CONTINUED Vegetation concentrations 4-48

. Ij and Yj:

Interception values and crop yields were determined in the afore-mentioned assessments based on geographic-specific crop yield data provided in Baes, et al., (1984) and the following types of crop-specific relationships estimating interception fraction based on yield (Y), also presented in Baes, et al., (1984):

Diagram V3 4-1

Judgments by Fries and Paustenbach (1990) on high, medium, and low yields of silage, hay, and pasture grass, and the use of the first two interception equations above (the first for silage, and the second for hay and grass), can give some guidance on interception fractions and yields for these crops:

Diagram V3 4-2

This information can be used for cattle intake of vegetation, and the resulting beef and milk concentrations. The medium values for grass, 0.15 kg/m2 yield and 0.35 interception, were used for the example setting in Chapter 5. An average of the medium values for hay and silage, 0.63 kg/m3 yield and 0.62 interception, were used for the second category of cattle vegetations for Chapter 5, the hay/silage/grain category.

Stevens and Gerbec (1988), using yields obtained from the Minnesota State Agricultural Office, derived the following yield and interception estimates, respectively, for vegetables for human consumption in their assessment:

lettuce - 8.6,0.72;

tomatoes - 12.0,0.55; and

beans - 2.7,0.18.

Average yields and interception fractions from their exercise: 7.8 kg/m2 and 0.48, were used in the example setting in Chapter 5. These vegetable yields are fresh weight, so they need to be converted to a dry weight basis in order to estimate a Cppa appropriate for use in Equation (4-23). Since vegetables are generally 80 ->90% water, a fresh to dry weight conversion factor of 0.15 was used, resulting in an average vegetable dry matter yield of 1.17 (7.8 * 0.15). This was used in the example settings in Chapter 5.

. Vd:

Particles settle to the ground surface and plant surfaces due to the forces of gravity. Gravitational settling velocity is a function of particle size, with more rapid settling occurring with larger particles. The algorithm used to estimate the concentration of contaminated particulates in air estimates the suspension of particles less than and equal to 10 m m, which is commonly referred to inhalable size particles. Seinfeld (1986) listed a gravitational deposition velocity of 1 cm/sec for 10 m m size particles. This deposition velocity will be used in this assessment, and in units of m/yr, this equals 315,360 m/y.

. RN:

Geraghty, et al. (1973) provides a map showing isolines average annual rainfall throughout the United States. This map shows low rates of 5 to 20 inches/year in the desert Southwest, moderate rates of 25 to 40 in/yr in the Midwest cornbelt, 40 to 60 in/yr in the South, and so on. The example scenarios of Chapter 5 were described as rural, with land in agricultural and non-agricultural settings. A rate of 1 m/yr (39 in/yr) will be used in the example scenarios.

. Rw:

It is assumed that dry depositions fully adhere to plant surfaces; the weathering constant, kw, models the loss of the vegetative reservoir of particle bound contaminants due to wind, rain, or other weathering process. However, it is not clear that wet deposition should also be assumed to fully adhere during a wet deposition event. Hence, the Rw parameter, or fraction of wet deposition adhering, was introduced. Prior modeling efforts of the impact of depositions of dioxin-like compounds to vegetations are unclear with regard to wet deposition.

Stevens and Gerbec (1988), Fries and Paustenbach (1990), Webster and Connett (1990), and Travis and Hattemer-Frey (1991) all model particle deposition impacts of 2,3,7,8-TCDD to vegetations in air-to-beef/milk modeling. None of them discuss the distinction in wet and dry deposition, and model "total deposition" impacts, describing total as wet and dry deposition, total deposition, or simply as deposition. On the other hand, McKone and Ryan (1989) reduce the wet deposition portion of total deposition. They promote use of a "b", which they define as the fraction of material retained on vegetation from wet deposition. They recommend a value between 0.1 and 0.3.

The clearest indication of the fate of wet deposition of particles can be found in Hoffman, et al. (1992). In that field study, simulated rain containing soluble radionuclides and insoluble particles labeled with radionuclides was applied to pasture-type vegetation under conditions similar to those found during convective storms. The fraction of the labeled particles found to remain on the vegetation after the rainfall varied from 0.24 to 0.37. Nine values comprised this range, including particle sizes of 3, 9, and 25 m m, and cover described as clover, fescue, and mixed (a site with old field vegetations including fescue, grasses, weeds, and wild flowers). Based on this work, the Rw will be assumed to be 0.30 for all vegetations and dioxin congeners of this assessment.

