Total Risk Integrated Methodology (TRIM) Air 

Pollutants Exposure Model Documentation 

(TRIM.Expo / APEX, Version 4.3) 

Volume II: Technical Support Document 

EPA-452/B-08-001b 

October 2008 

Total Risk Integrated Methodology (TRIM) Air Pollutants 

Exposure Model Documentation (TRIM.Expo / APEX, Version 4.3). 

Volume II: Technical Support Document 

U.S. Environmental Protection Agency 

Office of Air Quality Planning and Standards 

Health and Environmental Impacts Division 

Research Triangle Park, North Carolina 

DISCLAIMER 

 This document has been prepared by Alion Science and Technology, Inc. (through 

Contract No. EP-D-05-065, WAs 21 and 94). Any opinions, findings, conclusions, or 

recommendations are those of the authors and do not necessarily reflect the views of the EPA or 

Alion Science and Technology, Inc. Mention of trade names or commercial products is not 

intended to constitute endorsement or recommendation for use. Comments on this document 

should be addressed to John E. Langstaff, U.S. Environmental Protection Agency, C504-06, 

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

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ACKNOWLEDGEMENTS 

The primary authors of this document are Graham Glen and Kristin Isaacs, Alion Science and 

Technology, Inc. Contributions have also been made by Melissa Nysewander, Luther Smith, 

Casson Stallings (Alion Science and Technology, Inc.), Tom McCurdy, John Langstaff (EPA), 

and ICF Consulting. 

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CONTENTS 

CHAPTER 1. INTRODUCTION .............................................................................................. 1 

1.1 TRIM and The APEX Model........................................................................................... 1 

1.2 Scope and Organization of This Document ..................................................................... 1 

1.3 Introduction to APEX....................................................................................................... 1 

1.4 Strengths and Limitations of APEX................................................................................. 4 

1.4.1 ..................................................................................................................... 4 Strengths

1.4.2 Limitations.................................................................................................................. 5 

1.5 Applicability..................................................................................................................... 6 

1.6 Brief History of APEX..................................................................................................... 6 

CHAPTER 2. OVERVIEW OF MODEL DESIGN AND ALGORITHMS ............................. 8 

CHAPTER 3. USING PROBABILITY DISTRIBUTIONS IN APEX................................... 13 

3.1 The APEX Input Distribution Format............................................................................ 13 

3.2 Details of Distribution Sampling, Truncation, and Resampling .................................... 15 

3.2.1 Resampling Options.................................................................................................. 15 

3.2.2 Beta Distribution....................................................................................................... 17 

3.2.3 Cauchy Distribution.................................................................................................. 18 

3.2.4 Discrete Distribution................................................................................................. 19 

3.2.5 Exponential Distribution........................................................................................... 20 

3.2.6 Extreme Value Distribution ...................................................................................... 21 

3.2.7 Gamma Distribution.................................................................................................. 22 

3.2.8 Logistic Distribution ................................................................................................. 23 

3.2.9 Lognormal Distribution ............................................................................................ 24 

3.2.10 Loguniform Distribution....................................................................................... 25 

3.2.11 Normal Distribution.............................................................................................. 26 

3.2.12 Pareto Distribution................................................................................................ 27 

3.2.13 Triangle Distribution............................................................................................. 28 

3.2.14 Uniform Distribution ............................................................................................ 29 

3.2.15 Weibull Distribution ............................................................................................. 30 

CHAPTER 4. CHARACTERIZING THE STUDY AREA .................................................... 31 

4.1 APEX Spatial Units........................................................................................................ 31 

4.1.1 Initial Study Area...................................................................................................... 31 

4.1.2 ....................................................................................................................... 31 Sectors

4.1.3 Air Quality Districts.................................................................................................. 33 

4.1.4 Meteorological Zones............................................................................................... 34 

4.2 Determining the Final Study Area ................................................................................. 35 

4.2.1 Matching Sectors, Air Quality Districts, and Meteorological Zones........................ 35 

4.2.2 The Distance Algorithm............................................................................................ 35 

4.3 Modeling Commuting .................................................................................................... 36 

4.3.1 Nationwide Commuting Database for 2000 ............................................................. 37 

4.3.2 Implementation of Commuting in APEX ................................................................. 38 

CHAPTER 5. GENERATING SIMULATED INDIVIDUALS (PROFILES)........................ 40 

5.1 Demographic variables................................................................................................... 44 

5.2 Residential Variables...................................................................................................... 45 

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5.3 Physiological Profile Variables...................................................................................... 46 

5.4 Daily-Varying Variables................................................................................................ 50 

5.5 Modeling Variables........................................................................................................ 51 

CHAPTER 6. Constructing a Sequence of Diary Events ........................................................ 53 

6.1 Constructing the Diary Pool........................................................................................... 53 

6.1.1 Diary Data................................................................................................................. 53 

6.1.2 Grouping the Available Diaries into the Diary Pools............................................... 54 

6.2 Basic (Random) Composite Diary Construction............................................................ 55 

6.3 Longitudinal Activity Diary Assembly.......................................................................... 55 

6.3.1 The Longitudinal Diary Assembly Algorithm.......................................................... 56 

6.3.2 Selecting Appropriate D and A Values For a Simulated Population........................ 60 

CHAPTER 7. ESTIMATING ENERGY EXPENDITURES AND VENTILATION............. 62 

7.1 Generating the MET Time-Series.................................................................................. 62 

7.2

............................................................................................................................. 63 

Adjusting the MET Time-Series for Fatigue and Excess Post-Exercise Oxygen 

Consumption

7.2.1 Simulation of Oxygen Deficit................................................................................... 65 

7.2.1.1 Fast Processes ................................................................................................... 65 

7.2.1.2 Slow Processes.................................................................................................. 66 

7.2.1.3 Derivation of Appropriate Values for the Model Parameters........................... 67 

7.2.2 Adjustments to M for Fatigue................................................................................... 68 

7.2.3 Adjustments to M for EPOC..................................................................................... 69 

7.2.3.1 Fast Processes ................................................................................................... 69 

7.2.3.2 Slow Processes.................................................................................................. 69 

7.3 Calculating PAI and the Ventilation Rates .................................................................... 70 

7.3.1 Calculating PAI and Energy Expenditure................................................................. 70 

7.3.2 Calculating Oxygen Consumption and Ventilation Rates........................................ 71 

CHAPTER 8.

.......................................................................................................... 72 

CALCULATING POLLUTANT CONCENTRATIONS IN 

MICROENVIRONMENTS

8.1 Defining Microenvironments......................................................................................... 72 

8.2 Calculating Concentrations in Microenvironments........................................................ 77 

8.2.1 Microenvironmental Concentrations for Home/Work/Other Locations................... 78 

8.2.2 Mass Balance Method............................................................................................... 78 

8.2.3 Factors Method ......................................................................................................... 86 

8.2.4 Microenvironment Parameter Definitions................................................................ 87 

8.2.4.1 Time and Area Mappings.................................................................................. 90 

8.2.4.2 Conditional Variables........................................................................................ 91 

8.2.4.3 Correlation Settings .......................................................................................... 94 

8.2.4.4 Resampling Options.......................................................................................... 96 

8.2.4.5 Random Number Seeds..................................................................................... 97 

8.2.4.6 Source Strength Specification........................................................................... 98 

8.2.4.7 Specification of Distribution Data .................................................................. 100 

CHAPTER 9. CALCULATING EXPOSURES .................................................................... 102 

9.1 Estimating Exposure .................................................................................................... 102 

9.2 Exposure Summary Statistics....................................................................................... 103 

9.3 Exposure Summary Tables........................................................................................... 104 

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CHAPTER 10. CALCULATING DOSE............................................................................. 108 

10.1 Inhaled Dose Calculation........................................................................................ 108 

10.2 Carboxyhemoglobin (COHb) Calculation .............................................................. 109 

10.3 Calculating PM Dose .............................................................................................. 112 

10.3.1 Particle Sizes, Inhalability, and Diffusion Coefficient ....................................... 113 

10.3.2 The ICRP Deposition Equations......................................................................... 114 

10.3.2.1 Lung Volumes and Age Scaling Factors .................................................... 115 

10.3.2.2 Tidal Volume and Activity Level ............................................................... 117 

10.3.2.3 Inspiratory Ventilation................................................................................ 117 

10.3.2.4 Residence Times......................................................................................... 118 

10.3.2.5 Final Deposition Fractions and Deposited Masses..................................... 118 

10.4 Definition of Dose Summary Statistics................................................................... 119 

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LIST OF TABLES 

Table 3.1. Available Probability Distributions in APEX............................................................. 14 

Table 5.1. Profile Variables in APEX.......................................................................................... 41 

Table 6.1. D and A Statistics Derived from the Southern California Children’s Study.............. 61 

Table 8.1. Default Mapping of CHAD Location Codes to APEX Microenvironments.............. 73 

Table 8.2. Microenvironmental Parameters................................................................................. 84 

Table 10.1 The values of a, R, and P for each filter for oral and nasal breathing ...................... 115 

Table 10.2 Coefficients for the Lung Volumes and Scaling Factors.......................................... 116 

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LIST OF EXHIBITS 

Exhibit 8-1. Example of a Microenvironmental Parameter Description ..................................... 88 

Exhibit 8-2. Example of the Shortest Possible MP Description .................................................. 89 

Exhibit 8-3. Example of Defining Correlated Microparameters .................................................. 95 

Exhibit 8-4. Use of Source Number in MP Definition ................................................................. 98 

Exhibit 8-5. Second MP Definition with Source Number 2. ....................................................... 99 

Exhibit 8-6. Use of #sources Setting in the Pollutant Parameters section of the Simulation 

Control File................................................................................................................................... 99 

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ix 

LIST OF FIGURES 

Figure 2.1a. Overview of APEX, Part 1 ....................................................................................... 10 

Figure 3.1. The Beta Distribution in APEX................................................................................. 17 

Figure 3.2. The Cauchy Distribution in APEX............................................................................. 18 

Figure 3.3 The Discrete Distribution in APEX............................................................................ 19 

Figure 3.4. The Exponential Distribution in APEX...................................................................... 20 

Figure 3.5. The Extreme Value Distribution in APEX................................................................. 21 

Figure 3.6. The Gamma Distribution in APEX. ........................................................................... 22 

Figure 3.7. The Logistic Distribution in APEX........................................................................... 23 

Figure 3.8. The Lognormal Distribution in APEX. ...................................................................... 24 

Figure 3.9. The Loguniform Distribution in APEX...................................................................... 25 

Figure 3.10. The Normal Distribution in APEX........................................................................... 26 

Figure 3.11. The Pareto Distribution in APEX............................................................................. 27 

Figure 3.12. The Triangle Distribution in APEX. ........................................................................ 28 

Figure 3.13. The Uniform Distribution in APEX. ........................................................................ 29 

Figure 3.14. The Weibull Distribution in APEX. ......................................................................... 30 

Figure 4.1. Example of Study Areas, Air Quality Districts, Meteorological Zones, and Sectors 32 

Figure 5.1. Generating a Simulated Profile ................................................................................. 44 

Figure 6.1. Overview of the Longitudinal Diary Assembly Algorithm....................................... 57 

Figure 7.1. Fast Components of Oxygen Deficit and Recovery................................................... 66 

Figure 8.1. The Mass Balance (MASSBAL) Model.................................................................... 79 

Figure 10.1 Structure of the ICRP Deposition Model. ............................................................... 113 
CHAPTER 1. INTRODUCTION 

1.1 TRIM and The APEX Model 

The Air Pollutants Exposure model (APEX) is part of EPA’s overall Total Risk Integrated 

Methodology (TRIM) model framework (EPA, 1999), in particular the inhalation exposure 

component (TRIM.ExpoInhalation). TRIM is a time-series modeling system with multimedia 

capabilities for assessing human health and ecological risks from hazardous and criteria air 

pollutants; it is being developed to support evaluations with a scientifically sound, flexible, and 

user-friendly methodology. The TRIM design includes three modules: 

• Environmental Fate, Transport, and Ecological Exposure module (TRIM.FaTE); 

• Human Exposure-Event module (TRIM.Expo); and 

• Risk Characterization module (TRIM.Risk). 

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

and regional scales. The current release of the model is APEX4. Note that APEX has been 

extensively reviewed. Any changes to the computer code may lead to results that cannot be 

supported by this documentation. Model enhancements, bug fixes, and other changes are 

occasionally made to APEX, and thus users are encouraged to revisit the website 

http://www.epa.gov/ttn/fera/human_apex.html for notices of these changes. 

1.2 Scope and Organization of This Document 

The documentation of the APEX model is currently divided into two volumes. Volume II: 

Technical Support Guide (this document) is intended to be a reference on the scientific basis of 

the APEX model. The scientific background, original references, and equations for the APEX 

model algorithms are included in this volume. Topics covered include the methods implemented 

in APEX for sampling probability distributions, calculating microenvironmental concentrations, 

modeling ventilation, estimating exposure and dose, and assembling composite activity diaries. 

Other model algorithms, such as those for generating the study area and the simulated population 

are also described. 

Volume I: User’s Guide, is designed to be a hands-on guide to using APEX. It is applicable to all 

levels of expertise, from novice to advanced, and focuses on how to run the APEX computer 

model, develop the appropriate input files, and interpret the model output files. 

1.3 Introduction to APEX 

APEX estimates human exposure to criteria and toxic air pollutants using a stochastic, 

“microenvironmental” approach. That is, the model randomly selects data for a sample of 

1 
hypothetical individuals from an actual population database and simulates each individual’s 

movements over time, in different locations (e.g., at home, in vehicles) to estimate their exposure 

to (and, optionally, dose of) the modeled pollutants. APEX can assume people live and work in 

the same general area (i.e., that the ambient air quality is the same at home and at work) or 

optionally can model commuting and thus exposure at the work location for employed 

individuals. 

APEX is a multipollutant model. It can model the simultaneous exposure to any number of 

pollutants, assuming that the user can provide the necessary input air quality data and pollutant 

parameters. 

The APEX model uses the personal profile approach to generate simulated individuals, for whom 

exposure time series are calculated. The profile is a description of the characteristics of an 

individual that may affect either their activities or the concentrations in the microenvironments. 

Typically, the profile includes demographic variables such as age, gender, and employment 

status, as well as physiological variables such as height and weight, and finally some situational 

variables such as possession of a gas stove or air conditioning. The demographic variables are 

used in the selection of activity diaries from EPA’s Consolidated Human Activity Database 

(CHAD, McCurdy et al., 2000) to represent the individual, while the situational variables are 

used to help calculate the microenvironmental concentrations. The physiological variables are 

used in the calculation of pollutant dose. 

An APEX model run consists of calculating the exposure (and optionally dose) time series for a 

user-specified number of profiles. The time series can be calculated on different temporal scales. 

Collectively, these profiles are intended to be a representative random sample of the population 

in a given study area. To this end, tables of demographic data from the decennial census are 

used, so appropriate probabilities for any given geographical area can be derived. In APEX the 

geographical units are called sectors. Using the standard input files provided with the model, 

each sector is a census tract. Ambient air quality and meteorological data for the study area are 

also required by the model; the area covered by an air quality monitor is called a district, and the 

area covered by a meteorological monitor is called a zone. APEX matches up each sector of the 

study area with an appropriate air quality district and meteorological zone to provide all the data 

necessary to simulate exposure and dose for an individual. 

APEX can be thought of as a simulation of a field study that would involve selecting an actual 

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

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

pollutant during a specific period of time. The main differences between the model and an actual 

field study are that in the model: 

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

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

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

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

other microenvironments, the duration of time spent in each) are assumed by the model to 

be similar to individuals with similar demographic characteristics, according to activity 

2 
data such as diaries compiled in EPA’s Consolidated Human Activities Database 

(CHAD) (EPA, 2002; McCurdy et al., 2000); 

• The pollutant exposure concentrations and doses are estimated by the model using 

temporally and spatially varying ambient outdoor concentrations, coupled with 

information on the behavior of the pollutant in various microenvironments; and 

• Various reductions in ambient air quality levels due to potential emission reductions can 

be simulated by adjusting air quality concentrations to reflect the scenarios under 

consideration. 

Thus, the model accounts for the most significant factors contributing to inhalation exposure—

the temporal and spatial distribution of people and pollutant concentrations throughout the study 

area and among the microenvironments—while also allowing the flexibility to adjust some of 

these factors for regulatory assessments and other reasons. 

Nomenclature. The following terms are used throughout this guide: 

• Diary—a set of events or activities (e.g., cooking, sleeping) for an individual in a given 

time frame (e.g., a day). 

• Air quality district—the geographical area represented by a given set of ambient air 

quality data (either based on a fixed-site monitor or output from an air quality model). 

• Event—an activity (e.g., cooking) with a known starting time, duration, 

microenvironment, and location (usually home or work). 

• Microenvironment—a space in which human contact with an environmental pollutant 

takes place. 

• Profile—a set of characteristics that describe the person being simulated (e.g., age, 

gender, height, weight, employment status, whether an owner of a gas stove or air 

conditioner). 

• Sector—the basic geographical unit for the demographic input to and output from APEX 

(usually census tracts). 

• Study Area—the geographical area modeled. 

• Study Area Population—total population of persons who live in the study area. 

• Meteorological zone—the geographical area represented by a given set of meteorological 

data (either based on a meteorological station or output from a meteorological model. 

Labeling Conventions. The labeling used in this document is as follows. 

• Input and output file names are in italics. 

• Model Variables are in bold italics, generally only when first used in a section. 

3 
• KEYWORDS, which are used in the input files to identify variables and settings, are 

given in uppercase bold italics. 

• Input and output file excerpts are in a box surrounded by a single line, 

indicating that the text inside the box is shown exactly as it exists in electronic form. 

• This document also contains references to the APEX model code. Specifically, the 

discussions of the model algorithms include mention to the module and function or 

subroutine in which they are implemented. The code locations are given in bold nonitalic text in the format Module:Subroutine or Module:Function. 

1.4 Strengths and Limitations of APEX 

All models have strengths and limitations, and for each application it is important to carefully 

select the model that has the desired attributes. With this in mind, it is equally important to 

understand the strengths and weaknesses of the chosen model. The following sections provide a 

summary of the strengths and potential limitations of APEX. 

1.4.1 Strengths 

APEX simulates the movement of individuals through time and space to estimate their exposure 

to individual or multiple pollutants in indoor, outdoor, and in-vehicle microenvironments. 

Compared to conducting a field study that would involve identifying, interviewing, and 

monitoring specific individuals in a study area, APEX provides a vastly less expensive, more 

timely, and more flexible approach. The model also allows different air quality data, exposure 

scenarios, and other inputs and thus is very useful for decision making applications. 

An important feature of APEX is its versatility. The model is designed with a great deal of 

flexibility so that different levels of detail in input data can be applied for different applications. 

The input data sets supplied with APEX contain information for several microenvironments, 

covering the needs of most applications. The air quality data input to the model can be in the 

form of monitoring or modeling data. The data can be for specific locations, or geo-political 

units such as counties, or census units such as tracts, or the locations of air dispersion model 

receptors, or the grid cells of Eulerian model output. Criteria and hazardous air pollutants can be 

modeled by APEX. 

A key strength of APEX is the way it incorporates stochastic processes representing the natural 

variability of personal profile characteristics, activity patterns, and microenvironment 

parameters. In this way, APEX is able to represent much of the variability in the exposure 

estimates resulting from the variability of the factors effecting human exposure. 

Another strength of APEX is its ability to estimate exposures and doses on different timescales 

for all simulated individuals in the sample population from the study area. This ability allows for 

powerful statistical analysis of a number of exposure characteristics (e.g., acute and chronic 

exposure, correlations with activities and demographics), many of which are provided 

automatically by APEX in output tables. 

4 
APEX also estimates the exposures of workers in the areas where they work, in addition to the 

areas where they live. The pollutant concentrations in these respective locations may be very 

different from each other. 

The use of APEX has been facilitated by the availability of model-ready input files which have 

been developed from the databases discussed above: national population demographics and 

commuting information from the 2000 U.S. Census; CHAD activity data; and microenvironment 

definitions. 

1.4.2 Limitations 

The following limitations of APEX have been identified: 

• The population activity pattern data supplied with APEX (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. 

Nevertheless, the largest portion of CHAD is from random-sample studies of national 

scope, which could be extracted by the user if desired to create a representative sample. 

• The commuting data address only home-to-work travel; travel between sectors for other 

purposes is not modeled directly. APEX can model time spent in travel; however, based 

on the model settings, the ambient air quality during travel is assumed to be either 1) a 

composite of the air quality in all study area sectors or 2) a composite of the air quality in 

a randomly-selected group of sectors. 

• APEX creates seasonal or year-long sequences of activities for a simulated individual by 

sampling human activity data from more than one subject in CHAD. Thus, uncertainty 

exists about season-long exposure event sequences. This approach can tend to 

underestimate the variability from person to person, because each simulated person 

essentially becomes a composite or an “average” of several actual people in the 

underlying activity data (which tends to dampen the variability). At the same time, this 

approach may overestimate the day-to-day variability for any individual if each simulated 

person is represented by a sequence of potentially dissimilar activities from different 

people rather than more similar activities from one person. These uncertainties have been 

partly removed with the implementation in APEX of an algorithm for combining diaries 

which addresses these limitations to some extent. 

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

can impact microenvironmental concentrations (e.g., cigarette smoking leading to an 

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

the residence). 

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

every year (e.g., age). This is only an issue for simulations spanning several years. 

• At this point in time, no interactions between pollutants are modeled. 

5 
Other data and model limitations exist besides those identified above, including physiological, 

meteorological, and those associated with estimating concentrations in microenvironments. EPA 

will continue to refine the model and data to reduce these limitations to the extent possible. The 

uncertainties which result from these limitations of APEX have been characterized for an ozone 

assessment (Langstaff, 2007). 

1.5 Applicability 

APEX is an advanced air inhalation exposure model which can be used for a range of 

applications. APEX can be employed to model episodic "high-end" inhalation exposures that 

result from highly localized pollutant concentrations (e.g., residual risk assessments). APEX can 

also provide detailed probabilistic estimates of exposure for urban and greater metropolitan areas 

(e.g. for regulatory analyses supporting national decisions such as NAAQS reviews). APEX is 

appropriate for assessing both long-term chronic and short-term acute inhalation exposures of the 

general population or of specific segments of the population. The model is designed to look at 

the range of inhalation exposures of different groups of people across a population, for a range of 

averaging times, in a single simulation. The current version of APEX produces results for 

flexible averaging times. By default APEX produces results for 1 hour, 8 hours, 24 hours, and 

annual time periods (or the length of a simulation, if shorter than one year). However, APEX 

can optionally model results for timesteps on a much smaller scale (e.g. ever 5 minutes) by 

setting optional run parameters and providing air quality data on the appropriate time scale. 

Due to the computational demands (run time and disk space) of running APEX, it is not 

appropriate for national-level assessments of population exposure. However, this is not an 

inherent limitation in the model code or algorithms. 

1.6 Brief History of APEX 

APEX was originally derived from the probabilistic National Ambient Air Quality Standards 

Exposure Model (pNEM). The NEM series was developed to estimate exposure to the criteria 

pollutants (e.g., CO, ozone). In 1979, EPA began to develop NEM by assembling a database of 

human activity patterns that could be used to estimate exposures to outdoor pollutants (Roddin et 

al., 1979). The data were then combined with measured outdoor concentrations in NEM to 

estimate exposures to CO (Biller et al., 1981; Johnson and Paul, 1983). In 1988, OAQPS began 

to incorporate probabilistic elements into the NEM methodology, using activity pattern data 

based on various human activity diary studies in an early version of probabilistic NEM for ozone 

(pNEM/O3). In 1991, a probabilistic version of NEM was developed for CO (pNEM/CO) that 

included a one compartment mass-balance model to estimate CO concentrations in indoor 

microenvironments (Johnson et al., 1992). A newer version of pNEM/O3 was developed in the 

1990's and applied to nine urban areas for the general population, outdoor children, and outdoor 

workers (Johnson et al., 1996a,b,c). During 1999-2001, an updated version of pNEM/CO 

(versions 2) was developed that relied on activity diary data from CHAD and enhanced 

algorithms for simulating gas stove usage, estimating alveolar ventilation rate (a measure of 

human respiration), and modeling home-to-work commuting patterns. 

6 
APEX evolved from pNEM to provide greater applicability, flexibility, and accuracy. The 

APEX model was substantially different than pNEM, particularly in the use of a personal profile 

approach rather than a cohort simulation approach. APEX introduced a number of new features 

including automatic site selection from large (e.g., national) databases, a series of new output 

tables providing summary statistics, and a thoroughly reorganized method of describing 

microenvironments and their parameters. Most of the spatial and temporal constraints were 

removed or relaxed in APEX. Several major improvements to APEX have been introduced in 

the most recent version, APEX4. Specifically, APEX4 includes: 

• Multipollutant capability 

• algorithms for the assembly of multi-day (longitudinal) activity diaries that model intraindividual variance, inter-individual variance, and day-to-day autocorrelation in diary 

properties. 

• methods for adjusting diary-based energy expenditures for fatigue and excess postexercise oxygen consumption 

• new equations for estimation of ventilation 

• the ability to model commuters leaving the study area 

• the ability to model air quality and exposure on different time scales 

• the ability to model person-to-person variability in air quality within an air district 

• new output files containing diary event-level, timestep level, and hourly-level exposure, 

dose, and ventilation data, and hourly-level microenvironmental data 

• the ability to model the prevalence of disease states such as asthma 

• new output exposure tables that report exposure statistics for subpopulations such as 

children and active people under different ventilation levels. 

• the ability to model inhaled dose for pollutants 

• the inclusion of commuting data from the 2000 census 

• expanded options for modeling microenvironments 

 

7 
CHAPTER 2. OVERVIEW OF MODEL DESIGN AND 

ALGORITHMS 

This chapter provides a brief outline of the key modeling steps, logic processes, and databases 

used in APEX. 

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

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

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

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

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

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

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

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

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

ventilation (respiration) rate 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. The 

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

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

distribution of modeled individual exposures can be extrapolated to the larger population. 

The model simulation includes up to seven steps: 

1. Characterize the study area - APEX selects sectors (e.g., census tracts) within a study 

area—and thus identifies the potentially exposed population—based on the user-defined 

center and radius of the study area and availability of air quality and weather input data 

for the area. 

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

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

data (such as age-specific employment probabilities). The user can specify the size of the 

sample. The larger the sample, the more representative it is of the population in the study 

area (but also the longer the computing time). 

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

(activity pattern) spanning the period of simulation for each of the simulated persons 

(based on the supplied Consolidated Human Activity Database (CHAD) data, although 

other data could be used). 

4. Estimate energy expenditures and ventilation – APEX constructs a time-series of energy 

expenditures for each profile based on the activity event sequence. These expenditures 

are adjusted for physiological realism, and then used to estimate a number of ventilation 

8 
9 

metrics that are later used in estimating dose and in identifying an active subpopulation of 

active persons for use in creating exposure summary tables. 

5. Calculate timestep concentrations in microenvironments for each pollutant - APEX enables 

the user to define microenvironments that people in a study area would visit (e.g., by 

grouping location codes included in the supplied CHAD database). The model then 

calculates timestep concentrations of each pollutant in each of the microenvironments for 

the period of simulation, based on the user-provided ambient air quality data. All the 

timestep concentrations in the microenvironments are re-calculated for each simulated 

individual. 

6. Calculate exposures for each pollutant - APEX assigns a concentration to each exposure 

event based on the microenvironment occupied during the event and the person’s activity. 

These values are averaged by timestep and by clock hour to produce a sequence of 

timestep and hourly-average exposures spanning the specified exposure period (typically 

one year). These hourly values may be further aggregated to produce daily, monthly, and 

annual average exposure values. 

7. Calculate doses - APEX optionally calculates timestep, hourly, daily, monthly, and annual 

average dose values for each of the simulated individuals. 

The model simulation continues until exposures are calculated for the user-specified number of 

simulated individuals. Figure 2.1 presents these steps within a schematic of the APEX model 

design. The following chapters provide additional detail on the algorithms used in each of the 

above simulation steps. 

The above steps are largely self-contained in the APEX computer code and do not depend on 

subsequent steps. For example, the generation of simulated individuals (step 2) is independent of 

any other profile characteristics or modeling results. This means that the profile variables do not 

depend on the diaries assigned to that profile or to the properties of the microenvironments for 

that profile. The assignment of diaries to the profile (step 3) depends on the profile variables but 

not on the microenvironments, the exposure, the dose, or the properties of any other profile. The 

calculation of microenvironment concentrations (step 4) can depend on the profile variables 

through the use of conditional variables, but in APEX this step cannot depend on the contents of 

the selected activity diaries. Conceptually, this means that the microenvironments essentially 

have an existence of their own that is independent of the activities of the profile. For example, 

activities such as smoking and cooking can “occur” in a residence even when the person being 

profiled is not at home. In reality, the activities of the profiled person can have some effect on 

the microenvironments they visit, but this is not captured in the present version of the model. 

