1 Introduction

Zinc (Zn) is a trace metal that is biogeochemically important in the ocean because of its close involvement in biological activities. Previous studies found that the distribution of dissolved Zn is similar to that of silicate (Si) in the global ocean (Bruland 1980). However, while the distribution of silicate in the ocean is controlled by uptake of diatom opal, Zn is hardly found in diatom opal (Ellwood and Hunter 2000) but is rather present in organic matter in diatom cells (Twining and Baines 2013). In view of this fact, dissolved Zn distribution is expected to be similar to that of phosphate (P). However, the vertical distribution of Zn in the ocean is not similar to that of P but rather similar to that of Si. The mechanism of this coupling of Zn and Si, where the Zn distribution is similar to that of Si, has been discussed in previous studies. The recent progress of the GEOTRACES program (Anderson 2019) has led to a dramatic increase in observational data of dissolved Zn in the ocean and has accelerated the discussion of dissolved Zn cycling processes in the ocean (Kim et al. 2017; Vance et al. 2017; de Souza et al. 2018; Weber et al. 2018). Among them, the Southern Ocean hypothesis proposed by Vance et al. (2017) has received a great deal of attention.

The Southern Ocean hypothesis proposes that a combination of biogeochemical and physical oceanographic processes can explain the distribution of dissolved Zn in the ocean: the Zn-depleted water is formed due to the large Zn/P uptake ratio by phytoplankton in the surface Southern Ocean (biogeochemical process), and this Zn-depleted water in the surface is transported into the interior of the global ocean associated with the formation of mode water in the Southern Ocean (physical oceanographic process). It has been known that Si uptake by phytoplankton in the Southern Ocean is greater than in other areas, because these waters are dominated by diatoms; Si is depleted earlier than P in the upper Southern Ocean (Assmy et al. 2013). On the other hand, it has been reported that diatoms have a higher Zn/P uptake ratio in the Southern Ocean (Twining and Baines 2013). Therefore, the sub-Antarctic (50S–45S) surface water is not depleted in P but is depleted in Zn and Si (biogeochemical process). This sub-Antarctic surface water is located in the source area of SAMW (Sub-Antarctic Mode Water; McCartney MS 1977). Therefore, associated with the formation of SAMW, sub-Antarctic surface water with depletion of Zn/Si and non-depletion of P is transported into the ocean interior. Despite the fact that Zn and Si are included in two different components of the diatom cell and have different regeneration length scales, both are exported to the deep Southern Ocean together. Thus, water characterized by Zn and Si coupling in the Southern Ocean is transported to the north and causes global Zn and Si coupling. The fact that Zn and P are not coupled despite the same regeneration length scale can also be explained by the high Zn/P uptake ratio in the Southern Ocean. The Southern Ocean hypothesis argues that a coupling of Zn and Si is caused by the above-mentioned combination of biogeochemical and physical oceanographic processes.

To verify this hypothesis, Vance et al. (2017) conducted sensitivity experiments on the distribution of dissolved Zn in the ocean using a biogeochemical model. In their experiments, the Zn concentration was calculated in the same way as P concentration except that different phytoplankton uptake ratios were considered between Zn and P, while the Si concentration was calculated using a formulation independent of P or Zn (details are given in Sect. 2.3.3). Even though there is no direct link between Zn and Si cycles in the model formulation, the results showed that, under appropriate parameter settings, the scatter plots of Zn and Si concentrations in the global ocean reproduce the nearly linear relationships (coupling relationship) consistent with the observational data. This result supports the Southern Ocean hypothesis that high Zn/P uptake ratio by phytoplankton and SAMW formation in the Southern Ocean controls the global ocean Zn cycle.

However, it has also been known that locally zinc and silicon are not coupled. Jensen et al. (2019) reported that the biogeochemical cycling of dissolved zinc in the Arctic is different from in other oceans. Janssen and Cullen (2014) reported that waters above 400–500 m depth are characterized by elevated Zn compared to Si in the subarctic northeast Pacific. They argued that a removal process in low \({\mathrm{O}}_{2}\) waters could cause decoupling of Zn from Si in this region. Vance et al. (2019) showed from isotopic distributions that the decoupling of Zn and Si in the North Pacific could be explained mostly by differences in length-scales of regeneration between Zn and Si. Kim et al. (2017) also reported that Zn and Si are not coupled in the western and central subarctic North Pacific. They have highlighted the importance of an additional Zn supply from the continental shelf to the North Pacific. From modeling, Weber et al. (2018) reported that their model simulation based on Vance et al. (2017) does not sufficiently reproduce the Zn concentrations in the North Pacific. They proposed the importance of reversible scavenging in reproducing the vertical distribution of Zn in the North Pacific. Roshan et al. (2018) argued that reversible scavenging and hydrothermal Zn inputs are important sources of excess Zn to the deep ocean, causing the correlation between Zn and Si.

In this study, we conducted two types of model experiments by focusing on the distribution of Zn in the North Pacific. Based on these model experiments, we discuss the processes necessary to reproduce the collapse of the coupling relation between Zn and Si (Zn–Si decoupling) in the North Pacific, as reported from observations. First, we attempted to see if Zn–Si decoupling could be reproduced without additional biological or chemical processes as much as possible. Specifically, after conducting model experiments the same as those of Vance et al. (2017), additional experiments with widely varying model parameter values about Zn uptake ratio were performed. In those experiments, we examined whether the reproducibility of Zn distribution in the North Pacific can be improved by significantly modifying Zn uptake ratio parameters from the Vance et al. (2017) model. Second, other new experiments assuming Zn supply from continental coasts were also conducted. Recent studies, like those by Nishioka et al. (2020) have shown that the continental shelf is a source of trace elements in the North Pacific, such as iron. We discussed the role of continental shelf supply in controlling the Zn cycle in the North Pacific Ocean by performing model experiments, where additional Zn supply from the continental coasts in the Sea of Okhotsk and the Bering Sea are considered. Then, its role in Zn–Si decoupling in the North Pacific as highlighted by Kim et al. (2017) was discussed.

