EPA-450/2-77-024a
October 1977
(OAQPS NO. 1.2-083)
                  GUIDELINE SERIES

  GUIDELINE ON PROCEDURES
       FOR CONSTRUCTING AIR
         POLLUTION ISOPLETH
   PROFILES AND POPULATION
           EXPOSURE ANALYSIS
  U.S. ENVIRONMENTAL PROTECTION AGENCY
      Office of Air and Waste Management
   Office of Air Quality Planning and Standards
   Research Triangle Park, North Carolina 27711

-------
                               EPA-450/2-77-024a
                              (OAQPS NO. 1.2-083)
      GUIDELINE ON PROCEDURES
 FOR CONSTRUCTING AIR POLLUTION
ISOPLETH PROFILES AND POPULATION
           EXPOSURE ANALYSIS
                Monitoring and Reports Branch
               Monitoring and Data Analysis Division
            U.S. ENVIRONMENTAL PROTECTION AGENCY
               Office of Air and Waste Management
             Office of Air Quality Planning and Standards
             Research Triangle Park, North Carolina 27711

                    October 197?

-------
                   OAQPS GUIDELINE SERIES

The guideline series of reports is being issued by the Office of Air Quality
Planning and Standards (OAQPS) to provide information to state and local
air pollution control agencies; for example, to provide guidance on the
acquisition and processing of air quality data and on the planning and
analysis requisite for the maintenance of air quality ,  Reports published in
this series will be available - as  supplies permit - from the Library Services
Office (MD-35), Research Triangle Park. North Carolina 27711; or, for a
nominal fee, from the National Technical Information Service,  5285 Port
Royal Road, Springfield. Virginia 22161,
                  Publication No. EPA-450/2-77-024a

                         (OAQPS No.  1.2-083)
                                11

-------
                               PREFACE
     Development of air pollution isopleths  and  population  exposure  analysis
are components of the "Air Monitoring Strategy for State  Implementation  Plans"
(EPA-45Q/2-77-Q10).   The guideline document  is intended  to  provide assistance
in performing these activities.   A companion "Users Manual"  describes  existing
computer software applicable to  these tasks.
                                 iii

-------
                              ABSTRACT

     This guideline document provides  an overview of methodologies  that exist
for constructing pollutant isopleth displays  and for estimating population
exposure to air pollutants from air monitoring data.  Actual  examples  of the
methodologies are presented for applications  to data for the  New York-New Jersey-
Connecticut area and for the Los Angeles area.   This report  is  to assist the EPA's
Regional Offices and States in reviewing their data bases to determine feasibiltiy
of performing isopleth/population exposure analyses, and to  guide regional,  state,
and  local air pollution control agencies  in actually conducting  such analyses.
     Spatial presentation of air quality  monitoring information  in the  form of
isopleth maps is useful to  air pollution  control agencies and  highly informa-
tive to  the  public.  Steps  that must be taken  to obtain an isopleth map from
air  monitoring data measured at widely separated monitoring stations as well
as from  dispersion-moael-simulation outputs are described.  Currently available
methods  of developing an  isopleth map are documented for three  types:   manually
drawn maps,  character-printed maps, and line-drawn  maps.  Problems associated
with each type of  isopleth  map are discussed.
     A population  exposure  analysis, which combines air quality  data and demo-
graphic  data to estimate  population exposure to air pollution,  is outlined.
Data-set preparation and  analysis methods are  explained for estimating  both
long-term and short-term  exposure of the  population to  air pollution.   Exposure
to long-term average concentrations is described by the percentage of the
population exposed above  an annual National Ambient Air Quality  Standard
 (NAAQS).  Exposure to short-term  (e.g., 1 hr or  24  hr)  concentrations is
quantified by the  distribution of the population who are exposed above  an
hourly or 24-hour  NAAQS at  various percentages of the time (hours or days),
                                     IV

-------
                           TABLE OF CONTENTS

ABSTRACT	    ii
CHAPTER 1 - INTRODUCTION  	    1
     1.1  ANOTHER WAY TO STUDY AIR QUALITY	    2
     1.2  POTENTIAL BENEFITS  	    3
     1.3  PERFORMING A SPATIAL ANALYSIS .	    4
CHAPTER 2 - SPATIAL DISPLAY OF AIR QUALITY INFORMATION  	    6
     2.1  FIRST STEP IN SPATIAL ANALYSIS - FEASIBILITY  	    7
          2.1.1  Spatial Coverage of Monitoring Data  	    9
          2.1.2  Completeness of Air Quality Data	    13
          2.1.3  Other Considerations	    15
     2.2  MANUALLY DRAWN ISOPLETH MAPS  	    16
     2.3  SPATIAL REFINEMENT OF AIR QUALITY INFORMATION 	    19
          2.3.1  Spatial Interpolation of Air Monitoring Data ...    20
          2.3.2  Air Quality Simulation by Dispersion Model ....    27
     2.4  COMPUTER-DRAWN ISOPLETH MAPS  	    29
          2.4.1  Character-Printed Maps	    31
          2.4.2  Line-Drawn Maps	    36
          2.4.3  Hybrid Isopleth Map	    40
CHAPTER 3 - POPULATION EXPOSURE ANALYSIS  	    44
     3.1  DEVELOPMENT OF RECEPTOR NETWORKS  	    45
     3.2  PREPARATION OF DATA SETS	    49
          3.2.1  Population Data	    49
          3.2.2  Receptor Point Data	    52

-------
                     TABLE OF CONTENTS (Continued)

     3.3  CHARACTERIZATION OF POPULATION EXPOSURE TO AIR POLLUTION.  .   53
          3.3.1  Analysis of Long-Term Population Exposure  	   53
          3.3.2  Analysis of Short-Term Population Exposure 	   58
REFERENCES	63
APPENDIX A.  Locating Monitoring Stations on a Map  	   65
                            ACKNOWLEDGMENTS

      This  guideline  document  has  been  prepared  by  Neil  Frank,  Monitoring
 and  Reports  Branch,  Monitoring  and  Data Analysis Division,  Office  of  Air
 Quality Planning  and Standards  and  Yuji Horie,  Data  Sciences Division,
 Technology Service Corporation,  2811 Wilshire Boulevard,  Santa Monica,
 California 90403,  under contract No. 68-02-2318, project  No. DU-76-C190.
                                     VI

-------
 CHAPTER  1.   INTRODUCTION
    This  guideline  document is to assist the U.S. EPA, States and local air
 pollution control agencies in displaying air quality information in a geo-
 graphical  context and  reporting air quality progress to the public in a more
 meaningful  and  understandable form.  This  report provides guidelines on
 developing contour  lines  of air pollution  levels (isopleth map) from air
 quality  data and  presents an outline  of the methodology that has been
developed for analyzing population exposure to air  pollution.   To  assist air
pollution control  agencies in actually doing such analysis,  examples  of the
methodology and the computer programs  developed in  recent applications  to
the New York-New Jersey-Connecticut area and to the Los Angeles  area  are
presented.
     Isopleth maps are often  used to illustrate the spatial  variation of air
quality and other environmental  variables.   An isopleth map  can  be drawn
manually, or it can be drawn  mechanically by using  a readily available com-
puter program such as SYMAP [1],   Because environmental variables  are measured
at widely separated monitoring stations, the performance of  the  spatial-inter-
polation scheme being used may significantly affect the isopleth map.  Therefore,
numerous interpolation schemes employed in  meteorological  mapping  and in other
areas  are reviewed to determine  their  suitability for air pollution  applica-
tions.   The state  of the art  of spatial interpolation is discussed in regard
to preparing isopleth maps for air pollution studies.
     Although several reports [2,3,4,14] have  recently  been  published on popu-
lation exposure, the methods  used  need to be thoroughly explained  before
they can find wide application in  various  geographical  regions.  This report

-------
outlines the population exposure methodology that  we  have  developed  and
discusses problems that have arisen in two applications  -- one for the New
York-New Jersey-Connecticut area and one for the Los  Angeles  area.   Because
a  population  exposure analysis may be performed under  a  variety of situations,
alternative methods, as well as the currently applied methods, are discussed.
             WAY TO STUDY AIR QUALITY
     The nation's air quality is routinely measured by some 4,000 air
monitoring stations all over the United States.     While most studies of
air quality data have been made for individual  stations,  important knowledge
can be gained by collectively studying air quality information provided  by
an entire network of monitors in a specific geographic area.  Conventional
tabulations and graphs of air quality summary statistics,  given  separately
for individual stations, do not provide a convenient  basis  for studying
these spatial patterns of air quality.  When air-quality  monitoring infor-
mation is presented in a geographical context,  say through  use of an isopleth
map, one can readily comprehend the spatial variation in  air quality.
     A few economists and geographers have combined air quality  data with
socio-economic data, studying air pollution in  relation to  economic and
demographic variables [5,6,7].  Following their lead, air pollution researchers
have developed methods to quantify ambient air quality in terms  of population
exposure  to air pollution instead of concentration units  [2,3,8,9,14],   The
methodology to perform population exposure analyses is described in this
report.

-------
1.2  POTENTIAL BENEFITS


     Geographically oriented air-quality presentations supplement conventional


tabulations of air-quality sunmary statistics.   Therefore, an isopleth map


of air quality data is very effective for providing:


     •  A visual perspective of the spatial  variation in air quality and


        patterns of human exposure levels;


     t  A meaningful reference for evaluating air quality trends in relation


        to population-growth patterns, arid tempos1  arid spatial  emission


        trends;


     •  A spatially representative baseline of air quality for evaluating


        arid modifying r-gulsco! /  *,. ogratrc (e.g., State Implementation Plans


        and new source reviews).


     National Ambient Air Qun't'ty Standards (NAAQSs)  have been set to protect


the public health and welfare,   "-nibient air quality data provide the basic


means of quantifying whether th'  public benefits by trends in air pollution


levels.  To make this quantification  directly relatable to public health, it


is useful to report air quality in terms of population exposure  levels.  To


do so requires synthesis of population anj air quality data bases.