However, through the judicious use of source terms in microenvironments, APEX can simulate 

changes in concentrations due to the presence of the person (e.g., a “personal cloud” effect). 
- National

database

- Area-specific

input data

- Intermediate step

or data

- Data processor - Output data

Sector location data(latitude, longitude)

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

Sector population data 

(age/gender/race)

Population within 

the study area

Commuting flow data

(origin/destination sectors)

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

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

Locations of air quality and 

meteorological measurements; 

radii of influence

Stochastic 

profile generator

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

A simulatefollowing p• Home sec• Work sec• Age• Gender• Race• Employm• Home gas • Home gas • Home air • Car air co• Physiolog

(height, w

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

Age/gender/tract-specific 

employment probabilities

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

simulated individuals (pr

- National

database

- Area-specific

input data

- Intermediate step

or data

- Data processor - Output data

- National

database

- Area-specific

input data

- Intermediate step

or data

- Data processor - Output data

Sector location data(latitude, longitude)

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

Sector population data 

(age/gender/race)

Population within 

the study area

Commuting flow data

(origin/destination sectors)

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

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

Locations of air quality and 

meteorological measurements; 

radii of influence

Stochastic 

profile generator

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

A simulatefollowing p• Home sec• Work sec• Age• Gender• Race• Employm• Home gas • Home gas • Home air • Car air co• Physiolog

(height, w

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

Age/gender/tract-specific 

employment probabilities

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

simulated individuals (pr

Figure 2.1a. Overview of APEX, Part 1 

10 
Diary events/activities 

and personal information 

(e.g., from CHAD)

Maximum/mean daily

temperature data

Activity diary pools by day 

type/temperature category

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

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

Stochastic diary 

selector using age, 

gender, employment, 

and key diary statistic 

(for longitudinal diary 

assembly)

Stochastic

calculation of energy

expended per event (adjusted for

physiological limits and EPOC)

and ventilation

rates

Physiological 

parameters from 

profile

Sequence of event

individual

Profile for an 

individual

4. Construct sequence of activity events 

for each simulated individual

Diary events/activities 

and personal information 

(e.g., from CHAD)

Maximum/mean daily

temperature data

Activity diary pools by day 

type/temperature category

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

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

Stochastic diary 

selector using age, 

gender, employment, 

and key diary statistic 

(for longitudinal diary 

assembly)

Stochastic

calculation of energy

expended per event (adjusted for

physiological limits and EPOC)

and ventilation

rates

Physiological 

parameters from 

profile

Sequence of event

individual

Profile for an 

individual

4. Construct sequence of activity events 

for each simulated individual

Figure 2-1b. Overview of APEX, Part 2

11 
Hourly air quality 

data for all sectors

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

Concentrations for all events 

for each simulated individual

Hourly concentrations and minutes spent in each

microenvironment visited by 

the simulated individual

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

Microenvironments defined by 

grouping of CHAD location codes

Calculate hourly

concentrations in

microenvironments

visited

Population expoindicators for:• Total populati• Children• Asthmatic chi

Sequence of events for 

each simulated individual

Calculate

concentrations in all

microenvironments

5. Calculate concentrations in 

microenvironments for all events for 

each simulated individual

6. Calculate hourly 

exposures for each 

simulated individual

7. Calcu

population e

statisti

Input functions describing 

interpersonal, geographic, 

meteorological, 

and temporal variation in 

microenvironmental 

parameters

Repeat steps 

in t

Hourly air quality 

data for all sectors

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

Concentrations for all events 

for each simulated individual

Hourly concentrations and minutes spent in each

microenvironment visited by 

the simulated individual

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

Microenvironments defined by 

grouping of CHAD location codes

Calculate hourly

concentrations in

microenvironments

visited

Population expoindicators for:• Total populati• Children• Asthmatic chi

Sequence of events for 

each simulated individual

Calculate

concentrations in all

microenvironments

5. Calculate concentrations in 

microenvironments for all events for 

each simulated individual

6. Calculate hourly 

exposures for each 

simulated individual

7. Calcu

population e

statisti

Input functions describing 

interpersonal, geographic, 

meteorological, 

and temporal variation in 

microenvironmental 

parameters

Repeat steps 

in t

Timestep concentrations and minutes spent in eachmicroenvironment visited by the simulated individual

Calculate timestep 

concentrations in 

microenvironments 

visited

•Timestep•Hourly•Daily timestep max•Daily...

Timestep or hourly air quality data for all sectors

6. Calculate timestep / 

hourly exposures for 

each simulated 

individual

Figure 2-1c. Overview of APEX, Part 3

12 
13 

CHAPTER 3. USING PROBABILITY DISTRIBUTIONS IN 

APEX 

APEX is a stochastic model. It makes use of random sampling from probability distributions to 

model variability in a number of input model parameters. Specifically, distributions are used: 

1) To model variability in MET (energy expenditures) for different activities. Input MET 

distributions for each activity are defined in the Activity-Specific MET file. 

2) To model inter-person variability in physiological parameters. Physiological parameter 

distributions are defined for each different age-gender cohort in the Physiology file. 

3) To model timestep, hourly, daily, or geographic variability in microenvironment 

parameters. Distributions for microenvironmental parameters are defined in the 

Microparameter Descriptions file. 

4) To model person-to-person variation in hourly air quality data within an air district. 

Distributions for hourly air quality values can be defined in the Air Quality Data file. This is an 

optional feature of APEX. 

This chapter gives direction on how to define distributions in these input files. In addition, each 

distribution available in APEX and its parameters are defined in detail. 

3.1 The APEX Input Distribution Format 

In all APEX input files, distributions are defined in the same manner, via a standard APEX 

format. This format consists of the following items: 

• Distribution Shape. This variable gives the shape of the distribution. 

• Par1. Parameter 1 of the distribution. Depends on shape. 

• Par2. Parameter 2 of the distribution. Depends on shape. 

• Par3. Parameter 3 of the distribution. Depends on shape. 

• Par4. Parameter 4 of the distribution. Depends on shape. 

• LTrunc. Lower truncation point of the distribution. 

• UTrunc. Upper truncation point of the distribution. 

• ResampOut.: Distribution resampling flag. 

The distribution shape is a text keyword that defines the type of distribution to be used. The next 

four items (Par1-Par4) are numerical values defining the parameters of the distribution. The next 

two items (LTrunc and UTrunc) are the optional truncation limits for the distribution, and the last 

item is an optional character flag (ResampOut, set to either Y or N) indicating how sampled 

values outside of the truncation limits are handled. All the information is entered on a single line 

in the appropriate input file. Note that in each input file the distribution definition may be 

preceded on each line by additional data specific to that file; see sections on individual input 

files. 
The probability distributions allowed in APEX are listed in 

14 

Table 3.1. Equations for each of the 

distributions in the table are given in Section 3.2. 

Table 3.1. Available Probability Distributions in APEX. 

Distribution 

APEX SHAPE 

KEYWORD Par1 Par2 Par3 Par4 

LTrunc 

(Optional) 

UTrunc 

(Optional) 

ResampOut 

(Optional) 

Beta BETA Minimum Maximum 

Shape1 

(s1) >0 

Shape2 

(s2) >0 

Lower 

truncation 

limit 

Upper 

truncation 

limit 

Resample 

outside 

truncation? 

(Y/N) 

Cauchy CAUCHY Median 

Scale (b) > 

0 

Lower 

truncation 

limit 

Upper 

truncation 

limit 

Resample 

outside 

truncation? 

(Y/N) 

Discrete DISCRETE 

This type of distribution has no parameters, rather the keyword is simply followed by a 

space-delimited list of up to 100 discrete values. The distribution returns each of these 

values with equal probability.

Exponential EXPONENTIAL 

Decay 

constant, k 

> 0 Shift (a) 

Lower 

truncation 

limit 

Upper 

truncation 

limit 

Resample 

outside 

truncation? 

(Y/N) 

Extreme 

Value EVALUE 

Scale (b) > 

0 Shift (a) 

Lower 

truncation 

limit 

Upper 

truncation 

limit 

Resample 

outside 

truncation? 

(Y/N) 

Gamma GAMMA 

Shape (s) > 

0 

Scale (b) > 

0 Shift (a) 

Lower 

truncation 

limit 

Upper 

truncation 

limit 

Resample 

outside 

truncation? 

(Y/N) 

Logistic LGT Mean 

Scale (b) > 

0 

Lower 

truncation 

limit 

Upper 

truncation 

limit 

Resample 

outside 

truncation? 

(Y/N) 

Lognormal LOGNORMAL 

Geometric 

mean (gm) 

of unshifted 

dist 

Geometric 

standard 

deviation 

(gsd) >1 Shift (a) 

Lower 

truncation 

limit 

Upper 

truncation 

limit 

Resample 

outside 

truncation? 

(Y/N) 

Loguniform LUNIFORM 

Minimum > 

0 

Maximum > 

0 

Lower 

truncation 

limit 

Upper 

truncation 

limit 

Resample 

outside 

truncation? 

(Y/N) 

Normal NORMAL Mean 

Standard 

deviation 

Lower 

truncation 

limit 

Upper 

truncation 

limit 

Resample 

outside 

truncation? 

(Y/N) 

OffOn OFFON 

Probability 

of being 0 

(0-1) 

Pareto PARETO 

Shape (s) > 

0 

Scale (b) > 

0 Shift (a) 

Lower 

truncation 

limit 

Upper 

truncation 

limit 

Resample 

outside 

truncation? 

(Y/N) 

Point POINT Point Value 

Triangle TRIANGLE Minimum Maximum Peak 

Lower 

truncation 

limit 

Upper 

truncation 

limit 

Resample 

outside 

truncation? 

(Y/N) 

Uniform UNIFORM Minimum Maximum 

Lower 

truncation 

limit 

Upper 

truncation 

limit 

Resample 

outside 

truncation? 

(Y/N) 

Weibull WEIBULL 

Shape (s) > 

0 

Scale (b) > 

0 Shift 

Lower 

truncation 

limit 

Upper 

truncation 

limit 

Resample 

outside 

truncation? 

(Y/N) 
Cells that are grayed out in the table correspond to items not needed for a particular distribution, 

and data entered in these locations will be ignored by APEX. In addition, the LTrunc, UTrunc, 

and ResampOut items are in general optional. (If LTrunc and UTrunc are defined but 

ResampOut is not, the default value of ResampOut=Y is used.) Note however, that a 

placeholder period (“.”) must be used in the distribution definition for each item that is not 

used. 

15 

Consider each of the examples below (one from each input file using distributions): 

From the Activity-Specific MET file: 

Row Act Age Occ. Shape Par1 Par2 Par3 Par4 LTrunc UTrunc ResampOut 

 1 10000 0 ADMIN LogNormal 1.7 1.45 0 . 1.4 2.7 Y 

From the Physiology file: 

!Variable AgeMin AgeMax Gen Shape Par1 Par2 Par3 Par4 LTrunc UTrunc ResampOut 

NVO2MAX 0 0 M Normal 48.3 1.7 . . 44.3 52.2 Y 

From the Microparameter Descriptions file: 

Block DType Season Area C1 C2 C3 Shape Par1 Par2 Par3 Par4 LTrunc UTrunc ResampOut 

1 1 1 1 1 1 1 Normal 2 0.5 0 . 0.111 10.111 Y 

Note that in each case the distribution definitions follow the exact same format (starting with the 

Shape keyword). The only distribution type that does not follow this format is the Discrete 

distribution, see Section 3.2.4. 

Distributions are read from the various input files and stored in DistributionModule:ReadDist. 

3.2 Details of Distribution Sampling, Truncation, and Resampling 

Probability density functions (PDFs) for each of the APEX distributions, parameterized 

in terms of their input APEX parameters, are given in this section (with the exception of the 

OffOn and Point distributions, which are trivial). In addition, real examples (of 10000 samples 

each) from APEX are shown for untruncated distributions and for truncated distributions using 

both ResampOut=Y and ResampOut=N. 

When needed, stored distributions (which were read from the input files) are sampled in 

DistributionModule:SampleDist.

3.2.1 Resampling Options 

ResampOut determines how truncated distributions are handed by the APEX sampling routines. 

If ResampOut = N, then any generated sample outside the truncation points is set to the 

truncation limit; in this case, samples “stack up” at the truncation points, and the probability 
associated with the area under the PDF outside the truncation bounds is associated with the 

truncation limit. If ResampOut = Y, then a new random value is selected from inside the valid 

range. In this case, the probability outside the limits is spread over the valid values, and thus the 

probabilities inside the truncation limits will be higher than the theoretical untruncated PDF. 

16 

For each of the distributions defined in this section, the theoretical PDF is shown plotted against 

APEX results for each truncation case. (Note that the “untruncated” case is actually a truncated 

case with the truncation points set to the 0.1st and 99.9th percentiles where noted. These 

distributions had very long tails, and they were truncated so they would fit in the illustration). 
17 

3.2.2 Beta Distribution 

The PDF for the beta distribution in terms of the APEX input parameters is 

( ) ( )( )( ) 21

11 12

21

)21()()( )( ss

s s

minmaxss

minx ssxmax

xp +

− −

−ΓΓ

− +Γ− = (3-1) 

where Γ indicates the gamma function and S1 and S2 are shape parameters. See Table 3.1 for 

assignment of the parameters in this equation to the APEX parameters Par1-Par4. The 

theoretical PDF for the beta distribution is illustrated in Figure 3.1 along with real examples 

obtained from APEX using the different sampling options. 

Shape2=2.5

Shape1=2.5

Max=8

Min=2

BETA

1 2 3 4 5 6 7 8 9 10 0.00

0.05

0.10

0.15

0.20

0.25

2 3 4 5 6 7 8

0.00

0.05

0.10

0.15

0.20

0.25

0.30

PDF Untruncated 

2 3 4 5 6 7 8

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

2 3 4 5 6 7 8

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Truncated, range [3 - 7], ResampOut=N Truncated, range [3 - 7], ResampOut=Y 

Figure 3.1. The Beta Distribution in APEX. 
18 

3.2.3 Cauchy Distribution 

The PDF for the Cauchy distribution in terms of the APEX input parameters is 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − +

=

2

2 ( ) 1

1 )(

b

medianx b

xp

π

 (3-2) 

where b is a scale parameter. See Table 3.1 for assignment of the parameters in this equation to 

the APEX parameters Par1-Par4. The theoretical PDF for the Cauchy distribution is illustrated 

in Figure 3.2 along with real examples obtained from APEX using the different sampling 

options. 

Scale=2

Median=3

CAUCHY

-10 0 10 20 30 40 50 60 70 80 0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

-2 0 2 4 6 8 10

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Theoretical PDF Truncated at (0.1st and 99.9th percentiles) 

-2 0 2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

-2 0 2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Truncated, range [-1 - 8], ResampOut=N Truncated, range [-1 - 8], ResampOut=Y 

Truncated at 0.1st and 99.9th percentiles

Figure 3.2. The Cauchy Distribution in APEX. 
19 

3.2.4 Discrete Distribution 

The discrete distribution is a custom form of APEX distribution. Rather than being defined by 

the regular 7 parameters, the discrete distribution is just given as a space-separated list of up to 

100 values. APEX will return all values with equal probability. 

An example of a discrete distribution having 6 values is shown in Figure 3.3. 

2 4 6 8 10 12 14

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

DISCRETE 

Values= 

2.2 

4.4 

6.6 

8.8 

11.0 

13.2 

Figure 3.3 The Discrete Distribution in APEX 
20 

3.2.5 Exponential Distribution 

The PDF for the exponential distribution in terms of the APEX input parameters is

⎟

⎠

⎞ ⎜

⎝

⎛ −

= k

xa

)( kexp (3-3) 

where a is a shift parameter and k is the decay constant. See Table 3.1 for assignment of the 

parameters in this equation to the APEX parameters Par1-Par4. The theoretical PDF for the 

exponential distribution is illustrated in Figure 3.4 along with real examples obtained from 

APEX using the different sampling options. 

Shift=2

Decay=0.2

EXPONENTIAL

0 5 10 15 20 25 30 35

0.00

0.05

0.10

0.15

0.20

0.25

0 5 10 15 20 25

0.00

0.05

0.10

0.15

0.20

0.25

Theoretical PDF Untruncated 

0 5 10 15 20 25

0.00

0.05

0.10

0.15

0.20

0.25

0 5 10 15 20 25

0.00

0.05

0.10

0.15

0.20

0.25

Truncated, range [5-15], ResampOut=N Truncated, range [5-15], ResampOut=Y 

Figure 3.4. The Exponential Distribution in APEX. 
21 

3.2.6 Extreme Value Distribution 

The PDF for the extreme value distribution in terms of the APEX input parameters is

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

− − −

=

b

xa

e b

xa

e

b xp

1 ( ) (3-4) 

where a is a shift parameter and b is a scale parameter. See Table 3.1 for assignment of the 

parameters in this equation to the APEX parameters Par1-Par4. The theoretical PDF for the 

extreme value distribution is illustrated in Figure 3.5 along with real examples obtained from 

APEX using the different sampling options. 

Shift=2

Scale=3

EXTREME VALUE

-10 -5 0 5 10 15 20 0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

-5 0 5 10 15 20

0.00

0.05

0.10

0.15

0.20

0.25

Theoretical PDF Untruncated 

-5 0 5 10 15 20

0.00

0.05

0.10

0.15

0.20

0.25

-5 0 5 10 15 20

0.00

0.05

0.10

0.15

0.20

0.25

Truncated, range [-3 - 7], ResampOut=N Truncated, range [-3 - 7], ResampOut=Y 

Figure 3.5. The Extreme Value Distribution in APEX. 
22 

3.2.7 Gamma Distribution 

 The PDF for the gamma distribution in terms of the APEX input parameters is

( ) )( )( 1

s

e axbxp

b

xa

s s

Γ −=

−

− − (3-5) 

where a is a shift parameter and b is a scale parameter. See Table 3.1 for assignment of the 

parameters in this equation to the APEX parameters Par1-Par4. The theoretical PDF for the 

gamma distribution is illustrated in Figure 3.6 along with real examples obtained from APEX 

using the different sampling options. 

Shift=2

Scale=2

Shape=2

GAMMA

0 2 4 6 8 10 12 14 16 18

0.00

0.05

0.10

0.15

0.20

0.25

-5 0 5 10 15 20

0.00

0.05

0.10

0.15

0.20

0.25

Theoretical PDF Untruncated 

-5 0 5 10 15 20

0.00

0.05

0.10

0.15

0.20

0.25

-5 0 5 10 15 20

0.00

0.05

0.10

0.15

0.20

0.25

Truncated, range [2.5-14], ResampOut=N Truncated, range [2.5-14], ResampOut=Y 

Figure 3.6. The Gamma Distribution in APEX. 
23 

3.2.8 Logistic Distribution 

The PDF for the logistic distribution in terms of the APEX input parameters is

2

1

)(

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

= −

−

b

xa

b

xa

e

e

xp (3-6) 

where a is a shift parameter and b is a scale parameter. See Table 3.1 for assignment of the 

parameters in this equation to the APEX parameters Par1-Par4. The theoretical PDF for the 

logistic distribution is illustrated in Figure 3.7 along with real examples obtained from APEX 

using the different sampling options. 

Scale=1

Mean=2

LOGISTIC

-5 0 5 10 0.00

0.05

0.10

0.15

0.20

0.25

-3 -2 -1 0 1 2 3 4 5 6 7

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Theoretical PDF Untruncated 

-3 -2 -1 0 1 2 3 4 5 6 7

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

-3 -2 -1 0 1 2 3 4 5 6 7

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Truncated, range [0-4], ResampOut=N Truncated, range [0-4], ResampOut=Y 

Figure 3.7. The Logistic Distribution in APEX. 
24 

3.2.9 Lognormal Distribution 

The PDF for the lognormal distribution in terms of the APEX input parameters is

2

)log(

log

2

1

)log()(2

1 )(

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎣

⎡ ⎟

⎠

⎞ ⎜

⎝

⎛ −

−

− =

GSD

GM

ax

e

GSDax xp

π

 (3-7) 

where a is a shift parameter, GM is the geometric mean, and GSD is the geometric standard 

deviation. See Table 3.1 for assignment of the parameters in this equation to the APEX 

parameters Par1-Par4. The theoretical PDF for the lognormal distribution is illustrated in Figure 

3.8 along with real examples obtained from APEX using the different sampling options. 

Shift=2

GSD=1.5

GM=1

LOGNORMAL

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

0.0

0.2

0.4

0.6

0.8

1.0

2.0 2.5 3.0 3.5 4.0 4.5 5.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Theoretical PDF Untruncated 

2.0 2.5 3.0 3.5 4.0 4.5 5.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

2.0 2.5 3.0 3.5 4.0 4.5 5.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Truncated, range [2.5-4], ResampOut=N Truncated, range [2.5-4], ResampOut=Y 

Figure 3.8. The Lognormal Distribution in APEX. 
25 

3.2.10 Loguniform Distribution 

The PDF for the loguniform distribution in terms of the APEX input parameters is

x

min

max log

p(x)

⎟

⎠

⎞ ⎜

⎝

⎛ = 1 (3-8) 

where min and max are the minimum and maximum values of the untruncated distribution, 

respectively. See Table 3.1 for assignment of the parameters in this equation to the APEX 

parameters Par1-Par4. The theoretical PDF for the loguniform distribution is illustrated in 

Figure 3.9 along with real examples obtained from APEX using the different sampling options. 

Max=5

Min=1

LOGUNIFORM

0 1 2 3 4 5 6 7 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Theoretical PDF Untruncated 

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Truncated, range [2-4], ResampOut=N Truncated, range [2-4], ResampOut=Y 

Figure 3.9. The Loguniform Distribution in APEX. 
26 

3.2.11 Normal Distribution 

The PDF for the normal distribution in terms of the APEX input parameters is

( ) 2 2

2

1 )( SD

meanx

e

SD xp

−−

= π

 (3-9) 

where mean is the mean of the untruncated distribution and SD is the standard deviation. See 

Table 3.1 for assignment of the parameters in this equation to the APEX parameters Par1-Par4. 

The theoretical PDF for the normal distribution is illustrated in Figure 3.10 along with real 

examples obtained from APEX using the different sampling options. 

SD=1.7

Mean=8

NORMAL

0 2 4 6 8 10 12 14 16

0.00

0.05

0.10

0.15

0.20

0.25

5 10 15

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Theoretical PDF Untruncated 

5 10 15

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

5 10 15

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Truncated, range [4-12], ResampOut=N Truncated, range [4-12], ResampOut=Y 

Figure 3.10. The Normal Distribution in APEX. 
27 

3.2.12 Pareto Distribution 

The PDF for the Pareto distribution in terms of the APEX input parameters is

1 )( )( + − = s

s

ax

sb

xp (3-10) 

where a is a shift parameter and b is a scale parameter. See Table 3.1 for assignment of the 

parameters in this equation to the APEX parameters Par1-Par4. The theoretical PDF for the 

Pareto distribution is illustrated in Figure 3.11 along with real examples obtained from APEX 

using the different sampling options. 

Figure 3.11. The Pareto Distribution in APEX. 
28 

3.2.13 Triangle Distribution 

The PDF for the triangle distribution in terms of the APEX input parameters is

( )

( )( ) peakxmin minmaxminpeak

minx p(x) ≤≤ − −

− = 2 (3-11) 

( )

maxxpeak

minmax

minpeak 1minmax

max p(x) ≤≤

⎟

⎠

⎞ ⎜

⎝

⎛

−

− −−

= 2

2 

where min, max, and peak are the minimum, maximum, and peak of the untruncated distribution, 

respectively. See Table 3.1 for assignment of the parameters in this equation to the APEX 

parameters Par1-Par4. The theoretical PDF for the triangle distribution is illustrated in Figure 

3.12 along with real examples obtained from APEX using the different sampling options. 

Max=10

Peak=5

Min=3

TRIANGLE

0 5 10 15 0.00

0.05

0.10

0.15

0.20

0.25

3 4 5 6 7 8 9 10

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Theoretical PDF Untruncated 

3 4 5 6 7 8 9 10

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

3 4 5 6 7 8 9 10

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Truncated, range [4-9], ResampOut=N Truncated, range [4-9], ResampOut=Y 

Figure 3.12. The Triangle Distribution in APEX. 
29 

)

3.2.14 Uniform Distribution 

The PDF for the uniform distribution in terms of the APEX input parameters is

( minmax

1 p(x) − = (3-12) 

where min and max are the minimum and maximum values of the untruncated distribution, 

respectively. See Table 3.1 for assignment of the parameters in this equation to the APEX 

parameters Par1-Par4. The theoretical PDF for the uniform distribution is illustrated in Figure 

3.13 along with real examples obtained from APEX using the different sampling options. 

Max=10

Min=3

UNIFORM

0 5 10 15 0.00

0.05

0.10

0.15

0.20

0.25

1 2 3 4 5 6 7 8 9 10

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Theoretical PDF Untruncated 

1 2 3 4 5 6 7 8 9 10

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

1 2 3 4 5 6 7 8 9 10

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Truncated, range [4-8], ResampOut=N Truncated, range [4-8], ResampOut=Y 

Figure 3.13. The Uniform Distribution in APEX. 
30 

3.2.15 Weibull Distribution 

The PDF for the Weibull distribution in terms of the APEX input parameters is

( )

s

b

ax

s s eaxsbxp

⎟

⎠

⎞ ⎜

⎝

⎛ − − − − −= 1 ( ) (3-13) 

where a is a shift parameter and b is a scale parameter. See Table 3.1 for assignment of the 

parameters in this equation to the APEX parameters Par1-Par4. The theoretical PDF for the 

Weibull distribution is illustrated in Figure 3.14 along with real examples obtained from APEX 

using the different sampling options. 

Shift=3

Scale=2

Shape=2

WEIBULL

0 1 2 3 4 5 6 7 8 9 10 0.0

0.1

0.2

0.3

0.4

0.5

0.6

1 2 3 4 5 6 7 8 9 10

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Theoretical PDF Untruncated 

1 2 3 4 5 6 7 8 9 10

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1 2 3 4 5 6 7 8 9 10

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Truncated, range [4 - 8], ResampOut=N Truncated, range [4 - 8], ResampOut=Y 

Figure 3.14. The Weibull Distribution in APEX. 
31 

CHAPTER 4. CHARACTERIZING THE STUDY AREA 

An initial study area in an APEX analysis consists of a set of basic geographic units called 

sectors, typically defined as census tracts. (See Nomenclature, section 1.3) The user provides 

the geographic center (latitude/longitude) and radius of the study area. APEX calculates the 

distances to the center of the study area of all the sectors included in the sector location database, 

and then selects the sectors within the radius of the study area. One can also provide a list of 

counties or census tracts as part of the specification of the initial study area. APEX then maps 

the user-provided timestep air quality district and hourly meteorological zone data to the selected 

sectors. The sectors identified as having acceptable air and meteorological data within the radius 

of the study area are selected to comprise a final study area for the APEX simulation analysis. 

This final study area determines the population make-up of the simulated persons (profiles) to be 

modeled. 

The following sections describe in more detail how a final study area is determined in an APEX 

simulation analysis. 

4.1 APEX Spatial Units 

4.1.1 Initial Study Area 

The APEX study area has typically been the neighborhood around an emission source or on the 

scale of a city or larger metropolitan area. Larger study areas are possible to simulate, depending 

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

The user defines an initial study area by specifying the latitude and longitude of a central point 

(referred to here as the study area central location), together with a radius. The user also has the 

option of providing a list of counties or census tracts to be modeled. If present, this list further 

restricts the area to be modeled to the counties or tracts to be modeled which are within the 

specified study area radius. The final study area is a function of the availability of the usersupplied demographic data, pollutant concentration data, and the meteorological data within the 

initial study area, as determined respectively by population sectors, air quality districts, and 

meteorological zones. Figure 4.1 and the subsections below provide additional details about 

these geographical units. 

4.1.2 Sectors 

The demographic data used by the model to create personal profiles is provided at the sector 

level. For each sector the user must provide demographic information allowing the 

determination of age, gender, race, and work status. This is most commonly done by equating 

sectors with census tracts and providing input files with counts at the tract level for each age, 

gender, and race combination. The current release of APEX includes input files that already 

contain this demographic and location data for all census tracts in the 50 states and D.C., based 
on the 2000 Census. One of the APEX input files (generically named Sector Location file in this 

guide) lists the sector ID and location for all sectors that have associated population data. The 

supplied Sector Location file has been prepared listing all the census tracts in the 2000 U.S. 