This work is organized as follows. The observational data used in this study, the model setup, and the experimental designs are described in Sect. 2. The model results are described in Sect. 3. The insight into the Zn cycle in the North Pacific obtained from our results, and the comparison with previous studies are discussed in Sect. 4. A summary and concluding remarks are given in Sect. 5.

2 Materials and methods

2.1 Observational data

In this study, the GEOTRACES IDP2017 data set is used as the reference observational data set for dissolved Zn, Si, and P (Schlitzer et al. 2018). Figure 1a shows Zn observation stations in the GEOTRACES data used in this study: the sections of the West Atlantic (GA02; Middag et al. 2019), the North Atlantic (GA03; Shelley et al. 2018), the South Atlantic (GA10; Wyatt et al. 2014), the Pacific sectors of the Southern Ocean (GIPY02, GIPY11; Zhao et al. 2014), and the Western and Central Subarctic North Pacific (GP02; Kim et al. 2017).

Fig. 1
figure 1

Zn observational points in the ocean and sea area map defined in this study. a Observational stations plots from the GEOTRACES data set used in this study. b Sea area map defined in this study. Blue represents the Atlantic Ocean, green represents the Indian Ocean, and orange represents the Pacific Ocean. The section with the red dots is the observation line GP02 for the North Pacific Ocean in GEOTRACES. The red dots in b are selected to be located on a model grid and do not exactly match the point plots in a

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2.2 Ocean general circulation model

This study used the ocean general circulation model COCO version 4.0 (Hasumi 2006) which is the ocean part of the coupled atmosphere–ocean general circulation model MIROC (K-1 Model Developers 2004). The domain is the global ocean, with 44 vertical layers and about \({1.4}^{^\circ }\) horizontal resolution.

The sea surface boundary conditions for calculating heat, freshwater, and momentum fluxes in COCO were obtained from the pre-industrial MIROC simulation (Sasaki et al. 2022; Kobayashi et al. 2021, 2015; Oka et al. 2006, 2012). Then, the physical field calculated by COCO was used for the tracer calculation with the offline method (Oka et al. 2008, 2009, 2011). The details of the tracer calculation are described below.

2.3 Tracer calculations

In this study, dissolved P, Si, and Zn concentrations are calculated in the model. The equation of each tracer concentration is given as follows:

$$\frac{\partial C}{\partial t} =\mathrm{ Adv }+\mathrm{ Dif }+ {S}_{c},$$
(1)

where \(C\) is the tracer concentration, \(\mathrm{Adv}\) is the advection term, \(\mathrm{Dif}\) is the diffusion term, and \({S}_{c}\) is the source/sink term (e.g., Yamanaka and Tajika 1996). The advection term is a term that represents the effect of transport by large-scale currents in the ocean and is defined as follows:

$$\mathrm{Adv }= -u\frac{\partial C}{\partial x} - v\frac{\partial C}{\partial y} - w\frac{\partial C}{\partial z}.$$
(2)

The diffusion term, on the other hand, is a term that expresses the effect of transport of small-scale flows that cannot be directly expressed by the advection term and is described as follows:

$$\mathrm{Dif} ={K}_{H}{\nabla }_{H}^{2}C + {K}_{V}\frac{{\partial }^{2}C}{{\partial }^{2}z},$$
(3)

where \({K}_{H}\) and \({K}_{V}\) are horizontal and vertical diffusivities, respectively. Note that the isopycnal and layer thickness diffusions are not explicitly written in (3) but included in the model calculation. The velocity (u, v, and w) fields and diffusion coefficients (\({K}_{H}\) and \({K}_{V}\)) are both taken from the pre-industrial MIROC simulation. In this study, the horizontal resolution of these physical variables is reduced to be about \({2.8}^{^\circ }\) resolution in tracer calculations, for the sake of computational efficiency (Oka et al. 2011). The meridional overturning circulation referenced in this study is shown in Figs. 2a, b for the Atlantic and Pacific, respectively. The volume transport of the Atlantic meridional overturning circulation across the equator is about 15 Sv, which is comparable with an observed estimate of 14 Sv (Schmitz 1995). The Pacific meridional overturning circulation is also well-reproduced: its volume transport is about 10 Sv around 30S, close to the volume transport measured at the Samoan Passage (Roemmich et al. 1996). The \(\Delta {}^{14}\mathrm{C}\) distribution simulated under our circulation field (Fig. 2c, d) is also close to the observed climatology (Fig. 2e, f; Key et al. 2004), although the simulated water mass becomes somewhat younger in the deep Pacific Ocean than the observation.

Fig. 2
figure 2

Evaluation of the circulation field used in this study. The stream functions in a Atlantic and b Pacific are shown. \(\Delta {}^{14}\mathrm{C}\) distribution in the interior of c Atlantic and d Pacific calculated by the tracer model using the circulation field in this study. \(\Delta {}^{14}\mathrm{C}\) data by GLODAP in e Atlantic and f Pacific is also shown for comparison

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The source/sink term in the third term on the right-hand side of Eq. (1) depends on each tracer. The source/sink terms for P, Zn, and Si are described below.

