E. Halfon, S. Galassi, R. Brüggemann, A Provini

MANAGEMENT PERSPECTIVE

The hazard assessment of pesticides in ground water is evaluated using a ranking method based on graph theory coupled with data collected in Italy in the 1980's. In this paper we prove that the results obtained by our ranking method agree well with field data. To test whether the theoretical ranking is realistic, the list of identified compounds was compared with the results of monitoring studies carried out in Italian surficial waters. The assumption for this comparison is that if the ranking method is correct then the probability of finding chemicals identified as hazardous should be higher than the probability of finding less hazardous chemicals. Chemicals ranked lower have less probability of being found both because of lower usage and because they are less persistent and/or less leachable. This aspect is encouraging news as it means that only the pesticides ranked high in our assessment must be sought using analytical chemical techniques. The criteria we use for ranking are vapour pressure, water solubility, persistence and yearly usage. Here we have also studied which criteria are most important for ranking and to assess risk.

ABSTRACT

We assess the environmental hazard of 50 pesticides used in Italy by means of Hasse diagrams, a method based on graph theory. The criteria we use for ranking are persistence, and the physical-chemical properties, vapour pressure and water solubility, and yearly usage. When only the physical-chemicals properties plus persistence are used to assess environmental hazard of pesticides in soils, eleven out of the 50 compounds studied here, methylbromide, bentazone, dalapon, diquat, linuron, mancozeb, metham-Na, TCA, metolachlor, paraquat, and simazine are considered potentially hazardous for their mixture of long persistence in soil, high water solubility and low vapour pressure. Alachlor, atrazine, chloridazon, terbuthylazine and ziram are also a problem of concern because of their high loadings. To test whether the theoretical ranking is realistic, the list of identified compounds was compared with the results of monitoring studies carried out in Italian surficial waters. The assumption for this comparison is that, if the ranking method is correct, the probability of finding chemicals identified as hazardous should be higher than the probability of finding less hazardous chemicals. Chemicals ranked lower have less probability of being found both because of lower usage and because they are less persistent and/or less leachable. Results are quite encouraging since seven pesticides identified by our ranking method as most hazardous, alachlor, atrazine, bentazone, linuron, metolachlor, simazine and terbuthylazine of the 8 analyzed for (previous plus TCA) were found, a success ratio of 88%. Results for all the other chemicals are presented in the paper. The second purpose of this study was the identification of the most important criteria to assess the chemicals; this assessment was performed using a matrix W. We concluded that the elimination of the criterion "usage" affects ranking more than the elimination of water solubility. However, none of the criteria, water solubility, vapour pressure, persistence and yearly usage can be eliminated, too much information would be lost if they were omitted. This conclusion is consistent with our decision to use only few criteria to rank the chemicals, criteria that are deemed to be independent of each other.

Keywords: ground water, Hasse diagram, criteria, threat

INTRODUCTION

While hundreds of pesticides are used in Europe, only recently an EU Working Group (Fielding et al., 1992) collected data on their use in the different countries to assess the risk of pesticides to drinking and ground waters. Since pesticides are used differently in each country depending on agricultural cultivations and market laws, a risk assessment has to be done on a national basis.

The environmental fate of pesticides is determined by their physical-chemical properties, persistence in soil and their usage. A bibliography search has shown that a quantitative approach to evaluate which of these criteria have the greatest influence on the occurrence of pesticides in surface waters has never been tried. Our purpose is to assess the environmental hazard of some pesticides used in Italy by means of the Hasse diagrams (Halfon and Reggiani, 1986); the criteria we use for ranking are persistence, water solubility, vapour pressure and yearly usage; mathematically these criteria are stored as vectors with four elements. We also investigate two related issues: One is the identification of the most important criteria to assess the chemicals instead of combining a priori more criteria (Weber, 1977; Gustafson, 1989). The second one is the relation between the identification of the most hazardous pesticides through ranking and through identification in the field.

Hasse diagrams (Davey and Priestley, 1990) have been used to rank chemicals according to environmental hazard (Halfon and Reggiani, 1986; Brüggemann and Halfon, 1989), to compare waste disposal sites (Halfon, 1989), to compare mathematical models (Reggiani and Marchetti, 1975; Halfon, 1983a,b), in QSAR studies (Brüggemann and Altschuh, 1991; Randic, 1991), in problems of regional pollution (Brüggemann et al., 1994; Münzer et al., 1994) and in the evaluation of data sources (Voigt and Brüggemann, 1993). The main assumption is that we can perform a ranking while avoiding the use of an ordering index (Halfon and Reggiani, 1986).

RANKING METHODOLOGY

The analysis is performed in two parts. The first part is graphical, the development of a Hasse diagram, and the second is mathematical based on set theory. The first part uses the methodology developed by Halfon and Reggiani (1986) to rank toxic contaminants, while the second part of the analysis is based on a new sensitivity analysis of ranking (Brüggemann and Halfon, 1995). The textbooks of Harary (1969), Preparate and Yeh (1973), and Davey and Priestley (1990) present useful background information on graphs, sets, partially ordered sets (posets) and Hasse diagrams.

