The emission estimation methods for the constructed global Hg emission inventories used in this study are detailed in the literature . Table 1 outlines the global Hg emission inventories considered in this analysis, detailing grid resolution, years of emission inventory, sectoral aggregation used, estimation of uncertainties, and chemical speciation. Chemical speciation refers to the breakdown of chemical forms of emitted Hg into three forms, i.e., gaseous elemental mercury (GEM or Hg⁰), gaseous oxidized mercury (GOM or Hg²⁺), and particulate-bound mercury (PBM or Hg_p) . The dominant form of Hg in the atmosphere is Hg⁰ (>95 %) , which is the predominant form in the gaseous phase and facilitates global transport. None of the inventories provide information on intra-annual variation of monthly emissions. The AMAP/GMA inventory was developed based on national activity data and national/regional information on emission factors and the efficiency of air pollution control technology. The inventory is built by compiling and geolocating emission point (stacks) sources, as well as identifying the diffuse shares of 21 emission (industry) sectors. The diffuse emissions account for 62.1 % of the total emissions, and the spatial proxies used to distribute ASGM emissions significantly affect the sector representation. The EDGAR emissions from area (diffuse), line (road and water ways) and point sources are calculated as country-wide totals. EDGAR relies on activity data, emission factors, and control measures information from many data sources such as agencies (e.g. the International Energy Agency (IEA) , the United States Geological Survey (USGS) , specialized organizations, treaties, and extended scientific literature among others. EDGAR includes road, inland waterways and international shipping as Hg emission sources. The STREETS inventory uses IEA data for the fossil fuel combustion sector and considers the use of flue gas desulfurization (FGD) systems in the power sector. For the ASGM sector, the activity levels reported by GMA were adopted as anchor points for the year 2010 year, using a proxy approach, the emissions for 2010–2015 were estimated. The STREETS inventory obtained data from UNEP and USGS for industrial metal production and production and use of Hg in commercial products, respectively. The global WHET Hg emission estimate is based on the STREETS inventory (and EDGAR for ASGM emissions) and includes updated country-specific estimates for China, India, the US, and Western Europe. The WHET global Hg emission estimate takes into account the application of air pollution control devices (e.g. FGD) in the coal combustion sector in the US that shifts the speciation in emissions. This speciation change in the US is extrapolated to all other countries in North America, Western Europe, and Oceania and was derived by for China. WHET also takes into account the decline in emissions from the use and disposal of commercial products based on .

Figure 1 shows the latitudinal profiles of the annual anthropogenic Hg emissions (Mg yr⁻¹) and the spatial distribution of the TGM emissions range from the different inventories. Figure 2 presents the differences in emissions (Mg yr⁻¹) among the four different inventories by species and continent (in approximation using box masks). The percentage of emissions located in the Northern Hemisphere varies from 77.6 % to 88.5 % for the different inventories. There are multiple regions in Northern Canada, Alaska, the Sahel, northern Russia, and Australia where some inventories document zero emissions, and others report emissions. A comparison of inventories reveals large differences in Asia in terms of GOM and PBM emissions. Differences in GEM emissions are also pronounced in Asia, South America, and Africa. The overall chemical composition ratio GEM : (GOM + PBM) ranges between 1.83 and 4.57 for the different inventories.

We used the GEOS-Chem model (v 12.8.01) (https://geoschem.github.io/, last access: 22 April 2024) for the Hg simulation to estimate the effect of different uncertainties in modeling results at a horizontal resolution of 2° latitude by 2.5° longitude and 47 vertical levels. GEOS-Chem is driven by the assimilated meteorological MERRA-2 dataset and is parallelized using OpenMP. The simulations included three Hg tracers: GEM, GOM, and PBM. Both primary emissions and secondary re-emissions from soil and snow are included . The snow re-emissions are tied to solar radiation, and the re-emission rate used is based on the study of . Legacy Hg reemissions from the ocean were archived from the MITgcm model , and monthly Br fields were taken from full-chemistry GEOS-Chem simulations , respectively. Surface–atmosphere Hg exchange processes, including soil, snow, and ocean re-emissions, are included in GEOS-Chem but are prescribed independently of the anthropogenic emission inventory used in each simulation. As a result, differences among anthropogenic emission inventories do not propagate into inventory-specific legacy re-emissions. This modeling choice allows isolation of the atmospheric uncertainty attributable to inventories of direct anthropogenic emissions. The atmospheric GEM oxidation mechanism considers gas-phase Br as the primary oxidant in the troposphere and stratosphere, and second-stage oxidation of HgBr by a number of radical oxidants . For half of the simulations, we used an alternative GEM oxidation mechanism where the predominant oxidants are OH and O₃. More advanced chemical mechanisms have since been developed which incorporate the oxidation of Hg⁰ of both OH and Br, followed by oxidation by O₃ in a second-step . Nevertheless, by conducting two sets of simulations with radically different chemistry schemes (Br vs. OH/O₃), we can identify which regions of the atmosphere are most affected by chemical uncertainties. The model also calculates spatial fields of wet deposition of GOM and PBM consisting of scavenging in wet convective updrafts and rainout and washout in large-scale precipitation and dry deposition of all three species. GEOS-Chem uses a formulation consistent with a resistance-based GEM dry deposition .

