## 2 Materials and Methods
### Calculation of Hourly \(R_{e}\)  
To maintain physiological activities, plants respire CO\({}_{2}\) (\(R_{maintenance}\)). Vegetation biomass pools [69; 82; 83] were simply divided into foliage (\(bio_{t}{}^{flique}\)), wood (\(bio_{t}{}^{live-wood}\)\(+\)\(bio_{t}{}^{load-wood}\)), and root biomass (\(bio_{t}{}^{root}\)) for this study. Each was assigned a PFT-specific maintenance respiration rate that was proportional to the amount of biomass and ambient temperature. The \(R_{m}{}^{flique}\), \(R_{m}{}^{live-wood}\), and \(R_{m}{}^{root}\) equations are provided in the Supplementary Materials. \[R_{maintenance}=R_{m}{}^{flique}+R_{m}{}^{live-wood}+R_{m}{}^{root} \tag{6}\]  
To use the carbon captured during photosynthesis, a plant consumes a fraction of its \(GPP\) and emits CO\({}_{2}\) to grow. At annual- or daily-scale modeling, this growth respiration (\(R_{growth}\)) was assumed to be proportional to the difference between \(GPP\) and \(R_{maintenance}\)[69; 82; 83]. A similar assumption was made for this study at a sub-daily scale: hourly \(GPP\) is almost instantaneously exported and used by foliage, live-wood, and root areas to apply the same calculation method of \(R_{growth}\). \[R_{growth}=f_{Rg}\times(GPP_{BEAMS/TLM}-R_{maintenance}) \tag{7}\]  
where \(f_{Rg}\) stands for the fraction of growth respiration ([69; 83]: 0.14 in deciduous broadleaf forest (DBF), 0.055 in evergreen broadleaf forest (EBF), 0.11 in evergreen needleleaf forest, and 0.25 in grassland (GRS) after calibrations). With solved \(R_{growth}\) and \(R_{maintenance}\), autotrophic respiration \(R_{autotrophic}\) and net primary production (\(NPP\)) were calculated as follows:  
\[R_{autotrophic}=R_{maintenance}+R_{growth} \tag{8}\]  
\[NPP=GPP_{BEAMS/TLM}-R_{autotrophic} \tag{9}\]  
By assuming that live-wood and root biomass are proportional to foliage biomass in evergreen forests, live-wood biomass proportional to foliage biomass in DBF and root biomass proportional to foliage biomass in GRS, the allocation of hourly \(NPP\) was simplified for this study. In DBF, considering that some live roots might remain active and respire CO\({}_{2}\) even if foliage biomass appears to be 0 in early spring or late autumn, the root biomass was assumed as the accumulated result of \(NPP\) allocated to roots based on the formula of [PERSON] et al. [84] minus carbon loss because of maintenance respiration and root mortality. Although dead-wood biomass does not emit resyped CO\({}_{2}\), it contributes to the amount of litter fall, which eventually affects \(R_{heterotrophic}\). Therefore, a simple allocation scheme of \(NPP\) was applied to calculate dead-wood biomass in forests of the respective types. Additional details are presented in the Supplementary Materials. Compared to photosynthetic assimilation, the CO\({}_{2}\) emission rate attributable to soil organic carbon (\(SOC\)) decomposition is often lower, but \(SOC\) is estimated to store 2/3 of the carbon in terrestrial ecosystems [85]. Consequently, the total amount of CO\({}_{2}\) emit ted from soil carbon pools should not be neglected. In this study, three surface \(SOC\) pools (surface structural litter carbon (\(SOC_{surface}{}^{structural}\)), surface metabolic litter carbon (\(SOC_{surface}{}^{metabolic}\)), and surface microbe (\(SOC_{surface}{}^{micprobe}\))), and five soil \(SOC\) pools (root structural litter carbon (\(SOC_{root}{}^{structural}\)), root metabolic litter carbon (\(SOC_{root}{}^{metabolic}\)), soil microbe (\(SOC_{soil}{}^{micprobe}\)), soil slow carbon (\(SOC_{soil}{}^{slow}\)), and soil passive carbon (\(SOC_{soil}{}^{passive}\))) were identified from 0 to 28 cm-deep soil layers. Carbon flow among these \(SOC\) pools and emitted CO\({}_{2}\) via decomposition processes were simulated based on earlier studies of the CENTURY model [69; 86; 87; 88]. Followed the volcanic ash soil assumption of Japanese soil in [PERSON] et al. [89], the maximum decomposition rates [88] were adjusted by 1/2.3.