Climate Sensitivity From Both Physical and Carbon Cycle Feedbacks

The surface warming response to anthropogenic forcing is highly sensitive to the strength of feedbacks in both the physical climate and carbon cycle systems. However, the definitions of climate feedback, λClimate in W·m−2·K−1, and climate sensitivity, SClimate in K/(W/m2), explicitly exclude the impact of carbon cycle feedbacks. Here we provide a new framework to incorporate carbon feedback into the definitions of climate feedback and sensitivity. Applying our framework to the Global Carbon Budget reconstructions reveals a present‐day terrestrial carbon feedback of λCarbon = 0.31 ± 0.09 W·m−2·K−1 and an ocean carbon feedback of −0.06 to 0.015 W·m−2·K−1 in Earth system models. Observational constraints reveal a combined climate and carbon feedback of λClimate+Carbon = 1.48 W·m−2·K−1 with a 95% range of 0.76 to 2.32 W·m−2·K−1 on centennial time scales, corresponding to a combined climate and carbon sensitivity of SClimate+Carbon = 0.67 K/(W/m2) with a 95% range of 0.43 to 1.32 K/(W/m2).


Introduction
Climate change is driven by a combination of radiative forcing and climate feedbacks operating in the climate system (see review in Knutti et al., 2017). The climate feedback is usually expressed in terms of the change in surface temperature multiplied by a feedback parameter, λ in W·m −2 ·K −1 , defined in terms of a wide range of physical processes, including the Planck response of enhanced longwave emission from a warmer surface and physical feedbacks from changes in water vapor, lapse rate, cloud cover, and ice albedo (Andrews et al., 2012;Andrews et al., 2015;Armour et al., 2013;Ceppi & Gregory, 2017;Gregory et al., 2004). In contrast, the carbon cycle responses and feedbacks are usually defined in terms of how atmospheric carbon dioxide and temperature linearly combine to alter the carbon inventories of the climate system (Arora et al., 2013;Friedlingstein et al., 2003Friedlingstein et al., , 2006, which may be expressed in terms of a radiative feedback parameter in W·m −2 ·K −1 (Gregory et al., 2009). However, there are difficulties in applying this carbon feedback method due to nonlinearities in how the separate atmospheric carbon dioxide and temperature effects combine together (Schwinger et al., 2014) giving rise to errors in the overall carbon feedback (Arora et al., 2013). This linearization method also cannot be used to calculate the carbon feedback directly from observational reconstructions of the carbon cycle (e.g., le Quéré et al., 2018), since there is no observational method to generate the hypothetical state with a range of feedback processes turned off for the real world.
The separation of forcing and feedback is dependent upon the nature of the climate perturbation. In climate model experiments driven by an imposed atmospheric CO 2 trajectory, a radiative forcing is provided from the increase in atmospheric CO 2 that automatically includes the effects of carbon cycle feedbacks. In contrast, for climate model experiments driven by carbon emissions, a radiative forcing is provided from the increase in atmospheric CO 2 directly caused by the carbon emission together with a radiative feedback from the change in atmospheric CO 2 caused by changes in the terrestrial and ocean carbon reservoirs.
To understand this distinction between forcing and feedback, consider the response of a conceptual Earth system model to a pulse of carbon released to the atmosphere, which is partitioned between the atmosphere, ocean, and terrestrial systems ( Figure 1a). The original carbon release drives a radiative forcing from the increase in atmospheric CO 2 (Figure 1b, red line), which is augmented by a radiative feedback from both non-CO 2 and CO 2 changes ( Figure 1b). These feedbacks may act to enhance or oppose the original forcing perturbation.
Our aim is to define and evaluate a new feedback parameter for the carbon system that 1. takes into account the combined effects of the non-CO 2 and CO 2 feedbacks operating in the climate system, thus avoiding the need to make a linearizing assumption that introduces error; 2. allows direct comparison between magnitudes of, and uncertainties in, feedbacks in the climate and carbon systems; and 3. allows the practical application of real-world observational data to analyze carbon feedback.