. Wp:

Washout ratios are generally defined as the concentration of contaminant in rain to the concentration of contaminant in air. Concentrations of contaminants in air and rain water can be derived as a mass of contaminant divided by a mass of air/water or a volume of air/water. Mackay, et al. (1986) shows that volume-based washout ratios (mass of contaminant mixing in m3 air or water, e.g.) exceed mass-based washout ratios (mass of contaminant mixing in kg of air or water) by a factor of 815, which is the ratio of water and air densities. The washout ratio used in this assessment is a volumetric ratio based on methodologies described by Bidleman (1988). Using a volumetric ratio then allows for direct use of contaminant concentrations estimated in this methodology since they are already on a m g/m3 volume basis.

Bidleman (1988) defines the overall washout ratio as: (mass contaminant/volume rain) (mass contaminant)/(volume air). Bidleman (1988) also discusses that fact that overall washout includes both wet deposition of particulates and scouring of contaminants in the vapor phase. He includes methodologies for estimating the vapor/particulate ratios for semi-volatile organic compounds (abbreviated SOCs) and also for estimating the washout ratios for vapors. However, he claims that if H is sufficiently high, vapor dissolution in droplets is negligible and only the particulate fraction is removed by wet deposition.

He claims this to be the situation for n-alkanes, PCBs, chlordane, DDT, and 2,3,7,8-TCDD. Developing overall washout ratios for these and several other SOCs, he estimates that vapor scouring accounts for 1% of the overall washout ratio for 2,3,7,8-TCDD. For PCBs, he estimates similar percentages of 2, 4, and 28% for Aroclors 1260, 1254, and 1248, respectively. Based on this work, it will be assumed that vapor scouring of the dioxin-like compounds is small in comparison to wet deposition and the washout ratio for this assessment will only be applied to the air-borne particulate concentration of dioxin-like compounds.

Bidleman (1988) does not provide a chemical or site-specific equation which estimates the particle-phase washout ratio (which he does for the vapor-phase washout ratio). Rather, he summarizes available data and concludes that there is a wide range of the particle-phase washout ratio, Wp, for SOC: between 2x103 and 1x106. He claims that a typical range is 105 to 106, and uses a Wp of 2 x 105 in his exercises to estimate the overall washout ratio for several SOCs.

Koester and Hites (1992) list vapor and particle scavenging ratios for congener groups of dioxin-like compounds. To derive these ratios, they used air concentrations for congener groups that were taken at one time period in Bloomington and Indianapolis, Indiana, and rainfall depositions of these compounds at these sites measured during a second period of time. Using the Bidleman vapor/particle partitioning model used in this assessment, they estimate the vapor/split for the air concentrations. With these observations and models, they conclude that the overall washout ratio (sum of vapor and particle ratios) ranges from 104 to 105, which contrasts the typical range of 105 to 106 noted above from Bidleman (1988).

Also, their calculations indicate that vapor scavenging of dioxin-like compounds is comparable to particle scavenging, also in contrast to the Bidleman analysis summarized above. However, they did not state whether their washout ratios were volume or mass-based. If they were mass-based, then a conversion to volume based would put them in the 107 to 108 range, which seems improbable given the Bidleman summary above. Therefore, it will be assumed that are volume-based, and they are appropriate to use for this assessment. Since no clear trend for particle washout ratios with regard to the degree of chlorination increased appears in Koester and Hites' data, the midpoint of their calculated range, 5 * 104, will be used for all example compounds in this assessment.

As a final note, the multiplication of the above terms, Wp * Cpa * RN * Rw, does result in wet deposition in appropriate units of m g/m2-yr, although that is not immediately obvious. First, multiplication of Wp, in (m g contaminant/m3 rain) (m g/m3 air), and Cpa, in m g contaminant/m3 air, leaves a partial term in units of m g contaminant/m3 rain. Then, multiplication of this partial term times annual rainfall rate, thought of as m3/m2-yr instead of m/yr, gives the final quantity in the appropriate units.

