M6FLT004.WPD DRAFT 1 February 18, 1998

- Draft -

Soak Length Activity Factors for Hot Soak Emissions

Report Number M6.FLT.004

Edward L. Glover

David J. Brzezinski

U.S.EPA Assessment and Modeling Division

1.0 INTRODUCTION

MOBILE6 will compute and report (as a user option) hourly emission factors for

start, running, and evaporative emissions. These outputs will be in addition to the standard

daily emission estimates which are currently calculated by MOBILE5. The hourly

emission factors will allow the MOBILE6 model to provide more precise output that

accounts for the time of day that vehicle emissions occur. The temporal distribution of

emissions is an important factor in the formation of diurnal evaporative and start emissions.

The hourly emission estimates require considerable vehicle activity information and

analysis. The term “activity” refers to the vehicle’s operating mode, such as running,

idling, parked (soaking), etc. The specific activity information needed for emissions

estimates includes soak durations, time of soak, trip lengths, time of trip, and other

information. This document (M6.FLT.004) discusses the issue of vehicle soak time only

as it pertains to hot soak emissions. Other activity estimates needed to develop daily

emission factors for exhaust, diurnal, running loss or resting loss emissions will be

documented in other MOBILE6 documents listed with the report numbers “M6.FLT.XXX”.

2.0 DATA SOURCES USED

The primary data source for this analysis is an EPA instrumented vehicle studies

conducted in Baltimore and Spokane. In this studies, instrumentation to monitor vehicle

usage was installed with the motorists’ permission on 168 randomly selected vehicles while
M6FLT004.WPD DRAFT 2 February 18, 1998

they were tested at an Inspection / Maintenance (I/M) station. The motorists returned one

or two weeks later to have the instrumentation removed. Information from more than

8,500 vehicle-trips was recorded. The raw data collected from the studies were processed

by the Radian Corporation under EPA contract to create a “trip characteristics” file. This

processed file was used to develop the hourly soak time distributions. For more details

regarding the instrumented vehicle study and the data processing, please refer to the

document “Travel Trip Characteristics Analysis” Final Report under EPA Contract 68-C1-

0079 WA 2-05 with Sierra Research. 

3.0 METHODOLOGY

This section describes the basic methodology to develop the soak activity estimates

used to calculate hot soak emissions. The process consisted of several steps. These are

discussed below.

3.1 Definition of a Hot Soak

Hot Soak emissions are evaporative emissions which may be produced by a warm,

but no longer running vehicle. Operationally, hot soak emissions are defined as those

produced for a duration of time following a vehicle trip which lasted a minimum length of

time. This is a general definition. By convention (and assumption) a hot soak duration (the

length of time following the key off) is defined to range from a minimum of 1 second

(instantaneous) to a maximum of 1 hour. The one hour limit was chosen for consistency

with the Federal Test Procedure definition of a hot soak.

The length of time of the trip prior to the hot soak can vary considerably. However,

a minimum trip length of 4 minutes was chosen to qualify the subsequent soak as a valid

hot soak. The choice of 4 minutes was fairly arbitrary; however, it is believed that a trip

of less than 4 minutes will not sufficiently warm the engine or the fuel or over-saturate the

evaporative canister so as to produce sufficient hot soak emissions. Thus, trips less than

four minutes were assumed to produce no hot soaks and are not reflected in the hourly

activity factors for hotsoaks.

3.2 Hourly Intervals

The 24 hour day was divided into 14 different hourly groups. Thirteen of these

groups have a duration of one hour. These start at 6:00AM and run through 7:59:59PM.

The fourteenth hour contains the remaining nighttime hours as one interval. Collapsing

these hours into one group was done for three reasons: (1) the emissions contributed during

the night have a relatively smaller impact on daily ozone or CO formation than those

contributed during the morning or day, (2) there were relatively little data for these time

periods, and (3) what data were available produced results which showed very little hour
M6FLT004.WPD DRAFT 3 February 18, 1998

to hour variance. The hourly intervals are shown in Table 1. In addition to hot soak

activity estimates, they are the same hourly groups used in the calculation of activity

estimates for start emissions, running emissions, running loss emissions, resting loss

emissions, and diurnal emissions.

3.3 Factors Affecting Hot Soak Activity Values

3.3.1 Weekdays Versus Weekends

For a number of the activity parameters a significant difference existed between the

value for the weekday and the value for the weekend. Conceptually this make sense since

most motorists have different usage patterns for their vehicles on weekdays than on

weekends. Differences may also exist for the various days of the week; however, the

database was too small to reliably discern these differences. 

