MOBILE6 Model Development
                      Stakeholder Review Document
                                - Draft -

               Evaluating Resting Loss and Diurnal
             Evaporative Emissions Using RTD Tests

                            Larry C. Landman

                      Document Number M6.RTD.001


                               October 8,1997
                                 U.S. EPA
                       Assessment and Modeling Division
                 National Vehicle Fuel and Emissions Laboratory
                             2565 Plymouth Road
                        Ann Arbor, Michigan 48105-2425
                              313-741-7939 (fax)
                           mobile@epamail.epa.gov
                                 NOTICE

These reports do not necessarily represent final EPA decisions or positions. They are intended
to present technical analysis of issues using data which are currently available. The purpose in
release of these reports is to facilitate the exchange of technical information and to inform the
public of technical developments which may for the basis for a final EPA decision, position or
regulatory action.

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                                -1 -
                             ABSTRACT
     The Office of Mobile Sources, Assessment and Modeling
Division, announces the release of "Evaluating Resting Loss and
Diurnal Evaporative Emissions Using RTD Tests" for stakeholder
review and comment.  This document M6RTD001.PDF is available at
the MOBILES section of the QMS Web Site:

                http://www.epa.gov/omswww/models.htm

     This document reports both on the methodology used to analyze
the data from real-time diurnal (RTD)  tests on 270 vehicles and on
the results obtained from those analyses.  The purpose of the
analysis is to develop a proposal for a model of the diurnal and
resting loss emissions of the in-use fleet.  Since this draft
report is a proposal,  its analyses and conclusions may change to
reflect comments,  suggestions, and new data.

     Please note that EPA is seeking any input from stakeholders
and reviewers that might aid us in modeling any aspect of resting
loss or diurnal evaporative emissions.

     Comments on this report and its proposed use in MOBILES
should be sent to the attention of Larry Landman.   Comments may be
submitted electronically to mobile@epamail.epa.gov,  or by fax to
(313)741-7939, or by mail to "MOBILES Review Comments", US EPA
Assessment and Modeling Division,  2565 Plymouth Road,  Ann Arbor,
MI  48105.  Electronic submission of comments is preferred.  In
your comments, please note clearly the document that you are
commenting on including the report title and the code number
listed.  Please be sure to include your name, address,
affiliation, and any other pertinent information.

     This document is being released and posted on October 8,
1997. Comments will be accepted for sixty  (60) days, ending
December 7, 1997.   EPA will then review and consider all comments
received, and will provide a summary of those comments and how we
are responding to them in the form of a follow-up document within
30 days after the close of the comment period.

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                               -11-

                        TABLE OF CONTENTS
                                                     Page Number
 1.0 Introduction 	    1
 2.0 Vehicle Sample 	    2
 3.0 Vehicle  Testing	    4
 4.0 Weighting the EPA Data	    5
 5.0 Test Parameters	    7
 6.0 Consolidating Vehicle Parameters for 24-Hour RTD .  .    9
      6.1 Comparing TBI and PFI Vehicles   	10
      6.2 Comparing Carbureted and FI Vehicles  	   12
      6.3 Comparing Cars and Trucks    	15
      6.4 Summarizing Stratification Parameters   ....   17
      6.5 Evaluating  Untested Strata	18
 7.0 Evaporative Emissions Represented by the RTD   ...   19
      7.1 Resting Loss Emissions	19
      7.2 Diurnal Emissions  	   20
      7.3 Separating Out Gross Liquid Leakers   	   21
 8.0 Characterizing Resting Loss Emissions   	   23
 9.0 Characterizing 24-Hour Diurnal Emissions   	   27
10.0 Gross Liquid Leakers  	   29
     10.1 Frequency of  Gross  Liquid Leakers	29
     10.2 Magnitude of Emissions from Gross Liquid Leakers   32
     10.3 Effects of Vapor Pressure  Changes  Leakers  ...   34
11.0 On-Going Analyses   	   34
APPENDICES
 A.  Temperature Cycles  	   36
 B.  Vapor Pressure	37
 C.  Mean Emissions by Strata	39
 D.  Regression Curves of Diurnal Emissions by Strata .  .   42

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                       ***
                                      ***
           Evaluating  Resting  Loss  and  Diurnal
         Evaporative  Emissions  Using  RTD  Tests

                 Report  Number  M6. RTD. 001

                        Larry C . Landman
            U.S. EPA Assessment  and Modeling Division
1 . 0  Introduction

     In previous  versions of the highway vehicle emission factor
model (MOBILE), the estimates of the emissions resulting from the
daily rise  of  the ambient air temperature were based on a one-hour
test (adjusted to simulate an 8-hour test)  in which the heating
process was accelerated.  As part of the MOBILE model revision,  an
effort has  been undertaken to use the recently developed 72-hour
real-time diurnal  (RTD) test (or a shortened version) to more
accurately  estimate those temperature driven  (i.e., diurnal)
emissions,  as  well as the resting loss emissions.

     In the RTD test, the ambient temperatures gradually cycle
over a 24 degree  Fahrenheit range during the course of each 24
hour period as illustrated in Figure 1-1:

                           Figure  1-1
              Nominal  RTD  Temperature  Cycle
        (Temperatures  Cycling  Between  72°  and  96°
F)
          100
                                                     24

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                                -2-
The three hourly temperature cycles used in this study are given
in Appendix A.  These three temperature cycles are parallel  (i.e.,
identical hourly increases/decreases).   The temperatures peak at
hour nine.  The most rapid increase in temperatures occurs during
the fourth hour.  For RTD tests that exceed 24 hours  (i.e., 33,
38, or 72 hours), the cycle is simply repeated.

     This document reports both on the methodology used to analyze
the data from these RTD tests and on the results obtained from
those analyses.
2 . 0  Vehicle  Sample

     In this analysis, EPA used real-time diurnal  (RTD) test data
from two sources:

     1)   from  five  (5) individual testing programs  (i.e., work
          assignments) performed  for EPA by  its contractor, and

     2)   from  a testing program  performed for the Coordinating
          Research Council  (CRC).

     The RTD testing performed for EPA was done by its testing
contractor (Automotive Testing Laboratories)  over the course of
five (5) work assignments from 1994 through 1996  (performed under
three different EPA contracts).   A total of 119 light-duty
vehicles (LDVs)  and light-duty trucks (LDTs)  were tested in these
programs.   In the following table  (Table 2-1), the distribution of
those 119 test vehicles is given:

     1)   by work assignment  number,

     2)   by vehicle type  (LDV versus LOT),

     3)   by model year range, and

     4)   by fuel metering system
                carbureted  (Carb)
                port  fuel injected (PFI)
                throttle body  injection  (TBI).

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                                -3-


                            Table  2-1

                Distribution  of  EPA Test  Fleet
Work
Assignment No.
2-09

1 -05

0-05


0-07
0-1 1


Vehicle
Type
LDV

LDV

LOT
LDV


LDV
LOT


Model Year
Range
80-85
86-95
80-85
86-95
86-95
71-77
78-79
80-85
86-95
86-95
71-77
78-79
80-85
86-95
Fue
Garb
5
7
3
1
0
3
1
5
0
0
2
0
5
0
Meter
PFI
2
15
4
24
0
0
0
0
0
5
0
0
0
5
ing
TBI
0
1 0
3
1 2
2
0
0
0
0
1
0
0
0
4
     The recruitment method used for most of the vehicles in the
EPA sample was designed to recruit a larger number of vehicles
that had problems with their evaporative control systems.
Specifically, two tests of the integrity of each vehicle's
evaporative control system (a purge test and a pressure test)  were
used to screen the candidate vehicles.   This resulted,  among the
newer vehicles,  in a larger proportion of the test vehicles
failing either a purge test or pressure test (but not both)  than
did the corresponding vehicles in the in-use fleet.   EPA excluded
from its sample all those vehicles that failed both the purge and
pressure tests.   Any analyses performed on the EPA data must,
therefore,  account for this intentional bias toward problem
vehicles.  (See Section 4.0.)

     It is important to note that neither the purge test nor the
pressure test is a perfect identifier of vehicles that have
problems with their evaporative control systems.  While vehicles
that passed both the purge test and the pressure test had, on
average, lower RTD emissions than similar vehicles that failed
either or both tests, there was a wide overlap on the RTD
emissions of the vehicles that passed both tests with the RTD
emissions of similar vehicles that failed one or both of those
tests.   The size of the overlap varied with the strata (see
Section 6.4).  But, on average, the cleanest (i.e.,  lowest RTD
results) one-fourth of the vehicles failing the purge and/or
pressure test(s) had lower RTD test results than the dirtiest
(i.e.,  highest RTD results) similar vehicles that passed both the
purge and pressure tests.  In fact, the vehicle that had the

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                                -4-
highest RTD emissions (other than the seven gross liquid leakers,
see section 7.3)  was one that passed both tests.

     The CRC program involved performing RTD tests on a random
sample of 151 vehicles  (mostly LDTs) during 1996.  The
distribution of those 151 vehicles  (by vehicle type,  model year
range, and fuel metering system)  is given in the following table:

                            Table   2-2

                Distribution  of  CRC Test  Fleet
Vehicle
Type
Car
Truck
Truck
Truck
Model Year
Range
71-77
71-77
80-85
86-91
Garb
38
1 3
47
7
PFI
0
0
2
24
TBI
0
0
1
1 9
3 . 0  Vehicle  Testing

     The testing in the EPA study consisted of performing one or
more RTD tests on each vehicle in its "as-received" condition with
the exception that the tank fuel was replaced with specified
fuels.   (To restore the vehicle to its "as-received" condition for
subsequent tests, the canister was conditioned to return it to
approximately the condition it was in prior to the first test.)
Up to three temperature cycles were used. (In addition to the
standard 72°-96° F cycle,  60°-84°  and 82°-106°  cycles  were also
used.)   Similarly, up to four different fuel volatilities were
specified; specifically, fuels having nominal Reid vapor pressure
(RVP) of 6.3, 6.7, 6.9,  and 9.0 pounds per square inch (psi).
Since the actual RVP used in a given test may vary slightly from
the specified target RVP,  EPA felt that tests performed using the
6.7 or 6.9 psi RVP fuel could all be treated as equivalent to
tests performed using a fuel with a nominal RVP of 6.8 psi.