2.3.1 Calculation of dissolved phosphate

The dissolved nutrient P is taken up by phytoplankton in the surface ocean and sinks to the deep ocean in the particulate form. When it sinks to the deep ocean, it degrades and returns to its dissolved form. The vertical transport of P occurs associated with this biological process; its effect is expressed as \({S}_{c}\) in Eq. (1) as follows:

$${S}_{c}^{P}=\left\{\begin{array}{ll}-\mathrm{max}\left(\upgamma \left(\mathrm{P}-{\mathrm{P}}_{\mathrm{ref}}\right),0\right), &\left( z \le {\mathrm{z}}_{\mathrm{ref}}\right)\\ \frac{\partial {F}_{z}^{P}}{\partial z}.& \left(z > {z}_{\mathrm{ref}}\right)\end{array},\right.$$
(4)

where \(\gamma\) is the relaxation constant, P is the dissolved phosphate concentration, \({\mathrm{P}}_{\mathrm{ref}}\) is the reference P concentration in the euphotic layer, \({z}_{ref}\) is the euphotic depth, and \({F}_{z}^{P}\) is the vertical flux of P. In this study, we set \(\upgamma =\frac{1}{30\left[{\rm day}\right]}\) and \({z}_{ref}=100m\), and the observational data of World Ocean Atlas 2001 (WOA01, Conkright et al. 2002) is given as \({\mathrm{P}}_{\mathrm{ref}}\). Equation (4) expresses nutrient uptake by phytoplankton in the surface (\(z \le {\mathrm{z}}_{\mathrm{ref}}\)) and nutrient release by degradation from particulate to dissolved forms in the deeper ocean (\(z > {z}_{\mathrm{ref}})\). For \({F}_{z}^{P}\), we describe it as follows:

$${F}_{z}^{P} =\mathrm{ E}{\mathrm{P}}^{\mathrm{P}}{\left(\frac{\mathrm{z}}{{\mathrm{z}}_{\mathrm{ref}}}\right)}^{\mathrm{a}},$$
(5)

where \({\mathrm{EP}}^{\mathrm{P}}\) is the export production of P and is calculated as follows:

$${\mathrm{EP}}^{\mathrm{P}} = {\int }_{0}^{{z}_{\mathrm{ref}}}{S}_{c}^{P}\mathrm{d}z,$$
(6)

where a is set as − 0.858, an empirical constant determined from sediment trap data (Martin et al. 1987). Model simulations were initialized with WOA01 observational data in each experiment and integrated forward for 3000 model years. The average of the last 100 years of the integration was analyzed.

2.3.2 Calculation of dissolved silicate

The source/sink term of Si simulation is as follows:

$${S}_{c}^{Si}=\left\{\begin{array}{ll}-\mathrm{max}\left(\upgamma \left(\mathrm{Si}-{\mathrm{Si}}_{\mathrm{ref}}\right),0\right),& \left( z \le {\mathrm{z}}_{\mathrm{ref}}\right)\\ \frac{\partial {F}_{z}^{Si}}{\partial z}. &\left(z > {z}_{\mathrm{ref}}\right)\end{array}\right.$$
(7)

The parameter \(\gamma\) is the relaxation constant, Si is the dissolved silicate concentration, \({\mathrm{Si}}_{\mathrm{ref}}\) is the reference Si concentration in the euphotic layer, \({z}_{ref}\) is the euphotic depth, and \({F}_{z}^{Si}\) is the vertical flux of Si. The parameter settings are the same as for the calculation of P; \(\gamma =\frac{1}{30\left[day\right]}\),\({z}_{ref}=100m\), and we gave the observational data of WOA01 as \({\mathrm{Si}}_{\mathrm{ref}}\). For \({F}_{z}^{Si}\), we describe it as follows:

$${F}_{z}^{Si}={\mathrm{EP}}^{\mathrm{Si}}\cdot \mathrm{exp}{\left(\frac{{z}_{\mathrm{ref}}-z}{{z}_{op}}\right)}.$$
(8)

where \({\mathrm{EP}}^{\mathrm{Si}}\) is the export production of Si and is calculated as follows:

$${\mathrm{EP}}^{\mathrm{Si}}={\int }_{0}^{{z}_{ref}}{S}_{c}^{Si}\mathrm{d}z.$$
(9)

The parameter \({z}_{op}\) is an empirical constant that determines the depth scale of the vertical transport of Si. In this study, we set \({z}_{op}\)= 1 km. This formulation represents the process of the vertical transport of Si; Si is incorporated into diatom shells and sinks below the depth of \({z}_{\mathrm{ref}}\) with the exponential dissolution of diatom shells. Model simulations were initialized with WOA01 observational data in each experiment and integrated forward for 3000 model years. The average of the last 100 years of the integration was analyzed.

2.3.3 Calculation of dissolved zinc

The calculation of dissolved Zn concentration in this study is the same as that in Vance et al. (2017), which is tied to the calculation of the P simulation. The source/sink term of Zn is expressed as follows:

$${S}_{c}^{Zn}=\left\{\begin{array}{ll}-\mathrm{max}\left(\upgamma \cdot {\mathrm{r}}_{\mathrm{Zn}:\mathrm{P}}\cdot \left(\mathrm{P}-{\mathrm{P}}_{\mathrm{ref}}\right),0\right),& \left( z \le {\mathrm{z}}_{\mathrm{ref}}\right)\\ \frac{\partial {F}_{z}^{Zn}}{\partial z}.& \left(z > {z}_{\mathrm{ref}}\right)\end{array}\right.$$
(10)

