Joint Persistence of Transformation Products in Chemicals Assessment: Case Studies and Uncertainty Analysis

1. INTRODUCTION

To assess the possible hazard of environmental exposure to chemicals, persistence is frequently used as an indicator describing the duration of exposure. Because persistent chemicals are often also subject to long-range transport, which might lead to widespread contamination, persistence is regarded as an important criterion for the selection of chemicals that are deemed in need of global action. Persistence is thus part of many criteria sets for the selection of hazardous chemicals.

Many assessment procedures focus on identifying highly persistent parent chemicals. However, most of these procedures ignore the fact that exposure can result not only from the parent chemicals but also from their transformation products. In reality, the formation of transformation products can lead to higher spatial and temporal extents of exposure to chemicals. This might contribute significantly to the hazard a chemical poses, especially in the case of not exceedingly persistent parent chemicals. The Stockholm Convention on Persistent Organic Pollutants provides for this situation by defining a substance as “the parent compound and all its transformation products with POP characteristics.”⁽¹⁾ However, little instruction is given as to how transformation products could be included into the determination of the convention's selection criteria.

Recently, the joint persistence (JP) has been suggested as an indicator to assess the persistence of parent compounds and transformation products in combination.⁽²⁾ The JP indicates to what extent the transformation cascade originating from a certain parent compound increases the environmental exposure as compared to the parent compound alone. For its calculation, a multimedia box model was employed that accounts for the formation kinetics of transformation products. Similarly, Quartier and Müller-Herold⁽³⁾ integrated transformation products into the calculation of spatial range as a measure of the spatial dimension of exposure. Other studies investigating the fate of transformation products focus on risk-based indicators.^(4-6)

In a recent OECD/UNEP workshop on the use of multimedia models to calculate persistence and long-range transport potential,⁽⁷⁾ it was noted that although there is a broad consensus on the importance of persistence as an indicator for chemicals assessment, little is known about the uncertainties in its calculation. Open questions identified were, for example, how persistence values differ between models, how different mathematical persistence definitions compare, and what uncertainty intervals are to be expected due to uncertain and variable model input parameters.

The aim of this work is, first, to quantify the uncertainties in persistence calculations that are due to uncertainties in substance-specific input parameters and, second, to put a special focus on how inclusion of transformation products affects the calculation of persistence. This question can be regarded as an important decision rule concerning uncertainty in persistence calculations.

In Section 2, three chemical case studies are introduced and their PP and JP values are evaluated to illustrate three cases that differ with regard to the impact that the inclusion of transformation products has on the persistence values. The case studies are nonylphenol polyethoxylates (NPnEO), perchloroethylene (PCE), and atrazine, all including the respective transformation products. The case studies are further used in Section 3 to assess the main uncertainties in the calculation of PP and JP. These uncertainties include (1) variance in the results due to uncertainty in the substance-specific input parameters and (2) uncertainty due to the inclusion or exclusion of specific transformation products or generations of transformation products. With regard to parameter uncertainty, Monte Carlo simulations make it possible to estimate typical uncertainty ranges for persistence values and to determine which substance-specific input parameters dominate them. Regarding the importance of single transformation products, a mathematical expression is presented that allows one to determine their individual contribution to the joint persistence.

2. JOINT PERSISTENCE CALCULATIONS FOR THE NPnEO, PERCHLOROETHYLENE, AND ATRAZINE CASE STUDIES

To include transformation products into persistence calculations, several terms must first be defined.

The parent compound is the chemical (A) that is emitted, intentionally or accidentally, into the environment. The transformation products (B, C, …) are formed through biotic or abiotic degradation of the parent compound. Specific transformation products are transformation products that bear a clear structural similarity with the parent compound and for whose biodegradation no specific enzymes are available. Only specific transformation products are included in the calculation of persistence because it is assumed that if a chemical's structure allows it to enter one of the main metabolic pathways of microorganisms, it is readily biodegradable and no further persistent transformation products will be formed. The set of a parent compound and all its specific transformation products is termed a substance family. Further, generations of transformation products are distinguished, which are defined by the minimal number of transformation steps between a transformation product and its parent compound. Transformation products with the same minimal number of intermediate transformation reactions belong to the same generation.