Census. Corresponding Population files have been supplied as well. This allows the user to 

model any desired study area in the country without having to make any changes to these input 

files. 

Figure 4.1. Example of Study Areas, Air Quality Districts, Meteorological Zones, and Sectors 

If available, finer scales such as census block groups could be used instead. Also, data could be 

aggregated to larger regions such as counties if fewer sectors were desired. Regardless of the 

specific meaning for sectors, in APEX the shape of sectors is irrelevant in the sense that the 

model only uses the central location each sector, determined by the latitude and longitude for 

some representative point. 

In the Simulation Control file for an APEX run, the user specifies the area to be modeled by 

specifying the latitude and longitude of a central location for the study area, along with a radius 

(the CityRadius parameter). Optionally, the user may also provide a list of counties or census 

tracts to be modeled. If present, this list further restricts the study area. 

32 
For each model run, APEX selects the sectors that meet the study area conditions in the 

following way. First, the sector location must be within the specified distance (radius) of the 

designated center of the study area. Second, if the user provided a specific list of counties 

identified by their FIPS codes (using CountyList and County in the Control file) , then the sector 

must belong to one of these counties. This is achieved using the first five characters of the sector 

ID, which should contain the FIPS code for the county in which the sector is located. The user 

may also provide a list of census tracts (sectors) using the TractList and Tract variables. If no 

county or tract list is provided, the initial study area is roughly circular, consisting of all sectors 

with sector locations within the specified radius. The final study area consists of the subset of 

sectors in the initial study area for which air quality and meteorological data are available. This 

is discussed under the next two subsections (

33 

4.1.3 and 4.1.4).` 

One way to exert greater control over the selection of sectors is to edit the Census input files to 

eliminate any undesired sectors. However, the Sector Location file and the various Population 

files must all have the same set of sectors in them, so consistent editing is necessary. The 

Sectors and Population files provided with the current release of APEX contain data for all 

census tracts in the 50 states and D.C. from the 2000 Census. 

The sectors are read in SpaceTimeModule:ReadSiteLists. 

4.1.3 Air Quality Districts 

The spatial units for ambient air quality data are called air quality districts. Ambient air quality 

data are provided as timestep (e.g. hourly) time series at specific locations. These locations 

could be monitoring sites, or political units such as counties, or census units such as tracts, or 

receptor locations or grid points as used by some air quality models. As with sectors, each air 

quality district has a nominal central location consisting of a latitude and a longitude. The air 

quality district locations are stored in the Air Quality District Location input file. The user 

designates the maximum representative radius of the air quality districts as a modeling parameter 

called AirRadius. In a given APEX run, all air quality districts have the same maximum 

representative radius. The same set of air quality districts must be used for each pollutant. 

The model checks each air quality district listed in the Air Quality Data input files (one for each 

pollutant) to determine if the district has data covering the entire simulation period. Note that 

each air quality district may have a different period of operation (i.e., different start and/or stop 

dates), but there can be no missing data or gaps between the simulation start and stop dates. If 

the user is supplying monitoring data as inputs, for example, then any missing values within each 

monitoring period must be filled in. The monitoring period can exceed the simulation period for 

the model run because APEX extracts the portion of the input data that corresponds to the 

simulation period. If the monitoring period does not cover the entire simulation period, the air 

quality district is deleted in its entirety. 

APEX calculates the distance from each sector location to each air quality district center, and 

assigns the sector to the nearest air quality district, provided it is within the maximum 

representative air quality radius. If there is no air quality district within range (that is, all air 

quality district centers are further than AirRadius from the sector center), the sector is deleted 

from the study area and is not modeled. It is possible and perhaps even likely that some air 
quality districts in the Air Quality Data input files will have no sectors assigned to them. Such 

air quality districts are not used. This feature allows the user to prepare an input file in the 

simplest manner, perhaps containing more air quality districts than are necessary. For example, 

one might prepare a single Air Quality Data input file for a pollutant for all air quality districts in 

the state of Texas. This same input file could then be run on a study area around Houston, or 

Dallas, or some other location in Texas, without having to alter the input file. In principle, 

although the file would be very large, a single nationwide Air Quality Data file could be 

prepared and used for any pollutant of interest. 

34 

By default, APEX will assign each person within a sector the corresponding appropriate ambient 

values from the sector’s matching air district. Thus, for each timestep in the simulation, all 

persons within the same district will have the same air quality value. However, APEX can 

optionally model person-to-person variation in air quality within an air district. In this case, an 

optional form the the Air Quality Data file is provided, which lists air quality distributions for 

each hour for each air district. Each person in the district is assigned a randomly sampled value 

from the appropriate hourly distribution. See Volume I for details on using this option. Note that 

this option can only be used when the APEX timestep is equal to 1 hour (the APEX default). 

The air quality districts are read in from the input file in SpaceTimeModule:ReadSiteLists. 

The actual air quality is read from the Air Quality Data files in 

SpaceTimeModule:ReadAirQuality. If the Air Quality Data file uses hourly distributions for 

each district (an optional feature of APEX, see Volume I), then the air data for each simulated 

individual is sampled in SpaceTimeModule: GenerateAirQuality. 

4.1.4 Meteorological Zones 

Another spatial unit in APEX is the meteorological zone, which is the equivalent to air quality 

districts but for meteorological data. Most of the rules that apply to air quality districts also 

apply to meteorological zones. Each meteorological zone is associated with a central location 

(specified by latitude and longitude), a maximum representative radius given by ZoneRadius, a 

Start Date, and a Stop Date. The start and stop dates may differ for each meteorological zone, 

and must encompass the entire simulation period or else the meteorological zone is deleted. 

There can be no missing data between the start and stop dates of the simulation. 

APEX calculates the distance from each sector location to each meteorological zone center, and 

assigns each sector to the nearest meteorological zone if within range (ZoneRadius), or deletes 

the sector otherwise. 

The meteorological zone locations are read in from the Meteorological Zone Location input file 

in SpaceTimeModule:ReadSiteLists. The actual meteorological data is read from the 

Meteorology Data file in SpaceTimeModule:ReadMeteorologyData. When the data are read 

in, daily maximum and average temperatures are calculated for later use. 
4.2

35 

Determining the Final Study Area 

4.2.1 Matching Sectors, Air Quality Districts, and Meteorological Zones 

The APEX code for reading the locations of sectors, air quality districts, and meteorological 

zones, and for pairing the sectors to the nearest air quality districts and meteorological zones, is 

found in SpaceTimeModule: SelectSites. 

The final study area consists of all the sectors within CityRadius of the study area central 

location, restricted to the listed counties or tracts (if provided), that have both an air quality 

district and a meteorological zone within range. If both tracts and counties are listed, then the 

resulting study area is the union of the two lists. Sectors for which a valid air quality district 

(one within AirRadius) or a valid meteorological zone (one within ZoneRadius) cannot be found 

are discarded from the final study area. The study area population is the total population in the 

input Population files that reside in these sectors. 

The SelectSites subroutine makes use of the function SpaceTimeModule: Distance which 

calculates the distance between two points given their latitudes and longitudes. It is discussed 

below. 

4.2.2 The Distance Algorithm 

APEX uses a computational algorithm (implemented in SpaceTimeModule:Distance) to 

calculate the distances (e.g. study center to sector center, sector center to air quality district 

center) required to determine the final study area. The method is accurate, simple in terms of 

program code, and works well everywhere on the globe. It calculates the distance between two 

points based on their latitudes and longitudes. It is based on projecting the points onto a sphere, 

rather than onto a plane, using the following steps: 

• The latitude and longitude of the two points (locations) in question are identified 

• The two sets of angles, (θ1, φ1) and (θ2, φ2), subtended at the Earth's center by the radial

vectors to the two points are calculated 

• The net angle between these two radial vectors is found 

• The Earth's radius at the average latitude of the two points is calculated 

• The results from the previous 2 steps are multiplied to give the distance between the 

points, D 

All angles are measured in radians. In step 1, the angles φ subtended by the radial vectors at the 

Earth's center are the same as the longitudes of the points in question. However, calculating the 

θ from latitude is more complicated since it is affected by the flattening of the poles. The 

intersection of the Earth's surface with a plane through the poles is an ellipse. Let the 

eccentricity of the ellipse be given by e. Latitude measures the angle between the polar axis and 
a locally horizontal surface such as sea level (a tangent surface to the Earth). For a point on an 

ellipse at an angle θ from the semimajor axis, the tangent line has slope s: 

36 

( )cote1s (θ ) 2 −−= (4-1) 

where the square of the eccentricity of the earth is e2

 = 0.00672265. 

This slope is equal to the negative cotangent of the latitude. Hence 

θ [( )tan(lat)e1tan ] 1 2 −= − (4-2) 

When applied to both points, this gives angles θ1 and θ2. 

The radius of the Earth varies with latitude but not with longitude. At an angle theta relative to 

the semimajor axis, the distance from the center to a point on the ellipse is given by 

cose1 ( ) θ

e1 AR 22

2

−

− = (4-3) 

where A is the semimajor axis length, A = 6378.388. For purposes of the distance calculation, θ

is set to the average of θ1 and θ2. 

For two points at (θ1, φ1) and (θ2, φ2) on a sphere of radius R, the arc length of the great circle

connecting them, the distance D, is given by the product of the radius and the net angle between 

them: 

[ ( ) ( ) ( ) ( ) ( )] (4-4) 1 2 21 1 2

1 = cosRcosD θ cos θ cos +− sin θ sin θ − φφ

which follows from the formula for the dot product of the radial vectors, expressed in spherical 

coordinates. 

All of the above formulas are exact. The only approximation being made is in claiming that the 

arc of the Earth's surface between the two points lies exactly on a sphere. In most practical 

cases, the error resulting from this approximation is in the range of one to ten parts per million. 

4.3 Modeling Commuting 

APEX models commuting by assigning a work sector to each employed modeled individual 

based on commuting data for the individual’s home sector from the 2000 Census. A single 

nationwide file of commuting data (the Commuting file) is supplied with APEX. Both the 

nationwide Population Data and Commuting input files use census tracts as the sectors. The 

Population Data files contain year 2000 tract-level U.S. Census counts, tract locations, and 

national employment probabilities by age. The Commuting file contain adult commuting 

patterns based on the 2000 Census. As part of step 2 (Figure 2-1), APEX can extract the flows 

for the selected home sectors from this large Commuting file. The development of this file is 

described below. 
4.3.1

37 

Nationwide Commuting Database for 2000 

A national commuting database was generations from a set of US Census files listing the number 

of persons living in one tract and working in another. The original files, derived from the 2000 

Census, are distributed by the US DOT Bureau of Transportation Statistics at their web site 

http://transtats.bts.gov/. The data used were collected as part of the Census Transportation 

Planing Package (CTPP). The files used are from CTPP Part 3-The Journey To Work files. They 

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

geographic scales. Tract-to-tract data were used for the commuting databases. 

One concern identified from these data was that some home-work pairs are very widely 

separated geographically. For example, some people live in Alabama but work in Alaska. This 

may be the case for either military personnel, or others who are stationed in remote workplaces 

for weeks or months at a time, but in APEX the need is for daily commuting flows and there is 

no way to determine from these data which workers commute on a daily basis. A preliminary 

analysis of the home-work counts showed that a graph of Log(flows) versus Log(distance) had a 

near-constant slope up to somewhere around 100 kilometers. Beyond 150 kilometers the slope is 

also fairly constant but flatter, meaning that flows were not as sensitive to distance. Between 

these two distances there is a smooth transition from one slope to the other. A simple 

interpretation of this result is that at distances below 100 km the vast majority of the flow was 

due to persons traveling back and forth daily, and the numbers of such persons decrease fairly 

rapidly with increasing distance. At large distances the majority of the flow are persons who 

stay at the workplace for extended times, in which case the separation distance is not as crucial in 

determining the size of the flow. 

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

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

in more widely separated pairs commute daily. This meant that the list of destinations for each 

home tract can be restricted to only those work tracts that are within 120 km of the home. In 

practice, this cutoff has little impact in an APEX model run since persons who live and work 

more than 120 km apart are not likely to have both their home and work sectors inside the same 

study area. 

The resulting database contained a total of 64,958 distinct home sectors, and 65,075 work 

sectors, based on data from 117,792,172 persons. The home-work tract pairs were sorted by the 

home tract ID, and for each home tract the possible destinations were listed, one per line. The 

flows were converted to fractions of the home tract total, and then expressed as cumulative 

fractions since this is the form that will be needed by APEX. The work sectors were sorted by 

decreasing fraction of the home tract total, and the information was written to an ASCII text file. 

Every record in this file contains three variables: a tract ID, a flow fraction, and a distance. A 

convention was used that the flow fraction and distance were set to -1.0 to indicate a home tract. 

The first three records on the nationwide ASCII file are as follows: 
38 

01001020100 -1.00000 -1.0

01001020700 0.10412 5.5 

01101000100 0.20097 19.6

The first record contains the ID of the first home tract by sort order, followed by two placeholder 

values. The second record contains ID for the first destination tract for the current home tract. 

The destination tracts are sorted in order of decreasing commuting fraction The number 0.10412 

indicates that the largest percentage of commuters of the commuters who live in this home tract 

(around 10.4%) commute to tract 01001020700. The third number on each line is the separation 

distance in kilometers between the home and work tracts. The third record shows the second 

destination tract for this same home tract, followed by a cumulative fraction of 0.20097. This 

means that about 9.7% of the workers in that home tract go to second work tract, despite the two 

being greater than 19 kilometers apart. Further examination of this file reveals that this 

particular home tract has 38 destination tracts to which workers commute. Note that fractions 

down to 0.00001 (one in one hundred thousand) are reported. Fractions that round to zero at this 

precision are deleted from the database. 

The number of destinations per home tract is not constant. There are two ways to know when 

the last destination for a given home tract has been reached. First, the cumulative flow fraction 

for the last destination is always 1.00000. Second, the next record in the file has negative flow 

and distance indicators as placeholders, indicating that the record contains the ID of the next 

home tract. The mean number of associated work tracts per home tract is 79, with a minimum 

of 1 and a maximum (within 120 km) of 413. Overall, this file has over 5.2 million records and 

occupies 131 megabytes of disk space. 

4.3.2 Implementation of Commuting in APEX 

The APEX model only extracts the commuting data that pertains to the selected study area. For 

each sector in the study area (home sector) APEX reads in a list of possible work sectors and the 

cummulative probabilities associated with each. The cumulative probabilities range from 0 to 1; 

the work sectors having higher probabilities are associated with a larger “range” of this interval. 

For each worker (each profile with Employed=YES), a uniform random number R from zero to 

one is generated. This random number is used to select a corresponding work sector (the one 

that is associated with smallest cumulative probability that is ≥ R) for the profile. 

When a profile’s activity diary events are read from the Diary Events file, they are characterized 

as occurring in one of three places: “Work”, “Home” or “Other” based on the CHAD location 

and activity codes. For profiles who are commuters, all “Work” events will use the work 

sector’s air quality data when calculating microenvironmental concentrations. “Home” events 

will use the home sector data; “Other” events will use an average of data from different sectors 

(either all sectors in the area or a random selection, based on the APEX input settings). See 

Section 8.2.1 for more information on home, work, and other locations. 

It is likely that some profiles will commute to sectors outside of the final study area. The user 

may choose to include these profiles in the analysis or discard them by setting the Simulation 
Control file variable KeepLeavers. If KeepLeavers=YES, the air quality data for the work sector 

is unknown. Therefore, it is assumed to be related to the average concentration over all of the 

study area air quality districts at the same point in time. Calling this average C

39 

avg, the ambient 

concentration C for the person is: 

C=LeaverMult*Cavg+LeaverAdd (4-5)

where LeaverMult and LeaverAdd are also set in the Simulation Control file. If KeepLeavers = 

NO, then these individuals are not modeled. 
40 

CHAPTER 5. GENERATING SIMULATED INDIVIDUALS 

(PROFILES) 

APEX stochastically generates a user-specified number of simulated persons to represent the 

population in the study area. Each simulated person is represented by a “personal profile.” The 

personal profile (see step 2 in 2-1) is a set of parameters that describe the person being simulated. 

The simulated person has a specific age, a specific home sector, a specific work sector (or does 

not work), specific housing characteristics, specific physiological parameters, and so on. 

The profile does not belong to any particular real person, instead it is a fictional or simulated 

person. A single profile does not have much meaning in isolation, but a collection of profiles 

represents a random sample drawn from the study area population. This means that statistical 

properties of the collection of profiles should reflect statistical properties of the real population in 

the study area. 

APEX generates the simulated person or profile by probabilistically selecting values for a set of 

profile variables. The profile variables fall into five categories: 

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

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

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

distribution data; and 

• Daily varying variables, which (in most cases) are based on distribution data that change 

daily during the simulation period. 

• Modeling variables, which can have a variety of meanings, and are usually defined by the 

user. The individual profile variables are given in 

• Table 5.1. 

The profile variables do not depend on the results for any other profile, and in general do not 

depend on any results (diary selection, microenvironment concentrations, exposure, or dose) for 

the current profile. The exception is the person’s physical activity index (PAI), which is 

calculated using the activity diary. 

At present, APEX does not allow the user to select which variables are part of the personal 

profile. If such an enhancement were included, the user would be able to assign (say) a family 

size to each profile using input files rather than by reprogramming the source code. 

The process by which APEX generates the personal profile is illustrated in Figure 5.1. The 

demographic and residential variables are set in ProfileModule:GenerateProfiles, the 
physiological variables are generated in ProfileModule:GeneratePhysiology, and the dailyvarying variables are set in ProfileModule:GenerateDailyVars. 

41 

The following subsections describe the different categories of profile variables in more detail. 

Table 5.1. Profile Variables in APEX 

Variable Type Profile Variable Description 

Demographic 

variables 

Index Internal APEX profile index 

 Gender Male/Female 

 Race White, Black, Native American, 

Asian, and Other 

 Age Age (years) 

 Home sector Sector in which a simulated person 

lives 

 Work sector Sector in which a simulated person 

works 

 Home District Air quality district assigned to home 

sector 

 Work District Air quality district assigned to work 

sector 

 Meteorological zone Meteorological zone assigned to 

home sector 

 Employment Status Indicates employment outside home 

Gas stove Indicates presence of gas stove 

Gas pilot Indicates presence of gas pilot light 

Home air conditioning Indicates type of home ventilation/air 

conditioning system 

Residential variables 

Car air conditioner Indicates presence of air conditioning 

in the simulated person’s car 

Blood volume Blood volume of a simulated person 

(ml) 

Body Mass Mass of simulated person (kg) 

Weight Body weight of a simulated person 

(lbs) 

Physiological 

variables 

Height Height of a simulated person (in) 

Resting metabolic rate Resting metabolic activity rate 

(kcal/min) 

Body surface area Surface area of the body (m2) 

 

Maximum permitted MET value Maximum metabolic activity level 

(multiple of resting metabolic rate) 

that can obtained by the individual 

(dimensionless) 
42 

Variable Type Profile Variable Description 

Energy conversion factor Oxygen uptake per unit of energy 

expended (liters/kcal) 

Lung CO diffusivity Lung CO diffusivity parameter used 

in COHb calculation (ml/min/torr) 

Endogenous CO production rate 

#1 

Endogenous (internally produced) 

CO production rate #1 (ml/min) 

Endogenous CO production rate 

#2 

Endogenous CO production rate #2 

(ml/min) used only for women 

between ages of 12 and 50 for half 

the menstrual cycle 

 Hemoglobin altitude factor Correction for blood hemoglobin 

density at high altitudes 

 

Recovery Time Time to recover a maximum oxygen 

deficit (hours) 

 

Ventilation slope Slope term for MET to ventilation 

conversion 

 

Ventilation intercept Intercept term for MET to ventilation 

conversion 

 

Ventilation residual Residual term for MET to ventilation 

conversion 

 

Hemoglobin density in the blood Amount of hemoglobin in the blood 

(g/ml) 

 

Normalized maximum oxygen 

consumption 

Maximum rate of oxygen 

consumption by the individual, 

normalized to body mass (ml of 

oxygen/min/kg) 

Starting day of menstrual cycle The day during the first 28 days of 

the simulation period that 

menstruation begins; used for 

calculating endogenous CO 

Disease status Whether or not the person has the 

disease. Probability is determined by 

the input Prevalence file. 

 

Maximum oxygen deficit Maximum oxygen deficit obtainable 

by profile (ml/kg) 

Daily endogenous CO 

production rate 

Daily endogenous CO production 

rate in the simulation period (ml/min)

Diary number Index for the selected diary for the 

day 

Daily varying 

variables 

First event # Index of the first event for the day in 

the composite activity diary 

Diary ID CHAD (or other database) ID for the 

diary selected for the day 

Diary age Age of the CHAD diary selected for 

the day 
43 

Variable Type Profile Variable Description 

Diary employment Employment status of the CHAD 

diary selected for the day 

 

Last event # Index of the last event for the day in 

the composite activity diary 

 

Residence window position Daily residence window position 

(open or closed) during the 

simulation period 

 

Car window position Daily car window position (open or 

closed) during the simulation period 

 

Daily average car speed 

category 

Daily average car speed category 

during the simulation period 

 

Daily Conditional variable # 1 Generic user-defined daily 

conditional variable # 1 

 

Daily Conditional variable # 2 Generic user-defined daily 

conditional variable # 2 

 

Daily Conditional variable # 3 Generic user-defined daily 

conditional variable # 3 

PAI Daily physical activity index (MET, 

dimensionless) 

 

Diary key statistic Key diary statistic (such as outdoor 

time of vehicle time) for the day. 

Used for constructing longitudinal 

activity diary. Equal to 0 if not using 

longitudinal assembly. 

Modeling Variables Number of diaries Number of different activity diaries 

used to construct the composite 

activity diary for the person. 

Profile Conditional Variable #1 Generic user-defined conditional 

variable # 1. 

Profile Conditional Variable #2 Generic user-defined conditional 

variable # 2. 

Profile Conditional Variable #3 Generic user-defined conditional 

variable # 3. 

Profile Conditional Variable #4 Generic user-defined conditional 

variable # 4. 

Profile Conditional Variable #5 Generic user-defined conditional 

variable # 5. 

Regional Conditional Variable 

#1 

Regional user-defined conditional 

variable # 1. 

Regional Conditional Variable 

#2 

Regional user-defined conditional 

variable # 2. 

Regional Conditional Variable 

#3 

Regional user-defined conditional 

variable # 3. 

Regional Conditional Variable 

#4 

Regional user-defined conditional 

variable # 4. 
44 

Variable Type Profile Variable Description 

Regional Conditional Variable 

#5 

Regional user-defined conditional 

variable # 5. 

Loop over persons

Select population type

(Race/Gender combination)

Select home sector

Select age group within home 

sector

Assign age within age group

Check if age within range 

set in Simulation Control file

Generate employment status Select work sector 

(if modeling commuting)

Set demographic variables 

based on the above

Set residential variables

Set physiological variables

Set daily-varying variables

NO

YES

Profile 

Functions

file

Physiology file

Loop over persons

Select population type

(Race/Gender combination)

Select home sector

Select age group within home 

sector

Assign age within age group

Check if age within range 

set in Simulation Control file

Generate employment status Select work sector 

(if modeling commuting)

Set demographic variables 

based on the above

Set residential variables

Set physiological variables

Set daily-varying variables

NO

YES

Profile 

Functions

file

Physiology file

Figure 5.1. Generating a Simulated Profile 

5.1 Demographic variables 

The following are the profile variables of a demographic nature: 

• Age: Age in years (integer) 

• Employed: YES if employed outside home, NO otherwise 

• Gender: Male or Female 
•

45 

HomeD: Number of air quality district assigned to home sector 

• HomeSec: Number of home sector for this profile

• Race: White, Black, Native American, Asian, Other 

• WorkD: Number of air quality district assigned to work sector 

• WorkSec: Number of work sector (if any) 

• Index: Sequential number indexing the set of profiles 

• Zone: Number of meteorological zone for home sector 

The values of demographic variables (gender, age, etc.) for a simulated profile are selected 

probabilistically according to the following steps (see Figure 5.1): 

• The fractions of people in each of the gender/race combinations (“population types”) in 

the final study area are calculated and then used as probabilities to randomly select a 

gender/race type for a simulated individual. 

• The fractions of the selected population type in each sector within a study area are found 

and then used as probabilities to randomly select a home sector for the simulated person. 

• The fractions of people in each age group in the selected population type in the selected 

sector are calculated and then used as probabilities to randomly select an age group for 

the simulated person. 

• A specific age within the selected age group is randomly selected, assuming a uniform 

distribution. 

• The employment probability for the selected age group (for the home sector) is used to 

randomly determine whether a simulated person will work. 

• If the commuting option is used and a simulated person works, use the fractions of people 

commuting to each of the work sectors for the selected home sector to randomly select a 

work sector that a simulated person will commute to. If the commuting option is not 

used, assume a person who works does so in their home sector. 

5.2 Residential Variables 

The residential variables are set after the demographic variables described above. The residential 

variables are categorical variables that are used to indicate whether a residence or a car 

associated with a simulated person has a specified appliance or component that may affect 

exposure. The rules for assigning these four variables are specified by the user in the Profile 

Functions (Distributions) input file (see Volume I). The residential variables are: 
•

46 

AC_Home: An integer indicating the type of home ventilation systems (e.g., central air, 

attic fan, window unit, no A/C). 

• AC_Car: YES if has air conditioning in car, NO otherwise 

• HasGasStove: YES if has gas stove in home, NO otherwise 

• HasGasPilot: YES if has gas pilot for gas stove in home, NO otherwise 

APEX randomly determines the result for the variable based on the probabilities specified in the 

input files. For example, suppose a user specifies probabilities of 0.3 for not having a car 

conditioner (AC_Car= NO) and 0.7 for having a car air conditioner (AC_Car=YES). APEX 

randomly generates a value in the range of 0 to 1, assuming a uniform distribution. If this value 

is larger than 0.3, the simulated person will own an air conditioner, otherwise not. 

These variables may be used as conditional variables for calculating concentrations in 

microenvironments (see Chapter 8). 

5.3 Physiological Profile Variables 

The physiological variables are used for estimating ventilation, calculating dose (as described in 

Chapters 7 and 10) and classifying profiles in reporting results. This section covers the 

calculation of these variables. The profile variables relating to physiology are as follows: 

• Blood: Volume of blood (milliliters) 

• BM: Body mass (kilograms) 

• BSA: Body surface area (m2

) 

• Diff: Lung CO diffusivity(ml/min/torr) 

• ECF: Energy conversion factor (liters of oxygen per kcal) 

• Endgn1: Endogenous CO production rate #1 (ml/min) 

• Endgn2: Endogenous CO production rate #2 (ml/min) 

• Height: Body height (inches) 

• Hemfac: Hemoglobin altitude adjustment

• Hmglb: Hemoglobin density (grams per milliliter of blood) 

• METmax: Maximum obtainable MET value (unitless) 

• MOXD: Maximum obtainable oxygen debt (ml/kg body mass) 
•

47 

NVO2max: Maximum normalized oxygen consumption (milliliter of oxygen per minute 

per unit body mass) 

• PAI: Median daily physical activity index (MET, dimensionless) 

• RMR: Resting metabolic rate (kcal/min) 

• RecTime: Oxygen debt recovery time (hours)

• Start: Starting day (phase) for menstrual cycle (if applicable) 

• VeSlope: Slope for MET to ventilation rate conversion 

• VeInter : Intercept for MET to ventilation rate conversion 

• VeResid : Residual for MET to ventilation rate conversion 

• Weight: Body weight (pounds) 

• Ill: Flag indicating whether or not a person has the disease that is modeled in the 

Prevalence input file. 

The physiological profile variables do not affect the exposure calculations for individuals in any 

way, as none of them affect either the selection of diaries or the concentrations in the various 

microenvironments. However, the physiology of a profile affects the ventilation calculations and 

thus influences (1) the calculation of dose (see Chapter 10) and (2) the calculation of exertion 

level, which is used to group exposure results in the output Tables file (see Volume I). 

