The MIROC5.2 physical core comprises component models of the atmosphere, ocean, and land. The atmospheric model is based on a spectral dynamical core originally named the Center for Climate System Research–National Institute for Environmental Studies atmospheric general circulation model (CCSR-NIES AGCM; Numaguti et al., 1997), which is interactively coupled with an aerosol component model called the Spectral Radiation-Transport Model for Aerosol Species (SPRINTARS; Takemura et al., 2000, 2005). For the ocean, the CCSR Ocean Component (COCO) model (Hasumi, 2006) is used in conjunction with a sea ice component model. For land, the Minimal Advanced Treatments of Surface Interaction and Runoff (MATSIRO) model (Takata et al., 2003) is coupled to simulate the atmosphere–land boundary conditions and freshwater input into the ocean. Considering the application possibility of the ESM to long-term climate simulations of more than hundreds of years, e.g., paleoclimate studies (Ohgaito et al., 2013; Yamamoto et al., 2019), the horizontal resolution of the atmosphere is set to have T42 spectral truncation, which is approximately 2.8∘ intervals for latitude and longitude. The vertical resolution is 40 layers up to 3 hPa with a hybrid σ–p coordinate, as in MIROC5. The horizontal coordination for the ocean is changed from the bipolar system employed in MIROC5 to a tripolar system in MIROC5.2 that is divided horizontally into 360×256 grids. (To the south of 63∘ N, the longitudinal grid spacing is 1∘ and the meridional spacing becomes fine near the Equator. In the central Arctic Ocean, the grid spacing is finer than 1∘ because of the tripolar system.) The vertical levels increase from 44 to 62 with a hybrid σ–z coordinate system. For land, the same horizontal resolution as used for the atmosphere is employed; the vertical soil structure of the model has six layers down to the depth of 14 m. Subgrid fractions for two land use types (agriculture plus managed pasture and others) are considered for the physical processes.

For the AGCM, the schemes used for the dynamical core, radiation, cumulus convection, and cloud microphysics are mostly the same as in MIROC5; the major update of processes mainly concerns the aerosol module. The version used here treats atmospheric organic matter (OM) as one of the prognostic variables, and emissions of primary OM and precursors for secondary OM are diagnosed in the component. For land, the scheme for subgrid snow distribution is replaced by one incorporating a physically based approach (Nitta et al., 2014; Tatebe et al., 2019), and wetland formed temporarily in the snowmelt season is newly considered to reduce the warm bias in temperature in the European region during spring–summer (Nitta et al., 2017; Tatebe et al., 2019). The ocean and sea ice components are mostly the same as in MIROC5.

The model of the land ecosystem–biogeochemistry component in MIROC-ES2L is the Vegetation Integrative SImulator for Trace gases model (VISIT; Ito and Inatomi, 2012a). This model simulates carbon and nitrogen dynamics on land (schematics for the carbon cycle can be found in Ito and Oikawa, 2002, and for the nitrogen cycle in Supplement Fig. S1). It has been used for ecological studies of the site–global scale (e.g., Ito and Inatomi, 2012b), impact assessments of climate change (e.g., Warszawski et al., 2013; Ito et al., 2016a, b), CO2 flux inversion studies (e.g., Maksyutov et al., 2013; Niwa et al., 2017), and contemporary assessments of CO2, CH4, and N2O emissions in the Global Carbon Projects (Le Quéré et al., 2016; Saunois et al., 2016; Tian et al., 2018). The early version of the model (Sim-CYCLE; Ito and Oikawa, 2002) was actually used as the land carbon cycle component in the first stage of the C4MIP project (Friedlingstein et al., 2006; Yoshikawa et al., 2008). The model covers major processes relevant to the global carbon cycle. Photosynthesis or gross primary productivity (GPP) is simulated based on the Monsi–Saeki theory (Monsi and Saeki, 1953), which provides a conventional scheme to simulate leaf-level photosynthesis in a semiempirical manner and for upscaling to canopy-level primary productivity. The allocation of photosynthate between carbon pools in vegetation (e.g., leaf, stem, and root) is regulated dynamically following phenological stages. The transfer of vegetation carbon into litter–soil pools is simulated using constant turnover rates, and in deciduous forests, seasonal leaf shedding occurs at the end of the growing period. The model focuses on biogeochemical processes and it does not explicitly simulate dynamic change in vegetation composition; therefore, the biogeochemical processes are simulated under a fixed biome distribution (Supplement Fig. S2). The carbon stored in litter (i.e., foliage, stem, and root litter) and humus (i.e., active, slow, and passive) pools is decomposed and released as CO2 into the atmosphere under the influence of soil water and temperature. Further details on the carbon cycle processes in the model can be found in Ito and Oikawa (2002).

For the nitrogen cycle, the model considers two major nitrogen influxes to the ecosystem: biological nitrogen fixation (BNF) simulated based on the scheme of Cleveland et al. (1999) and external nitrogen sources such as fertilizer and atmospheric nitrogen deposition, which are prescribed in the forcing data. The fluxes of nitrogen out of the land ecosystem are simulated through N2 and N2O production during nitrification and denitrification in soils based on the scheme of Parton et al. (1996), leaching of inorganic nitrogen from soils, which is affected by the amount of soil nitrate and runoff rate, and NH3 volatilization from soils (Lin et al., 2000; Thornley, 1998). Within the vegetation–soil system, organic nitrogen in the soil is supplied from litter fall, whereas inorganic nitrogen is released through soil decomposition processes (soil mineralization) and stored as two chemical forms (NO3- and NH4+). Inorganic nitrogen is taken up by plants, allocated to two vegetation pools (canopy and structural pools), and immobilized into a microbe pool. Finally, mineral nitrogen is lost via biotic–abiotic processes as mentioned above.

Although the original land component model covers most major carbon–nitrogen processes, for the purposes of inclusion in the new ESM and making fully coupled climate–carbon–nitrogen projections, the land model was modified for this study (hereafter, the modified version is called VISIT-e). First, the modified model represents the close interaction between carbon and nitrogen in plants. This is because the original model has only a loose interaction between these two cycles, and thus it cannot precisely predict the nitrogen limitation on primary productivity. To achieve this, the photosynthetic capacity in VISIT-e is modified to be controlled by the amount of nitrogen in leaves (leaf nitrogen concentration), which is determined by the balance between the nitrogen demand of plants and potential supply from the soil. Thus, if sufficient inorganic nitrogen is not available for plants, the leaf nitrogen concentration is gradually lowered, which reduces photosynthetic capacity and the plant production rate. This process is required to simulate the observed downregulation in elevated CO2 experiments (e.g., Norby et al., 2010; Zaehle et al., 2014). Other modifications regarding the nitrogen cycle are described in Appendix A.

Second, although the original VISIT incorporates LUC and associated CO2 emission processes, to take full advantage of the latest LUC forcing dataset (Land-Use Harmonization 2; Ma et al., 2019), additional LUC-related processes have been newly introduced in VISIT-e. The model assumes five types of land cover (each represented on a separate tile) in each land grid box (i.e., primary vegetation, secondary vegetation, urban, cropland, and pasture) with the same structure of carbon–nitrogen pools. All processes are calculated separately for each tile (i.e., no lateral interaction), and then the variables in the tile are summed after weighting by the areal fraction of each land use type. The LUC impact is modeled assuming two types of land use impact on the biogeochemistry. The first impact considers status-driven LUC processes, which affect land biogeochemistry even when the areal fractions of the tiles are fixed. For example, even when a simulation is conducted with fixed areal fractions (e.g., a spin-up run under 1850 conditions), crop harvesting, nitrogen fixation by N-fixing crops, and the decay of OM in product pools occur. The second type of land use impact includes transition-driven processes that happen only when areal changes occur among the tiles. For example, when an areal fraction is changed within a year (e.g., conversion of forest to urban land use), carbon and nitrogen in the harvested biomass are translocated between product pools. When cropland is abandoned and the area is reclassified as secondary forest, the apparent mean mass density of secondary forest is first diluted because of the increase in the less vegetated area, and then secondary forest starts regrowth toward a new stabilization state. A further detailed description of LUC modeling is given in Appendix A.

The land ecosystem component runs with a daily time step in the ESM. It has fixed spatial distribution patterns of 12 vegetation categories (see Supplement Fig. S2), and the land biogeochemistry is affected by daily averaged atmospheric conditions (CO2 concentration, downward shortwave radiation, air temperature, and air pressure) and land abiotic conditions (soil water, soil temperature, and runoff rate as the base flow) simulated by the physical core of the ESM. In turn, daily averaged land variables simulated by VISIT-e are used by other components of the ESM (Fig. 1). For example, the simulated leaf area index (LAI) is referenced in the physical core of the model to simulate physical dynamics on the land surface (e.g., evapotranspiration, albedo, and surface roughness). Furthermore, the rate of net atmosphere–land CO2 flux is used in the calculation of the atmospheric CO2 concentration, and inorganic N leached from the soil is transported by rivers and subsequently used as an input of N nutrients to the ocean ecosystem. The chemical state of N in rivers is assumed conserved during transportation, and biogeochemical processes such as outgassing or sedimentation in freshwater systems are neglected in the present model. Additionally, although the model can simulate terrestrial carbon loss by erosion and dissolution of organic carbon, these processes are not activated to close the global mass conservation of carbon and nitrogen. Finally, although N2O and NH3 emissions are simulated, the emission fluxes are considered only for diagnostic purposes and they do not produce any change in the atmospheric radiation balance or air quality.

