United States
Environmental Protection
Agency
Office of Air Quality
Planning and Standards
Research Triangle Park NC 27711
EPA-450/4-86-002
February 1986
Air
oEPA
Evaluation of
Mobile Source Air
Quality Simulation
Models
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EPA-450/4-86-002
Evaluation of Mobile Source
Air Quality Simulation Models
By
David Wackter and Paul Bodner
TRC Environmental Consultants, Inc.
800 Connecticut Boulevard
East Hartford, CT06108
Contract No. 68-02-3886
U.S. Environmental Protection As'
r T i "h-"-q~*"Y I . - iJ -- - ' ,,
ST i^o^ st««. r.o- iov-
Cbiio, IL 60604
Prepared for
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Air Quality Planning and Standards
Monitoring and Data Analysis Division
Research Triangle Park, NC 27711
February 1986
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This report has been reviewed by the Office Of Air Quality Planning And Standards, U.S. Environmental
Protection Agency, and approved for publication as received from the contractor. Approval does not signify
that the contents necessarily reflect the views and policies of the Agency, neither does mention of trade
names or commercial products constitute endorsement or recommendation for use.
EPA-450/4-86-002
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TABLE OF CONTENTS
SECTION
1.0
2.0
2.1
2.2
2.3
2.4
2.5
3.0
3.1
3.2
3.3
3.4
3.5
4.0
4.1
4.2
4.3
5.0
5.1
5.2
5.3
5.4
5.5
6.0
7.0
PAGE
INTRODUCTION 1
DESCRIPTION OF THE MOBILE MODELS 3
CALINE3 3
GMLINE 5
HIWAY-2 5
PAL 6
Modifications to the Mobile Models 6
DESCRIPTION OF THE DATA SETS 11
California Department of Transportation -
Santa Monica Freeway (1974) 12
General Motors (1975) 15
New York State Long Island Expressway - CO (1977) . 18
New York State Long Island Expressway - SF6 (1976) 21
SRI Highway 101 (1975) 21
STATISTICS APPROACH 27
Pre-Analysis Data Handling Procedures 27
Statistical Performance Measures 30
Data Sets for Statistical Analysis 34
MODEL PERFORMANCE RESULTS 39
Statistics for "N" Highest Values 39
Statistics for Highest Concentration by Event ... 43
Statistics for All Concentrations Paired in Time
and Space 53
Statistics for Highest Concentration at Each
Station 57
Examples of Statistics by Subsets 61
SUMMARY AND CONCLUSIONS 69
REFERENCES 71
APPENDICES
A
B
C
D
STATISTICS FOR HIGHEST "N" VALUES
STATISTICS FOR VALUES PAIRED IN TIME, INCLUDING HIGH BY
EVENT AND PAIRED IN SPACE AND TIME
STATISTICS FOR HIGHEST CONCENTRATION BY STATION
STATISTICS FOR HIGHEST VALUES FOR VARIOUS PAIRINGS
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LIST OF FIGURES
FIGURE PAGE
3-1 Monitoring Configuration for the California Department of
Transportation CO Data Base (CAL74-CO) 13
3-2 Monitoring Configuration for the General Motors SFS Data
Base (GM75-SF6) 16
3-3 Monitoring Configuration for the New York CO Data Base
(NYS77-CO) 19
3-4 Monitoring Configuration for the New York SF6 Data Base
(NYS76-SF6) 22
3-5 Monitoring Configuration for the SRI CO Data Base (SRI75-CO)
CO Probes Shown in the Lower Diagram are at a Height of
1 Meter 23
5-1 Difference of Averages of Highest "N" Observed and Predicted
One Hour Concentrations 42
5-2 Average Difference of Highest Observed and Predicted One-Hour
Concentrations (Event by Event) 48
5-3 Average Difference of Highest Observed and Predicted One-Hour
Concentrations (Paired in Time and Space) 56
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LIST OF TABLES
TABLE PAGE
2-1 Comparison of Input Data Requirements for the Mobile Models . 4
4-1 Statistical Estimators and Basis for Confidence Limits on
Performance Measures 31
4-2 Array of Performance Measures and Statistics Calculated for
the "N" Highest (Unpaired) Mobile Data Sets (Where N is the
Lesser of 25 or 25%) 36
4-3 Array of Performance Measures and Statistics Calculated for
the Mobile Data Sets Paired in Time or Location 38
5-1 Comparison of "N" Highest Observed and Predicted One Hour
Concentration Values (Unpaired in Time or Location) .... 40
5-2 Comparison of "N" Highest Observed and Predicted Eight Hour
Concentration Values (Unpaired in Time or Location) .... 44
5-3 Comparison of Highest Observed and Predicted One Hour
Concentration Values Event by Event (Paired in Time) ... 46
5-4 Comparison of Highest Observed and Predicted Eight Hour
Concentration Values Event by Event (Paired in Time) ... 51
5-5 Comparison of All Observed and Predicted One Hour Concent-
ration Values (Paired in Time and Space) 54
5-6 Comparison of Highest and Second Highest Observed and
Predicted One Hour Concentration Values (Paired by Station) 58
5-7 Comparison of Highest and Second Highest Observed and
Predicted Eight Hour Concentration Values (Paired by Station) 60
5-8 Comparison of Difference of Averages for "N" Highest Observed
and Predicted SF6 Concentration Values (Unpaired in Time or
Location) for Various Subsets, Data Base: GM75, Averaging
Time: Half Hour 62
5-9 Comparison of Difference of Averages for "N" Highest Observed
and Predicted CO Concentration Values (Unpaired in Time or
Location) for Various Subsets, Data Base: NYS77-CO,
Averaging Time: 1 Hour 64
5-10 Comparison of Difference of Averages for Observed and
Predicted SFS Concentration Values Paired in Time and Space
for Various Subsets, Data Base: GM75, Averaging Time:
Half Hour 65
5-11 Comparison of Difference of Averages for Observed and
Predicted CO Concentration Values Paired in Time and Space
for Various Subsets, Data Base: NYS77, Averaging Time:
1 Hour 67
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1.0 INTRODUCTION
EPA is involved in an ongoing study to systematically evaluate the
performance of air quality simulation models using statistical measures
recommended by the American Meteorological Society (AMS). Results of the
study, in conjunction with scientific peer review, will provide EPA with
measures of accuracy and the degree of confidence that can be expected when
air quality models are applied in regulatory settings. Mobile source models
are one category of models to be evaluated.
In this study, the following mobile source models were evaluated:
CALINE3
GMLINE
HIWAY-2
PAL
Section 2 of this report contains a brief description of these models along
with a description of the procedures for implementing and testing the models
and the unique input data requirements.
The five data sets used for this evaluation are listed below:
GM75 - General Motors Sulfate Dispersion Experiment (SF6)
SRI75 - SRI, Highway 101 (CO)
NYS76 - New York State, Long Island Expressway (SF6)
NYS77 - New York State, Long Island Expressway (CO)
CAL74 - California Department of Transportation, Santa Monica
Freeway (CO)
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These data sets are described in Section 3 along with diagrams showing the
locations of monitoring sites relative to the roadways.
The statistical approach is presented in Section 4. Sets of observed and
predicted concentration values have been grouped in various ways to depict
performance for the high end of the frequency distribution as required for
regulatory applications, as well as performance for the full spectrum of
observed and predicted values.
In Section 5 the results of the study are presented. Summary tables of
the statistical measures recommended by the AMS are presented for each model
and data base. Examples of the tables by subsets of meteorological conditions
and monitoring station (the full set of which are shown in the appendices) are
also presented.
Four sets of appendices provide tables of statistical results for various
data groupings. Appendix A contains tables of High "N" results. Appendix B
contains the "All Paired" and "High by Event" analyses. The "High by Station"
tables are shown in Appendix C and single value comparisons are provided in
Appendix D.
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2.0 DESCRIPTION OF THE MOBILE MODELS
The four models evaluated in the mobile source category include CALINE3,
GMLINE, HIWAY-2, and PAL. As shown in Table 2-1, each model requires similar
inputs to determine concentrations. These inputs include descriptions of the
highway site, receptor locations and meteorology. While the inputs to each
model are similar, different methods are used by each model to simulate
dispersion near a roadway. A brief summary of each model follows, along with
a description of necessary coding changes made by TRC. The reader is referred
to the individual user's guides for a detailed description of each model.
2.1 CALINE3
The CALINE3 model (Benson, 1979) was developed by the California
Department of Transportation. It simulates dispersion of highway emissions by
dividing individual roadway links into a series of elements from which
incremental concentrations are computed using a finite line source equation.
The incremental concentrations are summed to obtain a total concentration
estimate at a particular receptor location.
CALINE3 simulates the region directly over the roadway as a zone of
uniform emissions and turbulence called the "mixing zone." This zone
experiences increased dispersion due to mechanical turbulence created by
moving vehicles as well as thermal turbulence created by hot vehicle exhaust.
CALINE3 adjusts the level of turbulence as a function of wind speed. At low
wind speeds residence time of an air parcel within the mixing zone is
increased, resulting in turbulence enhancement through the use of a larger
initial vertical sigma value.
The CALINE3 model includes options for simulating dispersion from four
types of roadways: at grade, elevated filled sections, elevated bridges, and
cut or depressed sections. Multiple lanes, links and orientations can be
simulated.
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TABLE 2-1
COMPARISON OF INPUT DATA REQUIREMENTS FOR THE MOBILE MODELS*
Function/Parameter
CALINE3
GMLINE
HIWAY-2
PAL
SOURCE/SITE
Number of Links, Lanes X
Link Coordinates X
Link Height X
Width of Highway or
Mixing Zone X
Median Width
Traffic Volume X
Emission Factor X
Emission Rate
Buoyancy Flux -
Surface Roughness X
Settling Velocity X
Deposition Velocity X
Initial Sigmas (cry, oz) -
Point, Area, Special Sources -
Averaging Time X
RECEPTORS
x,y,z Coordinates X
Background Concentration X
Output Units ppm (CO)
METEOROLOGY
Temperature
Wind Speed X
Wind Direction X
Stability Class X
Mixing Height X
Anemometer Height -
X
X
X
X
x,z
ppm or
ug/m3
X
X
X
X
X
X
X
X
ug/m ,
ppm (CO)
OPTIONS
Highway Type
Wind Speed
Emission Rate
DEVELOPMENT DATA
(See Section 3.0)
* X indicates required input data
At Grade,
Fill, Bridge,
Cut
At Grade,
(elevated)
X
X
X
X
At Grade,
(elevated)
Cut
X
X
X
X
X
X
CAL74,
GMT 5
GM75
GM75
X
X
X
g/m3
X
X
X
X
X
X
At Grade,
Bridge
Constant
or Height
Dependent
Constant
or Hourly
Varying
None
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This version of the model was developed with the use of data from two out of
the five field studies used for this evaluation: California Department of
Transportation's program at the Santa Monica site (CAL74) and General Motors
Research Laboratory's program at the Milford Proving Ground (GM75).
