Notice: Wiley Online Library will be unavailable on Saturday 27th February from 09:00-14:00 GMT / 04:00-09:00 EST / 17:00-22:00 SGT for essential maintenance. Apologies for the inconvenience.
 We examined climate-carbon cycle feedback by performing a global warming experiment using MIROC-based coupled climate-carbon cycle model. The model showed that by the end of the 21st century, warming leads to a further increase in carbon dioxide (CO2) level of 123 ppm by volume (ppmv). This positive feedback can mostly be attributed to land-based soil-carbon dynamics. On a regional scale, Siberia experienced intense positive feedback, because the acceleration of microbial respiration due to warming causes a decrease in the soil carbon level. Amazonia also had positive feedback resulting from accelerated microbial respiration. On the other hand, some regions, such as western and central North America and South Australia, experienced negative feedback, because enhanced litterfall surpassed the increased respiration in soil carbon. The oceanic contribution to the feedback was much weaker than the land contribution on global scale, but the positive feedback in the northern North Atlantic was as strong as those in Amazonia and Siberia in our model. In the northern North Atlantic, the weakening of winter mixing caused a reduction of CO2 absorption at the surface. Moreover, weakening of the formation of North Atlantic Deep Water caused reduced CO2 subduction to the deep water. Understanding such regional-scale differences may help to explain disparities in coupled climate-carbon cycle model results.
If you can't find a tool you're looking for, please click the link at the top of the page to "Go to old article view". Alternatively, view our Knowledge Base articles for additional help. Your feedback is important to us, so please let us know if you have comments or ideas for improvement.
 Feedback mechanisms exist between climate change and the carbon cycle; climate change caused by anthropogenic carbon dioxide (CO2) emission may influence the carbon cycle, by significantly changing terrestrial and oceanic uptake of CO2 thereby changing the atmospheric CO2 concentration [Cox et al., 2000; Friedlingstein et al., 2001]. All model results of the international Coupled Carbon-Cycle Climate Model Inter-comparison Project (C4MIP) indicate that the response of the carbon cycle to climate change enhances warming, although there is a large uncertainty about the magnitude of the enhancement [Friedlingstein et al., 2006]. It is therefore desirable to model the carbon cycle and climate change simultaneously, including their interactions, for use in projecting future climate change. Indeed, recently global warming projections have been performed using coupled climate-carbon cycle models, and many studies have been conducted to identify the cause of the feedback [e.g., Cox et al., 2000; Dufresne et al., 2002; Friedlingstein et al., 2003; Zeng et al., 2004; Kawamiya et al., 2005; Friedlingstein et al., 2006].
 In most of the previous studies climate-carbon cycle feedback has been examined on a global scale. However, since the response of the carbon cycle to climate change varies regionally, understanding of the feedback in each region is critically important to grasp the origin of the climate-carbon cycle feedback on a global scale and to reduce uncertainties. Cox et al.  and Betts et al.  have discussed Amazonian feedback in great detail. They have suggested that while the major contribution to the increased CO2 arises from reductions in soil carbon, Amazonian forest dieback, although small in area, also contributes to global-scale climate-carbon cycle feedback. In regions other than Amazonia, the carbon cycle is also thought to make significant contributions to climate-carbon cycle feedback. For example, the feedback of Siberia can cause major positive feedback on a global scale, because Siberia is a huge reservoir of soil carbon [Post et al., 1982]. For the ocean, the feedback of the northern North Atlantic, a region of intense anthropogenic CO2 absorption and subduction [Sabine et al., 2004], is also supposed to cause positive feedback, because deep circulation is likely to slow down as a result of warming [IPCC, 2001; Gregory et al., 2005]. In the present study, we examine more generally the geographical distribution of climate-carbon cycle feedback both on land and in the ocean and discuss the feedback mechanism with different characteristics in selected regions by using a coupled carbon cycle model.
 The next section describes our coupled climate-carbon cycle model and experimental methods. In section 3, the geographical distribution of climate-carbon cycle feedback is shown, and factors contributing to the feedback in each region are discussed. In section 4, the results of this study are summarized.
2. Description of the Model and Experiment
 The coupled climate-carbon cycle model used in the present study has been developed on the Earth Simulator as a part of the Japan Model Mission of the Kyousei-2 Project [Kawamiya et al., 2005]. Early result was submitted to the C4MIP under the name of “FRCGC” [Friedlingstein et al., 2006] and has been included in the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) [IPCC, 2007]. To develop the model, we coupled the existing biogeochemical and ecological process submodels with the already working physical climate model MIROC described later.
