Radium-228-derived ocean mixing and trace element inputs in the South Atlantic

. Trace elements (TEs) play important roles as micronutrients in modulating marine productivity in the global ocean. The South Atlantic around 40 ◦ S is a prominent region of high productivity and a transition zone between the nitrate-depleted subtropical gyre and the iron-limited Southern Ocean. However, the sources and ﬂuxes of trace elements to this region remain unclear. In this study, the distribution of the naturally occurring radioisotope 228 Ra in the water column of the South Atlantic (Cape Basin and Argentine Basin) has been investigated along a 40 ◦ S zonal transect to estimate ocean mixing and trace element supply to the surface ocean. Ra-228 proﬁles have been used to determine the horizontal and vertical mixing rates in the near-surface open ocean. In the Argentine Basin, horizontal mixing from the continental shelf to the open ocean shows an eddy diffusion of K x = 1 . 8 ± 1 . 4 (10 6 cm 2 s − 1 ) and an integrated advection velocity w = 0 . 6 ± 0 . 3


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Y.-T. Hsieh et al.: Radium-228-derived ocean mixing and trace element inputs al., 2004). However, the trace element sources and fluxes that fuel this region remain poorly constrained. Modelling and experimental studies have both suggested that this region is iron limited or co-limited (Moore et al., 2004;Browning et al., , 2017. It also has the lowest reported dissolved zinc concentrations in the global oceans (Wyatt et al., 2014), and the replacement for zinc by cobalt is crucial for phytoplankton, particularly in low-zinc regions (Price and Morel, 1990). Thus, knowing the sources and fluxes of iron, zinc, and cobalt can improve our understanding of the limiting factors for productivity in this highly productive region.
Oceanic mixing and advection facilitate the transport of nutrients to the euphotic zone (Oschlies, 2002). The distribution of TEs in the surface ocean is primarily controlled by the inputs from the continental shelves (i.e. rivers, submarine groundwater discharge (SGD), and sediments), deep ocean waters (regeneration, continental slopes, and hydrothermal vents) and aeolian inputs, with these mediated by lateral and vertical mixing (diffusive / turbulent mixing), advection, particle scavenging and biological uptake. In particular, deep winter mixing has been shown to be an important mechanism bringing TEs from below the mixed layer to the surface ocean (Tagliabue et al., 2014;Achterberg et al., 2018Achterberg et al., , 2020Rigby et al., 2020). Geochemical tracers for ocean mixing can therefore be used to indirectly estimate TE inputs and outputs in the upper ocean, e.g. tritium ( 3 He) (Jenkins, 1988;Schlitzer, 2016) and radium isotopes ( 228 Ra) (Cai et al., 2002;Ku et al., 1995;Nozaki and Yamamoto, 2001;Sarmiento et al., 1990;Moore, 2000;Charette et al., 2007;Sanial et al., 2018).
The four naturally occurring radium isotopes cover a wide range of half-lives ( 226 Ra, T 1/2 = 1600 years; 228 Ra, T 1/2 = 5.75 years; 223 Ra, T 1/2 = 11.4 d; 224 Ra, T 1/2 = 3.66 d), which enables us to study oceanic processes at different timescales. Ra-228 is continuously produced through the decay of 232 Th in shelf sediments, released into seawater, and then transported into the surface open ocean by mixing or advection. The half-life of 228 Ra is much shorter than the estimated Ra residence time by removal of ∼ 500 years (Moore and Dymond, 1991). The distribution of 228 Ra in the ocean is therefore mainly controlled by ocean transport and radioactive decay, and can be used to estimate lateral mixing from the coastal shelf or continental slope to the open ocean (Kaufman et al., 1973;Knauss et al., 1978;Yamada and Nozaki, 1986;Sanial et al., 2018). Subsequent downward mixing from the surface can also be used to assess vertical mixing in the upper water column (Charette et al., 2007;Sarmiento et al., 1976; van Beek et al., 2008). Radium-228 has also been used as a conservative tracer to estimate submarine groundwater discharge (SGD) (Windom et al., 2006;Moore et al., 2008;Kwon et al., 2014;Rodellas et al., 2015;Le Gland et al., 2017), river inputs , continental shelf (Rutgers van der Loeff et al., 1995;Charette et al., 2016;Sanial et al., 2018;Kipp et al., 2018a) and hydrothermal inputs (Kipp et al., 2018b).
Previous work has assessed TE inputs to the wider South Atlantic from rivers , atmospheric dust (Gaiero et al., 2013), shelf sediments (Graham et al., 2015), the Agulhas current (Paul et al., 2015) and hydrothermal vents . There are also studies of TE distributions and basin-scale inputs in some areas of the South Atlantic (e.g. Chever et al., 2010;Bown et al., 2011;Noble et al., 2012). Two UK GEOTRACES cruises in 2010-2012 provided a significant increase in such observations, focusing particularly on 40 • S (Homoky et al., 2013;Browning et al., 2014;Wyatt et al., 2014Wyatt et al., , 2020Chance et al., 2015;Menzel Barraqueta et al., 2019). These published studies did not assess the fluxes of TEs by ocean mixing and transport. In this study, we address this issue using samples taken on the two 40 • S Atlantic UK GEOTRACES cruises. We investigate the distributions of 228 Ra, as well as 226 Ra, in both the Argentine and Cape basins of a 40 • S latitudinal transect in the Atlantic Ocean. This is also the first exploration of the vertical and horizontal 228 Ra distributions reported for the Cape Basin. We investigate the application of seawater 228 Ra as a tracer for vertical and horizontal mixing in the surface South Atlantic, to provide estimates of the dissolved TE (dTE) fluxes, with a focus on cobalt, iron, and zinc, in the micronutrientdepleted euphotic zone.
2 Study sites and methods

Hydrographic setting
The study was conducted from the RRS Discovery and RRS James Cook during two UK GEOTRACES cruises, D357 and JC068, along the GA10 40 • S transect of the Atlantic Ocean (Fig. 1). The surface currents show dynamic interaction and mixing on both the western and eastern sides of this transect. In the Argentine Basin, the Río de la Plata estuary is located on the western margin of the transect. The boundary Brazil Current (BrC) and Malvinas Current (MC) meet between 33 and 45 • S along the continental margin of South America and these become the South Atlantic Current (SAC) transporting water eastwards along 40 • S. The water from the BrC is captured between Stn20 and Stn21 with a strong west to east gradient in salinity and other chemical and physical properties, which also suggests a limited exchange of water across the continental shelf break (see below). In the Cape Basin, the SAC turns northeast before reaching the continent of Africa, and the Agulhas Current (AC) adds warm water eddies from the Indian Ocean. The warm and salty water of the AC was sampled in the top 500 m at Stn2 (Fig. 1b). These currents meet and become the Benguela Current (BeC) flowing through the Cape Basin and into the South Atlantic.

