Introduction

Mercury (Hg) is a pervasive global pollutant with severe health impacts1. It is released into the environment from both human activities, such as fossil fuel burning and mining, and natural processes like oceanic emissions and wildfires2,3. Once in the atmosphere, Hg exists mainly as gaseous elemental mercury (Hg0), which makes up over 80% of atmospheric Hg and can remain airborne for months. The oxidized forms of mercury (HgII), including both gaseous [HgII(g)] and particle-bound species [HgII(p)], are less abundant but are rapidly removed by deposition4,5,6. Atmospheric deposition of HgII and Hg0 represents the major source of Hg to marine environments, influencing Hg biomagnification and cycling in the ocean7,8. However, the precise contributions of these Hg forms to oceanic Hg levels remain uncertain.

Direct observations of Hg0 and HgII deposition fluxes over the ocean are limited. Recent atmospheric model studies report varying ratios of HgII deposition compared to Hg0 uptake overs ocean, accompanied by distinct Hg deposition fluxes. The models, including different assumptions in Hg emissions and atmospheric redox chemistry, indicated that HgII deposition over the modern ocean is 2:1 to 3:1 compared to Hg0 uptake, with gross fluxes ranging from 3900 to 4600 Mg yr−1 and 1300 to 2000 Mg yr−1, respectively4,5. These models are often evaluated against atmospheric Hg concentration data near the ground and the troposphere, as well as wet deposition fluxes observed over the land, leaving such a ratio largely unconstrained.

Isotopic signatures provide a more reliable means of constraining these fluxes. Mercury has seven isotopes that exhibit both mass-dependent (MDF, δ202Hg) and mass-independent fractionation (MIF) signatures, including odd-MIF (Δ199Hg and Δ201Hg) and even-MIF (Δ200Hg and Δ204Hg)9,10. Even-MIF is known to be generated in the upper troposphere through photochemical reactions, making it a conservative tracer in surface environments that can be used to trace atmospheric inputs of Hg11,12,13. A recent study by Jiskra et al. 14 compared atmospheric and marine Δ200Hg signatures, suggesting an atmospheric HgII: Hg0 contribution ratio of 1:1. This ratio is significantly lower than those reported in previous modeling studies. Based on this, a recent coupled atmosphere-land-ocean model updated the global Hg budget, suggesting a ratio of 1.5:1, but with much higher fluxes across the air-sea interface, estimating HgII deposition and Hg0 uptake at 4860 Mg yr−1 and 3270 Mg yr−1, respectively15.

However, most of the atmospheric isotope data used by Jiskra et al. 14 are derived from measurements on land or in coastal regions. Relying on land-based observations to trace oceanic Hg sources may introduce significant uncertainties. Firstly, previous observations and modeling have revealed substantial global spatial variation in atmospheric Hg isotopes16,17,18,19. Secondly, current isotopic observations primarily focus on Hg0 and wet deposition, with a notable lack of isotopic characterization for dry deposition of Hg over the ocean. Accurate isotopic characterization of atmospheric end-members is crucial for effectively constraining sea-air Hg exchange using isotopes. But the absence of direct observations of Hg isotope signatures for different forms of Hg in the marine atmosphere limits the effectiveness of these constraints.

We propose that recent advancements in three-dimensional atmospheric Hg isotope modeling offer a promising opportunity to address this issue18,19. In this study, we aim to update the relative contributions of HgII and Hg0 to oceanic Hg by using more accurate Δ200Hg signatures in atmospheric end-members. We integrate Hg isotopes and isotopic fractionation into the GEOS-Chem model to develop an atmospheric Hg isotope model. Based on the even-MIF mechanisms outlined in our recent study (see Methods for details), we present an optimized modeling scenario for atmospheric even-MIF. This model elucidates the Δ200Hg signatures in global atmospheric Hg deposition, constrained by observed Δ200Hg in global atmospheric samples. By comparing these with observed oceanic Δ200Hg values, we propose an updated ratio of atmospheric HgII to Hg0 deposition to the ocean of over 2:1, higher than the previously reported 1:1 ratio. Our results indicate that spatial differentiation of atmospheric Δ200Hg signatures significantly impacts the findings, with important implications for understanding the global Hg cycle.