Definition of a Climate and Carbon Feedback Parameter
Consider the global energy balance for a climate system perturbed from an initial steady state (e.g., Figures 1a and 1b). The radiative forcing perturbation, ΔR′ , from the original forcing perturbation combined with subsequent feedback terms is balanced by additional outgoing longwave radiation emitted due to surface warming, λ Planck ΔT, and the net Earth system heat uptake, N, all terms defined in W/m 2 , Figure 1. Climate and carbon feedback over time for a 1,000 PgC emission experiment in a large ensemble of observationconstrained simulations. (a) Partitioning of a 1,000 PgC carbon emission (ΔI em , black line) between the terrestrial carbon (ΔI ter , light blue line and shading), ocean (ΔI ocean , red arrow), and atmospheric inventories (ΔI atmos , bright blue arrow). (b) Radiative forcing contributions from the CO 2 forcing from emissions without carbon feedbacks (red), plus the non-CO 2 feedbacks (blue), and from the carbon feedbacks (light blue). (c) Total climate feedback, λ Climate (light blue line and shading), and (d) total carbon feedback, λ Carbon (light blue line and shading), both showing contributions from individual feedback processes (dashed lines and arrows). On all panels, lines show the ensemble median, dark shading is 66% range, and light shading is the 95% range.
(1) where λ Planck is the Planck feedback parameter in W·m −2 ·K −1 and ΔT is the change in global-mean surface temperature in K. The radiative forcing, ΔR′, consists of an original forcing perturbation, ΔR forcing plus a subsequent feedback term, ΔR feedback , ΔR ′ = ΔR forcing +ΔR feedback , and the feedback may be written in terms of the separate non-CO 2 and CO 2 components, ΔR feedback non−CO2 and ΔR feedback CO2 , respectively (Figure 1b), such that The radiative feedback term from non-CO 2 feedbacks, ΔR feedback non−CO2 , includes the effects of changes in water vapor, lapse rate, clouds, and surface albedo, while the radiative feedback term from CO 2 , ΔR feedback CO2 , includes how radiative forcing from atmospheric CO 2 is altered by changes in the ocean and terrestrial carbon inventories.
The radiative response is often defined in terms of a climate feedback, λ Climate ΔT in W/m 2 , by combining the Planck response, λ Planck ΔT, with the radiative forcing from non-CO 2 feedbacks, ΔR feedback non−CO2 (e.g., see Intergovernmental Panel on Climate Change, 2013; Knutti et al., 2017), such that the energy balance in (1) may be reexpressed from (2) and (3) by The standard form of the climate feedback definition in (3) does not encapsulate the full sensitivity of the Earth system to perturbation, as the definition only accounts for the strength of the non-CO 2 feedbacks in the system and ignores the impact of carbon cycle feedbacks, which are instead treated as part of the forcing perturbation in (4). Here, we reexpress the energy balance relations (1) and (4) using a new combined carbon plus climate feedback, λ Climate+Carbon in W·m −2 ·K −1 , defined as the sum of the climate and carbon feedbacks, =ΔT. The energy balance in (1) may now be more explicitly written in terms of the original radiative forcing, ΔR forcing , balancing the radiative response from the combined climate and carbon responses, λ Climate+Carbon ΔT, plus the planetary heat uptake, N, such that To progress, we now wish to evaluate the carbon feedback λ Carbon in terms of changes in ocean and terrestrial carbon inventories.

Extracting the Feedback Component to CO 2 Change
A small carbon emission into a preindustrial state, δI em in PgC, is distributed between the atmospheric, ocean, and terrestrial carbon reservoirs (Figure 1a), where δI atmos = MδCO 2 is the change in atmospheric CO 2 inventory since the preindustrial, with M the molar volume of the atmosphere and CO 2 the atmospheric CO 2 mixing ratio; δI ocean = VδC DIC is the change in ocean dissolved inorganic carbon (DIC) inventory, with V the ocean volume and C DIC the mean ocean concentration of DIC; δI ter is the change in terrestrial (soil + vegetation) carbon inventory; and the symbol δ is used to indicate a small infinitesimal change since the preindustrial.
