In order to simulate the three-dimensional (3-D) distribution of dissolved Mn, we use the general circulation model “Océan PArallélisé” (OPA) that is part of NEMO, a framework for ocean models . We use the ORCA2-LIM configuration of NEMO. The spatial resolution is 2∘ by 2∘ cos⁡(ϕ) (where ϕ is the latitude) with an increased meridional resolution to 0.5∘ in the equatorial domain . The model has 30 vertical layers, with an increased vertical thickness from 10 m at the surface to 500 m at 5000 m depth. Representation of the topography is based on the partial-step thickness . Lateral mixing along isopycnal surfaces is performed both on tracers and momentum . The parameterisation of is applied from 10∘ poleward to represent the effects of non-resolved mesoscale eddies. Vertical mixing is modelled using the turbulent kinetic energy (TKE) scheme of , as modified by . The fluid dynamics used to drive our model is identical to that used in .

The model contains two tracers of Mn, referred to as dissolved (Mndiss) and oxidised (Mnox) manganese. These tracers are driven by the equations set out in this section, as well as the velocity fields obtained from OPA. Instead of calculating the dynamical variables of the model (velocity and mixing), we run it off-line, using a climatology with a resolution of 5 days.

Figure  presents the conceptual scheme of our manganese model. The internal processes include biological uptake and remineralisation (green arrows), reduction, oxidation, aggregation and burial (blue arrows in the figure), and are described in the following subsections. Manganese sources from rivers, the atmosphere, sediments and hydrothermal vents are presented as arrows at the top and bottom of the figure. These four Mn sources are presented in Fig. , and Table  lists the absolute contributions to the different basins by each of these sources, as well as the relative contribution of every source to the world ocean. The model parameters are summarised in Table . In the following subsections we will describe how the different sources and processes are included in the model.

The Reference simulation was spun up for 600 years to reach a steady state. From year 100 onwards two sensitivity simulations were forked off to run in parallel with Reference for another 500 years. These simulations are variations of the Reference simulation that uses the parameters listed in Table . Table  lists the simulations and their key parameters.

Our second simulation is without a biological cycle of Mn (NoBio). In this simulation Eq. () is removed from the model, or, equivalently, RMn:P is set to zero. This simulation should illustrate the consequences of the (lack of) biological incorporation and subsequent remineralisation of Mn.

The goal of LowHydro is to investigate whether the combination of the high hydrothermal input of Mndiss, and strong aggregation (modelled as a high settling velocity), is needed to obtain an accurate representation of the distribution of Mndiss, i.e. one where the predicted concentrations compare well with the observed concentrations. Specifically, we want to explain the sharp observed Mn plumes. To this end, we first decreased the settling velocity to a constant 1 md-1 (or, equivalently, Xthr→∞), which, as expected, resulted in a wide spreading of Mndiss and a too high [Mndiss] almost everywhere in the deep ocean (not presented). Decreasing only hydrothermal input would trivially result in a proportionally smaller [Mndiss] near the vents. For this reason LowHydro contains two changes compared to the Reference simulation: a tenfold decrease in both the hydrothermal flux and the maximum settling velocity.

In our fourth simulation, NoThreshold, we want to see if an aggregation threshold is needed for an accurate [Mndiss] simulation. The threshold is removed by setting Xthr in Eq. () to zero.

The fifth and final simulation, OxidThreshold, is one that has a threshold in the oxidation process instead of the particle sinking, setting effectively a minimum concentration of dissolved Mn.

In this study we mainly use data from the GEOTRACES programme, but for a worldwide global ocean comparison one also has to rely on data that were collected in the era before the reference samples of SAFe and GEOTRACES were available. Table  lists the datasets from GEOTRACES expeditions, as well as several other datasets; Fig.  shows the coordinates of the stations.

Most of these GEOTRACES datasets are part of the publicly available GEOTRACES Intermediate Data Product (IDP) 2014 , except for GP16 that will be released as part of the GEOTRACES IDP 2017.