2.2 GMLINE
GMLINE, "A Simple Line Source Model for Dispersion Near Roadways" (Chock,
1977a) was developed by General Motors Research Laboratories to describe
dispersion near straight-line, at-grade highways. Multiple parallel or
crossing roadway links can be simulated and the model allows for a variable
emissions height. Empirical relationships from the GM75 field study are
directly incorporated into the GMLINE model. The model was not designed to
treat cut-sections.
GMLINE simulates dispersion of vehicle emissions by dividing the roadway
into separate, straight-line sources, each with a uniform emission rate.
Downwind concentrations at a receptor are calculated for each infinite line
source, then summed to obtain a total concentration. The model accounts for
plume rise due to heated exhaust and includes a wind speed correction to
account for increased turbulence created by traffic wakes.
2.3 HIWAY-2
HIWAY-2 (Petersen, 1980) was developed by EPA to replace the HIWAY model
(Zimmerman and Thompson, 1975) for estimating roadway pollutant impacts. The
model was designed to determine concentrations at receptors downwind of
at-grade roadways and cut sections (outside of the cut only). HIWAY-2 was
developed with data from the GM75 field program.
HIWAY-2 simulates dispersion by treating highway emissions as a series of
finite line sources, each with a uniform emission rate. Concentrations
downwind are calculated by numerically integrating a Gaussian point-source
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plume along each line segment. The primary differences between HIWAY-2 and
HIWAY are that HIWAY-2 includes a new set of dispersion curves and an
aerodynamic drag factor to account for dispersion due to vehicle motion under
low wind speed conditions.
2.4 PAL
The PAL model (Petersen, 1978) was developed by EPA to estimate pollutant
dispersion from point, area and line sources. It was designed to simulate
dispersion from several types of roadway geometries including straight or
curved horizontal lines and straight or curved elevated lines with variable
emissions along each line segment. Model documentation specifies that
treatment of elevated line sources is appropriate for open bridge type road
segments but not for elevated filled roadways. Cut or depressed roadway
sections are not treated by PAL. None of the data sets employed for this
evaluation were used in developing the PAL model.
PAL determines concentrations at a receptor due to a line source by
numerically integrating the Gaussian point source equation. Calculations are
made for a number of points along the finite line, assuming a linear change in
concentration between these points. Subsequent estimates of concentration are
made by including additional points along the line. When the difference
between succeeding estimates becomes smaller than a prescribed value, the
calculations are complete.
2.5 Modifications to the Mobile Models
Each of the mobile models was installed and run on the EPA Univac 1100/82
computer at the National Computer Center. Although no changes were made to
the basic algorithms of any model, minor modifications were necessary for the
following reasons:
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To enable input of data directly from the archived data sets
To allow output of predictions to disk files for subsequent
statistical analysis
To accommodate unique features of each data set (such as hourly
varying emissions)
The first two I/O related changes were made through the addition of
subroutines MESSIN and MESSO. Subroutine MESSIN is called as one of the first
executable statements in each model. The function of MESSIN is to convert
units and reformat all model input data from EPA's Model Evaluation Support
System (MESS) formats (Computer Sciences Corporation, 1983) onto a file
formatted to the expectations of the respective model. The model-specific
formatting is done in subroutine MODLIN, which is called by MESSIN. MODLIN
performs three functions to create records of: 1) fixed model inputs, 2)
hourly model inputs (ENTRY MDHRLY), and 3) hourly model outputs (ENTRY
MESSO). MESSO is called hourly by each model after concentrations have been
calculated. The function of MESSO is to convert units of the predicted
concentrations and write them to a MESS formatted file. The observed and
predicted concentrations on the MESS files are in units of ppm for CO and ppb
for SF6.
Only the main programs for each model were modified by TRC (i.e., existing
subroutines were untouched). All changes were documented in the code as
follows to allow the respective model developers an opportunity to review and
approve their models before the statistics were generated:
New comment lines were clearly identified with "TRC" in the
comment.
New executable lines contain "TRC" in columns 73-75 (the
non-executable portion of an 80 character Fortran record).
For previously executable lines in the original GMLINE, a "comment
out" character "C" in column 1 was included.
Additional changes made to each model are summarized below.
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CALINE3
As described above, all coding changes incorporated into CALINE3 were
documented with comments in the source listing. Besides changes in I/O
(subroutine calls to MESSIN and MESSO), the CALINE3 model was modified to
include hourly varying rather than fixed line source emission rates.
To avoid any influence by mixing height on the results, a value of 9999
meters was used for all runs of the CALINE3 model. (Actually, any mixing
height greater than about 1000 meters would produce the same results.) It
should also be noted that no ambient background concentrations were included
in the model runs. Background levels were removed from observed
concentrations prior to statistical analysis (see section 4.1).
GMLINE
Major modifications to the GMLINE model were required in addition to the
I/O changes to allow an automated treatment of multiple discrete receptors
(either upwind or downwind of the roadway), hourly varying source emissions
and .variable buoyancy fluxes. To handle these enhancements, several variables
were redimensioned and additional loopings were added to the original computer
code. As a result, the modified model can now handle up to 10 line sources,
25 discrete receptors, and any number of hourly (or half-hourly)
meteorological conditions. Calculations of buoyancy fluxes,
lane-center/receptor distances and wind/roadway angle are now performed each
hour by the modified GMLINE.
Despite these major modifications, no changes were made to the empirical
parameters or mathematical algorithm upon which the original model was based.
This was verified by duplication of the example model runs in the GMLINE
user's guide.
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HIWAY-2
No additional modifications were necessary for the HIWAY-2 model.
However, for the CAL74 cut-section data set, the depressed highway was modeled
as two separate links, one in each direction of traffic flow. HIWAY-2
requires input of a parameter specifying the "width of the top of the cut" for
depressed roadways, but does not provide guidance on how to treat multiple
links in a cut-section. After reviewing the original HIWAY-2 code, it was
decided that, given the width to depth ratio of the cut, and to properly
account for emissions varying by lane, a value of half the cut width for each
of the two links would be appropriate for input to the model. This technique
causes the cut to be treated by the model as two separate cuts. The use of
this technique was reviewed and approved by William B. Petersen, the model
developer. To avoid influence by mixing height on the results, a value of
9999 meters was used for all runs of the HIWAY-2 model.
PAL
Changes made to the PAL model include subroutine calls to MESSIN and MESSO
for I/O and the inclusion of a new READ statement for hourly varying line
source emission rates. Following discussions with the model developer
(William B. Petersen), it was decided that the PAL inputs of initial mixing
(ayo and azo) should be allowed to vary hourly as is done internally
in the HIWAY-2 model. Two algorithms, for at-grade and cut sections, define
the initial sigmas as a function of wind speed. Rather than rerun the entire
input data sequence to the PAL model for each hour of data, the hourly sigmas
are calculated in a modified version of subroutine MODLIN and read by PAL with
the hourly varying emission rates.
All PAL runs specified the options for horizontal line sources, constant
wind speed with height, constant emission factors (hourly varying emissions
were permitted by the coding change noted above), and averaging for each
one-hour period. Mixing heights were set to 9999 meters for all model runs.
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3.0 DESCRIPTION OF THE DATA SETS
Five mobile source field studies were acquired and archived for this model
evaluation. The archive includes one cut-section and four at-grade data sets:
CAL74 - California Department of Transportation Santa Monica
Freeway - CO (cut-section)
GM75 - General Motors Sulfate Dispersion Experiment SFS
(at-grade)
NYS76 - New York State Long Island Expressway - SFs (at-grade)
NYS77 - New York State Long Island Expressway - CO (at-grade)
SRI75 - SRI Highway 101 Santa Clara - CO (at-grade)
These 5 data sets were selected from the 13 described in a Transportation
Research Board (TRB) report (Martinez, et al, 1982) for the following reasons:
Each selected data set contains enough quality data to enable
meaningful statistics to be generated for 1-hour and, in some
cases, 8-hour averaging periods.
Appropriate data were collected to provide the required inputs to
each of the mobile models.
The variety of data bases chosen allows model evaluation for both
at-grade and cut-section roadways and for emissions of both CO and
SF6 tracer.
Data collected in each study enable model evaluation over a wide
range of meteorological conditions.
Originally, most of the data needed for the mobile model evaluation was to
have come from the report and associated archive tape prepared for the
Transportation Research Board (Martinez et al., 1982). However, in order to
produce complete data sets which satisfy all input requirements of the models,
information had to be gathered from several additional sources. For example,
emissions for each CO data set were calculated using EPA's MOBILE2 or MOBILES
emissions models based on traffic information at each site. Data were only
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archived for hours containing complete information (source data, meteorology,
and air quality) needed to run and evaluate each model. Data sources for all
parameters archived or used as input to the emissions models are documented
for each data set in the sections that follow.
3.1 California Department of Transportation - Santa Monica Freeway (1974)
The archive for the CAL74 Santa Monica Freeway cut-section data set
includes 795 hours of data collected from April through July, 1974. The
monitoring configuration is shown in Figure 3-1. Carbon monoxide
concentrations measured at the six ground-level (1.5 meters) locations outside
the cut-section were archived. Ambient wind speed and wind direction measured
at the center of the median (6.7 meters above the top of the cut section and
14.0 meters above street level) were archived to provide the best available
representation of transport above the cut. Hourly stabilities were determined
from cloud cover and ceiling height observed at Los Angeles International
Airport (about 15 kilometers from the site) and on-site wind speeds measured
at 6.7 meters above the top of the cut section.
As described in Bemis, et al (1977), the Santa Monica Freeway site is
removed from other localized pollutant sources. There are no additional
freeways or main surface streets in the immediate area. The site is located
in a mixed single-double story residential area, with homes ranging from 20 to
30 feet in height.
Data from the CAL74 Santa Monica Freeway mobile source study were gathered
from several sources. Sources of all parameters archived or used in archiving
are given below:
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LEGEND
D CO PROBE
X TEMPERATURE
O ANEMOMETER
NOT TO SCALE
,13.4m
Ql4-0m
|-45.7-|-45.7-| - 12.5
4] [si [6] 1.5m
12.5 - 1-45 . 7^45 .
DISTANCE (m)
TOWER
14115(161
Figure 3-1. Monitoring configuration for the California Department of
Transportation CO data base (CAL74-CO).
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1. Martinez, et al (1982)
Road geometry
Anemometer location
- located at center of median, 6.7 m above grade and 14.0 m above
street level
CO receptor coordinates
Traffic hot/cold mode percentages
- 6.0% cold start and 2.0% hot start mode
Vehicle type distribution
- 77.0% light duty vehicles, 11.6% light duty trucks, 1.4% medium
duty trucks, 4.5% heavy duty gas trucks, 4.5% heavy duty diesel
trucks, and 1.0% motorcycles
Wind speed (from TRB computer tape)
Wind direction (from TRB computer tape)
Temperature (from TRB computer tape)
- measured at 13.4 m above grade at south edge of cut section
CO concentration (from TRB computer tape)
Sigma theta (from TRB computer tape)
- measured at the anemometer location described above
Traffic volume (from TRB computer tape)
* Traffic speed (from TRB computer tape)
* Ceiling height (from TRB computer tape)
- observed at Los Angeles International Airport NWS station
Cloud cover (from TRB computer tape)
- observed at Los Angeles International Airport NWS station
2. Benson (1979)
Surface roughness (100 cm)
Source length (5 km)
3. EPA (1977)
Stability (using wind speed, cloud cover, ceiling height,
sampling time and geographic location), from CRSTER
preprocessor program.
