DEVELOPMENT OF A SIMULATION MODEL
FOR .ESTIMATING GROUND LEVEL CONCENTRATIONS
OF PHOTOCHEMICAL POLLUTANTS
FINAL REPORT
Prepared by
Systems Applications, Inc.
Beverly Hills, California 90212
for the
Air Pollution Control Office
of the Environmental Protection Agency
Durham, North Carolina 27701
-------
DEVELOPMENT OF A SnfUIATION MODEL
FOR ESTIl1ATING GROUND LEVEL CONCENTRATIONS
OF PHOTOCHEMICAL POLLUTANTS
FINAL REPORT
Philip M. Roth
Steven D. Reynolds
Philip J. W. Roberts
John H. Seinfeld
Report 71SAI-2l
July 1971
Prepared by
Systems Applications, Inc.
Beverly Hills, California
90212
for the
Air Pollution Control Office
of the Environmental Protection Agency
Durham, North Carolina 27701
under Contract
CPA 70-148
-------
ABSTRACT
In this report we describe the progress that has been achieved
to date in the development and validation of a simulation model for
estimating ground level concentrations of photochemical pollutants.
This model is based on the finite difference solution of the equations
of conservation of mass, using the method of fractional steps. The
bulk of the effort reported here is developmental/ involving the
compilation of a comprehensive source emissions inventory, the
development and validation of a kinetic mechanism for photochemical
reactions, the adaptation of the method of fractional steps for
use in the solution of the governing equations, and the preparation
of maps displaying spatial and temporal variations in wind speed
and direction and in the height of the inversion base. The details
of these various efforts are described in a series of appendices
to this report. Although a validated kinetic mechanism has been
developed and incorporated in the simulation model, validation
efforts have thus far been restricted to carbon monoxide. Provisional
validation results for the Los Angeles Basin are presented.
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INT:RODUCTION
.;.
.;:
"
CONTENTS
. . .
. . .
, 'Page
. . . . . 1
. . .
. . . . . . .
. . . . . . . .
A.
AIRSHED MODELS BASED ON THE EQUATIONS OF CONSERVATION OF MASS
Moving Cell Approaches
. . . . .
6
I.
B.
c.
II.
. .
4
.......
. . . .
. . .
Fixed Coordinate Approaches
. . .
8
. . . . .
. . . . . . . .
l.
2.
3.
Finite Difference Methods
Particle-in-Cell Methods
Well-r1ixed Cell Model
. . . . . . . . . . . . . . . 9
. . . . . . . . . . . . . 11
. . . . . ., . . . . . . . . . . . 12
An Assessment. .
. . .
. . 14
. . . .
. . . .
......
THE MODEL DEVELOPED IN THIS STUDY
. . . . . . .
. . . .
. . . . . 15
III. VALIDATION OF TIlE MODEL
. . . .
. . . .
. . 22
. . . . .
IV.
RECOl-!11ENDATIONS
. . . . . . . . . .
. . . . . . .
. . 51
......
This final report includes the fOllowing Appendices,
each bound under separate cover.
Appendix A
Appendix B
Appendix C
Appendix D
Appendix E
Appendix F
Contaminant Emissions in the Los Angeles Basin--
Their Sources, Rates, and Distribution
A Kinetic Mechanism for Atmospheric Photochemical
Reactions
The Treatment of Meteorological Variables
Numerical Integration of the Continuity Equations
Air Quality Data Used in Model Validation
Description of the Computer Program
/
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INTRODUCTION
Urban airshed models are mathematical representations of atmospheric
transport and chemical reaction processes which, when combined with a
source emissions inventory and pertinent meteorological data, may be used
to predict pollutant concentrations at any point in the airshed. ~todcls
capable of accurate prediction \o1i11 serve as an important aid in urban and
regional planning. In particular, these models will be used for:
.
Simulation of the effects of alternative air pollution control
strategies on pollutant concentrations in the airshed
.
Planning for land use, So that projected freeways, industrial
sites, and power plants may be located where their air pollution
potential is minimized
u
.
Determination of the long-term air pollution control strategy
which accomplishes desired air quality objectives at least cost
.
Real-time prediction in an alert warning system, such that an
impending air pollution episode may be anticipatea and proper
preventive action taken.
An airshed simulation model that is to be generally useful in urban
planning studies must meet several requirements.
.
It should be capable of predicting accurately the ground level
concentrations of inert pollutants, as well as those formed in
the atmosphere through chemical reactions. Of immediate interest,
and the focus of this study, is the prediction of carbon mcmoxide,
nitrogen oxide, ozone, and hydrocarbon concentrations and their
variations in space and tine. Also of interest, particularly
for large Eastern and Midwestern cities, is the estimation of
sulfur dioxide and particulate concentrations. Finally, it should
be possible to incorporate into the model, when the means are
developed, the facility for estimating aerosol concentrations.
.
The model should have a spatial and temporal resolution appropriate
for the analysis of concentrat~on variations which occur in a
city througoout the course of day. For a typical large urban
area, the horizontal spatial resolution may be of the order of
a mile, and the temporal resolution, of the order of an hour.
The resolution of the model will, of course, be influenced by
the availability of data of similar resolution.
.
The complexity of the model, and thus the computing time and
computer storage requirements, should be such that the model
can be operated at a reasonable cost using computers of general
avaUabili ty . .
1
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Models that have been developed in L~e past, and that have l\ad wide application,
fail to satisfy all these requirements.
The simplest of the existing models is the so-called "box model",
wherein pollutant concentrations are assumed to be homogeneous throughout
the entire airshed. In addition, it is assumed that, within the airshed:
.
The sources are distributed uniformly
.
Emitted pollutants are instantaneously and uniformly mixed
.
A uniform wind characterizes transport
.
A constant inversion height is typical of time-averaged
meteorology
A model of this type has been employed by Smith (1961) to estimate pollutant
concentrations in an urban area. A variant of the box model, consisting
of a two-dimensional network of interconnected boxes or well-mixed cells,
has been developed by Reiquam (1970a, 1970b, 1970c) to estimate monthly
average pollutant concentrations in the ~'1illar,'ette Valley and in Northern
Europe. In this model, the assumptions listed above apply to each well-mixed
cell. The highly simplified box model clearly lacks the spatial resolution
needed to properly represent the distribution of sources or to estimate
spatial concentration variations in an urban airshed. However, its variant,
the well-mixed cell model, does not suffer this d~ficiency. In fact,
Reiquarn's formulation can be extended for application to the prediction
of' pollutant concentrations in urban areas and to incluC1.e photochenical
reactions. The well-mixed cell model is further discussed in Section I.B.3.
The second type of model that has been applied in the prediction of
pollutant concentrations is the plume model. This ~odel was originally
developed to describe the concentration distribution of an inert species
downwind of a point source. It has subsequently been extended for application
to line and area sources and, by imposing the principle of superposition,
to a distributed array of sources. In the usual applications of this modela
.
Only inert pollutants are considered
.
Wind shear is neglected
Measures of plume spread are assumed constant, are based
on experimental studies (usually carried out over rural
areas), are independent of height, and are a function of
atmospheric stability class.
While the plume model has been widely applied during the past decade in the
prediction of concentrations of sulfur dioxide and particulates in urban
areas (see, for example, Turner (1964), Clarke (1964), Miller and Holzworth
. (1967), Koogler, et ale (1967), Hilst (1967), Slade (1967), and Bowne (1969»,.
. it is of little use in the prediction of concentrations of pollutants formed
through chemical reaction. Nevertheless, gaussian plume models can often
provide useful estimates of concentrations downwind of strong isolated sources.
I
.
2
-;,..
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Reviews of gaussian plume and puff models* .have been presented by Lamb (1968),
Seinfeld (1970), and Neiburger and Chin (1970).
As models of a relatively simple nature are inadequate to meet the
requirements stated, we consider n~xt more fundamental approaches to the
simulation of transport. and reaction processes. The DOst complex of
these involves the solution of the turbulent planetary boundary layer
equations for the conservation of mass, r.\ornenturn, and energy. The solution
of these equations is a truly prodigious undertaking, the demands of which
exceed the computing speeds and storage capacities of the present generation
of computers. . Less ar.tbitious is the solution of Dne (or possibly two) of
these three classes of equations, at the SMae tir.\e supplying as data the
information that would not be computed by the model due to the omission
of one or n~re classes of equations from the system description.
One such approach to airshedmodeling is the solution of the partial
differential equations of conservation of mass. This approach has appeal
because it provides a means for including che::\ical reaction phenomena, time-
varying meteorological conditions, and complex source emissions patterns
while avoiding an undue level ~f complexity. However, the computational
requirements for the solution of these equations are still substantial,
both with respect to computing time and computer storage. Data require-
ments are also considerable; as those variables associated with the momentum
and energy equations, such as wind speed and direction and height of the
inversion base, must be treated as inputs to the ~odel. Thus, the questions
that must be answered in the development of such a model are:
1)
Will it predict ground level concentrations of frimary and
secondary pollutants** with acceptable accuracy?
