Sub-Daily Natural CO₂ Flux Simulation Based on Satellite Data: Diurnal and Seasonal Pattern Comparisons to Anthropogenic CO₂ Emissions in the Greater Tokyo Area

Abstract

During the last decade, advances in the remote sensing of greenhouse gas (GHG) concentrations by the Greenhouse Gases Observing SATellite-1 (GOSAT-1), GOSAT-2, and Orbiting Carbon Observatory-2 (OCO-2) have produced finer-resolution atmospheric carbon dioxide (CO₂) datasets. These data are applicable for a top-down approach towards the verification of anthropogenic CO₂ emissions from megacities and updating of the inventory. However, great uncertainties regarding natural CO₂ flux estimates remain when back-casting CO₂ emissions from concentration data, making accurate disaggregation of urban CO₂ sources difficult. For this study, we used Moderate Resolution Imaging Spectroradiometer (MODIS) land products, meso-scale meteorological data, SoilGrids250 m soil profile data, and sub-daily soil moisture datasets to calculate hourly photosynthetic CO₂ uptake and biogenic CO₂ emissions with 500 m resolution for the Kantō Plain, Japan, at the center of which is the Tokyo metropolis. Our hourly integrated modeling results obtained for the period 2010–2018 suggest that, collectively, the vegetated land within the Greater Tokyo Area served as a daytime carbon sink year-round, where the hourly integrated net atmospheric CO₂ removal was up to 14.15 ± 4.24% of hourly integrated anthropogenic emissions in winter and up to 55.42 ± 10.39% in summer. At night, plants and soil in the Greater Tokyo Area were natural carbon sources, with hourly integrated biogenic CO₂ emissions equivalent to 2.27 ± 0.11%–4.97 ± 1.17% of the anthropogenic emissions in winter and 13.71 ± 2.44%–23.62 ± 3.13% in summer. Between January and July, the hourly integrated biogenic CO₂ emissions of the Greater Tokyo Area increased sixfold, whereas the amplitude of the midday hourly integrated photosynthetic CO₂ uptake was enhanced by nearly five times and could offset up to 79.04 ± 12.31% of the hourly integrated anthropogenic CO₂ emissions in summer. The gridded hourly photosynthetic CO₂ uptake and biogenic respiration estimates not only provide reference data for the estimation of total natural CO₂ removal in our study area, but also supply prior input values for the disaggregation of anthropogenic CO₂ emissions and biogenic CO₂ fluxes when applying top-down approaches to update the megacity’s CO₂ emissions inventory. The latter contribution allows unprecedented amounts of GOSAT and ground measurement data regarding CO₂ concentration to be analyzed in inverse modeling of anthropogenic CO₂ emissions from Tokyo and the Kantō Plain.

1. Introduction

To address climate change, greenhouse gas inventories including both source emissions and sink removals have been exceedingly important for policymaking and for scientific studies. The primary greenhouse gas in the atmosphere affected by human activities is carbon dioxide (CO₂), with a global averaged concentration of 407.8 ± 0.1 parts per million (ppm) in 2018 [1]. Scientific reports such as the Global Carbon Budget 2019 [2] estimated sources and sinks of CO₂ globally. National greenhouse gas inventories have included annual totals and trends of CO₂ emissions and removals by sector. In addition to global and national inventories, the Integrated Global Greenhouse Gas Information System (IG³IS) advocates the necessity of advancing estimation and attribution of megacity GHG emissions to support the implementation of the ambition cycle and global stocktake in the Paris Agreement [3]. Cities are the focal points of climate action for the following reasons: more than half of the human population resides in urban areas [4], where cities and their affiliated power plants, airports and other infrastructure constitute the largest human-induced CO₂ emission sources, accounting for 50%–80% of the global total [3,5,6,7]; also, urban populations will continue growing to 68% of the global total by 2050 [4], with expected rapid rises occurring particularly in Africa, Asia, and Latin America, presumably increasing CO₂ emissions markedly [8,9].

Some city-scale anthropogenic CO₂ emission datasets already exist. Cities such as Los Angeles [10], Paris [11], and Tokyo [12], with abundant resources and the greatest commitments to addressing climate change, self-report their GHG annual emissions. Studies such as those by Gurney et al. [13] and Shan et al. [14] developed urban CO₂ emission inventory frameworks to estimate anthropogenic CO₂ emissions. Nangini et al. [15] synthesized anthropogenic CO₂ emissions in 343 cities from both developed and developing countries. However, a few aspects remain to be improved to acquire comprehensive and consistent urban CO₂ emission datasets. Because of variations in local resources and accounting capacities, global CO₂ emissions data at the city scale are incomplete. Moreover, the representativeness of cities is biased [7], and some cities in the global south are struggling with data scarcity challenges such as inadequate information collection [8,16,17]. Moreover, urban GHG inventory methods are yet to be standardized [7,16]. Because of inconsistent accounted emissions sources, inventory methods and incompatible boundaries [7,9], the contents and quality of city-scale CO₂ emission data are often incoherent, making city-to-city comparisons difficult.

Top-down approach might address the research challenges described above and update megacities’ anthropogenic CO₂ emission datasets extensively. In the field of atmospheric sciences, the top-down approach refers to the back-casting of CO₂ flux based on atmospheric concentration data. In fact, verification of greenhouse gas inventories via the top-down approach (atmospheric measurement and inverse model) has been highlighted by the Intergovernmental Panel on Climate Change (IPCC)’s Task Force on National Greenhouse Gas Inventories (IPCC-TFI) in the latest refinement of its 2006 guidelines [18], because this method allows the exploitation of independent observation datasets. Top-down approach can be applied flexibly at various scales. In particular, advances taking place during the last decade of global atmospheric greenhouse gas concentration observations derived from satellite retrievals (GOSAT-1, OCO-2, TanSat, GOSAT-2, and OCO-3) generated CO₂ and methane (CH₄) datasets in fine resolution to support such application of inverse models [19,20,21].

Several inversion frameworks have been proposed to study human-induced CO₂ 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 CO₂ fluxes represent the aggregated results of local anthropogenic CO₂ emissions, vegetation CO₂ uptake and biogenic respired CO₂ emissions [39,40,41,42], as well as transport of CO₂ in air mass/parcel by advection, turbulence, and convection [43], it is imperative to estimate biogenic CO₂ fluxes (photosynthetic uptake and biogenic respiration) accurately to assist inversion analysis of anthropogenic CO₂ emissions at a city scale.

Some of these studies accounted the net ecosystem exchange of CO₂ (NEE) in their study areas: Bréon et al. [33], Staufer et al. [34], Boon et al. [37], and Nickless et al. [38] used land surface models [44,45,46,47]; McKain et al. [22], Pillai et al. [35], and Sargent et al. [29] used a terrestrial biosphere model—the Vegetation Photosynthesis and Respiration Model (VPRM, [43,48]), or its urban version UrbanVPRM [49]; Hu et al. [30] used CarbonTracker results [50]. However, models such as VPRM, which calculate sub-daily photosynthetic CO₂ 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 [51,52,53,54]. 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 [52,53,54] 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. Gu et al. [51] 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 CO₂ uptake tends to be underestimated. Third, de Pury and Farquhar [55], Gu et al. [51], Urban et al. [56], Chen et al. [57], Luo et al. [58], and Ryu et al. [59] 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 CO₂ 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 [4]. Together with its neighboring prefectures, the Greater Tokyo Area, at the center of the Kantō Plain, is home to more than 37 million residents. Measurement, reporting, and verification [6] of anthropogenic CO₂ emissions in this megacity would help policymakers, local stakeholders, and the community to act against climate change. For example, Moriwaki and Kanda [39] conducted a one-year measurement of CO₂ flux in a residential area of Tokyo with a significant fraction of vegetation cover, and reported representative seasonal and diurnal variation patterns of anthropogenic CO₂ emission in the city. In addition, Hirano et al. [60] clarified the diurnal variation of CO₂ flux in a less vegetated residential area of Tokyo that was close to arterial roads. Imasu and Tanabe [61] summarized more than ten years of ground-based CO₂ concentration data measurements at five sites in the Greater Tokyo Area, finding different sub-daily and seasonal patterns of CO₂ concentrations from urban sites in Tokyo to rural ones in Saitama prefecture. In other efforts, GOSAT-1 and GOSAT-2 enhanced target mode observation, particularly addressing the Kantō Plain and provide an unprecedented amount of high-resolution atmospheric CO₂ concentration data to elucidate anthropogenic CO₂ emissions in Tokyo and to update its CO₂ inventory.

