United States        Air and Radiation      EPA420-R-01-012
            Environmental Protection                April 2001
            Agency                      M6.FLT.004
vvEPA     Soak Length Activity
            Factors for Hot Soak
            Emissions
                                   > Printed on Recycled Paper

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                                                                           EPA420-R-01-012
                                                                                 April 2001
                                             for

                                M6.FLT.004
                                Edward L. Glover
                                David J. Brzezinski

                         Assessment and Standards Division
                       Office of Transportation and Air Quality
                       U.S. Environmental Protection Agency
                                    NOTICE

    This technical report does not necessarily represent final EPA. decisions or positions.
It is intended to present technical analysis of issues using data which are currently available.
         The purpose in the release of such 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.

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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  MOBILES.  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 are documented
in MOBILE6 documents (M6FLT003, M6FLT005, and M6FLT006).
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
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,

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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:OOAM 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
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."

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Table 1
Hourly Ranges
Nominal Name
1
2
3
4
5
6
7
8
9
10
11
12
13
14-24
Military Time Range
6-7
7-8
8-9
9- 10
10- 11
11 - 12
12- 13
13- 14
14- 15
15- 16
16- 17
17- 18
18- 19
19 -24 and 24 -5
Time
6 am to 7 am
7 am to 8 am
8 am to 9 am
9 am to 10 am
10 am to 11 am
1 1 am to noon
noon to 1 pm
1 pm to 2 pm
2 pm to 3 pm
3 pm to 4 pm
4 pm to 5 pm
5 pm to 6 pm
6 pm to 7 pm
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.

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       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 Vehicle-Day

       The first necessary parameters in the model are the estimates for Hot Soaks/vehicle-
day. The starting point for this calculation are the trips/vehicle-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
database.  There is one estimate for each combination of car  versus truck and weekday
versus weekend.

       To calculate the number of hot soaks per vehicle 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 vehicle  from 7.28
trips/vehicle-day to 5.38 hs/vehicle-day.  The average number of hot soaks/vehicle-day are
shown in Table 2b.
Table 2a
Trips per Vehicle per Day
Cars
Weekday
7.28
Weekend
5.41
Trucks
Weekday
8.06
Weekend
5.68

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Table 2b
Hot Soaks per Vehicle per Day
Cars
Weekday
Reduction = 26.1%
5.38
Weekend
Reduction = 28.6%
3.86
Trucks
Weekday
Reduction = 26.1%
5.96
Weekend
Reduction = 28.6%
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
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

M6 Hour Index
1
2
3
4
5
6
7
8
9
10
Weekday
2.33
6.05
6.30
4.62
5.08
6.32
7.80
7.32
7.87
8.63
Dercent)
Weekend
0.99
2.26
3.38
6.41
6.98
8.80
9.23
7.40
8.10
6.62

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11
12
13
14-24
8.71
7.99
5.88
15.10
8.03
6.91
6.27
18.62
3.6    Hot Soak Length Distribution by Hourly Group

       Hot soaks are often interrupted by the beginning of a new trip. As a result, not all
hot soaks last the full hour. The distribution of the lengths of hot soaks can be obtained
from the instrumented vehicle data.

       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
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
bl - b2 * exp( -b3 * Soaklength"4)
Eqn 1
where bl, 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 (bl, b2, b3, and b4) and r-
squared values for each of the 28 hourly and weekday/weekend groups.  Figure  la 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

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generally typical of the fit of the other 27 hourly/week groups.
       501
      401

     03
     O
     (/) 30
       20'
     0
     0-  0
         Fig 1a -  Hot Soak  Distribution

         7AM to SAM Weekdays
Predicted Values

HOTSK_MIN


HOUR7

HOTSK MIN
         0     10     20      30     40     50      60



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

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Table 4a
Weekdays
Hot Soak Length Distribution Coefficients bv Hourly Group

Hourly
Index
1
2
3
4
5
6
7
8
9
10
11
12
13
14-24
Coefficient
Bl
1143.5
1749.6
2483.7
3212.9
4010.7
2985.7
3208.4
4042.0
3066.0
3207.6
2957.4
2435.8
2096.7
1906.5
Coefficient
B2
20.261
24.655
29.051
32.712
36.230
31.546
32.605
36.357
31.957
32.627
31.546
28.726
26.827
25.712
Coefficient
B3
-4.028
-4.259
-4.449
-4.589
-4.709
-4.552
-4.590
-4.714
-4.565
-4.590
-4.549
-4.440
-4.361
-4.306
Coefficient
B4
-0.001095
-0.001225
-0.000981
-0.001003
-0.000929
-0.001310
-0.001202
-0.009702
-0.001189
-0.001167
-0.001149
-0.001239
-0.001445
-0.000900
R- squared
Value
0.947
0.990
0.981
0.971
0.955
0.988
0.985
0.964
0.987
0.987
0.977
0.995
0.969
0.977

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Table 4b
Weekends
Hot Soak Length Distribution Coefficients bv Hourly Group

Hourly
Index
1
2
3
4
5
6
7
8
9
10
11
12
13
14-24
Coefficient
Bl
46.80
55.31
2732.31
2208.97
2706.57
2432.70
1824.07
1930.61
2424.95
1921.98
2129.29
1292.06
178.02
520.28
Coefficient
B2
47.35
0.0000633
0.1819
0.1645
0.1784
0.1674
0.1564
0.1506
0.1761
0.1496
0.1602
0.1333
0.0327
0.0902
Coefficient
B3
0.401
-13.695
-9.620
-9.507
-9.631
-9.591
-9.364
-9.464
-9.531
-9.464
-9.498
-9.183
-8.586
-8.653
Coefficient
B4
0.7685
-0.0325
-0.000651
-0.000750
-0.000628
-0.000862
-0.000857
-0.000904
-0.000692
-0.000861
-0.000819
-0.001161
-0.007661
-0.001729
R- squared
Value
0.935
0.924
0.943
0.978
0.951
0.945
0.972
0.950
0.980
0.922
0.978
0.969
0.957
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

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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-vehicle x 5.08 percent (Table 3) = 0.273 hot soaks/vehicle.
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
WtHS emissions(i) = HS emissions(i) * [HS activity(i+l) - HS activity(i)]       Eqn. 2

Average HS emissions(j) = SUM(WtHS 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 MOBILES.  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.
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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.
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