Manganese in the world ocean: a first global model

Dissolved manganese (Mn) is a biologically essential element. Moreover, its oxidised form is involved in the removal of itself and several other trace elements from ocean waters. Recently, a large number of highly accurate Mn measurements has been obtained in the Atlantic, Indian and Arctic oceans as part of the GEOTRACES programme. The goal of this study is to combine these new observations with state-of-the-art modelling to give new insights into the main sources and redistribution of Mn throughout the ocean. To this end, we simulate the distribution of dissolved Mn using a global-scale circulation model. 5 This first model includes simple parameterisations to account, realistically, for the sources, processes and sinks of Mn in the ocean. Whereas oxidation and (photo)reduction, as well as aggregation and settling are parameterised in the model, biological uptake is not yet taken into account by the model. Our model reproduces observations accurately and provides the following insights: – The high surface concentrations of manganese are caused by the combination of photoreduction and sources to the upper 10 ocean. The most important sources are dust, then sediments, and, more locally, rivers. – Results show that surface Mn in the Atlantic Ocean moves downwards into the North Atlantic Deep Water, but because of strong removal rates the Mn does not propagate southwards. – There is a mainly homogeneous background concentration of dissolved Mn of about 0.10 nM to 0.15 nM throughout most of the deep ocean. The model reproduces this by means of a threshold on particulate manganese oxides of 25 pM, 15 suggesting that a minimal concentration of particulate Mn is needed before aggregation and removal become efficient. – The observed sharp hydrothermal signals are produced by assuming both a high source and a strong removal of Mn near hydrothermal vents. *Postprints may be found at arXiv:1606.07128. 1 Biogeosciences Discuss., doi:10.5194/bg-2016-282, 2016 Manuscript under review for journal Biogeosciences Published: 11 July 2016 c © Author(s) 2016. CC-BY 3.0 License.


