Distribution of pump components from observational data
Figure 1 shows the horizontally averaged vertical distributions of each ocean carbon pump component. In Fig. 2, the vertical sections of ΔCorg, ΔCcaco3, ΔCgas, and ΔCfw along the track transecting the Atlantic, Southern, and Pacific Oceans are also displayed. Figure 1a and b suggest that ΔCorg (red line) and ΔAcaco3 (green line) are the most significant contributors to the deviation from the globally averaged values of DIC and ALK, respectively. The distribution of ΔCorg is determined solely from P (Fig. 2b), where the organic matter pump causes depletion at the surface and enrichment in the deep ocean (red line in Fig. 1a). At the same time, this pump causes surface enrichment of ΔAorg and its depletion in deeper water (red line in Fig. 1b). The distribution of ΔAcaco3 is similar to that of ALK (Fig. 2c); its enrichment occurs at greater depths than that of ΔAorg because of the different dissolution profiles between organic matter and calcium carbonate (Yamanaka and Tajika 1996; Oka et al. 2008; Kwon et al. 2009). The distribution of ΔCgas is determined as a result of both the air–sea gas exchange of CO2 at the surface and the ocean transport within the ocean (Fig. 2d). Figure 1a shows that ΔCgas is negative at the shallower depth and positive in the deeper ocean (purple line). Considering there is no source/sink term of ΔCgas within the ocean (i.e., Sgas is zero except at the surface), the enrichment of ΔCgas in the deep ocean can be explained only by the transport of positive ΔCgas from the ocean surface to the deep ocean. Figure 2d indicates that ΔCgas becomes positive mainly in the North Atlantic Ocean, whereas negative values are found in most of the Southern Ocean. This suggests that positive value of Cgas in the deep ocean is supplied from deep-water formation area in the North Atlantic Ocean. Figure 2e confirms that the distribution of ΔCfw becomes the same as that of salinity and the vertical profiles of ΔCfw and ΔAfw are also the same as that of salinity (blue line in Fig. 1a, b).
In our decomposition, Corg, ΔCcaco3ΔCgas, and ΔCfw were defined by the deviation from “globally averaged value” rather than “surface value” as seen in Eq. (1). Alternatively, previous decompositions usually referred “surface value” as a base value; the decomposition was usually defined from the deviation from the surface value. This traditional carbon pump decomposition is also demonstrated in Fig. 1c, d. The previous decomposition clearly demonstrates the enrichment of DIC and ALK in the deep ocean by the organic and alkalinity pumps, respectively. This decomposition is useful for focusing on the enrichment in the deep ocean but not directly used for evaluating the surface depletion of DIC which is important for controlling the oceanic pCO2. Contrary to previous decomposition, our decomposition can explicitly evaluate the surface depletion of DIC which will be discussed in detail below.
The surface distributions of ΔCorg, ΔCcaco3, ΔCgas, and ΔCfw are shown in Fig. 3a–d, respectively. Figure 3a and b indicate negative values for ΔCorg and ΔCcaco3 over the entire surface ocean. Note that each carbon pump component is defined such that its globally averaged value becomes zero; in the deeper ocean, they are positive, as seen in Fig. 1. Figure 3c shows that ΔCgas is negative over almost the entire surface, whereas it is positive in the deeper ocean (Fig. 1a). As discussed above, the positive value in the deep ocean appears to be transported from the deep-water formation area in the northern North Atlantic Ocean (Fig. 2d). Therefore, although the observational data of ΔCgas is missing over the Arctic Ocean and the northern North Atlantic Ocean, Cgas is expected to be positive in these regions (this is indeed supported from the results of CMIP5 ESM simulations). From Fig. 3d, it can be confirmed that the surface distribution of ΔCfw mirrors the pattern of sea surface salinity (SSS) as a matter of course. Although not shown here, the surface distribution of ΔAorg, ΔAcaco3, ΔAfw, and ΔAgas can also be discussed in the same manner.
Effects of ocean carbon pumps on oceanic pCO2
In the case where the surface ocean and atmosphere are in equilibrium, atmospheric pCO2 becomes very close to oceanic pCO2. The processes related to gas exchange between the atmosphere and ocean are faster than the other biogeochemical processes within the ocean, and oceanic pCO2 can be regarded as being in equilibrium with atmospheric pCO2 when focusing on the climatological state of the ocean carbon cycle. Oceanic pCO2 depends on DIC and ALK, and here, we try to evaluate how oceanic pCO2 is affected by the individual ocean carbon pumps defined above.
