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The Estimation of Commuting Patterns in Applications of the 

Hazardous Air Pollutant Exposure Model (HAPEM) 

Ted R. Johnson and James E. Capel 

IT Corporation 

South Square corporate Centre One 

3710 University Drive, Suite 201 

Durham, North Carolina 27707-6208 

Dianne M. Byrne 

Pollutant Assessment Branch 

Office of Air Quality Planning and standards 

U.S. Environmental Protection Agency 

Research Triangle Park, North Carolina 27711 

For Presentation at the 84th Annual Meeting of the 

Air and Waste Management Association 

Vancouver, British Columbia 

June 16-21, 1991 

Disclaimer: The statements and analytical conclusions presented 

in this paper are those of the authors. They do not necessarily 

reflect U.S. Environmental Protection Agency policy. 
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91-172.6 

The Office of Air Quality Planning and standards (OAQPS) of 

the U.S. Environmental Protection Agency (EPA) is responsible for 

developing national standards to reduce emissions of hazardous 

air pollutants. Within OAQPS, the Pollutant Assessment Branch 

(PAB) is responsible for assessing the health risks associated 

with exposure to these emissions. In accordance with this 

responsibility, the PAB continually evaluates and updates its 

exposure and risk assessment capabilities to reflect the current 

state of knowledge. 

In the past, the PAB's exposure assessments assumed that the 

population-at-risk was continuously exposed to the outdoor 

concentration estimated at the place of residence. This 

simplifying assumption does not consider the effects on exposure 

of time spent indoors or away from home. A more sophisticated 

methodology for estimating population exposure is currently being 

developed. This methodology is incorporated in a population 

exposure model developed by IT Corporation (formerly PEI 

Associates, inc.), under contract to EPA. The model is 

noteworthy in that it combines features from two exposure models 

used by EPA for risk assessment, the National Ambient Air Quality 

Standards Exposure Model (NEM) and the Human Exposure Model 

(HEM). This report presents a brief overview of NEM and HEM, a 

more detailed description of the new model referred to as the 

Hazardous Air Pollutant Exposure Model (HAPEM), and a summary of 

research efforts to develop an algorithm capable of estimating 

commuting patterns in areas where HAPEM is applied. 

THE EPA EXPOSURE MODELS 

The EPA routinely uses NEM and HEM to evaluate population 

exposure to air pollution. Historically, NEM has been applied to 

the criteria pollutants (e.g., ozone and carbon monoxide), whereas HEM has been applied to toxic pollutants (e.g., benzene). The 

structure of each model reflects the difference in application. 

The NEM is typically applied to a large urban area which has 

been subdivided into contiguous districts. The model simulates 

the movements of small population groups called cohorts through 

zones of varying air quality. The model accounts for the shortterm effects on exposure of geographic location (i.e., district 

occupied), microenvironment, and breathing rate. Ambient 

concentrations in, each district are usually determined from 

fixed-site monitoring data that have been adjusted to simulate a 

particular regulatory scenario. Cohort movements, which vary 

with age and occupation, are based on activity diary studies and 

local commuting data. Exposure estimates are provided for 

averaging times ranging from 1 hour to 1 year. A probabilistic 

version of NEM applicable to ozone (PNEM-03) has been described 

by Johnson et al. 
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The HEM is typically used to estimate annual average 

exposures and associated risks in an area surrounding a 

particular emission source, A polar coordinate grid is 

established for the source, and population centroids identified 

from census data are located on the grid system. A dispersion 

model is used to estimate the annual average ambient 

concentration at each receptor point on the grid and at the 

centroid locations. Early versions of HEM assumed that persons 

residing at each centroid location were constantly outdoors and 

remained at the same location. The PAB has recently developed 

HEM II, an improved version of HEM that accounts for the effecta 

of microenvironment. 

The HAPEM is a hybrid of NEM and HEM. Consistent with the 

NEM approach, HAPEM divides the population into cohorts that move 

through microenvironments and between home and work locations. 

