Astron. Astrophys. 333, 1092-1099 (1998)

3. Data analysis and modelling

3.1. Data calibration and determination of the line characteristics

The full transmission level of the spectra exhibits instrumental low frequency ripples. These were locally removed by fitting a Spline function to the continuum. As no absolute calibration of the data was available, the lines were rescaled to the continuum level, i.e. expressed as a fraction of the continuum, which is itself rescaled to its calculated value.

However it should be noticed that although not calibrated in absolute, the relative flux levels of the four 1991 spectra are consistent with the average albedos taken for the four different Mars areas sampled (see Sect. 3.2). About 30 ¹² CO lines were detected in the spectra. We selected among these lines those which were located in the parts of the spectra that have the best transmission level. We selected 25 such lines in the case of the 1990 spectrum, which all fall in the 4245-4330 cm^-1 region, and 17 for the four 1991 spectra (Fig. 2), which all fall in the 4250-4310 cm^-1 region. No isotopic CO lines were detected in the useful parts of the spectra (which is to be expected given our spectral resolution).

Fig. 2. The four 1991 spectra. The line identifications are given for Point 1. All are raw data.

The very high spectral resolution of the 1990 data allowed us to use three parameters to fit the 1990 lines: the depth at the center of the line, the depth at one FWHM (Full Width at Half Maximum) and the depth at two FWHMs. In the case of the 1991 data, the lower spectral resolution of the spectra resulted in the line widths to be entirely defined by the instrumental function. For this reason we fitted the 1991 data using the line depths only (Fig. 3). The estimated uncertainty on the measured line depths is given by the noise level as measured outside the filter plus the uncertainty on the position of the continuum level. We estimate its value to be of 10% of the continuum. This uncertainty on the line depths results in an equivalent uncertainty on the line FWHMs.

Fig. 3. Observed line absorptions for the 1991 data. The observed absorption (expressed as a percentage of the continuum level) is given as a function of line number (number 1 is for P2, number 2 is for P1, number 3 is for R0 and then number 4 to 17 are for R1 to R14).

3.2. Modelling of the 2.35 spectrum of Mars

At 2.35 , the emission of Mars is entirely dominated by its solar reflected component. The model used is quite comparable to the one we developed for the lines at 4.7µm (Billebaud et al., 1992): it consists of a multilayer radiative transfer code which generates synthetic CO lines. A major complication, however, is that at 2.35µm, the effects of light scattering by atmospheric dust are significant. Therefore, a complete scattering model, previously developed by Rosenqvist et al. (1992), was used to estimate the influence of the suspended dust on the depths and widths of the martian lines. It is a doubling-adding model consisting in 150 sublayers of 0.5 km thickness which finally provides the reflection coefficient of the total atmosphere. Conversely, the effects of scattering by ice clouds are neglected for two reasons: (i) their contribution is very small because the optical depth of these clouds is lower than 0.03 (Chassefière et al., 1992), (ii) the ice clouds are dispersed and small in dimension. Three main parameters define the scattering process: i/ the single scattering albedo a; ii/ the phase function and iii/ the total opacity. The single scattering albedo of the dust (0.9) was taken from Drossart et al. (1991), using results on the atmosphere of Mars obtained by the ISM instrument onboard the Phobos spacecraft. This value is also consistent with those from Pollack et al. (1977, 1979). The phase function is derived from Drossart et al. (1991). It can be described by a double Henyey-Greenstein function (Henyey and Greenstein, 1941; Rosenqvist, 1991) with a positive asymmetry parameter of 0.7 and a negative one of 0.5. These parameters are valid for the period of the Phobos observations (1989), but they can be extended to the period of our observations (January 1991), as the atmosphere of Mars did not exhibit large modifications (like global storms) between 1989 and 1991 (James et al., 1994). The surface reflectance property is assumed to be described by the Minnaert law with a coefficient of 0.85. The scale height of the dust ( 6 km) was taken from Chassefière et al. (1992) and Chassefière et al. (1995).

In the case of the 1990 data, we assumed an average surface pressure on the whole disk of the planet of 6 mbar. Concerning the 1991 data, for each spectrum (i.e. for each point on the planet), we determined a local average altitude, using the two available orographic datasets: the Consortium and the Digital Terrain Model. The altitude was then used to determine the surface pressure, under the assumption of a temperature profile, using Viking data (Seiff and Kirk, 1977). The pressures were compared to those obtained with the General Circulation Model (GCM) of Laboratoire de Météorologie Dynamique which accounts for local conditions, seasonal and diurnal variations as well as for the impact of atmospheric dynamics on the surface pressure distribution (Hourdin et al., 1993, 1995). The GCM pressures systematically lie in between the extreme values obtained by extrapolation of the Viking data. The albedos were taken from Kieffer et al. (1977) in order to check out the consistency with the flux levels (see 3.1). The temperature of the atmospheric level just above the surface was directly taken from the GCM simulations.

