United States
Environmental Protection
Agency
Environmental Monitoring Systems
Laboratory
Las Vegas NV 89114
Research and Development
EPA-600/S4-81-012 Apr. 1981
Project Summary
Optimum Meteorological and
Air Pollution Sampling
Network Selection in Cities:
Volume III. Objective
Variational Analysis Model
Walter D. Bach, Jr. and Fred M. Vukovich
This report is the third in a series of
reports on the development and appli-
cation of a procedure to establish an
optimum sampling network (OSN) for
ambient air quality in urban areas. In
the first report, the theoretical aspects
and the model algorithms for the
procedure and an optimum network
for St. Louis were presented (EPA-
600/4-78-030). The results of the
comparison of the wind field obtained
from the optimum network in St.
Louis and that obtained from all .avail-
able data were described in the second
report (EPA-60O/4-79-069). This
report discusses the development and
application to St. Louis of the Objec-
tive Variational Analysis Model which
is used to provide the air pollution
distribution.
The OSN technique provides an
objective method to develop a sampling
network for air pollution and meteor-
ological parameters that will yield a
representative distribution of those
parameters within the domain of the
network. Though the technique has
been used to develop an entire network,
probably the greatest utilization of the
technique can be in improving an
existing network in a given urban area.
Most urban areas already have a sam-
pling network and would not want to
undertake the economic burden to
establish a new network.
This Project Summary was devel-
oped by EPA's Environmental Moni-
toring Systems Laboratory, Las Vegas,
NV, to announce key findings of the
research project that is fully docu-
mented in a separate report of the
same title (see Project Report ordering
information at back).
Introduction
The research was motivated by the
realization that the cost of implementing
an air sampling network within budget-
ary constraints of a control agency may
result in fewer stations than desirable,
but the stations must be adequate for
the task in the present and future.
Conventional networks are often de-
signed to monitor specific sources or
concentration characteristics of a sub-
section of an urban area. With separate
source distributions for each pollutant,
a good site for one pollutant may not be
a good site for another. As sources are
added or deleted, the monitoring re-
quirements change. As stations are
moved, valuable time histories of pol-
lutants are lost.
Objective
This study takes the approach that
knowledge of the wind distribution
about the urban area should give a
principal guidance for design of a net-
work for air quality monitors. Distribu-
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tion of pollutants is controlled primarily
by the source distribution and the
meteorological conditions. Sources and
source distributions change as the
urban area changes, but the wind
characteristics are not a function of the
source and should remain relatively
unaffected by source changes. Thus, by
having a sampling network that will
accurately depict the distribution of
winds about the urban area, the distri-
bution of pollutants should followf rom a
knowledge of the source distribution.
The approach involves six steps.
Though, in the initial case, the tech-
nique was employed in St. Louis, Missouri,
the algorithms are generalized and can
be applied to any urban region. The six
steps are:
(1) A three-dimensional hydrodynamic
model was developed to generate
simulated wind fields for the urban
area under a variety of initial
meteorological conditions.
(2) A statistical model was chosen
from a class of statistical model
forms, relating wind to geographic
location and topography and giving
a reasonable approximation to the
simulated results for any of the
initial conditions.
(3) A site-selection methodology (back-
ward elimination) was developed,
and an optimum set of sites for
monitoring winds was selected
using the methodology and the
statistical model.
(4) An OSN was developed for St.
Louis, and wind and air quality
monitoring stations were estab-
lished at the indicated sites.
(5) Wind fields were created by fitting
statistical models (based on the
class of forms determined in step
2) to the observed data, and the
predicted data were compared to
observed data.
(6) An objective variational analysis
model was developed and tested
for estimating the pollution distri-
bution for an area by combining
the emissions inventory, the ob-
served pollutant concentrations,
and the estimated wind fields.
With minor modifications resulting
from practical and economic constraints,
the first four steps above have been
completed for the St. Louis area as
described in the first report (Vol. I).
Results of the comparison of the wind
field obtained from the OSN to that
obtained from all available data were
described in the second report (Vol. II).
Volume III discusses the development
and application of the Objective Varia-
tional Analysis Model (OVAM) to St.
Louis for the pollutant carbon monoxide
(CO).
