## 7 Conclusions  
When estimating the weak Sun-Induced chlorophyll Fluorescence (SIF) signal by resolving the strong O\({}_{2}\)-A absorption region and using passive remote sensing techniques, atmospheric effects must always be compensated, even at proximal-sensing scenarios. Among all possible atmospheric effects that can impact SIF retrievals on proximal-sensing scenarios, the accurate compensation of the oxygen absorption is of most importance. In this respect, incorporating the oxygen transmittance spectral function in the formulation of the classical SIF retrieval strategies, such as the Fraunhofer Line Discriminator (FLD) or the Spectral Fitting Method (SFM) family of techniques, involves applying some algebra between non-smooth spectral functions already convolved according to the instrument resolution, which leads to unduly mathematical formulations. In this paper, we reported that compensating for oxygen transmittance with the 3 FLD technique leads to a SIF estimation with relative errors between 8% (17%) and 20% (50%) for a spectral resolution (SR) of 0.1 nm (1 nm) and a target-sensor distance between 3 to 20 m. Similarly, estimated SIF at the bottom of the O\({}_{2}\)-A band when compensating for oxygen effects on SFM derives slightly more accurate results in all the sensor configurations evaluated, from 5% ( 6%) to 24% ( 31%) for a SR of 0.1 nm (1 nm). Hence, in order to simultaneously deal with the correction of the oxygen effects while defining a proper formulation that consistently operates the algebra at high spectral resolution, we proposed to adapt a classical airborne atmospheric correction strategy for proximal-sensing scenarios. The proposed strategy makes use of an atmospheric radiative transfer model (RTM) to characterize the target-sensor optical path. Assuming a perfect atmospheric modelling, the use of an airborne atmospheric correction scheme becomes the preferred strategy, being able to accurately estimate SIF within 10% of relative error for all the sensor spectral resolutions between 0.1 nm and 1 nm in the spectral region of 759-768 nm. Certainly, while the accuracy achieved by making use of an atmospheric RTM will be strongly dependent on the auxiliary data available to characterize the atmospheric state; no errors will be derived in this case due the mathematical formulation assumed. Finally, given the key role of the oxygen absorption effects on SIF retrievals, this work also addressed the need to take into account the dependence of oxygen absorption on air temperature (\(T\)) and pressure (\(p\)) conditions. This fact is of particular relevance for those experiments measuring long temporal SIF data series, especially at latitudes subject to strong \(T\) and \(p\) seasonality effects.  
The following are available at [[http://www.mdpi.com/2072-4292/10/10/1551/s1](http://www.mdpi.com/2072-4292/10/10/1551/s1)]([http://www.mdpi.com/2072-4292/10/10/1551/s1](http://www.mdpi.com/2072-4292/10/10/1551/s1)).  
[PERSON] performed the simulated analysis presented; [PERSON]. ([PERSON]), help in the analyses interpretation; [PERSON] contributed to the initial idea and many important comments; [PERSON]. ([PERSON]) polished the manuscript; [PERSON] reviewed the manuscript and scientifically contributed to the discussion; [PERSON]-C. contributed to the environmental parameters analyses discussion; and [PERSON] supervised the full work.  
This research was funded by the Spanish Ministry of Economy and Competitiveness grant number BES-C-2014-0087. [PERSON] was supported by the European Research Council (ERC) under the ERC-2017-STG SENTIFLEX project (grant agreement 755617).  
Thanks to the AVANFLEX (Advanced Products for the FLEX mission), ESP2016-79503-C2-1-P National Program for the Promotion of Scientific and Technical Research of Excellence Ministry of Economy and Competitiveness, Spain.  
The authors declare no conflict of interest.