These observations are used for a visual global ocean data–model comparison. Details on the statistical and visual model–data comparison are presented in Appendix . Of these observations, only the west Atlantic Ocean data (the GEOTRACES GA02 transect, consisting of 64 PE 319, PE 321 and JC 057; 1320 points) and the Zero-Meridian Southern Ocean data (GIPY5; 468 points) have been used for statistical comparison with the model. Moreover, only the data of the shipboard FIA have been used, which have five stations fewer than the on-shore mass spectrometry determinations (ICP-MS having 120 more measurements, thus 1440 in total). The focus of this study is the west Atlantic Ocean for several reasons. Firstly, recent measurements have been carried out in that region, resulting in a large consistent (one-method) dataset. Other regions generally contain fewer measurements and are mainly based on different methods by different analysts. Secondly, the west Atlantic Ocean is of importance to the Atlantic meridional overturning circulation, and hence the deep ocean cycling of for example the major nutrients. Therefore the west Atlantic Ocean was chosen as a key site for the ∼ 18 000 km long GEOTRACES GA02 transect for the collection of data for dissolved Mn and a suite of other trace elements and isotopes. The GEOTRACES GIPY5 transect at the Zero Meridian in the Southern Ocean complements the GA02 transect up to Antarctica, giving a more complete picture of the ocean circulation. For these reasons in this study we focus on the GA02 and GIPY5 transects.

The particulate [Mnox] measurements from were used to tune the redox model. The data from the CLIVAR P16 cruise are unpublished; sampling is from the surface up to 1000 m depth; its methods of analysis are described by .

Figure  shows the west Atlantic GEOTRACES transect at the top 500 m. The concentration of Mndiss near the ocean surface is high, going up to 4 nM and beyond. The highest surface concentrations are observed in the regions of high dust deposition, as previously observed for aluminium and consistent with dust as the main source of Mn to the surface open ocean. The Mndiss distribution is mainly homogeneous in the intermediate and deep ocean, where dissolved Mn has a concentration of about 0.10 to 0.15 nM.

North of 40∘ N, high concentrations of dissolved Mn reach deeper than the top couple of hundred metres, apparently because of vertical mixing. As can be seen in Fig. , some of it seems to go all the way down to about 3000 m. However, other sources may be (partly) responsible as well, including advection from diffusive sediments and hydrothermal vents. By plotting all deep waters at enhanced resolution of concentration (Fig. ), the Mn maxima of hydrothermal plumes and the O2 minimum zones are more discernible. Since Mn and Fe have a very similar redox chemistry in the oceans, not surprisingly the maxima of Mn and Fe generally overlap (the red dashed and black solid ellipses in Fig. ). Some of the Mn may be transported southwards by North Atlantic Deep Water (NADW), but this cannot be deduced from this transect: already around 35∘ N, [Mndiss] approaches near-constant deep background concentrations such that the NADW plume is no longer discernible. Similarly, at about 35∘ S, around 1000 m depth, we observe elevated concentrations in the northward advecting Antarctic Intermediate Water (AAIW), but once again concentrations already reach the typical background concentration around 20∘ S. In the Northern Hemisphere, the subsurface waters underlying the high dust deposition region near the Equator have relatively elevated Mndiss concentrations down to 750–1000 m depth, implying some influence of the dust deposition and particle export on the subsurface Mn concentrations, but yet again, the typical background concentration is reached further down. Elevated local features are located at almost 2 km depth on the Zero Meridian at 50∘ S their Fig. 2; also presented as dots from 52∘ S on our Fig.  and almost 3 km depth in the west Atlantic transect at, and just south of, the Equator, and at the Denmark Strait overflow (Fig. ). The elevated Mn in the Denmark Strait Overflow Water (DSOW) for a small part coincides with elevated aluminium attributed to sediment resuspension . However, there is a mismatch between the highest Al concentrations observed around 45∘ N and the highest Mn in the northernmost part of the transect . This implies the source of Mn is related to the DSOW rather than the sediment resuspension occurring while the DSOW advects into the North Atlantic Ocean. The elevated deep Mn at the other locations match with elevated Fe and is most likely of hydrothermal origin . Finally, at low latitudes, in the very deep ocean, [Mndiss] decreases with depth, suggesting a slower circulation in that region or an additional and/or enforced export of Mn to the sediment.

After 600 years, both the upper 100 m and the deep ocean relative Mn content changed by less than 25 ppm over a period of 10 years in the Reference simulation. This is about a factor of 4 less compared to the decadal change of 100 years ago. The small and reducing drift suggests that the simulation is practically in a steady state. Model output data are available on PANGAEA .