'C'''- .
2)
Assuming that the model is of acceptable accuracy, can it be
operated at a reasonable cost, given the large co~puting ti~a
and computer storage requirements associated with such an
,fi~U . ."
It has been the purpose of this study to develop and validate an airshed
.simulation model based on the solution of the equations of conservation of
mass, and, in so doing, to seek answers to these questions. In this report
we detail the progress that has been made to date in this effort. . In
Section I, we review the various approaches to airshed modeling that are
based on the solution of the continuity equations. We cor.unent on the virtues
and deficiencies inherent to each approach, and present a comparative
evaluation. In Section II, we describe in more detail the particular
approach adopted in this study. Progress to date in the validation of this
model is summarized in Section III, and we conclude, in Section IV, with
an outline of recommended future efforts.
* The puff model, described by Roberts, et al. (1970), is an extension of the
. plu~ 'modei, in that it is based on the gaussian distribution and the same
estimation pr~cedures for dispersion parameters. However, by assuming that
emissions can be treated as discrete puffs, certain assumptions nOrDally made.
for the plume model can be relaxed, notably that of steady state behavior'f
However, chemical reactions have yet to be treated in this approach.
*.Primary pollutants are those that do not undergo, or have not undergone,
chemical change subsequent to being emitted. Secondary pollutants are those
.pecie.s that are formed in the atmosphere through cl1el':\ical reaction processes.
3
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I.
AIRSHED MODELS BASED ON THE EQUATIONS OF
CONSERVATION OF l-tASS
There are several approaches to airshed modelin9 based On the solution
of the equations of conservation of mass.* These may' be divided into two
basic categories: .
. Moving cell models
. Fixed coordinate models
In the moving cell approach a hypothetical column of air, w~ich mayor may
not be well-mixed vertically, is followed through the airshed as it is
advected by the wind. Pollutants are injected into the column at its base
and chemical reactions may take place within the column. In the fixed
coordinate approach the airshed is divided into a three-dimensional grid,
which can be envisioned as stacked layers of cells, each cell being perhaps
one to two miles On a side and of the order of oJe hundred feet high.
. This three-dimensional grid is then used as a basis for the numerical solution
of the equations of conservation of mass. In the language of fluid mechanics,
the moving cell approach is termed Lagrangian, and the fixed coordinate approach,
Eulerian. Each of the approaches has characteJ::istics which suggest application
in the analysis of particular types of air pollution problems.
The modeling approach we have adopted and pursued in our study is
Eulerian in nature and is based on the finite difference solution of the
equations of conservation of mass. This approach, as do all others involving
the solution of the continuity equations, requires several components:
. A kinetic mechanism describing the rates of atmospheric
chemical reactions as a function of the concentrations of
the various species present~ ..
. ~
. A source description, giving the temporal and spatial
distribution of emissions from all significant pollutant
sources in the airshed. .
. A meteorological descriPtion, including wind speed and
direction at each location in the airshed as a function of ,
time, the vertical atmospheric temperature profile and
radiation intensity.
But it is to the overall model, in which these components are embedded, that
we must first direct our attention. For it is the nature and structure of
this model that will determine the degree to which the requirements that
are placed on an .irshed model will be met.
In this section, We review the various approaches that are currently
being pursued in the simulation of atmospheric transport and reaction
processes which are based on the solution of the. continuity equations. We
* Recall that we have restricted this discussion to models capable of
describing concentration changes in an urban airshed over time intervals
of the order of a day. We have also excluded from consideration urban air'
pOllution analyses of restricted scale, such as the prediction of concentrations
in the vicinity of major local sources, notablY freeways, ai~rts, power plants
and refineries.
4
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comment on the virtues and deficiencies inherent to each, and at the
conclusion present a comparative assessment. It is hoped that, as a
result of this review, the approach we have adopted can be better understood
and evaluated when compared with other modeling efforts under development.
We begin the discussion by presenting the equations upon which all models
to be described are based.
The time-averaged equation of conservation of mass for species
a turbulent flow is given by (see Bird, et ale (1960»:
i
in
a';i
-+
at
a (~i) a (~i) a (;;i) a (U';!) a (~. l a (~')
+ + 1 + i + i
ax ay + az ax 1y az
..
(a2c a2c alc-. )
i i '1
Di aXT + -ayT + ~ + Ri (cI
+ ci J"'"
-
c + c') + S1
P P .
(1)
where
---:-
1.1, .." W
t. = 1,2,...,p
= time-averaged wind velocity components in the
x, y and z directions respectively
u' ,v' ,wi
= instantaneous turbulent velocity fluctuations
Ci
= time-averaged concentration of species
i
= turbulent concentration fluctuation of species
i
c1
Di
= molecular diffusivity of species
i
in air
= rate of generation of species
Ri
Si
i
by chemical reaction
= rate ofernission of species
i
by elevated sources
If.
,,e.
Molecular diffusion is negligible when compared with turbulent
diffusion
b.
The contribution of turbulent concentration fluctuations to
Ri are neglected
c.
aU" av aw
The flow is incompressible, i.e., ax + ay + az a: 0
d.
Turbulent eddy diffusivities are defined by:
. \i'i?" ...
i
-
ac
i
-K -
x ax
aCt
V'C' = -K -
. i Y ay
aCi
-KzF
WiC' =
i
5
-------
'''. .
.~...., .
, .
It
then Equatioh (1) : simplifies to
aCi
- +
at
U aCi "+ v aCi + w' aCi =..!.. (K' aCi) + 1.../K aCi) + 1... (~ aCi)
"ax ay az ax x ax ay ~ y ay az z az
(2 )
+ Ri (~l'. .. '"Cp) + Si
i = 1,2,...,p
These p coupled equations provide a convenient basis from which to describe
both the moving cell and fixed coordinate approaches. It should be noted
that the coupling of the equations occurs through the nonlinear chemical.
reaction term~. The functional form of R. derives from the particular
formulation upon which the kinetic mechanis~ for the chemical reactions
- .
is based (see Appendix C).
A.
Moving Cell Approaches
, J
As we have noted, the principal feature of the moving cell 'approach
is that concentration changes in a hypothetical parcel of air are
computed a~ the parcel traverses the airshed.~~The parcel is visualized
as a vertical column of air of fixed cross-sectional area and variable
height, with the top of the column being defin~d by the base of an
elevated inversion or, in the absence of an inversion, by an estimated
maximum mixing height. The motion of the air column is assumed to
correspond to the local instantaneous wind speed and direction, thereby
tracing out a particular surface trajectory in the airshed.
The following assumptions are inherent in this model:
.
There is no horizontal transport of material across the
boundaries of the parcel (there is,' in fact, no means of
including horizontal diffusive transport between the
column and the environment).
.
There is no change in the horizontal wind velocity
with height.
. Vertical advection is neglected, i.e., w = o.
The basic assu~ption underlying the approach is that a parcel of air
maintains its integrity while traversing the airshed. It is highly
unlikely that this is ever the case in the atmosphere over the time
scales of interest.
Since horizontal transport across the boundaries of the column is
neglected, and since the column moves with the average ground-level
horizontal wind velocity, the moving cell approach may be represented
rather simply mathematically. If the contents of the column are
considered to be horizontally uniform but vertically non-uniform, the
only independent variables are time t and vertical distance z. The
concentration of species i, ci(z,t), is determined by integration of
the abridged form of Equations (2) I
6
-------
aCi a ( dCi)
it""" =: a; Kz a;- + Ri (cJ.'... ,cp) + Si
, (3)
i ... 1,2,...,p
The initial condition for this formulation is that the concentration
within the column at the,beginning of the traversal be given, i.e., ,
ci (z,O) = ci
o
The boundary conditions at the ground, z = 0, and at the inversion base
(or top of the column), z = H(t), are given by
dCi
- Kz az = Qi (t)
~ci
- Kz a;- = 0
Z ... 0
Z .. H(t)
where Q (t) is the flux of species i from ground-level sources, S is the
mass raie of emission of species i from elevated sources, and H(tt is the
height of the column as a function of time. The movement of the column
is reflected mathematically only in Q. (t) and H(t). An approach based
1
on Equations (3) has been developed for Los Angeles by Eschenroeder and
Martinez (1969). .
A simplified version of this model results if We neglect vertical
inhomogeneities in the column. Then Ci = ci(t) only, and Equations (3)
reduce to
d(Vci) - -
dt = VRi(cl"."cp) + AQi + VSi
(4 )
i . l,2,.~.,p
where the column is simply a well-mixed vessel having a volumn V, a base
area A, and a time varying pollutant input rate AQi + VSi. The advantage
of this approach, when compared to that based on Equations (3), is mainly
ease of computation, since Equations (4) consist of ordinary rather than
partial differential equations. Wayne, et a1. (1971) have utilized this
approach in developing a model of the Los Angeles Basin.
