EPA-R4-73-030B
July 1973
ENVIRONMENTAL MONITORING SERIES
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EPA-R4-73-030b
URBAN AIR SHED
PHOTOCHEMICAL SIMULATION MODEL STUDY
VOLUME I -
DEVELOPMENT AND EVALUATION
Appendix A -
Contaminant Emissions Model and Inventory for Los Angeles
by
P.J. Roberts, Mei-Kao Lui,
S.D. Reynolds, and P.M. Roth
Systems Applications, Inc.
9418 Wilshire Boulevard
Beverly Hills, California 90212
Contract No. 68-02-0339
Program Element No. 1A1009
EPA Project Officer: Herbert Viebrock
Meteorology Laboratory
National Environmental Research Center
Research Triangle Park, North Carolina 27711
Prepared for
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
July 1973
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This report has been reviewed by the Environmental Protection Agency and
approved for publication. Approval does not signify that the contents
necessarily reflect the views and policies of the Agency, nor does
mention of trade names or commercial products constitute endorsement
or recommendation for use.
11
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TABLE OF CONTENTS
Page
INTRODUCTION A-l
I. GENERAL A-2
II. AUTOMOTIVE EMISSIONS A-3
A. Summary of Changes A-3
1. Federal Driving Cycle A-3
2. Emissions/Average Speed
Correlation A-5
3. Correction for Nonuniform
Distribution of Vehicle Starts A-6
4. Modification in Treatment of
Emissions in the Downtown Area A-7
B. Discussion of Changes A-23
1. Federal Driving Cycle A-23
2. Emissions/Average Speed
Correlation A-26
3. Correction for Nonuniform
Distribution of Vehicle Starts A-28
III. REVISIONS OF THE AIRCRAFT EMISSIONS
INVENTORY A-40
IV. FIXED SOURCE EMISSIONS - POWER PLANTS A-43
A. Apportionment of Emissions A-43
B. Temporal Distribution of Emissions A-44
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TABLE OF CONTENTS (Contd.)
Page
C. Penetration of the Inversion Layer
by a Plume A-47
D. Calculation of Average Molecular
Weight of Emitted Hydrocarbpns A-49
V. FIXED SOURCE EMISSIONS - DISTRIBUTED
SOURCES AND REFINERIES A-50
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INTRODUCTION
During the last months of 1970, we prepared a pollutant emissions
inventory for the Los Angeles Basin for use in the modeling of the
transport, diffusion, and reaction of atmospheric contamination. Pol-
lutant sources were grouped into five categoriesautomobiles (and
other motor vehicles), aircraft, power plants, refineries and distri-
buted fixed sources. Emissions rates for a 2 x 2 mile grid system
covering the Basin were compiled for nitrogen oxides, carbon monoxide,
and hydrocarbons. Temporal variations in emissions rates were also
determined. The complete inventory is reported in "Contaminant Emissions
in the Los Angeles BasinTheir Sources, Rates, and Distribution," by
P.J.W. Roberts, P.M. Roth, and C.L. Nelson (1971).
Early in 1972, we had the opportunity to make a number of modi-
fications and extensions for the emissions inventory. The changes
which affected all segments of the original inventory, were motivated
by a variety of factors, but most heavily by a desire to improve the
accuracy or the resolution of the inventory, or to correct errors.
It is the purpose of this report to document all modifications and
extensions that were implemented. In general, this report is seg-
mented similarly to its predecessor, the exceptions being that (1)
changes applicable to all portions of the inventory are included in
an introductory general section and (2) the one modification to the
refinery inventory, as a matter of convenience, is included in the
section dealing with distributed fixed sources. Finally, we wish to
point out that only changes are reported here; we have not attempted
to present a final version of the inventory, either in summary or in
detail, in this document. One must read both this report and the
original to construct the complete inventory.
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I. GENERAL
In this brief section, we document two points of general
applicability concerning the treatment of nitrogen oxide emissions.
First, in using this inventory in conjunction with an airshed
model, it is necessary to specify the fraction of total NOX
emissions from each class of sources that is NC>2 As the measure-
ment of the individual oxides is rarely made, we can only estimate
the magnitude of the NO/NC>2 split. In order to obtain as accurate
an estimate as possible, we contacted Prof. Robert Sawyer of the
University of California (Berkeley), an expert in the field of com-
bustion. We solicited his opinion as to appropriate values for the
NO/N02 split for all categories of sources. After some discussion,
we arrived at the following figures:
Automobiles 1
Power Plants 5
Aircraft 1
Other fixed sources 2
However, these figures are at present uncertain and subject to revision.
Second, we wish to note that all NOX emissions rates reported in
Roberts et.al. (1971) are based on the assumption that the gases
emitted are 100% NC>2. As can be seen from the preceding table, NOX
emissions from all sources range from 95 to 99% NO. If we assume in
simplicity that NOX emissions are in fact 100% NO, then reported mass
rates (as NO2) must be multiplied by the following ratio:
molecular weight NO _ 3£
molecular weight N02 46
In this report the only instance in which NOX emissions are cited
as NO is in the section dealing with automotive emissions; in all
other instances, NOX rates should be adjusted.
A-2
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II. AUTOMOTIVE EMISSIONS
In this section, we describe extensions and modifications of the
motor vehicle emissions inventory. Because of the length of the section,
we first summarize the changes, then discuss them in detail.
A. Summary of Changes
We have modified and extended the original model describing
vehicular emissions of contaminants in the Los Angeles Basin (Roberts
et al. (1971)). The three major changes are (1) adoption of vehicle
emissions factors Q^ based on the Federal Driving Cycle, (2) inclusion
of a correlation between emissions rate and average speed to account
for temporal and spatial variations in emissions from freeways, and
(3) incorporation of a factor to account for variations in emissions
resulting from a nonuniform temporal distribution of vehicle starts.
We have also modified the treatment of emissions in the downtown area.
1. Federal Driving Cycle
We have adopted average emissions factors based on the Federal
Driving Cycle. These factors, which replace those estimated using
California Driving Cycle test results (as reported in Roberts et al.