Figure  shows the modelled and measured dissolved Mn concentrations at four depths; observations are shown as coloured dots (same scale). The dissolved Mn concentration is high in the surface of the Atlantic, Indian and Arctic oceans, mostly consistent with the observations (Fig. a). The model also reproduces the latitudinal gradient of [Mndiss] in the Atlantic and Indian oceans, reflecting dust deposition patterns (Fig. a).

Figure  shows the dissolved Mn concentrations at full depth in the Zero-Meridian Southern Ocean and the west Atlantic Ocean from the Reference simulation; observations are shown as coloured dots. Lower concentrations in the deep ocean are reproduced by the model (Figs. b–d and ). Both the model and observations present a mainly homogeneous distribution of just over 0.1 nM, though there are a number of sub-0.1 nM measurements in the polar oceans. The Mndiss concentrations are generally higher near the surface compared to the deep ocean, both in the observations and the model. This is caused by a combination of dust deposition and photoreduction. Also the penetration of Mndiss from Mn-rich surface waters into the deep ocean at around 50∘ N is reproduced by the model, but this is scavenged quickly before traversing southward in the NADW, which is consistent with early studies e.g.. Finally, the Reference simulation reproduces the measurements near hydrothermal vents in the Atlantic and Indian oceans (Figs. c and ).

Still, at many places, the Mndiss concentration is underestimated by the model, with the most notable exceptions of the Southern and Arctic oceans. The underestimation is especially pronounced at the surface of the Pacific Ocean (Fig. a). Furthermore, in the model the Mn-rich water from the Amazon does not reach the GA02 transect as opposed to the observations. This potentially explains the underestimated concentration of Mndiss in that region. The simulation overestimates measured [Mndiss] in the Arctic Ocean, except for some coordinates like near the Gakkel Ridge (the dark red dot in Fig. c at 90∘ E) . The Gakkel Ridge is not in our hydrothermal forcing field (Fig. d).

Figure  presents [Mndiss] of the GA03 west to east transect. Observations from are presented as coloured dots. Again, the general patterns are captured, but the concentration of Mndiss very close to the Mid-Atlantic Ridge is underestimated, while above the ridge (at about 2–3 km depth) it is overestimated. In other words, the modelled hydrothermal Mndiss gradient is not as sharp as in the observations. It is difficult to improve this feature because of the low vertical model resolution at that depth.

To more objectively compare the different simulations to each other, we list several goodness-of-fit statistics in Table . They compare the model simulations to observational data from the GEOTRACES GA02 transect. The model–data [Mndiss] Pearson correlation coefficient r has a value of 0.78 for the Reference simulation. The reliability index, the average factor by which model predictions differ from observations, shows that on average the model differs by a factor of 1.76 from observations and Appendix .

As Mn plays an important role as a trace nutrient, it is likely that biology has an impact on [Mndiss] at the ocean surface. Therefore, a simulation has been performed where biological incorporation and remineralisation of Mndiss was not included, henceforth named NoBio.

Across much of the surface ocean, the biological cycle of Mn in Reference causes a notable decrease of [Mndiss] compared to NoBio, though in the Pacific Ocean there is an increase at around 20∘ N and especially around 20∘ S (Fig. ). The decrease in the Pacific Ocean is up to 100 % near the Equator and up to 80 % at 40∘ S. In the Atlantic Ocean, [Mndiss] has not changed much between the two model simulations, explaining the insignificant change in the model–data comparison (Table ). Deeper in the Pacific Ocean, [Mndiss] is higher in Reference compared to NoBio.

Figure  shows [Mndiss] of the model compared with the observations at two depths for the NoBio simulation. The changes between the simulations are only big in the Pacific Ocean (Fig. ). Elsewhere biology does not appear to have a big effect on the Mndiss concentration. At the surface of the equatorial Pacific Ocean, concentrations are higher in the NoBio simulation. Since in Reference [Mndiss] is too low compared to the US East Pacific Zonal Transect (EPZT) (GP16), NoBio compares better with the observations. Deeper in the Pacific Ocean, Reference has higher [Mndiss], and hence is better than in NoBio.

We have shown that the Reference simulation gives an adequate representation of the effects of hydrothermal vents and the background concentration in the deep ocean. This is achieved by setting a large Mndiss flux from hydrothermal vents and a big maximum settling velocity at the depth of the vents to remove the hydrothermal Mn away from the source. The simulation presented in this section, LowHydro, is meant to test if the high flux is necessary for an accurately modelled Mndiss distribution.