Based on the inorganic chemistry of the carbon system, oceanic pCO2 is also controlled by temperature and salinity, and it can be expressed symbolically as below:
$$ {\mathrm{pCO}}_2=f\left(\mathrm{DIC},\mathrm{ALK},\mathrm{SST},\mathrm{SSS}\right), $$
(23)
where SST is sea surface temperature, SSS is sea surface salinity, and f represents a function determined from the inorganic chemistry of the carbon system (Millero 1995; Yoshikawa et al. 2008; Oka et al. 2011b). The pCO2 distribution calculated from the observational data of DIC, ALK, SST, and SSS are shown in Fig. 4a. Because of dependency on SST, the values tend to be larger in lower latitudes and smaller in higher latitudes. In addition, pCO2 is dependent on the distributions of DIC and ALK which we will mainly focus on. Here, we define the following pCO2(Pump) in order to discuss the effects of DIC and ALK on pCO2:
$$ {\mathrm{pCO}}_{2\left(\mathrm{Pump}\right)}=f\left(\mathrm{DIC},\mathrm{ALK},{\left[\mathrm{SST}\right]}_{\mathrm{sfc}},{\left[\mathrm{SSS}\right]}_{\mathrm{sfc}}\right). $$
(24)
We also define the following pCO2(NoPump) for reference:
$$ {\mathrm{pCO}}_{2\left(\mathrm{NoPump}\right)}=f\left({\left[\mathrm{DIC}\right]}_{\mathrm{avr}},{\left[\mathrm{ALK}\right]}_{\mathrm{avr}},{\left[\mathrm{SST}\right]}_{\mathrm{sfc}},{\left[\mathrm{SSS}\right]}_{\mathrm{sfc}}\right). $$
(25)
The pressure pCO2(NoPump) represents the reference pCO2 when no ocean carbon pump exists (i.e., ΔCorg = ΔCcaco3 = ΔCfw = ΔCgas = 0 and ΔAorg = ΔAcaco3 = ΔAfw = ΔAgas = 0). The difference between these two pressures can be referenced as the total effect of ocean carbon pumps, which is defined as
$$\delta \text{pCO}_{2(\text{Pump})} = \text{pCO}_{2(\text{Pump})} - \text{pCO}_{2(\text{NoPump})}. $$
(26)
The distribution of δpCO2(Pump) is displayed in Fig. 4b. Because pCO2(NoPump) is a scalar value, the horizontal pattern is determined solely by that of pCO2(Pump). By taking the surface average of δpCO2(Pump), the change of pCO2 caused by the ocean carbon pumps can be quantified; from the observational data, the globally averaged value of pCO2(Pump) (i.e., [pCO2(Pump)]sfc) is 289 ppm, the value of pCO2(NoPump) is 925 ppm, and their difference (i.e., [δpCO2(Pump)]sfc) is calculated as −636 ppm.
The next step is to decompose δpCO2(Pump) into the contributions from each ocean pump component. One way to evaluate the individual effects of each carbon pump on oceanic pCO2 may be expressed as:
$$ \begin{aligned} \delta\text{pCO}_{2(\text{org})} &= f \left([\text{DIC}]_{\text{avr}} + \Delta \text{C}_{\text{org}}, [\text{ALK}]_{\text{avr}}\right.\\
&\left.+\Delta \text{ALK}_{\text{org}}, [\text{SST}]_{\text{sfc}}, [\text{SSS}]_{\text{sfc}}\right) - \text{pCO}_{2(\text{NoPump})}, \end{aligned}$$
(27)
$$ \begin{aligned} \delta\text{pCO}_{2(\text{caco3})} &= f \left([\text{DIC}]_{\text{avr}} + \Delta \text{C}_{\text{caco3}}, [\text{ALK}]_{\text{avr}}\right.\\
&\left.+\Delta \text{ALK}_{\text{caco3}}, [\text{SST}]_{\text{sfc}}, [\text{SSS}]_{\text{sfc}}\right) - \text{pCO}_{2(\text{NoPump})}, \end{aligned}$$
(28)
$$ \begin{aligned} \delta\text{pCO}_{2(\text{gas})} &= f \left([\text{DIC}]_{\text{avr}} + \Delta \text{C}_{\text{gas}}, [\text{ALK}]_{\text{avr}}\right.\\
&\left.+\Delta \text{ALK}_{\text{gas}}, [\text{SST}]_{\text{sfc}}, [\text{SSS}]_{\text{sfc}}\right) - \text{pCO}_{2(\text{NoPump})}, \end{aligned}$$
(29)
$$ \begin{aligned} \delta\text{pCO}_{2(\text{fw})} &= f \left([\text{DIC}]_{\text{avr}} + \Delta \text{C}_{\text{fw}}, [\text{ALK}]_{\text{avr}}\right.\\
&\left.+\Delta \text{ALK}_{\text{fw}}, [\text{SST}]_{\text{sfc}}, [\text{SSS}]_{\text{sfc}}\right) - \text{pCO}_{2(\text{NoPump})}, \end{aligned}$$
(30)
