This study adopted the Vegetation Integrative SImulator for Trace gases (VISIT), a process-based terrestrial ecosystem model that is more fully described elsewhere (Ito, 2010; Inatomi et al., 2010; a schematic diagram is shown in Fig. S1 in the Supplement). In comparison to other carbon cycle models, the model has a computationally efficient structure, making it feasible to conduct large numbers of long-term simulations. The model has participated in several model intercomparison projects, making it possible to assess the limitations of a single-model study. The model is composed of biophysical and biogeochemical modules that simulate atmosphere–ecosystem exchange and matter flows within ecosystems. The hydrology module simulates land-surface radiation and water budgets using forcing meteorological data such as incoming radiation, precipitation, air temperature, humidity, cloudiness, and wind speed and biophysical properties such as fractional vegetation coverage, albedo, and soil water-holding capacity. The land-surface water budget is simulated using a two-layer soil water scheme that calculates evapotranspiration by the Penman–Monteith equation and runoff discharge by the bucket model (Manabe, 1969). Snow accumulation and melting are also simulated.

The carbon cycle is simulated with a box-flow scheme composed of eight carbon pools (leaf, stem, and root carbon for both C3 and C4 plants, plus soil litter and humus) and gross and net carbon flows. An early version of the model simulated only major carbon flows related to CO2 exchange (Ito and Oikawa, 2002), such as photosynthesis, plant (autotrophic) respiration (RA), and microbial (heterotrophic) respiration (RH). Net ecosystem production (NEP) is defined as follows: 1NEP=GPP-RA-RH. The total respiratory CO2 efflux (RA + RH) is called ecosystem respiration (RE). Thus, NEP represents net CO2 exchange with the atmosphere through ecosystem physiological processes (Gower, 2003). In the model, these processes are calculated using equations that include terms for responsiveness to environmental conditions such as light, temperature, CO2 concentration, and humidity.

Following carbon fixation by GPP, photosynthate is partitioned to the six plant carbon pools on the basis of production optimization and allometric constraints at every time step. Plant leaf phenology from leaf display to shedding is simulated in deciduous forests and grasslands, using an empirical procedure based mainly on threshold cumulative temperatures. From each vegetation carbon pool, a certain fraction of carbon is transferred to the soil litter pool, which has a specific turnover rate or residence time representing the decomposition of litter carbon into soil humus and eventually CO2. The VISIT model includes a nitrogen dynamics module that simulates nitrous oxide emission from the soil surface and other nitrogen flows, but this study was primarily focused on the carbon budget.

Note that the model has two separate layers: one for natural ecosystems and another for croplands. Almost all biogeochemical processes are simulated separately in the two layers and then weighted by their respective areas to obtain mean values for each grid cell. A transitional change in the fractions of natural ecosystems and cropland, associated with land-use conversion, results in interactions between the layers.

The VISIT model has been calibrated and validated with field data mostly related to the carbon cycle, such as plant productivity, biomass, leaf area index, and ecosystem CO2 fluxes (e.g., Ito and Oikawa, 2002; Inatomi et al., 2010; Hirata et al., 2014). Also, at regional to global scales, the model has been examined by comparisons with network and remote-sensing data (e.g., Ichii et al., 2013; Ito et al., 2017). Furthermore, the model has been part of model intercomparison projects. One was the Multi-scale Terrestrial Model Intercomparison Project, which examined terrestrial models in terms of the CO2 fertilization effect on GPP and its seasonal-cycle amplitude (Huntzinger et al., 2017; Ito et al., 2016) and soil carbon dynamics (Tian et al., 2015). Another was the Inter-Sectoral Impact Model Intercomparison Project, which compared terrestrial impact assessment models with various observational data such as satellite- and ground-measured GPP for benchmarking (Chen et al., 2017), responses to El Niño events (Fang et al., 2017), and turnover of carbon pools (Thurner et al., 2017). Moreover, the model participated in the TRENDY vegetation model intercomparison project and then contributed to the global CO2 synthesis (Le Quéré et al., 2018).

