The University of Victoria Earth System Climate model (UVic ESCM) version 2.9 (Weaver et al., 2001; Eby et al., 2009) is a model of intermediate complexity and consists of a terrestrial model based on TRIFFID and MOSES (Meissner et al., 2003) including weathering (Meissner et al., 2012), an atmospheric energy–moisture balance model (Fanning and Weaver, 1996), a CaCO3-sediment model (Archer, 1996), a sea-ice model (Semtner, 1976; Hibler, 1979; Hunke and Dukowicz, 1997) and a three-dimensional ocean circulation model (MOM2) (Pacanowski, 1995). The ocean model includes a marine ecosystem model based on a nutrient–phytoplankton–zooplankton–detritus model (Keller et al., 2012). The 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 at the sea surface to 500 m in the deep ocean. We use a sub-grid-scale bathymetry as described in Somes et al. (2013) to simulate benthic fluxes of phosphorus. The sub-grid bathymetry is inferred from the ETOPO2v2

https://www.ngdc.noaa.gov/mgg/global/etopo2.html

Earlier applications of the UVic ESCM assumed a fixed marine P inventory. We included a representation of the dynamic P cycle for this study. It consists of a modified terrestrial weathering module (Meissner et al., 2012) and a redox-sensitive transfer function for burial and benthic release of P (Floegel et al., 2011; Wallmann, 2010).

The continental weathering module developed earlier for fluxes of dissolved inorganic carbon (DIC) and alkalinity (Meissner et al., 2012; Lenton and Britton, 2006) is based on the following equations: FDIC,w=FDIC,w,0⋅⌊fSi+fCa⋅NPPNPP0⋅1+0.087⋅SAT-SAT0⌋=FDIC,w,0⋅fNPP,SATFAlk,w=FAlk,w,0⋅NPPNPP0⋅⌊fSi⋅1+0.038⋅SAT-SAT0⋅0.650.09⋅SAT-SAT0+fCa⋅1+0.087⋅SAT-SAT0, where FDIC,w and FAlk,w represent the globally integrated flux of DIC and alkalinity via river runoff; fSi and fCa stand for the fraction of silicate (0.25) and carbonate (0.75) weathering; and NPP and SAT are the global mean net primary production on land and global mean surface air temperature over land (in degrees Celsius). The index 0 stands for pre-industrial values.

We added the following flux to account for P weathering (FDP,w) with the same dependencies on globally and annually averaged net primary production (NPP) and surface air temperature (SAT) as those for DIC: FDP,w=FDP,0⋅fNPP,SAT. The global river input of DIP is the only continental source for P in the model. The global DIP input is distributed over all coastal points of discharge scaled according to their individual volume discharge. The pre-industrial DIP input to the ocean (FDP,0) is assumed to be in steady state and in equilibrium with the total globally integrated pre-industrial net burial of P (BURP): FDP,0=BURP,0. We use an empirical transfer function for BURP and for the benthic release of DIP (BENDIP) derived from observations across bottom-water oxygen gradients (Wallmann, 2010; Flögel et al., 2011). The release of dissolved inorganic P (BENDIP) is calculated as follows: BENDIP=BENDICrreg. Benthic release of dissolved inorganic carbon (BENDIC) is calculated from an empirical transfer function (Fig. 2 in Flögel et al., 2011) to determine BENDIP fluxes at the bottom of the ocean. In our model configuration, particulate organic carbon (POC) is remineralised completely at the ocean bottom and no ocean-to-sediment fluxes of POCs occur, i.e. BENDIC is equivalent to RRPOC, where RRPOC denotes the rain rate of particulate organic carbon to the sediment. Wallmann (2010) calculated rreg by a regression of observational data to bottom-water oxygen concentrations: rreg=RRPOCBENDIP=YF+A⋅exp⁡-[O2]r. The regeneration ratio is calculated by dividing the depth-integrated rate of organic matter degradation in surface sediments (RRPOC) by the benthic flux of dissolved inorganic P into the bottom water (BENDIP). Parameters are defined as YF= 123 ± 24, A = -112 ± 24 and r= 32 ± 19, and O2 is in µmol L-1 (Wallmann, 2010). Under oxic conditions rreg is higher than the Redfield ratio (106; Redfield et al., 1963) and under oxygen-depleted conditions rreg reduces to 10 (Wallmann, 2010).

