We used the MITgcm “checkpoint” 64w, which refers to a specific time and/or point within the development of the MITgcm code since it continuously undergoes updates. It was configured to solve the Boussinesq, hydrostatic Navier–Stokes equations with a nonlinear free surface (Marshall et al., 1997; Adcroft et al., 2004b). A cubed sphere grid was used which provided a nearly uniform resolution and avoided pole singularities (Adcroft et al., 2004a). It consisted of six faces, each of which comprised 32×32 grid cells, resulting in a horizontal resolution of approximately 2.8∘. There were 15 vertical levels, ranging in thickness from 50 m at the surface to 690 m at the seafloor, giving a maximum model depth of 5200 m. Associated with the nonlinear free surface is the possible vanishing of the upper layer. To avoid this problem, the rescaled vertical coordinate z* was employed (Adcroft and Campin, 2004). This approach scales the entire vertical grid with the surface elevation and not just the surface layer (cf. Fig. 1b in Adcroft and Campin, 2004). Furthermore, the shaved cell formulation was used, which reduced the representation error of the bathymetry (Adcroft et al., 1997). The model was coupled to a dynamic–thermodynamic sea ice model with a viscous–plastic rheology (Losch et al., 2010).

Isopycnal diffusion and eddy-induced mixing were parameterized with the GM/Redi scheme (Redi, 1982; Gent and McWilliams, 1990). Background vertical diffusivity for tracers was uniform at 3×10-5 (m2 s-1), and for the equation of state the polynomial approximation of Jackett and McDougall (1995) was used. Advection of tracers was computed using third-order advection with direct space–time treatment (Hundsdorfer and Trompert, 1994).

Atmospheric forcing (air temperature, specific humidity, zonal and meridional wind velocity, wind speed, (snow) precipitation, incoming shortwave and longwave radiation, as well as river runoff – 12 climatological monthly means) was obtained from the PI ocean state estimate by Kurahashi-Nakamura et al. (2017), which was based on the protocol of the Coordinated Ocean-ice Reference Experiments (COREs) project (Griffies et al., 2009). They optimized the forcing fields to reconstruct tracer distributions that were consistent with observations. Air–sea fluxes were internally computed in the model following the bulk forcing approach by Large and Yeager (2004). Furthermore, we globally balanced the freshwater flux by annually adjusting the precipitation field (Appendix A).

Our simulation was initialized with present-day salinity and temperature distributions (Levitus et al., 1994, and Levitus and Boyer, 1994, respectively) and spun up from the state of rest. We used asynchronous time stepping to accelerate computation with a time step of 1 day for the tracer equations and 20 min for the momentum equations.

We compiled the code using the GNU Fortran compiler gfortran version 5.3.0 and performed the simulation on six cores of a processor of type Intel Xeon E5-2630 v3. The simulation was integrated for 3000 years (1000 model years took ∼ 7.5 h CPU time) to reach a quasi-steady state (the global salinity, temperature and Atlantic meridional overturning circulation were approximately steady at 34.73 psu, 2.86 ∘C and 18.24 Sv (1 Sv = 106 m3 s-1), respectively) and continued for a further 3000 years with stable water isotopes as passive tracers. For analysis, the average of the last 100 years was used.

We implemented the stable water isotopes H216O, H218O and HDO as conservative, passive tracers in the ocean component of the MITgcm (wiso package). Isotopic variations at the sea surface were driven by evaporation (E), precipitation (P) and river runoff (R), while advection, diffusion and convection affected the distribution in the interior of the ocean. Monthly climatological means of the isotopic content of precipitation and water vapor were available from the National Center for Atmospheric Research Community Atmosphere Model including a water isotope scheme (NCAR IsoCAM; Tharammal et al., 2013). Note that the prescribed atmospheric forcing fields obtained from the PI ocean state estimate by Kurahashi-Nakamura et al. (2017) and the corresponding isotopic fluxes are not entirely consistent and might introduce an error in our model simulation. However, to minimize the uncertainty, we only took the ratio of the isotopic content of precipitation and water vapor and applied it to the corresponding atmospheric forcing fields. The isotopic composition of river runoff affects the isotopic composition of ocean water (δ18Ow and δDw) particularly in coastal regions. Since there was no land model in the MITgcm to calculate the amount and isotopic composition of continental runoff, we assumed that it equals the isotopic composition of the local precipitation at the river mouth and again applied it to the runoff forcing field.