Hasse diagrams, oriented graphs (acyclic digraphs), visualize the order relations of posets. A digraph consists of a set E of objects drawn as circles in Hasse diagrams. In our applications the circles near the top of the page (of the Hasse diagram) indicate chemicals that seem to be the most hazardous according to the criteria used to rank them. We use the word "seem" rather than "are" because when objects in a Hasse diagram are not connected by a line they cannot be compared. A line in the Hasse diagram indicates that the two objects (the two chemicals) connected by that line are "comparable" with each other, lack of sequences of connecting lines indicates that there are contradictions in the ranking according to the different criteria; these two chemicals are "incomparable"¹ , since these two chemicals have different physical-chemicals properties (a complete explanation with examples may be found in Halfon and Reggiani, 1986).

Ordering and partial ordering

Three conditions, reflexivity, antisymmetry and transitivity must be fulfilled at the same time for some objects to be said to be in an order relation. Order is not a property intrinsic to a single object, it concerns comparison of objects: 0 is smaller than 1; "Mars is farther from the Sun than Earth..." (Davey and Priestley, 1990). Antisymmetry means 5 is bigger than 3 but 3 is not bigger than 5 and transitivity means that from 0 < 1 and 1 < 1000 we can deduce that 0 < 1000. Reflexivity means that an object can be compared with itself. Furthermore, there are four descriptive terms of ordering relations, strict and non-strict, total and non-total. These relations are as fundamental to our purpose and in general in ecology as the previous two conditions of antisymmetry and transitivity. The statement "chemical x is more hazardous than chemical y" means that x is strictly more hazardous than y. In general if the statement "chemical x is as hazardous as chemical y" can not be excluded, the order is defined as non-strict. A total order ensues if all objects can be compared. However, the statement "chemical y is more hazardous because of property A and less hazardous because of property B than x" means that there is an ambiguity between the hazard to the environment exerted by x and y. The chemicals x and y are incomparable. The presence of such incomparable objects within an ordering scheme is explicitly denoted by the term non-total order or partial ordering. For the formal mathematical details see Davey and Priestley (1990). The number of levels in a Hasse diagram is, qualitatively, a rough measure of objects that are comparable to each other because, if the number of objects is the same, more levels mean more comparable objects.

Interpretation of Hasse diagrams in environmental assessment

Hasse diagrams are graphical tools that visualize posets. This visualization, however, must be interpreted by a user and this interpretation may be incomplete. Brüggemann and Halfon's (1995) method remedies this deficiency. Set theoretical and lattice theoretical concepts such as cardinality, successor sets and the intersection of these sets are used to compute their intersection matrix D. This matrix helps to understand the hidden structures of Hasse diagrams.

To study the importance that each attribute has for ranking, Brüggemann and Halfon (1995) also proposed the matrix W that quantifies the dissimilarity of different Hasse diagrams and helps to analyze the importance of criteria, by which chemical hazard is characterized.

DATA

Table 1 shows the 50 pesticides most used in Italy (> 50 metric tons year^-1); sales data refer to 1986-87 since Funari et al. (1989) published the most comprehensive list for herbicide sales. Consumption values for pesticides other than herbicides are taken from Italian National Statistics Office (ISTAT, 1989; 1992). All data refer to active ingredients with the exception of those on fungicides, because only data on commercial formulations are available.

Properties are half-life in soils ("persistence"), water solubility and vapour pressure. Their values are taken from The Agrochemical Handbook (1990) and from two databases (Wauchope et al., 1992; Augustijn-Beckers et al., 1994). Vapour pressure is handled as inverse quantity due to the improvement of the soil if the vapour pressure if high (volatilization from soil). Therefore, the vector half-life in soils, water solubility and (with a negative sign) vapour pressure describes the environmental hazard in surface waters.

RESULTS

Environmentally hazardous chemicals - potential

Figure 1 has only 49 circles and not fifty (See Table 1). The discrepancy is identified at the bottom of the Hasse diagram that indicates that the mancozeb (h2) and maneb (h3) are equivalent objects with the same properties. Table 1 shows that these two chemicals differ only in their usage in Italy, mancozeb is much more used than maneb.

The Hasse diagram in Fig. 1 indicates that when only the persistence and physical-chemicals properties are used to assess environmental hazard of pesticides in soils, four out of the 50 compounds studied here, bentazone (a7; 20, 2300000,-0.247), dalapon (c7; 30, 900000, 0), diquat (e1; 1000, 718000,0) and TCA (i4; 21, 1200000, 0) are the most environmentally hazardous for their mixture of long persistence in soil, high water solubility and low vapour pressure. These objects are called "maximals" in a Hasse diagram since they are not connected to any other chemicals with worse properties than theirs.

