EPA-420-P-98-022
            Calculation of Age Distributions in the Nonroad Model:
                              Growth and Scrappage

                                Report No. NR-007
                                   February 19, 1998

                        Nonroad Engine Emissions Modeling Team
                           Assessment and Modeling Division
                           US EPA, Office of Mobile Sources

Introduction

       The NONROAD model calculates nonroad equipment populations by age (i.e., an age
distribution) for given equipment types and scenario years.  This calculation is necessary for the
model to account for a number of factors which affect nonroad emissions over time, including
emissions deterioration, new emissions standards, technology changes, changes in equipment
sales and total equipment population, and scrappage programs.  The NONROAD model
calculates equipment age distributions for the base year (which in the beta version of the model is
1996) based on estimated 1996 engine populations and the scrappage function.  The model
calculates age distributions for future years by stepping through  each year between the base and
future years; for each year, the model projects equipment populations, scrappage for each model
year of equipment still in service, and equipment sales.

       The methods employed for these calculations, the manner in which these methods are
encoded in the NONROAD model, and the default assumptions  and inputs used by the
NONROAD model are described in this report.  The Methodology discussion is divided into
seven sections.  The first section describes the concept of base year populations and its use in
NONROAD.  The second section describes the model's use of population growth rates to project
equipment populations in future years.  The third section describes the methods used by the
model to calculate scrappage. The fourth section describes the method used by NONROAD to
calculate the age distribution in the base year. The fifth section  describes the method used by the
model to calculate annual sales based on  estimated scrappage and projected population growth in
each year.  The sixth section brings the methods presented in earlier sections together to describe
how NONROAD computes the age distribution for all future years. The seventh section
discusses the implications of and potential drawbacks to the methods used by the NONROAD
model to calculate age distributions and its relationship to the methods used by the California Air
Resources Board's OFFROAD model.

       The Calculations discussion describes the manner in which the methods presented in the
Methodology discussion are encoded in the NONROAD model. This discussion is divided into
three sections.  The first section describes the calculations used to calculate the growth rate for a
given equipment population.  The second section describes the algorithm used to determine the
age distribution, equipment population, and equipment sales for  the base year.  The third section

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describes the algorithm used to determine the age distribution, equipment population, and
equipment sales for future years.

       The Inputs discussion describes the information that must be provided to the NONROAD
model to perform the calculations necessary to determine equipment populations, age
distributions, and sales. This discussion includes separate sections on equipment populations,
growth indicators, scrappage functions, and activity data.

       The report ends with a glossary that defines the key terms used in this report. Those
terms are italicized the first time they appear in this report subsequent to this introduction.
Methodology

       The NONROAD model calculates equipment populations, the age distribution of those
populations, annual equipment sales, and equipment scrappage.  These calculations are
performed for the base year, the specified target year for the model run, and for all years
between the base year and target year. The methods used by the model to perform these
calculations are described below.  In general, the model uses the population growth rate to
project equipment populations from a base year (in which the equipment population is known)
through the target year. The model determines equipment sales by adding equipment scrappage
to the change in equipment population. The model calculates annual equipment sales using the
following equation:

       Sales(X+l) = [Population(X+l) - Population(X)] + Scrappage(X+l)

where

       Sales(X+l)          = Equipment sales in year X+l
       Population(X+l)     = Equipment population at the end of year X+l
       Population(X)        = Equipment population at the end of year X
       Scrappage(X+l)      = Equipment scrapped during year X+l

The model uses a scrappage curve to determine the proportion of equipment of a given age that
has been  removed from service. This proportion can then be multiplied by the annual sales for
the year in question to  determine the accumulated scrappage for equipment of that age.
Subtracting the accumulated scrappage from initial sales yields the population of equipment still
in service. With this information, the age distribution of the population can be calculated by
dividing the population at each age by the total population.  The  details of these calculations are
discussed more fully below.

