# Ozone Population Exposure Analysis for Selected Urban AreasEPA-452/R-07-010 July 2007



## Ozone Population Exposure Analys is 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 CarolinaDISCLAIMER

This document has been prep ared by staff from the Ambient Standards Group, Office of Air Quality Planning and Standard s, U.S. Environmental Protecti on 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 circ ulated to obtain review and comment from the Clean Air Scientific Adviso ry Committee (CASAC) and the general public. Comments on this document should be addresse d to John E. Langstaff, U.S. Environmental Protection Agency, Office of Air Quality Planni ng 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 Micr oenvironmental 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 Alte rnative 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 UNCE RTAINTIES OF THE MODELING APPROACH....................................................................................................................... . 43 4.1 Methodology ............................................................................................................. 43ii 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.................................................................................................................... 9 3

APPENDIX A. ANALYSIS OF AIR EXCHANGE RATE DATA
APPENDIX B. THEORETICAL DEV ELOPMENT 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 RE SIDENTIAL AIR CONDITIONERS AND THE EFFECTS OF SWAMP COOLERS
APPENDIX G. ANALYSIS OF NH IS ASTHMA PREVALENCE DATA
APPENDIX H. ALTERNATIVE LONGITUDINAL ACTIVITY PATTERN ALGORITHM
APPENDIX I. ESTIMATING NEAR ROADWAY POPULATIONSiii List of Tables

Table 1-1. Urban areas a nd time periods modeled ........................................................................ 2 Table 2-1. Profile Variables in APEX ......................................................................................... 1 1 Table 2-2. Mass Balance Model Parameters................................................................................ 14 Table 2-3. Factors Model Parameters .......................................................................................... 1 7 Table 2-4. Ventilation Re gression Parameters............................................................................. 19 Table 2-5. APEX Output Files.................................................................................................. ... 21 Table 3-1 The Numbers of Oz one Monitors in the Study Areas ............................................... 24 Table 3-2. List of the Current and Alternative 8-hour Ozone St andard Scenarios used in the Exposure Analysis .............................................................................................................. .. 25 Table 3-3 The Meteorological Stations for Each Study Area.................................................... 26 Table 3-3. Summary of St udies Used in CHAD.......................................................................... 30 Table 3-4. Microenvironment Parameter Information................................................................. 33 Table 3-5. List of Microenvironmen ts and Calculation Methods Used....................................... 34 Table 3-6. Mapping of CHAD activity locations to AP EX microenvironments ........................ 39 Table 4-1. Assignment of reside ntial air exchange rate dist ributions 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 th e current standard: 2002 counts of the general po pulation with any or three or mo re 8-hour ozone exposures above 0.07 ppm concomitant with modera te or greater exertion. ................................................... 65 Table 6-4. Sensitivity to activity database with air quality meeting th e current standard: 2002 counts of children (ages 5-18) with any or th ree or more 8-hour ozone exposures above 0.07 ppm concomitant with modera te 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 m oderate 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 m oderate 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 c ounts 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 populati on with any or three or more 8-hour ozone exposures above 0.07 ppm concomitant with moderate or greater exertion ....................................................................................................................... .......... 68iv 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 populat ion 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: 200 2 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 m oderate or greater exertion.......................................... 70 Table 6-14. Sensitivity to longitudinal activ ity pattern algorithm: 2002 counts of Boston population groups with any or three or mo re 8-hour ozone exposures above 0.07 ppm concomitant with moderate or greater exertion. ................................................................... 71 Table 6-15. Sensitivity to longitudinal diary algo rithm: 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 m oderate or greater exertion.......................................... 72 Table 6-16. Sensitivity to longitudinal diary algo rithm: 2002 days per person with 8-hour ozone exposures above 0.07 ppm concomitant with mo derate or greater exertion for Atlanta general population and ch ildren (ages 5-18)......................................................................... 72 Table 6-17. Sensitivity to near roadway proxim ity 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......................................................................................... 74v Acknowledgements

In addition to EPA staff, the following pe ople 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 Smithvi This page intentionally left blank.1 1. INTRODUCTION

The Clean Air Act, which was last ame nded in 1990, requires EPA to set National Ambient Air Quality Standards (NAAQS) for widesp read pollutants from numerous and diverse sources considered harmful to public health a nd 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 Ai r Act requires periodic review of the science upon which the standards are based a nd the standards themselves to (1) ensure that they provide adequate health and environmenta l protection and (2) update those standards as necessary. Under the NAAQS review process, EPA's O ffice of Research and Development (ORD) develops an “air quality criter ia document” – a compilation and evaluation by EPA scientific staff and other expert authors of the latest scie ntific knowledge useful in assessing the health and welfare effects of the air pollutant. In August 2005, the second external re view draft of the Air Quality Criteria for Ozone and Related Phot ochemical Oxidants was released for public comment and review by EPA's Clean Air Scientif ic Advisory Committee (CASAC), and a final document was released in 2006 (Ozone Criteri a Document, US EPA, 2006a). The Ozone Criteria Document presents the la test 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 inpu t 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 exposur e 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 pr esented and discussed in the Ozone Staff Paper (US EPA, 2007); only selected resu lts 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, genera lly 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 th e 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 di scussed 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 ge neral population residing in each area modeled, as well as for school-age children (age s 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 ri sk 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 pollu tants at the local, urban, and consolidated metropolitan levels. APEX, al so known as TRIM.Expo, is the human inhalation exposure module of EPA’s Total Risk Integrat ed Methodology (TRIM) model framework (EPA, 1999), a modeling system with multimedia cap abilities for assessing human health and ecological risks from hazardous and criteria air pollutants. It is being developed to support evaluations with a scie ntifically sound, flexible, and us er-friendly methodology. Additional information on the TRIM modeling system, as we ll 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 Am bient Air Quality Standards (NAAQS) Exposure Model (NEM) series of models. The NE M 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., 19 79). 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 pr obabilistic 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 in cluded a one-compartment mass-balance model to estimate CO concentrations in indoor microe nvironments. The application of this model to Denver, Colorado has been documented in Johnson et al. (1992). Severa l newer versions of pNEM/O3 were developed in th e early- to mid-1990’s, includ ing versions developed for applications to nine urban areas for the general population, out door 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 devel oped 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 measur e 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 ve rsion, APEX2, was substantially different, particularly in the us e of a personal profile approach rather than a cohort simulation approach. APEX3 introduced a number of new f eatures including automatic site selection from national databases, a series of new output tabl es providing summary expos ure and dose statistics, and a thoroughly reorganized method of describi ng 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 m ovements through time and space (e.g., at home, in vehi cles) to estimate their exposure to the subject pollutant. APEX models commuting and thus exposures at both home and work locations for individuals who wo rk in different areas than they live.
APEX can be conceptualized as a simulated field study that would involve selecting an actual sample of specific individu als who live in (or work and live in) a geographic area and then continuously monitoring their act ivities and subsequent inhalati on 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 possi ble) of the actual people in the study area;

• The activity patterns of the sampled indivi duals (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 simila r 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 es timated by the model using a set of userinput ambient outdoor concentrations and inform ation on the behavior of the pollutant in various microenvironments;

• Various reductions in ambient air quality leve ls can be simulated by either adjusting air quality concentrations to atta in alternative ambient standa rds under consideration or by reducing source emissions and obtaining resu lting air quality m odeling outputs that reflect these potential emission reductions, and

• The model attempts to account for the most significant factors contri buting to inhalation exposure – the temporal and spatial distribut ion of people and pollutant concentrations A microenvironmentis 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 micr oenvironments – while also allowing the flexibility to adjust some of these factor s for regulatory assessment and other reasons.
All models have limitations that require the us e of assumptions. Limitations of APEX lie primarily in the uncertainties associated with da ta distributions input to the model (e.g., human activity patterns). Primary uncertainties and as sumptions 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 em ployed outside the home is assumed to always remain in the residentia l 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 th e 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 th an one subject. Each simulated person essentially becomes a composite of several actual people in the unde rlying activity data.

• The model currently does not capture certain correlations among hu man 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 pr ofiles are held constant, tho ugh in reality they change as individuals age. This is ge nerally 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 expos ure to criteria and ai r toxic pollutants at local, urban, and regional scales. The user sp ecifies the geographic area to be modeled and the number of individuals to be simulated to repr esent this population. APEX then generates a personal profile for each simulated person that sp ecifies various parameter values required by the model. The model next uses diary-derived time/ac tivity data matched to each personal profile to generate an exposure event sequenc e (also referred to as “activity pattern” or “composite diary”) for the modeled individual that spans a specified ti me period, such as one year. Each event in the sequence specifies a start time, exposure dura tion, geographic location, microenvironment, and activity. Probabilistic algorithms are used to esti mate the pollutant concentration and ventilation6 (respiration) rate associated w ith each exposure event. The estimated pollutant concentrations account for the effects of ambient (outdoor) pollu tant concentration, penetration factors, air exchange rates, decay/deposition rates, and pr oximity 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 ra ndom sample of the population of interest, the distribution of modeled individual exposures can be extrapol ated 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 populat ion – based on user-defined criteria and availability of air quality and meteorol ogical data for the area. (Section 2.3.1)

2. Generate simulated individuals . APEX stochastically generates a sample of hypothetical individuals based on the census da ta for the study area and human profile distribution data (such as age- specific employment probabiliti es). 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 th e more stable the model resu lts 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 assi gning location codes in the supplied CHAD database to the user-specified microenvironments. The model then calculates hourly concentr ations 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 even t and the person’s activity. These values are averaged by clock hour to produce a se quence of hourly average exposures spanning the specified exposure period (typically one ye ar). These hourly values may be further aggregated to produce daily, monthly, and a nnual average exposure va lues. (Section 2.5)
The model simulation continues until expos ures 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- Nationaldatabase- Area-specificinput data- Intermediate stepor data- Simulationstep- Data processor- Output data- Nationaldatabase- Area-specificinput data- Intermediate stepor data- Simulationstep- Data processor- Output dataSector location data(latitude, longitude)Defined study area (sectorswithin a city radius and with airquality and meteorological datawithin their radii of influence)Sector population data(age/gender/race)Population withinthe study areaCommuting flow data(origin/destination sectors)Age/gender-specificphysiologicaldistribution data (bodyweight, height, etc)Distribution functions forprofile variables(e.g, probability of airconditioning)Locations of air quality andmeteorological measurements;radii of influenceStochasticprofile generatorDistribution functionsfor seasonal and dailyvarying profile variables(e.g., window status, carspeed)A simulated individual with thefollowing profile:• Home sector• Work sector (if employed)• Age• Gender• Race• Employment status• Home gas stove• Home gas pilot• Home air conditioner• Car air conditioner• Physiological parameters(height, weight, etc.)2000 Census tract-level data for the entire U.S. (sectors=tracts for the NAAQS ozone exposure application)Age/gender/tract-specificemployment probabilities1. Characterize study area2. Characterize study population3. Generate N number ofsimulated individuals (profiles)Figure 2-1. Overview of the APEX Model8Diary events/activitiesand personal information(e.g., from CHAD)Maximum/mean dailytemperature dataActivity diary pools by daytype/temperature categoryEach day in the simulationperiod is assigned to anactivity pool based on day typeand temperature categorySelected diary records for each day in the simulationperiod, resulting in a sequence of events(microenvironments visited, minutes spent, andactivity) in the simulation period, for an individualStochastic diaryselector usingage, gender, andemploymentStochasticcalculation of energyexpended per event (adjusted forphysiological limits and EPOC)and ventilationratesPhysiologicalparameters fromprofileSequence of events for anindividualProfile for anindividual4. Construct sequence of activity eventsfor each simulated individualFigure 2-1. Overview of the APEX Model, continued9Hourly air qualitydata for all sectorsSelect calculation method foreach microenvironment:• Factors• Mass balanceConcentrations for all eventsfor each simulated individualHourly concentrations andminutes spent in eachmicroenvironment visited bythe simulated individualAverage exposuresfor simulated person,stratified by ventilationrate:• Hourly• Daily 1-hour max• Daily 8-hour max• Daily...Microenvironments defined bygrouping of CHAD location codesCalculate hourlyconcentrations inmicroenvironmentsvisitedPopulation exposureindicators for:• Total population• Children• Asthmatic childrenSequence of events foreach simulated individualCalculateconcentrations in allmicroenvironments5. Calculate concentrations inmicroenvironments for all events foreach simulated individual6. Calculate hourlyexposures for eachsimulated individual7. Calculatepopulation exposurestatisticsFigure 2-1. Overview of the APEX Model, concluded10 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 provide d 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 specifi ed by latitude and longitude for some representative point (e.g., geographic ce nter). The current re lease 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 concentra tions to the tracts and microenvironments being modeled. The ambient air quality data are provi ded by the user as hourly time series for each district. As with tracts, each district has a representative lo cation (latitude and longitude). Districts can extend outsi de 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 locati on 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 (loca tions). As with districts, APEX calculates the distance from each tract to each temperature si te and assigns each tract to the nearest site.

2.3.2 Generate Simulated Individuals
APEX stochastically generates a user-speci fied number of simulated (hypothetical) persons to represent the populati on in the study area. Each simula ted person is represented by a “personal profile.” APEX genera tes 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 genera ted based on sets of distribution data;

• Physiological variables, which are gene rated based on age- and gender-specific distribution data; and

• Daily varying variables, which are generated based on distribu tion data that change daily during the simulation period.

APEX first selects and calculates demographic, residential, an d physiological variables (except for daily values) for all the specified number of simulated individuals, and then follows each individual over time and calculates exposures (a nd 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

Daily average car speed Daily average car speed In-vehicle 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 accordi ng to their joint distribution in th e 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 pe rson has the specified characteristic. These are randomly selected based on user-specified probab ilities. For example, a user could specify probabilities of 0.3 for not having an air conditioner and 0.7 for havi ng an air condit ioner in their home.
Physiological Profile Variables
The physiological variables are used for calculati ng ventilation rates. Input data to APEX provide gender- and age-specific di stributions for these variables.12 2.3.3 Construction of Activity Sequences
APEX probabilistically crea tes 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 supplie d with APEX for this purpose. A composite diary is a sequence of events that simulate s the movement of a modeled person through geographical locations and micr oenvironments during the simulation period. Each event is defined by geographic location, start time, dura tion, microenvironment vi sited, 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, employ ment status, occupation, day of week, daily maximum hourly average temp erature, 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 in to 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 th e 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 diar y 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 diar y days into a sequential longi tudinal diary for a simulated individual covering all days in the simulated period.
The method in APEX for creating longitudina l diaries that refl ect the tendency of individuals to repeat activities is based on reproducing realistic va riation in a user-selected key diary variable. APEX reads the va lues of the key variable from an external file. Currently, files have been constructed for both outdoor time a nd vehicle time for all CHAD diaries by summing the total time associated with “outdoor” and “v ehicle” CHAD location codes for each diary. The actual diary construction method ta rgets two statistics, D and A. The D statistic reflects the relative importance of within-p erson variance and between-person variance in the key variable. The A statistic quantifies the lag-one (day-to-da y) variable autocorrela tion. Desired D and A values for the key variable are selected by the us er and set in the APEX parameters file, and the method algorithm constructs a longitudinal diary th at preserves these parameters. Longitudinal diary data from a field study in children (Geyh et al., 2000), and s ubsequent 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 tw o 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 the13 model results are insensitive to small change s in these values. The longitudinal diary methodology is described further in Appendix C.

2.4 Algorithms for Calculating Micro environmental 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 th e various microenvironments visited by the simulated person by using the ambient air data fo r the relevant tracts and the user-specified method and parameters that are specific to each microenvironment. APEX calculates hourly concentrations in all the micr oenvironments at each hour of the simulation for each of the simulated individuals, based on the hourly ambien t air quality data specific to the geographic locations visited by the i ndividual. APEX provides two methods for calculating microenvironmental concentratio ns: 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; ther e 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 microe nvironment due to deposition, filtration, and chemical degradation; and

• Emissions from sources of a polluta nt inside the microenvironment.
Table 2-2 lists the parameters required by the ma ss balance method to calcul ate concentrations in a microenvironment. The proximity factor ( f

proximity ) 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 th e geographic location of the microenvironment (e.g., near a roadway). This fact or 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. R removal is defined as the removal rate of a pollutant fr om a microenvironment due to de position, filtration, and chemical reaction. The air exchange rate ( R air exchange ) is expressed in air change s 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 R removal ≥ 0

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

V

Volume of microenvironment m 3 V > 0

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

source removal out in C C C C Δ + Δ

− Δ

− Δ = dt (t) dC ME (2-1)

where:

d C ME (t) = Change in concentration in a microenvironment at time t (ppm),

) C in = Rate of change in microenvironmental concentration due to influx of air (ppm/hour),

) C out = Rate of change in microenvironm ental concentration due to outflux of air (ppm/hour),

) C removal = Rate of change in microenvironmental concentration due to removal processes (ppm/hour), and

) C source = 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, ) C in , ) C out , ) C removal , and ) C sourcel , is assumed to be constant.15 The change in microenvironmental concentration due to influx of air is represented by the following equation:

exchange air n penetratio proximity ambient in
in R x f x f x C dt t dC C = = Δ ) ( (2-2)

where:

C ambient = Ambient hourly outdoor concentration (ppm) f

proximity = Proximity factor (unitless) f penetration = Penetration factor (unitless) R air exchange = Air exchange rate (1/hour)
The change in microenvironmental concentra tion due to outflux of air is described by:

) ( ) ( t C R dt t dC C ME exchange air out

out × = = Δ (2-3)

The change in concentration due to deposition, filtration, and chemi cal degradation in a microenvironment is simulated based on the first-order equation:



### (t) C x R (t) )C R R (R dt (t) dC C ME removal ME chemical filtration deposition removal removal 

### = + + = = Δ (2-4)

where:

R deposition = Removal rate of a pollutant from a microenvironment due to deposition (1/hour) R

filtration = Removal rate of a pollutant from a microenvironment due to filtration (1/hour) R chemical = Removal rate of a pollutant from a microenvironment due to chemical degradation (1/hour) R removal = 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 ) C source will be uniformly equal to 0.0 for this study.

