## 4 Data Analysis
### Diurnal Variation in Radiant Spectra and Apparent Reflectance  
Several down-welling and up-welling radiance spectra covering the period from morning to afternoon observed on a clear day (7 September 2017) at the DM site are shown in Figure 8. The spectral range is from 649.3 nm to 805.4 nm, thus covering the full SIF emission spectrum. It can be seen that the absorption depth of the incoming radiation has distinct diurnal variations, which is consistent with our prior knowledge that the absorption depth of the radiation spectrum is greater in the morning and afternoon than that at noon, which can be explained by the increased radiation transfer path length for larger SZAs [52]. Also, the fraction of diffuse radiation is higher in the early morning and late afternoon than at noon time, and the transfer path of the direct radiation is shorter than that of the diffuse radiation, which results in a deeper absorption line for the diffuse radiation than for the direct radiation [53].  
Figure 7: An example of the diurnal variations in SIF results at the O\({}_{2}\)–A band as measured on 7 September 2017 at the DM site using four different retrieval methods (Fraunhofer line discrimination (FLD): red; 3 FLD: green; iFLD: blue; pFLD: black).  
The diurnal variations in the apparent reflectance spectrum (the ratio of up-welling to down-welling radiance) are also depicted in Figure 8. The approximate PAR values corresponding to the spectra are 648, 1283, 1525, 1277, and 947 umol m\({}^{-2}\) s\({}^{-1}\). A peak due to the in-filling effect of the SIF signal can be observed in the apparent reflectance spectra in the range from approximately 760 to 762 nm. The peak in the apparent reflectance contributed by the SIF is also an indicator for the data quality filtering--an obvious peak in the apparent reflectance indicates that the measurements are reliable. Comparing the diurnal variations in the apparent reflectance data, it can be seen that the magnitude of the apparent reflectance is larger in the morning and afternoon and smaller at noon. This is related to the bidirectional reflectance distribution function (BRDF) characteristics of the vegetation canopy, which result in different diurnal variations in reflectance for the direct and diffuse radiation [39; 54; 55].  
Furthermore, the relative height of the peak in the O\({}_{2}\)-A band is smaller at noon than that in the morning and afternoon, which is counterintuitive because the higher SIF value should produce a stronger in-filling effect for the same absorption depth. However, in the morning and afternoon, a stronger relative contribution of in-filling of the SIF to the apparent reflectance can be observed from the apparent reflectance than at noon. Three reasons or hypotheses can be used to explain this phenomenon. Firstly, although the absolute SIF value is larger at noon than in morning or afternoon, a smaller SIF excursion peak is present in the apparent reflectance because the depth of the absorption line is smaller at noon than in the early morning or late afternoon. Secondly, there is the negative in-filling effect of the direct radiation at noon [55]. According to the study in the previous work [55], both the SIF in-filling effect and the direct direct radiation contribute to the height of the peak in the apparent reflectance. Another possibility is the decreases in the SIF yield efficiency and the fraction of absorbed photosynthetically active radiation (fPAR) that occur at noon. [PERSON] et al. [56] pointed out that the SIF inside the absorption line can be calculated by multiplying the height of the peak of the apparent reflectance and the incoming solar radiation inside the absorption band. Thus, the decrease in the height of the peak at around 760 nm may also be the result of the decrease in the product of the SIF yield and fPAR. In general, the value of fPAR is lower at noon than in the morning and afternoon, but the diurnal variations in SIF yield need to be investigated in future research.