According to our simulation results with REcoM-2 embedded in the MITgcm, the oceanic carbon uptake requires about five years to equilibrate to ∼0.29 Pg C per Pg olivine in our STANDARD scenario (figure 1(a)). This scenario assumes an even distribution of 3 Pg of olivine per year over the entire open ocean surface and calculates the effects of both alkalinity and silicic acid input. If not mentioned otherwise results refer to this scenario. Our simulations show that alkalinity input is responsible for 92%, silicic acid input for ∼8% of the carbon sequestration (figure 1(a)). Both effects are cumulative. The carbon sequestration caused by alkalinity is with 0.25 Pg C per Pg olivine 10% smaller than previously assumed with a simpler model (Köhler et al 2010).

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The addition of silicic acid which accompanies the olivine dissolution improves growing conditions for diatoms in silicate limited waters. Our model predicts changes in the net primary production (NPP) of diatom and non-diatom species groups. Diatom NPP rises by 2.4 Pg C yr⁻¹ (+14%) to 19 Pg C yr⁻¹, while non-diatom NPP shrinks by 1.3 Pg C yr⁻¹ (−4%) towards 32 Pg C yr⁻¹ (figure 1(b)). Strong seasonal variations in diatom and non-diatom NPP partially compensate each other resulting in a rather constant increase in total NPP by 1 Pg C yr⁻¹ (+2%) (figure 1(b)). Consequently, the species shift towards diatoms alters the biological carbon pumps, leading to an increased export of organic matter by about 0.08 Pg C yr⁻¹ (+1%) and a decreased export of CaCO₃ by the similar amount (−5%) (figure 1(b)). CaCO₃ also has a ballasting effect on organic matter export (De La Rocha et al 2008). A decrease of CaCO₃ export could therefore also lead to a decrease of carbon export, a process which is so far not considered in our study.

There is little biological response to olivine dissolution in the Southern Ocean south of 60°S and throughout most regions of the Southern Hemisphere because of the high natural silicate concentrations there. The diatom NPP (figure 2(a)) increases in the equatorial regime, in the coastal regime, in the North Atlantic, and in the Southern Ocean just north of the opal belt. The maximum increase in both total and diatom NPP occurs in the North Atlantic where there is a low Si:N ratio and in the equatorial regime where silicate is limiting (Dugdale and Wilkerson 1998). The low latitudes from 20°S to 20°N experience a fairly uniform increase in diatom NPP. Conversely, the average nanophytoplankton NPP (figure 2(b)) was greatly reduced in the areas where diatom NPP was increased. Spatial explicit changes in export production of organic matter and CaCO₃ are related to the changes in diatom and non-diatom NPP, respectively (figures 2(c) and (d)).

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Olivine dissolution leads to a fairly uniform increase in sea surface pH (figure S4(b) available at stacks.iop.org/ERL/8/014009/mmedia) counteracting the ongoing acidification of the surface ocean to some extent. Mean sea surface pH is increased after ten years of olivine dissolution by 0.007 (figure 1(d)), which is to 85% caused by the rise in alkalinity and only to the minor 15% by changes in the marine biology. Changes in carbon uptake, NPP, export production of organic matter and CaCO₃, and pH saturate after a few years (figures 1(a), (b), (d)), which makes longer simulations unnecessary. The increase in oceanic carbon uptake with respect to the amount of olivine input is almost linear, with 1, 3, and 10 Pg of olivine addition leading to 0.29, 0.28, and 0.27 Pg C per Pg olivine, respectively (figure 1(c)).