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

) ( ) ( dt (t) dC ME t C R t C R C ME removal ME exchange air in −

− Δ = (2-5)

Solving the differential equati on in Equation 2-5 leads to:16 ) exp( ) ) 0 ( ( ) ( t R R C C R C t C combined combined in
ME combined in
ME − Δ

− + Δ

= (2-6)

where:

C ME (0) = Concentration of a pollutant in a microenvironment at the beginning of a hour (ppm) C

ME (t) = Concentration of a pollutant in a microenvironment at time t within the time period of a hour (ppm)

R combined = R air exchange + R removal (1/hour)

Based on Equation 2-6, the following three hou rly concentrations in a microenvironment are calculated:

combined in ME equil ME R C t C C Δ

= ∞ → = ) ( (2-7)

) ( exp ) ) 0 ( ( combined equil ME ME equil ME end hourly ME R C C C C

− − + = (2-8)

combined combined equil ME ME equil ME hourlymean ME R R C C C dt dt t C
C ) ( exp 1 ) ) 0 ( ( ) (

1

0 1

0 − −

− + = = 

## ∫

∫ (2-9)

where:

equil ME C = Equilibrium concentration in a microenvironment (ppm) C

ME (0) = Concentration in a microenvir onment at the beginning of an hour (ppm)

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

hourlymean ME C = 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 concentrati on for a specific hour. The calculation continues to the next hour by using end hourly ME C for the previous hour as C ME ( 0)

.
2.4.2 Factors Model
The factors method is simpler than the ma ss balance method. It does not calculate concentration in a microenvironment from the concentration in the pr evious hour and it has17 fewer parameters. Table 2-3 lists the paramete rs required by the factors method to calculate concentrations in a microenvironm ent 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 use r-provided hourly air quality data:

n penetratio proximity ambient hourlymean ME 

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

where:

hourlymean ME C = Hourly concentration in a microenvironment (ppm) C

ambient = Hourly concentration in ambient environment (ppm) f

proximity = Proximity factor (unitless) f

penetration = Penetration factor (unitless)

2.4.3 Commuting Outside of the Study Area
APEX allows for some flexibility in the tr eatment of persons in the modeled population who commute to destinations out side the study area. By specify ing “KeepLeavers = No” in the simulation control parameters file (see Section 3.1), people who work in side the study area but live outside of it ar e not modeled, nor are pe ople who live in the study area but work outside of it. By specifying “KeepLeavers = Yes,” these commu ters 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 concentra tion is assumed to be related to the average concentration over al l air districts at the same point in time, and is calculated as:

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

where:

Ambient Concentration = Calculated ambient air concen trations 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 concentra tion 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 loca tions outside of the st udy area are determined from this ambient concentra tion by the same function as ap plies inside the study area.

2.5 Algorithms for Calculating Dose
Probabilistic algorithms are used to estimate th e 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 r ealistically, inhalation exposure and dose. The ventilation rate is derived from an energy expe nditure rate estimated for the specified activity.

2.5.1 Ventilation
Ventilation is a general term fo r the movement of air into an d out of the lungs. Minute or total ventilation is the am ount of air moved in or out of the lu ngs per minute. Quantitatively, the amount of air breathed in per minute (V I ) is slightly grea ter than the amount expired per minute (V E ). Clinically, however, this difference is no t important, and by convention minute ventilation is always measured on an expired sample, V E . The oxygen ventilation rate V O2 (l of O 2 /min) is related to the energy expenditure rate for the given event activity and the gi ven profile’s physiol ogy in terms of oxygen ventilation per unit energy expenditure, or:

ECF x EE V

O =

2 (2-12)

where:

EE = Energy expenditure (kcal/min) ECF = Energy conversion factor (l of O 2 /kcal).
ECF is based on the physiology of the individual being modeled. EE is related to the activityspecific energy expenditure rate a nd the basal or resting energy e xpenditure (metabolic) rate of the given profile, or:

RMR x MET EE = (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 ba sal or resting energy ex penditure 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 requi re two times the basal19 energy expenditure, or two MET, for most people, w ith 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) a nd using equation 2-13, one obtains:

BM MET x ECF x RMR BM V

O / / 2 = (2-14)

Graham and McCurdy (2005) describe an approach to estimate V E directly from VO 2 using a series of regression-based equations. Us ing 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 f our age groups and both genders. The algorithm accounts for differences in ventila tion rate due to activ ity level, variability within age groups, and variation both between and within individuals . Their model is implemented in APEX as:

i i i i i O i ew eb gender b age b BM V b b BM VE + + + + + + = ) * ( )) 1 ln( * ( )) / ln( * ( ) / ln( 3 2 2 1 0 (2-15)

where:

the V O2 /BM term is given in terms of th e APEX variables by equation 2-14, age is the age of the i ndividual in years, and gender is a flag with value -1 for males and +1 for females.
Random error ( ε ) is allocated to two vari ance components used to es timate the between-person (inter-individual variability ) residuals distribution (e b ) and within-pers on (intra-individual variability) residua ls distribution (e w ). The regression parameters b 0 , b 1 , b 2 , b 3 , and e b are assumed to be constant over time fo r a given simulated person, whereas e w varies from event to event. These parameters are randomly drawn from normal distributions w ith means and standard deviations given in Table 2-4. e b and e w have mean zero.
Table 2-4. Ventilation Regression Parameters

Age range mean b 0 stdev b 0 mean b 1 stdev b 1 mean b 2 stdev b 2 mean b 3 stdev b 3 stdev

e b stdev

e w

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 0.067620 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 mi smatch, an individual’s energy needs are met by anaerobic processes. The magnitude of the mi smatch 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 expe nditure deteriorate. After exercise ceases, ventilation and oxygen consumption will remain elev ated above baseline levels. This increased oxygen consumption was historically labe led 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 ar ea (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 th at 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 sk in area was found to follow a lo gnormal distribution that is a function of body weight according to:

6821

. 0 2781

. 2 BM e BSA
− = (2-16)

where:

BSA = body surface area (m 2 ) 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 co ncentrations in each microenvironment based on these ambient air concentrations, and the minut es 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 determ ined using the following equation:



### T t C C N

j j hourlymean j ME

i 

# ∑

= 

### = 1 ) ( ) ( (2-17)

where:21 C i = Hourly exposure concentration at clock hour I of the simulation period (ppm) N

= Number of events (i.e., micr oenvironments visited) in clock hour I of the simulation period.
hourlymean j ME C ) ( = Hourly mean concentration in microenvironment j (ppm)

t (j) = Time spent in microenvironment j (minutes) T = 60 minutes
From the hourly exposures, APEX calculates tim e series of 8-hour and daily average exposure concentrations that a simulated individual w ould experience during the simulation period. APEX then statistically summarizes and tabul ates the hourly, 8-hour, and daily exposures.

2.7 Model Output
All of the output files written by APEX are AS CII 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 exposur e, ventilation, and energy expe nditures, 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 out put 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, th e log file indicates the input files and parameter settings used for the simulati on 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 poi nts used in these tables are defined in the simulation control parameters file.2223 3. PREPARATION OF MODEL INPUTS
The APEX model inputs require ex tensive analysis and preparat ion in order to ensure the model run gives valid and relevant results. This ch apter 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 criti cal parameters. The chapter goes on to describe the sources of data for the APEX input files. File formats a nd physical file structures are not discussed in detail, as this information is presente d 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 paramete rs 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 larg e enough sample size to provide stable model results. The parameters controlling the locati on and size of the simulated area we re set to include all counties in the study area CSA.
The settings that allow for replacemen t of CHAD data that are missing gender, employment or age values were all set to precl ude replacing missing data. The width of the age window was set to 20 percent to in crease the pool of diaries availabl e 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 sele ction. 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 th e key predictor of exposur e 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 autocorrelati on 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 th e 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 charac terized 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 concentrati ons at a set of site s 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 ex hibit the year-to-year variability that is characteristic of ozone form ation. All of the sites in AIRS within the boundaries of each CSA were used in this analys is. APEX uses the concentrations from the24 closest site to represent ambient concentrations at diffe rent 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-Michi gan 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. Vi rginia, DC-MD-VA-WV 28 28 26

3.2.1 Missing Data Replacement
Missing air quality data were estimated by th e following procedure. Where there were consecutive strings of missing va lues (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 R 2 for each hour of the day, subject to the constraints that R 2 be greater than 0.5 and the number of regression data values is at least 50. If there were any remaining missing va lues at this point, for gaps of less than 9 hours, missing values were es timated by linear interpol ation between the valid values at the ends of the gap. Any remaini ng missing values were repl aced 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 O 3 NAAQS of 0.08 ppm, as well as seven alternative standards. This was done using a quadr atic rollback approach to adjust the hourly O 3 concentrations observed in 2002-2004 to yield a design value corresponding to the standard being modeled. Design valu es for the current 8-hour O 3 NAAQS are calculated as the 3-year averages of the annual 4 th daily maximum 8-hr average concentration25 based on the maximum monitor within an urba n area. The quadratic rollback technique combines both linear and quadratic elements to reduce higher concentratio ns 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 standa rd scenarios can be found in the Ozone Staff Paper.

Table 3-2. List of the Current and Alternativ e 8-hour Ozone Standard Scenarios used in the Exposure Analysis

Attainment Threshold Form of Standard Labels for graphs 0.084 ppm 3 rd -highest form 4 th -highest form 85/3 85/4 0.080 ppm 4 th -highest form 81/4

0.074 ppm 3 rd -highest form 4 th -highest form 5 th -highest form 75/3 75/4 75/5 0.070 ppm 4 th -highest form 71/4 0.064 ppm 4 th -highest form 65/4

3.4 Meteorological Data
Hourly temperature data are from the Nati onal 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 fi le, contains the locations of meteorological data recordings, expressed in latitude and longitude coordinates. This file also c ontains start and end dates for the data recording periods. The temp erature data file contains the data from the locations in the temperature zone location file. This file cont ains daily maximum and da ily 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-Gainesvi lle, 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 acco unt to develop accurate representations of study area demographics. Specifically, populat ion counts by area and em ployment 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 us ed census tract level data.
Tract-level population counts come from th e 2000 Census of Population and Housing Summary File 1. Summary File 1 (SF 1) contai ns the 100-percent data, which is the information compiled from the questions asked of all people a nd 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 in to a single “Other” class (“O”) for modeling purposes. Hispanics are not separated, as the Cens us Bureau did not consid er Hispanic to be a

race.
In the 2000 U.S. Census, estimates of empl oyment were developed by census tract. Employment data from the 2000 census can be f ound 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 em ployment 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 e xposure of this group with AP EX 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 Nati onal 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 define d by NHIS are the Census Regions: “Midwest,” “Northeast,” “South,” and “West.” The reported survey response s were weighted to take into account the complex survey design of the NHIS survey. Standa rd 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 relations hips to age showed statistically significant differences between the prevalence functions fo r the two genders and for the four regions. Therefore the relationships of prevalence to ag e were estimated separately for each gender and region. A scatterplot smoothing technique using the LOESS smoot her was applied to smooth the prevalence curves and compute the standard e rrors and confidence intervals for the smoothed prevalence estimates.

3.7 Commuting Database
As part of the population demographics input s, it is important to integrate working patterns into the assessment. In addition to usi ng 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 (C TPP). These data are available from the U.S. DOT Bureau of Transportation St atistics (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. These28 files contain counts of individua ls commuting from home to wo rk 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 di fferentiate people that work at home from those that commute within their home tract.
Commuting Distance Cutoff
A preliminary data analysis of the home-wor k 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 relationshi p also had a fairly constant sl ope but it was flatter, meaning that flows were not as sensitive to distance. A si mple 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 rapi dly with increasing dist ance. Beyond 120 km, the majority of the flow is made up of persons w ho 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 patt erns 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 w ithin 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 worker s do not commute from home to work on a daily basis. It is expected th at the cutoff reduced the 20 00 data by similar amounts.

Eliminated Records
A number of tract-to-tract pairs were elimin ated from the database for various reasons. A fair number of tract-to-tract pair s represented workers who either worked outside of the U.S. (9,631 tract pairs with 107,595 workers) or wo rked in an unknown locat ion (120,830 tract pairs with 8,940,163 workers). An additional 515 work ers 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 ac tivity pattern data to pred ict and estimate exposure to pollutants. Different human activities, such as ou tdoor 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 ha ve 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 di aries, 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 wa s created. Individuals filled out diaries of their daily activities and this information was inpu t 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 responde nts through their various activities.
There are four CHAD-related input files used in the APEX system. Tw o 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 activ ities are specified as a single point value (for instance, sleep), while othe rs, such as athletic e ndeavors or manual labor, are normally, lognormally, or otherwise statistica lly distributed. APEX samples from these distributions and calculates values to simulate the variable nature of activity levels among different people.30Table 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) ReferenceBaltimore A singlebuilding inBaltimore01/1997-02/1997,07/1998-08/199872-93 26 391 Diary Williams et al, 2000CaliforniaAdolescents andAdults (CARB)California 10/1987-09/1988 12-1718-941831,5791831,579Recall; Random Robinson et al. (1989),Wiley et al. (1991a)CaliforniaChildren(CARB)California 04/1989- 02/1990 0-11 1,200 1,200 Recall; Random Wiley et al. (1991b)Cincinnati(EPRI)Cincinnatimetropolitanarea03/1985-04/1985, 08/1985 0-86 888 2,614 Diary; Random Johnson (1989)Denver (EPA) Denvermetropolitanarea11/1982- 02/1983 18-70 432 805 Diary; Random Johnson (1984), Aklandet al. (1985)Los Angeles:ElementarySchool ChildrenLos Angeles 10/1989 10-12 17 51 Diary Spier et al. (1992)31Los Angeles:High SchoolAdolescentsLos Angeles 09/1990-10/1990 13-17 19 43 Diary Spier et al. (1992)National:NHAPS-AirNational 09/1992-10/1994 0-934,723 4,723 Recall; Random Klepeis et al. (1995),Tsang and Klepeis (1996)National:NHAPS-WaterNational 09/1992-10/1994 0-934,663 4,663 Recall; Random Klepeis et al. (1995),Tsang and Klepeis (1996)Washington,D.C. (EPA)Wash., D.C.metropolitanarea11/1982-02/1983 18-98 699 699 Diary; Random Hartwell et al. (1984),Akland et al. (1985)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 th at 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 wh ich no data are included in the database

Diary Events file . The human activity diary data are cont ained in a file that is distributed with APEX. This is a large f ile because it contains diaries fo r about 23,000 people broken out at intervals ranging from one minute to one hour. Thes e 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 su bjects in order to ac curately model their pollutant intake via metabolic processes. This is because physiological differences may cause people with the same exposure and activity scenario s to have different pollu tant intake levels. The physiological parameters file distributed with APEX is described in th e 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 concentra tions in different types of environments (e.g., indoors, in cars, outdoors) within an area with the same estimate d ambient air concentration. There are two basic methods for calculating concen trations in microenviro nments: the transfer factors method and the mass balance method. The parameters for both factors and mass balance calculations used in this simula tion are listed in Table 3-4.

Table 3-4. Microenvironment Parameter Information

Calculation Method Parameter Type with Abbreviation Units Distribution

Proximity (PR) unitless Normal distribution Transfer Factors 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 con centrations are from the air quality data input file. There are two parameters that affect the pollutant concentration ca lculation in the factors method, the proximity and penetration factors. Th e proximity factor is a unitless parameter that represents the proximity of the microenvironment to a monitoring st ation. The penetration factor is a unitless parameter that represents the fracti on of pollutant entering a microenvironment from outside the microenvironment via air exchange. The development of the proximity factors and penetration factors used in this anal ysis 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 av erage 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 e xposure locations for modeled individuals. For exposures to be estimated accu rately, it is important to have realistic microenvironments that match closely to the locations where actua l people spend time on a daily basis.

As discussed above, the two methods availabl e in APEX for calcula ting 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 us ed to calculate the microenvironment concentrations can be found in Table 3-5.

Table 3-5. List of Microenvironme nts 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 diff erent microenvironments in the Microenvironment Mapping File (see Section 3.8.4). Th ere are many more CHAD locations than microenvironment locations (there are 113 CHAD codes versus 12 microenvironments in this assessment) and thus most of the microe nvironments 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 m odels the exchange of outside air with the microenvironment, while the decay rate models th e rate of ozone breakdown or removal within35 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 excha nge rate. An excerpt from th e input file describing this microenvironment appears af ter this paragraph.

The first section of the excer pt specifies the air exchange rate distributions for the microenvironment. Average temperature and air conditioning presence, wh ich 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 studi es, air exchange rate es timates 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 1.5336 lognormal distributions were genera ted. These functions are specifi c to the cities in the model run. For cities with similar climatic and othe r relevant characteristics, the same distributions were used (e.g., New York, Philadelphia, and Bo ston use the same distri butions). The data sources used and the development of these distribu tions are discussed in detail in Appendix A. The ozone decay rate is characterized as a lognorm al 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, ther e is a large block of numbers (w hich totals ten rows) in the air exchange rate portion of th e file. In this block, the fi fth 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 Fahr enheit, 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 stat us, 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 th e above example, there are actually four different distributions for each air conditioning setting; the last two distribu tions 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 esti mated that 85 percent of the population has air conditioning in the home, and 15 percent does no t (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. Us ing 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 th e 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 de veloping these functions are de tailed in Appendix A. An excerpt from the input file desc ribing one of these microenvironments is given on the next page.

As with the Indoor-Residence microenvironm ent, these microenvironments use both air exchange rates and decay rates to calculate e xposures 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 l ognormal 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 Ga rage/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 appl icable to outdoor environments. An excerpt from the file describing this microenvironment follows this paragraph.

The distribution for the proximity factor wa s 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). Ve hicle tests were conducted according to an experimental design specifying th e vehicle type, road type, vehi cle speed, and ventilation mode.

Microenvironment 10: Outdoors-General. The general outdoor environment concentrations should be well represented by the ambient monitors. Ther efore 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 1.5338 Microenvironments 11 and 12: In Vehicl e- 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 expo sure. 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 deve loped using the inside-vehicle to outsidevehicle ratios from the Cinci nnati ozone study previously men tioned (Johnson et al, 1995). Three proximity factor distributions were develo ped, 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 discusse d in Section 3.11. Again, thes e distributions were developed based on the Cincinna ti 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 m easured 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 deca y rates range from 0.95 to 8.05 hour -1 . A lognormal distribution was fit to the measurements from th is study, yielding a geometric mean of 2.5 and a geometric standard deviation of 1.5. These va lues are constrained to lie between 0.95 and 8.05 hour -1 . The specification of the decay ra te (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 0.16539 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_Transit40 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-Other41 3.11 Profile Functions

The Profile Functions file contains settings used to ge nerate results for variables related to simulated individuals. While certain settings for individuals are generated automatically by APEX based on other input files, including demogr aphic characteristics, others can be specified using this file. For example, the file may cont ain settings for determin ing 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 ex periment. APEX uses these fractions to stochastically ge nerate air conditioning status for profiled individuals. The derivation of this data is disc ussed 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 locati ons modeled, the percentage of vehicle miles traveled on each road type was generated fr om 2003 Federal Highway Administration data (FHWA, 2004). These percentages are listed as fractions on the fi fth 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 de velopment of the distributions in the microenvironments.43 4. PRINCIPAL LIMITATIONS AND UNCE RTAINTIES 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 ri sk. In general, the methods and the model used in this assessment c onform to the most contemporary modeling methodologies available. APEX is a powerful, hi ghly customizable modeling system that allows for the realistic estimation of air pollutant exposure to individuals. Sinc e it is based on human activity diaries and accounts for all important va riables known to affect exposure, it has the ability to effectively approximate actual conditions. In addition, th e data used to run the system were chosen because they were the best availabl e to ensure realistic and defensible results. However, there are constraints a nd uncertainties with the modeli ng approach and the input data that limit the realism and accu racy 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 f actors that were used to build the microenvironments in this assessment. A cons traint on this effort is that there are limited ozone exposure studies. In addi tion, there are geographical limita tions of the studies used to develop factors for this assessment. While th ese studies were genera lly 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 microe nvironments 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 conducte d 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 desp ite best efforts there could be different interpretations about which data sources and methodologies are appropri ate. Evaluation of several components of uncertain ty in specification of CSA-sp ecific 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 micr oenvironments that are used in the program are matched to CHAD data. Because there are fewer microenvironments than CHAD locations, there is some information lo st in this translation.