Radiative forcing is related to the log change in atmospheric CO 2 , R CO2 = aΔlnCO 2 (Myhre et al., 2013), so our goal is to find an expression for the change in log CO 2 due to some initial carbon emission, δI em , and subsequent responses to forcing and feedbacks within the atmosphere-ocean-terrestrial carbon system (7). The ocean inventory of carbon involves the DIC concentration C DIC , which may be expressed as a sum of process-driven components (Goodwin et al., 2008;Ito & Follows, 2005;Williams & Follows, 2011) involving the DIC concentration at chemical saturation with atmospheric CO 2 , C sat ; the disequilibrium concentration at subduction, C dis ; and the DIC contribution from regenerated biological material, C bio (C DIC = C sat + C dis + C bio ; Appendix A). Applying this ocean partitioning allows the perturbation to the global carbon inventory (7) to be reexpressed as where A pre is the global mean ocean preformed titration alkalinity; T oc is the global mean ocean temperature; B = ∂ln CO 2 /∂ln C sat is the Revelle buffer factor of seawater; and I atmos +(VC sat /B) = I B is the buffered carbon inventory of the air-sea system (Goodwin et al., 2007(Goodwin et al., , 2008(Goodwin et al., , 2015.
Rearranging (8) for δln CO 2 , and integrating for large changes using a constant buffered carbon inventory approximation (Goodwin et al., 2007, 2008, decomposes ΔR CO2 into the initial response to forcing from anthropogenic carbon emissions in the absence of feedbacks, ΔR forcing CO2 , plus components from terrestrial and ocean carbon cycle feedbacks, ΔR feedback where ΔR forcing CO2 is related to terms involving the carbon emission ΔI em and the change in ocean disequilibrium carbon ΔC dis from (8); ΔR feedback terrestrial is related to the feedback from the change in the terrestrial carbon inventory, ΔI ter ; and ΔR feedback ocean is related to the feedback from the changes in the ocean carbon inventory involving the saturated and regenerated carbon pools (8) from ΔC bio , ΔA pre , and ΔT oc (Appendix A).

Terrestrial Carbon Feedback
The change in the radiative forcing, ΔR feedback terrestrial in (9), is related to the change in the cumulative terrestrial carbon inventory relative to the preindustrial, ΔI ter in PgC (Figures 1a and 1b; Goodwin et al., 2007Goodwin et al., : 2008Goodwin et al., , 2011Goodwin et al., , 2015; Appendix A), which is given by The terrestrial carbon feedback λ Carbon is diagnosed from reconstructions of the change in the terrestrial carbon inventory and surface temperature record by substituting (10) into (5), This new relation (11) is now used to quantify terrestrial carbon feedback from observational reconstructions and Earth system model simulations. λ Carbon is estimated using the following parameters: the radiative forcing coefficient from CO 2 , a = 5.35 ± 0.27 W/m 2 (Myhre et al., 2013); the buffered carbon inventory, I B = 3451 ± 96 PgC (Williams et al., 2017); the global-mean surface temperature change ΔT from the Goddard Institute for Space Studies (GISS) Surface Temperature Analysis (GISTEMP) temperature record (Hansen et al., 2010), The terrestrial carbon feedback is now evaluated from four Coupled Model Intercomparison Project Phase 5 (CMIP5) Earth system models (CanESM2, HadGEM2-ES, HadGEM2-CC, and NorESM-ME), chosen as these have a reliable net export production (nep) variable allowing calculation of ΔI ter in (11). From the simulated ΔI ter and 11-year average ΔT (Figures 2a and 2b), and estimates of a and I B for each model (Williams et al., 2017), λ Carbon is evaluated from years 1959 to 2100 for the Representative Concentration Pathway 4.5 (RCP4.5) scenario (Figure 2c; Meinshausen et al., 2011). These four CMIP5 Earth system models have a smaller present-day terrestrial carbon feedback parameter ranging from 0.02 to 0.65 W·m −2 ·K −1 , broader than the 1σ range from observational reconstructions (Figure 2c, compare dashed lines to black line and shading). These differences between the Earth system models and the observational estimate arise from their discrepancy between the modeled and observational reconstructions of surface warming and terrestrial carbon uptake (Figures 2a and 2b). The future simulated λ Carbon remains stable under the RCP4.5 scenario, remaining close to the present-day values to year 2100 (Figure 2c).