7
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The moving cell approach has the fOllowing virtues:
. The lengthy integration of Equations (2) in all three
spatial dimensions and time is avoided.
. The concentration history along an air trajectory can
be traced, thereby permitting an assessment of the
effect of specific sources at locations downwind of
these sources.
and deficiencies:
. The concept of an identifiable parcel of air is an oversimplification
since such an entity never exists in a turbulent atmosphere
over time scales of interest.
. There is no way to ~nclude converge~ce and divergence
phenomena in the wind field, and the resulting vertical
advection of air.
. In order to determine the concentration at a given location
and time, it is necessary to trace the trajectory backward
in time to the point where it entered the airshed. Since
the only reason for this calculation is to ascertain the
starting-point of the trajectory, its inclusion constitutes
an inefficiency inherent in the approach, particularly
when a large number of trajectories must be computed.
one final observation. While the moving cell approach is a useful
technique for con~uting concentration histories along a given air
trajectory, it is not practical for full airshed modeling. This is
largely because of the great many trajectory calculations required to
construct maps of predicted concentrations for a wide area.
B.
Fixed Coordinate Approaches
In the fixed coordinate approach to airshed modeling, the airshed is
divided into a three-din\ensional grid for the numerical solution of some
form of Equations (2), the specific form being dependent upon the
simplifying assumptions made. We can classify the general mp.thods for
solution of the continuity equations as:
.
Conventional finite difference methods
..
Particle-in-cell methods
.
Variational methods
We will discuss in this section finite difference methods and particle--
in-cell methods. variational methods (of which a specific class,
Galerkin methods, are particularly pertinent) involve assuming the
form of the concentration distribution, usually in terms of an expansion
of known functions, and then evaluating coefficients in'the expansion. I
8
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There is currently very active interest in the development of these
techniques (see, for example, Douglas and DuPont (1970», however,
they are not included in this discussion, as experience to date in'
their application to complex systems of differential equations is very
limited.
,
The principal numerica~ problems associated with fixed coordinate
methods are that:
. Complex and lengthy calculations are required for the
integration of several coupled nonlinear partial differential
equations in three dimensions.
. Changes in elevation of the upper boundary (i.e., H(x,y,t»
with time require repeated reconfiguration of the grid
, on which the solution is carried out.
However, models based on a fixed coordinate approach may be used to
predict pollutant concentrations at all points of interest in the airshed
at any time. This is in contrast to the moving cell methods, wherein
predictions are confined to the paths along which concentration histories
are computed.
1.
Finite-Difference r.lethods
The numerical analysis literature abounds with finite~difference
methods for the numerical solution of partial differential equations.
Unfortunately, while these methods have been successfully applied in
the solution of tWo-di~ensional problems in fluid mechanics and
diffusion (see, for example, Peaccrnan and Rachford (1962) and Burstein (1967».
There is a dearth of reported experience in the solution of three-dimen-
sional, time-dependent, nonlinear problems. Application of these
techniques, then, must proceed by extending mathods successfully
applied in two-dimensional formulations to the more complex problem
of solving Equations (2). For general discussions of the various types
of finite-difference methods applicable in the solution of Fartial
differential equations, and their advantages and disadvantages, we
refer the reader to the books by von Rosenberg ~l969), Forsythe
and Wasow (1960), and Ames (1969). ' ,
The principal considerations in ohoosing a finite-difference method
for the solution of the continuity equations areaccuracYi stability,
computation time, and computer storage requirements. Accuracy of a
method refers to the degree to which the numerically computed temporal
and spatial derivatives approximate the true derivatives. Stability
considerations place restrictions on' the maximum time step tJ. t that can
be used in the in~egration. ~mplicit methods, L~ose involving the
simultaneous solution of difference equations at each step, are more
. suitable for the solution of nonlinear forms of the continuity e~ations
than are explicit methods, as the fo~r are stable over a wider range
of step ,sizes. Implicit methods, however, involve considerably
~re computation per time step than do explicit methods. Other
finite difference methods exist which are difficult to classify.
Typically, these ~echniques have'the characteristics of implicit methods,
9
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yet, because of some unique aspect of the particular method, involve
less burdensome calculations than are norn~lly expected with an
implicit method. Two such techniques that have the potential for
application in the solution of Equation (2) are the ~ethod of
fractional steps and the method of alternating directions (see Rich~~yer
and "lorton (1967) for a discussion of these techniques).
To date, there have been reported only two applications of finite-
difference methods to the solution of the equations of conservation
of mass as they pertain to urban air sheds, both for the Los Angeles
Basin. These are the '...ork of Eschenroeder and Hartinez (1969) and
that described in this report. Eschenroeder and foartinez applied the
crank - Nicolson implicit method to the simplified version of Equations (2),
aCi
-+
at
- ac i 3 ( 3Ct)
\1-=- K-+R
ax 3z z 3z 1
,
I
In a later paper (Eschenroeder and f.~rtinez (1971», they report that
a number of difficulties were encountered in using the Crank-Nicolson
method and the approach was abandoned. In the work we have carried
out, the method of fractional stc~s has been applied to the solution
of six equations of the form of Equations (2), four of which are
coupled. (t~ile horizontal dispersion was neglected in the final
formulation, it was originally incorporated through the use of
Equation (6». This work is described in Sections II and III and
in Appendix D.
The main advantage in using a finite-difference method in the
solution of Equations (2), as compared with other fixed coordinate
approaches, is that there has been extensive experience in applyins
these methods to a wide variety of partial differential equations.
Even though reported experience with three-dimensional, time-dependent,
nonlinear prob1e~s is scanty, experience with simpler syst~s provides
a sound basis for the development of feasible approaches. The
disadvantages of finite-difference methods are well known I
.
Inaccuracies in approximating the first-order advection
terms in the continuity equations give rise to errors
which have the mathematical characteristics of diffusion
processes. These inaccuracies, termed "numerical" or
-artificial" diffusion, often mask the representation
of true diffusion.
.
Computing time and storage requirements associated
with accurate, stab~e methods can be excessive for
problems involving several independent variables. (This.
is also true, however, for all fixed coordinate ~e~hods.)
When the equations are nonlinear, time-consuming iterations
or matrix inversions are often required in their solution.
10
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2;'.
Particlc"':in-Ccll Hethods
An alternative to the direct finite-difference solution of Equations
(2) ,is the so-called particle-in-cell (PIC) techniqUe. The distinguishing
feature of the PIC technique is that the continuous concentr.ation field
is:treatcd as a collection of mass points, each representing a given
amount of pollutant and ea~~ located at the center of mass of the
volut:\e of material it represents. . The m3.SS points, or particles, are
InOved 'by advection and diffusion. It is convenient, but not necessary,'
to: have each of ,the particles of a given contaminant: represent the
same mass of material. The application of the PIC technique in
hyp.iodynamic calculations is discussed by Harlo", (196<1). \'le consider
here the use of the PIC technique in the n~~erical solution of .
Eqqations (2).
. .
Given an initial, continuous concentration field in the airshed,
we:replace this field by discrete particles of pollutant i, each
rep~esenting a fixed mass. The particles are located within a three-
dtmensional fixed grid according to the t:\ass distribution 'of material.
Thus, each particle has a given set of coordinates. Con5id~r now a
sing::!-e time step tit in the nurr.crical solutidrl of the continuity equations
using. the PIC lI".cthod. \'le write Equations (2) in the form
a~i' - -
~ + V.~ici c R1 + 51
(5)
-
where the effective velocity U. is defined by
..1. '
~
U.i ~ V - - Vc.
Ci 1
(6)
Y:-c:: (\;,;,W"] and
K =
[KX ~KZ]
In the co~putational procedure,
eaCh'p~rtic1e of ~pecies i at location (x,y,z) is moved a distance
IYiAt~ in the direction of~. In addition, new particles are e~itted
during.the period t to t + 6t from the sources located in each cell,
the..number of .particles emitted being determined by, the product of the
source strength and ~~e time step. These neW particles are also advected
wffh'veiocity y.. After the convective step the average concentration of
each' sp~cies in~a cell is calculated, this concentration being equal
to:the total mass of particles occupying the cell, divided by the cell
volume. The cell contents are then allowed to react, resulting in a
conc~ntration ch~nge, RiAt. Finall~, the p~r~icles.are reconstituted,
wifh the change ~n mass due to chem~ca1 react~on be~ng reflected in
chang~s in the number of particles of each species~ The same procedure
ls:repeated for succeeding ti~e steps. The' PIC te~hniCIUe has been
adap~ed to air pollution modeling by Sk1arew ,~1970a, 1~70b).
~e PIC technique has the following advantages:
.
Artificial diffusion due to truncation errors in the
advection terms in Equations (2) is eliminated since
these terms are not approximated by finite-difference
representations.
11
-------
.
There are no stability restrictions on 6t (although 6t should
. -
be small enough so that the value of 21 is representative
of the movement of fluid particles). ' -
.
