The fraction χ of alkalinity that is released in the mixed layer can be calculated by integrating the alkalinity release profile down to the mixed layer depth (MLD), divided by the total alkalinity release per area and time, F. Here, we use the mean annual maximum mixed layer depth for MLD, representing the frequently ventilated ocean volume. For the uniform particle profile (Eq. ), the fraction dissolving in the mixed layer is given by 10χ=MLD/z0for MLD≤z01for MLD>z0.

Previous studies have calculated the fraction of alkalinity released in the mixed layer based on the decline in particle size during the mixed layer residence time tMLD in the shrinking core model, χ(tMLD)=1-R3(tMLD)/R3(0), assuming a constant sinking velocity within the mixed layer such that tMLD=MLDvsink(R(0)) . Our result (Eq. ) does not require this approximation and is equivalent to computing χ(tMLD) using the exact residence time obtained from ∫0tMLDvsink(R(t))dt=MLD for tMLD.

For the exponential PSD profile (Eq. ), integrating the alkalinity release profile down to the MLD and normalizing by F results in 11χ=1-exp⁡(-MLD/z0).

The analytical alkalinity release profiles from Sects.  and  make the assumption of constant environmental conditions throughout particle dissolution. In the ocean, however, temperature and pH typically decrease with depth. A decrease in temperature (T) reduces the area-normalized dissolution rate r , which, to a lesser extent, is countered by an increase in the dissolution rate from the co-occurring decrease in pH. In addition, a reduction in temperature will also increase dynamic viscosity, reducing the particles' sinking velocity. The impact of vertical temperature and pH variations on alkalinity release is further discussed in Sect. .

To obtain simple analytical alkalinity release profiles, in particular for non-uniform PSDs, we here use local vertically averaged temperature and pH to determine the penetration depths z0 for the dissolution profiles. However, z0 depends on the vertical range over which the mean temperature and pH are determined. For example, using average conditions over the upper 100 m will result in higher dissolution rates and a shallower penetration depth z0 than using average conditions over the upper 1000 m, due to the colder temperatures in the ocean interior. The former would be more appropriate for smaller particles that dissolve close to the surface while the latter would be more appropriate for larger particles. To take into account that larger particles experience colder temperatures (and a often lower pH), we calculate the penetration depth z0 from Eq. () with the mean conditions in temperature and pH between the surface and the penetration depth itself (T‾0→z0 and pH‾0→z0). In other words, z0 is calculated self-consistently with mean conditions in temperature and pH over the same vertical range. To do so, we solve 12z0=f(r(T‾0→z0,pH‾0→z0),μ(T‾0→z0)), numerically for z0. Following this approach, a particle that dissolves close to the surface (small z0) is modeled to dissolve under a warmer average temperature than a particle that penetrates the colder deep ocean (large z0).

In this study, we use the Earth system model GFDL ESM2M to determine OAE efficiency for the here developed alkalinity release profiles. GFDL ESM2M is a fully coupled carbon-climate Earth system model from NOAA GFDL, which contributed to the Coupled Model Intercomparison Project phase 5 (CMIP5). Its ocean component MOM4p1 uses a horizontal grid with 1° nominal resolution and 50 vertical layers with 10 m vertical resolution in the upper ocean. Ocean biogeochemistry is simulated by the Tracers of Ocean Phytoplankton with Allometric Zooplankton version two TOPAZv2, and carbonate chemistry follows the OCMIP2 recommendations with air-sea CO2 exchange determined by the bulk parameterization by .

