## 2 Materials and Methods
### Parameter Calibration and Model Validation at the Site Level  
According to the register of JapanFlux [90], 39 Japanese sites have been monitoring mass and energy fluxes over terrestrial ecosystems, including CO\({}_{2}\) fluxes. However, only the \(GPP\), \(R_{e}\), and \(NEE\) data of six sites are accessible in the Forestry and Forest Products Research Institute FluxNet Database (FFNet DB, [91]): Sapporo (SAP), Appi (API), Kawagoe, Fujiyoshida (FY), Kahoku, and Yamashiro (YMS). Additionally, the data of the Moshiri Birch Forest site and the Seto Mixed Forest site are included in the FLUXNET2015 dataset [92]. Nevertheless, no data of Japanese EBF or GRS were available when we developed our model. To complete parameter calibration and model validation for different ecosystem types, some \(GPP\) and \(R_{e}\) data from outside Japan (China and Malaysia) were used. To be more specific, half-hourly data of two FFNet DB sites (SAP [93; 94] and FJY [95; 96; 97]) and two FLUXNET2015 sites (Dinghushan DIN [98]) and Changeling CNG [99]) were obtained to calibrate PFT-specific parameters in hourly \(GPP_{BEAMS}\) and \(GPP_{TLM}\) modules. To validate the calibrated modeling settings, half-hourly data of one FFNet DB site (API [100; 101; 102; 103]) and three FLUXNET2015 sites (Qianyanzhou QIA [104], Pasoh forest reserve PSO [105], and Duolun DU2 [106]) were obtained. Table 1 presents site information such as the PFT type, coordinates, and period for which data were obtained. Half-hourly \(GPP\) data with air temperature, relative humidity, wind speed, downward shortwave solar radiation, and precipitation records were screened in each FFNet DB data subset. Only the best quality data (quality flag = 0) were retained in each FLUXNET2015 data subset. Post-screened data were then converted to the hourly average for model calibration and validation at the site level. Because continuous \(LAI\) records were not measured in either FFNet DB or FLUXNET2015 sites, it was extracted for the grid cell where each site was located from the MODIS \(LAI\) product (MCD15A3H v006 [107], 4-day 500 m) as proxies of the site conditions. Bad quality \(LAI\) data were replaced by interpolated values, as described further in the Supplementary Materials. Similarly, the canopy clumping index (\(\Omega\)) was extracted from the MODIS Bidirectional Reflectance Distribution Function (BRDF)-derived dataset [108] with 500 m resolution, and both \(\alpha_{black\_sky}\) and \(\alpha_{white\_sky}\) were based on the MODIS albedo product (MCD43A3 v006 [109], daily 500 m). Although some FFNet DB and FLUXNET2015 sites included 0-5 cm depth soil moisture data, this layer is too shallow to estimate the comprehensive effects of soil water availability on photosynthesis. Soil water content \(\theta_{k}\) (m\({}^{3}\) m\({}^{-3}\)) for the 0-7, 7-28, 28-100, and 100-289 cm soil layers was therefore extracted from the ERA-5 Land reanalysis dataset [110] (hourly 9 km), whereas the fractions of clay, sand, and silt and the amount of soil organic carbon for each site were obtained from the SoilGrids250m dataset [111]. In addition, cloud cover and atmospheric pressure conditions at each FFNet DB site were based on the hourly Meso-Spectral Model Grid Point Value (MSM-GPV) reanalysis dataset with 5 km resolution provided by the Japanese Meteorological Agency [112]. The ANNmethod developed for this study to estimate \(SR_{t}\textsuperscript{diffuse}\) was not applicable to FLUXNET2015 sites because of the lack of cloud cover data, and in such cases, the empirical method of [PERSON] et al. [58] was adopted instead.