     The testing in the CRC study consisted of performing a single
RTD test on each vehicle in its "as-received" condition.   Each
test used the standard temperature profile (i.e., temperatures
cycling between 72° and 96°  F)  and was performed using the fuel
already in each vehicle's fuel tank  (typically having an RVP which
ranged from 6.7 to 7.0 psi).  EPA felt these tests could also be
treated as equivalent to tests performed using a fuel with a
nominal RVP of 6.8 psi.

     For the purpose of the following analyses, we treated all
testing performed using fuels with RVPs from 6.7 through 7.0 as if
they were all performed using a fuel with a nominal RVP of 6.8
psi.  Thus, all the EPA testing performed using fuels with nominal

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                                -5-
RVPs of either 6.7 or 6.9 will be combined and then used with all
of the CRC tests.
4 . 0  Weighting the  EPA  Data

     To correct for the intentional sampling bias toward "problem"
vehicles in the EPA testing programs (described in Section 2.0),
we first determined the number of vehicles in each stratum in both
the recruited sample and the in-use fleet.

     Examining the purge/pressure data gathered in the I/M lanes
in Arizona and Indiana, we found 11,832 as-received vehicles for
which successful purge and pressure tests were performed.   (These
tested were conducted at the Phoenix,  Arizona I/M lane from June
1992 through August 1994 and at the Hammond,  Indiana I/M lane from
January 1990 through February 1995.)  The distributions of those
tests results are given in the following table:

                            Table   4-1

       Observed  Distribution  of  Purge/Pressure  Results
                        (by  Vehicle  Age)

     Vehicle    	 Purge / Pressure Test Results 	
        Age       F/F        F/P       P/F       P/P
           01          2        12       125
           1         5         24        48       986
           2         6         24        48       819
           3        12         30        44       889
           4        20         25        62       822
           5        19         54        76       972
           6        26         68        84     1,075
           7        32         91        82     1,092
           8        42         70        79       899
           9        31         89        68       752
          10        19         63        67       461
          11        30         47       105       304
          12        46         55        92       264
          13        30         38        77       191
          14        13         13        35         98
          15         3          3        11         28
          16         3          1         3         14
          17         3          0         2          6
          18         0          0         1          1
Modeling the preceding distributions with smooth curves produced
the distributions in Table 4-2.   Similar results can be obtained
by using the CRC data.  For example, of the 28 1989 through 1991
model year vehicles (average age of 6)  in the CRC sample,  24
passed both the purge and pressure tests (85.7%),  compared to 85.5
percent in Table 4-2.   For the 1983-85  model year vehicles in the

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                                -6-
CRC program (averaging 11.74 years of age), Table 4-2 predicts
that 23 vehicles pass both the purge and pressure tests (90
percent confidence interval from 18 through 27) which is
consistent with the 26 actually in the CRC sample.

                            Table  4-2

      Predicted  Distribution  of  Purge/Pressure  Results
        (By Vehicle  Age  --  Independent of  Model  Year)

                   —  Purge  /  Pressure  Test  Results  —
       Vehicle                   (Pass/  F ail)
        Age       F/F        F/P        P/F       PIP
           0
           1
           2
           3
           4
           5
           6
           7
           8
           9
          1 0
          1 1
          1 2
          1 3
          14
          15      11.0%     11.4%      29.4%     48.2%
Extrapolating these estimates beyond vehicles of 15 years of age
(i.e., beyond the data) produces unrealistic results (e.g.,
negative pass/pass rates for vehicles more than 21 years old).
Therefore, for vehicles more than 15 years of age, we simply used
the estimated rates for 15-year old vehicles.  Limiting these
estimated identification rates to the predictions at the 15-year
point would affect only the analyses of the pre-1980 vehicles,  and
then only when comparing the proportion of vehicles which past
both the purge and pressure tests with those that failed either
test.  And,  that situation never occurred in these analyses.

     This approach assumes that the purge/pressure results are
functions only of age  (i.e.,  independent of vehicle type, fuel
metering system, model year,  etc.).  To use these distribution
estimates within a given stratum (e.g., 1980-85 carbureted LDVs),
we determined the numbers of vehicles in each of the
purge/pressure categories that we would expect to find in a
randomly selected sample of the in-use fleet.  We then calculated
the ratio of those expected category sizes to the number of
vehicles actually recruited and tested within each of those four
0.7%
0.7%
0.8%
1.0%
1.3%
1.7%
2.2%
2.7%
3.4%
4.2%
5.1%
6.1%
7.2%
8.3%
9.6%
0.6%
1.6%
2.6%
3.5%
4.4%
5.3%
6.1%
6.9%
7.6%
8.3%
8.9%
9.5%
10.0%
10.5%
11.0%
3.9%
4.1%
4.4%
4.8%
5.1%
5.5%
6.2%
7.4%
8.8%
10.7%
12.9%
15.4%
18.4%
21.7%
25.3%
94.8%
93.5%
92.2%
90.7%
89.1%
87.5%
85.5%
83.0%
80.2%
76.9%
73.1%
69.0%
64.4%
59.5%
54.0%

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                                -7-
categories.   Those ratios then became the weighting factors for
the analysis of that stratum.

     NOTE:  Since no vehicles in the EPA testing programs were
recruited from among those that failed both the purge and the
pressure tests, we used the data from the CRC program to
characterize the RTD emissions of that category.  Since (as Table
4-2 indicates)  this stratum is quite small for newer vehicles, its
exclusion had only a slight affect on the estimate of fleet
emissions of those newer vehicles.   (See Section 6.5.)
5 . 0  Test   Parameters

     Since emissions from vehicles classified as gross liquid
leakers (vehicles identified as having substantial leaks of liquid
gasoline,  as opposed to simply vapor leaks) are characterized
separately from those of the remaining vehicles, the analyses in
this section were also performed with those vehicles omitted (see
section 7.3).

     There are three testing parameters in the EPA programs that
could affect the RTD test results.  Those are:

  1)  the RVP of the test fuel,

  2)  the temperature cycle, and

  3)  the site from which each vehicle was recruited.

     Since it is well known that both the ambient temperature and
the fuel volatility will affect evaporative emissions, these two
parameters were automatically included in the calculations.  All
of the analyses that used tests performed with fuels ranging from
6.7 to 7.0 psi RVP were conducted assuming the nominal RVP to be
6.8 psi, as noted previously.

     The question of whether the  "site" variable is significant
was raised because EPA's testing contractor (ATL)  recruited
vehicles from two different parts of the country.   Twenty-two (22)
vehicles were recruited from and tested in Indiana; the remaining
97 vehicles were recruited from and tested in Arizona.  Since the
higher temperatures in Arizona might have resulted in higher
canister loadings for those as-received vehicles,  we compared the
24-hour RTD results (weighted to correct for recruitment bias)  of
the 1986 and newer PFI LDVs tested at both sites (Figure 5-1)  and
of the 1986 and newer TBI LDVs tested at both sites (Figure 5-2).
All of these 24-hour RTD emissions were obtained using 6.7-6.9 psi
RVP fuel over the 72°-96°  F cycle.   Despite the small  sample sizes
in the Indiana data (only six PFIs and four TBIs),  the closeness
of the distribution curves is compelling and suggests that the
test data are comparable.   Therefore, the "site" parameter was
dropped from the remaining analyses.

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                       Figure  5-1



 Weighted  Cumulative  Distributions  at  Two  Sites

     RTD  Emissions  of  the  1986  and  Newer  PFIs
o
x

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                                -9-
6 . 0  Consolidating  Vehicle  Parameters  for  24-Hour  RTD

     Since emissions from vehicles classified as gross liquid
leakers (see section 7.3)  are characterized separately from those
of the remaining vehicles,  the analyses discussed in this section
were also performed with those vehicles omitted.

     When analyzing exhaust emissions, we note that some vehicle
technologies (sometimes identified by model year ranges)  have
distinct exhaust emission characteristics.  Before beginning the
primary analysis of these evaporative emissions, we examined the
data to determine if analogous technology groupings exist for the
RTD test results.  Specifically,  it was necessary to determine:

  1)  whether tests results from different model year ranges  (i.e.,
     1981-85 and 1986-93)  can be combined,

  2)  whether tests results from port fuel-injected vehicles  (PFIs)
     can be combined with throttle body injected vehicles  (TBIs)
     into a single stratum of fuel-injected vehicles,

  3)  whether tests results from carbureted vehicles can be
     combined with fuel-injected vehicles, and

  4)  whether tests results from cars and trucks can be combined
      (despite the differences in fuel tank size).


     We stratified the test vehicles using the following three  (3)
model year ranges:

  1)  1971 through 1979,

  2)  1980 through 1985, and

  3)  1986 through 1995.

