Environ. Sci. Technol. 2005, 39, 3186-3196
Illustrating Sensitivity and Uncertainty in Environmental Fate Models Using Partitioning Maps
when accurate and precise knowledge of physical chemical property data is crucial and when approximate numbers suffice to conduct a model investigation.
T O R S T E N M E Y E R , † F R A N K W A N I A , * ,† A N D KNUT BREIVIK‡ Department of Chemical Engineering and Applied Chemistry, and Department of Physical and Environmental Sciences, University of Toronto at Scarborough, 1265 Military Trail, Toronto, Ontario, Canada M1C 1A4, and NILU Norwegian Institute for Air Research, N-2027 Kjeller, Norway
Generic environmental multimedia fate models, such as those based on the fugacity approach, are recognized as important tools in the assessment of the impact of organic pollutants (1). Because of limited possibilities for evaluating such generic models by comparison with measured data and their increasing regulatory use, assessing the performance and reliability of these models is of considerable concern. This led to a demand for sensitivity and uncertainty analyses for the outputs of environmental fate models. Sensitivity analysis is an important validation method for simulation models (2) and is integrated into a range of quantitative techniques in risk analysis investigations (3). Sensitivity analyses are often conducted prior to uncertainty tests to exclude nonsensitive parameter from further investigations. Identification of those input parameters, which are of high influence for a chosen model scenario, makes it possible to decide which input parameters need to be known with high accuracy and precision, and for which parameters approximate knowledge can be tolerated. This can save time and effort, when certain parameters are both difficult to determine and of low relevance to the model output. Monte Carlo simulations are among the methods most commonly applied for the analysis of model uncertainty. Within a predefined input probability distribution, numerous random calculations are performed to obtain an output probability distribution. This method is independent of model formulation and treats nonlinear systems and combinations of different input parameter distributions. Although computationally intensive and demanding some user proficiency, it proved to be applicable in many cases (4-7). However, it is only one of several methods and should not be applied uncritically (8, 9). A major problem is the difficulty in determining appropriate probability distributions of input parameters if large datasets are not available, which is often the case. A Monte Carlo analysis needs a minimum of reliable measured field data and/or data received from previously modeling efforts to estimate mean values and standard deviations. Therefore, Monte Carlo analyses are usually performed for specific sites and certain substances. In general, sensitivity and uncertainty analyses with environmental fate models are performed for specific chemicals, implying that these investigations have to be repeated each time the fate of another substance is simulated. The ambition of the approach presented here is to describe comprehensively and simultaneously the sensitivity of model predictions for a very wide range of hypothetical chemicals in the environment. For this purpose, a “chemical space” is defined that identifies hypothetical chemicals by their partition coefficients KOA (octanol-air), KAW (air-water), and KOW (octanol-water). Sensitivity and uncertainty calculations are performed for the entire chemical space, and easily comprehensible maps can be constructed showing relations between hypothetical chemical properties and input parameters that are highly influential to the model output. Sensitivity analysis here means the study of the impact of input parameters on the value of the outputs, while uncertainty analysis means the study of the uncertainty of the input parameters on the uncertainty of the output parameters. A generic level III fugacity model is used to illustrate this approach.
Variations of model predictions of the environmental fate of organic contaminants are usually analyzed for only one or at most a few selected chemicals, even though parameter sensitivity and contribution to uncertainty are widely different for different chemicals. A graphical method is introduced that allows for the comprehensive investigation of model sensitivity and uncertainty for all persistent organic nonelectrolytes at the same time. This is achieved by defining a two-dimensional hypothetical “chemical space” as a function of the equilibrium partition coefficients between air, water, and octanol (KOW, KAW, KOA), and plotting sensitivity and/or uncertainty of a specific model result to each input parameter as a function of this chemical space. The approach is illustrated for the bulk phase concentrations in air, water, soil, and sediment calculated by a level III model. Colored contour maps facilitate the identification of those input parameters that cause a high output variation of hypothetical and real chemicals. They also allow for the easy categorization of chemicals in terms of common parameter sensitivities, and thus comparable environmental behavior. Sensitivity varies with the mode of emission and the degradability of the chemicals, making it necessary to develop multiple sets of contour maps. Comparison of these sets of maps in turn allows the investigation of how parameter sensitivities change as a result of changes in mode of emission and persistence. The presented method can be used for investigating the sensitivity of any prediction obtained with any linear fate model that characterizes the partitioning behavior of organic chemicals with KAW, KOW, and KOA. Once the sensitivity maps have been constructed for a given environmental scenario, it is possible to perform a sensitivity analysis for a specific chemical by simple placement of the substances’ partitioning combinations within the chemical space. The maps can further contribute to the mechanistic understanding of a model’s behavior, can aid in explaining observations of divergent environmental behavior of related substances, and can provide a rationale for grouping chemicals with similar model behavior, or for selecting representative example chemicals for a model investigation. They can also help in deciding * Corresponding author phone: (416)287-7225;
[email protected]. † University of Toronto at Scarborough. ‡ NILU Norwegian Institute for Air Research. 3186
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Introduction
10.1021/es048728t CCC: $30.25
2005 American Chemical Society Published on Web 03/09/2005
