Quick guide to environmental fate models

Environmental fate models are by no means compulsory for managing priority substances. Efficient source control can be done without them, i.e. by reducing emissions gradually and monitoring the environment to track changes. However we propose the use of environmental fate models for two reasons:

because the quantitative models can improve our understanding of the managed system, and

because the models can be used to predict long term impacts of planned actions.

The use of environmental fate models in decision making is not a new concept. It is routinely used in the framework of environmental risk assessment. Emissions are translated into concentrations in environmental media and organism tissue, and finally to risks using (modelled) toxicity estimates. Since our focus in strictly in emission reduction, the above mentioned framework can be simplified by ignoring the models associated with exposure and ecotoxicological effects (Figure 1).

Figure 1: The generic modelling framework of risk assessment applied to SOCOPSE (redrawn from US EPA 2007). The dotted stages have been taken into account in the definition of the environmental quality standards (EQS). In our suggested approach, environmental fate models are used to find the site-specific relation between emissions and concentrations. Bioaccumulation models are applied only when the EQS is defined as a biotic concentration.

Figure 2: Model output for decision making: simulated time trends with managed option and with autonomous development. This example depicts contaminated site recovery and the time required to reach the EQS is set as the benefit of management. Dotted lines depict simulation uncertainties.

1.1 Principles of environmental fate modelling
The principles behind fate modelling are fairly straightforward, and have been excellently described by Mackay (2001). This section will present a brief summary of some of the most basic principles and assumptions made, in order to clarify how these models apply as instruments in the management of priority substances. For further details, the reader is referred to the “blue book" (Mackay, 2001).

1.1.1  Description of the environment
The first basic assumption made when constructing an environmental fate model is that the world is a box, i.e. that the target ecosystem can be described as a set of individual boxes, or compartments, each representing a separate environmental matrix, e.g. water, air, biota etc. Each box is assumed to be well-mixed and unchanging with time, and they are parameterised according to the user´s knowledge with parameters such as total volumes, particle and organic carbon content and water content. For example, a lake would be regarded according to Figure 3.

Figure 3: An example of a simple conceptual box model of a lake.

1.1.2  Mass balance equations
Fundamental in all environmental fate models, is Lavoisier´s law of conservation of mass, which forms the basis for the mass balance equations used in the models. Despite the existence of nuclear decay processes, they are so rare, and are generally not relevant for the chemicals treated in environmental modelling and the law is treated as axiomatic. Once the environment has been defined and parameterised, it is possible to write down mass balance equations describing the movement processes of a chemical. Treating your model as a steady-state, equilibrated, closed system, and neglecting transformation processes such as degradation gives the following basic equation:

Total amount of chemical = sum of amounts in each compartment (mol)

Thus, if you release 10 mol of chemical A into the lake with given volumes Vw, Vw, VB and Vp (as in Figure 4):

10 = Cw×Vw + Cs×Vs + CB×VB + Cp×Vp mol

where C stands for the molar concentration in the different phases (mol/m3). This equation is solved easily if you know the volumes and the relationship between Cw, Cs, CB and Cp at chemical equilibrium i.e. the partition coefficients Kwb = Cw/CB, Kws = Cw/Cs, Kwp = Cw/Cp. Solving it will give you the resulting concentrations in each phase.
 
The above described equation is the most simple mass balance equation and it will give you a rough idea of the partitioning tendency of the chemical. In the case of managing priority pollutants you probably desire a more complex model, as you are likely to have continuous emissions as well as in- and outflows to the lake. You may also wish to include factors such as degradation and sediment burial. All this is possible by opening the system, perhaps adding some boxes and transport parameters, assuming that the environmental conditions are constant and that flow rates are continuous but constant. The mass balance assumptions are that the total chemical input equals the total chemical output and includes aspects such as non-equilibrium, degradation, sediment burial and volatilisation to the atmosphere. Naturally, each added transport process requires a new set of transport parameters that have to be determined.

Figure 4: Example of model where atmosphere has been added to the lake model and transport and degradation processes have been included.