4. Bemis, et al (1977)
Roadway angle (80° 12' 53" east of north)
Number of lanes (six in each direction; modeled as two links)
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5. Calculated using MOBILE2 Emissions Model (EPA, 1981)
CO Emission Factors
MOBILES could not be used because it does not have an option
for California emission factors. The following MOBILE2 input
options were used:
Identical speed for all vehicle types, varying by hour
- User supplied single VMT mix (from 1)
- MOBILE2 default registration and mileage distributions
- MOBILE2 default exhaust emission rates
- No I/M program
- No special correction factors
California emission factors
- 1974 calendar year
- Speeds, temperatures, and hot/cold mode
percentages as given in TRB report
MOBILE2 emission factors (grams/mile) were generated for each
combination of speed (5 to 55 mph) and ambient temperature (20
to 95°F). They were then matched with the traffic speed (to
the nearest mph for each direction of flow) and ambient
temperature (rounded to the nearest 5°F) for each hour during
which data were collected.
CO Emission Rates
Emission rates were obtained by multiplying the traffic volume
(for each direction of flow) by the MOBILE2 emission factor
(described above) for each hour of data collection. Emission
rate units are grams/meter/second.
3.2 General Motors (1975)
The archive for the GM75 tracer data set contains SF6 measurements for
62 periods of 30 minutes each from an at-grade oval test track at the GM
Proving Ground in Milford, Michigan. The site diagram is shown in Figure
3-2. Tracer was released from seven or eight pickup trucks distributed evenly
among 352 vehicles traveling on the track. Experiments were run during
October, 1975.
As described in Cadle, et al (1976), the GM Proving Ground site is located
in a rural area, surrounded by rolling hills and light woods. The site itself
is essentially flat and open. The nearest major highways are located 7 km to
the south and 6 km to the west.
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LEGEND
Q SFg PROBE
X TEMPERATURE
O ANEMOMETER
NOT TO SCALE
14. 5 m
)4.5 m
f/l 0.5m
h28.1-|L9(&8J11.8|6.8|3.3|11.2|-15.0-|20.0 |
-50.0-
DISTANCE (m)
Figure 3-2. Monitoring configuration for the General Motors SFfi data base
(GM75-SF6). °
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The GM archive contains half-hour averages of SF6 concentration for the
seven ground-level (0.5 meter), non-median monitoring locations. In addition,
wind speed, wind direction, and temperature at a height of approximately
4.5 meters were archived from the tower located 30 meters upwind of the track
(as determined for each sampling period) to represent ambient plume transport
conditions not affected by the roadway. The archive also includes SF6
emission rates for each sampling period.
Data from the General Motors Sulfate Dispersion Experiment were obtained
from several sources. Hourly averages contained on the Transportation
Research Board archive tape were not used in order to maintain the integrity
of the original 30 minute averaging periods. Sources of all parameters
archived for the mobile model evaluation are given below:
1. Chock (1977b)
Road geometry
Number of lanes (2 in each travel direction)
Traffic volume (equivalent of 5462 vehicles/hour, equally
divided between 4 lanes)
Source length (5000 m)
Anemometer location (30 upwind of road, at a height of 4.5 m)
2. Chock (1977a)
Buoyancy flux (0.052 mVsec3 for traffic volume stated
above)
3. Chock (1977c)
Stability (local Colder stability used in the model runs; also
archived Turner stability derived from Detroit Metropolitan
Airport NWS data)
Surface roughness (3 cm)
4. Cadle, et al (1976)
SFS emission rates
SFS emission factors
SF6 receptor locations
SF6 ambient concentrations
Wind direction
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Wind speed
Temperature (measured 30 m upwind of road, at a height of 4.5 m)
Ambient pressure
3.3 New York State Long Island Expressway - CO (1977)
A total of 303 hours of data were archived from an at-grade site along the
Long Island Expressway in New York State. The NYS77 study was conducted
during April and May, 1977. Figure 3-3 shows the site arrangement for this
study. Carbon monoxide concentrations from three ground-level (2 meter
height), non-median monitor locations were included in the archive. Wind
speed and wind direction recorded at a height of 2 meters on a tower located
37 meters north of the road edge were archived to represent ambient
plume-level transport conditions. Ambient temperature, measured at a height
of 4 meters, 21.5 south of the road edge, was also archived.
As described in Rao, et al (1978), the Long Island Expressway site is
situated in a relatively flat and open area, surrounded by sod farms. A small
grove of trees is located 200 meters to the south. The nearest major roads
are located approximately 0.5 and 1.5 km to the west of the site.
Data from the NYS77 Long Island Expressway CO field study were gathered
from several sources. Sources of all parameters archived are given below:
1. Martinez, et al (1982)
Traffic volumes and speeds (averages based on time of day and
day of week)
Traffic hot/cold start mode percentages
- 0% hot and 0% cold mode.
Vehicle type distribution (81% light duty vehicles, 9% light
duty trucks, 6.5% heavy duty gas trucks, and 3.5% heavy duty
diesel trucks)
Wind speed (from TRB computer tape)
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LEGEND
D CO PROBE
X TEMPERATURE
O ANEMOMETER
NOT TO SCALE
4m
2m-
s.
I
16 -
|-13.5H-20. 0-|-13. 5-|l.5|-20.0-|
DISTANCE (m)
O
X
Figure 3-3. Monitoring configuration for the New York CO data base
(NYS77-CO).
-19-
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Wind direction (from TRB computer tape)
Temperature (from TRB computer tape)
- measured at 4 m height, 21.5 m south of road edge
Stability (from TRB computer tape)
- Turner stability using data from Islip Airport NWS station
CO concentration (from TRB computer tape)
2. Rao, et al (1979)
Road angle (90° east of north)
Number of lanes (3 in each travel direction; modeled as two
links)
Road geometry
Source length (1500 m)
Anemometer location (37 m north of road edge at a height of 2 m)
CO receptor coordinates
Supplemental wind speed, wind direction, temperature,
stability, and CO concentration for hours not included on the
TRB tape
3. Rao, et al (1978)
Site description (used to determine surface roughness of 10 cm)
4. Calculated using the MOBILES Emissions Model (EPA, 1984)
CO Emission factors
Determined using available inputs from above and the
following MOBILES options:
- MOBILES tampering rates
- Identical speed for all vehicle types, varying by hour
- User supplied single VMT mix (from TRB report)
- MOBILES default registration and mileage distributions
- MOBILES default exhaust emission rates
- No I/M program
- No special correction factors
No anti-tampering program
- Low altitude emission factors
- 1977 calendar year
- Speeds, temperatures, and hot/cold mode percentages as
given in TRB report
MOBILES emission factors (grams/mile) were generated for each
combination of speed (5 to 55 mph) and ambient temperature (20
to 95°F). They were then matched with the average traffic
speed (to the nearest mph) for each direction of flow (by hour
and day of week) and ambient temperature (rounded to the
nearest 5°F) for each hour during which data were collected.
CO Emission rates
Emission rates were obtained by multiplying the traffic volume
(for each direction of flow) by the MOBILES emission factor
(described above) for each hour of data collection. Emission
rate units are grams/meter/second.
-20-
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3.4 New York State Long Island Expressway - SF6(1976)
The NYS77 CO program was preceded by NYS76, a series of SF6 tracer
experiments in October and November 1976. From these experiments, a total of
21 hours of complete data were available. SFS concentrations from eight
ground level (2 meter) non-median monitor locations were included in the
archive. These locations are shown in Figure 3-4.
Data from the 1976 tracer study were gathered from two references as given
below:
1. Rao, et al (1979)
Road angle (90° east of north)
Number of lanes (3 in each travel direction; modeled as two
links)
Road geometry
Source length (1160 m)
Anemometer location (center of median at 8 m height)
Wind speed
Wind direction
Turner stability
Local stability (used in model runs)
SF6 emission rates (determined by dividing hourly emissions
(g) by source length (1160 m) and then by time length of run
(3600 sec))
SF6 ambient concentrations
SF6 receptor coordinates
2. Rao, et al (1978)
Site description (used to determine surface roughness of 10 cm)
3.5 SRI Highway 101 (1975)
The archived SRI75 data set is made up of 45 hours of data collected on
six days in January and February, 1975 at an at-grade site (see Figure 3-5)
along Highway 101 in Santa Clara, California. Carbon monoxide concentrations
at 22 non-median receptor locations (18 at a height of one meter and 4 at a
height of three meters) were archived. Ambient wind speed and wind direction,
measured at a height of 3.8 meters on towers located 30.5 meters upwind of the
-21-
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LEGEND
O ANEMOMETER
D SF PROBE
NOT TO SCALE
8m
2m
O
20.
. 5-(20. 0-|-13. 5^. 5J-20. 0-1-16. 0-| 18.0
DISTANCE (m)
2 |3|
O
Figure 3-4. Monitoring configuration for the New York SFfi data base
(NYS76-SFg).
-22-
-------
LEGEND
D CO PROBE
X TEMPERATURE
O ANEMOMETER
NOT TO SCALE
TOWER
7-5- Ch
3.8- O
3.0-
i.o-
^**^ \
H]D r
HiE f-
~\ii\
-$7\
/
19.8 [-10.7-]-
36.6-
.L-iQ.7-1 19.8 '
DISTANCE (m)
TOWER
4 3 2 1
TOWER
-110m-
.110m.
Figure 3-5.
Monitoring configuration for the SRI CO data base (SRI75-CO).
CO probes shown in the lower diagram are at a height of 1 meter.
-23-
-------
road edge, were included in the archive to provide the best available ambient
representation of transport at plume height. Stability category was
determined using on-site radiation measurements, along with the wind speed at
a height of 7.5 meters, 30.5 meters upwind of the road edge.
As described in Dabberdt, et al (1981) The Highway 101 site is surrounded
by flat, low-cut grass fields, with two 7 meter high earth mounds 350 meters
to the east. The nearest major roadways are located 500 meters to the west
and east of the site.
Data from the SRI75 Highway 101 study were gathered from several sources.