Based on the assumption that changes to the EPA certification
requirements for evaporative emissions will result in changes to
vehicles'  evaporative control systems, we separated the RTD
results on the pre-1980 vehicles from the results  on the 1980 and
newer vehicles.   (For the same reason, data from the 1996 and
newer model year vehicles will form a new stratum once we begin to
test those vehicles.)   While a similar argument can be made for an
additional break at the 1978 model year point, we  lacked the data
to separately analyze the 1978-79 model year vehicles.  A second
break point was added between the 1985 and 1986 model years at the
recommendation of some of the automotive manufacturers who based
their suggestion on improvements in the control of evaporative
emissions.  Therefore,  this second break point was not based on

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                                -10-
any changes in EPA test requirements or applicable standards nor
on any analysis of the results of the RTD tests.

6 . 1  Comparing TBI  and  PFI  Vehicles

     To determine the appropriateness of combining the RTD test
results of PFIs with those of TBIs, we found two samples
containing otherwise similar vehicles:

  1)  1986 and newer trucks in the CRC testing program  (see Figure
     6 -1) and

  2)  1986 and newer LDVs in the EPA testing program  (see Figure 6-
     2) .

In each of those two samples, the testing was performed over the
72°-96° temperature cycle using  fuel  with an RVP ranging from 6.7
to 7.0 psi.   The similarity between PFI and TBI among the 1986 and
newer model year trucks in the CRC testing program is illustrated
in Figure 6-1.
                            Figure  6-1

          Cumulative Distributions  of  PFIs  and  TBIs
           RTD Emissions  in the  CRC  Testing  Program
      o
      in
      E
      ro
      in
      c
      O
      3)
      m
      O
      H
      OL
            40
            30 .-
20
10

• 	 'C
— — — c







RC 86-91 Truck
RC 86-91 Truck







TBI
PFI





• —













x -,/""
	 _..,:""'


	 I 	 i_
f

H
\Jj
~ 	 " 	 ' |


              0%
          20%     40%      60%     80%

              Cumulative Percentage  (%)
100%
Characterizing those two CRC samples yields:

-------
                                -11-
     1986-91  CRC
     Truck TBIs
Sample
 Size     Median
   19       3.13
                    Standard
           Mean     Deviation
            5.41       5.70
     1986-91  CRC
     Truck PFIs
   24
 2.05
5.85
7.87
The similarity between PFI and TBI among the 1986 and newer model
year LDVs in the EPA testing program is illustrated in Figure 6-2
                            Figure  6-2

     Weighted  Cumulative  Distributions  of  PFIs  and  TBIs
           RTD  Emissions  in  the  EPA  Testing  Program
      o
      in
      E
      ro
      in
      in
      Q
      H
      OL
      Tf
      tM
            60
            40
            20

—


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— - E




— ' —

PA 86-9
PA 86-S




r— ••

5 LDV
5 LDV




— —

TBI
PFI




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1 1
I 1
1
.•i
III
tl
It
J
I
•


              0%
 20%      40%      60%

      Cumulative Percentage  (%)
                 80%
              100%
     Both the distributions shown in Figure 6-2 and the
characterizations of those two EPA samples presented in the
following table have been weighted to correct for recruitment
bias.
     1986-95 EPA
      LDV TBIs
Sample
 Size
   21
Median
 4.52
Mean
9.84
     1986-95 EPA
      LDV PFIs
   41
 2.08
9.32

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                                -12-
Based on the similarity of the cumulative distribution curves and
on the close fit of the means (in the strata illustrated in
Figures 6-1 and 6-2),  the PFI and TBI strata were merged into a
single fuel-injected (FI) stratum for the remaining analyses.

6.2  Comparing Carbureted  and  Fuel  Injected  Vehicles

     To determine whether test results from carbureted vehicles
can be combined with those from fuel injected vehicles,  we
identified the only four samples containing otherwise similar
vehicles:

 1)  in the CRC testing program, 43 1986 and newer FI trucks and 7
     corresponding carbureted trucks  (see Figure 6-3),

 2)  in the EPA testing program, 64 1986 and newer FI LDVs and 6
     corresponding carbureted LDVs  (see Figure 6-4),

 3)  in the CRC testing program, 3 1980-85 FI trucks and 46
     corresponding carbureted trucks, and

 4)  in the EPA testing program, 6 1980-85 FI LDVs and 13
     corresponding carbureted LDVs.

However, the two comparisons using the 1980-85 model year vehicles
produced mixed results (possibly due to the small number of FI
vehicles in the samples).

     The differences in the distributions between carbureted
(Carb)  and FI among the 1986 and newer model year trucks in the
CRC testing program is illustrated in Figure 6-3.

-------
                                -13-
                            Figure  6-3
       Cumulative  Distributions of  FIs  and  Garb  Trucks
           RTD Emissions  in the  CRC  Testing  Program
      o
      in
      E
      ro
      in
      c
      O
      3)
      m
      O
      H
      OL
      Tf
      tM
            30
            20
            10







— •





CRC 86-91 Trk Carb


- — CRC 86-91 Trk FI





















, 	 '
I






I .-»
I 	 /"
| 	 / 	
. 1
I '
:: ^.' •
.•fl f
K1 "
m ii §
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.f I '
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11
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             0%
 20%      40%     60%      80%

      Cumulative Percentage  (%)
                         100%
Characterizing those two CRC samples yields:

           Comparing  Carbureted  LDTs  to  FI  LDTs
     1986-95 CRC
     LDT Carbs

     1986-95 CRC
      LDT FIs
Sample
 Size
    7
   43
Median
 6.15
 2.85
Mean
9.31
5.65
Standard
Deviation
  8.28
  6.92
The cumulative distributions of the carbureted (Carb) and the FI
among the 1986 and newer model year LDVs in the EPA testing
program is illustrated in Figure 6-4.

-------
                                -14-
                            Figure  6-4

     Weighted  Cumulative  Distributions  of  FIs  and  Garbs
           RTD  Emissions  in  the  EPA  Testing  Program
      o
      in
      E
      ro
      in
      c
      O
      m

      Q
      H
      OL
      3
      O
      Tf
      tM
            30
            20
10


— .









EPA 86-95 LDV Cart
- — EPA 86-95 LDV FI












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             0%
20%      40%      60%

     Cumulative  Percentage  (%)
                                    80%
         100%
     Both the distributions shown in Figure 6-4 and the
characterizations of those two EPA samples represented in the
following table have been weighted (using Table 4-2)  to correct
for recruitment bias.

          Comparing Carbureted  LDVs  to  FI  LDVs
          1986-95  EPA
           LDV Garbs

          1986-95  EPA
            LDV FIs
              Sample
               Size
                  6
                 64
              Median
              10.56


               3.41
 Mean
10.34
 9.50
     In each of the two preceding figures, the sample sizes of the
carbureted vehicles are relatively small.  However,  it is
noteworthy that every carbureted vehicle in each sample had RTD
test results higher than the median of the corresponding fuel
injected vehicle sample.

     Therefore, the carbureted vehicles and the FI vehicles were
treated as distinct strata for the remaining analyses.

-------
                                -15-
6 . 3  Comparing Cars  and Trucks

     Determining the appropriateness of combining the RTD test
results of LDVs with those of LDTs presented different problems.
Specifically, the CRC sample was exclusively trucks except for the
1971-77 stratum, and the EPA sample (using 6.7-6.9 RVP fuel)  was
almost exclusively cars.  The obvious solution was to compare the
CRC trucks with the EPA cars.  However,  because of the difference
in recruitment methods, we first had to omit from the CRC sample
those vehicles which would not have been recruited in the EPA
sample (i.e., those failing both purge and pressure), and we then
weighted the remaining results  (as we did with the EPA sample).
This produced the following two strata with which to investigate
the differences in RTD results between cars and trucks:

  1)  in the combined EPA and CRC testing programs, the weighted
     results of 13 1980-85 carbureted LDVs and 44 corresponding
     carbureted trucks  (Figure  6-5),  and

  2)  in the combined EPA and CRC testing programs, the weighted
     results of 62 1986 and newer FI LDVs and 42 corresponding
     carbureted trucks  (Figures 6-6 and 6-7).


     The distributions in Figures 6-5 and 6-6 and the
characterizations of those strata (in the following table) have
been weighted to correct for the actual recruitment bias in the
EPA sample and the simulated bias in the CRC sample.

                    Sample
                     Size     Median      Mean
    1980-85 LDVs       13      10.22      11.29
     Carbureted
    1980-85 LDTs       44      10.55      10.58
     Carbureted

    1986+ FI  LDVs       62       3.40       9.48
    1986+ FI  LDTs       42       3.11       5.99

-------
                            -16-
                        Figure  6-5
Weighted Cumulative  Distribution  of  Cars  and  Trucks
 RTD  Emissions  in  the  EPA  and  CRC  Testing Programs
      (1980-1985  Model  Year  Carbureted  Vehicles)
  o
  in
  E
  ro
  in
  c
  O
  3)
  m
  O
  H
  OL
  3
  O
        40
        30 •- _ _ _
20
10

• 	 E
L
- — — — c
T


: 	 73^*
PA 80-85 Carb
DVs
RC 80-85 Carb
rucks


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fr~; " -'


^r'


II '
= */; '
j*

— — 	 	 -
         0%
          20%      40%      60%      80%

               Cumulative  Percentage  (%)
        100%
                        Figure  6-6
Weighted Cumulative  Distribution  of  Cars  and  Trucks
 RTD  Emissions  in  the  EPA  and  CRC  Testing Programs
       (1986  and  Newer  Model  Year FI  Vehicles)
  o
  in
  E
  ro
  in
  in
  E
  m
  Tf
  tM
        40
        30 --
        20
        10
           EPA 86-95 FI LDVs


           CRC 86-91 FI Trucks
                   +
                                         '
                                        t ...... *-
         0%
          20%      40%      60%

