A model to predict the breathing zone concentrations of particles ...

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www.rsc.org/jem | Journal of Environmental Monitoring

A model to predict the breathing zone concentrations of particles emitted from surfaces Jonathan Thornburg,*a John Kominsky,b G. Gordon Brown,a Peter Frechtel,a William Barrettc and Glenn Shaulc

Downloaded by University of Nevada - Las Vegas on 01 September 2010 Published on 10 February 2010 on http://pubs.rsc.org | doi:10.1039/B919385E

Received 17th September 2009, Accepted 18th January 2010 First published as an Advance Article on the web 10th February 2010 DOI: 10.1039/b919385e Activity based sampling (ABS) is typically performed to assess inhalation exposure to particulate contaminants known to have low, heterogeneous concentrations on a surface. Activity based sampling determines the contaminant concentration in a person’s breathing zone as they perform a scripted activity, such as raking a specified area of soil, while wearing appropriate sample collection instrumentation. As an alternative approach, a probabilistic model based on aerosol physics and fluid dynamics was developed to predict the breathing zone concentration of a particulate contaminant emitted from a surface during activities of variable intensity. The model predicted the particle emission rate, tracked particle transport to the breathing zone, and calculated the breathing zone concentration for two scenarios. One scenario used an Eulerian model based on a Gaussian concentration distribution to quantify aerosol exposure in the trailing wake of a moving object. The second scenario modeled exposure in a quiescent environment. A Lagrangian model tracked the cumulative number of individual particles entering the breathing zone volume at a particular time. A Monte Carlo simulation calculated the breathing zone concentration probability distribution for each scenario. Both models predicted probability distributions of asbestos breathing zone concentrations that bracketed experimentally measured personal exposure concentrations. Modeled breathing zone concentrations were statistically correlated (p-value < 0.001) with independently collected ABS concentrations. The linear regression slope of 0.70 and intercept of 0.03 were influenced by the quantity of ABS data collected and model parameter input distributions at a site broader than those at other sites.

Introduction Personal exposure assessment measures or evaluates the quantity of a contaminant that reaches a target at a specific frequency for a known duration. Personal exposure assessment, if done properly, provides more representative exposure data than stationary area monitors. An advantage is that the duration and proximity of the person to the sources of the contaminant are accounted for by the measurement.1 Therefore, personal exposure measurements typically have a stronger statistical relation with dose and risk.2

a RTI International, 3040 Cornwallis Road, Research Triangle Park, NC, 27709, USA. E-mail: [email protected] b Environmental Quality Management Inc., 1800 Carillon Boulevard, Cincinnati, OH, 45240, USA c US EPA\ORD\NRMRL, 26 West Martin Luther King Drive, Cincinnati, OH, 45268, USA

Exposure assessment approaches for inhalation, dermal, and dietary routes include contaminant concentration measurements, biomarkers, surveys, historical reconstruction, deterministic models, and statistical models.3 Measurement of the contaminant concentration in the breathing zone is a common technique for inhalation exposure assessment. Accurate characterization of the breathing zone concentration is critical for the classical risk paradigm that links source emission rates to micro-environmental concentrations to a person’s exposure. Therefore, personal exposure measurements determine the inhalation rate and concentration dependent dose that can cause adverse health effects.4 General population studies and activity based sampling are common designs for obtaining experimentally measured breathing zone concentrations. General population studies characterize the personal exposure of a large cohort to a wide variety of air pollutants during their normal, daily activities.

Environmental impact Activity based sampling is the current standard method for assessing exposure to hazardous particles emitted from surfaces. This research presents an aerosol physics and fluid dynamics based model to predict the breathing zone concentration as a more economical alternative. This model is meant to be a screening tool to aid decision making. At one level, the model helps to identify whether the risk of adverse health outcomes is sufficient to justify collection of experimental data to confirm the modeled personal exposure estimates. Also, the model output extrapolates a limited range of experimental data to other exposure scenarios to understand the range of potential breathing zone concentrations. This journal is ª The Royal Society of Chemistry 2010

