Modelling iodine in the ocean

An ocean iodine cycling model is presented, which predicts upper ocean iodine speciation. The model comprises a three-layer advective and diffusive ocean circulation model of the upper ocean, and an iodine cycling model embedded within this circulation. The two primary reservoirs of iodine are represented, iodide and iodate. Iodate is reduced to iodide in the mixed layer in association with primary production, linked by an iodine to carbon (I:C) ratio. A satisfactory model fit with observations cannot be obtained with a globally constant I:C ratio, and the best fit is obtained when the I:C ratio is dependent on sea surface temperature, increasing at low temperatures. Comparisons with observed iodide distributions show that the best model fit is obtained when oxidation of iodide back to iodate is associated with mixed layer nitrification. Sensitivity tests, where model parameters and processes are perturbed, reveal that primary productivity, mixed layer depth, oxidation, advection, surface fresh water flux and the I:C ratio all have a role in determining surface iodide concentrations, and the timescale of iodide in the mixed layer is sufficiently long for non-local processes to be important. Comparisons of the modelled iodide surface field with parameterisations by other authors shows good agreement in regions where observations exist, but significant differences in regions without observations. This raises the question of whether the existing parameterisations are capturing the full range of processes involved in determining surface iodide, and shows the urgent need for observations in regions where there are currently none.


Introduction
The biogeochemical cycling and speciation of iodine in the oceans has been studied for many years, and it is recognised as a "bio-intermediate" element cycled between oxidised and reduced forms and removed from surface waters by biological activity (e.g. Truesdale et al., 2000).
Recently there has been increasing interest in understanding this speciation because of its potential utility as an indicator of productivity, (e.g. Ducklow et al., 2018, Campos et al., 1996, Wong, 2001, Tian et al., 1996, its application as a paleo-redox indicator (e.g. Lu et al., 2016;Zhou et al., 2016) and because reactions between iodide at the sea surface and ozone have been identified as a globally significant sink for tropospheric ozone, with implications for atmospheric chemistry and climate (Carpenter et al., 2013;Saiz-Lopez et al., 2014). The reaction of iodide and ozone is not only a sink for ozone (Ganzeveld et al., 2009) but also a source of molecular iodine (I2) and hypoiodous acid (HOI) to the atmosphere. These reactive iodine species photolyse to the highly reactive IO radical, influencing ozone cycling and other atmospheric chemistry reactions (e.g. Mahajan et al., 2010;Carpenter et al., 2013;Sherwen et al., 2016a). The iodine-driven sea surface ozone sink has been identified as the most uncertain part of the tropospheric sink of ozone (Hardacre et al., 2015), and has been estimated to account for around 12% of the total (Sherwen et al., 2016b), and thus an understanding of ocean iodine cycling is a key pre-requisite for adequate models of ozone and atmospheric oxidation processes.
Iodine is primarily present in the oceans as the dissolved inorganic ions iodide (I -) and iodate (IO3 -). In coastal surface water an additional organic iodine form has been identified as a significant component of the iodine pool, although this is not seen in the open ocean (Luther et al, 1991).
Iodine is known to be cycled biologically within the oceans leading to slight surface depletion of total iodine concentrations (I -+ IO3 -) and a marked interconversion of iodine oxidation species with a euphotic zone maxima in iodide relative to iodate. In deep oxygenated waters iodate is the overwhelmingly dominant species as predicted from its thermodynamic stability (Wong, 1991;Elderfield and Truesdale, 1980;Chance et al., 2014). The uptake of iodate and iodide and the ESSOAr | https:/doi.org/10.1002/essoar.10502078.1 | CC_BY_4.0 | First posted online: Wed, 29 Jan 2020 09:38:42 | This content has not been peer reviewed.
Confidential manuscript submitted to Global Biogeochemical Cycles 4 release of iodide have been demonstrated in microalgal (e.g. Chance et al., 2007;de la Cuesta and Manley, 2009) and bacterial laboratory cultures ) In coastal surface water an additional organic iodine form has been identified as a significant component of the iodine pool, although this is not seen in the open ocean (Luther et al., 1991). Surface water iodine speciation varies seasonally, with iodate decreases and iodide increases approximately in phase with cycles of primary production, although possibly with a time lag associated with delays between the uptake of iodate and its subsequent re-release as iodide (e.g. Chance et al., 2010). Oxidation of this iodide back to iodate is estimated to have a timescale of the order of months to years, although it has not been measured directly because it is so slow (Tsunogai, 1971;Campos et al., 1996;Edwards and Truesdale, 1997;Waite et al., 2006;de la Cuesta and Manley, 2009;Chance et al., 2010). Several authors have noted a relationship between iodide and nitrate concentrations in surface water and speculated that this may reflect a real biogeochemical coupling of these species, which could reflect the geochemical similarities of iodate and nitrate. The evidence for such coupling has until recently been equivocal at best (Hung et al., 2005;Waite and Truesdale, 2003;Campos et al., 1999;Truesdale et al., 2000). However, in a companion paper, Hughes et al. (2019) have demonstrated a link between the oxidation of ammonium to nitrite, and iodide to iodate, which has significant implications for our understanding of the ocean iodine cycle.
Although the global database for iodine speciation in ocean surface waters is rather limited, there are still clear large scale patterns evident with iodide concentrations (and iodide/iodate ratios) much higher in the oligotrophic surface ocean gyre waters (> 100 nM generally) than in high latitude waters (< 50 nM) , and this range of concentrations is sufficient to significantly affect the uptake of ozone and its global atmospheric cycling (Sherwen et al., 2016b).
The realisation of the importance of the role of iodine in surface ocean waters as a sink for ozone has led to efforts to incorporate this reaction into atmospheric models, which requires a global field of surface ocean iodide concentrations (Ganzeveld et al., 2009;Luhar et al., 2018). There have been some efforts to characterise the ocean surface iodide field in terms of other parameters that can be inferred indirectly or directly from satellite or other large scale ocean databases, such as temperature and nitrate, and use the derived statistical relationships to predict the ocean surface iodide field, which can provide a boundary condition for atmospheric chemistry models (Sherwen et al., 2016b). The iodide distributions predicted by these statistical relationships basically reflect ESSOAr | https:/doi.org/10.1002/essoar.10502078.1 | CC_BY_4.0 | First posted online: Wed, 29 Jan 2020 09:38:42 | This content has not been peer reviewed.
Confidential manuscript submitted to Global Biogeochemical Cycles 5 the large-scale ocean distribution of iodide with higher concentrations in low latitude, high temperature, low nitrate waters, and low iodide concentrations at high latitudes in seasonally overturning cooler waters MacDonald et al., 2014;Sherwen et al., 2019a).
However, while the statistical relationships developed provide a generally good fit to the data, they are not based on the biogeochemical cycling of iodine in the oceans and hence their extrapolation beyond the data range for which the relationships are derived cannot be done with confidence, and hence predictions of change in the ocean iodide field with climate change, for example, are unreliable. It is also evident that iodide exhibits interannual variations (Chance et al., 2010), which may compromise these statistical methods.
We therefore present here the first ocean iodine biogeochemical cycling model which includes realistic phytoplankton uptake and release parameterisations of iodine cycling based on ocean primary production fields and iodide oxidation derived from laboratory demonstrated mechanisms coupled to nitrogen cycling. This is all embedded within a realistic ocean physical mixing and transport field, allowing seasonal mixing between surface water where iodide is produced and subeuphotic zone waters, and redistribution by the local and global scale circulation. We demonstrate that all of these biological and physical iodine cycling processes interact together to yield the observed global iodine distribution.

