Evaluation of Data‐Based Estimates of Anthropogenic Carbon in the Arctic Ocean

Abstract The Arctic Ocean is particularly vulnerable to ocean acidification, a process that is mainly driven by the uptake of anthropogenic carbon (Cant) from the atmosphere. Although Cant concentrations cannot be measured directly in the ocean, they have been estimated using data‐based methods such as the transient time distribution (TTD) approach, which characterizes the ventilation of water masses with inert transient tracers, such as CFC‐12. Here, we evaluate the TTD approach in the Arctic Ocean using an eddying ocean model as a test bed. When the TTD approach is applied to simulated CFC‐12 in that model, it underestimates the same model's directly simulated Cant concentrations by up to 12%, a bias that stems from its idealized assumption of gas equilibrium between atmosphere and surface water, both for CFC‐12 and anthropogenic CO2. Unlike the idealized assumption, the simulated partial pressure of CFC‐12 (pCFC‐12) in Arctic surface waters is undersaturated relative to that in the atmosphere in regions and times of deep‐water formation, while the simulated equivalent for Cant is supersaturated. After accounting for the TTD approach's negative bias, the total amount of Cant in the Arctic Ocean in 2005 increases by 8% to 3.3 ± 0.3 Pg C. By combining the adjusted TTD approach with scenarios of future atmospheric CO2, it is estimated that all Arctic waters, from surface to depth, would become corrosive to aragonite by the middle of the next century even if atmospheric CO2 could be stabilized at 540 ppm.


Introduction
Ocean uptake of anthropogenic carbon (C ant ) drives reductions in ocean pH and carbonate ion concentration, the latter of which reduces the calcium carbonate (CaCO 3 ) saturation state (Orr et al., 2005). Surface waters in the high latitudes have naturally lower CaCO 3 saturation states; hence, as atmospheric CO 2 climbs, they are more susceptible to reaching saturation states below which they become undersaturated with respect to aragonite, a metastable form of CaCO 3 (Orr et al., 2005;Steinacher et al., 2009). Unlike in almost all other regions, surface waters in the Arctic Ocean are already partly undersaturated with respect to aragonite particularly near river mouths because of lower alkalinity freshwater input (Chierici & Fransson, 2009;Mathis et al., 2015;Semiletov et al., 2016). The Arctic Ocean's annual-mean conditions are projected to become entirely undersaturated with respect to aragonite by 2080 under the SRES A2 scenario (Steinacher et al., 2009).
The Arctic's aragonite saturation horizon (ASH), above which waters are supersaturated with respect to aragonite and below which they are undersaturated, is located at around 1,900 m . The Arctic ASH is projected to shoal by ∼100 m during the 21st century based on a coupled carbon-climate model forced under the SRES A2 scenario (Steinacher et al., 2009). The same model projects that the aragonite undersaturation in surface waters will propagate downwards rapidly, merging with the shoaling ASH at about 1,800 m by the end of the century. Conversely, a data-based approach that imposes exponentially increasing atmospheric CO 2 suggests that the deep ASH will shoal by much more (∼900 m) and will merge with the deepening undersaturation from the surface at about 1,000 m by the end of the century .
The main driver of acidification in the open ocean is the increase in atmospheric CO 2 during the industrial era and the resulting uptake of C ant by the ocean. Although this absorbed C ant cannot be measured directly, it has been estimated from other oceanographic data by various methods, such as the transit-time distribution (TTD) approach (Khatiwala et al., 2013;Waugh et al., 2006). For instance, the inverse Gaussian-TTD (IG-TTD) method, a specific solution of the TTD framework, aims to constrain the invasion of C ant into the interior ocean by using observations of transient tracers such as CFC-12, the tritium-helium pair ( 3 H∕ 3 He), and SF 6 (Hall et al., 2002;Waugh et al., 2004). With surface boundary conditions of the chosen tracer (e.g., CFC-12) as well as subsurface measurements of the same tracer, temperature (T), and salinity (S), the mean age of the water parcel can be determined by the IG-TTD approach. The resulting mean age is then used in combination with the atmospheric CO 2 history to estimate the C ant concentration in the respective water parcel.
The TTD approach was first applied to the global ocean by Waugh et al. (2006), who estimated a global ocean C ant uptake of 134 Pg C in 1994. Waugh et al. did not apply the TTD approach in the Arctic because tracer observations there were sparse. Later, with the advent of more tracer observations, Tanhua et al. (2009) applied the TTD method to the Arctic Ocean, estimating that it contained 2.5-3.3 Pg of anthropogenic carbon in 2005. From the TTD estimates of C ant concentrations along the 2005 Beringia section, Anderson et al. (2010) estimated that the Arctic Ocean's average depth of the ASH had shoaled by ∼190 m during the industrial era.