J. Environ. Monit., 2010, 12, 973–980 | 973


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Particulate matter exposure studies are one example of this type of study.5 Activity based sampling (ABS) targets a unique air pollutant or a single source during real or simulated activities. When breathing zone concentrations are expected to be large, measurements typically are collected as the person performs their routine tasks. However, investigation of a contaminant known to have low, intermittent concentrations often requires scripted activities at a source with a known emission rate. A scripted activity is a routine conducted by the subject in a deliberate manner in a specified area over a fixed time period. An example is measurement of inhalation exposure to a soil contaminant by raking a defined area of soil in a proscribed pattern for a set time period.6 A recent challenge in the ABS method is the assessment of a person’s inhalation exposure to serpentine or amphibole asbestos in soil. The asbestos in the soil results from either natural geological processes (e.g., naturally occurring asbestos) or the degradation of anthropogenic asbestos containing materials. Any activity that disturbs the soil aerosolizes the asbestos fibers and poses an inhalation risk. Typical recreational activities are the common exposure pathways for the general public. However, the exposure concentrations in these situations are much lower than occupational exposures due to the lower quantities in the source matrix and the intermittent nature of the exposures. Asbestos exposure typically is reported as the number of structures (str) per unit time (s) or volume (cm3). As a result, a representative personal exposure assessment for asbestos fibers aerosolized from soil is often prohibitively expensive. The number of samples required to provide the necessary statistical power, the required safety precautions due to the toxicity of asbestos, and the increased analytical costs resulting from the expected low concentrations are the significant cost factors. This research developed a new model framework for estimating asbestos breathing zone concentrations as a lower cost alternative to ABS. Although developed for asbestos fibers emitted from soil, the generic model formulation is applicable to any particulate contaminant found on a surface. This model is meant to be a screening tool to aid decision making. At one level, the model helps to identify whether the risk of adverse health outcomes is sufficient to justify collection of experimental data to confirm the modeled personal exposure estimates. Also, the model output extrapolates a limited range of experimental data to other exposure scenarios to understand the range of potential breathing zone concentrations.

ABS validated the model equations. The Monte Carlo approach also allowed a sensitivity analysis on the independent parameters to be performed. The model structure accounted for two different scenarios that used different particle emissions and aerosol transport equations. One scenario modeled particle emission and transport to the breathing zone of a person located in the turbulent, trailing wake generated by the source. For this research, motorcycle riding was the selected activity for this scenario. The equations for this scenario also are applicable to similar activities like bicycle riding or jogging. The second scenario modeled aerosol emission and transport when exposures were self-induced in a quiescent environment. Yard work (e.g., raking) was the selected activity for this scenario. This model formulation also applies to exposure in indoor environments. Four modules determined the general structure of the model for both scenarios (Fig. 1). The first module defined the characteristics of the person, their activity, and their environment. The second and third modules calculated the aerosol emission rate from the surface and the aerosol transport to the breathing zone, respectively, for the selected activity. The particle emission rate and aerosol transport equations were scenario specific. The fourth module calculated the pollutant concentration in the breathing zone. Tables 1 and 2 summarize the model variables required for each scenario. Values for input variables were selected from published distributions, an assumed distribution, or experimental data. Distributions published in the literature or data collected during the experimental phase of this research

Model description The model combined aerosol physics and fluid dynamics principles to develop mass balance equations to predict the breathing zone concentration of particles emitted from a surface by a person conducting activities of varying intensity. The equations predicted the particle emission rate, tracked particle transport to the breathing zone, and calculated the breathing zone concentration. A Monte Carlo algorithm calculated a breathing zone concentration distribution to account for the uncertainty associated in the results using randomly selected values from the independent variable input distributions in the model equations. Comparison of the modeled breathing zone concentration distribution against experimentally measured values collected by 974 | J. Environ. Monit., 2010, 12, 973–980

Fig. 1 Breathing zone concentration model flow chart.