Our model experiments (Table 2) are designed in three groups to compare the magnitudes of model uncertainties driven by anthropogenic emissions, chemistry, and meteorological data. Each group was constructed by varying one input while holding others constant to isolate its influence on model output. To assess anthropogenic emissions uncertainty, we conducted the Inventories simulations, consisting of four simulations with the Br oxidation scheme, each utilizing a different inventory of anthropogenic emissions. To evaluate chemistry uncertainty, the Chemistry simulations comprise eight simulations. This group includes four simulations using the Br oxidation scheme, each with a different inventory of anthropogenic emissions, as well as four simulations utilizing the OH/O₃ oxidation scheme, which are also based on different inventories of anthropogenic emissions. These simulations aim to highlight potential differences resulting from the selection of chemical mechanisms, clarifying their contribution to modeled atmospheric processes. The output variables from each set of simulations were averaged to obtain their means, which were then compared to represent the chemistry uncertainty. A 2-year spin-up period was used for the Inventories and Chemistry simulations and the results from the third, fourth, and fifth years, 2013, 2014, and 2015, were used for the analysis as a multi-annual mean (2013-2015). For the Meteo simulations group, we ran the model twice for the year 2015 using the Br oxidation scheme and the AMAP/GMA emission inventory, each time based on a different meteorological dataset: MERRA-2 and GEOS-FP.

GEM observations are obtained from the compilations of (courtesy of Hélène Angot) and AMAP/UNEP . The wet deposition flux observations are compiled by (courtesy of Hélène Angot), , AMAP/UNEP and . In this study, only observations collected between 2013 and 2015 are included.

SNR compares the level of a signal of interest with the level of background noise . There is a substantial body of research that has used the SNR measure in atmospheric sciences . In our study, the SNR is used to identify regions where the model-observation studies are suitable for the evaluation of anthropogenic emissions uncertainty. In this case, the signal is defined as the range (maximum minus minimum) of the model output variable across all simulations within a group (e.g., Inventories, Chemistry, or Meteo). The noise is quantified by first calculating the temporal standard deviation of the model output for each individual simulation, and then averaging those standard deviations across all simulations in the group. This average represents the typical intra-annual variability used in the denominator of the SNR. A high SNR indicates a large signal (high propagated uncertainty to modeling results) compared to the noise (relatively small intra-annual variability). We apply SNR to modeled atmospheric Hg concentrations and wet deposition output to extract the signal due to anthropogenic emissions and other model uncertainties in the presence of intra-annual variability. We use the SNR as defined by the following equation: 1SNR=rangeacrosssimulationsinagroupaverageoftemporalSDswithineachsimulation=maxxi-minxi1n∑i=1nσtxi where xi is the output variable from simulation i, σt(xi) is the temporal standard deviation for that simulation and n is the number of simulations in the group.

The range within each of the three simulation groups provides a representation of the uncertainties that arise from emissions, chemistry, and meteorology, respectively. We used the mean annual daily standard deviation (SD) as a direct measure of GEM, and weekly SD for wet deposition intra-annual variability. We used a weekly time frame for wet deposition because observation samples were collected on a weekly basis.

CTMs are typically evaluated based on their performance in simulating atmospheric Hg concentrations and deposition. In contrast, this study focuses on assessing how modeling choices affect the robustness of CTMs when used to evaluate anthropogenic Hg emission inventories. As the bottom-up method for Hg emission estimation suffers from various uncertainties and the current anthropogenic Hg inventories differ by substantial amounts, independent constraints from observations could shed light on primary anthropogenic Hg emissions uncertainties. Our simulations generate insight into which sites could provide or not the most relevant constraints on primary anthropogenic Hg emissions.

This modeling experiment reveals that different regions of the world exhibit varying levels of sensitivity to model components, such as emissions and atmospheric chemistry. The large differences in anthropogenic emissions estimates for Asia dominate the variability in modeled GEM. However, when considering aggregated monitoring sites across Asia, the resulting discrepancy in modeled GEM may not always be easily constrained by model-observation comparisons using the current observation sites. The reason is that, in this case, the range of the model results falls within the range of GEM measurement variability (Fig. 3a), which partly reflects spatial aggregation of heterogeneous monitoring locations. The spatial SNR patterns shown in Fig. 4c highlight subregional differences. For example, central China and Central Asia exhibit relatively high SNR values, whereas eastern China shows lower SNR. While the largest absolute uncertainties in anthropogenic Hg emissions occur in Asia and South America, our analysis identifies regions where background observations are most effective at isolating emission signals from other sources of variability, which is a distinct but complementary objective.

