Our results are based on the ocean-only model configuration of the Max Planck Institute Earth System Model MPI-ESM; version 1.2.00p4, which contains MPIOM version 1.6.2p3 (corresponding to revision 3997). MPI-ESM is a comprehensive Earth system model that consists of the atmosphere general circulation model ECHAM , the land surface scheme JSBACH , and the ocean circulation model MPIOM , which contains the ocean biogeochemistry model HAMOCC including a sediment module . MPI-ESM has been used successfully for millennial-scale atmosphere–ocean–carbon cycle simulations, including a transient simulation of the last millennium with fully interactive atmospheric CO2 . Since our aim is to isolate the effect of particle ballasting changes in the ocean during glacial–interglacial cycles on the atmosphere–ocean CO2 fluxes, rather than realistically simulating past climate evolution, we use the ocean–only configuration of MPI-ESM, namely MPIOM/HAMOCC in a stand-alone mode .

However, for the sensitivity experiments with LGM dust deposition fields, we do consider variable atmospheric pCO2 with a simple atmospheric CO2 box model based on atmosphere–ocean CO2 flux anomalies relative to a reference simulation with modern dust deposition and ballasting (PI_BALLAST). The flux anomalies are diagnosed at the end of each simulated year, and the prescribed atmospheric pCO2 is updated accordingly. For an accumulated net atmosphere–ocean CO2 flux anomaly of 2.1 Gt C into the ocean, the atmospheric CO2 concentration is reduced by 1 ppmv. Note that only the surface ocean biogeochemistry responds to this atmospheric pCO2 feedback. There is no effect on the atmospheric radiative transfer or climate; the prescribed climatological atmospheric forcing is unchanged. If the atmospheric CO2 concentration was not adjusted to the flux anomalies, for example, a positive anomalous ocean CO2 uptake would not result in a reduced atmospheric pCO2, the atmosphere would behave like a CO2 reservoir in our experiments, and the subsequent ocean CO2 uptake would be overestimated (as illustrated by an additional experiment in Sect.  with LGM dust deposition for particle ballasting but without adjusting atmospheric pCO2, shown as a blue dashed line in Fig. b). The long-term net ocean CO2 uptake in our reference simulations (Fig. b) would lead to a negative CO2 trend if absolute atmosphere–ocean CO2 fluxes were used; we avoid this effect by computing atmospheric CO2 from the flux anomalies relative to the reference simulation in each year. Moreover, this approach of computing flux anomalies each year, compared to, e.g., the alternative of subtracting the mean reference run flux imbalance, avoids additional atmospheric pCO2 variability due to, e.g., internal variability of the ocean circulation. By using this simple atmospheric pCO2 box model in combination with MPIOM/HAMOCC rather than using the coupled MPI-ESM, atmosphere and land surface feedbacks to the pCO2 variations – that would alter the ocean circulation and complicate the analysis of dust-related CO2 flux anomalies – are avoided and computational time is saved.

Another measure to save computational time is the use of a relatively coarse predefined, bipolar, curvilinear ocean grid (GR30L40) with a grid-point spacing of ∼3∘ and 40 levels, with thicknesses ranging from 10–12 m in the upper ocean to 600 m in the deepest ocean.

The ocean model MPIOM is forced by a repeating 1-year-long climatology of daily mean surface boundary conditions, including 2 m air temperature, zonal and meridional wind stress, wind speed, shortwave radiation, total cloud cover, precipitation, and river runoff, representing modern conditions based on the ERA40 and ERA15 reanalyses as in .

To avoid salinity trends due to imbalances in precipitation, evaporation, and river runoff, the surface salinity is restored with a relaxation coefficient of 3.3×10-7 s-1 to the annual salinity field of the Polar science center Hydrographic Climatology (PHC).

