Mercury is considered by the World Health Organization to be one of the top ten chemicals or substances to be of major concern to public health . This volatile and toxic element is found naturally in various environmental compartments and originates from both natural and anthropogenic sources, such as artisanal small scale gold mining, burning of fossil fuels and various industrial activities. As a gas, mercury is stable and has a long residence time in air, resulting in a global spread via the atmosphere to remote, pristine, and vulnerable environments such as the polar regions. Mercury is deposited from air by dry and wet deposition, often via oxidation from Hg⁰ to Hg^II. Oxidised mercury in seawater, for example, transforms more easily into methylmercury which can bioaccumulate in aquatic food chains. However, it can also reduce back to its elemental form and evade back to the atmosphere, where it is capable of fast long-range transport. Mercury evasion from sea surfaces accounts for almost 50 % of the annual contributions to the atmospheric mercury load. This is because much of the oceans' surfaces are supersaturated with elemental mercury compared to the atmosphere, resulting in net water-to-air evasion . Understanding the drivers behind formation of dissolved gaseous mercury (DGM) and subsequent flux is key to understand the bioavailability of methylmercury in seawater and supporting global models with information about spatial and temporal variability . Mercury flux models for seawater suggest that the flux, and thus the fluctuation of DGM concentration in surface waters, is mostly influenced by environmental factors such as wind speed, temperature, photochemistry and microbial activity . What controls the formation of DGM is also debated, and it is discussed that it is formed by demethylation processes of methyl- and dimethylmercury in the subsurface ocean . Demethylation could be either abiotic or biotic, with an abiotic process being photo-demethylation controlled by solar radiation . The connection between the formation of DGM and solar radiation has previously been studied in various environmental compartments such as the sea, lakes, soils, and salt marshes . In several studies, the relationship between DGM and solar radiation was quantified by determining correlation coefficients of 0.66 (Cane Creek Lake, USA; ), 0.99 (river near Knobesholm, Sweden; ), and 0.39 (coastal Minamata Bay, Japan; ), suggesting that solar radiation can be an important, though site-dependent, predictor of DGM. Other studies report similar relationships between mercury evasion and solar radiation with correlation coefficients of 0.7, (Adriatic Sea; ) and 0.5–0.9 (Wuijang River, China; ). However, there is probably more to the story of how the concentration of DGM is influenced by external factors such as solar radiation. hypothesised that the formation of DGM probably is affected by a combination of solar radiation and increased temperature. performed a Pearson analysis of DGM and various factors measured at Lake St. Pierre (Canada), including air and water temperature, wind speed and solar radiation. The analysis showed significant correlations between DGM and all of these factors. Other aspects, such as water depth, have also been shown to have an effect on how strong the influence of solar radiation is for the formation of DGM in surface seawater, since the correlation mainly has been observed at the coast . The reason has been suggested to be due to greater vertical and turbulence mixing , lower friction velocities and surface roughness , and the presence of dissolved organic carbon (DOC) and suspended particles .

In summary, we see that merely calculating and discussing correlations will not capture the underlying causal mechanisms by which different environmental forcings influence DGM. What is needed instead is an approach that can separate correlation from causation while also accounting for cause–effect relationships among the forcings themselves, such as solar radiation influencing temperature.

The intention of this paper is to provide a discussion of the role of graphical causal models in environmental research and to present suggestions on how effect sizes from observational data in environmental science can be systematically obtained and reported.

In Sect. , the paper describes the used case study of continuous measurements of gaseous elemental Hg (CMW) and calculated DGM in seawater, carried out on the west coast of Sweden in 2020. Section  introduces a framework for causal inference using observational data. Section  then describes how the proposed framework for causal inference is applied to the case data for inferring the effect sizes of different forcing, such as solar radiation, sea surface temperature, wind speed, and speed of the instrument feeding water pump on measured Hg concentrations CMW. Section  presents the results from the case study and in Sect.  these results and the application of the framework for causal inference using observational environmental data are discussed, leading to concluding remarks and suggestions for further research presented in Sect. .