An interesting aspect of Fig. 1 is the fact that no pesticide located in a lower layer is connected to, for example, EPTC (e6). This indicates that no other chemical, in this list of 50, has, at the same time, lower values of persistence, water solubility and (negatively taken) vapour pressure. In Hasse diagrams objects like EPTC are called minimal elements or simply "minimals." Minimal objects are not connected with other objects in a lower level. Other minimals in Fig. 1 are thiocarbazil (m0), butylate (b1), captan (b3), dichlofopmetyl (d6), fluazifopbutyl (f9), metamitron (h8), pendimethalin (j8), propanil (k6), trifluralin (m8), malathion (h1), endosulfan (e5), and methylbromide (i5). These chemicals have unique combinations of property values that distinguish them and make them the least hazardous in their group, in the sense that no other chemical has better properties.

Graphically, parathion (j6; 14., 24., -5.) and thiocarbazil (m0; 3., 2.5, -93.) seem to be the least hazardous chemicals (Fig. 1) because these two chemicals are the only ones that occupy the sixth and seventh level, however a careful analysis of Fig. 1 and of Table 1 shows that parathion and thiocarbazil do not have the best properties overall. For example EPTC (e6) has a high vapour pressure (6, 344, -4533) but its water solubility makes it potentially more hazardous than parathion and thiocarbazil. Gustafson (1989) identified EPTC as more hazardous than parathion. According to the properties in Table 1, GUS indices for the compounds are 1.88 (EPTC) and 1.27 (parathion), and 0.048 (thiocarbazil), respectively. The GUS index is defined as:

GUS = log T_0.5 (4 - log K_oc)

where T_0.5 is the half-life in soil [days] and Koc is calculated from solubility (Table 1) according to Karichoff et al. (1979) and Kenaga and Goring (1980). Figure 1 contains additional information: the missing line between EPTC and parathion indicates contradiction in the data used for ranking (parathion has a longer half-life than EPTC but a lower solubility and lower vapour pressure). While this ambiguity between the properties of these two chemicals is easily visualized in a Hasse diagram, a ranking index, like the GUS, forcing the objects to be linearly ordered (the usual ranking) hides this contradiction: information is lost.

Mecoprop (h5; 21, 660000, 0) is located on the second layer together with metham-Na (i0; 7, 963000, -0.0000027) and paraquat (j5; 1000, 620000,0). Contradictions between the properties of these three chemicals exist, for example, metham-Na has a lower persistence, a higher water solubility and higher vapour pressure than mecoprop. These chemicals are hazardous but they can not be compared directly. Again this shows that the set of 50 chemicals can only be partially ordered.

The complete analysis of the Hasse diagram, chemical by chemical, might become quite intricate, if it were done visually as done by Halfon and Reggiani (1986). Therefore Brüggemann and Halfon (1995) developed a method based on graph theory to automatize the analysis of any Hasse diagram. The matrix D summarizes all the relations between the chemicals; table 2 shows the part of the matrix that relates to the four maximal elements in Fig. 1. The diagonal elements of the matrix quantify the numbers of chemicals in lower layers directly connected by a line to the chemical of interest; in set theory these objects are called successors. For example the element D_1,1 indicates that bentazone (a7) is directly comparable with 12 less hazardous chemicals. The successors of bentazone are {Fig. 2; a "subtree" [defined as an order ideal (Davey and Priestley, 1990) generated by bentazone (a7)] of Fig. 1} dimethoate (d9), MCPA (h4), 2,4-D (c5), alachlor (a0), malathion (h1), EPTC (e6), propanil (k6), thiram (m1), methylparathion (s2), butylate (b1), parathion (j6) and thiocarbazil (m0). An interesting feature of Fig. 2 is that most of the chemicals in this subtree are not identified as very hazardous, since dimethoate belongs to the third layer and MCPA to the fourth.

Element D_2,2 has a value of 27, indicating that dalapon (c7) is more hazardous than 27 other chemicals. The off-diagonal matrix element D_1,2 = D_2,1 = 12, indicates that the successors of bentazone (a7) are also the successors of dalapon (c7), but that none of the other 15 (27-12) chemicals successors to dalapon are directly comparable to bentazone. The conclusion is that bentazone is hazardous, since it is located in the first layer, but it is definitively different from dalapon because of its high water solubility combined with a lower vapour pressure. This observation also applies to a comparison, on the basis of values of the matrix D, of bentazone with diquat (e1) and TCA (i4), since both D_1,3 and D_1,4 have a value of 12. The conclusions of this analysis are that the successors of bentazone (a7) are also the successors of the other three maximal elements. This can also be deduced from Fig. 1, because the neighbours of bentazone (a7), namely MCPA (h4) and dimethoate (d9) are also connected with the other maximals. Diquat (e1) is the most representative since it has a pattern of environmental hazard not in contradiction with other chemicals: 45 out of 50 chemicals are comparable to it. The representational order (defined as the number of elements in a subtree, generated by a maximal element) is e1 > i4 > c7 > a7 (diquat > TCA > dalapon > bentazone). All elements of a subtree have a combination of properties that do not contradict those of the maximal element. In this sense, the maximal element represents other elements.