To describe the persistence of entire substance families, the joint persistence (JP) is used in addition to the primary persistence (PP) that is usually calculated to express the lifetime of the parent compound.⁽²⁾ The JP can be used in chemicals assessment to describe the total exposure of the environment to all compounds of a substance family. Here, the JP and the PP are evaluated as key criteria for the persistence of substance families and discussed for the three case studies.

The three chemical case studies that were chosen to investigate the differences between PP and JP, as well as their applicability, significance, and uncertainty, are: (1) the widely used herbicide atrazine, (2) nonylphenol polyethoxylates (NPnEO) as a group of surfactants, and (3) perchloroethylene, a solvent used in metal degreasing and dry cleaning. The three chemicals have in common that they have been used historically in large amounts with, in the cases of perchloroethylene and NPnEO, little attention being paid to prevent their emission into the environment. Accordingly, all three chemicals are detected in the environment in considerable amounts. Also, each of them has transformation products that are present in the environment along with the parent compound and are known to possess potentially damaging properties. As a consequence of their widespread presence and known harmful effects, the three substance families have been investigated extensively and therefore the data availability is sufficiently good for them.

The three case studies differ with respect to the emission scenario for the parent compound (i.e., atrazine mainly to soil, perchloroethylene as fugitive emissions to air, NPnEO from sewage treatment plants to water), with respect to the main environmental residence compartments of parent compound and transformation products, and with respect to the number of identified specific transformation products, as well as the number of generations of transformation products. Lastly, the significance and behavior of the transformation products relative to their parent compound is different in the three case studies.

2.2. Primary and Joint Persistence Calculations

2.2.1. Methodology

The concentration functions on which the calculation of the persistence values is based are calculated with a generic three-box multimedia model with averaged global properties, including the media soil (s), water (w), and air (a). (Note that, if available, measured concentration-time profiles could be used instead to calculate persistence.) The multimedia model used here is similar to that described by Scheringer.⁽²⁹⁾ Modifications concern the depth of the water compartment, which has been increased to 200 m instead of 10 m to represent a global average depth of oceanic surface water, and the inclusion of suspended particles in water. The detailed mathematical formulations for the corresponding partition coefficients and intermedia transfer processes for the modified environments can be found in References 29 and 30.

To calculate the concentration functions of the transformation products y of any precursor x(x≠y), the rate equations describing formation, intermedia transfer processes, and degradation are set up for all transformation products (see Equation (1) in Fenner et al.⁽²⁾). They contain formation terms

(1)

with κ^xy_i denoting the rate constants of the formation of y out of x. κ^xy_i is proportional to the degradation rate constant of the precursor x, that is, κ^xy_i=ϑ^xy_i·κ^x_i with ϑ^xy_i denoting the fraction of formation for transformation of x to y in medium i.

The resulting media-specific rate equations for the parent compound and all of its transformation products form a system of 3 m linear differential equations that can be solved for a pulse release scenario to give concentration functions c^x_i(t) by calculating the eigenvectors and eigenvalues of the system.^(2,31,32)

Fenner et al.⁽²⁾ demonstrated how the PP and JP can be calculated from the media-specific concentration functions c^x_i(t) of the m chemical species x or y that make up a substance family with parent compound (A) and m− 1 transformation products y= B, C, …, see Equations (2) and (3) with media i= s, w, and a; media volumes V_i; media-specific release concentrations c_0,i (in mol/m³) at t= 0; and total released mass M^A₀ (in mol). The time integrals of c^A_i (t) and c^y_i(t) in Equations (2) and (3) are called media-specific exposures e^A_i and e^y_i (in d · mol/m³); denotes the time integral of the mass function M(t).

(2)

(3)

The overall persistence as defined in Equation (2) for the parent compound alone and in Equation (3) for the entire substance family depends on the release compartment. In the model calculations, each parent compound is released into its most likely release compartment, that is, atrazine into the soil, perchloroethylene into the air, and NPnEO into the water.

Substance-specific input data entering the three-box model are three degradation rate constants κ^x_i for each environmental medium i, the Henry's Law constant, K^x_H, and the octanol-water or the organic carbon-water partition coefficient, K^x_ow or K^x_oc. To obtain these substance-specific input parameters for the parent compound and all transformation products for all three case studies, an extensive literature search has been conducted, focusing, wherever possible, on original research papers.