Water sampling
Seawater samples for Ra analysis were collected from 14 stations on the D357 and JC068 cruises (Fig. 1). The first  Key et al., 1990Key et al., , 1992aGEOSECS: Ku and Lin, 1976;ANT XV/4: Hanfland, 2002). Surface currents are shown with arrows. (b) Salinity profiles along the cruise track of UK GEOTRACES GA10 are labelled with water masses. Vertical lines indicate the stations where vertical Ra water profiles are available. cruise (D357) took place in the SE Atlantic (Cape Basin) between October and November 2010; the second cruise (JC068) took place along the whole 40 • S transect between December 2011 and January 2012. For radium isotope analyses, the Cape Basin samples were only taken from D357, and the Argentine Basin samples were taken from JC068. For TEs, samples were taken from both D357 and JC068. Stations from these cruises are shown along with those from previous Ra studies (e.g. GEOSECS and TTO) in this region (Fig. 1a).
A total of 48 samples were analysed for 228 Ra / 226 Ra ratio and 228 Ra concentration, and 33 samples for 226 Ra concentration, collected using three different sampling techniques during the cruise. Surface seawater samples (80-100 L) at 5 m depth were collected via a trace-metal clean seawater supply (fish) using a Teflon bellow pump (Almatec-A15) and acid-cleaned tubing. Samples between 50 and 400 m were collected using a standard conductivity, temperature, and depth (CTD) rosette, typically sampling from four 20 L Niskin bottles. These samples were stored briefly in low-density polyethylene (LDPE) cubitainers and then filtered through Mn-fibre cartridges by gravity (flow rate < 0.5 L min −1 ) on board for the extraction of radium iso-topes (Moore et al., 1985;Reid et al., 1979). In addition, large-volume seawater sampling (300-600 L) was carried out using in situ stand-alone pump (SAP) systems, pumping seawater over Mn fibres in polypropylene cartridges (van Beek et al., 2008) at flow rate of 2-5 L min −1 at three selected sampling stations (Stn1, Stn3, and Stn4.5). As the cartridge Ra collection efficiency varies hugely, ranging from 70 % to 128 % (Geibert et al., 2013), all samples collected by these collection techniques (pump, CTD, and SAP) were only used for measurement of 228 Ra / 226 Ra ratios. To address the efficiency issue, for most samples, a separate sample of 250 mL seawater was also collected for measurement of 226 Ra concentration. This method provides the advantage of allowing a correction for variable efficiencies during the sample preparation.
Trace element samples were collected using a titanium CTD rosette fitted with trace-metal clean Tefloncoated Niskin bottles and filtered on board through 0.8/0.2 µm polyethersulfone (PES) membrane cartridge filters (AcroPak500™, Pall) before analysis. All the TE data and fluxes reported and discussed in this study refer to the dissolved fraction only. The data of zinc and cobalt were measured and published by Wyatt et al. (2014Wyatt et al. ( , 2020. Some of the iron data were determined and published by Browning et al. (2014) and Clough et al. (2016). All the TE data are available on the GEOTRACES Intermediate Data Product (IDP) 2017 (Schlitzer et al., 2018).
All the trace-metal cleaning procedures followed the GEOTRACES sampling protocols (Cutter et al., 2010). In brief, the sample tubing and bottles were rinsed with Milli-Q water and filled with 0.1 M HCl for 1 d. After emptying the acid, the tubing and bottles were rinsed thoroughly with Milli-Q water. The tubing and bottles were also rinsed with open-ocean seawater before sampling.

Ra isotopes analysis
Mn-fibre samples were first counted on board using a fourchannel radium delayed coincidence counting (RaDeCC) system for 224 Ra, 223 Ra, 228 Th, and 227 Ac (Moore and Arnold, 1996), but the data for 224 Ra, 223 Ra, 228 Th, and 227 Ac are not discussed in this paper. After the counting, Ra was purified using the following procedure for precisely measuring 228 Ra / 226 Ra ratios and 228 Ra concentrations by a Nu Instrument multi-collector inductively coupled plasma mass spectrometry (MC-ICP-MS) at the University of Oxford following the procedures established by Hsieh and Henderson (2011). Mn fibres were ashed at 550 • C for 6 h and then leached with distilled 6 N HCl to remove Ra from the ashed fibres. Ra was then co-precipitated with Sr(Ra)SO 4 in the leached solution, centrifuged, and cleaned with 3 N HCl and pure H 2 O a few times until the pH was > 4. To increase the dissolution rate, Sr(Ra)SO 4 was converted to Sr(Ra)CO 3 by adding 2 mL 1 M Na 2 CO 3 solution and heated on a hotplate for 3 h. After centrifuging and discarding the supernatant, Sr(Ra)CO 3 was finally dissolved in 2 mL 6 N HCl for ion exchange column chemistry, using Bio-Rad AG50-X8 cation exchange resin (to separate Ra and Ba from 228 Th and other matrix elements, e.g. Ca, Sr, and Mn) and Eichrom Sr-Spec resin (to separate Ra from Ba to avoid molecular interferences during MC-ICP-MS analysis).
Smaller seawater samples (250 mL) collected for 226 Ra were spiked with a 228 Ra spike (Hsieh and Henderson, 2011) and the Ra was purified by the precipitation of CaCO 3 and processing with ion exchange columns of AG1-X8, AG50-X8, and Sr-Spec resin for the measurement of 226 Ra concentrations by MC-ICP-MS (Foster et al., 2004). In general, the contribution of seawater 228 Ra (< 0.05 attomole) is negligible, compared to the spiked 228 Ra signal (≈ 70 attomole). Assessments of overall chemical blanks were conducted the same way as for the samples throughout the whole chemical procedures, except that there was no added seawater. The blanks were found to contribute less than 1 % of the 226 Ra in the sample and were not detectable for 228 Ra.
During the MC-ICP-MS analyses, 228 Ra and 226 Ra were measured simultaneously on two ion counters, and the uranium standard CRM-145 was used to bracket each sample for the mass bias and ion counter gain corrections. Instrumental memories of 228 Ra and 226 Ra were also detected on ion counters before each measurement. The machine memory was about 0.2 ± 0.1 cps (counts per second) (n = 16, 2 SE). The memory correction was insignificant for 226 Ra, because the ratio of memory to sample signal is small (< 10 −4 ). However, the memory correction could be significant for samples with low 228 Ra activities and count rates. For instance, the count rate during analysis of 228 Ra on the sample collected at 4741 m at Stn4.5 was only 0.5 cps. At this low count rate, instrumental memory contributed ∼ 40 % of the signal to the sample 228 Ra signal and the uncertainty of memory correction becomes substantial. In this study, most of the surface and deep waters in the South Atlantic were measured at count rates > 2 cps 228 Ra, which provides assurance that the contribution of the instrumental memory uncertainty to the total uncertainty is < 10 %.
For samples without accompanied 226 Ra measurements, silica data (Table 1) are used to assess 226 Ra activities (Appendix A). The Atlantic Ocean 226 Ra-Si relationship is based on the GEOTRACES (GA03), GEOSECS, and TTO datasets ( Fig. A1 in Appendix A, Ku and Lin, 1976;Key et al., 1990Key et al., , 1992aCharette et al., 2015). This relationship is used to determine 226 Ra activities in the 27 cases where no subsamples were collected for separate 226 Ra analysis (such 226 Ra estimates are shown in brackets in Table 1). The relationship has a slope of 0.119 dpm 100 L −1 of 226 Ra per µmol L −1 of Si and an intercept of 8.8 dpm 100 L −1 , which is comparable with the average slope of 0.1 observed by Broecker et al. (1976) in the Atlantic. The Si-extrapolated 226 Ra and measured 226 Ra activities (data from this study and the TTO) show a relatively consistent result although the extrapolated 226 Ra has a larger uncertainty (±11 % 2 SE) than the measured 226 Ra uncertainty (±4 %, 2 SE). The paired t test shows a p value of 0.55 (> 0.05), suggesting that the differences between the extrapolated 226 Ra and the measured 226 Ra data are not statistically significant. The uncertainties of 226 Ra activity have been used in the error propagation of 228 Ra activity; the total uncertainty of 228 Ra is typically about 6 %-12 % (2 SE).