4.2 Input Data
Modeling results are heavily dependent on the qu ality of the data th at 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 charact erized data as inputs to the model is that limitations and other problems with the data are well understood. Stil l, the limitations and uncertainties of each of the data streams affect the overall quality of the model output. These44 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 fr om monitoring stations in the a ssessment areas. One strength of these data is that it is relatively easy to see signifi cant 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, ther e are limitations in the use of these data. Because APEX only uses one te mperature 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 qua lity. Some data issues specific to air quality data result from the nature of pollutant forma tion and dispersion. Becau se many variables affect pollutant fate and transport, it is difficult to de termine 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 ot her unknowns may effect how well the data represent pollutant concentrati ons in the area. However, be cause APEX uses hourly average ozone concentrations, the model employs a tempor ally 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 fr om U.S. Census data from the year 2000. This is a high quality data source for natio nwide population data in the U.S. However, the data do have limitations. The Census used rando m 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 uncerta inty 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, cer tain simplifying assumptions were made in order to better match reality or to make the data match APEX input specif ications. 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 resu lts. 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 characteris tics. Furthermore, on a larger scale, it is possible that national phys iological characteristics have drif ted somewhat since the publication45 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 th e 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 possi ble that some differences do exis t. In addition, the CHAD data are taken from numerous surveys that were perf ormed 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 populatio n at large in order to fulfill their specific mission when they were conducted. These issues a ffect the overall quality of the data that now resides in CHAD. An investiga tion 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-speci fic residential air exchange rate distributions used for this analysis. Appendix D details an analyses of uncertainty due to extrapolation of air exchange rate distributions am ong CSAs , and of within-CSA uncertainty due to sampling variation. In Appendix E we desc ribe an analysis of the uncertainty due to estimating daily air exchange ra te distributions from air exchange rate measurements with varying averaging times. The results of t hose investigations are summarized here.
Extrapolation among cities CSA-specific distributions for use with the APEX ozone model were developed for 12 target CSAs, as deta iled 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 in fluence air exchange rates (see Table 4-1). Such factors include age composition of housing stock, construction me thods, and other meteor ological variables not explicitly treated in the analysis, such as humid ity 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 acro ss cities and studies.
The analysis showed a relatively wide varia tion across different citie s in the air exchange rate geometric mean and standard deviation, st ratified 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 se nsitive 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, th e 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. No te that this will result in a very different46 distribution to the current approa ch for St. Louis that fits a si ngle 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 th at CSAs like New York with most of the data values get the greatest statistical weight. Th e Monte Carlo approach gives the same total statistical weight for each CSA and fits a mixtur e of log-normal distributio ns 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 di fferent studies for a CSA.

In addition, we assessed th e within-city uncertainty by us ing a bootstrap distribution to estimate the effects of sampling va riation on the fitted geometric means and standard deviations for each CSA. The bootstrap distributions asse ss the uncertainty due to random sampling variation but do not address uncerta inties due to the lack of repr esentativeness of the available study data or the variation in the lengths of the AER monitori ng periods. The analysis showedthat 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 hr 1 ” 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 ex change rate distributio ns 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/C47 Varying measurement averaging times Although the averaging periods for the air exchange rates in the study databases varied fr om 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 av erages. To investigate the uncerta inty of this assumption, we investigated the correlations between consecutive 24-hour air ex change rates measured at the same house from the Research Triangle Park Pa nel Study. The results showed extremely strong correlations, providing support for the simplifie d 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 tim e 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 resu lted in a uniform air exchange rates for each 24- hour period and re-sampling of the 24-hour air ex change 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 statis tically independent. Although we have not identified sufficient data to test the assumpti on 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 m odeled CSA, the air conditioning status of the residential microenvironments is simulated random ly using the probability that a residence has an air conditioner, i.e., the resi dential air conditioner prevalence rate. For this study we used CSA-specific data from the American Hous ing 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 preval ence rates and confidence intervals developed from the Energy Information Administration’s Residential Energy Cons umption 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 in terval 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 pr esence 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 abse nce, 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 respec tively. 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 es timates 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 aver age 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 exceedan ces during moderate exertion.
The proportions are somewhat lower in Hous ton. For the children ’s subpopulations the proportion with at least one exceed ance of 0.07 ppm during moderate exertion is estimated to be between 32% and 37%, and w ith at least 3 exceedances between 3% and 4%.50 Figure 5-1

Person-Da y s of Exposure to 8-Hour Avera g e Concentrations Durin g Moderate Exertion

--Boston 2002--

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 0.1 1 0.1 3 0 . 1

5

Exposure Concentration (ppm)Person-Days
Children
Active children
Asthmatic children

Figure 5-2

Person-Da y s of Exposure to 8-Hour Avera g e Concentrations Durin g 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 . 0

9 0 . 1

1 0 . 1

3 0 . 1

5

Exposure Concentration (ppm)Person-Days
Children
Active children
Asthmatic children51 Figure 5-3

Person-Da y s of Exposure to 8-Hour Avera g e Concentrations Durin g Moderate Exertion

--Houston 2002--

1.E+00 1.E+02 1.E+04 1.E+06 1.E+08 1.E+10

0 0 . 0

2 0 . 0

4 0 .06 0 .08 0.1 0.12

Exposure Concentration (ppm)Person-days Children Active children Asthmatic children

Figure 5-4

Person-Da y s of Exposure to 8-Hour Avera g e Concentrations Durin g Moderate Exertion

--Houston 2004--

1.E+00 1.E+02 1.E+04 1.E+06 1.E+08 1.E+10

0 0 . 0

2 0 .04 0.06 0 . 0

8 0 . 1 0 . 1

2

Exposure Concentration (ppm)Person-days Children Active children Asthmatic children52 Figure 5-5

Exceedances of 8-Hour Avera g e 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 .0

6 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 Avera g e 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 . 0

6 0. 0

8 0.1

Exposure Concentration (ppm)Persons 1 exceedance
2 exceedances
3 exceedances
4 exceedances
5 exceedances53 Figure 5-7

Exceedances of 8-Hour Avera g e 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 . 0

2 0 . 0

4 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 Avera g e Exposure Concentrations Durin g 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 . 0

2 0.04 0 .06 0.0 8 0.1 0.12

Exposure Concentration (ppm)Persons 1 exceedance
2 exceedances
3 exceedances
4 exceedances
5 exceedances54 Figure 5-9

Exceedances of 8-Hour Avera g e Exposure Concentrations Durin g 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. 0

2 0.04 0.06 0. 0

8 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 Avera g e Exposure Concentrations Durin g 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+0600.010.020.030.040.050.060.070.080.090.10.110.12

Exposure Concentration (ppm)Persons 1 exceedance
2 exceedances
3 exceedances
4 exceedances
5 exceedances55 5.2 Attainment scenarios
The exposure projections presented in this se ction are based on the ai r quality projections discussed in section 3.3. Due to the uncertainti es in the air quality projections, these exposure projections should be viewed as demonstrating th e general range of possible changes in population exposure due to implementation of alte rnative 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 concentr ation 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 cu rves corresponding to potential air quality st andards specified as various combinations of concentration threshol ds 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 altern ative standards is estimated to reduce the proportion of the population subgroup exposed at l east 3 times to 8-hour average concentrations exceeding 0.07 ppm from about 12% (2002 base cas e) to between 0% and 2% depending on the alternative standard.
Figure 5-12 indicates that a re duction in exposures under the alternative standards, with the 95 th percentile 8-hour average exposure concentration decreas ing 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 exposur e concentration decrea ses 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 95 th percentile 8-hour average exposure concentration decrease s from approximately 0.045 ppm to approximately 0.035 ppm, while the maximum exposure concentrations decr eases 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 corre sponding 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 threshol d 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 Child ren 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 mod erate exertion, Houston, 2002.

Figure 5-18. Person-days (occurrences) above 8-hour exposure levels for different

alternative standards, for Active Child ren 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 Ch ildren 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-ho ur exposure levels fo r different alternative standards, for Asthmatic Children at moderate exertion, Houston, 2002.6263 6. SENSITIVITY STUDIES
In order to assess the sensitivity of the APEX predictions to some of the uncertain data inputs, several additional simu lations were conducted for 2002 c onditions. 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 met hod for constructing longterm activity patterns from short-term records.

6.1 Activity Pattern Database
Because many of the studies included in th e CHAD database are not national in scope, nor do they necessarily correspond to the CSAs ta rgeted here, it would be useful to know how similar the component studies are. Strong similar ity would suggest that ex trapolation of activity data gathered from one sample populati on 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 ac tive persons with moderate activity in Boston are presented in Figure 6-2. The figures present several pairs of cumulative dist ribution functions for the number of days/person that a given 8-hour average thresh old concentration is exceeded. The different curves represent different thresholds, ranging fr om 0.01 to 0.05 ppm-8hr, as indicated in the figure legends. Figure 6-1 shows little differen ce between the base case distributions and those for NHAPS activity patterns only, indicating th at 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 modera te 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 fo r 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 ex ceptions, 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 rela tively 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 patter n 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 averag e concentrations exceeding 0.07 ppm in the general population and for children with moderate exertion. Agai n, 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 st ep 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). Howe ver, the California activity data used alone were insufficient for stratifica tion into these 6 pools. Instead, 2 weekend pools (i.e., temperature = 55–84 °F, and >84 °F) were combined. In orde r 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 A ll 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 wi th moderate or greater exertion.

One or more exposures Th ree 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 databa se: 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 wi th moderate or greater exertion.

One or more exposures Th ree 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 th e 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 10 th percentile value and its 90th percentile value. The results are presente d 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 fi gures show only small changes in the rate of exceedances for these rather extreme decay rate s cenarios 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 re sults do show differences among the decay rate scenarios for these exposures to elevated concentrations.

Table 6-7. Sensitivity to ozone decay rate: 200 2 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 Th ree or more exposures Urban Area (CMSA) rate=90 th percentile Base case Rate=10 th percentile rate=90 th percentile Base case Rate=10 th 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: 200 2 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 Th ree or more exposures Urban Area (CMSA) rate=90 th percentile Base case Rate=10 th percentile rate=90 th percentile Base case Rate=10 th 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 predicti ons to the proximity f actor distribution, we compared the base case results with corres ponding results with the proximity factor set uniformly to its 10 th percentile value and its 90th percentil e 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 thes e 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 e xposures 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 Th ree or more exposures Urban Area (CMSA) Factor = 90 th percentile Base case 1 Factor = 10 th percentile Factor = 90 th percentile Base case 1 Factor = 10 th 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 th e modifications to APEX changed the magn itude of exposures, they did not change the relative differences for these sensitivity simulations.69 Table 6-10. Sensitivity to proximity factor: 20 02 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 Th ree or more exposures Urban Area (CMSA) Factor = 90 th percentile Base case 1 Factor = 10 th percentile Factor = 90 th percentile Base case 1 Factor = 10 th 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 predicti ons to the air exchange rate distributions, we compared the base case results with correspond ing results with the air exchange rates set uniformly to their 10 th percentile values and their 90th percentile values. The results are presented in Figure 6-7 for active persons with m oderate 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 CM SAs for the extremely high air exchange rate scenario.
Tables 6-11 and 6-12 present the results fo r 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 result s show a large increase in the number of people exposed to elevated concentrations for the scenario of high air exch ange rates, especially for the multiple exposure case.
In contrast with the sensitivity simulation fo r the ozone decay rate discussed above, this increase in the air exchange rates is sufficient to increase concentrati on 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 Th ree or more exposures Urban Area (CMSA) Rate = 10 th percentile Base case 1 Rate = 90 th percentile Rate = 10 th percentile Base case 1 Rate = 90 th 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 th e modifications to APEX changed the magn itude 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 Th ree or more exposures Urban Area (CMSA) Rate = 10 th percentile Base case 1 Rate = 90 th percentile Rate = 10 th percentile Base case 1 Rate = 90 th 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 measurem ents due to within-reside nce variations in air exchange rates, some recent studies have suggest ed that the reported rate s 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 fo r apartments a substant ial 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 th e 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 num ber 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 sens itive to a potential overestimate of air exchange rates by a factor of two.

Table 6-13. Sensitivity to air exchange ra te: 2002 simulated count s 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 wi th moderate or greater exertion.

One or more exposures Th ree 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 th e modifications to APEX changed the magn itude 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 correspondi ng results where (a) the new tr eatment 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 betw een APEX estimates for the base case and for the simulation that did not incorporate the ne w 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 averag e concentrations exceeding 0.07 ppm. Again, the results show very small di fferences among the scenarios for these exposures to elevated concentrations.

Table 6-14. Sensitivity to longitudinal activi ty 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 Th ree or more exposures Population group Base case 1 Simple resampling Div=0.75 Base case 1 Simple 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 l ongitudinal diaries was recently developed for another population exposure model, the Hazardous Air Pollutant Exposure Model (HAPEM). This approach, described in Appendix H, is de signed 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 anal ysis 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 si ngle activity pattern is selected from each cluster to represent the set of behaviors of the simulated individual. Next, cluster-to-cluster transition pr obabilities 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 th e modifications to APEX changed the magn itude of exposures, they did not change the relative differences for these sensitivity simulations72 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 num ber of persons in Atlanta population groups with moderate exertion exposed to 8-hour aver age concentrations exceeding 0.07 ppm. The results show that the predictions made with al ternative algorithm (“cluster”) are substantially different from those made with simple re-sam pling or with the new APEX algorithm (“base case”). Note that for the cluster algorithm approxi mately 30% of the individuals with 1 or more exposure have 3 or more exposures. The corresp onding values for the ot her algorithms range from about 13% to 21%.

Table 6-15. Sensitivity to longitudinal diar y algorithm: 2002 simula ted 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 wi th moderate or greater exertion.

One or more exposures Th ree or more exposures Population Group Simple resampling Base case 1 Cluster Simple resampling Base case 1 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 m ean and standard deviation of number of days/person with 8-hour average exposures ex ceeding 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 substa ntially higher, i.e., the cluster algorithm results in substantially higher inter- individual variabilit y. As described in Appendix H, limited evaluation of the cluster algorithm by compar ison 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 wi th moderate or g reater 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 th e modifications to APEX changed the magn itude 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 ve hicles, it does not account for depressed ozone concentrations in indoor microe nvironments that are near ma jor roadways. This issue was recently addressed in the HAPEM model by developi ng 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 th e 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 us ed 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-v ehicle 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 pr oximity 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 area s. These proportions were as follows:

Boston:

Interstate 0.05 Other major urban: 0.95

Houston:

Interstate 0.03 Other major urban: 0.9774 Combining these data resulted in the followi ng 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 fracti on of the residential population that live in the vicinity of the roadway, for this applic ation the same probabiliti es were applied to nonresidential indoor microenvironments as well.

6.6.2 Results
Table 6-17 presents the results for the num ber of children (5-18) exposed to 8-hour average concentrations exceeding 0.07 ppm with m oderate or greater exertion. The results show little difference in the predictions compared to the base case.

Table 6-17. Sensitivity to near roadway pr oximity 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 Th ree or more exposures Urban Area (CMSA) Base case 1 Near roadway Base case 1 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 ai r exchange rates. The results were also sensitive to the longitudinal activity algor ithm, the activity pattern data ba se, 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 PercentileDays/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 PercentileDays/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 PercentileDays/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 PercentileDays/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 PercentileDays/Person

All CHAD NHAPS only76 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 PercentileDays/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 PercentileDays/Person

DE= 10th percentile value

DE = 90th percentile value77 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 PercentileDays/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 PercentileDays/Person

PROX = 90th percentile value

PROX = 10th percentile value78 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 PercentileDays/Person

A ER= 90th percentile value

A ER = 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 PercentileDays/Person

A ER= 90th percentile value

A ER = 10th percentile value79 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 PercentilePerson-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 PercentileDays/Person 0.01 ppm

0.02 ppm

0.03 ppm

0.04 ppm

Base LD Off80 This page intentionally left blank.81 7. MODEL EVALUATION
In order to evaluate the performance of AP EX 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 fo r 6 consecutive days each month. The subjects resided in two separate areas of San Bernardino County: ur ban Upland CA, and the small mountain towns of Lake Arrowhead, Cr estline, and Running Springs, CA.
From the original dataset (Geyh et al. 2000), Xue et al. (2005) identi fied 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 eac h data set varies from 7 to 31. In the Upland area, where more than 95% of the subjects ha d air-conditioning in their homes, the maximum 6- day average exposure concentrati on was 0.029 ppm, and all other 6- day averages were less than 0.025 ppm. In the Lake Arrowhead area, wh ere none of the subjec ts’ 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 concentrati on 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 con centration values are assumed y the model to be spatially uniform throughout each respective modeling domain. The air exchange rates used were t hose developed for Sacramento from measurements taken in the inland portions of the Los Angeles area: Sacram ento, 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 expos ure 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 Appendi x 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 predic tions 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 distribu tion 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 factor s 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 measur ed outside the homes of the st udy subjects and those measured at the nearby fixed site monitors that ar e used as spatially un iform APEX inputs.82 In Figure 7-1, these comparisons show th at 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 concen tration 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 i ndoor residential distri butions shows that APEX estimates the average concentration well fo r 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 th e higher measured concentrations.
In Figure 7-2 for the same week in La ke Arrowhead, the distribution of APEX predictions of personal exposure concentrations matches the dist ribution 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 concen tration 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 residentia l predictions matches the median and upper end measurements well but overestimates the lo wer 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, re spectively, along with similar comparisons for outdoor and indoor concentrations.
Figure 7-3 shows that for the Upland ar ea the APEX mean and lower bound of the personal exposure concentration for each 6-da y 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. Ho wever, the predicted upper bounds for the weeks with higher concentrations are somewhat underpredicted, with di screpancies 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 con centration input undere stimates the mean measured values outside the subjects homes, es pecially for the weeks with higher measured concentrations, with discrepanc ies ranging up to 20 ppb, and an average discrepancy of 6 ppb. The discrepancies between the APEX outdoor c oncentration 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 averag es 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 conc entrations. 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 con centration input appear s to match the mean measured values outside the subjects homes reason ably well, with an av erage discrepancy of 1 ppb and a range of -12 ppb to 23 ppb. The discrepancies between the APEX outdoor concentration input and the uppe r bounds of the measured con centrations 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 disc repancies 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 con centration reasonably well, but underestimates the variability. Si milarly, the average prediction for the indoor residential microenvironment matches the measur ed value reasonably we ll, but underestimates the variability. Since the study subjects spent 67% of their sampling time on average inside their residences, the discrepancies for the indoor re sidential microenvironment are likely the main contributors to the discrepancies for the personal exposur e concentrations.
A contributing factor to this underestimation of the variabil ity in the indoor residential concentrations is likely to be an underestima tion of the spatial vari ability of the outdoor concentrations. It is also possible the variab ility of residential air exchange rates is underestimated.