The next step of complexity is to assume a non-steady state system, which is required if you need to predict system response time, i.e. if ceasing the emissions or other input sources, how long will it take for the concentrations to decrease and reach background levels? In this case you need a time-resolved or dynamic model and the mass balance equations are expressed as differential equations:
 
d(contents)/dt = total input rate — total output rate
 
Again, a time-resolved model requires additional input data such as time-resolved emission rates, but also allows the user to include other time-dependent or seasonal parameters such as temperature, precipitation, leaf coverage on vegetation etc.
 
1.1.3 Concentration versus fugacity
An additional note to make is the selection of parameters when writing the mathematical expressions. Above, concentration (C, mol/m3), has been used to describe the chemical content in an environmental phase. This is perceptually convenient as contaminant contents are generally reported in concentrations. In environmental fate models, concentrations or partition coefficients may be used in the equilibrium partitioning calculations. However, many modellers of organic contaminants today prefer to use another parameter, termed fugacity. The application of fugacity in chemical equilibrium calculations is old, but adopting it in large-scale to environmental modelling was initially done by Mackay (1979), who developed a large number of evaluative and site-specific models often referred to as “fugacity models" or “Mackay models". The principles are the same, only that another parameter is used in the mathematical expressions.

Fugacity was established as an equilibrium criterion in 1901 by the scientist G N Lewis. It is logarithmically related to chemical potential and has units of Pascal. In short, the fugacity of a chemical in a particular medium is the partial pressure that the chemical exerts when it tries to leave that medium, its ‘escaping tendency´. Fugacity is also related to concentration through the equation

C = Z x f,        

where C = concentration (mol/m3), Z = the fugacity capacity of the medium for the chemical of interest (mol/Pa.m3) and f is the fugacity of the chemical in that medium (Pa). The Z-value can be calculated for each medium and is dependent on the medium itself and on the chemical of interest. The fugacity ultimately drives the transport of a chemical in a phase as well as between phases, and at equilibrium between two phases, the fugacity is the same in both.          

It is optional to use concentration/partition coefficients or fugacity in mass balance equations, but as models and mathematical expressions become more complex, it is often algebraically more convenient to use fugacity. An additional advantage is that the fugacity ratio between two phases instantly reveals the direction of the chemical transport and the proximity to equilibrium.
 
1.1.4  Physical-chemical properties and partitioning
In the above, we have touched the subject of environmental partitioning, and it has been stated that different chemicals have different partitioning tendencies. More specifically, hydrophobic (water-repellent) substances tend to partition to media containing organic material such as soils, sediment, organic tissues (animals, humans and plants), whereas water-soluble substances tend to prefer the water phase. Some substances are very volatile and are mainly found in air and easily transported, whereas others are more “sticky" to their nature and remain close to the source. In environmental modelling, octanol is commonly used as “fat-surrogate" and thus partitioning to organic media is described as partitioning to octanol. Three partition coefficients are therefore used as key coefficients: the partition coefficient between air and water, KAW, the partition coefficient between octanol and air, KOA and the partition coefficient between octanol and water, KOW. A high KOW-value implies high tendency to partition to organic carbon containing media and lower tendency to partition to water. Similarly, a high KAW-value indicates that the substance volatilises from water to air and a high KOA-value implies preference of the aerosol rather than the air phase. The partitioning coefficients are normally obtained through measurements, i.e. by measuring the concentration of a substance in two phases when equilibrium is reached. If two partition coefficients are known, it is possible to determine the third, e.g. KAW = KOA/KOW etc.
 
One way of illustrating the partitioning properties of chemicals, is by plotting them against each other, resulting in a so-called chemical space diagram, which indicates which environmental media that are most likely to host the chemicals of interest. This is done in Figure X for the organic priority substances in the water framework directive. Distinguishing the phases from each other is done by running fate model simulations, and thus the phase borders vary slightly depending on the model used. Chemicals that place themselves within the phase borders can be regarded as “multi-compartmental", i.e. then can be expected to be found in similar levels in many environmental phases, whereas others are more likely to mainly reside in one. However, it should be noted that even substances mainly residing in e.g. sediment may be volatile enough to allow for existence of small amounts in air, thus enabling long-range transport, which is especially relevant for very persistent substances. Also the partitioning properties of chemicals change with temperature, so the actual partitioning is always dependent on the local ambient temperature.

