## 1 Introduction  
Trees play an important role in the urban ecosystem by reducing noise and air pollution, promoting urban biodiversity, and supporting storm water management [1, 2]. Furthermore, urban green spaces improve the physical and mental well-being of citizens and ameliorate urban climate issues resulting from climate change [3]. They play a crucial role in the sustainable development of cities and cooling effect in dense, tropical cities [3; 4]. An important input variable for urban climate, especially in the context of urban green spaces, is the amount of photosynthetically active radiation (PAR), and its fraction absorbed by green elements of healthy vegetation (fAPAR) [5]. It is an important factor in the estimation of vegetation health and plays an essential role in assessing the primary productivity of canopies, the associated fixation of atmospheric CO2 and the energy balance of the surface [6], and hence fAPAR is recognized as an essential variable that affects climate [7]. It is used in remote sensing techniques to assess gross primary productivity (GPP). An accurate estimation of photosynthetically active radiation is important for improving the design of urban green spaces [3] and is crucial for the effective implementation of ecophysiological models [8]. However, some of the methods and models used to measure fAPAR, are best suited for large, uniform canopies such as crops or forests, and might be less reliable when implemented in urban ecosystems. A vast majority of existing fAPAR research concerns crops and forests and relatively few studies focus on urban trees. Urban trees are usually either free-standing or distributed discontinuously (roadside and parkland scenes, potentially in proximity to buildings) with a relatively open, complex canopy structure. In such a setting, the characteristic of fAPAR of individual trees can differ significantly from that of vegetation which forms more uniform, continuous canopies due to the different environment. Urban trees often grow with a concrete background which exhibits much stronger reflectance than grass and soil. In addition, the illumination in urban areas is much more volatile and complex because of the built environment. It was demonstrated that shade cast by high-density high-rise build environment in Singapore might reduce daily PAR by nearly 50% [9]. Previous study demonstrate the effect of background and illumination conditions can introduce significant influence in the estimation of fAPAR for crops and forest [10; 11; 12]. However, how these factors influence urban individual tree fAPAR is still unknow. The distribution of sunlit and shaded leaves also influences the fAPAR of individual trees. At the leaf scale, the biochemistry of the photosynthetic response to solar radiation is well-understood and can be reliably modelled [13] or even measured in real-time [14; 15]. However, at the scale of vegetation canopies the effect of solar radiation on photosynthesis is more complex due to the differences in irradiance between direct and diffused solar radiation [16], and between sunlit and shaded regions across the entire canopy [17]. In addition, the illumination conditions can affect the distribution of sunlit and shaded leaves within individual trees, making its estimation particularly difficult [18]. In general, leaves in the shade suffer from lower exposure to incoming radiation, while those in direct sunlight are often saturated and can have relatively low light use efficiency. Under scattered light conditions the irradiance of the canopy is more uniform, resulting in higher light-use efficiency compared to direct sunlight [19]. Results of several studies have indicated that photosynthesis is more efficient under diffused radiation conditions [16; 20; 21]. The amount and type of solar radiation incident on a canopy or individual crown are important factors in the assessment of fAPAR since an overabundance of light might trigger a photo-protective reaction of the plant, reducing its gross primary production [22].