The underestimation of the outdoor concentr ation variability likely exacerbates the underestimation of the upper end of the pe rsonal exposure concentr ation 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 PercentileConcentration(ppb) measured

A PEX 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 PercentileConcentration(ppb) measured

A PEX 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 PercentileConcentration(ppb)

measured

A PEX n=2185 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=2786 Figure 7-3 

### Means of Weekly Average Personal Ozone ExposureConcentrations -- Upland --

0 20 40 60 80

1Concentration (ppb)

Measured APEX range measured APE X



### Means of Weekly Average Outdoor Ozone Concentrations -- Upland --

0 20 40 60 80 100

1Concentration (ppb)

Measured APEX range



### Means of Weekly Average Indoor Ozone Concentrations -- Upland --

0 10 20 30 40 50

1Concentration (ppb)

Measured APEX range measured APE X87 Figure 7-4 

### Means of Weekly Average Personal Ozone ExposureConcentrations -- Lake Arrowhead --

0 20 40 60 80

1Concentration (ppb)



### Measured APEX range measured APE X 

### Means of Weekly Average Outdoor Ozone Concentrations -- Lake Arrowhead --

0 50 100 150 200

1Concentration (ppb)

Measured APEX range



### Means of Weekly Average Indoor Ozone Concentrations -- Lake Arrowhead --

0 20 40 60 80

1Concentration (ppb)

Measured APEX range measured APE X88 This page intentionally left blank.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 w ith 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. Lognorma l distributions for skin area as a function of body weight. Risk Analysis , 18(1):27-32.

CASTNet 2004. Clean Air St atus 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 Transporta tion. 2004 (Publication Date). Highway Statistics 2003, Urbanized Areas, Miles and Daily Vehicl e Miles of Travel. Table HM-71. Website: http://www.fhwa.dot.gov/po licy/ohim/hs03/htm/hm71.htm

. Geyh, AS, Xue, J, Ozkaynak, H, and Spengl er, JD. 2000. The Harvard Southern California chronic ozone exposure study: A ssessing ozone exposure of grad e-school-age children in two Southern California communities. Environ Health Persp. 108:265-270.
Graham S.E. and T. McCurdy. 2005. Revised ventilation rate (V E ) 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 th e U.S. Environmental Agency by PEDCo Environmental Inc., Durham, N.C. under C ontract No. 68-02-3390. U.S. Environmental Protection Agency, Research Triangle Park, N.C.
Johnson, T., J. Capel, E. Olaguer, and L. W ijnberg. 1992. Estimation of Ozone Exposures Experienced by Residents of RO MNET Domain Using a Probabilis tic Version of NEM. Report prepared by IT Air Quality Services for the Offi ce of Air Quality Planning and Standards, U. S. Environmental Protection Agency, Research Triangle Park, North Carolina.
Johnson, T., A. Pakrasi, A. Wisbeth, G. Meiner s, W. M. Ollison. 1995. Ozone exposures within motor vehicles – results of a fi eld study in Cincinnati, Ohio. Proceedings 88 th annual meeting and exposition of the Air & Waste Manage ment 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 Proba bilistic Version of NEM a nd 1990 Population Data. Report prepared by IT Air Quality Services for the Offi ce of Air Quality Planning and Standards, U.S. Environmental Protection Agency, Research Triangle Park, North Carolina, September.90 Johnson, T., J. Capel, J. Mozier, and M. McCoy. 1996b. Estimation of Ozone Exposures Experienced by Outdoor Children in Nine Urban Areas Using a Pr obabilistic Version of NEM. Report prepared for the Air Quality Manageme nt Division under Contract No. 68-DO-30094, April.
Johnson, T., J. Capel, M. McCoy, and J. Mo zier. 1996c. Estimation of Ozone Exposures Experienced by Outdoor Workers in Nine Urban Areas Using a Pr obabilistic Version of NEM. Report prepared for the Air Quality Manageme nt Division under Contract No. 68-DO-30094, April.
Johnson, T. 2002. A Guide to Selected Algor ithms, Distributions, and Databases Used in Exposure Models Developed By the Office of Ai r Quality Planning and Standards. Revised Draft. Prepared for U.S. Environmental Protection Agency under EPA Grant No. CR827033.
Langstaff, J. E. 2007. OAQPS Staff Memora ndum to Ozone NAAQS Review Docket (OAR2005-0172). Subject: Analysis Of Uncertainty In Ozone Population Exposure Modeling. [January 31, 2007].
Lee, Vallarino, Dumyahn, Ozkaynak, and Spengl er. 1999. Ozone decay rates in residences. JAWMA. 49:1238-1244.
McCurdy, T. 2000. Conceptual basis for mu lti-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. De partment of Commerce, National Oceanic and Atmospheric Administration, Nati onal 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 Ad ministration (OSHA). 2005. http://www.osha.gov/dts/chemi calsampling/data/CH_259300.html . Last accessed: July 19, 2005.
Persily, A., J. Gorfain, G. Brunner. 2005. Vent ilation design and performance in U.S. office buildings. ASHRAE Journal. April 2005, 30-35.
Roddin, M.F., H.T. Ellis, and W.M. Siddiq ee. 1979. Background Data for Human Activity Patterns, Vols. 1, 2. Draft Final Report prepar ed 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/populat ion/www/cen2000/phc-t28.html

.91 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 documen tation 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 Qu ality 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 Pa rk, 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 Info rmation - OAQPS Staff Paper. Office of Air Quality Planning and Standards, U. S. Environmental Protection Agency, Research Triangle Park, NC. Available elec tronically 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 Sout hern California Chronic Ozone Exposure Study Data. J. Air & Waste Manage. Assoc. 55 :1508–1515.
Xue J, McCurdy T, Spengler J, Ozkaynak H. 2004. Understanding variabili ty in time spent in selected locations for 7-12-year old children. J Expo Anal Environ Epidemiol 14(3):222-33.92 This page intentionally left blank.APPENDIX A. ANALYSIS OF AIR EXCHANGE RATE DATA1 This page intentionally left blank.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. Anal ysis of Air Exchange Rate Data

EPA is planning to use the APEX exposure mode l 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 i nputs for the cities to be modeled. This memorandum describes the analysis of the AER data and the proposed APEX input distributions. Also in cluded 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) da ta 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. Da ta 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 a nd 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 st udy particulate matter concentrations and daily average AERs were measured at 37 residences in centra l North Carolina during 2000 and 2001 (averaging about 23 AER measurem ents per residence). The residences belong to two specific cohorts: a mostly Cau casian, 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 c ontrolled hypertension living in a low-tomoderate SES neighborhood in Raleigh. Da ta included the da ily average outdoor temperature, and the number of air conditione r 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 concentr ations 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. Meas urements were made at residences in Elizabeth, NJ, Houston TX, and Los Angele s CA. Residences in California were randomly selected. Residences in New Jersey and Texas were prefer entially selected to be close (< 0.5 km) to sources of air toxi cs. 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 cond itioning, room air conditioning, or a swamp (evaporative) cooler.

TEACH: Chillrud at al, 2004, Kinne y 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 expos ures to air toxics among hi gh 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 resi dences 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 (whi ch were converted to daily av erages 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 th e 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 cond itioner. We matched these data by month and zip code to the corresponding monthly average temperat ures obtained from EPA’s SCRAM website as well as from the archives in www.wunderground.com (personal and airport meteorological stations). Resi dences more than 25 miles aw ay 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 w ith one two-day test in the winter for each home. We obtained the data di rectly 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 cond itioner, 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 we bsite as well as from the archives in www.wunderground.com (personal and airport meteorol ogical stations). Residences more than 25 miles away from the nearest av ailable meteorological st ation were excluded from the analysis. For our analyses, the c ity/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 re sidential AER data from several studies conducted between 1982 and 1987. These data were originally compiled by the Lawrence Berkeley National Laboratory. We acknowle dge Mr. Murray’s assistance in obtainingA-3 these data for us. The available data consis ted of AER measurements, dates, cities, and degree-days. Information on air conditione r 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 de sign, although some of these studies included information on whether air conditioners or fa ns 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 th e homes were deliberatel y sampled from specific subsets of the population at a given location ra ther than the entire population: The RTP Panel study selected two specific cohorts of older subj ects 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 thes e 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 ofResidential Air Exchange RatesAvolRTP PanelRIOPATEACHWilson 1984Wilson 1991MurrayandBurmasterLocationsLancaster, LakeGregory,Riverside, SanDimas. All inSouthern CAResearch TrianglePark, NCCA; NJ; TXLos Angeles, CA;New York City, NYSouthern CA Southern CAAZ, CA, CO,CT, FL, ID,MD, MN, MT,NJYears1994 2000; 2001 1999; 2000; 2001 1999; 2000 1984, 1985 1984 1982 – 1987Months/SeasonsFeb; Mar; Apr;May; Jun; Jul;Aug; Sep; Oct;Nov2000 (Jun; Jul;Aug; Sep; Oct;Nov), 2001 (Jan;Feb; Apr; May)1999 (July toDec); 2000 (allmonths); 2001(Jan and Feb)1999 (Feb; Mar; Apr;Jul; Aug); 2000 (Jan;Feb; Mar; Sep; Oct)Mar 1984, Jul 1984, Jan1985 Jan, Mar, Jul VariousNumber ofHomes86 37 284 85 581 288 1,884Total AERMeasurements161 854 524 151 1,362 316 2,844AverageNumber ofMeasurementsper Home1.87 23.08 1.85 1.78 2.34 1.10 1.51MeasurementDurationNot Available 24 hour 24 to 96 hoursSample time (hours)reported. Rangesfrom about 1 to 7days. 7 days 7 days Not availableMeasurementTechniqueNot AvailablePerflourocarbontracer. PMCH tracerPerflourocarbontracer. Perflourocarbon tracer. Perflourocarbon tracer. Not availableMin AER Value0.01 0.02 0.08 0.12 0.03 0.01 0.01Max AER Value2.70 21.44 87.50 8.87 11.77 2.91 11.77Mean AERValue0.80 0.72 1.41 1.71 1.05 0.57 0.76MinTemperature(C)-0.04 -2.18 -6.82 -1.36 11.00 3.00 Not availableA-5AvolRTP PanelRIOPATEACHWilson 1984Wilson 1991MurrayandBurmasterMaxTemperature(C)36.25 30.81 32.50 32.00 28.00 25.00 Not availableAir ConditionerCategoriesNo A/C; Centralor Room A/C;Swamp Cooleronly; Swamp +[Central or Room]Central or RoomA/C (Y/N)Window A/C(Y/N); EvapCoolers (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) Not availableAir ConditionerMeasurementsA/C use inminutes Not AvailableDurationmeasurements inHrs and Mins Not Available Not Available Not Available Not availableFan CategoriesNot available Fan (Y/N) Fan (Y/N) Not Available Not Available Not Available Not availableFanMeasurementsTime on or off forvarious fan typesduring samplingwas recorded, butnot included indatabase provided.Not AvailableDurationmeasurements inHrs and MinsNot Available Not AvailableNot Available Not availableWindow Open/Closed DataDuration openbetween times6am-12 pm; 12pm- 6 pm; and 6pm -6amWindows (open /closed along withduration open ininch-hours unitsWindows (Open /Closed) along withwindow opendurationmeasurements Not Available Not Available Not Available Not availableCommentsCA sample was arandom sample ofhomes. NJ and TXhomes weredeliberatelychosen to be nearto ambientsources.Restricted to innercity homes with highschool students.Contemporaneoustemperature dataobtained for theseanalyses from SCRAMandwww.wunderground.commeteorological data.Contemporaneoustemperature dataobtained for theseanalyses from SCRAMandwww.wunderground.commeteorological 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 ty pe 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” “C entral and Room A/C” “Central or Room A/C” “No A/C” “Swamp + (Central or Ro om)” “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 a nd Burmaster data were excluded because of the absence of information on air conditioner presence. (However, a subset of these data was used for a supplemen tary analysis described below.) .

Based on our review of the AER data we excl uded seven outlying high AER values – above 10 per hour. The main data analysis used all th e 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 “C entral 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 preval ence for the subsequent ozone modeling cities was not available from the American Housing Su rvey. It is plausible that AER distributionsA-7 depend upon the presence or absence of a swamp cooler. It is also plausible that AER distributions also depend upon wh ether the residence sp ecifically has a cent ral 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 th e presence of a swamp cooler are approximately proportionately represented in the surveyed residences.

Most of the studies had more than one AER meas urement 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 si nce the AER will be affected by the use of the available ventilation (air c onditioners, windows, fans), which in turn will depend upon the outside meteorology. Therefore it is not appropriate to averag e 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 sa me house on different da ys 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 st udy, 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 Be rnardino. 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 temper ature 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 defi ned 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, 10 th , 20 th ... 90 th percentiles, Max)

These calculations exclude all seven outliers and resu lts are not used for strata with 10 or fewer values, since those summary statistics are extremely unreliable.
Examination of these summary tables clearly de monstrates that the AER distributions vary greatly across cities and A/C type s and temperatures, so that the selected AER distributions for the modeled cities should also depend upon the c ity, 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 m ean 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 th e A/C type and temperature is illustrated by theA-8 result that for residences with A/C and betw een 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 we re carried out between the different strata, for the AER and its logarith m. The various strata are define d 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 st atistically 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 th e Type of A/C and the temperature range; there are twelve such combinations. For each of th ese twelve combinations, we compare the AER distributions across differe nt cities. This analysis determin es whether the AER distribution is appropriately defined by the A/C type and temp erature 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 va lues 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 th e 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 si gnificantly different at the 5 pe rcent level. Those results are summarized in the last two colu mns of the above table “Summary of Comparisons of Means” which gives the number of cases where the m eans 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 st ratify by temperature range , A/C type, or both.A-9 The Kruskal-Wallis Statistic comparisons are non-p arametric 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 consis tent 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 th e test is non-parametric, the Kruskal-Wallis tests give identical results for AER and Log (AER).
The Mood Statistic comparisons are non-parametric te sts that compare the s cale statistics for two or more groups. The scale statistic measures va riation 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 th e 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-parametr ic, 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 comb ination 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 Wei bull distributions to the AER values.
The first analysis used the same stratificati ons as in the above “S ummary Statistics” and “Statistical Comparisons” secti ons. Results are not reported fo r 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), Ande rson-Darling (A-D). Each goodness-of-fit test compares the empirical distributi on of the AER values to the fitted distribution. The K-S and CM tests are different tests examining the overall fi t, 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-va lue and is marked by an x in th e final three columns. The mean and standard deviation (Std_Dev) are the values for the fitted di stribution. The scale and shape parameters are defined by:

• Exponential: density = σ -1 exp(-x/ σ ), where shape = mean = σ

• Log-normal: density = { σ x √ (2 π )} -1 exp{ -(log x - ζ ) 2 / (2 σ 2 )}, where shape = σ and scale = ζ . Thus the geometric mean and geomet ric standard deviation are given by exp( ζ ) and exp( σ ), respectively.

• Normal: density = { σ√ (2 π )} -1 exp{ -(x - μ ) 2 / (2 σ 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 = σA-10 Generally, the log-normal distribution was the best -fitting of the four di stributions, and so, for consistency, we recommend using the fitted log-normal distributions for all the cases.
One limitation of the initial analysis was that dist ributions 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 dist ributions were not available by using the AER distributions across all citie s and dates for a given temp erature range and A/C type.
Another important limitation of the initial analysis was that distributions we re 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 enti re range of temperatures from minus to plus infinity, although obviously the available data to fit these ranges ha ve finite temperatures. Stratifying by A/C type, city, and the new temperature ra nges produces results for four ci ties: Houston (AC and NA); Los Angeles (AC and NA); New York (AC and NA); Res earch Triangle Park (AC). For each of the fitted distributions we created histograms to co mpare the fitted distributions with the empirical distributions.

AER Distributions for Th e First Nine Cities. Based upon the results fo r the above four cities and the corresponding graphs, we propose using thos e fitted distributions for the three cities Houston, Los Angeles, and New York. For anothe r 6 of the cities to be modeled, we propose using the distribution for one of th e four cities thought to have similar charact eristics to the city to be modeled with respect to factors that mi ght influence AERs. These factors include the age composition of housing stock, construction met hods, and other meteorological variables not explicitly treated in the analysis, such as hum idity and wind speed patterns. The distributions proposed for these citi es are as follows:

• Atlanta, GA, A/C: Use log-normal distributi ons 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-norma l 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 ci ty using data from the same city, but this approach was chosen as a reasonable alte rnative, given the available AER data.

AER Distributions for Sa cramento 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 repr esent St. Louis. The results for the city Sacramento were obtained by combining all the av ailable 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 Burmaste r AER data for Maryland with AER data from each of those cities. The Murray and Burmaste r 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 distribut ions. Between Research Triangle Park and Maryland, the central values and the mean AE R values are not statistically significantly different, and the differences in the mean log (A ER) values are much less statistically significant than between New York and Maryland. The scal e statistic comparisons are not statistically significantly different between New York and Ma ryland, but were statistically significantly different between Research Triangle Park a nd Maryland. Since matching central and mean values is generally more important than matc hing the scales, we propos e to model Washington DC residences with air conditioning using the Res earch Triangle Park distributions, stratified by temperature:

• Washington DC, A/C: Use l og-normal distributions fo r 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 re sidences without air conditioning are discussed below.