As a first step, the penetration depth parameter z0 is calculated for forsterite (the most common form of olivine) for three different diameters, d = 1.72 µm, d = 2.58 µm, and d = 3.44 µm (hereafter rounded to 1.7, 2.6, and 3.4 µm for better readability), with environmental conditions from GFDL ESM2M. The three diameters were selected to show the transition from shallow to deep particle penetration depth. z0 is calculated for each vertical column of the ocean model grid separately, based on temporally averaged temperature and pH profiles over the period 2016–2025 and for five initial-condition ensemble members (50 years in total). The period 2016–2025, extending an emission-driven historical simulation , is forced with Global Carbon Budget CO2 emissions over 2016–2020 extended with NDCs for 2021–2025 , and non-CO2 forcing as well as land use changes prescribed from RCP2.6 . Since z0 is determined in a fixed time-period, the impact of climate change on the dissolution profiles is not considered here. We take the area-normalized dissolution rate of forsterite for geometric surfaces as a function of temperature and pH from , also validated in and (see Appendix Fig. ). Dynamic seawater viscosity as a function of temperature is interpolated from the tabulated data in . Forsterite density is taken from and seawater density is set to global surface ocean conditions of T = 18 °C and S = 35 PSU . Variations in seawater density are negligible for particle sinking velocity since they are small compared to the density difference between the mineral particles and seawater. Alkalinity release that is prescribed below the ocean bottom cell is added to the bottom cell.

Based on the spatially-varying penetration depths for the three diameters and the two alkalinity release profile types (uniform particles and exponential PSD), we run six OAE experiments with differing alkalinity release profiles in GFDL ESM2M. Following the CDRMIP protocol, alkalinity is continuously added to the global ocean between 60° S and 70° N, totaling to 0.14 Pmol alkalinity per year . For each of the six OAE experiments, GFDL ESM2M is run over the period 2026–2200, under a CO2 emission trajectory that stabilizes at 2 °C global warming relative to the preindustrial period in absence of OAE based on the AERA protocol;. These six simulations are compared to a simulation where alkalinity is added at the ocean surface. For the uniform alkalinity release profiles with d = 2.6 µm and d = 3.4 µm and for surface alkalinity addition, we ran four additional ensemble members for the period 2026–2035 to analyze the role of internal variability over the first 10 years of OAE. All simulations are run with interactive atmospheric CO2 rather than prescribed concentrations. Thus, the OAE efficiency; calculated as the difference in air-sea carbon uptake between the OAE experiment and the baseline simulation without OAE divided by the alkalinity addition; includes carbon cycle feedbacks between the ocean, atmosphere, and land biosphere. This net ocean capture efficiency including the carbon cycle feedbacks is lower than the gross efficiency, which is calculated without the adjustments in natural carbon reservoirs . The net efficiency is relevant for studying the carbon, climate and ocean acidification responses to OAE, while the gross efficiency characterizes the negative emissions due to OAE, thus important for emission budgets and carbon credits.

The penetration depth z0, calculated from Eqs. () and (), increases strongly with particle size (Fig. a–c). Globally averaged, z0 values are 165 m, 638 m, and 1945 m for particle diameters of d = 1.7 µm, d = 2.6 µm, and d = 3.4 µm, respectively. Thus, doubling the diameter from d = 1.7 µm to d = 3.4 µm increases z0 by about a factor of twelve. Under constant environmental conditions, Eq. () predicts a scaling of z0∝d3, corresponding to an eightfold increase. The stronger increase in z0 arises from overall cooler conditions experienced by larger particles that sink deeper into the water column as discussed in Sect. .

The penetration depth shows a pronounced latitudinal gradient (Fig. a–c). It is substantially greater at high latitudes than at low latitudes. For example, for d = 2.6 µm, the average penetration depth increases from 367 m in the tropics (10° S–10° N) to 1043 m in the Southern Ocean (60 to 45° S). This pattern arises primarily from lower water temperatures in high latitude regions, which suppress mineral dissolution rates and thereby increase penetration depth. The effect of reduced dissolution is partially counteracted by the higher viscosity of colder waters, which slows particle sinking and limits penetration. However, the change in dissolution rate with temperature dominates: a 1 °C cooling at 18 °C results in a 9.2 % decrease in area-normalized dissolution rate, whereas viscosity only increases by 2.6 %. Latitudinal variations in pH exert a negligible impact on mineral dissolution rate (Appendix Fig. ). Even variations in pH of ± 0.1 alter z0 by only a few meters.

