EPA420-P-99-027

- Draft -

Modeling Hourly Diurnal Emissions

and Interrupted Diurnal Emissions

Based on Real-Time Diurnal Data

Larry C. Landman

Document Number M6.EVP.002

July 1, 1999

U.S. EPA

Assessment and Modeling Division

National Vehicle Fuel and Emissions Laboratory

2000 Traverwood Drive

Ann Arbor, Michigan 48105-2425

734-214-4939 (fax)

mobile@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 form the basis for a final EPA decision,

position or regulatory action.
ABSTRACT

Evaporative emissions due to changes in ambient temperature

are an important source of hydrocarbons. These diurnal emissions

were described as daily averages in an earlier report

(M6.EVP.001). The current report proposes a model for

distributing these emissions among the hours of the day. This

document reports on both the methodology used to analyze data from

real-time diurnal (RTD) tests on 270 vehicles and the results from

those analyses. 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 MOBILE6

should be sent to the attention of Larry Landman. Comments may be

submitted electronically to mobile@epa.gov, or by fax to (734)

214-4939, or by mail to "MOBILE6 Review Comments", US EPA

Assessment and Modeling Division, 2000 Traverwood Drive, 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.

An earlier draft of this document was released and posted on

May 21, 1998 for stakeholder review. Comments were accepted for

sixty (60) days, ending July 18, 1998. In response to those

comments, we made substantial revisions to both our methodology

and to this document.

i
TABLE OF CONTENTS

Page Number

 1.0 Introduction . . . . . . . . . . . . . . . . . . 1

 2.0 Stratifying the Test Fleets . . . . . . . . . . . 3

2.1 Evaluating Untested Strata . . . . . . . . . 4

 3.0 Evaporative Emissions Represented by the RTD . . . . 5

 4.0 Hourly Diurnal Emissions . . . . . . . . . . . . 7

4.1 Characterizing Hourly Diurnal Emissions . . . . 7

4.2 Calculating Hourly Diurnal Emissions . . . . . 11

4.2.1 Carbureted Vehicles . . . . . . . . . . 11

4.2.2 Fuel Injected Vehicles . . . . . . . . 14

4.2.3 Gross Liquid Leakers . . . . . . . . . . 17

4.2.4 Summarizing All Strata . . . . . . . . . 20

 5.0 Interrupted Diurnal . . . . . . . . . . . . . . . 22

5.1 Example of an Interrupted Diurnal . . . . . . 22

5.2 Calculating Emissions of an Interrupted Diurnal 24

 6.0 Assumptions Related to Hourly Emissions . . . . . . 27

6.1 Distribution of Hourly Diurnal Emissions . . . 27

6.2 Assumptions for Interrupted Diurnals . . . . . 27

6.3 Temperature Ranges . . . . . . . . . . . . . 28

6.4 Estimating Vapor Pressure . . . . . . . . . . 29

6.5 Duration of Diurnal Soak Period . . . . . . . 29

ii
TABLE OF CONTENTS (Continued)

Page Number

APPENDICES

 A. Temperature Cycles . . . . . . . . . . . . . . . 31

 B. Vapor Pressure . . . . . . . . . . . . . . . . . 32

 C. Modeling 24-Hour Diurnal Emissions . . . . . . . . 34

 D. Regressions of Hourly Ratio of Diurnal . . . . . . 36

 E. Hourly RTD Emissions of Gross Liquid Leakers . . . . 43

 F. Modeling Hourly Resting Loss Emissions . . . . . . 44

iii
*** DDDD rrrr aaaa ffff tttt ***

Modeling Hourly Diurnal Emissions

and Interrupted Diurnal Emissions

Based on Real-Time Diurnal Data

Report Number M6.EVP.002

Larry C. Landman

U.S. EPA Assessment and Modeling Division

1.0 Introduction

In a recently released draft report,* the Environmental

Protection Agency (EPA) presented a model for estimating resting

loss and diurnal emissions over the course of a full day (i.e., 24

hours). (The diurnal emissions are the pressure-driven

evaporative HC emissions resulting from the daily increase in

temperature, while the resting loss emissions are the evaporative

HC emissions not related to pressure changes.) These estimates

were based on the results of 24-hour real-time diurnal (RTD) tests

during which the ambient temperature cycles over one of three

similar 24-degree Fahrenheit ranges. The three ambient

temperatures cycles used in those RTD tests are illustrated in

Figure 1-1; however, most of the testing was performed using the

72 to 96 degree cycle.** In that previous report, EPA proposed a

method for estimating resting loss and diurnal emissions on a

daily basis. In this report, EPA proposes a method for estimating

resting loss and diurnal emissions on an hourly basis. And then,

using those hourly estimates EPA proposes a method to calculate

the diurnal emissions that are delayed and do not start until

after the daily temperature rise has already begun.

As illustrated in Figure 1-1, these three temperature cycles

are parallel (i.e., have identical hourly increases/decreases).

The temperature profiles used in all of the RTD tests have the

ambient temperature rising gradually from the daily low

temperature to the daily high temperature nine hours later. Over

the course of the remaining 15 hours, the temperature slowly

returns to the daily low temperature. The three hourly

temperature cycles used in this study are given in Appendix A.

The most rapid increase in temperatures occurs during the fourth

________________________________

* Report numbered M6.EVP.001 is entitled "Evaluating Resting Loss and

Diurnal Evaporative Emissions Using RTD Tests."

* * Many of RTD tests were actually performed for periods of more than 24

hours. The results after the 24-hour point are analyzed in M6.EVP.003,

entitled "Evaluating Multiple Day Diurnal Evaporative Emissions Using RTD

Tests."
-2- DRAFT

hour. For RTD tests that exceed 24 hours, the cycle is simply

repeated. (Estimating the effects of alternate temperature

profiles is discussed in Section 6.3.)

Figure 1-1

Temperature Cycles for Real-Time Diurnal (RTD) Testing

Time (hours) 

Temperatures (°F) 

50 °

70 °

90 °

110 °

0 6 12 18 24 

The previous document analyzed RTD test results from 270

vehicles. In this document, we analyze the hourly results from

those same tests. This document reports on both the methodology

used to analyze the data from these RTD tests and the results

obtained from those analyses.

The cumulative hydrocarbon (HC) emissions were measured and

reported hourly. Subtracting successive cumulative results

produces the hourly emissions. However, using the hourly

emissions requires associating a clock time with each test hour.

The RTD test is modeled after a proposal by General Motors (GM).

(GM's proposal is documented in SAE Papers Numbered 891121 and

901110.) The cycle suggested by GM had its minimum temperature

occurring at 5 AM and its maximum temperature at 2 PM. For

MOBILE5, EPA analyzed 20-year averaged hourly temperatures by

month from Pittsburgh on high ozone days. EPA found that the

minimum daily temperature typically occurred between 6 and 7 AM,

while the maximum daily temperature typically occurred between 3

to 5 PM. Obviously, the local temperature curve depends on local

conditions. However, for MOBILE6, EPA proposes to combine the GM

and MOBILE5 time estimates and to assign the daily low temperature

to 6 AM, and the daily high temperature to at 3 PM. Applying this
-3- DRAFT

proposal to the temperature cycles in Appendix A results in having

the time zero correspond with 6 AM.

2.0 Stratifying the Test Fleet

It was necessary to stratify the test fleet for two reasons.

First, different mechanisms are involved in producing the diurnal

emissions for different groups of vehicles, thus, necessitating

different analytical approaches. Second, the recruitment of test

vehicles was intentionally biased to allow testing a larger number

of vehicles that most likely had problems with their evaporative

control systems. This stratified recruitment resulted in the

necessity of separate analyses within each of the recruitment

strata.

The test data used for these hourly analyses are the same

data used in the aforementioned EPA draft report. The data were

obtained by combining RTD tests performed on 270 vehicles tested

by the Coordinating Research Council (CRC) and EPA in separate

programs. The distribution of the fleet is given in Table 2-1.

Table 2-1

Distribution of Test Vehicles

Vehicle Type Program Cars Trucks

Pre-80 Carbureted CRC 38 13

EPA 4 2

80-85 Carbureted CRC 0 47

EPA 13 5

80-85 Fuel Injected CRC 0 3

EPA 9 0

86-95 Carbureted CRC 0 7

EPA 8 0

86-95 Fuel Injected CRC 0 43

EPA 67 11

In that previous draft report, EPA noted that the resting

loss and diurnal emissions from vehicles classified as "gross

liquid leakers" (i.e., vehicles identified as having substantial

leaks of liquid gasoline, as opposed to simply vapor leaks) are

significantly different from those of the remaining vehicles.

Based on that observation, those two groups were analyzed

separately in both reports.

The two testing parameters in the EPA programs that were

found (in M6.EVP.001) to affect the 24-hour RTD test results are:
-4- DRAFT

• the Reid vapor pressure (RVP) of the test fuel and

• the temperature cycle.

Similarly, the two vehicle parameters that were found to affect

the 24-hour RTD test results are:

• the model year range:

1) 1971 through 1979

2) 1980 through 1985

3) 1986 through 1995

• the fuel delivery system:

1) carbureted (Carb) or

2) fuel-injected (FI).

Also, since many of the EPA vehicles were recruited based on the

pass/fail results of two screening tests (i.e., canister purge

measured during a four-minute transient test and pressurizing the

fuel system using the tank lines to the canister), each of those

resulting stratum was further divided into the following three

substrata:

• vehicles that passed both the purge and pressure tests,

• vehicles that failed the purge test, but passed the

pressure test, and

• vehicles that failed the pressure test (including both

the vehicles that passed the purge test as well as those

that failed the purge test).*

This stratification was used in both the analysis of the 24-hour

diurnal emissions and in this current analysis (see Section 4.0).