Fractionation during evaporation, taking both equilibrium effects and kinetic effects into account, was treated explicitly in the MITgcm. The formulation for the isotopic composition of evaporation Ei (mol m-2 s-1) is Ei=Γi(qi-qsi). Here, qi is the specific humidity (kg kg-1) multiplied by the isotopic ratio derived from the NCAR IsoCAM, and qsi=qsJiαl-v is the tracer-specific humidity (kg kg-1) in thermodynamic equilibrium with the liquid at the ocean surface (Merlivat and Jouzel, 1979), while qs=0.98ρairqsat is the local sea surface humidity (kg kg-1) with qsat being the saturation-specific humidity (kg m-3) and ρair being the atmospheric density (kg m-3). Ji=c(i)⋅M(i)c(H216O)⋅M(H216O) is the local sea surface mass ratio with c being the concentration (mol m-3) and M the molar mass (g mol-1) of the respective stable water isotope. The equilibrium fractionation factor αl-v between liquid water and water vapor has been found empirically as a function of temperature and was given by Majoube (1971): αl-vδ18O=e1.137SST2×103-0.4156SST-2.0667×10-3αl-vδD=e24.844SST2×103-76.248SST+5.2612×10-2, with SST being the sea surface temperature (K).

Due to different molecular diffusivities of the isotopes, kinetic fractionation occurs. The kinetic fractionation factor K depends on wind speed U (m s-1) through the roughness of the air–sea interface (Merlivat and Jouzel, 1979; Jouzel et al., 1987): KH218O=0.006,ifU<7ms-10.000285⋅U+0.00082,ifU≥7ms-1KHDO=0.00528,ifU<7ms-10.0002508⋅U+0.0007216,ifU≥7ms-1. The kinetic fractionation factor was used to calculate the isotopic profile coefficient Γi following Γi=ρCEU(1-K), where ρ is the air density and CE is the transfer coefficient for evaporation as described in Large and Yeager (2004).

Fractionation during the formation of sea ice was neglected, because it is very small compared to other fractionation processes and thus only leads to minor effects on δ18Ow and δDw (Craig and Gordon, 1965). Due to the absence of isotopes in the sea ice, we approximated the isotopic surface flux Fi (mol m-3 s-1) by Fi=-Ei-Pi⋅1-Aice-Ri, with Aice being the ice-covered area fraction. Based on this approximation, there was no isotopic surface flux in areas covered by sea ice unless they were influenced by river runoff. Within the MITgcm, processes that affected the stable water isotopes were taken care of by the “gchem” and “ptracers” packages (Table 1). While the gchem package acted as an interface between the ptracers and wiso package and added Fi to the passive tracer surface tendency gPtri (mol m-3 s-1), gPtri=gPtri+Fi, the ptracers package mainly accounted for the transport of the isotopes by advecting and diffusing them. Furthermore, due to the freshwater flux that effectively changed the water column height, an additional tracer flux Fwi (mol m-2 s-1) associated with this input/output of freshwater (E-P-R (kg m-2 s-1)) was calculated following Fwi=(E-P-R)⋅ci⋅x, with x being a unit conversion factor. Fwi was then additionally added to the tracer surface tendency within the ptracers package: gPtri=gPtri+Fwi⋅1z, with z (m) being the surface grid cell thickness.

In the MITgcm, the stable water isotopes were not treated as ratios but as individual concentrations. Therefore, we initialized the ocean with homogenous concentrations of H216O, H218O and HDO matching present-day δ18Ow and δDw values of 0 ‰ with reference to the VSMOW. The ratios were calculated during the analysis of the results.

Furthermore, similar to the freshwater flux, a correction factor for the tracer-specific precipitation was applied, whereby the respective global tracer concentration in the ocean was conserved (cf. Appendix A).

We compare the simulated annual mean SST and sea surface salinity (SSS, upper 50 m) to the annual mean (averaged over the upper 50 m and interpolated to the cubed sphere grid) temperature (Fig. 1a, b) and salinity (Fig. 2a, b) of the World Ocean Atlas 2013 (WOA13; Locarnini et al. (2013), Zweng et al. (2013), respectively). In most regions of the global ocean, SST differences are around 1 ∘C or even less (root mean square error (RMSE) of 1.18 ∘C) and therefore in good agreement with the data. Larger differences are mainly located in regions of coastal and equatorial upwelling, in the Gulf Stream and around Indonesia.

A different picture emerges for the SSS anomaly. While most parts of the surface ocean are slightly too fresh, especially the Mediterranean Sea, Bay of Bengal, Hudson Bay and north of Iceland, both the Arctic Ocean and the east coast of North America are too salty. Nevertheless, we obtain a RMSE of 0.45 psu without using any salinity restoring.