Like HEM, HAPEM uses a dispersion model (ISCLT) to estimate 

annual average pollutant concentrations at population receptors 

and fenceline locations surrounding a source. The HAPEM is 

described in more detail in the next section. 

METHODOLOGY 

A five-step methodology is used to apply HAPEM to a 

particular facility. This process can be illustrated by 

describing how HAPEM would be used to estimate pollutant 

exposures and risks associated with a hypothetical emission 

source. 

step 1: Define Population-at-Risk, Exposure Districts, and 

Exposure Period. 

The HAPEM provides estimates of the distribution of 

pollutant exposure and associated risk within a defined 

population (the "population-at-risk") for a specified exposure 

period. The exposure period is usually a recent calendar year 

for which good meteorological and population data are available. 

The population-at-risk is usually defined as all persons residing 

within a specified distance frora a particular emission source. 

This circular area is referred to as the residential zone. 

Persons living within the residential zone are assumed to work 

within a larger circular area, the commuting zone. The commuting 

zone also has the emission source as its center. Radii of 10 

kilometers (km) and 50 km, respectively, are typically used to 

define the residential and commuting zones. 

The residential zone is divided into an exhaustive set of 

home districts. Each home district is defined as one or more 

geographic units for which Bureau of Census (BOC) data are 

available. The commuting area is divided into an exhaustive set 
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of work districts. These are also based on BOC units, but are 

generally much larger in size than the home districts. Within 

the residential zone, the work districts are defined as 

contiguous sets of home districts. 

step 2: Define cohorts. 

To apply HAPEM to a particular source, the analyst must 

specify a method of dividing the population-at-risk into cohorts. 

Each cohort is assumed to contain persons with identical 

exposures during the specified exposure period. In typical 

applications, the analyst identifies each cohort as a distinct 

combination of 1) home district, 2) demographic group, and 3) 

work district (if applicable). Specifying the home and work 

districts of a cohort provides a means of linking cohort exposure 

to ambient pollutant concentrations. The demographic group 

specification provides a means of linking cohort exposure to 

activity patterns that vary with age and work status. 

Table I lists nine demographic groups defined for a recent 

HAPEM analysis, in this application, the analyst defined 35 home 

districts and 20 work districts. Each of the 6 nonworking 

demographic groups was associated with 35 cohorts, one for each 

possible home district. Each of the three working demographic 

groups was associated with 700 cohorts, one for each possible 

combination of home district and work district. The total number 

of cohorts was (6 x 35) + (3 x 700) or 2310. 

Step 3: Estimate Fraction of Time Spent by Each Cohort in Each 

combination of Geographic Location and Microenvironment. 

The HAPEM provides an algorithm for estimating the fraction 

of time each cohort spends at home and at work in user-specified 

microenvironments. The algorithm assembles an exposure event 

sequence for each cohort spanning the exposure period (a calendar 

year). Each sequence consists of 365 person-days sampled from an 

activity diary data base. 

in past analyses, the Cincinnati Activity Diary study2 has 

served as the source of this data base. During this study over 

900 subjects completed 3-day activity diaries and detailed background questionnaires. Each person-day of Cincinnati diary data 

was classified according to the four indices: demographic group 

(Table I), season (summer or winter), day type (weekday or weekend), and temperature range (high or low). The demographic group 

index was determined by the demographic group to which the 

subject filling out the diary belonged. The season and day type 

indices were based on the calendar date of the diary data. The 

temperature range index was based on the daily maximum 

temperature in Cincinnati on that date. Further information 
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TABLE I. Number of cohorts defined for a HAPEM analysis 

using 9 demographic groups, 35 home districts, and 

20 work districts. 