Additional projections of carbon feedback are made using a very large ensemble of observation-constrained simulations from the Warming Acidification and Sea level Projector (WASP; Goodwin, 2016), for the RCP4.5 scenario (Figure 2, blue line and shading). We adopt the WASP model configuration of Goodwin (2018), with climate feedback including components from different processes operating on different response time scales (Figure 1). An ensemble is generated of many thousands of observation-consistent simulations using the Monte Carlo plus history matching (Williamson et al., 2015) methodology of Goodwin et al. (2018). First, the initial ensemble of 10 million Monte Carlo simulations is generated as in Goodwin (2018), with varied model input parameters, and we integrate each simulation from years 1765 to 2017 with historical forcing. Next the observation-consistency test of Goodwin (2018; see Table 2 therein) is applied with an updated terrestrial carbon range (supporting information Table S1) Table S1; Goodwin, 2018). Due to the observation-simulation agreement in ΔT and ΔI ter , the final WASP ensemble is also in good agreement with the observational reconstructions of terrestrial λ Carbon using (11)

Ocean Carbon Feedback
In a similar manner to how the terrestrial carbon feedback is defined relative to ΔI ter (11), the ocean carbon feedback is defined in relation to changes in the ocean DIC from regenerated carbon, ΔC bio , and changes in the ocean saturated carbon inventory from preformed alkalinity ΔA pre and ocean temperature ΔT oc (equations 8 and A8), via This ocean feedback term represents how changes in ocean temperature and ocean biological cycling of carbon and alkalinity from an initial carbon perturbation then feed back to alter the radiative forcing from atmospheric CO 2 . Based on Earth system models (evaluating ΔC bio , ΔA pre , and ΔT oc ), observational reconstructions for ocean heat uptake (Cheng et al., 2017), and the WASP ensemble (both evaluating ΔT oc only), the ocean carbon feedback is diagnosed as being much smaller than the terrestrial carbon feedback in the present day, ranging from −0.015 to 0.06 W·m −2 ·K −1 (Figures 2c and 2d), and remains small for the 21st century. The magnitude of the ocean carbon feedback might though increase beyond year 2100 due to continued climate-driven changes in ocean temperature, ΔT oc , and ocean biological carbon drawdown, ΔC bio .
Our estimate of ocean carbon feedback (Figure 2d) is much smaller than that implied by Gregory et al. (2009) because the previous approach (Friedlingstein et al., 2006) considers the transient disequilibrium of ocean DIC, C dis (eq. 8), to be part of the ocean carbon feedback, while our method considers C dis as part of the transient ocean response. An idealized feedback grows in magnitude over time, from zero the instant a forcing is applied to some final equilibrium value on long timescales. We do not consider C dis part of the ocean carbon feedback because the time evolution of C dis is the opposite sense: Ocean CO 2 disequilibrium is large the instant CO 2 is emitted into the atmosphere and then decays to zero over long time scales due to ocean carbon uptake (supporting information Figure S1).

Estimating the Combined Carbon-Climate Feedback and Sensitivity
We now place observational constraints on the combined climate plus carbon feedback, λ Climate+Carbon , and sensitivity, S Climate+Carbon in K/(W/m 2 ), by evaluating both λ Climate and λ Carbon for an idealized perturbation experiment in the observation-constrained WASP ensemble. Each of the 6,270 observation-consistent WASP ensemble members (Figure 2, blue line and shading) is reinitialized at a preindustrial spin-up and integrated for 500 years, forced with an idealized scenario consisting of a 1,000 PgC emission over the first 100 years (Figure 1a).
The total radiative forcing ΔR' is decomposed into the initial emission forcing, ΔR  terrestrial and smaller ocean temperature-CO 2 solubility effects (Figure 1d), but WASP does not simulate changes in C bio , which remain small in Earth system models (Figure 2d). For illustration purposes, λ Climate and λ Carbon contributions from individual processes are shown by integrating the WASP ensemble with combinations of feedback processes switched off (Figures 1c and 1d, dashed lines are ensemble median values).
Estimates of the carbon and climate feedback parameters, λ Carbon and λ Climate , applicable on century time scales, are made from the observation-consistent ensemble distributions at the end of the 1,000-PgC emission simulations (Figure 1). The 500-year carbon feedback after a 1,000-PgC emission has a median (and 95% range) of λ Carbon = 0.21 (−0.02 to 0.5) W·m −2 ·K −1 (Figure 1c), while the physical climate feedback after a 1,000-PgC emission is λ Climate = 1.27 (0.73 to 1.88) W·m −2 ·K −1 (Figures 1b and  3a, blue).