This good agreement also continues in the deeper parts of the Atlantic Ocean. Calculated weighted zonal means of the simulated annual mean temperature and salinity in the Atlantic Ocean correspond well with the observations (Fig. 3a and b, respectively; temperature and salinity provided by the GISS data – Schmidt et al., 1999). The simulated annual mean temperature gradually decreases with depth, as do the observational data. It is also recognizable that the boundary towards water masses colder than 4 ∘C appears slightly shallower in the southern than in the northern part of the Atlantic Ocean. Coldest temperatures occur in the deep southern Atlantic Ocean, both in the simulated as well as observational data. Interpolating the observational data to the nearest tracer grid point and comparing them to the simulated long-term monthly mean values of the respective month of sampling (as described in Sect. 2.3.1 for the GISS data) further underlines the agreement between simulated and observed values (Fig. 3c – r2=0.93, RMSE = 2.1 ∘C, n=660). The zonally averaged cross section of the simulated annual mean salinity clearly reveals the occurrence of different water masses. While most parts of the Atlantic Ocean are filled by the North Atlantic Deep Water (NADW) coming from the north with a salinity value of around 34.9 psu (reaching a water depth of ∼ 3500 m), the deepest parts of the Atlantic Ocean basin are occupied by less saline water (∼ 34.7 psu) of the Antarctic Bottom Water (AABW) flowing from the south. The Antarctic Intermediate Water (AAIW) is the freshest water mass (∼ 34.6 psu) and can be traced as a tongue, spreading from the south towards the north at a water depth of 1000 m. The most saline water appears in the upper water column of the northern tropics (∼ 30∘ N). This structure is also reflected in the observational data; however, both NADW and AAIW seem to be slightly fresher. Performing a model–data comparison for salinity, as outlined above for temperature, shows a good fit (Fig. 3d – r2=0.61, RMSE = 0.6 psu, n=691) in general, but a few points are clearly located above the 1 : 1 line. These data points correspond to simulated annual mean salinity values in the upper water column near the North American coast, one of the regions with the highest positive SSS anomalies (Fig. 2a) and will be discussed briefly in Sect. 4.1.

Even though measurements of δD exist, they are not as widespread as δ18O. Furthermore, the stable water isotope package will be used mainly for paleoclimatic reconstructions in conjunction with δ18Oc data from benthic foraminiferal shells. Hence, we chose to focus on the comparison for δ18O to validate our simulation.

The surface (upper 50 m) distribution of annual δ18Ow simulated by the MITgcm gradually decreases from the midlatitudes to high latitudes (Fig. 4a, b). Highest values of about 1 ‰ occur in the subtropical gyre of the Atlantic Ocean, which are slightly higher than in the Pacific Ocean, reflecting the net freshwater transport by the trade winds. The Mediterranean Sea and Red Sea are regions of net evaporation and therefore contain δ18Ow values of similar magnitude. The most depleted surface water is simulated in the high latitudes, showing values of -0.5 ‰ in the Southern Ocean and -1 ‰ in the Arctic Ocean. These depleted values result from negative δ18Ow values in precipitation in combination with river/glacial runoff. Similarly, depleted values occur in surface waters around Indonesia.

The large-scale patterns and latitudinal gradients of simulated annual mean δ18Ow values match fairly well with the observations. For example, the model captures the contrast between high and low latitudes and the Atlantic and Pacific oceans. However, some notable discrepancies are recognizable when comparing the absolute range of δ18Ow at the surface. In the MITgcm, the subtropical gyres are less enriched than in the observations (annual mean value of 0.6 ‰ as compared to 1.0 ‰, respectively). The same holds true for the Mediterranean Sea. For the Arctic Ocean, simulated δ18Ow values are not as depleted as in the observational data (annual mean value -0.6 ‰ as compared to -1.5 ‰, respectively). Especially near large river estuaries, the model–data mismatch is large.

A clear distinction between different water masses based on the annual mean isotopic composition of sea water is recognizable in our simulation, both for the Atlantic Ocean and the Pacific Ocean (Fig. 5a and b, respectively). In our model, the NADW in the Atlantic Ocean reaches down to approximately 3500 m depth and is rather enriched in H218O, resulting in an annual mean δ18Ow content of around 0.11 ‰ (cf. Table 3). Most enriched δ18Ow values (∼ 0.6 ‰) occur in the upper water column of the tropics (20–30∘ S and N). The NADW encounters the AAIW coming from the south at a water depth of approximately 1000 m. The latter is more depleted with an annual mean δ18Ow value of around 0 ‰. The deepest parts of the Atlantic Ocean are characterized by negative annual mean δ18Ow values of approximately -0.11 ‰ derived from AABW mixed with NADW. This water mass structure is in good agreement with the observational data. However, the NADW is not enriched enough compared to the observational data (0.21 ‰), whereby the deepest parts of the Atlantic Ocean reveal too depleted δ18Ow values. For the Pacific Ocean (Fig. 5b), the vertical structure is even more homogenous. Enriched waters (∼ 0.1 ‰) occur in the upper water column down to approximately 1000 m. Deeper parts of the Pacific are filled with depleted water of around -0.1 ‰. Compared to the observational data, the vertical and latitudinal gradients are in agreement. The large number of negative δ18Ow measurements at 50∘ N is obtained from the Okhotsk Sea and thus is not representative for a zonally averaged cross section of the North Pacific.

