Simulated effect of calcification feedback on atmospheric CO₂ and ocean acidification

Abstract

Ocean uptake of anthropogenic CO₂ reduces pH and saturation state of calcium carbonate materials of seawater, which could reduce the calcification rate of some marine organisms, triggering a negative feedback on the growth of atmospheric CO₂. We quantify the effect of this CO₂-calcification feedback by conducting a series of Earth system model simulations that incorporate different parameterization schemes describing the dependence of calcification rate on saturation state of CaCO₃. In a scenario with SRES A2 CO₂ emission until 2100 and zero emission afterwards, by year 3500, in the simulation without CO₂-calcification feedback, model projects an accumulated ocean CO₂ uptake of 1462 PgC, atmospheric CO₂ of 612 ppm and surface pH of 7.9. Inclusion of CO₂-calcification feedback increases ocean CO₂ uptake by 9 to 285 PgC, reduces atmospheric CO₂ by 4 to 70 ppm and mitigates the reduction in surface pH by 0.003 to 0.06, depending on the form of parameterization scheme used. It is also found that the effect of CO₂-calcification feedback on ocean carbon uptake is comparable and could be much larger than the effect from CO₂-induced warming. Our results highlight the potentially important role CO₂-calcification feedback plays in ocean carbon cycle and projections of future atmospheric CO₂ concentrations.

Introduction

Atmospheric CO₂ concentration has increased by 40% since the preindustrial time¹ primarily due to human activities of fossil fuel burning and deforestation. Between 1959 and 2011 total anthropogenic CO₂ emission is 436 PgC (1PgC = 10¹⁵ gram carbon = 1 billion ton carbon) with 44% of the emission stayed in the atmosphere, while 29% and 27% of emissions were absorbed by the terrestrial biosphere and the ocean, respectively². Increasing atmospheric CO₂ warms the Earth by trapping long wave radiation. In addition, the oceanic uptake of anthropogenic CO₂ perturbs ocean chemistry by making the ocean more acidic, a process known as ocean acidification³.

Global warming and ocean acidification would influence many processes of the marine carbon cycle, which in turn affect atmospheric CO₂ and climate change. For instance, rising atmospheric CO₂ concentration leads to an increase of sea surface temperature, reducing CO₂ solubility in the ocean. As a result, a warmer ocean reduces the oceanic CO₂ uptake, which provides a positive feedback to the growth of atmospheric CO₂^4,5. A warmer ocean could also accelerate respiration/remineralization rate of organic carbon and cause a reduction in the vertical flux of particulate organic carbon (POC) to the abyssal ocean. This reduced vertical transport of POC would weaken the ocean biological pump and decrease the ocean’s ability to take up carbon, providing a positive feedback to the growth of atmospheric CO₂⁶. On the other hand, increased C:N:P stoichiometry in seawater due to rising partial pressure of CO₂ in the ocean could enhance extracellular organic matter production, strengthening the ocean biological carbon pump and providing a negative feedback to rising atmospheric CO₂^7,8,9.

In addition to global warming, ocean acidification, through its effect on the ocean carbon cycle, could provide feedbacks to atmospheric CO₂. Global mean ocean surface pH, which can be used to quantify the degree of ocean acidification, has dropped by 0.1 units¹, representing a 26% increase in hydrogen ion concentration since the industrial revolution. The rise of hydrogen ion concentration would consequently lower carbonate ion concentration and in turn causes a reduction of seawater CaCO₃ (aragonite or calcite) saturation state, which is defined as

Here, is the stoichiometric solubility product for aragonite or calcite, which are two different polymorphs of CaCO₃¹⁰.

Calcifying organisms that use CaCO₃ to precipitate their shells or skeletons may not be able to acclimate to the reduction of CaCO₃ saturation state¹¹. Gattuso et al. detected a nonlinear relationship between calcification rate and CaCO₃ saturation state from experimental results of certain types of coral species and suggested calcification rate may drop substantially as a result of decreasing aragonite saturation state¹². Langdon et al. through mesocosm experiment results, argued that declining aragonite saturation state is a primary factor that attenuates coral reef calcification¹¹. Laboratory experiments with coccolithophorids^13,14 and analyses of foraminiferal shell weight observational record across glacial-interglacial Termination¹⁵ indicated a reduction in CaCO₃ production with increasing CO₂ concentration and resulting ocean acidification. More recent observational or experiment results also provided evidences of the negative response of calcification to ocean acidification^16,17,18. In spite of the abundant observational and experimental evidence, the sensitivity of the response of calcification to acidification varies dramatically between experiments using different species of calcifying groups or manipulation methods.

