Environ. Sci. Technol. 2001, 35, 142-148
Pollutant-Specific Scale of Multimedia Models and Its Implications for the Potential Dose E D G A R G . H E R T W I C H * ,† A N D THOMAS E. MCKONE‡ LCA-Laboratory, Norwegian University of Science and Technology, Kolbjørn Hejes vei 2b, 7491 Trondheim, Norway, and School of Public Health, University of California, Berkeley, California 94720-7360, and Lawrence Berkeley National Laboratory, Berkeley, California 94720
The spatial range is a generic indicator for how far pollutants are likely to travel. It also indicates the appropriate, pollutant-specific area of a multimedia model, which is the square of the spatial range. Formulations of the spatial range can be based on advective or dispersive transport. They differ in whether they take the extent and shape of the earth’s surface into account. We suggest the common element of the different approaches is that all account for the persistence and mobility of pollutants. The mobility is the expected travel speed and depends on the partitioning. This paper extends the concept of a pollutantspecific model scale through the introduction of a characteristic atmospheric scale height. It is the height of the atmosphere that would be needed to contain all the pollutant if the entire atmosphere had ground-level concentration, taking into account deposition and degradation. We define the spatial range as the expected advectiondriven travel distance of a pollutant molecule released to a specific compartment. This novel analytical formulation is more comprehensive but encompasses all previous advection-based proposals of a spatial range. We evaluate the spatial range and scale height of 288 chemicals for releases to air, surface water, and surface soil. We find a strong correlation between the spatial range for air releases and the scale height because both depend on persistence. We investigate the effect of the spatial scale on calculations of the human toxicity potential, a screeninglevel risk indicator based on toxicity and potential dose. The product of model area and potential dose is found to be the same for calculations using a fixed model area and those using the pollutant-specific spatial scale. The introduction of the scale height, however, can change the potential dose by more than 1 order of magnitude.
Introduction Pollutants differ in how far they can move before they are transformed and in how fast they move. The characteristic spatial range of a pollutant that partitions into multiple environmental compartments is an important pollutant attribute because it determines how many people are exposed * Corresponding author e-mail:
[email protected]; telephone: +47-73 55 0634; fax: +47-73 59 0110. † Norwegian University of Science and Technology. ‡ University of California and Lawrence Berkeley National Laboratory. 142
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to the pollutant and which political jurisdictions should address a pollution problem. A high spatial range may be of concern because adverse effects are more dispersed and therefore less likely to be identified and related to their cause. A low spatial range may be of concern because the exposure is more concentrated and the exceedance of toxicity thresholds more likely. The concept of a horizontal spatial range for persistent organic pollutants was introduced by Scheringer (1, 2) and its implications have been further considered by others (3-7). It is now a key issue in the international negotiations on a treaty on trans-boundary effects of persistent organic pollutants (8). In this paper, we propose to define the “range” of a pollutant as the mean distance that a molecule travels in a multimedia environment under conditions of advective transport, chemical partitioning, and reactive transformation. This proposal addresses a number of shortcomings in previous advection-based expressions for the spatial range. In particular, it allows for emissions to and transport in compartments other than air. In addition, we introduce a pollutant-specific vertical scale height for the air compartment, which depends on both the degradation of the pollutant in air and the advective removal of the pollutant from the air. Finally, we use our model to investigate the implications of different spatial scales on the evaluation of emissions in life cycle assessment. We do this by comparing the exposure/ toxicity ratios of 288 pollutants at a fixed spatial scale with their ratios when each pollutant has it own characteristic spatial scale. Existing approaches to calculating a spatial range differ in whether they account for advective or dispersive transport, whether this transport occurs in one or multiple compartments and whether and how the curvature of the earth’s surface is taken into account. The 1998 SETAC workshop on persistent pollutants held in Fairmont Hot Springs in Canada considered a number of the proposals (9). No single model is able to capture all factors that influence the transport of pollutants and therefore multiple approaches are useful in highlighting different aspects of long-range transport. The original model by Scheringer is based on a ring of adjacent boxes (2, 10). In this model, the spatial range is described as the fraction of the circumference of the earth that is needed to include 95% of a pollutant emitted at a single point in the ring. The model accounts for the dispersive transport in multiple compartments. Held extended this model to account for the