To take a closer look at the model–data fit, we interpolated the GISS data to the nearest tracer grid point and compared them to the simulated long-term monthly mean value of the respective month of sampling (see Sect. 2.3.1). The separation of the model–data comparison into different ocean basins (Atlantic Ocean – Fig. 6a, Pacific Ocean – Fig. 6b, Arctic Ocean – Fig. 6c and Indian Ocean – Fig. 6d) points to deviations that mainly occur in higher latitudes. The correlation and RMSE are quite diverse, showing strong correlation for the Indian (r2 = 0.77, RMSE = 0.19 ‰, n=593) and Pacific Ocean (r2 = 0.74, RMSE = 0.32 ‰, n=743), medium correlation for the Atlantic Ocean (r2=0.37, RMSE = 0.79 ‰, n=756) and no correlation for the Arctic Ocean (r2=0.05, RMSE = 1.18 ‰, n=1048). Overall, depleted δ18Ow values are not very well simulated in the MITgcm, which is particularly recognizable in the Arctic, a region highly influenced by negative δ18Ow values from precipitation, snowfall and river runoff (Yi et al., 2012).

Similar physical processes determine the salinity and δ18Ow distribution at the ocean surface. Thus, locally a linear relationship between those two quantities can be expected. Therefore, we compared the modeled δ18Ow–salinity relationship with the observed one by taking the closest long-term monthly mean tracer grid value of salinity and δ18Ow to the GISS data points of the respective month of sampling. Restricting the comparison to the upper 50 m and the salinity range to 28–38 psu in order to reflect open ocean conditions, the general features of the latter relationship are well captured in our model (Fig. 7).

The modeled δ18Ow–salinity relationship in the tropics (25∘ S–25∘ N) agrees quite well with the observed one (Fig. 7a). Here, we find a simulated slope of 0.15 ‰ psu-1, while the observed one is 0.22 ‰ psu-1. A steeper slope is visible in the midlatitudes (25–60∘ S/N) for both the simulated and observed relationships (Fig. 7b). However, the agreement between those two slopes is smaller than in the tropics, with a simulated slope of 0.28 ‰ psu-1 and an observed slope of 0.49 ‰ psu-1. Further, it underlines that we do not simulate salinity and δ18Ow values as low as represented in the GISS data.

The annual mean simulated δ18Oc distribution at the surface (upper 50 m) increases from the tropical regions (∼ 3 ‰) to high latitudes (∼ 3.5 ‰), reflecting the dependency on both δ18Ow and temperature (Fig. 8). Most depleted δ18Oc values develop in the Bay of Bengal and around Indonesia (< 3.5 ‰), while the transition towards positive δ18Oc values occurs from 40∘ S/N upwards. Even though the plankton tow data are rather sparsely distributed in the global ocean, a latitudinal increase in δ18Oc is also recognizable. Thus, the simulated large-scale pattern and latitudinal gradient match fairly well with the measurements. Nevertheless, some model–data mismatch occurs. Simulated annual mean calcite values in the tropics seem to be slightly too low (e.g., northeast of the Amazon delta), while regions in the North Atlantic and Arctic Ocean are slightly enriched compared to the observations. The influence of the seasonal cycle on the δ18Oc distribution depends on latitude (Fig. 9). The largest seasonal effects occur in the northern midlatitudes (30–60∘ N) with values of up to 3 ‰, whereas a weak or almost non-existent seasonal effect appears in low and high latitudes. Thus, when performing a model–data comparison, the respective month of plankton tow sampling must be considered. Figure 10a and b include not just the surface data but plankton tows taken in deeper parts of the ocean. The comparison reveals a good match (r2=0.88, RMSE = 0.83 ‰, n=183). Data points that are not located along the 1 : 1 line but rather above belong either to the deeper water columns of the model (Fig. 10b) within the tropics (Fig. 10a) or, as mentioned above, to the upper water column (Fig. 10b) in high latitudes (Fig. 10a).