Figure 3 shows the Hasse diagram when all four criteria included in Table 1 are used together: All 50 chemicals are condensed in four layers with a decreasing degree of hazard in a general sense from the top to the bottom. Inclusion of the "usage" criterion causes a shift of many chemicals that were in the fourth, fifth and sixth layers to the first or second layer. Furthermore, there is one isolated object, namely methylbromide (i5) with a loading of 3984 kg per year. In Fig. 1 methylbromide is a minimal indicating that its physical chemical properties are less hazardous than those of most others. Isolated objects are common in Hasse diagrams, this isolation indicates an extreme level of contradiction in their properties when they are compared with the other 49. In practice this isolation is quite meaningful,. As a matter of fact methylbromide is a fumigant and its occurrence should be limited to the aerial compartment. Nevertheless, due to its high solubility and large usage, a run-off into the aquatic environment might be expected in certain circumstances. since it signifies that the environmental hazard of methylbromide should be studied in more detail.

Apart from methylbromide, other pesticides of concern are alachlor (a0), atrazine (a4), bentazone (a7), chloridazon (b8), dalapon (c7), diquat (e1), linuron (h0), mancozeb (h2), metham-Na (i0), TCA (i4), metolachlor (i7), paraquat (j5), simazine (l3), terbuthylazine (l6), and ziram (n0). Out of these 16 chemicals, bentazone, dalapon, diquat, linuron, mancozeb, metham-Na, TCA, metolachlor, paraquat, and simazine are considered potentially hazardous (Fig. 1) because of their properties. The other five, alachlor, atrazine, chloridazon, terbuthylazine and ziram are a problem of concern because of their high loadings.

The chemicals that are ranked of least concern among the 50 in our list are dichlofopmetyl (d6), and ethofumesate (f0) and thiocarbazil (m0). Dichlofopmetyl (d6) is a minimal in Fig. 1, ethofumesate (f0) and thiocarbazil (m0) were already identified of low priority in Fig. 1 because of their physical-chemical properties and persistence. Thus these chemicals have low usage and their physical chemical properties are not of much concern. Figure 3 shows that there are 13 chemicals that are minimal, i.e., that should be considered chemicals of least concern. In addition to the ones mentioned above, they are endosulfan (e5), pendimethalin (j8), propanil (k6), trifluralin (m8), butylate (b1), captan (b3), EPTC (e6), fluazifopbutyl (f9), malathion (h1), and metamitron (h8).

Which criteria are important for ranking ?

This question is answered through the analysis of the W matrix (Table 3). Each element of W quantifies the difference between rankings when different combinations of criteria are used². The bottom of Table 3 shows all 15 possible combinations of the four criteria, case one (Table 3) indicates that the four criteria are used together, cases two to five indicate that three out of four are used, cases six to eleven indicates that two out of four criteria are analyzed and the last four cases indicate that each criterion is analyzed separately. Given the complexity of the information contained in the W matrix, here we concentrate on the analysis of the first row:

all 3 out of 4 2 out of 4 only one criterion

Case no. │ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

┼────────────────────────────────────────────────────────

1 │ 0 211 105 162 192 421 596 492 353 499 457 1092 1048 1076 1047

attribute Use VP WS T_0.5 other attribute combinations

Here we concentrate on the analysis of some few elements of the first row:

case i,j 1,1 1,2 1,3

entry of the matrix W_1,1 W_1,2 W_1,3

values 0 211 105

omitted attribute - usage vapour pressure

The (dimensionless) entry for W_1,1 is 0, indeed all diagonal elements of W are zero (Table 3), since the difference of a case from itself is zero. Since each element of W is the symmetrized differences between two successor sets for all elements of the poset the entry of matrix W quantifies the differences of the Hasse diagram of one case from the Hasse diagram of another case. The smaller the number the less important the missing criterion is. Element W_1,2 quantifies the difference between the Hasse diagrams in Figures 1 and 3. Since W_1,2 is relatively larger than W_1,3, W_1,4 or W_1,5 the conclusion is that knowledge of usage is relatively more important for ranking than the knowledge of the physical-chemical properties. The changes in topology can be seen, when Fig. 3 (all attributes (case 1)] is compared with Fig. 1 (usage omitted); the Hasse diagram (Fig. 3) resulting from case 1 (all criteria are used for ranking) and the Hasse diagram resulting from case 2 (Fig. 1) differ moderately, for example:

Case Fig. # isolated # maximals # minimals # levels

elements

all 4 parameters 3 1 15 13 4

usage omitted 1 0 4 13 8

Element W_1,3 has a value of 105. Compared with the theoretical maximal value (2450) for elements of a W matrix with 50 objects (Brüggemann and Halfon, 1995) this value of 105 is rather low and half of W_1,2. The vapour pressure, whose omission leads to case 3, has a minor importance on ranking, compared with the usage, whose omission leads to case 2. This value of 105 does not represent the difference in topology between Fig. 1 and Fig. 3, but it expresses the importance of the criterion, in this case vapour pressure. In cases 2 to 5 (Table 3) only one criterion at the time is removed, that is only three criteria are used for ranking. The values for W_1,2, W_1,4, and W_1,5 are relatively higher than W_1,3 namely 211, 162, and 192, respectively. The most important physical-chemical criterion for ranking is the half-life T_0.5.