Sources of all parameters archived or used in archiving are given below:
1. Wolf, et al (1981)
Road angle (110.6° east of north)
Number of lanes (3 in each travel direction)
Road geometry
Anemometer location (measured at 3.8 m height, either 30.5 m
north or south of road edge, depending on upwind direction)
CO receptor coordinates
Wind speed (from associated FHWA computer tape)
Wind direction (from associated FHWA computer tape)
Temperature (from associated FHWA computer tape)
- measured at a height of 3.8 m, either 30 m north or south of
road edge, depending on upwind direction
CO concentration (from associated FHWA computer tape)
Sigma theta (from associated FHWA computer tape)
- measured at same location as wind speed and direction
Solar radiation (from associated FHWA computer tape)
Traffic volume (from associated FHWA computer tape)
- total volume per lane per hour
Traffic speed (from associated FHWA computer tape)
- speed per lane per hour
2. Benson (1979)
Traffic hot/cold mode percentages {20% cold start mode, 27% hot
start mode)
Vehicle type distribution (81.5% light duty vehicles, 12.1%
light duty trucks, 1.3% medium duty trucks, 4.5% heavy duty gas
trucks, 0.5% heavy duty diesel trucks, and 0.1% motorcycles)
Surface roughness (10 cm)
Source length (6000 m)
3. Calculated using the method described by Ludwig and Dabberdt (1976)
-24-
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Stability (using solar radiation, 7.5 m height wind speed from
FHWA tape, and calculated sun angle)
4. Calculated using the MOBILE2 Emissions Model (EPA, 1981)
CO Emission Factors
MOBILE3 could not be used because it does not have an option for
California emission factors. The following MOBILE2 input options
were used:
- Identical speed for all vehicle types, varying by hour
- User supplied single VMT mix (from CALINE3 User's Guide)
- MOBILE2 default registration and mileage distribution
- MOBILE2 default exhaust emission rates
- No I/M program
- California emission factors
- 1975 calendar year
- Speeds, temperatures, and hot/cold mode percentages as given by
the FHWA tape and CALINE3 User's Guide
MOBILE2 emission factors (grams/mile) were generated for each
combination of speed (5 to 55 mph) and ambient temperature (20 to
95°F). They were then matched with the traffic speed (to the nearest
mph) for each lane and ambient temperature (rounded to the nearest 5°F)
for each hour during which data were collected.
CO Emission Rates
Emission rates were obtained by multiplying the traffic volume (for
each lane) by the MOBILE2 emission factor (described above) for each
hour of data collection. Emission rate units are grams/meter/second.
-25-
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4.0 STATISTICS APPROACH
The 1980 AMS Woods Hole Workshop on model performance evaluation (Fox,
1981) recommended a comprehensive list of performance measures and statistics
for evaluating air quality models. The workshop recommended that performance
evaluations be based on comparisons of the full set of observed-predicted data
pairs, of the highest observed and predicted concentrations per event (e.g., 1
or 8 hour time period), and of the highest "N" values (unpaired in time or
space). In addition, comparisons of observed and predicted concentrations for
data subsets representing individual monitoring stations or selected
meteorological conditions were recommended.
The statistical analyses performed for the mobile source model category
are based upon the recommendations of the 1980 AMS Workshop, together with
insights gained through evaluations of rural (Londergan, et al, 1982), urban
(Londergan, et al, 1983), and complex terrain (Wackter and Londergan, 1984)
model categories. The intent of the statistical analysis is to provide a
thorough assessment of model performance, avoiding redundant or uninformative
calculations.
4.1 Pre-Analysis Data Handling Procedures
A number of issues concerning analysis procedures can be addressed on a
generic basis, without regard for the differences among the selected data
sets. These issues include the selection of monitors; estimation of
background concentrations; averaging times; use of a concentration threshold;
and choice of meteorological subsets. Additional analysis issues must also be
discussed for the cut-section data set.
Monitor Selection. For regulatory applications, ambient concentrations at
ground level (or "breathing height") are the primary concern. Likewise,
-27-
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monitors located in the median of limit-access highways are not of concern for
the current evaluation. For the present study, analysis was restricted to
near-ground monitors, and excluded monitors in the median of a divided highway.
The SRI - at grade monitoring program utilized an array of 22 monitors
which were symmetrically located on both sides of the highway. Because the
models simulate transport and dispersion identically on both sides of the
roadway, the 11 sets of "twin" stations on opposite sides of the roadway were
treated as single stations for the "by station" subsets. This enabled a
reduction in the volume of statistics generated without any loss of
information, as well as an increase in the population sample size for those
statistics which were generated.
Background Concentrations. Each of the measurement programs included
monitors on both sides of the roadway. Background CO concentrations were
assumed to be evenly distributed over the study area and were estimated by the
lowest measured concentration in the network each hour. Observed
concentration values were calculated as the measured minus the background
concentration. A background level of zero ppb was assumed for the SF6 data
sets.
Averaging Times. National ambient air quality standards for carbon
monoxide exist for 1-hour and 8-hour averaging times. The basic prediction
unit for the models under consideration is one hour. The selected data sets,
except GM75, provide one-hour measurements of ambient concentrations, traffic,
-28-
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and meteorological variables. The GM75 data set is made up of half-hour
measurements. Statistical analyses were performed for half-hour (GM75 data
set only), 1-hour (all other data sets) and 8-hour averaging periods (CAL74
and NYS77-CO data sets only). A minimum of 6 hours of data were required to
estimate the 8-hour averages. Background values for the 8-hour data sets were
determined by calculating the average of the 8 individual hourly background
values.
Threshold. Near-zero observed and predicted concentration values are not
of great interest for testing model performance. For the mobile source data
sets, monitors located upwind of the roadway generally show negligible impact
from roadway emissions. To eliminate these data points from the statistical
analyses, a screening threshold of 0.5 ppm for CO, after background removal,
was used for the one-hour averaging period. This value represents a
characteristic measurement uncertainty as determined for an experimental
program in Texas (Bullin, et al, 1978). When both the observed and predicted
CO concentrations at a monitor were below this threshold for a given hour,
that data pair was eliminated from the data set. No threshold screening was
performed for 8-hour CO averages or for SF6 concentrations.
Meteorological Subsets. The key meteorological variables for estimating
pollutant concentrations within 25 m of a highway are wind speed and wind
angle (wind direction, relative to the highway direction). As the distance
from the roadway increases, atmospheric stability becomes increasingly
important. Meteorological subsets selected for statistical analysis are
summarized below:
Wind Speed (u): u < 2 m/s
2 < u < 4 m/s
u > 4 m/s
-29-
-------
Wind Angle (0): G < 20° (near parallel)
20° < 0 < 60° (oblique)
0 > 60° (near perpendicular)
Stability: unstable (Class A, B, C)
neutral (Class D)
stable (Class E, F, G)
Cut-Section Data Set (CAL74). Review of model provisions in HIWAY-2
suggests that predictions are only meaningful for receptor locations outside
of the cut-section. GMLINE and PAL V7ere not developed to treat cut-sections,
although PAL does allow the user to vary initial mixing on input. CALINE3 is
the only model which allows receptors to be located within the cut.
Conseguently, only the six ground-level monitors outside of the cut were used
to test model performance for the CAL74 Santa Monica data set. The CO
measurements were not taken simultaneously at all of the monitoring stations
for all measurement periods. To use any hour for statistical analysis, CO
concentrations at both upwind (to estimate background) and downwind locations
outside of the cut must have been available.
4.2 Statistical Performance Measures
The AMS workshop report recommended two somewhat different lists of
performance measures for comparing model predictions with observed air
guality, one appropriate for data sets representing pairs of observed and
predicted values, the other appropriate for unpaired data sets. Paired data
sets provide a means for assessing how well a model predicts on an event-by-
event basis, while unpaired sets do not. Table 4-1 summarizes the basic list
of performance measures, and the statistical methods recommended for
establishing confidence limits on each measure.
For data sets paired in time, statistical analyses based on residuals
(i.e., the differences between each pair of observed and predicted values) are
-30-
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TABLE 4-1
STATISTICAL ESTIMATORS AND BASIS FOR CONFIDENCE
LIMITS ON PERFORMANCE MEASURES
Performance
Measure
Bias
Woise/Scatter
Correlation
Basis for Confidence Interval
Estimator
Average
Median
Variance
Gross
variability
Average
absolute
residual
Pearson
correlation
coefficient
Paired Comparison
One sample "t," with
adjustment for serial
correlation
Wilcoxon match pair
Chi-squared test on
variance of residuals
None
None
Fisher "z"
Unpaired Comparison
Two sample "t"
Mann-Whitney
F test on variance
ratio
Not applicable
Not applicable
Not applicable
Frequency
distribution
comparison
Maximum
difference
between two
cumulative
distribution
functions
Not Applicable
Kolmogorov-Smi rnov
(K-S) test on f (obs.)
vs. f (pred.)
-31-
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appropriate for measuring model performance. If the time pairing for these
data sets is ignored, however, it is also possible to assess model performance
(in aggregate) by comparing the features of the composite set of all observed
values to those of the predicted values. Consequently, both paired and
unpaired comparisons were recommended by the AMS workshop for these data
sets. Data sets representing comparisons of the highest values, regardless of
time or space, provide no basis for paired analysis. For these sets only
unpaired comparisons were performed.
For paired comparisons, as noted above, the performance measures are based
on an analysis of residuals. Model bias is indicated by the average and/or
the median residual, with a value of zero representing no bias. The
characteristic magnitude of the residuals is an indicator of the scatter
between observed and predicted values on an event-by-event basis. Three
measures of noise or scatter were computed:
Variance 1 > (d, - d)2
N-l Z<
Gross variability
N
Average absolute residual 1 \ |dj
N * 1
where di is the residual (observed minus predicted) for data pair i, d is
the average residual, and N is the number of data pairs. The correlation of
paired observed and predicted values is measured by the Pearson correlation
coefficient.
For unpaired comparisons, the list of performance measures is somewhat
shorter. Model bias is indicated by the difference between the average (or
-32-
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median) observed value and the average (median) predicted value. A ratio of
the variances of the observed and predicted values is provided to indicate
whether the distribution of values in the two data sets is comparable.
Similarly, the frequency distribution of observed values is compared with that
for predicted values.
Standard statistical methods were used to estimate confidence limits for
each of the performance measures. Discussion of the statistical procedures
may be found in most statistics textbooks. For parametric procedures, the
reader is referred to Snedecor and Cochran (1967), while for nonparametric
procedures Hollander and Wolfe (1973) provide an appropriate description.
For paired comparisons, the confidence interval on the average residual
was estimated using the one-sample t test. This parametric test incorporates
the assumption that the residuals follow a normal distribution, but for large
M departures from normality are not critical. Serial correlation can affect
results, since the number of "independent events" could be overestimated and
the calculated variance could understate the magnitude of the actual random
error component. However, for the mobile data sets, this effect should be
minimized since much of the data is not continuous in time.
An analogous nonparametric indicator of model bias is the median
residual. The statistical method for estimating a confidence interval on the
median residual is provided by the Wilcoxon matched-pairs test. Wo
straightforward method of adjusting the confidence intervals from the Wilcoxon
test for serial correlation has been identified.