These expressions represent how much the oceanic pCO2 is changed from the state without ocean carbon pumps by adding the organic matter, calcium carbonate, gas exchange, and freshwater pumps, respectively. Figure 4c–f displays the distributions of δpCO2(org), δpCO2(caco3), δpCO2(gas), and δpCO2(fw), respectively, estimated from the observations with using the above equations. The figures suggest that the organic matter pump has the dominant role in reducing pCO2. The gas exchange pump also contributes to the reduction of pCO2. On the other hand, the calcium carbonate pump contributes to an increase of pCO2 because of alkalinity changes. Although the freshwater flux pump has significant effect on the concentrations of both DIC and ALK (Fig. 1a, b; Fig. 2e; Fig. 3d), their respective effects on pCO2 are negated by each other and their combined effect on pCO2 becomes very small. As for the surface-averaged value, it is calculated that [δpCO2(org)]sfc = − 600 ppm, [δpCO2(caco3)]sfc = 301 ppm, [δpCO2(gas)]sfc = − 246 ppm, and [δpCO2(fw)]sfc = − 5 ppm. In contrast to DIC and ALK, the total change of pCO2 cannot be represented by linear combinations of the four carbon pumps (i.e., δpCO2(Pump) ≠ δpCO2(org) + δpCO2(caco3) + δpCO2(gas) + δpCO2(fw)). This is because of the nonlinearity of function “f” of Eq. (23), which makes it difficult to obtain a simple decomposition of δpCO2(Pump) into the individual contributions from each ocean pump component.
Nonlinearity of ocean carbon chemistry
Instead of using Eqs. (27)–(30), the effects of each carbon pump on pCO2 can also be evaluated as below:
$$ {\delta \mathrm{pCO}}_{2\left(\mathrm{org}\right)}^{\prime }={\mathrm{pCO}}_{2\left(\mathrm{Pump}\right)}-f\left(\mathrm{DIC}-\Delta {C}_{\mathrm{org}},\mathrm{ALK}-{\Delta A}_{\mathrm{org}},{\left[\mathrm{SST}\right]}_{\mathrm{sfc}},{\left[\mathrm{SSS}\right]}_{\mathrm{sfc}}\right), $$
(31)
$$ {\delta \mathrm{pCO}}_{2\left(\mathrm{caco3}\right)}^{\prime }={\mathrm{pCO}}_{2\left(\mathrm{Pump}\right)}-f\left(\mathrm{DIC}-\Delta {C}_{\mathrm{caco3}},\mathrm{ALK}-{\Delta A}_{\mathrm{caco3}},{\left[\mathrm{SST}\right]}_{\mathrm{sfc}},{\left[\mathrm{SSS}\right]}_{\mathrm{sfc}}\right), $$
(32)
$$ {\delta \mathrm{pCO}}_{2\left(\mathrm{gas}\right)}^{\prime }={\mathrm{pCO}}_{2\left(\mathrm{Pump}\right)}-f\left(\mathrm{DIC}-\Delta {C}_{\mathrm{gas}},\mathrm{ALK}-{\Delta A}_{\mathrm{gas}},{\left[\mathrm{SST}\right]}_{\mathrm{sfc}},{\left[\mathrm{SSS}\right]}_{\mathrm{sfc}}\right), $$
(33)
$$ {\delta \mathrm{pCO}}_{2\left(\mathrm{fw}\right)}^{\prime }={\mathrm{pCO}}_{2\left(\mathrm{Pump}\right)}-f\left(\mathrm{DIC}-\Delta {C}_{\mathrm{fw}},\mathrm{ALK}-{\Delta A}_{\mathrm{fw}},{\left[\mathrm{SST}\right]}_{\mathrm{sfc}},{\left[\mathrm{SSS}\right]}_{\mathrm{sfc}}\right) $$
(34)
The above estimates are based on the changes in oceanic pCO2 when the organic matter, calcium carbonate, gas exchange, and freshwater pumps are removed from the present state of the ocean carbon pump, respectively. Figures 4g–j display the distributions of δpCO2(org)′, δpCO2(caco3)′, δpCO2(gas)′, and δpCO2(fw)′, respectively. They are similar to previous estimate in Fig. 4c–f but not the same; the values here tend to be moderate compared with those from previous estimate. From Eqs. (31)–(34), it can be calculated that [δpCO2(org)′]sfc = − 560 ppm, [δpCO2(caco3)′]sfc = 28 ppm, [δpCO2(gas)′]sfc = − 80 ppm, and [δpCO2(fw)′]sfc = − 0.3 ppm. This suggests that the organic matter pump is dominant, as established by the previous estimates from Eqs. (27)–(30); however, its absolute value is somewhat smaller (i.e., [δpCO2(org)′]sfc = − 560 and [δpCO2(org)] = − 600 ppm). Furthermore, the difference is more significant for the other carbon pumps, especially for the calcium carbonate pump; this is estimated at only 28 ppm, whereas the previous estimate was 301 ppm. Such a difference also arises from the nonlinearity of function “f.”