This temperature is 210 10 K for the four points and was used to compute a Viking-type thermal profile (Seiff, 1982), which is then used to calculate a CO absorption coefficient. It should be noted however that, as we work within the reflected component of the planetary emission, it is not required that the thermal profile be precisely determined. The local characteristics of the four points on the planet are given in Table 1. The effects of variations of the parameters on the integrated intensity of a typical line are given in Table 2. The CO spectroscopic data were taken from the GEISA databank (Husson et al., 1986) and the collisional broadening coefficients from Varanasi (1975). A Voigt profile was used to account for the simultaneous collision and Doppler broadening.

Table 1. Local characteristics for the four points on the planet - 1991 data.

Table 2. Relative effects of the parameter variations on the equivalent area (area multiplied by FWHM) of a line.

3.3. Results

The two unknowns in the model are the dust optical depth and of course the CO mixing ratio. We varied the dust optical depth within the 0.0 to 0.6 range, higher values being unrealistic (James et al., 1994) during periods without dust storms, as it was the case at the time of our observations. For the CO mixing ratio, we used values ranging from 3 10^-4 to 13 10^-4 for the 1990 data and from 3 10^-4 to 20 10^-4 for the 1991 data, by step of 1 10^-4 (see examples of fits with various CO mixing ratios on Figs. 4 and 5). Again, smaller or larger values are not realistic in the frame of what we presently know about the CO mixing ratio.

Fig. 4. Examples of fits of the line depths with various CO mixing ratios for a dust optical depth of 0.0 (no dust) in the case of the Point 1 (calculations done with the minimum value of the pressure), 1991 data.

Fig. 5. Examples of fits of the R14 line of the 1990 data, with the best model and two extreme models (which are outside the domain of solutions) with the same dust opacity of 0.20.

The presence of atmospheric dust complicates the analysis. Indeed, all the lines that we could use are strong CO lines. The prime effect of the dust is thus that the bottom of the lines is rising when the amount of dust is increased. As on the contrary, an increase in the CO mixing ratio deepens the lines, we see that the effects of the dust and of the CO mixing ratio go in opposite directions. The result of that is that we obtain domains of possible solutions that are not strongly constrained in the case of the 1991 data. For the 1990 data, as we could fit the line with three points (one at the center of the line and two in the wings, see Sect. 3.1) and as the effect of the dust scattering is different on the line core and line wings, the domain of solutions is narrower. In order to determine the domains of solutions, we made tests. The result of this test with a 2- confidence level in the case of the 1990 data gives a value of the dust optical depth between 0.13 and 0.23 and a value of the CO mixing ratio between 4.5 10^-4 and 8.5 10^-4 (which gives a column density of 1.0 10²⁰ cm^-1 to 2.0 10²⁰ cm^-1), stressing that not any combination of dust opacity and CO abundance is possible (see Fig. 6).

Fig. 6. Domain of solutions for the 1990 data.

The domains of solutions obtained after the tests (2- confidence level) for the four 1991 spectra are presented on Fig. 7 (note on Figs. 6 and 7 how the CO mixing ratio and dust optical depth appear to be correlated). They show that the CO abundance can take any value between 3.5 10^-4 and 20.5 10^-4 (column density of 1.3 to 6.5 10²⁰ cm^-1) for Point 1 and between 5.5 to 20. 10^-4 (column density of 1.3 to 4.2 10²⁰ cm^-1) for Point 2. In fact, the upper limit is artificial and corresponds to the highest value we introduced into the model, so we could have gone higher, as shown by the shape of the domains obtained for these two points. But as we said previously, this would not be realistic. The domains of solutions for the two other points give us a value of the CO abundance that can range from 3. to 17.5 10^-4 (column density of 8.5 10¹⁹ cm^-1 to 4.8 10²⁰ cm^-1) for Point 3 and from 3. to 18.5 10^-4 (column density of 8.9 10¹⁹ cm^-1 to 5.4 10²⁰ cm^-1) for Point 4. Concerning the dust opacity, it never exceeds 0.08 for Points 3 and 4 and can take any value for Point 1 and 2. However, again, as shown on Fig. 7, not any combination of CO mixing ratio and dust opacity is possible. Fig. 8 represents the intersection of the previous domains. It shows that a CO mixing ratio ranging from 5.5 to 11.5 10^-4 and a dust optical depth ranging from 0.03 to 0.08 provide a satisfactory fit to the ensemble of observations.

Fig. 7a-d. Domains of solutions for the four points of 1991. The solid, dotted, dash-dotted lines indicate respectively the limits of the domains of solutions obtained with the optimum, minimum and maximum values of the pressure. The sharpness of the contours is due to the discretization and therefore has no real meaning. This is also the case for the gap between the two domains of solution obtained for Point 3.

Fig. 8. Intersection of the domains obtained for the four points of 1991.

© European Southern Observatory (ESO) 1998

Online publication: April 28, 1998

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