<>EPA
United States
Environmental Protection
Agency
Office of Air Quality
Planning and Standards
Research Triangle Park NC 27711
EPA 450/4 79-036
December 1979
,:
Air
Application of
Photochemical Models
Volume IV
A Comparison of the
SAI Airshed Model and
the LIRAQ Model
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APPLICATION OF PHOTOCHEMICAL MODELS
Volune IV
A Comparison of the SAI Airshed Model and the LIRAQ Model
prepared by
Association of Bay Area Governments
Hotel Claremont
Berkeley, California 94705
in association with
Bay Area Air Quality Management District
San Francisco, California
Lawrence Livermore Laboratory
Liver-more, California
Systems Applications, Inc.
San Rafael, California
prepared for
U.S. Environmental Protection Agency
Office of Air Quality Planning and Standards
Research Triangle Park, North Carolina 27711
EPA Project Officer: John Summerhays
Contract No. 68-02-3046
Final Report, December 1979
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PREFACE
This document is one of four volumes intended to provide information
relevant to the application of photochemical models in the development
of State Implementation Plans. The reports are particularly directed
toward agencies and individuals responsible for preparation of
non-attainment plans and SIP revisions for ozone. The four volumes are
titled as follows:
Application of Photochemical Models
Volume I - The Use of Photochemical Models in Urban Ozone
Studies
Volume II - Applicability of Selected Models for Addressing
Ozone Control Strategy Issues
Volume HI - Recent Sensitivity Tests and Other Applications
of the LIRAQ Model
Volume IV - A Comparison of the SAI Airshed Model and the
LIRAQ Model
This work is to a large extent based on the photochemical modeling
experience gained In the San Francisco Bay Area in support of the 1979
Bay Area A1r Quality Plan. The following Individuals made significant
contributions to this work:
Association of Bay Area Governments - Ronald Y. Wada
(Project Manager)
- M. Jane Wong
- Eugene Y, Leong
Bay Area Air Quality Management District - Lewis H. Robinson
- Rob E. DeMandel
- Tom E. Perardi
- Michael Y. Kim
Lawrence Livennore Laboratory - William H. Duewer
Systems Applications, Inc. - Steven D. Reynolds
- Larry E. Reid
The authors wish to express their appreciation to John Summerhays, EPA
Project Officer in the Source Receptor Analysis Branch of OAQPS, for his
thoughtful review and comments on earlier drafts of this report.
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CONTENTS
ACKNOWLEDGMENTS
ILLUSTRATIONS
A COMPARISON OF THE TECHNICAL FEATURES OF THE SAI AIRSHED
MODEL AND THE LIVERMORE REGIONAL AIR QUALITY (LIRAQ) MODEL ..... 1
A. FORMULATION OF THE MODELS ... ................ 3
B. COMPONENTS OF THE MODELS ...... .............. 8
1 . Horizontal Transport .................... 8
2. Vertical Transport ..................... 10
3. Emissions ......................... 12
4. Chemistry ......................... 14
5. Other Processes .......... . ........... 18
6. Numerical Solution Procedures ............... 20
C. MODEL INPUTS .......................... 21
1. Emissions ...... ................... 22
2. Meteorological Inputs ................... 24
3. Chemistry Inputs ........ .............. 28
4. Initial Conditions ..................... 29
5. Boundary Conditions .................... 31
6. Other Inputs ........................ 32
D. MODEL OUTPUT ......... ..... - ............ 32
REFERENCES ............................. 40
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IV
ILLUSTRATIONS
1 Example of a Printed Map of Ground-Level Concentrations
Produced by the SAI Airshed Model 34
2 An Example of the Station Plots Produced by the LIRAQ Model . . 36
3 An Example of the Uopleth Plots Produced by the LIRAQ Model . 37
4 Example of Plots Generated by the SAI Graphics Package
Illustrating Computed and Actual Measured Concentrations ... 38
5 Example of a Plotted Contour Map of Ground-Level Concentration
Predictions Produced by the SAI Graphics Package 39
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A COMPARISON OF THE SAI AIRSHED MODEL
AND THE LI RAO. MODEL
Federal legislation requiring the preparation of various environmental
assessments—such as State Implementation Plans [SIP(s)] and New Source
Reviews [NSR(s)]--has motivated the development of several types of air
quality models. The primary purpose of these models is to provide a quan-
titative relationship between source emissions and the resulting ambient air
quality levels. Formulation of a suitable model for photochemical oxidants
is particularly difficult since complicated chemical transformations are
responsible for the process by which emissions of reactive organic compounds
and nitrogen oxides (mainly NO) lead to the formation of ozone, N02> peroxy-
acetylnitrate, and various other oxidants. Several models have been pub-
lished in the technical literature ranging from the relatively simple linear
and modified rollback schemes to the more sophisticated trajectory and grid
models.
At the present time, the Environmental Protection Agency (EPA) is faced
with the need to provide guidance to the various local and state agencies
responsible for preparing revisions to State Implementation Plans with regard
to the modeling procedures to be employed in carrying out photochemical oxi-
dant analyses. Over the past several years, considerable effort has been
devoted to the development of two sophisticated grid-based photochemical air
quality simulation models. Since 1970, the Systems Applications, Incorporated
(SAI) Airshed Model has been the subject of continued developmental work
funded largely by the EPA and U.S. Department of Transportation. The Livermore
Regional Air Quality (LIRAQ) model has similarly evolved from a multiyear
research and development effort conducted by the Lawrence Livermore Laboratory
(LLL) and funded by the Research Applied to National Needs (RANN) section of
the National Science Foundation. We note that these models are representative
of the state of the art in photochemical air quality simulation modeling at
the present time.
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The purpose of this report is to compare the various technical features
of the SAI Airshed Model and the LIRAQ model. Since detailed mathematical
descriptions of each model have been published in various technical journals
and reports, we confine our presentation here to a general description of the
similarities and differences of each model. We envision that this report
will fill three needs. First, it should give the participants in this study
a good overall description of the two models, which will be helpful in the
development of the guidance documents to be prepared in this contract effort.
Second, it should prove useful to potential model users who may be trying to
decide which of the two models to employ in some air quality assessment
study. A good understanding of each model is essential to sound decision-
making regarding model selection. And third, this document should help EPA
personnel in their ongoing photochemical model applications studies, espe-
cially those that involve direct comparisons of these two models.
Me note that this report is being prepared to aid the EPA Office of
Air Quality Planning and Standards (OAQPS) in its attempt to obtain a better
understanding of the relative strengths and shortcomings of these two rather
complex photochemical models. To this end, OAQPS personnel are going to
adapt the SAI Airshed Model for usage in the San Francisco Bay Area. Once
this is done, the two models will be exercised using inputs derived from the
same data base. Analysis of the results generated by each model should pro-
vide some insight into their relative performance. In a companion report
written by Reid and Reynolds (1979), guidelines are given for constructing
inputs for the SAI model using the information contained on the available
LIRAQ Input files.
In structuring our presentation in this report, we begin in Section A
by examining the governing equations of each model. In Section B, the dis-
cussion focuses on the various treatments of atmospheric processes, such as
emissions, transport, chemical reactions, and removal. Section C is devoted
to a comparison of model Inputs. We conclude this report in Section D by
considering the output produced by the two models.
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A. FORMULATION OF THE MODELS
The basis of both the LIRAQ model and the SAI Airshed Model is the con-
tinuity equation, which expresses the conservation of mass of each pollutant
in a turbulent fluid in which chemical reactions occur. This equation can
be written >n the following manner:
ac. a(uc.) 3(vc.)
—L + 1_ + !_ +
3t 3x 3y
Time Advection Turbulent Diffusion
Dependence
+ Ri + S. . (1)
Chemical Im1ssions
Reaction
where c- represents the pollutant concentration and is a function of space
(x,y,z) and time (t). This equation describing the dynamic behavior of
reactive pollutants is fully three-dimensional and is used directly in the
SAI Airshed Model. To obtain the governing equation of the LIRAQ model,
additional assumptions are invoked to derive a suitable two-dimensional
form of Eq. (1).
Examination of Eq. (1) indicates that the following physical and chem-
ical processes are considered in the Airshed Model:
> Pollutant advection. The model can treat a fully three-
dimensional wind field, where u, v, and w are the mean
wind velocity components in the x-, y-, and z-directions,
respectively.
> Turbulent diffusion. Pollutant transport resulting from the
influence of atmospheric turbulence is treated through the
use of the eddy diffusivity concept; KR and Ky are the
horizontal and vertical diffusivity coefficients, respec-
tively.