The number of data points found for each input parameter varied between 0 (e.g., for half-lives in soil, water, and air for all third and fourth generation transformation products of atrazine) and 100 (e.g., for the half-life of atrazine in soil). If no data could be retrieved for a certain model input parameter, quantitative structure-property relationships (QSPR) were used to estimate that parameter (EPIWIN by Meylan and Howard⁽³³⁾). To obtain estimates of degradation rate constants in soil and water, semi-quantitative estimates for primary biodegradation from BioWin⁽³⁴⁾ were translated into half-lives. In those cases in which more than one data point was available for a certain model input parameter, the set of all collected points was represented by geometric means (μ_GM). The geometric mean was chosen because it represents the central tendency of a set of data that spreads over several orders of magnitude, which is often the case for partition coefficients and degradation rate constants. In addition, it makes it possible to treat degradation data in a consistent manner independent of whether they are given as half-lives or rate constants. The substance-specific input parameters for all case study chemicals are compiled in Table AII of the Appendix.

As mentioned above, the media-specific fractions of formation as listed in Table AI are needed as an additional set of input parameters, representing the media-specific transformation schemes.

2.2.2. Results

The concentration functions c^x_i(t) obtained from solving the system of linear differential equations for each compound x in each medium are converted to overall mass profiles M^x(t) by multiplication with the compartments' volumes and summation over all compartments. The resulting mass profiles are displayed in Fig. 4 for all three case studies. The primary and joint persistences deduced from these mass profiles according to Equations (2) and (3) are listed in Table I.

Table 1. Point Estimates of the Primary and Joint Persistence Values for All Three Case Studies

Case Study	PP(d)	JP(d)	Q (=JP/PP)
NPnEO	27.3	111	4.06
PCE	62.2	139	2.24
Atrazine	66.4	83.1	1.25

A comparison of the primary mass profiles (PMP) with the joint mass profiles (JMP) in Fig. 4 shows that the transformation products make up large parts of the JMP in the case of NPnEO, whereas, in the case of atrazine, the JMP is still dominated by the PMP of atrazine itself. With regard to the persistence values, this translates into a quotient Q of 4.1 between JP and PP for NPnEO, of 2.2 for perchloroethylene, and a quotient of 1.3 for atrazine.

3. UNCERTAINTY ANALYSIS OF PRIMARY AND JOINT PERSISTENCE

Values of the PP and JP as calculated for the three case studies are subject to a number of uncertainties. These uncertainties stem, first, from concerns typical of using multimedia models, such as the appropriate selection and number of compartments to be modeled, the appropriate model geometry, and the fact that average values are used to represent large and heterogeneous regions. Second, in the context of JP calculations, additional uncertainty is introduced through questions specifically concerning transformation products, such as the selection of transformation products to be included, their substance-specific properties, and their pattern of formation, that is, their transformation scheme.

Here, general considerations regarding the structural uncertainty of multimedia models are excluded and the evaluation of uncertainty focuses on the variance in input parameters and on the inclusion of transformation products in persistence calculations.

First, it is of interest to quantify the actual uncertainty in PP and JP values and to discuss what consequences this has for the applicability of persistence in chemicals assessment. To this end, an uncertainty analysis is conducted for the PP and JP by means of Monte Carlo simulation. Additional insights gained from such an analysis are the identification of those input parameters that contribute most to the overall uncertainty and should therefore be investigated more thoroughly in order to reduce uncertainty and obtain as reliable persistence values as possible.

In a separate evaluation, the question of uncertainty in constructing the transformation scheme is discussed by evaluating how the inclusion or exclusion of certain transformation products affects the JP results. From these investigations, indication can also be obtained on how the number of transformation products that need to be included could possibly be reduced without significantly changing the value of the JP.

3.1. Parameter Uncertainty and Variability

3.1.1. Methodology

For the uncertainty analysis presented here, probabilistic distributions were attributed only to the substance-specific input parameters, while point estimates were used for the environmental parameters. The reasons for this are: (1) the focus of this analysis is on understanding the extent to which the parent compound and the different transformation products contribute to the uncertainty in the final JP value; (2) Hertwich et al.^(35,36) showed that for potential dose calculations in closed multimedia systems, most of the variance in the output is attributable to uncertainty in chemical-specific input parameters and that variance in the environmental parameters always contributes less than 10%; and (3) the results of sensitivity analyses for the JP, which are described in more detail in Reference 37, indicate that the environmental parameters generally have only a low influence on the JP value.