AER Distributions for Washi ngton DC and Atlanta GA Re sidences 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 Triangl e 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 f itted to all the study data for residences without A/C, stratified by temp erature. We propose applying the “No A/C”A-12 distributions for modeling these two cities for re sidences 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 valu es also need to be simulated using APEX in order to select the appropriat e AER distribution. Mean daily temperatures are one of the available APEX inputs for each modeled city, so that the temperature ra nge 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 “N o A/C.” For comparison with Washington DC and Atlanta, we have included the A/C type percen tage 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 Triangl e 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 cen tral 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 re sidential and non-residential AER studies that might provide additional information or data. In door / outdoor ozone and PAN distributions were studied by Jakobi and Fabian (1997). Liu et al (1995) studied resi dential ozone and AER distributions in Toronto, Cana da. Weschler and Shields (2000 ) describes a modeling study ofA-13 ventilation and air exchange rate s. Weschler (2000) includes a us eful overview of residential and non-residential AER studies.

AER Distributions for Other Indoor Environments

To estimate AER distributions for non-resident ial, indoor environments (e.g., offices and schools), we obtained and analyzed two AER data sets: “Turk” (T urk et al, 1989); and “Persily” (Persily and Gorfain 2004; Persily et al. 2005).
The earlier “Turk” data set (T urk et al, 1989) includes 40 AER m easurements from offices (25 values), schools (7 values), libraries (3 valu es), 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 Surv ey and Evaluation (BASE) study, which was conducted to assess indoor air qu ality, including ventilation, in a large number of randomly selected office buildings throughout the U.S. The data base co nsists of a total of 390 AER measurements in 96 large, mechanically ventilat ed 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 da ta, the AER values for each office space were averaged, rather using the individual measuremen ts, 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 th e two studies are presented in Table A-4.

Table A-4. AER summary statistics for of fices and other non-residential buildings

Study Variable N Mean Std Dev Min 25 th %ile Median 75 th %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 1.4110A-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 dist ributions were derived from the more recent Persily data only.
Similarly to the analyses of the residential AE R distributions, we fitted exponential, log-normal, normal, and Weibull distributions to the 96 o ffice 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-ValueKolmogorovSmirnov P-ValueCramervon Mises P-ValueAndersonDarling 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 reside ntial AER distributi ons above.) According to all three goodnessof-fit measures the best-fitting distribution is th e log-normal. Reasonable choices for the lower and upper bounds are the observed mi nimum 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 tr ansit micro-environments, an approach using proximity and penetra tion factors is proposed, as follows.

Outdoors Near Road

Penetration factor = 1.
For the Proximity factor, we pr opose 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 greate r Cincinnati metropolitan area in August and September, 1994. Vehicle tests were conducted ac cording to an experimental de sign 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 compac t car. Road types were interstate highways (interstate), principal ur ban arterial roads (urban), and local roads (local). Nominal vehicleA-15 speeds (typically met over one minute intervals w ithin 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 vehi cle, outside the vehicle, and at six fixed site monitors in the Cincinnati area.
The proximity factor can be estimated from the di stributions of the ratios of the outside-vehicle ozone concentrations to the fixe d-site ozone concentrations, repor ted 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 si x sites, as well as the nearest monitor to the test location). For this analysis we propose to use th e ratios of outside-vehicle concen trations to the concentrations at the nearest fixed site mon itor, as shown in Table A-6.

Table A-6. Ratio of outside-vehicle oz one to ozone at nearest fixed site 1

Road Type 1 Number of cases 1 Mean 1 Standard Deviation 1 25 th Percentile 1 50 th Percentile 1 75 th Percentile 1 Estimated 5 th Percentile 2 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 ex cluded 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 oz one exposure will occur on local roads. The summary data from the Cincinna ti Ozone Study are too limited to allow fitting of distributions, but the 25 th and 75 th percentiles appear to be approximate ly equidistant from the median (50 th percentile). Therefore we propos e 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 5 th percentile, as shown in the final column of th e above table. Therefore in summary we propose:

• Penetration factor for outdoors, near road: 1.A-16 • Proximity factor for outdoors, near road: No rmal 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 out doors-near-road microenvironment. We therefore recommend the same distributi ons 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 fo r outdoors, other: 1.

• Proximity factor for outdoors, other: 1.

In-Vehicle
For the proximity factor for in-vehicle, we also recommend using the resu lts of the Cincinnati Ozone Study presented in Table A-6. For this mi croenvironment, 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, a nd the lower bound to be the estimated 5 th percentile.

• Proximity factor for in-vehicle , local roads: Normal distribu tion. Mean = 0.755. Standard Deviation = 0.203. Lower Bound = 0.422. Upper Bound = 1.

• Proximity factor for in-vehicle, urban ro ads: Normal distribution. Mean = 0.754. Standard Deviation = 0.243. Lower Bound = 0.355. Upper Bound = 1.

• Proximity factor for in-vehicle , interstates: Normal distribu tion. Mean = 0.364. Standard Deviation = 0.165. Lower Bound = 0.093. Upper Bound = 1.
To complete the specification, th e 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 arte rial, 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 Urbani zed 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 combin ed with others for reporting purposes are not shown separately. The Illinois portion of R ound 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 Cincinna ti 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 ventil ation type are shown in Table A-8.

Table A-8. Ratio of inside-vehicle ozone to outside-vehicle ozone 1

Ventilation 1 Number of

cases 1 Mean 1 Standard Deviation 1 25 th Percentile 1 50 th Percentile 1 75 th Percentile 1 Estimated 5 th Percentile 2
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 0.000 3

All 812 0.300 0.232 0.117 0.251 0.463 0.000 3A-18 1. From Table 7 of Johnson et al .(1995). Data excluded if outsi de-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 in dicate that the inside-to-outside ozone ratios strongly depend upon the ventilation type, it would be very diff icult to find suitable data to estimate the ventilation type distributions for each modeled city. Furthermor e, 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 di stribution. 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 th e same APEX modeling approach:

• Proximity factor for mass transit, local ro ads: Normal distribution. Mean = 0.755. Standard Deviation = 0.203. Lower Bound = 0.422. Upper Bound = 1.

• Proximity factor for mass transit, urban ro ads: Normal distribution. Mean = 0.754. Standard Deviation = 0.243. Lower Bound = 0.355. Upper Bound = 1.

• Proximity factor for mass transit, intersta tes: 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
American Petroleum Institute (1997). Sensitivity testing of pNEM/O 3 exposure to changes in the model algorithms. Health and Environmental Sciences Department.

Avol, E. L., W. C. Navidi, a nd 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 exposur es 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.A-19 Colome, S.D., A. L. Wilson, Y. Tian (1994). California Residential Indoor Air Quality Study, Volume 2, Carbon Monoxide and Air Exchange Rate : An Univariate and Mu ltivariate Analysis. Chicago, IL. Report prepared for the Gas Research Inst itute, Pacific Gas & Electric Co., San Diego Gas & Electric Co., Southe rn California Gas Co. GRI-93/0224.3
Jakobi, G and Fabian, P. (1997). Indoor/outdoor con centrations of ozone and peroxyacetyl nitrate (PAN) . Int. J. Biometeorol. 40: 162-165.

. Johnson, T., A. Pakrasi, A. Wisbeth, G. Meiner s, W. M. Ollison (1995). Ozone exposures within motor vehicles – results of a fi eld study in Cincinnati, Ohio. Proceedings 88 th annual meeting and exposition of the Air & Waste Manage ment Association, June 18-23, 1995. San Antonio, TX. Preprint paper 95-WA84A.02.
Kinney, P. L., S. N. Chillrud, S. Ramstrom, J. Ro ss, 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. Brode r, (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 PM 2.5 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 Di stributions 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). Ventil ation 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.A-20 Weschler, C. J. (2000) Ozone in indoor envir onments: concentration a nd chemistry. Indoor Air 10: 269-288.
Weschler, C. J. and Shields, H. C. (2000) The influence of ventilation on reactions among indoor pollutants: modeling and e xperimental observations. Indoor Air . 10: 92-100.
Weisel, C. P., J. J. Zhang, B. J. Turpin, M. T. Morandi, S. Colome, T. H. Stock, D. M. Spektor, L. Korn, A. Winer, S. Alimokhtari, J. Kwon, K. Mohan, R. Harrington, R. Giovanetti, W. Cui, M. Afshar, S. Maberti, D. Shendell (2004). Re lationship of Indoor, Outdoor and Personal Air (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 Res earch Triangle Park particulate matter panel study: PM mass concentration relationships. Atmos Env 37, 5349-5363.
Williams, R., J. Suggs, A. Rea, L. Sheldon, C. Rodes, J. Thornburg (2003b). The Research Triangle Park particulate patter panel study: m odeling ambient source co ntribution to personal and residential PM mass concentrations. Atmos Env 37, 5365-5378.
Wilson, A. L., S. D. Colome, P. E. Baker, E. W. Becker (1986). Residential Indoor Air Quality 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. Bake r, E. W. Becker, D. W. Behrens, I. H. Billick, C. A. Garrison (1996). California residential air exchange rates and residence volumes. Journal of Exposure Analysis and Environ Epidemiology . Vol. 6, No. 3.APPENDIX B. THEORETICAL DEVELO PMENT 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 Lu ther 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 assi gns distributions for energy expenditure to each diary event, based on the reported event activity. This is don e using the MET paradigm , which uses ratios of activity-specific to basal energy expenditure. Ho wever, 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, th is means that the upper bound on MET is lowered if events in the recent past have been at unus ually high MET levels. Furthermore, once high activity levels have ended, peopl e tend to breathe heavily even wh ile 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 ab ove the ‘raw’ values pulled from the activitybased distributions.
Historically, the logic for the downward adju stments (downward limitations on the maximum MET with increasing fatigue) was developed befo re the EPOC adjustments. The pNEM model included downward adjustments, both for single ev ents and averages over many diary events. The rules for these adjustments are given in a report 1 by Ted Johnson describing the pNEM algorithms. These rules were inco rporated 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 an y of the SHEDS models.
Rather than separately accounti ng 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 met hod 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 effici ent than previous METadjustment algorithms, and eliminates some of th e problematic features of the current methods.B-2 II. THEORETICAL DEVELO PMENT OF THE METHOD

Background: Oxygen Deficit, Physiol ogical 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 i ndividual’s energy needs are met by anaerobic processes. The magnitude of the mismatch betw een 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 defi cit reaches a maximum value, and performance and energy expenditure deteriorate.
After exercise ceases, ventilation and oxygen cons umption will remain elevated above baseline levels. This increased oxygen consumption wa s historically labele d the “oxygen debt” or “recovery oxygen consumption.” However, re cently 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. Oxyge n deficit is measured as a percentage of the maximum oxygen deficit an indi vidual can attain prior to deterioration of performance. Limitations on MET levels corresp onding to post-exercise di ary events were based on maintaining an oxygen deficit below this maximu m 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 publishe d 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 ove r 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:

1 METS 1

METS M

max − −
= (1)

Using a normalized reserve assures that the method can be applied identica lly to a population of individuals having wi dely different MET max values.

Nomenclature
MET Metabolic equivalent (unitless) MET max Maximum achievable metabolic equivale nt for an indivi dual (unitless) M Normalized MET reserve (uni tless, M, bounded between 0 and 1) Δ M Change in M from one diary event to the next (M) D max Absolute maximum oxygen defic it that can be ob tained (M-hr) F Fractional oxygen deficit (percent of individual maximum, unitless) t e Duration of activity diary event (hours) t r

Time required to recover from an F of 1 to an F of 0 at rest (recovery time, hours)B-3 dF inc Rate of change of F due to deficit increase (F/hr, will have a positive value) dF rec Rate of change of F due to deficit recovery (F/hr, will have a negative value) dF tot Total rate of change of F, dF inc+ dF rec (F/hr) Δ F inc Increase in F due to anaerobic energy expenditure (F) Δ F rec Decrease in F due to re covery of oxygen deficit (F) Δ F tot Change in F due to simultaneous anaerobic work and oxygen recovery, Δ F inc+ Δ F rec (F) Δ F fast Total change in F during the fast recovery phase (F) S fast Magnitude of the rate of change in M during fast component (M/hr) EPOC fast Change in M due to fast-component EPOC (M) EPOC slow 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 theore tical 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 them selves, while the last section describes the determination of appropriate values for the model parameters.

Fast Processes. There exists a component of the accumu lated 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 assume d that these fast defici t 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 tria ngle associated with either a positive or negative change in M, normalized by the maximum obtainable accumulated oxygen deficit (D max ). The normalized area can thus be calculated as:

max fast fast D S Δ M Δ M 0.5 Δ F = (2)

where Δ M = M i -M i-1 and S fast is the slope of the change in M (in M/hr). Note that this change in F will be positive if Δ M is positive, and negative otherwise.

Slow Processes. The slow component of the increas e in oxygen deficit corresponds to the accumulation of deficit over a period of heavier exercise (rather th an that associated with an increase in activity level). The starting point for the analyses is the table of data 3-15 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 MET max , the MET value at which they exercised, and the corresponding norma lized reserve MET (M). (Note that the MET and MET max quantities in this table were derived from VO 2 and VO 2max measurements.) A plot of M versus duration is shown in Figure 2. There is one data point having M > 1, for one subjectB-4 who exercised briefly at a level above his/her MET max . The data indicate that oxygen deficit accumulates at a much faster rate when M is hi gh. 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 inc dF . Based upon the relationship depicted in Fig. 2, we postulate a simple nonlinear relationship between inc dF and M as a power law:

b inc aM dF = (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, esp ecially when using finite time-step models. In our exposure models, the time step may be as larg e 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 t r hours, the slow recovery of o xygen 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 t e is given by

rec inc slow dF dF dF + = (5)

and the associated change in F is

e

r b i slow t t 1 aM Δ F ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

− = (6)

For an individual starting with an F of 0 and ex ercising to exhaustion (neg lecting the transitory effects), the change in Δ F is 1.0. In this case, rearra nging and taking the logarithm gives


## ( ) log(M) b a log 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 ev ent (i +1), taking into account both the fast and slow changes in F, is thenB-5 Fast slow i 1 i Δ F Δ F F F + + = + (8)

Appropriate values for t r , 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 changi ng the structure of the algorithm.

Several of the studies in Table 1 reported t r 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 coul d 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 t r from a uniform distribution having a minimum of 8 and a maximum of 16 hours. (In practice, the values selected for t r do not affect the result significantly.) The user could replace this dist ribution, if desired.
Eq. 7 was fit to the data (Table 1) using different values of t r 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 5.20 a , (9)

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛
+ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

− = 2

r r t 3.66
t 3.57 3.93 b . (10)

Values for D max . Appropriate distributions for maxi mum oxygen debt (MOD) in ml/kg were derived from data from a num ber of studies in adults, 16-29 adolescents, 30 and children. 31-32 The studies covered multiple types of exercise protoc ols, some having more than one protocol per study. We chose to define normal distributio ns for MOD in all three age groups, based on average mean and standard devia tion 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 characterist ics. The bounds of these distributions were selected as two standard devi ations 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 D max, via a units conversion factor and the normalization needed for use with reserve MET:B-6 max D (M-hr) = 

## ( ) 1

max 2 1 METS METStoO 60 MOD

−

− ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ (12)

where METtoO 2 is the conversion factor 2 for mlO 2 to MET-min, 3.5 [(mlO2/min)/kg]/MET. Note that the variability in this factor is not addressed here.
Values for S fast. A number of studies on EPOC 33-42 were used to derive S fast . 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 en ough 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. Convert ing units and normalizing to M, one obtains:

fast S (M/hr) = 

## ( ) 1 METS 3.7) (0.6, Uniform 60

max − (13)

The data for all studies are given in Table 6.

Adjustments to M for Fatigue The equations provided in the previous section de scribe a method for keeping a running total of the fractional oxygen deficit (F) for each diary event for an indivi dual. 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 F i+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 M i for a value of F i+1 =1. However, the equa tions are non-linear in M i . The approach used here is to set M for each even t equal to the raw MET value, and test if F i+1 >1. If it is, then the M i value is reduced by a predetermined amount (currently 0.01) and F i+1 is recalculated. The process continues until an appropriate value of M i , called M max,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:

M i =min(M i , M max, i ) (14)

Adjustments to M for EPOC As noted above, it has been observed in many studi es 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 fa st and slow EPOC comp onents were modeled.

Fast Processes . The fast EPOC component, which take s place in the firs t few minutes after exercise, is also characterized by the slope S fast. The energy recovered during those first few minutes corresponds to the recovery triangle in Fig. 1, and this increase in the rate of energyB-7 expenditure for a post-exercise event is modeled as the area of the triangle divided by the event duration: 

## ( )

e fast 2

fast t S M 5

. 0 EPOC Δ

= (15)

EPOC fast will thus have units of M (normalized reserve MET). The M level for the post-exercise events will be incremented by EPOC fast.

Slow Processes . We estimate the increase in M associat ed with the slow EPOC component as the amount required to maintain the slow recovery of F. Since a deficit D max is recovered in full in the recovery time t r , the time-averaged adjustment to MET for the slow recovery process must be

EPOC slow =

r max t D (16)

Every diary event with the full rate of slow recovery will have its M value adjusted upward by EPOC slow . An appropriate fraction of EPOC slow is used if only partial r ecovery is needed to eliminate the deficit (i.e., return F to 0). The final adjusted M value for the diary event is thus

slow fast adj EPOC EPOC M M + + = (17)

and the new MET value for the event is

1 1) (METS M METS
max adj adj +

− = (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 ch ildren 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 ut ilized an earlier version of MET-adjustment, it is likely that the results pr esented 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 havi ng 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 M max assuming constant exercise at M max and a t r of 12 hours is given inB-8 Fig. 4 These results are very cl ose to those predicted by the Bink 43 equation (as modified by Erb 44 ), which was used in the previous method to limit MET. This demonstrates that for continuous exercise, the limits on intensity pred icted by the unified met hod 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, cons ider the case of the 3 year-old whose one, four, and nine-hour running MET averages are shown in Fig. 5. The flat dot ted lines represent the MET limits predicted by Bink 43 for constant exercise at these tim e intervals. In Fig. 5 note that the new method allows the MET curve to approa ch 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 MET max. Three examples for children of different age, gender, and MET max 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 ad justments were applied to a very short event. An example of a MET time series with EP OC adjustments is shown in Fig. 7.

As more conclusive data become available, th e slow EPOC processes could be modeled in a similar manner to the fast component, (i.e., with a slope term). Current ly, 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 modeli ng method for this component would have a negligible effect on M (and thus ventil ation and dose).

EFFECT ON PAI IN CHILDREN
Mean values of PAI for age and ge nder 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 highe r end of the distribution being most affected. That is, the unified algorithm mainly adjusted the highest values of PAI.

