# Scaling of FAPAR from the Field to the Satellite
## 1 Introduction  
The Fraction of Absorbed Photosynthetically Active Radiation (FAPAR) describes the efficiency of light absorption by plant and is a critical biophysical parameter in eco-environmental studies [1; 2]. It is defined as the fraction of Photosynthetically Active Radiation (PAR) absorbed by vegetation, where PAR refers to the incoming solar radiation within the spectral range 0.4-0.7 \(\upmu\)m [3]. FAPAR provides critical information on vegetation growth condition and reflects the energy-and-carbon exchange between biosphere and atmosphere. As a clearly defined quantitative parameter, it has been widely used as a key input into regional or global climate models [1; 4]. In view of the difficulties in ground measurements, sensors onboard satellite now provide the only available FAPAR estimates from local to global scales [5; 6; 7], such as moderate-resolution imaging spectroradiometer (MODIS) [8], Sea-Viewing Wide Field-of-View Sensor (SeaWiFS) [9],SPOT-VEGFATION [10] and the Medium Resolution Imaging Spectrometer (MERIS) [11]. The validity of these satellite FAPAR products now makes FAPAR a key terrestrial remote sensing product in the Global Climate Observing System [12]. In particular, in Production Efficiency Models (PEMs) for Gross and Net Primary Productivity (GPP/NPP), FAPAR often acts as the only satellite derived variable [5]. Because multiple satellite FAPAR products provide users various choices, it is essential to validate these global datasets before application at local or regional scale [13]. Large uncertainties resulting from data quality and retrieval accuracies were found in the currently available FAPAR products [5; 14]. Apparent inconsistencies among these FAPAR products were revealed in comparative studies, such as those conducted in [5; 14; 15; 16; 17; 18]. These uncertainties or inconsistencies have made continual validation and comparison with ground measurements imperative for real application or reducing the uncertainties. However, the validation of remote sensing FAPAR products is greatly limited as the spatially and temporally comparable _in-situ_ FAPAR data are very rare [7; 19]. Especially FAPAR is highly temporally variable, and its diurnal variations affected by the changing irradiation conditions can be dramatic [20]. This hindered the collection of FAPAR ground measurements. Most of the executed or ongoing field campaigns were focused on leaf area index (LAI) rather than FAPAR [3; 15; 21]. To take good advantage of the limited and valuable _in-situ_ FAPAR data, scaling of FAPAR from the field to the satellite is critical to achieve the comparability between _in-situ_ and satellite FAPAR data. To accomplish the scaling, spatial mismatch naturally poses the major challenge. While _in-situ_ FAPAR are representative of several meters at plot scale, a single pixel on the coarse resolution product extends a distance of 250 m-5 km, as defined in [22]. As land surface are commonly heterogeneous, the coarsening of spatial resolution results in the mismatches of spatial representative areas between field data and satellite data [3]. To guarantee the comparability between _in-situ_ and satellite data, homogeneous sites are always preferred and direct comparison can be performed after the representativeness of field sites to coarse-resolution pixel was verified, as conducted in [13; 15; 23; 24]. However, at heterogeneous sites that are more widely distributed, direct comparison between the pair of _in-situ_ and satellite data is unfeasible. This urges the need to consider the sub-pixel variability at coarse resolutions in scaling _in-situ_ data to coarse-resolution satellite product [16]. [PERSON] _et al._[25] proposed a bottom-up methodology for scaling ground measurements from field to elementary sampling units (ESUs), fine-resolution data and then moderate or coarse resolution data sequentially. It has been widely used in scaling field observations to coarse-resolution pixels, as those conducted in [9; 13; 16; 26; 27].