The new ocean biogeochemical component model OECO2 (see Supplement Fig. S3 for a schematic) is a nutrient–phytoplankton–zooplankton–detritus-type model that is an extension of the previous model (Watanabe et al., 2011). Although only an overview of OECO2 is presented here, a detailed description can be found in Appendix B.

In OECO2, ocean biogeochemical dynamics are simulated with 13 biogeochemical tracers. Three of them are associated with cycles of macronutrients (nitrate and phosphate) and a micronutrient (dissolved Fe). The model has four organic tracers of “ordinary” nondiazotrophic phytoplankton, diazotrophic phytoplankton (nitrogen fixer), zooplankton, and particulate detritus. All OM in these four tracers is assumed to have an identical nutrient, oxygen, and micronutrient iron composition following the Redfield ratio of C:N:P:O = 106:16:1:138 (Takahashi et al., 1985) and C:Fe = 150:10-3 (Gregg et al., 2003). Four other tracers are associated with carbon and/or calcium, i.e., dissolved inorganic carbon (DIC), total alkalinity, calcium, and calcium carbonate. The two other tracers are oxygen and nitrous oxide.

The nitrogen cycle in OECO2 is similar to that in the previous version (Yoshikawa et al., 2008; Watanabe et al., 2011), except the new model accounts for nitrogen influxes such as nitrogen deposition from the atmosphere (as external forcing), input of inorganic nitrogen from land via rivers, and BNF by diazotrophic phytoplankton (Fig. 1). Additionally, denitrification is also modeled as the dominant process of oceanic nitrogen loss, with an explicit distinction between the gaseous forms of N2O and N2 (see below for nitrogen fixation and denitrification processes). Loss of nitrogen through the sedimentation process is also considered. The phosphorus cycle is newly embedded in the model to represent strong phosphorous limitation on the growth of diazotrophic phytoplankton. The structure of the phosphorus cycle is generally similar to that of nitrogen except in two respects: (1) the riverine input of phosphate is the only process that introduces phosphorus into the ocean, and (2) there is no process of outgassing from the ocean, unlike the denitrification process in the nitrogen cycle. As the land ecosystem model cannot simulate the phosphorus cycle, the flux of phosphorous from rivers is diagnosed from the nitrogen flux, assuming that the phosphate brought to the river mouth satisfies the N:P ratio of 16:1, similar to the Redfield ratio.

The structure of the ocean iron cycle is also similar to that of nitrogen, except the following processes are modeled as iron input into the ocean. Two major sources of iron deposition from the atmosphere are included in the new model: lithogenic and pyrogenic sources. Mineral dust emission is diagnosed by the aerosol component module, depending on the near-surface wind speed, soil dryness, and bare ground cover, while iron emitted from biomass burning and the consumption of fossil fuel and biofuel follows external forcing. The latter emission dataset used in this study is shown in Supplement Fig. S4. The iron emissions from pyrogenic sources are estimated based on the iron content and emissions of particulate matter (Ito et al., 2018). A shift from coal to oil combustion is considered in relation to shipping (Fletcher, 1997; Endresen et al., 2007). The iron content of mineral dust is prescribed at 3.5 % (Duce and Tindale, 1991). The iron deposition from biomass burning is calculated from black carbon (BC) deposition and a ratio of 0.04 gFe gBC-1 in fine particles at emission (Ito, 2011). The emission, transportation, and deposition processes are simulated explicitly by the atmospheric aerosol component. The iron from different sources has different solubility in seawater, and thus different amounts of iron are available for phytoplankton. The solubility of iron is prescribed at 79 % for oil combustion, 11 % for coal combustion, and 18 % for biomass burning (Ito, 2013). The solubility of iron for mineral dust is prescribed at 2 % (Jickells et al., 2005).

In addition to the Fe input from the atmosphere, recent studies suggest contributions of Fe supply from sediment and hydrothermal vents to ecosystem activities (Tagliabue et al., 2017). The contributions of these two natural Fe sources to the determination of the atmospheric CO2 concentration and export production are similar to or greater than that of dust (Tagliabue et al., 2014). Therefore, these three Fe sources are also considered in the new ESM (Appendix B).

Ocean ecosystem dynamics are simulated based on the nutrient cycles of nitrate, phosphorous, and iron. The nutrient concentration, in conjunction with the controls of seawater temperature and the availability of light, regulates the primary productivity of the two types of phytoplankton. The model assumes that diazotrophic phytoplankton can prosper in regions in which phosphate is available but the nitrate concentration is small (<0.05 µmolL-1). In the model, zooplankton is assumed to be independent of abiotic conditions (e.g., seawater temperature) and dependent on biotic conditions (phytoplankton and zooplankton concentrations), as in the previous model. The denitrification process is modeled to occur only in suboxic waters (<5 µmolL-1) (Schmittner et al., 2008), and it is suppressed in water with a low nitrate concentration (<1 µmolL-1). Detritus contains nitrate, phosphorus, iron, and carbon, most of which is remineralized while sinking downward. The detritus that reaches the ocean floor is removed from the system; however, a fraction of OM in the sediment is assumed to return to the bottom layer of the water column at a constant rate in each location (Kobayashi and Oka, 2018).

The ocean carbon cycle is formed by atmosphere–ocean CO2 exchange, inorganic carbon chemistry, OM dynamics driven by marine ecosystem activities, and transportation and reallocation processes of ocean carbon within the interior. The formulations of atmosphere–ocean gas exchange, carbon chemistry, and related parameters follow protocols from the Ocean Model Intercomparison Project (OMIP; Orr et al., 2017). The production of DIC and total alkalinity is controlled by changes in inorganic nutrients and CaCO3, following Keller et al. (2012).

Finally, the flux of dimethyl sulfide (DMS) from the ocean, which is produced by plankton and is a precursor of atmospheric sulfate aerosols, is diagnosed in the original aerosol module from the surface downward shortwave radiation flux. In MIROC-ES2L, this emission scheme is modified and the flux is calculated from the sea surface DMS concentration that is diagnosed from the simulated surface water chlorophyll concentrations and the corresponding mixed-layer depth (Appendix B). In the present model, this is the only pathway via which ocean biogeochemistry affects climate if the model is driven by a prescribed CO2 concentration (Fig. 1). This modification of the DMS emission scheme increases the sulfate aerosol amount, particularly over high-latitude oceans during winter and in regions in which high surface wind speed occurs. The solar irradiance of the surface decreases in such regions; however, this effect is not sufficiently significant to change the mean physical climate states.

To evaluate the performance and sensitivities of MIROC-ES2L, we conducted four groups of experiments comprising 11 experiments in total (Tables 1 and 2). The first group was a control run that comprised two types of experiments: a normal control run (CTL) in which the external forcing was set to preindustrial conditions and an alternative control run (CTL-D) used for sensitivity analysis of the ocean biogeochemistry, which is described later.

The second group, used for historical simulations, comprised three types of experiments during the period 1850–2014. All three experiments were driven by the Coupled Model Intercomparison Project Phase 6 (Eyring et al., 2016) official forcing datasets (version 6.2.1; details on the forcing datasets used in the simulations are summarized in Appendix C), and the CO2 concentration was prescribed in the simulations (i.e., so-called concentration-driven experiments). The first comprised a conventional historical simulation (HIST), and the simulation result is used for direct comparison with observation-based studies to evaluate model performance. The second was a special experiment named HIST-NOLUC, which was designed to evaluate the impact of LUC on the climate and biogeochemistry. In this experiment, land use and agricultural management (fertilizer application) were fixed at preindustrial levels. This experimental configuration is the same as the LUMIP experiment in CMIP6 named land-noLu (Lawrence et al., 2016). The third experiment (HIST-BGC) was the same as HIST, except that the CO2 increase only affects the carbon cycle processes (named in C4MIP of CMIP6 as hist-bgc; Jones et al., 2016). Thus, there was no CO2-induced global warming in the experiment.

The third experimental group was used to evaluate the climate and carbon cycle feedbacks. This group comprised three types of idealized experiments, following experimental designs proposed by Eyring et al. (2016) and Jones et al. (2016). In the three experiments, the CO2 concentration was prescribed to increase at the rate of 1.0 % per year from the preindustrial state throughout the 140-year period (i.e., the concentration finally reached a value of approximately 1140 ppmv), while other external forcing was maintained at the preindustrial condition. The three experiments were configured as follows: (1) 1PPY was a normal experiment in which both climate and biogeochemical processes respond to the CO2 increase; (2) 1PPY-BGC was the same as 1PPY but the prescribed CO2 increase affects only the carbon cycle processes; and (3) 1PPY-RAD was the same as 1PPY but the CO2 increase affects only atmospheric radiation processes. In 1PPY-BGC, carbon cycle processes respond to the CO2 increase without CO2-induced global warming; thus, the result of this simulation is used to quantify the CO2–carbon feedback. In 1PPY-RAD, as there is no direct CO2 stimulation on the carbon cycle, climate change is the only cause of carbon cycle variation relative to the preindustrial control (CTL). Thus, this simulation result is used to evaluate the climate–carbon feedback (Arora et al., 2013; Schwinger et al., 2014).

