Ocean carbon uptake under aggressive emission mitigation

Abstract. Nearly every nation has signed the UNFCC Paris Agreement, committing to mitigate anthropogenic carbon emissions so as to limit the global mean temperature increase above pre-industrial levels to well below 2 ∘C, and ideally to no more than 1.5 ∘C. A consequence of emission mitigation that has received limited attention is a reduced efficiency of the ocean carbon sink. Historically, the roughly exponential increase in atmospheric CO2 has resulted in a proportional increase in anthropogenic carbon uptake by the ocean. We define growth of the ocean carbon sink exactly proportional to the atmospheric growth rate to be 100 % efficient. Using a model hierarchy consisting of a common reduced-form ocean carbon cycle model and the Community Earth System Model (CESM), we assess the mechanisms of future change in the efficiency of the ocean carbon sink under three emission scenarios: aggressive mitigation (1.5 ∘C), intermediate mitigation (RCP4.5), and high emissions (RCP8.5). The reduced-form ocean carbon cycle model is tuned to emulate the global-mean behavior of the CESM and then allows for mechanistic decomposition. With intermediate or no mitigation (RCP4.5, RCP8.5), changes in efficiency through 2080 are almost entirely the result of future reductions in the carbonate buffer capacity of the ocean. Under the 1.5 ∘C scenario, the dominant driver of efficiency decline is the ocean's reduced ability to transport anthropogenic carbon from surface to depth. As the global-mean upper-ocean gradient of anthropogenic carbon reverses sign, carbon can be re-entrained in surface waters where it slows further removal from the atmosphere. Reducing uncertainty in ocean circulation is critical to better understanding the transport of anthropogenic carbon from surface to depth and to improving quantification of its role in the future ocean carbon sink.



Introduction
The ocean has absorbed 39% of the CO 2 from industrial era fossil fuel combustion and cement production (Friedlingstein 20 et al., 2019). The rest of the CO 2 remains in the atmosphere where it acts as the primary driver of climate change. At the global scale, the partial pressure of CO 2 in the atmosphere (pCO atm 2 ) is greater than the partial pressure of CO 2 in the surface ocean (pCO ocn 2 ), thus there is a net ocean sink. The difference in partial pressures has grown over time, therefore ocean uptake of atmospheric CO 2 has increased over the industrial era (Khatiwala et al., 2009;DeVries, 2014). The carbon that has been added to the ocean and atmosphere as the result of anthropogenic CO 2 emissions is referred to as anthropogenic carbon, C ant .
The rate of ocean C ant uptake is controlled by the rate of physical removal of C ant from the surface ocean into the ocean interior. Various processes set the rate of physical C ant removal, with significant contributions coming from vertical diapycnal diffusion and isopycnal eddy diffusion (Bopp et al., 2015;Gnanadesikan et al., 2015). Advection dominates regional patterns C ant fluxes into (reemergence) and out of (subduction) the seasonal mixed layer (Bopp et al., 2015;Toyama et al., 2017). The large positive and negative signs of the advective flux mostly cancel when globally integrated (Bopp et al., 2015), thus advection 30 does not play a dominant role in setting the globally integrated C ant air-sea flux. In density space, C ant is primarily absorbed in lighter subtropical waters, and then transferred to denser mode and intermediate waters by diapycnal fluxes associated with watermass transformation (Iudicone et al. 2016). Using an effective surface diffusivity (K z,ef f ), i.e. summarizing the net removal by these processes as a single diffusive process, one-dimensional diffusion models have been shown to be consistent with observations and complex models (Gnanadesikan et al., 2015;Oeschger et al., 1975). 35 Growth of the natural sinks (land biosphere and ocean) has been outpaced by the growth of atmospheric CO 2 and thus sink efficiency has declined (Canadell et al., 2007;Raupach et al., 2014). Efficiency of land and ocean sinks is described by the CO 2 sink rate (k S ; Raupach et al., 2014), which is the combined ocean-land CO 2 uptake per unit atmospheric CO 2 above preindustrial levels (C ant,A ; Pg C):

40
Where F ant,L (Pg C yr −1 ) is the anthropogenic land sink and F ant,M (Pg C yr −1 ) is the anthropogenic ocean sink. Observations of k S from 1959-2012 indicate a robust declining trend, and thus the rate of increase in the natural sinks was slower than the accumulation of carbon in the atmosphere. Using a simple climate model, Raupach et al. (2014) attribute the declining trend to slower-than-exponential CO 2 emissions growth (∼35% of the trend), a decline in the size of major volcanic eruptions, which cause brief periods of global cooling (∼25%), response of the natural sinks to a warming climate (∼20%), and nonlinear 45 responses to increasing atmospheric CO 2 (mostly attributable to ocean chemistry; ∼20%).
Slowing of the emissions growth rate, and thus the pCO atm 2 growth rate, reduces the efficiency of ocean C ant uptake (McKinley et al., 2020;Raupach et al., 2014); this response is related to the timescales of C ant transfer to the ocean interior (Raupach et al. 2014). A reduced pCO atm 2 growth rate is inevitable, due either to climate policy, or by the eventual exhaustion of fossil fuel reservoirs. Nearly every nation has signed the Paris Agreement, which requires participating governments to 50 pledge to mitigate future greenhouse gas emissions in an attempt to limit the global mean temperature increase to 1.5 • C. While countries' emissions pledges are incompatible with the 1.5 • C goal (UNEP, 2019), continued commitment to these emissions pledges will inevitably end the historical pattern of exponential pCO atm 2 growth in coming decades.
The reductions to efficiency that are attributable to a slowing pCO atm 2 growth rate will be at least partially compensated by a decrease in the strength of the climate-carbon feedbacks that reduce efficiency of ocean C ant uptake (Friedlingstein et al.,55 2013; Raupach et al., 2014). Past studies have separated carbon cycle feedbacks into CO 2 concentration effects and climate driven effects . The CO 2 concentration driven effect is the net result of two effects: increased flux driven by increasing pCO atm 2 and reduced flux driven by a declining buffer capacity of the ocean. The buffering capacity of 2013; Randerson et al., 2015;Schwinger and Tjiputra, 2018). However, the idealized simulations used in these studies have not allowed for quantification of the additional contribution of reduced buffering capacity to reduced ocean carbon uptake.
This work expands upon previous work that has quantified future change in ocean C ant uptake by separately accounting for changes due to buffering. We will compare a future scenario with moderate levels of mitigation (RCP4.5; Meinshausen et al., 2011), and an aggressive mitigation scenario where the 1.5 • C target is met (1.5 • C; Sanderson et al., 2017) to RCP8.5 70 using an Earth System model (ESM). In the RCP8.5 scenario , pCO atm 2 increases exponentially and represents our no mitigation baseline. With our set of ocean carbon cycle simulations, we will calculate how warming and reduced buffering, referred to here as chemical capacity, affect ocean C ant uptake.
The contribution of ocean C ant uptake to k S is referred to as k M :