This journal is ª The Royal Society of Chemistry 2010

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Table 1 Input distributions for independent variables in equations used to simulate the contaminant breathing zone concentration for the trailing wake scenario (motorcycle riding). Data ranges, distribution types, and sources are identified Symbol

Parameter

Distribution description

Distribution type

Source

S (%) Sp/str per g M (%) Uf/cm s1 X/cm Q/ c

Soil silt loading Contaminant soil loading Soil moisture content Free-stream velocity Distance from source Angle from centerline Turbulence length scalar

See Table 3 See Table 3 See Table 3 Scale ¼ 671, shape ¼ 3, offset ¼ 313 Mean ¼ 500, SD ¼ 200 0 to 90 0.5 to 1

Uniform Uniform Normal Gamma Normal Uniform Uniform

Experimental data Experimental data Experimental data Assumed Assumed Assumed Assumed

Table 2 Input distributions for independent variables in equations used to simulate the contaminant breathing zone concentration for the quiescent environment scenario (yard work). Data ranges, distribution types, and sources are identified Symbol

Parameter

Distribution description

Distribution type

Source

H/cm

Age Gender Height

Uniform Uniform Normal

Assumed Assumed CDC (public domain)

W/kg

Weight

Normal

CDC (public domain)

qact/W Uf/cm s1 Eyard/str per s uz/cm s1 ux/cm s1 da/mm

Additional energy Ambient wind speed Yard work emission rate Thermal plume velocity Wake velocity Particle aerodynamic diameter

Adults: 16 to 60 years Male or female Male: mean ¼ 176, SD ¼ 7.5 Female: mean ¼ 161, SD ¼ 6.9 Male Mean ¼ 105.6 + (1.02 H) + (0.22 Age), SD ¼ (2.90 Mean)0.5 Female Mean ¼ 64.4 + (0.78 H) + (0.3 Age), SD ¼ (4.22 Mean)0.5 Yard work: 274 to 475 See Table 3 See Table 3 100 to 200 5 to 5 Mean ¼ 0.1, SD ¼ 1.06

Uniform Uniform Uniform Uniform (assumed) Uniform (assumed) Log-normal

Public domain Experimental data Experimental data

were preferred sources. When necessary, the authors assumed an input distribution based on their best judgment. The model used cgs units for all variables, except as noted in Table 2. The coordinate system had the origin at ground level and centered on the person. The z-axis represented the vertical direction. The y-axis went laterally from left to right across the person. The positive direction along the x-axis moved away from the person’s body. Trailing wake scenario The high turbulence generated by the unidirectional movement of a source was assumed to produce a steady aerosol cloud in the trailing wake of the source. The aerosol concentration gradient downstream of the source was assumed to be defined by a Gaussian distribution. Therefore, an Eulerian model was developed for this scenario. A Gaussian turbulent dispersion equation (eqn (1)) calculated the pollutant aerosol concentration in the breathing zone (Cbz) of a trailing person as a function of the pollutant emission rate (Em), the person’s relative free-stream velocity (Uf), the distance from the source to the trailing person (X), the offset angle of the trailing person from the centerline (Q), and the turbulent diffusivity (D).7

C¼

Em Uf X sin2 Q exp D pDX


(1)

12,11 12 19

This equation is applicable to all scenarios where the aerosol generated disperses in the trailing wake of an activity. Eqn (1) was modified to define measure variables that are difficult to measure experimentally. The modification replaced D with the product of the turbulent length scalar (c) and turbulent eddy velocity. For lack of a better approximation, the turbulent eddy velocity was assumed to be equal to Uf. This assumption is reasonable over small values of X, but as X increases the turbulent eddy velocity decreases at an unknown rate. By assuming a constant turbulent eddy velocity equal to Uf, the magnitude of Cbz possibly was underestimated. Therefore, the modified form of eqn (1) becomes: Em X sin2 Q $ (2) exp Cbz ¼ c p Uf c X Any appropriate particle emission rate equation or experimental data is suitable for calculating Em in eqn (2). This research used the empirical equation for PM2.5 generation from light duty vehicle travel on unpaved roads to calculate the soil emission rate.8 A literature review determined this equation was the most appropriate even though it was used out of context. The soil contaminant loading (Sp), silt content (S), and moisture content (M) were measured as part of this research, as described below. Multiplication of the soil emission rate equation by Sp yielded the pollutant emission rate (eqn (3)). Each numerical constant is listed individually to show the empirical constants in the emission rate equation and conversion factors to cgs units. J. Environ. Monit., 2010, 12, 973–980 | 975

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0:5 S Uf 3600 0:18 281:9 30 0:621 105 12 Em ¼ Sp Uf 0:2 105 M 0:5

(3)