Figure 5: The organic priority chemicals presented in a chemical space diagram. The logKAW (air-water partitioning) describes volatility/solubility and logKOW (octanol-water partitioning) describes hydrophobicity. The three contour lines indicate areas where over 90% of the chemical mass is found in one environmental compartment (water, air, sediment). The contour lines depend on the fate model and environment. Here they were calculated with the evaluative environment of the EQC model and assuming equilibrium partitioning (Level I). The colours describe the inverse of the EQS-norm (1/EQS): red-hazardous, green-less hazardous, blue intermediate hazard.

• Sorption to black carbon is important for very hydrophobic substances (benzo(a)pyrene, fluoranthene, DEHP, PBDE) especially PAH substances (Bucheli & Gustafsson, 2000; Ghosh et al., 2003). Modelling approaches including soot-carbon have recently been performed by Prevedouros et al. (2007) and Houck et al. (2007)
• Chemicals which are sorbed to particles are effectively scavenged by snow (Lei and Wania, 2004)If leaching from soil is an issue (e.g. for hydrophobic substances, pesticides and metals), vertical transport processes should be included (Cousins... McLachlan et al. 2002)
• If environmental temperatures deviate much from 20 C (e.g. in mountains,Northern Europe ), the partitioning coefficients can be corrected for temperature using phase change enthalpies. This feature is included in the models POPCYCLING_Baltic and CozMo-POP
• Metals and some organic compounds are sorbed to dissolved organic carbon, which can be a significant reservoir in humic waterbodies (especially inNorth Europe ).

www.trentu.ca/academic/aminss/envmodel/welcome.html

While the problem of non-volatile metal ions can be solved by simply changing the reference state, the sorption affinity of metals to non-organic surfaces is a more complex issue. As mentioned above, the sorption of organic compounds to solids can be predicted by the octanol-water partitioning coefficient (logKow). In contrast, metal sorption is controlled by the complex chemistry of complexation, precipitation, colloid formation and biofixation processes and properties such as salinity, pH, competing ions, redox-potential, surface site densities and nature of sorbent phases (US EPA, 2007). As an example Figure 6
shows the speciation behaviour of cadmium in a range of pH values using Finnish water chemistry values (VAHTI surface water monitoring). Since the environmental conditions affecting the sorption processes show considerable temporal and spatial variability, averaged partitioning coefficients (Kp) can only give approximate values. The differences in partitioning coefficients may be over an order of magnitude even in a single water body (Woodfine et al. 2000). Accurate modelling of the partitioning properties of metals requires a quantitative understanding of the metal sorption processes, i.e. the use of speciation models.

Figure 6: The speciation of cadmium in Finnish surface waters in a range of pH values, calculated with the biotic ligand models (Di Toro et al. 2001).

"Speciation refers to the occurrence of a metal in a variety of chemical forms. These forms may include free metal ions, metal complexes dissolved in solution and sorbed on solid surfaces, and metal species that have been coprecipitated in major metal solids or that occur in their own solids. The speciation of a metal affects not only its toxicity but also its volatilization, photolysis, sorption, atmospheric deposition, acid/base equilibria, polymerization, complexation, electron-transfer reactions, solubility and precipitation equilibria, microbial transformations, and diffusivity." (Bodek et al., 1988)
 
Modelling the speciation of metals is a key issue in ecotoxicology, since metal species have differing toxicities (US EPA 2007). A common assumption is that only the ionic form is bioavailable (MERAG 2007a). The recent developments of ecotoxicological speciation models (biotic ligand models, Di Toro et al. 2001) are outside the scope of this work, since our focus is on mass balance modelling. However, the WFD has the option of adjusting the EQSs based on the bioavailable fraction of metals. The speciation models described in the following chapters can be applied to that task, but here we outline their use in predicting the partitioning behaviour and concentration ratios of metal compounds in water and in sediment.

