Ozone Population Exposure Analysis for 

Selected Urban Areas 

EPA-452/R-07-010 

July 2007 

Ozone Population Exposure Analysis for Selected Urban Areas 

U.S. Environmental Protection Agency 

Office of Air Quality Planning and Standards 

Health and Environmental Impacts Division 

Ambient Standards Group 

Research Triangle Park, North Carolina 
DISCLAIMER 

 This document has been prepared by staff from the Ambient Standards Group, Office of 

Air Quality Planning and Standards, U.S. Environmental Protection Agency, in conjunction with 

ICF Consulting (through Contract No. 68-D-01-052) and Alion Science and Technology, Inc. 

(through Contract No. 68-D-00-206). Any opinions, findings, conclusions, or recommendations 

are those of the authors and do not necessarily reflect the views of the EPA, ICF Consulting, or 

Alion Science and Technology, Inc. This document is being circulated to obtain review and 

comment from the Clean Air Scientific Advisory Committee (CASAC) and the general public. 

Comments on this document should be addressed to John E. Langstaff, U.S. Environmental 

Protection Agency, Office of Air Quality Planning and Standards, C504-06, Research Triangle 

Park, North Carolina 27711 (email: langstaff.john@epa.gov). 
 i

Table of Contents 

1. INTRODUCTION................................................................................................................. 1

1.1 Selection of Urban Areas ............................................................................................ 1 

1.2 Exposure Periods ........................................................................................................ 2 

1.3 Populations Analyzed ................................................................................................. 2 

2. DESCRIPTION OF THE APEX MODEL......................................................................... 3

2.1 History of APEX......................................................................................................... 3 

2.2 Theoretical Basis and Limitations of APEX............................................................... 4 

2.3 Overview of Model ..................................................................................................... 5 

2.3.1 Characterize the Study Area........................................................................ 10 

2.3.2 Generate Simulated Individuals .................................................................. 10 

2.3.3 Construction of Activity Sequences............................................................ 12 

2.4 Algorithms for Calculating Microenvironmental Concentrations ............................ 13 

2.4.1 Mass Balance Model ................................................................................... 13 

2.4.2 Factors Model.............................................................................................. 16 

2.4.3 Commuting Outside of the Study Area ....................................................... 17 

2.5 Algorithms for Calculating Dose .............................................................................. 18 

2.5.1 Ventilation................................................................................................... 18 

2.5.2 Excess Post-Exercise Oxygen Consumption............................................... 20 

2.5.3 Body Surface Area ...................................................................................... 20 

2.6 Exposure Calculations .............................................................................................. 20 

2.7 Model Output ............................................................................................................ 21 

3. PREPARATION OF MODEL INPUTS........................................................................... 23

3.1 Model Options .......................................................................................................... 23 

3.2 Air Quality ................................................................................................................ 23 

3.3 Air Quality Projections for Alternative Standards Scenarios ................................... 24 

3.4 Meteorological Data.................................................................................................. 25 

3.5 Population Demographics......................................................................................... 26 

3.6 Asthma Prevalence Rates.......................................................................................... 27 

3.7 Commuting Database................................................................................................ 27 

3.8 Activity Patterns – CHAD ........................................................................................ 28 

3.9 Physiological Distributions....................................................................................... 32 

3.10 Microenvironment Specifications............................................................................. 33 

3.10.1 Microenvironments Modeled ...................................................................... 34 

3.10.2 Microenvironment Descriptions.................................................................. 35 

3.10.3 Ozone Decay and Deposition Rates ............................................................ 38 

3.10.4 Microenvironment Mapping ....................................................................... 39 

3.11 Profile Functions....................................................................................................... 41

4. PRINCIPAL LIMITATIONS AND UNCERTAINTIES OF THE MODELING 

APPROACH........................................................................................................................ 43

4.1 Methodology ............................................................................................................. 43 
 ii

4.2 Input Data.................................................................................................................. 43 

4.2.1 Meteorological Data.................................................................................... 44 

4.2.2 Air Quality Data .......................................................................................... 44 

4.2.3 Population and Commuting Data ................................................................ 44 

4.2.4 Physiological Data....................................................................................... 44 

4.2.5 Activity Pattern Data................................................................................... 45 

4.2.6 Air Exchange Rates..................................................................................... 45 

4.2.7 Air Conditioning Prevalence....................................................................... 47 

4.2.8 Evaporative Coolers .................................................................................... 47 

5. RESULTS OF EXPOSURE MODELING ....................................................................... 49

5.1 Base case................................................................................................................... 49 

5.2 Attainment scenarios................................................................................................. 55 

6. SENSITIVITY STUDIES................................................................................................... 63

6.1 Activity Pattern Database ......................................................................................... 63 

6.2 Ozone Decay Rate..................................................................................................... 67 

6.3 Proximity Factor ....................................................................................................... 68 

6.4 Air Exchange Rates................................................................................................... 69 

6.5 Long-term activity patterns....................................................................................... 71 

6.6 Near roadway locations............................................................................................. 73 

6.6.1 Proximity Probabilities................................................................................ 73 

6.6.2 Results ......................................................................................................... 74 

6.7 Sensitivity summary.................................................................................................. 74 

7. MODEL EVALUATION ................................................................................................... 81

8. REFERENCES.................................................................................................................... 93

 

APPENDIX A. ANALYSIS OF AIR EXCHANGE RATE DATA 

APPENDIX B. THEORETICAL DEVELOPMENT OF A UNIFIED ALGORITHM 

APPENDIX C. A NEW METHOD OF LONGITUDINAL DIARY ASSEMBLY 

APPENDIX D. UNCERTAINTY ANALYSIS OF RESIDENTIAL AIR EXCHANGE RATE 

DISTRIBUTIONS 

APPENDIX E. DISTRIBUTIONS OF AIR EXCHANGE RATE AVERAGES OVER 

MULTIPLE DAYS 

APPENDIX F. PREVALENCE OF RESIDENTIAL AIR CONDITIONERS AND THE 

EFFECTS OF SWAMP COOLERS 

APPENDIX G. ANALYSIS OF NHIS ASTHMA PREVALENCE DATA 

APPENDIX H. ALTERNATIVE LONGITUDINAL ACTIVITY PATTERN ALGORITHM 

APPENDIX I. ESTIMATING NEAR ROADWAY POPULATIONS 
 iii

List of Tables 

Table 1-1. Urban areas and time periods modeled ........................................................................ 2 

Table 2-1. Profile Variables in APEX ......................................................................................... 11 

Table 2-2. Mass Balance Model Parameters................................................................................ 14 

Table 2-3. Factors Model Parameters .......................................................................................... 17 

Table 2-4. Ventilation Regression Parameters............................................................................. 19 

Table 2-5. APEX Output Files..................................................................................................... 21 

Table 3-1 The Numbers of Ozone Monitors in the Study Areas ............................................... 24 

Table 3-2. List of the Current and Alternative 8-hour Ozone Standard Scenarios used in the 

Exposure Analysis ................................................................................................................ 25 

Table 3-3 The Meteorological Stations for Each Study Area.................................................... 26 

Table 3-3. Summary of Studies Used in CHAD.......................................................................... 30 

Table 3-4. Microenvironment Parameter Information................................................................. 33 

Table 3-5. List of Microenvironments and Calculation Methods Used....................................... 34 

Table 3-6. Mapping of CHAD activity locations to APEX microenvironments ........................ 39 

Table 4-1. Assignment of residential air exchange rate distributions to modeled CSAs ............ 46 

Table 6-1. Sensitivity to activity database with base case air quality: 2002 counts of the general 

population with any or three or more 8-hour ozone exposures above 0.07 ppm concomitant 

with moderate or greater exertion......................................................................................... 64 

Table 6-2. Sensitivity to activity database with base case air quality: 2002 counts of children 

(ages 5-18) with any or three or more 8-hour ozone exposures above 0.07 ppm concomitant 

with moderate or greater exertion......................................................................................... 64 

Table 6-3. Sensitivity to activity database with air quality meeting the current standard: 2002 

counts of the general population with any or three or more 8-hour ozone exposures above 

0.07 ppm concomitant with moderate or greater exertion. ................................................... 65 

Table 6-4. Sensitivity to activity database with air quality meeting the current standard: 2002 

counts of children (ages 5-18) with any or three or more 8-hour ozone exposures above 0.07 

ppm concomitant with moderate or greater exertion. ........................................................... 65 

Table 6-5. Sensitivity to activity database: 2002 simulated counts of Los Angeles CSA general 

population and children (ages 5-18) with any or three or more 8-hour ozone exposures 

above 0.07 ppm concomitant with moderate or greater exertion.......................................... 66 

Table 6-6. Sensitivity to activity database: 2002 simulated counts of Sacramento CSA general 

population and children (ages 5-18) with any or three or more 8-hour ozone exposures 

above 0.07 ppm concomitant with moderate or greater exertion.......................................... 67 

Table 6-7. Sensitivity to ozone decay rate: 2002 counts of general population with any or three 

or more 8-hour ozone exposures above 0.07 ppm concomitant with moderate or greater 

exertion. ................................................................................................................................ 67 

Table 6-8. Sensitivity to ozone decay rate: 2002 counts of children (ages 5-18) with any or three 

or more 8-hour ozone exposures above 0.07 ppm concomitant with moderate or greater 

exertion. ................................................................................................................................ 68 

Table 6-9. Sensitivity to proximity factor: 2002 counts of general population with any or three 

or more 8-hour ozone exposures above 0.07 ppm concomitant with moderate or greater 

exertion ................................................................................................................................. 68 
 iv

Table 6-10. Sensitivity to proximity factor: 2002 counts of children (ages 5-18) with any or 

three or more 8-hour ozone exposures above 0.07 ppm concomitant with moderate or 

greater exertion ..................................................................................................................... 69 

Table 6-11. Sensitivity to air exchange rate: 2002 counts of general population with any or three 

or more 8-hour ozone exposures above 0.07 ppm concomitant with moderate or greater 

exertion ................................................................................................................................. 69 

Table 6-12. Sensitivity to air exchange rate: 2002 counts of children (ages 5-18) with any or 

three or more 8-hour ozone exposures above 0.07 ppm concomitant with moderate or 

greater exertion ..................................................................................................................... 70 

Table 6-13. Sensitivity to air exchange rate: 2002 simulated counts of New York CSA general 

population and children (ages 5-18) with any or three or more 8-hour ozone exposures 

above 0.07 ppm concomitant with moderate or greater exertion.......................................... 70 

Table 6-14. Sensitivity to longitudinal activity pattern algorithm: 2002 counts of Boston 

population groups with any or three or more 8-hour ozone exposures above 0.07 ppm 

concomitant with moderate or greater exertion. ................................................................... 71 

Table 6-15. Sensitivity to longitudinal diary algorithm: 2002 simulated counts of Atlanta general 

population and children (ages 5-18) with any or three or more 8-hour ozone exposures 

above 0.07 ppm concomitant with moderate or greater exertion.......................................... 72 

Table 6-16. Sensitivity to longitudinal diary algorithm: 2002 days per person with 8-hour ozone 

exposures above 0.07 ppm concomitant with moderate or greater exertion for Atlanta 

general population and children (ages 5-18)......................................................................... 72 

Table 6-17. Sensitivity to near roadway proximity for indoor sources: 2002 counts of children 

(ages 5-18) with any or three or more 8-hour ozone exposures above 0.07 ppm concomitant 

with moderate or greater exertion......................................................................................... 74 
 v

Acknowledgements 

In addition to EPA staff, the following people contributed to writing this document. 

ICF Consulting, San Francisco, CA and RTP, NC 

Arlene Rosenbaum 

Jonathan Cohen 

Dan Bowman 

Alion Science and Technology Inc, RTP, NC 

Kristin Isaacs 

Graham Glen 

Luther Smith 
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1. INTRODUCTION 

The Clean Air Act, which was last amended in 1990, requires EPA to set National 

Ambient Air Quality Standards (NAAQS) for widespread pollutants from numerous and diverse 

sources considered harmful to public health and the environment. EPA has set NAAQS for the 

following pollutants, which are called “criteria” pollutants: ozone, particulate matter, carbon 

monoxide, sulfur dioxide, nitrogen oxides, and lead. The Clean Air Act requires periodic review 

of the science upon which the standards are based and the standards themselves to (1) ensure that 

they provide adequate health and environmental protection and (2) update those standards as 

necessary. 

Under the NAAQS review process, EPA's Office of Research and Development (ORD) 

develops an “air quality criteria document” – a compilation and evaluation by EPA scientific 

staff and other expert authors of the latest scientific knowledge useful in assessing the health and 

welfare effects of the air pollutant. In August 2005, the second external review draft of the Air 

Quality Criteria for Ozone and Related Photochemical Oxidants was released for public 

comment and review by EPA's Clean Air Scientific Advisory Committee (CASAC), and a final 

document was released in 2006 (Ozone Criteria Document, US EPA, 2006a). The Ozone 

Criteria Document presents the latest available pertinent information on atmospheric science, air 

quality, exposure, dosimetry, health effects, and environmental effects of ozone and other related 

photochemical oxidants. 

This report documents the methodology and input data used in the inhalation exposure 

assessment for ozone conducted in support of the current review of the ozone NAAQS. 

Specifically, this report includes the following: 

• Summary of the overall inhalation exposure assessment methodology; 

• Description of the inhalation exposure model used in this assessment; 

• Description of the input data used for the 12 selected urban areas; 

• Assessment of the quality and limitations of the input data for supporting the goals of 

the ozone NAAQS exposure analysis; and 

• Sensitivity analyses. 

 The results of the exposure modeling are presented and discussed in the Ozone Staff 

Paper (US EPA, 2007); only selected results are presented in this report. 

 An error was found in the exposure model in January 2007. This error has been corrected 

and the model runs have been redone, except where noted otherwise, generally resulting in small 

increases in the exposure estimates. The corrected results are presented in this Staff Paper and in 

the Exposure Analysis TSD. 
 2 

1.1 Selection of Urban Areas 

The selection of urban areas to include in the exposure analysis takes into consideration 

the location of ozone field and epidemiology studies, the availability of ambient monitoring data 

for ozone, and the desire to represent a range of geographic areas, population demographics, and 

ozone climatology. These selection criteria are discussed further in the Ozone Staff Paper. 

Based on these criteria, EPA selected the 12 urban areas in Table 1 for inclusion in the exposure 

analysis: 

1.2 Exposure Periods 

The exposure periods modeled were the ozone monitoring seasons for three years, 2002, 

2003, and 2004. The seasons modeled for each area are listed in Table 1-1. 

Table 1-1. Urban areas and time periods modeled 

Urban Area (CSA) Period modeled 

Atlanta-Sandy Springs-Gainesville, GA-AL March 1 to Oct. 31 

Boston-Worcester-Manchester, MA-NH April 1 to Sept. 30 

Chicago-Naperville-Michigan City, IL-IN-WI April 1 to Sept. 30 

Cleveland-Akron-Elyria, OH April 1 to Oct. 31 

Detroit-Warren-Flint, MI April 1 to Sept. 30 

Houston-Baytown-Huntsville, TX Jan. 1 to Dec. 30 

Los Angeles-Long Beach-Riverside, CA Jan. 1 to Dec. 30 

New York-Newark-Bridgeport, NY-NJ-CT-PA April 1 to Sept. 30 

Philadelphia-Camden-Vineland, PA-NJ-DE-MD April 1 to Oct. 31 

Sacramento--Arden-Arcade--Truckee, CA-NV Jan. 1 to Dec. 30 

St. Louis-St. Charles-Farmington, MO-IL April 1 to Oct. 31 

Washington-Baltimore-N. Virginia, DC-MD-VA-WV April 1 to Oct. 31 

1.3 Populations Analyzed 

Exposure modeling was conducted for the general population residing in each area 

modeled, as well as for school-age children (ages 5 to 18) and asthmatic school-age children. 

Due to the increased amount of time spent outdoors engaged in relatively high levels of physical 

activity, school-age children as a group are particularly at risk for experiencing ozone-related 

health effects. 
 3 

2. DESCRIPTION OF THE APEX MODEL 

The Air Pollutants Exposure model (APEX) is a personal computer (PC)-based program 

designed to estimate human exposure to criteria and air toxic pollutants at the local, urban, and 

consolidated metropolitan levels. APEX, also known as TRIM.Expo, is the human inhalation 

exposure module of EPA’s Total Risk Integrated Methodology (TRIM) model framework (EPA, 

1999), a modeling system with multimedia capabilities for assessing human health and 

ecological risks from hazardous and criteria air pollutants. It is being developed to support 

evaluations with a scientifically sound, flexible, and user-friendly methodology. Additional 

information on the TRIM modeling system, as well as downloads of the APEX Model, user’s 

guide, and other supporting documentation, can be found on EPA’s Technology Transfer 

Network (TTN) at http://www.epa.gov/ttn/fera. 

2.1 History of APEX 

APEX was derived from the National Ambient Air Quality Standards (NAAQS) 

Exposure Model (NEM) series of models. The NEM series was developed to estimate exposure 

to the criteria pollutants (e.g., CO, ozone). In 1979, EPA began to develop NEM by assembling 

a database of human activity patterns that could be used to estimate exposures to indoor and 

outdoor pollutants (Roddin et al., 1979). The data were then combined with measured outdoor 

concentrations in NEM to estimate exposures to CO (Biller et al., 1981; Johnson and Paul, 

1983). In 1988, OAQPS began to incorporate probabilistic elements into the NEM methodology 

and use activity pattern data based on various human activity diary studies to create an early 

version of probabilistic NEM for ozone (i.e., pNEM/O3). In 1991, a probabilistic version of 

NEM was developed for CO (pNEM/CO) that included a one-compartment mass-balance model 

to estimate CO concentrations in indoor microenvironments. The application of this model to 

Denver, Colorado has been documented in Johnson et al. (1992). Several newer versions of 

pNEM/O3 were developed in the early- to mid-1990’s, including versions developed for 

applications to nine urban areas for the general population, outdoor children, and outdoor 

workers (Johnson et al., 1996a,b,c). Between 1999 and 2001, updated versions of pNEM/CO 

(versions 2.0 and 2.1) were developed that rely on activity diary data from EPA’s Consolidated 

Human Activities Database (CHAD) and enhanced algorithms for simulating gas stove usage, 

estimating alveolar ventilation rate (a measure of human respiration), and modeling home-towork commuting patterns. 

The first version of APEX was essentially identical to pNEM/CO (version 2.0) except 

that it ran on a PC instead of a mainframe. The next version, APEX2, was substantially 

different, particularly in the use of a personal profile approach rather than a cohort simulation 

approach. APEX3 introduced a number of new features including automatic site selection from 

national databases, a series of new output tables providing summary exposure and dose statistics, 

and a thoroughly reorganized method of describing microenvironments and their parameters. 

Most of the spatial and temporal constraints of pNEM and APEX1 were removed or relaxed by 

version 3. 
 4 

The version of APEX used in this modeling analysis is APEX4, described in the APEX 

User’s Guide and the APEX Technical Support Document (EPA, 2006c,d), henceforth referred 

to as the APEX User’s Guide and TSD. 

2.2 Theoretical Basis and Limitations of APEX 

APEX estimates human exposure to criteria and toxic air pollutants at the local, urban, or 

consolidated metropolitan area levels using a stochastic, 

“microenvironmental” approach. The model randomly 

selects data for a sample of hypothetical individuals from 

an actual population database and simulates each 

hypothetical individual’s movements through time and 

space (e.g., at home, in vehicles) to estimate their 

exposure to the subject pollutant. APEX models 

commuting and thus exposures at both home and work 

locations for individuals who work in different areas than 

they live. 

APEX can be conceptualized as a simulated field study that would involve selecting an 

actual sample of specific individuals who live in (or work and live in) a geographic area and then 

continuously monitoring their activities and subsequent inhalation exposure to a specific air 

pollutant during a specific period of time. 

The main differences between APEX and an actual field study are that in APEX: 

• The sample of individuals is a “virtual” sample, created by the model according to 

various demographic variables and census data of relative frequencies, in order to obtain 

a representative sample (to the extent possible) of the actual people in the study area; 

• The activity patterns of the sampled individuals (e.g., the specification of indoor and 

other microenvironments visited and the time spent in each) are assumed by the model to 

be comparable to individuals with similar demographic characteristics, according to 

activity data such as diaries compiled in EPA’s CHAD (EPA, 2002; McCurdy et al., 

2000); 

• The pollutant exposure concentrations are estimated by the model using a set of userinput ambient outdoor concentrations and information on the behavior of the pollutant in 

various microenvironments; 

• Various reductions in ambient air quality levels can be simulated by either adjusting air 

quality concentrations to attain alternative ambient standards under consideration or by 

reducing source emissions and obtaining resulting air quality modeling outputs that 

reflect these potential emission reductions, and 

• The model attempts to account for the most significant factors contributing to inhalation 

exposure – the temporal and spatial distribution of people and pollutant concentrations 

A microenvironment is a threedimensional space in which human 

contact with an environmental 

pollutant takes place and which can 

be treated as a well-characterized, 

relatively homogeneous location with 

respect to pollutant concentrations for 

a specified time period. 
 5 

throughout the study area and among the microenvironments – while also allowing the 

flexibility to adjust some of these factors for regulatory assessment and other reasons. 

All models have limitations that require the use of assumptions. Limitations of APEX lie 

primarily in the uncertainties associated with data distributions input to the model (e.g., human 

activity patterns). Primary uncertainties and assumptions associated with these distributions 

include the following: 

• The population activity pattern data supplied with APEX (i.e., CHAD activity data) are 

compiled from a number of studies in different areas, and for different seasons and years. 

Therefore, the combined data set may not constitute a representative sample for a 

particular study scenario. Nevertheless, a large portion of CHAD is from a study of 

national scope (which could be extracted by the user if desired to create a representative 

sample). 

• Commuting pattern data were derived from the 2000 U.S. Census. The commuting data 

address only home-to-work travel. The population not employed outside the home is 

assumed to always remain in the residential census tract. Furthermore, although several 

of the APEX microenvironments account for time spent in travel, the travel is assumed to 

always occur in basically a composite of the home and work tract. No other provision is 

made for the possibility of passing through other tracts during travel. 

• APEX creates seasonal or annual sequences of daily activities for a simulated individual 

by sampling human activity data from more than one subject. Each simulated person 

essentially becomes a composite of several actual people in the underlying activity data. 

• The model currently does not capture certain correlations among human activities that 

can impact microenvironmental concentrations (for example, cigarette smoking leading 

to an individual opening a window, which in turn affects the amount of outdoor air 

penetrating the residence). 

• Certain aspects of the personal profiles are held constant, though in reality they change as 

individuals age. This is generally only an issue for simulations with long timeframes. 

These and other uncertainties are discussed in section 4. 

2.3 Overview of Model 

APEX is designed to simulate population exposure to criteria and air toxic pollutants at 

local, urban, and regional scales. The user specifies the geographic area to be modeled and the 

number of individuals to be simulated to represent this population. APEX then generates a 

personal profile for each simulated person that specifies various parameter values required by the 

model. The model next uses diary-derived time/activity data matched to each personal profile to 

generate an exposure event sequence (also referred to as “activity pattern” or “composite diary”) 

for the modeled individual that spans a specified time period, such as one year. Each event in the 

sequence specifies a start time, exposure duration, geographic location, microenvironment, and 

activity. Probabilistic algorithms are used to estimate the pollutant concentration and ventilation 
 6 

(respiration) rate associated with each exposure event. The estimated pollutant concentrations 

account for the effects of ambient (outdoor) pollutant concentration, penetration factors, air 

exchange rates, decay/deposition rates, and proximity to emission sources, depending on the 

microenvironment, available data, and estimation method selected by the user. The ventilation 

rate is derived from an energy expenditure rate estimated for the specified activity. Because the 

modeled individuals represent a random sample of the population of interest, the distribution of 

modeled individual exposures can be extrapolated to the larger population. The model 

simulation includes five steps, each of which is described in the sections indicated below: 

1. Characterize the study area. APEX selects census tracts within a study area – and thus 

identifies the potentially exposed population – based on user-defined criteria and 

availability of air quality and meteorological data for the area. (Section 2.3.1) 

2. Generate simulated individuals. APEX stochastically generates a sample of 

hypothetical individuals based on the census data for the study area and human profile 

distribution data (such as age-specific employment probabilities). The user must specify 

the size of the sample. The larger the sample, the more representative it is of the 

population in the study area and the more stable the model results are (but also the longer 

the computing time). (Section 2.3.2) 

3. Construct a sequence of activity events. APEX constructs an exposure event sequence 

(activity pattern) spanning the period of the simulation for each of the hypothetical 

individuals (based on the supplied CHAD data, although other data could be used). 

(Section 2.3.3) 

4. Calculate hourly concentrations in microenvironments. APEX users must define 

microenvironments that people in the study area would visit by assigning location codes 

in the supplied CHAD database to the user-specified microenvironments. The model 

then calculates hourly concentrations of a pollutant in each of these microenvironments 

for the period of simulation, based on the user-provided microenvironment descriptions 

and hourly ambient air quality data. All the hourly concentrations in the 

microenvironments are re-calculated for each of simulated individuals. (Section 2.4) 

5. Determine exposures. APEX assigns a concentration to each exposure event based on 

the microenvironment occupied during the event and the person’s activity. These values 

are averaged by clock hour to produce a sequence of hourly average exposures spanning 

the specified exposure period (typically one year). These hourly values may be further 

aggregated to produce daily, monthly, and annual average exposure values. (Section 2.5) 

 The model simulation continues until exposures are determined for entire modeling 

period for the user-specified number of simulated individuals. Figure 2-1 presents these steps 

within a schematic of the APEX model design. Subsections that follow provide addition detail 

on the key algorithms used in Steps 1 through 5. 
 7 

- National

database

- Area-specific

input data

- Intermediate step

or data

- Simulation

step

- Data processor - Output data

- National

database

- Area-specific

input data

- Intermediate step

or data

- Simulation

step

- Data processor - Output data

Sector location data

(latitude, longitude)

Defined study area (sectors within a city radius and with air quality and meteorological data within their radii of influence)

Sector population data 

(age/gender/race)

Population within 

the study area

Commuting flow data

(origin/destination sectors)

Age/gender-specific physiological distribution data (body weight, height, etc)

Distribution functions forprofile variables (e.g, probability of air conditioning)

Locations of air quality and 

meteorological measurements; 

radii of influence

Stochastic 

profile generator

Distribution functions for seasonal and daily varying profile variables (e.g., window status, car speed)

A fo• H• W• A• G• R• E• H• H• H• C• P

2000 Census tract-level data for the entire U.S. (sectors=tracts for the NAAQS ozone exposure application)

Age/gender/tract-spe

employment probabil

1. Characterize study area 2. Characterize study population 3. Generate N n

simulated individu

Figure 2-1. Overview of the APEX Model
 8 

Diary events/activities 

and personal information 

(e.g., from CHAD)

Maximum/mean daily

temperature data

Activity diary pools by day 

type/temperature category

Each day in the simulation period is assigned to an activity pool based on day type and temperature category

Selected diary records for each day in the simulation period, resulting in a sequence of events(microenvironments visited, minutes spent, and activity) in the simulation period, for an individual

Stochastic diary 

selector using 

age, gender, and 

employment

Stochastic

calculation of energy

expended per event (adjusted for

physiological limits and EPOC)

and ventilation

rates

Physiological 

parameters from 

profile

Sequence o

indi

Profile for an 

individual

4. Construct sequence of activity events 

for each simulated individual

Figure 2-1. Overview of the APEX Model, continued
 9 

Hourly air quality 

data for all sectors

Select calculation method for each microenvironment:• Factors• Mass balance

Concentrations for all events 

for each simulated individual

Hourly concentrations and minutes spent in each

microenvironment visited by 

the simulated individual

Average exposuresfor simulated person, stratified by ventilation rate:• Hourly• Daily 1-hour max• Daily 8-hour max• Daily...

Microenvironments defined by 

grouping of CHAD location codes

Calculate hourly

concentrations in

microenvironments

visited

Poind• T• C• A

Sequence of events for 

each simulated individual

Calculate

concentrations in all

microenvironments

5. Calculate concentrations in 

microenvironments for all events for 

each simulated individual

6. Calculate hourly 

exposures for each 

simulated individual

po

Figure 2-1. Overview of the APEX Model, concluded
 10 

2.3.1 Characterize the Study Area 

The APEX study area has traditionally been on the scale of a city or slightly larger 

metropolitan area, although it is now possible to model larger areas, depending primarily on 

computing capabilities, available data, and the desired precision of the run. 

In this analysis the study area is defined by a list of counties. The demographic data used 

by the model to create personal profiles is provided at the tract level. For each tract the model 

requires demographic information representing the distribution of age, gender, race, and work 

status within the study population. Each tract has a location specified by latitude and longitude 

for some representative point (e.g., geographic center). The current release of APEX includes 

input files that already contain this demographic and location data for all census tracts in the 50 

United States, based on the 2000 Census. 

The ambient air quality data are assigned to geographic areas called districts. The 

districts are used to assign pollutant concentrations to the tracts and microenvironments being 

modeled. The ambient air quality data are provided by the user as hourly time series for each 

district. As with tracts, each district has a representative location (latitude and longitude). 

Districts can extend outside of the study area. 

APEX calculates the distance from each tract to each district center, and assigns the tract 

to the nearest district, provided the tract’s representative location point (e.g., geographic center) 

is in the district. Each tract is assigned to only one district. 

Ambient temperatures are input to APEX for different sites (locations). As with districts, 

APEX calculates the distance from each tract to each temperature site and assigns each tract to 

the nearest site. 

2.3.2 Generate Simulated Individuals 

APEX stochastically generates a user-specified number of simulated (hypothetical) 

persons to represent the population in the study area. Each simulated person is represented by a 

“personal profile.” APEX generates the simulated person or profile by probabilistically selecting 

values for a set of profile variables (Table 2-1). The profile variables include: 

• Demographic variables, which are generated based on the census data; 

• Residential variables, which are generated based on sets of distribution data; 

• Physiological variables, which are generated based on age- and gender-specific 

distribution data; and 

• Daily varying variables, which are generated based on distribution data that change daily 

during the simulation period. 

APEX first selects and calculates demographic, residential, and physiological variables (except 

for daily values) for all the specified number of simulated individuals, and then follows each 

individual over time and calculates exposures (and optionally doses) for each simulated person. 

The following subsections describe these variables in more detail. 
 11 

Table 2-1. Profile Variables in APEX 

Variable 

Type Profile Variables Description

Age Age (years) 

Gender Male or Female 

Race White, Black, Native American, Asian, and Other 

Home tract Tract in which a simulated person lives 

Work tract Tract in which a simulated person works 

Demographic 

variables 

Employment status Indicates employment outside home 

Residential 

variables 

Air conditioner Indicates presence of air conditioning at home 

In-vehicle Daily average car speed Daily average car speed 

variables Car air conditioner Indicates presence of air conditioning in the vehicle 

Height Height of a simulated person (in) 

Weight Body weight of a simulated person (lbs) 

Resting metabolic rate Resting metabolic activity rate (kcal/min) 

Energy conversion factor Oxygen uptake per unit of energy expanded (liters/kcal) 

Physiological 

variables 

Maximum permitted 

metabolic value 

Maximum metabolic activity level that can be sustained for about 

five minutes (dimensionless) 

Demographic Variables 

The values of the demographic variables for a simulated profile are selected 

probabilistically according to their joint distribution in the input population files, which are 

derived from the 2000 U.S. Census. 

Residential Variables 

The residential variables are categorical variables that are used to indicate whether a 

residence or a car associated with a simulated person has the specified characteristic. These are 

randomly selected based on user-specified probabilities. For example, a user could specify 

probabilities of 0.3 for not having an air conditioner and 0.7 for having an air conditioner in their 

home. 

Physiological Profile Variables 

The physiological variables are used for calculating ventilation rates. Input data to APEX 

provide gender- and age-specific distributions for these variables. 
 12 

2.3.3 Construction of Activity Sequences 

 APEX probabilistically creates a composite diary for each of the simulated persons by 

selecting a 24-hour diary record – or diary day – from an activity database for each day of the 

simulation period. CHAD data have been supplied with APEX for this purpose. A composite 

diary is a sequence of events that simulates the movement of a modeled person through 

geographical locations and microenvironments during the simulation period. Each event is 

defined by geographic location, start time, duration, microenvironment visited, and an activity 

performed. The activity database input to APEX contains the following information for each 

person for each day in each person’s diary: age, gender, race, employment status, occupation, 

day of week, daily maximum hourly average temperature, the location, start time, duration, and 

type of each activity during the day. 

APEX develops a composite diary for each of the simulated individuals according to the 

following steps: 

1. Divide diary days in the CHAD database into user-defined activity pools, based on day 

type and temperature. 

2. Assign an activity pool number to each day of the simulation period, based on the userprovided daily maximum/average temperature data. 

3. Calculate a selection probability for each of the diary days in each of the activity pools, 

based on age/gender/employment similarity of a simulated person to a diary day. 

4. Probabilistically select a diary day from available diary days in the activity pool assigned 

to each day of the simulation period. 

5. Evaluate a metabolic value for each activity performed while in a CHAD location, based 

on the activity-specific metabolic distribution data. This is used to calculate a ventilation 

rate for the simulated person performing the activity. 

6. Map the CHAD locations in the selected diary to the user-defined modeled 

microenvironments. 

7. Concatenate the selected diary days into a sequential longitudinal diary for a simulated 

individual covering all days in the simulated period. 

The method in APEX for creating longitudinal diaries that reflect the tendency of 

individuals to repeat activities is based on reproducing realistic variation in a user-selected key 

diary variable. APEX reads the values of the key variable from an external file. Currently, files 

have been constructed for both outdoor time and vehicle time for all CHAD diaries by summing 

the total time associated with “outdoor” and “vehicle” CHAD location codes for each diary. The 

actual diary construction method targets two statistics, D and A. The D statistic reflects the 

relative importance of within-person variance and between-person variance in the key variable. 

The A statistic quantifies the lag-one (day-to-day) variable autocorrelation. Desired D and A 

values for the key variable are selected by the user and set in the APEX parameters file, and the 

method algorithm constructs a longitudinal diary that preserves these parameters. Longitudinal 

diary data from a field study in children (Geyh et al., 2000), and subsequent analyses (Xue et al., 

2004) suggest that D and A are stable over time (and perhaps over cohorts as well). Based on 

these studies, appropriate target values for the two statistics for outdoor time are estimated to be 

D=0.22 and A=0.19. A value of 0.2 is used for both of these parameters in the ozone exposure 

modeling, since precision beyond 0.1 is not warranted for these statistics. It turns out that the 
 13 

model results are insensitive to small changes in these values. The longitudinal diary 

methodology is described further in Appendix C. 

2.4 Algorithms for Calculating Microenvironmental Concentrations 

Probabilistic algorithms are used to estimate the pollutant concentration associated with 

each exposure event. The estimated pollutant concentrations account for the effects of ambient 

(outdoor) pollutant concentration, penetration factor, air exchange rate, decay/deposition rate, 

and proximity to emission sources, depending on the microenvironment, available data, and the 

estimation method selected by the user. 

APEX calculates air concentrations in the various microenvironments visited by the 

simulated person by using the ambient air data for the relevant tracts and the user-specified 

method and parameters that are specific to each microenvironment. APEX calculates hourly 

concentrations in all the microenvironments at each hour of the simulation for each of the 

simulated individuals, based on the hourly ambient air quality data specific to the geographic 

locations visited by the individual. APEX provides two methods for calculating 

microenvironmental concentrations: the mass balance method and the transfer factors method 

(described in Sections 2.4.1 and 2.4.2, respectively). The user is required to specify a calculation 

method for each of the microenvironments; there are no restrictions on the method specified for 

each microenvironment (e.g., some microenvironments can use the transfer factors method while 

the others use the mass balance method). 

2.4.1 Mass Balance Model 

The mass balance method models an enclosed microenvironment as a well-mixed volume 

in which the air concentration is spatially uniform at any specific time. The concentration of an 

air pollutant in such a microenvironment is estimated using the following four processes: 

• Inflow of air into the microenvironment; 

• Outflow of air from the microenvironment; 

• Removal of a pollutant from the microenvironment due to deposition, filtration, and 

chemical degradation; and 

• Emissions from sources of a pollutant inside the microenvironment. 

Table 2-2 lists the parameters required by the mass balance method to calculate concentrations in 

a microenvironment. The proximity factor (fproximity) is used to account for differences in 

ambient concentrations between the geographic location represented by the ambient air quality 

data (e.g., a regional fixed-site monitor) and the geographic location of the microenvironment 

(e.g., near a roadway). This factor could take a value either greater than or less than 1. 

Emission source (ES) represents the emission rate for the emission source and concentration 

source (CS) is the mean air concentration resulting from the source. Rremoval is defined as the 

removal rate of a pollutant from a microenvironment due to deposition, filtration, and chemical 

reaction. The air exchange rate (Rair exchange) is expressed in air changes per hour. This analysis 

of ozone exposures does not consider sources of ozone, and these terms are set to zero. 
 14 

Table 2-2. Mass Balance Model Parameters 

Variable Definition Units Value Range

f proximity Proximity factor unitless f proximity > 0 

CS Concentration source ppm CS ≥ 0 

ES Emission source μg/hr ES ≥ 0 

R removal Removal rate due to 

deposition, filtration, and 

chemical reaction 

1/hr Rremoval ≥ 0 

R air exchange Air exchange rate 1/hr Rair exchange ≥ 0 

V Volume of 

microenvironment 

m3 V > 0 

The mass balance equation for a pollutant in a microenvironment is described by: 

= ΔCin − ΔCout − ΔCremoval + ΔCsource dt

dC ME (t) (2-1) 

where: 

 dCME(t) = Change in concentration in a microenvironment at time t (ppm), 

)Cin = Rate of change in microenvironmental concentration due to influx 

of air (ppm/hour), 

)Cout = Rate of change in microenvironmental concentration due to outflux 

of air (ppm/hour), 

)Cremoval = Rate of change in microenvironmental concentration due to 

removal processes (ppm/hour), and 

)Csource = Rate of change in microenvironmental concentration due to an 

emission source inside the microenvironment (ppm/hour). 

Within the time period of an hour each of the rates of change, )Cin, )Cout, )Cremoval, and 

)Csourcel, is assumed to be constant. 
 15 

The change in microenvironmental concentration due to influx of air is represented by the 

following equation: 

ambient proximity penetration air exchange

in

in C x f x f x R

dt

dC t ΔC = = ( ) (2-2) 

where: 

Cambient = Ambient hourly outdoor concentration (ppm) 

fproximity = Proximity factor (unitless) 

 fpenetration = Penetration factor (unitless) 

Rair exchange = Air exchange rate (1/hour) 

The change in microenvironmental concentration due to outflux of air is described by: 

( ) ( ) R C t

dt

dC t C air exchange ME

out Δ out = = × (2-3) 

The change in concentration due to deposition, filtration, and chemical degradation in a 

microenvironment is simulated based on the first-order equation: 

(R R R )C (t) R xC (t) dt

dC (t) C deposition filtration chemical ME removal ME

removal Δ removal = = + + = (2-4) 

where: 

Rdeposition = Removal rate of a pollutant from a microenvironment due to 

deposition (1/hour) 

Rfiltration = Removal rate of a pollutant from a microenvironment due to 

filtration (1/hour) 

Rchemical = Removal rate of a pollutant from a microenvironment due to 

chemical degradation (1/hour) 

Rremoval = Removal rate of a pollutant from a microenvironment due to 

overall removal (1/hour) 

 We are not modeling indoor emissions of ozone, so the optional term )Csource will be 

uniformly equal to 0.0 for this study. 

Equation 2-1 combined with Equations 2-2, 2-3, and 2-4 leads to: 

( ) ( ) dt

dC ME (t) C R C t R C t = Δ in − air exchange ME − removal ME (2-5) 

Solving the differential equation in Equation 2-5 leads to: 
 16 

( ) ( (0) ) exp( R t) R

C C

R

C C t combined

combined

in

ME

combined

in

ME − Δ

+ − Δ = (2-6) 

where: 

CME(0) = Concentration of a pollutant in a microenvironment at the 

beginning of a hour (ppm) 

CME(t) = Concentration of a pollutant in a microenvironment at time t within 

the time period of a hour (ppm) 

Rcombined = Rair exchange + Rremoval (1/hour) 

Based on Equation 2-6, the following three hourly concentrations in a microenvironment 

are calculated: 

combined

in

ME

equil

ME R

C C C t

Δ = ( → ∞) = (2-7) 

( (0) ) exp( ) combined

equil

ME ME

equil

ME

hourly end CME =C + C −C −R (2-8) 

combined

equil combined

ME ME

equil

ME

hourlymean

ME R

R C C C

dt

C t dt

C 1 exp( ) ( (0) )

( )

1

0

1

0 − − = = + −

∫

∫

 (2-9) 

where: 

equil CME = Equilibrium concentration in a microenvironment (ppm) 

CME(0) = Concentration in a microenvironment at the beginning of an hour 

(ppm) 

hourly end CME = Concentration in a microenvironment at the end of an hour (ppm) 

hourlymean CME = Hourly mean concentration in a microenvironment (ppm) 

At each hour time step of the simulation period, APEX uses Equations 2-7, 2-8, and 2-9 to 

calculate the hourly equilibrium, hourly ending, and hourly mean concentrations. APEX reports 

hourly mean concentration as hourly concentration for a specific hour. The calculation continues 

to the next hour by using hourly end C ME for the previous hour as CME(0). 

2.4.2 Factors Model 

The factors method is simpler than the mass balance method. It does not calculate 

concentration in a microenvironment from the concentration in the previous hour and it has 
 17 

fewer parameters. Table 2-3 lists the parameters required by the factors method to calculate 

concentrations in a microenvironment without emissions sources. 

Table 2-3. Factors Model Parameters 

Variable Definition Units Value Range

f proximity Proximity factor unitless f proximity > 0 

f penetration Penetration factor unitless 0 ≤ f penetration ≤ 1 

The factors method uses the following equation to calculate hourly mean concentration in 

a microenvironment from the user-provided hourly air quality data: 

ambient proximity penetration

hourlymean

ME C =C x f x f (2-10) 

where: 

hourlymean CME = Hourly concentration in a microenvironment (ppm) 

Cambient = Hourly concentration in ambient environment (ppm) 

fproximity = Proximity factor (unitless) 

fpenetration = Penetration factor (unitless) 

2.4.3 Commuting Outside of the Study Area 

APEX allows for some flexibility in the treatment of persons in the modeled population 

who commute to destinations outside the study area. By specifying “KeepLeavers = No” in the 

simulation control parameters file (see Section 3.1), people who work inside the study area but 

live outside of it are not modeled, nor are people who live in the study area but work outside of 

it. By specifying “KeepLeavers = Yes,” these commuters are modeled. This triggers the use of 

two additional parameters, called LeaverMult and LeaverAdd. While a commuter is at work, if 

the workplace is outside the study area, then the ambient concentration is assumed to be related 

to the average concentration over all air districts at the same point in time, and is calculated as: 

Ambient Concentrat ion = LeaverMult × avg (t) + LeaverAdd (2-11) 

where: 

 Ambient Concentration = Calculated ambient air concentrations for locations outside 

of the study area (ppm or ppm) 

 LeaverMult = Multiplicative factor for city-wide average concentration, 

applied when working outside study area 

 avg(t) = Average ambient air concentration over all air districts in 

study area, for time t (ppm or ppm)
 18 

 LeaverAdd = Additive term applied when working outside study area 

All microenvironmental concentrations for locations outside of the study area are determined 

from this ambient concentration by the same function as applies inside the study area. 

2.5 Algorithms for Calculating Dose 

Probabilistic algorithms are used to estimate the ventilation (respiration) rate associated 

with each exposure event. Ventilation (as discussed in Section 2.5.1 below) is a measure of 

human respiration, which is activity and physiology dependent. It is used in APEX to simulate 

human activities in order to estimate, more realistically, inhalation exposure and dose. The 

ventilation rate is derived from an energy expenditure rate estimated for the specified activity. 

2.5.1 Ventilation 

 Ventilation is a general term for the movement of air into and out of the lungs. Minute or 

total ventilation is the amount of air moved in or out of the lungs per minute. Quantitatively, the 

amount of air breathed in per minute (VI) is slightly greater than the amount expired per minute 

(VE). Clinically, however, this difference is not important, and by convention minute ventilation 

is always measured on an expired sample, VE. 

The oxygen ventilation rate VO2 (l of O2/min) is related to the energy expenditure rate for 

the given event activity and the given profile’s physiology in terms of oxygen ventilation per unit 

energy expenditure, or: 

VO2 = EE x ECF (2-12) 

where: 

EE = Energy expenditure (kcal/min) 

ECF = Energy conversion factor (l of O2/kcal). 

ECF is based on the physiology of the individual being modeled. EE is related to the activityspecific energy expenditure rate and the basal or resting energy expenditure (metabolic) rate of 

the given profile, or: 

EE = MET x RMR (2-13) 

where: 

MET = Metabolic equivalent of work (the ratio of the rate of energy consumption 

for non-rest activities to the resting rate of energy consumption) (dimensionless) 

RMR = Resting metabolic rate (kcal/min). 

RMR is based on the physiology of the individual being modeled. MET is the ratio of the 

activity-specific energy expenditure rate to the basal or resting energy expenditure rate. While 

different people have very different basal metabolic rates, it is generally found that the metabolic 

ratios do not exhibit as much variability. Thus, standing still might require two times the basal 
 19 

energy expenditure, or two MET, for most people, with relatively little variation. Since the basal 

rate is constant for each profile, it only has to be determined once and the activity-specific 

metabolic ratio can be used to determine the absolute energy expenditure rate, EE, for each 

activity. 

Dividing equation 2-12 by body mass (BM) and using equation 2-13, one obtains: 

VO2 / BM = RMR x ECF x MET / BM (2-14) 

Graham and McCurdy (2005) describe an approach to estimate VE directly from VO2

using a series of regression-based equations. Using data compiled from 32 clinical exercise 

studies collected over a 25-year period by Dr. William C. Adams of the University of California 

at Davis, they developed an algorithm for four age groups and both genders. The algorithm 

accounts for differences in ventilation rate due to activity level, variability within age groups, 

and variation both between and within individuals. Their model is implemented in APEX as: 

i O i i i i i ln(VE / BM ) =b0 +(b1

*ln(V 2 / BM ))+(b2*ln(1+ age ))+(b3*gender )+eb +ew (2-15) 

where: 

the VO2/BM term is given in terms of the APEX variables by equation 2-14, 

age is the age of the individual in years, and 

gender is a flag with value -1 for males and +1 for females. 

Random error (ε) is allocated to two variance components used to estimate the between-person 

(inter-individual variability) residuals distribution (eb) and within-person (intra-individual 

variability) residuals distribution (ew). The regression parameters b0, b1, b2, b3, and eb are 

assumed to be constant over time for a given simulated person, whereas ew varies from event to 

event. These parameters are randomly drawn from normal distributions with means and standard 

deviations given in Table 2-4. eb and ew have mean zero. 

Table 2-4. Ventilation Regression Parameters 

Age 

range 

mean

b0

stdev

b0

mean

b1

stdev

b1

mean

b2

stdev

b2

mean

b3

stdev

b3

stdev

eb

stdev

ew

0-19 4.4329 0.0579 1.0864 0.0097 -0.2829 0.0124 0.0513 0.0045 0.0955 0.1117 

20-33 3.5718 0.0792 1.1702 0.0067 0.1138 0.0243 0.045 0.0031 0.1217 0.1296 

34-60 3.1876 0.1271 1.1224 0.012 0.1762 0.0335 0.0415 0.0095 0.126 0.1152 

>60 2.4487 0.3646 1.0437 0.0195 0.2681 0.0834 -0.0298 0.01 0.1064 0.0676 
 20 

2.5.2 Excess Post-Exercise Oxygen Consumption 

 At the beginning of exercise, there is a lag between work expended and oxygen 

consumption. During this work/ventilation mismatch, an individual’s energy needs are met by 

anaerobic processes. The magnitude of the mismatch between expenditure and consumption is 

termed the oxygen deficit. During heavy exercise, further oxygen deficit (in addition to that 

associated with the start of exercise) may be accumulated. At some point, oxygen deficit reaches 

a maximum value, and performance and energy expenditure deteriorate. After exercise ceases, 

ventilation and oxygen consumption will remain elevated above baseline levels. This increased 

oxygen consumption was historically labeled the “oxygen debt” or “recovery oxygen 

consumption.” However, recently the term “excess post-exercise oxygen consumption” (EPOC) 

has been adopted for the phenomenon. APEX has an algorithm for adjusting the MET values to 

account for EPOC. This algorithm is described in Appendix B. 

2.5.3 Body Surface Area 

The algorithm for calculating body surface area (BSA) in APEX was developed by 

Burmaster (1998), and uses a univariate model for total skin area as a function of body weight. 

Through regression analysis, Burmaster determined that weight alone does as well as weight and 

height together in predicting total skin area, with the advantage of requiring only a single 

explanatory variable. Total skin area was found to follow a lognormal distribution that is a 

function of body weight according to: 

2.2781 0.6821 BSA e BM − = (2-16) 

where: 

BSA = body surface area (m2) 

BM = body mass (kg). 

2.6 Exposure Calculations 

APEX calculates exposure as a time series of exposure concentrations that a simulated 

individual experiences during the simulation period. APEX determines the exposure using 

hourly ambient air concentrations, calculated concentrations in each microenvironment based on 

these ambient air concentrations, and the minutes spent in a sequence of microenvironments 

visited according to the composite diary. The hourly exposure concentration at any clock hour 

during the simulation period is determined using the following equation: 

T

C t

C

N

j

j

hourlymean

ME j

i

∑= = 1

( ) ( )

 (2-17) 

where: 
 21 

 Ci = Hourly exposure concentration at clock hour I of the simulation period 

(ppm) 

N = Number of events (i.e., microenvironments visited) in clock hour I of 

the simulation period. 

hourlymean CME( j) = Hourly mean concentration in microenvironment j (ppm) 

 t(j) = Time spent in microenvironment j (minutes) 

 T = 60 minutes 

From the hourly exposures, APEX calculates time series of 8-hour and daily average exposure 

concentrations that a simulated individual would experience during the simulation period. 

APEX then statistically summarizes and tabulates the hourly, 8-hour, and daily exposures. 

2.7 Model Output 

All of the output files written by APEX are ASCII text files. Table 2-5 lists each of the 

output data files written for these simulations and provides descriptions of their content. 

Additional output files that can produced by APEX are given in Table 5-1 of the APEX User’s 

Guide, and include hourly exposure, ventilation, and energy expenditures, and even detailed 

event-level information, if desired. The names and locations, as well as the output table levels 

(e.g., output percentiles, cut-points), for these output files are specified by the user in the 

simulation control parameters file. Specific output generated for the purposes of this document 

are discussed in Section 3.1. 

Table 2-5. APEX Output Files 

Output File Type Description

Log The Log file contains the record of the APEX model simulation as it progresses. 

If the simulation completes successfully, the log file indicates the input files and 

parameter settings used for the simulation and reports on a number of different 

factors. If the simulation ends prematurely, the log file contains error messages 

describing the critical errors that caused the simulation to end. 

Profile Summary The Profile Summary file provides a summary of each individual modeled in the 

simulation. 

Microenvironment 

Summary

The Microenvironment Summary file provides a summary of the time and 

exposure by microenvironment for each individual modeled in the simulation. 

Sites The Sites file lists the tracts, districts, and zones in the study area, and identifies 

the mapping between them. 

Output Tables The Output Tables file contains a series of tables summarizing the results of the 

simulation. The percentiles and cut-off points used in these tables are defined in 

the simulation control parameters file. 
 22 
 23 

3. PREPARATION OF MODEL INPUTS 

The APEX model inputs require extensive analysis and preparation in order to ensure the 

model run gives valid and relevant results. This chapter begins with a description of the selected 

model options and discusses their significance. Following this introduction is a discussion of the 

model input files and other critical parameters. The chapter goes on to describe the sources of 

data for the APEX input files. File formats and physical file structures are not discussed in 

detail, as this information is presented in the APEX User’s Guide (EPA, 2006c). 

3.1 Model Options 

Many of the important characteristics of a model run in APEX are set in the simulation 

control parameters file. In this file the user specifies the input and output files and their 

associated directories, as well as the basic parameters that characterize the run. The settings used 

for the model runs are described here. 

The number of simulated persons in each model run was set to 60,000, an amount that 

tests indicated would be a large enough sample size to provide stable model results. The 

parameters controlling the location and size of the simulated area were set to include all counties 

in the study area CSA. 

 The settings that allow for replacement of CHAD data that are missing gender, 

employment or age values were all set to preclude replacing missing data. The width of the age 

window was set to 20 percent to increase the pool of diaries available for selection. The variable 

that controls the use of additional ages outside the target age window was set to 0.1 to further 

enhance variability in diary selection. See the APEX User’s Guide for an explanation of these 

parameters. 

 The diary activity contributing the most to variability in exposure to ozone is the time 

spent outdoors, and we have selected that as the key predictor of exposure for the assembly of 

longitudinal diaries (see Appendix C). For school-age children, we take the diversity statistic D 

to be 0.2 and the autocorrelation to be 0.2. These values were derived from the Southern 

California Children's Study. We do not have data to base estimates of these parameters on for 

younger children and for adults, and we use the school-age children values for all ages. 

Levels of physical activity were categorized by the Physical Activity Index (PAI), which 

is discussed in Appendix B. Children were characterized as active if their median daily PAI over 

the period modeled is 1.75 or higher, a level characterized by exercise physiologists as being 

“moderately active” or “active” (McCurdy, 2000). 

3.2 Air Quality 

APEX requires hourly ambient ozone concentrations at a set of sites in the study area. 

These data were obtained from the EPA AIRS Air Quality Subsystem for the years 2002, 2003, 

and 2004. These years were modeled since they are recent years that exhibit the year-to-year 

variability that is characteristic of ozone formation. All of the sites in AIRS within the 

boundaries of each CSA were used in this analysis. APEX uses the concentrations from the 
 24 

closest site to represent ambient concentrations at different locations in the study area. Table 3-1 

lists the number of ozone monitors in each of the modeled CSAs. 

Table 3-1. The Numbers of Ozone Monitors in the Study Areas 

Number of monitors Urban area (CSA) 2002 2003 2004 

Atlanta-Sandy Springs-Gainesville, GA-AL 13 12 12 

Boston-Worcester-Manchester, MA-NH 17 19 15 

Chicago-Naperville-Michigan City, IL-IN-WI 32 30 27 

Cleveland-Akron-Elyria, OH 11 11 11 

Detroit-Warren-Flint, MI 10 10 10 

Houston-Baytown-Huntsville, TX 21 23 21 

Los Angeles-Long Beach-Riverside, CA 45 43 44 

New York-Newark-Bridgeport, NY-NJ-CT-PA 30 30 29 

Philadelphia-Camden-Vineland, PA-NJ-DE-MD 18 17 16 

Sacramento--Arden-Arcade--Truckee, CA-NV 21 22 22 

St. Louis-St. Charles-Farmington, MO-IL 18 18 17 

Washington-Baltimore-N. Virginia, DC-MD-VA-WV 28 28 26 

3.2.1 Missing Data Replacement 

 Missing air quality data were estimated by the following procedure. Where there were 

consecutive strings of missing values (data gaps of less than 6 hours, missing values were 

estimated by linear interpolation between the valid values at the ends of the gap. Remaining 

missing values at a monitor were estimated by fitting linear regression models for each hour of 

the day, with each of the other monitors, and choosing the model which maximizes R2

 for each 

hour of the day, subject to the constraints that R2

 be greater than 0.5 and the number of 

regression data values is at least 50. If there were any remaining missing values at this point, for 

gaps of less than 9 hours, missing values were estimated by linear interpolation between the valid 

values at the ends of the gap. Any remaining missing values were replaced with the regionwide 

mean for that hour. 

3.3 Air Quality Projections for Alternative Standards Scenarios 

 In addition to modeling exposures based on historical air quality, an analysis was 

conducted using air quality representative of just meeting the current 8-hour O3 NAAQS of 0.08 

ppm, as well as seven alternative standards. This was done using a quadratic rollback approach 

to adjust the hourly O3 concentrations observed in 2002-2004 to yield a design value 

corresponding to the standard being modeled. Design values for the current 8-hour O3 NAAQS 

are calculated as the 3-year averages of the annual 4th daily maximum 8-hr average concentration 
 25 

based on the maximum monitor within an urban area. The quadratic rollback technique 

combines both linear and quadratic elements to reduce higher concentrations more than lower 

concentrations near ambient background levels. Table 3-2 shows the alternative standards, their 

corresponding attainment thresholds and the form of the standard used for each scenario. 