In an alternative distribution scenario SHIP in which olivine input into the surface ocean is weighted by common ship track densities (also called ships of opportunity) very similar results are obtained with some more localized effects on marine biology and pH. While the marine carbon uptake is with 0.28 Pg C per Pg olivine almost identical in SHIP and STANDARD (figure 1(a)), changes in marine biology and sea surface pH are more localized in SHIP. Impacts on the marine biology are now the results of a combination of ship track density pattern with the spatial distribution of silicate limitation (figure S4 available at stacks.iop.org/ERL/8/014009/mmedia). In SHIP changes in sea surface pH are limited to areas north of 40°S, and they are much stronger in the Northern than in the Southern Hemisphere. In the North Atlantic, the impact of olivine dissolution on marine biology is larger in SHIP than in STANDARD because more olivine is dissolved. Marine biology in the North Pacific is not silicate limited, thus both scenarios lead to similar small changes in NPP and export production here. Land-based enhanced weathering (Köhler et al 2010) would lead to similar effects localized to river mouths, but the amount of silicic acid reaching the open ocean is unknown because of the extensive anthropogenic alteration of the land–ocean transition (Laruelle et al 2009).

We calculate the grain size depending dissolution from the residence time in the ocean surface layer and sea surface temperature (SST). For that purpose we generalize previous findings (Hangx and Spiers 2009), which compiled the dependency of olivine dissolution rate as a function of grain size and temperature. These authors assumed that olivine grains are spherical particles, which dissolve according to a shrinking core model. Using their results we can write the functional dependency of dissolution time (t_diss in years), fraction of dissolution after a given time (r_diss in %), sea surface temperature (T in °C), and initial grain size (diameter assuming spherical shapes d_grain in μm) as

$$\begin{eqnarray} {t}_{\mathrm{diss}}&=&{f}_{\mathrm{size}}\cdot {f}_{\mathrm{T}}\cdot {f}_{\mathrm{diss}} \end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray} {f}_{\mathrm{size}}&=&{d}_{\mathrm{grain}}/(1 0 0~\mu \mathrm{m}) \end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray} {f}_{\mathrm{T1}}&=&{\mathrm{e}}^{-((\mathrm{T}-2 5)/1 0)}\tqs \!\! \mathrm{or}\! \tqs {f}_{\mathrm{ T2}}=\frac{6}{{\cosh }^{2}(\frac{\mathrm{T}+2}{1 7.5})} \end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray} {f}_{\mathrm{diss}}&=&0.0 2 3\cdot {r}_{\mathrm{diss}}^{2}. \end{eqnarray} \tag{ 5 }$$

Briefly, the first factor in equation (2), f_size, normalizes to the standard case with grains of 100 μm. Previous results (Hangx and Spiers 2009) depend linearly on initial grain size in the range from 10 to 1000 μm and we here assume its linear extrapolation towards even smaller grain sizes. The second term, f_T, describes the temperature dependency. The dissolution time (Hangx and Spiers 2009) is given for SST of 25 °C (thus f_T=25 °C = 1), t_diss roughly increases by a factor of 3 when T is reduced from 25 to 15 °C (figure 3(a)). Uncertainties in dissolution are high for lower temperatures as demonstrated by our suggested two different fitting functions (figure 3(a)). However, this effect is limited to high latitudinal areas and contributes only a few percentages to the global relative dissolution. In the following we will use f_T1. The third term in equation (2), f_diss, is a second order polynomial fit to the empirically derived dependency between dissolution time and relative dissolution (figure 3(b)). Uncertainties on all these functions are high, at least of the order of 50%. Thus, this exercise should only illustrate the order of magnitude in the dissolution kinetics.

