We applied the University of Victoria (UVic) Earth system model (ESM) version 2.9 (Weaver et al., 2001), which has been used in several studies to investigate ocean oxygen dynamics (Schmittner et al., 2007; Oschlies et al., 2008; Getzlaff et al., 2016; Keller et al., 2016; Landolfi et al., 2017). The UVic model consists of a terrestrial model based on TRIFFID and MOSES (Meissner et al., 2003), an atmospheric energy–moisture balance model (Fanning and Weaver, 1996), a sea-ice model (Bitz and Lipscomb, 1999) and the general ocean circulation model MOM2 (Pacanowski, 1996). Horizontal resolution of all model components is 1.8∘ latitude × 3.6∘ longitude. The ocean model has 19 layers with layer thicknesses ranging from 50 m for the surface layer to 500 m in the deep ocean. The marine ecosystem was represented by a nutrients–phytoplankton–zooplankton–detritus (NPZD) model (Keller et al., 2012). Organic matter transformations (production, grazing, degradation) were parameterized using fixed stoichiometric molar ratios (C : N : P, 106 : 16 : 1) and directly related to the production and, in oxygenated waters, utilization of O2 (O : P, 160). When O2 is depleted in the model, organic matter is respired using nitrate (NO3-) (i.e. microbial denitrification). An O2 concentration of 5 mmol m-3 was used as the switching point from aerobic respiration to denitrification. Sedimentary denitrification was not considered in this model configuration so that water column denitrification and N2 fixation dictate the oceanic N balance. No explicit iron cycle was simulated and iron limitation was approximated with prescribed seasonally varying dissolved iron concentrations (Keller et al., 2012). Parameterizations of benthic and weathering fluxes of P were extended from the study of Niemeyer et al. (2017). A calcium carbonate sediment model (Archer, 1996) and a parameterization for silicate and carbonate weathering (Meissner et al., 2012) were applied in all simulations. When P weathering and anthropogenic P fluxes were applied (see Sect. 2.2), the global P flux was distributed over all river basins, in every grid box, weighted by river discharge rates.

In total, 12 different model simulations were performed to explore the range of uncertainties for the long-term development of the oceanic P inventory (Table 1). Each simulation started from an Earth system state close to equilibrium under pre-industrial atmospheric CO2 concentrations, prescribed wind fields and present-day orbital forcing. Spin-up runs lasting 20 000 simulation years or longer were made for each simulation to reach equilibrium. In the spin-up runs for simulations with benthic P burial (purple and red in Table 1), the marine P inventory was kept constant by instantaneously compensating oceanic P loss (burial) with P weathering fluxes to the ocean. For model simulations without benthic P burial (black and blue in Table 1), one common spin-up run was performed without P weathering fluxes.

All transient simulations started in the year 1765 and ended in the year 5000. Simulations were forced with anthropogenic CO2 emissions (fossil fuel and land use change) according to the extended RCP8.5 scenario until the year 2300 (Meinshausen et al., 2011), followed by a linear decline to zero CO2 emissions by the year 3000. Warming from non-CO2 greenhouse gases and the effect of sulfate aerosols were prescribed as radiative forcing (Eby et al., 2013). Non-CO2-emission effects from land-use change were not considered. The reference simulation (Ref) was performed without weathering and without burial fluxes of P, meaning that the P inventory of the ocean remained unchanged. The remaining transient simulations applied either variable climate-sensitive weathering anomalies (without burial) or time-variable burial fluxes (with constant weathering) to the ocean (Table 1).

The water column model is not coupled to a prognostic and vertically resolved sediment model. Instead, sinking organic matter interacts with the sediment via “transfer functions” (Wallmann, 2010) on a detailed subgrid bathymetry (Somes et al., 2013). Sinking organic matter is partially intercepted at the bottom of each grid box by a sediment layer and the intercepted amount depends linearly on the fractional coverage of the grid box by seafloor. The intercepted organic P is remineralized in accordance with Eqs. (1) and (2), whereby organic C and N are completely remineralized under oxygen or nitrate utilization without any burial.