The final group comprised a set of experiments to evaluate ocean biogeochemistry, focusing mainly on the processes newly introduced in MIROC-ES2L. This group comprised three types of experiments. The first experiment (NO-NR) was configured similarly to the CTL run, except the ocean component did not receive any riverine N input. Through this experiment, the impact of riverine N on ocean biogeochemistry could be evaluated. The second experiment (NO-NRD) was the same as NO-NR, except atmospheric N deposition additionally had no effect on ocean biogeochemistry. By evaluating the difference between NO-NR and NO-NRD, the impact of nitrogen deposition on ocean biogeochemistry could be evaluated. The final experiment (NO-FD) was configured with atmospheric Fe deposition onto the ocean surface switched off. To detect slight signals of ocean biogeochemistry arising from switching off the three processes (i.e., riverine N, N deposition, and Fe deposition), it was necessary to maintain consistency in the ocean physical fields between these experiments because a slight difference in the ocean physical fields produces perturbation on ocean biogeochemistry. In MIROC-ES2L, the ocean DMS emissions represent the feedback process of ocean biogeochemistry on the atmospheric physical processes; thus, biogeochemical change induced by the switching-off manipulations must change the DMS emission, which leads to inconsistency in the physical fields between the experiments. To avoid this occurrence, the DMS emission scheme in all three experiments was reverted to that used in the original aerosol component model, which is independent of the ocean ecosystem state (Appendix B). Similarly, the special control run (CTL-D), which was based on CTL, also had the DMS emission scheme changed to the same as NO-NR, NO-NRD, and NO-FD.

To conduct the experiments described above, preindustrial spin-up was performed in advance. Land and ocean biogeochemical components were decoupled from the ESM, and the spin-up run was conducted for 3000 years for the ocean component and 30 000 years for land by prescribing model-derived physical fields and other external forcing for the component models. In the final phase of the spin-up procedure, continuous spin-up, forced by the 1850-year condition of CMIP6 forcing, was performed for the entire system for 2483 years (Supplement Fig. S5). All the experiments listed in Table 1 were initiated from the final condition of this spin-up procedure.

To evaluate the climate and carbon cycle response to CO2 increase, we used the metrics of transient climate response (TCR), airborne fraction of CO2 (AF), and TCRE, which have been previously used to characterize the entire climate–carbon cycle response to CO2 increase in other models (Matthews et al., 2009; Hajima et al., 2012; Gillett et al., 2013). A similar analysis is made in this study, and the result is presented in Sect. 3.2.

First, TCRE is defined as the ratio of global mean near-surface air temperature change (T) to cumulative anthropogenic carbon emissions (CE) at the level of a doubled CO2 concentration from the preindustrial state (hereafter, 2×CO2PI): 1TCRE=T/CE, which can be written as follows: 2TCRE=(CA/CE)×(T/CA), where CA is the atmospheric carbon increase until reaching 2×CO2PI. The first term on the right-hand side (CA/CE) is identical to the definition of the cumulative airborne fraction of anthropogenic carbon emissions: 3CA/CE=AF. The second factor (T/CA) can be represented by TCR as follows: 4T/CA=TCR/CA, given that TCR is defined as T at 2×CO2PI. Thus, Eq. (2) can be expressed as follows: 5TCRE=AF×(TCR/CA). The result of the 1PPY simulation was used to evaluate TCRE, TCR, and AF. As CA is prescribed in the simulation, CE can be diagnosed by CE = CA + CL + CO, where CL and CO represent the change in land and ocean carbon storage, respectively. As shown by Matthews et al. (2009), AF summarizes the carbon cycle response to anthropogenic CE; the second term in Eq. (5) (TCR/CA) captures the global temperature response to CO2 increase in the models, and TCRE thus summarizes the two, i.e., the global temperature response to anthropogenic CO2 emissions in the model.

To evaluate the strength of carbon cycle feedbacks in the model, the feedback strength is quantified by the so-called β and γ quantities (Friedlingstein et al., 2006; Arora et al., 2013). The former is a feedback parameter for CO2–carbon feedback (carbon cycle response to atmospheric CO2 increase), which can be calculated as follows: 6βL=CL1PPY-BGC-CLCTL/CA1PPY,7βO=CO1PPY-BGC-COCTL/CA1PPY, where the subscripts L and O represent land and ocean, respectively, and the superscripts represent the experiment used for the calculation.

The quantity γ is a feedback parameter for climate–carbon feedback (carbon cycle response to climate change), which can be calculated using the results of the 1PPY-RAD and CTL simulations: 8γL=CL1PPY-RAD-CLCTL/T1PPY-RAD,9γO=CO1PPY-RAD-COCTL/T1PPY-RAD.

To evaluate the physical fields reproduced by MIROC-ES2L, the temporal evolutions of the global mean net radiation balance at the top of atmosphere (TOA) and anomalies of near-surface air temperature (SAT), sea surface temperature (SST), and upper-ocean (0–700 m) temperature were compared with observation datasets; the results are shown in Fig. 2. The model simulates a reasonably steady state of net TOA radiation balance in the CTL run, showing a trend of -4.6×10-5 W m-2 yr-1 during the 165-year period. When comparing the net TOA radiation balance of the HIST simulation with satellite measurements (CERES EBAF-TOA edition 4.0 constrained by in situ measurements; Loeb et al., 2012, 2018), the model result is -0.63 W m-2 (negative means net incoming radiation) during 2001–2010, which is within the range of -0.5±0.43 W m-2 estimated by Loeb et al. (2012) for the corresponding period (Fig. 2a).

Following the net increase in incoming radiation, the SAT anomaly increases in the latter half of the 20th century (Fig. 2b). The warming trend during 1951–2011 is simulated as 0.1 K per decade, which is consistent with that of HadCRUT4 (version 4.6; Morice et al., 2012), i.e., 0.11 K per decade (Stocker et al., 2013). Observation datasets of SST (HadSST version 3.1.1; Kennedy et al., 2011) and upper-ocean temperature (Levitus et al., 2012) clearly display increasing trends in the corresponding period, which are successfully reproduced by the model (Fig. 2c and d). In addition to the warming trend in the latter half of the 20th century, the model captures the slowdown of SAT increase both in the 1950s and in the 1960s. These changes are likely induced by increased anthropogenic aerosol emissions and resultant cooling through indirect aerosol effects, together with cooling attributable to large volcanic eruptions in the 1960s (Wilcox et al., 2013; Nozawa et al., 2005). However, distinct deviations of the model results from HadCRUT4 are found for SAT and SST in the 1860s and particularly in the 1900s. This might be due to inevitable asynchronization between the simulation and observations on the phasing of the internal variability of the climate, as identified by Kosaka and Xie (2016). They reported that there should have been four major cooling events due to tropical Pacific variability in the 20th century, one of which was found in the 1900s. They also reported that the other three events were around 1940, 1970, and 2000; however, discrepancies arising from these three events are not so evident in this study, likely because of the single ensemble simulation. The model also exhibits a short-term response of the TOA radiation balance following episodic volcanic events (Fig. 2a, vertical dashed lines), with resultant cooling of SAT and SST (Fig. 2a–c) and further propagation into the deeper ocean with an extended cooling duration (Fig. 2d). Overall, the historical SAT increase in MIROC-ES2L, taking the difference between the averages of 1850–1900 and 2003–2012, is 0.69 K, while the HadCRUT4-based estimate by Stocker et al. (2013) is 0.78 K for the corresponding period. The model shows good performance in reproducing global physical fields. This is likely attributable to the inherited robust performance of the physical core of the model (MIROC5.2) because MIROC-ES2L has only two feedback pathways of biophysical processes on climate (DMS emissions from the ocean and terrestrial processes associated with LAI dynamics) when the model is driven by a prescribed CO2 concentration. Both processes are likely to change the physical fields locally.

In addition to the radiation and temperature responses against historical external forcing, we briefly describe here the El Niño–Southern Oscillation (ENSO) and Atlantic meridional overturning circulation (AMOC) strength in MIROC-ES2L, both of which can affect interannual–multidecadal carbon cycle processes (Zickfeld et al., 2008; Pérez et al., 2013; Friedlingstein, 2015). In the HIST experiment, the standard deviation of the monthly SST anomaly in the Niño-3 region (5∘ S–5∘ N, 90–150∘ W) was 1.57 K in 1950–2009, which is larger than that of HadSST (0.94 K). This unrealistically large ENSO amplitude tends to influence the simulated interannual global temperature variability (Fig. 2b), which is suggestive of a further effect on the interannual variability in biogeochemical fields (e.g., CO2 flux in the tropics). The AMOC intensity, quantified by North Atlantic Deep Water transport across 26.5∘ N, was approximately 13 Sv (1 Sv =106 m3 s-1) as the 1850–2014 average, which is smaller than the observational estimates of 17.2 Sv (McCarthy et al., 2015). In the HIST run, the AMOC strength was weakened at a rate of 0.01 Sv yr-1 (i.e., reduction of 1.7 Sv during the 165 years of HIST), which seems slightly smaller than the recent estimate of AMOC weakening of 3±1 Sv from the mid-20th century (Caesar et al., 2018).