Based on these penetration depths, the fraction of alkalinity released within the annual maximum mixed layer can be calculated (Sect. , Fig. d–i). Because waters above the annual maximum MLD are well ventilated, alkalinity released in this layer directly contributes to oceanic carbon uptake. The fraction of alkalinity released in the mixed layer decreases with increasing particle size and is larger for the uniform particle profile than for the exponential profile, as larger particles in the latter are exported to greater depths. Globally, uniform particles with d = 1.7 µm release 72 % of their alkalinity within the annual maximum mixed layer (Fig. d), compared to 52 % for the exponential PSD profile with the same mean volume diameter (Fig. g). Increasing the (mean volume) diameter to d = 2.6 µm lowers the fraction to 20 % and 18 % for the uniform and exponential profile, respectively, and further to 6 % for both profiles at d = 3.4 µm. For large diameters, the penetration depth is often much larger than the mixed layer depth and the alkalinity release within the mixed layer between profiles is similar, because: 1-exp⁡(-MLD/z0)≈MLD/z0 for MLD/z0≪1.

Regionally, alkalinity release in the mixed layer is large either where penetration depths are shallow (low to mid-latitudes; Fig. a–c) or where mixed layers are deep (e.g., western boundary current extension in the North Atlantic and North Pacific, the mode water formation regions of the Southern Ocean, and deep convection zones in the North Atlantic and Weddell Sea; Appendix Fig. ). Since regions are often either warm, associated with shallow penetration depths, or have deep mixed layers, the latitudinal gradients of alkalinity release in the mixed layer are relatively small. For example, uniform particles with d = 2.6 µm release 14 % of their alkalinity in the mixed layer in the tropics (10° S–10° N) and 20 % in the Southern Ocean (60 to 45° S).

Each profile type (uniform and exponential PSD) and particle size results in a characteristic vertical distribution of additional alkalinity relative to the reference simulation without OAE (Fig. a, Appendix Fig. ). Averaged over 2026–2200, the additional alkalinity profile of the smallest mean volume diameter d = 1.7 µm closely resembles that from surface dissolution, with only slightly lower concentrations close to the surface (57 µmolkg-1 for surface dissolution vs. 55 and 52 µmolkg-1 for the uniform and exponential PSD profiles, respectively). With increasing particle diameter, additional alkalinity accumulates at larger depths. This is particularly the case for the exponential PSD profile, where 37 % of the alkalinity is released below z0 compared to no release below z0 for the uniform profile (global mean values for z0 are shown as dashed lines in Fig. a). As a result, additional alkalinity near the surface declines. For d = 3.4 µm, additional surface alkalinity reduces to 21 and 18 µmolkg-1 for the uniform and exponential PSD profiles, respectively.

Relative to surface alkalinity release, this deeper alkalinity release reduces OAE capture efficiency, defined as the ratio of additional carbon uptake to the alkalinity added (Fig. b). The reduction is most pronounced in the first decades of continuous alkalinity addition. Over the first 30 years, efficiency decreases by more than two thirds for d = 3.4 µm, to 0.20 and 0.18 molCT(molAT)-1 for the uniform and exponential PSD profiles, respectively, compared to 0.65 molCT(molAT)-1 for surface dissolution and alkalinity release. For reference, an efficiency of 0.65 molCT(molAT)-1 corresponds to an uptake of 0.81 Gt CO2 per Gt forsterite. For the intermediate mean volume diameter d = 2.6 µm, efficiency is reduced to 0.44 molCT(molAT)-1 (-32 %) and 0.39 molCT(molAT)-1(-40 %) for the uniform and exponential PSD profiles, respectively. For the exponential PSD profile with the smallest mean volume diameter d = 1.7 µm, we find a 16 % decrease in efficiency to 0.54 molCT(molAT)-1. Efficiency is further reduced during the first decade with 0.32 and 0.14 mol C_T (mol A_T)⁻¹ for uniform particles with d = 2.6 and 3.4 µm, respectively, compared to 0.65 molCT(molAT)-1 for surface dissolution (on ensemble mean, ensemble ranges are shown in Fig. b). As such, efficiency decreases by more than 75 % over the first 10 years for particles with 3.4 µm diameter. We also find a reduced efficiency of 0.47 molCT(molAT)-1 (-27 %) for uniform particles with d = 1.7 µm during the first decade.