To support analyses of these data in a top-down approach (i.e., inversion modeling system) for the megacity Tokyo, disaggregating anthropogenic CO₂ emissions from biogenic CO₂ flux at the order of a half-hour to several hours is necessary. To reduce biogenic CO₂ flux interference for city-scale CO₂ emissions estimation in particular, both photosynthetic CO₂ uptake and CO₂ emissions attributable to vegetation respiration, along with soil microbial and passive organic carbon decomposition within urban areas and surrounding vegetated land, should be explicitly considered.

This study was conducted to develop a terrestrial biosphere model calculating sub-daily variation of NEE based on satellite data and meteorological conditions, to be coupled with a regional CO₂ transport model for better estimation of anthropogenic CO₂ emissions from megacities, with Tokyo and the Kantō Plain (139°E–141°E, 35°N–36.33°N) as the target area of study. To set up boundary conditions of CO₂ in the transport model AIST-MM [62,63], the calculation of biogenic CO₂ fluxes was expanded further to the central area of Japan (134.5°E–142.5°E, 32.5°N–38.5°N). Moreover, the NEE results provide reference information that is useful to estimate net vegetation photosynthetic CO₂ removal from the atmosphere in the region, which itself is part of the CO₂ inventory.

2. Materials and Methods

The CO₂ flux from an ecosystem to the atmosphere is represented by NEE [64]. In terrestrial ecosystems, NEE is the difference between the gross primary production (GPP) and ecosystem respiration (R_e), where GPP represents the total photosynthetic CO₂ uptake at the ecosystem scale, whereas R_e denotes the sum of respired CO₂ by vegetation (R_autotrophic) and CO₂ emitted from organic carbon decomposition processes at the soil surface and in shallow soil layers (R_{heterotrophic}). Table S1 in the Supplementary Materials presents a list of variables used for the calculation of NEE.

NEE = R_e − GPP

(1)

R_e = R_autotrophic + R_{heterotrophic}

(2)

2.1. Calculation of Hourly GPP

One key step of GPP calculation is the quantification of the absorbed photosynthetically active photons flux density by the vegetation canopy at local time t (APPFD_t). By generalizing the sun/shade model described by de Pury and Farquhar [55] to various foliage clumping index conditions and types of leaf angle distribution, APPFD_t is calculable once diffuse PPFD (PPFD_t^diffuse) and direct PPFD (PPFD_t^direct) at the vegetation canopy top are known. For this study, PPFD_t^diffuse was calculated based on diffuse shortwave solar radiation (SR_t^diffuse), whereas PPFD_t^direct was based on direct shortwave solar radiation (SR_t^direct) using reference parameter settings in Ito and Oikawa [65]. To estimate SR_t^diffuse under various sky conditions (sunny to different degree of cloudiness), an artificial neural network (ANN) linear regression [59,66,67,68] method was developed using the following input variables: low cloud cover (LCDC), middle cloud cover (MCDC), high cloud cover (HCDC), surface atmospheric pressure (P_ambient), shortwave black-sky albedo (α_black-sky), shortwave white-sky albedo (α_white-sky), surface vapor pressure (VP) and cosine of solar zenith angle (θ_t^SZA) at local time t. The details of the generalized APPFD_t equations and ANN training processes are presented in the Supplementary Materials.

With solved hourly APPFD_t, it is then feasible to apply a terrestrial biosphere model, the Biosphere model integrating Eco-physiological And Mechanistic approaches using Satellite data (BEAMS, [69,70]), to estimate hourly GPP. BEAMS adopted the Monteith equation [71,72] with improvement of light use efficiency (LUE) calculation, assuming that GPP is proportional to APPFD_t and taking into account the photosynthetic Stress_t (unitless) caused by light, soil moisture conditions, surface temperature and relative humidity.

GPP_BEAMS = APPFD_t × LUE_max × Stress_t

(3)

Stress_t = P_t^actual/P_t^optimal

(4)

where LUE_max represents the maximal photosynthetic light use efficiency in each plant functional type (PFT), P_t^actual, denotes the actual photosynthetic assimilation rate at given conditions, and P_t^optimal stands for the optimal photosynthetic assimilation rate at optimal conditions (i.e., 100% surface relative humidity and no soil water stress). Additionally, APPFD_t was assumed to be evenly distributed in a big-leaf model [69] to calculate P_t^actual and P_t^optimal, which were solved by coupling a simplified Farquhar–von Caemmerer–Berry model [69,73,74,75,76] of a C3 plant to the stomatal conductance of CO₂ [73,77,78,79,80]. The Farquhar–von Caemmerer–Berry model, stomatal conductance and the iterative solution are described in the Supplementary Materials.

As reviewed in the Introduction, photosynthetic productivity at the canopy scale tends to be overestimated without differentiating sunlit leaves from shaded leaves, which is the case for a big-leaf model. Moreover, the vegetation density, represented by the Leaf Area Index (LAI), in our study area was often dense (LAI ≥ 5 m² m⁻²) during the growing season in summer, meaning that only a limited area (≤2 m² m⁻²) of leaves would be sunlit. To avoid GPP overestimation, a two-leaf (sunlit/shaded) up-scaling scheme [55,57,58,73,81] was also applied for this study to calculate hourly GPP, based on the average net photosynthetic assimilation rate in sunlit leaves (P_n^sunlit) and the average net photosynthetic assimilation rate for shaded leaves (P_n^shaded).

GPP_TLM = P_n^sunlit × LAI_t^sunlit + P_n^shaded × LAI_t^shaded

(5)

The equations used to calculate P_n^sunlit, P_n^shaded, LAI_t^sunlit, and LAI_t^shaded are given in the Supplementary Materials.

2.2. Caculation of Hourly R_e

To maintain physiological activities, plants respire CO₂ (R_maintenance). Vegetation biomass pools [69,82,83] were simply divided into foliage (bio_t^foliage), wood (bio_t^live-wood + bio_t^dead-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^foliage, R_m^live-wood, and R_m^root equations are provided in the Supplementary Materials.