Fractional coverage of every ocean grid box by seafloor was calculated on each model depth level according to the subgrid bathymetry (Somes et al., 2013). The subgrid bathymetry was inferred from the 2 min Gridded Global Relief Data (ETOPO2v2)

https://www.ngdc.noaa.gov/mgg/global/etopo2.html (last access: 15 July 2017)

P burial in the sediment (BURP) was determined in every grid box with sediment from the difference between the simulated detritus P rain rate to the sediment (RRP) and the benthic release of dissolved inorganic P from the sediment (BENP): 1BURP=RRP-BENP, where RRP is the detritus flux from the ocean (in P units). BENP was calculated locally by a “transfer function”, which parameterizes sediment/water exchange of P as a function of the rain rate of organic matter and the bottom water O2 concentration. Preferential P release, relative to carbon (C), is observed in sediments overlain by O2-depleted bottom waters (Ingall and Jahnke, 1994). Benthic P release was dependent on the dissolved inorganic carbon release (BENC) from organic matter degradation in the sediment and the C : P regeneration ratio rC:P (Wallmann, 2010; Eq. 2): 2BENP=BENCrC:P. BENC was computed (Eq. 3a) as the difference of the carbon rain rate to the sediment (RRC) and a “virtual” organic carbon burial flux (BURC). This flux is “virtual” as we do not account for changes in the C inventory and there is no explicit burial of organic C, which is remineralized in the deepest ocean layer. BURC is dependent on the simulated organic C rain rate and bathymetry (Flögel et al., 2011). Burial of organic C is more efficient on the shelf and continental margins (Eq. 3b) than for the deep sea (Eq. 3c, sediment below 1000 m water depth): 3aBENC=RRC-BURC3bBURC=0.14⋅RRC1.113cBURC=0.014⋅RRC1.05, where RRC is in mmol C m-2 a-1. rC:P (in Eq. 4) depends on the bottom water oxygen concentration and was calculated according to (Wallmann, 2010; Eq. 4) 4rC:P=YF-A⋅exp⁡-O2/r, where O2 is in mmol m-3 and the coefficients and their uncertainties are YF=123±24; A=112±24; r=32±19 mmol m-3. Under high O2 conditions, rC:P is 123, which is close to the Redfield ratio of 106. Under low O2 conditions, rC:P is lower than 106, which leads to a preferential P release from organic matter and, eventually, a net release of P from the sediment (BENP > RRP, in Eq. 1).

Burial fluxes of P were applied in the simulations Bur, Bur_Dun, Bur_low, Bur_high, Bur_noSG and Bur_res. The default Bur model configuration uses Eq. (3) (Flögel et al., 2011) and the subgrid-scale bathymetry. Uncertainties in benthic P burial were examined by modifying this default model configuration.

In the Bur_Dun simulation (i.e. burial parameterization from Dunne et al., 2007), BURC was calculated using Eq. (5) with RRC in mmol C m-2 d-1 (Dunne et al. 2007): 5BURC=RRC⋅0.013+0.53⋅RRC2c+RRC2, where c=7 mmol C m-2 d-1. This parameterization leads to high (low) organic C burial rates for high (low) organic C rain rates. This formulation is different from the standard formulation of burial in Eq. (3b, c), where burial depends on the C rain rates and in addition on the water depth. In the standard formulation, C burial is by definition 1 order of magnitude larger in slope and shelf regions compared to the deep ocean (see Eq. 3b, c).

We examined the sensitivity of P burial to the uncertainty of the parameters in Eq. (4), describing the carbon-to-phosphorus regeneration ratio rC:P. Given means and standard deviations for the parameters YF=123±24, A=112±24 and r=32±19 and assuming a Gaussian distribution, 100 000 independent coefficient combinations were assembled to calculate offline a range of global P burial estimates. For the offline calculation, pre-industrial fields of O2 and RRC were extracted from the simulation Bur with a temporal resolution fine enough to resolve seasonal variations in the data. Global P burial varied between 0.21 TmolP a-1 (Bur_low) and 0.60 TmolP a-1 (Bur_high) for a confidence interval of 90 % (coefficients are shown in Table 1). Individual spin-ups were performed for the Bur_low and Bur_high simulations to check that the offline calculated P burial corresponded to the online values from the spin-up. Only minor differences between the O2 fields of the Bur spin-up and the spin-ups for Bur_low and Bur_high simulations were noted (not shown), which implies negligible errors in the offline calculation of the pre-industrial global P burial.