The model parameters \(\upgamma , \mathrm{P},{\mathrm{P}}_{\mathrm{ref}}, \mathrm{and }\ {z}_{ref}\) are all the same as those used in the P calculation. However, the phytoplankton uptake ratio of Zn to P, \({\mathrm{r}}_{\mathrm{Zn}:\mathrm{P}}\), is a new model parameter introduced for the Zn calculation. Regarding \({\mathrm{r}}_{\mathrm{Zn}:\mathrm{P}}\), in this study, we use the following formulation as in Vance et al. (2017)

$${\mathrm{r}}_{\mathrm{Zn}:\mathrm{P}}=\frac{{\mathrm{a}}_{\mathrm{Zn}}\cdot {\mathrm{Zn}}^{2+}}{{\mathrm{b}}_{\mathrm{Zn}}+{\mathrm{Zn}}^{2+}}+{\mathrm{c}}_{\mathrm{Zn}}\cdot {\mathrm{Zn}}^{2+},$$
(11)

where \({\mathrm{a}}_{\mathrm{Zn}},{\mathrm{b}}_{\mathrm{Zn}}\ \mathrm{ and }\ {\mathrm{c}}_{\mathrm{Zn}}\) are model parameters introduced in Vance et al. (2017), and determine the Zn uptake ratio of phytoplankton (Sunda’ and Huntsman 1992). This formulation was found to reproduce dissolved Zn distribution better than the linear formulation between \({\mathrm{r}}_{\mathrm{Zn}:\mathrm{P}}\) and Zn (Vance et al. 2017). The specific parameter settings used in this study are described in Table 1. The \({\mathrm{Zn}}^{2+}\) concentration in Eq. (11) is calculated from the Zn concentration using the equilibrium equation as follows:

$${\mathrm{Zn}}^{2+} = \frac{{\mathrm{Zn}}^{\mathrm{^{\prime}}}}{\mathrm{\alpha }},$$
(12)

and

Table 1 Parameters of biological uptake ratio for CTL and U-series EXP
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$${\text{K}}_{L} \cdot {\text{ }}({\text{Zn}}^{\prime } )^{2} + \left( {{\text{K}}_{L} {\text{L}}^{T}- {\text{K}}_{L} {\text{Zn }} + 1} \right) \cdot {\text{Zn}}^{\prime } - {\text{ Zn}} = 0.$$
(13)

In Eq. (12), \({\mathrm{Zn}}^{\mathrm{^{\prime}}}\) is the non-ligand-bound dissolved zinc concentration, \(\mathrm{\alpha }=2.1\) is the inorganic side reaction coefficient of Zn in seawater. In Eq. (13), \({\mathrm{K}}_{\mathrm{L}}={10}^{10}{\mathrm{ M}}^{-1}\) is the conditional stability constant for the complexation of Zn by ligands, and \({\mathrm{L}}_{\mathrm{T}} = 1.2 \mathrm{nM}\) is the total concentration of ligands. All constants \(\mathrm{\alpha }\), \({\mathrm{K}}_{\mathrm{L}}\) and \({\mathrm{L}}_{\mathrm{T}}\) are the same as those in Vance et al. (2017). In Eq. (10), \({F}_{z}^{Zn}\) is the vertical flux of Zn. As in the case of P calculation, it is expressed as follows:

$${F}_{z}^{Zn} =\mathrm{ E}{\mathrm{P}}^{\mathrm{Zn}}{\left(\frac{z}{{z}_{ref}}\right)}^{a},$$
(14)

where a =  − 0.858 is the empirical constant also used in Eq. (5), and \({\mathrm{EP}}^{\mathrm{Zn}}\) is the export production of Zn. \({\mathrm{EP}}^{\mathrm{Zn}}\) is calculated as follows:

$${\mathrm{EP}}^{\mathrm{Zn}}={\int }_{0}^{{z}_{\mathrm{ref}}}{S}_{c}^{Zn}\mathrm{d}z.$$
(15)

In each experiment, model simulations were initialized with a globally uniform Zn concentration of 5.4 nM and integrated for 3000 model years. The average of the last 100 years of the integration was analyzed.

2.4 Experimental design

2.4.1 Control experiment

The parameter setting for the control experiment (CTL) in this study is the same as that for the case11 experiment in Vance et al. (2017), which best reproduced the observed coupling relationship between Zn and Si concentrations in the global ocean. Our CTL experiment will confirm that we can replicate the Vance et al. (2017) results. In this study, we will compare the results of our CTL experiment with the observational data by focusing on the North Pacific Ocean; in Vance et al. (2017), the discussion was focused on the global scale and the Southern Ocean, but not on the North Pacific Ocean.

2.4.2 Uptake experiment (U-series EXP)

Uptake experiments (U-series EXP) were conducted with different parameter values for \({\text{a}}_{\text{Zn}},{\text{b}}_{\text{Zn}}\text{ and }{\text{c}}_{\text{Zn}}\) in Eq. (11). We use the same parameter settings for Vcase7 to Vcase10 of U-series EXP, as in the case7–10 experiments of Vance et al. (2017), respectively (Table 1). The case7–10 in Vance et al. (2017) used the formulation of Eq. (11) in which the uptake ratio depends nonlinearly on the Zn concentration. Note that these parameter settings are obtained within the limits of laboratory experiments (Sunda and Huntsman 1992), and therefore, the biological uptake ratios simulated in case7–10 are within the range of what is biologically feasible. It has been highlighted by Vance et al. (2017) that these parameter settings can reproduce the observed Zn distribution well.

We also performed the simulation named WSOC in which the same parameter setting as Weber et al. (2018) were specified. Our simulation WSOC replicates SOC simulation in Weber et al. (2018), where the model parameters were optimized, so that the simulated Zn distribution becomes closest to the observations under the formulation of Eq. (11), the same as that used in the case7–10 of Vance et al. (2017) and our Vcase7–Vcase10. However, the optimized parameter setting was problematic, because Zn uptake becomes too large in the Southern Ocean and exceeds the biologically feasible range. Weber et al. (2018) proposed the necessity of introducing reversible scavenging to avoid such unrealistically large Zn uptake. In this study, we conducted the WSOC simulation, which uses the same parameter setting as the Weber et al. (2018) SOC simulation to compare their model results.