The rain rate of POP (RRPOP) is calculated by the rain rate of POC (RRPOC) divided by the Redfield ratio. As a result BURP can be calculated as follows: BURP=RRPOP-BENDIP. The burial of P (BURP) in the sediment is equal to the rain rate of particulate organic P (RRPOP) minus BENDIP (Floegel et al., 2011). If the benthic release overcomes the rain rate of POP at depths below 1000 m, the burial is set to zero. Following Floegel et al. (2011), this condition is not applied to shallower sediments because these deposits receive both marine particles and high fluxes of riverine particulate phosphorus.

Two model simulations were performed. Our control simulation, called simulation REF hereafter, includes neither weathering, benthic release nor burial of P. The global amount of P in the ocean is therefore conserved in this simulation over time. The second simulation, called WB, includes P weathering as well as benthic burial and release of P but excludes additional anthropogenic input. The spin-up was performed by computing the burial and benthic release according to Eq. (6). The weathering fluxes were set to a value to compensate the burial rate (Eq. 4) during the spin-up but not thereafter.

After a spin-up of 20 000 years under pre-industrial boundary conditions, we forced the model with anthropogenic CO2 concentrations following the RCP8.5 scenario of the IPCC AR5 assessment (Meinshausen et al., 2011; Riahi et al., 2011). The CO2 emissions in the UVic ESCM reach 105.6 Pg CO2 a-1 in year 2100. Between years 2100 and 2150, the models are forced with constant CO2 emissions (105 Pg CO2 a-1), followed by a linear decline until year 2250 to a level of 11.5 Pg CO2 a-1 and then linearly to zero emissions in year 3005 (see Fig. 2a). Simulated atmospheric CO2 concentrations peak in year 2250 with 2148.6 ppmv and equal 1835.8 ppmv in year 3005 (see Fig. 2a).

The UVic ESCM has been validated under present-day and pre-industrial conditions in numerous studies (Eby et al., 2009; Weaver et al., 2001). In particular, Keller et al. (2012) recently compared results of its ocean biogeochemical component to observations and previous model formulations. We therefore concentrate our validation on the new model component in this study, the P cycle.

Estimates of pre-industrial burial rates vary over a wide range in the literature. The comprehensive review by Slomp (2011) reported a burial rate of 0.032–0.35 Tmol P a-1 for the total ocean, while Baturin (2007) suggests a burial rate of 0.419 Tmol P a-1 based on observational data described in detail by Wallmann (2010). The burial rate diagnosed by the UVic ESCM in simulation WB for the total ocean under pre-industrial boundary conditions (0.38 Tmol P a-1) is within range of these earlier estimates. The burial at the continental margin (0–200 m) accounts for 50–84 % of total burial corresponding to 0.016–0.175 Tmol P a-1 calculated in Slomp (2011). Ruttenberg (2004) estimated a burial rate at continental margins of 0.15–0.22 Tmol P a-1, while the UVic ESCM calculated a burial rate of 0.33 Tmol P a-1 for the continental margins in year 1775. The open-ocean burial contributes only a minor part to total burial (0.04–0.13 Tmol P a-1; Ruttenberg, 2004; in the UVic it is 0.046 Tmol P a-1).

To conserve marine P during long model spin-ups, the dissolved weathering flux of P under pre-industrial conditions is set equal to the diagnosed total burial rate during the spin-up: 0.38 Tmol P a-1. Following the method of calculating the reactive P flux (defined in Ruttenberg, 2004 as the sum of > 50 % of total dissolved P (i.e. dissolved organic P) plus 25–40 % of particulate P flux), our result fits well with estimates summarised by Slomp (2011) ranging from 0.13 Tmol P a-1 (natural P flux) to 0.36 Tmol P a-1 (modern P flux) and Ruttenberg (2004) (0.16–0.32 Tmol P a-1).

Global values for benthic release under pre-industrial conditions equal 0.78 Tmol P a-1 in the UVic ESCM (simulation WB), while Ruttenberg (2004) described a range from 0.51 to 0.84 Tmol P a-1 based on pore water measurements (Colmann and Holland, 2000) for coastal regions. For the deep sea, Colmann and Holland (2000) specified the benthic release value with 0.41 Tmol P a-1. In the UVic ESCM, the benthic release for continental margins was calculated as 0.4816 Tmol P a-1 and for the open ocean as 0.2951 Tmol P a-1.

