The ESM was spun up under pre-industrial atmospheric CO2 (1850: 284.7 ppm) until the simulated climate was stable (2000 years) . Stability was defined as the point where the linear trend of global mean surface temperature change over the last 400 years of the spin-up was less than 0.015 ∘C century-1. The ocean and land carbon cycles were then spun up offline using separate ocean and land simulations, using the pre-industrial climate state of and the pre-industrial atmospheric CO2 until the drift in the global carbon exchanges was less than 0.1 PgC century-1. Finally, the climate and carbon states obtained above were incorporated in an ESM simulation that continued for another 1000 years to ensure that the global drifts in the climate and carbon were less than 0.015 ∘C and 0.1 PgC century-1.

From the spun-up initial climate and carbon state, the historical simulation (1850–2005) was performed using the historical atmospheric CO2 concentrations as prescribed by the CMIP5 simulation protocol. For the historical period, the atmospheric CO2 affects both the radiative properties of the atmosphere and the carbon cycle . From year 2006, four different future projections were made using the atmospheric CO2 concentration pathways of RCP8.5, RCP6, RCP4.5, and RCP2.6 as provided by CMIP5 (http://cmip-pcmdi.llnl.gov/cmip5/). The simulations made with prescribed atmospheric CO2 are subsequently called the concentration pathway (CP) simulations.

The future simulations were repeated using the CO2 emission scenarios that were used by the integrated assessment model to generate the future atmospheric CO2 concentrations used in the RCPs. We subsequently refer to these simulations as the emission pathway (EP) simulations. EP simulations have prescribed atmospheric carbon emissions, and the atmospheric CO2 is determined by considering how much carbon is absorbed by the land and ocean in our ESM. For each of the EP scenarios, the radiative forcing of non-CO2 gases was converted into an equivalent CO2 concentration and added to the simulated atmospheric CO2 to maintain the same radiative forcing of non-CO2 greenhouse gases as the corresponding CP simulation. This additional CO2 was not seen by the land and ocean carbon modules. From the difference between the EP and CP simulations, we quantify the carbon–climate feedbacks, and we use these differences to investigate how carbon–climate feedbacks influence future atmospheric CO2 concentration and ocean acidification.

The COAL simulations of the future carbon–climate feedbacks made with RCP8.5 and RCP2.6 were discussed by with a focus on how the feedbacks increased warming due to reduced carbon uptake by the land. showed the EP simulations had less than 0.4 ∘C more global surface warming than the corresponding CP simulations by 2100. Here, we add the RCP4.5 and RCP6 scenarios and focus our study on ocean acidification.

In all our simulations, the vegetation scenario used by remained unchanged over the simulation period following the CMIP5 experimental design. We also neglected changes in anthropogenic N deposition over the simulation period because of the large uncertainty in the future deposition rate and the small impact it has on net land carbon uptake . To account for possible drift in the simulated climate and carbon pools, a control simulation with the atmospheric CO2 held constant at 284.7 ppm was performed over the simulation period (1850–2100). Drifts in climate and carbon pool sizes were small (less than 0.015 ∘C century-1 and 0.1 Pg C century-1), and correcting the future scenarios with the control simulation had negligible impact on the future projections of ocean acidification and ocean warming.

An assessment of the simulated carbon and climate was made in , , and and here we briefly comment on the simulation over the historical period (1850–2005). Mk3L-COAL simulates the historical climate well, as compared to the models used for earlier IPCC assessments . Over the historical period, the global averaged surface warms by 0.57∘ ± 0.07 ∘C , which is comparable to the observed value of 0.76∘ ± 0.19 ∘C . The simulated land and ocean uptake were 85 ± 1 PgC and 116 ± 1 PgC, respectively, compared to observed land and ocean estimates of 135 ± 84 and 135 ± 25 PgC, respectively . The simulated responses of the land carbon cycle to increasing atmospheric CO2 and warming is consistent with those from CMIP5 , while the acidification of the ocean was also comparable to other CMIP5 simulations .

For 2002, we compare the simulated annual mean surface ocean aragonite saturation state to the values estimated from GLODAPv2 observational dataset (Fig. ). The simulated values are broadly consistent with the observations with the location of aragonite saturation value of 3 (purple line in Fig. ) being found at similar locations. However, the simulation slightly underestimates aragonite saturation state in the tropics.

