SH) and third hot (TH) bands of the main CO${}_{\mathrm{2}}$ isotopologue (hereafter 626). Despite the good general understanding of how the absorption of solar radiation and subsequent redistribution of vibrational energy generate the hot CO${}_{\mathrm{2}}$ band emissions, significant features present in the measured PFS spectra remain unexplained. Specifically, the majority of the daytime limb radiance measurements above approximately 90 km exhibit substantially stronger emissions than predicted by the non-LTE models in the spectral ranges 2290–2305 and 2345–2355 cm${}^{-\mathrm{1}}$ relative to the maxima of radiation at 2317 and 2335 cm${}^{-\mathrm{1}}$, respectively . An approach to explain this feature used in the previous studies was to treat the collisional rate coefficients as free parameters. However, the desired result was not reached, and it was speculated that remaining discrepancies might be due to contributions of some unidentified weak CO${}_{\mathrm{2}}$ 4.3 $\mathrm{\mu }$m bands not yet present in the HITRAN/HITEMP and GEISA spectroscopic databases. This issue remains unresolved until now. It prevents the scientific community from applying suitable retrieval algorithms for obtaining parameters of the Martian middle atmosphere from the PFS SWC limb spectra around 4.3 $\mathrm{\mu }$m.

In this paper we address this long-standing discrepancy and provide its clear physical explanation.

Modeling the 4.3 $\mathrm{\mu }$m emissions

The ALI-ARMS code

In this paper the CO${}_{\mathrm{2}}$ non-LTE populations and limb spectra are calculated using the ALI-ARMS (for Accelerated Lambda Iterations for Atmospheric Radiation and Molecular Spectra) non-LTE code package . ALI-ARMS utilizes the accelerated lambda iteration (ALI) technique developed in stellar astrophysics for calculating the non-LTE populations of a very large number of atomic and ionic levels in optically thick atmospheres. ALI has became a standard technique for spectrum formation calculations and for the computation of the non-LTE model stellar atmospheres. The ALI-ARMS code has been successfully applied to the diagnostics of a number of space infrared Earth's and Martian observations, both spectrally resolved and broadband signals , as well as to study the infrared radiative cooling/heating in planetary atmospheres .

Rotational LTE and non-LTE

In order to establish a nominal result for a pure vibrational non-LTE model (complete rotational LTE is assumed) as used in previous studies, we run ALI-ARMS for our extended reference CO${}_{\mathrm{2}}$ model for a dust-free atmospheric model retrieved from the Mars Climate Database (hereafter MCD)

http://www-mars.lmd.jussieu.fr/mars/access.html

, which matches the observation conditions. This reference model accounts for 150 vibrational levels of five CO${}_{\mathrm{2}}$ isotopologues and about 40 000 lines in calculating the non-LTE populations. The radiative transfer and solar absorption terms are calculated for all the 376 bands present in the task. We apply the same collisional rate coefficients for the lower vibrational levels as those used in previous studies. However, a different scaling of these basic rates for higher vibrational levels is performed based on the first-order perturbation theory as suggested by .

Once the CO${}_{\mathrm{2}}$ populations are known we simulate the limb spectra in the range 2200–2400 cm${}^{-\mathrm{1}}$ for different tangent altitudes both accounting for and not accounting for the overlapping and compare them to the PFS observations. In our model we include in total 60 bands of the five isotopologues that contribute to the CO${}_{\mathrm{2}}$ 4.3 $\mathrm{\mu }$m limb emission.

A random sample of the PFS measured spectrum is shown as a black curve in Fig. . This and other spectra have been kindly provided for this study by the PFS PI M. Giuranna. The shown spectrum is an average of 27 single scans taken for the following conditions: $L_{\mathrm{s}}=254$, latitude $=$ $-$67${}^{\circ }$, local time $=$ 18:00, and solar zenith angle (SZA) $=$ 69${}^{\circ }$, and tangent height of 115 km. As we already noted the effect addressed here is present in the majority of daytime spectra. Therefore, no special criteria in latitude/longitude or local time were applied to select these particular spectra for comparison with calculations here. The turquoise curve in Fig.  presents the spectrum for our nominal run (these and other simulated spectra in this figure were obtained for SZA $=$ 69${}^{\circ }$). We show here the synthetic radiance for tangent height of 120 km since for a given input atmospheric model it provides better agreement with measured spectrum at 115 km.

The mismatch of emission absolute values between measured and simulated spectra for the tangent altitude of 115 km (see also orange curve in Fig. , discussed below) may be attributed both to the mismatch of input model and to the simplifying assumptions applied in this and previous studies, namely, the missing field-of-view averaging.