       Base Year Populations

       Estimates of the base year equipment populations are contained in the NONROAD
model's input files. The basis for these estimates is discussed at length in the Population

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Estimates Technical Report (NR-006). The beta version of the NONROAD model uses 1996 as
its base year.

       Population Growth:  Growth Rates and Projected Populations

       The NONROAD model projects equipment populations in future (post-base year) years
by applying a growth rate to the base year equipment population. This growth rate is calculated
by determining the compound annual growth rate (CAGR) in equipment population between
1989 and 1996, as reported by PSR. This approach is discussed more fully in the Growth
Technical Report (NR-008). The model assumes that the population growth rate remains
constant during the years between the base and target years. EPA's Nonroad Engine Emissions
Modeling Team (NEEMT) has chosen this approach, instead of relying on economic indicator
variables, for the reasons discussed in NR-008.  Once the CAGR has been calculated, the model
uses this growth rate to project the total equipment population in each future year up to and
including the target year using the following equation:

       Total population in year X+l = [1+(CAGR/100)] *  [Total population in year X]

       Scrappage

       The NONROAD model uses a scrappage curve to determine the proportion of equipment
that has been scrapped as a function of equipment age. The model uses the scrappage curve
originally developed for the EPA NEVES project as its default scrappage curve for all equipment
types; the curve is scaled to the average lifetime of the equipment such that half of the units sold
in a given year will be scrapped by the time those units reach the average expected lifetime and
all units will be scrapped at twice the average lifetime. The  average lifetime  (in years) is
calculated as the average life (in hours at full load) divided by the activity level (hours/year) and
the load factor.  The default scrappage curve is shown in Figure 1 (the data plotted in Figure 1
are also provided in Table 1, located on p. 16 of this document). In Figure 1, age has been
transformed to a dimensionless quantity by dividing by the average lifetime for the type of
equipment under consideration. Note that in Figure 1, the proportion of equipment that has been
scrapped  represents the accumulated scrappage since the equipment was placed in service.

       The default scrappage curve used in the NONROAD model is based on a normal
distribution of accumulated scrappage versus age. Other distributions can be used; for example,
EPA's proposed standards for small spark-ignited engines uses a Weibull distribution to project
fleet turnover. This distribution results in reduced scrappage in the first few years and increased
scrappage in later years than is the case for a normal distribution.  The NONROAD model  allows
a user-specified curve to be substituted for the default curve for any or all equipment types. A
user-specified curve can vary the rate of scrappage with age (the shape of the curve) but must
conform to  the assumption that all units are scrapped within twice the average lifetime.

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                                 Default Scrappage Curve
                      100
                   HI
                   o.
                   Q.
                   2
                   o
                   w
                   :
                   c
                   c
                   01
                         0         0.5         1         1.5         2
                                         Age /Average Lifetime


        Figure 1. The default scrappage curve relating percent of units removed from
        service to age.
       The scrappage rate is defined as the percentage of equipment of a given age removed
from service in a given year.  The scrappage rate can be derived from the scrappage curve by
determining the slope of the scrappage curve at the age in question. Note that for the default
scrappage curve, the scrappage rate changes as the equipment age changes:  the scrappage rate is
low when units are new, reaches a maximum when unit age is equal to the average lifetime, and
then declines again for units that are older than the average lifetime.

       Age Distribution in the Base Year

       To determine the equipment population's actual age distribution as of the base year, one
would need to know past equipment sales and scrappage. However,  estimates of past equipment
sales suffer from missing or incomplete data, are of poor quality, or are based on estimation
methods that are incompatible with the methods used to  estimate the base year equipment
populations used in the NONROAD model. Given these uncertainties, the NEEMT has elected
to determine the age distribution as of the base year by assuming constant equipment sales over
the (N) years preceding the base year, where TV is two times the average lifetime for the
equipment type (in other words, the model does not backcast the effects of growth). Under this
assumption, the base year age distribution can be determined directly from the scrappage curve.