two-dimensional dispersion on the surface of a sphere (5). Another modeling approach assumes advective rather than dispersive transport. Both Bennett et al. (4) and van Pul et al. (3) have developed spatial range models based on a Lagrangian air cell. In these one-dimensional, linear models, the steady-state concentration decreases exponentially with distance, C(x)/C(0) ) exp(-x/L), where L is the characteristic travel distance. Hertwich (6) and the SETAC Fairmont group (9) have proposed to identify the spatial scale by determining the model size at which the transformation of pollutants within the model equals the advection of the pollutants out of the model. This spatial range is simply the square root of the area required for this mass-balance condition. Beyer et al. (7) have generalized the approach of Bennett et al. (4) and van Pul et al. (3) to other moving compartments and emissions to nonmoving compartments, but they have not evaluated the effect of several moving compartments. Rather than treating these methods as distinct and unrelated approaches to the formulation of a spatial range, we consider that they all derive from the same fundamental 10.1021/es9911061 CCC: $20.00
2001 American Chemical Society Published on Web 11/16/2000
FIGURE 2. Spatial ranges according to the definitions of Held and Scheringer can be obtained through a mathematical transformation of the spatial range calculated with a simple advection-based model as the one presented in this paper. FIGURE 1. Factors relating to the horizontal transport of pollutant considered in various multimedia models. The models are identified by citation number. approach and differ mainly in the number of factors taken into account. As indicated by Figure 1, all approaches consider both the persistence of a pollutant and its mobility, even though they do not explicitly define mobility. The dispersionbased approaches also take into consideration the direction of transport, or more accurately, the fact that the direction may change during the course of time. Just as molecular diffusion results from linear molecular motion randomized through collisions, macrodiffusion or dispersion results from the nearly-linear motion of air parcels influenced by the correolis force, temperature gradients, and friction. [While diffusion can be derived from molecular motion, dispersion cannot directly be deduced from the speed and angular momentum of air parcels because the equations are underdetermined (11).] The model by Scheringer also takes into account that the earth’s surface is finite. In addition, Held includes both the distribution across two dimensions and the curvature in the earth’s surfaces. We argue that mobility, defined here as the expected speed of the pollutant, is the common parameter underlying all models and that its importance has not yet been sufficiently appreciated. The more sophisticated models are in a sense more “realistic” because they include more factors influencing the spatial range. Dispersion dominates only longitudinal transport however. Latitudinal transport tends to be dominated by advection. This makes dispersive models more appropriate for north-south transport and advective models more suitable for east-west transport. The benefit of the advectionbased proposals is their simplicity, which allows us to investigate individual factors influencing the long-range transport of pollutants. The realism of dispersion-based models is limited because they use globally uniform landscapes and dispersion conditions, independent of actual atmospheric circulation patterns. The purpose of spatial range calculations is to provide an indicator of long-range transport; the explicit spatial distribution is more appropriately modeled with multiple-box models (12-16). Advection-based models highlight factors that differ between pollutants without accounting for the complications of geometry that are the same for all pollutants. The disadvantage is that not accounting for the finite surface leads to spatial ranges of many times the circumference of the earth. For transport in air, Scheringer et al. (17) indicate that there is a strong correlation between the results obtained from models of Scheringer and Bennett et al. Held (5) has shown that there is a 1-to-1 relationship between the results of his spherical model and Scheringer’s ring model. These relationships imply that the spatial range in the more detailed models can be derived through simple mathematical transformations of the results of the advective model, although the transformation equations have, to our knowledge, not yet been derived (Figure 2). The relationship among different spatial range models is further considered in the Supporting Information, Section C. In this paper, we investigate the advection-based spatial range without considering the shape
of the earth’s surface because this allows us to focus on important multimedia aspects of the spatial range.
Methods Multimedia Mass Balance Model. We describe the mass balance of the pollutant in terms of the pollutant inventory in mol in different compartments (18). This formulation is mathematically equivalent and simpler in terms of notation than a description in terms of concentration (13) or fugacity (19). Our multimedia model is described by a set of coupled, linear, first-order differential equations that can be written in the matrix form as in
dN h ) FN h + Sh dt where
(1)
() () (
N1 . N h ) . Nn
S1 . Sh ) . Sn
L1 T F ) 12 . .
T21 L2 . .
. . . .