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We furthermore estimate the available time for dissolution t_diss from the residence time of the olivine particles in the surface mixed layer t_ML. We here take the maximum of the monthly means of the surface mixed layer depth D_ML calculated in MITgcm, which has a global mean D_ML of 64 m. After Stokes law the settling velocity v_Stokes due to gravity can be calculated by

$$\begin{eqnarray} &&{v}_{\mathrm{Stokes}}=\frac{2}{9}\cdot \frac{{\rho }_{p}-{\rho }_{l}}{\mu }\cdot g\cdot \left (\frac{{d}_{\mathrm{grain}}}{2}\right )^{2} \end{eqnarray} \tag{ 6 }$$

with the densities of the olivine particles and the water fluid given by ρ_p = 3200 kg m⁻³ and ρ_l = 1000 kg m⁻³, respectively. The dynamic viscosity of water is μ = 10⁻³ kg (m s)⁻¹, g = 9.81 m s⁻² is the gravitational acceleration. We estimate the residence time t_ML in the surface mixed layer as ${t}_{\mathrm{ML}}=\frac{{D}_{\mathrm{ML}}}{{v}_{\mathrm{Stokes}}}$.

Our estimate leads to residence times of 3 yr, 10 d or 3 h for olivine particles with grain sizes of 1, 10 or 100 μm, respectively. Accordingly, ∼80% of olivine in 1 μm (initial diameter) grains would dissolve before leaving the mixed layer (figure 3(d)), whereas this percentage is already down to 5% for an initial grain size of 10 μm (figure 3(c)). Large particles will eventually dissolve in the deep ocean and not lead to an immediate oceanic carbon uptake. This maximum grain size estimate has also implications for enhanced weathering of olivine on land. If particles are distributed on land they might potentially be transported by winds to open ocean areas. A previous study on land-based enhanced weathering (Köhler et al 2010) discussed sequestration efficiency of 10 μm large olivine grains, a size which is easily transported by winds (Müller et al 2010). These large grains distributed on land and potentially dispersed by wind to the open ocean will according to our results sink largely undissolved to the deep ocean without the desired short-term carbon sequestration.

The dependences of the dissolution on both SST and mixed layer depth (figure 3(c)) also show that olivine dissolution is only feasible in the latitudinal band between 40°N and 40°S, and additionally in the areas of deep water production in the northern North Atlantic. However, the regions favourable for olivine dissolution largely overlap with commercial shipping tracks, especially in the Atlantic (figures 3(d), S3 available at stacks.iop.org/ERL/8/014009/mmedia) making a distribution scheme based on ships of opportunities a possible option.

Furthermore, scavenging by biogenic particles and physical aggregation, especially at high particle concentrations, might lead to larger, faster-sinking particles and aggregates. The addition of 3 Pg of olivine (as done in scenario STANDARD) with grain size of 1 μm homogeneously distributed over the world oceans would increase the number density by 10¹¹ particles per m³ in the mixed layer corresponding to 0.4 g olivine m⁻³. At a grain size of 1μm and below Brownian motion is the main process driving aggregation. In a recent study (Bressac et al 2012) it was shown that adding dust particles of a similar amount (0.8 g m⁻³) with a somewhat smaller grain size (the number size distribution peaks at 0.1 μm) would lead in a part of the distributed particles to fast particle aggregation resulting in sinking velocities on the order of 50 m d⁻¹. These velocities are orders of magnitude faster than our calculations implying residence times in the surface ocean of rather days than years. The experimental evidence (Bressac et al 2012) indicates that our calculated sinking velocities and the estimated fraction of olivine dissolution applies only at low rates of olivine addition.

The sequestration of CO₂ by olivine dissolution is restricted in our study to the immediate effects caused by alkalinity enhancement and ocean fertilization by addition of silicic acid. The transition of CO₂ from the atmosphere to the ocean pools is thus envisaged which might play a role on centennial to millennial timescales. On even longer timescales approaches which guarantee a deposition of C as part of the sediment on the ocean floor might need to be taken into consideration, e.g. using calcium silicates which might precipitate in the form of calcite (Lackner 2002, 2003). Here, other constraints such as source material availability might become important.