III. SUMMARY AN D CONCLUSIONS
We have developed a new method for simultane ously correcting MET values for fatigue and excess post-exercise oxygen consumption. Th e method is based on the calculation of an accumulated oxygen deficit. The method’s equati ons were derived from data from a large number of studies on oxygen defi cit and EPOC. Furthermore, th e model variables can be easily updated to incorporate data from future studies as they become available. However, the methodB-9 as presented here returns qualita tively 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 computa tionally efficient and theoretica lly straightforward than the previous ones. It requires no ma intenance of multiple running av erages of MET values (as was required by the previous algorithm) or recursive nonlin ear adjustment of oxygen deficit (as was required by the other methods).B-10 References

1. Johnson, T. and Capel, J. "Software for esti mating ventilation (respiration) rates for use in dosimetry models. May, 2002.

2. McArdle, WD, Katch, FI, and Katch, VL. Exercise Physio logy: Energy, Nutrition, and Human Performance, Fifth Ed ition. Lippincott, Williams, and Wilkins, Philadephia, 2001.
3. Bahr R. Excess postexercise oxygen consum ption--magnitude, mechanisms and practical implications. Acta Physiol Scand Suppl. 605:1-70, 1992.
4. Bahr R, Ingnes I, Vaage O, Sejersted OM, Newsholme EA. Effect of duration of exercise on excess postexercise O2 consumption. J Appl Physiol. 62(2):485-90, 1987.

5. Sedlock DA. Postexercise energy expenditure following upper body exercise. Res Q Exerc Sport. 62(2):213-6, 1991.

6. Sedlock DA. Effect of exer cise intensity on postexercise ener gy expenditure in women. Br J Sports Med. 25(1):38-40, 1991.
7. Bielinski R, Schutz Y, Jequier E. Energy metabolism during the postexercise recovery in man. Am J Clin Nutr. 42(1):69-82, 1985.
8. Brockman L, Berg K, Latin R. Oxygen uptake during recovery from intense intermittent running and prolonged walking. J Sports Med Phys Fitness. 33(4):330-6, 1993.
9. Gillette CA, Bullough RC, Melby CL. Postexer cise energy expenditure in response to acute aerobic or resistive exercise. Int J Sport Nutr. Dec;4(4):347-60, 1994.

10. Gore CJ, Withers RT. Effect of exercise intensity and duration on po stexercise metabolism. J Appl Physiol. 68(6):2362-8, 1990.
11. Hagberg JM, Hickson RC, Ehsani AA, Hollosz y JO. Faster adjustment to and recovery from submaximum exercise in the trained state.J Appl P hysiol. 48(2):218-24, 1980.
12. Maehlum S, Grandmontagne M, Newsholme EA, Sejersted OM. Magn itude and duration of excess postexercise oxygen consumption in he althy young subjects. Metabolism. 35(5):425-9, 1986.
13. Harris JM, Hobson EA, and Hollingsworth DF. Individual variations in energy expenditure and intake. Proc Nutr Soc. 21: 157-169, 1962.
14. Kaminsky LA, and Whaley MH. Effect of interval-type exercise on excess post-exercise oxygen consumption in obese and normal-weight women. Med Exer Nu tr Health. 2:106-111, 1993.B-11 15. Katch FI, Girandola RN, and Henry FM. Th e influence of the estimated oxygen cost of ventilation on oxygen deficit and recovery oxygen intake for moderately heavy bicycle ergometer exercise. Med Sc i Sports 4: 71-76, 1972.

16. Gastin PB, Costill DL, Lawson DL, Krze minski K, McConell GK. Accumulated oxygen deficit during supramaximum all-out and consta nt intensity exercise. Med Sci Sports Exerc. 27(2):255-63, 1995.

17. Gastin PB, Lawson DL. Variable resistance all-out test to generate accumulated oxygen deficit and predict anaerobic capacity. Eur J A ppl Physiol Occup Physio l. 69(4):331-6, 1994.

18. Weber CL, Schneider DA. Maximum accumulate d oxygen deficit expressed relative to the active muscle mass for cycling in untrained male and female subjects. Eur J Appl Physiol. 82(4):255-61, 2000.
19. Doherty M, Smith PM, Schroder K. Reproducibility of the maximum accumulated oxygen deficit and run time to exhaustion during short-dist ance running. J Sports Sci. 18(5):331-8, 2000.

20. Renoux JC, Petit B, Billat V, Kora lsztein JP. Oxygen deficit is related to the exercise time to exhaustion at maximum aerobic speed in middle di stance runners. 1: Arch Physiol Biochem. 107(4):280-5, 1999.

21. Roberts AD, Clark SA, Townsend NE, A nderson ME, Gore CJ, Hahn AG. Changes in performance, maximum oxygen uptake and maxi mum accumulated oxygen deficit after 5, 10 and 15 days of live high:train low altitude exposure. Eur J Appl Physiol. 88(4-5):390-5, 2003.

22. Maxwell NS, Nimmo MA. Anaer obic capacity: a maximum anaer obic running test versus the maximum accumulated oxygen deficit. Can J Appl Physiol. 21(1):35-47, 1996.
23. Buck D, McNaughton L. Maximum accumula ted oxygen debt must be calculated using 10 min time periods. Med Sci Sports Exerc. 31(9):1346-1349, 1999.
24. Hill DW, Ferguson CS, Ehler KL.An alterna tive method to determine maximum accumulated O2 deficit in runners. Eur J Appl Phys iol Occup Physiol. 79(1):114-7, 1998.
25. Demarle AP, Slawinski JJ, Laffite LP, Bocque t VG, Koralsztein JP, Billat VL. Decrease of O(2) deficit is a potential factor in increased time to exhaustion after specific endurance training. J Appl Physiol. 90(3):947-53, 2001.
26. Bickham D, Le Rossignol P, Gibbons C, Russell AP. Re-assessing accumulated oxygen deficit in middle-distance runners.J Sci Med Spor t. 5(4):372-82, 2002.
27. Faina M, Billat V, Squadrone R, De Angelis M, Koralsztein JP, Dal Monte A. Anaerobic contribution to the time to exhaustion at the minimal exercise intensity at which maximumB-12 oxygen uptake occurs in elite cy clists, kayakists and swimmers . Eur J Appl Physiol Occup Physiol. 76(1):13-20, 1997.
28. Billat V, Beillot J, Jan J, Rochcongar P, Carre F. Gender effect on the relationship of time limit at 100% VO2max with other bioenergetic characteristic s. Med Sci Sports Exerc. 28(8):1049-55, 1996.
29. Olesen HL. Accumulated oxygen deficit increas es with inclination of uphill running. J Appl Physiol. 73(3):1130-4, 1992.
30. Naughton GA, Carlson JS, Buttifant DC, Seli g SE, Meldrum K, McKenna MJ, Snow RJ. Accumulated oxygen deficit measurements during a nd after high-intensity exercise in trained male and female adolescents. Eur J Appl Physiol Occup Physiol. 76(6):525-31, 1998.
31. Carlson JS, Naughton GA. An examination of the anaerobic capacity of children using maximum accumulated oxygen debt. Pediatr Exerc Sci. 5:60-71, 1993.
32. Berthoin S, Baquet G, Dupont G, Blondel N, Mucci P. Critical velocity and anaerobic distance capacity in pr epubertal children. Can J A ppl Physiol. 28(4):561-75, 1996.
33. Knuttgen HG. Oxygen debt after submaxim um physical exercise. J Appl Physiol 29(5):651- 657, 1970.
34. Harms CA, Cordain L, Stager JM, Sockle r JM, and Harris M. Body fat mass affects postexercise oxygen metabolism in males of sim ilar lean body mass Me d Exer Nutr Health 4:33-39, 1995.

35. Trost S, Wilcox A, Gillis D. The effect of s ubstrate utilization, manipulated by nicotinic acid, on excess postexercise oxygen consumpti on Int J Sports Med 18(2):83-88, 1997.

36. Dawson B, Straton S, and Randall N. O xygen consumption during r ecovery from prolonged submaximum cycling below the anaerobic threshol d. J Sports Med Phys Fitness, 36:77-84, 1996.
37. Short KR, Sedlock DA. Excess postexercis e oxygen consumption and recovery rate in trained and untrained subjects. J Appl Physiol, 83(1):153-159, 1997.

38. Pivarnik JM, Wilkerson JE. Recovery me tabolism and thermoregulation of endurance trained and heat acclimatized men. Spor ts Med Phys Fitness 28(4):375-80, 1988.
39. Almuzaini KS, Potteiger JA, Green SB. Effects of split exercise sessions on excess postexercise oxygen consumption and resting metabolic rate. Can J Appl Physiol 23(5):433-43, 1998.
40. Frey GC, Byrnes WC, and Mazzeo RS. Factors influencing ex cess postexercise oxygen consumption in trained and untrained women. Metabolism 42(7):822-828, 1993.B-13 41. Kaminsky LA, Padjen S, LaHam-Saeger. J Effect of split exercise sessions on excess postexercise oxygen consumption. Br J Sports Med 1990 Jun;24(2):95-8.
42. Maresh CM, Abraham A, De Souza MJ, Deschenes MR, Kraemer WJ, Armstrong LE, Maguire MS, Gabaree CL, Hoffman JR. Oxygen c onsumption following exercise of moderate intensity and duration. Eu r J Appl Physiol Occup P hysiol 1992;65(5):421-6.
43. Bink B. The physical working capacity in relation to working time and age Ergonomics, 5(1):29-31, 1962.
44. Erb BD. Applying work physiology to occu pational medicine. Occup Health and Safety 50(6):20-24, 1981.B-14 Table 1. Data used for estimation of oxygen defic it. Table gives data fo r 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 0.668437B-15 Table 2. Values of a and b for different recovery times.

d (hours)

r a b R 2 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 0.79561B-16 Table 3. Mean PAI Values (Males). Unified al gorithm 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 EPAB-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 EPAB-18 Fast component of F: Recovery ( Δ M negative)

Δ M

M 1 M 2 Fast component of F: Accumulation ( Δ M positive)

Time Exercise Recovery
t= Δ M/ S

fast S

fast

Figure 1. Fast components of oxygen deficit and recovery. -S

fastB-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-20B-21 Figure 4. Maximum M (METS reserve) value that can be sustained during constant–intensity exercise of duration T. T (hours)

M maxB-22B-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 METS max =14.4

Male, 3 years METS max =5.7

Female, 5 years METS max =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 METSB-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 CHADB-26 Table 5. Data for Calculation of Maximum Accumulated Oxygen Deficit, D max

Stud y VO2Max SD SE Dmax SD SE a g e g ender (ml/k g -min) (ml/k g ) 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 = BothB-27 Table 6. Data for Calculation of th e 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 0.949B-28 This page intentionally left blank.APPENDIX C. A NEW METHOD OF LONGITUDINAL DIARY ASSEMBLYThis page intentionally left blank.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 AgencyC-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 suffici ent length. (Models are typically run for a year or more.) Various methods of assembling si ngle-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 larg e 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 so me 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 assemb led (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 appl y 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 met hod 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 realis tic 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 form ed 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 inC-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 vari able 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 cal culated 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 ofC-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 F w 2 in the group is the mean of these individual time variances. The between-person variance F b 2 is the variance across persons in the mean scores for each time series. The statistic D is then given by

D = F b 2 / ( F b 2 + F w 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 F b 2 is zero, or that each person has the same mean score. A small D means that F b 2 is substantially smaller than F w 2 . A D near one means that F b 2 is much larger than F w 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/J 2 ), 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 Calif ornia (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. TheC-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. Th en, 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 simulationC-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%, and14% 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. Fo r 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 a nd from simulations using the proposed method. Simulations constructed 20,000 longitudinal di aries 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 .14C-10 Table 3. Computation of the A statistic calculated from ranks and key variable values, both directly from the southern California study a nd from simulations using the proposed method. Simulations constructed 20,000 longitudinal di aries 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 .17C-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 -.99C-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 -.21C-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 differen ces between individuals while allowing the diary pools to define the distribution of the key variab le 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 we ll 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 theC-14 protocol for this study did not match the assumptions used in developing this method; in particular, different children reported diaries on di fferent 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 (Andersse n 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 sidesC-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 distributionresults, 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 valuesC-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 va ry 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 prev ent 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 signi ficant. Therefore, for simplicity, the basicC-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 reorde ring 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 differi ng 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 reor dering 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-d ay 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 eitherC-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, whic h 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. B ild, 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 th e 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 

### F i 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 

### F w 2 

### = (1/P) ' 

### F i 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 

### F b 2 

### = (1/P) ' 

### ( : i 

### - : 

### ) 2 

### = (1/P) ' 

### : i 2 

### - : 2 

### (1-7)
i =1 i =1

where ‘b’ stands for ‘between-persons’. In brief, F w 2 is the mean of the intra-personal variances, while F b 2 is the variance of the intra-personal means. An important result is that



### F w 2 

### + F b 2 

### = V 2 

### - : 2 

### = F 2 

### (1-8)

which follows from the three prior equations. Thus, for a given set of longitudinal diaries, F w 2

, F b 2 and F 2 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 F 2 can be calculated. This means that in longitudinal diary construction there is a direct trade-off between F w 2 and F b 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 F w 2 = 0 and F b 2 is maximized. Alternatively, if a new diary is chosen at random every day for each person, each individual tends to have a similar F i 2 , and F 2 is comprised mostly of F w 2 , while F b 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 F b 2 . The mean exposure will be correct for any unbiased method of long itudinal 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 = F b 2 

### / ( F b 2 

### + F w 2 

### ) = F b 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 F b 2 = 0) up to one (when F w 2 = 0). Using equations (1-7) and (1-8), the expression for D becomes

PC-S3 

### D = 1/(P F 2 

### ) ' 

### : i 2 

### - : 2 

### / F 2 

### (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 F i 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 T i 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 T i , 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 T i , all the beta distributions used in this approach have bounds zero and one, so the above formulas apply.C-S4 For the T i , 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 T i , the beta distribution from which their X-scores are drawn has a mean T i and a variance which follows from (2-5):



### F i 2 

### = T i 

### (1 - T i 

### ) / (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 F i 2 / J. Also, the expected value of the sample variance is



### s i 2 

### = (J-1) F i 2 

### / J . (2-10)

The within-person variance F w 2 is the mean across persons of the s i 2 . In the limit of a large simulated population, this is the same as the weighted average over T i .



### F w 2 

### = I 

### p(T i 

### ) s i 2 

### d T i


### = ((J-1)/J) I 

### p(T i 

### ) T i 

### (1 - T i 

### ) / (1 + S i 

### ) d T i 

### . (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 T i 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 T i is given by equation (2-8). Hence



### F w 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 F b 2 . It can be interpreted as the second moment about the overall mean : . (see equation 1-7). Here the mean of the T i is 1/2 by equation (2-7). For one value of T i , if several persons share this T i 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 F i / J 1/2

, hence the expected variance in : i for persons sharing the same T i is F i 2 / J , which by equation (2-9) is T i (1 - T i ) / (J + J S i ). To evaluate F b 2 , the variance in : i about T i must be converted to the second moment of : i about the overall population mean of 1/2.

Hence,

(2 nd moment of : i about 1/2 for given T i ) 

### = 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 

### - T i 

### +1/4 (2-13)

which follows since I p( : i ) : i d : i = T i and also I p( : i ) 1/4 d : i = 1/4.

The variance in : i is the second moment about the mean T i , or



### F i 2 

### / J = I 

### p( : i 

### ) ( : i 

### -T i 

### ) 2 

### d : i



### = I 

### p( : i 

### ) : i 2 

### d : i 

### - I 

### p( : i 

### ) 2 : i 

### T i 

### d : i 

### + I 

### p( : i 

### ) T i 2 

### d : i



### = I 

### p( : i 

### ) : i 2 

### d : i 

### - 2 T i 2 

### + T i 2 

### (2-14)

Substituting this expression into (2-13) givesC-S6 (2 nd moment of : i about 1/2 for given T i ) 

### = F i 2 

### / J + T i 2 

### - T i 

### +1/4

= F i 2 

### / J + (T i 

### - 1/2) 2



### = T i 

### (1-T i 

### ) / (J +J S i 

### ) + (T i 

### - 1/2) 2 

### . (2-15)

For a large simulated population, F b 2 is the mean of this quantity over all T i , namely



### F b 2 

### = I 

### p(T i 

### ) [ T i 

### (1 - T i 

### ) / (J + J S i 

### ) + (T i 

### - 1/2) 2 

### ] d T i 

### (2-16)

where p(T i ) 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 T i , which is given by equation (2-8). As for F w 2 , the first integral can be solved by assuming S i is constant for all persons. So



### F b 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 T i distribution about 1/2. The collective variance of the X-scores is related to F b 2 and F w 2 by equation (1-8). Hence



### F b 2 

### + F w 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 T i . Remembering thatC-S7 S = a+b, equation (2-2) can be written as



### a = S T i 

### = 2 T i 

### / (1 - 3 w 2 

### / (1 + 2 " 

### ) ) . (2-23)

Therefore


### b = S-a = 2 ( 1 - T i 

### ) / (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 T i 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:



### F b 2 

### = [1/(J + J (2/(1-D # 

### )))] [1/4 - D # 

### /12] + D # 

### /12. (2-26)

which can be solved for D # in terms of F b 2



### D # 

### = (12 J F b 2 

### -1 ) / ( J - 1) . (2-27)

Also, equation (1-9) together with (2-20) give



### D = F b 2 

### / ( F b 2 

### + F w 2 

### ) = 12 F b 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 pool s 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 dist ributions. 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



### w 2 

### = D # 

### . (2-33)

This choice results in a uniform distribution of the targets T i 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 equati on (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 T i 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 a i to each simulated individual. These targets can be drawn from any distribution that has a mean of A, provided that all a i 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 e nd 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 R j 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 

### ) ( R j+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 (K 2 -1)/12. Hence



### a i 

### = (12 / (K 2 

### -1)) E [(R j 

### - D 

### ) ( R j+1 

### - D 

### ) ]. (3-2)

The expectation value in equation (3-2) can be evaluated if we have the conditional probability p(R j+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(R j+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 distribu tion. Thus, a beta distribution for p(y|x) isC-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 R j+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 = (R j+1 

### -1/2) / K (3-4)

We wish to select the parameters for a beta distribution that give the selection probabilities for R

j+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 

### ) ( R j+1 

### - D 

### ) ] = ' ' 

### (R j 

### - D 

### ) ( R j+1 

### - D 

### ) p(R j 

### ) p(R j+1 

### | R j 

### ) (3-5)

where one sum is over all R j from 1 to K and the other is over all R j+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 R j+1 by an integral over all y, with R j+1 replaced by (Ky+1/2):


### E [(R j 

### - D 

### ) ( R j+1 

### - D 

### ) ] = (1/K) ' 

### (R j 

### - D 

### ) I 

### p(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 I p(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 

### ) ( R j+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), thereforeC-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 

### ) ( R j+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 

### ) ( R j+1 

### - D 

### ) ] = w (K 2 

### - 1) /12. (3-13)

With this choice of the beta distribution, equation (3-2) reduces to the very simple form



