## 3 Results
### Hourly \(R_{e}\) and NEE at the Site Level  
The comparison between hourly modeled \(R_{e}\) and FFNet DB/FLUXNET2015 estimation provides reference information about the modeling uncertainty of CO\({}_{2}\) emission via autotrophic and heterotrophic respiration in DBF, EBF, ENF, and GRS, as detailed in Figure 3a and Table S2. In DBF, ENF, and GRS, the hourly modeled \(R_{e}\) agreed well with the \(R_{e}\) estimates based on flux tower monitoring data (\(R^{2}\geq\) 0.71, 0.52, and 0.66, respectively). In EBF, the calculated hourly \(R_{e}\) agreed poorly with flux tower estimates at low latitude sites--DIN and PSO. At the mixed broadleaf forest site YMS in Japan, simulated hourly \(R_{e}\) using both DBF and EBF parameters agreed well with flux tower-estimated \(R_{e}\) (\(R^{2}\) was 0.68 and 0.76). In ecosystems of all four types, hourly \(R_{e}\) was overestimated. The standard deviation of hourly modeled \(R_{e}\) was 0.70-1.24 times (absolute difference within 0.66 \(\upmu\)molCO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\) that of the flux tower estimated one. Consequently, the RMSE of  
Figure 2: (a) Taylor diagram of hourly modeled \(GPP_{\mathit{BEAMS}}\) and hourly \(GPP\) estimates based on flux tower monitoring (\(\upmu\)mol m\({}^{-2}\) s\({}^{-1}\)) at selected FFNet DB/FLUXNET2015 sites. (b) Taylor diagram of hourly modeled \(GPP_{\mathit{TLM}}\) and hourly \(GPP\) estimates based on flux tower monitoring (\(\upmu\)mol m\({}^{-2}\) s\({}^{-1}\)) at selected FFNet DB/FLUXNET2015 sites. regional simulations of the latter were conducted and generated similar results. Figure 4a-g present hourly _GPP_ results of the study area from dawn to dusk on a summer day as examples of diurnal variations of vegetation CO\({}_{2}\) uptake. Hourly _GPP_ was generally low (<0.75 gC m\({}^{-2}\) h\({}^{-1}\)) in the early morning because of the limited availability of solar radiation. By virtue of the favorable weather conditions (e.g., 20-34 \({}^{\circ}\)C air temperature, 0.5-0.9 soil moisture wetness) in the study area, as the level of shortwave solar radiation increased, the hourly _GPP_ raised quickly (up to 1.5 gC m\({}^{-2}\) h\({}^{-1}\)) and peaked before noon. Then, in the late afternoon, the hourly _GPP_ dropped and became 0 after sunset. Spatially, the hourly _GPP_ was up to 1.19 \(\pm\) 0.27, 0.90 \(\pm\) 0.18, and 0.93 \(\pm\) 0.18 gC m\({}^{-2}\) h\({}^{-1}\) in ENF, EBF, and DBF, and 1.19 \(\pm\) 0.39 gC m\({}^{-2}\) h\({}^{-1}\) in GRS, as the means and standard deviations of hourly _GPP_ among all grid cells in Figure 6 show. In contrast, the hourly _GPP_ was only up to 0.69 \(\pm\) 0.19 gC m\({}^{-2}\) h\({}^{-1}\) in urban grid cells with partial vegetation cover. Depending on the distribution of cloud cover and vapor pressure, in cloudy summer periods with highly diffuse shortwave solar radiation ratios, plants in forests or grasslands effectively absorbed many of the available photosynthetically active photons, although the downward shortwave solar radiation was as low as 200-300 W m\({}^{-2}\). Consequently, the hourly _GPP_ in such cloudy conditions could reach 0.6-1.2 gC m\({}^{-2}\) h\({}^{-1}\). In raining  
Figure 4: Sub-daily variation of (**a–g**) hourly modeled _GPP_ (gC m\({}^{-2}\) h\({}^{-1}\)) and (**h–n**) hourly modeled fraction of _APPFD_ by plant canopy (-) in the study area on 3 July 2018.  
areas, precipitation interfered with stomatal conductance of CO\({}_{2}\) in photosynthesis, thereby temporarily reducing the hourly modeled _GPP_ to 0. Over seasons, the range and spatial distribution of the hourly _GPP_ varied according to the changes in meteorological and ecological conditions. Because of limited space, more examples of the hourly modeling results are not presented here. In addition, Figure 4 also includes diurnal variations of the modeled fraction of absorbed _PPFD_ on the same summer day.