# Modelling the mercury stable isotope distribution of Earth surface reservoirs: Implications for global Hg cycling

Ruoyu Sun, Martin Jiskra, Helen M. Amos, Yanxu Zhang, Elsie M.

Sunderland, Jeroen E. Sonke

► To cite this version:

Ruoyu Sun, Martin Jiskra, Helen M. Amos, Yanxu Zhang, Elsie M. Sunderland, et al.. Modelling the mercury stable isotope distribution of Earth surface reservoirs: Implications for global Hg cycling. Geochimica et Cosmochimica Acta, 2019, 246, pp.156-173. 10.1016/j.gca.2018.11.036. insu-03661426

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Accepted Manuscript

Modelling the mercury stable isotope distribution of Earth surface reservoirs: Implications for global Hg cycling

Ruoyu Sun, Martin Jiskra, Helen M. Amos, Yanxu Zhang, Elsie M. Sunderland, Jeroen E. Sonke

PII: S0016-7037(18)30666-5

DOI: https://doi.org/10.1016/j.gca.2018.11.036

Reference: GCA 11031

To appear in: *Geochimica et Cosmochimica Acta*

Received Date: 19 March 2018

Accepted Date: 26 November 2018

Please cite this article as: Sun, R., Jiskra, M., Amos, H.M., Zhang, Y., Sunderland, E.M., Sonke, J.E., Modelling the mercury stable isotope distribution of Earth surface reservoirs: Implications for global Hg cycling, *Geochimica et Cosmochimica Acta* (2018), doi: https://doi.org/10.1016/j.gca.2018.11.036

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# Modelling the mercury stable isotope distribution of Earth surface reservoirs: implications for global Hg cycling

Ruoyu Sun<sup>a*</sup>, Martin Jiskra<sup>b</sup>, Helen M. Amos<sup>c</sup>, Yanxu Zhang<sup>d</sup>, Elsie M. Sunderland<sup>c,e</sup>, Jeroen E. Sonke<sup>b*</sup>

<sup>a</sup>Institute of Surface-Earth System Science, Tianjin University, Tianjin 300072, China

<sup>b</sup>Observatoire Midi-Pyrénées, laboratoire Géosciences Environnement Toulouse, CNRS/IRD/Université Paul Sabatier Toulouse 3, France

<sup>c</sup>School of Public Health, Department of Environmental Health, Harvard University, Boston, MA, USA

<sup>d</sup>School of Atmospheric Sciences, Nanjing University, Jiangsu 210023, China

<sup>e</sup>School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

Corresponding authors, E-mail: ruoyu.sun@tju.edu.cn, jeroen.sonke@get.omp.eu
**Abstract**

Mercury (Hg) stable isotopes are useful to understand Hg biogeochemical cycling because physical, chemical and biological processes cause characteristic Hg isotope mass-dependent (MDF) and mass-independent (MIF) fractionation. Here, source Hg isotope signatures and process-based isotope fractionation factors are integrated into a fully coupled, global atmospheric-terrestrial-oceanic box model of MDF ($\delta^{202}\text{Hg}$), odd-MIF ($\Delta^{199}\text{Hg}$) and even-MIF ($\Delta^{200}\text{Hg}$). Using this bottom-up approach, we find that the simulated Hg isotope compositions are inconsistent with the observations. We then fit the Hg isotope enrichment factors for MDF, odd-MIF and even-MIF to observational Hg isotope constraints. The MDF model suggests that atmospheric Hg⁰ photo-oxidation should enrich heavy Hg isotopes in the reactant Hg⁰, in contrast to the experimental observations of Hg⁰ photo-oxidation by Br. The fitted enrichment factor of terrestrial Hg⁰ emission in the odd-MIF model (5‰) is likely biased high, suggesting that the terrestrial Hg⁰ emission flux (160 Mg yr⁻¹) used in our standard model is underestimated. In the even-MIF model, we find that a small positive atmospheric Hg⁰ photo-oxidation enrichment factor (0.22‰) along with enhanced atmospheric HgII photo-reduction and atmospheric Hg⁰ dry deposition (foliar uptake) fluxes to the terrestrial reservoir are needed to match $\Delta^{200}\text{Hg}$ observations. Marine Hg isotope measurements are needed to further expand the use of Hg isotopes in understanding global Hg cycling.

**Keywords**

Mercury isotope; Global Hg cycling; Box model; Mass-dependent fractionation; Mass-independent fractionation
# 1. Introduction

Mercury (Hg) is a globally distributed toxic element. Both geogenic processes and human activities liberate Hg from Earth's lithosphere into the surface environment. Geogenic Hg is mainly released into the atmosphere in forms of volcanic and hydrothermal degassing (Bagnato et al., 2014; Pyle and Mather, 2003). From ~3000 BCE, humans started to increase Hg releases by silver/gold mining, fossil fuel combustion and non-ferrous metal smelting (Nriagu, 1979; Streets et al., 2011). Following releases, Hg cycles among atmospheric, terrestrial and oceanic reservoirs before ultimately being buried in marine sediments and returning to the lithosphere (Amos et al., 2014; Andren and Nriagu, 1979; Mason et al., 1994). Understanding the natural and anthropogenic Hg cycles is critical to quantify the amounts of legacy Hg accumulated at the Earth's surface, and to predict how Hg emission reduction policies (e.g., Mercury Minimata Convention) will affect Hg budgets in biogeochemical reservoirs (Amos et al., 2014; Amos et al., 2013). However, large uncertainties still exist for the global Hg cycle regarding the magnitude of numerous fluxes and transformations including atmospheric Hg⁰ oxidation and Hg¹¹ reduction, Hg dry/wet deposition, and marine-atmospheric and terrestrial-atmospheric Hg⁰ exchange (Agnan et al., 2016; Engstrom et al., 2014; Holmes et al., 2010; Huang and Gustin, 2015; Lindberg et al., 2007; Obrist et al., 2014; Pongprueksa et al., 2008; Streets et al., 2011).

Mercury stable isotopes are a new tool to study Hg cycling at various spatiotemporal scales (Blum et al., 2014; Hintelmann, 2012; Sonke, 2011; Sonke and Blum, 2013; Yin et al., 2014). The seven Hg stable isotopes can be fractionated mass-dependently (MDF, indicated by δ²⁰²Hg) and mass-independently (odd-MIF for odd
mass number Hg isotopes indicated by $\Delta^{199}$Hg or $\Delta^{201}$Hg, and even-MIF for even mass number Hg isotopes indicated by $\Delta^{200}$Hg or $\Delta^{204}$Hg). MDF occurs during nearly all abiotic and biotic Hg transformations, and causes the separation between heavy and light Hg isotopes due to the differences in their nuclear masses and volumes (Blum et al., 2014; Yin et al., 2014). Odd-MIF occurs in specific processes that are selective to nuclear spin or nuclear volume, and causes the separation between even and odd mass number Hg isotopes due to the non-zero nuclear spins (magnetic isotope effect, MIE) (Bergquist and Blum, 2007; Buchachenko, 2001; Buchachenko, 2009) or the nuclear size/shape distortion of odd mass number Hg isotopes (nuclear volume effect, NVE) (Ghosh et al., 2013; Schauble, 2007; Zheng and Hintelmann, 2010b). More than 10‰ variation in both MDF and odd-MIF are reported across the Earth's reservoirs (Blum et al., 2014; Yin et al., 2014). Even-MIF is mainly observed in the atmosphere with more than 1‰ variation, but the underlying mechanisms are still unclear (Cai and Chen, 2015; Chen et al., 2012).

Physical, chemical and biological processes drive Hg mass transfer from one reservoir to another, and each process fractionates heavy/light and odd/even Hg isotopes along characteristic trajectories (Blum et al., 2014). The Hg mass transfer and Hg isotope fractionation processes result in biogeochemical reservoirs with distinct Hg isotope signatures. For example, the contrasting $\delta^{202}$Hg, $\Delta^{199}$Hg, and $\Delta^{200}$Hg signatures of atmospheric Hg$^0$ and Hg$^{II}$ lead to powerful applications in tracing Hg$^{II}$ wet and Hg$^0$ dry deposition pathways (Demers et al., 2013; Enrico et al., 2016; Obrist et al., 2017). Across the Arctic tundra, and the North American and European boreal and temperate forested ecosystems, Hg isotope signatures in soils show that Hg deposited through plant uptake of atmospheric Hg$^0$ exceeds Hg originating from atmospheric Hg$^{II}$ wet deposition by a factor 2-4 (Demers et al., 2013;
Enrico et al., 2016; Jiskra et al., 2015; Obrist et al., 2017; Zheng et al., 2016). We have only yet begun to understand the consequences of such a paradigm shift. Enrico et al. (2016) argued that plant uptake lowers atmospheric Hg⁰ lifetime to 4 months. Enrico et al. (2017) used a peat archive to reconstruct the first millennial record of plant Hg⁰ uptake, and found Holocene Hg⁰ levels to be more than 10 times lower than maximum 20th century Hg⁰. Obrist et al. (2017) showed how tundra uptake of Hg⁰ has loaded tundra soils with vast amounts of Hg, that risk being mobilized into the Arctic Ocean by rivers as permafrost soils thaw. We are therefore at a turning point in Hg isotope science, where isotope signatures provide strong constraints and insights on some of the lesser known Hg fluxes and processes at the Earth's surface.

Here we construct a global Hg isotope box model on the basis of the state-of-the-science global Hg chemistry and transport models (Amos et al., 2014; Zhang et al., 2015) where Hg sources and Hg mass transfer processes are complemented with Hg isotope signatures. The initial aim of this Hg isotope model is to examine if Hg isotope observations in atmospheric, terrestrial and oceanic reservoirs can be reproduced using current knowledge on the global Hg cycle, source Hg isotope signatures and Hg isotope fractionation processes. We then investigate how the observed Hg isotope compositions in the Earth's reservoirs can be used to further constrain global Hg mass transfer processes.

## 2. Methods

### 2.1. Hg isotope notations

The Hg isotope composition is expressed in delta notation (δ, ‰) by anchoring to a common NIST SRM 3133 Hg standard:
$$ \delta^{xxx} \text{Hg}(\text{\textperthousand}) = \left[ \left( {}^{xxx}\text{Hg} / {}^{198}\text{Hg} \right)_{\text{sample}} / \left( {}^{xxx}\text{Hg} / {}^{198}\text{Hg} \right)_{\text{NIST 3133}} - 1 \right] \times 1000 \quad (1) $$

Where the superscript XXX is Hg isotope mass number between 199 and 204, (XXXHg/¹⁹⁸Hg)sample is isotope ratio of the sample, and (XXXHg/¹⁹⁸Hg)NIST 3133 is the isotope ratio of the bracketing NIST SRM 3133 Hg standard. The Hg isotope MIF is expressed in capital delta notation (Δ, ‰), representing the difference between the measured δxxxHg and that predicted from δ²⁰²Hg using a kinetic MDF law (Blum and Bergquist, 2007):

$$ \Delta^{xxx} \text{Hg}(\text{\textperthousand}) = \delta^{xxx} \text{Hg} - {}^{xxx}\beta \times \delta^{202} \text{Hg} \quad (2) $$

The mass dependent scaling factor xxxβ is 0.2520 for ¹⁹⁹Hg, 0.5024 for ²⁰⁰Hg, 0.7520 for ²⁰¹Hg and 1.4930 for ²⁰⁴Hg. In this study, we use δ²⁰²Hg, Δ¹⁹⁹Hg and Δ²⁰⁰Hg as the tracers of MDF, odd-MIF and even-MIF, respectively.