Particles can be tagged as to their place of origin, thus
,making it possible to identify the sources of contaminants
observed at any location.
and weaknesses:
3.
.
Computer storage requirements can become excessive, as
the coordinates of a large number of particles must be
kept in memory.
.
If it is assu~ed that each particle of a given con-
taminant represents the same mass of material, then
every cell will have a residue th~t cannot be assigned
to a particle. On the average, this residual material
will equal one-half of a particle mass. For example,
for the simple case in which there are four particles
in every cell, then, on the average, 11\ of the total
material toTill not be included in particles.
Well-Mixed Cell Hodel
A conceptually simple approach is based on the representation
of the airshed by a three-dimensional network of well-mixed vf!Ml'!lf:
(see Seinfeld (1970». As before, we assume that the airshed has
been divided into an array of L cells. Instead of using the array
simply as a tool in the finite-difference solution of the continuity
equations, let us now assume that each of these cells is actual~y
a well-mixed reactor with inflows and outflows bet...-een adj.acent cells.
If we neglect diffusive transport across the boundaries of the cells
and consider only convective transport among cells, a mass balance
on species i in cell k is given by
-. L
dCik dVk ~
Vk ""'"d't'"'= - cik -cit + LJ QjkC1j
:)=0
whe'X'e
- Clk
L
L qk' + Sik +
j=O J
(7)
Ri
-------
Normally, dVk/dt is set equal to A,.. (ill\/dt) ,
of the base ,'of a cell having vertical sides
the top of the cell. In effect, the cell is
walls and a movable lid.
where 1Jc is the area
and Hk is the height of
a box with permeable
If we divide the airshed into L cells and consider p species,
Lp' ordinary differential equations of the form of Equations (7)
constitute the airshed model. As might be expected, this model bears
a direct relation to the partial differential equations of conservation
of mass. If we allow the cell size to become small, it can be shown
that Equations (7) are the same as the first-order spatial finite
difference representation of Equations (2) in which turbulent diffusive
transport is neglected, namely
aCi - aCi
1ft+uax-
- aCi
+v-
ay
~ Ri + Si
.J
Therefore, the well-mixed cell model can also be described as the
result of the finite difference approximation of the spatial derivations
of (2), that is, of the conservation equations in which diffusion has
been negleated.
The advantages of the well-mixed cell approach are as follows:
. The geometries of cell bases (which nay be both irregular
and variable from cell to cell) can be drawn to conform
with topographic features.
. Variations in inversion height with time are easily
incorporated in the model.
.
The model is conceptually easy to understand and implement
(only ordinary differential equations are involved).
Its disadvantages, however, are considerable.
. Due to the large variations that can occur in the
magnitudes of the flows, q. , Equations (7) are often
"stiff", thus requiring im~iicit integration techniques
, to insure stability in their solution.. If an implicit
technique is used, the inversion of an L~ x lp matrix is
necessary at each time step. Since computing the inverse
of large matrices can be very time-consuming, this require-
ment places a definite restriction of the size of L. For
example, if we were to consider 25 cells for our system
of four coupled equations, the repeated inversion of a
100 x 100 matrix would be required.
*See Appendix B, Section IV, for a discussion of the solution of "stiff"
systems of ordinary differential equations.
13
-------
.
Diffusive transport is neglected. This is a distinct
drawback in the case of vertical diffusion.
The mathematical formation of the well-mixed cell model,
Equations (7), is such that the expected accuracy of the
solution is equivalent to that expected from the application
of only a first order finite difference method to the -
solution of a corresponding model based on the partial
differential equations, Equations (2).
c.
An Assessment
Of the four models described that are based on the equations
of conservation of mass, all are at an initial stage of development.
It is thus premature to evaluate them. As has been pointed out,
the major distinction to be drawn among the models is that which
exists between the moving cell and fixed coordinate approaches.
Moving cell models have their most significa~t application in exploring
phenomena of a restricted scope in the spatial domain, such as examining
the possible sources of pollutants that are concentrated in a particular
region at a given time. Thus, while these models are not intended as
full airshed models, they have the advantage, when compared to fixed
coordinate approaches, of computational simplicity.
In contrast, the fixed coordinate approach is readily applicable
to the prediction of pollutant concentrations at all points in an
airshed at any time. These predictions can serve as the basis for
the preparation of contour plots of estimated concentration levels.
However, the costs that must be incurred to obtain these results are
high, due to the substantial computing time and storage requirements
associated with this approach. Huch less can be said, however, in
comparing the PIC and finite difference approaches to the solution
of Equations (2). Both have inherent sources of inaccuracy (the
discretization of the concentration field in creating a finite number
of particles in the PIC approach, the error of truncation and
resulting "artificial" diffusion in finite difference approaches)
that can be reduced only at a cost of substantially increasing computing
time and computer storage requirements (the creation of a larger number
of paiticles, each of a reduced mass, in the PIC approac~and the use
of a finer spatial grid and a higher order finite difference method in
the finite difference approach). The only means for assessing the
relative advantages of these approaches, in terms of accuracy and costs
incurred in their application, is through direct comparison. Models
are only now reaching a state of developnent at which such comparative
studies are feasible. As of this writing, however, there is no means
for assessing the relative merits of these airshed models.
The modeling approach that we have pursued in this study has been
the development of a comprehensive airshed model based on the finite
difference solution of the equations of conservation of mass. In the
next section, we present the details of this model aevelopment effort.
14
-------
II.
THE MODEL DEVELOPED IN THIS STUDY
The airshed simulation model we have developed is based on the
fOllowing formulation of the equations of conservation of mass*:
aCi aCi
~ +u-
lit ax
ac. aCi a ( aCi)
+v-2:.+ K +R( )+8
ay w a;- = a; z a;- i cl' c2'...' cp i
i = l,2,...,p
(8)
for
~~x~~
Ys ~ Y ; YN
h(x,y) ~ z ~H(y.,y,t)
t ;:. t
- 0
where
x,y = horizontal coordinates
z = vertical coordinate
u,v,w = three components of average
wind velocity vector
ci = time-averaged concentration of species
K = turbulent eddy diffusivity
z
8i = rate of emission of species i from
elevated sources
i
Ri .. rate of production of species
through chemical reaction
xw' xE' YS'YN= west, east, south, and north boundaries
i
h(x,y) = terrain elevation
H(x,y,t) = elevation of the inversion base above sea level
The initial and boundary conditions are:
initial
Ci(x,y,z,to) = fi(x,y,z)
boundary
(1)
aCi
--,.K - = Qi(x,y,t)
z az
at
z .. h(x,y)
* OVerbars (-) indicating averaged quantities will be omitted henceforth. .
All velocities and concentrations, however, oontinue to be time averaged
quanti ties.
15
-------
boundary
(2)
if W ~ 0, then
aCi
-K -"'0
z az
aCi
if W < 0, then W gi(x,y,z,t) ... W\ci - Kz az-
at z co H(x,y,t)
aH aH aH
where W... w - u ax - v 'iY - 'it
(3)
ci ... gi(x,y,z,t)
at x :... "w
Y. Ys
(or ~)
(or YN)
where
x and yare at boundaries through which the
prevailing winds enter.
and where
2i (x,y,t) = surface flux of species
fi(x,y,z) ... initial concentration distribution of
species i
i
gi(x,y,z,t) ... function expressing the concentration of
, species i on the boundary at points of
inflow.
In addition to the assumptions made in deriving Equations (2) in Section I,
several features of the formulation should be notedl .
. Horizontal turbulent diffusion is neglected.
. Due to changes in terrain elevations with x and y, the vertic~l
component of the wind will not, in general, be zero at the qround.
. The boundary condition 'at the inversion base (z . H) is the usual
flux condition if the transformed vertical velocity component W is
upward. If W is down into the airshed at z ... H, the concentration
of inflowing material is specified.
The most notable feature of the equations, however, is that they are coupled,
since they share a common argument through the tems Ri (cl' c2'...' c ).
We are thus confronted with the problems of solving p coupled, nonlfnear
partial differential equations in four dimensional space (x,y,z,t). '
up to this point we have described air shed models and modeling in the
abstract. When we plan to actually underta.1te solution of the equations,
however, we must do so fer a particular region. Source emissions rates
and their distribution in space and time and met~orological variables,
such as wind speed and direction and mixing depth, are inputs to the model..
In order to test (or validate) the model, it is necessary to include as inputs
the source distribution and meteorology appropriate for the area during the time
period in question, and to compare the pollutant concentrations predicted with
concentrations actually measUred in the area during that period.
16
-------
The Los Angeles Basin was the obvious choice for the prototype study,
largely because of the availability of a relatively rich data base. A
network of nearly three dozen wind speed and direction sensors and twelve
air quality monitoring stations dot the Basin. In addition, during the
summer of 1969, the Scott Research Laboratories (1970) c~rried out an
extensive data gathering program in Los Angeles. Particularly valuable.
were the vertical temperature profile data they gathered over three sites
in the Basin, thereby permitting much more accurate specification of the
. depth of the mixing layer than is norr.1ally possible. Finally, due to the
severity and persistence of the smog which plagues the region, Los Angeles is
the most appropriate area in which to apply such a model.