Hereafter, we present an overview of the performance of the mean state of the physical fields, atmosphere, and land–ocean basic variables of the model in comparison with various observational-based data. The variables examined here are SAT, precipitation, SST, sea ice concentration, land snow cover, and mixed-layer depth, all of which are representative physical states associated with biogeochemical processes. The mixed-layer depth is defined as the depth at which the potential density becomes larger than that of the sea surface by 0.125 kg m-3. Figure 3 shows the climatology of SAT (air temperature at 2 m of height) averaged over 1989–2009 for annual, December–February (DJF), and June–August (JJA) means and the biases in comparison with the ERA-Interim dataset (Dee et al., 2011). The comparison suggests that the model performs well (biases <2 ∘C) over the tropics and most of the global area in terms of both annual mean and seasonality. However, obvious warm biases exist over the Southern Ocean and Antarctica. This is a general tendency of CMIP5-class models, and both MIROC5 (Watanabe et al., 2010) and MIROC6 (Tatebe et al., 2019) also suffer from this problem. The warm bias in the Southern Ocean can be mainly attributed to a poor representation of cloud radiative processes (Bodas-Salcedo et al., 2012; Williams et al., 2013; Hyder et al., 2018) but also poor representations of the mixed-layer depth and deep convection in the open ocean attributable to the lack of modeled mesoscale processes in the Antarctic Circumpolar Current (Tatebe et al., 2019). A related warm bias in SST over the Southern Ocean is also confirmed, which is discussed later.

Figure 4 shows the precipitation distribution in the HIST experiment in comparison with the Global Precipitation Climatology Project (GPCP) dataset (Adler et al., 2003). Generally, the precipitation distribution is reasonably well represented in the model. The Intertropical Convergence Zone is reproduced well in the experiment, except that the simulated South Pacific Convergence Zone is shifted equatorward relative to the GPCP, which is the so-called double Intertropical Convergence Zone syndrome (Bellucci et al., 2010). Over continental areas, the model is effective in capturing the spatial pattern of both the annual mean precipitation and the seasonality. However, positive precipitation biases are evident in some tropical land regions such as central Africa, South and Southeast Asia, and South America. Additionally, arid and semiarid regions of central Asia, Australia, and the western side of North America also show a positive precipitation bias, although it is unclear in the bias map (see Supplement Fig. S6 for a comparison with the absolute precipitation rate of GPCP).

When projecting future climate change, it is important for a model to reproduce the observed climatological patterns of key physical variables, as suggested by Ohgaito and Abe-Ouchi (2009). The biogeochemical tracers are also affected by the representation of the physical fields. Figure 5 presents the modeled SST and its bias with respect to the World Ocean Atlas 2013 (Locarnini et al., 2013). Generally, the model performs well, confirmed by the large extent of the area with minimal bias (colored white in Fig. 5). However, obvious bias is evident, e.g., the warm bias in the Southern Ocean, as already explained above (Fig. 3). A cold bias is also evident over the western North Pacific Ocean, which is attributable to the lack of narrow and swift western boundary currents owing to the coarse horizontal resolution in the ocean parts of the present ESM.

The model performance in simulating sea ice concentration and snow cover over land for both March and September is shown in Fig. 6 in comparison with observational data (Special Sensor Microwave Imager (SSM/I; Kaleschke et al., 2001) for sea ice concentration and the Moderate-resolution Imaging Spectroradiometer (MODIS; Hall et al., 2006) for snow cover. Sea ice extent in the Northern Hemisphere is represented well for both months, although the summertime concentration minimum is slightly smaller than observed. In the Southern Hemisphere, however, the sea ice extent is unrealistically underestimated because of the persistent warm bias described above. The extent of the snow-covered area is also represented well, likely owing to the updated scheme for subgrid snow representation (Nitta et al., 2014; Tatebe et al., 2019). However, the fine structure of the snow cover is lost in the simulation, which is likely attributable to the coarse resolution of the modeled atmosphere and land. The reasonable performance in reproducing land snow seasonality in the boreal region is important for land biogeochemistry and the physical climate because snowmelt (accumulation) and leaf flush (shedding) processes are mutually associated (Supplement Fig. S7).

Figure 7 shows the mixed-layer depth in comparison with the mixed-layer dataset of Argo with grid point value (MILA_GPV; Hosoda et al., 2010). The HIST simulation captures both the spatial pattern and the seasonality change in mixed-layer depth. In the Northern Hemisphere winter, the structure of the deep mixed layer over the western North Pacific is consistent with observations; however, the actual depth is overestimated owing to the lack of mesoscale eddies. The deep mixed layer in the subarctic North Atlantic is also consistent with observations, except there is less deep water formed in the Labrador Sea. Additionally, the shallow mixed layer in low latitudes is generally captured well by the simulation, and the depth that is maintained at around 100 m over the Southern Ocean is consistent with observations. In austral winter, MILA_GPV shows that the mixed layer develops to more than 200 m over the Indian Ocean and the Pacific sector of the Southern Ocean, whereas it is shallow (around 50 m) in the tropics and the Northern Hemisphere (Fig. 7d). The model captures the general pattern in austral winter, although the extent of the simulated deeper mixed-layer depth of more than 200 m in the Southern Ocean is larger than that of MILA_GPV (Fig. 7c).

The simulated net CO2 uptake by land and ocean in cumulative values (i.e., changes in total carbon of land and ocean) is shown in Fig. 8a and b, respectively. For land, the CTL run shows a slight reduction of carbon of 7.6 PgC during the 165 years (i.e., 4.6 PgC per century), which is within the acceptable range for the CMIP6 exercise (10 PgC per century; Jones et al., 2016). The dashed gray line in Fig. 8a is the result from HIST-NOLUC and shows a natural land carbon sink in MIROC-ES2L of 200 PgC during 1850–2014. This is comparable with the estimate of 185±50 PgC by Le Quéré et al. (2018) for the same period (vertical gray bar in Fig. 8a), which was obtained from multiple offline terrestrial ecosystem models with fixed land use. Additionally, LUC is one of the factors that drastically changes the historical land carbon amount because positive (negative) LUC emissions are directly linked to a reduction (increase) in land carbon. Based on bookkeeping methods, Le Quéré et al. (2018) estimated the cumulative CE derived from LUC during 1850–2014 as 195±75 PgC, whereas the simulated cumulative emissions by MIROC-ES2L diagnosed by the difference in land carbon amount between HIST-NOLUC and HIST are 156 PgC.

Through being affected by both environmental changes and LUCs, MIROC-ES2L demonstrates in the HIST simulation that land carbon is reduced by approximately 60 PgC from the beginning of the simulation until the middle of the 20th century (black line in Fig. 8a). This reduction should reflect LUC during this period because HIST-NOLUC does not show such a trend of decrease in the corresponding period (dashed gray line in Fig. 8a). From the 1960s, the model shows continuous carbon sequestration on land, which results in a positive net CO2 uptake of 2.4 PgC yr-1 in the 2000s (Table 3). This continuous increase in the latter half of the 20th century is due to the combined effects of CO2 fertilization, vegetation recovery associated with LUC, and the increase in nitrogen input via deposition and the use of fertilizer. This is clearly displayed in Fig. 8c, where the historical land carbon change is decomposed into the responses to (1) CO2 increase (blue line, diagnosed by HIST-NOLUC + HIST-BGC – HIST; see Table 2), (2) climate change (red line, by HIST – HIST-BGC), and (3) LUC (green line, by HIST – HIST-NOLUC). In the latter half of the 20th century, land carbon sequestration accelerated by CO2 stimulation is clear, while climate change and the resultant terrestrial carbon loss also become evident. Additionally, land carbon reduction induced by LUC is slightly weakened in the corresponding period. During the historical period, MIROC-ES2L simulates a total land carbon change (CL) of 44 PgC. This number drops to within the independent estimate range of -10±90 PgC (vertical black bar in Fig. 8a), and the estimation uncertainties take into account both the terrestrial natural carbon sink and LUC emissions (calculated as (σLUC2+σSINK2)0.5, where σLUC and σSINK represent the uncertainty range of LUC emissions and the land sink, respectively, in Le Quéré et al., 2018). The possible range for CL can be changed if we estimate it as the residual of other global carbon budgets (i.e., CL = FF – CA – CO, where FF is the cumulative fossil fuel carbon emission). Using the estimated ranges of FF, CA, and CO reported by Le Quéré et al. (2018) (i.e., 400±20, 235±5, and 150±20 PgC, respectively; the budget imbalance of 25 PgC is ignored here), the CL range is suggested to be 15±29 PgC. In this case, the result of MIROC-ES2L (44 PgC) is still within the estimation boundaries, although it is at the upper end of the suggested range.

For the ocean, the model shows an increase in carbon accumulation in the CTL run (Fig. 8b). This is partly because of carbon removal by the sedimentation process that is newly introduced into MIROC-ES2L. In this process, an amount of carbon is extracted from the ocean bottom, which should be compensated for by an equivalent input of carbon from the atmosphere through gas exchange processes. In the CTL run, the rate of carbon extracted from the ocean bottom is 0.068 PgC yr-1 (Table 4), which suggests that the process removes 11 PgC throughout the entire simulation period of CTL (165 years). It is noted that Ciais et al. (2013) suggested that the ocean was a net source of CO2 in the preindustrial era to an amount of 0.7 PgC yr-1, whereas our model shows it as a net sink in the same condition. This is likely attributable to the lack of a process of riverine carbon input in our model. For example, Ciais et al. (2013) estimated that the ocean obtains an external carbon input of 0.9 PgC yr-1 from rivers, 0.2 PgC yr-1 of which is removed by ocean sedimentation and 0.7 PgC yr-1 is lost from the ocean to the atmosphere via gaseous exchange. The sedimentation process cannot explain all the increase in oceanic carbon in the CTL run (30 PgC). Therefore, the remainder should be attributed to other reasons, e.g., the shortness of the spin-up period or imperfect mass conservation in the ocean biogeochemical component.