The total Hg isotope fractionation factor (α) between reactant i (reservoir i) and product j (reservoir j) is defined as:

$$ \alpha^{xxx} \text{Hg}_{\text{TOT}(i \to j)} = \frac{\text{R}^{xxx} \text{Hg}_j}{\text{R}^{xxx} \text{Hg}_i} = \frac{\left( {}^{xxx}\text{Hg} / {}^{198}\text{Hg} \right)_j}{\left( {}^{xxx}\text{Hg} / {}^{198}\text{Hg} \right)_i} \quad (3) $$

and can be decomposed into MDF, odd-MIF and even-MIF components (Sonke, 2011):

$$ \alpha^{xxx} \text{Hg}_{\text{TOT}(i \to j)} = \alpha^{xxx} \text{Hg}_{\text{MDF}(i \to j)} \times \alpha^{xxx} \text{Hg}_{\text{odd-MIF}(i \to j)} \times \alpha^{xxx} \text{Hg}_{\text{even-MIF}(i \to j)} \quad (4) $$

Both α²⁰²Hgodd-MIF and α²⁰²Hgeven-MIF equal to 1 for α²⁰²HgTOT; α¹⁹⁹Hgeven-MIF equals to 1 for α¹⁹⁹HgTOT; α²⁰⁰Hgodd-MIF equals to 1 for α²⁰⁰HgTOT. The Hg isotope enrichment factor expressed in epsilon notation (ε or E) is used to denote ‘permil fractionation factor’, which we use from here on:
$$ 
\begin{aligned}
\varepsilon^{202}\text{Hg}(\%) &= 1000 \times (\alpha^{202}\text{Hg}_{\text{MDF}} - 1) \\
E^{199}\text{Hg}(\%) &= 1000 \times (\alpha^{199}\text{Hg}_{\text{odd-MIF}} - 1) \quad (5) \\
E^{200}\text{Hg}(\%) &= 1000 \times (\alpha^{200}\text{Hg}_{\text{even-MIF}} - 1)
\end{aligned}
$$

## 2.2. Model description

The basic structure of the global Hg isotope box model is based on the 7-box model of Amos et al. (2013, 2014) that is used to simulate global biogeochemical cycle of total Hg (THg). Here, we further separate the atmospheric THg box into gaseous elemental Hg⁰ and oxidized Hg¹¹ (including gaseous oxidized Hg¹¹ and particulate-bound HgP) based on the GEOS-Chem model of Holmes et al. (2010). THg in the surface, intermediate and deep ocean layers is also speciated as dissolved Hg⁰, dissolved Hg¹¹ and particulate-bound HgP based on a global 3D ocean general circulation model (MITgcm) (Zhang et al., 2015). Thus, the global Hg isotope box model comprises 14 Hg reservoirs (named as Global 14-Box Model of Hg Isotopes, user instruction and model codes are available at https://github.com/ruoyusun/GBM-Hg-ISO-14box-v1.git): atmospheric Hg⁰_atm, atmospheric Hg¹¹_atm, fast terrestrial Hgₜₜ, slow terrestrial Hgₜₛ, armored terrestrial Hgₜₐ, surface oceanic Hg⁰_ocs, surface oceanic Hg¹¹_ocs, surface oceanic HgP_ocs, intermediate oceanic Hg⁰_oci, intermediate oceanic Hg¹¹_oci, intermediate oceanic HgP_oci, deep oceanic Hg⁰_ocd, deep oceanic Hg¹¹_ocd, and deep oceanic HgP_ocd (Fig. 1). Organic Hg species (e.g. monomethylmercury and dimethylmercury) are not included in the model at this stage and are implicitly included in THg.

Mass transfer of Hg between boxes are controlled by first-order time-invariant rate coefficients (k, yr⁻¹), and are represented by a group of 14 coupled ordinary differential equations (ODEs):
$$ \frac{dM_i}{dt} = \sum_{j \neq i} (k_{j \to i} \times M_j) - \sum_{i \neq j} (k_{i \to j} \times M_i) + S \quad (6) $$

Where $M_i$ (Mg) is the Hg mass in box 'i', and $M_j$ (Mg) is the Hg mass in box 'j'. $k_{j \to i}$ = $F_{j \to i}/M_j$ and $k_{i \to j}$ = $F_{i \to j}/M_i$ are the first-order rate coefficients, in which $F_{j \to i}$ (Mg yr⁻¹) is Hg flux from box 'j' to box 'i' and $F_{i \to j}$ (Mg yr⁻¹) is Hg flux from box 'i' to box 'j'. S (Mg yr⁻¹) is external Hg input from the deep mineral reservoir by natural and/or anthropogenic processes (0 for all reservoirs except for the atmosphere and surfaceocean). Sequestration of riverine HgP in coastal margin sediments and HgP in deep oceanic sediments are treated as permanent Hg removal processes.

Fractionation of Hg isotopes between boxes are controlled by time-invariant Hg isotope enrichment factors (ε or E), and are also represented as a group of 14 coupled ODEs:

$$ \frac{d(M_i \times \delta^{202}Hg_i)}{dt} = \sum_{j \neq i} \left[ k_{j \to i} \times M_j \times (\delta^{202}Hg_j + \epsilon^{202}Hg_{(j \to i)}) \right] - \sum_{i \neq j} \left[ k_{i \to j} \times M_i \times (\delta^{202}Hg_i + \epsilon^{202}Hg_{(i \to j)}) \right] + S \times \delta^{202}Hg_S \quad (7) $$

for MDF, or

$$ \frac{d(M_i \times \Delta^{xxx}Hg_i)}{dt} = \sum_{j \neq i} \left[ k_{j \to i} \times M_j \times (\Delta^{xxx}Hg_j + E^{xxx}Hg_{(j \to i)}) \right] - \sum_{i \neq j} \left[ k_{i \to j} \times M_i \times (\Delta^{xxx}Hg_i + E^{xxx}Hg_{(i \to j)}) \right] + S \times \Delta^{xxx}Hg_S \quad (8) $$

for odd-MIF (Δ¹⁹⁹Hg) or even-MIF (Δ²⁰⁰Hg). Since Hg redox transformations are one-way kinetic processes, the MDF and MIF isotope enrichment factors represent kinetic isotope fractionation. The time-step (dt) of the ODE solver algorithm is small enough to avoid Rayleigh-type reservoir effects.
From the equations 6-8, the global Hg isotope model comprises four basic
components: rate coefficient k, geogenic/anthropogenic Hg input inventory S and its
isotope composition δ<sup>202</sup>Hg<sub>S</sub> or Δ<sup>xxx</sup>Hg<sub>S</sub>, and Hg isotope enrichment factor ε or E. The
rate coefficients are calculated from present-day reservoir Hg sizes and Hg fluxes
between reservoirs, based on the GEOS-Chem and MITgcm models (summarized in
Table EA-1 and explained in the Electronic Annex). We use the same Hg input
inventory as Amos et al. (2014), which includes geogenic (90 Mg/yr) (Bagnato et al.,
2011) and anthropogenic (2000 BCE to 2010 CE, cumulatively 460,000 Mg) Hg
emissions into the atmosphere (Horowitz et al., 2014; Streets et al., 2011) and
anthropogenic Hg discharges into the river (1850 CE -2010 CE, cumulatively 380,000
Mg) (Amos et al., 2014). The riverine Hg is then delivered to the surface ocean after
partial burial in coastal margin sediments (Amos et al., 2014). Previous studies have
evaluated the uncertainties of these Hg input inventories (Amos et al., 2014; Horowitz
et al., 2014; Streets et al., 2011), and demonstrated that their use in the Hg cycling
models could result in output compatible with observed Earth's budgets and fluxes
(Amos et al., 2014; Amos et al., 2013; Amos et al., 2015). The isotope composition of
Hg input inventory and Hg isotope enrichment factor are discussed below.

**2.2.1. Isotope composition of Hg input inventory**

The geogenic Hg emissions are derived from observations on volcanic plumes as
summarized by Bagnato et al. (2011). Volcanic fumarole plume THg has a mean
value of -0.76‰ ± 0.11‰ (1σ) for δ<sup>202</sup>Hg and of 0.05‰ ± 0.03‰ (1σ) for Δ<sup>199</sup>Hg
(Sun et al., 2016b; Zambardi et al., 2009). Thus, the geogenic Hg emissions are
assumed to have a δ<sup>202</sup>Hg value of -0.76‰ ± 0.11‰ (1σ). The anthropogenic Hg
emissions to the atmosphere are separated as gaseous Hg<sup>0</sup>, gaseous Hg<sup>II</sup> and
particulate-bound Hg<sup>P</sup>, and their Hg isotope compositions and associated uncertainties between 1850 and 2010 were estimated by Sun et al. (2016b) after correcting the isotope shifts during processing and combustion of anthropogenic source materials. Pre-1850 Hg emissions mostly originated from the intentional liquid Hg<sup>0</sup> use in silver production (58%) and Hg ore mining (30%) around the 16<sup>th</sup>-18<sup>th</sup> centuries in South/Central America (Streets et al., 2011). We assume these emissions to be near-quantitative and in the gaseous Hg<sup>0</sup> form, and should therefore conserve the Hg isotope signatures of source materials. According to anthropogenic Hg emission budgets of individual sectors before 1850 and their source material Hg isotope compositions, we estimate a median value of -0.91‰ (-1.49‰ to -0.49‰ at 80% confidence level) for δ<sup>202</sup>Hg and of 0.00‰ (-0.04‰ to 0.04‰ at 80% confidence level) for Δ<sup>199</sup>Hg, following Sun et al. (2016b). Since modern rivers mainly receive effluent Hg from industrial sectors that intentionally use liquid Hg<sup>0</sup> (Amos et al., 2014; Horowitz et al., 2014; Wiederhold et al., 2015), the direct anthropogenic Hg discharges into rivers are assumed to have the Hg isotope composition of commercial liquid Hg<sup>0</sup> (δ<sup>202</sup>Hg = -0.49‰ ± 0.40‰, Δ<sup>199</sup>Hg = -0.01‰ ± 0.05‰, 1σ) (Blum and Bergquist, 2007; Estrade et al., 2009; Foucher et al., 2009; Gray et al., 2013; Laffont et al., 2011; Mead et al., 2013; Ruaibarz et al., 2016; Sonke et al., 2008). As geogenic emissions and riverine discharges have very small Δ<sup>199</sup>Hg values, within the typical measurement uncertainty (± 0.05‰ to ± 0.10‰), we assume that they have no odd-MIF anomalies (i.e. Δ<sup>199</sup>Hg = 0.00‰). Following Sun et al. (2016b), we assume that geogenic and anthropogenic Hg sources have no even-MIF anomalies (i.e. Δ<sup>200</sup>Hg = 0.00‰).