In addition, this study also conducts simulations with parameter settings that have not been done in previous studies, as additional cases to analyze the distribution of Zn in the North Pacific. Specifically, one is the HyperL simulation, in which we choose the model parameter values, so that the Zn uptake ratio becomes extremely large. The other is the HyperS simulation, in which the Zn uptake ratio becomes extremely small. Note that while Vance et al. (2017) performed the model simulations within a biologically feasible parameter range obtained in Sunda and Huntsman (1992), the parameter settings in HyperL and HyperS are not necessarily biologically feasible (as in the WSOC simulation), by which we analyze the possible impacts of choice of model parameters on the simulated distribution of Zn, especially in the North Pacific.

Table 1 shows the parameter settings for each case, and the dependence of the Zn uptake ratio on Zn (increase in \({\mathrm{r}}_{\mathrm{Zn}:\mathrm{P}}\) with increasing Zn) calculated in Eq. (11) is shown in Fig. 8a.

2.4.3 Source experiment (S-series EXP)

Source experiments (S-series EXP) are performed in this study to incorporate the process of Zn supply from the continental shelf of the North Pacific Ocean into the model. The model setting of S-series EXP is similar to the CTL experiment except that the process of Zn supply from the North Pacific continental shelf is additionally considered. Specifically, the following term of \({S}_{c}^{Zn}(source)\) is added to the source/sink term of Zn:

$$S_{c}^{{Zn}} ({\text{source}}) = \left\{ \begin{array}{ll} - r\left( {{\text{Zn}} - {\text{Zn}}_{{{\text{ref}}}} } \right)&({\text{in}}\;{\text{the}}\;{\text{North}}\;{\text{Pacific}}\;{\text{continental}}\;{\text{shelf}}) \\ 0&({\text{outside}}\;{\text{the}}\;{\text{North}}\;{\text{Pacific}}\;{\text{continental}}\;{\text{shelf}}) \\ \end{array} , \right.$$
(16)

where r is the relaxation constant, and we set r = \(\frac{1}{30\left[\mathrm{day}\right]}\). The addition of the term \({S}_{c}^{Zn}(\mathrm{source})\) forces the value of Zn concentration to approach \({\mathrm{Zn}}_{\mathrm{ref}}\) by the term of \(-\mathrm{r}\left(\mathrm{Zn}-{\mathrm{Zn}}_{\mathrm{ref}}\right)\) within the specified region (the North Pacific continental shelf; see Fig. 9a). We define the North Pacific continental shelf as the area, where the depth is shallower than 2000 m in the model topography. Although the actual continental shelf is shallower than 2000 m, we chose 2000 m because of the model resolution, and to ensure that the continental shelf regions are sufficiently included in the model. The experiments are conducted by focusing on three possible source areas of Zn in the North Pacific continental shelf: the Sea of Okhotsk, the Bering Sea, or both. The Sea of Okhotsk and the Bering Sea continental shelves defined in the model are shown as green and red areas in Fig. 9a, respectively.

We then describe the treatment of the reference concentration (\({\mathrm{Zn}}_{\mathrm{ref}}\)), and for this purpose, we first define \({\mathrm{Zn}}^{*}\). In Conway and John (2015), \({\mathrm{Zn}}^{*}\) is introduced as an index of the coupling relationship between Zn and Si. In this study, we adopt the following equation proposed by Kim et al. (2017) as the definition of \({\mathrm{Zn}}^{*}\) in the North Pacific.

$${\mathrm{Zn}}^{*} =\mathrm{ Zn}\left[\mathrm{nM}\right] - 0.053 \times \mathrm{ Si}\left[\mathrm{\mu M}\right] - 0.33.$$
(17)

As the value of \({\mathrm{Zn}}^{*}\) is closer to 0, it is interpreted that a clearer coupling relationship between Zn and Si is realized. Kim et al. (2017) reported observational data obtained in the North Pacific. They reported that values of \({\mathrm{Zn}}^{*}\) around 3–7 are observed there, indicating that the coupling relationship between Zn and Si is broken in the North Pacific. Using the \({\mathrm{Zn}}^{*}\) values reported in Kim et al. (2017), the reference Zn concentration on the North Pacific continental shelf (i.e., \({\mathrm{Zn}}_{\mathrm{ref}}\) in Eq. 16) is given by the following equation:

$${\mathrm{Zn}}_{\mathrm{ref}} = 0.053 \times \mathrm{ Si}\left[\mathrm{\mu M}\right] + 0.33 + {{\mathrm{Zn}}_{\mathrm{ref}}}^{*},$$
(18)

where Si is the silicate concentration calculated in the model and \({{\mathrm{Zn}}_{\mathrm{ref}}}^{*}\) is the reference concentration of \({\mathrm{Zn}}^{*}\). We conducted experiments with five different values for \({{\mathrm{Zn}}_{\mathrm{ref}}}^{*}\) (\({{\mathrm{Zn}}_{\mathrm{ref}}}^{*}=3, 4, 5, 6, 7\)) within the range consistent with the observations of Kim et al. (2017) in this study. Therefore, we perform15 different simulations in total with three different settings of the region and five different settings of \({\mathrm{Zn}}_{\mathrm{ref}}\). The names of the simulations conducted in S-series EXP are summarized in Table 2.

Table 2 Names of simulations conducted in S-series EXP
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3 Results

3.1 GEOTRACES data

Figure 3a shows scatter plots of P and Zn concentrations in the global ocean from the observational GEOTRACES data. As shown in Vance et al. (2017), P and Zn have no coupling relationship (i.e., those scatter plots show no direct linear relationship between P and Zn), while the scatter plots of Si and Zn concentrations show a coupling relationship between Si and Zn concentrations (Fig. 3b). The scatter plots in each ocean basin of the Atlantic, Pacific, and Indian also show a coupling relationship between Si and Zn concentrations (Fig. 3c–e). However, if we focus on the North Pacific (Fig. 3f), we can see that Si and Zn concentrations are decoupled; the linear relationship between Si and Zn concentrations breaks down there as reported before (e.g.,Janssen and Cullen 2014; Kim et al. 2017; Weber et al. 2018; Vance et al. 2019).