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       The NEEMT recognizes that the assumption of constant sales for the years up to and
including the base year may introduce inaccuracies in estimating the rate at which existing
equipment is scrapped.  For example, to the extent that annual equipment sales increased during
the years preceding the base year, the model would overestimate the population of equipment
produced between N and N/2 years prior to the base year and would underestimate the population
of equipment produced between the base year and N/2 years prior to the base year. As a result,
the model would tend to overestimate the rate of scrappage of existing engines for the first N/2
years after the base year and then underestimate the rate of scrappage for the subsequent N/2
years. Furthermore, overestimating scrappage rates during the first N/2 years would tend to result
in overestimates of sales and the benefits of lower emission standards during those years. The
NEEMT plans to minimize these problems by updating its base year population estimates
periodically as new information becomes available, thereby helping to compensate for any
discrepancies between modeled and actual  scrappage. These updates would take the form of new
default population input files.  The NEEMT continues to investigate these issues and welcomes
suggestions regarding alternative sources of information about the age distribution in the base
year, scrappage rates, and other model inputs.

       Annual Sales for Future Years

       As the model steps through each year from the base year to the target year, it estimates the
sales expected to take place during each year. As discussed above, annual sales are determined
by adding the scrappage projected to occur during the year to the increase in equipment
population projected for that year:

       Sales(X+l) = [Population(X+l) - Population(X)] + Scrappage(X+l)

where

       Sales(X+l)          = Equipment sales in year X+l
       Population(X+l)     = Equipment population at the end of year X+l
       Population(X)        = Equipment population at the end of year X
       Scrappage(X+l)      = Equipment scrapped  during year X+l

The scrappage projected for equipment  sold in the target year depends on the type of scenario
being modeled.  For end-of-year scenarios, the projected scrappage of newly-sold equipment is
based on an average equipment age of 6 months. For mid-year scenarios, the projected scrappage
of newly-sold equipment is based on an average equipment age of 3 months.

       For a mid-year scenario, the target year sales estimated using the equation presented
above represent only one-half year of sales, including one-half year of equipment population
growth and one-half year of scrappage replacement.  To determine projected full-year sales
during the target year, the NONROAD model multiplies the calculated  sales by two.

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       Age Distribution for Future Years

       To calculate age distributions for future years, the NONROAD model steps through each
year between the base and target years, calculating the effects of growth and scrappage during
each step.  As the model steps through each year, it estimates the equipment population of each
age expected to remain in service using the scrappage curve mentioned above.  The age
distribution is determined by dividing the equipment population of each age by the total
equipment population.

       Discussion

       The methods used in the NONROAD model have considerable similarity to the methods
used in the CARB OFFROAD model. Both models use the same default scrappage curve and
similar methods for calculating an age distribution; both models also assume that equipment
durability remains constant over time. At the present time, the NEEMT is aware of two major
differences between the models. First, the CARB model is only capable of calculating year-end
age distributions, whereas NONROAD can calculate either a year-end or mid-year distribution.
Second, the CARB model appears to use a different method to adjust age distributions for
growth. This method is not fully understood by the NEEMT at this time but will be described in
a future technical report.
Calculations

       Calculation of Equipment Population Growth Rate

       The NONROAD model uses an exponential growth model to project equipment sales
over time, a model that is analogous to compound interest. The subroutine GRWFAC computes
the Compound Annual Growth Rate (CAGR) from default or user-specified indicator data.
CAGR is expressed as percent growth in total equipment population per year.  It is calculated by
fitting an exponential function to indicator data for 2 years that best match the time period of the
base and scenario years. Thus, at least 2 years of data are required for every growth indicator
used by the model.