### 2.2.2. Isotope enrichment factor
The Hg isotope enrichment factors in the model are derived from laboratory-
controlled experiments where possible, or empirically estimated from the literature, or
unknown. Table EA-2 lists the experimental enrichment factors for MDF (ε²⁰²Hg) and
odd-MIF (E¹⁹⁹Hg) during physical, chemical and biological transformation of
inorganic Hg. We note that these enrichment factors were obtained under controlled
laboratory conditions and their extrapolation to the natural environment is associated
with large uncertainties. In the following, we discuss the experimental conditions
under which enrichment factors were determined and the rationale for the selection of
specific literature values for the MDF and odd-MIF ‘standard model’ simulation in
Tables 1-2. A small amount of even-MIF (E²⁰⁰Hg<sub>atm (0-II)</sub> = 0.06‰ ± 0.01‰, 1σ) was
only observed in the photochemical reaction of Hg�0 + Br/Cl (Sun et al., 2016a). Thus,
we use a value of 0.05‰ for E²⁰⁰Hg<sub>atm (0-II)</sub> in even-MIF ‘standard model’ simulation
(Table 3).

2.2.2.1 Oxidation of gaseous Hg⁰

Gaseous Hg⁰ photo-oxidation experiments under normal atmospheric condition
(25 °C, 750 Torr) showed that the reaction of Hg⁰ + Br induced both MDF and odd-
MIF. The reactant Hg⁰ became progressively enriched in the light (ε²⁰²Hg = 0.74‰ ±
0.07, 1σ) and odd Hg isotopes (E¹⁹⁹Hg = -0.25‰ ± 0.05, 1σ) (Sun et al., 2016a). This
positive ε²⁰²Hg is unusual, as it is the first time that kinetic isotope fractionation
shows enrichment of the less reactive heavy isotopes in the product HgII. The reaction
of Hg⁰ + Cl was also studied by Sun et al. (2016a), and was found to induce MDF
(ε²⁰²Hg = -0.59‰ ± 0.03‰, 1σ), odd-MIF (E¹⁹⁹Hg = -0.37‰ ± 0.06‰, 1σ) and a
small amount of even-MIF (E²⁰⁰Hg = 0.06‰ ± 0.01‰, 1σ). Here the reactant Hg⁰
became enriched in the heavy and odd Hg isotopes, but also depleted in the even Hg
isotopes. However, the odd-MIF of Hg⁰ + Cl showed a Δ¹⁹⁹Hg/Δ²⁰¹Hg slope of 1.9, which is significantly higher than the slopes known for experimental MIE (1.0-1.3) (Bergquist and Blum, 2007; Zheng and Hintelmann, 2009) and NVE (~1.6) (Estrade et al., 2009; Ghosh et al., 2013). Both unusual observations on Hg isotope fractionation by Hg⁰ + Cl and Hg⁰ + Br pathways question their relevance for interpreting natural observations. Atmospheric Hg⁰ photo-oxidation pathways are currently not well understood as the HgII products have not been identified. Current global Hg models however suggest that Br rather than Cl radicals are the main oxidants (Holmes et al., 2010; Horowitz et al., 2017). Therefore, our standard model uses MDF and odd-MIF enrichment factors associated with atmospheric Hg⁰ photo-oxidation via the Hg⁰ + Br pathway from Sun et al., 2016a. As shown in Horowitz et al. (2007), the Hg⁰ + Br pathway has a second oxidation step that may involve NO₂ and HO₂. However, we don't know any Hg isotope enrichment factors for this step, implying that the used enrichment factor for Hg⁰ + Br pathway in our model has a large uncertainty.

### 2.2.2.2. Reduction of aqueous dissolved HgII

Reduction of HgII bound to dissolved organic matter (DOM) is extensively studied in laboratory-controlled experiments (Bergquist and Blum, 2007; Kritee et al., 2008; Kritee et al., 2007; Rose et al., 2015; Yang and Sturgeon, 2009; Zheng and Hintelmann, 2009, 2010a). Biotic and abiotic (photochemical and non-photochemical) reduction pathways exhibit distinct Hg isotope fractionation trajectories. MDF occurs in all these types of reduction, with a consistent enrichment of light Hg isotopes in the product Hg⁰. Additionally, abiotic HgII reduction can induce characteristic MIF via MIE (photochemical) (Bergquist and Blum, 2007;
Zheng and Hintelmann, 2009) or NVE (non-photochemical) (Zheng and Hintelmann, 2010b). Microbial Hg<sup>II</sup> reduction experiments showed that ε<sup>202</sup>Hg varies from -0.4‰ ± 0.2‰ (1σ) to -2.0‰ ± 0.2‰ (1σ), depending on the bacterial species and substrate Hg<sup>II</sup> concentrations (Kritee et al., 2008; Kritee et al., 2007). We assume that the natural bacteria un-adapted to high Hg concentrations are most representative for marine biota. Therefore, we choose a value of -0.4‰ for ε<sup>202</sup>Hg associated with marine, biotic Hg<sup>II</sup> reduction, which is at the lower end of the range reported for microbial Hg<sup>II</sup> reduction. Many photo-reduction experiments of Hg<sup>II</sup>-DOM indicated that the odd Hg isotopes are preferentially enriched in the reactant Hg<sup>II</sup> (Bergquist and Blum, 2007; Rose et al., 2015; Yang and Sturgeon, 2009; Zheng and Hintelmann, 2009). The large, positive Δ<sup>199</sup>Hg values observed in wet deposition (Chen et al., 2012; Demers et al., 2013; Donovan et al., 2013; Enrico et al., 2016; Gratz et al., 2010; Sherman et al., 2015; Sherman et al., 2012; Wang et al., 2015; Yuan et al., 2015) and coastal seawater samples (Štrok et al., 2015; Štrok et al., 2014) suggest that photo-reduction of Hg<sup>II</sup> in the atmosphere likely enrich odd Hg isotopes in the residual Hg<sup>II</sup>. The enrichment factors reported for Hg<sup>II</sup>-DOM photo-reduction experiments are very variable for different Hg/DOC ratios. The Zheng and Hintelmann (2009)'s experiment with lowest Hg/DOC ratio (35 ng mg<sup>-1</sup>) studied so far is most representative for natural systems. We therefore use its enrichment factors (ε<sup>202</sup>Hg = -0.77‰ ± 0.18‰; E<sup>199</sup>Hg = -2.75‰ ± 0.14‰, 1σ) for Hg<sup>II</sup> photo-reduction in atmospheric and oceanic reservoirs. Terrestrial Hg is mainly bound to -SH (thiol) ligands of organic matter in soils and in forms of thiolate complex (Hg(SR)<sub>2</sub>) or Hg-S nanoparticulate in plant leaves (Manceau et al., 2018; Skyllberg et al., 2006). Zheng et al. (2010a) showed that the photo-reduction of Hg<sup>II</sup> bound to low molecular weight -SH ligands is associated with a depletion of odd Hg isotopes in the reactant Hg<sup>II</sup>. The
enrichment factors ($\varepsilon^{202}\text{Hg} = -1.32\text{‰} \pm 0.04\text{‰}; \text{E}^{199}\text{Hg} = 1.02\text{‰} \pm 0.02\text{‰}, 1\sigma$) associated with photo-reduction of Hg$^{II}$ bound to cysteine (-SH) from Zheng et al. (2010a) are extrapolated to terrestrial Hg$^{II}$ photo-reduction based on their similar Hg bonding environments. Additionally, a previous Hg isotope MIF model by Sonke (2011) also suggested that soil Hg$^{II}$ photo-reduction most likely depletes odd isotopes in terrestrial reservoir, and gave a best-fitted E$^{199}$Hg of 1.4‰. Nevertheless, we have no experimental evidences for photochemical MIF occurring in upper soils. Following Jiskra et al. (2015), the enrichment factors ($\varepsilon^{202}\text{Hg} = -1.52 \pm 0.03\text{‰}; \text{E}^{199}\text{Hg} = 0.18\text{‰} \pm 0.03\text{‰}, 1\sigma$) determined by Zheng and Hintelmann (2010b) are used for non-photochemical reduction of terrestrial Hg$^{II}$.

### 2.2.2.3. Sorption of dissolved Hg$^{II}$ onto particles

The dissolved Hg$^{II}$ sorption was shown to associate with an enrichment in light Hg isotopes by -0.30‰ ± 0.04‰ (1σ) to -0.44‰ ± 0.04‰ (1σ) to the mineral surfaces (Jiskra et al., 2012), and -0.53‰ ± 0.08‰ (1σ) to -0.62‰ ± 0.09‰ (1σ) to the -SH ligands (Wiederhold et al., 2010) in $\delta^{202}\text{Hg}$. Insignificant to small odd-MIF (<0.1‰ in $\Delta^{199}\text{Hg}$) was also observed for both Hg$^{II}$ sorption experiments. We therefore chose a value of -0.50‰ for $\varepsilon^{202}\text{Hg}$ and of 0.00‰ for E$^{199}\text{Hg}$ for the partitioning of marine dissolved Hg$^{II}$ to Hg$^{P}$.

### 2.2.2.4. Evasion of dissolved gaseous Hg$^{0}$

The laboratory-controlled experiments showed that volatilization of dissolved Hg$^{0}$ from solution into the atmosphere enriches the light Hg isotopes in product gaseous Hg$^{0}$, with reported $\varepsilon^{202}\text{Hg}$ values of -0.44‰ ± 0.02‰ (1σ) and -0.47‰ ± 0.01‰ (1σ) (Zheng et al., 2007). No odd-MIF was observed during this experiment. Here, we use
a value of -0.45‰ to represent the ε²⁰²Hg associated with dissolved Hg⁰ evasion from
the surface ocean.

2.2.2.5. Plant uptake of atmospheric Hg⁰

Enrico et al. (2016) estimated an empirical ε²⁰²Hg of -2.6‰ for foliar Hg⁰ uptake based on the difference in Hg concentrations and δ²⁰²Hg values of atmospheric Hg⁰ between a peatland and the adjacent open mountain. This value agrees well with the δ²⁰²Hg difference (-3‰ to -2‰) between atmospheric gaseous Hg (primarily Hg⁰) and co-located plant leaves reported in most studies (Demers et al., 2013; Enrico et al., 2016; Obrist et al., 2017; Yin et al., 2013; Yu et al., 2016). Here, the value of -2.6‰ for foliar Hg⁰ uptake is used for atmospheric Hg⁰ dry deposition, following the notion that vegetation uptake is the dominant dry deposition pathway over terrestrial surfaces (Jiskra et al., 2018). Up to 0.3‰ negative shift in Δ¹⁹⁹Hg was observed in plant leaves relative to atmospheric Hg⁰ (Demers et al., 2013; Yu et al., 2016; Zheng et al., 2016), which was interpreted as photo-reduction of Hg¹¹ bound to -SH on foliage (Demers et al., 2013) and parameterized in the model as discussed above. A similar offset in Δ¹⁹⁹Hg was also observed during photo-microbial reduction of algal intracellular Hg¹¹ (Kritee et al., 2018).

3. Overview of Hg isotope compositions in Earth's reservoirs

To compare simulated Hg isotope compositions by the Hg isotope box model with
observations, we established a database of Hg isotope compositions measured in
Earth's reservoirs. Fig. 2 presents the statistic histograms for published values of
δ²⁰²Hg (A), Δ¹⁹⁹Hg (B) and Δ²⁰⁰Hg (C) in the atmospheric, terrestrial and oceanic
reservoirs.
## 3.1. Atmosphere

Due to difficulty in the separation of gaseous Hg�0 from gaseous HgII during atmospheric Hg species sampling, they are commonly collected together as total gaseous Hg. The bulk Hg isotope composition of total gaseous Hg is usually used to represent that of elemental Hg⁰_atm, due to the small fraction of gaseous HgII (<5%) in the atmospheric boundary layer (Demers et al., 2013; Demers et al., 2015; Enrico et al., 2016; Fu et al., 2016; Gratz et al., 2010; Sherman et al., 2010; Xu et al., 2017; Yu et al., 2016). The background levels of gaseous HgII and particulate-bound HgP are too low to precisely measure their isotope compositions. Wet deposition (rain or snow) scavenges both water-soluble gaseous HgII and particulate-bound HgP (Keeler et al., 1995; Lindberg and Stratton, 1998; Yuan et al., 2018). We assume that the Hg isotope composition in wet deposition (Chen et al., 2012; Demers et al., 2013; Donovan et al., 2013; Enrico et al., 2016; Gratz et al., 2010; Sherman et al., 2015; Sherman et al., 2012; Wang et al., 2015; Yuan et al., 2015) is representative for atmospheric oxidized HgII_atm comprised of gaseous and particulate forms in the model.