The effect of uncertainty in the substance-specific input parameters, that is, degradation rate constants, partition coefficients, and fractions of formation, on PP, JP, and quotient Q is analyzed with a Monte Carlo approach using Latin Hypercube sampling (LHS) as the sampling scheme.

The partition coefficients and degradation rate constants are assumed to be log-normally distributed and independent. The log-normal distribution is a good representation for quantities that are constrained to being nonnegative and that are expressed on an order-of-magnitude basis, which applies to both partition coefficients and degradation rate constants.⁽³⁸⁾ Log-normal distributions have the further advantage of providing the same distribution of the degradation data, independently of whether it is derived from log-transformed half-lives or degradation rate constants.⁽³⁹⁾ The distribution parameters that went into the model calculations are the logarithmic mean, μ_ln, and the logarithmic standard deviation, σ_ln, as defined in Equations (4) and (5) for an input parameter a.

(4)

(5)

These parameters of the distribution were determined in different ways depending on the number, n, of data points available for each input parameter.

• •

  If n≥ 3, μ_ln and σ_ln were determined according to Equations (4) and (5), that is, according to the maximum likelihood procedure for the estimation of the parameters of a log-normal distribution.⁽³⁸⁾

• •

  If n= 2, μ_ln was calculated as for n≥ 3 according to Equation (4) and σ_ln was calculated by assuming that the two data points represent the 5th and 95th percentile of the log-normal distribution. If this assumption resulted in a smaller σ_ln than the default values suggested in the model CalTOX,⁽⁴⁰⁾ the default σ_ln value from CalTOX was used instead to determine σ_ln.

• •

  If n= 1, the log-transformed data point was taken to be μ_ln and the default σ_ln value from CalTOX was used.⁽⁴⁰⁾

All μ_ln and σ_ln values, as well as the numbers of underlying data points, n, are listed in Tables AIII and AIV in the Appendix.

The fractions of formation in the uncertainty analysis were all described by triangular distributions between 0 and 1. The fractions of formation used for the point estimate calculations (given in Table AII) were chosen to represent the most likely values. However, there is a restriction for the choice of fractions of formation of parallel reactions since their sum must never exceed 1. Although this problem is easily solved for two fractions of formation that always add up to 1, the situation here is more complicated because it is possible that the fractions of formation do not add up to 1 because one or more unknown or irrelevant transformation products might be formed at the same time. The solution to this problem is described in detail in Reference 37.

To determine the number of runs providing sufficiently accurate results, simulations with different numbers of runs were performed (N= 100, 500, 1, 000, 2, 500, 10, 000) and the values of the corresponding summary statistics for PP and JP were monitored. It was found that the results for N= 2,500 always laid within 1% of the results for N= 10,000, which is assumed to be closest to the correct value. That precision was considered a good tradeoff between precision requirements and calculation time needed.

As mentioned, no correlations were assumed for the substance-specific input parameters, that is, degradation rate constants and partition coefficients, since their functional dependencies on environmental parameters such as temperature and pH are not covered by the model. There exists, however, a correlation between the analyzed model outputs, that is, PP and JP, because the JP value always contains the corresponding PP value (see Equation (3)). This correlation was taken into account by calculating the quotient of JP and PP for each scenario separately, which resulted in a third output distribution for the quotient, Q. Wherever the ratio between JP and PP needs to be investigated, the discussion should be based on the distribution of Q and not on the ratio of the summary statistics of the individual PP and JP distributions.

The three output parameters of the uncertainty analysis, namely, the PP, JP, and quotient Q, are analyzed in various ways. To determine the location and spread of the output distribution functions, their geometric mean, μ_GM, was calculated as a measure of central tendency, and the ratio of the 95th and the 5th percentile was evaluated to represent the spread of the distributions. These summary statistics are used to compare the output distributions with the point estimates from Section 2.2 and to learn about the uncertainty inherent in persistence calculations. Additionally, to compute the relative contribution of each input parameter to the total variance of the resulting output distribution, the contributions to variance (CTVs, denoted by Δ_a,b) were calculated based on the rank correlation coefficients, ρ_a,b, between input parameter a and output parameter b according to Equations (6) and (7).

(6)

(7)

N is the number of Monte Carlo runs; r(a_k) and r(b_k) denote the ranks of the values of input and output parameters a and b for a specific run k; is the mean rank of a total of N runs.