Additional details about rollback and the alternative standard scenarios can be found in the 

Ozone Staff Paper. 

Table 3-2. List of the Current and Alternative 8-hour Ozone Standard Scenarios used in 

the Exposure Analysis 

Attainment Threshold Form of Standard Labels for 

graphs 

0.084 ppm 3rd-highest form 

4th-highest form 

85/3 

85/4 

0.080 ppm 4th-highest form 81/4 

0.074 ppm 

3rd-highest form 

4th-highest form 

5th-highest form 

75/3 

75/4 

75/5 

0.070 ppm 4th-highest form 71/4 

0.064 ppm 4th-highest form 65/4 

3.4 Meteorological Data 

Hourly temperature data are from the National Climatic Data Center Surface Airways 

Hourly TD-3280 dataset (NCDC Surface Weather Observations). Daily average and 1-hour 

maxima are computed from these hourly data. 

There are two files that are used to provide meteorological data to APEX. One file, the 

meteorological station location file, contains the locations of meteorological data recordings, 

expressed in latitude and longitude coordinates. This file also contains start and end dates for the 

data recording periods. The temperature data file contains the data from the locations in the 

temperature zone location file. This file contains daily maximum and daily average temperature 

readings for the period being modeled for the meteorological stations in and around the study 

area. Table 3-3 lists the meteorological stations used for each modeled area. 
 26 

Table 3-3 The Meteorological Stations for Each Study Area 

Urban area (CSA) NWS station ID 

(WBAN) 

Atlanta-Sandy Springs-Gainesville, GA-AL 03813, 13873, 13874, 13882, 93842 

Boston-Worcester-Manchester, MA-NH 14739, 14745, 14765, 94746 

Chicago-Naperville-Michigan City, IL-IN-WI 14839, 14848, 94822, 94846 

Cleveland-Akron-Elyria, OH 14820, 14852, 

14860, 14891, 14895 

Detroit-Warren-Flint, MI 14822, 14826, 14836, 94830, 94847 

Houston-Baytown-Huntsville, TX 12912, 12917, 12960, 93987 

Los Angeles-Long Beach-Riverside, CA 23129, 23155, 23161, 23174, 23188, 

23190 

New York-Newark-Bridgeport, NY-NJ-CT-PA 04725, 04781, 13739, 14732, 14734, 

14737, 14740, 14765, 14777, 93730, 

94702, 94728, 94789 

Philadelphia-Camden-Vineland, PA-NJ-DE-MD 13739, 13781, 14737, 93730 

Sacramento--Arden-Arcade--Truckee, CA-NV 23185, 23232, 23237 

St. Louis-St. Charles-Farmington, MO-IL 13994, 93822 

Washington-Baltimore-N. Virginia, DC-MD-VA-WV 13740, 13743, 13781, 14711, 93721, 

93738, 93739 

3.5 Population Demographics 

APEX takes population characteristics into account to develop accurate representations of 

study area demographics. Specifically, population counts by area and employment probability 

estimates are used to develop representative profiles of hypothetical individuals for the 

simulation. 

APEX is very flexible in the resolution of population data provided. As long as the data 

are available, any resolution can be used (e.g., county, census tract, census block). For this 

application of the model, we used census tract level data. 

Tract-level population counts come from the 2000 Census of Population and Housing 

Summary File 1. Summary File 1 (SF 1) contains the 100-percent data, which is the information 

compiled from the questions asked of all people and about every housing unit. The first level of 

official Census race categories and their abbreviations are: 

• White (W) 

• Black or African American (B) 
 27 

• American Indian or Alaska native (N) 

• Asian (A) 

• Native Hawaiian or other Pacific Islander (OH) 

• Other single race (OO) 

• Two or more races combined (O2) 

The categories OH, OO, and O2 were combined into a single “Other” class (“O”) for modeling 

purposes. Hispanics are not separated, as the Census Bureau did not consider Hispanic to be a 

race. 

In the 2000 U.S. Census, estimates of employment were developed by census tract. 

Employment data from the 2000 census can be found on the U.S. census web site at the address 

http://www.census.gov/population/www/cen2000/phc-t28.html (Employment Status: 2000- 

Supplemental Tables). The file input to APEX is broken down by gender and age group, so that 

each gender/age group combination is given an employment probability fraction (ranging from 0 

to 1) within each census tract. The age groupings in this file are: 16-19, 20-21, 22-24, 25-29, 30-

34, 35-44, 45-54, 55-59, 60-61, 62-64, 65-69, 70-74, and >75. Children under 16 years of age 

are assumed to be not employed. 

3.6 Asthma Prevalence Rates 

One of the important population subgroups for the exposure assessment is asthmatic 

children. Evaluation of the exposure of this group with APEX requires the estimation of 

children’s asthma prevalence rates, detailed in Appendix G. The estimates are based on 

children’s asthma prevalence data from the National Health Interview Survey (NHIS) for 2003. 

Asthma prevalence rates for children aged 0 to 17 years were calculated for each age, gender, 

and region. The regions defined by NHIS are the Census Regions: “Midwest,” “Northeast,” 

“South,” and “West.” The reported survey responses were weighted to take into account the 

complex survey design of the NHIS survey. Standard errors and confidence intervals for the 

prevalence rates were calculated using a logistic model, taking into account the survey design. 

Logistic analysis of the prevalence relationships to age showed statistically significant 

differences between the prevalence functions for the two genders and for the four regions. 

Therefore the relationships of prevalence to age were estimated separately for each gender and 

region. A scatterplot smoothing technique using the LOESS smoother was applied to smooth the 

prevalence curves and compute the standard errors and confidence intervals for the smoothed 

prevalence estimates. 

3.7 Commuting Database 

As part of the population demographics inputs, it is important to integrate working 

patterns into the assessment. In addition to using estimates of employment by tract, APEX also 

incorporates home-to-work commuting data. 

Commuting data were originally derived from the 2000 Census and were collected as part 

of the Census Transportation Planning Package (CTPP). These data are available from the U.S. 

DOT Bureau of Transportation Statistics (BTS) at the web site http://transtats.bts.gov/. The data 

used to generate APEX inputs were taken from the “Part 3-The Journey To Work” files. These 
 28 

files contain counts of individuals commuting from home to work locations at a number of 

geographic scales. 

These data were processed to calculate fractions for each tract-to-tract flow to create the 

national commuting data distributed with APEX. This database contains commuting data for 

each of the 50 states and Washington, D.C. 

Commuting within the Home Tract

The APEX data set does not differentiate people that work at home from those that 

commute within their home tract. 

Commuting Distance Cutoff 

A preliminary data analysis of the home-work counts showed that a graph of log(flows) 

versus log(distance) had a near-constant slope out to a distance of around 120 kilometers. 

Beyond that distance, the relationship also had a fairly constant slope but it was flatter, meaning 

that flows were not as sensitive to distance. A simple interpretation of this result is that up to 

120 km, the majority of the flow was due to persons traveling back and forth daily, and the 

numbers of such persons decrease fairly rapidly with increasing distance. Beyond 120 km, the 

majority of the flow is made up of persons who stay at the workplace for extended times, in 

which case the separation distance is not as crucial in determining the flow. 

To apply the home-work data to commuting patterns in APEX, a simple rule was chosen. 

It was assumed that all persons in home-work flows up to 120 km are daily commuters, and no 

persons in more widely separated flows commute daily. This meant that the list of destinations 

for each home tract was restricted to only those work tracts that are within 120 km of the home 

tract. When the same cutoff was performed on the 1990 census data, it resulted in 4.75% of the 

home-work pairs in the nationwide database being eliminated, representing 1.3% of the workers. 

The assumption is that this 1.3% of workers do not commute from home to work on a daily 

basis. It is expected that the cutoff reduced the 2000 data by similar amounts. 

Eliminated Records 

A number of tract-to-tract pairs were eliminated from the database for various reasons. A 

fair number of tract-to-tract pairs represented workers who either worked outside of the U.S. 

(9,631 tract pairs with 107,595 workers) or worked in an unknown location (120,830 tract pairs 

with 8,940,163 workers). An additional 515 workers in the commuting database whose data 

were missing from the original files, possibly due to privacy concerns or errors, were also 

deleted. 

3.8 Activity Patterns – CHAD 

Exposure models use human activity pattern data to predict and estimate exposure to 

pollutants. Different human activities, such as outdoor exercise, indoor reading, or driving, have 

different pollutant exposure characteristics. In addition, different human activities require 

different metabolic rates, and higher rates lead to higher doses. To accurately model individuals 

and their exposure to pollutants, it is critical to have a firm understanding of their daily activities. 
 29 

The Consolidated Human Activity Database (CHAD) provides data on human activities 

through a database system of collected human diaries, or daily activity logs. The purpose of 

CHAD is to provide a basis for conducting multi-route, multi-media exposure assessments 

(McCurdy et al., 2000). 

The data contained within CHAD come from multiple surveys with varied structures 

(Table 3-3). In general, the surveys have a data foundation based on daily diaries of human 

activity. This is the foundation from which CHAD was created. Individuals filled out diaries of 

their daily activities and this information was input and stored in CHAD. Relevant data for these 

individuals, such as age, are included as well. In addition, CHAD contains activity-specific 

metabolic distributions developed from literature-derived data, which are used to provide an 

estimate of metabolic rates of respondents through their various activities. 

There are four CHAD-related input files used in the APEX system. Two of these files are 

downloaded directly from the “Query Questionnaire” link on the CHADNet 

(http://www.epa.gov/chadnet1) page, and then manipulated to fit into the APEX framework. 

These are the human activity diaries file and the personal data file. 

The third input file contains metabolic information for different activities listed in the diary file. 

These metabolic activity levels are in the form of distributions. Some activities are specified as a 

single point value (for instance, sleep), while others, such as athletic endeavors or manual labor, 

are normally, lognormally, or otherwise statistically distributed. APEX samples from these 

distributions and calculates values to simulate the variable nature of activity levels among 

different people. 
 30 

Table 3-3. Summary of Studies Used in CHAD 

Study name 

Geographic 

coverage 

Study time 

period 

Subject 

ages 

Number of 

persons 

Number of 

person-days 

Diary type 

and study 

design 

(random 

 or not) 

Reference 

Baltimore A single 

building in Baltimore 

01/1997-02/1997, 07/1998-08/1998 

72-93 26 391 Diary Wi

California Adolescents and Adults (CARB) 

California 10/1987-09/1988 12-17 

18-94 

183 1,579 

183 1,579 

Recall; Random Ro

Wi

California Children (CARB) 

California 04/1989- 02/1990 0-11 1,200 1,200 Recall; Random Wi

Cincinnati (EPRI) 

Cincinnati metropolitan area 

03/1985-04/1985, 08/1985 0-86 888 2,614 Diary; Random Joh

Denver (EPA) Denver 

metropolitan area 

11/1982- 02/1983 18-70 432 805 Diary; Random Joh

et a

Los Angeles: Elementary School Children 

Los Angeles 10/1989 10-12 17 51 Diary Sp
 31 

Los Angeles: High School Adolescents 

Los Angeles 09/1990-10/1990 13-17 19 43 Diary Sp

National: NHAPS-Air 

National 09/1992-10/1994 0-93 4,723 4,723 Recall; Random Kl

Ts

National: NHAPS-Water 

National 09/1992-10/1994 0-93 4,663 4,663 Recall; Random Kl

Ts

Washington, D.C. (EPA) 

Wash., D.C. metropolitan area 

11/1982-02/1983 18-98 699 699 Diary; Random Ha

Ak
 32 

The fourth input file maps five-digit location codes used in the diary file to APEX 

microenvironments. Because each simulation may contain different numbers and types of 

microenvironments, it is important to ensure that the codes map properly to the appropriate 

microenvironment. If this file does not represent a reasonable mapping, the model will not 

accurately simulate exposure related to daily activities. 

 Personal Information file. Personal data are contained in the CHAD questionnaire file 

that is distributed with APEX This file also has information for each day individuals have 

diaries. The different variables in this file are: 

• The study, person, and diary day identifiers 

• Day of week 

• Gender 

• Race 

• Employment status 

• Age in years 

• Maximum temperature in degrees Celsius for this diary day 

• Mean temperature in degrees Celsius for this diary day 

• Occupation code 

• Time, in minutes, during this diary day for which no data are included in the database 

Diary Events file. The human activity diary data are contained in a file that is distributed 

with APEX. This is a large file because it contains diaries for about 23,000 people broken out at 

intervals ranging from one minute to one hour. These diaries vary in length from one to 15 days. 

This file contains the following variables: 

• The study, person, and diary day identifiers 

• Start time of this activity 

• Number of minutes for this activity 

• Activity code 

• Location code 

Activity Specific Metabolic file. The third CHAD file is also distributed with APEX and 

contains the metabolic parameters for each of the CHAD activities. 

3.9 Physiological Distributions 

APEX requires physiological parameters for subjects in order to accurately model their 

pollutant intake via metabolic processes. This is because physiological differences may cause 

people with the same exposure and activity scenarios to have different pollutant intake levels. 

The physiological parameters file distributed with APEX is described in the APEX User’s Guide. 
 33 

3.10 Microenvironment Specifications 

 The microenvironments in APEX provide the specific locations within an air quality 

district where modeled individuals are exposed to pollutants. Microenvironments are used to 

capture the differences between exposure concentrations in different types of environments (e.g., 

indoors, in cars, outdoors) within an area with the same estimated ambient air concentration. 

There are two basic methods for calculating concentrations in microenvironments: the transfer 

factors method and the mass balance method. The parameters for both factors and mass balance 

calculations used in this simulation are listed in Table 3-4. 

Table 3-4. Microenvironment Parameter Information 

Calculation Method

Parameter 

Type with 

Abbreviation

Units Distribution

Transfer Factors Proximity (PR) unitless Normal distribution 

Penetration (PE) unitless Normal distribution 

Proximity (PR) unitless Normal distribution 

Decay Rate 

(DE) 1/hr Lognormal distribution 

Mass Balance 

Air exchange 

rate (AER) Air changes/hr Lognormal distribution 

 The factors method is used to model simple environments, like outdoor areas, that do not 

contain pollutant sources. The ambient ozone concentrations are from the air quality data input 

file. There are two parameters that affect the pollutant concentration calculation in the factors 

method, the proximity and penetration factors. The proximity factor is a unitless parameter that 

represents the proximity of the microenvironment to a monitoring station. The penetration factor 

is a unitless parameter that represents the fraction of pollutant entering a microenvironment from 

outside the microenvironment via air exchange. The development of the proximity factors and 

penetration factors used in this analysis is discussed in Appendix A. 

The mass balance method is more appropriate for complex environments. In addition to 

proximity factors and penetration factors, this method supports parameters for emissions sources, 

decay rate, air exchange rate, volume, and the average removal rate. Each of these parameters 

can be modeled within the microenvironment or left out of the simulation. Both decay rate and 

emissions sources have a default value of zero, which gives them no effect on the simulation. 

The air exchange rate and volume have no default values. They only effect the 

microenvironment calculation if they are specifically included in the definition of the 

microenvironment. Several microenvironments using the mass balance method utilize one or 

more of these additional parameters. See Appendix A for a full description of the values used for 

the development of these parameters. 
 34 

3.10.1 Microenvironments Modeled 

 In APEX, microenvironments provide the exposure locations for modeled individuals. 

For exposures to be estimated accurately, it is important to have realistic microenvironments that 

match closely to the locations where actual people spend time on a daily basis. 

As discussed above, the two methods available in APEX for calculating pollutant levels 

within microenvironments are: 1) factors and 2) mass balance. A list of microenvironments used 

in this study, the calculation method used, and the parameters used to calculate the 

microenvironment concentrations can be found in Table 3-5. 

Table 3-5. List of Microenvironments and Calculation Methods Used 

Microenvironment Calculation 

Method 

Parameter Types 

used 1

Indoors – Residence Mass balance AER and DE 

Indoors – Bars and restaurants Mass balance AER and DE 

Indoors – Schools Mass balance AER and DE 

Indoors – Day-care centers Mass balance AER and DE 

Indoors – Office Mass balance AER and DE 

Indoors – Shopping Mass balance AER and DE 

Indoors – Other Mass balance AER and DE 

Outdoors – Near road Factors PR 

Outdoors – Public garage - parking lot Factors PR 

Outdoors – Other Factors None 

In-vehicle – Cars and Trucks Factors PE and PR 

In-vehicle - Mass Transit (bus, 

subway, train) 

Factors PE and PR 

 1 AER=air exchange rate, DE=decay-deposition rate, PR=proximity factor, PE=penetration factor

Each of the microenvironments is designed to simulate an environment in which people 

spend time during the day. CHAD locations are linked to the different microenvironments in the 

Microenvironment Mapping File (see Section 3.8.4). There are many more CHAD locations 

than microenvironment locations (there are 113 CHAD codes versus 12 microenvironments in 

this assessment) and thus most of the microenvironments have multiple CHAD locations mapped 

to them. 

The mass balance microenvironments have two parameters defined, the air exchange rate 

and the decay rate. The air exchange rate models the exchange of outside air with the 

microenvironment, while the decay rate models the rate of ozone breakdown or removal within 
 35 

the microenvironment. The development of air exchange rate values for this analysis is 

discussed in Section 3.9.2 and Appendix A. The development of the decay rate distribution is 

described in Section 3.9.3. 

3.10.2 Microenvironment Descriptions 

Microenvironment #1: Indoors-Residence. The Indoors-Residence Microenvironment 

accounts for three variables that affect ozone exposure: whether or not air conditioning is 

present, the average outdoor temperature, and the ozone decay rate. The first two of these 

variables affect the air exchange rate. An excerpt from the input file describing this 

microenvironment appears after this paragraph. 

The first section of the excerpt specifies the air exchange rate distributions for the 

microenvironment. Average temperature and air conditioning presence, which are city-specific, 

were coded into air exchange rate conditional variables C1 and C2, respectively. Average 

temperatures were broken into five categories: less than 50 degrees F, 50 to 68, 68 to 77, 77 to 

86, and 86 and above. Using data from several studies, air exchange rate estimates in the form of 

Micro number = 1 ! Indoors - residence 

Parameter Type = AER 

Condition # 1 = AvgTempCat 

Condition # 2 = AC_Home 

ResampHours = NO 

ResampDays = YES 

ResampWork = YES 

Block DType Season Area C1 C2 C3 Shape Min Max Par1 Par2 

1 1 1 1 1 1 1 Lognormal .1 10 0.956 1.962 

1 1 1 1 2 1 1 Lognormal .1 10 0.517 2.017 

1 1 1 1 3 1 1 Lognormal .1 10 0.524 2.189 

1 1 1 1 4 1 1 Lognormal .1 10 0.392 2.076 

1 1 1 1 5 1 1 Lognormal .1 10 0.392 2.076 

1 1 1 1 1 2 1 Lognormal .1 10 0.754 2.317 

1 1 1 1 2 2 1 Lognormal .1 10 0.698 2.180 

1 1 1 1 3 2 1 Lognormal .1 10 1.367 2.292 

1 1 1 1 4 2 1 Lognormal .1 10 1.067 1.989 

1 1 1 1 5 2 1 Lognormal .1 10 1.067 1.989 

Micro number = 1 

Parameter Type = DE 

ResampHours = NO 

ResampDays = NO 

ResampWork = YES 

Block DType Season Area C1 C2 C3 Shape Min Max Par1 Par2 

1 1 1 1 1 1 1 LogNormal 0.95 8.05 2.51 1.53 
 36 

lognormal distributions were generated. These functions are specific to the cities in the model 

run. For cities with similar climatic and other relevant characteristics, the same distributions 

were used (e.g., New York, Philadelphia, and Boston use the same distributions). The data 

sources used and the development of these distributions are discussed in detail in Appendix A. 

The ozone decay rate is characterized as a lognormal distribution (as shown in the last section of 

the excerpt). The development of the decay rate is discussed in Section 3.9.3. 

In the input file excerpt, there is a large block of numbers (which totals ten rows) in the 

air exchange rate portion of the file. In this block, the fifth number across, which falls under 

“C1” in the excerpt, represents the temperature. The code “C1” represents “Conditional Variable 

1.” In this range, the numeral one represents temperatures below 50 Fahrenheit, two represents 

temperatures from 50 to 68, three represents 68 to 77, four represents 77 to 86, and five 

represents 86 and above. The sixth number in this block, which falls under “C2” and ranges 

from one to two, represents air conditioning status, with the numeral one representing having an 

air conditioning, and two not having it. There are five distributions listed for each value, for a 

total of ten distributions. In the above example, there are actually four different distributions for 

each air conditioning setting; the last two distributions for each air conditioning setting (which 

represent temperature ranges from 77 to 86, and 86 and above) are the same. 

An example of how this microenvironment would function may help to elucidate the 

code. For the city of Atlanta, it is estimated that 85 percent of the population has air 

conditioning in the home, and 15 percent does not (see Appendix A for more information on the 

origin of these data). These percentages are included in the Profile Functions file, which is 

discussed in Section 3.9. Using these percentages, APEX can stochastically generate air 

conditioning status for a profiled individual. In addition, APEX takes as input the daily average 

temperature in Atlanta. Based on the air conditioning status and the temperature, the appropriate 

one of the ten distributions listed is chosen for a particular profile. For example, if the profile 

had air conditioning and the average temperature was 70, the third row would be chosen to 

characterize the air exchange rate. If the profile had no air conditioning, and the average 

temperature was 90, the tenth row would be chosen. 

 Microenvironments 2-7: All other indoor microenvironments. The remaining five 

indoor microenvironments, which represent Bars and Restaurants, Schools, Day Care Centers, 

Office, Shopping, and Other environments, are all modeled using the same data and functions. 

The data and methodology for developing these functions are detailed in Appendix A. An 

excerpt from the input file describing one of these microenvironments is given on the next page. 

 As with the Indoor-Residence microenvironment, these microenvironments use both air 

exchange rates and decay rates to calculate exposures within the microenvironment. The air 

exchange rate distribution was developed based on an indoor air quality study (Persily et al, 

2005). This research indicated that the lognormal distributions should provide effective 

modeling of ozone exposure. The decay rate is the same as used in the Indoor-Residence 

microenvironment, and is discussed in Section 3.9.3. 
 37 

Microenvironments 8 and 9: Outdoor microenvironments. Two outdoor 

microenvironments, the Near Road and Public Garage/Parking Lot environments, are different 

from the indoor microenvironments in that they use the factors method to calculate pollutant 

exposure. Proximity factors were developed to estimate exposures in these microenvironments. 

Penetration factors are not applicable to outdoor environments. An excerpt from the file 

describing this microenvironment follows this paragraph. 

The distribution for the proximity factor was developed from an ozone study (Johnson et 

al, 1995) conducted in the greater Cincinnati metropolitan area in August and September, 1994 

(see Appendix A for details on this study). Vehicle tests were conducted according to an 

experimental design specifying the vehicle type, road type, vehicle speed, and ventilation mode. 

Microenvironment 10: Outdoors-General. The general outdoor environment 

concentrations should be well represented by the ambient monitors. Therefore the penetration 

factor and proximity factor for this microenvironment were set to 1. 

Micro number = 8 ! Outdoor near road 

Parameter Type = PR 

ResampHours = YES 

ResampDays = YES 

ResampWork = YES 

Block DType Season Area C1 C2 C3 Shape Min Max Par1 Par2 

1 1 1 1 1 1 1 Normal 0.422 1.0 0.755 0.203 

Micro number = 2 ! Bars & restaurants 

Parameter Type = AER 

ResampHours = NO 

ResampDays = YES 

ResampWork = YES 

Block DType Season Area C1 C2 C3 Shape Min Max Par1 Par2 

1 1 1 1 1 1 1 LogNormal 0.07 13.8 1.109 3.015 

Micro number = 2 

Parameter Type = DE 

ResampHours = NO 

ResampDays = YES 

ResampWork = YES 

Block DType Season Area C1 C2 C3 Shape Min Max Par1 Par2 

1 1 1 1 1 1 1 LogNormal 0.95 8.05 2.51 1.53 
 38 

Microenvironments 11 and 12: In Vehicle- Cars and Trucks, and Mass Transit. Both 

of these microenvironments were calculated using the same values. These microenvironments 

use the factors method to calculate pollutant exposure. Both proximity factors and penetration 

factors were developed to estimate exposures in the microenvironments. Again, the optional 

concentration source variable is not relevant to ozone studies and was not used. An excerpt from 

the file describing this microenvironment follows this discussion. 

The penetration factor distribution was developed using the inside-vehicle to outsidevehicle ratios from the Cincinnati ozone study previously mentioned (Johnson et al, 1995). 

Three proximity factor distributions were developed, one for local roads, one for urban roads, 

and one for interstates. The proportion of vehicle miles traveled in each city was estimated and 

used to weight the selection of the distributions. These weightings are included in the Profile 

Functions file, which is discussed in Section 3.11. Again, these distributions were developed 

based on the Cincinnati ozone study. 

 

3.10.3 Ozone Decay and Deposition Rates 

For this analysis, the same ozone decay rate distribution was used for all 

microenvironments that use the mass balance method. This distribution is based on data from an 

ozone decay study (Lee et al., 1999). This study measured decay rates in the living rooms of 43 

residences in Southern California. Measurements of decay rates in a second room were made in 

24 of these residences. The 67 decay rates range from 0.95 to 8.05 hour-1. A lognormal 

distribution was fit to the measurements from this study, yielding a geometric mean of 2.5 and a 

geometric standard deviation of 1.5. These values are constrained to lie between 0.95 and 8.05 

hour-1. The specification of the decay rate (parameter type = DE) is shown in the file excerpts for 

the residential microenvironment and the other indoor microenvironments above. 

Micro number = 11 ! Cars & trucks 

Parameter Type = PE 

ResampHours = YES 

ResampDays = YES 

ResampWork = YES 

Block DType Season Area C1 C2 C3 Shape Min Max Par1 Par2 

1 1 1 1 1 1 1 Normal 0.1 1.0 0.300 0.232 

Micro number = 11 

Parameter Type = PR 

Condition # 1 = Conditional1 

ResampHours = YES 

ResampDays = YES 

ResampWork = YES 

Block DType Season Area C1 C2 C3 Shape Min Max Par1 Par2 

1 1 1 1 1 1 1 Normal 0.422 1.0 0.755 0.203 

1 1 1 1 2 1 1 Normal 0.355 1.0 0.754 0.243 

1 1 1 1 3 1 1 Normal 0.093 1.0 0.364 0.165 
 39 

3.10.4 Microenvironment Mapping 

The Microenvironment Mapping file matches the APEX Microenvironments to CHAD 

Location codes. Table 3-6 gives the mapping used for the APEX simulations. 

Table 3-6. Mapping of CHAD activity locations to APEX microenvironments 

CHAD Loc. Description APEX micro 

--------- ------------------------------------------------- 

U Uncertain of correct code = -1 Unknown 

X No data = -1 Unknown 

30000 Residence, general = 1 Indoors-Residence 

30010 Your residence = 1 Indoors-Residence 

30020 Other residence = 1 Indoors-Residence 

30100 Residence, indoor = 1 Indoors-Residence 

30120 Your residence, indoor = 1 Indoors-Residence 

30121 ..., kitchen = 1 Indoors-Residence 

30122 ..., living room or family room = 1 Indoors-Residence 

30123 ..., dining room = 1 Indoors-Residence 

30124 ..., bathroom = 1 Indoors-Residence 

30125 ..., bedroom = 1 Indoors-Residence 

30126 ..., study or office = 1 Indoors-Residence 

30127 ..., basement = 1 Indoors-Residence 

30128 ..., utility or laundry room = 1 Indoors-Residence 

30129 ..., other indoor = 1 Indoors-Residence 

30130 Other residence, indoor = 1 Indoors-Residence 

30131 ..., kitchen = 1 Indoors-Residence 

30132 ..., living room or family room = 1 Indoors-Residence 

30133 ..., dining room = 1 Indoors-Residence 

30134 ..., bathroom = 1 Indoors-Residence 

30135 ..., bedroom = 1 Indoors-Residence 

30136 ..., study or office = 1 Indoors-Residence 

30137 ..., basement = 1 Indoors-Residence 

30138 ..., utility or laundry room = 1 Indoors-Residence 

30139 ..., other indoor = 1 Indoors-Residence 

30200 Residence, outdoor = 10 Outdoors-Other 

30210 Your residence, outdoor = 10 Outdoors-Other 

30211 ..., pool or spa = 10 Outdoors-Other 

30219 ..., other outdoor = 10 Outdoors-Other 

30220 Other residence, outdoor = 10 Outdoors-Other 

30221 ..., pool or spa = 10 Outdoors-Other 

30229 ..., other outdoor = 10 Outdoors-Other 

30300 Residential garage or carport = 7 Indoors-Other 

30310 ..., indoor = 7 Indoors-Other 

30320 ..., outdoor = 10 Outdoors-Other 

30330 Your garage or carport = 1 Indoors-Residence 

30331 ..., indoor = 1 Indoors-Residence 

30332 ..., outdoor = 10 Outdoors-Other 

30340 Other residential garage or carport = 1 Indoors-Residence 

30341 ..., indoor = 1 Indoors-Residence 

30342 ..., outdoor = 10 Outdoors-Other 

30400 Residence, none of the above = 1 Indoors-Residence 

31000 Travel, general = 11 In Vehicle-Cars_and_Trucks 

31100 Motorized travel = 11 In Vehicle-Cars_and_Trucks 

31110 Car = 11 In Vehicle-Cars_and_Trucks 

31120 Truck = 11 In Vehicle-Cars_and_Trucks 

31121 Truck (pickup or van) = 11 In Vehicle-Cars_and_Trucks 

31122 Truck (not pickup or van) = 11 In Vehicle-Cars_and_Trucks 

31130 Motorcycle or moped = 8 Outdoors-Near_Road 

31140 Bus = 12 In Vehicle-Mass_Transit 

31150 Train or subway = 12 In Vehicle-Mass_Transit 
 40 

31160 Airplane = 0 Zero_concentration 

31170 Boat = 10 Outdoors-Other 

31171 Boat, motorized = 10 Outdoors-Other 

31172 Boat, other = 10 Outdoors-Other 

31200 Non-motorized travel = 10 Outdoors-Other 

31210 Walk = 10 Outdoors-Other 

31220 Bicycle or inline skates/skateboard = 10 Outdoors-Other 

31230 In stroller or carried by adult = 10 Outdoors-Other 

31300 Waiting for travel = 10 Outdoors-Other 

31310 ..., bus or train stop = 8 Outdoors-Near_Road 

31320 ..., indoors = 7 Indoors-Other 

31900 Travel, other = 11 In Vehicle-Cars_and_Trucks 

31910 ..., other vehicle = 11 In Vehicle-Cars_and_Trucks 

32000 Non-residence indoor, general = 7 Indoors-Other 

32100 Office building/ bank/ post office = 5 Indoors-Office 

32200 Industrial/ factory/ warehouse = 5 Indoors-Office 

32300 Grocery store/ convenience store = 6 Indoors-Shopping 

32400 Shopping mall/ non-grocery store = 6 Indoors-Shopping 

32500 Bar/ night club/ bowling alley = 2 Indoors-Bars_and_Restaurants 

32510 Bar or night club = 2 Indoors-Bars_and_Restaurants 

32520 Bowling alley = 2 Indoors-Bars_and_Restaurants 

32600 Repair shop = 7 Indoors-Other 

32610 Auto repair shop/ gas station = 7 Indoors-Other 

32620 Other repair shop = 7 Indoors-Other 

32700 Indoor gym /health club = 7 Indoors-Other 

32800 Childcare facility = 4 Indoors-Day_Care_Centers 

32810 ..., house = 1 Indoors-Residence 

32820 ..., commercial = 4 Indoors-Day_Care_Centers 

32900 Large public building = 7 Indoors-Other 

32910 Auditorium/ arena/ concert hall = 7 Indoors-Other 

32920 Library/ courtroom/ museum/ theater = 7 Indoors-Other 

33100 Laundromat = 7 Indoors-Other 

33200 Hospital/ medical care facility = 7 Indoors-Other 

33300 Barber/ hair dresser/ beauty parlor = 7 Indoors-Other 

33400 Indoors, moving among locations = 7 Indoors-Other 

33500 School = 3 Indoors-Schools 

33600 Restaurant = 2 Indoors-Bars_and_Restaurants 

33700 Church = 7 Indoors-Other 

33800 Hotel/ motel = 7 Indoors-Other 

33900 Dry cleaners = 7 Indoors-Other 

34100 Indoor parking garage = 7 Indoors-Other 

34200 Laboratory = 7 Indoors-Other 

34300 Indoor, none of the above = 7 Indoors-Other 

35000 Non-residence outdoor, general = 10 Outdoors-Other 

35100 Sidewalk, street = 8 Outdoors-Near_Road 

35110 Within 10 yards of street = 8 Outdoors-Near_Road 

35200 Outdoor public parking lot /garage = 9 Outdoors-Public_Garage-Parking 

35210 ..., public garage = 9 Outdoors-Public_Garage-Parking 

35220 ..., parking lot = 9 Outdoors-Public_Garage-Parking 

35300 Service station/ gas station = 10 Outdoors-Other 

35400 Construction site = 10 Outdoors-Other 

35500 Amusement park = 10 Outdoors-Other 

35600 Playground = 10 Outdoors-Other 

35610 ..., school grounds = 10 Outdoors-Other 

35620 ..., public or park = 10 Outdoors-Other 

35700 Stadium or amphitheater = 10 Outdoors-Other 

35800 Park/ golf course = 10 Outdoors-Other 

35810 Park = 10 Outdoors-Other 

35820 Golf course = 10 Outdoors-Other 

35900 Pool/ river/ lake = 10 Outdoors-Other 

36100 Outdoor restaurant/ picnic = 10 Outdoors-Other 

36200 Farm = 10 Outdoors-Other 

36300 Outdoor, none of the above = 10 Outdoors-Other 
 41 

3.11 Profile Functions 

The Profile Functions file contains settings used to generate results for variables related 

to simulated individuals. While certain settings for individuals are generated automatically by 

APEX based on other input files, including demographic characteristics, others can be specified 

using this file. For example, the file may contain settings for determining whether the profiled 

individual has a car air conditioner, a gas stove, etc. The details and mechanics of this process 

are discussed in Section 2.3.2. 

As discussed in Section 3.8.2, the Profile Functions file contains fractions indicating the 

prevalence of air conditioning in the cities modeled in this experiment. APEX uses these 

fractions to stochastically generate air conditioning status for profiled individuals. The 

derivation of this data is discussed in Appendix A. An excerpt from the file describing this 

microenvironment follows this paragraph. 

 

One user-defined function was included in the Profile Functions file in order to reflect 

regional driving characteristics. The Conditional1 function is used to simulate In-vehicle 

penetration factors for modeled individuals. An excerpt from the file describing this 

microenvironment follows this paragraph. 

Conditional1 

! Penetration values for vehicles ME 11 and 12 

TABLE 

INPUT1 PROBABILITY 3 

0.14 0.55 0.31 

RESULT INTEGER 3 

1 2 3 

# 

AC_Home 

! Has air conditioning at home 

TABLE 

INPUT1 PROBABILITY 2 “A/C probabilities” 

0.85 0.15 

RESULT INTEGER 2 “Yes/No” 

1 2 

# 
 42 

The function contains different distributions for three road types: urban, local, and 

interstate. These distributions model how the road type affects pollutant level penetration into 

the microenvironment. For each of the 12 locations modeled, the percentage of vehicle miles 

traveled on each road type was generated from 2003 Federal Highway Administration data 

(FHWA, 2004). These percentages are listed as fractions on the fifth line of the above excerpt. 

Using these percentages, the function allowed each of the distributions, which are defined in the 

microenvironment file, to be selected based on the amount of vehicle miles traveled in the area. 

See Appendix A for more information on development of the distributions in the 

microenvironments. 
 43 

4. PRINCIPAL LIMITATIONS AND UNCERTAINTIES OF THE MODELING 

APPROACH 

Inhalation exposure and risk modeling attempts to simulate real world conditions in order 

to accurately estimate exposures to pollutants and their resulting risk. In general, the methods 

and the model used in this assessment conform to the most contemporary modeling 

methodologies available. APEX is a powerful, highly customizable modeling system that allows 

for the realistic estimation of air pollutant exposure to individuals. Since it is based on human 

activity diaries and accounts for all important variables known to affect exposure, it has the 

ability to effectively approximate actual conditions. In addition, the data used to run the system 

were chosen because they were the best available to ensure realistic and defensible results. 

However, there are constraints and uncertainties with the modeling approach and the input data 

that limit the realism and accuracy of the model results. 

4.1 Methodology 

As described in Appendix A, several ozone and air pollution studies were reviewed, and 

data from these studies were used to develop the parameters and factors that were used to build 

the microenvironments in this assessment. A constraint on this effort is that there are limited 

ozone exposure studies. In addition, there are geographical limitations of the studies used to 

develop factors for this assessment. While these studies were generally performed in the 

geographical areas modeled in this assessment or in similar areas, there were differences that 

could lend uncertainty. For example, the ozone study (Johnson et al, 1995) that was used to 

develop proximity factors for in-vehicle microenvironments for all 12 cities was performed in 

Cincinnati. In addition, the air exchange rate distributions used for Boston, Chicago, Cleveland, 

and Philadelphia were developed from a study conducted in New York City. It is possible that 

climatic and other differences among these cities would produce different results. Scientific 

judgments were made in choosing appropriate data and information sources to best model ozone 

exposures. However, it is possible that despite best efforts there could be different 

interpretations about which data sources and methodologies are appropriate. Evaluation of 

several components of uncertainty in specification of CSA-specific air exchange rates are 

discussed below. 

There are other areas of the modeling approach that have either assumptions or estimates 

that could affect results. For example, the microenvironments that are used in the program are 

matched to CHAD data. Because there are fewer microenvironments than CHAD locations, 

there is some information lost in this translation. 

4.2 Input Data 

Modeling results are heavily dependent on the quality of the data that are input to the 

system. The data for this analysis were selected in order to give the best opportunity to simulate 

actual conditions. One benefit of using well characterized data as inputs to the model is that 

limitations and other problems with the data are well understood. Still, the limitations and 

uncertainties of each of the data streams affect the overall quality of the model output. These 
 44 

issues and how they specifically affect each data stream are discussed in this section. The 

highest quality data streams are discussed first. 

4.2.1 Meteorological Data 

The least problematic of the data input to APEX are likely the meteorological data. 

These data are taken directly from monitoring stations in the assessment areas. One strength of 

these data is that it is relatively easy to see significant errors if they appear in the data. Because 

general climactic conditions are known for each area simulation, it would have been apparent 

upon review if there were outliers in the dataset. However, there are limitations in the use of 

these data. Because APEX only uses one temperature value per day, the model does not 

represent hour-to-hour variations in meteorological conditions throughout the day that may affect 

both ozone formation and exposure estimates within microenvironments. 

4.2.2 Air Quality Data 

The air quality data are taken directly from monitoring sites within each of the study 

areas, and thus the data are reliable and of high quality. Some data issues specific to air quality 

data result from the nature of pollutant formation and dispersion. Because many variables affect 

pollutant fate and transport, it is difficult to determine exactly how concentrations in the vicinity 

of a monitoring station may differ from the concentrations at other locations. Pollutant levels are 

highly dependent on weather and wind, and other unknowns may effect how well the data 

represent pollutant concentrations in the area. However, because APEX uses hourly average 

ozone concentrations, the model employs a temporally refined pollutant concentration record, 

which increases the accuracy of both ozone concentration and exposure estimates. 

4.2.3 Population and Commuting Data 

The population and commuting data are drawn from U.S. Census data from the year 

2000. This is a high quality data source for nationwide population data in the U.S. However, the 

data do have limitations. The Census used random sampling techniques instead of attempting to 

reach all households in the U.S., as it has in the past. While the sampling techniques are well 

established and trusted, they introduce some uncertainty to the system. The Census has a quality 

section (http://www.census.gov/quality/) that discusses these and other issues with Census data. 

In addition to these data quality issues, certain simplifying assumptions were made in 

order to better match reality or to make the data match APEX input specifications. For example, 

the APEX dataset does not differentiate people that work at home from those that commute 

within their home tract, and individuals that commute over 120 km a day were assumed to not 

commute daily. In addition to emphasizing some of the limitations of the input data, these 

assumptions introduce some uncertainty to the results. These issues were discussed in Sections 

3.5 and 3.6. 

4.2.4 Physiological Data 

Because the physiological data were drawn from a sample, it is possible that they do not 

accurately mirror national physiological characteristics. Furthermore, on a larger scale, it is 

possible that national physiological characteristics have drifted somewhat since the publication 
 45 

of these data. For example, both the marked rise in obesity and ongoing national demographic 

shifts could result in some inaccuracies. 

4.2.5 Activity Pattern Data 

It is probable that the CHAD data used in the system is the most subject to limitations 

and uncertainty of all the data used in the system. Much of the data used to generate the daily 

diaries are over 20 years old. Table 3-3 indicates the ages of the CHAD diaries used in this 

modeling analysis. While the specifics of people’s daily activities may not have changed much 

over the years, it is certainly possible that some differences do exist. In addition, the CHAD data 

are taken from numerous surveys that were performed for different purposes. Some of these 

surveys lasted only a day while others went on for weeks. Some of the studies were specifically 

designed not to be representative of the population at large in order to fulfill their specific 

mission when they were conducted. These issues affect the overall quality of the data that now 

resides in CHAD. An investigation on the sensitivity of the APEX results to the activity pattern 

database is discussed below. 

4.2.6 Air Exchange Rates 

 There are several components of uncertainty in the CSA-specific residential air exchange 

rate distributions used for this analysis. Appendix D details an analyses of uncertainty due to 

extrapolation of air exchange rate distributions among CSAs , and of within-CSA uncertainty 

due to sampling variation. In Appendix E we describe an analysis of the uncertainty due to 

estimating daily air exchange rate distributions from air exchange rate measurements with 

varying averaging times. The results of those investigations are summarized here. 

 Extrapolation among cities CSA-specific distributions for use with the APEX ozone 

model were developed for 12 target CSAs, as detailed in Appendix A. Because we did not have 

CSA-specific data for all the 12 CSAs targeted in this analysis, for many we used data from 

another CSA or a combinations of other CSAs thought to have similar characteristics with 

respect to factors that might influence air exchange rates (see Table 4-1). Such factors include 

age composition of housing stock, construction methods, and other meteorological variables not 

explicitly treated in the analysis, such as humidity and wind speed patterns. In order to assess the 

uncertainty associated with this extrapolation, we investigated the between-CSA uncertainty by 

examining the variation of the geometric means and standard deviations across cities and studies. 

 The analysis showed a relatively wide variation across different cities in the air exchange 

rate geometric mean and standard deviation, stratified by air-conditioning status and temperature 

range. This implies that the air exchange rate modeling results would be very different if the 

matching of modeled CSAs to study CSAs was changed, although a sensitivity study using the 

APEX model would be needed to assess the impact on the ozone exposure estimates. For 

example, the ozone exposure estimates may be sensitive to the assumption that the St. Louis air 

exchange rate distributions can be represented by the combined non-California air exchange rate 

data. One way to address this would to perform a Monte Carlo analysis where the first stage is to 

randomly select a CSA outside of California, the second stage picks the air conditioning status, 

and the third stage picks the air exchange rate value from the assigned distribution for the CSA, 

air conditioning status and temperature range. Note that this will result in a very different 
 46 

distribution to the current approach for St. Louis that fits a single log-normal distribution to all 

the non-California data for a given temperature range and air conditioning status. The current 

approach weights each data point equally, so that CSAs like New York with most of the data 

values get the greatest statistical weight. The Monte Carlo approach gives the same total 

statistical weight for each CSA and fits a mixture of log-normal distributions rather than a single 

distribution. 

 Within CSA uncertainty In general, there is also some variation within studies for the 

same CSA, but this is much smaller than the variation across CSAs. This finding tends to support 

the approach of combining different studies for a CSA. 

 In addition, we assessed the within-city uncertainty by using a bootstrap distribution to 

estimate the effects of sampling variation on the fitted geometric means and standard deviations 

for each CSA. The bootstrap distributions assess the uncertainty due to random sampling 

variation but do not address uncertainties due to the lack of representativeness of the available 

study data or the variation in the lengths of the AER monitoring periods. The analysis showed 

that the geometric standard deviation uncertainty for a given CSA/air-conditioningstatus/temperature-range combination tended to have a range of at most from “fitted GSD-1.0 hr1

” to “fitted GSD+1.0 hr-1”, but the intervals based on larger AER sample sizes were frequently 

much narrower. The ranges for the geometric means tended to be approximately from “fitted 

GM-0.5 hr-1” to “fitted GM+0.5 hr-1”, but in some cases were much smaller. 

Table 4-1. Assignment of residential air exchange rate distributions to modeled CSAs 

Modeled CSA Air exchange rate distribution 

Atlanta, GA, A/C Research Triangle Park, A/C only 

Atlanta, GA, no A/C All non-California, no A/C (“Outside California”) 

Boston, MA New York 

Chicago, IL New York 

Cleveland, OH New York 

Detroit, MI New York 

Houston, TX Houston 

Los Angeles, CA Los Angeles 

New York, NY New York 

Philadelphia, PA New York 

Sacramento Inland parts of Los Angeles (“Inland California”) 

St. Louis All non-California 

Washington, DC, A/C Research Triangle Park, A/C only 

Washington, DC, no A/C All non-California, no A/C 
 47 

 Varying measurement averaging times Although the averaging periods for the air 

exchange rates in the study databases varied from one day to seven days, our analyses did not 

take the measurement duration into account and treated the data as if they were a set of 

statistically independent daily averages. To investigate the uncertainty of this assumption, we 

investigated the correlations between consecutive 24-hour air exchange rates measured at the 

same house from the Research Triangle Park Panel Study. The results showed extremely strong 

correlations, providing support for the simplified approach of treating multi-day averaging 

periods as if they were 24-hour averages. 

 However, this finding raises another issue. In the current version of the APEX model, 

there are several options for stratification of time periods with respect to air exchange rates 

distributions, and for when to re-sample from a distribution for a given stratum. The options 

selected for this current set of simulations resulted in a uniform air exchange rates for each 24-

hour period and re-sampling of the 24-hour air exchange rates for each simulated day. This resampling for each simulated day implies that the simulated air exchange rates on consecutive 

days in the same microenvironment are statistically independent. Although we have not 

identified sufficient data to test the assumption of uniform air exchange rates throughout a 24-

hour period, the analyses described in Appendix D suggest that air exchange rates on consecutive 

days are highly correlated. Therefore, we performed sensitivity simulations to assess the impact 

of the assumption of temporally independent air exchange rates, but found little difference 

between APEX predictions for the two scenarios (i.e., temporally independent and autocorrelated 

air exchange rates). 

4.2.7 Air Conditioning Prevalence 

 Because the selection of an air exchange rate distribution is conditioned on the presence 

or absence of an air-conditioner, for each modeled CSA, the air conditioning status of the 

residential microenvironments is simulated randomly using the probability that a residence has 

an air conditioner, i.e., the residential air conditioner prevalence rate. For this study we used 

CSA-specific data from the American Housing Survey of 2003. Appendix F details the 

specification of uncertainty estimates in the form of confidence intervals for the air conditioner 

prevalence rate, and compares these with prevalence rates and confidence intervals developed 

from the Energy Information Administration’s Residential Energy Consumption Survey of 2001 

for more aggregate geographic subdivision (e.g., states, multi-state Census regions). 

 Air–conditioning prevalence rates for the 12 target CSAs from the American Housing 

Survey ranged from 55% for Los Angeles to 97% for Atlanta. Reported standard errors were 

relatively small, ranging from less than 1% for Houston to 3.4% for Cleveland. The 

corresponding 95% confidence interval spans range from approximately 4% to 14%. 

4.2.8 Evaporative Coolers 

 Some residences use evaporative coolers, also known as “swamp coolers,” for cooling. In 

our estimation of air exchange rate distributions from measurement data, we did not take into 

account the presence or absence of an evaporative cooler. 
 48 

 Although both the housing surveys discussed in section 4.2.7 specifically exclude 

evaporative coolers from their definitions of an air conditioner, it is plausible that the air 

exchange rate distributions might also depend upon the presence of an evaporative cooler. To 

evaluate this issue, Appendix F also details a comparison of the air exchange rate distributions 

estimated with and without accounting for the presence or absence of an evaporative cooler, 

using the available data from three air exchange rate measurement studies. The analysis showed 

no improvement in the statistical air exchange model when the data were also stratified by 

evaporative cooler presence or absence, given that they are already stratified by CSA, air 

conditioner presence or absence, and temperature range. 
 49 

5. RESULTS OF EXPOSURE MODELING 

5.1 Base case 

 In this section we present APEX results for population subgroups of interest in Boston 

and Houston for 2002 and 2004 as examples. Other CSAs show similar results. The population 

subgroups are: 

• Children 

• Active children 

• Asthmatic children 

 Figures 5-1 and 5-2 show the APEX estimates of the number of person-days of exposure 

to exceedances of various 8-hour average ozone exposure concentrations during moderate 

exertion in Boston for 2002 and 2004 conditions respectively. Comparison of the figures indicate 

generally higher exposure levels in 2002 with a maximum of 0.14 ppm-8hr. The corresponding 

value for 2004 is 0.10 ppm-8hr, respectively. 

 Figures 5-3 and 5-4 show the same APEX estimates for Houston, where exposure levels 

for 2002 and 2004 are similar with maxima of 0.14 and 0.13 ppm-8hr, respectively. 

 The remainder of the discussion of APEX estimates will be confined to 2002 only. 

 Figures 5-5 through 5-7 show the number of persons in Boston exposed to various 

numbers of exceedances of various 8-hour average ozone exposure concentrations during 

moderate exertion for 2002 conditions. Figures 5-8 through 5-10 show the same APEX estimates 

for Houston. 

 More than 45% of each child sub-population in Boston (i.e., children, active children, 

asthmatic children) is estimated to be exposed to at least one exceedance of an 8-hour average 

ozone concentration of 0.07 ppm during moderate exertion, and more than 10% are estimated to 

be exposed to at least 3 exceedances during moderate exertion. 

 The proportions are somewhat lower in Houston. For the children’s subpopulations the 

proportion with at least one exceedance of 0.07 ppm during moderate exertion is estimated to be 

between 32% and 37%, and with at least 3 exceedances between 3% and 4%. 
 50 

Figure 5-1 

Person-Days of Exposure to 8-Hour Average Concentrations During

Moderate Exertion

 --Boston 2002--

1.E+00

1.E+02

1.E+04

1.E+06

1.E+08

0.010.03

0.050.070.09

0.11

0.13

0.15

Exposure Concentration (ppm)

Person-Days

Children

Active children

Asthmatic children

Figure 5-2 

Person-Days of Exposure to 8-Hour Average Concentrations During

Moderate Exertion

 --Boston 2004--

1.E+00

1.E+02

1.E+04

1.E+06

1.E+08

0.01

0.03

0.05

0.07

0.09

0.11

0.13

0.15

Exposure Concentration (ppm)

Person-Days

Children

Active children

Asthmatic children
 51 

Figure 5-3 

Person-Days of Exposure to 8-Hour Average Concentrations During

Moderate Exertion

--Houston 2002--

1.E+00

1.E+02

1.E+04

1.E+06

1.E+08

1.E+10

0

0.02

0.04

0.06

0.08

0.1

0.12

Exposure Concentration (ppm)

Person-days

Children

Active children

Asthmatic children

Figure 5-4 

Person-Days of Exposure to 8-Hour Average Concentrations During

Moderate Exertion

--Houston 2004--

1.E+00

1.E+02

1.E+04

1.E+06

1.E+08

1.E+10

0

0.02

0.04

0.06

0.08

0.1

0.12

Exposure Concentration (ppm)

Person-days

Children

Active children

Asthmatic children
 52 

Figure 5-5 

Exceedances of 8-Hour Average Exposure Concentrations 

During Moderate Exertion

 --Children, Boston, 2002--

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

0

0.02

0.04

0.06

0.08

0.1

0.12

Exposure Concentration (ppm)

Persons

1 exceedance

2 exceedances

3 exceedances

4 exceedances

5 exceedances

Figure 5-6 

Exceedances of 8-Hour Average Exposure Concentrations 

During Moderate Exertion

 --Active Children, Boston, 2002--

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

0

0.02

0.04

0.06

0.08

0.1

Exposure Concentration (ppm)

Persons

1 exceedance

2 exceedances

3 exceedances

4 exceedances

5 exceedances
 53 

Figure 5-7 

Exceedances of 8-Hour Average Exposure Concentrations 

During Moderate Exertion

 --Asthmatic Children, Boston, 2002--

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

0

0.02

0.04

0.06

0.08

0.1

0.12

Exposure Concentration (ppm)

Persons

1 exceedance

2 exceedances

3 exceedances

4 exceedances

5 exceedances

Figure 5-8 

Exceedances of 8-Hour Average Exposure Concentrations During

Moderate Exertion 

 --Children, Houston, 2002--

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

0

0.02

0.04

0.06

0.08

0.1

0.12

Exposure Concentration (ppm)

Persons

1 exceedance

2 exceedances

3 exceedances

4 exceedances

5 exceedances
 54 

Figure 5-9 

Exceedances of 8-Hour Average Exposure Concentrations During

Moderate Exertion 

 --Active Children, Houston, 2002--

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

0

0.02

0.04

0.06

0.08

0.1

0.12

Exposure Concentration (ppm)

Persons

1 exceedance

2 exceedances

3 exceedances

4 exceedances

5 exceedances

Figure 5-10 

Exceedances of 8-Hour Average Exposure Concentrations During

Moderate Exertion 

 --Asthmatic Children, Houston, 2002--

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

0

0.010.020.030.040.050.060.070.080.09

0.1

0.110.12

Exposure Concentration (ppm)

Persons

1 exceedance

2 exceedances

3 exceedances

4 exceedances

5 exceedances
 55 

5.2 Attainment scenarios 

 The exposure projections presented in this section are based on the air quality projections 

discussed in section 3.3. Due to the uncertainties in the air quality projections, these exposure 

projections should be viewed as demonstrating the general range of possible changes in 

population exposure due to implementation of alternative NAAQS standards. They should not be 

considered as CSA-specific projections. 

 Figure 5-11 presents APEX projections of Boston children exposed to at least 3 

exceedances of various 8-hour average concentration levels, given attainment of various 

alternative NAAQS standards described in Section 3.3 above and 2002 meteorological 

conditions. Figure 5-12 presents the corresponding information for person-days of exceedances. 

Each figure contains a set of curves corresponding to potential air quality standards specified as 

various combinations of concentration thresholds and number of exceedances allowed. Table 3-

2 explains the meaning of the labels “85/4,” etc. 

 Figure 5-11 shows that each of the alternative standards is estimated to reduce the 

proportion of the population subgroup exposed at least 3 times to 8-hour average concentrations 

exceeding 0.07 ppm from about 12% (2002 base case) to between 0% and 2% depending on the 

alternative standard. 

 Figure 5-12 indicates that a reduction in exposures under the alternative standards, with 

the 95th percentile 8-hour average exposure concentration decreasing from approximately 0.055 

ppm (2002 base case) to a range of 0.040 to 0.045 ppm, depending on the alternative standard. 

Similarly, the maximum 8-hour average exposure concentration decreases from 0.13 ppm (2002 

base case) to a range of 0.08 to 0.11 ppm. 

 Figures 5-13 and 5-14 present the corresponding information for Houston. In this case the 

proportion of children exposed at least 3 times to 8-hour average concentrations exceeding 0.07 

ppm decreased from about 3% (2002 base case) to 0%. And the 95th percentile 8-hour average 

exposure concentration decreases from approximately 0.045 ppm to approximately 0.035 ppm, 

while the maximum exposure concentrations decreases from 0.13 ppm to a range of 0.07 to 0.09 

ppm, depending on the alternative standard. 

 Figures 5-15 through 5-18 present the corresponding information for active children, and 

Figures 5-19 through 5-22 for asthmatic children, with similar results. In general the figures 

suggest that changing the threshold concentration would have more influence on this measure of 

population exposure than changing the number of permitted exceedances. 
 56 

Figure 5-11. Number of persons with at least three 8-hour exposures above different levels, 

for Children at moderate exertion, Boston, 2002. 