75
In the past, k M has been influenced by a slowing of the CO 2 emissions growth rate (McKinley et al., 2020), volcanic aerosol induced cooling of the surface ocean (McKinley et al., 2020), changing ocean chemistry, and changes to physical climate .
Under exponentially increasing pCO atm 2 , constant gas solubility, and constant chemical capacity, k M , would remain constant, and thus by definition, the proportionality between increases in atmospheric CO 2 and increases in ocean C ant uptake 80 would also remain constant. Because these conditions approximately describe the historical conditions of the ocean carbon cycle, constant proportionality for ocean C ant uptake has been used as a null hypothesis in studies of the drivers of historical regional and global scale changes in the ocean carbon cycle (Lovenduski et al., 2008;Gruber et al., 2019a). Here we refer to this constant proportionality (i.e. k M = constant) as the "historical scaling", instead of the seemingly contradictory original term, the "transient steady state assumption" (Gammon et al., 1982;Tanhua et al., 2007;Lovenduski et al., 2008;Gruber et al., 85 2019a). With constant k M , the evolution of ocean C ant concentration at all points in space also follows the historical scaling.
This is because the exponential shape of pCO atm 2 is passed on to pCO ocn 2 by the C ant air-sea flux. The amplifying effect that approximately exponentially increasing pCO atm 2 has on the ocean C ant concentration and ocean C ant uptake can be removed using the historical scaling, and in previous work, deviations from the historical scaling for ocean C ant uptake and C ant concentrations have been attributed entirely to internal ocean mechanisms. However, we illustrate that previous work has likely 90 overestimated of the impacts of internal variability on the ocean carbon cycle, given the close relationship between the histor-ical scaling and k M , which is sensitive external mechanisms such as volcanic forcings and pCO atm 2 growth rate (McKinley et al., 2020).
The focus of this work is to determine the primary mechanisms in projections of future climate that will drive reductions to the efficiency of ocean C ant uptake under emission mitigation and, thus, a reduced growth rate of atmospheric CO 2 . Here 95 we consider efficiency of ocean C ant uptake as a measure of how effectively the input, pCO atm 2 , is converted into the desired output, ocean C ant uptake. More efficient ocean C ant uptake would result in the ocean absorbing more carbon at a given pCO atm 2 . In the following sections, we use a one-dimensional ocean carbon cycle model to diagnose the mechanisms of efficiency decline in climate projections from a complex ESM, with the goal of understanding future changes in the efficiency of ocean C ant uptake.

Methods
In this section, we develop equations for ocean sink efficiency and introduce our one-dimensional ocean carbon cycle model.
We identify the mechanisms driving changes in efficiency by comparing the behaviour of a one-dimensional ocean carbon cycle model to an ESM, the Community Earth System Model (CESM). CESM simulations are publicly available, provided by the National Center for Atmospheric Research (NCAR). The one-dimensional ocean carbon cycle model emulates the ocean 105 circulation and carbon cycling of the ESM, but allows for rapid integration to facilitate mechanistic exploration.

Efficiency Metric and Historical Scaling
Ocean sink rate (k M ; Equation 2) represents the efficiency of ocean C ant uptake. The efficiency metric used here, η, is k M referenced to the year 1990, so that efficiency may be expressed as a percentage: Referencing k M to 1990 values maximizes the time ocean C ant uptake is at 100% efficiency during the historical period, 1920-2006 ( Figure S1). The historical scaling for ocean C ant uptake (F ant ) is closely related to k M : * The rightmost expression in Equation 4 is the F ant historical scaling, and is based the assumption of constant efficiency, and thus mathematically equivalent to extrapolating F ant using a fixed k M (Equation 2,4). The overset "*" notation indicates 115 the variable that has been extrapolated with the historical scaling. When using the historical scaling, F ant (1990) is diagnosed from the CESM, and * F ant (t) is obtained mathematically by extrapolating F ant (1990) based on the relative increase in atmospheric C ant from 1990 values ( 1990) ). For example, F ant (1990) simulated by CESM was 1.7 Pg C ant yr −1 , and the atmospheric perturbation in 1990 was 74 ppm (∼157 Pg C). In the future, if the atmospheric perturbation is doubled from 1990 4 https://doi.org/10.5194/bg-2020-254 Preprint. Discussion started: 16 July 2020 c Author(s) 2020. CC BY 4.0 License. values to 148 ppm (∼314 Pg C), * F ant would also double to 3.4 Pg C ant yr −1 . Expressing ocean carbon sink efficiency (η) as 120 Equation 5 illustrates the link to the historical scaling:  (Lovenduski et al., 2008). In the future, as k M declines from 1990 values, F ant will be less than * F ant (t), and efficiency will decline. Here * F ant (t), extrapolated into the future with projected pCO atm 2 , will be used to represent an upper bound for future ocean C ant uptake.
While k M remains constant, the global mean ocean C ant profile (C ant (z, t)) can also be estimated ( * C ant (z, t)) using the historical scaling Gruber et al., 2019a): The C ant historical scaling exists because the C ant air-sea flux is effectively "pulling" pCO ocn are both exponential curves. Because ocean chemistry has remained relatively constant over the historical period, we have been able to assume that surface ocean C ant concentration is linearly related to pCO ocn 2 . Mathematically, surface ocean C ant concentration is closely related to the time integral of the 135 C ant air-sea flux (Methods 2.3). Therefore, because the integral of an exponential is also an exponential, surface C ant concentration has also increased exponentially, and that exponential is then propagated by ocean circulation to deeper layers. However, looking forward, the linear relationship between C ant concentration and pCO ocn 2 will end due to a decreasing chemical capacity for CO 2 . Also, the propagation of the surface exponential signal to depth by ocean circulation is not instantaneous, thus when emissions are mitigated, waters towards the surface will be changing in proportion to flattening atmospheric CO 2 , but 140 deeper in the water column they will be changing in proportion to the exponential atmospheric CO 2 signal from decades prior.
Future C ant (z), will deviate from * C ant (z).