The physiological variables are calculated from input data. The Physiology input file contains 

distributions that are used to set the physiological profile variables and parameters for each 

simulated person. Specifically, the physiology file contains distributions for the following 

variables and parameters for each age and gender cohort (see Volume I for more information): 

• NVO2max: normal distributions for NVO2max in ml O2/min/kg (Isaacs and Smith, 

2005) 

• BM lognormal distributions for BM in kg (Isaacs and Smith, 2005) 

• RMRSLP, RMRINT, and RMRERR: Point distributions for regression coefficients for 

RMR (slope, intercept, and error) as a function of BM in MJ/Day (Johnson et al., 2000, 

adapted from Schofield, 1985) 

• BLDF1 and BLDF2: Point distributions for blood volume factors for calculation of 

volume (ml) from height and weight (Johnson et al., 2002) 

• HMG: Normal distributions for blood hemoglobin density (g/lm of blood) (Johnson et 

al., 2002) 
•

48 

)

HTSLP, HTINT, and HTERR: Point distributions for regression coefficients for height 

in inches (slope, intercept, and error) as a function of age (children 0-17) or body mass 

(adults) (Johnson et al., 2000) 

• BSAEXP1 and BSAEXP2: Point distributions for exponential parameters for calculating 

body surface area (m2

) as a function of body mass (Burmaster, 1998) 

• MOXD: Normal distributions for maximum obtainable oxygen debt in ml per kg body 

weight (Isaacs et al., 2007) . MOXD is used in the adjustment of MET values; see section 

7.2. 

• ECF: Uniform distributions for the energy conversion factor for the person. Liters of 

oxygen per kcal. (Johnson et al., 2000, adapted from Esmail et al., 1995) 

• RecTime: Uniform distributions for the time required to recover a maximum oxygen 

deficit (hours). (Isaacs et al., 2007) RecTime is used in the adjustment of MET values; 

see section 7.2. 

• Endgn1 and Endgn2: Point distributions for endogenous CO production rates in ml/min. 

(ENDGN2 is used for women in 2nd half of menstrual cycle). 

The Ventilation input file contains data for a set of regression parameters used by APEX to 

estimate the ventilation-related profile variables VeSlope, VeInter, and VeResid. See Volume I

for an example of the Ventilation file; see Graham and McCurdy (2005) for the derivation of 

these parameters. The file contains the following parameters for 5 age groups: 

• VEB0 and VEB0SE: Mean and standard error for regression parameter b0 

• VEB1 and VEB1SE: Mean and standard error for regression parameter b1 

• VEB2 and VEB2SE: Mean and standard error for regression parameter b2 

• VEB3 and VEB3SE: Mean and standard error for regression parameter b3 

• VEEB: Interpersonal variance 

• VEEW: Intrapersonal variance 

Note: the standard error terms defined in the Ventilation file are not currently used by APEX, but 

could be used for future uncertainty analyses. 

Once the above parameters are read/set by APEX, the physiological profile variables are 

formulated as follows in ProfileModule:GeneratePhysiology using the appropriate parameter 

values for the profile age and gender. First, NVO2max, BM, RMR, HMG, BLDF1, BLDF2, 

HTSLP, HTINT, HTERR, MOXD, ECF, RecTime , BSAEXP1, BSAEXP2, Endgn1 and

Endgn2 are sampled from the appropriate input distribution (using the APEX sampling methods, 

Section 3.2) for the profile’s age and gender. Then the other profiles variables are calculated as 

follows: 

Weight = 2.2046 (BM (5-1) 
49 

where weight is given in pounds (lbs.). Body surface area (in m ) (Burmaster, 1998) is 

calculated as 

2

BSAEXP1 BSAEXP2 = BMeBSA (5-2) 

Resting metabolic rate (Johnson et al., 2000) is given in units of kcal/min by 

RMR = 0.166[ ( ) RMRSLP (BM ) + RMRINT + RMRERR] (5-3) 

where 0.166 is the conversion factor for converting MJ/day to kcal/min. 

The maximum MET value an individual can obtain is given by their personal maximum energy 

expenditure divided by their RMR. Personal maximum energy expenditure is simply maximum 

oxygen consumption converted to kcals via ECF, and thus METSmax can expressed as: 

( )( )( )

RMR*ECF

BM0.001 NVO2max METmax = (5-4) 

where 0.001 is the conversion factor for ml to liters O2 such that METmax is a unitless number. 

The lower bound for METmax is 5, and the higher bound is 20; values outside of this range are 

set to the corresponding bound. 

For children under the age of 18, height (in inches) is a function of age (in years): 

Height HTINT += HTSLP*age + HTERR (children under 18) (5-5) 

for adults, height (in inches) is a function of body weight (in pounds): 

Height HTINT += HTSLP*ln(weight) + HTERR (adults 18 and older) (5-6) 

Alion staff fit these equations for height, and derived the accompanying coefficients. 

Several physiological variables are calculated differently for males and females, including lung 

CO diffusivity in ml/min/torr (Johnson et al., 2000). This variable is only used in the APEX CO 

dose algorithm. 

Diff = 0.361( ) Height − ( )+16.3Age0.232 (males) (5-7) 

Diff = 0.556( ) Height − ( )−5.97Age0.115 (females) (5-8) 

where height is in inches and age in years. Blood volume in milliliters (Johnson et al., 2000) is 

calculated as: 

Blood BLDF1( ) Weight BLDF2(Height) 30 3 = + − (5-9) 

where weight is in pounds and height in inches. For males, VeInter is calculated as 

VeInter Intterm −= [VEB3] (males) (5-10) 
and for females 

50 

VeInter Intterm += [VEB3] (females) (5-11) 

where 

Intterm += ( ) VEEBZVEB0 + [ ][ ( + Age1lnVEB2 )] (5-12) 

where Z is a number drawn from a normal distribution ranging from -4 and 4. 

For both genders 

VeSlope =VEB1 (5-13) 

VeResid =VEEW (5-14) 

The variables VeSlope, VeInter, and VeResid are used in the APEX ventilation algorithm (see 

Chapter 7 and Graham and McCurdy, 2005). 

5.4 Daily-Varying Variables 

The daily varying variables are generated for each day in the model simulation for each profile in 

ProfileModule:GenerateDailyVars. There are eight daily-varying profile variables: 

• DailyConditional1 User-defined daily conditional variable #1 

• DailyConditional2 User-defined daily conditional variable #2 

• DailyConditional3 User-defined daily conditional variable #3 

• Endgn Endogenous CO production rate on given day (ml/min) 

• PAI Daily physical activity index (MET, dimensionless) 

• SpeedCat Category for average vehicle speed on given day 

• WindowRes Residence window status (open or closed) for given day 

• WindowCar Car window status (open or closed) for given day 

• DiaryID ID of the activity diary selected for the day (as it appears in the Diary 

Questionnaire and Diary Events files). 

• DiaryEmp. Employment status of the activity diary selected for the day. 

• DiaryAge. Age of the activity diary selected for the day. 
•

51 

 Stat. Value of the key diary statistic for the activity diary selected for the day.

The rules for defining WindowRes, WindowCar, SpeedCat, DailyConditional1, 

DailyConditional2, and DailyConditional3 are provided by the user in the Profile Functions 

(Distributions) input file. These variables may be used as conditional variables for use in 

calculating the concentrations in microenvironments. The Profile Functions file and conditional 

variables are covered in detail in Volume I. Conditional variables are also explained further in 

the Microenvironments chapter (Chapter 8) of this Volume. 

The variable Endgn is used in the evaluation of the blood COHb level. Even though it is stored 

in an array of daily values, for males it always has the same value from day to day, that is, it is 

always set to the physiological profile variable Endgn1. For females it may have one of two 

values (the physiological profile variables Endgn1 and Endgn2) depending on the phase of the 

menstrual cycle. 

The variable PAI is calculated as the time-averaged MET value for the entire simulation day. As 

it depends on the daily activity diaries, it is not set in the profile module, but rather later, in the 

ventilation subroutine ExposureDoseModule:Ventilation. 

The variables DiaryID, DiaryAge, and DiaryEmp are mainly for QA of the diary selection and 

diary assembly methods. The variable Stat contains the value for the key diary variable, which is 

used to construct the longitudinal diary, and thus is usually a variable important to exposure 

(such as time spent outdoors or time spent in vehicles). See Section 6.3. These variables are all 

set in DiaryModule:CompositeDiary. 

5.5 Modeling Variables 

The remaining profile variables are general modeling variables. They are: 

• Number of diaries. Number of different activity diaries used to construct the composite 

activity diary for the person. 

• Profile Conditional Variable #1-5. Generic user-defined profile conditional variables. 

Can be defined by the user model any property of the simulated person (for example, 

behavior or residential properties) that may affect microenvironmental parameters. 

• Regional Conditional Variable #1-5. Regional user-defined conditional variables. Can 

be defined by the user model any property of the simulated person (for example, behavior 

or residential properties) that vary by county or sector. 

The number of diaries is a convenience variable that is set during the diary assembly process, in 

DiaryModule:CompositeDiary. It depends on the number of appropriate diaries available in 

CHAD for the person, the diary pools, and other factors. It gives the modeler an idea of the 

heterogeneity in the diary selection for the person. 

The profile and regional conditional variables are defined by the user in the Profile Functions

file (see Volume I). They are set in ProfileModule:GenerateProfiles.
52 
53 

CHAPTER 6. Constructing a Sequence of Diary Events 

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

24-hour diary record—or diary day—from an activity database for each day of the simulation 

period. The Consolidated Human Activity Database (CHAD) has been supplied with APEX for 

this purpose. A composite diary is a sequence of events that simulate the movement of a 

modeled person through geographical locations and microenvironments during the simulation 

period. Each event is defined by geographic location, start time, duration, microenvironment 

visited, and activity performed. 

The APEX model generates sets of exposure time series, one for each simulated individual, and 

both mean exposures over time and variation in exposures are important. The ability to 

realistically reproduce these exposure metrics depends on the method used to construct the 

composite activity diaries for the simulated population. APEX provides two methods of 

assembling composite diaries. The first (basic) method, which is adequate for estimating mean 

exposures, simply involves randomly selecting an appropriate activity diary for the simulated 

individual from the available diary pool. The second method is a more complex algorithm for 

assembling longitudinal diaries that realistically simulates day-to-day (within-person) and 

between-person variation in activity patterns (and thus exposures). Both methods are covered in 

this chapter. 

As both methods of composite diary assembly require the creation of diary pools, their 

construction is covered first. 

6.1 Constructing the Diary Pool 

6.1.1 Diary Data 

The composite diary is created by concatenating individual one-day activity diaries from the 

CHAD database. APEX currently provides this database as two files: a file containing personal 

information of the studied individual, and one containing the actual diary events (see Volume I

for more information). The Diary Questionnaire (DiaryQuest) file contains the following 

variables, in this order, as comma-separated values: 

• CHAD ID 

• Day of the week (e.g., Monday) 

• Gender (M/F) 

• Race 

• Status of employment (Y/N) 
•

54 

Age (years) 

• Maximum hourly temperature on day of study (°F) 

• Average temperature on day of study (°F) 

• Occupation 

• Count of missing time in minutes (when activity and/or location codes are missing from 

the activity file) 

• Number of events 

The Diary Events file contains the following variables as comma-separated values: 

• CHAD ID 

• Start time (of the event) 

• Duration (minutes) 

• Activity code 

• Location code 

See Volume I for a description of the CHAD activity and location codes. The events file contains 

a record for each of the events indicated by the number of events in the diary questionnaire file. 

Note that while CHAD data are provided with APEX, other activity data could be used instead, 

as long as the input file formats are followed and the CHAD coding conventions are used. 

The APEX diary input files are read by DiaryModule:ReadDiaries. 

6.1.2 Grouping the Available Diaries into the Diary Pools 

A diary pool is a group of CHAD diaries, appropriate for a given simulation day, from which a 

daily diary may be drawn. The criteria for creation of the Diary Pools are defined using the 

DiaryPool variable in the Profile Functions (Distributions) input file (see Volume I). Briefly, the 

user can define different pools for different combinations of ranges of maximum temperature, 

average temperature, and day of the week. Thus, the definition of a diary pool for a single 

(hypothetical) simulated day may be something like “all CHAD activity diaries for a weekend 

day for which the maximum temperature was between 70 and 80 degrees, and the average 

temperature was between 50 and 80 degrees.” The idea behind this logic is that temperature and 

day of the week affect the type of activities people perform, and thus it is important to match 

these real properties of the activity diaries to corresponding simulated days. It should be noted 

that in APEX, CHAD diaries that are missing temperature data are thrown out (ie. not assigned 

to any diary pool.) 
The number of diary pools that are defined affects the number of diaries that available for 

selection on a given day. Therefore, it is important not to define the pools too narrowly, as it 

could result in the same activity diaries being selected over and over again, or could result in 

pools with no diaries in which case APEX will fail with a fatal error. 

55 

The diary pools are created in DiaryModule:ReadDiaries. 

6.2 Basic (Random) Composite Diary Construction 

Basic (random) composite diary construction is implemented in 

DiaryModule:CompositeDiary. In basic composite diary construction, APEX develops a 

composite diary for each of the simulated individuals (profiles) in the following manner: 

Once the diary pools have been created (based on temperature and day of the week as described 

above), a selection probability for each diary within the pool is calculated based on 

age/gender/employment similarity of the simulated person to the “real” diaries. The probabilities 

are calculated in DiaryModule:DairyProbabilities. The selection probability is actually a 

product of three probabilities between 0 and 1, one each for age, gender, and employment. The 

gender and employment probabilities are straightforward: if the gender or the employment status 

of the diary matches that of the profile, then the probability for these factors is set to 1. If they 

do not match, the probability is set to 0. The exception is for the employment probability for 

children under 16. Since APEX does not model employment status for children under sixteen 

(the employment profile variable will always be 0), then the employment probability is always 

set to 1 for this age group. This prevents APEX from discarding the CHAD activity diaries for 

children under age 16 that had an employment status=YES. 

The age selection probability is a bit more complicated. APEX provides the user with the option 

of using activity diaries that have an age close to that of the simulated profile, although it may 

not match exactly. This range is controlled by the Simulation Control file setting AgeCut2Pct

(see Volume I). Ages in this range will be given a probability of 1. In addition, APEX allows for 

the use of “shoulder ages,” which are the age ranges (of width AgeCutPct) above and below the 

main age window. These ages are given reduced probability equal to the value of the Simulation 

Control file setting the variable Age2Prob. 

If the employment status, gender, or age for an activity diary is missing, then the selection 

probability for that variable is determined directly from the Simulation Control file variables 

MissEmpl, MissGender, and MissAge, respectively. 

The final selection probability for each diary is the product of the age, gender, and employment 

selection probabilities. Then, on each day of the simulation period, APEX randomly selects a 

diary day from the appropriate diary pool, based on selection probability value. 

6.3 Longitudinal Activity Diary Assembly 

The second method of multi-day diary construction in APEX, which is required for 

characterizing within-person and between-person exposure variability, is a longitudinal diary 
assembly algorithm that constructs multi-day diaries based on reproducing realistic variation in a 

user-selected key diary variable. The variable may reflect any diary property, and is provided to 

APEX in the Diary Statistics input file. It is assumed that the key variable has a dominant 

influence on exposure. The APEX release provides Dairy Statistics files for outdoor time and 

vehicle time, which were constructed by summing the total time associated with “outdoor” and 

“vehicle” CHAD location codes for each diary (see Volume I). For some scenarios, the key 

variable might be travel time or time performing a particular activity. The key variable could 

also be a composite formed from several different variables, for example, a weighted average of 

diary 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. The method 

uses this key variable to preferentially select appropriate diaries from the available pool on the 

different days in order to produce a final longitudinal activity diary that has specific statistical 

properties. The method is primarily contained within DiaryModule:DiaryRanks, which is 

called from DairyModule:DiaryProbabilities. 

56 

The longitudinal diary construction method targets two statistics, D and A. The D statistic 

reflects the relative importance of within-person variance and between-person variance in the 

key variable. The A statistic quantifies the lag-one (day-to-day) variable autocorrelation, which 

characterizes the similarity in diaries from day to day. Desired D and A values for the key 

variable are selected by the user and set in the Simulation Control file, and the algorithm 

constructs a longitudinal diary that preserves these parameters. See Section 6.3.2 for guidance 

on selecting appropriate D and A values for a particular simulation. 

6.3.1 The Longitudinal Diary Assembly Algorithm 

The longitudinal diary selection method is based on the scaled rank, or “x-score” for the key 

variable for each diary. The x-scores are calculated within diary pools. First, a pool is sorted 

from lowest to highest on the key variable and given a corresponding rank, R. If there are K 

diaries in a pool, and each diary has equal statistical weight then the x-score for the diary at rank 

R is 

K

R

x

⎟

⎠

⎞ ⎜

⎝

⎛ −

= 2

1

(6-1) 

If the diaries have unequal statistical weight, then the x-scores will not be evenly spaced from 0 

to 1 (as some diaries will correspond to a greater “interval” on the 0 to 1 scale). In APEX, eq. 6-

1 is not used, but rather the x-scores are assigned to each diary by sorting the diary pool on the 

key statistic, and then applying the age, gender, and employment probabilities as described in 

Section 5.2. The diaries are then assigned to days in the simulation based on their x-scores by 

the algorithm described below. 

An overview of the longitudinal diary method is shown in Figure 6.1. For each simulated 

person, the following steps are performed: 
1.

57 

An individual target x-score Ti is selected from a beta distribution (β1) that depends on the 

value of D. 

2. For each day in the simulation, a daily scaled x-score (scaled rank) is generated. It is picked 

from a different beta distribution (β2) having a peak near Ti. 

3. An individual target correlation Ai is sampled from a beta distribution (β3) having a peak 

near the population autocorrelation A. 

4. The independently sampled daily x-score values are re-ordered to induce the target 

autocorrelation Ai. 

5. Diaries are assigned from the diary pool according to the final time-series of daily x-score 

values. 

Input START Results

Defined diary 

pools, sorted 

by rank of 

key variable

1. Pick personal target x score for key var

Loop over simulated persons

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96

Population

D Statistic

Loop over simulated days

Personal 

target rank 

(Ti

)

2. Pick daily x distributed about T

Var(Ti

s)=D 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96

3. Pick personal target 

autocorrelation (Ai

)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96

Population

A Statistic

4. Re-order daily x scores to match Ai

5. Assign diaries with appropriate 

x score to each day

Personal Ai

Personal 

daily 

x scores

Figure 6.1. Overview of the Longitudinal Diary Assembly Algorithm 

All of the random number generation in the new method involves drawing numbers from Beta 

distributions. All of the random number distributions are bounded both above and below, which 

is a natural property of the Beta distribution. Given these fixed end points, the Beta distribution 

has two shape parameters which allow a great variety of forms. Both shape parameters (for all 

the distributions) are positive. The means and shape parameters for each of the Beta 

distributions were formulated to 1) properly reproduce D for the population, while 2) producing 

unbiased x-scores across the population. The resulting equations for the parameters are given 
below. See Glen et al. (2007) for the derivation of these equations. Each of the above steps of 

the algorithm is described in detail below: 

58 

here 

1. An individual target x-score Ti is selected from a beta distribution (β1) that depends on 

the value of D. The distribution of Ti depends on the value of D. The β1 distributions for Ti

are symmetric about their midpoint, so the distribution shape parameters are equal. They are 

equal to α, w

( ( ) 3

α −= − D1D40.081 )

)

 (6-2) 

The mean of the distribution, μ, is equal to 0.05. The bounds of β1 are at (1/2-w1/2) and 

(1/2+w1/2), where w1 is a function of D and α: 

(

3

1D 2α

w1

+ = (6-3) 

Thus the final Ti for the profile is generated as: 

w0.5T β( ) ,( αα 0.5)- (6-4) i += 1

2. For each day in the simulation, a daily x-score is generated. To generate daily scores, a 

beta distribution (β2) dependent on D with a peak near the target value Ti is constructed. Since 

each individual has a personal value of Ti, each will have a unique β2. As D approaches zero, β2

flattens into a uniform distribution. As D approaches one, β2 narrows to a spike at Ti. One x 

value is selected randomly from the PDF for each day in the simulation, plus a few extra (15 

extra is sufficient for a one-year simulation). Since the β2 for two individuals differ, the 

between-person variance does not go to zero as the number of draws becomes large. The shape 

parameters a and b for β2 are a function of Ti and D: 

( ) D-1

2T

a i = (6-5) 

(

( )

)

D1

T12 b i

−

− = (6-6)

Thus for each day in the simulation, an x-score is generated as 

 x=β2 =β(a,b) (6-7) 

3. An individual target correlation Ai is sampled from a different beta distribution (β3) 

having a peak near the population autocorrelation A. The width of this distribution is w2: 

2 ( −= ,1A22minw )

)

 (6-8) 

The personal target for A, Ai, is then generated as: 

i += wAA 2 (β( ) 2.65,2.625 − 0.5 (6-9) 
4. The independently sampled daily x-scores are re-ordered to induce the target 

autocorrelation A

59 

i. This is done with a single pass, from first simulation day to the last. The 

reordering process involves selecting each x-score in the time series from another beta 

distribution (β4) that is a function of both the individual autocorrelation target Ai and the 

previous x-score. The “extra” diaries come into play here; they allow the avoidance of 

undesirable forced selections. The shape parameters c and d for β4 for day j are: 

⎟

⎠

⎞ ⎜

⎝

⎛ + − = 1-ji

i xA

2

A1

sc (6-10) 

⎟

⎠

⎞ ⎜

⎝

⎛ − + = 1-ji

i xA

2

A1 sd (6-11) 

where 

)A(1

2

s 2 − i

= (6-12) 

and xj-1 is the previous day’s x-score. The x-score for the first day is picked at random from a 

uniform distribution ranging from 0 to 1. Then, for day j, the x-score is selected as: 

x β( dc, (6-13) j = )

The APEX code for performing this process keeps track of which x-scores are picked. If the 

same score is selected more than once, then the algorithm finds the closest unused score. The 

process laid out by equations 6-10 through 6-13 continues until x-scores for all simulation days 

are selected. 

On very short time series (less than 30 days), the autocorrelation step has a slight effect on the 

resulting D for the population (a few percent increase). 

5. Assign the selected x-score (scaled rank) values to each day in the simulation, and assign 

corresponding diaries from the diary pool. The result of steps 1-4 is a time series of x-score 

values mapped to simulation days, for example, 

Jan 1 Jan 2 Jan 3 

0.148 0.372 0.324 

The diary pool has already been defined by APEX (typically by factors including age, gender, 

employment, day type, and season, and perhaps others, see Section 6.1). The pool is then sorted 

into rank order from lowest to highest score for the key variable, and sort order is mapped onto a 

corresponding x-score. The x-score reflects the behavior of an individual relative to their peer 

group (for example, a person with score 0.75 is above 75% of the people in the same cohort and 

pool, in terms of the key variable). Scores can be moved across diary pools, whereas absolute 

values for the key variable might not. Thus, 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 exists on all 

days. The use of scores also helps in ensuring that all the available diaries are collectively 
sampled with the correct frequency. Note that the use of scores does not destroy information. 

All that matters in terms of diary assembly is the ability 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 (for example) 73 minutes of outdoor 

time. 

APEX assigns the diary whose x-score is closest to the daily x-score value to the day. No 

distinction is made or needed between day types, seasons, etc., because that is already taken into 

account. Note that any diary matching criteria such as day type, season, temperature, rainfall, 

workday, holiday, etc., affect the list of diaries that belong to the pool for a given day, but have 

no effect on the x-scores. 

6.3.2 Selecting Appropriate D and A Values For a Simulated Population 

The statistic D for a population of individuals is given by 

D = σb

2

 / (σb

2

 + σw

2

 ) (6-14) 

where σb

2 and σw2

 are the between- and within- person variances in the key variable. Since both 

variances are non-negative, it is clear that D is in the interval [0,1]. D=0 means that σb

2

 is zero, 

or that each person has the same mean score. A small D means that σb

2

 is substantially smaller 

than σw

2

, indicating that the overall variability between people in the key diary statistic is smaller 

than the variability observed over days within the same person. A D near one means that σb

2

 is 

much larger than σw

2

, or that each person shows little variation over time relative to the 

variability between persons. 

The lag-one autocorrelation A is simpler to calculate than D, because each time series can be 

examined independently. The first step is to determine the x-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 x-score for that day is ( R-1/2 ) / J. The 

overall mean and variance in these scores for the time series is then calculated. 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 

) J

1 (1 12

1

σ 2

2 −= (6-15) 

which is very close to 1/12 for large J. The lag-one covariance is calculated by 

∑ ⎟

⎠

⎞ ⎜

⎝

⎛

⎟ −+ ⎠

⎞ ⎜

⎝

⎛ = − 2

1 1)x(j 21 x(j) J1 COV (6-16) 

where x(j) is the x-score on day j (see for example, Box et al., 1994). The lag-one 

autocorrelation for the individual time series is given by the ratio of the covariance to the 

variance: 

COV

σ A

2

i = (6-17) 

60 
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. 

61 

A study of children conducted in Southern California (Xue et al., 2004) provided about 60 days 

of data on each of 163 children. The time series are not continuous, as the monitoring consisted 

of twelve six-day periods, one per month over a year. Furthermore, only about 40 children were 

measured simultaneously, as the other children were sampled in different weeks. However, a 

sample size of 40 is sufficient to calculate reliable rankings across persons. The 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, 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 become very uncertain. The results 

for these analyses are given in Table 6.1. 

Table 6.1. D and A Statistics Derived from the Southern California Children’s Study 

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 0.2 

Indoor time girls 0.17 0.24

PAI all 0.16 0.23

PAI boys 0.16 0.2 

PAI girls 0.16 0.25

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. The values in Table 6.1

indicate that gender differences for both D and A are small, if present at all. The variance in A

over the population was also examined for the four diary variables. While the absolute values of 

A were different across variables, it was found the variance in individual autocorrelations was 

very similar (approximately 0.2) in all variables. This variance was used to derive the 

parameters for the target A distribution (eq. 6-9) in the APEX algorithm, and thus the method 

returns diaries that reproduce a variance of 0.2 in the daily autocorrelation, no matter what diary 

variable is modeled or what absolute A value is used. 
62 

CHAPTER 7. ESTIMATING ENERGY EXPENDITURES AND 

VENTILATION 

Ventilation rates are used in APEX for 

• Calculating exertion level for use in tabulating exposure summaries for the population 

• Estimating dose 

Ventilation does not influence the exposures for a simulated person. 

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

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

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

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

is always measured on an expired sample, Ve. Alveolar ventilation (Va) is the volume of air 

breathed in per minute that (1) reaches the alveoli and (2) takes part in gas exchange. The 

ventilation rate needed for the %COHb calculation is this ventilation rate, Va, and is derived for 

use in APEX based on work by Adams (1998), Astrand and Rodahl (1977), Burmaster and 

Crouch (1997), Esmail et al. (1995), Galetti (1959), Johnson (1998), Joumard et al. (1981), 

McCurdy (2000), McCurdy et al. (2000), Schofield (1985), and many others. Only a brief 

description of VA is described below; for the complete derivation, see Johnson (2002). 

Ventilation is calculated on an activity event-by-activity event basis. Ventilation is derived from 

the energy expenditure rate (MET, given as a multiple of resting metabolic rate), associated with 

the diary activities. The general steps in the estimating ventilation are 

• Generate the MET event time-series based on the diary activities 

• Adjust the resulting MET series for fatigue and excess post-exercise oxygen consumption 

• Convert the MET time-series into a ventilation rate time series 

These steps are covered in the following sections. 

7.1 Generating the MET Time-Series 

MET—which comes from “metabolic equivalents of task”—is a dimensionless ratio of the 

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

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

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

energy expenditure, or two MET, for most people, with relatively little variation. The basal rate 

is constant (it only has to be determined once per profile), while the activity-specific MET ratio 

is calculated for each of the activities reported on the composite activity diary. 
Each possible diary activity code (see Volume I), is mapped to a corresponding APEX MET 

distribution number the MET Mapping input file. Each of these distributions is then defined in 

the MET Distributions file. This file (see Volume I) gives the properties of the MET distribution 

for each type of activity, in some cases as a function of age or occupation. The distributions are 

defined in the standard APEX format (see Section 

63 

3.1) These distributions are based on many 

available data on energy expenditure, and in general should not be changed. This file is read into 

APEX in the DiaryModule:ReadMETS. In the subroutine DiaryModule:METSEval, APEX 

steps through the activity diary and assigns a MET value to each event by randomly selecting a 

value from the appropriate distribution as defined by the activity code and the profile. The result 

is consider the “raw” MET time-series, which is then adjusted to be physiologically realistic. 

The adjustments are covered in the next section. 

