United States
Environmental Protection
Agency
Environmental Sciences Research
Laboratory
Research Triangle Park NC 27711
*
Research and Development
EPA-600/S3-83-035 July 1983
Project Summary
A Regional Scale Model
(1000 km) of Photochemical
Air Pollution: Part 1.
Theoretical Formulation
Robert G. Lamb
A theoretical framework for a multi-
day, 1000-km scale simulation model
of photochemical oxidant is developed.
It is structured in a highly modular
form so that eventually the model can
be applied through straightforward
modifications to simulations of par-
ticulates, visibility and acid rain.
The model structure is based on
phenomenological concepts and con-
sists of three and one-half layers. The
interface surfaces separating the layers
are functions of both space and time
that respond to variations in the mete-
orological phenomena that each layer
is intended to treat. Among the physi-
cal and chemical processes affecting
passage and distribution of photo-
chemical concentrations that the model
is designed to handle are: horizontal
transport, photochemistry, nighttime
wind shear and the nocturnal jet;
cumulus cloud effects; mesoscale ver-
tical motion; mesoscale eddy effects;
terrain effects; subgrid scale chemis-
try processes; natural sources of hy-
drocarbons, NOX, and stratospheric
ozone; and wet and dry removal pro-
cesses, e.g., washout and deposition.
The predictability of pollutant con-
centrations at long range is considered,
along with such related problems as
the parameterization of "mesoscale"
diffusion andthe design of model "vali-
dation" experiments. A basis is estab-
lished for estimating quantitatively the
levels of uncertainty associated with
dispersion model predictions.
This report focuses on theoretical
aspects of the model and the question
of predictability. Results of the model's
performance and quantitative assess-
ments of its predictability will be pre-
sented in subsequent parts of this
report
This Project Summary was developed
by EPA's Environmental Sciences Re-
search Laboratory, Research Triangle
Park NC, to announce key findings of
the research project that is fully doc-
umented in a separate report of the
same title (see Project Report ordering
information at back).
Introduction
This project was begun in 1977 with
the objective of developing a model for
guiding the formulation of regional emis-
sions control strategies. Initially the prin-
cipal concern was with the photochemical
oxidant; but in the course of its develop-
ment, the model was constructed in a
highly modular form that would allow
straightforward applications to fine par-
ticulates, visibility, and, possibly, acid
deposition as well.
When this project was begun, there did
not exist an air pollution model that could
simulate all the physical and chemical
phenomena that are believed to control
the fate of photochemical pollutants over
large time and space domains. Among
these phenomena are (not necessarily in
order of importance):
' 1) Horizontal transport
2) Photochemistry, including the very
slow reactions
3) Nighttime chemistry of the products
and precursors of photochemical
reactions
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4) Nighttime wind shear, stability stra-
tification, and turbulence " episodes"
associated with the nocturnal jet
5) Cumulus cloud effects. Venting
pollutants from the mixed layer,
perturbing photochemical reac-
tions rates in the shadows, provid-
ing sites for liquid phase reactions,
influencing changes in the mixed
layer depth, perturbing horizontal
flow
6) Mesoscale eddy effects on urban
plume trajectories and growth rates
7) Terrain effects on horizontal flows,
removal, diffusion
8) Subgrid scale chemistry processes
-- resulting from emissions from
sources smaller than the model's
grid can resolve
9) Natural sources of hydrocarbons,
NOX, and stratospheric ozone
10) Wet and dry removal processes,
e.g., washout and deposition
A necessary condition for the credibility of
a long range transport model is that all of
these phenomena be taken into account,
at least until it has been demonstrated that
some of these processes play a negligible
role.
Of similar concern are several questions
regarding fundamental aspects of modeling
itself. Following are three questions that
are relevant not only to the utility of
pollution models in regulatory, decision-
making roles, but also to the meaningful
implementation of the model itself.
(1) What aspects of pollutant concen-
trations are models capable of pre-
dicting?
(2) Given our present state of knowledge,
what are the theoretical limits on the
accuracy with which these quantities
can be predicted (assuming perfect
emissions data chemical information,
etc.)?
(3) How does one assess the accuracy
of a given model?
These questions must be resolved before
a model can be verified or used in any
meaningful way.
Procedure
In order to design a viable model frame-
work consistent with all the anticipated
applications noted above, an attempt was
made to derive from the observational
evidence available at the time this program
was initiated an estimate of the minimum
vertical and horizontal resolutions neces-
sary to describe regional scale air pollution
phenomena. The aim was to arrive at the
best compromise between the restrictions
imposed upon the model by computer
time and memory limitations and the need
to describe as accurately as possible all of
the important physical and chemical pro-
cesses. The NO, 03, and meteorological
data reported by the participants of the
1975 Northeast Oxidant Transport Study
were analyzed and it was concluded that to
describe the phenomena revealed by those
data would require at the very least a three-
level model: one level assigned to the
surf ace layer, another layer assigned to the
remainder of the daytime mixed layer, and
an additional layer atop the mixed layer.
