Using the polygonal subdivision of the ocean introduced in , we selected 12 locations, spanning the range of the four different OAE uptake regimes identified by . The locations chosen are shown in Fig.  and listed in Table S1.

Since the ECCO-Darwin model uses a different grid (so-called Lat-Lon-Cap, (LLC270)) grid at 1/3° ) compared to the CESM2/MARBL model (1° spherical-polar grid), we re-projected the polygonal subdivisions onto the finer, 1/3° LLC270 grid. While the difference in gridding means that the release locations cannot be exactly replicated, the difference in the release area boundaries is very small and not expected to significantly alter the uptake curves. This assumption is supported by the observation that the CO2 uptake curves obtained previously vary across the ocean only gradually . In each location, alkalinity was released over the period of one month (in January) at a rate of 10 mol m⁻² yr⁻¹ uniformly across the selected polygon.

We conducted each of the pulsed alkalinity simulations using the standard LLC270 ECCO-Darwin 1/3° model set-up for 15 years . For each location, we investigated two pulses, one in 1992 and one in 1999 in two separate simulations. The latter matches the exact release year used in while the former provides an indication of the interannual variability. The year 1992 was not chosen for any particular climatological reasons, but rather, being the earliest year in ECCO-Darwin's data assimilative period, allows for potentially the longest continuous simulation. The atmospheric concentration of CO2 was set to historical values from the NOAA Greenhouse Gas Marine Boundary Layer Reference . Small differences in pCO2atm are not expected to change the OAE uptake curves, so long as the value is not responsive to induced CO2 uptake . The total volume-integrated amount of ocean DIC was then computed over the simulation period and the difference from a reference counterfactual simulation was obtained. This was then normalized by the total amount of alkalinity added initially to yield η(t)=ΔΣDIC(t)/ΔΣAlk as the metric of OAE efficiency , where the sums are over the entire ocean volume.

In the same way as described above, we also tested four additional locations (North Pacific, North Hawai'i, Equatorial Pacific and Gulf Stream) replicating exactly the experiments of . Here, 5 runs were conducted for 5 years each, with alkalinity addition pulses in January of 2000, 2003, 2006, 2009 and 2012, with the goal of quantifying interannual variability.

The CESM2/MARBL model configuration used in this study is described in detail in and references therein. Briefly, the CESM2/MARBL simulation is a global forced ocean-ice (FOSI) configuration of the Community Earth System Model v.2 (CESM2) . The ocean component is the Parallel Ocean Program v.2 (POP2) with nominal horizontal resolution of 1° × 1° and biogeochemistry simulated by MARBL . The model was forced with the Japanese 55-year atmospheric reanalysis dataset (JRA55) , spun up from 1850 to 2019. The simulation is not data constrained, and all simulations in this study were forced with historical atmospheric CO2. Further properties and features of the model are summarized in Table .

A detailed description of the ECCO-Darwin model set-up, observational constraints, optimization methodology, and model-data evaluation is presented in . The latest ECCO-Darwin solution (v05) used here is based on ocean circulation and physical tracers (i.e., temperature, salinity, and sea ice) from the Estimating the Circulation and Climate of the Ocean (ECCO) LLC270 global-ocean and sea-ice data synthesis . ECCO-Darwin is based on a global-ocean and sea-ice configuration of the Massachusetts Institute of Technology general circulation model (MITgcm) , which has been constrained by the ECCO project using nearly all available ocean observations for the 1992–near-present period and has horizontal grid spacing of 1/3° at the equator and ∼ 18 km at high latitudes, with 50 vertical levels. It should be noted that this configuration uses the ECCO LLC270 grid, which is a higher-resolution variant distinct from the more commonly used LLC90 production version . The ECCO circulation estimate is coupled online with the MIT Darwin ocean ecosystem model, which in turn drives and interacts with marine chemistry and ocean carbon variables , providing a data-constrained, property-conserving estimate of the three-dimensional, time-evolving ocean, sea ice, biogeochemical, and ecological state. An extensive global-ocean evaluation of v05 ECCO-Darwin against in-situ data is provided in . The ECCO-Darwin ecology includes five phytoplankton function types (diatoms, other large eukaryotes, Synechococcus, and low- and high-light adapted Prochlorococcus) and two zooplankton types with different preferential grazing behavior . The biological rates are driven by light, temperature, and macro/micronutrients (nitrogen, phosphorus, iron, and silica) but do not explicitly depend on DIC and Alk. Conversely the circulation does not depend on the tracers.