The iodine cycling model
The iodine cycling model aims to capture the dominant biogeochemical processes involved in the cycling of iodine in the oxygenated ocean, and embed these in a simplified three-dimensional circulation model of the upper ocean, driven by fields derived from climatologies and an ocean general circulation model. Further technical details and model equations can be found in the Appendix, and here we summarise the key features of the model and its development.
Confidential manuscript submitted to Global Biogeochemical Cycles 6 2.1 The physical ocean model The model is global in coverage, with a horizontal resolution of 1 o in latitude and longitude, and three layers in the vertical (Figure 1). The upper layer is the seasonal mixed layer, its thickness varying throughout the year (Monterey and Levitus, 1997). The middle layer extends from the base of the seasonal mixed layer to the maximum seasonal mixed layer depth (MLD), multiplied by 1.05, to prevent zero-layer thickness when the top layer is at maximum depth. The bottom layer has a thickness of 500 m, or extends to the ocean bottom (GEBCO -Becker et al., 2009) if this is less, or has a minimum depth of 0.05 times the maximum MLD if the mixed layer extends to the sea floor, to maintain a finite layer thickness. This simplification of the deep ocean structure reflects the constancy of iodine concentration and speciation at depth. Each layer is assumed to be completely mixed in the vertical. Changes in MLD result in the exchange of water and tracers between the upper two layers, and the exchanged tracers are mixed into the thickening layer. There is constant vertical mixing of 1x10 -4 m 2 s -1 between the middle and bottom layers. Each vertical column is subject to a horizontal mixing of 2000 m 2 s -1 , and advection by the depth-dependent horizontal ocean currents derived from the OCCAM ocean GCM (see Aksenov et al., 2010 for details). Vertical advection is derived from the horizontal divergence of this flow, and the precipitation minus evaporation and runoff flux is accounted for at the surface.
ESSOAr | https:/doi.org/10.1002/essoar.10502078.1 | CC_BY_4.0 | First posted online: Wed, 29 Jan 2020 09:38:42 | This content has not been peer reviewed. Figure 1: Schematic representation of the three-layer ocean model, in which the iodine cycling model is implemented. The upper layer is the mixed layer. The middle layer extends below this to the depth of the seasonal maximum mixed layer depth (multiplied by 1.05 to avoid zero depth in the model). The bottom layer extends either to the ocean floor, or to a thickness of 500m, whichever is less (but also has a minimum thickness of 0.05 times the maximum mixed layer depth to avoid zero thickness). Below the bottom box iodide and iodate are assumed to have concentrations of 0 nM and 500 nM respectively. Each box is subject to mixing and advection, and there is a fresh water flux due to precipitation, evaporation and runoff through the surface of the upper box. See text for more details.  .
Production of iodide only occurs in the mixed layer in the model, and is assumed to be biologically mediated consistent with all the available evidence (Campos et al., 1996;Tian et al., 1996;Wong, 2001;Chance et al., 2007;Chance et al., 2010;Ducklow et al., 2018;Hepach et al., 2019). It is linked to the uptake of carbon by primary production via an iodine to carbon ratio, thought to be in the range 10 -5 to 10 -3 (Elderfield andTruesdale, 1980, Jickells et al., 1988;Chance et al., 2010;Hepach et al., 2019). Primary productivity is taken from the climatology of Behrenfeld and Falkowski (1997), which uses satellite observations to determine chlorophyll concentrations, and hence has no data where and when solar irradiance is low or zero. We could simply assume productivity is zero under these conditions, and this is supported at most longitudes where productivity is essentially zero at the poleward extent of the data, but in the North Atlantic in spring the bloom extends to the northern limit of the data. We therefore extrapolate the productivity polewards from the last available data point to zero over 10 o of latitude. We also assume no productivity under sea ice through multiplying the productivity by (1 -sea ice concentration) (Stroeve and Meier, 2018). It should be noted that for most longitudes and seasons this results in the extrapolated productivity being zero in these regions beyond the data, so the correction is small.
We assume iodate is taken up by plankton cells, converted to iodide and release of iodide from cells is assumed to occur during the senescence phase, which is lagged 60 days from the iodide production (Chance et al., 2007;Chance et al., 2010;Bluhm et al., 2010;Hepach et al., 2019). It is found that the long-term equilibrium iodide concentrations are not sensitive to this lag timescale changing in the range 0 -120 days (see Section 4.3).