The VISIT version used in this study includes various MCFs, which play unique and important roles in terrestrial ecosystems. Eight MCFs were included in the VISIT model in a common manner (Fig. 1): emissions associated with land-use change (FLUC), biomass burning by wildfire (FBB), emission of biogenic volatile organic compounds or biogenic volatile organic compounds (BVOCs) (FBVOC), methane emissions from wetlands and methane oxidation in uplands (FCH4), agricultural practices from cropping to harvesting (FAP), wood harvesting in forests (FWH), export of dissolved organic carbon (DOC) by rivers (FDOC), and displacement of soil particulate organic carbon (POC) by water erosion (FPOC). The net carbon balance including MCFs, called net biome production (NBP: Schulze et al., 2000), is more closely related than NEP to the changes in the ecosystem carbon pool. Note that NBP has similarities with and differences from other terms such as NEP, which has scale dependence (Randerson et al., 2002), and net ecosystem carbon balance (Chapin et al., 2006). As discussed later (Sect. 4.4), there remain inconsistencies in the definition of net terrestrial productions, including riverine export, inland water sedimentation, and human harvest and consumption. In this study, NBP is defined as 2NBP=NEP-FLUC+FBB+FBVOC+FCH4+FAP+FWH+FDOC+FPOC. The MCFs differ markedly in their biogeochemical properties and therefore should be evaluated individually. For example, the first four flows are vertical exchanges with the atmosphere (FLUC, FBB, FBVOC, and FCH4), whereas the second four are lateral transportations induced by water and human activities (FAP, FWH, FDOC, and FPOC). Flows associated with disturbances, such as wildfire (FBB) and land-use conversion (FLUC), are heterogeneous in space and time. To avoid double counting, these two flows were calculated separately: FLUC includes burning of debris after deforestation, and FBB excludes human-induced ignition.

Global simulations were conducted from 1901 to 2016 at a spatial resolution of 0.5∘×0.5∘ in latitude and longitude. The VISIT model was applied to each grid cell, and lateral interactions such as riverine transport, food and timber export, and animal migration were ignored. To obtain the initial stable carbon balance, a spin-up calculation under stationary conditions was conducted for each grid cell for 300 to 3000 years, depending on climate conditions and the biome type. This section describes sensitivity simulations to analyze the impacts of different forcing variables, ensemble perturbation simulations to assess the effect of parameter uncertainty, and several supplementary simulations.

All simulations used climate conditions from CRU TS 3.25 (Harris et al., 2014), consisting of monthly temperature, precipitation, vapor pressure, and cloudiness. The historical change in atmospheric CO2 concentration was taken from observations (e.g., Keeling et al., 2009). The global distribution of natural vegetation was determined by Ramankutty and Foley (1998) for potential vegetation types and Olson et al. (1983) for actual vegetation types. This study classified natural vegetation into 28 types after Olson et al. (1983). Historical land-use status, transitional changes, and wood harvest in each grid cell were derived from the LUH data (Sect. 2.2.1). Until 2005, land-use data were compiled on the basis of statistics and various ancillary data, and after 2006 the data were extended by using an intermediate projection scenario (RCP4.5) produced with an integrated assessment model. The distribution of dominant crop types was determined from the global dataset of Monfreda et al. (2008) and used to calculate FAP and FCH4 (for paddy field). For the calculation of FCH4, the wetland fraction in each grid cell was determined from the GLWD (Global Lake and Wetland Dataset) (Sect. 2.2.4). For the estimation of FPOC, slope factors (L and K) were calculated from the GTOPO30 topography data (10.5066/F7DF6PQS; USGS, 1996), and the erodibility factor (S) was calculated from soil composition data (Reynolds et al., 1999). Vegetation coverage (C) and conservation practice (P) factors were determined from the dominant natural vegetation and cropland types, also considering the difference in management intensity between developed and developing countries.

This study focused on the carbon budget of terrestrial ecosystems and analyzed the following variables: GPP, RE, NEP, NBP, biomass carbon stock, and soil carbon stock. The mean residence time (MRT) of the biomass, soil, and total ecosystem carbon stocks at transitional states were approximately calculated in a similar manner to Carvalhais et al. (2014): 7MRT=Cstock/flux, where flux is net primary production (NPP) for biomass (= GPP - RA), RH for soil, and the sum of these fluxes (NPP + RH) for the total ecosystem carbon stock.