The optimization method of ECCO-Darwin uses the adjoint method for the physics, which adjusts initial conditions, surface-ocean boundary conditions, and 3-D time-invariant mixing coefficients; model biogeochemistry is optimized using a low-dimensional Green's Functions approach to adjust initial conditions and Darwin parameters. This results in a physically-consistent counterfactual solution with fully-closed property budgets (i.e., no nudging is used in the assimilation process). We note that ECCO-Darwin does not have a long spin-up period from pre-industrial conditions, as done in many forward-only ocean and Earth System Models, but uses the ECCO data assimilation methodology to both reduce spin-up and drift in a data-constrained simulation that starts in 1992. Table  summarizes the main features and parameterizations for both models.

In addition to quantifying the empirical differences in OAE-induced CO2 uptake between different ocean models, the goal of this paper is to estimate the relative importance of different model aspects to the overall variance. A better understanding of these sources of discrepancy will inform future model development and potentially inspire new sources of model-constraining data collection.

The main aspects of the ocean models which conceivably contribute to the CO2 equilibration dynamics are: horizontal and vertical transport (advection and mixing) of the excess alkalinity plume, the gas transfer velocities (which are a function of wind speed and sea-ice cover), the carbonate chemistry parameterization and any biological processes which can affect DIC or alkalinity concentrations. These aspects are strongly intertwined; for example, changes in horizontal transport will affect plume dispersal and therefore which gas transfer velocities will be encountered by the space-time evolving trajectory of the plume. Similarly temperature and salinity can affect the carbonate chemistry state and hence pCO₂.

We first compare these aspects in a generic way, comparing the wind forcing and carbonate parameters as function of latitude, longitude and time. These comparisons help identify overall differences in parameterization and are not specific to any given injection location. We then conduct a deeper analysis which compares the influence of each parameter to any given release location and alkalinity plume.

Another way to compare models is to conduct what is known in the machine learning community as “ablation”. Here, parts of a model are deliberately turned off or changed, and the simulations are repeated to examine their effects on the outcomes. We take this approach here with the biogeochemical model of ECCO-Darwin, which comprises 31 biogeochemical tracers, which, in addition to Alk and DIC, include Oxygen, Nitrate, Nitrite, Ammonia, Phosphate, Iron, Silica, Dissolved Organic Carbon and multiple phytoplankton functional type (PFT) tracers among others. These tracers are used to simulate biological activity, nutrient dynamics and carbonate precipitation and dissolution, in addition to inorganic processes such as gas exchange.

While biological processes modeled in ECCO-Darwin consume or produce CO2 and/or Alkalinity (through carbonate shell creation or dissolution), the growth rates are not explicitly coupled to DIC or Alk. We therefore reasoned that the majority of the biogeochemical model should have very little, if any, influence on the CO2 uptake curves, provided the background state of the DIC gradients (which biology helps establish) are present at the start of the simulation. If true, a significant fraction of computational cost could be saved in future simulations.

To test this hypothesis we created an ablated version of the ECCO-Darwin in which the marine ecosystem component was turned off in the code, i.e. an ocean without the soft tissue pump or calcifying activity. The only processes that remained active were the surface gas exchange, the advection of the tracers Alk and DIC, and the calculation of the carbonate system and pH. Alkalinity injections in eight different locations (plus an unperturbed reference run) were examined in this way, each with one run conducted with biological processes enabled and one run conducted without these features. Note that we did not spin up the system anew, or let the system reequilibrate into a new steady state which lacks the soft tissue pump and its associated DIC gradients before running the simulations. This was done intentionally to avoid changing the background carbonate state of the surface ocean, which would undoubtedly change the uptake kinetics. Instead, this experiment asks more narrowly: does the simulation of biological processes directly influence the CO2 uptake curves over a short timescale (15 years)? The sudden loss of the biological pump at the beginning of the simulations causes a steady departure of DIC from the regular ECCO-Darwin trajectory; however, those changes are still relatively small over the 15-year model period, such that the background ocean state still corresponds well to the full ECCO-Darwin carbonate state (See Fig. S3).