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> Chtmical reaction. The term FL represents the net rate at
which pollutant 1 Is generated by chemical reactions. The
reaction rate 1s a function of pollutant concentration,
temperature, and the Intensity of ultraviolet radiation.
> Emissions- The spatial and temporal distribution of the
source emissions are treated 1n the term S... For large
point sources, the total effective plume rise is calcu-
lated to enable the appropriate spatial placement of the
emissions aloft.
In addition, removal of pollutants by surface uptake processes is considered
in the boundary conditions of Eq. (1).
To derive En,. (1) from the fundamental continuity equation three
assumptions are necessary: first, pollutant transport effects due to
molecular diffusion are small relative to those attributable to turbulent
diffusion; second, pollutant transport due to turbulence can be adequately
parameterized through the use of the eddy di.ffusivity concept; and third,
turbulent concentration fluctuations have a. negligible influence on reaction
rates. For a more thorough discussion of the derivation of Eq. (1), we refer
the reader to the reports by Reynolds et al. (1973) and Reynolds, Seinfeld,
and Roth (1973).
Because the set of equations is both nonlinear and coupled (through the
reaction terms R.), Eq. (1) cannot be solved analytically; therefore,
appropriate numerical techniques must be utilized to find an approximate
solution. To facilitate the application of finite difference methods in the
SAI model, the vertical dimension is normalized to the distance between the
bottom and top of the modeling region. This step is accomplished by defining
a new independent variable p:
z - Hb(x,y,t)
p = Ht(x,y,t) - Hb(x,y,t)
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where H. and H are the elevations of the bottom and top of the region,
respectively. Upon performing this change of variable and neglecting
cross-derivative turbulent diffusion terms, Eq. (1) becomes (Reynolds,
Seinfeld, and Roth, 1973):
r I + R. An + SjAn
I 3o / 1 1
(2)
where
and
Ht(x,y,t) - Hb(x,y,t)
Basically, Eq. (2) with appropriate initial and boundary conditions is the
equation whose solution yields the predictions obtained from the SAI Airshed
Model.
The Airshed Model provides for segmenting the column of air above each
grid square into several cells. These cells may include all or part of
the mixed layer or can extend, if one exists, into an elevated inversion
layer. If, for example, calculations are performed in the mixed layer only,
then, the modeling region would be subdivided into several equally spaced
cells in the vertical direction bounded by the terrain and the base of the
inversion. To facilitate the calculation of pollutant concentrations within
the inversion, a second set of equally spaced cells can be added to the
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modeling region bounded, for example, by the base and top of the inversion
layer. When performing multiday simulations, these provisions for treating
the inversion layer may be important in properly accounting for the effect of
pollutant entralnment into the mixed layer as it deepens during the day.
To derive the governing equations for the LIRAQ model, 1t 1s first
assumed that the wind velocity components can be written in the following
manner:
u(x,y,z,t) • um(x,y,t)(f-j , (3)
v(x,y,z,t) * vm(x,y,t)(^-\ , (4)
* n
where um and vm are the velocity components at height zm. According to
MacCracken et al. (1978), n is normally set to a value of 1/7 to represent
neutral stability conditions in the mixed layer. Any other value (except -1)
nay also be chosen. By invoking further assumptions regarding the transport
and chemical reaction processes, MacCracken et al. argue that the concentration
profile at any point can be represented by the expression:
c^x.y.z.t) * a^x.y.t) * b^x.y.tkn- , (5)
where a., and b. are parameters that are a function of the mixing depth,
source strength, deposition velocity, and eddy diffusivity at a height ZQ
(taken to be 1 meter) above the ground, below which the concentration is assumed
uniform with height.
Substituting Eqs. (3) through (5) into Eq. (1) and performing a ver-
tical integration from ZQ to the base of an elevated inversion layer yields
the following governing equation for the LIRAQ model:
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wi
,. / I/!.... >,• i - . 3AH C-
where c. is the vertically averaged concentration of pollutant i, AH' is the
mixing depth, and e. = (n/n+1)(bi^). The term Wi represents the net effec-
tive flux of pollutant i transported through the top of the modeling region:
WHF.(x,y,H,t)- , WH > 0
Wi = { 0 * WH = °
WHCT,i ' WH < ° '
where Wu is the velocity at the top of the region H, and CT . is the assumed
H _ I »'
boundary concentration at H. S. and R. are the vertically averaged values of
the source and reaction terms given in Eq. (1). For further details regarding
the formulation of the LIRAQ model, we refer the reader to the paper by
MacCracken et al. (1978).
In the description presented by MacCracken et al. it is mentioned that
the parameter 6- in Eq. (6) was set to zero in the San Francisco applications.
Thus, comparing the governing equations for both models [Eqs. (2) and (6)],
we note that they are very similar. However, the concentrations predicted by
the LIRAQ model are vertically averaged values, though application of Eq. (5)
does enable one to obtain an estimate of the ground-level values. In using
Eq. (5), if the source flux is larger than deposition, then the near ground-
level concentration will be higher than the vertical average concentration,
and vice versa. The smaller the value of the turbulent diffusivity, the lar-
ger the difference between the ground-level and vertical average concentration.
Although the concentration profiles predicted by Eq. (5) are in general
agreement with observations, the adequacy of this procedure as a means for
calculating ground-level concentration values, especially for ozone, has
not been fully evaluated.
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8
No a priori assumptions are made concerning the vertical profile of the
winds or pollutant concentrations for the SAI model. The vertical resolu-
tion depends on the number of vertical levels used (the current limit is
10 levels) and on how many of those levels lie above the inversion base.
The ground-level concentration is taken as the concentration in the lowest
layer of cells. An option included in the SAI model (discussed later)
adjusts the concentrations in the lowest layer of cells to account for the
nonuniform distribution of sources.
Because the LIRAQ and SAI models have evolved from multiyear research
and development programs, the available technical documentation is rather
voluminous. Thereforet we suggest that anyone desiring additional informa-
tion regarding the LIRAQ model and its initial application to San Francisco
begin by examining the summary papers written by MacCracken et al. (1978),
Dickerson (1978), and Duewer, MacCracken, and Walton (1978). More detailed
descriptions of the model and a recent application to St. Louis are given
in the reports by MacCracken and Sauter (1975), MacCracken (1975), and
Duewer et al. (1978). The papers by Reynolds, Seinfeld, and Roth (1973),
Roth et al. (1974), and Reynolds et al. (1974) describe early developmental
work on the SAI model and its Initial application to Los Angeles. The recent
report by Reynolds et al. (1979) provides a summary description of the
technical features currently embodied 1n the SAI model and the results of
recent applications to Los Angeles, Sacramento, and Denver. A number of other
studies carried out by SAI using the Airshed Model are described in the report
by Reynolds, Tesche, and Reid (1979).
B. COMPONENTS OF THE MODELS
This section examines the ways in which atmospheric processes are treated
in the SAI Airshed Model and the LIRAQ model.
1. Horizontal Transport
Both models treat the two processes that transport pollutants in the hori-
zontal direction—advection and turbulent diffusion. Specification and use of
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the horizontal wind is straightforward. For the LIRAQ model, the mass flow at
each face of a grid cell is input. Use of nass flow rather than v.-ind soeed
takes into account any changes in the mixing depth from one edge of a cell to
the other. For the SAI model, the x- and y-components of the wind vector are
specified at the center of each grid cell. Since there can be more than one
level of cells, wind shear (including both speed and direction changes with
height) can be accounted for in the SAI model. Although this feature allows
the user to represent more realistically the actual three-dimensional wind
field, routine meteorological data collection efforts are frequently inade-
quate for characterizing spatial and temporal variations in the winds aloft.
In previous SAI model applications, estimates of upper level wind flows have
been generated through the use of available wind soundings and various diag-
nostic wind models (see Tesche and Burton, 1978; Reynolds et al., 1979;
Killus et al., 1977). In general, it is desirable to mount a special field
program to measure winds aloft several times during the day in the urban area
of interest. This program is important for both models since horizontal pol-
lutant transport is influenced by the winds throughout the mixed layer, not
just the winds near the surface (where routine wind data are usually measured)
Though generally less important than horizontal advection, both models
also consider horizontal transport by turbulent eddies. To approximate the
subgrid-scale transport due to turbulence, it is assumed that the pollutant
flux is proportional to the concentration gradient. The proportionality
factor is called the eddy diffusivity coefficient. In both models, the
horizontal diffusivity coefficients for turbulent transport in the x- and
y-directions are equal [as designated by KH in Eqs. (2) and (6)]. For the
LIRAQ model, the values of the horizontal diffusivity coefficients are cal-
culated outside the model by MASCON (described in a later section) using the
principles of similarity theory. Basically, the diffusivity coefficient is
a function of the wind speed and the mixing depth.