The mean annual global terrestrial GPP in 1990–2013 (a period when comparative estimates were available) was simulated as 144.0±4.4 Pg C yr-1 in EX0 and 125.4±4.0 Pg C yr-1 in EXALL (mean ± standard deviation of interannual variability). Ecosystem respiration (RE) was simulated as 141.0±3.6 Pg C yr-1 in EX0 and 118.8±3.2 Pg C yr-1 in EXALL. Mean vegetation and soil carbon storage differed in the two simulations: EX0 produced 648 Pg C in vegetation and 1560 Pg C in soil organic matter, and EXALL produced 477 Pg C in vegetation and 1290 Pg C in soil organic matter. The mean annual net CO2 budget determined by the major flows, NEP (= GPP - RE), was simulated as 2.99±1.18 Pg C yr-1 in EX0 (which ignores MCFs) and 6.57±1.07 Pg C yr-1 in EXALL. Because both simulations used the same climate, atmospheric CO2, and land-use data, these differences – lower carbon stocks, smaller GPP and RE flows, and a large sink by NEP – are attributable to the inclusion of the MCFs.

The individual MCFs had different impacts on the global terrestrial carbon budget. For the vegetation carbon stock, impacts were negligible (<1 Pg C) from methane emission, DOC and POC exports by water movement, and agricultural practices, whereas impacts were substantial from land-use change (-88.5 Pg C), biomass burning (-46.4 Pg C), wood harvest (-28.5 Pg C), and BVOC emission (-24.2 Pg C). For the soil carbon stock, the two largest negative impacts were from land-use change (-108 Pg C) and biomass burning (-71.2 Pg C). Interestingly, the inclusion of BVOC emission reduced the soil carbon stock (-18.1 Pg C) through the loss of photosynthate carbon and decreased carbon supply to the soil. The inclusion of agricultural carbon flows (planting and harvesting, other than land-use change) decreased the soil carbon stock (-55.6 Pg C), although planting enhanced vegetation productivity and carbon supply to the soil. The inclusion of DOC and POC exports moderately reduced the soil carbon stock (-5.9 and -3.6 Pg C, respectively).

Most of the difference in GPP between EX0 and EXALL was attributable to land-use change (-12.8 Pg C yr-1), wood harvest (-0.9 Pg C yr-1), and BVOC emission (-0.9 Pg C yr-1). Biomass burning, though it has substantial impacts on biomass, also slightly decreased GPP (-0.75 Pg C yr-1). The simulated impacts of MCFs on RE were mostly similar to those for GPP. The relatively high NEP in EXALL was largely attributable to compensatory regrowth in response to biomass burning (2.03 Pg C yr-1), BVOC emission (0.69 Pg C yr-1), and wood harvest (0.41 Pg C yr-1).

Human activities (EXATP) had greater impacts on terrestrial carbon stocks than biogeochemical processes (EXBGC), as mean ecosystem carbon stock decreased by 172 Pg C in EXBGC and 296 Pg C in EXATP. The sum of these two depressions in carbon stock, 467 Pg C, was larger than that estimated in the all-inclusive experiment (EXALL), 440 Pg C, which points to nonlinear offsetting effects among the MCFs.

The carbon budget including the MCFs (NBP) in 1990–2013 was estimated as 1.36±1.12 Pg C yr-1 of net sink in EXALL, that is, 20.7 % of NEP (see Table 1 for decadal summary). Figure 2 shows the temporal change in global annual NEPs and NBPs in each experiment for the 1901–2016 study period (see Fig. S3 for details of the 1990–2013 period). The inclusion of MCFs considerably altered the mean state of the terrestrial carbon budget throughout the simulation period. Little difference was found among the experiments in interannual variability and decadal trends. For example, linear trends of NBP in 1980–2013 were estimated as (0.0783 Pg C yr-1) yr-1 in EX0 and (0.0890 Pg C yr-1) yr-1 in EXALL. Interestingly, the larger differences among experiments for NEP (±1.15 Pg C yr-1, standard deviation among EX0 to EXALL) than for NBP (±0.52 Pg C yr-1) indicated a convergence of estimated carbon budgets after including MCFs.