2.1 Evaluating Untested Strata

As noted in M6.EVP.001, no pre-1980 model year, FI vehicles

were recruited because of the small numbers of those vehicles in

the in-use fleet (i.e., less than three percent).

Since the FI vehicles lack a carburetor bowl, they also lack

the evaporative emissions associated with that. This suggests

that the resting loss and diurnal emissions of the pre-1980 FI

vehicles are likely to be no higher than the corresponding

emissions of the pre-1980 carbureted vehicles. For MOBILE6, EPA

proposes to estimate the RTD emissions of the (untested) pre-1980

FI vehicles with the corresponding emissions of the pre-1980

________________________________

* For only one of the fuel delivery system/model year range groupings (i.e.,

pre-1980 carbureted vehicles) were there sufficient data to distinguish

between the vehicles that failed both the purge and pressure tests and

those that failed only the pressure test. Therefore, these two substrata

were combined into a single ("fail pressure") stratum.
-5- DRAFT

carbureted vehicles. This should be a reasonable assumption since

any actual differences between the emissions of these strata

should be balanced by the relatively small number of these FI

vehicles in the in-use fleet.

3.0 Evaporative Emissions Represented by the RTD Test

As described in M6.EVP.001, the results from the real-time

diurnal (RTD) tests actually measure the combination (sum) of two

types of evaporative emissions:

1) "Resting loss" emissions are always present and related

to the ambient temperature (see Section 7.1 of

M6.EVP.001) as opposed to diurnal emissions which are

related to the rise in ambient temperature.

That report calculated the hourly resting loss emissions

as being the mean of the RTD emissions from hours 19

through 24 at the nominal temperature for hour 24.

2) "Diurnal" emissions are the pressure-driven emissions

resulting from the daily increase in ambient temperature

(Section 7.2 of M6.EVP.001).

The 24-hour diurnal emissions were calculated by first

adjusting the resting loss value for each hour's ambient

temperature, and then subtracting that temperatureadjusted resting loss estimate from the full 24-hour RTD

test results.

A special case of each of these two categories consists of

evaporative emissions from vehicles that have significant leaks of

liquid gasoline. We defined these "gross liquid leakers" as

vehicles with resting loss emissions exceeding two grams per hour.

As stated in Section 2, these "gross liquid leakers" were analyzed

separately from the other vehicles. Alternative definitions of

these "gross liquid leakers" are possible; however, with each such

new definition, a new frequency distribution and mean emission

value would have to be determined.

The following graph (Figure 3-1) is an example of hourly RTD

emissions for vehicles that were not gross liquid leakers. For

this example, we averaged the RTD hourly results from 69 1986-95

model year, FI vehicles that had passed both the pressure and

purge tests. All were tested over the 72° to 96° cycle using a

6.8 RVP gasoline. We then plotted the temperature-adjusted hourly

resting loss and diurnal emissions.
-6- DRAFT

Figure 3-1

An Example of Hourly RTD Emissions

Duration (hours) 

Hourly Emissions (grams) 

0.0

0.2

0.4

0.6

0.8

1.0

1 4 7 10 13 16 19 22 

Diurnal 

Resting Loss 

This example represents the hourly resting loss and diurnal

emissions of the mean of a single stratum. Each combination of

the five parameters discussed in Section 2.0 can produce a

different graph. In the database used for these analyses, there

are:

• five combinations of fuel delivery system and model year

range,

• six combinations of temperature cycle and fuel RVP, and

• three combinations of results of the purge and pressure

tests.

Therefore, using the available data, we could construct 86 graphs

for which there are any data (58 are based on the average of no

more than four RTD tests). EPA chose to consolidate those strata

into the smaller number of groups that were actually used. The

selection of both the categorical variables (used to form the

strata) and the analytical variables is discussed in the following

section.
-7- DRAFT

4.0 Hourly Diurnal Emissions

4.1 Characterizing Hourly Diurnal Emissions by Strata

In Table 4-1 (below), to normalize the hourly diurnal

emissions (which can vary substantially), we divided each hour's

diurnal emissions by the full (i.e., total 24-hour) diurnal

Table 4-1

Distribution of Hourly Diurnal Emissions

Within the Strata Containing at Least 10 Tests

--- Hour During Which ---

Purge /

Total Hourly Reaches

Percent of Full-Day M a x

Pressure

Category

temp

cycle

MYR

Range

Fuel

Meter Cnt RVP 25% 50% 75%

Diurnal

Occur

Fail ONLY Purge 60.TO.84 86-95 FI 1 2 6.8 3.90 5.40 7.38 5

86-95 FI 1 7 9.0 4.16 5.89 7.86 6

72.TO.96 80-85 CARB 1 1 6.8 4.24 6.50 8.83 7

86-95 FI 1 9 6.8 3.52 5.50 7.65 6

86-95 FI 1 7 9.0 4.50 6.35 8.02 7

82.TO.106 86-95 FI 1 6 6.8 3.99 5.74 7.70 6

86-95 FI 1 2 9.0 5.01 6.71 8.58 7

Fail Pressure 60.TO.84 86-95 FI 1 1 6.8 4.06 5.73 7.54 7

86-95 FI 1 9 9.0 4.08 5.60 7.15 6

72.TO.96 Pre-80 CARB 3 3 6.8 4.39 6.28 8.35 6

80-85 CARB 1 0 6.8 4.18 6.04 8.10 6

86-95 FI 2 0 6.8 4.31 6.04 8.09 6

86-95 FI 1 9 9.0 4.37 6.06 7.84 6

82.TO.106 86-95 FI 1 7 6.8 4.26 5.98 7.79 7

86-95 FI 1 2 9.0 4.57 6.29 7.90 7

Passing Both 60.TO.84 86-95 FI 1 6 6.8 4.06 7.10 9.73 8

86-95 FI 3 2 9.0 5.49 7.88 10.36 8

72.TO.96 Pre-80 CARB 1 1 6.8 6.32 8.46 10.85 8

80-85 CARB 3 8 6.8 4.98 7.00 9.19 7

86-95 CARB 1 0 6.8 5.36 7.72 10.10 9

86-95 FI 7 0 6.8 4.62 6.73 8.98 7

86-95 FI 3 1 9.0 6.43 8.36 10.46 8

82.TO.106 86-95 FI 2 5 6.8 4.59 6.97 9.56 7

86-95 FI 2 2 9.0 6.73 8.06 9.72 8
-8- DRAFT

emissions within each of the strata described in Section 3.0.

Twenty-four of those strata were represented by at least ten

tests. Within each of those 24 strata, we estimated (by

interpolation) the time at which the cumulative hourly diurnal

emissions totaled 25, 50, and 75 percent of the full-days diurnal

emission. We also identified the test hour during which the day's

highest (i.e., peak) hourly diurnal emission occurred. No attempt

was made (in Table 4-1) to estimate the overall mean values.

A visual inspection of these results in Table 4-1 suggests

that:

 • These strata do not yield a complete representation of the

various technologies (i.e., not all of the combinations of

fuel delivery systems and model year ranges are present),

specifically:

• • The only strata containing fuel injected vehicles are

exclusively composed of the 1986-95 model year

vehicles.

• • The only strata containing the Pre-1980 or the 1980-85

model year vehicles are exclusively composed of the

carbureted vehicles.

Thus, we cannot treat as independent variables both the

type of fuel delivery system and the model year range.

Therefore, EPA proposes to select the type of fuel delivery

system (i.e., carbureted versus fuel injected) as the

stratifying variable.

• The emissions distribution as indicated by the "four

critical times" (i.e., the number of hours into the tests

that the maximum hourly diurnal emissions occur as well as

the number of hours into the tests necessary for the

cumulative hourly diurnal emissions to total 25, 50, and 75

percent of the full 24-hour diurnal) appear to be effected

by both the temperature cycle and the fuel RVP,

specifically:

• • The higher temperature cycles often correspond (but not

consistently) with a delay in the occurrence of some of

the four critical times in the distributions.

• • For the strata of vehicles that passed the pressure

test (either "Fail ONLY Purge" or "Passing Both"), a

higher fuel RVP corresponds with delaying the

occurrence of all four critical times in the

corresponding distributions.
-9- DRAFT

In the earlier analyses (M6.EVP.001), EPA used the RVP to

estimate the vapor pressure (VP) of the fuel at each point

in the temperature cycle. If we calculate the mean of the

VP at the highest and lowest temperatures, then that

midpoint value incorporates both the temperature cycle and

the fuel RVP. EPA proposes to use that value (in

kiloPascals) as one of the potential variables. (This

variable serves to distinguish among the three temperature

cycles in Appendix A. If RTD testing is performed over

different cycles, then this variable may need to be

modified.)

• There appears to be differences among the three purge /

pressure categories, specifically:

• • As noted above, the four critical times in the

distributions appear to be affected by the fuel RVP in

the strata that passed the pressure test. However, for

the strata of vehicles that failed the pressure test,

those times are fairly insensitive to differences in

fuel RVP.

• • For the strata of vehicles that passed both the purge

and pressure tests, the occurrence of all four critical

times in the corresponding distributions are delayed

(relative to the strata of vehicles the failed only the

purge test).

Based on these observations, EPA proposes to estimate the

hourly diurnal emissions separately for each of the three

purge / pressure categories.

Therefore, EPA proposes to model the hourly diurnal emissions

(as percentages of the full day diurnal):

 • separately for the category of "gross liquid leakers" (see

Section 4.2.3),

 • separately for each of the six combinations of fuel

delivery system (i.e., fuel injected versus carbureted) and

purge / pressure category,

 • using VP to distinguish among the temperature cycles and

the fuel RVP (for vehicles that are not "gross liquid

leakers"), and

 • using variables that describe the change in ambient

temperature (discussed on the following page).