For the future, the ESM simulated higher atmospheric CO2 in the EP simulations than the corresponding CP simulations and, by the end of the century, the atmosphere had 35, 60, 85 and 120 ppm more CO2 in the EP simulations (RCP2.6, 4.5, 6, and 8.5, respectively) than in the corresponding CP simulations (Fig. ). This atmospheric CO2 increase largely reflects more carbon being emitted to the atmosphere in the EP than the corresponding CP simulations. This is demonstrated by , who showed that for our ESM to track the atmospheric CO2 concentration prescribed by RCP2.6 and RCP8.5, the emissions over this century need to be reduced by 69 and 250 PgC, respectively. Therefore, the EP simulations have substantially more atmospheric CO2 emissions than the corresponding CP simulations.

Since the differences in land and ocean carbon uptake between the corresponding EP and CP simulations reflect their different atmospheric CO2 and global surface warming, one way to interpret these differences is in terms of the feedback parameters of warming (γ) and elevated CO2 (β) . assessed the feedback parameters of our ESM using the 1 % per year increase in atmospheric CO2 simulations following the classical methodology of .

For the ocean, our ESM feedback parameters (β=0.7 PgC ppm-1, and γ=-7.4 PgC K-1) are similar to the values from CMIP5 models (β=0.80 ± 0.07 PgC ppm-1 and γ=-7.8 ± 2.9 PgC K-1) . With higher atmospheric CO2 concentrations, the EP simulations have higher global averaged surface temperature (Fig. ) and increased oceanic uptake of CO2 (Fig. ) than the corresponding CP simulations. With higher atmospheric CO2 concentrations, more CO2 is taken up by the ocean; this in turn reduces the oceans buffering capacity of CO2, or Revelle factor , acting as a feedback to reduce ocean carbon uptake. These differential changes in buffering capacity across different scenarios explain why the changes in ocean carbon uptake are very similar. Ocean warming plays a small role in the change in oceanic uptake of CO2 because the changes in warming between the EP and CP simulations are small and similar for all scenarios (Fig. ).

For the land, our ESM warming feedback (γ=-34 PgC K-1) was within the range of the CMIP5 models (γ=-58.4 ± 28.5 PgC K-1) , however, the CO2 feedback (β=0.18 PgC ppm-1) was on the extreme low end of the CMIP5 model range (β=0.92 ± 0.44 PgC ppm-1) . Our ESM is consistent with the two ESMs used in the CMIP5 analysis that had land carbon models with carbon and nitrogen cycles (β=0.23 ± 0.01) . The β value of a land carbon model is strongly reduced by nutrient limitation, because the land CO2 fertilisation effect saturates as the land carbon uptake becomes nutrient limited . The simulated changes in land carbon uptake between the EP and CP simulations are small and similar for the various emissions scenarios. The similarity in the land uptake between scenarios reflects little difference in warming between the EP and CP simulations (Fig. ). However, the impact of the β feedback appears in the RCP8.5 scenario as a stabilisation, and subsequent decline in the cumulative land uptake difference onwards from 2060 (Fig. b).

A recent analysis of 11 ESMs of the RCP8.5 scenario showed atmospheric CO2 in 2100 would be 44 ± 97 ppm greater in the EP simulations than in the CP simulations. Our ESM simulated value is on the upper end of this range (120 ppm), but was consistent with one model used in the , which included nitrogen cycle and had a similar β land value.

The higher atmospheric CO2 translated into higher CO2 in the surface ocean. To quantify ocean acidification impacts, we show the aragonite saturation state values in the surface water for both the CP and EP simulations (Fig. ). Figure  illustrates how rising atmospheric CO2 impacts the carbon chemistry of the surface ocean. Two ways to quantify the ocean acidification in the surface water are to monitor where aragonite becomes chemically unstable or corrosive (aragonite saturation state of less than 1) and where aragonite saturation declines to less than 3, an approximate threshold for suitable coral reef habitat . In Fig. , the white lines denote annual mean aragonite saturation state values of 1, and the purple lines the annual mean aragonite saturation state values of 3. A quick way to assess the ocean acidification impacts is by comparing how the white and purple lines differ between RCP scenarios (e.g. differences in a column) and how the carbon–climate feedbacks alter the surface chemistry changes (i.e. differences across a row). As one goes to higher future emissions scenarios (e.g. RCP2.6 to RCP8.5), the atmospheric CO2 concentrations increase and the white lines move towards the Equator and the surface area of the water in which aragonite is chemically unstable expands. In contrast, as one goes to higher emissions scenarios, the suitable regions for coral reefs shrink. In the RCP6 and RCP8.5 scenarios, there are no suitable coral reef regions by 2100 and a substantial portion of the polar Southern and Northern Hemisphere have surface water corrosive to aragonite in agreement with previous studies . When the carbon–climate feedbacks are considered, there is a further expansion of aragonite undersaturated surface water, and a further reduction in the area suitable for coral reefs.