Comparison in Fig.  of simulated and measured signals obviously confirms the general conclusion of previous studies: above the altitude of 90 km, no matter the location and local time, taking into account all known weak bands of CO${}_{\mathrm{2}}$ does not improve the mismatch with the observed radiance in the “shoulders” (2290–2305 and 2345–2355 cm${}^{-\mathrm{1}}$) relative to the maximum at 2317 and 2335 cm${}^{-\mathrm{1}}$.

Comparison of measured (black) and simulated PFS SWC spectra. The observed spectrum is an average of 27 single scans taken for the following conditions: $L_{\mathrm{s}}=254$, latitude $=$ $-$67${}^{\circ }$, local time $=$ 18:00, SZA $=$ 69${}^{\circ }$, and tangent height of 115 km. The 1$\mathit{\sigma }$ random uncertainties for this measured spectrum are shown. The simulated spectra are shown for tangent height of 120 km including only vibrational non-LTE in CO${}_{\mathrm{2}}$ (turquoise), with vibrational–rotational non-LTE (green), and with vibrational–rotational non-LTE plus line overlapping along the line of sight (red). The spectra shown in orange color are calculated with the same assumptions as for red, but for tangent height 115 km as a demonstration (see text for detailed description).

[Figure omitted. See PDF]

The problem of “incorrect” radiance distribution between cores and wings of molecular bands is not a new one and has been theoretically investigated in a series of papers by , , and for CO${}_{\mathrm{2}}$ bands for atmospheric conditions of Mars and Venus, and for CO bands by for the Earth's atmosphere. In these studies it has been shown that in the Martian atmosphere the Boltzmann rotational distribution for CO${}_{\mathrm{2}}$ molecules in the ${\mathit{\nu }}_{\mathrm{3}}$-vibrationally excited states breaks down for altitudes above 80 km. At these altitudes the lifetime $\mathit{\tau }=\mathrm{1}/A$ of these vibrational levels, where $A\sim 200$ s${}^{-\mathrm{1}}$ is the Einstein coefficient for the spontaneous 4.3 $\mathrm{\mu }$m transitions, is not long enough for collisions to keep the rotation of excited molecules thermalized. Therefore, the need for complete vibrational–rotational non-LTE consideration had been identified already at that time.

In this study we relax the assumption of rotational LTE for two vibrational levels 10011 and 10012 (HITRAN notation) of main CO${}_{\mathrm{2}}$ isotope 626. These levels are strongly pumped by the absorption of solar radiation at 2.7 $\mathrm{\mu }$m and give origin to the two strong SH bands, which dominate the 4.3 $\mathrm{\mu }$m limb emissions of the Martian middle and upper atmosphere discussed here. We accounted for rotational sublevels up to $j=102$ for each of these vibrational levels. The state-to-state rate coefficients describing rotational relaxation of vibrationally excited CO${}_{\mathrm{2}}$ were calculated as described by , who applied the model of and based on infinite-order sudden (IOS) approximation results. The total rotational relaxation rate used in these calculations was estimated as $k_{\mathrm{rot}}\left(T\right)=\mathrm{2}\mathit{\pi }k(T/p)\mathrm{\Delta }{\mathit{\nu }}_{\mathrm{L}}\left(T_{\mathrm{o}}\right)(T/T_{\mathrm{o}}{)}^{0.7}$, where $\mathrm{\Delta }{\mathit{\nu }}_{\mathrm{L}}$ is the Lorentz line width. The validity of this approach is discussed in detail for linear and nonlinear molecules by . For our model we used mean Lorentz width $\mathrm{\Delta }{\mathit{\nu }}_{\mathrm{L}}$ of CO${}_{\mathrm{2}}$ rotational–vibrational lines from HITRAN12 . Accounting for temperature dependence of these widths, $k_{\mathrm{rot}}\approx \mathrm{3}\times {10}^{-10}$ cm${}^{\mathrm{3}}$ s${}^{-\mathrm{1}}$ for $T=200$ K.

Results and discussion

Importance of rotational non-LTE

The green curve in Fig.  shows the spectrum calculated accounting for the rotational non-LTE at vibrational levels 10011 and 10012 of main CO${}_{\mathrm{2}}$ isotope. One may see that this spectrum shows the redistribution of the radiances from SH band branch cores into their wings and, as a result, reproduces the measured signal shape significantly better than calculations based on the assumption of rotational LTE (turquoise curve).