State dependence about effects of ocean carbon pumps on oceanic pCO2
The abovementioned difference in the evaluation of pCO2 (i.e., the difference between Eqs. (27)–(30) and Eqs. (31)–(34)) can be understood easily from Fig. 5, which explicitly shows the nonlinearity of function “f.” Figure 5a and b visually demonstrate the estimations based on Eqs. (27)–(30) and Eqs. (31)–(34), respectively. The contours in the figure indicate the oceanic pCO2 as a function of DIC and ALK under a temperature of 18.16 °C and salinity of 34.59 psu, which are [SST]sfc and [SSS]sfc of the observation. These contours can be used as a measure of the impact of each carbon pump on pCO2. Due to the nonlinearity of function f, the contour interval becomes denser for higher DIC. The figure displays the vectors which represent ocean carbon pumps: the organic matter, calcium carbonate, gas exchange, and freshwater flux pumps are expressed as red, green, purple, and blue vectors, respectively. The red, green, purple, and blue vectors are defined from surface depletion of DIC and ALK by each carbon pump: i.e., ([ΔCorg]sfc, [ΔAorg]sfc), ([ΔCcaco3]sfc, [ΔAcaco3]sfc), ([ΔCgas]sfc, [ΔAgas]sfc), and ([ΔCfw]sfc, [ΔAfw]sfc), respectively. Also, note that the globally averaged concentrations are represented as a solid circle ([DIC]avr and [ALK]avr) and the open circle indicates the surface concentrations ([DIC]sfc and [ALK]sfc). In the first evaluation (i.e., Eqs. (27)–(30)), the “no-pump state” is selected as the reference. In this case, the starting point of the vectors is set at the globally averaged value of DIC and ALK in the figure. Based on this figure, [δpCO2(org)]sfc, [δpCO2(caco3)]sfc, [δpCO2(gas)]sfc, and [δpCO2(fw)]sfc are measured from the differences in the contour values between the start and ends of the red, green, purple, and blue vectors, respectively (Fig. 5a). On the other hand, in the second evaluation (i.e., Eqs. (31)–(34)), the reference state is the present ocean, and thus, the ends of the vectors are set at the surface average value of DIC and ALK (Fig. 5b). Because the contour interval is relatively sparse around this reference state, the evaluated values for [δpCO2(org)′]sfc, [δpCO2(caco3)′]sfc, [δpCO2(gas)′]sfc, and [δpCO2(fw)′]sfc become more moderate than in the first evaluation. Thus, in spite of the fact that the vectors used for the analysis are common between these two evaluations, their contributions to pCO2 are dependent on the selected reference state (i.e., start/end points of the vectors) because of the nonlinearity of function “f” (i.e., the unequally spaced contour intervals). In various sensitivity simulations, previous studies have reported that changes in atmospheric pCO2 are difficult to be decomposed linearly into separate factors (Cameron et al. 2005; Yoshikawa et al. 2008; Oka et al. 2011b; Chikamoto et al. 2012; Kobayashi et al. 2015); this is also largely attributable to the nonlinearity of “f.”
Vector diagram of ocean carbon pump
The decomposition of DIC and ALK into pump components is clearly defined by Eqs. (1)–(5) and (18)–(22), respectively. However, their effects on pCO2 are more difficult to quantify because of the nonlinearity of function “f.” Here, the vector diagram analysis is introduced (Baes 1982; Volk and Hoffert 1985), which can provide a clearer evaluation of the individual effects of each carbon pump on pCO2.
