## 4 Impact of Oxygen Transmittance Compensation on Different SIF Retrieval Strategies
### Oxygen Compensated SFM  
This section assesses the performance of the O\({}_{2}\) compensated SFM for a range of sensor heights above TOC (from 3 m to 20 m) on the O\({}_{2}\)-A absorption region and for the same instrument configurations evaluated in Section 4.2. For a specific sensor, the SFM depends strongly on: (1) the considered wavelength interval; (2) the use of weighting functions; and (3) the mathematical functions used to model the fluorescence, \(F\), and the reflectance, \(\rho\), spectra [24]. According to the results obtained in [PERSON] et al., 2010 [24] for noise-free data, the best SFM performance was obtained by modelling SIF (\(F\)) as a quadratic function and reflectance (\(\rho\)) as a cubic function for a narrow spectral interval ranging between 759.3-762.0 nm, without any weighting function. Due to multiple spectral configurations considered here, in order to ensure that enough bands are selected (specially for the lower resolutions evaluated), we have expanded the selected spectral interval to 759.3-767.5 nm (which corresponds to the third range interval described in [24]). For the SFM calculation, the first guess of the \(F\) polynomial coefficients was estimated by fitting the reference SIF spectrum to a quadratic function and distorting the derived coefficients by 10% of their value. Conversely, the first guess of the \(\rho\) polynomial coefficients was estimated by fitting the apparent reflectance spectrum \(\rho_{app}\) to a cubic function, in the spectral region around the O\({}_{2}\)-A, but avoiding the absorption band. The apparent reflectance spectrum, \(\rho_{app}\), was obtained as the ratio between the upward radiance and the incoming solar irradiance measured at sensor level. In Figure 9, \(\rho_{app}\) at the highest and lowest spectral resolution that we evaluated are presented for \"at-TOC\" surface level, and at 3 m and at 20 m heights. It can be observed that with increasing sensor height, peaks in the apparent reflectance become lower. In the particular case of the 20 m sensor height, peaks in the \(\rho_{app}\) have been transformed into depressions. Prior to showing the impact of the O\({}_{2}\) effects on the modified SFM formulation, we present as a reference point (Figure 10), the level of accuracy of the retrieved SIF when the SFM is applied at TOC surface level for the given surface reflectance and SIF spectra, with the polynomial functions used to model these signals, and the selected spectral interval. As can be seen in Figure 10, relative errors are lower than 10% for high resolution spectrometers. This error increases with decreasing spectral resolution, i.e., for sensors with wider bands. Therefore, following the same configuration (i.e., same spectral interval and polynomial functions to model \(\rho\) and \(F\)), the performance of the SFM is presented for the case when O\({}_{2}\) transmittance effects are compensated using Equation (11) (Figure 11). Figure 11 shows the estimated SIF for each of the above-evaluated set-ups 1-4. Errors on retrieved SIF are derived due to: (1) modelling the \(\rho\) and \(F\) signals as a cubic and a quadratic function, respectively; (2) introducing the O\({}_{2}\) transmittance compensation but ignoring the effects of multiplying atmospheric functions with absorption features already convolved (mentioned in  
Section 3.3); and (3) not restricting the modelled functions to realistic values. In set-ups 1 and 3, where the upward O\({}_{2}\) transmittance from target to sensor is corrected (\(t_{O_{2}}^{\dagger}\)) the estimations of values close to 0.97 [mW/m\({}^{2}\)/sr/nm] (which corresponds to the SIF reference value at the bottom of the O\({}_{2}\)-A band, see Figure A1) are accurately retrieved. However, estimated SIF values far away from the deepest region of the oxygen band are not successfully derived (not following the 1:1 line) due to not properly considering the convolution by the ISRF in the formulation.