(1971), Table A-2), form the basis for determining emissions rates as
a function of location and time, both for surface streets and free-
ways. Average hot and cold-start emissions factors, Q^1 and Q9
respectively, are given by:
Species
CO
HC (exhaust and
blowby only)
N0x/ as N02
as NO
(grams/mile)
h Oc
Qi Qi
68.6 91.0
10.8 11.7
4.16 4.16
2.71 2.71
where, for hydrocarbon:.;:
molecular weight (reactive species) = 47.8*
molecular weight (unreactive species) = 21.1
fraction reactive (mol %) =67.4
fraction unreactive (mol %) =32.6
We have assumed for the purposes of this inventory that methane,
ethane, propane, benzene, and acetylene are unreactive. All
other hydrocarbons are assumed to be reactive.
A-3
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Average emissions rates for surface streets are estimated by
(a) calculating
= y(t)Q
- y(t))g
(1)
where y(t) = fraction of the cars started at time t that are
11 cold-started"
time
0:00
6:00
9:00
11:30
13:30
16:30
18:30
21:00
period
- 6:00
- 9:00
- 11:30
- 13:30
- 16:30
- 18:30
- 21:00
- 24:00
y
0.90
0.85
0.25
0.30
0.20
0.50
0.15
0.20
and (b) correcting this estimate for variations in the average
emissions rate due to the nonuniform distribution of cold vehicle starts
during the day. See sections in the Summary and Discussion entitled
"Corrections for Nonuniform Distribution of Vehicle Starts" for
details concerning the cold start-corrections.
In calculating freewary emissions, we assume that all vehicles are
"hot-running". Average emissions rates are estimated as a function of
average vehicle speed using a relationship suggested by Rose et al.
(1965). Further details are presented in sections of the Summary and
Discussion entitled "Emissions/Average Speed Correlation."
A-4
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2. Emissions/Average Speed Correlation
Freeway emissions rates for species i (grams/minute) for a
particular grid square are given, as a function of average speed
and time, by
2i(t) = W jnf(t)°i[vf(t)1 +ns(t)oi[vs(t)1'
(2)
where
v ,v = average speed in the fast and slow directions respectively
f S (mph)
n ,n = number of vehicle miles driven per hour in the fast and
f s slow directions respectively
a. = "hot-running" emissions rate of species i in grams per
1 vehicle mile. a. is a function of average vehicle speed.
(Note: "Fast" and "slow" refer to an assignment of names to the
two opposing directions of flow on a freeway.) Values of cu are
computed from the following correlations, based on the work of Rose
et al. (1965) and modified as described later in this text:
a. = a. (v)
where
i
CO
HC
NO
X
a
295.
34.8
7.0
b
-0.49
-0.40
0
A-5
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Values of v for each direction of freeway traffic flow, at
the particular time noted, are given in Figures 1 through 8.
(v is assumed to be 60 mph before 6 a.m. and after 9 a.m.
over the daytime validation period.) Linear interpolation is
used to calculate average velocities for times falling between
those shown in the Figures. Finally nf and n are calcu-
lated from
Nf Nfx
nf = rTT ; ns = rT- (4a, 4b)
where
d. = fraction of daily (24-hour) freeway traffic counts
assignable to hourly period £ (Table A-l of
Roberts et al. (1971))
M = freeway vehicle mileage per day for the grid square
in question (Figure A-2 of Roberts et al.)
x = n /nf, as given in Figures 9 through 12.
S I
3. Correction for Nonuniform Distribution of Vehicle Starts
We have included a factor in the calculation of emissions rates
to account for variations in average rates that occur when the
total number of "cold-started" cars in operation changes rapidly,
as during the morning rush hours. These "correction" factors,
3.(t) , which are applied to the average emissions factors for
surface streets, Qf(t) , are given by the curves shown in Figures
13 and 14. (No correction is required for NOX .) Their entry
into the calculation of emissions rates is presented in the para-
graph that concludes this section. However, we strongly urge
that reader refer to the Discussion section entitled "Corrections
For Nonuniform Distribution of Vehicle Starts" for a full explana-
tion of the nature of, and need for, this correction.
A-6
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4. Modification in Treatment of Emissions in the Downtown Area
We have modified the treatment of auto emissions in the down-
town Los Angeles area in the following manner. We have shifted
the temporal distribution for surface traffic one hour later in
time for the three grid squares having the following column and
row numbers respectively: (12, 17), (11, 17), and (12, 16). (For
example, the fraction of daily surface traffic assignable to the
period 6 a.m. to 7 a.m. throughout the modeling region is applied
to the period 7 a.m. to 8 a.m. for these three grid squares.)
This shift provides a simple means to account for the fact that
these squares contain few residences and thus, in the net, re-
ceive vehicles rather than discharge them during the morning hours.
Total emissions for a particular grid square, in grams/minute,
are given by:
E. (t) = Ef (t) +
where
Ei(t) = ?6-Qi
and
d (t) = fraction of daily (24-hour) non-freeway traffic count
assignable to hourly period H (Table A-l of Roberts
et al. (1971))
non-freeway v(
in question (Figure A-3 of Roberts et al.(1971))
M = non-freeway vehicle mileage per day for the grid square
A-7
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In conclusion, the main changes described in this section may be
summarized as follows:
Average emissions factors
Correction for nonuniform
distribution included
Emissions/speed modifica-
tion included
Freeways
Average emissions rat
Hot-running factors
No
Yes
" (
Non-Freeways
:e based on the FDC
Weighted average of
cold-start and
hot-running factors
Yes
No
The net result, when compared to the original vehicle emissions model,
is to increase emissions from surface streets, to decrease emissions
from freeways (except for NOX ), to redistribute total emissions so
that emissions levels are greater during periods of congestion (ex-
cept for NOX ), and to maintain approximately the same total pollutant
loading of the atmosphere.
A-8
Figures 1 through 14 follow
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A-9
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A-13
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A-15
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-------
B. Discussion of Changes
In this section we present details pertaining to the modifications
and extensions outlined.
1. Federal Driving Cycle
Quoting from Roberts et al., p. A-29, "It should be understood
that while CDC (California Driving Cycle) emissions factors have
been adopted for the current study, we are unable to assess the
degree to which the two driving cycles* (or, for that matter, any
driving cycle) are representative of actual driving performance
in a particular locale. Hence, our figures may be subject to re-
vision as more data become available."