The HIST run shows the cumulative carbon uptake by the ocean, which is predominantly driven by CO2 increase (Fig. 8b and d). In comparison with land, ocean carbon shows a relatively small response to climate change (red line in Fig. 8d), which is consistent with analysis of the carbon cycle feedback in an idealized scenario (Arora et al., 2013). Furthermore, the model shows weak or almost no response against LUC (green line in Fig. 8d), although the ocean component in the model actually receives increased nitrogen input from rivers attributable to LUC and agriculture (Fig. 9, Table 4). This suggests that the increase in riverine nitrogen input due to LUC and agriculture would not induce a significant global-scale impact on ocean carbon uptake in the historical period. The model simulates a cumulative carbon uptake of 163 PgC for 1850–2014, which is within the range of 150±20 PgC (vertical black bar in Fig. 8b) reported by Le Quéré et al. (2018).

Overall, MIROC-ES2L qualitatively captures the temporal evolution of carbon dynamics in the historical period; the cumulative carbon uptake by both land and ocean is within the range of the estimates by Le Quéré et al. (2018). However, the model might overestimate the net carbon uptake by the land and/or ocean or underestimate LUC emissions. This is because the cumulative fossil fuel emissions, diagnosed from the simulated atmosphere–land–ocean CO2 fluxes and prescribed CO2 concentration change (FF = CA + CL + CO; Appendix D), were 447 PgC, i.e., larger than the estimate of 400±20 PgC of Le Quéré et al. (2018). Additionally, this speculation is also supported by the diagnosed CO2 concentration at the end of the HIST run (Appendix D); the diagnosed concentration is 376 ppmv, which is lower (by 22 ppmv) than that actually monitored. We note, however, that the likely biases in land–ocean carbon uptake, suggested by the larger diagnosed emissions and lower diagnosed CO2 concentration, could be partially alleviated if the model were driven by anthropogenic CO2 emissions. This is because in emission-driven mode, the relatively stronger land–ocean carbon uptake leads to a lower atmospheric CO2 concentration, which could weaken the land and ocean sink through a negative CO2–carbon feedback. Indeed, in emission-driven mode, the atmospheric CO2 concentration in the historical run (esm-historical; Jones et al., 2016) is simulated to be 384 ppmv in 2014 (as an average of three ensemble experiments; data not shown but available via the Earth System Grid Federation servers), which is closer to the actual level monitored (but still lower by 14 ppmv). Additionally, in emission-driven mode, the land and ocean are mutually interlinked via the atmospheric CO2 concentration; thus, a strong bias of CO2 flux in one component can be modulated by the other. This mechanism might reduce the bias of CO2 fluxes of the land and ocean simultaneously, or it might exacerbate the CO2 flux by imposing the flux bias of one onto the other. For more detail, simulations and multimodel analyses based on emission-driven configurations are necessary, as designed in C4MIP (Jones et al., 2016).

MIROC-ES2L can simulate the global nitrogen cycle under interaction with the climate and carbon cycle, and the global N budget for land and ocean in the HIST simulation is shown in Fig. 9 as the component fluxes. Comparison of the terrestrial nitrogen budget in the 2000s with the preindustrial condition (Table 3) reveals that the annual inputs of nitrogen via deposition and fertilizer, which are controlled by forcing data, increase to 65.5 and 114 TgN yr-1, respectively. Additionally, BNF is also increased by 40 % (39 TgN yr-1), which is caused by the areal expansion of agriculture for N-fixing crops (Fig. 9, Supplement Fig. S8). Previous studies have shown similar levels of increase. For example, Gruber and Galloway (2008) reported a value of 35 TgN yr-1, and the absolute magnitude of agricultural BNF in the present-day condition was estimated as 50–70 TgN yr-1 by Herridge et al. (2008) and 40 TgN yr-1 by Galloway et al. (2008).

For terrestrial nitrogen efflux, Gruber and Galloway (2008) reported N2 emissions in the unperturbed state as 100 TgN yr-1, i.e., larger than found in this study (72 TgN yr-1). However, in the present-day condition, they estimated the absolute magnitude of N2 emissions as 115 TgN yr-1, which is reasonably close to our model result (111 TgN yr-1). MIROC-ES2L simulates the historical increase in N2O emission from soil as 4.3 TgN yr-1 from the preindustrial condition to the 2000s, which is comparable with the estimate of approximately 4 TgN yr-1 for 1861–2015 derived from a model comparison study (Tian et al., 2018). However, the absolute magnitude of terrestrial N2O emission fluxes in preindustrial and present-day conditions is likely overestimated (Table 3; Hashimoto, 2012).

Although it is difficult to obtain observation-based estimates of how much nitrogen was accumulated by the land ecosystem in the historical period, the model demonstrates net nitrogen uptake by land in the 2000s as 37 TgN yr-1 (Table 3). This positive uptake is likely caused by increased total nitrogen input into the land ecosystem. In addition to the increasing N input, the net positive N uptake by land is likely accelerated by the increased nitrogen demand by plants and soils that have higher C:N ratios under elevated CO2 concentrations. This is because the net increase in land N uptake is also found in 1PPY-BGC (Supplement Table S1), even though the N inputs such as BNF, fertilizer, deposition, and climate conditions in the 1PPY-BGC simulation are almost unchanged from the CTL run. This suggests that atmospheric CO2 increase in HIST has changed the C:N ratios in plants and soil and hence stimulated ecosystem nitrogen demand. The model demonstrates nitrogen loss by LUC at a rate of >50 TgN yr-1 (Fig. 9). This is because the harvested biomass in the model is translocated to product pools, and the nitrogen contained in the biomass is assumed lost with implicit chemical form, together with carbon loss as CO2.

Compared with land, the model simulates relatively stable dynamics of the oceanic nitrogen budget but with larger interannual variation (Fig. 9b). In the 2000s, oceanic BNF is simulated as 126 TgN yr-1, which is almost at the same level (slightly below) as that of the preindustrial state, i.e., 129 TgN yr-1 (Table 4). This number is close to previously reported estimates of approximately 130 TgN yr-1 (Eugster and Gruber, 2012). The invariant behavior of BNF in the model suggests that the historical change in nitrogen input into the ocean is primarily attributable to two external sources: deposition and riverine input. Nitrogen deposition into the ocean, which is prescribed in the forcing data, shows an increase from 14 TgN yr-1 in the preindustrial condition to 35 TgN yr-1 in the 2000s. Riverine nitrogen input at a river mouth is shown to increase from 17.5 TgN yr-1 in the preindustrial condition to 33.9 TgN yr-1 in the 2000s (Table 4; this is discussed further in Sect. 3.1.5 and 3.2.3). In this study, the gross nitrogen input into the ocean in the present-day condition is simulated as 195 TgN yr-1. The value is reasonably close to the estimate of 200 TgN yr-1 by Wang et al. (2019) and that of 209 TgN yr-1 by Galloway et al. (2004); however, it is smaller than other published estimates (e.g., 294 TgN yr-1, Codispoti et al., 2001; 270 TgN yr-1, Gruber and Galloway, 2008). Denitrification, the main source of ocean nitrogen loss, is simulated as 142 TgN yr-1 for the preindustrial condition and 165 TgN yr-1 for the 2000s. These values are within the wide range of total denitrification rates estimated by previous studies, i.e., 145–450 TgN yr-1 (Eugster and Gruber, 2012). It should be noted that the present model used in this study does not include sedimentary denitrification. Thus, the expected N flux by sedimentary denitrification is imposed on water-column denitrification, and the rate of water-column denitrification is likely overestimated. Overall, the model exhibits an oceanic N imbalance of 26.1 TgN yr-1 in the present-day condition (Fig. 9, Table 4).

Model performance in relation to land biogeochemistry is evaluated based on the spatial distributions of three fundamental variables of the land carbon cycle in comparison with observation-based products. First, GPP in the HIST simulation is compared with the global product by Jung et al. (2011) (Fig. 10a–c). The model simulates high productivity (>2000 gC m-2) in the tropical forests of central Africa, Southeast Asia, and South America, although the productivity in these regions is generally still underestimated in comparison with the observation-based product. This underestimation is likely attributable to the use of the parameter values of photosynthetic capacities (KPSAT1 and KPSAT2 in Appendix A) from Kattge et al. (2009). This is because Kattge et al. (2009) also showed substantial depression of photosynthetic capacity in the tropics. The model captures the moderate productivity of vegetation in savanna regions such as the eastern side of South America and the marginal region surrounding central Africa. Moderate GPP is also found in the Northern Hemisphere in the region 20–45∘ N, where a large proportion of land cover is dominated by both natural and agricultural vegetation (Supplement Fig. S2). The GPP gradient from moderate to lower GPP in the boreal to tundra regions of Eurasia and North America is captured well by the model. The model estimates global GPP at 124 PgC yr-1 in the 2000s (Table 3), which is within the range of 106–140 PgC yr-1 produced by the CMIP5 ESMs and is reasonably close to the value of 119 PgC yr-1 derived from an observation product (1986–2005 average; Jung et al., 2011). The simulated GPP seasonality is also compared with that of Jung et al. (2011) (Supplement Fig. S9). It reveals a reasonable summertime peak and the seasonality of GPP in the extratropical Northern–Southern Hemisphere, where vegetation phenology is primarily controlled by air temperature. However, the region around 40∘ N displays a longer growing season than that of Jung et al. (2011), and the tropics (20∘ S–20∘ N) show less seasonality, suggesting room for improvement of the phenology-related processes and surface climate fields in the corresponding region or biome types.