The SAI model uses a constant value for the horizontal diffusivity
(50 m2/sec). Although the horizontal diffusivity treatment in the LIRAQ me
is more realistic, the effect on the predicted pollutant concentrations of
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10
using a constant coefficient should be small; studies reported by Liu, Whitney,
and Roth (1975) indicated that the model results are not very sensitive to the
value of this parameter. This effect occurs because gradients in the concentra-
tion field are often relatively small since emissions from point and line sources
are spatially averaged over relatively large grid cells. In addition many
of the important horizontal atmospheric motions can be represented explicitly
1n the advection terms of the governing equation through the use of a
relatively fine grid covering the urban area. The effects of the remaining
subgrid scale motions, which must be parameterized in the diffusivity
coefficient, are correspondingly somewhat less important.
2. Vertical
Exchange of material between vertical cells is characterized only in
the SAI mo4e1, though both models consider exchange of material across the
top of tfcf modeling region. As is the case for horizontal transport, there
are two components of vertical transport—adveetion (caused by the vertical
wind component) arid vertical turbulent diffusion. In addition, the height
of the cells can change, thereby causing a flux across the cell interfaces.
This tenr. is similar tQ that generated by the vertical wind component; in
both models, these te"« are combined to yield a net pollutant velocity
relative to each grid cell interface.
The LIRAQ model considers vertical transoort at the top of each cell.
It is assumed for this model that the effect of material exchange between
the mixed layer and the inversion layer as a result of a turbulent trans-
port can be combined into a net advective flux term. This flux at the top
of the modeling region is represented by a term that includes any vertical
mass flow needed to balance the horizontal mass flows, induced turbulent
ablation of the inversion that leads to changes in the cell height due to
a raisina or lowering of the inversion base in time, and horizontal transport
through a spatial gradient in the height of the inversion base. If pollutants
are transported or entrained into the inversion layer (and thus out of the
modeling region), they are excluded from all subsequent calculations
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in the LIRAQ model. As a result, they cannot be reentrained at a later time
in the simulation if, for example, the inversion base rises as a result of
surface heating effects. The concentration of pollutants in the air entrained
into the mixing layer is specified, in part, as a model input. The con-
centration of pollutants in the inversion is calculated by an empirical
function involving the predicted concentration just below the base of the
inversion and a user-specified concentration value and scaling parameter
(between 0 and 1).
The SAI model has the capability of modeling both the mixed layer and
nart or all of the inversion layer with one or more levels of cells within
each layer. The rate of turbulent diffusion, especially between levels
within the mixed layer, must be considered. Again, the assumption is made
that the effect of turbulent diffusion is proportional to the concentra-
tion gradient in the vertical direction with the proportionality factor, K ,
being the vertical diffusivity coefficient. The SAI model calculates this
coefficient for each grid cell interface on the basis of the wind speed, sur-
face roughness, height of the inversion base, height of the cell interface,
and the stability class. The stability class within the mixed layer is esti-
mated from the wind speed and solar insolation* (exposure class), and above
the mixed layer, it is estimated from the temperature gradient*. Different
algorithms for KV are used for the three possible stability classes: stable,
neutral, and unstable. For unstable conditions mixing is rapid, and as a
consequence, the vertical concentration gradients are small. Stable condi-
tions produce almost no mixing due to turbulence, and neutral conditions
result in rodest, but not insignificant, mixing.
The stability in the upper layer of grid cells can be either neutral or
stable, thus allowing the treatment of a surface-based inversion capped hy a
layer of neutrally stable air or a mixed layer capped by a stable layer. For
* At the present time these variables are assumed to vary temporally but
not spatially in the SAI model.
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12
grid cells within an elevated inversion layer, the values of the diffusivi-
ties are relatively small, effectively eliminating vertical transport by
turbulent diffusion. At the top of the modeling region, the vertical concen-
tration gradient is set to zero if the advective velocity of pollutants
relative to the top of the region is equal to zero or is directed out of the
region. Otherwise, if material is advected into the modeling region, then
the pollutant flux is calculated by multiplying the net velocity times the
boundary concentration just above the top of the region.
As in the L1RAQ model, the flow of pollutants relative to a cell inter-
face is made UD of three components. The SAI model differs only in the respect
that, for every cell except those adjacent to the qround, there is a mass flow
through the bottom, as well as the top, of the cell. The mass flow at the
top of a cell is calculated using a mass balan-ce that considers the net
amount of air carried into the cell by the horizontal wind components, the
amount of air injected through the bottom of the cell (from a previous mass
balance calculation for the cell belo*), and any change in height of the ce"!1
as a function of time.
The vertical resolution of the SAI model enables it to handle the entrair-
ment into the mixed layer of pollutants that enter the inversion either fror
elevated point source emissions or at the time the stable layer formed dur-
ing the previous night. In light of the limited treatment of the inversion
layer in the LIRAQ model, the SAI model would be better suited for applica-
tions in which large elevated point sources are important or multiple-day
simulations are to be performed.
3. Emissions
Emissions of pollutants are divided into two classes, those emanating
from either ground-level or elevated point sources. Emissions from mobile
sources, distributed area sources (such as space heating, gasoline marketing,
solvent usage, and so on), and other stationary sources that do not emit pol-
lutants from tall stacks are generally considered to be in the ground-level
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13
source category. The distinction between stationary sources treated as
ground-level sources and those treated as individual point sources is not
always clear-cut. The LIRAQ model application to San Francisco designated
elevated point sources as those with emissions higher than 30.5 meters. The
SAI model applications used a corresponding height of about 50 meters, the
usual height of the lowest layer of cells.
In the LIRAQ model the ground-level emissions affect the average concen-
tration in the grid cell and the shape of the assumed vertical concentration
profile that is used to estimate the surface pollutant concentration. The
larger the emissions rate, the larger the difference between the calculated
surface concentration and the vertical average concentration. Ground-level
emissions are injected into the lowest layer of cells in the SAI model.
The cells in this layer, as well as all other cells, are assumed to be well
mixed at all times. (This is not true of the special microscale layer,
which will be described later.) Subsequent to emission, the pollutants are
allowed to undergo vertical and horizontal transport, chemical transforma-
tions, and removal.
Elevated point source emissions contribute only to the vertical averaae
concentration in the LIRAQ model. To account for the fact that elevated
emissions may be injected into the stable inversion layer rather than the
mixed layer and that numerical stability problems may be encountered by includ-
ing sharp temporal changes in the emissions levels injected into a grid cell,
KacCracken et al. (1978) designed a special procedure for treating elevated
emissions when the mixing depth is relatively shallow. Basically, all elevated
source emissions are ignored if the mixing depth is less than 100 meters. The
emissions are scaled by a factor that varies smoothly from 0 to 1 as the
mixing depth increases from 100 to 150 meters. When the mixing depth is
greater than 150 meters, all elevated emissions are injected into the
mixed layer. The point source emissions not added to the cell average concentra-
tion are ignored in the simulation and cannot be reentrained when the mix-
ing depth rises.
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For the SA! model, the height at which the point source emissions are
injected is important, since it determines which vertical cell will receive
the emissions. Two methods are available for determining this height: The
first and easier method is simply ttf use the stack height; the other method
is to determine the plume rise relative to the too of the stack using the
Briggs' (1971) formulas, which require the heat flux of the effluents and
the local meteorological conditions as inputs. The effective stack height
(actual stack height + plume rise) is then used to determine the vertical
cell into which the emissions are to be injected. The emissions are com-
pletely mixed within this cell and can be transported into adjoining cells
according to the winds and turbulent diffusion coefficients. If the effec-
tive stack height 1s higher than the height of the modeling region, then the
emissions are not considered further in the simulation.
4. Chemistry
It is not practical to include explicitly within a chemical mechanism all
(or a large number) of the hydrocarbon compounds found in an urban atmosphere.
Therefore, on the basis of their common properties, the hydrocarbon species
must be condensed Into a few specific groups. The two most important charac-
teristics used for grouping are reactivity and products formed. The LIRAQ
model employs a mechanism similar to that developed by Hecht, Seinfeld, and
Dodge (1974), which groups species according to the types of reactions that a
compound undergoes In the atmosphere. Three classes of primary species are
defined: HC1. which reacts with oxygen atoms, ozone, and hydroxyl radicals
and which includes olefins; HC2, which reacts with oxygen atoms and hydroxyl
radicals and includes the paraffins and less reactive aromatic species;
and HC4. which reacts with oxygen atoms, light, and hydroxyl, peroxyl, and
nitrate radicals and which includes aldehydes and ketones. The rates and
mechanisms used for these species are representative of propylene for HC1,
n-butane for HC2, and a mixture of formaldehyde and acetaldehyde for HC4.
