EPA-650/4-74-001
THE APPLICATION
OF REPRO-MODELING
TO THE ANALYSIS
OF A PHOTOCHEMICAL
AIR POLLUTION MODEL
by
Alan Horowitz, William S. Meisel,
and David C. Collins
Technology Service Corporation
225 Santa Monica Boulevard,
Santa Monica, California 90401
Contract No. 68-02-1207
Program Element No. 1A1009
EPA Project Officer: Ronald E. Ruff
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
December 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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Ill
Abstract
Several physical models which simulate the impact of emissions and
meteorology on the creation and dispersion of photochemical smog have
been developed. Characteristics of most of these models are that they
are highly computational and require a great deal of input data; hence,
it is generally difficult to systematically explore the implications of
the models or to use them in a planning context where many model runs are
required. This paper explores "repro-modeling," the analysis and replica-
tion of the input/output characteristics of the model, as a means of
meeting these objectives. A study of the application of repro-modeling
to the SAI model developed for the Los Angeles Basin is described. The
major objectives of the study were threefold: (1) a feasibility test of
the repro-modeling approach; (2) a limited interpretation of the implica-
tions of the model; and (3) an efficient repro-model program which
duplicates input/output relationships of the original model. The repro-
model developed is analyzed in a particular application context (i.e.,
transportation emission control policy evaluation) and its general
implications are discussed. Examples of use of the repro-model, which
requires orders of magnitude less computer time than the original model,
are provided.
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TABLE OF CONTENTS
Abstract i i i
List of Figures vii
List of Tables xi
SECTION
1.0 INTRODUCTION 1
1.1 Major Objectives 2
1.2 Limitations of the Present Study 3
1.3 Outline 6
2.0 THE PHOTOCHEMICAL POLLUTION MODEL 8
2.1 Overview 8
2.2 Input Requirements of the SAI Model 10
2.3 Outputs of the SAI Model 11
2.4 Computational Requirements of the Model 12
3.0 AN APPLICATION CONTEXT 13
3.1 A Repro-Model for Evaluating Effects of
Transportation Control Strategies 13
3.2 The Policy Region 14
3.3 Outputs of the Repro-Model 22
3.4 SAI Model Runs 26
4.0 REPRO-MODEL DEVELOPMENT 32
4.1 The Technical Approach 32
4.1.1 Continuous Piecewise Linear Functions 34
4.2 Implications of the Precision of the SAI Model for
Statistical Analysis 43
4.3 Repro-Models Created and Accuracy Achieved 45
4.4 The Repro-Model Program 54
5.0 IMPLICATIONS OF THE MODEL 58
5.1 General Implications of the Model 58
5.2 Examples of Repro-Model Use 69
5.2.1 Impact of Emission Controls on Motor Vehicles. 69
5.2.2 Ratio of Hydrocarbon Emissions to NOX
Emissions 72
5.2.3 Effects of Single Day Emission Reduction 76
6/0 CONCLUSION -. 78
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VI
TABLE OF CONTENTS (Continued)
ACKNOWLEDGMENTS 81
REFERENCES 83
APPENDIX 85
A.1 Repro-Model Documentati on 85
A.2 Program Listing 88
A. 3 One Hundred SAI Model Runs 96
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VI1
LIST OF FIGURES
1.1 INPUT-OUTPUT STRUCTURE OF THE ORIGINAL MODEL AND
THE REPRO-MODEL 4
2.1 THE SAI COORDINATE SYSTEM AND LOCATIONS OF REPRO-MODELS 9
3.1 A PROJECTION ON THE (x1}x2) AXES OF THE FIVE-DIMENSIONAL
POLICY REGION 17
3.2 THE RANGE OF THE INITIAL CONDITION VARIABLES 19
3.3 RELATIONSHIP BETWEEN NOX MOBILE SOURCE EMISSION AND
INITIAL CONDITION VARIABLES 20
3.4 1969 VMT WITH VEHICLE MIX OF YEARS 1969-1980 23
3.5 EFFECT OF VMT CHANGES ON MOBILE SOURCE EMISSIONS 24
3.6 A PEAK OXIDANT "HISTOGRAM" FOR THE BASELINE RUN 27
4.1 THE OVERALL REPRO-MODEL AS A COLLECTION OF REPRO-MODELS
FOR EACH DEPENDENT VARIABLE 33
4.2 A CONTINUOUS PIECEWISE LINEAR FUNCTION OF ONE VARIABLE . 35
4.3(a) AN EXAMPLE OF A CONTINUOUS PIECEWISE LINEAR FUNCTION
IN TWO VARIABLES—AN OXIDANT REPRO-MODEL (10,24) 36
4.3(b) AN EXAMPLE OF A CONTINUOUS PIECEWISE LINEAR FUNCTION
IN TWO VARIABLES—AN N02 REPRO-MODEL (10,21) 37
4.4 AN EXAMPLE OF POSSIBLE SUBREGIONS FOR A TWO-VARIABLE
CONTINUOUS PIECEWISE LINEAR FUNCTION 39
4.5(a) FIT OF PERFECTLY PIECEWISE LINEAR DATA 44
4.5(b) SAME FIT AS 4.5(a) ON DATA WITH ROUNDOFF ERROR
INTRODUCED 44
4.6 EXAMPLE OF AN OUTPUT TABLE FROM ONE RUN OF THE
REPRO-MODEL 47
5.1 A "CUT" OF THE MODEL HOLDING THREE VARIABLES CONSTANT
AT ZONE (10,24) 59
5.2 A SIMPLE ILLUSTRATION OF THE POSSIBLE NEED FOR A
TRANSITORY SUBREGION 66
5.3 EFFECT OF VARYING NOX WHILE HOLDING HYDROCARBONS
CONSTANT ; 74
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LIST OF TABLES
3.1 POLICIES WHICH CAN BE EVALUATED USING THE REPRO-MODEL . 16
3.2 POLICY REGION CONSTRAINTS 21
3.3 DEPENDENCE OF ZONE PREDICTIONS 29
3.4 THE PEAK AS A PREDICTOR OF OTHER CONCENTRATIONS 30
4.1 TEN POLICIES USED IN TESTING REPRO-MODELS 46
4.2 COMPARISON OF CONTINUOUS PIECEWISE LINEAR FIT WITH
FIVE VARIABLE LINEAR AND QUADRATIC FITS 47
4.3 REPRO-MODEL COEFFICIENTS FOR OXIDANT 49
4.4 REPRO-MODEL COEFFICIENTS FOR N02 51
4.5 REPRO-MODEL SPECIFICATIONS FOR OXIDANT 52
4.6r REPRO-MODEL SPECIFICATIONS FOR N02 53
4.7(a) RMS ERROR OVER TEN TEST POLICIES N02 55
4.7(b) RMS ERROR OVER TEN TEST POLICIES OXIDANT 55
5.1 ANALYSIS DATA FOR OXIDANT REPRO-MODELS 63
5.2 COEFFICIENTS OF LINEAR FUNCTIONS FOR OXIDANT
REPRO-MODELS 67
5.3 ANALYSIS DATA FOR N02 REPRO-MODELS 70
5.4 IMPACT OF FEDERAL EMISSION CONTROL STANDARDS MOBILE .
SOURCES—OXIDANT 71
5.5 EFFECTS OF SINGLE DAY TRAFFIC REDUCTION POLICY ON
AIR QUALITY 77
A.I REPRO-MODEL POLICY INPUT FORMAT 86
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THE APPLICATION OF REPRO-MODELING TO THE
ANALYSIS OF A PHOTOCHEMICAL AIR POLLUTION MODEL
1.0 INTRODUCTION
In recent years several researchers have developed complex physical
models of the chemistry and dispersion of photochemical pollutants [e.g.,
1,2,3,4]. The major motivation for the models initially was to aid in the
evaluation of detailed plans for implementation of the Clean Air Act. For
an application of this sort, where a few complex strategies are to be
evaluated, the large amount of time required for data preparation and the
high computer cost per run of such models are justified by the resulting
benefits.
There are other uses for a pollution model, however, in which the
computational burden and complexity of data input are significant impedi-
ments. Such uses include (a) gaining detailed insight into the impact of
changes in emission levels and in ratios of pollutants as an aid to
judgment in designing policies; (b) estimating the air pollution impact
in a large-scale planning model measuring many environmental and socio-
economic impacts; and (c) rapidly evaluating hundreds or even thousands of
alternative policies as part of an optimization process, e.g., in develop-
ing an optimal fuel allocation plan.
Repro-modeling has been suggested as an approach to extending the
utility of complex models to such uses [5]. Briefly, repro-modeling
consists of using input/output data generated by the model to understand
its implications and to develop an efficient "model of the model" for
limited purposes. This final report on contract number 68-02-1207 with
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the Environmental Protection Agency explores the utility of repro-modeling
through application to a photochemical pollutant model developed by
Systems Applications, Inc.
1.1 Major Objectives
The major objectives of the present study are threefold:
(1) Feasibility of the repro-modeling approach—A major objective of
the study was a demonstration of the repro-modeling approach and a
test of its feasibility in application to a photochemical pollution
model. Questions in this regard include the following: Is the input/
output structure of the model sufficiently simple to allow repro-modeling
that relationship with a small number of input/output samples of the
model? Is the particular technical approach to the problem of modeling
that relationship practical? Can the implications of the model be
extracted from those input/output samples through the technical
approaches proposed?
(2) Limited interpretation of the present model—Can the results of
the study be phrased so that the implications of the model are made
clear? The interpretation of the relationship between those input
parameters changed and output variables measured for the present
version of the model provides insights into the implications of the
physical relationships embodied in the model and, to the degree of
validity of the model, those embodied in the real world. Since a
further version of the model is currently under development, any
intuitively unreasonable implications of the present version may lead
model developers into opportunities for further model improvement.
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(3) An efficient repro-mode1--We wish to summarize the input/output
implications of a model in relatively efficient equations which, to
the degree of accuracy of the model, yield the same results as running
the original model. This working repro-model, which can be embodied
in a relatively simple computer program, should run orders of magni-
tude faster than the original model. These differences between the
original model and the repro-model are illustrated in Figure 1.1.
1.2 Limitations of the Present Study
The present study has limited objectives and should be interpreted in
that light. Major limitations on the generality of the results include the
following: (a) the original model is calibrated for Los Angeles and the
meteorology was fixed; (b) not all aspects of the original model are
exercised; and (c) relationships implied by the original model are valid aids
for policy design only to the extent that the model represents reality. Let
us discuss these points in turn.
The model utilized was developed by Systems Applications, Inc., under
contract to the Environmental Protection Agency [1]. It was designed from
physical principles to be applicable to many regions, but has been cali-
brated and to some degree validated for the Los Angeles Basin. The study
is limited to one particular high pollution day which is reasonably well
documented and was included in the SAI study; our analysis is particular to
the meteorology on that day. This limitation is not as restrictive as it
might seem. One is usually interested in reducing pollution levels on
extreme days, not average days. In fact, the "rollback" model used in
designing many Clean Air Act implementation plans in effect chooses a
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SAI MODEL
(22 Minutes of
Processing)
40,000 WORDS
OF INPUT
30,000 WORDS
OF OUTPUT
5 WORDS
OF INPUT
REPRO-MODEL
(Milliseconds)
SEVERAL KEY
OUTPUTS
FIGURE 1.1
INPUT-OUTPUT STRUCTURE OF THE
ORIGINAL MODEL AND THE REPRO-MODEL
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a single high pollution day as the point from which to roll back.
Consistent with the philosophy of repro-modeling, the number of vari-
ables varied in the repro-model is orders of magnitudes less than the
number of variables which can be varied in the original model; however,
the repro-model variables are aggregate variables which vary many of the
original model inputs concurrently. The results must hence be qualified
in the sense that all the degrees of freedom of the model have not been
exercised and that the particular means chosen to aggregate the input
variables involve several assumptions. For example, in defining variables
such as the percent reduction in total reactive hydrocarbons emitted, the
assumption was made that basic items such as time and space distribution of
vehicular traffic would not change. Such assumptions, discussed in further
detail in the body of this report, limit the number of alternative policies
which can be evaluated by the repro-model, but are not inconsistent with a
large number of policies. It should be noted that the validity of such
assumptions depends to a large degree upon the outcome of the study; that
is, if the input/output structure of the model is sufficiently simple,
then more detailed assumptions probably are not justified.