Introduction
Dissolved manganese (Mn diss ) is taken up by phytoplankton, because Mn is crucial for photosynthesis and other biological functions (Raven, 1990). Furthermore, its oxidised form (Mn ox ) plays an important role in the removal of several other trace metals from seawater (Yamagata and Iwashima, 1963). While in the open ocean manganese (Mn) exists in small concentrations, it is the twelfth most plentiful element in the Earth's crust (Wedepohl, 1995). Seawater Mn occurs in many forms, among which 5 the bioavailable dissolved form which is available for incorporation in organisms and marine particles. After phytoplankton death, incorporated Mn sinks downwards together with the dead material, but most of the organic material remineralises before reaching the sea floor (Sarmiento and Gruber, 2006).
Another important mechanism of storing Mn in particles, besides biological incorporation, is the removal of dissolved Mn(II) via colloids on which the Mn is oxidised to insoluble Mn(IV) (and possibly other oxidation states), and the subsequent 10 aggregation by particulate matter. Oxidation occurs everywhere in the ocean where oxygen is available. This process may be strongly accelerated by Mn(II)-oxidising microorganisms, primarily bacteria and fungi Huntsman, 1988, 1994;Tebo et al., 2005), but we do not understand the role of these organisms quite well (Nealson, 2006).
The reverse process is the reduction of Mn oxides to bioavailable dissolved Mn(II), i.e. Mn 2+ . The full oxidation/reduction (redox) equilibrium reaction, in its most simple form, is given by (Froelich et al., 1979): where oxidation is towards the right and reduction towards the left. Reduction is significantly faster under the influence of sunlight. It is hence referred to as photoreduction when irradiance is the major contributor. This process, together with the atmospheric source, is responsible for the high Mn diss concentration in the euphotic zone. The relative speed of photoreduction compared to oxidation is important for Mn(II) availability. An overall net higher oxidation rate implies more scavenging, hence 20 more Mn export.
Manganese enters the open ocean through lithogenic dust deposition (Baker et al., in preparation) and lateral advection from reducing sediments (Homoky et al., in preparation). Surface [Mn diss ] is especially high in the central Atlantic Ocean and up to at least 30 • N because of high dust input from the Sahara in combination with photoreduction (Landing and Bruland, 1987;Jickells, 1995;Guieu et al., 1994;Baker et al., 2006;De Jong et al., 2007;Wu et al., 2014). Similarly, [Mn diss ] is high in the 25 northern Indian Ocean (Thi Dieu Vu and Sohrin, 2013). Dissolved Mn diffuses out of anoxic sediments, because sediment microorganisms reduce Mn ox if there is no more oxygen (or nitrate) left (Li et al., 1969;Landing and Bruland, 1980;Sundby and Silverberg, 1985;Pakhomova et al., 2007;Middag et al., 2012;Sarmiento and Gruber, 2006, p. 234). Rivers are another source of Mn to the ocean (Elderfield, 1976;Aguilar-Islas and Bruland, 2006). While much of the fluvial Mn sediments by scavenging and aggregation, a large part may finally be transported to the ocean by diffusion from and resuspension of the 30 sediments (Jeandel, in preparation; Charette et al., in preparation). Typically, the smaller sediment particles (0.5 µm to 4 µm) contain a lot of manganese, and, because of their small size, are able to reach the open ocean (Yeats et al., 1979;Sundby et al., 1981;Trefry and Presley, 1982). Manganese may also flux into the ocean by melting sea ice (Middag et al., 2011b). Finally, overwhelming evidence is found of manganese fluxing out of hydrothermal vents (Klinkhammer et al., , 1985Hydes et al., 1986;Klinkhammer et al., 2001;Middag et al., 2011b, a;German et al., in preparation).
Downward fluxes of settling particles that have been collected in sediment traps show a strong correlation between lithogenic particles and Mn (Roy-Barman et al., 2005). Therefore lithogenic particles are likely to play a significant role in the removal (oxidation, scavenging and aggregation) of Mn. Here the ballast effect of lithogenic particles, which typically have a density of about twice of that of seawater, is likely playing a major role for rapid settling of agglomerates of biogenic and lithogenic 5 particles including Mn-oxides coatings Balistrieri et al. (1981). This is consistent with the fact that most particles are small (less than 2 µm), but larger aggregates are significant contributors to the vertical flux (McCave, 1975;Bishop and Fleisher, 1987). The complete process may be more complicated than described above (Boyle et al., 2005), e.g. because Mn possibly binds to ligands such that it stays in solution (Sander and Koschinsky, 2011;Madison et al., 2013).
Manganese oxides are important scavengers of other trace metals like iron, cobalt, nickel and zinc (Yamagata and Iwashima,10 1963; Murray, 1975;Means et al., 1978;Saito et al., 2004;Tonkin et al., 2004), as well as insoluble radionuclides such as thorium and protactinium (e.g Reid et al., 1979;Hayes et al., 2015;Jeandel et al., 2015). Therefore, Mn availability does not only directly impact primary production but may also play a role in removing other elements from the surface ocean. These elements include biologically essential trace metals as well as many more trace elements. well as the West Atlantic Ocean at, and just south of, the equator, and at the Denmark Strait overflow (Fig. 1) Mn diss "background distribution" in the rest of the ocean. In this study, we will test a simple mechanism that should be able to give insight into this stable Mn diss concentration.
Until now only local model simulations of the Mn ocean cycle have been performed that focus on the processes most relevant for the respective regions. The case of hydrothermal activity has been studied by Lavelle et al. (1992) who modelled Mn in the 10 deep ocean near hydrothermal vents. They included four Mn tracers, namely, a dissolved form, small particles associated with bacteria, larger aggregate particles, and one in sediments as the model includes benthic fluxes. They found that "more than 80 % of the hydrothermal Mn is deposited within several hundred kilometres of the ridge crest though dissolved Mn concentrations beyond that distance exceed background levels by many times". This illustrates both the high Mn input from hydrothermal vents and the high removal rate. 15 The Mn diss distribution in the North Pacific Ocean has been modelled by Johnson et al. (1996) Except for the North Pacific, the OMZ is also present in other basins, amongst which the northwestern Indian Ocean (Saager et al., 1989;Lewis and Luther, 2000). Johnson et al. (1996) found that the combination of remineralisation rates and decreased 20 oxidation in the OMZ explained their [Mn diss ] profiles. In the euphotic zone Mn diss was incorporated in phytoplankton, while remineralised Mn diss in the aphotic (and disphotic) zone was lost by oxidation and scavenging.
While these modelling efforts are useful for their purposes, no studies exist in which the global ocean Mn diss distribution is modelled. To arrive at a more integrated understanding of the oceanic Mn cycle, we include a Mn model in an ocean general circulation model. This is the first time that a global ocean model for manganese has been written and assessed. It is 25 a basic model that should give a starting point for other studies. While there is of course uptake of Mn by phytoplankton, and sometimes it is even a limiting element , we do not include biology in the model. The reason is that at the moment there is no clear evidence for typical uptake-remineralisation processes as is the case for, e.g., iron. While we perform a model simulation on a global scale, we give more attention to the Mn diss distribution in the Atlantic Ocean. Specifically, two dense and high-accuracy datasets as part of the GEOTRACES programme were available at the time of this study, namely the 30 GA02 in the West Atlantic and the GIPY5 at the Zero Meridian in the Southern Ocean (Middag et al., 2011a, in preparation).
Furthermore, in those regions we can study potentially important properties of the ocean geochemistry of manganese and the interaction with circulation, among which the Atlantic overturning circulation and hydrothermal activity.
In this study our goal is to assess the fundamental processes that are the most important to realistically simulate [Mn diss ], including the aforementioned properties of the dissolved Mn distribution. To this end, we will first introduce our Mn model 5 with its processes, sources and sinks. We will show the results of a realistic reference simulation, which will be compared with recent high-accuracy observations. Also two sensitivity simulations will be presented, studying the effects of the intense nature of hydrothermal vents and a strong Mn removal that depends on specific conditions.