HC4 Is also a secondary species.
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In using the LIRAQ mechanism, it is necessary to distribute the hydro-
carbon emissions among the three classes cited above. This can be done
using emissions composition data for various source types, as discussed by
Duewer (1977). Each type of compound must be assigned to one or more LIRAQ
classes. In addition, a factor must be developed to account for the differ-
ences in reactivity between a particular compound and those compounds repre-
sentative of the three LIRAQ groups. This reactivity factor is then used
to adjust the hydrocarbon emissions inputs. Thus, reactivity is handled
by a complex mixture of species blending and total mass adjustment.
The latest version of the chemical mechanism employed in the SAI model
is based on a different approach. The SAI Carbon-Bond Mechanism groups
similarly bonded carbon atoms together rather than grouping entire molecules.
Six carbon-bond groups are defined: single-bonded, double-bonded (except
ethylene), and carbonyl-bonded carbon atoms as well as ethylene, aromatic
rings, and benzaldehyde. For example, using this scheme 1 mole of butene
would be composed of 2 moles of single-bonded and 1 mole of double-bonded
carbon atoms.
The total emissions of all reactive organic compounds are apportioned
directly among five of the six carbon-bond classes (no emissions of benzalde-
hyde are assumed). In contrast to the LIRAQ treatment, no adjustments are
made to the mass emissions rates to account for reactivity effects. This
is because the Carbon-Bond Mechanism takes advantage of the fact that, when
considered on a per carbon atom basis, the range of reactivity of carbon
atoms is considerably less than that of hydrocarbon molecules. In addition,
because the Carbon-Bond Mechanism follows carbon atoms rather than hydro-
carbon molecules, it is possible for the mechanism to maintain a formal mass
balance for carbon, a feature that is not an attribute of the LIRAQ mechanism.
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16
The preceding discussion has focused on the treatment of reactions
involving organic species to the exclusion of the inorganic reactions. In
general, both models treat the important inorganic chemical reactions in
about the same amount of detail.
It is important to note that the chemical mechanisms included in the SAI
and LIRAQ models are the subjects of ongoing research efforts. As a result,
they can be expected to change as new formulations are developed and evalu-
ated. As an example, the SAI mechanism has recently been updated to include
six, rather than four, hydrocarbon groups. In addition, this new version
of the mechanism includes recent information on the measured values of reac-
tion rate constants and improved treatments of the chemistry of single
carbon bonds as well as of aromatic and nitrate compounds.
For some studies, the effect of the previous day's emissions may be of
interest. These multiday simulations will necessarily include periods of
darkness. The chemical mechanism used for nighttime conditions must recog-
nize the fact that, during periods with no sunlight, the chemistry is no
longer driven by the photochemical reactions. Both LIRAQ and the SAI model
are at least theoretically capable of treating nighttime chemistry. Basically,
the SAI model contains a separate mechanism derived by simplifying the nominal
Carbon-Bond Mechanism to reflect only those reactions thought to be important
at night. This simplification significantly reduces the amount of computa-
tion required to evaluate the reaction rate expressions during the night-
time portion of a simulation. The LIRAQ model employs the same mechanism
for both day and night conditions, though different parts of the mechanism
are important during each of these periods.
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17
Some difficulties have been experienced in using both the SAI and
LIRAQ models to simulate the transition period between daytime and night-
time conditions. During the development stages, the SAI model sometimes
predicted negative concentrations during this transition period, but this
problem has been virtually eliminated. The numerical method used in the
LIRAQ model (a modified Gear routine) can be computationally very slow
during a transition period under some conditions. For example, in the
St. Louis application, more computer time was required for the period
covering sunset than for the entire daylight period. Once the transition
period is passed, however, neither model exhibits any further problems.
During daylight hours when the photolysis rates are constantly changing,
the LIRAQ model updates each photolysis rate constant for every time step on
the basis of the solar zenith angle at that time (each rate constant is inde-
pendently tabulated versus zenith angle). All the values are adjusted by a
transmissivity value for that grid square for that tine period. The trans-
missivity values are derived from Eppley pyranometer data and are a measure
of the amount of sunlight reaching the ground to account for clouds, fog, or
particulates that may reduce the available sunlight.
The SAI model also updates the photolysis rate constants for every time
step but a different procedure is used: The photolysis rates are not all
independent; instead, each is defined as the ratio of the particular photol-
ysis rate constant to that for N02-* The N02 rate is input at the begin-
ning and end of every input data time period. To obtain a value at each
time step, the rate constant is determined by linear interpolation within
the time period. If aerosols are simulated, then the rate constants are
subject to a linear variation with height throughout the column of cells
on the basis of the aerosol concentration within the column. This
* Basically, the SAI model assumes that each photolysis rate constant has
the same dependence on the solar zenith angle, though several rate con-
stants are known to exhibit a different dependence from 1 to 2 hours
just after sunrise and just before sunset.
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18
procedure accounts for the effects of light scattering due to the presence
of aerosols on the available UV radiation in each grid cell. No provision
is included for spatially varying the photolysis rate constants to account
for clouds or fog in one part of the region but not in another.
Spatial and temporal variations in the photolysis rate constants are
treated in more detial in the LIRAQ model than in the present version of
the SAI model. In some situations, such as those periods when the zenith
angle is close to 90° (at sunrise and sunset) and when the cloud cover
over the modeling region is not uniform, this detail may be important.
5. Other Processes
The removal of pollutants at ground level by physical and chemical
processes is treated by both models. Surface deposition is calculated in
the LIRAQ model by multiplying the deposition velocity by the calculated
pollutant concentration at 1 meter above the surface. Although the depo-
sition velocity is only a function of the pollutant (i.e., it is assumed
to possess no spatial variability), the ground-level pollutant concentra-
tion is dependent on the diffusivity near the surface, which does vary
over the modeling region. Basically, the loss of material dufc to surface
sinks affects the value of the predicted ground-level concentration and
also influences the cell average concentration.
In the SAI model the rate of deposition depends upon the pollutant con-
centration in the lowest cell. In contrast to the LIRAQ model, the deposi-
tion velocity used by the SAI model is not uniform over the entire grid.
Pollutant removal is assumed to take place in two steps—diffusion to the
surface followed by absorption, adsorption, or chemical reaction at the sur-
face. The rate of diffusion is calculated from the wind speed, atmospheric
stability, and surface roughness for each grid square. The rate of removal
for each species at the surface is a nominal value, which is scaled by a
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19
land use factor. This scaling factor is based on surface characteristics;
for example, in previous studies thick vegetation has been assumed to
result in relatively fast pollutant removal, and concrete has been assumed
not to absorb pollutants at all.
The SAI model includes some consideration of the effects of subgrid-
scale concentration variations on the reaction rate; there is no correspond-
ing capability in the LIRAQ model at this time. This optional routine,
referred to as the microscale module, requires additional input data and
is used to account for nonuniform mixing in the lowest layer of cells. It
should be noted that this module has only been exercised in a few studies,
and thus, its performance characteristics have not been well established.
Near sources of NO, the local ozone is rapidly consumed to form NOp
until the NO, N0?, and 0~ come to equilibrium. This subqrid-scale ozone
depletion effect is important in the area immediately downwind of the NO
source. At the present time, ozone suppression is only treated around road-
ways. Although considerable effort has been devoted to developing appropri-
ate means for treating ozone suppression in point source NO plumes, these
procedures have not been implemented in the SAI model to date. Thus, NO
emissions from motor vehicles are allowed to react only with the ambient
ozone in the immediate vicinity of the roadway. The microscale routine
adjusts the pollutant concentration in the lowest layer, usually 20 meters
high, to account for this localized chemistry effect as well as to calculate
a measure of the spatial variation of pollutant concentrations within the
cell. If this optional module is not exercised, then the lowest layer is
assumed to be well mixed, and the chemistry proceeds from this assumption.
The assumption that the lowest layer is well mixed allows any NO emitted to
react with any ozone in the grid square, thereby reducing the ozone concen-
tration more than it would actually be reduced.
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20
The additional data required for this microscale option are the NO emis-
sions from the major roadways and a factor related to the number of cars oper-
ating on the major roadways and their average speed, for each grid square.
These data can usually be derived from the information produced by the trans-
portation model used to calculate the mobile source emissions.