The use of speciation models is by no means compulsory for modelling the transport of metals. Measured values or model fits to data can be used to deduce the ratios and partitioning coefficients. This approach has been successfully used by Macleod et al. (2005). Compared to measured species concentrations, models have the advantage of predicting metal behaviour in rapidly changing environmental conditions, which are hard to capture by measurements (e.g. pulses of humic substances in the autumn, development of anoxia). Figure 7 depicts the annual variation of zinc compounds in RossLake (modelled using the aquivalence approach by Bhavsar et al. 2004b). Achieving similar results with experimental species ratios would require extensive monitoring to make sure that the long term dynamics are correctly captured.

Figure 7: The annual variation in the concentrations of zinc compounds in Ross Lake in the year 1999 (Bhavsar et al. 2004b). The modelled rise of concentrations in the water column during summer and autumn is caused by increased sediment resuspension and oxidation of sediments resulting in larger diffusion of Zn2+ ions.

In principle the speciation models can be used to predict speciation in sediment pore waters, however the local redox-conditions and microbial activity may not be properly described in the models and rules-of-thumb may have to be used to fine-tune the results (no diffusion if sulfides are present, etc.) (Woodfine et al. 2000; Bhavsar et al. 2004a).
 
3.2 Modelling metal concentration as the sum of interconverting metal species
The environmental quality standards (EQS) for metals are defined as dissolved concentrations of the metal and its compounds (e.g. ?Hg or ?Pb). Focusing on dissolved concentrations, the particle bound fraction can be ignored, but in mass balances that fraction must be accurately assessed. The problem is complicated by several interconverting metal species with different partitioning properties. In order to calculate the dissolved concentration of e.g. "mercury and compounds", the dissolved concentration must be calculated separately for elemental, ionic and methyl mercury and the results added to get to the total dissolved concentration.

However one of the challenges of interconverting metal compounds is that their fate has to be solved simultaneously for each species. Organic degradation chains can be solved step-wise by looping the degradation products of one compound as the emissions of another. In contrast reversible interconversion of metal species requires that the model equations are solved for all of the chemical species simultaneously - otherwise key chemical cycles may be missed. Focusing on total metal concentrations and ignoring speciation would be a work-around solution, but the partitioning coefficients would be difficult to calculate for the total metal.

 
A detailed mechanistic model can be used to model the interactions between interconverting species in a transparent way. Transport and interspecies conversion rate-equations are solved for a time-dependent solution of chemical species concentrations. Di Toro (2001) has applied this approach to Ni, Mn and Cd in freshwater and marine sediments. However the problem with sophisticated transport models is that they are data intensive: the interconversion rates should be known for all species. Since some of the conversion processes are microbiological (e.g. methylation of mercury) the rates depend on the local conditions in sediment and water column. The use of detailed mechanistic models will thus require plenty of field data for calibration of submodules. However the process of calibration and data acquisition may prove too costly, when empirical models can be used to get similar results (Malve, 2007). In data-rich situations, mechanistic models provide a thorough analysis fluxes in the system. In most situations the interconversion rates are unknown, but the concentration ratios between species are known and simpler modelling approaches may be more suitable.
 
Toose and Mackay (2004) developed a method for applying multimedia models to interconverting multispecies substances. It comprised of a few steps:

• Obtaining the physicochemical properties and calculating the D and Z values for each species in the specified environment
• Obtaining species concentration ratios (measured or modelled) and using these to weight the D-values into a D-value of the total metal transport
• Total metal D-values are used to solve the fugacity of one of the species (key species) and other fugacities are calculated using the concentration ratios
• Original species-specific D-values are used to calculate the mass balance for each of the species.

Figure 8: Mass balance for all species

Figure 9: Cumulative probability distributions of exposure and effects/toxicity with grey bands describing 90 % uncertainty. The dotted lines describe different ways of making risk estimates. (Merag Fact sheet 07, 2007).