The global mean atmospheric surface temperature, as simulated by the WB run, increases until year 2835 and peaks at 23.1 ∘C, i.e. 9.9 ∘C above pre-industrial levels. Simulation REF shows similar changes in temperature with an increase until year 2855 and a peak at 23.3 ∘C (see Fig. 2a). Both simulations show a slight recovery in temperatures after the peak (REF: 23.2 ∘C; WB: 23.1 ∘C; year 3005). Atmospheric temperatures in the WB simulation are slightly lower than in the reference simulation, due to slightly lower carbon dioxide concentrations in the atmosphere, caused by increased global ocean alkalinity (REF: 2.498 mol m-3; WB: 2.481 mol m-3; both for year 3005), the enhanced biological pump and a rise in detritus export rate (see Sect. 3.2) and therefore increased marine uptake of atmospheric CO2. The impact of the negative feedback via enhanced biotically and chemically induced marine uptake of atmospheric CO2 on surface air temperatures is thus small compared to the CO2-induced warming in a high-emission scenario.

Given that the response in temperature is similar for both simulations compared to considerable differences in biological productivity (see below), differences in oxygen concentration mainly originate from biogeochemical changes, which will be discussed in Sect. 3.3.

The weathering rate (see Fig. 3b) and associated flux of P into the ocean via river discharge more than doubles relative to the pre-industrial situation in our WB simulation and leads to an enhancement in global mean oceanic P concentrations by 27 % over 1000 years (see Fig. 2b). At the same time, benthic burial acts as the only P sink in our model (see the Supplement, Fig. S1), mitigating the total increase in marine P. The P concentration remains constant in the control run REF.

The weathering input in the WB simulation is largest north of 30∘ N (0.338 Tmol P a-1 in year 3005; see Fig. 3a), while south of 30∘ S (0.138 Tmol P a-1) and in the low-latitude Pacific Ocean the input is lowest (0.117 Tmol P a-1). Weathering fluxes into the low-latitude Indian and Atlantic oceans equal 0.187 and 0.267 Tmol P a-1, respectively.

Increasing P concentrations as well as climate warming result in an increase in net primary production in the ocean (ONPP). Globally integrated ONPP ranges between 43.8 Tmol P a-1 (REF) and 44.1 Tmol P a-1 (WB) under pre-industrial conditions and 65 Tmol P a-1 (REF) and 116.4 Tmol P a-1 (WB) in year 3005 (see Fig. S1). The main areas of ONPP increase are located in the tropical ocean, where higher temperatures favour net primary production in the model (results not shown).

Due to enhanced P inventory and enhanced ONPP, the WB simulation also has a higher export rate (8.6 Tmol P a-1, computed at 130 m depth; see Fig. 2b) when compared to the reference run (5.5 Tmol P a-1) in year 3005. In the REF simulation, the export rate declines until year 2175 (4.8 Tmol P a-1) in response to enhanced stratification, associated declining nutrient supply and stronger nutrient recycling in the upper layers (Schmittner et al., 2008; Steinacher et al., 2010; Bopp et al., 2013; Moore et al., 2013; Yool et al., 2013; Kvale et al., 2015). The export rate recovers to reach 5.5 Tmol P a-1 at the end of the simulation in experiment REF.

The globally integrated remineralisation rate in the aphotic zone (results not shown) ranges between 5.1 Tmol P a-1 (WB) and 5.2 Tmol P a-1 (REF) in year 1775. Simulation WB is characterised by a strong increase in remineralisation until 3005 with a maximum of 8.1 Tmol P a-1 (in year 3005), while in the reference run the remineralisation rate first decreases, followed by a moderate increase to 5.3 Tmol P a-1. Regions with highest remineralisation are located on the continental margins, especially in the Indian Ocean.

The P burial in the WB simulation equals 0.38 Tmol P a-1 in year 1775 and decreases by 44.3 % to 0.2 Tmol P a-1 in year 3005 (see Fig. S1). One reason for this decrease is the redox state of the bottom water. The strong expansion of the area of ocean bottom waters with O2 concentrations below 0.005 mol m-3 (see Fig. 2d) in the WB simulation leads to a decrease in benthic burial of P despite an increase in the rain rate of particulate organic P, RRPOP. In general, burial rates are largest along the coastal margins, where 87.9 % of the total flux is buried in 1775. Highest increases in burial rates between years 1775 and 3005 are located in the Arctic Ocean (see Fig. 4a), whereas burial rates decrease in the Bay of Bengal and the Gulf of Mexico where low-oxygen bottom waters expand (see Fig. 5).