       Calculation of the Age Distribution and Equipment Population for the Base Year
       and Prior Years

       The calculation of the age distribution of engines for the base year and any previous year
is performed in the MODYR subroutine. The steps employed are:

       1.     Calculate the hours accumulated in service for units of each model year using
             activity data for each year. NONROAD assumes that all engines of a given
             application, size,  and engine type which are still in service operate for the same
             number of hours during any given time period. Note that the hours accumulated
             by units sold in the base year must be adjusted downward to reflect the units'

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       average age at the time of evaluation. For an end-of-year scenario, base year units
       were on average sold in June and therefore have accumulated only half a year's
       activity. For a mid-year scenario, base year units have accumulated only a quarter
       of a year's activity, on average. A mid-year scenario is defined as spring or
       summer season scenario, or a monthly scenario earlier than October. All other
       scenarios are defined as end-of-year scenarios.

2.      Calculate the average equipment lifetime (in years) as the number of years at
       which the accumulated hours of service equal the average equipment life (in
       hours), adjusted for the average load that the equipment's engine experiences,
       using the  following equation:

           .       T.,, ..   ,    ,         Average Life (hrs)
          Average Lifetime (years) =               J  ^   '
                                   Activity (hrslyr) * Load Factor
       where the average life is expressed in terms of hours of operation at full load and
       the load factor is expressed in terms of the average fraction of available power
       that is used by the equipment during operation.

3.      Use the average equipment lifetime to transform the dimensionless scrappage
       curve (Figure 1) to an annualizedscrappage curve.

4.      Use the annualized scrappage curve to estimate the in-service fraction for each
       model year, which is the fraction of units that were produced in each year from the
       base year back to twice the average equipment lifetime and which are still in
       service as of the base year. The NONROAD model calls this fraction modfrc; the
       fraction for a specific year Mis called modfrc(M). Figure 2 shows an example for
       equipment with a ten-year life.

5.      Calculate the base year age distribution. Assume that the sales in each  year were
       the same so that the population of units still in service during the base year for a
       given model year (M) is proportional to modfrc(M). The model year fraction is
       the proportion of in-service equipment of a specific model  year M and is called
       modscp(M); as of the base year, it is given by:

       modscp(M) = modfrc(M) /  modfrc(Z)

       where ^[jnodfrc(L) is summed  over the TV years between  the base year and (N-l)
       years prior to the base year (N = twice the average equipment lifetime).

6.      To calculate a given model year's equipment population as of the base year, the
       model year fraction is multiplied by the application's total  base year equipment
       population.

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       Note that step 5 calculates an age distribution based on the assumption that sales did not
vary over the TV years prior to and including the base year. This assumption is equivalent to
assuming that total equipment populations did not vary over those years.  The age distribution
for later model years can be adjusted to account for changes in population, as discussed below.
                            Percent Units in Service by Age
              100
       Figure 2.  Fraction of equipment still in service versus equipment age,
       assuming an average equipment lifetime often years.
       Calculation of the Age Distribution and Equipment Population for Future Years

       The key difference between base year and future year age distributions, equipment
population, and equipment sales is that future year calculations are adjusted to account for
growth in equipment populations and sales. The adjustment of age distributions to account for
population and sales growth is performed in the GRWCLC subroutine. The steps employed are:

       1.     Calculate populations of each model year back to twice the average equipment
             lifetime prior to the base year by multiplying the base year population by the
             model year fractions as of the base year (i.e., by the base year age distribution).
             Save these populations for use in future calculations.

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2.      Step from the base year out to the target year in one year increments and perform
       the following steps at each year until the target year is reached:

       A.     Grow the total population by multiplying the previous year's population by
              (1 + CAGR/100), where CAGR is the compound annual growth rate.

       B.     For all model years prior to the current year, recalculate the model year
              populations. Conceptually, this calculation is performed by multiplying
              the sales for each model year by the fraction of equipment projected to
              remain in use in the current year based on the scrappage curve. For model
              years prior to or including the base year, the NONROAD model uses a
              computational shortcut to calculate populations: the model re-uses the set
              of base year populations by model year shifted by a year. This approach is
              mathematically equivalent to direct calculation of model year populations
              for these years because the model assumes that sales were constant for all
              years up to and including the base year.

