EPA-600/4-81-012
March 1981
OPTIMUM METEOROLOGICAL AND AIR POLLUTION
SAMPLING NETWORK SELECTION
IN CITIES
Volume III: Objective Variational Analysis Model
by
Walter D. Bach, Jr. and Fred M. Vukovich
Research Triangle Institute
P.O. Box 12194
Research Triangle Park
North Carolina 27707
Contract No. 68-03-2187
Project Officer
James L. McElroy
Advanced Monitoring Systems Division
Environmental Monitoring System Laboratory
Las Vegas, Nevada 89114
ENVIRONMENTAL MONITORING SYSTEMS LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
LAS VEGAS, NEVADA 89114
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EPA-600/4-81-012
March 1981
OPTIMUM METEOROLOGICAL AND AIR POLLUTION
SAMPLING NETWORK SELECTION
IN CITIES
Volume III: Objective Variational Analysis Model
by
Walter D. Bach, Jr. and Fred M. Vukovich
Research Triangle Institute
P.O. Box 12194
Research Triangle Park
. North Carolina 27707
Contract No. 68-03-2187
Project Officer
James L. McElroy
Advanced Monitoring Systems Division
Environmental Monitoring System Laboratory
Las Vegas, Nevada 89114
ENVIRONMENTAL MONITORING SYSTEMS LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
LAS VEGAS, NEVADA 89114
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DISCLAIMER
•This report has been reviewed by the Environmental Monitoring Systems
Laboratory, U.S. Environmental Protection Agency, and approved for
publication. Approval does not signify that the contents necessarily reflect
the views and policies of the U.S. Environmental Protection Agency, nor does
mention of trade names or commercial products constitute endorsement or
recommendation for use.
ii
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SUMMARY
This report is the third in a series treating a method for developing
optimum meteorological and air quality networks and the application of the
methodology for St. Louis. (EPA-600/4-78-030 describes the method and the
network for St. Louis and EPA-600/4-79-069 presents an evaluation of the
meteorological (wind field) network for St. Louis.) This particular report
discusses the development and application to St. Louis of the Objective
Variational Analysis Model (OVAM), which is used to provide estimates of the
air pollution distribution.
The OVAM produces an analysis of air quality in an area by solving an
Euler-Lagrange equation that minimizes the weighted error variance between the
analysis and observations and between the analysis and the solution from the
equation of mass continuity. The OVAM was applied to obtain analyses of
carbon monoxide, CO, in the St. Louis area for selected days in August, 1975
and February, 1976, periods of intensive study by the Regional Air Pollution
Study. Measurements of CO concentration and winds at a 19-station optimum
sampling network and the emission inventory were used by the OVAM to estimate
the concentrations in a 20-km square area centered on the city. Four cases,
totalling 26 hours, were selected for detailed study.
Methodologies to incorporate point sources were developed. Studies of
the sensitivity of the analyses to various user-defined parameters showed that
the relative weights given to the observations and to the constraint equation
were the most important factors. The analytical results became smoother as
the depth of the volume increased. The model was insensitive to changes in
the radius of influence of an observation.
The OVAM analyses appeared more consistent with the distribution of
sources and winds than were found using conventional objective analyses,
particularly when emissions were large and consistent with the observations.
Plumes of high concentration appeared downwind of the major sources, except
when observations indicated otherwise. In areas of low emissions, the OVAM
did not change the results significantly. The error variance throughout the
area of analysis decreased by about 25 percent from its initial value. At
night, the •emissions were small compared to the observations and were
insufficient to alter the Initial estimate of the distribution. For these
situations, the effects of adjustments to boundary conditions and advection
p red oml nat ed.
ill
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The GVAK generally predicted the trends v-eil but of uen failed .to
accurately predict the absolute magnitudes of CO concentrations at rionnetwork
stations. In addition to model errors, the discrepancies arose because:
1. 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 observations not
necessarily representative of an area, and
2. OVAM values used for comparisons were at grid points up to 0.7 km
from an observation, and plumes dovmwind 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 consequences of randomly deleting two, four or six observations from
the analyses were investigated to develop guidance as to which, if any, of the
observations could be deleted from the analysis, without significantly
affecting the analysis. This was done to determine if all the stations in the
optimum network needed to monitor CO. The analyses showed the average error
variance reduction did not change, although large percentage changes were
noted in localized sections of -the analyses. Some changes were due to changes
in the initial analysis; other changes (usually increases) were due to the
dominance of the mass continuity equation, where observations, which had been
removed, had previously dominated.
When stations were deleted in regions 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 observations, suggesting that if initial conditions 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 required
on the initialization methodology before conclusive statements can be made.
Though the optimization technique has been used to develop an entire
network, probably its greatest practical utility 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 economic burden to
establish a new network.
iv
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CONTENTS
Page
Summary ill
Figures vi
Tables . vii
Introduction. . . 1
Background 1
Objective variational analysis model 4
Research objectives. 5
Model Development 7
Model equations 7
Study area 11
Point sources. ............... 11
Profile parameter. 11
Aerometric data 14
Objective analysis 14
Relaxation procedure ........... 14
Options 15
Model Applications 18
Selection of cases ....... ....... 18
Model performance. .._. 18
Model sensitivity... 26
Time sequence.-of analyses: 12 August 1975 _ 27
Deletion of observations . ..... 36
Effects: of boundary conditions on analyses 47
Error variance 51
Accuracy estimates ........... 51
Discussion of Results 54
Major findings 54
Limitations and further research 55
Utilization of the OSN technique . 57
References 58
Appendix A.... ........... 60
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FIGURES
i
Number Page j
1 Location of stations in the RTI network and other non-network
stations used in the evaluation in the St. Louis
metropolitan area 3
2 OSN network and OVAM analysis area 12
3 Response of OVAM analysis to point source plume rise above and
below the top of the model, Z 13
4 Ratio of weights, oVa, as a function of ALFA and RAD . 17
5 Hourly CO concentrations at OSN locations 19
6 Wind vectors, area sources, and CO isopleths, August 12, 1975 at
1300 CST 25
7 Isopleths of CO concentration for basic state of sensitivity
analyses and isopleths of percent change from basic state
induced by indicated parameter value 28
8 Spatial cross section of OVAM analysis for sensitivity tests
indicated in key 30
9 OVAM concentration analyses and area emissions by hour for
August 12, 1975 32
10 Time series of observed and interpolated CO concentrations for
indicated number of missing.observations for August 12 39
11 Isopleths of concentration for basic case and percent change
with two, four or six stations deleted, August 12, 1975 41
12 Isopleths of concentration for basic case and percent change with
two, four, or six stations deleted, February 27, 1976 48
13 Time series of CO concentrations for OSN and non-OSN locations
from observations, Barnes interpolation and OVAM analysis with
zero or six stations missing 50
vi
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TABLES
Number Page
1 Parameters of Sensitivity Analysis. 27
2 CO Concentrations Observed and Interpolated by the Barnes and
OVAM for OSN Stations Within the Analysis Grid. . . 37
3 Missing and Deleted Observations, August 12, 1975 38
A Non-Dimensional Error Variance of Analyses. . . 52
vii
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INTRODUCTION
BACKGROUND
The Research Triangle Institute (RTI) has been engaged in a long-term
program with the United States Environmental Protection Agency (EPA) to
develop and test a methodology to determine an optimum sampling network (OSN)
for a major urban area. The research has been motivated by the realization
that the costs of implementing a sampling network within budgetary constraints
of a control agency may result in fewer stations than desirable but that the
stations must be adequate for the task in the present and the future.
Conventional networks are often designed to monitor specific sources or
concentration characteristics of a large subsection of the urban area. With
different source distributions for different pollutants, a good site for one
pollutant may not be good for another. As sources are added or deleted, the
monitoring requirements change. As stations are moved, valuable time
histories of pollutants are lost.
RTI has taken the approach, contrary to conventional applications, that
knowledge of the wind distributions about the urban area should give principal
guidance to the design of a network of air quality monitors. The distribution
of pollutants is controlled primarily by their sources and by the wind speed
and direction. Sources and source distributions change as the urban area
changes, but the wind characteristics are not a function of 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 distribution of pollutants should follow from a knowledge of the
source distribution.
The RTI approach Involves six steps. Though in the initial case, the
technique 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 for the St. Louis urban area.
(2) A statistical model was chosen from a class of statistical model
forms, relating winds to the geographic location and topography and
giving a reasonable approximation to the simulated results for any
of the Initial conditions.
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(3) A site selection methodology was developed, and an optimum set of
sites for monitoring winds was selected using the methodology and
the statistical model.
(4) Wind and air quality monitoring stations were established at the
indicated sites in St. Louis.
(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 model was developed and tested to estimate
pollution concentrations over the area by combining the emissions
inventory, the observed pollutant concentration, and the estimated
wind fields.
With minor modifications resulting from practical and economic constraints,
the first four steps above were completed for the St. Louis area as described 1
in Volume I (Vukovich, Bach, and Clayton, 1978, hereafter referred to as VBC). |
Analysis of the wind field obtained from the OSN (Step 5) was described in j
Volume II (Vukovich and Clayton, 1979). This volume provides the description j
of the development of the objective variational analysis model, its
application, and the results obtained.
The three-dimensional primitive equation model was used to create the
wind field in the St. Louis area over a variety of meteorological conditions. •
These data were used to develop a statistical model to characterize the wind :
field. The statistical model was combined with a backward elimination site
selection technique to produce the OSN. From an initial field of over 500
candidate sites, the resulting OSN had 19 stations.
The major emphasis of the second phase of the research project involved
the preparation and execution of a summer and winter field program in St.
Louis. These field programs were held during August 1975, and February and ?
March; 1976 when EPA was performing intensive studies of the Regional Air j
Pollution Study (RAPS). During this time there was a concerted effort to ;
maintain a high level of performance of the twenty-four RAPS surface
monitoring stations.