6. Numerical Solution Procedures
Since the mass conservation relationships that form the basis for these
models cannot be solved analytically, it is necessary to employ numerical
techniques to obtain approximate solutions. There are two aspects of the
governing equations that are particularly troublesome numerically: the
calculation of horizontal advection and the treatment of the chemical reac-
tion term. One of the main drawbacks of the grid modeling approach, as
noted by Liu and Seinfeld (1975), is that the horizontal advection portion
of the governing equation is difficult to solve accurately.
A first-order finite difference scheme is used in the LIRAQ model to
calculate the advective flux between grid cells. In contrast, the SAI
model employs the flux-corrected SHASTA* procedure developed by Boris and
Book (1973). Tests conducted it SAI have indicated that the SHASTA pro-
cedure is a more accurate means of treating horizontal advection (Reynolds
et al., 1976; Killus et al., 1977), especially when there are relatively
sharp gradients in the concentration field. We note that the SHASTA pro-
cedure is used in the LIRAQ-1 model, which is limited to the consideration
of pollutants that are inert or those that undergo first-order reactions.
Experience reported by Duewer, MacCracken, and Walton (1978) based on actual
LIRAQ model applications to San Francisco indicates that the numberical results
generated by the two versions of the LIRAQ model that employ the first-order
and SHASTA difference scher.s, respectively, seem to agree fairly well.
Killus et al. (1977) obtained similar results when applying the SAI model
to Los Angeles using both a second-order difference scheme and the SHASTA
technique. Thus, it can probably be concluded that the SHASTA procedure would
be expected to yield more accurate results in those areas on the qrid for
which horizontal concentration gradients are relatively large. In other areas,
the results from the two procedures should not differ substantially.
SHASTA is an abbreviation for Sharp and Smooth Transport Algorithm.
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21
To handle the chemical reaction terms, the LIRAQ model employs an LLL-
modified version of the numerical method developed by Gear (1971). We note
that this technique is frequently used in chemical mechanism development
studies and is acknowledged to be a good procedure for solving systems of
stiff ordinary differential equations. However, it was not feasible to
adapt the more accurate SHASTA treatment of horizontal advection for use in
the Gear routine; thus, the simpler first-order difference scheme was used.
The reaction terms in the SAI model are integrated by employing a Crank-
Nicolson difference scheme. Basically, this scheme yields a set of nonlin-
ear algebraic equations at each time, step, which are solved using a Newton
iterative procedure. . In comparisons involving the Crank-Nicolson and Gear
techniques, predicted, concentrations generally agreed with one another to
within 10 to 15 percent after a few hours of simulation. A major advantage
of the method implemented in the SAI model is computational speed. The
computing time required by the SAI model for a region segmented into five
vertical layers of grid cells is about one-half that required by the LIRAQ
model for the same sized two-dimensional grid.
C. MODEL INP'JTS
The first step in preparing the input files to a grid model entails the
collection and processing of the available aeronetric and emissions data as
well as other miscellaneous information such as that pertaining to the topo-
graphy and land use of the area. The form of these data varies widely frorr
one urban area to another. In most cases, the available data require
reformatting prior to their use as inputs to the preprocessor programs that
create the input files. Both the LIRAQ and SAI models include series of
programs that create the appropriate data files in a form suitable for
input to each model. The following discussion describes the types of data
needed as input for the existing preprocessor programs, the data manipula-
tions that are necessary in addition to any reformatting, and the input
data requirements of each model.
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22
Input preparation is more flexible with the SAI model than with the LIRAg
model; in the SAI model, different methods are available for creating the
input files, each with different data requirements. The choice of method is
determined by the user on the basis of the amount of data available and the
general characteristics of the physical and chemical phenomena that influence
pollutant concentrations in the region. In general, data preparation proce-
dures should be adapted to the region of interest. The primary objective of
this effort is to identify and implement algorithms that make the best possi-
ble use of available data and knowledge. The selection of an appropriate
algorithm is especially important in situations in which a particular model
input is not well characterized by the data. In light of the previous com-
ments, the existing algorithms for preparing model inputs may not represent
the best choice for some new application. In such circumstances, more suit-
able procedures should be developed and implemented in the models.
1. Emissions Inputs
The treatment of ground-level emissions is very similar in both models.
Basically, emissions from different sources, such as dry cleaners, gasoline
marketing, space heating, and motor vehicle operation, are summed and gridded.
In addition, a temporal distribution and hydrocarbon splits must be specified
for each source or source category. The primary difference between the two
emissions files are the hydrocarbon species.
In the discussion of the chemical mechanism used by each model, it was
pointed out that the reactive hydrocarbons have to be apportioned among dif-
ferent classes. The criteria for assigning a molecule to a particular class
is quite different for the two models, and the determination of emissions
splitting factors requires a good understanding of how organic species are
treated in the chemical mechanisms. The actual methods employed for splitting
the hydrocarbons for an application range from using average factors for the
entire emissions inventory to deriving splits on the basis of detailed hydro-
carbon breakdowns for two or more source categories. The amount of disaggre-
gation (by source category) in the emissions inventory and the availability
of information with which to derive emissions splits determine how the sources
should be lumped into categories.
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23
Individual point sources can be divided into two categories — those that
emit pollutants at heights significantly above the surface and those that
inject contaminants into the atmosphere at or near the ground. A stack height
of 30.5 meters is used as the cfiteria in the LIRAQ model for deciding whether
point source emissions are included in the ground-level or elevated point source
category. This height can be easily changed if desired. For the LIRAQ model,
the only inputs for the point sources are the location of the source and the
emissions of each pollutant. Since the SAI model has multiple layers of grid
cells, the height at which the pollutants enter the modeling region is impor-
tant. Source emissions that are not expected to be injected into grid .cells
above the surface layer are treated as ground-level sources. For other point
sources, the plume rise is calculated and used to allocate emissions on the
grid. Therefore, an effective stack height (the actual stack height plus the
plume rise relative to the top of the stack), as well as the location and
emission rates of each source must be input.
The effective stack height can be specified by the SAI preprocessor
program in either of two ways: The simpler method involves inputting the
actual stack height and having the program ignore buoyant plume rise
calculations; the preferred approach entails inputting both the stack
height and other pertinent effluent characteristics to enable the estimation
of the effective stack height using the Brigg's (1971) formulas. These
formulas require estimates of the heat flux from the stack. The SAI
preprocessor routine that calculates the plume rise estimates the heat flux
from input values for the exit temperature and flow rate. The stack
diameter and velocity can be substituted for the flow rate. Calcula-
tion of the plume rise gives a more accurate representation than use of
the stack height in determining the place at which the emissions should
be injected on the grid. For both models, if the effective stack height
is above the top of the modeling region, then the emissions are ignored
In subsequent model calculations.
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24
2. Meteorological Inputs
a. Winds
One of the most important tasks of input preparation is creation of
the wind field. The data typically available for this task are surface-
level wind measurements throughout the region and instantaneous ver-
tical soundings taken at a few locations usually one to three times a day.
To prepare wind inputs, the LIRAQ model uses a diagnostic model called MASCON
(Dickerson, 1978). The inputs to MASCON are the inversion height data, the
wind measurements, and the topography of the region. For the application to
San Francisco, additional wind data were synthesized to give a reasonable
wind field. Since wind data do not usually exist for every part of the
region, judgments must often be made with regard to the way in which wind
velocities should be estimated in these areas and whether the calculated
velocities are an adequate representation of the expected flow fields. Mak-
ing such judgments requires experience and a knowledge of the meteorology of
the area.
MASCON was developed to provide a self consistent mass flux field for
the LIRAQ model. The mass flux into each grid cell is balanced by the out-
ward flux and changes in the mixing depth so that there is no accumulation
or depletion of mass within a cell. This is a necessary condition for any
wind field to be used in urban-scale air pollution modeling. Another fea-
ture of MASCON is the turning of the wind around the topography and channel-
ing of the winds through valleys and mountain passes. The channeling is very
important since it determines the ways in which pollutants generated in the
urban area will be transported to suburban and rural areas.
SAI has used several methods to construct wind fields for use in the
Airshed Model. The appropriate method for use in a given application depends
on the topography of the region and the data available. An algorithm devel-
oped at SAI by Killus et al. (1977) was tailored for use with the St. Louis
Regional Air Pollution Study (RAPS) data base. It is valid only for rela-
tively flat terrain and makes maximum use of the aloft wind data. This
method is not appropriate for use in areas where the terrain significantly
Influences the wind field.