A major simplification in the approach is the assumption that all input parameters are independent. This assumption only affects the uncertainty analysis, whereas sensitivities are invariant with respect to correlations. Previous work suggests that correlations between environmental parameters have in most cases a negligible effect on model uncertainty (9, 10). After tentative identification of the input parameters contributing most to output uncertainty, further efforts may be made to investigate covariance with other parameters (11). The choice of input variable distribution appears to be more important to model prediction than correlations. The applied approach assumes a log-normal distribution of the input parameter variation, which is an expedient way to estimate nonnegative data of physical processes covering several orders of magnitude (8, 12). Sensitivity and uncertainty tests in this study are based on the local sensitivity approach and require linearity between input and output, which is the case for the level III model (20). Local sensitivity concentrates on the local impact of the input parameters on the model output. When the presented approach is applied to a nonlinear model, special emphasis needs to be placed on the chosen environmental scenario and highly uncertain parameters may additionally require a global sensitivity analysis. In this case, the entire parameter range could be taken into account, provided that sufficient reliable data are available. In the analysis of uncertainty, variability and “true” uncertainty are often distinguished (13, 14). Variability refers to the spatial and temporal variations in the characteristics of the environment of interest and therefore cannot be reduced. “True” uncertainty describes deficiencies of knowledge relating to these characteristics and is often reducible (15, 16). For specific environmental fate investigations, it is often useful to determine both kinds of uncertainties separately to facilitate the interpretation of results (14, 17). It is particularly useful for risk assessments in providing decision-makers a tool to evaluate reducible uncertainty (15). If input variation stems mostly from variability, improvement of parameter accuracy is often not meaningful considering the balance of costs and benefit. Whereas previous modeling efforts sought to determine the relative contribution of variability and true uncertainty to overall input variation (14, 17-19), variability and “true” uncertainty of particular input parameters are not distinguished in the present investigation. Uncertainty of model formulation is a special issue and very difficult to determine quantitatively but can be decreased by permanently comparing and reconsidering the applied concepts (17).
Methods Model Description. The level III unit world model by Mackay and Paterson (20) is used to illustrate the proposed method. This commonly used generic model is based on the fugacity concept and includes four bulk compartments, air, water, soil, and sediment. A bulk compartment consists of subcompartments describing solid, aqueous, and gaseous phases. The model assumes equilibrium within bulk compartments, but not between them. It also assumes steady state; that is, there is no change in time. The level III model is linear; that is, emissions are linearly related to output concentrations (20). Chemical transfer between compartments can occur by diffusive and nondiffusive processes. Partitioning is quantified through fugacity capacities or Z-values in units of mol/(Pa‚m3h), whereas transport and degradation processes are expressed with D-values in units of mol/(Pa‚h). The model outlines a simple picture of an organic chemical’s fate by identifying major environmental transport and degradation pathways. The original model was modified in three respects. The gas/particle partitioning equilibrium in the atmosphere is described using KOA (21), assuming that
the molecular mass of the organic matter in particles and its interaction with chemicals is the same as for octanol. Another modification relates to chemical exchange between air and soil. Adopting the suggestion by McLachlan et al. (22), an additional mass transfer coefficient was introduced to account for vertical sorbed phase transport in surface soil. This process affects the effective diffusivity in soil of chemicals with log KOW > 2 and log KOA > 6. Finally, the gas scavenging ratio, estimated as the reciprocal of the Henry’s law constant, was limited to a maximum value of 106 (23). Selection of Input Parameter Values and Uncertainty. Although the model is generic in character, the environmental input parameters for the illustrative calculations presented in this study are describing a real environment, the Baltic Sea region. The parameters, taken from Wania et al. (24), are listed in Table 1. Diffusive and nondiffusive transfer parameters are assumed to be the same for all chemicals. Determination of input parameter uncertainty in an evaluative model is only possible by expert judgment in a very approximate way. Adopting the approach of MacLeod et al. (11), the variability and true uncertainty of these input parameters is expressed using confidence factors (CF). The use of CFs leads to convenient interpretability of results (8). With a probability of 95%, the input parameter lies between the mean value (Table 1, applied value) divided by CF and the mean value multiplied by CF. The mean µ and standard deviation σ of the normal distribution on the log scale is related to CF by σ ) 0.5 ln CF (11). In model scenarios where the applied input parameter uncertainties are much larger than in this study and the assumption of a log-normal distribution cannot be justified, this local sensitivity approach is not applicable. The Chemical Space. The intention was to quantify model sensitivity and uncertainty not for one or a few selected chemicals, but for the entire range of organic substances to which a model may be applied. Adopting an approach we introduced a few years ago (25), a two-dimensional “chemical partitioning space” was defined as a function of log KOA (xaxis) and log KAW (y-axis) (Figure 1). Each point in this space corresponds to a hypothetical chemical with a specific combination of partitioning properties. If the effect of the mutual solubility of water and octanol on the chemical’s solvation in water and octanol is neglected, log KOW equals log KOA + log KAW, and diagonal lines from the upper left to the lower right of this space correspond to chemicals of equal log KOW. Real chemicals can also be placed within this space, if their partitioning properties are known. The boundaries of the investigated space (0 < log KOA < 14, -14 < log KAW < 4, -2 < log KOW < 10) are chosen such that most known chemicals fall within the defined space. In the model, the environmentally relevant partition coefficients, for example, between water and organic carbon KOC, and between atmospheric particles and the gas-phase KPA, are estimated from KOW and KOA using simple linear free energy relationships. For example, log KOC is assumed to equal 0.35 × log KOW (26). Although such equations are applicable to nonpolar organic substances, they likely are less appropriate for more polar chemicals (27). Real chemicals for which these relationships do not hold could nevertheless be placed on the partitioning space by deriving hypothetical KOW and KOA values that correspond to empirically determined KOC and KPA values, for example, log KOW ) log KOC/0.35. The partition coefficients KOA and KAW are highly dependent on temperature. A chemical will shift its location on the partitioning space to the lower right in response to decreasing temperatures. In addition to the partitioning properties, organic chemicals are characterized by their degradability. Most of the sensitivity maps presented below were calculated with the assumption that the hypothetical chemicals are completely VOL. 39, NO. 9, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 1. Environmental Model Input Parameters and Their Confidence Factorsa acronym