To evaluate the simulated vegetation carbon, we compare the model results of forest carbon, not total vegetation carbon, with those of Kindermann et al. (2008) (Fig. 10d–f). The model reproduces the reasonably high density of biomass in tropical forests, although the values are smaller than the observation product (Fig. 10f). This is partly attributable to the underestimation of GPP in this region, as described above. In high-latitude regions of the Northern Hemisphere (around 50∘ N), the model overestimates biomass density, particularly in terms of the evergreen coniferous forests that extend across western Siberia and North America. GPP in these regions is captured reasonably well by the model (Fig. 10a and b), and thus the overestimation of boreal forest biomass is likely due to the underestimated turnover rate of forest carbon. A slight overestimation of biomass is also found in regions where intensive cultivation has occurred, i.e., Europe, Southeast–East Asia, and eastern America. The model estimates global vegetation carbon content including all types of vegetation at 543 PgC (Table 3).

In Fig. 10g–i, the model results of soil organic carbon (SOC) are compared with two different types of SOC products: harmonized soil property values for broad-scale modeling (WISE30sec) by Batjes (2016) and the Northern Circumpolar Soil Carbon Database version 2 (NCSCDv2) by Hugelius et al. (2013). The former is a global dataset that represents soil column SOC down to the depth of 2 m, whereas the latter targets only the high-latitudinal region of the Northern Hemisphere at different soil depths (∼1, ∼2, and ∼3 m). Comparison with WISE30sec confirms that the model successfully captures the spatial distribution of lower carbon accumulation in arid and tropical regions and higher SOC in boreal regions in the Northern Hemisphere. However, the simulated zonal mean SOC in the boreal regions is about half that of WISE30sec (Fig. 10i). This is likely attributable to the different treatment of frozen carbon in deeper soils in permafrost regions; i.e., WISE30sec covers the total SOC down to 2 m of depth including frozen carbon, while the model does not consider the frozen carbon and instead simulates only upper SOC as litter and lower SOC as humus. The model result in the boreal region is comparable with the NCSCDv2 estimation for 1 m of depth. We note, as mentioned by Todd-Brown et al. (2012), that large uncertainty remains in the estimation of the SOC amount, especially in boreal regions. Globally, SOC is simulated as 1491 PgC (Table 3) in this study, which is smaller than the value of 2060±215 PgC of WISE30sec (Batjes, 2016) but comparable with the range of 890–1660 PgC, as estimated by Todd-Brown et al. (2012) based on the Harmonized World Soil Database v1.2 (FAO/IIASA/ISRIC/ISS-CAS/JRC, 2012).

In this section, we evaluate the simulated surface and vertical distributions of nitrate, phosphate, dissolved Fe, NPP, oxygen, DIC, and alkalinity against observations (Fig. 11). Additionally, the ocean CO2 flux is also compared with an observation-based estimation (Fig. 12). The observations comprise the World Ocean Atlas 2013 (WOA2013; Garcia et al., 2014a, b) for macronutrients and oxygen, the GEOTRACES dataset (updated to its 2015 version; Tagliabue et al., 2012) for dissolved iron, the Global Ocean Data Analysis Project version 2 (GLODAPv2; Lauvset et al., 2016) for DIC and alkalinity, and SeaWiFS (Behrenfeld and Falkowski, 1997) satellite observations for NPP.

Owing to the long spin-up, the drift in global averaged concentrations of biogeochemical tracers becomes close to zero. The linear drift of dissolved oxygen, NO3, and Alk–DIC over the final 250 years of the spin-up is less than 3 % kyr-1 (Supplement Table S3). This small bias is significant in providing results on ocean biogeochemistry and carbon cycle feedbacks that are quantitatively more correct (Séférian et al., 2016).

The simulated surface distributions of nitrate and phosphate are generally in agreement with the WOA2013 datasets (Fig. 11a and b). The surface macronutrient concentrations in HNLC regions (e.g., the Southern Ocean, North Pacific Ocean, and eastern equatorial Pacific Ocean) are higher than those produced by the ocean biogeochemical component of our previous model (Watanabe et al., 2011), and they are more consistent with the observed values. This increase in macronutrients in HNLC regions is reasonable because the implementation of the iron cycle and the iron limitation on phytoplankton growth can reduce macronutrient utilization in these regions. Ocean circulation also influences the distribution of nutrient concentrations. In the Southern Ocean, the deep mixed-layer depths simulated by the model can cause an overestimation of nutrient entrainment to the surface and thus produce a high nutrient bias (Fig. 7). The simulated global mean vertical profile of nitrate concentrations compares reasonably well with observed values, likely because the ocean circulation is represented adequately (Fig. 11a). To check the influence of ocean circulation on the tracer distributions, we compared the apparent oxygen utilization (AOU) between the model and observations (Supplement Fig. S10). Although the model captures the observed AOU distributions, the strong and deep AMOC causes an underestimation of AOU values in the Atlantic Ocean deep water. The largest bias is an underestimation in the North Pacific Ocean, which is caused by the strong deep circulation of the Pacific Ocean. It should be noted that the difficulty of simulating the Pacific Ocean deep circulation appears to be a general problem in present coarse-resolution models (Hasumi et al., 2010). Model–data agreement on vertical nitrate concentrations is also the result of the near balance between nitrogen cycle sources (i.e., nitrogen fixation, atmospheric nitrogen deposition, and riverine nitrogen input) and sinks (i.e., denitrification, N2O emissions, and sedimentary loss) over the long spin-up period.

The concentration of dissolved iron in the open ocean is highest in the subtropical North Atlantic Ocean and in the Arabian Sea (Fig. 11c), which is consistent with the pattern observed in GEOTRACES. Such high concentrations are caused by enhanced dust deposition from the Sahara. In the remainder of the open ocean, dissolved iron concentrations are generally <0.2 µmolm-3, especially in HNLC regions. The model captures the main observed patterns in the surface ocean well. The very high iron concentrations (>1 µmolm-3) both observed and simulated along coasts and over continental margins are the result of iron input from sediment. The average simulated dissolved Fe concentration in the surface ocean (0–100 m) is 0.39 µmolm-3, which is lower than observed (0.52 µmolm-3) but within the range of the iron model intercomparison project (FeMIP; Tagliabue et al., 2016). One factor not accounted for in our model is the variation in the solubility of iron in aerosols, which depends not only on the source chemical composition but also on atmospheric processing during transport (Ito et al., 2019a). Consideration of different degrees of atmospheric Fe processing could reduce the overestimations of dissolved Fe concentration in the North Atlantic Ocean and North Pacific Ocean (Ito et al., 2019b). Our model also neglects variations in sedimentary iron flux. Observations have found that iron release or burial in sediment is dependent on the oxygen concentration of bottom water (Noffke et al., 2012), ambient temperature (Sanz-Lázaro et al., 2011), and the amount of OM that reaches the sea floor and is remineralized therein (Elrod et al., 2004). To simulate more realistic iron distributions, these processes should be considered in future studies.

Reproducing the spatial pattern of nutrient limitation on phytoplankton growth is crucial for the accurate prediction of primary production and for reflecting in the simulations the consequences of ongoing anthropogenic perturbations to oceanic nutrient cycles (Moore et al., 2013). The model reasonably reproduces the HNLC regions because of the iron limitation in the subarctic North Pacific Ocean, the equatorial Pacific Ocean, and the Southern Ocean (Supplement Fig. S11), although the subarctic North Pacific Ocean and the equatorial Pacific Ocean have larger HNLC zones than observed upwelling regions. This is likely because of an underestimation of surface iron concentrations and/or a relatively high half-saturation constant for iron uptake (Appendix B). Nitrogen limitation occurs throughout much of the low-latitude surface ocean where the nitrogen supply from the subsurface is relatively slow.

Based on the distribution pattern of nutrients and the limitations, annual NPP is simulated as 28.6 PgC yr-1 (Table 4). This value is lower than a satellite-based estimate of 35–78 PgC yr-1 (Carr et al., 2006), and it is also lower than the range of 30.9–78.7 PgC yr-1 derived from the CMIP5 models (Bopp et al., 2013). This is likely attributable to the high half-saturation constant for iron uptake, as mentioned above. Although intense primary productivity in coastal regions is not resolved by the coarse grid, the modeled NPP agrees with the basin-scale patterns of observation-based NPP. The values of both modeled and observed NPP are high in regions of equatorial upwelling, the North Atlantic Ocean, and the Southern Ocean north of the polar front, whereas they are low in subtropical gyres (Fig. 11g). Global export production is estimated as 7.9 PgC yr-1, which is the upper bound of the CMIP5 models (4.9–7.9 PgC yr-1; Bopp et al., 2013).

The simulated surface distribution of dissolved oxygen compares reasonably well with observations (not shown). This is because the surface oxygen concentration is close to its solubility value, and it is strongly constrained by SST. At depth, oxygen minimum zones in the eastern equatorial Pacific Ocean, eastern tropical Atlantic Ocean, Arabian Sea, and Bay of Bengal are reproduced well (Fig. 11f). However, the model produces oxygen concentration values higher than observed; thus, it underestimates the hypoxic volume ([O2] <80 mmol m-3) by a factor of 3 in comparison with data-based estimates (Bianchi et al., 2012). Note that existing global ocean biogeochemical models have difficulty in reproducing oxygen minimum zones owing to their coarse resolution and simple globally tuned parameterizations of vertical fluxes of OM (Cocco et al., 2013; Bopp et al., 2013). The positive bias in oxygen might be driven by wintertime mixing in the Southern Ocean and the North Pacific Ocean that is too intense (Fig. 7), which transports too much oxygen from the surface to depth.