For the Bur_noSG simulation (i.e. without subgrid-scale parameterization), P fluxes at the sediment–ocean interface were calculated using the coarser standard model bathymetry, which barely reproduces the global coverage of shelf areas (compare hypsometries in Fig. S1 in the Supplement). This does not affect other processes like circulation, advection or mixing.

The implemented transfer functions (Eqs. 2 and 4) assume unlimited local reservoirs of sedimentary P, meaning that the cumulative release of P may exceed the local inventory of P in the sediment if the benthic release is sustained over a longer period of time. In the Bur_res simulation (i.e. restricted release or P reservoir), we tested the impact of this simplification by applying sediment inventory restrictions to sediment P release. In accordance with Flögel et al. (2011), release of P from the deeper ocean (>1000 m) cannot exceed the rain rate of organic P to the sediment. For the continental shelf and slope, an upper limit sediment P inventory was calculated based on the following assumptions. We assume that the top 10 cm of the sediment column are mixed by organisms and are hence regarded as the active surface layer that is in contact with the overlying bottom water. Considering a mean porosity of 0.8 and a mean density of dry particles of 2.5 g cm-3, the mass of solids in this layer is 5 g cm-2 (Burwicz et al., 2011). The mean concentration of total P in continental shelf and slope sediments is 0.07 wt %, equal to 22.6 µmol g-1 (Baturin, 2007). Together, these assumptions convert to a maximum local inventory of total solid P in the active surface layer of RESP,max=113 µmol cm-2 (Eq. 6a). We assume that shelf and slope sediments can release up to 100 % of the total solid P under low-oxygen conditions. The local P inventory (RESP) can be fully replenished by P supply from the water column and any excess P is assumed to be permanently buried: 6aRESP∈R|0≥RESP≥RESP,max6bΔRESPΔt=RRP-BENP.

Local values of RESP adjust during the spin-up according to the environmental conditions. Our pragmatic sediment inventory approach most likely overestimates the upper limit of P that can be released from the sediments. For example, under low O2 conditions, part of the releasable or reactive P is transformed into authigenic P and permanently buried (Filippelli, 2001).

All Bur experiments applied a constant global weathering flux (WP,const) as established during the respective spin-up run (see Table 1 for values of WP,const for the different Bur experiments). 7WP=WP,const

Uncertainties in the ocean P inventory due to weathering processes and anthropogenic fluxes of P were examined with the model simulations Anthr, Weath0.05, Weath0.10, Weath0.15 and Weath0.38.