       C.     Sum the populations for all model years up to the current year minus one.
              Subtract this sum from the total population to get the current model year
              population.

       D.     Calculate the number of engines scrapped during the current year by
              summing the scrappage for each model year. For model years prior to the
              current year, scrappage amounts to one full year of scrappage.  For the
              current model year, scrappage equals 1/2 year's worth of scrappage for an
              end-of-year scenario and 1/4 year's worth of scrappage for a mid-year
              scenario.  Scrappage for a given model year is calculated by subtracting
              the model year's accumulated  scrappage as of the year prior to the current
              year from the model year's accumulated scrappage as of the current year.

       E.     Calculate the the current model year sales and save this value to use in
              subsequent calculations. For end-of-year scenarios, sales for the current
              model year are calculated by adding the total scrappage calculated in step
              2D to the current model year population calculated in step 2C. For mid-
              year scenarios, the sum of total scrappage and current model year
              population must be multiplied by two in order to place the current model
              year sales on a full-year basis.

3.      Step 2 gives populations by model year for the future year scenario. To convert to
       model year fractions, divide by the total population.  Note that in GRWCLC, the
       base year population is used as the divisor to give model year fractions relative to
       the base year population (i.e., the fractions do not sum to one).

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       An example calculation using this algorithm is shown in Figure 3. Figure 3 shows the
age distribution in the base year for equipment with a life often years. Also shown are the age
distributions incorporating 2 percent per annum growth in population for 5, 10 and 20 years after
the base year.  Since the model year fractions in Figure 3 are shown relative to the base year
population, the divisor in each curve is the same and the curves are effectively a direct measure
of population by model year, making it easier to compare curves. Note that after 5 years of
growth, the populations for the first 5 years have risen above the base year curve, but for years  6-
20 the populations remain the same as for the base year. This makes clear the point that the
growth algorithm does not perform any backcasting; thus, populations for model years prior to
the base year are always assumed to be based on sales at the base year level. After 10 years of
growth, effects have propagated into model years 1-10. After 20 years of growth, effects have
propagated through the entire distribution.
                        Age Distributions Adjusted for 2% Growth
                                                        base year
                                                        base + Syr
                                                        base + 10yr
                                                        base + 20 yr
                  0.00
           Figure 3. Model year fractions after adjustment for 2% annual growth
           beginning in the base year, shown for the base year, base + 5 years, and
           base +10 years. Model year populations are expressed as fractions
           relative to the total equipment population in the base year.

       Growth may be negative.  Equipment populations may decrease due to economic factors
or because of changes in technology (e.g., shift from 2-cycle to 4-cycle engines). Figure 4 shows
the effects of negative 2% per annum growth for the same example as used in Figure 3. Note that
the 5, 10 and 20 year curves drop below the base year curve.
                                           10

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       If population data predict a strongly negative growth rate, the population could drop faster
than the rate of attrition, resulting in a prediction of negative sales and therefore negative model
year fractions. Figure 5 shows that such a situation occurs if negative 15% growth is assumed for
the scenario used in Figures 3 and 4.  The GRWCLC subroutine traps negative sales to zero
which effectively limits the rate of population decrease to be no greater than the rate of attrition.
                      Age Distributions Adjusted for Negative 2% Growth
              ta
              Q
              01
                0.12
              . 0.10  
            C
             a
            i= 3
            -5 9-
0.08  
                                       base year
                                       base + 5 yr
                                       base + 10 yr
                                       base + 20 yr
                0.06  
            11
                0.04  
                0.02  
                0.00
                                             10
                                            Age
                                                         15
                                                                      20
         Figure 4. Model year fractions after adjustment for negative 2% annual
         growth beginning in the base year, for the base year, base + 5 years, and
         base +10 years. Populations are expressed in terms of fractions of the
         total equipment population in the base year.
                                            11