The MOBILE6 model will distinguish between weekend and weekday in terms of

activity and emissions, and a user input will be required to tell the model which one is to

be reported. The default will likely be the “weekday.”

Table 1

Hourly Ranges

Nominal Name Hourly Range Time

6 6 - 7 6 am to 7 am

7 7 - 8 7 am to 8 am

8 8 - 9 8 am to 9 am

9 9 - 10 9 am to 10 am

10 10 - 11 10 am to 11 am

11 11 - 12 11 am to noon

12 12 - 13 noon to 1 pm

13 13 - 14 1 pm to 2 pm

14 14 - 15 2 pm to 3 pm

15 15 - 16 3 pm to 4 pm

16 16 - 17 4 pm to 5 pm
M6FLT004.WPD DRAFT 4 February 18, 1998

17 17 - 18 5 pm to 6 pm

18 18 - 19 6 pm to 7 pm

24 19 - 24 and 24 - 5 7 pm to 6 am

3.3.2 Vehicle Type and Model Year

The hot soak activity parameters such as the number of trips per day, and the

distribution of soak time after the trip end were also investigated by vehicle type or vehicle

age. Slight differences were found between cars and trucks in terms of trips per day, with

trucks having slightly more trips per day (shown in Tables 2a and 2b). However, little

significant difference in the hourly distributions were found between cars and trucks or

even by vehicle model year. The lack of difference in the hourly distributions between cars

and trucks was not particularly surprising since the number of trips per day are fairly

similar, and most light trucks today play virtually the same role as cars. Exceptions might

be in rural areas or heavily industrial areas where trucks frequently are used to haul

equipment or products. 

The lack of difference between model years is a little more surprising. One would

expect an older vehicle to have a higher percentage of longer soaks, and possibly shorter

trips (i.e., the vehicle sits more and goes on fewer long trips because it is a second vehicle).

However, a limited analysis of the data did not conclusively demonstrate these hypotheses.

One reason might be the relatively small sample of older vehicles. For example, less than

15 percent of the vehicle sample were more than 10 years old at the time of the testing.

This was also too small a sub-sample to further split into 28 hourly and weekday/weekend

groups, and still obtain reasonable results. The other reason might be recruitment process

which was biased to obtain vehicles which were primary vehicles rather than spare second

vehicles. As a result, the hourly distributions shown in Tables 3, 4a and 4b represent both

cars and trucks and all vehicle ages. 

Since the default MOBILE6 hourly activity estimates are based exclusively on 168

vehicles, and cannot possibility reflect all geographical areas, times, or other variables, the

user will have the option of providing hot soak activity data into the MOBILE6 model from

an external file. 

3.4 Hot Soaks per Car-Day

The first necessary parameters in the model are the estimates for Hot Soaks/car-day.

The starting point for this calculation are the trips/car-day values shown in Table 2a. This

is a convenient starting point because by definition each hot soak must have a

corresponding trip. Four different estimates were obtained from the instrumented vehicle
M6FLT004.WPD DRAFT 5 February 18, 1998

database. There is one estimate for each combination of car versus truck and weekday

versus weekend.

To calculate the number of hot soaks per car per day, the values shown in Table 2a

were reduced to account for trips which were less than 4 minutes in length. The reduction

is a simple percentage of the total trips which were less than 4 minutes. For weekdays, the

reduction is 26.1 percent and for weekends it is 28.6 percent. For example, this reduces the

average number of weekday trips per day per car from 7.28 trips/car-day to 5.38 hs/car-day.

The average number of hot soaks/car-day are shown in Table 2b.

These estimates are subject to revision pending completion of a thorough analysis

of national trip data by an EPA contractor. The values could potentially vary considerably

from those shown here.