Demographic group 

Includes 

commuting 

cohorts 

Number of cohorts 

associated with 

group 

1. Children 0 to 5 

2. Children 6 to 13 

3. Children 14 to 18 years 

4. Workers with low probability 

of outdoor work 

5. Workers with moderate 

probability of outdoor work 

6. Workers with high probability 

of outdoor work 

7. Nonworking adults under 

35 years 

8. Nonworking adults 35 to 

54 years 

9. Nonworking adults 55+ years 

No 

No 

No 

yes 

Ves 

Yes 

No 

No 

No 

35 

35 

35 

700 

700 

700 

35 

35 

2310 

oncerning the classification procedure is provided by Johnson et 

l.1 con 

a 

To run the algorithm, the analyst provides a sequence of 

daily maximum temperatures for the study area for the calendar 

year under analysis (e.g., 1989). These data are used to assign 

each calendar day to one of the temperature ranges used in 

classifying the Cincinnati diary data. To construct the exposure 

event sequence for a particular cohort, the algorithm selects a 

person-day of Cincinnati diary data for each calendar day in 1989 

according to the demographic group of the cohort and the season, 

day type, and temperature range associated with the calendar day. 

Each exposure event sequence consists of a series of events 

with durations varying from 1 to 60 minutes. Each exposure event 

assigns the cohort to a particular combination of geographic 

location and microenvironment. The geographic location is either 

the home district or the work location associated with the 

cohort. The home/work decision is based on the activity diary 

data associated with the exposure event. The microenvironment 

assignment is typically either indoors or outdoors. Microenvironment codes appearing in the Cincinnati activity diary data 

base are used to determine these assignments. 
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The exposure event sequences are analyzed to determine the 

fraction of time spent by each cohort in each combination of 

geographic location and microenvironment. Table II lists these 

fractions for 9 cohorts. Each cohort represents 1 of the 9 

demographic groups in Table I. Fractions are specific to a 

location in North Carolina during 1989. 

Step 4: Estimate the Annual Average Exposure of Each Cohort. 

The annual average exposure of each cohort is estimated by 

the expression 

C(d,h,w) = s F(d,h,w,i,j) x M(i) x A(j) (l) 

where C(d,h,w) is the annual average pollutant concentration to 

which the cohort is exposed, d is the demographic group 

identifier, h is the home location identifier, w is the work 

location identifier (if applicable), F(d,h,w,i,j) is the fraction 

of time spent by the cohort in microenvironment i at location j, 

M(i) is the microenvironment factor associated with microenvironment i, and A(j) is the annual average ambient pollutant 

concentration for location j. The summation is carried out for 

all values of i and j. 

The values for F(d,h,w,i,j) are developed in Step 3. values 

of M(i) for the outdoor microenvironment [M(outdoors)] and for 

the indoor microenvironment [M(indoors)] are specified by the 

analyst. The value of M(outdoors) is typically assumed to be 

1.0. The value of M(indoors) is selected to represent a reasonable indoor/outdoor ratio for the pollutant in the absence of 

indoor sources. The value will be less than 1.0 if a pollutant 

has reactive properties or is adsorbed onto indoor surfaces. 

The location index (j) indicates either the cohort's home 

district or the cohort's work district. The value of A(j) for 

each home or work district is assumed to be constant over the 

entire district and to be equal to the average of the pollutant 

concentrations estimated for all receptors which fall within the 

district. 

Pollutant concentrations at the receptors are estimated by 

the industrial source complex long term (ISCLT) dispersion model. 

Input data for the ISCLT model include local meteorological data 

and an estimate of the pollutant emissions from the source. In a 

typical HAPEM application, the ISCLT dispersion model is used to 

estimate the annual average pollutant concentration at the 

centroid of each of the census units used to define the home and 

work districts, 36 fenceline locations spaced at 10' increments, 

and 396 receptors in 11 rings of 36 receptors each at various 

distances between 500 m and 10,000 m. The 10,000 ra ring defines 

the outer boundary of the residential zone. 
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TABLE II. Fraction of time spent by a cohort representing 

each demographic group in each combination of 

geographic location and microenvironment. 

