## 2 Materials and Methods
### Hourly GPP and \(R_{e}\) Modeling at the Regional Scale  
The Kanto Plain, circumjacent to Tokyo, is a region of heterogeneous land cover and complex terrain (Figure 1). To assign PFT-specific parameters to each forest and grassland grid cell, the MODIS land cover type dataset (MCD12Q1 v006 [117], annual 500 m) was used as a reference after quality control screening (only retaining classified land and forest type changed land). Because of insufficient access of Japanese urban vegetation CO\({}_{2}\) flux data, its land-cover-specific traits were based on grassland parameter values in non-tree vegetated parts. Because valid _LAI_ values of partially vegetated urban land presented clear appearing-disappearing seasonal patterns in our study area, the parameters of urban trees were temporarily set to those of DBF. For each urban grid cell, the relative fractions of tree cover and non-tree vegetation cover were obtained from the MODIS vegetation continuous fields product (MOD44B v006 [118], annual 250 m) after quality control screening (count of bad quality period \(\leq\) 1) to calculate the fraction of partial vegetation cover.  
To calculate the hourly 500 m \(\times\) 500 m _GPP_ and \(R_{e}\) in the study area during the period 2010-2018, the MODIS _LAI_ dataset (MCD15A3H v006 [107], 4-day 500 m), Land Cover Dynamics dataset (MCD12Q2 v006 [119], annual 500 m), and BRDF-derived Clumping Index [108] were applied to quantify the regional vegetation canopy structure after quality control screening (details are presented in the Supplementary Materials). The surface albedo was set by the MODIS albedo product (MCD43A3 v006 [109]). The fractions of clay, sand, and silt and the amount of organic carbon in the 0-200 cm soil layers were converted from the SoilGrids250m dataset [111]. Before March 2015, soil moisture and temperature data were based on the ERA-5 Land reanalysis dataset [110]. After March 2015, root zone soil moisture data were also extracted from the Soil Moisture Active Passive (SMAP) Root Zone (0-100 cm) Soil Moisture Geophysical Dataset (SMAPL4 SMGPU v5 [120], 3-h 9 km) to calculate the effects of soil water availability on photosynthesis and to calculate the hydraulic limit of transpiration. Hourly surface air temperature, relative humidity, atmospheric pressure, wind speed, precipitation, cloud covers, and downward shortwave solar radiation in the MSM-GPV reanalysis dataset [112] were also processed as input data for the calculations. Depending on the data file format, the resampling of the input data to geographic projection was realized using the HDF-EOS to GeoTIFF Conversion Tool [121], Geospatial Data Abstraction Library [122] or wgrib2 [123]. Smoothing iteration in gdal_fillmodata.py [122] was applied to fill missing edge data of soil moisture or temperature. Similar to the modeling at the site level, a spin-up simulation was conducted regionally to initialize _SOC_ in the study area: input data of the period 2010-2018 were used repeatedly until the carbon stock in the 0-28 cm soil layers (Figure S1 in the Supplementary Materials) reached approximately 6.95 \(\pm\) 3.25 kg m\({}^{-2}\)[116].  
Furthermore, hourly modeling results were aggregated and compared to the MODIS Gross Primary Productivity (MOD/MYD17A2 HGF v006 [124; 125], 8-day 500 m), the Global OCO-2 Solar-Induced Chlorophyll Fluorescence (SIF) Gross Primary Production (GOSIF _GPP_[126], 8-day 5 km), and the MODIS Net Primary Production (MOD/MYD17A3 HGF v006 [127; 128], annual 500 m). By calculating the difference between the modeling output and existing satellite datasets, the performances of our _GPP_ and \(R_{e}\) model were analyzed further.