These proposals result in modeling the hourly diurnal emissions

separately within each of the following seven strata:
-10- DRAFT

1) carbureted vehicles (not "gross liquid leakers") that pass

both the purge and pressure tests,

2) carbureted vehicles (not "gross liquid leakers") that fail

the pressure test,

3) carbureted vehicles (not "gross liquid leakers") that fail

only the purge test,

4) FI vehicles (not "gross liquid leakers") that pass both the

purge and pressure tests,

5) FI vehicles (not "gross liquid leakers") that fail the

pressure test,

6) FI vehicles (not "gross liquid leakers") that fail only the

purge test, and

7) the vehicles classified as "gross liquid leakers" (see

Section 4.2.3).

Those seven strata can be illustrated in the following table. The

numbering of the cells within the table (1 through 7) coincides

with both the numbering in the preceding list as well as with the

numbering of the seven equations in Section 4.2.

Passing Both

Purge and

Pressure

Failing the

Pressure

Test

Failing ONLY

the Purge

Test

Gross Liquid

Leakers

Carbureted (1) (2) (3)

Fuel

Injected (4) (5) (6) (7)

As stated in Section 3.0, the diurnal emissions are the

pressure-driven emissions resulting from the daily increase in the

temperature of both the fuel and the vapor. Although the fuel

temperature is not a readily available variable, it does follow

the daily cycle of the ambient temperature. On 80 of the 119

vehicles that EPA tested using the RTD cycles, EPA measured both

the ambient temperature and the fuel tank temperature. We then

shifted the graph of the tank temperatures to minimize the sum of

the squares of the temperature differences. The amounts of those

shifts are the times (in minutes) by which the fuel tank

temperatures lagged behind the corresponding ambient temperatures.

Those shifts are given below:

Lag Time

Ambient Temperature Cycle (minutes)

60 to 84° Cycle 44.4

72 to 96° Cycle 67.0

82 to 106° Cycle 108.4
-11- DRAFT

Since the changes in fuel temperature can lag by one to two hours

behind the corresponding changes in the ambient temperature, EPA

considered the following three variables (and multiplicative

combinations of them to allow for interactions) in modeling the

hourly diurnal emissions:

• the change in ambient temperature during that specific

hour,

• the change in ambient temperature during the previous

hour, and

• the total change in temperature from the start of the

cycle until the start of the previous hour.

Since all three of those temperature terms are actually

differences of temperatures, it was not necessary to convert the

temperature units from Fahrenheit to an absolute temperature. For

the three temperature cycles used, these three temperature

variables are given in Appendix A.

4.2 Calculating Hourly Diurnal Emissions by Strata

EPA proposes to estimate the mean hourly diurnal emissions by

multiplying the full day's diurnal emissions (estimated in the

previous report (M6.EVP.001 and reproduced in Appendix C) by the

hourly percentages predicted in Sections 4.2.1 through 4.2.3 of

this report.

4.2.1 Carbureted Vehicles

As noted in the discussion associated with Table 4-1, within

each of the various strata of carbureted vehicles, the only

combination of temperature cycle and fuel RVP represented by at

least 10 tests was that of the 72 to 96 degree cycle using the 6.8

RVP fuel. That condition persisted even after eliminating the

model year groupings as a stratifying factor. EPA, therefore, had

the option of either performing analyses based on a small number

of carbureted vehicles or applying the results of the analyses of

the FI vehicles directly to the carbureted vehicles. EPA decided

to proceed using the limited test results on carbureted vehicles.

The distribution of the tests is given on the following page in

Table 4-2.
-12- DRAFT

Table 4-2

Distribution of RTD Tests of Carbureted Vehicles

Purge/Pressure

Category 

temperature

 cycle RVP 

Number

of Tests

Fail ONLY Purge 60 to 84 6.8 4

9.0 6

72 to 96 6.8 1 9

9.0 6

82 to 106 6.8 5

9.0 4

Fail Pressure 60 to 84 6.8 4

9.0 8

72 to 96 6.8 4 5

9.0 8

82 to 106 6.8 6

9.0 4

Passing Both 60 to 84 6.8 4

9.0 9

72 to 96 6.8 5 9

9.0 9

82 to 106 6.8 6

9.0 4

EPA chose to use stepwise* linear regressions to identify the

variables that were the most influential in determining the shape

of the hourly diurnal emissions. The mean hourly diurnal

emissions were calculated within each of the 18 sub-stratum

determined by the purge/pressure category, the temperature cycle,

and fuel RVP. The emissions were positive for hours one through

18, and were zero for hours 19 through 24. The emissions for each

hour were divided by the full (i.e., total 24-hour) diurnal

emissions to calculate the percentage (ratio) of the total diurnal

the percentage for hour 19 always zero). Therefore, each

________________________________

* The stepwise regression process first uses the Pearson Product-Moment to

select the independent variable that has the highest correlation with the

"Ratio of Hourly Diurnal." The difference between the best linear estimate

using that variable and that "Ratio of Hourly Diurnal" (i.e., the residuals)

is then compared with the set of remaining variables to identify the

variable having the next highest correlation. This process continues as

long as the "prob" values do not exceed 5%, thus, creating a sequence of

variables in descending order of statistical correlation.
-13- DRAFT

purge/pressure stratum contained 19 hourly percentages for each of

six combinations of temperature cycles and fuel RVP (for a total

of 114 results). Within each purge/pressure stratum, a stepwise

linear regression of those 114 hourly diurnal ratios was performed

to estimate the "Ratio of Hourly Diurnal" as a linear function of the

temperature variables (from page 10) and multiplicative

combinations of them, as well as, multiplicative combinations of

them with the VP term (calculated as the midpoint of the VP at the

highest and lowest temperatures of the day in kiloPascals). The

stepwise regression process produced the following three equations

that predict the ratios of hourly diurnal emissions from

carbureted vehicles:

For Carbureted Vehicles Passing Both Purge and Pressure Tests: ( 1 )

Ratio of Hourly Diurnal = 0.007032

+ 0.000023 * [ ( Midpoint VP ) *

( Change in Ambient During Previous Hr )

( Change in Ambient Prior to Previous Hr ) ]

+ 0.003586 * ( Change Prior to Previous Hr )

- 0.001111 * ( Sqr of Change During Previous Hr )

For Carbureted Vehicles Failing the Pressure Test: ( 2 )

Ratio of Hourly Diurnal = 0.010549

+ 0.001138 * [ ( Change During Previous Hr ) *

( Change in Ambient Prior to Previous Hr ) ]

+ 0.001758 * ( Change Prior to Previous Hr )

+ 0.001765 * ( Sqr of Change During Current Hr )

For Carbureted Vehicles Failing ONLY the Purge Test: ( 3 )

Ratio of Hourly Diurnal = 0.006724

+ 0.000023 * [ ( Midpoint VP ) *

( Change in Ambient During Previous Hr )

( Change in Ambient Prior to Previous Hr ) ]

+ 0.003966 * ( Change Prior to Previous Hr )

- 0.001122 * ( Sqr of Change During Previous Hr )

+ 0.000019 * [ ( Midpoint VP ) *

( Sqr of Change During Current Hr ) ]

- 0.000018 * [ ( Midpoint VP ) *

( Change Prior to Previous Hr ) ]
-14- DRAFT

More details can be found in Appendix D which contains the

regression tables and graphs comparing the actual and predicted

hourly ratios. The solid lines in each of the graphs in Appendix

D are not regression lines; they are unity lines. (That is, if

the predicted values exactly matched the actual values, then the

points of predicted versus actual pairs would exactly lie on those

lines.) EPA proposes to use equations (1) through (3) to predict

the ratios of hourly diurnal emissions of the carbureted vehicles

that were not gross liquid leakers. EPA then proposes to multiply

those percentages by the full (24-hour) diurnals estimated by

using the corresponding equations in Appendix C to obtain the

hourly emissions (in grams of HC).

4.2.2 Strata of FI Vehicles

The distribution of the tests of fuel injected vehicles is

given below in Table 4-3. This table is similar to the previous

table on the distribution of the tests of carbureted vehicles

(Table 4-2).

Table 4-3

Distribution of RTD Tests of FI Vehicles

Purge/Pressure

Category 

temperature

 cycle RVP 

Number

of Tests

Fail ONLY Purge 60 to 84 6.8 1 5

9.0 21

72 to 96 6.8 2 1

9.0 21

82 to 106 6.8 1 8

9.0 16

Fail Pressure 60 to 84 6.8 1 3

9.0 21

72 to 96 6.8 2 3

9.0 21

82 to 106 6.8 1 8

9.0 14

Passing Both 60 to 84 6.8 1 7

9.0 33

72 to 96 6.8 7 3

9.0 33

82 to 106 6.8 2 6

9.0 22
-15- DRAFT

For the strata of fuel injected vehicles, the analytical

approach was similar to that used for the carbureted vehicles.

That is, the mean hourly diurnal emissions were calculated within

each of the 18 sub-stratum determined by the purge/pressure

category, the temperature cycle, and fuel RVP. The emissions were

positive for hours one through 18, and were zero for hours 19

through 24. The percent of the total diurnal emissions

represented by each hour was calculated for hours one through 19

(with the percentage for hour 19 always zero). Therefore, each

purge/pressure stratum contained 19 hourly percentages for each of

six combinations of temperature cycles and fuel RVP (for a total

of 114 results).