               Cumulative  Percentage  (%)
80%
100%

-------
                               -17-
     In Figure 6-6, the distributions of the FI 1986 and newer
cars and trucks are virtually identical up to about the 50
percentile point,  after which they diverge.   However,  much of that
divergence is the result of a RTD test on a single truck in the
CRC sample (vehicle 9143).   If that single truck had not been
recruited, then the (re-weighted)  distribution of the remaining 41
FI trucks (given below in Figure 6-7)  is quite similar to that of
the corresponding 62 FI cars.
                            Figure  6-7
    Weighted  Cumulative  Distribution  of  Cars  and  Trucks
     RTD  Emissions  in  the  EPA and  CRC  Testing  Programs
           (1986  and  Newer  Model  Year FI  Vehicles)
                  (Excluding  CRC LDT  No.  9143)
     o
      E
      ro
      ^
      D)
m
c
O

-
E
LLJ

O
           40
      30 --
           20
           10
1 	

- •







'EPA 86-95 FI LDVs
- — CRC 86-91 FI Trucks
(minus 9143)








—













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„ ,iniur
1 — —

1"

'« i
II' 1
	 l> 	 f 	
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             0%
20%      40%      60%

     Cumulative  Percentage  (%)
                                          80%
100%
Based on the similarity of the cumulative distribution curves,  the
close fit of the means for the 1980-85 vehicles,  and on the close
fit of all of the medians, we merged the cars and trucks into a
single stratum for the remaining analyses.   This  conclusion seems
reasonable based on the fact that the large fuel  tanks (and hence
potentially larger vapor volumes) of trucks are offset by the
reportedly larger canister volumes.

6.4  Summarizing  Stratification   Parameters

     For each combination of the pass/fail results on the
(screening) purge test and pressure  test (i.e., recruitment
groups),  we stratified the combined  119 vehicle EPA and 151
vehicle CRC data into the following  five strata:

-------
    Model  Year  Range
          1971-1979
                               -18-
 Number  of
Carbureted
 Vehicles
      57
  Number  of
Fuel  Injected
   Vehicles
         1980-1985       |         65      _ [[[ 12
            and Newer    (         15              121
       * No data were available for this stratum.  We simply
        applied the results of the 1971-79 carbureted vehicles to
        characterize this stratum.

These five (tested)  strata,  in the above table,  were then
subdivided to include the recruitment criteria and yielded the 20
substrata listed in Appendix C.   Three of these 20 strata were not
tested, and two of the remaining had only limited coverage.   These
five missing or poorly covered strata are comprised of  vehicles
that failed both the purge and pressure tests.

6 . 5  Evaluating  Untested  Strata

     As noted in the previous section, the strata that  are either
missing or poorly represented in our sample fall into two
categories :

     1)   No pre-1980 model year vehicles equipped with fuel
          injection were recruited because of the small numbers of
          pre-1980 model year vehicles in the in-use fleet.

     2)   The vehicles that failed both the purge and the pressure
          tests :

          •  were systematically excluded from the EPA  sample and

          •  were missing or poorly represented in CRC ' s  sample of
             the newer model year vehicles due to their relative
             rarity (see  Table 4-2) .

     For the MOBILE model, we will assume that the RTD  emissions
of the (untested)  pre-1980 fuel injected vehicles are identical to
the corresponding emissions  of the pre-1980 carbureted  vehicles.
This should be a safe assumption since any actual differences
between these strata should  be balanced by the relatively small
number of these vehicles  in  the in-use fleet.

     Eighteen vehicles that  failed both the purge and the pressure
tests were tested (all by CRC) .   Four of those were identified as
gross liquid leakers and analyzed separately.   Thirteen (of the
remaining 14)  were pre-1980  carbureted vehicles.  For those 13
vehicles,  the mean (24 -hour) RTD emissions was 25.11 grams (with a
standard deviation of 12.00).   The corresponding stratum  of pre-
1980 vehicles that passed the purge test but failed the pressure
test contains 20 vehicles (18 CRC and 2 EPA)  has a mean (24-hour)

-------
                                -19-
Based on the similarity of those means,  we will use the test
results of vehicles that failed the pressure test but passed the
purge test to represent the corresponding untested strata of
vehicles that failed both screening tests.
7 . 0  Evaporative  Emissions  Represented by  the  RTD

     The results from the real-time diurnal  (RTD) tests can be
used to model the following two types of evaporative emissions:

     1)    "Diurnal" emissions are the pressure-driven emissions
           resulting from the daily increase  in temperature.

     2)    "Resting loss" emissions are the relatively stable
           emissions that are always present.

7 . 1  Resting  Loss Emissions

     Examinations of the RTD data suggest that, for virtually all
of the tests (regardless of the temperature cycle,  fuel RVP,  or
vehicle type),  the hourly HC evaporative emissions  had stabilized
and were relatively constant for hours 19 through 24.   (See Figure
7-1.)  This suggests that the average hourly emissions during the
final six  (6) hours of the 24-hour RTD cycle correspond to what
this paper refers to (in the previous section)  as hourly "resting
loss" emissions.

     The "resting loss" emissions component of each RTD test was
calculated as the average (i.e., mean) hourly RTD emissions for
hours 19 through 24,  at the nominal temperature for the twenty-
fourth hour.  In this  example,  the average emissions for that 6-
hour period  (0.10 grams per hour)  would represent this vehicle's
hourly resting losses  at a stable 72°F with a fuel  having RVP of
6.8 psi.  The mean hourly resting loss emissions (temperatures of
60°,  72°  and 82°) for each of the  strata  in Section 6.4  are given
in Appendix C.

-------
                               -20-


                            Figure  7-1

                 Identifying  Resting   Losses
           (Stable  Portion  of RTD Hourly Emissions)
        100
         90°  -
      0)
      Q.
      E
      0)
      0)
      !5
      E
         80°  -
         70'
0.0
                                                   2 4
7 . 2  Diurnal   Emissions

     Subtracting the hourly resting loss emissions (calculated in
Section 7.1)  from the hourly RTD emissions,  should yield an
estimate of the hourly emissions that result from the daily rise
in temperature (i.e., "diurnal"  emissions).   Although the hourly
resting loss emissions will vary as the ambient temperature cycles
over the full  range of the RTD test (see Section 8.0),  the
variation is small relative to the RTD hourly emissions.
Therefore,  using a constant resting loss value rather than a
"temperature adjusted" value will not affect the analysis.   (Using
a "temperature adjusted" resting loss value  will result in a
slightly higher level of resting loss emissions over  the day,  and
a corresponding lower level of diurnal emissions over that day.
The total emissions will be unchanged.)
     In the following figure, the hourly resting loss emissions
correspond to the unshaded area.   The remaining (i.e.,  shaded)
area then corresponds to the hourly diurnal emissions which are
primarily pressure-driven vapor leaks.   This approach produces
calculated hourly diurnal emissions that approach zero as  the SHED

-------
                                -21-
(i.e., "ambient")  temperature drops to near the starting
temperature.

                            Figure  7-2

               Estimating  Diurnal  Emissions
                 (Pressure  Driven Vapor  Leaks)
      1.5
   in
   E
   2
   O)
   (A
   (A
   E
   m
   3
   O
   I
      1.0
      0.5   • -
Pressure  Driven
  Vapor Leaks
      0.0
                          12      18

                           Time  (hours)
                  2 4
3 0
     The average  (mean) 24-hour diurnal emissions for each of the
strata in Section 6.4 are given in Appendix C.

7 . 3  Separating  Out  Gross   Liquid  Leakers

     The largest quantity of RTD data  (combining data from the EPA
and CRC programs) was generated using fuel with an RVP ranging
between 6.7 and  7.0 psi over  the 72°-96° F temperature cycle.
These test conditions were used by a total of 96 vehicles in the
EPA program and all 151 vehicles in the CRC program.   Using the
preceding method to estimate hourly resting loss emissions (at
72°F)  for each of those 247  vehicles,  we then plotted the full 24-
hour RTD emissions versus those hourly resting loss emissions
(Figure 7-3).
     This graph  (Figure 7-3) clearly illustrates that the test
results of all but five of the vehicles are tightly clustered with
RTD results under 100 grams (per 24-hours)  and with hourly resting
losses under 1.5 grams per hour.  The test  results from each of

-------
                                -22-
the remaining five vehicles are quite distinct from those of the
corresponding 242 tightly clustered vehicles.  Each of these five
extremely high emitting vehicles was identified, by the mechanics
who examined them, as having significant leaks of liquid gasoline
(as opposed to simply vapor leaks).

                            Figure  7-3
       Comparison  of  RTD  versus  Resting  Loss  Emissions
            (72°-96°F  Cycle  Using  6.7-7.0   RVP Fuel)
      o
      E
      ro
      ^
      D)
      c
      O
      
-------
                                -23-
EPA study as likely gross liquid leakers.   (These two are only
"likely" gross liquid leakers because no mechanic's inspections
were performed.  We inferred their status based solely on their
resting loss emissions.)   These two additional gross liquid
leakers do not appear in Figure 7-3 because they were tested only
on 6.3 and 9.0 psi RVP fuels.
8 . 0  Characterizing  Resting  Loss  Emissions

     Resting loss evaporative emissions, like all evaporative
emissions, are functions of both fuel volatility and ambient
temperature which are themselves interdependent.   There are
several distinct mechanisms contributing to resting loss
emissions:

     •  permeation of the liquid fuel through the walls of both
       hoses and (if applicable) plastic fuel tanks,
     •  seepage of vaporized fuel at connectors and through cracks
       in hoses, fuel tanks,  etc.,
     •  at the canister,  and
     •  undetected (minor)  liquid leaks of fuel.