The spatial distribution of carbon budgets shows that EX0 identified a vast area of tropical, temperate, and boreal forests as moderate net carbon sinks (Fig. 3a). The inclusion of MCFs in EXALL (Fig. 3b) intensified this net sink in tropical forests and parts of the temperate and boreal forests, but it decreased NEP in grasslands and pastures in central North America and Europe, turning parts of them into net carbon sources (Fig. 3d). The spatial distribution of NBP in EXALL (Fig. 3c) was a heterogeneous pattern of sink and source. Several tropical and subtropical forests had negative NBP, although NEP in these areas was estimated as positive or neutral. As shown in Fig. 3e, with the addition of MCFs, a large part of the terrestrial ecosystem was simulated to lose carbon. The contributions of each flow are described in the next section.

The decrease in carbon stocks in terrestrial ecosystems after the addition of MCFs indicates that the mean residence time (MRT) of these stocks became shorter than would be estimated solely from major carbon flows (see Fig. S4 for the spatial distribution of stocks and MRTs). As shown in Fig. 4, simulated terrestrial carbon stocks in EXALL were steady or slightly declining until around 1960, especially when land-use change (e.g., tropical deforestation) was included. After 1960, carbon stocks in vegetation and soil began to gradually increase. As described earlier, the simulated carbon stocks differed among the experiments by as much as 440 Pg C as a consequence of including MCFs. Also, the inclusion of MCFs made large impacts on GPP and RE (Fig. S5) by altering vegetation structure and soil carbon storage. Simulated MRTs grew clearly shorter (i.e., turnover was accelerated), as a result of global changes such as temperature rise enhancing respiratory emissions. Note that MRTs also grew shorter in the result of EX0, which ignored MCFs, but including the MCFs increased the difference in MRT among the experiments. For example, the difference in MRT of vegetation biomass between EX0 and EXALL grew from 0.89 years in the 1900s to 1.54 years in the 2000s, and the difference for soil carbon stock grew from 0.10 years in the 1900s to 0.24 years in the 2000s. The definition of MRT (Eq. 7) means that shortened MRTs could result from increases in NPP and respiration.

Figure 5 shows the temporal changes in the eight simulated MCFs in their individual sensitivity simulations (EXLUC to EXPOC) as well as the EXALL simulation. The emissions associated with land-use change (FLUC) peaked around the 1950s at 1.2–1.4 Pg C yr-1 and then gradually decreased. Biomass burning emission (FBB) remained around 1 Pg C yr-1 until the 1970s and then increased slightly to 1.5 Pg C yr-1, with a large interannual variability. BVOC emission (FBVOC) increased gradually from 0.5 Pg C yr-1 in the early 20th century to 0.6 Pg C yr-1 in the 21st century. Methane emission (FCH4) gradually increased from 0.11 Pg C yr-1 in the first decades of the 1900s to 0.13 Pg C yr-1 in the 2000s (representing 160–170 Tg CH4 yr-1). Wood harvest (FWH) likewise increased from 0.5 Pg C yr-1 in the 1900s to 1.1 Pg C yr-1 in the 2000s, as did POC export by water erosion (FPOC), which increased from 0.55 Pg C yr-1 in the 1900s to 0.95 Pg C yr-1 in the 2000s. Crop planting and harvest (FAP) had a mixed effect on the terrestrial carbon budget because planting enhances productivity, whereas harvesting is a direct carbon loss. As a result, FAP had both negative (net uptake) and positive (net emission) values. DOC export (FDOC) remained steady at around 0.14±0.004 Pg C yr-1 throughout the simulation period.

The supplementary simulations showed that temporal changes in the MCFs were caused by different forcing factors. For example, when the atmospheric CO2 concentration was fixed at its level in 1901 (EXfxCO2, data not shown), the increasing trend in FBVOC (Fig. 5c) nearly vanished, whereas other flows such as FWH and FPOC were insensitive to CO2. When climate conditions were held fixed (EXfxCL), FBB showed only a decadal trend in response to changes in fuel load, and climate-induced interannual variability in burned area and fire-induced emissions (Fig. 5b) disappeared.

