The Bern3D v2.0 EMIC (Roth et al., 2014) consists of a dynamic geostrophic-frictional balance model (Edwards et al., 1998; Müller et al., 2006) featuring an isopycnal diffusion scheme and Gent–McWilliams parametrization for eddy-induced transport (Griffies, 1998). The horizontal resolution comprises 40 × 41 grid cells with 32 logarithmically scaled depth layers. The ocean model is coupled to a single-layer energy–moisture balance model on the same horizontal grid (Ritz et al., 2011). Cloud cover and wind stress are prescribed from satellite re-analysis data of monthly climatologies (ERA40; Kalnay et al., 1996). Biogeochemical cycling is implemented as described by Parekh et al. (2008) and Tschumi et al. (2011). In brief, export production of particulate organic matter (POM), calcium carbonate (CaCO3), and biogenic opal is computed from prognostic equations considering new production of POM and dissolved organic carbon as functions of light, iron, phosphate, and temperature as described by Doney et al. (2006). Following the OCMIP-2 protocol, the euphotic zone is set to 75 m below which particles are remineralized following global uniform, exponential profiles for CaCO3 and opal and a power-law profile based on Martin et al. (1987) for POM. The aeolian dust flux (Fdu(θ, ϕ), where θ and ϕ represent latitude and longitude) is prescribed based on Mahowald et al. (2006) and is not remineralized in the water column. All simulations were performed under pre-industrial boundary conditions corresponding to 1765 CE with greenhouse gas concentrations set to CO2=278 ppm, CH4=722 ppb, and N2O = 273 ppb (Köhler et al., 2017).

We implemented both oxidation states, Cr(III) and Cr(VI), as independent tracers subject to advection, diffusion, and convection. The total Cr concentration, [Cr]tot, is defined as the sum of the concentrations of both oxidation states. 1Crtot=CrIII+CrVI For most Cr sources to the ocean, constraints related to the relative distribution of its chemical species are insufficient. We therefore estimated speciation factors for each source based on available information from the literature (Table 1) in order to derive the individual Cr(III) and Cr(VI) source terms.

In total, we consider three Cr sources to the ocean: mineral dust, rivers, and a benthic source. The former two are well-constrained vectors of trace metals to the ocean. Yet, during the past years it emerged that for a number of trace metals benthic sources may also play an important role for their respective oceanic inventories (e.g., rare earth elements, Jeandel, 2016; Fe, Mn, and Co, Viera et al., 2019). A benthic Cr source has also been invoked (Cranston, 1983; Jeandel and Minster, 1987), though quantitative estimates of source magnitude are limited by sparse data and are approximate at present (Janssen et al., 2021). Removal of Cr is thought to be controlled by reversible scavenging, which describes the process of adsorption onto sinking particles and subsequent release to the water column during particle remineralization at depth ultimately leading to burial in the underlying sediments.

The Arctic Ocean experiences only limited water mass exchange with the adjacent ocean basins via narrow straits. At the same time, it exhibits a high sediment surface-to-ocean volume ratio. Both these circumstances dramatically increase the impact of a benthic flux on the regional tracer budget. Thus, in order to explore the relationship between the benthic flux and the mean Arctic Cr concentration, we conducted an idealized experiment in which we set the benthic flux of Cr to zero north of 70∘ N (simulation NoArcticBFlux).

Further, due to data constraints, the model tuning was based solely on total Cr concentrations, yet the internal redox cycling and the resulting distribution between Cr(III) and Cr(VI) are also of crucial importance for the potential applicability of Cr and its isotopes as a paleo-redox proxy. To date, a relatively limited amount of information regarding open ocean Cr speciation is available, yet observations suggest widespread Cr reduction in OMZs below a threshold O2 concentration (Goring-Harford et al., 2018; Huang et al., 2021; Moos et al., 2020; Rue et al., 1997). In order to explore the consequences of OMZ Cr reduction on the global Cr inventory, we performed a number of idealized sensitivity experiments. As noted in Sect. 2.1, in our standard configuration POM remineralization is prescribed as a globally uniform power-law profile (Martin et al., 1987). Even though total export fluxes are in good agreement with observations using such parametrization (Parekh et al., 2008), the POM remineralization in OMZs is not adequately represented. Recently, Battaglia and Joos (2018) introduced a new formulation in the Bern3D model that assigns POM remineralization to aerobic or anaerobic pathways depending on the dissolved O2 concentration. Both are defined as power-law profiles yet with different remineralization length scales, yielding reduced remineralization rates under anaerobic conditions (see Battaglia Battaglia and Joos, 2018 for details). We therefore performed a set of sensitivity experiments in which we replaced the globally uniform POM remineralization with the improved parametrization introduced by Battaglia and Joos (2018) (simulation OMZrem).