Measuring DGM in water is commonly performed by manually collecting a water sample which is purged using an inert gas, resulting in that gaseous Hg is released and pre-concentrated on an adsorbent trap (typically gold), which is anlalysed with thermal desorption and detection using cold vapour atomic flourescence spectrometry (CVAFS) or cold vapour atomic absorption spectrometry (CVAAS). With manual sampling, DGM is easily calculated by dividing the total amount of Hg captured on the adsorbant trap with the sample volume . However, continuous sampling is often preferable to increase time resolution which is needed for studying the dynamics of DGM in surface waters. Continuous sampling methods are normally divided by two different approaches; one where the aim is to extract all Hg from the continuous inflow of water and a second approach which aims to establish an equilibrium between Hg in the water phase and the gas phase. In the second approach, which is used in this study, the DGM concentration is normally recalculated by dividing the measured Hg concentration in outgoing air by the dimensionless Henry´s law constant that describes the partitioning of mercury between the gaseous and aqueous phase. Henry's law constant for mercury in seawater has previously been determined by to be temperature dependent and is calculated as 1H′=e(-2404.3/T(K))+6.92.

The automatic continuous equilibrium system used in this study, developed by and further used in e.g.,  and in , consist of an inner cylinder in which incoming seawater enters continuously from the top, see Fig. b. A purging system, consisting of a glass frit, was installed at the bottom of the inner cylinder. The air used for purging was pumped using an air pump. A massflow controller regulated the air flow (ra) to a fixated 1.5 L min⁻¹. Ambient air normally contains small amount of Hg (ca0 in Fig. b), but in our set-up, a coal canister was used to remove Hg from the purging air. After purging through the water in the inner cylinder, the air outflow, now containing the equilibrium concentration of extracted gaseous mercury (CMW), was first led through a soda lime trap and a polytetrafluoroethylene (PTFE, 2 µm pore size, 47 mm diameter) filter to prevent particles and moisture from entering the analyser. The purged sea water flowed out via the bottom of the inner cylinder, moving upwards inside the outer cylinder and was then discharged back to the sea via a rubber tubing. The purpose of the backflow system using an outer cylinder is to serve as isolation to keep the temperature in the inner cylinder as stable as possible during purging. All small tubing in the system was made of FEP (fluorinated ethylene propylene).

Finally, the equilibrium concentration of extracted gaseous elemental mercury (CMW) in the air outflow was analysed every minute using a Lumex RA-914+ CVAAS. Calibration of the instrument was performed automatically every three hours by adjusting the baseline using mercury free air. The detection limit of the instrument has previously been determined to be 0.5 ng m⁻³, having a precision of ±5 % . The blank of the automated continuous equilibrium system was determined by turning off the water pump, letting water within the system be depleted of gaseous Hg. The detection limit of the system was determined to 0.32 pg L⁻¹, calculated as three times the standard deviation of the blanks.

CMW measured with the analyser can be used to calculate the concentration of dissolved gaseous mercury (DGM) in incoming seawater. If Ca0 is removed from Hg, the equation to calculate DGM can be simplified to : 2DGM=CMW1H′+rArw, where CMW is the measured Hg concentration in the air outflow from the purging system (pg L⁻¹), H′ is the dimensionless Henry's law constant that describes the partitioning of mercury between the gaseous and aqueous phase. The variables rA and rw denote the flow rates of purging air and seawater (L min⁻¹), respectively. When studying Eqs. () and () it becomes clear that sea water temperature is already integrated into the calculation of DGM, which can cause uncontrollable feedback loops when studying direct effects between DGM and sea surface temperature in our model. To avoid this problem, CMW was chosen as a outcome variable instead of DGM in this study. Calculated DGM concentrations, which in this study only are presented for comparison, are presented in Table  and Fig. f in Sect. .

The measurements were conducted in shallow waters (< 10 m depth) at the harbour of Kristineberg. At the sampling site, a commercial 12 V bilge pump

Art. no. 25-9741, Biltema

Solar radiation, denoted as Sol, was measured using a pyranometer sensor from Renke, model RS-TBQ measuring both direct and diffuse solar irradiance with a measurement range of 0–2000 W m⁻², a resolution of 1 W m⁻² and an accuracy of ±3 %. The sensor was installed on the roof of the measurement box, having no shadowing. The output of the sensor was read by an Arduino embedded computer which transformed the output voltage into irradiance in W m⁻² and sent the result to a central computer for logging alongside the other measurements. The temperature of the incoming seawater was measured at the inlet to the automated continuous equilibrium system using a DS18B20 temperature probe connected and processed by the same Arduino embedded computer.