Sixteen existing stations in St. Louis were situated near the OSN station ;
locations, and were used as part of the OSN. Four of the existing stations '
were St. Louis city/county air pollution stations and twelve were RAPS |
stations. RTI set up three temporary stations specifically for this research. '
The stations comprising the OSN network and the non-network in the St. Louis j
area are shown in Figure 1.
Following the field program, processed network and non-network wind data i
were used to evaluate the wind field determined from the optimum network. The ;
principal result of that study showed that application of the stepwise >
regression to a 13-term model (the chosen statistical model) with the wind •
data from the 19-station OSN predicted wind fields comparable to those \
obtained by more general procedures, using more terms and a larger network. ' j
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Figure 1. Location of stations in the RTI network (solid dots) and other
non-network stations (open dots) used in the evaluation (interior
grid spacing • 1 km) in the St. Louis metropolitan area.
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This substantiated the results of the theoretical analysis which selected urse
13-term model and the 19-station OSN on the basis that adding terms to the
model and/or stations to the network would not markedly improve the analysis
of the wind field.
OBJECTIVE VARIATIONS ANALYSIS MODEL
Within an urban area, the pattern of pollutant concentrations is not
generally apparent from a set of concentration measurements at fixed
locations. The presence of more sources than sampling stations and the
variability in the wind field often mask the true distribution from those
obtained by conventonal subjective or objective analysis. In conventional
objective analysis, the estimated value of a variable at a given location is
extrapolated/interpolated from observed values of the variable at specified
locations. Cressman (1959) and Barnes (1964) used different distance-
dependent weight functions to interpolate within a given radius of an
observation. Endlich and Mancuso (1968) used an elliptical weight function
oriented along the wind direction and proportional to the wind .speed. These
techniques smooth the distributions and are generally incapable of showing
maxima or minima where there are no observations.
Sasaki (1958, 197Oa, b, c) proposed an analysis technique that uses the
observed variables to produce analysis which is consistent with both the
observations and the model. The technique is based on minimizing the weighted
error variance of 1) the arbitrary variable, <(> , and its observation,^, and 2)
the model equations, E(<|>), over the domain of the integration. The total
weighted error variance, EV, is given by:
r ~ ~:
= J cr() + ctE () is being minimized rather than
E(4>). The distinction is significant since E() is normally zero.
The distribution of $ which minimized the intergral is given by the
solution to the Euler-Lagrange equations (Lanczos, 1970). The equations .
specify the partial differential equation of 4> which .must be satisfied on the
interior of the domain and the boundary conditions. The solution is generally
obtained by numerical integration. • .
Sasaki and Lewis (1970) used the technique to analyze three-dimensional
mesoscale distributions of wind components, temperature, and moisture
associated with severe storms. Stephens (1970) obtained synoptic scale
distributions of pressure height fields consistent with the balance equation.
In those studies, the solution technique acted as a low-pass filter for real
or induced (simulated) errors in the observation field.
Wilkins (1971, 1972) applying the objective variational analysis
principles to urban air pollution analyses, described a method of adjusting a
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p";t«r:. of concentration isopleths using the classical diffusion equation as a
constraint. The technique reduced discrepancies in temporal continuity '
between two successive analyses. Errors arising from misanalysis or from a _!
variable wind field were also considered. Wilkins showed that the analysis '•
error of the sequences of an analysis could be reduced to one-tenth the '
initial error. He also outlined the potential application of the methodology j
as a part of the continuous urban air monitoring surveillance program. j
}'
The approach used in this research project reverts to more basic forms. j
The differential form of the mass continuity equation for a trace material ;
instead of an integrated form is used as a constraint, and the observed '
concentrations are used where and when they are available. Wilkins1 approach
could be used to adjust the resulting analyses.
The purpose of an objective analysis is to obtain an estimate of the
concentrations where observations are missing. The variational analysis
approach requires that the analysis fit the observed concentrations and the
emissions, transport, and diffusion characteristics throughout the urban area.
The "best analysis" is defined as the distribution which minimizes the
weighted sum of the error variance a) between the observed and analyzed
concentrations, and b) the departure of the results from a steady state.
In VBC, the essential elements of ttie objective variational analysis
model (OVAM) were developed and explored, through idealized cases and a
sensitivity analysis. In the case studies, the OVAM developed a solution very
similar to an analytic solution even when'only a few "observations" were
known. When a random error was added to those observations, the OVAM still
produced an analysis in close agreement with the analytic solution. The error
variance of the initial analysis was reduced by an order of magnitude. The
ratio of weights, oVo, for the analyses and the boundary conditions had the
greatest impact upon the characteristics of the'solution obtained.
RESEARCH OBJECTIVES
The primary purpose of this research project was to produce an OVAM that
gives better analysis of inert pollutants than conventional objective analysis
techniques. In order to accomplish this objective, the following tasks were
undertaken:
• The OVAM algorithm was modified to incorporate temporal variability
of the air pollutant and to include a more rapidly convergent
relaxation technique.
• The results of the OVAM analysis were studied in three cases:
a) Stagnation Cases (V < 2 ms"1),
b) Mild Ventilation Cases (2 ms"1 £ V £ 5 ms"1),
c) Strong Ventilation Cases (V > 5 ms"1)
where V is horizontal wind speed.
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The reliability of the CO analysis using the OVAM and a limited
number of air pollution stations in the optimum network was
determined to establish guidelines as to how many monitoring >
stations must be wind stations only and how many must observe both |
wind and air pollution. j
i
The effect of missing air pollution data in the optimum network was [
determined.
Due to limitations in the quantity of CO data available from the
intensive field programs, an assessment of the OVAM using conventional
statistical procedures was not possible. The research was conducted on a case
study basis choosing cases that would represent extremes in the CO
concentrations.
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MODEL DEVELOPMENT
MODEL EQUATIONS
Consider a volume encompassing an urban area. Observations of the pol-
lution concentration, "ty , are giyen^at various, locations. The volume emissions
density rate, Q (x, y ).»* JHT wnl V-ajTTkha. ambient wind velocity components, u, v, w
(in the x, y and z directions, respectively) are alga specified. The conser-
vation equation for the pollutant, fy, undergoing a first order decay in the
atmosphere is
where
^ is the concentration
KH is. the eddy diffusivity in the horizontal (m2/s) ,
K2 is the eddy diffusivity in the vertical (m2/s), and
T is the decay rate (s~l)
The following assumptions are made:
1)
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g(z) = 1.0 - K (z/Z)2, (2)
where K is a parameter (positive or negative) to be determined.
Integrating (1) from z = 0 to Z, gives
'
where
Z
y.
i|» = J fy dz,
T)
and
2 * 32~ + 32~
9x _?y_
By Assumption 2,
The functional form of ip becomes
iz • •
'o (4)
i.
I ~f — \ i— ~ ,\. r*rt\ v-'/
$ = t|Jo(x,y,o) y g(z) dz = ijMKZ),
o
where G (Z) = Z (l-K/3). The integral form of the vertical diffusion term is
evaluated.
*o ^-y-0) • g
(z) *Cx,y,o) • C2K/Z) (6)
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K
8t{»
z 3z
s 0
(7)
Substitution of Eqs (4)-(7) into (3) gives:
2K K (Z) * « QZ + TO* = 0. (g)
z z °
Since the observed concentrations are averaged values over a time
increment, the time variability of the concentration over that increment •
cannot be accounted for. If the emissions data, Q, and the wind data are
appropriate for that time interval, a near steady state (i.e., -|T- = 0) may
d t
be assumed for the time interval. Applying that assumption, the emissions
must be locally balanced by advection and diffusion. The assumption of a
steady state is not a requirement of the analysis model. If only one set of
observations is available, it is the best assumption. If data for more than
one time are available, then the time variability can be included.
A dimensional analysis-was applied to show the relative contribution of
each term and to aid in computations by reducing truncation errors. The
following definitions are formed.
it - $ • 9', K = K • K',
(9)
x,y = L • Oc'.y'). u,v = U-(u'.v'),
Q = Q - Q',
where
^ is a characteristic magnitude of Vo, (gm/m^) ,
L is a characteristic length of the urban pollution system (m) ,
Q is a characteristic rate of emission density (gm/m^s) ,
• U is a characteristic wind speed1 (m/s),
and K is the characteristic magnitude of Kg or Kg (m^/s).
Substituting (9) into (8) gives
'« CIO)
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Dividing (10) by !f • and dropping the prime (') from the non-dimensional
Irf
variables, gives . -
where . R = K/UL,
H = (LQZ/GU40,
«. _ 2KK iL
GUZ tJ '
The advection terms, u ~- , and v-|^-> are on the order of unity and the
o 3C 0V »
other terms are scaled by the non-dimensional coefficients. The magnitude of
the non-dimensional coefficients determines the relative contribution of each
term of the equation. It was shown in VBC that R«l; therefore
A = uf* + vf*-+ C*- OQS-0. (12)
Eq. (12) is identical in form to the constraint equation in VBC. The
only difference occurs in the definition of £. Following the developemnt VBC,
the Euler-Lagrange equation 'that minimizes the error variance is
„
= 0 . 03)
Substituting (12) into (13) and combining terms leads to the following form of
the Euler-Lagrange equation:
3j| [3u2 3uv\ 3iJ) ( 3v2 3uv)
3x \3x By 3y \3x 3x /
2 3 ib 3 ill 2
u —? + 2uv ——_ + v • .. ... . _ • • _
,, 2 3x3y . 2 3x \3x 3y / 3y
3x J By j / j
f £,2. ** i -\ \ *** t *T f •* *+. 90 oOx
(C + a/a) ijj =-a/a «Jj - q (CQ - u ^ - v ^ )•
In order to obtain a solution to eq. (14), the spatial distributions of
^^
the wind components (u,v), observed concentration (^), the relative weights
(S7a), the decay rate (T), the profile parameter (K), and the sources (Q) are
required.