Within each of the three purge/pressure strata, a stepwise

linear regression of those 114 hourly diurnal ratios was performed

to estimate the "Ratio of Hourly Diurnal" as a linear function of the

temperature variables (from page 10) and multiplicative

combinations of them, as well as, multiplicative combinations of

them with the VP term (calculated as the midpoint of the VP at the

highest and lowest temperatures of the day in kiloPascals). The

stepwise regression process produced the following three equations

that predict the ratios of hourly diurnal emissions from fuel

injected vehicles:

For Fuel Injected Vehicles Passing Both Purge and Pressure Tests: ( 4 )

Ratio of Hourly Diurnal = 0.008001

+ 0.001961 * ( Change Prior to Previous Hr )

+ 0.000535 * [ ( Change During Previous Hr) *

( Change in Ambient Prior to Previous Hr ) ]

- 0.000060 * [ ( Midpoint VP ) *

( Sqr of Change During Previous Hr ) ]

+ 0.005964 * ( Change During Current Hr )

+ 0.000056 * [ ( Midpoint VP ) *

( Change in Ambient Prior to Previous Hr ) ]
-16- DRAFT

For Fuel Injected Vehicles Failing the Pressure Test: ( 5 )

Ratio of Hourly Diurnal = 0.006515

+ 0.001194 * [ ( Change During Previous Hr ) *

( Change in Ambient Prior to Previous Hr ) ]

+ 0.001963 * ( Change Prior to Previous Hr )

+ 0.001329 * ( Sqr of Change During Current Hr )

+ 0.000574 * ( Sqr of Change During Previous Hr )

For Fuel Injected Vehicles Failing ONLY the Purge Test: ( 6 )

Ratio of Hourly Diurnal = 0.007882

+ 0.000855 * [ ( Change During Previous Hr ) *

( Change in Ambient Prior to Previous Hr ) ]

+ 0.000084 * [ ( Midpoint VP ) *

( Change in Ambient Prior to Previous Hr ) ]

+ 0.006960 * ( Sqr of Change During Current Hr )

- 0.000160 * [ ( Midpoint VP ) *

( Sqr of Change During Current Hr ) ]

- 0.001172 * ( Change Prior to Previous Hr )

+ 0.000118 * [ ( Midpoint VP ) *

( Change in Ambient During Current Hr ) ]

+ 0.000825 * ( Sqr of Change During Previous Hr )

More details can be found in Appendix D which contains the

regression tables and graphs comparing the actual and predicted

hourly ratios. The solid lines in each of the graphs in Appendix

D are unity lines. (That is, if the predicted values exactly

matched the actual values, then the points of predicted versus

actual pairs would exactly lie on those lines.) EPA proposes to

use equations (4) through (6) to predict the ratios of hourly

diurnal emissions of the fuel injected vehicles that were not

gross liquid leakers.

In the observations following Table 4-1, it was noted that

the shape of the hourly distribution curve (i.e., the ratios not

the actual magnitude) for FI vehicles that failed the pressure

test seemed insensitive to changes in the fuel RVP. The

regression in Appendix D confirms that observation. The

regression table indicates that more than 95 percent of the

variability in the hourly diurnal emissions can be explained using

only the variables involving changes in the temperature. (A
-17- DRAFT

similar condition holds true for carbureted vehicles that failed

the pressure test.)

4.2.3 "Gross Liquid Leaker" Vehicles

In the previous report (M6.EVP.001), vehicles classified as

"gross liquid leakers" were analyzed separately from the other

vehicles due to both:

• the large differences in both resting loss and diurnal

emissions, as well as,

• the mechanisms that produce those high emissions.

For these vehicles, the primary source of the evaporative

emissions is the leakage of liquid (as opposed to gaseous) fuel.

Therefore, we would expect the diurnal emissions from these

vehicles to be less sensitive to changes in ambient temperature

than the diurnal emissions from vehicles that do not have

significant leaks of liquid gasoline.

The analyses in Sections 4.2.1 and 4.2.2 were repeated for

the vehicles identified as being gross liquid leakers. The hourly

RTD results for those test vehicles are given in Appendix E.

These tests indicate that several of the higher emitting vehicles

exhibited unusually high emissions during the first one or two

hours of the test (relative to their emissions for the next few

hours). One possible explanation is that during the first two

hours of the RTD test, the analyzer was measuring gasoline vapors

that resulted from leaks that occurred prior to the start of the

test. These additional evaporative emissions (if they existed as

hypothesized) would have resulted in a higher RTD result than this

vehicle would actually have produced in a 24 hour period. In the

last column of Appendix E, we attempt to compensate (as explained

in the footnote in Appendix E) for what appears to be simply an

artifact of the test procedure. The modified RTD evaporative

emissions were then converted to diurnals by assuming that the

hourly resting loss for these vehicles is completely independent

of ambient temperature, subtracting that amount (8.52 grams per

hour which is the average RTD emissions of hours 19 through 24)

from each hour's modified RTD emissions, and then dividing by the

total diurnal to yield the hourly percentages in Table 4-4 on the

following page.
-18- DRAFT

Table 4-4

Distribution of Hourly Diurnal Emissions

of Gross Liquid Leakers

(Hourly Emissions as Percent of 24-Hour Diurnal)

Hour Time of Day Emissions Hour Time of Day Emissions

1 6 - 7 AM 1.82% 1 3 6 - 7 PM 4.53%

2 7 - 8 AM 3.64% 1 4 7 - 8 PM 2.99%

3 8 - 9 AM 7.27% 1 5 8 - 9 PM 1.95%

4 9 - 10 AM 8.63% 1 6 9 - 10 PM 1.73%

5 10 - 11 AM 9.19% 1 7 10 - 11 PM 1.48%

6 11 AM - Noon 9.80% 1 8 11 PM - Midnight 1.28%

7 Noon - 1 PM 9.64% 19 Midnight - 1 AM 0 %

8 1 - 2 PM 9.61% 2 0 1 - 2 AM 0 %

9 2 - 3 PM 7.95% 2 1 2 - 3 AM 0 %

1 0 3 - 4 PM 7.50% 2 2 3 - 4 AM 0 %

1 1 4 - 5 PM 5.89% 2 3 4 - 5 AM 0 %

1 2 5 - 6 PM 5.09% 2 4 5 - 6 AM 0 %

A stepwise linear regression of those hourly diurnal ratios

(for hours 1 through 19) was performed to estimate the "Ratio of

Hourly Diurnal" as a linear function of the temperature variables

(from page 10) and multiplicative combinations of them, as well

as, multiplicative combinations of them with the VP term

(calculated as the midpoint of the VP at the highest and lowest

temperatures of the day in kiloPascals). The stepwise regression

process produced the following equation that predict the ratios of

hourly diurnal emissions from vehicles with gross liquid leaks:

For "Gross Liquid Leaker" Vehicles: ( 7 )

Ratio of Hourly Diurnal = 0.021349

+ 0.010137 * ( Change During Previous Hr )

+ 0.002065 * ( Change Prior to Previous Hr )

More details can be found in Appendix D which contains the

regression table and graph comparing the actual and predicted

hourly ratios. A second graph comparing the actual and predicted

hourly ratios appears in Figure 4-1 in which equation (7) is

plotted as a solid line and the data from Table 4-4 as a bar

chart. Based on those two graphs which depict close matches

between the predicted and actual ratios of hourly diurnal

emissions, EPA proposes to use equation (7) to predict the ratios

of hourly diurnal emissions of the gross liquid leakers.
-19- DRAFT

Figure 4-1

Distribution of Hourly Diurnal Emissions

from "Gross Liquid Leakers"

Duration (hours) 

Hourly Diurnal Emissions 

(Percentage of Daily Diurnal) 

0 %

4 %

8 %

12%

1 4 7 10 13 16

In the earlier report (from Section 10.2 of M6.EVP.001), it

was determined that the mean 24-hour diurnal emissions from "gross

liquid leakers" (for any of the three temperature cycles in

Appendix A and independent of the fuel RVP) was 104.36 grams.

Multiplying the hourly ratios in equation (7) by that value

produces, on the following page, equation (7a) which predicts the

mean hourly diurnal emissions (in grams of HC) for vehicles that

are gross liquid leakers.

For "Gross Liquid Leaker" Vehicles: (7a)

Hourly Diurnal Emissions (grams of HC) =

+ 2.22798

 + 1.057897 * ( Change During Previous Hr )

 + 0.215503 * ( Change Prior to Previous Hr )
-20- DRAFT

In that earlier report, we predicted the full 24-hour diurnal

emissions from vehicles that were not gross liquid leakers for all

temperature cycles in which the hourly changes in temperatures are

proportional to the cycles in Appendix A. Unfortunately, the

corresponding data on the "gross liquid leakers" were limited

(i.e., practically all of the tests were performed using the same

temperature cycle), and we did not make similar predictions for

the gross liquid leakers. However, if we apply equation (7a) to

each hour of any temperature cycle (with the hourly changes in

temperatures proportional to the cycles in Appendix A) and then

add these hourly predictions together, we obtain equation (7b):

 Total 24-Hour Diurnal Emissions (grams) (7b)

= 40.10367 + ( 2.616201 * Diurnal_Temperature _Range )

Where the Diurnal_Temperature_Range is the difference of the daily

high temperature minus the daily low temperature.

Note, equation (7b) predicts a 24-hour total diurnal emission

of 40.10 grams for a day during which the temperatures do not

change. This is not reasonable since diurnal emissions result

from the daily rise in ambient temperatures. Therefore, EPA

proposes to set the 24-hour diurnal equal to zero for a diurnal

temperature range of zero degrees Fahrenheit. For diurnal

temperature ranges between zero and ten degrees Fahrenheit, EPA

proposes to calculate the 24-hour diurnal for gross liquid leakers

as increasing linearly from zero to 66.27 grams (i.e., the value

predicted by the equation for a diurnal temperature range of 10

degrees).

Of the seven regression analyses performed (and displayed in

Appendix D), the simplest equation (in terms both of number of

variables and complexity of the variables) is the equation that

predicts the hourly diurnal emissions of gross liquid leaking

vehicles. This most likely results from the simplicity of the

primary mechanism that produces the emissions for the vehicles in

this stratum (i.e., a significant leakage of liquid fuel).