10
In order to simulate the three-dimensional (3-D) distribution of dissolved Mn, we use the general circulation model Océan PArallélisé (OPA) (Madec et al., 1998) that is part of NEMO, a framework for ocean models (Madec, 2008). We use the ORCA2-LIM configuration of NEMO. The spatial resolution is about 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- 15 step thickness (Barnier et al., 2006). Lateral mixing along isopycnal surfaces is performed both on tracers and momentum (Lengaigne et al., 2003). The parameterisation of Gent and McWilliams (1990) 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 Gaspar et al. (1990), as modified by Madec (2008). The fluid dynamics used to drive our model is identical to that used in Aumont et al. (2015). 20

Manganese model
There are two tracers of Mn, referred to as dissolved (Mn diss ) and oxidised (Mn ox ) manganese. The dissolved phase is operationally defined, and may contain phases different from Mn(II). These tracers are driven by the equations set out in this section, as well as the velocity fields obtained from OPA, the dynamical component of NEMO. Instead of calculating the dynamical variables of the model (velocity and mixing), we run it off-line, using a five-daily climatology.  Table 1 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.
In the following subsections we will describe how the different sources and processes are included in the model. The model 30 parameters are summarised in Table 2.

Atmospheric dust source
Manganese is added to the pool of Mn diss in the upper model layer, according to where D is the dissolved Mn concentration, α is the solubility of Mn in dust, f Mn,dust is the mass fraction of Mn in dust, m is the molar mass of Mn, ∆z 1 = 10 m is the upper model layer thickness. The lithogenic dust deposition flux, Φ dust , is derived 5 from the Interaction with Chemistry and Aerosols (INCA) model (Hauglustaine et al., 2004). Here we use a 12 mo climatology of INCA's output as a forcing.
The average mass fraction of Mn in the Earth's upper crust is 527 ppm (Wedepohl, 1995 The Southern Ocean is defined as the ocean south of 58.7 • S. The line "total amount" denotes how much world-wide Mn is added to the ocean due to a specific flux; "relative amount" is normalised to the total Mn input flux.  Buck et al. (2010). Several studies report even higher values (> 50 %), which are, however, mainly from anthropogenic or otherwise processed dust, while the lower reported values (< 50 %) are from natural dust, mainly 5 of Saharan origin. Figure 3a presents the average Mn dissolution flux of the 12 mo climatology.

River source
The manganese river source is modelled analogously to iron, which is part of the biogeochemical model PISCES (Aumont et al., 2015). This means that our manganese influx is proportional to the total dissolved (organic and inorganic) carbon flux, 10 just like for iron (Aumont et al., 2015). Hence, the modelled concentration change of Mn diss caused by river input is given by where [Fe diss ] is the dissolved iron concentration, and r Mn:Fe,river is the effective manganese/iron flux ratio, here set to 0.214, based on river dissolved concentrations (Sarmiento and Gruber, 2006, p. 2). For comparison, it is much higher than the crustal ratio, which is around 0.02 (Wedepohl, 1995), but probably underestimated as we do not consider external sources of particulate 15 manganese. The effective Mn diss input into the ocean by rivers is presented in Fig. 3b.