228 Ra-derived 1-D mixing models
The distribution of seawater 228 Ra in the ocean is mainly controlled by mixing, advection, radioactive decay, and additional removal/input. It has been widely used as a tracer for measuring diffusion coefficients and advection rates on a basin-wide scale in the surface or at intermediate depths in the ocean (e.g. Cochran, 1992;Ku and Luo, 2008;Sanial et al., 2018). The one-dimensional (1-D) 228 Ra advectiondiffusion model is commonly expressed by the following formula (e.g. Moore, 2015): where A is activity of 228 Ra, t is time, K x is horizontal eddy diffusion coefficient, w is advection velocity, x is offshore distance, λ is decay constant (λ Ra228 = 3.82×10 −9 s −1 ), and J is additional input or removal of 228 Ra. To use the model to accurately calculate the mixing rates, several assumptions need to be made.

Steady state (∂A/∂t = 0)
This assumption requires long-term monitoring of 228 Ra activities in the ocean due to the long half-life of 228 Ra. Charette et al. (2015) compared the 228 Ra data in the North Atlantic from the US GEOTRACES and the TTO programmes, and found that the upper ocean 228 Ra inventories have remained constant over the past 30 years. Although 228 Ra seasonality in coastal areas may introduce uncertainty to the mixing model, the assumption of steady state is likely to be valid for 228 Ra on decadal timescales and at ocean basin scales. The comparison between our 228 Ra data and the limited data from the TTO in this region shows good agreement ( Fig. 2b), supporting this assumption for the South Atlantic.

No additional input or removal of 228 Ra (±J = 0)
Based on particle removal, Ra residence time is estimated to be ∼ 500 years in the surface ocean (Moore and Dymond, 1991). However, there is no measurable particle removal of Ra in the surface open ocean at the timescale of 228 Ra halflife (5.75 years) (Moore, 2015). In theory, the distribution of seawater 228 Ra is controlled by both vertical and horizontal mixing. For example, vertical mixing could potentially introduce additional "removal" of 228 Ra from the surface water and affect the horizontal distribution of 228 Ra in the surface ocean, which would require 2-D models and a high sample resolution dataset to resolve the problem. However, vertical mixing (∼ 0.1-1 cm 2 s −1 ) is typically 5 to 8 orders of magnitude smaller than horizontal mixing (∼ 10 5 -10 7 cm 2 s −1 ), and the sample resolution is not good enough for precise 2-D modelling in this study. Therefore, we only apply the 1-D model to estimate the maximum horizontal mixing rates by neglecting the term of downward mixing.
Similar assumptions need to be made for the 228 Ra-derived vertical mixing -the gradient of 228 Ra with depth mainly reflects the vertical mixing rates, and the vertical 228 Ra distribution is not affected by additional input of horizontal 228 Ra below the mixed layer. These assumptions are mostly true in the upper open ocean, where horizonal 228 Ra mainly comes from the continental margins (shelf and slope sediments) and there is a lack of other important 228 Ra sources in the middle of the ocean. However, if the lateral input becomes important and starts to interfere with the 228 Ra vertical profiles (e.g. receiving strong advective shelf water or profiles closer to the seafloor), the 1-D 228 Ra-derived vertical mixing rates can be significantly overestimated.

Boundary conditions (
It has been pointed out that the boundary condition of A = 0 at x → ∞ is incorrect for using 228 Ra to determine coastal mixing as the distribution of 228 Ra could be controlled by water mass mixing within the coastal distance scale (< 50 km) rather than eddy diffusion (Moore, 2000). In theory, this boundary condition may be valid on the ocean basin scale, as the major sink of 228 Ra in the ocean is radioactive decay. However, observed seawater 228 Ra is still not completely zero in the remote ocean. To avoid this problem, we follow the suggestion of Moore (2015) and define the 228 Ra excess ( 228 Ra ex = 228 Ra − 228 Ra bg ) by subtracting the background value in the middle of the South Atlantic, 228 Ra bg : 0.23 ± 0.06 dpm 100 L −1 (1 SE, n = 6). This value is determined by the average of the observed values at (1) the remote surface waters in a previous study around the 40 • S transect (Hanfland, 2002;Fig. 1, ANT XV/4 station S8, S10, and S11); and (2) the water depth between 1000 and 3500 m in this study (except for 2580 m at Stn1 on the continental slope). The mid-depth 228 Ra background (1000-3500 m) shares a similar background as the remote surface waters (∼ 0.2 dpm 100 L −1 ), suggesting that the 228 Ra background needs to be corrected in both horizontal and vertical mixing calculations. For comparison, the central North Atlantic shows a similar mid-depth 228 Ra background value (∼ 0.16 dpm 100 L −1 ) between 1000 and 3000 m depth from the GEOTRACES GA03 transect (Stn12-20; Charette et al., 2015). However, the surface value in the central North Atlantic (∼ 2.2 dpm 100 L −1 ) is significantly higher than that in the South Atlantic (∼ 0.2 dpm 100 L −1 ), which has also been observed by Moore et al. (2008). We therefore use a background value of 228 Ra bg : 0.23 ± 0.06 dpm 100 L −1 determined from the South Atlantic. The boundary condition can now be rewritten as A ex_0 = A 0 − A bg at x = 0 and A ex = 0 at x = ∞. Considering the assumptions discussed above, Eq. (1) can be written as In this study, we consider two scenarios in the horizontal 228 Ra calculations: (1) mixing only (w = 0) and (2) advection only (K x = 0). We use these two scenarios to provide independent assessments of chemical fluxes in the surface ocean, to bracket the range of possible TE fluxes that are consistent with the 228 Ra data regardless of the combination of mixing and advection in the real ocean. The advection model is only applied to the Argentine Basin data after the shelf break where the advection signal is strong because of the Brazil Current. Although the advection only scenario is an unrealistic one, it provides an end-member for comparisons of TE fluxes under different settings. Using the boundary (2) can be solved for diffusive mixing only: and for advection only: where A ex_0 is the activity of 228 Ra ex at x = 0 (i.e. Stn0 or Stn25); X 1/2 is the distance at which A ex = 0.5A ex_0 ; and T 1/2 is the half-life of 228 Ra (5.75 years). The exponential fit of the surface 228 Ra data provides the estimate of the maximum diffusion coefficients (K x ) at both ends of the transect, and the linear fit of the surface 228 Ra data after the shelf break in the Argentine Basin provides the minimum estimate of the advection water transport (w) along the west end of the transect (see discussion below). For vertical mixing, the calculation of K z is based on a situation in which 228 Ra is mixed horizontally away from the coast in the surface mixed layer and then down into the subsurface. The 1-D mixing model can therefore be applied to the depth profiles of 228 Ra to calculate K z near the surface ocean. Under similar boundary conditions A ez_0 = A 0 − A bg at z = 0 and A ez = 0 at z = ∞, the diffusion equation can be solved for vertical mixing to fit the vertical 228 Ra profiles: where A ez_0 is the activity of 228 Ra ex at z = 0 (i.e. the mixed layer). In the 1-D mixing model, the term for diapycnal ad-vection is generally negligible, as the oceanic vertical advection velocity is usually very small, i.e. 10 −3 -10 −5 cm s −1 (Liang et al., 2017).