4. Uncertainty and sensitivity analysis of models
Why perform an uncertainty analysis — isn´t model result interpretation hard enough already?

• The purpose of uncertainty and sensitivity analysis is to:
• increase communication between the decision maker and the model
• builder make result interpretation easier and more transparent
• improve understanding about the modelled environmental system

It is easy to criticize the use of models in decision making: “You can get any kind of result you want." “There are so many unknown factors, how can you say anything about the situation." Much of this criticism is warranted. Models have been used in decision making in a deterministic manner, resulting in decisions being made based on suspicious assumptions. For example, Refsgaard et al. (2006) cite a groundwater modelling study, where five different consultants were asked to model the most sensitive regions in the CountyofCopenhagen to prioritize for protection. All consultants used the same datasets for model construction and calibration, but obtained five completely different prioritizations. Naturally future groundwater quality could not be measured, so the models could not be validated experimentally. Since none of the prioritizations included uncertainty analysis, the reliability of the results could not be assessed. As a result, no management decisions could be made based on the five (costly) modelling studies. Similar problems with model validation and transparency have resulted in the modelling credibility crisis experienced in the RIVM Laboratories´ in the Netherlands (Van der Sluijs, 2002).

Not performing uncertainty analysis moves responsibility away from the decision maker and to the modeller. If the assumptions made during modelling are not expressed clearly, they become a “black box" to the decision maker. He has to accept or reject them at face value. Instead of making a fair judgement, the decision maker has to trust the modellers expertise about the subject, i.e. decisions are not based on scientific facts but on personal trust between modeller and manager (Van der Sluijs, 2007). In contrast, keeping uncertainty analysis in the modelling process informs the decision maker about the scientific acceptability of the assumptions made during the modelling process (Refsgaard et al. 2007). Accordingly the JRC recommends that uncertainty and sensitivity analyses should be included in every modelling study meant to serve decision making or public debate (Saltelli, 2006).

4.1  Variability and uncertainty in parameters  
One of the pitfalls of using sophisticated models is that their input data contains variability and uncertainty (variability is a property of nature, it can't be reduced by further studies, in contrast uncertainty can). Unless the effect of this uncertainty in input parameters can be determined, it is difficult to trust the obtained results. The phenomenon of using inaccurate input data with an accurate model has been labelled as "garbage-in-garbage-out". The problem of determining the effects of input variability and prioritizing the most sensitive parameters is usually solved by applying methods of technical uncertainty and sensitivity analysis. The output of such an analysis is usually a confidence interval of possible outputs and an explanation on which factors cause the variability (Figure 9).

Figure 9: Cumulative probability distributions of exposure and effects/toxicity with grey bands describing 90 % uncertainty. The dotted lines describe different ways of making risk estimates. (Merag Fact sheet 07, 2007).

Much can be learned from previous uncertainty analyses of environmental fate models. Webster and Mackay (2003) concluded that the major sources of uncertainty in environmental fate modelling are chemical data, environmental data and emission inventories. Of these sources, models are the most sensitive to inaccuracies in the chemical data, but variability of environmental factors usually has the most effect on results.

Meyer et al. (2005) discovered that the sensitivity of fate models to uncertain parameters is determined to a large extent by the properties of the chemical modeled. They illustrated their discovery with the aid of chemical space diagrams labelled as uncertainty maps. The concept has been applied to the fate of priority substances in the Baltic Sea (Figure 10). Using the map, substances can be divided in to distinct groups which have differing sources of uncertainty. Very hydrophobic and volatile compounds (Group 1) are sensitive to suspended solid dynamics in water and sediment; Hydrophobic and volatile compounds (Group 2) are sensitive to the amount of particulate organic matter and volatilization mass transfer (water-side); Chemicals in Group 3 are sensitive to the amount of particulate organic matter; Volatile compounds (Group 4) are sensitive to water surface area and mass transfer (water-side); Group 5 is sensitive to air-side mass transfer; and finally low volatility- low hydrophobicity (Group 6) substances are sensitive mainly to water flow.

