## 1 Introduction
Several inversion frameworks have been proposed to study human-induced CO\({}_{2}\) emissions in Salt Lake City [22; 23], Los Angeles [24; 25], Indianapolis [26; 27; 28], Boston [29], Saint Paul [30], Washington DC-Baltimore [31] in North America, Davos [32], Paris [33; 34], Berlin [35; 36], and London [37] in Europe, and Cape Town [38] in Africa. Because urban CO\({}_{2}\) fluxes represent the aggregated results of local anthropogenic CO\({}_{2}\) emissions, vegetation CO\({}_{2}\) uptake and biogenic respired CO\({}_{2}\) emissions [39; 40; 41; 42], as well as transport of CO\({}_{2}\) in air mass/parcel by advection, turbulence, and convection [43], it is imperative toestimate biogenic CO\({}_{2}\) fluxes (photosynthetic uptake and biogenic respiration) accurately to assist inversion analysis of anthropogenic CO\({}_{2}\) emissions at a city scale. Some of these studies accounted the net ecosystem exchange of CO\({}_{2}\) (\(NEE\)) in their study areas: [PERSON] et al. (2013), [PERSON] et al. (2014), [PERSON] et al. (2016), and [PERSON] et al. (2018) used land surface models ([PERSON] et al., 2014; [PERSON] et al., 2015; [PERSON] et al., 2016; [PERSON] et al., 2017); [PERSON] et al. (2018); [PERSON] et al. (2018), and [PERSON] et al. (2019) used a terrestrial biosphere model--the Vegetation Photosynthesis and Respiration Model (VPRM, ([PERSON] et al., 2014; [PERSON] et al., 2017)), or its urban version UrbanVPRM ([PERSON] et al., 2014); [PERSON] et al. (2018) used CarbonTracker results ([PERSON] et al., 2018). However, models such as VPRM, which calculate sub-daily photosynthetic CO\({}_{2}\) uptake based on simple empirical relations to air temperature and photosynthetically active radiation (\(PAR\)), neglect diurnal variation of vegetation-absorbed \(PAR\) attributable to cloud conditions and the vegetation canopy structure ([PERSON] et al., 2018; [PERSON] et al., 2016; [PERSON] et al., 2017; [PERSON] et al., 2018). First, the flux density of diffuse and direct photosynthetically active photons in the shortwave spectrum of solar radiation varies considerably according to changes in cloud cover, atmospheric aerosols and ozone, solar elevation angle, surface elevation, and terrain ([PERSON] et al., 2018; [PERSON] et al., 2016; [PERSON] et al., 2017) conditions. For instance, the presence of clouds reduces the total photosynthetically active photon flux density (\(PPFD\)) reaching the top of the vegetation canopy, whereas the fraction of diffuse photons increases. Compared to clear-sky noon, the fraction of diffuse photons reaching the ground is higher at times near sunrise and sunset. Second, when diffuse and direct photosynthetically active photons pass through a vegetation canopy, they present different absorption, scattering, and transmittance characteristics. [PERSON] et al. (2018) analyzed seasonal patterns of photosynthetic parameters based on flux tower measurements. They concluded that without separating diffuse photosynthetically active photons from the total (diffuse + direct), the photosynthetic CO\({}_{2}\) uptake tends to be underestimated. Third, [PERSON] and [PERSON] (2018), [PERSON] et al. (2018), [PERSON] et al. (2018), [PERSON] et al. (2018), [PERSON] et al. (2018), and [PERSON] et al. (2018) discussed light saturation effects in sunlit leaves vs. light limitation effects on shaded leaves of a plant canopy. The results of those studies suggest that photosynthetic CO\({}_{2}\) uptake tends to be overestimated if leaves of the two types are not separated. Tokyo, the capital of Japan, is the world's largest city ([PERSON] et al., 2016). Together with its neighboring prefectures, the Greater Tokyo Area, at the center of the Kanto Plain, is home to more than 37 million residents. Measurement, reporting, and verification ([PERSON] et al., 2016) of anthropogenic CO\({}_{2}\) emissions in this megacity would help policymakers, local stakeholders, and the community to act against climate change.