Table 2a

Trips per Car per Day

Cars Trucks

Weekday Weekend Weekday Weekend

7.28 5.41 8.06 5.68

Table 2b

Hot Soaks per Car per Day

Cars Trucks

Weekday Weekend Weekday Weekend

Reduction = 26.1% Reduction = 28.6% Reduction = 26.1% Reduction = 28.6%

5.38 3.86 5.96 4.06

3.5 Daily Hot Soak Distribution by Time of Day Increment

Table 3 contains the distribution of the vehicle hot soaks by time of day. An

estimate is provided for each of the fourteen groups, and separate estimates are provided

for weekends and weekdays. All of the estimates were calculated after removing the hot

soaks which had preceding trip durations less than 4 minutes. For example, Table 3 shows

that approximately 2.33% percent of the weekday hot soaks occur during the period from
M6FLT004.WPD DRAFT 6 February 18, 1998

6:00 AM to 6:59:59 AM. The data which underlies Table 3 were obtained from the

instrumented vehicle database. Each column sums to 100 percent.

Table 3

Daily Distribution of Hot Soaks (in percent)

Hour Weekday Weekend

6 2.33 0.99

7 6.05 2.26

8 6.30 3.38

9 4.62 6.41

10 5.08 6.98

11 6.32 8.80

12 7.80 9.23

13 7.32 7.40

14 7.87 8.10

15 8.63 6.62

16 8.71 8.03

17 7.99 6.91

18 5.88 6.27

24 15.10 18.62

3.6 Hot Soak Length Distribution by Hourly Group

The MOBILE6 model will contain a cumulative soak length distribution for each

of the 14 hourly groups, and for both weekdays and weekends. As a result, there will be

28 cumulative soak length distributions. These 28 distributions are based on data from the

instrumented vehicle study. To make the distributions smoother for use in the MOBILE6

model, a Weibull function fit was generated for each of the 28 soak length distributions

using the non-linear fit algorithms in the statistical software package SPSS. Only the first

59 minutes of the cumulative distribution were fitted. Since the 60 minute (the last minute)

contained all of the soaks which were 60 minutes or greater in length it produced a
Predicted Values

HOTSK_MIN

HOUR7

HOTSK_MIN

Fig 1a - Hot Soak Distribution

7AM to 8AM Weekdays

Hot Soak Length (0-59 Minutes) 60 has remainder

0 10 20 30 40 50 60

Percent of Hot Soaks

50

40

30

20

10

0

M6FLT004.WPD DRAFT 7 February 18, 1998

discontinuous function which jumped up to 100 percent. The 60 minute point will be

accounted for separately in the MOBILE6 model by coding the value of 100 percent for the

60 minute point. Also, in a few cases negative values for the Weibull distribution function

were obtained for short duration soaks (1 or 2 minutes). In these cases, a value of zero will

be assumed. Overall, the Weibull function produced a fairly close fit for all of the 28

distributions. The typical r-squared value was 0.97 or better for weekdays, and 0.92 or

better for weekends. The better fit for the weekdays versus the weekends is the result of

a considerably larger weekday database.

The Weibull function fit is of the form:

Y = b1 - b2 * exp( -b3 * Soaklength ) Eqn 1 b4

where b1, b2, b3 and b4 are regression coefficients, and soaklength in minutes (0 to 59) is

the independent variable. The variable Y is the cumulative distribution in percent.

Tables 4a and 4b lists all of the regression coefficients (b1, b2, b3, and b4) and rsquared values for each of the 28 hourly and weekday/weekend groups. Figure 1a shows

the raw data distribution and the corresponding Weibull fit for the 7 to 8 AM weekday

group. The heavier dots in the figure are the points fitted by the weibull function, the

lighter dots are the actual data points. The 7 to 8 AM function was plotted because it is

generally typical of the fit of the other 27 hourly/week groups.
M6FLT004.WPD DRAFT 8 February 18, 1998