When calculating concentrations in below ground fruit and vegetables using Equation (4-23), Cbgv is on a fresh weight basis since the RCF developed by Briggs, et al. (1982) is on a fresh weight basis, and no correction for estimating exposures is necessary. However, Cabv as estimated in Equation (4-24) is on a dry weight basis, and should be multiplied by a dry weight to fresh weight conversion factor when applied to above ground fruits and vegetables. A reasonable estimate for this parameter for fruits and vegetables is 0.15 (which assumes 85% water), which was used in this assessment. When using Equation (4-24) to estimate Cabv for the beef and milk food chain algorithm, a conversion to fresh weight is not required, however, since the algorithms were developed assuming dry weight concentrations. Beef and milk concentrations

The algorithm to estimate the concentration of contaminant in beef and/or milk was based on methods developed by Fries and Paustenbach (1990). They developed the beef bioconcentration factor for 2,3,7,8-TCDD, which is defined as the ratio of the concentration of the contaminant in beef fat to the concentration in the dry matter dietary intake of the beef cattle. They discussed bioavailability, which, as they define it, is the fraction of ingested contaminant which is absorbed into the body.

It depends on the vehicle of ingestion - dioxin in corn oil has a bioavailability in the range of 0.7 to 0.8, in rodent feed it has an estimate of 0.5, while in soil it has a range of 0.3 to 0.4. They emphasized the importance of the differences in diet between cattle raised for beef and those which are lactating in explaining different food product concentrations. Although there is likely to be some difference in the bioconcentration tendencies for lactating cattle and beef cattle, Fries and Paustenbach in fact used the same bioconcentration for beef fat and milk fat, and the same will be done here.

The concentration in the fat of cattle products is given as:

Equation V3 4-32

The following is offered as brief guidance to these terms and also the justification for the values selected in the example Scenarios in Chapter 5.

. BCF:

Fries and Paustenbach (1990) developed the concept of a beef/milk bioconcentration ratio and applied it to 2,3,7,8-TCDD. BCF is defined as the concentration of contaminant in fat of cattle products (i.e., dairy and beef) divided by the concentration in dry matter intake. The key difference in the dietary intake of cattle raised for beef versus cattle raised for dairy is that cattle raised for beef tend to be pastured more than dairy cattle and be more exposed to contaminated soil, whereas lactating cattle are more often fed high quality feed, including grains which are expected to be substantially residue free since they are a protected vegetation.

Based on literature studies of cattle consuming feed contaminated with dioxin-like compounds, Fries and Paustenbach (1990) calculated a BCF of between 4 and 6, and assumed a value of 5.0 for 2,3,7,8-TCDD.  Being developed directly from data of cattle ingesting contaminated feed, this BCF value of 5.0 already considers the bioavailability of the experimental contaminated feed.

It will be assumed that the bioavailability of the cattle vegetations in this assessment equal that of the experimental feed. Therefore, a value of 5.0 can go directly into Equation (4-32) when applied to concentrations in grass and pasture. However, this value should not be applied to soil, since it has been shown that TCDD on soil is less bioavailable than TCDD on other vehicles. This is why a Bs appears in Equation (4-32) - it adjusts BCF when applied to a soil concentration. The value of Bs is described below. The Fries and Paustenbach (1990) literature review is reproduced in Table 4-3, which additionally shows results generated based on information in McLachlan, et al. (1990).

Although the BCF of 5 determined by Fries and Paustenbach (1990) for 2,3,7,8-TCDD appears high based on the literature for this compound, Fries and Paustenbach (1990) discuss how short duration feeding trials (the 21 days of Jensen and Hummel

table Table 4-3. Ratios of dioxins and furans in milk fat (MF) and body fat (BF) to concentrations in diets of farm animals..
(1982) and the 28 days of Jensen, et al. (1981)) do not result in steady state bioconcentration ratios. Extrapolating the data to a point where steady state is speculated to be reached, Fries and Paustenbach (1990) developed the arguments for the range of 4 to 6 for 2,3,7,8-TCDD.
The second example compound in Chapter 5 was 2,3,4,7,8-PCDF. Fries and Paustenbach (1990) observed that bioconcentration ratios for PCDDs and PCDFs decreased significantly as chlorination increased, although their literature seems to imply that this effect is most pronounced for hepta- and octa- PCDDs and PCDFs. They could not locate data in the literature for penta-PCDDs or PCDFs.
expand table Table V3 4-3

McLachlan, et al. (1990) was the only source found where BCFs for cow milk could be generated for furan congeners. They conducted a mass balance of dioxin and furan congeners in a lactating cow. They carefully accounted for 16 of the 17 dioxin and furan congeners of toxicity equivalency to 2,3,7,8-TCDD in the intake of a lactating cow in food, air, and water, and measured amounts in feces, urine, and milk, while attributing the rest of the intake to a compartment they termed, storage/degradation/experimental error.