R_maintenance = R_m^foliage + R_m^live-wood + R_m^root

(6)

To use the carbon captured during photosynthesis, a plant consumes a fraction of its GPP and emits CO₂ 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 × (GPP_BEAMS/TLM − R_maintenance)

(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

(8)

NPP = GPP_BEAMS/TLM − R_autotrophic

(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 CO₂ 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 Friedlingstein et al. [84] minus carbon loss because of maintenance respiration and root mortality. Although dead-wood biomass does not emit respired CO₂, 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 CO₂ 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 CO₂ emitted 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^microbe)), and five soil SOC pools (root structural litter carbon (SOC_root^structural), root metabolic litter carbon (SOC_root^metabolic), soil microbe (SOC_soil^microbe), 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 CO₂ 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 Hashimoto et al. [89], the maximum decomposition rates [88] were adjusted by 1/2.3. The equations of carbon influx and efflux flows are presented in the Supplementary Materials, including CO₂ emission R_hSOC in each SOC pool, as shown below:

R_{heterotrophic} = (R_hSOC_surface^structural + R_hSOC_surface^metabolic + R_hSOC_surface^microbe) + (R_hSOC_root^structural + R_hSOC_root^metabolic) + (R_hSOC_soil^microbe + R_hSOC_soil^slow + R_hSOC_soil^passive)

(10)

2.3. Parameter Calibration and Model Validation at the Site Level

According to the register of JapanFlux [90], 39 Japanese sites have been monitoring mass and energy fluxes over terrestrial ecosystems, including CO₂ fluxes. However, only the GPP, R_e, and NEE data of six sites are accessible in the Forestry and Forest Products Research Institute FluxNet Database (FFNet DB, [91]): Sapporo (SAP), Appi (API), Kawagoe, Fujiyoshida (FJY), Kahoku, and Yamashiro (YMS). Additionally, the data of the Moshiri Birch Forest site and the Seto Mixed Forest site are included in the FLUXNET2015 dataset [92]. Nevertheless, no data of Japanese EBF or GRS were available when we developed our model. To complete parameter calibration and model validation for different ecosystem types, some GPP and R_e data from outside Japan (China and Malaysia) were used. To be more specific, half-hourly data of two FFNet DB sites (SAP [93,94] and FJY [95,96,97]) and two FLUXNET2015 sites (Dinghushan DIN [98]) and Changeling CNG [99]) were obtained to calibrate PFT-specific parameters in hourly GPP_BEAMS and GPP_TLM modules. To validate the calibrated modeling settings, half-hourly data of one FFNet DB site (API [100,101,102,103]) and three FLUXNET2015 sites (Qianyanzhou QIA [104], Pasoh forest reserve PSO [105], and Duolun DU2 [106]) were obtained.

Table 1. List of FFNet DB and FLUXNET2015 sites used for parameter calibration and model validation.

Dataset	Site	Site Code	Longitude	Latitude	Plant Functional Type	Modeling Group	Extraction Period
FLUXNET2015	Changeling	CNG	123.5092E	44.5934N	GRS	Calibration	2007–2010
	Dinghushan	DIN	112.5361E	23.1733N	EBF	Calibration	2003–2005
	Duolun	DU2	116.2836E	42.0467N	GRS	Validation	2006–2008
	Pasoh forest reserve	PSO	102.3062E	2.9730N	EBF	Validation	2003–2009
	Qianyanzhou	QIA	115.0581E	26.7414N	ENF	Validation	2003–2005
FFNet DB	Appi	API	140.9375E	40.0001N	DBF	Validation	2010–2011
	Fuji Yoshida	FJY	138.76225E	35.45454N	ENF	Calibration	2010–2011
	Sapporo	SAP	141.3853E	42.9868N	DBF	Calibration	2010–2014
	Yamashiro	YMS	135.840884E	34.7940252N	Mixed Forest	Validation	2003–2011

presents site information such as the PFT type, coordinates, and period for which data were obtained. Half-hourly GPP data with air temperature, relative humidity, wind speed, downward shortwave solar radiation, and precipitation records were screened in each FFNet DB data subset. Only the best quality data (quality flag = 0) were retained in each FLUXNET2015 data subset. Post-screened data were then converted to the hourly average for model calibration and validation at the site level.

Because continuous LAI records were not measured in either FFNet DB or FLUXNET2015 sites, it was extracted for the grid cell where each site was located from the MODIS LAI product (MCD15A3H v006 [107], 4-day 500 m) as proxies of the site conditions. Bad quality LAI data were replaced by interpolated values, as described further in the Supplementary Materials. Similarly, the canopy clumping index (Ω) was extracted from the MODIS Bidirectional Reflectance Distribution Function (BRDF)-derived dataset [108] with 500 m resolution, and both α_black-sky and α_white-sky were based on the MODIS albedo product (MCD43A3 v006 [109], daily 500 m). Although some FFNet DB and FLUXNET2015 sites included 0–5 cm depth soil moisture data, this layer is too shallow to estimate the comprehensive effects of soil water availability on photosynthesis. Soil water content θ_k (m³ m⁻³) for the 0–7, 7–28, 28–100, and 100–289 cm soil layers was therefore extracted from the ERA-5 Land reanalysis dataset [110] (hourly 9 km), whereas the fractions of clay, sand, and silt and the amount of soil organic carbon for each site were obtained from the SoilGrids250m dataset [111]. In addition, cloud cover and atmospheric pressure conditions at each FFNet DB site were based on the hourly Meso-Spectral Model Grid Point Value (MSM-GPV) reanalysis dataset with 5 km resolution provided by the Japanese Meteorological Agency [112]. The ANN method developed for this study to estimate SR_t^diffuse was not applicable to FLUXNET2015 sites because of the lack of cloud cover data, and in such cases, the empirical method of Luo et al. [58] was adopted instead.

During calibration, each PFT-specific parameter for DBF, EBF, ENF, and GRS was increased or decreased by 10% until: (1) the correlation coefficient between hourly flux tower estimate (GPP_tower) and modeled GPP was as close to 1 as possible and this change in parameter did not conflict with (2) or (3); (2) the root mean square error (RMSE) between hourly GPP_tower and modeled GPP was as low as possible and this change in parameter did not conflict with (1) or (3); (3) the standard deviations of hourly GPP_tower and modeled GPP were as similar as possible and this change in parameter did not conflict with (1) or (2).

Table 2. Plant functional type-specific parameters used to calculate hourly GPP.

Symbol	Parameter Name	Unit	GPPBEAMS Module				GPPTLM Module
			DBF	EBF	ENF	GRS	DBF	EBF	ENF	GRS
fPAV	Fraction of APPFDt absorbed by photosynthetic active vegetation part	-	0.85	0.765	0.85	0.85	0.36	0.33	0.56	0.85
Kb	Extinction coefficient of PPFDtdirect	-	0.94	0.86	0.94	0.94	0.94	0.94	0.94	0.78
Kn	Extinction coefficient of leaf nitrogen content	-	-	-	-	-	0.33	0.3	0.36	0.3
LUEmax	Maximal photosynthetic light use efficiency	-	0.02	0.02	0.0293	0.022	-	-	-	-
Ntop	Leaf nitrogen content per leaf area at vegetation canopy top	g m−2	-	-	-	-	1.57	2.34	3.1	1.69
Vcmax25	Maximal carboxylation rate at 25 °C	μmol m−2 s−1	57.7	31.9	68.7	86.0	-	-	-	-
Vcmax25top	Vcmax25 at the top of vegetation canopy		-	-	-	-	42.0	31.9	62.5	46.2
θleaf	Leaf response curvature to electron supply	-	0.63	0.63	0.7	0.77	0.5	0.56	0.51	0.63
σ	Vegetation canopy reflection coefficient of PPFD	-	0.09	0.08	0.07	0.09	0.1	0.11	0.07	0.11
τ	Vegetation canopy transmissivity of PPFD	-	0.045	0.04	0.05	0.05	0.05	0.06	0.05	0.07
χn	Empirical coefficient of Vcmax25 variation attributable to Nleaf	m2 g−1	-	-	-	-	0.59	0.48	0.33	0.54

presents the calibrated parameters used to calculate hourly GPP. After calibration, hourly GPP values at the validation sites were also calculated and compared with GPP_tower.