Fig. 3
figure 3

Scatter plots for Zn, Si, and P from GEOTRACES data set. a Global scatter plots of P–Zn concentrations. b Global scatter plots of Si–Zn concentrations. The coloration of the points represents relative frequencies which are defined as the percentage of plots within the grid out of the total number of plots, delimiting the plot area into 70 × 70 grids. Scatter plots of Si–Zn concentrations c in the Atlantic, d in the Pacific, e in the Indian Ocean, and f along the North Pacific line (GP02). See Fig. 1b for the definition of each ocean basin

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3.2 Control experiment

3.2.1 Zn–P/Zn–Si scatter plots

Figure 4a shows the surface distribution of the Zn concentration simulated in the CTL experiment. The distribution is broadly similar to nutrients, with larger concentrations in the Southern Ocean and North Pacific and smaller concentrations in the tropics. In the CTL experiment, the Zn cycle was assumed to be related to the P cycle with the larger Zn uptake ratio to P in the Southern Ocean (Fig. 4b), and the global characteristics of the Zn distribution become similar to the P distribution as consistent with the GEOTRACES observations (Fig. 4c–f). It is also confirmed that the result obtained in our CTL experiment is similar to that of Vance et al. (2017).

Fig. 4
figure 4

CTL experiment results. a Surface distribution of Zn concentration and b Zn/P uptake ratio in CTL experiment. The contour intervals are 1 nM in a and 1 mmol/mol in b. Zn concentration of zonal mean c in the Atlantic, d in the Pacific, and e in the Indian. The colored dots represent the observation of GEOTRACES data set

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Then, we compare the Zn concentration in the CTL experiment with Si and P concentrations simulated in our model. Note that not only Zn but also Si and P are both model-computed, so each contains errors from observations. The reproducibility of our model (Fig. 5) is comparable with the previous model study (e.g., Fig. S3 of Vance et al. 2017), with the correlation coefficients between model and observation above 0.9 for both Si and P. The Zn–P scatter plots (Fig. 6a) show that the decoupling relationship between P and Zn concentrations is reproduced in our model, as seen in the observations (Fig. 3a). Also consistent with observational data (Fig. 3b), the Zn–Si scatter plots (Fig. 6b) show that our model reproduces the global coupling relationship between Si and Zn. Therefore, from the scatter plots in the global ocean, it is confirmed that the model in this study can reproduce similar results to the previous study of Vance et al. (2017).

Fig. 5
figure 5

Evaluation of P and Si model skill. Taylor diagram comparing the three-dimensional simulated P and Si tracer fields to the data

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Fig. 6
figure 6

Zn, Si, P scatter plots from CTL experiment in the same manner as Fig. 3

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3.2.2 Reproducibility of observed Zn distribution in the North Pacific

In the CTL experiment, the Zn–Si coupling relationship is found in the global ocean and the Atlantic, the entire Pacific, and the Indian Oceans (Fig. 6c–e). The observational data can also confirm this relationship (Fig. 3c–e).

However, as mentioned above and reported by Kim et al. (2017), this coupling relationship breaks down in the North Pacific (Fig. 3f). Such a collapse of Zn–Si coupling (Zn–Si decoupling) in the North Pacific is not reproduced well in the CTL experiment, as confirmed from the Si–Zn scatter plots in the North Pacific (Fig. 6f). In contrast to the observational data (Fig. 3f), the model shows a coupling relationship similar to that in other regions in the model. To focus on the distribution in the North Pacific, the vertical section of the Zn distribution along the GP02 line of the GEOTRACES project is shown in Fig. 7a. In the interior of the North Pacific, the model results generally underestimate the observed Zn concentration. \({\mathrm{Zn}}^{*}\) distribution also tends to be underestimated compared to observations (Fig. 7b).

Fig. 7
figure 7

Comparison of CTL experiment and observations at the North Pacific line (GEOTRACES GP02 section). a Distribution of Zn concentration [nM] and b \({\mathrm{Zn}}^{*}\) at the North Pacific line. The colored contours represent the results of the CTL experiment (along with red plots in Fig. 1b), and the colored points represent the observations at the GEOTRACES GP02 section (see Fig. 1a)

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3.3 U-series EXP

We conducted U-series EXP to assess how much the model of Vance et al. (2017) could be improved by changing the model parameters associated with the Zn uptake ratio. The results show that Zn–Si decoupling in the North Pacific does not occur in all simulations of U-series EXP (Fig. 8c–e). The results of the WSOC (Fig. 8c) and HyperL (Fig. 8d) simulations, in which the Zn uptake ratio is much larger than in the CTL experiment, do not differ significantly from the results of the CTL experiment (Fig. 6f). In addition, the small concentration bias of Zn in the North Pacific seen in the CTL experiment does not see any significant improvement (not shown). The same is true for the HyperS simulation (Fig. 8e), in which the Zn uptake ratio is much smaller than that in the CTL experiment. In the HyperS, the slope of the scatter plots becomes smaller than in the CTL experiment. This is due to an overall increase in Zn concentration in the surface ocean and a decrease in Zn concentration in the deep ocean because of smaller Zn uptake in the surface ocean and an associated decrease in the amount of Zn vertically transported to the deep ocean.

Fig. 8
figure 8

Zn uptake ratio and Si–Zn scatter plots in the North Pacific for U-series EXP. a Zn uptake ratio as a function of Zn concentration assumed in each simulation of U-series EXP. Scatter plots of Si–Zn concentration in the North Pacific for b GEOTRACES data, c WSOC, d HyperL, and e HyperS simulations of U-series EXP

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In conclusion, our U-series EXP suggests that the same model as Vance et al. (2017) has difficulty in reproducing the Zn–Si decoupling in the North Pacific and leads to the smaller Zn and \({\mathrm{Zn}}^{*}\) concentrations than the observations no matter how the Zn uptake ratio parameter is adjusted.