Trace element flux calculations
In this study, we use three different 228 Ra approaches to quantify the horizontal and diffusive vertical dTE fluxes in the Cape Basin and Argentine. More details of the calculations are provided in Appendix D.

228 Ra-derived diffusive TE fluxes
To calculate both lateral and vertical TE fluxes, the 228 Raderived diffusion coefficients (K z or K x ) are applied to Fick's first law of molecular diffusion in the following equation: where F TE−d is the diffusive flux of the TEs, and TE/ x or z is the gradient of TE concentration over either the horizontal distance x to the coasts or the vertical depth z below the mixed layer, which can be obtained from the linear regression of horizontal and vertical TE profiles (Sect. 3.2).

228 Ra-derived advective TE fluxes
Surface water after the boundary of the shelf break and the Brazil Current in the Argentine Basin carries strong offshore advection signals along the SAC towards the open ocean ( Fig. 1). Assuming that the mixing of TE is conservative, the advective TE fluxes can be calculated using the following equation: where F TE−a is the offshore advective flux of TE, w is the net offshore advection velocity along the SAC in the Argentine Basin, and [TE] ave−0 is the average concentrations of dissolved TEs in the initial advective waters around where the Brazil Current merges into the SAC (around Stn21).

TE/ 228 Ra-ratio-derived TE fluxes
Previous studies have combined the use of the shelf 228 Ra fluxes with the ratios of TE/ 228 Ra in the surface waters between continental shelves and open oceans to estimate the shelf-ocean TE inputs from the continental margins to the open oceans (Charette et al., 2016;Sanial et al., 2018;Vieira et al., 2020). This method provides the integrated net fluxes of TEs, considering all the possible inputs (e.g. rivers, SGD, and sediments) and outputs (e.g. particle scavenging, biological uptake, and radioactive decay) of 228 Ra and TEs during water mixing between the continental shelf and the open ocean. More details of the method are given in Charette et al. (2016). In brief, assuming that the net shelf-ocean exchange is mainly driven by eddy diffusion, the cross-shelf  (Ku and Lin, 1976); the triangles show Ra data from the TTO programme (Key et al., , 1992a. Different water masses are characterised in the (a) 226 Ra profile (see details in text). Error bars are ±2 SE.
TE fluxes can be calculated using the following equation: where F 228Ra is the cross-shelf 228 Ra flux (Appendix D); TE shelf and 228 Ra shelf are the average concentrations of the TE and 228 Ra in the surface waters on the shelf (GA10W: between Stn23 and Stn25; GA10E: between Stn0 and Stn1), respectively; and TE oecan and 228 Ra ocean are the average concentrations in the open ocean (GA10W: between Stn18 and Stn19; GA10E: between Stn4 and Stn4.5). The ratios of TE/ 228 Ra are reported in Table D1 in Appendix D.

Ra isotope concentrations
The results of 226 Ra and 228 Ra activities and the activity ratios of 228 Ra / 226 Ra are presented in Table 1 (with ±2 SE). The vertical profiles of measured 226 Ra show good agreement with the data from the closest GEOSECS and TTO stations in this region (e.g. Ku and Lin, 1976;Key et al., 1990Key et al., , 1992a (Fig. 2a). Ra-226 activities range from 8.2 to 22.4 dpm 100 L −1 . In this study, the results of 226 Ra are mainly used for calculating 228 Ra activities, and will not be discussed in further detail. The activity ratios of 228 Ra / 226 Ra range from 0.017 to 1.599 in the surface water and are comparable with the ratios from 0.080 to 2.810 observed in previous studies in this region (TTO data, Windom et al., 2006;Hanfland, 2002). The vertical profiles of 228 Ra activity are shown in Fig. 2b. In surface waters, the activities of 228 Ra ranging from 1.02 to 17.66 dpm 100 L −1 in the Argentine Basin are consistent with the observed values from 0.07 to 24.0 dpm 100 L −1 from the previous studies (TTO data and Windom et al., 2006), and the activities of 228 Ra ranging from 0.99 to 3.22 dpm 100 L −1 in the Cape Basin are consistent with the observed values from 0.67 to 4.23 dpm 100 L −1 from the previous study (Hanfland, 2002). Between 600 and 4000 m, 228 Ra / 226 Ra ratios decrease to 0.015-0.030 and 228 Ra activities decrease to 0.29-0.32 dpm 100 L −1 . In the 100 m closest to the ocean floor, the ratios of 228 Ra / 226 Ra increase to 0.048-0.088 and the activities of 228 Ra also increase to 1.07-1.94 dpm 100 L −1 . This is the first dataset of seawater 228 Ra reported in the intermediate and deep waters in the Cape Basin. The 228 Ra values in the Cape Basin are noticeably higher than those observed in intermediate (< 0.1 dpm 100 L −1 ) and deep waters (0.22-0.28 dpm 100 L −1 ) to the south in the Southern Ocean (Charette et al., 2007;van Beek et al., 2008). The vertical profiles of seawater 228 Ra in the Cape Basin are consistent with GEOSECS and TTO observations elsewhere in the South Atlantic Ocean (Moore et al., 1985). The samples collected by pump (fish), CTD, and SAP within the mixed layer at each station show consistent 228 Ra and 226 Ra results, suggesting that there is no significant difference in the Ra results between these three sampling methods.