Our work shows that open ocean dissolution of olivine is ocean fertilization (Lampitt et al 2008). It might also affect oxygen concentration below the surface if more organic matter is respired there. Nowadays ∼5% of the ocean volume has hypoxic conditions located in the highly productive equatorial upwelling regions (Matear and Elliott 2004, Lampitt et al 2008, Deutsch et al 2011). One study (Deutsch et al 2011) indicates that low-O₂ waters are prone to further expansion, with the increase in anoxic water generally confined to intermediate waters of the equatorial Indian and Pacific. The olivine dissolution leads to regionally relatively large impacts of up to ±30% in diatom and non-diatom NPP patterns (figures S5(a), (b) available at stacks.iop.org/ERL/8/014009/mmedia), but our simulations show less than a 10% change in regional export production of organic matter (figures S5(c), (d) available at stacks.iop.org/ERL/8/014009/mmedia). In the upwelling regions export production increases by only a few per cent suggesting that the expansion of hypoxic regions due to olivine dissolution might be small.

Olivine dissolution might also lead to a substantial input of iron into the ocean. Its impact on the marine biology might be a subject for future studies. Back-of-the-envelope calculations reveal that an annual dissolution of 3 Pg of olivine with a Mg:Fe ratio of 9:1 is connected with an annual input of 0.2 Pg Fe. This is an order of magnitude larger than the natural iron input connected with dust deposition (Mahowald et al 2005). Because iron solubility (and thus bio-availability) varies by several orders of magnitude between 0.01 and 80% and is not well understood (Baker and Croot 2010), it is not directly clear, what the impact on marine biology would be. Acid processing of aeolian dust particles seems to be an important factor to enhance iron solubility in terrestrial dust (Baker and Croot 2010). As this process is missing in open ocean dissolution of olivine iron solubility from these particles is expected to be on the lower end of the known range. Furthermore, other trace metals found in olivine-containing rocks, e.g. nickel or cadmium (see geochemistry of rocks database GEOROC, http://georoc.mpch-mainz.gwdg.de/georoc), might get dissolved and their effects on marine ecosystems need to be considered.

The suspended olivine density of 0.4 g olivine m⁻³ corresponds to a flux of ∼8 g m⁻² yr⁻¹. Natural biogenic fluxes, e.g. our calculated export production of organic matter (figure S2(e) available at stacks.iop.org/ERL/8/014009/mmedia) range from less than 10 to more than 200 g organic matter m⁻² yr⁻¹ assuming a carbon content of organic matter of 50%. This implies that especially in low-productive open ocean waters of the subtropical region light transparency is expected to be reduced by the olivine input, but—as little NPP or export production occurs there—with only marginal effects on global biological fluxes. In high productivity areas the relative change in the particle flux is on the order of 10%. Global dust deposition in the world oceans is estimated to about 0.5 Pg yr⁻¹ (Mahowald et al 2005) corresponding to about 1 g m⁻² yr⁻¹, although the input is spatially very heterogeneous. Furthermore, riverine input of suspended matter is on the order of 20 Pg yr⁻¹ (Peucker-Ehrenbrink 2009). The mass concentration of suspended particulate matter in coastal waters around Europe is in the range of 0.02 to 50 g m⁻³ (Babin et al 2003). This implies that in coastal waters (so-called 'case 2' waters) natural suspended matter concentrations are for most cases larger than our olivine input rates. All-together, geoengineering large scale distribution of olivine in the open ocean surface waters might have a small negative effect on marine photosynthesis due to shading.

These multiple effects of olivine dissolution on the marine biology—silicic acid input, input of iron and other trace metals, reduced water transparency—would certainly alter our results. The addition of silicic acid added about 10% to the CO₂ uptake, corresponding to 0.1 Pg C yr⁻¹ in our STANDARD scenario. The upper limit of CO₂ uptake potential for large scale iron fertilization is in the order of 1 Pg C yr⁻¹ (Aumont and Bopp 2006), but 90% of this CO₂ draw down is restricted to the Southern Ocean, where olivine dissolution is according to our results very slow. The combined effect of ocean fertilization by both silicic acid and iron input was so far not investigated and might lead to some surprising synergistic impacts.

