PB83-165191
Evaluation of the Empirical
Kinetic Modeling Approach (EKMA)
SRI International
Menlo Park, CA
Prepared for
Environmental Sciences Research Lab.
Research Triangle Park, NC
Feb 83
U.S. Department of Commerce
Nations! Tedsacal Information Service
lb
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EPA-600/3-83-003
February 1983
PUQ3-16S191
EVALUATION OF THE EMPIRICAL KINETIC
MODELING APPROACH (EKMA)
by
J. R. Martinez
Atmospheric Science Center'
C. Maxwell
H. S. Javitz
R. Bawol
Statistical Analysis Department
SRI International
Menlo Park, California 94025
EPA Contract 68-02-2984
Project Officer
Basil Dimv ".riades
Atmospheric Chemistry and Physics Division
Environmental Sciences Research Laboratory
Research Triangle Park, North Carolina 27711
ENVIRONMENTAL SCIENCES RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U. S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NORTH CAROLINA 27711
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TECHNICAL REPORT DATA
IPlease read Instructions on the rciersc be/ore completing)
1. REPORT NO. 2.
EPA-600/3-83"003
3. RECIPIENT'S ACCESSION NO.
P53* 16 5191
4. TITLE AND SUBTITLE
EVALUATION OF THE EMPIRICAL KINETIC MODELING
APPROACH (EKMA)
S. REPORftfAfE
February 1983
6. PERFORMING ORGANIZATION CODE
7. AUTHOH(S)
J. R. Martinez, C. Maxwell, H. S. Javitz, and R. Bawol
B. PERFORMING ORGANIZATION REPORT NO.
SRI Project 7936
9. PERFORMING ORGANIZATION NAME AND ADORESS
SRI International
333 Ravenswood Avenue
Menlo Park, California 94025
10. PROGRAM ELEMENT NO.
CDWA1A/01 - 0649 (FY-83)
11. CONTRACT/GRANT NO.
68-02-2984
12. SPONSORING AGENCY NAME AND ADORESS
Environmental Sciences Research Laboratory-RTP, NC
Office of Research and Development
U. S. Environmental Protection Agency
Research Triangle Park, NC 277.11
13. TYPE OF REPORT AND PERIOD CiVERED
14. SPONSORING AGENCY CODE
EPA/600/09
15. SUPPLEMENTARY NOTES
16. ABSTRACT t
The EKMA 1s a Lagrangiar photochemical air quality simulation model that calculates
ozone from Its precursors: nonmethane organic compounds (NMOC) and nitrogen oxides
(N0y). This study evaluated the performance of the EKMA when it 1s used to estimate
the maximum ozone concentration that can occur 1n an urban area and its environs. The
evaluation was conducted using data for five U.S. cities: St. Louis, Houston,'
Philadelphia, Los Angeles, and Tulsa.
A novel statistical evaluation procedure was developed to measure the accuracy of the
EKMA o.-one estimates. The accuracy parameter fs defined as the ratio of observed to
estimated ozone. Associated with this ratio is an accuracy probability, which is
definee. as the probability that the ratio lies within a predefined percent, (e.g. ±20
percent) of unity, a unit value of the ratio denoting perfect agreement between observa
tion and prediction. The evaluation procedure uses NMOC and N0X as inputs to calculate
the accuracy probability of the EKMA ozone estimate. The full range of accuracy
probabilities associated with the EKMA ozone estimates is displayed in graphical form
on the NM0C-N0x plane.
The report describes the results for the various cities, and discusses potential
appli cations of the methodology to other models and to the assessment of ozone control
strategies.
17. KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS
b. IDE NT IF IE RS'OPEN ENDED TERMS
C. COSATI [ wld/GtOUp
18. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
10. SECURITY CLASS (This Report/
UNCLASSIFIED
21. NO. OF PAGES
123
2'1. SECURITY CLASS (This page!
UNCLASSIFIED
22. PRICE
EPA Fen* 2110-1 (R«*. 4-77) previous edition is OBiourt
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NOTICE
This document has been reviewed in accordance with
U.S. Environmental Protection Agency policy and
approved for publication. Mention of trade names
or commercial products does not constitute endorse-
ment or recommendation for use.
ii
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ABSTRACT
The EKMA is a Lagranglan photochemical air quality simulation model that
calculates ozone from its precursors: nonaethane organic compounds (NMGC) and
nitrogen oxides (NOx). This study evaluated the performance of the EKKA when
it is used to estimate the maximum ozone concentration that can occur in an
urban area and its environs. The evaluation was conducted using data for five
U.S. cities: St. Louis, Houston, Philadelphia, Los Angeles, and Tulsa.
A novel statistical evaluation procedure was developed to measure the
accuracy of the EKKA ozone estimates. The accuracy parameter is defined as
the ratio of observed to estimated ozone. Associated with this ratio is an
accuracy probability, which is defined as the probability that the ratio lies
within a predefined percent (e.g. ±20 percent) of unity, a unit value of the
ratio denoting perfect agreement between observation and prediction. The
evaluation procedure uses NMGC and N0X as Inputs to calculate the accuracy
probability of the EKMA ozone estimate. The full range of accuracy probabili-
ties associated with the EKMA ozone estimates is displayed in graphical form
on the NM0C-N0x plane.
The report describes the results for the various citi"s, and discusses
potential applications of the methodology to other models and to the assess-
ment of ozone control strategies.
This report was submitted in partial fulfillment of Contract 68-02-2984
by SRI International under sponsorship of the U.S. Environmental Protection
Agency. This report covers the period June 1979 to December 1981 and work was
completed as of March 1982.
Ill
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CONTENTS
Abs tract Hi
Figures vli
Tables x
1. introduction... 1
Objective .1
Background... 1
Report Organization.... 2
2. Methodology » 3
Overview of the Data Bases.... 3
Data Review, Analysts, And Selection of Days...., 3
EBticaatlon of Ozone Using EKMA 6
Statistical Evaluation 7
3. EKMA Evaluation for the St. Louis Area... 11
Data Review and Analysis 11
Definition of Evaluation Data Set........ 16
Evaluation of Standard EKMA 16
Evaluation of City-Specific EKMA......... 31
Discussion. 42
4. EKXft Evaluation for the Houston Area.... 44
Data Review and Analysis 44
Definition of Evaluation Data Set.......................... 44
Evaluation of Standard EKMA 45
Evaluation of City-Specific EKMA 59
Discussion 63
5. EKMA Evaluation for the Philadelphia Area................ 66
Data Review and Analysis. 66
Definition of Evaluation Data Set 66
Evaluation of Standard EKMA 69
Evaluation of City-Specific EKMA.. 74
Discussion. 78
6. Evaluation Using Data for the Loa Angeles Area................. 61
Data Review and Analysis. 81
Definition of Evaluation Data Set.......................... 83
Evaluation of Standard EKMA..,.,... S3
Evaluation of City-Specific EKMA...................;."...... 97
Discussion....101
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7. Evaluation Using Data for the Tulsa Area 104
Data Review and Analysis 104
Definition of Evaluation Data Set 104
Evaluation of Standard EKMA 107
Evaluation of City-Specific EKMA 107
Discussion Ill
8. Conclusions, Implications, and Recommendations 113
Discussion of Results 113
Implications for EKMA Applications 114
Recommendations 117
Concluding Remarks 118
Appendix—Equations for Standard-EKMA Ozone Estimates 119
References 120
vi
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FIGURES
Number Page
1 Location of Regional Air Monitoring Systems (RAMS)
Stations 12
2 Scatterplot of Maximum Rally Ozone Concentration
as a Function of Dally Maximum Temperature for the 1976
St. Louis Data.. 14
3 Scatterplot of Daily Maximum Ozone Concentration
as a Function of Daily Core-City 0600-0900 (CDT) Average
Ratio of NMHC to N0X for the 1976 St. Louis Data IS
4 Scatterplot of Observed Ozone and Standard-EKMA Ozone
Estimate for St. Louis... . 22
5 Scatterplot of 0600-0900 (CDT) Concentrations of NMCC
and N0X for St. Louis 27
6 Scatterplot of 0BS/EST as a Function of 1/N0X
for Standard-EKMA Ozone Estimate in St. Louis....* 28
7 Accuracy Probability Plot for Standard-EKMA Ozone
Estimates for St. Louis 30
8 Plot of Constant-Z Curves on NM0C-N0x Plane
for Standard-EKMA Estimates for St. Louis 32
9 Accuracy Probability Curves for Standard-EKMA Evaluation
for St. Louis 33
10 Scatterplot of City-Specific and Standard EKMA Ozone
Estimates for St. Louis.............. 36
11 Scatterplot of Observed Ozone and City-Specific EKMA
Ozone Estimates for St. Louis 37
12 Accuracy Probability Plot for City-Specific EKMA Ozone
Estimates for St. Louis 40
13 Plot of Conscant-Z Lines on NM0C-N0x Plane
for City-Specific EKMA Estimates for St. Louis. 41
vii
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Nurcber Page
14 Scatterplot of Observed Ozone and Standard-EKMA Ozone
Estimate for HAOS Data Set 49
15 Scatterploc of Observed Ozone and Standard-EKMA Ozone
Estimate for HOMS Data Set 50
16 Scatterplot of N0X and NMOC for the HAOS Dita Set 54
17 Scatterplot of N0X and NMOC for the HOMS Data Set 56
18 Accuracy Probability for Standard-EKMA Ozone Estimates
for the HAOS Data Set 57
19 Conptant-Z Plot for Standard-EKMA Ozone Estimates
for the HAOS Data Set 58
20 Scatterplot of Observed Ozone and Clty-Spec'lfic EKMA
Ozone Estimates for the HAOS Data 61
21 Scatterplot of Observed Ozone and City-Specific EKMA
Ozone Estimates for the HOMS Data 62
22 Accuracy Probability for City-Specific EKMA Ozone
Estimates for the HAOS Data Set... 64
23 Constant-Z Plot for City-Specific EKMA Ozone Estimates
for the HAOS Data Set 65
24 Air Quality Monitoring Network for the Philadelphia Area 67
25 Scatterplot of Observed Ozone and Standard-EKMA Ozone
Estimate for Philadelphia................ 70
26 Scatterplot of 0600-0900 (EDT) Concentrations of NMOC
and N0X for Philadelphia ¦, 72
27 Accuracy Probability Plot for Standard-EKMA Ozone
Estimates for Philadelphia 73
28 Constant-Z Plot for Standard-EKMA Ozone Estimates
for Philadelphia........ 75
29 Scatterplot of Observed Ozone and City-Specific EKMA
Ozone Estimate for Philadelphia
30 Accuracy Probability Plot fur City-Specific Ozone
Estimates for Philadelphia 79
~ill
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Number Page
31 Constant-Z Plot for City-Specific EKMA Ozone Estimates
for Philadelphia 80
32 Air-Quality Monitoring Network for the Los Angeles Area 82
33 Scatterplot of Observed Ozone and Standard-EKMA Ozone
Estimate for Los Angeles 91
34 Scatterplot of 0600-0900 NM0C and N0X for Los Angeles 93
35 Accuracy Probability Plot for Standard-EKMA Ozone
Estimates for Los Angeles . 95
36 Plot of Cor.stant-Z Curves on NM0C-N0x Plane
for Standard-EKMA Ozone Estimates for Los Angeles.............. 96
3/ Scatterplot of City-Specific EKMA Ozone Estimates
and Standard-EKMA Ozone Estimates for Los Angeles *. 99
38 Scatterplot of Observed Ozone and City-Specific Ozone
Estimate for Los Angeles 100
39 Accuracy Probability Plot for City-Specific EKMA
Ozone Estimates for Los Angeles 102
40 Plot of Constant-Z Curves on NMOC-NOx Plane
for City-Specific EKMA Ozone Estimates for Los Angeles... 103
41 Map of Tulsa, Oklahoma, and Vicinity 105
42 Scatterplot of Observed Ozone and Standard-EKMA
Ozone Estimate for Tulsa 108
43 Scatterplot of 0600-0900 NM0C and N0X for Tulsa.. 109
44 Scatterplot of Observed Ozone and City-Specific EKMA
Ozone Estimate for Tulsa 112
45 Flowchart for the Application of the EKMA
as a Screening Tool for Analyzing the Impact
of a Control Strategy 116
ix
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TABLES
Number Page
1 Data Bases Used in EKMA Evaluation 4
2 0600-0900 (CDT) Ratios of NMHC/N0X Cop ntrations
for St. Louis Area 13
3 Evaluation Data Set for St. Louis 17
4 Selected 0600-0900 NMOC and N(>x Concentrations
at Source-Region Monitoring Sites In St. Louis 24
5 Meanj. Standard Deviations, and Correlations
for Selected Variables In the St. Louis
Evaluation Data Set. * 25
6 Summary of Input Parameters for Obtaining
City-Specific EKMA Ozone Estimates for St. Louis 34
7 Means, Standard Deviations, ail Correlations
for City-Speclflc EKMA Evaluation for St. Louis 39
6 Evaluation Data Set for Houston: HAOS Data... 46
9 Evaluation Data Set for Houston: H0MS Data 48
10 Statistical Parameters for Selected Variables
in the HAOS Data Set 52
11 Statistical Parameters for Selected Variables
in the H0MS Data Set 53
12 Summary of Input Parameters for Obtaining
City-Specific EKMA Ozone Estimates for Houston 60
13 Evaluation Data Set for Philadelphia * t>4
14 Means, Standard Deviations, and Correlations
for Selected Variables in the Philadelphia Data Set 71
15 Summary of Input Parameters for Obtaining
City-Specific EKMA Ozone Estimates for Philadelphia 76
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Number Page
16 Evaluation Data Set for Los Angeles 84
17 Means, Standard Deviations, and Correlations
for Selectt-'j Variables ir. the Los Angeles Data Set. 92
18 Sueaary ol Input Parameters for Obtaining
Clty-Speclfic EKMA Ozone Estimates for Los Angeles. 98
19 Evaluation Data Set for Tulsa 106
20 Summary of Input Parameters for Obtaining
Clty-Speclfic EKMA Ozone Estimates for Tul6a 110
xi
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SECTION 1
INTRODUCTION
OBJECTIVE
The objective of this study is to assess the performance of the Empirical
Kinetic Modeling Approach (EKMA) when it is used to estimate the maximum ozone
(O3) concentration that could occur in an urban area and its environs. Speci-
fically, the study quantitatively measures EKMA's ability to predict maximum
O3, defines conditions under which O3 estimates can achieve specific accuracy
levels, and examines the application of EKMA as an estimator of maximum O3.
BACKGROUND
A common problem in air pollution control requires estimating the reduc-
tion in the level of O3 precursors, I.e. nonmethane organic compounds (NMOC)*
and nitrogen oxides (NOx)» needed to achieve a prescribed decrease in O3 con-
centration. To tackle this problem, one must have a model that relates O3 to
NMOC and N0X; the EKMA, which was developed by the U.S. Environmental Protec-
tion Agency (EPA), is one such model. The EKMA has been extensively docu-
mented, and the reader should consult the references for technical details
(EPA, 1977, 1978; Dodge, 1977; Trijonis and Hunsaker, 1978; FPA, 1960). EPA
has prepared and disseminated a computer program that performs the calcula-
tions that relate O3 to NMOC and NOx (Whitten and Hogo, 1978). The output of
the computer program is a graph that contains constant-03 contours (O3 Iso-
pleths) as a function of NMOC and NOx; hereafter we will refer to this graph
as the "O3 isopleth diagram."
Basically, the EKMA takes two forms: standard and city-specific. The
standard EKMA is based on conditions that prevail in the Los Angeles area; the
city-specific version, as the name implies, tailors the model to a particular
city. We will evaluate the performance of both forms of EKMA using data for
five cities.
In a typical application, the EKMA has been used to calculate the percen-
tage reduction, in NMOC and NOx that would be required to reduce O3 from a high
observed value to some desired lower level. Under current EPA guidelines
*Much of the EKMA literature refers to the organic compounds as nonmethani
hydrocarbons (NKHC). This term has recently been replaced by NMOC (EPA, .
1960), and we will conform to this usage throughout this report.
1
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(EPA, 1977; 1980), such an application uses the observed ozone level and the
median 0600-0900 (LDT) NM0C/N0x ratio to find the NMOC and N0X concentrationr,
that the model requires to produce the observed-.ozone. These NMOC and NOx
concentrations then become the base data used in the calculation of percent
reduction of NMOC and NOx. Thus, in this procedure the NMOC and NOx conceni-
trations are not necessarily the precursor levels that prevailed when the
ozone was observed. Rather, they are the presumed precursor levels defined'by
the model.
Our assessment of the EKMA as a predictor of maximum O3 shifts the focus
of EKMA from using observed O3 and the NMOC/NOx ratio to define precursor lev-
els, as was mentioned above, to using precursor levels to estimate O3 concen-
tration. Thus, the EKMA could be used to estimate the O3 level produced by a
given emission control strategy that yields particular levels of NMOC and N0X.
In such applications, it would be helpful for the analyst to know whether ther
EKMA estimate is an upper bound for the O3 that would actually occur, and if
so, to know the accuracy of the upper bound. Our study is concerned with such
questions.
REPORT ORGANIZATION
Section Two describes the evaluation methodology. The results of the
EKMA evaluation using data for five cities are presented in Sections Three
through Seven. Section Eight contains conclusions and recommendations. An
appendix defines several equations used in the study.
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SECTION 2
METHODOLOCY
OVERVIEW OF THE DATA BASES
The first step in the evaluation process identified and obtained the data
bases for the five cities of interest: St. Louis, Missouri; Houston, Texas;
Philadelphia, Pennsylvania; Los Angeles, California; and Tulsa, Oklahoma. For
each city, the model assessment procedure consisted of three steps:
0 Review and analyze data and select days for the evaluation data set.
• Obtain ozone estimates using both standard and city-specific EKMA.
• Conduct a statistical evaluation of EKMA performance as a predictor of
maximum O3.
Table 1 lists the five cities and briefly describes each data base. Both
air quality and meteorological data were included in each data base, but the
quantity of data and the spatial coverage are by no means uniform for all the
data bases. Because the data for four of the cities were obtained in special
studies, the spatial coverage of pollutant patterns for these cities is more
thorough than usual. For Houston in 1978, and for Tulsa and Philadelphia, the
duration of the monitoring program was short, and this, in combination with
other data selection criteria, resulted in small data sets being used in the
EKMA evaluation.
Routinely collected monitoring data were used for Los Angeles, but this
is a rich data base because the monitoring network is extensive. Los Angeles
data for the period 1976-1978 were examined; 1978 was selected because it con-
rained the highest ozone levels.
The sections below describe the steps in the evaluation process.
DATA REVIEW, ANALYSIS, AND SELECTION OF DAYS
The objectives of the data review and analysis process are to identify
the available data and to define the criteria.for selecting the days for the
EKMA evaluation data set.
Each data base was examined to determine what correlations, if any, exist
between high ozone concentrations and other pollutants and meteorological
parameters. These correlations were used to define criteria for selecting
days to test the city-specific and the standard EKMA. We seek to identify
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TABLE 1. DATA BASES USED IN EKMA EVALUATION
Dara Base
City
Date
Type
Title
Source
Reference
St. Louis,
Missouri
May-Oct 1976
Special
Regional Air
Pollution Study
(RAPS)
EPA
Card veil (1980)
Houston,
Texas
May-Oct 1977
Special
Houston Area
Oxidant study
(HAOS)
SRI
Ludvlg and Martinez (1979)
Ludvlg et al. (1979)
IS Sep -
12 Oct 1978
Special
Houston Oxidant
Modeling Study
(HOMS)
EPA
Martinez (1982)
Nitz and Martinez (1982)
Philadelphia,
Pennsylvania
Jul-Aug 1979
Special
Philadelphia
Oxidant Data
Enhancement Study
EPA
Westberg and Sweeny (1980)
Los Angeles,
California
May-Oct 1978
Routine
Monitoring
California
Air Resources
Board
—
Tulsa,
Oklahoma
Jul-Sep 1977
Special
EPA
Eaton and Dlomock (1979)
Eaton et al. (1979)
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precursor and meteorological conditions associated with ozone concentrations
that equal or exceed 100 ppb; these conditions are necessary, but may not be
sufficient, for such concentrations of ozone to occur. (That is, high ozone
concentrations never occur in the absence of such conditions, but may not
occur even if the conditions are present.) This approach yields a set of
selected modeling days that encompasses the high-ozone-concentration events,
but that also contains a number of low-ozone cases. Although the latter may
strain the worst-case assumptions of the EKMA, we have retained them to exter
the range of ozone concentrations in the evaluation.
The data were also analyzed to identify monitoring sites within the urba
area that can be considered to be good Indicators of 0600-0900 (LDT) NMOC and
N0X concentrations, which EKMA considers to be the principal cause of the
ozone maximum that occurs downwind of the source region. We will refer to
these sites as source-region monitors.
The initial step of the analysis was to compile daily summaries for each
data set. The dally summary provides information on pollutant and meteorolog
ical data, including the date, the maximum ozone concentration observed
throughout the monitoring area, the station where the peak ozone concentratio
was observed, and the first: or only hour when the peak was recorded. The
daily summaries also incli.da average 0600-0900 NMOC and NOj. concentration for
the source-region monitors, and the ratio of the two averages. Additional
information is listed indicating whether the selected source-region monitors
had missing data for the times for which the average NMOC and N0X concentra-
tions were calculated. Meteorological data contained in the daily summaries
include the dally maximum temperature, the norning minimum temperature, the
0600-1400 (LDT) average wind speed and direction, and the standard deviations
of the wind speed and direction at one selected rural location, if available.