Overall the elimination of the criterion "usage" (case 2) affects ranking more than the elimination of half-life T_0.5, water solubility or vapour pressure. However, none of these criteria should be eliminated due to the similar values of W_1,2 to W_1,5. Too much information in ranking would be lost if these attributes were omitted.

This trend of loss of information is evident from the increase in the value of the matrix elements as more and more criteria are dropped. Analysis of the first line shows that the values of W_1,k, k=2 to 5 (one criterion at the time is dropped) are in the range of 105 to 211, the values of W_1,k, k=6 to 11 (only two criteria at the time are used for ranking) increase to a range of 353 to 596, and the values of W_1,k, k =12 to 15 (only one criterion at the time is used) are in the range of 1047 to 1092.

A CASE STUDY

To test whether the selection of the properties is realistic, the ranking (Fig. 3) is compared with the results of monitoring studies carried out in Italian surface waters (Galassi et al., 1993; Readman et al., 1993; Daví personal communication) since 1986. All the available Italian analytical data are used here taking into account that usage data were rather constant in Italy in this period with the exception of atrazine, which was regulated in 1986 and banned in 1989.

The assumption for this comparison is that if the ranking method is correct then the probability of finding chemicals identified as hazardous should be higher than the probability of finding less hazardous chemicals. Chemicals ranked lower have less probability of being found both because of lower usage and because they are less persistent and do not tend to reside on ground water. Only 24 out of the 50 active ingredients considered here have been analyzed for in surface waters, basically because they can be detected by a multiresidual method. As these methods have different detection limits for different compounds, a limit of 50 ng L^-1 was set as a threshold for a positive finding. This value is approximately the detection limit of the least sensitive analytical procedures. used in the monitoring studies mentioned before.

Table 4 shows results for the 50 compounds grouped in 4 classes, corresponding to the layers of the Hasse diagram (Fig. 3). This table shows the relation between the ranking, the number of chemicals found in ground water, the number of chemicals searched for and the percentage of chemicals found in relation to the chemicals sought for. Results are quite encouraging. Out of the 16 chemicals identified as most hazardous, seven pesticides [namely alachlor (a0), atrazine (a4), bentazone (a7), linuron (h0), metolachlor (i7), simazine (l3) and terbuthylazine (l6)] of the 8 analyzed for (previous plus TCA) were found, a success ratio of 88%. Five of the pesticides sought in the second layer [dimethoate (d9), MCPA (h4), molinate (j1), propanil (k6), thiobencarb (l9)] were found of the 10 analyzed for [previous plus alachlor azinfosmethyl (p0), 2,4-D (c5), endosulfan (e5), pendimethalin (j8), phorate (k0)]. In line 3 of the Hasse diagram only one pesticide EPTC (e6) of the 6 analyzed for [previous plus captan (b3), diazinon (d0), malathion (h1), parathion (j6), methylparathion (s2)] was found; compounds in line 4 were never analyzed for.

DISCUSSION

We have used a ranking method we developed, method based on partially ordered set theory, to asses the environmental pollution due to xenobiotics. The outcome of this ranking analysis is displayed by Hasse diagrams. Hasse diagrams avoid the loss of information that occurs when data are aggregated into a ranking index. The use of an index has the disadvantage that information from each test is lost because it is aggregated. Our ranking method (Halfon and Reggiani, 1986; Halfon, 1989) preserves the information collected at each site. Our method does not merge results from different tests, e.g. toxicity with quality tests, as it is done in the construction of a ranking index. The method can be used to explain which properties are important in the ranking and which may be eliminated without loss of information. Besides the amount used, which undoubtedly greatly influence the hazard of pesticides to all targets, the choice of other attributes was made with the aim of detecting priority pollutants of surface waters.

Persistence and volatility are the properties that mainly influence the occurrence of a compound in soil and water. Water solubility gives indications of the mobility from soil to the surface waters. Other properties usually considered in the environmental models (e.g., K_ow and K_oc) are no needed because they are correlated with water solubility (Kenaga and Goring, 1980; Brüggemann and Altschuh, 1991).

We have also studied the importance that each attribute has for ranking. For this purpose we have used the W matrix that quantifies the dissimilarity of different Hasse diagrams. Several benefits have derived from this ranking analysis: Identification of the chemicals most hazardous to the Italian environment: Typically the Hasse diagram technique lists more than one chemical as most hazardous, each identified by a different combination of physical-chemical properties and persistence. Furthermore, this technique identifies the more important and the less important criteria to rank the chemicals, which leads to a reduction in costs in environmental monitoring. This identification is of great value for environmental studies, where uncertainty and sampling costs are often big issues. In fact, in the Italian scenario we have considered, more methods are needed at least for covering priority pesticides grouped in line 1.

In the case study, the percentage of positive findings decreases from class 1 to 4 is in agreement with the theoretical predictions of the Hasse diagram. This fact shows that the choice of the attributes is correct and the model can be used for ranking pesticides. Nevertheless, it has to be shown whether the analytical protocols have been set up independently from the pesticides properties and usage or the criteria for setting analytical procedures empirically followed the same approach. However the model offers the advantage of being applicable to a great number of compounds, giving indications on the uncertainty in the chemical ranking.