. . . Ln
)
Ni represents the inventory of the pollutant in compartment i (measured in mol, molecules, or kg); Si is the source or emissions rate; n represents the number of compartments in the model; and F is the invariant fate matrix. The positive off-diagonal elements, Tij, represent the transfer coefficients from compartment i to compartment j. The diagonal elements Li are the loss terms and are always negative. Li is the negative sum of the transformation rate ki, the transfer rate of the pollutant from compartment i to outside the model system through advection Tio, and the transfer coefficients Tij:
Li ) -ki - Tio -
∑T
(2)
ij
i*j
We use the CalTOX multimedia fate and exposure model (18, 20, 21) to calculate transfer rates and loss coefficients, but any other multimedia model could be used as well. CalTOX represents the environment with seven compartments: air, surface water, plants, sediments, surface soil, root-zone soil, and vadose-zone soil. A compartment is described by its total mass, total volume, solid-phase mass, liquid-phase mass, and gas-phase mass. It is assumed that each compartment is well-mixed and therefore has a uniform concentration. The contaminant concentration in different phases within a single compartment (e.g., the gas and particulate phases in air) are in equilibrium with each other, i.e., chemical partitioning among phases maintains equal fugacities. CalTOX calculates transfer factors, which express the likelihood that, over a given period of time, the chemical will be transported to some other compartment or be transformed into some other chemical species. The model and a detailed description can be downloaded from the internet (22). The model settings, the data, and the data sources used here are documented in Hertwich et al. (23). VOL. 35, NO. 1, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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The only modification to CalTOX is that we use a pollutantspecific atmospheric scale height. Scale Height of the Air Compartment. Multimedia models commonly assume a uniform vertical distribution of the pollutant up to 800 m (18), 1000 m (13), or the height of the troposphere. For the assessment of contaminated sites, CalTOX uses a height that depends on the area of the site modeled, following an approach used by Hanna et al. (24). Jolliet and Crettaz (25) base the height of the atmosphere in their model on a correlation between the observed vertical distribution of a number of pollutants and their atmospheric lifetime. The vertical distribution of pollutants, however, will depend on the strength of unidirectional advection through wet deposition and gravitational settling as well as the persistence of pollutants in air. A detailed modeling of the vertical distribution taking into account local meteorological conditions as practiced in air dispersion modeling (11) would be inappropriate for multimedia models. Instead, we adopt the concept of a scale height, originally developed for inert atmospheric constituents, to the modeling of pollutants. Assuming uniform atmospheric conditions in terms of vertical dispersion, degradation, temperature, and gravity as well as emissions at the ground level, the partial pressure of a pollutant can be represented by
p(z)/p0 ) exp(-z/h)
(3)
The scale height h can be interpreted as the height of a uniformly mixed air compartment with a partial pressure p0 that contains the same amount of pollutant as the atmosphere represented by the pressure profile in eq 3. The derivation of the pollutant-specific scale height is presented in the Supporting Information, Section A. The scale height is defined by
(
1
∑v K 1 2
x(
)
h
i i
i
D
+
MW × g RT
∑v K
+
+ D
) ) 2
i i
i
FIGURE 3. Dynamic fate and mobility of 1 mol of 2,3,7,8tetrachlorodibenzo[p]dioxin released to the atmosphere at t ) 0. Panel a shows the first 10 d, while panel b shows 10 yr.
MW × g RT
+
4k D
(4)
where vi is the advection (or deposition) speed, Ki is the partitioning ratio between the advecting medium (rain, particulate matter) and the gas phase, D is the vertical dispersion coefficient [D ) 0.5-5 m2/s (ref 11, p 942)], and k is the degradation rate. We consider three advection pathways i: dry and wet deposition of particles and partition into rain. We use D ) 0.5 m2/s. Mobility of Pollutants. The pulse release of a pollutant into a single release compartment j in a dynamic multimedia model is described by the initial conditions
Nj(0) ) 1, Ni*j(0) ) 0, Si ) 0 Given these initial conditions, the solutions to eq 1, Ni(t), define the probability that the pollutant is present in compartment i at time t. To account for the entire time that a pollutant is present in the moving compartment, we ignore advection out of the model system (Tio ) 0 in eq 2). Figure 3 illustrates Ni(t) for the case of a pulse release of 1 mol of TCDD into the atmosphere. We assume that in each compartment pollutants move horizontally with a characteristic velocity, ui, the advection velocity of the compartment. We use 379 km/d (4.4 m/s) for air and 2 km/d for surface water. We define the mobility of a pollutant released to 144
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compartment j (mj) as calculated by a population-weighted average of travel speeds in the different compartments (eq 5). As noted in the Introduction, advection-based spatial range and mobility formulations do not consider potential differences in the direction of advection.