The skill of related data-based approaches has been tested in general ocean circulation models (Matear et al., 2003;Matsumoto & Gruber, 2005). In a similar fashion, the TTD approach can be applied to simulated CFC-12 concentrations to obtain a TTD-based estimate of C ant in the same model as where C ant is simulated directly (reference C ant ), for example, using the perturbation approach for C ant from Sarmiento et al. (1992). The first such TTD evaluation by Waugh et al. (2006) indicated that the TTD-derived C ant is similar to the directly simulated C ant reference in all modeled ocean regions except for the Southern Ocean. The issue in the Southern Ocean stems from its upwelled deeper waters, which are impoverished in CFC-12 and C ant and spend only about 4 months at the surface before being subducted into the ocean interior (Weiss et al., 1979). Although that period is sufficient for air-sea equilibration of CFC-12, such is not the case for C ant whose complete air-sea equilibration takes longer (Broecker & Peng, 1974). Conversely, the TTD approach assumes equilibrium between the atmosphere and surface ocean for both C ant and CFC-12. Hence, that data-based approach systematically overestimates C ant in the Southern Ocean (Matear et al., 2003;Waugh et al., 2006).
In the Arctic Ocean, differences between C ant and CFC-12 in terms of surface-water saturation relative to the atmosphere are also thought to cause biases in the TTD-based C ant estimates. But in that region, the sign and magnitude of these biases have not been evaluated (Tanhua et al., 2009). Recently, Rajasakaren et al. (2019) revised upward the C ant inventory estimate for the Arctic Ocean to 3.6 Pg C in 2005 after accounting for the undersaturation of surface-water CFC-12 relative to the atmosphere. However, the associated uncertainty is large. Moreover, they did not account for the related air-sea disequilibrium for C ant , which could be larger in magnitude owing to its longer air-sea equilibration time. They also changed other parameters of the TTD approach, making it impossible to isolate the effect of differences in surface saturation of CFC-12. In this study, our goals are (1) to evaluate the TTD method in the Arctic Ocean with an ocean model and (2) to use results from that assessment to adjust the existing TTD data-based estimate of the Arctic C ant inventory (Tanhua et al., 2009).

Arctic Ocean and Its Water Masses
The boundaries of the Arctic Ocean are defined following Bates and Mathis (2009), that is, at the Fram Strait, the Barents Sea Opening, the Bering Strait, and the Canadian Arctic Archipelago (between Smith Sound and Baffin Bay).
Arctic Ocean water masses are also defined based on previous studies (Table S1). The Pacific Water (PW) is divided into (1) the Summer Pacific Water (SPW), having temperatures between −1.0 • C and 0.4 • C and salinities between 31 and 33 (Bourgain et al., 2013;Steele et al., 2004;Woodgate et al., 2010), and (2) the Winter Pacific Water (WPW), having temperatures below −1.4 • C and salinities above 32.4 (Pickart et al., 2005). Water from the Atlantic Ocean splits into two branches. The first branch enters the Arctic Ocean through the Fram Strait at intermediate depths and is generally warmer than 0 • C and saltier than 34 (Woodgate, 2013). Being disconnected from the surface, it tends to conserve these characteristics and is thus named Atlantic Water (AW). The second branch enters the Arctic Ocean through the Barents Sea Opening. Being 10.1029/2020JC016124 mainly located at the surface, it cools to less than 0 • C and its salinity increases to values above 34.6 owing to brine rejection (Midttun, 1985). Consequently, the density of this water mass increases, which drives its descent into the deep Arctic Ocean basins through the St Anna Trough (Gammelsrød et al., 2009;Schauer et al., 2002;Smedsrud et al., 2013). Water masses from this second Atlantic branch are named Barents Sea Water (BSW).