Without the screening limitation of PPFD in the GPP module, more FFNet DB and FLUXNET2015 data (extraction periods expanded to 2003–2011 at API, 2003–2011 at FJY and 2006–2014 at SAP) were obtained to calibrate and validate hourly R_e and NEE. Validation experiments using YMS [113,114,115] data were also added, and flux tower estimates of the mixed broadleaf forest with both deciduous and evergreen species were compared against DBF modeling results and EBF modeling results, respectively. Half-hourly GPP, R_e, and NEE data with complete air temperature record were selected in each FFNet DB data subset. Only the best quality half-hourly GPP, R_e, NEE, and air temperature data (quality flag = 0) were selected in each FLUXNET2015 data subset. Hourly averages were then calculated for R_e modeling calibration and validation at the site level. Additional required variables such as LAI, θ_k, soil temperature T_k^soil, and fractions of the respective soil components in the 0–7 and 7–28 cm soil layers were assumed with grid values of the MODIS LAI product (MCD15A3H [107]), the ERA-5 Land reanalysis dataset [110], and the SoilGrids250m dataset [111], respectively, same as the case of GPP. To set up initial SOC conditions, hourly R_e simulations based on CENTURY [86,87,88] were first conducted in spin-up mode to accumulate organic carbon, until the carbon stock in the 0–28 cm soil layers approximately reached 6.95 ± 3.25 kg m⁻², a range estimated based on the National Forest Soil Carbon Inventory of Japan [116]. Then, hourly R_e and NEE were modeled to calibrate the parameters and to validate the R_e model. The details of the related equations and parameter settings are available in the Supplementary Materials.

2.4. Hourly GPP and R_e Modeling at the Regional Scale

The Kantō 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 CO₂ 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 ≤ 1) to calculate the fraction of partial vegetation cover.

To calculate the hourly 500 m × 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 (SMAPL4SMGPH 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_fillnodata.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 ± 3.25 kg m⁻² [116].

Furthermore, hourly modeling results were aggregated and compared to the MODIS Gross Primary Productivity (MOD/MYD17A2HGF 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/MYD17A3HGF 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.

2.5. Estimation of Integrated Anthropogenic CO₂ Emissions in the Greater Tokyo Area

Finally, the calculation results in Section 2.4 were compared with anthropogenic CO₂ emissions data in the Greater Tokyo Area spatially and at various time scales. Annual anthropogenic CO₂ emission data by sector (TotalE_sector²⁰¹⁸, e.g., construction, industry, agricultural waste burning, vehicle, ship, aircraft) in Japan in 2018 were obtained at as high a rate as possible from the national greenhouse gas emissions report provided by the Ministry of the Environment of Japan [129]. For our study area specifically, hourly human-induced CO₂ emissions in January to December were estimated based on the East Asian Air Pollutant Emissions Grid Database (EAGrid2000Japan [130]), where the value of each grid cell by sector (GridCellE_sector^{EAGrid2000Japan}) was adjusted using a constant ratio (f_sector) of total CO₂ emissions in 2000 to that in 2018:

f_sector = TotalE_sector²⁰¹⁸/TotalE_sector²⁰⁰⁰

(11)

GridCellE_sector²⁰¹⁸ = f_sector × GridCellE_sector^{EAGrid2000Japan}

(12)

In addition, integrated anthropogenic CO₂ emission of all source sectors, GPP, R_e, and NEE of the Greater Tokyo Area were calculated to elucidate the patterns of sub-daily and seasonal variations: the mean and standard deviation of biogenic integrated fluxes were calculated based on hourly results of all the days in each month during the period 2010–2018.

3. Results

3.1. Hourly GPP at the Site Level

Comparison between hourly modeled GPP and FFNet DB/FLUXNET2015 estimation provides reference information about the modeling uncertainty of CO₂ uptake via photosynthesis in DBF, EBF, ENF, and GRS. As presented in Figure 2a (the evaluation metrics values also detailed in Table S2), the degree of similarity [131] between hourly GPP_BEAMS (Big-Leaf upscaling scheme) and GPP_tower was greater than 0.6 in both calibration and validation groups. Stated more specifically, the hourly GPP_BEAMS agreed closely with GPP_tower in ENF (R² ≥ 0.75), followed by DBF (R² ≥ 0.63), EBF (R² ≥ 0.53), and GRS (R² ≥ 0.49). The difference between flux tower-estimated and modeled standard deviation of hourly GPP at the site level was always within 1.22 μmolCO₂ m⁻² s⁻¹, and therefore was acceptable. The RMSE of the hourly GPP_BEAMS was less than 6.1 μmolCO₂ m⁻² s⁻¹ or 0.26 gC m⁻² h⁻¹, where the largest was found for DBF and the smallest was found for GRS.

The accuracy of the hourly modeled GPP_TLM (two-leaf upscaling scheme) was better than that of the hourly modeled GPP_BEAMS when compared to GPP_tower, but with one exception in the validation group of ENF (QIA). As with GPP_BEAMS, the similarity between hourly GPP_TLM and GPP_tower was greater than 0.6 in both the calibration and validation groups, according to Figure 2b and Table S2. Hourly GPP_TLM also showed very good agreement with GPP_tower in ENF (R² ≥ 0.74), DBF (R² ≥ 0.67), EBF (R² ≥ 0.61), and GRS (R² ≥ 0.50). The difference between the flux tower estimated and modeled standard deviation of hourly GPP in the two-leaf module was within 1.05 μmolCO₂ m⁻² s⁻¹, smaller than that in the case of GPP_BEAMS. The RMSE of hourly GPP_TLM was less than 5.55 μmolCO₂ m⁻² s⁻¹, or 0.24 gC m⁻² h⁻¹, which was again smaller than the value of hourly GPP_BEAMS.

3.2. 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 CO₂ 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 (R² ≥ 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 (R² 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 μmolCO₂ m⁻² s⁻¹ that of the flux tower estimated one. Consequently, the RMSE of hourly R_e was up to 2.61 μmolCO₂ m⁻² s⁻¹, or 0.11 gC m⁻² h⁻¹ in EBF, followed by ENF, DBF, and GRS, in descending order.

Hourly R_e was approximately one to two thirds of hourly GPP in terms of the absolute value, while the former often presented much less sub-daily variations than the latter. As a result, their difference, hourly modeled NEE, agreed well with flux tower estimates at the site level simulations (Figure 3b and Table S2), though hourly modeled R_e tended to be overestimated. In DBF, the correlation coefficient of hourly NEE was equal to or larger than 0.95, followed by ENF (R² ≥ 0.79), EBF (R² ≥ 0.74), and GRS (R² ≥ 0.41). Contrary to the hourly modeled R_e, the standard deviation of the hourly modeled NEE was only 0.80–0.98 times (the difference of the absolute values was within 1.33 μmolCO₂ m⁻² s⁻¹) that of the flux tower estimated one. The RMSE of the hourly modeled NEE was up to 5.43 μmolCO₂ m⁻² s⁻¹, or 0.23 gC m⁻² h⁻¹ in EBF, followed by ENF, DBF, and GRS, in descending order. The standard deviation of the hourly modeled NEE at YMS was close to that of the flux tower-estimated NEE, when assuming with either DBF or EBF parameters; the RMSE of the hourly modeled NEE was 3.21 and 3.37 μmolCO₂ m⁻² s⁻¹, while the correlation coefficient was 0.51 and 0.50, respectively. These results might be partially attributable to the overestimation of hourly R_e: overestimated R_e can engender a positive NEE value, representing a false net carbon release, when the actual R_e was smaller than GPP and there was actually net carbon uptake.