The vector diagram illustrates the quantitative impact of each carbon pump on oceanic pCO2, as shown in Fig. 5c, in which the organic matter, calcium carbonate, gas exchange, and freshwater flux pumps are again expressed as red, green, purple, and blue vectors, respectively. The difference from Fig. 5a and b is that the starting or endpoints of individual vectors are not located in the same point but the vectors line up in order and are connected together from the solid circle ([DIC]avr, [ALK]avr) to the open circle ([DIC]sfc, [ALK]sfc). Note that decompositions of DIC and ALK into pump components are linear as confirmed from Eqs. (1) and (18), respectively. This means that the solid circle ([DIC]avr, [ALK]avr) and the open circle ([DIC]sfc, [ALK]sfc) can be always strictly connected by combinations of four carbon pumps.
Figure 5c clearly demonstrates how the carbon pumps operate and affect the oceanic pCO2.. In the case of no carbon pump, DIC and ALK become uniform everywhere and their surface values become the same as the globally averaged concentrations. With no ocean carbon pump, Fig. 5c suggests that pCO2 is around 900 ppm (i.e., a solid circle lies on the contour of 900 ppm). The red vector (i.e., organic matter pump) accounts for a considerable proportion of pCO2 depletion. Although the green vector (i.e., carbonate pump) has the second-largest magnitude, its effect on pCO2 is much smaller than that of the red vector because the direction of the green vector is aligned more along the pCO2 contours. The blue vector (i.e., freshwater pump) has very little effect on pCO2 despite the large spatial variation of ΔCfw (Fig. 2e; Fig. 3d). The purple vector (i.e., gas exchange pump) is oriented near perpendicular to the pCO2 contours, and thus, it has some effect on pCO2 although its magnitude is not large. It is demonstrated here that the vector diagram can display the individual contributions of the carbon pumps to pCO2 in an easily comprehensible manner without omitting the abovementioned nonlinear dependency.
Application to CMIP5 simulations
In the same manner as for the observational data, the decomposition of the ocean carbon pumps was applied to the CMIP5 ESM simulations; the climatological three-dimensional fields of DIC, ALK, phosphate, and salinity obtained from the CMIP5 outputs were utilized for this decomposition. As mentioned in the “Methods” section, nine CMIP5 models were used here; their vertical profiles of ΔCorg, ΔCcaco3, ΔCgas, and ΔCfw are displayed in Fig. 6. Although the formulation of the incorporated ocean biogeochemical processes is different among the models (Bopp et al. 2001; Nakamura and Oka 2019), all the model results captured the overall pattern of the observation (black line). Interestingly, the CMIP5 model mean (i.e., average of nice CMIP5 model results; shown as gray line in Fig. 6) tends to show better agreement with the observation than the individual model results (especially for ΔCorg) as seen in other climate variables (Phillips and Gleckler 2006). As for the CMIP5 model mean, the surface distributions of ΔCorg, ΔCcaco3, ΔCgas, and ΔCfw are shown in Fig. 7a–d, respectively. These figures also indicate that the model captures the overall pattern of the observation (Fig. 3). Note that ΔCgas is positive in the Arctic and northern North Atlantic Oceans where the observational data is missing; this supports the previously mentioned explanation that positive ΔCgas observed in the deeper ocean (Fig. 1a) is transported from the northern North Atlantic and Arctic Oceans.
Based on the obtained decomposition of DIC and ALK into the four carbon pump components, the vector diagrams for the CMIP5 models are displayed in Fig. 8. Together with individual model results (Fig. 8c–k), the observation (Fig. 8a same as Fig. 5c) and the CMIP5 model mean (Fig. 8b) are also shown in the figure. In all the models, the simulated surface average concentrations of DIC and ALK (i.e., ([DIC]sfc, [ALK]sfc); open circles in Fig. 8) are located around the 300 ppm contour value, which agrees with the observation (this agreement is guaranteed from the experimental design of the CMIP5 historical simulation, in which the atmospheric CO2 concentration is prescribed). In the same time, the figures also show that they are separately distributed along the 300 ppm contour line, suggesting that the carbon pumps operate differently among the models. Figure 8c–k illustrate how the organic matter, calcium carbonate, gas exchange, and freshwater carbon pumps are operating in the individual models by the red, green, purple, and blue vectors, respectively. The individual effects of these four ocean carbon pumps on the surface pCO2 can also be measured from the difference in the contour values between the start and end of each vector. In the same way as the observational data, Fig. 8 clearly visualizes the individual effects of the four ocean carbon pumps on the surface pCO2 in each CMIP5 model, which demonstrates that the vector diagram is a useful and simple diagnosis for ocean carbon pumps of each CMIP5 model.