In this study, we applied Equations (8) to the prediction of pollutant
concentrations over a fifty mile Square area that includes virtually all
centers of population in the Los Angeles Basin. This region, shown in
Figure 1, was divided into a grid of 625 ~ mile x 2 ~ile squares. Source
emissions and meteorological variables are 'distributed according to this
grid, i.e., two miles is the resolution of the model, or the spatial
dimension over which:al1 quantities are averaged. Furthermore, for reasons
to be discussed, the grid actually used in the solution of Equations (8)
is a three-dimensional array of ten layers of cells occupying the space
between the ground and the base of the inversion and lying directly over
the larea shown in Figure 1. Thus, each cell has abase two miles square and
a height of (H - h)/lO. The center of each cell, or node, is the point to
which values of all variables are assigned or referenced. Unfortunately,
due to variations in both H and h with x and y and, in the case
of H, with t, the three-dimensional modeling region has an irregular "roof"
and "floor". To eliminate these irregularities, which har.per the solution
of, the equations, we performed the following change of variables
X
(::~-~
TI c:
YN - Y5
y
z - h(x,y)
P c: ,
H(x,y,t) - h(x,y)
thereby transforming Equations (8) to Equations (D-4), given in Appendix D.
The entire airshed is thus transformed into a cube, one unit on a side,
in the (t,TI,p) space. The actual model is then based on the sQlution
of Equations (D-4) over a dimensionless region comprised of 25 x 25 x 10
rectangular para1lelOpipeds.
The objective of this study,. then, is to solve Equations (8), or
'equivalently, the transformed Equations (D-4), over a particular period
of time, comparing the predicted concentrations with those measured at
local air quality monitoring stations. A number of factors enter into
the accompl~shment of such a task:
17
-------
. , l-T:tT~'-s.- ,J~-r?_t o~-...!£ ).Lr'2_-~.'!,!..t,-.-!r. .J...6;...!.'!...!.!..;..L2.!.. !L.J-I-J~![~-~"
~~ fTtt "i;F;;\---,---_~~~+i~~;;;~l:::~-Ji: ~:trtL ;:
23 :.~, FEIJlIr.!ID~ i I! i! . ,t:CUN,TAIN~ I "'.1 0; ! 23
2 : 'YAt~l- -~--T--I' ---:-,-r-o", ---"--'____,_0: -t--j7--r
1 -~lI.J-- ~._1-_cir.J.ffJ:tL. -_..L...-_~._--- ,....i.--- I -~ --.:.L..L---!-.-1- 2.'2.
1 I " ,I / i Par:k :' Pasadena.. I' I. i I . I ., .
I' I' I. ')( " ' : i ..
2D si.J..rrA ~1)~uiA--L- ,---L-. j - .;.. - ! -~''""-~----'' _.~_._~.__~_.~~a_~_L.L_~ 20
,q i ; I 'IOUIITAI 5 j ,I : I : :. Iii i ',!;:,:!I
~ I! ~ ,.,. 'I I " 1
IS i i !' I -',' --!~ii~I';; ~dr-'f-~,:--:-- _1--1; J - ~rT-:-i 18
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:-=~ ~.--.i..- -t- ~_! -:2-.~os Ang~~s .!! ._- " L{-:"-r--+- '7
I' ; ; , ,Sa ta I : " ,!:' i: I. ! '
. . . , ! X Mo iea> :. '.:', I # !:.
IS !! "i::!: ~ iu;; I!::; IS"
t--L-- ' I --~--I...- -'---~-- ."~ ___LPIlE!iIt.-' ~
, i I ii' . I I I,' I t' H-' j
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:; I:: 'I i . ,; I I ", :
'.: ,. I I . I .
I. °t-- ;0'''0_-1"- -1°-r--!1 :--r'-llo---t--j- _"0,_. ---- --T--T--
'0 1 ; ;: I I ii' i i . ; i ~ I Ii: i
: '. : I t- --_1._[ -- ;_1-__':-0-'-- _o'~'_"':'T-sn anA---.-L
, I . , .. I" " ..,,,. I
, , . . --.1.-- --i-.._~-- - .-1_~. _1_---1- -'-li--L-'T-~ _~_o~_L-L_~ '
II : I .: . I ! I : ,',! . I I I 0 I 0
" ," ,I PALOS VERQ~S ',long,: : I t I I ~
7 -"~-~--~-:'- -; --rPEl;i;;SUL~- ~;:7.'-~eac~- --'r-;-~I ..- -r-t 7
. --1. ! :; t ~-~--~ ~~ : -.JI'--~- --,--t-l 1-- - -1--_,1 .- "
.. " ! 0 " i. I : 1 I r.: i '~I S~"ta ~nl '
S i ;. I I J 1 ! ;' '", I L j " , j S
. . ~ :-~==r:. ~ +R-. -H+ -I - j -- J- -~~l= -- ~ 4
.; : t-~ +II-~ +~+~-~H,F +~.~t - ~.
- -6-_~-
., 2. ) 0 t,. 5 "7 . 0 II 12. '3 ,,, ., S" 1'7 . & .. 'I lOLl 2. 2 1J 2.4- 2S
lit
I)
11
11
1/
10
Figure 1.
The MOdeling Region
18
-------
.
The development of a kinetic mechanism capable of describing
the rates of chemical reactions occurring in the atmosphere,
and the adaptation of this mechanism for inclusion in the airshed
simulation model.
.
The selection and adaptation of a finite difference technique
suitable for use in the numerical integration of ~quations (D-4),
the development of a computer program embodying the method, and
subsequent testing of the method to determine its stability
and accuracy characteristics.
.
The development of a contaminant emissions inventory for the
LOS Angeles Basin.
.
The development of a means for treating the various meteorological
parameters, including the winds aloft.
Upon selection of particular validation daYs, in our case 29 and 30 September
1969:
.
Maps must be prepared expressing toe spatial and temporal distribu-
tions of surface wind speed and direction and the height of the
inversion base.
.
. Air quality data must be gathered.
Validation of the model is undertaken upon completion of these various efforts
And is comprised of three parts, to be carried out in sequence. .
(1) - Validation for carbon monoxide. The main purpose of this part is
to provide a test of the meteorological facets of the model.
If the model can be validated for CO, then confidence may be
placed in the treatment of the winds and the inversion, and
validation of the photochemistry may proceed. Validation for CO
also constitutes a test of portions of the source emissions
inventory and the numerical integration technique.
(2)
Sensitivity studies. Exploration of the effects on predicted
CO concentrations of changes in meteorological variables, such
as winds, inversion height, and diffusivities. Also, study of
the effects of varying the order of the numerical technique, the
size of the grid system (for example, one mile instead of two
mile squares), the number of horizontal strata of cells, and the
size of the integration time step.
(3)
Upon successful completion of (1) and (2), and upon incorporating
modifications suggested by the results of the studies, carry out
validation runs and. sensitivity studies for hydrocarbons, nitrogen
oxides, and ozone.
Clearly, the size and scope of such an undertaking is great. Since
the inception of the project last July, we have fully completed the
developmental effort, but we have undertaken only a small portion of the
19
-------
",l.
validation segment. In particular, we have carried out validation studies
for CO for 29 September 1969 and have explored a few questions concerning
sensitivity of the model. In section III, we report on our accomplis~ents
to date in validation of the model. In the remainder of this section,
we outline briefly what has been achieved in model development. The details
of these various efforts are reported in S1-X accompanying appendices.
.
We have completed a comprehensive emissions inventory for the
Los Angeles Basin. Particular emphasis was placed on the
spatial and temporal distribution of emissions from motor
vehicles, as vehicular emissions account for a preponderance
of carbon monoxide, hydrocarbons, and nitrogen oxides in the
Los Angeles atmosphere. Attention was also given to those
sources which, while responsible for only a small proportion
of emissions on: an area-wide basis, contribute heavily to
pollutant concentration levels in their own locale--airports,
power plants,. and refineries. See Appendix A, "Contaminant
Emissions in the Los Angeles Basin--Their Sources, Rates, and
Distribution", for a complete description of this effort.
.
We have incorporated into the airshed model a new kinetic
mechanism developed by Thomas A. Hecht and John H. Seinfeld
of the California Institute of Technology. The results of
validation studies demonstrate that this model is capabl~
of predicting with acceptable accuracy the concentration/time
behavior of smog chamber experiments for propylene, isobutylene,
n-butane, and a mixture of propylene and n-butane at initial
NO to hydrocarbon ratios of 1/3 to 1. The mechanism has also
be~n shown to simulate accurately the effect on photo-oxidation
rates of variations in CO cpncentrations, as well as the
inhibitory effect of high initial concentrations of nitric
oxide on the maximum concentration of ozone obtained. A
full discussion of the mechanism and the validation
results is given in Appendix B, "A Kinetic Hechanism for
Atmospheric Photochemical Reactions."