3.3. Hourly GPP at the Regional Scale

Because point-scale modelling results suggest that hourly modeled GPP_TLM was close to or more accurate than hourly modeled GPP_BEAMS, only the GPP_TLM estimates at the regional scale were presented in the following analyses for simplicity, although 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 CO₂ 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 °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 ± 0.27, 0.90 ± 0.18, and 0.93 ± 0.18 gC m⁻² h⁻¹ in ENF, EBF, and DBF, and 1.19 ± 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 ± 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 areas, precipitation interfered with stomatal conductance of CO₂ 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. By virtue of the density of the leaf area in summer, the fraction of absorbed PPFD by the vegetation canopy was high (>0.7) in most of the forests in the study area but lower (0.2–0.6) in less densely vegetated urban grid cells. In agreement with earlier studies [57,132], this variable also exhibited diurnal change, higher in the early morning and late afternoon of a sunny day, when the ratio of diffuse PPFD was relatively high, as Figure 4h,i,m,n show.

3.4. Hourly R_e at the Regional Scale

Figure 5 presents hourly R_e results on the same summer day as in Figure 4 and Figure 6, to give examples of sub-daily variations of biogenic CO₂ emission. At night, in evergreen forests in the southeast, northeast and west of the study area, hourly R_e was strong (about 0.18 ± 0.06 to 0.22 ± 0.10 gC m⁻² h⁻¹), probably because of active microbial and chemical decomposition of SOC under favorable soil temperatures and moisture conditions, where litter carbon was abundant. In contrast, hourly R_e was lower in DBF near the eastern coastline and in most urban grid cells with partial vegetated cover. The latter hourly R_e was roughly 0.04 ± 0.01 gC m⁻² h⁻¹ according to Figure 6. In the daytime, the total of autotrophic and heterotrophic respiration in all types of ecosystem increased, up to 0.35 ± 0.13 gC m⁻² h⁻¹ in forests, 0.35 ± 0.27 gC m⁻² h⁻¹ in grassland, and 0.19 ± 0.06 gC m⁻² h⁻¹ in partially vegetated urban area. Diurnal temperature difference and additional growth respiration of plants to use photosynthesis-captured carbon most likely caused such a day–night difference of hourly R_e.

Hourly NEE (the difference of R_e and GPP) in different types of ecosystem was also presented by the mean and standard deviation among all grid cells in Figure 6. At night, R_e was the sole contributor of hourly NEE, and therefore the latter shared the same range of values described in the paragraph above. In the daytime, the strongest net carbon uptake occurred in ENF, up to –0.82 ± 0.22 gC m⁻² h⁻¹, followed by DBF, EBF, urban land with partial vegetated cover, and GRS, up to −0.66 ± 0.13, −0.65 ± 0.16, −0.49 ± 0.15, and −0.35 ± 0.41 gC m⁻² h⁻¹, respectively.

Furthermore,

Table 3. Annual averaged and integrated GPP and R_e estimates in deciduous broadleaf forest (DBF), evergreen broadleaf forest (EBF), evergreen needleleaf forest (ENF), grassland (GRS), and partially vegetated urban area of the Greater Tokyo Area (139°E–141°E, 35°N–36.33°N) during the period 2010–2018.

Plant Functional Type	Total Area 1	Annual Averaged GPP	Annual Averaged Re	Integrated Annual GPP	Integrated Annual Re
	km2	gC m−2 Year 1	gC m−2 Year 1	106 tonCO2 Year 1	106 tonCO2 Year 1
DBF	3131.06 ± 100.40	1254.42 ± 67.63	667.66 ± 73.21	14.39 ± 0.78	7.66 ± 0.84
EBF	3669.55 ± 72.73	1484.26 ± 22.22	801.43 ± 82.38	19.96 ± 0.30	10.78 ± 1.11
ENF	3337.77 ± 48.05	1834.27 ± 38.60	1035.43 ± 105.79	22.43 ± 0.47	12.66 ± 1.29
GRS	159.22 ± 14.04	1409.33 ± 185.44	1308.89 ± 280.83	0.82 ± 0.11	0.76 ± 0.16
Partially vegetated URBAN (0 < LAI)	1374.62 ± 134.05	1020.77 ± 93.59	393.85 ± 38.41	5.14 ± 0.47	1.98 ± 0.19

¹ Total area of each plant functional type (PFT) was estimated based on the number of 500 m × 500 m grid cells in the MODIS land cover type product (MCD12Q1) and the vegetated cover fraction per grid cell in the MODIS vegetation continuous fields product (MOD44B).

summarizes the annual averaged GPP and R_e during the period 2010–2018 in different types of ecosystem within the study area. According to our calculation, the highest annual averaged GPP occurred in ENF, about 1834.27 ± 38.60 gC m⁻² year⁻¹. By virtue of the longer photosynthetic active period in EBF than in DBF, the annual averaged GPP in EBF (1484.26 ± 22.22 gC m⁻² year⁻¹) was significantly higher than that in DBF (1254.42 ± 67.63 gC m⁻² year⁻¹), even though the hourly averaged GPP in these two types of broadleaf forest was similar from May to October. In GRS, the annual averaged GPP was 1409.33 ± 185.44 gC m⁻² year⁻¹. The annual averaged GPP in partially vegetated urban areas was 1020.77 ± 93.59 gC m⁻² year⁻¹, probably because of a less dense LAI level than that in forests or grassland. The strongest annual averaged R_e occurred in GRS, about 1308.89 ± 280.83 gC m⁻² year⁻¹, followed by ENF, EBF, and DBF in descending order. The annual averaged R_e in partially vegetated urban area was only 393.85 ± 38.41 gC m⁻² year⁻¹; both the limited SOC-decomposition-induced CO₂ emissions and less dense LAI level probably caused this.

3.5. Comparison of Regional Scale Modeling Results and Satellite Data

Hourly modeled GPP at the regional scale also presented clear seasonal changes. Figure 7a–d depict examples of 8-day sums of hourly modeled GPP from winter to autumn. Because little or no valid MODIS LAI was detected in the urban land close to the Tokyo bay in our study area year-round, GPP was zero there. In January, our model estimated up to 10.0 gC m⁻² 8-day⁻¹ photosynthetic carbon uptake in deciduous forests and urban vegetated land. In contrast, GPP was almost 30.0 gC m⁻² 8-day⁻¹ in evergreen forests, even in winter. When spring approached and temperatures increased, so did GPP in such evergreen forests. The GPP remained low in deciduous forests and some urban vegetated land, as the leaf area had not fully expanded yet. Summertime GPP was about 40.0–90.0 gC m⁻² 8-day⁻¹ in ecosystems of all types because of favorable solar radiation and temperature conditions. It then decreased to 10.0–70.0 gC m⁻² 8-day⁻¹ in autumn until leaf fall occurred.

The reason to calculate 8-day GPP of the study area was that few GPP datasets or reference values in earlier studies were available at the sub-daily scale. In fact, only Bodesheim et al. [133] has modeled global half-hourly biogenic CO₂ flux data, but the spatial resolution (0.5°) of this dataset was too coarse to validate our modeling results. Therefore, comparisons between our 8-day GPP results and MODIS GPP [124,125] or GOSIF GPP [126] (Figure 7e–p) were presented. As Figure 7e-h show, our model estimated higher (0.0–30.0 gC m⁻²) 8-day GPP than the MODIS one in evergreen forests in the northeast and west of the study area. In contrast, the modeled 8-day GPP was 0.0–20.0 gC m⁻² lower compared to MODIS 8-day GPP in the western deciduous forests and southeastern evergreen forests; for the latter, the discrepancy was up to 30.0 gC m⁻² in summertime (Figure 7g). Over seasons, the range of difference was larger in summer than in winter while the spatial patterns remained the same, as the average and standard deviation of the difference between the modeled and MODIS 8-day GPP during the period 2010–2018 in Figure 7m-o indicate.

