where M is the number of measurements and m is the estimated measurement error.
The second step consists in separating, for each altitude z, the contribution of the active atmospheric components to the total extinction coefficient by solving the system:
K*i (z) = EN0 ni (z)<cl Y&z) = £ N0 ni (z)<c2
To validate our procedure, we have built a batch of simulated data based on the MSISE-90 model (Hedin 1991) for the atmospheric constituents vertical distributions and on the Science softCon database (Nolle et al. 2005) for their respective cross-sections (once again, scattering was neglected). The absorption cross-section variations with the temperature have been neglected so far. Their introduction in the model is to be considered in the future.
The component distributions and cross-sections were introduced in the forward model together with a chosen spatial profile of solar irradiance to estimate the atmospheric transmittance for a given set of tangential point altitudes. The vertical sampling was 2 km. A random noise of 10-4 order of magnitude for Zr channel and 10-5 elsewhere was added to the attenuated and unattenuated signals (i.e., the numerator and denominator of Eq. (7)). This amount of noise is representative of what we expect with LYRA for acquisition cadences of the order of 1 Hz.
In a first attempt, we have postulated that I2(y, /¿) is constant all over the solar disk. A second step would involve introducing the limb brightening for Al and Zr channels (see e.g., Warren et al. 2001) and a limb darkening for Hz channel (see e.g., Bonnet and Blamont 1968; Samain 1979). The solar emission radial variation for the Ly channel is still subject to discussion and should be carefully evaluated. This will be part of a future paper. Our final objective is to use a more realistic model, taking into account the quiet Sun regions, active regions, and coronal holes as well. The spatial distribution of these regions would be determined using information from imaging telescopes such as SWAP (Sun Watcher with APS detectors and image Processing), also on-board PROBA2.
Afterwards, we have used the noisy simulated data as input of the retrieval process and compared the output with the initial simulated values.
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