Ocean Component of the Earth System Model
The CESM provides a realistic simulation of the response of the ocean carbon cycle to climate change. The CESM's ocean . For the 1.5 • C scenario, a concentration pathway was designed that limited warming 155 the CESM to 1.5 • C, for the purpose of investigating avoided climate impacts (Sanderson et al., 2017). This scenario features the same forcing as RCP8.5 until 2017, except for CO 2 . The projected CO 2 forcing was not smoothly joined to the historical CO 2 forcing, creating a period of low C ant flux, which the ocean C ant sink recovers from by 2017 ( Figure S2).  Sanderson et al., 2017). Ocean biogeochemistry output is limited to 9 members for the medium ensemble and the 3 for the low warming ensemble, thus we also only use 9 ensemble members for the RCP8.5 experiment.
In coupled climate models, historical climate variability of the carbon sink is not expected to match observations because 165 the phasing of ENSO or other internal climate variability is different in each ensemble member. Averaging across an ensemble removes the imprint of internal variability leaving only the climate system response to external forcing. With only a single coupled climate simulation, decadal means are used to smooth internal climate variability, but with an ensemble, a single year of the ensemble mean provides a snapshot of the climate response to external forcing. All output analyzed here is the ensemble mean because we are focused on the externally forced signal. CESM is used for maps and sections, and we tune a 170 one-dimensional model to replicate its global mean behavior to elucidate the underlying mechanisms.

One-Dimensional Ocean Carbon Cycle Model
The behavior of the one-dimensional ocean carbon cycle model is more easily interpreted than the behavior of the complex ESM. Here we employ an established one-dimensional ocean carbon cycle model that is based on impulse response functions.
This model is easily interpretable and has been used for decades to emulate ocean carbon uptake simulated by complex ESMs 175 (Joos et al., 1996;Meinshausen et al., 2011;Raupach et al., 2014). The impulse response function form of our model has been used to convert emissions projections into the CO 2 concentration pathways (RCP4.5, RCP8.5) that are used to force the CESM, as well as others in the CMIP5 suite of ESMs ) used in IPCC AR5 (Cias et al., 2013.
Impulse response functions can be used to characterize the response of dynamical systems to small perturbations around a steady state. In our case, the small perturbation is the C ant perturbation to the preindustrial carbon cycle. With this method, 180 the full response of the system is considered to be the sum of the system's response to infinitely many discrete pulses. For the ocean carbon cycle, a pulse is the C ant added to the surface ocean by air-sea exchange for a time frame specified by the onedimensional model's time step. The impulse response function describes how long that C ant pulse remains in surface ocean.
C ant air-sea flux and surface C ant concentration are calculated at each time step, while the response function is fixed. The surface ocean C ant is mathematically expressed as the convolution integral of the impulse (C ant air-sea flux) and the impulse 185 response function (lifetime of that C ant pulse). A conceptual version of this approach is illustrated in Appendix A.
The one-dimensional model is forced with the same historical and projected pCO atm This is the convolution integral of C ant air-sea flux (F ant ) and the mixed-layer impulse response function, r(t). A convolution integral calculates the concentration at time t by calculating the fraction of previous pulses (F ant (u)), that entered the ocean at times u (from t i = 0 to t), that remain in the surface ocean at time t. The effective mixed layer depth, h, converts the The mixed-layer impulse response function (r(t)) used here is from Joos et al. (1996), and was diagnosed by those authors from the box-diffusion model, HILDA (HIgh Latitude-exchange/interior Diffusion-Advection). With this method, the response 200 function is fixed throughout time, which is equivalent to the assumption that ocean circulation is constant.
The convolution integral (Equation 7) represents the time integral of a box-diffusion model's surface C ant tendency equation: Where h again, is the effective mixed layer depth (same as Equation 7) and K z,ef f is the effective vertical diffusivity of the 205 one-dimensional model. The one-dimensional model's K z,ef f must match that of the ocean component of the ESM in order for the growth of C ant uptake of the one-dimensional model to match that of the ocean component of the ESM (Gnanadesikan et al., 2015). Diagnosing an ocean model's mixed layer impulse response function diagnoses the net C ant removal by simulated physical processes, and thus the K z,ef f of the ocean model. However, diagnosing the mixed layer impulse response function requires special simulations (Joos et al., 1996), and is unnecessary if one instead uses h as tuning parameter (Meinshausen et al.,210 2011). Experiments with one-dimensional carbon cycle models show that K z,ef f is indirectly tuned by adjusting h (Oeschger et al., 1975). Thus by changing h of the one-dimensional model, we can match the K z,ef f of the CESM and therefore the one-dimensional model replicates CESM ocean C ant uptake over the historical period.
C ant (t) and F ant are calculated explicitly by the one-dimensional model, and the second term on inside the integral in Equation 9, the diffusive C ant flux, is not modeled explicitly by the one-dimensional model, but can be determined exactly by 215 residual. In the one-dimensional model, the C ant air-sea flux is calculated as follows: F ant is the ocean flux of anthropogenic carbon, which is dependent on the air-sea partial pressure gradient and the gas ex- is based on a parameterization that includes effects of changing buffer capacity and temperature (Appendix B). and ∆C cgrad , combine to make ∆C total lower than the historical scaling (∆ * C hs ):