10
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STUDY AREA
The OSN grid for the St. Louis area was centered at UTM coordinates of
738.5 km Easting, 4279.8 Northing (the intersection of Lindell Blvd. with
Kings highway). The area emissions inventory, developed by EPA, is designated •
in 1.0 km or larger increments, and is coincident with the UTM coordinate ;
system. Rather than make'the emissions inventory conform to the OSN grid, the I
center of the grid for these analyses was shifted to 738.0 km E and 4279.0 km \~
N. The analysis area and the OSN network are shown in Figure 2. A 20 km x 20 j
km regular grid with 1 km spacing (thus, 441 grid points) was adopted for the ;
tests of the OVAM. The sources are normalized to a 1 km^ area. |.
POINT SOURCES ;
Operationally, only the point sources of CO that emit more than 50 kg/hr
are used in the analysis. These account for approximately 98 percent of point :
source emissions of CO in the summer and reduces the number of sources from
200 to about 20. The point sources are further stratified into those with [
effective source heights (stack height plus plume rise) above the top of the ?
model (Z) and those below. '••
The effects of each point source are included by establishing the upper ;
and lower boundary concentrations and the concentration profile. Some point •
sources have an effective emission height (stack height plus plume rise) •- • .
greater than the top of the -modeled volume (~ 50 m). Those sources do not
occur in the volume and are not included in the source term, but are included '-.
in the analysis indirectly through the estimation of the profile parameter.
The remaining point sources are smoothed over the grid square and are included
as area sources in the constraint (continuity) equation because the equation
does not discriminate among source types.
The consequence of this treatment is demonstrated in Figure 3 by
considering two such point sources having different stack heights but
otherwise identical emission characteristics placed in a uniform air flow
field with a minimal background. The greatest impact of the source below the
top of the model is in the immediate surroundings. The analysis creates an .
anomalous negative concentration upwind of the source and overpredicts the
concentration in the first few kilometers downwind of the source (this feature
was shown and discussed in VBC). If the source is above the top of the model, ;
and not considered by the analysis, the location and magnitude of the maximum ;
are predicted nearly correctly. Clearly, the inclusion of the point source,.
as an area source in the analysis equation, creates a problem for this
analysis technique.
'PROFILE PARAMETER
The profile parameter, K, is obtained by estimating the concentration at
the ground, (x,y,0), and at the top of the volume, iKx,y,Z), at each grid
'point from the point and area sources.- The value is determined-using the
definition of K from eq. (2) i.e.,
K = 1.0 - 0|»(x,y,Z)+«|iB)/Glf(x,y,0)+»|fB)
11
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Figure 2. OSN network and OVAM analysis area.
12
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Gaussian Solution
OVAK Solution
Figure 3. Response of OVAM analysis to point source plume rise above
and below the top of the model, Z.
13
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where i|>g is a background value of ^. Concentration estimates at the ground
and model top are carried out for area and point sources independently, using
a modified version of. the RAM dispersion model (Nov_ak and Turner, 1976).
Plume rise is based on source parameters, wind speed, stability, and ambient
temperature. The computations are extracted from the plume rise coding of the
RAM model.
AEROMETRIC DATA
The 19 station OSN and eight additional stations provided data for this
study (Figure 1). The 'data consisted of five-minute average values from the
EPA and RTI stations and three-minute average values from the St. Louis
city/county stations. Five-point running averages centered about the hour and
half-hour were computed. At least three of the five readings were required
for a valid average. The averaging period is consistent with the averaging
performed in the hydrodynamic model which produced the simulated wind fields
upon which the OSN was based.
All CO concentrations were measured at 10 m. Winds were measured at 10 m
at the three RTI stations, the St. Louis city/county stations, and three RAPS
stations (EPA 108, EPA 110 and EPA 118). Measurements at the remaining 13
RAPS stations were made at the 30-m level. Those data were extrapolated
downward to 10 m using the procedure described in Volume II (Vukovich and
Clayton, 1979).
OBJECTIVE ANALYSIS
The OVAM formulation assumes that the winds and concentration, ^, are
known throughout the domain of interest. In reality, they are known at a few
scattered observation points. Estimates of the winds and concentration at
each grid point were determined using the procedure developed by Barnes
(Appendix A) which uses an exponential weighting function to interpolate the
value for a grid point from nearby observation. The interpolated values are
corrected, based?on the error of the interpolation at the observation points ._-.
using an exponential weight function that is more restrictive in its area of
influence.
The Barnes analysis produced initial values at the 441 grid points in tlie
model. The non-dimensional concentrations were determined by dividing the
initial concentration by $ (see equation 9). The concentration, $, was
defined as the mean value of the 441 interpolated grid values.
RELAXATION PROCEDURE
The analysis equation (14) was solved using the sequential over-
relaxation (Liebmann) technique outlined in Thompson (1962). Previous
experience (VBC) indicated that a solution could be attained using point-to-
point relaxation. The Liebmann procedure was used to speed convergence.
The analysis produces negative concentration estimates in regions upwind
of sources where observed contentrations were small. While that result is
consistent with the mathematics of the analysis model and was found in VBC, it
is physically unrealistic. Two additional requirements to the analysis have
14
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overcome the problem. A "background" concentration was subtracted from all
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at inflow boundaries
at outflow boundaries
where 7 is the Barnes analysis. This formulation does not permit mass inflow
from sources outside the modeled region, but mass can be lost by outflow.
Hence, mass is not fully conserved in the OVAM. While there can be wide
discussion of various modifications of the open boundary conditions, these
conditions gave more reasonable results than the others tested.
Ratio of Weights
The choice of the value given to the weight for the interpolated
concentration, OL , and to the weight for the constraint equation,a , has been
shown .(VBC) to have significant influence on the analysis. Increasing the
weight given to the constraint equation (decreasing of /a) in areas without
observations made the OVAM analysis much more compatible with the analytic
solution, and the error variance was substantially reduced.
The weights can be interpreted as measures of the user's confidence that
an observation is "representative" of the concentration within a given
distance of the observing point. At grid points adjacent to observation
point, the interpolated concentration should he similar to the observaton. At
more distant grid points, the interpolated value may not be dependent upon the
nearest observation.
Chaney (1979) studied variations in CO concentrations within a one km
radius of selected RAPS surface monitoring stations. He showed very poor
correlation (r = 0.10) of area averaged concentrations with an urban RAPS
station. At a rural RAPS site, the correlation was 0.80 principally because
of lower concentrations. The mean percentage difference of area averaged
concentrations and concentrations at the RAPS site was about -35 percent in
both urban and rural sites. Ott (1977), Ott and Eliassen (1973), and Ludwig
and Kealoha (1975) address the problem of CO variability in street canyon and
urban areas. They show 200 or 300 percent concentration changes by changing
sampling location by less than 100 m.
The value of a* or a is not significant to the resultant analysis, but the
ratio o7a is. To provide an opportunity to examine the effects of the results
upon the distance of the grid point from the nearest observing location, d,
the ratio otVa was given the form:
**•* /
a /a
100, d/RAD < 0.1
1.0/(ALFA • (d/RAD)2), 0.1 < d/RAD £ 1.0
1.0/ALFA, d/RAD > 1.0.
16
-------
where d is the distance to the nearest observation, but less than RAD, the
radius of influence of a point. Thus," the weight is dependent on RAD and a
given value, ALFA, as shown in Figure 4. Ix^ this case, RAD = 2.5 km. The
choice of the RAD is large in view of Chaney's data. However, the area
emissions data are known to one-km square, so the minimum detectable scale of
variability due to source influence is two km. At that "distance, u7a ~0.2
with the choice of RAD and ALFA. Since o7a is not made a function of land use
(e.g., urban, suburban, or rural), the choice was a reasonable compromise.
5/a
1000
100
0.001
0.5
1.0
d / RAD
Figure 4. Ratio of weights, "a/a, as a function of ALFA and RAD.
17
-------
MODEL APPLICATIONS
SELECTION OF CASES
Besides the criteria mentioned in the Introduction Section, an additional
criterion was applied for the selection of case studies. Valid wind and CO
data were required at 13 of the 19 OSN locations. The criterion was based on
the order of variability of the wind field in S.t. Louis which requires a
minimum of 13 stations to be accurately specified (VBC). Initially, it was
assumed that the CO distribution had at least the same order of variability as
the wind field, thus requiring a minimum of 13 observations from the OSN.
Selection of case studies was made after the wind and CO data were screened
using hourly plots (Figure 5) for each OSN station.
In August 1975, the CO concentrations were quite small and. showed very
little variation. One day was nearly indistinguishable from another. The
wind direction was usually from the southwest. August 12, 1975' (Julian date
75224) from 1100 to 1800 CST was chosen for analysis; Winds were .westerly in
the late morning but by evening they became predominantly southerly. Wind
speeds between 5 and 7 m/s were reported, making this a strong ventilation
case.
In February 1976, U;e CO conci- nt; £ i.' o;.i ;:nov'td
and in space. Several short periods qualify for analysis. February 18, 1976
from 1800 to 2100 (Julian date 76049) was chosen because the larger CO
concentrations were about the highest found during the winter when there was
sufficient data, and because the winds were 3 .to 4 n/s (i.e., moderate
ventilation). The 26 February 1976 (Julian date 76057) from 1800 to 2300 CST
was chosen because it had the highest CO concentrations observed throughout
the network and because the winds were light and variable (i.e., mild
ventilation). The last case, 27 February 1976, from 0000 to 0800 CST, (Julian
date 76058), was chosen to observe the decreasing CO during the night and
increasing CO during morning rush hour (27 February 1976 was a Friday). By
choosing- these events, a wide spectrum of cases was taken from a limited
number of available cases.
MODEL PERFORMANCE
The consequences of the OVAM can be understood by first considering the
Barnes analysis. The analysis (Figure 6) was performed without considering
the winds. Within the network, the resultant wind was from the
south-southwest at 2.5 m/s. The Lambert Field winds were westerly at 5.2 m/s.