The Model
The OVAM obtains an analysis of air
quality in an area by solving a Euler-
Lagrange equation that minimizes the
weighted error variance between the
analysis and observations and between
the analysis and the solution from the
mass continuity equation (the analysis
being assumed to be in a steady-state).
In this manner, the source inventory
serves as another set of observations,
allowing the analysis to have a greater
order of variability than is possible using
the observations alone.
Methodology
The OVAM was adapted for field data
and applied to the CO concentrations
obtained from the OSN for St. Louis for
selected days in the August 1975 and
February 1976 periods of intensive
study by the Regional Air Pollution
Study (RAPS) program. Measurements
of CO concentrations and winds at the
19-station OSN and CO emissions
inventory were used to estimate the
concentrations in a 20-km square area
centered about the city. Seven additional
nonnetwork stations were available for
verification. Four cases, totaling 26
hours, were selected for study. Cases
were chosen on the basis of wind speed
and of the pollutant concentration
magnitudes. Initialization of the OVAM
was accomplished by utilizing the CO
data from the 19-station OSN and an
objective analysis model (the Barnes
method). The OVAM, essentially, ad-
justed the initial field to conform simul-
taneously with the observations, the
transport associated with the wind
distribution, and the emissions inven-
tory.
Methodologies to incorporate point
sources were developed. Studies of the
sensitivity of the analysis to various
user-defined parameters were conducted.
Afterwards, the model was applied to
the case studies and an error analysis
was applied. Finally, tests were made to
determine whether all 19 stations in the
OSN needed to monitor CO. The results
of these studies are described below.
The principal parameters in the OVAM
were the weights which placed emphasis
on an observation (if the grid point was
near an observation point) or the con-
tinuity equation (if the grid point was not
near an observation point); the radius of
influence which defined how rapidly the
value of the weight related to the
observation decreased away from a grid
point associated with an observation;
and the depth of volume over which the
OVAM determines an analysis. The
OVAM analysis was particularly sensi-
tive to the ratio of the weights for the
observations and the continuity equa-
tion, but was insensitive to the radius of
influence of the observations. For the
OVAM, the grid spacing (1 km) was a
practical lower limit to the radius of
influence since it was half the resolvable
spatial scale in the model. However,
other RAPS studies have shown ob-
served CO concentrations to often be
highly variable on a scale of about 1 km,
suggesting that a smaller radius of
influence should be utilized. The OVAM
analyses became smoother and less
sensitive to the emissions as the depth
of the volume in the model increased.
Increasing the volume depth, and there-
fore the volume, allowed for a greater
dilution of the emissions. A practical
upper limit to the volume depth might be
the atmospheric mixing height. The
choice of the volume depth was also
important because point sources that
failed to rise above the volume depth
were treated as area sources.
Results and Discussion
Results of the application of the
OVAM to the 12 August 1975 case, a
daytime period with low wind speeds
and small CO concentrations, showed
strong dependence upon the distribu-
tion of sources and winds. Upwind of
the stronger area sources, the concen-
trations tended to decrease; downwind,
they increased. Large percentage
changes between the initial CO distri-
bution and the results from the OVAM
analysis were found in the vicinity of
principal sources. Since concentrations
were on the order of 0.5 ppm, which is
near the practical lower limit for CO
measurements, the percent changes
were relatively meaningless except to
help identify the ongoing processes.
For the 27 February 1976 case, a
nighttime period with large wind speeds
and CO concentrations, the CO emissions
decreased by an order of magnitude,
whereas the concentrations remained
large. The OVAM produced analyses
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hat varied little from the initial distri-
butions. The principal adjustments to
the initial distribution were due to the
boundary conditions and the winds
because the magnitude of the sources
was small.
In order to determine whether all 19
stations in the OSN were required to
monitor CO, two, four, and six observa-
tions were randomly deleted from the
OSN to gain insight into the effect on the
CO analysis. The error variance which
the OVAM attempts to minimize de-
creased by 20 to 30 percent of its initial
value regardless of the number of
stations deleted. However, large per-
cent changes of concentration occurred,
depending upon the location of the
deleted data. In most daytime cases, the
largest changes occurred when obser-
vations upwind or downwind of the
principal source areas were deleted,
and when the deleted observations
were not near other observations which
were near principal sources. Concen-
tration changes were primarily con-
trolled by changes in the initial distri-
bution that resulted from the deleted
observations.