As shown in Figs. 2A-B, Hg⁰_atm is ~0.5‰ higher than HgII_atm in δ²⁰²Hg (0.10‰ ± 0.65‰ vs. -0.41‰ ± 0.48‰, 1σ), but is ~ 0.5‰ lower than HgII_atm in Δ¹⁹⁹Hg (-0.11‰ ± 0.12‰ vs. 0.39‰ ± 0.28‰, 1σ). Significant and positive Δ²⁰⁰Hg observed in HgII_atm (0.17‰ ± 0.08‰, 1σ) is balanced by the small and negative Δ²⁰⁰Hg in Hg⁰_atm (-0.04 ± 0.05‰, 1σ) (Fig. 2C). Significant Hg isotope differences are observed between Hg⁰_atm samples collected from rural sites in Europe/North America and mostly urban-industrial sites in China. Hg⁰_atm in Europe/North America (δ²⁰²Hg = 0.61‰ ± 0.44‰; Δ¹⁹⁹Hg = -0.20‰ ± 0.08‰, Δ²⁰⁰Hg = -0.07‰ ± 0.05‰, 1σ, n = 98) (Demers et al., 2013; Demers et al., 2015; Enrico et al., 2016; Fu et al., 2016; Gratz et al., 2010;
Sherman et al., 2010) is more enriched in heavy and depleted in odd Hg isotopes than China (δ<sup>202</sup>Hg= -0.30‰ ± 0.48‰; Δ<sup>199</sup>Hg = -0.04‰ ± 0.09‰, Δ<sup>200</sup>Hg = -0.01‰ ± 0.03‰, 1σ, n = 122) (Xu et al., 2017; Yu et al., 2016). This difference may be explained by a higher contribution of Hg from primary anthropogenic sources in the Chinese samples, reflected also in higher Hg concentrations in China compared to Europe/North America. The regional differences are not considered in our global Hg box model.

## 3.2. Terrestrial reservoir

We compiled Hg isotope compositions reported in forest ecosystem including foliage, litter, organic and mineral soil (Demers et al., 2013; Enrico et al., 2016; Jiskra et al., 2015; Wang et al., 2017; Yu et al., 2016; Zhang et al., 2013; Zheng et al., 2016). δ<sup>202</sup>Hg in the terrestrial reservoir increases significantly from foliage/litter (-2.56‰ ± 0.64‰, 1σ, n = 156) to organic surface soils (-1.79‰ ± 0.45‰, 1σ, n = 85) and to mineral soil (-1.39‰ ± 0.43‰, 1σ, n = 50) (Fig. 2A). Δ<sup>199</sup>Hg only shows a small increase from foliage/ litter (-0.31‰ ± 0.13‰, 1σ, n = 156) to organic surface soil (-0.25‰ ± 0.14‰, 1σ, n = 85) and mineral soil (-0.25‰ ± 0.14‰, 1σ, n = 50) (Fig. 2B). No significant anomalies in Δ<sup>200</sup>Hg were observed for the terrestrial reservoirs (Fig. 2C). Foliage and litters collected in China (δ<sup>202</sup>Hg = -2.95‰ ± 0.36‰; Δ<sup>199</sup>Hg = -0.34‰ ± 0.12‰, 1σ, n = 57) (Wang et al., 2017; Yu et al., 2016) are also significantly different from those collected in Europe/North America (δ<sup>202</sup>Hg = -1.89‰ ± 0.44‰; Δ<sup>199</sup>Hg = -0.25‰ ± 0.12‰, 1σ, n = 99) (Demers et al., 2013; Enrico et al., 2016; Jiskra et al., 2015; Zhang et al., 2013; Zheng et al., 2016). Thus, foliage/litter is likely biased towards low mean δ<sup>202</sup>Hg value, because the database contains >60% of Chinese samples that are characterized by very negative δ<sup>202</sup>Hg.
### 3.3. Ocean

Low Hg levels in ocean waters make measurements of Hg isotope ratios very challenging and therefore only limited data exist. Štrok et al., (2014) reported the first analyses of coastal seawater samples, and showed that $δ^{202}Hg$ varies from -1.5‰ to -0.5‰ with small, positive $Δ^{199}Hg$ (-0.01‰ to 0.14‰) and $Δ^{200}Hg$ (0.05‰ to 0.53‰). A further study by Štrok et al., (2015) showed that the coastal filtered seawater near the Canadian Arctic Archipelago had more negative $δ^{202}Hg$ (-2.85% to -1.10%), and also positive $Δ^{199}Hg$ (0.17‰ to 0.29‰) and $Δ^{200}Hg$ (0.05‰ to 0.52‰). Dissolved Hg<sup>II</sup> is the primary Hg pool in the ocean, and is likely the main Hg form in these reported seawater samples (Lamborg et al., 2014; Zhang et al., 2014). Up until now, Hg isotope data for open ocean waters are not reported. Blum et al. (2013) proposed that the dissolved Hg<sup>II</sup> in the open Pacific Ocean likely had small positive $δ^{202}Hg$ and $Δ^{199}Hg$, similar to the Pacific coastal rainwater ($δ^{202}Hg$ = 0‰ to 0.2‰; $Δ^{199}Hg$ = 0.25‰ to 0.35‰) (Donovan et al., 2013; Sherman et al., 2012). It is noted that seawater in coastal and shelf areas might be significantly affected by Hg inputs from terrestrial reservoirs, while the open ocean mainly receives Hg from atmospheric deposition (Amos et al., 2014; Holmes et al., 2010).

Therefore, based on the availability of Hg stable isotope measurements, we consider the Hg isotope composition of the atmospheric reservoir as the primary observational constraint followed by the terrestrial reservoir. The Hg isotope composition of the oceanic reservoir is used as the least well-known constraint. In the following, the simulated results of the models are first compared against the Hg isotope composition of atmospheric reservoir followed by those of terrestrial and oceanic reservoirs.
4. Modelling results and evaluation

The Hg isotope box model simulation is first run for MDF, odd-MIF and even-MIF
until natural steady-state in both Hg masses (i.e. dMᵢ/dt = 0) and Hg isotope
compositions (i.e. d(δ²⁰²Hgᵢ)/dt = 0, d(Δ¹⁹⁹Hgᵢ)/dt = 0 and d(Δ²⁰⁰Hgᵢ)/dt = 0) of all
reservoirs. The initial spin-up uses geogenic Hg emissions to the atmosphere only (S
= 90 Mg a⁻¹) with a constant Hg isotope composition (δ²⁰²Hg_s = -0.76‰; Δ¹⁹⁹Hg_s =
0.00‰; Δ²⁰⁰Hg_s = 0.00‰). Then, following Amos et al. (2014), the reservoir Hg
masses and Hg isotope compositions in natural steady-state are used as the initial
conditions for the standard model run from 2000 BCE until present (2010). In the
standard model all-time anthropogenic Hg emissions to the atmosphere are introduced
with a time-dependent Hg isotope composition (1850-2010: data from Sun et al.
(2016b); pre-1850: δ²⁰²Hg_s = -0.91‰; Δ¹⁹⁹Hg_s = 0.00‰; Δ²⁰⁰Hg_s = 0.00‰) and direct
anthropogenic Hg discharges into rivers with a constant Hg isotope composition
(δ²⁰²Hg_s = -0.49‰; Δ¹⁹⁹Hg_s = 0.00‰; Δ²⁰⁰Hg_s = 0.00‰) (Tables 1-3). The simulated
Hg budgets and isotope compositions of environmental reservoirs (boxes) are not at
steady-state due to human perturbations since 2000 BCE.

Table EA-3 lists the simulated Hg sizes in various reservoirs under natural steady-
state and in 1850 and 2010. The simulated present-day (2010) Hg size is 5500 Mg for
atmosphere, 12,300 Mg (i.e. 1.14 pM) for the upper ocean (surface and intermediate
ocean) and 250,000 Mg for the terrestrial soils. The atmospheric Hg deposition in
modern days (1990-2010) is elevated by a factor of 3.8 relative to the pre-industrial
period (1760-1880). These data are comparable to those derived from contemporary
measurements and various models (atmosphere: 4600-5600 Mg; upper ocean: 0.5-2.0
pM; terrestrial soils: >200,000; pre-industrial Hg enrichment factor: 2-5) (Amos et al.,
2014; Amos et al., 2013; Biester et al., 2007; Bowman et al., 2015; Hararuk et al., 2013; Horowitz et al., 2014; Horowitz et al., 2017; Lamborg et al., 2002; Lamborg et al., 2014; Mason et al., 2012; Selin et al., 2008; Sunderland and Mason, 2007; Zhang et al., 2014).

Fig. 3 shows that the simulated modern-day δ<sup>202</sup>Hg and Δ<sup>199</sup>Hg values in the atmospheric, terrestrial and oceanic reservoirs are very different from their observed isotope compositions. For example, the standard model predicts that δ<sup>202</sup>Hg values of Hg<sup>II</sup><sub>atm</sub> are more than 1‰ higher than Hg<sup>0</sup><sub>atm</sub>, which is contrary to the observations of higher δ<sup>202</sup>Hg values of gaseous Hg<sup>0</sup> compared to wet deposition (Table 1). The simulated atmospheric and terrestrial Δ<sup>199</sup>Hg values are underestimated by over 1‰ compared to their observed values (Table 2). The simulated Δ<sup>200</sup>Hg values are too small to explain the observed large Δ<sup>200</sup>Hg in the wet deposition (Table 3). Thus, it appears that the direct use of experimentally determined Hg isotope enrichment factors is unrealistic or some key Hg isotope enrichment factors are missing in the standard Hg isotope model. To a lesser extent, the uncertainties in source Hg isotope compositions and Hg mass transfer processes in our Hg cycling box model also potentially bias the simulated output.

**5. Discussion on Hg isotope box model**

In the following, we first discuss how the source Hg isotope uncertainties affect the simulated Hg isotope compositions. Then, we test the sensitivity of simulated Hg isotope compositions to Hg isotope enrichment factors, with the aim of finding the best-fitted enrichment factors that reproduce the observed Hg isotope compositions. Lastly, we examine the sensitivity of simulated Hg isotope compositions to some key but controversial Hg mass transfer processes.
## 5.1. Uncertainties in source Hg isotope compositions

The Hg input inventory for the Hg isotope model include three categories: geogenic Hg emissions to the atmosphere, all-time anthropogenic Hg emissions to the atmosphere and anthropogenic Hg discharges to rivers and ultimately oceans. $\Delta^{199}\text{Hg}$ and $\Delta^{200}\text{Hg}$ values in all these sources are very small, and are generally around zero within the measurement uncertainty (±0.10‰). Setting $\Delta^{199}\text{Hg}$ values of all-time anthropogenic Hg emissions as zeros has no significant effect (<0.03‰ increase) on the simulated $\Delta^{199}\text{Hg}$ in all the Earth's reservoirs. Thus, we only discuss the model sensitivity to the uncertainties of source $\delta^{202}\text{Hg}$ values.

