## 4 Discussion  
The sub-daily scale terrestrial biosphere model developed for this study was based on earlier studies [55; 69; 88]. It required multiple satellite datasets as input. Our main motivation of \(GPP\) and \(R_{e}\) simulation in such short time-steps was to disaggregate biogenic CO\({}_{2}\) fluxes from the anthropogenic CO\({}_{2}\) emissions of the Tokyo megacity and surrounding industrial areas in future inversion studies. Even though some driving forces of the model (i.e., temperature, solar radiation, and soil moisture data) are available hourly or every few hours, sub-daily scale modeling of biogenic CO\({}_{2}\) flux remained challenging. In terms of \(GPP\) calculation, earlier satellite-based models often applied the light use efficiency concept [71; 72], which requires \(APPFD\) by plant canopy or its equivalent in \(W\) m\({}^{-2}\) as input. However, global daily satellite datasets to calculate \(APPFD\), let alone sub-daily ones, are not available yet. Furthermore, after removing cloud-contaminated points, valid data obtained from existing dataset such as MODIS 4-day \(LAI\)/Fraction of Photosynthetically Active Radiation ([107]) are incomplete, especially in regions such as our study area, where the rain period is long in summer. To prepare complete and continuous hourly \(APPFD\) estimates for \(GPP\) calculation, we introduced the satellite-derived clumping index \(\Omega\) and interpolated \(LAI\) as the input. An ANN was also trained to estimate hourly diffuse shortwave solar radiation under various weather conditions. This combination allowed the generalization of \(APPFD\) modeling method proposed in [PERSON] and [PERSON] [55]. Because both diffuse and direct \(PPFD\) were accounted for in hourly \(APPFD\) modeling processes, underestimation of \(GPP\)[51] was alleviated in our model. It also means simulating more realistic diurnal variations of photosynthetic CO\({}_{2}\) uptake compared to existing terrestrial biosphere models, for instance, VPRM [43; 48; 49], which were applied in the field of top-down CO\({}_{2}\) emissions verification studies at a city scale. Figure 11: Monthly integrated anthropogenic CO\({}_{2}\) emissions (\(10^{6}\) ton CO\({}_{2}\) month\({}^{-1}\)) in 2018, compared to biogenic CO\({}_{2}\) emissions, photosynthetic CO\({}_{2}\) uptake, and net biogenic CO\({}_{2}\) flux of the Greater Tokyo Area (\(10^{6}\) ton CO\({}_{2}\) month\({}^{-1}\)) during the period 2010–2018. Shadows represent the variation (the minimum to the maximum) of monthly integrated biogenic CO\({}_{2}\) emission (red), photosynthetic CO\({}_{2}\) uptake (green), and net biogenic CO\({}_{2}\) flux (blue). Accurate temporal variation and spatial distribution of both \(LAI\) and the clumping index are the key to obtaining more realistic hourly _APPFD_ estimates and subsequently more realistic hourly _GPP_. For this study, we set the clumping index of vegetated land to fixed values [108], assuming that the temporal variation of \(\Omega\) was small within a growing season [57] and interannually (2010-2018). This assumption reflected a compromise because of dataset accessibility: it should be improved for future studies by introducing a clumping index dataset with finer temporal resolution, such as the Global Vegetation Clumping Index Products LIS-CI-A1 [134]. Until daily satellite \(LAI\) datasets become accessible, improvements to \(LAI\) data quality rely on better interpolation and smoothing algorithms. By introducing a satellite dataset of phenological metrics [119], we were able to smooth trends of 4-day \(LAI\) in deciduous forest and grassland areas. However, it is difficult to constrain satellite-observed \(LAI\) in evergreen forests by checking against date of vegetation green-up or dormancy. Our results of both hourly modeled _GPP_ at the site level and comparison to existing _GPP_ data at the regional scale suggest that temporal linear averaging interpolated \(LAI\) of evergreen forests was sufficient for accurate simulation of hourly _GPP_.