In simulations Weath0.05, Weath0.10, Weath0.15 and Weath0.38 (i.e. the number represents the pre-industrial weathering flux), the global weathering flux of P to the ocean (WP) was parameterized in terms of an anomaly relative to a pre-industrial P weathering flux (WP,0) according to Eq. (8). 8WP=WP,0⋅fNPP,SAT-1 The weathering function f is given in Eq. (9). Values of WP,0 are given in Table 1 and derived below. The chosen anomaly approach assumes that, at steady state, WP,0 is balanced by a respective global burial flux and hence can be neglected during the spin-up. In these simulations, no benthic P burial was applied, and for pre-industrial conditions the weathering function f(NPP,SAT) equals 1, and hence WP equals 0 TmolP a-1. The dynamic weathering function f (Eq. 9) was adopted from Niemeyer et al. (2017) and is originally based on an equation from Lenton and Britton (2006) for carbonate and silicate weathering. Following Niemeyer et al. (2017), we assumed that the release of P is proportional to the chemical weathering of silicates and carbonates on a global scale. Equation (9) describes the sensitivity of terrestrial weathering to the change of global terrestrial net primary production (NPP) and global mean surface air temperature (SAT): 9f=0.25+0.75⋅NPP/NPP0⋅1+0.087SAT-SAT0, with NPP0 and SAT0 being the respective pre-industrial values. Increasing SAT and NPP led to enhanced weathering. The upper estimate of WP,0 in Weath0.38 was inferred from the P burial reference simulation Bur, assuming that the global integral of burial is compensated by the pre-industrial global weathering flux (i.e. the global marine P inventory is in steady state). With the simulations Weath0.05, Weath0.10, Weath0.15, and Weath0.38, we explored the range of WP,0 estimates as derived from observational studies, which range from 0.05 to 0.30 TmolP a-1 (see Fig. 1, Benitez-Nelson, 2000; Compton et al., 2000; Ruttenberg, 2003). These studies give a range of total P fluxes to the oceans, which are higher than derived from dissolved inorganic P fluxes shown already in previous studies (e.g. Martin and Meybeck, 1979; Rao and Berner, 1993) and in the Global News Model (Seitzinger et al., 2005). A small amount of fluvial P is delivered to the ocean as dissolved inorganic P, but the majority (90 %) is particulate (inorganic and organic) P (Compton et al., 2000). The fast transformations between dissolved and particulate P in rivers (seconds to hours) (Withers and Jarvie, 2008) suggest a much higher amount of P that is available for marine organisms than derived from dissolved inorganic P concentrations. A large amount of bioavailable P in rivers is present as loosely sorbed and iron-bound P. Estimates of bioavailable P are given in Fig. 1 (Benitez-Nelson, 2000; Compton et al., 2000; Ruttenberg, 2003), which are much higher than the estimates for dissolved inorganic P (0.018 TmolP a-1 from Seitzinger et al., 2005, or 0.03 TmolP a-1 from Filippelli, 2002). Taking into account only fluxes of dissolved inorganic P would strongly underestimate the effect of weathering fluxes as a P source to the ocean. The weathering parametrization (Eq. 9) was used to scale pre-industrial fluvial fluxes of bioavailable P that is delivered in UVic to the ocean as dissolved inorganic P. In the model, no distinction was made between particular and dissolved fluvial fluxes of P.

Uncertainties to other weathering parameterizations were not investigated in this study. Our parameterization predicts similar weathering rates to other weathering formulations (Meissner et al., 2012, their Fig. 6a). Since weathering is calculated on a global scale, we cannot study the effects of regional lithology and soil shielding on weathered P (Hartmann et al., 2014). UVic does not resolve the P cycle in the rivers, which is an active field for scientific research (Beusen et al., 2016; Harrison et al., 2019).

Finally, global anthropogenic P fluxes from fertilization, soil loss due to deforestation and sewage as projected by Filippelli (2008) were prescribed in the simulation Anthr (anthropogenic).

Largest uncertainties in the P inventory are related to the large range of P weathering fluxes (Fig. 2, blue curves). Upper and lower estimates of P weathering fluxes differ by a factor of 6 (Fig. 2a, blue lines). In our weathering simulations, weathering anomalies depend linearly on the pre-industrial weathering flux (WP,0) estimate (see Eq. 8) because the climate development is essentially equal across the simulations. Therefore, the choice of WP,0 (Fig. 1a) is a major source of uncertainty for projected future land–ocean P fluxes.

Weathering fluxes increased from the pre-industrial value by a factor of 2.5 until the year 5000 for atmospheric CO2 concentrations of 1100 ppmv. This is comparable with the 2- to 4-fold increase in weathering fluxes estimated during OAE 2 approximately 91 Myr ago (Pogge von Strandmann et al., 2013) when atmospheric CO2 concentrations increased to about 1000 ppmv (Damsté et al., 2008).

In contrast to weathering-induced P input, anthropogenic P fluxes (Filippelli, 2008) influence the global marine P inventory only in the near future (Fig. 2a, dashed black line). A decline in anthropogenic P fluxes after the year 2100 is expected due to the depletion of the easily reachable phosphorite mining reserves (Filippelli, 2008).