Thus far, our analysis has compared the parameter sets of the two models as a whole, however, for each release location the relative importance of various contributing factors to the CO2 uptake will vary, depending on the trajectory of the spreading alkalinity plume. In this section we develop a framework which attempts to disambiguate, to an extent possible, different contributions in a plume-specific way.

This is illustrated in Fig.  for an alkalinity release near Alaska. The extent of the alkalinity plume from three different runs is overlaid on the local gas-exchange parameter k. One can see how the intersection of the plume with k (as well as the other gas-exchange parameters) will determine the overall equilibration rate. Different models will not only have different gas-exchange parameters, they will also predict different plume trajectories – both contributing to the overall observed variance between models. The goal of the following section is to develop a framework to be able to attribute the differences to the various contributing aspects. The central idea is to reconstruct the equilibration rate of a given run (i.e. the gradient of the observed η(t) uptake curve) from the spatial extent of the plume at any given time t and the gas-exchange parameters that this plume is intersecting at that time. Then, an individual term in this expression may be swapped out to examine the sensitivity of the overall rate to that term. We develop this framework in the following section.

Figure  shows a comparison of the OAE equilibration curves (η(t)) for 12 different locations, obtained from one-month pulse additions of alkalinity in January. For the ECCO-Darwin model, two runs were conducted at each location in 1992 and 1999 to obtain a measure of interannual variability. In many locations, substantial differences between the models are observed, typically larger in magnitude than the interannual difference between the two ECCO-Darwin model runs. In general, the ECCO-Darwin model appears to predict faster equilibration than CESM2/MARBL, the only exception being the alkalinity release in the Kuroshio Current (labelled “Japan”). The largest differences are observed on the west coast of the Sahara, off the coast of Oman and for releases in the North Atlantic Ocean. The most extreme difference is observed at the Oman location in the Indian Ocean, where the two models disagree up to 50 % over the majority of the simulation period, with the discrepancy reducing to 25 % by 15 years. Locations near deep-water formation regions, such as offshore of Iceland and Norway, also yield substantially different results, with CESM2/MARBL having 25 % lower uptake compared to ECCO-Darwin.

In all locations, uptake differences are most pronounced during the first 7 years after release, where η(t) can vary up to 50 % in extreme cases (such as Oman) but generally differs by ≈10 %–20 %. Subsequently, in some locations, the equilibration curves then begin to converge again, as the equilibration proceeds towards the theoretically maximal value of ≈0.85 – the value of which is determined solely by the carbonate chemistry equilibria . This suggests that the models have relatively good agreement in terms of carbonate chemistry, which is expected. However, this convergence is not observed in the North Atlantic Ocean, where the equilibration differences developed by year 7 do not begin to dissipate. Likewise, the residual differences for the Kerguelen location appear stable even after 15 years. Near deep-water formation areas any differences in the initial rate of equilibration have an outsized effect on the progress of the overall equilibration state because equilibration ceases to make progress once the excess alkalinity has been subducted to depth and is isolated from the mixed layer and atmosphere. In other ocean regions, however, un-equilibrated alkalinity is not subducted deep enough and can be transported back into the mixed layer on a 5–20 year timescale , accounting for the continued equilibration and convergence of the equilibration curves, despite the initial divergence. In the cases of Oman and West Sahara, a substantial difference remains in year 15, even though the lagging CESM2/MARBL equilibration is still slowly rising. We note that our simulations were not long enough to determine if there would, eventually, be convergence or not.

The divergence between different models results immediately after alkalinity injection. It is therefore instructive to compare the gradient of the η(t) curves, shown in Fig. , which compares the normalized rates of equilibration (i.e. dη(t)/dt) with units yr⁻¹ between the same twelve runs. By far the largest differences between models is observed in the first 6–24 months, after which the rates tend to converge to more similar values. In the most extreme case (Kerguelen), the rates converge by month 4. This means that the majority of the divergence is accumulated in these first months and thus reflects model differences relatively close to the addition site. The strong seasonality of the equilibration rate is also very evident, with peaks occurring in boreal winter for locations located in the northern hemisphere, likely due to winter storms driving vigorous air-sea exchange and deepening of the mixed layer.