Some of these components of resting loss emissions are strongly
related to temperature changes while others are more closely
related to changes in volatility.  Of course, the portion due to
the minor liquid leaks (as distinguished from the gross liquid
leakers in Section 10) are unaffected by either temperature or
volatility changes.

     As the first step in characterizing the effects of changes in
temperature and volatility on the hourly evaporative emissions,  we
identified 57 vehicles in the EPA program that were each tested:

     •  using both the 6.8 and the 9.0 RVP fuels and
     •  over all three temperature cycles.

Using this sample permitted us to have exactly the same vehicles
being tested at each combination of fuel RVP and temperature;
thus, avoiding many of the problems associated with vehicle-to-
vehicle test variability.   This sample of 57 vehicles consisted
of:

     •  12 1974-85 model  year carbureted vehicles and
     •  45 1985-94 model  year fuel injected vehicles.

In the following graph (Figure 8-1), we plotted the mean hourly
resting loss emissions for the carbureted vehicles and the fuel
injected vehicles.

-------
                                -24-
                            Figure  8-1

         Mean  Hourly  Resting  Loss   Versus  Temperature
     (averaged  at  each  temperature  and  RVP  combination)
          0.3
          0.2
       o>
       (A
       (A
       O
       O)
       (A
       0)
       re
       o>
0.1 --
          0.0
                1974-85  Carbu eted
                   (12 vehicles)
      1985-94 Fl
     (45  vehicles)
                                    9.0  RVP
                                    6.8  RVP
                                               9.0 RVP
                                               6.8 RVP
             4 0
                 60            80

             Ambient Temperature  (  °F)
1 00
     Based on the graphs  in  Figure  8-1,  we  can make the following
observations:
     •  Hourly resting loss emissions  increase with  increasing
       temperature.
     •  Hourly resting loss emissions  increase with  increasing fuel
       RVP.
     •  The effects of RVP and temperature  changes appear to be
       interrelated.
     •  For the fuel injected  (i.e., the  larger  sub-sample,  the
       plots at each fuel RVP appear  to  be linear in  log-space.

     For the fuel injected vehicles,  the function that most
reasonably models the hourly resting  loss  emissions  (within the
tested range) is that the logarithm of the emissions  is a linear
function of both RVP and temperature.  That is:

-------
                                -25-
       Hourly Resting Loss= exp [ A + (  B * Temperature ( °F) ) + (  C * RVP ) ]

Where:

        N A"         ii B"         ii C"
     -6.38000    0.039163    0.116588   For FI Vehicles

     Before attempting  to model the  resting  loss emissions of
those 12 carbureted vehicles,  we observe  (in Figure 8-1)  that  the
average emissions at 72° with  the 6.8 RVP fuel are suspiciously
high.  This suspect value may  simply be a result of the  small
number of carbureted vehicles  in this sample.  If we first delete
that suspicious value,  and then use a linear regression  (through
the remaining five points) to  model the logarithm of the emissions
as a linear function of both RVP and temperature, we obtain:

       Hourly Resting Loss= exp [ A + (  B * Temperature ( °F) ) + (  C * RVP ) ]

Where:

        ii A"         ii B"         ii C"
     -3.39291    0.016599    0.059795   For Garb Vehicles


     These equations predict resting loss emissions of  the
carbureted vehicles to  be higher than for the fuel injected
vehicles, but the emissions from the fuel injected vehicles would
increase at a faster rate with increasing temperature.   Adding
those regression curves to the values in Figure 8-1 produces
Figure 8-2.  The "dotted" portion of the regression curves extends
the curves beyond the limits of the tested data.  While  these
regressions can be used to calculate reasonable estimates  of
resting loss emissions  within  the range of temperature and fuel
RVPs that were actually tested, we must determine  (see Section 11)
how to extrapolate beyond the  limits of the test data.

-------
                                -26-
                            Figure  8-2

         Mean  Hourly  Resting  Loss  Versus  Temperature
                     (with  regression  curve)
     (averaged  at  each  temperature  and RVP  combination)
          0.3
          0.2
       o>
       (A
       (A
       O
       O)
       W  01
       Q)
       re
       o>
          0.0
                                                  X     X
                                                 /     «
                                               *     X   ,
                     1974-85  Carbureted
                                          1985-94  Fl
             4 0
    60            80

Ambient  Temperature   ( °F)
1 00
     For each of the strata identified in Section 6.4, we
calculated the value of "A" (in the previous regression equations)
that would minimize the difference between the predicted and the
actual resting losses.   If more tests had been conducted at a
given combination of temperature and fuel RVP  (e.g.,  72 °F using
6.8 psi RVP fuel),  then the average resting loss emissions at that
combination was then more heavily weighted in the process to
calculate the value "A".

     Only the test results from the 57 vehicles that were tested
over a range of fuel RVPs and temperature cycles were used to
determine the coefficients (B and C)  which determine the shapes of
the curves.  The full data set was used only to solve for the
constant term (A).   In this type of equation (i.e.,  an exponential
function),  the constant term (A) has a multiplicative effect rather
than an additive effect.

-------
                                -27-
     This process produced  a  regression equation for each of the
24 strata.  The regression  equations  are unique for each stratum
for which tests were performed.   Each untested stratum (see
Section 6.5) used the regression  equation of  a similar tested
stratum.

     Using  these 24 equations,  we calculated an estimate of the
hourly resting loss emissions associated with each fuel RVP at
each hour of the three temperature  cycles.   Then,  adding the
hourly estimates for the  first  24  hours of each test produced the
daily resting loss emissions  (for each of the 24 strata).
Subtracting those values  from the mean RTD emissions (for each of
the 24 strata) yielded the  estimated  diurnal  emissions (by strata)
that are listed in Appendix C.


9.0   Characterizing  24-Hour  Diurnal  Emissions

     Diurnal evaporative  emissions,  like other evaporative
emissions, are functions  of both  fuel volatility and ambient
temperature which are themselves  interdependent.  The RVP is a
measure of vapor pressure*  (VP) at a  single temperature, 100°F.
The Clausius-Clapeyron relationship was used to estimate the vapor
pressure at each temperature and  for  each of  the fuels (RVPs of
6.8 and 9.0 psi) used in  this testing program.   (See Appendix B.)

     To characterize the  diurnal  emissions,  we again (see Section
8.0)  identified the 57 vehicles EPA program that were tested over
a wide range of vapor pressures.   These test  vehicles were then
distributed into 12 tested  strata (of the 24  potential strata
identified in Section 6.4).

     The attempt to use this  approach to characterize resting loss
emissions (see previous section)  had  been unsuccessful.  However,
this approach produced more satisfactory results in characterizing
the diurnal emissions even  in strata  that were sparsely tested.
Most likely this difference was due to the effect that the test-
to-test variability was substantially larger relative to the
resting loss emissions than to  the  diurnal emissions.  Therefore,
any test-to-test variability was  less likely to hide patterns
evidenced in the diurnal  emissions  measurements.

     For each RTD test, the Clausius-Clapeyron relationship was
used to estimate the vapor  pressure at both the low and the high
   Evaporative emissions are functions of  both fuel volatility and  ambient
   temperature which are themselves interdependent.  The  RVP is one  measure
   of vapor pressure  (VP)  at  a  single temperature,  100°F.   In order to
   analyze  the diurnal emissions as a  function of  VP, we  used the Clausius-
   Clapeyron  relationship  to  estimate  the VP  at each combination of
   temperature and fuel  RVPs. See Appendix B.

-------
                                -28-
temperatures.   Using these estimates, we calculated both the
average of the low and the high vapor pressures, as well as the
difference between the low and the high vapor pressures (both in
kPa).   Multiplying these two quantities together produced a single
product term  (VP*AVP) that incorporates the parameters of the RTD
test.

     The mean diurnal emissions  (calculated in the previous
section by subtracting a daily resting loss value from the RTD
test results)  were repeatedly regressed against a polynomial of
that product term of vapor pressures within each stratum.   The
independent variable used in the regressions was either:

     1)   the product term  (i.e., the average vapor pressures
          times the  difference of the vapor pressures) or

     2)   both the square and the cube of that product term  (to
          allow for  expected non-linearity).

Therefore, in each of those 12 strata, we generated both nonlinear
(i.e.,  quadratic and cubic)  models and a linear model.  A two step
process was used to choose among those three models:

     1)   We  performed a visual  inspection of the data.   (This
          approach,  in and of itself, is not very precise, but we
          wanted to  make certain that the model selected would be
          both reasonable and accurately represent the test data.)

     2)   We  compared the statistical parameters associated with
          each of those regressions.   (That is, we identified the
          model that optimized:  the  F-ratio, the statistical
          significance of the independent variable, and the R-
          squared value.)

     In all but two  (2)  of the strata, the data strongly suggest a
non-linear relationship (usually cubic)  between the diurnal
emissions and that product term.   Those two strata in which the
diurnal emissions are a linear function of that product term are
the 1980-85 model year vehicles  (both FI and carbureted) that
failed the pressure test.   In two of the strata in which non-
linear curve fits were superior to the linear,  the quadratic was a
slightly better fit than the cubic,  but we elected to use the
cubic to be consistent with the form of the majority of the non-
linear regression equations.  (Those two strata were the 1980-85
and 1986 and newer FI vehicles that failed the purge test but
passed the pressure test.)

     Additionally, the regressions within several of the strata
produced mediocre correlations,  resulting in our decision to merge
some of the strata.