.
We have prepared hourly maps for each of the validation days
that display spatial and temporal variations in surface wind
speed and direction and in the height of the inversion base.
We have also explored several approaches to the estimation
of the wind field aloft, one :of which appears to be a useful
method for the automatic generation of these winds. We have
investigated the use of computer graphics in the preparation
and conversion to digital form of wind maps, and have attempted
to develop a simple model to describe variations in mixing
depth with time and location. A complete description of these
efforts is presented in Appendix C, "The Treabnent of Meteorological
Variables. "
.
We have adapted the method of fractional steps for use in the
finite difference solution of the equations of conservation of
mass. Details of the method, and an evaluation of its stability
and accuracy characteristics, are given in Appendix D, "Numerical,
Integration of the Continuity Equations."
20
-------
.
We have gathered together all the available air quality data
for the validation days 29 and 30 September 1969. These data
are presented in Appendix E, "Air Quality Data Used in Model
Validation. "
.
We have prepared a computer program to carry out the many
calculations required in an airshed simulation. A general
discussion of the program is presented in Appendix F, "Descrip-
tion of the Computer Program.."
21
-------
III. VALIDATION OF THE HODEL
The major validation result obtained as of this writing is the
prediction of the distribution of carbon ~onoxide concentrations over the
Los Angeles Basin for the period 5 AU to 5 PH PST (6 AH to 6 PH PDT) on
29 September 1969. This validation run constituted a pivotal test of the
treatment of meteorological variables, as well as of the accuracy of the
emissions inventory and the suitability of the numerical method. (Actually,
the integration of the coupl,ed equations, with photochemical reaction terms
included, is a r.\Uch more severe test of the numerical technique.) The
conditions under which the run was made are as follows:
.
Meteorology - Hourly naps of wind speed, wind direction, and
mixing depth were prepared, as described (and examples of which
,are shown) in Appendix C, Sections I and II. Wind variables
and inversion height were maintaincd constant throughout each
hourly interval, co~encing at the half hour. ~fuen the inversion
base was raised, the concentration of carbon monoxide in the air
newly included under the inversion was taken to be equal to the
CO concentration at the inversion ,base iPst prior to its
displacement upward. Vertical turbulent diffusivity was treated
as shmln in Appendix C, Section IV. The second method for
constructing the wind field aloft, as described in Appendix C,
Section III (p. 40, paragraph 2), was used.
Emissions - Carbon monoxide emissions fro~ automobiles and aircraft
(both on the ground and in flight) were included, as described
in Appendix A. One modification, not discussed in Appendix A,
was made in the treabment of vehicle emissions. To account for
the higher emissions rates due to cold starts in the morning, we
assumed that
r. grams ~
QCO lvehicle mileJ
/63.9 (4:~t)
63.9
5
-------
instantaneous values of concentration. Thus, the average of
the 4 AH to 5 AN and 5 AH to 6 M.I hourly averages was used
to estimate the instantaneous values at 5 MI.
The validation run \-las carried out on an IBI1 360-67 computer. 'lVenty-nine
~inutes of computing time were required to simulate twelve hours, a ratio
of 1:24. contemplated modifications, as noted in Section- IV, are expected
to substantially reduce this ratio.
The results of the validation effort are displayed in Figures 4 through
10 and twelve computer printouts.
.
Figure 4. A summary of comparisons between predicted and.
measured concentrations at eleven sites scattered throughout
the aasin. (The locations of the monitoring stations, along
with their proximity to najor emissions sources, are shown
in Figure 2.) Both the predicted and the measured concentrations
.represent hourly averages beginning at the hour given.*
Since a two-minute ti~e step was used, each reported hourly
prediction is the average of thirty calculated values.
Figures 5 through 10. Plots of predicted and measured
concentrations vs. time of day for each of the eleven
moni toring sta tions. These plots convey the same infor-
mation shown in Figure 4.**
.
.
Computer Printouts. Twelve ~aps of predicted average hourly
concentrations throughout the day (except for the maps
representing the time periods 8~1 to 8:20 AM and
8: 20 1\1-1 to 9 A1-1). The indexing syster:t (ro\., and column
numbers) shown on the printouts corresponds exactly to that
used in Figures 1 and 2; thus, a predicted value of co
concentration can be located geographically, and its
proximity to freeways, airport~, and monitoring stations
noted, by reference to these fi~ures.
It is perhaps wise to precede the discussion of these results with a few
comments concerning ~hat should be expected in a co~parison of predicted
and measured carbon monoxide concentrations.
In any interpretation of results, it is important to note that a
measurement, if presumed accurate, is representative of the CO concentration
in only a: SI:".all portion of the 2 mile x 2 mile grid square for which the
concentration is predicted. The prediction represents the average concen-
tration over the entire grid square; higher concentrations, as well as lO\fer
* All predicted values are reported as truncated integers (e.g., an average
concentration of 5.85 is reported as 5, and not 6), all aeasured values as
rounded integers. Rounding and truncation to integers adds a possible
discrepancy of up to 1.5 ppm to that which already exists between predicted
and measured values. .
**Note that in Figures 5 through 10 the lines connecting both experimental
and predicted values of concentration are merely s~olic links. They do
Dot represent interpolated values. Links are not drawn through experimental
points of questionable accuracy, but these points a~e indicated on the maps.
Furthermore, links are not drawn for periods in which experimental data are
unavailable, as the resulting plots may be visually misleading.
23
-------
concentrations, very likely exist in portions of the square. Thus,
recognizing that line sources are not well represented by a grid system
and that sensors are generally located near freeways or arterials (see
Appendix E, Table E-2), predicted and measured values may be expected
to aiffer. .
Returning now to the results, and with the preceding comments in mind,
it may be observed from Figures 5 through 10 that reasonable agreement has
been achieved at a majority of the monitoring stations over the course of the
'twelve hour validation period. At certain stations, however, comparisons
are poor--in so~e cases during the early hours, in others, over a period of
several hours.. These discrepancies may be categorized into two classes,
each attributable to an identifiable deficiency in the model, in its for-
mulation,'or in the ~ethod of solution. Two of the deficiencies are
correctable, and one is inherent to the model.
, . Comparisons ~ade at the Azusa (AZU) and El Monte (EU~) stations,
both located in the San Gabriel Valley, are poor during the
II10rning hours. This appears to be attributable to the means
by which temporal variations in the height of the inversion base
are treated in the ~odel. The mixed layer is very shallow over
the San Gabriel Valley early in the morning, increasing rapidly
in depth through the morning hours. Recall, however, that the
depth of the layer is altered only once an hour in the
calculation. t'lhen the base of the inversion is displaced
upward, the value of concentration at the base just prior to
its vertical displacement is assigned to the entire volume of
air newly included under the displaced inversion. While this
hourly displac~~ent occurs OVer all grid squares in the Basin,
its effect on the calculation is most pronounced over the
San Gabriel Valley, where the estimated mixing depth during
the morning hours varies as £ollo\.,s:
Time (AH PST) Mixinq CepUt (feet)
0500 - 0530 60
0530 - 0630 60
0630 - 0730 ," . 150
0730 - 0830 200
0830 - 0930 400
0930 - 1030 650
, Since the inversion is shallow, high concentrations build up
rapidlY at the top of the mixed layer, and when the inversion
bas~ is displaced upward, the equivalent of a large elevated
source of CO is introduced. We believe that by altering the height,
. The,Pomona'~onitoring station lies one mile east of the eastern boundary
of the modeling region. The concentration calculated at the closest 9rid
square is compared with that measured at Po~ona.
24
-------
of the inversion base at each time step in the integration,
(i.e., every two minutes), this effect can be alleviated.*
. Predictions of peak CO concentrations, bebleen 7 Af.l and 9 AH,
are typically too low. Extreme examples occur at Lennox (LENX), West
~s Angeles (WEST), and \'lhittier (\-:HTR); others. occur at Cor.unerce
(VER) and Reseda (RESD). Since all monitoring sites, except
for the station at Azusa, are focated near major local sources,
particularly freew'ays and arterials, the stations are probably
"seeing" local high concentrations. The rodel, having a two-mile
horizontal spatial resolution, will be incapable of predictihg
these local peak concentrations. This thesis may be explored
further by applying the model to a smaller region, using a
finer horizontal resolution.