The model also captures the global-scale patterns of observed DIC and alkalinity (Fig. 11d and e). High values of these tracers in subtropical gyres (and in the Southern Ocean for DIC) are found in the model output and observations. Salinity bias and the parameterization of calcium carbonate production in the model can contribute to the alkalinity bias. Overestimation of alkalinity in subtropical gyres leads to an overestimation of DIC because alkalinity affects the ocean's capacity to take up and store atmospheric CO2.

Figure 12a shows the simulated annual mean air–sea CO2 fluxes for the period 1985–2014 with observational estimates by Landschützer et al. (2014). Generally, the simulated spatial pattern is consistent with the data-derived estimates. The strongest carbon source to the atmosphere is found in the equatorial Pacific Ocean, and the most intense carbon sink is found in the North Atlantic Ocean. Model outgassing is weaker than the observational estimate in the North Pacific and equatorial Indian oceans. The model–data discrepancies are pronounced in the seasonal cycle of air–sea CO2 fluxes in the Southern Ocean and the North Atlantic Ocean (Fig. 12b and c). In the Southern Ocean, the model simulates an opposite CO2 flux seasonal phase, which could be driven by the bias in SST variability (Kessler and Tjiputra, 2016). In the North Atlantic Ocean, although the simulated seasonal phasing of CO2 fluxes agrees with the observational estimate, the amplitude is overestimated. The processes driving the seasonal cycle should be investigated in future studies because simulating a proper regional seasonal cycle of air–sea CO2 fluxes is important for future projections (Kessler and Tjiputra, 2016; Goris et al., 2018).

To evaluate the sensitivities of modeled land biogeochemistry, we focus on GPP and its response to external forcing in the terrestrial system because this carbon flux is the primary driver of land carbon input. GPP change was calculated by taking the difference of the 2005–2014 averages between the HIST and CTL runs. Then, as diagnosed in Fig. 8c, the GPP change was decomposed into the response to (1) CO2 increase, (2) climate change, and (3) LUC and agricultural change (Fig. 13) based on the simulation results of HIST, HIST-NOLUC, and HIST-BGC (Tables 1 and 2). Additionally, the GPP changes were further decomposed into the contributions from non-crop (i.e., the contribution of primary and secondary vegetation, urban areas, and pasture) and crop tiles by weighting the GPP of each tile by their areal fractions on a grid.

Figure 13d–f shows that CO2 increase in the historical period is the main driver of change in the land carbon cycle and that the CO2 fertilization effect prevails over most land areas except desert regions. Conversely, the GPP response to climate change shows both positive and negative signs (Fig. 13g–i) with relatively smaller magnitudes. Midlatitude and high-latitude regions of the Northern Hemisphere show a positive change in GPP that is likely attributable to lengthening of the vegetation growth season, enhanced plant growth following accelerated soil mineralization due to warming, and other mechanisms (e.g., soil water increase via precipitation and permafrost melting). In semiarid regions (i.e., Africa, South Asia, northern Australia, and the eastern side of South America), GPP shows a slight reduction. As these regions have less precipitation in comparison with the tropics, the reduction in GPP is likely associated with precipitation change.

In addition to the responses to CO2 increase and climate change, the model demonstrates spatial variation in the response of GPP to LUC (Fig. 13j). Historical LUC reduces the non-crop GPP contribution (Fig. 13k), while the crop contribution is enhanced (Fig. 13l). In the tropics, LUC reduces the non-crop GPP but weakly increases crop GPP, which results in a net negative reduction of GPP as grid averages (Fig. 13j). Meanwhile, regions with intensive agriculture with nitrogen fertilizer input (e.g., western Europe, East Asia, and parts of North America) show a net positive change in GPP as grid averages, whereby increases in the crop contribution overcome reductions in the non-crop contribution (Figs. 13k and 12l). In the model, the crop contribution to GPP can be intensified by the following: (1) increasing the areal fraction of the crop tile following LUC forcing; (2) changing the vegetation type from natural vegetation to crop, whereby the latter has higher photosynthetic capacity than natural plant functional types (given as parameters that relate photosynthetic capacity to leaf nitrogen concentration; Appendix A); (3) applying nitrogen fertilizer to crop tiles; and (4) increasing nitrogen input via nitrogen-fixing crops, which is considered in the model to be a subcategory of crop tiles. Indeed, the total area of cropland increases in the 20th century in the HIST simulation (Supplement Fig. S2), which is reflected by the model producing an increase in nitrogen input via fertilizer application and biological fixation on the global scale (Fig. 9a).

By responding to CO2 increase, climate change, and LUC, most land areas show increased GPP in the historical period (Fig. 13a), and regions with intensive agriculture show a greater increase in GPP than induced solely by the CO2 fertilization effect (Fig. 13a and d). This suggests that modeled GPP is sensitive to land use and agricultural management forcing in addition to the increase in CO2, and this might be one of the reasons for the slowing of LUC-induced land carbon reduction in the latter half of the 20th century in the HIST simulation (green line in Fig. 8c).

In this section, we investigate the sensitivity of oceanic NPP to external nutrient inputs from atmospheric deposition and river discharge processes under preindustrial conditions because these processes are newly incorporated into the ESM. Through the combination of the simulation results of CTL-D, NO-NR, NO-NRD, and NO-FD (Tables 1 and 2), the impacts of nutrient input on both the nutrient concentration and primary productivity are analyzed (Fig. 14 for N input assessment and Fig. 15 for Fe), and the spatial patterns of simulated nutrient limitation on NPP in the four experiments are examined (Fig. 16). Here, NO3, Fe, and PO4 limitation is diagnosed using the equations NO3/(kN + NO3), Fe/(kFe + Fe), and PO4/(kP + PO4), respectively, as simulated in MIROC-ES2L (Eq. B17); Fig. 16 presents the strength of each limitation visualized by the intensity of each of the three primary colors (red, blue, and green). In the simulations, because changes in NPP and surface nutrient concentrations continued to change over several decades following the abrupt switching-off manipulation, the average over the final 10 years is used for the following analysis. The rapid response of NPP to changes in nutrient input is consistent with that found in previous research (Somes et al., 2016).

First, the impacts of riverine N input on the surface nutrient concentration and NPP are assessed by subtracting the zero-input scenario NO-NR from the control experiment CTL-D (Tables 1 and 2). Surface NPP is increased by riverine N input (by >10 gC m-3 yr-1) in coastal areas such as the North Brazil Shelf and the Gulf of Mexico (Fig. 14a). In comparison with the pattern of the distribution of nutrient limitation (Fig. 16a and b), it is clear that a strong NPP increase in the open ocean occurs mainly in the Atlantic Ocean, which is under an N-limited condition. Conversely, NPP decreases in Fe-limited regions because the NPP increase in N-limited regions consumes surface dissolved Fe. Surface NO3 concentrations increase only slightly in N-limited regions because NO3 is immediately consumed locally by phytoplankton. A remarkable increase in surface NO3 concentrations is found in Fe-limited regions such as the Kara Sea, North Atlantic Ocean, Hudson Bay, and Subantarctic Ocean. Global NPP increases by 0.7 PgC yr-1 (by 2.5 % in comparison with NO-NR). This value is comparable with the finding of da Cunha et al. (2007), who estimated a 5 % increase in primary production due to riverine nutrient input. Note that nutrient retention in estuarine areas is not considered in our model. Thus, most nitrogen supplied from river mouths can easily be conveyed to the open ocean. Given that a recent modeling study estimated that approximately 75 % of riverine nitrogen globally escapes from shelf areas to the open ocean (Sharples et al., 2017), our results on the impact of riverine N on NPP should be viewed as an upper limit for the estimation.

Second, the effects of atmospheric N deposition on the surface nutrient concentration and NPP are evaluated by subtracting the zero-input scenario NO-NRD from the NO-NR experiment (Tables 1 and 2). Similar to riverine N input, atmospheric N deposition causes an increase in NPP in N-limited regions and a global increase in NO3 (Figs. 14b, 16a and c). According to deposition flux, significant changes in NPP are found in coastal areas and low-latitude regions of the Pacific Ocean. Global NPP increases by 0.3 PgC yr-1 (by 1 % in comparison with NO-NR), which is consistent with previous estimates (Duce et al., 2008; Moore et al., 2013).

Finally, changes in the surface nutrient concentration and NPP, driven by atmospheric Fe deposition, are calculated by subtracting the zero-input scenario NO-FD from the control experiment CTL-D (Tables 1 and 2). In contrast to N input, atmospheric Fe deposition causes an increase in NPP in Fe-limited regions and a decrease in N-limited regions (Figs. 15, 16a and d). A significant Fe increase is found in N-limited regions. Global NPP and export production increase by 1.8 and 0.8 PgC yr-1, respectively (by 6.7 % and 11 %, respectively, in comparison with NO-FD). These percentage increases are consistent with previous estimations by Moore et al. (2013). However, the sensitivity of export production to Fe deposition from dust is higher than reported by Tagliabue et al. (2014), who estimated that export production increases by 0.06–0.11 PgC yr-1. Therefore, it seems difficult to obtain robust sensitivity for both iron and the biological cycle to iron input because of the high uncertainty regarding the iron cycle among models. Although nitrogen input from both deposition and rivers has little effect on the spatial patterns of the distribution of nutrient limitation (Fig. 16a–c), iron input from the atmosphere changes the pattern in low-latitude regions from iron limitation to nitrogen limitation (Fig. 16a and d).