Sediment source
The largest contribution of Mn to the upper ocean is dust deposition, but over large shelf and slope regions (e.g. polar oceans) the flux of Mn diss from the sediment can be of the same order of magnitude as the dust deposition flux (e.g. Middag et al., 2013, for the Southern Ocean). 20 As long as there is oxygen in the sediment, the organic carbon is remineralised by using this oxygen as an electron acceptor.
This process produces CO 2 that fluxes out of the sediments. As soon as oxygen is mostly depleted, nitrate is used as an oxidiser, producing both N 2 and CO 2 ; this is called denitrification. Around the same time, Mn reduction takes place, converting MnO 2 to dissolved Mn(II) that fluxes out of the sediment into bottom waters (Pakhomova et al., 2007;Middag et al., 2011a). After that iron reduction takes over as the primary redox reaction. Oxygen oxidation has the most negative free energy change, 25 then manganese and nitrate (depending on the MnO 2 phase being reduced), and so on; this determines the order of reactions (Froelich et al., 1979).
The (redox) reactions in the sediment are not explicitly modelled, since the sediment is not part of our model domain.
Therefore, Mn addition from the sediment is modelled as a prescribed source. Since we do not have global maps of Mn diss sediment-seawater flux, we parameterise the flux based on existing parameterisations of nitrate and iron. Middelburg et al. (1996) derived an empirical model for calculating the denitrification rate as a function of the seafloor depth: 9 Biogeosciences Discuss., doi: 10.5194/bg-2016-282, 2016 Manuscript under review for journal Biogeosciences Published: 11 July 2016 c Author(s) 2016. CC-BY 3.0 License. Aumont et al. (2015) used this model for their sediment source of dissolved Fe in the PISCES model. They used a highresolution bathymetric map to account for the shallow shelves, and modulated the seafloor depth (z → z Fsed ) as follows: They set the maximum iron flux to 2 µmol m −2 s −1 . Assuming a porewater ratio r Mn:Fe,sed = 0.2, and following the same method as Aumont et al. (2015), our final sediment addition of Mn diss into bottom water is given by: where z sed is the gridbox thickness of the bottom gridbox (just above the seafloor). With this prescribed source, the Mn flux is limited to a maximum of about 150 µmol m −2 yr −1 . This can be seen in Fig. 3c: the higher-than-140 µmol m −2 yr −1 regions on the shelves is especially notable as it falls in the upper (red) part of the colour scale.

Hydrothermal source 15
Hydrothermal vent Mn diss fluxes are modelled proportional to that of 3 He in Rüth et al. (2000) and Dutay et al. (2004). This approach is shown to have worked for iron (Bowers et al., 1988;Douville et al., 2002;Tagliabue et al., 2010;Resing et al., 2015). The basic equation for the change of Mn diss from hydrothermal vent influx is where r Mn : 3 He,hydro = 0.1 × 10 9 is the ratio between the Mn diss and 3 He effective inflow from hydrothermal vents into the This high "solubility fraction" means that the hydrothermal vents are a large source of Mn diss compared to Fe (Tagliabue et al., 2010;Resing et al., 2015). In our simulations we will show that such a large flux is necessary. This choice also relates to 25 the fast modelled removal rate of Mn near the depth of hydrothermal vents (explained later). The hydrothermal Mn diss source is presented in Fig. 3d.

Redox processes
Reduction and oxidation of Mn within the water column is a combination of several processes. Firstly, Mn ox is subject to nonbiological reduction, significantly stimulated by sunlight (e.g. Sunda and Huntsman, 1994). Secondly, the rate of oxidation is enhanced by microbes (bacteria and fungi) in regions where Mn diss supply is high (Sunda and Huntsman, 1994;Tebo et al., between the euphotic and oxygen minimum zones. At this stage we decide to not include a dependency on [O 2 ] to the model. Hence, here we choose to model Mn following a pseudo-first-order reaction where k ox and k red are pseudo-first-order rate 10 constants (conventional primes omitted, e.g. Stone and Morgan, 1990): where X is the particulate oxidised Mn concentration, and 15 with k red,light k red,dark , since reduction is much stimulated by sunlight ( Table 2). The euphotic zone is defined as the depths where the sunlight penetration is at least 1 %.

Settling and burial
Manganese oxides settle, resulting in a concentration change according to The rationale for increasing the settling velocity above a certain threshold is that if Mn ox is large enough, dense aggregates 25 form that have faster sinking rates. Notably mineral particles (sand, clay, carbonate) of high density in the order of 2-3 times that of seawater are responsible for this (McCave, 1975). Particulate organic carbon may play an important role as well (Passow and De La Rocha, 2006 where z is the depth, MLD is the mixed layer depth, H the Heaviside step function, and X thr is the aggregation threshold set to 25 pM. Simulation name r Mn: 3 He,hydro wox(m d −1 ) Xthr Reference 0.10 × 10 9 1-10 25 pM LowHydro 0.01 × 10 9 1 − NoThreshold 0.10 × 10 9 1-10 0 Table 3. List of simulations with the parameters changed compared to the reference simulation in boldface.

Simulations
The base simulation, Reference, was spun up for 500 yr to reach a steady state. Reference uses the parameters listed in Table 2.
From year 100 onwards two sensitivity simulations were forked off to run in parallel with Reference for another 400 yr. These simulations are variations of the reference simulation. Table 3 lists the simulations and key parameters.
The simulation LowHydro is intended to test if the high Mn diss input from hydrothermal vents is necessary or realistic. 5 We first decreased the settling velocity to a constant 1 m d −1 (or, equivalently, X thr → ∞), which, as expected, resulted in a wide spreading of Mn diss and a too high [Mn diss ] almost everywhere in the deep ocean (not presented). Then we decreased the hydrothermal flux by a factor of 10 to see whether the concentration of Mn diss would become reasonable again without removing the hydrothermal plume signal. Thus LowHydro contains two changes compared to the Reference simulation: a tenfold decrease in both the hydrothermal flux and the maximum settling velocity. 10 In our third and final simulation, NoThreshold, we want to see if an aggregation threshold is needed for a realistic [Mn diss ] simulation. The threshold is removed by setting X thr to zero.