Results and discussion

Model evaluation

We developed a three-dimensional isotopic model for atmospheric Hg, incorporating state-of-the-art Hg chemistry, to elucidate the potential processes driving even-MIF. Our model results show comparable spatial variability with globally observed Hg concentrations and wet deposition fluxes (Supplementary Discussion, Text1, Supplementary Fig. 1). Additionally, our modeling results reveal pronounced spatial variations in atmospheric Δ200Hg, particularly for HgII species, a phenomenon not previously documented (Fig. 1). Since the model outputs are annual averages, we utilize background observations, from various environments—including the poles, remote mountains, coastal regions, and marine boundary layer (MBL) areas—for modeling validation. The model results reproduce the observed Δ200Hg signatures in global atmospheric samples, including Hg0 (represented by Δ200Hg0), HgII(g) [represented by Δ200HgII(g)], HgII(p) [represented by Δ200HgII(p)], and precipitation [represented by Δ200HgII(pre)]. As illustrated in Fig. 1a, the observed Δ200Hg0 shows a mean value − 0.07 ± 0.02‰ (n = 48), which is closely matched by modeled Δ200Hg0 of −0.07 ± 0.01‰ (n = 48). The modeled mean Δ200Hg0 also aligns with observations from the Arctic (about −0.07‰)20,21,22,23, remote mountain regions (about −0.07‰)11,24,25,26, and MBL (about −0.06‰)27,28,29,30. Similarly, the observed Δ200HgII(p) has a mean value of 0.06 ± 0.05‰ (n = 13), and our model yields a consistent value of 0.06 ± 0.06‰ (n = 13) (Fig. 1b). Specifically, the model successfully reproduces the mean Δ200HgII(p) values observed in remote mountain regions (about 0.10‰)11,28,31,32 and coast MBL regions (about 0.06‰)28,33,34,35,36, including the Huaniao Island (about 0.08‰) at Northwest Pacific Ocean32.

Fig. 1: Distribution patterns of modeled Δ200Hg signatures in surface atmosphere.
figure 1

a Comparison of modeled and observed Δ200Hg0 values. b Comparison of modeled and observed Δ200HgII(p) values. c Comparison of modeled and observed Δ200HgII(g) values. d Comparison of modeled and observed Δ200HgII(pre) values. The circles and the color they carry represent the location and the Δ200Hg values of observations, respectively. e Comparison of simulated and observed latitudinal Δ200Hg signatures in precipitation. The green and red squares represent observations and modeling data, respectively. f Comparison of observed and modeled annual mean Δ200Hg values in atmospheric samples. The abbreviation MBL represents the marine boundary layer. Error bars represent the reported stand deviation of measured Δ200Hg for: Hg0 (yellow), HgII(g) (blue), and wet-deposited HgII(green) (1δ). Error bars for HgII(p) represent spatial variability in observational and modeled datasets (1δ).

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The modeled Δ200HgII(g) distribution closely mirrors that of Δ200HgII(p) (Fig. 1c), which can be attributed to the degassing process that produces HgII(g) from HgII(p)4. Although observations of Δ200HgII(g) are limited, two studies have measured Δ200HgII(g) in Grand Bay, USA (0.18 ± 0.07‰)34 and Pic du Midi, France (0.15 ± 0.06‰)11, with our model yielding comparable mean values of 0.16‰ and 0.17‰, respectively. The modeled Δ200HgII(pre) also exhibits a consistent mean value with observations, at 0.15 ± 0.04‰ (n = 15, Fig. 1d), and shows a significant positive correlation with observed data, with a correlation coefficient of 0.62, reproducing the latitudinal variation of observations (Fig. 1e). Notably, the modeled Δ200HgII(pre) values (0.10‰ and 0.07‰) aligns well with observations from the Island of Hawaii (0.14 ± 0.05‰) and the R/V Kilo Moana (open ocean station ALOHA, 0.08‰)37, which are representative of Δ200HgII(pre) observed over the open Pacific Ocean. In summary, our model successfully simulates the gradient of Δ200Hg values, with the highest values in precipitation samples, followed by HgII(p), and the lowest in Hg0. The close agreement between our modeled and observed values, which approximate a 1:1 relationship (Fig. 1f), underscores the reliable performance of our Hg isotope model.