Other weather data, such as wind speed, were downloaded from a weather station situated in the Gullmarsfjord close to the research station. These measurements are run by the University of Gothenburg and are available online .

All variables have been resampled to 5 min intervals using a moving average filter. This has been done for two reasons: firstly, we did not suspect that the dynamics of the observed effects are faster than 10 min, which is twice the new sampling rate and therefore fulfils the Nyquist–Shannon sampling theorem. Secondly, we reduced the amount of datapoints which allowed for faster processing in the modelling steps. The measurements of solar radiation, seawater temperature and wind speed are presented in Table  and Fig. a, b and d, respectively.

All steps of the framework were implemented using open-source software. DAGs and implied conditional independence relations were derived using DAGitty . Bayesian statistical models were specified in R with the rethinking package and Stan as underlying inference engine. Data preprocessing and visualisations were performed in both R and Python using standard specific libraries. No commercial causal inference software or simulation software was used. All code and data required to reproduce the steps of the causal framework are provided in the replication package accompanying this manuscript.

The data used for this study were collected between 1 April 2020 (13:20 UTC+1) and April 25th 2020 (02:29 UTC+1). Figure  and Table  summarise and present the observed data. The data have a coverage rate of 92 % for all measured parameters with 6149 valid data points. The month of April was chosen due to the good data coverage, which makes it already visually possible to see some co-variations between the variables in the data.

The measured CMW in Fig. c show clear diurnal patterns with peaking concentrations during daytime and lower concentrations during night-time. This coincides with the measured solar radiation shown in Fig. a. Solar radiation shows clear diurnal patterns with higher values during the day and lower values during the night, as to be expected. It is even possible to see in the patterns of the data that 11 April was a cloudy day, as less radiation was measured at noon. This explains why the peak in measured CMW was lower at this time. The measured surface water temperature, plotted in Fig. b, also shows variations with higher temperatures during the day and lower temperatures during the night, suggesting an association between solar radiation and surface water temperature. In Fig. d we also plotted CMW to show the distinct covariation of the pump speed rW and the measured Hg concentration CMW. Calculated DGM, shown in Fig. f, show similar diurnal patterns as for CMW. The average concentration during the measurement period was 14 pg L⁻¹ (Table ). During the summers in 1997 and 1998, measured DGM by manual sampling at 20 cm depth in open seawater, about 1 km from the Kristineberg Marine Research Station, resulting in DGM concentrations varying between 40 and 100 pg L⁻¹. However, it differs about 20 years between their and our measurements. More recent continuous measurements of DGM, performed in spring 2015 at the Råö/Rörvik station in Sweden (about 160 km south of Kristineberg), showed an average DGM surface concentration of 13 pg L⁻¹ , which is in good agreement with our study. The literature review presented in show surface DGM concentrations varying between 11 and 32 pg L⁻¹ in the Baltic Sea (15–20 pg L⁻¹ in spring), 11–52 pg L⁻¹ in the North Sea, 12 pg L⁻¹ in the North Atlantic Ocean (summer) and about 20–30 pg L⁻¹ in the Mediterranean Sea.

After fitting the models to the observed data, we obtained posterior distributions for each parameter of the models. Figure  shows the estimates for the constant parameters aC and aT of the models listed in Table . The first parameter aC is the constant offset in the Sol → CMW ← TS part of the models. It is approximately equal to the mean of the CMW values in data which is 2.4 pg L⁻¹. The estimate for aT is close to zero for all models because we have standardised the predictor parameters Sol and TS. Figure  provides the estimates for the coefficients of effect sizes bt,s, bc,s, and bc,t. These estimates are important to answer what the direct and indirect effect of solar radiation on Hg concentration are (RQ1).

None of the effect size estimates are zero, which means that we cannot assume any statistical independence between the variables. We confirmed these results using manual examination of scatter plots, which is outlined as supplementary material in Appendix . Hereafter, we propose model m3 is the most plausible causal model for the variables of interest.