 In the terrestrial carbon-cycle component model, Sim-CYCLE, originally developed by Ito and Oikawa , carbon storage is divided into five compartments: leaves, stems, roots, litter or dead biota, and soil organic matter. Processes representing flow among carbon pools, including exchanges among the atmosphere, the vegetation, and the soil, are included. The biota is classified into 20 plant function types, and their geographical distributions are fixed; thus, changes in vegetation types caused by climate change are not represented. In previous models [Kawamiya et al., 2005], the initialized value for carbon storage on land was larger than that in typical simulations [Prentice et al., 1993; François et al., 1998] but was still within the range of uncertainty suggested by an observation-based study [Adams and Faure, 1998]. In the present study, parameters of the terrestrial carbon-cycle component have been tuned so that the initialized state of land carbon storage is closer to typical values in many simulation studies [IPCC, 2001]. This model was used in offline calculations of the response of terrestrial carbon storage to some projected future climate changes [Ito, 2005a, 2005b].
 Ocean ecological and biogeochemical processes are represented by a four-compartment model consisting of nutrients, phytoplankton, zooplankton, and detritus [Oschlies and Garçon, 1999; Oschlies, 2001] as the ecosystem-process model. In addition, a series of inorganic carbon reactions were introduced in the form recommended by the Ocean Carbon Cycle Model Intercomparison Project (OCMIP) [Orr et al., 1999].
 The physical climate-system model in which these carbon-cycle components were embedded is a medium-resolution version of the Model for Interdisciplinary Research on Climate (MIROC), developed jointly by the Center for Climate System Research (CCSR) of the University of Tokyo, the National Institute for Environmental Studies (NIES), and the Frontier Research Center for Global Change (FRCGC) of Japan Agency for Marine-Earth Science and Technology (JAMSTEC). The atmospheric model has a horizontal resolution of T42, approximately equivalent to a 2.8° grid size with 20 vertical levels. The ocean model has a zonal resolution of 1.4° and a spatially varying meridional resolution that is about 0.56° at latitudes lower than 8° and 1.4° at latitudes higher than 65° and changes smoothly in between. The model has 44 vertical layers, including a bottom boundary layer. No flux adjustment was applied for the coupling. Further details of the coupled model are provided in a dedicated report [K-1 Model Developers, 2004].
 An experiment was carried out to examine the positive feedback between global warming and the carbon cycle found in previous studies [Cox et al., 2000; Friedlingstein et al., 2001]. The offline spin-up run was conducted by only running the Sim-CYCLE for 1000 years under steady preindustrial climate conditions to create the initial data of terrestrial carbon pools. Then, the online spin-up was conducted by running the integrated model for 250 years, starting with the initial conditions based on climatologic data sets. (Specifically, the results of MIROC spin-up were provided for the physical climate system by the K-1 Model Developers , the results of Sim-CYCLE offline spin-up were provided for the terrestrial carbon cycle, the data of the Global Ocean Data Analysis Project [GLODAP] were provided for the marine CO2 system, and the data of the World Ocean Atlas 1998 [WOA98] were provided for the marine ecosystem model.) As a result, an equilibrium state was reached such that the net CO2 fluxes on land and sea surfaces were near zero (Terrestrial drift: +0.1 PgC year−1; Marine drift: −0.2 PgC year−1). The resultant initial states of ocean carbon (35,390 PgC), vegetation carbon (762 PgC), soil carbon (1579 PgC), and terrestrial net primary production (NPP) (63 PgC year−1) and ocean primary productivity (27 PgC year−1) are comparable with observations and other estimates [Melillo et al., 1995; Antoine et al., 1996; IPCC, 2007]. Three different runs for the period from 1850 to 2100 were performed after the spin-up: the control run, in which the atmospheric CO2 concentration was fixed at 285 ppmv throughout the entire integration period; and the coupled and uncoupled runs having the same format as used for C4MIP [Friedlingstein et al., 2006], in which the observed anthropogenic fossil fuel emission was given for 1850–1999 [Marland et al., 2005] and the A2 Scenario of the Special Report on Emissions Scenarios (SRES A2) was given for 2000–2100 [IPCC, 1992]. Atmospheric CO2 concentration was allowed to vary as calculated by the carbon-cycle components in both runs. In the coupled run, the changing CO2 concentration was used for the radiation module, so that climate change occurred. In the uncoupled run, in contrast, the fixed value of 285 ppmv was used for radiation routines, so that the changing CO2 concentration had no effect on climate.