Micronutrient concentrations
Dissolved Co, Fe, and Zn concentration data (Wyatt et al., 2014Browning et al., 2014;Clough et al., 2016;Schlitzer et al., 2018) are summarised in Appendix B (Tables B1 and B2). At the continental margins, surface shelf waters show much higher trace element concentrations (Co: 146.2 pM, Fe: 1.53 nM, and Zn: 0.59 nM in the Argentine Basin margin; Co: 46.9 pM, Fe: 0.35 nM, and Zn: 0.14 nM in the Cape Basin margin) than observed in the open-ocean surface waters along the 40 • S transect (Fig. 3). In the Argentine Basin, the distribution of trace elements generally follows the salinity in the surface waters. The low-salinity waters (< 29 psu) around 200 km from the South America coast show high TE concentrations (Co: > 80 pM, Fe: > 1 nM, and Zn: > 0.5 nM). In contrast, the high-salinity waters (> 35 psu) in the Brazil Current show much lower TE concentrations (Co: < 60 pM, Fe: < 0.5 nM, and Zn: < 0.2 nM). Similar correlations between trace elements and salinity have been observed along other western boundaries of the Atlantic as well (e.g. the North American shelf; Bruland and Franks, 1983;Noble et al., 2017). In the upper ocean (< 600 m), these trace element concentrations are generally low in the surface mixed layer and increase with depth below the mixed layer (Fig. 4). Co concentrations range from 1.6 to 61.2 pM, and Fe and Zn concentrations range from 0.05 to 0.54 and 0.01 to 0.53 nM, respectively. In general, these trace element concentrations (< 600 m) are slightly higher in Stn1 than other stations further away from the continental shelf. The distribution of 228 Ra ex in the Argentine Basin (GA10W) is controlled by the Rio de la Plata river plume and the Brazil Current (Fig. 5a), and this is supported by a good correlation with salinity (linear regression R 2 = 0.96; Fig. C1 in Appendix C). If we apply the 1-D mixing model (Eq. 3) to fit the 228 Ra ex data between Stn25 and Stn21, across the boundary of the Brazil Current, the gradient of the exponential fit (a) is 0.0047 ± 0.0027 and the estimate of the offshore horizontal diffusion coefficient K x is 1.8 ± 1.4 × 10 6 cm 2 s −1 , which is likely to be an overestimate due to the influence of the river plume and the advection of the boundary current. Nevertheless, this estimate is still within the range of other estimates of K x between 10 5 and 10 8 cm 2 s −1 in a variety of margin and open-ocean settings (e.g. Kaufman et al., 1973;Knauss et al., 1978;Yamada and Nozaki, 1986).
Across the boundary of the Brazil Current, the advection of the eastward flowing SAC shows a significant impact on the distribution of 228 Ra ex in the surface Argentine Basin (Fig. 5a). If we apply the 1-D advection model (Eq. 4) to fit the data between Stn21 and Stn18 (Fig. 5a), the X 1/2 is 1116 ± 600 km (from Stn 21) and the estimate of average advection velocity w is 0.6 ± 0.3 cm s −1 . Although the 228 Ra-derived velocity is smaller than the typical velocities (2-4 cm s −1 ) around the South Atlantic subtropical gyre (Schlitzer, 1996), similar advective 228 Ra signals have been previously observed in other surface ocean current systems, including the Peru and Kuroshio currents in the Pacific (Knauss et al., 1978;Yamada and Nozaki, 1986).

Cape Basin
Ra-228 data from the Cape Basin transect (GA10E) are used to calculate the offshore horizontal diffusion coefficient (K x ) in the Cape Basin (Fig. 5b). Applying the simple 1-D mixing model, assuming w = 0, to fit the surface 228 Ra ex data in the Cape Basin (Fig. 5b), the gradient of the exponential fit (a) is 0.0012 ± 0.0003 and the estimate of K x is 2.7 ± 0.8 × 10 7 cm 2 s −1 , which is an order of magnitude higher than the value observed in the Argentine Basin (see above) but within the range of other observed values in the oceans (10 5 -10 8 cm 2 s −1 ).
The horizontal diffusion coefficient K x is likely to be overestimated in the Cape Basin due to the influence of episodic water advection. The Agulhas Current leakage (ACL) is known for transporting water from the Indian Ocean into the South Atlantic and episodically introduces eddies (Agulhas rings) into the Cape Basin (Beal et al., 2011). However, the signals of mixing and advection cannot be easily separated with the 228 Ra data alone (Fig. 5b). For example, the distribution of 228 Ra ex in the surface Cape Basin shows elevated values (Stn2 and Stn4.5) above the fitted curve and coincides with the elevated salinity and temperature data (Fig. 5d), which indicates that the elevated 228 Ra ex is likely to come from an advective signal (e.g. ACL). The ACL signal has also been identified with a distinct Pb isotope signature in the upper water column at Stn2 (Paul et al., 2015). The application of a 1-D mixing model may actually be biased by the addition of these high 228 Ra ex waters; therefore, the horizontal diffusion coefficient K x is likely to be a maximum estimate for the Cape Basin. Nevertheless, the overall gradient of 228 Ra ex , decreasing along the distance away from the shore, is driven by the loss of 228 Ra through both water mixing and radioactive decay.
Despite uncertainty in the diffusion coefficients due to advection of other sources, the 228 Ra data do place bounds on maximum horizontal mixing in the surface ocean away from the eastern and western boundaries of the Atlantic at 40 • S. These bounds can be used to quantify the trace element inputs from the continental margins to the South Atlantic (see Sect. 4.3).