We have already established that model m3 and its extension with external influences to model m4 are most plausible. Furthermore, all models are workable meaning that it is computationally possible to fit the models to the data provided. Evidence for this claim is that the R2 values for all parameters in all models are close to 1 indicating stable posterior distributions as listed in Table F1 in Appendix F. Further evidence of the workability of the models are the effective sample sizes neff which indicate that the samples contain sufficient information to infer the model parameters. The overall sample size was n = 6149. The smallest effective sample size occurred for parameter br,t of model m4 with neff = 811 which is more than the recommended ratio of at least 10 % of the total sample size. We did not receive any numerical warnings during the training of the models. Finally, we also checked that the models are adequate by comparing the posterior predictive plots with the empirical data as shown in Fig. a–d. The closer the points in these plots are to the black diagonal line, the better a model can predict the outcome variable. It is obvious that model m3 and m4 seem most adequate to predict CMW. This is further confirmed by plotting the posterior distribution densities, as shown in Fig. e. The posterior density of CMW in this plot is closest to the observed data density for model m4. We have also calculated the R2-values, shown in Fig. f), using the mean of the posterior predictions for CMW for all models. Model m3 has an R2 value of 0.544 and model m4 has the highest R2 value of all models with a value of 0.626, which indicates a moderate to good fit to the data. It is important to remember that model m3 only accounts for solar radiation, temperature changes and the interaction between these two external variables, and model m4 adds the additional influences of wind and variation of the water speed pump. The models ignore any additional external factors that might influence CMW. It is therefore a rather simple model of CMW, but yet the fit to the data is quite acceptable.

Finally, we calculated the WAIC information criterion which allows us to make a relative comparison of the statistical models. Figure  suggests that model m4 has the lowest deviance and is therefore the most adequate model. A lower deviance calculated by WAIC indicates a smaller statistical distance between the estimated posterior distribution of the model and the probability distribution of the observed data which we have also checked manually using the posterior distribution density plots in Fig. e.

The causal framework in this study did not aim to discover previously unknown physical processes governing the formation of gaseous mercury in the oceans. Instead, the contribution lies in quantifying how known processes jointly contribute to observed variability under observational conditions outside of a laboratory. Specifically, using the suggested causal framework, it is possible to (i) separate total observed association between solar radiation and measured mercury into direct and temperature-mediated components, (ii) quantify the relative importance of these causal pathways, and (iii) adjust effect estimates for confounding influences such as environmental influences and instrument-intrinsic factors that are difficult to control in field observations. While laboratory and field experiments showed that solar radiation and sea surface temperature influence mercury emissions, the proposed causal framework allows these effects to be estimated simultaneously from observational data under explicitly and transparently stated causal assumptions. This causal inference technique therefore provides effect size estimates that are directly interpretable for large-scale modelling efforts or policy assessments, where controlled experiments may be infeasible. Causal conclusions, however, are conditional on the assumed causal models. DAGs, as graphical representations of causal knowledge, make prior causal knowledge explicit which allows other researchers to understand and criticise more easily the underlying assumptions. Such criticism is important because causal models are not immune to misspecification, such as by omitting unobserved but relevant confounders, leaving out, or misdirecting edges, which may lead to biased effect estimates. Table  lists a set of possible misspecifications and their mitigation strategies.

In the following, we revisit the research questions and summarise and discuss the answers we found and their implications for the mercury research community. Then, based on the findings and learnings from the case study, we discuss the use of causal inference in combination with prior knowledge in terms of its applicability to environmental research in general.

As mentioned in Sect. , several studies report an observed significant correlation between measured gaseous mercury and solar radiation. However, considering the regression only between these two factors results in a very simple model, comparable to our model m1 (Fig. a). This model is not comprehensive enough to allow for drawing correct causal conclusions. In contrast, model m4 (Fig. ) explicitly incorporates both mediation by sea surface temperature (TS), confounding by wind speed (W), and an instrument-intrinsic influence through the pump speed (rW). The model is more reliable because it reduces bias from additional competing effects, confounders, and background conditions that, if ignored, would give a misleading picture of the underlying causal relationship. Figure  illustrates the practical implication of this difference. For an increase in solar radiation from 600 to 800 W m⁻², model m1 predicts an increase in measured mercury of about 0.56 pg L⁻¹. In contrast, the causally adjusted model m4 predicts a smaller increase of only about 0.42 pg L⁻¹. Thus, the estimated effect size of solar radiation on mercury emission is about 25 % lower if causal relationships are accounted for. In summary, if causal relationships are ignored, there is a risk of overestimating the effect of solar radiation on gaseous mercury.