In January (Figure 7i) and October (Figure 7l), the difference between the modeled and GOSIF 8-day GPP was similar to the case of the modeled and MODIS 8-day GPP comparisons. Interestingly, GOSIF 8-day GPP was lower (up to 40.0 gC m⁻²) than our modeled results or MODIS GPP in April (Figure 7j), and then became much larger than the latter two estimates in July (Figure 7k). The favorable conditions (e.g., warm temperature and sufficient solar radiation) in spring and frequent rain in summer shaped the seasonal patterns of our modeled GPP, which probably led to the discrepancy with GOSIF 8-day GPP. The average and standard deviation of the difference between the modeled and GOSIF 8-day GPP during the period 2010–2018 are presented in Figure 7n–p. In addition to forests and partially vegetated urban area, MODIS GPP [124,125] also provides GPP estimates in agricultural land in the northeast of the study area that was not included in our simulations. GOSIF GPP [126] estimated a photosynthetic carbon uptake of 0–10.0 gC m⁻² 8-day⁻¹ in winter and 10.0–30.0 gC m⁻² 8-day⁻¹ in summer in the highly urbanized areas next to the Tokyo bay, which both our model and the MODIS GPP dataset considered non-vegetated.

In terms of NPP, our annual modeled NPP (Figure 8a) was about 0.6–2.0 kgC m⁻² year⁻¹ in forests and up to 0.6 kgC m⁻² year⁻¹ in urban vegetated land in 2018. Evergreen forests in particular presented high NPP, 1.2–2.0 kgC m⁻² year⁻¹, by virtue of a longer photosynthetic active period. Our modeled NPP was larger compared to annual MODIS NPP (Figure 8b,c) values, especially in evergreen forests in the northeast and west of the study area. This was probably because of lower estimates of autotrophic respiration and growth respiration rate of plants in particular, considering that the modeled GPP showed good agreement with MODIS GPP and that the algorithm of maintenance respiration in this study was similar to the MODIS method. Because of limited space, comparisons of 8-day GPP and annual NPP to satellite data in 2010–2017 are not presented, but were very similar to those obtained for cases of 2018.

3.6. Biogenic CO₂ Fluxes and Anthropogenic CO₂ Emissions in the Greater Tokyo Area

The spatial distribution of anthropogenic CO₂ emissions and biogenic CO₂ fluxes in the Greater Tokyo Area barely overlapped and exhibited some asynchronous characteristics, as the examples of our modeling results in Figure 4, Figure 5 and Figure 9 demonstrate. On one hand, Tokyo was surrounded by evergreen and deciduous forests in Ibaraki, Chiba, Saitama, and Kanagawa prefectures, which were sources of biogenic CO₂. On the other hand, strong anthropogenic CO₂ emissions occurred from the Tokyo metropolis, as well as from the Keihin and Keiyou industrial areas near Tokyo and the Kashima seaside industrial area (marked by dashed cycles in Figure 1, respectively), where power plants and factories are concentrated. If the range of the biogenic CO₂ flux in our study area was much smaller than that of anthropogenic CO₂ emissions, then neglecting the former in a top-down approach modeling would not cause much error in back-casting results. Otherwise, accurate calculation of the biogenic CO₂ flux is essential for updating the anthropogenic CO₂ emission inventory in the megacity of Tokyo. The comparisons of hourly integrated GPP (photosynthetic CO₂ uptake), R_e (biogenic CO₂ emission), and NEE (net biogenic CO₂ flux) to hourly anthropogenic CO₂ emissions in the Greater Tokyo Area (Figure 10) provide some reference to evaluate this question. For our study, “hourly integrated” refers to the sum of modeled results in all grid cells within 139°E–141°E, 35°N–36.33°N, averaged over all days in each month during the period 2010–2018. The mean and standard deviation of hourly integrated biogenic CO₂ fluxes are elaborated as below.

To elaborate, first, hourly integrated anthropogenic CO₂ emissions of the Greater Tokyo Area presented similar diurnal variations year-round; the lowest level (2.37–2.64 × 10⁴ ton CO₂ h⁻¹) was found after midnight when human activities were least active. As traffic rush hours started in the morning, hourly integrated anthropogenic CO₂ emissions increased gradually and almost doubled by around 9 a.m. to 4.05–4.63 × 10⁴ ton CO₂ h⁻¹. From then until late afternoon, the integrated anthropogenic CO₂ emissions entered a plateau phase and then started to drop at about 8 pm, after the evening traffic rush hours.

Secondly, the hourly integrated biogenic CO₂ emissions of the Greater Tokyo Area, the total of vegetation-respired CO₂ and CO₂ emitted via SOC decomposition processes, exhibited both sub-daily and seasonal variations. At night, the lowest hourly integrated biogenic CO₂ emissions (0.09 ± 0.01 × 10⁴ ton CO₂ h⁻¹), which was about 3.07 ± 0.51% of the hourly integrated anthropogenic CO₂ emission in the area, occurred at 4 a.m. in January. In the daytime, the hourly integrated biogenic CO₂ emissions became stronger and peaked in the early afternoon (around 3 p.m.). The peak biogenic CO₂ emission (0.16 ± 0.03 × 10⁴ ton CO₂ h⁻¹) was equivalent to about 3.55 ± 0.79% of the hourly integrated anthropogenic CO₂ emissions in January. Such a rise in integrated biogenic CO₂ emissions was probably attributable to increased temperatures and additional vegetation growth respiration when photosynthesis was active during the day.

As meteorological conditions became more favorable for SOC decomposition from winter to summer and vegetation became more active in terms of both maintenance and growing activities, hourly integrated biogenic CO₂ emissions of the Greater Tokyo Area increased considerably. In July, the lowest hourly integrated biogenic CO₂ emissions were at 5 a.m. and was estimated to be 0.56 ± 0.08 × 10⁴ ton CO₂ h⁻¹, roughly 18.76 ± 2.80% of the hourly integrated anthropogenic CO₂ emissions in the Greater Tokyo Area and 6.35 times the biogenic value in January. The strongest hourly integrated biogenic CO₂ emissions were found at noon and were estimated to be 0.96 ± 0.13 × 10⁴ ton CO₂ h⁻¹, which was 6.39 times that of January’s biogenic level, and 23.62 ± 3.13% of the hourly integrated anthropogenic CO₂ emissions, as the latter also increased after several hour.

Thirdly, hourly integrated photosynthetic CO₂ uptake of the Greater Tokyo Area represents the amount of absorbed carbon by forests, grassland or urban vegetation, varying both diurnally and seasonally. Because the calculation of GPP in our model was under the assumption that the supply of CO₂ for photosynthetic reactions in C3 plants is controlled by stomata in daytime only, the hourly integrated photosynthetic CO₂ uptake at night was 0. In winter, the absolute value of hourly integrated photosynthetic CO₂ uptake in both the early morning and late afternoon was low and was the lowest (0.04 ± 0.06 × 10⁴ ton CO₂ h⁻¹ and 1.34 ± 2.03% of the hourly integrated anthropogenic CO₂ emissions in the Greater Tokyo Area) at 5 a.m. in January. Because photosynthetic enzymes became more active at higher winter temperatures and because more photosynthetically active radiation was available around midday, the hourly integrated photosynthetic CO₂ uptake was enhanced. For January, the highest absolute value was obtained around 2 p.m., and that value (0.62 ± 0.17 × 10⁴ ton CO₂ h⁻¹) was 14.08 ± 3.89% of the hourly integrated anthropogenic CO₂ emissions. As the seasons changed, hourly integrated photosynthetic CO₂ uptake of the Greater Tokyo Area reached the highest level in July, with an absolute value of 3.22 ± 0.50 × 10⁴ ton CO₂ h⁻¹ at noon and 5.42 times the January value. This amount was 79.04 ± 12.31% of the hourly integrated anthropogenic CO₂ emissions.