The benthic P release in the WB simulation increases by 119 % until year 3005 to 1.7 Tmol P a-1 (see Fig. S1). As mentioned above, the benthic release is a redox-dependent process, which commonly takes place at the coastal margins (Wallmann, 2010; in our model, under pre-industrial conditions, 62 % of total release is from coastal margins). This means that an increase in suboxic bottom water area (see Fig. 2d) leads to an enhanced release of benthic P in WB. A rapid increase between years 1775 and 3005 can be found in the Bay of Bengal, the Gulf of Mexico and in the Arctic Ocean (see Fig. 4b).

In our model simulations, both the weathering-induced P flux into the ocean (see Fig. 2c) as well as the net P released from the sediments (see Fig. 2c) show a strong increase under continued global warming, which explains the increase in the marine P inventory in the WB simulation (see Fig. 2b). However, the simulated increase in the weathering input has a much stronger (about 4 times larger) impact on the P budget and therefore on the expansion of OMZs than the benthic release feedback (see Fig. 2c). We note that even at the end of the 1000-year simulation, the P cycle has not yet reached a new steady state in experiment WB. Weathering rates are high in the warm climate and burial of P has not increased to counteract the supply by weathering (see Figs. 3b and S1). The release of P from sediments also adds to this imbalance. As a result, the marine P inventory is still increasing almost linearly at the end of our simulation. Extending the simulation until year 10 000 reveals that the ocean – as well as the coastal regions – does not become anoxic despite a more than 3-fold increase in oceanic P inventory (see Sect. 3.3 and Fig. S2) while the P cycle still exhibits a strong imbalance between sources and sinks.

The black contours in Fig. 5 indicate the lateral extent of OMZs for a depth of 300 m (see Fig. S3 for a depth of 900 m). In year 1775, the suboxic volume, defined here as waters with oxygen concentrations of less than 5 mmol m-3, equals 3.9 × 106 km3 in both simulations (see Fig. 2d). An observational estimate of today's suboxic water volume equals 102 × 106 ± 15 × 106 km3 for oxygen concentrations less than 20 mmol m-3 (Paulmier and Ruiz-Pino, 2009), which is considerably larger than the volume of O2 concentrations less than 20 mmol m-3 in our WB simulation (WB2005= 15.8 × 106 km3). However, in consideration of the studies of Bianchi et al. (2012) and their calculated OMZ volume of 2.28–2.78 × 106 km3, as well as the World Ocean Atlas (WOA2005= 4.12 × 105 km3), it can be concluded that estimations of the volume of OMZs vary over a wide range and that our results are within this range. Comparing our results with observational data from the WOA, a generally good agreement can be found with regard to the spatial distribution of low-oxygen waters (see Fig. 5). The suboxic areas are located in the upwelling regions of the tropical eastern Pacific and eastern Atlantic as well as in the Indian Ocean (see Fig. 5; representative for both simulations in 1775).

During our transient simulations, we find a considerable expansion of OMZs until year 3005 in both simulations (see Figs. 2d and 5). The expansion of the suboxic volume between 300 and 900 m is particularly pronounced in the WB simulation where the OMZs account for 4.85 × 107 km3 in year 3005, i.e. an increase by a factor of 12.4. The control simulation (REF) shows a much smaller increase in the volume of OMZs (1.12 × 107 km3 between 300 and 900 m depth). As both simulations display similar climates (see Fig. 2a), the difference in the oxygen fields is largely due to the differences in the simulated P cycle.

The sea-floor area in contact with suboxic bottom waters, which directly impacts the redox-sensitive benthic burial and P release, shows an increase by more than a factor of 19 (WB1775= 3.59 × 105 km2; WB3005= 6.95 × 106 km2) in the WB simulation (see Fig. 2d) compared to a factor of 4 increase in the REF simulation (REF1775= 2.79 × 105 km2; REF3005= 1.2 × 106 km2). Our present-day results (WB2005= 3.8 × 105 km2) compare well with data of the WOA (WOA2005= 2.48 × 105 km2).

Somewhat unexpectedly, in our study, an increase in continental weathering does not result in an anoxic ocean under current topography and seawater chemistry – at least not until year 10 000. At the pre-industrial state (year 1775), 0.12 % of all coastal margins are characterised by oxygen concentrations below 0.005 mol m-3. While this portion increases by about a factor of 50 to 5.57 % by year 3005, this is too low for the generation of widespread coastal anoxia. Conversely, the global mean oxygen concentration starts to increase again in year 3415 when it has reached a minimum of about two-thirds of the pre-industrial oxygen inventory in the WB simulation (see Fig. S1). This suggests that the positive feedback between the release of benthic P and marine net primary production is – in this study, for present-day bathymetry and geography – not the decisive factor for a rapid transition into an anoxic ocean.