Over time, the difference in efficiency relative to surface alkalinity release decreases, reflecting the gradual transport of alkalinity released at depth back to the surface. Nevertheless, the average efficiency over 2026–2200 remains less than half of that of surface addition for d = 3.4 µm (0.29 and 0.25 molCT(molAT)-1, respectively, compared to 0.60 molCT(molAT)-1). Year-to-year variability in OAE efficiency is substantial in all experiments (standard deviation around 0.18 molCT(molAT)-1). These strong fluctuations in carbon uptake mainly arise because we run the experiments in a fully coupled Earth system model, where natural variations in air-sea CO2 flux in the OAE experiment and the baseline simulation are superimposed onto the carbon uptake signal from OAE. For larger particle sizes, the standard deviation of OAE efficiency approaches mean efficiency (coefficients of variation are 0.56 and 0.72 for the uniform and exponential PSD profiles with d = 3.4 µm). Thus, the OAE carbon uptake signal is less significant compared to flux variability when alkalinity is released from larger particles.

During the first 10 years of alkalinity addition, OAE with vertical alkalinity release profiles results in additional carbon uptake over most of the ocean (see Fig. a for the additional CO2 uptake for uniform particles with diameter d = 2.6 µm). However, carbon uptake and efficiency are generally lower than when alkalinity is released directly at the surface (Fig. c). As expected, regions with particularly low alkalinity release in the mixed layer (Fig. e) partially overlap with regions of low carbon uptake (Fig. a), such as in the northern and eastern North Pacific or the Atlantic section of the Southern Ocean. Carbon uptake is higher in the Kuroshio current extension, the Gulf Stream region in the North Atlantic, and mode water source regions in the Southern Ocean, where the fraction of alkalinity release in the mixed layer is also relatively high. However, despite relatively low alkalinity release in the mixed layer, the tropical upwelling regions show considerable carbon uptake, which may indicate the upwelling of alkalinity back to the surface. Overall, the fraction of alkalinity release in the annual maximum mixed layer only partially explains the regional variations in carbon uptake even on short timescales such as 10 years. The pattern correlation between the fraction of alkalinity release in the mixed layer and OAE-induced carbon uptake for d = 2.6 µm particles, averaged over the 5 ensemble members, is only 0.34 between 60° S and 70° N. However, the carbon uptake pattern also varies strongly among the five ensemble members. We analyze this by calculating the pattern correlation coefficients between the carbon uptake patterns of the different ensemble members over the first 10 years of experiment. The mean of the ten pairwise pattern correlation coefficients across the five ensemble members is 0.15 and 0.37 for uniform d = 3.4 µm and d = 2.6 µm particles, respectively. As such, regional carbon uptake is more uncertain for larger particles where alkalinity is released deeper in the water column.

At longer timescales, ocean carbon uptake increases in regions with deep mixed layers (cf. Fig. b and Appendix Fig. ), in the upwelling region of the tropical Pacific, as well as in Eastern Boundary upwelling systems (Fig. b). The increase in carbon uptake in these regions suggests that additional alkalinity released at subsurface in other regions is transported there, where it comes in contact with the atmosphere. In the eastern and central equatorial Pacific, for example, we find a distinct buildup of alkalinity in the upper 1000 m, likely due to an inflow of alkalinity from North and South of the equator (Appendix Fig. f). As these waters with additional alkalinity have not yet equilibrated with the atmosphere, additional carbon is taken up. As a result, carbon uptake becomes larger than in the simulation with direct alkalinity addition at the surface in these regions (Fig. d). Increased carbon uptake is also observed south of 60° S where no alkalinity is added, indicating an increased southward transport of alkalinity from regions north of 60° S when alkalinity is released at subsurface. Yet, carbon uptake remains lower over most of the low-to-mid latitudes, such that global carbon uptake remains 16 % lower than when alkalinity is added to the surface (Fig. b).