### w = a i 

### . (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 k th 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

= I 

### p(x) dx I 

### y k 

### p(y|x) dy . (3-16)

The second integral is the k th moment of the beta distribution p(y|x). The first moment is given by equation (3-10). The second moment of a be ta 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 w 2 

### ) x + S w 2 

### x 2 

### ] / (S+1). (3-17)

Hence the first moment of ‘y’ is


### E(y ) = I 

### p(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 m 1 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 w 2 

### )/2 + S w 2 

### /3 ] / (S+1)

= (6 + 3 S + S w 2 

### ) / (12 + 12 S) (3-19)

Matching E(y 2 ) to the second moment m 2 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 m 3 = E (y 3 ) 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 a i 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 a i 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 withinC-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 autoco rrelations 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 A j for each day-type. For each individual, a target a i j is required for each A j . 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



### R

j+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 x j+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 D j+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(D j+1 

### x j+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 theC-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 R j+1 has been used before, the result must be shifted to the nearest unused rank. However, if this is not the same rank as R j , then the shift is equally likely to move the rank closer to R j 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 DISTRIBUTIONSThis page intentionally left blank.D-2 

### MEMORANDUM

To: John Langstaff, EPA OAQPS
From: Jonathan Cohen, Arlene Ro senbaum, 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 th e uncertainty of cityspecific distributions of residentia l air exchange rates that were f itted to the available study data. City-specific distributions for use with the AP EX ozone model were de veloped for 12 modeling cities, as detailed in the memorandum by Cohen, Mallya and Rosenbaum, 2005 7 (Appendix A of this report). In the first part of the memora ndum, we analyze the between-city uncertainty by examining the variation of the geometric means a nd standard deviations ac ross 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 variati on on the fitted geometric means and standard deviations for each city. The bootst rap 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, 2005 8 (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 c onditioner (central or window). In each case we chose to fit a log-normal distribu tion to the AER data, so that the logarithm of the AER for a given city, temperature range, and A/C type is as sumed to be normally distributed. If the AER data has geometric mean GM and geometric standa rd 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 th e non-California data for houses

7 Cohen, J., H. Mallya, and A. Rosen baum. 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 repres ent the AER distributions for h ouses without A/C. Sacramento, CA AER distributions were estimat ed using the AER data from the inland California counties of Sacramento, Riverside, and San Bernardino; thes e combined data are referred to by the City Name “Inland California.” St Louis, MO AER di stributions were estima ted 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-Californi a, 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 Lo s Angeles (“Inland California”)
St. Louis All non-California (“Outside California”) Washington, DC, A/C Resear ch 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 fi rst 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 th at 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 variati on of the fitted log-normal distributions across the cities with AER data. In this manner we can ex amine 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 da ta, 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 de signed to represent theD-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 car diac defibrillators livi ng in Chapel Hill; a group of non-smoking, African Amer icans aged at leas t 50 years with cont rolled 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 pref erentially 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 loca tions is to evaluate the varia tion of the fitted log-normal distributions within ea ch modeled city across the different studies.

We evaluated the variation between cities, and the variation within cities and betw een studies, by tabulating and plotting the AER di stributions 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 th e outside temperature and the A/ C type (whether or not the residence has air conditioning), th is analysis was stratified by th e outside temperature range and the A/C type. Otherwise, st udy or city differences woul d have been confounded by the temperature and A/C type differe nces and you would not be able to tell how much of the AER difference was due to the variati on of temperature and A/C type acr oss cities or studies. In order to be able to compare cities and studies we could not use different te mperature ranges for the different modeled cities as we did for the origin al 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 temp erature and A/C type strata.
Table D-2 shows the geometric means and stan dard deviations by city and study. These geometric mean and standard deviation pairs ar e plotted in Figure D-1 through D-8. Each figure shows the variation across cities and studies for a given temper ature 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 i ndividual 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 1.00D-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 2.14D-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 availa ble 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 und efined 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 m odeled 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 pa rticular 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 CarloD-7 analysis where the first stage is to randomly sele ct a city outside of Ca lifornia, the second stage picks the A/C type, and the third stage picks th e AER value from the assigned distribution for the city, A/C type and temperature range. Note that th is will result in a very different distribution to the current approach that fits a single log-normal distri bution to all the non- California data for a given temperature range and A/C t ype. The current approach weight s 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 statisti cal weight for each city and fits a mixture of log-normal distributions rather than a single distribution.
In general, there is also some va riation 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 da ta points are less precise and the differences would not be statistically signifi cant. 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, Wils on 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 st udy 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 th eir allocation to the 12 modeled c ities 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 thes e 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 <=10D-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 >25D-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 ex ample figures D-9 through D-19 corresponds to a single GM/GSD “Original Data” pa ir. The GM and GSD values fo r the “Original Data” are at the intersection of the horizontal and vertical lines that are parall el to the x- and y-axes in the figures.D-10 Table D-4. Geometric means and standard devi ations 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 2.0373D-11 Table D-4. Geometric means and standard devi ations 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 GS D values, a bootstrap si mulation was performed, as follows. Suppose that a given AER subset ha s N values. A bootstrap sample is obtained by sampling N times at random with replacement fr om the N AER values. The first AER value in the bootstrap sample is selected randomly from the N values, so that eac h of the N values is equally likely. The second, third, ..., N’th valu es in the bootstrap sample are also selected randomly from the N values, so that for each selec tion, each of the N values is equally likely. The same value can be selected more than on ce. 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 s ubset, producing a set of 1,000 geometric mean and geometric standard deviation pairs, which were plotted in exampl e 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 di stribution of AER values for the given city, temperature range, and A/C type. On that basis, the 1,000 bootst rap GM and GSD pairs estimate the variation of the GM and GSD across all possi ble samples of N values from the population. Since each GM, GSD pair uniquely defines a f itted log-normal distribution, the pairs also estimate the uncertainty of the fitted log-normal distribution. Th e 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 pair s, the uncertainty distri bution would still be an estimate of the true uncertainty be cause the N is finite, so that the empirical distribution of the N measured AER values does not equa l 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 largeD-12 and/or the variability is small, so that there are a large number of valu es that are all close together.
The bootstrap analyses show that the geometri c 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 geomet ric 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 uncerta inty due to the random sampling. It does not account for the uncertainty due to th e lack of representativeness, whic h in turn is due to the fact that the samples were not always random sample s from the entire population of residences in a city, and were sometimes used to represent di fferent cities. Since only the GM and GSD were used, the bootstrap analyses does not account fo r uncertainties about th e true distributional shape, which may not necessarily be log-normal. Furthermore, the bootstr ap uncertainty does not account for the effect of the calen dar year (possible tre nds in AER values) or of the uncertainty due to the AER measurement period; the distributi ons were intended to repr esent distributions of 24 hour average AER values although the study AE R 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 AP EX model. Instead of using the Original Data distributions, a bootstrap GM, GSD pair could be selected at ra ndom and the AER value could be selected randomly from the log-normal di stribution with the boot strap GM and GSD.Figure D-1D-14Figure D-2D-15Figure D-3D-16Figure D-4D-17Figure D-5D-18Figure D-6D-19Figure D-7D-20Figure D-8D-21Figure D-9D-22Figure D-10D-23Figure D-11D-24Figure D-12D-25Figure D-13D-26Figure D-14D-27Figure D-15D-28Figure D-16D-29Figure D-17D-30Figure D-18D-31D-32Figure D-19APPENDIX E. DISTRIBUTIONS OF AI R EXCHANGE RATE AVERAGES OVER MULTIPLE DAYSThis page intentionally left blank.E-1 

### MEMORANDUM

To: John Langstaff, EPA OAQPS From: Jonathan Cohen, Arlene Ro senbaum, 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, 2005 9 (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 Triang le 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 averagi ng periods as if they were 24- hour averages.

In the current version of the AP EX model, there are several options for stratification of time periods with respect to AER distributions, and fo r when to re-sample from a distribution for a given stratum. The options selected for this curre nt 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 independ ent. Although we have not identified sufficient data to test the assumption of uniform AERs th roughout a 24-hour period, the analyses described in this memorandum suggest that AERs on consecutiv e days are highly correlated. Therefore, we performed sensitivity simulati ons 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. Rosen baum. 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 av erages 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 co mpare 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 temperatur e, and the daily temper atures often varied considerably. Two altern ative 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 actua l number of groups was 124. For the second approach, B, we again sort ed the data by the HOUSE_ID number and date, but this time we began a new group of days fo r 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 temp erature ranges chosen for the analysis in the Cohen, Mallya, and Rosenbaum, 2005, memora ndum (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 trea t 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 follo wing a transition to a different house or season. Us ing the second approach we tr eat groups of days as being independent following a transiti on to a different house or season or temperature range.
To evaluate the distributions of multi-day air ex change 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 c ontinued this process to obtain three-, four-, five-, six-, and seven-day averag es. There were insufficiently re presentative data for averaging periods longer then seven days. Averages ove r 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 A pproach A, some or all of th e days in the averaging period might be in different temperatur e 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, st andard 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 geom etric standard deviation equals e raised to the power Std Dev log (AER). The results are shown in Tabl es 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 ( o C) 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 sa me temperature range bu t different averaging periods. This is expected if the daily AER valu es 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 a pproximately 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 av eraging 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 diffe rent values of K in the same temperature range (except for the relatively limite d data at > 25 oC), this shows that the daily AER values are strongly correlated. Of course the correlation is not perfect, sin ce otherwise the AER for a given day would be identical to the AE R 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 ( o C) 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 th e 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, alt hough it does depend upon the av erage temperature. This supports the methodology used in the Cohen, Mallya, and Rosenbaum, 2005, analyses that did not take into account the le ngth of the averaging period.
The above argument suggests that the assumpti on that daily AER valu es are statistically independent is not justified. St atistical modeling of the correlati on structure between consecutive daily AER values is not easy because of the prob lem of accounting for temp erature 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 eff ects are the populationE-5 average values of AER or log(AER), and ar e assumed to depend upon the temperature range. The random effects have expected values of zero and define the correla tions between pairs of measurements from the same Group, where the Gr oups 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 mixe d model analyses we in cluded 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 th at 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. Ther e is a different overall mean value for each of the four temperature ranges.
A(Group, Temp Range) is the random effect of te mperature. For each Group, four error terms are independently drawn from four different norma l 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 defi ned so that the first day of a Group has day number 1, the next calend ar 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 covari ance between B(Group g, day i) a nd 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-re gressive 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 ar e 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 additi onal correlation if they are in the same temperature range.
Probably the most interes ting 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 corre lation) although values exactly equal to +1 or -1 are impossible for a stationary model. Nega tive values of d would be unusual since theyE-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 “r andom” 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 dis tinguish from the other te rms. 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, sh owing the very strong co rrelations between AER measurements on consecutive or almost consecutive days.

Impact of accounting for daily average AER auto-correlation

In the current version of the AP EX model, there are several options for stratification of time periods with respect to AER distributions, and fo r when to re-sample from a distribution for a given stratum. The options selected for this curre nt 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 independ ent. Although we have not identified sufficient data to test the assumption of uniform AERs th roughout 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 intr oduced into the APEX estimates with respect to either the magnitudes or vari ability of exposure concentra tions by implicitly assuming uncorrelated air exchange rates, we re-ran the 20 02 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 micr oenvironments 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 exce edances 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 PercentileDays/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 PercentileDays/Person base-.01 rsoff - .01
base - .02 rsoff - .02
base -.03 rsoff - .03
base - .04 rsoff - .04
base - .05 rsoff - .05E-8APPENDIX F. PREVALENCE OF RE SIDENTIAL AIR CONDITIONERS AND THE EFFECTS OF SWAMP COOLERSThis page intentionally left blank.F-1 

### MEMORANDUM

To: John Langstaff, EPA OAQPS From: Jonathan Cohen, Arlene Ro senbaum, ICF International Date: June 6, 2006 Re: Prevalence of residential air conditioners and the e ffects of swamp coolers

This memorandum describes our analysis of the pr evalence of air conditione rs in the 12 cities being modeled using the APEX. As detailed in the memorandum by Cohen, Mallya and Rosenbaum, 2005 10 (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 ai r conditioner type, define d 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 usin g the probability that a residence has an air conditioner, which is the air c onditioner prevalence. Our propose d 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 interval s developed from the Energy Information Administration’s Residential Energy Consumption Survey of 2001.
Some residences use evaporative coolers, also known as “swamp” cooler s, 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 al so 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). Th e survey questions ask whether the housing unit ha s central and room air conditioners, central air conditioners only, room air conditioners only, or no air conditioners. The following de finition was used to define air conditioning. Note that evaporative or “swamp” coolers are specifically excluded.

10 Cohen, J., H. Mallya, and A. Rosen baum. 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 calcul ated using the data and survey weights from the American Housing Survey, together with 95 % confidence intervals. The confidence intervals were computed using the formul as provided in the “Source and Accuracy Statement for the 2003 AHS-N Data Chart” ( http://www.census.gov/hhes/www/h ousing/ahs/03dtchrt/source.html ):

) ( Error Standard 96

. 1 ) ( Interval Confidence , 1 3850 ) ( Error Standard

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 Amer ican 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 Resi dential Energy Consum ption Survey of 2001 provides estimates of air conditione r prevalence for four states, ni ne Census Divisions and four Census Regions. Summary data we re 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/g lossary/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.
Has A/C Uses A/C Area (US, State, 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 7.2F-4 Table F-2. Prevalence estimates from RECS 2001.
Has A/C Uses A/C Area (US, State, 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:

) ( Error Standard 96

. 1 ) ( Interval Confidence , 100 / RSE ) ( Error Standard Factor RSE Column Factor RSE Row (%) Error Standard Relative RSE

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 SouthF-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 in tervals 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 nec essary 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 syst em 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 wa s 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 conditionerprevalence estimates. RECS prevalence forhouseholds owningair conditioners.*CityAHS %AHS LowerAHS UpperDivision %Division LowerDivision UpperRegion %Region LowerRegion UpperAtlanta97.0194.69 99.33 95.00 92.13 97.87 95.70 93.6097.80Boston85.2381.03 89.43 58.40 52.36 64.44 71.60 66.9776.23Chicago87.0984.37 89.81 79.80 75.67 83.93 83.60 80.0087.20Cleveland74.6468.01 81.27 79.80 75.67 83.93 83.60 80.0087.20Detroit81.4177.96 84.86 79.80 75.67 83.93 83.60 80.0087.20Houston98.7097.39 100.01 97.50 93.49 101.51 95.70 93.6097.80LosAngeles55.0551.72 58.38 43.60 36.32 50.88 45.70 39.3452.06New York81.5779.08 84.06 76.40 69.98 82.82 71.60 66.9776.23Philadelphia90.6188.07 93.15 76.40 69.98 82.82 71.60 66.9776.23Sacramento94.6390.84 98.42 43.60 36.32 50.88 45.70 39.3452.06St. Louis95.5392.26 98.80 92.40 86.42 98.38 83.60 80.0087.20WashingtonDC96.4794.51 98.43 95.00 92.13 97.87 95.70 93.6097.80*AHS % = AHS estimated prevalence. [AHS Lower, AHS Upper] = 95 %confidence interval for AHS prevalence. Division % = RECS estimatedprevalence based on the Census Division. [Division Lower, Division Upper] = 95 % confidence interval for RECS prevalence basedon CensusDivision. Region % = RECS estimated prevalence based on the Census Region. [Region Lower, Region Upper] = 95 % confidence interval forRECS prevalence based on Census Region.Table F-5. AHS and RECS air conditionerprevalence estimates. RECS prevalence for households using air conditioners.*CityAHS %AHS LowerAHS UpperDivision %Division LowerDivision UpperRegion %Region LowerRegion UpperAtlanta97.0194.69 99.33 93.70 90.47 96.93 94.60 92.23 96.97Boston85.2381.03 89.43 58.40 52.17 64.63 70.20 65.52 74.88Chicago87.0984.37 89.81 78.50 74.25 82.75 82.30 78.59 86.01Cleveland74.6468.01 81.27 78.50 74.25 82.75 82.30 78.59 86.01Detroit81.4177.96 84.86 78.50 74.25 82.75 82.30 78.59 86.01Houston98.7097.39 100.01 97.00 92.44 101.56 94.60 92.23 96.97LosAngeles55.0551.72 58.38 38.30 31.81 44.79 41.00 35.21 46.79F-7Table F-5. AHS and RECS air conditionerprevalence estimates. RECS prevalence for households using air conditioners.*CityAHS %AHS LowerAHS UpperDivision %Division LowerDivision UpperRegion %Region LowerRegion UpperNew York81.5779.08 84.06 74.50 68.05 80.95 70.20 65.52 74.88Philadelphia90.6188.07 93.15 74.50 68.05 80.95 70.20 65.52 74.88Sacramento94.6390.84 98.42 38.30 31.81 44.79 41.00 35.21 46.79St. Louis95.5392.26 98.80 91.10 84.94 97.26 82.30 78.59 86.01WashingtonDC96.4794.51 98.43 93.70 90.47 96.93 94.60 92.23 96.97*AHS % = AHS estimated prevalence. [AHS Lower, AHS Upper] = 95 %confidence interval for AHS prevalence. Division % = RECS estimatedprevalence based on the Census Division. [Division Lower, Division Upper] = 95 % confidence interval for RECS prevalence basedon CensusDivision. Region % = RECS estimated prevalence based on the Census Region. [Region Lower, Region Upper] = 95 % confidence interval forRECS 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 cool er 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 aF-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 absen ce, given that we already stratify by city, air conditioner presence or absence, and temperature range.F-10 This page intentionally left blank.APPENDIX G. ANALYSIS OF NHIS ASTHMA PREVALENCE DATAThis page intentionally left blank.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 child ren’s asthma prevalence data from the National Health Interview Survey (NHIS) for 2003. Asth ma prevalence rates for children aged 0 to 17 years were calculated for each age, gender, and region. The regi ons 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 que stion CASHMEV: “Ever be en 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 desi gn of the NHIS survey. Standard errors and confidence intervals for the prevalence were ca lculated 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 pl otted. 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 signifi cant differences in pr evalence by gender and by region. Therefore we did not combine the prev alence 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 uncertain ties 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 wa s initially used, two problems are that the distributions of the estimat ed prevalence rates are not well approximated by normal distributions, and that the estimate d confidence intervals based on the normal approximation often extend outside the [0, 1] interv al. 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 variab les 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 be ta 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 conf idence intervals for beta, the co rresponding confidence intervals for prob (asthma) will always be inside [0, 1]. A nother advantage of the logistic modeling is that it can be used to compare alternative statistica l models, such as models where the prevalence probability depends upon age, region, and ge nder, or on age and region but not gender.
A variety of logistic models for asthma preval ence were fit and compared, where the transformed probability variable beta is a given function of age, gender, and region. SAS’s SURVEYLOGISTIC procedure was us ed 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 lo g-likelihood goodness-of-fit measures. 16 models were fitted. The Strata co lumn 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 independent ly 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 32G-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 describe s 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 × age 2 where α β and γ vary with the strata. Cubic in age: Beta = α + β × age + γ × age 2 + δ × age 3 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 pol ynomial 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 co mplex model (16) has a prevalence that is an arbitrary function of age, gender, and region. Mo del 16 is equivalent to calculating independent prevalence estimates for each of the 144 combina tions 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, wher e r is the difference in the DF. This is a likelihood ratio test. For all pairs of models from Table G-1, a ll the differences are at least 70,000 and the likelihood ratios ar e all extremely statis tically significant at levels well below 5 percent. Therefore the model 16 is clearly pref erred and was used to model the prevalences.
The SURVEYLOGISTIC model predictions are ta bulated 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 scatte rplot smoother, as discussed below.
The SURVEYLOGISTIC procedure produces estimat es 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 (b eta) × exp(- beta) / (1 + exp(beta) ) 2

, which follows from the delta method (a fi rst 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 f unctions of age modeled by SURV EYLOGISTIC were one strategy for smoothing the curves, but they did not prov ide a good fit to the data. One reason for this might be due to the attempt to fit a global regressi on 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 regre ssion 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 smoo thing 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 fitte d these local regression curves to the beta values, the logits of the asthma prevalence estimates, and then c onverted them back to estimated prevalence rates by applying the inverse logit functi on exp(beta) / (1 + exp(be ta) ). 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 avoi d 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 ra w 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 para meter of 0.2 cannot be used becau se 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 Figu res 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 applicati on 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 estimat ed standard errors by 1 / estimated σ , and adjusted the widths of the c onfidence intervals by the same factor.