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SAI has also developed a three-dimensional diagnostic wind model for
use in areas with complex terrain. The basic characteristics of the wind
field produced by this wind model, mass consistency and the wind turning
around obstacles, are similar to those of MASCON, but the mathematical
formulations of the models are quite different. The inputs to the SAI
wind model are the surface temperature field, the surface roughness, the
elevation for each grid cell, and thr wind velocity along the boundaries
of the region. The topography and boundary conditions have a dominant
influence on the calculated wind field; thermal circulations estimated
from the temperature inputs and surface roughness effects have relatively
small influences on the wind field. Surface and upper air wind neasurenents
are used to specify the boundary conditions for each level of the wind
model. In order to exercise some influence on the wind velocities cor>-
puted by MASCON, fictitious wind stations and data are sometimes defined
and employed in the model. A similar type of control is possible in the
SAI wind model by making suitable adjustments to the values of the wind
velocities along the boundaries. Again, the modeler must have a good
expectation of what a reasonable wind field looks like before adjustments
can be made.
In addition to the above approaches, an interpolation routine is also
available as part of the SAI data preparation programs. The routine calcu-
lates the x- and y-component of the wind velocity for each surface grid square
by averaging the observed wind vectors within a specified radius of the grid
square. Each measurement is weighted by the inverse of the distance fror
the grid square to the wind station. This method also lends itself to the
use of synthesized wind data as a possible means of rectifying deficiencies
in the calculated wind fields resulting from inadequacies in the available
data.
The algorithm developed by Killus et al. (1977) and the three-dimensional
wind model both calculate a fully three-dimensional wind field. The wind
shear predicted by these models depends almost entirely upon the aloft wind
data input to the routines. Since there are usually very limited upper air
wind data and all the data are instantaneous measurements, care should be
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26
taken when specifying these inputs. The interpolation routine calculates
only the surface wind field; therefore, some additional methodology is
needed to generate the wind field for the other grid levels of the modeling
region. SAI has used several methods including one that produces no wind
shear (i.e., the upper level flows are the same as those at the surface)
(Reynolds et al., 1973; Anderson et a!., 1977) and another that assumes the
wind velocity aloft is a function of the calculated local surface wind velocity
and some scaling function derived from the available upper air soundings
(Reynolds et al., 1979). Since each method was developed for a specific
application, we refer the reader to the indicated reports for further
details regarding these procedures.
b. Mixing Depths
The depth of the ir,ixed layer directly affects the dilution of emissions
and hence has a direct impact on ambient concentrations. The data available
for estimating the mixing depth are vertical temperature soundings and sur-
face temperature data. HASCON uses this data along with the wind data to
construct "-he mass-consistent wind and mixing depth field for the LIRAQ model.
The winds and mixing depths are linked, and one cannot be changed indepen-
dently of the other without nullifying the mass-consistency of the wind
field.
The SAI model calculates a vertical velocity for each grid cell to sat-
isfy mass conservation. Since this calculation only considers the cell heights
and the horizontal wind components in each level of grid cells, the mixing
depth inputs for the SAI model can be specified independently of the horizontal
wind field inputs. Using the same types of data input to MASCON, the SAI
data preparation programs will construct a spatially and temporally varying
mixing depth field. We note that the extent to which the changes in the
mixing depth are consistent with convergence and divergence effects in the
wind field is dependent on the technical features of the preprocessor used
to prepare wind and mixing depth inputs to the SAI model.
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c. Other Meteo'-clogical Inputs
To estimate the ground-level pollutant concentrations frorr. the cell
average concentration, the LIRAQ model calculates a vertical profile for
each pollutant. Besides the emissions and deposition velocity, another
parameter enters into the calculation of the vertical profiles. This parar-
eter is the turbulent diffusivity coefficient near the surface. This
coefficient is calculated by MASCON using a procedure proposed by von Karmar
as explained by Sutton (1953). In general, if the wind speed is high, the
vertical mixing is fast, and the vertical profile is relatively flat. At low
wind speeds, the diffusivity is smaller, and the resulting concentration oro-
file exhibits a steeper gradient near the surface. The diffusivity coefficient
is also used in the SAI model to estimate turbulent transport between vertical
layers; howeve^, in that model, this parameter is calculated internally rather
than being input from a preprocessor program.
Another variable input to the LI RAG model, but not to the SAI model,
is the atmospheric transmissivity coefficient. This coefficient is a mea-
sure of the effect of clouds, aerosol, and atmospheric scattering on the
amount of solar radiation that is available for photodissociation reactions.
Gridded values of this variable are interpolated from pyranometer station
data. We note that the effects of light scattering on the photolysis rate
constants are treated internally in the SAI model.
There are also some meteorologically-related data that are input to the
SAI model, but not to the LIRAQ model. Chief among these inputs is the top
of the modeling region. For the LIRAQ model, the mixing height is also used
as the height of the grid cells, whereas the SAI model allows the height of
the top of the modeling region to be different from the mixing height. The
height of the region can be a function of the mixing depth, can vary accord-
ing to some other criteria, or can be constant for the entire grid. The
choice usually depends on the importance and height of elevated point source
emissions, the existence of strata of pollutants within the inversion, and
the type of simulation to be performed (i.e., single daylight period or
multiple-day run).
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Zti
Studies in smog chambers indicate that ozone formation is dependent on
temperature. This dependence has been quantified by characterizing the tem-
perature dependence of individual reaction rate constants through the use of
the Arrhenius relationship. To employ this relationship, it is necessary to
input values of the reaction rate constant at some reference temperature and
the value of the activation energy for the reaction. Both models include
provisions for treating this temperature effect, but the LIRAQ model pro-
vides for only one temperature to be input for an entire simulation, whereas
the SAI model provides the option of employing a spatially and temporally
varying temperature field. Basically, the user must prepare a file contain-
ing gridded surface temperature inputs. If a temperature file is not used,
then the value of the rate constants at 25°C are employed in the chemistry
routine. The gridded surface temperature data are used as an estimate of
the temperature throughout each column of grid cells. This process is
straightforward, though the addition of synthesized data may be necessary
to obtain realistic gridded surface fields, especially if part of the region
is covered by a body of water.
Tne SAI model also requires the values of five variables that are varied
temporally but not spatially: the atmospheric pressure, concentration of water
vapor (derived from humidity data), temperature gradient above and below the
inversion base, and exposure class. The temperature gradients are used in
the calculation of the plume rise for large point sources and as an indica-
tion of the atmospheric stability of the air above the lower layer of grid
cells. These gradients are calculated from the vertical temperature pro-
files. The exposure class is a measure of the solar insolation, and it is
used to calculate the atmospheric stability within the lower layer of cells.
3. Chemistry Inputs
Although the rate constants and activation energy for each nonphotolysis
chemical reaction are input to the models, they differ from the other inputs
because they are specific to the mechanism rather than dependent upon the
region and the date of the simulation. In general, the rate constants
are an integral part of the chemical mechanism, and therefore, any single
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29
rate constant should not be updated or changed without analyzing the effect
of the change on the overall performance of the entire mechanism at various
hydrocarbon and NO concentration levels.
A
The two models differ as to the amount of information used to estimate
the photolysis rate constants. The SAI input is the NCL photolysis rate
constant' at set times, usually one-hour intervals. Interpolation is used
to calculate the photolysis rate constant at each integration time step,
and the other photolysis rate constants are assumed to be proportional to
this value. The LIRAQ input files include a table of photolysis rate con-
stants versus the cosine of the zenith angle for all nine of the photodis-
sociation reactions in the LIRAQ mechanism. At each time step, the zenith
angle is calculated by the model, and this table is used to obtain the nine
photolysis rate constants. This technique produces a more accurate
temporal variation of the individual rate constants than does the
SAI methodology.
4. Initial Conditions
The pollutant concentrations at the start of a simulation must be input
to both grid models. The initial concentration has to be specified for each
grid cell and for each species. Local air quality management districts usu-
ally monitor the concentrations of NO, NO^, 03, CO, and hydrocarbons as well
as S0? and particulates at tir.es. Their data are usually reported as 1-
hour or 24-hour averages. Both models use interpolation procedures and the
available monitoring data to derive initial concentration fields for those
species for which there are sufficient data.
The schemes used to contruct the initial concentration fields from the
measurements are somewhat similar for the LIRAQ model and the Airshed Model.
In LIRAQ, the measured surface concentrations at the start of the simulation
are converted to vertically averaged values through the use of Eq. (5) on page 6.
These average concentration values are then employed in an inverse distance
weighted interpolation scheme to calculate the vertically averaged initial
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30
concentration for each grid cell. In the SAI model, the surface observations
are used directly in a similar interpolation algorithm to estimate the initial
concentrations in each ground-level grid cell.