In a third experiment, we investigated the impact of a substantially stronger Cr reduction rate in OMZs as suggested by field observations (Huang et al., 2021; Moos et al., 2020; Rue et al., 1997). For this simulation we increased the OMZ reduction rate from 4 nmol m-3 yr-1 in the control run to 20 nmol m-3 yr-1 while also using the improved two-pathway POM remineralization of Battaglia and Joos (2018) (simulation OMZrem20). Finally, we performed an experiment with an even higher reduction rate of 30 nmol m-3 yr-1 (OMZrem30). All these experiments were branched off from the fully equilibrated control (CTRL) run under pre-industrial boundary conditions and are summarized in Table 2.

A wide array of estimates for the oceanic residence time of Cr exists (defined as the total inventory divided by the sum of all source fluxes) ranging from 2 to 40 kyr (McClain and Maher, 2016; Sirinawin et al., 2000; Wei et al., 2018). In our parametrization, the mean ocean residence time of Cr is strongly influenced by the magnitude of the newly introduced benthic flux representing the largest source in nearly all runs of the 500-member tuning ensemble. From this tuning ensemble, we already obtain first constraints on the magnitude of the benthic flux, as well as the mean ocean residence time of Cr, as both converge towards low MAEs (Fig. 2). In the ensemble, the best model–data agreement is achieved with benthic fluxes in the range of 0.1 to 0.2 nmol cm-2 yr-1, substantially lower than the estimate from the Tasman Basin that suggested a benthic flux of ∼ 3.2 nmol cm-2 yr-1 (Janssen et al., 2021). Overall, simulations with large benthic fluxes on the order of 1 nmol cm-2 yr-1 produce either Cr concentrations that are too high or unrealistically strong vertical gradients (due to the large bottom source in combination with strong particle scavenging that is required under such conditions to balance the large benthic source flux). The clear trend in the model–data misfit of the ensemble (Fig. 2a) indicates that reduced benthic fluxes are a fairly robust result with the parametrization applied (i.e., globally uniform flux). Thus, we suspect that the benthic flux observed in the Tasman Basin may not be fully representative of the global ocean seafloor. However, missing processes in the internal cycling of the model that could be responsible for the mismatch cannot be fully excluded at this point. Further, we note that we cannot distinguish whether the benthic Cr is of authigenic or lithogenic origin in the model since we do not employ a sediment module for the calculation of the pore-water chemistry. It is thus possible that the benthic Cr is to some extent recycled primary Cr from dust and rivers and not “new” Cr that is added to the marine reservoir from the sediments. In that case, the ocean residence time of Cr would increase proportionally to the fraction of recycled Cr of the benthic source. As benthic sources account for approximately two-thirds of the total Cr source in our model (Table 1), this would yield a maximal increase of approximately a factor of 3 for our calculated residence times.

The trend in the residence time versus model–data mismatch is somewhat less distinct than that for the benthic flux (Fig. 2b), but it still clearly converges towards the lower end of previous estimates. The simulations that best fit the observational data all exhibit Cr residence times between 5 and 8 kyr (Fig. 2d). These relatively short residence times, compared to previous upper-limit estimates, are to some degree expected considering that benthic fluxes were either neglected or assumed to be fairly small in previous studies (e.g., Reinhard et al., 2013) but are in contrast to the dominant Cr source in our model simulations. Yet, previous lower-limit estimates also did not include significant benthic sources but instead included anthropogenically contaminated rivers with exceedingly high Cr concentrations (e.g., the Panuco River; McClain and Maher, 2016), which are not considered here.