Demography 

group* 

l 

2 

3 

4 

5 

6 

7 

8 

9 

a

 See Table 

Lc 

I 

Home 

Indoors 

0.926 

0.888 

0.921 

0.737 

0.752 

0.747 

0.938 

0.943 

0.951 

Fraction 

District 

outdoors 

0.074 

0.111 

0.079 

0.044 

0.053 

0.038 

0.062 

0.056 

0.049 

of time 

Work District 

Indoors 

0 

0 

0 

0.215 

0.164 

0.138 

0 

0 

0 

Outdoors 

0 

0 

0 

0.005 

0.031 

0.078 

0 

0 

0 

Step 5: Extrapolate Cohort Exposures to Population-at-Risk and 

Estimate Associated Risk. 

The cohort-specific exposure estimates developed in Step 4 

are extrapolated to the population-at-risk by estimating the size 

of each cohort. A special computer program estimates cohort 3ize 

directly from census and commuting data specific to each home 

district. These data are obtained from the BOC. 

A two-step process is used to determine cohort population. 

In Step 1, the population of each demographic group residing in a 

particular home district is calculated using detailed BOC data. 

This step provides the populations of all nonworking cohorts. 

The populations of the working cohorts are determined by further 

subdividing the populations of the working demographic groups 

associated with each home district. The formula used for this 

step is: 

Com(d,h,w) = Pop(d,h) x F(h,w) (2) 

where Cora(d,h,w) is the number of persons in the commuting cohort 

associated with demographic group d, home district h, and work 

district w; P(d,h) is the number of persons in demographic group 

d in home district h; and F(h,w) is the fraction of all workers 

residing in home district h who commute to work district w. 

Values of F(h,w) are obtained from an origin-destination 
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(0-D) table produced by a special commuting model. This model is 

described in detail in the next section of this paper. 

The population exposure estimate for a particular cohort is 

converted to an expected annual cancer incidence [I(d,h,w)] using 

the expression 

I(d,h,w) = C(d,h,w) x P(d,h,w) x URE/70 (3) 

where C(d,h,w) is the annual average pollutant concentration 

associated with the cohort, P(d,h,w) is the estimated population 

of the cohort, and URE is the lifetime (70-year) unit risk 

estimate for the pollutant. An exposure and risk value are 

estimated for each cohort, and the results are summed over all 

cohorts. The HAPEM provides histograms of annual average 

exposure concentrations for the population-at-risk. It also 

provides annual and lifetime cancer incidence estimates for each 

' home district and for the population-at-risk. The lifetime 

^incidence values are calculated by assuming the annual incidence 

estimated for each home district is repeated for 70 years. 

THE HAPEM COMMUTING MODEL 

The HAPEM and NEM are similar in that each model accounts 

for the mobility of working cohorts. Each uses Equation 2 to 

estimate the populations of these cohorts, and thus they require 

a table listing values for F(h,w). Each calculates F(h,w) by the 

expression: 

F(h,w) = Com(h,w)/Work(h) (4) 

where Com(h,w) is the number of workers in all demographic groups 

that commute from home district h to work district w and Work(h) 

is the total number of workers in home district h. The basic 

requirement for these calculations is an origin-destination (O-D) 

table listing Com(h,w) values for all combinations of h and w. 

In current NEM applications, Com(h,w) values are obtained 

from a special commuting data base. This data base, the Sixty 

Cities Data File (SCDF), contains o-D tables by census tract for 

60 cities based on surveys conducted by the BOC from 1975 to 

1977. The BOC asked each member of a random sample of commuters 

in each city to provide the addresses of his residence and 

workplace. These addresses were converted to census tracts to 

produce an O-D table. It should be noted that only O-D 

combinations specified by the sampled commuters appear in these 

tables. As the sampled commuters represent only a small fraction 

of the possible O-D combinations for a given city, the SCDF is 

best used for estimating general intercity commuting patterns 

rather than the number of commuters associated with a particular 

pair of home and work census tracts. 