However, to succeed with the challenging task of evaluating for example the effectiveness of the Minamata Convention on Mercury , better and more reliable computer models are needed to support sparse mercury measurements. Re-emissions of volatile mercury from sea surfaces is one of the largest contributors to the mercury load in the atmosphere, which is highly depending on the concentration of mercury. To build better computer models we need reliable predictors. One of our contributions towards finding more reliable predictors is showing the importance of modelling prior causal knowledge and including it in statistical models to correctly identify and connect competing and confounding factors to measured gaseous mercury. The use of graphical causal models strengthens reliability in the results because these models make the underlying causal assumptions transparent and guide the choice of which predictors to include in the regression analysis.

Previous attempts to apply causal inference in environmental research have often avoided using prior knowledge. Instead, they tried to discover causal relationships in time series using methods such as Granger causality tests , potential outcome framework , or by mimicking randomised controlled trials . However, these approaches rely on strong and often non-transparent assumptions . Graphical causal models, on the other hand, allow to encode prior assumptions transparently such that the necessary restricting conditions for causal inference from observational data are provided. This does not mean that graphical causal models remove the need for prior assumptions, nor do they guarantee the correctness or completeness of prior causal knowledge. As with other causal frameworks, such as potential outcome frameworks or Granger causality, the validity of any causal claim depends on the underlying prior assumptions and the adequacy of the data. Other causal frameworks are not inherently “non-transparent” but they use different, and often more implicit, mechanisms to communicate prior assumptions such as exchangeability assumptions or stationarity requirements. In this sense, the primary contribution of graphical causal models is to offer a particularly explicit and inspectable representation of prior causal knowledge. The importance of defining prior causal knowledge as graphical causal models has been recognised in other scientific disciplines, such as medicine , economy , social science , and software engineering . Scientists in these fields proposed a set of different workflows to work with graphical causal models.

In addition to workflows developed in other disciplines, it is important to distinguish the proposed causal inference framework from conventional scientific modelling in environmental science. Scientific modelling aims to formalise the understanding of researchers into mathematical or computational models (physical, empirical, statistical, or hybrid) that generate verifiable predictions of system dynamics . Such models are calibrated and validated against observational data and progressively refined as new data becomes available. In these models, causal assumptions are embedded implicitly in functional forms and governing equations. In contrast, the primary aim of the causal inferences framework is not the predictive reproduction of system dynamics but the quantification of direct and indirect effect sizes under explicitly stated causal assumptions represented by graphical models. Similar to conventional modelling, parameter estimation and model evaluation are governed by real observational data. The two approaches therefore address complementary research questions. While scientific modelling aims to predict how a system behaves, causal inference aims to disentangle and quantify the causal contributions of different factors to observed outcomes.

Here, we propose a framework for causal inference using observational data in environmental research with three general elements:

First, we suggest incorporating prior knowledge about (assumed) cause-effect relationships in form of a DAG. If a researcher is uncertain about some of the cause-effect relationships, we proposed to define different possible causal models for a given scientific question. Based on mathematical operations that can be performed on the graphical models, known as d-separation , independence criteria can be derived for each model. These independence criteria, applied on the observational data, can be used to provide evidence for the selection of one or several candidate causal models.

There are limitations to using causal models as a guide for inferring causal knowledge from observational data in environmental research. For example, we have shown that the results of causal inference can be highly sensitive to confounding factors, such as the presence of unmeasured external factors. Future research should explore how to inform future data collection by identifying sensitivity to unmeasured confounders using causal models. Furthermore, missing and noisy data should be explicitly modelled, as their causes may be entangled with the variables under study.

Another limitation of our approach is that independence criteria alone may not be sufficient to select a correct causal model for analysis. There are situations where several causal models may have identical independence criteria, and we cannot distinguish between them. Future research can explore how the proposed framework can be extended with causal discovery approaches to suggest candidate causal models . We discussed earlier that current approaches to automatic causal discovery from observational data require too strong and non-transparent assumptions to be useful. However, combining automatic causal discovery with prior expert knowledge could be a promising approach.

Finally, the case study is limited by the limited amount of available data. In future research, it would be interesting to validate effect sizes using long-term measurements over several months or even years. Also, we only studied a few identified confounding factors. An improvement to this study could be to include for example measurements of dissolved organic carbon since this has been suggested to influence DGM concentration .