     Air pollution concentration? alone are not indicative of population


health risks, because they do not specify what fraction of the population


is exposed to various concentration levels.   Fo>~ example, it may be more


meaningful for residents of an urban  area to learn that the percentage of


the urban population living in areas  above the primary national  standard


for particulates decreased from 60* in 1970 to 10";. in l^S, than to learn that

                                                                 "*
the annual mean pollutant concentrations decreased from 69.5 ug/m0 to 64.3 ;,q/m


in the same period.  In the latter statement, even tho people whc know the

-------
              3                            3
NAAQS (75 vg/m  for the primary and 60 pg/m  for the secondary)  may misinterpret
the implications of meeting the primary NAAQS but failing to meet the secondary
standard in both 1970 and 1975.  The former statement tells people, regardless
of their knowledge, that the particulate air pollution in the urban area
improved from 1970 to 1975 and that the number of people exposed to health
risks from particulate matter was less in 1975 than in 1970.
     The Population Exposure Methodology discussed in this report focuses  on
exposure to air pollution above established air quality standards.   Exposure
to long-term average concentrations is characterized by that percentage of
the population exposed to air pollution above the yearly average NAAQS.  Ex-
posure to short-term (e.g., one hr or 24 hr) concentrations is quantified  by
the average percentage of the time (hours or days) that people were exposed
above the short-term NAAQS.  A more complete characterization of population
exposure is given by cumulative distributions of people's exposures to long-
term average or short-term concentrations.
1.3  PERFORMING A SPATIAL ANALYSIS
     To develop an isopleth map from air monitoring data, a network of
air monitoring stations must adequately cover the area of interest.  The
required size may vary from one pollutant to another.  If sufficient
monitoring sites are not available, isopleth analysis might depend on the re-
sults  of a calibrated dispersion model.  As few as three stations may
be needed for estimating a spatial concentration distribution of photochemical
oxidant and other secondary pollutants.  For the primary pollutants such as

-------
CO, TSP, and S02, a larger number of stations are required to obtain a
meaningful isopleth map over a study area.  In addition, these stations
must be clustered so that concentration in the neighborhood of the monitor-
ing sites can be inferred from those measured by the stations.
     Isopleth maps can be used in several  ways to describe air quality.
First, an isopleth map for a single year can be used to inform the public
of the spatial variation in air quality.  Second, a series of isopleth maps
for selected years can be used to present the trends in the spatial  patterns
of air quality over time.  Third, by computing the land area within each
isopleth level, both the regional air quality level and the percentage of
land area above the NAAQS can be determined.  Fourth, by combing air quality
data with demographic data, exposure of the population to air pollution can
be determined.
     In obtaining an accurate isopleth map or in determining population
exposure to air pollution, a rather ']-ate jwlysts method and some
computer software are required.  The analyses method for dev:-]opiny an
isopleth rr:ap  Is discussed in Chapter :/; that for perfonpbig a population
exposure analysis ~'3 describe-"' in C 3p+er 3.  The computer programs for
actually doing such analyses are presanted in a separate volume of the
User's Manual.

-------
CHAPTER 2  SPATIAL DISPLAY OF AIR QUALITY  INFORMATION
     Ambient air quality in most major U.S.  cities  is  routinely measured
by a network of air monitoring stations.   The display  of air quality  monitor-
ing information in a spatial context is useful to air  pollution control
agencies and highly informative for the public.   However, many factors  have
to be considered in displaying air quality data from a finite set of  mon-
itors on a spatial scale.  Considerations  may include  the number of stations,
configuration of monitoring sites, spatial gradient of pollutant concentra-
tions, emission source inventory, geographical features, and local  climatic
characteristics.
     When air monitoring stations are too  few, too far apart or clustered
in too small an area, a spatial display of air quality monitoring informa-
tion cannot be made in a meaningful manner.   A spatial analysis might depend
on the results of a validated dispersion mode.  The first section discusses
items to be included in checking feasibility of a spatial display of  monitor-
ing information.
      The simplest method of displaying monitoring  information  in a spatial  con-
text  is  to  plot monitoring sites  and  air  quality values  on  a map and to manual 1
draw  an  air-quality isopleth map.   In drawing an isopleth line,  one employs
either consciously  or  unconsciously,  an "eyeball estimate"  of  air quality
at nonstation  locations  from air  quality  values measured at nearby monitoring
stations.   This eyeball  interpolation involves all  the  considerations of
pollutant-concentration  dispersion  characteristics  that  the person perceives.
The importance  of these  subjective  factors  in drawing an isopleth map is  dis-
cussed in Section  2.2.

-------
     Isopleth displays have been used more frequently for dispersion-
model outputs than for air monitoring data.  The main reason is that air-
quality monitoring information was not adequate for developing an isopleth
map in many urban areas.  In recent years, however, the air monitoring network
in metropolitan areas has expanded considerably and its data quality has
improved measurably.  Section 2.3 discusses two alternate methods of estimating
air quality at nonstation locations by 1) spatially interpolating air-quality
monitoring information, and 2) applying an air quality dispersion model.  Pro-
cedures involved in each of the two methods are described in separate sub-
sections.  Advantages and disadvantages of each method under various situations
are also stated.
     Modern computer graphic techniques can be used for drawing an isopleth
map after air quality values are estimated at sufficiently dense grid points.
Section 2.4 presents an overview of currently available computer mapping
techniques  and several examples of computer-drawn isopleth  maps of air
quality parameters.
2.1  FIRST STEP IN SPATIAL ANALYSIS -  FEASIBILITY
     Given a study pollutant and a geographical  area,  the first thing to
be considered is whether an isopleth analysis will  be  feasible.  It is
suggested that the isopleth analysis be based on monitoring data.  This is
the easiest way to establish trends over time and provides a basis for
convenient updates.  If this is not possible, then  the isopleth analysis
might be based on the believable results of a calibrated dispersion model.

-------
                                     8
     Several  items are useful  for establishing the feasibility of an
isopleth analysis based on monitoring data.   These items  include previously
published isopleth maps, monitoring location maps and a check of data com-
pleteness.
     As obvious as it may sound, a good starting point is to check if
isopleth maps have been previously published.  These could be based on a
past year of monitoring data or the results  of a modeling exercise.   This
basically indicates that an isopleth analysis can be done and will provide
a basis for comparison of relative spatial  patterns with  new analysis. This
comparison will also ensure that contradictory new results won't be pro-
duced.
     Another important item is a map which shows the location of existing
monitors plus those which previously produced historical  data.  This  will
show if monitoring data might serve as the basis for the  isopleth analysis.
This map will help to establish the spatial  coverage of the monitors  and
also help to define the boundaries of the possible study area.  Some hints
on locating monitoring sites on a map is discussed in Appendix A.
     Next, air quality data completeness must be checked for all candidate
monitors.  The check list must include:
     a.  Validity .of air monitoring data over a time period of interest,
say a year or a season, and
     b.  Historical continuity of data over several years for a trend
analyses.

-------
jLl.l  Spatial Coverage of Monitoring Data
     Suppose that 5 stations report hourly CO concentrations with an
acceptable data quality at three locations near highway and at two urban
background sites.  In this case, it may not be feasible to draw a concen-
tration isopleth map from the CO monitoring data because each station read-
ing of CO concentration is representative for such a small area (less than
1 mi around a station) that CO concentrations at a place apart from a station
site may differ considerably from concentration readings at that station.
     On the other hand, if the above example is for 0 , it is quite possible
                                                     /\
to develop an isopleth map by interpolating the station readings to places
between stations.  The reason is that the concentration gradients of Ox are
generally so small  that Ox concentration at any place within the urban area
can be estimated reasonably well from concentration readings at the nearby
stations.
     A "representative area" of a monitoring station may be defined as a
distance from the station at which a pollutant concentration remains almost
constant, say it does not change more than ±20% from the reading at that
station.  Then, based on expected pollution gradient of long-term concen-
tration statistics  (e.g., annual mean and annual percentile concentration),
the "representative area" presented in Table 1  may be used as a guide of how
far from a station  air monitoring data can be extrapolated for various
pollutants.  The representative areas specified in Table 1 are only a guide
and are open to user modifications.  For example, a site affected by local
emission sources may have a much smaller representative area than the repre-
sentive area listed in Table 1.  Similarly, a monitoring site in a high

-------
                                     10

pollution gradient area (e.g., due to complex terrain or due to high emission
density) may have a smaller representative area.   On the other hand, a
representative area by a monitor located in a uniform land use zone (e.g.,
agricultural land) may be substantially larger than the typical representative
area of Table 1.  As a matter of fact, areas with a similar land use tend to
have a similar level of air pollution.  In many cases, a land use map will
be quite useful  for refining a representative area on a site-by-site basis.
     Although a representative area for the primary pollutant is influenced
strongly by a particular site characteristic, this may not be a problem
with the secondary pollutants (e.g., Ox and SO^)  whose concentration
gradients tend to be moderate.  One exception is  that 0Y concentration
                                                       /\
gradient near a heavily traveled highway is quite sharp.  Therefore, 0
                                                                      J\
monitoring site near a busy highway will have a much smaller representative
area than the typical representative area for 0  monitors.
                                               /\
     Using the representative area listed in Table 1, one can check the
feasibility of an isopleth analysis for a given set of air monitoring stations
and a given pollutant.  Various configurations of air monitoring stations
are given in Figure 1 to illustrate how to check the feasibility of an
isopleth analysis and to determine the study area.
     Suppose that, after quality and completeness of air monitoring data
have been checked, the stations whose locations are designated by dots in
Figure 1 have been selected for a spatial analysis.  By drawing a circle around
each station, with the radius being equal to the representative area, one can
determine a potential study area for a given configuration of station sites.
Figure 1-a shows that the stations are located so far apart from each other

-------
                                     11
compared to the representative area for TSP that one cannot form a  contiguous

study area.  On the other hand, Figure 1-b shows that although two  stations

are too distant from any other station, the rest of the stations form a con-

tiguous study area.
Table 1.  Typical "Representative Area" of a Monitoring Station Estimated
          for Each Major Pollutant from the Expected Pollution Gradients
          of Long-Term Concentration Statistics.
Pollutant
CO
S02
TSP
N02
°x
so=
Representati
Distance from a
Less than 1 mi
3 mi
3 mi
5 mi
10 mi
20 mi
ve Area
Station






     Figures 1-c and 1-d are for 0 .  Although the stations of Fig. 1-c are
                                  X

scattered as far apart from each other as those of Fig. 1-a, the large

representative area for Ox monitoring sites makes it possible to form a

contiguous study area.  In Fig. 1-d, the three stations are so far apart

from the rest of the stations that the study area is split into two areas.