The MCFs considered in this study showed distinct spatial patterns (Fig. 6). FLUC occurred mainly in the tropical forests of South America, Africa, and South Asia. FBB occurred in subtropical areas in Africa, tropical forests in South America and Southeast Asia, the Mediterranean area, and boreal forests in North America and east Siberia. FBVOC was highest in tropical forests and elevated in other forested areas. For FCH4, major sources included monsoon-affected parts of Asia dominated by paddy fields, tropical wetlands including floodplains of big rivers, and northern wetlands, whereas other uplands were weak sinks. For FAP, croplands in Europe, East Asia, and North America exported large amounts of carbon (see Fig. 6f for the crop harvesting effect alone). FWH occurred mainly in tropical forests in southern East Asia, South America, and southern North America. FPOC occurred mainly in humid and steep areas such as mountainous regions of monsoon Asia and cultivated areas. FDOC occurred mainly in warm and humid areas such as tropical forests in South America, Africa, and Southeast Asia.

The effects of the eight studied MCFs on the global carbon budget, resulting in a lower net sink by NBP than by NEP, were dominated by five MCFs: biomass burning (FBB), wood harvest (FWH), POC export by water erosion (FPOC), BVOC emission (FBVOC), and emission caused by land-use change (FLUC) (Fig. 7a). The contributions of MCFs differed among regions. FAP and FBB had dominant effects in Europe (Fig. 7b) and North America (Fig. 7g), where the effects of FLUC and FDOC were negligible. In Africa (Fig. 7c), South America (Fig. 7h), and the global tropics (Fig. 7i), all five MCFs had similar effects. In Asia (Fig. 7e), FPOC and FAP had the largest effects, and FCH4 emissions from the vast area of paddy fields were considerable. In semiarid regions (Fig. 7j), FAP and FBB were the largest.

Certain spatial tendencies become clearer in a global aggregation of the simulated results (Fig. 8) related to the dominant land-cover type in each grid cell, the cropland fraction, and aridity represented by annual precipitation. In forest-dominated grid cells (Fig. 8a), FBB made the largest (>30 %) contribution, followed by FWH, FBVOC, and FLUC, and in cropland-dominated cells, about half of the influence of MCFs was due to agricultural practices (FAP). Because grassland-dominated cells contain fractions of woodland and cropland, FAP and FWH as well as FPOC made contributions in these cells. In desert-dominated cells, FBB made up the majority of the contributions. In cells with small fractions of cropland including tropical forests (Fig. 8b), FWH, FBB, and FBVOC made strong contributions, whereas in cells dominated by crops, FCH4 made a substantial contribution reflecting the vast area of paddy fields in Asia. FPOC made large contributions at all cultivation intensities, but particularly in moderately cultivated areas. An analysis based on precipitation was also informative (Fig. 8c). In arid areas (annual precipitation <500 mm), FBB had the largest impacts, as expected from the dominance of fire-prone ecosystems such as boreal forests and subtropical woodlands. In wet areas (precipitation >1500 mm), FLUC and FPOC made large contributions, and FBB had a minor effect. The influence of FWH was strongest in moderately humid to wet areas.

This study showed that MCFs have notable impacts on the terrestrial carbon budget; they disequilibrate ecosystem carbon stocks and affect MRTs. Most of the simulated magnitudes of MCFs were comparable to results of previous studies (Fig. 5 and Table 2), and their impacts on the carbon budget were consistent with other model studies (e.g., Yue et al., 2015; Naipal et al., 2018). In terms of FLUC, the model estimated clearly lower emissions than the Global Carbon Project (GCP) synthesis (Le Quéré et al., 2018) and other studies, surely because this study did not use actual land-use data after 2005. Updated data would likely improve the VISIT model's performance. The fact that the simulated FBB was slightly low compared to previous estimates implies that there is a need to refine the fire module in the model (discussed further in Sect. 4.5). The simulated FPOC was comparable to results in other studies, but there remain inconsistencies in the fate terms (riverine transport, burial, and CO2 evasion) and the ratio of ocean and inland water export. Similarly, the simulated FAP and FWH appear comparable to results in other studies, but this study largely ignored their transport and consumption. Further detailed comparisons and comprehensive assessments are clearly required.