We have very few new data that are pertinent. During the last
two years, however, the Federal Driving Cycle (FDC) has come to
replace the CDC as the standard emissions test procedure. We
have adopted FDC-based factors in conformance with this trend.
The new values adopted, with the exception of those for NOX ,
have been estimated by the Environmental Protection Agency, as
reported on p. A-26 of Roberts et al. (1971). Unfortunately,
we are still unable to assess the degree to which these factors
represent actual vehicle emissions in Los Angeles.
Establishing an emissions rate for nitrogen oxides was some-
what more involved. In carrying out a series of validation runs
for the airshed model, we found to our dismay that NO emissions
levels were far too high. In pursuing the possible reasons for
the high NO emissions rate, we discovered that the 7.0 grams/
mile figure supplied to us by EPA is based on 100% N02 As auto
emissions are about 99% NO , the rate we have used is too high
by a factor of
3°
* Referring to the California and Federal Driving Cycles.
A-23
-------
Pursuing this further, we discussed the matter of NOX
emissions from automobiles with Dave Kircher of EPA. Studies
carried out by him and his colleagues indicate that the emissions
rate of 7.0 grams/mile, as NC>2 , is also too high. To correct
this, he provided us with newly available data, average emissions
rates of NOX , as measured in vehicle surveillance studies in
Los Angeles in December 1971, for model years 1957 through 1971.
Using his figures, we calculated the average NOX emissions rate
(as NC>2 ), as of September 1969, to be 4.16 grams/mile. Ex-
pressed as emissions of NO , we have 30/46 x 4.16 , or 2.71 grams/
mile. Undoubtedly, the fact that these measurements were made in
1971, and not in 1969, biases the result. However, we have not
attempted to account for this.
Mr. Kircher also provided us with information which indicates
that we had overestimated the methane content of auto emissions.
We thus revised our earlier estimates for average molecular weight
and fraction reactive, which were based on the distribution of
hydrocarbons in auto exhaust reported by Mayrsohn et al. (1969).
The figures we have adopted are as follows:
MW (reactive species) 47.8*
MW (unreactive species) 21.1
fraction reactive (mol%) 67.4
fraction unreactive (mol%) 32.6
The data that served as the basis for these calculations were taken
from Papa (1967).
In our current vehicle emissions model, freeways and non-freeways
(surface streets, including major and minor arterials and residential
streets) are treated separately. "Hot-start" emissions factors form
the basis for calculating freeway emissions rates, a weighted average
of "hot" and "cold-start" factors form the basis for calculating sur-
face street emissions rates. The cold-start emissions factors are those
We have assumed for the purposes of this inventory that methane,
ethane, propane, benzene, and acetylene are unreactive. All other
hydrocarbons are assumed to be reactive.
A-24
-------
reported by Sigworth (1971).
the exception of
equation:
"Hot-running" emissions factors (with
NO *) were estimated through the following
X
oh -
Qi
c
i
x<
ZP
-------
We emphasize that both Q^ and Q![ are based on the FDC, which
is defined to simulate a trip having an average speed of about
19.6 miles/hour. We thus "assume" that vehicles travel at approxi-
mately this average speed throughout the day (and throughout the
Basin) on surface streets. However, we treat freeway emissions as
a function of average speed, which varies both spatially and temp-
orally (see next section).
Finally, we shall mention two relatively minor factors that in-
fluence the estimation of non-freeway emissions of CO and hydrocarbons.
First, the city traffic department estimates average surface route
speeds in Los Angeles to be somewhat higher than the FDC average speed
of 19.6 mph. These estimates range from 21 to 23 mph. Compensating
for the decrease in emissions rate expected at these higher average
speeds is the second factor, the inclusion of vehicle operations in
excess of 50 mph in the FDC. If freeway emissions are to be treated
separately, it is appropriate to increase average emissions values
by removing the "freeway portions" of the cycle and computing a re-
vised average emissions rate. The net effect of introducing these
two modifications is to leave the initial value of Q^ virtually
unchanged, as the effects tend to cancel each other. For this reason,
and because the degree of representativeness of the Q? values re-
mains unclear, we elected to ignore these factors in estimating sur-
face street emissions rates.
2. Emissions/Average Speed Correlation
In the original formulation of the vehicle emissions model, we
assumed that emissions rates from freeways may be treated as con-
stants, independent of driving conditions and route speeds. A major
weakness of this formulation is that it fails to account for both
the high emissions rates that occur during the rush hour congestion
and the reduced emissions rates associated with higher average speeds.
Rose et al. (1965) have shown that, while variations in emissions
rates are attributable to factors such as route conditions and the
percentage of time in accelerate, decelerate, idle, and cruise modes
(these factors being reflected in traffic volume, average route speed,
and the nature of the local terrain), average emissions rates for Los
Angeles correlate well with average route speed alone. Furthermore,
this single index is sufficient to provide estimates of emissions
rates. Their correlations are based on a linear relationship between
the logarithm of average emissions rates and the logarithm of average
route speed. _ It is on these findings that we have based our correlations,
A-26
-------
The following information was required to develop the emissions
rate/average speed correlation presented in the summary:
1) The slopes of emissions rate/average speed curves for CO,
hydrocarbons and nitrogen oxides. However, as these values
are estimated from tests of vehicles of 1955 to 1963 man-
ufacture, we have modified the a^ and b^ in a manner
to be described.
2) Average emissions rates for "hot-running" conditions at a
known average speed. These rates, reported in the summary,
were estimated as described in the preceding section.
3) Average freeway speed as a function of time for both
directions on all freeways in the Los Angeles Basin.
These data were obtained from the State Division of
Highways (Arcineaux (1971)).
4) Average vehicle flow as a function of time for both
directions on all freeways. Individual flows were estimated
from the data base discussed on p. A-18 of Roberts et al. (1971)
Values of x (= ns/nf) were computed using these data.
The data under 1) and 2) were needed to estimate emissions rate
as a function of average speed, the data under 3) and 4), average
speed as a function of location and time.
