## 4 Discussion
### The Uncertainty of Using fIPAR as a Proxy for fAPAR  
In order to simplify the measurement requirements in terms of hardware, cost, and time, fIPAR has been used as a proxy for fAPAR. [PERSON] compared five different fAPAR estimation schemes in open-canopy forest in order to assess the uncertainty which such approximation entails [54]. All these schemes are essentially reduced forms of the energy conservation equation. He concluded that out of the assessed approaches the 2-flux fAPAR (fIPAR) estimator performs best which suggests that fIPAR is a good approximation of fAPAR for open forests. However, in the case of urban individual trees, fIPAR overestimates fAPAR by approximately 10% (Figure 5). In addition, the overall relative differences between fAPAR and fIPAR obtained in this study were almost twice as high as the ones reported in earlier studies in the case of full plant cover, which were generally no greater than 5% [56; 57]. Such a difference would be non-negligible when considering, e.g., the GPP of urban greenery. Similar to the previous study [54], the current study shows that the differences between fIPAR and fAPAR also depend on the illumination condition, foliage colour and background (Figures 5 and 6). While the increase in the simulated difference between the two indices resulting from increased background reflectance (in this case grass and concrete backgrounds, with background reflectance of approximately 0.06 and 0.25, respectively) is consistent with the results of fAPAR estimations for sparse vegetation based on remote sensing data [23], in our case the fIPAR value is higher than fAPAR. This is likely due to the fact, that in the present study the leaves are not assumed to be completely absorbing. Instead, the leaves are assigned C\({}_{\text{ab}}\) values ranging from 10 to 100, which includes green and brown leaves. Previous study as well as the optical field instrument DHP and LAI2200 would assume the leaves complete black when they take fIPAR as a proxy of fAPAR. The assumption is true for green, healthy leaves, while in reality, the concentration of pigments varies depending on the health of the tree and the season. Newly-grown leaves, mature leaves, and senescent leaves have different absorption ability in the PAR band. Previous study show that the presence of yellow leaves leads to an overestimation when using fIPAR to approximate fAPAR because yellow leaves are characterized by a higher brightness than green leaves [54; 58; 59]. Furthermore, the high spatial resolution of the simulated images makes the scattering effect of the non-photosynthetically active material such as the trunk or the branches non-negligible. Thus, although the background reflected radiance can increase the fAPAR, the radiance scattered from the trunk and leaves which is intercepted, but not absorbed is the main reason for the bias towards fIPAR. This supports the results of field measurements using DHP, AccuPAR and LAI-2200 reported by [PERSON] et al. [28]. Another factor that might influence the differences between fIPAR and fAPAR is plant leaf density. [PERSON] found fAPAR to be significantly higher than fIPAR for low LAI, while lower than fIPAR for high LAI [11]. Urban trees tend to have a denser distribution of leaves than grass in the referenced study which might result in fIPAR being larger than fAPAR. 3D radiative transferer models play an important role in assessing the uncertainty of field measurement methods [60] and were even believed to be the only means to find the proper measurement strategy for field-based validation campaigns [54]. The five fAPAR estimation schemes explored by [PERSON] using the 3D radiative transfer model were only based on vertical flux [54]. [PERSON] et al. compared the differences between fAPAR and fIPAR using 3D radiative transfer simulation [23]. However, their comparison was based on a single scattering regime under direct illumination. They concluded that the differences between the two indices were minute for forests with vegetation understory.