An important limitation of the study that should be emphasized at the
outset is that we are modeling a model, and only indirectly the physical
system. Hence, the utility of the results in policy planning is determined
by the validity of the original model. Tests of model validity will not be
evaluated here, but it should be noted that those tests performed were
related to forecasting absolute pollution levels. The repro-model is
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oriented more toward determining relative effects of changing different
variables than predicting absolute pollution levels. If the major char-
acteristics of the physical system are embodied reasonably in the model,
then the relative effects and nonlinearities involved in the process
should be modeled adequately. However, the original model is still under
continuing development, and implications of future versions of the model
may differ. On the positive side, an important aspect of working with
models rather than directly with data from the physical system is that
all variables can be controlled. The physical system is not so coopera-
tive; the difference in pollution levels from one day to another is due
to a large number of factors including changing traffic distributions and
meteorology. In the physical model we can hold traffic distribution and
meteorology constant while manipulating other factors. Hence, for the ex-
ploration of the relative effects of a large number of alternatives, model-
ing the model might in some cases be more to the point than a direct model
of the physical world. From another point of view, the investigation of
the implications of the model in terms of general effects is another form
of model validation. If the model predicts effects which are strongly
counter-intuitive and difficult to justify, this suggests that the compon-
ents of the model contributing to those effects be examined carefully to
suggest improvements in the model.
1.3 Outline
In Section 2.0 the photochemical pollutant model under study is
described briefly. Section 3.0 discusses the application context for the
repro-model; that is, the aggregate input variables and output variables
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chosen are described, the policies to which they correspond are indicated,
and the ranges of the policy variables are specified. Section 4.0 contains
discussion of the repro-models created, the accuracy achieved, and the form
of the results produced by the repro-model program. Section 5.0 discusses
the general implications of the model revealed by the analysis and exempli-
fies the use of the repro-model to examine policy tradeoffs. Section 6.0
reviews and summarizes the results of the study.
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2.0 THE PHOTOCHEMICAL POLLUTION MODEL
2.1 Overview
The photochemical pollution model developed at Systems Applications,
*
Inc., was the focus of analysis in this study. The purpose of the SAI
model is, given emission levels, meteorology, and other data, to
accurately predict pollutant concentration over a wide area (to date, the
Los Angeles areaj. The model, as used in this study, divides the region
into 62b 2x2 mile squares, the atmosphere above ground level and below
the inversion into five vertical strata and time into five minute
intervals with hourly summaries. A ten-hour simulation was used in
this study. Figure 2.1 illustrates the positioning of the model region
over the Los Angeles Basin.
The SAI model is one of the most comprehensive photochemical pollution
models developed. Based on the Eulerian (fixed coordinate) approach, the
SAI model repeatedly solves the conservation of mass differential equations
for the whole basin. A total of six atmospheric pollutants are simulated
with a fifteen-step photochemical reaction model. These pollutants are
reactive and unreactive hydrocarbons, nitrogen dioxide, nitric oxide,
carbon monoxide, and ozone. The model requires two types of inputs:
meterological inputs such as wind speed and direction and inversion
heights, and emission inputs such as hydrocarbon and NO production from
A
both fixed and mobile sources. Outputs of the model take the form of
estimates of the six pollutants' hourly average concentrations in most
*
The SAI model is documented in great detail in a lengthy report. The
reader should consult this report for a complete description of the SAI
model [I].
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FIGURE 2.1
THE SAI COORDINATE SYSTEM
AND LOCATIONS OF REPRO-MODELS
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10
of the four-square-mile zones. The SAI model can be characterized,
therefore, as a transfer function between very detailed and complex
inputs and very comprehensive outputs.
The SAI model is undergoing further development. The latest available
version [l ] of the model was used in this study. As newer versions of the
SAI model are released, we can expect improvements in accuracy and possibly
in computational efficiency.
2.2 Input Requirements of the SAI Model
Raw emissions and meteorological data are preprocessed before they
are input into the model. Parts of this preprocessing are accomplished by
hand; however, much of the data preparation procedure has been computerized
in the current version.
The SAI model requires a complete and detailed emissions inventory
for any day that is simulated. Traffic volumes on all surface streets
and speeds and volumes of traffic on all freeways are used to obtain
emissions from mobile sources. Cold start information, the temporal dis-
tribution of traffic, ground operations at airports are also used. Fixed
source emissions are aggregated for each of the 625 zones. Stack emission
information is also required. Approximately 15,000 words of emission
input is used to simulate a single day in Los Angeles.
The SAI model further requires a complex statement of the simulated
day's meteorology. Unlike emission inventories which can remain useful
for several months, meteorological data can change drastically from one day
to the next. Besides demanding wind speed and direction and inversion height
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11
in each zone for each hour, the SAI model requires initial and boundary
condition concentrations of all the pollutants. In all, approximately
25,000 words of meteorological input must be respecified for each day
simulated.
2.3 Outputs of the SAI model
In the course of one model run, approximately 37,500 words of output
are generated. This breaks down into six pollutant concentrations in
625 zones for 10 hours. Each output is the average of several concen-
trations computed for each zone and each hour. Only ground level
concentrations are normally reported, although the average concentrations
in each of the four highest strata are also available. Additionally, the
SAI model interpolates to obtain the expected concentrations at each of the
air pollution monitoring station locations within the simulation boundaries.
In order not to convey the misleading impression that the SAI model is
extremely accurate, the outputs are presented as rounded integers. The
units of concentration for each pollutant are chosen such that the results
contain about two digits of information. Where the results involve only
one digit (e.g., 6 pphmj the error introduced by rounding can be a signifi-
cantly high fraction of the pollution level. This feature of the model pre-
sents little problem to the typical user, since the accuracy of the model
simply does not warrant more significant figures.
The rounding, however, presents a problem when doing statistical
analyses of the model: it adds a pseudo-random component to the model
output. This problem will be discussed in more detail later -;n this report.
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12
2.4 Computational Requirements of the Model
The SAI model requires a computer with approximately 300K bytes of
memory. The ten-hour simulation takes about seventy-three minutes [1]
on the IBM 370-155 and about twenty-two minutes on the IBM 370-165.
Furthermore, the program requires computer facilities which have available
a minimum of three disk or tape drives, with two additional disk areas
needed for full utilization.
In the course of this study, the SAI model was executed one hundred
times. These computations were carried out by the staff at the Environ-
mental Protection Agency on an IBM 370-165, according to specifications
developed jointly by Technology Service Corporation and EPA personnel.
Only the emission input data was modified in this study. Otherwise, the
model was run exactly as specified by SAI. The results of the model runs
were analyzed at TSC.
All the SAI model runs used the meteorological conditions of September
30, 1969. The test day had high average oxidant readings (36 pphm at
Pasadena) and was typified by slight winds and a strong inversion.
Total NO emissions for the test day were 772 tons in Los Angeles
A
County and 119 tons in Orange County. Approximately 62% of the emissions
were from motor vehicles. Los Angeles County contributed 1237 tons of
high-reactivity organic gases and 804 tons of low-reactivity organic gases.
Orange County was responsible for 220 tons of high-reactivity organic
gases and 79 tons of low-reactivity organic gases. Motor vehicles were
the cause of approximately 84% of these emissions.
A detailed breakdown of emission by sources can be obtained in the
appendix to an early SAI report [1].
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13
3.0 AN APPLICATION CONTEXT
3.1 A Repro-Model for Evaluating Effects of Transportation Control
Strategies
The SAI model (as with any comprehensive model) lends itself to
analysis from many different viewpoints. The number and variety of
repro-models that could be constructed from any model of this size are
virtually infinite. The content of a repro-model's input/output relation-
ships can be defined by first delineating a decision or analysis context.
Once this context has been carefully defined a repro-model can be built
which specifically answers certain pre-specified questions.
The application context chosen for this study centers around trans-
portation control strategies. The objective of the application is to
gain insight into how across-the-board emission controls affect overall
air quality. The inputs to the repro-model are aggregate emission
measures. The outputs of the repro-model are selected measures of
pollution concentration at various locations in the South Coast Air Basin.
The relationship between the SAI model and the repro-model was
illustrated in Figure 1.1. While the SAI model represents an indirect
relationship between tens of thousands of disaggregated variables, the
repro-model selects only a few aggregated inputs and directly produces
several meaningful outputs. Within its limited scope, the repro-model
is in effect equivalent to the original SAI model.
The repro-model deals in the language of the decision-maker or planner
rather than the language of the environmental engineer or meteorologist.
For example, when the planner wishes to test the impact of a certain
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14
percentage reduction in vehicle miles of travel (VMT) in a specified year,
the repro-model will accept this input with very little preprocessing. The
outputs of the repro-model are phrased to convey the maximum of information
to the decision-maker. Instead of producing volumes of uninterpreted data,
the repro-model's results are phrased for comparison with the national
ambient air quality standards.
3.2 The Policy Region
Because only one hundred air pollution model runs were made, the
*
number of decision variables and their ranges were carefully selected.
For this repro-model, the variables were restricted to those which describe
short-run emission reduction policies.
This repro-model is directed, particularly, toward changes in pollutant
production from motor vehicles. Two control variables for primary motor
vehicle pollutants (NO ,HC), two variables for initial and boundary pollution
A
concentration (NO ,HC), and one variable for area source hydrocarbons have
A
been defined. Meteorological, geographical, and developmental variables
have all been assumed constant and equal to the values for the test day.
Each variable is defined in terms of the fraction of the values used
for the selected test day. The oxides of nitrogen variable, for instance,
is the fraction of NO emitted from each zone as compared with the actual
A
values for the test day. The fraction is specified constant over all zones.
That is, a fifty percent reduction in NO emissions implies a fifty percent
A
reduction in every zone. The initial condition variables specify the
The "curse of dimensionality" makes careful choice necessary; for
example, if one simply looked at combinations of 5 values of each of 5
variables, the number of model runs required would be 5^ = 3,125.
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15
initial and boundary pollutant concentrations as a fixed fraction of the
test day's initial and boundary concentrations.
While this variable set may seem somewhat restrictive, the number .and
types of policy alternatives which can be investigated in this manner is
quite large. Table 3.1 on the following page shows which of the most com-
monly suggested control strategies the repro-model can handle. Of the short-
run control measures only those which imply a transportation demand change
or deal in an unmodeled pollutant cannot be analyzed using the repro-model.
Most commonly applied control measures do not radically reduce one
pollutant while leaving all other pollutants unchanged. For example, if
fuel was rationed we might expect to see emissions of all pollutants
decrease roughly in proportion to the decrease in fuel consumption. Over
the short run, one would not expect to see great variations between pollu-
tants in the amount of reduction. Under a fifty percent gas rationing
proposal, for instance, we would not expect to see in the short run a
seventy percent reduction in HC and only a thirty percent reduction in NO
X
from mobile sources.
The policy region has been defined assuming that reductions in mobile
source emissions will be highly correlated. A thirty percent variation from
an equal reduction rule is permitted for control strategies which do not
greatly affect the status quo, and as much as a two hundred percent varia-
tion off the equal reduction line is permitted for radical policy alterna-
tives. A projection of the feasible policy region is shown in Figure 3.1.
The equal reduction line is the set of points such that: x, = x^, where
x-, is the NO mobile source emission variable and x0 is the hydrocarbon
I A £
mobile source emission variable.
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16
TABLE 3.1
POLICIES WHICH CAN BE EVALUATED USING THE REPRO-MODEL
Short-Run Control Measures
Can repro-model aid
decision making?
A. Inspection Maintenance Yes
B. Retrofit Yes
C. Fuels Modification
1. Lowering Reid Vapor Pressure Yes
2. Replacing Reactive Hydrocarbons Yes
3. Lead Removal No
4. Gaseous Fuel Conversion Yes
D. Traffic System Improvements Yes
E. Vehicle Exchange Yes
F. Vehicle Travel Reduction
1. Limited Registration Yes
2. Fuel Rationing Yes
3. Travel Rationing Yes
4. Parking Limitations No
5. Free Zones No
6. Work Schedule Shifts No
G. Pricing
1. Increase Cost of Ownership Yes
2. Increase Fuel Taxes Yes
H. Demand Shift
1. Improve Mass Transit No
2. Slow Traffic Improvement No
J. Household and Industrial Emission Reduction No
Long-Run Control Measures
K. Land Use Planning
1. Population Shifts Due to Transportation
Improvement
2. Population Increases
3. Green Belts—Open Space
4. Industrial Location/Stationary Source Location
Long-run strategies
must be tested with
a new repro-model
designed to handle
the specific problem.