They obtained data well into steady state, and provided information necessary to estimate milk BCFs including: average daily wet weight food ingestion intake by the cattle (dry weight assumed to be 30% of wet weight for cattle feed); ng/day congeners in feed, water, and air; L/day milk production (density assumed to be 0.9 g/cm3); and percent fat in milk. The BCFs generated are shown in Table 4-3, and the one noted for 2,3,4,7,8-PCDF is 3.10. It is clear that the data in Table 4-3 is not definitive in establishing BCFs for specific congeners. Only the McLachlan data is complete, and it includes one cow and one lactating period. The data of Firestone, et al. (1979), as interpreted by Fries and Paustenbach, shows a BCF for milk fat of 5.7 for 1,2,3,6,7,8-HxCDD, compared to the milk fat BCF of 1.74 developed from McLachlan data.

In Chapter 5, the McLachlan data will be used for purposes of demonstration. The BCF value for 2,3,7,8-TCDD value is 4.3 and the BCF for 2,3,4,7,8-PCDF is 3.1, in the demonstration scenarios which include a dioxin, a furan, and a PCB. For the demonstation of the incinerator, the suite of dioxin-like compounds are demonstrated, and the full BCF set developed by McLachlan and coworkers will be used.

A review of the literature for PCBs is given in Table 4-4. Although PCBs, dioxins, and furans are related compounds in terms of environmental fate characteristics, a difference in bioaccumulation potential is noted with higher degrees of chlorination, based

table Table 4-4. Ratios of PCBs in milk fat (MF) and body fat (BF) to concentrations in diets of lactating cowsa.
on the study of Tuinstra, et al. (1981). Their work implies increasing bioaccumulation potential as the degree of chlorination increases. They developed BCF values (defined in the same manner as in this assessment) for a suite of congeners identified to occur in Aroclor 1260 administered to lactating cows. Therefore, their data allowed for a partial examination on congener bioaccumulation patterns. The results given in Table 4-4 are interpreted from the data supplied in Tuinstra, et al. (1981). Tuinstra determined the identity and percentage of specific congeners which comprise Aroclor 1260. He was able to identify 36 congeners, but could only quantify 27 of them (because of the unavailability of standards for 9 congeners).
expand table Table V3 4-4

These 27 comprised 81%, by mass, of the Aroclor 1260. Tuinstra was able to estimate BCF values for most, but not all, of the identified congeners - for 23 of the 27 congeners they identified (which equaled 77% of the congeners, by mass, of Aroclor 1260). As seen in Table 4-4, the average congener-group BCF value increases from about 2 to 4 going from hexa- to nanochloro-PCBs. However, there was a wide range of measured BCF values for specific congeners. In the heptagroup, for example, Tuinstra estimated BCF values between 0.4 and 5.2. Fries, et al. (1973) showed increasing BCF values in milk fat at 20, 40, and 60 days for Aroclor 1254 up to a value of 4.8 at day 60. The body fat BCF value at 60 days, the only time such a measurement was taken, was 3.4.

The trend of having a higher BCF value for milk fat as compared to body fat for lactating cows was also noted by Willett, et al. (1987). They fed lactating cattle Aroclor 1254 sorbed to ground corn. In three sequential periods of 60 days, they fed the cattle 10, 100, and then 1000 mg/day of Aroclor 1254. Given their average daily dry matter intake of 19.5 kg during the experiment, the concentration during each of those 3 periods was 0.51, 5.13, and 51.28 mg/kg (ppm). However, milk and body fat concentrations of PCBs were given after 60, 120, and 180 days, so that for estimation of the BCF value, what is needed is average concentration of Aroclor intake after these periods.

These averages are 0.51, 2.82, and 18.97 mg/kg. Given the reported concentrations of PCBs in milk and body fat after these experimental periods, BCF values were estimated and given in Table 4-4. Two studies, that of Willett and Liu (1982) and Perry, et al. (1981), contained data from which estimates of BCF could be made, except that these studies did not report daily dry matter intake. An estimate of 19.5 kg/day was assumed for lactating cattle for these studies, which was the experimental dry matter intake noted by Willett, et al. (1987). Willett and Liu (1982) dosed cattle for only 20 days, and arrived at the lowest noted BCF value for Aroclor 1254, 1.2.