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            Age Distributions Adjusted for Negative 15% Growth
                                              base year
                                              base + 5 yr
                                              base + 10 yr
                                              base + 20 yr
                                   Age
Figure 5. Model year fractions after adjustment for negative 15% annual
growth beginning in the base year, for the base year, base + 5 years, and
base +10 years.  Populations are expressed as fractions of the total
equipment population in the base year.
                                 12

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       The calculation of age distributions requires the following data to be supplied to the
NONROAD model:

      Equipment Populations
      Growth Indicators
      Scrappage Curve
      Activity Data

       These data are input to the model using data files. The format of the data files is
described below, examples of data are given, and the location of the data is specified.

       Equipment Populations

       Equipment population data for each state are provided in the directory "data/pop." If
estimates are provided for more than one year, the NONRO AD model will use the closest year
which comes before the target year.

       The format of the data in the /POPULATION/ packet is as follows:

1 -  5        FIPS code
7-11        Subregion code (used for subcounty estimates)
13-  16      Year of population estimates
18-27      SCC code (no globals accepted)
29 -  68      Equipment description (ignored)
70 -  74      Minimum HP range
76 -  80      Maximum HP range (ranges must match those internal to model)
82-  86      Expected average life (in hours of use)
87 -  96      Flag for scrappage  distribution curve (DEFAULT = standard curve)
100 - 116     Population estimate

       An example of data from a /POPULATION/ packet is given below (note that lines are
wrapped to fit the page).
02000
16
02000
25
02000
40
02000
50

25

40

50

100
1990 2260001010
750 DEFAULT
1990 2260001010
1500 DEFAULT
1990 2260001010
1500 DEFAULT
1990 2260001010
3000 DEFAULT
2

2

2

2

-Stroke

-Stroke

-Stroke

-Stroke

Motorcycles :
7
Motorcycles :
525
Motorcycles :
131
Motorcycles :
482
Off-Road

Off-Road

Off-Road

Off-Road

                                         13

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       Growth Indicators

       The default data are based on national growth estimates for the various source category
groups. Data are located in the "data/growth" directory in a single file that contains both data
packets:

       /INDICATORS/      Cross reference between SCC code and growth indicator code.
       /GROWTH/         Numerical values for different growth indicator codes.

       An indicator code is an alphanumerical code used to identify an actual growth indicator,
such as population or employment growth. The growth indicator codes used in the
/INDICATORS/ packet must match one of the codes provided in the /GROWTH/ packet. Cross
referencing between the /INDICATORS/ and /GROWTH/ packets is based on FIPS code, SCC
code, horsepower (HP) range, and technology type. The model uses the best match to the codes
provided, falling back on global values if a unique match is not found.

       The format of the data in the /INDICATORS/ packet is as follows:

1-5          FIPS code    (00000 = applies to entire nation)
                          (ssOOO = applies to all of state ss)
7-10         Indicator code (arbitrary alphanumeric code)
12-21        SCC code     (2260004000 = applies to all 2-stroke lawn and garden)
                          (2600000000 = applies to all 2-stroke)
23-27        Beginning of HP range
28-32        Ending of HP range
34-43        Technology type (ALL = applies to all tech types)

       An example data record from the /INDICATORS/ packet is given below.
 00000  001  2260001000     0  9999 ALL         2-Stroke Recreational Vehicles
       The format of the data in the /GROWTH/ packet is as follows:

1-5          FIPS code    (00000 = applies to entire nation)
                          (ssOOO = applies to all of state ss)
6-10         Subregion code (blank = applies to all subregions)
11-15        Year of estimate (4-digit year)
17-20        Indicator code (arbitrary alphanumeric code)
26-45        Indicator value
                                         14

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      An example data record from the /GROWTH/ packet is given below.
02000
02000
02000
02000
1992
2000
2005
2010
001
001
001
001
15
20
22
24
8
4
7
7
      Scrappage Curve