       •  The four (4) pre-carbureted vehicles were combined into a
         single stratum.   For those data,  both the second and
         third degree polynomials were each better fits than the

-------
                                -29-
         linear.  Although the quadratic was a slightly better fit
         than the cubic, we elected to use the cubic to be
         consistent with the form of the majority of the
         regression equations.

       •  The tests on the single 1980-85 FI vehicle the passed
         both the purge and pressure tests were combined with the
         tests on the three 1980-85 FI vehicles the failed the
         purge test but passed the pressure test into a single
         stratum.  The cubic equation that modeled this stratum
         was used only for the stratum of 1980-85 FI vehicles the
         passed both the purge and pressure tests.

     Once the coefficient values of the equation were determined
for each stratum, we then transformed the constant term (for each
stratum)  to minimize the sum of the differences between the
predicted and calculated diurnal emissions.  The resulting
equations are given in Appendix D.


10.0   Gross  Liquid  Leakers

     Three issues related to vehicles with gross liquid leaks need
to be addressed:

     1)   the frequency of the occurrence of gross liquid leakers
           (possibly as a function of vehicle age),

     2)   the magnitude of the emissions from gross liquid
          leakers, and

     3)   the effects of changes  in vapor pressure on the diurnal
          and resting loss emissions of these gross liquid
          leakers.

Analyses of these issues were hampered by a lack of a substantial
number of identified gross liquid leakers.   However,  we anticipate
receiving additional data.   (CRC recently completed a running loss
testing program in which data on gross liquid leakers were
gathered.)

10.1   Frequency  of  Gross  Liquid  Leakers

     To estimate the frequency of these gross liquid leakers, we
examined data on the seven (7) vehicles in the two studies that
were determined to be gross liquid leakers:

     1)   In the CRC RTD testing program, four  (7.8%) of 51 of the
          1971  to 1977 model year vehicles were gross liquid
          leakers.   (All four of  these vehicles failed both the
          purge and the pressure  tests.  This was the stratum of
          vehicles not recruited  in the EPA program.)

-------
                                -30-
     2)   In the EPA testing program, one of the five non-randomly
          selected 1971 to 1977 model year vehicles was a gross
          liquid leaker.   (That single vehicle was one of three
          that passed the purge test but failed the pressure test.
          The weighting factors  (from Table 4-2) suggest that this
          single vehicle would represent 8.4% of the 1971 to 1977
          model year vehicles.)

     3)   In the CRC testing program, one  (2.0%) of the 50 1980 to
          1985 model year vehicles was a gross liquid leaker.

     4)   In the EPA non-random sample of only 27 1980-85 model
          year vehicles, no gross liquid leaker was identified;
          this is consistent with the 2.0 percent rate in the
          corresponding CRC sample.

     5)   In the EPA testing program, one of the 86  (not randomly
          selected) 1986 to 1995 model year vehicles was a gross
          liquid leaker.   (The weighting factors suggest that this
          single vehicle would represent 0.45% of the 1986 to 1995
          model year vehicles.)

     6)   In the CRC testing program, none of the 50 1986 and
          newer model year vehicles was a gross liquid leaker.
           (This suggests that the true ratio of the gross liquid
          leakers to the other vehicles in this model year group
          is most likely less that 1.34 percent which is not
          inconsistent with the 0.45 percent in the previous
          point.)

Plotting these four estimates of the frequency of gross liquid
leakers versus model year range yields Figure 10-1.   The dotted
line in that figure is an exponential regression (the
corresponding linear regression in log-space has an R-squared of
99.9%).  The curve's formula is the frequency equals the
exponential of 10.4160 minus the product of -0.174475 with the
mid-point model year of the stratum.

-------
                                -31-


                           Figure   10-1

               Frequency  of  Gross  Liquid  Leakers
          10%
        (A
        0)

           8% -h
        (A
        g  6% --
        O

        o  4% -|-

        o
        0)
           2% 4-
           0%
              70
75      80      85

         Model Year
90
95
     Transforming the frequency relationship from a function of
model year into a function of vehicle age yields the following
equation (graphed in Figure 10-2)

         Frequency = exp [-6.159125  +( 0.174475  * V EHICLE_AGE) ]

This formula predicts that for vehicles that are 30 years of age
(i.e.,  well beyond the actual data) 40 percent will be gross
liquid leakers, and that rate would reach 50 percent before the
vehicles reach 32 years of age.  If these predicted rates for
older vehicles turn out to be excessive,  the impact of that excess
will be minimal due to the relatively small number of vehicles
older than 25 years (approximately one percent of the in-use fleet
for LDGV).

     This equation predicts that one-fourth of one percent of
vehicles under the age of one year will be gross liquid leakers;
that percentage slowly climbs to one-half of a percent for five
year old vehicles, and to one percent for nine year old vehicles.
While frequencies of those sizes appear small,  the high emission
levels associated with these vehicles (see Section 10.2)  make them
consequential.

-------
                                -32-


                           Figure  10-2

         Predicted  Frequency  of  Gross  Liquid Leakers
1 */ /O •
in
0)
re
0)
w 10% -
in
0
0
11-
0
> 5% -
0
c
0)
o-
0)
£ 0% J
I ii I ii
I I I !

Js
~ 	 t 	 i 	 t 	 i 	 if 	 "
i I i I ™
I ii ii ii ""
I i I i 	 r
! I ! A
i \ i . "4" 	 i
il i ii ,'-""™ i
I I _ 2^'' I

ii - .— ~1' ' ''" '" ii I
	 .-====!-='. -• 	 :- 	 ' - ' 	 | I |

0 5 10 15 20 25
                           Vehicle Age  (years)
     It is important to note that this model of the frequency of
gross liquid leakers is based on the assumption that modern
technology vehicles will show the same tendency toward leaks as do
the older technology vehicles at the same age.   However,  if the
modern technology vehicles exhibit a lower tendency to leak (due
to the more stringent demands imposed by the new evaporative
emissions certification procedure as well as heightened attention
to safety, e.g.,  fuel tank protection and elimination of fuel line
leaks),  the effect would be to replace the single curve (in
Figures 10-1 and 10-2)  with two or three curves.  That would lower
the predicted rate of such leakers in the current and future in-
use fleets.

10.2  Magnitude  of Emissions  from  Gross Liquid  Leakers

     In Section 10.1, we concluded that the frequency of gross
liquid leakers is a function of vehicle age.  The question as to
whether the magnitude of the emissions are also a function of age
cannot be answered with the available data.
     Seven vehicles  (five in the CRC study and two in the EPA
study)  have been identified as gross liquid leakers.   However,
of the five CRC vehicles exhibited questionable results.
Specifically:
two
     1)   For vehicle number 9111, the RTD test was aborted at the
          sixteenth hour due to the high evaporative emissions.
          CRC used the emissions measured during the first 16

-------
                                -33-
          hours to estimate the emissions during the final eight
          hours.   (Cumulative HC through 16 hours was 616.71 grams
          which was extrapolated to 777.14 for the full 24 hours.)
          Therefore, the calculated resting loss emissions  (i.e.,
          the mean of the untested hours 19 through 24) might be
          in error.  Also, this vehicle exhibited unusually high
          emissions during the first two hours of the test
           (relative to its emissions for the next few hours).
          This might suggest that while the vehicle was in the
          SHED, prior to the test, some gasoline leaked out and
          then evaporated after the test had begun.  These
          additional evaporative emissions  (if they existed) would
          have resulted in a higher RTD result than this vehicle
          would actually have produced.

     2)   Vehicle number 9129 exhibited relatively normal
          emissions for the about the first nine hours of the RTD
          test, after which the hourly emissions quickly rose then
          stabilized at about 11 grams per hour.  This suggests
          that the leak actually developed during the RTD test
           (around the tenth hour).  Therefore, while this
          vehicle's resting losses  (i.e., the mean of hours 19
          through 24) were representative of other gross leakers,
          the calculated diurnal emissions are likely not
          representative of other gross leakers.   (The calculated
          resting loss emissions from this vehicle were 10.77
          grams per hour.  Had that level of emissions simply
          continued for the full 24 hours, the total resting loss
          emissions would have been 258.48 grams compared to the
          181.79 grams actually measured for the entire 24-hour
          RTD test.  Computationally, this would result in a
          substantial negative estimate of diurnal emissions.)

     An additional difficulty is caused by the two vehicles in the
EPA sample not being tested with the same fuel as the five CRC
test vehicles.   However,  since the major mechanism driving the
emissions of these vehicles is the leaks of liquid gasoline,  the
effects of changes in temperature or fuel RVP should be relatively
small  (see Section 10.3).   If we,  therefore,  simply average the
emissions of these two vehicles,  we obtain the following table:
Veh No
5002
5082
RVP
9.0
9.0
Temp Cycle
72.to.96
82. to. 106
Means:
6.3
6.3
9.0
72.to.96
82. to. 106
72.to.96
Means:
RTD
91.09
158.80
124.95
54.80
99.35
87.26
80.47
Hourly RL
1.88
3.81
2.85
1.45
2.88
2.07
2.13

-------
                                -34-
     If we then average the preceding two means with the results
from the five vehicles in the CRC sample, we obtain:
Veh No
9049
9054
9087
9111
9129
5002
5082
Means:
Std Dev:
RTD
181.35
316.59
478.16
777.14
Ignore
124.95
80.47
326.44
263.97
Hourly RL
4.87
10.58
14.12
16.51
10.77
2.85
2.13
8.83
5.63
     and
      •  DIURNAL
     Based on the means in the preceding table, we propose  to use,
in MOBILES, for the category of gross liquid leakers:

       •  DAILY RESTING Loss   =  24  *  HOURLYRESTINGL.OSS
                          =  24  *  8.83
                          =  211.92  (GRAMS / DAY )

                          =  RTD - DAILY RESTING Loss
                          =  326.44 - 211.92
                          =  114.52  (GRAMS/DAY)

     These equations suggest that  the daily evaporative  emissions
associated with gross liquid leakers average about 316 grams per
vehicle.   Thus,  while the occurrence of these gross liquid  leakers
is relatively rare among newer vehicles (Section 10.1),  their
presence has a substantial effect on the total evaporative
emissions.