Due to the large amount of anthropogenic Hg released, any uncertainty in geogenic $\delta^{202}\text{Hg}$ only has a very little effect on the modern reservoir $\delta^{202}\text{Hg}$ values. Varying geogenic $\delta^{202}\text{Hg}$ by 1‰ only changes <0.1‰ in the modern $\delta^{202}\text{Hg}$ values of reservoirs except for the armored terrestrial reservoir and deep ocean. Similarly, the simulated reservoir $\delta^{202}\text{Hg}$ values are also insensitive to the $\delta^{202}\text{Hg}$ variation in anthropogenic Hg discharges to rivers from 1850 to 2010. This is because >90% of riverine Hg exists as Hg$^P$ of which ~70% is thought to be buried in the shelf and coastal areas before entering into open ocean (Amos et al., 2014; Zhang et al., 2015). Varying the $\delta^{202}\text{Hg}$ values of anthropogenic riverine discharges between mean (-0.5‰) and mean-1σ (-0.9‰) or mean+1σ (-0.1‰) only slightly changes modern reservoir $\delta^{202}\text{Hg}$ values (<0.1‰ for atmospheric and terrestrial reservoirs; 0.10‰-0.15‰ for oceanic reservoirs). In contrast, the simulated reservoir $\delta^{202}\text{Hg}$ values are very sensitive to the $\delta^{202}\text{Hg}$ variation in all-time anthropogenic Hg emissions. The use of the lower (P10) or upper (P90) boundary $\delta^{202}\text{Hg}$ values (Sun et al., 2016b) changes the modern reservoir $\delta^{202}\text{Hg}$ values by 0.12‰ to 0.27‰. Taken together, the $\delta^{202}\text{Hg}$
uncertainties of Hg release sources may account for up to 0.5‰ variation in δ²⁰²Hg values of modern Earth's reservoirs.

## 5.2. Fitting of Hg isotope enrichment factors

The fitting of Hg isotope enrichment factors adopts the following steps on basis of the observational constraints as discussed in section 3. 1) the enrichment factors associated with atmospheric redox processes are initially fitted to reproduce the relative difference of observed Hg isotope compositions between Hg⁰_atm and HgII_atm. 2) The enrichment factors associated with terrestrial and oceanic redox processes are then fitted to match the absolute values of observed Hg isotope compositions of Hg⁰_atm and HgII_atm. 3) The simulated Hg isotope compositions of terrestrial and upper oceanic HgII are compared with their observed values to find the optimized combination of enrichment factors. Model fitting runs are indicated as 'model #1-x' in contrast with the 'standard model' that is only based on published enrichments factors (Tables 1-3).

### 5.2.1. Mass dependent fractionation (MDF) model

In the standard MDF model, both photo-reduction of HgII_atm and photo-oxidation of Hg⁰_atm enrich heavy Hg isotopes in HgII_atm, causing δ²⁰²HgII_atm to be significantly higher than δ²⁰²Hg⁰_atm. This is contrary to observed δ²⁰²Hg in the atmosphere where δ²⁰²Hg⁰_atm exceeds δ²⁰²HgII_atm by ~0.5‰ (Fig. 3). Here, we optimize photo-oxidation ε²⁰²Hg_atm (0-II) to enrich the light Hg isotopes in the product HgII_atm which would be coherent with kinetic isotope fractionation theory (i.e. light isotopes are preferably enriched in products) (Hoefs, 2015; Wiederhold, 2015). We find that a value of -0.85‰ for ε²⁰²Hg_atm (0-II) results in ~0.5‰ relative difference between the simulated
$\delta^{202}\text{Hg}^0_{\text{atm}}$ (-0.1‰) and $\delta^{202}\text{Hg}^{\text{II}}_{\text{atm}}$ (-0.6‰) (MDF model #1 in Table 1). This suggests that the photo-oxidation $\varepsilon^{202}\text{Hg}_{\text{atm (0-II)}}$ based on the $\text{Hg}^0 + \text{Br}$ pathway in Sun et al., (2016a) used in the standard MDF model (discussed in section 2.2.2.1) is not representative for atmospheric $\text{Hg}^0$ oxidation. Although the simulated $\delta^{202}\text{Hg}^0_{\text{atm}}$ and $\delta^{202}\text{Hg}^{\text{II}}_{\text{atm}}$ are ~0.2‰ lower than their observed values (Table 1), they are within the 0.5‰ variation attributed to the Hg input source uncertainties in $\delta^{202}\text{Hg}$. The simulated $\delta^{202}\text{Hg}_{\text{tf}}$ (-1.8‰) is higher than the average $\delta^{202}\text{Hg}$ value of Chinese foliage/litter (-3.0‰) that is affected by anthropogenic $\text{Hg}^0$ with low $\delta^{202}\text{Hg}$, but is similar to the average $\delta^{202}\text{Hg}$ values of European/North American foliage/litter (-1.9‰) and global organic surface soils (-1.8‰) (Fig. 2B). The simulated $\delta^{202}\text{Hg}_{\text{ts}}$ (-1.2‰) is comparable to the global mineral soils (-1.39‰) (Fig. 2B). The simulated upper oceanic $\delta^{202}\text{Hg}^{\text{II}}$ values (0.2-0.5‰) are compatible with the slightly positive $\delta^{202}\text{Hg}$ values proposed for open surface ocean (0‰ to 0.2‰) by Blum et al. (2013). Thus, it appears that the optimization (i.e. sign inversion) of atmospheric photo-oxidation $\varepsilon^{202}\text{Hg}_{\text{atm (0-II)}}$ is critical to attain satisfactory simulated reservoir $\delta^{202}\text{Hg}$ values. Given the multitude of fractionating processes, further assessment of marine and terrestrial redox $\varepsilon^{202}\text{Hg}$ is difficult in the MDF model.

### 5.2.2. Odd-mass independent fractionation (odd-MIF) model

Compared to the observations, the odd-MIF standard model predicts too low $\Delta^{199}\text{Hg}$ values for atmospheric and terrestrial reservoirs, and too high $\Delta^{199}\text{Hg}$ values for upper oceanic $\text{Hg}^{\text{II}}$ reservoir (Fig. 3). This is because the simulated surface ocean $\text{Hg}^0_{\text{ocs}}$ has a very negative $\Delta^{199}\text{Hg}$ value (-1.5‰, Table 2) due to the large negative marine photo-reduction $\text{E}^{199}\text{Hg}_{\text{ocean (II-0)}}$ (-2.70‰), which propagates to atmospheric and terrestrial reservoirs. This effect was shown previously for a global Hg odd-MIF
model by Sonke (2011), who suggested that marine Hg odd-MIF is not needed to
explain global Δ¹⁹⁹Hg distribution. Additionally, the same large negative atmospheric
photo-reduction E¹⁹⁹Hg_atm (II-0) (-2.70‰) results in low atmospheric and terrestrial
Δ¹⁹⁹Hg values as well. Therefore, E¹⁹⁹Hg_ocean (II-0) and E¹⁹⁹Hg_atm (II-0) are fitted to
increase atmospheric and terrestrial Δ¹⁹⁹Hg values. The odd-MIF model #1 in Table 2
shows that a less strong atmospheric and marine photo-reductive odd-MIF (E¹⁹⁹Hg_atm
(II-0) = -1.75‰; E¹⁹⁹Hg_ocean (II-0) = 0.55‰) results in non-biased atmospheric Δ¹⁹⁹Hg
values (Δ¹⁹⁹Hg⁰_atm = -0.11‰; Δ¹⁹⁹Hg¹¹_atm = 0.41‰). However, the simulated Δ¹⁹⁹Hg
values are positive for the terrestrial reservoir and negative for the oceanic Hg¹¹
reservoir (Table 2), which is inconsistent with observations on vegetation, soils and
marine waters (Fig. 2B).

In the odd-MIF standard model, E¹⁹⁹Hg<sub>ter</sub> (II-0) associated with photo- and non-
photo-reduction of Hg<sup>II</sup> in the terrestrial reservoirs are assigned values of 1‰ (MIE)
and 0.2‰ (NVE), respectively (Table 2). An increase in terrestrial reduction E¹⁹⁹Hg<sub>ter</sub>
(II-0) would reduce the Δ¹⁹⁹Hg value of terrestrial reservoir and increase the Δ¹⁹⁹Hg
value of the atmospheric reservoir. Here, the odd-MIF model #1 is modified to
include a larger E¹⁹⁹Hg<sub>ter</sub> (II-0) value. Simulation results show that a value of 5‰ for
E¹⁹⁹Hg<sub>ter</sub> (II-0) along with a less strong atmospheric and marine photo-reductive odd-
MIF (E¹⁹⁹Hg<sub>ocean</sub> (II-0) = 0.00‰; E¹⁹⁹Hg<sub>atm</sub> (II-0) = -1.75‰) could well reproduce the
observed Δ¹⁹⁹Hg values of fast/slow terrestrial and atmospheric reservoirs (odd-MIF
model #2 in Table 2). However, such a large E¹⁹⁹Hg<sub>ter</sub> (II-0) value is not reported in the
literature and seems implausible. This implies that the terrestrial Hg⁰ emission flux in
the model is incorrect (see discussion in section 5.3).
Marine Hg reduction and oxidation MIF factors are not studied experimentally. If we assume a zero value for the unknown oxidation E¹⁹⁹Hg_ocean (0-II), the fitted reduction E¹⁹⁹Hg_ocean (II-0) value is also zero. If E¹⁹⁹Hg_ocean (0-II) is assigned with a non-zero value, the fitted E¹⁹⁹Hg_ocean (II-0) will also change to this non-zero value. This implies that E¹⁹⁹Hg_ocean (0-II) and E¹⁹⁹Hg_ocean (II-0) is comparable in magnitudes or that the marine photo-oxidation and photo-reduction do not necessarily produce odd-MIF as argued by Sonke et al. (2011). Experimental or field studies of marine Hg odd-MIF are lacking thus far. A recent study did observe intracellular photomicrobial odd-MIF in laboratory incubations of marine microalaga where the enrichment factor E¹⁹⁹Hg_(II-0) was around -1‰. However, the importance of such photo-biological odd-MIF appears limited as the estimated reduction flux of 5 Mmol yr⁻¹ is much smaller than estimates of the abiotic photo-reduction flux of >10,000 Mmol yr⁻¹ (Kritee et al., 2018; Zhang et al., 2015).

In summary, optimization analysis of odd-MIF models suggests that a large terrestrial reduction E¹⁹⁹Hg_ter (II-0) is important to model global Δ¹⁹⁹Hg distribution, and the magnitudes of odd-MIF associated with photo-oxidation and photo-reduction in the ocean are likely both very small.