The processes governing the oxidation of iodide to iodate have not been well understood, but it is clear that the oxidation is slow with estimates varying from months to decades (Tsunogai, 1971; ESSOAr | https:/doi.org/10.1002/essoar.10502078.1 | CC_BY_4.0 | First posted online: Wed, 29 Jan 2020 09:38:42 | This content has not been peer reviewed. Confidential manuscript submitted to Global Biogeochemical Cycles 9 Jickells et al., 1988;Luther et al., 1995;Campos et al., 1996;Edwards and Truesdale, 1997;Campos et al., 1999;Truesdale et al., 2000;Waite and Truesdale, 2003), allowing time for physical water transport processes to play an important role in the iodide distribution. This uncertainty in oxidation rate estimates is at least, in part, due to a lack of knowledge as to whether or not the oxidation is biologically mediated. Truesdale et al.'s (2001) study in the Black Sea pointed to a possible role for nitrifying bacteria, and Long et al. (2015) found that iodide oxidation varied proportionally with nitrification in the South China Sea. In a companion paper, recent work by Hughes et al. (2019) reports on results from bacterial culture experiments, which supported a link between nitrification and the oxidation of iodide to iodate. Mixed layer nitrification results in the oxidation of ammonium, produced by the senescence of cells, to nitrite, and then nitrate ( Figure   2), with the former transformation being linked to the oxidation of iodide. However, this is not the only route for ammonium loss in the euphotic zone, since it is also taken up by primary production, and is subject to physical mixing and advection by the ocean circulation. The uptake of nitrite is thought to be negligible, and nitrate from mixed layer nitrification is available, together with 'new' nitrate derived from upwelling, for driving primary production. A biogeochemical model including the process of mixed layer nitrification has been developed by Yool et al. (2007), resolved globally at a resolution of 1 o latitude and longitude, and we have used this approach to allow us to separate the nitrogen cycle into the deep ocean nitrification route, and the mixed layer nitrification route,  originating from below the mixed layer, nitrate from nitrification within the mixed layer, and also ammonium (NH4 + ). Uptake of nitrite (NO2 -) is much less and assumed to be zero. The proportion of nitrate supplied from below and within the mixed layer has been determined by Yool et al. (2007), allowing D/(D+E) to be calculated, and hence the proportion of ammonium which undergoes oxidation to nitrite. It is this flux which is also associated with oxidation of iodide to iodate .
Production of iodide is linked to carbon fixation by an iodine to carbon (I:C) ratio, and hence via the Redfield ratio, is also linked to nitrogen uptake. Linking oxidation of iodide to nitrification in turn requires a stoichiometric link to nitrogen and carbon. We achieve this by using the wellestablished Redfield ratio of C:N = 106:16, and I:C = 3 x 10 -4 reflecting the range reported in the literature, giving I:N = 0.002 for the oxidation of iodide with respect to nitrogen during mixed layer nitrification, provided we assume that the I:C and C:N associated with primary production is the same for bacterial nitrification. The experiments reported by Hughes et al. (2019) show that iodide oxidation only occurs when ammonium oxidising bacteria are present in culture media, and ESSOAr | https:/doi.org/10.1002/essoar.10502078.1 | CC_BY_4.0 | First posted online: Wed, 29 Jan 2020 09:38:42 | This content has not been peer reviewed.
suggest a much higher ratio for I:N of 4.5, but this is in the experimental context of a much higher nitrate concentration environment than is found in the ocean. Indeed, it cannot be the case that the ratio is this high in the ocean, as the much lower surface ocean concentrations of iodine compared with nitrogen would result in the complete oxidation of iodide back to iodate, and near zero iodide concentrations, given the short timescale of order 2 days for mixed layer nitrification to occur (Yool et al., 2007).
We will see below that iodide oxidation by this mechanism has a profound effect on the iodide concentrations, as it results in a spatially variable, rapid, partial oxidation of the iodide inventory, with the remainder being subject to removal by ocean mixing and advection, and much slower chemical oxidation to iodate, which occurs implicitly below the layers represented in the model. This may also provide an explanation for the huge range of oxidation timescales reported in the literature (Chance et al., 2010;Campos et al., 1996;Waite et al., 2006;de la Cuesta and Manley, 2009;Edwards and Truesdale, 1997), with long timescales associated with environments where nitrification is weak/absent, and much shorter timescales where nitrification is active.
The deep ocean iodine cycle is represented in the model by the downwelling of iodide to the deep ocean, and the return of iodate to the bottom model level by upwelling, with a concentration of 500 nM. This assumes that iodide oxidation rates in the deep ocean are fast relative to deep ocean water residence times of decades to millenia, and takes no account of low oxygen environments where iodate reduction could occur, although these are of very limited extent in the present day ocean.