. Perhaps equally significant is the effect on the accuracy of
prediction of assuming that automotive emissions can be
represented by a constant factor, Qc. As we discussed in
Appendix A (see pages A-I to A-4, A-£9 and A-26), the representa-
tiveness of the vehicular emissions factors depends on the extent
to which the driving cycle upon which they are based actually
simulat~s average vehicular emissions. Even if the cycle is
adjudged to be representative, cognizance must be given to the
fact that carbon monoxide emissions rates varY with percentage
of time in an individual operating mode. In particular,
increased contaminant emissions rates result from the increased
frequency of acceleration, deceleration, and idle at the low
average speeds that occur during periods of congestion. Thus,
the CO emissions rate, taken to be constant in the validation
run, does not properly represent the norning rush period. This
deficiency in the treatnent of emissions ~ay be alleviated by
assuming that Ceo has a higher value durin9 periods of congestion
than during periods of normal traffic.
Discrepancies between prediction and measurement can be only partially
rectified by correcting deficiencies in the model. ~he accuracy of prediction
is dependent upon the quality and quantity of available meteorological and
emissions data, as well as upon the "goodness" of .the nodel. Furthermore,
the magnitude of the discrepancies in the results depend, not only on the
accUracy of the model's predictions, but also upon the accuracy of the
air quality data. Thus, it would be inappropriate to reflect further on the
results without commenting on the accuracy of the data.
The inversion maps, as was discussed in Appendix C, . are based on temporal
and spatial interpolation of vertical temperature profiles taken at about.
8 AM and I PM at three points located between Los Angeles International Airport
and El Honte. All values outside these ranges are extrapolated, and the
accuracy of these extrapolated values .is questionable. (The accuracy
of the temperature profiles, themselves, is questionable, as altimeter readings
sometimes registered 25 to 75 feet 'below ground eleva~ion.) In addition,
sensitivity studies have indicated that modest changes in the depth of
. Since mixing depths over the San Fernando Valley are about the same as
those over the San Gabriel Valley during the morning hours, similar discrepancies
might be expected in the former location. These discrepancies are not observed,
however due to the existence of a diverging surface wind field in the San
Fernand~ Valley. This divergence necessitates the supply of air from above, .
thereby reducing the concentrations at the base of the inversion and thus dimin-
ishing the magnitude of the elevated artificial source.
25
I
~ .
.
;
,
,
I
-------
the mixed layer have a significant effect on predicted ground concentrations.
It is therefore apparent that the number of sites at which vertical temperature
soundings were made, and the number of soundings carried out daily at each
site, are inadequate. In addition, the need for extrapolation in the early
morning hours, and out to the borders of the modeling area (including the
San Fernando Valley), should be minimized. .
While the number of wind monitoring stations in the Basin is sufficient
to give adequate definition to the surface wind field, the accuracy of the
readings is often questionable. A substantial number of wind speed and
direction measurements, taken at identical or adjacent sites at the same
time, differ markedly. At El Honte, for example, Scott and LACAPCD made
w~rld measurements at virtually the sarne site; their reported readings typically
differ by 30% in speed and 30° to 45° in direction, and, on occasion, by
200% and 180°, respectively. Measurements made simultaneously at. the Encino,
Van Nuys, and Reseda stations in the San Fernando Valley often varied by
as much as l80~, making the construction of wind ~ps in that area a
dubious undertaking. ,-
We turn at this point to the computer printouts, representations of
predicted values of average hourly concentrations of carbon monoxide over
the entire 50 mile x 50 mile grid. (Note that the period 8 AN to 9 AM is
represented by two maps--8:00-8:20 and 8:20 - 9:00.) The reader should
refer to Figures 1 and 2 to establish the correspondence betweeu predicted
concentrations and geography. In general, the predicted values shown on
the printouts appear to give a reasonable representation of temporal
variations in the concentration field. The morning buildup of carbon
monoxide is clearly demonstrated, followed by a mid-day cleansing of the
Basin as the winds blow the pollutants northward and out of the modeling
area. Low afternoon concentrations then generally prevail. .
Large concentration gradients and apparently random. fluctuations
may be noted at certain locations on virtually all the maps. When these
occur in the vicinity of a monitoring station, an average value of
concentration, weighted according to distance from the four closest node
points, is reported in Figure 4 (and thus in Figures 5 to 10). For example,
ELM, located in the northwest quadrant of ground square (18, 18), has a
predicted average hourly CO concentration of 19 ppm between 9 AM and 10 AM PST.
The average hourly concentrations in the local area, as may be seen from the
computer printout, and as shown here, .
14 16
X
ELM
17 21
vary greatly. Thus, the predicted valu~ of concentration in areas of large
gradients has a relatively large uncertainty associated with it. This should
be kept in mind when evaluat~ng the results of Figures 5 to 10.
Two problems arise in the northwestern portion of the Basin, which
includes the San Fernando Valley, that become apparent upon viewing these
maps. The first is that the difficulties encounte~ed in representing the
26
-------
wind field in this area manifest themselves in peculiar ways. Very often
large vertical components of the wind are required in order to satisfy.
continuity, and, as these appear to be distributed somewhat randornl~
throughout the Valley, the resulting concentration field is more a series
of fluctuations than the smooth field characteristic of .the rest of the
modeling region. Second, anomalies sometimes occur in regions in which
horizontal spatial gradients in emissions rates are steep. For example,
row 21 in the northwest includes a large emissions source, the Ventura
Freeway, while row 20 lies along the Santa Y.onica Mountains, a region in
which virtually no emissions occur. The finite difference method, in
approximating the large concentration gradients that exist in this region,
often predicts depressed and, on occasion, negative values of concentration.
The use of higher order approximations may be needed to eliminate this
probleI:1.
To summarize, then, we believe that reasonable agree~ent has been
achieved at a majority of monitoring stations. ~ihere discrepancies between
prediction and measurement are great, assignable causes can be identified.
Some are correctable, others are inherent in the nature of the approach and
in the spatial resolution of the model. Finally, inaccuracies in source
emissions and meteorological data and in their representation contribute
significantly to the discrepancies that are observed.
The remaining validation efforts of interest can be described very
briefly. We carried out a validation run for 30 September 1969 similar
to that of 29 September--prediction of carbon ~onoxide concentrations from
5 Az.1 to 1 PH. Comparisons beb/een precU.ction and measurement "Tere less
satisfactory than those obtained for 29 September. We believe that the
relatively large discrepancies observed are attributable to poor definition
of the wind field in the morning. Wind speeds were consistently I to'2
miles per hour over much of the Basin from 5 AM to 8 N1,.a speed that is
below the reported threshold of the mecsurement apparatus. We plan to
. examine the actual meteorological data in detail before proceeding further
with validation runs on the 30th. (It should be noted, however, that the
high concentrations experienced on that day make it most interesting for
study.) We have not yet undertaken validation of the full photochemical
model (including hydrocarbons, nitrogen oxides, and ozone) for either of
the validation days as of this writing, although tests of the nunerical
method, as applied to the coupled ~ations, have been carried out.
A number of sensitivity runs were perfo~~d during the validation
process, and the following observations were made. Modest variations in
specification of the wind field and the inversion have significant effects
on the magnitude and distribution of predicted concentrations. Sensitivity
'of the calculation to changes in the vertical diffusivity profile have
not been investigated; however, .vertical gradients are gener~lly small, and
predictions should not be greatly influenced by ~Ddest changes in the profile.
Recent tests of the finite difference method, comparing the accuracy of
the second and fourth order approximations in the horizontal when a second
order approximation is applied in the vertical, indicate that only minor
differences in predicted values result when' the higher order method is
used. However, for the validation run reported here, large concentration
9radients are present and the two approximations may give somewhat different
results in the lnunediate locale of these gradients. Finally, variations in
27
-------
Qco as a function of "degree of congestion" has not been investigated.
However, it is expected that inclusion of a variable emissions rate will
result in more realistic predictions of morning CO peaks.
28
-------
, ,:1 ~-.£.r~..€!-,-1r-1-.8-T!T!.~-'LT!~-r'3-r.!.~r!:>" ..!.!...'_t, ;8...!..9 : :, l''-r'Yf'" J4I~lS'
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Figure 2. Locations of r-tonitoring Stations Relative
to Major Contaminant Sources in the Los Angeles Basin
" - freeways
. - oil retineries
. - power plants
. airports
o - contaminant monitoring stations
29
-------
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for 29 September 1969, 500 PST (in ppm)
30
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Figure 4.
Summary of Validation Results for Carbon Monoxide for 29 September 1969 (in ppm)*
~
..