Figure 5-12. Person-days (occurrences) above 8-hour exposure levels for different 

alternative standards, for Children at moderate exertion, Boston, 2002. 
 57 

Figure 5-13. Number of persons with at least three 8-hour exposures above different levels, 

for Children at moderate exertion, Houston, 2002. 

Figure 5-14. Person-days (occurrences) above 8-hour exposure levels for different 

alternative standards, for Children at moderate exertion, Houston, 2002. 
 58 

Figure 5-15. Number of persons with at least three 8-hour exposures above different levels, 

for Active Children at moderate exertion, Boston, 2002. 

Figure 5-16. Person-days (occurrences) above 8-hour exposure levels for different 

alternative standards, for Active Children at moderate exertion, Boston, 2002. 
 59 

Figure 5-17. Number of persons with at least three 8-hour exposures above different levels, 

for Active Children at moderate exertion, Houston, 2002. 

Figure 5-18. Person-days (occurrences) above 8-hour exposure levels for different 

alternative standards, for Active Children at moderate exertion, Houston, 2002. 
 60 

Figure 5-19. Number of persons with at least three 8-hour exposures above different levels, 

for Asthmatic Children at moderate exertion, Boston, 2002. 

Figure 5-20. Person-days (occurrences) above 8-hour exposure levels for different 

alternative standards, for Asthmatic Children at moderate exertion, Boston, 2002. 
 61 

Figure 5-21. Number of persons with at least three 8-hour exposures above different levels, 

for Asthmatic Children at moderate exertion, Houston, 2002. 

Figure 10. Person-days (occurrences) above 8-hour exposure levels for different alternative 

standards, for Asthmatic Children at moderate exertion, Houston, 2002. 
 62 
 63 

6. SENSITIVITY STUDIES 

 In order to assess the sensitivity of the APEX predictions to some of the uncertain data 

inputs, several additional simulations were conducted for 2002 conditions. The inputs analyzed 

were the activity pattern database, the ozone decay rate, the proximity factor, and the air 

exchange rate. In addition, we evaluated the impact of the new method for constructing longterm activity patterns from short-term records. 

6.1 Activity Pattern Database 

 Because many of the studies included in the CHAD database are not national in scope, 

nor do they necessarily correspond to the CSAs targeted here, it would be useful to know how 

similar the component studies are. Strong similarity would suggest that extrapolation of activity 

data gathered from one sample population to another population is appropriate. 

 The most comprehensive individual study is probably the National Human Activity 

Pattern Study (NHAPS), so we compared the base case exposure results with corresponding 

results using only the NHAPS data. The results for all persons at all activity levels in Boston are 

presented in Figure 6-1 and for active persons with moderate activity in Boston are presented in 

Figure 6-2. The figures present several pairs of cumulative distribution functions for the number 

of days/person that a given 8-hour average threshold concentration is exceeded. The different 

curves represent different thresholds, ranging from 0.01 to 0.05 ppm-8hr, as indicated in the 

figure legends. Figure 6-1 shows little difference between the base case distributions and those 

for NHAPS activity patterns only, indicating that both the average number of exceedances and 

the variability among individuals are similar. This suggests that the composite database is similar 

to NHAPS. 

 However, Figure 6-2 does show moderate differences, with the NHAPS results 

systematically lower than the base case. This suggests that the activity patterns for active people 

in the NHAPS data base may differ somewhat from those in the other component data bases of 

CHAD. 

 Tables 6-1 through 6-4 present the results for the number of persons exposed to 8-hour 

average concentrations exceeding 0.07 ppm in the general population and for children, 

respectively, with moderate exertion. Simulations were performed both with the base case air 

quality and with a scenario of attainment of the current NAAQS. 

 The results show that, with a few notable exceptions, use of the NHAPS database leads to 

exposure predictions generally lower than use of the complete CHAD database. The percentage 

differences are generally small when there are relatively high numbers of exposures, e.g., for one 

or more exposures with base case air quality. As the number of exposures decreases the 

percentage differences increase. 

 
 64 

Table 6-1. Sensitivity to activity database with base case air quality: 2002 counts of the 

general population with any or three or more 8-hour ozone exposures above 0.07 ppm 

concomitant with moderate or greater exertion. 

 One or more exposures Three or more exposures 

CSA All CHAD NHAPS 

only 

Difference All CHAD NHAPS 

only 

Difference 

Atlanta 985,748 896,458 -9% 173,122 154,779 -11%

Boston 1,386,985 1,222,219 -12% 256,958 202,100 -21%

Chicago 2,260,651 1,895,204 -16% 336,429 260,080 -23%

Cleveland 1,037,486 918,103 -12% 327,470 258,647 -21%

Detroit 1,505,255 1,297,412 -14% 281,767 225,967 -20%

Houston 832,053 732,309 -12% 61,467 62,510 2%

Los Angeles 3,153,096 3,154,187 0% 780,634 854,577 9%

New York 6,200,771 5,443,294 -12% 1,517,089 1,233,391 -19%

Philadelphia 2,008,319 1,745,857 -13% 666,264 512,773 -23%

Sacramento 443,771 393,884 -11% 89,417 82,051 -8%

St. Louis 795,121 675,697 -15% 171,747 143,796 -16%

Washington DC 2,155,893 1,896,060 -12% 531,528 438,397 -18%

Table 6-2. Sensitivity to activity database with base case air quality: 2002 counts of 

children (ages 5-18) with any or three or more 8-hour ozone exposures above 0.07 ppm 

concomitant with moderate or greater exertion. 

One or more exposures Three or more exposures 

CSA All CHAD NHAPS 

only 

Difference All CHAD NHAPS 

only 

Difference

Atlanta 392,859 357,916 -9% 85,954 76,631 -11%

Boston 504,012 447,344 -11% 122,574 100,669 -18%

Chicago 860,159 748,430 -13% 157,197 148,817 -5%

Cleveland 373,613 331,446 -11% 161,845 134,404 -17%

Detroit 571,568 494,252 -14% 142,580 129,455 -9%

Houston 333,174 300,836 -10% 28,567 34,104 19%

Los Angeles 1,302,603 1,219,656 -6% 375,719 380,631 1%

New York 2,251,072 1,994,783 -11% 717,609 621,145 -13%

Philadelphia 716,034 633,894 -11% 320,203 262,267 -18%

Sacramento 158,763 144,514 -9% 38,565 38,887 1%

St. Louis 294,981 248,395 -16% 82,890 79,723 -4%

Washington DC 792,244 706,432 -11% 257,435 224,372 -13%
 65 

Table 6-3. Sensitivity to activity database with air quality meeting the current standard: 

2002 counts of the general population with any or three or more 8-hour ozone exposures 

above 0.07 ppm concomitant with moderate or greater exertion. 

One or more exposures Three or more exposures 

CSA All CHAD NHAPS 

only 

Difference All CHAD NHAPS 

only 

Difference 

Atlanta 481,845 445,766 -7% 29,030 26,984 -7%

Boston 820,876 725,445 -12% 68,573 61,144 -11%

Chicago 1,077,875 900,815 -16% 56,020 58,347 4%

Cleveland 575,808 499,918 -13% 71,277 65,435 -8%

Detroit 858,334 758,520 -12% 56,425 57,764 2%

Houston 206,468 199,006 -4% 2,086 2,086 0%

Los Angeles 98,500 126,877 29% 1,637 3,001 83%

New York 1,815,025 1,751,308 -4% 92,905 97,888 5%

Philadelphia 1,131,891 972,469 -14% 155,144 131,911 -15%

Sacramento 102,540 103,955 1% 4,278 4,439 4%

St. Louis 583,581 506,291 -13% 73,344 72,426 -1%

Washington DC 1,139,150 1,001,347 -12% 110,672 96,538 -13%

Table 6-4. Sensitivity to activity database with air quality meeting the current standard: 

2002 counts of children (ages 5-18) with any or three or more 8-hour ozone exposures 

above 0.07 ppm concomitant with moderate or greater exertion. 

One or more exposures Three or more exposures 

CSA All CHAD NHAPS 

only 

Difference All CHAD NHAPS 

only 

Difference 

Atlanta 193,360 171,303 -11% 13,340 8,868 -34%

Boston 311,531 280,292 -10% 33,048 29,048 -12%

Chicago 389,345 375,068 -4% 23,587 38,640 64%

Cleveland 226,151 196,452 -13% 37,209 36,865 -1%

Detroit 322,299 305,336 -5% 27,320 34,373 26%

Houston 80,004 82,411 3% 1,043 963 -8%

Los Angeles 28,104 43,929 56% 273 1,364 400%

New York 674,539 654,249 -3% 37,731 42,359 12%

Philadelphia 438,894 387,083 -12% 84,279 72,614 -14%

Sacramento 30,170 32,357 7% 1,126 1,576 40%

St. Louis 213,835 189,142 -12% 32,449 41,307 27%

Washington DC 434,737 384,765 -11% 48,585 41,139 -15%
 66 

 An additional set of sensitivity simulations was conducted to test the differences between 

using the complete CHAD database and using a regional-specific subset corresponding to the 

CSA of interest. The Los Angeles and Sacramento CSAs were selected for the test, because of 

the relative abundance of activity pattern data for California (see Table 3-3). 

 Tables 6-5 and 6-6 present the results for Los Angeles and Sacramento, respectively, for 

the number of persons exposed to 8-hour average concentrations exceeding 0.07 ppm in the 

general population and for children with moderate exertion. Again, simulations were performed 

both with the base case air quality and with a scenario of attainment of the current NAAQS. 

 As explained in Section 2.3.3, the first step in constructing a multi-day activity sequence 

for a simulated individual is the stratification of the activity pattern data by day-type and ambient 

temperature. For the simulations reported here the activity pattern database was stratified into 6 

pools, each defined by a combination of day type (weekday or weekend) and ambient temperature 

(maximum temperature < 55, 55-84, >84 °F). However, the California activity data used alone 

were insufficient for stratification into these 6 pools. Instead, 2 weekend pools (i.e., temperature 

= 55–84 °F, and >84 °F) were combined. In order to make a fair comparison with the AllCHAD case, for these simulations we stratified the All CHAD database into the same 5 pools. 

Tables 6-5 and 6-6 show the results for All CHAD using both the 6 pool and the 5 pool 

stratifications for reference. 

 As was the case for Tables 6-1 through 6-4, the percentage differences are generally 

small when there are relatively high numbers of exposures, but as the number of exposures 

decreases the percentage differences increase. 

Table 6-5. Sensitivity to activity database: 2002 simulated counts of Los Angeles CMSA 

general population and children (ages 5-18) with any or three or more 8-hour ozone 

exposures above 0.07 ppm concomitant with moderate or greater exertion. 

One or more exposures Three or more exposures 

Population 

Group 

All CHAD 

(6 pools) 

All CHAD 

(5 pools) 

CA only 

(5 pools) 

All CHAD 

(6 pools) 

All CHAD 

(5 pools) 

CA only 

(5 pools) 

Base Case

General 

Population 

3,153,096 2,905,345 2,693,065 

 (-7%) 

780,634 675,858 713,239 

(+6%) 

Children (5-

18) 

1,302,603 1,239,847 1,208,196 

(-3%) 

375,719 326,606 368,625 

(+13%) 

Current Standard 

General 

Population 

98,500 85,676 50,751 

(-41%) 

1,637 1,364 3,274 

(+140%) 

Children (5-

18) 

28,104 23,465 11,733 

(-50%) 

273 0 0 

(N/A) 
 67 

Table 6-6. Sensitivity to activity database: 2002 simulated counts of Sacramento CMSA 

general population and children (ages 5-18) with any or three or more 8-hour ozone 

exposures above 0.07 ppm concomitant with moderate or greater exertion. 

One or more exposures Three or more exposures 

Population 

Group 

All CHAD 

(6 pools) 

All CHAD 

(5 pools) 

CA only 

(5 pools) 

All CHAD 

(6 pools) 

All CHAD 

(5 pools) 

CA only 

(5 pools) 

Base Case

General 

Population 

443,771 442,935 422,704 

(-5%) 

89,417 89,674 113,218 

(+26%) 

Children (5-

18) 

158,763 157,251 153,263 

(-3%) 

38,565 37,922 41,460 

(+9%) 

Current Standard 

General 

Population 

102,540 102,540 99,709 

(-3%) 

4,278 4,567 5,693 

 (+25%) 

Children (5-

18) 

30,170 30,556 24,477 

(-20%) 

1,126 1,319 901 

 (-32%) 

 

6.2 Ozone Decay Rate 

 To test the sensitivity of the APEX predictions to the ozone decay rate distribution, we 

compared the base case results with corresponding results with the decay rate set uniformly to its 

10th percentile value and its 90th percentile value. The results are presented in Figures 6-3 and 6-

4 for active persons with moderate activity in Houston and Boston, respectively, for exceedances 

of an 8-hour average 0.05 ppm threshold. The figures show only small changes in the rate of 

exceedances for these rather extreme decay rate scenarios in Houston, and moderate changes for 

the higher decay rate in Boston. 

 Tables 6-7 and 6-8 present the results for the number of persons exposed to 8-hour 

average concentrations exceeding 0.07 ppm in the general population and for children, 

respectively, with moderate exertion. These results do show differences among the decay rate 

scenarios for these exposures to elevated concentrations. 

Table 6-7. Sensitivity to ozone decay rate: 2002 counts of general population with any or 

three or more 8-hour ozone exposures above 0.07 ppm concomitant with moderate or 

greater exertion. 

One or more exposures Three or more exposures 

Urban Area 

(CMSA) 

rate=90th

percentile Base case

Rate=10th

percentile

rate=90th

percentile Base case 

Rate=10th

percentile

Boston 1,089,073 

(-212%) 

1,387,175 1,551,845

(+12%)

134,596

(-48%)

258,577 335,532

(+30%)

Houston 737,926 

(-11%) 

824,590 861,743

(+5%)

48,869

(-22%)

62,751 69,251

(+10%)
 68 

Table 6-8. Sensitivity to ozone decay rate: 2002 counts of children (ages 5-18) with any or 

three or more 8-hour ozone exposures above 0.07 ppm concomitant with moderate or 

greater exertion. 

One or more exposures Three or more exposures 

Urban Area 

(CMSA) 

rate=90th

percentile Base case

Rate=10th

percentile

rate=90th

percentile Base case 

Rate=10th

percentile

Boston 409.438 

(-18%) 

499,821 542,870

(+9%)

67,049

(-47%)

126,003 160,289

(+27%)

Houston 295,299 

(-11%) 

331,088 346,334

(+5%)

21,826

(-27%)

30,011 34,184

(+14%)

6.3 Proximity Factor 

 To test the sensitivity of the APEX predictions to the proximity factor distribution, we 

compared the base case results with corresponding results with the proximity factor set 

uniformly to its 10th percentile value and its 90th percentile value. The results are presented in 

Figures 6-5 and 6-6 for active persons with moderate activity in Houston and Boston, 

respectively, for exceedances of an 8-hour average 0.05 ppm threshold. The figures shows only 

small changes in the rate of exceedances for these rather extreme proximity factor scenarios. 

 Tables 6-9 and 6-10 present the results for the number of persons exposed to 8-hour 

average concentrations exceeding 0.07 ppm in the general population and for children, 

respectively, with moderate exertion. Again, the results show larger differences among the 

proximity factor scenarios for these exposures to elevated concentrations. 

Table 6-9. Sensitivity to proximity factor: 2002 counts of general population with any or 

three or more 8-hour ozone exposures above 0.07 ppm concomitant with moderate or 

greater exertion 

One or more exposures Three or more exposures 

Urban Area 

(CMSA) 

Factor = 90th

percentile Base case1

Factor = 10th

percentile

Factor = 90th

percentile Base case1

Factor = 10th

percentile

Boston 1,133,360 

(-4%) 

1,183,742 1,283,268

(+8%)

136,098

(-12%)

154,575 196,671

(+27%)

Houston 662,416 

(-4%) 

691,705 756,944

(+9%)

23,752

(-14%)

27,765 37,795

(+36%)

 

1 These base case values are somewhat different than those presented above, because these sensitivity simulations were made 

with an earlier version of APEX. Although the modifications to APEX changed the magnitude of exposures, they did not change 

the relative differences for these sensitivity simulations.
 69 

Table 6-10. Sensitivity to proximity factor: 2002 counts of children (ages 5-18) with any or 

three or more 8-hour ozone exposures above 0.07 ppm concomitant with moderate or 

greater exertion 

One or more exposures Three or more exposures 

Urban Area 

(CMSA) 

Factor = 90th

percentile Base case1

Factor = 10th

percentile

Factor = 90th

percentile Base case1

Factor = 10th

percentile

Boston 421,724 

(-5%) 

444,963 496,773

(+12%)

61,525

(-17%)

73,811 100,764

(+37%)

Houston 271,547 

(-4%) 

284,225 323,705

(+14%)

10,833

(-20%)

13,561 19,580

(+44%)

6.4 Air Exchange Rates 

 To test the sensitivity of the APEX predictions to the air exchange rate distributions, we 

compared the base case results with corresponding results with the air exchange rates set 

uniformly to their 10th percentile values and their 90th percentile values. The results are 

presented in Figure 6-7 for active persons with moderate activity in Houston for exceedances of 

an 8-hour average 0.05 ppm threshold and Figure 6-8 for active persons with moderate activity in 

Boston for exceedances of an 8-hour average 0.05 ppm threshold. The figures show a moderate 

increase in the rate of exceedances in both CMSAs for the extremely high air exchange rate 

scenario. 

 Tables 6-11 and 6-12 present the results for the number of persons exposed to 8-hour 

average concentrations exceeding 0.07 ppm in the general population and for children, 

respectively, with moderate exertion. The results show a large increase in the number of people 

exposed to elevated concentrations for the scenario of high air exchange rates, especially for the 

multiple exposure case. 

 In contrast with the sensitivity simulation for the ozone decay rate discussed above, this 

increase in the air exchange rates is sufficient to increase concentration exceedances of 0.05 ppm 

in the indoor microenvironments compared to the base case. 

Table 6-11. Sensitivity to air exchange rate: 2002 counts of general population with any or 

three or more 8-hour ozone exposures above 0.07 ppm concomitant with moderate or 

greater exertion 

One or more exposures Three or more exposures 

Urban Area 

(CMSA) 

Rate = 10th

percentile Base case1

Rate = 90th

percentile

Rate = 10th

percentile Base case1 

Rate = 90th

percentile

Boston 835,924 

(-29%) 

1,183,742 2,403,294

(+103%)

53,239

(-66%)

154,575 1,074,596

(+595%)

Houston 595,894 

(-14%) 

691,705 1,816,088

(+135%)

17,333

(-38%)

27,765 659,527

(+2275%)

 

1 These base case values are somewhat different than those presented above, because these sensitivity simulations were made 

with an earlier version of APEX. Although the modifications to APEX changed the magnitude of exposures, they did not change 

the relative differences for these sensitivity simulations.
 70 

Table 6-12. Sensitivity to air exchange rate: 2002 counts of children (ages 5-18) with any or 

three or more 8-hour ozone exposures above 0.07 ppm concomitant with moderate or 

greater exertion 

One or more exposures Three or more exposures 

Urban Area 

(CMSA) 

Rate = 10th

percentile Base case1

Rate = 90th

percentile

Rate = 10th

percentile Base case1 

Rate = 90th

percentile

Boston 320,293 

(-28%) 

444,963 756,875

(+70%)

24,001

(-67%)

73,811 420,296

(+469%)

Houston 243,060 

(-14%) 

284,225 652,386

(+130%)

7,142

(-47%)

13,561 262,720

(+1837%)

 In addition to lack of precision in measurements due to within-residence variations in air 

exchange rates, some recent studies have suggested that the reported rates may be biased upward 

from actual rates by as much as a factor of two (Wallace, L., personal communication). Primary 

reasons for such potential bias include (a) the typical placement of tracer emitters in relatively 

isolated locations, such as bathrooms and bedrooms, so that the tracer gas is constrained from 

reaching the collector, and (b) the fact that for apartments a substantial portion of air is 

exchanged with indoor common areas, such as hallways, rather than to the outdoors. 

 In order to determine the sensitivity of APEX predictions to such bias, if present, a set of 

sensitivity simulations was performed for the New York CMSA, setting the residential air 

exchange rates to half the value selected from the air exchange rate distribution. The New York 

CMSA was selected because it is known to contain a high density of apartment buildings. 

 Table 6-13 presents the results for the number of persons exposed to 8-hour average 

concentrations exceeding 0.07 ppm in the general population and for children, respectively, with 

moderate exertion. The results suggest that the results are not sensitive to a potential 

overestimate of air exchange rates by a factor of two. 

Table 6-13. Sensitivity to air exchange rate: 2002 simulated counts of New York CMSA 

general population and children (ages 5-18) with any or three or more 8-hour ozone 

exposures above 0.07 ppm concomitant with moderate or greater exertion. 

One or more exposures Three or more exposures 

Population 

Group Base case 

Residential 

AER=1/2 Base case

Residential 

AER=1/2

General 

Population 

5,439,379 5,420,869 

(-0.3%) 

958,948 953,253 

(-0.6%) 

Children (5-18) 2,033,582 2,030,023 

(-0.2%) 

494,780 495,136 

(+0.1%) 

 

1 These base case values are somewhat different than those presented above, because these sensitivity simulations were made 

with an earlier version of APEX. Although the modifications to APEX changed the magnitude of exposures, they did not change 

the relative differences for these sensitivity simulations.
 71 

6.5 Long-term activity patterns 

 The version of APEX used for this analysis includes a new treatment of activity patterns 

to construct long-term individual activity patterns, as described in section 2.3.3 and Appendix C. 

To test the sensitivity of the APEX results to this new treatment we compared the base case 

exposure results with corresponding results where (a) the new treatment was not implemented, 

and (b) the D statistic was set to 0.75 instead of 0.2. The comparisons of the days/person with 

exceedances of 8-hour average concentrations for active persons on Boston during moderate 

exertion (Figure 6-9) shows little difference between APEX estimates for the base case and for 

the simulation that did not incorporate the new long-term activity pattern treatment. The 

comparison between the base case and the sensitivity simulation with the diversity statistic, D, 

set to 0.75 (Figure 6-10) shows a slight elevation of the exposure rate for the highest 5% to 10% 

or the exposed population compared to the base case for this rather extreme scenario. 

 Table 6-14 presents the results for the number of persons in Boston population groups 

with moderate exertion exposed to 8-hour average concentrations exceeding 0.07 ppm. Again, 

the results show very small differences among the scenarios for these exposures to elevated 

concentrations. 

Table 6-14. Sensitivity to longitudinal activity pattern algorithm: 2002 counts of Boston 

population groups with any or three or more 8-hour ozone exposures above 0.07 ppm 

concomitant with moderate or greater exertion. 

One or more exposures Three or more exposures 

Population 

group Base case1 

Simple resampling Div=0.75 Base case1Simple resampling Div=0.75

General 

population 

1,183,742 1,212,409 

(-2%) 

1,101,740 

(+6%) 

154,575 140,765 

(-9%) 

169,718 

(+10%) 

Children (ages 

5-18) 

444,963 458,773 

(-3%) 

408,962 

(+8%) 

73,811 70,478 

(-5%) 

80,097 

(+9%) 

 An alternative algorithm for constructing longitudinal diaries was recently developed for 

another population exposure model, the Hazardous Air Pollutant Exposure Model (HAPEM). 

This approach, described in Appendix H, is designed to better represent the variability among 

individuals by limiting the number of selected activity diaries used to represent an individual. 

 This approach was adapted to use in APEX as follows. For each simulated 

individual/diary pool combination, cluster analysis is used to group the corresponding diaries 

into three clusters of similar patterns. (There are 18 clusters for each selected individual: 3 

temperature categories × 2 day-of-week types × 3 clusters = 18.) A single activity pattern is 

selected from each cluster to represent the set of behaviors of the simulated individual. Next, 

cluster-to-cluster transition probabilities are defined both within diary pools and across diary 

pools, and used in a Markov process to select a cluster for each day of the modeling period. 

 

1 These base case values are somewhat different than those presented above, because these sensitivity simulations were made 

with an earlier version of APEX. Although the modifications to APEX changed the magnitude of exposures, they did not change 

the relative differences for these sensitivity simulations
 72 

 A special version of APEX was developed that incorporated this approach for testing the 

sensitivity of the model. A set of sensitivity simulations was performed for the Atlanta CMSA 

using (a) the alternative algorithm, and (b) simple re-sampling. 

 Table 6-15 presents the results for the number of persons in Atlanta population groups 

with moderate exertion exposed to 8-hour average concentrations exceeding 0.07 ppm. The 

results show that the predictions made with alternative algorithm (“cluster”) are substantially 

different from those made with simple re-sampling or with the new APEX algorithm (“base 

case”). Note that for the cluster algorithm approximately 30% of the individuals with 1 or more 

exposure have 3 or more exposures. The corresponding values for the other algorithms range 

from about 13% to 21%. 

Table 6-15. Sensitivity to longitudinal diary algorithm: 2002 simulated counts of Atlanta 

general population and children (ages 5-18) with any or three or more 8-hour ozone 

exposures above 0.07 ppm concomitant with moderate or greater exertion. 

One or more exposures Three or more exposures 

Population 

Group Simple resampling Base case1 Cluster

Simple resampling Base case1 Cluster

General 

Population 

979,533 939,663 

(-4%) 

668,004 

(-32%) 

124,687 144,470 

(+16%) 

188,509 

(+51%) 

Children (5-18) 411,429 389,372 

(-5%) 

295,004 

(-28%) 

71,174 83,377 

(+17%) 

94,216 

(+32%) 

 Table 6-16 presents the results for the mean and standard deviation of number of 

days/person with 8-hour average exposures exceeding 0.07 ppm with moderate or greater 

exertion. The results show that although the mean for the cluster algorithm is very similar to the 

other approaches, the standard deviation is substantially higher, i.e., the cluster algorithm results 

in substantially higher inter-individual variability. As described in Appendix H, limited 

evaluation of the cluster algorithm by comparison to measurement data shows reasonably good 

agreement. 

Table 6-16. Sensitivity to longitudinal diary algorithm: 2002 days per person with 8-hour 

ozone exposures above 0.07 ppm concomitant with moderate or greater exertion for 

Atlanta general population and children (ages 5-18). 

Mean Days/Person Standard Deviation 

Population 

Group Simple resampling Base case Cluster

Simple resampling Base case Cluster

General 

Population 

0.332 0.335

(+1%)

0.342

(+3%)

0.757 0.802 

(+6%) 

1.197

(+58%)

Children (5-18) 0.746 0.755

(+1%)

0.758

(+2%)

1.077 1.171 

(+9%) 

1.652

(+53%)

 

1 These base case values are somewhat different than those presented above, because these sensitivity simulations were made 

with an earlier version of APEX. Although the modifications to APEX changed the magnitude of exposures, they did not change 

the relative differences for these sensitivity simulations.
 73 

6.6 Near roadway locations 

 Although APEX accounts for depressed ozone concentrations near roadways for 

activities that occur outdoors, including in vehicles, it does not account for depressed ozone 

concentrations in indoor microenvironments that are near major roadways. This issue was 

recently addressed in the HAPEM model by developing a national data base of estimates of the 

fraction of the population of each census tract that resides in the vicinity of a major roadway, 

either 0 – 75m or 75m-200m. Although the data specify only the fraction of the residential 

population of each tract that live in the vicinity of the roadway, it was assumed that the same 

proportion of non-residential indoor venues are in the vicinity of major roadways for each tract. 

The development of the data base is described in Appendix I. 

 In order to test the sensitivity of APEX to the potential overestimate of concentrations in 

indoor microenvironments near roadways, we used the roadway proximity data developed for 

HAPEM to estimate the probability of a randomly selected individual living in proximity to 

either an interstate or a major urban road, as described below. Based on these estimated 

probabilities, a simulated individual’s residence (and other frequented indoor 

microenvironments) were assigned roadway-category-specific proximity factor distributions as 

previously described for in-vehicle microenvironments. 

6.6.1 Proximity Probabilities 

 Given the specifications of the near roadway proximity factors, described in Appendix A, 

for this application we defined near-roadway proximity as being located within 75 meters of a 

major roadway, i.e., the first category in the HAPEM database. The probabilities for Boston and 

Houston were estimated by averaging the HAPEM data across the tracts in the respective 

modeling domains, and are as follows. 

Boston: 27% 

Houston: 20% 

 Next, we allocated these fractions between the categories used to develop the nearroadway proximity factors (i.e., interstate and other major urban road) according to the 

proportions of roadway miles in the respective categories as specified by the Federal Highway 

Administration (FHWA 2004) for the urban areas. These proportions were as follows: 

Boston: 

 Interstate 0.05 

 Other major urban: 0.95 

Houston: 

 Interstate 0.03 

 Other major urban: 0.97 
 74 

 Combining these data resulted in the following probabilities for residing within 75 meters 

of an interstate or another major urban road. 

Boston: 

Interstate 1% 

 Other major urban: 26% 

 Not within 75 meters of a major roadway: 73% 

Houston: 

Interstate 1% 

 Other major urban: 19% 

 Not within 75 meters of a major roadway: 80% 

 Although the HAPEM data specify only the fraction of the residential population that live 

in the vicinity of the roadway, for this application the same probabilities were applied to nonresidential indoor microenvironments as well. 

6.6.2 Results 

 Table 6-17 presents the results for the number of children (5-18) exposed to 8-hour 

average concentrations exceeding 0.07 ppm with moderate or greater exertion. The results show 

little difference in the predictions compared to the base case. 

Table 6-17. Sensitivity to near roadway proximity for indoor sources: 2002 counts of 

children (ages 5-18) with any or three or more 8-hour ozone exposures above 0.07 ppm 

concomitant with moderate or greater exertion. 

One or more exposures Three or more exposures 

Urban Area 

(CMSA) Base case1 

Near 

roadway Base case1

Near 

roadway

Boston 444,963 432,772

(-3%)

73,811 64,859

(-12%)

Houston 284,225 281,256

(-1%)

13,561 12,358

(-9%)

6.7 Sensitivity summary 

 Of the data, parameters, and algorithms tested for this sensitivity analysis, the model 

results were most sensitive to increases in the air exchange rates. The results were also sensitive 

to the longitudinal activity algorithm, the activity pattern data base, the decay rate, and decreases 

in the proximity factors. 
 75 

Figure 6-1 

Figure 6-2 

Days/Person with Exceedances of 8-Hour Average Concentrations During Moderate 

Exertion 

--Active Persons, Boston, 2002-- 

Days/Person with Exceedances of 

8-Hour Average Concentrations During Any Exertion

--All Persons, Boston, 2002--

0

20

40

60

80

100

120

140

160

180

200

0 20 40 60 80 100 120

Cumulative Percentile

Days/Person

0.01 ppm

0.02 ppm

0.04 ppm

0.05 ppm

0.03 ppm

All CHAD

NHAPS only 

0.04 ppm

0

20

40

60

80

100

120

140

160

180

0 10 20 30 40 50 60 70 80 90 100

Cumulative Percentile

Days/Person

All CHAD

NHAPS only

0.03 ppm

0

20

40

60

80

100

120

140

160

180

0 10 20 30 40 50 60 70 80 90 100

Cumulative Percentile

Days/Person

All CHAD

NHAPS only

0.02 ppm

0

20

40

60

80

100

120

140

160

180

0 10 20 30 40 50 60 70 80 90 100

Cumulative Percentile

Days/Person

All CHAD

NHAPS only

0.01 ppm

0

20

40

60

80

100

120

140

160

180

0 10 20 30 40 50 60 70 80 90 100

Cumulative Percentile

Days/Person

All CHAD

NHAPS only
 76 

Figure 6-3 

Decay Rate Sensitivity:

Days/Person with Exceedances of 0.05 ppm

 8-Hour Average Exposure Concentration During Moderate Exertion

--Active Persons, Houston, 2002--

0

5

10

15

20

25

30

0 20 40 60 80 100

Cumulative Percentile

Days/Person

DE= 10th percentile value

DE = 90th percentile value

Figure 6-4 

Decay Rate Sensitivity:

Days/Person with Exceedances of 0.05 ppm

 8-Hour Average Exposure Concentration During Moderate Exertion

--Active Persons, Boston, 2002--

0

5

10

15

20

25

30

35

0 20 40 60 80 100

Cumulative Percentile

Days/Person

DE= 10th percentile value

DE = 90th percentile value
 77 

Figure 6-5

Proximity Factor Sensitivity:

Days/Person with Exceedances of 0.05 ppm

 8-Hour Average Exposure Concentration During Moderate Exertion

--Active Persons, Houston, 2002--

0

5

10

15

20

25

30

0 20 40 60 80 100

Cumulative Percentile

Days/Person

PROX = 90th percentile value

PROX = 10th percentile value

Figure 6-6

Proximity Factor Sensitivity:

Days/Person with Exceedances of 0.05 ppm

 8-Hour Average Exposure Concentration During Moderate Exertion

--Active Persons, Boston, 2002--

0

5

10

15

20

25

30

35

0 20 40 60 80 100

Cumulative Percentile

Days/Person

PROX = 90th percentile value

PROX = 10th percentile value
 78 

Figure 6-7

Air Exchange Rate Sensitivity:

Days/Person with Exceedances of 0.05 ppm

 8-Hour Average Exposure Concentration During Moderate Exertion

--Active Persons, Houston, 2002--

0

10

20

30

40

50

60

0 20 40 60 80 100

Cumulative Percentile

Days/Person

AER= 90th percentile value

AER = 10th percentile value

Figure 6-8

Air Exchange Rate Sensitivity:

Days/Person with Exceedances of 0.05 ppm

 8-Hour Average Exposure Concentration During Moderate Exertion

--Active Persons, Boston, 2002--

0

10

20

30

40

50

60

70

80

90

0 20 40 60 80 100

Cumulative Percentile

Days/Person

AER= 90th percentile value

AER = 10th percentile value
 79 

Figure 6-9 

Figure 6-10 

Diversity Statistic Sensitivity:

Days/Person with Exceedances of 

 8-Hour Average Exposure Concentration During Moderate Exertion

--Active Persons, Boston, 2002--

0

20

40

60

80

100

120

140

160

180

200

0 20 40 60 80 100

Cumulative Percentile

Person-Days

0.01 ppm

0.02 ppm

0.03 ppm

0.04 ppm

Base

D=0.75

Long-term Activity Pattern Sensitivity:

Days/Person with Exceedances of 

 8-Hour Average Exposure Concentration During Moderate Exertion

--Active Persons, Boston, 2002--

0

20

40

60

80

100

120

140

160

180

200

0 20 40 60 80 100

Cumulative Percentile

Days/Person

0.01 ppm

0.02 ppm

0.03 ppm

0.04 ppm

Base

LD Off
 80 

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 81 

7. MODEL EVALUATION 

 In order to evaluate the performance of APEX we compared APEX simulation results to 

personal ozone concentration measurements taken from the Harvard Southern California Chronic 

Ozone Exposure Study (Xue et al. 2005, Geyh et al. 2000). In this study, 224 children in ages 

between 7 and 12 yr were followed for 1 year from June 1995 to May 1996. Passive ozone 

samplers were used to measure ozone personal ozone concentrations, as well as indoor and 

outdoor concentrations at participants homes for 6 consecutive days each month. The subjects 

resided in two separate areas of San Bernardino County: urban Upland CA, and the small 

mountain towns of Lake Arrowhead, Crestline, and Running Springs, CA. 

 From the original dataset (Geyh et al. 2000), Xue et al. (2005) identified 160 subjects on 

which longitudinal ozone concentrations have been made at least in 6 of the 12 months of study 

period. This dataset was used for the APEX model evaluation. The number of 6-day average 

measured personal exposure concentrations in each data set varies from 7 to 31. In the Upland 

area, where more than 95% of the subjects had air-conditioning in their homes, the maximum 6-

day average exposure concentration was 0.029 ppm, and all other 6-day averages were less than 

0.025 ppm. In the Lake Arrowhead area, where none of the subjects’ homes were airconditioned, the maximum exposure concentration was 0.034 ppm with five 6-day periods that 

had at least one subject with an exposure concentration greater than 0.025 ppm. 

 For the APEX simulations we used hourly outdoor concentrations from fixed site 

monitors located in Upland and Crestline as inputs. The outdoor concentration values are 

assumed y the model to be spatially uniform throughout each respective modeling domain. The 

air exchange rates used were those developed for Sacramento from measurements taken in the 

inland portions of the Los Angeles area: Sacramento, Riverside, and San Bernardino Counties. 

For each 6-day period for which personal measurements were available we simulated 10,000 

subjects in the 7 – 12 age range in each of the two study areas. For each case the distribution of 

simulated 6-day average exposure concentrations was compared to the corresponding 

distribution of measured values. 

 Example comparisons of weekly (i.e., 6-day) distributions for Upland and Lake 

Arrowhead are presented in Figures 7-1 and 7-2 respectively. (See Appendix J for a full set of 

weekly comparison figures for all weeks in each location when at least one personal exposure 

concentration exceeding 30 ppb was measured.). 

 In Figure 7-1 the distribution of APEX predictions of personal exposure concentrations in 

Upland matches the distribution of measured values closely for the lower half of the distribution, 

but underestimates the upper end of the distribution by up to 17 ppb. The coefficient of variation 

(CV = standard_deviation ÷ mean) for the APEX distribution is 20% compared to 41% for the 

measured values. 

 To provide some insight into the factors driving these comparisons, the figure also 

presents comparisons between the measurements made inside the subjects’ homes and the APEX 

indoor residential concentration predictions. In addition, comparisons are also shown between 

the ozone concentrations measured outside the homes of the study subjects and those measured 

at the nearby fixed site monitors that are used as spatially uniform APEX inputs. 
 82 

 In Figure 7-1, these comparisons show that the model-to-monitor discrepancy in the 

upper end of the personal exposure distributions is similar to the discrepancy between the APEX 

(spatially uniform) outdoor concentration input and the upper end of the measured values outside 

the subjects homes, with a median difference of about 7 ppb and a maximum difference of about 

19 ppb. The CV for the APEX outdoor inputs is 0% compared to 12% for the measured values. 

 The model-to-monitor comparison of the indoor residential distributions shows that 

APEX estimates the average concentration well for this data set, but shows a smaller CV (34% 

compared to 78%) with a small overestimate of the lower concentrations (about 5 ppb) and 

underestimates up to about 10 ppb for the higher measured concentrations. 

 In Figure 7-2 for the same week in Lake Arrowhead, the distribution of APEX 

predictions of personal exposure concentrations matches the distribution of measured values 

closely throughout, although with a somewhat lower CV (21% compared to 45%) , i.e., 

overestimates of about 5 ppb at the lower end and underestimates of about 5 ppb at the upper 

end. 

 The APEX (spatially uniform) outdoor concentration input matches the median measured 

outdoor concentration well, but overestimates the minimum by about 15 ppb and underestimates 

the maximum by about the same amount (i.e., APEX CV of 0% compared to a measured CV of 

11%). 

 The distribution of APEX indoor residential predictions matches the median and upper 

end measurements well but overestimates the lower values by up to 10 ppb (i.e., APEX CV of 

33% compared to a measured CV of 70%) . 

 Figures 7-3 and 7-4 show the full sets of Upland and Lake Arrowhead weekly average 

personal exposure concentration comparisons, respectively, along with similar comparisons for 

outdoor and indoor concentrations. 

 Figure 7-3 shows that for the Upland area the APEX mean and lower bound of the 

personal exposure concentration for each 6-day period generally match the mean and lower 

bound of the measurements closely. The average discrepancy between the weekly means is less 

than 1 ppb, with a range of -11 ppb to 8 ppb. However, the predicted upper bounds for the weeks 

with higher concentrations are somewhat underpredicted, with discrepancies up to 24 ppb. The 

average weekly CV for the APEX predictions is 19% compared to 53% for the weekly measured 

values. 

 The APEX (spatially uniform) outdoor concentration input underestimates the mean 

measured values outside the subjects homes, especially for the weeks with higher measured 

concentrations, with discrepancies ranging up to 20 ppb, and an average discrepancy of 6 ppb. 

The discrepancies between the APEX outdoor concentration input and the upper bounds of the 

measured concentrations range up to 43 ppb with and average of 17 ppb. The average of the 

weekly CVs of the measured values is 22%. 
 83 

 APEX shows some underestimation of the weekly average indoor residential 

concentrations and CV’s for the weeks with higher measured concentration. The discrepancies 

between the weekly means averages less than 2 ppb, and ranges from -6 ppb to 11 ppb. The 

average CV for the APEX predictions is 23% compared to 73% measured values. 

 Figure 7-4 shows that for the Lake Arrowhead area the APEX predictions overestimate 

the weekly average personal concentrations and CV for the weeks with lower concentrations and 

underestimate them for weeks with higher concentrations. The average discrepancy for the 

means is 3 ppb with a range of -4 ppb to 16 ppb. The average weekly CV of the APEX 

predictions is 21% compared to 56% for the measured values. 

 The APEX (spatially uniform) outdoor concentration input appears to match the mean 

measured values outside the subjects homes reasonably well, with an average discrepancy of 1 

ppb and a range of -12 ppb to 23 ppb. The discrepancies between the APEX outdoor 

concentration input and the upper bounds of the measured concentrations range up to 95 ppb 

with and average of 16 ppb. The average of the weekly CVs of the measured values is 17%. 

 Like the personal exposure concentrations, the APEX predictions overestimate the 

weekly average indoor concentrations and CVs for the weeks with lower concentrations and 

underestimate them for weeks with higher concentrations. The discrepancies between the weekly 

means averages less than 1 ppb, and ranges from -9 ppb to 14 ppb. The average CV for the 

APEX predictions is 25% compared to 83% measured values. 

 In summary, APEX predicts the average personal exposure concentration reasonably 

well, but underestimates the variability. Similarly, the average prediction for the indoor 

residential microenvironment matches the measured value reasonably well, but underestimates 

the variability. Since the study subjects spent 67% of their sampling time on average inside their 

residences, the discrepancies for the indoor residential microenvironment are likely the main 

contributors to the discrepancies for the personal exposure concentrations. 

 A contributing factor to this underestimation of the variability in the indoor residential 

concentrations is likely to be an underestimation of the spatial variability of the outdoor 

concentrations. It is also possible the variability of residential air exchange rates is 

underestimated. 

 The underestimation of the outdoor concentration variability likely exacerbates the 

underestimation of the upper end of the personal exposure concentration distribution. 
 84 

Figure 7-1 

Figure 7-2 

Weekly Average Personal Ozone Concentration

--Upland, Week of 6/7/95--

0

10

20

30

40

50

60

0 20 40 60 80 100

Cumulative Percentile

Concentration 

(ppb)

measured

APEX n=24

Weekly Average Outdoor Ozone Concentration

--Upland, Week of 6/7/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration 

(ppb)

measured

APEX

n=21

Weekly Average Indoor Ozone Concentration

--Upland, Week of 6/7/95--

0

10

20

30

40

50

0 20 40 60 80 100

Cumulative Percentile

Concentration 

(ppb)

measured

APEX n=21
 85 

Figure 7-2 

We ekly Average Indoor Ozone Concentration

--Lake Arrowhe ad, Week of 6/7/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

measured

APEX n=22

We ekly Average Outdoor Ozone Concentration

--Lake Arrowhead, We ek of 6/7/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

measured

APEX

n=22

We ekly Average Personal Ozone Concentration

--Lake Arrowhe ad, Wee k of 6/7/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

measured

APEX

n=27
 86 

Figure 7-3 

Means of Weekly Average 

Personal Ozone ExposureConcentrations

-- Upland --

0

20

40

60

80

1

Concentration (ppb)

Measured APEX range

measured APEX

Means of Weekly Average 

Outdoor Ozone Concentrations

-- Upland --

0

20

40

60

80

100

1

Concentration (ppb)

Measured APEX range

Means of Weekly Average 

Indoor Ozone Concentrations

-- Upland --

0

10

20

30

40

50

1

Concentration (ppb)

Measured APEX range

measured APEX
 87 

Figure 7-4 

Means of Weekly Average 

Personal Ozone ExposureConcentrations

-- Lake Arrowhead --

0

20

40

60

80

1

Concentration (ppb)

Measured APEX range

measured APEX

Means of Weekly Average 

Outdoor Ozone Concentrations

-- Lake Arrowhead --

0

50

100

150

200

1

Concentration (ppb)

Measured APEX range

Means of Weekly Average 

Indoor Ozone Concentrations

-- Lake Arrowhead --

0

20

40

60

80

1

Concentration (ppb)

Measured APEX range

measured APEX
 88 

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 89 

7. REFERENCES 

Biller, W.F., T.B. Feagans, T.R. Johnson, G.M. Duggan, R.A. Paul, T. McCurdy, and H.C. 

Thomas. 1981. A general model for estimating exposure associated with alternative NAAQS. 

Paper No. 81-18.4 in Proceedings of the 74th Annual Meeting of the Air Pollution Control 

Association, Philadelphia, Pa. 

Burmaster, D.E. 1998. Lognormal distributions for skin area as a function of body weight. Risk 

Analysis, 18(1):27-32. 

CASTNet 2004. Clean Air Status and Trends Network (CASTNet) 2003 Annual Report, 

Prepared by: MACTEC Engineering and Consulting, Inc. Prepared for: 

U.S. Environmental Protection Agency, Office of Air and Radiation, Clean Air Markets 

Division, Washington, DC. Available at http://www.epa.gov/CASTNet . 

Federal Highway Administration, U.S. Department of Transportation. 2004 (Publication Date). 

Highway Statistics 2003, Urbanized Areas, Miles and Daily Vehicle Miles of Travel. Table 

HM-71. Website: http://www.fhwa.dot.gov/policy/ohim/hs03/htm/hm71.htm. 

Geyh, AS, Xue, J, Ozkaynak, H, and Spengler, JD. 2000. The Harvard Southern California 

chronic ozone exposure study: Assessing ozone exposure of grade-school-age children in two 

Southern California communities. Environ Health Persp. 108:265-270. 

Graham S.E. and T. McCurdy. 2005. Revised ventilation rate (VE) equations for use in 

inhalation-oriented exposure models. EPA/600/X-05/008. 

Johnson, T.R., and R.A. Paul. 1983. The NAAQS Exposure Model (NEM) Applied to Carbon 

Monoxide. EPA-450/5-83-003. Prepared for the U.S. Environmental Agency by PEDCo 

Environmental Inc., Durham, N.C. under Contract No. 68-02-3390. U.S. Environmental 

Protection Agency, Research Triangle Park, N.C. 

Johnson, T., J. Capel, E. Olaguer, and L. Wijnberg. 1992. Estimation of Ozone Exposures 

Experienced by Residents of ROMNET Domain Using a Probabilistic Version of NEM. Report 

prepared by IT Air Quality Services for the Office of Air Quality Planning and Standards, U. S. 

Environmental Protection Agency, Research Triangle Park, North Carolina. 

Johnson, T., A. Pakrasi, A. Wisbeth, G. Meiners, W. M. Ollison. 1995. Ozone exposures within 

motor vehicles – results of a field study in Cincinnati, Ohio. Proceedings 88th annual meeting 

and exposition of the Air & Waste Management Association, June 18-23, 1995. San Antonio, 

TX. Preprint paper 95-WA84A.02. 

Johnson, T., J. Capel, and M. McCoy. 1996a. Estimation of Ozone Exposures Experienced by 

Urban Residents Using a Probabilistic Version of NEM and 1990 Population Data. Report 

prepared by IT Air Quality Services for the Office of Air Quality Planning and Standards, U.S. 

Environmental Protection Agency, Research Triangle Park, North Carolina, September. 
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Johnson, T., J. Capel, J. Mozier, and M. McCoy. 1996b. Estimation of Ozone Exposures 

Experienced by Outdoor Children in Nine Urban Areas Using a Probabilistic Version of NEM. 

Report prepared for the Air Quality Management Division under Contract No. 68-DO-30094, 

April. 

Johnson, T., J. Capel, M. McCoy, and J. Mozier. 1996c. Estimation of Ozone Exposures 

Experienced by Outdoor Workers in Nine Urban Areas Using a Probabilistic Version of NEM. 

Report prepared for the Air Quality Management Division under Contract No. 68-DO-30094, 

April. 

Johnson, T. 2002. A Guide to Selected Algorithms, Distributions, and Databases Used in 

Exposure Models Developed By the Office of Air Quality Planning and Standards. Revised 

Draft. Prepared for U.S. Environmental Protection Agency under EPA Grant No. CR827033. 

Langstaff, J. E. 2007. OAQPS Staff Memorandum to Ozone NAAQS Review Docket (OAR2005-0172). Subject: Analysis Of Uncertainty In Ozone Population Exposure Modeling. 

[January 31, 2007]. 

Lee, Vallarino, Dumyahn, Ozkaynak, and Spengler. 1999. Ozone decay rates in residences. 

JAWMA. 49:1238-1244. 

McCurdy, T. 2000. Conceptual basis for multi-route intake dose modeling using an energy 

expenditure approach. Journal of Exposure Analysis and Environmental Epidemiology. 10:1-12. 

McCurdy, T., G. Glen, L. Smith, and Y. Lakkadi. 2000. The National Exposure Research 

Laboratory’s Consolidated Human Activity Database, Journal of Exposure Analysis and 

Environmental Epidemiology 10: 566-578. 

NCDC Surface Weather Observations. U.S. Department of Commerce, National Oceanic and 

Atmospheric Administration, National Environmental Satellite Data and Information Service, 

National Climatic Data Center, Asheville, North Carolina. 

http://lwf.ncdc.noaa.gov/oa/ncdc.html

Occupational Health and Safety Administration (OSHA). 2005. 

http://www.osha.gov/dts/chemicalsampling/data/CH_259300.html. Last accessed: July 19, 2005. 

Persily, A., J. Gorfain, G. Brunner. 2005. Ventilation design and performance in U.S. office 

buildings. ASHRAE Journal. April 2005, 30-35. 

Roddin, M.F., H.T. Ellis, and W.M. Siddiqee. 1979. Background Data for Human Activity 

Patterns, Vols. 1, 2. Draft Final Report prepared for Strategies and Air Standards Division, 

Office of Air Quality Planning and Standards, U.S. Environmental Protection Agency, Research 

Triangle Park, N.C. 

U.S. Census Bureau, Employment Status: 2000- Supplemental Tables. Housing and Household 

Economic Statistics Division. http://www.census.gov/population/www/cen2000/phc-t28.html. 
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U.S. Environmental Protection Agency. 1999. Total Risk Integrated Methodology. Website: 

http://www.epa.gov/ttnatw01/urban/trim/trimpg.html. 

U.S. Environmental Protection Agency. 2002. Consolidated Human Activities Database 

(CHAD) Users Guide. The database and documentation are available electronically on the 

internet at: http://www.epa.gov/chadnet1/.

U.S. Environmental Protection Agency. 2006a. Air Quality Criteria for Ozone and Related 

Photochemical Oxidants (Final). National Center for Environmental Assessment, U.S. 

Environmental Protection Agency, Research Triangle Park, NC, EPA/600/R-05/004aF-cF. 

Available electronically on the internet at: 

http://cfpub.epa.gov/ncea/cfm/recordisplay.cfm?deid=149923

U.S. Environmental Protection Agency. 2006c. Total Risk Integrated Methodology (TRIM) - 

Air Pollutants Exposure Model Documentation (TRIM.Expo / APEX, Version 4) Volume I: 

User’s Guide. Office of Air Quality Planning and Standards, U.S. Environmental Protection 

Agency, Research Triangle Park, NC. June 2006. Available at: 

http://www.epa.gov/ttn/fera/human_apex.html. 

U.S. Environmental Protection Agency. 2006d. Total Risk Integrated Methodology (TRIM) - 

Air Pollutants Exposure Model Documentation (TRIM.Expo / APEX, Version 4) Volume II: 

Technical Support Document. Office of Air Quality Planning and Standards, U.S. Environmental 

Protection Agency, Research Triangle Park, NC. June 2006. Available at: 

http://www.epa.gov/ttn/fera/human_apex.html. 

U.S. Environmental Protection Agency. 2007. Review of National Ambient Air Quality 

Standards for Ozone: Assessment of Scientific and Technical Information - OAQPS Staff Paper. 

Office of Air Quality Planning and Standards, U.S. Environmental Protection Agency, Research 

Triangle Park, NC. Available electronically on the internet at: 

http://www.epa.gov/ttn/naaqs/standards/ozone/s_o3_cr_sp.html. 

Xue J, Liu SV, Ozkaynak H, Spengler J. 2005. Parameter evaluation and model validation of 

ozone exposure assessment using Harvard Southern California Chronic Ozone Exposure Study 

Data. J. Air & Waste Manage. Assoc. 55:1508–1515. 

Xue J, McCurdy T, Spengler J, Ozkaynak H. 2004. Understanding variability in time spent in 

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 92 

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APPENDIX A. ANALYSIS OF AIR EXCHANGE RATE DATA 
 1 

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 A-1

DRAFT MEMORANDUM 

To: John Langstaff 

From: Jonathan Cohen, Hemant Mallya, Arlene Rosenbaum 

Date: September 30, 2005 

Re: EPA 68D01052, Work Assignment 3-08. Analysis of Air Exchange Rate Data 

 

EPA is planning to use the APEX exposure model to estimate ozone exposure in 12 cities / 

metropolitan areas: Atlanta, GA; Boston, MA; Chicago, IL; Cleveland, OH; Detroit, MI; 

Houston, TX; Los Angeles, CA; New York, NY; Philadelphia, PA; Sacramento, CA; St. Louis, 

MO-IL; Washington, DC. As part of this effort, ICF Consulting has developed distributions of 

residential and non-residential air exchange rates (AER) for use as APEX inputs for the cities to 

be modeled. This memorandum describes the analysis of the AER data and the proposed APEX 

input distributions. Also included in this memorandum are proposed APEX inputs for 

penetration and proximity factors for selected microenvironments. 

Residential Air Exchange Rates

Studies. Residential air exchange rate (AER) data were obtained from the following seven 

studies: 

Avol: Avol et al, 1998. In this study, ozone concentrations and AERs were measured at 

126 residences in the greater Los Angeles metropolitan area between February and 

December, 1994. Measurements were taken in four communities: Lancaster, Lake 

Gregory, Riverside, and San Dimas. Data included the daily average outdoor 

temperature, the presence or absence of an air conditioner (either central or room), and 

the presence or absence of a swamp (evaporative) cooler. Air exchange rates were 

computed based on the total house volume and based on the total house volume corrected 

for the furniture. These data analyses used the corrected AERs. 

RTP Panel: Williams et al, 2003a, 2003b. In this study particulate matter concentrations 

and daily average AERs were measured at 37 residences in central North Carolina during 

2000 and 2001 (averaging about 23 AER measurements per residence). The residences 

belong to two specific cohorts: a mostly Caucasian, non-smoking group aged at least 50 

years having cardiac defibrillators living in Chapel Hill; a group of non-smoking, African 

Americans aged at least 50 years with controlled hypertension living in a low-tomoderate SES neighborhood in Raleigh. Data included the daily average outdoor 

temperature, and the number of air conditioner units (either central or room). Every 

residence had at least one air conditioner unit. 

RIOPA: Meng et al, 2004, Weisel et al, 2004. The Relationship of Indoor, Outdoor, and 

Personal Air (RIOPA) study was undertaken to estimate the impact of outdoor sources of 

air toxics to indoor concentrations and personal exposures. Volatile organic compounds, 
 A-2

carbonyls, fine particles and AERs were measured once or twice at 310 non-smoking 

residences from summer 1999 to spring 2001. Measurements were made at residences in 

Elizabeth, NJ, Houston TX, and Los Angeles CA. Residences in California were 

randomly selected. Residences in New Jersey and Texas were preferentially selected to 

be close (< 0.5 km) to sources of air toxics. The AER measurements (generally over 48 

hours) used a PMCH tracer. Data included the daily average outdoor temperature, and the 

presence or absence of central air conditioning, room air conditioning, or a swamp 

(evaporative) cooler. 

TEACH: Chillrud at al, 2004, Kinney et al, 2002, Sax et al, 2004. The Toxic Exposure 

Assessment, a Columbia/Harvard (TEACH) study was designed to characterize levels of 

and factors influencing exposures to air toxics among high school students living in 

inner-city neighborhoods of New York City and Los Angeles, CA. Volatile organic 

compounds, aldehydes, fine particles, selected trace elements, and AER were measured at 

87 high school student’s residences in New York City and Los Angeles in 1999 and 

2000. Data included the presence or absence of an air conditioner (central or room) and 

hourly outdoor temperatures (which were converted to daily averages for these analyses). 