The process of calcification decreases , suppressing the ocean’s ability to absorb atmospheric CO₂. Therefore, the potential reduction of calcification as a result of CO₂-induced ocean acidification could enhance the ocean’s uptake of carbon, providing a negative feedback for rising atmospheric CO₂¹⁹, which is termed as CO₂-calcification feedback here. Recently, a few modeling studies have been conducted to examine effects of the CO₂-calcification feedback. In these studies, the parameterization schemes that link CaCO₃ production to CaCO₃ saturation state (Ω) are based on different results of experimental studies and as a consequence, estimates of the effect on oceanic uptake of atmospheric CO₂ from CO₂-calcification feedback varies among studies^{20,21,22,23,24}.

As an extension of previous studies, here we further examine the effect of CO₂-calcification feedback on the oceanic uptake of atmospheric CO₂. We incorporate the calcification-Ω dependence into an Earth system model of intermediate complexity to quantify the strength of the CO₂-calcification feedback in mitigating the growth of atmospheric CO₂ and ocean acidification. Usually, previous studies on CO₂-calcification feedback assume a single type of calcification-Ω parameterization scheme. Here, different types of calcification-Ω parameterization schemes are used, which enables us to assess the importance in the parameter value (parameter uncertainty) and the equation form (model structural uncertainty) of the calcification response to ocean acidification. Also, we compare the strength of CO₂-calcification feedback with the feedback induced by climate change. Furthermore, we assess the effect of different parameterization of CO₂-calcification feedback on projected ocean acidification. This study aims to further our understanding in the role of the CO₂-calcification feedback on the ocean carbon cycle and atmospheric CO₂, which is important for a reliable projection of future atmospheric CO₂ concentrations and climate change.

Results

To quantify the effect of CO₂-calcification feedback, we conduct a series of Earth system model simulations that incorporate different parameterization schemes representing the dependence of calcification rate on saturation state of CaCO₃ (refer to Method section and Fig. 1). All model simulations last from year 1800 to 3500 with SRES A2 CO₂ emission scenario until year 2100 and zero CO₂ emission afterwards. Total cumulative anthropogenic CO₂ emissions amount to 2270 PgC.

Figure 1

Dependence of CaCO₃: POC production ratio on (CaCO₃ saturation state) used in model parameterizations.

Detailed configuration of different model versions is provided in Table 1.

To quantify the effect of climate change on the carbon cycle, we also conduct additional simulation experiments in which CO₂-induced warming does not affect the carbon cycle. A detailed description of the model and simulation experiments can be found in the Method section.

Model-observation comparison

To test the performance of the UVic model in simulating present day carbon cycle, the model-simulated distributions of key variables of the ocean carbon cycle are compared with GLODAP observations²⁵. As shown in Fig. 2, the simulated vertical profiles of alkalinity and dissolved inorganic carbon (DIC) are in close agreement with observational estimates and their vertical profiles of different model versions are almost indistinguishable. This is because in different model parameterizations, in equation (3) and in equation (4) was back-calculated to ensure that the global mean value of at preindustrial time is the same for all model versions.

Figure 2

Model-simulated global mean vertical distribution of dissolved inorganic carbon (DIC) and alkalinity (ALK) in mid 1990s compared with observed GLODAP data (including published errors as gray shaded areas)²⁵.

Model results are shown for different parameterization schemes of CO₂-calcification feedbacks. Detailed configuration of different model versions is provided in Table 1.

In the simulations with climate change modeled CaCO₃ productions with different parameterizations of in year 2000 range from 0.69–0.73 PgC yr⁻¹, which are within the estimate range of 0.6–1.6 PgC yr⁻¹ calculated from observations of satellite and sediment trap²⁰.

Future projections

In the following, we first present results from simulations including the effect of CO₂-induced warming on the ocean carbon cycle. Then we compare the effect of CO₂-calcification feedback with that from CO₂-induced warming, which is obtained by the differences between the simulations with and without CO₂-induced warming.