Cloud cover data for 1200 (LDT) and any available solar radiation data are
also listed. Estimates of the background ozone concentrations, which would
include transport effects, are listed for each day, but these were not avail-
able for all the cities.
Several restrictions were imposed on the data used for calculating the
average 0600-0900 NMOC and N0X concentrations at the source-region monitors.
kt each individual monitoring site, an average 0600-0900 NMOC and N0X concen-
tration would be calculated only if no Less than two.of the possible three
hours of pollutant data were available; otherwise, the 0600-0900 concentratioi
was considered to be missing. The composite (spatial) average of the 0600-
D900 pollutant concentrations would be calculated If averages existed for at
least half of the source-region monitors; otherwise the spatial average was
considered to be missing.
The daily average wind speeds and directions were calculated for the
hours from 0600-1400 (LDT). These hours were selected to indicate the genera]
transport between the hours of peak NMOC and N0X emissions and the time of the
peak ozone concentrations.
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The background (including transported) ozone concentration was determined
as follows. Based on the average 0600-140Q wind oirection, the background
ozone concentration was assumed to equal the peak* ozone concentration
recorded at the upwind station most distant from the urban area. This method
of determining background ozone differs from the method suggested in the EKMA
literature, which uses the 1100-1300 average ozone.at an upwind location (EPA,
1977). It is recognized that as the transported ozone enters the urban area
its level can be reduced due to reaction with nitric oxide; however, the
amount of ozone scavenging is not well defined. By using the peak upwind
ozone, we are conservatively assured of having the worst-case background ozone
?evel.
The essential criteria for selecting days for the evaluation data set
comprised:
• Data availability
• The time of occurrence of the daily ozone maximum
• The prevalence of meteorological conditions that are necessary, but
may not be sufficient, for the C3 level to be at least 100 ppb.
The 100-ppb cutoff was chosen to ensure that all days when the ozone national
ambient air quality standard (NAAQS) of 17.0 ppb was exceeded are included in
the evaluation. Such days should be included because FKMA is based on worst-
case assumptions and cannot be expected to perform well for days that do not
meet these conditions. Because we are interested in maximum ozone potential
with reference to an air quality standard, days with conditions associated
with low ozone concentrations are not critical to our evaluation.
ESTIMATION OF OZONE USING EKMA
Estimates of O3 concentration were obtained using both standard and
city-specific EKMA. The standard-EKMA estimates were computed using equations
fitted by Holton (1980) to the standard O3 isopleth diagram. These equations
were independently tested at SRI. The test verified that the fit was very
good, but a slight bias was detected and corrected by u.ean3 of supplemental
equations. Holton's formulas and the adjustment equations are presented In
the appendix of this report.
The city-specific ozone estimates were obtained using the EKMA computer
code. For each cityc the NMOC and NOjj precursors in the evaluation data set
were the model's inputs, and the code competed th2 ozone maximum using the
CALCULATE option (Whitten and Hogo, 1978).
*As used in this report, the term "peak ozone" refers to the maximum 1-hour
average ozoae.
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For both standard' and city-specific EKMA, the inputs used to estimate O3
were the 0600-0900 (LDT) NMOC and N0X, spatially averaged over all the
source-region monitors. Of course, the same NMOC and N0X coordinates were
used to obtain both standard and city-specific O3 estimates.
STATISTICAL EVALUATION
Approach
The evaluation is designed to test whether EKMA can be used to estimate
an upper bound for the maximum ozone concentration that can occur in a given
geographical region. To test this usage of EKMA we must define the dally max-
imum ozone concentration.
Daily Maximum—The maximum 1-hr average O3 concentration that occurs at
some time and location during a day in an urban region: The observed maximum
value recorded at a monitoring site, which may differ from the true daily max-
imum. (The latter may occur in a location where there is no monitor.) This
is the variable with which the EKMA ozone estimate will be compared.
The question of EKMA performance is, then, How well do EKMA estimates
serve as an upper bound for observed daily maximum ozone concentrations? EKMA
estimates are an upper bound if they are equal to or higher than the observed
maximum on every day. Denoting the observed dally O3 maximum by OBS and the
EKMA estimate by EST, then we want to test whether the inequality OBS < EST
holds. However, this criterion alone is inadequate, because it does not indi-
cate whether an upper bound is higher than necessary: An excessively high
upper bound could lead to unduly conservative decisions about allowable levels
of precursors. Both underprediction and overpredlction must be considered in
evaluating the performance of the EKMA. But, as we will show, it is appropri-
ate to relax the strict requirement that OBS EST to allow a certain amount
of underprediction. Such considerations are discussed below.
In evaluating the performance of the EKMA, we must recognize that the
measurements of O3, NMOC, and N0X are not exact; they are inevitably corrupted
by random and systematic errors. Recent analyseu of the quality of pollutant
measurements made in monitoring programs in the Houston area indicate that
most of the measurement errors for O3, NMOC and N0x fall within an Interval of
±20 percent (Ludwlg et al., 1979; Martinez, 1981). Thus, even If EKMA vcre
perfect, O3 estimates and observations would be expected to differ. Conse-
quently, using the ±20 percent figure, we define the following regions of
varying accuracy for the ratio of observed daily maximum to estimated O3
(denoted by OBS/EST):
• Region 1: 1.2 < OBS/EST
• Region 2: 0.8 < OBS/EST < 1.2
• Region 3: OBS/EST < C.8.
Region 1 contains ratios representing cases of substantial underpredic-
tion. Such cases are of special concern because they represent instances
7
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where the EKMA does not produce an upper bound for the observation. Ratios in
Regions 2 and 3 satisfy the inequality OBS/EST < 1.2, which allows for the
possibility of an apparent underestimation of at most 20 percent. Such
underestimation could be the result of measurement error, and we consider
it acceptable. Consequently, In testing whether EKMA estimates are upper
bounds for observed O3, we will relax the requirement OBS £ EST, and substi-
tute ORS £1*2 GST instead. We consider ratios in Region 2 to represent the
most accurate predictions that can be made, because the error is at most 20
percent. Region 3 contains ratios representing cases of substantial overpred-
lction. Such cases would be of concern in applications of EKMA only if the
estimate is over 120 ppb, which is the NAAQS.
To evaluate EKMA, we devised a method for calculating the likelihood that
a given EKMA estimate falls in one of the three regions defined above. In
general, the evaluation procedure consists of three steps:
Step 1: Compare observed (OBS) and estimated (EST) ozone.
Step 2: Investigate relationships between OBS/EST ratio and NMOC, N0X, and
other variables.
Step 3: Define regions on the NMOC-NOjj plane where the EKMA estimates attain
prescribed levels of predictive accuracy.
Descriptions of these three steps are presented below.
Step 1: Compare Observed and Estimated Ozone
To compare observed and estimated ozone, we began by plotting a scatter
diagram of OBS as a function of EST. We could t!>en define the three regions
of varying OBS/EST ratio and examine the location of the points with respect
to the three regions. In addition, we investigated the correlation, u' my,
between OBS and EST.
Step 2: Investigate the Relationships Between the Variables
In this step we examined the correlation between OBS/EST and NMOC, NOjj,
and other variables such as temperature and background ozone. We also inves-
tigated the correlation between NMOC and NO*, and between pairs of the other
variables. When possible, a multiple regression equation wan derived using
stepwise regression that relates the OBS/EST ratio to a subset of the vari-
ables of Interest. This multiple regression equation was used in the third
step of the analysis to define regions of prescribed accuracy on the O3 iso-
pleth diagram.
In preparing for the third step of the evaluation, we used the correla-
tion, if any, between NMOC and NOjj to define an evaluation region on the O3
lsopleth diagram. (The evaluation region is defined to limit the results, of
the EKMA evaluation to the portion of the O3 lsopleth diagram where the data
are located.) The evaluation region was defined by regressing NOjj on NMOC and
placing a band around the regression line so as to capture approximately 95
percent of the joint distribution of NMOC and NO^. Thus, the evaluation
8
-------
region is defined by NOx = a + b (NMOC) ± 1.96s, where a and b are the coeffi-
cients of the regression line, and s is the srdndard error of estimate for the
regression. The evaluation region may be modified further as a result of cri-
teria used to select the evaluation data set.
Step 3: Define Regions of Predictive Accuracy
Because the performance of the EKMA model could vary as a function of
NC^, NMOC, and other variables (e.g. temperature and background ozone), we
sought to estimate the likelihood that the ratio OBS/EST falls in Region 1, 2
or 3 as a function of these variables. Our approach is as follows.
The ratio ORS/EST is used as the dependent variable in a multiple linear
regression equation of the form
N
OBS/EST = aQ + ]T) atXi - F(X)
1=1
where
Xl o Independent variable, such as NO^, NMOC, temperature
- regression coefficient
N » number of Independent variables.
and F(X) is shorthand notation for the regression equation. The standard
error of estimate, s, is also obtained for this regression.
Define R = OBS/EST, Rj = 1.2, and = 0.8. We wish to find the proba-
bility that R > 1.2, or 0.8 < R < 1.2, or K < 0.8. Let P(R < R«) - probabil-
ity that R£ Rj, j >» 1,2. Then
P(R < Rj) - *
Rj - F(X)
J - 1,2
where $ Is the cumulative normaJ probability distribution function. Then for
the three accuracy regions we tvve
• Region 1:
• Region 2:
• Region 3:
P(R > 1.2) - 1 - P(R < Rj)
P(0.8 < R < 1.2) - P(R < Rt) - P(R < R2)
(la)
(lb)
P(R < 0.8) - P(R < R2)
(lc)
9
-------
(Note that the above equation for P(R _< Rj) is general and thus valid not only
for Rj equal to 1.2 and 0.8, but also for any other values of Rj).
The variables Rj include either N0X or NMOC or both (or a transformation
thereof, e.g. 1/N0X) and possibly other variables such as temperature. In the
most general case, let Rj = f(N0x>, R2 = g(NM()C) and R^, k = 3, ..., N, where'
f and g denote transformations of N0X and NMOC, respectively. Then we can
calculate- and plot the probabilities in Eq. 1 as functions of (R}Ri -I- R2R2^
for fixed values of R^. The plot allows us to estimate the probability that
for a given (NMOC, N0X) pair the ratio OBS/EST falls in one of the three accu-
racy regions in Eq. 1. The accuracy regions and their probabilities are then
identified on the ozone isopleth diagram.
For EKMA to provide an upper bound for the maximum ozone, we require that
the ratio OBS/EST have a high probability of being in Region 2 or 3. Con-
versely, EKMA fails to produce an upper bound if there is a high probability
that the ratio falls in Region 1. The most desirable outcome is to have a
high probability that the ratio falls in Region 2. We still get an upper
bound if the ratio falls in Region 3, but the bound is not sharp, because the
overpredlction would be greater than 20 percent.
A question remains about what values would be acceptable for the proba-
bilities associated with the three accuracy regions. We have purposely
refrained from specifying any probability thresholds at this time, and will
let the data speak for themselves instead.
10
-------
SECTION 3
EKMA EVALUATION FOR THE ST. LOUIS AREA
DATA REVIEW AND ANALYSIS
The St. Louis data were collected during the Regional Air Pollution Study
(RAPS) from May through October 197b. Twer;./-five monitoring stations were
used during RAPS; t'leir locations are shown in Figure 1. Four source-region
monitors (Sites 101, 105, 106, and 107) were selected to determine spatially
averaged 0600-0900 (CDT) NMOC and N0X concentrations. Meteorological data
used in the analysis were collected at a rural site south of St. Louis (Site
124).
Six monitoring stations that measured NMOC and N0X were investigated to
determine whether they should be classified as source-region sites. The six
stations are 101, 102, 105, 1C6, 107 and 111. Figure 1 shows that all are
within the metropolitan area. In relation to the downtown area, Sites 101 and
105 are closest, Stations 106 and 107 are about 6 km west, Station 102 is
approximately 7 km north-northwest, and Station 111 is about 8 km south-
southwest. Table 2 compares the 0600-0900 (CDT) NM0C/N0x ratios at these
sites, showing range, mean, standard deviation, and median ratio. It is evi-
dent from Table 2 that Stations 102 and 111 have similar ratios, which tend to
be lower than at the other four stations. Thus, Stations 101, 105, 106, and
107, which are closest to downtown St. Louis, show the highest mean and median
ratios; the difference in their mean ratios is not statistically significant.
Consequently, stations 101, 105, 106, and 107 were selected as the source-
region monitors that determine the spatially averaged 0600-0900 (CDT) NMOC and
NOx concentrations.
To define the necessary conditions for high-ozone-concentration day3, we
analyzed the relationship between ozone and precursor and meteorological vari-
ables. Figure 2 plots the maximum observed dally ozone concentration against
the maximum dally temperature recorded at the rural site. Overall, there is a
good linear correlation (r - 0.7). The data distribution in Figure 2 suggests
that the envelope of the points may have an exponential form. Of particular
interest Is that no peak ozone concentrations exceeding 100 ppb occurred when
the maximum temperature was below 24.0°C. However, as befits a necessary but
not sufficient condition, Figure 2 shows that a number of ozone maxima below
100 ppb were recorded on occasions when the maximum temperature exceeded 24°C.
The distribution of the maximum ozone concentrations as a function of the
ratio of the average 0600-0900 NMOC and N0X concentrations recorded at the
source monitors is shown in Figure 3. Ozone concentrations exceeding 100 ppb
occurred only when the NMOC/N0x ratio exceeded 5.0.
11
-------
Figure 1. Location of Regional Air Monitoring Systems (RAMS) stations.
12
-------
TABLE 2. 0600-0900 (CDT) RAl'US OK NMHC/NOx CONCENTRATIONS
FOR ST. LOUIS AREA
Station
Number
Range
of Ratios
Mean
Standard
Deviation
Median
Number
of Ratios
101
0. 5-61.6
9.4
7.4
8.1
110
102
0.2-39.0
5.5
4.1
5.3
104
105
2.7-26.1
8.5
4.1
7.3
89
106
0.3-56.4
9.2
6.0
7.9
121
107
2.2-29.1
9.2
3.6
8.5
149
111
0-79.2
5.1
7.3
4.4
118
13
-------
944.00
223 00
202.00
I
§ 181.00
P
«
K
H
5 'MOO
o
z
u 09 00
O
hi
o
j IU.00
<
o
s
2 97 00
5
«
5
70 OO
• ¦
• 2 ¦ •
• •
• 2**
• # 2 •
• •« 2
• • • •
22 • •
99 00
34 OO t i ¦
6 00 10 00 14 00 16 00 22 OO 26.OO 30 00 9m 00 38 00
MAXIMUM DAILY TEMPER ATURE-°C
J/ 00 46 00
Figure 2. Scatterplot of maximum daily ozone concentration at a function of
daily maximum temperature for the 1976 St. Louis data.
-------
244.00 t
223.00
V»
I
z
o
h
<
oc
H
z
Mi
o
z
o
(J
UJ
z
o
N
O
>
J
5
Q
2
3
2
X
<
181.00
139.00
116.00
97.00
76.00
* ¦ ¦
2 2 ¦ •
* a ¦
¦ « « ¦ I
• a m m 2*
It a a •
¦ 3 ¦
¦ 2*
•3 * 2
¦ " * 2
55.00
• ¦ ¦
»¦ a
a ¦
2 •
3 00 5.00 7.00 9.00 11.00 13.00 13.00
DAM.Y CORE-CITY AVERAGE 0600-0900 RATIO OF
17.00 19.00
NMHC TO N0„
2» .00
+
- - - ~
23.00
Figure 3. Scatter plot of daily maximum ozone concentration as a function of
daily corc-city 0600-0900 (CDT) average ratio of NMHC to N0X for
the 1976 St. Louis data.
-------
We also investigated several other variables to see whether they imposed
any restrictions on the occurrence of ozone levels above 100 ppb. variables
examined included cloud cover, dew point temperature, and wind spaed and
direction. For cloud cover, it was found that although the highest ozone lev-
els occurred on days when cloud cover was low, ozone concentrations exceeding
120 ppb were observed for all cloud cover conditions. Accordingly, cloud
cover was not used as a selection criterion. Similar negative findings apply
to dew point and wind direction.
DEFINITION OF EVALUATION DATA SET
Based on the analysis discussed previously, the selection criteria are:
• Maximum temperature higher than 24°C
• Ratio of NMOC to N0X greater than 5.0.
Two additional criteria were applied:*
• Time of maximum ozone 1200 (LT)—A daily maximum that occurs before
noon indicates an unusual event that probably cannot be predicted by
EKMA (EPA, 1977).
• Concurrent dally maximum O3 and 0600-0900 NMOC and NOx spatially aver-
aged over the source-region monitors are required. At a given moni-
tor, 0600-0900 NMOC or NOjj was considered missing if data for two
hours were missing. The spatially averaged 0600-0900 NMOC or NOx was
considered to be missing if more than half of the monitors have miss-
ing data.
The evaluation data set for St. Louis is listed in Table 3, which
includes the standard and city-specific ozone estimates. The number of cases
in the set is 100.
EVALUATION OF STANDARD EKMA
Comparison of Observed and Estimated Ozone
Figure 4 shows a scatterplot of OBS as a function of EST. Of the 100
points plotted, four are in Region 1, 18 in Region 2, and 78 in Region 3.
Thus, 4 percent of the cases are underpredlcted and the remainder satisfy the
inequality OBS jC 1.2 EST.
The observed and estimated O3 depicted in Figure 4 are correlated: the
correlation coefficient Is r» 0.49, and is highly statistically significant
(p < 0.0001). However, there is a fair amount of scatter. The regression
line relating OBS and EST, shown in Figure 4, is defined by $ « 0.232 EST +
74.4, where the standard error of estimate is s ¦ 32.4, all the units are ppb,
*These two criteria also apply to the other four cities.
16
-------
TABL2 3. EVALUATION DATA SET FOR ST. LOUIS
Precursors Observed Maximum Ozone SKMA Otone Estimate (ppb)
Date
^19761
11 Hay
NMOC
,(PPbC>.