Process Decomposition Using One-Dimensional Ocean Carbon Cycle Model Simulations
Changes in ocean chemical capacity, ∆C chem , are the change in C ant in a one-dimensional model simulation with all effects, ∆C total , minus the change in C ant in a one-dimensional model simulation with constant chemical capacity, ∆C ccc (Table   1). The carbon gradient effect, ∆C cgrad , is the difference between ∆C ccc and the time integral of * Because circulation is fixed in the one-dimensional ocean carbon cycle model, changes to the carbon gradient effect are not 235 due to changes in circulation. In the results, we show that ocean C ant uptake has a low sensitivity to simulated changes in circulation from 1920-2080.

C ant Air-Sea Flux Decomposition
We use the one-dimensional model to identify the dominant controls on ocean C ant uptake, by decomposing the C ant air-sea flux into multiple terms. In order to perform this decomposition, surface ocean pCO ocn The first term on the right hand side is the impact of the atmospheric CO 2 growth rate on the flux (atmosphere component) and the second term is the impact of the ocean CO 2 growth rate on the flux (ocean component). In Equation 12, ∂Fant ∂pCO atm 2 = ∂Fant ∂pCO ocn 2 , and is constant, thus variations in F ant are solely due to variations in the atmospheric CO 2 growth rate and the 250 ocean CO 2 growth rate. The pCO ocn 2 closely follows pCO atm 2 , and the sign of their growth rates is the same. When the atmospheric CO 2 growth rate is positive, the atmospheric CO 2 growth rate acts to enhance F ant , and the ocean CO 2 growth rate acts to decrease F ant (Equation 10). The atmospheric CO 2 growth rate is prescribed, and cannot be separated further in this framework, while the ocean component is expanded into the following terms: The two ocean terms are the product of the change in C ant times the buffer factor, and the change in temperature times the We refer to the three terms on the right hand side, from left to right, as the impact of the air-sea flux on pCO ocn 2 , the impact of ocean circulation on pCO ocn 2 , and the impact of warming on pCO ocn 2 . Because the impact of warming is small, the ocean 260 CO 2 growth rate is a balance between the impact of the air-sea flux on pCO ocn 2 and the impact of ocean circulation on pCO ocn 2 . The sign of F ant is always positive in all scenarios, thus the impact of the air-sea flux always acts to increase pCO ocn 2 . The sign of the vertical gradient ( ∂Cant ∂z ) is always negative, thus the impact of ocean circulation always acts to decrease pCO ocn 2 . In the ∆C total experiment (Table 1), F ant , the vertical C ant gradient, the buffer factor, and sensitivity to warming, are freely evolving (Equation 14). In the ∆C ccc experiment, the buffer factor is fixed at preindustrial values. The ∆ * C hs experiment is equivalent 265 to a constant buffer factor, a warming sensitivity of 0, and, as shown in the results, setting the C ant profile to that predicted by historical scaling. The vertical profile alters pCO ocn 2 through the vertical gradient (Equation 14). In the results we will use Equation 14 to illustrate how changes to the impact of ocean circulation result in reduced efficiency of ocean C ant uptake in response to emission mitigation.

270
In the following sections, we use ocean output from the ocean component of the ESM to calculate the efficiency of ocean C ant uptake (Results 3.1) and determine if the evolution of C ant concentration along meridional sections is consistent with historical scaling (Results 3.2). We then use the one-dimensional model to attribute changes in the efficiency of C ant uptake to physical and/or chemical mechanisms (Results 3.3). Changes to the air-sea flux arising from changes to the atmospheric CO 2 growth rate and ocean CO 2 growth rate are also diagnosed (Results 3.4). Our analysis includes scenarios with aggressive 275 emission mitigation (1.5 • C), intermediate emission mitigation (RCP4.5), and no emission mitigation (RCP8.5). See Figure 2c for the pCO atm 2 forcing for these scenarios.

Projected Spatial Redistribution of the C ant Air-Sea Flux
Using output from the ocean component of the ESM, we diagnose C ant air-sea flux for three future scenarios: 1.5 • C, RCP4.5, RCP8.5. Here we focus on the projected spatial distribution of C ant air-sea flux from 2020-2080. Ocean C ant uptake persists throughout the simulation.
In the RCP4.5 scenario, changes to the spatial pattern lie somewhere between RCP8.5 and the 1.5 • C scenario. Equatorial Pacific outgassing of C ant grows over time, but is less widespread and intense than in the 1.5 • C scenario (Figure 1 the equatorial Pacific, the spatial pattern of C ant air-sea flux is similar to the RCP8.5 scenario, but the amplitude of uptake is reduced. Relative to the scenarios with emission mitigation (1.5 • C and RCP4.5) the RCP8.5 scenario features a consistent spatial pattern of the C ant air-sea flux (Figure 1, top row). The primary change over time is an amplification of magnitude, with the highest flux intensity occurring in 2080.