Our study suggests a shallower release of alkalinity compared to , who estimated that about 80 % of alkalinity from forsterite olivine particles with a 1 µm diameter is released within the maximum mixed layer. Repeating the analysis from Sect.  for particles of 1 µm diameter, we find a release of 98 % in the annual maximum mixed layer. The shallower release of alkalinity in our study primarily arises from the higher area-normalized dissolution rate adopted here, based on geometric surfaces from . For example, the dissolution rate is 84 % higher at 25 °C than the rate from used in . A secondary contribution stems from the deeper maximum MLD in our model, 123 m on global average 34 m deeper than observations;, compared to 64 m in . As the dissolution rate from has been validated against observations in multiple studies , the mixed layer alkalinity release fractions obtained here are likely more robust. Nonetheless, the comparison underscores the strong sensitivity of vertical alkalinity release to the assumed mineral dissolution rate. Despite the shallower release, the spatial patterns of mixed layer alkalinity release are broadly consistent with those of (cf. Fig.  and their Fig. 3d).

Our results are also qualitatively consistent with , who modeled alkalinity release using a more complex mineral particle model that includes particle aggregation and zooplankton interaction. Their study employed an experimental PSD from , in which 80 % of particle mass is contained in particles smaller than 10 µm in diameter. To enable comparison, we discretize the experimental PSD into 14 discrete size classes and convert the experimentally determined mass fractions per size class into particle number fractions (see Appendix Sect.  and Fig. a). The resulting cumulative alkalinity release profiles (Fig. b) are qualitatively similar to those reported by though our model predicts a shallower release. While found 25 % to 45 % of alkalinity release in the upper 80 m, with increased release for higher feedstock application rates where aggregates are less likely packed into zooplankton fecal pellets, we obtain 54 % to 61 % for temperatures of 10 to 25 °C. This difference suggests that including particle aggregation and zooplankton ingestion, as in , may further reduce the efficiency of olivine-based ocean alkalinity enhancement by enhancing particle settling velocities.

The analytical framework presented here involves several simplifying assumptions. The main limitations include (i) the idealized representation of particle geometry and sinking, (ii) the omission of particle interactions with the environment such as aggregation, scavenging, or the formation of coating layers, (iii) the use of mean rather than depth-resolved environmental conditions, and (iv) the omission of particle advection during dissolution.

First, the shrinking core model assumes smooth, spherical particles. We use an area-normalized dissolution rate determined for geometric spherical particles with equivalent diameters determined by sieving the mineral grains . The particles' sinking velocity, on the other hand, is characterized by the equivalent diameter from Stokes settling. While the two equivalent diameters are often similar , implying that the treatment of dissolution and sinking in our study is consistent, this may not always be the case. When the two equivalent diameters diverge, one cannot assign a single equivalent spherical diameter to a mineral particle that is representative for both dissolution and sinking as assumed in our alkalinity release profiles. Additionally, when mineral particles are added over a small area such that high mineral particle concentrations near 15 gL-1 are reached, fluid instabilities may considerably enhance the sinking velocity . While such mineral particle concentrations in the mixed layer are not reached in our idealized global experiments, where only 15 g olivine per square meter and year are added, instabilities may occur in more realistic localized application schemes.

Second, we also neglect potential particle interactions with the environment. Smaller mineral particles may aggregate, forming larger particles that sink faster . Mineral particles may also attach to biogenic particles through scavenging or zooplankton ingestion, suppressing near-surface alkalinity release . Mineral or microbial coating layers may form on the particles' surfaces , which can reduce the contact area with the surrounding water and mineral dissolution.

