## 1 Introduction
In scenarios with high vegetation heterogeneity, the effect of illumination conditions on sunlit and shaded parts of an individual tree is no longer negligible and should be considered when assessing the applicability of a particular model. The fraction of intercepted photosynthetically active radiation (fIPAR) has been taken as a good approximation of fAPAR [23; 24]. Due to the difficulty of accurately measuring the flux in different directions for fAPAR estimation, fIPAR has been regularly acquired at many flux tower sites and long-term validation sites for remote sensing of fAPAR products, e.g., [25; 26]. The fIPAR measured by the optical field instruments, such as digital hemispherical photography (DHP), tracking radiation and architecture of canopies (TRAC) [27], and LAI-2200 (LI-COR Inc., Lincoln, Nebraska, USA) has been widely used in fAPAR studies as ground truth. However, the above methods are based on the assumption that fIPAR and fAPAR are equivalent. This assumption has been shown to hold for crops using field measurements [28] and forests using simulations [23]. Unlike continuous (or closed), homogeneous crop or forest canopies, urban individual trees have distribution patterns of low plant cover and bright backgrounds. Whether the fIPAR can be used to approximate fAPAR for the urban individual trees remains unknown. Considering the growing awareness of the significance of trees in urban ecosystems, in situ fAPAR measurements will be increasingly needed. Thus, it is important to carefully examine the uncertainty of using the above efficient approach in fIPAR measurement to approximates fAPAR for trees in complex urban environments. Considering the difficulty of acquiring true values of fAPAR of trees, simulation methods are a good approach for its evaluation. [PERSON] and [PERSON] [29] were among the first to demonstrate that fPAR of inhomogeneous canopies can be reliably assessed using computer-generated 3D models of vegetation to evaluate the effect of factors such as background reflectance, optical properties of canopy elements, or solar view geometries. In 1996, [PERSON] et al. developed the discrete anisotropic radiative transfer (DART) model which enables detailed simulations of radiative transfer in heterogeneous 3d scenes which comprise features such as leaves, grass, trunks, etc. [30]. DART is aimed at high accuracy, and so the radiative budget is simulated with high accuracy for all sun directions and atmospheric conditions [31]. It has been validated against results of field measurements and compared with other radiation transfer models, performing favorably in heterogeneous scenes [32; 33]. The capability of the DART model to accurately assess the radiative budget of vegetation can be further enhanced by combining it with the PROSPECT radiative transfer model which accounts for the optical properties of plant leaves such as spectral refractive index [34]. Absorption is modelled using, among other input variables, the concentration of chlorophyll a and b and carotenoids. The coupling of both models (PROSPECT-DART) enables a comprehensive assessment of the radiative budget considering the health of vegetation. It was successfully used, e.g., to simulate the leaf pigment content in heterogeneous conifer forests [35], to retrieve spruce chlorophyll content from airborne images [36], and to simulate reflectance spectra and LiDAR data for tree canopies [37; 38; 39]. In addition, radiative budget (absorbed, scattered, and intercepted radiation) produced using the PROSPECT-DART model which has been demonstrated to be well-suited to simulating urban landscapes [40]. The two main goals of this study were 1) to explore the influences of background and illumination conditions on fAPAR and fIPAR for individual trees in the context of urban greenery, and 2) to evaluate the differences between fAPAR and fIPAR and corresponding factors that influence such scenarios.