The Lloyd's Register Fairplay (Kaluza et al 2010) counted in year 2007 16 363 cargo ships and tankers with a total capacity of 665 × 10⁶ gross tonnage (deadweight tonnage DWT). Using an estimate for net tonnage as 50% of DWT gives a total net tonnage of 0.33 Pg. With an average of 32 ports called per ship per year this gives a total transport capacity of 10 Pg per year. About 100 large ships (net tonnage of 300 000 t each) with a year-round commitment including 32 port calls each would be necessary to distribute 1 Pg of olivine. Alternatively, olivine might be distributed in the ships of opportunity scenario via ballast water, which weighs at least 30% of the DWT of ships running empty (Australian Quarantine and Inspection Service 1993) summing up in the Lloyd Register (Kaluza et al 2010) to a global ballast water capacity of 0.2 Pg. Assuming all ships run empty every second run results in an annual ballast water capacity of 3.2 Pg (see also http://globallast.imo.org/ for similar estimates), in which 0.9 Pg of olivine can be dissolved considering that olivine dissolution is limited by the saturation concentration of silicic acid of 2 mmol kg⁻¹ (Van Cappellen and Qiu 1997) derived from biogenic silica reactivity. However, we like to emphasize that the estimation of this limitation is subject to uncertainty, because direct olivine dissolution rates available to us were so far obtained for silicic acid concentration below 1 mmol kg⁻¹, thus at least a factor of 2 below its saturation concentration (Oelkers 2001, Pokrovsky and Schott 2000, Rimstidt et al 2012), although the decline of olivine dissolution rates for rising silicic acid concentrations (Pokrovsky and Schott 2000) hints already at a saturation effect.

Grinding particles to 1 μm grain size is a practical challenge which consumes by far the most energy in the whole processing chain, at least an order of magnitude more than mining and transport (Hangx and Spiers 2009, Köhler et al 2010, Renforth 2012). Energy costs for grinding 80% of the particles down to 1 μm with present day technology are as high as 300–350 kWh t⁻¹ (Renforth 2012). Depending on the type of energy production (Rubin et al 2007) this might release as much as 350 (gas) to 800 (coal) g of CO₂ per kWh reducing carbon sequestration efficiency by up to 30%.

Implementation of enhanced weathering would require an operation on a global scale that will bring olivine mining to one of the world's largest mining sector (Schuiling and Krijgsman 2006, Mohr and Evans 2009). CO₂ and other greenhouse gases produced by grinding, mining, and transport of olivine would offset sequestration capacity of enhanced weathering. An estimate (Köhler et al 2010) assuming local mining and restricted transport (less than 1000 km and mainly by ships) for the total CO₂ expenditure is close to 10%, which gives a carbon sequestration efficiency of 90%. This does not include the fuel required for ships that would distribute olivine nor the energy demand necessary for grinding to small grain sizes of 1 μm as calculated above. If they are included, carbon sequestration efficiency falls below 60% and makes open ocean dissolution of olivine a rather inefficient geoengineering technique.

Our results show that enhanced weathering might help to reduce atmospheric CO₂. However, with a carbon uptake rate of 0.28 g carbon per g of olivine (neglecting reduced efficiency as discussed above) the recent fossil emissions of about 9 Pg C yr⁻¹ (Peters et al 2012) are difficult if not impossible to be reduced solely based on olivine dissolution. An upper limit for the open ocean distribution of olivine is difficult to estimate, but such a limit certainly depends on shipping capacities, exploitation of olivine, and low distribution rates to prevent particle aggregation. In our STANDARD scenario (3 Pg of olivine dissolution per year) about 9% of the anthropogenic CO₂ emissions would be compensated. This is slightly higher than the compensation rate of about 7% after ten years of implementation for the ongoing surface ocean acidification of nowadays 0.1 pH-units (Doney et al 2009).