The Barnes analysis and the CO observations showed small variations over the
domain. CO ranged from 500 ppb in the southwest to 80 ppb in the southeastern
quarter. The OVAM analysis changed the Barnes analysis along the southern
border where CO concentrations increased substantially in a narrow finger
18
-------
ftUGUST CO STATIONS 1-10
a 10 u
Ull UliUUlIlM |M~I|I I. IlllIK
lift
«dl buua
12 13 I H 15
iuill.1 lu
IbQu I ui Biua ill DikuiQ
l
• If
II iMlUmJl JLu«DlllIlll UbuudllllllB inJb Illlll I L Id I
nJin
aujii itfl
IL
I
DIM
ll
1111.
ii L JBI «-4fcA..~tt.....JBi*jhli m...mi*itmi. —Jh iJl I j Judl Ji
IklhMMbOTrttffc •^JwlltoMikHlkt lMHUlLi«AA«iiti %uJB|j IttKl I M l4*At ftt
I .I Jhi bl
IIII Jll i.LliJk,«Uhl LiJLii *i kJ4wMJui
16
STL 008
RTI 202
STL 009
STL 006
RTI 205
STL 002
RTI 207
EPA 101
EPA 102
EPA 104
Figure 5. Hourly CO concentrations at OSN locations, August 9^to 16, 1975 and
February 14 to 29, 1976. Vertical tick increment; is ~
-------
tsj
O
.
-
-
-
-
-
RUGUST CO SJHTIONS 10-19
9 10 11 . 12 13 11 15 16
lid j||jtil.kU..«4kl Ujtti At tnflftt-ntfiVjK-nti till J * Jbi kl.^jllbl . li. EPA 104
llfl Hi, ...,A.,.....I T T^T •- I »-*"-««« MM IHl 1 J Ub. 01 taJtl 1 I. EPA 105
III L. •**»**-*• -jLa_l . Ju „*, M- .ttl 1 a JM! iilii*jk«i . li EPA 106
bl
l*i JiaftMuJlt iJliliiM<
-------
ro
-
.
"
-
-
-
-
-
FEBRUARY CO STftTU
H IS 16 17. 18 J 19
11 ULfc»
1 +*t\ t«MMMl llllMllMrf lUI Iw
......
-_.
t i iiMMu
Atkhkf^l rfiMMMMMMA
htllVll 1 kMMMJ
i
, .__ ,«... .*_
1 Brill iflLlU-. lUlW,
INS 1-10
20 21
MMI .-*... . STL 008
bhi --M. RTI 202
li.i .w-. STL 009
«.. . .«.. STL 006
Brtt .«•« RTI 205
ri*l .M.. STL 002
« >.«.. .«>.».. >i * ^ . . RTI 207
1 'I
! i~. ,JL.^- i ,i-Ji ~, . EPA 101
EPA 102
kAiJli IhilMi^i iWUtA llhui I.AIU EPA 104
-
.
-
-
- •
-
-
^
Figure 5. (continued)
-------
KJ
FEBRUARY CO S
22 23 ,24 25 26
. J
Ml
1-10
mlL.L MI
.MUWtaWWil MM «
29
I i Itfllt
llill'.*._
. d,
. J,
Mil tattMtU IM
tJL.
L U Jl
Li-jiMiiktb. liUti
.MA. IMlMH^.^.1
h..J L
.JkMi<.J , A^u^lkibj. llliJfcjiAil tkkiii
STL 008
RTI 202
STL
STL 006
Jbl MA.MUMMMI RTI 205
STL 002
207
EPA 101
EPA 102
/W*u«,i EPA 104
Figure 5. (continued)
-------
K>
FEBRI+
„
^
•
_
;
M
«
-
U 15
IttMftll tiMMMM
1 ^
^jliflU
mr co STATIONS 10-19
..i
U
16 17 18 1 19 ,, 20 21
, JU . iml.i^i ,llLa IJfcM. . U-.I. . EPA 104
jj MllN.«uJ |d,M 1
1 1
Jj IL.^ jiJn
il U
*• *~~~~*l JI..I-II II » fcH»» i.i il ttttmmm
-_*, .«-.,
_ J J,a
i
•IIMll kJ^jl iJ
— •l^-
U
iJ
.AlH.« lh«l^>H«_rf till *_
- "J-"1-
u., «u-b EPA 105
u«l .L». EPA 106
k .. -•.. EPA 108
U . EPA 109
1... l«k EPA 110
U* *««,.. EPA 113
**•••• M «t* • tr M 1 1 0
- ». -... - EPA 119
M - i --. ,. EPA 120
_
—
-
-
I
_
-
L-
Figure 5. (continued)
-------
FEBi
22
- . i
A
CO STATIONS
fl
... dtiuUifthf U. **uL.liki &.
Jti A 4 *•!.•• kitJl Mil i
*. Aki«Aki ».jl flu.
MM M<| «J«» atwl •*•• i
I LhjL*JLl i mm~l
IlkiJlLnl
ll
i EPA 108
EPA 109
EPA 110
EPA 113
EPA 118
llluku.il!
EPA 119
^i EPA 120
Figure 5. (continued)
-------
EMISSIONS
224/1300
CO (PPBJ
229/1300
BflRNES
CO (PPB)
*K
22V1300
CBRSIC3
Figure 6. Wind vectors, area-sources, and CO isopleths, August 12, 1975
at 1300 CST. Source isopleths are in increments of Q. Observed
concentrations are plotted above the station nark (+); interpolated
values at nearest grid point, below the mark.
25
-------
extending along the local wind direction and downwind of the larger emissions.
The Barnes.analysis interpolated a value of 430 ppb at the grid point adjacent
to the missing location, but the OVAM increased that concentration to 755 ppb.
The OVAM developed several other maxima near the center of the grid that are
unsupported by the observations, but where the emissions were large.
Centers are justified, by being located downwind of principal source
regions. The relative minimum, upwind of the sources, a common feature of the
OVAM, occurs because the analysis tends to suppress concentration estimates
(VBC). Since the observations are several kilometers away from this area, the
constraint equation is dominant Co/a. « 0.1) and is attempting to conserve mass
in that local area. The increase in mass (concentration) downwind is
compensated by a reduction in mass upwind of the source. The amount of
reduction is related to the along-wind gradient of emission rate.
The concentration in the north-northeastern and northwest sections also
increases in response to the emissions. Thus, the wind and emission patterns
of the area has a major impact upon OVAM results. The concentration estimates
are changed dramatically at EPA 106 (from 181 to 327 ppb) and at EPA 102 (from
107 to 208 ppb). Both stations were downwind of large sources, contributing
to an increase even though "a/a ~1.0 near the stations. Furthermore, the
predicted concentration gradient is large in that area, so the .displacement of
the grid point from the observation is important.
MODEL SENSITIVITY
The ratio "ex /a and Z, the depth of the volume, have been shown to be
;-^"tir.ulE.rly 5.!J.flufr.l:i?l ?.n the OY.AM an^yric (VBC). In rbe precr-nt
dvv-&lop2}£nt, with point L-ources incixjoco &r,d 'with questions E.S to Lh.e
correlation of nearby concentrations to the measured concentrations, the
selection of Z and of/a and of RAD, the maximum radius of the observation's
influence, are important. The impact of these user-defined parameters was
examined using the data for August 12, 1975 at 1300 CST (1400 CDT). The
values of the three parameters in the basic (reference) case and the test
cases are given in Table 1. The studies were carried out a) using the initial
distribution of V and the wind field developed using the Barnes analysis with
interpolation along the wind vector, and b) without the influence of the local
wind vector. The difference of results between cases was minor due to small
wind speeds, so only the case (b) results are given. Effects were shown by
computing the percentage change of the concentrations (Figure 7) with the
varied conditions related to the basic condition. Differences are also
examined along the south to north line, approximately in the direction of the
wind, 12 km from the western edge of the domain (Figure 8). All of the
features of the analyses do not occur along the line, but salient features can
be illustrated.
The cross section analysis (Figures 8) clearly shows that the choice of
ALFA is the primary factor in changing the concentration estimates. When ALFA
is reduced to 5, the concentration changes are small and negative. When ALFA
increases, the impact of sources upon the analysis increases and all values of
concentration increase. The concentration gradient along the cross section
for all curves is essentially the same for the first 10 km, but increases more
rapidly for the next two km (for ALFA > 10) in response to strong area sources
just to the west. There are changes in the gradient in response to emissions
further north. For the smaller value of ALFA (5.0), the gradient shows
26
-------
TABLE 1. PARAMETERS OF SENSITIVITY ANALYSIS
Test ALFA RAD
Test ALFA RAD
BASIC
1
2
3
10
5
50
100
2.5
2.5
2.5
2.5
50
50
50
50
4
5
6
7
10
10
10
10
5.0
1.5
2.5
2.5
50
50
100
200
similar trends away from sources and responds less to the sources than does
the basic case.
The higher values of ALFA increase concentrations when emissions are
large. The initial, upwind difference among the concentrations is due to the
strong source region at the upwind (south) boundary. The principal response
seems to occur in areas where the actual emissions are two or more times
larger than the average emissions over the total analysis area.
Changing RAD from 1.5 to 5.0 has little effect upon the concentrations.
The smaller value produced the least change. The larger value produced a
decrease in the concentration toward the north (Figure 8) in response to the
influence of a nearby observation and to a lesser degree in response to nearby
sources. The same feature is shown in the percentage change (Figure 7) in
concentration at the northern border of the area.
Increasing Z produces a much smoother analysis along the cross section,
because the pollution is being averaged over a much deeper layer and the
effects of the vertical profile are much smaller, thereby decreasing the
effects of strong area sources. Upwind of sources, the percentage change
exceeds 200 percent and the concentrations have increased, because the
influence of a strong gradient associated with area sources has been reduced
by averaging the'emissions over a deeper volume.
The results of the sensitivity analysis shows that the choice of ALFA has
the primary impact upon the OVAM analysis. The initial concentration has
little impact upon the choice of the parameter. Larger values of Z smooth the
analysis, de-emphasizing the source. The analyses are least sensitive to the
choice of RAD.