10.3   Effects  of Vapor  Pressure  Changes  on Gross  Liquid
       Leakers

     Since only two of the seven vehicles  that have been
identified as gross liquid leakers were tested over a  range of
vapor pressures, there are not enough data to relate changes in
diurnal and resting loss emissions to changes in temperature and
fuel RVP.  However, as noted in the preceding section, changes in
temperature and fuel RVP have only minimal (proportional) effects
on the total diurnal and resting loss emissions.  Thus,  until
additional data are available, we will treat the diurnal and
resting loss emissions of the gross liquid leakers as  independent
of temperature and fuel RVP.   This will most likely be the
approach used in MOBILE6.

-------
                                -35-
11.0  On-Going  Analyses

     In Sections 8 and 9, equations were developed that would
estimate diurnal and resting loss emissions (within each of the
strata identified in Section 6.4) based on temperature (or
temperature cycle)  and the fuel RVP.  Those estimates are
reasonable within the range of temperatures and fuel RVPs that
were actually tested.  Still to be determined is how to
extrapolate beyond the limits of those temperature and RVP data.

     In the preceding analyses, three temperature cycles were used
(Appendix I).   While the three starting temperatures were
different  (i.e., 60°, 72°,  and 82°  F) ,  the corresponding hourly
temperature changes were identical.  This yields three parallel
temperature profiles.  This limitation on the variety of
temperature cycles produces the following questions not addressed
in this report:

     1)    Given the  RTD  evaporative emissions of a vehicle on our
          standard cycle, how can  the vehicle's daily RTD
          emissions  be estimated over different cycles  (e.g.,
          cycles whose minimum and maximum temperatures vary by
          amounts different  from 24°F)?

     2)    How  are RTD emissions  for periods of less than 24 hours
           (i.e., partial day diurnals) to be estimated?

     3)    How  are RTD emissions  for periods of more than 24 hours
           (i.e., multiple day diurnals) to be estimated?

     We are currently completing analyses that will answer these
questions.  These analyses make use of the hourly RTD emissions
instead of just the total 24-hour results plus the resting loss
portion.  These results will appear in the next report
(M6.RTD.002).

-------
                               -36-
                           Appendix A

                     Temperature Cycles (°F)
Hour
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
---Temperatures
60°-84°F I 72°
60.0 I
60.5 I
63.5 I
68.3 I
73.2 I
77.4 I
81.1 jj
83.1 I
83.8 I
84.0 I
83.5 I
82.1 I
79.7 I
76.6 I
73.5 jj
70.8 I
68.9 I
67.0 I
65.2 I
63.8 I
62.7 I
61.9 I
61.3 jj
60.6 I
60.0 I
Cycling
-96 °F* I
72.0 I
72.5 I
75.5 jj
80.3 I
85.2 I
89.4 I
93.1 I
95.1 I
95.8 I
96.0 I
95.5 jj
94.1 I
91.7 I
88.6 I
85.5 I
82.8 I
80.9 I
79.0 I
77.2 jj
75.8 I
74.7 I
73.9 I
73.3 I
72.6 I
72.0 I
Between
82 °-1 06 °F
82.0
82.5
85.5
90.3
95.2
99.4
103.1
105.1
105.8
106.0
105.5
104.1
101.7
98.6
95.5
92.8
90.9
89.0
87.2
85.8
84.7
83.9
83.3
82.6
82.0
• Change in
Temperature
—
0.5
3.0
4.8
4.9
4.2
3.7
2.0
0.7
0.2
-0.5
-1.4
-2.4
-3.1
-3.1
-2.7
-1.9
-1.9
-1.8
-1.4
-1.1
-0.8
-0.6
-0.7
-0.6
    The temperature  versus  time values  for the 72-to-96 cycle are
    reproduced from Table  1  of Appendix II of 40CFR86.
These three temperature cycles  are  parallel  (i.e.,  identical
hourly increases/decreases).  The temperatures peak at hour nine.
The most rapid increase in temperatures  occurs during the  fourth
hour (i.e., a 4.9° F rise).
For cycles in excess of 24  hours,  the  pattern  is  repeated.

-------
                                -37-
                            Appendix B

                          Vapor Pressure
Using   the  Clausius-Clapeyron  Relationship

     The Clausius-Clapeyron  relationship  is  a reasonable estimate
of vapor pressure over the moderate  temperature  range (i.e.,  60°
to 106°F)  being considered for adjusting  the  diurnal  emissions.*
This relationship assumes that the logarithm  of  the vapor pressure
is a linear function of the  (absolute)  temperature.

     In a previous EPA work  assignment, similar  RVP  fuels were
tested, and their vapor pressures  (in kilo Pascals) at  three
temperatures were measured.  The results  of  those  tests  are given
in the following table:
Nominal
RVP
7.0
9.0
Measured
RVP
7.1
8.7
Vapor Pressure (kPa)
75° F
30.7
38.2
100 ° F
49.3
60.1
130 ° F
80.3
96.5
Plotting these six vapor pressures  (using  a  logarithm  scale  for
the vapor pressure) yields the graph  (Figure B-l)  on the  following
page.

For each of those two RVP fuels, the  Clausius-Clapeyron
relationship estimates that, for temperature in  degrees Kelvin,
the vapor pressure  (VP) in kPa will be:

     Ln(VP) = A +  (B / Absolute Temperature),  where:
                   RVP
                    8.7
                    7.1
13.5791
13.7338
               B
-2950.47
-3060.95
   C. Lindhjem and D. Korotney, "Running Loss Emissions from Gasoline-Fueled
   Motor Vehicles",  SAE Paper 931991,  1993.

-------
                                -38-


                            Figure  B-l

         Comparison  of Vapor  Pressure  to  Temperature
         100
       re
       Q.
       £
       3
       (A
       (A
       0)
       O
       Q.
       re
          1 0
- - * -  RVP 8.7

   A    RVP 7.1
           0.0030     0.0031     0.0032    0.0033

                       Reciprocal  of Temp  (1/ °K)
                                    0.0034
Extrapolating the trends in either  the  "A"  or "B"  values to fuels
with nominal RVPs of 6.3,  7.0,  and  9.0  psi;  and then requiring the
lines  (in log-space) to pass  through  the  appropriate pressures at
100°F,  yields the linear equations  with coefficients:
                   RVP
                    6.3
                    6.8
                    9.0
                           B
             13.810
             13.773
             13.554
-3121.05
-3085.79
-2930.67
We will use the above to estimate  vapor  pressures for the 6.3,
6.8, and 9.0 psi RVP fuels.

-------
               -39-
            Appendix C

Mean Evaporative Emissions by Strata
    By Vapor Pressure Products
Strata
Pre-1980 Carbureted
Fail Purge/
Fail Pressure
Pre-1980 Carbureted
Fail Purge/
Pass Pressure

Pre-1980 Carbureted
Pass Purge/
Fail Pressure
Pre-1980 Carbureted
Pass Purge/
Pass Pressure



1980-85 Carbureted
Fail Purge/
Fail Pressure
1980-85 Carbureted
Fail Purge/
Pass Pressure
1980-85 Carbureted
Pass Purge/
Fail Pressure
Fuel
RVP
6.8
6.8
6.8
9.0
6.8
9.0
9.0
6.8
6.3
6.8
9.0
6.3
6.8
9.0
9.0
6.8
6.8
9.0
6.8
9.0
9.0
6.8
6.8
6.3
6.8
9.0
6.3
6.8
9.0
9.0
6.8
6.3
6.8
9.0
6.3
6.8
9.0
9.0
Temp.
Cvcle
72. TO. 96
60. TO. 84
72. TO. 96
60. TO. 84
82. TO. 106
72. TO. 96
82. TO. 106
60. TO. 84
72. TO. 96
72. TO. 96
60. TO. 84
82. TO. 106
82. TO. 106
72. TO. 96
82. TO. 106
60. TO. 84
72. TO. 96
60. TO. 84
82. TO. 106
72. TO. 96
82. TO. 106
72. TO. 96
60. TO. 84
72. TO. 96
72. TO. 96
60. TO. 84
82. TO. 106
82. TO. 106
72. TO. 96
82. TO. 106
60. TO. 84
72. TO. 96
72. TO. 96
60. TO. 84
82. TO. 106
82. TO. 106
72. TO. 96
82. TO. 106
VP
times
AVP
567.02
374.77
567.02
655.07
789.30
968.66
1323.87
374.77
489.32
567.02
655.07
683.98
789.30
968.66
1323.87
374.77
567.02
655.07
789.30
968.66
1323.87
567.02
374.77
489.32
567.02
655.07
683.98
789.30
968.66
1323.87
374.77
489.32
567.02
655.07
683.98
789.30
968.66
1323.87
Count
13
1
7
1
1
1
1
2
1
20
3
1
2
3
2
1
11
1
1
1
1
1
3
1
11
4
1
3
4
3
2
1
8
3
1
2
3
2
Mean
Mean Resting
Diurnal I Loss
11.883 I 0.452
8.910 | 0.250
12.059 I 0.218
11.129 | 0.307
30.349 I 0.204
36.903 | 0.250
69.219 I 0.259
14.331 | 0.238
13.327 I 0.140
17.747 | 0.103
18.566 I 0.227
19.205 | 0.175
37.705 I 0.174
32.199 | 0.107
64.241 I 0.274
2.972 | 0.167
5.527 I 0.239
10.426 | 0.263
23.714 I 0.293
32.325 | 0.204
98.279 I 0.062
19.643 I 0.265
5.214 I 0.124
11.125 | 0.185
12.981 I 0.163
11.780 | 0.172
10.688 I 0.146
14.731 I 0.169
20.650 I 0.163
50.581 | 0.162
9.855 I 0.121
13.334 I 0.253
12.453 I 0.139
24.050 | 0.127
30.386 I 0.444
25.641 I 0.216
37.239 I 0.276
44.598 | 0.308

