## 2 Materials and Methods
### Calculation of Hourly GPP  
One key step of _GPP_ calculation is the quantification of the absorbed photosynthetically active photons flux density by the vegetation canopy at local time \(t\) (_APPFD\({}_{t}\)_). By generalizing the sun/shade model described by [PERSON] and [PERSON] [55] to various foliage clumping index conditions and types of leaf angle distribution, _APPFD\({}_{t}\)_ is calculable once diffuse _PPFD_(_PPFD\({}_{t}\)diffuse_) and direct _PPFD_(_PPFD\({}_{t}\)direct_) at the vegetation canopy top are known. For this study, _PPFD\({}_{t}\)diffuse_ was calculated based on diffuse shortwave solar radiation (_SR\({}_{t}\)diffuse_), whereas _PPFD\({}_{t}\)direct_ was based on direct shortwave solar radiation (_SR\({}_{t}\)direct_) using reference parameter settings in Ito and Oikawa [65]. To estimate _SR\({}_{t}\)diffuse_ under various sky conditions (sunny to different degree of cloudiness), an artificial neural network (ANN) linear regression [66; 67; 59; 68] method was developed using the following input variables: low cloud cover (_LCDC_), middle cloud cover (_MCDC_), high cloud cover (_HCDC_), surface atmospheric pressure (_Pambient_), shortwave black-sky albedo (_\(\alpha_{black-sky}\)_), shortwave white-sky albedo (_\(\alpha_{white-sky}\)_), surface vapor pressure (_VP_) and cosine of solar zenith angle (\(\theta_{t}\)SZA) at local time \(t\). The details of the generalized _APPFD\({}_{t}\)_ equations and ANN training processes are presented in the Supplementary Materials. With solved hourly _APPFD\({}_{t}\)_, it is then feasible to apply a terrestrial biosphere model, the Biosphere model integrating Eco-physiological And Mechanistic approaches using Satellite data (BEAMS, [69; 70]), to estimate hourly _GPP_. BEAMS adopted the Monteith equation [71; 72] with improvement of light use efficiency (_LUE_) calculation, assuming that _GPP_ is proportional to _APPFD\({}_{t}\)_ and taking into account the photosynthetic _Stress\({}_{t}\)_ (unitless) caused by light, soil moisture conditions, surface temperature and relative humidity. \[GPP_{BEAMS}=APPFD_{t}\times LUE_{max}\times\textit{Stress}_{t} \tag{3}\]  
\[\textit{Stress}_{t}=P_{t}{}^{actual}/P_{t}{}^{optimal} \tag{4}\]  
where _LUE\({}_{max}\)_ represents the maximal photosynthetic light use efficiency in each plant functional type (PFT), \(P^{actual}\), denotes the actual photosynthetic assimilation rate at given conditions, and \(P_{t}{}^{optimal}\) stands for the optimal photosynthetic assimilation rate at optimal conditions (i.e., 100% surface relative humidity and no soil water stress). Additionally, _APPFD\({}_{t}\)_ was assumed to be evenly distributed in a big-leaf model [69] to calculate \(P_{t}{}^{actual}\) and \(P_{t}{}^{optimal}\), which were solved by coupling a simplified Farquhar-von Caemmerer-Berry model [69; 73; 74; 75; 76] of a C3 plant to the stomatal conductance of CO\({}_{2}\)[73; 77; 78; 79; 80]. The Farquhar-von Caemmerer-Berry model, stomatal conductance and the iterative solution are described in the Supplementary Materials. As reviewed in the Introduction, photosynthetic productivity at the canopy scale tends to be overestimated without differentiating sunlit leaves from shaded leaves, which is the case for a big-leaf model. Moreover, the vegetation density, represented by the Leaf Area Index (_LAI_), in our study area was often dense (\(LAI\geq 5\) m\({}^{2}\) m\({}^{-2}\)) during the growing season in summer, meaning that only a limited area (\(\leq\)2 m\({}^{2}\) m\({}^{-2}\)) of leaves would be sunlit. To avoid \(GPP\) overestimation, a two-leaf (sunlit/shaded) up-scaling scheme [55; 57; 58; 73; 81] was also applied for this study to calculate hourly \(GPP\), based on the average net photosynthetic assimilation rate in sunlit leaves (\(P_{n}{}^{sunlit}\)) and the average net photosynthetic assimilation rate for shaded leaves (\(P_{n}{}^{shaden}\)).