TIME SEQUENCE OF ANALYSES: 12 AUGUST 1975
At 1100 and 1200 CST on 12 August, the winds were westerly to
southwesterly over much of the area. A concentration maxima developed along
27
-------
BASIC
ALFA * 5 '
Al.FA « 50 '
ALFA « 100 '
Figure 7. Isopleths of CO concentration for basic state of sensitivity
analyses and isopleths of percent change from basic state (interval
33%) induced by indicated parameter value. Zero percent change
isopleth is indicated.
28
-------
C\
RAD - 5.0'
RAO - 1.5 '
Z - 100
Figure 7. (continued)
29
-------
CROSS SECTION ftLFft VflRIED
6 8 10 12
DISTftNCE. KM.
16 18 20
KEY
10.0
5.0
50.0
100.0
CROSS SECTION RRD VflRIED
6 8 10 12 14
DISTflNCE. KM.
16 18 20
KEY
_ 2.5
1.5 I
5.0 !
CROSS SECTION ZMftX VflRIED
6 8 10 12 14 16 18
DISTflNCE. KM.
20
KEY
— 50
o 100
A 200
Figure 8. Spatial cross section of OVAM analysis (ppm) for sensitivity
tests indicated in key.
30
-------
the Mississippi River downwind of the primary area sources (Figure 9).
Concentration minina developed along the northwestern city limits and to the
routh-central portion of the city. To the southwest, RTI 205 did not report
at 1100 CST, but data were available at 1200 CST, producing marked changes in
the CO distribution in that area. The largest differences between the Barnes
analysis and the OVAM analysis occurred near two network stations close to
each other which are affected by major sources.
By 1300 and 1400 CST, the winds shifted to the south-southwest. The
naxinum associated with the emissions near the river, shifted to a more
north-south orientation, encroaching on the minimum in the south-central part
of the city. The minimum in the northwest persisted. A maximum concentration
just north of the center of the area developed because of a large area source
just upwind of the maximum. In the previous two hours, the OVAM had been
tempered by the observation at EPA 106, missing during these hours, and had
attempted to increase the concentration at EPA 106, by 25 to 40 percent.
Without the restriction of the observation, the relative weight of the
analysis, "ff/a, locally decreases from~1.0 to 0.1 and favors the constraint
equation.
At 1500 and 1600 CST, the winds were more southerly throughout the grid.
An OSN station (STL 002) at the south-central location STL reported the
largest CO concentration of any station. Furthermore, these were the only
times this station reported during the eight-hour period. The large value
dominates the analysis throughout the southwestern portion of the area. The
area sources were inconsistent (smaller) with the observation in that area and
did little to modify the impact of the initial interpolation. The influence
of the observation did not extend to the east because of advective affects.
Sources would have caused larger concentrations there thus making the maxima
larger rather than smaller. Several streaks of higher concentration, downwind
of sources were present. The maximum in the center of the area remained in
. about the same position at 1500 but was markedly reduced when EPA 106 reported
data at 1600 CST. , i
|
From 1600 to 1700 CST, the concentration at EPA 120 more than doubled and j
dominated the analysis over the western half of the area. At other locations, .
the observations and OVAM concentrations showed small differences. Emissions
had decreased markedly, especially along the river, thus, having less impact •
upon.the analysis. !
i
These analyses clearly show the influences of emissions and winds (the i
constraint equation) upon the resulting analyses. The 1500-1700 CST analyses ;
clearly show that a large concentration observed in an area where the j
emissions does not justify such a large value, will dominate the analysis in
that region. The area dominated is a function of the initial interpolation. |
The observation at EPA 120 at 1700 CST could be produced by sampling very j
close to a source though no major source is indicated in the emissions [
analysis. The large concentration at STL 002 at 1500 and 1600 CST was j
suggested by analyses at 1300 and 1400 CST. However, the magnitude of j
observed values at 1500 and 1600 CST, which are point observations, do not j
correspond to those of the emissions, which are area-averaged values. The . I
discrepancy produced by employing point observations with area-averaged source |
31
-------
CO (PPB)
JJ435
f*\,' '•$y,<''y
'-J8—\.'^~-''t%S.-' »
224/1200
(BflSIC)
22V1200
Figure 9. OVAM concentration analyses and area emissions by hour
for August 12, 1975.
32
-------
-„ SM ,' S~\ ««
)* / / / A"H1
-.. '• L/ ^»7/
—"-. / :T-i~* .^//i
y / .-•^'^Af2|o'
1 ( ( />*
I HO \ \ /
"v* * » y
v *r vvy
7P lv "
^
22V1%00
CBftSIC)
Figure 9. (continued)
33
-------
• ^y9u^
CO CPP0)
224/1
CBflSICl
Figure 9. '(continued)
34
-------
CO CPPB)
HO
224/1700
C8RSIC)
trUSSlUNS
modiuno x"
*•* t i / •
* 'J /
22V1700
CO CPPB)
SOD
224/1800
CBftSlC)
EMISSIONS
224/1800
Figure 9. (continued)
35
-------
emissions is a significant problem that will always be encountered in
utilizing an OVAM—or prediction models. The 1300 and 1400 CST analyses
indicated that the large sources near STL 002 affected only a small area about
the station, when the observation at that station was missing. The large area
of influence demonstrated in the 1500 and 1600 CST analyses was due to the
initial field created by the Barnes analysis.
The impact of the sources on the analyses appears significant. However,
the concentrations are on the order of 0.5 ppm. The largest hourly
concentration is on the order of 2 ppm or about one-fourth the NAAQS for
eight-hour running averages for CO. The case study treats CO concentrations
which are near the measurement capability of the instrument used to measure
CO. A comparison of observed and interpolated concentrations nearest the
observing locations is given in Table 2.
DELETION OF OBSERVATIONS
The summer case study was primarily chosen to examine the effects of
missing observations. This analysis was carried out by randomly deleting
observations from the set of available observations for a given hour. The
selection procedure was random so that user bias would not be an influence.
It also needed to be repeatable from analysis to analysis. The number of OSN
observations to be deleted and an initial number for the random number
generator are input parameters for the selection procedure. The random number
generator develops a number between 1 and the total number of OSN stations.
If that observation is not missing or already deleted, it becomes a missing
observation. The procedure repeats until the prescribed number of
observations are deleted. The Barnes analyses are rerun on these revised data
bases; the Barnes analysis is used to initialize the OVAM. In this manner,
the whole analysis procedure is compared, not just the OVAM procedure. The
status of the OSN stations in the various analyses is given in Table 3.
The OVAM value at the grid point nearest two non-network stations (EPA
107 and EPA 111) were plotted versus time (Figure 10). Concentrations at two
OSN network locations were similarly identified. One of those stations (EPA
105) had CO observations for the entire period; the other (EPA 106) did not
report from 1300 to 1500 CST.
Station EPA 105 was deleted from all hours when six data points were
removed and from the 1300 to 1500 CST when two data points were removed. When
the data were retained, the OVAM value at the nearest grid point and the 1
observed value at the point are in good agreement. When the observations were [
removed, the OVAM overpredlcts, especially when station EPA 106 is also [
missing. EPA 105 was downwind of large area sources (Figure 9). The
discrepancy between observation and prediction suggests either the emissions
were too large or the observations were too small. ;
Station EPA 106 was not used in the analyses when two stations were
removed and at 1600 CST when six stations were removed. When the data were
not missing or removed, the OVAM showed reasonable agreement with the
observation. The substantial difference in the OVAM and the observations in
other cases was a result of the station's proximity to the large area source,
. \
36
-------
TABLE 2. CO CONCENTRATIONS (ppb) OBSERVED AND INTERPOLATED BY THE BARNES AND OVAM FOR OSN
STATIONS WITHIN THE ANALYSIS GRID (AUGUST 12, 1975)
Station
RTI 202
STL 009
RTI 205
STL 002
EPA 101
EPA 102
EPA 104
EPA 105
EPA 106
EPA 110
EPA 119
OBS
420
500
M
M
280
100
380
560
300
120
80
1100
Barnes
423
501
54
.179
295
107
365
498
320
165
80
OVAM
416
489
137
361
318
144
427
447
369
221
38
OBS
420
440
500
M
300
120
380
200
M
80
100
1300
Barnes
369
383
381
375
257
107
304
181
207
100
111
OVAM
426
411
403
755
320
208
326
327
569
122
115
OBS
400
920
640
1,820
400
100
580
200
M
80
140
1500
Barnes
409
921
552
1,809
384
109
515
221
265
141
156
OVAM
406
833
548
1,843
492
356
480
378
714
165
147
OBS
460
1,700
640
M
340
160
400
300
140
120
400
1700
Barnes
479
1,723
616
453
328
176
376
263
174
155
415
OVAM
461
1,632
603
478
332
279
330
244
162
136
390
M « missing observation
-------
HISSING AND DELETED OBSERVATIONS (August 12, 1975)
Station
1100
1200
1300
1400
1500
1600
1700
1800
STL 008
RTI 202
STL 009
STL 006
RTI 205
STL 002
RTI 207
EPA 101
EPA 102
EPA 104
EPA 105
EPA 106
EPA 108
EPA 109
EPA 110
EPA 113
EPA 118
EPA 119
EPA 120
M
4
2,4
M
M
M
M
6
6
6
6
2 6
___
4,6
4
•
___
"• — ' *
M
4
2,4
M
4,6
M
M
6
6
-.-—
6
2 6
_».
__
4,6
—
—
— — —
M
4
2,4
M
4,6
M
M
6
6
6
2 6
M
___
M
4,6
_-_
.___
— — —
M
4
2,4
M
4,6
M
M
6
6
6
2 6
M
___
M
4,6
— --
___
—
M
4
2,4
M
4,6
6
M
6
6
___
2 6
M
. —
M
4,6
• ___
___
— — —
M
4
2,4
M
4,6
6
M
6
6
___
6
2
—
M
4,6
_ _
—
M
4
2,4
M
4,6
M
M
6
6
___
6
2 6
___
M
4,6
___
___
M .