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17
150_
C\J
X
oo
o
i—i
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18
The initial condition variables adjust both the initial conditions
and boundary conditions together. These variables are permitted to vary
around the values that would typically be found under the various emission
control strategies. That is,
= 38 + 0.62X, +6 (3.1)
X5 = 0.84x2 + 0.16x3 + 6 , (3.2)
where x. is the NO initial condition variable, xg is the hydrocarbon
initial condition variable, and x3 is the fixed source hydrocarbon-emission
*
control variable. Figure 3.2 shows the range (<5) that the initial condi-
tion variables may be varied around their typical values. The relationship
between x. and x, is shown in Figure 3.3.
The formal statement of the policy region constraints is provided
in Table 3.2.
Carbon monoxide concentration does not greatly affect the reaction
equation. CO production from automobiles has, therefore, been made an
endogenous variable in this model. Because CO emissions are expected to
vary roughly with NO and HC emissions, we assume CO reduction is proper-
/\
tional to the average reduction in HC and NO .
J\
The two-dimensional projection of the policy region with respect to
NO and HC mobile source emissions is a rectangle tilted at 45°. In
The coefficients in these two equations result from the 62 percent
contribution of NOX from mobile sources and the 84 percent contribution
of HC from mobile sources.
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19
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20
150 t-
o
o
X
o
50
0
50
TOO
150
MOBILE SOURCE NOX EMISSIONS
FIGURE 3.3
RELATIONSHIP BETWEEN NOV MOBILE SOURCE EMISSION
A
AND INITIAL CONDITION VARIABLES
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21
TABLE 3.2
POLICY REGION CONSTRAINTS
x + Xo > 30 (D
1 9 wW * *
X] + x2 < 240 (2)
X] - X2 < 40 (3)
-x + x2 < 20 (4)
x2 > 0 (5)
x3 > 0 (6)
x3 < 100 (7)
x4 - 0.558Xl > 29.2 (8)
x4 - 0.682x1 < 46.8 (9)
-x5 + 0.756x2 + 0.144x3 < 5 (10)
x5 - 0.924x2 - 0.176x3 < 5 (11)
x5 > 0 (12)
x = % of test day's mobile source NO emissions
1 x
x2 = % of test day's mobile source hydrocarbon emissions
x3 = % of test day's fixed source hydrocarbon emissions
x, = % of test day's initial and boundary conditions for NO
* /\
XE = % of test day's initial and boundary conditions for hydrocarbons
-------
22
Figure 3.4 the policies representing vehicl9 emission controls has been
superimposed on the policy region [8]. The resulting curve falls well
within the policy region. While Figure 3.4 holds vehicle miles of travel
(VMT) constant, Figure 3.5 shows the effects of VMT changes in any year
between 1969 and 1980. While these curves do not take into consideration
secondary reductions or increases in emissions due to vehicle speed
changes, all but very radical VMT change policies fall within the policy
region. By varying both the VMT and the emission control policy, and
adjusting for secondary effects, an infinite variety of control policies
can be simulated within the specified policy region.
As insurance, two vectors well outside the policy region were included
in the repro-model design to improve the accuracy of extrapolation beyond
the chosen policy region.
3.3 Outputs of the Repro-Model
The outputs of the SAI model provide the ability to construct literally
thousands of repro-models. We are given the concentrations of six pollu-
tants, ten time periods, and six hundred and twenty-five zones. Not all
of this information is particularly useful for present purposes, and the
number of relevant dependent variables can be quite small.
The pollutant which violates national primary and secondary ambient air
quality standards most frequently in the Los Angeles Basin is photochemical
oxidant. While the eight-hour average carbon monoxide standard is often
exceeded, photochemical oxidant is considered the critical pollutant for
air quality control in Los Angeles. The repro-model accordingly emphasizes
measures of peak one-hour average oxidant. Time average nitric oxide
concentrations are also studied, but to a lesser extent.
-------
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Two classes of peak oxidant readings are considered in this modeling
effort. First, we consider the peak one-hour average for eight selected
zones in the basin, no matter when these peaks occur. Second, one repro-
model will predict peak one-hour concentrations no matter where or when
this peak occurs. These types of models are designed to answer the question
of whether a particular control strategy will produce sufficiently reduced
oxidant readings to satisfy air quality standards. Further, these repro-
models will indicate where the oxidant concentration is expected to be a
problem in a day similar to the conditions of the test day.
For three locations on the 625-zone grid, repro-models were constructed
for ten-hour average N02. The time averaging phrases the N02 concentration
in similar terms as the national ambient air quality standards, helps over-
come roundoff error problems, and allows some determination of the ease of
repro-modeling average pollutant concentrations.
The eight zones which were used for the repro-models were spread over
the basin. Four of the zones correspond to the location of monitoring
stations. Four of the zones were selected because of particularly inter-
esting repro-model features. The eight zones are:
1. Sunland (10,24). This zone consistently yielded levels near the
peak oxidant value for runs which simulated high emissions. (O^)
2. Pasadena (15,20). Location of monitoring station 75. (Oo)
3. Burbank (10,21). Location of monitoring station 69. (03 and N02)
4. Downtown Los Angeles. Location of monitoring station 1. (0~ and N02)
In the zone designation (a,b), "a" refers to the east-west coordinate
and (b) refers to the north-south coordinate. See Figure 2.1.
-------
26
5. Duarte (20,20). Example of a high pollution area east of
downtown Los Angeles. (03)
6. Carbon Canyon (25,13). Easternmost high pollution zone
considered. (0,J
7. West Los Angeles (7,17). Typical of many low pollution zones.
Located near monitoring station number 71. (03 and NO,,)
8. North Long Beach (12,9). A low pollution zone located in the
industrialized South Bay area.
A separate repro-model was constructed of the peak oxidant value whenever
and wherever it occurred.
3.4 SAI Model Runs
One hundred well-spaced points within the policy region were used as
a basis for the SAI model runs. These points are listed in the Appendix.
The first run is referred to as the "baseline." It represents the
100% case, and it uses the data exactly as provided by SAI for September 30,
1969. A peak oxidant "histogram" for this baseline case is shown in
Figure 3.6. The boundaries of the simulation are clearly defined, especi-
ally along the coastline. Two local maximums are evident. One maximum
occurs in the Northeast San Fernando Valley near Sunland. A second
maximum occurs along the eastern boundary of the 25x25 grid. In general,
this "histogram" and others for different runs exhibit a continuity in
the peak oxidant function with a noticeable absence of isolated peaks
and steep troughs. High concentration gradients visible in the northern
portion of the graph indicate the model's sensitivity to meteorological
factors.
-------
27
FIGURE 3.6
A PEAK OXIDANT "HISTOGRAM"
FOR THE BASELINE RUN
-------
28
The shape of the peak oxidant function remains nearly the same
throughout all the runs. This characteristic of the SAI model can
be more precisely stated by the correlation matrix shown in Table 3.3.
Each term in the matrix represents the correlation between the peak
*
oxidant readings at two zones over ninety of the one hundred runs.
The near perfect correlations found in most of the table demonstrate
this shape-retaining property of the SAI model. The last row on the
table is the expected correlation between the particular peak oxidant
readings and the same reading without any roundoff error, i.e., the
value that would be obtained if the only source of error was roundoff
**
error. This row indicates that, after roundoff error is accounted
for, zone (12,9) is behaving in nearly direct proportion to the other
zones while zone (7,17) is not.
The column associated with the peak oxidant over all zones shows the
typically high correlation with all other zones. Table 3.4 shows the
proportionality constants between the peak zone and all other zones.
Although only eight bivariate regressions were performed for this table,
approximations of any peak oxidant reading can be arrived at in this
manner. The fact that a simple linear relationship closely predicts
the peak levels in most zones given the overall peak suggests that the
aggregate output measures chosen summarize succinctly much of the model
output.
*
Ten runs were removed at random for later independent tests.
**
This effect of roundoff error is discussed further in Section 4.2.
-------
29
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TABLE 3.4
THE PEAK AS A PREDICTOR OF
OTHER CONCENTRATIONS (pphm)
[Zone level = SLOPE x Peak level + CONSTANT]
ZONE SLOPE CONSTANT
10,24
10,21
15,20
20,20
7,17
12,17
25,13
12,9
1.10
0.61
0.69
0.36
0.11
0.30
0.38
0.02
-3.91
-3.48
-3.15
-0.82
2.15
-1.78
-0.36
0.80
-------
31
Three other points are of particular significance. One run of the
SAI model represents the 87% hydrocarbon reduction control strategy for
Los Angeles [9]. The results of this run were that over most of the basin
the Oo concentrations were between 1 and 3 pphm. Two other runs were made
which represent points well outside the policy region. These points
insure that the repro-model will extrapolate well in regions which are
not completely explored.
-------
32
4.0 REPRO-MODEL DEVELOPMENT
This section outlines the technical approach employed in creating
the repro-models; discusses the limiting accuracy that can be achieved
due to roundoff of the model output; lists the parameters of the repro-
models developed; and discusses their accuracy, their efficiency, and the
particular output format chosen for the delivered software. Discussion
of the implications of the repro-models is postponed to section 5.0.
4.1 The Technical Approach
The general philosophy and approaches employed in repro-modeling
have been discussed elsewhere [5]. Some discussion of the technical
approach will aid exposition of the results of this study; however,
the remainder of the report does not lean heavily on the present section.
In the 100 runs of the SAI model used in this study, five independent
variables were varied. Each set of values of the independent variables
produced a set of values of the dependent variables. Because a separate
functional relationship is derived for each dependent variable, we will
speak in terms of a repro-model with five independent variables and one
dependent variable. In fact, the repro-model of the entire model is a
collection of smaller repro-models having identical inputs (Figure 4.1).
This semantic confusion will hopefully be unraveled through context.
The means by which these repro-models, i.e., functional forms
modeling the input/output relationship implicit in the original model,
are constructed is through the use of many samples of the input/output
process. A hundred such samples were available for each repro-model;
ninety were used to construct the repro-model, and ten set aside for a
later test of consistency.
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Using a small set of multivariate samples to define a nonlinear
relationship is a procedure which requires great care to avoid under-
fitting (neglecting substantial information contained in the data) or
over-fitting (imputing meaning to statistical fluctuations). This
problem can be approached formally [7], but perhaps the most straight-
forward way of expressing the objective of such a problem is in terms of
the "efficiency" of the approximating functional form. The number of free
parameters adjusted and the accuracy of fit resulting determine the effi-
ciency of the functional form used in the approximation. The fewer para-
meters used to obtain a given degree of fit, the more efficient the approxi-
mation obtained. An efficient approximation minimizes the possibility of
fitting statistical anomalies rather than fundamental relationships in the
data.
4.1.1 Continuous Piecewise Linear Functions
Continuous piecewise linear functions have the potential of being a
very efficient class of approximating functions, as well as other advan-
tages in terms of interpretability. A piecewise linear function is a func-
tion for which one can find a partition of the space of independent variables
such that the function is linear on every subregion. If the function is
continuous piecewise linear, there are no discontinuities in the function
at the boundaries between subregions. A continuous piecewise linear function
of one variable is shown in Figure 4.2. Figures 4.3(a) and (b) illustrate
continuous piecewise linear functions of two variables. In both cases the
-------
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OTHER VARIABLES = 50%
FIGURE 4.3(a)
AN EXAMPLE OF A CONTINUOUS PIECEWISE LINEAR
FUNCTION IN TWO VARIABLES—AN OXIDANT
REPRO-MODEL (10,24)
-------
37
OTHER VARIABLES =
FIGURE 4.3(b)
AN EXAMPLE OF A CONTINUOUS PIECEWISE LINEAR
FUNCTION IN TWO VARIABLES—AN N0?
REPRO-MODEL (10.21)
-------
38
continuity constraint requires that the hyperplanes defining the function
in any subregion meet at the boundaries of the subregions. Thus, in Figure
4.2, the values of the linear functions on the first and second subregions
must be the same at the boundaries between those subregions, i.e., the point
a, and the values of the linear functions on the second and third subregions
must be the same at the boundary between those subregions, i.e., the point b.
In higher dimensions the subregions can become considerably more complex, as
indicated in Figure 4.4, and the problem of ensuring continuity is a more
difficult technical problem. The general formula for a piecewise linear
function is given by
F(xr...,xn) =
14.1)
for x in X
R
where x. = (x,>x ,...,x ) and X, ,X2,...,XR are subregions partitioning the
space.
For any given set of subregions X,,X^,...,XR> one could (with diffi-
culty) find the optimal coefficients b.. with a constraint of continuity
' J
at the boundaries. Since the choice of subregions is not obvious, the
problem of simultaneously finding the optimal subregions makes the
A hyperplane is a generalization of lines in the two-dimensional
case and planes in the three-dimensional case to any dimensionality.