Observed iodide concentrations
In any modelling study, observations are crucial to validate the model. Here we have used a compilation of most of the iodide observations in the literature prior to 2014. A compilation of these observations is described in Chance et al. (2014). To this we have added recent observations from the Indian Ocean , and some unpublished data from the coast off Peru (Croot, unpublished, included in the database described in Chance et al. (2019b)). The individual observations of iodide were then binned into a one-degree latitude and longitude grid, for each of ESSOAr | https:/doi.org/10.1002/essoar.10502078.1 | CC_BY_4.0 | First posted online: Wed, 29 Jan 2020 09:38:42 | This content has not been peer reviewed. the three model levels, for each month of the year, and averaged where multiple observations occurred. Comparisons with the model were then made for the same month, in each location where observed iodide concentration data was present.

Modelling strategy
In order to refine the iodine cycling model, we need to determine the I:C ratio, and oxidation rate/mechanism which allows us to achieve the best spatial fit to the observed iodide distribution.
Ideally, we would like to find universal parameters that allow us to fit the data globally, both in coastal and open ocean locations, and are within the range reported in the literature. Iodide concentrations will be determined by a balance between production and loss, with production and weaker oxidation acting to increase the biogeochemical residence time (and vice versa), in conjunction with the residence time for water in the mixed layer, which is dependent on advection and mixing.
We will therefore run two suites of model experiments, one with the oxidation of iodide over a defined timescale, and the other with oxidation linked to nitrification. In both of these the I:C ratio will be varied over a range consistent with the values reported in the literature.

Results from a simple iodine cycling model
Before considering the results from the full iodine cycling model, we will consider a much simpler, conceptual box model, which will aid interpretation of the full model results.
The production and loss of iodide over an annual cycle can be captured by considering the dominant processes involved, and assuming a physical mixing timescale for iodide in the mixed layer of around one year. In the subtropical gyres this timescale is likely to be considerably longer (e.g. Jickells et al., 1988), but elsewhere it is plausible, and provides a simple approach to investigate the dominant processes involved in determining iodide concentrations. In this simple model, the annual production of iodide is assumed to be equal to the production of organic carbon, multiplied by an I:C ratio. Following an annual cycle of mixed layer deepening and shoaling, the proportion of iodide remaining in the mixed layer is assumed to equal MLDmin/MLDmax, with the remainder removed from the mixed layer during shoaling. The oxidation pathway driven by mixed layer nitrification converts a proportion of the iodide produced back to iodate. The residual iodide inventory is then distributed throughout the annual mean mixed layer to give a mean mixed layer concentration. there is upwelling. This favours high iodide in these regions. Oxidation of iodide by nitrification is greatest in the subtropical gyres, lower in equatorial regions, and lowest at high latitudes, resulting from the link to the nitrification model of Yool et al. (2007). This results in the greatest oxidation of iodide in the subtropical gyres and lower latitudes outside of equatorial regions. MLD variations are generally greatest at high latitudes, resulting in the greatest loss of iodide through mixing, so long as the lifetime of iodide with respect to oxidation is comparable to the seasonal timescale of mixed layer cycling. The MLD itself is also greatest at high latitudes, although this has strong seasonal variability. These competing factors result in generally higher iodide concentrations at low latitudes, with the highest concentrations occurring where productivity is high, MLDs are shallow, seasonal MLD variations are small, and oxidation by nitrification is weak. In both the Atlantic and Pacific this is on the eastern side of the basin, where predicted iodide concentrations are greatest. High iodide is also predicted in the Arctic, where productivity is lower, but MLDs are shallow, and have little seasonal variation. The subtropical gyres have low iodide, due to low productivity and strong oxidation of iodide linked to mixed layer nitrification.
The full model (Section 4) will show that the iodide residence time is considerably longer than a year in these gyres, resulting in an underestimate by this simple model. proportion of ammonium subject to nitrification in the mixed layer (Yool et al., 2007), (d) ocean productivity (Behrenfeld and Falkowski, 1997), (e) predicted mixed layer iodide inventory, and (f) predicted mixed layer iodide concentration.

The full iodine cycling model
The model was run for a range of I:C ratios, from 4.7 x 10 -6 to 1.2 x 10 -3 , increasing in multiples of two. This range of values covers that reported in the literature (Elderfield andTruesdale, 1980, Jickells et al., 1988;Chance et al., 2010;Hepach et al., 2019). Two methods of iodide oxidation were used, firstly a simple parameterisation representing the actual processes by a timescale for ESSOAr | https:/doi.org/10.1002/essoar.10502078.1 | CC_BY_4.0 | First posted online: Wed, 29 Jan 2020 09:38:42 | This content has not been peer reviewed.
Confidential manuscript submitted to Global Biogeochemical Cycles 15 conversion of iodide to iodate, and secondly via a coupling to the nitrogen cycle through nitrification.