Before we discuss the δ18Ow distribution in the MITgcm, the general model performance will be briefly assessed, because an accurate presentation of the ocean circulation is essential for a reasonable simulation of stable water isotopes. Therefore, we investigate the temperature and salinity distribution, because these two quantities determine the density and thus are one of the main factors influencing the vertical movement of ocean waters. The results for the simulated annual mean temperature and salinity are quite promising. Large biases at the sea surface occur in the North Atlantic, both for the SST and SSS. These biases are quite common in ocean models, especially with a low resolution, since the proper simulation of the structure, pathways and extensions of western boundary currents are difficult to achieve (cf. Griffies et al., 2009). Here, the Gulf Stream remains attached to the coast far to the north, and due to the coarse grid resolution, subpolar surface water displaces the North Atlantic Current resulting in SST and SSS biases. Regarding the SST, warm biases also occur in the upwelling regions along the west coasts of Africa and North and South America (intruding far into the open ocean basin), which are mainly driven by the poorly resolved coastal upwelling process. In terms of SSS biases, surface boundary conditions like P and E should be considered. In general, the large-scale patterns for P and E are accurately presented (not shown here). The prescribed precipitation field P clearly depicts the intertropical convergence zones (ITCZs) in the Atlantic and Pacific oceans. Further, extremely dry ocean regions in the subtropics that are associated with high pressure zones are visible. The simulated evaporation field E is mainly zonally oriented, with increased values occurring in subtropical areas and decreased values along the Equator and high latitudes. This zonal pattern is interrupted in regions of western boundary currents, where E is enhanced along the pathways. For a more precise estimate, we calculated annual anomalies for P and E (Fig. 11a and b, respectively) using data from rain gauge stations from the Global Precipitation Climatology Project (GPCP; Huffman et al., 1997) and the latent heat flux (converted to E by dividing it by the constant latent heat of evaporation (2.5×106 (J kg-1); Hartmann, 1994)) from the National Oceanography Centre (NOC) version 2.0 Surface Flux and Meteorological Dataset (Berry et al., 2009). Unfortunately, no data exist for E in high latitudes, whereby no model–data comparison can be carried out in these regions. Since E, among others, depends on the SST, a similar picture for the anomaly should emerge. Indeed, regions with warmer (colder) SST simulated by the MITgcm also experience elevated (reduced) E values. The precipitation, however, is too small in the North Atlantic, the Bay of Bengal, the equatorial Atlantic and along 60∘ S, while it is too large mainly in the tropics (especially in the Pacific) and high latitudes. Regarding the SSS, the bias in the North Atlantic appears to be caused by an interaction between the coarse grid resolution and a bias in the evaporation. Besides the Mediterranean Sea, where enhanced P and reduced E can lead to a fresh bias, there is no other apparent correlation between P, E and SSS anomalies. With a RMSE of 1.18 ∘C and 0.45 psu, respectively, our SST and SSS results are comparable to Danabasoglu et al. (2012), who reported a RMSE of 0.58 ∘C and 0.41 psu for the POP2 ocean component of the Community Climate System Model 4 (CCSM4) using a weak salinity restoring, and Griffies et al. (2011), who got a RMSE of 1.3 ∘C and 0.77 psu with the Geophysical Fluid Dynamics Laboratory Climate Model version 3.

Likewise, the comparison with observed data for the deep Atlantic Ocean basin is good. The main water masses AAIW, NADW and AABW can be detected. Core properties of the water masses (AAIW: salinity of ∼ 34.6 psu, temperature of ∼ 5 ∘C; NADW: salinity of ∼ 34.9 psu, temperature of ∼ 3 ∘C; AABW: salinity of ∼ 34.7 psu, temperature of ∼ 0 ∘C; visual estimation based on Fig. 3) fit reasonably well with the temperature and salinity ranges reported by Emery and Meincke (1986 – Fig. 14, rectangles). However, both NADW and AABW might be slightly too salty, while the AABW seems to be too cold. To maintain a realistic ocean climate, not just the water mass structure is of importance but also the circulation strength. The maximum meridional transport at 48∘ N simulated in the MITgcm is 17.8 Sv, consistent with 16 ± 2 Sv reported by Ganachaud (2003) and Lumpkin et al. (2008).

Thus, we find that the general model performance is reasonable and comparable to both observations and other climate simulations.

Results of the δ18Ow distribution at the sea surface showed relatively large mismatches between modeled and observed data in the Arctic Ocean. As indicated by Eq. (11), there is no isotopic surface flux in areas that are covered by sea ice unless they are influenced by river runoff. Since parts of the Arctic Ocean are covered by sea ice all year round and others are seasonally influenced (not shown here), these areas do not experience any isotopic surface flux during most of the year. In this way, the impact of precipitation and snowfall that is highly depleted is neglected, which could explain too-high δ18Ow values in the Arctic Ocean.