Quiescent environment scenario A Lagrangian model suited the quiescent environment scenario because the low turbulence of the activity did not guarantee a significant percentage of contaminant particles emitted from the surface would reach the breathing zone. In some instances, the person’s orientation to the convective air flow possibly prevented any particles from entering the breathing zone. Therefore, the model structure tracked the position of individual particles in the x–z plane. Particles that successfully entered the breathing zone were included into a rolling average concentration determined by their respective velocities. Calculation of the breathing zone concentration required the characteristics of the person, their activity, and their environment to be defined. Full definition of the modeled person’s physical characteristics, age, and gender was potentially important for this scenario. For each model iteration, a person’s gender and age were assumed from a uniform distribution. These values defined the normal distributions for their height (H) and mass (W) (Table 2). From these distributions, a single random value for height and mass was selected per iteration. Their activity contributed to the amount of body heat (qbody) generated by the person. Their environment defined the distributions for Uf, the particle emission rate, and contaminant aerosol size. A thorough literature review did not identify a suitable empirical or theoretical equation to predict particle emission rates from the soil during yard work (Eyard). Therefore, a uniform distribution of contaminant emission rates was developed, as described in the next section. However, emission rate data or equations for other activities, such as particle resuspension from carpet, exist.9,10 Existing equations provided the theoretical basis for modeling transport of aerosolized particles from immediately above the surface to the breathing zone.11,12 In quiescent, low turbulence conditions, particle transport to the breathing zone is dominated by the vertical updraft created by a person’s body heat. This thermal plume velocity varies from 100 to 200 cm s1, and is capable of transporting particles from ground level to the breathing zone in less than 2 s. For thermal convection to dominate particle transport, the thermal plume velocity must dominate the free-stream velocity. In outdoor locations, the ambient wind dominates the thermal plume unless the person faced in the direction of the free-stream such that their body acted as a shield. In this case, the wake velocity in the x-direction represents the free-stream. Therefore, the model assumed the person was properly oriented 25% of the time. Free-stream velocities indoors typically are less than 400 cm s1 such that the person’s orientation is not a factor.13 The Richardson number (Ri) is a dimensionless number that describes the thermal convection to inertial convection ratio.12 gqbody Ri ¼ 0:5 H2 r Uf3 Cp T 3 976 | J. Environ. Monit., 2010, 12, 973–980

(4)

where g is the gravitational constant, r is the air density, Cp is the air heat capacity, and T is the air temperature. Previous experimental research indicates thermal convection dominates when Ri is between 0.04 and 0.2.11,12,14,15 For this research, a low Ri number of 0.04 was selected as the boundary between thermal and inertial dominated convection to maximize the potential breathing zone concentration. The qbody generated by the person performing the activity is a function of their basal metabolic rate (BMR) and the extra heat produced conducting the activity (qact) with a coefficient to account for the 25% of body heat lost via perspiration.16 qbody ¼ (1 0.25)(BMR + qact)

(5)

Harris and Benedict developed the gender specific equation for BMR that is a function of the person’s weight (W), height (H) and age.17 4:184ð66 þ 13:7W þ 5H 6:8ageÞ 86400

(6)

4:184ð655 þ 9:6W þ 1:8H 4:7ageÞ 86400

(7)

BMRM ¼

BMRF ¼

Particle transport from ground level to the breathing zone was calculated from the Navier–Stokes equations. The solved equations for particle velocity (vx, vz) and location (x, z) in the x–z planes are shown in eqn (8)–(11), respectively. Particle movement in the y-direction (left to right across body) was assumed to be negligible. vx(t) ¼ ux + (vx,t1 ux)et/s

(8)

vz(t) ¼ uz 981s + (vz,t1 + uz 981s)et/s

(9)

x(t) ¼ uxt + s(vx,t1 ux)(1 et/s)

(10)

z(t) ¼ (uz 981s)t + s(vz,t1 + uz 981s)(1 et/s)

(11)

For this scenario, uz is the thermal plume velocity and ux is the wake velocity.12 The particle relaxation time (s) is a function of the particle aerodynamic diameter (da), air density (r), air viscosity (m), and Cunningham correction factor (Cc). s¼

Cc ¼ 1 þ

ðda rÞ2 Cc 18 m

2 :0687 1:257 þ 0:4e1:1da =2:0687 da

(12)

(13)