The trend of increasing BCF value over time of dosing was noted by Fries, et al. (1973). Willett, et al. (1990) conclude that steady state is reached after about 60 days, so that estimates of BCF made from experiments less than 60 days may not reflect steady state conditions. Perry, et al. (1984) had a high BCF value, 4.2, despite the dosing period being only 32 days. This would appear to be the result of having a high concentration in the diet. Similarly high BCF values with corresponding high concentration in dosed intake were noted in Fries, et al. (1973) and Willett, et al. (1987). It should be noted that the concentrations in body fat in the studies of Willett and Liu (1982) and Perry, et al. (1981) were corrected as recommended by Willett, et al. (1990) in estimating BCF values.

Five trends for PCBs were discussed above:

1) that steady state is reached after approximately 60 days,

2) that higher BCF values appear to result with higher concentrations in feed,

3) that BCF values for milk fat may exceed those of body fat for lactating cows (this also seems true for dioxins/furans; see Table 4-3),

4) that the BCF values tend to increase with increasing chlorination of PCB congener groups, and

5) that this fourth trend is based on a limited set of data and much variability exists within specific congener groups.

Generally there is a sparsity and inconsistency in the data which would allow for definitive estimation of BCF values for the example heptachloro-PCB example compound in Chapter 5, 2,3,3',4,4',5,5'-PCB. Most of the data noted is for Aroclor 1254, and this data implies BCF values between 1.2 and 4.8. Based on the results from Tuinstra, et al. (1981) for the average of eight heptachloro-PCBs, a BCF value of 2.3 will be assigned to 2,3,3',4,4',5,5'-PCB.

It should be noted that all bioconcentration or biotransfer parameters, such as the BCF, are qualified as second order defaults for purposes of general use. Section 6.2. of Chapter 6 discusses the use of parameter values selected for the demonstration scenarios, including a categorization of parameters. Second order defaults are defined there as parameters which are theoretical and not site specific, but whose values are uncertain in the published literature. The parameter values in this category should be considered carefully by users of the methodology.

. Soil bioavailability, Bs:

This parameter reduces the bioconcentration ratio, F, considering that soil is a less efficient vehicle of transfer compared to feed. Remember that the values of BCF appropriate for Equation (4-32) already consider bioavailability and were developed from experimental data placing the BCF of 2,3,7,8-TCDD in the 4 to 6 range. Fries and Paustenbach (1990) reviewed several studies on the oral bioavailability of TCDD in soil in the diet of rats, and concluded that soil is a less efficient vehicle of transfer as compared to rat feed.

If the same is true for cattle - that soil is less efficient than their feed - than the BCF value must be reduced when applied to soil ingestion. Most studies reviewed by Fries and Paustenbach used corn oil as the positive control, since there is a high absorption of TCDD in rats when corn oil is used as the vehicle, with 70-83% of the administered TCDD dose absorbed. Their literature review on rat data showed that the bioavailability of TCDD in soil was between 0.4 and 0.5 that in corn oil, or 0.3 to 0.4 overall. The literature implied a range of 0.5 to 0.6 of TCDD in standard rat feed is absorbed, and although few studies were available, a similar 50% absorption rate of TCDD in cattle feed was noted.

They concluded, therefore, that the rat data was a reasonable surrogate for cattle. The Bs can be thought of as the ratio of BCF values between soil and feed, or, (BCFsoil)/(BCFfeed). If the difference in BCFsoil and BCFfeed is explained solely by bioavailability differences, than the ratio of overall bioavailability of soil to feed should equal this ratio. As described above for rat data, the overall bioavailability of soil was 0.3-0.4, and the overall bioavailability of feed was 0.5-0.6. The ratio of overall bioavailabilities is, therefore, (0.3-0.4)/(0.5-0.6).

If the argument that this ratio equals the ratio of BCFs is valid, than this would lead to a Bs of 0.5 to 0.8. This implies that absorption of TCDD when soil is the vehicle is 50 to 80% of what it would be if feed were the vehicle. These assumptions and implications are made for this assessment, and the soil bioavailability term, Bs, used for all example compounds in Chapter 5 is 0.65.

. Soil diet fraction, DFs:

Fries and Paustenbach (1990) report that soil intake by cattle feeding on pasture varies between 2 and 18% of total dry matter intake, depending on whether the grazing area is lush or not. The soil diet fraction would be lower for cattle which are barn-fed with minimal opportunity for contaminated soil intake. Cattle raised for milk are rarely pastured, so one possible assumption for estimating milk fat concentrations would be a DFs of 0.0. Fries and Paustenbach (1990) assumed between 0 and 2% of the dry matter intake by lactating cattle was soil in various sensitivity tests.