As shown in Fig. 3, in the control simulation (S0), by year 2100, the global ocean has absorbed 581 PgC of anthropogenic CO₂. After the cessation of CO₂ emission at 2100, the ocean continues to absorb CO₂ and by year 3500, the global ocean has a total CO₂ uptake of 1462 PgC (Fig. 3b, also see Supplementary Table S1). As for the carbon uptake by the terrestrial biosphere, by year 2100 and 3500 the land has absorbed 629 and 2236 Pg C, respectively (Fig. 3d). Atmospheric CO₂ reaches a peak value of 897 ppm at year 2100 (Fig. 3e). A cessation of CO₂ emission leads to a gradual decline of atmospheric CO₂. By year 3500, atmospheric CO₂ concentration is 612 ppm with a global mean surface warming of 3.9 °C (Fig. 3f). The ocean’s absorption of anthropogenic CO₂ acidifies the global ocean (Fig. 4). By year 2100, relative to the preindustrial values, surface mean pH drops by 0.42 units, corresponding to a 50.6% reduction in surface . With the gradual decrease of atmospheric CO₂, surface ocean acidification slowly recovers. By year 3500, surface mean pH reduces by 0.29 units, corresponding to a 37.8% decrease of relative to the preindustrial values (see Supplementary Table S1 online).

Figure 3

Model-simulated time series of annual and global mean variables for (a) ocean CO₂ uptake, (b) cumulative ocean CO₂ uptake, (c) land CO₂ uptake, (d) cumulative land CO₂ uptake (e) atmospheric CO₂ concentration, (f) surface air temperature (SAT).

Model results are shown for different parameterization schemes of CO₂-calcification feedbacks. Detailed configuration of different model versions is provided in Table 1.

Figure 4

Model-simulated time series of global mean variables as a function of year for (a) ocean surface dissolved inorganic carbon (DIC) concentration, (b) ocean mean DIC concentration, (c) ocean surface alkalinity concentration, (d) ocean mean alkalinity concentration, (e) ocean surface pH, (f) ocean mean pH, (g) ocean surface , (h) ocean mean .

Detailed configuration of different model versions is provided in Table 1.

The introduction of dependence on calcite saturation state affects the ocean carbon cycle through its impact on the production of CaCO₃. In the S0 simulation, CaCO₃ production increases with time (Fig. 5) mainly as a result of increasing ocean temperature that boosts the growth of phytoplankton, which CaCO₃ production depends on according to equation (2). In the simulations with -dependent , CaCO₃ productions are under the influence of both changing temperature and . As shown in Fig. 5, except for S1, relative to the preindustrial value, there is a general decrease of CaCO₃ production with time, indicating the dominant influence of decreasing . After around year 2150, there appears to be a recovery of CaCO₃ production as a result of the recovery of surface (Fig. 5). In the simulation of S2, after year 2350, the change of CaCO₃ production becomes positive again, indicating the increasing influence of rising ocean temperature. Overall, compared to the simulation of S0, the introduction of -dependent greatly decreases the production of CaCO₃, which has great implication for the oceanic uptake of CO₂ as discussed below.

Figure 5

Model-simulated time series of annual and global mean change in CaCO₃ production rate for different parameterization schemes of CO₂-calcification feedbacks.

Detailed configuration of different model versions is provided in Table 1.

The change in CaCO₃ production has great impact on the ocean alkalinity. In the simulation of S0, an increase in CaCO₃ production (Fig. 5) leads to a decrease in ocean-mean alkalinity (Fig. 4). In the simulations with the -dependent , ocean-mean alkalinity generally increases with time. For example, in the simulation of R3, by year 3500, ocean-mean and surface-mean alkalinity have increased by 25 and 24 μmol kg⁻¹ respectively (see Supplementary Table S1 online). Meanwhile, in the simulations that include the -dependent , the vertical gradient of alkalinity diminishes due to the reduced CaCO₃ production rate and the consequent weaker CaCO₃ pump (Fig. 6, see Supplementary Fig. S1 online).

Figure 6

Model-simulated latitude-depth distribution of the change in DIC (year 3500 minus year 1800) ∆DIC (a,d,g), the change in ALK (year 3500 minus year 1800) ∆ALK (b,e,h) and the change in (year 3500 minus year 1800) ∆ (c,f,i).