Note that biogeochemical changes do not affect the ocean circulation in the default (and our) configuration of MPIOM/HAMOCC. That means, for example, that any effect of phytoplankton concentration changes on light absorption is neglected in MPIOM. Differences in the ocean circulation between our simulations with the standard MPIOM/HAMOCC set-up and the set-up that includes particle ballasting are only due to the fact that, unfortunately, different numbers of CPUs were used for the computations (Fig. a: black line covers the coloured lines, but not the dark grey line of the set-up without ballasting). For binary-identical results, the parameter “nprocx” must not be changed. Otherwise, the spatial and temporal variations in the ocean circulation would be identical in the spin-up with the standard model and the simulations with ballasting.

In the standard version of HAMOCC, particle ballasting is not accounted for. Calcite and opal shells sink at a prescribed, constant speed of 30 m d-1; dust sinks at a speed of only 0.05 m d-1, resulting from the assumption of spherical dust particles with a diameter of 1 µm following Stokes' law (Stokes' drag is balanced by gravitational force minus buoyancy force); the sinking speed of detritus wdet is constant in the euphotic zone and increases with depth z below the euphotic zone (z>100 m) following : 1wdet(z)=weu+0,z≤100mλdetb(z-100m),z>100m, where weu=3.5 m d-1 is the sinking speed in the euphotic zone, the parameter b is set to 2, and the remineralization rate for detritus λdet is set to 0.026 d-1, resulting in sinking speeds of up to 80 m d-1 (Fig. b).

To account for particle ballasting, we add a simple parameterization of particle sinking speeds to HAMOCC. We assume that all particulate matter forms aggregates and sinks together at a common speed wballast. As suggested by , the common speed is proportional to the difference between the mean density of all particles ρparticles and the density of the seawater ρsw in each model grid box: 2wballast=w0⋅ρparticles-ρswρdet-ρsw. w0 is the proportionality factor and can be interpreted as the sinking speed of the aggregate in the absence of particle ballast. The density difference ρparticles-ρsw is also called excess density. The mean density of all particles ρparticles is given by the mass of all particles per unit volume of seawater, divided by the volume of all particles per unit volume of seawater. In contrast to , here, dust also contributes to the ballasting of detritus: 3ρparticles=cdust+∑bmbΨb1ρdustcdust+∑bmbρbΨb, where cdust is the mass concentration of dust (mass of dust per unit volume of seawater, in g cm-3), ρdust is the density of dust (2.50 g cm-3), Ψb is the molar concentration of the biogenic particle types b (namely: detritus, calcite, and opal, in mol C and mol Si cm-3, respectively), mb is their molar mass (32.7 g (mol C)-1 for detritus, 100.0 g (mol C)-1 for calcite, and 72.8 g (mol Si)-1 for opal), and ρb is their density (1.06 g cm-3 for detritus, 2.71 g cm-3 for calcite, and 2.10 g cm-3 for opal).

Monthly mean dust deposition rates are prescribed based on numerical reconstructions of modern and LGM boundary conditions, including glacigenic dust Fig. a–b;. The dust deposition fields not only affect the sinking speed in our ballasting parameterization, but also the availability of iron. It is assumed that 3.5 % (weight) of the dust in the water column is iron, of which 1 % is soluble and bioavailable.

Before starting our experiments with particle ballasting, we spin up the standard version of MPIOM/HAMOCC without particle ballasting for over 10 000 years (Fig. ). During the spin-up phase, the ocean model, which is initialized from three-dimensional PHC temperature and salinity fields, approaches an equilibrium state (thanks to the salinity restoration at the surface). The simulated ocean circulation is characterized by deep-water formation in the Atlantic and Southern oceans, and no deep-water formation in the Pacific; the Atlantic meridional overturning at 26∘ N amounts to about 17 Sv (sverdrup; 106 m3 s-1; Fig. a).