8 
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Although the SCDF is currently the preferred source of O-D 

data for NEM, it has three significant deficiencies. First, the 

data are now 15 years old and may not accurately represent 

current urban commuting patterns. Second, the data exclude many 

smaller urbanized areas and all rural areas. Third, the data are 

"grainy" at the census tract level. As discussed above, this 

graininess reflects the small number of commuters who were 

surveyed in each of the 60 cities by the BOC. 

For HAPEM applications, PAB has investigated an indirect 

method for constructing o-D tables that uses trip duration data. 

Trip duration data are collected during each census for all areas 

of the U.S. The data are reported as the number of persons in 

each census unit with one-way commute times that fall into each 

of the following 8 commute duration ranges: 

1. Less than 5 minutes. 

2. 5 to 9 minutes. 

3. 10 to 14 minutes. 

4. 15 to 19 minutes. 

5. 20 to 29 minutes. 

6. 30 to 44 minutes. 

7. 45 to 59 minutes. 

8. 60+ minutes. 

The method assumes that each commute duration range can be 

converted into a corresponding range of geodesic distances. 

Geodesic distance is defined here as the shortest distance 

between two points on the globe, i.e., the distance "as the crow 

flies." 

Consider a commuter in a large urbanized area who reports 

that his commute takes between 20 and 29 minutes. If the average 

geodesic commute speed in the area is 0.3 kilometers per minute 

(km/min), the commute duration range of 20 to 29 minutes is 

equivalent to a geodesic distance range (GDR) of 6 to 8.7 km. 

In a similar manner, each of the eight commute distance 

ranges is converted to a GDR indexed as i = 1, 2, ..., 8. The 

location of each exposure district is represented by its 

geographic centroid. If the district is an origin location for 

commuters (i.e., a "home" district), one can delineate eight 

concentric rings centered on the centroid, one for each GDR. The 

i-th GDR centered on home district h is identified as GDR(h,i). 

Other useful terms are defined below. 

com(h): the number of commuters residing in home 

district h 

Com(h,i): the number of commuters residing in home 

district h who commute to a work district in 

GDR(h,i) 
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Com(h,i,w): the number of commuters residing in home 

district h who commute to work district w 

where work district w is in GDR(h,i) 

N(h,i): the number of work districts in GDR(h,i) 

Tot(h,i,w): the total number of commuters who work in 

work district w in GDR(h,i) 

Tot(h,i): the total number of commuters that work in 

GDR(h,i) (includes commuters frora all home 

districts) 

The indirect method for developing an o-D table can be 

stated as follows: 

1. com(h,i) and N(h,i) are known. Make an initial estimate 

of com(h,i,w) using the expression 

Cora(h,i,w) = [Com(h,i)]/[N(h,i)]. (5) 

2. Calculate Tot(h,i,w) by summing Com(h,i,w) values 

associated with specified w value. 

3. Calculate Tot(h,i) by summing Tot(h,i,w) values for all 

work districts in GDR(h,i). 

4. Make a new estimate of com(h,i,w) using the expression 

com(h,i,w) - [Com(h,i)][Tot(h,i,w)]/[Tot(h,i)]. (6) 

5. Go to Step 2. 

In Step l, commuters associated with a particular combination of 

home district and GDR are evenly distributed across the work 

districts in the GDR. This step is Iteration 0. Steps 2 through 

4 are repeated n times where n is determined by the user. In 

each iteration of Steps 2 through 4, the commuters are 

redistributed across the work districts in the GDR in proportion 

to the number of workers assigned to each work district during 

the last iteration. 

Test Using A Hypothetical Data Set 

As an initial test of the indirect method, analysts created 

a hypothetical study area containing 16 exposure districts. 

Based on the distances between the centroids of these districts, 

a hypothetical o-D table was developed in which short commutes 

were more numerous than long commutes. 