-------
                -40-
Mean Evaporative Emissions by Strata
By Vapor Pressure Products (continued)


Strata
1980-85 Carbureted
Pass Purge/
Pass Pressure





1986+ Carbureted
Fail Purge/
Fail Pressure
1986+ Carbureted
Fail Purge/
Pass Pressure

1986+ Carbureted
Pass Purge/
Fail Pressure

1986+ Carbureted
Pass Purge/
Pass Pressure

1980-85 Fuel Injected
Fail Purge/
Fail Pressure
1980-85 Fuel Injected
Fail Purge/
Pass Pressure



1980-85 Fuel Injected
Pass Purge/
Fail Pressure



1980-85 Fuel Injected
Pass Purge/
Pass Pressure




Fuel
RVP
6.8
	 §T§ 	
	 §T§ 	
	 ITo 	
	 §73 	
	 §7§ 	
	 ITo 	
	 ITo 	
N/A


6.8
	 ITo 	
	 §7§ 	
	 ITo 	
6.8
	 ITo 	
	 §7§ 	
	 ITo 	
6.8
	 ITo 	
	 §7§ 	
	 ITo 	
N/A


6.8
	 §7§ 	
	 iTo 	
	 §T§ 	
	 ITo 	
	 iTo 	
6.8
	 §T§ 	
	 ITo 	
	 §T§ 	
	 ITo 	
	 ITo 	
6.8
	 §T§ 	
	 ITo 	
	 §T§ 	
	 ITo 	
	 ITo 	

Temp.
Cycle
60. TO. 84
	 72"foTl6
_____

,,,,___ 	
	 §2TfoTl"06 	
	 82TfoT'l"06
_____

,,,,____ 	
N/A


72. TO. 96
	 eoTfoT§4 	
	 giTfoTT'oI 	
	 72"fo7l6 	
72. TO. 96
	 eoTfoT§4 	
	 giTfoTT'oI 	
	 72"fo7l6 	
72. TO. 96
	 eoTfoT§4 	
	 giTfoTT'oI 	
	 72"fo7l6 	
N/A


60. TO. 84
	 72"foTl6 	
	 eoTfoT§4 	
	 giTfoTT'oI 	
	 72"fo7l6 	
	 giTfoTT'oI 	
60. TO. 84
	 72"foTl6 	
	 eoTfoT§4 	
	 giTfoTT'oI 	
	 72"fo7l6 	
	 giTfoTT'oI 	
60. TO. 84
	 72"foTl6 	
	 eoTfoT§4 	
	 giTfoTT'oI 	
	 72"7fSTl6 	
	 giTfoTT'oI 	
VP
times
AVP
374.77
489.32
567.02
655.07
683.18
789.30
168.66
1323.87
N/A


567.02
655.07
789.30
168.66
567.02
655.07
789.30
168.66
567.02
655.07
789.30
168.66
N/A


374.77
567.02
655.07
789.30
168.66
1323.87
374.77
567.02
655.07
789.30
168.66
1323.87
374.77
567.02
655.07
789.30
168.66
1323.87


1 Count
! 3
! 	 § 	
f 	 38 	 '
! 	 7 	
f 	 3 	
! 	 4 	
f 	 7 	 '
! 	 3 	
1 °


1 1
f 	 1 	
! 	 i 	
f 	 i 	
1 2
f 	 2 	
! 	 2 	
f 	 2 	
I 10
f 	 1 	
! 	 i 	
f 	 i 	
1 °


! 3
! 	 § 	
| 	 4 	
! 	 3 	
| 	 4 	
! 	 4 	
! 2
! 	 § 	
| 	 2 	
! 	 2 	
| 	 2 	
! 	 2 	
! 1
! 	 4 	
| 	 2 	
! 	 2 	
| 	 2 	
! 	 i 	

Mean
Diurnal
3.399
	 I'oTIII 	
	 5TI40 	
	 7"036 	
	 17"060 	
ToToIe
	 l"5"4l'8 	
	 35"§8"§ 	
N/A


7.302
ToTooo
	 2"l"Tl"82 	
	 l"3"337 	
9.058
	 l"l""767 	
	 17"§50 	
	 17"248 	
5.447
	 §"747 	
	 57644 	
	 57144 	
N/A


3.946
	 7T474 	
	 47782 	
	 ITT'TI 	
	 §T088 	
	 2l"T845 	
11.777
	 1l"331 	
	 l"§"5§9 	
	 27T554 	
	 2lTI'30 	
	 40"287 	
1.212
	 5T370 	
	 l'T622 	
	 §7221 	
	 4.353 	
	 T"i.7ii 	
Mean
Resting
Loss
0.065
	 oTTI'i 	
	 o"Ti"o7 	
	 oTl°47 	
	 oTiTo 	
	 oTT'i'I 	
	 o"Ti"l4 	
	 (1274 	
N/A


0.100
o"Tol7
	 oT'l"55
0"T148
0.233
	 0"T342
	 oT'l"24
67308
0.138
6UI2
oTl02
0°075
N/A


0.010
oTo 1 1
0°045
oTbli
0°086
	 oT'l"23
0.198
oTIoe
6"Tl84
oTIoo
	 0°231
	 b"252
0.296
oToso
	 bTl°57
	 0~2 1 8
	 0°227
b"348

-------
                -41-
Mean Evaporative Emissions by Strata
By Vapor Pressure Products (continued)


Strata
1986+ Fuel Injected
Fail Purge/
Fail Pressure
1986+ Fuel Injected
Fail Purge/
Pass Pressure






1986+ Fuel Injected
Pass Purge/
Fail Pressure






1986+ Fuel Injected
Pass Purge/
Pass Pressure







Fuel
RVP
N/A


6.3
6.8
6.3
6.8
9.0
6.3
6.8
9.0
9.0
6.3
6.8
6.3
6.8
9.0
6.3
6.8
9.0
9.0
6.3
6.8
6.3
6.8
9.0
6.3
6.8
9.0
9.0

Temp.
Cycle
N/A


60. TO. 84
60. TO. 84
72. TO. 96
72. TO. 96
60. TO. 84
82. TO. 106
82. TO. 106
72. TO. 96
82. TO. 106
60. TO. 84
60. TO. 84
72. TO. 96
72. TO. 96
60. TO. 84
82. TO. 106
82. TO. 106
72. TO. 96
82. TO. 106
60. TO. 84
60. TO. 84
72. TO. 96
72. TO. 96
60. TO. 84
82. TO. 106
82. TO. 106
72. TO. 96
82. TO. 106
VP
times
AVP
N/A


321.73
374.77
489.32
567.02
655.07
683.98
789.30
968.66
1323.87
321.73
374.77
489.32
567.02
655.07
683.98
789.30
968.66
1323.87
321.73
374.77
489.32
567.02
655.07
683.98
789.30
968.66
1323.87


I Count
0


! 3
! 12
I 5
! 18
I 17
! 5
I 15
! 17
! 12
I 1
I 12
! 4
I 19
! 19
I 4
! 16
I 19
! 12
! 2
! 16
I 6
! 69
I 31
! 6
I 24
! 31
! 21

Mean
Diurnal
N/A


3.372
4.960
5.068
6.698
6.464
8.524
11.624
9.508
20.457
3.740
4.919
8.763
5.470
6.519
11.364
11.457
11.656
27.014
0.622
0.524
1.077
4.725
1.042
1.654
2.579
1.889
8.782
Mean
Resting
Loss
N/A


-0.009
0.011
0.024
0.060
0.034
0.064
0.073
0.056
0.087
0.037
0.042
0.038
0.094
0.053
0.088
0.110
0.114
0.129
-0.001
0.027
0.032
0.062
0.034
0.049
0.073
0.064
0.123

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                       -42-
                   Appendix D



Regression Curves of Diurnal  Emissions for All Strata
Strata
Pre-80 Carb F/F
F/P
P/F
PIP
80-85 Carb F/F
F/P
P/F
PIP
86-95 Carb F/F
F/P
P/F
P/P
Pre-80 Fl F/F
F/P
P/F
P/P
80-85 Fl F/F
F/P
P/F
P/P
86-95 Fl F/F
F/P
P/F
P/P
Constant
6.995852
8.167144
12.162899
47127629
-1.589121
6.872729
-4.323279
3.812881
-1.589121
2T8T8923
-16.520726
0.224599
6.995852
8TT67144
T27T62899
4.127629
-2.524013
4.241510
-2.524013
1.843499
4.396049
5.676831
4.396049
1.773854
Coefficient of
VP * AVP



0.037445

0.037445

0.037445
0.037445



0.032554

0.032554





Coefficient of
(VP * AVP)A3
0.026810
0.026810
0.026810
07026810

0.018974

0.014217
67018974

0.014217
0.026810
07026810
67026810
0.026810

0.006868

0.004744
0.009876
0.005993
0.009876
0.002850

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