Ocean Model
In this study, we used the global ocean circulation model Nucleus for European Modeling of the Ocean-version 3.2 (NEMO-v3.2) (Madec, 2008) combined with a single-tracer perturbation approach to simulate C ant (Lachkar et al., 2007;Palmiéri et al., 2015;Sarmiento et al., 1992). This approach is computationally less expensive than a full biogeochemical model, which facilitates running the physical model at higher resolution. The atmospheric CO 2 forcing for years 1765-1869 comes from Meinshausen et al. (2017) while that for years 1870-2012 is from Le Quéré et al. (2015). To calculate the anthropogenic change in surface-ocean partial pressure of CO 2 (pCO 2 ), referred to as δpCO 2 , the perturbation approach exploits the nearly linear relationship between δpCO 2 and the ratio between the corresponding perturbation in total dissolved inorganic carbon (δC T ) and δpCO 2 (Sarmiento et al., 1992) where z 0 and z 1 are each quadratic functions of surface temperature ( • C): The fitted parameters a 0 , a 1 , a 2 , b 0 , b 1 , and b 2 are taken from Terhaar et al. (2019, Table 4) and were calculated with the K 1 and K 2 dissociation constants from Lueker et al. (2000), the dissociation constant for boric acid from Dickson (1990), and the total boron-to-salinity ratio from Uppström (1974). For perturbations in atmospheric CO 2 of up to 280 ppm (a doubling of the preindustrial level), the relationship between δpCO 2 ∕δC T and δpCO 2 is essentially linear under the assumption of constant total alkalinity A T (2300 molkg −1 ) and salinity (35). Hence, it depends only on surface ocean temperature. Rearranging (1) yields the equation by which simulated surface temperature and δC T are used to compute surface δpCO 2 , as needed to compute the air-sea C ant flux: where is the solubility of CO 2 (Weiss, 1974), k w is the gas transfer velocity (Wanninkhof, 1992), and δpCO atm 2 and δpCO oce 2 are the anthropogenic changes in partial pressure in the atmosphere and the surface ocean, respectively. For brevity, δpCO oce 2 is usually indicated here as δpCO 2 . The experimentally derived gas transfer velocity implicitly accounts for some effects of bubbles on the air-sea C ant flux, but not the direct effect of bubbles on gas saturation anomalies from bubble dissolution (Hamme et al., 2017). While bubbles enhance the gas saturation of less soluble gases, for example, O 2 (Atamanchuk et al., 2020) and SF 6 (Stöven et al., 2015), they have little effect on the saturation of CO 2 and CFC-12, which are more soluble (Hamme et al., 2017;Stöven et al., 2015). Once transferred to the ocean, C ant was treated as a passive tracer with no internal sources nor sinks.
Despite these approximations, the simulated Arctic Ocean C ant inventory (total mass in the ocean) from the perturbation approach agrees within 3% with the C ant inventory in 2005 simulated by the more costly full biogeochemical approach (Terhaar et al., 2019). This relatively small difference between the two approaches probably results from most of the C ant in the Arctic Ocean interior being taken up in the Atlantic Ocean or the Barents Sea, where the sea surface alkalinity is close to the perturbation approach's assumed 2,300μmol kg −1 . Thus, alkalinity and salinity anomalies at the Arctic Ocean surface due to freshwater input from rivers and sea ice melt (Chierici & Fransson, 2009;Mathis et al., 2015;Semiletov et al., 2016) have little impact beyond its shallow surface waters. Because of limited computational resources, we used a coarser resolution version of the model (ORCA05, nominal resolution of 0.5 • ) from 1765 to 1957 and the higher resolution version (ORCA025, nominal resolution of 0.25 • ) only for the final 1958-2012 period. Also included in the model is CFC-12, an inert tracer that is simulated from 1932 onwards following the OCMIP-2 protocol (Dutay et al., 2002) but with the atmospheric boundary conditions from Bullister (2015).

TTD Calculation
The TTD approach was applied following Hall et al. (2002), Waugh et al. (2004), and Tanhua et al. (2009). The concentration of a tracer c(r, t) was calculated at each point r and time t (in years) using the equation where G r (t ′ ) is the commonly applied inverse Gaussian of the Green's function (e.g., Olsen et al., 2010;Tanhua et al., 2009;Waugh et al., 2004;Waugh et al., 2006) and c 0 (t − t ′ ) is the tracer's surface-ocean time history with t being the year when the tracer concentration in the water cell is calculated and t ′ being the transit time of the water mass in years since it left the sea surface. The surface ocean time history of C ant is calculated as the difference between C T at time t−t ′ and preindustrial C T (year 1765), where C T is calculated from the simulated temperature in the water cell, fixed salinity (35), and A T (2,300μmol kg −1 ), consistent with the perturbation simulation and the atmospheric pCO 2 in the respective year (Le Quéré et al., 2015;Meinshausen et al., 2017), assuming equilibrium between the atmosphere and the surface ocean. To calculate C T from A T and pCO 2 , we used the MATLAB version of the routine CO2SYS (van Heuven et al., 2011) with K 1 and K 2 dissociation constants from Millero et al. (2002), the dissociation constant for boric acid from Dickson (1990), and the total boron-to-salinity ratio from Uppström (1974). The solubility of CO 2 was calculated following Weiss (1974). For these calculations, nutrient concentrations are assumed to be zero. Although phosphoric and silicic acid systems contribute to A T and thus should be corrected for when calculating C T , their effect is assumed to be negligible when calculating C ant , a difference between C T at time t − t ′ and preindustrial C T , both being biased similarly in the same direction.
For every water parcel r, G r (t ′ ) is expressed as where Δ represents the width of the TTD and Γ the mean age of the water parcel. The mean age was calculated at each point r, assuming Δ∕Γ = 1, from the measured CFC-12 concentration at time t (c(r, t)) and the surface ocean CFC-12 history (c 0 (t − t ′ )) calculated from the atmospheric history of the partial pressure of CFC-12 (pCFC-12) (Bullister, 2015), assuming equilibrium between pCFC-12 in the atmosphere and that in the surface ocean. The solubility of CFC-12 was calculated following Warner and Weiss (1985). Based on the mean age, G r (t ′ ) was derived at every point r.