We only examined a single location in the southern hemisphere where these peaks would be expected in the boreal summer. However, the location in question, Kerguelen, does not appear to display any seasonal variation in equilibration rate, possibly because equilibration is so fast that it is nearly complete by the second year post injection. The Oman location also displays a strong peaking in equilibration rate in the boreal summer, however this is considerably more pronounced in ECCO-Darwin and appears to be the primary reason for the much faster equilibration in this model. This increased summer equilibration is evident until year 4 or 5 and is much more pronounced in 1999 compared to 1992, accounting for the interannual differences observed.

As found by a previous study , interannual variability within an ocean model is generally non-negligible, making comparison between single runs of different models statistically less meaningful. In order to gain insight into the significance of the inter-model differences, we repeated the ECCO-Darwin runs for two different years (1992 and 1999), see Fig. .

We found that some locations, such as the Amazon and Kerguelen, exhibited virtually no variability, while subtropical locations such as Hawai'i and the west-Saharan coast have substantial differences. Consistent with prior work , interannual variability itself varies between locations. In general, the interannual differences were significantly smaller than the inter-model differences. A notable exception was the alkalinity release south of Hawai'i, where the two runs diverged considerably; here the CESM2/MARBL run predicts a CO2 uptake curve intermediate between the two ECCO-Darwin runs.

Alkalinity additions in different years are subject to different circulation patterns and gas-exchange conditions, both of which can in principle affect the equilibration curve. Changes in how much alkalinity remains at the ocean surface in the short term, as well as changes in wind speeds, can have a significant effect on the e-folding time of equilibration. Differences in the amount of deep subduction can also affect the apparent ηmax if more or less alkalinity is transported to deep waters where it could remain out of contact with the atmosphere for centuries.

To further investigate the interannual variability and compare to the previous study of , we repeated the same runs in four of the same locations and in the same years (2000, 2003, 2006, 2009 and 2012) as in their study, with all injections occurring in January. The alkalinity injections occurred in the same geographical regions (as far as the different grids allowed). The results are shown in Fig. .

First, we note that the amount of interannual variability in ECCO-Darwin and in CESM2/MARBL are correlated, with the largest amount observed in the Gulf Stream location, although it is larger in magnitude in ECCO-Darwin compared to CESM2/MARBL for all four cases. Second, it is evident that the model differences are considerably larger than the interannual variability in all four cases, validating the results from Fig. . For all four locations, we found that ECCO-Darwin resulted in substantially faster equilibration during the first 5 years compared to CESM2/MARBL, consistent with our results in the other 12 locations presented earlier.

For the injection locations North Pacific, Equatorial Pacific and the Gulf Stream, the interannual variability appears to decrease from year 1–2 to year 5 in both models. For the North Hawai'i location, the interannual variability appears to stay constant in both models. Since our simulations are limited to 5 years here, it is unclear if the interannual variability will eventually converge entirely or not. This likely depends on whether in some years there is deeper subduction than in others, in which case the interannual variability could be persistent over many decades or more.

If, however, the initial variability is due to other factors, one would expect eventual convergence, as has been observed before . An interesting case is the injection north of Hawai'i, which exhibited relatively small interannual variability in ECCO-Darwin as well as CESM2/MARBL. This is in stark contrast to the injection south of Hawai'i (Fig. d). It is unclear whether the latter is an outlier or whether the interannual variability is much greater south of Hawai'i.

The equilibration process is dependent on a balance between the rate of CO2 exchange at the surface ocean and that of subduction processes transporting DIC-deficient water parcels from the surface to depth and hence out of contact with the mixed layer and atmosphere.

Because the excess alkalinity can only contribute to enhanced CO2 uptake in the surface-ocean layer of the model and because alkalinity is an almost conservative tracer, the fraction of the excess alkalinity retained in the surface ocean is an excellent proxy for monitoring the subduction process of the plume . The surface-ocean grid cell in both models is 10 m thick, allowing for direct comparison. Figure  shows the surface-ocean fraction of excess alkalinity over time for all 12 locations tested (dashed lines). We find that, in general, a more persistent surface residence of alkalinity also coincides with faster equilibration and vice versa (cf Figs.  and ). Thus differences in the models' predictions of surface alkalinity fraction appear to have a direct effect on the observed equilibration speed. Locations where CESM2/MARBL predicts a smaller surface alkalinity fraction such as Oman, West coast of USA and West Sahara also have slower OAE uptake behavior. For most locations there is a clear qualitative correspondence between a smaller surfaceocean alkalinity fraction and slower equilibration. Likewise, patterns (such as seasonal variations) apparent in one, are visible also in the other.