The tuning ensemble member that best fits the observational data of dissolved Cr concentrations (defined as the control run) yields an MAE of 0.48 nmol kg-1. A few other simulations performed virtually as well as the control run, all of which exhibited similar values for the benthic flux and the scavenging factors. However, the parameters that describe the internal cycling (i.e., oxidation rate and OMZ reduction rate) exhibit a wider spread among these simulations. This is related to the fact that our tuning target was solely the total Cr concentration, and we did not consider the individual oxidation states in assessing model performance due to insufficient data coverage to achieve statistical significance. The parameters of the control run are listed in Table 1.

In the control run, the total flux of Cr entering the ocean amounts to 8.77 × 108 mol yr-1 with the smallest contribution from dust (∼ 3 %), followed by the riverine source (∼ 29 %), and by far the largest contribution from the benthic flux (∼ 68 %) (Table 1). Even though the global benthic flux of 0.16 nmol cm-2 yr-1 in the control run is much smaller than the first local estimate (Janssen et al., 2021), it still dwarfs the combined contributions from dust and rivers. In contrast, assuming both dust and river sources as in the control run but a benthic flux comparable to the first local estimate (∼ 3 nmol cm-2 yr-1) would yield a benthic flux contribution of ∼ 98 % and be about 50 times larger than the riverine source. As previously noted by Janssen et al. (2021), it thus appears that this first observational estimate for the benthic flux from the Tasman Basin may not be fully representative of the global ocean, and further research regarding the impacts of sediment composition, porosity, and bottom and pore-water chemistry is required to better constrain this presumably significant Cr source to the ocean.

Oxygen minimum zones are thought to represent important environments where Cr is removed from the ocean and deposited in the underlying sediments (Moos et al., 2020; Rue et al., 1997) as they promote the reduction of soluble Cr(VI) to scavenging-prone Cr(III). In the model, about one-fourth of the entire Cr removal (calculated from the particulate concentrations of the bottommost grid cells) takes place at the sediments below OMZs (representing an area of 7.37 % of the seafloor; Table 3). Yet, the simulated Cr(III) concentrations of ∼ 0.15 nmol kg-1 are partly in disagreement with observed Cr(III) concentrations in OMZs that can even exceed 1 nmol kg-1 (Huang et al., 2021; Moos et al., 2020; Rue et al., 1997). We consider this to be the result of the model tuning not taking into account the spatial distribution of Cr(III) due to the insufficient data coverage. Generally, modeled Cr(III) concentrations are only slightly elevated in OMZs (Fig. 7b) in contrast to observations that suggest strong reduction rates and subsequent removal of Cr (e.g., Rue et al., 1997).

In a first sensitivity experiment (OMZrem) we therefore replaced the globally uniform POM remineralization profile with the O2-dependent parametrization introduced by Battaglia and Joos (2018) (see Sect. 2.3). This reduces the horizontal expansion of OMZs in the model but at the same time increases their vertical extent (see Fig. 7a). Consequently, the difference in ocean volume where [O2] < 5 µmol kg-1 is relatively moderate with a decrease from 0.93 % in CTRL to 0.75 % of the total volume with the O2-dependent remineralization (Fig. 8). However, this is still an overestimation of the modern expansion of OMZs by a factor of about 5 (see Bianchi et al., 2012). This is a persistent issue with Earth system models of various complexity and is mostly related to insufficient spatial resolution to adequately represent these highly dynamic regions even with considerably better spatially resolved models (Cocco et al., 2013).

The greater vertical extent and the strongly attenuated particle remineralization in the OMZs associated with the O2-dependent parametrization has a profound impact on the vertical [Cr(III)] and [Cr]tot profiles (illustrated for the eastern equatorial Pacific OMZ in Fig. 7b). In the upper part of the OMZ, Cr(III) concentrations are lower compared to CTRL due to the higher particle concentrations enhancing the scavenging efficiency. In contrast, in the lower part (below 1 km) the effect of the deepened OMZ promoting Cr reduction (local Cr(III) source) dominates over the elevated particle concentrations associated with the vertical expansion (local Cr(III) sink). Both the elevated particle concentration in general and the greater vertical extent of the OMZ increasing Cr reduction (integrated over the entire water column) lead to a decrease in total Cr concentration throughout the water column, yet this effect is most pronounced in the depth range of the OMZ.