Observations
In this study we will mainly use data from the GEOTRACES programme, but for a worldwide global ocean comparison one has to rely also on data that were collected in the era before the reference samples of SAFe and GEOTRACES were available. ments 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. For these reasons the West Atlantic was chosen as the 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. For these reasons all quantitative arguments in this study concern the West Atlantic GEOTRACES section. 20 The particulate [Mn ox ] measurements from Landing and Bruland (1987) 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 depths; its methods of analysis are described by Milne et al. (2010).  Table 4 for an overview with references and the number of observations.

Reference simulation
25 Figure 5 shows the modelled and measured dissolved Mn concentrations at four depths; observations as coloured dots (same scale). The dissolved Mn concentration is high in the surface of the Atlantic, Indian and Arctic oceans. The order of magnitude is reproduced by the model (Fig. 5a). The model also reproduces the latitudinal gradient of [Mn diss ], reflecting dust deposition patterns (Fig. 3a). Ocean from the Reference simulation; observations as coloured dots. Lower concentrations in the deep ocean are reproduced by the model (Fig. 5b-d and 6). Both the model and observations present a mainly homogeneous distribution of just over  Observations are presented as coloured dots; white is the land mask of the model grid.
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 North Atlantic Deep Water (NADW), which is consistent with early studies (e.g. Bender et al., 1977). Finally, the measurements near hydrothermal vents in the Atlantic and Indian oceans are reproduced by Reference (Fig. 5c and 6).
Still, at many places, the Mn diss concentration is underestimated by the model, with the exception of the Southern and Arctic oceans. The underestimation is especially pronounced at the surface of the Atlantic and Pacific oceans (Fig. 5a), as well as at 5 500 m depth in the Arctic and Pacific oceans and some parts of the Atlantic and Southern oceans (Fig. 5b). Furthermore, the relatively high concentration of Mn diss near the Amazon outflow of the West Atlantic transect is not reproduced.   To more objectively compare the different simulations to each other, we list several goodness-of-fit statistics in Table 5.
They compare the model simulations to observational data from the GEOTRACES GA02 and GIPY5 transects. The model-data

Reduced hydrothermal flux and export
We have shown that the Reference simulation gives a reasonably realistic distribution of the effects of hydrothermal vents and   Furthermore, the statistics of LowHydro compared to Reference unambiguously show that [Mn diss ] worsened ( Table 5). The LowHydro simulation is significantly worse in all three statistics: the gradients from hydrothermal vents have disappeared, and [Mn diss ] is much too high throughout the ocean compared to Reference.

No aggregation threshold 5
The simulation NoThreshold does not impose the Mn ox condition, meaning that settling occurs unconstrainedly in this simulation (no aggregation threshold). Figure 10 presents [Mn diss ] from NoThreshold. In the intermediate and deep ocean south of 40 • N, compared to Reference (Fig. 6), the concentration of Mn diss decreases by more than 50 % in much of the ocean.
Neither the correlation coefficient nor the root-mean-square deviation of [Mn diss ] in NoThreshold significantly differ from that of Reference, because the homogeneous, already low background concentration of Mn diss is reduced to close to zero,  while the hydrothermal signals are still correctly represented in the NoThreshold simulation. This means that away from ocean ridges the spatial variation of the modelled [Mn diss ] is similar to that of the observations (Stow et al., 2009). However, the reliability index, the average factor by which model predictions differ from observations, has changed from 1.82 to 2.77, which is significant by over thirty standard deviations. Therefore, the NoThreshold simulation is much worse than the Reference simulation. 15

Discussion
Many of the properties of the Mn diss distribution in the world ocean are reproduced by the Reference simulation (Sect. 3.1).
Shortcomings of the predicted [Mn diss ] are relatively minor. However, some discussion on the assumptions of the underlying processes in the model is required.

Margin sediments 5
Here we chose to use a simple sediment flux parameterisation for this study. In our model Mn diss is added to bottom water from anoxic sediments analogously to the iron flux in the model PISCES (Aumont et al., 2015). This first-order approach works well mostly, but shortcomings can be identified.  On the one hand, the flux may be overall underestimated, for instance because Mn reduction releases a higher free energy than Fe reduction, so that Mn oxides reduce more easily and hence before Fe reduction takes place (Sarmiento and Gruber, To summarise, we chose to use a simple sediment flux parameterisation for this study. While out of the scope of this study, a better parameterisation, or even an explicit sediment model, could make for a more realistic simulation and should be pursued in future studies.