∑N (t)u i
mj(t) )
i
i
∑
(5) Ni(t)
i
In many cases, it will be sufficient to know the timeaveraged mobility, as defined by eq 6. Due to the mathematical properties of the linear model (eq 1), we can express the time-integrated pollutant inventories in terms of steadystate solutions, which are more easily solved. The timeintegrated inventories in the initial conditions problem correspond to the inventory in the steady-state problem if the steady-state source S replaces N(0) (26, 27). Steady-state inventories Nss i are the solutions to eq 1 under steady-state conditions:
Sj(t) ) 1, Si*j(t) ) 0,
dN h )0 dt
The average mobility can hence be calculated both from initial conditions and steady-state conditions:
∫ ∑N (t) u dt ∑N ∞
i
0
mj )
i
i
i
)
∫ ∑N (t) dt
∑
∞
i
0
ss i ui
i
(6) Nss i
i
Spatial Range of Pollutants. We define the spatial range R as the mean distance that a pollutant travels once it is released. On the basis of the simple definition that distance is the product of speed and time, the spatial range for emissions to compartment j is
Rj )
∫ P(t)m (t) dt ∞
(7)
j
0
where P(t) ) ∑iPi(t) ) ∑iNi(t)/∑iNi(0) represents the probability that the pollutant emitted at t ) 0 is still present at time t. Pi(t) is the probability that the pollutant is in compartment i at time t. Using eqs 5 and 6, this can be expressed in terms of compartmental inventories and advection speeds, both under initial conditions (eq 8) and in steady state (eq 9):
Rj )
∑∫ P (t)u dt ∞
i
0
i
(8)
i
∑u N i
ss i
i
Rj )
∑
(9) Si
i
Scheringer (2, 26) has defined the persistence of a pollutant as
τj )
∑∫ P (t) dt ) ∞
i
0
i
∑N
ss i
i
∑S
(10)
i
i
A simple comparison of eqs 6 and 8-10 indicates that, for both steady-state and initial conditions, the spatial range equals the product of persistence and average mobility, Rj ) mjτj. Potential Dose Calculations. The potential dose is a quantity that is used together with the toxicity of a pollutant to determine the relative importance of a pollutant in life cycle assessment (21). The potential dose is the dose taken in from all pathways of exposure by a randomly selected individual as a result of a continuous, uniform release of 1 kg/d into a fixed model area and is calculated by CalTOX. To investigate the importance of the characteristic model scale on the potential dose calculations, we calculate the spatial scale (spatial range and scale height) and potential dose of 288 organic pollutants and compare them to the potential dose calculated with a fixed-model scale. The potential dose calculations, the model settings, and the chemical specific data have been described in detail by Hertwich et al. (23). An investigation of the uncertainty in the potential dose calculations has revealed that the atmospheric residence time and the potential dose are sensitive to whether it rains or not (28). Because of the advection term, the scale height also depends on the rain. We present calculations for both rain and no-rain conditions.
Results An illustrative calculation for the mobility is presented in Figure 3. This calculation indicates that the mobility of dioxin decreases rapidly in the first 4 d after being released to air.
FIGURE 4. Spatial range R and scale height h of pollutants for both surface water and air emissions, evaluated at no-rain conditions. Each point represents a pollutant. It continues to decrease more slowly for another 2.5 yr as dioxin is removed from the tightly coupled plant-air compartments to the soil and aquatic compartments. After that, it increases slightly as runoff from the soil increases the partitioning into the aquatic compartments. The spatial range and atmospheric scale height for air and surface water emissions are presented in Figure 4. The calculations reflect a situation without rainfall. The spatial range (horizontal scale) varies between 100 m and 1 million km, the scale height between 10 and 5000 m. For a spatial range of more than the radius of the earth (6380 km), it is important to also take the geometry of the earth’s surface into account because the pollutants come back to their emissions source. Note that the atmospheric scale height (vertical scale) is independent of the release compartment, but the spatial range is not. For chemicals with a low Henry’s law constant, both the spatial range and the scale height can be substantially smaller in a situation with rain than in a situation without rain, as Figures A and B in the Supporting Information indicate. The spatial ranges for emission to air, surface water, and surface soil and the scale height of selected chemicals are listed in Table 1. Table S1 of the Supporting Information contains the spatial ranges and scale heights of all 288 chemicals. An investigation of the spatial range and persistence is presented Figure 5. The two straight lines indicate that many chemicals travel either at the wind speed or the speed of the surface water current. These are chemicals that partition predominantly into one those two compartments. The relationship of mobility and partitioning is displayed in Figure 6 and further explored below. For most chemicals emitted to air, mobility is determined by transport in air. For emissions to surface water, however, either transport in air or in surface water can be dominant. Figure 7 presents an investigation of the effect of using the characteristic spatial scale in potential dose calculations as compared to potential dose calculations conducted at a fixed scale. It indicates that with increasing spatial scale, the potential dose from a unit release decreases due to mixing in a larger volume. If the same atmospheric height is used in both calculations, the relationship between the dose ratio and the spatial range is represented by a straight line. The individual points represent the ratio of the potential dose calculated using the chemical-specific spatial scale (h and R) to the potential dose calculated using a fixed model VOL. 35, NO. 1, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 1. Spatial Range and Scale Height of Selected Pollutantsa scale height (m)b
spatial range (km) chemical
CAS No.