Table 4a

Weekdays

Hot Soak Length Distribution Coefficients by Hourly Group

Hourly Coefficient Coefficient Coefficient Coefficient R-squared

Group B1 B2 B3 B4 Value

6 1143.5 20.261 -4.028 -0.001095 0.947

7 1749.6 24.655 -4.259 -0.001225 0.990

8 2483.7 29.051 -4.449 -0.000981 0.981

9 3212.9 32.712 -4.589 -0.001003 0.971

10 4010.7 36.230 -4.709 -0.000929 0.955

11 2985.7 31.546 -4.552 -0.001310 0.988

12 3208.4 32.605 -4.590 -0.001202 0.985

13 4042.0 36.357 -4.714 -0.009702 0.964

14 3066.0 31.957 -4.565 -0.001189 0.987

15 3207.6 32.627 -4.590 -0.001167 0.987

16 2957.4 31.546 -4.549 -0.001149 0.977

17 2435.8 28.726 -4.440 -0.001239 0.995

18 2096.7 26.827 -4.361 -0.001445 0.969

24 1906.5 25.712 -4.306 -0.000900 0.977
M6FLT004.WPD DRAFT 9 February 18, 1998

Table 4b

Weekends

Hot Soak Length Distribution Coefficients by Hourly Group

Hourly Coefficient Coefficient Coefficient Coefficient R-squared

Group B1 B2 B3 B4 Value

6 51.25 5.911 -18.036 -0.0359 0.935

7 55.31 0.0000633 -13.695 -0.0325 0.924

8 2732.31 0.1819 -9.620 -0.000651 0.943

9 2208.97 0.1645 -9.507 -0.000750 0.978

10 2706.57 0.1784 -9.631 -0.000628 0.951

11 2432.70 0.1674 -9.591 -0.000862 0.945

12 1824.07 0.1564 -9.364 -0.000857 0.972

13 1930.61 0.1506 -9.464 -0.000904 0.950

14 2424.95 0.1761 -9.531 -0.000692 0.980

15 1921.98 0.1496 -9.464 -0.000861 0.922

16 2129.29 0.1602 -9.498 -0.000819 0.978

17 1292.06 0.1333 -9.183 -0.001161 0.969

18 178.02 0.0327 -8.586 -0.007661 0.957

24 520.28 0.0902 -8.653 -0.001729 0.991

3.7 Using the Hourly Hot Soak Activities in MOBILE6

3.7.1 Average Hourly Hot Soak Emissions

The average hourly hot soak emissions will be calculated by multiplying the hot

soak emissions function (discussed in document M6.EVP.003) with the corresponding hot

soak activity function (calculated from the coefficients in Tables 4a and 4b and Eqn. 1), and

summing the products to produce an overall hourly average. This average is then

multiplied by the number of hot soaks per day per vehicle which occur in the given hourly
M6FLT004.WPD DRAFT 10 February 18, 1998

group to produce the average hot soak emission emission level for the given hourly group.

In the MOBILE6 model this is done by multiplying the 60 (one for each minute of the hot

soak) hot soak emission estimates with the 60 activity values (activity distribution at each

one minute point), and summing the result. This calculation will be done separately for

each of the 28 hourly and weekday/weekend groups to produce hourly hot soak emission

estimates. The number of hot soaks per day per vehicle is obtained in Table 2b, and the

factors which determine how many hot soaks to allocate to a particular hourly group is

shown in Table 3. For example, the 10 to 11 AM weekday hourly group for cars would be

allocated 5.38 hot soaks/day-car x 5.08 percent (Table 3) = 0.273 hot soaks/car.

Calculation of the average hourly hot soak is shown mathematically as:

given: HS emissions[soak length] 

HS activity[soak length]

Soak length: i = 1, 59 minutes

Hourly group: j = 1, 28 hourly/weekday-weekend groups 

Wt HS emissions(i) = HS emissions(i) * [HS activity(i+1) - HS activity(i)] Eqn. 2

Average HS emissions(j) = SUM(Wt HS emissions(i)) 

where the range of the SUM(Wt HS emissions(i)) is: i = 1, 59 minutes

Both the activity function (Weibull fit) and the hot soak emissions function are

continuous functions. However, both were turned into discrete functions with 60 intervals

in the MOBILE6 model. This was done for computation purposes, and to allow the

MOBILE6 user to input a set of alternative hot soak activity values in an attached file rather

than a set of different Weibull function parameters.

3.7.2 Average Daily Hot Soak Emissions

An average daily hot soak value will also be calculated in the MOBILE6 model.

This hot soak emission value is analogous to the hot soak emission values reported by

MOBILE4 and MOBILE5. It will be the product of the number of hot soaks per day, and

a weighted average of the individual hourly average hot soaks. The average number of hot

soaks per day are shown in Table 2a. The weighting factors used to weight the hourly

groups together are the values shown in Table 3.
M6FLT004.WPD DRAFT 11 February 18, 1998

COMMENTS

Comments on this report and its proposed use in MOBILE6 should be sent to the attention

of the author, and submitted electronically to mobile@epamail.epa.gov, or by fax to

(313)741-7939, or by mail to MOBILE6 Review Comments, US EPA Assessment and

Modeling Division, 2565 Plymouth Road, Ann Arbor MI 48105. Electronic submission

of comments is preferred, since we will make any comments available on our web site. 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.