3.1.2. Results and Discussion

The summary statistics for the output distributions resulting from the Monte Carlo analysis of the PP, JP, and Q are listed in Table II for the three case studies.

Table 2. Summary Statistics for Results of Uncertainty Analysis: PP, JP, and Quotient Q for the Three Case Studies

NPnEO	PP	JP	Q
μ GM	27.3 d	143 d	5.39 (−)
GSD	3.2 (−)	2.4 (−)	3.1 (−)
5th percentile	4.10 d	41.0 d	1.30 (−)
95th percentile	180 d	665 d	45.1 (−)
95th/5th percentile	43.8 (−)	16.2 (−)	34.8 (−)

Perchloroethylene	PP	JP	Q
μ GM	62.7 d	156 d	2.49 (−)
GSD	2.0 (−)	2.3 (−)	2.3 (−)
5th percentile	20.9 d	55.1 d	1.14 (−)
95th percentile	186 d	674 d	12.0 (−)
95th/5th percentile	8.86 (−)	12.2 (−)	10.5 (−)

Atrazine	PP	JP	Q
μ GM	97.4 d	158 d	1.62 (−)
GSD	3.2 (−)	2.6 (−)	1.5 (−)
5th percentile	23.7 d	58.1 d	1.03 (−)
95th percentile	1020 d	1060 d	3.55 (−)
95th/5th percentile	43.0 (−)	18.3 (−)	3.44 (−)

• μ _GM : geometric mean. GSD: geometric standard deviation.

Comparison of the geometric means from Table II with the point estimates from Table I shows that the μ_GM values lie between a factor of 1–2 above the point estimates. This is mostly due to the fact that the fractions of formation are allowed to vary between 0 and 1 in the uncertainty analysis as opposed to being set to a fixed, rather low, value for the point estimate calculations.

The results of the uncertainty analysis further reveal that the variance of PP and JP values—as defined by the ratio of the 95th to the 5th percentile—varies between 10 and 40. The typical uncertainty in persistence calculations therefore seems to lie between 1–2 orders of magnitude. If these rather large calculated confidence intervals are compared to the ratios typically encountered between persistence values of individual compounds, for example, a set of persistence rank-ordered POPs, it becomes obvious that the persistence confidence interval of one compound might overlap considerably with the persistence confidence interval of a neighboring compound.

A comparison of the uncertainty range of the PP with that of the JP for each separate case study reveals another important point. It shows that in two of three cases (NPnEO and atrazine), the uncertainty range of the JP is smaller than that of the PP. This clearly contradicts the presumption that through the inclusion of transformation products the model complexity and, therefore, also the uncertainty in the model outputs is augmented. The explanation of the smaller uncertainty range of the JP of NPnEO and atrazine as compared to that of the PP is that, in these two cases, the most influential input parameters of the JP show smaller uncertainties than the most influential input parameters of the PP.

The analysis of the Δ_a,b values, whose results are depicted in Fig. 5, indicates that for all three case studies over 70% of the uncertainty of persistence calculations is due to variance in the degradation rate constants. That variance is due to the combined effect of true parameter uncertainty (scatter in measurement results) and stochastic variability due to differences in the global environment represented by the model. The latter cause for variance cannot be excluded from a model using global averages for many parameters. Since preliminary investigations suggest that it is variability that dominates the variance of the degradation rate constants,⁽³⁷⁾ most of the considerable variance in the persistence values must be regarded as irreducible too. It follows that rather than assessing single compounds on grounds of their persistence (and other indicators), it might be more appropriate to assign them to groups of chemicals that are defined by ranges of substance properties and to develop risk management strategies for such groups as a whole.⁽⁴¹⁾

The contributions to variance of the fractions of formation lie between 7–25% and are thus clearly lower than those of the degradation rates. This is explained by the fact that the fractions of formation are always bound by 0 and 1, while the degradation data can vary over much larger ranges. This means that the fractions of formation, which are often poorly known and therefore have been suspected to be prejudicial to the dynamic modeling of transformation products, do not contribute greatly to the variance in the JP. Therefore, it seems that reasonably good JP values can be calculated by using relatively rough guesses for the fractions of formation.

