## 5 Conclusions  
Remote sensing retrieval of Solar Induced chlorophyll Fluorescence (SIF) from Top-Of-Atmosphere (TOA) is challenging due to the tininess of the SIF signal. For this reason, the multiple strategies developed in the last few years to retrieve SIF from satellite data make use of the solar and terrestrial absorption regions where radiance at TOA is considerably reduced. In the particular case of the O\({}_{2}\)-B and O\({}_{2}\)-A bands, these are conveniently located in the SIF spectrum, i.e., close to each of the typical SIF emission peaks, being wider and deeper than the solar lines and thus more sensitive for SIF detection. However, oxygen bands are highly affected by atmospheric effects, especially by the aerosols scattering and surface pressure. For this reason, the FLuorescence EXplorer (FLEX)/Sentinel-3 tandem space mission proposes an SIF retrieval strategy based on a two-step approach: (1) performing the Atmospheric Correction (AC), and (2) applying a Spectral Fitting (SF) technique to retrieve SIF. Given the tininess of the SIF signal, it is well-known that any inaccuracy in the atmospheric state characterization can lead to errors in the estimated SIF. However, just as important as the atmospheric parameters characterization is the use of an appropriate formulation to infer surface apparent reflectance from TOA radiance and to apply a consistent coupling process between the AC and SF strategies. Thus, assuming the atmospheric state as known, we evaluated the mathematical formulation of the FLEX data processing scheme, from the TOA radiance inversion to its coupling with the at-surface level SF method. It was shown that the impact on TOA radiance of the approximations assumed by FLEX is around one order of magnitude lower than an expected variation caused by increasing 10% of the value of a typically SIF emission spectrum. It was also demonstrated that an inconsistent AC-SF coupling process derives errors that depend on the atmospheric transfer functions because of the formulation involved in the process. One of the advantages of using a two-step approach resides in the intermediate products generated, such as the apparent reflectance (\(\rho_{app}\)). Using simulated data with SCOPE and MODTRAN radiative transfer models, we subsequently analysed the spectral distortions propagated to \(\rho_{app}\) due to inaccuracies in the estimation of aerosol optical properties. As it was expected, different distortion patterns appear in the \(\rho_{app}\) due to the over-/under-estimation of each of the key aerosol optical properties: the AOT, the Angstrom exponent (\(\alpha\)) and the Henyey-Greenstein (HG) scattering anisotropy parameter (\(g\)). This leads us to proposing to exploit the use of the \(\rho_{app}\) as a quality indicator of the AC. As a proof of concept, a simple exercise was performed over \(\sim\)8\(\cdot\)10\({}^{4}\) incorrectly atmospherically corrected \(\rho_{app}\) database by using a multivariate linear regression technique to predict the over-/under-estimation of the aerosol optical properties. First, results showed that the AOT, \(\alpha\) and the \(g\) parameters can be corrected with a relative error lower than 0.5%, 8% and 3%, respectively, for 75% of the evaluated data. In the context of the FLEX/Sentinel-3 tandem mission, the exploitation of the apparent reflectance spectral distortions can open up new opportunities to refine the atmospheric parameters obtained from the AC process. The authors extend their thanks to [PERSON] for the contribution to this work. Thanks also go to the Spanish Ministry of Economy and Competitiveness predoctoral grant BES-C-2014-0087 for funding, the AVANFLEX (Advanced Products for the FLEX mission), and the ESP2016-79503-C2-1-P National Program for the Promotion of Scientific and Technical Research of Excellence Ministry of Economy and Competitiveness, Spain.