The spatial distribution of δ18Ow in P is also a matter of debate. The Global Network of Isotopes in Precipitation (GNIP; IAEA/WMO, 2010) provides a database with δ18Ow in P at more than 950 stations all around the globe. For the comparison with modeled annual δ18Ow in P, only data with continuous sampling for a minimum of 5 years have been considered, resulting in 127 data points. Unfortunately, most of the data are continental, whereby a significant conclusion for the δ18Ow in P over the ocean is difficult. Nevertheless, all the main characteristics in δ18Ow in P can be identified (Fig. 12a). Due to the temperature effect on the fractionation during condensation (Dansgaard, 1964), δ18Ow in P decreases from middle to high latitudes. While most enriched values occur in the regions of trade winds with slightly more depleted values along the ITCZ, the strongest depletion can be found over the polar ice sheets. For a more straightforward statement, we performed a model–data comparison (Fig. 12b) by interpolating the GNIP data to the closest tracer grid point of the MITgcm, revealing a good agreement between modeled and measured data (r2=0.72, RMSE = 2.4 ‰, n=91). Linking these results to the large δ18Ow mismatches that emerged in the Arctic Ocean, subtropical gyres and the Mediterranean Sea let us conclude that the decreased δ18Ow values at the ocean surface in the latter two regions are caused by an interaction of P, E and δ18Ow in E. Enhanced P in the MITgcm has a dilutional effect on the water, while due to reduced E not enough 16O is removed from the ocean surface. It appears that δ18Ow in P is reasonably well simulated. Unfortunately, we cannot compare our simulated δ18Ow in E to any observational data, but it could be that it is also slightly too enriched. Regarding the Arctic Ocean, except for the isotopic surface flux calculation as outlined above, insufficient river discharge and neglecting the fractionation during sea ice formation could be further sources for the model–data deviations. As part of the Pan-Arctic River Transport of Nutrients, Organic Matter and Suspended Sediments (PARTNERS) project, Cooper et al. (2008) published flow-weighted annual mean discharge and δ18Ow data (collected between 2003 and 2006) from the six largest Arctic rivers (Table 2). According to their estimates, δ18Ow values of Eurasian rivers decrease from west to east; thus, the Ob' River discharges the most enriched freshwater (-14.9 ‰) while the water of the Kolyma River is most depleted in heavy isotopes (-22.2 ‰). This west-to-east trend is also recognizable in our model (Fig. 13b), where the Ob' River contributes freshwater with a δ18Ow value of around -15.6 ‰ and the Kolyma River of around -20.5 ‰. Even though it seems that the isotopic composition of the Ob' River is too depleted, all the other three Russian rivers are not as depleted as seen in the PARTNERS data.

Measurements of the Yukon and Mackenzie rivers reveal intermediate isotopic signals (-20.2 and -19.1 ‰, respectively). In the MITgcm, these signals are slightly more enriched with δ18Ow values of around -17.1 and -18.9 ‰ for the Yukon and Mackenzie rivers, respectively. A consideration of the overall river discharge to the Arctic Ocean reveals a slight underestimation as the flow-weighted average for all six rivers is -18.8 ‰, while in the model it is only -18.0 ‰. Not only does the isotopic signal of the river discharge matter but also the discharge amount. Estimating the annual discharge amount in the MITgcm is difficult, because determining the grid cells that belong to the respective river is based on visually assigning them according to the location of the river mouth. This may lead to deviations compared to observational data. While simulated annual discharge for the Yenisey, Lena, Yukon and Mackenzie rivers is in good agreement with reported values by Cooper et al. (2008 – Table 2), the amounts discharged by the Ob' and Kolyma rivers differ substantially. However, deviations of the annual discharge for all six rivers are tolerable (∼ 400 km3 a-1). Cooper et al. (2008) further reported that the Arctic Ocean basin receives 10 % of the global river runoff (1.3 Sv; Trenberth et al., 2007). The MITgcm fits right into this magnitude with 9.3 % of the simulated global river runoff (1.17 Sv) received by the Arctic Ocean (> 60∘ N). Thus, the deviations that appeared for the Ob' and Kolyma rivers are most likely attributable to the grid cell assignment described above and should not matter significantly. Therefore, both the isotopic signal of river runoff and the discharge amount are rather insignificant for the model–data mismatch in the Arctic Ocean. The general pattern of the simulated isotopic river discharge shows that river runoff is more enriched in low and middle latitudes (Fig. 13a), which is in accordance with observations (IAEA, 2012). Thus, simulating the isotopic composition of river runoff by taking the isotopic composition of the local precipitation is a reasonable first approximation but should be overcome by implementing a bucket model in the MITgcm which calculates the river discharge and its isotopic content for individual catchment areas over land.

Further discrepancies between model and observations might be due to the formation and transport of sea ice. During the formation of sea ice, the heavier isotopes are entrapped in the solid ice structure, while depleted sea ice brine is expelled (O'Neil, 1968). However, this fractionation process is relatively small. Lehmann and Siegenthaler (1991) reported an equilibrium fractionation constant of 2.91×10-3 between pure water and ice under equilibrium laboratory conditions, while Melling and Moore (1995) estimated a fractionation constant of 2.09×10-3 for ∼ 1 m thick ice in the Canadian Beaufort Sea. So, even though sea ice is highly dynamic, excluding not only the fractionation during the formation of sea ice but also the transportation of isotopes within the sea ice might lead to minor local changes but should not be one of the main sources of error. Indeed, Brennan et al. (2013) investigated the impact of a fractionation factor for sea ice on δ18Ow in the University of Victoria Earth System Climate Model (UVic ESCM). They conclude that local changes in δ18Ow due to the contribution of sea ice are smaller than 0.14 ‰ and therefore rather negligible.