input parameter
CF
applied value
AWat vQ vA vW 1 - vS vP vOrgQ fOrgWat fOrgSoil fOrgSed δOM MTCAW MTCWW MTCE MTCA MTCW MTCS MTCXW UDep URes UBur UWW USW ULS URain Q UP GAir GWat
area of water compartment volume fraction of particles in air volume fraction of air in soil volume fraction of water in soil volume fraction of particles in sediment volume fraction of particles in water volume fraction of organic carbon on aerosols fraction of organic carbon on water particles fraction of organic carbon on soil particles fraction of organic carbon on sediment particles density of organic matter mass transfer coefficient air-water (air side) mass transfer coefficient air-water (water side) mass transfer coefficient air-soil (boundary layer) mass transfer coefficient air-soil (air phase) mass transfer coefficient air-soil (water phase) mass transfer coefficient air-soil (particle sorbed phase) mass transfer coefficient water-sediment sediment deposition rate sediment resuspension rate burial rate soil water runoff soil solids runoff leaching into groundwater rain ratio scavenging rate dry particle deposition advective flow in air advective flow in water
1.1 3 1.1 1.1 1.1 3 3 1.5 1.58 1.5 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1.5 1.5
25.2% 2.0 × 10-11 0.25 0.25 0.2 5.0 × 10-6 0.1 0.2 0.018 0.032 1000 kg/m3 5 m/h 0.05 m/h 1 m/h 0.02 m/h 1.0 × 10-5 m/h 1.0 × 10-6 m/h 0.02 m/h 5.0 × 10-7 m/h 3.5 × 10-7 m/h 1.5 × 10-7 m/h 2.0 × 10-5 m/h 5.0 × 10-9 m/h 6.0 × 10-6 m/h 6.5 × 10-5 m/h 200 000 10 m/h 5.00 × 10+13 m3/h 2.54 × 10+8 m3/h
a The CFs for most of the input parameters are taken from MacLeod et al. (11). The CF of MTC is set to 3 in accordance with those of the other S mass transfer coefficients. The CFs of Q, vOrgQ, and δOM are also assumed to be 3. The CF of advective flow in air GAir and water GWat was set to 1.5, consistent with the CF for the regional air and water residence time specified in ref 11.
FIGURE 1. Chemical partitioning space used in the construction of sensitivity and uncertainty maps. Colors indicate the % distribution among the compartments air, water, soil, and sediment as calculated with a level III model assuming emission of a persistent chemical into air (A), water (B), and soil (C), and assuming emission of degradable chemicals into air (D, E). persistent. It is conceivable that input parameter sensitivities change with a chemical’s degradability. To test this, additional sensitivity tests were conducted for degradable hypothetical chemicals, and the resulting sensitivity maps were compared to those derived from the scenarios assuming perfect persistence. Two different degradation scenarios were used, 3188
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which assume that the rates of degradation in different surface media are correlated. A proportion between half-lives (HL) in water, soil, and sediment of 1:2:6.5 was considered reasonable. The first degradability scenario applied half-lives of 12 h in air, and 2, 4, and 13 months in water, soil, and sediments, respectively. The second set of hypothetical
chemicals was more persistent in air (HLair is 1 week), but somewhat more degradable in surface compartments (HLwater 1 month, HLsoil 2 months, HLsediment 6.5 months). Constructing Sensitivity and Uncertainty Maps. The local sensitivity S is defined as the relative deviation of the output value Y deriving from variation in an input value Xi (29):
S(xi) ) ∂Y/Y ‚ Xi/∂Xi
(1)
where ∂Y and ∂Xi are the absolute change of output value and input parameter, respectively. In this study, the concentrations in the four bulk compartments air, water, soil, and sediment in the level III model are chosen as output values. Several approaches to probing sensitivity of model results to changes in environmental input parameter have been applied. Whereas in some studies all input parameters are changed by a certain percentage simultaneously (29), more commonly individual parameters are increased or decreased separately (14, 30-32). Here, every environmental input parameter is increased individually by 10%, and the sensitivity of the four output values to these changes is plotted as a function of log KOA and log KAW. Sensitivity maps are constructed for three level III simulations that differ in terms of the mode of emission (emission into air, water, and soil, respectively). The resulting plots are maps delineating partitioning regions of similar sensitivity to an environmental input parameter. Regions of high sensitivity to a parameter can clearly be identified. In addition to the sensitivity maps, segments within the chemical space are identified that display similar input parameter sensitivity. For every segment, the specific input parameters causing large sensitivity are compiled. At the edges of the segments, definite assignments to input parameters of influence become blurry. Therefore, the aggregated segmentation maps can only reflect the main sensitivity patterns within the chemical space and cannot replace sensitivity maps for individual input parameters. Following MacLeod et al. (11), uncertainty is calculated on the basis of Taylor expansion calculations described by Morgan and Henrion (12). An output confidence factor CFout is calculated using only the input confidence factor CFin and the local sensitivity S resulting from a 10% increase of each individual input parameter:
CFout ) (CFin)|S|
(2)
When previously applied to a regional contaminant fate model and a food web bioaccumulation model, this approach proved consistent with a Monte Carlo analysis using similar assumptions (11). CFOuts are calculated and presented as uncertainty maps for the chemical space. The model outputs are the same as above, that is, the bulk phase concentration for three different modes of emission. All noninfluential input parameters were excluded from the uncertainty analysis. Moreover, maps for parameters with calculated sensitivities and uncertainties that lay below a defined threshold for the entire partitioning space were excluded from presentation in this paper. We should stress that this analysis is restricted to the sensitivity and uncertainty of environmental properties and thus does not cover the full range of possible uncertainties. The uncertainty of degradation rates, in particular, which is often considerable, is not considered here. Although different degradation scenarios were investigated to gain a picture of the impact of degradability on the sensitivity to environmental parameters, this is no replacement for an uncertainty analysis that includes degradation rates.