-------
Figure 1.  Determination of Study Area from a Set of Monitoring Stations by
           Using the Range of Influence (a and b for TSP, c and d for 0 ).

-------
                                     13

     When a set of monitoring stations cannot form a contiguous study area
covering the region of interest, the spatial  distribution of pollutant
concentrations must be estimated by knowledge about pollution behavior
in addition to the air monitoring data.  If it is known that the pollution
levels are intermediate between those of adjacent monitoring stations, then
these areas can be estimated by a credible interpolation formula.  Also a
dispersion model may be helpful for depicting a spatial concentration dis-
tribution of a primary pollutant.  In addition, pollution level in areas
with no monitors may be guessed from the concentration readings of monitors
in areas with the same or similar land use and similar adjacent emission
sources.  AQDM [10] and COM [11] computer models are useful for S02 and
TSP, while APRAC [12] and HIWAY [13] computer models are useful for CO.
The use of these dispersion models for estimating a spatial distribution
of concentration is discussed in Section 2.3.2.
2.1.2  Completeness of Air QualityData
     When air monitoring data are used for developing an air quality isopleth
map, credibility of the monitoring data must be checked.  The check list
must include  a) completeness of air monitoring data over a time period of
interest, and  b) historical continuity of data over several years for a
trend analysis.
     In reporting a seasonal or annual air quality, we have to check, for
each station, the number of valid concentration measurements during the
period of interest.  In distinguishing valid stations from invalid stations,
we need a specific criterion as to the minimum number of valid concentration
measurements per station-year or station-season.  The criterion for a valid

-------
                                     14
station-year used by the U.S.  Environmental  Protection  Agency's  National
Aerometric Data Bank (NADB) will  serve as  a  preliminary data  screening
tool.
     The NADB uses separate criteria for continuous  and intermittent  moni-
toring.  For continuous monitoring,  a year (or quarter) of data  is  valid
if at least 75% of the total number  of possible observations  were  recorded.
For intermittent monitoring a year of data is valid  if  it has four valid
quarters of data.  For a valid quarter, a  minimum of five observations  is
required.   In addition, if one month has no  measurements, the other two
months must have at least two observations.
     In order to establish air quality trends, spatial  analysis  of air
monitoring data would be performed for a multi-year  period rather  than  for
a single year.  This would entail at least two isopleth maps  within a
several year study period.  A series of maps would show the change in the
spatial pattern of air quality and can specifically  show the  change in  the
study area having air quality values above established  air quality standards.
     Ideallys only "trend" stations  meeting  the valid Nation-year criteria
in every year during the study period should be selected for  the analysis.
In actual  situations, however, such  stations are usually too  few to ade-
quately depict the spatial variation in air quality.  One solution to this
problem is to use those stations  that reported air quality data  in several
years.  Then the air quality at stations in the missing years can  be estimated
from other data.  If isopleth maps were developed only from the  reporting
stations in a given year some bias might be introduced into the  trend
analysis.

-------
                                     15
     There are several possible approahces for estimating missing values.
If the changes in air quality is gradual, then linear interpolation of air
quality values between neighboring years might be used.   Because of the
problem of what to do with missing data in the start and end years, an
alternate approach is to make use of the region-wide average change in air
quality between successive years.
     The average year-to-year change can be established from all sites with
data for each successive two year period.  This change can then be applied
to estimate missing values.  A third potential approach is to use a gener-
alized linear model with class variables for years and sites.  Unfortunately,
this analysis of variance procedure will probably involve an unbalanced
design due to the missing values and this may not be computationally con-
venient without the aid of a statistical analysis computer package.  The
missing values would be estimated from a term which describes the average
air quality value for each year and from a term which describes the average
air quality value for each site.  For each of the above procedures, we can
make use of emission density and/or land use maps to select an appropriate
subset of sites that should be used for the estimation procedures.
2.1.3  Other Considerations
     An adequate "area representativeness" of each monitoring site is
essential to correctly estimate a spatial distribution of air quality from
air monitoring data.  If a monitoring station reports an extraordinary con-
centration caused by a local "hot soot", that station must be given special
consideration in the analysis.  The "hot spot" might be indicated on the
isopleth maps as a localized condition.  Because it is not representative

-------
                                     16

of a wide area, it should not be included in a spatial  analysis  that
estimates air quality by spatial interpolation from neighboring  monitoring
stations or in a population exposure analysis to be described in later
sections of this guideline.
     Site characteristics are another important factor.  Since a pollutant
concentration varies greatly with height above the ground, some adjustment
of air monitoring data might be necessary to account for the height effects
on concentration readings.  Concentration readings at an elevated monitoring
site, say, 50 ft above the ground, could be low because of the greater dilu-
tion at  that elevation compared to the one at 5 ft above the ground.   The
height effect  is great for CO and the other primary pollutants, but is not
so great for 0  arid  the  other secondary pollutants.  Therefore, careful con-
              A
si deration of site characteristics such as height and local emission influ-
ence must be given for selecting a set of stations reporting concentrations
of a primary pollutant.

2.2,_ MANUALLY  DRAWN ISOPLETH MAPS
      When air monitoring data are available at several  station  sites,  the
 first step  necessary for obtaining an isopleth map is  to  plot the  station
 locations and concentration  (or other air quality parameter) levels  on a
 skeleton map as shown in Fig. 2.
      Figure 2-a illustrates  a standard procedure for drawing an isopleth map
 when one has concentration/station site information only.   Starting  with the
 stations where the highest concentration occurs, straight lines are  drawn
 connecting  adjacent station  sites.  When the concentration levels  at two

-------
                               17
       036
                      o
                      42
      50
      o
o 53
            037
 lu
 o
                       15
                       o
a.  Without Subjective
      Considerations
                               36
                       o se
53
 o
                                  o 37
                                                 22
                                             o
                                             42
                                             ll
                      b.  With Subjective
                           Considerations
Figure 2.   Illustration of the  Stepwise  Procedure  for  Preparing
           Isopleth flaps with and without  Subjective Considerations,

-------
adjacent station sites are considered, an intermediate grid point is assigned
to one or more location on the edge where one or more isopleth levels fall.
To find such an intermediate point between two stations, we use an eyeball
interpolation of the two station values, which is usually similar tc a linear
interpolation.  As seen in the second illustration of Figure 2-a, we car, draw
an isopleth line around the station with the highest concentration bj con-
necting the intermediate points with the isopleth level of 50.  Then, proceed to
the next isopleth  level,  40.   Now,  we  consider all stations with  concentrations
near 40, plus   their neighboring stations.   By repeating the  above procedure,
an isopleth map is completed in the third illustration  of Figure  2-a.   Here,
intermediate points and station values are  removed to have a  clear isopleth map.
     The procedures described above are quite similar to those used in  computer
software for drawing an isopleth map.   Figure 2-b illustrates a typical
isopleth-drawing procedure employed by an air pollution expert and an
experienced meteorologist.   These experts also plot  the station locations
and concentration  levels  on a skeleton map.   However,  because they know the
geographical  feature of the area and its effect on the  concentration field,
they incorporate their subjective considerations in  drying an isopleth map.
     In Figure 2-b, the locations of mountains are designated by hatched areas.
Because an air pollution expert knows  that a polluted air mass on one side
of the mountains does not mix with the one on the other side of the mountains,
he may draw an isopleth line separately for each of the two polluted valleys
as shown in the second illustration of Figure 2-b.  With his  subjective con-
sideration of the mountains, his final isopleth map, shown in the third

-------
                                     19
illustration of Figure 2-b, is totally different from the isopleth map obtained
without considering the mountains (Figure 2-a).
     The above example considers only the effect of mountains  on a concentration
field.  An air pollution expert may also consider potential  effects on a con-
centration field of wind-flow patterns and configuration of major emission
sources.  Because the effects of mountains, emissions, and wind patterns on
a pollutant concentration field are difficult to quantify, very little ela-
boration has been made in incorporating the subjective considerations men-
tioned above in a computer-drawn isopleth map.   A technique  to  incorporate
some of the subjective considerations in a spatial interpolation scheme is
discussed in the next section.
2.3  SPATIAL REFINEMENT OF AIR QUALITY INFORMATION
        The estimate of the spatial  variation of air quality can be refined
by two methods — spatial interpolation of air monitoring data, and air
quality simulation by a dispersion model.  The former method is appropriate
when air quality data are available at closely spaced network  points.  The
latter method is more suitable when air quality data are not available at
all (e.g., future air quality) or are available  only at a few  sites.
        For most applications, a spatial distribution of pollutant concentra-
tion was obtained from dispersion-model outputs.  The reason has been that,
in early years of air quality surveillance, there were only a  few air
monitoring stations even in a large metropolitan area.  Therefore, it was
almost impossible to estimate a spatial distribution of pollutant concen-
tration from concentration readings  at a few widely separated  monitoring sites.