Emissions/average speed data are very scarce; measurements of this
type are rarely made. Thus, while Rose's data are somewhat out of
date (less than 50% of the vehicles on the road in September 1969
are represented by this test group), they are the best available
that pertain to the period of interest. However, when correlations
based on these data are used to estimate average emissions rates
at high speeds under hot-running conditions, the estimates appear
to be rather low. For example, while the values of 91 and 68.6
grams/mile represent FDC-based average CO emissions rates under
cold and hot-running conditions respectively, we predict an average
rate of only 26 1/2 grams/mile at 65 mph using a correlation based
on Rose's slope (bco = -.89). We thus decided to modify Rose's
values for use in the present work.
A-27
-------
We have based our modifications on the premise that, since the
California and the Federal Driving Cycles have been the standard
for testing new emissions control systems, automobile manufacturers
design their systems with the expectation that they will be tested
at low average speeds (22.2 mph and 19.6 mph respectively for the
two test cycles). Thus, contrasting 1963 (the last year of manu-
facture for Rose's test vehicles, a time during which vehicles
were uncontrolled) with the present, it may be expected that
average emissions rates at low average speeds have decreased more
rapidly, from model year to model year, than average emissions
rates at high average speeds. The net effect would be that the
b^ values that were estimated for CO and hydrocarbons at the time
of Rose's study would increase with each engine or exhaust system
modification, becoming less negative with each succeeding year.
We have no data on which to base an estimate of a revised slope.
In the absence of appropriate information, we have estimated the
slopes b^ reported in the summary using two points, the hot-
running emissions rates at 19.6 mph, and the rates at 60 mph, the
latter computed from
0^(60) + l/3[Qj(19.6) - Qh(60)] (7)
where Q^(19.6) are FDC values, modified for "hot-running" con-
ditions, and Q"(60) are the rates computed using Rose's correla-
tion equation and his estimates of slopes. The factor of 1/3 is
a guess as to the relative decrease in emissions rates at high
and low average speeds. It must be made clear that this factor
might be anywhere between 0.1 and 0.5; the value of 1/3 is merely
a guess and is certainly subject to revision as data become available.
3. Correction for Nonuniform Distribution of Vehicle Starts
In the original form of our model, we assumed that "hot-running"
CDC tests adequately represent vehicle emissions rates. We have
now adopted average emissions factors for surface streets, Qf (t) ,
based on a weighted average of "hot" and "cold-running" emissions
factors, as shown in equation (1). However, one further modifica-
tion in the treatment of surface street emissions is required,
accounting for the effect on average emissions rates of sudden
variations in the number of vehicle starts. We can best illustrate
the need for this modification through a simple example.
A-28
-------
Let us assume that all vehicles on the road are operated as
prescribed by the FDC, namely that they are run for 23 minutes/
and that steady-state engine temperature is attained about 8-1/2
minutes after start-up. Emissions from an individual vehicle as
a function of time might thus be described as shown in Figure 15.
If we further assume (1) that trip starts are distributed uniformly
in time, and (2) that all vehicles on the road were "cold" when
started, then, at any time, about 100(8.5/23)% , or 37%, of
vehicles on the road have not yet achieved steady-state operating
temperature. Under these conditions the average emissions for all
vehicles is given by the horizontal dotted line in Figure 15.
Suppose now that 10,000 vehicles are currently in operation,
under the circumstances stated, in some region of interest. Suppose
further that an additional 5000 vehicles are started in the next
three minutes (all "cold"). The immediate effect of adding these
additional vehicles to the pool of autos in use, each emitting at
relatively high rates owing to their "cold" operation, would be
to temporarily increase the average emissions of all 15,000 vehicles
in operation to a value in excess of that given by the dotted line.
Suppose, however, that we maintain vehicle starts at the increased
rate of 5000 starts every three minutes for the next several hours.
After about 20 minutes (i.e., 23 minutes less 3 minutes), we would
find that we are again terminating trips at the same rate that we
are initiating them and that, as before, 37% of vehicles on the road
are still in the "warm-up" period. The average emissions rate for
all vehicles is once again given by the dotted line, despite the
fact that the total number of cars in operation has increased
dramatically.
Thus, we observe that the effect of suddenly increasing the rate
of vehicle starts, and maintaining that rate at a constant level
thereafter, is to temporarily increase the fraction of cars in
warm-up to a value greater than 0.37. Since vehicles in warm-up
emit carbon monoxide and hydrocarbons at a higher rate than do
"hot-running" vehicles, the average emissions rate of all cars in
operation increases. After sufficient time passes to equalize the
rate of start-ups and trip terminations (23 minutes), the original
value of average emissions rate again applies.
A-29
Figure 15 follows
-------
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o
(0
u
0)
4-'
tn
C
o
(0
H
300
200
189.6
100.
Notes:
Areas under solid and dashed curves
are equal.
W = Assumed v.'arm-up time.
T = Length of Federal Driving Cycle
Average cold-start emissions rate
(FDC-based estimate) =91.0 grams/mile
Average hot-running emissions rate
= 68.6 grams/mile
VL L
I
10 15
Time (minutes)
20
25
Figure 15. Estimated Variation in Emissions Rate as a Function of
Time (Example: Carbon Monoxide)
A-30
-------
The phenomenon that this example illustrates, the inducement of
variations in average emissions rate due to variations in the rate
of vehicle start-ups, is best exemplified during the morning rush
hours. The rapidly increasing rate of vehicle starts in the early
morning has the effect of increasing average emissions rates until
some time when the rate of starts begins to taper off. Soon, more
trips will be terminated than initiated and the average emissions
rate will drop, not only returning to its original level, but
falling below that given by the dotted line in Figure 15. Eventually,
however, an approximately steady rate of vehicle starts will be
attained (immediately following the "rush" period) and the average
"dotted line" rate will again apply.
We have accounted for the effects of variations in the rate of
vehicle starts through the correction function, 3^(t) , that appears
in equation (5). The curves shown in Figures 13 and 14 describe
the variation in 8i(t) with time for carbon monoxide and hydrocarbons.