3.4 S-series EXP

We discuss the results of S-series EXP in which the Zn supply from the North Pacific continental shelf is additionally considered. The results show that the Zn–Si decoupling relationship tends to be reproduced in all 15 simulations conducted in the S-series EXP (Fig. 9b–p). To select the most realistic model simulations, the Root Mean Squared Error (RMSE) between the observational data and each model simulation is calculated in the North Pacific for Zn and \({\mathrm{Zn}}^{*}\) (Table 3). As a result, we found that the simulation with the highest reproducibility of Zn concentration is B7 and the simulation with the highest reproducibility of \({\mathrm{Zn}}^{*}\) is B4. This means that no simulation has the lowest RMSE for both Zn and \({\mathrm{Zn}}^{*}\). The simulation in which the sum of the RMSE for Zn and \({\mathrm{Zn}}^{*}\) becomes the smallest is B5. In this study, we treated B5 (an experiment with \({\mathrm{Zn}}^{*}=5\) in the Bering Sea), a case with small RMSE in both Zn and \({\mathrm{Zn}}^{*}\), as the best case. We focused on the B5 case and compared its result with observations in the following.

Fig. 9
figure 9

Scatter plots of Si–Zn concentration in the North Pacific Ocean for S-series EXP. a Sea of Okhotsk continental shelf (green) and the Bering Sea continental shelf (red) defined in S-series EXP. The orange dots indicate the GEOTRACES GP02 section (the same as the red dots of Fig. 1b) used for the Si–Zn concentration scatter plots in b–p. b–p Si–Zn scatter plots for all simulations of S-series EXP along the GP02 section in the North Pacific. Note that red dots show the results of forcing Zn concentration only in the Bering Sea (b, e, h, k, and n), green dots show the results of forcing Zn concentration only in the Sea of Okhotsk (c, f, i, l, and o), and black dots (d, g, j, m, and p) show the results of forcing Zn concentration in both the Bering Sea and the Sea of Okhotsk. Forced concentrations (\({\mathrm{Zn}}^{*}\)) are indicated by the numbers on the labels

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Table 3 Root mean square errors between each model simulation and observational data in the North Pacific
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3.4.1 B5 simulation

Figure 10f shows scatter plots of Zn and Si in the North Pacific for the B5 case. The figure shows an upward convex shape, reproducing the Si–Zn decoupling, which was difficult to reproduce in the CTL and U-series experiments (Figs. 6f and ). Regarding the distribution in the North Pacific, the Zn concentration and \({\mathrm{Zn}}^{*}\) are increased in the deeper ocean (Fig. 11) compared to the CTL experiment (Fig. 7), confirming that the observational data are well-reproduced there. Because there is a concern that additional sources from the North Pacific continental shelf could also increase the concentration of Zn in other regions and affect the coupling relationship between Zn and Si there, we also check the results of the B5 case outside the North Pacific. In the B5 experiment, the global correlation between P and Zn (Fig. 10a) and the Si and Zn coupling correlation (Fig. 10b) does not change significantly from the CTL experiment; in the Atlantic (Fig. 10c), the entire Pacific (Fig. 10d), and the Indian (Fig. 10e), the coupling relationship between Si and Zn is confirmed as in the CTL experiment. This suggests that sources on the North Pacific continental shelf affect the Zn concentration in the North Pacific but have less effect on the rest of the ocean.

Fig. 10
figure 10

Scatter plots for Zn, Si, P from B5 experiment in the same manner as Fig. 3

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Fig. 11
figure 11

Comparison of B5 simulation and observations at the North Pacific line (GP02) in the same manner as Fig. 7

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4 Discussion

4.1 Zn supply from the North Pacific continental shelf

In this study, we show that the reproducibility of Zn distribution in the North Pacific Ocean can be improved by incorporating Zn supply processes from continental shelves in the Sea of Okhotsk and the Bering Sea into the model. We demonstrated that the existence of Zn supply from the North Pacific continental shelf can cause the Zn–Si decoupling in the North Pacific, as noted by Kim et al. (2017). Recent studies discuss the possibility that various trace elements are transported long distances from the continental shelf to the open ocean (e.g., Conway and John 2015; Nishioka et al. 2020). This study shows consistent result with this idea: Zn supply from the continental shelf has an important role in determining Zn distribution throughout the North Pacific.

In our model experiment, the Sea of Okhotsk continental shelf and the Bering Sea continental shelf are assumed to be Zn supply sources, but detailed observational data do not exist for both continental shelves yet. If more detailed observations of Zn concentrations near the North Pacific continental shelf are obtained in the future, the existence of Zn supply from the continental shelf can be verified more directly. In addition, although the simulations in this study assumed an ideal value for \({\mathrm{Zn}}^{*}\) in the continental shelf, numerical experiments under more realistic source fluxes would be possible when observational data on the continental shelf become available.

Although we focus on supply from the continental shelf of only Zn, it should be noted that some studies have suggested the possibility of an additional Si supply. Hou et al. (2019) estimate the benthic fluxes of Si in the North Pacific based on observations. Hautala and Hammond (2020) argues that incorporating the bottom source of silica into the model can explain the silica maximum in the northeast Pacific basin. If such additional Si supply is important for controlling Si concentration in the North Pacific, the quantification of \({\mathrm{Zn}}^{*}\) there is also affected by not only Zn supply but also Si supply. Because this study did not consider additional Si supply, its role needs to be discussed in future studies.