-------
                                      20
 The  monitoring  data  have  been used to validate the model calculations. How-
 ever,  in recent years, most major U.S. cities and metropolitan areas have
 a large and dense  network of air monitoring stations.  Because of this
 development of  air monitoring networks, we can now develop an isopleth TOP
 of various air  quality parameters from air monitoring data and monitoring
 site information.
 2.3.1   Spatial  Interpolation of Air Monitoring Data
      To obtain  a reproducible air quality isopleth map from air monitoring
 data,  a credible spatial-interpolation scheme must be used to estimate con-
 centrations at  places other than monitoring sites.
      The most commonly used interpolation scheme is  linear interpolation.
 There are two types  of linear  interpolation formulas; true  linear interpo-
 lation and pseudo  linear interpolation.   When  applied to  estimate a  con-
 centration at a place other than monitoring sites, the  linear interpolation
 formulas may be written  as
                                                                          (1)
where d. is the distance between  the ith  grid (or receptor)  point  and  the  jth
station site.   C.,   j=l,2,3s  is  the observed  air  quality  at  each of  the  three
                J
stations nearest to the i   grid  point.   The sign parameter a^ takes only

-------
                                   21
+1 inside the triangle formed by the three stations for both the true



linear and pseudo linear interpolation formulas.   However, outside the



triangle, a- of the true linear interpolation formula takes either +1
           j


or -1 depending upon the position of the grid point, while a- of the
                                                            J


pjeudjo linear formula takes +1 only irrespective of the position of the



grid point.



     The performance of the linear interpolation formulas, Eq. (1), is



shown in Figs. 3 and 4 for a hypothetical case where observed concentrations



of 85, 15, and 60 (in arbitrary units) are assumed at points A, B, and C,



respectively.  In both figures the spatial distribution of the interpo-



lated concentrations inside the triangle is generally in fair agreement



with what we would expect from the concentrations at A, B, and C.  Outside



the triangle, however, the true interpolation formula tends to over-



extrapolate the concentration values assigned at A, B, and C (Fig. 3).



This over-extrapolation tendency of the true linear interpolation formula



is very undesirable for air pollution applications.  The pseudo linear



interpolation formula does not show such over-extrapolation tendency (Fig. 4),



In the resulting isopleth i,;ap, however, we miss both the highest observed



concentration, 85, and the lowest, 15.  Therefore, the pseudo 1inear inter-



polation formula is said to be over-smoothing particularly for its applica-



tion to air quality mapping.



     To avoid the problems of over-smoothing as well as over-extrapolation,



the performance of various candidate interpolation formulas was examined.



Among the interpolation formulas examined, the parabolic interpolation



formula, given by Eq. (2), showed the most satisfactory performance [2].

-------
                             22
LLJ
O
cn
                     DISTANCE X
            Figure 3.   Performance of the True Linear
                      Interpolation Formula [2].

-------
                             23
UJ
O
                      DISTANCE X
            Figure 4.  Performance of the Pseudo Linear
                      Interpolation Formula [2].

-------
                                     24
                     Cn- =   7 C,       J.  Vd     •                   (2)
     The concentration isopleth map obtained by the parabolic inf-: po^
formula is shown in Fig. 5 .  It shews the isopleths of the highes"  85,
lowest, 15, observed concentrations.  Although the parabolic -inte^po
formula is not perfect in its performance, it certainly mininiz-   rhc prob-
lem of over-smoothing as seen in the pseudo linear interpolation formula
(Fig. 4).  The conservative characteristic that no estimated value exceeds
the maximum observed  concentration nor is any estimated value less than
the minimum observed concentration is also desirable for air pollution
applications.
       In Eq. (2) k the s'jrT>piat"'0" can hp 
-------
                         25
Ul
O
CO
o
                     DISTANCE  X
           Figure 5.  Performance of the Parabolic
                    Interpolation Formula [2].

-------
                                     26
grid points should be closer to the real  spatial  distribution  of air  quality
than a computer map drawn to the air monitoring  data  at the  stations  alone.
       Any interpolation formula by itself cannot Incorporate,  the effects
of mountains, prevailing wind patterns,  and configuration  of major emission
sources on the concentration pattern.   Some computer  algorithms  (e.g.,  SYMAP,
LPEM, and SHEW in user's Manual; can incorporate into air  quality Interpo-
lation schemes the effects which geographical  features exert on  pollutant
concentration fields.  For example, when stations are located  on boeh sides
of mountains, the interpolated concentration at  a receptor point will be
determined primarily from the concentration readings  at the  stations  located
on the same side of the mountains as that receptor grid point.  This  effect
can be accomplished by imposing a penalty distance to the  stations on the
opposite side of the mountain.  This penalty distance simulates  the difficulty
of an air mass crossing the mountain.   The location of mountains or other
barriers would be approximated by a series of piecewise™linear penalty
functions having a particular penalty value at each node.   The technique can
be applied to take into account the effects of the prevailing  wind pattern,
the configuration of large bodies of water and major emission  sources.
These techniques are incorporated into spatial interpolation schemes  used
in LPEM and SPEM computer models as well as the SYMAP graphics package (see
User's Manual).
       Spatial interpolation of air monitoring data should not be applied
without constraints imposed by the physical reality of air pollution.  The
concentration reading at a station is representative only of a specified
area about that station.  As discussed in Section 2.1, the "representative
area" depends on the type of pollutant and emission source pattern and is

-------
                                      27
 inversely associated with concentration gradient.  A yajid  interpolated


 concentration will be limited to a receptor point lying within the  repre-


 sentative area  from the nearest station.   Interpolated  concentrations at



 receptor  points outside  the representative area of the nearest station


 should  be denoted by some warning symbol  (e.g., asterisks  (*)).  In this


 manner, the  air quality  in the  study area will be estimated from concen-


 tration readings at appropriate monitoring stations.  The  study area


 may  turn  out to be one  of the four cases  illustrated in Fig. 1.  In case


 (1-a),  we would have to  resort  to a dispersion model or some other method


 then spatial  interpolation of air monitoring data to estimate air quality


 dt intermediate nonstation grid  point,


 2.3,2  Air Q'.«a^iiy SlwulaTior1 by inversion Mode1
      Dispersion models ara widely urcd to simulate tr.e  spatial  distribution



of air  quality unde" various situation.  The so-r;Jlc:-d ,-.-l iinatological  dis-



persion irodel—-which uses, as imji cM,3, the Piiii^iu';  inventory  and the



joint frequency distribution cf V'in- ..t;eed} wind direct/: jn,  and atmospheric



stability—1:;  considered useful lor *-:;tirr
-------
                                     28
     A dispersion model  should first  be  calibrated by comparing the simu-
lated values with the observed air quality  at  the monitoring station(s).
Air quality at places including but not  limited  to the station sites would
then be given by the predictions of the  calibrated model.  For additional
details on modeling, refer to an upcoming OAQPS  Guideline on Air Quality
Models.
     A dispersion model  can  be used  to  estimate the spatial distribution
of future air quality when a proposed project is  completed or when a pro-
posed control strategy  is  implemented.  First,  the  dispersion model is
applied to  the jsresent  emission inventory  and present meteorology to simu-
late present air quality.  Second, the  simulated  values are compared with
the observed air qualities at several monitoring  stations to calibrate
the dispersion model.   Then, the calibrated model  is applied to the
postulated emission  inventory and multi-year average meteorology to simulate
the air quality  likely in the future.
      A critical limitation of a climatological  dispersion model is  that  it
 cannot be  applied to complex terrain.   When applied to  flat or gentle terrain,
 a climatological dispersion model does  generate useful  spatial information of
 pollutant  concentration, although it may  not  predict accurately a  level  of
 pollutant  concentration.  Therefore, there exists a possibility of obtaining
 a more accurate isopleth map by combining  the spatial  information  from air
 monitoring data and  from dispersion-model  outputs  than  an  isopleth map ob-
 tainable from air monitoring data or dispersion model  outputs alone.
      The following discussion presents  a conceptual  approach to accomplish
 the above  objective.  Specific guidelines  are not yet available at  this  time.

-------
                                     29
     Suppose that a predicted value o ve re sti "is. *.?><•: a concentration level at
one monitoring site in the south and underestimates at the other two monitoring
sites in the north.  Further, suppose that the emission inventory data used
for a dispersion model are so complete that at least the spatial distribution
pattern of predicted concentration is believable.  One could then obtain a
better isopleth map by superimposing the spatial distribution over an error
field, as shown in Fig. 6.   The error field is a plane that passes through
the three points (xm, ym, em),m=l,2,3, where (xm»ym) is the x-y coordinates
of the m   monitoring station and em is the prediction error at that station,
i.e., the observed concentration minus the predicted concentration.
     When there are more than three monitoring stations, the study area should
be divided into several sub-areas formed by three adjacent stations.  Then,
the above adjustment can be made separately on the predicted spatial distri-
bution for each sub-area.  When a dispersion model is applied to complex
terrain, the study area should be divided into several flat segments.  Then,
the  adjustment can be made separately for each flat segment.
2.4  COMPUTER-DRAWN ISOPLETH MAPS
      Before  deciding  to  use a computer for  drawing an air quality isopleth
map,  one has  to consider advantages and disadvantages of employing a computer-
graphics technique to  his particular problems.  Although a  computer-drawn
isopleth map  is neat  and objective, it  requires some familiarity with  computer
graphics and  a  lot of data-base  preparation.  When prepared carelessly, a
computer-drawn  isopleth  map can  be quite erroneous.  As mentioned  in Section  2.2,
one can  incorporate into his hand-drawn isopleth  all the considerations of
pollutant-dispersion  characteristics in a particular geographical area.
These subjective factors often play a vital role  in  determining  a pattern
of  isopleth  lines, as  demonstrated in Figure 2.

-------
                                 30
                Adjusted Concentration  Field
                Simulated Concentration Field
                       Error Field
Figure 6,  Adjustment of a Simulated Concentration Field According
           to Differences Between the Observed and Predicted Concentrations,

-------
                                    31
     To draw an isopleth map by computer, all  the data points and data values
must be numerically specified in either computer cards or magnetic data tapes.
In addition, isopleth levels and boundary of a study area must be numerically
specified.  This preparatory work requires substantial time and effort.
Therefore, it may not be practical  to use a computer for drawing a single
isopleth map.  Computer mapping is  the most advantageous for drawing many
isopleth maps repetitiously for similar applications.   Here, a study area
does not have to be the same as long as the type of isopleth mapping is
similar.
    Two types of computer-drawn maps are discussed in  this report:  character-
printed maps and line-drawn maps.  Character-printed maps are produced by a
standard computer printer, which prints typewriter-like characters or,
standard corT!pijt9r-pr''ntOL|t. paper.  Line-drawn  maps ?,^e produced by eithe1"
a pen plotter or a cathode ray tube (CRT).  A  brief description of the two
types of computer mapping is presented in the  first two subsections.  In
the third subsection, a hybrid method incorporating manually drawn and computer-
drawn isopleth maps is explained.  Computer software for these applications
is presented in the User's Manual of this guideline document.
2.4.1  Character-Printed Maps
     Character~printing--given  access  to a standard highspeed  computer—is
probably  the r,;ost  cc~;ncn  nsans  of  drav/ing an  iscpleth rrap,   SYMAP  is  a
widely used  corrpjter  progrcr-, for era,/ing a variety of naps  [1].  When  SYMAP
is used,  the basic requirements are to specify the cap boundaries  numeri-
cally and to select the type of isopleth map from among three options:
Conformal, Contour and Proximal [1].