The derivation of these functions is detailed in the remainder of
this section. However, before turning to this discussion, we wish
to note three points. First, since the "hot" and "cold-running"
emissions rates for NOX are assumed to be equal, BNO^) = 1 f°r
all t . Second, even though the rate of trip starts varies
throughout the day (as may be seen from Table 1, which is reproduced
in part in Figure 16), we have considered the effect of these varia-
tions only for the period 6 a.m. to 9:23 a.m. We have not included
the effect on B^Ct) of the "midday bump" in Figure 16, as the
majority of vehicles operating during that period are "hot-started"*
and the bump is small compared with the rush-hour bumps. Neither
have we included the effect of the "evening bump", as we do not plan
to validate our model for that time period. Third, it should be evident
that, in order to properly evaluate 3i(t) , large quantities of data
are needed. Pertinent data include those involving driving patterns
in the Los Angeles area, trip length, average speed, time between
trips, etc. Also needed are emissions data as functions of time
for both "cold" and "hot-starts". As such data are, for the most
part, unavailable, we have based our model on what data we were able
to obtain. In the absence of full information, we have made what we
believe are reasonable simplifying assumptions in deriving 3j_(t) .
Note that if all vehicles are "hot-running", and there is a sudden
increase in vehicle starts (all "hot"), there will be no effect on the
average emissions rate. For the effect to be noticeable, a reasonable
percentage of vehicle starts must be "cold".
A-31
Figure 16 follows
-------
120
100
80
60
40
_L
_L
J.
6 7 8 9 10 11 12 13
Figure 16. Distribution of Weekday Trip Start Times in Los Angeles (Kearin, et al. (1971))
14
15
Time
-------
a. General Mathematical Statement of Problem
The relationship for B j_(t) was derived in the following
manner: Let
t = time of day
T = length of FDC (minutes)
c(t) = distribution of vehicle trip-start times, such
that the number of vehicles started between times
t and t + dt equals c(t)dt
T = time elapsed after vehicle start-up (minutes)
e"?(T) = emissions from a vehicle at time T after a 00.10-
start (grams/mile)
e.(T) = emissions from a vehicle at time T after a hot-start
(grams/mile)
y(t) = ratio of cold-starts to total starts during time
interval dt
The number of vehicles started between time t-x-di and
t-x is given by c(t-T)dT (see Figure 17). The emissions
rate of species i from a vehicle at time t , cold-started at
the time t-T , is E?(T) . Assuming that the average trip length
for all vehicles is T , the total emissions rate of species i
at time t is given by
/[y(t-r)e°(T) + (l-y(t-T))e£(T)]c(t-T)dT
_
and the average emissions rate from each vehicle by
f
/
(l-y(t-T))eh(T)] c(t-T)dt
q ' - - 1
Ei(t) -
c
I c(t-T)dT
A-33
Figure 17 follows
-------
-p
t)
Area under the curve
equals the number of
trip starts dur.ing
the time period
designated.
c(t) is defined such that the number of trips started between times t
and t + dt equals c(t)dt.
T is the length of the Federal Driving Cycle (23 minutes) assumed
equal to the average trip length.
T is a dummy variable of integration but is also equal to the length
of time a car has been runn.ing at time t which was started at time t-T
Figure 17. Explanatory Diagram for Derivation of Equation 8.
A-34
-------
The correction factor is then defined as
ES(t)
B. (t) = -i (9)
Qj(t)
g
where Q.(t) is given in equation (1).
b. Evaluation of 3-i
In order to integrate equation (8), it is necessary to
establish a functional form for eij-(T) and £^(1) . Recent
data obtained from the EPA (Sigworth (1972)) show that engine
operating temperatures reach steady-state levels about 7-1/2
minutes after a "cold-start". Based on this information, we
have assumed that a simple relationship exists between E?(T)
and time, as shown in Figure 15. We have postulated a linear
decrease in emissions rate during the first 7-1/2 minutes of
operation and a constant emissions rate thereafter. This rate
is equal to £^(T) , and, being constant over time is also equal
to Q^ . The slope of the GC(T) curve during the warm-up
period is calculated by equating the area under the solid line
to the average "cold-start" emissions rate, given by the dotted
line.
In order to calculate 3i(t) for carbon monoxide and hydro-
carbons using equations (8) and (9), we also need to know the
temporal dependence of c(t) . Kearin et al. (1971) recently
carried out a survey of average driving patterns for six urban
areas in the United States. In their survey, based on a sample
of 946 drivers (169 drivers in the Los Angeles area)*, they
Kearin, et al. note that "...when one considers the number of auto-
mobile trips made daily in even the smallest of the cities sampled, it
becomes clear that our sample sizes are puny". Thus, while the
statistics employed in this analysis are the most useful available,
their reliability is clearly subject to question and they must be used
with caution.
A-35
Table 1 follows
-------
Table 1.
Distribution of Weekday Trip Start Times in Los Angeles, c .
Time
From
0001
0016
0031
0046
0101
0116
0131
0146
0201
0216
0231
0246
0301
0316
0331
0346
0401
0416
0431
0446
0501
0516
0531
0546
0601
0616
0631
0646
0701
0716
0731
0746
0801
0816
0831
0846
period, n
To
0015
0030
0045
0100
0115
0130
0145
0200
0215
0230
0245
0300
0315
0330
0345
0400
0415
0430
0445
0500
0515
0530
0545
0600
0615
0630
0645
0700
0715
0730
0745
0800
0815
0830
0845
0900
No. of
Trips
15
5
4
4
1
1
2
1
2
4
2
4
2
2
0
3
1
3
1
1
0
1
2
13
32
51
74
76
127
92
84
77
50
31
40
21
Time
From
0901
0916
0931
0946
1001
1016
1031
1046
1101
1116
1131
1146
1201
1216
1231
1246
1301
1316
1331
1346
1401
1416
1431
1446
1501
1516
1531
1546
1601
1616
1631
1646
1701
1716
1731
1746
period, n
To
0915
0930
0945
1000
1015
1030
1045
1100
1115
1130
1145
1200
1215
1230
1245
1300
1315
1330
1345
1400
1415
1430
1445
1500
1515
1530
1545
1600
1615
1630
1645
1700
1715
1730
1745
1800
No. of
Trips
19
21
22
30
24
21
24
26
34
31
37
75
47
57
47
56
45
37
36
26
23
25
27
34
38
44
39
48
45
83
155
128
119
147
105
97
Time
period, n
From To
1801
1816
1831
1846
1901
1916
1931
1946
2001
2016
2031
2046
2101
2116
2131
2146
2201
2216
2231
2246
2301
2316
2331
2346
1815
1830
1845
1900
1915
1930
1945
2000
2015
2030
2045
2100
2115
2130
2145
2200
2215
2230
2245
2300
2315
2330
2345
0000
No. of
Trips
69
78
74
66
58
62
63
52
50
53
58
51
22
31
21
35
21
17
14
9
16
10
11
7
A-36
-------
The calculation of 8-(t) was carried out as follows.