The ocean carbon cycle is not so easily tamed, since it remains an open system in our model (no restoring). To reach a stable equilibrium of the carbon cycle in the water column and the sediment, the net fluxes of organic carbon, calcite, and opal from the ocean column to the sediment – which are computed in HAMOCC – need to be balanced by the fluxes into the ocean of organic matter, calcite, and silicate from weathering on land – which are prescribed as namelist parameters (called deltaorg, deltacal, and deltasil). The weathering fluxes are adjusted several times during the spin-up phase, aimed at (1) balancing the sediment burial fluxes as diagnosed from the trends in the sediment inventory over several hundred years prior to each weathering flux adjustment, (2) a stable calcite export production at 90 m depth of about 1 Gt C yr-1, and (3) a rain ratio (ratio of calcite export to detritus export at 90 m depth) of about 10 % (Fig. f). An equilibrium of the sediment, however, is not reached in our simulations. Note that the selection of the weathering fluxes itself affects the simulated biogeochemistry. For example, if the silicate weathering flux is increased, more opal can be produced, and calcite production is suppressed see Eqs. 12–14 of.

The simulations with particle ballasting are initialized from year 6500 of the reference simulation without particle ballasting (PI_MARTIN; Fig. b). Using a no-ballast reference speed w0 (Eq. ) of 0.5 m d-1 leads to global mean sinking speeds wballast of the virtual aggregates between about 5 m d-1 at the surface and about 120 m d-1 below 5 km depth (Fig. b). A larger w0, such as 3.5 m d-1 as used by , would lead to much higher global mean sinking speeds. The advantage of using the small w0 is that it yields global mean aggregate sinking speeds that are comparable to the depth-dependent, Martin-type sinking speed of detritus that is prescribed in PI_MARTIN (Fig. b) and to a similar POC flux profile (Fig. a), which allows us to avoid a re-tuning of the remineralization rate of detritus.

The dissolution rate of opal, however, needs to be re-tuned, since the sinking speed of opal is reduced from previously 30 m d-1 to now only ∼5 m d-1 in the euphotic zone (Fig. b). Consequently, more opal is dissolved within the euphotic zone, leading to higher silicate concentrations, a higher opal production rate (Fig. e), and a very low rain ratio (Fig. f) due to a completely suppressed calcite production. Without adjusting the river input (weathering) of calcite to the reduced calcite precipitation and burial, surface alkalinity and dissolved inorganic carbon (DIC) rise (Fig. b–c). For a reduction in the opal dissolution rate by a factor of 6, the trends in alkalinity and DIC become small and comparable to (or actually smaller than) the trend in the control simulation without ballasting (Fig. b–c), and, even without readjusting the weathering fluxes, a stable carbon cycle simulation with particle ballasting (PI_BALLAST) is achieved that is similar to PI_MARTIN.

For pre-industrial GHGs (pCO2=278 ppmv), modern ocean circulation, and modern dust deposition (Fig. a), the simulated atmosphere–ocean CO2 fluxes in the standard set-up (PI_MARTIN) and the set-up with particle ballasting (PI_BALLAST) are hardly distinguishable (Fig. b–c). There are, however, clear differences compared to the observed modern CO2 fluxes (Fig. a). Most notably, the observed flux of CO2 from the atmosphere into the ocean between 30 and 60∘ S in the South Atlantic, Indian Ocean, and west Pacific is underestimated, due to an overestimation of the ocean surface pCO2, as previously reported for HAMOCC within the coupled MPI-ESM . Also note that the CO2 flux data are based on modern observations, while pre-industrial GHGs are prescribed in the model simulations.

A comparison of simulated to observed nutrient concentrations is shown in Fig. d–f for phosphate at the surface and in a Taylor diagram (Fig. ) at the surface, 100 m depth, and 2 km depth for phosphate, nitrate, and silicate. The surface dissolved phosphate concentrations are hardly distinguishable in the simulations with particle ballasting (PI_BALLAST) and without particle ballasting (PI_MARTIN). Compared to World Ocean Atlas data (WOA; ), the simulated phosphate concentrations in the Southern Ocean, Indian Ocean, equatorial Pacific, and the North Pacific are underestimated (Fig. d–f), and these biases are again similar to previous HAMOCC studies . This similarity between the simulated phosphate concentrations is not only true at the surface, but also at depth (Fig. ). The large overestimation of the spatial variability of the phosphate concentrations at 2 km depth in both simulations is due to an underestimation of the concentrations in the Atlantic and an overestimation in the eastern tropical Pacific (not shown). For nitrate, the observed high concentrations in the Antarctic circumpolar region at the surface and 100 m depth are underestimated in both simulations, leading to an underestimated spatial variability at these depths (Fig. ). At 2 km depth, the simulation with particle ballasting fits better to observations (Fig. ), especially due to an improved fit in the eastern Pacific (nitrate concentrations are overestimated in the eastern Pacific in PI_MARTIN, while they fit relatively well in PI_BALLAST; not shown). For silicate concentrations, the fit to observations is improved at the surface and at 100 m depth in the simulation with particle ballasting, mostly because the concentrations in the Antarctic circumpolar region match observations well in PI_BALLAST, while they are overestimated in PI_MARTIN. At 2 km depth, the fit is also improved in PI_BALLAST due to a reduction in the positive concentration bias in the eastern Pacific (compared to PI_MARTIN).