In waters where pCFC-12 is supersaturated with respect to the current atmospheric pCFC-12, G r (t ′ ) cannot be derived; hence, the TTD method cannot be applied. Oceanic pCFC-12 can exceed atmospheric pCFC-12 because atmospheric CFC-12 levels have declined since 2002. Thus, when comparing C ant calculated by the TTD method to that which is simulated directly, we masked out model grid cells where ocean pCFC-12 is above atmospheric pCFC-12, amounting to 6.5% of the total Arctic Ocean C ant inventory in 2005 based on directly simulated C ant (section 2.4). While the TTD method could not be evaluated in these supersaturated waters, they are included in data-based C ant estimate from Tanhua et al. (2009) assuming a mean age of zero.
The ratio of Δ to Γ determines the relative importance of advection versus diffusion, with Δ∕Γ < 1 indicating a larger advective than diffusive share. Here, we used the typical Δ∕Γ ratio of 1.0 (Tanhua et al., 2009;Waugh et al., 2006) as the standard case and assume the related ±1 uncertainty to be ±5% following Tanhua et al. (2008Tanhua et al. ( ,2009). Furthermore, we made a series of sensitivity tests over a range of Δ∕Γ ratios. When that ratio is varied between 0.6 and 1.8, vertical profiles of C TTD ant concentrations averaged over the Arctic Ocean still agree within the applied uncertainty of ±5% ( Figure S1). In another study, Rajasakaren et al. (2019) compared mean ages derived from SF 6 with those derived from CFC-12 while varying the Δ∕Γ ratio to identify the value of that ratio where the mean ages derived from both tracers agreed best. From their comparison, they provide a regionally varying best estimate of Δ∕Γ for each Arctic Ocean water mass. Their estimates 10.1029/2020JC016124 range from 0.6 for Atlantic Water in the Amerasian basin to 1.2 for waters below the Atlantic Water layer. Their results also indicate that the C TTD ant concentration uncertainty related to the Δ∕Γ ratio is at most ±5% (Rajasakaren et al., 2019, figures 8 and 11) in accord with our uncertainty estimation.
The TTD approach assumes that ocean circulation is in steady-state, that it can be represented by a 1-D advection-diffusion equation (G r (t ′ )), and that there is one surface-ocean source region for both tracers, C ant and CFC-12. It also assumes that there is conservative mixing between water masses from different source regions and that the air-sea disequilibrium for both tracers is constant in time. In the standard case for TTD, it is assumed that there is no air-sea disequilibrium for either tracer.

Evaluation of TTD
To evaluate the TTD method, we applied it to simulated CFC-12 and temperature from the summer of 2005, that is, the year and months used for the TTD estimate from Tanhua et al. (2009). This TTD-based C ant is denoted as C TTD ant . For consistency with the perturbation simulations, the A T was fixed at 2,300 μmol kg −1 , the salinity at 35, and the atmospheric boundary conditions for CO 2 were identical. The TTD method was evaluated separately for SPW, WPW, AW, and BSW.
The TTD approach could not be evaluated in some parts of the Arctic Ocean because of our simulation strategy, which initialized all variables in the high-resolution configuration ORCA025 in 1958 with results from the coarse-resolution configuration ORCA05. Around 41% of the oceanic invasion of the directly simulated anthropogenic carbon (C NEMO ant ) occurs before 1958 (with ORCA05), while only 2% of the oceanic CFC-12 invasion occurs before 1958 (with ORCA025) because of its more recent perturbation. While this 1958 initialization of ORCA025 with output of ORCA05 poses no problem for the evaluation of the TTD method in relatively young water masses, it biases the evaluation for older water masses where the circulation in ORCA05 differs largely from ORCA025. The largest differences between the two configurations is in the deep Arctic Ocean, where separate CFC-12 simulations indicate that waters are ventilated to 1,300-min ORCA05 and to 1,800-min ORCA025 (Terhaar et al., 2019). Thus, in the combined CFC-12 simulation (ORCA05 for 1932-1957, then ORCA025 for 1958-2012, simulated CFC-12 in year 2005 is relatively more abundant below 1,300 m, a signature of ORCA025, when compared to C NEMO ant (ORCA05 for 1765-1957, then ORCA025 for 1958-2012 in the same year because the anthropogenic carbon invasion began much earlier. That is, C NEMO ant depends more on the characteristics of the simulated circulation in ORCA05. Hence, in waters below 1,300 m, which represent 54% of the Arctic Ocean volume and 10% of the simulated Arctic Ocean C ant inventory, it is inappropriate to evaluate the TTD method. Furthermore, the evaluation should only be performed in regions where the model represents the Arctic Ocean circulation reasonably well. That is the case for most parts of the Arctic Ocean above 1,300 m except for the western end of the Canada basin, which receives no AW in the model (Terhaar et al., 2019). Consequently, the simulated CFC-12 concentrations remain close to zero and well below those observed (Tanhua et al., 2009). Hence, the TTD method is also not evaluated in that region, which represents 6% of Arctic Ocean volume and 10% of the simulated Arctic Ocean C ant inventory. After excluding surface waters that were found to be supersaturated with respect to CFC-12 (3% of the Arctic Ocean's volume and 7% of its C ant inventory), the TTD evaluation was performed in water masses representing 37% of the Arctic Ocean volume and 69% of the simulated Arctic Ocean C ant inventory. Yet despite this partial coverage, results from the TTD evaluation were expanded upon by classifying each water parcel as a member of one of the Arctic's four dominant water masses and then applying the corresponding corrective factors.

