## 1 Introduction  
Photosynthetically active radiation (PAR) refers to the radiation with the spectral range from 400-700 nm that is used by plants in photosynthesis. The fraction of absorbed photosynthetically active radiation (FPAR) is the ratio of the PAR absorbed by vegetation to the PAR across an integrated plant canopy [1]. FPAR is closely linked to canopy functioning processes such as canopy photosynthesis, carbon assimilation and evapotranspiration rates. It is a key biophysical variable for vegetation productivity estimation, vegetation growth condition monitoring, and climate change analysis [2]. An accurate specification of FPAR is an important detail in large scale productivity and carbon budget models [3]. FPAR is recognized by the global climate observing system (GCOS) as essential climate variables (ECVs) [4]. Traditionally, the canopy total FPAR is directly measured in the field through optical instruments including hemispherical photographs [5], the tracking radiation and architecture of canopies (TRAC) instrument [6], the burr Brown data acquisition system (BBDAS) [7]. Traditional method is time-consuming and expensive. This makes assessment of FAPR on the landscape and ecosystem scales impractical. As an alternative solution, FPAR can be derived through remote measures of surface spectral reflectance, and remote sensing-based methods are currently the only feasible way of acquiring FPAR estimates at the temporal and spatial scales [8; 9; 10; 11]. A number of state of the art algorithms have been proposed to estimate the important environmental variable. They can be categorized as, (a) empirical methods based on relationships between FPAR and vegetation indices,LAI (Leaf area index); (b) physical methods based on the physics of radiation interaction with elements of a canopy and transport within the vegetative medium; (c) machine learning algorithms [12; 13]. Moreover, the number of researches utilizing hybrid regression methods combining radiative transfer model simulations with machine learning regression methods to derive vegetation FPAR is increasing [14]. During the recent decades, a series of satellite FPAR products have been developed based on different definitions, assumptions, retrieval algorithms, and sensors including MODerate-resolution Imaging Spectroradiometer (MODIS), Multi-angle Imaging SpectroRadiometer (MISR), MEdium Resolution Imaging Spectrometer (MERIS), Sea-Viewing Wide Field-of-View Sensor (SeaWiFS), GEOV1,Global Land Surface Satellite (GLASS), CYCLOPES, Visible Infrared Imaging Radiometer (VIIRS), FPAR3 g, Copernicus Global Land Service (CGLS), Earth Polychromatic Imaging Camera (EPIC) and Sentinel-3 Ocean and Land Colour Instrument (OLCI) [13; 15]. For woody plants, the canopy is composed of photosynthetically active vegetation (PAV, mostly green leaves) and non-photosynthetically active vegetation (NPV, e.g., braches, stems) [16]. PAV and NPV absorb PAR, but only the PAR absorbed by PAV is used for photosynthesis [17; 18]. Obviously, this quantity of FPAR determined by PAV is lower than the canopy total FPAR because it does not include PAR absorption by wood materials. For forest ecosystems, NPV can increase canopy FPAR by 10-40% when leaf area index is less than 3.0 [8]. If the NPV contribution to canopy FPAR is not removed, the PAR used to photosynthesis will be overestimated [19]. Additionally, the total FPAR cannot accurately reflect the spatiotemporal variations in photosynthesis due to the varying fractions of NPV [20; 21]. Therefore, for the canopy consist of PAV and NPV, the FPAR should be partitioned into FPARPAV (green FPAR) and FPARNPV, and FPARPAV should be estimated instead of the canopy total FPAR in order to improve the estimation accuracy of vegetation productivity. Any model that accounts for FAPARPAV is likely to substantially improve estimation of GPP or NPP of forests, given a known value of light-use efficiency [22]. However, there is no practical direct method of separating the PAR absorbed by the green leaves [23; 24].