4
2,4
M
4,6
M
M
6
6
___
6
2 6
__
—
4,6
___
• ___
•" •
2 - deleted, one of two
4 - deleted, one of four
6 — deleted, one of six
M-- missing observation
suggesting, as in the case of EPA 105, that the emissions were too large or
the observations were too small.
At the non-network stations (EPA 107 and 111), the OVAM value does not
generally follow the trends of the observed concentration. However, the
observed concentrations are so small that differences with analyses are not
necessarily meaningful. The presence or absence of data does not usually
affect the concentration estimates. However, the concentrations at EPA 111 at
1500 CST results from a complex interaction of sources, observations, and
deleted observations. The best estimate occurs with six stations missing, the
poorest with two. This station is just downwind from the large area source
and the reported large concentration at STL 002. With EPA 105 (and one other
38
-------
STATION: EPA105
STATION: EPA107
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station) deleted and EPA 106 missing, the concentration at EPA 111 is
dominated by the large concentration at STL 002. However, when six stations
are deleted, STL 002 .is also deleted, so the OVAM estimate is more consistent
with those at the earlier hours.
The consequences of deleting measurements upon the spatial distribution
of CO produced by the OVAM are shown in Figure 11. For each hour, the.
isopleths of CO for the basic case and the spatial distribution of the
percentage change of concentration as a result of removing two, four, and six
observations from those available are shown. The removed observations are
indicated by a large dot in each frame of the figure.
t
The random selection process produced a diverse set of data deletions.
When four observations are deleted, three of the four stations are in the
western extremity of the analysis region, and one is on the southeast border.
For most of the hours, only one observation (EPA 119) remains in the southern
and western third of the analysis area. The same six stations are not deleted
each time, but five are in the eastern half of the area, often being adjacent
to the river and sources. One southwestern station is deleted.
The impact of removing an observation depends upon the wind direction.
When the winds were westerly (1100 and 1200 CST), a large percentage increase
occurred near EPA 102 along the axis of the wind when the observation from
that station was deleted (one of six stations only). As the winds turned
southerly (1300 to 1600 CST), the axis of the increase became oriented south
to north. The changes around EPA 106 (two stations removed) at 1100, 1200,
and 1600 CST show the same rotation of axes.
The removal of the three western stations invariably produced a one-half
to three-fourths reduction in the OVAM predictions through the western half of
the domain.- The reduction is attributable to reduced concentration estimates
for the Barnes analysis and the fact that no large sources are found in the
immediate vicinity. The deletion of those data tended to reduce the
concentration slightly in the eastern portion of the area, (except to the
southeast of the river) regardless of the wind direction.
To the southeast of the Mississippi River in an area almost devoid of
sources, the removal of the observation at EPA 110 has a dramatic impact upon
the concentrations that persist through all analyses.. The concentrations in
that area are controlled by the background concentrations (i.e., the minimum
concentration permitted in the analysis). For the four- and six-station
deleted analyses, the background concentrations were two to five times the
background of the basic case, particularly upwind of EPA 106.
Almost all analyses show a major percentage increase from the basic case
when EPA 106, the most central station, is removed from the analysis. The
OVAM analysis increased the concentration near EPA 106 in response to the
nearby source. When the station value is missing or deleted, the increases
are not constrained as when the data are present.
The 27 February 1976 case was also used to examine some effects of
missing observations. The deletion of six observations from the OVAM network
40
-------
PERCENT DIFFERENOT //
fTVim
Figure 11. Isopleths of concentration for basic case and percent change with
two, four or six stations deleted, August 12, 1975. Deleted stations are
indicated (•). Isopleths of percent change are -67, -33, 0, 33, 67,
100, 200, and 400.
41
-------
CO CPPB)~
too /
If*
224/1200
800 CBfiSIC3
Figure 11. (continued)
42
-------
PERCENTDIFFER
PERCENT DIFFERENp£
o^-N W
*Y! ' f>
224/1900
Figure 11. (continued)
43
-------
ZH/lfOO
(BASIC)
PERCENT.DIFFERENCE'
S> v/
22%/HOD
0 (TWO)
PERCENT DIFFERi
'
Figure 11. (continued)
44
-------
PERCENTJJIFFERENpE'
22V15DO
PERCENT DIFFEJlENpE'
Figure 11. (continued)
45
-------
PERCENT DIFFERENBT
PERCENT DIFFERENCE
Figure 11. (continued)
46
-------
during the early morning of 27 February, produced substantial percentage
changes of the analysis (Figure 12). Between 0000 to 0800 CST, the same five
stations (STL 008, EPA 110, STL 002, EPA 105 and EPA 101) were deleted. For
the first four hours, EPA 106 was deleted; and for the remaining hours, RTI
205 was deleted.
Throughout the night, station EPA 109 reported the highest concentrations
of any station and dominated the analysis over a wide region. For the first
four hours, the largest change occurred in the locality of EPA 106, a deleted
station. Adjacent stations EPA 101 and EPA 105 were also deleted, leaving a
void in the center of the grid. The initial interpolation in those areas was
controlled by OSN stations giving higher concentrations than'observed. At
night, area sources diminished by an order of magnitude over daytime values,
so that the emissions were too small, once again signalling a disparity
between emissions and observed concentrations. Solutions were achieved in a
few iterations. Local percent changes from the Barnes analysis to the OVAM
analysis were generally less than + 25 percent. Changes arose from changes in
the initial conditions, rather than from the requirements of the constraint
equation.
Comparison of observed concentration with OVAM predictions prior to 0600
CST suggest reasonable agreement (Figure 13). The OSN stations, EPA 106 and
EPA 105, maintain reasonable agreement with the observations during this
period. At 0700 and 0800 CST, when the observations at EPA 107, EPA 111 and
EPA 106 increase five fold, that at EPA-105 remains about the same. The OVAM
values, however, show an increase at EPA 105 of about five fold. The response
of the OVAM to the high initial values and to the overall increase in
emissions are probably responsible for this increase.
The concentration estimates for non-network stations, EPA 107 and EPA
111, show trends similar to the observed values. However, differences between
predictions and observations for the non-network stations are generally
greater than those for the network stations, especially between 0600 and 0800
CST. The observations at only"EPA 107 are better predicted when six stations
are missing. Also, the OVAM values generally differ little from the initial
Barnes values, at both non-network and network stations.
EFFECTS OF BOUNDARY CONDITIONS ON ANALYSES
The OVAM predictions obtained with six stations withheld from the Barnes
analysis were examined at OSN and non-network stations to de-termine error
reduction and the number of iterations required to attain a solution for two
sets of boundary conditions, the open boundary condition and 6 (•!=•-) = 0.
dn
For the August case study, the mean difference between the two sets of
analyses was less than 60 ppb for all hours. The integrated error variance
associated with the two solutions differed by less than two percent for each
hour. The number of iterations occasionally varied but only because
convergence had not occurred in less than ten locations in one analysis and
did occur in others. However, a steady state of error reduction was attained
in almost the same number of iterations. Thus, the boundary conditions did
not have a major impact upon the results obtained.
47
-------
PERCENT
05B/OQOO
Figure 12. Isopleths of concentration for basic case and percent change
with two, four, or six stations deleted, February 27, 1976.
Deleted stations are indicated (•).
48
-------
PERCENT DIFFERENCE //
(SDH
CO CPPB)
2S40
PERCENT DIFFERENCE //
osg/oano
Figure 12. (continued)
49
-------
STflTIOH: EPfUOS
Ul
o
5-°r. i iii i i i
I.Ot-
KEY
- OBSERV
3 0|- J" ° BARNES
; i «• OVAM - o
2.0
1.0
0.
(
— ^ .
^\*j • ~
) 1 2 3 4 5, 6 7 t
+ OVAM - 6
'v.
TIME OF DOT
i i
! .1
1
5.0
3.0
3.0
t.O
0.
<
STRTION: EFfll06 ;
1 1 1 • . 1 ' 1 1 1
\
•
* " ' /
•a*^"s>Ns— -4-~-^JL__-_/
i i i~~I T T i
) 1 2 3 H 5 6 7 8
TIME OF DflY
5.0
1.0
9.0
2.0
1.0
0.
STATION: EPR107
5.0
1.0
3.0
2.0
1.0
I
I
I I
945
TIME OF DflY
STATION: EPfllll
I I I I I I
TIME OF DflY
Figure 13. Time series of CO concentrations (ppm) for.OSN and non^-OSN locations from observations,
Barnes Interpolation and OVAM analysis with zero or six stations missing, February 27, 1976.
-------
ERROR VARIANCE
The OVAM is-designed to reduce the integrated error variance (EV) of the
analysis over an area. In VBC, the EV was reduced to one-tenth of its initial
value where the initial value was determined from an inverse square inter-
polation of randomly located, but analytically determined, "observations". The
integrated EV of the Barnes and OVAM analysis are given in Table 4. The
values were computed from the non-dimensional values with background
subtracted. The daytime analyses show the largest variance with both the
Barnes and the OVAM analyses. The EV increases through the day to a peak,
then decreases rapidly as emissions diminish toward evening. Typically, the
EV is reduced to about 78 percent of its initial value.
Removing observations from the input to the analyses has different
effects upon the initial variance and its reduction by the OVAM. Removing two
observations usually leads to a larger initial and final EV. When four
observations are removed the initial EV is reduced. An exception occurred at
1500 and 1600 CST in August, 1975 and the initial error variance increased
when the large concentration at STL 002 was reported. The interpolated values
in the western third were lower and more in keeping with the lower emissions
in the areas (Figure 9). The mean EV with four stations removed is only
slightly -larger than that without removing data,' even though the mean
fractional decrease is larger. Removing six stations usually produces larger
initial EV than found with no stations removed. At 1500 and 1600 CST, when
the STL 002 data were not included in the interpolation, the reduction of the
EV is slightly greater, but not enough to reduce the EV relative to the basic
case.