Correction of C ant
Each data-based C ant concentration from Tanhua et al. (2009) was adjusted based on its assigned water mass, determined from its associated physical characteristics (Table S1), and the pertinent water-mass specific corrective factor from our evaluation of the TTD approach (section 3). Water masses between 250 and 800 m across the Arctic Ocean were mainly identified as AW (Smethie et al., 2000), while those below 800 m were largely identified as WPW (Aagaard, 1981;Swift et al., 1997) or BSW (Jones, 2001;Jones et al., 1995;Smedsrud et al., 2013).

Future C ant
Coarse-resolution ocean models tend to underestimate the storage of C ant in the Arctic Ocean and the resulting shoaling of the deep ASH (Terhaar et al., 2019). Yet 21st century projections with high-resolution 10.1029/2020JC016124 ocean-biogeochemical models remain prohibitive due to their computational costs. A simpler alternative is to estimate future C ant concentrations based on the TTD approach.
Following Anderson et al. (2010), the TTD approach was used here to estimate C ant concentrations along the Beringia 2005 section over the 21st century, but this time with atmospheric CO 2 from the four Representative Concentration Pathways RCP2.6, RCP4.5, RCP6.0, and RCP8.5 (Meinshausen et al., 2011) instead of with an exponentially increasing atmospheric CO 2 . The TTD was estimated based on observed CFC-12, temperature, and salinity, while A T was computed from salinity based on an Arctic-specific relationship (MacGilchrist et al., 2014). The computed TTD from observed CFC-12 in 2005 (equation 7) was then applied to atmospheric CO 2 levels for 13 different years spanning from 2014 to 2107 in each of the four RCP scenarios. The resulting ocean C ant concentrations were then adjusted based on the corrective factors that were obtained from the TTD evaluation (section 3).
This TTD-based approach implicitly assumes no physical changes, for example, in ocean circulation, sea-ice extent, river discharge, temperature, salinity, and mixed-layer depth. It also assumes that the air-sea disequilibrium does not change with time. Furthermore, the TTD approach is based on tracers that started to invade the ocean more recently than anthropogenic carbon. To test if the accuracy of the TTD method changes when being applied to a tracer with a longer atmospheric history, we replicated our TTD-based future estimates and compared them to model estimates using the computationally efficient, coarse-resolution version of the model (ORCA2, nominal horizontal resolution of 2 • ). In ORCA2, we simulated CFC-12 over 1932-2005 and C ant over 1765-2100. The simulated CFC-12 concentrations in 2005 were used to derive the TTD. This TTD was then combined with atmospheric CO 2 levels over 1765-2005 and over 1765-2100 to estimate C ant concentrations in the ocean. Despite the considerably longer atmospheric history of C ant in 2100, the relative uncertainty of the TTD estimated C ant concentrations remains almost the same ( Figure S2). Although ORCA2 does not simulate the Arctic Ocean circulation as well as ORCA025 (Terhaar et al., 2019), the relative uncertainty of its C TTD ant concentrations in 2005 remains similar to that in 2100 over the range of observed CFC-12 concentrations and thus over the range of observed mean ages. Thus, it appears that the TTD computed from present-day CFC-12 may be used to estimate C ant uptake over 1765-2100 for the idealized case where atmospheric CO 2 increases but climate and the air-sea disequilibrium do not change.

A and Undersaturation Index
The aragonite saturation state Ω A was calculated using mocsy (Orr & Epitalon, 2015) with dissociation constants recommended for best practices (Dickson et al., 2007). Combined standard uncertainties in Ω A were computed from the standard uncertainties in the dissociation constants and the solubility product for aragonite (Mucci, 1983) using mocsy's uncertainty propagation routine from Orr et al. (2018). Due to the idealized nature of our simulated future estimates, we neglected measurement uncertainties for the CO 2 system input variables (A T and C T ).
Present-day Ω A was calculated from observed temperature, salinity, C T , A T , total dissolved inorganic phosphorus (P T ), total dissolved silicon (Si T ), and depth along the Beringia 2005 section. Preindustrial Ω A was computed after subtracting the adjusted C ant concentration estimates in 2005 from measured C T and assuming that the other variables did not change over the industrial period. For estimates of Ω A over the 21st century, the changes in the C ant concentrations since 2005 were added to C T measurements taken in 2005, while also neglecting changes in all other variables.