Let the total number of trips started in the fifteen minute
interval denoted by n equal cn . If we assume the trip
start rate to be uniform during each fifteen minute interval,
then we can approximate the integral of equation (8) by:
n-2 h
- y )en + y I.}
n i n i
30
n-1
where:
(10)
n
= denotes a fifteen minute time interval
E.(t ) = Average emissions rate of species i evaluated
at the mid-point of time interval n .
e. = Average emissions rate of species i from an
automobile over the time period between 7-1/2
and 22-1/2 minutes after a cold^-start.
e. = Average emissions rate of species i from an
automobile over the time period between zero
and 7-1/2 minutes after a cold-start.
Using the emissions factors given earlier we have
estimated e". and e. as:
Species
CO
HC
e .
i
(grams/
69.1
10.82
£.
i
mile)
136.2
13.52
A-37
-------
In using the results of Kearin et al., we elected to segment
the weekday into eight time periods, as suggested by the
slope of the curve in Figure 16. We assigned to each period
a constant value of y , the ratio of cold starts to total
starts. These values of y given in Table 2, the values
of Qf(t) given in the same table, the emissions curve of
Figure 15, and the distribution of vehicle start-ups Cn
shown in Figure 16 form the basis for evaluating equation (10)
to obtain SCQ^ an(^ &HC^ The results of these inte-
grations are given in Figures 13 and 14. Note, again, that
3110^ = 1 ' as QhQ = Q^ .
X X
A-38
Table 2 follows
-------
TABLE 2. TEMPORAL DISTRIBUTION OF "COLD-STARTS"
n Time Period
% of daily
trips started
fraction of
cold starts to
total starts
Q
y
3**
CO
HC
grams/mile]
1
2
3
4
5
6
7
8
0:00
6:00
9:00
11:30
13:30
16:30
18:30
.21:00
- 5
- 8
- 11
- 13
- 16
- 18
- 20
- 23
:59
:59
:29
:29
:29
:29
:59
:59
2
21
6
10
12
24
16
6
.0
.0
.9
.7
.1
.7
.1
.5
0
0
0
0
0
0
0
0
.90
.85
.25
.30
.20
.50
.15
.20
88
87
74
75
73
79
72
73
.8
.6
.2
.3
.1
.8
.0
.1
11
11
11
11
10
11
10
10
.61
.57
.03
.07
.98
.25
.94
.98
Note: Kearin, et al. (1971) have estimated that a vehicle in Los Angeles
makes an average of 4.66 trips per weekday. Of these 4.66 trips,
we have estimated that 2 are "cold-started" and 2.66 are "hot-
started". Thus:
8 8
Ey c = 42.92, and V* (1-y )c = 57.08
n n / j n n
n=l n =1
Using the figures from the above table:
8 8
Eye = 43%, and V* (1-y )c = 57%
n n / j n n
n=l
n=l
Estimated from Figure 16.
**
(Figures 13 and 14) to obtain
These figures should be multipled by 3^ (t
the surface street emissions factors, Es(t) . (S.(t) = 1, except
for the period 6:00 - 9:23 a.m. ) 1 1
A-39
-------
III. REVISIONS OF THE AIRCRAFT EMISSIONS INVENTORY
Since the completion of the original emissions inventory, the
results of two studies dealing with the emissions from aircraft have
become available.
(1) Emissions tests of reciprocating aircraft engines were
performed recently by Scott Research Labs (1970). Based
on their findings, entries in Table A-14 of Roberts et al.
(1971), have been updated. Changes are shown in Table 3.
(2) New information involving the average number of jet
aircraft flights per day at Los Angeles International
Airport has been reported by the Los Angeles APCD (1971).
We have correspondingly altered the appropriate statistics
in Table A-18 of Roberts et al. (1971), as shown in
Table 4.
The change in total emissions from each square as reflected by these
alterations is very small; the revisions are made primarily for the
sake of completeness and consistency.
Finally, we have assumed, for lack of better information, that
aircraft exhaust has approximately the same hydrocarbon composition
as automobile exhaust, and thus the same molecular weights for the
reactive and unreactive groupings.
The inventory, as reported by Roberts et al. (1971) and herein,
should be considered representative of airport and aircraft emissions.
However, we note here that we do not include emissions released from
elevated sources, i.e., from aircraft during ascent and descent, in
the airshed model due to the small contribution of these sources to
the total emissions load in cells adjacent to the airports.