-------
39
t
FIGURE 4.4
AN EXAMPLE OF POSSIBLE SUBREGIONS FOR A
TWO-VARIABLE CONTINUOUS PIECEWISE LINEAR FUNCTION
-------
40
procedure quite difficult. The approach employed in the present work is
the specification of the piecewise linear function in an alternate form
which insures continuity as the parameters are varied and which defines
the boundaries of the subregions implicitly as a function of the parameters
defining the linear function on each subregion [5].
Specifically, equation (4.2) defines a continuous convex piecewise
*
linear function:
14.2)
P(xrx2,...,xn)= Max L aij
'~~lj<-5'«85^v'vJ '
Referring to equation (4.1), note that F(x-,,...,x ) = P(x,,...,x )
if b-. = a.. and X. is the region where the i hyperplane is
largest, i.e.,
X. =
X
for alI k ( .
Figures 4.2 and 4.3 (b) illustrate convex and non-convex piecewise linear
functions respectively. Figure 4.2 illustrates this definition graphi-
cally. Note that the value of the function P(x) is obtained quite simply
by calculating the values of the three linear functions
*
A convex function is roughly, one which has the property that all
the points on a line connecting two points on the surface of the function
take values greater than or equal to the function.
-------
41
g (x) = -1.5x + 9
g2(x) = 0.25x + 2
g3(xj = x -6
and taking the largest value which results. The subregions are defined
implicitly; for example, in Figure 4.2, X2 is the region where
0.25x + 2 > x -6
and
0.25x + 2 > -1.5x + 9 .
A simple extension of the approach will yield non-convex functions:
N
F(xr..,xn) = wkPk(Xl xnj , (4.3)
where
Pk(x,s...,x ) = Max "J (k) (k) I ,
K ' n ,-_i o i/ ) a-- x. + a. „, , i
"•••"Nk
& aU AJ ai,n+lj
i.e., F is a sum of functions of the form (4.2). The function F may be
non-convex if the weights wk differ in sign. Note that F is a "para-
meterized" function: to fully specify F, we must choose the values
(k]
WI,...,WN and aL' for k=l,2,...,N; i = l ,2,... ,Kk; and j= 1,2,... ,n.
Some of these parameters are redundant; the total number of free
parameters is
-------
42
The parameters b. . in equation ^4.1) are related to the parameters wk
and a-- by a linear equation on each subregion.
I J
The procedure used was to test whether a convex function of the
form in (4.2) was sufficient to represent the input/output relationship;
this would be the case only if the relationship itself were convex or
nearly so. If a convex function was insufficient, then a functional ap-
proximation of the form (4.3) was employed. This procedure yields the
fringe benefit of detecting whether the model input/output relationship
is itself essentially convex.
The means used to find the parameters of the function minimizing
the least-mean-square error in the input/output approximation is not
of particular concern here and is discussed elsewhere [5].
We note one important characteristic of continuous piecewise linear
functions that makes them attractive for the present application. Since
the functions are linear in any subregion, they will extrapolate linearly
to points outside the region in which the input/output samples were taken;
they can to some degree be trusted to extrapolate reasonably (particularly
in comparison to other functional forms such as higher order multivariate
polynomials).
Another key characteristic of the continuous piecewise linear form
is its ease of interpretability. In any small region (other than a point
on the boundary between regions), the function is linear, and the
relationship can be interpreted much as in linear regression. That
is, in a particular region of space, the dependent variable is given
-------
43
by a linear function of the independent variables and the effect on the
output of small changes in the independent variables is clearly evident.
This approach to interpretation will be employed in Section 5.0.
4.2 Implications of the Precision of the SAI Model for Statistical Analysis
The SAI model reports its results to only one or two significant
figures. The roundoff error due to this form of presentation can range
from .5% to 50% of the reported concentration. The problem of statisti-
cally fitting this data is< illustrated in Figures 4.5(a) and 4.5(b). In
a set of data modeled perfectly by a piecewise linear function (Figure 4. 5(a))>
a rounding error has been introduced. The perfect fit which was achieved
before rounding has an error associated with it after rounding. A perfect
fit to the rounded data would clearly be distorted relative to the under-
lying physical relationship.
The rounding puts a lower bound on the error one should attempt to
achieve with any functional fit. If an error of a fit less than this
lower bound is achieved, there is a tendency for the resulting functional
form to follow the error-distorted data rather than the original unrounded
data. An attempt must, therefore, be made to choose the number of free
parameters such that the resulting error of the fit approaches but does
not become substantially less than a theoretical rounding error.
The theoretical RMS error of a perfect fit with only rounding errors
introduced is 0.289. This assumes that the rounding error is uniformly
and independently distributed over an interval of +.5 about the unrounded
data, an assumption sufficiently representative for present purposes. In
-------
f(x)
14 L
44
13
12
11
RMS ERROR = 0
10
FIT OF PERFECTLY PIECEWISE
LINEAR DATA
FIGURE 4.5 (a)
f(x
14
)
N
\
13
12
O
\
\
\
O
11
RMS ERROR = 0. 3
10
SAME FIT AS 4.5 (a) OH
DATA WITH ROUNDOFF
ERROR INTRODUCED
FIGURE 4.5 (b)
-------
45
the case of the NO- data, however, ten numbers were averaged. This reduces
the error somewhat, but only by a factor of vT5~. The theoretical RMS
error of a perfect fit of ten averaged rounded numbers is 0.091. There is,
of course, a logical upper bound on the fraction of variance explained by
any statistical fit of rounded data. This fraction will vary, however,
from one dependent variable to another. For unaveraged data however,
22 2
this number is l-(.289) /a where a is the variance of the dependent
variable. The "limiting correlation" coefficients used in Table 3.3 are
the square roots of this fraction.
4.3 Repro-Models Created and Accuracy Achieved
The oxidant dependent variables as previously defined were statisti-
cally fit using three basic functional forms: linear, quadratic, and
continuous piecewise linear. In all cases, ninety data points were used.
Ten of the hundred data points (Table 4.1) were withheld at random for
later testing.
A comparison of errors resulting from all these fits is shown in
Table 4.2. The linear regression with six free parameters provided the
worst error statistics in every instance. The 5-variable quadratic fit,
which involved twenty-one free parameters, did consistently better than
the linear regression (as it must), but still did not approach the roundoff
error limit. The piecewise linear approximations, with 12 to 18 free
parameters, performed better than either the quadratic or the linear fits.
The improvements over the linear regression are by factors of between 2
and 8 and over the quadratic fit by factors of between 1.2 and 4. Since
the error in the piecewise linear fit was uniformly smaller than the
-------
46
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
TABLE 4.1
TEN POLICIES USED IN TESTING REPRO-MODELS
MOBILE
NOX
85.0
100.0
30.0
60.0
45.0
70.0
75.0
105.0
125.0
125.0
MOBILE
HC
80.0
65.0
13.0
30.0
45.0
50.0
60.0
90.0
100.0
115.0
FIXED
HC
10.0
70.0
13.0
100.0
45.0
75.0
100.0
40.0
70.0
20.0
INITIAL
N0x
93.0
100.0
57.0
87.0
54.0
87.0
72.0
103.0
130.0
132.0
INITIAL
HC
69.0
66.0
13.0
41.0
35.0
59.0
54.0
95.0
88.0
108.0
-------
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quadratic fit, even though obtained with fewer free parameters, the piece-
wise linear form is clearly more efficient for this application and repre-
sents the model more naturally. Note that, in one case, a linear form was
sufficient to achieve the limiting accuracy.
Table 4.3 and Table 4.4 provide the parameters of the twelve repro-
models developed. The entries are labeled to correspond to equations (4.1)
and (4.2). The number of free parameters on each piecewise linear approxi-
mation was adjusted separately. The numbers of hyperplanes that were used
in each case were selected on the basis of the smoothness and convexity
of the data being analyzed. Since there are six free parameters in each
hyperplane, the number of free parameters for each repro-model ranged
from six (counting the linear case) to twenty-four (including the NO
/\
repro-models). In each case, care was taken not to "overfit" the data,
that is, to allow the piecewise linear approximation to be strongly
affected by the roundoff error.
The statistical characteristics of each of the twelve repro-models
are shown in Tables 4.5 and 4.6. In each case the percent variance
explained and the RMS error approached their respective practical limits.
It should be noted that the averaging of the N02 data allowed a substan-
tially better approximation to be calculated. The two N0~ fits which
required twenty-four free parameters behave very much like an eighteen
parameter approximation. The nonconvexity of the data and the nature
of the algorithm required the addition of a fourth hyperplane, although
in both instances it explains an extremely small portion of the policy
space (a point discussed further in section 5.0).
-------
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The ten test policies were simulated on the repro-models. The results
of these simulations were compared with the results of the SAI model for
these policies. The RMS errors for each repro-model were calculated, and
these are listed in Tables 4.7(a) and 4.7(b). For each of the twelve repro-
models, the RMS error for the test cases was close to the error on the de-
sign set. This substantiates the expectation that the repro-models are
valid for data points which were not among the set that was used to
create the models in the first place.
It should be noted that the repro-models, to all intents and
purposes, perfectly duplicate the behavior of the original model. This
is a much better result than necessary in most repro-modeling applica-
tions, where it is usually assumed that it is sufficient to approximate
only to the degree of accuracy with which the original model corresponds
to reality. Since in the present application, validation results are
often stated as the percentage of time the model is within a factor of
two of reality, we have easily achieved this basic objective.
4.4 The Repro-Model Program
Since the repro-model requires no iterative calculation, it can
run several orders of magnitude faster than the SAI model. Even with the
relatively elaborate input/output routines of the repro-model package,
the program will execute a single policy evaluation (twelve repro-models)
*
in about 0.2 seconds. If a single repro-model were to be embedded into
an iterative calculation, such as an optimization routine, where the
*
These runs were made on the CDC-6400.
-------
55
TABLE 4.7(a)
RMS ERROR OVER TEN TEST POLICIES
N02
Zone RMS Error
10,21 .214
12,17 .284
7,17 .157
TABLE 4.7(b)
RMS ERROR OVER TEN TEST POLICIES
OXIDANT
Zone RMS Error
Peak 0.47
10,24 0.48
15,20 0.51
10,21 0.79
12,17 0.60
20,20 0.40
25,13 0.37
7,17 0.24
12, 9 0.39
-------
56
input-output overhead is minimal, the time of evaluation would be on the
order of 10 milliseconds.
The repro-model package evaluates all twelve of the repro-models.
On input it checks that all policy region constraints are satisfied.and
prints a specific warning message if one or more constraints are violated.
After the policy is evaluated by the piecewise linear approximations, the
program displays the linear sensitivities about the policy evaluated, i.e.,
indicates how small changes in policy variables would affect the result.
An example of an output page from the repro-model is shown in Figure 4.6.
A complete description of the repro-model program, a program listing, and
an explanation of the output are found in the Appendix to this report.
-------
57
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58
5.0 IMPLICATIONS OF THE MODEL
In the previous section, the form, efficiency, and accuracy of the
repro-model were discussed. The present section describes the implications of
the repro-model, i.e., the implications of the SAI model. The discussion
is in two parts: (1) an outline of the general conclusions implied by
the input/output relationships of the model; and (2) several examples of
the use of the repro-model to examine model implications for particular
policy questions.
5.1 General Implications of the Model
One of the most valuable uses of an air pollution model is to provide
qualitative insights and rough quantitative estimates about a process in
general, rather than about the specific outcome of a particular policy.
This type of information aids innovative policy design by indicating which
variables have the most effect on pollutant levels and the approximate
degree of that effect.
One means of studying the input/output relationship of the model
is through graphical aids. Because the repro-model has five independent
variables, however, one is limited to plots such as Figure 5.1, holding at
least three variables constant. Similar information is displayed in 3-D
plots holding three variables fixed, such as in Figures 4.3(a,b). While
such plots do give some feel for overall model structure, one would be
forced to look at a large number to fully explore the model; even then,
it would be difficult to gain an intuitive feel for the five-variable
relationship by such an approach. Graphical aids, however, are extremely
useful in providing insight into particular questions, as will be illus-
trated in section 5.2.
-------
16
59
14
12
10
IE
Q.
CL
X
o
ALL OTHERS = 50%
I
10 20 30 40 50 60 70
HYDROCARBON MOBILE SOURCE EMISSIONS (% OF TEST DAY)
FIGURE 5.1
A "CUT" OF THE MODEL HOLDING THREE
VARIABLES CONSTANT AT ZONE (10,24)
80
-------
60
In this section we examine overall model implications by exploiting
the piecewise-linear form of the repro-models.