Results are shown for simulation S0 (a–c), simulation S3 (d–f) and simulation R3 (g–i), respectively. Detailed configuration of different model versions is provided in Table 1. The figures were generated using UV-CDAT (http://uvcdat.llnl.gov/).

As a result of modification of the ocean alkalinity, the -dependent affects the ocean’s uptake of CO₂. By year 2100, compared to the S0 simulation, the inclusion of -dependent increases accumulated oceanic CO₂ uptake by 1 PgC (0.1%) to 36 PgC (6.2%), depending on the exact form of CaCO₃ production parameterization (Fig. 3). By year 3500, the increase in accumulated oceanic CO₂ uptake relative to the simulation of S0 ranges from 9 PgC (0.6%) to 285 PgC (19.5%) across different CaCO₃ production parameterization schemes (Fig. 3, see Supplementary Table S1 online). As a consequence, by year 3500, simulated atmospheric CO₂ ranges from 608 to 542 ppm with the inclusion of dependence of on , compared with 612 ppm in the S0 simulation (Fig. 3). Moreover, by year 3500, the inclusion of -dependent acts to reduce the amount of surface warming by 0.04 to 0.6 K relative to the S0 simulation, depending on the parameterization scheme used (see Supplementary Table S1 online).

The inclusion of dependence on also has a great influence on ocean acidification (Fig. 4 e, f, g, h). For example, by year 3500, the difference of surface mean pH between R3 and S0 becomes 0.06 units, corresponding to a 15% difference of (see Supplementary Table S1 online). Thus, the inclusion of -dependent increases the ocean uptake of CO₂, but mitigates ocean acidification. The mitigation of ocean acidification in the simulations with dependence of , relative to the simulation with fixed is mainly a result of increased alkalinity, which dominates the effect of increased DIC on ocean acidification.

In the above, we have discussed model-simulated results with the inclusion of CO₂-induced warming. To test the importance of CO₂-induced warming on the ocean carbon cycle, we have performed additional simulations that do not include the radiative effect of increasing atmospheric CO₂. Our simulations show that, by year 3500, in the S0 case, in the absence of CO₂-induced warming effect, model-simulated cumulative ocean’s uptake of CO₂ is 122 PgC greater than that in the simulation with CO₂-induced warming (Fig. 7, see Supplementary Fig. S2, Supplementary Table S1 online). For comparison, relative to the S0 simulation, by year 3500, the inclusion of -dependent increases the ocean’s uptake of CO₂ by 9 to 285 PgC (Fig. 7, see Supplementary Fig. S2, Supplementary Table S1 online). This comparison shows that in terms of the magnitude of oceanic CO₂ uptake, the effect of CO₂-calcification feedback could be comparable to or even much larger than that from the feedback of CO₂-induced warming.

Figure 7

Simulated effects of different CO₂-calcification feedback parameterization schemes (colored bars) compared with the effect of CO₂-induced warming (black bars) in year 3500 for (a) cumulative ocean CO₂ uptake, (b) atmospheric CO₂ concentration.

The effect of CO₂-calcification feedback is represented by the difference between S1 (S2, S3, R1, R2, R3) simulation with the inclusion of CO₂-induced warming and the S0 simulation with the inclusion of CO₂-induced warming. The effect of CO₂-induced warming is represented by the difference between S0 simulation with the inclusion of CO₂-induced warming and the S0 simulation without it. Detailed configuration of different model versions is provided in Table 1.

Discussion

Here, we use the UVic model to quantify the effect of potential CO₂-calcification feedback on the projections of the ocean carbon cycle and climate change. To evaluate the effect of CO₂-calcification feedback on the ocean carbon cycle and associated uncertainties, we include two different types of parameterization schemes that link CaCO₃ production with saturation state of calcite. In each scheme, a set of different parameters is used. As atmospheric CO₂ increases and the ocean becomes more acidic, the introduction of -dependent decreases the production of CaCO₃, increasing ocean alkalinity and enhancing the oceanic uptake of atmospheric CO₂. Therefore, it triggers negative feedbacks on the growth of atmospheric CO₂ and curbs global warming to a certain degree. Under SRES A2 CO₂ emission scenario with zero emission after year 2100 and a total cumulative emission of 2270 PgC, relative to the simulation with fixed CaCO₃: POC production ratio, by year 2100, the simulations that include CO₂-calcification feedback decrease modeled atmospheric CO₂ by 0.1 to 7 ppm; by year 3500, the simulations that include CO₂-calcification feedback decrease modeled atmospheric CO₂ concentration by 4 to 70 ppm. The magnitude of the CO₂-calcification feedback depends on the calcification- parameterization scheme used and parameter values used, demonstrating the importance of both the model structure uncertainty and parameter uncertainty of the CO₂-calcification feedback in regulating the ocean carbon cycle. While the inclusion of the CO₂-calcification feedback enhances the ocean’s uptake of atmospheric CO₂, it acts to mitigate ocean acidification mainly as a result of increased ocean alkalinity. For example, by year 3500, the inclusion of -dependent increases surface mean pH and by 0.8% and 15.0% in R3 relative to S0. Furthermore, our simulations show that the effect of CO₂-calcification feedback on ocean’s uptake of atmospheric CO₂ is comparable to and in some cases, much larger than the effect from CO₂-induced warming.