265
NOx
(ppb)
41
Maximum
Temperature( C)
Background
O-j(ppb)
Station
Time
(CDT)
Concentration
(ppb)
Standard
Cltv-Speclflc
27.5
74
24
1700
100
117
1C8
IS May
324
36
24.9
80
24
1500
80
124
112
22 May
318
37
30.7
98
25
1500
118
124
112
24 May
383
65
24.1
76
24
1700
96
151
126
29 May
682
83
28.5
106
21
1400
139
230
174
30 May
171
24
29.6
76
14
1600
100
86
92
31 May
403
48
26.3
47
23
1300
89
146
125
1 Jun
42S
47
29.6
98
24
1400
151
148
126
2 Jun
43S
50
29.1
82
18
1700
93
152
128
3 Jun
308
65
27.7
86
24
1300
94
174
140
4 Jun
471
48
28.1
98
22
1500
98
155
130
3 Jun
465
34
28.8
60
22
1700
91
136
120
6 Jun
504
50
30.9
107
14
1800
118
160
134
7 Jun
1656
187
32.5
137
22
1600
198
388
261
8 Jun
1111
75
33.9
115
15
1700
221
237
176
9 Jun
615
59
31.2
88
23
120C
121
181
146
11 Jun
601
66
34.4
91
15
1500
133
186
148
14 Jun
807
95
33.4
84
14
1800
93
2/*:
174
19 Jun
186
28
26.2
55
24
1500
69
92
95
21 Jun
1436
175
25.3
67
19
1400
86
345
240
22 Jun
947
145
28.1
86
21
1500
112
274
197
23 Jun
806
108
32.2
65
11
1200
154
239
179
-------
Precursors
Date
NMOC
NO,
Maximum
(1976)
(ppbC)
(ppb)
Temperaturef°C>
26 Jun
552
76
33.6
27 Jun
354
44
37.0
28 Jun
698
63
33.3
29 Jun
333
66
29.7
30 Jun
299
36
25.2
1 July
697
103
30.6
4 July
223
28
29.7
7 July
504
66
31.5
8 July
289
34
34.0
9 July
357
5C
33.2
10 July
275
23
24.8
12 July
146
13
34.8
13 July
228
45
32.2
17 July
691
85
27.9
18 July
587
70
30.6
19 July
951
56
30.9
20 July
448
60
34.3
21 July
337
46
34.7
22 July
487
68
36.6
23 July
451
44
37.4
24 July
147
14
38.4
2} July
324
48
35.1
27 July
516
69
30.1
29 July
383
14
29.1
30 July
1216
98
35.1
TABLE 3 (continued)
Observed Maximum Otore
Background
07(ppb)
Station
Time
(CDT)
Concentration
(ppb)
107
22
1600
138
80
15
1300
116
58
16
1200
90
57
22
1700
74
54
24
1600
f.3
61
9
1600
112
67
20
1200
89
80
14
130C
103
73
18
1700
141
73
14
1200
112
50
15
1400
102
60
10
1600
105
106
14
1600
223
55
5
1600
sis
102
21
1600
126
83
22
1300
148
63
14
1200
76
51
15
1300
108
73
16
1600
107
56
23
1500
141
87
18
1600
112
93
20
1500
126
69
22
1700
121
145
20
1600
155
93
8
1300
170
EKMA Prone Estimate (ppM
Standard
Cltv-Speclflc
187
147
135
118
193
153
'.78
143
120
110
221
167
100
99
174
140
117
108
143
122
101
101
68
83
121
103
211
162
188
149
202
155
161
133
134
117
172
139
148
127
70
84
133
116
177
142
140
121
270
196
-------
Precursors
Date
moc
N°„
Maxlmtn
(1976)
(ppbC)
(ppb)
Tempera ture (0O
1 August
203
26
26.6
2 August
433
38
27.4
3 August
701
83
28.6
4 August
707
101
28.9
3 August
387
64
31.3
6 August
442
44
28.0
7 August
28S
35
26.1
8 August
348
33
27.3
11 August
701
33.2
12 August
622
65
35.3
13 August
728
86
33.7
14 August
263
30
31.5
16 August
484
38
28.4
17 August
819
76
28.5
18 August
967
100
29.2
19 August
808
96
30.6
20 August
1320
141
32.3
21 August
1324
114
S3.7
22 August
313
43
34.6
23 August
1432
159
33.5
24 August
1704
127
33.3
25 August
1330
158
33.1
29 August
321
44
29.6
30 August
342
55
28.9
31 August
833
:i2
30.0
TABLE 3 (continued)
Observed Kanlnum Orrne EKW Oione Estimate (ppbl
Background
O^fppb)
Station
Tine
fCDTl
Concentration
fppb)
Standard
Cltv-Speclflc
55
18
1600
70
94
96
68
14
1700
80
158
131
90
19
1600
145
211
162
100
14
1300
147
222
168
82
14
1200
113
152
126
71
24
1600
105
147
126
(6
24
1600
86
117
108
90
23
1800
124
126
114
82
13
1400
117
229
173
68
17
1400
166
188
149
109
9
1200
180
216
166
84
19
1400
160
109
104
68
21
1400
93
165
136
76
25
1700"
148
217
167
92
25
1600
168
252
137
85
25
1600
133
233
175
95
21
1500
127
314
221
105
14
1500
169
293
209
89
18
1300
128
128
114
88
20
1200
136
336
235
112
20
1200
176
329
224
111
15
1400
192
325
228
64
10
1400
75
130
115
68
22
1500
109
170
139
75
24
1300
130
245
181
-------
TABLE 3 (continued)
Precuraora
Date
112251
HHOC
(ppbC)
Kaxlmua
Temperature (°C)
1
Sept
1098
105
29.1
2
Sept
529
58
29.7
3
Sept
573
61
27.2
4
Sept
592
27
35.0
3
Sept
639
50
29.8
6
Sept
483
42
29.9
7
Sept
697
84
31.5
8
Sept
895
65
31.4
10
Sept
737
102
23.2
11
Sept
73S
76
26.9
13
Sept
900
90
30.3
14
Sept
1076
103
31.4
15
Sept
1010
106
30.2
16
Sept
454
63
27.3
17
Sept
2055
189
28.6
18
Sept
1267
118
31.S
19
Sept
559
42
31.9
23
Sept
717
97
24.4
24
Sept
424
65
27.2
25
Sept
694
86
25.6
26
Sept
659
41
27.9
30
Sept
548
93
24.7
1
Oct
1884
210
31.5
2
Oct
2838
302
33.4
3
Oct
1088
ISO
30.5
Obaerved Maxlmun Otone . EKMA Prone Eatlnate (ppb)
Ion
Time
(CCT)
1200
Concentration
(ert)
Standard
Clt« Specific
8
134
2
8
195
1
1600
109
1
1
139
2
1500
126
1
9
144
8
1400
149
1
2
117
8
1500
111
1
3
142
8
1700
107
1
9
127
8
1400
114
2
1
162
1
1300
107
2
1
163
0
1300
58
2
7
170
2
1400
99
2
1
163
2
1400
117
2
7
178
4
1600
118
2
4
193
8
1600
107
2
1
151
4
1600
94
1
4
134
2
1300
188
403
267
4
1400
132
292
209
4
1300
91
156
132
8
1400
75
222
168
5
1600
106
160
131
8
1600
80
212
163
8
1200
73
162
134
3
1500
102
192
148
2
1500
244
405
272
5
1700
186
528
333
4
1300
125
295
210
Background
2ji£E^l
104
74
80
67
59
82
72
63
52
60
41
82
78
68
70
74
54
53
58
56
52
61
78
81
105
-------
TABLE 3 (concluded)
Precursors
Osserved
Maximum Ozone
EKMA Ozone
Esttmate
Date
fl976>
NMOC
(onbC)
(ppb)
73
Maxlmua
Temperature (°C)
Background
0,(ppb)
Station
Time
(COT)
Concentration
(ppb)
Standard
Cltv-Speclflc
I Oct
593
29.1
83
18
1300
104
191
ISO
! Oct
890
124
29.7
73
22
1300
78
258
189
1 Oct
686
97
29.7
51
18
ISOO
58
217
164
-------
SI.00 137 00 163.00 2Z#.00 273.00 321.00 367 00 413 00 459 00 SOS 00
6a.00 114.00 160.00 206.00 232.00 296.00 344 00 390 00 436.00 462.00 326.00
STANDARD-EKMA 03 ESTIMATE (EST) — >pb
Figure 4.
Scatterplot of observed ozone and ttandard-EKMA ozone estimate
for St. Louis. Number of points plotted is 100.
-------
and ? represents the value of OBS obtained from the regression line. The ten-
dency of EST to overestimate OBS is reflected in the value of the slope of thi
regression line. The regression li.ie Implies that, on the average, ?/EST >
1.2 for EST < 77 ppb, and ?/EST <.1*2 otherwise. However, the regression lint
serves only as a rough guide to the location of a point in one of the three
regions of Figure 4: We want to know the probability that a point is located
In a particular region as a function of NMOC and NC^. This will be examined
in connection with the definition of the accuracy regions of the NMOC-NOx
plane.
The four points located in Region 1 (see Figure 4) are distinguished by
having very low concentrations of NMOC or N0X. Table 4 shows the 0600-0900
NMOC and K'0X levels at the Individual monitoring sites and the corresponding
spatial averages. (The spatial averages also appear in Table 3). For all the
days in the evaluation data set, the spatially averaged NMOC range from 146 tc
2858 ppbC and have a median concentration of 577 ppbC. Ranked in order of
increasing concentration, the four NMOC spatial averages in Table 4 were
lowest (146), second lowest (147), sixth lowest (228), and eighth lowest
(265), where the number in parentheses is the NMOC concentration. flOx ranged
from 13 to 302 ppb, with a median level of 65 ppb. The NOx spatial averages
In Table 4 ranked lowest (13), second lowest (14), ninth lowest ('30), and 27th
lowest (45). The levels of both NMOC and N0X for 12 and 24 July i.ere the
lowest in the evaluation data set. Sites 101 and 107 are solely responsible
for the low N0X on these two days; the NO,; data are missing for the other two
sites. This raises the possibility that Sites 101 and 107 may not be
representative of the areawide N0X level on these two days; the same argument
applies to NMOC.
Table 4 shows that on 13 July the EKMA estimate underpredicted the
observed value by a large margin. In this case the problem appears to be Che
NMOC rather than the N0X. As Table 4 shows, Site 101 reported a very low NMOC
of 41 ppbC while the NOx was 48 ppb, for en NM0C/N0x ratio of 0.85. [This low
ratio does not violate our _ata selection criterion (NM0C/N0x > 5) because the
criterion pertains to the spatially averaged NMOC and N0X, not to the indivi-
dual monitoring sites.] Such a low ratio is unusual and suggests that this
NMOC measurement at Site 101 may be incDrrect. The low value of NMOC causes
the spatial average to be low, which in turn produces a low ozone estimate.
This situation recurs on 14 August, when Table 4 shows that Site 105 reported
a relatively high value of NMOC, but that Site 106 has a very low value. The
latter site also has a very low NM0C/N0x ratio.
All four cases of substantial underpredictlon are associated with data of
questionable reliability; but, because vagaries in the data will always occur,
these four cases will be retained and used in subsequent analyses.
Relationships Between the Variables
Table 5 shows the correlation coefficients for selected variables in the
St. Louis evaluation data set. NMOC and NOx are highly correlated; the impli-
cations of this relationship will be discussed below. The tabls shows that
EST is highly correlated with NMOC and NOx. This is expected, because It
reflects the strong correlation between NMOC and NOx. However, the
23
-------
TABLE 4. SELECT CO 0600-0900 NMOC ANIi NO CONCENTRATIONS*
AT SOURCE-MWIOU MONITORING SITES IN ST. LOUIS
Date
Monitoring Site
Spatial
Average
Ozone (ppb)
101
105
106
107
Observed
Standard EKMA
Estimate
NMOC
MOx
NMOC
N0X
NMOC
N0X
NMOC
N0X
NMOC
N0X
12 Jul
115
13
270
—
53
13
146
13
105
63
13 Jul
41
46
273
—
371
43
228
45
223
121
24 Jul
50
14
—
245
15
147
14
112
70
14 Aug
—
501
29
23
38
265
30
160
109
*NMOC in ppbC N0X and ozone In ppb. Dashes denoce missing data*
-------
TABLE 5. MEANS, STANDARD DEVIATIONS AND CORRELATIONS
FUR SELECTED VARIABLES IN THE ST. LOUIS EVALUATION DATA SET
Variable
Mean
Srandard
Deviation
Correlation Coefficient*
N0*
1/NMOC
l/NO„
M^xlnun
Temperature
Background
°3
OBS
EST*
OBS/EST
NMOC (ppbC)
690.6
448.1
0.93
-0.72
-0.63
—
0.2 7
0.54
0.98
-".49
N0X (ppb)
76.5
46.1
-0.69
-0.70
—
0.23
0.44
0.97
-0.55
I/NMOC (ppbC"1)
0.0020
0.0013
0.90
—
-0.19
-0.31
-O. 79
0.72
1/NO, (ppb"1)
0.0180
0.0! 18
—
0
N
©
1
-0.26
-0.74
0.73
Maximum teoperature (°C>
20.4
3.2
0.30
0.47
0.09
0.35
Background Oj (ppb)
78.0
19.6
0.63
0.2 7
0.22
OBS (ppb)
119.9
37.0
0.49
.0.32
EST (ppb)*
196.0
74.4
-0.58
OBS/EST
0.676
0.280
1.0
£ '
Ail correlations significant at the 0.05 lev?] or better. Taahea denote that correlation
Is not statistically significant.
^Standard-ERM esttaate.
-------
correlation between OBS and NMOC and OBS and N0X is not high; the coefficients
are 0.54 and 0.44, respectively. The variables 1/NOx and 1/NMOC correlate
best with the ratio OBS/EST, the former being slightly better. Temperature
correlates best with observed 03, which reflects the indications of Figure 2.
There is no statistically significant correlation between temperature and
NMOC, N0X, their respective Inverses, and EST.
The scatterplot of NOx and NMOC concentrations (Figure 5) shows the com-
binations of these precursors represented in the evaluation data set. The
shaded region of the scatterplot is excluded from consideration by the selec-
tion criterion of NMOC/NOx greater than 5.0. Figure 5 provides graphic evi-
dence of the high correlation between N0X and NMOC (r ¦ 0.93).
The strong linear relationship between NMOC and N0X indicates that the
source-region sites are influenced by sources with a relatively uniform
NMOC/NOx ratio. Such uniformity suggests that area sources, mainly mobile
sources, are the primary contributors of NMOC and N0X in the area of central
St. Louis during 0600-0900.
As is evident in Figure 5, the interdependence of NMOC and N0X causes the
points to fall along a narrow band. This limits the region of the EKMA
diagram in which the evaluation can be performed. In this region, NMOC varies
from 146 to 2,858 ppbC and NOx from 13 to 302 ppb. This region may be defined
by the 95-percent confidence band for the linear regression of NOx. on NMOC.
The fitted regression equation is
NOx - 10.4 + 0.0958(NMOC),
where NOx is in ppb, NMOC is in ppbC, and the standard error of estimate is
s ¦ 16.8. The upper and lower boundaries of the region are defined by the
lines N0x 11.96s. In what follows, we will refer to the region bounded by
these lines as the evaluation region. (To be technically correct, the confi-
dence limits drawn on the scatterplot should be concave arcs rather than
straight lines; however, the amount of curvature is small and the straight-
line approximation is satisfactory for this application.)
As Table 5 Indicates, the OBS/EST ratio correlates Lest with the variable
1/N0x« The 3catterplot of OBS/EST and 1/N0x (Figure 6) shows a nicely corre-
lated linear relationship (r - 0.730) that is well behaved, because the resi-
dual variance about the fitted regression line appears to be constant. The
fitted regression line is OBS/EST - 0.365 + 17.3(l/NOK), where NOx is in ppb,
and the standard error of estimate Is s ¦ 0.193. This regression line is
plotted in Figure 6*
Because NOx an<* NMOC are correlated, the relationship between OBS/EST and
1/NMOC is similar to that with 1/NOx, but, as Table 5 shows, t.hc correlation
coefficient is slightly smaller for 1/NMOC. These dependencies will be
exploited in the next section to derive a multiple regression equation for
OBS/EST as a function of several variables.
26
-------
281 60 SS2 80 824 00 1095 20 1366 40 1637 60 1908 80 2180 00 2451 20 2722 40
NMOC ppbC
Figure 5. Scatterpiot of 0600-0900 (CDT) concentrations of NMOC and NOx for St. Louis.
-------
0.0070 0.0144 0.0217 0.0291 0.0364 0.0438 0.0512 0.0585 0.0659 0.0732
ro
oo
in
UJ
B
O
1.84
1.6J
1.52
1.36
1.21
1.06
0.63
0.73
0.57
0.41
0.25
• • ¦
0.0033 0.0107 0.0180 0.0254 0
-------
Definition of Accuracy Regions
To define the accuracy regions, and associated probabilities, in the O3
isopleth diagram, a multiple regression equation was derived for the OBS/EST
ratio as a linear function of 1/N0X, 1/NMOC, daily maximum temperature (T),
and background ozone (B03). The equation is:
OBS/EST = -0.628 + 8.68(l/NOx) + 99.23(1/NMOC)
+ 0.00451(B03) + 0.0196(T) (2]
where NOj; and B03 are in ppb, NMOC in ppbC, and T in °C. All the coefflclenti
of the regression are statistically significant (p < 0.005); the multiple
regression coefficient is 0.86, and the standard error of estimate is
s - 0.146.
Using Eq. 2, we can estimate the probability that OBS/EST > 1.2, or
0.8 _< OBS/EST jC 1.2, or OBS/EST < 0.8 as a function of NMOC end NOjj for any
specified values of B03 and T. This is illustrated below.
Following the notation of Section Two, define R = OBS/EST, Rj = 1.2,
R2 = 0.8; denote Eq. 2 by R = F(N0X, NMOC, B03, T); and let P(R < Rj) = proba'
bility that R _< R^, j = 1,2. Then
[Rj - F(N0X,NM0C,B03,T)]
P(R < Rj) - *
s (3.
where ( is the cumulative normal probability distribution function and s =
0.146, the standard error of estimate of Eq. 2. Then we can use Eq. 1 in con-
junction with Eq. 3 to calculate the probability that the ratio R » OBS/EST
located in one of the three accuracy regions, i.e. P(R > 1.2), P(0.8 R <
1.2), and P(R < 0.8). The procedure is simple: First, fix B03 and T by, for
example, setting them equal to their mean values, which were defined in Table
5. Thus, B03 3 78.0 ppb, and T •» 30.4°C. Substituting these values in Eq. 2
yields
F(NOX,NMOC,78.0,30.4) - 0.3196 + 8.68/NOx + 99.23/(NM0C) (4
Equation 4 is then substituted in Eq. 3 to obtain the desired probabilities.
Figure 7 shows a plot of the probability as a function of a new variable
Z «¦ 8.68/NOx + 99.23/NMOC. Using Figure 7, one can calculate the probability
associated with each accuracy region for a given (NMOC, N0X) pair. In gen-
eral, Figure 7 indicates that there is a high probability of overprediction
[i.e. P(R<0.8)] when NMOC and N0X are large (which corresponds to low values
of Z). It is also apparent from Figure 7 that there is a high probability of
underprediction [I.e. P(R > 1.2)] for low values of NMOC and NOjj. Relatively
accurate predictions occur in the interval 0.56 jC Z £ 0.80, where P(0.8 < R <
1.2) varies between 0.70 and 0.83, the maximum probability of 0.83 occurring
in the neighborhood of Z ° 0.68.
29
-------
Z = 8.68/NOx + 99.23/NMOC
Figure 7. Accuracy probability plot for standard-EKMA ozone estimates for St. Louis.
Mean values are assumed for background ozone and maximum daily temperature.
30
-------
Given specific values of NMOC and N0X, it is easy to compute the
corresponding value of Z to find the probability in Figure 7. Figure 8 com-
plements Figure 7 by showing the values of NMOC and N0X that correspond to
selected values of Z. Figure 8 also displays the evaluation region for NMOC
and N0X that was previously defined in Figure 5. Each constant-Z curve.in
Figure 8 ran be related to the probability plots of Figure 7; for example, th<
shaded aiea in Figure 7, which corresponds to the interval 0.56 £ Z _< 0.80,
maps into the shaded area of Figure 8, which defines the values of NMOC and
N0X that are associated with the most accurate predictions. High probabili-
ties of overprediction, where P(R < 0.8) > 0.70, occur for Z 0.3; these
curves are seen in Figure 8 to be linked to high values of NH0C and N0X. A
high probability of underpredictlon occurs for Z ;> 1.0; Figure 8 shows that/
this is a very small area within the evaluation region.
In view of the above, the standard-EKMA ozone estimate can be considered
to be an upper bound for the observed daily maximum in the region defined by
Z £ 0.8 in Figures 7 and 8. In this region, the probability that R < 1.2 is
approximately 0.7 at Z = 0.8 and Increases rapidly for Z < 0.8.
The effect of changing B03 and T is shown in Figure 9, which contains
probability plotr> similar to those in Figure 7 but with B03 and T set to theli
respective mean value plus two standard deviations, viz., B03 = 117 ppb and T
«» 37°C. Comparison of Figures 7 and 9 shows that the higher B03 and T have
shifted the location of the probability curves to the left, the shift causing
the curves for P(R < 0.8) and P(0.8 £ R 1.2) to be truncated for Z £ 0.1.
The new location of the probability curves implies that accurate predictions
are most likely in the interval 0.25 <, Z £ 0.49, with the maximum located
approximately at Z = 0.37. Referring to Figure 8, it can be seen that within
the evaluation region the area corresponding to 0.25 < Z < 0^49 is larger than
the shaded area. However, in Figure 9 underpredictlon is most likely to occur
for Z 0.65, and the corresponding area in Figure 8 is larger than the under-
predictlon region associated with Figure 7. In Figure 9, the standard-EKMA
ozone estimate can be considered an upper bound of the observed daily maximum
for Z 0.49, whereas in Figure 7 it was for Z 0.8.
In general, increasing either B03 or T, or both, will shift the probabil-
ity curves to the left. This lowers the probability of overprediction,
expands the area of highest accuracy, and increases the area where the likeli-
hood of underprediction is high. Lowering B03 or T shifts the probability
curves to the right, thus reversing the effect associated' with the leftward
shift.
EVALUATION OF CITY-SPECIFIC EKMA
City-Specific Ozone Estimates
The EKMA computer program was run using the input listed in Table 6 to
generate city-specific (C-S)03 estimates for St. Louis. Table 3 lists the
values of the C-S ozone estimates, hereafter denoted by CS03. The date shown
in Table 6 was used to calculate CS03 because the highest observed ozone level
In the evaluation data set occurred on that date (r.f. Table 3). The inversion
31
-------
500
200
EVALUATION REGION
BOUNDARIES
too
.0
Q.
Q.
I so
x
o
20
10 h
0.2 I
-0.3
-0.4
0.5
— 0.6
0.7
1.8
1.9
¦1.0
1.1
-1.2
_L
500
1000
1500
NMOC — ppbC
2000
2500
30C
Figure & Plot of constant-2 curves on NMOC-NOx plane for rtandard-EKMA estimates
for St. Louis. Shading denotes area where ozone estimates are most accurate,
assuming average conditions for temperature and background ozone.
32
-------
Z = 8.68/NOx + 99.23/NMOC
Figure 9. Accuracy probability curves for standard-EKMA evaluation for St. Louis.
Background ozone equals 117 ppb and maximum temperature equals 37° C.
33
-------
TABLE 6. SUMMARY OF IHP1JJ PARAMETERS FOR OBTAINING
CITY-SPECIFIC EKMA OZOUK ESTIMATES FOR ST. LOUIS
Parameter
Value
Date
1 October 1976 •
Location
Latitude 38.4°N,
Longitude 90.15°W
Inversion height data
Initial height (ra)
400
Final height (m)
1500
Start time of rise
0900
Ending tine of rise
1300
Post-0800 hourly N0X and NMOC
hourly emissions fractions
by ending hour
0900
0.24
1000
0.21
1100
0.09
1200
0.09
1300
0.06
1400
0.03
Reactivity, N02/N0X
0.59
Background ozone
concentration (ppm)
0.092
34
-------
height data represent an average estimated from several days of temperature
soundings. Post-0800 emissions fractions are average values calculated from
trajectories for the five days with the highest observed ozone in the evalua-
tion data set. The /N0X ratio and the background ozone level are the uean
values of these quantities for all the days in Table 3 for which the observed
ozone exceeded 120 ppb.