### 5.2.3. Even-mass dependent fractionation (even-MIF) model

The even-MIF standard model does not reproduce the observed large Δ²⁰⁰Hg in wet deposition (Fig. 2C). The even-MIF standard model used a small atmospheric photo-oxidation E²⁰⁰Hg_atm (0-II) of 0.05‰ (Table 3), a value based on the recent Hg⁰ oxidation experiment (Sun et al., 2016a). Fig. EA-1 shows that the relative difference (~0.2‰) between the observed Δ²⁰⁰Hg⁰_atm (-0.04‰) and Δ²⁰⁰Hg²_atm (0.17‰) (Fig. 2C) can only be achieved by fitting a value of 0.22‰ for E²⁰⁰Hg_atm (0-II). However, the
simulated $\Delta^{200}\text{Hg}^0_{\text{atm}}$ (-0.13‰) and $\Delta^{200}\text{Hg}^{\text{II}}_{\text{atm}}$ (0.08‰) (Fig. EA-1) are still ~0.10‰ lower than their observed values (even-MIF model #1 in Table 3). If we presume that even-MIF also occurs during marine $\text{Hg}^0$ photo-oxidation in the ocean and $\text{E}^{200}\text{Hg}_{\text{ocean}}$ (0-II) has a value of -0.2‰, the model reproduces the observed $\Delta^{200}\text{Hg}$ values of the atmospheric reservoir. However, the oceanic $\text{Hg}^{\text{II}}$ would develop negative $\Delta^{200}\text{Hg}$ values, which are unlikely considering the observed positive $\Delta^{200}\text{Hg}$ in coastal seawater (Štrok et al., 2015; Štrok et al., 2014) and the near-zero $\Delta^{200}\text{Hg}$ of marine sediments (Gehrke et al., 2009; Mil-Homens et al., 2013; Yin et al., 2015). Whatever the oxidative even-MIF mechanism, it appears not to operate in the aqueous marine environment. Alternatively, the even-MIF model suggests that the uncertainties in Hg mass transfer processes likely bias the simulated $\Delta^{200}\text{Hg}$ values (see below).

### 5.3. Uncertainties in Hg mass transfer processes

Three Hg fluxes deserve particular attention. Firstly, in the standard model, the atmospheric $\text{Hg}^0_{\text{atm}}$ dry and $\text{Hg}^{\text{II}}_{\text{atm}}$ wet deposition ratio to the terrestrial reservoir ($\text{Hg}^0_{\text{atm-ter}}/\text{Hg}^{\text{II}}_{\text{atm-ter}}$) has a value of 1 (Table EA-1). As discussed in the introduction section, the surface soil primarily receives $\text{Hg}^0_{\text{atm}}$ deposition via plant uptake, with a net $\text{Hg}^0_{\text{atm-ter}}/\text{Hg}^{\text{II}}_{\text{atm-ter}}$ ratio of 2-4 (Demers et al., 2013; Enrico et al., 2016; Jiskra et al., 2015; Obrist et al., 2017; Zheng et al., 2016). Secondly, Horowitz et al. (2017) recently implemented a fast two-step atmospheric $\text{Hg}^0$ oxidation mechanism in the GEOS-Chem model, reducing $\text{Hg}^0$ lifetime to <3 months, and requiring a significant increase of in-cloud aqueous $\text{Hg}^{\text{II}}$ photo-reduction rate to match global $\text{Hg}^0$ and $\text{Hg}^{\text{II}}$ deposition observations. Compared to the mass transfer rate coefficients for atmospheric photo-oxidation ($k_{\text{atm (0-II)}}$) and in-cloud photo-reduction ($k_{\text{atm (II-0)}}$) in our standard model, Table EA-1), both *k* values are increased by a factor of ~2 and ~7,
respectively, in Horowitz et al. (2017). Thirdly, the terrestrial Hg⁰ emission flux used to derive terrestrial Hg⁰ emission rate coefficient ($k_{\text{ter (II-0)}}$) is only 160 Mg yr⁻¹ (reflecting greater soil Hg retention as suggested by Amos et al., 2014) (Table EA-1), which is much lower than the value (~600 Mg yr⁻¹, from ~500 Mg yr⁻¹ at 37.5th percentile to 1350 Mg yr⁻¹ at 67.5th percentile) established in a recent review (Agnan et al., 2016). We thus examine the sensitivity of simulated δ²⁰²Hg (Fig. 4), Δ¹⁹⁹Hg (Fig. 5) and Δ²⁰⁰Hg (Fig. 6) to the following Hg mass transfer parameters: atmospheric Hg⁰ photo-oxidation $k_{\text{atm (0-II)}}$ (A), atmospheric HgII photo-reduction $k_{\text{atm (II-0)}}$ (B), Hg⁰$_{\text{atm-ter}}$/HgII$_{\text{atm-ter}}$ ratio (C) and terrestrial Hg⁰ emission $k_{\text{ter (II-0)}}$ (D).

As shown in Fig. 4, the simulated atmospheric Hg⁰$_{\text{atm}}$ and HgII$_{\text{atm}}$ approach to their observed mean values when either atmospheric photo-reduction $k_{\text{atm (II-0)}}$ (B) or Hg⁰$_{\text{atm-ter}}$/HgII$_{\text{atm-ter}}$ ratio (C) is slightly increased. A prominent feature of Fig. 5 is that an increase in terrestrial emission $k_{\text{ter (II-0)}}$ could effectively decrease terrestrial Δ¹⁹⁹Hg values (D), implying that a smaller terrestrial photo-reduction E¹⁹⁹Hg$_{\text{ter (II-0)}}$ in odd-MIF model #2 (Table 2) can be fitted. If we increase $k_{\text{ter (II-0)}}$ by a factor of 4 (resulting in an increase of terrestrial Hg⁰ emission flux from 160 to ~600 Mg yr⁻¹ as suggested by Agnan et al., 2016) in odd-MIF model #2, the fitted E¹⁹⁹Hg$_{\text{ter (II-0)}}$ can be decreased from 5‰ to a more plausible value of 2‰. This indicates that the terrestrial Hg⁰ emission flux of 160 Mg yr⁻¹ in the standard model (Table EA-1) may be underestimated.

Even-MIF is thought to occur during atmospheric (net) Hg⁰ oxidation. We have shown in the even-MIF model #1 that a fitted value of 0.22‰ for E²⁰⁰Hg$_{\text{atm (0-II)}}$ could match the relative difference between the observed Δ²⁰⁰Hg⁰$_{\text{atm}}$ and Δ²⁰⁰HgII$_{\text{atm}}$, but not the absolute values. To increase simulated Δ²⁰⁰Hg⁰$_{\text{atm}}$ (-0.13‰) and Δ²⁰⁰HgII$_{\text{atm}}$
(0.08‰), it requires an increase of atmospheric photo-reduction $k_{\text{atm (II-0)}}$ (Fig. 6B) or $\text{Hg}^0_{\text{atm-ter}}/\text{Hg}^{\text{II}}_{\text{atm-ter}}$ (Fig. 6C). Sensitivity analysis (even-MIF model #2) shows that an increase in the default atmospheric photo-reduction $k_{\text{atm (II-0)}}$ by a factor of 12 reproduces both $\Delta^{200}\text{Hg}^0_{\text{atm}}$ (-0.04‰) and $\Delta^{200}\text{Hg}^{\text{II}}_{\text{atm}}$ (0.17‰) (Fig. EA-2A; Table 3). However, the even-MIF model #2 predicts a much larger $\text{Hg}^0_{\text{atm}}$ (8500 Mg) and smaller $\text{Hg}^{\text{II}}_{\text{atm}}$ (370 Mg) reservoirs in the atmosphere, and an atmospheric THg mass about two times of modern values (4000-5600 Mg) (Fig. EA-2B) (Amos et al., 2014; Amos et al., 2013; Horowitz et al., 2014; Horowitz et al., 2017; Mason et al., 2012; Selin et al., 2008). A further sensitivity analysis (even-MIF model #3) shows that a 6 times larger $k_{\text{atm (II-0)}}$ along with a $\text{Hg}^0_{\text{atm-ter}}/\text{Hg}^{\text{II}}_{\text{atm-ter}}$ ratio of 2.5 (within the range of $\text{Hg}^0_{\text{atm-ter}}/\text{Hg}^{\text{II}}_{\text{atm-ter}}$ ratio suggested by the new plant $\text{Hg}^0$ uptake paradigm) also results in unbiased atmospheric $\Delta^{200}\text{Hg}$ values (Fig. EA-2A; Table 3), and a reasonable atmospheric THg budget (4500 Mg) (Fig. EA-2B). Thus, it appears that fast atmospheric $\text{Hg}^0$ dry deposition rate to terrestrial plants (i.e. foliar uptake, followed by intracellular oxidation, and limited re-emission, Manceau et al., 2018) is able to reconcile both MDF and MIF constraints. This reconciles with recent observations that vegetation uptake of atmospheric $\text{Hg}^0$ drives seasonal and diurnal dynamics of atmospheric $\text{Hg}^0$ (Jiskra et al., 2018).

The above discussion on Hg isotope enrichment factors and Hg mass transfer processes in our Hg isotope models indicates that MDF model #1 (fractionation sign inversion of atmospheric $\text{Hg}^0$ photo-oxidation by Br, Table 1, Fig. 3), odd-MIF model #2 (strong fractionation of terrestrial $\text{Hg}^{\text{II}}$ reduction, Table 2, Fig. 3) and even-MIF #3 (enhanced in-cloud aqueous $\text{Hg}^{\text{II}}$ photo-reduction and plant $\text{Hg}^0$ uptake, Table 3) could well reproduce the observed Hg isotope compositions across different Earth's reservoirs. For example, atmospheric $\text{Hg}^0$ source tracing studies showed that
continental background and marine-influenced Hg⁰ have apparently higher δ²⁰²Hg values than recent anthropogenic Hg⁰ emissions (Demers et al., 2015; Fu et al., 2016; Yu et al., 2016). The input of terrestrial Hg into the coastal regions explains the reported low δ²⁰²Hg and Δ¹⁹⁹Hg values in the seawater, sediments and fish tissues from coastal areas (Das et al., 2013; Li et al., 2014; Perrot et al., 2012; Senn et al., 2010; Štrok et al., 2015; Štrok et al., 2014; Yin et al., 2015). The fitted models also indicate that upper oceanic HgII reservoir has positive δ²⁰²Hg (0.2-0.5‰), Δ¹⁹⁹Hg (0.1-0.2‰) and Δ²⁰⁰Hg (0.02-0.03‰) (Fig. 3), similar to the values proposed for the open Pacific Ocean (Blum et al., 2013). Additionally, the Hg isotope difference between coastal and open ocean seawaters supports the observations that pelagic ocean fish has higher δ²⁰²Hg and Δ¹⁹⁹Hg than costal and freshwater fish (Blum et al., 2013; Li et al., 2014; Perrot et al., 2012; Senn et al., 2010).

**6. Concluding remarks**

We provide a mechanistic model framework to examine the controls of sources and biogeochemical processes on the Hg isotope distribution in various Earth's surface reservoirs. The ensemble of MDF, odd-MIF and even-MIF sensitivity analyses indicates that 1) the limited set of available experimentally derived MDF and MIF factors cannot explain current Hg isotope observations; 2) MDF associated with atmospheric photo-oxidation likely enriches product HgII with light Hg isotopes; 3) terrestrial reduction odd-MIF is likely significant and marine odd-MIF associated with photo-oxidation and photo-reduction is possibly negligible in magnitude; 4) the following Hg fluxes are potentially not correct in global Hg models: atmospheric HgII photo-reduction, Hg⁰ dry deposition via plant uptake, terrestrial Hg⁰ emission.
Currently, the enrichment factors (or fractionation factors) used in the Hg isotope model are associated with large uncertainties, and the enrichment factors of some important Hg redox reactions (e.g. dissolved Hg⁰ oxidation in the ocean) are still lacking. An important future research avenue would be the determination of these enrichment factors under experimental conditions that are more representative of natural ecosystems. Further, the assembled Hg isotope observations used for simulation evaluation are potentially biased both spatially and temporally, and show high between-site heterogeneity. More measurements of Hg isotope compositions in various biogeochemical reservoirs, particularly the open ocean, are needed, which would provide more robust constraints on the global Hg cycling.