The most pronounced of these differences in our dataset is found at the Oman location. Here, CESM2/MARBL predicts rapid subduction with equilibration slowing significantly after the first two years but then continuing at a slow pace, due to gradual remixing of the subducted excess alkalinity. In ECCO-Darwin however, a very different kinetics is observed. Here, subduction occurs much more gradually and the equilibration curve does not exhibit a double exponential shape with two characteristic temporal peaks, as was found by . In the west Sahara location, both models exhibit the steep subduction followed by rebound, but in ECCO-Darwin the rebound is considerably more dramatic and occurs over a different timescale. A more detailed plot of this rebound is shown in Fig. S1 in the Supplement. Overall, equilibration can proceed further at an earlier stage and surface-ocean alkalinity remains higher in ECCO-Darwin compared to CESM2/MARBL.

We note that the surface-ocean alkalinity fraction differs substantially starting from the first data point in the time series, i.e., within one month of alkalinity addition, even though the alkalinity is added only into the surface layer grid cell. Figure a shows that surface-ocean fraction of alkalinity during month 1 of the simulations is systematically higher in ECCO-Darwin compared to CESM2, accounting for a significant fraction of the immediate discrepancies in equilibration rate. Since we expect surface-added alkalinity to mix and dilute into the mixed layer around the injection site rapidly, the degree of initial surface-ocean dilution should be directly correlated to the mixed layer depths.

Figure b shows that for both models the surface-ocean alkalinity fraction correlates quite well with what would be expected from the estimate of the mixed layer depth (MLD) estimated by the method of (estimated from the density profile as the shallowest depth where the potential density exceeds its surface value by 0.03 kg m⁻³). For this comparison, we assumed the excess alkalinity would spread evenly throughout the local mixed layer. The excellent agreement demonstrates that mixed layer depth predicted by the models play a central role in determining CO2 equilibration speeds. In general, it appears that CESM2/MARBL has a considerably deeper mixed layer depth compared to ECCO-Darwin and thus this difference explains a large proportion of the differences in the predicted CO2 equilibration rate. A direct comparison of the seasonal MLD for both models, for each location, is shown in Fig. S2, together with MLD data from ARGO floats . In general we observe that the MLDs in ECCO-Darwin agree more closely with the ARGO data than the CESM2/MARBL model.

However, vertical mixing clearly does not explain all the observed differences in equilibration speed. For example, the vertical dilution in the Norway location (Fig. a) is quite similar between the models, but the overall equilibration is markedly slower in CESM2. Thus, other factors must contribute more significantly in this location, which will be analyzed further below.

In addition to surface-ocean alkalinity, Fig.  also shows the surface DIC (dotted lines) and the surface-ocean deficit (solid lines) as calculated from ΔDIC and ΔAlk (see methods). By definition, in every location where there is initially a higher concentration of surface-ocean excess alkalinity, there is also a greater concentration of deficit and the rate of DIC increase in the surface-ocean layer is proportionally greater. This greater DIC influx, however, begins to quickly reduce the surface-ocean deficit. In many locations, this leads to a convergence of the surface-ocean deficit in the two simulations within the first 6–18 months, even though the difference in excess surface-ocean alkalinity persists. Since it is the deficit that drives CO2 uptake, this explains the earlier noted convergence of the CO2 uptake rates. In some cases (Hawaii, Brazil, West Sahara, Alaska), the simulation with the initially higher surface-ocean deficit (ECCO-Darwin) depletes its surface deficit so rapidly that it actually drops below that of the CESM2/MARBL simulation, allowing the latter to catch up in terms of equilibration.

The evolution of the deficit over time is complex, because it is a function both of surface-ocean equilibration (which is determined not only by available surface deficit but also the surface gas-exchange parameters) and subduction below, and remixing of deeper excess alkalinity back into the mixed layer. Such complex dynamics are evident in the Kuroshio current, where, especially in the ECCO-Darwin simulation, the surface-ocean alkalinity and deficit exhibit sharp spikes around March (Fig. f). However, in other locations where fresh (unequilibrated) excess alkalinity is brought to the surface over a slower timescale, such as Hawaii (Fig. j in years 3–9 and West Sahara (Fig. h) in years 6–12 after injection, the deficit does not rise to the same extent, presumably because this signal can equilibrate faster than the influx of fresh, unequilibrated alkalinity.