The release of P from the sediment is strongly dependent on the O2 concentration in the water above the sediments (Wallmann, 2003; Flögel et al., 2011). Climate warming reduces O2 solubility and ventilation of the ocean, which decreases the global O2 content (more details in Sect. 4). The general decrease in ocean O2 content may therefore cause preferential release of P from marine sediments. Differences in sediment P fluxes in our simulations are related to uncertainties in the parameterization of the transfer function (Fig. 2, red lines, -0.01 to 0.22 TmolP a-1 by the year 5000), to different representations of the bathymetry (Fig. 2, dashed purple line: 0.06 (without subgrid) and 0.12 (Bur) TmolP a-1) and to the way sediment P reservoirs in the sediment are represented (Fig. 2, solid purple line: -0.01 (limited reservoir) and 0.12 (unlimited reservoir, Bur) TmolP a-1).

The global P burial of approximately 0.2 TmolP a-1 (Fig. 3) (Filippelli and Delaney, 1996; Benitez-Nelson, 2000; Ruttenberg, 2003) is relatively well reproduced by simulations Bur_low and Bur_Dun. The simulation with the standard UVic bathymetry (Bur_noSG) underestimates P burial by 60 %, while simulations Bur_high, Bur and Bur_res overestimate P burial by 180 %, 90 % and 80 % with respect to estimates based on observations. The transient response of the P release to O2 was stronger for simulations with low burial, and vice versa (Fig. 2), except for simulation Bur_res. In Bur_res, a significant reduction in the transient P release occurred due to the implementation of a finite P reservoir, with net global P loss due to enhanced burial at the end of the simulation. In the year 5000, global P concentrations increased in Bur_res by only 0.06 mmolP m-3 compared to the global mean pre-industrial concentration of 2.17 mmolP m-3. This is 6-fold smaller than the increase of 0.36 mmolP m-3 in simulation Bur with an assumed unlimited P reservoir. The small increase in the oceanic P inventory in Bur_res can be explained by the reduction in P sediment inventory rather than by changes in the rain rate of particulate organic matter to the sediment (RRC). In Bur, a rapid increase in the benthic P release appeared in areas where the water turned suboxic and thus drove a positive benthic feedback between P release, productivity and deoxygenation (Fig. 2a). A limited supply of P from the sediment (Bur_Res) dampens this feedback.

Simulated pre-industrial RRC increased significantly from 180 to 1040 TgC a-1 on the shelf and globally from 900 to 1500 TgC a-1 compared to simulations without subgrid bathymetry. Pre-industrial RRC with subgrid bathymetry agrees better to estimates by Bohlen et al. (2012) (Table 2) and to other field data studies reporting a range from 900 to 2300 TgC a-1 (Fig. 4) (Muller-Karger et al., 2005; Burdige, 2007; Dunne et al., 2007; Bohlen et al., 2012).

In summary, subgrid bathymetry leads to a substantial improvement of the representation of RRC to the sediment. More realistic benthic fluxes of P could be also attained by adjusting parameters for rC:P (Eq. 4) or by using the function of Dunne et al. (2007) to calculate BURC (Eq. 5). The implementation of a finite P reservoir in the sediment has a substantial impact on the transient development of the global P inventory on millennial timescales. This is an important improvement relative to earlier work and should be considered in future studies.

The biological carbon pump can be summarized as the supply of biologically sequestered CO2 to the deep ocean. In the euphotic zone, phytoplankton and diazotrophs take up CO2, a process that is intensified by elevated PO4 concentrations in the surface ocean (Fig. 6a). Part of the organic matter sinks out of the euphotic zone (Fig. 6b) to the ocean interior, where it is respired using O2. It is therefore P supply to the surface waters that explains the differences in deoxygenation between the simulations. Circulation changes could also affect the supply of O2 to the ocean interior. However, no significant differences in climate and circulation appeared among the simulations, and therefore the global-warming-induced circulation changes affected all simulations in the same way.