We have previously noted that all the oxidant repro-models are
convex. Thus, there is no tendency within the range of the repro-model
for the process to saturate; as any emissions or initial condition variable
is increased with the others held fixed, the rate of increase of oxidant
will not decline, but will increase or stay constant. This is not the case
for the NC>2 repro-models, two of which are non-convex.
We can examine the repro-models more deeply by noting once more that
they are linear in large subregions of the space; for example, for the
larger values of the variables, the oxidant level (in parts-per-hundred-
million) for the repro-model at the peak is given by
OXIDANT (pphm) = 0.067-MSNOV + 0.342-MSHC + 0.122-FSHC +
X
0.097-ICNO + 0.237-ICHC - 41.6 , (5.1)
X
where the independent variables are respectively mobile source NO , mobile
X
source hydrocarbons, fixed source hydrocarbons, NO initial conditions, and
A.
hydrocarbon initial conditions, all expressed in percent of test day. For
example, setting all variables at 100% yields 45 pphm oxidant, which is
indeed the peak predicted by the SAI model for the test day. It is easy to
see from this equation that mobile source NOV and initial conditions for NO
A X
have little effect on the oxidant level. Reducing both variables by 20%
will reduce the oxidant level by only 3 pphm (a 7% reduction). On the other
hand, the hydrocarbon variables have the predominant effect; reducing MSHC
-------
61
and I CMC by 20% (and leaving fixed sources unchanged) reduces the peak by
12 pphm (a 27% reduction). Hence, the oxidant level at the peak is domi-
nated by hydrocarbon emissions.
The effect of the fixed source hydrocarbon variable is approximately
one-third that of mobile source hydrocarbons (by the ratio of their
coefficients), indicating that, while mobile sources have the predominant
effect as usually assumed, reductions in fixed source emissions can have
a significant impact.
A final point can be extracted from equation (5.1): assumptions
regarding the levels of initial and boundary conditions have a major
impact on model output. The coefficient of ICHC is comparable with the
coefficient of MSHC and dominates that of FSHC; the coefficient of ICNO
X
is comparable with that of MSNO . Since initial and boundary conditions
A
can be predicted only with a great deal of uncertainty, this uncertainty
should be reflected in model use. For example, a change of +20% in
initial/boundary condition assumptions for the 100% case would yield an
estimate of 45 pphm +_ 7 pphm.
At lower levels of emissions, the equation yielded by the repro-model
at the peak is
OXIDANT = -0.~005-MSNOV + 0.003-MSHC - 0.001-FSHC +
X
0.005-ICNO + 0.001-ICHC + 6.86 . (5.2)
At lower levels, the model indicates in effect a floor on oxidant levels of
about 7 pphm; none of the variables have a significant effect on oxidant
-------
62
levels. By referring to the functional form of the repro-model, one can
easily see that the boundary between the region where (5.1) holds and (5.2)
holds is obtained by equating the two, i.e., (5.1) holds if
0.072-MSNOY + 0.339-MCHC + 0.123-FSHC +
/\
0.092-ICNO + 0.236-ICHC ^48.5 , (5.3)
/\
or, less precisely, when the oxidant level predicted by equation (5.1) is
above 7 pphm.
The repro-model of the peak contains only two hyperplanes and hence is
completely described by equations (5.1), (5.2), and, redundantly, (5.3).
Table 5.1 lists the coefficients of the hyperplanes for all the oxidant
repro-models with other pertinent data. The table includes the following
aids to interpretation:
(a) Standard deviation of the dependent variable: This column lists
the standard deviation of oxidant in parts per hundred million at the
particular zone over all ninety points used in constructing the repro-
model. This number in general is larger for the zones experiencing
high pollutant levels. This standard deviation thus serves to char-
acterize the zone and also measures the variability to be explained.
Zones with little variability are typically low in oxidant and are
of only minor interest because there is little change in the dependent
variable under any condition.
(b) Subregion label: There may be several linear functions associated
with each repro-model, depending upon its complexity. They are
labeled simply for reference.
-------
63
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64
(c) Population: This is the percentage of the 90 sample points which
fell in the subregion where the particular linear function is active.
Since the samples were uniformly distributed, this gives an estimate
of the size of the subregion where the given linear function is used.
(d) Average policy: This is the average policy vector for the sub-
region corresponding to the given linear function, obtained by taking
the mean of all policy vectors falling in the subregion. This data
provides an insight into the typical policy for which the linear
*
function is appropriate.
(e) Linear coefficients and constant term: If the six entries in the
table are a,, a2, a-, a,, a5, ag, then the equation for policies in
the corresponding subregion is
OXIDANT (pphm) = a-^SNC^ + a2MSHC +
a3FSHC + a4ICNOx + aglCHC + a6 , (5.4)
where the variables are as before. '
(f) Normalized coefficients: If a,, a^, a3, a^, a5, ag are the entries
discussed under (e), and b, , b», b.,, b^, b5 are the entries in the
columns presently under discussion, then
b, = a./o (5.5)
k k zone
*
The subregions for the oxidant repro-models are themselves convex
regions; hence, the mean policy vector is likely to fall near the centroid
of the region.
-------
65
where a is the standard deviation of the dependent variable for
the repro-model in question and is listed in the first column discussed
[see (a)]. The constant term is not listed. These normalized coeffi-
cients use standard deviations as scale factors to provide a means of
comparing coefficients between repro-models, i.e., between zones with
differing ranges of dependent variable. The dependent variable pre-
dicted by the linear function corresponding to these coefficients can
be thought of as the oxidant level stated in units of standard devia-
tions particular to the zone rather than as an absolute level.
The reader will note several subregions with few sample points. The
inclusion of a small subregion indicates that reduction of function param-
eters to eliminate the subregion resulted in a significant increase in
approximation error; i.e., the subregion was necessary. Figure 5.2 indicates
how such a situation might occur. Such subregions usually occur at transi-
tions or extremes, and their location should be of interest as anomalies in
model behavior. We will simply note here, however, that one should attribute
little significance to the coefficients corresponding to a region with low
population.
Let us use Table 5.1 to examine differences in the repro-models
for different zones. Table 5.2 abstracts the most pertinent data for
this purpose. Two sets of normalized linear function coefficients are
listed, corresponding to higher emission levels and to intermediate or
lower levels. Also listed is the standard deviation of the oxidant
level for each zone. Where there existed multiple linear functions
corresponding to intermediate or low emissions, the one corresponding to
-------
66
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68
highest emissions was chosen. (Linear functions corresponding to popula-
tions of 1 percent were ignored.)
Consider first the high emission case. Note that the coefficients
for zone No. 2, where the peak most often occurs with high emissions, are
essentially identical to those for the peak (zone No. 1). In fact, the
coefficients have essentially the same implications for most of the zones
with high and intermediate pollution levels (zones 2-6). These implica-
tions have been discussed in terms of the peak model. One exception to
this consistency is a marked decrease in the value of the coefficient for
mobile source NO as the pollution level of the zone decreases; the co-
A
efficient even changes sign. This trend suggests that, in regions with
higher pollution levels, an increase in NO emissions results in an increase
/\
in oxidant, but at intermediate and lower levels results in no change or a
decrease in oxidant levels.
The coefficients for NO initial conditions are positive for all zones
s\
and of similar magnitudes. We thus have contradictory effects at the
lower pollution levels: an increase in NO initial/boundary conditions
X
leads to an increase in oxidant concentrations, while an increase in mobile
source NOV emissions leads to a decrease in oxidant concentrations. Having
X '' " " '
noted this characteristic, we shall leave its meaning an open question.
Marked differences in the effect of boundary conditions is consistent
with the location of zones 6 and 7. The normalized coefficients for zones
8 and 9 are included for completeness, but there is too little variability
in pollution levels in these zones to merit close examination.
-------
69
At low emission levels, the variables have much less effect on oxidant
concentrations, but one effect is consistent and pronounced. Except in
zone No. 2, mobile source NO becomes the prime determinant of oxidant
X
level, with oxidant decreasing as mobile source NO increases.
/\
It remains to analyze the three NOp repro-models (Table 5.3). At the
highest emission levels in the highest pollution zones, increasing any of the
three hydrocarbon variables reduces average N02 (perhaps by converting it
into oxidant). In all cases, the NO initial and boundary conditions (and
X
not mobile source NO ) are the prime determinant of the average NOo levels.
We have outlined the predominant implications of the model; the energetic
reader may wish to probe further into the data provided.
5.2 Examples of Repro-Model Use
The repro-model is intended to aid transportation control policy
evaluation. Three sets of examples of repro-model runs presented in this
section illustrate the usage of the model. It should be emphasized that
these examples represent a small fraction of the types of questions that
can be addressed using the model. The repro-model program is designed to
permit rapid evaluation of many more control policies. In the following
analyses and in using the repro-model, the reader should recall the limita-
tions of the repro-model (section 1.0).
5.2.1 Impact of Emission Controls on Motor Vehicles
Several repro-model evaluations were produced which simulate the change
in air quality due to changes in the motor vehicle emission standards. The
policies shown in Figure 3.5 and listed in Table 5.4 were used as input to
the repro-model. Fixed source emissions of all types and VMT were held
-------
70
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72
constant at the 1969 level, and initial conditions were varied to corre-
spond to levels normally expected under the particular control policy.
The policies were derived from calculations performed by the Los Angeles
Air Pollution Control District [8] assuming federal standards are met on
schedule. The calculations included changes in vehicle mix over the
years and automobile aging and mortality.
The results of the repro-model evaluations are shown in Table 5.4.
This table indicates that if VMT were to be held at the 1969 level, the
peak concentration of oxidants on a day similar to the test day, as pre-
dicted by the SAI model, would dip below 8 pphm by the year 1975. Table
5.4 demonstrates a relatively early predicted improvement in air quality as
emissions are reduced. This improvement can be considerably reduced,
however, by increases in VMT and fixed source emissions and by delays in
implementing emission controls. A planner or engineer interested in
evaluating other alternative policies, such as effects of delays in control
implementation or changes in VMT, can do so easily using the repro-model.
Note that the results of the model do not correspond to the assumptions
of the rollback model; e.g., a reduction in hydrocarbon emissions of 55%
results in a reduction in peak oxidant of 76% rather than 55%.
5.2.2 Ratio of Hydrocarbon Emissions to NO Emissions
X
The California mobile source emission standards differ from those of
the federal government. The principal difference between the standards is
California's higher permissible NO emissions. The Los Angeles APCD
/\
asserts [8] that the California standards provide a more favorable ratio
of NOX to hydrocarbons than the federal standards. An exploratory
-------
73
investigation as to the importance of this ratio at a particular location
on air quality was made using the repro-model for Sun!and (10,24). While
holding fixed source emissions constant and while varying NO emissions,
A
constant hydrocarbon contours were generated using the repro-model. Fig-
ure 5.3 displays the contours. The "HC = 70" contour, for example, fixes
all hydrocarbon emissions at the 70% level and fixed source NO at the
X
test day level and varies NO mobile source emissions between 10% and 140%.
A
The hash marks on the contours denote the boundaries of the policy region.
Over most of the policies, especially with high hydrocarbon emissions,
the SAI model, as interpreted by the repro-model, behaves very regularly.
At a constant hydrocarbon emission level, for the most part, reducing NO
A
causes a linear reduction in 0^. At lower emission levels, however, the
behavior of the SAI model changes. As the hydrocarbon emissions are
reduced to the 50% level, the rate of reduction in 0_ concentration with
respect to a reduction in NO is smaller. At the 40% level, the slope of
A
the contour starts to become negative. At lower hydrocarbon levels, a
decrease in NO emissions causes an increase in the 0-, concentration.
A O
This analysis would normally be carried out for the Peak model. The
interesting effects, however, are hidden in the case of the Peak repro-model
by the fixed source contributions. Therefore, zone (10,24), the zone which
seems most affected by mobile source emissions, was used instead.
This discussion by no means resolves the controversy; however, the SAI
model behaves such that at low emissions the ratio of NO to hydrocarbons
A
is very important. For low levels of hydrocarbon emissions there appears
to be an optimum level (other than zero) of NO emissions for maximum
A
oxidant reduction.