3. Results and Discussion
3.1. Climate-Carbon Cycle Feedback
Figure 1 shows model results of atmospheric CO2 concentration (Figure 1a), global mean surface air temperature (Figure 1b), and total CO2 uptake by land and ocean, along with CO2 emissions from 1850 to 2100 (Figure 1c). In the coupled run (thick line), in response to anthropogenic CO2 emission (thick dashed line), the CO2 concentration increases and the temperature rises, while in the uncoupled run (thin line), the CO2 concentration increases but the temperature remains constant. This is because climate interacts with the carbon cycle in the coupled run but does not in the uncoupled run. The difference in CO2 concentrations between the coupled and uncoupled runs represents the response of the carbon cycle to climate change.
 The atmospheric CO2 concentration reaches 382 ppmv by the end of the 20th century (Figure 1a), and the temperature rises by 0.4°C from 1850 to 2000 (Figure 1b) in the coupled run. These results for global warming and CO2 increase are similar to the present-day observed levels: 375 ppmv for the atmospheric CO2 and 0.6°C for temperature rise. In the future projection run the atmospheric CO2 concentration at the year 2100 is 123 ppmv higher in the coupled run than in the uncoupled run (Figure 1a), indicating that climate change leads to reduced total CO2 uptake by land and ocean (Figure 1c) and to further increases in atmospheric CO2 concentration. The magnitude of further warming induced by the CO2 increase is estimated to be 0.7°C in the total warming of 4.6°C at 2100, by multiplying 123 ppmv by the rate of temperature increase per unit of CO2 concentration increase (i.e., α = 0.0059 K ppmv−1; Table 1). Thus, the effect of global warming on the carbon cycle is to increase atmospheric CO2; in other words, there is positive feedback for global warming. The resultant increase of positive feedback due to climate-carbon cycle interactions is 123 ppmv at the year 2100 in our model, whereas other models show a variety of feedback intensities i.e., 20–250 ppmv, according to C4MIP models [Friedlingstein et al., 2006].
Table 1. Carbon Cycle Gain, g, Along With Component Sensitivities of Climate to CO2 (α), Land and Ocean Carbon Storage to CO2 (βL, βO), and Land and Ocean Carbon Storage to Climate (γL, γO)a
α (K ppm−1)
βL (GtC ppm−1)
βO (GtC ppm−1)
γL (GtC K−1)
γO (GtC K−1)
Calculations are done for 2100.
C4MIP models average
 A method of analysis has been devised to facilitate comparison among different models [Friedlingstein et al., 2003] by breaking down the climate-carbon cycle feedback into elements: the climate sensitivity to atmospheric CO2 (α) and the sensitivities of land and ocean carbon storage to atmospheric CO2 (βL and βO, respectively) and land and ocean carbon storage to temperature change (γL and γO, respectively). The method has been applied to results of the Hadley Centre model [Cox et al., 2000], the IPSL model [Dufresne et al., 2002], and the C4MIP models [Friedlingstein et al., 2006]. Results for the present model and from other experiments are listed in Table 1.
 The gain factor (g), which shows the relative increase in atmospheric CO2 concentration due to the climate-carbon cycle feedback, was estimated to be 0.16 in our model, similar to the g-value of 0.17 in the IPSL model and the average g for the 11 C4MIP models (0.15) but much weaker than the g-value 0.41 of the Hadley Centre model. The sensitivity of carbon storage to temperature (γ) in our model is much larger for land than in the ocean, as in the other models, i.e., the positive feedback can be attributed mainly to the land. The sensitivity of land carbon storage to temperature (γL) in our model, −71, is less than half of that of the Hadley Centre model (−201) but is close to the average of the C4MIP models (−79) and the −90 of the IPSL model. As pointed out in a previous report [Dufresne et al., 2002], possible reasons for the reduced sensitivity in our model relative to the Hadley Centre model are that in our model the increased CO2 level induces only slightly larger increase in carbon storage in the soil than in vegetation thus preventing large increase of CO2 emission from the soil due to warming. Moreover, processes leading to the Amazonian forest dieback suggested by Cox et al.  and Betts et al.  cannot be precisely duplicated here due to the lack of representation of vegetation dynamics in our model.