The table provided 256 "actual" Com(h,i,w) values, one for 

each possible combination of home and work district. The table 

also provided a value for the distance separating each pair of 

10 
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home and work districts. These distances were converted to 

commute times. Based on these commute times, each work district 

was assigned to a GDR with respect to each home district. 

These assignments provided a means of constructing a trip 

duration table similar in format to that which would be provided 

by the BOC. If 50 commuters in home district h traveled to work 

districts within the GDR denoted as 5 to 9 minutes, it was 

assumed that BOC records would indicate that 50 residents of home 

district h commuted 5 to 9 minutes. Applying this procedure to 

all home districts and all GDR's, analysts were able to create a 

trip duration table that was completely consistent with the 

"source" O-D table. 

The indirect procedure described above was applied to this 

trip duration table with the goal of recreating the source 0-D 

table. The result was a pair of values for each combination of 

home and work district: the "actual" Com(h,i,w) value and the 

model estimate. If the procedure performed perfectly, then the 

actual and estimated values would be identical for each combination. A linear regression analysis of actual versus estimate 

would yield a slope value of 1.00, an intercept of 0, and an Rsquared value of l.oo. Regression results close to these values 

indicate that the model performs well. 

In performing the test, analysts found that model performance improved with each iteration of the procedure. Table 

III lists the slope, intercept, and R-squared value for selected 

values of n, where n is the number of iterations. Note that n -

0 indicates even distribution of commuters among work districts 

(i.e., implementation of Step l only). The R-squared values in 

Table III increase as n increases. Model performance at n • 10 

is quite good: slope = 1.0511, intercept = -2.0005 commuters, 

and R-squared value = 0.9319. At n = 100, performance is 

excellent: slope = 0.9973, intercept = 0.0931 commuter, and Rsquared value - 0.9705. 

These results probably represent the upper bound of model 

performance that can be expected when real trip duration data are 

used for model input. The test used hypothetical trip duration 

data that were complete and internally consistent. The model 

output (i.e., the estimated O-D table) was compared to an 

"actual" o-D table that was perfectly consistent with the input 

trip duration data. Tests using real data will be affected by 

errors and missing values in both the input trip duration data 

obtained from the BOC and the O-D table used to validate the 

model output. The next section of this paper presents the 

results of tests using real data. 

11 
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TABLE III. Results for hypothetical study area of linear 

regression analyses of actual versus estimated 

number of commuters 

Results of linear regression analysis of actual 

versus estimated values (n-256) 

Iteration 

o

a 

r-l 2 

5 

10 

15 

20 

30 

50 

100 

Slope 

0.9988 

1.1183 

1.0992 

1.0662 

1.0511 

1.0378 

1.0253 

1.0092 

0.9991 

0.9973 

Intercept 

0.0784 

4.6067 

3.8827 

2.6105 

2.0005 

1.4912 

0.9820 

0.3676 

0.0115 

0.0931 

0.4831 

0.7026 

0.7810 

0.8753 

0.9319 

0.9539 

0.9629 

0.9685 

0.9703 

0.9705 

d Even distribution of commuters within each geodesic distance 

range. 

Test Using Atlanta Data 

Atlanta, Georgia was selected for testing purposes because 

validation data were available for Atlanta from the SCDF. Test 

data were prepared as follows. Trip duration data for 1980 were 

obtained for the city at the census tract level from the BOC. 

The SCDF provided o-D data for Atlanta for 1975, also at the 

census tract level. As the two data sets did not use a 

consistent set of census tract boundaries, a special program was 

developed to aggregate the census tracts used in each data set 

into a set of exposure districts with boundaries consistent with 

both data sets. 

Two impact areas were defined. The residential zone (Zone 

R) included the 103 exposure districts within 10 km of an imaginary emission source positioned near the city center. The commuting zone (Zone C) was defined as including the 232 exposure 

districts within 50 km of the emission source. Zone R was 

assumed to include all home and work locations with significant 

ambient pollutant concentrations associated with the source. We 

assumed that impact Zone c, which contains all of Zone R, included all possible work locations associated with residents of 

Zone R. 