7.2 Adjusting the MET Time-Series for Fatigue and Excess Post-Exercise 

Oxygen Consumption 

As discussed in the previous section, APEX assigns distributions for MET level to each diary 

event, based on the reported event activity (and in some cases, age and occupation). However, 

these raw MET time-series do not consider the sequence of the events (i.e., the order in which 

they occur). It is well known that a person’s capacity for work will diminish as they get tired, 

and in practice, this means that the upper bound on MET is lowered if events in the recent past 

have been at unusually high MET levels. Furthermore, once high activity levels have ended, 

people tend to breathe heavily even while resting, as they recover their accumulated oxygen 

deficit. This effect is called excess post-exercise oxygen consumption (EPOC), and results in 

raising the MET levels above the ‘raw’ values pulled from the activity-based distributions. 

APEX contains an algorithm for adjusting the MET time series for both of these effects. The 

algorithm is implemented in ExposureDoseModule:Ventilation. 

The adjustment method is based on keeping a running total of the oxygen deficit as a simulated 

individual proceeds chronologically through his or her activity diary. The oxygen deficit is the 

amount of energy supplied to the muscles by non-aerobic systems during exercise. It reflects a 

need for increased post-exercise ventilation to “pay back” this energy. The oxygen deficit 

calculations were derived from a synthesis of numerous published studies (see below). 

Oxygen deficit is measured as a percentage of the maximum oxygen deficit an individual can 

attain prior to deterioration of exercise performance. Limitations on MET levels corresponding 

to post-exercise diary events were based on maintaining an oxygen deficit below this maximum 

value. In addition, adjustments to MET were simultaneously made for EPOC. The EPOC 

adjustments are based in part on the modeled oxygen deficit and in part on data from published 

studies on EPOC, oxygen deficit, and oxygen consumption. 

The methods are constructed in terms of reserve MET, which is the amount over the basal rate 

(MET=1). Furthermore, we defined M as the normalized reserve, so that M=0 at MET=1, and 

M=1 at maximum MET: 

1MET

1MET M

max −

− = (7-1)
(Recall that MET

64 

max is a profile variable assigned for each simulated profile; see Section 5.3). 

Using a normalized reserve assures that the method can be applied identically to the entire 

population of profiles, each having a unique METmax value. 

A number of terms will be used in the description of the algorithm. They are defined below: 

• MET Metabolic equivalent of task (unitless) 

• METmax Maximum achievable metabolic equivalent for an individual (unitless) 

• M Normalized MET reserve (unitless, M, bounded between 0 and 1) 

• ΔM Change in M from one diary event to the next (M) 

• Dmax Absolute maximum oxygen deficit that can be obtained (M-hr) 

• F Fractional oxygen deficit (percent of individual maximum, unitless) 

• te Duration of activity diary event (hours) 

• tr Time required to recover from an F of 1 to an F of 0 at rest (recovery time, 

hours) 

• dFinc Rate of change of F due to deficit increase (F/hr, will have a positive 

value) 

• dFrec Rate of change of F due to deficit recovery (F/hr, will have a negative 

value) 

• dFtot Total rate of change of F, dFinc+ dFrec (F/hr) 

• ΔFinc Increase in F due to anaerobic energy expenditure (F) 

• ΔFrec Decrease in F due to recovery of oxygen deficit (F) 

• ΔFtot Change in F due to simultaneous anaerobic work and oxygen recovery, 

ΔFinc+ΔFrec (F) 

• ΔFfast Total change in F during the fast recovery phase (F) 

• Sfast Magnitude of the rate of change in M during fast component (M/hr) 

• EPOC fast Change in M due to fast-component EPOC (M) 

• EPOCslow Change in M due to slow-component EPOC (M) 

See Isaacs et al. (2007) for a complete derivation of the method. 
7.2.1

65 

Simulation of Oxygen Deficit 

This section presents the theoretical development of the equations describing the accumulation of 

oxygen deficit. The method was developed using a large number of studies on oxygen 

consumption, oxygen deficit, and EPOC. Individual studies will be referenced below. The first 

two subsections below describe the equations themselves, while the last section describes the 

determination of the values for the model parameters. 

7.2.1.1 Fast Processes 

There exists a component of the accumulated oxygen deficit that is due to transition from one M 

level to another (McArdle et al., 2001). This component derives from the anaerobic work that is 

required by sudden muscular motion. There is also a corresponding fast component of oxygen 

recovery which occurs very quickly after a change from a high M level to a lower one. In the 

absence of any data to the contrary, it is assumed that these fast deficit accumulation and fast 

recovery processes occur at the same rate. These processes are illustrated in Figure 7.1. The 

adjustment to F is equal to the area of the triangle associated with either a positive or negative 

change in M, normalized by the maximum obtainable accumulated oxygen deficit (Dmax). The 

normalized area can thus be calculated as:

maxfast

fast DS

ΔM ΔM

ΔF = 0.5 (7-2) 

where ΔM = Mi-Mi-1 and Sfast is the slope of the change in M (in M/hr). Note that this change in 

F will be positive if ΔM is positive, and negative otherwise. 
66 

Fast component of 

F: Recovery 

(ΔM negative)

ΔM

M1

M2

Fast component 

of F: Accumulation

(ΔM positive)

Time

Exercise Recovery

t= ΔM/Sfast

Sfast -Sfast

Fast Component of F:

Accumulation

(ΔM Positive)

M2

M1

Time Exercise Recovery

Time

Fast Component of F:

Recovery

(ΔM Negative)

ΔM

Sfast -Sfast

Figure 7.1. Fast Components of Oxygen Deficit and Recovery 

7.2.1.2 Slow Processes 

The slow component of the increase in oxygen deficit corresponds to the accumulation of deficit 

over a period of heavier exercise (rather than that associated with an increase in activity level). 

The method was derived from the analysis of a number of studies on exercise and EPOC 

including Bahr (1992), Bahr et al. (1987), Bielinski et al. (1985), Brockman et al. (1993), Gillette 

et al. (1994), Gore and Withers (1990), Hagberg et al. (1980), Harris et al. (1962), Kaminsky and 

Whaley (1993), and Katch et al. (1972), Maehlum et al. (1986), Sedlock (1991a,b). The 

following data were considered: the time it took for subjects to reach exhaustion, their 

accumulated oxygen deficit, their METmax, the MET value at which they exercised, and the 

corresponding normalized reserve MET (M). (Note that the MET and METmax quantities were 

derived from the published VO2 and VO2max measurements). The data indicated that oxygen 

deficit accumulates at a much faster rate when M is high. For example, an M value near 0.5 

requires about 5 times longer to reach exhaustion than an M value near 0.75 (on average), 

indicating that F is nonlinear in M. 

Let the rate of increase in F be given by . The relationship between and M is a power 

law: 

dFinc dFinc

 (7-3) b

inc = aMdF

where a and b were estimated from available data. The slow recovery of oxygen deficit must 

also be accounted for, as it occurs simultaneously with debt accumulation. A slow, but 

continual, process for recovering oxygen deficit is modeled, independent of the MET level. 

EPOC recovery is modeled as constant over time until the oxygen deficit is erased. Assuming 

this takes tr hours, the slow recovery of oxygen deficit occurs at a rate 
67 

r

rec t

1 dF −= (7-4) 

The total net rate of change in F from slow processes during an event with duration te is given by 

slow = inc + dFdFdF rec (7-5) 

and the associated change in F is 

e

r

b

slow i t

t

1 ΔF aM ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ −= (7-6) 

For an individual starting with an F of 0 and exercising to exhaustion (neglecting the transitory 

effects), the change in ΔF is 1.0. In this case, rearranging and taking the logarithm gives 

( ) log(M)balog t

1

t

1 log

r

+=⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ (7-7) 

This equation can be used to fit data to estimate the parameters a and b (this will be discussed in 

the next subsection). 

The starting normalized oxygen deficit for the next event (i +1), taking into account both the fast 

and slow changes in F, is then 

+ i1i += ΔFFF slow + ΔFFast (7-8) 

7.2.1.3 Derivation of Appropriate Values for the Model Parameters 

The values of the model parameters tr, a, and b, were derived from summaries of published data 

on EPOC and oxygen debt (see references listed in Section 7.2. Several of the these studies 

reported tr values, however, due to variability in measurement and protocol differences, these 

recovery times varied from 0.5 hours to 24 hours. From a modeling viewpoint, it would be 

unacceptable to allow recovery to significantly carry over from one day to the next. To do so 

could lead to a perpetual delay in recovering an oxygen deficit, for example, by repeatedly 

encountering new exercise events before recovery is complete. In APEX, tr, which is a profile 

variable, is selected from a uniform distribution having a minimum of 8 and a maximum of 16 

hours. 

In APEX, a and b are modeled as a function of tr: 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ −= 2

r r t

3.92

t

1.54 5.20a (7-9) 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ −= 2

r r t

3.66

t

3.57 3.93b (7-10) 
These expressions were derived from the experimental data. 

Appropriate distributions for maximum oxygen debt (MOD) in ml/kg were derived from data 

from a number of studies in adults (Bickham et al., 2002, Billat et al., 1996, Buck and 

McNaughton, 1999, Demarle et al., 2001, Doherty et al., 2000, Faina et al., 1997, Gastin and 

Lawson, 1994, Gastin et al., 1995, Hill et al., 1998, Maxwell and Nimmo, 1996, Olesen,1992, 

Renoux et al., 1999, Roberts et al., 2003, Weber and Schneider, 2000) adolescents (Naughton et 

al., 1998) and children (Berthoin et al., 1996, Carlson and Naughton, 1993). The studies covered 

multiple types of exercise protocols, some having more than one protocol per study. Normal 

distributions for MOD were defined for all three age groups, based on average mean and 

standard deviation values from the studies: 

• adults (>17 yrs): 54.95±14.46 (ml/kg) 

• adolescents (12-17 yrs): 63.95±21.12 (ml/kg) 

• children (<12 yrs): 34.74±13.10 (ml/kg) 

(These mean and standard deviations are read in from the Physiology file; see Section 5.3.) 

Values are selected from normal distributions with these characteristics. These values are 

constant for an individual over the simulation period. The bounds of these distributions are 

selected as two standard deviations from the mean; these ranges were found to be reasonable 

when compared to reported ranges (Olesen 1992). These values are transformed to Dmax, via a 

units conversion factor and the normalization needed for use with reserve MET: 

Dmax (M-hr) = ( 1

max

2

METS 1

60 METStoO

MOD − − ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ ) (7-11) 

where METStoO2 is the conversion factor for ml O2 to MET-min, 3.5 [(ml O2/min)/kg]/MET. 

Note that the variability in this factor is not addressed here. 

A number of studies on EPOC (Almuzaini et al., 1998, Dawson et al., 1996, Frey et al., 1993, 

Harms et al., 1995, Kaminsky et al., 1990, Knuttgen, 1970, Maresh et al., 1992, Pivarnik and 

Wilkerson, 1988, Short and Sedlock, 1997, Trost et al., 1997) were used to derive Sfast. These 

were all studies in which oxygen consumption was measured relatively soon (within a few 

minutes) after the end of exercise and at a frequency high enough to capture the kinetics of the 

change in oxygen consumption. The data were found to be relatively uniform from the minimum 

(0.6 MET/min) to the maximum (3.7 MET/min) slope values, and so values were selected from a 

uniform distribution having these bounds. Converting units and normalizing to M, one obtains: 

 (M/hr) = Sfast ( ) METS 1

Uniform60 3.7)(0.6,

max − (7-12) 

7.2.2 Adjustments to M for Fatigue 

The equations provided in the previous section describe a method for keeping a running total of 

the fractional oxygen deficit (F) for each diary event for an individual. These event F values are 

68 
used 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

69 

i+1 (eq. 7-8) equal to 1 (i.e., 

the maximum value) at the end of the diary event. The approach used in APEX is to set M for 

each event equal to the raw MET value, and test if Fi+1>1. If it is, then the Mi value is reduced 

by a predetermined amount (currently 0.01) and Fi+1 is recalculated. The process continues until 

an appropriate value of Mi, called Mmax,i is found. As the exposure model marches through the 

events of the activity diary, the M values associated with each event are adjusted if necessary: 

Mi=min(Mi, Mmax, i) (7-13) 

7.2.3 Adjustments to M for EPOC 

As noted above, it has been observed in many studies that EPOC is characterized by both slow 

and fast components. The fast increase in oxygen consumption occurs within minutes of 

exercise, while the slow component may persist for many hours. Both fast and slow EPOC 

components were modeled. 

7.2.3.1 Fast Processes 

The fast EPOC component, which takes place in the first few minutes after exercise, is also 

characterized by the slope Sfast. The energy recovered during those first few minutes 

corresponds to the recovery triangle in Figure 7.1 and this increase in the rate of energy 

expenditure for a post-exercise event is modeled as the area of the triangle divided by the event 

duration: 

( )

efast

2

fast tS

ΔM EPOC = 0.5 (7-14) 

EPOCfast will thus have units of M (normalized reserve MET). The M level for the post-exercise 

events will be incremented by EPOCfast.

7.2.3.2 Slow Processes 

The increase in M associated with the slow EPOC component is estimated as the amount 

required to maintain the slow recovery of F. Since the deficit Dmax is recovered in full in the 

recovery time tr, the time-averaged adjustment to MET for the slow recovery process must be 

EPOCslow=

r

max

t

D (7-15) 

Every diary event with the full rate of slow recovery will have its M value adjusted upward by 

EPOCslow. An appropriate fraction of EPOCslow is used if only partial recovery is needed to 

eliminate the deficit (i.e., return F to 0). The final adjusted M value for the diary event is thus 

adj += EPOCMM fast + EPOCslow (7-16) 
and the new MET value for the event is 

70 

)

METS (METSM 11) (7-17) adj = adj max +−

7.3 Calculating PAI and the Ventilation Rates 

APEX calculates three different ventilation rates from the adjusted MET time series. These are 

the expired ventilation rate (Ve) the alveolar ventilation rate (Va), and the effective ventilation 

rate (EVR). All three are reported for each hour in the simulation in the APEX output files. Va

is used in the CO dose calculations, and EVR is used in compiling summary exposure tables for 

different populations during different levels of exertion. 

In addition, the final MET time-series is used to calculate a physical activity index (PAI) for 

each individual. Finally, an intermediate rate, oxygen consumption (VO2), is also calculated. 

The equations for calculating these rates from the MET time series are given below. All of these 

calculations are implemented in ExposureDoseModule:Ventilation. 

7.3.1 Calculating PAI and Energy Expenditure 

Once the final MET time series is calculated, the timestep and hourly physical activity index 

(PAI) for each hour in the simulation for the simulated individual is calculated as the timeweighted average of MET: 

( )(

t

tMETS

PAI

Nevents

1i

∑ ii

= = (7-18) 

where METi is the MET value for event i, ti is the event duration in minutes, and t is the length 

of the timestep in minutes (or 60 minutes, if calculating hourly values). Nevents is the number of 

diary events in the considered timestep or hour. These PAI values can be written to the Timestep

or Hourly files. The daily PAI value is simply the average of the 24 hourly values. Finally, a 

median daily PAI value is calculated for each profile. The daily and median daily PAI values are 

saved as a profile variables (see Section 5.3). The median daily PAI value is used in the 

characterization of persons as “active” when creating the output exposure summary tables (see 

Volume I and Section 9.2). 

The energy expenditure (kcal/min) is 

EE I×= RMRPA (7-19) 

where RMR is the profile resting metabolic rate in kcal per minute. EE is calculated for both 

timesteps and hours, and can be written to the corresponding output files. 
7.3.2

71 

Calculating Oxygen Consumption and Ventilation Rates 

The oxygen consumption rate in ml/min/kg (McCurdy, 2000), normalized to body mass, is given 

by 

BM

METS ECF RMR VO2

× × = (7-20) 

where ECF is the profile energy conversion factor in liters of oxygen per kcal and BM is the 

profile body mass. The alveolar ventilation rate is also calculated from MET using: 

a METSV ×= 19630 ×ECF ×RMR (7-21) 

where the constant 19630 is the oxygen to air conversion factor (19,630 ml of air/l of O2). 

The calculation of Ve is based on the VeSlope, VeResid, and VeInter profile variables (see 

Section 5.3). The calculation of those variables and the following equations for Ve comprise the 

Ve regression equations derived by Graham and McCurdy (2005). Ve is calculated as 

( ) X

e = eBMV (7-22) 

where BM is the profile body mass and the exponent term X is given by 

VeInterX VeSlope( ) (VeResidZVO ) += 2 + (7-23) 

where Z is a random number pulled from a normal distribution every event. EVR is then 

BSA

V EVR e = (7-24) 

where BSA is the profile body surface area. 

Using the above equations, APEX generates an event time-series for Ve and Va and EVR. Ve 

and Va are output on the Events output file. Timestep and hourly values (time-weighted timestep 

and hourly averages of the event values) for EVR, Va, Ve, are calculated and can be written to 

the Timestep and Hourly output files (see Volume I). 

CHAPTER 8.
72 

APEX calculates concentrations of all modeled air pollutants in all microenvironments at each 

 are 

8.1 Defining Microenvironments 

APEX gives the user great flexibility in defining the number and properties of the 

nt is generally 

There are three input files that relate to microenvironments. The first is the Microenvironment 

 file, 

 as 

The Microenvironment Mapping file gives the user control over how many microenvironments 

n 

 See 

Table 8.1 lists the 115 location codes currently in CHAD and the microenvironment to which 

e. 

CALCULATING POLLUTANT 

CONCENTRATIONS IN 

MICROENVIRONMENTS 

timestep of the simulation period for each of the simulated individuals. The default APEX 

timestep is 1 hour (See Volume I). The microenvironmental concentrations are set in 

MicroEnvModule:MicroConcs. The input files and algorithms for these calculations

described in the following sections. 

microenvironments (see step 4 in Figure 2-1). (Note that the term microenvironme

shortened to micro in the computer code and files.) Along with this flexibility, however, is the 

need for the user to specify a substantial amount of information about the microenvironments in

the input files. 

Mapping file, which contains the mapping from the location categories used in the activity 

diaries to the APEX microenvironments. The second is the Microenvironment Descriptions

which contains rules for calculating pollutant concentrations in each microenvironment. The 

third file is the Profile Functions (Distributions) file, in which profile (person) variables (such

the presence of air conditioning or a gas stove in the home) influencing the microenvironmental 

concentrations can be defined. See Volume I for a discussion of the Profile Functions 

(Distributions) file. 

will be modeled and what CHAD (or other activity database) locations should be grouped into 

each of microenvironment. The file contains one row for each CHAD location code, indicating

which APEX microenvironment is to be used whenever that CHAD code is encountered. Thus, 

the more than 100 location codes defined in the activity (CHAD) database are mapped into a 

smaller subset of user-defined microenvironments amenable to modeling. In addition, locatio

codes are also mapped to concentration locations (Home, Work, Other, H/W/O), which tell 

APEX which set of microenvironmental concentrations to use for a particular location code.

Section 8.2.1 for details. 

each is assigned in the default Microenvironment Mapping file included with the APEX releas
73 

Table 8.1. Default Mapping of CHAD Location Codes to APEX Microenvironments 

CHAD 

Location 

Code 

CHAD Location 

Description 

APEX 

Microenv. 

Code 

APEX 

Microenviroment 

Description 

Location 

(see Section 

8.2.1) 

U Uncertain of correct code −1 Use previous 

microenvironment U 

X No data −1 Use previous 

microenvironment U 

30000 Residence, general 1 Indoors −

Residence H 

30010 Your residence 1 Indoors −

Residence H 

30020 Other residence 1 Indoors −

Residence H 

30100 Residence, indoor 1 Indoors −

Residence H 

30120 Your residence, indoor 1 Indoors −

Residence H 

30121 ..., kitchen 1 Indoors −

Residence H 

30122 ..., living room or family 

room 

1 Indoors −

Residence H 

30123 ..., dining room 1 Indoors −

Residence H 

30124 ..., bathroom 1 Indoors −

Residence H 

30125 ..., bedroom 1 Indoors −

Residence H 

30126 ..., study or office 1 Indoors −

Residence H 

30127 ..., basement 1 Indoors −

Residence H 

30128 ..., utility or laundry room 1 Indoors −

Residence H 

30129 ..., other indoor 1 Indoors −

Residence H 

30130 Other residence, indoor 1 Indoors −

Residence H 

30131 ..., kitchen 1 Indoors −

Residence H 

30132 ..., living room or family 

room 

1 Indoors −

Residence H 
74 

CHAD 

Location 

Code 

CHAD Location 

Description 

APEX 

Microenv. 

Code 

APEX 

Microenviroment 

Description 

Location 

(see Section 

8.2.1) 

30133 ..., dining room 1 Indoors −

Residence H 

30134 ..., bathroom 1 Indoors −

Residence H 

30135 ..., bedroom 1 Indoors −

Residence H 

30136 ..., study or office 1 Indoors −

Residence H 

30137 ..., basement 1 Indoors −

Residence H 

30138 ..., utility or laundry room 1 Indoors −

Residence H 

30139 ..., other indoor 1 Indoors −

Residence H 

30200 Residence, outdoor 10 Outdoors − Other H 

30210 Your residence, outdoor 10 Outdoors − Other H 

30211 ..., pool or spa 10 Outdoors − Other H 

30219 ..., other outdoor 10 Outdoors − Other H 

30220 Other residence, outdoor 10 Outdoors − Other H 

30221 ..., pool or spa 10 Outdoors − Other H 

30229 ..., other outdoor 10 Outdoors − Other H 

30300 Residential garage or carport 7 Indoors − Other H 

30310 ..., indoor 7 Indoors − Other H 

30320 ..., outdoor 10 Outdoors − Other H 

30330 Your garage or carport 1 Indoors −

Residence H 

30331 ..., indoor 1 Indoors −

Residence H 

30332 ..., outdoor 10 Outdoors − Other H 

30340 Other residential garage or 

carport 

1 Indoors −

Residence H 

30341 ..., indoor 1 Indoors −

Residence H 

30342 ..., outdoor 10 Outdoors − Other H 

30400 Residence, none of the above 1 Indoors −

Residence H 

31000 Travel, general 11 InVehicle − Cars 

and Trucks O 

31100 Motorized travel 11 InVehicle − Cars 

and Trucks O 

31110 Car 11 InVehicle − Cars 

and Trucks O 
75 

CHAD 

Location 

Code 

CHAD Location 

Description 

APEX 

Microenv. 

Code 

APEX 

Microenviroment 

Description 

Location 

(see Section 

8.2.1) 

31120 Truck 11 InVehicle − Cars 

and Trucks O 

31121 Truck (pickup or van) 11 InVehicle − Cars 

and Trucks O 

31122 Truck (not pickup or van) 11 InVehicle − Cars 

and Trucks O 

31130 Motorcycle or moped 8 Outdoors − Near 

Road O 

31140 Bus 12 InVehicle − Mass 

Transit O 

31150 Train or subway 12 InVehicle − Mass 

Transit O 

31160 Airplane 0 Zero concentration O 

31170 Boat 10 Outdoors − Other O 

31171 Boat, motorized 10 Outdoors − Other O 

31172 Boat, other 10 Outdoors − Other O 

31200 Non-motorized travel 10 Outdoors − Other O 

31210 Walk 10 Outdoors − Other O 

31220 Bicycle or inline 

skates/skateboard 

10 Outdoors − Other 

O 

31230 In stroller or carried by adult 10 Outdoors − Other O 

31300 Waiting for travel 10 Outdoors − Other O 

31310 ..., bus or train stop 8 Outdoors − Near 

Road O 

31320 ..., indoors 7 Indoors − Other O 

31900 Travel, other 11 InVehicle − Cars 

and Trucks O 

31910 ..., other vehicle 11 InVehicle − Cars 

and Trucks O 

32000 Non-residence indoor, 

general 

7 Indoors − Other 

O 

32100 Office building/ bank/ post 

office 

5 Indoors − Office 

O 

32200 Industrial/ factory/ 

warehouse 

5 Indoors − Office 

O 

32300 Grocery store/ convenience 

store 

6 Indoors −

Shopping H 

32400 Shopping mall/ non-grocery 

store 

6 Indoors −

Shopping O 

32500 Bar/ night club/ bowling 

alley 

2 Indoors − Bars and 

Restaurants O 

32510 Bar or night club 2 Indoors − Bars and 

Restaurants O 
76 

CHAD 

Location 

Code 

CHAD Location 

Description 

APEX 

Microenv. 

Code 

APEX 

Microenviroment 

Description 

Location 

(see Section 

8.2.1) 

32520 Bowling alley 2 Indoors − Bars and 

Restaurants O 

32600 Repair shop 7 Indoors − Other O 

32610 Auto repair shop/ gas station 7 Indoors − Other O 

32620 Other repair shop 7 Indoors − Other O 

32700 Indoor gym /health club 7 Indoors − Other O 

32800 Childcare facility 4 Indoors − Day 

Care Centers O 

32810 ..., house 1 Indoors −

Residence O 

32820 ..., commercial 4 Indoors − Day 

Care Centers O 

32900 Large public building 7 Indoors − Other O 

32910 Auditorium/ arena/ concert 

hall 

7 Indoors − Other 

O 

32920 Library/ courtroom/ museum/ 

theater 

7 Indoors − Other 

O 

33100 Laundromat 7 Indoors − Other H 

33200 Hospital/ medical care 

facility 

7 Indoors − Other 

O 

33300 Barber/ hair dresser/ beauty 

parlor 

7 Indoors − Other 

H 

33400 Indoors, moving among 

locations 

7 Indoors − Other 

O 

33500 School 3 Indoors − Schools O 

33600 Restaurant 2 Indoors − Bars and 

Restaurants O 

33700 Church 7 Indoors − Other H 

33800 Hotel/ motel 7 Indoors − Other O 

33900 Dry cleaners 7 Indoors − Other H 

34100 Indoor parking garage 7 Indoors − Other O 

34200 Laboratory 7 Indoors − Other O 

34300 Indoor, none of the above 7 Indoors − Other O 

35000 Non-residence outdoor, 

general 

10 Outdoors − Other 

O 

35100 Sidewalk, street 8 Outdoors − Near 

Road O 

35110 Within 10 yards of street 8 Outdoors − Near 

Road O 

35200 Outdoor public parking lot 

/garage 

9 Outdoors − Public 

Garage / Parking O 

35210 ..., public garage 9 Outdoors − Public 

Garage / Parking O 
77 

CHAD 

Location 

Code 

CHAD Location 

Description 

APEX 

Microenv. 

Code 

APEX 

Microenviroment 

Description 

Location 

(see Section 

8.2.1) 

35220 ..., parking lot 9 Outdoors − Public 

Garage / Parking O 

35300 Service station/ gas station 10 Outdoors − Other O 

35400 Construction site 10 Outdoors − Other O 

35500 Amusement park 10 Outdoors − Other O 

35600 Playground 10 Outdoors − Other H 

35610 ..., school grounds 10 Outdoors − Other O 

35620 ..., public or park 10 Outdoors − Other H 

35700 Stadium or amphitheater 10 Outdoors − Other O 

35800 Park/ golf course 10 Outdoors − Other O 

35810 Park 10 Outdoors − Other O 

35820 Golf course 10 Outdoors − Other O 

35900 Pool/ river/ lake 10 Outdoors − Other O 

36100 Outdoor restaurant/ picnic 10 Outdoors − Other O 

36200 Farm 10 Outdoors − Other O 

36300 Outdoor, none of the above 10 Outdoors − Other O 

All of the other properties of the microenvironments are provided in the Microenvironment 

Descriptions file. All microenvironments assigned locations in the Microenvironment Mapping 

file must be defined in the Microenvironment Descriptions file. More microenvironments may 

be described than are assigned locations, but they will not be used by APEX (since in this case 

simulated people will never enter the microenvironment). The total number of 

microenvironments described in the Microenvironment Descriptions file must also be indicated 

in the Simulation Control input file. (These input files are also covered in Volume I.) 

Definition of the microenvironments using the Microenvironment Descriptions file is covered in 

Section 8.2.4. 

8.2 Calculating Concentrations in Microenvironments 

APEX calculates concentrations of all the air pollutants in all the microenvironments at each 

timestep of the simulation period for each of the simulated individuals, based on the ambient air 

quality data specific to the geographic locations visited by the individual. APEX provides two 

methods for calculating microenvironmental concentrations: the mass balance (MASSBAL) 

method and the simpler factors (FACTORS) method. The MASSBAL method starts with the 

previous timestep’s concentration in each microenvironment, which is modified over time by 

exchange with the ambient air. The FACTORS method uses a simple equation to relate the 

concentration in each microenvironment to the current ambient concentration. Both methods 

require that a number of parameters including proximity, penetration and pollutant sources be 

specified over time, while the MASSBAL method uses some additional parameters, such as air 

exchange, volume, and decay rates. All pollutants use the same method in each 

microenvironment. These methods are described in the next two subsections. The user is 

required to specify the calculation methods for each of the microenvironments in the simulation 
in the Microenvironment Descriptions file (see Volume I). Microenvironments within a single 

simulation may use either method; mixing the methods (across micros, not pollutants) is allowed 

with no restrictions. 