The distinct variations in Δ200Hg values among HgII species—including gaseous (HgII(g)), particulate (HgII(p)), and precipitation-derived (HgII(pre))—arise from chemical fractionation processes. Comparison with the global atmospheric Hg redox rate (Supplementary Fig. 2a, d) reveals that regions dominated by net Hg oxidation, such as parts of the central Indian and Pacific Oceans, exhibit relatively lower Δ200Hg values in HgII(g), HgII(p), and wet deposition (Fig. 1b, d). These patterns reflect the influence of specific fractionation mechanisms: Br-initiated oxidation dominates in the marine boundary layer (Supplementary Fig. 2a), while even-MIF processes occur during OH-initiated oxidation and HgII(p) photoreduction (see Methods). Elevated Δ200HgII values in African regions further highlight the spatial variability of chemical fractionation. High PM2.5 concentrations driven by dust emissions (Supplementary Fig. 2e) promote HgII(p) formation, while concurrent high photolysis frequencies (Supplementary Fig. 2f) induce strong net HgII(p) reduction (Supplementary Fig. 2d). Additionally, significant OH-initiated chemical activity (Supplementary Fig. 2b) also contributes to this regional Δ200Hg signal. We decompose the fractionation process and find that the OH-initiated chemistry and HgII(p) photoreduction pathways induce distinct Δ200HgII distribution patterns, as these reactions prevail in distinct atmospheric layers (Supplementary Fig. 3). Both processes contribute to the elevated Δ200HgII values over the African landmass (Supplementary Fig. 3). The modeled Δ200HgII signatures at the surface are also influenced by the upper atmosphere. The free troposphere, marked by intense redox rates4,5 (Supplementary Fig. 2g and h), generates high Δ200Hg values in HgII species (Supplementary Fig. 2f). Subsequent convective transport (Supplementary Fig. 4d, e) delivers these species to the surface, thereby affecting surface Δ200HgII signatures. Moreover, compared with regions such as East and South Asia, the African region has relatively lower anthropogenic Hg emissions that is characterized with a close to zero Δ200Hg signal, further enhancing the importance of chemical fractionation processes in this area.

Isotope signature of atmospheric deposition

The model elucidates the Δ200Hg signatures of atmospheric sources deposited into the ocean, including Hg0 uptake, HgII dry deposition, and HgII wet deposition. The Δ200Hg signatures in deposited Hg are influenced by the corresponding signatures in atmospheric Hg. As shown in Fig. 2a, Hg0 uptake by the ocean generally shows negative Δ200Hg0 signatures, with a median value of −0.06‰ [interquartile range (IQR), −0.07‰ to −0.05‰]. In contrast, HgII dry deposition, encompassing both HgII(g) and HgII(p), displays distinct spatial variations in Δ200Hg signatures (Fig. 2b). Globally, HgII dry deposition to the ocean has a median Δ200Hg value of 0.00‰ (IQR, −0.02‰ to 0.03‰). And near-shore regions show higher Δ200Hg values compared to the open ocean, with median values of 0.04‰ (IQR, 0.01‰ to 0.09‰) and 0.01‰ (IQR, −0.01‰ to 0.03‰), respectively. The modeled Δ200Hg values in wet deposition to the ocean are generally positive, with a median of 0.08‰ (IQR, 0.06‰ to 0.12‰) for the global ocean and 0.11‰ (IQR, 0.09‰ to 0.13‰) for near-shore regions (Fig. 2c). The spatial patterns in both dry and wet deposition display similar trends, largely driven by the Δ200HgII distributions (Fig. 1 and Supplementary Fig. 4). Although HgII dry deposition occurs primarily in the boundary layer, the Δ200Hg signatures of HgII(g) and HgII(p) therein are significantly influenced by upper-atmospheric processes—similar to the Δ200Hg observed in precipitation due to the washout of HgII species from higher altitudes. Moreover, elevated Δ200Hg values in both dry and wet deposition near coastal regions are also influenced by terrestrial transport, as on-land Hg chemistry exhibits stronger reduction rates (Supplementary Fig. 2), leading to higher Δ200Hg in HgII species.

Fig. 2: Annual mean Δ200Hg signatures of atmospheric Hg deposited to the ocean.
figure 2

a Δ200Hg in Hg0 uptake by the ocean. b Δ200Hg in the dry deposition of HgII, including both direct deposition and uptake by sea salt. c Δ200Hg in the wet deposition of HgII. Hg0 uptake by the ocean is calculated using Eqs. (1) and (2) as described in “Method” section, representing the uptake of atmospheric Hg0. HgII deposition includes both dry and wet deposition of HgII(g) and HgII(p).