Most models have been calibrated and validated with observational data of major carbon flows (e.g., GPP, RE, and NEP) and carbon stocks. Although recent models have begun to take account of land-use change and biomass burning, most still ignore the contributions of many other minor flows. The global GPP simulated in this study is similar to a satellite-based product of the Breathing Earth System Simulator (BESS) of Jiang and Ryu (2016): for the 2001–2013 period, the coefficient of determination (R2) was 0.77 for EX0 and 0.71 for EXALL (Fig. S5). All three simulations show increasing trends. In contrast, the upscaled flux measurement data of FLUXCOM (Tramontana et al., 2016) and the MOD15 satellite product (Zhao et al., 2006) show smaller interannual variability and trends, and they were only weakly correlated with the VISIT simulations (R2=0.21–0.39). Compared with the terrestrial carbon budget in the integrated synthesis of the GCP for 1959–2016 (Le Quéré et al., 2018), the simulated NEP in EXALL was much higher in the same period: 5.7 Pg C yr-1 in EXALL and 2.1 Pg C yr-1 in GCP. Removing the land-use emission of 1.3 Pg C yr-1 would reduce the provisional NBP from GCP to 0.85 Pg C yr-1, putting it closer to the simulated NBP in EXALL (0.68 Pg C yr-1) than to the NBP in EX0 (2.33 Pg C yr-1). (Figures S6 and S7 compare the results of NEP and FLUC from the individual models in the GCP synthesis.) EXALL successfully captured the large aboveground vegetation biomass stock in the tropics and the small stock in boreal zones seen in observations (Fig. S8a). A similar comparison of soil carbon (Fig. S8b) also indicates the model's ability to capture the spatial gradient in this stock; an overestimation in the northern midlatitudes (around 30∘ N) is attributable to high soil carbon accumulation in the Tibetan Plateau simulated by the model in frigid regions. It is not clear, however, whether EXALL (with MCFs) captured the global patterns with greater accuracy than EX0 (without MCFs), because observational datasets show considerable discrepancies, and the differences between the model simulations were relatively small. The estimated MRT of the ecosystem carbon stock in EXALL (14–17 years) was shorter than the MRT of 23 years (95 % confidence interval, 18–29 years) found by the data-oriented study of Carvalhais et al. (2014). This difference is attributable to the high soil carbon stock in the latter study (2397 Pg C) rather than to differences in the vegetation carbon stock and flows; both studies had similar spatial patterns of MRT.

Considering the remaining uncertainties in observational terrestrial carbon accounting, it is still difficult to perform a conclusive validation. Nevertheless, this study demonstrated the possibility of integrating various carbon flows into a single model framework.

The simulated MCFs affect the amount of the terrestrial carbon stock by as much as 440 Pg C. The size of this difference is comparable to differences, or the model estimation uncertainty, found among biome models (e.g., Friend et al., 2014; Tian et al., 2015). By definition, NBP including the effect of MCFs is likely to correspond closely to carbon stock change as well as carbon budgets obtained by atmospheric inversions. MCFs affect the carbon budget in two major ways: first by their instantaneous carbon exports and second by the ensuing carbon uptake during recovery from these disturbances, which occurs with time lags of decadal to centennial scale, depending on the types of disturbance and their intensities (e.g., Fu et al., 2017). Assessments of MCFs would help characterize the “missing sink”, which is now primarily ascribed to terrestrial carbon uptake (Houghton et al., 1998; Le Quéré et al., 2018) by mechanisms that are still arguable. Although previous studies (e.g., Jung et al., 2011; Zscheischler et al., 2017) have noted the potential importance of MCFs and the difference between NEP and NBP (or corresponding metrics such as the net ecosystem carbon balance of Chapin et al., 2006), these issues have not been comprehensively evaluated by global and regional carbon syntheses, such as the REgional Carbon Cycle Assessment and Processes (RECCAP; Sitch et al., 2015). Indeed, biome models used to simulate the terrestrial carbon cycle in RECCAP differ in how they parameterize the MCFs, and their estimations of net budget are not easily compared.

In the VISIT model simulation, interannual variability of NBP and NEP were closely correlated (Fig. S9), although several MCFs such as FBB and FCH4 did not share in that correlation. These interannual variations were largely determined by the major flows, except for extreme events such as huge fires in 1997 and 2015 (e.g., Huijnen et al., 2016). Therefore, establishing an empirical model may make it possible to approximately estimate NBP from NEP. To evaluate the similarities and differences between these two quantities, further observation data are required for each flow and its determinant processes.