Oxidation parameterised by a timescale conversion of iodide to iodate
The model was run with oxidation timescales of 1, 2, 4, 8 and 16 years, reflecting the large range of rates estimated in the literature (e.g. Campos et al., 1996;Edwards and Truesdale, 1997). hence broadly latitude. Increasing the I:C ratio increases production of iodide, and decreasing the oxidation timescale increases the rate of conversion back to iodate. Hence with a low I:C ratio and long oxidation timescale, the predicted concentrations are generally higher than observed, whereas with a small I:C ratio, and short oxidation timescale, the model underestimates iodide concentrations relative to observed values.
At low SSTs (< 5 o C) agreement between model and observations is only achieved with higher I:C ratios, with the oxidation timescale having little influence. This is because there is a strong seasonal cycle in MLD, which acts to remove iodide from the mixed layer within an annual timescale, and is the dominating iodide loss process.  Above 15 o C the model/observation fit is more problematic. There is a consistent tendency across the I:C and oxidation timescale parameter space for a relative overestimation of modelled iodide compared to the available data between 15 o C and 25 o C (in the subtropical gyres), compared with an underestimation above these temperatures (in equatorial regions). This is the case in both coastal and open ocean locations. This could indicate that the I:C ratio is higher in equatorial regions than in the gyres, or that oxidation is more rapid in the subtropical gyres. A variation in I:C ratio could be due to different types of plankton dominating primary production. An analysis of plankton type distributions (Alvain et al., 2008) does indeed show a separation of types between these regions, with Synechococcus dominating in equatorial regions, whereas Prochlorococcus dominates in the subtropical gyres. The difference between model and observed iodide is consistent with work by Wong et al. (2002), who found that Synechococcus have some of the highest rates of iodide production.
A sensitivity experiment was performed, in which the rate of production of iodide from iodate was temperature dependent, increasing by 2, 4, 8 and 16-fold for a doubling of SST. It was found that an eight-fold increase in production of iodide for a doubling in SST was required to remove the equatorial low-iodide bias, which is a far greater temperature dependency than permitted by physical chemistry alone (Luther et al., 1995). We therefore conclude that this is unlikely to be the reason for the model bias.
The dependence of iodide production on productivity is well established, but it is also noted that the model iodide biases are consistent with this dependency, with over prediction in mid-latitude coastal regions, and an under prediction in the low latitudes. A sensitivity experiment was performed in which the observed productivity was replaced with its globally averaged seasonal cycle. Interestingly, this considerably reduced the model biases, and we will see in Section 4.2 that this is consistent with a link between production and oxidation, via the process of nitrification.
Another possible explanation for the poor fit of the model in some regions lies with the oxidation rate, which may vary spatially in the ocean. The representation of oxidation by a timescale is a simple approach designed to avoid use of a mechanism-dependent parameterisation, be it physical chemistry (and therefore temperature dependent) or biologically mediated, which may also be temperature dependent. It should be noted that removal by mixing occurs in parallel to these processes, and is represented by the model. With the exception of processes in the sea surface ESSOAr | https:/doi.org/10.1002/essoar.10502078.1 | CC_BY_4.0 | First posted online: Wed, 29 Jan 2020 09:38:42 | This content has not been peer reviewed. microlayer, the purely chemical oxidation of iodide in the seawater is thought to be so slow it can be considered insignificant (Luther et al., 1995). This rate would increase with temperature, and therefore result in a greater oxidation of iodide in equatorial regions, where the model is underestimating concentrations. Inclusion of a temperature-dependent oxidation rate would therefore increase the tendency for the model to underestimate concentrations in equatorial regions.

Oxidation driven by mixed layer nitrification
Biologically mediated iodide oxidation by bacteria has been shown to occur (Gozlan, 1968;Fuse et al., 2003;Amachi et al., 2004;Amachi et al., 2005) and recent laboratory microcosm experiments have demonstrated that it may be brought about by nitrifying bacteria . This recent discovery prompted the inclusion of nitrification-linked oxidation in the model. This mechanism is discussed in Section 2.2, and is described by Equation 4b in the Appendix. The linking of the oxidation of iodide to nitrification, at a ratio stochiometrically consistent with that of iodide production, results in a proportion of the iodide produced being oxidised to iodate over a timescale of days, assuming iodide is released during senescence and ammonium oxidation has a timescale of days (Yool et al., 2007) while the remainder is subject to oxidation by an unspecified, possibly purely chemical process (which we will assume has a much longer timescale), and physical mixing. Figure 3 (top-right) shows the proportion of mixed layer nitrate supplied by nitrification, corresponding to the proportion of iodide subject to oxidation, as calculated by Yool et al. (2007). It is immediately apparent that the largest proportion of iodide subject to oxidation is in the subtropical gyres, where the model overestimates iodide concentrations.
The model was run with the same range of I:C ratios, but with this alternative oxidation mechanism. The general response to changing I:C ratio is the same as with oxidation over a prescribed timescale ( Figure 5), but the overestimation of iodide for SSTs in the range 15 o C -25 o C is considerably reduced, both for coastal and open ocean locations, with the best fit obtained using an I:C ratio of 3.75 x 10 -5 similar but about two times lower than in previous model runs.