The particles position and velocity were calculated iteratively over time steps starting at 0.001 s and doubling until the cumulative time equaled 2 s. If at any time the particle moved more than 9 cm from the body or if the particle did not reach the breathing zone height within 2 s, no exposure occurred and tallied as a zero concentration.14 Otherwise, the particle entered the breathing zone, defined to have a mid-point at 90% of the person’s height.18 This journal is ª The Royal Society of Chemistry 2010

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The previous two paragraphs apply to a single particle. The position and velocity calculations were repeated for each contaminant particle emitted per second, as defined by Eyard. Each particle was tracked to determine the number of particles per second entering the breathing zone (Nbz). The breathing zone volume was assumed to be a sphere with a diameter of 9 cm (dbz). The average particle residence time (t) within the breathing zone volume was calculated from the average particle velocity. Eqn (14) used Nbz, dbz and t to calculate the average breathing zone concentration (Cbz).


Cbz ¼

Nbz t 3 pdbz =6

(14)

Monte Carlo simulation The breathing zone concentration model equations and Monte Carlo algorithms were written in SAS v.9 (SAS Inc., Cary NC). Equations and input distributions are easily modified as exposure scenarios of interest change or new data become available. Values for the parameters in the trailing wake scenario equations were selected randomly from the input distributions described in Table 3 Experimental data collected at seven sites for modeling breathing zone concentrations. The number of experimental measurements for each variable is shown in parentheses

Location

Model scenario

Experimental input data

Clear Creek Management Area (CCMA), King City, CA

Trailing wake

M Sp S

Swift Creek (SCWA), Nooksack, WA

Trailing wake

M Sp S

Quiescent

Eyard Uf

North Ridge Estates (NREO), Klamath Falls, OR

Quiescent

Eyard Uf

Coalinga Operable Unit 2 (COAL), Coalinga, CA

Quiescent

Eyard Uf

Big Tex Site (BGTX), San Antonio, TX

Quiescent

Eyard Uf

Vermont Asbestos Group (VTAG), Eden, VT

Quiescent

Eyard Uf

Sapphire Mine (SMNC), Sapphire, NC

Quiescent

Eyard Uf

2.8% 1.9% (n ¼ 48) 1.37 10+9 to 2.10 10+10 (n ¼ 8) 1.9% to 7.9% (n ¼ 18) 5.1% 1.0% (n ¼ 120) 1.03 10+8 to 7.22 10+9 (n ¼ 8) 2.6% to 3.1% (n ¼ 24) 70 to 303 (n ¼ 10) 49 to 219 (n ¼ 28) 1 to 30 (n ¼ 12) 201 to 452 (n ¼ 12) 27 to 2933 (n ¼ 11) 49 to 228 (n ¼ 13) 1 to 4 (n ¼ 3) 215 to 344 (n ¼ 12) 3 to 875 (n ¼ 16) 67 to 350 (n ¼ 15) 0.3 to 13 (n ¼ 13) 0 to 148 (n ¼ 12)


Tables 1 and 3. Similarly, input variable values for the quiescent environment scenario equations were selected randomly from the input distributions described in Tables 2 and 3. One iteration of the model completed a single pass through each of the four modules; a total of 10 000 iterations were performed. The breathing zone concentration and corresponding input variable values were tabulated for interpretation and data quality assessment. An input parameter sensitivity analysis was also conducted for each scenario. This analysis determined the sensitivity of the model outputs to variations in the model inputs. The analysis was performed iteratively. The value of one input parameter was changed in discrete increments from minimum to maximum value while all other input parameters were held constant at their median value. At each increment, the model output was calculated and tallied. The sensitivity analysis ranked the model input parameters with respect to their contribution to the model output variability. The metric was the magnitude of the geometric standard deviation of the Cbz distribution.