The impact of carbon feedbacks is therefore to increase the overall carbon plus climate feedback above λ Climate , with an observation-constrained distribution of λ Climate+Carbon = λ Carbon +λ Climate = 1.48 (0.76 to 2.32) W·m −2 ·K −1 (Figure 3a). Consequently, the climate sensitivity, S = 1/λ, from non-CO 2 feedbacks alone, S Climate = 0.79 (0.53 to 1.37) K/(W/m 2 ), is reduced to S Climate+Carbon = 0.67 (0.43 to 1.32) K/(W/m 2 ), when encapsulating both non-CO 2 and CO 2 feedbacks acting together (Figure 3b). This estimate of S Climate+Carbon (Figure 3b, black) represents the total sensitivity of the climate system to perturbation by carbon emission over century time scales, including both physical climate and carbon-cycle feedbacks.

Conclusions
A new method is presented to constrain the carbon feedback parameter, finding for the present-day terrestrial carbon system λ Carbon = 0.33 ± 0.09 W·m −2 ·K −1 (Figure 2c) based on observational reconstructions of carbon uptake and warming (Hansen et al., 2010;le Quéré et al., 2018) and λ Carbon = 0.02 to 0.65 W·m −2 ·K −1 in four CMIP5 models. This compares to a previous method implying terrestrial carbon feedback of λ Carbon = 0.7±0.5 W·m −2 ·K −1 , based on analysis of the earlier Coupled Climate-Carbon Cycle Model Intercomparison Project (C4MIP) climate model ensemble (Arneth et al., 2010;Friedlingstein et al., 2006;Gregory et al., 2009) and comprising a linearization of separate CO 2 -carbon (1.1 ± 0.5 W·m −2 ·K −1 ) and climate-carbon (−0.4 ± 0.2 W·m −2 ·K −1 ) components. The linearization assumed by the previous method introduces errors (Arora et al., 2013;Schwinger et al., 2014), and this means the method cannot be applied to observational reconstructions. To avoid making the linearization assumption, and so be applicable to observational reconstructions, our method assumes a constant buffered carbon inventory (Appendix A), a good approximation for carbon perturbations up to~5,000 PgC or for atmospheric CO 2 reaching~1,100 ppm (Goodwin et al., 2007(Goodwin et al., , 2008).
The Equilibrium Climate Response to Emission (ECRE), in K/1,000 PgC, expresses the warming per unit carbon emitted once ocean heat uptake approaches zero over centennial to multicentennial time scales, ECRE = ΔT/ΔI em (Frölicher & Paynter, 2015). This atmosphere-ocean equilibrium is approached over many centuries, but not necessarily reached due to the effect of other longer time scale carbon and climate feedbacks, such as from ice sheet-albedo feedbacks  and multimillennial CaCO 3 sediment and weathering responses (Archer, 2005). In the absence of carbon feedbacks, Williams et al. (2012) related the ECRE to climate feedback, λ Climate , via ECRE = a/(λ Climate I B ). Here we extend the relationship to include the effects of both climate and carbon feedbacks, ECRE = a/ (λ Climate+Carbon I B ), applicable after ocean CO 2 invasion and heat uptake but prior to significant CaCO 3 sediment and weathering responses (Archer, 2005;Goodwin et al., 2007Goodwin et al., , 2008Goodwin et al., , 2015. Our historically constrained feedback estimates (Figures 3a and 3b) imply ECRE =1.0 (0.6 to 2.0) K/1,000 PgC emitted (Figure 3c), with the upper half of our range (from 1 to 2 K/1,000 PgC) consistent with a CMIP5-based estimate (Frölicher & Paynter, 2015). Carbon and climate feedbacks not constrained historically (e.g., MacDougall & Knutti, 2016;Pugh et al., 2018;Rohling et al., 2018;Zickfeld et al., 2013) may alter future λ Climate+Carbon and so alter ECRE. We anticipate this relationship, ECRE = a/(λ Climate+Carbon I B ), will be useful in elucidating how different carbon and climate feedbacks contribute to the multicentury warming response to carbon emission.

Appendix A: Connecting Radiative Feedbacks to Changes in Carbon Inventories
Our aim is to separate the total CO 2 radiative forcing into a sum of linearly separable terms representing different processes and feedbacks. We start by considering how carbon emissions perturb carbon storage across the atmosphere-ocean-terrestrial system. We now write identities for the changes in atmospheric and ocean carbon inventories containing terms with δln CO 2 . Using the identity for small perturbations in x, δx = xδln x, we write an identity for a small perturbation in atmospheric CO 2 inventory, δI atmos , in terms of a small perturbation to the logarithm of atmospheric CO 2 , δln CO 2 , δI atmos ¼ I atmos δ lnCO 2 ; (A1) where I atmos is the initial atmospheric CO 2 inventory at the unperturbed preindustrial state.