12 
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The model was applied to trip duration data for the 

residents of Zone R using a series of assumed geodesic speeds 

between 0.26 km/min and 0.52 km/min. Ten iterations were 

specified for each model run. Each run produced an 0-D table 

listing an estimate of the number of commuters associated with 

each of 23,896 o-D combinations (i.e., 103 home districts x 232 

work districts). 

A similar O-D table was developed from the SCDF. Because 

the SCDF data are based on a relatively small sample of Atlanta 

commuters, only 2307 of the 23,896 modeled 0-D combinations 

appeared in the SCDF O-D table. To provide a means of comparing 

the detailed model estimates with the "grainy" SCDF data, 

analysts aggregated the 232 districts within Zone C into 20 

"super districts." The super districts were defined by radial 

lines from the emission source at the four compass points and by 

five circles with centers at the source and radii of 2 km, 5 km, 

10 km, 20 km, and 50 km. This scheme produced 12 super districts 

within zone R and 8 outside Zone R. Two of the super districts 

near the source in Zone R were subsequently found to contain no 

exposure districts and were omitted from the comparison. Thus, 

the comparison included io super districts in Zone R and 8 super 

districts outside Zone R. 

The comparison was conducted as follows. A super district 

o-D table was developed from the model estimates for a particular 

geodesic speed. A corresponding super district O-D table was 

developed from the SCDF. The two tables were combined to produce 

a table which listed a model estimate and a SCDF estimate for 

each combination of home super district and work super district. 

The table provided data for 180 0-D combinations: 10 home super 

districts in Zone R x 18 work super districts in Zone C. As 

discussed above, only commuting trips originating in zone R were 

considered in the analysis. 

Several statistically-derived indicators were used to assess 

the level-of-agreement between the modeled and SCDF values. 

Three of these indicators were obtained through linear regression 

analyses where the SCDF value was the dependent value and the 

modeled value was the independent value. Each analysis yielded 

an intercept value, a slope value, and an R-squared value. A 

perfect match-up would produce an intercept of zero, a slope of 

0.79, and an R-squared value of 1.0. The specified slope value 

(0.79) is not unity because the population represented by the 

SCDF data (140,106) is less than the population represented by 

the model estimates (177,730). The ratio of these populations is 

0.79. If the two populations were equal, the slope value 

associated with a perfect match-up would be 1.0. 

13 
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91-172.6 

We also used the Spearman rank coefficient as an indicator 

of the level-of-agreement between modeled and SCDF values. As an 

indicator of correlation, this statistic may be preferable to the 

R-squared value, as the Spearman coefficient is not based on any 

assumptions concerning the distribution of the values being 

compared. 

Table IV provides modeling results for 5 assumed geodesic 

speeds. For each geodesic speed, the linear regression coefficients and the Spearman coefficient are provided for each of 

two work location categories: l) inside Zone R only and 2) all 

work locations within Zone C. Based on the Spearman rank coefficient, the geodesic speed producing the best possible match-up 

of model and SCDF values appears to fall somewhere between 0.30 

km/min and 0.35 km/min. The Spearman rank coefficient exceeds 

0.72 within this range for both work location categories. 

Table IV also provides model-derived estimates for the 

fraction of commuters residing in Zone R that work outside 

Zone R. Estimates range from 0.097 to 0.540, suggesting that 

this fraction is highly sensitive to the choice of geodesic 

speed. Based on the 0-D table derived from the SCDF, we would 

estimate the "true" fraction to be 0.244. The closest modeled 

value (0.218) corresponds to a geodesic speed of 0.35 km/min. 

These analyses suggest that 0.35 is close to the optimum 

geodesic speed for the modeled area. Similar analyses can be 

conducted for other areas to determine whether a "rule-of-thumb" 

geodesic speed exists which is applicable to most areas. 