The C-S and standard-EKM\ ozone estimates are highly correlated. Figure
10 shows a scatterplot of CS03 and EST, where EST denotes the standard ozone
estimate. The correlation coefficient is r » 0.99; the regression line is
CS03 = 0.563(EST) + 42.8, where the standard error of the regression is
8 - 1.65, and the units are ppb. The fitted line implies that the ratio
CS03/EST < 1 for EST 98 ppb and that CS03/EST > 1 for EST < 98 ppb. The
presence of a statistically significant intercept in the regression line indi-
cates that the location of the C-S isopleths has been shifted with respect to
the standard-EKMA isopleths.
Comparison of Observed and City-Specific Ozone Estimate
Figure 11 shows a scatterplot of OBS as a function of CS03. Of the 100
cases, eight are in Region 1, 36 are In Region 2, and 56 are in Region 3. By
contrast, 4 percent of the standard-EKMA estimates were located in Region 1,
18 percent in Region 2, and 78 percent in Region 3. Thus, although the C-S.
estimates tend to underpredict the observations more frequently, the fraction
of cases in Region 2 Tor the C-S method is twice that for the standard F.KMA.
Overall, the percentages of cases satisfying the inequalities OBS/EST < 1.2
EST and 0BS/CS03 < 1.2 were 96 and 92 percent, respectively, which is a rela-
tively small difference. Hence, the C-S estimates also produce an upper bound
for the observed ozone, but more cases are underestimated.
As was the case with EST, OBS and CS03 are correlated. The correlation
coefficient Is r - 0.49, and is highly statistically significant. The regres-
sion line relating OBS and CS03 is plotted in Figure 11, and Is defined by
OBS » 0.407(CS03) + 32.5, where the units are ppb, and the standard error of
the regression is s- => 32.5 ppb. Figure 11 shows that the estimates obtained
from the regression equation always are in Regions 2 and 3 for CS03 > 83 ppb.
The eight points in Region 1 of Figure 11 include the four points in
Region 1 of Figure 4 and four additional points for 8 June, 8 and 29 July, and
4 September. Two of the points in Region 1 of Figure 11 appear to have NO*
levels that are considerably lower than would be expected for the concurrent
NMOC concentration. One of the two points In question is 8 June, which has
NMOC ° 1,111 ppbC and N0X « 75 ppb. The NMOC level is one of the highest in
She evaluation data set, ranking 87th out of 100, where the rank increases
«lth increasing concentration. By contrast, 75 ppb ranked 60th among all the
ttOx values, and is more than two standard errors smaller than the NOx tsti-
nated from the regression equation relating NOx and NMOC (see Figure 5). The
latter is also true for 4 September, which has NMOC = 592 ppbC and NOx ™ 27
ppb. In this case, NMOC ranked 52nd, but NOg ranked sixth. The NMOC and N0X
Levels for the remaining two points (for 8 and 29 July) appear to be con-
sistent with each other.
35
-------
u
999.00 ~
906.00
91.00 197.00 109.00 829.00 879.00 981.00 907.00 413.00 499.00 909.00
I
?
^ 809.00
8
8
<
2 899.00
ui
2
O
fj
o
<
s
X
o
ui
899.00
199.00
199.00
109.00
99i
9
92
• 22
49
• •
98
8»«
84«
88
48
• ¦
99.00 *8
2«
82*
6$.00 114.00 160.00 206.00 292.00 899.00 944.00 990.00 436.00 *62.00 926.00
STANDARD-EKMA OZONE ESTIMATE (EST) — ppb
Figure 10. Sc9ttcrplot of city-specific and standard EKMA ozone estimates for St. Louis.
-------
99.50 120.50 145.50 170.50 195.50 220.50 249.50 270.50 295 50 320.50
SX-1.00 ~
REGION 1
/ REGION 2 / j
/ Y REGION 2
-------
.Relationships Between the Variables
Table 7 shows the means, standard deviations and pairwise correlations
for the variables of interest; the table is abbreviated because some of the
information was previously presented in Table 5. As with the standard-EKMA
ozone estimate, CS03 is strongly correlated with NMOC and N0X. The table alsc
shows that CS03 is correlated with background O3, although the correlation is
low. The ratio 0BS/CS03 correlates best and about equally well with 1/N0* and
1/NMOC, followed by maximum dally temperature.
Definition of Accuracy Regions
A multiple regression equation was derived for 0BS/CS03 as a function of
1/NMOC, daily maximum temperature (T), and background (>3(B03). The equation
Is
0BS/CS03 *» -0.584 + 118.39( 1/NMOC)
+ 0.024KT) + 0.00543VB03) (5)
where the units are as defined in Table 7. All the regression coefficients
are statistically significant (p < 0.002), the multiple regression coefficient
is 0.74, and the standard error of the regression is 0.182. In contrast to
Eq. 2 for OBS/EST, the variable 1/N0X does not appear in the regression. The
stepwise regression procedure attempted to include l/NOjj, but its. coefficient
was not significant at the 0.05 level; NO* was also tried with the same
result. Equation 5 also has a smaller multiple regression coefficient, 0.74,
compared to 0.86 for Eq. 2. Hence, Eq. 5 explains a smaller fraction of the
variance than does Eq. 2. Moreover, the standard error for Eq. 5 (s = 0.182)
is greater than that for Eq. 2 (s = 0.146).
Using Eq. 5, we plotted the accuracy probabilities as a function cf
Z «¦ 118.39/NMOC after setting T = 30.4°C and B03 = 78.0 ppb, which are their
respective means; the plot is shown in Figure 12. Complementing Figure 12, a
family of lines for several values of Z is displayed in Figure 13, which also
shows the evaluation region in the NM0C-N0x plane.
Figure 12 shows that there is at least a 75 percent probability of satis-
fying the inequality R _< 1.2 for Z jC 0.50, which is the area to the left of
the dashed vertical line shown in Figure 12. Thj area of Figure 12 in which
Z jC 0.50 corresponds to the region of Figure 13 in which NMOC )> 237 ppbC; the
left boundary of the shaded area in Figure 13 is the line NMOC «* 237 ppoC.
Thus, inside the evaluation region of Figure 13, (NMOC, NO*) combinations
within and to the right of the shaded area have at least a 75-percent proba-
bility of producing an ozone estimate that is an upper bound for the observed
daily maximum ozone.
The shaded area of Figure 12 is the region where the probability P(0.8 <
Rj< 1.2) attains its highest values, hence it is associated'with ozone esti-
mates that are most likely to be accurate. Within the shaded area, the vari-
able Z varies from 0.35 to 0.50, and P(0.8 .< R <, 1*2) varies from 0.70 to
0*73, reaching its maximum value of 0.73 In the neighborhood of Z « 0.43. The
38
-------
TABLK 7. MEANS, STANDARD DEVIATIONS, AND CORRELATIONS
FOR CIIY-SP2CIFIC EKMA EVALUATION FOR ST. LOUIS
Standard
Deviation
Correlation*
Variable
Mean
CS03
OBS/CS03
NMOC (ppbC)
690.6
448.2
0.97
-0.34
N0X (ppb)
76.5
46.1
0.97
-0.41
1/NMOC (ppbC-1)
0.0020
0.0013
-0.79
0.49
l/NOx (ppb*1)
0.0180
0.0118
-0.74
0.49
Maximum
temperature (°C)
30. A
3./
__
0.41
Background 0^ (ppb)
78.0
i9.6
0.26
0.38
OBS (ppb)
119.9
37.0
0.49
0.55
CS03 (ppb)
153.2
44.1
1.0
-0.42
03S/CS03
0.814
0.266
-0.42
1.0
^Significant at the 0.05 level or better. Dashes indicate
correlation is not statistically significant.
39
-------
Z- 118.39/NMOC
Figure 12. Accuracy probability plot for city-specific EKMA ozone estimates for St. Louis.
Mean values are assumed for background ozone and maximum daily temperatures.
40
-------
5 i i i 1 1 r i i ¦ ¦ « ¦
0 500 1000 >500 2000 2500 3000
NMOC — ppbC
Figure 13. Plot of constant-Z lines on NM0C-N0x plane (or city-specific EKMA estimates
for St. Louis. Shading denotes area where ozone estimates tend to be most
accurate, assuming average conditions for maximum temperature and background ozone.
41
-------
shaded area of Figure 13 corresponds to that of Figure 12. Inside the shaded
area of Figure 13, NMOC is defined by 237 < NMOC < 338 ppbC, and N0X is lim-
ited by the boundaries of the evaluation region. Thus, (NMOC, NO,;) combina-
tions in the shaded area of Figure 13 are associated with the C-S ozone esti-
mates most likely to be accurate.
The maximum value of P(0.8 < R < J.2) in Figure 7 is higher than that in
Figure 12—the respective maxima being 0.83 and 0.73—largely because the
standard deviation for Eq. 2 is smaller than that for Eq. 5 (s = 0.146 and
s = 0.182, respectively). The smaller standard deviation yields a narrower
and taller probability curve for Eq. 2 (cf. Figure 7) in comparison with that
of Eq. 5 (see Figure 12).
Comparison of Figures 8 and 13 shows that the location of the shaded a-'ea
has been shifted upward in Figure 13. As a result, the values of NMOC and NOx
associated with the ozone estimates most likely to be accurate are lower for
the standard EKMA (Figure 8) than for the C-S case (Figure 13). The relative
placement of the shaded area In Figures 8 and 13 is also indicative of the
difference in the predictive performance of standard and C-S EKMA. Thus,
overprediction is more common for the standard than foi* C-S EKMA, as reflected
by the size of the region above the shaded area in Figure 8. This situation
is reversed in the case of underpredlction; the region below the shaded area
is smaller in Figure 8 than in Figure 13.
DISCUSSION
The results presented above indicate that both standard and C-S EKMA can
be used to obtain ozone estimates that are upper bounds for the observations,
where the upper bound criterion is observed O3 1.2 estimated O3. Ko;e pre-
cisely, an estimate has a high probability of being an upper bound if its
(NMOC, NOx) coordinates fall in certain specific areas of the NK0C-N0x plane
(see Figures 8 and 13). In general, high NMOC and N0X lead tc upper bound
estimates, and low NMOC and NOx to underestimates, in which observed
O3 > 1.2 times estimated O3.
The analysis showed that, within certain bounds, the standard EKMA can be
uued to provide realistic estimates of maximum ozone levels for the St. Louis
area. Three regions of predictive accuracy were defined wherein the ratio of
observed to estimated ozone is greater than 1.2 between 0.8 and 1.2, and less
than 0.8. Of the 100 estiuates, 78 fell in the tiiird region, which is indica-
tive of substantial overprediction (as expected). Eighteen estimates fell in
the second regton, where EKMA is accurale to within ±20 percent, indicating
that reasonably credible estimates can be obtained with the standard EKMA.
Four cases fell in the first region, where an underestimate occurs, which sug-
gests that the standard EKMA could be used as a screening tool with the expec-
tation that there is a low probability that its predictions would be exceeded.
The C-S EKMA'8 ozone estimates were generally more accurate than the
standard EKMA's. Thus, although the C-S EKMA also produced upper bounds for
the observatlms, 36 percent of the C-S estimates fell in the region where
0.8 < observed/estimated < 1.2, compared to 18 percent for the standard-EKMA
42
-------
estimates. However, the C-S EKMA displayed a greater tendency to underesti-
mate the observations than did the standard EKMA (8 percent compared to 4 per
cent, respectively).
The accuracy regions for the standard-EKMA estimates were shown to be
functions of NMOC, N0X, background ozone, and maximum daily temperature.
Thus, to define the accuracy regions on the NMOC-NOx plane It is necessary to
assign a value to background ozone and temperature. One of the two examples
presented used mean values for these two quantities (cf. Figures 7 and 8); th
other used the mean value plus two standard deviations (cf. Figure 9). These
two examples demonstrated how the accuracy regions are defined and mapped on
the NMOC-NOx plane. They also showed the effect of changing the background
ozone and temperature on the position and size of the accuracy regions. When
applied to a particular problem, it is desirable to tailor the accuracy
regions to the specific prevailing background ozone and temperature. Having
defined the values of these two variables, it is a simple matter to use Eq. 2
and 3 to generate a plot similar to Figure 7. In so doing, care must be takei
to use values of background ozone and temperature that fall within the range
of values shown in Table 3, because these were used-to derive Eq; 2. Similar
considerations apply to the accuracy regions associated with the C-S
estimates.
In discussing the probability P(0.8 jC R < 1.2) in connection with Figurec
7, 9, and 12, we used 0.70 as the minimum probability that defines the region
where the ozone estimates are most likely to achieve the highest accuracy.
The value of 0.70 was selected because we desired to have a relatively high
probability of being in the high-accuracy region, but not one so high that the
size of the region would be minuscule. Examination of Figures 7, 9, and 12
suggested that 0.70 would be adequate. For another problem, it may be more
appropriate to use some other probability threshold to define the boundaries
of the high-accuracy region.
43
-------
SECTION 4
EKMA EVALUATION FOR THE HOUSTON AREA
DATA REVIEW AND ANALYSIS
The data used were collected during the Houston Area Oxidant Study (HAOS
and the Houston Oxidant Modeling Study (HOMS). The HAOS data span the period
May-October 1977; the IIOMS data cover about one month, from 13 September
through 12 October 1978. Comprehensive analyses and descriptions of these tw
data bases are found in the references given in Table 1.
Analysis of the Houston data did not reveal any strong linear correla-
tions between maximum ozone and other pollutants or meteorological parameters
The low correlation between peak ozone concentration and daily maximum tem-
perature can be explained by the consistently high daily maximum temperature
observed in the Houston area during the period of interest. The best correla
tion (r = 0.53) was found between the maximum ozone concentration and the
difference between the daily maximum temperature and the morning minimum tem-
perature, where the latter is defined as the lowest temperature between mid-
night and 0800. A low but statistically significant correlation was found
between maximum dally ozone with dally peak hourly solar radiation and with
the 1000-1400 averaged solar radiation values for the HAOS data. The data
also suggest that there is a minimum level of solar radiation that must exist
for high ozone concentrations to occur (Maxwell, 1981).
Five mor.itoring sites, located at Aldlne, Mae Drive, Crawford, Clinton,
and Parkhurst, were selected as source-region monitors that define the
0600-0900 (CDT) NM0C and NO* concentrations. The analysis that led to this
selection was previously reported by Ludwlg and Martinez (1979). Briefly, thi
analysis showed that these five sites have similar NM0C/N0x ratios, and that
mobile source emissions predominate during 0600-0900.
DEFINITION OF EVALUATION DATA SET
The review of the HAOS data showed that NMOC and N0g measurements were
very sparse during the period August-October. As a result, the HAOS evalua-
tion data set is almost entirely composed of data for the period May-July
-------
1977. Other data availability considerations also reduced the size of the
HOMS evaluation data set. The criteria used to select Houston test days for
evaluating EKMA are as follows:
• Maximum daily temperature at least 24°C.
• Difference between maximum and morning temperature greater than 6°C.
• 0600-0900 areawide average N0X at least 36 ppb.
• Average 1000-1400 solar radiation at least 0.22 ly/min.
(Recall that the conditions represented by these criteria are always present
when the daily maximum ozone is at least 100 ppb.) The fourth criterion was
applied only to the HA0S data, because no solar radiation data were available
for the HOMS. A few days were discarded because thunderstorms or rain showei
preceded the time of the observed peak ozone concentration. Other days were
rejected because the ozone maximum occurred before 1200. Missing values of
the area-wide average 0600-0900 NOx concentration resulted in more days being
discarded than did any other criterion.
The HAOS and HOMS evaluation data sets are shown in Tables 8 and 9,
respectively. The nunber of days in the HAOS data set is 61; the HOMS data
set contains 17 days. (A complete evaluation of EKMA could not be performed
using the HOMS data set because of its small size.)
The performance of the EKMA was investigated separately using the HAOS
and HOMS data because the two data sets differ significantly in several
aspects. The NMOC and N0X concentrations in the HAOS data set (Table 8) are
generally lower than in the HOMS data set (Table 9). The mean NMOC is 987.4
ppbC for Table 8 (with s = 545.0) and 2368.9 for Table 9 (with s = 1148.3).
The difference between these two means is highly statistically significant.
The same is true for N0X, whose mean value 5s 89.5 ppb for Table 8 (with
8 ° 56.0) and 139.2 for Table 9 (with s = 86.6). Another important differenc
is that the network of ozone monitors used in the HAOS was not the same as
that used in the HOMS, although the two networks overlapped.
EVALUATION OF STANDARD EKMA
Comparison of Observed and Estimated Ozone
Figure 14 shows a scatterplot of 0BS and EST for the HAOS data set.
Region 1 contains two points, Region 2 has 11, and Region 3 has 48. (One of
the points in Region 2 is plotted just below the line 0BS = 0.8 EST.) Thus,
about 3 percent of the cases are underpredicted, and the remainder satisfy th
inequality 0BS 1.2 EST. These percentages are similar to those previously
obtained for the RAPS data (see Figure 4).
The observed and estimated ozone for the HOMS data set are compared in
Figure 15. The figure shows that there are no points in Region 1, one point
In Region 2, and the rest are in Region 3. The pattern of substantial over-
prediction depicted in Figure 15 Is a consequence of the high values of NMOC
and NOx in the HOMS data set. The single point in Region 2 of Figure 15
45
-------
TABLE 8. EVALUATION DATA SET FOR HOUSTON: HAOS DATA
1
Precursors
Temperature (°C)
Solar Radiation*
1000-1400
ibserved Maximum Ozone
EHtA Ozone
Estimate (ppb)
Date
NMOC
NOx
Dally
Horning
Average
Station
Time
°3
City-
(1977)
(ppbC)
(ppb)
Maximum
Minimum
(ly/mln)
Name
(CDT)
(ppb)
Standard
Speclflc
I Mar
330
57
27.1
17.8
0.68
Parkhurst
1500
79
137
58
2 May
470
53
29.4
20.0
0.49
Aldlne
1400
90
159
65
3 May
157S
141
27.8
16.1
0.26
Parkhurst
1300
95
334
126
4 May
1543
89
28.3
20.6
0.65
Parkhurst
1200
62
277
114
6 May
1103
94
28.9
17.8
0.54
Aldlne
1200
64
258
100
7 May
803
63
30.0
20.6
0.37
Parkhurst
1300
89
202
82
8 Hay
943
41
30.6
21.7
0.53
Parkhurst
1400
141
176
79
9 May
1457
188
27.8
19.4
0.31
Clinton
1700
103
354
117
12 May
625
46
30.0
15.0
0.67
Mae Drive
1300
169
167
71
19 May
1107
53
28.3
21.7
0.38
Parkhurst
1200
65
205
88
20 Ma -
66]
72
27.8
20.6
0.42
Parkhurst
1200
58
198
77
23 May
563
47
27.8
19.4
0.39
Fugua
1J:00
92
163
69
25 May
2396
203
31.1
16.1
0.64
Parkhurst
1200
302
435
65
27 May
1018
99
31.7
19.4
0.63
Fugua
1400
141
256
97
28 May
1650
69
31.7
17.2
0.68
Aldlr.e
1500
80
252
108
2V May
1420
42
33.3
17.8
X
Aldlne
1500
95
195
87
31 May
1545
no
33.9
17.8
0.79
Parkhurst
1500
264
302
120
1 Jun
957
89
31.1
20.6
0.41
Fugua
1500
280
242
94
2 Jun
1400
no
33.3
20.0
0.69
Aldlne
1600
270
29'
115
3 Jun
745
123
33.3
18.9
0.64
Aldlne
1200
258
235
86
4 Jun
930
99
34.4
18.3
0.63
Lang
1200
256
248
92
5 Jun
990
100
35.0
18.9
0.68
Fugua
1400
180
254
95
6 Jun
460
54
35.0
21.1
0.69
Fugua
1300
186
159
64
8 Jun
555
43
32.2
16.7
0.71
Crawford
1500
309
157
64
9 Jun
1567
242
33.9
17.2
0.67
Crawford
1300
267
385
128
10 Jun
1087
91
33.9
18.3
0.57
Parkhurst
1500
119
254
99
12 Jun
700
43
29.4
22.8
0.24
Lang
1500
111
167
72
13 Jun
863
39
31.7
21.1
0.4*
Lang
1300
77
169
75
16 Jun
1010
54
31.1
24.4
0.44
Westhollov
1700
62
202
86
17 Jun
833
45
32.8
22.8
0.66
Vesthollov
'1400
87
178
77
18 Jun
700
43
32.8
22.2
0.66
Fugua
1200
73
If 7
72
21 Jun
850
54
32.2
24.4
0.44
Westhollov
1800
70
193
81
23 Jun
1053
63
32.2
23.3
0.60
Vesthollov
1600
108
218
91
24 Jun
1860
45
32.8
22.2
0.58
Fugua
1500
50
213
94
27 Jun
740
53
31.1
22.2
0.30
Westhollov
1500
94
185
77
28 Jun
625
58
33.9
21.7
0.62
Westhollov
1300
92
181
73
-------
TABLE 6 (concluded)
Precursors
Temperature (°C)
Solar Radiation*
1000-1400
Observed Haxlmum Ozone
EiQtA Ozone
Estlaate (ppb)
Date
NMOC
NOx
Dally
Horning
Average
Station
Time
°3
City-
(1977)
(ppbC)
(ppb)
Haximum
Minimum
(ly/min)
Naree
(CDT)
(ppb)
Standard
Specific
3 Jul
937
56
35.6
20.0
0.70
Aldlne
1500
134
201
85
4 Jul
963
56
33.9
21.1
0.60
Jackrabblt
1500
149
203
86
5 Jul
1060
98
33.3
21.1
0.57
Parkhurst
1300
140
258
99
6 Jul
1165
115
32.2
22.2
0.53
Parkhurst
1200
143
281
106
7 Jul
1240
136
33.9
20.6
0. 58
Parkhurst
1300
124
303
110
8 Jul
1150
134
33.3
21.1
0.45
Aldlne
1200
112
293
105
9 Jul
660
101
34.4
21-7
0.62
Mae Drive
1300
152
215
79
10 Jul
473
60
33.9
22.2
0.61
Parkhurst
1300
63
165
66
12 Jul
677
98
35.6
23.3
0.67
Prrkhurst
1200
107
216
79
IS Jul
873
70
34.4
21.1
0.55
MacGregor
1300
178
215
86
18 Jul
1597
82
32.8
21.1
0.48
Jackrabblt
1400
125
270
113
19 Jul
940
83
31.1
21.7
0.39
Parkhurst
1300
163
234
92
20 Jul
730
125
31.7
22.8
0.48
Parkhurst
1600
60
231
66
22 Jul
600
154
35.0
21.7
0.57
Mae Drive
1500
134
207
81
23 Jul
253
66
36.7
23.9
0.66
'rlac Drive
1500
160
120
54
24 Jul
210
39
35.6
23.9
0.67
Aldlne
1400
107
116
4?