To investigate the effect of near-coast ocean dynamics, which could differ substantially between the two models due to their different horizontal grid resolutions and representation of lateral fluxes, we chose four of the earlier locations and repeated the comparisons in a nearby polygon further out in the ocean. The results are shown in Fig. . We found that in all four cases, the agreement between the two models is considerably greater for offshore locations than for near-shore locations. Furthermore, the interannual variation between the ECCO-Darwin runs conducted in year 1999 and 1992 is also reduced in offshore locations compared to their respective near-shore locations. For all four locations, the final values of η(t) at 15 years agreed within ±0.025, but varied as much as ±0.1 for the equivalent near-shore location. These results are consistent with the idea that the coastal 3-D ocean dynamics are complex and difficult to capture correctly in coarse-resolution ocean models, and may differ more between models compared to simulations of open-ocean waters. In particular, one may expect that lower-resolution models might perform more poorly in the near-coast regimes, and that only higher-resolution models can hope to resolve the complex coastal dynamics. Since near-coast dynamics could lead to substantial upwelling or downwelling currents and intense mixing, such differences would be particularly important for OAE equilibration, since only surface-ocean alkalinity can contribute to CO2 uptake.

We strengthen this hypothesis by comparing the surface-ocean alkalinity fraction for the same four location pairs (Fig. ). In all four cases, the difference in total excess surface-ocean alkalinity proceeds much more similarly in both models compared to each respective near-coast location. This confirms that near-coast subduction and mixed-layer modelling is of primary importance in order to predict the equilibration of near-coast releases. Given that near-coast release of alkalinity is likely to be more economically favorable, this points to a need for greater model certainty in such complex flow regimes. However, the two models we have compared differ in both resolution and parameterization such that we cannot disambiguate which aspect is responsible for the observed differences. recently reported comparisons between different resolution versions of the same model and found relatively small differences between simulations at 1 and 0.1° resolution; however, locations closer and further from the coast were not explicitly compared.

The carbonate chemistry model, in particular at the surface ocean, plays an integral role in the modelling of OAE equilibration. We therefore compare several key quantities between different models, as well as from the data-based OceanSODA product in Fig. .

Starting with the basic carbonate system tracers [DIC] and [Alk], we find significant differences between the models across latitudes. Compared to OceanSODA, CESM2/MARBL has consistently higher values for both parameters across nearly all latitudes (Fig. a, b). ECCO-Darwin exhibits more closely aligned values, although slightly lower than OceanSODA in tropical latitudes. In the Arctic Ocean however, ECCO-Darwin begins to deviate from the observational data, while CESM2/MARBL agrees much more closely. However, because [DIC] and [Alk] have compensatory effects on pH and pCO₂, the differences in pCO₂ are somewhat smaller, with the models showing better agreement with each other and with OceanSODA, and mean discrepancies on the order of 10–20 ppm (Fig. d). For comparison, the sea-surface temperature (Fig. c) exhibits considerably closer agreement between the two models.

Two important sensitivities are of particular importance for OAE. In the short term, the fact that CO2 is in comparatively fast equilibrium with bicarbonate ions, vastly increases the capacity of seawater to absorb CO2, but also increases the e-folding time for air-sea CO2 equilibration. The term ∂[DIC]/∂[CO2] is a key sensitivity which quantifies this effect . It is therefore an important parameter to compare between model implementations. Figure e shows its mean values across the latitudes, with larger values leading to slower equilibration. Generally there is quite good agreement, with both models slightly overestimating this sensitivity compared to OceanSODA and therefore overestimating the equilibration e-folding times. The deviation is up to 8 %–10 % for CESM2/MARBL and 2 %–4 % for ECCO-Darwin, with commensurate deviations expected for the equilibration rate constant.