**Acknowledgments**

This work was supported by the National Key Research and Development Plan (2017YFC0212700; 2016YFC0201600), the National Natural Science Foundation of China (41773104; 41602167; U1612442), and the Tianjin Natural Science Foundation (17JCYBJC23500). J.E.S acknowledges support by research grant ERC-2010-StG_20091028 from the European Research Council. M.J. has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 657195. We thank the associate editor (Jan Wiederhold) and four anonymous reviewers for their insightful criticisms and thorough corrections.

**Electronic Annex (EA). SUPPLEMENTARY DATA**

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<figure><img src="image_3.png" /></figure>
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** The basic structure of global Hg isotope box model where the numbers in boxes represent the each Hg reservoir size (Mg), the numbers beside the black arrows represent Hg mass transfer fluxes (Mg yr⁻¹), and the numbers and functions besides the red arrows represent the geogenic and anthropogenic input Hg fluxes (Mg yr⁻¹) in modern days. The multiple Hg mass transfer fluxes from one box to another are differentiated by arrows with processes identifiers (pho: photochemical; bio: biotic; bb: biomass burning; res: respiration; adv: advection; diff: diffusion; sed: sedimentation; par: particle-setting. See Table A1 in the electronic annex for details.</figcaption></figure>
<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>
<figure><img src="image_7.png" /><figcaption>**Fig. 2.** Summary of published δ<sup>202</sup>Hg (A), Δ<sup>199</sup>Hg (B) and Δ<sup>200</sup>Hg (C) in the atmospheric, terrestrial and oceanic reservoirs. Data sources: atmospheric gaseous Hg (Demers et al., 2013; Demers et al., 2015; Enrico et al., 2016; Fu et al., 2016; Gratz et al., 2010; Sherman et al., 2010; Xu et al., 2017; Yu et al., 2016); wet deposition without direct anthropogenic influences (Chen et al., 2012; Demers et al., 2013; Donovan et al., 2013; Enrico et al., 2016; Gratz et al., 2010; Sherman et al., 2015; Sherman et al., 2012; Wang et al., 2015; Yuan et al., 2015); folaige/litter, organic and mineral soil (Demers et al., 2013; Enrico et al., 2016; Jiskra et al., 2015; Wang et al., 2017; Yu et al., 2016; Zhang et al., 2013; Zheng et al., 2016); coastal seawater (Štrok et al., 2015; Štrok et al., 2014). Samples with extreme δ<sup>202</sup>Hg or Δ<sup>199</sup>Hg or Δ<sup>200</sup>Hg were removed based on statistical outlier analysis where their values higher than 3rd quartile + 1.5 × IQR (the interquartile range) or lower than 1st quartile - 1.5 × IQR are deemed as outliers.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**Fig. 3.** The simulated modern-day (2010) δ<sup>202</sup>Hg and Δ<sup>199</sup>Hg in atmospheric Hg<sup>0</sup><sub>atm</sub>, atmospheric Hg<sup>II</sup><sub>atm</sub>, fast terrestrial Hg<sub>tf</sub>, slow terrestrial Hg<sub>ts</sub>, upper oceanic Hg<sup>0</sup><sub>ocs</sub> and oceanic Hg<sup>II</sup> (surface Hg<sup>II</sup><sub>ocs</sub>, intermediate Hg<sup>II</sup><sub>oci</sub>, deep Hg<sup>II</sup><sub>ocd</sub>) reservoirs using the MDF and odd-MIF standard models (hollow symbols), and the MDF model #1 (i.e. fractionation sign inversion of atmospheric Hg<sup>0</sup> photo-oxidation by Br) and odd-MIF model #2 (i.e. strong fractionation for terrestrial Hg<sup>II</sup> reduction) (filled symbols) (Tables 1-2). The observed δ<sup>202</sup>Hg and Δ<sup>199</sup>Hg values are indicated by ellipses where the center, horizontal axe and vertical axe denote the means of δ<sup>202</sup>Hg and Δ<sup>199</sup>Hg, 1SD on δ<sup>202</sup>Hg and 1SD on Δ<sup>199</sup>Hg, respectively. The mean anthropogenic isotope compositions of Hg<sup>0</sup><sub>anthro</sub> and Hg<sup>II</sup><sub>anthro</sub> into atmosphere are shown in black filled symbols. The arrows indicate the shift in Hg isotope signatures from the standard model to the fitted models.</figcaption></figure>
<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>
<figure><img src="image_11.png" /><figcaption>**Fig. 4.** Sensitivity of δ<sup>202</sup>Hg values (simulated by MDF model #1 in Table 1) in modern atmospheric, terrestrial and upper oceanic Hg<sup>II</sup> reservoirs to variations in atmospheric Hg<sup>0</sup> photo-oxidation rate coefficient (k<sub>atm (0-II)</sub>) (A), atmospheric Hg<sup>II</sup> photo-reduction rate coefficient (k<sub>atm (II-0)</sub>) (B), atmospheric Hg dry and wet deposition ratio to the terrestrial reservoir (Hg<sup>0</sup><sub>atm-ter</sub>/Hg<sup>II</sup><sub>atm-ter</sub>) (C) and terrestrial Hg<sup>0</sup> emission rate coefficient (k<sub>ter (II-0)</sub>) (D). The grey bars denote the observed atmospheric δ<sup>202</sup>Hg values.</figcaption></figure>
<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>
<figure><img src="image_14.png" /><figcaption>**Fig. 5.** Sensitivity of Δ¹⁹⁹Hg values (simulated by odd-MIF model #2 in Table 2) in modern atmospheric, terrestrial and upper oceanic HgII reservoirs to variations in atmospheric Hg⁰ photo-oxidation rate coefficient ($k_{atm (0-II)}$) (A), atmospheric HgII photo-reduction rate coefficient ($k_{atm (II-0)}$) (B), atmospheric Hg dry and wet deposition ratio to the terrestrial reservoir (Hg⁰$_{atm-ter}$/HgII$_{atm-ter}$) (C) and terrestrial Hg⁰ emission rate coefficient ($k_{ter (II-0)}$) (D). The grey bars denote the observed atmospheric Δ¹⁹⁹Hg values.</figcaption></figure>
<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /></figure>
<figure><img src="image_17.png" /><figcaption>**Fig. 6.** Sensitivity of $\Delta^{200}\text{Hg}$ values (simulated by even-MIF model #1 in Table 3) in modern atmospheric, terrestrial and upper oceanic $\text{Hg}^{\text{II}}$ reservoirs to variations in atmospheric $\text{Hg}^{0}$ photo-oxidation rate coefficient ($k_{\text{atm (0-II)}}$) (A), atmospheric $\text{Hg}^{\text{II}}$ photo-reduction rate coefficient ($k_{\text{atm (II-0)}}$) (B), atmospheric Hg dry and wet deposition ratio to the terrestrial reservoir ($\text{Hg}^{0}_{\text{atm-ter}}/\text{Hg}^{\text{II}}_{\text{atm-ter}}$) (C) and terrestrial $\text{Hg}^{0}$ emission rate coefficient ($k_{\text{ter (II-0)}}$) (D). The grey bars denote the observed atmospheric $\Delta^{200}\text{Hg}$ values.</figcaption></figure>

<caption>**Table 1.** Observed and simulated $\delta^{202}\text{Hg}$ (‰) in the Earth's reservoirs by standard and fitted MDF box models (the fitted enrichment factors are shown in bold)</caption>

Enrichment factor (‰)
$\delta^{202}\text{Hg}_{\text{atm (0-II)}}$ (atmospheric $\text{Hg}^{0}$ oxidation, photo-)

| Observed mean±1SD | Model simulation standard #1 | Model simulation standard #1 |
|---|---|---|
<table><tbody><tr><td>ε<sup>202</sup>Hg<sub>ocean (0-II)</sub> (marine Hg<sup>0</sup> oxidation, photo-)</td><td>0.00</td><td>0.00</td></tr><tr><td>ε<sup>202</sup>Hg<sub>atm (II-0)</sub> (atmospheric Hg<sup>II</sup> reduction, photo-)</td><td>-0.80</td><td>-0.80</td></tr><tr><td>ε<sup>202</sup>Hg<sub>ocean (II-0)</sub> (marine Hg<sup>II</sup> reduction, photo-)</td><td>-0.80</td><td>-0.80</td></tr><tr><td>ε<sup>202</sup>Hg<sub>ocean (II-0)</sub> (marine Hg<sup>II</sup> reduction, biotic-)</td><td>-0.40</td><td>-0.40</td></tr><tr><td>ε<sup>202</sup>Hg<sub>ocean (II-P)</sub> (marine Hg<sup>II</sup> partition to Hg<sup>P</sup>)</td><td>-0.50</td><td>-0.50</td></tr><tr><td>ε<sup>202</sup>Hg<sub>ter (II-0)</sub> (terrestrial Hg<sup>0</sup> emission, photo-)</td><td>-1.30</td><td>-1.30</td></tr><tr><td>ε<sup>202</sup>Hg<sub>ter (II-0)</sub> (terrestrial Hg<sup>0</sup> emission, nonphoto-)</td><td>-1.50</td><td>-1.50</td></tr><tr><td>ε<sup>202</sup>Hg<sub>atm-ter (0-II)</sub> (atmospheric Hg<sup>0</sup> deposition, foliar uptake)</td><td>-2.60</td><td>-2.60</td></tr><tr><td>ε<sup>202</sup>Hg<sub>ocs-atm (0-0)</sub> (surface marine Hg<sup>0</sup> volatilization)</td><td>-0.45</td><td>-0.45</td></tr></tbody></table>

Source δ<sup>202</sup>Hg (‰) input

<table><tr><td>Natural emissions</td><td>-0.76</td><td>-0.76</td></tr><tr><td>Anthropogenic emissions</td><td>P50<sup>a</sup></td><td>P50<sup>a</sup></td></tr><tr><td>Anthropogenic river discharges</td><td>-0.49</td><td>-0.49</td></tr></table>

δ<sup>202</sup>Hg (‰) in modern Earth's reservoirs

<table><tbody><tr><td>Hg<sup>0</sup><sub>atm</sub></td><td>0.10±0.65</td><td>-1.02</td><td>-0.11</td></tr><tr><td>Hg<sup>II</sup><sub>atm</sub></td><td>-0.41±0.48</td><td>0.00</td><td>-0.61</td></tr><tr><td>Hg<sup>b</sup><sub>tf</sub></td><td></td><td>-2.06</td><td>-1.75</td></tr><tr><td>Hg<sup>c</sup><sub>ts</sub></td><td>-1.39±0.43</td><td>-1.11</td><td>-1.22</td></tr><tr><td>Hg<sub>ta</sub></td><td></td><td>0.26</td><td>-0.40</td></tr><tr><td>Hg<sup>0</sup><sub>ocs</sub></td><td></td><td>-0.23</td><td>-0.31</td></tr><tr><td>Hg<sup>II</sup><sub>ocs</sub></td><td></td><td>0.57</td><td>0.49</td></tr><tr><td>Hg<sup>P</sup><sub>ocs</sub></td><td></td><td>-0.13</td><td>-0.18</td></tr><tr><td>Hg<sup>0</sup><sub>oci</sub></td><td></td><td>-0.52</td><td>-0.59</td></tr><tr><td>Hg<sup>II</sup><sub>oci</sub></td><td></td><td>0.27</td><td>0.20</td></tr><tr><td>Hg<sup>P</sup><sub>oci</sub></td><td></td><td>-0.15</td><td>-0.21</td></tr><tr><td>Hg<sup>0</sup><sub>ocd</sub></td><td></td><td>-0.42</td><td>-0.50</td></tr><tr><td>Hg<sup>II</sup><sub>ocd</sub></td><td></td><td>0.16</td><td>0.09</td></tr><tr><td>Hg<sup>P</sup><sub>ocd</sub></td><td></td><td>-0.15</td><td>-0.21</td></tr></tbody></table>

<sup>a</sup>median value of all-time anthropogenic Hg emissions to the atmosphere from 2000 BCE to 2010;

<sup>b</sup>observed value is represented by foliage/litter (-2.56‰ ± 0.64‰) and organic surface soils (-1.79‰ ± 0.45‰); <sup>c</sup>observed value is represented by mineral soils (-1.39‰ ± 0.43‰).