Third, to obtain analytical alkalinity release profiles, we assume that dissolution occurs at the mean temperature and pH between surface and penetration depth z0 (Sect. ). This simplification neglects vertical and seasonal gradients that could enhance dissolution in warmer surface waters and reduce it at depth. The approximation performs best where such gradients are small (e.g., at high latitudes or for shallow-sinking particles). For instance, in a subtropical Atlantic column with a 9.2 °C temperature range between surface and a particle's penetration depth of 300 m, surface alkalinity release is 27 % higher and deep release is 28 % lower than predicted using mean conditions, whereas in the Southern Ocean (1.8 °C range) the differences are only 9 % and 2 %, respectively (Fig. a,b). The stronger mismatch at low latitudes thus reflects the larger vertical temperature contrast. The use of mean environmental conditions to determine a particle’s penetration depth also neglects the nonlinear dependence of dissolution rate on temperature and pH . Because the dissolution rate is a convex function of these variables, the rate at vertically averaged conditions is slightly lower than the average rate computed over the full profile, resulting in a deeper predicted penetration depth. This effect is generally small: across the global ocean, penetration depths differ by less than 10 % over 90 % of the area for 2.6 µm particles (Fig. d). For these particles, explicit profiles yield a globally averaged penetration depth that is only 14 m shallower than the idealized case, though mixed-layer release fractions increase by about 6 % (a relative rise of 28 %, Fig. f). Hence, while vertically resolved profiles yield higher surface release, the idealized treatment remains a good first-order approximation. For the exponential PSD profile, we also assume that all particle sizes experience identical mean temperature and pH, although larger particles typically penetrate into colder, more acidic waters than smaller ones. Accounting for these variations would increase the spread in penetration depth across the PSD, resulting in a deeper alkalinity export for larger particles.

Fourth, the present framework neglects the horizontal and vertical advection of mineral particles during dissolution. Because dissolution can span several years (Appendix Fig. a), advection of mineral particles in the subsurface may modify the depth and spatial patterns of alkalinity release. This aspect should be assessed in subsequent studies.

Overall, these simplifications may lead to a modest underestimation of mineral export and deep alkalinity release, primarily due to the omission of particle aggregation. Nevertheless, the simplified vertical profiles developed here capture the first-order effects of environmental conditions and feedstock properties on alkalinity release, providing a robust basis for sensitivity analyses of ocean alkalinity enhancement efficiency.

Our study confirms that olivine must be milled to grain sizes near 1 µm to achieve feasible carbon removal through open-ocean alkalinity enhancement . When particles are uniformly milled to a diameter of 1.7 µm, carbon capture efficiency is reduced over the first decade but comparable to that of instantaneous surface dissolution on longer timescales. In contrast, doubling the diameter to 3.4 µm reduces the efficiency to less than one third within the first decades.

Olivine powder with an exponential PSD at a mean volume diameter of 1.7 µm marks a transition between near-optimal and considerably reduced capture efficiency. In this case, efficiency is 16 % lower than with direct surface alkalinity addition over the first 3 decades, with full efficiency reached only by the end of the 21st century (Fig. b). These long timescales until full efficiency result from an overproportionally larger fraction of alkalinity stored in the larger particles that sink deeper. While 80 % of particles are smaller than 2 µm, they only contain 48 % of the alkalinity. In contrast, the largest 0.3 % of particles in the PSD, exceeding 3.1 µm, still contain 2 % of the alkalinity. In natural or industrially milled powders, more heavy-tailed PSDs can further exacerbate this problem. For example, in the experimental PSD from , 73 % of the alkalinity resides in the largest 0.3 % of particles, resembling a power law distribution (Fig. a). For this heavy-tailed PSD, 20 % of the alkalinity is contained in particles with diameters larger than 10 µm, compared to only 2.5 µm for the exponential PSD, despite a smaller mean particle volume in the experimental PSD. Thus, beyond minimizing mean volume diameter, achieving a rapid decay of particle abundance at larger sizes is essential for efficient OAE. As such, separating and regrinding the largest particles in the mineral powder would, if possible, improve OAE efficiency.