3.2. Terrestrial Carbon-Cycle Response
Figure 2 shows model calculations of the flux due to CO2 uptake by land (Figure 2a) together with the carbon storages by vegetation (Figure 2b) and soil (Figure 2c), which represent the accumulated amount of CO2 uptake, from 1850 for both of the coupled and uncoupled cases shown by thick and thin solid lines, respectively. The land CO2 uptake flux in the coupled run is 1.5 PgC year−1 in the 1980s and 1.2 PgC year−1 in the 1990s (Figure 2a); these values are within the range of observations and other estimates summarized by the IPCC , namely −0.2 ∼ 3.4 PgC year−1 for the 1980s and 0.9 ∼ 4.3 PgC year−1 for the 1990s. The interannual variability of land CO2 uptake is ±3 PgC year−1 between the extremes. The calculations indicate that CO2 uptake by land is reduced as a result of climate change after around 2050 (Figure 2a). By the end of the 21st century, climate change feedback causes a 31 PgC increase in vegetation carbon level (Figure 2b) and a 277 PgC decrease in soil carbon level (Figure 2c), leading to a net reduction of 246 PgC in accumulated CO2 uptake by land (Table 2). The decrease in the amount of CO2 taken up by land is 93% of the total decrease in the CO2 uptake by land and ocean (265 PgC). The positive feedback in our model is mainly attributable to the land. Incidentally, the percentage of land CO2 uptake is relatively higher than that expected from the ratio between terrestrial and marine sensitivities of carbon storage to temperature (γL = −71 GtC K−1 and γO = −29 GtC K−1, respectively, in Table 1). These sensitivities are represented by:
where ΔCarbonL, ΔCarbonO, ΔCO2, and ΔTemp are the differences between coupled and uncoupled runs in land (−246 PgC) and ocean (−20 PgC) carbon storages, the atmospheric CO2 concentration (123 ppmv), and temperature (4.6°C) at the year 2100, respectively, and βL and βO are the sensitivities of land (0.8 GtC ppmv−1) and ocean (0.9 GtC ppmv−1) carbon storage to the atmospheric CO2 shown in Table 1. The second terms of the numerators represent the additional carbon to the land and ocean carbon storages induced by the increase of CO2 level due to positive feedback (land: 98 PgC; ocean: 110 PgC). Thus, while the additional carbon to the land carbon storage is much smaller than the loss in existing land carbon (numerator of equation 1, 344 PgC), the additional carbon to the ocean carbon storage is almost equal to the loss in existing ocean carbon (130 PgC). Therefore, the total carbon loss is mostly by land rather than by the ocean.
Table 2. Difference in Mean Land Carbon Storage Between Coupled and Uncoupled Run by the End of the 21st Century for Each Box of Figure 3
C. N. America
W. N. America
Δ Accumulated land CO2 uptake (PgC)
ΔVegetation carbon storage (PgC)
ΔSoil carbon storage (PgC)
Figure 3 shows geographical distributions of differences in accumulated land CO2 uptake (Figure 3a), vegetation carbon storage (Figure 3b), and soil carbon storage (Figure 3c) between the coupled and uncoupled runs in the 2090s. The difference in accumulated land CO2 uptake is equal to the difference in land carbon storage (i.e., the sum of the differences in the vegetation carbon storage and soil carbon storages). In most regions a slight increase in vegetation carbon storage is seen which is primarily a result of extended growing season in the boreal regions due to warming and enhancement of photosynthesis due to CO2 increase, the fertilization effort (Figure 3b). A large decrease in soil carbon storage is also seen, primarily as a result of enhanced microbial respiration due to warming (Figure 3c). Thus, reduction in accumulated land CO2 uptake, or positive feedback, is obtained in most of the land regions (Figure 3a). On the other hand, in some regions (western and central North America and South Australia) enhanced land CO2 uptake, or negative feedback is found. These regions exhibit an increase or a small decrease in soil carbon storage (Figure 3c). The similarity between distributions of accumulated land CO2 uptake and soil carbon storage suggests that terrestrial feedback is mainly determined by soil carbon dynamics on regional scale.
 To investigate the mechanism of feedback between climate change and carbon cycle on regional scale, we chose six distinct regions, indicated by boxes in Figure 3, which are representative of various regions with different characteristics, such as northern North America, central Africa, and India. Figure 4 shows area-averaged differences in land carbon storage (Figure 4a) and accumulated carbon fluxes (Figure 4b) between the coupled and uncoupled runs in the 2090s for each region. Table 2 lists area-integrated differences in land carbon storage between the coupled and uncoupled runs by the end of the 21st century in each region for estimation of the relative role of each region in the global feedback. Table 3 lists characteristics of the background environment for each region for examination of factors of the response of the terrestrial carbon cycle to climate change; differences in the values of temperature functions for maintenance respiration (ARM) and soil respiration (HR) between the coupled and uncoupled runs for each region are also listed. ARM and HR are calculated from the following equations:
where SARM and SHR are specific respiration rates, WP is plant biomass, WS is soil organic carbon, and FHR(WA) and FHR(EA) are functions that depend on soil moisture and soil air space, respectively. In addition, FARM(TG) and FHR(TS) represent the temperature dependences of for maintenance respiration and microbial respiration, given as
where TG and TS are ground temperature and soil temperature, respectively [Ito and Oikawa, 2002]. The increases of temperature-dependent functions are not always large in regions where large temperature increases are calculated, if the base temperatures are low because of the functional forms. Therefore, we compared the temperature-dependent functions among regions to investigate the effect of temperature on respiration.