Based on our modeling results, we show that current SH monitoring networks are not ideal to help evaluate anthropogenic emissions uncertainties, but they could be instrumental in addressing uncertainties related to chemical processes. Current observations in the SH are insufficient to evaluate anthropogenic emissions uncertainties due to distances from areas with positive SNR (apart from the Nieuw Nickerie and Manaus sites) and their limited spatial coverage (Fig. 4c). The majority of GEM observation sites in the SH are located in areas where chemistry uncertainty and intra-annual variability completely impede detection signals of anthropogenic emissions uncertainty. For instance, when analyzing the annual averaged results for the SH mid-latitudes and Antarctica, the response of the model across different emission inventories remains below 0.06 and 0.04 ng m⁻³ range of GEM, respectively. The low sensitivity to the different inventories in conjunction with up to 0.2 ng m⁻³ intra-annual variability of GEM leads to very low SNR across much of the Southern Hemisphere monitoring network. However, this result should not be interpreted solely as evidence of a true physical insensitivity of Southern Hemisphere Hg concentrations to anthropogenic emissions. The weak emissions SNR may also reflect limitations in currently available anthropogenic Hg emission inventories for the Southern Hemisphere, where emissions from ASGM and industrial sources are known to be poorly constrained . Future studies could address this point using new emissions inventories that have been published after these simulations were completed . In this context, a low SNR may arise from an under-representation or misallocation of anthropogenic emissions in the input data. Improved bottom-up emission estimates and enhanced observational coverage in the Southern Hemisphere could therefore improve the ability of monitoring networks to constrain anthropogenic Hg emissions uncertainties.

The chemistry and meteorological data model settings and the intra-annual Hg variability have less impact on model-simulated Hg concentrations and wet deposition in Europe, the USA, and the Arctic. The model and the observations agree that the SD of GEM for the Arctic Circle (Fig. 3h), USA (Fig. A1i), and Europe (Fig. A1h) monitoring systems is low (smaller than 0.09 ng m⁻³) for any month of the year. Distinguishing emissions uncertainty signals over intra-annual variability of GEM in the sites of the Arctic Circle is feasible, as the former is more than twice as large as the latter. In winter, SNR exceeds the value of 5.5 in both Greenland sites. Similarly, sites that could help constrain the uncertainties of anthropogenic emissions are those in South Europe and the East US. While the SNR analysis identifies regions such as the Arctic and specifically Arctic Russia, Greenland, as theoretically optimal for isolating anthropogenic Hg emission signals – particularly during winter – these findings should be interpreted in the context of substantial real-world constraints. Harsh environmental conditions, including extreme cold, prolonged darkness, snow and ice cover, and limited accessibility, pose significant operational challenges for sustained monitoring in the Arctic. In addition, strengthening monitoring coverage in remote areas such as Greenland and Arctic Russia faces logistical, infrastructural, and geopolitical constraints.

Studies of Hg emissions and atmospheric processes that are performed using a single model present advantages but also limitations. One advantage of employing one model is that it allows a controlled and consistent framework to systematically evaluate specific uncertainties, such as those arising from emission inventories, chemical mechanisms, or meteorological datasets. With this approach, it is possible to focus on specific sources of modeling uncertainty and derive more accurate conclusions within a specific, invariant model architecture. Additionally, an experiment with a single model often reduces computational costs and complexity, facilitating performing a group of simulations within a consistent modeling environment. Despite its benefits, this method entails certain limitations. A single model inherently reflects the biases and limitations of its design, such as its specific treatment of Hg chemistry or resolution constraints. Such biases may result in overconfidence in findings, which might not apply to other models. On the other hand, multi-model studies enable exploration of the diversity of outcomes, which commonly improve the robustness of the analysis of uncertainty and confidence in predictions. To address this issue, our study incorporated two fundamentally different chemistry schemes, representing distinct oxidation pathways (Br and OH/O₃-based chemistry), within the same modeling framework. Using these different chemical schemes allowed us to cover a broad range of chemical uncertainties and reduce the potential for bias linked to dependence on a single chemical mechanism. Future studies could conduct similar analysis using other global mercury models , as well as updated Hg chemistry schemes .

One limitation of the present analysis is that inventory-dependent re-emissions are not represented. The modeled response to anthropogenic emission differences likely underestimates the full influence of emissions on atmospheric Hg. Such an approach is beyond the scope of the present work and would complicate attribution of modeled atmospheric differences to specific sources of uncertainty. Therefore, our results should be interpreted as a lower-bound estimate of the relative importance of anthropogenic emission uncertainties compared to chemistry and meteorology. Additionally, the Meteo simulations are intended to assess sensitivity to commonly used assimilated meteorological datasets within the GEOS-Chem framework rather than to represent the full range of meteorological model uncertainty.