Figure  shows the relative change in [Mndiss] at four depths when both the hydrothermal input and the maximum settling velocity are decreased by a factor of 10 (LowHydro). In the surface ocean (Fig. a) there are both moderate increases and decreases. However, there are very large increases in places with deep convection that connect with the deep ocean (over 500 % in the Weddell Sea). In the deep ocean below about 1 km depth, such a large increase is not limited to the Weddell Sea but stretches over much of the Atlantic and Indian oceans (Fig. c and d). Exceptions are the locations near the oceanic ridges, where there is hydrothermal activity. At those locations [Mndiss] decreased by up to 80 %.

The [Mndiss] transects in Fig.  show that LowHydro performs worse than the Reference simulation. For instance, the high [Mndiss] with a clear hydrothermal origin at 54∘ S has disappeared, while at the same time the deep ocean filled up with Mndiss, resulting in a consistent overestimation of about a factor of 5 in most of the deep west Atlantic Ocean. In the South Pacific Ocean and the Indian Ocean the signature of hydrothermal input of Mndiss is – though smaller and worse than in Reference – still clearly present, with [Mndiss] values near the ridges distinctly different from the “background” concentration (results not presented). Furthermore, the statistics on the points at the west Atlantic GA02 transect of LowHydro compared to Reference unambiguously show that [Mndiss] worsened (Table ). The LowHydro simulation is significantly worse in all three statistics: the gradients from hydrothermal vents have disappeared, and [Mndiss] is much too high throughout the ocean compared to Reference.

The simulation NoThreshold does not impose the aggregation threshold, meaning that settling is unconstrained in this simulation. Figure  presents [Mndiss] from NoThreshold at the GA02 and GIPY5 transects. In the intermediate and deep ocean south of 40∘ N the concentration of Mndiss is generally more than 50 % smaller than that in Reference (Fig. ).

The homogeneous, already low background concentration of Mndiss is reduced to close to zero (at least in the deep South Atlantic Ocean), while the hydrothermal signals are still correctly represented in the NoThreshold simulation. This explains that neither the correlation coefficient nor the root-mean-square deviation, based on the west Atlantic GA02 data, of [Mndiss] in NoThreshold differ significantly from those of Reference. This means that away from ocean ridges the spatial variation of the modelled [Mndiss] is similar to that of the observations . However, the reliability index, the average factor by which model predictions differ from observations, here also based on the GA02 data, has changed from 1.76 to 2.03, a change that is significant by six standard deviations (Table ). Therefore, the NoThreshold simulation is much worse than the Reference simulation.

As a final simulation, we limited the oxidation, rather than the settling of the manganese oxides. The resulting dissolved Mn concentrations are similar to those of Reference which has an aggregation threshold. Figure  shows the Mnox/Mndiss concentration ratio of the two simulations as well as observations at (155∘ W, 28∘ N). The blue squares represent the ratios between the particulate and dissolved Mn measurements taken during the VERTEX-IV cruise . The left panel shows that this ratio lies near 0.005 in the upper 100 m, and the right panel shows the deep ocean that has higher values. The green line is the Mnox/Mndiss concentration ratio from the Reference simulation, and the red, dashed line is the OxidThreshold simulation. For the Reference simulation, the modelled X/D generally lies at the lower end of the observed ratio, while only between 200 and 400 m are particles overestimated compared to dissolved Mn. Whereas in the upper 100 m of the ocean both simulations are consistent with those from the VERTEX-IV cruise, in the deep ocean only the Reference simulation compares well with the observations. In OxidThreshold the ratio is underestimated.

We have chosen to use a simple sediment flux parameterisation for this study. In our model, Mndiss is added to bottom water from anoxic sediments analogously to the iron flux in the model PISCES .