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Our results reveal distinct differences between the Δ200Hg signatures of atmospheric dry deposition HgII and wet deposition HgII over the ocean—a detail not fully emphasized in previous studies14. Since dry deposition of HgII occurs primarily in the boundary layer, while wet deposition of HgII originates mainly from higher atmospheric layers, the Δ200Hg values for wet deposition are considerably higher than those for dry deposition. In Jiskra’s study14, the Δ200Hg characteristics of dry- and wet-deposited HgII were not distinguished; instead, they were combined into a HgII end-member with Δ200Hg values ranging from 0.13‰ to 0.15‰. Compared to our modeling results, this approach likely overestimates the Δ200Hg of the dry deposition HgII, leading to an underestimation of HgII deposition’s contribution to oceanic Hg. Our model provides more detailed Δ200Hg signatures of atmospheric Hg sources, offering a more accurate resolution of the contribution of atmospheric Hg to oceanic Hg.

Atmospheric sources to ocean

We use Δ200Hg data to evaluate the atmospheric contribution of Hg to the ocean, as Δ200Hg is uniquely produced in the atmosphere and remains conserved in ocean. We exclude other potential marine Hg sources, such as hydrothermal emissions and river inputs, since hydrothermal Hg flux is minimal38 and riverine Hg primarily affects coastal regions39. Figure 3a compares the modeled latitudinal variations of Δ200Hg in atmospheric Hg depositions with observations in ocean samples (see method). The deposited Δ200Hg values exhibit three different gradients, with wet deposition showing the highest values, followed by HgII dry deposition, and then Hg0 uptake. The observed interquartile ranges (P25–P75) of Δ200Hg values in ocean samples fall between these three end-members of Hg depositions, suggesting that the relative proportions of these three depositions to oceanic Hg can be differentiated based on Δ200Hg isotope mass balance.

Fig. 3: Comparison of Δ200Hg signatures in modeled atmospheric mercury deposition versus measured oceanic samples.
figure 3

a Latitudinal variation of Δ200Hg values in atmospheric deposited Hg and oceanic Hg. The boxes represent Δ200Hg observations (interquartile range, P25–P75) in ocean samples, including seawater, particle-bound Hg, sediment, and biota14, aggregated by contiguous latitudes. The bold line in boxes represents the median, the boxes represent the IQR, the whiskers represent 1.5× the IQR, and outliers are represented by dots. The yellow line indicates modeled Δ200Hg signatures in Hg0 uptake by the ocean. The green and red lines represent modeled Δ200Hg signatures in dry and wet deposition HgII over the ocean. The shaded area represents the standard deviation of the latitudinal mean. b Comparison of Δ200Hg values in modeled total deposited Hg with ocean observations. The pink dotted line and shaded area represent the modeled Δ200Hg signatures and standard deviation of total Hg deposited from the atmosphere to the ocean, encompassing Hg0 uptake, dry deposition of HgII, and wet deposition of HgII. c Modeled fraction of the three categories of depositions relative to total atmospheric Hg deposition to the ocean.

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The Δ200Hg0 values exhibit minimal variation with latitude, with only a slight downward trend observed in lower latitudes (Fig. 3a). In contrast, Δ200Hg in both dry and wet deposition of HgII shows distinct latitudinal variations, with an increasing trend in low-latitude regions. This corresponds with an upward trend in oceanic Δ200Hg values in the same areas, suggesting a greater contribution of atmospheric HgII to oceanic Hg compared to atmospheric Hg0. Additionally, both Hg0 and dry-deposited HgII display lower Δ200Hg values compared to observed values in certain regions, such as between 20°S and 40°S and 50°N and 70°N, indicating a more significant role for wet deposition in these areas. The overall Δ200Hg values in both wet and dry deposition of HgII align more closely with observed oceanic Δ200Hg, indicating that atmospheric HgII might be a more substantial contributor to the global ocean Hg pool than atmospheric Hg0.

The Hg deposition proportions and isotopic signatures of this model can be further used to quantify the contribution of atmospheric Hg to marine Hg. As illustrated in Fig. 3b, the majority of Δ200Hg values in the modeled total atmospheric deposition (purple area) are comparable to the interquartile range of oceanic observations. This suggests that the relative proportions of the three types of Hg deposition in our model are largely reasonable for explaining the oceanic Δ200Hg. However, the modeled Δ200Hg values are also slightly lower than the observations between 20°S to 40°S, 10°N to 20°N, and 50°N to 70°N, implying a potential underestimation of the relative contribution from HgII wet deposition or, alternatively, an overestimation of Hg0 uptake and HgII dry deposition in these regions. Indeed, previous studies have shown that the GEOS-Chem model underestimates HgII precipitation in equatorial tropical areas, partly due to its limitations in accurately predicting cloud mass in these regions7,40. Additionally, when combined our modeled Δ200Hg with Jiskra’s Hg deposition flux data14, the total Δ200Hg also shows lower values in the regions between 20°S to 40°S and 50°N to 70°N (Supplementary Fig. 5), further supporting this conclusion.