Nevertheless, Cr(III) concentrations also remain lower in simulation OMZrem than observations of OMZs indicate (of up to 1 nmol kg-1; Huang et al., 2021). We therefore performed two additional sensitivity experiments with substantially increased OMZ reduction rates of 20 and 30 nmol m-3 yr-1 (simulations OMZrem20, OMZrem30, respectively) (compared to 4 nmol m-3 yr-1 in CTRL), including the parametrization of O2-dependent remineralization (Fig. 7c). For both these simulations, Cr(III) concentrations are strongly elevated in OMZs, for instance, peaking at 0.33 and 0.44 nmol kg-1 in the core of the eastern equatorial Pacific OMZ for OMZrem20 and OMZrem30, respectively, compared to a maximum of ∼ 0.20 nmol kg-1 in CTRL. At the same time, the effect of increased OMZ Cr reduction on [Cr]tot within OMZs is relatively small with a minor decrease in concentrations in the top 1 km and only slightly higher concentrations below. This redistribution in the water column is a direct consequence of the higher Cr(III) concentrations enhancing Cr downward transport and ultimately also removal. Globally this results in 7 % and 12 % more Cr removal below OMZs for simulations OMZrem20 and OMZrem30, respectively, compared to OMZrem (Table 3). As such, the higher OMZ reduction rates, together with the O2-dependent remineralization, do indeed provide an improved representation of OMZ Cr concentration characteristics (Cr(III) and Crtot) consistent with observations (see Moos et al., 2020; Rue et al., 1997). However, it is worthy of note that observations indicate that the Cr(III) maximum in OMZ depth profiles is shifted toward shallower depths (Huang et al., 2021; Rue et al., 1997) and not in the middle or bottom of the OMZ as simulated here. Thus, additional processes such as organic complexation, which stabilizes Cr(III), or elevated Cr reduction at shallow depths might be at play in OMZs that are not explicitly implemented here.

This study describes the first implementation of the modern marine Cr cycle and more specifically of the two oxidation states, Cr(III) and Cr(VI), into an EMIC. We implemented three Cr sources, namely an aeolian, a riverine, and a benthic flux, that are balanced by the removal associated with reversible scavenging transferring particulate Cr to the sediment. The comparison of our 500-member tuning ensemble to a comprehensive and quality-controlled seawater database provides a best estimate for the mean ocean Cr residence time between 5 and 8 kyr, which is at the lower end of previous first-order approximations (Campbell and Yeats, 1984; Reinhard et al., 2013; Wang et al., 2020). At the same time, we find that the best model–data agreement is achieved with benthic fluxes in the order of 0.1 to 0.2 nmol cm-2 yr-1, substantially lower than the first local estimates (Janssen et al., 2021). Nevertheless, a benthic flux of such magnitude is substantially larger than the aeolian and riverine source fluxes (for the control run: 68 % benthic, 29 % riverine, and 3 % aeolian).

Overall, the control run simulates the vertical, meridional, and inter-basin [Cr]tot gradients in good agreement with observational data. Thus, total Cr concentrations increase with depth, as well as with water mass age, which leads to [Cr]tot > 4.5 nmol kg-1 in the deep North Pacific. Similarly, the vertical gradient increases from Δ[Cr]tot≈1 nmol kg-1 in the North Atlantic to Δ[Cr]tot>2.5 nmol kg-1 in the North Pacific. The only major model–data mismatch is observed in the Arctic Ocean basin where simulated concentrations are far too high compared to observations. We attribute this to the poor spatial representation due to the coarse model resolution and to the simplified benthic flux parametrization causing it to have an impact that is too large on this semi-enclosed basin with a large sediment surface area compared to its volume.