When stations were deleted in re-
gions with small or no emissions (the
outlying regions of the city) and far from
stations influenced by large sources,
the impact was significant in those
regions but relatively insignificant in the
large emissions' areas. The impact of
the deleted stations in the outlying
region was primarily due to the initial
values being different from the obser-
vations, suggesting that if initial condi-
tions can be treated properly in the
outlying regions, some of the stations in
this region would not be required as CO
monitors. Thirteen of the 19 stations
were in such regions; possibly as many
as half of these need not monitor CO,
though they all must monitor the winds.
However, further investigation is re-
quired on the initialization methodology
before conclusive statements can be
made.
The OVAM generally predicted the
trends well but often failed to accurately
predict the absolute magnitudes of CO
concentrations at nonnetwork stations.
In addition to model errors, the discrep-
ancies arose because:
(1) The CO concentrations are often
very source-oriented and sources
were smoothed to a 1 -km square
area by the inventory (the problem
affects all CO data), whereas the
observations are point observa-
tions not necessarily representa-
tive of an area, and
(2) The OVAM values used for com-
parisons were at grid points up to
0.7 km from an observation, and
plumes downwind of principal
sources developed with strong
gradients which may have a slight
influence at the grid point which
actually affects the station, or
vice-versa.
These are shortcomings faced by modelers
and analysts every day.
The OVAM relied upon the initial
conditions generated by another objec-
tive analysis procedure to determine the
initial concentration field. The initiali-
zation technique extended the influence
of an observation over too large an area.
For example, the OVAM analysis for
1300 and 1400 CST 12 August, when
one of the stations did not report,
showed large concentrations in a narrow
plume over and downwind of that station.
At 1500 and 1600 CST, when that
station reported a very large CO concen-
tration, the plume extended over almost
half the southern region of the grid
because the initialization technique
produced an initial field where the
observation at that station dominated
the southern area. The OVAM results
were considerably different from the
observations at many of the other OSN
stations as well as nonnetwork stations.
As part of a test, that station was deleted
at 1500 and 1600 CST and a new set of
initial conditions was developed. These
OVAM results compared more favorably
with both the OSN and nonnetwork
observations at those hours and were
consistent with the analyses at 1300
and 1400 CST. Though part of the
problem in this case resulted from the
data mixture, the difference in the area
influenced by the large sources around
the particular station of interest with
and without the observation at the
station was completely dependent on
the initialization technique.
Conclusions
Except for some improvements needed
for the OVAM, the essential ingredients
for the OSN technique have been devel-
oped and tested, and the test results
have been shown to be reasonable. The
OSN technique provides an objective
method to develop a sampling network
for air pollution and meteorological
parameters that will yield a representa-
tive distribution of those parameters
within the domain of the network.
Though the technique has been used to
develop an entire network, probably the
greatest utilization of the technique can
be in improving an existing network in a
given urban area. Most urban areas
already have a sampling network and
would not want to undertake the eco-
nomic burden to establish a new network.
The site-selection algorithm of the
OSN technique can be altered so as to
maintain certain sites as part of the
improved network (stations in the exist-
ing network). The algorithm would then
establish the minimum number and
disposition of stations to be added to the
existing network in order to determine a
reasonable analysis of the wind field.
The OVAM is, of course, independent of
the network design; but since the wind
field is an input to the OVAM, an
accurate description of the wind field is
necessary. Given the emissions inven-
tory, then the air pollution distribution
can be determined using the OVAM.
Walter D. Bach, Jr. and Fred M. Vukovich are with Research Triangle Institute,
Research Triangle Park, NC 27707.
James L. McElroy is the EPA Project Officer (see below).
The complete report, entitled "Optimum Meteorological and Air Pollution
Sampling Network Selection in Cities: Volume III. Objective Variational
A nalysis Model," (Order No. PB 81 -172 256; Cost: $8.00, 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 Project Officer can be contacted at:
Environmental Monitoring Systems Laboratory
U.S. Environmental Protect/on Agency
P. O. Box 15027
Las Vegas, NV98114
it U.S GOVERNMENT PRINTING OFFICE-1801 -757-012/7082
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