## 4 Impact of Oxygen Transmittance Compensation on Different SIF Retrieval Strategies
### Oxygen Compensated SFM
In the cases of set-ups 2 and 4, neither the values at the bottom of the O\({}_{2}\)-A band nor nearby vicinities have been successfully retrieved. Figure 10: Scatter plots of the reference spectra and estimated SIF spectra values (black circles) in the interval between 759.0–767.5 nm, for different instrumental spectral resolutions (SR) and sampling interval (SSI). Estimated SIF was derived by applying the SFM at TOC surface level. Red solid line represents the 1:1 line, and red dashed lines define the region for a SIF relative error lower than 10%. Figure 9: Apparent reflectance (\(\rho_{app}\)) derived at: (**a**) high (SSI 0.1 nm - SR 0.1 nm); and (**b**) low (SSI 1 nm-SR 2 nm) instrument resolutions for 3 m (red circles) and 20 m (blue squares) sensor heights above the TOC. The solid thin black lines correspond to the \(\rho_{app}\) derived at surface level. The solid thick black line corresponds to the surface reflectance used here as a reference. Airborne Atmospheric Correction Scheme Applied to Proximal Sensing Data: O\({}_{2}\) and ISRF Compensated SFM  
As it has been demonstrated during this section, O\({}_{2}\) transmittance effects must be compensated when retrieving SIF from proximal remote sensing data. However, significant errors in estimating SIF can occur, even when applying an O\({}_{2}\) transmittance compensation factor (or spectrum) in the formulations of the 3 FLD (or SFM) approach(es). Thus, here we assess errors derived in the estimated SIF under scenario 1 when following the strategy detailed in Figure 4, which properly includes the ISRF convolution as part of the SFM minimization process. Figure 12 shows the estimated SIF at multiple sensor heights above the TOC when applying the proposed strategy (adaptation from classic airborne correction strategies) and considering the same conditions presented in Section 4.3, i.e., the same spectral interval and the same polynomial functions used to model \(F\) and \(\rho\). Although higher relative errors are derived at lower spectral resolution, errors have significantly improved in comparison to the situation described by set-up 1 from Section 4.3, where the O\({}_{2}\) compensated SFM approach was used while ignoring the effect of multiplying spectrally convolved functions. Therefore, in this case a successful SIF estimation was achieved, including those values that were not close to the bottom of the O\({}_{2}\)-A, i.e., SIF from 0.7-1 [mW/m\({}^{2}\)/sr/nm], for high spectral resolution cases. Finally, in order to evaluate the impact of excluding the aerosol compensation on the upward transmittance from the TOC level to the sensor, we quantified the impact of replacing the O\({}_{2}\) transmittance with the total atmospheric transmittance function, i.e., replacing \(t_{O2}^{\uparrow}\) by \(t^{\uparrow}\). Since the accuracy improvement achieved for estimated SIF was not significant, to better show the slight gain, Figure 13 presents a scatter plot between estimated SIF (labelled as \(SIF_{O_{2}}\)), with compensation only for O\({}_{2}\) transmittance, versus compensation for the total atmospheric transmittance (labelled as \(SIF_{tot}\)). Figure 11: Scatter plots of reference SIF versus estimated SIF spectra in the interval between 759.0–767.5 nm using the SFM retrieval approach and O\({}_{2}\) compensation while ignoring instrument spectral convolution effects for set–up configurations 1–4. Simulations are shown for different instrument resolutions (rows 1–4) and sensor heights between 3 m to 20 m (colour scale). Solid lines are regression lines. Actual estimations are presented as circles. For more details, the Supplementary Material also presents a scatter plot relating reference SIF and \(SIF_{tot}\) spectra (Figure S3). In addition, since the SFM also provides the reflected surface spectrum, scatter plots comparing reference and estimated surface reflectance when compensating for either oxygen transmittance only, or for total atmospheric transmittance, are also included in the Supplementary Material (Figures S4 and S5).