Here, we examine model sensitivity against global inputs of both N and Fe into the ocean through atmospheric deposition and river discharge in the preindustrial condition. We note, however, that these two types of nutrient input have increased significantly since the preindustrial era because of human activities (Duce et al., 2008; Seitzinger et al., 2010; Krishnamurthy et al., 2010). Additionally, ongoing nutrient input increase can lead to a future increase in biological production, which might partly negate the production decrease driven by global warming. Conversely, the resultant increase in the export of OM would accelerate CO2-induced ocean acidification and warming-induced deoxygenation in subsurface waters, which leads to major environmental pressures. Thus, the combined effects of global warming and anthropogenic nutrient input on ocean biogeochemical cycles should be explored in the future.

The coupling of land and ocean ecosystems via riverine nitrogen is one of the new features of MIROC-ES2L, and the potential impact of the process on ocean biogeochemistry has already been examined and discussed in Sect. 3.2.2. Here, we examine the response of river nitrogen loading itself against anthropogenic forcing by comparing the results of the CTL, HIST-NOLUC, and HIST simulations. As mentioned in Sect. 3.1.3, the global flux of riverine nitrogen input into the ocean is simulated at 17.5 TgN yr-1 in the CTL experiment (Table 4), and the flux is almost doubled in the 2000s at 33.9 TgN yr-1 in the HIST run. This number is larger than previous estimates of 19–25 TgN yr-1 for the present-day condition (Smith et al., 2003; Mayorga et al., 2010; Dumont et al., 2005). This overestimation might be caused by the inability of the model to simulate all forms of nitrogen in rivers. For example, the model simulates only the dissolved inorganic nitrogen (DIN) flux; thus, the expected nitrogen flux with non-DIN forms (e.g., dissolved organic and particulate matter) might be partly imposed on the DIN flux in the simulations. Indeed, the global total nitrogen flux, including DIN, dissolved organic nitrogen, and particulate nitrogen, is estimated at 37–66 TgN yr-1 (Beusen et al., 2016; Mayorga et al., 2010; Boyer et al., 2006; Seitzinger et al., 2005), which is closer to the result of MIROC-ES2L.

Another possible reason for the above overestimation is precipitation bias, which results in the overestimation of BNF on land. As mentioned in Sect. 3.1.1, the model has a positive precipitation bias on land in arid and desert regions (Supplement Fig. S6). As the scheme for the natural BNF flux employed in MIROC-ES2L is modeled to be controlled by the actual evapotranspiration rate (Cleveland et al., 1999), the precipitation bias in arid regions could easily lead to an overestimation of the BNF flux and an increase in riverine nitrogen loading. This is also evident when decomposing the global riverine flux into river basins and comparing the findings with a previous study by Dumont et al. (2005) (Fig. 17). MIROC-ES2L overestimates the DIN fluxes of large rivers such as the Amazon, Mississippi, and Yangtze rivers, even in the CTL experiment, in which all anthropogenic forcings are fixed at preindustrial levels. This suggests the necessity of improvement of the baseline flux of riverine nitrogen in the model. For more in-depth discussion, it will be necessary to explicitly simulate the organic and particulate nitrogen fluxes in rivers, and it might be necessary to simulate the explicit sedimentary and chemical reaction processes in freshwater and coastal zone systems.

In Fig. 17, the difference between the results of CTL and HIST-NOLUC mainly reflect the change induced by nitrogen deposition (and historical climate change) (Table 2), and the model demonstrates that deposition has increased N fluxes in many rivers. Additionally, the difference between HIST-NOLUC and HIST demonstrates the impact of LUC and agricultural management change (Table 2), and regions that have intensive agriculture within their watersheds (e.g., the basins of the Mississippi, Indus, Yellow, and Yangtze rivers) are simulated as strongly affected by the forcing change. The DIN discharge in each river is not always smaller in HIST-NOLUC than in HIST. This is because LAI in HIST-NOLUC is different to that in HIST, which is sometimes accompanied by a slight change in the surface climate via biophysical feedback. If the soil temperature is slightly warmer in HIST-NOLUC than in HIST, the soil mineralization rate in HIST-NOLUC should be accelerated, and thus the DIN loadings of rivers could be increased. This simulated trend in the historical period is qualitatively consistent with previous studies (Gruber and Galloway, 2008). Furthermore, the model simulates the global riverine flux to be increased by 16.4 TgN yr-1 in the historical period. This value is quantitatively consistent with previous estimates, e.g., 16 TgN yr-1 by Dumont et al. (2005) for DIN flux and 18 and 19 TgN yr-1 by Beusen et al. (2016) and by Green et al. (2004), respectively, for total N flux. Although bias exists in the magnitude of riverine nitrogen flux both globally and locally, we confirm that the model can qualitatively capture the changes in riverine nitrogen flux during the historical period.

Here, the model sensitivity of the global climate–carbon cycle against CO2 increase is analyzed by calculating TCR, AF, and TCRE from the results of the 1PPY, 1PPY-BGC, and 1PPY-RAD experiments (see Sect. 2.2.2 for the method). These quantities summarize the total performance of the climate, carbon cycle, and coupled climate–carbon cycle system in the models, which enables us to compare them with existing ESMs.

The TCR, AF, and TCRE derived from the 1PPY simulation are displayed in Table 5. The TCR of MIROC-ES2L is 1.5 K, which is lower than the multimodel mean of the CMIP5 ESMs but within the range of spread (1.8±0.5 K; Gillet et al., 2013). Compared with our previous ESM (i.e., MIROC-ESM; Watanabe et al., 2011), the TCR has decreased by 32 % because of the replacement of the physical core of the ESM from the MIROC3-based model to that of MIROC5 (Watanabe et al., 2010). The value of AF, which is a quantity that characterizes the carbon cycle response in an ESM but is dependent on TCR, was simulated at 0.61 in MIROC-ESM. This value is reduced to 0.52 in MIROC-ES2L; i.e., the new model has a stronger carbon sink than the previous version. The value of AF in the new model is of similar magnitude to the CMIP5 model average (0.53±0.06; Gillet et al., 2013). The lowered TCR and the moderate AF cause the new model to have moderate TCRE (1.3 K EgC-1), which is smaller than that of the CMIP5 model average (1.6±0.5 K EgC-1) by 19 %. Using TCRE, we can approximate the value of CE until the global temperature exceeds a specific mitigation target; CE for the 2 ∘C warming target should be approximately 1540 PgC for MIROC-ES2L, 910 PgC for MIROC-ESM, and 950–1820 PgC for the CMIP5 models.

To further explore why AF is lowered in MIROC-ES2L, the strengths of the carbon cycle feedbacks were analyzed using the 1PPY-BGC and 1PPY-RAD simulation results (Table 6), and the findings were compared with the CMIP5 ESMs (Arora et al., 2013). The strength of the CO2–carbon feedback (β) of land is simulated to be 0.52 PgC PgC-1, which is slightly higher than the CMIP5 model average (0.43±0.21 PgC PgC-1) and larger than that of MIROC-ESM by 48 %. The strength of oceanic CO2–carbon feedback in the CMIP5 ESMs displays less spread among the models (0.38±0.03 PgC PgC-1), and the result of MIROC-ES2L is within this spread (0.35 PgC PgC-1). The absolute magnitude of the climate–carbon feedback (γ) for land and ocean in MIROC-ES2L is -71 and -4.5 PgC K-1, respectively, both of which are less negative than the result of MIROC-ESM by 20 % for land and 63 % for ocean. Consequently, the land γ in MIROC-ES2L is within the range of the CMIP5 ESMs (-58±29 PgC K-1), while the ocean γ is slightly larger than the upper range of the CMIP5 ESMs (-7.8±2.9 PgC K-1).

As the quantities β and γ have different units, it is difficult to conclude which feedback process contributes most to the AF change. To compare them with the same unit, we used the quantity u proposed by Gregory et al. (2009). This quantity, which is defined as uβ=β and uγ=γ×T/CA (PgC PgC-1), can relate the carbon cycle feedback parameters to AF, as AF =1/(1+uβL+uβO+uγL+uγO) (see Appendix E for the derivation). When comparing the u quantities of MIROC-ES2L with the CMIP5 models (Fig. 18), it is evident that the ocean component of MIROC-ES2L is less sensitive than the previous model for both CO2–carbon and climate–carbon feedbacks. These two changes almost counteract each other; thus, the ocean component does not explain the reduced AF in the new model (Table 5). For land, the climate–carbon feedback (uγ) in MIROC-ES2L is intermediate, while MIROC-ESM was one of the most sensitive models of the CMIP5 ESMs. Additionally, the magnitude of the land CO2–carbon feedback (uβ) is increased from MIROC-ESM to MIROC-ES2L by 48 % (uβ=β). Therefore, the land component is the main cause of the lower AF, making the magnitude of both the CO2–carbon and the climate–carbon feedbacks more positive and less negative, respectively, i.e., strengthening the land carbon sink.