Footnotes:

1 We also call this "a contradiction" or "an ambiguity"

2 The derivation of the W matrix is presented in Brüggemann and Halfon (1995). The ranking of the objects is sensitive to the set of criteria. To quantify the importance of a criterion on ranking the basic idea is to compare with each other all Hasse diagrams induced by different sets of criteria. The concept of successor sets [G(k,A) or G(k,Ai)] is used for this purpose, where G is the successor set, k denotes some arbitrary chosen key element, A is the full set of criteria and Ai is a subset of criteria, Ai _ A. The influence of each criterion can be quantified by counting the elements of the symmetrized difference between two successor sets as follows:

W(k,Ai ,Aj ) := card{ [ G(k,Ai ) \ G(k,Aj )] _ [G(k,Aj ) \ G(k,Ai ) ] } (1)

For a given key-element, two Hasse diagrams (given by two arbitrary sets of criterions) are more dissimilar, the more the successor sets G(k,Ai ) and G(k,Aj ) differ. The equivalent form of the symmetrized difference is

[ G(k,Ai ) _ G(k,Aj )] \ [G*'

19* G(k,Aj ) ] (2)

which is easier to evaluate than the right hand side of Eq. 1. The cardinality of the symmetrized set difference is also called the Hamming-distance (Bollobás, 1986) between sets. To simplify notation, we write W(k,i,j) for W(k,Ai ,Aj ). We also note that each

W(k,i,j) > 0 and W(k,i,j) = W(k,j,i). *19*0 matrix itself is denoted by W(k). Thus we have:

W(k,1,1), W(k,1,2), ...., W(k,1,p)

W(k,2,1), W(k,2,2), ...., W(k,2,p)

W(k) = .................................. (4)

..................................

W(k,p,1), W(k,p,2), ...., W(k,p,p)

with p = 2n -1. This matrix W is the key for the sensitivity analysis of ranking, each entry of W is the cardinality of the symmetrized difference (Eq. 1) of two successor sets which are constructed from a given key element k and the two Hasse diagrams induced by two criterion subsets.

LITERATURE CITED

(The) Agrochemical Handbook. 1990. Second Edition. Royal Society of Chemistry, London, U. K., 1990 Update.

Augustijn-Beckers, P. W. M., Hornsby, A. G. and Wauchope, R. D. 1994. The SCS/ARS/CES Pesticide properties database for environmental decision-making. II Additional Compounds. Rev. Environ. Contam. Toxicol., 137: 1-82.

Bollobás, B. 1986. Combinatorics. Cambridge University Press, 177 pp.

Brüggemann, R. and Altschuh, J. 1991. A validation study for the estimation of aqueous solubility from n-octanol/water partition coefficients. Sci. Tot. Env. 109/110: 41-57.

Brüggemann, R. and Halfon, E. 1990. Ranking the environmental hazard of the chemicals spilled in the Sandoz accident in November 1986. Sci. Tot. Env., 97/98: 827-837.

Brüggemann, R. and Halfon, E. 1995. Sensitivity analysis of partially ordered sets and ranking objects of environmental interest. IIIE Systems Man and Cybernetics (in preparation).

Brüggemann, R., Münzer, B., and Halfon, E. 1994. An algebraic/graphical tool to compare ecosystems with respect to their pollution - The German river Elbe as an example. Comparative regional analysis - I. Hasse-Diagrams, Chemosphere 28: 863-872.

Davey, B.A. and Priestley, H.A. 1990. Introduction to Lattices and Order. Cambridge Mathematical Textbooks, Cambridge University Press, Cambridge, 248 pp.

Funari, E., Bastone, A., Bottoni, P., Camoni, I., Miniero, R., Beretta Anguissola, M., Bortolosso, C., Brun, F., Coccino, S., Ferraro, P and Salamana M. 1989. Erbicidi nelle acque destinate al consumo umano in Italia. Acqua-Aria, 9: 1011-1024.

Galassi, S., Mingazzini, M. and Battegazzore, M. 1993. The Use of biological methods for pesticide monitoring. Sci. Total Environ., 132: 399-414.

Gustafson, D. I. 1989. Ground water ubiquity score: a simple method for assessing pesticide leachability. Environ. Toxicol. Chem., 8: 339-357.

Halfon, E., 1983a. Is there a best model structure? I Modelling the fate of a toxic substance in a lake. Ecological Modelling, 20:135-152.

Halfon, E., 1983b. Is there a best model structure? II Comparing model structures of different fate models. Ecological Modelling, 20:153-163.

Halfon, E. and Reggiani, M.G., 1986. On ranking chemicals for environmental hazard. Environ. Science Tech., 23: 1173-1179.

Halfon, E. 1989. Comparison of an index function and a vectorial approach method for ranking waste disposal sites. Environ. Science Technol., 23: 600-609.

Harary, F. 1969. Graph Theory. Addison-Wesley, Reading, Mass.