-------
74
20
40 60 80
PERCENT OF TEST DAY'S
120
FIGURE 5.3
EFFECT OF VARYING NOX WHILE
HOLDING HYDROCARBONS CONSTANT
-------
75
The well-behaved nature of the repro-model for oxidant at Sunland
at high pollution levels allows for the derivation of a simple alterna-
tive to the rollback model. If HC and NOX are derived variables, where
HC represents the appropriate policy for an across-the-board decrease
in hydrocarbon emissions and where NOX represents the appropriate policy
for an across-the-board decrease in mobile source NO^ emissions, the
oxidant concentration at Sunland can be represented by the equation:
OXIDANT = 0.70-HC + 0.13-NOX - 38 . (5.6)
The region where this linear equation remains valid can be clearly seen in
Figure 5.3. Both the derived variables, HC and NOX, are expressed in
percent of the test day.
The dependence on the test day can be lessened somewhat by expressing
*
equation 5.6 in terms of percent reduction. That is,
% REDUCTION in 03 = -1.55-HC - 0.30-NOX + 185 . (5.7)
When NOX and HC are both set at 100, the percentage reduction in oxidant is,
of course, zero. We see that this simple model predicts a 1.6% reduction in
oxidant concentration for each 1% decrease in the hydrocarbon emissions vari-
able and a 0.3% reduction in oxidant concentration for each 1% decrease in the
NO emissions variable. This linear equation holds up to about an 80% reduc-
/\
tion. Also, the coefficients for the Sunland model and the peak model are almost
**
identical for this range.
Section 2.4 for a listing of test day emission levels.
Specifically, the appropriate constants for the peak model are
-1.56, 0.28, and 184.
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76
5.2.3 Effects of Single Day Emission Reduction
Control policies have been proposed for Los Angeles whereby air
quality standards are achieved by cutting VMT for a single day. Two
scenarios which are representative of such policies were simulated
using the repro-model. The first case was that of a twenty percent
reduction in mobile source emissions while initial conditions remain
at their original level. When compared with the "baseline" (100%) case,
this one day emission reduction produced approximately a 20% overall
reduction in oxidant concentrations. (See Table 5.5.) When a twenty
percent decrease in emissions was tried at a lower emission level, some
reductions in oxidant concentrations were achieved. In this case the
reductions were not as dramatic.
-------
77
TABLE 5.5
EFFECTS OF SINGLE DAY TRAFFIC REDUCTION POLICY
ON AIR QUALITY (OXIDANT, pphm)
20% Reduction
in Mobile
50% of
20% Reduction
of" Mobile
Source Emissions
Zone
Peak
10,24
10,21
15,20
20,20
7,17
12,17
25,13
12, 9
Baseline
45
45
25
30
16
3
14
16
2
Source Emissions
37
37
20
25
13
3
11
14
1
Baseline
7
6
3
4
3
2
2
3
1
from 50% Base4
7
4
3
3
3
2
1
3
2
Policy: 100,100,100,100,100 (NO and HC mobile source emissions,
HC fixed source emissions, and NOX and HC initial
condition, respectively.)
2Policy: 80, 80,100,100,100
3Policy: 50, 50, 50, 69, 50. The 69% value for NOX initial
condition variable results from the uncontrolled NO
fixed sources.
'Policy: 40, 40, 50, 69, 50
-------
78
6.0 CONCLUSION
In the introduction, we listed three objectives: (1) a feasibility
test for repro-modeling in the context of pollution models; (2) an
interpretation of some of the implications of the SAI model; and (3) the
creation of an efficient repro-model to allow further analysis. The
following is a review of the study in the light of these objectives.
Since the SAI model had tens of thousands of numbers constituting
input and thousands of numbers as output, it was neither feasible nor
desirable to explore the input/output relationships of the model in full
variety. Five aggregate input variables were defined: mobile source NOV,
A
mobile source hydrocarbon, fixed source hydrocarbon, NO initial/boundary
A
conditions, and hydrocarbon initial/boundary conditions. These independent
variables were expressed as percent of level on test day. Twelve outputs
(dependent variables) were examined: the peak one-hour-average oxidant con-
centration over the Los Angeles basin, the peak one-hour-average at eight
specific locations in the basin, and IMOp ten-hour-average concentrations
at three specific locations. Twelve repro-models, each relating the five
independent variables to one of the dependent variables, were constructed
to create the overall repro-model. Ninety model runs were used to create
the repro-models; ten additional runs were used for independent testing.
The feasibility of the approach was clearly demonstrated. The input/
output relationship implied by the SAI model was relatively simple and
fully defined by the set of model runs. The resulting repro-models essen-
tially duplicated the SAI model output; accuracy of approximation was close
to the limiting accuracy with which the output was reported and certainly
-------
79
well within the accuracy with which the model corresponds to reality.
The continuous piecewise linear functional form used to represent the
input/output relationship proved to be efficient relative to multivariate
polynomials. The independent test on ten model runs provided convincing
verification of the repro-models.
The objective of efficiency was clearly met. While a run of the
original model took 22 minutes of computer time, the repro-models took
milliseconds on a comparable computer. A computer program was developed
and delivered to the Environmental Protection Agency.
The study yielded an extensive interpretation of the implications of
the SAI model regarding the relationship between the five aggregate input
variables and the twelve output variables. Characteristics noted included
the following:
(1) The oxidant models were convex; the rate of increase of oxidant
concentration never decreased with increasing values of the indepen-
dent variables. Two of the three N02 repro-models were non-convex.
(2) Over most of the policy region hydrocarbon emissions are signifi-
cantly more important than NO emissions in the formation of ozone.
A
(3) Assumptions on the magnitude of initial and boundary conditions
have a major impact on the predicted air quality.
(4) As emissions are reduced the impact on oxidant formation of NO
A
emissions becomes relatively less. In fact, increasing NO emissions
X
reduces oxidant concentration for very low emission policies.
(5) At low pollution levels, increasing mobile source NO emissions
A
decreases oxidant concentrations, but increasing NO initial/boundary
A
-------
80
conditions increases oxidant concentrations.
(6) The major determinant of average N0? concentrations in the
model is NO initial and boundary conditions and not mobile
X
source NO emissions.
X
(7) Simplified models to aid planning may be extracted by exploiting
the locally linear nature of the repro-model form. For example, in
the limited context of this study, the results suggested the following
rule-of-thumb relationship between the percent reduction of peak
oxidant concentration and the level of fixed and mobile-source hydro-
carbon emissions (HC) and mobile source NO emissions (NOX), expressed
X
as percent of test day:
% REDUCTION in 03 = -1.55-HC - 0.30-NOX +185 .
This formula holds up to about an 80% reduction and indicates the
predominant effect of hydrocarbons. (Section 5.2 details the
assumptions involved.)
It is appropriate to conclude this report by referring the reader to
the limitations, discussed in the introduction, on the generality of the
repro-model and the generality of its implications. In particular, we
have been discussing the characteristics of a model, and it is not our
purpose to make a judgment on the correspondence of the model characteristics
to reality. We have hopefully demonstrated that repro-modeling is a powerful
tool for understanding the implications and extending the utility of complex
physical models.
-------
81
ACKNOWLEDGMENTS
This project was a joint effort between Technology Service Corpora-
tion and the Environmental Protection Agency. We wish to thank Mr. Dale
Coventry for performing all the SAI model runs and delivering the output
data to us with a minimum of delay. We would also like to thank Dr. Ron
Ruff, the EPA project monitor, for many helpful discussions and suggestions
throughout the project.
Mr. Harry Knobel and Mr. Ross Bettinger at TSC were responsible for
data management and programming.
We would also like to thank Drs. Philip Roth and Mei-Kao Liu at
Systems Applications, Inc., who patiently answered our questions about
their model. Helpful suggestions about application context of the repro-
model were given by Mr. Arnold Den and Mr. Robert Frommer of Region IX EPA.
-------
83
REFERENCES
1. The following volumes constitute the documentation of the SAI model.
Roth, Philip M., Steven D. Reynolds, Philip J. W. Roberts, and John H.
Seinfeld, Development of A Simulation Model for Estimating Ground Level
Concentrations of Photochemical Pollutants, Report 71SAI-21, Systems
Applications, Inc., Beverly Hills, California, July 1971. (Final Report
and six appendices)
Reynolds, Steven D., Mei-Kao Liu, Thomas A. Hecht, Philip M. Roth, and
John H. Seinfeld, Further Development and Evaluation of a Simulation
Model for Estimating Ground Level Concentrations of Photochemical
Pollutants, Report R73-19. Systems Applications, Inc.. Beverly Hills.
California, February 1973. (Final Report in three volumes and five
appendices)
2. Wayne, Lowell G., Allan Kokin, and Melvin I. Weisburd, Controlled
Evaluation of the Reactive Environmental Simulation Model (REM),
Report EPA R4-73-013a, Pacific Environmental Services, Inc., Santa
Monica, California, February 1973.
3. Eschenroeder, A. Q., J. R. Martinez, and R. A. Nordsieck, Evaluation
of a Diffusion Model for Photochemical Smog Simulation, Report EPA
R4-73-012a, General Research Corporation, October 1973.
4. Sklarew, Ralph C., Allan J. Fabrick, and Judith Prager, "Mathematical
Modeling of Photochemical Smog Using the PICK Method," Journal of the
Air Pollution Control Association, Vol. 22, No. 11, November 1972.
5. Meisel, William S., and David C. Collins, "Repro-Modeling: An Approach
to Efficient Model Utilization and Interpretation," IEEE Transactions
on Systems, Man, and Cybernetics, Vol. SMC-3, No. 4, July 1973, pp. 349-58.
6. Meisel; William S., Computer-Oriented Approaches to Pattern Recognition,
Academic Press, New York, 1972.
7. Breiman, L., and W. S. Meisel, "Estimates of the Intrinsic Variability
of Data in Nonlinear Regression Models," submitted for publication
(available as a TSC Report), November 1973.
8. Hamming, Walter J., Robert L. Chass, Janet E. Dickinson, William G.
MacBeth, "Motor Vehicle Control and Air Quality: The Path to Clean Air
for Los Angeles," Proceedings of the 66th Annual Meeting, Air Pollution
Control Assoc., Paper 73-73, June 1973.
9. Environmental Protection Agency Region IX, Technical Support Document
for the Metropolitan Los Angeles Intrastate Air Quality Control Region,
January 15, 1973.
-------
85
APPENDIX
A.I Repro-Model Documentation
The several piecewise linear representations of the SAI model have
been included in a repro-model computer program. The program is user-
oriented and is suitable for both batch and on-line processing. A listing
of the program appears at the end of this documentation.
The policies which are to be evaluated are input after the program
deck. One policy (five numbers) is punched on a card. The format is
5F10.1. The five fields contain the information in Table A.I. The
program will accept up to 500 different policies (i.e., 500 cards). The
program will cease reading policy cards when it reaches an end-of-file.
(An end-of-file card must follow the last policy.)
Figure 4.6 shows a typical page of output from the repro-model program.
The policy variables are printed first. Also, if any policy region con-
straints are violated by that particular policy, these violated constraints
are listed. The table contains the repro-model results. The first column
is the name of the zone, and the next two columns list the east-west and
north-south coordinates of that zone, corresponding to Figure 4.5. The
pollutant name appears in the fifth column. The repro-model results are
printed in the next column, followed by a time period designation. The
remainder of the page contains a listing of the net hyperplanes which were
used to obtain the concentration estimates and indicate the sensitivity
of the result for small changes in the independent variable.
The formula,
5
y = £ a^.+ ag
-------
86
en
o
CM
I
O
ro
o
o
i— C\J
o
«*
I
I—
CO
o
in
i
a:
o
o
oo
0)
J3
>'i
ro LU
Q
E
•P O
to J2
CU S-
h~ rO
O
4- O
0 S-
-o
•+-> >>
CU
o
cu
o.
cu
o
£-
3
0
CO
to
•o E
CU 0
X -r-
•r- tO
u_ to
• r—
>> E
ra LU
f"i
c
•P 0
to -Q
CU &-
1— (0
O
4- 0
0 S-
"O
-*-> >>
E 31
CU
O
i-
cu
Q.
s_
0 CU
4- -C
to
C "
O s/>
•i— C •
+-> ra -a
•i- i— tO
C_> 4- CO
CU ra
^— r—
ra CD
•r- S- J3
4J O
C O ^
1 1 •!—
O S
>>4->
rO CU
Q i— 3
ro i—
-»-> 3 ro
to CT >
CU CU
1— r-
-tj ro
M- CU S
O tO T-
CL
O-i^
QJ
(_)
S-
OJ
a_
S-
o cu
to
c ••
o -^
•r- E .
-P ra T3
•r- i— CU
•a _a E
c~ ^
0 4-> (/>
C_) 4- to
CU rO
r~ i— •
ra CU
•r" y, , (^
•(-> O
'E 0 r^
1— 1 •!-
O •£.
ra CU
Q i— 3
ro i—
-P 3 rO
CO CT >
CU CU
\— ,—
4- gj o
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a.