The reason for this alteration lies in the production of excited 626 molecules in vibrational states 10011 and 10012 due to the absorption of the 2.7 $\mathrm{\mu }$m radiation in the altitude region of 80–140 km. In Fig.  (left panel) we show these production rates, normalized over the rotational quantum number $j$, for state 10011 at an altitude of 120 km for SZA $=$ 69${}^{\circ }$ (red), which corresponds to simulated spectra presented in Fig. . Additionally, the same pumping rates at 100 km for SZA $=$ 60 and 80${}^{\circ }$ (green and blue, respectively) are shown for comparison. Similar production rates were also obtained for level 10012. In general the molecules in level 10011 are most efficiently generated at the altitude of 120 km in rotational states with $j=25$–40 (30–50 for altitude of 100 km). The low production for $j<30$ is caused by a strong absorption of solar radiance in the cores of the 2.7 $\mathrm{\mu }$m band branches in the upper atmosphere, which, however, remain transparent in the branch wings. At the altitudes above 90 km the collisions are not able to completely restore the Boltzmann rotational distribution of molecules in the vibrational states 10011 and 10012, and the latter takes the form shown in the right panel of Fig. . Compared to the Boltzmann distribution (red with circles), rotational non-LTE curve (red) demonstrates enhanced tail for $j>30$, which reflects intensive radiative pumping of these levels shown in the left panel. The same is also true for two other curves (green and blue) shown in this panel for altitude 100 km. The latter demonstrate obvious dependence of the rotational LTE distortion on the SZA in agreement with corresponding production rate variation shown in the right panel of this figure.

Left – normalized distribution of radiative pumping at level 10011 of ${}^{12}$C${}^{16}$O${}_{\mathrm{2}}$ due to the absorption of the 2.7 $\mathrm{\mu }$m solar radiation for altitudes of 100 and 120 km. Right – normalized rotational distribution at level 10011 of ${}^{12}$C${}^{16}$O${}_{\mathrm{2}}$ for altitudes of 100 and 120 km.

[Figure omitted. See PDF]

Importance of line overlapping along the limb LOS

The rotational non-LTE spectrum in Fig.  (green curve) reproduces the general shape of measured signal (black curve) significantly better compared to that calculated with the rotational LTE assumption (turquoise curve). However, there are a number of small- and medium-size spectral features visible in the measured spectrum not present in the simulated one (green curve). So far the synthetic spectra discussed here were calculated ignoring line overlapping along the LOS.

We note here also that, although previous studies report using a forward model capable of treating line overlapping in limb calculations, its effects on PFS spectra were not discussed.

In this study we employed our radiance model in both non-overlapping and overlapping mode. In the latter case the calculations treat spectral line overlapping of all bands (within a band and between lines of different bands) of all isotopes in the line-by-line (LBL) fashion (technical discussion is detailed in ).

The effect of accounting for line overlapping is clearly demonstrated in spectrum plotted in red color. Two well-developed absorption features appeared, one around 2344 cm${}^{-\mathrm{1}}$ and another one around 2324 cm${}^{-\mathrm{1}}$, which overlay well the corresponding features of measured spectrum. We found that the first of these features is caused by the absorption of radiation, which is emitted in the line R22e (here and below the line notations are taken from HITRAN) of the main isotope 10012–10002 SH band, by the nearly coincidental line R16e, which belongs to the fundamental band of isotope 628. The same is also true for the feature at 2324 cm${}^{-\mathrm{1}}$: here the emission line P4e of the 626 SH band 10012–10002 is blanketed by the line P15e of the first hot band 01111–01101 of the same isotope.

In addition, the “rotational non-LTE $+$ overlapping on limb” spectrum (red curve) has an absorption feature around 2316 cm${}^{-\mathrm{1}}$, which is, however, much less pronounced than the one in the measured spectrum. The formation mechanism of this signature is rather complex. Here, the emission line, R9e, belonging to the 10011–10001 SH band of the 628 isotope (pumped by the 2.7 $\mathrm{\mu }$m solar radiation), is attenuated by the two nearby lines Q31f and Q74f, from the 628 and 626 FH bands, respectively. To a smaller degree, several other lines located very closely to the R9e and belonging to various isotopic bands may also contribute to this absorption signature. It should be noted that none of the vibrational levels of bands whose lines are involved in the formation of this absorption feature were treated accounting for the rotational non-LTE in this study. In general, rotational non-LTE at the lower vibrational level can influence the band absorption, whereas at the upper level the band emission is impacted. To get a better agreement with the measured spectrum, regarding the said absorption feature, as well as in the region 2285–2305 cm${}^{-\mathrm{1}}$, where the synthetic spectrum does not reproduce a number of fine “wavy” features, we plan (a) to apply more detailed rotational non-LTE model and (b) to use the exact procedure of spectra convolution, such as the “zero padding”, as applied to the PFS interferograms . This signal processing technique certainly contributes to the formation of these “wavy” features of measured spectra.