Since cattle raised for beef are commonly pastured, a conservative assumption would be a high DFs of 0.15 (15%), although a more reasonable assumption which would consider grazing in lush conditions and/or a portion of diet in feed or supplemental feed leads to DFs less than 0.10. Fries and Paustenbach (1990) assumed DFs of between 0 and 0.08 for beef cattle in various sensitivity tests. The example settings in Chapter 5 assume 0.02 (2%) for lactating cattle, and 0.04 (4%) for beef cattle.

. Feed and grass diet fractions, DFf and DFg:

The sum of the three diet fractions, DFs + DFf + DFg must equal 1.0. Setting DFs equal to 0.02 (2%) for lactating cattle assumed that they are pastured to some extent or could be taking in residues of soil sticking to home grown feed. Assuming lactating cattle graze a small amount of time, the DFg for lactating cattle will be 0.08 (8%).

This assessment simplifies the definitions of dairy and beef cattle diets by defining non-pasture grass vegetation simply as "feed". Feeds include hay, silage, grain, or other supplements. While dairy cattle are lactating, 90% of their dietary intake is assumed to be in this general category. Beef cattle spend a significant amount of time pasturing. However, their diet is supplemented with hays, silages, and grains, and particularly so in colder climates where they need to be housed during the winter. In this assessment, the simple assumption that they ingest equal proportions of pasture grass and feeds is made. Therefore, with 4% soil ingestion, DFf and DFg are both 48% for beef cattle.

Fries and Paustenbach (1990) summarize pertinent literature to conclude that cattle raised for beef are not slaughtered without an intervening period of high-level grain feeding. Agricultural statistics (USDA, 1992) show that 32.9 million cattle were slaughtered in 1991. Of this number, 6.1 million were cows and bulls that likely did not go through a feedlot prior to slaughter. Quarterly statistics from 1991 show that at any time, cattle and calves on feed for slaughter range from 10 to 12 million.

Fries uses these statistics to conclude that 75 to 80% of the total beef supply is from animals that went through a feedlot finishing process, and that the portion of beef that did not go through a feedlot process are (generally speaking) those 6.1 million cows and bulls (personal communication, G. Fries, USDA Agricultural Research Service, Beltsville, Maryland, 20705). He suggests that a representative feedlot finishing process would include a length of 120 days and diet consisting of 20% corn silage and 80% grain. The grains can be assumed to be residue-free, since grains are protected and, as discussed above, little within plant translocation of outer contamination can be assumed. Also, the ears of the corn silage are in the same category, leaving only the stalks and leaves of the corn silage impacted by atmospheric transfers of dioxin-like compounds.

A feedlot finishing process is important to consider if assessing beef impacts in a site-specific assessment. However, data could not be found in the literature which measured the impact of this process to beef concentrations. Such impacts could occur as the result of increased weight gain from substantially residue-free feeds. Fries and Paustenbach (1990) and Stevens and Gerbec (1988) modeled the impact of a residue-free grain-only diet for four months prior to slaughter. Based on within-cow dilution and depuration considerations, both efforts estimated that the feedlot process would reduce beef concentrations by about one-half. This was the assumption used in the beef food chain validation exercise described in Chapter 7, Section

The demonstration scenarios of Chapter 5 assume that farming families slaughter a portion of their cattle for home consumption. A dilution/depuration reduction is not assumed for these demonstrations.

. Average contaminant soil concentration, ACs:

The simplest assumption for ACs would be that it equals the initial level of contamination, Cs. However, this would be too high if the cattle also graze in uncontaminated areas. Where cattle have random access to all portions of a grazing area with contaminated and uncontaminated portions, a ratio of the spatial average of the contaminated area to the total area should be multiplied by Cs to estimate ACs. If cattle spend more time in certain areas, these areas should be weighted proportionally higher.

Different assumptions for determining ACs might also be in order when using Equation (4-32) to estimate milk fat as compared to beef fat concentrations. Lactating cattle, if pastured, might graze on different areas than beef cattle. After determining a spatial average based on current conditions, a second consideration might be given to temporal changes. If soil levels are expected to change over time (due to changes in source strength or other factors) then the concentrations should be averaged over the exposure duration as well.

The example scenarios in Chapter 5 where beef and milk exposures were estimated were termed "farms". The methodologies in this chapter were used to estimate the average soil concentration over the entire farm property. Assuming the cattle are raised on the farm property, than 100% of their intake of soil comes from the farm. This means that the average soil concentration, ACs in Equation (4-32), is equal to the level of contamination given as the initial level, or determined as average for the farm based on fate and transport algorithms.