Karickhoff, S.W., Brown, D.S. and Scott, T.A. 1979. Sorption of hydrodynamic pollutants on natural sediments. Wat. Res. 13; 241-248

Kenaga, E. E. and Goring, C. A. I. 1980. Relationship between water solubility, soil sorption, octanol-water partitioning, and concentration of chemicals in biota. In: Eaton, J. G., Parrish, P. R., Hendricks, A. C. (eds) Aquatic Toxicology. ASTM, STP 707, Philadelphia, PA, pp 78-115.

ISTAT (Italian National Statistics Office). 1992. Statistiche dell'agricoltura, zootecnia e mezzi di produzione. Annuario N° 37, Roma.

Münzer, B., Brüggemann, R. and Halfon, E. 1994. An Algebraic/graphical tool to compare ecosystems with respect to their pollution II: Comparative regional analysis. Chemosphere 28: 873-879.

Preparate, F.P. and Yeh, R.T. 1973. Introduction to Discrete Structures. Addison-Wesley, Reading, Mass.

Randic, M. 1991. The nature of chemical structure. J. Math. Chem., 4: 157-184.

Readman, J.W., Albanis, T. A., Barcelò, D., Galassi,S., Tronczynsky, J. and Gabrielides, G. P. 1993. Herbicide contamination of Mediterranean estuarine waters: Results from a MED POL pilot survey. Mar. Poll. Bull., 26: 613-619.

Reggiani, M.G. and Marchetti, F.E. 1975. On assessing model adequacy. IEEE Trans. Systems Man Cyber., SMC-5: 322-330.

Voigt, K and Brüggemann, R., 1993. Metadatabases of data-sources for environmental chemicals: Online Information 93: Proc. 17th International Information Meeting, pp: 495-505.

Wauchope, R. D., Buttler, T. M., Hornsby, A. G., Beckers, P. W. M and Burt, J. P. 1992. The SCS/ARS/CES pesticide properties database for environmental decision-making. Rev. Environ. Contam. Toxicol., 123: 1-155.

Weber, J. B. 1977. The pesticide scorecard. Environ. Sci. Technol., 11: 756-766.

Figure Captions:

Figure 1: Hasse diagram showing the ranking of 50 pesticides used in Italy in 1986 in amounts above 50 metric tons per year. Table 1 identifies the chemicals. Bentazone (a7), dalapon (c7), diquat (e1) and TCA (i4) are the most environmentally hazardous for their mixture of long persistence in soil, high water solubility and low vapour pressure. The minimal elements EPTC (e6), thiocarbazil (m0), butylate (b1), captan (b3), dichlofopmetyl (d6), fluazifopbutyl (f9), metamitron (h8), pendimethalin (j8), propanil (k6), trifluralin (m8), malathion (h1), endosulfan (e5), and methylbromide (i5) are the least hazardous chemicals. The ranking criteria are the half-life, T_0.5, water solubility, and vapour pressure.

Figure 2: Hasse diagram showing the successors of Bentazone (a7). This diagram if a subtree of Fig. 1.

Figure 3: Hasse diagram showing the ranking of 50 pesticides used in Italy in 1986 in amounts larger than 50 metric tons per year. Table 1 identifies the chemicals. The number of levels is smaller than in Figure 1 since the additional criterion, usage, creates some contradictions between physico-chemical properties plus persistence, and usage. Pesticides of concern are methylbromide (i5), alachlor (a0), atrazine (a4), bentazone (a7), chloridazon (b8), dalapon (c7), diquat (e1), linuron (h0), mancozeb (h2), metham-Na (i0), TCA (i4), metolachlor (i7), paraquat (j5), simazine (l3), terbuthylazine (l6), and ziram (n0). The minimal elements are endosulfan (e5), pendimethalin (j8), propanil (k6), trifluralin (m8), butylate (b1), captan (b3), EPTC (e6), fluazifopbutyl (f9), malathion (h1), metamitron (h8), dichlofopmetyl (d6), ethofumesate (f0) and thiocarbazil (m0). These are the chemicals of least concern. The ranking criteria are the half-life, T_0.5, water solubility, vapour pressure and usage in metric tons per year.

Table 1: Physical-chemical properties, persistence and usage data in Italy in 1986-87. Fifty compounds are included. The alphanumeric digits identify the chemicals in the Hasse diagrams. The negative sign in the fifth column has been added to reverse the ranking order. Chemicals with low vapour pressure are considered most hazardous since they do not readily volatilize from soils. Since, in this analysis the assumption is that the higher the value of the criterion, the higher the environmental hazard of the chemical, the vapour pressure order has been inverted by changing the sign. Properties are half-life in soil, T_0.5, water solubility (WS), and vapour pressure (v.p.).