Hydrothermal source
In the model, hydrothermal Mn diss is added to the ocean based on a model proxy of 3 He (Dutay et al., 2004). For Reference and NoThreshold the Mn diss addition has been set to 0.10 × 10 9 mole Mn for each mole of 3 He. There is no reference to literature values in Table 2 since they are very uncertain. For instance, Klinkhammer and Bender (1980) note that " Corliss and Dymond (1979) reported that the Mn : 3 He ratios vary by over a factor of 2 in the Galapagos vents, and as we discuss below, similar 25 variations are found at 21 • N". Rather a value is chosen to yield an acceptable distribution of Mn diss .
The goal of LowHydro is to investigate whether the combination of the high hydrothermal input of Mn diss , and strong aggregation (modelled as a high settling velocity), is needed to get a realistic distribution of Mn diss , namely that of Reference.  (Fig. 9). Decreasing hydrothermal input and the settling velocity by a smaller factor than 10 results in a Mn diss distribution that is better than LowHydro but not as good as in Reference (not presented). In any case, the main result is that the high hydrothermal input used in the Reference simulation is needed for a realistic simulation of [Mn diss ].
According to observations a negligible amount of Mn from hydrothermal vents reaches the surface ocean. As Bruland and Lohan (2006) (Tagliabue et al., 2010). Similarly, hydrothermal Mn may not be completely removed from the ocean 5 before reaching the surface by currents and vertical mixing. There are different potential reasons for this. First, the oxidation of Mn(II) is thermodynamically favoured, but the large activation energy of Mn(II) oxidation renders Mn(II) stable in aquatic environments (Nealson, 2006). In our model we made a choice in assuming that the activation energy is not an issue, and the background "dissolved" Mn particles are not Mn 2+ ions but rather suspended colloids or complexes. Candidates include colloidal Mn ox and Mn bound to ligands, respectively the second and third potential reasons for the observed background Mn ox is much higher near hydrothermal vents (up to 10 m d −1 ) than in the surface ocean (1 m d −1 ). The modelling study by Lavelle et al. (1992) suggests a settling velocity much higher than our w ox . They used a model with an additional tracer of large particles (aggregate products) that had settling speeds of up to 175 m d −1 (near hydrothermal vents, as they model those regions). This shows that there is justification in using an increasing settling velocity, but also that at least two particle tracers may be needed in the model. It is worth investigating in future studies if this would make for a more realistic and useful model.

Biological cycle
Our model does not include biological processes involving manganese, because at the moment there is not enough data available that would constrain these processes. Specifically, while Mn correlates well with the nutrients PO 4 and NO 3 (Middag et al., 2011a), there is no clear evidence for typical uptake-remineralisation processes. On the one hand, of course, Mn plays in important role in biology. It even limits primary production in parts of the Southern Ocean (Coale, 1991;Middag et al., 2011a, 25 2013; Browning et al., 2014), although the micro-nutrient iron often appears more significant (Buma et al., 1991). This is even suggested by our model-data comparison: at the Zero-Meridian GIPY5_e transect south of 62 • N, Mn diss is depleted at the surface, but between ∼50 m to 250 m there is a maximum of [Mn diss ] that may very well be due to remineralised plankton (Fig. 6, left transect). The maximum is only visible in the observations (Middag et al., 2011a), which suggests that a remineralisation process of Mn is missing in the model. On the other hand, this does not mean that primary production always 30 has an important impact on the dissolved manganese concentration (not identified in the West Atlantic transect, Fig. 6, right transect). If future studies will show that the impact is higher than here assumed, and it is due to biological incorporation, this process should be included in future versions of the model. Possibly, limitation of Mn diss for the growth of phytoplankton, and co-limitation with iron in the Southern Ocean, plays an important role for the carbon cycle (Peers and Price, 2004;Middag et al., 2013). Hence, such a limitation function could be added to carbon cycle models as well. In other words, assuming approximate equilibrium, the ratio k ox /k red could be too high. However, the k values in our model are optimised to get values consistent with the ratio of concentration measurements of Mn ox and Mn diss . Figure 11   One may introduce a threshold on the oxidation process instead of the settling of the particles. In that case, oxidation only 5 takes place when higher than 0.1 nM (k ox is multiplied by H(X −0.1 nM)). While this yields a reasonable distribution of Mn diss (not significantly worse than Reference), the Mn ox /Mn diss concentration ratio below 250 m is then strongly underestimated compared to the VERTEX data (Fig. 12, not discussed elsewhere in the paper). This pleads for using an aggregation rather than an oxidation threshold.