Results and Discussion Sensitivity to Environmental Input Parameters in Level III Calculations. The level III model provides a simple picture
of a chemical’s fate within the environment. The presence of transfer resistances between the bulk compartments makes the model predictions dependent on the mode of emission (Figure 1A, B, and C). Thus, the parameter sensitivities differ depending on whether a chemical is released into air, water, or soil (emission into sediment is uncommon). Sensitivity, that is, the change in a phase concentration in response to a change in an input parameter, was calculated twodimensionally as a function of KOA and KAW for all four bulk compartments. This was done by increasing each of the input parameters in Table 1 individually by 10% and recording the change in the bulk phase concentration for each hypothetical property combination in the chemical partitioning space. Dry and wet soil conditions were simulated by increasing air and water fractions within soil (vA, vW), while the counterpart was decreased keeping the overall pore space volume constant. Sensitivity maps for the calculation assuming emission to air are shown in Figure 2. Only sensitivity maps of input parameters related to sensitivities above 0.1 or below -0.1 are included. In these sensitivity maps (Figure 2), yellow to red indicates an increase in output media concentration in response to increases in input parameters, whereas blue indicates a decrease. Green colored areas of the chemical space refer to negligible output sensitivities. Areas of different sensitivities are defined by horizontal, vertical, and diagonal boundaries, revealing their dependence on the three major partition coefficients. The different patterns revealed in the sensitivity maps of Figure 2 clearly show that sensitivity to environmental input parameters depends on the partitioning properties of a chemical. It is often quite easy to explain why parameter sensitivities occur in certain parts of the partitioning space. For example, parameters related to transport processes of chemicals in the dissolved phase (ULS, UWW, GWat) only affect water-soluble chemicals in the lower left of the partitioning space (low KAW and low KOW values, Figure 2), whereas parameters related to sediment exchange processes (UDep, URes, UBur) affect hydrophobic chemicals in the upper right of the maps (high KOW). In general, parameters describing nondiffusive intermedia transfer processes, such as the rain rate (URain), sediment exchange processes (UDep, URes, UBur), soil water runoff (UWW), and advective flow of air (GAir) and water (GWat), have a higher influence on output concentration than parameters describing diffusive processes. This may reflect that an increase of a diffusive mass transfer coefficient enhances transmissibility of chemicals in both directions. Some parameters are influencing the concentrations of all hypothetical chemicals (e.g., advection rate in air, GAir), whereas others have an impact on model results for only a very small subset of the investigated partitioning property combinations (e.g., the mass transfer coefficients for diffusive air-water exchange MTCAW and MTCWW). The sensitivity maps for some input parameters are very similar for the concentrations in all four media. For example, an increase in URain decreases the air concentrations and increases the water, soil, and sediment concentrations of all water-soluble (with a low KAW below -4) and particle-sorbed (with a log KOA > 10) chemicals. In other cases, concentrations in different compartments respond very differently to changes in input parameters. For example, the organic matter content in soil, fOrgSoil, affects the soil concentrations of a very large segment of the partitioning space, but impacts the water concentration of only the most hydrophobic chemicals, for which soil solids runoff is important. Differences in the sensitivity map for the same parameter and different compartment concentrations occur when that parameter is important in the description of several processes. Some parameters result in identical sensitivity maps. This is, for example, the case for the parameters that determine the capacity of atmospheric particles for contaminants (volume VOL. 39, NO. 9, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 2. Partitioning space maps displaying the sensitivity of the concentration in various bulk media, calculated with a level III model assuming emissions to air, to changes in environmental input parameter as a function of the equilibrium partitioning coefficients KOA and KAW. fraction of aerosols in air vQ, organic matter content of aerosols vOrgQ) or the parameters determining the rate of deposition of these particles (scavenging ratio Q, dry particle deposition velocity UP). Based on the maps in Figure 2, the chemical partitioning space was divided into segments of common parameter sensitivities. To each of the numbered segments within the chemical space, all input parameters were assigned that cause elevated sensitivities to the output concentration. Thereby, only sensitivities above 0.5, occurring for the concentration in water, soil, and sediment, and sensitivities above 0.1, occurring in the air compartment, were included. Figure 3 shows the partitioning space segmentation for the scenario with emission into air and lists the input parameter relevant for each segment. Also, the partitioning properties of some real persistent chemicals are placed within the partitioning space. The maps in Figure 3 have three types of thresholds, depending on the governing partition coefficient. The horizontal thresholds relate to KAW, vertical thresholds relate to KOA, and diagonal thresholds show the importance of KOW. Remarkably, only a single horizontal threshold occurs, indicating sensitivity to KAW. It occurs for all four compart3190
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ments at a log KAW between -3 (soil) to -5 (air). Below this threshold is the part of the partitioning space, which is sensitive to the input parameters rain rate URain (influencing air and soil concentrations), water advection rate GWat (influencing water and sediment concentrations), and soil water runoff rate UWW (influencing soil concentrations). All three parameters characterize processes that involve the transport of chemical dissolved in water, and our analysis suggests that they only become relevant for highly watersoluble chemicals with a low log KAW below around -4. This horizontal threshold further only extends to a log KOA value of 11 for concentrations in air and to a log KOW of around 5-6 for concentrations in water, soil, and sediment, because chemicals with higher KOA and KOW values are more likely to associate with particles in air and water than to dissolve in water. We should note that the exact location of these thresholds is specific for a given model and a chosen scenario. For instance, a different rain scenario (with no-rain being an extreme case) would move the horizontal KAW thresholds up or down. Vertical thresholds, related to KOA, are particularly pronounced in Figure 3A and generally determine when various