Our study shows a noticeable CO₂-calcification feedback on atmospheric CO₂. Different estimates of this feedback are reported in previous modeling studies^21,22,23,24. For example, Ridgwell et al. by using the function form of equation (4) to represent CO₂-calcification feedback, reported that under a CO₂ emission scenario that reaches a total of 4,000 PgC, the inclusion of CO₂-calcification feedback would lower atmospheric CO₂ concentration by 29–93 ppm by year 3000, depending on the parameter values used²¹. Hofmann and Schellnhuber²², using an exponential form that links calcification rate to carbonate ion concentration, predicted a 125 ppm decrease in atmospheric CO₂ by year 3000 as a result of CO₂-calcification feedback under a scenario with total anthropogenic CO₂ emission of 4,075 PgC. Other studies show relatively small effects from the CO₂-calcification feedback. For instance, Heinze, using a linear relationship that links calcification to seawater CO₂ partial pressure, projected a CO₂ decrease of 12 ppm due to CO₂-calcification feedback when atmospheric CO₂ reaches about 1400 ppm²³; Gangstø et al.²⁴, by using both Michaelis-Menten type formula and linear relationship to link calcification and CaCO₃ saturation, showed that by year 2100, the CO₂-calcification feedback acts to reduce atmospheric CO₂ concentration by 1 to 11 ppm under a range of parameterization schemes and IPCC scenarios of RCP8.5 and RCP6.0. Although these studies, including our study here, are not directly comparable because of different CO₂ pathways used and different inherent model structures in ocean dynamics and biogeochemistry, at least part of the difference is associated with different representations of CO₂-calcification feedback. Uncertainties in our model results here reflect uncertainties in modeled parameterization of CO₂-calcification feedback, which actually reflects uncertainties in our understanding of the calcification response to changing ocean chemistry. The reported response of the CaCO₃ production rate to ocean acidification varies dramatically between experiments using different species of calcifying groups or manipulation methods^20,26. Therefore, modeling simulations based on different results of experimental studies would result in different estimates of the effect of CO₂-calcification feedback. More coordinated experimental and observational studies on the CaCO₃ production response to ocean acidification are needed for a more reliable appraisal of the CO₂-calcification feedback.

In this study, we have investigated the response of calcification to acidification and its feedback to the ocean carbon cycle. Other processes relevant to CaCO₃ cycle that are not included in this study could also have important effect on the ocean carbon cycle. For example, inclusion of the dependence of CaCO₃ dissolution rate on CaCO₃ saturation state would further alter the ocean carbon cycle^19,27. In addition, the ballast effect, i.e., the link between the fluxes of particulate organic carbon (POC) and particulate inorganic carbon (PIC) to the abyssal ocean^28,29, is not included in the model. It is possible that reduced CaCO₃ production could result in a decrease in PIC export rate, which consequently lowers POC export rate. This reduced vertical transport of POC would weaken the oceanic carbon pump and decrease the capacity for the global ocean to absorb atmospheric CO₂, acting as a positive feedback to atmospheric CO₂^22,30. The feedback from the ballast effect could partly counteract the CO₂-calcification feedback, which merits further study.

This study demonstrates the potential important effect of CO₂-calcification feedback on the ocean carbon cycle and atmospheric CO₂ on the timescale from centuries to millennia. Further experimental and modeling studies are needed to acquire a better understanding of the CO₂-calcification feedback, which is crucial for a reliable projection of future atmospheric CO₂ concentrations and climate change.