-33-
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A confidence interval for the variance of the residuals was calculated
using a chi-sguared test. No adjustment was made for serial correlation. No
standard method is available for estimating confidence intervals for the gross
variability or average absolute deviation measures. For the Pearson
correlation coefficient, the Fisher z test provided a method of estimating the
confidence interval.
Comparison of two cumulative distribution functions was accomplished using
the Kolmogorov-Smirnov (K-S) test. For this test, the two distribution
functions are compared across the full range of concentration (or residual)
values, and the maximum frequency difference between the two functions is
identified.
For unpaired comparisons, two bias measures were computed. The average of
the observed values was compared with the average of the predicted values.
The confidence interval on the difference of the averages was estimated with a
two-sample t test. The median difference was also computed, and the
confidence interval was estimated using the Mann-Whitney nonparametric test.
The variance of observed values was compared with the variance of
predicted values for unpaired data sets. The performance measure is the ratio
of the variances; the F test provides confidence limits on the ratio. The
frequency distribution comparison for unpaired data sets provided a measure of
the difference between the observed and predicted distribution functions. The
K-S test was again used to assess the statistical significance of the maximum
frequency difference.
4.3 Data Sets For Statistical Analysis
Twenty basic data sets were compiled as a product of the data from the
five field programs run through each of the four mobile models. Each of these
basic data sets were screened and processed for missing data, threshold,
-34-
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background and averaging times as described above and then sorted into subsets
by station and meteorological conditions. Various unpaired and paired data
groups were then developed for subsequent statistical analysis.
The statistical measures generated for the mobile source model evaluation
are very similar to those utilized for the urban and complex terrain model
evaluations, except for some of the selected data sets the amount of available
experimental data limited the extent of the analyses. Statistical measures
are discussed separately for the unpaired (N highest values) and paired data
sets.
Unpaired (M Highest Values). The array of statistical analyses performed
for the N highest observed and predicted values, regardless of time or
location, are summarized in Table 4-2. The principal change from earlier
model categories concerns the choice of N, the number of peak values
analyzed. Previously, this number had been fixed at 25. In light of the
small number of measurement hours available for three of the data sets, the
number of peak values analyzed in this study was reduced to 25 percent of the
available hours or 25 hours, whichever was less. (Otherwise, the data set
would not accurately reflect the "top end" of the frequency distribution. ) To
reduce spatial correlation, not more than one observed and predicted value
from any hour was chosen. This prevented the high-N analysis from being
unduly influenced by one or two hours of overall high concentrations. The
confidence intervals for these data sets are based upon a two-sample t-test.
These confidence intervals should be viewed with caution, since the N highest
values are selected based on their rank within the distribution. The data
set, therefore, does not represent a random sample of N independent values.
As noted previously, data from "twin" stations from the SRI data set were
combined for the subset analysis by station. Meteorological subsets for the
one-hour data were also defined in an earlier discussion.
-35-
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Analysis of the "highest N" 8-hour average values was only undertaken for
the CAL74 cut-section and NYS77 CO data sets. For the New York data set,
fewer than 100 8-hour periods were available, so the selected N value was 25
percent of the available number, rather than 25. Statistics for
meteorological subsets were not computed for the 8-hour data sets.
Paired in Time and/or Location
Statistical analyses undertaken for paired data sets are summarized in
Table 4-3. The first two columns represent subsets of the full basic data
set. For column one, the highest observed and predicted values are selected
for each time period (paired in time but not necessarily in space), and then
analyzed statistically as a group. Similarly the highest observed and
predicted values at each station for the period of record (data paired by
station but not necessarily in time) are grouped for statistical analysis in
column two. The full basic data set is represented in column three by the
group of all observed and predicted values paired for each time period at each
station. Fully paired comparisions are also made for observed and predicted
concentrations at each station (column four) and for each meteorological data
subset (column five).
-37-
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TABLE 4-3
ARRAY OF PERFORMANCE MEASURES AND STATISTICS CALCULATED
FOR THE MOBILE DATA SETS PAIRED IN TIME OR LOCATION
Highest Highest All Data All Events Meteorological
per event per station paired in at each Subsets of
paired in paired by time and station events paired
time location location paired in in time
time and location
Number of events
Averaged observed
Average Predicted
Difference of Averages
Average difference
Fraction Co > Cp
Characteristics
Discrepancies
ad
RMSE
AAD
X
X
X
X (C.I.)*
X (C.I.)
X
X (C.I.)
X
X
X
X
X
-
X (C.I.)
X
X (C.I.)
X
X
X
X
X
X (C.I.)
X (C.I.)
X
X (C.I.)
X
X
X
X
X
X (C.I.)
X (C.I.)
X
X (C.I.)
X
X
X
X
X
X
X
X
X
X
X
(C.I.)
(C.I.)
(C.I.)
Correlation coefficient
Pearson R
Variance comparison
Maximum frequency
difference
X (C.I.)
X (C.I.)
X (C.I.)
X (C.I.)
-
-
X (C.I.)
X(C.I.)
X(C.I. )
X (C.I.)
X (C.I.)
X (C.I.)
X
X
X
(C.I.)
(C.I.)
(C.I.)
* C.I. = 95% confidence interval
-38-
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5.0 MODEL PERFORMANCE RESULTS
Statistics comparing observed and predicted concentrations were generated
for each combination of the four mobile source models and five data bases
using the approach described in Section 4.0. Statistics were produced for the
"N" highest observed and predicted values, highest concentrations by event,
highest concentrations by station, and all observed and predicted
concentrations paired in space and time. A summary of results for each of
these data groupings is presented in this section. Complete tables of
statistics, including breakdowns by station and meteorological subset, are
presented in Appendices A through D.
5.1 Statistics for "N" Highest Values
One-Hour
Summary statistics for the "N" highest observed and "N" highest predicted
1-hour average CO and SFs concentrations are presented in Table 5-1 for each
model and data base. Because some of the data bases are fairly small, the
value of "N" for each data set was determined by selecting either the highest
25 percent or highest 25 concentration values, whichever was less. Caution
should be exercised when interpreting the meaning of statistics generated
using the smaller data sets.
The number of events used to calculate statistics for each model and data
base is given in the first column of Table 5-1. Averages of the "N" highest
observed and predicted values for each data set are listed in columns two and
three, respectively. The first performance measure, presented in column four,
is the difference between the two averages. A positive value implies model
underprediction. In parentheses adjacent to the calculated differences are 95
percent confidence intervals, determined by using the two-sample Student's t
test. Confidence limits which contain zero imply that there is no significant
-39-
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-40-
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difference between modeled and observed concentrations at the 95 percent
confidence level.
Results for the "difference of averages" comparison, as displayed
graphically in Figure 5-1, show differences both between models and between
data bases. The best model performance occurs with the two tracer data bases,
GM75 and NYS76. Little bias is observed for these two data bases except with
the PAL and HIWAY-2 models which show significant overpredictions for GM75 and
NYS76, respectively. The least bias and smallest confidence bounds are
exhibited by GMLINE. In general, much poorer model performance is exhibited
for the three CO data bases. GMLINE performed best for both at-grade data
sets (NYS77 and SRI75) while PAL performed worst. The cut-section data base
(CAL74) appears to be an exception, with large underpredictions by three of
the models and unbiased performance by PAL.
The second performance measure shown in Table 5-1 is the difference of
medians between ranked pairings of the "N" highest observed and predicted
concentrations. It should be noted that the 95 percent confidence interval is
determined with the nonparametric Mann-Whitney test for the median
difference. Results for the difference of medians are very similar to those
for the difference of averages.
The last performance measure shown in Table 5-1 is the variance
comparison. This statistic was obtained by dividing the variance of the "N"
highest observed values by the variance of the "N" highest predicted
concentrations. A quotient of 1 indicates equal scatter of observed and
predicted concentrations. The F test was used to calculate the 95 percent
confidence levels. Results of the variance comparison for the at-grade data
sets vary. Of the at-grade data sets, the most notable observation is that
the models tend to predict with much more variability than the observed data
(values less than 1). The GMLINE model performed relatively better than the
-41-
-------
1-HOUR AVERAGE
8-HOUR AVERAGE
10
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Figure 5-1. Difference of averages of highest "N" observed and predicted
one hour concentrations.
-42-
-------
other models while PAL performed poorest; however the 95 percent confidence
intervals on this measure are fairly large. For the cut-section data set
(CAL74), only CALINE3 predicted with a variance comparable to the observed
variance, while GMLINE and HIWAY-2 predicted with much less variability than
observed.
Eight-Hour
Summary statistics for the "N" highest observed and predicted 8-hour
average CO concentrations are presented in Table 5-2 and Figure 5-1 for the
two largest data bases (NYS77 and CAL74). In general, the 8-hour model
results show the same tendencies as the 1-hour results. For the at-grade data
set (NYS77), only the GMLINE model produces results which are not
significantly different from observed concentrations for any performance
measure listed. The other models all overpredict by a significant margin and
produce much more scatter than observed.
For the cut-section data base (CAL74), all of the models underpredict
significantly at the 95 percent level of confidence, as indicated by both the
difference of averages and difference of medians. Only HIWAY2 produces a
variance similar to the observed variance. The GMLINE model displays less
scatter than observed while both CALINE3 and PAL produce more scatter than
observed.
5.2 Statistics for Highest Concentration by Event
A second statistical grouping compares the highest observed and predicted
concentrations over the monitoring network for each sampling period, paired in
time (i.e., one pair of values for each sampling period). Statistics were
generated for both 1-hour and 8-hour sampling periods.
-43-
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One-Hour
A summary of high by event results for the 1-hour averaging period is
given in Table 5-3. This table is divided into two parts which present
results for paired (part one) and unpaired (part two) performance
comparisons. The number of events, average observed value, and average
difference are listed in the first three columns of the paired part of the
table. The average differences are also shown graphically in Figure 5-2. In
general, all models perform better using the SF6 tracer data than they do
using the CO data, indicating problems either with quantifying CO emissions or
background concentrations. There is no clear tendency for one model to
perform better than another, although the PAL model overpredicted
significantly for the at-grade CO data sets. All four models significantly
underpredicted for the cut-section data set.
A second measure of bias, the fraction of events with the highest observed
concentration greater than the highest predicted concentration, is presented
in column four of Table 5-3. The residual is defined as an observed minus
predicted value. Both GMLINE and CALINE3 underpredict the highest
concentrations per event at least half of the time for all of the at-grade
data bases, while both PAL and HIWAY2 overpredict the highest concentrations
per event at least half of the time for all the at-grade data bases except
GM75. Each of the four models underpredict the highest concentrations for
virtually all events of the cut-section (CAL74) data base.
The next three columns in Table 5-3 present performance measures
estimating scatter, and are titled characteristic discrepancies. They include
the standard deviation of residuals (noise) with 95 percent confidence limits
calculated from a Chi-Square test, the root mean square error, and the average
absolute difference. Results for the at-grade data bases show that GMLINE
nearly always has the smallest values (best performance) in all three
-45-
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-------
GM75
Co = 2.5
(PPB)
N= 62
NYS76
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LEGEND
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OF AVERAGES
Co =
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CONFIDENCE. C
BOUNDS P
H
Average Observed
Concentration
Number of Events
GMLINE
CALINE3
PAL
HIWAY2
Figure 5-2. Average difference of highest observed and predicted one
hour concentrations (event by event).
