## 4 Impact of Oxygen Transmittance Compensation on Different SIF Retrieval Strategies
### High Spectral Resolution  
An initial simulated experiment was conducted to estimate the impact of ignoring oxygen effects on the retrieved SIF at a high spectral resolution of 0.06 nm, regardless of the retrieval technique implemented. To do so, four instrumental configuration set-ups were evaluated: \((1)\)\(L\) corrected for target-sensor O\({}_{2}\) absorption and \(\overline{E}\) measured at TOC (Figure 5a); \((2)\)\(L\)**not** corrected for target-sensor O\({}_{2}\) absorption and \(\overline{E}\) measured at TOC (Figure 5b); \((3)\)\(L\) corrected for target-sensor O\({}_{2}\) absorption and \(E\) measured at sensor level on a tower (Figure 5c); and \((4)\)\(L\)**not** corrected for target-sensor O\({}_{2}\) absorption and \(E\) measured at sensor level on a tower (Figure 5d). In all cases, SIF was estimated by isolating \(F\) from Equation (3), assuming the surface reflectance spectrum was known. Thus, the resulting expression used to estimate SIF in each experimental set-up was:  
* Set-up (1): \(F=L/t_{O_{2}}^{\uparrow}-(\overline{E}\cdot\rho)/\pi\)
* Set-up (2): \(F=L-(\overline{E}\cdot\rho)/\pi\)
* Set-up (3): \(F=L/t_{O_{2}}^{\uparrow}-(E\cdot\rho)/\pi\)
* Set-up (4): \(F=L-(E\cdot\rho)/\pi\)The retrieved O\({}_{2}\)-A band SIF from all set-up configurations \((1-4)\) was obtained for a nadir observation geometry and covering sensor mounted-heights from 3 m to 20 m on a tower (Figure 6). At greater sensor heights above the TOC, the impact of aerosol and molecular oxygen on retrieved SIF becomes more critical. According to Figure 6, estimated (coloured lines) and reference (black solid line) SIF values inside the O\({}_{2}\)-A absorption band are reasonably close, especially for bands deep inside the absorption dip, and particularly in cases where the O\({}_{2}\) correction was applied, i.e., set-up configurations \((1)\) and \((3)\). However, when no O\({}_{2}\) absorption correction on the target-to-sensor optical path is applied, i.e., set-up configurations \((2)\) and \((4)\), then retrieved SIF is highly underestimated. Outside the O\({}_{2}\)-A absorption region, retrieved SIF is biased compared with the reference SIF (black solid line) for all the scenarios, and this effect increases as the sensor height increases. This is attributed to limiting the correction of the atmospheric transmittance (\(t^{\uparrow}\)) to only the O\({}_{2}\) transmittance (\(t^{\uparrow}_{\text{O}_{2}}\)). This effect is demonstrated in Figure 7a where SIF was estimated by correcting the at-sensor radiance for only the aerosol transmittance (\(t^{\uparrow}_{\text{a}er}\)). As it can be observed, the earlier existing bias in the spectral region outside of the O\({}_{2}\) absorption band has disappeared. In addition, in Figure 7b, we evaluated the impact of using the solar irradiance at sensor level instead of at TOC. To do so, SIF was estimated by correcting the at-sensor radiance using the total atmospheric transmittance (\(t^{\uparrow}\)). This case is similar to the set-up configuration 3, but residuals in the estimated SIF are now exclusively caused by the at-sensor measured solar irradiance. In both cases of Figure 7, because the at-sensor radiance has been corrected for the total or aerosol transmittance, there are no residuals caused by aerosols out of the absorption band (i.e., no bias is observed). Figure 5: Diagrams in (**a–d**) corresponding to the instrument set–up configurations (1), (2), (3) and (4), respectively, described in Section 4.1. (**d**) represents the common configuration of tower–mounted instruments to measure SIF at tower–scale. In some cases, downward looking sensors mounted at the tower ‘s top allow multi–angular data collections. Down–welling solar irradiance is typically acquired with upward looking hemispherical or conical systems or by measuring a reference panel with a downward looking sensor. Here \(t^{\uparrow}\) is the upward atmospheric transmittance. Likewise, an analogous analysis was conducted for the O\({}_{2}\)-B region and for a wider spectral range from 650 nm to 800 nm.