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C i — I j_>
cu
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i.
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CX
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3
ra
•a
to
cu
cu
-------
87
can be used to compute the pollutant concentration, where the a.'s are
respective net hyperplane coefficients (ag is the constant term).
-------
88
A.2 Program Listing
The following is a FORTRAN listing of the repro-model program.
-------
89
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
POLICY ARRAY CONTAINING POLICIES OF VARYING EMISSIONS
ZONE ARRAY CONTAINING ALPHAMERIC LABELLING INFORMATION
HOUR ARRAY CONTAINING ALPHAMERIC LABELLING INFORMATION
NPFUNQ ARRAY CONTAINING NUMBER OF PIECEwISE-LINEAR FUNCTIONS USED.IN EACH
POLICY-ZONE EVALUATION
NMYPER ARRAY CONTAINING NUMBER OF HYPERPLANES PER P-FUNCTIONI PER ZONE
XCOORD, YCOORD ARRAYS DESCRIBING ZONE LOCATION ON GRID
VARIABLE LIST AND DESCRIPTION OF PURPOSE OF EACH VARIABLE
POLLUT ARRAY CONTAINING ALPHAMERIC LABELLING INFORMATION DESCRIBING TYPE OF
POLLUTANT
CONCEN ARRAY CONTAINING ALPHAMERIC LABELLING INFORMATION DESCRIBING UNITS OF
CONCENTRATION OF POLLUTANT
PFUNCM ARRAY CONTAINING PJECEWISE-LINEAR FUNCTION WEIGHTS
PFUNCC ARRAY CONTAINING PIECEWlSE-LlNEAR FUNCTION CONSTANTS
HYPER ARRAY CONTAINING HYPERPLANES
K VARIABLE CONTAINING NUMBER OF ZONES INPUT
POLCON ARRAY CONTAINING CALCULATED POLLUTION CONCENTRATION FOR THE
ZONE UNDER CONSIDERATION
HYPMAX ARRAY CONTAINING MAXIMUM HYPERPLANE FOR THE ZONE UNDER CONSIDERATION
DRIVER FOR REPRO MODEL POLICY EVALUATION PROGRAM
1000
DO 1000
CALL
INPUT POLICY VARIABLES XI
1=1,500
TO XS
CALL CALC
CALL HEADER(I)
CONTINUE
END
SUBROUTINE
rut ATP tycoon unnp
Vh«t»rtt»- i * »~. r «** t > w V? t~
SUBROUTINE TO CALCULATE CONCENTRATION OF POLLUTANT IN A QIVEN
ZONE FOR A PARTICULAR SET OF VALUES OF POLLUTANT SOURCES
COMMON/TACTiC/POLICYtb)
DIMENSION NPFUNCC20), NHYPER(20), PFUNCW(20,3),PPUNCC(20),
HYPER(1BO,6)
COMMON/RE8ULT/PQLCON(20),HYPMAX(20,6)
UAT A'NrrUNU/ 1
DATANHYPER/2
DATAPFUNCWt
DATAPFUNCrtf
DATAPFUNC*(
DATAPFUNCwC
DATAPFUNCwt
DATAPFUNC*(
DATAPf-UNChC
DATAPFUNCW(
DATAPFUNC*C
DATAPFUNCC(
DATAPFUNCC(
DATAPFUNCCC
DATAPFUNCIC
DATAPFUNCCC
DATAPf-UNCCC
DATAPFUNCCt
DATAPf-UNCC(
, 1 ,
,T>,
1,1
2,1
3,1
4,1
5,1
6,1
7,1
8.1
9,1
I)/
2)/
3)/
4) /
5)/
b) /
7)/
8)/
1 , 1 , 1, 1 , 1 , 1 , 1 »£»
3,3,3,2,2,3,1,2,
)/12,83 /
)/ 6.5U5/
)/ S.293/
)/ 5.770/
)/ 4.694/
}/ 3,514,'
)/ 2,749/
)/ ,9727/
)/ l.OOO/
9, 19b/
tl,8bO/
fe,UO/
3,20b/
0.2909/
3.0660/
«,2340/
1.8160/
-------
90
DATAPFUNCC
DATAHYPERC
DATAHYPE.RC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPf.RC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPERC
DATAHYPfcRC
DATAHYPfcRC
DATAHYPERC
DATAHYPtR(
DATAHYPfcR(
DATAHYPERC
DATAHYPE«(
DATAHYPtR(
DATAHYPtR(
DATAHYPERC
DATAHYPERC
DATAHYPf-R(
( 9)
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9,
9,
9,
10,
10,
10,
11,
11,
11,
12,
12,
12,
13,
13,
13,
14,
14,
14,
15,
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1 t>,
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OOOOS479X,
00009567X,
00523000X,
00953100X,
01849000X,
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0003J8BOX,
00370700X,
00667700X,
oossbaoox,
0158JOOOX,
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01876000X,
03S4b"OOOX,
02749000X,
.0030870X,
01027000X,
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00224800X ,
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3 ) X i
03178000X,
00366700X,
00991600X,
0002S530X,
00139900X,
00352500X,
00001323X,
01615000X,
0'I143000X,
0348QOOOX,
00330600X,
00996100X,
00161800X,
00086b*UOX,
0014280 X,
0067120 X,
0171700 X,
0407900 X,
00379500X,
00070330X,
00643200X,
00263600X,
01369000X,
0520aOOOX,
00138SOOX,
0003b"OfcOX,
01'j6SOOOX,
00111000X,
OOb50700X,
06853000X,
036U1000X,
000326UOX,
00838900X,
00460300X,
OOOS6S70X,
OOU83700X,
0?1 4MOQOX ,
OOd«>/600X,
0 i 9 ?> 1 0 0 0 X ,
OOabbOOOX,
00151000X,
HYPER{
U V O C D t
n T r C* n \
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPFRC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPFRC
HYPERC
HYPERC
HYPERC
HYPERC
HYPEiRC
HYPFRC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPERC
HYPE'W(
HYPS tf (
HYPt R(
HYH H(
HYPEKC
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HYPERC
1,2)X
1 ,4)X
1,6)X
2, 2) X
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2,6)X
3,2)X
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4,6)X
5,g)X
5, 4) X
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12,6)X
13,2)X
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14,2)X
14,4)X
14,6JX
15,2)X
1 b, 4) X
15,6)X
16,2)X
16,4)X
16,6)X
17,2)X
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17,6)X
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18, 4) X
18,6)X
19, 2)X
19,4)X
19,6)X
20,2)X
20,
-------
1006
C
C
C
1005
26, 2)/
DATAHYPERC 22,5j/ ,ooo76000,/,HYPERC 22,
DATAPFUNCH(ll,l)/2,7ia /,PFUNCW(U,2)/»
DATAPFUNCW(10,l)/3,599 /,PFUNC«(
DATAPFUNCrtCi2,l)/i,581 /
DATAPFUNCCClOJ/16,77 /
DATAPFUNCCC11)/13,1« /
DATAPFUNCCU2)/ 9.833X
DATAHYPERC 23,I)/ ,008l9200/,HYPER(
DATAHYPERC 23,3)/ ,OOl92800/»HYPERC
OATAHYPERC 23,5)/ ,00765800/,HYPERC
DATAHYPERC 2«,1)/ .OlSUOOO/, HYPERC
DATAHYPERC 2«,3)/ ,OOa88100/»HYPERC
DATAHYPERC 2«,5)/ ,01OSaOOO/,HYPERC
DATAHYPERC 25,I)/ .00173100/,HYPERC
DATAHYPERC 25,3)/*,00178900/,HYPERC
DATAHYPERC 25,5)/-,OOS8?000/,HYPERC
DATAHYPERC 26, !)/•>, 0046950 0/t HYPERC
DATAHYPfcR( 26,3)/ ,00765100/,HYPERC
DATAHYPERC 26,S)/ ,0ia66000/,HYPERC
DATAHYPERC 27,I)/ .00805600/,HYPERC
DATAHYPERC 27,3)/ ,QG3lbl00/,HYPERC
DATAHYPERC 27,5)/ ,010B7000/»HYPERC
DATAHYPERC 28,I)/ .01835000/,HYPER(
DATAHYPERC 28,3)/ ,0109QOOO/,HYPERC
DATAHYPERC 28,S)/ .02322000/,HYPERC
DATAHYPERC 29,I)/ .00239800/,HYPERC
DATAHYPtRC 29,3)/*,00100200/,HYPERC
DATAHYPERC 29,5) /- ,00«aiJ600/, HYPERC
DATAHYPERC 30,1)/*,011S2000/,HYPERC
DATAHYPERC 30,3)/ ,01110000/,HYPERC
DATAHYPERC 30,5)/ ,0196«000/,HYPERC
DATAHYPERC 31,i)/ ,0063b800/,HYPERC
DATAHYPER? 31.3)/ .00l89000/tHYPER(
DATAHYPERC 3l)5)/ J0076330C/,HYPERC
DATAHYPERC 32,U/ ,01139000/,HYPERC
DATAHYPERC 32,3)/ ,00488900/fHYPERC
DATAHYPERC 32,S)/ .02S44000/,HYPER(
DATAHYPERC 33,1J/ ,026?9000/,HYPERC
DATAHYPERC 33,3)/ .00236000/,HYPERC
DATAHYPERC 33,5)/ .01155000/,HYPERC
K«12
23, 2)/
.00976500/
,03«9«000/
«,8730000/
.02165000/
23,6)/
24, 2)/
2a,a)/
24,6)/«7,8290000/
2S,2)/«,00/ ,00«31900/
30,6)/«j,75fcOOOO/
31, 2)/ .00799100/
51, a)/
32, 2)/
.OH32000/
.07528000/
32,6}/«10,l20000/
33, 2)/ ,00«12000/
33, a)/ .02871000/
33,6)/"6,0090000/
ARRAY POLCUN
J»TH ZONE JN
DO 1006 Jsl,20
POLCDNCJJsO
CONTINUE
CONTAINS THE POLLUTION CONCENTRATION FOR THE;
CELL POLCON(J)
FOR EACH ZONE CALCULATE POLLUTION CONCENTRATION AND MAXIMUM
HYPERPLANE
DO 1007 KK*1,K
DO 1005 1=1,b
HYPMAXCKK,I)sO
CONTINUE
CUMHYP=0
ITERATE ON PIECEWISE-LINEAR FUNCTIONS
NPFUNKBNPFUNC(KK)
DO 1000 L°1,NPFUNK
HYPIJ»«i,E»50
ITERATE ON HYPERPLANES
NHYPK»NHYPER(KK)
FORM DOT PRODUCT OF HYPERPLANE AND POLICY
DO 1001 Msi,NHYPK
SUMsQ
DO 1003 NNsi,5
-------
92
1003
tooi
C
1004
C
1000
C
1007
1002
+ POHCY(NN) * HYPEKtMM+M,NNJ
CONTINUE
SUM=SUM + HYPER(MM+M,6)
IFCHYP1J ,LE, SUM) HAXHYPsMM*M
HYPIJsAMAXiC SUN,HYPIJ )
MH»MM + NHYPK
PO 100« 1=1,6
HYPMAX(KK,I)sHYPMAX(KK,I)
CONTINUE
* PFUNCN(KK,L)*HYPERCMAXHYP,I)
CUMHYP=CUMHYP
CONTINUE
* HYPU*PFUNCW(KK,L)
HYPMAX(KK,6)s HYPMAX(KK,6)* PFUNCC(KK)
POLCON(KK)=CUMHYP * PFUNCC(KK)
CONTINUE
CONTINUE
RETURN
END
SUBROUTINE EVAL
C
C
C
C
100
101
102
103
104
105
106
107
10B
109
HO
m
112
C
SUBROUTINE TO DETERMINE POSSIBLE VIOLATION OF POL
CONSTRAINTS
COMMON/TACTIC/POL ICY (5)
DIMENSION FLAGC12)
LOGICAL FLAG.YIOLAT
FQRMATC/10X,43H*** VIOLATED POLICY REGION CONSTRAINT (S)"-%)
FORMATC 21X,17HX1 + X2 ,GE, 30 )
FORMATC 2jX,17HXi + X2 ,LE, 240 )
FQRMA.TC 2iX;17HXl - X2 tl£t 40 )
FORMATC 21X,17HX2 * XI ,LE, 20 )
FORMATC 2l*,15HX2 ,GE, 0 )
FORMATC 21X,15HX3 ,GE, 0 )
FORMAT( 2JX,17HX3 ,LE, 100 )
FORMATC 21X,24HX4 • 0,558X1 ,GE, 29,2 )
FORMATC 21X,
FORMATC 21X,
FURHATC 21X,
FORMATC 21X,
2aHX« - 0,682X
30HO,
30HX5
11HX5
756X2 *
- 0,92
.GE,
0
ux
3
1 .Lfc
,144X3
2 •• 0,
)
,
9
46,8
X5 ,
176X3 ,
)
LE, 5)
UE, 5)
VJOLAT=, FALSE,
DO 1000 J=l,
12
FLAGCJ)=, FALSE,
1000
C
C
C
CONTINUE
LOGICAL CASCADE TO
DO 1001 J=l,
IF((POLICYC
IF<(POLICY(
IFCCPOLICYC
IKCPOL1CYC
IF( POLICYC
IF( PULICYC
IF( POLICYC
IFCCPOLICYC
IFCCPOLICYC
12
1) *
1)
I)
2)
2)
3)
3)
4)
a)
POLICY
POLICY
POLICY
POLICY
LT, 0)
LT, 0)
GT.100,
f 7 J O * r
C
C
C
C
)
OL
,682*POL
2)) ,
2)) ,
2)) ,
in .