25 Jul
680
89
35.6
22.2
0.62
Aldlne
1500
138
212
78
26 Jul
727
70
34.4
23.3
0.56
Clinton
1300
133
203
80
27 Jul
BOO
no
32.2
22.2
0.37
Mae Drive
1800
110
239
86
31 Jul
450
66
35.6
22.8
0.63
Parkhurst
1500
71
165
65
21 Oct
1206
126
26.7
18.3
0.37
Parkhurst
1600
93
293
108
23 Oct
570
58
26.7
15.6
0.40
MacGregor
1500
156
176
71
2) Oct
758
95
25.0
16.1
0.39
Clinton
1500
68
226
83
26 Oct
3710
378
28.9
13.9
0.53
Clinton
1400
122
523
223
*X denotes no data available*'
-------
TABLE 9* EVALUATION DATA SET FOR HOUSTON: KOHS DATA
00
Precursors
Temperature (°C)
Observed Maximum Ozone
EWiA Ozone
Estimate (ppb)
Dace
NMOC
B0*
Dally
Horning
Tine
°3
Cley-
(1978)
(ppbC)
(ppb)
Haxlauo
Mlnlmun
Site
(CUT)
(ppb)
Standard
Speclflc
21 Sep
2208
86
31.1
22.8
Jaekrabblt
1200
117
301
89
22 Sep
2489
61
31.1
23.3
Pearland
1500
119
260
79
23 Sep
2622
92
28.9
17.8
Pearland
1400
164
319
93
2t Sep
1411
80
29.4
20.0
Pearland
1200
182
259
81
27 Sep
867
8 8
28.9
21.7
PearZand
1400
106
233
75
29 Sep
1908
84
27.8
19.4
Pearland
1600
141
285
86
30 Sep
900
71
30.6
20.0
Darlinghurat
1500
105
218
71
1 Oct
1067
134
31.1
17.8
Hornwood
1400
310
285
87
2 Oct
2133
216
30.6
18.9
Aldlne
1200
210
427
121
3 Oct
4542
122
28.3
21.7
Aldlne
1200
100
408
117
4 Oct
2425
118
28.9
19.4
Aldlne
1400
150
350
100
5 Oct
4900
157
30.0
21.1
Crawford
1330
190
467
133
7 Oct
1823
69
25.6
15.6
Darllnghurst
1600
163
258
80
9 Oct
2575
136
26.1
16.7
Aldlne
1500
120
461
125
10 Oct
3133
194
27.8
15.0
Aldlne
1200
150
461
125
11 Oct
3500
263
29.4
17.8
Sheldon
1300
133
537
143
12 Oct
1758
394
30.6
15.6
Hornwood
1500
120
448
117
-------
141.39 192.05 242.79 293.49 344.19 394.69 449.93 496.29 946.99 997.69
116.00 166.70 217.40 266.10 316.60 369.90 420.20 470.90 921.60 372.30 623.
STANDARD-EKMA OZONE ESTIMATE (EST) — ppb
Figure 14. Scatterplot of observed ozone and standard-EKMA ozone estimate
for HAOS data set Number of points plotted is 61.
-------
233.99 86S.es 297.78 329.63 Ml.88 3S3.43 423.33 437.28 469.18 821.OS
216.00 249.90 261.60 310.70 049.60 377.BO 409.40 441.30 473.20 SOS.10 837.
STANDARD-EKMA OZONE ESTIMATE (EST) — ppb
Figure 15. Scatterplot of observed ozone and standard-EKMA ozone estimate
for HOMS data set. Number of points plotted is 17.
-------
corresponds to 1 October, when Che observed ozone was 310 ppb and Che estimate
was 285 ppb, hen~e R = 1.09. The orone level of 310 ppb was the highest
observed during Che HOMS monitoring program (6ee Table 9). The NM0C/N0x ratio
for 1 October is abouc 8, Che second lowesC .ratio ir. Table 9. (The lowesc
NM0C/N0x racio was 4.5, which occurred on 12 OcCober.)
The two points in Region 1 of Figure 14 correspond to 8 June and 23 July
(see Table 8). The OBS/EST ratio for these two days was 1.97 and 1.33,
respectively. The ozone level of 309 ppb recorded on 8 June was the highest
reported in the Houston area in 1977. It was measured at the Crawford moni-
toring site, which is located in downtown Houston. Analysis of the NMOC and
N0X data for 8 June showed that 0600-0900 measurements were not available for
the Crawford site, and the precursor levels shown in Table 8 for this date
were determined solely from data for Aldine and Parkhurst. The Crawford site
tends to have the highest levels of NMOC and N0X, which suggests the possibil-
ity that the precursor values used for 8 June may be low, thus inducing the
underestimate. The data of 23 July exhibited the second lowest NMOC in Table
8. (The lowest was 210 ppbC, which occurred on 24 July). For 23 July, the
NMOC was determined from measurements made at Aldine, Crawford, and Mae Drive.
The 0600-0900 NMOC at Aldine and Crawford was 230 ppbC and at Parkhurst, 3.00
ppbC. Thus, although NMOC was quite low on this date, the data for Che Chree
sites appear to be consistent, and could well be valid.
The observed and estimated ozone shown in Figure 14 are correlated; the
correlation is low (r = 0.26) but statistically significant (p < 0.025). The
regression line is defined by 0BS = 0.220 EST + 79.4, and has a standard error
of 65.3, where all Che unics are ppb. By contrasc, there Is no staciscically
signif'canC correlation beCween OBS and EST in Figure 15.
Relationships Between the Variables
Tables 10 and 11 show the correlation coefficients for selected variables
for the HAOS and HOMS data sets, respectively. For convenience, the tables
include variables associated with the city-specific ozone estimates; they will
be dealt wich in a later section.
Tables 10 and 11 show that temperature difference is correlated with both
NOx and OBS. OBS and N0X are correlated in the HAOS data set (Table 10) but
not in the HOMS data sec (Table 11). The standard-EKMA ozone estimate,
denoted by EST in the tables, is highly correlated with both NMOC and NOx, the
correlation being higher in the HAOS data set. Table 10 also shows that EST
is slightly correlaCed wich temperature difference in the HAOS data set but
not in the HOMS data set (Table 11). Table 10 indicates that the ratio
OBS/EST is correlated with 1/NM0C, NMOC, and temperature d'.fferincef which
will be exploited in deriving a multiple regression equation for OBS/EST.
NMOC and NOx are highly correlaCed in the HAOS data set, but ther is no
significant correlation between these two variables in the HOMS data sec..
For the HAOS data set, NOx and NMOC are related by the regression equation
NOx = 15.95 4- 0.0745(Wh")C). The significance level of the intercept is 0.065
and of the slope, 0.00001; the standard error of the regression Is s - 38.96
ppb. Figure 16 shows the regression line and the evaluation region boundaries
51
-------
TABLE 10. STATISTICAL PARAMETERS FOR SELECTED VARIABLES IN THE HAOS DATA SET*
S/i
K)
Correlation Coefficient^
Variable
Mean
Standard
Deviation
N0*
1/NMOC
l/NO,
Temp.
Dlff •
OBS
EST*
OBS/EST
CS038
OBS/CS03
KHOJ (ppbC)
987.4
34S.0
0.72
-0.70
0.46
0.23
—
0.90
-0.33
0.96
-0.30
BO, (ppb)
89>3
36.0
-0.40
-0.80
0.31
0.27
0.92
—
0.83
—
1/NMOC (ppbC"1)
0.0013
0.0008
0.41
—
—
-0.64
0.38
-0.68
0.33
l/NOx (ppb"1)
0.0141
0.0060
-0.27
-0.28
-0.7>
—
-0.66
—
Teoperature
difference (°C)
11.6
2.7
0.61
0.28
0.44
0.2&
0.49
OBS (; pb)
130.1
67.0
0.2C-
0.78
0.24
0.84
EST (opb)*
230.2
79.8
-C.28
0.98
—
OBS/EST
0.396
0.319
-0.29
0.99
CS03 (ppb)*
90.3
26.6
-0.24
OBS/CS03
1.49
0.770
1.0
'statistics based on 61 points.
^Significant at 0.0S level or better* Dashes Indicate that correlation Is not significant*
^Standird-EKMA estimate.
^Clty-opecifle EKMA estimate.
-------
TABLE 11. STATISTICAL PARAMETERS FOR SELECTED VARIABLES IN THE HOHS DATA SET*
in
u>
Variable
Mean
Standard
Deviation
Correlation Coefficient^
NOx
1/NMOC
i/uox
Temp.
Dlff.
OBS
EST*
OBS/EST
CS038
OBS/CS03
NHOC (ppbC)
2363.9
1148.3
—
-0.86
—
—
—
0.71
-0.54
0.75
-0.50
NOx (ppb)
139.2
86.6
—
-0.87
0.71
—
0.77
—
0.72
—
1/KMOC (ppbC-1)
0.0005
0.0003
—
—
—
-0.69
0.52
-0.69
0.46
1/NO, (ppb-1)
0.0092
0.0040
-0.59
—
-0.89
—
-0.86
—
Teitperature
difference (°C)
to.i
2.3
0.44
•—
—
--
—
OBS (ppb)
lit.8
SI.7
—
0.81
—
0.86
EST (ppb)*
346.7
96.3
-0.56
0. 99
•0.48
OBS/EST
0.47
0.20
-0.53
0.99
CSOJ (ppb)'
100.2
22.1
-0.46
OBS/CS03
1.37
0.63
1.0
^Statistics based on 17 points*
^Significant at 0*05 level or better* Dashes Indicate that correlation Is not significant*
^Standard-EKHA estimate*
®City-speelflc EKMA estimate-
-------
MS.00 730.00 1088.00 1439.00 1709.00 <139.00 2409.00 8890.00 31*9.00 3933.00
210.00 800.00 010.00 1200.00 lOIO.OO 1000.00 2310.00 2000.00 3010.00 3300.00 3710.1
NMOC — PpbC
Figure 16. Scatterplot of N0X and NMOC for the HAOS data set.
Number of points plotted it 61.
-------
A multiple regression equation was derived for OBS/EST as a function of
NMOC and temperature difference (denoted by DT) for the HAOS data set. The
equation is defined by
OBS/EST - 0.1145 - 0.0002681 (NMOC) + 0.06425 (DT) (6)
where the units of the variables were defined in Table 10. The multiple
correlation coefficient is r = 0.63 and the standard error of the regression
is s ° 0.25. The significance level of the regression and of the coefficients
of NMOC and DT is p < 0.0001, but the constant term is not statistically sig-
nificant at the 0.05 level. An expression analogous to Eq. 6 was not obtained
for the H0MS data set because the sample size is too small to yield meaningful
results.
Following the procedures previously described in Sections TVo and Three,
a plot of the accuracy probability was obtained using Eq. 6 after setting
DT » 17°C, which is its mean value plus two standard deviations. Figure 18
displays the probability curves for the three accuracy regions as a function
of the variable Z = -0.0002681 (NMOC). The figure shows that ?(' 1.2) > 0.5
for Z < -0.175, which corresponds to NMOC > 654 ppbC. This reflects the stan-
dard EKMA s tendency to overpredlct. The propensity for overpredlction
becomes even more pronounced if the value of DT in Eq. 6 is lowered from 17°C
to its mean value of 11.6°C. To illustrate, consider the circled point in
Figure 18, which is located at Z ¦ -0.45. Setting DT » to 11.6°C would shift
the curves in Figure 18 to the right, changing the Z-coordinate of the circled
point from -0.45 to -0.10. Thus, nearly all of Figure 18 to the right of the
circled point would be truncated, and P(R < 0.8) > 0.5 over the entire range
of NMOC and N0X concentrations.
Figure 18 shows that the curve for P(0.8 < R 1.2) is flattened and
spread out, in sharp contrast to the relatively narrow curve shown for St.
Louis in Figure 7. (Note, however, that the Z-scales are not equal in Figures
7 and 18.) The maximum value of P(0.8 <. R <. 1*2) is 0.58 In Figure 18, com-
pared to the maximum of 0.83 in Figure 7. The curves in Figures 7 and 18
differ In shape because the standard error of the regression is smaller for
Eq. 2 (s = 0.15) than for Eq. 6 (s » 0.25). The maximum probability of 0.58
in Figure 18 occurs in the neighborhood of Z * -0.21, which corresponds to
NMOC = 783 ppbC. The shaded region in Figure 18 is where P(0.8 jC R jC 1.2) >
0.50 and is defined by -0.35 < Z < -0.060, which corresponds to *224 < NMOC <
1305 ppbC.
Figure 19 displays constant-Z lines on the NM0C-N0x plane, along with the
evaluation region previously defined in Figure 16. The shaded area corre-
sponds to the region where P(0.8 R < 1.2) 0.50. Inside the evaluation
region, (NMOC, N0X) combinations that fall within and to the right of the
shaded area satisfy the inequality P(R < 1.2) > 0.60. Points to the left of
the shaded area satisfy the relation P(R > 1.2) > 0.42, and thus are more
55
-------
toeo.es 1471.99 1075.89 2876.99 8661.99 9069.19 9466.49 9601.79 4809.09 4606.39
904.00 ~ • I I
I I I
I I t
I t I
I I I
960.70 ~ I t
< I I
I I I
I I I
I I f
987.40 ~ I I
I I I
I I I
I I I
t I I
804.»0 ~ I I
860.60
£27.90
104.80
160.00 ~ I
I I
I t
I I
I I
187.60 ~ • t
I I
I I •
I I
I I
04.90 « I
I • ¦ I
I » I
I * I
I ¦ ¦ I
01.00 ~ I ¦
e«?.00 1870.90 1679.60 8076.OO 84S0.80 8669.90 9861*.60 3600.10 4003.40 4406.70 4900.
NMOC — ppbC
Figure 17. Scatterplot of N0X and NMOC for the HOMS data set.
Number of points plotted is 17.
-------
2 = -0.0002681 (NMOC)
Figure 18. Accuracy probability for standard-EKMA ozone estimates
for the HAOS data set. Temperature difference set to 17.0PC.
57
-------
NMOC — ppbC
Figure 19. Constant-Z plot for standard-EKMA ozone estimates for the HAOS data set.
Shading indicates area where ozone estimates tend to be most accurate,
assuming a temperature difference of 17.CP C.
58
-------
likely to yield underestimates of observed ozone. The tendency of the stan-
dard EKMA to overpredict ozone is reflected in the large difference in the
respective sizes of the regions that flank the shaded area in Figure 19. If
the figure were redrawn to correspond to a value of DT = 11.6°C, the shaded
area of Figure 19 would be confined to a narrow slice at the lower left hand
corner of the diagram, and the region of overprediction would cover essen-
tially the entire evaluation region.
EVALUATION OF CITY-SPECIFIC EKMA
City-Specific Ozone Estlnates
Table 12 shows the input parameters used to obtain the city-specific
ozone estimates for both the HAOS and HOMS data sets. The criteria for defin-
ing this input follow those used with the St. Louis data. Inversion height
data were derived from soundings obtained for 8 June 1977. The dates shown ii
Table 12 correspond to the days with the highest observed ozone for each data
set.
As in the St. Louis case, the C-S and standard-EKMA ozone estimates were
highly correlated for both HAOS and HOMS. Tables 10 and 11 show that the
correlation coefficient between C-S and standard-EKMA estimates is r = 0.98
for the HAOS, and r *¦ 0.99 for the HOMS. The regression line for the HAOS
data is CS03 = 15.02 + 0.33 * EST, and that for the HOMS is CS03 = 21.02 +
0.23 * EST, where the units are ppb.
Comparison of Observed Ozone and City-Specific Estimates
Figures 20 and 21 show scatterplots of observed and estimated ozone for
the HAOS and HOMS data, respectively. Whereas the standard-EKMA estimates
showed a marked tendency to overpredict, the C-S estimates show the opposite:.
The majority of the points in both figures are in Region 1, the region of
underprediction. For the HAOS, Figure 20 has 33 points (54 percent) in Regior
1, 16 points (26 percent) in Region 2, and 12 points (20 percent) in Region 3.
Figure 21 for the HOMS has 12 points (71 percent) in Region 1, 5 points (29
percent) in Region 2, and none in Region 3. Observed and estimated ozone are
correlated for the HAOS data; the correlation is low (r ¦= 0.24) but statisti-
cally significant (p < 0.04). No significant correlation exists between the
two quantities in the HOMS data.
Definition of Accuracy Regions
A multiple regression equation analogous to Eq. 6 was derived for the
ratio OBS/CS03 for the HAOS data set. The equation is
0BS/CS03 = 0.1718 - 0.0006191 (NM0C)
+ 0.1664 (DT) . (7)
The units and symbols in Eq. 7 were previously defined. The multiple correla-
tion coefficient is r - 0.65 and the standard error is s = 0.60. As In Eq. 6,
the significance level of, the coefficients of NM0C and DT is p < 0.0001, but
59
-------
TABLE 12. SUMMARY OF INPUT PARAMETERS
FOR OBT/tnING CITY-SPECIFIC EKMA
OZONE ESTIMATES FOR HOUSTON
Parameter
Value
Date
HAOS
8 June 1977
HOMS
1 October 1978
Location
Latitude 29.75°N,
Longitude 95.40°W
Inversion height data
Initial height (m)
105
Final height (d)
1510
Starting time of rise
0700
Ending tine of rise
1400
Post-0800 emissions
by ending hour
0900
NMOC
0.23
NO
0.23
1000
NMOC
0.07
N0„
0.05
1100
NMOC
0.08
NO
0.06
1200
NMOC
0.03
NO
0.03
1300
NMOC
0.04
NO
0.03
1400
NMOC
0.01
NO*
0.03
Reactivity, N02/N0x
0.33
Background ozone
concentration (ppm)
0.040
60
-------
97.70 79.10 *3.80 109.00 1S7.30 144.70 102.10 179.90 190.90 214.30
49.00 66.40 S3.60 101.80 IIS.SO 136.00 193.40 170.60 188.20 203.60 273.00
CITY-SPECIFIC EKMA OZONE ESTIMATE ICS03) — ppb
Figure 20. Scatterplot of observed ozone and city-specific EKMA ozone estimates for the HAOS data.
-------
74.60 61.60 60.00 66.80 100.40 110.60 117.60 ISO.00 132.20 106.40
0>
M
910.00 ~
866.00
t
g
O
o
Nl
o
>
-------
the constant term is not statistically significant at the 0.05 level. Equa-
tions 6 and 7 have the same form, but different coefficients; both equations
explain approximately the same amount of variance (about AO percent). How-
ever, the standard error of Cq. 7 is more than twice as big as that for Eq. 6.
Thue, there is more scatter, and less precision, associated with Eq. 7. As a
result, the accuracy probability plot will show distributions that are flat
and broad.
Figure 22 displays the probability curves for the three accuracy regions
as a function of the variable Z = -0.0006191 (NMOC). The curves are computed
for DT = 11.6°C, which is its mean value. The probability P(R 1.2) exceeds
0.5 for Z < -0.90, which corresponds to NMOC > 1454 ppbC. Thus, the C-S ozone
estimates can be considered to be upper bounds generally for high values of
NMOC. In contrast to the corresponding plots for St. Louis (cf. Figure 12),
the probability curve for Region 2 is very flat and broad. This is a conse-
quence of the large standard error associated with Eq. 7. The curve for P(0.t
^ R 1.2) covers the entire range of NMOC concentrations, but the probability
is low that & given NMOC value will fall in Region 2. The highest probability
of an accurate prediction is about 0.26, and occurs for Z » -1.11, which
corresponds approximately to NMOC = 1793 ppbC.