      A single default scrappage curve is used by the NONROAD model. The scrappage curve
is read in from the same data file as the growth data in the "data/growth" directory.
                                         15

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                          Table 1. Default Scrappage Curve.
Age/
Average
Life
0
0.06
0.12
0.17
0.22
0.24
0.26
0.3
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
Percent
Scrapped
0
1
2
O
4
4.5
5
6
8
10
11
13
14
15
18
19
21
24
25
31
50
Age/
Average
Life
1.05
1.1
1.15
1.2
1.25
1.3
1.35
1.4
1.45
1.5
1.55
1.6
1.7
1.72
1.74
1.78
1.83
1.88
1.94
2

Percent
Scrapped
69
75
76
79
81
82
85
86
87
89
90
92
94
95
95.5
96
97
98
99
100

      Activity

      The /ACTIVITY/ packet defines how often a piece of equipment is used in a year. The
file also contains some other information about the equipment, such as average load factor and
tank volume.
1-10
12-51
The format of the /ACTIVITY/ packet is as follows:

      SCC code
      Equipment description (not used)
                                         16

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52-56        Region code
57-66        Technology type
67-71        Minimum HP
72-76        Maximum HP
77-81        Load factor
82-86        Tank volume (gallons)
87-96        Activity level units
97-106       Activity level

      An example data record from the /ACTIVITY/ packet is (note that lines are wrapped to fit
on page):
    2260001010  2-Stroke Motorcycles:  Off-Road
    ALL    0  9999   76  0.5     Hrs/Yr        120        0.0
For more information on equipment populations and equipment activity, load factors and average
life, see EPA's technical reports on these subjects, NR-006 and NR-005.
                                         17

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                                   Glossary of Terms
Term
Accumulated scrappage



Activity level


Age distribution



Annual equipment sales

Annualized scrappage curve


Average life


Average lifetime



Base year
Compound Annual Growth Rate
 (CAGR)

Current year
End-of-year
Definition
The total amount of scrappage that has occurred for
equipment of a given model year since its introduction into
service

The number of hours per year that the equipment in
question operates

The function that describes the proportion of in-service
equipment by age; consists of the full set of model year
fractions for a given year

Total sales during a given calendar year

The result of scaling the scrappage curve by the average
lifetime of the equipment in question

The average number of hours that a given type of
equipment operates at full load

The age (in years) at which half of the equipment will have
been removed from service; one-half the age at which all of
the equipment will have been scrapped

The year for which the population of equipment in service
is known

The rate at which the population is projected to grow each
year in order to reach a specified level

The year for which the model is currently calculating
quantities such as population, sales, scrappage, and
emissions

Refers to model runs for which the target date is October 1
or later
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                                   Glossary of Terms
Term
Definition
In-service fraction



Load factor


Mid-year


Model year
 Model year fraction


Population growth rate


Scrappage curve

Scrappage function
Scrappage rate


Target year
The fraction of the engines originally sold in a given year
which are still in service; the inverse of accumulated
scrappage

The average power level at which the engine operates
divided by the maximum available power

Refers to model runs for which the target date is September
30 or earlier

Refers to the year in which equipment was produced.
Equipment of the same model year was produced in the
same year.  To clarify the relationship between age and
model year, consider the following example:  1990-model
year equipment is (on average) six years  old in 1996 and
ten years old in 2000.

The fraction of the total equipment population represented
by a given model year at a given point in time

The rate at which the equipment population increases each
year

A graphical representation of the scrappage function

The relationship between equipment age (expressed in
terms of the fraction of average lifetime) and the proportion
of equipment that has been removed from service, i.e.,
scrapped

The percentage of equipment of a given age removed from
service in a given year

The year for which the NONROAD model's user wishes to
estimate emissions and other quantities
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                                  Glossary of Terms

Term                            Definition
Total equipment population         The total number of pieces of equipment in service at a
                                 given point in time; the sum of the populations of each
                                 model year still in service
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