4.2.4 Summarizing All Strata

Examining the seven stepwise regression analyses in Appendix

D (one for each of the strata identified on page 10), we note that

not every possible variable described on page 11 (along with their

multiplicative combinations) were found to be statistically

significant in one or more of those analyses; only 11 variables

and products of variables were found to be statistically

significant:

 • Delta (change) in previous hour's temperature,

 • Delta (change) in current hour's temperature,
-21- DRAFT

 • Total (change in temperature) prior to previous hour,

 • Square of the delta in previous hour's temperature,

 • Square of the delta in current hour's temperature,

 • Product of the delta in previous hour's temperature times

the total (change in temperature) prior to the previous

hour,

 • Product of the VP times the delta in current hour's

temperature,

 • Product of the VP times the total prior to the previous

hour,

 • Product of the VP times the square of the delta in previous

hour's temperature,

 • Product of the VP times the square of the delta in current

hour's temperature, and

 • Product of the VP times the delta in previous hour's

temperature times the total prior to the previous hour.

On further examination of Appendix D, we note that some of those

variables are statistically significant in most of the strata:

 • The total (change in temperature) prior to the previous

hour, possibly combined with its interaction (i.e.,

product) with the midpoint VP, is statistically significant

in all seven strata.

 • The product of the delta in previous hour's temperature

times the total (change in temperature) prior to the

previous hour, possibly combined with its interaction

(i.e., product) with the midpoint VP, is statistically

significant in the six strata that do not include gross

liquid leakers.

 • The square of the delta in the previous hour's temperature,

possibly combined with its interaction (i.e., product) with

the midpoint VP, is statistically significant in the five

strata that do not include either gross liquid leakers or

carbureted vehicles that failed the pressure test.

 • The square of the delta in the current hour's temperature,

possibly combined with its interaction (i.e., product) with

the midpoint VP, is statistically significant in the four

strata of vehicles that failed either the pressure or the

purge test but which are not gross liquid leakers.

This "universality" of the variable "total (change in temperature)

prior to the previous hour" will be the basis for a critical

assumption in estimating interrupted diurnals (in Section 5.2)
-22- DRAFT

5.0 Interrupted Diurnal

Many vehicles do not actually experience a full (i.e., 24-

hour) diurnal. That is, their soak is interrupted by a trip of

some duration. This results in what this report refers to as an

"interrupted diurnal." The following example illustrates such an

interrupted diurnal.

5.1 Example of an Interrupted Diurnal

For the purpose of this example, we will use the type of

vehicle and conditions in Figure 3-1 (i.e., a 1986-95 model year

FI vehicle that passes both the purge and pressure tests, uses a

6.8 RVP fuel, and experiences a daily temperature profile of the

standard 72° to 96° F cycle from Appendix A). For those

conditions, we will assume the following vehicle activity:

1. The vehicle soaks overnight and into the early morning.

2. Shortly after 9 AM (corresponding to the fourth hour of

the RTD test), the vehicle is driven for 30 minutes.

The vehicle reaches its destination and is parked by

10 AM. (That is, the entire drive takes place during

the fourth hour of the RTD test.)

3. The vehicle remains parked until the following morning.

The resting loss emissions would continue throughout the entire

24-hour period of this example. However, the other types of

evaporative emissions would occur for only limited periods.

1. The first segment of this example (from 6 AM through 9

AM) corresponds to the first three hours of the RTD

test. Therefore, the diurnal emissions are represented

by the first three hours in Figure 3-1.

2. The evaporative emissions associated with the morning

drive are the "running loss" emissions and the

continuing resting loss emissions. Thus, the running

loss emissions replace the diurnal emissions for the

fourth hour (from 9 AM through 10 AM). We will allocate

the entire hour interval (rather than fractional

intervals) to running loss emissions even if the actual

drive is much shorter than one hour. (Since running

loss emissions are calculated as a function of distance,

rather than of time, this approach will not change the

total running loss emissions. Also, since MOBILE6 will

not report emissions for intervals smaller than one

hour, this approach will not change the calculated

emissions.)
-23- DRAFT

3. While the vehicle was being driven, the temperature in

its fuel tank rose by about 20 degrees Fahrenheit*.

After the vehicle stops and until this elevated fuel

temperature drops to become equal to the ambient air

temperature, the vehicle will be experiencing what is

referred to as "hot soak" emissions.

In MOBILE5 (and MOBILE4.1), EPA determined the time

required to stabilize the temperatures was two hours.

Therefore, the hot soak emissions replace the diurnal

emissions for the fifth and sixth hours (from 10 AM

through noon). For calculation purposes, in MOBILE the

entire hot soak emissions will be credited to the first

hour (see reports M6.EVP.004 and M6.FLT.004). Thus, in

this example, from 11 AM to noon, only resting losses

will be calculated.

4. At noon, we assume the fuel temperature has cooled to

the ambient temperature of 93.1° F (from the temperature

profile). The hourly diurnal emission will resume but

in the modified form of an "interrupted diurnal" due to

the effects of the drive on canister loading and fuel

temperature. To modify the hourly diurnal emissions, we

will make the following assumption:

• The pressure that is driving the interrupted diurnal

emissions (starting at noon) results from the fuel

being heated to above the temperature which occurred

at the end of the hot soak (in this example, 93.1°

F). Therefore, had the ambient temperature not

risen above 93.1° F, there would have been no

further diurnal emissions for the remainder of that

day, only resting loss emissions.

• This suggests that the interrupted diurnal emissions

will end once the ambient temperature returns to its

starting point (i.e., 93.1° F in this example).

• From the temperature profile, the ambient

temperature will return to 93.1° at 5:25 PM. We

will assume that after 5:25 PM, there are only

resting loss emissions.

________________________________

* In SAE Paper Number 931991 (referenced in Appendix B), the authors discuss

the increase in tank temperatures as a function of trip duration. The

data presented in that report (in Table 4) suggest that for trips of over

five minutes in duration, fuel tank temperature increases as a function of

the trip duration. A 15 minute trip would be associated (on average) with

an increase in tank temperature of about 12 to 13 degrees Fahrenheit. A

30 minute trip would be associated with an increase in tank temperature of

about 20 degrees Fahrenheit, while a one hour trip would be associated

with an increase in tank temperature of about 30 degrees Fahrenheit.
-24- DRAFT

Therefore, we need to modify the estimated hourly

diurnal emissions so that the modified values are

zero after 6 PM (i.e., from test hour 13 through

24). In the following section (Section 5.2), EPA

proposes a method of modifying the hourly diurnal

emissions following such an interruption to the soak

period.

5.2 Calculating Emissions of an Interrupted Diurnal

Based on the discussions in the preceding sections, EPA

proposes to make the following three key assumptions in estimating

interrupted diurnals:

 • The ambient temperature at the beginning of the interrupted

diurnal (i.e., the end of the hot soak) will be used as the

starting temperature for that interrupted diurnal.

 • In Section 4.2.4, we commented on the "universality" of the

variable "total (change in temperature) prior to the

previous hour." In those analyses of diurnals that were

not interrupted, that variable was calculated by

subtracting the daily low temperature (i.e., the starting

temperature of the full day's diurnal) from the temperature

at the start of the previous hour. EPA proposes for

interrupted diurnals that the daily low temperature in that

subtraction be replaced with that new starting temperature.

 • The estimate of hourly diurnal emissions from that

interrupted diurnal will be modified so that they cease

once the ambient temperature drops below that new starting

temperature.

In the preceding paragraphs, we analyzed one theoretical

situation in which the diurnal emissions (following the morning

drive) resumed at noon when the ambient temperature reached 93.1°F

and, then, continued until the temperatures declined to that

93.1°F (at 5:25 PM). Using the 72° to 96° F temperature cycle

given in Appendix A, we can repeat those calculations for

interrupted diurnals that begin at each hour of the day. Those

results appear in Table 5-1 (on the following page).

While the starting temperatures (the second column in Table

5-1) would vary with the daily temperature cycle, the time at

which each (interrupted) diurnal ends would be unchanged for any

of the three temperature cycles in Appendix A or for any cycle

based on those three. Table 5-1, therefore, provides the time

intervals during which diurnal emissions could occur following an

interruption to the soak period.
-25- DRAFT

Table 5-1

Starting and Ending Times and Temperatures

For Interrupted Diurnals

For the 72° to 96° Fahrenheit Cycle

Diurnal Begins Time

Time Temperature

Diurnal

Ends

Midnight thru

6 AM*

72.0° Midnight* *

 7:00 AM 72.5° Midnight* *

 8:00 AM 75.5° Midnight* *

 9:00 AM 80.3° 10:18PM

10:00 AM 85.2° 8:06PM

11:00 AM 89.4° 6:44PM

Noon 93.1° 5:25PM

 1:00 PM 95.1° 4:17PM

 2:00 PM 95.8° 3:24PM

 3 PM thru

Midnight

N/A*** N/A***

Therefore, EPA will modify the predicted hourly emissions of

full day's diurnals (from equations (1) through (7)) using the

following four-step process:

1.) In each of the seven regression equations (in Sections

4.2.1 through 4.2.3), the variable "Change Prior to Previous

Hr" appears. For an interrupted diurnal, that variable

is calculated by subtracting the temperature at the

start of the interrupted diurnal from the temperature at

the beginning of the previous hour. This step will

produce an estimate of the percent of the full day's

diurnal occurring each hour of the interrupted diurnal.

________________________________

 * In Section 4.2.1, it was noted that diurnal emissions are zero for hours

19 through 24 (i.e., midnight through 6AM). Thus, any diurnal that

begins between midnight and 6AM effectively begins at 6AM, and that

diurnal is actually a full 24-hour diurnal.