Figure 10: The chemical space segmented according to the most sensitive parameters in a level III fugacity model of the Baltic Sea (adapted from Meyer et al. 2005). The modelled variable is bulk concentration in water phase. The numbered grouping is explained in the text.

Some of the priority substances are near contour borders (e.g. DEHP, PBDEs, benzo(a)pyrene, nonylphenol, chloroalkanes, lindane and PCP), indicating that the chemical properties of these substances should be determined as accurately as possible. For these substances small deviations in chemical properties will result in large changes in the relative sensitivity of parameters. However since it is difficult to get an accurate estimate of the partitioning coefficients in environmental conditions, uncertainty and sensitivity analysis should be done simultaneously for chemical and environmental parameters.

4.2 Limited knowledge — model structure uncertainty
In many cases the structural uncertainty is greater than the one associated with parameter variability (Fenner et al. 2004 on long-range transport of pollutants, Refsgaard et al. 2006 more generally). The previous treatment assumes that there is only one correct description of the system, and that the uncertainties lie in the variation of individual parameters. However in most cases, several models can be formulated, which all fit the experimental data sufficiently well (Refsgaard et al. 2006; Saltelli 2006). It could also be argued that the previous approach depends on the assumption that uncertainty is something that can be controlled technically by quantifying and reducing it through measurements (Van der Sluijs, 2007). Uncertainty can be reduced to a certain extent through analysis and refinement of information. Assessment of structural uncertainty however requires either plenty of experimental work to validate and improve the models, or expert judgement on the differences between models (MERAG, 2007b; Refsgaard et al., 2007 for examples of application).

Webster and Mackay (2003) found that the process equations in different environmental fate models are similar, showing a common understanding of the key transport processes in the scientific community (i.e. there are no competing theories or schools of thought). However some process equations are still uncertain estimates of reality. In particular processes such as chemical uptake by plants, photodegradation, ice and snow dynamics, bioaccumulation and microbial transformation are still highly uncertain. For example, microbial biodegradation rates have uncertainty factors of 1/10 to 10 (e.g. one log-unit). In cases where any of these processes is detected as the key process governing chemical fate, caution should be taken in interpreting the results.

Currently there are no standard methods for assessing structural uncertainty and it is questionable whether there are resources in a modelling case to estimate the structural uncertainties of environmental fate models. In many cases, it however is informative to do a qualitative uncertainty analysis at the beginning of the modelling study. This can take the form of a literature search on contrasting opinions or an uncertainty matrix (see Refsgaard et al. 2007; Refsgaard et al. 2006 for details). This stage is best applied at the problem formulation stage (step 1) both to increase understanding about what can be feasibly be answered and to pinpoint key issues for further investigations.
 
5. Selecting suitable models

• Modelling is not cheap: information costs, etc. It is rational only if not modelling will be even more expensive. Because of this, it is of utmost importance to make sure that the model will give answers to the right questions.
• Moreover, sediment and biota remain important matrices for the monitoring of substances with significant accumulation potential and against whose indirect effect EQS for surface water currently offer no protection. Such monitoring should be carried out in order to advance the future technical and scientific work on EQS in sediment and biota for the monitored substances, where this is proven necessary. (Amendment of the Parliament, A6-0125/2007 of 22 May 2007) at the proposal for a - the set of questions presented in the benchmark criteria for water management models (Saloranta et al. 2003). Main focus in determining the question that the model should answer.
• A good example for applying those questions to a model can be found from Saloranta 2006
• Does the model describe all the key processes? can the model variables explain the behaviour of the "real world system"

In the context of SOCOPSE, there are two separate questions that need to be answered by the model:

• What will happen to priority substance concentrations in the water body if no-action is taken (autonomous development)?
• What effect will the available emission reduction methods have on the priority substance concentrations?

Obviously the answers to those questions depend on both the source of the problem (chemical emission) and the nature of the local environment.

Modelling approach must suit the chemical type: