## 4 Discussion
### Apparent Reflectance Spectral Distortion Analysis and Exploitation  
An initial analysis was designed to evaluate the apparent reflectance spectral distortions produced in the oxygen regions by over-/under-estimating three different aerosol optical properties. The selected varying aerosol optical properties were the AOT, the Angstrom exponent (\(\alpha\)) and the asymmetry parameter of the HG scattering phase function (\(g\)), related to the aerosol load, aerosol size, and aerosol scattering anisotropy. Among them, the AOT and the \(g\) are the driving aerosol optical parameters, as they have a higher impact on the spectral distortions of the surface apparent reflectance (\(\rho_{app(atm)}\)). These results are in agreement with the aerosol sensitivity analyses performed in ([PERSON], 2012; [PERSON], 2011). From this analysis, it was found that the spectral distortions produced by each evaluated aerosol property differ not only in magnitude but also in the spectral shape. This suggests that spectral distortions in the \(\rho_{app}\) could be used to refine the estimation of atmospheric parameters in the AC process. Therefore, we investigated the possibility of using the apparent reflectance to detect inaccuracies in the AC. A simple exercise was performed as a proof of concept, creating a DB of erroneously corrected \(\rho^{\prime}_{app(atm)}\). Using a simple multivariate linear regression algorithm, 30% of the DB was used for training and the remaining 70% of the DB was used for validation. Results suggest that the driving aerosol optical properties, i.e., AOT and \(g\), can be predicted with an error below 0.5% (for the AOT) and 3% (for \(g\)) for 75% of the cases. Despite the low sensitivity to the Angstrom exponent, the proposed method can still reduce its errors below 8% for 75% of the cases. However, some limitations are worth noting. Although these results support the hypothesis that the retrieval of aerosol optical properties from an inaccurate AC could be refined due to the distinct spectral pattern produced, the study should be extended to a more complex DB in a future work. Regarding expected improvements related to atmospheric simulations, they should not be limited to the spectral distortions produced by the AOT, \(\alpha\) and \(g\) aerosol properties, but should be extended to other aerosol parameters such as the aerosol vertical distribution or the single scattering albedo. In the particular case of the aerosol vertical distribution, its radiometric effect on TOA radiance will strongly depend on the mathematical function assumed to model the vertical distribution, e.g., Gaussian [13] or exponential [42]. Thus, a more extensive aerosol sensitivity analysis would be beneficial to identify the driving aerosol parameters to be included in a future DB simulation, i.e., to identify those parameters that highly distort the TOA radiance at the oxygen regions under realistic scenarios. With respect to how other atmospheric parameters affect the DB training statistics, e.g., WV or surface pressure, this will strongly depend on the range of the values covered. While the used DB included two different WV and surface pressure (surface height) values, in a new DB design, a wider range and a larger number of grid-points values should be incorporated. Also regarding the surface level, not only simulated but real surface reflectance and SIF spectra should be considered. Additionally, cases where each reflectance spectrum is associated to a range of SIF spectra should also be incorporated. At the same time, more efforts are required to study the impact of an inaccurate ISRF characterization on the predictive power of \(\rho_{app}\), as well as other instrumental effects, such as radiometric noises, residual polarisation effects, or stray-light contamination. In the particular case of the FLEX mission, a polarization scramble will be located in front of the telescope to cover the full pupil.