 ** In the previous footnote, it was noted that diurnal emissions are zero

after midnight. Thus, even if the ambient temperature has not returned

to the temperature at which the (interrupted) diurnal began, the diurnal

effectively ends by the following midnight.

*** Any interrupted diurnal that begins while the ambient temperatures are

declining (i.e., 3 PM or later) does not exist (has zero emissions).
-26- DRAFT

2.) Those hourly percentages would then be modified so that

any negative estimates would be changed to zero, and any

estimates for hours beyond the "Time Diurnal Ends" column

in Table 5-1 would be replaced by zero.

3.) The total 24-hour diurnal emissions are then predicted

using the regression equations from Appendix C.

4.) Finally, the hourly (interrupted) diurnal emissions are

estimated by multiplying the predicted full 24-hour

diurnal emissions by the individual hourly percentages.

To illustrate the use of this four-step process, we return to

the example in Section 5.1.

 • Both Table 5-1 and the discussion at the end of Section 5.1

indicate that the interrupted diurnal emissions would begin

at noon and continue until 6 PM. For each of those six

hours, we can use Appendix A to construct a table of hourly

temperatures and changes in temperatures. (We will assume

that the changes in temperature prior to noon are zero.)

Those temperature values are given in Table 5-2 on the

following page.

 • Using the changes in temperature in Table 5-2 we use

equation (4) (to estimate hourly emissions from FI vehicles

that pass both the pressure and purge tests) to calculate

the estimated percentages of the full 24-hour diurnal

emissions that occur each hour of this interrupted diurnal.

Those hourly fractions are given (as percentages) in the

seventh column of Table 5-2.

 • For the purpose of that example, we assumed a 1986-95 model

year, FI vehicle that passed both the purge and pressure

tests, that used a 6.8 RVP fuel, and where the daily

temperature profile was the standard 72° to 96° F cycle

from Appendix A. The equation in Appendix C predicts the

full 24-hour diurnal in this case would be 2.55 grams (per

day).

 • Multiplying the predicted full 24-hour diurnal (2.55 grams)

emissions by the six hourly percentages then produces the

estimated hourly emissions (in grams) which appear as the

eighth column of Table 5-2. (The negative value for the

second hour is then rounded up to zero.)
-27- DRAFT

Table 5-2

Example of Calculating Hourly Diurnal Emissions

From an Interrupted Diurnal

Initial Final Change in Change in Change Hourly Hourly

Time Temp Temp Previous Current Prior to Diurnal Diurnal

Of Day (°F) (°F) Hr Temp Hr Temp Previous (pct) (grams)

Noon - 1PM 93.1 95.1 0 2.0 0 0.80% 0.020

1PM - 2PM 95.1 95.8 2.0 0.7 0.0 -0.06% 0.000

2PM - 3PM 95.8 96.0 0.7 0.2 2.0 1.16% 0.030

3PM - 4PM 96.0 95.5 0.2 -0.5 2.7 1.35% 0.034

4PM - 5PM 95.5 94.1 -0.5 -1.4 2.9 1.23% 0.031

5PM - 6PM 94.1 91.7 -1.4 -2.4 2.4 0.66% 0.017

EPA believes that while this approach is not perfect (as

evidenced by the prediction of negative emissions during the

second hour that needed to be rounded up to zero), it does provide

a reasonable estimate of hourly diurnal emissions during an

interrupted diurnal; therefore, EPA proposes to use this method in

MOBILE6.

6.0 Assumptions Related to Hourly Emissions

Several basic assumptions related to estimating hourly

emissions were made in this analysis due to the lack of test data.

6.1 Distribution of Hourly Diurnal Emissions

In Section 4, the key assumption is that once the hourly

diurnal emissions are divided by the full 24-hour diurnal

emissions, the distribution (within each of the seven strata

identified on page 10) of those fractions is a function of the

temperature change variables and the midpoint VP.

As a direct result of that assumption, the hourly diurnal

emissions (in grams) can be predicted by simply multiplying the

estimated full 24-hour diurnal emissions (from Appendix C) by the

fractions calculated in Section 4.2. EPA proposes using those

products to estimate the diurnal emission from each individual

hour.

6.2 Assumptions for Interrupted Diurnals

The discussion of interrupted diurnals (in Sections 5.1 and

5.2) requires a number of assumptions. Three of these assumptions

are stated at the beginning of Section 5.2.
-28- DRAFT

The fourth assumption deals with estimating how much time

must elapse following the driving cycle for the diurnal to resume.

It is an accepted fact that interrupting the diurnal with a trip

will result in a temporary increase in fuel tank temperature. The

time required after the trip for the fuel temperature to return to

(i.e., achieve equilibrium with) the ambient temperature depends

on many factors (e.g., duration of the trip, fuel delivery system,

fuel tank design, fuel tank materials, air flow, etc.). However,

EPA proposes to continue the approach used since MOBILE4.1 of

assuming that exactly two hours is necessary to stabilize the

temperatures. (Also, this approach of rounding off the vehicle

activity periods to whole hours is also consistent with the

vehicle activity data that will be used in MOBILE6.)

6.3 Temperature Ranges

All of the tests used in this analysis were performed using

one of the three temperature cycles in Appendix A. Thus, all of

the resting loss data were measured at only three temperatures

(i.e., 60, 72, and 82 °F). In Appendix F, we present regression

equations (developed in M6.EVP.001) to estimate hourly resting

loss emissions at any temperature. We will limit that potentially

infinite temperature range as we did in the previous version of

MOBILE, specifically:

1) We will assume, for vehicles other than gross liquid leakers,

there are no resting loss emissions when the temperatures are

below or equal to 40°F. (This assumption was used

consistently for all evaporative emissions in MOBILE5.)

For temperatures between 40°F and 50°F, EPA proposes to

interpolate between an hourly resting loss of zero and the

value predicted in Appendix F for 50°F.

2) We will assume, for vehicles other than gross liquid leakers,

that when the ambient temperatures are above 105°F that the

resting loss emissions are the same as those calculated at

105°F.

Since vehicles classified as gross liquid leakers were not handled

separately in MOBILE5, we will now make a new assumption

concerning the resting loss emissions of those vehicles as relates

to temperatures. Specifically:

3) For the vehicles classified as gross liquid leakers, we will

assume the resting loss emissions are completely independent

of temperature, averaging 9.16 grams per hour. (from report

number M6.EVP.009, entitled "Evaporative Emissions of Gross

Liquid Leakers in MOBILE6").

In a similar fashion, the equations developed in this report

to estimate hourly diurnal emissions theoretically could also be
-29- DRAFT

applied to any temperature cycle. EPA proposes to limit those

functions by making the following assumptions:

1) Regardless of the increase in ambient temperatures, there are

no diurnal emissions until the temperature exceeds 40°F.

(This assumption was used consistently for all evaporative

emissions in MOBILE5.)

For a temperature cycle in which the daily low temperature is

below 40°F, EPA proposes to calculate the diurnal emissions

for that day as an interrupted diurnal that begins when the

ambient temperature reaches 40 °F.

2) The 24-hour diurnal emissions will be zero for any

temperature cycle in which the difference between the daily

high and low temperatures (i.e., the "diurnal temperature

range") is no more than zero degrees Fahrenheit. For

temperature cycles in which the diurnal temperature range is

between zero and ten degrees Fahrenheit, the 24-hour diurnal

emissions will be the linear interpolation of the predicted

value for the ten-degree cycle and zero.

6.4 Estimating Vapor Pressure

EPA proposes using the fuel's RVP and the Clausius-Clapeyron

relationship to calculate the fuel's vapor pressure at each

ambient temperature (see Figure B-1). This approach is the

equivalent of attempting to draw a straight line based on only a

single point since RVP is the vapor pressure calculated at a

single temperature (100° F). Since two different fuels could have

the same vapor pressure at a single temperature, it is possible

for two fuels to have the same RVP but different relationships

between the vapor pressure and the temperature. However, the two

vapor pressure curves would yield similar results near the point

where they coincide (i.e., at 100° F). Thus, at temperatures

where ozone exceedences are likely to occur, this assumption

should produce reasonable estimates of diurnal emissions.

6.5 Duration of Diurnal Soak Period

The analyses in this report were based on diurnals of 24

hours or less in length. In the real-world, vehicles could soak

for longer periods of time. Estimating diurnal emissions when the

soak period is a multiple of 24 hours will be analyzed in report

M6.EVP.003. For the purpose of this analysis, a full 24-hour

diurnal takes place between 6 AM and 6 AM of the following day

(with hourly diurnal emissions of zero between midnight and 6 AM).

If a diurnal period extends beyond 6 AM, then the emissions during

the hours beyond 6 AM will be calculated using equations (1)

through (7) (in Sections 4.2.1 through 4.2.3).

EPA's proposal on classifying a diurnal that follows a

diurnal of less than 24 hours is based on EPA's hypothesis of why
-30- DRAFT

a single-day diurnal is different from a multiple-day diurnal.

EPA believes that as the time progresses (during a multiple day

diurnal), the vehicle's evaporative canister becomes more heavily

loaded (with a possible back purge occurring during the night

hours). Therefore, if the first day's interrupted diurnal is

almost equivalent to a full 24-hour diurnal, EPA proposes to treat

the subsequent days as if the first day's diurnal were a complete

(i.e., a full-day) diurnal.

To determine the meaning of an interrupted diurnal being

"almost equivalent" to a full 24-hour diurnal, we applied the

equations (1) through (6) to various combinations of fuel RVP,

temperature cycle, and starting time of an interrupted diurnal.

This analysis determined that:

• Interrupted diurnals that began at 10 AM (i.e., the

start of the fourth hour of the RTD test) exhibited only

about one-third of the emissions of the full 24-hour

diurnal.