FIGURE 3. Chemical space segments of identical input parameter sensitivities for the bulk phase concentrations in air, water, soil, and sediment in a level III model calculation with emissions to air. The location of the partitioning properties of selected PCBs and HCHs, taken from Li et al. (41) and Xiao et al. (42), in the partitioning space is also indicated. parameters related to atmospheric particles become influential. If emitted into air, the air concentration of chemicals with a log KOA of less than 10 is insensitive to virtually all input parameters. The air concentration of such chemicals is solely determined by the air advection rate GAir (segment 1) and, for chemicals with log KAW below -5, the precipitation rate URain (segment 2). This implies that only wet gaseous deposition can compete with the atmospheric transport out of the model environment. For involatile chemicals with log KOA values higher than 11, input parameters describing the rate of particle deposition (URain, particle scavenging ratio Q, dry particle deposition velocity UP) and the capacity of the atmospheric particle phase (volume fraction particles in air vQ, volume fraction organic matter in particles vOrgQ, density of organic matter δOM) become important (segment 3). The latter three parameters are no longer influential for the least volatile chemicals (log KOA > 12, segment 4), because they are associated with particles irrespective of the particle concentration and composition. The segmentation maps for the bulk phase concentrations in surface media (Figure 3B, C, and D) also have a vertical threshold at log KOA 12. At higher log KOA values, that is, for chemicals that are completely particle-bound in the atmosphere, the atmospheric advection rate GAir and the rain rate URain are losing influence on the concentrations in the surface compartments. Another vertical threshold at log KOA 1.5 indicates when chemicals become so volatile that air-filled soil pore space (vA) becomes a notable contributor to the amount in soil (Figure 3C).
Diagonal thresholds, related to log KOW, are particularly important for concentrations in the bulk water phase. A threshold at a log KOW of around 6 separates chemicals whose water concentration only depends on the advection rates of air and water (GAir, GWat) from those whose water concentration depends on the dynamics of solids in the aqueous phase, and which therefore are influenced by numerous parameter describing the transport of solids between soil, water, and sediment compartments (UDep, URes, USW), and the capacity of solids in soil, water, and sediment (fOrgSoil, fOrgWat, fOrgSed). Figure 3C and D also has diagonal thresholds at a log KOW around 5.5-6. Soil concentrations of chemicals above this threshold depend strongly on the soil solids runoff rate (USW), whereas those of chemicals below the threshold are more dependent on the soil water runoff rate (UWW) and the organic matter content of the soil (fOrgSoil) (Figure 3C). The equivalent threshold in Figure 3D separates chemicals whose sediment concentration is governed mostly by the relative size of the aquatic environment (AWat) and the sediment burial rate (UBur) and those that are more influenced by the water advection rate (GWat) and the organic matter content of the sediments. This implies that the soil and sediment concentrations of the less hydrophobic chemicals are governed by capacity terms (fOrgSoil, fOrgsed) and kinetic terms related to water movement (UWW, GWat), whereas the more hydrophobic chemicals’ concentrations in these media are more dependent on kinetic terms related to the movement of solids (USW, UBur). In Figure 3C and D, an additional diagonal threshold VOL. 39, NO. 9, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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at log KOW 1.5 separates chemicals, which are so water soluble that the water-filled pore space in soils (vW) or sediments (1 - vS) is a notable reservoir, from those chemicals for which the organic matter fraction in soil (fOrgSoil) and sediment solids (fOrgSed) becomes the dominant reservoir. Influence of Mode of Emission on Input Parameter Sensitivity. Sensitivity maps were also constructed for bulk phase concentrations calculated assuming emission is occurring into water and soil (Figures S1 and S2 in the Supporting Information). The maps with segments of similar input parameter sensitivity for emissions to water and soil are shown in Figures S3 and S4. A comparison of Figures 2, S1, and S2 and Figures 3, S3, and S4 reveals similarities and differences in the parameter sensitivities depending on the mode of emission. In general, it appears that emission to surface media (Figures S3, S4) results in a larger number of influential input parameters than the emission to the atmosphere (Figure 3). In particular, parameters influencing diffusive mass transfer processes, such as the mass transfer coefficients describing air-soil (MTCE, MTCA, MTCS) and air-water exchange (MTCWW, MTCAW), and the surface area of the water compartment (AWat) are now becoming important, because diffusive transfer to air is now the only way by which a chemical enters the atmosphere. The number of parameters influencing the concentration in a compartment is particularly large, if there is no direct connection between that compartment and the compartment receiving emission. Examples are the concentrations in sediment (Figure S4D) when emission occurs to soil, and the concentration in soil (Figure S3C) when emission is into the water compartment. As there is no transport process delivering chemical directly from water to soil, a chemical first has to volatilize into the atmosphere to reach the soil compartment. Interestingly, this suggests that model predictions may become increasingly uncertain as compartments further away from the emission compartment are being considered. The number of influential parameters is generally also large for the concentrations in the water compartment when emission occurs to air or soil, because water is the only