The global primary production in the simulation with ballasting amounts to about 39 Gt C yr-1 compared to 44 Gt C yr-1 in the simulation without particle ballasting (Fig. d), not including the primary production by diazotrophs, which amounts to additional 5 and 4 Gt C yr-1 for PI_BALLAST and PI_MARTIN, respectively. The global organic matter export is slightly reduced (7.0 Gt C yr-1 compared to 7.5 Gt C yr-1 without ballasting), and the global calcite production and export are only moderately larger (1 Gt C yr-1 compared to 0.85 Gt C yr-1 without ballasting, not shown), leading to an elevated rain ratio of about 13 % compared to 11 % in the simulation without ballasting (Fig. f). Opal production (Fig. e) and opal export at 90 m (not shown) are reduced by about 30 % in the simulation with modern dust and ballasting compared to the run without ballasting (production: 76 versus 108 Tmol Si yr-1; export: 72 versus 103 Tmol Si yr-1).

The simulated spatial pattern of the carbon export at 90 m depth (export production) in PI_MARTIN and PI_BALLAST are very similar to each other, with the area of high export production in the equatorial Pacific extending further into the subtropics in PI_MARTIN (Fig. h–i). Compared to estimates based on sediment trap data and satellite data , the simulated export production in both simulations is underestimated in the North Atlantic and overestimated in the equatorial Pacific (Fig. g–i).

Only a fraction of this export production from the euphotic zone reaches the deep ocean. This fraction, also called transfer efficiency, is a measure for the efficiency of the biological pump. The range of simulated transfer efficiencies through the mesopelagic zone (here computed as the simulated POC flux at 2080 m depth divided by the POC flux at 90 m depth in PI_BALLAST and PI_MARTIN) compares well with the range of transfer efficiency estimates based on sediment trap data (; Fig. j–l). In the simulation without particle ballasting (PI_MARTIN), the same sinking speed profile for POC is prescribed everywhere. Hence, the variations in the transfer efficiency are only due to local differences in the organic matter remineralization rate, which depends on oxygen availability. Denitrification and sulfate reduction remineralization rates combined are lower than aerobic remineralization rates see Eq. 6 of, leading to higher transfer efficiencies in oxygen minimum zones (OMZs), e.g. in the eastern equatorial Pacific, Arabian Sea, and Bay of Bengal (Fig. k). In the simulation with particle ballasting (PI_BALLAST), this effect of lower remineralization rates in OMZs is at least partly compensated for by reduced ballasting by calcite due to the corrosive waters, resulting in lower settling speeds and transfer efficiencies (Fig. l). The relatively high transfer efficiencies in the midlatitudes in PI_BALLAST compared to PI_MARTIN are in line with high particle sinking speeds mostly due to ballasting by calcite particles (compare Fig. d to Fig. l).

However, as far as we understand, even qualitatively, the global pattern of transfer efficiencies is uncertain: on the one hand, suggested that, based on satellite data, in large areas of the tropics and subtropics except in the eastern equatorial Pacific cold tongue, over 30 % of the export production at 100 m depth reach the deep ocean below 2000 m, while at high latitudes (>50∘) less than 10 % of the export production reaches that depth. On the other hand, from nutrient distributions reconstructed a “global pattern of transfer efficiency to 1000 m that is high (∼25 %) at high latitudes and low (∼5 %) in subtropical gyres, with intermediate values in the tropics”.