In contrast, the poor spatial data coverage of Cr(III) observations precludes not only its incorporation in the tuning metric but also a robust model–data assessment that can only be improved by more seawater measurements. The only exception are OMZs that are fairly well-studied with respect to Cr reduction and hence Cr(III) concentrations (e.g., Huang et al., 2021; Moos et al., 2020; Murray et al., 1983; Rue et al., 1997). Yet, as a consequence of not including Cr(III) in the tuning metric, its representation in OMZs is somewhat deficient. We therefore performed three sensitivity experiments to improve simulated Cr(III) concentrations in these highly reducing regions. By introducing an O2-dependent parametrization of POM remineralization and a strongly increased OMZ reduction rate, we are able to simulate high Cr(III) concentrations and elevated Crtot removal in OMZs that are in much improved agreement with observational data.

The fairly long mean ocean residence time of Cr puts serious constraints on its implementation in Earth system models. In order to obtain an equilibrated state of the marine Cr cycle, model integrations of several tens of thousands of years are required. This can currently only be achieved with highly computationally efficient, coarse-resolution, intermediate complexity models such as Bern3D. At the same time this limits the representation of the Cr cycle as small-scale processes, for instance at coastal regions, can inherently only be approximated in these models. Furthermore, because of the scarcity of data, processes such as redox reactions, particle scavenging, and sedimentary release of Cr remain critically under-constrained to date, which contributes to substantial uncertainty in the understanding of the marine Cr cycle and thus also impedes its robust implementation in models. As a consequence, only large-scale features of the Cr distributions presented here can be considered as robust. Future improvements in the understanding of, for example, the spatial variability in the benthic flux or the Cr behavior in OMZs, might however bolster our ability to also simulate regional variations in better agreement with observations.

One such more local, yet important, model–data discrepancy relates to the simulated surface depletion of [Cr]tot that is most pronounced above OMZs but not observed to the same extent in existing seawater profiles (see Figs. 6 and 7; Goring-Harford et al., 2018; Moos et al., 2020; Nasemann et al., 2020). The reversible scavenging scheme linearly scales with the particle concentration. From this follows that Cr removal is strongest in the surface ocean where no remineralization takes place in the model (euphotic zone) and in high-productivity regions that are also responsible for OMZs. One possible explanation to account for the high particle concentrations in these regions not leading to strong surface Cr depletions in the real ocean could relate to complexation with organic ligands. Complexation has been found to be an important process increasing the solubility of a number of trace metals such as rare earth elements (Byrne and Kim, 1990), Cu, Zn, Cd, and most notably Fe (Bruland and Lohan, 2003). Similarly, investigations showed that Cr(III) readily binds with organic ligands (Saad et al., 2017), in contrast to Cr(VI), which seems to be far less affected by complexation (Richard and Bourg, 1991). The dominance of Cr(VI) in oxygenated water therefore indicates that this process is unable to fully explain the simulated surface Cr depletion. Instead, we speculate that internal recycling processes in the mixed layer, not considered in our reversible scavenging parametrization, might be responsible for the observed relatively stable Cr concentrations in the uppermost water column. This could also explain the depleted surface concentrations of other geochemical tracers implemented in the Bern3D model that also make use of the same reversible scavenging formulation (Nd: Pöppelmeier et al., 2020; Pa: Rempfer et al., 2017).

Despite the uncertainties persisting in the understanding of key processes of the marine Cr cycle, the two main oxidation states of Cr were successfully implemented in the coarse-resolution Bern3D model. This thus provides us with a powerful tool to investigate the biogeochemical cycle of Cr and its isotopes and their tight interconnection with past oceanic and atmospheric oxygenation and biological productivity.

One main focus of future Cr modeling may encompass exploring the impact of expanded OMZs on Cr removal rates. For such endeavors it may be valuable to further improve the parametrization of OMZ-related processes, which should be guided by, for example, new observations of the microbial influence on Cr reduction, as recently suggested by Huang et al. (2021). Furthermore, the Bern3D model is also well-suited for simulations over glacial–interglacial cycles that involve drastic changes not only of the biogeochemistry but also of the ocean circulation and their complex feedbacks.

Finally, past changes in the stable isotopic ratios associated with the fractionation during redox transformations may also be successfully extracted from ocean sediments in the future, which would allow for (semi-)direct comparisons to the Bern3D model.