<table><caption>**Table 2.** Observed and simulated Δ<sup>199</sup>Hg (‰) in the Earth's reservoirs by standard and fitted odd-MIF models (the fitted enrichment factors are shown in bold)</caption><thead><tr><th rowspan="2">Enrichment factor (‰)</th><th rowspan="2">Observed<br>mean±1SD</th><th colspan="3">Model simulation</th></tr><tr><th>standard</th><th>#1</th><th>#2</th></tr></thead><tbody><tr><td>E<sup>199</sup>Hg<sub>atm (0-II)</sub> (atmospheric Hg<sup>0</sup> oxidation, photo-)</td><td></td><td>-0.25</td><td>-0.25</td><td>-0.25</td></tr><tr><td>E<sup>199</sup>Hg<sub>ocean (0-II)</sub> (marine Hg<sup>0</sup> oxidation, photo-)</td><td></td><td>0.00</td><td>0.00</td><td>0.00</td></tr></tbody></table>
<table><tr><td>E<sup>199</sup>Hg<sub>atm (II-0)</sub> (atmospheric Hg<sup>II</sup> reduction, photo-)</td><td>-2.70</td><td><strong>-1.75</strong></td><td><strong>-1.75</strong></td></tr><tr><td>E<sup>199</sup>Hg<sub>ocean (II-0)</sub> (marine Hg<sup>II</sup> reduction, photo-)</td><td>-2.70</td><td><strong>0.55</strong></td><td><strong>0.00</strong></td></tr><tr><td>E<sup>199</sup>Hg<sub>ter (II-0)</sub> (terrestrial Hg<sup>0</sup> emission, photo-)</td><td>1.00</td><td>1.00</td><td><strong>5.00</strong></td></tr><tr><td>E<sup>199</sup>Hg<sub>ter (II-0)</sub> (terrestrial Hg<sup>0</sup> emission, nonphoto-)</td><td>0.20</td><td>0.20</td><td><strong>5.00</strong></td></tr></table>

Source Δ<sup>199</sup>Hg (‰) input

<table><tr><td>Natural emissions</td><td>0.00</td><td>0.00</td><td>0.00</td></tr><tr><td>Anthropogenic emissions</td><td>P50<sup>a</sup></td><td>P50<sup>a</sup></td><td>P50<sup>a</sup></td></tr><tr><td>Anthropogenic river discharges</td><td>0.00</td><td>0.00</td><td>0.00</td></tr></table>

Δ<sup>199</sup>Hg (‰) in modern Earth's reservoirs

<table><tr><td>Hg<sup>0</sup><sub>atm</sub></td><td>-0.11±0.12</td><td>-1.67</td><td>-0.11</td><td>-0.11</td></tr><tr><td>Hg<sup>II</sup><sub>atm</sub></td><td>0.39±0.28</td><td>-0.58</td><td>0.41</td><td>0.40</td></tr><tr><td>Hg<sub>tf</sub><sup>b</sup></td><td></td><td>-1.27</td><td>0.05</td><td>-0.30</td></tr><tr><td>Hg<sub>ts</sub><sup>c</sup></td><td>-0.25±0.14</td><td>-0.92</td><td>0.20</td><td>-0.24</td></tr><tr><td>Hg<sub>ta</sub></td><td></td><td>-0.32</td><td>0.37</td><td>0.30</td></tr><tr><td>Hg<sup>0</sup><sub>ocs</sub></td><td></td><td>-1.46</td><td>0.33</td><td>0.18</td></tr><tr><td>Hg<sup>II</sup><sub>ocs</sub></td><td></td><td>1.23</td><td>-0.21</td><td>0.18</td></tr><tr><td>Hg<sup>P</sup><sub>ocs</sub></td><td></td><td>0.90</td><td>-0.16</td><td>0.12</td></tr><tr><td>Hg<sup>0</sup><sub>oci</sub></td><td></td><td>-1.12</td><td>0.25</td><td>0.15</td></tr><tr><td>Hg<sup>II</sup><sub>oci</sub></td><td></td><td>1.53</td><td>-0.28</td><td>0.15</td></tr><tr><td>Hg<sup>P</sup><sub>oci</sub></td><td></td><td>1.04</td><td>-0.19</td><td>0.13</td></tr><tr><td>Hg<sup>0</sup><sub>ocd</sub></td><td></td><td>-0.31</td><td>0.10</td><td>0.17</td></tr><tr><td>Hg<sup>II</sup><sub>ocd</sub></td><td></td><td>1.35</td><td>-0.24</td><td>0.16</td></tr><tr><td>Hg<sup>P</sup><sub>ocd</sub></td><td></td><td>1.04</td><td>-0.19</td><td>0.13</td></tr></table>

<sup>a</sup>median value of all-time anthropogenic Hg emissions to the atmosphere from 2000 BCE to 2010;

<sup>b</sup>observed value is represented by foliage/litter (-0.31‰ ± 0.13‰) and organic surface soils (-0.25‰ ± 0.14‰); <sup>c</sup>observed value is represented by mineral soils (-0.25‰ ± 0.14‰).

<table><caption>**Table 3.** Observed and simulated Δ<sup>200</sup>Hg (‰) in the Earth's reservoirs by standard and fitted even-MIF models (the fitted rate coefficients are shown in bold)</caption><thead><tr><th rowspan="2">Enrichment factor (‰)</th><th rowspan="2">Observed mean±1SD</th><th colspan="4">Model simulation</th></tr><tr><th>standard</th><th>#1</th><th>#2</th><th>#3</th></tr></thead><tbody><tr><td>E<sup>200</sup>Hg<sub>atm (0-II)</sub> (atmospheric Hg<sup>0</sup> oxidation, photo-)</td><td></td><td>0.05</td><td>0.22</td><td>0.22</td><td>0.22</td></tr><tr><td colspan="6" style="text-align: left; font-weight: bold;">Source Δ<sup>200</sup>Hg (‰) input</td></tr><tr><td>Natural emissions</td><td></td><td>0.00</td><td>0.00</td><td>0.00</td><td>0.00</td></tr></tbody></table>
<table><tbody><tr><td>Anthropogenic emissions</td><td>0.00</td><td>0.00</td><td>0.00</td><td>0.00</td></tr><tr><td>Anthropogenic river discharges</td><td>0.00</td><td>0.00</td><td>0.00</td><td>0.00</td></tr><tr><td colspan="5"><strong>Hg mass transfer rate coefficient (yr<sup>-1</sup>)</strong></td></tr><tr><td>× k<sub>atm (0-II)</sub> (atmospheric Hg<sup>0</sup> oxidation, photo-)</td><td>1</td><td>1</td><td>1</td><td>1</td></tr><tr><td>× k<sub>atm (II-0)</sub> (atmospheric Hg<sup>II</sup> reduction, photo-)</td><td>1</td><td>1</td><td><strong>12</strong></td><td><strong>6</strong></td></tr><tr><td>× k<sub>ter (II-0)</sub> (terrestrial Hg<sup>0</sup> emission)</td><td>1</td><td>1</td><td>1</td><td>1</td></tr><tr><td>× k<sub>atm-ter (0-II)</sub> (atmospheric Hg<sup>0</sup> dry deposition, foliar uptake)</td><td>1</td><td>1</td><td>1</td><td><strong>2.5</strong></td></tr><tr><td colspan="5"><strong>Δ<sup>200</sup>Hg (‰) in modern Earth's reservoirs</strong></td></tr><tr><td>Hg<sup>0</sup><sub>atm</sub></td><td>-0.04±0.05</td><td>-0.03</td><td>-0.13</td><td>-0.04</td><td>-0.04</td></tr><tr><td>Hg<sup>II</sup><sub>atm</sub></td><td>0.17±0.08</td><td>0.02</td><td>0.08</td><td>0.17</td><td>0.16</td></tr><tr><td>Hg<sup>a</sup><sub>tf</sub></td><td></td><td>-0.01</td><td>-0.04</td><td>-0.02</td><td>-0.02</td></tr><tr><td>Hg<sup>b</sup><sub>ts</sub></td><td>0.02±0.04</td><td>0.00</td><td>0.02</td><td>0.01</td><td>0.00</td></tr><tr><td>Hg<sub>ta</sub></td><td></td><td>0.02</td><td>0.09</td><td>0.13</td><td>0.12</td></tr><tr><td>Hg<sup>0</sup><sub>ocs</sub></td><td></td><td>0.00</td><td>0.01</td><td>0.01</td><td>0.03</td></tr><tr><td>Hg<sup>II</sup><sub>ocs</sub></td><td></td><td>0.00</td><td>0.01</td><td>0.01</td><td>0.03</td></tr><tr><td>Hg<sup>P</sup><sub>ocs</sub></td><td></td><td>0.00</td><td>0.01</td><td>0.01</td><td>0.02</td></tr><tr><td>Hg<sup>0</sup><sub>oci</sub></td><td></td><td>0.00</td><td>0.01</td><td>0.01</td><td>0.02</td></tr><tr><td>Hg<sup>II</sup><sub>oci</sub></td><td></td><td>0.00</td><td>0.01</td><td>0.01</td><td>0.02</td></tr><tr><td>Hg<sup>P</sup><sub>oci</sub></td><td></td><td>0.00</td><td>0.01</td><td>0.01</td><td>0.02</td></tr><tr><td>Hg<sup>0</sup><sub>ocd</sub></td><td></td><td>0.00</td><td>0.01</td><td>0.01</td><td>0.02</td></tr><tr><td>Hg<sup>II</sup><sub>ocd</sub></td><td></td><td>0.00</td><td>0.01</td><td>0.01</td><td>0.02</td></tr><tr><td>Hg<sup>P</sup><sub>ocd</sub></td><td></td><td>0.00</td><td>0.01</td><td>0.01</td><td>0.02</td></tr></tbody></table>

<footnote><sup>a</sup>observed value is represented by foliage/litter (-0.01‰ ± 0.05‰) and organic surface soils (-0.01‰ ± 0.03‰); <sup>b</sup>observed value is represented by mineral soils (0.02‰ ± 0.04‰).</footnote>