Table 3. Mean Land Surface Temperature, Mean Soil Temperature, and Soil Carbon Storage in 1990s, and Differences in Mean Land Surface Temperature, Temperature Functions for Respiration Equations Between Coupled and Uncoupled Run in 2090s for Each Box in Figure 3
C. N. America
W. N. America
Land surface temperature in 1990s (°C)
Soil temperature in 1990s (°C)
Soil carbon storage in 1990s (kgC m−2)
Δ Land surface temperature (°C)
Δ Temp. coefficient function for maintenance respiration
Δ Temp. coefficient function for microbial respiration
 Siberia shows intense positive feedback (a reduction of 3.1 kgC m−2 in accumulated land CO2 uptake) and a significant decrease in soil carbon (decrease of 4.0 kgC m−2; Figure 4a). Litterfall is also enhanced (an increase of 4.2 kgC m−2), but microbial respiration is enhanced even more (an increase of 8.6 kgC m−2) (Figure 4b). The microbial respiration is affected mainly by soil temperature conditions and amounts of soil organic carbon. In Siberia, land surface temperature rises by 7.7°C by the 2090s, but background soil-surface temperature is very low, −6.9°C (Table 3). Therefore, the increase of temperature-dependent function for the microbial respiration rate (0.38) is not so large. However, the soil carbon storage volume, 33.2 kgC m−2, is very large (Table 3). Thus, microbial respiration increases, leading to a significant decrease in soil carbon level and the intense positive feedback in Siberia. The reduction of 3.1 kgC m−2 in accumulated land CO2 uptake in Siberia is 15% of the global reduction (Table 2). The carbon cycle in Siberia makes a significant contribution to the climate-carbon cycle feedback in our model.
 Amazonia also exhibits positive feedback (reduction of 2.2 kgC m−2 in accumulated land CO2 uptake) because of a large decrease in soil carbon, 2.9 kgC m−2 (Figure 4). As in Siberia, microbial respiration is more enhanced than litterfall (microbial respiration: increase of 5.0 kgC m−2; litterfall: increase of 1.7 kgC m−2). In Amazonia, land surface temperature rises by 4.7°C by the 2090s and background soil temperature is high, 24.9°C (Table 3). Therefore, the increase of temperature coefficient function for microbial respiration is quite high, 0.97, while soil carbon storage has a moderate value of 14.4 kgC m−2 (Table 3). As a result, microbial respiration significantly accelerates and leads to a large decrease in soil carbon and the positive feedback in Amazonia. The decreased CO2 uptake by Amazonia is 4% of the global reduction (Table 2). While Cox et al.  suggested that Amazonian forest dieback occurs in the Hadley Centre model due to global warming, carbon storage in vegetation increased by 0.7 kgC m−2 in our model. Although the model does not simulate vegetation dynamics, the simulated increase of carbon storage suggests that the warming and drying of Amazonia in our model are weaker than in the Hadley Centre model. In the Hadley Centre model, Amazonian surface air temperature and precipitation are 310.6 K and 1.7 mm day−1 in the 2090s, respectively. In contrast, air temperature and precipitation in our model are 302.0 K and 3.8 mm day−1; this environmental condition is close to that of the Hadley Centre model, in the 2030s, that is, before Amazonian forest dieback begins.
 The Sahel also shows intense positive feedback (a reduction of 4.2 kgC m−2 in accumulated land CO2 uptake), with decrease in vegetation carbon volume (−1.1 kgC m−2) and soil carbon (−3.0 kgC m−2; Figure 4). Soil carbon decreases because litterfall decreases by 7.3 kgC m−2 but accumulated amount of microbial respiration decreases by 4.0 kgC m−2, unlike the increases in Siberia and Amazonia (Figure 4). The reduced microbial respiration is attributed to the reduction in background soil carbon storage (Figure 4a). The reduced litterfall is attributed to a decline of 12.1 kgC m−2 in gross primary production (GPP). Because climate change induces an increase in soil moisture due to the enhanced rainfall around this region, water stress is not the reason for the reduction of GPP as generally seen. The optimal temperature for photosynthesis of C4 plants does not increase with increasing CO2 concentration [Ito and Oikawa, 2002]. Therefore, temperatures in low latitudes, where the fractional land coverage by C4 plants is high, exceed the optimal value for photosynthesis by warming. Consequently, GPP, vegetation carbon storage, soil carbon storage, and microbial respiration are all reduced. The decrease of CO2 uptake in the Sahel amounts to 13% of the global reduction (Table 2). The carbon cycle in the Sahel also contributes significantly to the climate-carbon cycle feedback in our model, through a totally different mechanism from those in Siberia or Amazonia.