-------
                                    32
    In each of these maps, the study region is represented as a series of
polygons.  The polygons can be used to depict sub-areas such as counties.
These polygons must be numerically specified and are used as basic input
data of the package.  Ideographical features can also be incorporated into
the resultant figure.
    When the Conformal option is chosen, each polygonal area must be
associated with a data value.   Figure 7 is an example of the Conformal
option.  In this case, each polygonal area represents a sub-county census
division.  Solid lines, showing the boundaries of various counties, are
overlayed over the Conformal SYMAP output.  The SYMAP program simply
compared each data value with the ranges of average earnings of male workers
and printed the appropriate character in the polygonal area.
    The Contour option is based on a concentration field established by
linear interpolation among existing data points.  With this option, the
points at which data values are available must be specified by the X-Y
coordinates.  The contour intervals are pre-specified and interpolated
values at intermediate data points are compared with the specified ranges
of the variable.  Then,  the computer prints the appropriate symbol at
each data point.  The print positions at boundaries of one contour level
and another can be  left blank so  that the shaded region of one contour
level  is clearly separated  from the other shaded regions by a  blank space.
Due to the use of linear interpolation, spurious results can occur in areas
of sharp pollutant  gradients among existing  data points.
    Figure 8  is an  example  of the Contour option.   In-the figure,  the
geographical  boundaries of  the United States are featured by including Mexico

-------
                                                     33
                A
DISTORTION IS CAUSED BY COMPUTER SYSTEM LIMITATION,
RESULTING IN APPROXIMATE SCALES OF 1 IN. = 19Mi,(VERTICALt
AND ? IN. - 24 ML(HOBIZONTAL).
                                                                        TRI-8TATE REGIONAL PLANNING COMMISSION
                                                                    County  Boundaries Overlayed  on
                                                                    Conformal  SYMAP Output
                                                      1970 AVERAGE EARNINGS OF  MALE

                                                                       :"  Less than  $ 8000

                                                                       H*  $ 8000 to $ 8999
                                                                       ooo $ 9000 to $10499
                                                                       000
                                                                       |«» $10500 to $12999
                                                                          $13000 or More
                         Figure  7.  Example of Conformal Option, Showing Spatial
                                     Distribution of  1970 Average Earnings  of Male
                                     Workers in the New York-New Jersey-Connect!cut
                                     Tri-State  Region [12],

-------
           0   OOOOOOOP   00
          OPOOOOO      OOCO
          ooooo  oooeeee  o

          t'lOOO
        nooo
        ooo e
        ooo
    4-  oooo
    ocoo  e
    ooooo  &
   OOOOO 96866866666
   t »00
    ,100  9966899699 KHf
  OOOO 99998699666 Mil
 -OOOO .,	 „_,-,   _„-,-
                                            OOOO
4- OOOO 8686666696 •••VCIIIIIIIM 6668666666866 0000
  OOOO 66696699069 •fllllllllli 66884689668868 000'
 oooooo  eees&eeaeee ••••••§••* aeeeeweeeaaee ooooo
  OOOOO  869969866998  •&••••• 8966969ft9*68966 OOOOO
 + OOOftO  609966^66669      6686666666664666 HQQOO
  noOGOQOO 66660666688886866866986898668^696 OOOOO
   OOOOOOOO  99609666^0666869666666666966666 OOOOO
    ooooooooo eeef0e6eeee0eie&ee9909e9eeee9e oooooo
      OOOOOOO 09868866896869996966916969  OOOOOOO
                     OOOOOOO.
                      OOOOO .
                  66960 OOPO
                  feepeo roo
                        ooo
                        000  K.
    ooooo erteeaeeaeueewee ooo 4  «
   ooooooo  eee«e66ee**ee OPO 4»JKN
    ooroooco  eeeeaetfee oooo    2.
  oooooooooooo    e   oooo
  00000000000,10000 ooooo
.oooooooonoooooorooooo
                        BeaebAda&eeaoefii>eoe Ov>'.""oo  UJf*
                        seeoeeye'jee^tibt'deoeH oo^oo  i-li ft
                        6Si83ftl:J60Ortfl63H08Ht*f TOJO1" * t { 4 r (
                        (iB*»8ei*-*O»it'titvi*es!(iiJflt,*i CU.J  -) i ^ ( J , 1
                        $ •*•*       fleeetoaetfj^ ooi : 4-ftl;f-
eeeeeeeo^
66046096  6P
                                                                             SO000  69666666666669086868696 OOCOOCOO
                                                                             003000 6866£666666669866     OCOOO003O
                                                                             OOOOOO  666666666      OOOOCOOOOOOOO
                                                                             OOOOOOOO        OOOOOOOOOOOOCOOOOO
                                                                             t ooocoooooooooooooooooooooooccooo
                                                                               oooooooocoooo
                                                                                ooooooco
                                                                                                               oooooo
                                                                                                             ooooooooc
                                                                                                              ooooooooo
                                                                                                                ooooocoo
                                                                                                                ooooocon
                                                                                                                ooooooooo
                                                                                                                0 10OOOOOO
                                                                                                                 OQOOOOOOO  ,
                                                                                                                 oooooooooo
                                                                                                                  ooocoooooo
                                                                                                                     oooooon
                                                                                                                     ooao-joo
                                                                                                                      OOtlOPO
                                                                                                                         0
                                                                         __,...}	^	2	+	3	-t	U	+	5	4	6	+	7	4	8
                           "oorjocnr
                           ro .coooar
                           ooooooooo
r?t<-},        j        15

   *Bsoi!)^r  fiice HIKCU
   c   «*7* SO'IPCh:  >PCO, fcaT'I- NtTWC^K, F. TADPfi  AND B. 1CCOPHICK

      1-XJtO Df SIGHl •'•S'j RY K»  «"*TflCKTTT PY »,  HIP CAT* HXTVSAS  PY H.
MAX.
                                                        PPM(SOj)
                Figure  8.   Example  of  Contour  Option,  Showing  Spatial  Variation  of  504  =
                                Washout  Concentration  Over  the  Contiguous  United  States  M3l

-------
                                    35
 (designated by M), the Nantucket  Islands  (designated by N), and Cape Hatteras
 (designated by H).  The spatial variation of sulfate washout concentration
 over the United States is illustrated with the use of five different
 characters, each corresponding to a certain range of sulfate concentration.
     In the Proximal option, the  specifications of map boundaries, data
 points, and grid-point interval are made  in the sar
-------
                                    36
     Line-drawn isopleth maps can be generated by a number of plotting
devices.  These devices can be separated into two basic categories,  Cathode
Ray Tubes (CRTs) and Pen Plotters.   CRTs are usually equipped with a photo-
graphic device so that the desired picture can also be printed on film or
photo-sensitive paper.
     Whereas a character-printed map is obtained by using a simple proce-
dural language described in the user's manual of SYMAP, a line-drawn map
usually requires special programming.  To generate a character-printed map,
a computer simply calculates a variable value at every grid point, using a
certain interpolation formula (e.g., linear interpolation), and prints a
particular symbol according to the range in which the computed value falls.
In contrast, to obtain a line-drawn map, the computer must command the
plotting device to draw a contour line connecting the points at which the
computed values are equal to the isopleth value.
     Data points can be connected by a number of methods.  From among the
many methods, we recommend using either a piecewise linear fit, which is
used in the computer program called TRICON listed in the User's Manual, or
a splines-under- tension method, computer program for which is obtainable from
the University of Colorado [17].  Under no circumstance should polynomial
fit be  used for drawing isopleth lines.  Polynomial fit exhibits very poor
performance with undesirable oscillations.
     Figure 9 shows two weather maps produced by a CRT.  In this figure,
the first contour map was drawn using a piecewise linear fit; the second

-------
                      37
                            a.  Piecewise linear fit
     b,   Splines  under  tension
Figure 9.   Contour Maps  of Barometric  Pressure  Drawn  by a
           Piecewise Linear Fit and  by Splines  under  Tension  p8].

-------
                                    38
contour map was drawn using splines under tension [18].   The former map
was probably drawn from regularly spaced data points of  barometric pressure
by either writing a small computer program or simply using a procedural
language of some preprogrammed package for computer graphics.   Although the
latter contour map has more aesthetic appeal  than the former,  it requires
a large program and considerably longer computing time.
     In the above examples, the data values were given at regularly spaced
data points.  The mechanism for determining an isopleth  line for regularly
spaced data points is illustrated in Figure 10a.  For every edge whose two
vertices have a data value greater than or equal to the  isopleth level at
one end and less than or equal to the isopleth level at  the other, the
isopleth point is determined by linearly interpolating the data values at
the two vertices to that isopleth level.  The isopleth line is then drawn
by connecting all those isopleth points.
     Air monitoring data (and population exposure variables to be discussed
later) are available only at scattered data points, i.e., monitoring station
sites and/or receptor points.  A method of obtaining an  isopleth map from
such randomly spaced data points involves triangulation  of data points as
shown in Figure lOb.  The triangulation can be performed in many ways.  How-
ever, it is recommended that the outlying data points be connected first by straight
 lines  to  form  a  polygon, and  the  triangulation  proceed  inward.   In  forming
 a polygon by connecting  the  outlying data  points,  it  is,  to a  certain extent,
 possible  to make the polygonal  area  resemble  the study  region.
      Once the  triangulation  is  completed  for  randomly spaced  data points,
 the steps for  drawing an isopleth map are  similar to  those used for regularly

-------
 26        25        24         23
14
                 V
21    	I 23
                      18
          16
                   _J	1
                      15         18
 a.   Regularly spaced  data  points
                                                                                 24
                                                                                          24
                                           b.   Randomly spaced data points
                                                                                                         co
                Figure 10. Concentration  Isopleths Resulting  from  Regularly  and
                          Randomly Spaced Data Points.