295
Ocean C ant uptake is greatest in RCP8.5, and is the lowest in 1.5 • C (Figure 2a). In all scenarios ocean C ant inventory increases throughout the period (Figure 2d). In the RCP4.5 scenario, C ant air sea flux peaks in 2050, and then gradually declines. In the 1.5 • C scenario, ocean C ant uptake peaks in 2020, and is almost zero by 2080. In the RCP4.5 scenario ocean C ant uptake initially increases and then returns to 2020 values by 2080.
Extrapolation of the ocean C ant uptake based on the historical scaling ( *   Figure S2).
The efficiency decrease is linear in RCP8.5 and RCP4.5, but exponential in the 1.5 • C scenario. The 1.5 • C scenario is the only scenario with negative pCO atm 2 growth rates, which substantially modifies the ocean carbon cycle response, as shown below.

Projected Changes in the Ocean Interior
Here we analyze the evolution of the C ant vertical gradient by applying the historical scaling to the vertical profile of C ant (Equation 6). A weakening of the vertical gradient of C ant would reduce the ability of physical removal of C ant to 310 maintain the C ant air-sea flux (F ant ; Equation 14). Thus, via the vertical C ant gradient, interior C ant can alter the airsea flux. Deviations of globally averaged C ant profiles (C ant (z)) from the C ant historical scaling ( * C ant (z)) are defined as , more carbon is stored at that location than predicted by the C ant historical scaling (Equation 6) and the deviation is positive. Assuming ocean circulation remains constant, if deviations are less at the surface relative to the interior, the vertical gradient would be weaker than expected by the historical scaling, and thus ocean 315 C ant uptake would be less efficient. Therefore the historical scaling may be used to identify how the pattern of changing interior C ant (z) deviates from the historical scaling ( Figure 3) and thus reduces the efficiency of the C ant air-sea flux ( Figure   2b). With more rapid emission mitigation, globally average profiles reveal a pattern of increasingly positive deviations from the historical scaling at depth (Figure 3).
In the RCP8.5 and RCP4.5 scenarios, C ant (z) increases from 2020-2080 at all depths, but at the surface, C ant (z) increase 320 is less than * C ant (z) increase (Figure 3a). In the RCP4.5 scenario, the C ant at depth is greater than * C ant (z), while in the RCP8.5 scenario it is less than * C ant (z) (Figure 3b). In both the RCP8.5 and RCP4.5 scenarios, the increase in C ant is surface https://doi.org/10.5194/bg-2020-254 Preprint. Discussion started: 16 July 2020 c Author(s) 2020. CC BY 4.0 License. intensified, which enhances the vertical gradient. The enhanced vertical gradient allows for increased vertical diffusion of C ant , and thus increased ocean C ant uptake. However, in RCP4.5 and RCP8.5 the enhancement of the vertical gradient is not as strong as the historical scaling would suggest (Figure 3b). In the 1.5 • C scenario, the largest change in C ant (z) is at depth, 325 and at the surface C ant decreases. This results in a much weaker vertical gradient, weaker vertical diffusion, and thus a reduced ocean C ant uptake. The surface loss of C ant is a short term response to declines in pCO atm 2 that began in 2036, while the increase in C ant (z) at depth is from the long-term increase in pCO atm 2 relative to preindustrial times (Figure 3c).
The signals found in C ant (z) are found throughout the ocean (Figure 4). In the RCP8.5 scenario (Figure 4, top row), the surface layer exhibits the strongest negative deviation, but there is no positive deviation in the interior. The negative deviation 330 is seen in deep waters between 25 • N and 60 • N, and also in the bowls of the northern and southern subtropical gyres. The negative deviation grows from 2020-2080, and appears to propagate into the ocean interior with NADW. The historical scaling alone cannot identify whether buffering or solubility is the driver of lower C ant (z) than * C ant (z) in the interior.
In the RCP4.5 scenario, the surface layer exhibits a growing negative deviation (Figure 4, middle). The negative surface deviation spans from the southern to the northern end of the zonal mean section. In the interior, however, there is a growing  (Figure 1). In the next section, we will evaluate the relative role of buffering for all scenarios.

Drivers of Simulated Changes in Efficiency
We utilize projections of ocean C ant uptake from the one-dimensional model to provide mechanistic understanding of the changes in ocean carbon uptake efficiency simulated by the full model. Changes in ocean C ant are examined to determine 345 what drives projected changes in efficiency. These changes that are quantified with the one-dimensional model are separated into the carbon gradient effect, ∆C cgrad (Table 1), and effects related to the ocean's chemical capacity to absorb carbon, ∆C chem (Table 1)  The cumulative error is 4 Pg C ant , only 3% of the 2080 cumulative flux, again indicating that the one-dimensional model is a useful diagnostic tool for quantifying changes in the efficiency of ocean uptake .
Over the historical forcing period  ∆C cgrad drives ∆C total to be slightly lower than the historical scaling    Figure 5). This indicates that if ocean chemical capacity remains constant, the ocean would absorb an additional 158 Pg C ant . The positive ∆C cgrad is attributable to fitting CESM C ant uptake to a not-quite exponential pCO atm 2 in the 360 historical period. Changes in ocean C ant uptake due to warming were calculated, but are not shown as warming effects are small relative to ∆C chem , making up <5% of the total efficiency decline. This small contribution is consistent with the change due to warming calculated in studies of climate-carbon feedbacks (Randerson et al., 2015, Schwinger et al., 2018.  (PI buffer factor) with variable solubility. The black line is the one-dimensional model simulation that includes all effects (variable chemical capacity and variable solubility). Light green shading represents decreases in uptake related to the carbon gradient effect (∆C cgrad ), teal shading represents decreases in uptake related to chemical capacity (∆C chem ). Negative indicates loss of ocean carbon.