Figure 23 depicts constant-Z lines on the NM0C-N0x plane, along with the
evaluation region. The area to the left of the line Z ° -1.0 is associated
with underprediction and that to the right of the line Z » -1.25 with overpre-
diction. The area between the lines Z = -1.0 and Z = -1.25 is associated witi
the highest probability of an accurate prediction, but, as shown in Figure 22,
the probability is low.
DISCUSSION
For both HA03 and H0MS data, the EKMA Substantially overpredicted in the
standard mode, and underpredicted in the city-specific mode. As a result, th<
probability of an accurate prediction for the HA0S data was generally low. Ii
the city-specific case, the multiple regression fit to the ratio 0BS/CS03 had
a large standard error that is indicative of a low-precision fit. In general,
it appears that in either mode the EKMA tends to be a low-accuracy predictor
of ozone for the Houston area. If it is desired to obtain an upper bound for
the maximum potential ozone in the Houston area, then the standard-EKMA mode
is the appropriate choice, because it has a low probability of underestimating
the ozone level.
63
-------
Figure 22. Accuracy probability for city-specific EKMA ozone estimates for the HAOS data set.
Temperature difference is set to its mean value of 11.6*C.
64
-------
NMOC —ppbC
Figure 23. Constant-Z plot for city-specific EKMA ozone estimates for the HAOS data set
Temperature difference is set to its mean value of 11.6°C.
65
-------
SECTION 5
EKMA EVALUATION FOR TH^ PHILADELPHIA AREA
DATA REVIEW AND ANALYSIS
The EKMA has also been evaluated using data collected in the Philadelphia
area during the period July-Septeraber 1979. Figure 24 shows the 17 air-
quality monitoring stations used during the field program.
The statistical analyses performed using the Philadelphia data found
relationships similar to those found for St. Louis and Houston. The daily
maximum ozone was found to have a significant positive correlation with the
daily maximum temperature and the morning minimum to afternoon-maximum tem-
perature difference. A low negative correlation was found between the daily
peak ozone concentration and the 0600-1400 average wind speed.
The 0600-0900 EDT spatial average NM0C and N0X concentrations were calcu-
lated usip.g data for three source-region monitors located in downtown Phi-
ladelphia at South Broad and Spruce Streets (Site 13), at the Franklin Insti-
tute (Site 14), and at the American Meteorological Society Laboratory (Site
15).
DEFINITION OF EVALUATION DATA SET
Based on the (iata analysis, the following criteria were used to select
the evaluation data set for Philadelphia:
• Maximum dally temperature at least 24°C.
• Difference between maximum and morning minimum temperature at least
7°C.
• 0600-0900 areawide average N0X at least 34 ppb.
• 1000-1400 average wind speed less than 5 ra/s.
Note that the first three criteria are similar to those used in connection
with the Houston data. (Recall again that these meteorological conditions arc
always present whenever the daily maximum ozone is at least 100 ppb.)
Application of these criteria yielded an evaluation data set for Phi-
ladelphia that contains 29 days. Table 13 shows the data set including date,
precursor levels, temperature, and observed and estimated ozone. .The observe*
maximum 0-j exceeded 120 ppb on 12 of the 29 days.
66
-------
Figure 24. Air quality monitoring network for the Philadelphia area.
67
-------
TABLE 13. EVALUATION DATA SET FOR PHILADELPHIA
Precursors
Temperature (°C)
Observed Maximum Ozone
EKMA Ozune
Estimate (ppb)
Date
twoc
NOx
Dally
Horning
Time
°3
City-
(1979)
(ppbC)
(ppb)
Maximum
Hlnloum
Site*
(EDT)
(ppb)
Standard
Speclflc
7 Jul
800
97
24
II
11
1400
105
232
230
8 Jul
1267
133
26
12
10
1600
126
304
285
9 Jul
1230
90
26
13
10
1700
109
263
239
10 Jul
1567
93
25
14
13
1600
90
234
243
U Jul
283
51
26
17
11
1700
110
124
137
12 Jul
783
81
30
18
11
1400
147
219
215
13 Jul
1083
144
31
19
6
1300
183
292
282
U Jul
183
43
28
20
2
1200
84
101
110
17 Jul
300
53
30
20
5
1500
161
129
141
19 Jul
308
43
26
18
15
1700
160
123
137
20 Jul
450
87
27
17
2
1600
101
188
181
22 Jul
889
63
26
16
5
1600
141
208
199
23 Jul
3U9
48
26
19
2
1300
76
144
152
24 Jul
983
75
27
18
7
1500
120
229
216
25 Jul
767
57
29
20
5
1500
77
192
188
28 Jul
217
52
28
19
3
1300
146
11
120
31 Jul
317
52
29
20
2
1400
147
133
145
1 Aug
783
81
32
22
7
1500
114
219
215
10 Aug
783
63
31
19
15
1600
170
200
195
13 Aug
26}
38
23
13
2
1700
70
116
127
14 Aug
983
96
27
17
5
1500
115
250
239
21 Aug
200
69
26
17
7
1700
99
80
104
22 Aug
900
111
28
16
14
1500
140
253
247
23 Aug
300
88
28
16
7
1600
77
121
135
25 Aug
223
36
28
21"
7
1600
116
102
118
27 Aug
383
53
28
21
7
1600
101
146
155
2B Aug
4 22
59
27
20
7
1600
118
156
165
30 Aug
356
80
29
21
3
1400
126
189
195
JI Aug
367
91
27
19
11
1600
124
153
158
*Slte numbers are keyed to Figure 24.
68
-------
EVALUATION OF STANDARD EKMA
Comparison of Observed and Estimated Ozone
Figure 25 shows a scatterplot of ORS as a function of EST, which is the
mnemonic for the standard-CKMA ozone estimate. Of the 29 points plotted, fou
(14 percent) are in Region 1, five (17 percent) are in Region 2, and the
remainder in Region 'J. N'ute, however, that the four points In Region 1 are
not grossly underpredlcted.
Thus, as in St. Louis and Houston, the standard-EKMA shows a marked ten-
dency to overpredict. Unlike the St. Louis case, there is no statistically
significant correlation between OBS and EST.
Relationships Between Ihe Variables
Table 14 shows the pairwise correlation coefficients, mean, and standard
deviation for selected variables in the Philadelphia data set; the table con-
tains variables for both standard- and city-specific EKMA ozone estimates.
The table shows that EST is highly correlated with both NMOC and NOx, which
was expected. However, there is no significant correlation between OBS and
NMOC and OBS and N0X. Maximum temperature is correlated only with OBS. The
variable 1/NMOC correlates with EST and with OBS/EST because NMOC does.
Figure 26 shows a scatterplot of NMOC and N0X. The plot clearly portray
the linear correlation between these two variables. As Table 14 indicates,
the correlation coefficient is r = 0.70, and is highly statistically signifi-
cant (p < 0.00001). The figure also shows the regression line that relates
NOx and NMOC. The regression equation is NOx = 42.26 -I- 0.0501(NM0C), and has
a standard error s = 19.8 ppb. As in previous cases, the regression equation
has been used to define an evaluation region for the NM0C-N0x plane that is
shown in Figure 26.
Definition of Accuracy Regions
The multiple regression equation derived for the OBS/EST ratio is
OBS/EST « -0.653 + 162.45/NMOC + 0.0365(T) (8
where T denotes maximum temperature in °C, and the other symbols and units ar
as previously defined. The multiple regression coefficient for Eq. 8 is
r <• 0.79 and the standard error is s = 0.198. The coefficients of NMOC and T
are statistically significant at the 0.05 level, but the constant is not.
Neither iIOx nor 1/N0X appear in Eq. 8 because both are correlated with 1/NM0C
and do not provide any statistically significant improvement in the amount of
variance explained.
Figure 27 displays the accuracy probability plot for OBS/EST as a func-
tion of Z ¦ 162.45/NMOC for the mean value of T, which is 27.5°C. The proba-
bility P(R < 1.2) exceeds 0.5 for Z < 0.85, wnich corresponds to NMOC > 191
ppbC. The shaded area in Figure 27 defines the region with fhe highest proba
bility of an accurate prediction, i.e. where 0.8 < OBS/EST < 1.2. In the
69
-------
STANDARD-EKMA OZONE ESTIMATE (EST) — PPb
Figure 25. Scatterplot of observed ozone end standard-EKMA ozone estimate for Philadelphia.
-------
TABLE 14. MEANS, STANDARD DEVIATIONS, AND CORRELATIONS
FOR SELECTED VARIABLES IN THE PHILADELPHIA DATA SET
Correlation
Coefficient*
Variable
Mean
Standard
Deviation
1
! *
iM
i
I/NMOC
Maximum
Temperature
OBS
EST
OBS/EST
CS03
OBS/CS03
NMOC (ppbC)
620.9
379.8
0.70
-0.88
—
—
0.96
-0.71
0.92
-0.65
N0X (ppb)
73.3
27.2
-0.65
—
—
0.81
-0.54
0.84
-0.51
1/NMOC (ppbC"1)
0.0023
0.0014
—
—
-0.92
0.75
-0.92
0.66
Temperature
difference (°C)
27.5
2.1
0.52
__
OBS (ppb)
119.1
29.8
—
0.42
--
0.54
EST (ppb)*
181.4
64.1
1
©
0.99
-0.66
OBS/EST
0. 73
0.29
-0. 71
0.98
CS03 (ppb)*
181.8
51.9
—0.64
08S/CS03
©
-g
O
0.24
1.0
*All correlations significant at the 0.05 level or better*
Dashes denote that correlation Is not statistically significant*
^Standard-EKMA ozone estimate.
'citjr-speclflc EKMA ozone estimate.
-------
on.*io + ¦
NMOC — ppbC
Figure 26. Scatterplot of 0600—0900 (EDT) concentrations of NMOC and NOx for Philadelphia.
-------
Z =¦ 162.45/NMOC
Figure 27. Accuracy probability plot for standard-EKMA ozcne estimates for Philadelphia.
Mean value is assumed for maximum daily temperature.
73
-------
shaded area, the maximum probability Is approximately 0.71, and occurs for
Z = 0.65, which corresponds to NMOC = 250 ppbC. For the shaded area the vari-
able Z Is bounded by 0.51 < Z < 0.79, for P(0.8 0.6.
The accuracy regions are illustrated in the NM0C-N0x plane in Figure 28.
The shaded area of the figure corresponds to that in Figure 27 and is defined
by 206 < NMOC < 319 ppbC. Thus, {NMOC, N0x) combinations within the shaded
area have the highest probability of yielding an accurate ozone estimate.
Values of NMOC and NOx to the right of the shaded area have a high probability
that the ratio 0BS/EST < 0.8; hence, this is the region of overpredlction.
Underprediction is most probable in the thin slice to the left of the shaded
area. Thus, the vast majority of the evaluation region is associated with
OBS/GST ratios smaller than 1.2.
EVALUATION OF CITY-SPECIFIC EKMA
City-Specific Ozone Estimates
Table 15 lists the input parameters used to calculate the city-specific
ozone estimates for Philadelphia. As Table 13 showed, the highest observed
ozone occurred on 13 July, which is the date used as the input for the model.
The other parameters in Table 15 were obtained following the same procedures
used in the cases p~ lously described.
Continuing the pattern of the St. Louis and Houston data, the city-
specific and standard-EKMA ozone estimates are strongly correlated, with
r = 0.99 (see Table 14). The regression equation relating C-S and standard-
EKMA ozone is CS03 = 36.01 + 0.804 * EST, with standard error s >» 6.29, and
units in ppb; the regression is highly statistically significant (p <
0.00001). The equation indicates that CS03 > EST for EST < 180 ppb. This
range is greater than that for St. Louis, for which CS03 > EST for EST < 9£
ppb.
Comparison of Observed Ozone and City-Specific Estimates
Figure 29 compares OUS and CS03 concentrations. The figure shows that
Region 1 contains no points, Region 2 has eight points (28 percent) and Region
3 has 21 (72 percent). Thus, in contrast to the standard-EKMA estimates (cf.
Figure 25), the C-S estimates include no underpredlctions. Continuing the
pattern of the standard-EKMA estimates, there is no statistically significant
correlation between OBS and CS03.
Definition of Accuracy Regions
The multiple regression equation derived for the ratio OBS/CP03 is
OBS/CS03 = -0.580 + 117.72/NM0C + 0.0364(T) (9)
The multiple regression coefficient for Eq. 9 is r = 0.73, and the standard
error is s « 0.167. The coefficients of 1/NM0C and T are statistically signi-
ficant (p < 0.025), but the constant is not significant at the 0.05 level.
74
-------
NMOC — ppbC
Figure 28. Constant-2 plot for standard-EKMA ozone estimates for Philadelphia.
Shading defines area wfiere ozone estimates have the highest probability
of being accurate, assuming a maximum daily temperature of 27.b°C,
which is its mean value.
75
-------
TABLE 15. SUMMARY OF INPUT PARAMETERS
FO-\ OBTAINING CITY-SPECIFIC EKMA
ozo;;e estimates for Philadelphia
Paraneter
Value
Date
13 July 1979
Locat ion
Latitude 40.00°N,
Longitude 75.44°W
laversion height data
Initial height (n)
Final height (n)
Start tine of rise
Ending tine of rise
600
1800
0700
1400
Post-0800 onissions
by ending hour
0900
It IOC
NO
1000'
IMOC
1100
HiOC
*>,
1200
M10C
N0:<
1300
NMOC
NOx
0.25
0.25
0.04
0.04
0.13
0.13
0.28
0.28
0.35
0.35
Reactivity,
0.53
Background ozone
concentration (ppn)
0.070
76
-------
103.00
171.70
100.40
140.10
107.00
3
o
V
111
g 106.00
O
> 110.SO
c
s
o
103.90
oa.ea
at. 30
70.00 ~
104.00 Its.10 140.00 ISA.SO 170.40 104.BO 218.60 *30.70 240.SO 288.90 268.00
CITY-SPECIFIC EKMA OZONE ESTIMATE (CS03) — ppb
Figure 29. Scatterpiot of observed ozone and city-specific EKMA ozone estimate for Philadelphia.
-------
Equations 8 and 9 are very similar, which is a consequence of the strong
correlation between EST and CS03. Moreover, the 95-percent confidence inter-
vals of the coefficients of 1/NMOC and T foi Eq. C overlap the corresponding
intervals for Eq. 9.
Figure 30 shows the plot of the accuracy probabilities associated with
Eq. 9 for T = 27.5°C, which is its nean value. The graph shows probability as
a function of the variable Z =¦ 117.72/NMOO. The region.where P(R < 1.2) > 0.5
is defined by L < 0.78. In this region, the ozone estimate has a better than
50-percent probability of yielding an upper bound to the observed ozone. The
shaded area in Figure 30 marks the region where P(0.8 _< k 1.2) > 0.6.
Values of Z within the stiaded area are defined by 0.43 < Z < 0.73, and
correspond to 161 < NMOC < 274 ppbC. Thus, the C-S ozone estimates are most
likely to be accurate where NMOC is within these bounds.
The accuracy regions are displayed on the NM0C-N0x plane in Figure 31.
The shaded area of this figure corresponds to that of Figure 30; here C-S
ozone estimates have the highest probability of being accurate. The upper-
bound region, i.e. were R 1.2, includes the shaded area and all of the
evaluation region to the right of the shaded area. Only a very narrow slice
of the NMGC-NOx plane to the left of the shaded area corresponds to the region
of underprediction, and that slice is actually outside the bounds of the
evaluation region. This is, of course, a reflection of the fact that no
points fell in Region 1 of Figure 29.
DISCUSSION
For Philadelphia, the standard- and city-specific EKMA ozone estimates
were very similar. However, in a reversal of roles from the St. Louis and
Houston cases, the Philadelphia C-S estimates were more accurate and displayed
a lower tendency toward underprediction than did the standard-EKMA estimates.
However, in keeplag with previous results, Che standard-EKMA ozone estimates
showed a pronounced tendency toward overprediction. Because the city-specific
EKMA yielded more accurate estimates, and because its upper-bounfl properties
are similar to the standard EKMA's, it is recommended that the city-specific
EKMA, rather than the standard EKMA, should be the method used for application
to the Philadelphia area. This contrasts with the Houston situation, In which
the underpredlctive tendency of the city-specific EKMA renders it useless for
an upper-bound type of analysis.
78
-------
2= 117.72/NMOC
Figure 30. Accuracy probability plot for city-specific orciie estimates for Philadelphia.
Mean value is assumed for maximum daily temperature.
79
-------
NMOC — ppbC
Figure 31. Constant-Z plot for city-specific EKMA ">zone estimates for Philadelphia.
Shaded area denotes region where ozone estimates have the highest probability
of being accurate, assuming the mean value of 27.5° C for the maximum daily
temperature.
RO
-------
SECTION 6
EVALUATION USING DATA FOR THE LOS ANGELES AREA
DATA REVIEW AND ANALYSIS
The EKMA was evaluated using data from the South Coast Air Basin (the Lo
Angeles Basin) air monitoring network, operated by the California Air
Resources Board and the South Coast Air Quality Management District. The dat
were collected at thirty monitoring stations in the South Coast Air Basin
(Figure 32) during the period May through October 1978. Data for 1976 and
1977 were also examined; 1978 was chosen because it had the highest ozone
levels.
From a total of 184 days, only 20 days did not have observed ozone con-
centrations exceeding the NAAQS for ozone of 120 ppb. The highest observed
hourly averaged ozone concentration was 460 ppb. The dally maximum hourly
ozone concentrations were significantly correlated with dally maximum tempera-
ture; however, the correlation coefficient was low (r = 0.2*0., Ab with the
Houston data, the low correlation between peak ozone and peak tempera'ujre is
probably due to the narrow range in daily maximum temperatures. Tne daily
maximum ozone was also correlated with the 0600-0900 average source region
NM0C and NOx concentrations, but the correlation was low, although statisti-
cally significant.
Six monitoring sites were used to calculate the 0600-0900 average source
region NMOC and N0X concentrations:
•
Site
1—downtown Los Angeles
•
Site
3—Surbarik
•
Site
4—Long Beach
•
Sice
6—Pomona
•
Site
7—Lennox
•
Site
8—Whittier.
Results from an analysis of variance performed on the 0600-0900 average HM0C
and NOx concentrations monitored at each of these six sites showed that the
number of sites could not be condensed on a statistical basis.
81
-------
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-------
DEFINITION OF EVALUATION DATA SET
No selection criteria were used to decrease the number of test days
selected from the Los Angeles data base. Because the peak ozone concentration
exceeded the 120 ppb NAAQS for ozone on most days, the only days excluded from
the data base were those that had the 0600-0900 average source region flMOC or
NOx concentrations missing. Two additional days (14 September and 30 October)
were excluded because the dally maximum ozone concentrations (90 ppb and 80
ppb) occurred at 0300 and 1000, respectively.
The evaluation data set is; listed In Table 16. Included in the table are
the dally 0600-0900 average source region core city NM0C and N0X concentra-
tions; daily maximum temperature; the site, time, and magnitude of the
observed daily maximum ozone concentration; and the standard-EKMA and city-
specific ozone estimates. The number of test days Is 176.
EVALUATION OF STANDARD EK.MA
Comparison of Observed and Estimated Ozone
Figure 33 is a scatterplot of OBS and EST for Los Angeles.
scatter suggests, no statistically significant correlation exists between
observation and prediction. Nevertheless, the distribution of the points
among the three accuracy regions is of interest. Region 1 contains 62 points
(35 percent), Region has 51 (29 percent), and Region 3 has 63 (36 percent).
Thus, overpredictions, underpredictions, and accurate predictions are about
equally probable. This is surprising, because the standard-EKMA is supposed
to simulate worst-case ozone conditions in the Los Angeles area. However, the
figure shows. that 35 percent of the cases are underpredicted, which implies
that the standard-EKMA is not useful for obtaining upper bounds for maximum
ozone potential in the Los Angeles area.
Relationships Between the Variables
Table 17 show: correlation coefficients for selected variables In the Los
Angeles data set. Both standard-EKMA and city-specific ozone estimates are
included in tbe table, but the latter will be discussed in another section.
The table shows that OBS is weakly correlated with 1/NM0C and 1/N0x. By con-
trast, EST is strongly correlated with NM0C, N0X, 1/NMOC and l/NO*. and, as a
consequence, the ratio OBS/EST is also correlated with these variables. Max-
imum temperature is also correlated with NM0C, NOx, 1/NMOC, 1/N0X. and EST,
which contrasts with the situation in St. Louis, where no significant correla-
tion existed.
Table 17 indicates that NM0C and NOx are strongly correlated. This is
evident in Figure 34, which displays the strong linear relationship between
the two variables. The correlation coefficient is r = 0.92, and the regres-
sion line (which is plotted on the graph) is NOx " 41.68 + 0.142 (NMOC), where
the units ?re as defined in Table 17. The standard error of the regression is
s •> 29.96 ppb, which was used in conjunction with the regression line to
define the evaluation region in Figure 34.