The nighttime winter cases showed a more variable error reduction,
averaging about 28 percent regardless of the number of observations deleted.
The analyses seem to produce a 22 to 28 percent decrease in EV regardless of
the concentration or number of stations removed. The reduction is generally
less (nearer 22 percent) during the daytime. The resultant error appears to
be a result of the initial error.
ACCURACY ESTIMATES
In the summer case, the average CO observed concentration was 0.6 ppm and
ranged from 0.1 ppm to 2.0 ppm. The RMS difference between the observed and
predicted concentrations at non-network stations was +0.6 ppm. When two or
four stations were deleted, the RMS difference did not change; but when six
stations were deleted, the RMS difference decreased slightly to + 0.4 ppm.
The decrease was primarily due to the deletion of EPA 105 and STL 002 which
had observed concentrations inconsistent with the local emissions. When these
stations were included, their observations markedly influenced the initial
conditions produced by the Barnes algorithm and the resultant OVAM analysis
over a broad area. When these stations were deleted, the concentrations
increased near the center of the city and decreased to the south relative to
the case when these stations were included, in response to the local
emission—and, thus, increased the accuracy at non-network stations. The
inconsistencies were likely due at least in part to differences in the nature
of the data—point observations and area-averaged sources—and to location
51
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TABLE 4. NON-DIMENSIONAL ERROR VARIANCE OF ANALYSES
Wn
to
Date
Aug
14
Feb
18
Feb
26
Feb
27
Hour
11
12
13
14
15
16
17
18
18
19
20
21
18
19
20
21
22
23
00
01
2
3
4
5
6
7
8
Barnes
197
202
260
331
487
369
132
65
.533
.389
1.40
1.65
.517
1.69
2.25
8.65
1.59
3.01
1.49
0.827
0.395
0.115
11.11
.842
1.68
5.31
None
OVAM
158
174
216
259
357
271
97
53
.378
.275
1.20
1.15
•
.368
1.23
1.78
5.69
1.15
1.54
1.26
.615
.320
.098
6.83
.663
1.16
2.64
Stations Removed
Two
% DECR Barnes OVAM % DECR Barnes
20 236 173 27 181
14 234 196 16 188
16 283 236 17 269
22 355 281 21 328
25 543 394 27 523
27 388 279 28 390
26 119 96 19 112
19 63
21.1 22.1
29
29
14
30
25.5
29
27
21
34
28
27.8
49
16
26
19
15
38
22
31
50
29.5
2370
Four
OVAM % DECR Barnes
149 18 295
167 11 248
229 15 284
265 19 354
393 25 419
295 24 309
95 14 171
52 16 67
17.8
1.36
.634
4.31
3.92
1.10
2.64
3.11
7.53
4.01
4.06
3.48
1.68
.77
1.53
11.72
71.69
1.57
3.73
Six
OVAM
195
195
231
267
314
247
118
51
.998
.469
3.32
2.56
.762
2.01
2.52
4.70
2.73
2.76
2.47
1.38
0.61
1.01
5.69
58.77
1.18
2.70
% DECK
34
21
19
25
25
20
31
24
24.9
21
20
23
35
27. »
31
24
19
38
32
28.8
32
29
. 18
21
35
51
1«
25
28
28. ()
27. J
-------
differences becv.-een the observatier, and the grid point—grid points were up to
0.7 km from the observations.
In the winter, the average observed CO concentration was 5.3 ppm and
ranged from 1.0 to 15 ppm. The RMS difference was + 4.2 ppm. When six
stations were deleted, the RMS difference increased to ^ 6.5 ppm. During the
early morning hours of 27 February 1976, the concentrations that would be
produced by the emissions were considerably smaller than the actual
observations (by an order of magnitude). The emissions decreased due to the
inactivity in the city. The CO concentrations remained large and were
apparently left over from the rush hour emissions. The OVAM analysis was
controlled by the initial conditions and the dynamic effect of the wind, the
influence of the former dominating. At night when emissions are small, the
initial conditions must very nearly represent the actual field. This can be
accomplished by utilizing the previous hours analysis updated with existing
observations as the initial field, but this procedure must begin during
periods of large emissions.
53
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DISCUSSION OF RESULTS
MAJOR FINDINGS
The OVAM was adapted for field data and applied to CO concentrations
obtained from the OSN. Several cases representing a variety of conditions
were examined with the objective of assessing the model sensitivity to input
parameters, the response characteristics of the analyses, the reduction of
error variance, the effects of missing data, and the overall effectiveness of
the model.
The OVAM analysis was particularly sensitive to the ratio of weights for
the observations and constraint equation but was insensitive to the radius of
influence of the observation. The grid spacing was a practical lower limit to
the radius of influence since it was half the resolvable spatial scale.
However, CO concentrations are highly variable on a small scale, suggesting a
small radius of influence should be utilized. OVAM analyses became smoother
and less sensitive to emissions as the depth of the volume, Z, increased.
Increasing Z diluted the emissions over a large volume. A practical upper
limit to Z might be the atmospheric mixing height. The choice of Z was also
important because point sources that fail to rise above Z were treated as area
sources.
Results of the application of the OVAM to the August 12, 1975 case
(daytime) showed a strong dependence upon the spatial distribution of sources
and winds. Upwind of the stronger area sources, the concentrations tend to
decrease; downwind, they increase. Large percentage changes between the
initial guess and the OVAM analysis were found in the vicinity of principal
sources. Since concentrations were on the order of 0.5 ppm, which is rear the
practical limit of observations for CO, the percent changes are relatively
meaningless, except to help Identify the on-going processes.
For the 27 February 1976 case (nighttime), the CO emissions decreased by
an order of magnitude, whereas the concentrations remained high. The OVAM
produced analysis that did not differ greatly from the initial guess. The
principal adjustments of the analysis were due to boundary conditions and
winds because the magnitude of the source emissions were inconsistent with the
magnitude of the observed concentrations.
The response of the analyses to deleting two, four, or six observations
from the OSN produced inconclusive and, at times, conflicting results. The
error variance decreased by 20 to 30 percent of its initial value regardless
of the number of stations deleted. However, large percentage changes of
concentration occurred, depending upon the location of deleted data. In most
daytime cases, the largest changes occurred when observations upwind or
54
-------
downwind of principal source areas were deleted, and when the deleted
observations were not near other observations which were near principal
sources. Large changes were also found when changes in background
concentration occurred. In all cases, the concentration changes were
primarily controlled by changes in the initial guess resulting from the
deleted observations.
When stations, which were in regions where the emissions were small or
non-existent (the outlying regions of the city) and which were not near
stat:ions influenced by large sources, were deleted, the impact was significant
in those regions, but relatively insignificant in the large emission regions.
The impact at the deleted stations in the outlying regions was primarily due
to the interpolated initial value being different from the observation,
suggesting that, if initial conditions can be treated properly in the outlying
regions, some of the stations in this region would not be required as a CO
monitoring station. Thirteen of the nineteen OSN stations were in such
regions. Possibly as many as half of these need not monitor CO, though they
all must monitor the wind. However, further investigation is required on
initialization methodology before conclusive statements can be made. The
sample is too small and the relationship of the 1 km square sources to the
point measurements is not well-defined. The cause-effect relationships are
tied to the density of the stations, the initial guess of the concentrations
at those stations and, of course, upon the meteorological conditions.
In several instances the OVAM did not predict concentrations in agreement
with observed concentrations at the non-network stations. The discrepancies
arose because 1) the CO concentrations tend to be source-oriented, and sources
are smoothed to a 1 km square area by the inventory (this problem affects all
CO data) whereas the observations are point observations not necessarily
representative of an area; and 2) the OVAM values used for comparison were at
grid points up to .7 km from the observation. The OVAM developed plumes with
strong gradients perpendicular to the wind downwind of principal sources.
Those plumes may be slightly offset from the grid point while actually
affecting the station.
The impact of boundary conditions upon the analyses was not significant,
but the boundary conditions currently used were somewhat arbitrary. Further
study is needed to determine if a set of boundary conditions can be
established which have a better foundation.
LIMITATIONS AND FURTHER RESEARCH
The OVAM analysis was limited by the inconsistency in the mixture of data
available for application in the model. Time-averaged, point observations and
area-averaged emissions were two of the primary data inputs. Time-averaged CO
concentrations at a point are poor representations of an area-averaged
concentration, especially in urban areas. The location of a sampler relative
to a nearby source is extremely critical for determining the CO concentration.
The area-averaged emission smoothes the local variability of CO sources.
Thus, the local source/receptor relationship so often found with CO
measurements is not necessarily identifiable using area averaged data. The
inconsistency went both ways: sometimes the concentrations were higher than
55
-------
that developed by the emissions inventory, and other times they were lower.
This is a shortcoming faced by modellers and analysts everyday.
Sophisticated analysis algorithms such as the OVAM will produce results
in accordance to the input data and model parameters. Consistent analyses can
usually be acquired only if consistent input data are available. However,
there is a possibility to obtain a consistent analyses utilizing the OVAM
through manipulation of certain model parameters, namely the weights. In its
present form, the model places total emphasis on the observation at the
location of the observations. Two and one-half kilometers from that point,
the entire emphasis is placed on the constraint equation. The present
concensus is that a certain amount of emphasis, which can be achieved by
manipulation of the weights, should be placed on the constraint equation at
the location where the observations are found. This procedure will force the
observation and the emissions to become mutually consistent. Proper selection
of the weights which would produce a more consistent analysis must be left to
research. Such research is essential for proper application of the OVAM.
The OVAM relied upon the initial conditions generated by the Barnes
analysis to determine the concentration in data-sparce areas. The CO
concentration is uncorrelated at distances as small as 1 km; yet the Barnes
analysis extends the radius of influence of an observation considerably
farther than 1 km. For example, the OVAM analysis for 1300 and 1400 CST 12
August, when station STL 002 did not report, showed large concentrations in a
narrow plume over and downwind from STL 002. At 1500 and 1600 CST, when STL
002 reported a very large CO concentration, the plume extended over almost
half the southern region of the grid because the Barnes analysis produced an
initial field in which the observation at STL 002 dominated the southern area.