SUMMARY AND DISCUSSION 

The HAPEM methodology attempts to account for various 

factors that are expected to affect exposure to hazardous air 

pollutants in populations residing near emission sources. These 

factors include age, work status, residential location, and work 

location. Considered together, they provide a means for defining 

a collection of cohorts, each with a distinct pattern of 

exposure. 

An 0-D table listing the number of commuters associated with 

each combination of home location and work location is necessary 

for estimating the size of each working cohort. A commuting 

model that estimates values in the O-D table based on BOC trip 

duration data has been developed and applied to Atlanta, GA. The 

correlation between O-D table values estimated by the model and 

corresponding values obtained from the SCDF exceeded 0.72 for 

assumed geodesic speeds between 0.30 km/min and 0.35 km/min. 

Additional testing of the commuting model is planned. 

14 
TABLE IV. CasparISOB of coamnting model estiaates Mitb 'lita obtained frcm 

tbe sixty cities data file. 

Geodesic 

Speed, to/Min 

0.26 

0.30 

0.35 

0.42 

0.52 

Itart Location" 

Zone C 

Zone R 

2o«ie C 

Zone R 

Zone C 

Zone B 

Zone C 

Zone E 

Zone C 

Zone R 

n 

ieo 

100 

180 

100 

180 

100 

180 

100 

180 

100 

Linear Regression Gesults 

Intercept 

230 

200 

109 

34 

36 

71 

17 

224 

265 

392 

Slope 

0.554 

0.535 

0.676 

0.672 

0.748 

0.708 

0.767 

0.716 

0.516 

0.810 

R

2 

0.392 

0.370 

0.442 

0.425 

0.443 

0.388 

0.377 

0.305 

0.184 

0.208 

Spearaan 

Rank 

Coefficient 

0.683 

0.754 

0.720 

0.766 

0.767 

0.727 

0.733 

0.648 

0.603 

0.557 

Estinated Fraction 

Counting Outside 

Zone R 

0.097 

0.141 

0.213 

0.347 

0.540 

* Zone C: all mit districts within 50 in of source 

Zone P.: all wart districts to thia 10 km of source 

I 

"^1 

Csi 

TJ 

O) 
P.17 

91-172.6 

The HAPEM is an evolving model that the PAB intends to update and refine as new data become available. For example, PAB 

is currently reviewing new research which provides estimates of 

M(indoors), the ratio of indoor to outdoor concentration, for a 

number of hazardous pollutants. The PAB also intends to add an 

area source modeling capability to HAPEM and to provide 

algorithms for estimating exposure by nonair routes such as 

ingestion. 

ACKNOWLEDGMENTS 

The authors would like to thank Roy Paul for obtaining 

the BOC data used for testing the commuting model. Jim Capel 

processed these data for input into the commuting model* 

Ted Johnson developed the commuting model and performed the tests 

described in this report. 

This study was funded by EPA under Contract No. 68-DO-0062. 

Mr. Tom Lahre served as EPA Work Assignment Manager for the 

project. Ms. Dianne Byrne is the chief of the Program Analysis 

and Technology Section of the Pollutant Assessment Branch. 

Ms. Byrne's section is responsible for developing and maintaining 

exposure models used to assess risk from hazardous air 

pollutants. 

REFERENCES 

1. T. Johnson, R. Paul, J. Capel, and T. McCurdy, "Estimation of 

Ozone Exposure in Houston Using a Probabilistic Version of NEM," 

Paper No. 90-150.1, Presented at 83rd Annual Meeting of the Air 

and waste Management Association, Pittsburgh, June 1990. 

2. T. Johnson, A Study of Human Activity Patterns in Cincinnati. 

Ohio, Electric Power Research Institute, Palo Alto, November 

1987. 

3. 1977 Nationwide Personal Transportation Study Home-tn-Work 

TrJPs and Travel. U.S. Department of Transportation, Federal 

Highway Administration, FHWA/PL/81/002, December 1980. 

16 

TOTAL P.17