In the long term, after extensive mixing, the equilibration curves will approach a value given by the sensitivity of the carbonate system [DIC] to increases in alkalinity, typically written as ∂[DIC]/∂[Alk], since it determines the amount of DIC deficit created per unit alkalinity added. The long-term effect on radiative cooling effected by OAE, given the typical lifetime of CO2 in the atmosphere, occurs on timescales of hundreds of years, by which point alkalinity releases from most locations (other than those near deep-water formation areas) will be thoroughly equilibrated. Thus, the end point of the equilibration, i.e., the value of ∂[DIC]/∂[Alk] is of long-term importance and it is interesting to compare this factor between models. Figure f shows that both models agree quite closely, with deviations on the order of a few percent. This suggests that the long-term CO2 predictions from both models are likely in very good agreement, even if the short-term equilibration e-folding times may differ in each model. This is consistent with a general understanding that the ocean carbonate chemistry is well understood and therefore not a major contributor to the inter-model-variance of OAE efficiency. It is also consistent with our observation that the η(t) curves appear to converge in many locations towards the end of the 15-year period simulated here.

Wind speed plays a central role in determining the rate of gas exchange across the ocean-atmosphere boundary, as the gas transfer velocity k is typically parameterized as a function of the square of the wind speed . Greater wind stress can also increase vertical mixing in the upper ocean, contributing to changes in the surface-ocean fraction of alkalinity.

Figure  compares the k parameters calculated for the two models being compared here and for OceanSODA. The contribution of sea ice has been included in this comparison. The values for k agree in general, but the details differ substantially. In the boreal summer for example, in the subtropical zones around ±18°, ECCO-Darwin has k parameters that are nearly 40 % higher than those observed in CESM2/MARBL.

This can be partially explained by the different gas exchange parameterizations in the two models, as noted by . ECCO-Darwin uses the older, but widely- adopted parameterization from with a higher coefficient of 0.337, while CESM2/MARBL uses a more recent estimate from with a coefficient of 0.251, which is roughly 25 % lower. However, the observed differences in k differ in a more complex way than a simple scaling; the k values in ECCO-Darwin are higher than those from CESM2/MARBL in equatorial regions but lower in polar regions, therefore affecting alkalinity releases at different latitudes in different ways (as will be shown later).

As described in the methods, we examined the importance of simulating the soft tissue pump and other biological processes on the equilibration curve by comparing the results of the regular ECCO-Darwin model with an ablated version in which computation of these systems was disabled. The results are shown in Fig. .

Despite the rather abrupt perturbation to the model (Fig. S3), the results show virtually no difference in the equilibration curves with or without biological processes enabled. Despite the sudden removal of biological activity, which causes a steady change in surface-ocean DIC and Alk, these changes are virtually equal in the perturbed and the reference simulations and thus for the purpose of calculating the ΔDIC induced by the alkalinity pulse, they appear to cancel. This suggests that OAE impulse response functions can be simulated relatively accurately without reliance on detailed biological models, provided the background carbonate state (vertical DIC and Alk gradients) is accurate to start with. A small difference was observed at the Oman location, however its root cause could not be determined at this time.

We note that the quantities of alkalinity added in these simulations are quite small and ocean variables such as pH and carbonate saturation are not dramatically changed. Thus, the rate of biological processes is not impacted significantly. For real-world deployments of OAE, this situation may be quite different and these results here do not apply to the question whether large-scale deployments of OAE could affect biological processes, or cause secondary positive or negative CO2 uptake feedbacks.

It should be noted that 29 out of 31 tracers were turned off for this experiment, which reduces the computational load substantially. Given the small impact of biology relative to the large impact of circulation, and in particular vertical processes and subduction, it is likely beneficial to focus computational expenditure on higher-resolution models rather than sophistication of biological modelling for the purpose of calculating accurate OAE impulse response functions. We note that for each deployment time a no-biology reference simulation must also be branched off the main simulation. However, if many OAE perturbations are being tested at different locations (as in ), the computational cost savings can be substantial overall.

Thus far, the analysis has focused on the various aspects of the ocean models which conceivably contribute to CO2 equilibration dynamics, one at a time: overall surface-ocean dilution and parameterization of gas transfer (i.e., wind speeds, carbonate chemistry parameters and biological processes). However, for any particular release location, the relative importance of these parameters is dependent on the particular model trajectory the DIC deficient plume takes, for example, which gas transfer velocities will be encountered by the space-time evolving plume. To disentangle these effects, at least to the extent feasible, we devised a more specific approach which examines changes to the equilibration rate based on changing one component of the plume at a time as described in detail in the methods section.