Methods

Model description

An Earth system model of intermediate complexity, UVic ESCM (the University of Victoria Earth System Climate Model) version 2.9³¹, was used for this study. UVic consists of a 3D ocean general circulation model (Modular Ocean Model 2 or MOM2) with a resolution of 1.8° latitude by 3.6° longitude and 19 vertical layers in the ocean. The ocean component is coupled to a vertically integrated energy-moisture balance atmospheric model and a thermodynamic/dynamic sea ice model³². The land carbon cycle component is represented by a dynamic vegetation model (the Hadley Center model TRIFFID) and a land surface model (the Met Office surface exchange scheme or MOSES)³³. The ocean carbon cycle is represented by an inorganic carbon cycle model following the protocol of the Ocean Carbon-Cycle Model Intercomparison Project (OCMIP)³⁴ and a nutrient-phytoplankton-zooplankton-detritus (NPZD) marine ecosystem model³¹. The ocean carbon cycle model also comprises a sediment component that calculates CaCO₃ concentration from CaCO₃ dissolution and burial rates^35,36.

The CaCO₃ production in the model is calculated as

where Pr(CaCO₃) represents CaCO₃ production, denotes the zooplankton (Z) grazing of phytoplankton , represents the mortality of phytoplankton, denotes the mortality of zooplankton, represents the ratio of CaCO₃ production to the production of particulate organic carbon and is the carbon to nitrogen Redfield ratio³¹.

Parameterization of CaCO₃ production

In the original model, CaCO₃: POC production ratio in equation (2) is fixed at a constant value of 0.018. In this study, two types of parameterization functions of that link CaCO₃ production with saturation state of calcite are introduced into the UVic model.

The first type of parameterization follows the Michaelis-Menten function based on Pinsonneault et al.³⁷:

Where denotes the specified maximum value of (the CaCO₃: POC production ratio) and is a half-saturation constant^37,38. Different model versions based on this parameterization are denoted as “series S” (Table 1). In series S, the values of are selected to be 0.07, 1.5 and 20, which covers the range of values used by Pinsonneault et al.³⁷. For each , we calculate the corresponding value of by using the modeled preindustrial global mean sea surface calcite saturation state of 5.2 to ensure that the preindustrial surface mean CaCO₃: POC production ratio in each model version has the same value of 0.018, i.e., the fixed constant used in the original model.

Table 1 Summary of configurations of different model versions with different parameterizations of the dependence of calcification rate on saturation state of CaCO₃.

The second type of parameterization follows the thermodynamically-based function based on Ridgwell et al.^21,39:

Where represents a spatially-uniform constant and is a thermodynamically-based modifier with the power parameter η^21,39. Different model versions based on this parameterization are denoted as “series R” (Table 1). In series R, we set the values of η to be 0.53, 0.81 and 1.09, which covers the range of η values used by Ridgwell et al.²¹ and for each η we obtain the value of in the same way as in series S.

All together, we have a set of model versions with different parameterizations of (S1 to S3 and R1 to R3 in Table 1). In addition, we have the original model configuration with fixed (S0 in Table 1). For each parameterization, the dependence of CaCO₃: POC production ratio on are presented in Fig. 1.

Simulation experiments

All of the model versions mentioned above are integrated for 10,000 model years with fixed preindustrial atmospheric CO₂ concentration of 280 ppm to reach a quasi-equilibrium preindustrial state of global climate and carbon cycle. Using the preindustrial climate state as initial condition for the nominal year of 1800, two sets of 1700-year transient simulations are performed (from year 1800 to 3500). The first set of simulation includes the feedback from CO₂-induced warming on the ocean carbon cycle, whereas the second set of simulation does not include the radiative effect of increasing CO₂ on global climate. Each set of experiments includes seven simulations, corresponding to the seven model versions listed in Table 1. All these 14 simulations are integrated under the IPCC CO₂ emission scenario SRES A2 (“business-as-usual”) until year 2100. After year 2100, emissions are set to zero. During this spinup stage, at each time step continental weathering CaCO₃ flux via river discharge is set equal to the model-simulated accumulation flux of CaCO₃ from open ocean to deep-sea sediment. For transient simulations, weathering flux is held fixed at the rate that is diagnosed from the spinup run, whereas CaCO₃ accumulation flux is allowed to evolve freely.