The SAI model requires the initial concentration at every grid level,
but the interpolation routine calculates only surface concentrations. A few
options have been included in the data preparation programs for calculating
the initial concentrations in grid cells above the surface layer. If desired,
a different method can be used for each species. Possibilities include using
exactly the sane concentrations for the upper layers as for the surface layer,
or inputting a vertical profile, that is scaled according to the surface con-
centration or according to the surface concentration and the boundary concen-
tration at the top of the region. The vertical profile can be related to the
mixing depth such that the profile will always have the same value at the tot
of the mixed layer no matter how the height of the mixed layer might vary over
the modeling region at the start of the simulation.
An important computational difference between the routines is that
the LIRAQ routine uses the boundary conditions as well as the station
observations in the interpolation scheme. Other minor differences exist
in the actual equations and the treatment of "barriers," such as mountains.
Both methods contain provisions for employing synthesized data to supple-
ment the data bases.
Measurements 'for some pollutants are not always available. Some
species, such as S02, may not be measured, though they are known to exist
in the atmosphere at measurable (but low) concentrations. For these species,
initial concentrations are often set to some nominal background level.
In addition, ambient measurements for some of the products of photochemical
reactions for which there are no standards are rarely available in
urban areas. Since most simulations start just before or just after dawn,
the initial concentrations of this class of species would be expected to
be very low. Zero or near zero (to avoid division by zero) concentrations
are used for these species.
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5. Boundary Conditions
The boundary conditions* specify the concentration of pollutants in the
air entering the modeling region through the side as a result of horizontal
advection or through the top of the region as a result of vertical advection
and entrainnent caused by changes in the region height. The inputs to
the SAI model specify time varying boundary concentrations along the region
edges and at the top of the region. The concentrations along each boundary
are independent; furthermore, it is even possible for the concentrations to
vary spatially along a boundary segment if a given situation warrants the
increased detail. Measurements taken at locations just inside or outside
the region can aid in estimating the boundary values. If no data are available,
background concentration levels or some other suitable values can be used.
Pollutant concentrations at the top of the region are even harder to esti-
mate, though special field studies are sometimes carried out (such as, in
Los Angeles, St. Louis, Denver, and other cities) that yield information
pertaining to the pollutant concentrations aloft. Again, if no data are
available, one can assume the presence of background levels or some other
appropriate values. However, the edge and aloft boundary conditions may be
influenced by large upwind sources or an upwind urban area. If this is the
case the boundary conditions could have a significant effect on the pollutant
concentrations within the modeling region, and an accurate specification of
these boundary concentrations is important. The time scale over which the
boundary conditions vary is usually an hour, but this time period can be
changed to fit each particular application.
The LIRAQ boundary conditions are treated differently. In that model,
boundary conditions are established using the following equation:
CB . (C0 *. A/'"2
where CD is the boundary concentration, C is the background concentration,
B 0
and C is the concentration computed by the model for the cell adjacent to the
3
* In this section we omit the vertical boundary condition applied at the
surface of the models. Basically, emissions, surface uptake, and pol-
lutant transport from the microscale layer (if this option is exercised)
are combined to yield a pollutant flux into the lowest layer of grid cells.
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32
boundary. The parameter 6 is set to a value between 0 to 1. Both CQ and 6 are
specified by the user for each boundary and are held constant throughout the
simulation. This technique does not allow the user to specify the diurnal
variation of boundary concentration that might be expected if there were large
upwind sources outside of the modeling region. Such a situation, which may
exist in some eastern cities, could be handled in the SAI model.
We note that if the air is flowing out of the modeling region at some
point on the boundary, then each model simply allows the material in the cell
adjacent to the boundary to advect out of the region.
6. Other Inputs
The differing model formulations and assumptions lead to different
input requirements. This section will discuss those additional inputs that
are needed by either the LIRAQ model or the SAI Airshed Model.
The ' IRAQ model discounts any emissions from a grid square in which
the land is 25 meters above the regionally interpolated inversion height;
therefore, the emissions from areas such as mountain tops that break through
the inversion base do not affect the pollutant concentrations in the grid cell
above that area. (There must be a cell for every grid square, even if the
mixing depth is zero. A minimum height of 50 meters is used.) The MASCON
program calculates those areas that lie above the mixed layer according to
the meteorological inputs and the average elevation of each grid square.
These topographic data are contained on the LIRAQ file QGEO, which is
calculated from the U.S. Geological Survey tapes or maps for the region. The
file QGEO also contains other map data used in the LIRAQ plotting routines,
including information pertaining to the shoreline, river courses, political
boundaries, and measurement station locations. Topographical data are not
input directly to the simulation portion of the SAI model, but if the wind
model is used, this information is needed to calculate the wind field. In
addition, topographical data are often used in the preparation of mixing depths.
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33
The SAI inputs include an optional file, TERRAIN, which describes two
surface characteristics—the surface roughness and a surface deposition
factor. The surface deposition factor is a scaling factor representing
the ratio of the average surface uptake velocity for a grid square to that
of alfalfa. This factor, which is indenendent of the pollutant, depends upon
the relative amounts of vegetation and man-made surfaces in the grid
square. For example, trees have been assumed to have a greater capacity for
removing pollutants than grasses, and concrete and asphalt have been assumed to
have almost no capacity for uptake of pollutants. Both the surface rough-
ness and the deposition factor can be estimated fro^ land use information.
If gridded values cannot be estimated for these two variables, then a single
value is used for each variable for the entire grid.
D. MODEL OUTPUT
Since the oxidant standard is based on one-hour average concentrations,
the models calculate one-hour averages for each hour of the simulation for
each species and each grid cell. The instantaneous concentrations at any
time are also available, but they are usually employed only for diagnosing
problems that have arisen in a simulation. The hourly average concentration
grids constitute the basis of all the output options. The simplest forrr, of
output, though not the easiest to use, is a printout of the concentrations in
grid format as shown in Figure 1. This type of output provides the maximu-
amount of information regarding the computed ground-level concentration
field at each hour.
Comparison of the model predictions with the actual station observa-
tions is usually of interest for assessing model performance. The LIRA.:
model uses the calculated concentrations within the grid square in which
the station is located for the comparison. The SAI model interpolates
between the four surface grid cells closest to the station to calculate a
predicted concentration for station comparisons. The observed and pre-
dicted concentrations can be tabulated by hour or can both be plotted versus
time on the same graph. These plots show how well the model reproduces
-------
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riOURE 1. EXAMPLE OF A PRINTED MAP OF GROUND LEVEL CONCENTRATION PREDICTIONS PRODUCED BY THE
SAI AIRSHED MODEL. Averaqe qrnund-level 03 concrntrations (pphm) are qiven for Los
Anqeles on 1 Auqust 1975 hpfwopn 1:00 and 2:00 p.m. PST.
CO
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35
the observed diurnal variation of pollutant concentrations and readily
indicate any discrepancies between computed and measured values. Such
plots can be produced automatically by the LIRAQ model; an example is
given in Figure 2.
To quantify further the model's performance, the station observations
and predictions can be statistically analyzed. A statistical package is
currently available for the LIRAQ model that calculates the mean value,
standard deviation, rms error, and the correlation coefficient for the set
of observations and predictions at each station.
The most illustrative presentation of the results is isopletn plots.
These plots show the regional pattern of the contours of pollutant concen-
trations with the station locations and other geographical information
included for reference. Again, this type of plot can be prepared auto-
matically by the LIRAC model. Figure 3 is a typical exanple of one such plot
prepared for the San Francisco application.
At the present time, the graphical and statistical programs for display-
ing the output of the SA1 model have not been documented and formally included
in the computer codes delivered to the EPA. However, these programs have
been employed in previous Airshed Model applications. Examples of station
and contour plots are shown in Figures 4 and 5, respectively. In addition,
a statistical package is currently being developed by SAI to aid in the
analysis of the model results.
-------
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SURFACE
CORRELATION COEFF « 0.93
CSAMPLE SIZE - 161
MODEL OBS
MEAN ^.3E»00 3.9E*00
STD DEV ««.3E*00 3.6E*00
RMS ERROR = I.6?6E*00
« a
TIME (PACIFIC STANDARD)
STATION DSL - SAN LEANDRO
VTBI »VO
FIGURE ?. AN FXAMPLE OF THE STATTf™ PIOTS PRnnUCEO BY THE LIRAQ
rr>
-------
SURr CONCEN CONTOURSOF
TIME
10: 0.