The basin-wide undersaturation with respect to aragonite was characterized by the undersaturation index (UI), the fraction of the total Arctic Ocean volume where Ω A < 1. Here, UI is based on Ω A at the measurement points along the Beringia section, weighted by depth and distance. It is not extrapolated beyond the Beringia section to other parts of the Arctic basin.

Evaluation of TTD Method in the Arctic Ocean
In the Arctic Ocean, the ORCA025 configuration of NEMO-PISCES, which is initialized in 1958 with output from the ORCA05 configuration, simulates a total C NEMO ant inventory of 2.5 Pg C in 2005. That simulated inventory lies at the lower end of the uncertainty range of the data-based estimate from Tanhua et al. (2009) (2.5-3.3 Pg C in 2005 because of (1) the model's inadequate horizontal extension of Atlantic Waters at intermediate depths and (2) its insufficient deep-water formation (Terhaar et al., 2019). After masking out cells where the pCFC-12 level in the ocean exceeds that in the atmosphere, owing to the decline in atmospheric The difference between C TTD ant and C NEMO ant would be expected to be larger had we used ORCA025 before 1958 instead of the coarser configuration ORCA05, which simulates less storage of C ant (Terhaar et al., 2019). Indeed, when evaluating the TTD approach in the model's younger waters that are affected little by the change in resolution in 1958, the calculated C TTD ant concentrations are seen to underestimate the reference C NEMO ant concentrations by 7 ± 2% (2.5 ± 0.9 μmol kg −1 ) in SPW, by 12 ± 3% (4.9 ± 1.3 μmol kg −1 ) in WPW, by 4 ± 2% (1.1 ± 0.6 μmol kg −1 ) in AW, and by 12 ± 2% (5.0 ± 1.1 μmol kg −1 ) in BSW (Table S1).
The general underestimation of C ant by the TTD method can be explained by its simplified assumption for the saturation of surface ocean δpCO 2 and pCFC-12 relative to the atmosphere during deep-water formation in the Arctic Ocean (Figure 1). Contrary to the TTD assumption of perfect equilibrium between the atmosphere and the surface ocean for both δpCO 2 and pCFC-12, during deep-water formation in February and March, simulated δpCO 2 in the surface ocean is higher than atmospheric δpCO 2 ; it is supersaturated. Conversely, surface ocean pCFC-12 is lower than atmospheric pCFC-12; it is undersaturated. This disequilibrium between the surface ocean and atmosphere for both δpCO 2 and pCFC-12 can be attributed to the rapid heat loss of inflowing PW and AW (Kaltin & Anderson, 2005;Midttun, 1985). For any gas (e.g., CFC-12), when surface cooling is faster than its air-sea equilibration, then the dissolved gas concentration changes little and its partial pressure must decline (e.g., see Orr et al., 2017, eq. 21). Conversely, δpCO 2 (the anthropogenic change in pCO 2 ) depends on ocean chemistry. Cooling causes oceanic δpCO 2 to increase because it reduces the carbonate ion concentration and thus the buffer capacity, making the water less able to retain anthropogenic carbon.
Air-sea equilibration also depends on how long waters remain at the surface and the extent to which those surface waters are ice free. Surface-water transit times in the Barents and Chukchi Seas are around 6 months each (Loeng, 1991;Spall, 2007). During that transit, the surface waters undergo continual cooling in the Barents Sea and are isolated by substantial sea-ice cover in the Chukchi Sea. Hence, gas equilibrium between air and sea is not reached, neither for δpCO 2 nor for pCFC-12, before those surface waters are subducted. Thus, the TTD assumption that both δpCO 2 and pCFC-12 in those surface waters equilibrate entirely with the atmosphere causes the TTD-based estimates of C ant concentrations to be too low in the deep waters that were formed from surface waters in the Chukchi and Barents Seas.
The TTD approach's largest underestimates are found in WPW in the Chukchi Sea, delimited by the S = 33 contour in Figure 2, and in the BSW, delimited by the 0 • C isotherm in the same figure. The extent of underestimation diminishes as these water masses mix with others ( Figure 2). The bias in the BSW is reduced once it enters the Nansen basin and mixes with AW. A signature of this mixing in the model is its decrease in the temperature gradient in the AW along the shelf-break of the Nansen basin, a feature that is also observed (Gammelsrød et al., 2009;Schauer et al., 2002).

Correction of Data-Based Estimate of C ant
To refine the data-based estimate from Tanhua et al. (2009), we adjusted their TTD-based estimates upward based on the extent of underestimation in each water mass indicated by our model-based assessment. That is, we assigned corrective factors for the C ant concentrations to each water mass: +4% for AW, +12% for WPW and BSW, and +7% for SPW (section 3, Table S1). After this adjustment of the TTD-based C ant concentrations, the best estimate for the Arctic Ocean C ant inventory increases from 3.0 to 3.3 Pg C in 2005 while the uncertainty range changes from 2.5-3.3 to 3.0-3.6 Pg C. The lower bound of the uncertainty range increases by 0.2 Pg C more than the upper bound, reducing the overall uncertainty range. The former lower bound accounted for the additional uncertainty for the bias between surface saturations of δpCO 2 and pCFC-12 (Tanhua et al., 2009), an estimate that was based on results from the Southern Ocean (Waugh et al., 2006). Here, we explicitly account for the sign and magnitude of these saturation differences in the Arctic.
