# Scaling of FAPAR from the Field to the Satellite
## 1 Introduction
Spatial discrepancies can be bridged by the use of fine-resolution data, while temporal mismatch is another critical issue and even a more challenging task for scaling FAPAR from the field to the satellite. Two aspects should be considered here: temporal normalization to match the specific time stamp and temporal interpolation to match the acquisition dates of field measurements to satellite data. The dramatic diurnal variations of FAPAR lead to fluctuations in ground measurements at varying hours. Ideally FAPAR _in-situ_ data are expected to be measured at the satellite overpass time. However, given the limited labor, time and instrument, it is impractical to measure FAPAR for all field sites at the same time. Multiple sites are always measured one by one at different hours. Temporal normalization is thus required to match the _in-situ_ FAPAR to the time of satellite overpass in the scaling-up process. [PERSON] _et al._[13] found that daily averages of FAPAR from 9:00 a.m. to 3:00 p.m. approximated the value at 10:30 a.m. from the field measured FAPAR diurnal courses. However, such diurnal FAPAR data cannot be conveniently obtained at multiple sites in field measurements, which limits the use of this normalization method in future applications. The diurnal FAPAR variations are attributed to the changing conditions of incident solar radiations, including the solar zenith angle (SZA) and the diffuse skylight proportions [20]. [PERSON] _et al._[7] attempted to characterize the effects of SZA and the fraction of skylight on diurnal FAPAR by fitting the _in-situ_ FAPAR at different SZAs. The fitted result represented the diurnal variation of FAPAR simply, which could be the basis for temporal normalization. However, in real application, difficulties in field measurements are also major limits. [PERSON] _et al._[28] suggested that the effects of SZA on FAPAR measurements should be directly addressed in future studies. However, to date, few studies have addressed the issue in temporal normalization based on easily available _in-situ_ data. Despite the fact that coarse-resolution FAPAR products are now available daily, field measurements do not always coincide with the acquisition dates of satellite data [29]. [PERSON] _et al._ and [PERSON] _et al._[13; 16] interpolated satellite products to the acquisition dates of ground measurements linearly, while [PERSON] _et al._[29] employed a cubic function to interpolate the _in-situ_ data to the dates of satellite data. The linear interpolation adopts a simple linear assumption for crop growth, yet it can hardly capture the smooth temporal shape at the fast-growing stage of vegetation. The cubic interpolation could derive smooth and consistent temporal shape at high measurement frequency, but might produce unfeasible results when the available measurements are limited or random errors occur in the limited measurements. A more precise representation of crop growth is thus necessary for temporal interpolation. In brief summary, scaling of FAPAR from the field to the satellite confronts spatial and temporal mismatches. While spatial mismatch has been widely concerned and studied, the temporal mismatches received far less attention. Further investigation is urged to strengthen the spatial and temporal comparability between _in-situ_ and satellite FAPAR in the scaling. In this study, the aim is to develop a general methodology for scaling the _in-situ_ FAPAR to the coarse-resolution satellite product. To achieve the objective, the spatial scaling framework by [PERSON] _et al._[25] and the general scale transfer framework in [30; 31] were combined. The spatial and temporal mismatches were addressed in three steps. Firstly, an FAPAR analytical model was integrated with an atmospheric radiative transfer model to simulate FAPAR with different conditions accurately. Then the coefficients for temporal normalization can be derived by fitting those simulated data with a simplified semi-experienced model.