Partition coefficients, even when varied over the whole uncertainty range attributed to them, have little influence on the uncertainty range of persistence calculations. This is in agreement with the results of Hertwich et al.,⁽³⁵⁾ who showed that most of the variance in their calculated exposure values is due to chemical-specific input parameters and, in particular, to half-lives. The low influence of the partition coefficients is due to the fact that their σ_ln values are somewhat lower than the σ_ln values of the degradation rates for most compounds. This situation is also due to the fact that the values of the partition coefficients do not fall into the domain of pronounced multimedia behavior so that changes of the partition coefficients do not strongly affect the chemicals' environmental fate.

4. CONCLUSIONS

A first important finding of the uncertainty analysis for primary and joint persistence is that the primary persistences alone exhibit considerable variances of about a factor of 10 in one case and 40 in two cases. Since the compounds investigated are relatively well known, these variances are not mainly due to uncertainty but to explicitly documented variability, in this case of the degradation rate constants. In the NPnEO case study, for example, the degradation rate constant of NPnEO in water with a geometric standard deviation of 4.3 (which is based on 12 data points) leads to a factor of 43.8 between the 95th and the 5th percentile. It is likely that similar variabilities also occur for persistence calculations of other chemicals.

Because of these considerable uncertainties, chemical rankings in terms of persistence should include information about the ranges of the persistence values whenever possible. Rankings based on point estimates alone can serve as a first illustration but should be complemented by uncertainty and variability data if they are to be used as a basis for decisions about chemicals. It might be useful to devise ranking schemes in terms of ranges of substance properties and to develop research priorities, as well as management strategies, for such groups of compounds. A research need following from these results is that the environmental variability of degradation rate constants should be better characterized by investigation of a broad spectrum of degradation processes and environmental conditions.

As for the joint persistence, there are several points to mention. The point estimates of the joint persistence, if compared to the PP values (see Table I), show that significant contributions to the environmental exposure and thus persistence from the transformation products are possible. In the case studies considered, a maximum factor of 4 between joint persistence and primary persistence is found; it is likely that similar or even higher values could be found in other cases such as DDT/DDE and other persistent organic pollutants or fluorinated hydrocarbons used as CFC substitutes.

The main obstacle to including transformation products into persistence calculations is the task of compiling a reliable transformation scheme. It requires an extensive and often time-consuming search for different types of data, evaluation of these sometimes conflicting data, and combination of all information to an overall picture of the degradation processes of a substance family. Specific steps are (1) the selection of relevant transformation products, (2) determination of transformation rate constants, and (3) quantification of fractions of formation.

The most important finding from the uncertainty analysis is that even complex transformation schemes do not necessarily lead to high uncertainties in the joint persistence. Although a transformation scheme might contain many parameters, these additional model parameters differ with respect to their influence on the joint persistence results, as is shown by the CTVs in Fig. 5. In the case studies investigated, the joint persistence is dominated by only a few most influential parameters and at least some of these parameters are not more uncertain than those dominating the primary persistence. Therefore, in two of the cases considered here (NPnEO and atrazine), the variance observed for the joint persistence is even smaller than that of the primary persistence. To some extent, this is due to the fact that the default coefficients of variation taken from CalTOX for poorly characterized compounds are lower than the spread of the data for relatively well-characterized parent compounds. Again, this points to the necessity of a better understanding of the environmental variability of degradation rate constants.

A tentative conclusion from the case studies investigated is that the joint persistence is not necessarily more uncertain than the primary persistence.

Another conclusion is that because of the dominating influence of a few parameters, the JP values are rather robust against errors or changes in the transformation scheme. This, in turn, implies that it is not necessary to strive for a complete transformation scheme (which would be not possible anyway because of the complexity of the environmental transformation pathways) but that, for the purpose of calculating the joint persistence, estimates and simplified schemes are sufficient.

Specifically, the quality of a transformation scheme depends on the following points. The main error in setting up a transformation scheme would be to overlook a major metabolite. If the relevant metabolites are known and data (or estimates) for their properties are available, a first transformation scheme can be established with generic fractions of formation. Once the transformation scheme has been set up, the calculation procedure for the joint persistence can easily be included into existing level III multimedia models; it does not require much computational effort. The first transformation scheme and the corresponding joint persistence can be refined by including more specific fractions of formation.

It must be kept in mind that all findings presented here are derived from three examples. To improve the understanding of how important different generations of transformation products are in persistence calculations, additional substance families should be investigated.

APPENDIX