This study demonstrated that the VISIT modeling approach is effective in integrating the major and minor carbon flows into a single framework and obtaining a consistent carbon budget, although this approach has its own uncertainties and biases, as shown by benchmarking and intercomparison studies (e.g., Arneth et al., 2017; Huntzinger et al., 2017). Biogeochemical models like VISIT have advantages in reconciling inconsistencies, filling gaps, and specifying underlying mechanisms, as well as reconstructing historical changes and making future projections. Intimate collaborations between modeling and observational studies (Sitch et al., 2015; Schimel et al., 2015) should lead to more reliable carbon accounting.

This study focused on the terrestrial carbon budget, but the MCFs also affect the hydrological properties of land systems. As shown in Fig. S10, land-use change, biomass burning, and BVOC emission lead to a loss of vegetation leaf area, except in croplands. The loss in turn decreases evapotranspiration and increases runoff discharge regionally by as much as 20 mm yr-1. In the simulation, runoff discharge increased through time, more steeply in EXALL than in EX0. This effect was evident in many tropical to temperate regions, implying the importance of a comprehensive understanding of carbon–water interactions.

However, it should be noted that the actual impacts of MCFs on land systems can be much more complicated than assumed here. For example, loss of soil organic carbon by biomass burning and water erosion may decrease the water-holding capacity of soils, leading to higher runoff discharge and lower tolerance to droughts. Also, several MCFs should change along with translocations and biogeochemical reactions of nutrients such as nitrogen and phosphorus, followed by changes in vegetation productivity and water use. To fully include these processes in the model, a comprehensive understanding of biogeochemistry and ecohydrology is required.

Although this study incorporated some of the known MCFs, fully or partially, others are unrecognized or assumed to be negligible. Indeed, many studies have investigated MCFs that were not included in this and most previous carbon cycle studies (Table 3). Few studies have taken comprehensive account of all carbon flows. For example, for lack of parameterization data, this study did not explicitly consider carbon sequestration in pyrogenic organic matter or charcoal (e.g., Santín et al., 2015), in phytoliths (Song et al., 2017), or by means of abiotic geochemical processes (Schlesinger, 2017). This study tried to include the effects of DOC and POC exports and obtained results comparable to other studies (e.g., Dai et al., 2012; Galy et al., 2015; Chappell et al., 2016). However, this study did not explicitly consider lateral displacement of carbon between adjacent grid cells and associated emissions, such as river transport and international commerce (e.g., Battin et al., 2009; Bastviken et al., 2011; Peters et al., 2012), and reservoir effects on riverine transport (e.g., Mendonça et al., 2017). In this regard, modeling of agricultural practices should be improved to obtain more reliable regional carbon budgets. It is particularly important to evaluate efforts to enhance harvest index and to raise carbon sequestration into cropland soils, as proposed by the “4 per 1000” initiative (Dignac et al., 2017; Minasny et al., 2017).

More clarity is needed in the parameterization of disturbances. This study considered the impacts of wildfires and land-use conversion, but in a conventional manner, possibly leading to biased results (see Sect. 4.5 for biomass burning). Other potentially influential disturbances, such as pest outbreaks and drought-induced dieback associated with climate extremes, were not explicitly considered, although they can perturb ecosystem carbon budgets (Reichstein et al., 2013). In the long term, ecosystem degradation induced by forest fragmentation, overgrazing, and soil loss by wind erosion can further affect carbon budgets (e.g., Paustian et al., 2016; Brinck et al., 2017). Integration of these processes awaits future studies.

This study is an early attempt to evaluate the effects of various MCFs. The results have convinced me that changes in MCFs will have considerable influences on the global carbon budget (e.g., Piao et al., 2018; Lal, 2019; Pugh et al., 2019), and more such attempts are required to improve our understanding of the global carbon cycle, which plays a critical role in future climate projections. However, given the imperfect state of knowledge about these MCFs, their inclusion can introduce other errors and biases. I took the estimation uncertainty into account by perturbing representative parameters, but this study did not examine other sources of uncertainties such as differences among ecosystem models and forcing data. Indeed, many ecosystem models have been developed with different degrees of complexity (e.g., dynamic global vegetation models), and intercomparison studies have shown that existing ecosystem models differ widely in their environmental responsiveness to changes in major carbon flows (e.g., Friend et al., 2014; Huntzinger et al., 2017). For example, the models differ in global GPP by more than 30 %, even though the processes contributing to primary production are well understood and increasingly constrained by observations (Anav et al., 2015). This single-model study was necessarily limited in searching the full range of estimation uncertainty, and further studies using multiple MCF-implemented models are highly desirable.