-48-
-------
categories. In general, the PAL model performs worst for this measure. For
the cut-section data base, PAL produces the largest standard deviations, with
little difference between the models for the other measures of scatter.
The last column of the first part of Table 5-3 lists the Pearson
correlation of observed and predicted concentration pairs for the highest by
event data sets. Results show that GMLINE generally produces the highest
correlation coefficients for the at-grade data sets, ranging from .53 to .91;
while PAL produces the lowest correlations from .16 to .77. HIWAY-2 and
GMLINE produce similar correlations for the tracer data sets. All the models
exhibit poor correlation (.25 or less) for the cut-section data base.
The second page of Table 5-3 (Part 2) summarizes unpaired performance
measures for the highest per event one-hour concentration values. The first
two columns of Part 2 repeat the number of events and average observed value
for each data set. The ratio of observed to predicted variances, along with
95 percent confidence bounds determined by an F test, are presented in column
three. Variance ratios close to 1.0 indicate good model performance. Results
show the GMLINE model performs best using this performance statistic for each
of the at-grade data sets. For the cut-section data set (CAL74), predicted
variances are small relative to observed, except for PAL which continues to
predict with a larger variance than observed.
A comparison of observed and predicted frequency distributions is provided
in the last column of Table 5-3. The value listed for each data set and model
represents the largest fractional difference between the observed and
predicted distribution functions when compared at the same concentration
value. For this measure, positive fractional difference implies model
overprediction. The value given in parentheses is the maximum absolute
difference which is significantly different from zero, at a 95 percent
confidence level, as given by the Kolmogorov-Smirnov (K-S) test. Results for
the two at-grade tracer data sets show all models underpredicting the highest
-49-
-------
concentrations by event, with none of the distributions significantly
different from observed for the NYS76 data set. For the two at-grade CO data
sets, the models generally overpredict, with no distributions significantly
different from observed for the SRI75 data set. The frequency distribution
comparison for the cut-section data base shows virtually no overlap between
distributions of the high by event data sets for any of the models.
Eight-Hour
A summary of high by event results for the eight-hour averaging period is
given in the top half of Table 5-4. The comparison of "all concentrations" is
discussed in the next section. This table is also divided into two parts
which present results for paired (part 1) and unpaired (part 2) performance
comparisons. Statistics were only generated for the two largest data bases.
Paired results for the at-grade data set (NYS77) show that GMLINE
outperforms the other models for each of the measures. GMLINE is the only
model which does not predict highest concentrations by event that are
significantly different from observed. It also produces the lowest values for
all three measures of characteristic discrepancies and the highest correlation
coefficient. All models perform poorly for the cut-section data base (CAL74),
substantially underpredicting concentrations and producing extremely small
correlation coefficients.
Similar results were obtained for the unpaired analysis of high by event
eight-hour concentrations (Part 2 of Table 5-4). GMLINE performs best for the
at-grade data base, producing the most favorable values for both the variance
comparison and the frequency distribution comparison. For these measures all
models perform poorly with the cut-section data base.
-50-
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5.3 Statistics for All Concentrations Paired in Time and Space
One-Hour
The largest data sets considered in this evaluation represent all
concentration values paired in time and location. One-hour statistics are
summarized in Table 5-5 for both paired (part one) and unpaired (part two)
performance comparisons. Statistics are presented in the same columns
described for the high by event analysis. Figure 5-3 presents graphically the
average difference of all observed and predicted one-hour concentrations.
Results for the one-hour analysis of all paired at-grade data differed for
the SF6 and CO data sets. HIWAY2 outperformed the other models using the
tracer data bases, producing the lowest values of bias and characteristic
discrepancies and the highest correlation coefficients. GMLINE performed
better overall for the two CO at-grade sets, although CALINE3 performed
comparably with the SRI75 data. Once again, all models underpredicted
significantly and with little correlation for the cut-section data base
(CAL74).
The unpaired comparisons are shown in Part 2 of Table 5-5 for the one-hour
analysis of all data paired in time and space. For the variance comparison,
GMLINE predicted with essentially the same amount of scatter as was observed
for three of the at-grade data sets, while PAL consistently predicted with
less scatter than was observed. The observed and predicted cumulative
distribution functions are significantly different (at the 95% confidence
level) for all models and data sets except PAL with GM75 and CALINE3 with
NYS76.
Results for the cut-section data base were generally poor for all models.
PAL did produce the lowest variance comparison, but its predicted variance was
significantly less than observed.
-53-
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Figure 5-3. Average difference of all observed and predicted one hour
concentrations (paired in time and space).
-56-
-------
Eight-Hour
Summary statistics for the "all paired" analysis of eight-hour data are
given in the bottom half of Table 5-4 (part 1). Results for the at-grade data
set (NYS77) show that GMLINE produced the lowest bias and scatter and the
highest correlation of observed to predicted values. CALINE3 and HIWAY-2
perform comparably, while PAL produced the largest bias and scatter and lowest
correlation. All models perform equally for the cut-section data set (CAL74),
except the correlation by PAL is somewhat lower.
As shown in Part 2 of Table 5-4, the variance comparison for the "all
concentration" data sets indicates opposite performance between the at-grade
and cut-section data bases. The ratio of variances were significantly
different from unity at a 95% confidence level for all models and both data
sets (except GMLINE for NYS77). Also for NYS77, all models except PAL
produced frequency distributions which were similar to the observed at a 95%
level of confidence. The cut-section data base resulted in significantly less
predicted scatter than observed for all models, but to a lesser degree for PAL.
5.4 Statistics for Highest Concentration at Each Station
One-Hour
Performance statistics are presented in Table 5-6 for the comparison of
highest and second highest onehour concentrations observed and predicted at
each station over the duration of each of the five monitoring programs.
Because of the small number of events (i.e., number of monitoring stations)
for most of the data bases, caution should be exercised when interpreting the
statistics.
The statistics provided in this table compare observed and predicted
one-hour values for the number of data pairs shown in the first column. This
number ranges from 3 for the NYS77-CO study to 22 for the SRI75-CO program.
-57-
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The next two columns present the average of the observed concentrations and
the average difference between observed and predicted values. Results show
that GMLINE produces the smallest bias of highest concentrations by station
for each at-grade data set. The model also produces the smallest bias of
second highest concentractions by station for three of the four at-grade data
bases. PAL overpredicts by an extreme margin for the NYS77 data base. For
the cut-section data set 3 of the 4 models underpredict, while PAL
overpredicts.
GMLINE performs with the lowest noise (or standard deviations of the
residuals) for the at-grade high by station concentrations. GMLINE also
produces the lowest noise for three of the four at-grade data sets when second
highest concentrations are compared. The largest values of noise are found
with the PAL model for NYS77 and CAL74.
As can be seen from the results presented here, the high by station
statistics are very unstable, with large differences between the high and
second high data sets.
Eight-Hour
Results of the eight-hour high and second high by station analyses are
presented in Table 5-7. All of the models overpredicted for NYS77, with
GMLINE showing the least bias and PAL the greatest. Underprediction was the
rule with CAL74 data, except for the PAL results for high by station which
overpredicted. The lowest values of noise are found for GMLINE with NYS77.
This statistic is unstable, however, as evidenced by PAL for CAL74, which
exhibits the largest noise for the high concentrations and the smallest noise
for the second high concentrations. Again, caution should be exercised when
analyzing the confidence intervals for these small data sets, since many of
the assumptions are not met.
-59-
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-60-
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5.5 Examples of Statistics by Subsets
While the model performance statistics presented earlier are informative
for comparing model performance for applications in regulatory settings, the
results do not provide much information as to why individual models are
performing good or badly. A better understanding of model performance can be
obtained by analyzing results for different subsets of the basic data base.
In this section examples of the subset results are presented for two of the
data bases, GM75 and NYS77. The General Motors data base was selected because
it probably contains the best quality data. Since it was a tracer (SF6)
study, there is no contamination of ambient air quality data by background or
other nearby sources. As shown in the previous results sections, the models
perform best for the GM data base. The 1977 New York State (Long Island
Expressway) CO data base was selected because it is typical of highway
modeling applications and it produced distinct differences between overall
model performances. The NYS77 data base also contains a large number of
events (over 300) for statistical analysis.
Results by subset are presented for "N" highest and paired in time and
space data sets only.
"N" Highest Observed and Predicted Values
In Table 5-8 the difference of averages are presented for the "N" highest
observed and predicted SF6 concentrations for the GM75 data base. In this
table the first column of data contains the average observed value for all
stations combined, by station and by subsets of meteorological conditions.
The difference of averages for GMLINE shows little bias for any of the
subsets. However, the largest underprediction (positive value) occurs near
the roadway at Station 3 (see Section 3 figures), and for higher wind speeds,
unstable conditions and near parallel wind/road angles. It should be noted
-61-
-------
TABLE 5-8
COMPARISON OF DIFFERENCE OF AVERAGES .FOR "N" HIGHEST
OBSERVED AND PREDICTED SF6 CONCENTRATION VALUES
(UNPAIRED IN TIME OR LOCATION) FOR VARIOUS SUBSETS
DATA BASE: GM75 AVERAGING TIME: HALF HOUR
Data Sets
("N" of Events)
Lesser of
25 or 25%
Average
Observed
Value (Co)
(PPB)
Difference of Averages (C0-CP)
Model
GMLINE CALINE3
PAL HIWAY2
1. All Stations/All
Events(16)
3.4
.1
-1.9 -1.9 -.1
2. By Station/All
Events
Station 1(16)
Station 2(16)
Station 3(16)
Station 4(16)
Station 5(16)
Station 6(16)
Station 7(16)
3. By Meteorology
A. Wind Speed
< 2.0 sec (7)
2.0 to 4.0 (9)
> 4.0 sec (0)
B. Stability Group
Class UNST (7)
Class NEUT (2)
Class STAB (7)
C. Wind/Road Angle
<20. Degrees (6)
20. to 60. (6)
>60. Degrees (5)
.9
2.8
3.1
1.9
1.2
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3.4
3.3
2.9
2.9
3.7
3.7
3.3
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-.7
-.8
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-1.2
-1.3
-1.4
-3.3
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-62-
-------
that the GM75 data base contains no averaging periods with wind speed greater
than 4.0 m/s and only eight periods of neutral stability (i.e., N = 2).
Therefore the statistics for some of the subsets are fairly unstable and the
results should be viewed with this in mind.
The CALINE3 and PAL models in general overpredict the "N" highest values
by a much greater extent than GMLINE underpredicts (or HIWAY-2 overpredicts).
These overpredictions by CALINE3 and PAL seem to occur under different
circumstances for the two models. The largest overpredictions by CALINE3
occur for light wind speeds, neutral stabilities and low wind/road angles,
while PAL overpredicts more for higher wind speeds, stable conditions and low
wind/road angles.