Figure 3c exhibits the proportions of the three types of depositions to the ocean calculated by the model. The proportion of Hg0 tends to decrease in low-latitude tropical regions, while the proportion of HgII wet deposition tends to increase. This trend may explain why ocean samples from these regions exhibit higher Δ200Hg values (Fig. 3a), as wet deposition in these areas is associated with high positive Δ200Hg values (Fig. 3b). Globally, atmospheric Hg0 contributes 34% to oceanic Hg, while atmospheric HgII accounts for the remaining 66%, with 38% from dry deposition and 28% from wet deposition. This indicates a 2:1 ratio of atmospheric HgII to Hg0 deposition over the ocean. Given the potential underestimation of wet deposition’s contribution in the model as indicated above, we suggest this ratio likely exceeds 2:1, significantly higher than the 1:1 ratio reported in the previous study14. This also implies that the contribution of atmospheric HgII wet deposition to marine Hg may be greater than 28%, suggesting that the combined contribution of HgII dry deposition and Hg0 uptake could be less than 72%.

Uncertainty

The uncertainties in this study may stem from the simulation of even-MIF of atmospheric Hg. While our model can replicate Δ200Hg values comparable to atmospheric observations, the fractionation mechanisms and enrichment factors for even-MIF in the model have not been definitively established. Therefore, we advocate for further experimental and theoretical investigations on this matter. Additionally, the Hg isotope signatures of source emissions exhibit standard deviations ranging from 0.02‰ to 0.05‰, as indicated in Table 1. To evaluate the impact of the upper and lower bounds (maximum or minimum isotopic composition) of various emission sources on the modeling results, we performed a sensitivity analysis. The findings indicate that uncertainties in source emissions can lead to shifts of ±0.02‰ to ±0.03‰ in the simulated Δ200Hg0, Δ200HgII(g), Δ200HgII(p), and Δ200HgII(pre), which minimally impact the analysis of these Δ200Hg values. Another uncertainty arises from the assumption that all oceanic Hg originates from the atmosphere, which may not be applicable to coastal regions where rivers are the predominant source39. Uncertainties may also result from the limited observational coverage of the ocean. Current observations do not encompass the entire ocean, particularly in open ocean regions like the central Indian Ocean and the Pacific Ocean. This uneven spatial distribution of observations may influence the analysis of the results.

Table 1 Mercury flux and Δ200Hg signatures of source emissions
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Another source of uncertainty arises from the delineation of the Hg cycle of our isotope model. However, the impact on our conclusion is limited as the simulation of deposition fluxes and their isotopes in our model operates relatively independently. To validate this, we conducted sensitivity tests using different enrichment factors (E200Hg) during the chemical fractionation process. As illustrated in Supplementary Fig. 6, two scenarios with various E200Hg yielded consistent ratios of the three forms of Hg occupancy, although the simulated Δ200Hg values varied significantly. Moreover, the isotopic observations in atmospheric and ocean samples are independent of the simulations, providing robust constraints on the modeled Δ200Hg signatures in both atmospheric Hg and its deposition. This confirms the feasibility of using modeled Δ200Hg values to trace oceanic Hg sources.

The modeling uncertainties may arise from the omission of the lightning process that induces even-MIF, as proposed by recent experimental studies41. As a result, this could influence the simulation of Δ200Hg signatures in wet deposition, given that precipitation events are often associated with lightning. However, according Sun et al.41, it is still unrealistic to attribute global significance to Hg(3P)-induced oxidation (Supplementary Discussion, Text S2). Another potential source of bias is the model resolution. For example, the 4° × 5° GEOS-Chem model may fail to accurately capture high-altitude precipitation events in North America42, potentially leading to an underestimation of Hg elution with positive Δ200HgII values from higher altitudes in this region. Additionally, although the model reproduces the existing observations well, these are primarily concentrated in East Asia, North America, Europe, and parts of the Arctic. Consequently, we recommend that future studies focus on more remote regions, such as South America, Africa, and the open ocean.