Considering the shortcomings of broad-scale and long-term observations of MCFs, estimation uncertainties could be larger than presently thought. For example, each of the coefficient factors of the erosion scheme (Eq. 6) can be expected to have large ranges of uncertainty, and few data are available to constrain for the fate of laterally transported POC and DOC. Data related to land-use changes (e.g., gross vs. net land-use transition) and procedures to implement them in models are not standardized (e.g., Fuchs et al., 2015). One exception is that multiple satellites have produced long global records of biomass burning. Indeed, a comparison of FBB in the VISIT model simulation and these observations clearly shows a problem in this study (Fig. 5b): the VISIT model systematically underestimated fire-induced CO2 emission in most years relative to the BB4CMIP6 multi-satellite (combined with proxies) product of biomass burning (van Marle et al., 2017). It also showed an increasing trend of fire activity after 1998, a trend inconsistent with a recent analysis of global burned area (Andela et al., 2017) that showed a declining trend of burned area due to human activities such as agricultural expansion and intensification.

To evaluate the bias caused by this inconsistency, a simulation was conducted (EXBB1) in which interannual anomalies of burned area were prescribed by the GFED4s satellite product in 1998–2016 (Fig. S11, green line). As a result, the model-simulated FBB showed a decreasing trend, implying that prognostic modeling of fire regimes is problematic. Additionally, the high fire-induced emission in 1998, a strong El Niño year, was appropriately captured. The model, however, was likely to overestimate average burned area (561×106 ha yr-1) relative to satellite-based estimates. Therefore, another simulation was conducted (EXBB2) in which not only anomalous but also average burned area were prescribed by GFED4s. That simulation (Fig. S11, orange line) yielded an even lower FBB resulting from a smaller burned area (437×106 ha yr-1), although its interannual variability was little changed. The low FBB despite a large burned area indicates that fire intensity or emission factors in the model were not properly determined. Such estimation biases and uncertainties can remain in other carbon flows and should be clarified and reduced using observational data.

This study has implications not only for improving models, but also for strategic observations of the carbon cycle. MCFs may account for much or all of the discrepancy among top–down atmospheric inversions, CO2 flux measurements, and bottom–up biometric carbon stock surveys (e.g., Jung et al., 2011; Kondo et al., 2015; Takata et al., 2017). Furthermore, investigations of MCFs may help reveal the mechanisms underlying the apparent net carbon sequestration by mature forests (Luyssaert et al., 2008), as observed in CO2 flux measurements and biometric surveys. Major carbon flows (GPP, RE, and NEP) have been observed using the standardized FLUXNET method at many flux measurement sites (Baldocchi et al., 2001). These observations have given us an overview of the terrestrial carbon budget and its tendencies (e.g., Jung et al., 2017). Recent satellite observations allow us to monitor vegetation coverage and biomass globally at fine spatial resolutions (e.g., Saatchi et al., 2011; Baccini et al., 2017). Nevertheless, it is still difficult to directly observe some MCFs, including non-CO2 trace gases, disturbance-induced non-periodic emissions, and subsurface transport and sequestration. For example, flux measurements of BVOC emissions are technically challenging (Guenther et al., 1996; Geron et al., 2016) because of the low concentrations of BVOC compounds, their wide variety, and their spatial and temporal heterogeneity. Quantification of DOC and POC dynamics at the landscape scale appears to require intensive observation networks (e.g., Dai et al., 2012; Raymond et al., 2013). Emissions associated with land-use change, which have attracted much attention from researchers, still have large uncertainties (Houghton and Nassikas, 2017; Erb et al., 2018). Further integrated studies of ground-based, airborne, and satellite observations of carbon flows are necessary that include minor flows, pools, and relevant properties (e.g., isotope ratios). The spatial and temporal patterns of influential MCFs obtained in this study will be useful for planning effective observational strategies.