ML" n 1971
OZONE
• eooar-ei
• IOOOC-OF
INTfHVAL 9 OOOOC-OJ
tl SCALING I OOOOOOO
CCW.E* 9 • m
I
FIGURE 3. AN EXAMPLE OF THE ISOPLETH PLOTS PRODUCED BY THE LIRAQ MODEL. The numbers
in the boxes refer to the observed concentrations and have been superimposed
on the computer qenerat.ed qraphical output.
-------
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BBSERVCD
PREDICTED
6 12 IB
TtNt INflURS)
60
SO
12
- 0RSHRVCO
- PRIOICHO
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SO
90
FIGURE 4. FXAMPLE OF PLOTS GENERATED BY THE SAI GRAPHICS PACKAGE ILLUSTRATING COMPUTER AND ACTUAL
MEASURED CONCENTRATIONS. Ozone concentrations measured at two stations in the Los
Angeles area on 4 August 1975 are compared with the corresponding concentrations
calculated by the Airshed Model.
to
no
-------
NVWTN
vXv.vl'yXv.v.vXv.
0 10
Source: Tcsche and Burton (1978).
30
SiUTH
FIGURE 5. EXAMPLE OF A PLOTTED CONTOUR Mflp np GROUND-LEVEL CONCENTRATION PREDICTIONS
PRODUCED BY THE SAI GRAPHICS PACKAGE. Average ground-level 0-j concentrations
(pphm) are given for Los Angeles on 4 August 1975 between 1:00 and 2:00 p.m. PST.
. .>
u ,
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40
REFERENCES
Anderson, G. E., et al. (1977), "Air Quality in the Denver Metropolitan
Region: 1974-2000," EPA-908/1-77-002, Systems Applications, Incor-
porated, San Rafael, California.
Boris, J. P., and D. L. Book (1973), "Flux Corrected Transport. I. SHASTA,
an Algorithm That Works," J. Comp. Phys., Vol. 11, pp. 38-69.
Briggs, G. A. (1971), "Plume Rise: A Recent Critical Review," Nuclear
Safety, Vol. 12, pp. 15-24. ~~
Dickerson, M. H. (1978), "MASCON--A Mass Consistent Atmospheric Flux Model
for Regions with Complex Terrain," J. Appl. Meteor., Vol. 17, No. 3,
pp. 241-253.
Duewer, W. H. (1977), "Suggested Revision of the LIRAQ Hydrocarbon Emissions
Inventory," Memorandum, Lawrence Livermore Laboratory, Livermore,
California
Duewer, W. H., M. C. MacCracken, and J. J. Walton (197E), "The Livermore
Regional Air Quality Model: II. Verification and Sample Application
In the San Francisco Bay Area," J. Appl. Meteor., Vol. 17, No. 3,
pp. 273-311.
Duewer, W. H., et al. (1978), "Livermore Regional Air Quality (LIRAQ)
Model Application to St. Louis, Missouri," UCRL-52432, Lawrence
Livermore Laboratory, Livermore, California.
Gear, C. W. (1971), "The Automatic Integration of Ordinary Differential
Equations," Comm. A.C.M.. Vol. 14, No. 3, pp. 176-179.
Hecht, T. A., J. H. Seinfeld, and M. C. Dodge (1974), "Further Development
of a Generalized Kinetic Mechanism for Photochemical Smog," Environ.
Sci. Techno!., Vol. 8, pp. 327-339.
Killus, J. P., et al. (1977), "Continued Research in Mesoscale Air Pollution
Simulation Modeling--Vol. V: Refinements in Numerical Analysis,
Transport, Chemistry, and Pollutant Removal," EF77-142, Systems
Applications, Incorporated, San Rafael, California.
Liu, M. K., and J. H. Seinfeld (1975), "On the Validity of Grid and Tra-
jectory Models of Urban Air Pollution," Atmos. Environ., Vol. 9,
pp. 555-574.
Liu, M. K., D. C. Whitney, and P. M. Roth (1976), "Effects of Atmospheric
Parameters on the Concentration of Photochemical Pollutants,"
J. Appl. Meteorol., Vol. 15, pp. 829-835
-------
MacCracken, M. C. (1975), "User's Guide to the LIRAQ Model: An Air
Pollution Model for the San Francisco Bay Area," UCRL-51983,
Lawrence Livermore Laboratory, Livermore, California
MacCracken, M. C.,-et al. (1978), "The Liver-more Regional Air Quality
Model: I. Concept and Development." J. Appl. Meteor., Vol. 17,
No. 3, pp. 254-272.
MacCracken, M. C., and G. D. Sauter, eds (1975), "Development of an Air
Pollution Model for the San Francisco Bay Area, Final Report,"
UCRL-51920, Vols. I and II, Lawrence Livermore Laboratory, Livermore,
California.
Reid, L. £., and S. D. Reynolds (1979), "The Conversion of LIRAQ Inputs to
SAI Airshed Model Inputs," EF79-30, Systems Applications, Incorporated,
San Rafael, California.
Reynolds, S. D., J. H. Seinfeld, and P. M. Roth (1973), "Mathematical Model-
ing of Photochemical Air Pollution--!. Formulation of the Model,"
Atmos. Environ., Vol. 7, pp. 1033-1061.
Reynolds, S. D., T, W. Tesche, and L. E. Reid (1979), "An Introduction
to the SAI Airshed Model and Its Usage," EF78-53R4-EF79-31, Systems
Applications, Incorporated, San Rafael, California.
Reynolds, S. D., et al. (1979), "Photochemical Modeling of Transportation
Control Strategies, Vol. I. Model Development, Performance Evaluation,
and Strategy Assessment," FHVIA-RD-78-173, Systems Applications, Incor-
porated, ban Rafael, California.
(1976), "Continued Research in Mesoscale Air Pollution Simulation
Modeling--Volume II: Refinements in the treatments of Chemistry,
Meteorology, and Numerical Integration Procedures," EPA-600/4-76-016b,
Systems Applications, Incorporated, San Rafael, California.
(1974), "Mathematical Modeling of Photochemical Air Pollution--
Ill. Evaluation of the Model," Atmos. Environ., Vol. 8, pp. 563-596.
_ (1973), "Urban Airshed Photochemical Simulation Model Study,"
EPA-R4-73-030, Systems Applications, Incorporated, San Rafael,
California.
Roth, P M., et al. (1974), "Mathematical Modeling of Photochemical Air
Pollution—II. A Model and Inventory of Pollutant Emissions," Atmos.
Environ.. Vol. 8, pp. 97-130.
Sutton, 0. G. (1953), Wcj^teorqlosy. (McGraw-Hill, New York, New York).
Tesche, T. W., and C. S. Burton (1978), "Simulated Impact of Alternative
Emissions Control Strategies on Photochemical Oxidants in Los Angeles,
EF78-22R, Systems Applications, Incorporated, San Rafael, Can forma.
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TECHNICAL REPORT DATA
(Please read Inunctions on the reverse before completing)
1 Rl J;^f*T NO
EPA-450/4-79-036
J. Tilt.I ANL1 SUBTITLE
Application of Photochemical Models
Volume IV: A Comparison of the SAI Airshed Model and the
L.IRAQ Model
7 AUTHORISI
Wada, Ronald Y., et al.
3. RECIPIENT'S ACCESSION-NO.
5. REPORT DATE
1 Q7Q
6. PERFORMING ORGANIZATION CODE
B. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Association of Bay Area Governments
Hotel Claremont
Berkeley, California 94705
10. PROGRAM ELEMENT NO.
2AA635
11. CONTRACT/GRANT NO.
68-02-3046
12. SPONSORING AGENCY NAME AND ADDRESS
13. TYPE OF REPORT AND PERIOD COVERED
U. S. Environmental Protection Agency
Office of Air Quality Planning and Standards
Research Triangle Park, North Carolina 27711
14. SPONSORING AGENCY CODE
16. SUPPLEMENTARY NOTES
16. ABSTRACT
This document compares the technical features of the SAI Airshed Model with the Liver-
more Regional Air Quality (LIRAQ) Model. These two state-of-the-art photochemical
dispersion models are compared according to their theoretical formulation, com-
ponents, inputs, and outputs. The model components compared include horizontal
transport, vertical transport, emissions, chemistry, and numerical solution pro-
cedures .
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b IDENTIFIERS/OPEN ENDED TERMS C. COSATI Field/Group
Photochemical Modeling
SIP Development
IS. DISTRIBUTION STATEMENT
RELEASE UNLIMITED
19. SECURITY CLASS (ThisKtporl/
Unclassified
21. NO. OF PAGES
2O
This page/
22. PRICE
EPA Form 2220-1 (»-73)
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