4.2 Other processes not considered in our model

We successfully reproduced the observed Zn distribution in the North Pacific in our S-series EXP without introducing reversible scavenging process considered in Weber et al. (2018). Weber et al. (2018) did not mention the Zn–Si decoupling relationship in the North Pacific in detail, but there is a possibility that their model also reproduces the Zn–Si decoupling relationship as in our S-series EXP. Here, the model results in this study and those of Weber et al. (2018) give different interpretations about the key process of Zn circulation in the North Pacific: the continental Zn supply or reversible scavenging.

One possible reason for this discrepancy is the differences in the ocean circulation field between the two models. For example, despite the same parameter settings for the Zn cycle (WSOC of this study and SOC of Weber et al. 2018), the reproduced vertical distribution of Zn in the North Pacific is different between this study and Weber et al. (2018). Compared to observations at all depths, the WSOC simulation of this study underestimated concentrations (solid black line in Fig. 12). However, Zn concentrations in the upper North Pacific are overestimated in Weber et al. (2018) SOC simulation compared to observations, whereas concentrations in the deeper region are underestimated (North Pacific profile in their Fig. S3). Considering that reversible scavenging acts to transport Zn from the surface to the deeper oceans, it is understandable that Weber et al. (2018) can improve their SOC simulation by introducing reversible scavenging. However, as for our model, even if reversible scavenging is introduced, the model results are unlikely to improve, because the Zn concentration in the North Pacific was underestimated at both the surface and deep in the WSOC simulation of this study. Unlike reversible scavenging, the supply of Zn on the North Pacific continental shelf is expected to improve such underestimation; in fact, our B5 simulation can reproduce a vertical distribution close to observations (red line in Fig. 12). Therefore, we infer that Zn supply on the North Pacific continental shelf is more important than reversible scavenging. Note that the underestimation of Zn concentration in the North Pacific was not improved even in our study’s HyperL and HyperS simulations, where the Zn uptake ratio is extremely large and small, respectively. This means that it is difficult to improve this underestimation by adjusting the Zn uptake model parameters in our model, which supports the idea that the difference between our study and Weber et al. (2018) arises from differences in the circulation field.

Fig. 12
figure 12

Vertical profiles of Zn concentration averaged over the GEOTRACES GP02 section. The red dots represent the observed data. The blue, black-solid, black-dashed, black-chain, and red-solid lines represents the CTL, WSOC, HyperL, HyperS, and B5 simulations, respectively

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Specifically, as confirmed in Fig. 2c, deep water in the Pacific Ocean is somewhat younger in our model than in the real ocean. In Vance et al. (2019), it is argued that the difference in the Zn and Si regenerations length scales is responsible for the decoupling in the North Pacific Ocean. Due to younger water mass bias of the Pacific deep ocean, our model tends to underestimate the effect of such regeneration effects. It is possible that slight differences in the circulation field in the Pacific could significantly affect the reproducibility of Zn. In the future, the reproducibility of the North Pacific circulation field in the ocean model needs to be examined in detail.

In the S-series EXP of this study, we do not directly consider the process of Zn removal (the process of Zn loss to the outside of the ocean, such as sedimentation) necessary to balance the Zn supply specified in the continental shelves in the North Pacific. Reversible scavenging process (and the associated sedimentation process) needs to be considered to introduce such removal processes into the model explicitly. In the future, it is desirable to evaluate this process by conducting numerical experiments directly considering both the supply and removal processes. Observational knowledge about the process related to the Zn cycle such as adsorption on particles would also be important for evaluating the effect of reversible scavenging correctly.

Based on our model results, we demonstrated that inclusion of Zn supply from the continental regions can improve the reproducibility of Zn concentration in the North Pacific. However, there is possibility that this conclusion could be model-dependent because, for example, the circulation field in the Pacific Ocean has the important role in controlling the Zn and Si cycles there, as described above. Therefore, our conclusion needs to be evaluated again with various ocean models and/or under different ocean circulation fields. In addition, role of processes not explicitly considered in this study, such as reversible scavenging (Weber et al. 2018), additional Si supply (Hou et al. 2019), hydrothermal Zn inputs, a benthic supply of Zn (Roshan et al. 2018), and a removal process in low \({\mathrm{O}}_{2}\) waters (Janssen and Cullen, 2014) needs to be investigated more quantitatively in future studies.

5 Summary and concluding remarks

This study performed numerical model experiments to investigate zinc cycle in the ocean, with a particular focus on the observational evidence that the coupling relationship between Zn and Si breaks down in the North Pacific. We confirmed that our model reproduced the global Zn–Si coupling relationship that is consistent with observations in the CTL simulation, which followed the previous simulation of Vance et al. (2017). We found that the CTL simulation did not reproduce the Zn–Si decoupling in the North Pacific and underestimated the Zn concentration there. No significant improvement from the CTL simulation was obtained in U-series EXP, where the range of Zn uptake ratio parameters significantly changed; the experiments failed to reproduce Zn–Si decoupling in the North Pacific, and the concentration of Zn there remained underestimated even if the uptake ratio increased or decreased. We showed that S-series EXP, which introduces an additional Zn supply from the continental shelf of the North Pacific, reproduced the Zn–Si decoupling in the North Pacific and resolved the underestimation of the Zn concentration in the North Pacific. The results are consistent with the idea that Zn supply from the North Pacific continental shelf to the ocean is the cause of Zn–Si decoupling in the North Pacific.

The results of this study suggest the importance of Zn supply processes from the continental shelf for understanding the Zn cycle in the North Pacific. Many recent studies have revealed the importance of continental shelves as a source of trace elements (e.g., Conway and John 2015; Nishioka et al. 2020; Oka et al. 2021). These studies discuss the possibility that various trace elements are being transported long distances from the continental shelf to the open ocean. This study supports this idea by suggesting that Zn supply from the continental shelf has an important role in determining Zn distribution throughout the North Pacific. Although this study performed a model experiment for Zn, we hope our study could also contribute to further understanding other trace metal cycling processes, such as Fe, that are important for biogeochemistry.