Wilson 1984: Wilson et al, 1986, 1996. In this 1984 study, AER and other data were 

collected at about 600 southern California homes with three seven-day tests (in March 

and July 1984, and January, 1985) for each home. We obtained the data directly from Mr. 

Wilson. The available data consisted of the three seven-day averages, the month, the 

residence zip code, the presence or absence of a central air conditioner, and the presence 

or absence of a window air conditioner. We matched these data by month and zip code to 

the corresponding monthly average temperatures obtained from EPA’s SCRAM website 

as well as from the archives in www.wunderground.com (personal and airport 

meteorological stations). Residences more than 25 miles away from the nearest available 

meteorological station were excluded from the analysis. For our analyses, the 

city/location was defined by the meteorological station, since grouping the data by zip 

code would not have produced sufficient data for most of the zip codes. 

Wilson 1991: Wilson et al, 1996. Colome et al, 1993, 1994. In this 1991 study, AER and 

other data were collected at about 300 California homes with one two-day test in the 

winter for each home. We obtained the data directly from Mr. Wilson. The available data 

consisted of the two-day averages, the date, city name, the residence zip code, the 

presence or absence of a central air conditioner, the presence or absence of a swamp 

(evaporative) cooler, and the presence or absence of a window air conditioner . We 

matched these data by date, city, and zip code to the corresponding daily average 

temperatures obtained from EPA’s SCRAM website as well as from the archives in 

www.wunderground.com (personal and airport meteorological stations). Residences 

more than 25 miles away from the nearest available meteorological station were excluded 

from the analysis. For our analyses, the city/location was defined by the meteorological 

station, since grouping the data by zip code would not have produced sufficient data for 

most of the zip codes. 

 

Murray and Burmaster: Murray and Burmaster (1995). For this article, Murray and 

Burmaster corrected and compiled nationwide residential AER data from several studies 

conducted between 1982 and 1987. These data were originally compiled by the Lawrence 

Berkeley National Laboratory. We acknowledge Mr. Murray’s assistance in obtaining 
 A-3

these data for us. The available data consisted of AER measurements, dates, cities, and 

degree-days. Information on air conditioner presence or absence was not available. 

Table A-1 summarizes these studies. 

For each of the studies, air conditioner usage, window status (open or closed), and fan status (on 

or off) was not part of the experimental design, although some of these studies included 

information on whether air conditioners or fans were used (and for how long) and whether 

windows were closed during the AER measurements (and for how long). 

As described above, in the following studies the homes were deliberately sampled from specific 

subsets of the population at a given location rather than the entire population: The RTP Panel 

study selected two specific cohorts of older subjects with specific diseases. The RIOPA study 

was biased towards residences near air toxics sources. The TEACH study focused on inner-city 

neighborhoods. Nevertheless, we included all these studies because we determined that any 

potential bias would be likely to be small and we preferred to keep as much data as possible. 
Table A-1. Summary of Studies of Residential Air Exchange Rates 

Avol RTP Panel RIOPA TEACH Wilson 1984 Wilson 1991 

Locations 

Lancaster, Lake Gregory, Riverside, San Dimas. All in Southern CA 

Research Triangle Park, NC CA; NJ; TX 

Los Angeles, CA; New York City, NY Southern CA Southern CA 

Years 1994 2000; 2001 1999; 2000; 2001 1999; 2000 1984, 1985 1984 Months/Seasons 

Feb; Mar; Apr; May; Jun; Jul; Aug; Sep; Oct; Nov 

2000 (Jun; Jul; Aug; Sep; Oct; Nov), 2001 (Jan; Feb; Apr; May) 

1999 (July to Dec); 2000 (all months); 2001 (Jan and Feb) 

1999 (Feb; Mar; Apr; Jul; Aug); 2000 (Jan; Feb; Mar; Sep; Oct) 

Mar 1984, Jul 1984, Jan 1985 Jan, Mar, Jul 

Number of Homes 86 37 284 85 581 288 Total AER Measurements 161 854 524 151 1,362 316 Average Number of Measurements per Home 1.87 23.08 1.85 1.78 2.34 1.10 Measurement Duration 

Not Available 24 hour 24 to 96 hours 

Sample time (hours) reported. Ranges from about 1 to 7 days. 7 days 7 days 

Measurement Technique Not Available 

Perflourocarbon tracer. PMCH tracer 

Perflourocarbon tracer. Perflourocarbon tracer. Perflourocarbon tracer. 

Min AER Value 0.01 0.02 0.08 0.12 0.03 0.01 Max AER Value 2.70 21.44 87.50 8.87 11.77 2.91 Mean AER Value 0.80 0.72 1.41 1.71 1.05 0.57 Min Temperature (C) -0.04 -2.18 -6.82 -1.36 11.00 3.00 
A-5

Avol RTP Panel RIOPA TEACH Wilson 1984 Wilson 1991 

Max Temperature (C) 36.25 30.81 32.50 32.00 28.00 25.00 Air Conditioner Categories 

No A/C; Central or Room A/C; Swamp Cooler only; Swamp + [Central or Room] 

Central or Room A/C (Y/N) 

Window A/C (Y/N); Evap Coolers (Y/N) 

Central or Room A/C (Y/N) 

Central A/C (Y/N); Room A/C (Y/N); 

Central A/C (Y/N); Room A/C (Y/N); Swamp Cooler(Y/N) 

Air Conditioner Measurements A/C use in minutes Not Available 

Duration measurements in Hrs and Mins Not Available Not Available Not Available 

Fan Categories Not available Fan (Y/N) Fan (Y/N) Not Available Not Available Not Available Fan Measurements 

Time on or off for various fan types during sampling was recorded, but not included in database provided. Not Available 

Duration measurements in Hrs and Mins Not Available Not Available Not Available 

Window Open/ Closed Data 

Duration open between times 6am-12 pm; 12pm - 6 pm; and 6pm - 6am 

Windows (open / closed along with duration open in inch-hours units 

Windows (Open / Closed) along with window open duration measurements Not Available Not Available Not Available 

Comments 

CA sample was a random sample of homes. NJ and TX homes were deliberately chosen to be near to ambient sources. 

Restricted to innercity homes with high school students. 

Contemporaneous temperature data obtained for these analyses from SCRAM and www.wunderground.com meteorological data. 

Contemporaneous temperature data obtained for these analyses from SCRAM and www.wunderground.com meteorological data. 
 A-6

We compiled the data from these seven studies to create the following variables, of which some 

had missing values: 

• Study 

• Date 

• Time – Time of the day that the AER measurement was made 

• House_ID – Residence identifier 

• Measurement_ID – Uniquely identifies each AER measurement for a given study 

• AER – Air Exchange Rate (per hour) 

• AER_Duration – Length of AER measurement period 

• Have_AC – Indicates if the residence has any type of air conditioner (A/C), either a room 

A/C or central A/C or swamp cooler or any of them in combination. “Y” = “Yes.” “N” = 

“No.” 

• Type_of_AC1 – Indicates the types of A/C or swamp cooler available in each house 

measured. Possible values: “Central A/C” “Central and Room A/C” “Central or Room 

A/C” “No A/C” “Swamp + (Central or Room)” “Swamp Cooler only” “Window A/C” 

“Window and Evap” 

• Type_of_AC2 – Indicates if a house measured has either no A/C or some A/C. Possible 

values are “No A/C” and “Central or Room A/C.” 

• Have_Fan – Indicates if the house studied has any fans 

• Mean_Temp – Daily average outside temperature 

• Min_Temp – Minimum hourly outside temperature 

• Max_Temp – Maximum hourly outside temperature 

• State 

• City 

• Location – Two character abbreviation 

• Flag – Data status. Murray and Burmaster study: “Used” or “Not Used.” Other studies: 

“Used”; “Missing” (missing values for AER, Type_of_AC2, and/or Mean_Temp); 

“Outlier”. 

The main data analysis was based on the first six studies. The Murray and Burmaster data were 

excluded because of the absence of information on air conditioner presence. (However, a subset 

of these data was used for a supplementary analysis described below.) . 

Based on our review of the AER data we excluded seven outlying high AER values – above 10 

per hour. The main data analysis used all the remaining data that had non-missing values for 

AER, Type_of_AC2, and Mean_Temp. We decided to base the A/C type variable on the broad 

characterization “No A/C” versus “Central or Room A/C” since this variable could be calculated 

from all of the studies (excluding Murray and Burmaster). Information on the presence or 

absence of swamp coolers was not available from all the studies, and, also importantly, the 

corresponding information on swamp cooler prevalence for the subsequent ozone modeling cities 

was not available from the American Housing Survey. It is plausible that AER distributions 
 A-7

depend upon the presence or absence of a swamp cooler. It is also plausible that AER 

distributions also depend upon whether the residence specifically has a central A/C, room or 

window A/C, or both. However we determined to use the broader A/C type definition, which in 

effect assumes that the exact A/C type and the presence of a swamp cooler are approximately 

proportionately represented in the surveyed residences. 

Most of the studies had more than one AER measurement for the same house. It is reasonable to 

assume that the AER varies with the house as well as other factors such as the temperature. (The 

A/C type can be assumed to be the same for each measurement of the same house). We expected 

the temperature to be an important factor since the AER will be affected by the use of the 

available ventilation (air conditioners, windows, fans), which in turn will depend upon the 

outside meteorology. Therefore it is not appropriate to average data for the same house under 

different conditions, which might have been one way to account for dependence between 

multiple measurements on the same house. To simplify the data analysis, we chose to ignore 

possible dependence between measurements on the same house on different days and treat all the 

AER values as if they were statistically independent. 

Summary Statistics. We computed summary statistics for AER and its natural logarithm 

LOG_AER on selected strata defined from the study, city, A/C type, and mean temperature. 

Cities were defined as in the original databases, except that for Los Angeles we combined all the 

data in the Los Angeles ozone modeling region, i.e. the counties of Los Angeles, Orange, 

Ventura, Riverside, and San Bernardino. A/C type was defined from the Type_of_AC2 variable, 

which we abbreviated as “NA” = “No A/C” and “AC” = “Central or Room A/C.” The mean 

temperature was grouped into the following temperature bins: -10 to 0 oC, 0 to 10 oC, 10 to 20 

oC, 20 to 25 oC, 25 to 30 oC, 30 to 40 oC.(Values equal to the lower bounds are excluded from 

each interval.) Also included were strata defined by study = “All” and/or city = “All,” and/or 

A/C type = “All” and/or temperature bin = “All.” The following summary statistics for AER and 

LOG_AER were computed: 

• Number of values 

• Arithmetic Mean 

• Arithmetic Standard Deviation 

• Arithmetic Variance 

• Deciles (Min, 10th, 20th ... 90th percentiles, Max) 

These calculations exclude all seven outliers and results are not used for strata with 10 or fewer 

values, since those summary statistics are extremely unreliable. 

Examination of these summary tables clearly demonstrates that the AER distributions vary 

greatly across cities and A/C types and temperatures, so that the selected AER distributions for 

the modeled cities should also depend upon the city, A/C type and temperature. For example, the 

mean AER for residences with A/C ranges from 0.39 for Los Angeles between 30 and 40 oC to 

1.73 for New York between 20 and 25 oC. The mean AER for residences without A/C ranges 

from 0.46 for San Francisco between 10 and 20 oC to 2.29 for New York between 20 and 25 oC. 

The need to account for the city as well as the A/C type and temperature is illustrated by the 
 A-8

result that for residences with A/C and between 20 and 25 oC, the mean AER ranges from 0.52 

for Research Triangle Park to 1.73 for New York. Statistical comparisons are described below. 

Statistical Comparisons. Various statistical comparisons were carried out between the different 

strata, for the AER and its logarithm. The various strata are defined as in the Summary Statistics 

section, excluding the “All” cases. For each analysis, we fixed one or two of the variables Study, 

City, A/C type, temperature, and tested for statistically significant differences among other 

variables. The comparisons are listed in Table A-2. 

Table A-2. Summary of Comparisons of Means 

Cases with significantly 

different means (5 % 

level) 

Comparison 

Analysis 

Number. 

Comparison 

Variable(s) 

“Groups 

Compared” 

Stratification 

Variable(s) 

(not missing in 

worksheet) 

Total 

Comparisons

AER Log AER 

1. City Type of A/C AND 

Temp. Range 

12 8 8 

2. Temp. Range Study AND City 12 5 5 

3. Type of A/C Study AND City 15 5 5 

4. City Type of A/C 2 2 2 

5. City Temp. Range 6 5 6 

6. Type of A/C 

AND Temp. 

Range 

Study AND City 17 6 6 

For example, the first set of comparisons fix the Type of A/C and the temperature range; there 

are twelve such combinations. For each of these twelve combinations, we compare the AER 

distributions across different cities. This analysis determines whether the AER distribution is 

appropriately defined by the A/C type and temperature range, without specifying the city. 

Similarly, for the sixth set of comparisons, the study and city are held fixed (17 combinations) 

and in each case we compare AER distributions across groups defined by the combination of the 

A/C type and the temperature range. 

The F Statistic comparisons compare the mean values between groups using a one way analysis 

of variance (ANOVA). This test assumes that the AER or log(AER) values are normally 

distributed with a mean that may vary with the comparison variable(s) and a constant variance. 

We calculated the F Statistic and its P-value. P-values above 0.05 indicate cases where all the 

group means are not statistically significantly different at the 5 percent level. Those results are 

summarized in the last two columns of the above table “Summary of Comparisons of Means” 

which gives the number of cases where the means are significantly different. Comparison 

analyses 2, 3, and 6 show that for a given study and city, slightly less than half of the 

comparisons show significant differences in the means across temperature ranges, A/C types, or 

both. Comparison analyses 1, 4, and 5 show that for the majority of cases, means vary 

significantly across cities, whether you first stratify by temperature range, A/C type, or both. 
 A-9

The Kruskal-Wallis Statistic comparisons are non-parametric tests that are extensions of the 

more familiar Wilcoxon tests to two or more groups. The analysis is valid if the AER minus the 

group median has the same distribution for each group, and tests whether the group medians are 

equal. (The test is also consistent under weaker assumptions against more general alternatives) 

The P-values show similar patterns to the parametric F test comparisons of the means. Since the 

logarithm is a strictly increasing function and the test is non-parametric, the Kruskal-Wallis tests 

give identical results for AER and Log (AER). 

The Mood Statistic comparisons are non-parametric tests that compare the scale statistics for two 

or more groups. The scale statistic measures variation about the central value, which is a nonparametric generalization of the standard deviation. Specifically, suppose there is a total of N 

AER or log(AER) values, summing across all the groups. These N values are ranked from 1 to 

N, and the j’th highest value is given a score of {j - (N+1)/2}2

. The Mood statistic uses a one 

way ANOVA statistic to compare the total scores for each group. Generally, the Mood statistics 

show that in most cases the scale statistics are not statistically significantly different. Since the 

logarithm is a strictly increasing function and the test is non-parametric, the Mood tests give 

identical results for AER and Log (AER). 

Fitting Distributions. Based on the summary statistics and the statistical comparisons, the need 

to fit different AER distributions to each combination of A/C type, city, and temperature is 

apparent. For each combination with a minimum of 11 AER values, we fitted and compared 

exponential, log-normal, normal, and Weibull distributions to the AER values. 

The first analysis used the same stratifications as in the above “Summary Statistics” and 

“Statistical Comparisons” sections. Results are not reported for all strata because of the 

minimum data requirement of 11 values. Results for each combination of A/C type, city, and 

temperature (i.e., A, C, and T) were analyzed. Each combination has four rows, one for each 

fitted distribution. For each distribution we report the fitted parameters (mean, standard 

deviation, scale, shape) and the p-value for three standard goodness-of-fit tests: KolmogorovSmirnov (K-S), Cramer-Von-Mises (C-M), Anderson-Darling (A-D). Each goodness-of-fit test 

compares the empirical distribution of the AER values to the fitted distribution. The K-S and CM tests are different tests examining the overall fit, while the Anderson-Darling test gives more 

weight to the fit in the tails of the distribution. For each combination, the best-fitting of the four 

distributions has the highest p-value and is marked by an x in the final three columns. The mean 

and standard deviation (Std_Dev) are the values for the fitted distribution. The scale and shape 

parameters are defined by: 

 

• Exponential: density = σ

-1 exp(-x/σ), where shape = mean = σ

• Log-normal: density = {σx√(2π)}-1 exp{ -(log x - ζ)

2

 / (2σ

2

)}, where shape = σ and 

scale = ζ. Thus the geometric mean and geometric standard deviation are given by 

exp(ζ) and exp(σ), respectively. 

• Normal: density = {σ√(2π)}-1 exp{ -(x - μ)

2

 / (2σ

2

)}, where mean = μ and standard 

deviation = σ

• Weibull: density = (c/σ) (x/σ)

c-1 exp{-(x/σ)c

}, where shape = c and scale = σ
 A-10

Generally, the log-normal distribution was the best-fitting of the four distributions, and so, for 

consistency, we recommend using the fitted log-normal distributions for all the cases. 

One limitation of the initial analysis was that distributions were available only for selected cities, 

and yet the summary statistics and comparisons demonstrate that the AER distributions depend 

upon the city as well as the temperature range and A/C type. As one option to address this issue, 

we considered modeling cities for which distributions were not available by using the AER 

distributions across all cities and dates for a given temperature range and A/C type. 

Another important limitation of the initial analysis was that distributions were not fitted to all of 

the temperature ranges due to inadequate data. There are missing values between temperature 

ranges, and the temperature ranges are all bounded. To address this issue, the temperature ranges 

were regrouped to cover the entire range of temperatures from minus to plus infinity, although 

obviously the available data to fit these ranges have finite temperatures. Stratifying by A/C type, 

city, and the new temperature ranges produces results for four cities: Houston (AC and NA); Los 

Angeles (AC and NA); New York (AC and NA); Research Triangle Park (AC). For each of the 

fitted distributions we created histograms to compare the fitted distributions with the empirical 

distributions. 

AER Distributions for The First Nine Cities. Based upon the results for the above four cities 

and the corresponding graphs, we propose using those fitted distributions for the three cities 

Houston, Los Angeles, and New York. For another 6 of the cities to be modeled, we propose 

using the distribution for one of the four cities thought to have similar characteristics to the city 

to be modeled with respect to factors that might influence AERs. These factors include the age 

composition of housing stock, construction methods, and other meteorological variables not 

explicitly treated in the analysis, such as humidity and wind speed patterns. The distributions 

proposed for these cities are as follows: 

• Atlanta, GA, A/C: Use log-normal distributions for Research Triangle Park. Residences 

with A/C only. 

• Boston, MA: Use log-normal distributions for New York 

• Chicago, IL: Use log-normal distributions for New York 

• Cleveland, OH: Use log-normal distributions for New York 

• Detroit, MI: Use log-normal distributions for New York 

• Houston, TX: Use log-normal distributions for Houston 

• Los Angeles, CA: Use log-normal distributions for Los Angeles 

• New York, NY: Use log-normal distributions for New York 

• Philadelphia, PA: Use log-normal distributions for New York 

Since the AER data for Research Triangle Park was only available for residences with air 

conditioning, AER distributions for Atlanta residences without air conditioning are discussed 

below. 

To avoid unusually extreme simulated AER values, we propose to set a minimum AER value of 

0.01 and a maximum AER value of 10. 
 A-11

Obviously, we would be prefer to model each city using data from the same city, but this 

approach was chosen as a reasonable alternative, given the available AER data. 

AER Distributions for Sacramento and St. Louis. For these two cities, a direct mapping to one 

of the four cities Houston, Los Angeles, New York, and Research Triangle Park is not 

recommended because the cities are likely to be too dissimilar. Instead, we decided to use the 

distribution for the inland parts of Los Angeles to represent Sacramento and to use the aggregate 

distributions for all cities outside of California to represent St. Louis. The results for the city 

Sacramento were obtained by combining all the available AER data for Sacramento, Riverside, 

and San Bernardino counties. The results for the city St. Louis were obtained by combining all 

non-California AER data. 

AER Distributions for Washington DC. Washington DC was judged likely to have similar 

characteristics both to Research Triangle Park and to New York City. To choose between these 

two cities, we compared the Murray and Burmaster AER data for Maryland with AER data from 

each of those cities. The Murray and Burmaster study included AER data for Baltimore and for 

Gaithersburg and Rockville, primarily collected in March. April, and May 1987, although there 

is no information on mean daily temperatures or A/C type. We collected all the March, April, 

and May AER data for Research Triangle Park and for New York City, and compared those 

distributions with the Murray and Burmaster Maryland data for the same three months. 

 

The results for the means and central values show significant differences at the 5 percent level 

between the New York and Maryland distributions. Between Research Triangle Park and 

Maryland, the central values and the mean AER values are not statistically significantly 

different, and the differences in the mean log (AER) values are much less statistically significant 

than between New York and Maryland. The scale statistic comparisons are not statistically 

significantly different between New York and Maryland, but were statistically significantly 

different between Research Triangle Park and Maryland. Since matching central and mean 

values is generally more important than matching the scales, we propose to model Washington 

DC residences with air conditioning using the Research Triangle Park distributions, stratified by 

temperature: 

• Washington DC, A/C: Use log-normal distributions for Research Triangle Park. 

Residences with A/C only. 

Since the AER data for Research Triangle Park was only available for residences with air 

conditioning, the estimated AER distributions for Washington DC residences without air 

conditioning are discussed below. 

AER Distributions for Washington DC and Atlanta GA Residences With No A/C. For 

Atlanta and Washington DC we have proposed to use the AER distributions for Research 

Triangle Park. However, all the Research Triangle Park data (from the RTP Panel study) were 

from houses with air conditioning, so there are no available distributions for the “No A/C” cases. 

For these two cities, one option is to use AER distributions fitted to all the study data for 

residences without A/C, stratified by temperature. We propose applying the “No A/C” 
 A-12

distributions for modeling these two cities for residences without A/C. However, since Atlanta 

and Washington DC residences are expected to be better represented by residences outside of 

California, we instead propose to use the “No A/C” AER distributions aggregated across cities 

outside of California, which is the same as the recommended choice for the St. Louis “No A/C” 

AER distributions.

A/C Type and Temperature Distributions. Since the proposed AER distribution is conditional 

on the A/C type and temperature range, these values also need to be simulated using APEX in 

order to select the appropriate AER distribution. Mean daily temperatures are one of the 

available APEX inputs for each modeled city, so that the temperature range can be determined 

for each modeled day according to the mean daily temperature. To simulate the A/C type, we 

obtained estimates of A/C prevalence from the American Housing Survey. Thus for each 

city/metropolitan area, we obtained the estimated fraction of residences with Central or Room 

A/C (see Table A-3), which gives the probability p for selecting the A/C type “Central or Room 

A/C.” Obviously, 1-p is the probability for “No A/C.” For comparison with Washington DC and 

Atlanta, we have included the A/C type percentage for Charlotte, NC (representing Research 

Triangle Park, NC). As discussed above, we propose modeling the 96-97 % of Washington DC 

and Atlanta residences with A/C using the Research Triangle Park AER distributions, and 

modeling the 3-4 % of Washington DC and Atlanta residences without A/C using the combined 

study No A/C AER distributions. 

Table A-3. Fraction of residences with central or room A/C (from American Housing 

Survey) 

 

CITY SURVEY AREA & YEAR PERCENTAGE 

Atlanta Atlanta, 2003 97.01 

Boston Boston, 2003 85.23 

Chicago Chicago, 2003 87.09 

Cleveland Cleveland, 2003 74.64 

Detroit Detroit, 2003 81.41 

Houston Houston, 2003 98.70 

Los Angeles Los Angeles, 2003 55.05 

New York New York, 2003 81.57 

Philadelphia Philadelphia, 2003 90.61 

Sacramento Sacramento, 2003 94.63 

St. Louis St. Louis, 2003 95.53 

Washington DC Washington DC, 2003 96.47 

Research Triangle Park Charlotte, 2002 96.56 

Other AER Studies 

We recently became aware of some additional residential and non-residential AER studies that 

might provide additional information or data. Indoor / outdoor ozone and PAN distributions were 

studied by Jakobi and Fabian (1997). Liu et al (1995) studied residential ozone and AER 

distributions in Toronto, Canada. Weschler and Shields (2000) describes a modeling study of 
 A-13

ventilation and air exchange rates. Weschler (2000) includes a useful overview of residential and 

non-residential AER studies. 

AER Distributions for Other Indoor Environments

To estimate AER distributions for non-residential, indoor environments (e.g., offices and 

schools), we obtained and analyzed two AER data sets: “Turk” (Turk et al, 1989); and “Persily” 

(Persily and Gorfain 2004; Persily et al. 2005). 

The earlier “Turk” data set (Turk et al, 1989) includes 40 AER measurements from offices (25 

values), schools (7 values), libraries (3 values), and multi-purpose (5 values), each measured 

using an SF6 tracer over two- or four-hours in different seasons of the year. 

The more recent “Persily” data (Persily and Gorfain 2004; Persily et al. 2005) were derived 

from the U.S. EPA Building Assessment Survey and Evaluation (BASE) study, which was 

conducted to assess indoor air quality, including ventilation, in a large number of randomly 

selected office buildings throughout the U.S. The data base consists of a total of 390 AER 

measurements in 96 large, mechanically ventilated offices; each office was measured up to four 

times over two days, Wednesday and Thursday AM and PM. The office spaces were relatively 

large, with at least 25 occupants, and preferably 50 to 60 occupants. AERs were measured both 

by a volumetric method and by a CO2 ratio method, and included their uncertainty estimates. For 

these analyses, we used the recommended “Best Estimates” defined by the values with the lower 

estimated uncertainty; in the vast majority of cases the best estimate was from the volumetric 

method. 

Another study of non-residential AERs was performed by Lagus Applied Technology (1995) 

using a tracer gas method. That study was a survey of AERs in 16 small office buildings, 6 large 

office buildings, 13 retail establishments, and 14 schools. We plan to obtain and analyze these 

data and compare those results with the Turk and Persily studies. 

Due to the small sample size of the Turk data, the data were analyzed without stratification by 

building type and/or season. For the Persily data, the AER values for each office space were 

averaged, rather using the individual measurements, to account for the strong dependence of the 

AER measurements for the same office space over a relatively short period. 

Summary statistics of AER and log (AER) for the two studies are presented in Table A-4. 

Table A-4. AER summary statistics for offices and other non-residential buildings 

Study Variable N Mean Std Dev Min 25th %ile Median 75th %ile Max 

Persily AER 96 1.9616 2.3252 0.0712 0.5009 1.0795 2.7557 13.8237 

Turk AER 40 1.5400 0.8808 0.3000 0.8500 1.5000 2.0500 4.1000 

Persily Log(AER) 96 0.1038 1.1036 -2.6417 -0.6936 0.0765 1.0121 2.6264 

Turk Log(AER) 40 0.2544 0.6390 -1.2040 -0.1643 0.4055 0.7152 1.4110 

 
 A-14

The mean values are similar for the two studies, but the standard deviations are about twice as 

high for the Persily data. The proposed AER distributions were derived from the more recent 

Persily data only. 

Similarly to the analyses of the residential AER distributions, we fitted exponential, log-normal, 

normal, and Weibull distributions to the 96 office space average AER values. The results are 

shown in Table A-5. 

Table A-5. Best fitting office AER distributions from the Persily et al. (2004, 2005) 

Scale Shape Mean Std_Dev Distribution

P-Value 

KolmogorovSmirnov 

P-Value 

Cramervon 

Mises 

P-Value 

AndersonDarling 

1.9616 1.9616 1.9616 Exponential 0.13 0.04 0.05 

0.1038 1.1036 2.0397 3.1469 Lognormal 0.15 0.46 0.47 

 1.9616 2.3252 Normal 0.01 0.01 0.01 

1.9197 0.9579 1.9568 2.0433 Weibull 0.01 0.01 

(For an explanation of the Kolmogorov-Smirnov, Cramer-von Mises, and Anderson-Darling Pvalues see the discussion residential AER distributions above.) According to all three goodnessof-fit measures the best-fitting distribution is the log-normal. Reasonable choices for the lower 

and upper bounds are the observed minimum and maximum AER values. 

We therefore propose the following indoor, non-residential AER distributions. 

• AER distribution for indoor, non-residential microenvironments: Lognormal, with scale 

and shape parameters 0.1038 and 1.1036, i.e., geometric mean = 1.1094, geometric 

standard deviation = 3.0150. Lower Bound = 0.07. Upper bound = 13.8. 

Proximity and Penetration Factors For Outdoors, In-vehicle, and Mass Transit

For the APEX modeling of the outdoor, in-vehicle, and mass transit micro-environments, an 

approach using proximity and penetration factors is proposed, as follows. 

Outdoors Near Road

Penetration factor = 1. 

For the Proximity factor, we propose using ratio distributions developed from the Cincinnati 

Ozone Study (American Petroleum Institute, 1997, Appendix B; Johnson et al. 1995). The field 

study was conducted in the greater Cincinnati metropolitan area in August and September, 1994. 

Vehicle tests were conducted according to an experimental design specifying the vehicle type, 

road type, vehicle speed, and ventilation mode. Vehicle types were defined by the three study 

vehicles: a minivan, a full-size car, and a compact car. Road types were interstate highways 

(interstate), principal urban arterial roads (urban), and local roads (local). Nominal vehicle 
 A-15

speeds (typically met over one minute intervals within 5 mph) were at 35 mph, 45 mph, or 55 

mph. Ventilation modes were as follows: 

• Vent Open: Air conditioner off. Ventilation fan at medium. Driver’s window half open. 

Other windows closed. 

• Normal A/C. Air conditioner at normal. All windows closed. 

• Max A/C: Air conditioner at maximum. All windows closed. 

Ozone concentrations were measured inside the vehicle, outside the vehicle, and at six fixed site 

monitors in the Cincinnati area. 

The proximity factor can be estimated from the distributions of the ratios of the outside-vehicle 

ozone concentrations to the fixed-site ozone concentrations, reported in Table 8 of Johnson et al. 

(1995). Ratio distributions were computed by road type (local, urban, interstate, all) and by the 

fixed-site monitor (each of the six sites, as well as the nearest monitor to the test location). For 

this analysis we propose to use the ratios of outside-vehicle concentrations to the concentrations 

at the nearest fixed site monitor, as shown in Table A-6. 

Table A-6. Ratio of outside-vehicle ozone to ozone at nearest fixed site1

Road 

Type1

Number 

of cases1

Mean1 Standard 

Deviation1

25th

Percentile1

50th

Percentile1

75th

Percentile1

Estimated 

5th

Percentile2

Local 191 0.755 0.203 0.645 0.742 0.911 0.422 

Urban 299 0.754 0.243 0.585 0.722 0.896 0.355 

Interstate 241 0.364 0.165 0.232 0.369 0.484 0.093 

All 731 0.626 0.278 0.417 0.623 0.808 0.170 

 

1. From Table 8 of Johnson et al. (1995). Data excluded if fixed-site concentration < 40 

ppb. 

2. Estimated using a normal approximation as Mean – 1.64 × Standard Deviation 

For the outdoors-near- road microenvironment, we recommend using the distribution for local 

roads, since most of the outdoors-near-road ozone exposure will occur on local roads. The 

summary data from the Cincinnati Ozone Study are too limited to allow fitting of distributions, 

but the 25th and 75th percentiles appear to be approximately equidistant from the median (50th

percentile). Therefore we propose using a normal distribution with the observed mean and 

standard deviation. A plausible upper bound for the proximity factor equals 1. Although the 

normal distribution allows small positive values and can even produce impossible, negative 

values (with a very low probability), the titration of ozone concentrations near a road is limited. 

Therefore, as an empirical approach, we recommend a lower bound of the estimated 5th

percentile, as shown in the final column of the above table. Therefore in summary we propose: 

• Penetration factor for outdoors, near road: 1.
 A-16

• Proximity factor for outdoors, near road: Normal distribution. Mean = 0.755. Standard 

Deviation = 0.203. Lower Bound = 0.422. Upper Bound = 1.

Outdoors, Public Garage / Parking Lot

This micro-environment is similar to the outdoors-near-road microenvironment. We therefore 

recommend the same distributions as for outdoors-near-road: 

• Penetration factor for outdoors, public garage / parking lot: 1.

• Proximity factor for outdoors, public garage / parking lot: Normal distribution. Mean = 

0.755. Standard Deviation = 0.203. Lower Bound = 0.422. Upper Bound = 1.

Outdoors, Other

The outdoors, other ozone concentrations should be well represented by the ambient monitors. 

Therefore we propose: 

• Penetration factor for outdoors, other: 1.

• Proximity factor for outdoors, other: 1.

In-Vehicle

For the proximity factor for in-vehicle, we also recommend using the results of the Cincinnati 

Ozone Study presented in Table A-6. For this microenvironment, the ratios depend upon the road 

type, and the relative prevalences of the road types can be estimated by the proportions of 

vehicle miles traveled in each city. The proximity factors are assumed, as before, to be normally 

distributed, the upper bound to be 1, and the lower bound to be the estimated 5th percentile. 

• Proximity factor for in-vehicle, local roads: Normal distribution. Mean = 0.755. Standard 

Deviation = 0.203. Lower Bound = 0.422. Upper Bound = 1.

• Proximity factor for in-vehicle, urban roads: Normal distribution. Mean = 0.754. 

Standard Deviation = 0.243. Lower Bound = 0.355. Upper Bound = 1.

• Proximity factor for in-vehicle, interstates: Normal distribution. Mean = 0.364. Standard 

Deviation = 0.165. Lower Bound = 0.093. Upper Bound = 1.

To complete the specification, the distribution of road type needs to be estimated for each city to 

be modeled. Vehicle miles traveled (VMT) in 2003 by city (defined by the Federal-Aid 

urbanized area) and road type were obtained from the Federal Highway Administration. 

(http://www.fhwa.dot.gov/policy/ohim/hs03/htm/hm71.htm). For local and interstate road types, 

the VMT for the same DOT categories were used. For urban roads, the VMT for all other road 

types was summed (Other freeways/expressways, Other principal arterial, Minor arterial, 

Collector). The computed VMT ratios for each city are shown in Table A-7. 
 A-17

Table A-7. Vehicle Miles Traveled by City and Road Type in 2003 (FHWA, October 2004) 

FRACTION VMT BY ROAD TYPE 

FEDERAL-AID URBANIZED 

AREA INTERSTATE URBAN LOCAL 

Atlanta 0.38 0.45 0.18 

Boston 0.31 0.55 0.14 

Chicago 0.30 0.59 0.12 

Cleveland 0.39 0.45 0.16 

Detroit 0.26 0.63 0.11 

Houston 0.24 0.72 0.04 

Los Angeles 0.29 0.65 0.06 

New York 0.18 0.67 0.15 

Philadelphia 0.23 0.65 0.11 

Sacramento 0.21 0.69 0.09 

St. Louis 0.36 0.45 0.19 

Washington 0.31 0.61 0.08 

Note that a “Federal-Aid Urbanized Area" is an area with 50,000 or more persons that at a 

minimum encompasses the land area delineated as the urbanized area by the Bureau of the 

Census. Urbanized areas that have been combined with others for reporting purposes are not 

shown separately. The Illinois portion of Round Lake Beach-McHenry-Grayslake has been 

reported with Chicago. 

 

Thus to simulate the proximity factor in APEX, we propose to first select the road type according 

to the above probability table of road types, then select the AER distribution (normal) for that 

road type as defined in the last set of bullets. 

For the penetration factor for in-vehicle, we recommend using the inside-vehicle to outsidevehicle ratios from the Cincinnati Ozone Study. The ratio distributions were summarized for all 

the data and for stratifications by vehicle type, vehicle speed, road type, traffic (light, moderate, 

or heavy), and ventilation. The overall results and results by ventilation type are shown in Table 

A-8.

Table A-8. Ratio of inside-vehicle ozone to outside-vehicle ozone1

Ventilation1

Number 

of 

cases1

Mean1 Standard 

Deviation1

25th

Percentile1

50th

Percentile1

75th

Percentile1

Estimated 

5th

Percentile2

Vent Open 226 0.361 0.217 0.199 0.307 0.519 0.005 

Normal 

A/C 332 0.417 0.211 0.236 0.408 0.585 0.071 

Maximum 

A/C 254 0.093 0.088 0.016 0.071 0.149 0.0003

All 812 0.300 0.232 0.117 0.251 0.463 0.0003
 A-18

 

1. From Table 7 of Johnson et al.(1995). Data excluded if outside-vehicle concentration < 

20 ppb. 

2. Estimated using a normal approximation as Mean – 1.64 × Standard Deviation 

3. Negative estimate (impossible value) replaced by zero. 

Although the data in Table A-8 indicate that the inside-to-outside ozone ratios strongly depend 

upon the ventilation type, it would be very difficult to find suitable data to estimate the 

ventilation type distributions for each modeled city. Furthermore, since the Cincinnati Ozone 

Study was scripted, the ventilation conditions may not represent real-world vehicle ventilation 

scenarios. Therefore, we propose to use the overall average distributions. 

• Penetration factor for in-vehicle: Normal distribution. Mean = 0.300. Standard Deviation 

= 0.232. Lower Bound = 0.000. Upper Bound = 1. 

Mass Transit

The mass transit microenvironment is expected to be similar to the in-vehicle microenvironment. 

Therefore we recommend using the same APEX modeling approach: 

• Proximity factor for mass transit, local roads: Normal distribution. Mean = 0.755. 

Standard Deviation = 0.203. Lower Bound = 0.422. Upper Bound = 1.

• Proximity factor for mass transit, urban roads: Normal distribution. Mean = 0.754. 

Standard Deviation = 0.243. Lower Bound = 0.355. Upper Bound = 1.

• Proximity factor for mass transit, interstates: Normal distribution. Mean = 0.364. 

Standard Deviation = 0.165. Lower Bound = 0.093. Upper Bound = 1.

• Road type distributions for mass transit: See Table A-6 

• Penetration factor for mass transit: Normal distribution. Mean = 0.300. Standard 

Deviation = 0.232. Lower Bound = 0.000. Upper Bound = 1. 

References 

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model algorithms. Health and Environmental Sciences Department. 

Avol, E. L., W. C. Navidi, and S. D. Colome (1998) Modeling ozone levels in and around 

southern California homes. Environ. Sci. Technol. 32, 463-468. 

Chilrud, S. N., D. Epstein, J. M. Ross, S. N. Sax, D. Pederson, J. D. Spengler, P. L. Kinney 

(2004). Elevated airborne exposures of teenagers to manganese, chromium, and iron from steel 

dust and New York City's subway system. Environ. Sci. Technol. 38, 732-737. 

Colome, S.D., A. L. Wilson, Y. Tian (1993). California Residential Indoor Air Quality Study, 

Volume 1, Methodology and Descriptive Statistics. Report prepared for the Gas Research 

Institute, Pacific Gas & Electric Co., San Diego Gas & Electric Co., Southern California Gas Co. 
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Volume 2, Carbon Monoxide and Air Exchange Rate: An Univariate and Multivariate Analysis. 

Chicago, IL. Report prepared for the Gas Research Institute, Pacific Gas & Electric Co., San 

Diego Gas & Electric Co., Southern California Gas Co. GRI-93/0224.3 

Jakobi, G and Fabian, P. (1997). Indoor/outdoor concentrations of ozone and peroxyacetyl nitrate 

(PAN). Int. J. Biometeorol. 40: 162-165.. 

Johnson, T., A. Pakrasi, A. Wisbeth, G. Meiners, W. M. Ollison (1995). Ozone exposures within 

motor vehicles – results of a field study in Cincinnati, Ohio. Proceedings 88th annual meeting 

and exposition of the Air & Waste Management Association, June 18-23, 1995. San Antonio, 

TX. Preprint paper 95-WA84A.02. 

Kinney, P. L., S. N. Chillrud, S. Ramstrom, J. Ross, J. D. Spengler (2002). Exposures to multiple 

air toxics in New York City. Environ Health Perspect 110, 539-546. 

Lagus Applied Technology, Inc. (1995) Air change rates in non-residential buildings in 

California. Sacramento CA, California Energy Commission, contract 400-91-034. 

Liu, L.-J. S, P. Koutrakis, J. Leech, I. Broder, (1995) Assessment of ozone exposures in the 

greater metropolitan Toronto area. J. Air Waste Manage. Assoc. 45: 223-234. 

Meng, Q. Y., B. J. Turpin, L. Korn, C. P. Weisel, M. Morandi, S. Colome, J. J. Zhang, T. Stock, 

D. Spektor, A. Winer, L. Zhang, J. H. Lee, R. Giovanetti, W. Cui, J. Kwon, S. Alimokhtari, D. 

Shendell, J. Jones, C. Farrar, S. Maberti (2004). Influence of ambient (outdoor) sources on 

residential indoor and personal PM2.5 concentrations: Analyses of RIOPA data. Journal of 

Exposure Analysis and Environ Epidemiology. Preprint. 

Murray, D. M. and D. E. Burmaster (1995). Residential Air Exchange Rates in the United 

States: Empirical and Estimated Parametric Distributions by Season and Climatic Region. Risk 

Analysis, Vol. 15, No. 4, 459-465. 

Persily, A. and J. Gorfain.(2004). Analysis of ventilation data from the U.S. Environmental 

Protection Agency Building Assessment Survey and Evaluation (BASE) Study. National Institute 

of Standards and Technology, NISTIR 7145, December 2004. 

Persily, A., J. Gorfain, G. Brunner.(2005). Ventilation design and performance in U.S. office 

buildings. ASHRAE Journal. April 2005, 30-35. 

Sax, S. N., D. H. Bennett, S. N. Chillrud, P. L. Kinney, J. D. Spengler (2004) Differences in 

source emission rates of volatile organic compounds in inner-city residences of New York City 

and Los Angeles. Journal of Exposure Analysis and Environ Epidemiology. Preprint. 

Turk, B. H., D. T. Grimsrud, J. T. Brown, K. L. Geisling-Sobotka, J. Harrison, R. J. Prill (1989). 

Commercial building ventilation rates and particle concentrations. ASHRAE, No. 3248. 
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Weschler, C. J. (2000) Ozone in indoor environments: concentration and chemistry. Indoor Air 

10: 269-288. 

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pollutants: modeling and experimental observations. Indoor Air. 10: 92-100. 

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L. Korn, A. Winer, S. Alimokhtari, J. Kwon, K. Mohan, R. Harrington, R. Giovanetti, W. Cui, 

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(RIOPA) study; study design, methods and quality assurance / control results. Journal of 

Exposure Analysis and Environ Epidemiology. Preprint. 

Williams, R., J. Suggs, A. Rea, K. Leovic, A. Vette, C. Croghan, L. Sheldon, C. Rodes, J. 

Thornburg, A. Ejire, M. Herbst, W. Sanders Jr. (2003a). The Research Triangle Park particulate 

matter panel study: PM mass concentration relationships. Atmos Env 37, 5349-5363. 

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Triangle Park particulate patter panel study: modeling ambient source contribution to personal 

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Characterization Study of Nitrogen Dioxide, Phase I, Final Report. Prepared for Southern 

California Gas Company, Los Angeles. 

Wilson, A. L., S. D. Colome, Y. Tian, P. E. Baker, E. W. Becker, D. W. Behrens, I. H. Billick, 

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of Exposure Analysis and Environ Epidemiology. Vol. 6, No. 3. 
 

APPENDIX B. THEORETICAL DEVELOPMENT OF A UNIFIED ALGORITHM 

FOR ADJUSTING MET VALUES IN HUMAN EXPOSURE MODELING FOR 

FATIGUE AND EXCESS POST-EXERCISE OXYGEN CONSUMPTION (EPOC) 
This page intentionally left blank.
B-1 

TECHNICAL MEMORANDUM 

TO: Tom McCurdy, U.S. EPA, WA Manager, NERL WA 131 

FROM: Kristin Isaacs, Graham Glen, and Luther Smith, Alion Science and Technology Inc.

DATE: June 16, 2005 

SUBJECT: Theoretical Development of a Unified Algorithm for Adjusting MET Values 

 in Human Exposure Modeling for Fatigue and EPOC 

I. INTRODUCTION 

The CHAD activity database assigns distributions for energy expenditure to each diary event, 

based on the reported event activity. This is done using the MET paradigm, which uses ratios of 

activity-specific to basal energy expenditure. However, the basic or “raw” MET distributions do 

not consider sequences of events. It is well known that a person’s capacity for work will 

diminish as they get tired, and in practice, this means that the upper bound on MET is lowered if 

events in the recent past have been at unusually high MET levels. Furthermore, once high 

activity levels have ended, people tend to breathe heavily even while resting, as they recover 

their accumulated oxygen deficit. This effect is called excess post-exercise oxygen consumption 

(EPOC), and results in raising the MET levels above the ‘raw’ values pulled from the activitybased distributions. 

Historically, the logic for the downward adjustments (downward limitations on the maximum 

MET with increasing fatigue) was developed before the EPOC adjustments. The pNEM model 

included downward adjustments, both for single events and averages over many diary events. 

The rules for these adjustments are given in a report1

 by Ted Johnson describing the pNEM 

algorithms. These rules were incorporated into CHAD and APEX without alteration. The rules 

for the EPOC adjustments were developed later by G. Glen and added to CHAD. They were not 

included in APEX or any of the SHEDS models. 

Rather than separately accounting for these effects, it is more logical to make both adjustments 

simultaneously. This would prevent the possibility of making a downward adjustment so that the 

MET average conforms to a given limit, but then have the EPOC adjustment boost the average 

back above that limit. Also, the current method of making the adjustments is computationally 

burdensome. For these reasons, we have developed a new approach. 

The proposed adjustment algorithm imposes limits on MET via the value of an oxygen deficit an 

individual has incurred. The method is more computationally efficient than previous METadjustment algorithms, and eliminates some of the problematic features of the current methods. 
B-2 

II. THEORETICAL DEVELOPMENT OF THE METHOD 

Background: Oxygen Deficit, Physiological Limits on MET, and EPOC 

At the beginning of exercise, there is a lag between work expended and oxygen consumption.2 

During this work/ventilation mismatch, an individual’s energy needs are met by anaerobic 

processes. The magnitude of the mismatch between expenditure and consumption is termed the 

oxygen deficit. During heavy exercise, further oxygen deficit (in addition to that associated with 

the start of exercise) may be accumulated. At some point, oxygen deficit reaches a maximum 

value, and performance and energy expenditure deteriorate. 

After exercise ceases, ventilation and oxygen consumption will remain elevated above baseline 

levels. This increased oxygen consumption was historically labeled the “oxygen debt” or 

“recovery oxygen consumption.” However, recently the term “excess post-exercise oxygen 

consumption” (EPOC) has been adopted for the phenomenon. 

The new method for adjusting the MET values is based on keeping a running total of the oxygen 

deficit as one proceeds chronologically through an activity diary. The oxygen deficit 

calculations were derived from numerous published studies. Oxygen deficit is measured as a 

percentage of the maximum oxygen deficit an individual can attain prior to deterioration of 

performance. Limitations on MET levels corresponding to post-exercise diary events were based 

on maintaining an oxygen deficit below this maximum value. In addition, adjustments to MET 

were simultaneously made for EPOC. The EPOC adjustments are based in part on the modeled 

oxygen deficit and in part on data from published studies on EPOC, oxygen deficit, and oxygen 

consumption. 

As instructed by the EPA WAM, the methods were constructed in terms of reserve MET rather 

than total MET. The reserve is the amount over the basal rate (MET=1). Furthermore, we 

defined M as the normalized reserve, so that M=0 at MET=1, and M=1 at maximum MET: 

METS 1

METS 1 M

max −

− = (1)

Using a normalized reserve assures that the method can be applied identically to a population of 

individuals having widely different METmax values. 

Nomenclature

MET Metabolic equivalent (unitless) 

METmax Maximum achievable metabolic equivalent for an individual (unitless) 

M Normalized MET reserve (unitless, M, bounded between 0 and 1) 

ΔM Change in M from one diary event to the next (M) 

Dmax Absolute maximum oxygen deficit that can be obtained (M-hr) 

F Fractional oxygen deficit (percent of individual maximum, unitless) 

te Duration of activity diary event (hours) 

tr Time required to recover from an F of 1 to an F of 0 at rest (recovery time, hours) 
B-3 

dFinc Rate of change of F due to deficit increase (F/hr, will have a positive value) 

dFrec Rate of change of F due to deficit recovery (F/hr, will have a negative value) 

dFtot Total rate of change of F, dFinc+ dFrec (F/hr) 

ΔFinc Increase in F due to anaerobic energy expenditure (F)

ΔFrec Decrease in F due to recovery of oxygen deficit (F)

ΔFtot Change in F due to simultaneous anaerobic work and oxygen recovery, 

ΔFinc+ΔFrec (F) 

ΔFfast Total change in F during the fast recovery phase (F) 

Sfast Magnitude of the rate of change in M during fast component (M/hr) 

EPOC fast Change in M due to fast-component EPOC (M) 

EPOCslow Change in M due to slow-component EPOC (M) 

PAI Physical activity index (median of daily average MET, dimensionless) 

Simulation of Oxygen Deficit 

This section presents the theoretical development of the equations describing the accumulation of 

oxygen deficit. We developed the method using a large number of studies on oxygen 

consumption, oxygen deficit, and EPOC. Individual studies will be referenced below. The first 

two sections below describe the equations themselves, while the last section describes the 

determination of appropriate values for the model parameters. 

Fast Processes. There exists a component of the accumulated oxygen deficit that is due to 

transition from one M level to another.2

 This component derives from the anaerobic work that is 

required by sudden muscular motion. There is also a corresponding fast component of oxygen 

recovery which occurs very quickly after a change from a high M level to a lower one. In the 

absence of any data to the contrary, it is assumed that these fast deficit accumulation and fast 

recovery processes occur at the same rate. These processes are illustrated in the Figure 1. The 

adjustment to F is equal to the area of the triangle associated with either a positive or negative 

change in M, normalized by the maximum obtainable accumulated oxygen deficit (Dmax). The 

normalized area can thus be calculated as:

fast max

fast S D

ΔM ΔM

ΔF = 0.5 (2) 

where ΔM = Mi-Mi-1 and Sfast is the slope of the change in M (in M/hr). Note that this change in F 

will be positive if ΔM is positive, and negative otherwise. 

Slow Processes. The slow component of the increase in oxygen deficit corresponds to the 

accumulation of deficit over a period of heavier exercise (rather than that associated with an 

increase in activity level). The starting point for the analyses is the table of data3-15 assembled by 

T. McCurdy for the 1998 and 1999 EPOC work. Data from a selection of these studies in which 

persons exercised to exhaustion are given in Table 1. The table includes the time it took for 

subjects to reach exhaustion, their accumulated oxygen deficit, their METmax, the MET value at 

which they exercised, and the corresponding normalized reserve MET (M). (Note that the MET 

and METmax quantities in this table were derived from VO2 and VO2max measurements.) A plot of 

M versus duration is shown in Figure 2. There is one data point having M > 1, for one subject 
B-4 

who exercised briefly at a level above his/her METmax. The data indicate that oxygen deficit 

accumulates at a much faster rate when M is high. For example, an M value near 0.5 requires 

about 5 times longer to reach exhaustion than an M value near 0.75 (on average), indicating that 

F is nonlinear in M. 

Let the rate of increase in F be given by dF . Based upon the relationship inc depicted in Fig. 2, we 

postulate a simple nonlinear relationship between dF and M as a power law: inc

b

inc dF = aM (3) 

However, before estimating a and b, one must account for slow recovery of oxygen debt, as it 

occurs simultaneously with debt accumulation. We assume a slow, but continual, process for 

recovering oxygen deficit that is independent of the MET level. For modeling purposes, timevarying processes are very difficult to handle, especially when using finite time-step models. In 

our exposure models, the time step may be as large as one hour. To avoid problems, we model 

the slow EPOC recovery as constant over time, until the oxygen deficit is erased. Assuming this 

takes tr hours, the slow recovery of oxygen deficit occurs at a rate 

r

rec t

1 dF = − (4) 

The total net rate of change in F from slow processes during an event i with duration te is given 

by 

dFslow = dFinc + dFrec (5) 

and the associated change in F is 

e

r

b

slow i t

t

1 ΔF aM ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = − (6) 

For an individual starting with an F of 0 and exercising to exhaustion (neglecting the transitory 

effects), the change in ΔF is 1.0. In this case, rearranging and taking the logarithm gives 

log( ) a b log(M) t

1

t

1 log

r

= + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ (7) 

This equation can be used to fit data to estimate the parameters a and b (this will be discussed in 

the next section). 

The starting normalized oxygen deficit for the next event (i +1), taking into account both the fast 

and slow changes in F, is then 
B-5 

Fi+1 = Fi + ΔFslow + ΔFFast (8) 

Appropriate values for tr , a, and b. These parameters were derived from summaries of 

published data that were supplied by EPA (i.e., the data in Table 1). It should be noted that these 

data were collected and analyzed some years ago and should be updated to include any recent 

additions to the literature. As additional data become available, the parameter values estimated 

here may be adjusted without changing the structure of the algorithm. 

Several of the studies in Table 1 reported tr values. However, due to variability in measurement 

and protocol differences, these recovery times varied from 0.5 hours to 24 hours. From a 

modeling viewpoint, it would be unacceptable to allow recovery to significantly carry over from 

one day to the next. To do so could lead to a perpetual delay in recovering an oxygen deficit, for 

example, by repeatedly encountering new exercise events before recovery is complete. For the 

results section, we chose tr from a uniform distribution having a minimum of 8 and a maximum 

of 16 hours. (In practice, the values selected for tr do not affect the result significantly.) The 

user could replace this distribution, if desired. 

Eq. 7 was fit to the data (Table 1) using different values of tr to obtain estimates of a and b. The 

results are shown in Table 2. The results were summarized to obtain the following expressions 

for a and b: 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = − 2

r r t

3.92

t

1.54 a , (9) 5.20

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = − 2

r r t

3.66

t

3.57 b . (10) 3.93

Values for Dmax. Appropriate distributions for maximum oxygen debt (MOD) in ml/kg were 

derived from data from a number of studies in adults,16-29 adolescents,30 and children.31-32 The 

studies covered multiple types of exercise protocols, some having more than one protocol per 

study. We chose to define normal distributions for MOD in all three age groups, based on 

average mean and standard deviation values from the studies: 

 

 adults: 54.95±14.46 (ml/kg) 

 adolescents: 63.95±21.12 (ml/kg) 

 children: 34.74±13.10 (ml/kg) 

Values were selected from normal distributions with these characteristics. The bounds of these 

distributions were selected as two standard deviations from the mean; these ranges were found to 

be reasonable when compared to reported ranges.29 The means for each exercise protocol from 

the studies for all three age groups are shown in the plots in Fig. 3, and the data for all the studies 

are given in Table 5. For use in Eq. 2, we transformed these values to Dmax, via a units 

conversion factor and the normalization needed for use with reserve MET: 
B-6 

D (M-hr) = max ( ) 1

max

2

METS 1

60 METStoO

MOD − − ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ (12) 

where METtoO2 is the conversion factor2

 for mlO2 to MET-min, 3.5 [(mlO2/min)/kg]/MET. 

Note that the variability in this factor is not addressed here. 

Values for Sfast. A number of studies on EPOC33-42 were used to derive Sfast. These were all 

studies in which oxygen consumption was measured relatively soon (within a few minutes) after 

the end of exercise and at a frequency high enough to capture the kinetics of the change in 

oxygen consumption. The data were found to be relatively uniform from the minimum (0.6 

MET/min) to the maximum (3.7 MET/min) slope values, and so values were selected from a 

uniform distribution having these bounds. Converting units and normalizing to M, one obtains: 

S (M/hr) = fast ( ) METS 1

60 Uniform (0.6, 3.7)

max − (13) 

The data for all studies are given in Table 6. 

Adjustments to M for Fatigue 

The equations provided in the previous section describe a method for keeping a running total of 

the fractional oxygen deficit (F) for each diary event for an individual. We used these event F 

values to limit M for each event to appropriate values. Basically, the maximum M value that can 

be maintained for an entire event is the value that would result in an Fi+1 (eq. 8) equal to 1 (i.e., 

the maximum value) at the end of the diary event. Ideally, one would wish to solve Eqs. 2, 6, 

and 8 explicitly for Mi for a value of Fi+1 =1. However, the equations are non-linear in Mi. The 

approach used here is to set M for each event equal to the raw MET value, and test if Fi+1>1. If it 

is, then the Mi value is reduced by a predetermined amount (currently 0.01) and Fi+1 is 

recalculated. The process continues until an appropriate value of Mi, called Mmax,i, is found. As 

the exposure model marches through the events of the activity diary, the M values associated 

with each event are adjusted if necessary: 

Mi=min(Mi, Mmax, i) (14) 

Adjustments to M for EPOC 

As noted above, it has been observed in many studies that EPOC is characterized by both slow 

and fast components. The fast component occurs within minutes of exercise, while the slow 

component may persist for many hours. Both fast and slow EPOC components were modeled. 