On the one hand, our model may underestimate the flux. In fact, with Mn reduction a larger free energy is released compared to Fe reduction, so that Mn oxides reduce more easily . Furthermore, high benthic Mn fluxes have been observed from eastern North Pacific marine sediments . On the other hand, at some large-shelf regions, like in parts of the Arctic Ocean, the Mn flux is overestimated, because the low model resolution does not handle shelf regions well. This problem is similar for iron their Fig. 8c, d.

measured pore water concentrations of dissolved Fe and Mn. The Mn/Fe ratios based on their pore water concentrations typically range from 0.2 to 0.5, but sometimes up to 2.5. The reduction rate found by their reaction–diffusion model yields a Mn/Fe reduction rate ratio of 0.02 to 0.2. reports fluxes from sediment to bottom water of dissolved Mn and Fe that yield an average ratio of 0.5. The value that we used, 0.2, lies between the intermediate and lower end of the reported values. This choice is mainly due to the fact that the crude iron flux parameterisation results in increases of the Mn flux that are out of proportion in some regions of the ocean, like the eastern Arctic Ocean and the Indonesian throughflow. This is a known shortcoming of this parameterisation that can also be seen in the modelled iron distribution . In the Arctic Ocean, a higher sedimentary Mn input would induce an even stronger overestimation than it already does with Mn/Fe=0.2 (Fig. c). The shortcoming had also been concluded by who presented a sensitivity study that used the same parameterisation for aluminium sediment input as for Mn here.

Nevertheless, a higher Mndiss input would be beneficial for the simulation in the Atlantic, and especially the Pacific Ocean, where [Mndiss] is underestimated everywhere but south of 50∘ S. This general underestimation may be due to underestimation of the enhanced dissolved Mn as previously measured in coastal upwelling regions and their underlying OMZs. Reports of elevated dissolved Mn in major Pacific coastal upwelling regions are in the California Current of the northeast Pacific , and the Peru Current (also known as the Humboldt Current) of the southeast Pacific (GP16, ). The mobilisation of Mn in these two Pacific upwelling systems is comparable to the elevated dissolved Mn in two other classical upwelling systems, off Namibia in the southeast Atlantic (CoFeMUG, ), and in the northwest Indian Ocean (GI04, ). Indeed in the surface waters (Fig. a) the model does predict elevated dissolved Mn off California and off Peru, but simulated concentrations in the ∼0.6 to ∼2 nM range are lower than measured values up to 4 or even 10 nM off California, and up to ∼3.4 nM off Peru (Fig. a). Otherwise off Namibia there appears to be more agreement between the simulated and the measured dissolved Mn in surface waters. The upwelling regions are also characterised by an extensive OMZ in the subsurface waters. In the eastern Pacific a tongue of very low dissolved O2 is most apparent at around 300 m depth their Fig. 1 and would yield elevated dissolved Mn. In our model at the 500 m depth horizon (Fig. b) this is indeed seen off California and off Namibia, but is not reproduced very well off Peru where some higher measured Mn up to ∼ 2 nM was in fact observed. The very low dissolved O2 and high dissolved Mn in these OMZ waters lead to strong spatial gradients, and a more fine resolution of the model in upwelling and OMZ regions would be required.

To summarise, we had chosen to use a simple sediment flux parameterisation, which is not completely adequate for representing Mndiss fluxes from OMZ sediments. For future work a finer regional resolution of the model in upwelling and/or OMZ regions, better parameterisation or even an explicit sediment submodel should be taken into consideration.

Although we chose to model Mn reduction and oxidation as first-order-reaction kinetics, redox of Mn within the water column is a combination of several processes. Firstly, Mnox is subject to non-biological reduction, significantly stimulated by sunlight e.g.. This is taken into account by using different kred for the euphotic and aphotic zones of the ocean. Secondly, the rate of oxidation is enhanced by microbes (bacteria and fungi) in regions where Mndiss supply is high , and it depends on the O2 concentration and pH. This has been observed in the North Pacific Ocean and references therein, as well as in some GEOTRACES transects in the Atlantic Ocean. Measurements from the west Atlantic Ocean and Zero-Meridian Southern Ocean GEOTRACES cruises show some variations with depth, e.g. near 10∘ N and near 40–47∘ N (top of Fig. ). This corresponds to the maximum of dissolved Fe associated with the oxygen minimum as reported for the same cruise by . Our model does not reproduce such a maximum of dissolved Mn, because in the model the Mn oxidation rate does not depend on [O2]. Furthermore, fluxes from reducing sediments are not expected to reproduce the feature either . This means that at least for those regions it would be logical to include a dependence on [O2]. However, this is not the pattern that attracts the most attention when looking at the full transect. The striking patterns are rather the high concentration at the surface and near the Equator around 2.5 to 3 km depth (Fig. ). For this reason we have not included a dependency on [O2] to the model. In other words, while kox depends on oxygen, we assumed here that the oxygen concentration is generally so high that its variation does not affect kox.