air
air rain
surface water
soil
no rain
rain
1,1-dimethylhydrazine 2,3,7,8-TCDD 2,4,5-T 2,4,6-trichlorophenol benzo[a]pyrene DDT tetrachloroethylene
57-14-7 1746-01-6 93-76-5 88-06-2 50-32-8 50-29-3 127-18-4
2.8 e+1 2.7 e+2 7.4 e+1 3.3 e+3 1.3 e+1 4.6 e+2 2.8 e+4
2.4 e+1 1.3 e+2 7.5 e+0 3.1 e+3 8.3 e+0 3.2 e+2 2.8 e+4
3.4 e+1 7.6 e+2 2.0 e+1 1.3 e+1 6.7 e+0 4.5 e+2 1.7 e+4
2.4 e+1 8.6 e+1 8.7 e+0 2.1 e+3 1.1 e-1 3.1 e+2 2.8 e+4
6.1 e+1 t 5.2 e+2 g 2.9 e+2 t 5.6 e+2 t 5.9 e+1 t 3.3 e+2 t 1.0 e+3 g
2.0 e+0 r 1.9 e+2 w 6.8 e+0 r 5.3 e+2 t 4.3 e+1 t 2.1 e+2 t 1.0 e+3 g
a The spatial range for air emissions and the atmospheric scale height are presented for both no-rain and rain conditions. The spatial range for emissions to surface water and surface soil are presented only for the no rain scenario. b The letter after the scale height indicates the limiting factor: g, gravity; r, advection of dissolved pollutant in rain; w, wet deposition of particle-bound pollutant; t, transformation (decay).
FIGURE 7. Ratio of the potential dose calculated at the characteristic model scale to the potential dose calculated at a fixed model scale as a function of the spatial range. FIGURE 5. Spatial range R versus the persistence τ of pollutants for both surface water and air emissions, evaluated at no-rain conditions. The straight lines indicate the wind speed and the speed of the surface water current.
TABLE 2. Correlation Coefficient between Logarithms of Different Calculated Quantitiesa Rair-Rsoil Rair-Rsw Rsw-Rsoil H -h Rair-h
no rain
rain
0.83 0.74 0.80 0.26 0.86
0.94 0.79 0.81 0.91 0.59
rain-no rain
Rair Rsw Rsoil h
0.93 1.00 0.99 0.30
a The columns to the left list the correlations between the spatial ranges for emissions to different compartments as well as between the scale height h and the Henry’s law constant H and the spatial range of air emissions. The columns to the right present the correlations for the four calculated quantities between rain and no-rain scenarios; air, air emissions; sw, surface water emissions; soil, surface soil emissions.