Fast Processes. The fast EPOC component, which takes place in the first few minutes after 

exercise, is also characterized by the slope Sfast. The energy recovered during those first few 

minutes corresponds to the recovery triangle in Fig. 1, and this increase in the rate of energy 
B-7 

expenditure for a post-exercise event is modeled as the area of the triangle divided by the event 

duration: 

 ( )

fast e

2

fast S t

M EPOC 0.5 Δ = (15) 

EPOCfast will thus have units of M (normalized reserve MET). The M level for the post-exercise 

events will be incremented by EPOCfast.

Slow Processes. We estimate the increase in M associated with the slow EPOC component as 

the amount required to maintain the slow recovery of F. Since a deficit Dmax is recovered in full 

in the recovery time tr, the time-averaged adjustment to MET for the slow recovery process must 

be 

EPOCslow=

r

max

t

D (16) 

Every diary event with the full rate of slow recovery will have its M value adjusted upward by 

EPOCslow. An appropriate fraction of EPOC slow is used if only partial recovery is needed to 

eliminate the deficit (i.e., return F to 0). The final adjusted M value for the diary event is thus 

Madj = M + EPOCfast + EPOCslow (17) 

and the new MET value for the event is 

METSadj = Madj(METSmax −1) +1 (18) 

II. DISCUSSION 

Note: As the main focus of this document was the presentation of the method, only a general 

summary of the modeling results are presented here. An in-depth analysis of PAI, dose, and 

ventilation modeling results for children within 36 age and gender cohorts were presented in the 

report Analysis of Data Relating to EPOC and Duration-Dependent Limits on MET ( Kristin 

Isaacs and Graham Glen, February 5, 2005). Though that report utilized an earlier version of 

MET-adjustment, it is likely that the results presented there would not vary greatly from those 

obtained using the method discussed here. The PAI results presented herein demonstrate that the 

new method decreases MET (and thus PAI) a bit more than the earlier method. However, it is 

expected that this decrease will be fairly uniform across cohorts. 

MET Limits for Fatigue 

For periods of constant exercise, Eq. 7 results in a function having a horizontal asymptote. This 

asymptote is the M level that the individual can sustain indefinitely, and above which oxygen 

deficit accumulates. At this M, the net change in F is zero because recovery exactly balances the 

increase in F. A plot of Mmax assuming constant exercise at Mmax and a tr of 12 hours is given in 
B-8 

Fig. 4 These results are very close to those predicted by the Bink43 equation (as modified by 

Erb44), which was used in the previous method to limit MET. This demonstrates that for 

continuous exercise, the limits on intensity predicted by the unified method decline appropriately 

with time. 

Existing methods have a tendency to overcorrect MET values for relatively low-activity events 

to fulfill limits on subsequent high-MET events. By imposing limits on MET via the current 

value of the oxygen deficit, the unified method avoids overcorrection and implements more 

localized adjustments in MET. For example, consider the case of the 3 year-old whose one, four, 

and nine-hour running MET averages are shown in Fig. 5. The flat dotted lines represent the 

MET limits predicted by Bink43 for constant exercise at these time intervals. In Fig. 5 note that 

the new method allows the MET curve to approach the Bink limit without exceeding it, whereas 

overcorrection in the earlier methods prevents MET from even approaching this limit. 

The actual adjustments made to MET time series varied greatly. Much of this variation was 

dependent on individual differences in METmax. Three examples for children of different age, 

gender, and METmax are given in Figure 6. 

EPOC 

The adjustments to single-event MET for EPOC when the algorithm was applied to CHAD were 

very small compared to the adjustments made for fatigue. In general, the increases in MET for 

EPOC were small, usually less than one MET. In a few cases the adjustments were bigger (on 

the order of 4-6 MET), due to the fact that the adjustments were applied to a very short event. 

An example of a MET time series with EPOC adjustments is shown in Fig. 7. 

As more conclusive data become available, the slow EPOC processes could be modeled in a 

similar manner to the fast component, (i.e., with a slope term). Currently, data on the duration 

and magnitude of the slow EPOC component are inconclusive and vary greatly from study to 

study. However, the change in M for slow EPOC is extremely small, and thus it would be 

expected that a different modeling method for this component would have a negligible effect on 

M (and thus ventilation and dose).

EFFECT ON PAI IN CHILDREN 

Mean values of PAI for age and gender cohorts are given in Tables 3 and 4. In general, the 

unified algorithm resulted in a decreased PAI. A frequency distribution for PAI is given in Fig. 

8. The algorithm shifted the distribution of PAI to the left, with the higher end of the distribution 

being most affected. That is, the unified algorithm mainly adjusted the highest values of PAI. 

III. SUMMARY AND CONCLUSIONS 

We have developed a new method for simultaneously correcting MET values for fatigue and 

excess post-exercise oxygen consumption. The method is based on the calculation of an 

accumulated oxygen deficit. The method’s equations were derived from data from a large 

number of studies on oxygen deficit and EPOC. Furthermore, the model variables can be easily 

updated to incorporate data from future studies as they become available. However, the method 
B-9 

as presented here returns qualitatively appropriate results for time-dependent averages of MET 

levels for children, though fine tuning of the results might be obtained by updating the model 

parameter estimates using new data. 

The new method is more computationally efficient and theoretically straightforward than the 

previous ones. It requires no maintenance of multiple running averages of MET values (as was 

required by the previous algorithm) or recursive nonlinear adjustment of oxygen deficit (as was 

required by the other methods). 
B-10 

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B-14 

Table 1. Data used for estimation of oxygen deficit. Table gives data for 22 subjects exercising 

to exhaustion. Oxygen deficit was assumed to be 0 at the start of exercise. 

Observation Oxygen Deficit

Time to 

Reach Exhaustion METSMax METS M

(ml/kg) (Hours)

1 153.52 1.00 13.3 9.31 0.67561

2 109.95 1.17 13.8 10.35 0.730469

3 106.43 1.33 13.46 9.57 0.687801

4 93.92 1.27 16.11 11.43 0.690271

5 68.23 0.75 13.3 9.31 0.67561

6 57.86 1.33 19.18 13.426 0.683498

7 57.14 1.33 17.8 12.46 0.682143

8 55.13 0.10 15.51 16.7508 1.085513

9 44.42 0.67 15.86 10.9434 0.669139

10 39.76 0.83 17.8 12.46 0.682143

11 37.08 3.00 19.86 10.30734 0.493496

12 32.88 3.00 17.8 8.9 0.470238

13 31.09 0.58 11.3 9.2773 0.803621

14 29.16 0.40 15.4 12.32 0.786111

15 29 0.50 13.3 9.31 0.67561

16 27.88 0.50 20.95 14.665 0.684962

17 24.87 0.33 17.94 13.1859 0.719357

18 24.27 0.33 15.8 11.85 0.733108

19 21.08 0.75 11.3 7.458 0.62699

20 19.57 0.33 13.8 11.04 0.784375

21 18.32 0.17 18.87 15.30357 0.800424

22 13.72 0.83 7.79 5.53869 0.668437
B-15 

Table 2. Values of a and b for different recovery times. 

 d (hours) r a b R2

8 5.08538 3.54442 0.79008 

9 5.09260 3.58195 0.79121 

10 5.09932 3.61289 0.79216 

11 5.10550 3.63885 0.73296 

12 5.11114 3.66094 0.79364 

13 5.11627 3.67997 0.79423 

14 5.12095 3.69653 0.79475 

15 5.12522 3.71109 0.79520 

16 5.12912 3.72398 0.79561 

 
B-16 

Table 3. Mean PAI Values (Males). Unified algorithm values are for a 50000-person simulation 

(~1400 persons per cohort). 

Age CHAD (UNCORRECTED) UNIFIED 

ALGORITHM 

LITERATURE 

VALUE* 

0 1.84 1.59 - 

0.33 - - 1.15 

0.50 - - 1.23 

0.75 - - 1.34 

1 1.83 1.58 1.32 

2 1.89 1.59 1.38 

3 1.88 1.62 - 

4 1.86 1.65 - 

5 1.91 1.71 1.36 

6 1.91 1.75 1.39 

7 1.93 1.77 1.33 

8 1.91 1.79 1.39 

9 1.90 1.79 1.41 

10 1.90 1.81 1.59 

11 1.86 1.74 1.65 

12 1.85 1.78 1.74 

13 1.84 1.78 1.46 

14 1.86 1.81 1.73 

15 1.85 1.81 1.89 

16 1.94 1.90 - 

17 1.93 1.89 - 

* Provided by EPA 
B-17 

Table 4. Mean PAI Values (Females). Values are for a 50000-person simulation (~1400 persons 

per cohort). 

Age CHAD (UNCORRECTED) UNIFIED 

ALGORITHM 

LITERATURE 

VALUE* 

0 1.85 1.57 - 

0.33 - - 1.2 

0.50 - - 1.31 

0.75 - - 1.29 

1 1.86 1.56 1.3 

2 1.88 1.57 1.36 

3 1.86 1.59 - 

4 1.87 1.66 - 

5 1.85 1.69 1.33 

6 1.86 1.73 1.35 

7 1.84 1.75 1.41 

8 1.85 1.76 1.47 

9 1.85 1.77 1.6 

10 1.83 1.76 1.55 

11 1.83 1.78 1.59 

12 1.80 1.77 - 

13 1.79 1.76 1.60 

14 1.79 1.76 1.66 

15 1.77 1.75 1.74 

16 1.94 1.90 - 

17 1.83 1.81 - 

*Provided by EPA 
B-18 

Fast component of 

F: Recovery 

(ΔM negative)

ΔM

M1

M2

Fast component 

of F: Accumulation

(ΔM positive)

Time

Exercise Recovery

t= ΔM/Sfast

Sfast

Figure 1. Fast components of oxygen deficit and recovery.

-Sfast
B-19 

0

0.5

1

1.5

2

2.5

3

3.5

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

Normalized Reserve METS (M)

Time to 

Exhaustion

(Hours)

Figure 2. Exercise level in normalized reserve METS (M) versus time 

to reach exhaustion. Note nonlinear relationship.
B-20 
B-21 

Figure 4. Maximum M (METS reserve) value that can be sustained during constant–intensity 

exercise of duration T.

T (hours)

Mmax
B-22 
B-23 

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0

1

2

3

4

5

6

7

8

9

0

1

2

3

4

5

6

7

8

9

10

Final METS

Original METS

O2 Deficit, F

Final METS

Original METS

O2 Deficit, F

Final METS

Original METS

O2 Deficit, F

Male, 16 years

METSmax=14.4

Male, 3 years

METSmax=5.7

Female, 5 years

METSmax=8.4

12am 6am 12pm 6pm 12am

12am 6am 12pm 6pm 12am

12am 6am 12pm 6pm 12am

METS

METS

METS

Figure 6. Three examples of original and corrected METS event time series. In the 

example in the top panel, the METS values pulled from the CHAD diary required no 

adjustment. The METS series for the individuals represented in the bottom two 

panels were adjusted for fatigue. 
B-24 

Figure 7. Event series for a 13-year-old female (METSmax=14), showing small upwards

adjustments in METS for EPOC.

0

2

4

6

8

10

12

14

Final METS

Original METS

O2 Deficit, F

6am 8am 10am 12pm 2pm 4pm 6pm

EPOC

METS
B-25 

0

200

400

600

800

1000

1200

0123456

PAI

#

Individuals

Figure 8. PAI distributions calculated using the uncorrected CHAD METS 

values compared with the values resulting from the unified algorithm.

Unified algorithm

Uncorrected CHAD
B-26 

Table 5. Data for Calculation of Maximum Accumulated Oxygen Deficit, Dmax

Study VO2Max SD SE Dmax SD SE age gender

(ml/kg-min) (ml/kg)

Berthoin et al. 2003 43.3 5.3 34.3 11.8 c f

Berthoin et al. 2003 48.7 8.1 33.6 13.6 c m

Bickham et al. 2002 64.4 6.1 43.3 a b

Billat et al. 1996 63.2 4.2 40.1 14.9 a f

Billat et al. 1996 77 6.4 48.9 21.3 a m

Buck and McNaughton 1999 57.5 2.4 53.4 a m

Carlson and Naughton 1993 43.3 1 41 14.4 2.4 c f

Carlson and Naughton 1993 43.3 1 35 13.2 2.2 c f

Carlson and Naughton 1993 43.3 1 32 13.8 2.3 c f

Carlson and Naughton 1993 53.9 2.3 33 25.8 4.3 c m

Carlson and Naughton 1993 53.9 2.3 35 22.2 3.7 c m

Carlson and Naughton 1993 53.9 2.3 34 19.2 3.2 c m

Doherty et al. 2000 58 4.6 69 a m

Doherty et al. 2000 58 4.6 70.4 a m

Doherty et al. 2000 58 4.6 71.4 a m

Faina et al. 1997 72 4 45.9 19 a m

Gastin et al. 1995 57 3 42 a b

Gastin et al. 1995 57 3 43.9 a b

Gastin et al. 1995 57 3 44.1 a b

Gastin et al. 1995 55 3 51.2 a b

Gastin et al. 1995 55 3 52.1 a b

Gastin and Lawson 1994 53.1 2.1 47.6 a m

Gastin and Lawson 1994 53.1 2.1 49 a m

Gastin and Lawson 1994 53.1 2.1 49.6 a m

Hill et al.1998 48.2 9.1 42 22 a b

Maxwell and Nimmo 1996 112.2 5.2 74.6 a m

Naughton et al. 1997 49.6 3.5 58.6 22.2 3.7 ad f

Naughton et al. 1997 49.6 3.5 58.1 28.2 4.7 ad f

Naughton et al. 1997 61.7 2.2 71.5 35.4 5.9 ad m

Naughton et al. 1997 61.7 2.2 67.6 38.4 6.4 ad m

Olesen 1992 53.5 40 11 a b

Olesen 1992 62.5 57 8 a b

Olesen 1992 53.5 69 8 a b

Olesen 1992 53.5 72 20 a b

Roberts et al. 2003 62.3 9 49.1 13 a b

Roberts et al. 2003 62.3 9 50.5 14.1 a b

Weber and Schneider 2000 38.5 1.8 38.2 15.6 2.6 a f

Weber and Schneider 2000 43.4 1.5 46.3 14.4 2.4 a m

Woolford et al. 1999 74.2 2.3 38.7 5.4 ad b

Woolford et al. 1999 74.4 3.5 54.4 9.7 ad b

Woolford et al. 1999 76.2 2.9 56.8 9.1 ad b

Abbreviations

SD = Standard deviation 

SE = Standard error 

c = Children 

ad = Adolescents 

a = Adults 

m = Males 

f = Females 

b = Both 
B-27 

Table 6. Data for Calculation of the Slope of the Fast EPOC Component 

Study Peak VO2 Baseline VO2 post-EPOCfast Duration of EPOCfast Slope Slope

(ml/min) (ml/min) ml/min min ml/min/min METS/min

Dawson et al. 1996 1900 250 450 2.5 580.00 2.320

Almuzaini et al. 1998 2500 250 425 2.75 754.55 3.018

Knuttgen 1970 2500 250 400 2.5 840.00 3.360

Short and Sedlock 1997 1800 250 575 2 612.50 2.450

Short and Sedlock 1997 1500 250 400 2 550.00 2.200

Harms et al. 1995 2976 300 399 7 368.14 1.227

Harms et al. 1995 2688 300 420 7 324.00 1.080

Trost et al. 1997 1900 250 550 4 337.50 1.350

Pivarnik and Wilkerson 1988 3300 250 900 5 480.00 1.920

Pivarnik and Wilkerson 1988 2600 250 650 5 390.00 1.560

Pivarnik and Wilkerson 1988 1650 250 520 5 226.00 0.904

Frey et al. 1993 2610 350 725 5 377.00 1.077

Frey et al. 1993 2003 350 580 5 284.60 0.813

Frey et al. 1993 1688 300 609 5 215.80 0.719

Frey et al. 1993 1373 300 493 5 176.00 0.587

Kaminsky et al. 1990 2100 220 475 2 812.50 3.693

Maresh et al. 1992 2262 312 624 5 327.60 1.050

Maresh et al. 1992 2340 312 702 5 327.60 1.050

MEAN 4.263888889 443.54 1.688

Std dev 1.605304219 204.55 0.949
B-28 

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APPENDIX C. A NEW METHOD OF LONGITUDINAL DIARY ASSEMBLY 
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C-1

A New Method of Longitudinal Diary Assembly

Graham Glen and Luther Smith

June, 2005 (revised October, 2005)

Alion Science and Technology, Inc.

Durham, NC 27713

prepared for WA 131

EPA Contract 68-D-00-206

Tom McCurdy

Work Assignment Contract Officer’s Representative

National Exposure Research Laboratory

U. S. Environmental Protection Agency
C-2

Introduction

Exposure models like APEX and SHEDS are microenvironmental personal simulation models. 

The determination of exposure requires time series for both (a) microenvironmental pollutant

concentrations and (b) personal time-activity patterns. To estimate longitudinal exposure

patterns, it is necessary to produce a longitudinal time-activity diary for each simulated person

which covers the entire simulation period. The human time-activity databases used by exposure

models contain no longitudinal diaries of sufficient length. (Models are typically run for a year

or more.) Various methods of assembling single-day diaries into a longitudinal pattern are

currently implemented in EPA exposure models. This report describes a new method that

correctly meets user-defined targets for both variance and autocorrelation.

The output from an exposure model like APEX or SHEDS consists of a set of exposure time

series, one for each simulated individual. Of course, the mean exposure is important, both within

an individual (the mean over time) and across individuals (the population mean). The existing

diary assembly methods are good at determining these means. However, there is a growing

recognition that variation in exposure is also important. One such aspect is within-person

variation, which is useful for determining the frequency and intensity of high-exposure events,

even for persons whose mean exposure is low. Another aspect is the between-person variance,

especially in some long-term measure of exposure. For example, to assess the carcinogenic risk

from pollutants that slowly accumulate in the body, the average daily dose (ADD) over a period

of several years may be a useful measure of exposure. Then the distribution of risk across the

population depends on the distribution of ADD. A large part of the variance in this distribution

may be due to persistent differences in activities among individuals. To characterize this

distribution correctly, it is necessary to have longitudinal activity diaries with persistent

differences in activities between individuals, even for persons in the same age-gender cohort.

 

Another aspect of longitudinal diary assembly is similarity in diaries from day to day, reflecting

the degree of repetitiveness in human behavior. Statistically, this can be measured by

autocorrelation. The proposed method uses a one day lag. Longer lag times could be

considered, but the strength of the correlation decreases rapidly with elapsed time (Xue et al.,

2004; MacIntosh, 2001). 

Cohorts and Diary Pools

Nearly all diary assembly methods depend on some method of cohort specification. Diaries are

drawn from cohorts, which are population subgroups whose members have certain common

characteristics. It is reasonable to expect that at least on average, people who are closely

matched in age and gender (and possibly other properties such as employment status) would

have activity patterns that are more similar than people of widely differing demographic status. 

Hence, if one were attempting to construct a longitudinal activity diary for a 30 year old working

female, it is reasonable to use a set of single-day diaries belonging to (say) the cohort of working

females ages 25-44. Note that the cohort cannot be defined too narrowly, or there might not be

enough single-day diaries in the database to allow the proper variation in activities. This is the

main reason why cohorts often consist of a range of ages, rather than a single year of age. 
C-3

The creation of cohorts involves a trade-off between two factors. A narrower or smaller age

range for each cohort increases the similarity between the people supplying the diaries and the

target individual for whom the diary is assembled (Graham and McCurdy, 2004). However, for

statistical stability it is necessary that the pool of available diaries from which the selections are

made does not get too small. 

Within cohorts, additional criteria for diary selection may be imposed. For example, it is often

the case that diaries are matched by day of week and season, and sometimes by temperature

and/or rainfall as well. The set of diaries available for possible selection on a given simulation

day is called a diary pool or subgroup. In short, the term ‘cohort’ refers to restrictions on the

universe of available diaries that apply to a given person throughout the entire simulation,

whereas ‘pool’ refers to restrictions that apply on a particular simulation day, but may change on

subsequent days. Each simulated person belongs to only one cohort, but may move through

several diary pools as the simulation progresses. It is permissible for the diaries in the diary pool

to have unequal selection probabilities. For example, perhaps a diary that is an exact match in

age to the simulated individual is given a higher a priori selection probability than a diary from a

person of slightly different age. 

This appendix does not address the questions of cohort or pool definition. Once these definitions

are given, the next step is to specify the method of selecting one-day diaries from each pool for

assembly into a single longitudinal diary. This selection process should result in a ‘realistic’

distribution of the dominant exposure-related variable on the diaries. One of the strengths of the

proposed diary assembly method is that it does not directly depend on the cohort or pool

definitions; the same method (and computer code) is applicable in all cases. 

Indexing the diary database by scores for a key variable

For this discussion, it is assumed that there is some measurable property of the diaries that has a

dominant influence on exposure. To obtain credible exposure estimates, it is necessary to

assemble longitudinal diaries that have a realistic distribution for this key property. A specific

example of this key property could be the total time spent outdoors, which is currently used by

the SHEDS-Wood model for assembling longitudinal activity diaries. For other pollutants the

key variable might be travel time or time performing a particular activity, for example. The key

or index variable could also be a composite formed from several different variables, for example,

a sum or perhaps a weighted average of other variables. The necessary condition for

implementing the method is that every single-day diary be assigned a numeric value for this key

variable. This allows the set of available diaries in every diary pool to be ranked in terms of this

key variable, from lowest to highest. While the diary assembly method does not depend on how

this key variable is defined, in examples given below it is assumed (for specificity) that the key

variable is outdoor time.

An important aspect of this approach is that all references to the key variable are in terms of

scores. This means that within every pool of diaries, the individual diaries are ranked from

lowest to highest in terms of the key variable and assigned a score which indicates their place in
C-4

the list. This score is bounded between zero and one. If there are K diaries in a pool, and each

diary has equal statistical weight, then the score for the diary at rank R is

score = ( R - 1/2 ) / K (1)

Similarly, when individuals are being ranked within a group of P persons, then the score for the

person at rank R in the group is 

score = ( R-1/2 ) / P. (2)

The scores are useful for several reasons. First, the distributional properties are known, whereas

the distributional properties of the key variable itself would depend on its definition and,

furthermore, might well vary from cohort to cohort and from pool to pool. Knowing the

distributional properties allows the specification of methods that target certain statistics. Second,

the score reflects the behavior of an individual relative to their peer group (for example, a score

of 0.75 means that the person ranks above 75% of the people in the same cohort and pool, in

terms of the key variable). Third, scores can be moved across diary pools, whereas absolute

values for the key variable might not. For example, there might be a diary with six hours of

outdoor time in the Sunday pool, but no such diary in the Monday pool. But a score of 0.75 has

meaning on all days and can be mapped to a specific diary. The ability to move scores across

day types is important in the autocorrelation matching, as described below. Fourth, the use of

scores helps in ensuring that all the available diaries are collectively sampled with the correct

frequency. 

Note that the use of ranks or scores does not preclude the ability to return to the original key

variable. In terms of diary assembly, it is necessary to specify which diary should be used on a

given simulation day. For this purpose, requesting the available diary nearest to score 0.38 is no

different than requesting the available diary nearest to (say) 73 minutes of outdoor time. Once

the diary is chosen, the exact value of the key variable on that diary can be recovered. 

The statistics D and A

For this assessment, two statistics are used. The first is called ‘D’, which measures long-term

differences between persons in the same cohort. The second is called ‘A’; it is the mean across

persons of the daily autocorrelation coefficient of the scores. Detailed mathematical properties

of D and A are given in the appendix. Both D and A are collective properties of a group of

persons. To calculate them, a time series for the key variable is needed for each person. There

may be some gaps or missing values in the time series, but to calculate D it is necessary that

there is substantial temporal overlap between persons, as each person is ranked relative to the

others on each day.

The following discussion of how D and A are calculated assumes that a longitudinal diary is

available for each individual. The discussion of how one constructs longitudinal diaries that

collectively have desired values of D and A for model simulation runs comes later. 

D is calculated as follows. For each day, rank each person relative to their cohort and use

equation (2) to generate a score. Here P may possibly vary from day to day; it is the number of
C-5

persons with non-missing values on each day. The underlying assumption is that the sample on

any given day is representative, so that a score of 0.38 would mean that the person ranks above

about 38% of all the other persons in the cohort, even if only part of the cohort was sampled on

that particular day. Days with a very small diary pool should therefore be excluded from the

analysis.

This yields a time series of daily scores for each person. Find the mean and variance of the

scores for each person over their time series. The overall within-person variance Fw

2

 in the

group is the mean of these individual time variances. The between-person variance Fb

2

 is the

variance across persons in the mean scores for each time series. The statistic D is then given by

D = Fb

2

 / (Fb

2

 + Fw

2

 ). (3)

Since both variances must be non-negative, it is clear that D is a proper fraction, bounded

between zero and one. D=0 means that Fb

2

 is zero, or that each person has the same mean score. 

A small D means that Fb

2

 is substantially smaller than Fw

2

. A D near one means that Fb

2

 is much

larger than Fw

2

, or that each person shows little variation over time relative to the variability

between persons. 

The criteria for defining cohorts and diary pools are determined by the user, and the proposed

method places no restrictions on these criteria. However, the calculation of D can provide a

useful indicator of whether cohorts have been reasonably defined. A large value for D indicates

large variability in long-term behavior between the individuals, and this is contradictory to the

concept of cohorts.

The autocorrelation A is even simpler to calculate than D, because each time series can be

examined independently. The first step is to determine the score for each day, relative to the

entire time series. If there are J days in the time series, and a given day is at rank R in terms of

the rank for the key variable among the J days, then the score for that day is ( R-1/2 ) / J. The

overall mean and variance in these scores for the time series is then calculated. However, due to

the properties of the discrete uniform distribution of the scores (neglecting tied scores), the mean

must be 1/2 and the variance is (1/12) (1-1/J2 ), which is very close to 1/12 for J large. The lagone covariance is also determined; it is (1/J) times the sum of the paired products 

(score(j)-1/2)*(score(j+1)-1/2), where score(j) is the score on day ‘j’ (see, for example, Box et

al., 1994). The lag-one autocorrelation for the time series is given by the ratio of the covariance

to the variance. This calculation is repeated for each time series, and the statistic A is the mean

of these individual autocorrelations. The statistic A has a range from -1 to +1, with positive

values indicating that each day has a tendency to resemble the day before. Random selection of

diaries from day to day produces A values near zero. Negative A values imply dissimilarity

between consecutive days. 

A study of children conducted in Southern California (see Xue et al. 2004) provides about 60

days of data on each of 163 children. The time series are not continuous, as the monitoring

consisted of twelve six-day periods, one per month over a year. Furthermore, only about 40

children were measured simultaneously, as the other children were sampled in different weeks. 

However, a sample size of 40 is sufficient to calculate reliable rankings across persons. The
C-6

number of consecutive day pairs was substantially less than the number of days, due to the gaps

in the time series. However, D and A statistics were calculated for three variables directly

recorded on the activity diaries (outdoor time, travel time, and indoor time), and also for a fourth

variable, the physical activity index or PAI (McCurdy et al., 2000). The analyses were

performed for all children together and for two gender cohorts. The separation into two cohorts

reduces the number of children measured simultaneously to fewer than 20. Further division into

more cohorts is therefore not practical, as the reliability of the scores would decrease. The results

for these analyses are given in Table 1.
C-7

Table 1: D and A statistics derived from the Southern California study data

Variable Group D A

outdoor time all 0.19 0.22

outdoor time boys 0.21 0.21

outdoor time girls 0.15 0.24

travel time all 0.18 0.07

travel time boys 0.18 0.05

travel time girls 0.18 0.08

indoor time all 0.17 0.22

indoor time boys 0.21 0.20

indoor time girls 0.17 0.24

physical activity all 0.16 0.23

physical activity boys 0.16 0.20

physical activity girls 0.16 0.25

Here ‘physical activity’ is measured by PAI, which is the ratio of total energy expenditure per

day to the basal metabolic energy expenditure per day, estimated from the diary times. For all

variables and each group, the standard deviation between persons for autocorrelation was about

0.20, and the standard error in the mean A was about 0.02. Table 1 indicates that gender

differences for both D and A are small, if present at all. 

It should be noted that the variables in Table 1 are not really independent. The sum of the three

time variables equals 24 hours in all cases. Furthermore, PAI is derived from the same three

times, so part of the similarity across variables is due to these relationships.

Generating longitudinal diaries

Exposure models like APEX and SHEDS construct a number of ‘simulated individuals’, whose

demographic characteristics are intended to be representative of the target population. A

longitudinal activity diary is constructed for each such person; it is to be hoped that the

collective properties of these diaries are also representative of the target population, or at least

the distribution of the key variable affecting exposure. As mentioned earlier, the new diary

assembly method does not impose any constraints on the methods of constructing cohorts and

diary pools, so it is up to the modeler to ensure that these are defined appropriately. The new

method just ensures that the selections from these pools match the requested targets for D

(variance ratio) and A (autocorrelation). The target values for D and A are supplied by the

modeler.

First, construct a beta distribution (with parameters as specified in the Supplement) for the

distribution of personal mean scores. For each simulated person, first select a mean target score

T at random from this beta distribution. Then, for each individual, construct another beta

distribution with mean equal to T. From this second beta distribution, pick a set of independent

random values containing approximately 3% more numbers than there are days in the simulation
C-8

period. Call this the set of X-scores and let K be the number of scores selected. At this point,

one has P sets of X-scores, each containing K values. 

The second part of the process is to generate the requested autocorrelation by reordering the

collection of selected values. First, choose a target autocorrelation for each individual. This is

selected from a beta distribution with a mean of A. For each individual, the set of X-scores are

ranked from lowest to highest. For the first simulation day, choose any X-score at random. For

each subsequent day, construct a new beta distribution (the parameters of the beta depend on A

and the selected value for the prior day, as detailed in the Supplement), and pick one value Y

from it. Find the nearest X-score (in rank) to K*Y that has not already been assigned to a prior

day in the time series. Continue this process until all simulation days are assigned values. The

reason for the extra values is that without them, the last few days of the simulation would have

very few choices left, and this lack of freedom would inhibit meeting the requested

autocorrelation.

The result of these steps is a vector of X-scores, one value per simulation day, for each person. 

It remains to now associate a diary with each X-score. Recall that the user has specified the

appropriate diary pool for each simulation day. The diaries in the pool are assigned a

cumulative probability distribution as follows. First, they are sorted by the key variable. Then a

selection probability is assigned to each diary as determined by the diary pool structure (for

many models, equal probabilities are used). 

The following example illustrates how a diary is assigned to an X-score. Suppose the pool for a

particular day had only four diaries, with probabilities in sorted order of 12%, 33%, 41%, and

14% of being used. The cumulative probability vector is then (0.12, 0.45,0.86,1.00). The Xscore assigned to this day is then used to determine which diary is selected. If the X-score is

lower than 0.12 then the diary ranked lowest on the key variable is chosen. If X is between 0.12

and 0.45 the second lowest diary is picked. For X between 0.45 and 0.86 the next highest diary

is used. Finally, if X is greater than 0.86 then the diary ranked highest on the key variable is

selected. This process is repeated for each day of the simulation period.

Results

The following tables present some results obtained using the new method. Tables 2 and 3

present comparisons of D and A statistics, respectively, calculated both from ranks and from key

variable values, for both the Southern California data and simulations using the new method. 

Table 4 displays the performance of the new method over the full range of both D and A. Table

5 shows the performance of the proposed method for different simulation lengths, for a variety of

D and A values.
C-9

Table 2. Computation of the D statistic calculated from ranks and key variable values, both

directly from the southern California study and from simulations using the proposed method.

Simulations constructed 20,000 longitudinal diaries for periods of forty-eight days.

Key

variable

Group Ranks Values

Study Simulation Study Simulation

outdoor time all .19 .19 .12 .14

outdoor time girls .15 .15 .11 .11

outdoor time boys .21 .21 .17 .18

travel time all .18 .18 .10 .13

travel time girls .18 .18 .10 .13

travel time boys .18 .18 .12 .14

indoor time all .17 .17 .12 .14

indoor time girls .17 .17 .11 .13

indoor time boys .21 .21 .16 .17

PAI all .16 .16 .12 .13

PAI girls .16 .16 .13 .12

PAI boys .16 .16 .13 .14
C-10

Table 3. Computation of the A statistic calculated from ranks and key variable values, both

directly from the southern California study and from simulations using the proposed method.

Simulations constructed 20,000 longitudinal diaries for periods of forty-eight days.

Key

variable

Group Ranks Values

Study Simulation Study Simulation

outdoor time all .22 .21 .24 .19

outdoor time girls .24 .23 .26 .20

outdoor time boys .21 .20 .21 .19

travel time all .07 .07 .06 .06

travel time girls .08 .08 .07 .06

travel time boys .05 .06 .04 .05

indoor time all .22 .21 .23 .19

indoor time girls .24 .23 .26 .20

indoor time boys .20 .19 .19 .18

PAI all .23 .22 .26 .19

PAI girls .25 .24 .29 .21

PAI boys .20 .20 .23 .17
C-11

Table 4. Performance of proposed method in hitting targeted values at selected points across the

ranges of the D and A statistics.

Requested Obtained

DADA

0 0 .00 .00

0 .50 .01 .50

0 .99 .03 .99

0 -.50 .00 -.49

0 -.99 .00 -.99

.50 0 .51 .01

.50 .50 .51 .50

.50 .99 .53 .99

.50 -.50 .50 -.49

.50 -.99 .51 -.99

.99 0 .99 .01

.99 .50 .99 .50

.99 .99 .99 .99

.99 -.50 .99 -.49

.99 -.99 .99 -.99
C-12

Table 5. Performance of proposed method in hitting targeted values of the D and A statistics

over different lengths of the simulation period. The values of D=.19 and A=.22 are the values for

outdoor time obtained from the southern California study.

Simulation

period length

Requested Obtained

DADA

30 days .19 .22 .20 .24

90 days .19 .22 .20 .24

1 year .19 .22 .20 .22

30 days .10 .40 .11 .40

90 days .10 .40 .10 .41

1 year .10 .40 .10 .40

30 days .40 .10 .41 .13

90 days .40 .10 .41 .12

1 year .40 .10 .41 .10

30 days .81 -.22 .81 -.17

90 days .81 -.22 .81 -.20

1 year .81 -.22 .82 -.21
C-13

Discussion

1) Use of ranks rather than the original key variable

2) Use of beta distributions rather than other forms

3) Ensuring no sampling bias within diary pools 

4) Performance over full range of D and A values

5) Performance of simulations of various lengths

6) Varying targets for D and/or A within a simulation

7) Movement of X-scores across day-types

8) The frequency distribution for relatively rare diary events

9) Ease of use 

1) Use of ranks rather than the original key variable

The new method makes use of rankings of the key variable in computing D and A statistics and

in the generation of X-scores, rather than using the original values of the key variable. This

provides both a modeling advantage and a mathematical advantage. The modeling advantage is

that it permits the maintenance of persistent differences while allowing a natural transition across

diary pools. A person with a mean or target X-score of T has a tendency for a higher value for

the key variable than a fraction T of his/her peer group. In the absence of information to the

contrary, it is reasonable to suppose that this tendency would persist. If the key variable is

outdoor time, on cold and rainy days the entire group may spend less time outdoors, but this does

not suggest that the relative position of individuals within the group would change. Once the

diaries are assembled, most persons will show drops in outdoor time on such days due to the

change in the diary pool, even though the X-scores themselves do not drop on such days. This

combination of maintaining persistent differences between individuals while allowing the diary

pools to define the distribution of the key variable would be very difficult to attain using the

original (non-ranked) variable.

The mathematical argument for using ranks is that the method becomes much more general,

since the distribution of ranks does not depend on the choice of the key variable, or on the

definition of cohorts, diary pools, or day-types. By contrast, the development of a parametric

method that tried to match statistics on the original values of the key variable would have to

depend on characterizing the distribution of that variable for the specific application of the

model. For some variables like outdoor time, the distribution has a relatively low mean and

positive skewness (a long tail to the right), but for indoor time the mean is high and the

distribution is negatively skewed. Furthermore, the distribution would depend on the specific

definition of the cohort, and would change as well with day-type and season. It would also be

likely to change when going from one geographic region to another. Every time the distribution

changes, the mathematical algorithms would have to change to reproduce the given distribution

while simultaneously meeting targets for both variability (here represented by D) and episodic

behavioral tendencies (here represented by A). The complexity of such approaches would add

both a computational burden and a quality assurance burden to the exposure model.

The performance of the proposed method was numerically evaluated against measured key

variable values using data from the southern California study (see Tables 2 and 3). Note that the
C-14

protocol for this study did not match the assumptions used in developing this method; in

particular, different children reported diaries on different days, and each child had breaks in their

time series. The new method was applied to three different key variables (outdoor time, travel

time, and indoor time), each with two cohort groupings (all children together, and separated by

gender). Synthetic longitudinal diaries were constructed from the single-day diaries reported

during this study. Both D and A statistics were calculated for the study and for the synthetic

diaries, using both the ranks and the key variable values. 

The D statistics on rankings were essentially the same for the original diaries and the synthetic

diaries. The D statistics on ranks were consistently higher than those on key variable values

(average D on ranks ~ 0.18, average D on key variable ~ 0.12). This is consistent with the

observation in the physical activity literature that people have more fixed tendencies in terms of

rankings than in the original variable (Anderssen et al., 1996; Kelder et al.,1994; Schwab et al.,

1992). However, this may not apply universally to all variables (DeBourdeauhuij et al.,2002). 

More within-person consistency translates to less within-person variance for the rankings than

for the original variable. By the form of the definition of D, this implies higher values for D for

the rankings. This effect is evident in Table 2 for the four variables considered there. For D

calculated on key variable values, the synthetic diaries (average D ~ 0.14) tended to exceed the

study (average D ~ 0.12) by only a small amount. 

Autocorrelations in the key variable values proved to be close to the autocorrelations in ranks,

for both the study and for the simulated diaries. The simulated diaries were consistently close in

A to the study when measured using ranks. Using the key variable values to calculate A, the

synthetic diaries tended to be lower than the study (differences ranging from 0.01 to 0.07),

except when the key variable was time spent in travel.

2) Use of beta distributions

All of the random number generation in the new method involves drawing numbers from beta

distributions. This is convenient though not strictly necessary. All of the random number

distributions are bounded both above and below, which is a natural property of the beta

distribution. For instance, it would be quite feasible to select personal targets for autocorrelation

that were normally distributed about the overall population mean A, but since autocorrelation is

bounded between -1 and +1, it would then be necessary to truncate the normal on both ends. 

Most programming languages have built-in beta distribution functions, and for the ones that do

not (like Fortran), there are a number of well-tested algorithms developed for this purpose. 

Alternate distributions for generating the X-scores have been tested, for example a two-level

uniform (one probability inside a given sub-interval and a different probability elsewhere) has

been successfully used for this purpose. 

Given fixed end points, the beta distribution has two shape parameters which allow a great

variety of forms. Both shape parameters must be positive. If both parameters exceed one, then

the distribution has the ‘usual’ form of a central peak, monotonically decreasing on either side

until reaching the bounds. The location and width of this peak can be targeted separately, which

is convenient for targeting both a mean and a variance. If the parameters fall on different sides
C-15

of unity, then the distribution is monotonic over its entire range (either increasing or decreasing),

often called a J-shaped beta. If both parameters are less than one, a U-shaped distribution

results, with peak probability at each end. Such U-shaped distributions are never used for Xscores or diary reordering, but may be used to assign individual targets T. A beta distribution

with both shape parameters equal to one is a uniform distribution. In fact, if D=0 is requested,

then all the X-scores are chosen from such uniform beta distributions, and all persons have a

common target mean of T=0.5. If D is set to one, then the targets T have a uniform distribution,

but the X-scores all become equal to T since the beta for them narrows to zero variance. In

practice this would lead to numerical difficulties, so in implementation the code would usually

contain a restriction that D<0.99 (or some similar bound). If a simulated person is given a target

autocorrelation of zero, then the beta distributions used to order the X-scores all reduce to

uniform distributions.

3) Ensuring no sampling bias within dairy pools

If a given pool of one-day diaries is believed to be representative for a given cohort on a given

day, then to avoid any bias it is necessary that over a large population of simulated individuals,

all the diaries in the pool be used about equally often. That is, the mean and variance of any

variable on that day for the group of simulated individuals should match the mean and variance

seen in the diary pool itself, since the pool is supposed to be representative of the real

population. This is most easily achieved by the simple expedient of uniformly sampling from

the diary pool.

In the new method, the selection probabilities from the diary pool are not uniform for one

individual; they tend to be higher for diaries near to the target score T than for ones further

away. To avoid overall biases, it is necessary that the mixture of all the personal betas over a

large group of persons be very close to uniform. So that, for example, a person who

preferentially samples diaries at the low end of the rankings should be balanced by a person who

preferentially samples the upper end. An important constraint on the beta distributions used for

the T scores and the X-scores, is that the overall distribution of X-scores over a large simulated

population should be close to uniform. In general, exact uniformity cannot be achieved by

mixing betas; some particular X-scores may remain oversampled or undersampled by about 2%

relative to others. However, it is possible to arrange these effects so that both the mean and

variance of the beta mixture match the mean and variance of a uniform distribution, which

ensures that the mean and variance of the key variable on the diaries is the same for the group of

simulated individuals as for the diary pool itself (in the limit of a very large number of

individuals), on each simulation day. See the Supplement for details.

4) Performance over the full range of D and A

The D statistic is bounded between zero and one, and A is bounded between minus one and one.

There are no restrictions on D and A together; any A may be used with any D. The limiting

values on both parameters imply total order, which is incompatible with the concept of a 

stochastic simulation. Furthermore, there is a minimum possible value for D that depends on the

simulation length; for a simulation of J days, D cannot be below 1/J.

Table 4 presents results at selected points over the full range of both D and A, using the new

method. The values of D and A achieved with this new method agree with the target values
C-16

within 0.02 in nearly all cases, and within 0.01 much of the time. Thus, if D is requested to be

0.25, it will nearly always fall between 0.23 and 0.27 for any sizeable simulation. The same

holds for A, at least for A values greater than -0.5. Large negative A targets do not match quite

as well, unless a correction factor is included in the algorithm. Such a correction can be

implemented fairly easily, but in practice should not be necessary since such large negative A

values are not normally seen in human behavior patterns. 

Some other small but reproducible effects may be seen. For example, if a very large and positive

autocorrelation is requested, it is achieved but the target D statistic becomes slightly larger than

requested (by about 0.02 for A=1). This effect is negligible for A<0.5, which means it is unlikely

to be an issue for human behavior simulations. If it were deemed to be important, one could

compensate for it by suppressing the target D value in such cases.

5) Performance over various simulation lengths

The method has been tested successfully over a wide range of simulation lengths, ranging from a

few days up to six years. Table 5 presents some results from these simulations. For all lengths

over 30 days, the match for both D and A is very good. For very short simulations, it is difficult

to precisely target these statistics. For one thing, the sample mean of the X-scores for any

individual does not necessarily come close to the target mean score T, when only a few scores

are drawn. For another, it is very difficult to target particular autocorrelations merely by

rearranging the order of the values. In fact, for three data points the autocorrelation cannot be

positive, no matter what their values or how they are rearranged. For any simulation below one

week in length, the autocorrelation step is nearly irrelevant, although there is no harm in

allowing it to rearrange the scores. For long simulations the performance is always good, with D

and A extremely close to the target values for simulations of six years in length. 

6) Varying targets for D and/or A within a simulation

In certain applications the user might wish to vary D or A over time. For example, different daytypes might each have their own targets, or perhaps D or A might change with seasons or with

age over a long simulation period. The new method is easily extended to such a situation. 

Basically, the method would be applied separately to each set of days with a distinct D. For

each set, define a distribution of target T scores, pick one for each person (keeping the percentile

the same for all sets), and pick enough X-scores for the given set of days. The reordering would

be done within each distinct set of days, to prevent mixing X-scores from different distributions. 

The final time series would then merge the vectors for the various sets of days, according to the

calendar sequence. 

The implementation of multiple targets for A is extremely easy. A new beta distribution is

required every day since its parameters depend on both the target autocorrelation and on the rank

of the X-score assigned to the prior day, and this latter quantity changes every day. Instead of

supplying the target autocorrelation as a scalar, use a vector indexed by the day number, and use

A(j) everywhere that A is currently used.

While it is not difficult to vary D and/or A by day-type, there is no evidence in the southern

California study data that this effect is significant. Therefore, for simplicity, the basic
C-17

explanation of the new method does not include this possibility directly. However, nothing is

fundamentally different if these extensions are used.

7) Movement of X-scores across day-types

The basic method does not distinguish differing D and A targets for differing day-types, as

discussed in the previous subsection. But even if A depended on day-type, the X-scores could

be moved freely across day-types during the reordering step, as long as D and T did not change. 

This is because the X-scores are independently randomly sampled, and as long as the distribution

remains the same, the scores can be interchanged. 

As discussed in subsection (1) above, this is one of the advantages in using X-scores that are

based on relative rankings rather than employing the original variable. The same distribution of

rankings exists on all day-types, although the distribution of the original key variable will differ

across day-types (if it did not, there is no reason to separate the day-types). The proposed

method recognizes this difference through the differing diary pools. For example, an X score of

0.25 may correspond to 40 minutes of outdoor time on a weekday, but correspond to 70 minutes

of outdoor time on a weekend. The reason why the reordering has an overall null effect on the

mean and variance of the key variable is that it is just as likely for an X score of 0.25 to be

shifted from a weekday to a weekend as vice versa. Therefore, over a large enough sample of

persons, the distribution of X-scores before reordering and after reordering are indistinguishable.

8) The frequency distribution for relatively rare diary events

One concern with many of the existing longitudinal diary assembly methods currently used in

exposure models is that they limit the within-person variance (and thereby induce behavioral

habits) by selecting relatively few different one-day diaries for each simulated individual. This

leads to the forced re-use of each of the selected diaries many times. Thus, a model that selects

only eight diaries to represent one year must use each diary an average of 45 times. For such 

methods, each particular kind of diary event will occur with the correct overall frequency in the

population as a whole, but the frequency within individuals is highly distorted.

As an example, suppose the pollutant of concern is ozone. The combination of high breathing

ventilation rate, outdoor activity, and warm daytime conditions will lead to high ozone exposure. 

Then a relatively rare event like a long distance run (for example, a marathon) is significant to

the exposure model. Under the model where only eight diaries are used, if a long distance run

occurs at all (which is not likely), it occurs every time the diary is reused. This leads to a

situation where the vast majority of the population have no such events, and a small number have

(say) 45 such events packed into one year (or even one season), with no one having only a few

such events.

With the new method, if the diary pool contains one diary with a long distance run (and hence

much outdoor time on that day), this diary might be selected not at all or perhaps once, for a

person whose target T has little outdoor time. For persons with larger T , this diary might be

chosen a handful of times in a year. For a person whose target T matches this diary closely, it

might be picked a couple of dozen times. The point is that the population has a quasi-continuous

frequency distribution for this event, rather than a discontinuous one (having it occur either
C-18

never or at least 45 times). Thus, the proposed method better reproduces the variance in

exposure across the population.

9) Ease of use

The proposed method places a minimal burden on the user in terms of required input. Beyond

the definitions of cohorts and diary pools, which are always required (either as user input or

hard-coded into the model), the new method only requires the designation of the key variable

and the targets for D and A. The various beta distributions are constructed by the model code

from these inputs without further user intervention. 

Summary

The new method is very flexible and succeeds in reproducing target D and A values over the

entire possible range, for any choice of key variable. The D statistic of diaries assembled by the

new method is independent of the length of the simulation, unlike most existing diary assembly

methods. The new method avoids forced repetitions of the same activity diary from one day to

another, and therefore allows for some events to occur uniquely or rarely on a given longitudinal

diary. It imposes as much habitual behavior as is requested through the D and A statistics, no

more and no less. The method is relatively simple to implement in computer models, requiring

the ability to sort lists and to draw random numbers from beta distributions. A great advantage

over many other methods is that the computer code for generating the vectors of X-scores does

not depend on the choice of cohorts or diary pools.
C-19

References

Anderssen, N., D. R. Jacobs, S. Sidney, D. E. Bild, B. Sternfeld, M. L. Slattery, and P. Hannan,

1996, "Change and Secular Trends in Physical Activity Patterns in Young Adults", Amer. J.

Epidemiology 143:351-362.

Box, G. E. P., G. M. Jenkins, and G. C. Reinsel, 1994, Time Series Analysis: Forecasting and

Control, Prentice Hall, Englewood Cliffs, NJ, 598 pp.

DeBourdeaudhuij, I., J. Sallis, and C. Vandelanotte, 2002, "Tracking an Explanation of Physical

Activity in Young Adults over a Seven Year Period", Res. Q. Exer. Sport 73:376-385.

Graham, S. E. and T. McCurdy, 2004, "Developing Meaningful Cohorts for Human Exposure

Models", J. Exposure Anal. Environ. Epidem. 14: 23-43.

Hogg, R. V. and A. T. Craig, 1995, Introduction to Mathematical Statistics, Prentice Hall,

Englewood Cliffs, NJ, 564 pp.

Johnson, N. L., S. Kotz, and N. Balakrishnan, 1994, Continuous Univariate Distributions - 2 , 

John Wiley and Sons, New York, NY, 306 pp.

Kelder, S. H., C. L. Perry, K.-I. Klepp, and L. L. Lyttle, 1994, "Longitudinal Tracking of

Adolescent Smoking, Physical Activity, and Food Choice Behaviors", Amer. J. Public Health

84:1121-1126.

MacIntosh, D., 2001, "Refinements to EPA/NERL's Aggregate SHEDS-Pesticides Model", EPA

Contract OD-5537-NTTX, Research Triangle Park, North Carolina.

McCurdy, T., G. Glen, L. Smith, and Y. Lakkadi, 2000, “The National Exposure Research

Laboratory’s Consolidated Human Activity Database” J. Exposure Anal. Environ. Epidem. 10: 

566-578.

 

Schwab, M., A. McDermott, and J. Spengler, 1992, "Using Longitudinal Data to Understand

Children's Activity Patterns in an Exposure Context" Environ. Intern. 18:173-189.

Xue, J., T. McCurdy, J. Spengler, and H. Özkaynak, 2004, "Understanding Variability in the

Time Spent in Selected Locations for 7-12 year old Children" J. Exposure Anal. Environ.

Epidem. 14 : 222-233.
C-S1

SUPPLEMENT

1) Statistical properties of longitudinal diaries

Consider a set of longitudinal diaries for P persons, each diary covering the same J days. For

this analysis we will assume that there are no time gaps, so that all days are consecutive. Let ‘j’

be an index that runs over simulation days, and let ‘i’ be an index that runs over persons. 

Consider just one variable and one cohort of persons, so all persons share the same pool of

available diaries on any given day. Let t i j be the value of the variable of interest on day ‘j’ of

the longitudinal diary for person ‘i’. Note that in this analysis, variance calculations use

division by the number of data points, without the convention of subtracting one to account for

degrees of freedom (Hogg and Craig (1995), Box et al. (1994) ). 

Let : i be the average value for the given variable for person ‘i’, so for i=1,...,P we have

 J

: i = ( 1/J ) ' t i j (1-1)

 j =1

where J is the number of days in the simulation. There is also an intra-personal (within-person)

variance for ‘t’ which may differ from one person to another:

 J J

Fi 

2 = ( 1/J ) ' ( t i j - : i

 ) 2 = ( 1/J ) ' t i j

2 - : i 2 (1-2)

 j =1 j =1

For convenience, define V 2 as

 P J

V 2 = 1/(JP ) ' ' t i j

2

 . (1-3)

 i =1 j =1

The mean for the variable : i over all persons is given by

 P P J

: = (1/P) ' : i = 1/(JP) ' ' t i j (1-4)

 i =1 i =1 j =1

which is also the mean of all the t i j. The total variance of the t i j is given by 

 P J P J

F 2 = 1/(JP ) ' ' ( t i j - : )2 = 1/(JP ) ' ' t i j

2

 - :2 = V 2 - :2 (1-5)

 i =1 j =1 i =1 j =1

The mean of the intra-personal variances across all persons is given by

 P P J P

Fw

2

 = (1/P) ' Fi

2

 = 1/(JP) ' ' (t i j - :i)

 2 = V 2 - (1/P) ' :i

2 (1-6)
C-S2

 i =1 i =1 j =1 i =1

where the subscript ‘w’ stands for ‘within-person’. There is also an inter-person (between

person) variance, which is the variance in the personal means :i

 P P

Fb

2

 = (1/P) ' ( :i - : ) 2 = (1/P) ' : i

2 - : 2

 (1-7)

 i =1 i =1 

where ‘b’ stands for ‘between-persons’. In brief, Fw

2

 is the mean of the intra-personal

variances, while Fb

2

 is the variance of the intra-personal means. An important result is that 

Fw

2

 + Fb

2

 = V 2 - : 2 = F 2 (1-8)

which follows from the three prior equations. Thus, for a given set of longitudinal diaries, Fw

2

,

Fb

2

 and F2 are tied together by equation (1-8). This has important implications when targeting

variance. For a given set of diary pools from which the longitudinal dairies are to be

constructed, the total variance F2 can be calculated. This means that in longitudinal diary

construction there is a direct trade-off between Fw

2

 and Fb

2

 ; one can only be made larger if the

other is made smaller, given that the diaries are to be sampled in an unbiased manner. 

This is starkly illustrated by considering two extreme approaches to assembling longitudinal

diaries. If, for each person, one simply chooses a single diary and reuses it each day, then Fw

2

 =

0 and Fb

2

 is maximized. Alternatively, if a new diary is chosen at random every day for each

person, each individual tends to have a similar Fi 

2

, and F 2 is comprised mostly of Fw

2

, while Fb

2

tends to zero (particularly for large J).

The population variability in typical measures of long-term exposure like annual average daily

dose (ADD) or lifetime average daily dose (LADD) is proportional to Fb

2

. The mean exposure

will be correct for any unbiased method of longitudinal diary construction. But for a fixed

mean, a higher variance implies that the high end of the exposure distribution will be at higher

values (and also that the low end is at lower values). The high-end exposures are often of

interest, and the estimates of these exposures will be sensitive to the method of constructing

longitudinal diaries. Hence it is important that the method be matched to experimental data as

far as possible.

Define D as 

D = Fb

2

 / (Fb

2

 + Fw

2

 ) = Fb

2

 / F 2 (1-9)

This definition is similar to the definition of ICC used by Xue et. al. (2004). The value of D may

range from zero (when Fb

2

 = 0) up to one (when Fw

2

 = 0). Using equations (1-7) and (1-8), the

expression for D becomes

 P 
C-S3

D = 1/(P F2) ' :i

2 - :2

 / F2 (1-10)

 i =1 

So this statistic reflects the distribution of the personal means :i. It does not reflect any patterns

or ordering of the t i j within a diary. Note that it is possible to interchange two or more days

(interchange t i j and t i k for two days ‘j’ and ‘k’), without changing :i

 or Fi

2 (or : or F 2

). 

Thus, longitudinal diary construction can be separated into two problems, the first being the

selection of the set of t i j values without any particular regard to day order, and the second being

to reorder them to match the patterns expected within individual longitudinal diaries. These

patterns are summarized by autocorrelation statistics, discussed in section 3 below.

2) Specifying the parameters of the beta distributions for the Ti

 and X-scores

To complete the description of the proposed method, formulas for the parameters of the beta

distributions are required. Each person simulated is assigned a personal target score Ti , which is

the mean of the distribution from which their X-scores are drawn. For this analysis, the t i j are

the X-scores. There are two constraints to be met. The set of selected values t i j should produce

a sample D statistic close to the requested value, and the set of t i j (across all persons) should be

as uniformly distributed between zero and one as is possible. 

