## 4 Impact of Oxygen Transmittance Compensation on Different SIF Retrieval Strategies
### Oxygen Compensated 3 FLD  
A second simulation experiment was performed by varying the sensor height above TOC (from 3 m to 20 m), and the instrument spectral configuration for the 4 set-up configurations as described in Section 4.1. In this section, we applied the 3 FLD method with the approximation to compensate for the O\({}_{2}\)-A transmittance effect, as given in Equation (8). The selected sensor specifications, i.e., Spectral Resolution (SR) and the Spectral Sampling Interval (SSI), are listed in the legend of Figure 8 and are based on configurations evaluated by [46].  
Figure 8 shows the performance of the 3 FLD method under set-up configurations 1-4 for different sensor specifications. Since the 3 FLD method depends strongly on the wavelength locations, especially for the wavelength at the bottom of the O\({}_{2}\)-A absorption region, we have kept the central wavelength of the band located at the bottom of the O\({}_{2}\)-A absorption region constant at 760.6 nm in all of the sensor specifications evaluated. Consistent with results shown in Figure 6, as the sensor height above TOC increases, set-up configurations 2 and 4 underestimate the retrieved SIF and produce negative values. For set-up(s) 1 and 3, where O\({}_{2}\) transmittance between the target and the sensor is  
Figure 8: Relative error (%) on retrieved SIF in the O\({}_{2}\)–A region when applying the 3 FLD method according to Equation (8) for a range of spectral resolutions, applied to set-up configurations 1–4 (red symbols and lines) from left to right panels, respectively. The SIF relative error obtained when applying the 3 FLD at TOC surface level is indicated with black symbols and lines.  
Figure 7: SIF in the O\({}_{2}\)–A region was estimated by: (**a**) correcting the at-sensor radiance for the aerosol transmittance (\(t^{\uparrow}_{\text{a}or}\)) and measuring the solar irradiance at TOC surface level; (**b**) correcting the at-sensor radiance for the total transmittance (\(t^{\uparrow}\)) and measuring the solar irradiance at sensor level. The black dashed line in (**a**) shows the lower y–axis limit established in (**b**). Notice that (**a,b**) have different SIF ranges.  
corrected, SIF was overestimated as the sensor height increases and as the sensor resolution decreases. In addition, according to Figure 6, we could expect that SIF estimations from set-up 1 were more accurate (provide lower relative errors \([\%]\)) than from set-up 3. However, this is not the case. This can be attributed to a compensation between the overestimation produced by the 3 FLD technique and the stronger SIF underestimation produced in set-up 3 by measuring the solar irradiance at sensor level. Note, that for all the configurations, SIF was also retrieved at TOC level using the 3 FLD method to identify the relative error baseline for each of the sensor configurations evaluated (black symbols and lines in Figure 8), for comparison.  
SIF relative errors in Figure 8 have been limited to a range of \(\pm\)50%. For set-up 4, where no O\({}_{2}\) compensation is applied, the application of the 3 FLD method produces high underestimations of the SIF values, even for sensors located as close to the surface as 3 m, regardless of the instrument configuration used. For configurations 1 and 3, only in the particular cases where the instrument acquires the signal at high spectral resolution (i.e., SSI \(<\) 0.2 nm and SR \(<\) 0.4 nm), does the compensation for the O\({}_{2}\) effects lead to SIF relative errors less than 30% for all sensor heights.