Decomposition of the C ant Air-Sea Flux
Here we diagnose the mechanisms controlling the C ant air-sea flux (F ant ) in the one-dimensional model ∆C total simulations.
The one-dimensional model has been tuned so the ∆C total simulation matches the CESM (Figure 2d). The one-dimensional  In the RCP8.5 scenario, the atmosphere component acts to enhance F ant , and the ocean component acts to reduce the F ant (Figure 6a-b). The actual F ant (Figure 6, green) is a small residual of these tendencies. Increasing pCO atm 2 acts to increase the air-sea pCO 2 difference, while increasing pCO ocn 2 acts to decrease F ant (Equation 12). If pCO ocn 2 , increased only very 385 slightly, such as the hypothetical scenario where the ocean is well mixed from surface to deep, ocean C ant uptake would be the magnitude of the atmospheric component (Figure 6a-b). In fact, the ocean component is also subject to a balance between two large terms. The increase in pCO

Drivers of Future Efficiency Declines
Ocean carbon uptake will decline as a result of emission mitigation. We also show that the efficiency of ocean carbon uptake, i.e. how closely ocean carbon uptake follows the observed proportionality between uptake and atmospheric CO 2 , is also reduced as mitigation becomes more rapid, consistent with the results of Raupach et al. (2014). Under exponentially increasing pCO atm 2 (RCP8.5), reductions in efficiency of ocean C ant uptake are almost entirely due to reduced buffer capacity. We find ). With rapid mitigation, the vertical C ant profile, which is set by the integrated effects of past C ant accumulation at depth, does not change to immediately to adjust to the trajectory of pCO atm 2 . We find that in a scenario featuring rapid 415 emission mitigation (1.5 • C), the C ant concentration change from 2020-2080 is greatest in the thermocline, a behavior that has been identified in other simulations of rapid emission mitigation (Tokarska et al., 2019). The past C ant accumulation at depth weakens the vertical C ant gradient compared to a vertical C ant profile that reaching the same pCO atm 2 under exponential pCO atm 2 increase, constant ocean chemistry, and constant circulation (Figure 3).
The air-sea flux is a balance between the atmospheric CO 2 growth rate and the ocean CO 2 growth rate (Equation 12), and in 420 all scenarios the atmospheric CO 2 growth rate dominates the balance. The positive atmospheric CO 2 growth rates throughout the RCP8.5 and RCP4.5 scenarios acts to enhance the air-sea flux. In the 1.5 • C scenario, ocean pCO atm 2 declines after 2036, and the negative atmospheric CO 2 growth rate acts to decrease the air-sea flux, while the negative ocean CO 2 growth rate acts to enhance the air-sea flux. The negative growth rates of the 1.5 • C scenario occur in the only scenario where efficiency declines exponentially.

425
The dominant mechanisms governing the decline in efficiency are different in each scenario, due to the differing degrees of emission mitigation. Internal ocean mechanisms (reduced chemical capacity) dominate the reduction of efficiency in the RCP8.5 scenario, and external mechanisms (increasing carbon gradient effect) dominate the reduction of efficiency in the 1.5 • C scenario. For the ocean, warming effects have a small impact relative to the carbon gradient and chemical capacity effects.

430
The growing carbon gradient effect in the 1.5 • C scenario is due to a weakening of the C ant vertical gradient, thus a declining rate at which C ant mixes and diffuses into the ocean interior. The magnitude of the C ant air-sea flux is limited by the rate of surface C ant removal (Graven et al., 2012), thus slower removal results in a reduced growth rate of ocean C ant uptake. The vertical gradient is weaker in scenarios with slower than exponential pCO atm 2 increase, compared to the vertical gradient at the same pCO atm 2 concentration in an exponentially increasing pCO atm 2 scenario, because C ant concentration is enhanced at 435 depth relative to exponential scenarios (Figure 3,4). The C ant concentration is elevated at depth because it takes longer for the slower than exponential scenarios to reach the same pCO atm 2 , allowing more cumulative C ant transfer to deeper waters. The waters at depth effectively push back on the changes occurring at the surface due to changing pCO atm 2 , which is qualitatively similar to how back-pressure in a pipe slows the flow of fluid through the pipe. It is the C ant at depth that is providing the "backpressure", resisting the flow of C ant into the interior. The faster emissions are mitigated, the more evident the back-pressure 440 exerted by ocean interior C ant becomes (Figure 3,4,5,6). However, delaying emission mitigation would act to increase the total back-pressure effect that would eventually occur. If the RCP8.5 scenario is followed into the 22nd century, future emissions would be flat from 2100 to 2150 and then decline dramatically (van Vuuren et al., 2011). As pCO atm 2 growth slows in response to the declining rate of emissions, the back-pressure effect from the ocean will appear, but at a greater magnitude due to the much greater load of C ant in the interior ocean. Therefore, climate simulations extending beyond 2100 are needed to quantify 445 the back-pressure effect in high emission scenarios.
With aggressive emission mitigation, regional patterns of the C ant air-sea flux shift, with implications for regional carbon cycle monitoring (Peters et al., 2017). The surface waters of regions that trend towards C ant outgassing under emission mitigation ( Figure 1; bottom row) are renewed by advection with waters that are much older than the waters that renew the waters of the subtropics (Toyama et al., 2017). As emissions are mitigated from 2020-2080, there is a positive change in C ant concentration 450 in the ocean interior, with this back-pressure effect being most pronounced at ∼400m (Figure 3). Regionally, advective fluxes are important drivers of C ant reemergence (Bopp et al., 2015), thus the regional impacts of ocean circulation on pCO ocn 2 (Equation 14) would include the effects of advective fluxes in addition to mixing/diffusive fluxes (which dominate globally). In the outgassing regions of Figure 1 (bottom row), advective fluxes bring waters with an increasing load of C ant to the surface, thus reemergence is increasing, acting to increase pCO ocn 2 . The increase in reemergence ultimately overwhelms the weakening 455 downwards diffusive C ant flux that acts to decrease pCO ocn 2 . Therefore, advection of C ant is driving the C ant air-sea flux further towards outgassing in the equatorial Pacific, supbolar and mid-latitude North Atlantic, SAMW outcrop region, and the Kuroshio (Toyama et al., 2017). The Circumpolar Deep Water (CDW) that is upwelled into the surface of the Southern Ocean south of 50 • S, is old relative to the subtropics, but it is uncontaminated by C ant . Below ∼400m the magnitude of the backpressure decreases, therefore upwelling of CDW does not result in an increasing load of C ant being brought to the surface.