-------
                                   40
spaced data points.  An isopleth point is determined on each edge whose two
vertices have a data value greater than or equal  to the isopleth level  at
one end and less than or equal  to the isopleth level at the other end.
Then, the isopleth line is drawn by connecting all  those isopleth points
(Figure 10b). A computer program doing the above tasks has been developed
by Martin Cohen at Technology Service Corporation.   Listings of the computer
program called TRICON are given in the User's Manual.
     Figure 11 shows an example of a computer-drawn isopleth mao for randomly
spaced data points.  In the figure, the boundary of the study area is drawn
separately from the isopleth lines.  The map boundary was drawn for the
input data produced by a digitizer whose pencil-like probe traced the
boundary of the original geographic map, starting from the bottom (note
the small gap there).  When such a convenient digitizing device is not
available, the boundary can be  numerically specified by reading off the
X-Y coordinates of major vertices on the boundary line from an overlayed
graph paper.  A simpler approach, as mentioned before,  is  that  of overlaying
a transparent map of the study  area on the computer-drawn isopleth lines.
     The isopleth lines obtained from the randomly  spaced data points cover
the study area quite well.  When data points sufficiently cover a study
area, as seen in Figure 11, data values need not be computed for every
regularly spaced data point; an isopleth map obtained from triangulation
of randomly spaced data points  is sufficient for most cases.
2.4.3  Hybrid Isopleth Map
     Even when one cannot trust a computer-drawn isopleth map or computer
software to draw an isopleth map is not readily available, a computer
plotting device still can be a  useful tool to draw an isopleth map.  For

-------
Figure 11-   Computer-Drawn  Isopleth  Map,  Showing  Oxidant Air Quality
            over the Los  Angeles  Region  in  Percentage  of Days on
            which the NAAQS was  Exceeded  During  1973/74 [3].

-------
                                    42
instance, a pen plotter will  draw a specific symbol  at an exact data point
(monitoring station and/or receptor grid point) according to a range of
data values.   Then, one can easily draw an isopleth  line by following the
same symbols  and procedures described  in Section 2.2.
     Figure 12 shows an example of a hybrid isopleth map.  Three data sets
are required:
(1)  A set of annual air quality statistics (here,  percentage of days the
     Ox NAAQS was exceeded during 1973/74 period),
(2)  X-Y coordinates of non-uniformaly spaced data  points (here, receptor
     grid points at which the air quality was estimated from air monitoring
     data), and
(3)  A set of X-Y coordinates describing polygonal  areas that represent
     the study region.
The computer sorts each data value into an appropriate range of data values
and commands the pen plotter to draw the corresponding symbol at the data
point.  Note that Figure 12 is drawn for the same data used to produce
Figure 11.
     With this hybrid approach, one can save some time by using a computer
and at the same time can manually draw an isopleth map that the person
perceives to be the most likely.  The  listing of the computer program to
produce the  hybrid map  is given in the User's Manual.

-------
Symbol
  9
  8
  7
  6
  5
  4
  3
   % of days
above Ox NAAQS
     50-59
     40-49
     30-39
     20-29
     15-20
     10-14
      5-9
                                                                                                                 -p*
                                                                                                                 co
                Figure 12.   Hybrid Isopleth Map, Showing Oxidant Air  Quality  over the Los  Angeles
                             Region in Percentage of Days on Which  the NAAQS was  Exceeded During
                                                         1973/74

-------
                                    44
CHAPTER 3.  POPULATION EXPOSURE ANALYSIS

     One can extend a spatial  analysis of air quality information a  step
further by combining air quality data and demographic data.   Ambient air
quality can be quantified by the percentage of the population living in
areas above an air quality standard instead of concentration units.
     A population exposure analysis can report ambient air quality by a
statement such as, "The percentage of the urban population living in areas
above the primary national ambient air quality standard for  particulates
decreased from 60% in 1970 to 10% in 1975."  This statement  may be more
informative to the public than telling them that the annual-mean-particulate
                                       3             3
concentrations decreased from 69.5 yg/m  to 64.3 ug/m  in the same period.
     The following three different methods have been used to quantify
population exposures from air monitoring information:
     1.  Associating populations to a monitoring site [5,6,7,14],
     2.  Transcribing air pollution isopleth patterns on a map of census
         tracts [8,9].
     3.  Interfacing air quality and population data at strategically located
         receptor grid points [2,3,14],
This guideline document describes the third method that provides the most
objective estimates of population exposure and lends itself  to computer
processing.
     The proposed population exposure analysis requires several steps.  The
first step is a search for a proper regional map and population data in a
convenient form.  The second step is development of a receptor network of
artificial grid points that are used to approximate the spatially distributed

-------
                                    45

population.  The study area boundary is determined by the methods of
Chapter 2.  The location of the receptor points and the monitoring stations
must be specified in a digital form, based on the coordinate system of the
regional map. The third step involves the preparation of computer-ready
data sets and computation of population exposure variables by computer
software.  The fourth step included analysis of the computed population
exposure variables and presentation of the results.
     The details of each step are discussed in the sections which follow.
3.1  DEVELOPMENT OF RECEPTOR NETWORK
     Instead of employing the assumption that the population exposure level
in various parts of a region is represented by the concentration reading at
a single air monitoring station, we propose the use of a receptor network of
artificial grid points.   The development of this network is based on the
spatial distribution of the population and is used to interface the population
data and the air quality data at each receptor point.  A receptor point is
used to represent the local population in the areas where they reside.  The
location and density of receptor points are selected so that the distribution
of receptor points reflects the spatial distribution of population density
and adequately covers the land area  throughout the study region.  Air quality
is estimated at each receptor point  by spatial  interpolation of air quality
observed at neighboring  monitoring sites.
     To develop  a  receptor network,  one has to  have  population  data  and  a
 regional  map.  Population  data  are  always  obtainable  from  census  population
 summaries.   However, because  it takes  time and effort  to reduce these data
 into a form  that  is  practical  for population exposure  analysis, it may be

-------
                                    46

worthwhile to contact a regional planning agency.  The regional  planning
agency often has not only conveniently aggregated population data into
properly aggregated statistical areas, but has also prepared a regional map
showing boundaries of the statistical areas, cities, and counties.
     When such a convenient source of information is not available, census
population data must be used.  Although every census summary contains maps
showing tracts and statistical areas, a regional map covering the entire
study area, say for an AQCR, may not be found in the census summary.  There-
fore, it is necessary either to look for other map sources  (such as street
and geographical maps) or to create a new regional map by combining several
maps found in the census summaries.
     The census population summarires range from detailed demographic data
for each census tract to aggregated population data for each state and each
standard metropolitan statistical area (SMSA).  For a single city or small
SMSA, the census tracts provide a basis for establishing a  receptor network.
The center of each census tract will serve as a receptor point.   For a
larger study area covering many cities and/or counties, the number of census
tracts included in the study area may become too large.  For the larger areas,
the most convenient census statistics may be the population summaries for
subcounties [19].  These summaries provide the population size of statistical
areas that often correspond to administrative jurisdictions such as cities,
towns, villages, or boroughs.
     When a planning agency's statistical areas, census subcountry or census
tract population statistics are found to be suitable for the analysis, re-
ceptor points are assigned to each "statistical" area according  to the size

-------
                                    47
of the population and the land area.   Assuming  that  the  population  is
uniformly distributed within each statistical area,  the  location of re-
ceptors (in most cases just one receptor) is determined  such that the
receptor points represent properly the spatial  location  and boundary of
that statistical area.  Empirically, we have found that  the following
method yields the proper number of receptor points to each statistical  area:

      1,  Regardless  of  the size of the population and the land area, each
         statistical  area is  represented by at least one receptor point.
                                                                2
      2.  An additional  receptor point is assigned for each 50 mi  increment
         land area or each 200,000-person increment of resident population.
      3.  Take the number of receptor points representing the larger increment
         (land  or population).
      A question arises  here as to why the monitoring stations themselves are
not  included as receptor points in computing population exposure variables.
The  following two paragraphs  provide some explanation.
      Because the spatial interpolation scheme used in the population exposure
methodology smoothes  out the  observed air qualities at the three nearest
neighboring stations to each  receptor point, the  highest and lowest observed
air  qualities among  the monitoring stations sometimes do not appear on the
concentrations  at the receptor points.  Therefore, a population exposure
analysis may indicate that the study population is exposed to concentrations
either slightly above the lowest observed concentration or slightly below
the  highest observed concentration.

-------
                                   48

     The problem of missing the highest and  lowest  concentrations,  however,
is already inherent in the limited number of monitoring  sites.  Although
the spatial  interpolation scheme used may further smooth out  those  highest
and lowest concentrations, the conservative  nature  of  population  exposure
methods should be a merit rather than a demerit.  The  population  exposure
analysis is  less affected by the extreme values observed than  is  the  air
quality analysis that is applied directly to the  air monitoring data.   The
smoothing effect of a spatial  interpolation  of air  monitoring  data  is  not
necessarily undesirable for estimating population exposure  because  it is
partially equivalent to people moving around and  smoothing  out their  exposure
levels.
    When the receptor network is developed,  both  the receptor points  and
the monitoring stations have to be located on the same digitized  regional
map, e.g., a map on graph paper.  To correctly locate  a  monitoring  station
on the map is not as easy as one might think; the regional  map used may not
contain any landmarks helpful  in locating the station  at the  right  place.
The larger the study region, the more difficult the placement of  the  stations
on the regional map.  For a large, ummarked regional map, one's prior know-
ledge of the station sites does not work effectively.   A mathematical  method
of correctly locating monitoring stations on a skeleton  map,  discussed in
Appendix,A.should be used for such a case.