The top level would be used in conjunction
with the mixed layer to account for down-
ward fluxes of stratospheric ozone as well
as upward fluxes of ozone and its pre-
cursors into the subsidence inversion layer
above. Material that entered this top layer
could be transported by winds aloft to
areas outside the modeling region; it could
reenter the mixed layer by subsidence or
entrainment; it could enter precipitating
clouds and be rained out of the atmosphere;
or it could undergo chemical transforma-
tion. Representing the subsidence inver-
sion, where cumulus clouds often form
under stagnant high pressure conditions,
the top level of the model would be in-
strumental in simulating the chemical sink
effects of heterogeneous (within cloud
droplets) reactions among ozone, its pre-
cursors, and other natural and pollutant
species. Including cloud effects in the
model would be especially important in
simulating S02 and sulfates. An extra
"half layer" would be necessary adjacent
to the ground to parameterize dry deposi-
tion and subgrid scale chemistry processes
induced by point and line sources of
pollutants.
Having three layers in a model is insuf-
ficient in itself to simulate the phenomena
we have discussed above. The need is,
rather for three "dynamic" layers that are
free to expand and contract locally in
response to changes in the phenomena
being modeled The model developed in
this program possesses these properties.
The surfaces that comprise the interfaces
of adjacent layers are variable in both
space and time in order that each layer can
fully account for the changes that occur in
its own domain of phenomena. Working
in concert, the model's three and one-half
layers can effect the simulation of all of the
phenomena cited above.
To address the questions of what models
are capable of predicting, how accurately
they can predict given variables and how
one would proceed to verify the validity of
a model, we considered the basic problem
of model formulation from the viewpoint
of fundamental mathematical principles.
The aim was to delineate in mathematical
terms the nature of the statements that
one can deduce about natural phenomena,
such as air pollutant concentrations, given
descriptions of the universal laws govern-
ing those phenomena and values of the
parameters, in terms qf discrete observa-
tions, involved in those laws.
Conclusions
Special numerical techniques were de-
veloped to meet the rather unique needs of
this model. One of these techniques is a
high-order, explicit differencing scheme
that suppresses errors in the advection
and diffusion simulation that the nonlinear
chemical processes would amplify. This
scheme also permits the model domain to
be handled in a piecewise fashion. Without
this capability, awkward, inefficient com-
puting procedures would be required to
operate this large model on EPA's UNIVAC
computer. Tests of this numerical method
showed that its performance is superior in
a number of important respects to that of
existing alternative algorithms.
Another special numerical technique
developed for this project is a scheme that
allows the set of nonlinear differential
equations that describe air pollution chem-
istry to be handled in their full form rather
than in pseudosteady-state form. Coupling
of the chemistry with the vertical fluxes of
material among the model's three layers is
accomplished with the aid of still another
new algorithm that is computationally stable
over virtually an infinite range of parameter
values. Tests of these two numerical
schemes showed that they provide an
acceptable level of accuracy in much less
computation time than alternative methods.
The mathematical analyses of predicta-
bility, model accuracy, and validation pro-
cedures showed that physical laws anc
discrete descriptions of atmospheric vari-
ables are insufficient to define uniquely
such variables as pollutant concentration
distributions. As a consequence, even il
all data used in the model were precise and
the mathematical equations that describe
the governing physical laws could be solvec
exactly, a model still could not predict the
concentration that would occur at a giver
place at a given time. Rather, it coulc
prescribe only a range of values in which
the observed value would fall. Thus, the
utility of a model in a given application is
determined by the width of this interval o
possible values. An ongoing aspect of this
research program is to quantify the predic-
tability of pollutant concentrations as £
function of averaging time, distance be-
tween the source and receptor, the pol-
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lutant species, meteorological conditions,
and other relevant parameters. Results of
this work will be presented in a future
report.
The EPA author Robert G. Lamb is with the Environmental Sciences Research
Laboratory. Research Triangle Park, NC 27711.
The complete report, entitled "A Regional Scale (1000 km) Model of Photo-
chemical Air Pollution: Part 1. Theoretical Formulation," (Order No. PB 83-207
688; Cost: $20.50, subject to change) will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield. VA 22161
Telephone: 703-487-4650
The EPA author can be contacted at:
Environmental Sciences Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
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