A beta distribution with parameters ‘a’ and ‘b’, bounded by zero and one, has a probability

density function (pdf) given by 

p(x) = '(a+b) x a-1 (1- x) b-1 / [ '(a) '(b) ] (2-1)

which has a mean of

: (a,b) = a / (a+b) (2-2)

and a variance

F 2 (a,b) = a b / [(a+b)2 (1+a+b)] (2-3)

(see for example Johnson, Kotz, and Balakrishnan, 1994). Replacing ‘a’ and ‘b’ by the mean :

and the sum S (where S = a+b) results in 

p(x) = '(S) x : S - 1 (1- x) S - : S - 1 / [ '(: S) '(S - : S) ] (2-4)

F 2 (:,S) = : (1- :) / (1+S) . (2-5)

Except for the beta distribution that is used for selecting the personal targets Ti , all the beta

distributions used in this approach have bounds zero and one, so the above formulas apply. 
C-S4

For the Ti, the bounds of the beta distributions are at (1/2-w/2) and (1/2+w/2), where ‘w’ is a

function of ‘D’ and may range from zero to one. These beta distributions are symmetric about

their midpoint, so ‘a’ = ‘b’ = " . The pdf in such cases is

p(x) = '(2") ( 1 - (2x-1) 2 / w 2 ) "-1 / [ w '(") 2 2 2 "-2 ] , 

 for (1/2-w/2) < x < (1/2+w/2) (2-6)

and the statistics for this distribution are mean 

: = 1/2 (2-7)

which is obvious from the symmetry, and variance

F 2 = w 2 / (4 + 8 ") . (2-8)

For a particular person with a target score Ti , the beta distribution from which their X-scores are

drawn has a mean Ti and a variance which follows from (2-5):

Fi 

2

 = Ti (1 - Ti ) / (1 + S i ) (2-9)

where S i is the sum of the ‘a’ and ‘b’ parameters for that particular person. For a sample of size

J drawn from this distribution, the square of the standard error of the mean is Fi 

2

 / J. Also, the

expected value of the sample variance is

 si 

2 = (J-1) Fi 2

 / J . (2-10)

The within-person variance Fw

2

 is the mean across persons of the si 

2

. In the limit of a large

simulated population, this is the same as the weighted average over Ti . 

Fw

2

 = I p(Ti) si 

2

 d Ti 

 = ((J-1)/J) I p(Ti) Ti (1 - Ti ) / (1 + S i ) d Ti . (2-11)

This integral has a simple solution if the denominator can be factored out, which is possible

when the sum of the parameters of the beta distribution for the X-scores, which is S i, is the same

for all persons (or all T i ). Assume that such a solution exists that also meets all the other

constraints; that is, assume S i is equal to a constant S for all persons. The remaining terms in

the integral consist of the difference between the first and second moments of Ti

 about the origin. 

The first moment is the mean (which is 1/2), while the second moment about the origin is the

variance plus the square of the mean. The variance of the Ti

 is given by equation (2-8). Hence

Fw

2

 = [(J-1)/(J + J S)] [ 1/2 - ( 1/4 + w 2 / (4 + 8 ") ) ]
C-S5

 = [(J-1)/(J + J S)] [1/4 - w 2 / (4 + 8 ") ] . (2-12)

Now consider the between-person variance Fb

2

. It can be interpreted as the second moment

about the overall mean :. (see equation 1-7). Here the mean of the Ti

 is 1/2 by equation (2-7). 

For one value of Ti

, if several persons share this Ti then the expected variance in : i for this

subgroup is the square of the standard error of the mean. Each person is assigned J X-scores,

one per simulation day. The standard error of the mean of these scores is given by Fi / J1/2, 

hence the expected variance in : i for persons sharing the same Ti is Fi 

2

 / J , which by equation

(2-9) is Ti

 (1 - Ti ) / (J + J Si ). To evaluate Fb

2

 , the variance in : i about Ti must be converted

to the second moment of : i

 about the overall population mean of 1/2. 

Hence, 

(2nd moment of : i

 about 1/2 for given Ti) = I p(:i) (:i -1/2) 2 d:i

 

 = I p(:i

) (:i

2

 - :i +1/4) d:i

 = I p(:i

) :i

2

 d:i - Ti +1/4 (2-13)

which follows since I p(:i) :i d:i = Ti and also I p(:i) 1/4 d:i = 1/4. 

The variance in :i is the second moment about the mean Ti , or 

Fi 

2

 / J = I p(:i) (:i -Ti )2 d:i

 = I p(:i

) :i

2

 d:i - I p(:i ) 2 :i Ti d:i + I p(:i ) Ti

2

 d:i

 = I p(:i

) :i

2

 d:i - 2 Ti

2

 + Ti

2

 (2-14)

Substituting this expression into (2-13) gives 
C-S6

(2nd moment of :i

 about 1/2 for given Ti) = Fi 

2

 / J + Ti

2

 - Ti +1/4

 = Fi 

2

 / J + (Ti - 1/2)2

 = Ti

 (1-Ti) / (J +J Si) + (Ti - 1/2)2 . (2-15)

For a large simulated population, Fb

2

 is the mean of this quantity over all Ti, namely

Fb

2

 = I p(Ti) [ Ti (1 - Ti ) / (J + J Si) + (Ti - 1/2)2 ] d Ti (2-16)

where p(Ti) is given by equation (2-6). This integral can be split in two; the first part is the

same integral as in (2-11), while the second part is just the variance in Ti, which is given by

equation (2-8). As for Fw

2

, the first integral can be solved by assuming Si is constant for all

persons. So

Fb

2

 = [1/(J + J S)] [1/4 - w 2 / (4 + 8 ") ] + w 2 / (4 + 8 ") . (2-17)

Collectively, the X-scores for all the simulated persons should be as close to uniformly

distributed as possible, to ensure no net bias in the usage of the diaries. In general this cannot be

achieved exactly, but it is possible to ensure that the X-scores collectively have the same mean

and variance as a uniform distribution, which for a uniform bounded by zero and one is

mean of X-scores = 1/2 , (2-18)

variance of X-scores = 1/12 . (2-19)

The mean will be 1/2 by the symmetry of the Ti distribution about 1/2. The collective variance

of the X-scores is related to Fb

2

 and Fw

2

 by equation (1-8). Hence

Fb

2

 + Fw

2

 = 1/12 . (2-20)

Substituting in the expressions from (2-12) and (2-17), one obtains

[1/(1+S)] [1/4 - w 2 / (4 + 8 ") ] + w 2 / (4 + 8 ") = 1/12 (2-21)

which when solved for S results in

S = 2 / (1 - 3 w 2 / (1 + 2 ") ) . (2-22)

This result permits the specification of the parameters for the beta distribution for person 'i' from

which all their X-scores are drawn. This distribution has a mean of Ti

. Remembering that 
C-S7

S = a+b, equation (2-2) can be written as

a = S Ti = 2 Ti / (1 - 3 w 2 / (1 + 2 ") ) . (2-23)

Therefore

b = S-a = 2 ( 1 - Ti ) / (1 - 3 w 2 / (1 + 2 ") ) . (2-24)

From equation (2-6), the parameters w and " define the beta distribution from which all the

personal target scores Ti are drawn. This distribution must match the requirements of the D

statistic. To simplify the equations, define a new parameter 

D# = 3 w 2 / (1 + 2 ") (2-25)

and rewrite equation (2-17) in terms of this new parameter:

Fb

2

 = [1/(J + J (2/(1-D#)))] [1/4 - D# /12] + D# /12. (2-26)

which can be solved for D# in terms of Fb

2

D# = (12 J Fb

2

 -1 ) / ( J - 1) . (2-27)

Also, equation (1-9) together with (2-20) give

 D = Fb

2 / (Fb2

 + Fw

2

 ) = 12 Fb

2 . (2-28)

Hence

D# = (J D - 1 ) / (J - 1 ) (2-29)

As J becomes large, D# approaches D. Therefore, D# may be seen as a modified D statistic that

accounts for the effects of short simulation periods. Since the user specifies the simulation

length J and the diversity statistic D directly, D# is therefore also specified. However, equation

(2-25) still contains two unknowns (w and "). Thus, there is no unique solution. 

Let R be the square root of D#

R = (D# ) 1/2 . (2-30)

It is found empirically that the following relationship between " and R gives a nearly uniform

distribution of X-scores:

" = 1 - (4/5) [4 R (1 - R)] 3 (2-31)
C-S8

In practice, the above formulas give a nearly uniform collective distribution of X-scores, and

hence a nearly uniform usage of the available diaries. For example, suppose one year time series

are generated for a large number of simulated persons, using a pool of 100 diaries. (For this

purpose, neglect the effects of altering diary pools throughout the year.) Strict uniformity would

result in each diary being assigned an average of 3.65 times per person (365 days divided by 100

diaries). The above formulae using beta distributions result in each diary being used between

3.50 and 4.0 times per person. Furthermore, both the mean and variance of the key variable on

the assembled time series match the mean and variance seen in the diary pool. If even better

uniformity in diary usage is desired, it is possible to use a smoothing function on the X-scores, at

a slight cost in departing from strict beta distributions. This is usually not necessary and is not

detailed here. 

Unlike the other equations in this derivation, there is no necessity to use equation (2-31) when

implementing this method. Any functions for " and ‘w’ that produce valid beta distributions and

satisfy equation (2-25) may be used. Another choice which is simpler than (2-31) is 

" = 1 (2-32)

whereupon equation (2-25) reduces to 

w2 = D# . (2-33)

This choice results in a uniform distribution of the targets Ti between the limits (1/2-D#/2) and

(1/2+D# /2). However, while the D statistic is matched, and the mean and variance of the Xscores match those of a uniform distribution, overall the X-scores are slightly less uniformly

distributed than is obtained by using equation (2-31). The choice of functions for " and ‘w’

could be based on preferences for statistics other than D; for example, one might wish to match

statistics on the distribution of the Ti targets themselves.

3) Method of reordering the diaries to match a target value of A

The second step in the proposed method for constructing longitudinal activity diaries is the

reordering of the selected X-scores to match a target value for ‘A’. It should be noted that

autocorrelation is hard to measure on short time series. Box, Jenkins and Reinsel (1994)

recommend a minimum of 50 data points to adequately characterize the autocorrelation of a time

series. The method described below does a reasonable job for 30 days or more. The method can

be applied to shorter time series, but the results will not match the target autocorrelation as

closely as for longer simulations. 

 

For purposes of autocorrelation, the ranks that matter are the ranks relative to the other days in

the same time series. These ranks may differ substantially from the original X-scores. Note that

the X-scores are uniformly distributed across persons and hence the mean (across persons) is 1/2,
C-S9

but the mean within a time series for a given person is :i . Hence the ranking of X-scores across

persons may differ substantially from the ranking within persons. 

To start the process of targeting the desired overall autocorrelation A, assign a target

autocorrelation ai

 to each simulated individual. These targets can be drawn from any distribution

that has a mean of A, provided that all ai are between -1 and 1. 

Sort the X-scores within each simulated individual’s time series and rank them from smallest to

largest. Suppose there are J days in the simulation period. Recall that some extra X-scores

(approximately 3%) should be selected for each person. The extra ones are needed to prevent a

severe loss of degrees of freedom towards the end of each individual’s reordering. Let K be the

number of X-scores selected per person, including the extras. When sorted and ranked, the set of

available ranks will be the integers from 1 to K. For example, rank 1 will correspond to the

lowest of the X-scores assigned to this person, rank 2 is the second lowest X-score, and so on. 

Ties will not generally occur, as the X-scores are real numbers selected from continuous

distributions; ties are ignored in practice. The goal is to reorder these ranks in a stochastic

manner that will (on average) reproduce the requested autocorrelation. The reordering process

will stop once J values are selected, any extras are discarded.

Let Rj be the rank assigned to day ‘j’ by this reordering process. The lag-one autocorrelation ‘a i’

of the time series for person ‘i’ is the ratio of the lag-one covariance to the variance, or

a i = E [ (R j - D) ( Rj+1 - D) ] / E [ (R j - D)

2

 ] (3-1)

where D is the mean of the ranks. Here E [arg] means the expected value of the argument ‘arg’. 

There is a slight difference in the autocorrelation of the entire set of K ranks as compared to the

autocorrelation of the J ranks of the selected subset, although this difference is quite small for J

close to K. One difficulty is that while the latter is a measurable output from the diary assembly

process, it is the former that is accessible during the reordering process. Thus, the ranks, means,

and variances in equation (3-1) and subsequent equations apply to the full list of K values.

The denominator in equation (3-1) is the variance of the set of integers from 1 to K, which is 

(K2

-1)/12. Hence

a i = (12 / (K2 -1)) E [(R j - D) ( Rj+1 - D) ]. (3-2)

The expectation value in equation (3-2) can be evaluated if we have the conditional probability

p(Rj+1 | R j ); that is, the probability for each rank being chosen on day ‘j+1', given the rank R j

chosen on day ‘j’.

The conditional probability distribution p(Rj+1 | R j ) is a discrete distribution, since the set of

ranks is discrete. However, the number of ranks is often in the hundreds, and it is more

convenient to use a continuous probability distribution. Thus, a beta distribution for p(y|x) is
C-S10

developed, where ‘x’ and ‘y’ are continuous variables ranging from zero to one that are mapped

onto the ranks:

 R j = ceil(K x), and Rj+1 = ceil(K y) (3-3)

where ‘ceil’ is the ceiling or least integer function that rounds up to the next integer. To invert

these relationships, note that on average the ceiling function adds 1/2 to the argument, so the

mean values of x and y that correspond to given ranks are

x = (R j -1/2) / K, and y = (Rj+1 -1/2) / K (3-4)

We wish to select the parameters for a beta distribution that give the selection probabilities for

Rj+1 , based on the value of R j and the other constants in equation (3-2). The expected value

appearing in equation (3-2) is given by weighting the sum over all outcomes by the probability

of occurrence:

E [(R j - D) ( Rj+1 - D) ] = ' ' (R j - D) ( Rj+1 - D) p(R j) p(Rj+1 | R j) (3-5)

where one sum is over all R j from 1 to K and the other is over all Rj+1 from 1 to K. All values

for R j should be equally likely, that is, p(R j) =1/K for all cases. Replace the sum over all Rj+1 by

an integral over all y, with Rj+1 replaced by (Ky+1/2):

E [(R j - D) ( Rj+1 - D) ] = (1/K) ' (R j - D) Ip(y|x) (Ky+1/2- D) dy (3-6)

The integral over ‘y’ consists of two parts. Factoring out the K, the first part is the mean value

of ‘y’ for the given ‘x’, which can be symbolized as E(y|x). The second part equals (1/2-D),

since the integrand is independent of y, and Ip(y|x) dy = 1. Also note that for the integers from 1

to K, the mean is D = (K+1)/2, so (1/2-D) = -K/2. Thus,

E [(R j - D) ( Rj+1 - D) ] = ' (R j - D) ( E(y|x) - 1/2) (3-7)

The value of E(y|x) will depend on the parameters of the beta distribution. As in section 2, let

‘a’ and ‘b’ be the parameters of the beta distribution and let S = a+b. Consider the following:

a = S/2 - S w/2 + S w x . (3-8)

Then 

 b = S-a = S/2 + S w/2 - S w x. (3-9)

The mean of a beta distribution bounded by zero and one is given by equation (2-2), therefore
C-S11

E (y|x) = a / (a+b) = a /S = 1/2 - w/2 + w x . (3-10)

Thus, equation (3-7) becomes 

E [(R j - D) ( Rj+1 - D) ] = ' (R j - K/2 - 1/2) w (x-1/2). (3-11)

Replacing x by (R j -1/2)/K and noting that the sums evaluate to 

' R j

2

 = K (K+1) (2K+1)/6, ' R j = K (K+1)/2, ' 1 = K, (3-12)

 then equation (3-11) can be expanded and evaluated to give

E [(R j - D) ( Rj+1 - D) ] = w (K2 - 1) /12. (3-13)

With this choice of the beta distribution, equation (3-2) reduces to the very simple form

w = ai. (3-14)

To completely specify the parameters of the beta distribution, a form for the sum of parameters 

S = a+b must be given. The second requirement is that the distribution of ‘y’ be essentially

uniform, when averaged over all values of ‘x’. In practice, this condition cannot be met exactly. 

Instead, a reasonable match can be made by matching the first few moments of the distribution

for ‘y’ to the moments of a uniform distribution.

The kth moment about zero of a uniform distribution from zero to one is

 

m k = I x k p(x) dx = 1/ (k+1) (3-15)

since p(x) =1 for a uniform. The moments of the ‘y’ values are

E(y k) = I I y k p(y|x) p(x) dy dx

= Ip(x) dx I y k p(y|x) dy . (3-16)

The second integral is the kth moment of the beta distribution p(y|x). The first moment is given

by equation (3-10). The second moment of a beta distribution (Johnson, Kotz, and Balakrishnan,

1994) is

M 2 = a (a+1) / ( S (S+1) )

 

 = (S/2 - S w /2 + S w x ) (1+S/2 -S w/2 + S w x) / [S (S+1) ]
C-S12

 = [ (1-w)(2+S-S w)/4 + (w + S w - s w2 ) x + S w2 x2 ] / (S+1). (3-17)

Hence the first moment of ‘y’ is

E(y ) = Ip(x) (1/2 - w/2 + w x) dx

 = 1/2 - w/2 + w (1/2)

 = 1/2 (3-18)

which agrees with the first moment m1 of a uniform (0,1) distribution. For the second moment,

equation (3-17) must be integrated over x from zero to one, giving

E(y 2 ) = [(1-w)(2+S-S w)/4 + (w+S w - S w2)/2 + S w2/3 ] / (S+1)

 

 = (6 + 3 S + S w 2 ) / (12 + 12 S) (3-19)

Matching E(y2) to the second moment m2 of a uniform (0,1) distribution (which is 1/3) and

solving for S gives

S = 2 / (1- w 2) (3-20)

Matching the third moments m3 = E (y3) results in the same relationship S = 2 / (1- w 2). 

Moments higher than this generally will not match.

To summarize, the parameter values should be

w = a i

S = 2 / (1- w 2). (3-21)

The preceding development is in terms of the target autocorrelation ‘a i’ that is specific to one

individual ‘i’. The population statistic A is the mean of the ai across persons. An examination

of the data used in Xue et al. (2004) indicates that people within the same cohort may differ

greatly in their personal autocorrelations. For four different choices of the key variable, the

standard deviation of ai across persons was 0.20. A symmetric beta distribution centered on A

with a standard deviation of 0.20 was chosen for the results reported here. The bounds on this

beta are (A-1/2) to (A+1/2), provided these do not extend past 1 or -1. If A is less than -1/2 or

greater than 1/2, the beta distribution is “squeezed” symmetrically until the bounds are within
C-S13

limits. Other choices of the key variable or data from other studies may lead to alternative

choices for the distribution of ‘a i’ .

The proposed method could allow differing autocorrelations for different points in the time

series. For example, suppose that there is one autocorrelation for the case where both days ‘j’

and ‘j+1’ are of the same day-type, and another if the days are of differing day-types. The

average autocorrelation is the weighted average. The user would specify the overall target 

autocorrelations Aj for each day-type. For each individual, a target a i j is required for each Aj. 

Since a new beta distribution is generated every day, one merely replaces a i by a i j in equations

(3-21), so that ‘w’ and ‘s’ become functions of ‘j’. Note that there are few data sets extensive

enough to determine if this effect is significant. Furthermore, the stability of each

autocorrelation target will decrease when it is applied to fewer and fewer days. Hence, the

derivation does not emphasize this possibility.

4) Mapping the X-scores back to activity diaries

For the first day of the simulation, select any of the ranks from 1 to K at random. For each

subsequent day, a beta distribution with parameters determined by (3-21) and (3-8) is used to

select the next rank. The beta distribution will return a real number between zero and one; call

this value ‘y’. Convert this to a rank R from 1 to K by

Rj+1 = ceil(K y) (4-1)

where ‘ceil’ is the ceiling function. The only complication is if this rank has already been

assigned to a prior day, in which case the nearest rank that has not already been used is assigned

instead. The X-score corresponding to this rank is recorded (call it xj+1 ), and the assigned rank

is used to adjust the parameters of the beta distribution to be used for the next day. Continue

until J values have been assigned. 

To connect the time series of X-scores with actual diaries, the pool of available diaries for each

day must be identified. If there are Dj+1 available diaries in the pool for simulation day ‘j+1’, 

then use the diary at position d j+1 in the sorted list of available diaries, where 

d j+1 = ceil(Dj+1 xj+1 ). (4-2)

5) Possible Modifications

There are several reasons why the derivation of the parameters needed to match a target

autocorrelation yields an approximate, but not analytically exact, solution. First, and most

importantly for short simulations, the correspondence between the discrete nature of the ranks

and the continuous beta distribution can become a difficulty. Mathematically, this means that

larger segments of x and y space map onto a single rank. The implicit assumption in the
C-S14

derivation is that ranks can be mapped to the midpoint of these segments, and vice versa. This is

a good approximation as long as the probability is not rapidly changing within each segment,

which is the case when each segment is small (meaning many days in the simulation).

Secondly, the beta distribution for reordering may select the same rank on two days in a row, in

which case the second rank must be shifted away from the first, which lowers autocorrelation. In

fact, anytime selected rank Rj+1 has been used before, the result must be shifted to the nearest

unused rank. However, if this is not the same rank as Rj, then the shift is equally likely to move

the rank closer to Rj as moving it further away, so the net effect on autocorrelation is small.

Additionally, near the end of the simulation, there are relatively few unused ranks, and in

practice these ranks may be near to each other. So when examined in detail, the time series may

show a tendency for autocorrelation to increase toward the end.

The final point is that within each time series the rankings for the J selected X-scores will differ

from the rankings with respect to all K of the X-scores. Usually, this is not a problem since the

mean and variance of the subset are close to the mean and variance of the larger set. In

exceptional cases, the autocorrelation measured on the original rankings (based on K) may differ

from the autocorrelation based on the rankings within the subset; this could happen when the

omitted X-scores are congregated near one end of the ranking scale.

Accounting for the above factors may be possible by modifying the proposed method, though at

a cost of complicating the approach. However, in total, these effects tend to be small for

simulations over 30 days in length. Also, some of the potential problems have a tendency to

cancel out. It is found in simulations that D and A are usually within 0.02 of the requested value,

an excellent agreement. 

APPENDIX D. UNCERTAINTY ANALYSIS OF RESIDENTIAL AIR EXCHANGE 

RATE DISTRIBUTIONS 
This page intentionally left blank. 
D-2

MEMORANDUM 

To: John Langstaff, EPA OAQPS 

From: Jonathan Cohen, Arlene Rosenbaum, ICF International 

Date: June 5, 2006 

Re: Uncertainty analysis of residential air exchange rate distributions 

This memorandum describes our assessment of some of the sources of the uncertainty of cityspecific distributions of residential air exchange rates that were fitted to the available study data. 

City-specific distributions for use with the APEX ozone model were developed for 12 modeling 

cities, as detailed in the memorandum by Cohen, Mallya and Rosenbaum, 20057

 (Appendix A of 

this report). In the first part of the memorandum, we analyze the between-city uncertainty by 

examining the variation of the geometric means and standard deviations across cities and studies. 

In the second part of the memorandum, we assess the within-city uncertainty by using a 

bootstrap distribution to estimate the effects of sampling variation on the fitted geometric means 

and standard deviations for each city. The bootstrap distributions assess the uncertainty due to 

random sampling variation but do not address uncertainties due to the lack of representativeness 

of the available study data, the matching of the study locations to the modeled cities, and the 

variation in the lengths of the AER monitoring periods. 

Variation of geometric means and standard deviations across cities and studies 

The memorandum by Cohen, Mallya and Rosenbaum, 20058 (Appendix A of this report) 

describes the analysis of residential air exchange rate (AER) data that were obtained from seven 

studies. The AER data were subset by location, outside temperature range, and the A/C type, as 

defined by the presence or absence of an air conditioner (central or window). In each case we 

chose to fit a log-normal distribution to the AER data, so that the logarithm of the AER for a 

given city, temperature range, and A/C type is assumed to be normally distributed. If the AER 

data has geometric mean GM and geometric standard deviation GSD, then the logarithm of the 

AER is assumed to have a normal distribution with mean log(GM) and standard deviation 

log(GSD). 

Table D-1 shows the assignment of the AER data to the 12 modeled cities. Note that for Atlanta, 

GA and Washington DC, the Research Triangle Park, NC data for houses with A/C was used to 

represent the AER distributions for houses with A/C, and the non-California data for houses 

 

7

 Cohen, J., H. Mallya, and A. Rosenbaum. 2005. Memorandum to John Langstaff. EPA 68D01052, Work 

Assignment 3-08. Analysis of Air Exchange Rate Data. September 30, 2005. 8 Op. Cit.
D-3

without A/C was used to represent the AER distributions for houses without A/C. Sacramento, 

CA AER distributions were estimated using the AER data from the inland California counties of 

Sacramento, Riverside, and San Bernardino; these combined data are referred to by the City 

Name “Inland California.” St Louis, MO AER distributions were estimated using the AER data 

from all states except for California and so are referred to be the City Name “Outside 

California.” 

Table D-1. Assignment of Residential AER distributions to modeled cities 

Modeled city AER distribution 

Atlanta, GA, A/C Research Triangle Park, A/C only 

Atlanta, GA, no A/C All non-California, no A/C (“Outside California”) 

Boston, MA New York 

Chicago, IL New York 

Cleveland, OH New York 

Detroit, MI New York 

Houston, TX Houston 

Los Angeles, CA Los Angeles 

New York, NY New York 

Philadelphia, PA New York 

Sacramento Inland parts of Los Angeles (“Inland California”) 

St. Louis All non-California (“Outside California”) 

Washington, DC, A/C Research Triangle Park, A/C only 

Washington, DC, no 

A/C All non-California, no A/C (“Outside California”) 

It is evident from Table D-1 that for some of the modeled cities, some potentially large 

uncertainty was introduced because we modeled their AER distributions using available data 

from another city or group of cities thought to be representative of the first city on the basis of 

geography and other characteristics. This was necessary for cities where we did not have any or 

sufficient AER data measured in the same city that also included the necessary temperature and 

A/C type information. One way to assess the impact of these assignments on the uncertainty of 

the AER distributions is to evaluate the variation of the fitted log-normal distributions across the 

cities with AER data. In this manner we can examine the effect on the AER distribution if a 

different allocation of study data to the modeled cities had been used. 

Even for the cities where we have study AER data, there is uncertainty about the fitted AER 

distributions. First, the studies used different measurement and residence selection methods. In 

some cases the residences were selected by a random sampling method designed to represent the 
D-4

entire population. In other cases the residences were selected to represent sub-populations. For 

example, for the RTP study, the residences belong to two specific cohorts: a mostly Caucasian, 

non-smoking group aged at least 50 years having cardiac defibrillators living in Chapel Hill; a 

group of non-smoking, African Americans aged at least 50 years with controlled hypertension 

living in a low-to-moderate SES neighborhood in Raleigh. The TEACH study was restricted to 

residences of inner-city high school students. The RIOPA study was a random sample for Los 

Angeles, but was designed to preferentially sample locations near major air toxics sources for 

Elizabeth, NJ and Houston TX. Furthermore, some of the studies focused on different towns or 

cities within the larger metropolitan areas, so that, for example, the Los Angeles data from the 

Avol study was only measured in Lancaster, Lake Gregory, Riverside, and San Dimas but the 

Los Angeles data from the Wilson studies were measured in multiple cities in Southern 

California. One way to assess the uncertainty of the AER distributions due to variations of study 

methodologies and study sampling locations is to evaluate the variation of the fitted log-normal 

distributions within each modeled city across the different studies. 

We evaluated the variation between cities, and the variation within cities and between studies, by 

tabulating and plotting the AER distributions for all the study/city combinations. Since the 

original analyses by Cohen, Mallya and Rosenbaum, 2005 clearly showed that the AER 

distribution depends strongly on the outside temperature and the A/C type (whether or not the 

residence has air conditioning), this analysis was stratified by the outside temperature range and 

the A/C type. Otherwise, study or city differences would have been confounded by the 

temperature and A/C type differences and you would not be able to tell how much of the AER 

difference was due to the variation of temperature and A/C type across cities or studies. In order 

to be able to compare cities and studies we could not use different temperature ranges for the 

different modeled cities as we did for the original AER distribution modeling. For these analyses 

we stratified the temperature into the ranges <= 10, 10-20, 20-25, and >25 oC and categorized the 

A/C type as “Central or Window A/C” versus ‘No A/C,” giving 8 temperature and A/C type 

strata. 

Table D-2 shows the geometric means and standard deviations by city and study. These 

geometric mean and standard deviation pairs are plotted in Figure D-1 through D-8. Each figure 

shows the variation across cities and studies for a given temperature range and A/C type. The 

results for a city with only one available study are shown with a blank study name. For cities 

with multiple studies, results are shown for the individual studies and the city overall distribution 

is designated by a blank value for the study name. 

Table D-2. Geometric means and standard deviations by city and study. 

A/C Type Temperature City Study* N Geo Mean Geo Std Dev**

Central or Room A/C <= 10 Houston 2 0.32 1.80 

Central or Room A/C <= 10 Los Angeles 5 0.62 1.51 

Central or Room A/C <= 10 Los Angeles Avol 2 0.72 1.22 

Central or Room A/C <= 10 Los Angeles RIOPA 1 0.31 

Central or Room A/C <= 10 Los Angeles Wilson 1991 2 0.77 1.12 

Central or Room A/C <= 10 New York City 20 0.71 2.02 

Central or Room A/C <= 10 Research Triangle Park 157 0.96 1.81 

Central or Room A/C <= 10 Sacramento 3 0.38 1.82 

Central or Room A/C <= 10 San Francisco 2 0.43 1.00 
D-5

Table D-2. Geometric means and standard deviations by city and study. 

A/C Type Temperature City Study* N Geo Mean Geo Std Dev**

Central or Room A/C <= 10 Stockton 7 0.48 1.64 

Central or Room A/C 10-20 Arcata 1 0.17 

Central or Room A/C 10-20 Bakersfield 2 0.36 1.34 

Central or Room A/C 10-20 Fresno 8 0.30 1.62 

Central or Room A/C 10-20 Houston 13 0.42 2.19 

Central or Room A/C 10-20 Los Angeles 716 0.59 1.90 

Central or Room A/C 10-20 Los Angeles Avol 33 0.48 1.87 

Central or Room A/C 10-20 Los Angeles RIOPA 11 0.60 1.87 

Central or Room A/C 10-20 Los Angeles TEACH 1 0.68 

Central or Room A/C 10-20 Los Angeles Wilson 1984 634 0.59 1.89 

Central or Room A/C 10-20 Los Angeles Wilson 1991 37 0.64 2.11 

Central or Room A/C 10-20 New York City 5 1.36 2.34 

Central or Room A/C 10-20 New York City RIOPA 4 1.20 2.53 

Central or Room A/C 10-20 New York City TEACH 1 2.26 

Central or Room A/C 10-20 Redding 1 0.31 

Central or Room A/C 10-20 Research Triangle Park 320 0.56 1.91 

Central or Room A/C 10-20 Sacramento 7 0.26 1.67 

Central or Room A/C 10-20 San Diego 23 0.41 1.55 

Central or Room A/C 10-20 San Francisco 5 0.42 1.25 

Central or Room A/C 10-20 Santa Maria 1 0.23 

Central or Room A/C 10-20 Stockton 4 0.73 1.42 

Central or Room A/C 20-25 Houston 20 0.47 1.94 

Central or Room A/C 20-25 Los Angeles 273 1.10 2.36 

Central or Room A/C 20-25 Los Angeles Avol 32 0.61 1.95 

Central or Room A/C 20-25 Los Angeles RIOPA 26 0.90 2.42 

Central or Room A/C 20-25 Los Angeles Wilson 1984 215 1.23 2.33 

Central or Room A/C 20-25 New York City 37 1.11 2.74 

Central or Room A/C 20-25 New York City RIOPA 20 0.93 2.91 

Central or Room A/C 20-25 New York City TEACH 17 1.37 2.52 

Central or Room A/C 20-25 Red Bluff 2 0.61 3.20 

Central or Room A/C 20-25 Research Triangle Park 196 0.40 1.89 

Central or Room A/C > 25 Houston 79 0.43 2.17 

Central or Room A/C > 25 Los Angeles 114 0.72 2.60 

Central or Room A/C > 25 Los Angeles Avol 25 0.37 3.10 

Central or Room A/C > 25 Los Angeles RIOPA 10 0.94 1.71 

Central or Room A/C > 25 Los Angeles Wilson 1984 79 0.86 2.33 

Central or Room A/C > 25 New York City 19 1.24 2.18 

Central or Room A/C > 25 New York City RIOPA 14 1.23 2.28 

Central or Room A/C > 25 New York City TEACH 5 1.29 2.04 

Central or Room A/C > 25 Research Triangle Park 145 0.38 1.71 

No A/C <= 10 Houston 13 0.66 1.68 

No A/C <= 10 Los Angeles 18 0.54 3.09 

No A/C <= 10 Los Angeles Avol 14 0.51 3.60 

No A/C <= 10 Los Angeles RIOPA 2 0.72 1.11 

No A/C <= 10 Los Angeles Wilson 1991 2 0.60 1.00 

No A/C <= 10 New York City 48 1.02 2.14 
D-6

Table D-2. Geometric means and standard deviations by city and study. 

A/C Type Temperature City Study* N Geo Mean Geo Std Dev**

No A/C <= 10 New York City RIOPA 44 1.04 2.20 

No A/C <= 10 New York City TEACH 4 0.79 1.28 

No A/C <= 10 Sacramento 3 0.58 1.30 

No A/C <= 10 San Francisco 9 0.39 1.42 

No A/C 10-20 Bakersfield 1 0.85 

No A/C 10-20 Fresno 4 0.90 2.42 

No A/C 10-20 Houston 28 0.63 2.92 

No A/C 10-20 Los Angeles 390 0.75 2.09 

No A/C 10-20 Los Angeles Avol 23 0.78 2.55 

No A/C 10-20 Los Angeles RIOPA 87 0.78 1.96 

No A/C 10-20 Los Angeles TEACH 9 2.32 2.05 

No A/C 10-20 Los Angeles Wilson 1984 241 0.70 2.06 

No A/C 10-20 Los Angeles Wilson 1991 30 0.75 1.82 

No A/C 10-20 New York City 59 0.79 2.04 

No A/C 10-20 Sacramento 1 1.09 

No A/C 10-20 San Diego 49 0.47 1.95 

No A/C 10-20 San Francisco 15 0.34 3.05 

No A/C 10-20 Santa Maria 2 0.27 1.23 

No A/C 20-25 Houston 10 0.92 2.41 

No A/C 20-25 Los Angeles 148 1.37 2.28 

No A/C 20-25 Los Angeles Avol 19 0.95 1.87 

No A/C 20-25 Los Angeles RIOPA 38 1.30 2.11 

No A/C 20-25 Los Angeles Wilson 1984 91 1.52 2.40 

No A/C 20-25 New York City 26 1.62 2.24 

No A/C 20-25 New York City RIOPA 19 1.50 2.30 

No A/C 20-25 New York City TEACH 7 1.99 2.11 

No A/C 20-25 Red Bluff 1 0.55 

No A/C > 25 Houston 2 0.92 3.96 

No A/C > 25 Los Angeles 25 0.99 1.97 

No A/C > 25 Los Angeles Avol 6 1.56 1.36 

No A/C > 25 Los Angeles RIOPA 4 1.33 1.37 

No A/C > 25 Los Angeles TEACH 3 0.86 1.02 

No A/C > 25 Los Angeles Wilson 1984 12 0.74 2.29 

No A/C > 25 New York City 6 1.54 1.65 

No A/C > 25 New York City RIOPA 3 1.73 2.00 

No A/C > 25 New York City TEACH 3 1.37 1.38 

* For a given city, if AER data were available from only one study, then the study name is missing. If AER data were available 

for two or more studies, then the overall city distribution is shown in the row where the study name is missing, and the 

distributions by study and city are shown in the rows with a specific study name. 

** The geometric standard deviation is undefined if the sample size equals 1.

In general, there is a relatively wide variation across different cities. This implies that the AER 

modeling results would be very different if the matching of modeled cities to study cities was 

changed, although a sensitivity study using the APEX model would be needed to assess the 

impact on the ozone exposure estimates. In particular the ozone exposure estimates may be 

sensitive to the assumption that the St. Louis AER distributions can be represented by the 

combined non-California AER data. One way to address this is to perform a Monte Carlo 
D-7

analysis where the first stage is to randomly select a city outside of California, the second stage 

picks the A/C type, and the third stage picks the AER value from the assigned distribution for the 

city, A/C type and temperature range. Note that this will result in a very different distribution to 

the current approach that fits a single log-normal distribution to all the non-California data for a 

given temperature range and A/C type. The current approach weights each data point equally, so 

that cities like New York with most of the data values get the greatest statistical weight. The 

Monte Carlo approach gives the same total statistical weight for each city and fits a mixture of 

log-normal distributions rather than a single distribution. 

In general, there is also some variation within studies for the same city, but this is much smaller 

than the variation across cities. This finding tends to support the approach of combining different 

studies. Note that the graphs can be deceptive in this regard because some of the data points are 

based on very small sample sizes (N) ; those data points are less precise and the differences 

would not be statistically significant. For example, for the No A/C data in the range 10-20 oC, 

the Los Angeles TEACH study had a geometric mean of 2.32 based on only nine AER values, 

but the overall geometric mean, based on 390 values, was 0.75 and the geometric means for the 

Los Angeles Avol, RIOPA, Wilson 1984, and Wilson 1991 studies were each close to 0.75. One 

noticeable case where the studies show big differences for the same city is for the A/C houses in 

Los Angeles in the range 20-25 oC where the study geometric means are 0.61 (Avol, N=32), 0.90 

(RIOPA, N=26) and 1.23 (Wilson 1984, N=215). 

Bootstrap analyses

The 39 AER subsets defined in the Cohen, Mallya, and Rosenbaum, 2005 memorandum 

(Appendix A of this report) and their allocation to the 12 modeled cities are shown in Table D-3. 

To make the distributions sufficiently precise in each AER subset and still capture the variation 

across temperature and A/C type, different modeled cities were assigned different temperature 

range and A/C type groupings. Therefore these temperature range groupings are sometimes 

different to those used to develop Table D-2 and Figure D-1 through D-8. 

Table D-3. AER subsets by city, A/C type, and temperature range. 

Subset City 

Name 

Study Cities Represents 

Modeled Cities: 

A/C Type Temperature 

Range (oC) 

Houston Houston Houston, TX Central or Room A/C <=20 

Houston Houston Houston, TX Central or Room A/C 20-25 

Houston Houston Houston, TX Central or Room A/C 25-30 

Houston Houston Houston, TX Central or Room A/C >30 

Houston Houston Houston, TX No A/C <=10 

Houston Houston Houston, TX No A/C 10-20 

 Houston Houston, TX No A/C >20 

Inland California Sacramento, Riverside, 

and San Bernardino 

counties, CA 

Sacramento, CA Central or Room A/C <=25 

Inland California Sacramento, Riverside, 

and San Bernardino 

counties, CA 

Sacramento, CA Central or Room A/C >25 

Inland California Sacramento, Riverside, 

and San Bernardino 

counties, CA 

Sacramento, CA No A/C <=10 
D-8

Table D-3. AER subsets by city, A/C type, and temperature range. 

Subset City 

Name 

Study Cities Represents 

Modeled Cities: 

A/C Type Temperature 

Range (oC) 

Inland California Sacramento, Riverside, 

and San Bernardino 

counties, CA 

Sacramento, CA No A/C 10-20 

Inland California Sacramento, Riverside, 

and San Bernardino 

counties, CA 

Sacramento, CA No A/C 20-25 

Inland California Sacramento, Riverside, 

and San Bernardino 

counties, CA 

Sacramento, CA No A/C >25 

Los Angeles Los Angeles, Orange, 

Riverside, San 

Bernardino, and 

Ventura counties, CA 

Los Angeles, CA Central or Room A/C <=20 

Los Angeles Los Angeles, Orange, 

Riverside, San 

Bernardino, and 

Ventura counties, CA 

Los Angeles, CA Central or Room A/C 20-25 

Los Angeles Los Angeles, Orange, 

Riverside, San 

Bernardino, and 

Ventura counties, CA 

Los Angeles, CA Central or Room A/C 25-30 

Los Angeles Los Angeles, Orange, 

Riverside, San 

Bernardino, and 

Ventura counties, CA 

Los Angeles, CA Central or Room A/C >30 

Los Angeles Los Angeles, Orange, 

Riverside, San 

Bernardino, and 

Ventura counties, CA 

Los Angeles, CA No A/C <=10 

Los Angeles Los Angeles, Orange, 

Riverside, San 

Bernardino, and 

Ventura counties, CA 

Los Angeles, CA No A/C 10-20 

Los Angeles Los Angeles, Orange, 

Riverside, San 

Bernardino, and 

Ventura counties, CA 

Los Angeles, CA No A/C 20-25 

Los Angeles Los Angeles, Orange, 

Riverside, San 

Bernardino, and 

Ventura counties, CA 

Los Angeles, CA No A/C >25 

New York City New York, NY Boston, MA, 

Chicago, IL, 

Cleveland, OH, 

Detroit, MI, 

New York, NY, 

Philadelphia, PA 

Central or Room A/C <=10 

New York City New York, NY Boston, MA, 

Chicago, IL, 

Cleveland, OH, 

Detroit, MI, 

New York, NY, 

Philadelphia, PA 

Central or Room A/C 10-25 

New York City New York, NY Boston, MA, 

Chicago, IL, 

Cleveland, OH, 

Detroit, MI, 

Central or Room A/C >25 
D-9

Table D-3. AER subsets by city, A/C type, and temperature range. 

Subset City 

Name 

Study Cities Represents 

Modeled Cities: 

A/C Type Temperature 

Range (oC) 

New York, NY, 

Philadelphia, PA 

New York City New York, NY Boston, MA, 

Chicago, IL, 

Cleveland, OH, 

Detroit, MI, 

New York, NY, 

Philadelphia, PA 

No A/C <=10 

New York City New York, NY Boston, MA, 

Chicago, IL, 

Cleveland, OH, 

Detroit, MI, 

New York, NY, 

Philadelphia, PA 

No A/C 10-20 

New York City New York, NY Boston, MA, 

Chicago, IL, 

Cleveland, OH, 

Detroit, MI, 

New York, NY, 

Philadelphia, PA 

No A/C >20 

Outside California Cities outside CA St. Louis, MO Central or Room A/C <=10 

Outside California Cities outside CA St. Louis, MO Central or Room A/C 10-20 

Outside California Cities outside CA St. Louis, MO Central or Room A/C 20-25 

Outside California Cities outside CA St. Louis, MO Central or Room A/C 25-30 

Outside California Cities outside CA St. Louis, MO Central or Room A/C >30 

Outside California Cities outside CA St. Louis, MO 

Atlanta, GA 

Washington DC 

No A/C <=10 

Outside California Cities outside CA St. Louis, MO 

Atlanta, GA 

Washington DC 

No A/C 10-20 

Outside California Cities outside CA St. Louis, MO 

Atlanta, GA 

Washington DC 

No A/C >20 

Research Triangle Park Research Triangle 

Park, NC 

Atlanta, GA 

Washington DC 

Central or Room A/C <=10 

Research Triangle Park Research Triangle 

Park, NC 

Atlanta, GA 

Washington DC 

Central or Room A/C 10-20 

Research Triangle Park Research Triangle 

Park, NC 

Atlanta, GA 

Washington DC 

Central or Room A/C 20-25 

Research Triangle Park Research Triangle 

Park, NC 

Atlanta, GA 

Washington DC 

Central or Room A/C >25 

The GM and GSD values that define the fitted log-normal distributions for these 39 AER subsets 

are shown in Table D-4. Examples of these pairs are also plotted in Figures D-9 through D-19, to 

be further described below. Each of the example figures D-9 through D-19 corresponds to a 

single GM/GSD “Original Data” pair. The GM and GSD values for the “Original Data” are at 

the intersection of the horizontal and vertical lines that are parallel to the x- and y-axes in the 

figures. 
D-10

Table D-4. Geometric means and standard deviations for AER subsets by city, A/C type, 

and temperature range. 

Subset City 

Name A/C Type Temperature Range (oC) N Geometric Mean 

Geometric 

Standard 

Deviation 

Houston Central or Room 

A/C <=20 15 0.4075 2.1135 

Houston Central or Room 

A/C 20-25 20 0.4675 1.9381 

Houston Central or Room 

A/C 25-30 65 0.4221 2.2579 

Houston Central or Room 

A/C >30 14 0.4989 1.7174 

Houston No A/C <=10 13 0.6557 1.6794 

Houston No A/C 10-20 28 0.6254 2.9162 

 No A/C >20 12 0.9161 2.4512 

Inland California Central or Room 

A/C <=25 226 0.5033 1.9210 

Inland California Central or Room 

A/C >25 83 0.8299 2.3534 

Inland California No A/C <=10 17 0.5256 3.1920 

Inland California No A/C 10-20 52 0.6649 2.1743 

Inland California No A/C 20-25 13 1.0536 1.7110 

Inland California No A/C >25 14 0.8271 2.2646 

Los Angeles Central or Room 

A/C <=20 721 0.5894 1.8948 

Los Angeles Central or Room 

A/C 20-25 273 1.1003 2.3648 

Los Angeles Central or Room 

A/C 25-30 102 0.8128 2.4151 

Los Angeles Central or Room 

A/C >30 12 0.2664 2.7899 

Los Angeles No A/C <=10 18 0.5427 3.0872 

Los Angeles No A/C 10-20 390 0.7470 2.0852 

Los Angeles No A/C 20-25 148 1.3718 2.2828 

Los Angeles No A/C >25 25 0.9884 1.9666 

New York City Central or Room 

A/C <=10 20 0.7108 2.0184 

New York City Central or Room 

A/C 10-25 42 1.1392 2.6773 

New York City Central or Room 

A/C >25 19 1.2435 2.1768 

New York City No A/C <=10 48 1.0165 2.1382 

New York City No A/C 10-20 59 0.7909 2.0417 

New York City No A/C >20 32 1.6062 2.1189 

Outside California Central or Room 

A/C <=10 179 0.9185 1.8589 

Outside California Central or Room 

A/C 10-20 338 0.5636 1.9396 

Outside California Central or Room 

A/C 20-25 253 0.4676 2.2011 

Outside California Central or Room 

A/C 25-30 219 0.4235 2.0373 
D-11

Table D-4. Geometric means and standard deviations for AER subsets by city, A/C type, 

and temperature range. 

Subset City 

Name A/C Type Temperature Range (oC) N Geometric Mean 

Geometric 

Standard 

Deviation 

Outside California Central or Room 

A/C >30 24 0.5667 1.9447 

Outside California No A/C <=10 61 0.9258 2.0836 

Outside California No A/C 10-20 87 0.7333 2.3299 

Outside California No A/C >20 44 1.3782 2.2757 

Research Triangle 

Park 

Central or Room 

A/C <=10 157 0.9617 1.8094 

Research Triangle 

Park 

Central or Room 

A/C 10-20 320 0.5624 1.9058 

Research Triangle 

Park 

Central or Room 

A/C 20-25 196 0.3970 1.8887 

Research Triangle 

Park 

Central or Room 

A/C >25 145 0.3803 1.7092 

To evaluate the uncertainty of the GM and GSD values, a bootstrap simulation was performed, 

as follows. Suppose that a given AER subset has N values. A bootstrap sample is obtained by 

sampling N times at random with replacement from the N AER values. The first AER value in 

the bootstrap sample is selected randomly from the N values, so that each of the N values is 

equally likely. The second, third, ..., N’th values in the bootstrap sample are also selected 

randomly from the N values, so that for each selection, each of the N values is equally likely. 

The same value can be selected more than once. Using this bootstrap sample, the geometric 

mean and geometric standard deviation of the N values in the bootstrap sample was calculated. 

This pair of values is plotted as one of the points in a figure for that AER subset. 1,000 bootstrap 

samples were randomly generated for each AER subset, producing a set of 1,000 geometric mean 

and geometric standard deviation pairs, which were plotted in example Figures D-9 through D19. 

The bootstrap distributions display the part of the uncertainty of the GM and GSD that is entirely 

due to random sampling variation. The analysis is based on the assumption that the study AER 

data are a random sample from the population distribution of AER values for the given city, 

temperature range, and A/C type. On that basis, the 1,000 bootstrap GM and GSD pairs estimate 

the variation of the GM and GSD across all possible samples of N values from the population. 

Since each GM, GSD pair uniquely defines a fitted log-normal distribution, the pairs also 

estimate the uncertainty of the fitted log-normal distribution. The choice of 1,000 was made as a 

compromise between having enough pairs to accurately estimate the GM, GSD distribution and 

not having too many pairs so that the graph appears as a smudge of overlapped points. Note that 

even if there were infinitely many bootstrap pairs, the uncertainty distribution would still be an 

estimate of the true uncertainty because the N is finite, so that the empirical distribution of the N 

measured AER values does not equal the unknown population distribution. 

In most cases the uncertainty distribution appears to be a roughly circular or elliptical geometric 

mean and standard deviation region. The size of the region depends upon the sample size and on 

the variability of the AER values; the region will be smallest when the sample size N is large 
D-12

and/or the variability is small, so that there are a large number of values that are all close 

together. 

The bootstrap analyses show that the geometric standard deviation uncertainty for a given 

CSA/air-conditioning-status/temperature-range combination tends to have a range of at most 

from “fitted GSD-1.0 hr-1” to “fitted GSD+1.0 hr-1”, but the intervals based on larger AER 

sample sizes are frequently much narrower. The ranges for the geometric means tend to be 

approximately from “fitted GM-0.5 hr-1” to “fitted GM+0.5 hr-1”, but in some cases were much 

smaller. 

The bootstrap analysis only evaluates the uncertainty due to the random sampling. It does not 

account for the uncertainty due to the lack of representativeness, which in turn is due to the fact 

that the samples were not always random samples from the entire population of residences in a 

city, and were sometimes used to represent different cities. Since only the GM and GSD were 

used, the bootstrap analyses does not account for uncertainties about the true distributional 

shape, which may not necessarily be log-normal. Furthermore, the bootstrap uncertainty does not 

account for the effect of the calendar year (possible trends in AER values) or of the uncertainty 

due to the AER measurement period; the distributions were intended to represent distributions of 

24 hour average AER values although the study AER data were measured over a variety of 

measurement periods. 

To use the bootstrap distributions to estimate the impact of sample size on the fitted distributions, 

a Monte Carlo approach could be used with the APEX model. Instead of using the Original Data 

distributions, a bootstrap GM, GSD pair could be selected at random and the AER value could be 

selected randomly from the log-normal distribution with the bootstrap GM and GSD. 
Figure D-1 
D-14 

Figure D-2 
D-15 

Figure D-3 
D-16 

Figure D-4 
D-17 

Figure D-5 
D-18 

Figure D-6 
D-19 

Figure D-7 
D-20 

Figure D-8 
D-21 

Figure D-9 
D-22 

Figure D-10 
D-23 

Figure D-11 
D-24 

Figure D-12 
D-25 

Figure D-13 
D-26 

Figure D-14 
D-27 

Figure D-15 
D-28 

Figure D-16 
D-29 

Figure D-17 
D-30 

Figure D-18 
D-31
D-32

Figure D-19 

APPENDIX E. DISTRIBUTIONS OF AIR EXCHANGE RATE AVERAGES OVER 

MULTIPLE DAYS 
This page intentionally left blank. 
E-1 

MEMORANDUM 

To: John Langstaff, EPA OAQPS 

From: Jonathan Cohen, Arlene Rosenbaum, ICF International 

Date: June 8, 2006 

Re: Distributions of air exchange rate averages over multiple days 

As detailed in the memorandum by Cohen, Mallya and Rosenbaum, 20059 (Appendix A of this 

report) we have proposed to use the APEX model to simulate the residential air exchange rate 

(AER) using different log-normal distributions for each combination of outside temperature 

range and the air conditioner type, defined as the presence or absence of an air conditioner 

(central or room). 

Although the averaging periods for the air exchange rates in the study databases varied from one 

day to seven days, our analyses did not take the measurement duration into account and treated 

the data as if they were a set of statistically independent daily averages. In this memorandum we 

present some analyses of the Research Triangle Park Panel Study that show extremely strong 

correlations between consecutive 24-hour air exchange rates measured at the same house. This 

provides support for the simplified approach of treating all averaging periods as if they were 24-

hour averages. 

In the current version of the APEX model, there are several options for stratification of time 

periods with respect to AER distributions, and for when to re-sample from a distribution for a 

given stratum. The options selected for this current set of simulations resulted in a uniform AER 

for each 24-hour period and re-sampling of the 24-hour AER for each simulated day. This resampling for each simulated day implies that the simulated AERs on consecutive days in the 

same microenvironment are statistically independent. Although we have not identified sufficient 

data to test the assumption of uniform AERs throughout a 24-hour period, the analyses described 

in this memorandum suggest that AERs on consecutive days are highly correlated. Therefore, we 

performed sensitivity simulations to assess the impact of the assumption of temporally 

independent air exchange rates, but found little difference between APEX predictions for the two 

scenarios (i.e., temporally independent and autocorrelated air exchange rates). 

 

9

 Cohen, J., H. Mallya, and A. Rosenbaum. 2005. Memorandum to John Langstaff. EPA 68D01052, Work 

Assignment 3-08. Analysis of Air Exchange Rate Data. September 30, 2005. 
E-2 

Distributions of multi-day averages from the RTP Panel Study

The RTP Panel study included measurements of 24-hour averages at 38 residences for up to four 

periods of at least seven days. These periods were in different seasons and/or calendar years. 

Daily outside temperatures were also provided. All the residences had either window or room air 

conditioners or both. We used these data to compare the distributions of daily averages taken 

over 1, 2, 3, .. 7 days. 

The analysis is made more complicated because the previous analyses showed the dependence of 

the air exchange rate on the outside temperature, and the daily temperatures often varied 

considerably. Two alternative approaches were employed to group consecutive days. For the first 

approach, A, we sorted the data by the HOUSE_ID number and date and began a new group of 

days for each new HOUSE_ID and whenever the sorted measurement days on the same 

HOUSE_ID were 30 days or more apart. In most cases, a home was measured over four different 

seasons for seven days, potentially giving 38 × 4 = 152 groups; the actual number of groups was 

124. For the second approach, B, we again sorted the data by the HOUSE_ID number and date, 

but this time we began a new group of days for each new HOUSE_ID and whenever the sorted 

measurement days on the same HOUSE_ID were 30 days or more apart or were for different 

temperature ranges. We used the same four temperature ranges chosen for the analysis in the 

Cohen, Mallya, and Rosenbaum, 2005, memorandum (Appendix A): <= 10, 10-20, 20-25, and > 

25 oC. For example, if the first week of measurements on a given HOUSE_ID had the first three 

days in the <= 10 oC range, the next day in the 10-20 oC range, and the last three days in the <= 

10 oC range, then the first approach would treat this as a single group of days. The second 

approach would treat this as three groups of days, i.e., the first three days, the fourth day, and the 

last three days. Using the first approach, the days in each group can be in different temperature 

ranges. Using the second approach, every day in a group is in the same temperature range. Using 

the first approach we treat groups of days as being independent following a transition to a 

different house or season. Using the second approach we treat groups of days as being 

independent following a transition to a different house or season or temperature range. 

To evaluate the distributions of multi-day air exchange rate (AER) averages, we averaged the 

AERs over consecutive days in each group. To obtain a set of one-day averages, we took the 

AERs for the first day of each group. To obtain a set of two-day averages, we took the average 

AER over the first two days from each group. We continued this process to obtain three-, four-, 

five-, six-, and seven-day averages. There were insufficiently representative data for averaging 

periods longer then seven days. Averages over non-consecutive days were excluded. Each 

averaging period was assigned the temperature range using the average of the daily temperatures 

for the averaging period. Using Approach A, some or all of the days in the averaging period 

might be in different temperature ranges than the overall average. . Using Approach B, every day 

is in the same temperature range as the overall average. For each averaging period and 

temperature range, we calculated the mean, standard deviation, and variance of the period 

average AER and of its natural logarithm. Note than the geometric mean equals e raised to the 

power Mean log (AER) and the geometric standard deviation equals e raised to the power Std 

Dev log (AER). The results are shown in Tables E-1 (Approach A) and E-2 (Approach B). 
E-3 

Table E-1. Distribution of AER averaged over K days and its logarithm. Groups defined by Approach A. 