• Interrupted diurnals that began at 9 AM (i.e., the start

of the third hour of the RTD test) exhibited only about

one-half of the emissions of the full 24-hour diurnal.

• Interrupted diurnals that began no later than 8 AM

(i.e., at least by the start of the second hour of the

RTD test) exhibited at least 80 percent of the emissions

of the full 24-hour diurnal.

Based on these observations, if a vehicle's first day's incomplete

(i.e., interrupted) diurnal begins no later than 8 AM, EPA proposes

to treat the subsequent days as if the first day's diurnal were a

complete diurnal. Otherwise, we treat the subsequent day as the

first day of the diurnal.
-31- DRAFT

Appendix A

Temperature Cycles (°F)

Temperatures Cycling Between Change in Change in Change

Previous Hr Current Hr Prior to

Hour 60-84°F 72-96°F * 82-106°F Temp (°F) Temp (°F) Previous Hr

0 60.0 72.0 82.0 - - - - - - - - -

1 60.5 72.5 82.5 0.0 0.5 0.0

2 63.5 75.5 85.5 0.5 3.0 0.5

3 68.3 80.3 90.3 3.0 4.8 3.5

4 73.2 85.2 95.2 4.8 4.9 8.3

5 77.4 89.4 99.4 4.9 4.2 13.2

6 81.1 93.1 103.1 4.2 3.7 17.4

7 83.1 95.1 105.1 3.7 2.0 21.1

8 83.8 95.8 105.8 2.0 0.7 23.1

9 84.0 96.0 106.0 0.7 0.2 23.8

10 83.5 95.5 105.5 0.2 -0.5 24.0

11 82.1 94.1 104.1 -0.5 -1.4 23.5

12 79.7 91.7 101.7 -1.4 -2.4 22.1

13 76.6 88.6 98.6 -2.4 -3.1 19.7

14 73.5 85.5 95.5 -3.1 -3.1 16.6

15 70.8 82.8 92.8 -3.1 -2.7 13.5

16 68.9 80.9 90.9 -2.7 -1.9 10.8

17 67.0 79.0 89.0 -1.9 -1.9 8.9

18 65.2 77.2 87.2 -1.9 -1.8 7.0

19 63.8 75.8 85.8 -1.8 -1.4 5.2

20 62.7 74.7 84.7 -1.4 -1.1 3.8

21 61.9 73.9 83.9 -1.1 -0.8 2.7

22 61.3 73.3 83.3 -0.8 -0.6 1.9

23 60.6 72.6 82.6 -0.6 -0.7 1.3

24 60.0 72.0 82.0 -0.7 -0.6 0.6

* The temperature versus time values for the 72-to-96 cycle are

reproduced from Table 1 of Appendix II of 40 CFR 86.

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.
-32- DRAFT

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 reciprocal (absolute) temperature.

In a previous EPA work assignment, fuels with similar Reid

vapor pressures (RVP) were tested, and their vapor pressures (in

kiloPascals) at three temperatures were measured. The results of

those tests are given in the following table:

Nominal Measured Vapor Pressure (kPa)

RVP RVP 75° F 100° F* * 130° F

7.0 7.1 30.7 49.3 80.3

9.0 8.7 38.2 60.1 96.5

** The VPs at 100° F are the fuels' RVPs (in kiloPascals).

Plotting these six vapor pressures (using a logarithm scale for

the vapor pressure) yields the graph (Figure B-1) 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 A B 

8.7 13.5791 -2950.47

7.1 13.7338 -3060.95

________________________________

* C. Lindhjem and D. Korotney, "Running Loss Emissions from Gasoline-Fueled

Motor Vehicles", SAE Paper 931991, 1993.
-33- DRAFT

Figure B-1

Comparison of Vapor Pressure to Temperature

Reciprocal of Temp (1/°K) 

Vapor Pressure (kPa) 

1 0

100

0.0030 0.0031 0.0032 0.0033 0.0034

RVP 8.7

RVP 7.1

We will assume that the specific fuels used in the vehicles that

were tested in this analysis had vapor pressure versus temperature

curves similar to the curves for these to two test fuels.

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 A B 

6.3 13.810 -3121.05

6.8 13.773 -3085.79

9.0 13.554 -2930.67

We will use the above to estimate vapor pressures for the 6.3,

6.8, and 9.0 psi RVP fuels.

In general, given the fuel RVP, we can approximate A and B with

these equations:

B = -3565.2707 + ( 70.5114 * RVP )

and

A = Ln( 6.89286 * RVP ) - ( B / 310.9 )
-34- DRAFT

Appendix C

Modeling 24-Hour Diurnal Emissions

As Functions of Vapor Pressure (kPa) and RVP (psi)

(Reproduced from M6.EVP.001)

In each of the following 18 strata, 24-hour diurnal emissions

are modeled using four constants:

A ,B, C, D. Where,

24-Hour Diurnal (grams) =

= A

+ B * RVP (in psi)

+ C * [(Mean VP) * (Change in VP)]

+ D * [(Mean VP) * (Change in VP)]2 / 1,000

For each of the 9 strata, the four constants used to model

diurnal emissions are given below in the following table.

Within each cell of this table, the four constants are listed

vertically (i.e., with "A" at the top and "D" at the bottom).

Fuel Delivery

Model Year

 Range 

Fail

Pressure

 Test 

Fail Only

Purge Test

Pass Both

Purge and

Pressure

Carbureted 1972-79* -0.29374

-0.62160

0.039905

0

21.94883

-2.23907

0

0.02990

21.13354

-2.42617

0

0.024053

1980-1985 -1.22213

-0.62160

0.039905

0

16.69934

-2.23907

0

0.02990

15.50536

-2.42617

0

0.024053

1986-

1995* *

18.97709

-1.81237

0

0.017098

13.90647

-2.14898

0.021368

0

8.37118

-0.767027

0

0.005934

 * The B, C, and D values are based on 1980-85 carbureted

vehicles.

 ** The B, C, and D values are based on 1986-95 FI vehicles.
-35- DRAFT

Appendix C (Continued)

Modeling 24-Hour Diurnal Emissions

As Functions of Vapor Pressure (kPa) and RVP (psi)

(Reproduced from M6.EVP.001)

In each of the following 18 strata, 24-hour diurnal emissions

are modeled using four constants:

A ,B, C, D. Where,

24-Hour Diurnal (grams) =

= A

+ B * RVP (in psi)

+ C * [(Mean VP) * (Change in VP)]

+ D * [(Mean VP) * (Change in VP)]2 / 1,000

Fuel Delivery

Model Year

 Range 

Fail

Pressure

 Test 

Fail Only

Purge Test

Pass Both

Purge and

Pressure

Fuel Injected 1972-79* -0.29374

-0.62160

0.039905

0

21.94883

-2.23907

0

0.02990

21.13354

-2.42617

0

0.024053

1980-1985 7.11253

-1.25128

0.036373

0

7.48130

-0.701002

0

0.010466

5.62111

-0.701002

0

0.010466

1986-1995 14.19286

-1.81237

0

0.017098

9.93656

-2.14898

0.021368

0

5.85926

-0.767027

0

0.005934

 * The three untested strata of Pre-1980 FI vehicles were

represented using the Pre-1980 model year carbureted

vehicles (which were themselves based on the 1980-85 model

year carbureted vehicles).
-36- DRAFT

Appendix D

Regression of Ratio of Mean Hourly Diurnal Emissions

Carbureted Vehicles Passing Both Purge and Pressure Tests

Dependent variable is: Ratio of Hourly Diurnal

No Selector

R squared = 91.6% R squared (adjusted) = 91.4%

s = 0.0146 with 114 - 4 = 110 degrees of freedom

Source Sum of Squares df Mean Square F-ratio

Regression 0.257692 3 0.085897 400

Residual 0.023597 110 0.000215

Variable Coefficient s.e. of Coeff t-ratio prob

Constant 0.007032 0.0033 2.15 0.0336

VP * Previous

* Total Prior

to Previous

0.000023 0.0000 23.1 < 0.0001

Total Prior to

Previous

0.003586 0.0002 20.7 < 0.0001

Sqr_Delta

Previous

-0.001111 0.0002 -5.01 < 0.0001

Plotting Predicted Versus Actual Values

Predicted Hourly Diurnal (pct) 

Actual Hourly Diurnal (pct) 

0 %

10%

20%

0 % 10% 20%
-37- DRAFT

Appendix D (continued)

Regression of Ratio of Mean Hourly Diurnal Emissions

Carbureted Vehicles Failing the Pressure Test

Dependent variable is: Ratio of Hourly Diurnal

No Selector

R squared = 95.1% R squared (adjusted) = 95.0%

s = 0.0119 with 114 - 4 = 110 degrees of freedom

Source Sum of Squares df Mean Square F-ratio

Regression 0.300208 3 0.100069 710

Residual 0.015505 110 0.000141

Variable Coefficient s.e. of Coeff t-ratio prob

Constant 0.010549 0.0029 3.60 0.0005

Previous *

Total Prior

to Previous

0.001138 0.0000 37.4 < 0.0001

Total Prior to

Previous

0.001758 0.0001 11.8 < 0.0001

Sqr_Delta

Current

0.001765 0.0002 10.4 < 0.0001

Plotting Predicted Versus Actual Values

Predicted Hourly Diurnal (pct) 

Actual Hourly Diurnal (pct) 

0 %

10%

20%

0 % 10% 20%
-38- DRAFT

Appendix D (continued)