Implications

Current observations lack the direct measurement of fluxes in both HgII and Hg0 deposition over the ocean. The Δ200Hg data and modeling indicate that previous findings, which suggested an equal contribution (1:1) of atmospheric HgII and Hg0 to the ocean14, may be biased. Our analysis proposes a higher relative contribution of HgII, with a ratio of might over 2:1, and highlights the significant spatial heterogeneity of Δ200Hg in atmospheric Hg deposition as a key factor in resolving isotopic signatures at the Earth’s surface, including both land and ocean. The greater relative contribution of atmospheric HgII to marine Hg may impact the marine ecosystems, as various forms of Hg in the ocean affect methylmercury production43,44. This has direct implications for human health due to the consumption of seafood containing methylmercury. Conversely, since Hg0 constitutes the majority of atmospheric Hg, its smaller relative contribution to oceanic Hg affects its atmospheric lifetime and ultimately influences the benefits of reducing anthropogenic Hg emissions.

The updated ratio provides an important constraint for the global Hg budget, offering insights into the sea-air Hg fluxes. In global modeling studies, sea-air exchange fluxes can be adjusted within the model by modifying relevant parameters to achieve a self-consistent Hg balance between sea and air4,5,15. For example, a coupled atmosphere-land-ocean model15 suggests atmospheric Hg0 and HgII deposition fluxes of 3270 Mg yr−1 and 4860 Mg yr−1, respectively, constrained by the previously believed 1:1 HgII to Hg0 ratio. This indicates an ocean Hg0 emission of 7220 Mg yr−1 resulted from adapting faster air-sea exchange velocities. Our study suggests that the oceanic Δ200Hg data may not fully support this budget.

Our results effectively differentiate the spatial variation of Δ200Hg in atmospheric Hg and distinguish between the Δ200Hg signatures of dry and wet deposition over the ocean. This demonstrates the advantages of three-dimensional atmospheric Hg isotope modeling, which effectively captures global variations in atmospheric Hg isotopes, compensates for the inhomogeneity of observational data, and provides new perspectives on using Hg isotopes to analyze the global Hg cycle. To better constrain the global Hg cycle, we propose that both atmospheric and oceanic Hg balance and isotopic composition should be integrated. Future research should focus on developing coupled atmosphere-land-ocean isotope models, which could serve as a powerful tool for constraining the global Hg cycle.

Methods

Model description

The GEOS-Chem (version 12.9.0) platform is used to develop the Hg isotope model, featuring a resolution of 4°latitude by 5° longitude and 47 vertical layers18,19. The model employs the native MERRA-2 (4° × 5°) meteorological reanalysis data produced by NASA’s Global Modeling and Assimilation Office (GMAO). Anthropogenic Hg emissions are sourced from Streets et al. 45, while natural emissions are cited from Shah et al. 4. Atmospheric HgII, including HgII(g) and HgII(p), experiences both dry and wet deposition over the ocean. Dry deposition of Hg following the resistance-in-series scheme of Wesely (1989)46. Over the ocean, dry deposition velocity for the atmospheric HgII(g) is biologically unreactive and has a highly high Henry’s law constant47. Dry deposition of HgII(p) is calculated according to the aerosol deposition scheme48,49. Sea-salt aerosol uptake of HgII also acts as a dry deposition sink of Hg in the marine boundary layer6. And wet scavenging of HgII follows the scheme proposed by Amos et al. 50 and Liu et al. 51. The exchange of Hg0 between the air-sea interface is controlled by the following equations48:

$${{{\rm{Flux}}}}_{-{{\rm{up}}}}={{{\rm{K}}}}_{{{\rm{w}}}}\times {{{\rm{CHg}}}}_{0}$$
(1)
$${{{\rm{Flux}}}}_{-{{\rm{down}}}}={{{\rm{K}}}}_{{{\rm{w}}}}\times {{{\rm{CHg}}}}_{{{\rm{a}}}}/{{\rm{H}}}$$
(2)