 Western and central North America and South Australia show negative feedback (enhancement of about 0.9 kgC m−2 in accumulated land CO2 uptake), with an increase in vegetation carbon of about 0.9 kgC m−2 and a slight increase or no change in soil carbon storage (Figure 4a). Unlike in Siberia and Amazonia, litterfall is enhanced more than, or as much as, microbial respiration (litterfall: increase of about 7.3 kgC m−2; microbial respiration: increase of about 7.5 kgC m−2; Figure 4b). In western and central North America and South Australia, GPP significantly increases, by about 18.0 kgC m−2. In addition, the temperature function for maintenance respiration only slightly increases, by 0.26, because background temperature is relatively low, 8.2°C, although temperature rises by about 5°C (Table 3). As a result, the annual litterfall, which should be equal to annual NPP in an equilibrium state, is accelerated by climate change and leads to the slight increase or no change in soil carbon and the negative feedback.
3.3. Marine Carbon-Cycle Response
Figure 5 shows model results of oceanic CO2 uptake and dissolved inorganic carbon storage from 1850 to 2100. The oceanic CO2 uptake in the coupled run is 1.8 PgC year−1 in the 1980s and 2.2 PgC year−1 in the 1990s (Figure 5a); these values are within the range of observations and other estimates summarized by the IPCC  (1980s: 1.8 ± 0.8 PgC year−1, 1990s: 2.2 ± 0.4 PgC year−1). The interannual variability of oceanic CO2 uptake (±0.3 PgC year−1 between the extremes) is much smaller than that of land (±3 PgC year−1 between the extremes), as discussed by the IPCC . Like the land CO2 uptake, the oceanic CO2 uptake is also reduced by climate change (Figure 5a). At the end of the 21st century, the warming brings about a reduction of dissolved inorganic carbon level of 20 PgC (Figure 5b). The reduction is less for the ocean (20 PgC) than for land (246 PgC).
 Marine CO2 flux is calculated from the difference between atmospheric and oceanic fugacity of carbon dioxide (fCO2) and coefficient functions. Factors affecting fCO2 are temperature (T), salinity (S), total carbonic acid (TCO2), and alkalinity (Alk) of surface water. To evaluate the effect of these factors on the changes in ocean CO2 uptake due to climate change, we divided the change in fCO2 into the changes effected by these four factors. fCO2 is represented by:
where F is a function describing the relation between fCO2 and the four factors [Millero, 1995]. The response of fCO2 to climate change is expressed by the following equation:
The first term on the right side of the equation is evaluated in the following equation:
where subscripts c and u denote coupled and uncoupled runs, respectively. The other terms are evaluated in the same manner. The changes in global mean fCO2 as affected by changes in each factor (ΔT, ΔS, ΔTCO2, and ΔAlk) attributable to climate change until the 2090s are shown in Figure 6. The rise of oceanic surface temperature is the largest factor affecting the increase of fCO2 and the decrease of ocean CO2 flux. The second-largest positive contribution comes from alkalinity, but the negative contribution of TCO2 is nearly as large. In our model, the surface distributions of differences in alkalinity and TCO2 between the coupled and uncoupled runs are very similar to the distribution of surface salinity differences, suggesting that changes in alkalinity and TCO2 are determined by the change in surface water budget in our model. When the values for alkalinity and TCO2 change equally, the change in partial pressure of CO2 by the change in alkalinity almost cancels out that by the change in TCO2. Therefore, we consider the positive feedback found in the ocean to be primarily caused by the effect of temperature on the CO2 system at the ocean surface.