Additionally, because the true value of σ equals 1, the best choi ces of smoothing parameter should give residual standard erro rs close to one. Using this cr iterion 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, combini ng all the studentized residuals across genders, regions, and ages. The plots for smoothing para meters seem to be equally straight for each smoothing parameter.
The final regression diagnostic is a plot of the studentized resi duals against the smoothed beta values. Ideally there should be no obvious patt ern and an average studentized residual close to zero. The plots indeed showed no unusual patterns, and the result s 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 c hoices of 0.5 or 0.6. We therefore chose the final value of 0.5. These predictions, standard errors, and confidence inte rvals 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 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=Northeast

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 17G-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 17G-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 17G-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 17G-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 17G-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 17G-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 17G-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 17G-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 0.31309G-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 0.25769G-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 0.20515G-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 0.15872G-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 0.28447G-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 0.19510G-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 0.23012G-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 0.35487G-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 0.10573G-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 0.24569G-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 0.31153H-1 APPENDIX H. ALTERNATIVE LONGITUDINAL ACTIVITY PATTERN ALGORITHMH-2 This page intentionally left blank.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 al gorithm for creating longitudinal activity patterns.

BACKGROUND
In previous work ICF reviewed the HAPEM4 m odeling approach for developing annual average activity patterns from the CHAD database a nd recommended an approach to improve the model’s pattern selection process to better re present the variability among individuals. This section summarizes the recommended approach. (For details see the me morandum of July 23, 2002 from ICF Consulting to Ted Palma.)
Using cluster analysis, first the CHAD daily activ ity 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 demogra phic group (males or females; age groups: 0- 4, 5-11, 12-17, 18-64, 65+). Next, for each comb ination of day type and demographic group, category-to-category transition probabilities ar e 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. (Consecu tive 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 cate gory 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 aver age activity pattern to represent an individual in a give n demographic group and census tract.
The weighting for each of the 9 act ivity patterns used in the aver aging process is determined by the product of two factors. The firs t 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 weighti ng for the selected ac tivity pattern is determined by simulating a sequence of category-types as a one-stage Markov chain process using the transitionH-2 probabilities. The category for the first day is se lected 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 fo r the first day. The category for the third day is selected according to the transi tion 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 seque nce 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 explai ned in this section.

Data Preparation

Step 1 : Each daily activity pa ttern in the CHAD data base is su mmarized by the total minutes in each of five micro-environments: indoors – reside nce; 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 activ ity pattern for their exposure impact.

Step 2: All CHAD activity patterns for a given day-type and demogr aphic group are subjected to cluster analysis, resulting in 2 or 3 cluster catego ries. 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 an alyzed to determine th e category-to-category transition frequencies in the CHAD data base. These transition fre quencies 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 P BA = the probability that a type B patte rn is followed by a type A pattern (P BA = 1 – P BB ).

Activity Pattern Selection
For each day-type and demographic group in each census tract

Step 5: One activity pattern is randomly selected fr om 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 ca tegory 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-cate gory transition probabilities.

Step 8 : The relative frequency of eac h 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 frequenc ies (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 ar e averaged together using the relative frequency of day-types as we ights, 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 aver age 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 mu lti-day activity pa tterns with respect to demographic group means and inter-individual variability , while using one-day selection.
In order to accomplish this we propose to ap ply 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 ge nerated 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 se lected from a uniform distribution.

Step 3: The employment status is simula ted 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 equa l 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 divi ded 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 AP EX activity selection algorithm can cross temperature bins, we woul d propose to use broad temperature bins for the clustering and transition probability calculat ions so that the cluste r 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 ac tivity patterns may be important in APEX. Therefore, for Step 4 transition probabilities would be specified fo r 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 exampl e, transition probabilitie s 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 th e 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 considerati on of age in the cluste ring 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 a ssumption could be tested by examination of the cluster categories stratified by age group that we re developed for HAPEM5. If the assumption is found to be valid, then the cluster categories coul d be pre-determined for input to APEX, whileH-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 co uld be implemented that would create overlapping age groups for purpos es 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 catego ries and transition prob abilities would be predetermined for input into APEX and the appropria te 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 P AB where A is the cluster for the first day’s activity pattern and B is the cluster for a given activity patte rn 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 P AB divided by the total of the products of age weight and P AB 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 mu lti-day data set. For purposes of clustering we characterized the activity pa ttern 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 calcula ting transition probabilities we divided the activity patter n 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 ag e 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 prob abilities. To evaluate the algorithm we calculated the following statis tics 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 micr oenvironment, the average of the withinperson variance across all simulated persons (W e 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 microenvironmentH-6 In each case we compared the predicted statis tic for the stratum to the statistic for the corresponding stratum in the actual diary data. 14

We also calculated the mean normalized bias fo r the statistic, which is a common performance measure used in dispersion model performa nce and which is calculated as follows.


# ∑ −
= N observed observed predicted 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 fo r 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 predicte d time-in-microenvironment averages match well with the observed values. For combinations of microenvironment/a ge/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 acro ss 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 combina tions = 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 pr edicted variances have bias between –22% and +24%. The mean normalized bi as across any microenvironment ranges from –10% to +28%. Eighteen predictions have posit ive 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 bi as 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, wher e 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 degree s of freedom using analysis of variance.H-7 microenvironment/age/gender/season. Seventy per cent of the predicted variances have bias between –25% and +30%. The mean normalized bi as across any microenvironment ranges from –11% to +47%. Twenty-eight predictions have positive bias and 12 have negative bias, suggesting some tendency for overp rediction of this variance m easure. 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 vari ance was significantly overpredicted. Still, Figure 4 suggests a reasonably good match of pred icted to observed varian ce in most cases, with a few overpredicting outliers at the higher end of th e distribution. So altho ugh the positive bias is significant in a statistical sense (i.e., the vari ance is more likely to be overpredicted than underpredicted), it is not cl ear 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 varian ce 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 th is approach. Two earlier approaches were:

1. Select a single activity pattern for ea ch 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 da y in the multi-day sequence from the appropriate set for the corres ponding day-type and season.

Goodness-of-fit statistics could be developed to compare the thr ee approaches and find which model best fits the data for a given stratum.H-8 Table 1. Average time spent in each microen vironment: 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 sp ent 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-14Figure 1. Flow diagram of proposed algorithm for creating annual average activity patterns for HAPEM5.Consolidated Human Activity Database - CHADCluster AnalysisCluster 1PatternGroupCluster 2PatternGroupCluster 3PatternGroupTransitionAnalysisTransitionProbabilitiesMarkov SelectionIndividual Annual Average ActivityWinter WeekdayPattern GroupSummer WeekdayPattern GroupWeekendPattern GroupCluster 1PatternCluster 2PatternCluster 3PatternWeightsAverage WinterWeekday Pattern0.54Cluster AnalysisCluster AnalysisH-15Figure 2. Comparison of predicted and observed average timein each of 5 microenvironments for age/gender groups andseasons.Figure 3. Comparison of predicted and observed average timein each of 4 microenvironments for age/gender groups andseasons.051015200 5 10 15 20Observed (hours/day)

Predicted (hours/day)Indoor, homeIndoor, schoolindoor, otherOutdoorIn vehicle012345012345Observed (hours/day)

Predicted (hours/day)Indoor, schoolindoor, otherOutdoorIn vehicleH-16Figure 4. Comparison of predicted and observed variance across persons for time spent in each of 5 microenvironments forage/gender groups and seasons.Figure 5. Comparison of predicted andobserved the average within-person variance for time spent in each of 5microenvironments by age/gender groups and seasons.010203040506070800 20 40 60 80Observed

Simulatedgirls, 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 inter0510152025300 10 20 30Observed

Simulatedgirls, 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 interAPPENDIX I. ESTIMATING NEAR ROADWAY POPULATIONSThis page intentionally left blank.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 “M SAT Rule”) EPA’s Office of Transportation and Air Quality (OTAQ) co mmitted to further study of the range of concentrations to which people are exposed for cons ideration in future rulemaking. As part of the Technical Analysis Plan outlined in that res earch, OTAQ undertook resear ch activity looking at the air quality in immediate proximity of bus y 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 spatia l 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 microenvironmen t visited are combined into a time-weighted average concentration, which is assigne d to members of the demographic group.

Indoor microenvironment concentrations are estima ted by applying scalar f actors to outdoor tract concentrations, which are some of the required inputs. These scalar factors are derived from published studies of concurrent concentr ation measurements indoors and outdoors. In the previous version, HAPEM5, if only a si ngle 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 th e model to account for the spatial variability of outdoor concentrations within a tr act due to enhanced outdoor c oncentrations 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 expos ure concentrations within each Census tract by accounting for some of the spatial variability in the outdoor concentrations w ithin the tract, and by extension some of the spatial variability in indoor concentrations within the tract. Accomplishing this refinement to HAPEM require d several activities, in cluding 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 memorandu m 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 bl ock 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 Cent er (ESRI) StreetMap US roadway geographic database (which includes NavTech, GDT and TeleAtlas rectified street data)

• A geographic database of US Census bloc k boundaries, extracted using the PCensus 2000 Census data extraction to ol 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 interm ediate product for this project, it will be retained to facilitate the re-specification of demographic groups for po ssible future analyses. Therefore, this file contains the most resolved age-gender groups ava ilable at the block leve l 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 (b lock level only) are:

• non-Hispanic White (alone or in combination - P010003)

• non-Hispanic Black (alone or in combination - P010004)

• non-Hispanic American Indian /Alaskan Na tive (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 me ters 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 op erations in this study ICF utilized ArcInfo software. ArcInfo is the most extensive versi on of ArcGIS 9.1, the industry’s standard for Geographic Information Systems, produ ced by ESRI of Redlands, CA.
Due to the size of the roadway and block geograp hy 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 fe w 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 ev enly distributed w ithin 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 cr eate a 150-meter buffer around all roadways within the block. This buffer served as a “clipped” block boundary defining theI-4 portion of the block containing residen tial 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” bl ock area that that fell within each buffer was calculated. This area fraction was a ssumed to equal the population fraction that fell within each buffer, and the fract ions 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 th e 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 stratif ications 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 follo wing 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 me ters of a major roadway

o population residing between 75 and 2 00 meters from a major roadway

o population residing more than 200 meters from a major roadway

• sum of race/ethnic populations (note; this may di ffer 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 me ters of a major roadway

o population residing between 75 and 2 00 meters from a major roadway

o population residing more than 200 meters from a major roadway

Note that because of the limit ations of the US Census dat a the block level populations could not be stratified by age, gender, and race together,I-5 The tract file contains the fo llowing 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 with in 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 th an 200 meters from a major roadway

To date only a subset of stat es have been completely processed. For this subset state summaries of the fraction of population li ving 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. Distance from major roadways STATE < 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 0.33J-1 APPENDIX J. WEEKLY MODEL-TO-MONITOR COMPARISONSJ-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 PercentileConcentration(ppb) measured

A PEX 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 PercentileConcentration(ppb) measured

A PEX 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 PercentileConcentration(ppb)

measured

A PEX n=21J-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 PercentileConcentration(ppb) measured

A PE X 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 PercentileConcentration(ppb) measured

A PE X

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 PercentileConcentration(ppb) measured

A PE X

n=24J-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 PercentileConcentration(ppb) measured

A PEX 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 PercentileConcentration(ppb) measured

A PEX

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 PercentileConcentration(ppb) measured

A PEX n=15J-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 PercentileConcentration (ppb)

measured

A PEX 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 PercentileConcentration (ppb)

measured

A PEX
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 PercentileConcentration(ppb) measured

A PEX n=10J-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 PercentileConcentration (ppb)

measured

A PE X 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 PercentileConcentration (ppb)

measured

A PE X

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 PercentileConcentration (ppb)

measured

A PE X n=14J-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 PercentileConcentration (ppb)

measured

A PE X
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 PercentileConcentration (ppb)

measured

A PE X

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 PercentileConcentration (ppb)

measured A PEX

n=15J-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 PercentileConcentration (ppb)

measured A PE X

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 PercentileConcentration (ppb)

measured

A PE X 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 PercentileConcentration (ppb)

measured A PE X

n=13J-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 PercentileConcentration (ppb)

measured

A PEX 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 PercentileConcentration (ppb)

measured

A PEX

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 PercentileConcentration (ppb)

measured

A PEX n=18J-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 PercentileConcentration (ppb)

measured A PE X

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 PercentileConcentration (ppb)

measured

A PEX
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 PercentileConcentration (ppb)

measured
APEX n=16J-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 PercentileConcentration (ppb)

measured
A PEX 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 PercentileConcentration (ppb)

measured

A PEX

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 PercentileConcentration (ppb)

measured A PEX

n=23J-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 PercentileConcentration (ppb)

measured

A PE X 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 PercentileConcentration (ppb)

measured

A PE X 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 PercentileConcentration (ppb)

measured
A PEX n=17J-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 PercentileConcentration (ppb)

measured

A PE X 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 PercentileConcentration (ppb)

measured

A PEX

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 PercentileConcentration (ppb)

measured

A PE X

n=18J-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 PercentileConcentration (ppb)

measured

A PE X 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 PercentileConcentration (ppb)

measured

A PEX 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 PercentileConcentration (ppb)

measured

A PE X n=12J-15 Weekly Average Indoor Ozone Concentration --Upland, Week of 4/24/95--

0 10 20 30 40

0 20 40 60 80 100
Cumulative PercentileConcentration (ppb)

measured

A PEX 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 PercentileConcentration (ppb)

measured

A PE X 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 PercentileConcentration(ppb) measured

A PE X n=15J-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 PercentileConcentration (ppb)

measured

A PEX 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 PercentileConcentration (ppb)

measured A PE X

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 PercentileConcentration (ppb)

measured

A PEX n=10J-17 Weekly Average Indoor Ozone Concentration --Upland, Week of 5/15/95--

0 10 20 30 40

0 20 40 60 80 100
Cumulative PercentileConcentration (ppb)

measured

A PEX 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 PercentileConcentration (ppb)

measured

A PEX 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 PercentileConcentration (ppb)

measured

A PEX n=17J-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=27J-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 PercentileConcentration(ppb) measured

A PE X 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 PercentileConcentration(ppb) measured

A PE X

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 PercentileConcentration(ppb) measured

A PE X n=31J-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 PercentileConcentration(ppb)

measured A PE X

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 PercentileConcentration (ppb)

measured A PE X

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 PercentileConcentration(ppb) measured

A PE X n=12J-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 PercentileConcentration (ppb)

measured

APE X 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 PercentileConcentration (ppb)

measured A PE X

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 PercentileConcentration(ppb)

measured A PE X

n=17J-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 PercentileConcentration (ppb)

measured

A PE X 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 PercentileConcentration (ppb)

measured A PE X 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 PercentileConcentration (ppb)

measured

A PE X n=20J-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 PercentileConcentration (ppb)

measured

A PE X 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 PercentileConcentration (ppb)

measured A PE X

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 PercentileConcentration (ppb)

measured

A PE X

n=18J-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 PercentileConcentration (ppb)

measured
A PE X

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 PercentileConcentration (ppb)

measured A PE X

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 PercentileConcentration (ppb)

measured

A PE X n=14J-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 PercentileConcentration (ppb)

measured

A PE X 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 PercentileConcentration (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 PercentileConcentration (ppb)

measured

A PE X

n=19J-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 PercentileConcentration (ppb)

measured

A PE X

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 PercentileConcentration (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 PercentileConcentration (ppb)

measured

APEX n=13J-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 PercentileConcentration (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 PercentileConcentration (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 PercentileConcentration (ppb)

measured

APEX n=22J-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 PercentileConcentration (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 PercentileConcentration (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 PercentileConcentration (ppb)

measured

APEX n=12J-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 PercentileConcentration (ppb)

measured

A PE X 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 PercentileConcentration (ppb)

measured A PEX

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 PercentileConcentration (ppb)

measured

A PEX n=25J-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 PercentileConcentration (ppb)

measured

A PE X 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 PercentileConcentration (ppb)

measured A PE X

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 PercentileConcentration (ppb)

measured

A PEX n=16J-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 PercentileConcentration (ppb)

measured

A PE X 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 PercentileConcentration (ppb)

measured A PE X

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 PercentileConcentration (ppb)

measured

A PE X

n=22J-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 PercentileConcentration (ppb)

measured

A PEX

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 PercentileConcentration (ppb)

measured

A PEX 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 PercentileConcentration(ppb)

measured APEXJ-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 PercentileConcentration(ppb) measured

A PEX 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 PercentileConcentration(ppb)

measured A PEX

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 PercentileConcentration (ppb)

measured

A PEX n=17J-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 PercentileConcentration(ppb) measured

A PEX

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 PercentileConcentration(ppb) measured

A PEX

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 PercentileConcentration(ppb) measured

A PEX n=16United StatesEnvironmental ProtectionAgencyOffice of Air Quality Planning and StandardsHealth and Environmental Impacts DivisionResearch Triangle Park, NCPublication No. EPA-452/R-07-010July 2007