medium receiving input from all other compartments. On the other hand, the concentration in the compartment receiving emissions tends to be influenced by only a small number of input parameters (Figures S3B, S4C). This is understandable, because the concentration in the compartment receiving emission is largely determined by how quickly the persistent chemical is lost by transport from that compartment. The sensitivity maps therefore can reveal the major transport route and rate-controlling parameter for that loss. For example, from Figure S4C we can deduce that for chemicals with a log KAW above -3 emitted to soil volatilization is the dominant route of loss from soil, and depending on volatility (log KOA), the rate-controlling parameter is the mass transfer coefficient describing diffusion in the air-filled soil pore space (MTCA, log KOA < 6, segments 1 and 2), the diffusivity describing sorbed phase movement within the soil (MTCS, 6 < log KOA < 8, segment 3), or the mass transfer coefficient through the air layer above the soil (MTCE, 8 < log KOA < 10, segment 4). If the chemical is even less volatile (log KOA > 10, segment 5), the solid-phase runoff to the water compartment becomes the most important route of loss from the soil and USW is the rate controlling parameter. Chemicals with a log KAW of less than -3 and a log KOW of less than -6.5 (segments 6 and 7) finally are lost by dissolving in the runoff water, and UWW becomes the most important parameter. Figure S3B can be read in a similar fashion to reveal for which chemicals volatilization (segments 2, 4, and 5), transfer to the sediment (segment 1), and water advection (segment 6) is the dominant loss route from the water compartment. The segmentation maps for the different modes of emission, air, water, and soil (Figures 3, S3, and S4, 3192
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respectively), are similar in that horizontal thresholds occur only in an intermediate log KAW range of -4 to -2. In addition to deciding when URain, GWat, and UWW become influential (Figure 3), these log KAW thresholds now also determine whether the air (MTCAW) or the water side (MTCWW) resistance is controlling diffusive air-water gas exchange (see, e.g., Figures S3C and D, S4B and S4D). A major difference, on the other hand, is related to the vertical thresholds, describing dependence on KOA. The thresholds at high log KOA values that are dominant at emission to air (Figure 3) no longer occur for emissions to water and soil (Figures S3, S4), and the aerosol-related input parameters, such as vQ, UP, vOrgQ, Q, are not influencing any of the bulk phase concentrations when emission is to water and soil. This suggests that the gas/particle partitioning process is only of importance, if emission of a chemical occurs into the atmosphere. On the other hand, a set of new vertical thresholds at lower log KOA values occurs, in particular if emission is to soil (Figure S4). These are related to the soil evaporation process discussed above and determine which mass transfer coefficient is controlling the overall soil-to-air transfer. A detailed discussion of this process, which is obviously of crucial importance for understanding the fate of soil emitted chemicals with a log KOA between 6 and 10 and a log KAW above -4, is given in McLachlan et al. (22). Very few input parameters, the advection rates of air and water, cause high sensitivity to volatile chemicals in bulk air (segment 1 in Figures 3A and S4A, segment 4 in Figure S3A) and to soluble chemicals in bulk water (segments 3 and 4 in Figure 3B, segment 6 in Figure S3B, segment 12 in Figure S4B) regardless of the mode of emission. This highlights that multimedia fate models are poorly suited for simulating the atmospheric behavior of very volatile substances or the behavior of very water-soluble substances in rivers, lakes, and oceans. The most important processes in such simulations are the advection of air and water, which are much better described in atmospheric dispersion or hydrodynamic models. The calculation of a characteristic travel distance in the context of the assessment of a chemical’s long-range transport potential relies on the calculation of an air concentration in a level III model assuming emission to air (33). Figure 3A suggests that for chemicals that are persistent in air, a level III approach has a fairly limited potential to discriminate between the atmospheric long-range transport potential of most reasonably volatile chemicals (log KOA less than approximately 10). For these persistent chemicals, alone the extent to which they are scavenged by precipitation will determine the value of their characteristic travel distance. Contribution to Output Uncertainty in Level III Calculations. Uncertainties of the level III model output expressed in CF values were also calculated and mapped. The results for all three modes of emission are presented in the Supporting Information (Figures S5-S7). Only maps exhibiting CFs above 1.4 are being displayed to avoid clutter and focus the discussion. In general, the uncertainty maps resemble the sensitivity maps quite closely, which may not be too surprising considering that many environmental input parameters were assumed to have the same uncertainty (CF values in Table 1). Noticeable is the large number of input parameters causing high output CFs for the concentrations of very hydrophobic substances (log KOW > 7.25) and substances that are both hydrophobic (log KOW > 5.5) and involatile (log KOA > 9.75). On the other hand, no input parameter causes CFs above 2.2 for chemicals that are very volatile and nonhydrophobic. The uncertainty of the parameter rain rate is responsible for high output CFs of the entire fraction of water-soluble substances. Because of high assigned uncertainty (CF of 3), the transport parameters (U and MTC) are more prominent in the uncertainty maps than