In the Ref simulation, NPP (Fig. 6a, black line) increased from 45 to 70 TmolP a-1 (57 to 89 GtC a-1) by the end of the simulation. In Weath0.15, enhanced P supply to the ocean led to a doubling of NPP compared to the Ref simulation. The P inventory increased continuously, but NPP did not follow this trend and instead peaked in the year 4000. In the year 5000, all simulations, excluding Weath0.38, showed a similar response of NPP to the P addition, with an increase in NPP of 19 TmolP a-1 (relative to the Ref simulation) per 10 % increase in P inventory. In Weath0.38, the response was weaker and NPP increased by 8 TmolP a-1 per 10 % rise in the P concentration. P is less effectively utilized in simulations with large oceanic P inventories. Higher ocean temperatures enhanced remineralization of organic matter in the shallower ocean so that the overall export to NPP ratio decreased from its pre-industrial value of 0.12 to an average value among all simulations of 0.08 by the year 5000. This is because despite the warming-driven enhanced remineralization, the warming-driven intensification of ocean stratification leads to a decline in supply of nutrients to the surface layer and reduced export production, in line with earlier studies (e.g. Bopp et al., 2013; Landolfi et al., 2017).

To summarize, NPP and export of organic matter are sensitive to P addition. However, the proposed positive feedback between P, NPP, export of organic matter and deoxygenation was limited in our simulations due to a negative feedback related to nitrate availability. This is shown and explored in the following section. We acknowledge that accounting for P burial in weathering simulations may limit the P increase. However, the effect of P burial has been shown to be small relative to the increase in benthic release of P due to the feedback involving redox-sensitive benthic P fluxes associated with the expansion of OMZ (Niemeyer et al. 2017, Fig. S1).

At the end of the spin-up, the N sink by denitrification and the N source by N2 fixation were balanced. In the Ref simulation, climate warming enlarged the oxygen minimum zones, which enhanced denitrification in the tropics (not shown). In our model, diazotrophs are limited by P and Fe and are not limited by N. Their growth rate, which depends on temperature being zero below 15 ∘C, is slower relative to non-fixing phytoplankton. These characteristics allow them to succeed in warm, low-N and high-P environments that receive sufficient iron. In all simulations, N2 fixation was stimulated by the addition of P to the ocean and was sensitive to rapid changes in the supply of P (compare Figs. 7a and 2a). However, N2 fixers (Fig. 7a) were not able to use the extra P supply in polar and iron-limited regions where low temperatures and iron limitation, respectively, inhibit their growth (Fig. 8). This led to a substantial amount of excess phosphate in the surface waters of these regions (Fig. S2). Because N2 fixers were not able to balance the loss by denitrification, nitrate decreased globally by 4 mmol N m-3 by the year 5000 (Fig. 7b). The loss in nitrate led to a decrease in globally averaged N-to-P ratios. In the Ref simulation, N : P decreased from 14 to 12, and for the Weath0.15 simulation it decreased to 10, which contributed further to a N-limiting ocean. The nitrogen cycle was not able to recover from the decrease in N : P ratio with respect to pre-industrial values. We acknowledge that in the current study we did not account for potential future changes in iron concentrations (from atmospheric deposition, shelf inputs) and that the lack of a fully prognostic iron model may lead to a different sensitivity of the response of diazotrophs. Similarly, we did not account for the ability of phytoplankton to adapt to changing N : P ratios, which may affect marine biological productivity and in turn deoxygenation. These would require further studies.

Anomalies in circulation, ocean temperature and remineralization of organic matter affect oceanic O2 levels in a climate-warming scenario. In the Ref simulation, the O2 inventory (Fig. 9a) decreased by 60 Pmol O2 by the year 3000 and then reached present-day values again by the year 5000. In Weath0.15, weathered P enhanced deoxygenation and led to a greater decrease in O2 than in the Ref simulation. The O2 decrease was up to 70 Pmol by the year 3300 and O2 still showed a negative anomaly of 24 Pmol O2 by the year 5000. Global anomalies in O2 were due to changes of the apparent oxygen utilization (AOU; Fig. 9b) and the O2 saturation level (Fig. 9c). AOU is calculated from the difference between the O2 saturation concentration and the in situ O2 concentration assuming that all ocean water leaves the surface layer saturated in O2. The calculation of AOU is in general biased towards higher values, because in polar regions the water that is subducted and mixed into the deep water is undersaturated with respect to O2 as a result of reduced air–sea gas transfer by sea ice (Ito et al., 2004). In UVic, this leads to an overestimation of AOU by 30 % (Duteil et al., 2013). Sea ice cover reduces in a warming ocean that leads to an underestimation of the AOU anomaly in Fig. 9c. Changes in O2 saturation were similar across the model simulations and lagged behinds surface ocean temperature changes. The circulation and ventilation of the ocean were similar in the model simulations because differences in surface temperatures were negligible and the atmospheric forcing of the ocean circulation was identical so that differences in AOU depended almost only on biological O2 consumption and AOU anomalies were directly yet inversely related to the changes in O2 levels. Hence, biological consumption explained variations in O2 content among the different model simulations (compare Fig. 9a and b). Increasing O2 utilization contributed to the decrease of O2 levels until the year 3000. Thereafter, a distinct negative trend in AOU with a similar slope was observed among all simulations and contributed to a re-oxygenation of the ocean. For simulations with larger P inventories, the AOU had a larger positive offset to the Ref simulation.