The remaining uncertainty of the C ant inventory is considered the same as previously estimated by Tanhua et al. (2008Tanhua et al. ( , 2009. It includes uncertainties from the Δ∕Γ ratio (±5%), from the spatial extrapolation (±5%), and from either very low CFC-12 concentrations in old waters or supersaturation of CFC-12 in young waters owing to the decline in atmospheric CFC-12 since 2002 (±7%). Rajasakaren et al. (2019) also estimated uncertainties from the Δ∕Γ ratio and from their lateral extrapolation of C TTD ant concentrations from the Beringia section to the entire Arctic Ocean. While their uncertainty from the Δ∕Γ ratio is also around ±5%

Arctic Ocean Acidification
Using the data-based C obs ant concentration estimates from Tanhua et al. (2009 calculated that the average depth of the ASH on the Beringia section was 1,890 m in 2005 and that it had shoaled by 190 m between 1765 and 2005. Based on our refined C ant concentration estimates, the distance-weighted mean ASH along that section is located at 1,950 ± 260 m in 2005 and it has shoaled by 270 ± 60 m during 1765-2005, that is, by 37% more on average than estimated by Anderson et al. (2010). Error bars represent plus or minus one combined standard uncertainty from the propagation of the standard uncertainties of the dissociation constants and the solubility product for aragonite. Furthermore, we assessed the spatial variability of the depth of the ASH along the Beringia section. In 2005, that section's deepest ASH (2,450 ± 300m) is found on the continental rise next to the Beaufort Sea, while its shallowest ASH (1,590 ± 300 m) is 500 km away in the center of the Canada basin (Figure 3). Shoaling also varies along the section, from as low as 80 m in the southern part of the Canada basin to as much as 550 m in the center of the Canada basin.
For the future scenarios, we applied the same basic approach as used by Anderson et al. (2010), which considers that changes in Ω A are only due to the direct effect of increasing atmospheric CO 2 on ocean chemistry; effects from climate change are ignored. Thus, we applied the observation-based TTD obtained for 2005 along the Beringia section to the four future RCP scenarios to estimate the evolution of C ant concentrations and UI along the same section as described in section 2.7 ( Figure 3). Between 2005 to 2037, the UI follows the same trajectory under all four RCPs, increasing from 39-50% to 45-64%. Afterwards, it diverges. Under RCP2.6, the UI rises more slowly reaching 63-78% in 2087 and remains constant thereafter. Under the three other RCP scenarios, the UI increases more quickly, for example, in 2100 reaching [80][81][82][83][84][85][86][87][88][89][90][91][92][93][94][95][96][97][90][91][92][93][94][95][96][97][98][99][100][97][98][99][100] Our idealized TTD-based estimates were also compared to simulated changes in Ω A from Steinacher et al. (2009), who made projections with the NCAR CSM1.4 climate-carbon model. During the 21st century, their model is forced under the Special Report on Emissions Scenarios (SRES) B1 and A2, which are similar to the more recent RCP2.6 and RCP8.5 scenarios used here. Steinacher et al. found that in 2100, the entire water column in the Arctic Ocean becomes undersaturated with respect to aragonite under the A2 scenario but not under the B1 scenario. That complete undersaturation under the A2 scenario occurs in 2090 when atmospheric CO 2 reaches 765 ppm. Likewise, our results suggest that the Arctic water column would become entirely undersaturated by 2100 (Figure 3) under the RCP8.5 scenario, when atmospheric CO 2 reaches 936 ppm, but not under the lower atmospheric CO 2 levels of the RCP2.6 scenario, which reaches 443 ppm in 2052 and subsequently declines. Our results also suggest that the Arctic Ocean would eventually become almost entirely undersaturated (UI > 95%) even at atmospheric CO 2 levels less than 765 ppm.
With the two intermediate RCP scenarios, the UI reaches 93-99% in 2150 under RCP4.5 and 94-100% under RCP6.0. The lowest atmospheric CO 2 level at which nearly complete undersaturation (UI > 95%) is reached is 540 ppm, the atmospheric CO 2 value at which RCP4.5 levels out. Under the RCP8.5 scenario, the 540 ppm threshold is reached sooner, in 2051, but the entire Arctic water column does not become undersaturated until 2080 because it takes time to ventilate intermediate and deep waters. These findings emphasize that the year in which the entire Arctic Ocean water column would become undersaturated with respect to aragonite depends not only on reaching a specific atmospheric CO 2 level but also on the rates of increase and future decline. Complete undersaturation of the Arctic Ocean appears inevitable if atmospheric CO 2 would reach twice the preindustrial level unless just afterwards there were a sharp decline.