FIGURE 4. Comparison of the partitioning space maps displaying the sensitivity of the bulk concentrations of persistent and degradable chemicals in various media to changes in environmental input parameters. A level III model was used, assuming emissions to air. the compositional parameters or the air and water advection rates. Perusing the maps in Figures S5-S7, a number of input parameters stand out as consistently contributing greatly to the uncertainty of the calculated bulk phase concentrations. For example, large uncertainty (CF > 2) in the predictions of highly hydrophobic chemicals is due to the input parameters particle fraction in water (vP), soil solids runoff rate (USW), sediment deposition (UDep), and burial rate (UBur). This highlights the importance of the dynamics of particles, or more specifically particulate organic carbon (POC), when aiming to simulate the multimedia fate of highly hydrophobic organic chemicals. When trying to improve a model of the fate of such chemicals in a water body, it would be advisable to expend effort on constraining the parameters describing the transport of POC in that system. When emission takes place to water or soil (Figures S6 and S7), the mass transfer coefficients describing the diffusive exchange between air and the surface media also contribute significantly to output uncertainty. Influence of Chemical Degradability on Input Parameter Sensitivity. The assumption of total persistence is inappropriate for most chemicals. To obtain an idea about the extent to which the sensitivity maps differ for degradable chemicals, additional sensitivity calculations for two sets of hypothetical chemicals with different combinations of compartmental degradation half-lives were conducted and compared to those for perfectly persistent chemicals. Only selected sensitivity maps pertaining to level III calculations of bulk phase concentrations assuming emission into air are presented (Figure 4). The first set of degradable chemicals reacts fast in air and is somewhat persistent in the surface media, whereas the second set is more stable in air and slightly more reactive in surface media.
Introducing degradability did not or only slightly affected the sensitivity of the calculated concentrations to many of the input parameters. Several parameters cease to be influential for some or all partitioning combinations. For example, the particle concentration in water (vP) is no longer influential for the sediment concentration of any of the degradable chemicals (Figure 4), and the soil water runoff rate (UWW) only affects the soil and water concentrations of the least hydrophobic degradable chemicals. Similarly, the rain rate (URain) no longer affects the air concentrations of degradable chemicals with a low KAW, because atmospheric degradation is now so fast to compete effectively with vapor scavenging in removing chemical from the air compartment. For the same reason, the influence of the atmospheric advection rate (GAir) on the calculated concentrations is gradually diminished as the chemical degrades faster in air. However, the sensitivity of the air concentrations of the least volatile chemicals (log KOA > 12) is not affected, because they are completely particle sorbed and only gas-phase chemicals are assumed to undergo degradation in air. The gas/particle partitioning equilibrium is also at the root of more complex changes in sensitivity. For example, increasing the volume fraction of particles in air (vQ) decreased the air concentration of persistent chemicals with log KOA between 11 and 12, but increased them for chemicals with the same partitioning combinations when they are very degradable in air. In the case of persistent chemicals, a higher particle load increases particle-associated deposition processes, whereas for degradable chemicals, it decreases the fraction that is in the gas phase and can therefore react. In general, it appears that input parameters describing diffusive phase exchange processes, such as MTCAW and MTCA, are more influential for degradable chemicals than VOL. 39, NO. 9, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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for the persistent chemicals. When a chemical degrades much faster in air than in the surface media, more rapid diffusive transfer to the surface media can notably increase the concentration in surface media. This is particularly the case for the transfer of chemicals with intermediate log KAW around -3 to -5 to water (see sensitivity map for MTCAW), and chemicals with intermediate log KOA around 5-7 to soils (see map for MTCA). Interestingly, for the latter chemicals the influence of the organic matter content of soil (fOrgSoil) on the soil concentration is diminished upon introducing degradability, which means that a capacity term (fOrgSoil) is superseded in importance by a kinetic term (MTCA). Because the lifetime of degradable chemicals in the environment is limited, the rate of phase transfer is increasing in relative importance to the phase capacity. Although the results of the respective calculations are not shown here, we would like to note that the influence of the degradability on the sensitivities of the input parameters is smaller when emission occurs to the surface media. Application and Benefits of Sensitivity Maps. In principle, sensitivity to input parameters can be illustrated with partitioning space maps for any result of any linear model in which phase partitioning of organic chemicals is expressed in terms of the partition coefficients between air, water, and octanol. This includes not only most multimedia environmental fate models, but also many comprehensive bioaccumulation and human exposure models (34-36). It should be particularly worthwhile to construct sensitivity maps for highly aggregated model results with use in chemical evaluation and assessment, such as an intake fraction (36) or measures of long-range transport potential, such as a Spatial Range (37) or the Arctic Contamination Potential (28). The approach is most useful when a large number of diverse chemicals are modeled with a fixed environmental scenario. Models that are to be applied to only one or a few chemicals or models that yield a large number of outputs are less amenable to this approach to sensitivity analysis. Similarly, it is not useful when using a large number of environmental scenarios. The effort, involved in conducting the necessary calculations and producing the sensitivity maps, may be substantial, but the benefits that can be derived are also considerable. Once the sensitivity maps have been constructed, it is possible to perform a sensitivity analysis for a specific chemical or a group of chemicals by simple placement of the substances’ partitioning combinations on the sensitivity maps. We recently illustrated this procedure for a number of persistent organic pollutants (38). A sensitivity analysis could, for example, be accomplished with a transparent template that locates the substances in the partitioning space. By overlaying this template on the maps displayed in Figures 2, 3, and S1-S4, the influential parameters can be identified easily. As the chemical partitioning properties KOA and KAW are highly temperature dependent, the location of a substance in the partitioning space shifts to the right (higher KOA) and to the bottom (lower KAW) upon a drop in temperature (see, e.g., ref 23). In other words, a chemical occupies not merely a point in the partitioning space, but moves along a line from the upper right to the lower right depending on temperature. This implies that this simple graphical method even allows the evaluation of how the sensitivities to environmental input parameters change with temperature. Another major benefit of the sensitivity maps is that they can contribute a great deal to the mechanistic understanding of a model’s behavior, in particular in regard to how chemical with different partitioning properties are described by the model. Even simple models, such as those used for illustration of the method here, can be quite inaccessible and difficult to comprehend in terms of their dependencies on processes and parameters. For more complex models, these depend3194