19
This value is within the range reported in the literature, and corresponds well to the ratio found for some types of phytoplankton  and in oceanic studies (Campos et al., 1996;Chance et al., 2010). Linking oxidation to nitrification fundamentally changes the way iodine is cycled between iodate and iodide. Previous assertions that oxidation occurred at a given rate, which is possibly temperature dependent, and/or biologically mediated, and hence spatially variable, fail to capture a key aspect of the process which results from the link to nitrification. The oxidation of iodide back to iodate in tandem with the oxidation of ammonium results in a proportion of the iodide being oxidised rapidly in the surface layer (time scale order days, Yool et al., 2007), whilst the remainder is removed from the mixed layer by a slower physical mixing pathway to the ocean interior where much slower oxidation occurs. In regions where vertical mixing is strong (e.g. high latitudes), mixing is the dominant removal mechanism, and iodide has a residence time in the surface waters of around one year. However, where vertical mixing is much less intense (e.g. the sub-tropical gyres), the proportion of iodide remains unoxidized and therefore accumulates year-ESSOAr | https:/doi.org/10.1002/essoar.10502078.1 | CC_BY_4.0 | First posted online: Wed, 29 Jan 2020 09:38:42 | This content has not been peer reviewed.
Confidential manuscript submitted to Global Biogeochemical Cycles 20 on-year, and is slowly mixed out, resulting in a much longer residence time of the iodide in the surface waters. This coupling of iodide oxidation to the euphotic zone biogeochemistry of nitrogen may help explain why there is such a large range of oxidation timescales reported in the literature (Tsunogai, 1971;Campos et al., 1996;Edwards and Truesdale, 1997;Truesdale, 2001;Zic and Branica, 2006;Zic et al., 2013), as the actual removal process comprises rapid oxidation of part of the iodide inventory in conjunction with nitrification, and the relatively slow physical removal of the remainder by mixing to the ocean interior, followed by slow chemical oxidation.

Comparison with observed ocean sections
We will now make comparisons between the modelled and observed iodide for five ocean sections: a trans-Atlantic meridional section (Truesdale et al., 2000), a South Atlantic meridional section (Campos et al., 1999), a South Atlantic zonal/meridional section (Bluhm et al., 2011), an East Atlantic meridional section (Baker (unpublished)), and an Indian Ocean section . Data used for this comparison is available in Chance et al. (2019b). Data from the first four were taken from the database in Chance et al. (2014), and the Indian Ocean data is from Chance et al. (2019a). Data used for this comparison is available in Chance et al. (2019b). Model comparisons with ocean sections allows spatial and inter-basin comparisons to be made.
We have seen in Section 4.2 that whilst a best fit between model and observations can be made by selecting an appropriate I:C ratio, there is still considerable variation between the model and observations at each particular SST. Figure 6 shows comparisons between model and observed iodide concentrations for each section, and for a range of I:C ratios. Taking each section in turn, it can be seen that the model can be made to fit each section with considerable skill, but that a different I:C ratio is required for each section. The two meridional Atlantic sections (extending from 45 o S to 45 o N) require a relatively low ratio of 1.9 x 10 -5 . The two south Atlantic sections require a higher I:C ratio, and it is apparent that within the latitudinal range of these sections the best fit requires an increasing I:C ratio with increasing latitude. The Campos et al. (1999)  Confidential manuscript submitted to Global Biogeochemical Cycles 21 lower value of around 1 x 10 -5 near the equator. It is clear that the I:C ratio required to fit the model to the observations is around ten times greater at high latitudes than low latitudes. However, it is also interesting to note that a relatively high ratio is required in the Indian Ocean south of only 20 o S.

Discussion
Having established that the model is capable of reproducing the observed iodide distributions with an appropriate I:C ratio consistent with the relatively wide range of values reported in the literature, and an oxidation mechanism that has been shown to occur in microcosm experiments, we will now use the model to broaden our understanding of the role of processes in the ocean iodine cycle.

Spatial variation of the I:C ratio
The finding that the I:C ratio varies spatially raises the question of whether a global field of I:C can be derived from the model. There is no reason to expect the I:C ratio to be globally constant; even the Redfield ratio of C:N:P has in reality some variability, and the variability for other elements may be greater (Moore et al., 2013). The RMS error between the model and iodide observations was calculated for each model I:C ratio, in bins of 5 o C increments in SST. An empirical function describing the optimum I:C ratio required to minimise the model RMS error is shown in Figure 7. The optimum I:C ratio decreases with increasing SST from 3 x 10 -4 at 0 o C to 3.8 x 10 -5 at SSTs of > 15 o C. The spatial distribution of I:C derived from this function is shown in Figure 8a.  An alternative approach is to derive a zonally constant I:C, taking the zonal mean of the best fit I:C ratio for each iodide observation point. We have already seen that the best fit I:C ratios in the Indian Ocean south of 20 o S are greater than in the Atlantic, so we derive a separate zonal mean for the Indian Ocean from the Atlantic and poorly observed Pacific oceans, with a smooth transition between the ocean basins. It should be noted that in the absence of any observations in the Arctic, the I:C ratio was set to that at the latitude of the northern most observation in the Atlantic. This I:C field is shown in Figure 8b. The SST-derived field has a much higher I:C ratio in the Arctic, which is a result of the observational evidence from the Southern Ocean with similar SSTs. The zonal mean approach results in more latitudinal structure in the I:C ratio, including a marked asymmetry in the subtropical Atlantic, and a much greater I:C in the subtropical Indian Ocean. Confidential manuscript submitted to Global Biogeochemical Cycles 24 Figure 8: I:C production ratio derived from (a) a best fit to SST, using the relationship in Figure   7, and (b) using the zonal mean of the best fit I:C for the Atlantic and Pacific, and Indian oceans. constant I:C production ratio, the second for an SST dependent I:C production ratio (see Figure   8a), and the last a zonal mean I:C production ratio for the Atlantic and Pacific, and Indian oceans.
Overall, the modelled iodide is in best agreement with observations when the I:C ratio is parameterised as a function of SST, as shown by the RMS errors ( Figure 10). The model still tends to underestimate iodide where SST > 20 o C, and overestimate for 5 o C < SST < 15 o C. It might be expected that the dependency of the I:C ratio on SST would eliminate this bias completely, but the residual differences between the model and observations is consistent with the ocean circulation playing an important role in redistributing iodide across SST contours. Selection of the best fit I:C ratio assumed the iodide depended only on the local I:C ratio, whereas advection could potentially bring iodide from lower latitude regions where the best fit I:C is lower, and higher latitude regions where the best fit I:C is greater. Since the I:C ratio was globally constant in the suite of model runs from which the local best fits were determined, the I:C ratio and iodide concentrations at lower latitudes would be too great, and at higher latitudes too small with respect to the SST-dependent I:C ratio case. Thus, in the runs used to determine the best fit I:C ratio, advection of iodide from regions with higher SST and I:C ratio is too great, and from lower SST and I:C ratio, too small. This is consistent with the tendency of the model to underestimate iodide at low latitudes, and overestimate at mid latitudes. This suggests that the surface water iodide residence time is sufficiently long that horizontal as well as vertical mixing processes may be important. We also suggest that the I:C ratio may vary systematically with SST which probably implies a variation with phytoplankton species and communities.