Temperature 

(oC) K Groups 

Mean 

AER 

Mean 

log(AER) 

Std 

Dev 

AER 

Std Dev 

log(AER) 

Variance 

AER 

Variance 

log(AER) 

<= 10 1 35 1.109 -0.066 0.741 0.568 0.549 0.322 

<= 10 2 30 1.149 -0.009 0.689 0.542 0.474 0.294 

<= 10 3 28 1.065 -0.088 0.663 0.546 0.440 0.298 

<= 10 4 28 1.081 -0.090 0.690 0.584 0.476 0.341 

<= 10 5 24 1.103 -0.082 0.754 0.598 0.568 0.358 

<= 10 6 24 1.098 -0.083 0.753 0.589 0.567 0.347 

<= 10 7 29 1.054 -0.109 0.704 0.556 0.496 0.309 

10-20 1 48 0.652 -0.659 0.417 0.791 0.174 0.625 

10-20 2 55 0.654 -0.598 0.411 0.607 0.169 0.368 

10-20 3 51 0.641 -0.622 0.416 0.603 0.173 0.363 

10-20 4 50 0.683 -0.564 0.440 0.619 0.194 0.384 

10-20 5 53 0.686 -0.546 0.419 0.596 0.175 0.355 

10-20 6 49 0.677 -0.533 0.379 0.544 0.144 0.296 

10-20 7 34 0.638 -0.593 0.343 0.555 0.118 0.308 

20-25 1 32 0.500 -1.005 0.528 0.760 0.279 0.577 

20-25 2 28 0.484 -0.972 0.509 0.623 0.259 0.388 

20-25 3 27 0.495 -0.933 0.491 0.604 0.241 0.365 

20-25 4 17 0.536 -0.905 0.623 0.652 0.389 0.425 

20-25 5 17 0.543 -0.905 0.672 0.649 0.452 0.421 

20-25 6 17 0.529 -0.899 0.608 0.617 0.370 0.381 

20-25 7 14 0.571 -0.889 0.745 0.683 0.555 0.466 

> 25 1 9 0.470 -1.058 0.423 0.857 0.179 0.734 

> 25 2 11 0.412 -1.123 0.314 0.742 0.098 0.551 

> 25 3 12 0.411 -1.036 0.243 0.582 0.059 0.339 

> 25 4 23 0.385 -1.044 0.176 0.429 0.031 0.184 

> 25 5 23 0.390 -1.028 0.175 0.425 0.031 0.181 

> 25 6 23 0.399 -1.010 0.193 0.435 0.037 0.189 

> 25 7 17 0.438 -0.950 0.248 0.506 0.061 0.256 

Using both approaches, Tables E-1 and E-2 show that the mean values for the AER and its 

logarithm are approximately constant for the same temperature range but different averaging 

periods. This is expected if the daily AER values all have the same statistical distribution, 

regardless of whether or not they are independent. More interesting is the observation that the 

standard deviations and variances are also approximately constant for the same temperature 

range but different averaging periods, except for the data at > 25 oC where the standard 

deviations and variances tend to decrease as the length of the averaging period increases. If the 

daily AER values were statistically independent, then the variance of an average over K days is 

given by Var / K, where Var is the variance of a single daily AER value. Clearly this formula 

does not apply. Since the variance is approximately constant for different values of K in the same 

temperature range (except for the relatively limited data at > 25 oC), this shows that the daily 

AER values are strongly correlated. Of course the correlation is not perfect, since otherwise the 

AER for a given day would be identical to the AER for the next day, if the temperature range 

were the same, which did not occur. 
E-4 

Table E-2. Distribution of AER averaged over K days and its logarithm. Groups defined by Approach B. 

Temperature 

(oC) K Groups 

Mean 

AER 

Mean 

log(AER) 

Std 

Dev 

AER 

Std Dev 

log(AER) 

Variance 

AER 

Variance 

log(AER) 

<= 10 1 62 1.125 -0.081 0.832 0.610 0.692 0.372 

<= 10 2 41 1.059 -0.063 0.595 0.481 0.355 0.231 

<= 10 3 32 1.104 -0.040 0.643 0.530 0.413 0.281 

<= 10 4 17 1.292 0.115 0.768 0.531 0.590 0.282 

<= 10 5 5 1.534 0.264 1.087 0.608 1.182 0.370 

10-20 1 109 0.778 -0.482 0.579 0.721 0.336 0.520 

10-20 2 81 0.702 -0.532 0.451 0.603 0.204 0.363 

10-20 3 63 0.684 -0.540 0.409 0.580 0.167 0.336 

10-20 4 27 0.650 -0.626 0.414 0.663 0.171 0.440 

10-20 5 22 0.629 -0.660 0.417 0.654 0.174 0.428 

10-20 6 12 0.614 -0.679 0.418 0.638 0.175 0.407 

10-20 7 6 0.720 -0.587 0.529 0.816 0.280 0.667 

20-25 1 107 0.514 -0.915 0.518 0.639 0.269 0.409 

20-25 2 63 0.511 -0.930 0.584 0.603 0.341 0.364 

20-25 3 23 0.577 -0.837 0.641 0.659 0.411 0.434 

20-25 4 3 1.308 -0.484 1.810 1.479 3.277 2.187 

> 25 1 54 0.488 -0.949 0.448 0.626 0.201 0.392 

> 25 2 32 0.486 -0.900 0.351 0.595 0.123 0.354 

> 25 3 23 0.427 -0.970 0.218 0.506 0.048 0.256 

> 25 4 12 0.401 -1.029 0.207 0.509 0.043 0.259 

> 25 5 12 0.410 -1.003 0.207 0.507 0.043 0.257 

> 25 6 6 0.341 -1.164 0.129 0.510 0.017 0.261 

> 25 7 6 0.346 -1.144 0.125 0.494 0.016 0.244 

These arguments suggest that, based on the RTP Panel study data, to a reasonable 

approximation, the distribution of an AER measurement does not depend upon the length of the 

averaging period for the measurement, although it does depend upon the average temperature. 

This supports the methodology used in the Cohen, Mallya, and Rosenbaum, 2005, analyses that 

did not take into account the length of the averaging period. 

The above argument suggests that the assumption that daily AER values are statistically 

independent is not justified. Statistical modeling of the correlation structure between consecutive 

daily AER values is not easy because of the problem of accounting for temperature effects, since 

temperatures vary from day to day. In the next section we present some statistical models of the 

daily AER values from the RTP Panel Study. 

Statistical models of AER auto-correlations from the RTP Panel Study

 

We used the MIXED procedure from SAS to fit several mixed models with fixed effects and 

random effects to the daily values of AER and log(AER). The fixed effects are the population 
E-5 

average values of AER or log(AER), and are assumed to depend upon the temperature range. 

The random effects have expected values of zero and define the correlations between pairs of 

measurements from the same Group, where the Groups are defined either using Approach A or 

Approach B above. As described above, a Group is a period of up to 14 consecutive days of 

measurements at the same house. For these mixed model analyses we included periods with one 

or more missing days. For all the statistical models, we assume that AER values in different 

Groups are statistically independent, which implies that data from different houses or in different 

seasons are independent. 

The main statistical model for AER was defined as follows: 

AER = Mean(Temp Range) + A(Group, Temp Range) 

 + B(Group, Day Number) + Error(Group, Day Number) 

Mean(Temp Range) is the fixed effects term. There is a different overall mean value for each of 

the four temperature ranges. 

A(Group, Temp Range) is the random effect of temperature. For each Group, four error terms are 

independently drawn from four different normal distributions, one for each temperature range. 

These normal distributions all have mean zero, but may have different variances. Because of this 

term, there is a correlation between AER values measured in the same Group of days for a pair 

of days in the same temperature range. 

B(Group, Day Number) is the repeated effects term. The day number is defined so that the first 

day of a Group has day number 1, the next calendar day has day number 2, and so on. In some 

cases AER’s were missing for some of the day numbers. B(Group, Day Number) is a normally 

distributed error term for each AER measurement. The expected value (i.e., the mean) is zero. 

The variance is V. The covariance between B(Group g, day i) and B(Group h, day j) is zero for 

days in different Groups g and h, and equals V × exp(d × |i-j|) for days in the same Group. V and 

d are fitted parameters. This is a first order auto-regressive model. Because of this term, there is a 

correlation between AER values measured in the same Group of days, and the correlation 

decreases if the days are further apart. 

Finally, Error(Group, Day Number) is the Residual Error term. There is one such error term for 

every AER measurement, and all these terms are independently drawn from the same normal 

distribution, with mean 0 and variance W. 

We can summarize this rather complicated model as follows. The AER measurements are 

uncorrelated if they are from different Groups. If they are in the same Group, they have a 

correlation that decreases with the day difference, and they have an additional correlation if they 

are in the same temperature range. 

Probably the most interesting parameter for these models is the parameter d, which defines the 

strength of the auto-correlation between pairs of days. This parameter d lies between -1 (perfect 

negative correlation) and +1 (perfect positive correlation) although values exactly equal to +1 or 

-1 are impossible for a stationary model. Negative values of d would be unusual since they 
E-6 

would imply a tendency for a high AER day to be followed by a low AER day, and vice versa. 

The case d=0 is for no auto-correlation. 

Table E-3 gives the fitted values of d for various versions of the model. The variants considered 

were: 

• model AER or log(AER) 

• include or exclude the term A(Group, Temp Range) (the “random” statement in the SAS 

code) 

• use Approach A or Approach B to define the Groups 

Since Approach B forces the temperature ranges to be the same for very day in a Group, the 

random temperature effect term is difficult to distinguish from the other terms. Therefore this 

term was not fitted using Approach B. 

Table E-3. Autoregressive parameter d for various statistical models for the RTP Panel 

Study AERs. 

Dependent variable Include A(Group, 

Temp Range)? Approach d 

AER Yes A 0.80 

AER No A 0.82 

AER No B 0.80 

Log(AER) Yes A 0.87 

Log(AER) No A 0.87 

Log(AER) No B 0.85 

 

In all cases, the parameter d is 0.8 or above, showing the very strong correlations between AER 

measurements on consecutive or almost consecutive days. 

Impact of accounting for daily average AER auto-correlation 

In the current version of the APEX model, there are several options for stratification of time 

periods with respect to AER distributions, and for when to re-sample from a distribution for a 

given stratum. The options selected for this current set of simulations resulted in a uniform AER 

for each 24-hour period and re-sampling of the 24-hour AER for each simulated day. This resampling for each simulated day implies that the simulated AERs on consecutive days in the 

same microenvironment are statistically independent. Although we have not identified sufficient 

data to test the assumption of uniform AERs throughout a 24-hour period, the analyses described 

in this memorandum suggest that AERs on consecutive days are highly correlated. 

Therefore, in order to determine if bias was introduced into the APEX estimates with respect to 

either the magnitudes or variability of exposure concentrations by implicitly assuming 

uncorrelated air exchange rates, we re-ran the 2002 base case simulations using the option to not 

re-sample the AERs. For this option APEX selects a single AER for each 

microenvironment/stratum combination and uses it throughout the simulation. 
E-7 

The comparison of the two scenarios indicates little difference in APEX predictions, probably 

because the AERs pertain only to indoor microenvironments and for the base cases most 

exposure to elevated concentrations occurs in the “other outdoors” microenvironment. Figures E1 and E-2 below present the comparison for exceedances of 8-hour average concentration during 

moderate exertion for active person in Boston and Houston, respectively.

Figure E-1 

Air Exchange Rate Resampling Sensitivity:

Days/Person with Exceedances of 

 8-Hour Average Exposure Concentration During Moderate Exertion

--Active Persons, Boston, 2002--

0

50

100

150

200

0 20 40 60 80 100

Cumulative Percentile

Days/Person

base-.01

rsoff - .01

base - .02

rsoff - .02

base -.03

rsoff - .03

base - .04

rsoff - .04

base - .05

rsoff - .05

Figure E-2 

Air Exchange Rate Resampling Sensitivity:

Days/Person with Exceedances of 

 8-Hour Average Exposure Concentration During Moderate Exertion

--Active Persons, Houston, 2002--

0

50

100

150

200

250

300

350

0 20 40 60 80 100

Cumulative Percentile

Days/Person

base-.01

rsoff - .01

base - .02

rsoff - .02

base -.03

rsoff - .03

base - .04

rsoff - .04

base - .05

rsoff - .05
E-8 
APPENDIX F. PREVALENCE OF RESIDENTIAL AIR CONDITIONERS AND THE 

EFFECTS OF SWAMP COOLERS 
This page intentionally left blank. 
F-1 

MEMORANDUM 

To: John Langstaff, EPA OAQPS 

From: Jonathan Cohen, Arlene Rosenbaum, ICF International 

Date: June 6, 2006 

Re: Prevalence of residential air conditioners and the effects of swamp coolers 

This memorandum describes our analysis of the prevalence of air conditioners in the 12 cities 

being modeled using the APEX. As detailed in the memorandum by Cohen, Mallya and 

Rosenbaum, 200510 (Appendix A of this report) we have proposed to use the APEX model to 

simulate the residential air exchange rate (AER) using different log-normal distributions for each 

combination of outside temperature range and the air conditioner type, defined as the presence or 

absence of an air conditioner (central or room). For each modeled city, the presence or absence 

of an air conditioner is simulated randomly using the probability that a residence has an air 

conditioner, which is the air conditioner prevalence. Our proposed approach used city-specific 

data from the American Housing Survey of 2003. In this memorandum we present uncertainty 

estimates in the form of confidence intervals for the air conditioner prevalence. We compare 

these with confidence intervals developed from the Energy Information Administration’s 

Residential Energy Consumption Survey of 2001. 

Some residences use evaporative coolers, also known as “swamp” coolers, for cooling. Although 

both the housing surveys specifically exclude swamp coolers from their definitions of an air 

conditioner, it is plausible that the AER distributions might also depend upon the presence of a 

swamp cooler. To evaluate this issue, we also present a comparison of the AER distributions 

with and without swamp coolers using the available data from three of the AER studies. 

American Housing Survey air conditioner prevalence 

Data from the American Housing Survey for 2003, a continuous Census Bureau survey of 

selected cities, (http://www.census.gov/hhes/www/housing/ahs/ahs.html) was used to estimate 

the air conditioner prevalence in the memorandum by Cohen, Mallya, and Rosenbaum, 2005 

(Appendix A of this report). The survey questions ask whether the housing unit has central and 

room air conditioners, central air conditioners only, room air conditioners only, or no air 

conditioners. The following definition was used to define air conditioning. Note that evaporative 

or “swamp” coolers are specifically excluded. 

 

10 Cohen, J., H. Mallya, and A. Rosenbaum. 2005. Memorandum to John Langstaff. EPA 68D01052, 

Work Assignment 3-08. Analysis of Air Exchange Rate Data. September 30, 2005. 
F-2 

“Air conditioning. Air conditioning is defined as the cooling of air by a refrigeration unit; 

excluded are evaporative coolers, fans, or blowers that are not connected to a 

refrigeration unit. A room air-conditioning unit is an individual air conditioner that is 

installed in a window or an outside wall and generally intended to cool one room, 

although it may sometimes be used to cool several rooms. A central system is a central 

installation that air conditions the entire housing unit or major portions of it. In an 

apartment building, a central system may cool all apartments in the building; each 

apartment may have its own central system; or there may be several systems, each 

providing central air conditioning for a group of apartments. A central installation with 

individual room controls is a central air-conditioning system.11” 

Table F-1 shows the prevalence estimates calculated using the data and survey weights from 

the American Housing Survey, together with 95 % confidence intervals. The confidence 

intervals were computed using the formulas provided in the “Source and Accuracy Statement 

for the 2003 AHS-N Data Chart”

(http://www.census.gov/hhes/www/housing/ahs/03dtchrt/source.html): 

Confidence Interval( ) 1.96 Standard Error ( )

, 3850 1 Standard Error ( )

P P P

N

 P ( P) P

= ± ×

− =

where P is the estimated percentage and N is the estimated total number of housing units. 

Table F-1. Prevalence estimates from the American Housing Survey with 95 % Confidence 

Intervals. 

AHS Survey Percentage 

(A/Cs) 

Housing Units Std 

Error 

Lower 

Bound 

Upper 

Bound 

Atlanta, 2003 97.01 797,687 1.18 94.69 99.33 

Boston, 2003 85.23 1,056,874 2.14 81.03 89.43 

Chicago, 2003 87.09 2,253,540 1.39 84.37 89.81 

Cleveland, 2003 74.64 637,081 3.38 68.01 81.27 

Detroit, 2003 81.41 1,877,178 1.76 77.96 84.86 

Houston, 2003 98.7 1,106,268 0.67 97.39 100.01 

Los Angeles, 2003 55.05 3,296,819 1.70 51.72 58.38 

New York, 2003 81.57 3,575,019 1.27 79.08 84.06 

Philadelphia, 2003 90.61 1,943,492 1.30 88.07 93.15 

Sacramento, 2003 94.63 524,252 1.93 90.84 98.42 

St. Louis, 2003 95.53 592,086 1.67 92.26 98.80 

Washington DC, 2003 96.47 1,305,811 1.00 94.51 98.43 

 

11 Codebook for the American Housing Survey, Public Use File: 1997 and later. Version 1.77. December 

2004. 
F-3 

Residential Energy Consumption Survey air conditioner prevalence 

The Energy Information Administration’s Residential Energy Consumption Survey of 2001 

provides estimates of air conditioner prevalence for four states, nine Census Divisions and four 

Census Regions. Summary data were obtained from the website 

http://www.eia.doe.gov/emeu/recs/recs2001_hc/2001tblhp.html using the “Appliances” tables 

HC5-7b, HC5-9b, HC5-10b, HC5-11b, and HC5-12b. This survey uses the following definition 

of air conditioning (see http://www.eia.doe.gov/glossary/glossary_a.htm): 

“Air conditioning: Cooling and dehumidifying the air in an enclosed space by use of a 

refrigeration unit powered by electricity or natural gas. Note: Fans, blowers, and evaporative 

cooling systems ("swamp coolers") that are not connected to a refrigeration unit are excluded.” 

Note again that evaporative or “swamp” coolers are specifically excluded. 

The relevant data extracted from the “Appliances” tables are presented in Table F-2. The RECS 

summary tables provide separate prevalence estimates for the households that have air 

conditioners and for the households that use their air conditioners. The estimates include the 

small number of households where the fuel for central air-conditioning equipment was 

something other than electricity. 

Table F-2. Prevalence estimates from RECS 2001. 

Area (US, State, Has A/C Uses A/C 

Census Division, 

or Census 

Region) 

Prevalence 

(%) 

Row RSE Factor 

(Has) 

Column RSE Factor 

(Has or Uses) 

Prevalence 

(%) 

Row RSE 

Factor (Uses) 

US 77.5 2.4 0.4 75.5 2.6 

NY 68.6 2.4 1.2 66.5 2.6 

CA 48.3 2.4 1.1 41.8 2.6 

TX 96.7 2.4 1.4 95.9 2.6 

FL 98.0 2.4 1.3 95.7 2.6 

North East 71.6 3.3 1.0 70.2 3.4 

Middle Atlantic 76.4 3.3 1.3 74.5 3.4 

New England 58.4 3.3 1.6 58.4 3.4 

Mid West 83.6 2.2 1.0 82.3 2.3 

East North Central 79.8 2.2 1.2 78.5 2.3 

West North 

Central 

92.4 2.2 1.5 91.1 2.3 

South 95.7 1.4 0.8 94.6 1.6 

South Atlantic 95.0 1.4 1.1 93.7 1.6 

East South Central 94.3 1.4 1.4 93.5 1.6 

West South 

Central 

97.5 1.4 1.5 97.0 1.6 

West 45.7 7.1 1.0 41.0 7.2 
F-4 

Table F-2. Prevalence estimates from RECS 2001. 

Area (US, State, Has A/C Uses A/C 

Census Division, 

or Census 

Region) 

Prevalence 

(%) 

Row RSE Factor 

(Has) 

Column RSE Factor 

(Has or Uses) 

Prevalence 

(%) 

Row RSE 

Factor (Uses) 

Mountain 50.9 7.1 1.7 47.7 7.2 

Pacific 43.6 7.1 1.2 38.3 7.2 

The row and column RSE factors are used to calculate 95 % confidence intervals, as follows: 

Confidence Interval( ) 1.96 Standard Error ( )

Standard Error ( ) RSE /100,

RSE RelativeStandard Error (%) Row RSE Factor Column RSE Factor

P P P

P P

= ± ×

= ×

= = ×

To apply these results, Table F-3 gives the Census Divisions and Regions for the 12 modeled 

cities. These Census groupings are defined as groups of States, together with Washington DC 

included in the South Atlantic Division. 

Table F-3. Census Divisions and Regions for 12 cities. 

City Census Division Census 

Region 

Atlanta South Atlantic South 

Boston New England Northeast 

Chicago East North Central Midwest 

Cleveland East North Central Midwest 

Detroit East North Central Midwest 

Houston West South Central South 

Los Angeles Pacific West 

New York Middle Atlantic Northeast 

Philadelphia Middle Atlantic Northeast 

Sacramento Pacific West 

St. Louis West North Central Midwest 

Washington 

DC 

South Atlantic South 
F-5 

The RECS prevalence estimates and confidence intervals are presented along with the AHS 

estimates in Tables F-4 and F-5. Table F-4 uses the RECS estimates of households owning air 

conditioners. Table F-5 uses the slightly lower RECS estimates of households using air 

conditioners. The agreement depends upon the city. For Boston and Sacramento, the two 

surveys give extremely different results, the AHS estimates being much higher. Good 

agreements between the AHS and RECS confidence intervals is found for Atlanta, Cleveland, 

Detroit, Houston, and Washington DC. Poor agreement (but not as bad as for Boston and 

Sacramento) with the AHS for either the Census Region or Census Division estimates is found 

for Chicago, Los Angeles, New York, Philadelphia, and St. Louis. 

Since the AHS survey results are city-specific and were based on a more recent survey, we 

recommend using the AHS prevalence estimates for the APEX modeling. 

Air conditioner prevalence versus use. 

The approach taken in the Cohen, Mallya, and Rosenbaum, 2005, memorandum (Appendix A of 

this report) was to stratify the data based on the ownership of an air conditioner. It is very 

plausible that the AER is more directly related to the actual use of an air conditioner. The Avol 

and RIOPA studies provided data on the duration of air conditioner use during the AER 

measurement. However, in order to directly include air conditioner usage in the AER 

distributions for the APEX model, it would be necessary to know the residential probability of 

AER usage for each city. The AHS survey did not ask about air conditioner use. The RECS 

survey asked the following question about central air conditioner usage and also asked the 

same question about room or wall air conditioner usage: 

“USECENAC Please look at Exhibit F-6. Which of the statements shown best describes the way your 

household (if before July 1, insert will use; if between July 1 and August 30, insert uses; if after 

August 30, insert used) the central air-conditioning system during the summer of 2001? 

Not used at all ....................................................................... 0 

Turned on only a few days or nights when really needed ..... 1 

Turned on quite a bit ............................................................. 2 

Turned on just about all summer .......................................... 3 

Other ..................................................................................... 5”

It is not clear exactly how these answers was used to define “Air Conditioner Not Used” for the 

summary tables. Furthermore, the RECS data was not city-specific and was an older survey 

than the AHS. 

We do not recommend directly modeling the AER data as a function of air conditioner use 

instead of air conditioner ownership in view of the limited data on the prevalence of air 

conditioner use and the limited AER data where air conditioner use is also recorded. 
Table F-4. AHS and RECS air conditioner prevalence estimates. RECS prevalence for households owning air conditioners.* 

City AHS % AHS Lower AHS Upper Division % Division Lower Division Upper Region % 

Atlanta 97.01 94.69 99.33 95.00 92.13 97.87 95.70 Boston 85.23 81.03 89.43 58.40 52.36 64.44 71.60 Chicago 87.09 84.37 89.81 79.80 75.67 83.93 83.60 Cleveland 74.64 68.01 81.27 79.80 75.67 83.93 83.60 Detroit 81.41 77.96 84.86 79.80 75.67 83.93 83.60 Houston 98.70 97.39 100.01 97.50 93.49 101.51 95.70 Los Angeles 55.05 51.72 58.38 43.60 36.32 50.88 45.70 New York 81.57 79.08 84.06 76.40 69.98 82.82 71.60 Philadelphia 90.61 88.07 93.15 76.40 69.98 82.82 71.60 Sacramento 94.63 90.84 98.42 43.60 36.32 50.88 45.70 St. Louis 95.53 92.26 98.80 92.40 86.42 98.38 83.60 Washington DC 96.47 94.51 98.43 95.00 92.13 97.87 95.70 *AHS % = AHS estimated prevalence. [AHS Lower, AHS Upper] = 95 % confidence interval for AHS prevalence. Di

prevalence based on the Census Division. [Division Lower, Division Upper] = 95 % confidence interval for RECS pr

Division. Region % = RECS estimated prevalence based on the Census Region. [Region Lower, Region Upper] = 9

RECS prevalence based on Census Region. 

Table F-5. AHS and RECS air conditioner prevalence estimates. RECS prevalence for households using air conditioners.* 

City AHS % AHS Lower AHS Upper Division % Division Lower Division Upper Region % 

Atlanta 97.01 94.69 99.33 93.70 90.47 96.93 94.60 Boston 85.23 81.03 89.43 58.40 52.17 64.63 70.20 Chicago 87.09 84.37 89.81 78.50 74.25 82.75 82.30 Cleveland 74.64 68.01 81.27 78.50 74.25 82.75 82.30 Detroit 81.41 77.96 84.86 78.50 74.25 82.75 82.30 Houston 98.70 97.39 100.01 97.00 92.44 101.56 94.60 Los Angeles 55.05 51.72 58.38 38.30 31.81 44.79 41.00 
F-7 

Table F-5. AHS and RECS air conditioner prevalence estimates. RECS prevalence for households using air conditioners.* 

City AHS % AHS Lower AHS Upper Division % Division Lower Division Upper Region % 

New York 81.57 79.08 84.06 74.50 68.05 80.95 70.20 Philadelphia 90.61 88.07 93.15 74.50 68.05 80.95 70.20 Sacramento 94.63 90.84 98.42 38.30 31.81 44.79 41.00 St. Louis 95.53 92.26 98.80 91.10 84.94 97.26 82.30 Washington DC 96.47 94.51 98.43 93.70 90.47 96.93 94.60 *AHS % = AHS estimated prevalence. [AHS Lower, AHS Upper] = 95 % confidence interval for AHS prevalence. Di

prevalence based on the Census Division. [Division Lower, Division Upper] = 95 % confidence interval for RECS pr

Division. Region % = RECS estimated prevalence based on the Census Region. [Region Lower, Region Upper] = 9

RECS prevalence based on Census Region.
F-8 

Evaporative or “Swamp” Coolers

As discussed above, neither the AHS not the RECS provide estimates of the prevalence of 

swamp coolers, which were specifically excluded from the definition of air conditioning. This 

means that an AER model stratified by the presence or absence of swamp coolers is not 

feasible, unless another survey with swamp cooler prevalence estimates becomes available. 

Nevertheless, we used the data from the RIOPA (CA, NJ, and TX), Avol (Southern CA), and 

Wilson 1991 (CA) studies to evaluate the effects of swamp coolers on the AER. The results 

generally showed no statistically significant differences between the AER distributions for 

residences with or without swamp coolers, after stratifying by state, city, study, air conditioner 

type (presence or absence), and temperature range. 

First we calculated summary statistics for the AERs for each combination of State (including 

All), city (including All), study (including All), A/C ownership (presence or absence of a central or 

room air conditioner), temperature range (<= 10. 10-20, 20-30, > 30 oC), and swamp cooler 

ownership. The summary statistics included the average, standard deviation, variance, 

minimum, maximum, and various percentile values. Summary statistics of the natural logarithms 

of the AERs were also calculated. 

Then we compared the distributions with and without swamp coolers. For each stratum, defined 

by a combination of State, city, study, A/C ownership, and temperature range, an F-Statistic was 

calculated to compare the mean values between groups using a one way analysis of variance 

(ANOVA). This test assumes that the AER or log(AER) values are normally distributed with a 

mean that may depend upon swamp cooler ownership and a constant variance.. 

The Kruskal-Wallis Statistics were also computed as a non-parametric test for equal group 

medians. It is equivalent to the more familiar Wilcoxon test, since there are only two groups 

compared (presence or absence of swamp coolers). The analysis is valid if the AER minus the 

group median has the same distribution for each group. (The test is also consistent under 

weaker assumptions against more general alternatives). Since the logarithm is a strictly 

increasing function and the test is non-parametric, the Kruskal-Wallis tests give identical results 

for AER and Log (AER). 

In addition the Mood Statistics were computed as a non-parametric test to the scale statistics for 

each pair of groups. The scale statistic measures variation about the central value, which is a 

non-parametric generalization of the standard deviation. Specifically, suppose there is a total of 

N AER or log(AER) values, summing across both groups. These N values are ranked from 1 to 

N, and the j’th highest value is given a score of {j - (N+1)/2}2

. The Mood statistic uses a one 

way ANOVA statistic to compare the total scores for each group. Since the logarithm is a strictly 

increasing function and the test is non-parametric, the Mood tests give identical results for AER 

and Log (AER). 

For each statistic (i.e., F, Kruskal-Wallis, Mood) a P-value was determined. P-values above 0.05 

indicate cases where the two group means are not statistically significantly different at the 5 

percent level. Most of the p-values were above 0.05, indicating no significant differences. (There 

are a few anomalous significant differences for very small sample sizes when the estimated 

variances are zero). This appears to justify treating a residence with a swamp cooler but no A/C 

the same as a residence without a swamp cooler and no A/C; and treating a residence with a 
F-9 

swamp cooler and with A/C the same as a residence without a swamp cooler but with A/C. In 

other words, this analysis shows that there is no improvement in the statistical AER model if we 

also stratify by swamp cooler presence or absence, given that we already stratify by city, air 

conditioner presence or absence, and temperature range. 
F-10 

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APPENDIX G. ANALYSIS OF NHIS ASTHMA PREVALENCE DATA 
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G-1 

DRAFT MEMORANDUM 

To: John Langstaff 

From: Jonathan Cohen, Arlene Rosenbaum 

Date: September 30, 2005 

Re: EPA 68D01052, Work Assignment 3-08. Analysis of NHIS Asthma Prevalence 

Data 

This memorandum describes our analysis of children’s asthma prevalence data from the National 

Health Interview Survey (NHIS) for 2003. Asthma prevalence rates for children aged 0 to 17 

years were calculated for each age, gender, and region. The regions defined by NHIS are 

“Midwest,” “Northeast,” “South,” and “West.” For this project, asthma prevalence was defined 

as the probability of a Yes response to the question CASHMEV: “Ever been told that ... had 

asthma?” among those that responded Yes or No to this question. The responses were weighted 

to take into account the complex survey design of the NHIS survey. Standard errors and 

confidence intervals for the prevalence were calculated using a logistic model, taking into 

account the survey design. Prevalence curves showing the variation of asthma prevalence 

against age for a given gender and region were plotted. A scatterplot smoothing technique using 

the LOESS smoother was applied to smooth the prevalence curves and compute the standard 

errors and confidence intervals for the smoothed prevalence estimates. Logistic analysis of the 

prevalence curves shows statistically significant differences in prevalence by gender and by 

region. Therefore we did not combine the prevalence rates for different genders or regions. 

Logistic Models

NHIS survey data for 2003 were provided by EPA. One obvious approach to calculate 

prevalence rates and their uncertainties for a given gender, region, and age is to calculate the 

proportion of Yes responses among the Yes and No responses for that demographic group, 

weighting each response by the survey weight. Although that approach was initially used, two 

problems are that the distributions of the estimated prevalence rates are not well approximated by 

normal distributions, and that the estimated confidence intervals based on the normal 

approximation often extend outside the [0, 1] interval. A better approach is to use a logistic 

transformation and fit a model of the form: 

Prob (asthma) = exp(beta) / (1 + exp(beta) ), 
G-2 

where beta may depend on the explanatory variables for age, gender, or region. This is 

equivalent to the model: 

 Beta = logit {prob (asthma) } = log { prob (asthma) / [1 – prob (asthma)] }. 

The distribution of the estimated values of beta is more closely approximated by a normal 

distribution than the distribution of the corresponding estimates of prob (asthma). By applying a 

logit transformation to the confidence intervals for beta, the corresponding confidence intervals 

for prob (asthma) will always be inside [0, 1]. Another advantage of the logistic modeling is that 

it can be used to compare alternative statistical models, such as models where the prevalence 

probability depends upon age, region, and gender, or on age and region but not gender. 

A variety of logistic models for asthma prevalence were fit and compared, where the transformed 

probability variable beta is a given function of age, gender, and region. SAS’s 

SURVEYLOGISTIC procedure was used to fit the logistic models, taking into account the NHIS 

survey weights and survey design (stratification and clustering). 

The following Table G-1 lists the models fitted and their log-likelihood goodness-of-fit 

measures. 16 models were fitted. The Strata column lists the four possible stratifications: no 

stratification, by gender, by region, by region and gender. For example, “4. region, gender” 

means that separate prevalence estimates were made for each combination of region and gender. 

As another example, “2. gender” means that separate prevalence estimates were made for each 

gender, so that for each gender, the prevalence is assumed to be the same for each region. The 

prevalence estimates are independently calculated for each stratum. 

Table G-1. Alternative logistic models for asthma prevalence. 

Model Description Strata - 2 Log Likelihood DF

1 1. logit(prob) = linear in age 1. none 54168194.62 2

2 1. logit(prob) = linear in age 2. gender 53974657.17 4

3 1. logit(prob) = linear in age 3. region 54048602.57 8

4 1. logit(prob) = linear in age 4. region, gender 53837594.97 16

5 2. logit(prob) = quadratic in age 1. none 53958021.20 3

6 2. logit(prob) = quadratic in age 2. gender 53758240.99 6

7 2. logit(prob) = quadratic in age 3. region 53818198.13 12

8 2. logit(prob) = quadratic in age 4. region, gender 53593569.84 24

9 3. logit(prob) = cubic in age 1. none 53849072.76 4

10 3. logit(prob) = cubic in age 2. gender 53639181.24 8

11 3. logit(prob) = cubic in age 3. region 53694710.66 16

12 3. logit(prob) = cubic in age 4. region, gender 53441122.98 32
G-3 

Model Description Strata - 2 Log Likelihood DF

13 4. logit(prob) = f(age) 1. none 53610093.48 18

14 4. logit(prob) = f(age) 2. gender 53226610.02 36

15 4. logit(prob) = f(age) 3. region 53099749.33 72

16 4. logit(prob) = f(age) 4. region, gender 52380000.19 144

The Description column describes how beta depends upon the age: 

 Linear in age: Beta = α + β × age, where α and β vary with the strata. 

Quadratic in age: Beta = α + β × age + γ × age2

 where α β and γ vary with the 

strata. 

Cubic in age: Beta = α + β × age + γ × age2

 + δ × age3 where α β, γ, and δ vary 

with the strata. 

f(age) Beta = arbitrary function of age, with different functions for 

different strata 

The category f(age) is equivalent to making age one of the stratification variables, and is also 

equivalent to making beta a polynomial of degree 16 in age (since the maximum age for children 

is 17), with coefficients that may vary with the strata. 

The fitted models are listed in order of complexity, where the simplest model (1) is an 

unstratified linear model in age and the most complex model (16) has a prevalence that is an 

arbitrary function of age, gender, and region. Model 16 is equivalent to calculating independent 

prevalence estimates for each of the 144 combinations of age, gender, and region. 

Table G-1 also includes the -2 Log Likelihood, a goodness-of-fit measure, and the degrees of 

freedom, DF, which is the total number of estimated parameters. Two models can be compared 

using their -2 Log Likelihood values; lower values are preferred. If the first model is a special 

case of the second model, then the approximate statistical significance of the first model is 

estimated by comparing the difference in the -2 Log Likelihood values with a chi-squared 

random variable with r degrees of freedom, where r is the difference in the DF. This is a 

likelihood ratio test. For all pairs of models from Table G-1, all the differences are at least 

70,000 and the likelihood ratios are all extremely statistically significant at levels well below 5 

percent. Therefore the model 16 is clearly preferred and was used to model the prevalences. 

The SURVEYLOGISTIC model predictions are tabulated in Table G-2 below and plotted in 

Figures 1 and 3 below. Also shown in Table G-2 and in Figures 2 and 4 are results for smoothed 

curves calculated using a LOESS scatterplot smoother, as discussed below. 

The SURVEYLOGISTIC procedure produces estimates of the beta values and their 95 % 

confidence intervals for each combination of age, region, and gender. Applying the inverse logit 

transformation, 

Prob (asthma) = exp( beta) / (1 + exp(beta) ), 
G-4 

converted the beta values and 95 % confidence intervals into predictions and 95 % confidence 

intervals for the prevalence, as shown in Table G-2 and Figures 1 and 3. The standard error for 

the prevalence was estimated as 

Std Error {Prob (asthma)} = Std Error (beta) × exp(- beta) / (1 + exp(beta) )2

, 

which follows from the delta method (a first order Taylor series approximation). 

Loess Smoother

The estimated prevalence curves shows that the prevalence is not a smooth function of age. The 

linear, quadratic, and cubic functions of age modeled by SURVEYLOGISTIC were one strategy 

for smoothing the curves, but they did not provide a good fit to the data. One reason for this 

might be due to the attempt to fit a global regression curve to all the age groups, which means 

that the predictions for age A are affected by data for very different ages. We instead chose to 

use a local regression approach that separately fits a regression curve to each age A and its 

neighboring ages, giving a regression weight of 1 to the age A, and lower weights to the 

neighboring ages using a tri-weight function: 

 Weight = {1 – [ |age – A| / q ] 3

}, where | age – A| <= q. 

The parameter q defines the number of points in the neighborhood of the age a. Instead of calling 

q the smoothing parameter, SAS defines the smoothing parameter as the proportion of points in 

each neighborhood. We fitted a quadratic function of age to each age neighborhood, separately 

for each gender and region combination. We fitted these local regression curves to the beta 

values, the logits of the asthma prevalence estimates, and then converted them back to estimated 

prevalence rates by applying the inverse logit function exp(beta) / (1 + exp(beta) ). In addition to 

the tri-weight variable, each beta value was assigned a weight of 

1 / [std error (beta)]2

, to account for their uncertainties. 

The SAS LOESS procedure was applied to estimate smoothed curves for beta, the logit of the 

prevalence, as a function of age, separately for each region and gender. We fitted curves using 

the choices 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 for the smoothing parameter in an effort to 

determine the optimum choice based on various regression diagnostics.12,13 

 

12 Two outlier cases were adjusted to avoid wild variations in the “smoothed” curves: For the West region, males, 

age 0, there were 97 children surveyed that all gave No answers to the asthma question, leading to an estimated 

value of -15.2029 for beta with a standard error of 0.14. For the Northeast region, females, age 0, there were 29 

children surveyed that all gave No answers to the asthma question, leading to an estimated value of -15.2029 for 

beta with a standard error of 0.19. In both cases the raw probability of asthma equals zero, so the corresponding 

estimated beta would be negative infinity, but SAS’s software gives -15.2029 instead. To reduce the impact of these 

outlier cases, we replaced their estimated standard errors by 4, which is approximately four times the maximum 

standard error for all other region, gender, and age combinations. 

13 With only 18 points, a smoothing parameter of 0.2 cannot be used because the weight function assigns zero 

weights to all ages except age A, and a quadratic model cannot be uniquely fitted to a single value. A smoothing 

parameter of 0.3 also cannot be used because that choice assigns a neighborhood of 5 points only (0.3 × 18 = 5, 
G-5 

Quantities predicted in these smoothing parameter tests were the predicted value, standard error, 

confidence interval lower bound and confidence interval upper bound for the betas, and the 

corresponding values for the prevalence rates. 

The polygonal curves joining values for different ages show the predicted values with vertical 

lines indicating the confidence intervals in Figures 3 and 4 for smoothing parameters 0 (i.e., no 

smoothing) and 0.5, respectively. Note that the confidence intervals are not symmetric about the 

predicted values because of the inverse logit transformation. 

Note that in our application of LOESS, we used weights of 1 / [std error (beta)] 2

, so that σ

2

 = 1 

for this application. The LOESS procedure estimates σ

2

 from the weighted sum of squares. Since 

in our application we assume σ

2

 = 1, we multiplied the estimated standard errors by 1 / 

estimated σ, and adjusted the widths of the confidence intervals by the same factor. 

Additionally, because the true value of σ equals 1, the best choices of smoothing parameter 

should give residual standard errors close to one. Using this criterion the best choice varies with 

gender and region between smoothing parameters 0.4 (3 cases), 0.5 (2 cases), 0.6 (1 case), and 

0.7 (1 case). 

 As a further regression diagnostic the residual errors from the LOESS model were divided by 

std error (beta) to make their variances approximately constant. These approximately studentized 

residuals, ‘student,’ should be approximately normally distributed with a mean of zero and a 

variance of σ

2

 = 1. To test this assumption, normal probability plots of the residuals were 

created for each smoothing parameter, combining all the studentized residuals across genders, 

regions, and ages. The plots for smoothing parameters seem to be equally straight for each 

smoothing parameter. 

The final regression diagnostic is a plot of the studentized residuals against the smoothed beta 

values. Ideally there should be no obvious pattern and an average studentized residual close to 

zero. The plots indeed showed no unusual patterns, and the results for smoothing parameters 0.5 

and 0.6 seem to showed a fitted LOESS close to the studentized residual equals zero line. 

The regression diagnostics suggested the choice of smoothing parameter as 0.4 or 0.5. Normal 

probability plots did not suggest any preferred choices. The plots of residuals against smoothed 

predictions suggest the choices of 0.5 or 0.6. We therefore chose the final value of 0.5. These 

predictions, standard errors, and confidence intervals are presented in tabular form below as 

Table G-2. 

 rounded down), of which the two outside ages have assigned weight zero, making the local quadratic model fit 

exactly at every point except for the end points (ages 0, 1, 16 and 17). Usually one uses a smoothing parameter 

below one so that not all the data are used for the local regression at a given x value. 
G-6 

region=Midwest

gender Female Male

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0.32

0.34

age

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
G-7 

region=South

gender Female Male

prev

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

age

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

region=West

gender Female Male

prev

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

age

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
G-8 

region=Midwest

gender Female Male

predprob

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

age

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

region=Northeast

gender Female Male

predprob

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

age

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
G-9 

region=South

gender Female Male

predprob

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

age

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

region=West

gender Female Male

predprob

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

age

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
G-10 

region=Midwest

gender Female Male

prev

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

age

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

region=Northeast

gender Female Male

prev

0.0

0.1

0.2

0.3

0.4

0.5

0.6

age

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
G-11 

region=South

gender Female Male

prev

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

age

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

region=West

gender Female Male

prev

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

age

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
G-12 

region=Midwest

gender Female Male

prev

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

age

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

region=Northeast

gender Female Male

prev

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

age

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
G-13 

region=South

gender Female Male

prev

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

age

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

region=West

gender Female Male

prev

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

age

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
G-14 

Table G-2. Raw and smoothed prevalence rates, with confidence intervals, by region, 

gender, and age. 