The strong dependence of carbon capture efficiency on the particle size distribution makes particle comminution to grain sizes near 1 µm for olivine-based open-ocean OAE imperative. However, grinding olivine to such fine grain sizes strongly increases energy demand and associated costs and emissions. estimated CO2 emissions to increase from 0.04 tCO2(1.25tolivine)-1 for 10 µm particles to about 0.21 tCO2(1.25tolivine)-1 for 1 µm particles from comminution alone, translating to reductions in OAE capture efficiency by 0.03 and 0.13 molC(molAT)-1, respectively. Additionally, such fine olivine powders may increase particle aggregation , negatively impact zooplankton , and pose risks to human health . These problems with olivine grain sizes near 1 µm call into question the feasibility of olivine-based OAE in the open ocean. However, olivine may remain suitable for coastal applications where the mixed layer extends to the seafloor, such that alkalinity released from coarser olivine grains in the sediments enhances carbon uptake from the atmosphere . Future research should therefore focus on shallow coastal seas. The micrometer scale olivine grain size necessary for open-ocean OAE and associated high particle amounts may also impact marine ecosystems due to increases in turbidity. While no detrimental impacts were observed for coastal plankton communities with coarser olivine powder , turbidity-associated impacts on plankton should be investigated with micrometer-scale olivine powder, and ideally also for open-ocean ecosystems.

Alternative alkaline materials with higher dissolution rates, such as brucite, relax the particle-size constraints. Using Eq. (), one can calculate the permissible increase in particle volume for a more quickly dissolving material (indicated by primes) such that the penetration depth stays constant: 13Vd′Vd=r′r⋅Vmol′Vmol⋅ρp-ρwρp′-ρw

Because brucite dissolves roughly 100 times faster than forsterite at T = 25 °C and pH = 8 , the allowable particle volume increases by a factor of 90, corresponding to an increase in diameter by a factor of 4.5. Thus, an exponential PSD with mean volume diameter of 1.7 µm for forsterite corresponds to an equally efficient PSD with mean volume diameter of 7.7 µm for brucite. Importantly, dissolution rates of brucite have been shown to vary by orders of magnitude depending on crystalline structure , making particle size constraints for effective brucite-based OAE in the open ocean uncertain.

The framework developed here can be generalized to other PSDs by deriving corresponding vertical alkalinity release profiles, as illustrated for the exponential and discrete PSDs. This approach provides a direct estimate of the alkalinity released within the mixed layer (Sect. ), improving on earlier approaches assuming constant sinking velocity in the mixed layer . Our Earth system model simulations indicate, however, that regional variation in oceanic carbon uptake is only partly explained by mixed-layer dissolution. The remaining differences highlight the role of ocean circulation and alkalinity redistribution, which can only be captured with ocean-biogeochemical models.

Such ocean-biogeochemical models are also essential for assessing how mineral OAE with subsurface alkalinity release affects ocean acidification (OA). Relative to surface dissolution, and averaged over 2026–2200, mineral OAE with an exponential PSD at a mean volume diameter of 3.4 µm results in a 0.015 unit lower pH (weaker OA mitigation) in the upper 482 m of the water column, and a 0.015 unit higher pH (stronger OA mitigation) at greater depths (Appendix Fig. c). Notably, OA mitigation is increased below 482 m even though the alkalinity enhancement is smaller than under surface dissolution down to 792 m (Fig. a). This occurs because waters contain lower dissolved inorganic carbon concentrations as a result of the lower ocean carbon uptake under subsurface alkalinity addition. Overall, these results indicate a downward shift in the depth of OA mitigation and an enhanced mitigation potential driven by the reduced carbon uptake and efficiency of the mineral-based OAE.