Finally, the hourly integrated net biogenic CO₂ flux of the Greater Tokyo Area represents the amount of CO₂ flow from ecosystems to the atmosphere. At night, such flow was one-way, from forests, grasslands, and urban vegetated areas into the air. The nighttime vegetated land of the Greater Tokyo Area was a natural carbon source, collectively emitting 0.08 ± 0.01 × 10⁴ to 0.09 ± 0.01 × 10⁴ ton CO₂ h⁻¹ in January and 0.56 ± 0.09 × 10⁴ to 0.60 ± 0.10 × 10⁴ ton CO₂ h⁻¹ in July, which were 3.07 ± 0.51% to 2.34 ± 0.41% and 21.97 ± 3.38% to 17.80 ± 2.97% of the hourly integrated anthropogenic CO₂ emissions for January and July, respectively. Depending on whether the photosynthetic CO₂ uptake would completely compensate for the biogenic CO₂ emission in each grid cell or not, the daytime net biogenic CO₂ flux from ecosystems to the atmosphere was either negative or positive. Here, negative net biogenic CO₂ flux values mean that the direction of carbon flow is reversed (from atmosphere to the ecosystem): a natural carbon sink. The maximal negative hourly integrated net biogenic CO₂ flux of the Greater Tokyo Area often occurred around 12 a.m. to 2 p.m. in all seasons, −0.46 ± 0.14 × 10⁴ ton CO₂ h⁻¹ in January in winter to −2.26 ± 0.42 × 10⁴ ton CO₂ h⁻¹ in July in summer, would potentially offset 10.52 ± 3.17% to 55.42 ± 10.39% of the hourly anthropogenic emissions.

Overall, the sub-daily patterns of hourly integrated biogenic CO₂ emissions, photosynthetic CO₂ uptake, and net biogenic CO₂ flux of the Greater Tokyo Area were bell-shaped, whereas the ranges of hourly integrated values increased from winter to spring and from spring to summer, subsequently dropping in autumn. The intraday peaks almost always occurred around midday, but the highest hourly integrated biogenic CO₂ emissions often appeared several hours later than the photosynthetic CO₂ uptake. In each month, the variation of hourly integrated photosynthetic CO₂ uptake of the Greater Tokyo Area was much greater than that of biogenic CO₂ emissions. As a result, the integrated net biogenic CO₂ flux fluctuated between positive and negative figures within a day.

Figure 11 presents the integrated anthropogenic CO₂ emissions, biogenic CO₂ emissions, photosynthetic CO₂ uptake, and net biogenic CO₂ flux of the Greater Tokyo Area at the monthly scale. In winter to early spring (December to March), the integrated biogenic CO₂ flux was lower than the anthropogenic one by more than one order of magnitude (the ratio of integrated biogenic CO₂ flux to anthropogenic emission was only 3.34 ± 0.54% in February). From April to November, both photosynthesis and biogenic respiration became more active, up to 34.29 ± 5.92% and 20.46 ± 1.96% of the integrated anthropogenic CO₂ emissions. Consequently, the integrated biogenic CO₂ flux was up to 17.06 ± 5.44% of the anthropogenic one in June.

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 CO₂ fluxes from the anthropogenic CO₂ 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 CO₂ 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 Ω 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 de Pury and Farquhar [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 CO₂ uptake compared to existing terrestrial biosphere models, for instance, VPRM [43,48,49], which were applied in the field of top-down CO₂ emissions verification studies at a city scale.

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 Ω 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. However, frequently fluctuated LAI in evergreen forests can be expected to trigger abnormal amounts of leaf litter fall, which can lead to overestimation of SOC and risks of overestimating hourly R_e. In this case, data assimilation of LAI [135,136,137,138,139] might provide an alternative for model improvement in future work.

Additionally, we recognized that in recent years, satellite-observed SIF has become a promising proxy for GPP because the two variables presented a strong linear relation [140,141,142]. Although we already used a SIF-based GPP dataset [126] to assess our modeled GPP results, it was difficult to apply this type of SIF-based GPP algorithm directly at sub-daily scale modeling because of similar challenges discussed in earlier paragraphs: temporally continuous, sub-daily SIF satellite datasets are not yet available. The ECOsystem Spaceborne Thermal Radiometer Experiment on Space Station (ECOSTRESS) and the Orbiting Carbon Observatory-3 (OCO-3) aboard the International Space Station (ISS) have diurnal sampling capability to some extent. ECOSTRESS has been used to develop instantaneous GPP estimates for different times of day [143], but neither ECOSTRESS nor OCO-3 could provide temporally continuous observations throughout the day due to the orbit nature of the ISS. Consequently, the diurnal variability of GPP cannot be simulated accordingly [144,145].

Because GPP modeling in this study was process-based, our last discussion point about photosynthetic CO₂ removal estimation is about PFT-specific parameters. Following Wullschleger [76], we assumed that, in each PFT, the maximal electron transport rate J_max in photosynthetic reactions was linearly related to the maximal carboxylation rate at 25 °C V_cmax25, where the latter was set as a constant. However, studies such as that by Kosugi et al. [146] observed a seasonal change in V_cmax25, which has been reflected in some global GPP models [147] and which should be included in our future model optimizations. Furthermore, the values of empirical parameters to calculate V_cmax25 based J_max reported by Medlyn et al. [148] and Walker et al. [149] differ from those reference settings [76] for this study, which should be compared in further sensitivity tests of our GPP modeling.

In terms of R_e modeling, hourly R_e calculations in this study considered the effects of biomass amount in all vegetation biomass pools and SOC pools [69,70,86,87,88] instead of simple R_e correlations to ambient temperature and soil moistures. This consideration is both a benefit and a challenge of our model because below-ground biomass was rarely obtained via satellite observations, if not impossible. Hourly modeled R_e results at the site level suggest that our sub-daily model tended to overestimate biogenic CO₂ emissions, which led to an overestimated natural carbon source at night and underestimated negative biogenic CO₂ flux during the day.

Several parts of the hourly R_e model might contribute to such results. To start with, we assumed that live-wood and root biomass were proportional to the foliage biomass in most cases (except for root biomass in DBF) for the allocation of hourly NPP, with a fixed specific leaf area (SLA) setting [82] in each PFT. Our forest NPP results fluctuate above or below the calculated values presented by Sasai et al. [69]: 1200 gC m⁻² year⁻¹ NPP in 1982–2000. These results also exceed the estimates of Ise et al. [150]. In that study, NPP of temperate forest was no more than 500 gC m⁻² year⁻¹. Occasionally, because the change in biomass was only constrained using the difference of LAI over time, carbon flow in and out of the plants was not fully balanced. This imbalance can cause errors of maintenance respiration and then biogenic CO₂ emissions. To reduce modeling errors of this type, the data quality of the input LAI should be improved, as discussed in earlier paragraphs. Additionally, more representative values of PFT-specific parameters should be updated from the latest literature or from research datasets such as the TRY Plant Trait Database [151]. Another point to be addressed in future work is the assumption about growth respiration. Bruggemann et al. [152] reviewed existing isotope studies of plant and pointed out a time lag of transport and allocation of carbon from leaves to the root tissues belowground, suggesting that our assumption of almost instantaneous GPP export to root utilization should be converted to a lagged one once measurement data are available to set the delay time range.