In our model, oxidation takes place everywhere with the same kox=0.341×10-3 h-1. Based on the underestimation of the concentrations in the surface of the Atlantic and Pacific oceans, one may think that [Mnox] is too high compared to [Mndiss]. In other words, assuming approximate equilibrium, the ratio kox/kred could be too high. However, the k values in our model are chosen to get values consistent with the ratio of concentration measurements of Mnox and Mndiss. To this end we set kred,light to the mean value found by , then used the dissolved and particulate profiles in Fig. 4 of to derive kox and kred,dark. If we were to ignore that ratio, and increase the first-order rate constants for reduction with a factor of 5 (a factor of 3 higher than the upper value of the range found by ), the model would still not yield sufficiently high [Mndiss] (results not presented).

Still, one may introduce a threshold on the oxidation process (instead of the settling of the particles). The purpose would be to find out if this would result in higher surface [Mndiss], without having a significant effect on the ratio between the dissolved manganese and the oxides. In such a model simulation, oxidation only takes place when [Mndiss] is higher than a certain threshold Dthr, equal to 0.125 nM in OxidThreshold. While this yields a distribution of Mndiss not significantly worse in the west Atlantic Ocean than that in Reference, the Mnox/Mndiss concentration ratio around 500 m and below is then strongly underestimated compared to the VERTEX data (Fig. , right panel, red dashed line). While [Mndiss] stays at realistic values, [Mnox] does not and approaches zero. This is an argument for using an aggregation rather than an oxidation threshold.

The very homogeneous low dissolved concentration of Mn at ∼ 0.1 nM in the deep waters of the west Atlantic GA02 section is remarkable (Fig. ). Such deep water values of ∼ 0.1 nM were also found in the deep waters of the Antarctic Ocean , as well as deep waters of the Mediterranean Sea (2013 cruise, data will be published at http://www.geotraces.org/dp/intermediate-data-product-2017 IDP 2017). For the Atlantic Ocean, these deep concentrations are much lower than the dissolved Mn values of ∼ 0.5–0.6 nM reported for deep samples at several Atlantic stations in the 1990s . The sampling resolution is too coarse to exclude spatial variation, but it appears the values produced by pioneering efforts to study the oceanic Mn distributions are overestimations.

The new ultraclean sampling methods , rigorous calibrations and excellent accuracy at the Bermuda crossover station for 12 trace metals now yield a much larger database of uniformly very low Mn ∼ 0.1 nM in deep waters. Given these very uniform and much lower background Mn concentrations, the hydrothermal Mn plumes are better discernible and much more widespread than realised in the 1990s. Exactly over or very near the ridge crest this has recently been shown dramatically in a plume more than 500 km wide over the Gakkel Ridge in the high-latitude Arctic Ocean , and in the Antarctic Ocean with a plume that extends more than 1000 km, at a site near the Bouvet triple junction where three ocean ridges meet . A similar long-range extent of the Mn hydrothermal plume has recently been discerned in the Pacific Ocean .

Although the west Atlantic GA02 section is quite far west from the Mid-Atlantic Ridge, the impact of the hydrothermal plume is still visible. Dissolved Mn reaches a maximum of 0.2–0.3 nM in the 2500 to 3000 m depth range just south of the Equator. This is consistent with observations along two zonal (east–west) sections across the Mid-Atlantic Ridge. These are (i) the part of the GEOTRACES GA03 section that passes over the TAG hydrothermal site (USGT11-16 at 26.14∘ N, 44.83∘ W) , and (ii) at ∼ 12∘ S in the South Atlantic Ocean their Fig. 1. In both sections a plume of dissolved Mn is visible that extends for 500 km in both zonal directions.