Comparisons with statistically-derived surface iodide fields
Modelling the ocean iodine cycle has produced a new estimate of surface iodide concentrations, which can be compared with other estimates from existing statistical and non-parametric machine learning methods. These statistical methods attempt to fit the observed iodide data using a suite of correlations to other more widely observed ocean variables including temperature, salinity, mixed layer depth and nitrate. Here we will use the model configuration that uses an SST-dependent I:C Confidential manuscript submitted to Global Biogeochemical Cycles 28 ratio, as this has a lower RMS error with observations than the latitude/basin I:C dependent approach. Comparing the model iodide field with observations, where they exist, shows a generally good agreement between the model and observed values (Figure 11a -c), with the model tending to slightly over-estimate iodide in the Atlantic, and under-estimate iodide in the Indian Oceans, as we have seen in previous sections. Elevated concentrations are generally confined to the eastern and coastal regions of the low and mid latitude ocean basins, and it is interesting to note that the majority of the observations are in these regions. High iodide is also predicted in the Arctic, but no direct observations are available to support this. However, periods of low tropospheric ozone in the atmospheric boundary layer during spring, driven from the ocean surface, have been observed in the Arctic (Wessel et al., 1998). This depletion of tropospheric ozone could be driven by iodine emissions from the Arctic Ocean. Chance et al. (2014) proposed a parameterisation of iodide in terms of a number of oceanic variables (Figure 11d). This has a strong dependency on latitude, but does not predict much variation with longitude. Where observations exist, agreement with iodide concentrations predicted by the model and those predicted by the Chance et al. (2014) equation is good, but elsewhere large differences exist (Figure 11e).
MacDonald et al. (2014) also parameterised iodide concentrations, but used a simpler approach, relating ln(I -) with SST -1 using a subset of the observational database in Chance et al. (2014) ( Figure 11f). This parameterisation is currently the most widely used in atmospheric models (e.g. Sherwen, 2016;Sarwar, 2016). Iodide fields predicted using this relationship are again broadly consistent with observations where they exist, but are lower than the Chance et al. parameterisation over much of the low and mid latitudes, away from the regions with observations. The MacDonald parameterisation generally predicts lower iodide concentrations than the model at high latitudes, and higher concentrations at low latitudes ( Figure 11g). This pattern is consistent with using just SST as a predictor of iodide, compared to the model approach which incorporates a range of processes.
Sherwen et al. (2019a) adopted a machine-learning approach to predict iodide from an expanded compilation of iodide observations . This approach assigns an iodide concentration to each oceanic location based on observed iodide values at locations with related combinations of biogeochemical and oceanographic properties. This machine learning based parameterisation yields a similar iodide distribution to that predicted by the multivariate equation in Chance et al., but with generally greater iodide at higher latitudes ( Figure 11h). This is consistent with both methods using similar oceanic properties (e.g. SST, salinity, nitrate) to predict iodide.
Comparison of model and machine learning predictions shows the latter technique predicts higher iodide throughout most of the ocean (Figure 11i).
In each comparison, the modelled iodide has more longitudinal variation than the statistical methods suggest. Observations are currently insufficient to assess whether such a longitudinal  with the supply of iodate from below the mixed layer. In the South Pacific subtropical gyre this depletion is sufficient to limit iodide production. Doubling the MLD effectively doubles the volume of water in which the iodide is stored, and therefore reduces iodide concentrations accordingly (Figure 12d). Iodide increases in some high latitude locations, but this is because the MLD increase is limited by the ocean depth, so where the maximum MLD extends near to the ocean floor, the seasonal MLD variation is effectively reduced, reducing the seasonal loss each year.
Oxidation of iodide to iodate acts to reduce iodide concentrations, hence removing the oxidation process increases iodide, especially in the subtropical gyres. It is here that oxidation is the dominant removal process, as vertical mixing is weak. At high latitudes, where removal is dominated by the seasonal cycle of MLD, oxidation has a much smaller impact (Figure 12e).
Advection redistributes heat and salt, and also all other tracers, around the ocean. The impact of this advection depends on the life time of the tracers, and their spatial gradients. Removal of advection from the model results in increased iodide everywhere except the Arctic (Figure 12f).
This shows that the vertical component of the circulation acts either to reduce iodide through the upwelling of iodide-depleted water, or remove iodide through the downwelling of iodide-rich water, the net effect of both of which is to remove iodide to depth, where it undergoes long-term oxidation to iodate. In the Arctic, however, iodide decreases without advection, showing that at least part of the iodide results from advection from the North Atlantic, probably associated with the spring bloom. Truesdale et al. (2003) also found iodide concentrations to be dependent on advection in the Skagerrak.
Iodide is thought to be released from most types of phytoplankton cells during the senescence phase (Bluhm et al., 2010), with a lag estimated at around 60 days. The sensitivity of iodide concentrations to this lag was tested by using lags of zero and 120 days in the model. Earlier release results in an increase in iodide in some coastal locations, and the Arabian Sea. Delayed release results in a small decrease in iodide in some mid latitude locations (Figure 12g, h). These changes are due to the interaction of the release of iodide with seasonal MLD variations.
The net surface fresh water flux, resulting from precipitation, evaporation and runoff, acts to dilute/concentrate the mixed layer. Removal of the freshwater flux has a corresponding impact on iodide concentrations. Net freshwater input dilutes iodide at high latitudes, whereas net freshwater loss concentrates iodide. This has a significant impact where MLDs are shallow, and the flux is large (Figure 12i), for example the Arctic.
Lastly, the I:C ratio for the production of iodide acts as a multiplier to the production of C, and the impact of changes in the I:C ratio correspond to changes in productivity (Figure 12j, b).
These model sensitivity tests give an important insight into the processes driving ocean iodide concentrations, and show that surface iodide concentrations result from the interaction of several processes, which are dominated by primary productivity, the I:C ratio, MLD, oxidation, advection, and the oceanic fresh water flux. All of these are likely to change during the coming decades and centuries as atmospheric greenhouse gas concentrations increase, and impact climate and ocean chemistry. For instance, heating of the upper layers of the ocean may reduce MLDs, and nitrification rates may decrease due to ocean acidification (Beman et al., 2011), resulting in less oxidation. Both of these changes would act to increase iodide concentrations. Further studies would be needed to quantify potential future changes in the ocean iodide cycle.