In a model with constant stoichiometry for elemental exchange by biological processes, anomalies in AOU (Fig. 10, blue lines) can be explained by the difference between total integrated nutrients (Fig. 10, solid red and black lines as anomalies) and preformed nutrients (Fig. 10, dashed red and black lines as anomalies). Preformed nutrients correspond to the fraction that leaves the surface ocean unutilized by phytoplankton (Ito and Follows, 2005). For example, in the Southern Ocean, a large fraction of nutrients that leaves the surface is preformed. The fraction of utilized and preformed nutrients can change during a transient simulation and could affect the oxygen state of the ocean.

In the Ref simulation (Fig. 10a), the anomaly of preformed dissolved inorganic P was directly inverse to the anomaly of AOU because the oceanic P Inventory was conserved in this simulation. Until the year 2200, changes in circulation and climate are the main cause for the reduction in preformed N and P in the Ref simulation since global N and P inventories were almost constant in this time period (Fig. 9a, solid red and black line). During continuous and intense ocean warming, a weakening of the meridional overturning (not shown) reduced ocean ventilation. The meridional overturning maximum decreased from 17 Sv (pre-industrial) to 11 Sv in the year 2200. The continuous warming and stratification of the ocean reduces the supply of nutrients to the surface layer from the deep ocean. This is consistent with a reduction of the export of organic matter until the year 2200 (Fig. 6b). The balance between exported P out of the surface ocean and supplied P controls changes in AOU. We suggest that a weaker overturning increased the residence time of water and nutrients in the surface ocean. Nutrients staying longer in the euphotic zone are more likely to be biologically consumed. This implies more efficient utilization of nutrients and hence the reduction in preformed nutrients and an increase in AOU.

Enhanced suboxia after the year 2200 drove excess denitrification and a decline in nitrate (Fig. 10a, solid red line) in the Ref simulation. The decline in nitrate could explain the negative trend in AOU anomalies (Fig. 10a, solid blue line) and therefore a negative feedback on the global deoxygenation. In the year 2200, overturning had started to recover quickly and increased to 21 Sv in the year 3000 (+24 % relative to pre-industrial values), leading to faster overturning of organic matter in the surface ocean and a decrease in global AOU. This suggests that the slight increase in export by 5 % (relative to pre-industrial values) was not strong enough to compensate for the 24 % faster overturning, which reduced the residence time of nutrients in the surface ocean.

P addition in the Weath0.15 simulation stimulated N2 fixation by diazotrophs and counteracted N loss by denitrification (Fig. 10b, solid red line). This led to an increase in N inventory by 17 Pmol O2 equivalents compared to the Ref simulation. Furthermore, the high availability of P seems to reduce preformed N by 6 Pmol O2 equivalents. Both explain the difference in AOU between Weath0.15 and Ref of 24 Pmol O2 at the end of the simulation (Fig. 9b). However, denitrification still exceeded N2 fixation, which led to low levels of nitrate. From the year 5000, approximately all of the added P in the Weath0.15 simulation remained unused by phytoplankton, left at the surface ocean as preformed P, and was afterwards stored in the deep ocean. Phytoplankton was unable to utilize the extra P because it was limited by nitrate. Diazotrophs could not counteract the lack of N due to iron limitation and low surface temperatures in the polar oceans. The denitrification feedback driven by the spread of suboxic conditions in the tropics had reduced further the N availability for phytoplankton and limited the effect of P addition on the global oxygen level.