Remarkably, the background concentration of dissolved Mn is quite uniform in the 0.10 to 0.15 nM range. Preliminary equilibrium calculations predict an equilibrium of 0.19 nM total dissolved Mn with the solid phase pyrochroite Mn(OH)2(s). This total dissolved equilibrium concentration is quite close to the observed 0.10 to 0.15 nM background range measured in the oceans. Please note that in pyrochroite the Mn is divalent Mn(II) just as the dissolved Mn forms. Disregarding organic complexes, the latter dissolved equilibrium Mn(II) forms would comprise 0.148 nM (78 %) free Mn2+ ion, 0.027 nM (∼14%) MnCl+ ion, 0.011 nM (∼5.8%) MnCl20(aq) and a very low abundance 0.000028 nM (∼ 0.0015 %) MnOH+ ion. The above most simple Reaction () for oxidation removal from seawater may perhaps be split into several reaction steps as follows: Mn2+⇋equil.MnOH+(aq)⟶slowMn(OH)2(s)⟶fastMn(III,IV)solidstate(s), where the dominant (78 %) dissolved Mn2+ species is via the minor dissolved MnOH+ species converted to solid Mn(OH)2, and next this is oxidised to one or several of various oxide forms, for example hausmannite Mn3O4 that is a mixed valency state (III, IV) Mn-oxide, or Mn(IV)O2 pyrolusite or birnessite. Please note that in the Reference simulation an aggregation threshold for particulate Mn at 25 pM was invoked, which via redox rate constants is based on typical background dissolved Mn concentrations that was chosen at 0.125 nM. The latter threshold value of 0.125 nM was required to have the model simulate the observed data, and is quite close to the equilibrium concentration of 0.19 nM versus pyrochroite. The notion of perhaps an equilibrium control is not new. Previous pioneering measurements led to an apparent background concentration of Mn of 0.4 nM or higher, that is now shown to be too high, yet otherwise attempts were made to compare these values in terms of equilibrium versus hausmannite Mn3O4 . A reaction mechanism was proposed by which also involves conversion of Mn2+ via Mn(OH)+ as in the above Reaction (). Further research is needed to verify and confirm the hypothesis of equilibrium of dissolved Mn at ∼0.19 nM versus pyrochroite discussed here.

In the NoThreshold simulation [Mndiss] is underestimated in much of the ocean. When removing the threshold, the RMSD significantly worsens: it appears that the threshold is needed to reasonably simulate [Mndiss]. But there are several alternatives to the aggregation threshold that may keep Mndiss at a relatively homogeneous concentration.

Firstly, instead of an aggregation threshold, a criterion on oxidation may be imposed, because, hypothetically, there may be a lower limit below which oxidising microbes would not proliferate and the pseudo-first-order rate constant would then be lower. The simulation with an oxidation threshold based on this idea gives similar [Mndiss] as the aggregation threshold; but as we saw in the previous section, it would significantly influence the Mnox/Mndiss concentration ratio in the deep ocean, making for a less realistic simulation. Therefore, this alternative should probably not be pursued.

Secondly, the process of oxidation is strongly mediated by adsorption onto particles, after which they form larger aggregates that settle faster. This is now parameterised by increasing the settling velocity of particles with depth. However, a more explicit model for adsorption/desorption could be useful. Possibly, much of the Mnox does not settle efficiently. In that case, another tracer of adsorbed Mn is needed that would export oxidised Mn (in adsorbed or aggregated form), but not too fast to account for the background [Mndiss]. The adsorption should not take place onto a homogeneous pool of particles as is effectively done in our model, but rather onto a component, for example calcium carbonate (CaCO3) and lithogenic particles . Sediment samples show a strong correlation between authigenic manganese and lithogenic particles, though Mn does not show any correlation with biogenic silica, POC or CaCO3 according to recent observations and modelling . On the one hand, this suggests that only lithogenic particles are a scavenger of Mn. On the other hand, we do not know whether the correlation comes from Mn adsorption onto lithogenic particles, or if it is lithogenic in itself.

Thirdly, oxidation is mediated by microbes (mainly bacteria) . They possibly prolong the time of Mnox particles spent in the euphotic zone, but this has not been tested. In the model we assume that these processes are included in the redox rate constant. If we want the redox rate constants to depend on inhomogeneously distributed quantities like the bacterial distribution or the oxygen concentration, the equations need to be modified, and our model may need to be extended. Subsequently, more Mn would stay suspended.

Fourthly, it has been suggested that dissolved Mn ligands keep Mn in solution . That would result in less conversion to manganese oxide aggregates, and hence may solve the removal problem, but this would yield wrong Mnox/Mndiss concentration ratios like we saw for OxidThreshold. Similarly, nanoparticles, which have a size that falls within the operationally defined dissolved Mn, keep Mn afloat as long as they do not aggregate.