Discussion
FIGURE 6. Mobility as a function of the partitioning into air of the pollutants for both surface water and air emissions, evaluated at no-rain conditions. The partitioning represents the fraction of the total pollutant inventory (time-average or in steady state) that resides in the air compartment. dimensions. Deviations from the straight line are hence explained by the effect of the scale height on potential dose calculations. The correlations between various calculated quantities as well as between the scale height and the Henry’s law constant are presented in Table 2. 146
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Our investigation shows a close relationship between the advective spatial range, the persistence, and the partitioning of a chemical. We will further elaborate this relationship and discuss the relevance of the model scale for the potential dose calculations. Characteristic Model Scale. A relationship between spatial range and persistence is readily apparent in Figure 5. The two edges apparent in the graph represent the advection speeds of the air and surface water compartments. The chemicals that form the two edges are chemicals that partition predominantly into air, or surface water. The ratio of the spatial range to persistence represents the mobility or average speed of the pollutant. In Figure 6, we see that the value of this ratio can to a large degree be explained by the relative
partitioning of the pollutant into the air compartment. Deviations from the diagonal line represent pollutants for which transport in surface water is more important than transport in air. A pollutant that partitions almost entirely into surface water would travel at the speed of the surface water current, 2 km/d. We suggest that mobility is the quantity that underlies all definitions of spatial range based on multimedia models. While they take different aspects of the earth’s geometry into account, they all consider intermedia partitioning and persistence in the same manner. Mobility is the connection between persistence and spatial range that Beyer et al. (7) have speculated about. While we have calculated the mobility and spatial range over a land surface, we expect that the mobility over oceans will be significantly different for lipophilic pollutants because they can no longer partition into plants and soils. The concept of mobility allows us to distinguish between transport over oceans, over land, over snow-covered surfaces, etc. and avoids assuming a uniform surface consisting of 70% ocean and 30% land, a feature of most current spatial range models. In the Supporting Information, we demonstrate that the proposed analytical expression of the spatial range is very similar to but more general than previous advection-based approaches (3, 4, 6, 7, 9). Its strength is that it can take into account transport in several compartments, which is important especially for emissions to surface water, as Figure 6 indicates. We suggest that mobility and persistence are the common properties that also underlie dispersion-based spatial range definitions (2, 5). If this is correct, it opens the path to a deeper understanding of the elements that determine long-range transport. It may eventually lead to a uniform definition of a quantity expressing long-range transport. The proposed expression for a scale height offers a way to account for differences in the vertical distribution of pollutants due to differences in persistence and deposition rates. The calculated scale height is sensitive not only to the parameters determining persistence and deposition (investigated in the Supporting Information), but also to the dispersion factor D. A higher D indicates better mixing and produces more similar scale heights for common pollutants. The dispersion factor and the ability of the scale height concept to represent the appropriate atmospheric volume for multimedia models need to be investigated through comparisons with empirical data and the results of more detailed atmospheric models. The role of persistence in air explains the correlation between the scale height and the spatial range. This correlation is apparent in Figure 4 and in the results listed in Table 2. An investigation of the scale height in the Supporting Information indicates that, for the no-rain scenario, the persistence limits the upward transport for 214 of 292 chemicals. As is the case for inert gases O2, N2, Ne, ..., the remaining chemicals are limited by gravity. For most surface water emissions, transport in water is more important, and there is little or no correlation with scale height. These results indicate that spatial range calculations for air emissions should take the differences of the atmospheric scale height into account. Implications for Potential Dose Calculations. Figure 7 provides a comparison among the 288 chemicals of the ratio of the potential dose calculated at a chemical-specific model scale to the potential dose calculated at a fixed scale. Figure 7 shows that, for the same total emissions, the product of potential dose and model area, PD × R2, is equal for calculations at a fixed model area and for calculations at the characteristic model scale. This result applies when both calculations are done using the same atmospheric height, as indicted by the diagonal line in Figure 7. If calculations at
the fixed scale also use a fixed atmospheric height, the potential dose for chemicals with a small spatial range will be underestimated. This underestimation is a result of the correlation between scale height and spatial range (Table 2). A higher atmosphere in the fixed-scale calculations not only results in a lower air concentration due to dilution but also results in lower concentrations in other compartments. Concentrations are lower because the transfer rate from air to other compartments is proportional to the atmospheric concentration. The potential dose is reduced correspondingly. For chemicals with a range of 100 km or less, a fixed atmospheric height leads to an underestimate of the potential dose for air emissions by around 1 order of magnitude. This error is comparable to the effect of uncertainties in the input parameters (28). We therefore conclude that the spatial range does not need to be considered in potential dose calculations but that the atmospheric scale height should be included.
Acknowledgments Funding for the research reported in this paper was provided by the U.S. Environmental Protection Agency (Cooperative Research Grant CR-826925-01-0) and the P2005 Program of the Norwegian Research Council. Helpful comments were provided by three anonymous reviewers.
Supporting Information Available Contains derivation of the scale height, discussion of relationship among advection-based formulations of spatial range, and scale height and spatial range for 288 chemicals (21 pages). This material is available free of charge via the Internet at http://pubs.acs.org.
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Received for review September 28, 1999. Revised manuscript received September 29, 2000. Accepted October 2, 2000. ES9911061