-------
                                    49
3.2  PREPARATION OF DATA SETS
     The population exposure analysis requires careful preparation of several
data sets.  These include data on the resident population, receptor points,
air quality, and monitoring stations.  The data sets of air quality and
monitoring stations similar to those required for performing a spatial analysis
of air quality.  Air quality data used for a population exposure analysis are
commonly available statistical summaries:  annual mean concentrations for
analyzing long-term average population exposure, and percentage of the time
above the air quality standard or percentile concentrations for analyzing
short-term population exposure.
     Population and receptor data sets to be prepared for performing a
population exposure analysis are described in the following two subsections.
These data sets, together with those of air quality and monitoring stations,
are used as input data to one of the two computer software systems (LPEM and
SPEM) described in the User's Manual.

3.2.1  Population Data
Sources of Population Data
     National census data are the primary source for almost all demographic
data.  Detailed demographic data are available in both magnetic data tapes
and published reports for some 35,000 census tracts in 241 Standard Metropolitan
Statistical Areas (SMSAs) and the remaining unincorporated census statistical
areas.  However, it is rather difficult to transform these census data into
a form useful for a population exposure analysis.  Unless an in-house capa-
bility of handling the census data tapes exists, a search for pre-existing
sources of conveniently aggregated population data is recommended.

-------
                                    50
     Census statistical summaries issued from the Bureau of Census and
local planning agencies are the two major sources of such aggregated popu-
lation data.  Among the census statistical summaries, the following two
series provide useful population data for performing a population exposure
analysis:  PC(1)-A series [19], which summarizes the number of inhabitants
for political  jurisdictions (boroughs, towns, cities, counties, etc.), and
PHC(l) series  [20J, which provides data on population characteristics
(e.g., sub-populations by age group, nativity, place of work, worker and
nonworker status) for each census tract.  These two series also contain
maps showing boundaries of political jurisdictions arid/or census tracts.
Some of these maps may be useful for a population exposure study.
     Local planning,agencies that may have useful population data include
state highway departments, regional planning agencies, state housing
administrations, and civil defense agencies.  These agencies may have not
only conveniently aggregated population data for regional statistical areas
but also a high quality map showing boundaries of counties and regional
statistical areas.
Sub-Population Data
     Population exposure methodology discussed in this text assumes that
people are locationally fixed at their residence location.  This simplifying
assumption may not be valid for working-age population, but may be good
for  sub-populations  such as school-age and elderly who tend to stay near
their residence location most of the time.  Furthermore, these sub-populations
are believed to be the most susceptible to air pollution.  Therefore, population

-------
                                    51
exposure analysis should be performed not only for total population but
also for sub-populations including school-age children and elderly people.
     Because all statistics of the sub-populations mentioned above are given
for place of residenee, the data for sub-populations should be converted to
a percentage of the total resident population in each aggregated statistical
area.  Then, we can perform a population exposure analysis for various sub-
populations by using the same receptor network developed for the total
resident population.
     For working-age population, its large diurnal mobility may invalidate
the stationarity assumption employed in the population exposure methodology.
However, a way exists to incorporate population mobility into the current
population exposure methodology.  It can be assumed that population exposure
during working time occurs at work place, while population exposure during
non-working time,occurs at residence location[3].  To compute exposure of
the workers during working  time requires employment statistics that
provide the number of workers at their place of employment.  This type of
sub-population data should be given by the actual size of the sub-population
in each aggregated statistical area, instead of the percentage of the total
population.
Population Data for Off-Survey Years
     When the analysis is made for many years, the population statistics should
be computed for each year by interpolating known population statistics or
population projections for other years to that year.   For example,  the size
of resident population in New Y ork County (Manhattan borough) in 1965 is
estimated as 1,618,757 by linearly interpolating the  1960 population,  1,698,281,

-------
                                   52
and the 1970 population, 1,539,233,  to the year 1965.   The 1973 population
may be approximated by the 1970 census population or may be estimated by
interpolating the 1970 population and the population projected to 1980.
     When the study period is only for a few years or when the spatial
distribution of population over the study period remains almost the seme,
the population data of a single survey year can be used for population
exposure analyses over the entire study period.

3.2.2  Receptor Point Data
     In a population exposure analysis, a receptor point is used for several
purposes.  A receptor point represents both the size, the spatial location,
and the spatial spread of the local population,  The spatial location of the
local  populace is given by the x-y coordinates of the receptor point in the
digitized regional map.  Specifications for the formats are given in the
User's Manual.
     Air quality  data measured at air  monitoring  stations  are  spatially inter-
polated  to  each  receptor point and are merged  with  the  population data at  the
receptor points  to compute various population  exposure  variables.  Thus, the
receptor points  can  also be  used to  develop  an  isopleth map of air quality
and population exposure variables from the values computed at  each receptor
point.   For example,  the isopleth map  of  long-term  exposure to annual mean
concentrations over  the study region  is developed from  the values computed
at each  of  the receptor points.  Guidelines  for producing  isopleth maps
of air quality and population exposure variables are given in Chapter 2.

-------
                                    53
3.3  CHARACTERIZATION OF POPULATION EXPOSURE TO AIR POLLUTION
     Pollutant concentrations over an urban area are constantly changing in
time and space.  Exposure of people to these concentrations can be analyzed
with respect to both long-term average exposure and statistical distribution
of short-term exposures over a long period (usually a year).  To make the
analysis tractable, the resident population (the type of data available
from the census summaries) is used, and individual members of the population
are assumed to be locationally fixed at their residence location.
3.3.1  Analysis of Long-Term Population Exposure
     An annual mean concentration is used to designate the long-term average
pollution level to which people are exposed.  The long-term average pollution
level at each receptor point is estimated by spatially interpolating the
annual mean concentrations observed at the three nearest neighboring stations
to that receptor point by using Eq. (2).  For a given receptor point,
{x-,y-). the computer program call ad Long-Term Population Exposure Model
(LPEM) automatically searches among all the stations used for the
analysis for the three nearest stations, (x.,y.}» j - 1.2,3, to that receptor
                                           J  J
point (see User's Manual).
     Once the annual mean concentration, C^, is determined for each receptor
point, population exposure can be calculated by combining the air quality
and population statistics.  The LPEM compute^ program compares C- with a
                                *
given concentration threshold, C ; enters the local population, P.; and
determines population exposure for the entire region, R.   Mathematically,
this can be expressed by

-------
                                    54
                       P(C*) -  £ P,  U(C,-C*)/E  ?<   »              (3)
                                ieR             ieR   1
                                        *                                *
v/here an indicator step functiontU(C.j-C ), takes the value one for C^>C
                  *                                     *
and zero for C-
-------
                                           55
O)

-------
     1.0
     0.8

-------
                                     57
 longer black bars indicating the percentage of the population exposed  to
 annual mean N02 above 130 yg/m .  The decrease in  population  exposure  in
 1973/74 is noted by the shorter black bar  and the  longer gray bar, which
 indicates the percentage of the population exposed to N02 between  100  and
 130 yg/m3.
      The LPEM computer program also  calculates three  regional  indices  for
 characterizing long-term air quality and population exposure:   station average
 concentration, space average concentration, and population average  concen-
 tration.  The station average concentration is given  by an arithmetic  mean
 of annual mean concentrations observed at  individual  stations.  The  space
 average concentration is given by an area  weighted average of the  concen-
 trations at the receptor points.  The population average concentration is
 given by a population weighted average of  the receptor concentrations  and
 indicates the air quality level most representative of the population.
 Mathematically, the space average concentration^ At) . and the population
                                                    o
 average concentration, AQ , are expressed  respectively, by

                       AQ. =   £  S.C./ £ S.                          (4)
                         s          n n  icR  n
                       AQp =  E P. C./  £  P                          (5)
                                  7  1  ieR   7
where C.. is the annual mean concentration at the i    receptor point,
and Si and P..  are, respectively, the land area and  the local  population
size represented by the i    receptor point.

-------
                                    58
3.3.2 _ Analysis of  Short-Term  Population Exposure



     Analysis of  population  exposure to short-term peak concentrations  is



more difficult than  the  analysis  for long-term average concentrations.   The



reason is that long-term average  exposure involves only one pollution  variable,



i.e., concentration  level, but short-term exposure involves at  least  two pol-



lution variables,  i.e.,  concentration level  and frequency of occurrence or



duration of that  concentration level.



     It is extremely costly  to compute each  instantaneous exposure  level  In-



dividually over a  long  time  period.   Instead of using each  instantaneous con-



centration value,  a  percentage of the time that the short-term  (1-hr  or 24-hr)



NAAO^ was exceeded  is  used to  characterize short-term exposures  of  the popula-



tion over a long  period.  The  quantity, "percentage of the  time  above  the



standard,'' is termed a  "risk frequency" because it indicates how frequently



^••.oplf: are exposed  to  a  lovel  of  air pollution above the standard.



     I he risk frequency  can  be computed either from the number  of standard



violations or from the  percent!le concentrations.  When a number of standard



v;- lotions are .jvailable, the  risk frequency at each monitoring  station is



ustd a-, input fldt.fi  t.o  the I PI M computer proqram.  Then, the LPHM spatially



interpo loter, thf-  risk  frequencies observed  concentra-



i. i'jris ai f-i'jht so let, ted  perceiii. i les  ,ire usetl 
-------
                                    59
spatially interpolates the percentile concentrations at the monitoring sta-

tions to those at receptor points.  Then, the SPEM compares each of the

eight interpolated percentile concentrations with the air quality standard

to determine the risk frequency at each receptor point (see User's Manual).

     The risk frequency computed at each receptor point is used to draw an

isopleth map of risk frequencies over the study region.  The risk frequency

map is an excellent aid in visualizing the spatial variation of short-term

air quality levels.

     When the risk frequencies are determined for all the receptor points,

short-term exposure levels can be calculated for the entire study region.