1
S~ation/Ti.me 1
(PST) 5.- 6 6 - 7 7 - 8 8 - 9 9 - 10 10 - 11 i 11 - 12 12 - 13 13 - 14 14 - 15 15 - 16 16 - 17
:
1 CAP 3'(5) 7 (12) 17 (17) 18 (20) - (19) - (13) 16 (7)' 3 (4) 3 (4) 2 (4) 6 (5) 6 (6)
60 AZU 10 (9) 10 (11) 10 (13) 11 (13) 10 (14) 8 (16) 6 (15) 7 (3) 9 (6) 6 (4) 6 (4) 4 (5)
69 BURK 13 ( 8) 15 (11) 18 ( 14) 17 (14) 9 (13) 11 ( 12) 10 (9) 11 (9) 7 (4) 7 (3) 5 (3) 5 (4)
71 WEST 5 (6~ 9 (9) 17 ( 10) 17 (10) 8 (8) - (8) 5 (7) 4 (5) 4 (4) 4 (4)' 4 (5) 5 (5)
72 LONB 7 (4) 9 (5) 13 (7) 11 (7) 9 (4) 6 (4) 6 (4) 6 (4) 5 (4) 5 (4) 5 (4) 5 (4)
74 RESD 10 (9) 12 (10) 16 (12) 11 (10) 8 (10) 6 (11) 4 (8) 5 (4) 3 (3) 3 (4) 5 (4) 5 (4)
I
75 POMA 7 (6) 8 (6) 9 (5) 9 (5) - (5) 6 (5) 5 (8) 4 (9) 5 (7) 6 (6) '6 (4) 6 (3)
76 LENX 6 (5) 15 (5) 9 (6) 5 (5) 5 (4) 6 (4) - (4) 3 (3) 3 (3) 4 (3) 6 (3) 6 (3)
80 WHTR - (6) 11 (5 ) 14 ( 7) 11 (11) 11 (13) 13 ( 13) - (10) ,2 (2) 1 (4) 1 '(4) 1 (4) 1 (4)
(SC) ELM - (8) .. (11) - (16) 8 (17) 6 (19) 6 (14) 9 (8) 5 (6) 3 (3) 2 (2) 2 (3) - (3)
- .
(SC) VER 9 (8) 12 (8) 17 (11) 15 (13) 15 ( 11) 9 (8) 6 (7) 4 (5) 3 (5) 3 (4) 4 (4) 3 (5)
. .
*The left-hand fiqure in each square is the measured valuel the figure in parenthesis is the predicted value.
All values are in parts per million of carbon monoxide, averaged over a period of one hour.
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Figure 5. Ter:1pora1 Variations in Predicted and r:easured Carbon r.lonoxide
: Concentrations for 29 Septer.mer 1969: Downto\'tn Los J\nseles
32
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'Figure 6. Temporal Variations in Predicted and Measured Carbon Monoxide
Concentrations for 29 September 19€9: West Los Angeles and Lennox
33
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Figure 7.
Temporal Variations in Predicted and Measured Carbon Monoxide'
Concentrations for 29 September 1969: Azusa and Pomona
34
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Figure 8. Temporal Variations in Pr~c!ictcd and llcasurcd CClr~on rlonc~idc
. Concentrations for 29 'September 1969: E1 r'tonte and Commerce
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AIIERA!;!' G_R_OJLN!LI..E'y'r;-L~-~~N.!.R~!.l..tNS OF cc It ET WEEN THE Ht1U R!i: OF 9QO. ANn 1000. P'IT
1 2 3 ~ 5 6 1 8 9 10 11 12 13 1~ 15 16 11 18 19 20 21 22 23 2~ 25
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AVERA!;E GROUND lE~~LtQ..."-C_ENTRAT1DNS OF CO BETtlEEN THE HOURS OF 10.Q!). ANn 1100. PI:T
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AVERAGe GRO~~tD_NCENTRATICNS OF CO 8ETIIUN THE HOU~L.1ZJI.O.......A~D 1300. PH
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10 3 2 2 ) 2 '] 2 ] .. ] 5 4 .. .. .. .. '] ] .. 5 6 5 5 5 4
'I 3 2 ] 2 3 2 '] '] 3 ] .. .. 5 5 5 5 .. 4 L.. .. II 5 5 5 ..
8 2 ] 'I ] 2 ] 3 '3 ] 3 .. .. 4 5 .. 5 5 5 5 5 5 7 II 5 ~
7 3 2 '3 2 '] 2 ] ] 2 ] 3 ] ] ~ ] ] ] 4 4 5 5 5 5 5 ..
6 2 ] 2 ] 2 2 3 2 ] ] ] 2 2 2 2 2 ] ] ] ] .. 4 ~ 4 4
5 3 2 2 2 2 -] 2 2 ] 2 2 2 2 2 ] 2 ] 2 '] '] .. 4 .. .. 3
~ 2 3 2 2 '] 2 ,. '] 2 ] 3 ] ] 3 ] 2 ] 2 ] ] 3 .. 4 .. 3
] 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 '] 2 2 " '3 '3 '3 3
2 '3 '] 2 2 '3 2 ] 2 ] 2 '] 2 '] 2 '] 2 3 2 2 3 3 '] 3 3
2 2 2 2 3 2 '/ 2 '] 2 ]- 2 2 2 ] 2 3 2 3 2 3 2 ] 3 2
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IV.
RECOMHENDATIONS
The accomplishments of the past year have been described in detail
in earlier sections and in the Appendices. These include the formulation
and development of an airshed model, the acquisition and preparation of.
emissions inventories and meteorological data, and the completion of the
initial phase in model validation. The potential of the model for accurate
prediction of the concentration distribution of inert species such as
carbon monoxide may be assessed from the results described in Section III.
But much remains to be accomplished. In this section, we present our
recommendations for future efforts.
The recommendations which follow are divided into two categories,
those to be undertaken in the near term and those ,to be initiated upon
validation of \!he model for photochemical pollutants. (These latter
recommendations will be referred to as "intermediate term".) The near-
term efforts consist of the correction of model deficiencies which Were
noted in the discussion of the validation results, and validation of the
model for photochemical pollutants. Also, we WQuld investigate the
reliability of the meteorological data base--in particular, wind measurement
in near-calm conditions--and ascertain the effect on prediction of the
probable imprecision of measurements made under these conditions. Upon
successful validation of the model we would begin the intermediate-term
efforts. These include the automation of meteorological calculations, the
initiation of extensive validation studies and the optimization of the
computer program to reduce computing time and computer storage requir~~ents.
More specifically, the tasks envisaged are as follows:
Near Tervn
A.
Exploration and correction of model deficiencies revealed to date.
1.
Incorporate means to account for high vehicle emissions
occurring under conditions of heavy traffic congestion,
especially on freeways.
rates
2.
Explore
aspects
include
surf ace
the effect on accuracy of prediction of certain
of the numerical technique. In particular, these
the order of integration metl10d, the size of the
grid, and the number of horizontal strata employed.
3.
Investigate sources of error and degree of inaccuracy of
wind measurements made at low wind speed, especially in
relationship to the early morning September 30 data.
4.
Evaluate the sensitivity of calculation to theforrn of the
diffusivity relationship.
B.
Validation of Model for Photochemical Pollutants. In addition to
the usual aspects of validation, this effort will inolude:
51
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A.
B.
C.
1.
Adaptation of the kinetic mechanism to describe the
atmospheric reaction mixture (thus far the mechanism
has only been applied to smog chamber data, as described
in Appendix B). Also, inclusion of the effects on reaction
rates of the changing composition of the atmospheric
hydrocarbon mixture and the presence of carbon monoxide
and water. These efforts are directed toward establishing
guidelines for selecting generalized rate constants and
stoichiometric coefficients.
2.
Determination of the best method for representing the.
atmospheric hydrocarbon mixture. This effort will focus
on the choice of the number of groupings of hydrocarbons
that are to be employed, with consideration being given to
both accuracy of prediction and computing time.
Intepmediate Term
Automation of Meteorological Calculation
1.
Develop a new method, or modify an existing technique, for
the automatic calculation of wind speed and direction 1n
each cell ~sing meteorological data obtained at ground
stations scattered throughout the Basin. Such a method,
most likely based on the interpolation of ground data, must
be suitably adapted to Los Angeles' unique topography.
2.
Codification and extension of Edinger's model of inversion
behavior to provide for automatic calculation of mixing depth.
Model Improvements
1.
Examine alternative computational methods to determine
whether computing time can be shortened without 105.5 in
accuracy, and whether accuracy can be improved without
an increas e in compu ting time.
2.
Redefine the mOdeling area to exclude many of the cells
lying over the ocean.
3.
Investigate the possibility of carrying out a simulation
throughout the night and into the next day. A major problem
associated with such a calculation is the lack of vertical
temperature profile data at night, h~iever, it may be possible
to consider just one shallow well-mixed layer for this period.
4.
Optimize the current computer program to reduce computing
time and computer storage requirements.
Sensitivity and Validation Studies
1.
Investigate sensitivity of predicted concentrations to
variations in model parameters and boundary conditions.
Carry out extensive validation studies for differing types
of meteorological conditions.
2..
52
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It should be kept in mind that as progress is made and improvements
in prediction are realized, an ever greater proportion of the discrepancy
between predicted and measured values of pollutant concentrations will be
attributable to the limitations in quantity, representativeness, and
accuracy of. meteorological, source emissions, and air quality data. Thus,
in addition to the refinements recommended above, attention must be given
to the acquisition and incorporation of a richer and more accurate data
base as efforts in modeling proceed.
~
53
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