Dust substantially affects sinking speeds and the transfer efficiencies in the Southern Ocean and South Atlantic off Patagonia, as well as in the equatorial Atlantic due to Saharan dust deposition, in the North Atlantic, and in the Arctic Ocean. Note, however, that, in particular in the Arctic Ocean, where POC concentrations are low, even small quantities of dust can lead to high sinking speeds (Fig. c and f), since our simple particle ballasting parameterization only takes into account the density of the dust (for POC concentrations tending to zero), and not its diameter. This leads to high sinking speeds in the model, while in reality, when POC concentrations are so low that particle collisions and aggregate formation are unlikely, the small and mostly individual dust particles sink very slowly according to Stoke's law. While this illustrates a limitation of the simple particle ballasting parameterization, the effect of the erroneously high sinking speeds in the Arctic on the carbon export is small: the integrated carbon export at 90 m depth north of 80∘ N amounts to only 0.01 Gt C yr-1 or just over 0.1 % of the global export of about 7 Gt C yr-1.

In summary, although the simulated sinking speeds substantially differ between the simulations with and without particle ballasting, the biases of the set-up with particle ballasting compared to observations remain similar to the biases of the standard set-up. But the set-up with particle ballasting now enables us to estimate the effect of glacial dust deposition on atmospheric pCO2.

The largest ballasting effect of the LGM dust in our sensitivity experiments occurs in the Southern Ocean off Patagonia. Here, the higher dust deposition rates lead to about 5 to 10 m d-1 faster particle sinking at 100 m depth (Fig. e), which is equivalent to about a doubling of the sinking speed (compared to Fig. c). This faster sinking locally leads to a higher export production (Fig. f), to a reduced surface dissolved inorganic carbon concentration (Fig. i), and consequently to a positive downward net atmosphere–ocean CO2 flux anomaly (Fig. d), which, accumulated over the first ∼3000 years, causes an atmospheric pCO2 drawdown by about 4.5 ppmv (Fig. c). This anomalous ocean CO2 uptake occurs despite a reduction in the globally integrated export production (Fig. d), as opposed to the locally enhanced export production off Patagonia (Fig. f). The smaller globally integrated export production is due to a reduced primary production over wide areas of the Atlantic, Pacific, and Indian Ocean, as well as parts of the Southern Ocean, just north of the area off Patagonia with enhanced organic matter export (Fig. g and f). This reduced primary production is consistent with a stronger nitrate depletion in surface waters (not shown) due to increased particle sinking speeds (Fig. e). Note that this nitrate depletion can have an effect on primary production globally, since nitrate is the least available nutrient for non-diazotroph phytoplankton everywhere in our model. However, at the same time, the production and export of calcite shells is reduced in the sensitivity simulation (Fig. h). Due to higher surface silicate concentrations (not shown), this calcite export reduction is disproportionately large (compared to the POC export reduction), which leads to a reduced rain ratio (Fig. f). This weakening of the calcium carbonate counter pump has a larger effect on the atmosphere–ocean CO2 fluxes than the global reduction in the organic matter export, leading to a net ocean CO2 uptake in the first ∼3000 years of our sensitivity experiment.

After about 3000 years, the ocean begins to release CO2 into the atmosphere again, due to (1) the continuously decreasing export production (Fig. d; in response to nitrate depletion) and (2) the slowly recovering calcite production leading to an increasing particulate-inorganic-carbon-to-POC (PIC/POC) export ratio anomaly (Fig. f).