Both computer programs (LPEM and SPEM) compare the risk frequency, F., at

each receptor point with a given frequency threshold, F*; enter the local

population, P.; and scan the entire study region, R,  Mathematically, this

process can be expressed by




                 P(F*) -  E  P.UCF.-F*)/  Y P,-      ,                (6)
                         i R       ]       ifR

where an indicator step function L:(F.~F*} takes the value one for F^>F*

and zero for F..
-------
                                   60
illustrates how much the population exposure decreased (or increased)  in
a given time period, how the decrease (or increase)  in population  exposure
was distributed over the population, and how the frequency of dangerous
exposures changed.  For instance, Fig.  15 shows the  percentage of  the
population exposed to total suspended particulate above the national
secondary 24-hr standard (150 yg/m ) at least 10$ of the days dropped
from 33% in 1971 to 4% in 1974.
    The bar graph shown in Fig. 16 is convenient for illustrating  year-
to-year variations in population exposure over a long period.  The increase
in population exposure during the middle years, 1967-72, is represented  by
the rhorter white bars, indicating the  percentage of the population  ex-
posed to hourly NOo above the California standard less than 6% of  the
days.  The decrease in population exposure in 1973/74 is noted by  the
longer white bar and the shorter gray bar, indicating those who were
exposed above the California standard between 6% and 12% of the days.
     Both computer programs compute two regional  indices for character-
izing short-term air quality and population exposure:   the percentage  of
time (hours or days) exceeding the standard, area weighted average over
the study region; and the percentage of time exceeding the standard, popu-
lation weighted average over the region.  The latter quantity is the
average percentage of time the standard is exceeded  among all the  people
in the study region.  Mathematically, the two regional indices, F$ and F  ,
are expressed, respectively, by

                    Fs =   £ S. F  /  £ S.                         (7)
                     *    ieR     n   ieR
F  _
FP "
                           E P, F. /  L P..                        (8)
                           ieR  n  1   ifR  n

-------
                                         61
c
QJ
£
o
T3
O)
(/)
O
OL
X
c
o ,

•£> >,
03 O
r— C
3 O)
CL 3
o cr
O- O)

it- Li_
O
  -o

-------
            U3
            VO
            ID
            1C
                  CO
C\J
r--
100
90
80
70
2:
o
i — i
1 60
O.
O
Q-
-i 50
•3.
O
U- 40
o
«—
z
UJ ~n
<_> ou
C£
yj
o.
20
10
0
MM*





, ',•.*.•,' " * ]
••<<•: ilis
• :•••:•:•:•:: !]
,:x:>fv:::->M*«
1 X




•
Bffl-::';;:r::

i i :ii:a £ i
CA. standar




d
P IS I OF DAYS STANDARD EXCEEDED
p < 6
'.:'. 6 £ p < 1 2


                                                                                    01
                                                                                    ro
Figure 16. Changes in Population Exposure to NC^ During  Five 2-Year

           Periods in the  Los  Angeles Region [3].

-------
                                    63
                          REFERENCES
 1.    Harvard Laboratory  for  Computer  Graphics,  "User's  Reference Manual
      for Synagraphic  Computer  Mapping 'SYMAP1 Version V,"  Harvard
      University,  Cambridge,  MA,  1968.

 2.    Horie,  Y.,  and A. C.  Stern,  "Analysis of Population Exposure to
      Air Pollution  in New  York-New Jersey-Connecticut Tri-State Region,"
      U.S.  EPA/OAQPS Publication  No. EPA-450/3-76-027, University of
      North Carolina,  Chapel  Hill, NC,  March  1976.

 3.    Horie,Y., ejt a_]_. , "Population Exposure  to  Oxidants and Nitrogen
      Dioxide in  Los Angeles:   Volumes I,  II, and  III,"  U.S. EPA/OAQPS
      Publication  No.  EPA-450/3-77-004a, b, and  c, Technology Service
      Corporation, SantG  Monica,  CA, January  1977.

 4.    U.S.  Erivironmenta i  Protection Agency, "National Air Quality and
      Emissions Trends Report,  1975,"  U.S. EPA/OAQPS Publication No.
      EPA-450/1-76-002, Monitoring and Data Analysis Division, Office
      of Air Quality Planning and  Standards,  Research Triangle Park,
      NC, November 1976.

 5.    Zupan,  J.M., The Distribution of Air Quality in the New York
      Region, Resources of  the  Future,  Inc.,  Washington, DC, 1973.

 6.    McHarg, I.  L., Design with  Nature, Published for the American Museum
      of Natural  History, Doubleday/Natural History Press, Garden City,
      NY, 1971.

 7.    Anderson, J. A.  et  al.,   "Correlation between Air  Pollution and
      Socio Economic Factors  in Los Angeles County," submitted to
      Urban Ecology, Department of Chemistry  and Energy  Center, University
      of California, San  Diego, CA, January 1977.

 8.    Brian,  J.L., Berry, et  al.  The Social Burdens of Environmental
      Pollution:   A  Comparative Metropolitan  Data  Source, Department of
      Geography,  University of  Chicago, 1976.

 9.    Istvan,Takacs  and G.  Bradford Shea.  Estimations of Human Population-
      at-Risk to  Existing Levels  of Air Quality, EPA Contract No. 68-01-2820,
      Enviro Control,  Inc., Rockville,  Maryland, February 1975.

10.    TRW Systems  Group, "Air  Quality Display  Model," prepared for Department
      of Health,  Education  and  Welfare, National Air Pollution Control
      Administration,  Washington,  DC,  Contract No. Ph-22-68-60, and
      Available from NTIS,  Springfield, VA, 22151  as PB-189-194, 1969.

-------
                                     64
11.   Busse, A.D.,  and J.  R.  Zimmerman,  "User's Guide for the Climatological
      Dispersion Model," U.S.  EPA Publication No.  EPA-R4-73-024,  National
      Environmental  Research  Center, U.S.  EPA, Research Triangle  Park,   NC,
      December 1973.

12.   Ludwig, F. L.,  W.  B.  Johnson,  A.  E.  Moon, and R.  L. Mancuso,
      "A Practical  Multipurpose Diffusion  Model for Carbon Monoxide,"
      Stanford Research  Institute,  Menlo Park, CA,  Contracts  CAPA-3-68
      and CPA 22-69-64,  1970.

13.   Zimmerman, J.  R.,  and R.  S.  Thompson,  "User's Guide for HIWAY, A
      Highway Air Pollution Model,"  U.S. EPA Publication No.  EPA-650/
      4-74-008,  National Environmental  Research Center,  U.S.  EPA,
      Research Triangle  Park,  NC,  February 1975.

'.4.   Fran!,, N.  H.,  W.  F.  nunt, ;-., and W.  H. Cox, "Population Exposure:
      An Indicator of Air Quality Improvement," Paper #77-44.2 presented
      at the 70th Annual Meeting of the  Air Pollution Control Association,
      Toronto, Canada, U.S. Environmental  Protection Agency,  Research
      Triangle Park, NC, June 1977.

•3-   Tri-State  Regional Planning Commission,  Re g iona1 Profi1e--Regiona1
      Employment 1970,  Vol. II, No.6, New York, NY, December 1973.

16.   Wolaver,  T. G., "The Dsstribution of Natural and Anthropogenic
      Elements  and Compounds in Precipitation Across the U.S.:  Theory
      and Quantitative  Models," Botany  Department, University of
      North  Carolina, Chapel Hill, NC, October 1972.  Copies available
      through Division  of  Ecological Research, U.S. EPA/NERC, Research
      Triangle  Park, NC.

17.   Cline, A.  K.,  "Curve Fitting Using Splines Under Tension,"
      Atmospheric Technology, National  Center for Atmospheric Research,
      No. 3,  pp  60-65,  September 1973.

18.   Wright, T. J., "Utility Plotting  Programs," Atmospheric Techno1ogy,
      National  Center for  Atmospheric Research, No.  3,  pp 51-57, September
      1973.

19.   Bureau of the  Census, "Number  of  Inhabitants," PC(1)-A Series,
      U.S.  Department of Commerce,  Washington,  DC, May  1972.

20.   Bureau of the  Census, "Census  Tracts,"  PHC(l)  Series,  li.S. Department
      of Commerce, Washington,  DC,  May  1972.

-------
                                    65
             APPENDIX A.  USE OF COORDINATE TRANSFORMATION FOR
                          LOCATING MONITORING STATIONS ON A SKELTON MAP


     When the study region is large, a mathematical method of  locating

monitoring stations on a skeleton map of the study region often works

more effectively and more accurately than heuristic methods, such as

those based on the street address of station site or on knowledge •/   •=•

relative location of one station to another.  The mathematical method

utilizes the UTM coordinates given in the SAROAD format and applies a co-

ordinate transformation on the UTM coordinates of an individual station.

     When the mathematical method is used, the first step is to locate

the two most familiar stations on the skeleton map.  The location of

other stations on the map is then determined by a coordinate transfor-

mation of their UTM coordinates into the coordinate^ used in the map.


The map coordinates  (x,  y) of a station  whose UTM coordinates are (p, q)

are given by the following equations:

                       x = m(p - pj) + x]

                       y = m(q - q,) + y,


and the  slope, m, is given by
                       m =	-	      ,             (A-2)
                           (P1-P2)y2 - (q1-q2)x2



where (x,,y,) and (x2,y2) are the map coordinates of the two known stations

and (p,,q,) and (p2,q2) are their UTM coordinates.

-------
ENVIRONMENTAL PROTECTION AGENCY
     Technical Publications Branch
       Office of Administration
Research Triangle Park, North Carolina 27711
         OFFICIAL BUSINESS
   AN EQUAL OPPORTUNITY EMPLOYER
     POSTAGE AND FEES PAID
ENVIRONMENTAL PROTECTION AGENCY
           EPA - 335
                                                                             SPECIAL FOURTH-CLASR RATE
                                                                                     BOOK
                               Return this sheet if you do NOT wish to receive this material
                               or if change of address is needed [	].  (Indicate change, including
                               ZIP code.)
                            PUBLICATION NO.  EPA-450/2-77-024a
                                         (OAQPS NO. 1.2-083)

-------