228 Ra-derived vertical mixing
Vertical diffusion coefficients (K z ) are calculated at six stations where the depth profiles of 228 Ra ex are available (Stn1, Stn2, Stn3, Stn4.5, Stn18, and Stn21). The best-fit exponential curve gradients (a) from the depth (z) profiles of 228 Ra ex activities below the surface mixed layer are used in the same 1-D mixing model (Eq. 5) to calculate the vertical mixing coefficient K z for the upper ≈ 600 m of each station in both the Argentine and Cape basins (Fig. 6), and resulting K z values range from 1 to 53 cm 2 s −1 at these stations. It should be noted that Stn2 only has one Ra data point below the mixed layer, and hence it is not considered in the vertical TE input calculations (Sect. 4.3), but the estimate of K z shows a similar value as other stations with more data points. The high K z values of 53 cm 2 s −1 and 7 cm 2 s −1 at Stn18 and Stn21, respectively, are most likely biased by the lateral inputs of 228 Ra below the mixed layer (see later discussion). Excluding the values of Stn18 and Stn21, the range of K z values from 1.0 to 1.7 cm 2 s −1 is broadly comparable to the average K z of 1.5 cm 2 s −1 assessed from tritium measurements in the South Atlantic (Li et al., 1984). These estimates are also consistent with the range of observed vertical mixing from 0.1 to 10 cm 2 s −1 using different methods (e.g. 7 Be, SF 6 dye release and microstructure shear probe methods) in different ocean basin settings (Kunze and Sanford, 1996;Ledwell et al., 1993;Martin et al., 2010;Painter et al., 2014;Kadko et al., 2020).
Given that the calculation of K z is based on the vertical gradients of 228 Ra driven by vertical mixing and radioactive decay only, it therefore relies on the assumption that the vertical gradients are not dominated by lateral input of 228 Ra at depths below the surface mixed layer. This assumption is supported by an inspection of horizontal 228 Ra gradients at depths below the mixed layer (Fig. 7). Due to the sample resolution, detailed inspection is only available for the Cape Basin. Here, unlike the exponential change seen in the surface layer, 228 Ra ex activities at 50 m and deeper do not show an increasing gradient towards the continental margin. This therefore argues against lateral mixing away from the shore as the major mechanism driving subsurface 228 Ra concentrations in the Cape Basin. In addition, the distribution of 228 Ra on an isopycnal surface (≈ 200 m depth) is largely constant and shows no lateral gradient (Fig. 7). Studies using theoretical models to simulate seawater 228 Ra distribution have also shown that the horizontal eddy mixing (K x ) has little effect on the vertical distribution of 228 Ra (Lamontagne and Webster, 2019). The depth profiles of 228 Ra ex in the Argentine Basin show evidence of advective 228 Ra below the mixed layer, potentially from the nearer-shore shelf waters. For example, elevated 228 Ra ex values are seen around 400 m at Stn18 and 200 m at Stn21 (Fig. 6a and b) and these may explain the extremely high K z values at these stations. Although the pos-sibility of lateral inputs cannot be entirely excluded, particularly in the Argentine Basin, the vertical variation of 228 Ra near the surface mixed layer still provides the first estimates of maximum vertical mixing and the upper limits of trace element inputs from vertical mixing to the surface ocean along the 40 • S transect.

Trace element inputs in the South Atlantic
TEs are important micronutrients for marine productivity in the surface ocean. Atmospheric dust deposition is an important source of TEs to the surface ocean. The soluble atmospheric dust deposition fluxes to the surface 40 • S Atlantic transect have been assessed from the same cruise as this study: these are 0.02-0.05 nmol Co m −2 d −1 , 1.6-5.2 nmol Fe m −2 d −1 and 0.6-6 nmol Zn m −2 d −1 (Chance et al., 2015). However, other inputs of these TEs to the euphotic zone in the South Atlantic are still unknown (e.g. shelf-ocean and vertical mixing). In this study, we consider three different 228 Ra approaches to quantify the horizontal and vertical TE fluxes in the Cape Basin and Argentine Basin along the 40 • S transect: (1) 228 Ra-derived diffusive, (2) 228 Raderived advective, and (3) TE/ 228 Ra-ratio-derived TE fluxes (Sect. 2.5 and Appendix D). The results of the TE fluxes are summarised in Table 2 (shelf-ocean, horizontal) and Table 3 (vertical). For comparison, the horizontal TE fluxes are normalised to the areas of shelf-ocean cross section (Table D2; Urien and Ewing, 1974;Nelson et al., 1998;Emery, 1966;Windom et al., 2006;Carr and Botha, 2012;Hooker et al., 2013;Vieira et al., 2020) (illustrated in Fig. 8) unless otherwise specified.
Surprisingly, the estimates of shelf-ocean TE fluxes show relatively good agreements (within uncertainties) between these three approaches (Table 2), given the limitations of the 1-D 228 Ra-mixing model (Moore, 2015). A similar observation has also been found in the 228 Ra study in the Peruvian continental shelf , which suggests that the assumptions made for the 1-D 228 Ra-mixing model are reasonable. In addition, the TE fluxes show consistent results between the D357 and JC068 data in the Cape Basin. These observations are likely to be a result of the gradients of 228 Ra and TEs representing a long-term average at an ocean basin scale and being closer to a steady-state condition in the upper water column (e.g. the 228 Ra and TEs in the North Atlantic; Charette et al., 2015).
are about 1 and 2 orders of magnitude, respectively, higher than the estimates in the South Atlantic, these regions are also associated with low oxygen which increases dissolution of Mn and Fe oxides in sediments and is prone to result in higher Co fluxes (e.g. Hawco et al., 2016). A low shelf-ocean Co flux has been reported in the eastern South Atlantic conti-nental shelf (11-18 × 10 3 nmol m −2 d −1 ; Bown et al., 2011), which is very close to this study region in the Cape Basin. Along the 40 • S transect, the 228 Ra-derived shelf-ocean Fe fluxes range from 8 to 19 × 10 4 nmol m −2 d −1 in the Argentine Basin margin and from 1.2 to 3.1 × 10 4 nmol m −2 d −1 in the Cape Basin margin, which are slightly lower than the es- 1.2 ± 0.6 7 ± 4 * Fluxes are normalised to the surface area. All errors are ±1 SD.
timates of the shelf-ocean Fe flux (4.5 × 10 5 nmol m −2 d −1 ) in the western North Atlantic (Charette et al., 2016). However, these fluxes are significantly lower than those high Fe fluxes observed in regions with river plumes (e.g. Congo River; 4.1 × 10 8 nmol m −2 d −1 ; Vieira et al., 2020), submarine groundwater discharge (1.3 × 10 8 nmol m −2 d −1 , Windom et al., 2006) and the oxygen minimum zone (2.1 × 10 6 nmol m −2 d −1 , Sanial et al., 2018). Lastly, the 228 Ra-derived shelf-ocean Zn fluxes range from 2.7 to 6.3 × 10 4 nmol m −2 d −1 in the Argentine and from 0.9 to 1.2 × 10 4 nmol m −2 d −1 in the Cape Basin mar-gins. When compared with the only available shelf-ocean Zn flux value (1.8×10 6 nmol m −2 d −1 ) in the western North Atlantic (Charette et al., 2016), the Zn fluxes from this study indicate low Zn inputs in the South Atlantic. The different shelf-ocean Zn inputs between the North and South Atlantic require more detailed study to understand the processes supplying and removing Zn in the shelf waters and the influence of anthropogenic Zn. Nevertheless, the low Zn inputs support the previous observation that surface water along the 40 • S transect has some of the lowest reported dissolved Zn concentrations in the global oceans (Wyatt et al., 2014). From below the mixed layer, the vertical dissolved TE fluxes range from 0.1 to 1.2 nmol Co m −2 d −1 , from 6 to 9 nmol Fe m −2 d −1 , and from 5 to 7 nmol Zn m −2 d −1 along the 40 • S transect (Table 3)