Figure 7 shows the spatial distribution of differences of accumulated oceanic CO2 uptake in the 2090s between coupled and uncoupled runs. Most of the oceanic regions show reductions in accumulated oceanic CO2 uptake, or positive feedback, mostly as a result of the rise in sea surface temperature, as discussed above. In particular, a positive feedback in the northern North Atlantic is strong. The feedback intensity expressed as the difference between coupled and uncoupled runs is more than 2 kgC m−2 and comparable to the feedback intensities due to land of Siberia, Amazonia, and the Sahel in our model. The reduction in CO2 uptake by the northern North Atlantic is 4% of the global reduction. On the other hand, the Barents Sea shows enhancement of accumulated oceanic CO2 uptake, or negative feedback. Sea ice completely disappears from this region by 2100. Therefore, gas exchange is enhanced by longer exposure resulting in intense negative feedback in the Barents Sea. The Southern Ocean also shows enhancements in accumulated oceanic CO2 uptake, or negative feedback. Friedlingstein et al.  suggested that the difference between the IPSL and Hadley models is greatest in the Southern Ocean and that the strength of CO2 uptake in the Southern Ocean is a key process for the difference in feedback between the two models. In our model, CO2 uptake in a high atmospheric CO2 concentration is not conspicuously large in the Southern Ocean, which is also the case for the Hadley model while not for the IPSL model. This is one of the reasons why the sensitivity of ocean carbon storage to atmospheric CO2 (βO) in our model is much smaller than that for the IPSL model and similar to that for the Hadley model. However, in our model, deep convection prevents a rise in the sea surface temperature (SST) in this region. Thus, there is no effect of temperature on the surface CO2 system or the mixed layer depth in this region. Therefore, in our model, CO2 uptake is not reduced but rather is enhanced by the effect of the CO2 increase arising from positive feedback on land. Moreover, the equatorial divergence and convergence zones show remarkable negative and positive feedbacks, respectively, the results of weakening of the equatorial upwelling system caused by stratification due to surface warming.
 The mechanism of the intense positive feedback in the northern North Atlantic is explored in Figure 8, which shows the distributions of differences in factors affecting the change in CO2 absorption between coupled and uncoupled runs in the 2090s. CO2 uptake is reduced by more than 2.0 kgC m−2 near the coast of Greenland, where the North Atlantic Deep Water (NADW) is being formed (Figure 8a). The rise in SST is smaller in this region than in the other regions because of deep convection; in the subduction area in particular, SST does not rise (Figure 8c). On the other hand, the mixed layer depth in winter becomes much shallower in this region by the reduction of salinity and the slight rise of temperature (Figures 8a, 8b, and 8d). Thus, the reduction of CO2 uptake is largely due to the weakening of winter mixing than a direct result of the effect of temperature on the surface CO2 system in this region.
 The northern North Atlantic is a region of strong CO2 absorption and also a region of subduction. Then the absorbed excess CO2 is subducted around the northern North Atlantic and is transported to the ocean interior by deep circulation. In our study, the anthropogenic CO2 level in the seawater was estimated as the difference of TCO2 from the corresponding value in the control run with the fixed atmospheric CO2, 285 ppmv. The estimate of the anthropogenic CO2 distribution accumulated until 1994 from our model and the observation-based estimate of Sabine et al.  are in overall agreement [Kawamiya et al., 2005]. The estimated total amount of anthropogenic CO2 in the global ocean accumulated until 1994 (94 PgC) is slightly below the observed range of 118 ± 19 PgC [Sabine et al., 2004], but Matsumoto and Gruber  suggested a bias of +7% in the estimation by Sabine et al.  drawn from the ΔC*-derived global inventory of anthropogenic CO2. Figure 9 shows distributions of vertically integrated anthropogenic CO2 in the ocean until the 2090s from the coupled (Figure 9a) and uncoupled (Figure 9b) runs, as well as the difference between these runs (Figure 9c). The total amount of anthropogenic CO2 accumulated until the end of the 21st century are 580 PgC in the coupled run and 600 PgC in the uncoupled run. In both the coupled and uncoupled runs, it is apparent that the northern North Atlantic is capable of carrying much CO2 (Figures 9a and 9b). The anthropogenic CO2 accumulated in the northern North Atlantic region in the coupled run is much less than that in the uncoupled run (Figure 9c). That is, CO2 subduction in the northern North Atlantic is reduced by climate change.
Figure 10 shows meridional-vertical distributions of zonally averaged anthropogenic CO2 concentration in the Atlantic Ocean until the 2090s from the coupled (Figure 10a) and uncoupled (Figure 10b) runs, and the difference between these runs (Figure 10c). The anthropogenic CO2 accumulated around the northern North Atlantic in the coupled run is much less than that in the uncoupled run, both above and below the mixed layer depth in winter (Figures 10a, 10b, and 10c). The reduction in anthropogenic accumulated CO2 in surface water is caused by the weakening of winter mixing, as mentioned above, but the reduction in the deeper water is a result of the weakening of the North Atlantic deep circulation. In our model, the North Atlantic deep circulation weakens by about 6 Sverdrup (Sv) as a result of changes in global heat flux [Gregory et al., 2005]. The anthropogenic CO2 accumulated in the ocean is reduced mainly after the decrease in CO2 subduction in the northern North Atlantic, which is in turn caused by the weakening of NADW formation.