Conclusions
We present the first physical and biogeochemical model for the cycling of iodine in the ocean. In the model production of iodide from iodate is driven by primary production, and it is found that the I:C ratio for production of iodide increases by an order of magnitude between low and high latitudes, yet this range lies within those reported in the literature. Evidence from oceanic and laboratory-based studies show a link between the oxidation of iodide and ammonium by nitrification. In the model it is found that the spatial distribution of observed iodide can best be reproduced if oxidation is also linked to nitrification, which has a distinctive spatial pattern. Using the model to explore the sensitivity of surface iodide reveals that the distribution results from several interacting processes, both physical and biogeochemical, and that changes in any of these is likely to result in changes to surface iodide concentrations. Significant differences are found between global surface iodide distributions derived from parameterisations, and those predicted by the model. The model predicts much greater longitudinal variations of iodide within ocean basins, which cannot be captured statistically from the predominantly meridional observational transects. The model also predicts high iodide concentrations in the Arctic, where there are currently no observations. These aspects of the iodide distribution are consistent with advection of iodide within the ocean gyres and major currents linking ocean basins, reflecting the relatively long lifetime of iodide in surface waters, which cannot be captured by statistical relationships between iodide and local oceanic variables. The model predicted surface iodide distribution differs sufficiently from that derived by statistical and machine learning techniques to impact atmospheric model predictions of ozone and air quality. We now await new observations of iodide in regions currently without observations (in particular the Arctic and centres of the subtropical gyres) to further validate our process-based prediction of surface iodide concentrations.
runs. Iodide production occurs only in the mixed layer (Eq. 1), and results in a corresponding loss of iodate, and vice versa (Eq. 2).
Two mechanisms for the oxidation of iodide to iodate are explored in this paper. In the first, oxidation occurs over a specified timescale, which parameterises the actual processes involved (Eq. 4a). Experiments with the model show that linking oxidation to nitrification in the mixed layer ) significantly improves the model fit to observations. The production of iodide, driven by the assimilation of carbon, also has an implied link to the nitrogen flux, which can be determined by a Redfield ratio. With oxidation driven by nitrification, the proportion of iodide oxidised to iodate is given by the proportion of nitrogen (in the form of ammonium) that is oxidised to nitrite in the surface ocean layer (Eq. 4b).
The tracers iodide and iodate are subject to advection by the monthly mean velocities from the OCCAM ocean general circulation model (Aksenov et al., 2010) (Eq. 5, 6 and 7), and horizontal and vertical mixing at rates of Kh = 2000 m 2 s -1 and Kz = 1 x 10 -4 m 2 s -1 respectively. In addition, seasonal mixed layer depth changes result in the exchange of tracers between the upper two model layers, and complete mixing of existing and additional tracers in the thickening layer.

Model equations
In the mixed layer where PROD is the monthly mean production of carbon, LAG is the time lag for iodide production from carbon assimilation (60 days), IC is the ratio of iodide to carbon production, MLD is the seasonally varying mixed layer depth, and is the iodide saturation term, where IO3limit = 50 nM.
Oxidation is represented by either a timescale, such that or is linked to mixed layer nitrification, such that where REGEN is the proportion of nitrogen subject to nitrification in the mixed layer (Yool et al., 2007).
The transport of iodide and iodate (represented by tracer T) is given by where u, v and w are the layer-dependent zonal, meridional and vertical velocities.
Below the mixed layer there is no production or oxidation of iodide, with changes in iodide and iodate being driven by advection and mixing (Eq. 6 and 7).

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In the deep ocean iodide and iodate are assumed to have concentrations of 0 nM and 500 nM respectively , and upward advection transports iodide and iodate with these concentrations into the bottom model layer (Figure 1).
Each model simulation was run for 100 years, which allowed iodide and iodate concentrations to reach an equilibrium.