78 

8.2.1 Microenvironmental Concentrations for Home/Work/Other Locations 

APEX calculates up to three sets of microenvironmental concentrations for each person. In 

general, these concentrations represent the geographical locations a person moves through in a 

day. These three locations are “Home” (H), “Work” (W), and “Other” (O). (A person who is 

not employed only has H and O locations.) The H and W concentrations are calculated from the 

air quality data in a person’s home and work sectors respectively. The concentrations in the O 

location are calculated from a composite of set of air districts. By default, APEX uses the cityaverage air concentration to calculate O concentrations. However, the user can customize this 

average concentration using the Control file settings SampleOtherLocs, #OtherDistricts, and 

HomeProbab (see Volume I). 

Location is determined event-by-event for each simulated person. In general, APEX determines 

which set of concentrations to use for each event via the diary (CHAD or other) location code 

The Microenvironment Mapping file assign locations definitions to each activity database 

location code (see Table 8.1). However, APEX also assigns diary events with a “work” activity 

code to the W location. This assignment overrides the location assignment based on location 

code. By default, APEX assigns CHAD activity codes 10000-10300 to the work location (see 

Table 4-5 in Volume I). However, the user also has the ability to customize this setting using the 

Control file variable CustomWork.

APEX only defines a single set of micro parameter distributions for each micro (i.e. there are no 

unique distributions for the H, W, O locations.) However, the values of the parameters 

themselves may differ between locations. By using the ResampleWork keyword in a micro 

parameter description, APEX will select a different value from the distribution to use for the W 

location (see Section 8.2.4.3 for details). If ResampleWork is used, then the micro parameters 

for the O location will be the average of the parameters for the H and W locations. If not, the H, 

W, and O locations will all use the same values of the parameters for the micro. In addition, if 

the simulated person (profile) is not employed, there is no W location, and the values of the 

parameters for the O location are equal to the H values. 

8.2.2 Mass Balance Method 

The mass balance method assumes that an enclosed microenvironment (e.g., a room in a 

residence) is a single well-mixed volume in which the air concentration is approximately 

spatially uniform. The concentration of an air pollutant in such a microenvironment is estimated 

using the following four processes (as illustrated in Figure 8.1): 

• Inflow of air into the microenvironment; 

• Outflow of air from the microenvironment; 
•

79 

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

chemical degradation; and 

• Emissions from sources of a pollutant inside the microenvironment. 

Air

inflow

Indoor sources

Removal due to:

•Chemical reactions

•Deposition

•Filtration

Air

outflow

Microenvironment

Air

inflow

Indoor sources

Removal due to:

•Chemical reactions

•Deposition

•Filtration

Air

outflow

Microenvironment

Figure 8.1. The Mass Balance (MASSBAL) Model 

It is assumed that the flow of outside air into the microenvironment is equal to that flowing out 

of the microenvironment, and this rate is given by the air exchange rate, Rair exchange. Rair exchange is 

given in units of hr-1. The air exchange rate can be interpreted as the number of times per hour 

the entire volume of air in the microenvironment is replaced. 

Considering the microenvironment as a distinct, well-mixed volume of air, the mass balance 

equation for a pollutant can be described by: 

( )

in out removal CCCC source dt

tdC  +−−= (8-1) 

where: 

C(t) = Concentration in the microenvironment at time t (μg/m3) 

 = Rate of change in C(t) due to air entering the micro Cin



 = Rate of change in C(t) due to air leaving the micro Cout


80 

 = Rate of change in C(t) due to all removal processes Cremoval



 = Rate of change in C(t) due to all source terms Csource



(Note that concentration must be in the same units as the ambient air quality data, i.e., either ppm 

or μg/m3

, although throughout these equations concentration is shown only in μg/m3 for brevity. 

The change in microenvironmental concentration due to influx of air, , is Cin



 (8-2) in ambient proximity penetratio ×××= RffCC airn exchange 

where: 

Cambient = Ambient timestep concentration (μg/m3) 

fproximity = Proximity factor (unitless) 

fpenetration = Penetration factor (unitless) 

The proximity factor fproximity is used to account for differences in ambient concentrations 

between the geographic location represented by the ambient air quality data (e.g., a regional 

fixed-site monitor) and the geographic location of the microenvironment. That is, the outdoor air 

at a particular location may differ systematically from the outdoor air at the center of the air 

quality district. For example, a house might be located next to a busy road in which case the air 

outside the house would have elevated levels for mobile source pollutants such as carbon 

monoxide. The concentration Coutdoor in the air directly outside the microenvironment is given by 

the product of the ambient concentration and fproximity: 

 (8-3) outdoor = proximityCfC ambient

For some pollutants (especially particulate matter), the process of infiltration may remove a 

fraction of the pollutant from the air. The fraction that is retained in the air is given by the 

penetration factor fpenetration. During exploratory analyses, the user may examine how a 

microenvironment affects overall exposure by setting the microenvironment’s proximity or 

penetration factor to zero, thus effectively eliminating the microenvironment. 

Change in microenvironmental concentration due to outflux of air is calculated as the 

concentration in the microenvironment C(t) multiplied by the air exchange rate: 

RC (tC ) out = air exchange ×  (8-4) 

The third term in the MASSBAL calculation represents removal processes within the 

microenvironment. There are three such processes in general: chemical reaction, deposition, 

and filtration. Chemical reactions are significant for ozone, for example, but not for carbon 

monoxide. The amount lost to chemical reactions will generally be proportional to the amount 

present, which in the absence of any other factors would result in an exponential decay in the 

concentration with time. Similarly, deposition rates are usually given by the product of a 
(constant) deposition velocity and a (time-varying) concentration, also resulting in an 

exponential decay. The third removal process is filtration, usually as part of a forced air 

circulation or HVAC system. Filtration will normally remove particles but not gases. In any 

case, filtration rates are also proportional to concentration. Change in concentration due to 

deposition, filtration, and chemical degradation in a microenvironment is simulated based on the 

first-order equation: 

C ( ) R ( ) (tCRtCRR ) removal = deposition filtration ++ chemical removal ×=  (8-5) 

where: 

 = Change in microenvironmental concentration due to removal 

processes (μg/m3/hour) 

Cremoval



RR

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

deposition (1/hour) 

RR

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

filtration (1/hour) 

RR

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

chemical degradation (1/hour) 

RR

removal = Removal rate of a pollutant from a microenvironment due to the 

combined effects of deposition, filtration, and chemical 

degradation (1/hour) 

For unreactive gases like carbon monoxide, all three removal terms could be zero, in which case 

RR

removal =0. 

The fourth term in the MASSBAL calculation represents pollutant sources within the 

microenvironment. This is the most complicated term, in part because several sources may be 

present. APEX allows two methods of specifying source strengths: emission sources (ESource 

or ES) or concentration sources (CSource or CS). Either may be used for MASSBAL 

microenvironments, and both can be used within the same microenvironment. The source 

strength values are used to calculate the source term , which has standard units of 

μg/m

Csource



3

/hr. 

Emission sources are expressed as emission rates in units of μg/hr. To determine the source term 

associated with an emission source, ES must be divided by the volume V of the 

microenvironment in m3

: 

V

ES C ESsource, =  (8-6) 

Concentration sources however, are expressed in units of concentration. These must be the same 

units as used for the ambient concentration (e.g., μg/m3

). Concentration sources are normally 

81 
used as additive terms for microenvironments using the FACTORS method. Strictly speaking, 

they are somewhat inconsistent with the MASSBAL method, since concentrations should not be 

inputs but should be consequences of the dynamics of the system. Nevertheless, a suitable 

meaning can be found by determining the source strength that would result in a mean 

increase of CS in the concentration, given constant parameters and equilibrium conditions, in this 

way: 

82 

Csource



Assume that a microenvironment is always in contact with clean air (ambient = zero), and it 

contains one concentration source. Then the mean concentration over time in this 

microenvironment from this source should be numerically equal to CS. The mean source 

strength expressed in ppm/hr or μg/m3

/hr is the rate of change in concentration In 

equilibrium, 

. C CS source, 

air exchange removal

CS source,

R R

C

CS

+ =

 (8-7) 

C CS source,  can be written as 

 (8-8) C CS source, ×= RCS mean 

where Rmean is the chemical removal rate. From eq. 8-7, Rmean is equal to the sum of the air 

exchange rate and the removal rate (Rair exchange+Rremoval) under equilibrium conditions. In 

general, however, the microenvironment will not be in equilibrium, but in such conditions there 

is no clear meaning to attach to since there is no fixed emission rate that will lead to a 

fixed increase in concentration. The simplest solution is to use R

C CS source, 

mean = Rair exchange+Rremoval. 

However, the user is given the option of specifically specifying Rmean (see discussion of 

parameters below). This may be used to generate a truly constant source strength by 

making CS and R

C CS source, 

CS 

mean both constant in time. If this is not done, then Rmean is simply set to the 

sum of (Rair exchange + Rremoval). If these parameters change over time, then also 

changes. Physically, the reason for this is that in order to maintain a fixed elevation of 

concentration over the base conditions, then the source emission rate would have to rise if the air 

exchange rate were to rise. 

Csource, 

Multiple emission and concentration sources within a single microenvironment are combined 

into the final total source term by combining equations 8-6 and 8-8: 

∑∑= =

= + = + e nc

1i

mean i

n

1i

source ESsource, CSsource, i CSRES

V

1 CC C (8-9) 

where: 

ESi = Emission source strength for emission source i (μg/hour) 

CSi = Emission source strength for concentration source i (μg/m3) 
83 

ne = Number of emission sources in the microenvironment 

nc = Number of concentration sources in the microenvironment 

(A note on units: The above equation is modified if the units of air quality are ppm rather than 

μg/m3

. Specifically, 1/V is replaced by f/V, where f = 1/ppmFact. The value of ppmFact is a 

user-supplied in the Simulation Control input file; it expresses the number of μg/m3

 that equate 

to 1 ppm. For the pollutant CO, ppmFact=1,145. The conversion factor ppmfactor could also be 

used to convert μg/m3

 to other units.) 

Equations 8-2, 8-4, 8-5,and 8-9 can now be combined with 8-1 to form the differential equation 

for the microenvironmental concentration C(t). Within the time period of an timestep, and 

are assumed to be constant. Using 

Csource



Cin

 Ccombined

 = + leads to: Csource

 Cin



( ) () ()tCRtCR-C

dt

tdC = combined exchange air − removal 

C (tCR ) combined −= mean  (8-10) 

Solving this differential equation leads to: 

( ) ( ) R- meant

mean

combined

mean

combined e

R

C 0C

R

C tC ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = −+   (8-11) 

where: 

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

beginning of a timestep (μg/m3

) 

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

the time period of a timestep (μg/m3

). 

Based on eq. 8-11, the following three concentrations in a microenvironment are calculated: 

( )

air exchange removal

source in

mean

combined

equil R R

CC

R

C tCC

+

+

=∞→= =   (8-12) 

( ( ) ) Rmean t

end equil equil eC0CCC − −+= (8-13) 

( ) ( ) ( ) t

t

mean

R

1 equil equil

0

1

0

mean R

e1 C0CC

dt

dttC

C

− mean − = −+=

∫

∫ (8-14) 

where: 

 t = length of the APEX timestep (hours) 
84 

Cequil = Concentration in a microenvironment (μg/m3) if t → ∞

(equilibrium state). 

C(0) = Concentration in a microenvironment at the beginning of the 

timestep (μg/m3

) 

C end = Concentration in a microenvironment at the end of the timestep 

(μg/m3

) 

 C mean = Mean concentration in a microenvironment for timestep (μg/m3) 

RR

mean = RRair exchange + RRremoval (1/hour) 

At each timestep of the simulation period, APEX uses Eqs. 8-12, 8-13, and 8-14 to calculate the 

equilibrium, ending, and mean concentrations. APEX reports mean concentration as the 

concentration for a specific timestep. The calculation continues to the next timestep by using C 

end for the previous timestep as C(0). 

The microenvironmental parameters for the MASSBAL method that can be defined by the user 

in the Microenvironment Descriptions file are summarized in the Table 8.2, with their valid 

ranges and their corresponding names in the file. 

Table 8.2. Microenvironmental Parameters

Parameter Definition Units Range 

Default 

Value Namea

f proximity Proximity factor unitless fproximity ≥ 0 1 PR 

f penetration Penetration factor unitless 0 ≤ fpenetration ≤ 1 1 PE 

CS Concentration source μg/m3

 or 

ppm 

CS ≥ 0 0 CS 

ES Emission source μg/hr ES ≥ 0 0 ES 

RR

 removal

Removal rate due to 

deposition, filtration, 

and chemical reaction 

1/hr RR

removal ≥ 0 0 DE 

RR

 air exchange Air exchange rate 1/hr RRair exchange ≥ 0 none AE 

RR

mean

Mean removal rate: 1/hr RR

mean ≥ 0 RR

removal + 

RR

air exchange

MR 

V Volume of 

microenvironment m3 V > 0 none V 

a Designation in Microenvironment Descriptions file 
Not all of the possible parameters are always needed, and several of them have natural default 

values. Based on the above equations, the following generalizations can be made about the 

definition of the MASSBAL parameters in the Microenvironment Descriptions file: 

85 

• Air exchange rate is a critical parameter that is always needed in a MASSBAL 

calculation. It must always be defined in the file as it has no default value. 

• Air exchange rate and volume are not pollutant-specific, and therefore are defined only 

once for each micro. All other parameters must be defined for each pollutant. 

• Removal rate must also be user-defined in the file if not assumed to be zero. For some 

pollutants it can be assumed to have a natural default value of zero. 

• The proximity and penetration factors must be defined in the file unless assumed to be 

unity, which is the natural default value for both factors that should be used in the 

absence of data to the contrary. 

• If any emission source terms are present then volume must be defined. Volume has no 

default value. 

• If any concentration source terms are present then the mean removal rate may be userdefined, but if appropriate, it may assume a default value of (Rair exchange + Rremoval). 

The details for specifying these input parameters in the Microenvironment Descriptions file are 

provided in the Volume I of this User’s Guide. Further details on the options for designating 

these parameters are given in Section 8.2.4. 

In APEX, it is assumed that the outdoor concentration and the other modeling parameters for the 

MASSBAL method remain constant during any timestep. . Of course, recalling that the APEX 

default timestep is one hour, in many cases the MASSBAL parameters may not remain constant 

for an timestep at a time. For example, a person may enter a microenvironment and smoke a 

cigarette for five or ten minutes and then leave. Or, someone might enter a kitchen and cook for 

a few minutes using a gas stove. Or one might alter an air exchange rate by opening or closing a 

window. There are two reasons why it is difficult to model such events in APEX. First, there is 

already a large computational burden in calculating concentrations in every microenvironment 

for every timestep for every simulated person. This burden is substantially large if very fine time 

resolution were demanded. Second, most examples of fine-scale parameter variation are driven 

by human actions. The CHAD activity diaries generally do not contain enough detail to 

determine when each cigarette is lit or each time a stove is used or a window is opened or closed. 

Furthermore, the diaries only follow the activities of a single person. It is quite possible for these 

actions to be performed by other people. For example, if the activity diary follows a child, then 

the child’s parents may be doing these things that affect the properties of the microenvironments 

that the child is in. Since the diaries do not reliably report such information, it was decided that a 

very fine time resolution could not reliably be used for the calculation of concentrations. 

In a MASSBAL microenvironment, the concentration during any timestep depends on the 

concentration for the timestepbefore. Ultimately, all timestepsdepend on some method for 

establishing initial conditions. To avoid the problem of establishing new initial conditions every 
time the activity diary indicates that a MASSBAL microenvironment is entered, the time series is 

evaluated for all timestepsin the simulation period. An extra 24 hour period is added prior to the 

start of the APEX simulation period by duplicating the properties from the first day of the 

simulation period. It is assumed that 24 hours is sufficient so that the initial concentration 

becomes irrelevant. The entire simulation period is then evaluated timestepby timestepwithout 

gaps, with each timestepbeing used to determine the next. 

8.2.3 Factors Method 

The FACTORS method is simpler than the mass balance method. In this method, the value of 

the concentration in a microenvironment is not dependent on the concentration during the 

previous timestep. Rather, the method uses the following equation to calculate 

timestepconcentration in a microenvironment from the user-provided air quality data: 

∑=

= +

nC

1i

timestep ambient proximity penetration CSi ffCC

 (8-15) 

where: 

 Ctimestep = Timestep concentration in a microenvironment (μg/m3

) 

 Cambient = Timestep concentration in ambient environment (μg/m3

) 

 fproximity = Proximity factor (unitless) 

 fpenetration = Penetration factor (unitless) 

 CSi = Mean air concentration resulting from source i (μg/m3

) 

 nc = number of concentration sources in the microenvironment 

The user may provide values for proximity, penetration, and any concentration source terms, or 

may allow them to assume default values (see Table 8.2); however, it is not mandatory that the 

user supply any values if the default values are suitable. An undefined proximity or penetration 

is assumed to be unity at all times. Missing (i.e., undefined) sources are assumed to be zero. 

Parameters are left undefined by simply omitting them from the Microenvironment Descriptions

input file. If all parameters are missing, then the concentration in the microenvironment is 

always the same as the ambient concentration. All of the parameters in the above equation are 

evaluated for each timestep, although these values might remain constant for several hours, 

entire days, or even for the entire simulation. For the ambient concentration, the timestep values 

come from the input Air Quality Data file, and may be either measurements or modeled results, 

or may be sampled for each hour from a distribution (see Volume I for available formats of this 

file). For the other parameters, the timestep values are the result of the calculations based on the 

information specified in the Microenvironment Descriptions input file. 

86 
8.2.4

87 

Microenvironment Parameter Definitions 

The second section of the Microenvironment Descriptions input file contains the rules for 

determining the values of the parameters used in the MASSBAL and FACTORS methods. 

Instructions for specifying microenvironmental input parameters (those in Table 8.2) in the 

Microenvironment Descriptions file are provided in Volume I of this User’s Guide, but further 

details on the options for using resampling rates, conditional variables, periodic (daily, weekly, 

and monthly) groupings, and random seeds, are provided in this section. This includes an 

explanation of ways to specify CS terms as products of distributions. 

Both of the concentration calculation methods require multiple user-defined input parameters. 

These microenvironmental parameters are defined by probability distributions defined in the 

Microenvironment Descriptions input file, with values being assigned to each timestep of the 

simulation. The file is read in MicroEnvModule:ReadMicroData. Any of the following 

distribution types in Table 3.1 can be used for microparameters. 

The user may provide different distribution data for the parameter for any combination of the 

following temporal and spatial variables: 

• Hour in a day 

• Day in a week 

• Month in a year (i.e., season) 

• Air quality district 

For example, the user can define probability distributions for a parameter that vary depending on 

the time of day and whether the simulated timestep is on a weekday or a weekend, or the user 

can define a distribution that changes with the season of the year and with the air quality district 

associated with the microenvironment being considered (recall that home and work sectors for 

each profile will be associated with a unique air quality district). 

The distributions for the microenvironmental parameters may also depend on conditional 

variables that are a subset of the profile variables for an individual. A single microenvironmental 

parameter may depend on up to three of the above conditional variables. Conditional variables 

may change on an interpersonal, geographic, meteorological, or temporal basis, influencing the 

microparameters accordingly. 

The rules for determining any microenvironmental parameter (MP) are unique to each 

microenvironment. For example, the rules for proximity for a house may differ completely from 

the rules for proximity for a car. Every combination of parameter, pollutant, and 

microenvironment is distinct (with the exception of air exchange rate and volume, which can 

only be defined once per micro). The order in which the MP definitions are presented is not 

significant to APEX, although it might help the user to group them by microenvironment, 

pollutant, or MP. Note that the entire definition of an MP can be omitted if its default value is 

acceptable, so for example if proximity is always to be unity in some microenvironment, then no 

MP definition is needed for proximity in that microenvironment. The example in Exhibit 8-1

shows one possibility for the proximity parameter for microenvironment #1. The actual data are 
only for illustrative purposes and are not intended to properly represent this MP in any real 

scenario. 

Micro number = 1 

Pollutant = 3 

Parameter Type = Proximity 

Hours - Block = 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 

Weekday-DayType = 1 1 1 1 1 1 1 

Month-Season = 1 1 2 2 2 3 3 3 4 4 4 1 

District-Area = 1 1 1 1 1 1 

Condition #1 = 0 

Condition #2 = 0 

Condition #3 = 0 

ResampHours = NO 

ResampDays = YES 

ResampWork = YES 

RandomSeed = 0 

Block DType Season Area C1 C2 C3 Shape Par1 Par2 Par3 Par4 LTrunc UTrunc ResampOut 

1 1 1 1 1 1 1 Normal 1.5 1.2 . . 0 4.0 Y 

2 1 1 1 1 1 1 Point 2.0 . . . . . . 

1 1 2 1 1 1 1 Lognormal 1.2 1.5 . . 0 10 Y 

2 1 2 1 1 1 1 Lognormal 0.4 1.2 . . 0 10 Y 

1 1 3 1 1 1 1 Triangle 0 3 2 . . . Y 

2 1 3 1 1 1 1 Normal 2.5 1.5 . . . . Y 

1 1 4 1 1 1 1 Uniform 0 3 . . . . Y 

2 1 4 1 1 1 1 Lognormal 3 2 . . 0 10 Y

Exhibit 8-1. Example of a Microenvironmental Parameter Description 

The general format is the same for all MPs. The first three lines are mandatory and specify the 

microenvironment number, the pollutant (indicated by its order in the Control file), and the MP, 

or parameter type (the Pollutant line may be absent for AER and Vol). This combination should 

be unique for every MP in the input file, with the possible exception of enumerated sources 

(discussed later). 

The parameter types are indicated using standard keywords (given in Table 8.2). Note that only 

the first two characters of the parameter type are checked by APEX, and the keyword is not case 

sensitive, so the example above could use “PR”. The user may spell out the parameter types if 

desired, providing greater clarity. 

After the microenvironment number and parameter type, any or all of the remaining lines 

containing an equal sign may be omitted. These indicate the settings for various options, all of 

which have default values. These settings may appear in any order within the description; they 

are recognized via the keyword that precedes the equal sign. One option, missing in the above 

example since it only applies to parameter types ES and CS, is the source number. See section 

8.2.4.6 for an example using this option. The other seven options in this example are the 

mappings that determine the values for the seven indices that label each distribution. This is 

followed by three resampling options and a random seed initialization option. These options are 

covered in the following subsections. 

After all the options are specified, the next line (starting with “Block”) indicates that the 

following lines contain descriptions of distributions. At least one distribution is always required; 

the exact number needed depends on the settings of the seven indexing options. The shortest 

possible MP description (other than one completely missing) consists of four lines. Such a 

description would have the first three mandatory lines, the header line indicating that 

distributions follow, and a single distribution that applies to all timesteps of the simulation, as in 

Exhibit 8-2. 

88 
Micro number = 1 

89 

Parameter Type = Proximity 

Block DType Season Area C1 C2 C3 Shape Par1 Par2 Par3 Par4 LTrunc UTrunc ResampOut 

1 1 1 1 1 1 1 Normal 1.5 1.2 . . 0 4 Y 

Exhibit 8-2. Example of the Shortest Possible MP Description 

These rules state that the proximity in microenvironment #1 is to be drawn from a normal 

distribution with mean 1.5 and standard deviation 1.2. If the value drawn is below zero or above 

4.0 then another value is drawn, until one is found that is within bounds. This single value is 

then applied to all timesteps of the simulation, for that particular simulated individual, for their 

home air quality district. A separate single value is applied to that individual for all timesteps in 

their work district. Actually, a third value, the average of the first two, is applied to all timesteps 

in the “other” (non-home, non-work) air quality district. In effect, all the microenvironments are 

modeled in triplicate to account for the three different places. In the above example the three 

values would all be the same if an extra line “ResampleWork =NO” were added 

after the second line. Each simulated individual is modeled independently so new values are 

drawn for all parameters when starting another profile. 

It is necessary that all the parameter distribution data be given in the correct units (i.e. those that 

are compatible with the data in the Air Quality Data input files.) 

The motivation for the rather complex programming that defines and evaluates the MP is that the 

various parameters that enter the MASSBAL and FACTORS equations may have widely 

divergent properties. For example, a parameter like house volume should have a single value 

that does not change over time. Another parameter such as an air exchange rate may change 

every hour. Some parameters like source strengths from cooking or from traffic may show 

strong diurnal patterns that may repeat on a daily or a weekly basis. Parameters that relate to 

temperature may show seasonal variation. 

There are a number of possibilities for each optional rule in the MP definitions. The options fall 

into the following categories: 

• Time and area mappings; 

• Conditional variables; 

• Correlation settings; 

• Resampling options; 

• Random number seeds; and 

• Source number specification. 

Each of these are discussed in the following subsections, after which comes a brief subsection on 

the specification of distributions. 
8.2.4.1

90 

Time and Area Mappings 

Each MP is evaluated for every timestep of the simulation period. Normally this is done by 

drawing a value at random from a distribution. The user may specify that different distributions 

apply at timesteps within different hours of the day. Furthermore, the frequency of sampling can 

be controlled by the user. It is not the case that a new value must be drawn every timestep, 

instead values drawn for other times may be reused. The primary purpose of the time and area 

mappings is to specify which distribution applies to each timestep. The secondary purpose, in 

conjunction with the resampling options, is to establish periodic reuse of values on a daily, 

weekly, monthly, or geographical basis. 

As an example, suppose some parameter should be sampled from one distribution during typical 

working hours and from another distribution at other times. This can be accomplished by 

defining two “blocks” and assigning each hour of the day to either block #1 or block #2. Perhaps 

hours 1-7 (midnight to 7 a.m.) and hours 19-24 (6 p.m. to midnight) belong to block #1, while 

hours 8-18 (7 a.m. to 6 p.m.) belong to block #2. Then distributions must be defined for block 

#1 and block #2. Hours that fall into block #1 will have their parameter values drawn from the 

distribution that applies to block #1, and so on. If, for example, the distribution for block #2 has 

the higher mean, then the daytime values for the parameter will generally be higher than the 

nighttime values, generating a diurnal pattern. Similarly, weekly and seasonal patterns may be 

generated. 

The Hour-Block (HB) mapping indicates the block to which each hour of the day belongs. The 

mapping must contain 24 numbers. The first is the block number for hour 1 (midnight to 1 a.m.), 

and so on. All timesteps belonging to the same block use the same distribution. The block 

numbers range from 1 upwards; there can be anything from 1 to 24 blocks. The number of 

blocks (#blocks) is determined from this mapping itself. If the Hour-Block mapping is missing it 

is assumed that there is only one block, which implies that the parameter values for all 24 hours 

of the day (that is, all timesteps) are taken from the same distribution. The term “Block” might 

suggest that the hours belonging to a given block should be adjacent chronologically, but this is 

not necessary in APEX. It is also not necessary for each block to contain the same number of 

hours. 

The Weekday-Daytype (WT) mapping is similar to the Hour-Block mapping, except that it 

contains seven values instead of 24. The first value is the day type for Sunday, the second is for 

Monday, and so on until the last which is the day type for Saturday. The seven days of the week 

are in the same order as on a standard calendar. Thus if day type 1 is weekday and 2 is weekend, 

the vector should be ( 2 1 1 1 1 1 2), but without the parentheses. The mapping (1 2 2 2 2 2 1) 

would be equivalent if the distributions presented further down were appropriately renumbered. 

If the WT mapping is missing in the Microenvironment Descriptions input file, then only one 

day type is assumed, that is, the default mapping is (1 1 1 1 1 1 1). 

The Month-Season (MS) mapping is similar to the previous two, except that 12 numbers are 

needed. The first number indicates the season for January, and so on through December. Again, 

if this mapping is missing then a single season is assumed to apply to all months. 

The District-Area (DA) mapping is similar to the others, except that the number of air quality 

districts is not a universal constant, but may vary from one simulation to another. If the mapping 
is present, the user must ensure that it contains the correct number of terms (one area assignment 

for each air quality district in the study area). The district indices represent the APEX air district 

numbers, as enumerated in the Sites output file. 