Obs Region Gender Age Smoothed Prevalence 

Std 

Error 

95 % Conf 

Interval – 

Lower 

Bound 

95 % Conf 

Interval – 

Upper 

Bound 

1 Midwest Female 0 No 0.04161 0.02965 0.01001 0.15717

2 Midwest Female 0 Yes 0.06956 0.03574 0.02143 0.20330

3 Midwest Female 1 No 0.10790 0.04254 0.04840 0.22336

4 Midwest Female 1 Yes 0.07078 0.01995 0.03736 0.13008

5 Midwest Female 2 No 0.05469 0.02578 0.02131 0.13325

6 Midwest Female 2 Yes 0.07324 0.01778 0.04228 0.12395

7 Midwest Female 3 No 0.06094 0.03474 0.01936 0.17579

8 Midwest Female 3 Yes 0.07542 0.01944 0.04205 0.13163

9 Midwest Female 4 No 0.09049 0.03407 0.04233 0.18298

10 Midwest Female 4 Yes 0.08100 0.02163 0.04417 0.14393

11 Midwest Female 5 No 0.08463 0.03917 0.03317 0.19942

12 Midwest Female 5 Yes 0.09540 0.02613 0.05106 0.17131

13 Midwest Female 6 No 0.14869 0.08250 0.04643 0.38520

14 Midwest Female 6 Yes 0.09210 0.02854 0.04534 0.17808

15 Midwest Female 7 No 0.04757 0.02927 0.01389 0.15051

16 Midwest Female 7 Yes 0.09032 0.02563 0.04728 0.16571

17 Midwest Female 8 No 0.10444 0.03638 0.05160 0.19997

18 Midwest Female 8 Yes 0.08612 0.02181 0.04842 0.14857

19 Midwest Female 9 No 0.09836 0.04283 0.04062 0.21943

20 Midwest Female 9 Yes 0.11040 0.02709 0.06298 0.18643

21 Midwest Female 10 No 0.10916 0.04859 0.04400 0.24600

22 Midwest Female 10 Yes 0.16190 0.03486 0.09838 0.25484

23 Midwest Female 11 No 0.27341 0.06817 0.16112 0.42437

24 Midwest Female 11 Yes 0.19597 0.03920 0.12296 0.29763

25 Midwest Female 12 No 0.10055 0.04780 0.03816 0.23952

26 Midwest Female 12 Yes 0.21214 0.03957 0.13724 0.31309
G-15 

Obs Region Gender Age Smoothed Prevalence 

Std 

Error 

95 % Conf 

Interval – 

Lower 

Bound 

95 % Conf 

Interval – 

Upper 

Bound 

27 Midwest Female 13 No 0.22388 0.05905 0.12907 0.35959

28 Midwest Female 13 Yes 0.16966 0.03371 0.10716 0.25807

29 Midwest Female 14 No 0.10511 0.04233 0.04637 0.22104

30 Midwest Female 14 Yes 0.14020 0.02603 0.09164 0.20857

31 Midwest Female 15 No 0.12026 0.03805 0.06327 0.21670

32 Midwest Female 15 Yes 0.13341 0.02266 0.09056 0.19226

33 Midwest Female 16 No 0.13299 0.03933 0.07288 0.23037

34 Midwest Female 16 Yes 0.14040 0.02235 0.09764 0.19777

35 Midwest Female 17 No 0.17497 0.04786 0.09970 0.28884

36 Midwest Female 17 Yes 0.16478 0.04037 0.09320 0.27468

37 Midwest Male 0 No 0.06419 0.03612 0.02068 0.18227

38 Midwest Male 0 Yes 0.03134 0.01537 0.01042 0.09046

39 Midwest Male 1 No 0.02824 0.01694 0.00859 0.08879

40 Midwest Male 1 Yes 0.06250 0.01751 0.03321 0.11457

41 Midwest Male 2 No 0.05102 0.02343 0.02040 0.12189

42 Midwest Male 2 Yes 0.10780 0.02078 0.06960 0.16328

43 Midwest Male 3 No 0.18650 0.04864 0.10898 0.30057

44 Midwest Male 3 Yes 0.15821 0.02705 0.10696 0.22775

45 Midwest Male 4 No 0.24649 0.05823 0.15035 0.37686

46 Midwest Male 4 Yes 0.21572 0.03661 0.14543 0.30774

47 Midwest Male 5 No 0.11609 0.04818 0.04973 0.24793

48 Midwest Male 5 Yes 0.17822 0.03525 0.11280 0.27003

49 Midwest Male 6 No 0.14158 0.05280 0.06576 0.27873

50 Midwest Male 6 Yes 0.12788 0.02799 0.07751 0.20375

51 Midwest Male 7 No 0.09726 0.03614 0.04588 0.19448

52 Midwest Male 7 Yes 0.12145 0.02642 0.07391 0.19317

53 Midwest Male 8 No 0.16718 0.05814 0.08134 0.31276

54 Midwest Male 8 Yes 0.12757 0.02700 0.07864 0.20031

55 Midwest Male 9 No 0.13406 0.04783 0.06458 0.25769
G-16 

Obs Region Gender Age Smoothed Prevalence 

Std 

Error 

95 % Conf 

Interval – 

Lower 

Bound 

95 % Conf 

Interval – 

Upper 

Bound 

56 Midwest Male 9 Yes 0.14718 0.02976 0.09254 0.22603

57 Midwest Male 10 No 0.13986 0.04422 0.07331 0.25050

58 Midwest Male 10 Yes 0.17728 0.02996 0.12020 0.25366

59 Midwest Male 11 No 0.23907 0.05031 0.15449 0.35075

60 Midwest Male 11 Yes 0.18961 0.03044 0.13100 0.26639

61 Midwest Male 12 No 0.13660 0.04784 0.06668 0.25946

62 Midwest Male 12 Yes 0.19487 0.03078 0.13541 0.27221

63 Midwest Male 13 No 0.18501 0.04498 0.11230 0.28945

64 Midwest Male 13 Yes 0.16939 0.02841 0.11528 0.24195

65 Midwest Male 14 No 0.16673 0.05094 0.08886 0.29104

66 Midwest Male 14 Yes 0.16795 0.02631 0.11734 0.23459

67 Midwest Male 15 No 0.14583 0.04241 0.08054 0.24967

68 Midwest Male 15 Yes 0.17953 0.02561 0.12951 0.24347

69 Midwest Male 16 No 0.24965 0.06037 0.15033 0.38489

70 Midwest Male 16 Yes 0.20116 0.03048 0.14187 0.27721

71 Midwest Male 17 No 0.21152 0.06481 0.11131 0.36490

72 Midwest Male 17 Yes 0.23741 0.05816 0.13243 0.38835

73 Northeast Female 0 No 0.00000 0.00000 0.00000 0.00000

74 Northeast Female 0 Yes 0.06807 0.06565 0.00670 0.44174

75 Northeast Female 1 No 0.12262 0.07443 0.03476 0.35164

76 Northeast Female 1 Yes 0.07219 0.03765 0.02088 0.22109

77 Northeast Female 2 No 0.07217 0.03707 0.02561 0.18713

78 Northeast Female 2 Yes 0.07522 0.02212 0.03764 0.14468

79 Northeast Female 3 No 0.08550 0.03991 0.03324 0.20269

80 Northeast Female 3 Yes 0.07709 0.02021 0.04162 0.13840

81 Northeast Female 4 No 0.08704 0.03804 0.03596 0.19592

82 Northeast Female 4 Yes 0.08171 0.02252 0.04269 0.15080

83 Northeast Female 5 No 0.07597 0.03754 0.02801 0.18998

84 Northeast Female 5 Yes 0.11603 0.03012 0.06258 0.20515
G-17 

Obs Region Gender Age Smoothed Prevalence 

Std 

Error 

95 % Conf 

Interval – 

Lower 

Bound 

95 % Conf 

Interval – 

Upper 

Bound 

85 Northeast Female 6 No 0.19149 0.06960 0.08937 0.36372

86 Northeast Female 6 Yes 0.16106 0.03737 0.09219 0.26629

87 Northeast Female 7 No 0.22034 0.07076 0.11195 0.38783

88 Northeast Female 7 Yes 0.18503 0.04087 0.10844 0.29764

89 Northeast Female 8 No 0.11002 0.05128 0.04241 0.25654

90 Northeast Female 8 Yes 0.17054 0.04039 0.09628 0.28407

91 Northeast Female 9 No 0.17541 0.07488 0.07159 0.36981

92 Northeast Female 9 Yes 0.14457 0.03538 0.08042 0.24618

93 Northeast Female 10 No 0.12980 0.04964 0.05930 0.26087

94 Northeast Female 10 Yes 0.13487 0.03098 0.07799 0.22319

95 Northeast Female 11 No 0.15128 0.05287 0.07366 0.28547

96 Northeast Female 11 Yes 0.14072 0.03068 0.08367 0.22704

97 Northeast Female 12 No 0.11890 0.04426 0.05568 0.23597

98 Northeast Female 12 Yes 0.16615 0.03375 0.10211 0.25877

99 Northeast Female 13 No 0.22638 0.06285 0.12650 0.37158

100 Northeast Female 13 Yes 0.17374 0.03402 0.10861 0.26626

101 Northeast Female 14 No 0.15807 0.05513 0.07694 0.29719

102 Northeast Female 14 Yes 0.15137 0.02946 0.09519 0.23220

103 Northeast Female 15 No 0.07460 0.03409 0.02971 0.17506

104 Northeast Female 15 Yes 0.14564 0.02761 0.09279 0.22127

105 Northeast Female 16 No 0.13603 0.05328 0.06081 0.27686

106 Northeast Female 16 Yes 0.14601 0.03095 0.08805 0.23241

107 Northeast Female 17 No 0.19074 0.07382 0.08451 0.37568

108 Northeast Female 17 Yes 0.15662 0.05374 0.06784 0.32151

109 Northeast Male 0 No 0.03904 0.03829 0.00547 0.23095

110 Northeast Male 0 Yes 0.04768 0.03299 0.00991 0.20023

111 Northeast Male 1 No 0.05533 0.03425 0.01596 0.17461

112 Northeast Male 1 Yes 0.04564 0.01831 0.01850 0.10821

113 Northeast Male 2 No 0.05525 0.03119 0.01781 0.15872
G-18 

Obs Region Gender Age Smoothed Prevalence 

Std 

Error 

95 % Conf 

Interval – 

Lower 

Bound 

95 % Conf 

Interval – 

Upper 

Bound 

114 Northeast Male 2 Yes 0.05161 0.01505 0.02680 0.09709

115 Northeast Male 3 No 0.03842 0.02923 0.00840 0.15853

116 Northeast Male 3 Yes 0.06766 0.01784 0.03734 0.11955

117 Northeast Male 4 No 0.07436 0.02906 0.03393 0.15522

118 Northeast Male 4 Yes 0.09964 0.02330 0.05859 0.16441

119 Northeast Male 5 No 0.17601 0.04519 0.10393 0.28234

120 Northeast Male 5 Yes 0.14854 0.02948 0.09428 0.22623

121 Northeast Male 6 No 0.23271 0.09319 0.09832 0.45756

122 Northeast Male 6 Yes 0.20731 0.04235 0.12875 0.31640

123 Northeast Male 7 No 0.13074 0.05195 0.05785 0.26922

124 Northeast Male 7 Yes 0.22820 0.04524 0.14338 0.34311

125 Northeast Male 8 No 0.33970 0.08456 0.19726 0.51855

126 Northeast Male 8 Yes 0.22240 0.04298 0.14157 0.33157

127 Northeast Male 9 No 0.13761 0.05024 0.06507 0.26785

128 Northeast Male 9 Yes 0.21238 0.04071 0.13589 0.31617

129 Northeast Male 10 No 0.21785 0.06659 0.11464 0.37465

130 Northeast Male 10 Yes 0.17652 0.03731 0.10824 0.27460

131 Northeast Male 11 No 0.11448 0.05849 0.04005 0.28601

132 Northeast Male 11 Yes 0.16617 0.03516 0.10200 0.25907

133 Northeast Male 12 No 0.17736 0.05489 0.09349 0.31067

134 Northeast Male 12 Yes 0.18279 0.03589 0.11611 0.27581

135 Northeast Male 13 No 0.19837 0.05450 0.11222 0.32635

136 Northeast Male 13 Yes 0.17078 0.03078 0.11288 0.25000

137 Northeast Male 14 No 0.16201 0.04973 0.08618 0.28386

138 Northeast Male 14 Yes 0.17033 0.02889 0.11547 0.24408

139 Northeast Male 15 No 0.11894 0.04584 0.05417 0.24139

140 Northeast Male 15 Yes 0.18246 0.02858 0.12740 0.25438

141 Northeast Male 16 No 0.24306 0.05798 0.14759 0.37326

142 Northeast Male 16 Yes 0.20406 0.03216 0.14187 0.28447
G-19 

Obs Region Gender Age Smoothed Prevalence 

Std 

Error 

95 % Conf 

Interval – 

Lower 

Bound 

95 % Conf 

Interval – 

Upper 

Bound 

143 Northeast Male 17 No 0.22559 0.06980 0.11748 0.38930

144 Northeast Male 17 Yes 0.24185 0.06066 0.13291 0.39898

145 South Female 0 No 0.02459 0.01116 0.01002 0.05906

146 South Female 0 Yes 0.03407 0.01282 0.01465 0.07723

147 South Female 1 No 0.08869 0.03373 0.04118 0.18067

148 South Female 1 Yes 0.05182 0.01167 0.03127 0.08472

149 South Female 2 No 0.05097 0.02373 0.02012 0.12319

150 South Female 2 Yes 0.07110 0.01386 0.04584 0.10869

151 South Female 3 No 0.08717 0.03240 0.04122 0.17500

152 South Female 3 Yes 0.08759 0.01718 0.05624 0.13394

153 South Female 4 No 0.11010 0.03209 0.06113 0.19035

154 South Female 4 Yes 0.09897 0.01914 0.06387 0.15025

155 South Female 5 No 0.09409 0.02943 0.05015 0.16968

156 South Female 5 Yes 0.11870 0.02157 0.07855 0.17548

157 South Female 6 No 0.15318 0.04317 0.08611 0.25777

158 South Female 6 Yes 0.12150 0.02282 0.07925 0.18182

159 South Female 7 No 0.09608 0.03538 0.04565 0.19105

160 South Female 7 Yes 0.11192 0.02171 0.07204 0.16985

161 South Female 8 No 0.09955 0.03288 0.05111 0.18493

162 South Female 8 Yes 0.09287 0.01897 0.05850 0.14436

163 South Female 9 No 0.07477 0.02719 0.03606 0.14864

164 South Female 9 Yes 0.09117 0.01786 0.05855 0.13929

165 South Female 10 No 0.10602 0.03214 0.05750 0.18732

166 South Female 10 Yes 0.10821 0.02026 0.07077 0.16201

167 South Female 11 No 0.14411 0.04267 0.07875 0.24907

168 South Female 11 Yes 0.13237 0.02251 0.08989 0.19071

169 South Female 12 No 0.12646 0.02981 0.07860 0.19723

170 South Female 12 Yes 0.12346 0.02004 0.08543 0.17519

171 South Female 13 No 0.11376 0.03270 0.06365 0.19510
G-20 

Obs Region Gender Age Smoothed Prevalence 

Std 

Error 

95 % Conf 

Interval – 

Lower 

Bound 

95 % Conf 

Interval – 

Upper 

Bound 

172 South Female 13 Yes 0.09653 0.01717 0.06458 0.14190

173 South Female 14 No 0.02915 0.01339 0.01174 0.07054

174 South Female 14 Yes 0.09469 0.01619 0.06436 0.13721

175 South Female 15 No 0.11985 0.03357 0.06801 0.20259

176 South Female 15 Yes 0.09988 0.01586 0.06978 0.14099

177 South Female 16 No 0.14183 0.03685 0.08366 0.23028

178 South Female 16 Yes 0.11501 0.01620 0.08365 0.15612

179 South Female 17 No 0.13141 0.03007 0.08280 0.20226

180 South Female 17 Yes 0.14466 0.02946 0.09067 0.22291

181 South Male 0 No 0.01164 0.00852 0.00275 0.04790

182 South Male 0 Yes 0.04132 0.01867 0.01487 0.10956

183 South Male 1 No 0.10465 0.03216 0.05629 0.18635

184 South Male 1 Yes 0.06981 0.01623 0.04125 0.11576

185 South Male 2 No 0.11644 0.03486 0.06353 0.20382

186 South Male 2 Yes 0.10189 0.01672 0.07024 0.14557

187 South Male 3 No 0.10794 0.03253 0.05874 0.19005

188 South Male 3 Yes 0.12852 0.02139 0.08793 0.18405

189 South Male 4 No 0.08480 0.02973 0.04190 0.16410

190 South Male 4 Yes 0.14393 0.02379 0.09861 0.20534

191 South Male 5 No 0.22243 0.04227 0.15052 0.31592

192 South Male 5 Yes 0.16450 0.02373 0.11821 0.22430

193 South Male 6 No 0.13908 0.03392 0.08485 0.21964

194 South Male 6 Yes 0.16386 0.02460 0.11613 0.22617

195 South Male 7 No 0.10695 0.04272 0.04747 0.22347

196 South Male 7 Yes 0.13329 0.02322 0.08951 0.19392

197 South Male 8 No 0.13660 0.03841 0.07712 0.23049

198 South Male 8 Yes 0.13818 0.02276 0.09484 0.19702

199 South Male 9 No 0.15978 0.03742 0.09920 0.24720

200 South Male 9 Yes 0.16839 0.02450 0.12062 0.23012
G-21 

Obs Region Gender Age Smoothed Prevalence 

Std 

Error 

95 % Conf 

Interval – 

Lower 

Bound 

95 % Conf 

Interval – 

Upper 

Bound 

201 South Male 10 No 0.21482 0.04702 0.13676 0.32086

202 South Male 10 Yes 0.17848 0.02453 0.13021 0.23972

203 South Male 11 No 0.15078 0.03440 0.09492 0.23112

204 South Male 11 Yes 0.16247 0.02224 0.11881 0.21820

205 South Male 12 No 0.13727 0.03260 0.08489 0.21438

206 South Male 12 Yes 0.14480 0.01976 0.10610 0.19453

207 South Male 13 No 0.14136 0.03119 0.09049 0.21409

208 South Male 13 Yes 0.14318 0.01928 0.10537 0.19165

209 South Male 14 No 0.16110 0.03444 0.10438 0.24037

210 South Male 14 Yes 0.15339 0.01875 0.11612 0.19992

211 South Male 15 No 0.16172 0.03519 0.10394 0.24291

212 South Male 15 Yes 0.15088 0.01746 0.11598 0.19398

213 South Male 16 No 0.15836 0.03879 0.09614 0.24974

214 South Male 16 Yes 0.14038 0.01773 0.10533 0.18467

215 South Male 17 No 0.11156 0.02737 0.06810 0.17746

216 South Male 17 Yes 0.12247 0.02596 0.07537 0.19286

217 West Female 0 No 0.00983 0.00990 0.00135 0.06802

218 West Female 0 Yes 0.01318 0.00987 0.00248 0.06700

219 West Female 1 No 0.02367 0.01862 0.00497 0.10522

220 West Female 1 Yes 0.03105 0.01312 0.01204 0.07769

221 West Female 2 No 0.08097 0.03759 0.03170 0.19166

222 West Female 2 Yes 0.05440 0.01482 0.02948 0.09825

223 West Female 3 No 0.07528 0.03851 0.02679 0.19404

224 West Female 3 Yes 0.07444 0.01842 0.04257 0.12701

225 West Female 4 No 0.09263 0.03196 0.04621 0.17703

226 West Female 4 Yes 0.07696 0.02064 0.04194 0.13701

227 West Female 5 No 0.01976 0.01347 0.00513 0.07302

228 West Female 5 Yes 0.07737 0.02123 0.04157 0.13949

229 West Female 6 No 0.15792 0.07301 0.06009 0.35487
G-22 

Obs Region Gender Age Smoothed Prevalence 

Std 

Error 

95 % Conf 

Interval – 

Lower 

Bound 

95 % Conf 

Interval – 

Upper 

Bound 

230 West Female 6 Yes 0.07298 0.01985 0.03947 0.13107

231 West Female 7 No 0.06955 0.02567 0.03321 0.13989

232 West Female 7 Yes 0.08146 0.01987 0.04691 0.13776

233 West Female 8 No 0.07753 0.02825 0.03731 0.15417

234 West Female 8 Yes 0.09062 0.01994 0.05507 0.14558

235 West Female 9 No 0.13440 0.04481 0.06802 0.24832

236 West Female 9 Yes 0.10215 0.02347 0.06061 0.16709

237 West Female 10 No 0.06573 0.03719 0.02102 0.18736

238 West Female 10 Yes 0.12152 0.02660 0.07376 0.19374

239 West Female 11 No 0.15354 0.04584 0.08329 0.26584

240 West Female 11 Yes 0.12719 0.02688 0.07852 0.19950

241 West Female 12 No 0.10120 0.03594 0.04934 0.19631

242 West Female 12 Yes 0.13054 0.02498 0.08440 0.19650

243 West Female 13 No 0.14759 0.04125 0.08346 0.24769

244 West Female 13 Yes 0.11968 0.02369 0.07629 0.18284

245 West Female 14 No 0.08748 0.03284 0.04105 0.17675

246 West Female 14 Yes 0.11063 0.02132 0.07145 0.16744

247 West Female 15 No 0.10099 0.03841 0.04674 0.20471

248 West Female 15 Yes 0.11236 0.02051 0.07428 0.16645

249 West Female 16 No 0.12538 0.04343 0.06188 0.23755

250 West Female 16 Yes 0.12224 0.02210 0.08108 0.18021

251 West Female 17 No 0.14672 0.04582 0.07743 0.26052

252 West Female 17 Yes 0.14371 0.03992 0.07558 0.25621

253 West Male 0 No 0.00000 0.00000 0.00000 0.00000

254 West Male 0 Yes 0.03075 0.02534 0.00437 0.18642

255 West Male 1 No 0.05457 0.02662 0.02056 0.13695

256 West Male 1 Yes 0.04584 0.01889 0.01729 0.11595

257 West Male 2 No 0.07833 0.02789 0.03833 0.15342

258 West Male 2 Yes 0.06254 0.01442 0.03627 0.10573
G-23 

Obs Region Gender Age Smoothed Prevalence 

Std 

Error 

95 % Conf 

Interval – 

Lower 

Bound 

95 % Conf 

Interval – 

Upper 

Bound 

259 West Male 3 No 0.05897 0.02530 0.02500 0.13281

260 West Male 3 Yes 0.07844 0.01913 0.04398 0.13607

261 West Male 4 No 0.07267 0.03354 0.02870 0.17208

262 West Male 4 Yes 0.09122 0.02482 0.04765 0.16763

263 West Male 5 No 0.19732 0.10033 0.06632 0.45969

264 West Male 5 Yes 0.11262 0.02937 0.06021 0.20092

265 West Male 6 No 0.13335 0.04859 0.06322 0.25970

266 West Male 6 Yes 0.12119 0.02916 0.06799 0.20680

267 West Male 7 No 0.08881 0.03493 0.04015 0.18508

268 West Male 7 Yes 0.12691 0.02806 0.07464 0.20758

269 West Male 8 No 0.15183 0.05484 0.07210 0.29200

270 West Male 8 Yes 0.13161 0.02705 0.08037 0.20811

271 West Male 9 No 0.17199 0.05164 0.09260 0.29715

272 West Male 9 Yes 0.15079 0.02837 0.09590 0.22915

273 West Male 10 No 0.12897 0.03747 0.07151 0.22159

274 West Male 10 Yes 0.16356 0.02584 0.11192 0.23279

275 West Male 11 No 0.19469 0.04002 0.12785 0.28505

276 West Male 11 Yes 0.16965 0.02623 0.11699 0.23956

277 West Male 12 No 0.13214 0.04542 0.06547 0.24865

278 West Male 12 Yes 0.17494 0.02738 0.12002 0.24792

279 West Male 13 No 0.19947 0.04814 0.12127 0.31029

280 West Male 13 Yes 0.16217 0.02773 0.10747 0.23732

281 West Male 14 No 0.10759 0.03838 0.05220 0.20880

282 West Male 14 Yes 0.16487 0.02644 0.11214 0.23582

283 West Male 15 No 0.18459 0.05348 0.10138 0.31235

284 West Male 15 Yes 0.17018 0.02480 0.11996 0.23578

285 West Male 16 No 0.19757 0.04862 0.11892 0.30993

286 West Male 16 Yes 0.17888 0.02540 0.12718 0.24569
G-24 

Obs Region Gender Age Smoothed Prevalence 

Std 

Error 

95 % Conf 

Interval – 

Lower 

Bound 

95 % Conf 

Interval – 

Upper 

Bound 

287 West Male 17 No 0.18078 0.04735 0.10548 0.29227

288 West Male 17 Yes 0.19218 0.04291 0.11118 0.31153

 

 
H-1 

APPENDIX H. 

ALTERNATIVE LONGITUDINAL ACTIVITY PATTERN ALGORITHM 
H-2 

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H-1 

TECHNICAL MEMORANDUM 

To: Ted Palma, US EPA 

From: Arlene Rosenbaum and Jonathan Cohen 

Date: November 4, 2004 

Re: Evaluation of a multi-day activity pattern algorithm for creating longitudinal activity 

patterns. 

BACKGROUND 

In previous work ICF reviewed the HAPEM4 modeling approach for developing annual average 

activity patterns from the CHAD database and recommended an approach to improve the 

model’s pattern selection process to better represent the variability among individuals. This 

section summarizes the recommended approach. (For details see the memorandum of July 23, 

2002 from ICF Consulting to Ted Palma.) 

Using cluster analysis, first the CHAD daily activity patterns are grouped into either two or three 

categories of similar patterns for each of the 30 combinations of day type (summer weekday, 

non-summer weekday, and weekend) and demographic group (males or females; age groups: 0-

4, 5-11, 12-17, 18-64, 65+). Next, for each combination of day type and demographic group, 

category-to-category transition probabilities are defined by the relative frequencies of each 

second-day category associated with each given first-day category, where the same individual 

was observed for two consecutive days. (Consecutive day activity pattern records for a single 

individual constitute a small subset of the CHAD data.) 

To implement the proposed algorithm, for each day type and demographic group, one daily 

activity pattern per category is randomly selected from the corresponding CHAD data to 

represent that category. That is, if there are 3 cluster categories for each of 3 day types, 9 unique 

activity patterns are selected to be averaged together to create an annual average activity pattern 

to represent an individual in a given demographic group and census tract. 

The weighting for each of the 9 activity patterns used in the averaging process is determined by 

the product of two factors. The first is the relative frequency of its day type, i.e., 0.18 for summer 

weekdays, 0.54 for non-summer weekdays, and 0.28 for weekends. 

The second factor in the weighting for the selected activity pattern is determined by simulating a 

sequence of category-types as a one-stage Markov chain process using the transition 
H-2 

probabilities. The category for the first day is selected according to the relative frequencies of 

each category. The category for the second day is selected according to the category-to-category 

transition probabilities for the category selected for the first day. The category for the third day is 

selected according to the transition probabilities for the category selected for the second day. 

This is repeated for all days in the day type (65 for summer weekdays, 195 for non-summer 

weekdays, 104 for weekends), producing a sequence of daily categories. The relative frequency 

of the category-type in the sequence associated with the selected activity pattern is the second 

factor in the weighting. 

PROPOSED ALGORITHM STEPS 

The proposed algorithm is summarized in Figure 1. Each step is explained in this section. 

Data Preparation 

Step 1: Each daily activity pattern in the CHAD data base is summarized by the total minutes in 

each of five micro-environments: indoors – residence; indoors – other building; outdoors – near 

road; outdoors – away from road; in vehicle. These five numbers are assumed to represent the 

most important features of the activity pattern for their exposure impact. 

Step 2: All CHAD activity patterns for a given day-type and demographic group are subjected to 

cluster analysis, resulting in 2 or 3 cluster categories. Each daily activity pattern is tagged with a 

cluster category. 

Step 3: For each day-type and demographic group, the relative frequency of each day-type in the 

CHAD data base is determined. 

Step 4: All CHAD activity patterns for a given day-type and demographic group that are 

consecutive days for a single individual, are analyzed to determine the category-to-category 

transition frequencies in the CHAD data base. These transition frequencies are used to calculate 

category-to-category transition probabilities. 

For example, if there are 2 categories, A and B, then 

PAA = the probability that a type A pattern is followed by a type A pattern, 

PAB = the probability that a type A pattern is followed by a type B pattern (PAB = 1 – PAA), 

PBB = the probability that a type B pattern is followed by a type B pattern, and 

PBA = the probability that a type B pattern is followed by a type A pattern (PBA = 1 – PBB). 

Activity Pattern Selection 

For each day-type and demographic group in each census tract 

Step 5: One activity pattern is randomly selected from each cluster category group (i.e., 2 to 3 

activity patterns) 
H-3 

Creating Weights for Day-type Averaging

For each day-type and demographic group in each census tract 

Step 6: A cluster category is selected for the first day of the day-type sequence, according to the 

relative frequency of the cluster category days in the CHAD data set. 

Step 7: A cluster category is selected for each subsequent day in the day-type sequence day by 

day using the category-to-category transition probabilities. 

Step 8: The relative frequency of each cluster category in the day-type sequence is determined. 

Step 9: The activity patterns selected for each cluster category (Step 5) are averaged together 

using the cluster category frequencies (Step 8) as weights, to create a day-type average activity 

pattern. 

Creating Annual Average Activity Patterns 

For each demographic group in each census tract 

Step 10: The day-type average activity patterns are averaged together using the relative 

frequency of day-types as weights, to create an annual average activity pattern. 

Creating Replicates 

For each demographic group in each census tract 

Step 11: Steps 5 through 10 are repeated 29 times to create 30 annual average activity patterns. 

EVALUATING THE ALGORITHM 

The purpose of this study is to evaluate how well the proposed one-stage Markov chain 

algorithm can reproduce observed multi-day activity patterns with respect to demographic group 

means and inter-individual variability, while using one-day selection. 

In order to accomplish this we propose to apply the algorithm to observed multi-day activity 

patterns provided by the WAM, and compare the means and variances of the predicted multi-day 

patterns with the observed patterns. 

Current APEX Algorithm 

Because the algorithm is being considered for incorporation into APEX, we would like the 

evaluation to be consistent with the approach taken in APEX for selection of activity patterns for 

creating multi-day sequences. The APEX approach for creating multi-day activity sequences is 

as follows. 
H-4 

Step1: A profile for a simulated individual is generated by selection of gender, race (not 

implemented?), age group, and home sector from a given set of distributions consistent with the 

population of the study area. 

Step 2: A specific age within the age group is selected from a uniform distribution. 

Step 3: The employment status is simulated as a function of the age. 

Step 4: For each simulated day, the user defines an initial pool of possible diary days based on a 

user-specified function of the day type (e.g., weekday/weekend) and temperature. 

Step 5: The pool is further restricted to match the target gender and employment status exactly 

and the age within 2A years for some parameter A. The diary days within the pool are assigned a 

weight of 1 if the age is within A years of the target age and a weight of w (user-defined 

parameter) if the age difference is between A and 2A years. For each simulated day, the 

probability of selecting a given diary day is equal to the age weight divided by the total of the 

age weights for all diary days in the pool for that day. 

Approach to Incorporation of Day-to-Day Dependence into APEX Algorithm 

If we were going to incorporate day-to-day dependence of activity patterns into the APEX 

model, we would propose preparing the data with cluster analysis and transition probabilities as 

described in Steps 1-4 for the proposed HAPEM 5 algorithm, with the following modifications. 

• For Step 2 the activity patterns would be divided into groups based on day-type (weekday, 

weekend), temperature, gender, employment status, and age, with cluster analysis applied to 

each group. However, because the day-to-day transitions in the APEX activity selection 

algorithm can cross temperature bins, we would propose to use broad temperature bins for 

the clustering and transition probability calculations so that the cluster definitions would be 

fairly uniform across temperature bins. Thus we would probably define the bins according 

to season (e.g., summer, non-summer). 

• In contrast to HAPEM, the sequence of activity patterns may be important in APEX. 

Therefore, for Step 4 transition probabilities would be specified for transitions between 

days with the same day-type and season, as in HAPEM, and also between days with 

different day-types and/or seasons. For example, transition probabilities would be specified 

for transitions between summer weekdays of each category and summer weekends of each 

category. 

Another issue for dividing the CHAD activity records for the purposes of clustering and 

calculating transition probabilities is that the diary pools specified for the APEX activity 

selection algorithm use varying and overlapping age ranges. One way to address this problem 

would be to simply not include consideration of age in the clustering process, under the 

assumption that cluster categories are similar across age groups, even if the frequency of each 

cluster category varies by age group. This assumption could be tested by examination of the 

cluster categories stratified by age group that were developed for HAPEM5. If the assumption is 

found to be valid, then the cluster categories could be pre-determined for input to APEX, while 
H-5 

the transition probabilities could be calculated within APEX during the simulation for each age 

range specified for dairy pools. 

If the assumption is found to be invalid, then an alternative approach could be implemented that 

would create overlapping age groups for purposes of clustering as follows. APEX age group 

ranges and age window percentages would be constrained to some maximum values. Then a set 

of overlapping age ranges that would be at least as large as the largest possible dairy pool age 

ranges would be defined for the purposes of cluster analysis and transition probability 

calculation. The resulting sets of cluster categories and transition probabilities would be predetermined for input into APEX and the appropriate set used by APEX for each diary pool used 

during the simulation. 

The actual activity pattern sequence selection would be implemented as follows. The activity 

pattern for first day in the year would be selected exactly as is currently done in APEX, as 

described above. For the selecting the second day’s activity pattern, each age weight would be 

multiplied by the transition probability PAB where A is the cluster for the first day’s activity 

pattern and B is the cluster for a given activity pattern in the available pool of diary days for day 

2. (Note that day 2 may be a different day-type and/or season than day 1.) The probability of 

selecting a given diary day on day 2 is equal to the age weight times PAB divided by the total of 

the products of age weight and PAB for all diary days in the pool for day 2. Similarly, for the 

transitions from day 2 to day 3, day 3 to day 4, etc. 

 

Testing the Approach with the Multi-day Data set 

We tested this approach using the available multi-day data set. For purposes of clustering we 

characterized the activity pattern records according to time spent in each of 5 

microenvironments: indoors-home, indoors-school, indoors-other, outdoors (aggregate of the 3 

outdoor microenvironments), and in-transit. 

For purposes of defining diary pools and for clustering and calculating transition probabilities we 

divided the activity pattern records by day type (i.e., weekday, weekend), season (i.e., summer or 

ozone season, non-summer or non-ozone season), age (6-10 and 11-12), and gender. Since all the 

subjects are 6-12 years of age and all are presumably unemployed, we need not account for 

differences in employment status. For each day type, season, age, and gender, we found that the 

activity patterns appeared to group in three clusters. 

In this case, we simulated week-long sequences (Wednesday through Tuesday) for each of 100 

people in each age/gender group for each season, using the transition probabilities. To evaluate 

the algorithm we calculated the following statistics for the predicted multi-day activity patterns 

for comparison with the actual multi-day diary data. 

• For each age/gender group for each season, the average time in each microenvironment 

• For each age/gender group, season, and microenvironment, the average of the withinperson variance across all simulated persons (We defined the within-person variance as the 

variance of the total time per day spent in the microenvironment across the week.) 

• For each age/gender group, season, and microenvironment, the variance across persons of 

the mean time spent in that microenvironment 
H-6 

In each case we compared the predicted statistic for the stratum to the statistic for the 

corresponding stratum in the actual diary data.14 

We also calculated the mean normalized bias for the statistic, which is a common performance 

measure used in dispersion model performance and which is calculated as follows. 

∑ − =

N

observed

predicted observed

N

NBIAS

1

100 ( )

 % 

RESULTS 

Comparisons of simulated and observed data for time in each of the 5 microenvironments are 

presented in Tables 1 – 3 and Figures 2-5. 

Average Time in Microenvironment 

Table 1 and Figure 2 show the comparisons for the average time spent in each of the 5 

microenvironments for each age/gender group and season. Figure 3 shows the comparison for all 

the microenvironments except indoor, home in order to highlight the lower values. 

Table 1 and the figures show that the predicted time-in-microenvironment averages match well 

with the observed values. For combinations of microenvironment/age/gender/season the 

normalized bias ranges from –35% to +41%. Sixty percent of the predicted averages have bias 

between –9% and +9%, and the mean bias across any microenvironment ranges from -9% to 

+4%. Fourteen predictions have positive bias and 23 have negative bias. A Wilcoxon signed rank 

test that the median bias across the 40 combinations = 0 % was not significant (p-value = 0.40) 

supporting the conclusion of no overall bias. 

Variance Across Persons 

Table 2 and Figure 4 show the comparisons for the variance across persons for the average time 

spent in each microenvironment. In this case the bias ranges from –40% to +120% for any 

microenvironment/age/gender/season. Sixty-five percent of the predicted variances have bias 

between –22% and +24%. The mean normalized bias across any microenvironment ranges from 

–10% to +28%. Eighteen predictions have positive bias and 20 have negative bias. Figure 4 

suggests a reasonably good match of predicted to observed variance in spite of 2 or 3 outliers. A 

Wilcoxon signed rank test that the median bias across the 40 combinations = 0 % was not 

significant (p-value = 0.93) supporting the conclusion of no overall bias. 

Within-Person Variance for Persons 

Table 3 and Figure 5 show the comparisons for the within-person variance for time spent in each 

microenvironment. In this case the bias ranges from –47% to +150% for any 

 

14 For the diary data, because the number of days per person varies, the average of the within-person 

variances was calculated as a weighted average, where the weight is the degrees of freedom, i.e., one 

less than the number of days simulated. Similarly, the variance across persons of the mean time was 

appropriately adjusted for the different degrees of freedom using analysis of variance. 
H-7 

microenvironment/age/gender/season. Seventy percent of the predicted variances have bias 

between –25% and +30%. The mean normalized bias across any microenvironment ranges from 

–11% to +47%. Twenty-eight predictions have positive bias and 12 have negative bias, 

suggesting some tendency for overprediction of this variance measure. And indeed a Wilcoxon 

signed rank test that the median bias across the 40 combinations = 0 % was very significant (pvalue = 0.01) showing that the within-person variance was significantly overpredicted. Still, 

Figure 4 suggests a reasonably good match of predicted to observed variance in most cases, with 

a few overpredicting outliers at the higher end of the distribution. So although the positive bias is 

significant in a statistical sense (i.e., the variance is more likely to be overpredicted than 

underpredicted), it is not clear whether the bias is large enough to be important. 

CONCLUSIONS 

The proposed algorithm appears to be able to replicate the observed data reasonably well, 

although the within-person variance is somewhat overpredicted. 

It would be informative to compare this algorithm with the earlier alternative approaches in order 

to gain perspective on the degree of improvement, if any, afforded by this approach. Two earlier 

approaches were: 

1. Select a single activity pattern for each day-type/season combination from the 

appropriate set, and use that pattern for every day in the multi-day sequence that 

corresponds to that day-type and season. 

2. Re-select an activity pattern for each day in the multi-day sequence from the 

appropriate set for the corresponding day-type and season. 

Goodness-of-fit statistics could be developed to compare the three approaches and find which 

model best fits the data for a given stratum.
H-8 

Table 1. Average time spent in each microenvironment: comparison of predicted and observed. 

Microenvironment Demographic 

Group 

Season Observed 

(hours/day) Predicted 

(hours/day) 

Normalized 

Bias 

Indoor, home Girls, 6-10 Summer 

15.5 16.5 6% 

 Not Summer 15.8 15.5 -2% 

 Boys, 6-10 Summer 15.7 15.2 -3% 

 Not Summer 15.8 16.4 4% 

 Girls, 11-12 Summer 16.2 15.3 -5% 

 Not Summer 16.5 16.5 0% 

 Boys, 11-12 Summer 16.0 15.6 -3% 

 Not Summer 16.2 16.1 -1% 

MEAN 

 -1% 

Indoor, school 

Girls, 6-10 Summer 

0.7 0.7 -9% 

 Not Summer 2.3 2.5 7% 

 Boys, 6-10 Summer 0.8 0.5 -34% 

 Not Summer 2.2 2.2 0% 

 Girls, 11-12 Summer 0.7 0.7 6% 

 Not Summer 2.1 2.4 13% 

 Boys, 11-12 Summer 0.6 0.9 38% 

 Not Summer 2.4 2.7 11% 

MEAN 

 4% 

Indoor, other 

Girls, 6-10 Summer 

2.9 2.4 -14% 

 Not Summer 2.4 2.7 13% 

 Boys, 6-10 Summer 2.2 2.7 21% 

 Not Summer 1.9 1.8 -3% 

 Girls, 11-12 Summer 2.2 1.6 -25% 

 Not Summer 2.2 2.1 -2% 

 Boys, 11-12 Summer 2.3 2.2 -5% 

 Not Summer 1.9 2.0 4% 

MEAN 

 -2% 

Outdoors 

Girls, 6-10 Summer 

3.7 3.5 -6% 

 Not Summer 2.5 2.5 0% 

 Boys, 6-10 Summer 4.1 4.3 4% 

 Not Summer 3.1 2.7 -12% 

 Girls, 11-12 Summer 3.7 5.2 41% 

 Not Summer 2.3 2.1 -5% 

 Boys, 11-12 Summer 3.9 4.3 9% 

 Not Summer 2.6 2.4 -7% 

MEAN 

 3% 
H-9 

In-vehicle 

Girls, 6-10 Summer 

1.1 0.9 -20% 

 Not Summer 1.0 0.9 -13% 

 Boys, 6-10 Summer 1.1 1.3 13% 

 Not Summer 1.0 0.9 -16% 

 Girls, 11-12 Summer 1.2 1.1 -12% 

 Not Summer 0.9 0.8 -15% 

 Boys, 11-12 Summer 1.1 1.0 -5% 

 Not Summer 0.9 0.8 -7% 

MEAN 

 -9% 
H-10 

Table 2. Variance across persons for time spent in each microenvironment: comparison of 

predicted and observed. 

Microenvironment Demographic 

Group 

Season Observed 

(hours/day)2 Predicted 

(hours/day)2

Normalized 

Bias 

Indoor, home Girls, 6-10 Summer 

70 42 -40% 

 Not Summer 67 60 -9% 

 Boys, 6-10 Summer 54 49 -9% 

 Not Summer 35 30 -12% 

 Girls, 11-12 Summer 56 47 -17% 

 Not Summer 42 38 -10% 

 Boys, 11-12 Summer 57 63 12% 

 Not Summer 39 42 8% 

MEAN 

 -10% 

Indoor, school 

Girls, 6-10 Summer 

6.0 5.2 -13% 

 Not Summer 9.5 5.9 -38% 

 Boys, 6-10 Summer 5.6 3.8 -32% 

 Not Summer 5.3 8.2 53% 

 Girls, 11-12 Summer 4.9 5.5 11% 

 Not Summer 5.4 5.3 -1% 

 Boys, 11-12 Summer 5.6 6.0 6% 

 Not Summer 9.2 11 23% 

MEAN 

 1% 

Indoor, other 

Girls, 6-10 Summer 

46 32 -30% 

 Not Summer 44 46. 6% 

 Boys, 6-10 Summer 34 33 -4% 

 Not Summer 23 16 -27% 

 Girls, 11-12 Summer 21 18 -15% 

 Not Summer 28 22 -22% 

 Boys, 11-12 Summer 33 31 -6% 

 Not Summer 30 30 0% 

MEAN 

 -12% 

Outdoors 

Girls, 6-10 Summer 

17 23 37% 

 Not Summer 9.3 6.8 -27% 

 Boys, 6-10 Summer 17 18 3% 

 Not Summer 8.3 7.6 -8% 

 Girls, 11-12 Summer 22 22 0% 

 Not Summer 9.0 9.1 1% 

 Boys, 11-12 Summer 13 29 120% 

 Not Summer 10 11 8% 

MEAN 

 17% 
H-11 

In-vehicle 

Girls, 6-10 Summer 

1.9 2.3 24% 

 Not Summer 1.8 1.6 -11% 

 Boys, 6-10 Summer 2.5 4.7 93% 

 Not Summer 1.5 1.6 9% 

 Girls, 11-12 Summer 3.5 4.7 34% 

 Not Summer 2.8 2.0 -28% 

 Boys, 11-12 Summer 3.2 5.4 69% 

 Not Summer 1.3 1.7 35% 

MEAN 

 28% 
H-12 

Table 3. Average within person variance for time spent in each microenvironment: comparison of 

predicted and observed. 

Microenvironment Demographic 

Group 

Season Observed 

(hours/day)2 Predicted 

(hours/day)2

Normalized 

Bias 

Indoor, home Girls, 6-10 Summer 

20 29 49% 

 Not Summer 18 23 25% 

 Boys, 6-10 Summer 17 30 75% 

 Not Summer 15 24 64% 

 Girls, 11-12 Summer 22 42 93% 

 Not Summer 22 25 13% 

 Boys, 11-12 Summer 21 24 16% 

 Not Summer 17 24 38% 

MEAN 

 47% 

Indoor, school 

Girls, 6-10 Summer 

2.3 2.4 5% 

 Not Summer 7.3 6.4 -12% 

 Boys, 6-10 Summer 2.0 1.5 -25% 

 Not Summer 6.7 5.8 -14% 

 Girls, 11-12 Summer 1.7 2.1 29% 

 Not Summer 7.4 7.6 3% 

 Boys, 11-12 Summer 1.4 2.9 101% 

 Not Summer 7.3 7.8 6% 

MEAN 

 12% 

Indoor, other 

Girls, 6-10 Summer 

14 14 -4% 

 Not Summer 14 18 30% 

 Boys, 6-10 Summer 12 17 42% 

 Not Summer 10 13 26% 

 Girls, 11-12 Summer 10 10 1% 

 Not Summer 14 15 7% 

 Boys, 11-12 Summer 11 14 26% 

 Not Summer 12 13 7% 

MEAN 

 17% 

Outdoors 

Girls, 6-10 Summer 

8.4 9.5 13% 

 Not Summer 3.4 3.2 -3% 

 Boys, 8-10 Summer 6.7 9.5 42% 

 Not Summer 3.4 4.4 28% 

 Girls, 11-12 Summer 10 25 150% 

 Not Summer 4.0 4.5 11% 

 Boys, 11-12 Summer 9.2 7.4 -20% 

 Not Summer 4.3 3.7 -15% 

MEAN 

 26% 
H-13 

In-vehicle 

Girls, 6-10 Summer 

1.0 0.90 -13% 

 Not Summer 0.90 0.48 -47% 

 Boys, 6-10 Summer 1.1 1.4 31% 

 Not Summer 0.81 0.71 -12% 

 Girls, 11-12 Summer 1.3 1.3 4% 

 Not Summer 1.3 1.1 -16% 

 Boys, 11-12 Summer 2.4 1.6 -34% 

 Not Summer 0.85 0.85 1% 

MEAN 

 -11% 
H-14 

Figure 1. Flow diagram of proposed algorithm for creating annual average activity patterns for HAPEM5

Consolidated Human Activity Database - CHAD 

Cluster Analysis

Cluster 1 

Pattern 

Group 

Cluster 2 

Pattern 

Group 

Cluster 3 

Pattern 

Group 

Transition Analysis 

Transition 

Probabilities 

Markov Selection

Individual Annual Average Activity 

Winter Weekday 

Pattern Group 

Summer Weekday 

Pattern Group 

Weekend 

Pattern Group 

Cluster 1 

Pattern 

Cluster 2 

Pattern 

Cluster 3 

Pattern 

Weights Average Winter Weekday Pattern 

0.54 

Cluster Analysis Cluster Analys
H-15 

Figure 2. Comparison of predicted and observed average time in each of 5 microenvironments for age/genseasons. Figure 3. Comparison of predicted and observed average time in each of 4 microenvironments for age/genseasons. 

05

101520

0 5 10 15 20

Observed (hours/day)

Predicted (hours/day) Indoor, home Indoor, school indoor, other Outdoor In vehicle

012345

012345

Observed (hours/day)

Predicted (hours/day) Indoor, school indoor, other Outdoor In vehicle
H-16 

Figure 4. Comparison of predicted and observed variance across persons for time spent in each of 5 microage/gender groups and seasons. Figure 5. Comparison of predicted and observed the average within-person variance for time spent in each 

microenvironments by age/gender groups and seasons.

0

1020304050607080

0 20 40 60 80

Observed

Simulated

girls, 6-10, summergirls, 6-10, w interboys , 6-10, summerboys, 6-10, w intergirls, 11-12, summergirls, 11-12, w interboys, 11-12, summerboys, 11-12, w inter

05

1015202530

0 10 20 30

Observed

Simulated

girls, 6-10, summergirls, 6-10, w interboys , 6-10, summerboys, 6-10, w intergirls, 11-12, summergirls, 11-12, w interboys, 11-12, summerboys, 11-12, w inter
APPENDIX I. ESTIMATING NEAR ROADWAY POPULATIONS 
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I-1 

MEMORANDUM 

To: Chad Bailey 

From: Arlene Rosenbaum and Kevin Wright 

Date: December 28, 2005 

Re: Estimating near roadway populations and areas for HAPEM6

PURPOSE AND BACKGROUND 

In its 2001 regulation of mobile source air toxics (the “MSAT Rule”) EPA’s Office of 

Transportation and Air Quality (OTAQ) committed to further study of the range of 

concentrations to which people are exposed for consideration in future rulemaking. As part of the 

Technical Analysis Plan outlined in that research, OTAQ undertook research activity looking at 

the air quality in immediate proximity of busy roadways and highways. Concentrations of 

pollutants directly emitted by motor vehicles show statistically significant elevation in 

concentrations with increased proximity to busy roadways. 

The Hazardous Air Pollutant Exposure Model (HAPEM) is a screening-level exposure model 

appropriate for assessing average long-term inhalation exposures of the general population, or a 

specific sub-population, over spatial scales ranging from urban to national. HAPEM uses the 

general approach of tracking representatives of specified demographic groups as they move 

among indoor and outdoor microenvironments and among geographic locations. The estimated 

pollutant concentrations in each microenvironment visited are combined into a time-weighted 

average concentration, which is assigned to members of the demographic group. 

 

Indoor microenvironment concentrations are estimated by applying scalar factors to outdoor tract 

concentrations, which are some of the required inputs. These scalar factors are derived from 

published studies of concurrent concentration measurements indoors and outdoors. 

In the previous version, HAPEM5, if only a single outdoor concentration is provided for each 

Census tract, as is typical, this concentration is assumed to uniformly apply to the entire Census 

tract. For this version, HAPEM6, we refined the model to account for the spatial variability of 

outdoor concentrations within a tract due to enhanced outdoor concentrations of onroad mobile 

source pollutants at locations near major roadways. The term “major roadway” is used to 

describe a “Limited Access Highway”, “Highway”, “Major Road” or “Ramp”, as defined by the 

Census Feature Class Codes (CFCC). The new version of HAPEM more accurately reflects the 

average and variability of exposure concentrations within each Census tract by accounting for 

some of the spatial variability in the outdoor concentrations within the tract, and by extension 

some of the spatial variability in indoor concentrations within the tract. 

Accomplishing this refinement to HAPEM required several activities, including the development 

and implementation of an approach for creating a database of the fraction of people within each 

US Census tract living near major roadways. This memorandum describes that activity. 
I-2 

OVERVIEW AND SPECIFICATIONS 

The objective of this task was to estimate the fraction of people in each of 6 demographic groups 

in each US Census tract living near major roadways. 

The basic analysis was conducted at the US Census block level for populations stratified by age, 

gender, and race/ethnicity. The block level data was then aggregated up to the tract level for 

populations stratified by age only for use in HAPEM6. 

The data bases used for this task were: 

• The Environmental Sciences Research Center (ESRI) StreetMap US roadway geographic 

database (which includes NavTech, GDT and TeleAtlas rectified street data) 

• A geographic database of US Census block boundaries, extracted using the PCensus 2000 

Census data extraction tool for Census file SF1 

• A geographic data for US Census block boundaries in Puerto Rico and the US Virgin Islands 

obtained from Proximity 

Although the block file is an intermediate product for this project, it will be retained to facilitate 

the re-specification of demographic groups for possible future analyses. Therefore, this file 

contains the most resolved age-gender groups available at the block level from the US Census 

STF1. The age groups for the block level data are as follows: 

• 19 single-year age groups from 0-19 (P14) 

• 2 single-year age groups 20-21 (P12) 

• 16 age groups (P12) 

o 22 to 24 years 

o 25 to 29 years 

o 30 to 34 years 

o 35 to 39 years 

o 40 to 44 years 

o 45 to 49 years 

o 50 to 54 years 

o 55 to 59 years 

o 60 and 61 years 

o 62 to 64 years 

o 65 and 66 years 

o 67 to 69 years 

o 70 to 74 years 

o 75 to 79 years 

o 80 to 84 years 

o 85 years and over. 
I-3 

The aggregated age groups for the tract level data are: 

• 0-1 

• 2-4 

• 5-15 

• 16-17 

• 18-64 

• 65+

The race/ethnic groups (block level only) are: 

• non-Hispanic White (alone or in combination - P010003) 

• non-Hispanic Black (alone or in combination - P010004) 

• non-Hispanic American Indian /Alaskan Native (alone or in combination - P010005) 

• non-Hispanic Asian (alone or in combination - P010006) 

• non-Hispanic Native Hawaiian/ Pacific Isalander (P010007) 

• non-Hispanic other (alone or in combination - P010008) 

• Hispanic (alone or in combination - P010009)

The spatial stratifications of the populations (block and tract level) are: 

• Those residing within 75 meters of a major roadway 

• Those residing from 75 to 200 meters from a major roadway 

• Those residing at greater than 200 meters from a roadway.

In addition, the fraction of the area of each Census block and tract that is located within the same 

distance ranges from a major roadway was determined. 

PROCEDURES 

For all the spatial modeling and geoprocessing operations in this study ICF utilized ArcInfo 

software. ArcInfo is the most extensive version of ArcGIS 9.1, the industry’s standard for 

Geographic Information Systems, produced by ESRI of Redlands, CA. 

Due to the size of the roadway and block geography files, most of the processing was conducted 

on a county-by-county basis. The files for some counties, however, still exceeded ArcInfo’s 

capacity and were processed tract-by-tract. A few counties in Arizona needed special handling 

because even at the tract level they exceeded ArcInfo’s capacity and were disaggregated into 

smaller pieces for processing. 

1. Because populations are not generally evenly distributed within blocks, it was 

assumed that the block populations all reside within 150 meters of any road within the 

block of designation “local” or greater as defined by the Census Feature Class Codes 

(CFCC). Thus, the first step was to create a 150-meter buffer around all roadways 

within the block. This buffer served as a “clipped” block boundary defining the 
I-4 

portion of the block containing residential populations. The block population was 

assumed to be uniformly distributed within the “clipped” block boundary. 

2. Next a 75-meter buffer and a 200-meter buffer were created around all major 

roadways within the block. These buffers were overlaid on the “clipped” block 

boundary, and the fraction of the “clipped” block area that that fell within each buffer 

was calculated. This area fraction was assumed to equal the population fraction that 

fell within each buffer, and the fractions were applied to each population 

stratification. 

3. The 75-meter buffer and the 200-meter buffer were also overlaid on the unclipped 

block boundary to determine the fraction of the total block area that fell with each of 

the buffers. 

4. The block level fractions for area and populations were then aggregated up to the tract 

level, and the population stratifications were aggregated up to the 6 tract age groups 

only. 

RESULTS 

The resulting database consists of 2 files types: (1) a block file for each state, and (2) a nationwide tract file. 

The block files contains the following 249 fields for each block: 

• block FIPS code 

• total population 

• total area 

• area within 75 meters of a major roadway 

• area from 75 to 200 meters from a major roadway 

• for each of 74 age-gender groups: 

o population residing within 75 meters of a major roadway 

o population residing between 75 and 200 meters from a major roadway 

o population residing more than 200 meters from a major roadway 

• sum of race/ethnic populations (note; this may differ slightly from the total population due to 

some double-counting of persons with more than 1 race/ethnicity) 

• for each of 7 race/ethnic groups: 

o population residing within 75 meters of a major roadway 

o population residing between 75 and 200 meters from a major roadway 

o population residing more than 200 meters from a major roadway 

Note that because of the limitations of the US Census data the block level populations 

could not be stratified by age, gender, and race together, 
I-5 

The tract file contains the following 22 fields for each tract 

• tract FIPS code 

• fraction of area within 75 meters of a major roadway 

• fraction of area between 75 and 200 meters from a major roadway 

• fraction of area more than 200 meters from a major roadway 

• for each of 6 age groups: 

o fraction of population residing within 75 meters of a major roadway 

o fraction of population residing between 75 and 200 meters from a major roadway 

o fraction of population residing more than 200 meters from a major roadway 

To date only a subset of states have been completely processed. For this subset state 

summaries of the fraction of population living within various distances of major 

roadways are presented in Table 1. 

Table 1. Fraction of population residing at various distances from major roadways for 

selected states. 

STATE Distance from major roadways 

< 75 meters 75 – 200 meters > 200 meters 

Colorado 0.22 0.33 0.45 

Georgia 0.17 0.24 0.59 

New York 0.31 0.36 0.33 

J-1 

APPENDIX J. WEEKLY MODEL-TO-MONITOR COMPARISONS 
J-2 

Weekly Average Personal Ozone Concentration

--Upland, Week of 6/7/95--

0

10

20

30

40

50

60

0 20 40 60 80 100

Cumulative Percentile

Concentration 

(ppb)

measured

APEX n=24

Weekly Average Outdoor Ozone Concentration

--Upland, Week of 6/7/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration 

(ppb)

measured

APEX

n=21

Weekly Average Indoor Ozone Concentration

--Upland, Week of 6/7/95--

0

10

20

30

40

50

0 20 40 60 80 100

Cumulative Percentile

Concentration 

(ppb)

measured

APEX n=21
J-3 

Weekly Average Indoor Ozone Concentration

--Upland, Week of 6/21/95--

0

10

20

30

40

50

0 20 40 60 80 100

Cumulative Percentile

Concentration 

(ppb)

measured

APEX n=19

Weekly Average Outdoor Ozone Concentration

--Upland, Week of 6/21/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration 

(ppb)

measured

APEX

n=19

Weekly Average Personal Ozone Concentration

--Upland, Week of 6/21/95--

0

10

20

30

40

50

60

0 20 40 60 80 100

Cumulative Percentile

Concentration 

(ppb)

measured

APEX

n=24
J-4 

Weekly Average Personal Ozone Concentration

--Upland, Week of 6/28/95--

0

10

20

30

40

50

60

0 20 40 60 80 100

Cumulative Percentile

Concentration 

(ppb)

measured

APEX

n=19

Weekly Average Outdoor Ozone Concentration

--Upland, Week of 6/28/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration 

(ppb)

measured

APEX

n=14

Weekly Average Indoor Ozone Concentration

--Upland, Week of 6/28/95--

0

10

20

30

40

50

0 20 40 60 80 100

Cumulative Percentile

Concentration 

(ppb)

measured

APEX n=15
J-5 

Weekly Average Indoor Ozone Concentration

--Upland, Week of 7/05/95--

0

10

20

30

40

50

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX n=12

Weekly Average Outdoor Ozone Concentration

--Upland, Week of 7/05/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=14

Weekly Average Personal Ozone Concentration

--Upland, Week of 7/05/95--

0

10

20

30

40

50

60

0 20 40 60 80 100

Cumulative Percentile

Concentration 

(ppb)

measured

APEX

n=10
J-6 

Weekly Average Personal Ozone Concentration

--Upland, Week of 7/19/95--

0

10

20

30

40

50

60

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=15

Weekly Average Outdoor Ozone Concentration

--Upland, Week of 7/19/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=14

Weekly Average Indoor Ozone Concentration

--Upland, Week of 7/19/95--

0

10

20

30

40

50

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX n=14
J-7 

Weekly Average Indoor Ozone Concentration

--Upland, Week of 8/02/95--

0

10

20

30

40

50

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=11

Weekly Average Outdoor Ozone Concentration

--Upland, Week of 8/02/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=11

Weekly Average Personal Ozone Concentration

--Upland, Week of 8/02/95--

0

10

20

30

40

50

60

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=15
J-8 

Weekly Average Personal Ozone Concentration

--Upland, Week of 8/09/95--

0

10

20

30

40

50

60

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=18

Weekly Average Outdoor Ozone Concentration

--Upland, Week of 8/09/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=14

Weekly Average Indoor Ozone Concentration

--Upland, Week of 8/09/95--

0

10

20

30

40

50

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=13
J-9 

Weekly Average Indoor Ozone Concentration

--Upland, Week of 8/16/95--

0

10

20

30

40

50

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX n=17

Weekly Average Outdoor Ozone Concentration

--Upland, Week of 8/16/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=17

Weekly Average Personal Ozone Concentration

--Upland, Week of 8/16/95--

0

10

20

30

40

50

60

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=18
J-10 

Weekly Average Personal Ozone Concentration

--Upland, Week of 8/23/95--

0

10

20

30

40

50

60

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=20

Weekly Average Outdoor Ozone Concentration

--Upland, Week of 8/23/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=15

Weekly Average Indoor Ozone Concentration

--Upland, Week of 8/23/95--

0

10

20

30

40

50

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX n=16
J-11 

Weekly Average Indoor Ozone Concentration

--Upland, Week of 8/30/95--

0

10

20

30

40

50

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX n=15

Weekly Average Outdoor Ozone Concentration

--Upland, Week of 8/30/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=14

Weekly Average Personal Ozone Concentration

--Upland, Week of 8/30/95--

0

10

20

30

40

50

60

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=23
J-12 

Weekly Average Personal Ozone Concentration

--Upland, Week of 9/06/95--

0

10

20

30

40

50

60

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=20

Weekly Average Outdoor Ozone Concentration

--Upland, Week of 9/06/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=17

Weekly Average Indoor Ozone Concentration

--Upland, Week of 9/06/95--

0

10

20

30

40

50

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX n=17
J-13 

Weekly Average Indoor Ozone Concentration

--Upland, Week of 9/13/95--

0

10

20

30

40

50

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX n=17

Weekly Average Outdoor Ozone Concentration

--Upland, Week of 9/13/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=16

Weekly Average Personal Ozone Concentration

--Upland, Week of 9/13/95--

0

10

20

30

40

50

60

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=18
J-14 

Weekly Average Personal Ozone Concentration

--Upland, Week of 9/20/95--

0

10

20

30

40

50

60

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=14

Weekly Average Outdoor Ozone Concentration

--Upland, Week of 9/20/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=12

Weekly Average Indoor Ozone Concentration

--Upland, Week of 9/20/95--

0

10

20

30

40

50

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX n=12
J-15 

Weekly Average Indoor Ozone Concentration

--Upland, Week of 4/24/95--

0

10

20

30

40

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX n=14

Weekly Average Outdoor Ozone Concentration

--Upland, Week of 4/24/96--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=14

Weekly Average Personal Ozone Concentration

--Upland, Week of 4/24/96--

0

10

20

30

40

50

60

0 20 40 60 80 100

Cumulative Percentile

Concentration 

(ppb)

measured

APEX

n=15
J-16 

Weekly Average Personal Ozone Concentration

--Upland, Week of 5/08/96--

0

10

20

30

40

50

60

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=15

Weekly Average Outdoor Ozone Concentration

--Upland, Week of 5/08/96--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=10

Weekly Average Indoor Ozone Concentration

--Upland, Week of 5/08/95--

0

10

20

30

40

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=10
J-17 

Weekly Average Indoor Ozone Concentration

--Upland, Week of 5/15/95--

0

10

20

30

40

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX n=13

Weekly Average Outdoor Ozone Concentration

--Upland, Week of 5/15/96--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=12

Weekly Average Personal Ozone Concentration

--Upland, Week of 5/15/96--

0

10

20

30

40

50

60

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX n=17
J-18 

We ekly Average Indoor Ozone Concentration

--Lake Arrowhe ad, Week of 6/7/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

measured

APEX n=22

We ekly Average Outdoor Ozone Concentration

--Lake Arrowhead, We ek of 6/7/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

measured

APEX

n=22

We ekly Average Personal Ozone Concentration

--Lake Arrowhe ad, Wee k of 6/7/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

measured

APEX

n=27
J-19 

Weekly Average Indoor Ozone Concentration

--Lake Arrowhead, Week of 6/21/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration 

(ppb)

measured

APEX

Weekly Average Outdoor Ozone Concentration

--Lake Arrowhead, Week of 6/21/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration 

(ppb)

measured

APEX

n=21

Weekly Average Personal Ozone Concentration

--Lake Arrowhead, Week of 6/21/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration 

(ppb)

measured

APEX

n=31
J-20 

Weekly Average Personal Ozone Concentration

--Lake Arrowhead, Week of 6/28/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration 

(ppb)

measured

APEX

n=15

Weekly Average Outdoor Ozone Concentration

--Lake Arrowhead, Week of 6/28/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=13

Weekly Average Indoor Ozone Concentration

--Lake Arrowhead, Week of 6/28/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration 

(ppb)

measured

APEX n=12
J-21 

Weekly Average Indoor Ozone Concentration

--Lake Arrowhead, Week of 7/05/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX n=11

Weekly Average Outdoor Ozone Concentration

--Lake Arrowhead, Week of 7/05/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=11

Weekly Average Personal Ozone Concentration

--Lake Arrowhead, Week of 7/05/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration 

(ppb)

measured

APEX

n=17
J-22 

Weekly Average Indoor Ozone Concentration

--Lake Arrowhead, Week of 7/12/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

Weekly Average Outdoor Ozone Concentration

--Lake Arrowhead, Week of 7/12/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

Weekly Average Personal Ozone Concentration

--Lake Arrowhead, Week of 7/12/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=20
J-23 

Weekly Average Indoor Ozone Concentration

--Lake Arrowhead, Week of 7/19/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=13

Weekly Average Outdoor Ozone Concentration

--Lake Arrowhead, Week of 7/19/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=14

Weekly Average Personal Ozone Concentration

--Lake Arrowhead, Week of 7/19/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=18
J-24 

Weekly Average Personal Ozone Concentration

--Lake Arrowhead, Week of 8/02/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=18

Weekly Average Outdoor Ozone Concentration

--Lake Arrowhead, Week of 8/02/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=13

Weekly Average Indoor Ozone Concentration

--Lake Arrowhead, Week of 8/02/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX n=14
J-25 

Weekly Average Indoor Ozone Concentration

--Lake Arrowhead, Week of 8/09/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX n=10

Weekly Average Outdoor Ozone Concentration

--Lake Arrowhead, Week of 8/09/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=10

Weekly Average Personal Ozone Concentration

--Lake Arrowhead, Week of 8/09/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=19
J-26 

Weekly Average Personal Ozone Concentration

--Lake Arrowhead, Week of 8/16/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=17

Weekly Average Outdoor Ozone Concentration

--Lake Arrowhead, Week of 8/16/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=13

Weekly Average Indoor Ozone Concentration

--Lake Arrowhead, Week of 8/16/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX n=13
J-27 

Weekly Average Indoor Ozone Concentration

--Lake Arrowhead, Week of 8/23/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX n=16

Weekly Average Outdoor Ozone Concentration

--Lake Arrowhead, Week of 8/23/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=17

Weekly Average Personal Ozone Concentration

--Lake Arrowhead, Week of 8/23/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=22
J-28 

Weekly Average Personal Ozone Concentration

--Lake Arrowhead, Week of 8/30/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=17

Weekly Average Outdoor Ozone Concentration

--Lake Arrowhead, Week of 8/30/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=12

Weekly Average Indoor Ozone Concentration

--Lake Arrowhead, Week of 8/30/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=12
J-29 

Weekly Average Indoor Ozone Concentration

--Lake Arrowhead, Week of 9/06/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX n=15

Weekly Average Outdoor Ozone Concentration

--Lake Arrowhead, Week of 9/06/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=15

Weekly Average Personal Ozone Concentration

--Lake Arrowhead, Week of 9/06/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=25
J-30 

Weekly Average Personal Ozone Concentration

--Lake Arrowhead, Week of 9/13/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=18

Weekly Average Outdoor Ozone Concentration

--Lake Arrowhead, Week of 9/13/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=16

Weekly Average Indoor Ozone Concentration

--Lake Arrowhead, Week of 9/13/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX n=16
J-31 

Weekly Average Indoor Ozone Concentration

--Lake Arrowhead, Week of 9/20/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX n=16

Weekly Average Outdoor Ozone Concentration

--Lake Arrowhead, Week of 9/20/95--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=17

Weekly Average Personal Ozone Concentration

--Lake Arrowhead, Week of 9/20/95--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=22
J-32 

Weekly Average Personal Ozone Concentration

--Lake Arrowhead, Week of 4/24/96--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

Weekly Average Indoor Ozone Concentration

--Lake Arrowhead, Week of 4/24/96--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

Weekly Average Outdoor Ozone Concentration

--Lake Arrowhead, Week of 4/24/96--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration 

(ppb)

measured

APEX
J-33 

Weekly Average Indoor Ozone Concentration

--Lake Arrowhead, Week of 5/01/96--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration 

(ppb)

measured

APEX n=12

Weekly Average Outdoor Ozone Concentration

--Lake Arrowhead, Week of 5/01/96--

0

20

40

60

80

100

0 20 40 60 80 100

Cumulative Percentile

Concentration 

(ppb)

measured

APEX

n=7

Weekly Average Personal Ozone Concentration

--Lake Arrowhead, Week of 5/01/96--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration (ppb)

measured

APEX

n=17
J-34 

Weekly Average Personal Ozone Concentration

--Lake Arrowhead, Week of 5/08/96--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration 

(ppb)

measured

APEX

n=23

Weekly Average Outdoor Ozone Concentration

--Lake Arrowhead, Week of 5/08/96--

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100

Cumulative Percentile

Concentration 

(ppb)

measured

APEX

n=15

Weekly Average Indoor Ozone Concentration

--Lake Arrowhead, Week of 5/08/96--

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Cumulative Percentile

Concentration 

(ppb)

measured

APEX n=16
United States 

Environmental Protection Agency 

Office of Air Quality Planning and Standards 

Health and Environmental Impacts Division 

Research Triangle Park, NC 

Publication N