To effectively reduce anthropogenic Hg emission estimate uncertainties and support global Hg policy goals, the design of Hg monitoring networks could better target regions with high SNR of anthropogenic emissions uncertainties and minimal overlapping signals from multiple other sources (e.g., chemistry, and meteorology). The eastern US, Greenland, and Arctic Russia (Fig. 4c), are ideal locations for year-round monitoring to evaluate the potential uncertainties of anthropogenic Hg emission inventories. Such regions with high SNR can effectively minimize background noise and isolate clear signals of anthropogenic Hg emissions. For example, the whole Arctic's high SNR during winter months (Fig. 5) makes it an excellent location for studying Northern Hemisphere background Hg concentrations, independent of other chemical or meteorological errors in modeling results (Figs. 4d and A4). Additionally, regions like Eurasia, northern Canada, and central North America show high SNR during specific seasons (Fig. 5), making them key areas for detecting emissions uncertainty, particularly in seasons when Hg transformation or deposition processes are more stable.

Key regions for intensive monitoring include high-emission regions such as Asia, South America, and Africa, where ASGM and industrial activities prevail. With China and India producing high industrial, and coal combustion Hg emissions, Asia is the biggest emitter . Identifying and quantifying such sources of high emission remains a major challenge, and an enhanced strategy and dense monitoring are needed to reduce associated uncertainties. Monitoring stations could be densely distributed in these regions to capture the full range of emissions and their shifts in space and time (Fig. 2a, d and g) and better estimate anthropogenic Hg emissions. The main sources of emissions in South America and Africa are ASGM, fuel combustion, and industrial activities , and targeted monitoring strategies are necessary to address the significant uncertainties in Hg emissions from these activities. Large portions of the globe remain undersampled, including parts of Africa, South America, and Asia. Measurements in these areas are important for improving the understanding of Hg sources. Expanding the global monitoring network would complement observations in high-emission and high-SNR regions and strengthen model–observation comparisons used to evaluate Hg emissions and atmospheric processes. In addition, tailored wet deposition monitoring in regions like Asia and South Africa, where emission estimates vary widely, is essential to constraining emissions, as the high SNR suggests strong potential to constrain model uncertainties (Fig. 3e). Although enhanced wet deposition monitoring in regions such as South Africa may be informative from a modeling perspective, such recommendations must be considered alongside regional climatology. Much of southern Africa is characterized by arid or semi-arid conditions and recurrent droughts, limiting the feasibility and interpretability of continuous wet deposition measurements.

In addition to high-emission zones, remote receptor regions, such as the Arctic, are instrumental in capturing long-range Hg transport and deposition. The Arctic, as a receptor region, is of considerable importance in understanding global Hg transport, especially from major emitting regions such as Asia, Europe, and North America. However, current modeling underestimates GEM in this region (Fig. 3b, e and h), making it imperative to enhance monitoring efforts in Greenland and Arctic Russia (Fig. 4c). Monitoring in these remote locations will provide baseline data to shed light on the causes of model-observation discrepancies as well as anthropogenic emission uncertainties.

Observations should be consistently used in model–observation comparison studies with CTMs such as GEOS-Chem to ensure that the monitoring network provides actionable insights for policy-makers and the Minamata Convention on Mercury. In this way, refinement of Hg emission estimates would be possible, especially in regions where significant discrepancies exist between observed and modeled data. The benefits of using inverse modeling techniques are also important in constraining emission inventories based on observations. Inverse modeling refines Hg emission estimates by adjusting model inputs to better match observations like GEM or wet deposition. Using models such as GEOS-Chem, emissions are iteratively optimized to minimize differences between simulations and observations. This top-down approach is especially useful to identify and correct inventory biases. Therefore, strengthening the monitoring network would not only enhance our understanding of the Hg global distribution and deposition but also provide critical data to guide future policy interventions aimed at reducing global Hg emissions.

For the Hg modeling community, this study points to the importance of addressing both emissions and other model uncertainties simultaneously rather than in isolation. The complex interactions between emission inputs, chemical processes, and meteorological data require models to be tested holistically. As demonstrated in this work, emission uncertainties could mask the impacts of other model errors regarding Hg wet deposition (Central America, Fig. 4c and d), and vice versa. Therefore, to minimize overall uncertainty, model developers and users should not only improve the accuracy of emission input data but also refine the representation of key atmospheric processes within models, such as Hg oxidation and deposition mechanisms. This dual approach is essential because, as shown in this study, uncertainties in emissions and chemistry can interact and amplify total model uncertainty in complex ways.