83
-------
TABLE 16. EVALUATION DATA SET FOR LOS ANGELES
08SCRVC0 OZONE EKHA OZOUE ESTIMATES (ppb>
m~mm--
PATE
NMOC
NOX
TEMP
PEAK
PEAK
(1978)
(ppbC)
-------
pA?f
( IfTII
*7
MAT
11
tut
29
PUT
31
PUT
1
JII*
7
Ju*
3
J»*
4
Ju*
1
Jo*
t
JO*
?
Ju*
•
JO*
9
JO*
1#
Jo*
If
Jo*
13
JO*
14
JV*
14
J 9*
;•
JO*
1 7
JO*
19
JV*
19
Jon
29
JU*
91
JO*
It
JV*
it
ittn
•»0C «0*
tppPC* Ippto)
1017 l*t
1297 1*7
ifttr 1*4
197 72
m «•
(M I)
*)» 113
233 • *
CI 99
4*7 Itl
470 Iff'
ill VI
••• 1)4
JV» If
If?' Ml
lift 242
»e« wi
*23 122
126# l«ft
IS 49 2*1
9*9 144
I24« 271
1179 227
lift 147
94) t%9
irit ni
TABLE 16 (continued)
TW
01'* • >
oBsriv
*
070*1
C«MA JrONt (SrtNAT
S1*"0A«D
CIT*
I ppb I
CM IC
1
2
2
2
-------
UTf
•woe
•0.
i r«*t
74 JQ«
I13»
193
n Ju*
»7f
• ft
76 Jtm
303
7ft
*9 jua
377
10ft
30 JVM
613
160
i Jin.
t)l
110
t JUL
SI 3
91
3 JVl
31ft
101
• J CI
70ft
•a
1 J VI
37*
130
• Jin
»:«
Iftft
7 JUL
«»
9ft
0 J 51
933
na
> J Ml
4ftft
0ft
10 JUL
)M
*03
II JIM.
373
90
11 JUL
Iff
163
13 JUL
'.07 3
700
M JUL
1100
249
1ft Jvt
992
160
16 JUL
397
ez
•» ti i)
•74
130
10 JUL
770
1*7
19 JUL
560
117
70 JUL
747
173
71 JUL
863
174
TABU 16 (continued)
STAND
one (STIHAT
•D CITV-
tff>to >
-------
OAT!
<1978)
22
JUL
23
out
24
JUL
25
JUL
26
JUL
27
JUL
28
JUL
29
JUL
30
JUL
31
JUL
1
AUG
2
AUG
3
AUG
4
AUG
5
AUG
6
AUG
7
AUG
8
AUG
9
AUG
10
AUG
11
AUG
12
AUG
14
AUG
IS
AUG
16
AUG
17
AUG
NO*
(ppb >
17!
108
161
138
173
146
187
140
75
130
115
1 IS
139
126
139
106
i:>e
103
125
1 10
97
6**
95
127
176
J 50
NMOC
{ppbC>
852
741
688
601
945
747
848
420
342
630
411
495
476
471
440
448
502
336
475
467
303
238
303
485
933
602
TABLE 16 (continued)
08SEKVC0 0?0N£
TtMr
OEG r )
PEAK
ST*
z
28
28
2
2
9
28
2
2
9
23
9
29
12
6
3
2
29
28
29
29
2
2
Z
26
2
rpB
260
360
330
300
S30
31*
300
320
290
280
780
240
320
360
390
270
320
290
230
290
230
2 20
100
230
190
170
IKHA OZONt CSTIMAT
STANOARD CITV-
2C4
2 30
237
218
307
761
2/7
132
153
232
153
191
163
149
176
176
125
1 76
163
113
105
115
178
304
210
I ppb >
cjtic
-------
CAT!
I I9?#>
WKOC
IfpbC I
It
AUC
1
If
At*
1#
AUC
11
AUC
22
AVC
23
iUC
24
AUC
1
2t
AUC
2$
AUC
21
AUC
29
AtfC
1
Jl
AUC
IS
A9C
91
At*
1
up
1
up
MP
I
up
«
«p
•
UP
?
up
•
UP
1
9
UP
1#
MP
It
MP
If
MP
TARMv 16 (continued)
Pf AK
tin
ft
HO
PPi
?S#
*7#
?J#
18#
r?«
;t#
19#
210
74#
76#
XI
• I#
31#
SI#
XI
>7#
I 9#
7#
7#
IT#
?«#
IT#
l>#
17#
129
out (STIMAT
RO CITt
(ppb >
ciric
-------
TAM.r !*
(ronl |n«»*4>
0411 ftvf 0 r*70«4
9ITI
M*OC
ftCt Tt«f
MAC
»l *r
1 !«?•>
¦
«OV» 7
II uf
ur
IM 71
If
14 -I
1* m
1#«!
24# 73
77
It u»
n«
10ft 73
1#
13
it tir
till
2*9 7ft
74
17 1
t* sir
Itlf
477 at
12
14
2# »l»
1997
347 91
12
17 1
t* if
III!
349 IS
2
1ft I
7#44
s;i 92
7
14 7
23 »t»
11'?
ru im
17
13 7
n if
I2#2
1*7 If*
7
Ift 7
n it*
n?i
m
12
14 7
2* It'
7477
«7
I*
14 3
27 *«»
im
)l< 47
9
Ift 1
i« tir
14*7
7*4 17
12
14 J
Ul
1941
Sit 44
2
14 <
)i tcr
Mt
177 44
24
14 7
1 OCT
• IS
47 74
t
II 2
* OCT
IP*
71 74
•
14 7
3 OCT
Iftl
147 74
9
14 1
4 OCT
If/
144 »3
24
IC 3
1 XT
*77
117 74
2
Ift 3
• OCT
77*
i44 ;i
9
14 3
t OCT
• 17
121 74
9
It 3
• OCT
SIS
121 74
2
14 :
* OCT
Mil
244 77
2
Ift 1
1# OCT
114)
342 7*
21
Ift 7
0«t rtllMAT
•0 CIT».
< rr» I
ClfIC
-------
DATE
< 1978)
NHOC
IppbC)
NOX
t ppb)
11 OCT
1648
3«8
12 OCT
2123
305
13 OCT
16S7
2*3
14 OCT
1204
212
IS CCT
1232
197
16 OCT
989
182
17 OCT
303
90
18 OCT
1148
217
19 OCT
198A
326
20 OCT
723
135
21 OCT
835
135
22 OCT
758
80
23 OCT
714
145
24 OCT
234S
315
25 OCT
665
128
26 OCT
1475
308
27 OCT
1213
2JB
28 OCT
898
103
29 OCT
648
80
31 OCT
1058
206
16 (concluded)
OBSERVED OZONE EKMA OZONE ESTIMATE?
-------
69.*S 133.23 180.79 226.23 271.73 117.23 30i.7? 408.23 433 73 490 23
er oo its so ts» oo roi so 24« oo tm bo 3*0.00 »•» eo 431 00 470 so 8?2 00
STAMDARD-CKMA OZONE ESTIMATE (ESTI —pppb
Figure 33. Scinerplnt ol observed orone «rxJ ttanderd-EKMA orone estimate for Lot Angeles.
-------
Tklll 17. W*TM>tURD in'-VUTtnHS. AKT) CuRKIXATlONS
rot tuxctu) vAtuiLt-s u rut u>$ Maaixs da:a sit
Corr»l»llci> Cort Mr 1»nt*
n*an
1'ttuSi r4
OrtlltlAfl
J.'BO.
Flail Asa
«tur«
MS
tsi
oss/rsr
C50J
OBS/CSCi)
r?wc c)
•54.4
«K.)
o.»:
-O.M
-0. JB
0. 59
—
0. 9«
-0. >7
0. 94
-0. 51
w, »r»»>
i*:.p
?*.~
-0. 75
-0. »fc
o.s;
—
o.«;
-0.5)
G.*7
-0.45
iwx (tftc'h
0.001*
0.0009
o. p:
-0. 42
-0.l*t
-j.a*
0.->J
-0.9)
0.61
I/SO.
o.«m
0.00)
-0.4)
-0.1*'
-O. f<
0. 46
-0. 79
1. 39
r«. i
t.t
0.1)
0. 54
-0. lb'
0. 50
--
c»j <»*%>'
:».«
9>.r
—
0. 56
0. -.4"
0. 5l
trr **
1.10
til.)
0.5»
its. J
-•J. bh
-0.6)
00J/CM)
0.H
O.K
t.O
'#11 corfvltf le>«* ttpKUnf at 0*001 Irvtl onleit noted i*tWr*|«f«
&•«*#* tndtct* tMt (9r(vtit1rA It Not »tgfiI(lraM *t the 0.0} JfVfl*
^3!ftn|!t<»*t 1ml < 0.0|«
^Ub*cr»*d Aiwt
|ml ¦ O.OIt.
t»v«I « 0#0)•
lUiH'tCU MOM t(tl(X.tfi
(PU mm* Ht
-------
909.69 996.99 770 » 1009 99 1299.99 1470. 19 1709 49 1990 79 3170 09 9409 99
197.00 420.30 (99.60 686.90 1120.20 1999.90 1966.60 1920.TO 2099.40 ?266 70 2920.
NMOC ppbC
Figure 34. Scatterptot of 0600*0900 NMOC and N0X for Los Angeles.
-------
Definition of Accuracy Regions
A multiple regression equation was derived for the ratio OBS/EST as a
function of several variables:
OBS/EST = -0.244 - 39.06/N0x ~ 371.60/NMOC (10)
-0.0004 56 (NMOC ) + 0.0187(T)
where T denotes dally ma:.lroum temperature In °F and the other syobols and
units are as previously defined. The multiple regression coefficient Is
r = 0.68, and the standard error of the regression is s ¦ 0.43. All the coef-
ficients of Eq. 10 are statistically significant at better than the 0.05 Jevel
except the constant, which is not.
Equation 10 resembles Eq. 4 for St. Louis because It Includes both 1/KMOC
and 1/NOx. However, in Eq. 4 these two variables had positive coefficients,
which Is not the case in Eq. 10. Another difference between Eq. 4 and 10 19
that the latter includes NMOC; despite the fact that 1/NHOC, 1/N0X, and NMOC
are intercorrelated (see Table 17) the latter two variables increase the
amount of variance explained. By far the most Important variable in terac of
amount of variances explained is 1/NMGC, which by itself explains about 40
percent of the variance. The remaining three variables—T, NMOC and l/NOjj—
together add another 6 percent to the total explained variance. Thus, NMOC or
its reciprocal continues to play a lar^e role in explaining the predictive
performance of the EKiMA.
Figure 35 displays a plot of accuracy probability derived froa Eq. 10
after setting T 3 76.1°F, which is its mean value. The variable Z ¦ -39.06/
NOx + 371.60/NMOC - 0.000456 (NMOC) is the right side of Eq. 10 without the
constant and the factor for T. Reflecting the Indications of Figure 33, Fig-
ure 35 shows that the probability of an accurate prediction is relatively low,
with P (0.8 R < 1.2) < 0.37. Moreover, the magnitude of the three probabil-
ities is about the same in the neighborhood where P(0.8 < R < 1.2) has Its
maximum. Thus, relatively small changes In the value of Z in this neighbor-
hood can radically shift the probability of an accurate prediction in favor of
an increased probability of overpredlction or underpredlctlon. The steepness
of the curves for P(R < 0.8) and for P(R > 1.2) suggests a similarly sensitive
behavior in the overpredlction and underpredlctlon regimes, respectively. The
sensitivity of the probabilities causes the standard-EKMA ozone estimates to
be of limited usefulness for obtaining upper bounds for ozone In Los Angclet.
Figure 36 is the companion to Figure 35, depicting constant-Z contours In
the NM0C-N0x plane. For mean daily maximum temperature, the area to the right
of the curve Z » -0.50 represents the region where overpredlction is nost
probable. Conversely, the area to the left of rhe curve Z - 0.25 denotes the
region of underpredlctlon. Th» area between Z ¦ -0.5 and Z ¦ C.25 nay be con-
sidered a transition region where the three possibilities, i.e. overpredlc-
tion, accurate prediction, and underpredlctlon, have similar probabilities.
Qi
-------
2 - -39 08 NO, • 3M 6/NWOC - O.OOMStlNMOCI
31 AftvKv pfobot>l
-------
NMOC — ppbC
Plot of cmtwi7 curvet on NMOC-NO, plan* for lUndtrd-EKMA
atom HiuiMtn to* tw Angt*M.
9«
-------
EVALUATION OF CITY-SPECIFIC EKMA
Clty-Speclflc Ozone Estimates
Table 18 shows the Input parameters used with the EKMA computer program
to obtain the C- S ozone estimates.. As with the others, the date used, 23
June, was when the highest ozone level, 460 ppb, was observed. (This is one
day after the summer solstice.) Default values were used for the inversion
height; they are the same as for the standard EKMA. The city-specific EKMA
differs from the standard EKMA mainly in that the former has post-0800 emis-
sions, and the N02/N0x ratio is 0.41 rather than the standard value of C.25.
As in the other tost cities the city-specific EKMA ozont estimates for
Los Angeles, are highly correlated with the standard-EKMA estimates. Figure
37 shows a scatterplot of CS03 and EST that illustrates the strong relation-
ship between the two variables. The correlation coefficient is p - 0.98, and
is significant with p < 0.00001. The regression equation relating the two
variables Is CS02 = 78.35 + 1.62(EST), and has a standard error s <¦ 30.31,
where units are ppb. Actually, the figure Indicates a nonlinear relationship
exists between CS03 and EST, as evidenced by the slight curvature of the point
swarm.
Like Philadelphia, but unlike St. l,ouls and Houston, the Los Angeles C-S
estimates are greater than the Los Angeles standard-EKMA estimates. This is
reflected in the Intercept and slope of the regression equation, the slope
Indicating a scaling factor of 162 percent. This will lead to fewer
underpredictious and ta more overpredlctlons.
Comparison of Observed Ozone
and City-Specific Ozone Estimate
Figure 38 shows a scatterplot of OBS and CS03. In contrast to Figure 33,
Figure 38 has a preponderance of overpredlctlons and feu underpredictions.
Region i contains six points (3 percent of the total), Region 2 has 25 (14
percent), and Region 3 has 145 (83 percent). Thus, the nunber of undarpredlc-
tions has been reduced by more than a factor of ten, but the nuaber of accu-
rate predictions has decreased by a factor of two. Although the magnitude of
the overpredlctlons can be very large, more than a factor of ten in some
cases, for purposes of estimating u*>per bounds titc C-S EKMA is more appropri-
ate then the standard-EKMA because of its low probability of underprediction.
Definition of Accuracy Regions
The multiple regression equation derived for the ratio 0BS/0S03 la
OBS/CS03 - 0.0756 -54.999/NO* ~ 286.822/NMOC
-0.001687(NOX) + 0.00932(T) (11)
where symbols and units are as defined for Eq. 10. The multiple regression
coefficient is r - 0.69, and the standard error of the regression is s - 0.22.
97
-------
TAHLE 18. SUMMARY OK INPUT PARAMETERS
FOR OBTAINING CITi'-Sl'lICIFIC EKMA
OZONE ESTIMATES FOR LOS ANCELES
Paraneter
Value
Dace
23 June 197R
Locatton
Latitude 24.00°N,
Longitude 118.5°U
Inversion data
Default values used
Post-OROO enicsions
by ending hour
0900
MMiiC
0.61
;;°x
0.64
1000
nm;:c
0.57
"°x
0.51
1100
KMilC
0.35
NOx
0.34
1200
rfiiic
0.30
NOx
0.29
1300
NMilC
0.25
N°x
0.25
1400
NM1IC
0.16
110
0.15
1500
KMilC
0.14
N0X
0.14
Kcact lvity
N°,/N°x
0.41
Background ozone
concentration (ppn)
0.04
98
-------
••.79 199 29 190.79 226.*9 271.79 317.29 962 79 406.29 493.79 499.29
•99 00 ~
VO
SO
711.20
•37.90
<
s
O
<
S 419*5
X
u*
u
>
~-
u
• 22
9 ••
ia ••2*
*2**2-
• • 3«
• 32
3*
• ••
• 2 •
• *22* • • -
• • •• »
• i *2*
• • ,
• 4 •
2« *2
• 2* •
*• 2 *3 •
3*
¦ 2* •
• ¦
• 2*
120 00
+ + 1
•7.00 112.90 194.00 ?J3.90 249.00 294.90 340.00 369 90 431.00 476.90 922.00
STANDARD-EKMA OZONE ESTIMATE (ESTI — ppb
Figure 37. Scatierplot of city-spncific EKMA ozone estimate* and ttandard-EKMA
ozone estimates for Lm Angeles.
-------
196 99 *30 69 904 79 37® 69 492 99 926 49 600 39 074 29 746. 15 6?2 09
120.00 199.90 267.60 441.70 419.60 469.90 963.40 637.30 711.20 769 10 699.00
CITY-SPECIFIC Er.MA OZONE ESTIMATE (C503> — ppb
Figure 38. Scatterplot of observed ozone and city-specific ozone estimate for Los Angeles.
-------
All the coefficients are statistically significant ( p < 0.001), but the con-
stant is not significant at the 0.05 level.
Equation 11 differs from Eq. 10 in the presence of the variable N0X in
the former instead of the NMOC that appeared in the latter. Nevertheless, in
both aquations l/NMOC explained approximately the same amount: of-variance,
37 percent in Eq. 1! and 40 percent in Eq. 10. The remaining three variables
in Eq. 11, l/NO*, N0X and T, together account for about 10 percent of the
variance.
Figure 39 displays the plot of accuracy probability corresponding to
Eq. 11 with T = 76.1°F, which is its mean value. The probability is plotted
as a function of the variable Z = -54.999/N0x + 286.822/NMOC - 0.001687(NOX),
which is part of the right side of Eq. 1?. The figure shows that the proba-
bility of underprediction is low for most values of Z. The probability of an
accurate prediction is moderately high, with P(0.8 R < 1.2) reaching a max-
imum value of approximately 0.64 in the neighborhood of Z = 0.22. The ten-
dency to overpredict is apparent in the fact that P(R < 0.8) > 0.5 for Z < 0.
The highest probabilities of an accurate prediction range from 0.6 to 0.64 ani
"ccur for values of Z in the interval 0.1 < Z < 0.3.
Constant-Z contours are displayed on the NM0C-N0x plane in Figure 40.
The shaded area of Figure 40 corresponds to the interval 0.1 < Z < 0.3 in Fig'
ure 39 in which P(0.8 _< R _< 1.2) > 0.60. Thus, (NM0C,N0x) combinations in thi
shaded are& have the highest probability of yielding accurate estimates. The
small area to the left of the shaded slice is the region where underpredictioi
becomes more probable. The part of the evaluation region to the right of the
shaded area is associated with an increasing probability of overprediction.
The tendency toward overprediction is thu; made apparent, because most of the
evaluation region is to the right of the shaded area.
DISCUSSION
It was surprising that the standard-EKMA yielded so many underestimates,
indicating that the worst-case conditions supposedly embodied in the standard
EKMA do not in fact define a worst case. The city-specific EKMA, by co.itrast
yielded a large majority of overestimates. This, suggests that the city-
specific EKMA is the operational mode of choice for uhe purpose of obtaining,
an upper bound for ozone, although the magnitude of the overpr'.diction can be
very large.
101
-------
Z = -54.999/NOx + 286.6I2/NMOC - 0.
-------
450
400
£
c.
O
z
350 H
300
250
200
1000 1600
NMOC — ppbC
2000
2500
Figure 40. Plot of conttant- Z curvet on NH0C-N0x plans for city-tpccific EKMA
o/one etlimatet lor Lot Angeiet. Shaded area denotet rogion where accurate
ettimatet are moil probable, at turning mean maximum daily temperature.
103
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SECTION
EVALUATION USING DATA FOR THE TULSA AREA
DATA REVIEW AND ANALYSIS
Data collected during a field study conducted In the Tulsa, Oklahoma,
area frora July from September 1977 (Eaton et al., 1979) were used in the EKMA
evaluation. Ten monitoring locations were used to observe the production and
transport of ozone and ozone precursors, particularly when the winds were from
the soutli (Figure 41).
In comparison with the other da'.a bases used in the EKMA evaluation, peak
ozone concentrations in the Tulsa area were generally lower and occurred later
in the day. Hovuver, the peak ozone concentrations were significantly corre-
lated with the observed daily maximum temperature, although higher.tempera-
tures are apparently needed «:o produce ozone concentrations exceeding the
NAAQS ozone standard of 120 ppb. The 0600-0900 areawide-average source-region
NMOC and NOx concentrations are consistently lower in Tulsa than in the other
test cities. P«.ak ozone concentrations were also significantly correlated
with the morning-minimum to afternoon-maximum temperature difference.
NOx at>d NMOC were measured at two monitors located within the Tulsa city
limits. These iwo sites, the Tulsa Post Office and the Tulsa Health Depart- .
ment, were used to calculate the 0600-0900 average source-region NMOC and NOx
concentrations.
DEFINITION OF EVi^UATION DATA SET
The criteria used to select the evaluation data set for Tulsa were:
• Maximum daily temperature at least 30.6°C
• Difference between daily maximum and morning minimum temperature at
least 10.6°C.
M^ny days were excluded from the data set due to missing NMOC or NOx data.
One day with e maximum ozone level of 115 ppb watt excluded because the maximum
occurred before noon.
