A simple, autonomous, non-linear inversion method for the analysis of occultation observation of the dusty atmosphere of Mars.

editorial reviewedOzone (O3) is an important atmospheric specie of planet Mars, capable of absorbing ultraviolet (UV) radiation. Occultation of solar (or stellar) radiation and measurement of the extinction of UV photons by the atmosphere is a standard O3 remote sensing method. Both O3 and carbon dioxide (CO2) absorb UV photons in the 200 – 300 nm range, the O3 Hartley absorption band peaking near 250 nm. Dusts also contribute to, and sometimes dominate, the UV extinction by the atmosphere of Mars. The wavelength-dependent dust extinction coefficient (k) is often described using a power law k=k0 (λ0/ λ)α with reference value k0 at wavelength λ0. The ad-hoc α exponent stems from the properties of the dusts. We develop a simple autonomous, nonlinear method to retrieve the vertical profiles of CO2, O3 and dust properties from solar occultation profiles, under a spherical symmetry assumption. The gas concentration and dust reference extinction (k0) are represented using a combination of triangle functions of the radial distance (r), producing a piecewise linear profile. The α parameter is represented similarly using triangle functions of log(r). Slant line-of-sight optical thickness results from the Abel transform of these profiles, producing hypergeometric 2F1 functions for the dusts. The different parameters are retrieved by inverse Abel transform using a least squares minimization, which depends linearly on the CO2, O3 and k0 profiles, and non-linearly on α. The linear parameters are considered as functions of the α, reducing the fitting to a non-linear minimization over the α parameter profile only. This drastically reduces the number of dimensions of the parameter space. We show that this method allows efficient retrieval of all the parameters. Noise is however expected to be present when analyzing occultation data from the NOMAD-TGO instrument, which can reduce the ability to retrieve the minimization parameters. The k0 and O3 profiles can, nevertheless, be expected to be retrieved over about two orders of magnitude, while the CO2 density profile can be expected to be fairly retrieved at relatively low altitude

Inversion of occultation observation of a dusty atmosphere using hypergeometric functions.

Occultation of solar radiation by a planetary atmosphere is a very accurate method to obtain high signal vs noise spectral measurement of the properties of the atmospheric gas, not only owing to the overwhelmingly large photon flux from our host star, but also because the method is nearly not dependent on instrument calibration. On the other hand, the method can only be applied near the terminator. Using occultation techniques in other regions of the atmosphere can nevertheless be done using stars as a radiation source, but the instrument then has to be more sensitive to cope with the severely reduced photon flux. The method nevertheless remains independent on the absolute calibration of the instrument. Occultation observation directly provides the optical thickness (or the extinction coefficient) of the absorbing and scattering constituents when multiple scattering can be safely neglected. Under those conditions, the measurement gives the line-of-sight integrated density of the absorbing and scattering constituents, and simultaneous measurements at several wavelength are then needed to discriminate between the effects of the several species. Retrieval of the vertical density profile of the different constituents requires an inversion method, basically an inverse Abel transform when a spherical (or cylindrical) symmetry assumption can be made. Efficient inverse Abel transform methods rely on least squares fit techniques taking advantage of easy-to-compute analytical indefinite integrals constructed from the Abel transform integral operator. In the case of a dusty atmosphere, the contribution of dusts to the extinction depends on the properties of the dust grains controlling their scattering cross section, which is generally represented using the so-called alpha parameter appearing as an exponent of the wavelength in the expression of the cross section. As the properties of the dusts vary with altitude, so does the alpha parameter, which severely complicates the computation of the indefinite integrals needed for the inverse Abel transform fitting. We propose a method that allows to express those indefinite integrals using Gauss’s hypergeometric 2F1 function, which can be applied to the observation of the Earth as well as of planet Mars, as it is done by the ESA EXOMARS-NOMAD instrument