Figure  shows more clearly how carbon–climate feedbacks alter the rate of ocean acidification. The figure shows how the global surface area of aragonite undersaturation (a) and the global surface area of suitable coral reef habitat (b) change with time for the various scenarios. All EP scenarios show an acceleration in ocean acidification (dotted lines) compared to the corresponding CP simulations (solid lines).

For undersaturated aragonite surface water, the EP simulations all display a similar evolution to the corresponding CP simulations but with a more rapid onset of undersaturated conditions. For RCP8.5, the EP simulation leads the CP simulation by about 5 years. For RCP6, the EP simulation leads the CP simulation by about 10 years. For RCP4.5, the lead is nearly 20 years. While for RCP2.6, there is a similar 20-year lead in the emissions simulation but the area of undersaturated water is small due to the low atmospheric CO2, which makes quantifying the lead uncertain. Further, in the RCP2.6 scenario, the atmospheric CO2 starts to decline after 2050 (Fig. ) because the scenario has negative emissions in the second half of the century, which enables some recovery in ocean acidification. Associated with the decline in atmospheric CO2 is a reduction in surface ocean acidification (Fig. b); hence, in this scenario there is a small reduction in the area of undersaturated water by 2100 from the maximum value in the 2060s.

For all scenarios, the carbon–climate feedbacks accelerate the onset of undersaturated aragonite conditions. However, it is in the medium- to low-emissions scenarios (RCP4.5 and RCP2.6) where the differences between EP and CP simulations are greatest and, hence, where the carbon–climate feedbacks are most significant.

For the surface ocean area suitable for coral reefs, the evolution of the EP simulations is similar to the corresponding CP simulations, but, again, they lead the CP simulations. The more rapid onset of ocean acidification produces the largest difference in the RCP4.5 scenario where, by the end of the century, the suitable area for coral reefs in the EP simulation (18 %) is less than half the CP simulation (37 %). Under the high-emissions scenarios (RCP6.0 and RCP8.5), there is no suitable habitat for coral reefs by 2100, with the time of disappearance occurring 15 and 6 years earlier in the EP simulations than in the CP simulations for RCP6 and RCP8.5, respectively. With the highest emission scenario (RCP8.5), there is such a large and rapid release of CO2 to the atmosphere and ocean acidification impacts are so substantial that the differences between the EP and CP simulations are similar, but with a slight acceleration in the EP simulation.

The differences between the EP and CP simulations extend into the ocean interior. By 2100, the EP simulations show a shoaling of the aragonite saturation horizon (depth of where the aragonite goes undersaturated) than the corresponding CP simulations (Fig. ). For the RCP2.6, the difference is generally small because the rate of atmospheric CO2 rise is weak and the penetration of carbon is not very different between the two EP and CP simulations. However, for the other emissions scenarios, the differences between the EP and CP simulations are substantial, particularly in the Southern Ocean and North Pacific (Fig. b, c, d). Under the RCP4.5 scenario in the Southern Ocean, the EP simulated aragonite saturation horizon is more than 400 m shallower than the CP simulation. In this scenario, the surface water does not become undersaturated with respect to aragonite (Fig. b), but the increase in ocean carbon uptake in the EP simulation is sufficient to significantly shoal the aragonite saturation horizon. Such a shoaling of the aragonite saturation horizon would have a detrimental impact on calcifying organisms such as pteropods inhabiting the Southern Ocean . The RCP8.5 and RCP6 scenarios also display regions where the aragonite saturation horizon is more than 400 m shallower in the EP simulation than in the CP simulation. In both these scenarios, most of the Southern Ocean surface water is undersaturated with respect to aragonite (Fig. c, d) and the largest shoaling occurs just outside of the Southern Ocean, where anthropogenic carbon taken up in the Southern Ocean is stored . As more anthropogenic carbon is transported into the ocean interior in the EP simulations, it is the regions where the carbon is stored that show the greatest shoaling of the aragonite saturation horizon. The projected increased shoaling of the aragonite saturation horizon in the Southern Hemisphere with carbon–climate feedbacks could be important to the future viability of deep water corals found in regions like south of Australia, where living corals are generally confined to water above the aragonite saturation horizon .