Conclusions

We present our first modeling results of the Mars Express PFS SWC daytime limb 4.3 $\mathrm{\mu }$m spectra for the altitude region above 90 km. We show that the long-standing discrepancy between observed and calculated spectra in the cores and wings of the 4.3 $\mathrm{\mu }$m region is explained by the non-thermal rotational distribution of the ${}^{12}$C${}^{16}$O${}_{\mathrm{2}}$ molecules in upper vibrational levels 10011 and 10012 of the strong SH bands. The enhancement of the SH band wing emissions is caused (a) by intensive production of the CO${}_{\mathrm{2}}$ molecules in rotational states with $j>30$ due to the absorption of solar radiation in optically thin wings of 2.7 $\mathrm{\mu }$m bands and (b) by a short radiative lifetime of molecules in these states, which is insufficient at altitudes above 90 km for collisions to maintain rotation of excited molecules thermalized. As a result, redistribution of SH band intensities takes place going from band branch cores into their wings. This result confirms significant impact of rotational non-LTE on the CO${}_{\mathrm{2}}$ 4.3 $\mathrm{\mu }$m emissions of Martian and Venusian atmospheres, which was predicted by and . The PFS spectra provide the first strong evidence of this effect.

Although the rotational non-LTE on the levels 10011 and 10012 does an excellent job explaining the radiance redistribution observed in the measured spectra, more detailed simulations are still needed to investigate whether there are smaller-order effects caused by the rotational non-LTE at other CO${}_{\mathrm{2}}$ vibrational levels. However, accounting for rotational non-LTE significantly slows down the non-LTE calculations by an order of magnitude for the problem discussed in this paper.

Additional improvement in matching the 4.3 $\mathrm{\mu }$m band shape/structure between simulated and PFS measured spectra was reached by accounting for spectral line overlapping (within each band and among lines of different bands) along the limb LOS. This allowed the reproduction of some fine absorption features in measured spectra that were missing in previous calculations, causing, however, a factor of 10 increase of the limb emission computing time. This additional computing time increase indicates the need for significant efforts aimed at optimizing the rotational non-LTE/line overlapping calculations to allow massive processing of measured PFS spectra.

The presented results are also important for diagnostics of other similar observations. For instance, the Venus Express VIRTIS spectra around 4.3 $\mathrm{\mu }$m for tangent heights above 100–110 km, which are discussed in and , demonstrate remarkable resemblance of Mars Express PFS spectra analyzed in this study. Due to a well-known similarity of the CO${}_{\mathrm{2}}$ daytime emission formation mechanisms for both planets the Venus spectra obviously also require detailed rotational non-LTE/line overlapping analysis. These results may also be relevant for the analysis of limb mode measurements of the Trace Gas Orbiter/NOMAD instrument, which will start scientific operation in late 2017.

At last, we note that, as in previous studies, the following simplifications were applied in our simulations: (a) infinite-narrow field-of-view (FOV) approximation was used, and (b) detailed spectra convolution was not performed; only simple (1 cm${}^{-\mathrm{1}}$)-triangle window (to match the instrument spectral resolution) averaging of monochromatic spectra calculated on a fine grid was applied. Neither of these, however, influence the main results of this study. Nevertheless, missing FOV averaging (in combination with insufficient matching of applied pressure/temperature model) may explain better agreement (see Fig. ) between absolute emission values of an average spectrum measured for the tangent altitude of 115 km and the spectrum simulated for 120 km (compare black, red and orange lines in this figure). Additionally, simplified averaging of monochromatic spectra in combination with missing FOV averaging may cause certain fine structure inconsistencies between measured and simulated spectra compared in this study.

Data availability

The PFS data are available in the ESA Planetary Science Archive: ftp://psa.esac.esa.int/pub/mirror/MARS-EXPRESS/PFS/ (Giuranna, 2016). The results of calculations presented in Figs. 1 and 2 are available on the Open Science Framework website: 10.17605/OSF.IO/6S6UJ (Kutepov et al., 2017).

Acknowledgements

The authors cordially thank Marco Giuranna, the PI of PFS/MEX for providing us samples of PFS limb spectra with the emission features unexplained by the nominal non-LTE models, and for a very helpful discussion on the data quality and the general performance of the instrument. The work of AAK was supported by the NASA grant NNX08AL12G and the NSF grant AGS-1301762. The work of LR was partly supported by the DFG grant HA3261/7-1. The work of AGF was supported during his employment in the USA by the NASA grant NNX08AL12G and in France by the project “Towards a better interpretation of atmospheric phenomena” of the French National Program LEFE/INSU. Edited by: M. Rapp Reviewed by: two anonymous referees