Vector diagram as a tool for model evaluation and comparison
Because the carbon pump components can be decomposed linearly (Eqs. (1) and (18)), the differences in ΔDIC and ΔALK between the models and the observation can also be decomposed into the four carbon pump components. For comparing the models with the observation more closely, Fig. 9 is presented. In this figure, the surface concentrations in the model and observation (two open circles) are connected by the four pump vectors; here, the vectors are defined in the form of the differences between the observation and the models. In other words, the vector of Fig. 9 represents the model bias of each carbon component against the observation.
As for the CMIP5 model mean (Fig. 9b), the calcium carbonate pump (green arrow) is somewhat weaker than the observation, which is compensated by the weaker gas exchange pump (purple arrow). The freshwater flux pump (blue arrow) also shows fresher bias, but its contribution to pCO2 is small. Bias of organic matter pump (red arrow) is small with regard to the CMIP5 model mean. As for individual CMIP5 model results, they are also summarized in Fig. 9c–k. The organic matter pump has the largest model spread, which confirms that the small bias of the model mean is a result of cancellation between individual model biases. It is worthy to note that the strength of the organic matter pump is not simply determined from the ocean net primary production (NPP) or export production (EP). For example, although it was reported that GFDL-ESM2M has the most largest NPP among the other models (Bopp et al. 2013), Fig. 9e shows that this model has the significant weaker bias of the organic matter pump. This is because the organic matter pump is controlled not only by NPP/EP but also by the ocean transport. For example, the stronger upwelling tends to increase surface phosphate concentration, which means that the organic matter pump tends to be weaker. At the same time, the stronger upwelling also causes the larger NPP/EP, which in turn reduces the surface phosphate concentration contributing to the strengthening of the carbon pump. Therefore, the strength of the organic matter pump is controlled under the balance between NPP/EP and the ocean transport. The figure suggests that all the models have significant fresher bias of freshwater flux pump. It is known that CMIP5 models have systematic fresher salinity bias especially over the subtropical gyre in the South Atlantic Ocean (Mecking et al. 2017), which appears to cause such systematic bias of the freshwater flux pump. All the models except CESM1-BGC, GFDL-ESM2M, and MPI-ESM-LR show weaker bias of calcium carbonate pump. The reason for this weaker bias appears to come from various reasons depending on models. For example, GFDL-ESM2G and NorESM1-ME have shallower maximum of ΔCcaco3 than the observation (Fig. 6b), which makes the calcium carbonate pump weaker (Yamanaka and Tajika 1996; Oka et al. 2008). IPSL-CM5A-LA and IPSL-CM5A-MR have the weaker bias of the carbonate pump in spite of their stronger bias of the organic matter pump, which implies that their rain ratio is smaller. As for the gas exchange pump, the models tend to have weaker bias. This weaker bias is considered to be a result of the compensation for weaker bias of the sum of remaining three carbon pumps (mainly due to weaker bias of calcium carbonate pump). Because the atmospheric pCO2 level is prescribed in the model from the experimental design of CMIP5 historical simulation, all the models are forced to be located around the specified pCO2 level (around 300 ppm contour line in Fig. 9a). This adjustment is done by the air–sea gas exchange; namely, the gas exchange pump works in such a way that the model’s open circle becomes located close to 300 ppm pCO2 contour line in Fig. 9. Therefore, if the total effects of three carbon pumps have a weaker bias, the gas exchange pump needs to compensate such bias by adjusting its own strength to be also weaker.
Note that the difference in two open circles is not fully explained from the combination of four carbon pumps in Fig. 9 (i.e., the end point of blue vector is not located at the model’s open circle). This is simply because the globally averaged values of DIC and ALK (i.e., ([DIC]avr, [ALK]avr); solid circles in Fig. 8) are not the same as those of the observation. In other words, the difference between the end point of blue vector and the model’s open circle corresponds to the difference in ([DIC]avr, [ALK]avr) between the model and the observation. The CMIP5 models tend to show the larger values of globally averaged DIC and ALK than the observation. This difference originates from initial conditions of CMIP5 historical simulation; the reason for the larger initial values may come partly from the fact that models were usually spin up under recent conditions (anthropogenic carbon is included therein) rather than the condition before the year 1860.