Export dynamics
In the NoThreshold simulation [Mn diss ] is underestimated in much of the ocean. When removing the threshold, the RMSD 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. A simulation with an oxidation threshold based on this idea gives similar results as the aggregation threshold, but as we saw in the previous section, it would influence significantly the Mn ox /Mn diss ratio in the deep ocean, making for a less realistic simulation. Therefore, this alternative should probably not pursued.
Secondly, the process of oxidation is strongly mediated by adsorption onto particles, after which it forms larger aggregates that settle faster. This is now parameterised by increasing the settling velocity of particles with depth. However, a more explicit  Thirdly, oxidation is mediated by microbes (mainly bacteria) (Sunda and Huntsman, 1994;Von Langen et al., 1997;Tebo et al., 2005;Fraústo da Silva and Williams, 2001). Possibly they prolong the time of Mn ox particles spent in the euphotic zone, but this has not been tested. In the model we assume that these are included in the redox rate constant. As of yet, there are no oxidising microbes in our model. If we want the redox rate constants to depend on inhomogeneously distributed quantities like the bacterial distribution or the oxygen concentration, the equations may need to be modified, and our model may need to be 20 extended. If this is done, more Mn may stay suspended ('dissolved Mn') as a consequence.
Fourthly, there have been suggestions that Mn ligands keep Mn in solution (Sander and Koschinsky, 2011;Madison et al., 2013). That would result in less conversion to manganese oxide aggregates, and hence may solve the removal problem, but this may yield wrong Mn ox /Mn diss concentration ratios like in the previous section. Similarly, colloids, which have a size that falls within the operationally defined dissolved Mn, keep Mn floating as long as they do not aggregate. 25

Conclusions
This is the first study in which the 3-D distribution of Mn diss has been modelled. The distribution of Mn diss is captured reasonably well by our model when compared to the recent observations from the GEOTRACES programme. A combination of photoreduction and Mn sources to the upper ocean mostly yields the high surface concentrations of manganese. However, they are somewhat underestimated by the model, which may be due to too low surface Mn input or a too strong sink (among Since accounting for these sinks could alter the structure of [Mn diss ] throughout the ocean a lot, this would imply it be necessary to make other fundamental changes in the model as well. At any rate, including these scavenging processes should be considered for future simulations. Our model does not include biology, because at the moment there is no clear evidence for typical uptake-remineralisation 15 processes as for iron. If future studies show that such a process has a significant impact on the Mn(II) concentration, biological incorporation should be included in future versions of the model. Besides processes in the photic zone, it may also be needed to model microbial activity throughout the ocean, as that is not homogeneously distributed. This means that our chemical first-order reaction may be insufficient for many modelling purposes.
Hydrothermal fluxes of Mn were set to such a high rate that we must assume 96 % is scavenged near the outflow of the 20 vents. This choice was made to account for the local high Mn diss near the oceanic ridges. This is combined with a high w ox in the deep ocean to prevent too much hydrothermal Mn diss spreading far away from the oceanic ridges. As an alternative, settling may not need to be set as high as 10 m d −1 in the deep ocean, but then it is unclear how to simulate the local nature of [Mn diss ] anomalies near the ocean ridges. One possibility is to include extra species of Mn, that may include a very fast sinking particle and a very reactive Mn species. 25 Process studies of Mn are necessary to determine the rate constants, and possibly thresholds, for redox, scavenging and aggregation. More measurements of particulate Mn ox concentrations would be useful as well. When measuring Mn ox it needs to be clear what is measured exactly. It would for instance be useful if (1) a range of particle sizes was measured, and (2) a structural analysis of the particles was performed, such that one can unambiguously say onto which particle Mn is adsorbed or into which particle it is incorporated.

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Appendix A: Shipboard methods

A1 Sample collection
For the determination of tracer concentrations, notably dissolved aluminium and dissolved manganese, samples were collected along the GEOTRACES Atlantic Meridional GA02 transect of the Netherlands (Fig. 4). Sampling was done with an all-titanium ultraclean CTD sampling system for trace metals (De Baar et al., 2008) with novel PVDF samplers Middag et al., 2015). Immediately upon recovery, the complete titanium frame with its 24 PVDF samplers was placed inside a clean room environment sampling from where the sub-samples for trace metal analysis were collected. The water was filtered from the PVDF samplers over a 0.2 µm filter cartridge (Sartobran-300, Sartorius) under pressure (1.5 atm) of (inline prefiltered) nitrogen gas. Sub-samples for dissolved metals were taken in cleaned (Middag et al., 2009, for (Landing et al., 1986) to remove interfering iron ions in the 20 carrier solution (Doi et al., 2004). Hereafter the carrier mixed with 0.7 M ammonium hydroxide (Suprapure Merck) and a luminol solution.
The The system was calibrated using standard additions from a 5000 nM Mn stock solution (Fluka) to filtered acidified seawater of low Mn concentration that was collected in the sampling region. A five-point calibration line (0, 0.1, 0.2, 0.6 and 1.2 nM standard additions) and blank determination were made every day. The three lowest points (0, 0.1 and 0.2 nM) of the calibration line were measured in triplicate and the two highest points (0.6 and 1.2 nM) in duplicate in order to add more weight to the lower part of the calibration line. The blank was determined by measuring acidified MQ which was below the detection limit and subsequently no blank was substracted. The limit of detection defined as three times the standard deviation of the lowest value observed was < 0.01 nM. The flow injection system was rinsed every day with a 0.5 M HCl solution.