91 

If the user defines 2 blocks, 2 day types, 4 seasons, and 3 areas, then a total of 48 distributions 

(that is, 2 x 2 x 4 x 3) must be specified, one for each possible combination. The number would 

be even larger if any conditional variables were used. To ease the burden of data requirements 

the number of cases should be kept to a minimum. For example, if the seasonal dependence of 

this parameter were weak, one could eliminate it and reduce the number of distributions from 48 

to just 12. If this is too extreme, perhaps two seasons would suffice to capture the variation. The 

number of seasons (or blocks, day types, or areas) can be defined differently for each MP, even 

ones that belong to the same microenvironment. Each MP is evaluated for all timesteps in the 

simulation period, independently of other MP, so there is no reason why the rules for one MP 

should match or correspond with the rules for any other MP. 

8.2.4.2 Conditional Variables 

Selected profile variables may be used to influence the parameter values in the MASSBAL or 

FACTORS equations. These profile variables are known as Conditional Variables. Conditional 

variables can be used to vary parameters on a profile, daily, hourly, or timestep basis. The list of 

variables to use for the current simulation are set in ProfileModule: SetCVlist. The allowable 

conditional profile variables are: 

• Gender 

• Population category (Race/gender combination) 

• Employed 

• HasGasStove 

• HasGasPilot 

• AC_Home 

• AC_Car 

• Window_Res 

• Window_Car 

• SpeedCat 

• ProfileConditional1 

• ProfileConditional2 
•

92 

ProfileConditional3 

• RegionalConditional1 

• RegionalConditional2 

• RegionalConditional3 

• RegionalConditional4 

• RegionalConditional5 

These variables influence the parameters on a profile basis. See Chapter 5 for definition of these 

variables. With the exception of the first three, rules for setting these variables for each profile 

are defined in the Profile Functions (Distributions) input file. In addition to these variables, the 

MPs can also depend on seven meteorological variables: 

• TempCat Hourly temperature, binned into categories.

• HumidCat Hourly humidity, binned into categories.

• PrecipCat Hourly precipitation category.

• WindCat Hourly windspeed, binned into categories.

• DirCat Hourly wind direction, binned into categories.

• MaxTempCat Daily maximum temperature, binned into categories.

• AvgTempCat Daily average temperature, binned into categories

The first five can influence parameters on an hourly basis, while the last 2 are daily-varying 

parameters.

Finally, the MPs can depend daily on 5 user-defined daily varying functions. 

• DailyConditional1 

• DailyConditional2 

• DailyConditional3 

• DailyConditional4 

• DailyConditional5 

. These hourly and daily varying variables are not profile variables. However, rules for defining 

them are also designated in the Profile Functions (Distributions) input file (see Volume I). 
Note that Conditional Variables must be integer, since their values are used as indices to select 

the distribution to be sampled. In practice, the number of categories must be fairly small 

(generally 2 or 3) or else defining distributions for every case becomes burdensome. It should be 

noted that while the concentrations in various microenvironments may depend on the profile 

through the conditional variables, these concentrations do not depend on the activity diaries or 

the event structure. 

93 

The user may select up to three Conditional Variables from the list for each MP. If one is used, 

it does not matter whether conditional variable #1, #2, or #3 is used. If more than one is used 

then the order they are designated does not matter. 

The conditional variable to be applied is identified by its name. For example, if a parameter 

were to depend on gender then it would be indicated as follows in the input file: 

Condition # 1 = Gender 

Note that the word “Gender” must be spelled out in full as in the above list, but it is not case 

sensitive. There are two ways to indicate that a conditional variable is not used. Either the line 

for it can be omitted, or else the variable name can be set to anything that is not on the list. The 

standard practice (if the line is not simply omitted) is to set the right hand side to zero: 

Condition # 1 = 0

There is a complication for the user when it comes to specifying the distributions that are 

applicable to conditional variables. Each distribution has seven indices (four for time and area 

mappings and three for Conditional Variables). But the values that any index may have must be 

integers. Thus, if gender is used as a Conditional Variable then the user must specify 

distributions for gender=1 and for gender=2. The user cannot use mnemonic devices such as 

“M” or “F” instead. The numerical codes for the Conditional Variable are set as constants in 

GlobalModule and are as follows: 

• Gender: 1=Male, 2=Female 

• Employed: 1=YES, 2=NO 

• HasGasStove 1=YES, 2=NO 

• HasGasPilot: 1=YES, 2=NO 

• AC_Car: 1=YES, 2=NO 

• Window_Res: 1=OPEN, 2=CLOSED 

• Window_Car: 1=OPEN, 2=CLOSED 

For the population category conditional variable, the conditional variable value codes are 

integers that represent the order in which the population categories are defined in the “Population 

file” definitions in the Control file. For example, if “Native American females” is the third 
population file defined, then the code for that population category would be 3. The other 

Conditional Variables, the numerical values are provided by the user in the Profile Functions

input file, so there are no pre-assigned ranges or interpretations. The list of conditional variables 

to be used in defining MPs is set in DistributionModule:SetCVList. 

94 

8.2.4.3 Correlation Settings 

In APEX the user has the option of correlating samples for microenvironmental parameters. 

Such correlation would make sense, for example, when the value of the parameter is assumed to 

be mainly a function of the properties of a simulated individual’s home and the pollutants have 

similar properties (for example, are all particles). In addition, in some cases it may be that the 

same parameters may be correlated in different microenvironments. 

APEX uses a simple method of correlation microparameters - by sampling them using the same 

random numbers. This results in values being selected for correlated parameters at the same 

percentile from the appropriate distributions. The percentiles will correspond each hour as long 

as the 2 (or more) parameters use the same conditional variables, time and area mappings, and 

resampling rates and thus have the same number of required distributions and samples. 

Otherwise the samples get out of phase and any correlation is lost. APEX checks that the 

conditionals, mappings, and resampling are the same when correlating parameters, and writes a 

warning if they are not. APEX will still run, but the user should be aware that the correlation is 

lost. 

Correlation is handled by an optional keyword in the microparameter definition, CORRNUM. 

Each subset of microparameters that the user desires be correlated (sampled at the same 

percentile each hour) are assigned a unique integer 1-N, where N is the total number of 

correlated subsets. For example, assume that the user wants to correlate the penetration and 

decay values for residences (micro #1) for 2 pollutants. Valid MP definitions for this case are 

shown in 
! PENETRATION FACTOR 

Micro number = 1 

POLLUTANT = 1 

CorrNum = 1 

Parameter Type = PE 

Month - Season = 1 1 1 1 2 2 2 2 2 2 1 1 

ResampHours = NO 

ResampDays = YES 

ResampWork = YES 

Block DType Season Area C1 C2 C3 Shape Par1 Par2 Par3 Par4 LTrunc UTrunc ResampOut

1 1 1 1 1 1 1 Normal 0.5 0.2 . . 0.1 1.0 Y 

1 1 2 1 1 1 1 Normal 0.8 0.2 . . 0.1 1.0 Y 

 

Micro number = 1 

POLLUTANT = 2 

CorrNum = 1 

Parameter Type = PE 

Month - Season = 1 1 1 1 2 2 2 2 2 2 1 1 

ResampHours = NO 

ResampDays = YES 

ResampWork = YES 

Block DType Season Area C1 C2 C3 Shape Par1 Par2 Par3 Par4 LTrunc UTrunc ResampOut

1 1 1 1 1 1 1 Normal 0.4 0.1 . . 0.1 1.0 Y 

1 1 2 1 1 1 1 Normal 0.7 0.1 . . 0.1 1.0 Y 

! DECAY RATES 

Micro number = 1 

POLLUTANT = 1 

CorrNum = 2 

Parameter Type = DE 

ResampHours = NO 

ResampDays = NO 

ResampWork = YES 

Block DType Season Area C1 C2 C3 Shape Par1 Par2 Par3 Par4 LTrunc UTrunc ResampOut

1 1 1 1 1 1 1 LogNormal 2.51 1.53 0 . 0.95 8.05 Y 

 

Micro number = 1 

POLLUTANT = 2 

CorrNum = 2 

Parameter Type = DE 

ResampHours = NO 

ResampDays = YES 

ResampWork = YES 

Block DType Season Area C1 C2 C3 Shape Par1 Par2 Par3 Par4 LTrunc UTrunc ResampOut

1 1 1 1 1 1 1 LogNormal 2.51 1.53 0 . 0.95 8.05 Y 

95 

Exhibit 8-3. Example of Defining Correlated Microparameters 

In this example, the 2 penetrations are correlated, as are the decays, but the decays and 

penetration are not correlated with each other. (If for some reason this was desirable, all four 

descriptions could be set to have CorrNum=1). 

Note that if the same distributions are assigned to each pollutant (which is true for decay in this 

example), the pollutants will use the exact same parameter values (samples) for that pollutant for 

each hour. 

Note that the user can specify random number seeds for each microparameter using the 

RandomSeed keyword (see section 8.2.4.5). This can also be used to correlate microparameters. 

However, in this case the hourly microparameter samples will be the same for all persons in the 
simulation, while using the CorrNum setting will produce different sets of correlated samples for 

each person. 

96 

8.2.4.4 Resampling Options 

The time and area mappings indicate which cases are to have their parameter values drawn from 

the same distribution. However, they do not distinguish between cases when a single parameter 

value is to be drawn and applied to multiple timesteps and when separate values from the same 

distribution are to be drawn. The concept is called resampling, and the two specific cases 

mentioned above correspond to ResampTS=NO and ResampTS=YES. 

There are four resampling options, namely for timesteps, hours, days, and work air quality 

district. Each may be set to either YES or NO. If ResampTS=NO and ResampleHours=NO, 

then all timesteps within a block on any day of the simulation will share the same value. 

Timesteps in different blocks have their values drawn from different distributions, so these 

values are never shared. If Resample TS=NO and ResampHours=YES, then only timesteps 

within each hour will share values. If ResampTS=YES, then each timestep in the same block on 

the same day will have its own value drawn, so Ntimestep values will be drawn no matter how 

many blocks there are. In this case the blocks serve only to determine which parent distribution 

is used for each particular hour. The defaults are ResampTS=NO and ResampHours=NO. If the 

Control file variable TimeStepsPerDay is equal to 24 (the APEX default), then ResampTS and 

ResampHours are interchangeable. If TimeStepsPerDay < 24, then the ResampHours flag has 

no meaning and is ignored (because the microconcentrations are only calculated for each 

timestep, which in this case is greater than an hour). 

 The second resampling option is ResampDays. If ResampDays=NO, then the same daily profile 

is used on all days in the same category. If ResampDays=YES, then all days have new sets of 

values drawn for them. The category for days is defined by the combination of day type, season, 

and conditional variables. An example might be all winter weekdays with windows open, if day 

type = weekday and season = winter and condition #1 = (WindowPos==OPEN), assuming these 

terms have been defined appropriately. If ResampDays=NO (which is the default) then all such 

days in the simulation period will share the same set of values. 

The third resampling option is ResampWork. APEX normally generates different parameter 

values for home and work locations. However, there are cases when this is not logical. For 

example, if a car is defined to be a microenvironment and it uses the mass balance method, the 

volume of the car should be the same whether the car is at home or at work. If 

ResampWork=YES, then home and work always draw parameter values independently. If 

ResampWork=NO, then the same values are used for work as for home. Since such cases are 

rare, ResampWork=YES is the default, meaning that the workplace will have its values sampled 

independently of the home. 

To summarize, the default values for ResampTS, ResampHours and ResampDays are NO, and 

for ResampWork it is YES. This means that the default is to draw only two values (one for 

home and one for work) from each distribution listed for that MP and to apply those values 

whenever possible. If a default is to be used then the line may be omitted from the input file, but 

it does not hurt to show the lines anyway for purposes of clarity. 
8.2.4.5

97 

Random Number Seeds 

One of the features of the APEX model is the ability to conduct paired runs by controlling the 

random number seeds. In normal use the model stochastically generates random profiles, selects 

diaries, and generates MP values from distributions. If multiple model runs are to be 

independent then the main RandomSeed value in the Simulation Control input file should be set 

to zero or to different values. If model runs are to be paired, then identical streams of random 

numbers are desired, in which case RandomSeed should be set to the same positive number in 

both runs. 

Creating paired runs in which everything is identical will create results that are identical as well. 

Thus, the usual mode of operation is to have one specific difference between the two runs and 

then see how much effect it has on the results. The difficulty from a programming point of view 

is that it is not sufficient to simply start both runs with the same random number seed. In 

addition, multiple random number streams are required. As an example, suppose one of the 

paired runs contains an extra source term, and there was only one random number stream. The 

first profile in both runs would be the same, as would all random numbers evaluated until values 

are drawn for the new source. From then on the two runs will be drawing random numbers out 

of phase, meaning at different points in the stream. This means that the next profile will differ 

between the two runs. 

In APEX the solution to the problem of getting out of phase is to set up multiple random number 

streams. Then, for example, it is possible to generate the profile variables by sampling from one 

stream while generating sources from another. This ensures that even if the sources differ, the 

same profiles will be generated in both runs, since the random numbers used for the profiles 

always will stay in step. The “extra” random numbers used for the additional source are drawn 

from a separate stream and therefore do not affect the status of any of the other streams. 

In general, paired runs using the same microparameters will stay in phase (even if the definitions 

for these microparameters change). However, if a different number of microparameters are 

defined (if, for example, a different number of sources are used for 2 different runs), then APEX 

will get out of phase. The solution to this is to allow a definition random number seed for each 

MP. 

Each MP has an optional line for setting a RandomSeed specific to that MP. There are two 

choices. If RandomSeed is set to a positive value, then that sets an absolute starting point for the 

stream for that MP that can be set the same in another run. If RandomSeed = 0 (which is the 

default) then the seed is chosen internally. This internal seed is fixed relative to the overall 

model seed as defined in the Simulation Control file, based on the order of the MP definitions. 

Thus, if the first MP defined in the Microenvironment Descriptions input file has RandomSeed 

= 0, then this stream will begin at a fixed offset from the main stream for the model run. There 

are two cases, depending on whether the main seed has a fixed value or is set to zero. If the main 

seed is fixed (as for two paired runs), then the starting seed value for any MP will be the same in 

both runs, provided the MP are in exactly the same order in both runs. However, this is not the 

case unless the run with “extra” MP has them all appear in the input file after the MP that are in 

common to both runs. To avoid this restriction, it is better in paired runs to set each MP to have 

a non-zero random seed of its own. If the main seed is 0 and an MP seed is greater than 0, runs 
can be generated in which: 1) the MP values are reproduced exactly and 2) all other random 

aspects of the model (for example, the profiles) change. 

98 

If an MP has RandomSeed = 0 and the Simulation Control file also has RandomSeed = 0, then 

the MP will have a starting seed that has a fixed offset from a randomly chosen main seed. This 

means that the MP will draw random numbers independently from one run to another. 

In summary there are three cases. If independent, random runs are desired then set the main 

RandomSeed in the Simulation Control file to zero and for each MP either set the RandomSeed 

to zero or simply omit the option. If paired runs are desired and the MP are not altered between 

runs, then the main seed in the Simulation Control file should be nonzero and it does not matter 

whether the seeds for each MP are zero or not (although if they are not zero the seeds should be 

the same in both runs). If paired runs involve changes to the list of MP then all seeds should be 

set to positive values, matching seeds in the MP common to both runs. 

A limitation of using the RandomSeed keyword is that it will produce the same stream of random 

numbers (and thus the same set of hourly microparameter samples) for each person in the 

simulation. 

8.2.4.6 Source Strength Specification 

As described in the sections on the MASSBAL and FACTORS methods (Sections 8.2.1 and 

8.2.3), APEX allows two types of sources to be defined. ESource terms are emission sources 

expressed in units of micrograms per hour. CSource terms are sources expressed in 

concentration units of μg/m3

 (or ppm). ESource and CSource strengths can optionally be 

specified as the product of two or more values drawn from different distributions. 

As an example, an ESource term representing emissions from gas stoves can be constructed as 

the product of three terms: a binary switch for Use/Non-use for each timestep, a duration of 

usage term, and an emission rate per minute of usage. One advantage of separating this term into 

three pieces is that different rules for the time and area mappings and the resampling rate can be 

defined for each of the three pieces. 

Each source in APEX, meaning each MP of type ES or CS, may be assigned an optional source 

number. This is done by adding a line to the MP definition as inExhibit 8-3: 

Micro number = 4 

Parameter Type = ES 

Source number = 2 

Block DType Season Area C1 C2 C3 Shape Par1 Par2 Par3 Par4 LTrunc UTrunc ResampOut 

1 1 1 1 1 1 1 Lognormal 1000 2 . . 100 10000 Y 

Exhibit 8-4. Use of Source Number in MP Definition 

For clarity, the source number should appear right after the parameter type. It cannot appear 

earlier nor can it appear after the header line starting with “Block”. It only applies to types ES or 

CS and is not relevant for other parameter types. If the source number is omitted then it is 

assumed to be zero, which is the catch-all category for additive source terms. 

All MP of type ES or CS that share the same microenvironment number and source number are 

evaluated separately for all timesteps according to their own rules, then the results are multiplied 
together on an timestep basis. For example, if another MP has the description shown in 

99 

Exhibit 

8-5, then both this MP and the previous one are evaluated for each timestep and then the results 

are multiplied together, timestep by timestep. 

Micro number = 4 

Parameter Type= ES 

Source number = 2 

Hours – Block = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 1 1 

Block DType Season Area C1 C2 C3 Shape Par1 Par2 Par3 Par4 LTrunc UTrunc ResampOut 

1 1 1 1 1 1 1 Normal 10 10 . . 0 60 Y 

2 1 1 1 1 1 1 Point 45 . . . . . . 

Exhibit 8-5. Second MP Definition with Source Number 2. 

Since the first MP was not resampled, only one value is generated per person and that value 

remains constant over the simulation. The second MP is resampled every hour (although the 

timesteps using the Point distribution will all return the same value). 

It is possible to have a large number of terms sharing the same microenvironment and source 

numbers, in which case all terms are evaluated separately and the timestep results are multiplied. 

Note that all terms sharing the same microenvironment and nonzero source numbers must also 

share the same parameter type; one cannot mix ES and CS types since it does not make sense to 

multiply them together. APEX will generate an error message if this is attempted. It is possible 

for some sources to be ES while others are CS, even in the same microenvironment, as long as 

they are not assigned the same nonzero source numbers. 

Once the product is evaluated, the result is treated exactly the same as any additive sources for 

that microenvironment. All ESource terms are added together timestep by timestep, whether 

each resulted from a product or was a separate term by itself. The same applies to all CSource 

terms in the same microenvironment. In effect there is no change at all to either the MASSBAL 

or the FACTORS equations, there is simply a change in how the ESource and CSource terms are 

determined. 

When defining product terms, a line must be added to the Simulation Control input file 

indicating the largest source number used in the run for each pollutant. This line has the 

keyword #SOURCES and it might appear as in the pollutant parameters section of the 

Simulation Control file as shown in Exhibit 8-6. 

 Pollutant = CO 

 DoDose = YES 

 InputUnits = ug/m3 

 OutputUnits = ug/m3 

 #Sources = 3 

Exhibit 8-6. Use of #sources Setting in the Pollutant Parameters section of the Simulation 

Control File. 

This value reported here (3 in this case) is echoed to the Log file after “#microenvironments” and 

it is called “#Enumerated sources”. Actually, like #microenvironments, this value is only used to 

allocate array space, and APEX will run correctly as long as #sources is large enough to 
accommodate the source numbers used in the Microenvironment Descriptions input file. If 

#sources is larger than is needed, no error occurs although job execution will be slightly less 

efficient. This line can only be omitted from the Simulation Control file if no source numbers 

are assigned to any MP. 

100 

Not all sources need be expressed as products. These sources can either be left without source 

numbers or can explicitly have source number of zero, or may even have a positive source 

number. If there is only one MP with a given microenvironment number and source number, 

then it essentially constitutes a product with only one term. If only source numbers = 0 are used 

(i.e. only additive terms are defined), then #Sources may be set to 0 in the control file or omitted. 

8.2.4.7 Specification of Distribution Data 

The number of distributions that the user must supply for each MP is the product of these 

numbers: 

 NDistributions = Nblocks x Ndaytypes x Nseasons * Nareas x NC1 * NC2 * NC3 (8-16) 

Here NC1-NC3 are the number of possible responses for conditional variables #1-#3. If a 

conditional variable is not used, then it has one possible value (its index is always equal to 1). 

The number of possible responses varies from one conditional variable to another. All preset 

Conditional Variables have two values. Population Category has as many values as population 

files are defined in the Control file. For other Conditional Variables the number is determined 

from the definition supplied by the user in the Profile Functions (Distributions) input file. 

Each distribution occupies one line in the Microenvironment Descriptions input file. Every 

combination of the seven indices must have a distribution defined, even if that specific 

combination never occurs during the simulation. For example, if a winter season exists then it 

must have a set of distributions defined, even if the simulation period only covers the summer. 

The reason is that the distributions are stored in an array with room for all possible combinations 

of index values, and this array is checked once for gaps (missing data) before the first profile is 

begun. This is more efficient than checking to see if a distribution exists every time it is called, 

as a model run can contain millions or even billions of calls to distributions. The price is that 

distributions that ultimately are never called must still exist in the array. 

The user does not need to number the distributions, this is done internally by the program. The 

distributions are assigned index numbers in standard Fortran order (the block index changes 

fastest, and Condition #3 changes slowest). Thus, distribution#1 is for (1,1,1,1,1,1,1), and if 

there is more than one block then distribution#2 is for (2,1,1,1,1,1,1), etc. In the input file the 

distributions can appear in any order, but the standard order is preferred for consistency. 

Each line describing a distribution contains the following information First, the seven indices 

are listed; block, day type, season, area, c1, c2, and c3. The seven indices must all appear 

explicitly in the set order. Any superfluous indices must be given a value of one. Thus if a 

conditional variable such as c3 is not used then the c3 index number is 1 for all distributions for 

that MP. 
After the seven indices comes the distribution definition in standard APEX distribution format 

(Section 

101 

3.1). Any of the APEX distributions can be used; the available shapes and their 

parameters are given in Table 3.1. 
102 

CHAPTER 9. CALCULATING EXPOSURES 

Below is a description of how the microenvironment concentrations and other information are 

used by APEX to estimate exposure (see step 6 in Figure 2-1), and how the model then presents 

and summarizes the exposure results. Exposures are calculated in 

ExposureDoseModule:Exposure. 

9.1 Estimating Exposure 

For inhaled pollutants such as the ones APEX models, exposure is defined as the time integrated 

concentration of the pollutant in the breathing zone of a person. We refer to the concentration to 

which a person is exposed as the exposure concentration. This concentration is assumed to be 

approximately spatially uniform within each microenvironment and also approximately 

temporally uniform for the duration of any one activity event (at most one hour). A time series 

of exposure concentrations can be constructed by following the sequence of microenvironments 

and locations (“Home,” “Work,” or “Other”) visited according to the composite activity dairy 

assembled for the target profile. 

As an example, assume the activity diary indicates that the first 40 minutes of the simulation are 

spent in microenvironment #3 (“Home”), the next 20 minutes in microenvironment #2 (“Other”), 

and the next 60 minutes in microenvironment #5 (“Work”), and so on. Then the exposure time 

series has its first 40 minutes at the concentration for hour 1 in microenvironment #3 in location 

“Home,” the next 20 minutes at the concentration for hour 1 in microenvironment #2 for location 

“Other,” and the next 60 minutes at the concentration for hour 2 in microenvironment #5 for 

location “Work,” and so on. The exposure itself depends neither on the activities that the person 

is performing nor on any personal physiological properties. 

The user may select the units for reporting the exposure output. Either ppm or μg/m3

 may be 

chosen. This applies both to concentration and to exposure. It also applies to the levels used as 

cutpoints in the various exposure tables. The parameter OutputUnits in the Simulation Control

file controls this; if set to PPM (actually, to anything beginning with “P”) then parts per million 

(ppm) are used, otherwise micrograms per cubic meter (μg/m3

) are used. 

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

experiences during the simulation period. APEX calculates the exposure by identifying the 

concentrations in the microenvironments visited by the person according to the composite 

activity diary. In this manner, a time-series of event exposures are found. Then, the timestep 

exposure concentration at any clock hour during the simulation period is calculated using the 

following equation: 

()() ( )

T

tC

C

N

1j

jjtimestep

i

∑= = (9-1) 

where: 
103 

Ci = Timestep exposure concentration at clock hour i of the simulation 

period (μg/m3

 or ppm) 

N = Number of events (i.e., microenvironments visited) in timestep i of 

the simulation period. 

Ctimestep (j) = Timestep concentration in microenvironment j (μg/m3 or ppm) 

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

T = Length of timestep (minutes) 

From the timestep exposures, APEX calculates time series of 1-hour, 8-hour and daily average 

exposures that a simulated individual would experience during the simulation period. APEX then 

statistically summarizes and tabulates the timestep, hourly, 8-hour, and daily exposures. Note 

that if the APEX timestep is greater than an hour, the 1-hour and 8-hour exposures are not 

calculated and the corresponding tables are not produced. Exposures are calculated 

independently for all pollutants in the simulation. 

9.2 Exposure Summary Statistics 

The exposure time series provides a wealth of detail on the exposure experienced by each profile. 

However, it is difficult to analyze since the number of events differs for each profile and even the 

number of events on any given calendar day is unpredictable. Also, a model run may consist of 

thousands of profiles, so it is not practical to retain the exposure time series for all profiles in 

memory. For output tables and for analysis, summaries of the exposure time series are required. 

Exposure summary statistics are calculated for each pollutant in the simulation, and are written 

to pollutant-specific output files: the Micro Summary file, the Micro Results file, and the Tables

file. Each exposure metric in this section is thus calculated for each pollutant, and the Control

file keywords listed below are pollutant-specific. (See Volume I). 

The first step in summarizing exposure is to calculate the time series of event-level, timesteplevel, and hourly average exposures for the profile. The event exposures for all pollutants are 

written to the Events output file (if the Simulation Control file setting EventsOut = YES), while 

the timestep values are written to the Timestep output file (if the Simulation Control file setting 

TimestepOut = YES). Daily averages and maxima for each pollutant can be written to the Daily

output file as well. The timestep values are used to derive most of the other exposure summary 

statistics. 

There are two exposure time series reported on an hourly basis, namely the series of 1-hour 

averages and running eight hour averages. These are stored in other vectors. For the first seven 

hours of the simulation the averages are taken over fewer than eight values, otherwise it is 

always the current hour and the previous seven hours. These hours may cross day, month, or 

even yearly boundaries. The 1-hour and 8-hour averages are not calculated for timesteps greater 

than 1 hour (ie. when the Control file variable TimestepsPerDay is less than 24). 

There are three exposure statistics calculated on a daily basis. The first is the daily average 

exposure or DAvgExp. This is this arithmetic mean of the 24 values of hourly exposures that fall 

on a given calendar day. Note that all days contain 24 hours in APEX; the effect of Daylight 

Savings Time is removed from the model. The daily average exposure is then binned into levels 
according to the cutpoints provided by the user in the Simulation Control file. For example, the 

input line 

DAvgExp = 2, 5, 8, 12, 20 

indicates that the first bin for daily average exposure extends from 0.0 to 2.0 (ppm or μg/m3

), 

and the second bin from 2.0 to 5.0, et cetera. The final or sixth bin in this example contains all 

values over 20.0. The number of days at each level is recorded for each profile. 

The second daily exposure statistic is the maximum timestep average for each calendar day, or 

DMTSExp in the code (for Daily Maximum Timestep Exposure). It is the highest of the 

timestep values on each day. Like DAvgExp, these are also converted to bins or levels using 

cutpoints from the Simulation Control input file. The number of days at each level is recorded 

for each profile. 

The third daily exposure statistic is the maximum 1-hour average for each calendar day, or 

DM1HExp in the code (for Daily Maximum 1-Hour Exposure). It is the highest of the 24 hourly 

values on each day. Like DAvgExp, these are also converted to bins or levels using cutpoints 

from the Simulation Control input file. The number of days at each level is recorded for each 

profile. 

The final daily summary statistic for exposure is DM8HExp which is the Daily Maximum 8-

Hour Exposure. It is the largest of the 24 8-hour running averages for each calendar day. As for 

the other daily statistics, it is also binned into levels and recorded for each profile. 

The average exposure over the entire simulation period is also calculated. As for the daily 

summary statistics, the average exposure is binned using the cutpoints designated in the 

Simulation Control input file by SAvgExp. 

In addition to the exposure statistics described above, there are a few others that are derived 

directly from the event-based exposure time series. The variable TimeExp represents the 

number of minutes spent in each bin in each micro, based not on hourly averages but on the 

original event exposures. Again, the cutpoints for the TimeExp bins are provided by the user in 

the Simulation Control input file. 