Regression of Ratio of Mean Hourly Diurnal Emissions

Carbureted Vehicles Failing ONLY the Purge Test

Dependent variable is: Ratio of Hourly Diurnal

No Selector

R squared = 93.5% R squared (adjusted) = 93.1%

s = 0.0124 with 114 - 6 = 108 degrees of freedom

Source Sum of Squares df Mean Square F-ratio

Regression 0.236796 5 0.047359 308

Residual 0.01659 108 0.000154

Variable Coefficient s.e. of Coeff t-ratio prob

Constant 0.006724 0.0030 2.23 0.0276

VP * Previous

* Total Prior

to Previous

0.000023 0.0000 27.1 < 0.0001

Total Prior to

Previous

0.003966 0.0004 10.1 < 0.0001

Sqr_Delta

Previous

-0.001122 0.0003 -4.05 < 0.0001

VP * Sqr_Delta

Current

0.000019 0.0000 3.14 0.0022

VP * Tot Prior

to Previous

-0.000018 0.0000 -2.24 0.0272

Plotting Predicted Versus Actual Values

Predicted Hourly Diurnal (pct) 

Actual Hourly Diurnal (pct) 

0 %

10%

20%

0 % 10% 20%
-39- DRAFT

Appendix D (continued)

Regression of Ratio of Mean Hourly Diurnal Emissions

FI Vehicles Passing Both Purge and Pressure Tests

Dependent variable is: Ratio of Hourly Diurnal

No Selector

R squared = 85.2% R squared (adjusted) = 84.5%

s = 0.0188 with 114 - 6 = 108 degrees of freedom

Source Sum of Squares df Mean Square F-ratio

Regression 0.220626 5 0.044125 124

Residual 0.03832 108 0.000355

Variable Coefficient s.e. of Coeff t-ratio prob

Constant 0.008001 0.0046 1.75 0.0834

Total Prior to

Previous

0.001961 0.0006 3.33 0.0012

Previous *

Total Prior

to Previous

0.000535 0.0000 5.61 < 0.0001

VP * Sqr_Delta

Previous

-0.000060 0.0000 -8.75 < 0.0001

Delta Current 0.005964 0.0015 4.11 < 0.0001

VP * Tot Prior

to Previous

0.000056 0.0000 4.47 < 0.0001

Plotting Predicted Versus Actual Values

Predicted Hourly Diurnal (pct) 

Actual Hourly Diurnal (pct) 

0 %

10%

20%

0 % 10% 20%
-40- DRAFT

Appendix D (continued)

Regression of Ratio of Mean Hourly Diurnal Emissions

FI Vehicles Failing the Pressure Test

Dependent variable is: Ratio of Hourly Diurnal

No Selector

R squared = 95.9% R squared (adjusted) = 95.7%

s = 0.0118 with 114 - 5 = 109 degrees of freedom

Source Sum of Squares df Mean Square F-ratio

Regression 0.350423 4 0.087606 634

Residual 0.015068 109 0.000138

Variable Coefficient s.e. of Coeff t-ratio prob

Constant 0.006515 0.0029 2.25 0.0267

Previous *

Total Prior

to Previous

0.001194 0.0000 33.9 < 0.0001

Total Prior to

Previous

0.001963 0.0002 12.9 < 0.0001

Sqr_Delta

Current

0.001329 0.0003 5.04 < 0.0001

Sqr_Delta

Previous

0.000574 0.0003 2.03 0.0449

Plotting Predicted Versus Actual Values

Predicted Hourly Diurnal (pct) 

Actual Hourly Diurnal (pct) 

0 %

10%

20%

0 % 10% 20%
-41- DRAFT

Appendix D (continued)

FI Vehicles Failing ONLY the Purge Test

Dependent variable is: Ratio of Hourly Diurnal

No Selector

R squared = 95.6% R squared (adjusted) = 95.3%

s = 0.0120 with 114 - 8 = 106 degrees of freedom

Source Sum of Squares df Mean Square F-ratio

Regression 43.7687 2 21.8844 50.8

Residual 1.29117 3 0.43039

Variable Coefficient s.e. of Coeff t-ratio prob

Constant 0.007882 0.0030 2.66 0.0090

Previous *

Total Prior

to Previous

0.000855 0.0001 7.87 < 0.0001

VP * Tot Prior

to Previous

0.000084 0.0000 8.82 < 0.0001

Sqr_Delta

Current

0.006960 0.0007 10.7 < 0.0001

VP * Sqr_Delta

Current

-0.000160 0.0000 -10.0 < 0.0001

Total Prior to

Previous

-0.001172 0.0004 -2.88 0.0048

VP * Delta

Current

0.000118 0.0000 2.98 0.0036

Sqr_Delta

Previous

0.000825 0.0004 2.06 0.0419

Plotting Predicted Versus Actual Values

Predicted Hourly Diurnal (pct) 

Actual Hourly Diurnal (pct) 

0 %

10%

20%

0 % 10% 20%
-42- DRAFT

Appendix D (continued)

Regression of Ratio of Mean Hourly Diurnal Emissions

"Gross Liquid Leaker" Vehicles

Dependent variable is: Ratio of Hourly Diurnal

No Selector

R squared = 96.2% R squared (adjusted) = 95.7%

s = 0.0070 with 19 - 3 = 16 degrees of freedom

Source Sum of Squares df Mean Square F-ratio

Regression 0.019576 2 0.009788 200

Residual 0.000783 16 0.000049

Variable Coefficient s.e. of Coeff t-ratio prob

Constant 0.021349 0.0032 6.67 ≤ 0.0001

Delta Previous 0.010137 0.0006 16.90 ≤ 0.0001

Total Prior to

Previous

0.002065 0.0002 10.30 ≤ 0.0001

Plotting Predicted Versus Actual Values

Predicted Hourly Diurnal (pct) 

Actual Hourly Diurnal (pct) 

0 %

6 %

12%

0 % 6 % 12%
-43- DRAFT

Appendix E

Hourly Real-Time Diurnal (RTD) Emissions (in grams)

From Six Gross Liquid Leakers

 -------- Vehicle Number --------

Hour 5002 5082 9049 9054 9087 9111 Mean Modified*

1 4.56 2.23 11.88 10.99 27.67 55.95 18.88 10.48

2 4.71 2.41 8.79 11.24 28.50 46.77 17.07 12.45

3 6.12 3.18 10.24 9.78 24.65 44.26 16.37 16.37

4 7.93 4.00 11.74 13.05 25.98 44.32 17.84 17.84

5 9.55 4.63 11.62 14.28 25.06 45.49 18.44 18.44

6 11.29 5.14 11.19 14.69 24.61 47.67 19.10 19.10

7 9.41 5.39 10.99 14.00 25.70 48.07 18.93 18.93

8 9.78 5.11 9.74 16.08 25.22 47.46 18.90 18.90

9 7.14 4.73 9.04 15.05 24.21 42.41 17.10 17.10

1 0 6.06 4.36 8.02 14.06 23.36 43.84 16.62 16.62

1 1 5.35 4.30 7.42 14.85 20.95 36.43 14.88 14.88

1 2 4.18 4.10 6.91 15.53 19.67 33.72 14.02 14.02

1 3 3.66 3.51 6.91 14.93 18.50 32.96 13.41 13.41

1 4 3.08 2.76 6.25 15.03 17.58 25.79 11.75 11.75

1 5 2.89 2.55 5.63 14.60 16.57 21.55 10.63 10.63

1 6 2.83 2.23 5.78 13.93 16.31 21.24 10.39 10.39

1 7 2.97 2.22 5.09 16.37 13.59 20.46 10.12 10.12

1 8 2.76 2.20 4.91 14.65 15.29 19.64 9.91 9.91

1 9 2.91 2.18 4.93 11.54 13.86 17.60 8.84 8.84

2 0 2.82 2.09 4.89 11.30 13.46 16.85 8.57 8.57

2 1 3.01 2.06 4.70 11.12 13.69 16.52 8.52 8.52

2 2 3.06 2.09 5.02 9.89 13.62 15.89 8.26 8.26

2 3 3.01 1.97 4.78 10.36 13.04 15.82 8.16 8.16

2 4 2.96 2.13 4.88 9.28 17.05 16.40 8.78 8.78

________________________________

 * Mean emissions for the first two hours have been

"MODIFIED" (see Section 4.2.3) to fit the following

assumed pattern:

• The diurnal emissions (i.e., RTD minus resting loss

of 8.52) during the first hour were assumed to be

one-half the diurnal emissions during the second

hour.

• The diurnal emissions during the second hour were

assumed to be one-half the diurnal emissions during

the third hour.
-44- DRAFT

Appendix F

Modeling Hourly Resting Loss Emissions

As Functions of Temperature (°F)

In each of the following 12 strata, resting loss emissions (in

grams per hour) are modeled using a pair of numbers (A and B),

where:

 Hourly Resting Loss (grams) = A + ( B * Temperature in °F )

B = 0.002812 (for ALL strata) and

"A" is given in the following table:

Fuel Delivery

Model Year

 Range 

Pass Pressure

 Test 

Fail Pressure

 Test 

Carbureted Pre-1980 0.05530 0.07454

1980-1985 -0.05957 -0.02163

1986-1995 -0.07551 0.05044

Fuel Injected Pre-1980* 0.05530 0.07454

1980-1985 -0.09867 0.02565

1986-1995 -0.14067 -0.10924

 * The untested stratum (Pre-1980 FI vehicles) was represented

using the Pre-1980 model year carbureted vehicles. (See

report M6.EVP.001 for additional details.)

These equations can then be applied (in each stratum) to each of

the hourly temperatures in Appendix A to obtain the resting loss

emissions released in a 24 hour period. If we use an alternate

temperature profile in which the hourly change in temperature is

proportional to the cycles in Appendix A, we find that:

24-Hour Resting Loss (grams) = ( 24 * A ) + ( B * C )

Where A and B are given above, and where

C = 0.002632 + (24 * Low Temperature)

+ (11.3535 * Diurnal_Temperature _Range)

Where the Diurnal_Temperature_Range is the difference of the daily

high temperature minus the daily low temperature.