Furthermore, the coarse resolution of our model may cause some of the model–data discrepancies, since it is not able to resolve all of the physical processes. For instance, water that is transported towards the Nordic Seas as part of the Gulf Stream system is displaced by water from the Labrador Sea due to the coarse horizontal grid system. Likewise, the vertical resolution might introduce some additional errors because the thermocline might not be as pronounced and shifted compared to the real ocean since, e.g., the upper 500 m in the MITgcm are only represented by four layers. Observational data corresponding to depths within that transition layer might reflect a different signal than that resolved by the ocean model.

Since δ18Ow is a passive tracer, shifts at the ocean surface might propagate in the ocean interior. Errors in the general model performance might further add to the deviations in the deeper ocean. However, the water masses in the MITgcm in terms of structure, extent and magnitude are faithfully simulated (cf. Sect. 4.1) and thus can be ruled out as a significant error source.

Additionally, our isotopic forcing was not obtained from the same source as the atmospheric forcing for the freshwater, heat and momentum flux, whereby a maximum consistency cannot be ensured and an additional uncertainty to our sources of error is added.

Despite these sources of error, the simulated pattern of δ18Ow both at the sea surface as well as in the deep ocean agrees fairly well with other recent studies such as the study by Xu et al. (2012) with an OGCM as well as the studies by Roche and Caley (2013) and Werner et al. (2016) with fully coupled models.

The seawater oxygen isotope ratio and salinity are controlled by the same processes such as evaporation, precipitation, river runoff and sea ice formation. In this way, they are locally linearly related, resulting in a slope that varies between 0.1 ‰ psu-1 in low latitudes and up to 1 ‰ psu-1 in high latitudes. However, water that is evaporated from the ocean surface does not carry any salt, but it contains stable water isotopes. The agreement between the simulated slope and observational slope in the tropical regions is good but significantly weaker in the midlatitudes. This mismatch is mainly caused by the stable water isotopes since the overall comparison to observed SSS is quite good and comparable with other ocean models (cf. Sect. 4.1).

Subtropical gyres are characterized by high salinity and δ18Ow values. While the model shows reasonable salinities in these regions (Fig. 2a), its surface water is too depleted (Fig. 4a). As discussed in Sect. 4.2, these discrepancies rather stem from an interaction of reduced E, whereby not enough 16O is removed from the ocean surface, δ18Ow in E that is probably slightly too enriched and the dilutional effect of enhanced P. In contrast to this are the values of low salinity and δ18Ow at the other end of the slope. They are mainly located around the upper boundary of the midlatitudes (∼ 60∘ N/S) near the coast (e.g., the Okhotsk Sea and Bering Sea) and within the western boundary currents (e.g., the Gulf Stream). While the modeled salinity is slightly too salty, the δ18Ow values are not as depleted as seen in observations, causing the deviations in the slope of the δ18Ow–salinity relationship. We infer that the coarse grid resolution is the main driver for this mismatch.

Despite these discrepancies at the sea surface, the investigation of the water mass structure of the deeper parts of the ocean reveals that the model is suitable to determine the large-scale distribution of water masses in terms of the δ18Ow signature. Water mass formation regions are mainly located in the high-latitude Atlantic Ocean and produce large parts of the deep and bottom waters of the global ocean. Hence, our investigation focuses on the main water masses (AAIW, AABW and NADW) within that basin. Emery and Meincke (1986) used published temperature and salinity data to determine the core properties of the main water masses of the global ocean. Applying these characteristics of the Atlantic Ocean to both the GISS data and modeled values (Fig. 14; Table 3) clearly shows the resemblance. All three water masses are found in the ocean model, but their temperature–salinity ranges differ slightly from those given by Emery and Meincke (1986) as discussed in Sect. 4.1. Nevertheless, even though the absolute range of δ18Ow values is narrower in the model than in the observations, the modeled mean values are remarkably close to the observations (cf. Table 3). Our results are quite encouraging, suggesting that the nonlinear free surface and real freshwater flux boundary conditions of the MITgcm indeed lead to an improvement compared to other ocean models using salinity restoring (e.g., Paul et al., 1999; Xu et al., 2012).

Overall, even though some regions at the surface reveal localized biases regarding the δ18Ow distribution, the water mass structure of the deeper parts of the ocean and their characteristic δ18Ow values are successfully simulated. Hence, the ocean model is well suited to perform long-term simulations in a paleoclimatic context and investigate the respective δ18Ow changes.

To address questions regarding the evolution and history of the ocean and climate, oxygen isotopic records derived from measurements of foraminiferal shells have been used extensively. Particularly, the last glacial maximum (LGM) and last deglaciation are time periods for which the evidence comes from proxy data recorded as oxygen isotopes in CaCO3. Hence, before using the model for paleostudies, an evaluation of modeled and measured δ18Oc for the PI climate is necessary.