ICYC
ICYC
EVALUATE
LT
GT
GT
GT
n
i)
. 30,
,240.
• aO ,
, 20,
) tLT,
) ,GT,
INEQUALITIES
) FLAS(
) FLAG(
) FLAG(
) FLAG(
FLAG(
FLAG(
FLAG(
1 )
2)
3)
4)
5)
6)
7)
29,2) FLAG
st
s i
s »
s«
~ •
= •
= •
C
46,8) FLAG(
TRUE,
TRUE,
TRUE,
TRUE,
TRUE,
TRUE,
TRUE,
8)=, TRUE,
9)=, TRUE,
2)»,144*PULICYC 3)»POLICY( b)),GT,b)
IK(PUL1CYC b)-,92«*POLICY( 2) - , 1 76*POL 1C Y ( 3)),GT,5)
*FLAG(11)=,TRUE,
IF(POLICY( 5) ,LT, 0)
FLAG(12)=,TRUE,
-------
93
100}
c
100?
C
c
c
c
CONTINUt
DO 1002 Jsjfl*
IFC FLAGCJ) ) VIOLATE,TRUE,
CONTINUE
IFC VIOLAT ) GOTO i
RETURN
WRITE(6f100)
IFC FLAGCl) ) WRITECfcflOl)
IFC FLAGC2 )) WRITE(fa,102)
IFC FLAC(3))WRITF-C6f 103)
IFC
FLAG(5))W*ITEC6»105)
FLAG(6))W«ITE(6,10fc)
FLAGC7))wmTE(6,107)
FLAG(8))WRIT£(6,10fl)
IFCFLAG(lU)KRITEC6,lin
if U/«HPEAK/fZONE(
2f l)/4HSUNL/fZQNEC
/,ZDNEC
/,ZONEC
RETURN
END
SUBROUTINE HEADER(I)
SUBROUTINE TO OUTPUT P(JLICY«ZONF. RELATIONSHIPS AND POLLUTION
CONCENTRATIONS RESULTING FROM GIVEN POLICY
COMMON/TACTIC/POL 1CYCb)
COMMON/KESULT/PUUON(20),HYPMAXC20»6)
DIMENSION ZONt(20,3),HOUR(20f3),XCOORDC20)fYCUORDC20}fPOLLUTCHO,3)
I ,CONCENC20,3)
INTEGER ZONE,HOUR,PULLUTfCONCtN
N^LANK IS USED TO BLANK OUT COORDINATE FIELD
DATA NBLANK/flH /
DATAZONtC
DATAZONEC
DATAZONEC
DATAZONEC
DATAZUNEC
DATAZONEC 6,i)/4HDUAR/fZONE(
DATAZONEC
DATAZUNEC
DATAZONEC 9,U/4HN UO/,ZONEC
DATAHOURC
DATAHOUKC
DATAHUURC
DATAHOURC
DATAHUURC
DATAHOURC
DATAHUURC
DATAHQURC
DATAHUURC 9
DATACONCENC
DATACUNCENC
DATACUNCENC
/
/
LA /
7,1)/4MCARB/,ZON£(
/fZUNLC i
C/rZUNtC '
LA /,ZONE(
i)/4HPEAK/,HOUR(
HOU/»HUUR(
HOU/fHOURC
9,3)/«HEACH/
3f3)/«HR
HOURC a,z
5, l)/<4HPEAK/f HOUR( S,£
6,l)/aHPEAK//HDURC 6f2
7,l)/
-------
94
C
109
HI
112
113
115
116
C
C
100
101
117
118
DATAXCOORDt
DATAXCOORDC
DATAXCOUROC
DATAXCUURDt
DATAPOLLUH
DATAPOLLUTt
DATAPOLLUTC
DATAPOLLUH
DATAPOLLUTt
DATAPULLUTC
DATAPOUUTC
DATAPOLLUK
DATAPOLLim
DATAZONECJO
DATAZONtCU
DATAZONEU2
DATAHOUKUO
DATAHULIKUl
DATAHQURU2
DATACONCENt
DATACONCENC
DATACQNCF.NC
DATAXCOORD,
DATAXCOORDt
DATAXCOUROC
DATAPULLUTC
DATAPOLLUTt
OATAPOLLUT(
KM2
fe)/20,/,YCQORUC *••
7)/
-------
95
C
C PRINT (K) ZONES FOR I»TH POLICY
00 JOOO Jrl,K
IF((XCDORDCJ),LE,0),OR«CYCOURD(J),Lt,0)) GO TO 10
WRITE (6,117) (ZON6(J,L),L = l,.5),XCUORO(J),YCQORD(J),(POLLUTCjfl)»
1 L=t»2)»POLCON(J),CONCEN(J,l),(HOUR(J,LJ*L*1t3)i(HYPMAX{J,L)»L*1
2 »6)
GO TO 1000
JO WRITE(6»118) (ZONE:(J»L),L=lr3),NBUNK ,NBl,ANK , (POLUUT {J> U) ,
\ Ut!l,2),POLCON(J),CONtEN(J,nf (HOljRC J,U f L«i f i)» (HYPMAX (J,L) ,l,si
2 >6)
1000 CONTINUE.
WRITEC6,100)
RETURN
END
SUBROUTINE INPOL
C
C SUBROUTINE TO INPUT POUICItS TO BE USED IN DETERMINING AJR
C POLLUTION CONCENTRATIONS FOR ZONES UNDER CONSIDERATION
C'
COMMON/TACTIC/POLICY(5)
c
100 PORMAT(5F10,0)
c
RCAD(S,100,ENP=1) (POLICY(J),J=l,5)
C INSERTION OF INITIAL CONDITIONS
« IF(POi.ICY(«) ,UE, 0) POl.ICy(«)e,62*PQLlCY(i)*38
IF(POLICY(5) ,Lt, OJ POLICY(5;s,8a*POlICY(2)+,l6*POLICY(3)
C
RETURN
1 CONTINUE
STOP
END
-------
96
A.3 One Hundred SAI Model Runs
The five input variables used for each of the SAI model runs are
listed in the following table.
-------
97
Independent Variables
1 100 100 100 100 100
2 25 5 20 58 13
3 20 10 40 45 9
4 15 15 60 57 15
5 10 20 80 54 30
6 5 25 100 34 43
1 30 13 13 57 13
8 35 10 25 65 15
9 30 15 45 46 27
10 25 20 65 49 22
11 20 25 85 60 35
12 15 30 10 47 27
13 40 5 30 73 9
14 45 15 50 78 13
15 40 20 70 62 24
16 35 25 90 65 44
17 30 30 15 48 36
18 25 35 35 50 27
19 20 40 55 60 42
20 50 10 75 61 16
21 50 25 95 62 40
22 45 30 0 66 18
23 40 35 20 63 28
24 35 40 40 70 49
25 30 45 60 46 57
26 55 20 80 71 32
27 60 30 100 87 41
28 55 35 5 72 30
29 50 40 25 74 42
30 45 45 45 54 35
31 40 50 65 57 47
32 35 55 85 68 71
33 65 25 10 84 23
34 65 40 30 70 29
35 60 45 50 75 46
36 55 50 70 78 58
37 50 55 90 63 55
38 45 60 15 77 63
39 70 35 35 70 28
40 75 45 55 84 47
41 70 50 75 87 59
42 65 55 95 72 56
43 60 60 0 87 50
-------
98
Independent Variables (Cont.)
xl X2 X3 X4 X5
44 55 6F 2^ 84 69"
45 50 70 40 58 55
46 80 40 60 88 49
47 80 55 80 94 54
48 75 60 100 72 54
49 70 65 5 74 61
50 65 70 15 89 70
51 60 75 30 75 80
52 85 50 45 104 49
53 90 60 60 80 60
54 85 65 75 91 67
55 80 70 85 94 77
56 75 75 95 99 65
57 70 80 5 77 62
58 65 85 25 90 87
59 95 55 45 88 ' 53
60 95 70 65 82 57
61 90 75 85 99 77
62 85 80 10 93 69
63 80 85 30 82 83
64 75 90 50 85 71
65 100 65 70 100 ; 66
66 105 75 90 us 90
67 100 80 15 85 80
68 95 85 35 97 65
69 90 90 55 80 84
70 85 95 75 91 106
71 80 100 95 inn 9
72 110 70 0 116 5
73 110 85 20 110 74
74 105 90 40 103 95
75 100 95 60 93 97
76 95 100 80 no 96
77 90 105 100 85 89
78 115 80 5 93 • 68
79 120 90 25 m 93
80 115 95 45 96 100
81 110 100 65 106 80
82 105 105 85 117 .102
83 100 110 10 104 94
84 95 115 30 90 JOS
85 125 85 50 115 79
86 125 100 70 130 88
87 120 105 90 gs 118
88 115 110 15 93 109
89 110 115 35 106 112
90 105 120 55 103 110
-------
99
Independent Variables (Cont.)
91 130 90 75 125
92 135 105 95 138
93 130 110 0 110 92
94 125 115 20 132 108
95 120 120 40 100 123
96 115 125 60 100 109
97 110 130 80 113 139
98 135 100 100 97 100
99 100 20 50 100 25
100 20 100 50 50 92
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-650/4-74-001
2.
3. RECIPIENT'S ACCESSIOONO.
4. TITLE AND SUBTITLE
5. REPORT DATE
The Application of Repro-Modeling to the Analysis of
a Photochemical Air Pollution Model
Dprpmhpr., 19 73
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Alan Horowitz, William S. Meisel, David C. Collins
8. PERFORMING ORGANIZATION REPORT NO
9. PERFORMING OR~ANIZATION NAME AND ADDRESS
Technology Service Corporation
225 Santa Monica Boulevard
Santa Monica, Ca. 90401
10. PROGRAM ELEMENT NO.
3RAM ELE
1A1009
11. CONTRACT/GRANT NO.
68-02-1207
12. SPONSORING AGENCY NAME AND ADDRESS
13. TYPE OF REPORT AND PERIOD COVERED
Meteorology Laboratory, EPA
National Environmental Research Center
Research Triangle Park, N. C. 27711
Final Report
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
16. ABSTRACT
Several physical models which simulate the impact of emissions and meteorology on
the creation and dispersion of photochemical smog have been developed. Characteris-
tics of most of these models are that they are highly computational and require a
great deal of input data; hence, it is generally difficult to systematically explore
the implications of the models or to use them in a planning context where many
model runs are required. This paper explores "repro-modeling," the analysis and
replication of the input/output characteristics of the model, as a means of
meeting these objectives. A study of the application of repro-modeling to the
SAI model developed for the Los Angeles Basin is described. The major objectives
of the study were threefold: (1) a feasibility test of the repro-modeling approach;
(2) a limited interpretation of the implications of the model; and (3) an efficient
repro-model program which duplicates input/output relationships of the original
model. The repro-model developed is analyzed in a particular application context
(i.e., transportation emission control policy evaluation) and its general implica-
tions are discussed. Examples of use of the repro-model, which requires orders
of magnitude less computer time than the original model, are provided.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS C. COS AT I Field/Group
Air Pollution
Mathematical Modeling
Repro-modeling
3. DISTRIBUTION STATEMENT
19. SECURITY CLASS (ThisReport}
Unclassified
21. NO. OF PAGES
109
20. SECURITY CLASS (Thispage)
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
-------
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------- |