Mass-balance budgets for trace elements in the South Atlantic
The mass-balance budgets of dissolved TEs from different sources (horizontal shelf inputs, vertical upward mixing, and atmospheric dust deposition) and sinks (exported fluxes) in the surface South Atlantic (40 • S transect) are calculated and summarised in Table 4 and Fig. 8. The vertical upward mixing appears to be a more important source supplying TEs to the surface water at 40 • S compared to atmospheric dust and continental shelf inputs. However, the dominant source or seasonal variation of the vertical TE inputs cannot be identified in this study. Apart from the internal regeneration, TEs from a subsurface lateral input from the continental margin can subsequently be brought to the surface by vertical mixing (e.g. Rijkenberg et al., 2014). Deep winter convective mixing has also been shown as an important source of TEs to the surface ocean (e.g. Achterberg et al., 2018Achterberg et al., , 2020Rigby et al., 2020). A bulk estimate of the dissolved TE exported fluxes from the surface ocean, supported by new production biological uptake, can be made using a sinking particulate organic carbon (POC) flux and an estimated TE/C uptake ratio. In this study region, previous studies have reported the 234 Th-derived POC fluxes ranging from 3.1 to 9.7 mmol C m −2 d −1 in the top 100 m integration depth (7.0±2.2 mmol C m −2 d −1 ; Thomalla et al., 2006; 6.4 ± 3.3 mmol C m −2 d −1 ; Owens et al., 2015). The estimates of cellular TE/C ratios are 0.3-3, 10-100, and 5-10 µmol mol −1 for Co / C, Fe / C, and Zn / C, respectively, based on the measurements in marine phytoplankton under different TE concentrations in surface waters (e.g. Co: 10 −12 to 10 −11 mol L −1 , Sunda and Huntsman, 1995; Fe: 10 −8 to 10 −7 mol L −1 , Sunda and Huntsman, 1997; Zn: 10 −11 to 10 −10 mol L −1 , Sunda and Huntsman, 2000). These concentrations were chosen to represent the ranges of TE concentrations found in the surface waters of this region. Multiplying the POC fluxes with the TE/C ratios, the exported fluxes of Co, Fe, and Zn are 1-29, 31-970, and 16-97 nmol m −2 d −1 , respectively. The results agree with the estimates of particulate TE removal fluxes in the North Atlantic (e.g. Co: 0.27-6.8 and Fe: 274-2740 nmol m −2 d −1 ; Hayes et al., 2018), even though the North Atlantic assessments have accounted for both biological uptake and particle scavenging fluxes by directly using TE / 234 Th ratios.
In general, the exported TE fluxes are higher than the net dissolved TE inputs that we have identified in this study (Table 4). Taking Fe as an example, the total dissolved Fe inputs (22-45 × 10 6 mol yr −1 ) only contribute 1 %-56 % of the biological consumption of dissolved Fe, which is not enough to balance the iron budget in the surface ocean. This could imply that (1) the spatial and temporal variability in 234 Thderived POC flux is crucial (given the mean life of 234 Th is 35 d); (2) much lower TE/C ratios are required; or (3) other sources of TEs need to be considered (e.g. lateral-transport particulate TE or winter deep mixing).
In the calculations of TE removal fluxes, we have considered a reasonable range of 234 Th-derived POC fluxes and the TE/C ratios, which helps to bring the lower end of the TE removal fluxes closer to the upper end of the total TE input fluxes. This may be enough to explain the offsets of Zn and Co budgets, considering the uncertainties, but it is still not enough to explain the offset of Fe. The range of observed phytoplankton TE/C ratios in the global oceans can vary widely (e.g. Co/C: 0.00047-25.6 µmol mol −1 ; Fe/C: 2.1-  Table 4 are shown and colour coded according to the sources. The vertical red cross sections are used to normalise the shelf-ocean TE and 228 Ra fluxes. The net shelf-ocean TE fluxes represent the total inputs from rivers, SGD, and shelf sediments, and the outputs by particle or biological removal between the shelf-ocean mixing from both sides of the continental margins. The blue surface area is used to estimate the net TE inputs from dust and vertical mixing, and the red cross section above the mixed layer is used to estimate the net shelf-ocean TE fluxes (Table 4). (4) Removal dTE fluxes 24-752 80-2507 40-251 * The high-productivity zone is illustrated in Fig. 8. The net dTE fluxes of (1) shelf-ocean inputs (Table 2) are multiplied by the area of cross-shelf section above the removal flux integration depth (100 m). The net TE fluxes of (2) vertical mixing (Table 3), (3) atmospheric inputs (Chance et al., 2015), and (4) the exported fluxes (assessed from the 234 Th-POC fluxes and TE/C ratios) are multiplied by the surface area. 258 µmol mol −1 ; Zn/C: 0.02-110 µmol mol −1 ; Moore et al., 2013). Direct measurements of the TE/C ratios in the suspended particles in the South Atlantic are required to constrain the removal TE fluxes. The Fe released from lateraltransport particles has been suggested as a potential source to explain the high dissolved Fe concentration observed in the upper 800 m waters in the Southwest Atlantic (Rijkenberg et al., 2014). It is not possible to evaluate this flux or to provide more discussion at this stage. Further studies are needed to understand the sources and the TE concentrations of these particles and the mechanism releasing TEs from these particles in the ocean.