Thirteen days were selected fo the evaluation data set for Tulsa, which
is shown in Table 19. A complete statistical evaluation of the EKMA, similar
to that performed for the other four test cities, could not be performed for
104
-------
SOURCE: Eaton et al. (1979)
Figure 41. Map of Tulsa, Oklahoma, and vicinity.
105
-------
TABLE 19. EVALUATION DATA SET FOR TULSA
Precursors
Tenperaturo (°C)
Observed flixinun Ozone
EKMA Ozon<*
Estimate (ppb)
Date
tcioc
;;ox
Daily
.'.ornin,j
Tiae
o3
City-
(197?)
(ppbC)
(ppb )
Maxlnura
Mini:aur>
Site*
(COT)
(ppb)
Standard
Spec If lc
25 Jul
460
42
41.7
26.7
7
1900
123
147
101
29 Jul
440
53
34.4
23.3
1
1800
127
155
107
30 Jul
270
84
35.6
21.1
6
1300
128
108
85
2 Aug
960
65
35.0
19.4
1
1900
117
215
136
3 Aug
490
50
35.0
22.8
6
1500
151
159
108
4 Aug
500
59
35.0
23.9
7
1400
111
168
115
6 Aug
210
79
37. Z
25.0
6
1600
79
74
70
7 Aug
220
107
>5.2
25.0
6
1500
94
48
59
8 Aug
390
101
38.9
26.1
6
1500
84
156
109
9 Aug
410
76
33.3
25.0
6
1800
74
177
112
11 Aug
370
29
31.1
20.6
1
1600
95
120
85
14 Aug
170
10
33.9
il.7
8
1400
95
65
53
IS Aug
570
56
34.4
21.7
7
1300
106
174
117
*Slte nunbera arc keyed to Figure 41.
-------
Tulsa because of the small size of the data set. Consequently, we present an
abbreviated analysis In the sections that follow.
EVALUATION OF STANDARD F.KMA
Comparison of Observed and Estlnated Ozone
figure 42 shows a scafterplot of OBS and EST. Because the number of
points Is so Bmall, the plot yields no statistically meaningful pattern. How-
ever, each of the three regions contains some points, and the respective
number of points In Regions 2 and 3 differs only by one. Moreover, there is
no statistically significant correlation between OBS and EST. The paucity of
data prevents us fron inferring any trends from Figure 42.
Relationship Between the Variables
A scatterplot of 0600-0900 NMOC and N0X ia shown in Figure 43. In con-
trast to tlie other four test cities, «:he NMOC and N0x in Tulsa are not corre-
lated. One possible implication of this lack of correlation is that the
source region, if it exists, has not been properly characterized by the two
oonltor'.ng stations used to compute average NMOC and N0x. Another possible
explanation Is that stationary sources may be affecting one or both putative
"source-region" monitors, wliith would weaken the correlation between NMOC and
NO*. In fart. Figure 43 shows three clusters of points, one comprising five
points In the upper left haaJ corners of the graph, one seven points that are
aligned along the figure's main diagonal, and one a single point located In
the middle of the right-most margin. The seven-point cluster suggests a
linear relationship between Jf-jOC and N0X, but the dichotomy between the five-
point and seven-point clusters could be Indicative of the presence of multiple
uncorrelated sources affecting the precursor levels. It is thus apparent that
the two monitors arc Inadequate to characterize the Tulsa source region, if
Indeed It exists.
No slgplflcan: correlation vis found between OBS and NMOC and N0X. How-
ever, EST 1s strongly correlated with NMOC (r ¦ 0.87, p < 0.001) and with
1/NM0C (r » -0.94, p < 0.001). But KST Is not correlated with NO* or 1/N0-X,
which Is another Indication of the possible Influence of stationary sources on
the 0600-0900 NO*.
EVALUATION OF ClTlf-SPEClFIC EKMA
Ctty-Speclf1c Ozone Estimates
Table 20 shows the input paraoeters for the clty-speclflc calculations.
The trajectories calculated for estimating post-0800 emissions all left the
source area after 0900; hence, there are no post-0900 ealeslona. The absence
of post-0900 calsslons la a consequence of the small size of the urban area
and of the fact that Tulsa Is surrounded by open lands.
107
-------
96.39 73.09 69.79 106.49 129.19 139.69 196.99 173.29 169.99 206.69
O
00
. ~
191.00 ~
143.30
.70 61.40 96.10 114.60 131.90 146.20 164.90 161.60 196.30 219.
STANDARD-EKMA OZONE ESTIMATE (EST) — ppb
Figure 42. Scatterplot of observed ozone and standard-EKMA ozone estimate for Tulsa.
-------
100 50 860 50 307.90 440 50 523.90 €04.90 669.50 702 30 641 30 920.90
107.00 \ • I t
I I I
t * t
t t I
j • | I
•7 *0 ~ t I
I I I
> I I
a i i
i i i
07.0* ~ I I
I I I
1*1 I
I I I
I I I
77.00 ~ • t I
00. to
56 90
40 00
79.10 ~ I I
I I I
I I t
I t I
I I I
26 40 ~ I (
I ¦ I I
I I I
I I I
I I I
to 70 « 1 t
I I I
i a (
l t t
I t i
to oo •• a i
1 TO 00 240 00 020 00 407.00 400 00 569.00 *44 00 7*» 00 60t 00 061.00 900
NMOC — pp&C
Figuro 4X Scofterptot of 0600-0900 NMOC and N0k for Tutia.
-------
TABLE 20. SUMMARY OF INPUT PARAMETERS
FOR OBTAINIKC ClTf-SPECIFIC EKMA OZO.'fE ESTIMATES
FOR TULSA
Par-iriuter
Value
Dace
3 August 1977
Location
Latitude 36.92°N,
Longitude 95.92®U
Inversion height data
Initial height (a)
Final height (n)
Starting tlae of rlbe
Ending tine of rise
400
1800
0700
UOO
Poat-0600 enlaelonB*
twoc
HOx
0,50
0. SO
Reactivity, KOj/HO^
0.52
Zackgrouod osone
concentration (ppo)
0.04
*Endlng hour 0900.
HO
-------
As in the other four test cities, the C-S ozone estimates are strongly
correlated with the standard-EKMA predictions (r = 0.99, p < 0.001). The C-S
estimates are also correlated with NMOC (r = 0.88, p < 0.001), with 1/NMOC
(r » -0.95, p < 0.001), but not with N0X or 1/N0X.
Comparison of Observed Ozone
and Cit.'--Specific Ozone Estimates
Figure 44 shows the scatterplot of 0EJ and CS03. Comparison with Figure
42 shows that the C-S estimates display an increased frequency of underpredic-
tion with a corresponding decrease in overprediction. The frequency of accu-
rate predictions remains about the same as for the standard-EKMA case.
DISCUSSION
Although the small sample size precludes drawing general conclusions
about EKMA performance in the Tulsa area, a few cautionary remarks can
nonetheless be made. In using the EKMA, it is important to have a reasonably
well-defined source region. The Tulsa application revealed that the source
region was either inadequately defined or it does not exist. In either case,
the use of EKMA in the Tulsa context would be inappropriate. Thus, any
further attempts to apply the EKMA to Tulea should be preceded by an investi-
gation of the source distribution, with the aim of determining whether the
source-region concept that underlies the EKMA fits Tulsa's conditions.
Ill
-------
CITY-SPECIFIC EKMA OZONE ESTIMATE (CS03) — ppb
Figure 44. Scatterplot of observed ozone and city-specific EKMA ozone estimate for Tulsa.
-------
SECTION 8
CONCLUSIONS, IMPLICATIONS, AND RECOMMENDATIONS
DISCUSSION OF RESULTS
This study has:
• Demonstrated the feasibility of using the EKMA to estimate upper
bounds for daily maximum ozone, given the concentration of NMOC and
NOx.
• Shown that the accuracy of the EKMA ozone estimates is a function of
the position of the estimate on the O3 isopleth diagram, the posltlo
being determined by the (NMOC, NOx) coordinates.
• Developed a general method for evaluating EKMA performance as a pre-
dictor of maximum ozone.
The results indicate that it is possible to use the EKMA, in eithsr the
standard or city-specific form, to estimate an upper bound for daily maximum
ozone, given the concentration of NMOC and N0X. However, for a certain rangi
of values of NMOC and N0X the upper bound can be very loose, and thus of lim-
ited usefulness. The EKMA also can produce ozone estimates that are accurati
to within ±20 percent of the observations. Estimates of this accuracy can b<
obtained only for a restricted range of values of NMOC and NOx. In some
cases, e.g. for St. Louis, the range of values of NMOC and N0X that detorwini
the accuracy of the estimates is dependent in turn on such other variables at
background ozone level and maximum dally temperature.
Three levels of accuracy were defined based on the tatlo R ¦» observed/
estimated: R > 1.2, 0.8 jC R £ 1.2, and R < 0.8. The interval R > 1.2 defint
cas>s of underestimation; R < 0.8 defines cases of overpredlction. The close
Interval 0.8^ R£ 1.2 defines the most accurate estimates. The accuracy of
the ozone estimates depended not only on the level of pollutant and neteoro-
logical variables, but also on whether the standard or city-specific EKMA was
used. Moreover, the frequency of occurence of ozone estimates that fall in
each of the three accuracy Intervals was different for all the data sets stu-
died. Nevertheless, a general pattern emerged that relates low, medium, and
high values of NMOC and NOx to tlic 'hree accuracy intervals: Low values ten-
ded to yield R > 1.2, medium values, 0.8 .< R <. 1.2, and high values, R < 0.8.
The precise va?.ues of NMOC and NOx that mark the boundaries of the three accu
racy intervals differed among the individual data sets. St. Louis and Housto
exhibited a general trend toward a high frequency of overestlmatlou, and a lo
frequency of underprediction, for the standard EKMA. Although for St. Louis
and Houston the standard EKMA yielded estimates in the interval 0.8 < R < 1.2
-------
the frequency was low, and the range of NMOC and !J0X values that produced such
estimates with high probability was narrow.
The situation vas different for the city-specific EKMA, which tended to
have a higher frequency of estimates In the Interval 0.8 < R < 1.2. The
clty-speciflc F.KMA also tended to undcrpredlct more frequently, and to over-
predict less frequently, than the s.-'ndard KKMA. Thus, although the city-
specific EKMA offers n higher probability of producing an accurate estimate
(for which 0.8 _< R <_ 1.2), the standard KKMA has a higher probability of
yielding an upper bound estimate (for which R < 1.2). This has implications
for EKMA applications that are discussed in the next section.
The situation described above for St. Louis and Houston was reversed for
Philadelphia and Los Angeles. For the latter two test cities the standard
EKMA had a higher frequency of undorprediction and a lower frequency of over-
prediction than the city-specific EKMA. Consequently, the clty-specl.fic EKMA
is core useful for obtaining upper bounds on roaxlroun ozone potential for Phi-
ladelphia and Los Angeles.
A major thrust of the study was to quantify the probable error associated
with the estimates. Equations were derived for calculating the probability
that the observed/estimated ratio for a given estimate was in one of the three
accuracy intervals, namely R > 1.2, 0.8 _< R £ 1.2, and R < 0.8. Depending on
the data set studied, the probability was a function of NMOC and/or N0X and
other variables. Accuracy regions were identified in the NM0C-N0x plane
wherein an estimate can be assigned a probability of having attained a pre-
scribed accuracy level. Although our computations were aimed at the three
specific accuracy levels previously mentioned, the equations derived are gen-
eral and can be applied to any arbitrarily defined accuracy levels*
The study's use of several distinct data bases lends generality to the
patterns and trends discussed above. Nevertheless, the scope of the numerical
results is limited, in the sense that they strictly apply only to the particu-
lar data sets examined. Unless these data sets can be considered to be
representative of conditions In their respective geographical areas, the
application of the equations and graphs derived in tills study to other geo-
graphical regions, or to the same regions in other years, oust be regarded
with caution. Such restrictions are, of course, typical of most data-analytic
studies.
We regard the evaluation methodology developed In the study as an Impor-
tant contribution. The methods are general, and the numerical results
reported are real-life examples of what can be accomplished with these tech-
niques. In the future, the same raethodology can be applied to other data
bases to extend and generalize further the results reported here, as recom-
mended below.
IMPLICATIONS FOR EKMA APPLICATIONS
Using the EKMA to estimate maximum ozone from its NMOC and NOx precursors
implies that the EKMA could be used to assess the effect on ozone of actions
114
-------
that modify thp concentration of NMOC and N0X, e.^. emission control stra-
tegies. A corollary is that tl,e EKMA could also be used in the design of con'
trol strategies by performing a sequence of analyses of the effect on ozone oi
a variety of postulated control measures. Below we examine the possibilities
and pitfalls of using the EKMA in this fashion in light of the results of this
study. The discussion will be cast in terms of emission control strategies,
because we consider this to be the most common applicai.ior. of the EKMA. How-
ever, it should be understood that any action that modifies precursor levels
is implicitly treated. The discussion assumes that the reader is fanuHar
with the principles and assumptions of the EKMA as presently formulated.
The problem at issue is to evaluate the effectiveness of a control stra-
tegy aimed at reducing ozone bv curtailing emissions of NMOC or N0X, or both.
In this context, the EKMA could be used to estimate the maximum ozone associ-
ated with the control strategy in an attempt to answer the following
questions:
(1) What is the probability that the maximum ozone will exceed 120 ?pb?
(2) If it appears that 120 ppb will be exceeded, is the estimated ozone
close to or much greater than 120 ppb?
The general procedure is depicted in the flow chart in Figure 45. The
EKMA could be used to answer the first question provided that the ozone esti-
mate is less than or equal to 120 prb, and there is a high probability that
the estimate is an upper bound for the actual concentration. This corresponds
to taking the right-hand branch of Figure 45. In this case, the answer to
Question 1 above is that the probability is very low that the control strategy
will produce ozone levels that exceed 120 ppb; che precise value of the proba-
bility would be obtained from a probability graph such as Figure 7. Note that
the accuracy of the ozone estimate is not important in this situation because
an upper bound estimate is all that is needed. Hence, the standard EKMA may
be satisfactory for this application.
The EKMA is not as helpful in answering Question 1 if the estimate is
under 120 ppb but there is a high probability of underprediction. As indi-
cated in the right-most branch of Figure 45 in this case, the analysis must be
refined to establish the accuracy of the estimate and the probability associ-
ated with that accuracy. The methods developed in this study allow a user to
perform such a refined analysis. Because accuracy is important in these cir-
cumstances, it may be necessary to resort to the city-specific EKMA to obtain
the ozone estimate. However, this must be tempered by the knowledge that the
city-specific EKMA has a tendency to underpredict.
Answering Question 2 requires analyzing the accuracy of the estimate and
its associated probability. As depicted in the left branch o£ Figure 45,
three cases arc to be considered when the estimate is over 120 ppb:
(1) There is a high probability of overprediction
(2) There is a high probability of underprediction
(3) There is a relatively high probability that the estimate Is accu-
rate, for example, to within ±20 percent.
115
-------
CALCULATE
LOW
CALCULATE
YES / \ NO
¦+—C03>12C ~
CALCULATE
LOW
CALCULATE
P(R>1.2)
P(0.8
-------
The EKMA is least helpful In the first case (the left-most branch of Figure
45) because although the control strategy may actually reduce ozone below 120
ppb, the overpredictlor. masks the effect. This case thus requires a very
thorough analysis of the accuracy of the estimate. In the second case, it is
clear that the control strategy does not work, and the margin of ineffective-
ness should be assessed by analyzing the accuracy of the estimate as a means
of guiding the reformulation of the control strategy. The third case is where
the EKMA is most useful, because the estimate Is relatively accurate. Such ai
estimate can also be used to guide the design of a new control strategy.
Used In the fashion described above, the EKMA can be considered to be a
screening tool, albeit coarse at times, that allows one to analyze the poten-
tial impact of a control strategy. Coupled with the analysis of the accuracy
of £he estimates, the F.KMA couid also be used to help formulate a control
strategy by sequentially screening a series of control strategies. In gen-
eral, we recommend applying the standard EKMA first, then going to the city-
specific mode if the results obtained with the standard mode warrant it.
To apply the F.KMA in the manner described, one must have a means of cal-
culating the accuracy, and its associated probability, of the ozone estimate.
This, of course, presumes that EKMA performance has been already evaluated
following the methods described in this report. Hence, one would have avail-
able probability curves similar to Figure 7 and equations such as Eq. 2 for
analyzing the acuracy of the estimates. Because such curves and equations
would be based on a particular set of existing data, one is faced with the
perennial problem of deciding whether it 16 appropriate to use them for
predictive purposes; in effect, to extrapolate using equations and graphs
based on historical data. This Judgment is not unique to this EKMA applica-
tion; all models are tested and verified urflng historical data and are then
applied predictively. The prudent course Is not to stray too far froa the
known conditions.
RECOMMENDATIONS
We propose three extensions of the current research, first that further
evaluations of the EKMA be conducted using the methods developed in this
study. Specifically, evaluations should be performed using data for other
years in St. Louis, Houston, Philadelphia, and Los Angeles. This suggestion
is motivated by the need to establish whether the pattern of EWIA performance
associated with a single data set for each of these ««reas Is general In
nature. Only these four urban areas are recommended, because the Tulsa data
base that is normally available Is not sufficiently detailed for such
analysis. Adding some new areas to the extended evaluation should also be
considered, provided that at least two years of data are used for each area.
Second, we recommend investigating the appli-r.Ation of the results of this
study to the analysis and design of ozone control strategies. A procedure cat
he developed that uses EKMA ozone estimates and associated accuracy probabili-
ties to analyze the effectiveness of ;» control strategy with respect to its
effect on ozone levels. The analysis can be converted into design by sequen-
tially examining the impact of a series of control strategies. The results oJ
117
-------
the studies described in chis report lend themselves to the use of Monte Carlo
simulation techniques in conjunction with the £KMA to predict the distribution
of ozone maxima. This approach uses the entire joint distribution of NMOC and
N0X as the model input and produces the distribution of ozone maxima as out-
put. Thus, EKMA applications would not be United to using only the median
0600-0900 NM0C/NOx ratio and the single observed ozone design value as the
aole- EKMA Inputs.
The third reconrendation is prompted by the finding that the standard and
city-specific EKMA ozone estimates are highly correlated. The linear rela-
tionship between the two sets of estimates indicates that the city-specific
estimates are scaled versions of the standard estimates and the standard
scale/; versions of the city-specific. The presence of a nonzero constant terra
in the linear equation indicates that the two sets of ozone isopleths are
shifted with respect to one another. The well-defined linear transformation
between the two sets of estimates suggests that the transformation can perhaps
be generalized and parameterized so that the city-specific estimates can be
obtained directly from the standard estimates. Thi'3 would eliminate the
necessity of running the EKMA computer code in the city-specific mode, which
would simplify considerably the use of EKMA: equations already exist that fit
the standard EKMA ozone lsopleth diagram (see the appendix of this report).
Hence, a pocket calculator could be used to compute the estimated ozone for
both standard and city-specific EKMA. Thus, it is recommended that EPA spon-
sor an effort to derive a general transformation between standard and city-
specinc Z '.MA ozone estimates.
CONCLUDING REMARKS
The model evaluation methodology developed In this study has several
valuable features, namely:
• It la independent of the model evaluated. Hence It can be used with
other models besides EKMA.
• The accuracy of the model predictions can be calculated from che model
inputs.
• Accuracy ooup.da can be expressed in terms of probabilities.
These attributes make the methodology useful for application to a variety
of model evaluation studies. The methodology is especially easy to apply in
connection with trajectory models such as EKMA or ELSTAR. Such models have a
relatively otaall of lnpi'ts, and this facilitates the derivation of the
regression equation that describes the predictive behavior of the model.
Ileiice, we urge that the methodology bp considered for use in other uodel
evaluation studies. For example, It could be applied to Cipson and Meyer's
(1981) recent atudy.
118
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APPENDIX
EQUATIONS FOR STANPARD-EKMA OZONE ESTIMATES
The standard-EKMA ozone estimates were obtained using a set of equations
fitted to the ozone isopleth diagram by researchers at the University of Nortl
Carolina (Holton, 1980; Holton and Jeffries, 1979). An independent test of
the equations was performed at SRI for this study that detected a slight bias
in the equations. The bias was corrected by means of adjustment equations
that we derived using regression analysis. The ozone isopleth equations and
the correction expressions are defined below.
Following the notation of Holtor. and Jeffries (1979), let
0 » tan * (1/5.49)
L >» (NMOC) cos 0 + (N0X) sin 6
D = (NMOC) sin 6 - (N0X) cos 9
For D > 0, the uncorrected ozone is given by
0.683 , , _ , .1.97 ,0.518
0'3 = 0.282 L (1 - (5.49 D/L) ]
The corrected ozone is given by
03 = 0.00338337 + 1.00075 (0'3)
For D < 0, the uncorrected ozone is given by
0"3 = 0.282 l0,683 exp [-9.11 ( |D|/L)1 *68 ] .
The corrected value is obtained from
03 •» 0.00912572 + 1.08471 (0"3) .
119
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the Mature of Ozone, Oxides of Nitrogen, and Nonmethane Hydrocarbons in
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Gipson, G.L., and E.L. Meye?-, 1981: "Simplified Trajectory Analysis Approach
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Holton, G.A., 1980: Private communication, University of North Carolina,
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