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encies are virtually impossible to anticipate intuitively. Segmentation maps, such as those displayed in Figures 3, S3, and S4, highlight which processes are important for which chemicals, which input parameters have similar or even identical influence on a model result, and where the thresholds occur, at which a process starts or ceases to be of relevance. Input parameters and processes causing high output uncertainty can easily be ascertained, and emphasis can be laid on their improved specification. Another application of the approach presented here is that it can provide a rationale for grouping chemicals with similar model behavior or for selecting representative example chemicals for a model investigation, which is, for example, relevant when conducting risk assessment for chemical mixtures. Many chemicals are used or occur in complex mixtures. Examples are chlorinated paraffins or the polychlorinated dibenzo-p-dioxins and -furans. MacLeod et al. (39) grouped 300 hydrocarbon components of gasoline into 24 blocks displaying similar characteristics and then performed fate and bioaccumulation model simulations on these blocks rather than on the individual chemicals. We believe that segmentations maps such as those shown in Figures 3, S3, and S4 would constitute a rigorous means of establishing the minimum number of “blocks” required to describe a complex mixture in a particular model investigation and aid in assigning the components of the mixture to these blocks. The segmentation maps can further aid in explaining observations of divergent environmental behavior of structurally related substances. Li et al. (40), for example, noted a remarkably different distribution and transport behavior of β-hexachlorocyclohexane (β-HCH) in the Northern Pacific and Arctic Ocean when compared to R-HCH, even though both are structurally very similar and have identical sources. Even though the KAW of β-HCH is only 1 order of magnitude lower than that of R-HCH, the two chemicals happen to fall into segments on either side of the horizontal log KAW threshold identified above (Figures 3, S3, and S4). This suggests that, despite fairly minor differences in partitioning properties, different processes are controlling the fate of the two isomers. Specifically, the lower KAW of β-HCH makes it considerably more susceptible to precipitation scavenging than R-HCH (40) (Figure 3). However, we should note that different degradation behavior of the two isomers might also contribute to the observed divergence in environmental behavior. Similarly, it is noteworthy that polychlorinated biphenyls (PCBs) of different degree of chlorination straddle several segments within the partitioning space maps of Figures 3, S3, and S4, suggesting that they differ in terms of the controlling fate processes. Whereas the lightest PCBs are essentially atmospheric pollutants, whose concentrations are governed by atmospheric advection rates and organic matter content in surface media, the number of influential parameters increases with degree of chlorination. The heaviest PCBs sorb to particles in both air and water, and thus many additional processes become important. This divergent environmental behavior explains differences in terms of longrange transport and persistence of PCB congeners (21). Yet another application of the approach delineated here is that it can assist in deciding when accurate and precise knowledge of physical chemical property data is crucial and when approximate numbers suffice to conduct a model investigation. We had discussed above that horizontal thresholds in Figures 3, S3, and S4, indicating dependence of level III model results on log KAW, are few in number, occur only in a very limited, intermediate KAW range, and do not extend to very high KOA and KOW values. Interestingly, this implies that for a level III calculation using the model and environmental scenario of this study, it is only important to know a chemical’s log KAW very precisely and accurately,
if it falls within the fairly narrow range between -2.5 and -5.5, and if its log KOW is below 5 and its log KOA is below 11. Very high (log KAW > -2) and very low (log KAW < -6) KAWs and KAWs of very involatile and very hydrophobic chemicals need not be known very precisely, because they have no influence on the model results. It may often suffice to know, for example, from estimation techniques, that the log KAW is below -6, and no measurement is required. This is a very useful piece of information, because very low KAW values are very difficult to obtain experimentally. On the other hand, the occurrence of several diagonal thresholds suggests that the accurate description of the solid/water partitioning equilibrium estimated through KOW is key to obtaining reasonable concentration estimates in level III model calculations.
Acknowledgments We are grateful to the Long-Range Research Initiative (LRI) of the European Chemical Industry Association (CEFIC) for funding.
Supporting Information Available Figures with the partitioning space maps displaying the sensitivity of the concentration in various bulk media, calculated with a level III model assuming emissions to water or soil, to changes in environmental input parameter, and figures with the partitioning space maps displaying the contribution to model output uncertainty (CFs) for the level III model calculations. This material is available free of charge via the Internet at http://pubs.acs.org.
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Received for review August 16, 2004. Revised manuscript received January 27, 2005. Accepted February 4, 2005. ES048728T