Where Flux-up represents the flux of Hg0 from the ocean to the atmosphere, and Kw denotes the mass transfer coefficient, which was developed based on field experiments with volatile and nonvolatile tracers52. CHg0 is the concentration of dissolved Hg0 in seawater. We utilize the state-of-the-art chemistry mechanism of atmospheric Hg, which includes mainly four redox pathways4: (i) the oxidation of Hg0 to HgII by Br; (ii) the oxidation of Hg0 to HgII by OH; (iii) the oxidation of Hg0 to HgII by Cl; (iv) photoreduction of HgII(p) to Hg0. This mechanism also integrates the photoreduction of gaseous HgII53, a process that occurs primarily within the Br-initiated pathway and significantly influences global Hg deposition. The oxidant field includes debromination from sea-salt aerosol in the marine atmosphere54,55, which enhances the Br radicle concentration in the marine boundary compared to previous Br fields56. The model simulation covers the period from 2016 to 2018, with the first two years used for model initialization and the third year dedicated to result analysis.

Isotope notion and fractionation

We follow the notation established by Blum and Bergquist10 to express the modeled isotope signatures. These notations are defined as the isotopic ratio difference simulated species and the NIST-3133 standard, measured in permil (‰):

$${{{\rm{\delta }}}}^{{{\rm{xxx}}}}{{\rm{Hg}}}({{\textperthousand }})=[({}^{{{\rm{xxx}}}/198}{{{\rm{Hg}}}/}^{{{\rm{xxx}}}/198}{{{\rm{Hg}}}}_{{{\rm{NIST}}}3133})-1]\times 1000$$
(3)

MIF is calcuated as below:

$$\Delta {}^{199}{{\rm{H}}}{{\rm{g}}}={{{\rm{\delta }}}}^{199}{{\rm{Hg}}}-{{{\rm{\delta }}}}^{202}{{\rm{Hg}}}\times 0.252$$
(4)
$$\Delta {}^{200}{{\rm{H}}}{{\rm{g}}}={{{\rm{\delta }}}}^{200}{{\rm{Hg}}}-{{{\rm{\delta }}}}^{202}{{\rm{Hg}}}\times 0.502$$
(5)
$$\Delta {}^{201}{{\rm{H}}}{{\rm{g}}}={{{\rm{\delta }}}}^{201}{{\rm{Hg}}}-{{{\rm{\delta }}}}^{202}{{\rm{Hg}}}\times 0.752$$
(6)
$${\Delta }^{204}{{\rm{Hg}}}={{\rm{\delta }}}{}^{204}{{\rm{H}}}{{\rm{g}}}-{{\rm{\delta }}}{}^{202}{{\rm{H}}}{{\rm{g}}}\times 1.493$$
(7)

In our calculations, the xxx/198HgNIST3133 ratios are treated as constants, derived from the atomic abundances of Hg isotopes in the NIST-3133 standard10,57: 196Hg = 0.155%, 198Hg = 10.04%, 199Hg = 16.94%, 200Hg = 23.14%, 201Hg = 13.17%, 202Hg = 29.73%, and 204Hg = 6.83%. For the Hg isotope inventories, we synthesize the Hg isotopic composition of each source and calculate its isotopic ratio (xxx/198Hg) using Eqs. (3)–(7) (Table 1). These ratios allow us to divide total Hg emissions into seven isotopes, which can be input into the model as individual tracers. After running the model, it outputs the concentrations and fluxes of these isotopes, enabling us to calculate the isotope signatures using Eqs. (3)–(7).

Our model incorporates isotopic fractionation during chemical processes, treating these fractionations as kinetic processes. The chemical reaction coefficients are slightly adjusted for various isotopes by applying multiple fractionation factors (α), thus achieving isotope fractionation during these chemical reactions18,19. In the model, 198Hg is treated as the reference isotope, maintaining the chemical reaction coefficients (K198) consistent with the standard GEOS-Chem. The calculations of Kxxx for other six isotopes follow the MDF kinetic laws and utilizes reported enrichment factors for specifically processes. The Kxxx is for calculating Kxxx is as follows:

$${\mathrm{ln}}({{{\rm{\alpha }}}}^{{{\rm{xxx}}}/198}{{{\rm{Hg}}}}_{{{\rm{MDF}}}})={{{\rm{\varepsilon }}}}^{{{\rm{xxx}}}}{{\rm{Hg}}}/1000$$
(8)
$${\mathrm{ln}}({{{\rm{\alpha }}}}^{{{\rm{xxx}}}/198}{{{\rm{Hg}}}}_{{{\rm{MIF}}}})={{{\rm{E}}}}^{{{\rm{xxx}}}}{{\rm{Hg}}}/1000$$
(9)
$${\mathrm{ln}}({{{\rm{\alpha }}}}^{{{\rm{xxx}}}/198}{{{\rm{Hg}}}}_{{{\rm{MDF}}}})={{{\rm{\beta }}}}_{{{\rm{xxx}}}}\times \,{\mathrm{ln}}({{{\rm{\alpha }}}}^{202/198}{{\rm{Hg}}})$$
(10)
$${{{\rm{\alpha }}}}^{{{\rm{xxx}}}/198}{{{\rm{Hg}}}}_{{{\rm{tot}}}}={{{\rm{\alpha }}}}^{{{\rm{xxx}}}/198}{{{\rm{Hg}}}}_{{{\rm{MDF}}}}\times {{{\rm{\alpha }}}}^{{{\rm{xxx}}}/198}{{{\rm{Hg}}}}_{{{\rm{MIF}}}}$$
(11)
$${{{\rm{K}}}}_{{{\rm{xxx}}}}={{{\rm{K}}}}_{198}\times {{{\rm{\alpha }}}}^{{{\rm{xxx}}}/198}{{{\rm{Hg}}}}_{{{\rm{tot}}}}$$
(12)

Where the εxxx and Exxx represent the reported enrichment factors for MDF and MIF, respectively. These factors are calculated as the difference between the MDF and MIF signatures as product over reactant Hg pool. The calculation of αxxx/198HgMDF follows the kinetic laws governing Hg transfer, where β takes values as −0.507, 0.252, 0.502, 0.752, and 1.493 for 196Hg, 199Hg, 200Hg, 201Hg, 202Hg, and 204Hg, respectively10. The αxxx/198Hgtot represents the processes-based kinetic fractionation factors and is defined as the ratio of xxx/198Hg for the product to that in the reactant. The αxxx/198Hgtot comprises two parts: αxxx/198HgMDF and αxxx/198HgMIF.

In this study, we focus on the mass-independent fractionations of even mass isotopes (represented by Δ200Hg). While previous studies11,12,13,41,58 have documented elevated Δ200Hg values in precipitation and aerosols, the mechanisms driving even-MIF remain poorly constrained. Chemical processes of Hg0 photo-oxidation in the tropopause12,13 and HgII photolysis on aerosols mediated by magnetic halogen nuclei11 have been proposed as potential sources. Experimental evidence further implicates mercuric oxide photodissociation in UVC-exposed Hg–O2 systems41. Recent detections of positive Δ200Hg in high-altitude gaseous HgII(g), particulate Hg (HgII(p)), and marine/urban aerosols59,60,61,62,63 underscore the spatial complexity of these processes. Here, we evaluate atmospheric Hg redox pathways using the state-of-the-art atmospheric Hg chemical frameworks4, identifying HgII(p) photoreduction and OH-initiated reactions are plausible dominant even-MIF drivers. Our model successfully reproduces global Δ200Hg distributions (Supplementary Discussion Text S2), resolving key uncertainties in the environmental contexts and chemical pathways of even-MIF generation.

Mercury isotope data

We synthesized representative atmospheric observations of Δ200Hg. These observations are far away from high anthropogenic emission areas, especially for East Asia, where the atmospheric Δ200Hg signatures are significant influenced by anthropogenic emissions. The selected observations are conducted at poles, remote mountain regions, coast areas, marine boundary layer. Most of the land-based observations are from Asia and North America and are presented as average values, including Hg0, HgII(p), and precipitation [HgII(pre)] samples. All the atmospheric isotope data are presented in Supplementary Table 1. For oceanic Hg isotopic signatures, we utilize the synthesized data from Jiskra et al. 14, which includes total Hg in seawater, particle-bound Hg, sediment, and biota samples. These data are collected from four oceans: the Mediterranean Sea, Atlantic Ocean, Pacific Ocean, and Southern Ocean. The median Δ200Hg for oceanic samples are as follows: 0.03‰ (IQR, 0.01‰ to 0.05‰; n = 87) for the Mediterranean Sea, 0.02‰ (IQR, −0.01‰ to 0.05‰; n = 122) for the Atlantic Ocean, 0.06‰ (IQR, 0.03‰ to 0.08‰; n = 295) for the Pacific Ocean, 0.00‰ (IQR, −0.03‰ to 0.08‰; n = 110) for the Southern Ocean. All Δ200Hg signatures for various sample categories in the oceans are detailed in Jiskra et al. 14.