The observed long-term CO2 trends may also be affected by interactions with the sediment and by imbalances between sediment burial and weathering fluxes see, e.g.,. Since the weathering fluxes are the same in all sensitivity experiments (unchanged after the spin-up phase), a rough estimate of the role of sediment interactions can be derived from time series of the total organic carbon and calcite pools in the sediment (not shown). The organic carbon pool in the sediment in the experiment with LGM dust (LGM_BALL) grows faster than in the reference run with modern dust for ballasting (PI_BALLAST), which potentially contributes to the simulated ocean CO2 uptake. This anomalous organic carbon pool trend amounts to an uptake of about 0.01 Gt C per year by the sediment, which is comparable in magnitude to the atmosphere–ocean CO2 flux anomalies (Fig. b). Moreover, relative to PI_BALLAST, the sediment calcite pool in LGM_BALL is reduced by about 0.2×1016 mol Ca after the first 3000 years of the sensitivity experiment, which can be translated into a global mean ocean alkalinity increase of ∼3 mmol m-3, also potentially contributing to the simulated ∼10 mmol m-3 alkalinity increase in LGM_BALL at the surface.

Iron fertilization, due to the iron contained in the dust (Sect. ), also leads to a net CO2 flux anomaly into the ocean. In our simulations, this anomalous CO2 flux leads to an atmospheric pCO2 drawdown by about 10 ppmv within 6500 years (Fig. c).

However, as evident from the lack of CO2 flux anomalies in the Southern Ocean (Fig. j), this CO2 drawdown in our sensitivity experiment is not due to the expected fertilization of phytoplankton growth by enhanced dust deposition in the Southern Ocean. Hence, the mechanism at work in our iron sensitivity experiment differs from the frequently studied classical iron hypothesis . The reason for this difference is, that, in contrast to observations seefor a review, non-diazotroph phytoplankton growth in our reference simulations (for the standard set-up, PI_MARTIN, and the set-up with particle ballasting, PI_BALLAST) is limited by nitrate everywhere and nowhere by iron.

The simulated nitrogen-fixing cyanobacteria, on the other hand, have a higher iron demand than non-diazotroph phytoplankton , which is also taken into account here by applying a Michaelis–Menten type iron limitation function with a high half-saturation constant . Moreover, since the diazotroph growth rate, unlike the non-diazotroph phytoplankton growth rate in our model, is not limited by the least available nutrient Eq. 2 of but is proportional to the product of the limiting functions for temperature, iron, phosphate, and light Eqs. 3 and 8 of, the addition of iron can always lead to enhanced diazotroph growth. Consequently, we find enhanced diazotroph growth in particular in the tropical Pacific (Fig. k), which leads to a net positive downward atmosphere–ocean CO2 flux anomaly locally (a reduced net CO2 outgassing in the tropical Pacific; Fig. j). This CO2 flux anomaly is caused by (1) enhanced organic matter export due to the enhanced diazotroph production (Fig. d) and (2) the associated reduction in the rain ratio in the tropical Pacific leading to a weakening of the calcium carbonate counter pump (Figs. f and l). A relative shift from calcifying to silicifying organisms, as reflected by enhanced opal export production (Fig. e), also contributes to the weakening of the calcium carbonate counter pump. However, the global mean sinking speed in LGM_IRON hardly differs from that in the reference run with modern dust (PI_BALLAST; Fig. a), suggesting that the ballasting effect of the additional opal is balanced by the effect of the reduced calcite export.

Even after 6500 years, the ocean still takes up additional CO2 from the atmosphere. We attribute most of this long-term trend to a continuously enhanced organic matter export production (Fig. d) while the calcite export remains reduced, leading to a continuously lower PIC/POC ratio (Fig. f) and to a reduced export of alkalinity. A slightly reduced calcite pool in the sediment in LGM_IRON compared to PI_BALLAST also potentially contributes a small portion to the simulated long-term atmospheric pCO2 drawdown. The sediment calcite pool reduction is equivalent to an alkalinity increase in the water column of less than 2 mmol m-3, compared to a surface alkalinity increase of about 16 mmol m-3 after 6500 years in LGM_IRON. Less organic carbon is stored in the sediment in LGM_IRON compared to PI_BALLAST (not shown), which means that the exchange of organic matter between the sediment and the water column does not contribute to the simulated long-term ocean CO2 uptake in LGM_IRON.