## 4 Discussion
### Uncertainties in MODTRAN Simulations and Field Measurements  
In this study, the estimates of the atmosphere transmittances were based on the MODTRAN simulations. Therefore, the reliability of the results is directly related to the accuracy of the MODTRAN simulations. Although MODTRAN has been widely used for the modelling of atmospheric radiative transfer, in the case of this study, there are some uncertainties. First, to match with the observations, the MODTRAN simulations need to be convolved with the ISRF of the specific spectrometers used. In this study, a Gaussian function with an FWHM of 0.31 nm  
Figure 8: Simulated diurnal variation in direct and diffuse radiation canopy reflectance at 760.6 nm using the Soil Canopy Observation, Photochemistry and Energy fluxes (SCOPE) model for an LAI of 4 and spherical leaf inclination distribution function (LIDF). was used as the ISRF for the Ocean Optic QE pro spectrometer. The difference between the Gaussian function and the real ISRF will lead to some error in the simulated atmosphere transmittances. But as the spectral resolution of the spectrometer is high and the O\({}_{2}\)-A absorption band is relatively wide, the uncertainties related to FWHM should be ignorable. Figure 9 shows the MODTRAN simulated up-welling transmittance convolved with Gaussian, rectangular, and triangular ISRF with an FWHM of 0.31 nm and resampled with spectral interval of 0.155 nm (Sensor height = 25 m, Surface elevation = 1.5 km, VZA = 25\({}^{\circ}\), AOD\({}_{550}\) = 0.1). For this case, the transmittances convolved by Gaussian, rectangular, and triangular functions at 760.6 nm are 0.9939, 0.9941, and 0.9937, respectively. The results indicate that the difference of transmittance caused by the ISRF is less than 0.04%, which is very tiny. The mismatch between the spectral sampling of simulations and observations may also lead to uncertainties in the estimation of atmospheric transmittances. Secondly, for tower-based SIF observations, the RTPL is relatively short and the atmospheric absorption effect is relatively weak, which means that accurate radiative transfer modelling is required. MODTRAN has been widely used and is regarded as a highly accurate radiative transfer model [31; 40; 41], and the LUT-based method used in this study could also improve the robust of the estimation of transmittance. In this study, synchronous measurements on the ground and on the tower were carried out to validate the results of atmospheric correction. Although the two spectrometers were with very similar configurations and had been cross-calibrated, there could still be mismatch between the measurements by the two spectrometers. Besides, the footprints of the tower-based and ground-based measurements were somewhat different due to the different height of sensors. But as the surface as relatively homogeneous and the canopy was closed, it is reasonable to ignore the influence by different footprints. In addition, although the tower-based measurements of downwelling and upwelling radiance were conducted with the same spectrometer, two fibers were used (see Figure 3). The two fibers were connected to the same spectrometer using a Y-shaped assembly. So there can be slight difference in the light path of the downwelling and upwelling radiance, consequently leading to some spectral shift. [PERSON] et al. [42] pointed out that the spectral shift has an obvious influence on  
Figure 9: MODTRAN simulated up-welling transmittance convolved with Gaussian, Rectangular and Triangular instrument spectral response function (ISRF) with a full-width at half maximum (FWHM) of 0.31 nm and resampled with spectral interval of 0.155 nm. The FWHM of the original simulation (grey line) is 1 cm\({}^{-1}\) (-0.06 nm at 760 nm), the sensor height is 25 m, the surface elevation is 1.5 km, the view zenith angle (VZA) is 25\({}^{\circ}\), and the AOD\({}_{550}\) is 0.1.