The user can also set a threshold exposure level in the Simulation Control file. This variable is 

called AlertThresh. If the exposure time series exceeds AlertThresh for any event then the 

following three things occur. First, the count of high exposure events for this profile is 

incremented by one. Second, the total duration over the threshold exposure is incremented by 

the duration of this event. Third, the exposure is checked to see if it exceeds the maximum 

exposure previously experienced by this profile. These results are reported in the Log file for the 

model run for each profile that exceeds the threshold. 

9.3 Exposure Summary Tables 

APEX writes out up to 130 different exposure summary tables for the statistics described above. 

The content and interpretation of these tables (including examples) are covered in Volume I. 

104 
There are 11 basic types of tables; the tables are written to the Tables files (one for each 

pollutant) and optionally the Log file in ExposureDoseModule:Output: 

105 

1. Minutes in each Exposure Interval by Microenvironment (TimeExp) 

2. Minutes at or above each Exposure Level by Microenvironment (TimeExp) 

3. Person-Days at or above each Daily Maximum 1-Hour Exposure Level (DM1HExp) 

4. Person-Days at or above each Daily Maximum 8-Hour Exposure Level (DM8HExp) 

5. Person-days at or above each Daily Maximum Timestep Exposure Level (DMTSExp) 

6. Number of Simulated Persons with Multiple Exposures at or above each Daily Maximum 

1-Hour Exposure Level (DM1HExp) 

7. Number of Simulated Persons with Multiple Exposures at or above each Daily Maximum 

8-Hour Exposure Level (DM8HExp) 

8. Number of Simulated Persons with Multiple Exposures at or above each Daily Maximum 

Timestep Exposure Level (DMTSExp) 

9. Number of Simulated Persons with Multiple Exceedances (in the Simulation) of the 

Threshold Timestep Exposure Levels (TSExp). 

10. Person-Days at or above each Daily Average Exposure Level (DAvgExp) 

11. Persons at or above each Overall Average Exposure Level (SAvgExp) 

The levels written to each table are given by the Simulation Control file keywords in 

parentheses. The definition of terms in the titles of these tables are as follows: 

• Person-day: A single simulated day for one simulated individual. A 100-day simulation 

of 10 persons contains 1000 person-days, as does a single-day simulation of 1000 

persons. APEX in general counts exposures in Person-days. Multiple exposures (at a 

single level) during single day are counted as one Person-day of exposure. 

• Multiple Exposures: Multiple exposures for the same person on different simulation 

days. This term refers to multiple person-days of exposure in a simulation corresponding 

to the same profile. Multiple exposures (at a single level) during single day are counted as 

one Person-day of exposure. 

• Multiple Exceedances: Multiple exposures for the same person on different timesteps of 

the simulation. Multiple exposures during the same day (at a single level) DO count as 

different exceedances. 

Table types 1, 2, 10, and 11 are generated only once, for the entire population. Table types 3 to 9 

are generated for six population subgroups, under three exertion levels. . The six population 

subgroups are as follows: 

1. All Persons. The table statistics are based on the entire population. 

2. Children. The table statistics are based on the population of children, as defined by the age 

range given by the Control file settings ChildMin and ChildMax. 
3. Active Persons. The table statistics are based on the population of people having a median 

Physical Activity Index (PAI, mean MET) over the whole simulation period that exceeds the 

value designated by the Control file setting ActivePAI. 

106 

4. Active Children. The table statistics are based on the population of active children, as 

determined by the Control file settings ChildMin, ChildMax, and ActivePAI. 

5. Ill Persons. The table statistics are based on the population of ill people. The population is 

determined by the probabilities given in the Prevalence file. This population is only considered 

if the input variable Disease is set in the Control file. 

6. Ill Children. The table statistics are based on the population of ill people. The population is 

determined by the probabilities given in the Prevalence file and the Control file settings 

ChildMin and ChildMax. This population is only considered if the input variable Disease is set 

in the Control file. 

The three exertion levels are: 

1. All Exertion Conditions. The table statistics are based on exposures experienced by the 

population subgroup under any ventilatory conditions. 

2. Moderate Exertion. The table statistics are based on exposures experienced by the 

population subgroup only during periods in which their average equivalent ventilation rate 

(EVR) is in the “moderate” range. The period of time during which EVR is averaged is either 1 

hours or 8 hours, based on the table being generated. The “moderate” EVR ranges are defined 

by the Simulation Control file settings ModEVR1 (for timestep exposures), ModEVR1 (for 1-

hour exposures) and ModEVR8 (for 8-hour exposures). An individual’s EVR is in the moderate 

range if it is greater than or equal to the ModEVR# setting and less than the HeavyEVR# setting 

for the exposure period. 

3. Heavy Exertion. The table statistics are based on exposures experienced by the population 

subgroup only during periods in which their average equivalent ventilation rate (EVR) is in the 

“heavy” range. The period of time during which EVR is averaged is either 1 hours or 8 hours, 

based on the table being generated. The “heavy” EVR ranges are defined by the Simulation 

Control file settings HeavyEVRTS (for timestep exposures), HeavyEVR1 (for 1-hour 

exposures) and HeavyEVR8 (for 8-hour exposures). An individual’s EVR is in the heavy range 

if it is greater than or equal to the HeavyEVR# setting for the exposure period. 

The exertion level statistics are calculated in the following manner: For each day in the 

simulation, the mean EVR level during every timestep, one hour, and running eight hour time 

period is calculated. If the mean timestep, 1-hour or 8-hour EVR is higher then the EVR levels 

indicated (in the Simulation Control file) for moderate or heavy exertion, then the exposure 

during the same time period is compared with the levels given in the Simulation Control file, and 

the statistics and tables are updated if the exposure exceeds the level. 

NOTE: Many of the tables can include statistics at the 0.0 exposure level, if it is indicated on the 

Simulation Control file. This can be used to obtain some useful statistics (such as total final 

study area of the subpopulation population), since all persons will have exposures equal to or 

exceeding 0.0 level exposures on all person-days. However, use caution in examining these 
“0.0” level statistics in the case of the exertion-level tables. If a simulated person has no 

timestep, 1-hour or 8-hour periods at Moderate or Heavy EVR, then they will NOT have an 

exposure in that table for the 0.0 level, and the 0.0 level statistics will not correspond to the 

entire subpopulation. 

107 
108 

CHAPTER 10. CALCULATING DOSE 

APEX contains algorithms for estimating pollutant doses. The term “dose” refers to some 

measure of the amount of pollutant in the body of the target person. The situation is not as clear 

as for exposure since there are numerous specific definitions of dose that are used in various 

contexts. For an airborne pollutant, dose could refer to the amount inhaled, or the amount 

currently in the lungs, or the amount crossing from the lungs to the body, or the total amount in 

the body, or the total in some specific target organ, or a number of other things. Dose may be 

more useful or accurate than exposure for evaluating the effects of air pollutants because it 

accounts better for differences in pollutant uptake resulting from (1) the variation in physiology 

and activities across populations and (2) the variation in physiological responses to activities 

within an individual. In APEX, dose is generally defined at the amount inhaled. APEX 

contains a special algorithm for the pollutant CO, in which the model calculates the percent of 

carboxyhemoglobin (%COHb) in the blood. Carboxyhemoglobin is hemoglobin that has carbon 

monoxide instead of the normal oxygen bound to it. In addition, APEX contains algorithms to 

estimate the deposited lung dose in the case of particulate matter (PM). When the APEX model 

is extended to other pollutants, it will likely require the development of specific dose algorithms 

for each new pollutant, or at least for each class of pollutant. 

The simple algorithm for calculating inhaled dose is discussed in the next section, followed by 

the algorithm for the %COHb calculation. The final topic relating to dose is the explanation of 

the summary statistics for reporting dose. Doses are calculated in ExposureDoseModule:Dose.

10.1 Inhaled Dose Calculation 

Currently, for all pollutants other than CO, APEX calculated inhaled dose. Inhaled dose is 

simply the amount of pollutant inhaled over the course of a specified time period. In APEX, 

inhaled dose for each timestep is calculated as 

 (10-1) = ei CVD i

where 

Ci = Timestep exposure concentration at timestep hour i of the simulation 

period (μg/m3

 or ppm) 

 Ve = Expired ventilation rate (ml/min) 

The calculation of the expired ventilation rate Ve is discussed in Section 7.3. The exposure Ci is 

discussed in Section 9.1. From the timestep doses, APEX calculates time series of 1-hour, 8-

hour and daily average dose that a simulated individual would experience during the simulation 

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

Note that if the APEX timestep is greater than an hour, the 1-hour and 8-hour dose are not 

calculated and the corresponding tables are not produced. Doses are calculated independently 

for all pollutants in the simulation. 
109 

10.2 Carboxyhemoglobin (COHb) Calculation 

The calculation of CO dose is complex. It starts with the exposure time series, which indicates 

the pollutant concentration in the inhaled air at each moment in time. It also requires the 

ventilation rate which is activity dependent, knowledge of a number of physiological parameters, 

and the %COHb level depends not only on current conditions but on recent history as well. The 

discussion of physiological parameters is in the chapter on personal profiles. In APEX, dose is 

the delivered dose of CO as measured by the biotransformation product carboxyhemoglobin 

(COHb)—specifically %COHb—in the blood. The estimated %COHb, in addition to being a 

more refined measure of exposure compared to exposure concentration, is useful for comparing 

to health-based benchmarks of %COHb. A normal carboxyhemoglobin level is less than two 

percent for non-smokers. Overt signs of toxic effects usually appear at carboxyhemoglobin 

levels of 15 to 20 percent, and a level of 25 percent is an index of severe poisoning, which may 

lead to sudden loss of consciousness. 

Conceptually, APEX uses a number of factors, in particular a time series estimate of alveolar 

ventilation rate Va (which is activity and physiology dependent) and a time-series estimate of 

exposure (which indicates the pollutant concentration in the inhaled air for specific moments in 

time), to calculate %COHb. The ventilation rate algorithm is discussed in Section 7.3 and the 

%COHb algorithm is discussed in the following subsections. For other factors and additional 

detail, see Johnson (2002). 

The %COHb calculation in APEX uses the time series for exposure to CO and the time series for 

alveolar ventilation rate, VA, as inputs (among other factors). The dose calculation is based on 

the solution to the non-linear Coburn, Forster, Kane (CFK) equation, as detailed in Johnson 

(2002). As pointed out by that report, the CFK equation does not have an explicit solution, so an 

iterative solution or approximation is needed to calculate the %COHb. An iterative solution, 

however, was determined to be unsuitable because of the model execution time necessary (a 

typical model run of one calendar year represents roughly 14,000 events per person and several 

thousand people, or tens of millions of diary events). Therefore, the CFK equation is solved 

using a modified Taylor’s series method in which the event duration is restricted in time (if 

necessary) to ensure convergence with only a few terms. This method avoids the dangers of 

non-convergence that arise in some other methods. 

As the mathematical derivation in the above report is very detailed, only the main results are 

presented here. First, it should be noted that the literature discusses two forms of the CFK 

equation, namely a linear and a non-linear form. The linear form itself is an approximation that 

allows an explicit solution, but is not accurate under all conditions. The non-linear form is 

considered to be more correct and is the one being discussed here. 

Restricting %COHb(t) to between 0 and 100 (percent), the CFK equation takes the form of the 

following differential equation: 
110 

100 %COHb(t)

%COHb(t) CC(t)b%COH 10 − ′ ×−= (10-2) 

where C0 and C1 are constants over the duration of one event that depend on physical and 

physiological parameters, including Va and the CO exposure. C0 is given by 

BloodBRH

B

P Endgn C

0

CO

0 +

+ = (10-3) 

where Endgn and Blood are physiological profile variables (Section 5.3). PCO is the partial 

pressure of CO (torr) 

 (10-4) -6

CO PP gases ×= Exposure ×10

where Exposure is the event CO exposure concentration and Pgases is the partial pressure (torr) of 

dry gases at the study altitude (EPA, 1978): 

P 760e 47 (10-5) 0.0000386Altitude

gases = − −

where altitude is in feet. The variable RHB0 is the total reduced blood hemoglobin level (ml O2 

or ml CO per ml blood), adjusted for altitude (as in EPA, 1978) 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ ×××= +

100

2.76e RHB 0.011.39 0.995 1Hmglb

0.0001429Altitude

0 (10-6) 

where Hmglb is the profile variable for hemoglobin density. The factor B is given by 

a

gases

V

P

DIFF

1 B += (10-7) 

Va is the event alveolar ventilation (see Section 7.3) and DIFF is lung CO diffusivity 

(ml/min/torr) adjusted for ventilation rate 

DiffDIFF += 0.000845Va − 5.7 (10-8) 

where Diff is the CO diffusivity profile variable (which corresponds to a baseline ventilation). 

The constant C1 is given by 

69.76 RHB Blood

PO0.321 C

0

2

1 ××

+ × = (10-9) 

where P02 is the partial pressure of oxygen in the lungs (torr) 

PO2 = 0.209Pgases − 49 (10-10) 

See Johnson et al. (2002) for a detailed derivation of the above equations for C1 and C2. 
111 

Time zero represents the start of the current event. The concentration %COHb(0) (at time zero) 

is assumed to be known. The first derivative, %COHb′(0), can easily be found from the above 

equation. The solution %COHb(t) is a smoothly varying function of time without sudden 

discontinuities or changes in slope. It therefore can be expanded in a Taylor’s series about t = 0, 

which should converge fairly rapidly. One simplification is to rescale the time variable to the 

unitless parameter z: 

( )

( ) 00

10

DD100

tCC

z ××

×+ = (10-11) 

where 

100

1 %COHb(0) D0

− = (10-12) 

The Taylor’s series up to the fourth order term is: 

+

××× = −××+

2

DzDA100 (z)T %COHb(0) DzD100

2

01

4 0

( ) +

×−××××

6

z2DADDA100 3

01 1

( )

24

z6D8DAADDA100 42

1

2

01 1 ×+−×××× (10-13) 

where 

10

1

1 CC

C A

+ = (10-14) 

 (10-15) −= ADD 10

For typical values for the constants C0, C1, and %COHb(0), convergence occurs for z<1. For z 

values below this limit but still close to one, the convergence is slow, so the terms beyond fourth 

order would be needed if high accuracy were desired. It is found that z<1 generally corresponds 

to %COHb(0) values below 40 to 50% for one-hour events. 

The z value is proportional to t. In APEX, an event can have a duration of no more than one 

hour. For one hour events there are conditions where z is close to one and convergence of the 

Taylor’s series may require more than four terms. However, it is not necessary to evaluate the 

entire hour in one step. By dividing the event into shorter subevents, each will have a smaller z 

value. For example, if a one-hour activity diary event has initial conditions that correspond to 

z=0.9, then by dividing this into three 20 minute subevents, each will have a z value around 0.3. 

Actually, the first subevent will have exactly z=0.3. The others will be slightly different as the 

initial conditions for those subevents will have changed slightly. In practice, a dimensionless 
subevent duration is used, and all the subevents have equivalent length. An accumulated dose is 

calculated as the running sum of the average %COHb level over the subevents. At the end of all 

subevents, the average dose is this accumulated dose divided by the number of subevents while 

the final value of the dose is simply the final value of COHb itself. These values are saved and 

the next diary event is processed. 

112 

th 

 each filter. 

10.3 Calculating PM Dose 

In APEX PM dose is modeled as the mass of PM depositing in the entire respiratory system, 

including the extrathoracic regions (mouth, nose, and oropharynx) and the lungs. The PM dose 

algorithm was developed from the empirical lung deposition equations of the International 

Commission on Radiological Protection’s Human Respiratory Tract Model for Radiological 

Protection (ICRP 1994). 

The algorithm calculates the deposition fraction (f) in each of 9 filters (see Figure 10.1) and 

determines the PM mass deposited in each for each event. The 9 filters correspond to the 

following regions of the respiratory system: 1. Nose (inhalation, fN) 2. Oropharynx (inhalation, 

fO) 3. Tracheobronchi (inhalation, fTB,i) 4. Bronchioles (inhalation, fB), 5. Alveoli (fA), 6.

Bronchioles (exhalation, fB), 7. Tracheobronchi (exhalation, fTB,e) 8. Oropharynx (exhalation, 

fO) and 9. Nose (exhalation, fN). The f values determine the fraction of the particle mass 

entering the region that deposits. Only the fraction in the Tracheobronchial filters differs for 

inhalation versus exhalation, for the other filters the value of the fraction is the same in bo

cases. Deposition via both aerodynamic and thermodynamic (diffusive) mechanisms are 

estimated for
113 

fN

fO

fTB,e

fB

Inhaled 

Particles

Exhaled 

Particles

fA

fN

fO

fTB,i

fB

Figure 10.1 Structure of the ICRP Deposition Model. 

The fractions f and the resulting deposited doses are calculated for each particle size considered. 

The size-specific mass are summed to get the mass deposited in each filter. The deposited filter 

masses are then combined into 4 deposited masses corresponding to total PM dose in the entire 

respiratory system and in the extrathoracic (ET, nose + oropharynx), tracheobronchial (TB), and 

pulmonary (Pulm, bronchiole + alveoli) regions. 

10.3.1 Particle Sizes, Inhalability, and Diffusion Coefficient 

The particle size used by the ICRP algorithm is the aerodynamic diameter. Aerodynamic 

diameter (dae) is the property of particles measured by the majority of particle samplers, and the 

EPA designations of PM2.5 and PM10 are based on aerodynamic diameter. The aerodynamic 

diameter is provided to the model in the Control file using the pollutant-specific keyword Size

(see Volume I). 

Particle inhalability is defined as the fraction of the ambient particles that are inhaled. This 

fraction is calculated as: 

)1]d10[7.60.5(11f 2 1

iae,

4

iinh,

− − ×−−= + (10.16) 

The particle diffusion coefficient Di is also required to calculate the deposition fractions. Di is 

calculated using Equation 10.17: 
114 

ith,

thC

i

π d3

)kT(dC D i

μ = (cm2 s

-1) (10.17) 

where k is the Boltzmann's constant 1.38 x 10-16 g cm2 s-1 K-1

dth,i is an equivalent thermodynamic diameter of particle size i 

T is absolute temperature (Kelvin) 

 μ is the absolute viscosity of air (1.82 X 10-4 g cm-1 s-1) 

and CC is the Cunningham correction factor, given in Equation 10.18: 

)] 2λ

d1.1

[1.257 exp(0.4 d

2λ 1)(dC ith,

ith,

ith,C

∗

+= + − (10.18) 

where λ is the mean free path of air, 6.5 X 10-6 cm. 

The thermodynamic diameter is calculated from the aerodynamic diameter: 

)(dC

)(dC

1.5

ρ d

ith,c

iae,c

ith, = (microns) (10.19) 

where ρ is the particle density in g/cm3

. The value of dth,i is found by recursively solving this 

equation using an initial guess of dae,i(ρ)

-1/2. 

10.3.2 The ICRP Deposition Equations 

As described above, the ICRP model considers the respiratory system as a system of 9 filters 

corresponding to the particles deposited in the nose (N), oropharynx (O), trachea/bronchi (TB), 

bronchioles (B), and alveoli (A) during inhalation and exhalation. The ICRP equations considers 

fractions for both aerodynamic (ae) and thermodynamic (th) deposition processes in each region. 

These fractions in each filter j are exponential functions of 3 empirical coefficients a, R, and p, as 

shown in Equations 10.20 and 10.21. 

Aerodynamic Deposition Fraction

)Raexp(1f p jae,

jae, −−= jae,jae, (10.20)

Thermodynamic Deposition Fraction 

)Raexp(1f p jth,

jth, −−= jth,jth, (10.21)
There is an a, R, and p coefficient for each filter for both aerodynamic and thermodynamic 

mechanisms. The coefficients may be constant or may be functions of parameters describing the 

respiratory system physiology and activity level of the individual being modeled. The 

coefficients, which may also be a function of the mode of breathing (nasal or oral), are given in 

115 

Table 10.1. 

Table 10.1 The values of a, R, and P for each filter for oral and nasal breathing 

Nose 

(N) 

Oropharynx 

(O) 

Tracheobronchial 

(TB) 

Bronchioles 

(B) 

Alveoli 

(A) 

Aerodynamic Deposition 

a 0.0003 nose breathing: 

0.000055 

oral breathing: 

0.00011 

inhalation: 

0.00000408 

exhalation: 

0.00000204 

0.1147 0.146S3

0.98

R 

d2 •

Vn(S1)

3 nose breathing: 

d2 •

Vn(S1)

3 

oral breathing: 

d2

(

•

V)

0.6(VT)-0.2(S1)1.4

d2 •

V(S1)

2.3 

25.-0

B 1.5 t + B dt0.056 d2

tA

P 1 nose breathing: 

1.17 

oral breathing: 

1.4 

1.152 1.173 0.6495 

Thermodynamic Deposition 

a 18 nose breathing: 

15.1 

oral breathing: 

9 

22.02(S1)

1.24 ×

100e-[1 ]

2

0.9 10 )] d

10 − (100log[ +

-76.8+167S2

0.65 170+103S32.13

R 

D •

VnS1

-0.25 nose breathing: 

D •

VnS1

-0.25 

oral breathing: 

d2

(

•

V)

0.6(VT)-0.2(S1)1.4

DtTB DtB DtA

p 0.5 nose breathing: 

0.538 

oral breathing: 

0.5 

0.6391 0.5676 0.6101 

As indicated in the table, several of the a, R, and P coefficients are a function of a number of 

physiological variables, including lung volumes, inspiratory flow rates, and residence times. 

These are described below. 

10.3.2.1 Lung Volumes and Age Scaling Factors 

The ICRP Publication provides reference values for the required lung volumes as a function of 

subject age and gender. The volumes are: (1) the dead spaces for the entire lung (Vd), and for 

the ET, TB, and B regions (Vd,ET, Vd,TB, Vd,B) and (2) the functional residual capacity (FRC). 

The ICRP model also makes use of three scaling factors to adjust some of the a and R mo

coefficients as a function of age. Physiologically, these factors represent ratios of specific 

airways of a modeled person to those of a reference adult male. S

del 

1 gives the ratio for the 
trachea, S

116 

n of the form: 

2 for the 9th airway generation, and S3 for the 16th airway generation. Both the 

volumes and the scaling factors are modeled in APEX based on the reference values, using an 

equatio

 P=Ah2+Bh+C (10.22) 

The variable P is the volume or scaling factor of interest and h is the individual’s height (in cm). 

The values of the A,B,C coefficients for the different parameters for males and females were 

calculated by fitting eq 10.22 to the ICRP parameters; they are given in Table 10.2. 

Table 10.2 Coefficients for the Lung Volumes and Scaling Factors 

A B C 

Volumes 

Male 

 FRC 0.0002 -0.0279 1.0353 

 Vd 0.0078 -0.7135 29.316 

 Vd,ET 0.0031 -0.3175 10.907 

 Vd,TB 0.0026 -0.2392 9.7143 

 Vd,B 0.0023 -0.2119 11.375 

Female 

 FRC 0.0002 -0.0265 0.96 

 Vd 0.0079 -0.7403 30.381 

 Vd,ET 0.0029 -0.2861 9.5306 

 Vd,TB 0.0022 -0.1523 5.9635 

 Vd,B 0.0029 -0.3225 16.098 

Scaling Factors

Male 

 S1 1.1354E-04 -4.0700E-02 4.6711 

 S2 2.3020E-05 -1.1168E-02 2.2567 

 S3 7.8360E-05 -3.2100E-02 4.2381 
117 

Female 

 S1 1.2800E-04 -4.3542E-02 4.7975 

 S2 2.3200E-05 1.1225E-02 2.2597 

 S3 8.0500E-05 -3.2543E-02 4.2585 

10.3.2.2 Tidal Volume and Activity Level 

Tidal volumes (Vt) were calculated as a function of age, gender, and activity level. The starting 

point for the Vt calculations are the ICRP reference values for men and women of reference ages 

for four different activity levels: sleep, sitting, light exercise, and heavy exercise. Other ages are 

interpolated from the values at the reference ages. After age 30, the values are assumed to be 

constant with increasing age. The correct Vt for each event is determined as a function of age, 

gender, and activity level. Activity level is determined by the event METS values for the 

individual being studied. Activity level was based on normalized METS (M), defined in 

Equation 10.23. 

METSmax -1

1-METS M = (10.23) 

METSmax is the maximum obtainable MET value for the person. If M was less than or equal to 

0, then activity level was assumed to be “sleep.” If M was greater than 0, then the activity level 

was assigned as follows: 

M ≤ 0.333 : activity level = sitting 

0.333 < M ≤ 0.667 : activity level = light exercise 

M > 0.667 : activity level = heavy exercise 

10.3.2.3 Inspiratory Ventilation 

Several of the model parameters are a function of the inspiratory ventilation. This flow rate was 

calculated as 

e

.

= V2V (ml/s) (10.24) 

where Ve is the exhaled ventilation rate. 
10.3.2.4

118 

Residence Times 

The residence times in the lungs are required to calculate deposition via diffusive mechanisms. 

Residence times are a function of the flow rate, the dead spaces, FRC, and Vt. The residence 

times in the tracheobronchial, bronchial, and alveolar regions are given by: 

⎟

⎠

⎞ ⎜

⎝

⎛ +=

FRC

0.5V 1

V

V

t tTBd, t

TB  (s) (10.25) 

⎟

⎠

⎞ ⎜

⎝

⎛ +=

FRC

0.5V 1

V

V

t Bd, t

B  (10.26) 

[ ]

V

FRC

V 1VVVV

t

t

ETd,t Bd,TBd,

A 

⎟

⎠

⎞ ⎜

⎝

⎛ ++−−

= (10.27) 

10.3.2.5 Final Deposition Fractions and Deposited Masses 

 The total deposition efficiency for filter j is: 

Error! Objects cannot be created from editing field codes. (10.28) 

The total mass deposited in each filter j is: 

∑ (10.29) 

−

=

−=

1j

1k

j inh jk (mm )fm

The variable minh is the total inhaled PM mass that is calculated for each event, Equation 10.30. 

 minh= finh * VE * minutes * CPM (10.30)

CPM is the microenvironmental PM concentration for the event, VE is the exhaled ventilation, 

and minutes is the event duration. 

The mass deposited in each region of the respiratory tract can be calculated by summing the 

mass deposited by the inhalation and exhalation filters associated with that region. The total 

deposited mass is given by 

= ∑ (10.31) tot mm j
10.4

119 

Definition of Dose Summary Statistics 

A flag called DODOSE is available in the Simulation Control file. The default is DODOSE = 

YES. If DODOSE = NO then the dose calculation in APEX is skipped. 

If the dose calculation is performed, the initial result is the dose level for each event in the 

simulation. Unlike exposure, there are actually three doses calculated per event. The first is the 

time-average dose over the event. The second is the running 8-hour average of event doses. The 

third is the final instantaneous dose at the end of the event. For CO, The final dose is found 

directly using the series T4(z) given in the previous section. The average dose is easily found 

since T4(z) is a polynomial in time and therefore can be integrated without difficulty. For all 

other pollutants, the instantaneous end-of-event dose has no meaning and is simply equal to the 

value calculated in Eq. 10-1. 

Most of the summary statistics for dose are analogous to those for exposure. The average dose 

values over an event and the instantaneous dose at the end of the event are written to Events

output file (if it exists). Timestep and hourly-average dose time series are created by taking 

appropriate duration-weighted averages of dose over the events in each clock hour. These doses 

may be written to the Timestep and Hourly output files. A vector of instantaneous dose at the 

end of each hour (FDose) is also saved, for the calculation of a daily statistic for maximum endof-hour dose (see next section). This is not an average, but simply a subset of the values of the 

event-end dose corresponding to the events that end on a clock hour. For pollutants other than 

CO, this end-of-hour dose is simply the dose on the last event of the hour. 

There are five daily summary statistics for dose. The first is DAvgDose (Daily Average Dose) 

which is the average of the 24 hourly average dose values that fall on the same calendar day. The 

result for each day is binned according to the levels defined by the cutpoints set in the Simulation 

Control file. The second summary statistic is DMTSDose (Daily Maximum Timestep Dose), the 

largest dose over all the timestep values for the day. The third summary statistic is DM1HDose 

(Daily Maximum 1-Hour Dose) which is the largest of the 24 hourly dose values for a day. The 

fourth is DM8HDose (Daily Maximum 8-Hour Dose) which is the largest of the 24 8-hour 

running dose averages. The fifth is DMEHDose (Daily Maximum End-of-Hour Dose), which is 

the largest of the 24 values of the instantaneous dose level at the end of each clock hour on a day. 

All four daily summaries are binned according to the appropriate set of cutpoints in the 

Simulation Control file. Finally, there is the average dose over the entire simulation period, 

SAvgDose. It too is binned and tabulated according to cutpoints set in the Simulation Control

file. 
120 

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