HIWAY-2 shows a small amount of negative bias (overprediction) overall,
with little distinction between the subsets by station or meteorology.
Table 5-9 shows similar results for the NYS77 data base. This data base
shows more distinct differences between the models than GM75. GMLINE
overpredicts to a lesser degree than the other three models. Only minor
difference exist between stations for all the models. The largest GMLINE
overpredictions are for light wind speeds, neutral stabilities and near
parallel wind/road angles, while underpredictions occur for higher wind
speeds. In fact, this same tendency is found for all four models, with the
largest overpredictions by PAL.
Observed and Predicted Values Paired in Space and Time
Table 5-10 presents model performance statistics (difference of averages)
for subsets of events paired in space and time for the GM75 data base. The
same subsets are shown in the previous section for "N" highest values. The
number of events is much larger for each of the paired subsets, while the
average observed and predicted values are somewhat lower since the full set of
-63-
-------
TABLE 5-9
COMPARISON OF DIFFERENCE OF AVERAGES FOR "N" HIGHEST
OBSERVED AND PREDICTED CO CONCENTRATION VALUES
(UNPAIRED IN TIME OR LOCATION) FOR VARIOUS SUBSETS
DATA BASE: NYS77-CO AVERAGING TIME: 1 HOUR
Data Sets
("N" of Events)
Lesser of
25 or 25%
Average
Observed
Value (Co)
(ppm)
Difference of Averages (C0-CP)
Model
GMLINE CALINE3 PAL HIWAY2
1. All Stations/All
Events(25)
4.7
-2.4 -12.5 -37.3 -8.7
2. By Station/All
Events
Station 1(25)
Station 2(25)
Station 3(25)
3. .By Meteorology
A. Wind Speed
< 2.0 sec (25)
2.0 to 4.0 ,(25)
> 4.0 sec (14)
B. Stability Group
Class UNST (11)
Class NEUT (25)
Class STAB (14)
C. Wind/Road Angle
<20. Degrees (15)
20. to 60. (25)
>60. Degrees (25)
2.2
4.2
3.9
3.9
3.8
3.8
3.6
4.6
2.0
4.0
3.8
3.8
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-64-
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values are included in this analysis. For the GMLINE model a slight
underprediction occurs for the all-paired data set, but the analysis by
station shows that underprediction at Stations 2 through 4 are primarily
responsible for this. Very little difference exists between meteorological
subsets for the GMLINE model. CALINE3 and PAL show nearly equivalent
overprediction as indicated by the all-paired in time and space data set.
CALINE3 shows more pronounced overprediction for light wind speed, neutral
stability and near parallel wind/road angles, while PAL's largest
overpredictions occur with both neutral and stable conditions and also for
near parallel wind/road angles. The HIWAY-2 model shows no significant bias
for any of the GM75 data sets shown.
Similar results for the NYS77 data base are displayed in Table 5-11.
There were only three monitoring stations for this data base, but the number
of events is somewhat larger than for GM75. All four models tend to
overpredict for each station and meteorological subset, except for the highest
wind speed (greater than 4 m/s). All four models underpredict for the higher
wind speeds. GMLINE also shows some slight underprediction for unstable
conditions.
Again, the tendency by all four models is to produce the largest
overpredictions for light wind speeds and near parallel wind/road angles.
Differences between the models, though, show GMLINE overpredicting the least
and PAL overpredicting the most.
-66-
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-------
6.0 SUMMARY AND CONCLUSIONS
A systematic evaluation of model performance has been carried out for
mobile source air quality models. The evaluation approach involves
comparisons of observed concentrations and model predictions. Statistical
measures recommended by the American Meteorological Society have been used to
assess model performance. As with the previous evaluation studies for other
model categories, the primary objective of the current project is to produce
performance statistics so that EPA and a group of reviewers may judge the
relative merits of different models.
No diagnostic analyses have been performed to better understand why
individual models perform the way they do. Statistics were generated though,
for subsets of events by station, wind speed, stability category, and
wind/roadway angles. The volume of information provided in the appendix
tables should provide a useful starting point for such diagnostic analysis.
Summary of Procedures
Data from five field studies were prepared for use in the evaluation of
four mobile source models. The data bases and models are listed below:
Models Data Bases
CALINE3 GM75 - General Motors (SFS)
GMLINE NYS76 - Long Island Expressway (SF6)
HIWAY-2 SRI75 - SRI Highway 101 (CO)
PAL NYS77 - Long Island Expressway (CO)
CAL74 - Santa Monica Freeway (CO)
A summary of the data bases, models, and statistics to be generated was
prepared as part of a test run package, which also included two-hour test runs
for each model with each data base. This test run package was submitted to
the respective model developers for review and comment. Responses to the
-69-
-------
comments were then made, the models were run for the full data bases and
statistics were generated.
Summary of Results
The results are presented in Section 5 and in the Appendix A through D
tables. The most distinct results are highlighted in the following statements:
Better model performance was found for the SF6 tracer data bases
than for the CO data sets.
The models exhibit distinct differences in performance within any
individual data set.
Bias for the 1-hour and 8-hour averages showed similarities for
each model.
All of the models underpredicted significantly for the cut-section
-------
7.0 REFERENCES
Bemis, G.R., P.E. Benson, A.J. Ranzieri and K.O. Pinkerman, 1977: Air
Pollution and Roadway Location, Design and Operation - Project Overview.
FHWA-RD-77-102.
Benson, P.E., 1979: CALINE3 - A Versatile Dispersion Model for Predicting
Air Pollutant Levels Near Highways and Arterial Streets.
FHWA/CA/TL-79/23, California Department of Transportation, Sacramento, CA.
Bullin, J.A., J.C. Polasek and N.J. Green, 1978: Analytical and Experimental
Assessment of Highway Impact on Air Quality. FHWA/TX-79/11-218-4, Federal
Highway Administration, Washington, D.C.
Cadle, S.H., D.P. Chock, J.M. Heuss, and P.R. Monson, 1976: Results of the
General Motors Sulfate Dispersion Experiment. G.M. Research Publ. No.
2107, General Motors Research Laboratories, Warren, MI.
Chock, D.P., 1977a: A Simple Line Source Model for Dispersion Near
Roadways. GMR-2407, General Motors Research Laboratories, Warren, MI.
(see also Atmospheric Environment, Vol. 12, pp. 823-829 (1978).)
Chock, D.P., 1977b: General Motors Sulfate Dispersion Experiment - An
Overview of the Wind, Temperature and Concentration Fields. Atmospheric
Environment, Vol. 11, pp 553-559.
Chock, D.P., 1977c: General Motors Sulfate Dispersion Experiment:
Assessment of the EPA HIWAY Model. J. Air Poll. Control Assoc., Vol. 27,
pp 39-45.
Computer Sciences Corporation, 1983: Modeling Evaluation Support System
(MESS) Data Management Subsystem (DMSS) User's Manual. Computer Sciences
Corporation, Durham, NC.
Dabberdt, W.F., E. Shelar, D. Marimont, and G. Skinner, 1981: Analyses,
Experimental Studies, and Evaluations of Control Measures for Air Flow and
Air Quality On and Near Highways, Vol. I: Experimental Studies, Analyses,
and Model Development. FHWA-RD-78-179, SRI International, Menlo Park, CA.
EPA, 1977: User's Manual for Single-Source (CRSTER) Model.
EPA-450/2-77-013, U.S. EPA, Research Triangle Park, NC.
EPA, 1981: User's Guide to MOBILE2 (Mobile Source Emissions Model).
EPA-406/3-81-006, U.S. EPA, Research Triangle Park, NC.
EPA, 1984: Draft User's Guide to MOBILES (Mobile Source Emissions Model).
EPA-406/3-84-002, U.S. EPA, Research Triangle Park, NC.
Fox, D.G., 1981: Judging Air Quality Model Performance (A Summary of the AMS
Workshop on Dispersion Model Performance, Woods Hole, MA, 8-11 September
1980). Bull. Am. Meteorol. Soc., 62, 599-609.
Hirtzel, C.S. and J.E. Quon, 1981: Estimating Precision of Autocorrelated
Air Quality Measurements. Summary of Proceedings Envirometrics 81,
200-201.
-71-
-------
Hollander, M. and R.A. Wolfe, 1973: Nonparametric Statistical Methods. John
Wiley and Sons, New York, NY.
Londergan, R.J., D.H., Minott, D.J. Wackter, T.M. Kincaid and D.M. Bonitata,
1982: Evaluation of Rural Air Quality Simulation Models. EPA-450/4-83-003,
OAQPS, Research Triange Park, NC.
Londergan, R.J., D.H. Minott, D.J. Wackter and R.R. Fizz, 1983: Evaluation of
Urban Air Quality Simulation Models. EPA-450/4-83-020, OAQPS, Research
Triangle Park, NC.
Ludwig, F.L., and W.F. Dabberdt, 1976: Comparison of Two Practical
Atmospheric Stability Classification Schemes in an Urban Application. J.
Applied Meteorology, 15, 1172-1176.
Martinez, J.R., H.S. Javitz, R.E. Ruff, A. Valdes, K.C. Nitz, and W.F.
Dabberdt, 1982: Development and Application of Methodology for Evaluating
Highway Air Pollution Dispersion Models. Prepared by SRI for the
Transportation Research Board of the National Research Council, National
Cooperative Highway Research Program Report 245, Washington, D.C. (SRI
Project 8363)
Petersen, W.B., 1978: User's Guide for PAL, A Gaussian Plume Algorithm for
Point, Area, and Line Sources. EPA-600/4-78-013, U.S. EPA, Research
Triangle Park, NC.
Petersen, W.B., 1980: User's Guide for HIWAY-2, A Highway Air Pollution
Model. EPA-600/8-80-018, U.S. EPA, Research Triangle Park, NC.
Rao, S.T., M. Chen, M. Keenan, G. Sistla, R. Peddada, G. Wotzak and N. Kolak,
1978: Dispersion of Pollutants Near Highways. Experimental Design and
Data Acquisition Procedures. EPA-600/4-78-037, U.S. EPA, Research
Triangle Park, NC.
Rao, S.T., M. Keenan, G. Sistla and P. Samson, 1979: "Dispersion of
Pollutants Near Highways. Data Analysis and Model Evaluation."
EPA-600/4-79-011. U.S. EPA, Research Triangle Park, NC.
Snedecor, G.W. and W.G. Cochran, 1967: Statistical Methods, 6th Edition.
Iowa State University Press, Ames, IA.
Wolf, D.E., E. Shelar, R.E. Ruff, and W.F. Dabberdt, 1981: Analyses,
Experimental Studies, and Evaluations of Control Measures for Air Flow and
Air Quality On and Near Highways; Volume III - User's Manual for FHWA Data
Base and Retrieval Programs. FHWA/RD-81/054, Federal Highway
Administration, Washington, D.C.