Experimental Experimental data for model input parameters were collected at seven sites with elevated asbestos concentrations in the soil (Table 3). The experimental Eyard data collected with the Releasable Asbestos Field Sampler were used for model input into the quiescent environment scenario.19 Briefly, this instrument uses a rake mechanism to aerosolize soil particles. Plug air flow induced by a fan carries the resuspended particles to the outlet of the instrument where open-faced filter cassettes isokinetically collect samples for gravimetric analysis, transmission electron microscopy (TEM), and/or chemical speciation. TEM analysis of samples collected on 25 mm, 0.8 mm pore mixed-cellulose ester (MCE) filters was conducted following ISO 10312:1995 to measure the asbestos fiber emission rate (Eyard).20 M was measured with a ML2 Theta Soil Moisture Probe (Dynamax Inc., Houston TX). Multiple soil samples collected at each site determined the range for Sp. Soil was prepared for asbestos concentration determination by following US EPA’s ‘‘Method for Determination of Asbestos in Bulk Building Materials’’.21 This method reduces a representative portion of the soil to a residue that is directly transferred to 0.8 mm pore MCE filters for TEM analysis following ISO 10312:1995. ASTM Method D6913-04e1 was used to determine S.22 This method determines the particlesize distribution (gradation) of a soil sample to quantify the mass percentage of silt, particles smaller than 70 mm, in the soil sample. To validate the model, US EPA independently collected ABS data at the same seven sites (Table 4). We did not participate in the collection and analysis of these samples. Experimental ABS data for the trailing wake scenario were collected at CCMA and SCWA only. Measurements in the breathing zone of a motorcycle rider following a lead motorcycle were collected at CCMA. Breathing zone samples were collected for a trailing person during combined jogging–biking–walking activity at SCWA. Experimental ABS data for the quiescent environment were collected at all sites except CCMA. Raking was the activity selected to simulate yard work at these sites. The exposure scenario had the subject rake a 3 m by 3 m area for 120 min in a scripted manner.6 J. Environ. Monit., 2010, 12, 973–980 | 977

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Table 4 Activity based sampling (ABS) activities and range of experimentally measured breathing zone concentrations (Cbz) at the seven sites Location

Model scenario


Clear Creek Management Area (CCMA) Swift Creek (SCWA)

Number Cbz range/str of samples per cm3

Motorcycle 11 riding Jog/bike/walk 6 Raking 7 North Ridge Estates (NREO) Raking 7 Coalinga Operable Unit 2 Raking 9 (COAL) Big Tex Site (BGTX) Raking 4 Vermont Asbestos Group Raking 9 (VTAG) Sapphire Mine (SMNC) Raking 5

0.140 to 2.000 0.006 to 0.093 0.024 to 0.043 0.003 to 0.088 0.000 to 0.037 0.000 to 0.001 0.002 to 0.420 0 to 0.005

The ABS median breathing zone concentrations at each site were compared against the modeled median values. Linear regression analysis assessed the accuracy and correlation of the modeled results with ABS values. We chose median model and ABS values for the linear regression analysis because the median, unlike the mean, is unaffected by the magnitude of the observations at the tails of the distributions. When the distribution covers a broad range, like the modeled breathing zone concentrations, or is comprised of a limited number of measurements, like the ABS concentrations, extreme values will greatly bias the group mean and the median is a better metric.23

Results Initial modeling of the trailing wake and quiescent scenarios confirmed the model equations and parameter input distributions provided modeled breathing zone concentrations that compared favorably with ABS concentrations. Fig. 2 compares the box-whisker plots for the modeled breathing zone concentrations with the ABS data at CCMA and SCWA. Modeled breathing zone concentrations for both scenarios were log-normally distributed. Motorcycle riding (Fig. 2A) modeled concentrations at CCMA spanned four orders of magnitude from minimum to maximum. All iterations yielded a concentration greater than zero. The median modeled breathing zone concentration was 0.59 asbestos structures (str) per cm3. The 25th to 75th percentiles were within a factor of 3.5. The modeled values were compared against the range of experimental breathing zone concentrations, 0.14 to 2.0 str per cm3, measured during motorcycle riding.19 Fig. 2B shows the box-whisker plot for the modeled breathing zone concentration during the raking scenario at SCWA. The box-whisker plot shows only concentrations that were greater than zero. Half of the Monte Carlo iterations produced a concentration of zero because Ri was less than 0.04. For half of the iterations where Ri was greater than 0.04, median breathing zone concentrations were 0.031 str per cm3. The distribution of modeled breathing zone concentrations during yard work covered a smaller range than motorcycle riding, 0.01 to 0.08 str per cm3. Modeled breathing zone concentrations bracketed the experimentally measured values, 0.024 to 0.043 str per cm3. Fig. 3 compares the corresponding ABS and modeled median breathing zone concentrations at each site as described in Tables 978 | J. Environ. Monit., 2010, 12, 973–980

Fig. 2 Distribution of modeled (box-whisker plot) and experimental (X) breathing zone concentrations for the two scenarios modeled: (A) motorcycle riding at CCMA; (B) yard work at Swift Creek (only showing non-zero concentrations). Box shows the median and quartiles. Whiskers show maximum and minimum.