The δ18Oc of planktonic foraminifera is not only determined by δ18Ow and temperature of the ambient water in which the calcification takes place but also altered by vital effects and modifications after death. Vital effects involve, for example, the photosynthetic activity of algal symbionts. Species like G. ruber (w) and G. sacculifer harbor symbionts (Kucera, 2007) that change the microenvironment around the shell by increasing the calcification rates through CO2 uptake and thus shifting the pH towards more alkaline conditions corresponding to elevated carbonate ion concentrations ([CO32-]). This mechanism will induce a kinetic fractionation that leads to relatively 18O-depleted shells (Ravelo and Hillaire-Marcel, 2007). Furthermore, in the course of ontogenesis, successive shell chambers reveal more enriched δ18Oc values (Bemis et al., 1998), while significant changes also occur during reproduction. Bé (1980), Duplessy et al. (1981) and Mulitza et al. (2004) as well as others argue that some planktonic foraminifera add an additional layer of calcite during reproduction (gametogenic calcification). This additional calcite layer is secreted in deeper and cooler water masses, introducing an 18O enrichment in the shell. Duplessy et al. (1981) ascertained a δ18O mean enrichment of 0.78 and 0.92 ‰ in the shells of G. ruber and G. sacculifer from core-top sediments, respectively. Mulitza et al. (2004) also showed that foraminiferal shells from the sediment are increased in δ18O by approximately 0.5–1 ‰. The average δ18O composition recorded by a foraminiferal species at the sea floor is further influenced not only by the vertical migration within the water column, whereby signals from different depths are incorporated into the foraminiferal shell, but also by seasonal variations in shell production. Species that prefer polar waters (e.g., N. pachyderma (s)) rather peak during summer, whereas species that are distributed in warm provinces (e.g., G. bulloides) reflect a spring signal followed by a smaller autumn peak (Kucera, 2007). Additionally, the isotopic composition of foraminiferal shells can also be altered after deposition due to dissolution. This is especially the case if the initial shell is dissolved rather than the crust formed during gametogenesis (gametogenic calcite is often more resistant to dissolution; Bé et al., 1975), further shifting the δ18O towards higher values.

All these mechanisms described above cannot be captured in our model, because it does not have an ecosystem module included, which could represent the life cycle of foraminifera and factors that determine the incorporation of oxygen isotopes in foraminiferal shells. Neglecting these processes might lead to additional model–data discrepancies. To avoid them, a comparison with plankton tow data is more reliable for testing the general capability of the model to simulate δ18Oc, since the depth and month of sampling are known (thus excluding any deviations due to seasonality or depth habitat) and the foraminifera are sampled alive (thus excluding any deviations due to gametogenic calcification or modifications after death).

For the surface distribution of δ18Oc, the largest discrepancies between model and data occurred in the Arctic Ocean. While the SST is too low, the δ18Ow is not depleted enough in this region. These two effects could compensate each other, but the δ18Oc reveals a slight overestimate, which results from the underestimated SST. To disentangle the background of any model–data mismatch, it is best to investigate the model–data fit considering individual species (Fig. 15). Therefore, we use species-specific paleotemperature equations published by Mulitza et al. (2003 – Table 4). First, we notice that the correlation is weaker when individual species are considered compared to investigating them grouped together. The best model–data fit is captured for G. bulloides (r2=0.72, RMSE = 0.65 ‰, n=35), while it is significantly weaker for N. pachyderma ((s); r2=0.41, RMSE = 0.71 ‰, n=61). While the largest deviations for N. pachyderma (s) occur in the upper surface column, data points that deviate from the 1 : 1 line for the other three species mainly correspond to depths larger than 100 m (not shown here). This becomes clearer when the model–data comparison is carried out for data that only fall in the upper level (< 50 m) of the ocean model, resulting in a significant improvement of the RMSE and r2 for G. ruber ((w); r2=0.86, RMSE = 0.41 ‰), G. sacculifer (r2=0.80, RMSE = 0.37 ‰) and G. bulloides (r2=0.83, RMSE = 0.56 ‰), while the RMSE worsens for N. pachyderma ((s); r2=0.46, RMSE = 0.89 ‰). Even though the sampling depth of the plankton tow data is known and was used for interpolation to the respective grid cell, we suppose that the δ18Oc signal recorded by the living foraminifera rather corresponds to a shallower water depth (at least for the first three species mentioned before). Schiebel and Hemleben (2005) illustrated the average depth inhabited by planktonic foraminifera (cf. Fig. 2 therein). While G. ruber (w), G. sacculifer and G. bulloides inhabit the upper surface column (∼ 25, ∼ 40 and ∼ 50 m, respectively), N. pachyderma (s) lives on average in deeper parts (∼ 90 m) and thus might confirm the assumption above. Another source of error may be the coarse vertical resolution of the model.

Overall, modeled δ18Oc values can be compared to data successfully with a better result when all species are grouped together compared to individual species. Taking into account the processes that potentially affect the δ18Oc of foraminifera and considering the species-specific influence by habitat depth and seasonality, a comparison with δ18Oc collected from sediment cores appears to be feasible in a future study.