Text S1. Details of the retrieval concept
The transmission spectrum is calculated using well-known Beer-Lambert law, taking into account all altitude layers above the considered one. Free parameters of the fitting are temperature, concentrations of CO2 and H2O, and the aerosol slant opacity. We do not consider any atmospheric scattering effect, neither Rayleigh one, which is negligible in the middle IR range, nor the aerosol one, which is rather weak relative to the directly incoming solar flux. In the fitting procedure, an optimal search is based on partial derivatives of the transmission on each of the free parameters. Here, the key contribution comes from the cross section derivative with respect to temperature: ∂σ/∂T (Fig. 3b). The first guess (a priori) values for the considered atmospheric parameters are taken from the Mars Climate Database (MCD 5.3; Millour et al., 2018) adapted for the ACS occultation climatology in MY 34 and 35.
Since the altitude, z , profiles of temperature T (z ) and CO2 density N CO2(z ) are simultaneously fitted, the pressure p (z ) is calculated by integrating T (z ) using the equation of hydrostatic equilibrium:\(p\left(z\right)=p_{o}\exp\left[-\int_{z_{o}}^{z}\frac{g\left(h\right)M(h)}{k_{B}T(h)}dh\right]\). Here, kB – Boltzmann constant, g(z) is the gravity acceleration, and M(z) is the atmospheric molecular weight (taken from MCD). A reference pressure pois calculated for a specified altitude zo from the ideal gas law:\(p_{o}=p\left(z_{o}\right)=\left(\frac{N_{\text{CO}2}\left(z_{o}\right)}{f_{\text{CO}2}\left(z_{o}\right)}\right)k_{B}T(z_{o})\). The CO2 volume mixing ratio \(f_{CO2}(z_{o})\) is also derived from MCD. In all occultations, zo is selected between 20 and 60 km (Fig. 1d), where the retrieval uncertainties are minimal. Once the hydrostatic pressure profile is derived, we keep it fixed when a new temperature and CO2density are retrieved on the next iteration. We repeat this procedure about 5-6 iterations while the profiles reach a convergence. Here, the values on an (i -1)th step are used as a priori for the i th one. When sounding the CO2-rich atmosphere by CO2 spectroscopy, the fitting of N CO2 with the hydrostatic pressure assumption is physically reasonable, rather than using the directly fitted pressure while keeping N CO2 fixed.
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