The change in ocean DIC is considered, via a process-driven viewpoint (Goodwin et al., 2008;Ito & Follows, 2005;Williams & Follows, 2011), in terms of the sum of components from the change in chemically saturated DIC arising from changes in atmospheric CO 2 and seawater properties, δC sat ; the change in chemical disequilibrium of ocean DIC relative to atmospheric CO 2 , δC dis ; and the combined change in ocean DIC from regenerated soft tissue and CaCO 3 drawdown, δC bio : Due to the carbonate chemistry system, the perturbation to C sat is a function of the change to the logarithm of atmospheric CO 2 , δln CO 2 ; the change in mean ocean preformed titration alkalinity, δA pre ; the change in mean seawater temperature, δT oc ; and the change in mean seawater salinity, δS: δC sat = δC sat (δ ln CO 2 , δA pre , δT oc , δS). This small perturbation to C sat is now expanded after Goodwin and Lenton (2009) into components from δln CO 2 , δA pre , δT oc , and δS: where the salinity term, (∂C sat /∂S)δS, is small and henceforth will be omitted.
Again, using the identity for small perturbations in a variable x, δx = xδln x, but applying to C sat , the term for the sensitivity of C sat to ln CO 2 in (A3) becomes where B = (∂ln CO 2 /∂ln C sat ) is the Revelle buffer factor expressing how fractional chemical in atmospheric CO 2 is much larger than fractional changes in DIC with B, the order 10 for the present ocean (e.g., Williams & Follows, 2011). Substituting (A4) into (A3), and noting that I ocean = VC DIC , produces an identity for δI ocean containing a term in δln CO 2 : where I sat ocean ¼ VC sat is the ocean inventory of saturated DIC at current atmospheric CO 2 . Substituting δI ocean (A5) and δI atmos (A1) into (7), and rearranging to solve for the log change in atmospheric CO 2 mixing ratio to small perturbations to I em , I ter , C dis , C bio , A pre , and T oc , reveals The issue now is that this identity for δln CO 2 (A7) applies only to small infinitesimal perturbations, and we wish to solve for the change in log CO 2 for large finite perturbations. The next step is therefore to integrate (A6) over large finite perturbations in I em , I ter , C dis , C bio , A pre , and T oc .
To integrate (A6), we note that the left-hand side contains the buffered carbon inventory, I B (Goodwin et al., 2007(Goodwin et al., , 2008, defined as the atmospheric carbon inventory added to the ocean saturated-DIC inventory divided by the Revelle buffer factor, I B ¼ I atmos þ I sat ocean =B À Á . I B represents the total buffered CO 2 and DIC in the atmosphere-ocean system that is available for redistribution between the CO 2 and carbonate ion pools , given that the majority of ocean DIC is in the form of bicarbonate ions. At the preindustrial state, I B = 3,451 ± 96 PgC in the CMIP5 models analyzed by Williams et al. (2017).
Using this constant buffered carbon inventory approach (supporting information), we integrate (A6) to find the change in atmospheric CO 2 for large finite perturbations to total carbon emitted, ΔI em ; the change in terrestrial carbon storage, ΔI ter ; and the large changes in mean ocean values of ΔC dis , ΔC bio , ΔA pre , and ΔT oc , so that Multiplying (A7) by the CO 2 -radiative forcing coefficient, a, produces an expression for the radiative forcing from CO 2 in (9), as a sum of separable terms representing different processes, each linked to a different change in a carbon inventory. The CO 2 radiative forcing, represents the direct effect of the emitted carbon partitioned between the atmosphere and ocean, including both chemical equilibrium (ΔI em ) and the transient chemical disequilibrium between the atmosphere and ocean (ΔC dis ) of the carbon emitted, but without subsequent carbon feedbacks. The radiative forcing from the carbon feedbacks for the terrestrial, depends on the change in terrestrial carbon storage since the preindustrial, and that for the ocean, depends on the changes to the ocean biological drawdown of soft tissue and CaCO 3 , including the titration alkalinity effects, and on the changes in the seawater temperature since the preindustrial, altering the solubility of CO 2 in seawater.