There are two different approaches this analysis takes. First, we investigate the effect of changing parameters sets or individual parameters, given a fixed plume trajectory. This probes the parameterization of the gas exchange, separate from the question of how each model predicts the trajectory of any given plume. As described in the methods, each parameter can be considered in isolation. Second, we investigate the effect of different horizontal plume trajectories intersecting a constant set of gas exchange parameters (gas-exchange velocity k and carbonate sensitivity β). This probes the importance of the predicted flow pattern of each model, separate from the parameterization itself.

Figure  illustrates an example of alkalinity release near Alaska where three different plume trajectories are overlaid over the gas exchange parameter k. One can clearly see how equilibration will speed up if the plume intersects high-wind regions in the North Pacific and avoids the sea-ice covered regions north of Bering Strait. Likewise, changes in the k parameter would only influence the equilibration if the changes occur along the actual DIC-deficient plume trajectory.

Figure  shows the changes in the equilibration rate with respect to the exchange of changing different components of the rate constant expression (Eq. ). In most locations, the wind parameterizations appear to play a large role in determining equilibration rates. Interestingly, in polar locations the equilibration appears to be consistently slower in ECCO-Darwin (e.g. Norway, Iceland, Alaska and Kerguelen), while for tropical and subtropical locations it appears to be somewhat faster (e.g., Gulf of Mexico, Oman and Brazil). This is consistent with the general observation that kw values from ECCO-Darwin exceed those from CESM2/MARBL in the tropics, but are generally lower compared to those from CESM2/MARBL towards the poles (see Fig. ). This pattern is especially pronounced in the boreal winter. The most extreme difference is found in the Alaska release location, where considerably slower winds are encountered in the ECCO-Darwin 1999 run compared to CESM2/MARBL, especially during the first 6 months of the simulation.

The influence of the sea-ice parameterization was not separated in this plot, since its influence is very small compared to the other parameters (<0.01 yr⁻¹), however it is singled out in Fig. S6 for the interested reader. As expected, sea-ice cover only influence the three most northern injection locations, Norway, Iceland and Alaska (Fig. S6a, b and c). The influence only appears after 1 year, once part of the plume has had a chance to reach sea-ice covered areas. As expected, for more equatorial release locations, sea-ice coverage has no influence (Fig. S6e–l), except for the Gulf Stream location (East USA) (Fig. S6d), where some differences are evident after year three when the alkalinity reaches the North Atlantic Ocean and encounters the presence of sea ice.

Figure  also shows the influence of the carbonate system (β, in red), which is much more modest compared to wind effects. In general, the carbonate parameters in ECCO-Darwin favor a slightly faster equilibration compared to CESM2/MARBL. This is consistent with earlier observations that the carbonate system description is very similar in the different models. These results are consistent with the earlier comparison of β across latitudes (see Fig.  e), where β in ECCO-Darwin is consistently smaller than in CESM2/MARBL, resulting in faster equilibration. Once the plumes have spread widely, its contribution becomes practically negligible; however, early, when the plume is more localized, the difference can be significant in some locations (e.g., East USA, Brazil and Kerguelen). In particular, on the east coast of North America the carbonate parameterization of ECCO-Darwin predicts a considerably faster equilibration compared to CESM2/MARBL in the first 3 months after injection (Fig. d); however, the effect is somewhat counteracted by a slower wind parameterization during the same time period.

Finally, Fig.  also shows the relative change in the CO2 equilibration rate, when the horizontal distribution of the surface-ocean deficit is changed from ECCO-Darwin to CESM2/MARBL, while keeping the parameters and the total amount of surface-ocean deficit constant. Since the horizontal transport and time evolution of the plume reflect physical bulk flow predicted by each model, these curves represent the extent in which these flow predictions can cause changes in the CO2 equilibration. We note that these changes are relatively modest in most cases, similar in magnitude as model differences in carbonate system parameterization. However, in the locations Oman and Brazil, they appear to be on par with changes in wind parameterization. Especially in Oman, the horizontal plume trajectory appears to be a major contributor to the peak equilibration events that occur during boreal summer (i.e., in months 6, 18, 30 etc).