Chemical Identifier T_0.5 Water vapour Usage

solubility pressure

[days] [mg L^-1] [m Pa] [kg yr^-1]

alachlor a0 15 240 -1.87 1537

atrazine a4 60 33 -0.039 725

azinfosmethyl p0 10 29 -0.027 422

bentazone a7 20 2300000 -0.2 95

butylate b1 13 44 -1733 175

captan b3 2.5 5.1 -0.011 557

carbaryl b4 10 120 -0.16 590

chloridazon b8 31 400 -0.01 268

chlortoluron c2 135 70 -0.017 67

2,4-D (ph <5) c5 8 620 -1400 314

dalapon c7 30 900000 0 170

diazinon d0 40 60 -8 105

dichlofopmetyl d6 30 0.8 -0.47 52

dimethoate d9 7 39800 -3.33 446

diquat e1 1000 718000 0 52

endosulfan e5 50 0.32 -0.023 131

EPTC e6 6 344 -4533 90

ethofumesate f0 30 50 -0.65 50

fluazifopbutyl f9 15 2 -0.033 60

glyphosate g4 47 12000 0 109

linuron h0 60 75 -2.27 271

malathion h1 1 130 -1.07 205

mancozeb h2 70 6 0 3465

maneb h3 70 6 0 116

MCPA h4 15 825 -0.2 225

mecoprop h5 21 660000 0 102

metamitron h8 28 1.8 -13 226

metham-Na i0 7 963000 -0.0000027 5075

methabenzthiazuron i1 135 59 -0.133 59

TCA i4 21 1200000 0 889

methylbromide i5 55 13400 -243000000 3984

metolachlor i7 90 530 -4.18 544

molinate j1 21 970 -746 185

paraquat j5 1000 620000 0 172

parathion j6 14 24 -5 257

pendimethalin j8 90 0.275 -1.25 163

phenmedipham j9 30 4.7 -0.000001 56

phorate k0 60 22 -85 120

propanil k6 1 200 -5.3 694

simazine l3 60 6.2 -0.0029 194

terbuthylazine l6 114 8.5 -0.15 207

thiobencarb l9 21 28 -2.93 150

thiocarbazil m0 3 2.5 -93 97

thiram m1 15 30 -1.33 1180

trifluralin m8 60 0.3 -14.7 140

ziram n0 30 65 -0.0013 3151

zineb n1 30 10 -0.01 2359

dodine s0 20 700 -0.013 216

dinocap s1 5 4 -0.0053 432

methylparathion s2 5 60 -2 212

Table 2: D Matrix, Used Attributes: 1,2,3. The diagonal elements of the matrix quantify the numbers of chemicals in lower layers directly connected by a line to the chemical of interest; in set theory these objects are called successors. The off-diagonal elements quantify the number of chemicals that are successors to both. For example W_1,1 (the entry for a0 (alachlor) has a value of 5, W_2,2 the entry for a4 (atrazine) has a value of 8, and W_1,2 = W_2,1 = 2. Thus, alachlor has five chemicals with properties directly comparable with it, atrazine has eight, but only two chemicals, parathion and thiocarbazil, are common to both (this information can be extracted from the Hasse diagram, Fig. 3).

│ a7 c7 e1 i4

───┼───────────────

a7 │ 12 12 12 12

c7 │ 12 27 27 21

e1 │ 12 27 45 21

i4 │ 12 21 21 22

Table 3: Each element of W is the symmetrized differences between two successor sets for all elements of the poset. The theoretical maximal value for the elements of this W matrix with 50 objects is 2450.

│ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

───┼──────────────────────────────────────────────────────────────

1 │ 0 211 105 162 192 421 596 492 353 499 457 1092 1048 1076 1047

2 │ 211 0 316 373 403 210 385 281 564 710 668 881 837 865 1258

3 │ 105 316 0 267 297 316 701 597 248 394 562 987 943 1181 942

4 │ 162 373 267 0 354 583 434 654 191 661 295 930 1210 914 885

5 │ 192 403 297 354 0 613 788 300 545 307 265 1284 856 884 855

6 │ 421 210 316 583 613 0 595 491 564 710 878 671 627 1075 1258

7 │ 596 385 701 434 788 595 0 666 625 1095 729 496 1222 480 1319

8 │ 492 281 597 654 300 491 666 0 845 607 565 1162 556 584 1155

9 │ 353 564 248 191 545 564 625 845 0 642 486 739 1191 1105 694

10 │ 499 710 394 661 307 710 1095 607 642 0 572 1381 549 1191 548

11 │ 457 668 562 295 265 878 729 565 486 572 0 1225 1121 619 590

12 │1092 881 987 930 1284 671 496 1162 739 1381 1225 0 1298 976 1433

13 │1048 837 943 1210 856 627 1222 556 1191 549 1121 1298 0 1140 1097

14 │1076 865 1181 914 884 1075 480 584 1105 1191 619 976 1140 0 1209

15 │1047 1258 942 885 855 1258 1319 1155 694 548 590 1433 1097 1209 0

Cases:

1 X X X X Each X represents a case where each criterion is used

2 X X X in the comparison. Each element in the W matrix

3 X X X represents the ranking distance between two cases.

4 X X X The lower the number the less the distance and the less

5 X X X important the missing criterion (or criteria for cases

6 X X 6 and higher) is.

7 X X

8 X X

9 X X

10 X X

11 X X

12 X

13 X

14 X

15 X

T_0.5 WS VP Use

Table 4: Proportion of pesticides sought and found in Italian surface waters according to environmental hazard.

Total number of Found Analyzed Found/analyzed for

chemicals in line for %

1 16 7 8 88

2 20 5 10 50

3 11 1 6 17

4 3 0 0 N/A^*