A-40
Tables 3 and 4 follow
-------
Table 3. Corrections to Table A-14 of Roberts
et al. (1971), Emissions Factors, fj*
and ffj (Northern Research (1966))
Emission factors, f^u and f£
(pounds/1000 pounds of fuel)
Aircraft Operating
Class Mode
u = 1 Idle & Taxi
Approach
LTC*
2 Idle & Taxi
Approach
LTC
3 Idle & Taxi
Approach
LTC
4 Idle & Taxi
Approach
LTC
5 Idle
Taxi
Approach
LTC
6 Idle
Taxi
Approach
LTC
7 Idle & Taxi
Approach
Climb-out
CO
174
8.7
0.7
50
6.6
1.2
118
11
4
24.8
1.6
2.3
600 8^6
-966-9)0
000 S*-i>
1250
--6SQ- S9fo
900 910
000 3i£
1050
118
11
4
Organics
75
16
0.1
9.6
1.4
0.6
11.5
0.6
0.3
8.1
0
3.2
±tt~ 11
-96- 4$
-66- iOt
190
-i&6- -3£
^96-^3
-66-104
110
11.5
0.6
0.3
NOx
2.0
2.7
4.3
2.0
2.7
4.3
2.0
2.7
4.3
3.7
2.9
3.1
e- 7
*- L
-s- 3
0
-6- 7
-9- Z
-5- 3
1
2.0
2.7
4.3
*Land, Take-Off and Climb-Out
A-4.1
-------
4^
ro
Table 4. Corrections to Table A-18 of Roberts et al. (1971),
Average Number of Aircraft Flights Per Day at. ^os Anyeles Basin Airports
^v. Aircraft
Airport\Class 1. 2_ 3_ _4 5_ £A °
0
0
0
0
0
0
0
0
0
0
0
47(2.5)
0
2& °
f\ \ ^^ 1 f\f / *") Q \
\j j j^TTT \ £* ^? /
12(2.0)
0
0
0
0
0
6(1.5)
0
125(1.0)
0
0
19(2.0)
2(2.0)
3005(1.0)
9(1.0)
0
0
3(2.0)
0
25(2.0)
0
0
0
0
0
0
4(2.8)
0
0
57(2.9)
0
0
0
0
0
0
0
0
0
0
0
25(4.0)
67(4.0)
50(2.0)
21(3.2)
0
0
0
0
14(4.0)
0
288(1.0)
191(1.0)
21(1.9)
700(1.0)
428(1.0)
225(1.6)
591(1.4)3
0
159(1.4)3
850(1.4)3
100(1.1)
525(1.1)
500(1.1)
720(1.0)
200(1.1)
10(1.0)
0
20(1.0)
0
0
10(1.0)
25(1.0)
0
58(2.0)
0
0
25(1.0)
0
125(1.0)
0
-1968 data.
2Nuitibers in parentheses are average number of engines per aircraft.
Total national averageFAA controlled terminals (Northern Research (1968)).
4Airport closed March 1, 1971.
Class 3 activity at this terminal is mostly military aircraft. Military engines are estimated to be
equivalent to six Clas? 3 aircraft engines. Thus, numbers of flights shown are actual flights
multiplied by six*
-------
IV. FIXED SOURCE EMISSIONS - POWER PLANTS
We carried out a thorough review of the inventory and model of
pollutant emissions from power plants in the Los Angeles Basin. Based
in this review, we felt that the emissions model needed both revision
and extension, particularly with regard to
the apportionment of emissions from a power plant among cells
downwind of the source
the inclusion of temporal variations in emissions rates
the treatment of "inversion penetration"
the calculation of the average molecular weight of emitted
hydrocarbons
The original model and inventory for power plant emissions is discussed
in Chapter III of Roberts et al. (1971). We describe only the modifica-
tions to that model and inventory in the presentation that follows.
A. Apportionment of Emissions
The original model for apportioning emissions among downwind
squares can be summarized as follows:
1. Draw a straight line, beginning at the source, in the
downwind direction parallel to the direction of wind
flow.
2. Continue the line until it passes through portions of
no more than three squares including the square in which
the source is located (only two if it passes through a
corner).
3. Apportion emissions among the three squares in proportion
to the length of the segment passing through each square
See p. A-49 of Roberts et al. (1971) for a full description of the
model.
A-43
-------
While the model was intended to be simple and therefore could
be expected to provide only a rough basis for allocating emissions, it
nevertheless displayed a major defect. Under low wind conditionssay,
one to two mphemissions were advected too far and too quickly by the
model, thus providing estimates that were too low near the source and
too high downwind.
To rectify this flaw in the model, we now apportion power plant
emissions in the following manner. The fraction rj/ (r^ + r2 + r3)
of power plant emissions is allocated to each of the three downwind grid
squares, where
r + r + r < 3.5 miles (11)
and
rn + r_ + r_< (60 minutes) x (wind speed in ft./min.)
1 2. 3
(12)
(See Figure 18a.) If the situation depicted in Figure 18b. occurs,
the segment r. is ignored, and apportionment is carried out in
proportion to the lengths ri ' r9 ' anc^ r3 Note that inequal-
ities (11) and (12) both must apply.
B. Temporal Distribution of Emissions
We found in reviewing data obtained from the Southern California
Edison Company, that diurnal temporal variations in NOX emissions
are substantial and must be taken into account in our airshed model.
Inclusion of these variations is particularly important in the vicinity
of the Pasadena, Burbank, and Haynes plants, as each is located in
immediate proximity, and often upwind, of a LAAPCD monitoring station.
After analyzing the Southern California Edison data, we contacted
the Los Angeles Department of Water and Power, and the Cities of Pasadena,
Burbank, and Glendale to obtain the additional data needed. The data,
summarized in Table 5 are of somewhat varying specificity and reliability.
Yet, be believe the improvement in accuracy realized by their inclusion
far outweighs the inconsistencies introducedsay, by including data for
one day in the case of the SCE plants, and data averaged over a season
for the remaining plants.
A-44
Figure 18 and Table 5 follow
-------
(a)
win<
Power
Plant
(b)
wind
0 1 mile
Figure 18. Apportionment of Power Plant Emissions
A-45
-------
TABLE 5 - TFMPORAL DISTRIBUTION OF POWFR PLANT EMISSIONS
TIME (LOCAL)
10
11
12
13
15
16
RFMAPKS
Southern Cal. Fdison
Los Alamitos
Fl Segundo
Redondo Beach
Hunt ing ton Beach
LA Pept. of V/ater
a nd Powe r
C i ty of Pasadena
C i ty of Burbank
City of Glendale
44.3 48.9 ''3.7 59.7 78.9
51.4 56.8 52.3 63.2 82.7
65.2 77.3 ^5.6 85.4 94.4
38.? 38.0 74.4 82.2 100.0
59.1 60.5 69.6 81.9 91.3
55.1 62.7 71.0 81.6 85.5
33.9 33.n 34.8 ''0.9 51.3
25.7 22.2 29.6 35.7 42.2
44.8 '-6.6 56.9 70.1 77.6
41.4 47.1 58.0 69.0 71.3
35.9 37.3 ''-2.5 51.0 60.1
32.0 35.9 ''6.4 55.6 5°.5
71.3 ^.9 100.8 113.0 121.3 123.9 121.7
79.5 84.1 75.P 96.P 105.9 110.5 1o8-2
90.8 <^3.° 90.3 97.5 10?..0 106.5 104.3
98.3 °8.3 03.3 102.2 102.2 10^.4 104.4
96.8 100.4 100.8 104.0 104.4 105.1 103.7
87.0 86.3 8C.3 8y.fi 87.4 85.5 f!i,.i
61.3 67.0 70.4 72.2 74.8 76,5 76.1
47.0 1*7.8 ''7.0 46.5 ''-6.5 46.1 45.7
83. ? 88.5 90.2 96.6 97.7 100.6 5)8.3
71.8 71.8 69.0 70.1 70.7 67.0 65.5
68.6 74.5 78.': 81.0 86.3 RQ. 5 01.5
62.1 f>2.1 62.1 60.1 60.1 5q.8 57.5
September 30, 1969
September 30, 1969
September 30, 1 969
September 30, 1969
Summer
Winter
Summer
Winter
Summer
Wi nter
Summer
Winter
MOTE: The entries are percentages of nominal hourly emission rates estimated in Appendix A.