Conclusions
This study investigates the distribution of 228 Ra in the 40 • S Atlantic transect and provides constraints on ocean mixing and dissolved TE fluxes (Co, Fe, and Zn) to the highproductivity region in the South Atlantic. Although the 228 Ra 1-D mixing model shows some limitations in the assumptions, the 228 Ra data do place bounds on maximum mixing rates in this study and the estimates are within the range of observed values in the global oceans. Three different 228 Ra approaches (1-D diffusion, advection, and 228 Ra/TE ratio) have been applied to estimate the dissolved TE fluxes to the 40 • S Atlantic transect, and the results are comparable to each other. The net dissolved TE fluxes suggest that vertical upward mixing is more important than atmospheric dust deposition and continental shelf supply as the main source supplying dissolved TEs to the surface 40 • S Atlantic transect. However, considering the biological uptake, these dissolved TE inputs are generally not enough to balance the TE budgets in the surface ocean of this region, particularly for Fe. Apart from vertical upward mixing, continental shelves, and atmospheric dust inputs, other TE inputs (e.g. particulate or winter deep mixing) may need to be considered to improve our understanding of micronutrient limitations in the high-productivity region in the South Atlantic.
Appendix A: Seawater 226 Ra and silica concentrations Figure A1. (a) Relationship between the Atlantic seawater 226 Ra activity and silica concentration (GEOTRACES GA03, GEOSECS, and TTO datasets; Ku and Lin, 1976;Key et al., 1990Key et al., , 1992aCharette et al., 2015). The dashed line shows a linear regression through all the data. (b) Plots of Si-extrapolated 226 Ra against measured 226 Ra in this study and the TTO programme. The paired t test shows a p value of 0.55 (> 0.05). The solid line is 1 : 1, and the dashed purple lines show the linear regressions with the error bars of ±11 % (2 SE). To calculate both lateral and vertical TE fluxes, the 228 Raderived diffusion coefficients (K z or K x ) are applied to Eq. (6) with the gradient of TE concentration ( TE/ x or z) over either the horizontal distance x to the coasts or the vertical depth z below the mixed layer, which can be obtained from the linear regression of horizontal and vertical TE profiles in Figs. 3 and 4, respectively. In the Argentine Basin, the cross-shelf horizontal gradients of TEs (Fig. 3a, c, and e) and 228 Ra-derived K x (Fig. 5a) have been used to assess the TE fluxes cross the shelf break and the Brazil Current. In the Cape Basin, where the TE gradients (Co and Fe) from both cruises (D357 and JC068) are used for comparison ( Fig. 3b  and d), the differences are generally less than 20 % (except for the vertical gradient of Co at Stn3). As the vertical gradients and 228 Ra-derived K z in the Argentine Basin are likely to be biased by lateral inputs, the vertical TE fluxes are not assessed in the western transect here. The 228 Ra-derived diffusive TE fluxes are summarised in Table 2 (horizontal) and Table 3 (vertical).

D2 228 Ra-derived advective TE fluxes
The advective TE fluxes after the boundary of the shelf break and the Brazil Current in the Argentine Basin can be calculated using Eq. (7) with the net offshore advection velocity (w = 0.6 ± 0.3 cm s −1 ) along the SAC in the Argentine Basin and the average concentrations of dissolved TEs in the initial advective waters around where the Brazil Current merges into the SAC (around Stn21; Fig. 3 Table 2 for comparison. As the advective signals cannot be easily separated from the mixing in the Cape Basin, the advective TE fluxes are not assessed in the eastern transect here.

D3 TE/ 228 Ra-ratio-derived TE fluxes
The cross-shelf TE/ 228 Ra-ratio-derived TE fluxes can be calculated using Eq. (8) with the TE/ 228 Ra ratios reported in Table D1 and the estimates of shelf 228 Ra flux (F 228Ra ) based on the inverse models using the global seawater 228 Ra database and inventory (Kwon et al., 2014;Le Gland et al., 2017). In the South Atlantic, the average shelf 228 Ra flux is 1.7 ± 0.3 × 10 10 atoms m 2 yr −1 around the Uruguayan and South African continental margins (normalised to shelf area; Charette et al., 2016). For comparison, the flux is converted to the shelf-ocean cross-sectional flux by multiplying the average continental shelf widths (Cape Basin: 80 km; Argentine Basin: 120 km) and then dividing by the water depths at the shelf break (Cape Basin: 150 m; Argentine Basin: 160 m) (Urien and Ewing, 1974;Nelson et al., 1998;Carr and Botha, 2012). The shelf length is shared between the two surfaces (the shelf horizontal plane and vertical section in Fig. 8) and cancelled out during the calculation (Table D2). The cross-shelf 228 Ra flux (F 228Ra ) becomes 1.3 ± 0.2 × 10 13 atoms m 2 yr −1 in the Argentine Basin and 0.9±0.2×10 13 atoms m 2 yr −1 in the Cape Basin. The calculated TE fluxes are summarised in Table 2.
It is important to remember that when considering the sources of 228 Ra and TEs in the ocean, TEs may have their maximum source term at a different depth than 228 Ra. Whereas 228 Ra has a clear maximum from the continental shelf in the surface mixed layer, redox-sensitive, more particle-bound or hydrothermal-related TEs may see a maximum at deeper levels, due to particle resuspension, low oxygen saturation, or hydrothermal activity. In this sense, our model calculations provide the estimates of lateral TE inputs in the surface mixed layer with a clear source from the continental shelf. The vertical TE inputs, however, do not separate the TE inputs between internal cycling, hydrothermal, or lateral transport from the continental margin at greater depths. Nevertheless, all these inputs would only become relevant for productivity if they reach the surface mixed layer later, e.g. by vertical mixing as quantified here. Table D1. Shelf and open-ocean average dTE and 228 Ra concentrations and TE/ 228 Ra ratios * . 228 Ra dCo dFe dZn (10 5 atoms L −1 ) (pmol L −1 ) (nmol L −1 ) (nmol L −1 ) Argentine Basin Shelf 6.4 ± 1.1 99 ± 42 1.44 ± 0.12 0.58 ± 0.01 Open ocean 1.3 ± 0.5 15 ± 5 0.28 ± 0.12 0.18 ± 0.05 Cape Basin Shelf 1.3 ± 0.1 30 ± 8 0.22 ± 0.09 0.08 ± 0.03 Open ocean 0.5 ± 0.1 9 ± 5 0.11 ± 0.06 0.05 ± 0.05 TE/ 228 Ra (10 −7 nmol atom −1 ) Argentine Basin margin 1.6 ± 1.1 22 ± 14 7.7 ± 3.9 Cape Basin margin 2.5 ± 1.5 12 ± 8 3.6 ± 4.2 * Only JC068 TE data are used. All errors are ±1 SD. a Shelf-ocean TE or 228 Ra fluxes presented in this study are normalised to the area of shelf-ocean cross section (by default, the cross section at shelf break is equal to shelf length multiplied by the shelf-break water depth). To convert the shelf TE or 228 Ra flux (usually normalised by shelf area) from previous studies, the shelf fluxes are multiplied by the shelf width and length, and then divided by the area of the cross section. Shelf length should drop off from the flux conversion. a Congo River margin TE fluxes are divided by a defined cross section (the width of river plume multiplied by the mixed layer depth). b Brazilian margin Fe flux is divided by a defined cross section (the width of a defined coastline multiplied by the mixed layer depth).
Data availability. All the original and supporting data are shown in the paper. The data are also available publicly at the GEOTRACES IDP2017 (https://www.bodc.ac.uk/geotraces/data/ idp2017/, Schlitzer et al., 2018).
Author contributions. YTH, WG, and GMH designed the radium projects. YTH conducted the Ra-228 and Ra-226 analyses. EMSW conducted the Si measurements. NJW, MCL, and EPA contributed the TE data and interpretation. YTH prepared the manuscript with contributions from all co-authors.
Competing interests. The authors declare that they have no conflict of interest.