## 5 Temporal Analysis on Temperature and Pressure Environmental Conditions  
As previously pointed out, when using a RTM the accuracy of the retrieved SIF will strongly depend on the accuracy achieved in modelling the atmospheric conditions. As concluded in Section 4, oxygen transmittance compensation becomes essential to accurately estimate SIF for proximal sensing. In the particular case of conducting a long temporal data series analysis of measured SIF from tower, oxygen transmittance variations caused by seasonal \(p\) and \(T\) changes within the year must also be carefully considered. As an illustrative example, we analysed the expected variation, first for the oxygen transmittance and then for the acquired at-sensor radiance, caused by changes in \(T\) and \(p\) conditions (see Appendix B for details). In this example, we reproduced the radiance variations that would be observed by an instrument mounted on a tower located at the Hyytiala Forestry Field Station in Finland, due only to changes in the meteorological conditions while keeping the surface properties, i.e., reflectance and emitted SIF, invariant. The rationale behind keeping the surface properties invariant is to evaluate changes in sensor radiance exclusively attributed to changes in the meteorological conditions. This is because we were interested in whether these pressure and thermal influences on O\({}_{2}\) transmittance could be incorrectly translated into perceived changes in the retrieved SIF signal if not appropriately compensated. Thus, for the at-surface level we took the reference surface reflectance and SIF spectra shown in Figure 11. For the atmospheric simulation we did the exercise in three steps: (1) taking the \(T\) and \(p\) registered in Hyytiala, we computed the transmittance following the empirical approximations presented in Equations (9) and (10); and (2) the resulting transmittance spectra were scaled to a high resolution MODTRAN spectra (0.1 cm\({}^{-1}\)). Finally, in (3) we used the MODTRAN oxygen transmittance spectra to compute sensor radiance over a full one year period using Equation (3). Regarding the simulation protocol, while \(T\) was directly measured at the top of the tower (\(\sim\)30 m), air pressure was measured at surface level. Therefore, surface pressure at the top of the tower was computed following Equation (13), resulting from combining the hydrostatic equation together with the ideal gas law, assuming the measured total pressure as dry air pressure. \[p_{sen}=p\cdot\exp\left(\frac{gM_{0}Z}{R_{0}T}\right) \tag{13}\]  
In Equation (13), \(p_{sen}\) is the pressure at sensor level, \(p\) and \(T\) are the pressure and T temperature measured at TOC surface level, \(M_{0}\) is the molar mass of the dry air, \(R_{0}\) is the ideal gas constant, and \(g\) is the standard gravity constant. In this simulation exercise, we evaluated how variations in the meteorological conditions impacted on the O\({}_{2}\) transmittance locally. Since the selected Hyytiala tower height is around 30 m tall, about 15 above the evergreen forest canopy that it monitors, and assuming nadir acquisition geometry, we fixed the optical path as 15 m, i.e., the \(Z\) term in Equation (10). Figure 14 shows oxygen molecular transmittance in the O\({}_{2}\)-A and O\({}_{2}\)-B absorption bands caused by \(T\) and \(p\) changes throughout a full year (2016) for the tower geometrical configuration in the Hyytiala Forestry Field Station. As observed, the band depth in both, the O\({}_{2}\)-A and O\({}_{2}\)-B regions tracks the expected thermal dynamics related to seasonality, i.e., as \(T\) increases from winter minima (\(DOY\) 0, \(\sim\)350) to reach maximum values in the summer season (e.g., \(DOY\), \(\sim\)180), the O\({}_{2}\) absorption band depth becomes shorter. For the O\({}_{2}\)-A band, the seasonal change in transmittance is 0.01 [\(-\)] (Figure 14a), whereas for the O\({}_{2}\)-B case is only 0.002 [\(-\)] (Figure 14b).