 To examine climate-carbon cycle feedback, we developed a coupled climate-carbon cycle model and carried out a global warming experiment. In our model, climate change leads to reduced CO2 uptake by land and ocean and consequently a further increase in CO2 of 123 ppmv, which may result in warming by 0.7°C, by the end of the 21st century. The intensity of this positive feedback is the middle of the C4MIP range (20–250 ppmv) [Friedlingstein et al., 2006], and the feedback is mainly attributed to land.
 Most land regions show a slight increase in vegetation carbon storage and a large decrease in soil carbon storage and, as a result, a reduction in accumulated land CO2 uptake, or positive feedback. According to regional-scale investigations, Siberia is a region with intense positive feedback, where, because of the low background temperature, the effect of temperature rises on microbial respiration is not so large, but soil carbon volume is very high. Therefore, the acceleration of microbial respiration leads to a significant decrease in soil carbon level, and an intense positive feedback in Siberia. Amazonia also shows a positive feedback resulting from the large acceleration of microbial respiration due to the temperature rise with high background temperature. The Sahel also shows an intense positive feedback resulting from a decrease in vegetation carbon storage in addition to a decrease in soil carbon. Since fractionation of the areas with C4 plants is high in this region, the temperature becomes above the optimal value for photosynthesis as a result of warming. Therefore GPP, vegetation carbon storage, and soil carbon storage are reduced, resulting in an intense positive feedback in the Sahel region. On the other hand, some regions such as western and central North America and South Australia exhibit negative feedback. Contrary to the situation for Siberia, Amazonia, and the Sahel, enhancement of litterfall leads to a slight increase or no net change in soil carbon irrespective of enhancement of microbial activity and thus negative feedback. Thus, the terrestrial feedback is mainly determined by soil carbon dynamics in our model. In this study, the model did not simulate vegetation dynamics. Cramer et al.  suggested that changes in vegetation structure influence the magnitude and spatial pattern of the carbon balance. Therefore, the distribution of positive/negative feedback may also change when vegetation dynamics is considered.
 Most ocean regions show a reduction in accumulated oceanic CO2 uptake, or positive feedback. Breakdown of the change in fCO2 into the changes effected by four factors suggests that the positive feedback is caused mainly by the effect of temperature dependence of the CO2 solubility at the ocean surface. The contribution of alkalinity is secondary but is almost canceled out by that of TCO2. In our model, alkalinity and TCO2 fluctuate synchronously and are affected by changes in the surface fresh water budget. According to our regional-scale analysis, positive feedback is especially strong in the northern North Atlantic ocean, where the feedback intensity is similar to that of Amazonia in our model. In the northern North Atlantic, the reduction in surface CO2 absorption is largely due to the weakening of winter mixing than the temperature effect on the CO2 system. Moreover, CO2 subduction in the northern North Atlantic is also reduced, as a result of a decline in CO2 transport into the deep layers by the NADW after its formation is weakened by ocean dynamical process [IPCC, 2001; Gregory et al., 2005].
 The mechanisms by which carbon cycles changes by climate change differ among regions. An understanding of such regional-scale differences helps in the understanding of differences among the C4MIP models. For example, our results suggest that the carbon cycles in Siberia and the Sahel make significant contributions (more than 13% of the total) to climate-carbon cycle feedback. Improvements focused on these regions are expected to help reduce spreads of climate-carbon cycle projection. More importantly model analysis of the changes of regional carbon cycle caused by climate change with different characteristics (different processes) as reported in this study may give a clue of validation of models by careful comparison with actually occurring changes. If such comparisons give clear and robust answers to the validity of some of the modeled processes they would give firm basis for the future projection.
 The authors would like to thank the members of the Kyousei-1 Project (principal investigator, A. Sumi), who kindly provided their climate model for extension in the Kyousei-2 project. S. Emori and A. Ito helped to incorporate Sim-CYCLE into our atmospheric general circulation model. M. Aita-Noguchi helped to install the carbon-cycle component in our ocean general circulation model. This study was conducted as a part of the Japan Model Mission of the Kyousei-2 Project. The computational calculation was carried out with the Earth Simulator of Japan Agency for Marine-Earth Science and Technology.