3 and 4. The linear regression was statistically significant (p-value < 0.001) with a slope statistically different from unity (p-value < 0.001) and an intercept not different from zero (p-value ¼ 0.080). Table 5 presents the parameter sensitivity analysis results for both scenarios. For the trailing wake scenario, the person’s distance from the leading person (X), the trailing person’s angle to the leading person (Q), the asbestos soil loading (Sp) had the largest influence on the model. For yard work, a meaningful parameter sensitivity analysis required inclusion of only non-zero concentrations. The asbestos emission rate (Eyard), thermal plume velocity (uz) and the ambient wind speed (Uf) influenced modeled concentrations from the yard work scenario when the modeled Ri was greater than 0.04. This journal is ª The Royal Society of Chemistry 2010


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Fig. 3 Comparison of modeled and ABS median breathing zone concentrations for the eight scenarios conducted at the seven test sites. Modeled concentrations of 0 str per cm3, caused by orientations to the ambient wind except ‘‘facing away’’, were not included in the calculation of the median.

Discussion The modeled breathing zone concentrations for each scenario bracketed the experimentally measured values, indicating the model accurately predicted the expected range of breathing zone concentrations. The larger span of the modeled breathing zone concentration distributions compared to the experimental data reflected the random variation or experimental error in the input data for each scenario. To validate the model equations, modeled breathing zone concentrations were compared against independently measured ABS breathing zone concentrations. The statistically significant correlation provided confidence that the model equations are valid. The difference between modeled and ABS breathing zone concentrations at COAL and BGTX determined the regression slope and intercept. At COAL, the Eyard range used as model input spanned two orders of magnitude; compared to Eyard

ranges at other sites that spanned ranges from 5 to 40 (Table 3). The larger Eyard range at COAL possibly introduced a positive bias to the modeled median breathing zone concentration. The small amount of ABS data collected at BGTX (n ¼ 4) and concentrations less than 0.001 str per cm3 increase the probability that the median ABS value was biased low. The agreement between modeled and ABS values at concentrations less than 0.01 str per cm3 was encouraging. Typical analytical detection limits applied to TEM analysis are 0.001 to 0.005 str per cm3 to control the cost per sample. In these cases, only 1 or 2 asbestos fibers may be counted over the filter area analyzed thereby limiting one’s confidence the measured concentration is correct. A large number of asbestos structures per unit filter area (e.g., higher concentration) reduces the analytical costs and increases one’s confidence in the measurement. The ability to accurately predict breathing zone concentrations less than 0.005 str per cm3 at a site can reduce analytical costs and increase confidence in ABS breathing zone concentrations near the analytical detection limit. Assumed values and distribution types for key independent variables may have caused the random variation in the input data that affected the modeled breathing zone concentrations and the resulting linear regression slope. For example, the two most important parameters for the trailing wake scenario used assumed input distribution ranges and shapes. We created reasonable estimates of X and Q from limited experimental notes collected by US EPA and conversations with observers of the ABS measurements. Similarly, the assumed input distribution shape for uz for the quiescent environment scenario had a similar effect on the breadth of the modeled breathing zone concentrations. The assumed uniform distribution provided an equal probability that a velocity from the extremes of the range was selected. A normal distribution for this parameter should reduce the breadth of the modeled breathing zone concentrations. However, the limited experimental data published in the literature were not sufficient to develop a different distribution.11,12 Conversely, assumed input distributions for certain input parameters did not influence the breathing zone concentrations. Examples included c and ux for the trailing wake and quiescent scenarios, respectively. The input distributions for these two variables covered narrow ranges, thereby limiting their impact on the model results.

Table 5 Sensitivity analysis for input parameters used to model the breathing zone concentration for trailing wake and quiescent environment scenarios Trailing wake

Quiescent

Ranking

Parameter

p-Value

Ranking

Parameter

p-Value

1

Distance from source (X)