460
Southern Ocean C ant uptake persists because the positive C ant tendency is absent in the upwelling watermass.
The back-pressure from C ant at depth is an unavoidable consequence of emission mitigation. While more efficient ocean C ant uptake is desirable when drawing down pCO atm 2 , in fact, peak sink efficiency occurs under exponential growth of pCO atm 2 . How long the ocean will remain a net sink depends on the strength of the back-pressure effect, which depends on the strength of surface ocean C ant removal. If the back-pressure effect is stronger, due to more vigorous ocean circulation 465 transfer of C ant to depth in the years prior to mitigation, the sink will disappear at a faster rate. With rapid mitigation, the ocean C ant uptake peaks in approximately 2030 and nearly disappears by 2080. Despite the decline in the efficiency of ocean C ant uptake under rapid mitigation, ESMs indicate that the ocean becomes the primary C ant sink in scenarios with aggressive mitigation  and without mitigation (Randerson et al., 2015) because the land uptake declines more rapidly than ocean uptake (Zickfeld et al., 2016). The ocean will ultimately remove most atmospheric C ant over tens of thousands of 470 years (Archer, 2005, Archer et al., 2009.

Validity of the One-Dimensional Model Representation of Ocean Physics
Our one-dimensional ocean carbon cycle model represents multiple physical removal process as a single diffusive process (Equation 8). Parameterizing these various processes in this manner requires defining an effective vertical diffusivity of the ocean, K z,ef f and better observational estimates of ocean mixing are required to in order to recreate the effective diffusivity 475 of the actual ocean. In the three-dimensional ocean models used in ESMs, up to ∼30% of simulated K z,ef f is attributable to isopycnal eddy mixing (Gnanadesikan et al., 2015). Varying a three-dimensional ocean model's isopycnal eddy diffusivity within the range of typical model values results in a 92 Pg C range of cumulative ocean C ant uptake under instantaneous CO 2 doubling (Gnanadesikan et al., 2015), thus the sensitivity of ocean C ant uptake to isopycnal eddy mixing is much larger than the sensitivity to changing ocean circulation. Models with spatially varying isopycnal eddy diffusivities, such as the 480 NCAR CESM and GFDL ESM2G, have parameterizations that produce a range of diffusivities from ∼300 m 2 s −1 in gyres, to ∼1500 m 2 s −1 in boundary currents (Dunne et al., 2012;Danabasoglu et al., 2011). Observational estimates of isopycnal eddy diffusivity from tracers (Ledwell et al., 1998) and satellite altimetry (Abernathey and Marshall, 2013) are uncertain, but consistently suggest that real world eddy diffusivities could be much higher, with ranges from ∼1000 m 2 s −1 in gyres, to ∼10,000 m 2 s −1 in boundary currents.

485
While the mean state of ocean circulation is most important over the never 60 years, as warming increases, the magnitude climate-carbon feedbacks increase, such as changes to ocean circulation driving changes in ocean carbon uptake (Randerson et al., 2015), which is not represented by our one-dimensional ocean carbon cycle model. The small effect of changing ocean circulation in our simulation is likely because changes due to declines in AMOC are not yet evident by 2080 (Sarmiento and LeQuéré, 1996;Randerson et al., 2015). While assuming that ocean climate-carbon feedbacks are small prior to 2080 490 is consistent with the behavior of the CESM (Randerson et al., 2015), this may not be hold true for the Earth System itself.
The uncertainties associated with the timing and magnitude of climate-carbon feedbacks can be avoided by mitigating climate change (Randerson et al., 2015).

Identification of the Impacts of Internal Ocean Variability using the Historical Scaling
Given the direct relationship between the efficiency of ocean C ant uptake and the deviations from the historical scaling, we 495 suggest that future work quantify the impact of external mechanisms on observed interannual variability of ocean carbon uptake. The historical scaling relies on the assumption of fixed sink efficiency due to exponential growth of pCO atm 2 . While most of the industrial era is consistent with an exponential CO 2 growth, variability in emissions drives variability in the atmospheric growth rate that then results in decadal variability in the ocean carbon sink (McKinley et al., 2020). If the historical scaling is used to identify changes in observations of C ant concentration (Gruber et al., 2019a), and the atmospheric growth 500 rate has recently slowed, changes due to internal variability are mixed with signals related to the carbon gradient effect, and the changes due to internal variability (Gruber et al., 2019a) would be overestimated. We also emphasize that in a future with emission mitigation, deviations from historical scaling will not be driven by changes due to internal ocean variability alone, given the dynamic response of the ocean to changes in pCO atm 2 .