The distribution for the LA Department of Water and Power is the averace for their
four power plants -- Harbor, Maynes, S>cattergood, and Valley -- and, as such, is
applied to each.
A-46
-------
C. Penetration of the Inversion Layer by a Plume
Oftentimes, during the early morning hours, the base of the in-
version overlying the Los Angeles Basin is sufficiently low that it
can be penetrated by plumes emenating from tall stacks. In order to
include this phenomena in an airshed model, it is necessary to specify
the conditions under which penetration will occur.
The maximum height of the base of an elevated inversion above a
stack, Ah , that a buoyant plume can penetrate is expressed by
Ah =. 1.128 I "m I (moderate wind) (13)
where Q = heat emissions from the stack
H
u = average wind speed at the stack height
P = average density of ambient air
C = specific heat of air at constant pressure
P
AT. = temperature difference between top and
bottom of the elevated inversion
as given by Briggs (1971). For calm conditions Briggs suggests the
use of
Cow wind)
A-47
-------
If Ah + H is less than the local mixing depth, where H is the stack
height, emissions are apportioned as described in part A of this section.
If Ah + H is greater than the local mixing depth, emissions are assumed
to be injected into or above the inversion layer and are thus not appor-
tioned below the inversion base.
In order to implement these formulae, we need to establish a critical
wind speed, uc , to determine which of these two formulae will apply under
specific conditions. To estimate uc , we have equated ATj_ in equations
(13) and (14),
(AT,) = (AT,)
moderate wind low wind
By doing thus, we obtain the relationship,
/ 9QH \
Jf. = Q.k I i_)
VvTZ/
where Z is the range of elevation of interest. Hence the following
classifications will be made,
u > u moderate wind
u < uc low wind
For a typical power plant in Los Angeles, QH = 10 cal/sec. Assuming
that the elevation of the inversion base is 400 ft.,
A-48
-------
u -1.9 ft/sec
= 1.25 mph.
D. Calculation of Average Molecular Weight of
Emitted Hydrocarbons
Since power plants burned natural gas during the validation
period, we have assumed that the molecular weight of unreactive species
is between that of Cj_ and £-2 hydrocarbons, but much closer to
that of C^ (about 18). For reactive hydrocarbons, we have assumed
the molecular weight to lie between that of C4 and C^ hydrocarbons,
but closer to C4 (about 60).
A-49
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V. FIXED SOURCE EMISSIONS - DISTRIBUTED SOURCES
AND REFINERIES
We have reviewed the treatment of fixed source emissions rates
(from sources other than power plants) and their spatial and temporal
distribution, as reported in Roberts et al. (1971). The only source of
the data on which the inventory is based is the LAAPCD's published
emissions profile, in which only total emissions rates for a 5 mi. x 5 mi.
grid are reported. With the exception of hydrocarbon emissions, which we
will discuss shortly, we found no reason to alter the treatment of these
emissions, given the limitations in accuracy inherent in the inventory
due to the spatial "lumping" process. However, it would be most helpful
if the APCD would furnish emissions data (locations, rates and temporal
distributions) for
(1) large sources, such as steel and aluminum plants
(2) sources located near monitoring stations.
With respect to hydrocarbon emissions from fixed sources, the
LAAPCD has classified these as follows:
Unreactive (U) - all paraffins
Reactive (R) - all aromatics, olefins, and acetylenes
We, in contrast, have classified GI to C$ paraffins, benzene, and
acetylene as unreactive, all other hydrocarbons as reactive. In order
to place hydrocarbons emissions from all sources on the same basis in
terms of reactivity, we have re-evaluated previously estimated HC emissions
rates from (1) refineries (Tables A-15 and A-16 of Roberts et al. (1971))
and (2) other distributed fixed sources (Tables A-20 and A-21). Emission
rates in tons per day from these sources, based on classifications of the
APCD (old) and ourselves (new), are given in Table 6. The net result is
that entries in the tables in Roberts et al. (1971) must be multiplied
by the following factors to convert from the APCD classification system
to our classification system:
Figure (in Roberts et al. (1971)) Source Reactivity Multiplier
A-15 Refineries R 5.000
A-16 Refineries U 0.555
A-20 Petroleum R 3.233
marketing and
organic solvents
A-21 Petroleum U 0.355
marketing and
production and
organic solvents
A-50
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Finally, since refineries and other fixed sources primarily
burned natural gas during the validation period, we have assumed
that the molecular weight of unreactive species is the same as that
for unreactive hydrocarbons emitted from power plants, i.e., be-
tween C-, and C2 / but much closer to C^ (about 18) , and that
of reactive species between C4 and 05 , but closer to C^ (about
60) .
A-51
Table 6 follows
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TABLE 6. Hydrocarbon Emissions From Fixed Sources
Source
Refineries
Other Distributed
Fixed Sources
Petroleum Production
Petroleum Marketing
Solvent Evaporation
Total
Old (APCD)
U
<*5
60
60
kQQ
520
R
5
0
50
100
150
New (SAI)
U
25
60
0
125
185
R
25
0
110
375
485
Total
50
60
1 10
500
670
A-52
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