In addition to temperature and moisture conditions, initial SOC amounts also greatly affected the heterotrophic part of hourly R_e. On one hand, active soil biomass pools such as SOC_surface^metabolic, SOC_surface^microbe, SOC_root^metabolic, and SOC_soil^microbe reached equilibrium (annual carbon change remained several grams or even larger by our calculations) rapidly during the spin-up. On the other hand, it would take more than one thousand years to stabilize SOC_soil^passive. However, hourly R_e estimates based on these fully stabilized initial SOC settings were almost twice those of observed ones. Thereby, the number of years for spin-up was shortened to reduce SOC and R_{heterotrophic} overestimation.

To improve this aspect of modeling further, a few aspects must be addressed. As reported by Fierer et al. [153] and by Pugh et al. [154], both the quantity and quality of litter can be expected to affect the biomass amount in SOC and its decomposition rate. Estimating the hourly litter fall rate more accurately requires good estimation of plant biomass change in foliage, wood, and root parts, as described above. However, plant biomass loss attributable to biogenic volatile organic compound (VOC) emission [152], herbivore consumption [155], and litter loss because of dissolved carbon [64] should be updated or tuned to more accurately estimate SOC. From a quality perspective, PFT-specific parameters such as the lignin fraction and the lignin:nitrogen ratio can be further calibrated or adjusted with reference values from the TRY Plant Trait Database [151]. Our R_e modeling only included carbon cycling, and coupling C and N might improve the simulations [85,87,88].

Because of the limited availability of GPP, R_e, and NEE datasets for Japanese forests and grasslands, some (n = 5) flux tower sites’ data outside our study area and the 33°N–38°N range were used in model calibration and validation experiments. To improve the representativeness of model calibration, future availability of data from more observational sites is expected to reduce site-specific errors [133]. This point also addresses future application of our sub-daily scale model to provide fine-resolution biogenic CO₂ flux data in an inversion analysis of anthropogenic CO₂ emissions of other megacities, which requires both globally available satellite input datasets and well-tuned model parameters.

Furthermore, although biogenic CO₂ fluxes induced by urban forest and greenspace were estimated in our sub-daily scale model, these calculations were based on natural vegetation parameters because of the scarcity of observational data. Such assumptions should be replaced in future work because urban vegetated land might present unique characteristics that are different from natural forests [49,156]. Although CO₂ emissions attributable to agricultural biomass waste burning were counted in the anthropogenic emission data [129,130] that we used, photosynthetic CO₂ uptake and crop-soil CO₂ emissions in agricultural systems distributed in our study area were not included and could potentially be calculable based on a model described by Sasai et al. [157].

According to our hourly integrated biogenic CO₂ emission, photosynthetic CO₂ uptake and net biogenic CO₂ flux results discussed in Section 3.6, the range of integrated hourly biogenic to anthropogenic CO₂ emissions ratio in winter (2.27 ± 0.11%–4.97 ± 1.17%) was similar to the value (4–5%) estimated in earlier urban CO₂ flux studies [24,42,158]. However, the modeled ratio range in summer (13.71 ± 2.44%–23.62 ± 3.13%) was much higher than reference values, probably because our study area included much more vegetated land than Los Angeles [24], or a higher vegetation fraction than the neighborhood-scale studies in Singapore and Mexico City [42,158].

In terms of CO₂ removal, the range of integrated hourly photosynthetic uptake to anthropogenic CO₂ emission ratio in winter (up to 19.07 ± 5.33%) was comparable to the series of 1.4% in Velasco et al. [158], 8% in Velasco et al. [42], 10% in Brioude et al. [24], 14% in Hardiman et al. [49], and 20–24% in Park et al. [159]. In summer, the ratio of photosynthetic uptake to anthropogenic emissions (79.04 ± 12.31%) was higher than the estimate (69%) for a July afternoon in Boston [29]. The summer daytime integrated hourly net biogenic to anthropogenic CO₂ flux ratio (up to 55.42 ± 10.39%) was higher than the 20% offset by daytime NEE in Paris [33] and up to 31% estimated by Menzer et al. [41] while our winter daytime estimates was only up to 14.15 ± 4.24%. Forests, grasslands, and urban greenspaces in the Greater Tokyo Area showed potential to offset Tokyo’s anthropogenic CO₂ emissions, especially during the growing season.

According to Table 3, our model estimated 5.14 ± 0.47 × 10⁶ tonCO₂ year⁻¹ of photosynthetic uptake and 1.98 ± 0.19 × 10⁶ tonCO₂ year⁻¹ of biogenic emission in the partially vegetated urban land (1374.62 ± 134.05 km²) in the Greater Tokyo Area. Another 1665.31 km² of urban land in the study area was also identified as having partial vegetation cover by the MODIS vegetation continuous fields product (MOD44B), but was without valid LAI data to proceed any simulation. Additionally, if the rest of the urban land (about 7065.07 km²) in our study area was fully covered by DBF, EBF, ENF or GRS instead, 3.25 ± 0.18 × 10⁷, 3.84 ± 0.06 × 10⁷, 4.75 ± 0.10 × 10⁷ or 3.64 ± 0.49 × 10⁷ ton year⁻¹ more CO₂ would be captured by photosynthesis, while 1.73 ± 0.19 × 10⁷, 2.08 ± 0.21 × 10⁷, 2.68 ± 0.27 × 10⁷ or 3.37 ± 0.71 × 10⁷ ton year⁻¹ more CO₂ would be emitted via biogenic respiration and SOC decomposition. Nonetheless, one must bear in mind that once the spatial range of hourly integrated calculation changed, so would the results [49,160]. These values were the total of GPP, R_e, and NEE in ecosystems of different types under various environmental conditions. It is too complicated to make an interpretation without discussing factors such as near-ground CO₂ storage [161,162,163], which affect the actual biogenic offset of anthropogenic CO₂ emissions. For that reason, the gridded estimates of sub-daily biogenic CO₂ flux are supplied to the transport model AIST-MM for inversion analysis of anthropogenic CO₂ emissions in cities such as Tokyo.

5. Conclusions

Sub-daily photosynthetic CO₂ uptake and biogenic CO₂ emissions in DBF, EBF, ENF, GRS, and urban vegetated lands located in Tokyo and its surrounding areas were estimated via a terrestrial biosphere model driven by multiple satellite inputs and meteorological datasets. After calibrations, our modeled results were found to be consistent with both point-scale observed values and existing satellite-based data. The order of hourly integrated photosynthetic CO₂ uptake and NEE values in the Greater Tokyo Area was up to about 80%, or approximately half of the total anthropogenic CO₂ emissions in summer, and lower than one-tenth of the human-induced values in winter. Such modeling results not only provide reference data for the estimation of total natural CO₂ removal in our study area but also provide prior input values for the disaggregation of anthropogenic CO₂ emission and biogenic CO₂ flux when applying top-down approaches to update the megacity’s CO₂ emissions inventory. This allows for unprecedented amounts of GOSAT and ground measurement data of CO₂ concentrations to be analyzed using inverse modeling of anthropogenic CO₂ emissions from Tokyo and the Greater Tokyo Area. The updated megacity CO₂ emissions inventory based on observations of CO₂ concentration will serve to detect changes in emission and to improve the understanding of source patterns over space and time. The updating of the urban CO₂ emissions inventory will also support the assessment of emission reduction efforts pledged and implemented by cities such as Tokyo.