505
Atmospheric CO 2 has grown exponentially over the industrial era, and so has ocean C ant concentration at all depths (DeVries, 2014;Gruber et al., 2019). Under the exponential forcing regime, ocean C ant uptake also grows exponentially and, over the historical era, maintains high efficiency of ocean C ant uptake as we have defined it here. In future scenarios, regardless of whether countries mitigate emissions, efficiency of ocean C ant uptake will decline. However the mechanisms differ depending on the degree of mitigation. In the RCP8.5 scenario, a scenario with no emission mitigation, reduced buffer capacity explains 510 nearly all of the loss in efficiency of ocean C ant uptake by 2080, 158 Pg C. In the case of scenarios with emission mitigation, such as RCP4.5 and the 1.5 • C scenario, the loss of efficiency is more due to the carbon gradient effect. The carbon gradient effect explains 38% of efficiency loss in RCP4.5 scenario, and 71% of the efficiency loss in the 1.  However, the ocean interior C ant concentration response lags the surface response. Below 100m in the rapid mitigation scenario, C ant concentration increases from 2020-2080, while above 100m, the C ant concentration decreases, thus the downward C ant concentration gradient is greatly reduced. A reduced downward vertical gradient results in less effective downward dif-fusion of C ant . Ocean C ant uptake is limited by surface ocean C ant removal (Graven et al., 2012), thus this results in reduced uptake in the future, relative to ocean C ant uptake under the same pCO atm 2 concentration in the historical period. This reduc-525 tion of the vertical gradient, an unavoidable result of emission mitigation, is the driver of efficiency declines.
Under emission mitigation, the carbon gradient effect results in a enhanced outgassing of C ant in the equatorial Pacific, and a transition from C ant uptake to C ant outgassing in the subpolar and mid-latitude North Atlantic, Kurshio, and SAMW outcrop region. These regions are also hotspots for reemergence (Bopp et al., 2015, Toyama et al., 2017. Reemergence of older watermasses, from depths where C ant continues to increase, drives a tendency towards outgassing in these regions. The waters 530 of the subtropics are renewed with shallower waters, above where the continued C ant increase occurs in the ocean component of ESM, and the surface waters of the Southern Ocean are renewed with waters below the C ant increase. Thus, in subtropics and Southern Ocean, the air-sea C ant uptake continues. Diffusive processes control the removal of C ant from the surface ocean, and because the diffusivity of the surface ocean is highly uncertain, it creates large uncertainties in C ant uptake (Gnanadesikan et al., 2015). Determining the effective vertical 535 diffusivity of the upper ocean is essential to reducing uncertainty in future ocean C ant uptake, particularly under 21st century emission mitigation scenarios.
Code and data availability. The code used to run the one-dimensional model is provided by the authors in a GitHub repository (https: //qoccm.readthedocs.io/en/latest/). Raw output from the coupled ocean model simulations can download from NCAR's Earth System Grid (https://www.earthsystemgrid.org/).

540
Appendix A: Physical Interpretation of the Impulse Response Function Based Model one-dimensional model Impulse response functions are a powerful tool in dynamical system analysis. With a response function, one can understand the response of a system to any pulse, as long as the response is linear. The response function used in our one-dimensional model has the same shape as the conceptual example in Figure A1. For the one-dimensional model case, the response function was derived by equilibrating HILDA to a doubling CO 2 , and then tracking fraction of C ant that remained in the surface box (the 545 mixed layer) (Joos et al. 1996).
In our conceptual example of the mixed layer response function, at t = 0 100% of the tracer remains in the mixed layer, while 200 years later, only 10% of the tracer remains ( Figure A1). This is a general example of response function that can be applied to any transient tracer, but the values in this example have been scaled so that it is most similar to the evolution C ant .
Ocean circulation, with vertical diffusion playing the largest role for short lived transient tracers, sets the time that it takes 550 to reach this value. The mixed layer pulse response function must be calculated for each transient tracer of interest because the spatial distribution of flux is tracer dependent, thus each tracer flux distribution uniquely samples the spatially variable vertical diffusivity of the ocean. The mixed layer pulse response function for C ant is determined by simulating the exposure of the surface ocean to a pulse of atmospheric CO 2 . In order to use a single case as our pulse response function, the size of the pulse we give our model cannot affect the time it would take that pulse to reach 10%. In other words, the time it takes for any 555 subsequent pulse to reach 10% in the mixed layer must also remain constant. In theory, the timescale could change as result of changes to ocean circulation, and as seen in the results this does occur, but minimally affects the response (Figure 2c).
One can use the convolution integral of the pulse and the response function to determine the surface ocean concentration of a transient tracer: This is a slightly simplified version of the one-dimensional model equation, where C o is the surface concentration of a tracer, F c is the flux, and r is the response function. In our case, the pulse, F c , is the change in carbon concentration at the surface each year. By taking the convolution integral of the pulse, and its response function, we can determine the change in mixedlayer concentration ( Figure A2). A convolution integral (Equation A1) calculates the concentration at time t by calculating the fraction of previous pulses (F c (u)), that entered the ocean at times u (from t i = 0 to t), that remain in the surface ocean at time 565 t. This is generalizable to any tracer that is initially absent in the ocean. An intuition for convolution integral can be formed by visualizing it in discrete form ( Figure A2). By summing all of the discrete pulses that are present in the mixed layer at a given time, one can arrive at an approximation of the exact convolution integral ( Figure A2c,d). In this case the exact solution is the ocean concentration of the transient tracer. In this generalized example, we show the effect of pulse sampling frequency ( Figure A2c). With more frequent pulse sampling, the more accurate the approximation of the convolution integral (A2c,d), thus with infinitely many pulses one can capture the full convolution integral (concentration of some transient tracer). In the one-dimensional model case, the pulse is sampled annually, with no benefit to sampling at sub-annual frequencies.
Interestingly, the convolution integral can be used to solve for the flux. All we need to know is the flux at t = 0. The flux of transient tracer can be described with the following equation: In this equation F C is the flux of tracer in units of quantity (µmol, mol, kg, etc) per m 3 . On the right hand side, the air-sea difference is multiplied by the gas transfer velocity, k (m yr −1 ), and the mixed layer depth, h (m).
1. Calculate the air-sea flux (Equation A2) 2. Sum up the pulses still present in the mixed layer to determine concentration at the next timestep (Equation A1).
This process is repeated to calculate the next year's air-sea flux. After many time steps, the flux is responding to the change in concentration that occurred in the previous year due to the previous year's flux, and any pulses that remain in the mixed layer.

585
Appendix B: One-Dimensional Ocean Carbon Cycle Model Chemistry The pCO ocn 2 of the one-dimensional ocean carbon cycle model is calculated as follows: pCO ocn 2 = [pCO ocn,P I 2 + δpCO ocn 2 (C ant , T 0 )]exp(α T δT ) The response of pCO ocn 2 to warming is parameterized as an exponential function as in Takahashi et al. (1993), with α T set