Unlike model studies (Steinacher et al., 2009;Steiner et al., 2013), our future estimates are based on data-based estimates of the ventilation age and future RCP scenarios of atmospheric CO 2 . This simplified approach suggests that during the 21st century under RCP8.5, the deep ASH would shoal by 900 m, nine times as much as found with the model studies. In contrast, the model studies suggest much greater deepening of undersaturated waters from the surface before there is a merge with the models' more Journal of Geophysical Research: Oceans 10.1029/2020JC016124 slowly shoaling deep ASH, at which time the entire water column becomes undersaturated. However, these coarse-resolution ocean models largely underestimate lateral input of C ant into the Arctic Ocean (Terhaar et al., 2019). Their resulting underestimated storage of C ant in intermediate waters implies that they also underestimate the shoaling of the deep ASH.
Our TTD-based estimates of increasing C ant concentrations and resulting acidification during the 21st century account for future invasion of C ant but neglect climate change and its affect on the ocean. Yet the Arctic Ocean is already experiencing changes in sea-ice extent (Serreze & Stroeve, 2015) and primary production (Arrigo & van Dijken, 2015). During this century, the Arctic Ocean is also projected to experience large increases in summertime sea-surface temperature (Carton et al., 2015). All of these changes will affect Arctic Ocean uptake of C ant and hence its acidification. Steinacher et al. (2009) estimate with their model projection that the dominant climate-change effect on Ω A is a reduction due to dilution of C T and A T from sea-ice melt. Climate change is also expected to alter the Arctic Ocean circulation and the associated transport of C ant into the deep Arctic Ocean, although the primary driver of overall change in Ω A is the increase in C ant . Lique et al. (2018) found that the climate-change-induced brine rejection from sea-ice melt intensified deep-water convection in the Eurasian basin in the HiGEM climate model forced under a 4×CO 2 scenario. Some indication for this projected increase in deep-water formation in the Arctic Ocean appears to have already been observed, namely, through an increased contribution of Arctic waters to deep water masses in the Nordic Seas (Langehaug & Falck, 2012;Somavilla et al., 2013). More Arctic deep convection would further enhance Arctic storage of C ant and thus deep-water acidification and shoaling of the deep ASH. Steinacher et al. (2009) found that the effects of climate change will enhance the reduction of Ω A in the Arctic Ocean. Thus, our estimate of the future reduction in Arctic Ocean Ω A , which neglects climate change, should be considered as a lower bound. Despite the uncertainties associated with the idealized nature of our study, including its neglect of climate change and observational uncertainties, it is consistent with previous studies in estimating that in coming years the Arctic Ocean will experience widespread undersaturation with respect to aragonite, a dramatic chemical change that is expected to degrade the Arctic Ocean ecosystem (Fabry et al., 2008;Gattuso & Hansson, 2011;Riebesell et al., 2013).

Conclusion
Our model-based evaluation has demonstrated that the TTD approach underestimates C ant concentrations in the Arctic Ocean by up to 12% depending on the water mass considered. These underestimates occur throughout the water column, being tied through water-mass formation to biases in surface waters. The surface C ant concentrations estimated by TTD are generally too low because of that approach's assumption of perfect gas equilibrium between the surface ocean and the atmosphere for both δpCO 2 and pCFC-12. In contrast, our ocean model produces surface-ocean δpCO 2 that is supersaturated with respect to atmospheric δpCO 2 at the time of deep-water formation, while also producing surface ocean pCFC-12 that is undersaturated relative to atmospheric pCFC-12. Not accounting for these contrasting tendencies biases the TTD approach. After adjusting the 2005 Arctic Ocean C ant inventory from Tanhua et al. (2009) for these biases, the best estimate of that inventory increases from 3.0 to 3.3 Pg C while the uncertainty range moves from 2.5-3.3 to 3.0-3.6 Pg C.
By using the bias-corrected TTD approach with future atmospheric CO 2 scenarios, we provide an estimate of future conditions for an idealized case where effects from climate change are neglected. Results from that simplified analysis suggest that the Arctic Ocean would eventually become entirely undersaturated with respect to aragonite unless atmospheric CO 2 were stabilized below 540 ppm. Avoiding an entirely undersaturated Arctic Ocean would thus not be possible under the RCP4.5 scenario, which maintains that CO 2 level after 2100. Effects from climate change would probably reduce that atmospheric CO 2 threshold. Retaining some Arctic Ocean waters that are not corrosive to aragonite appears feasible only under more optimistic scenarios such as RCP2.6. To better characterize the atmospheric CO 2 stabilization threshold at which the Arctic Ocean would eventually become entirely undersaturated with respect to aragonite, more studies are needed with Earth System Models forced under stabilization scenarios beyond 2100.