While it is natural to compare the impact of climate-carbon feedbacks on ocean acidification to previous estimates of intermodel variability from CP simulations, we emphasise that all the CP simulations prescribe the future atmospheric CO2 concentrations. However, to broaden the discussion, we review the current results of intermodel differences for ocean acidification. provided a seminal study of the intermodel variability in the projected ocean acidification from CP simulations with different emissions scenarios. For the four emission scenarios considered here, showed that the global change in surface aragonite saturation state had a small intermodel range (less than 10 %) and they concluded that atmospheric CO2 dominated the model behaviour. This is consistent with , who observed similar behaviour in the ocean carbon responses between CMIP5 projections for a given scenario.

Regionally, showed significant intermodel differences that are comparable to the magnitude of the carbon–climate feedbacks we simulated. For example, in the Southern Ocean (south of 60∘ S), showed mean aragonite saturation of the surface water occurs in 2067 and 2092 for RCP8.5 and RCP6.0, respectively, but from the intermodel variability it could occur 7 and 13 years earlier for RCP8.5 and RCP6, respectively. While the intermodel differences are large, showed that much of these regional differences is attributed to differences in spin-up protocol, which influence both a model simulated pre-industrial state and the amount of drift that occurs in the subsequent scenario simulation. Thus suggest that much of the estimated model–model uncertainty reflects inconsistencies in spin-up protocol and initial conditions across CMIP5 ESM simulations rather than how these models parameterise key biogeochemical processes. Further, if the carbon–climate feedbacks increase the projected atmospheric CO2, then all these models would simulate an earlier onset of aragonite saturation in the surface water. Hence, our study complements model–model analysis by introducing an independent modification to their analysis associated with carbon–climate feedbacks. We next assess the robustness of our simulated carbon–climate feedbacks by comparing our ESM to other CMIP5 models.

The World Climate Research Program (WCRP) identified Carbon Feedbacks in the Climate System as one of their Grand Challenges (https://www.wcrp-climate.org/grand-challenges/gc-carbon-feedbacks) due to the potential influence the feedbacks may have on future climate change . A key conclusion of our study is that the carbon–climate feedbacks may also be important to the future trajectory of ocean acidification. Our estimates of the impact of the carbon–climate feedbacks on ocean acidification are only based on a single model, and to help assess the robustness of our results we compare our ESM with other CMIP5 simulations. To compare our ESM to other CMIP5 models, we compare the land and ocean feedback parameters of warming (γ) and elevated CO2 (β) .

assessed the feedback parameters of our ESM and showed that our ocean response was consistent with CMIP5 models . Nutrient limitation had the greatest impact on our ESM land β feedback parameter, which significantly reduced land carbon uptake with rising atmospheric CO2. Hence, in emission scenarios with high atmospheric CO2 concentrations (RCP8.5), our ESM had less land carbon uptake and higher atmospheric CO2 than most CMIP5 models . While this behaviour is on the extreme end of the CMIP5 models it partially reflects the omission of nutrient limitation in most CMIP5 land models, and the models that do include nutrient limitation have β values similar to our ESM.

Recent studies show the carbon–climate feedbacks are dominated by the land carbon cycle response to warming . From the CMIP5 simulations, for the historical period, the land γ was -49 ± 40 PgC K-1 . For comparison, the ESM used in this study the land γ for the historical period was -35 PgC K-1, which is within the range of the CMIP5 models. Recent analysis using the short-term variability to further constrain the model simulations reduces the range of the land γ to -44 ± 14 PgC K-1 Our ESM again falls within this reduced range but, when compared to the weighted mean of the CMIP5 models, our ESM is at the lower range of these estimates.

An ESM with a weaker land γ feedback parameter equates to lower atmospheric CO2 concentrations in future projections. Therefore, in the scenarios with relatively low atmospheric CO2 concentrations (RCP2.6 and RCP4.5), where the land β feedback is small and the land γ feedback dominates, our ESM is on the low side of the CMIP5 models and could be providing a lower bound estimate of the carbon–climate feedbacks on future ocean acidification.