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An internal reference sample was measured in triplicate every day. This was a sub-sample of a 25 dm 3 volume of filtered seawater that was taken at the beginning of Leg 1 (also used during Leg 2, i.e. Iceland to the equator) and Leg 3 (Punta Arenas, Chile, to the equator).
The relative standard deviation (i.e. the precision) of this replicate analysis seawater sample that was analysed 40 times on different days in triplicate was 2.57 % (Leg 1 and 2) and 1.21 % for 17 analyses during Leg 3. The relative standard deviation on single days was on average 1.37 % and the absolute values were 0.45 and 0.61 nM for the first two legs and Leg 3, respectively.
As external comparison the international reference samples collected on the GEOTRACES Intercalibration Cruise (www.geotraces.org) as well as from the SAFe cruise (Johnson et al., 2007) were analysed for Mn. At the cross-over station we obtained the results listed in Table A1.    Besides the good agreement with the consensus values, the measurements also agreed well with those of an independent lab. The profiles of both laboratories at BATS are presented in Fig. A1. The difference between the two profiles is significant mostly in the mixed layer.

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Furthermore, these Mn profiles are also consistent with the profiles determined by Landing et al. (1995). Figure A2 shows the correlation between the two methods of analysis for the determination of [Mndiss], shipboard and laboratory measurements, by NIOZ. There is a very good agreement between the shipboard and mass spectrometer analyses, which strongly suggests a high observational accuracy. In this study we used the observational data obtained from the shipboard FIA for the comparison with the model simulations.

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These data, and those of Wu et al. (2014), can be found online in the GEOTRACES Intermediate Data Product (IDP) (Mawji et al., 2015).

Appendix B: Data-model comparison
To compare quantitatively the model results of this study with the observations, the focus is on the West Atlantic and Zero-Meridian Southern oceans (GA02 and GPIY4). The data points of the GEOTRACES transects in those regions are used. First the model output is horizontally interpolated onto the station coordinates, keeping the vertical model grid (10 m at the surface up to 500 m thickness near the bottom).
Then the model output that lies closest to each of the observations are associated with each other. To be precise, for each observation, we take the shallowest gridbox whoes upper bound lies deeper than the observation, after which residuals can be defined as Pi − Oi, where Oi is the observed and Pi the modelled [Mndiss], for each i ∈ {1, ..., N }, with N the number of data points. The interpolation introduces a representative error that is taken to be part of the residual (Van Hulten, 2014). Then several statistics are determined, namely the Root Mean Square Deviation (RMSD), the Reliability Index (RI) and the correlation coefficient r.
In addition to classical statistical indices (r, RMSD), another additional performance indicator has been used as suggested in previous skill assessment studies (Stow et al., 2009;Vichi and Masina, 2009): The reliability index (Leggett and Williams, 1981). The reliability index "quantifies the average factor by which model predictions differ from observations". (Stow et al., 2009). It is in essence the root-mean-square deviation, but it uses the logarithm of the residual. This is useful when both large and small values need to be considered (as for this case).
The RI is given by where Oi is the measured concentration with index i, Pi is the model prediction associated to the respective observation i, and N is the number of observations. Furthermore, for each sensitivity simulation the significance of the change in each goodness-of-fit statistic compared with the corresponding reference simulation is calculated. This is determined by means of a Monte Carlo simulation on the reference simulation for which a subsample of 400 has been randomly selected from the original set of 1800 or 1650 data-model points. They are the pairs of observations and model output, both on the model grid. This is done 50 000 times, and from this the 2σ confidence interval is calculated (the mean ± two times the standard deviation). Suppose that we wish to simulate q, and assume q is in steady state. Given a simulation X, for each model 10 simulation Y resulting in qY (x), the average RMSD of the Monte Carlo simulation of qY (x) must be outside the 2σ confidence range of the RMSD distribution of qX (x) to say that Y is a significant improvement or worsening compared to X.