Wackter, D.J. and R.J. Londergan, 1984: Evaluation of Complex Terrain Air
Quality Models. EPA-450/4-84-017, OAQPS, Research Triangle Park, NC.
Zimmerman, J.R. and R.J. Thompson, 1975: User's Guide for HIWAY, a Highway
Air Pollution Model. EPA-650/4-74-008, U.S. EPA, Research Triangle Park,
NC.
-72-
-------
APPENDIX A
STATISTICS FOR HIGHEST "N" VALUES
-------
In the high N tables, model performance statistics are presented which
compare the highest "N" (lesser of 25 percent or the 25 highest) observed and
predicted concentration values, unpaired in time or location. Each table
contains the results for one model, one data base base and one averaging time
(1 or 8 hours). In each table, results are presented for the entire data set
(all stations/all events) and for subsets representing either a single
monitoring station or particular meteorological conditions. Subsets based on
meteorology were developed only for the 1-hour averaging time. In an effort
to mitigate statistical problems due to spatial correlation, selection rules
stipulated that only one value could be selected from a given event.
The first two columns of results in the Appendix A tables are simply the
average of the "N" highest observed values and the average of the "N" highest
predicted values for each data set. The first performance measure (third
column) is the difference between these averages. A positive value implies
model underprediction. In parentheses following the calculated value is the
95 percent confidence interval, determined by using the two-sample Student's t
test.
The second performance measure is the difference between the medians of
the observed and predicted values. The 95 percent confidence interval (in
parentheses) is determined using the nonparametric Mann-Whitney test.
The third performance measure is the variance comparison. The variance of
the highest observed values was divided by the variance of the predicted
values. The variance ratio is presented, together with the 95 percent
confidence interval (in parentheses), determined using an F test.
The final performance measure in Table A is the frequency distribution
comparison. The cumulative distribution function f(C) represents the fraction
of the data set (in this case, the fraction of the "N" highest data points)
with concentrations values less than or equal to C. The value presented in
A-l
-------
this column is the largest difference between the observed and predicted
distribution functions (for the same concentration values) obtained when the
two functions are compared for all concentration values.
A positive fractional difference implies model overprediction. At the
concentration value where the maximum difference occurs, the fraction of
observed values less than or equal to that concentration value is larger than
the fraction of predicted values. Conversely, the fraction of observed values
higher than that concentration value is smaller than the fraction of predicted
values.
The value given in parentheses is the maximum difference which is
significantly different from zero, at a 95 percent confidence level, as given
by the Kolmogorov-Smirnov (K-S) test. This confidence interval is a function
of the number of cases.
A-2
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TABLE A19
COMPARISON OF "N" HIGHEST OBSERVED AND PREDICTED
CO CONCENTRATION VALUES (UNPAIRED IN TIME OR LOCATION)
SES STATISTICS FOR MODEL/DATA BASE: PAL/CAL74 AVERAGING TIME: 1 HOUR
AVERAGE AVERAGE DIFFEREHCE DIFFERENCE VARIANCE FREQUENCY
DATA SETS OBSERVED PREDICTED OF AVERAGES* OF MrDIANS* COMPARISON* DISTRIBUTION
("N" OF EVENTS) VALUE (CO) VALUE (CP) (CO - CP) (CO - CP) ( SO**2/SP**2 ) COMPARISON*
LESSER OF (PPM) (PPM) (PPM) (PPM) (F03S-FPRED
25 OR 25X (FRACTION)
1. ALL STATIONS/ALL
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APPENDIX B
STATISTICS FOR VALUES PAIRED IN TIME, INCLUDING
HIGH BY EVENT AND PAIRED IN SPACE AND TIME
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In the Appendix B tables, model performance statistics are presented for
all events with either the predicted or the observed concentration above a
threshold value. As in the previous section, each table contains the results
for one model, one data base, and one averaging time. In each two page table,
results are first presented based on comparisons of the highest observed and
predicted concentration values event-by-event, regardless of location.
Results are then presented for observed and predicted concentration values
paired in time and location, including results for all stations combined, for
each individual monitoring station, and for subsets of events based on
meteorological conditions. As noted previously, subsets by meteorology were
employed only for the 1-hour averaging time.
In establishing the sets of observed and predicted concentration data, a
small threshold concentration was used to eliminate events when both the
observed and predicted values at a monitoring station were insignificant. The
threshold value for 1-hour average carbon monoxide concentrations was 0.5
ppm. No threshold was used for 8-hour average CO concentrations or SF6
concentrations.
Each table of results is presented in two parts, due to the large number
of performance measures recommended for these data sets. Part 1 provides
results based on statistics appropriate to unpaired data. Part 2 gives
results obtained for the same data sets using statistics appropriate for
paired data.
In Part 1, the first column presents the number of events (or data pairs)
in each data set. The second and third columns present, respectively, the
average observed and average predicted concentration values. The fourth
column presents the difference between the observed and predicted averages,
followed in parentheses by a 95 percent confidence interval calculated with a
two-sample t test. The fifth column (variance comparison) presents the ratio
B-l
-------
of the observed variance divided by the predicted variance, with 95 percent
confidence bounds in parentheses as calculated with an F test.
The frequency distribution comparison (sixth column) is equivalent to the
performance measure previously described in Appendix A. The cumulative
frequency distribution of observed values is compared to the distribution of
predicted values. The maximum fractional difference is listed; a positive
difference implies model overprediction. The value in parentheses is the
maximum difference significant at a 95 percent confidence level, as given by
the K-S test.
In Part 2, the number of events (i.e., data pairs) is repeated in the
first column. The average difference between observed and predicted values is
presented in the second column. In parentheses, the 95 percent confidence
interval calculated with a one-sample t test is given.
The fraction of positive residuals is presented in the third column. This
performance measure indicates the fraction of observed-predicted data pairs
for which the observed concentration value is larger than the predicted
value. In the fourth column, the standard deviation of the residuals is
presented, with 95 percent confidence bounds (from a Chi-Square test) in
parentheses. The root mean square error of the residuals (i.e., the square
root of the average squared residual) is given next, followed by the average
absolute residual.
The Pearson correlation coefficient of observed and predicted
concentration values is presented in the seventh column. In parentheses, 95
percent confidence bounds on the correlation coefficient are listed, as
calculated with the Fisher z test. The Part 2 tables are also continued on a
second page for presentation of meteorological subsets.
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TABLE B25. (PART 1) COMPARISON OF OBSERVED AND PREDICTED
CO CONCENTRATION VALUES EVENT-BY-EVENT (PAIRED IN TIME)
SES STATISTICS FOR MODEL/DATA BASE-' GMLH/CAL74 AVERAGING TIME: 8 HOUR
PERFORMANCE MEASURES - UNPAIRED COMPAPISOMS
AVERAGE AVERAGE DIFFERENCE VARIANCE FREQUENCY DISTRIBUTION
DATA SETS NUMBER OBSERVED PREDICTED OF AVERAGES* COMPARISON* COMPARISON*
OF VALUE (CO) VALUE (CP) (CO - CP) (F(CO) - F(CP)) MAX
EVENTS (PPM) (PPM) (PPM) (SO**2/SP**2 ) (FRACTION)
1. HIGHEST CONCENTRATION,
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APPENDIX C
STATISTICS FOR HIGHEST CONCENTRATION BY STATION
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In the high by station tables, model performance statistics are presented
which compare the maximum observed and predicted concentrations over all time
periods at each monitoring station. Each table contains results for one
model, one data base, and one averaging time. The performance measures are
analogous to those in Part 2 of the Appendix B tables.
Statistical analyses in these tables compare the N pairs of observed-
predicted values, where N represents the number of stations. The first two
columns present the averages of the maximum observed and predicted
concentration values at each station. The third column presents the average
difference between observed and predicted values, with the 95 percent
confidence interval in parentheses (calculated with a one-sample t test). The
fourth column indicates the fraction of observed- predicted data pairs for
which the observed value is greater than the predicted. The standard
deviation of the residuals (differences) is presented in the fifth column,
with 95 percent confidence bounds as given by a Chi-Square test. The root
mean square error (square root of the average squared residual) is listed
next, followed by the average absolute residual. The Pearson correlation
coefficient indicates the spatial correlation of the maximum concentration
values at each station. The 95 percent confidence bounds for the correlation
coefficient were calculated using a Fisher z test.
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APPENDIX D
STATISTICS FOR HIGHEST VALUES FOR VARIOUS PAIRINGS
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The high value tables present single-value residuals representing the
difference between the highest observed (or predicted) value over all events
and locations and the corresponding predicted (observed) value for the same
event or location. Each table contains results for one model, one data base,
and one averaging time. The tables contain no statistical measures, since
confidence intervals cannot be assigned for single-value comparisons.
The first row presents the highest observed and highest predicted
concentration values, over all events and locations. The difference between
»
observed and predicted values is given in the third column. A positive
difference indicates model underprediction.
The second row presents the maximum observed concentration, over all
events and locations, and the corresponding predicted value at the same time
and location. Row three presents the same observed value, but with the
maximum value at any location during the same time period as the observed.
Row four again presents the same maximum observed value, but matches it with
the maximum predicted value for any event at the same location as the observed.
The last three rows repeat the analogous single-value residuals obtained
using maximum predicted values instead of observed. Again, results are
presented representing pairings in space and time, pairings in time but not
space, and pairings in space but not time.
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-450/4-86-002
2.
3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
Evaluation of Mobile Source Air Quality Simulation
Models
5. REPORT DATE
February 1986
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
8. PERFORMING ORGANIZATION REPORT NO.
David Wackter and Paul Bodner
9. PERFORMING ORGANIZATION NAME AND ADDRESS
TRC Environmental Consultants, Inc.
800 Connecticut Boulevard
East Hartford, Connecticut 06108
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
68-02-3886
12. SPONSORING AGENCY NAME AND ADDRESS
U.S. EPA
OAQPS, MDAD, SRAB (MD-14)
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
16. ABSTRACT
This report summarizes the result of a comprehensive evaluation of four mobile
source air quality simulation models using data collected from five field measurement
programs. The report contains numerous tabulations of each model's performance in
terms of statistical measures of performance recommended by the American Meteorologica
Society.
The purpose of the report is two-fold. First, it serves to document for the
models considered, and similar models, their relative performance. Second, it pro-
vides the basis for a peer scientific review of the models. To stay within the spirit
of this latter purpose, the report is limited to a factual presentation of information
and performance statistics. No attempt is made to interpret the statistics or to
provide direction to the reader, lest reviewers might be biased.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS C. COS AT I Field/Group
Mobile Source Air Quality Models
Carbon Monoxide
Statistical Measures
Performance Evaluation
Mobile Source Data Sets
18. DISTRIBUTION STATEMENT
19. SECURITY CLASS (This Report/
21. NO. OF PAGES
236
20. SECURITY CLASS (TMs page)
22. PRICE
EPA Form 2220-1 (Rev. 4-77) PREVIOUS EDITION is OBSOLETE
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DAT
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