The OVAM results were not in agreement with the observations at many of the
other OSN stations as well as non-network stations. When STL 002 was deleted
at 1500 and 1600 CST and a new set of initial conditions were developed, the
OVAM results were in better agreement with both the OSN and the non-network
observations at those hours and with the analyses at 1300 and 1400 CST.
Though part of the problem in this case resulted from inconsistencies in the
data mixture, the differences in the area influenced by the large sources
around STL 002 with and without the observation at STL 002 was completely
dependent on the initial conditions generated by the Barnes method.
Better initialization procedures are highly desirable. Other
interpolation procedures would undoubtedly produce similar results as those
produced by the Barnes method. Research into initialization procedures is
necessary to obtain a high quality analysis from the OVAM. One procedure with
a high potential for success is the-use of the observations at the specified
grid points, filling in the remaining grid points with a background value
defined to be the network average or minimum•value. In this manner, the
influence of the observation is initially confined to a specific grid point in
accordance with the notion that CO becomes rapidly uncorrelated in space.
Initial conditions specified in this manner would allow the OVAM to develop
completely the distribution rather than altering some initial distribution.
The problems with data mixture and initialization are the most dominant
problems confronted in utilization of the OVAM. They can interact, producing
56
-------
analyses that are inconsistent in time, and, at a given hour, are in poor
agreement with the OSN and non-network observations. It is essential that
research continues to solve these problem areas. Other problem areas
involving boundary conditions and the choice of the top of the model should
also be investigated.
UTILIZATION OF THE OSM TECHNIQUE
Except for some improvements needed for the OVAM, the essential
ingredients for the OSN technique had been developed 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 representative distribution of the
air pollution and 'meteorological 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 may 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 economic 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 (the stations in the
existing network). The algorithm would then establish the minimum number of
stations and their locations needed to be added to the existing network in
order to determine a reasonable analysis of the wind field. The OVAM, the
model used to obtain the air pollution distribution is independent of the
network design. However, since the wind field is an input to the OVAM, an
accurate description of the wind field is necessary. Given the emissions
inventory, then the air pollution distribution can be determined.
The procedure of updating existing networks has not been tested nor has
the site selection algorithm been adjusted to accommodate the procedure. The
existing data for St. Louis can be utilized to test of the OSN technique for
updating networks. A nine-station sampling network presently exists in St.
Louis. RAPS and RTI stations can be used as a part of the updated network.
Case studies would be identical to those utilized for the OSN developed for
St. Louis, simplifying the analysis.
57
-------
REFERENCES
Barnes, S. L. 1964. "A Technique for Maximizing Details in Numerical Weather
• Map Analysis:, J. Appl. Meteor., 3^ 396-409.
Chaney, L. W. 1979. "Microscale Variations in Ambient Concentrations of
Pollutants in St. Louis Air", EPA-600/2-79-183, US EPA Environmental
Sciences Research Laboratory, Research Triangle Park, NC 27711.
Cressman, G. P. 1959. "An Operational Objective Analysis Systems", Mon. Wea.
Rev., 87, 367-374.
Endlich, R. M. and R..L. Mancuso. 1968. "Objective Analysis of Environmental
Conditions Associated with Severe Thunderstorms and Tornadoes", Mon. Wea.
Rev., 96, 342-350.
Lanczos, C. 1970. The Variational Principles of Mechanics, Fourth Edition,
University of Toronto Press, Toronto.
Ludwig, F. L. and J. H. S. Kealoha. 1975. "Selecting Sites for Carbon
Monoxide Monitoring", EPA-450/3-75-007, US EPA, Research Triangle Park,
NC 27711.
Novak, J. H. and D. B. Turner. 1976. "An Efficient Gaussian Plume Multiple
Source Air Quality Algorithm", J. Air Poll. Control Assoc., 26, 570-575.
Ott, W. R. and R. Eliassen. 1973. "A Survey Technique for Determining the
Representativeness of Urban Air Monitoring Stations with Respect to
Carbon Monoxide", J. Air Poll. Control Assoc., 23, 685.
Ott, W. R. 1977. "Development of Criteria for Siting Air Monitoring
Stations", J. Air Poll. Control Assoc. ,27^, 543.
Sasaki, Y. 1958. "An Objective Analysis Based on the Variational Method", J.
Meteor. Soc., Japan, ^6_, 77-88.
1970a. "Some Basic Formalisms in Numerical Variational
Analysis", Mon. Wea. Rev., 98, 875-883.
. 1970b. "Numerical Variational Analysis Formulated Under the
Constraints as Determined by Long-Wave Equations and a Low-Pass Filter",
Mon. Wea. Rev., 98, 884-898.
. 1970c. "Numerical Variational Analysis with Weak Constraint and
Application to Surface Analysis of Severe Storm Gusts", Mon. Wea. Rev.,
JJ8, 899-910
58
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and J. M. Lewis. 1970. "Numerical Variationel Objective Analysis
of the Planetary Boundary Layer in Conjunction with Squall Line
Formation", J. Meteor. Soc. of Japan, 48, 381-398.
Stephens, J. J. 1970. "Variational Initialization with the Balance
Equation", J. -Appl. Meteor., 9_, 732-739.
Thompson, P. D. 1961. Numerical Weather Analysis and Prediction, The
MacMillan Company, New York.
Vukovich, F. M., W. D. Bach, Jr. and C. A. Clayton. 1978. "Optimum
Meteorological and Air Pollution Sampling Network Selection in Cities,
Vol. I: Theory and Design for St. Louis", EPA-600/4-78-030, US EPA
Environmental Monitoring Systems Laboratory, Las Vegas, NV 89114
, and C. A. Clayton. 1979. "Optimum Meteorological and Air
Pollution Sampling Network in Cities, Vol. II: Evaluation of Wind Field
Predictions for St. Louis", EPA-600/4-79-069, US EPA Environmental
Monitoring Systems Laboratory, Las Vegas, NV 89114
Wilkins, E. M. 1971. "Variational Principle Applied to Numerical Objective
Analysis of Urban Air Pollution Distribution", J. Appl. Meteor., 10,
974-981.
. 1972. "Variationally Optimized Numerical Analysis Equations for
Urban Air Pollution Monitoring Networks", J. Appl. Meteor., 11,
1334-1341.
59
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APPENDIX A
OBJECTIVE ANALYSIS TECHNIQUE
. Barnes used a weighted space-time interpolative procedure to ascertain
winds, temperature, and moisture in the vicinity of a moving thunderstorm.
The procedure is fairly simple and straightforward. If $o = 4>(xo,yo,to)
is the scalar variable to be interpolated from a set of observations
^i n ° $(*±*yi»*-Ti)> then a weighted interpolation analysis technique
is'written:
where r2 = x2 + y2.
Barnes chooses
w, the weight function, as
w(rltr0,tn,t0) - o exp I- R2/4k*2 - T2/4v2j/8ir 3/2k*v
where
R2
(y±-y0)2
Tot — t
1 tn 'o
and
4k*2 » 4k* (1 + 8 cos2*)
B o Vj/V* for V* > 0, « 0 otherwise,
* = the angle between the position vector from ro
to r^ and the wind velocity vector V
V * = a characteristic speed of the system moving past
the observing locations.
The parameters k and v are chosen according to the data density and the scale
of motions represented by the analyses. The term a represents the confidence
in the data. If the data is suspect, then a is small «1); whereas with total
confidence in the data, a » 1.0.
60
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Weighted interpolation analyses fall.short by smoothing the analysis in a
highly variable scalar and by underestimating large values and overestimating
small ones. Maxima and minima occur only near maxima and minima in the input
field. Barnes improves the initial analysis byAinterpolating the differences
of the observed and interpolated values 6i>n = $i>n ~-^i,n over a small
area near the observation. By adding the two fields, the new estimate of $ at
the observation time and place should be improved. For the second inter-
polation, Barnes shows that using WY as the weight function for the 6^ n
analysis is equivalent to using an iterative error reduction. In practice, Y,
exceeds 2 but is usually less than 5.
61
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••'"•• ti ~J :- '"•..'-.•• ;- ;
i. ! -. • <_ -,"• :. "„-. 2.
t. TITLE AN'Ot-u'STITLE
OPTIMUM METEOROLOGICAL AND AIR POLLUTION SAMPLING KET- .
WORK SELECTION IK CITIES. Volume III: Objective
Variational Analysis Model
7. AUTHOR(S)
W. D. Bach, Jr. , and F. M. Vukovich
3. FERFOF..V.IKG ORGANIZATION NAME AND ADDRESS
Research Triangle Institute
P.O. Box 12194
Research Triangle Park
North Carolina 27707
12. SPONSORING AGENCY NAME AND ADDRESS
U.S. Environmental Protection Agency — Las Vegas, NV
Office of Research and Development
Environmental Monitoring Systems Laboratory
Las Vegas, NV 89114
;:- Ki.cir.Ex-. •:. ACCECE!O=. no.
E. REPORT DATE
5. PERFORMING ORGANIZATION
8. PERFORMING ORGANIZATION
1
r
1
CODE 1
i
!
REPORT NC
!
TO. rROGRAM ELEMENT NO. i
11. CONTRACT/GRANT NO.
68-03-2187
i
13. TYPE OF REPORT AND PERIOD COVERED'
14. SPONSORING AGENCY CODE
EPA/600/07
T
i
!
i
15. SUPPLEMENTARY NOTES • '
J. L. McElrov. EMSL-LV. Proiect Officer i
16. ABSTRACT
This report is the third in a series of reports on the development and
application of a procedure to establish an optimum sampling network for ambient
i
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 available data were described
in the second report (EPA-600/4-79-069). This report discusses the development and
application to St. Louis of the Objective Variational Analysis Model which is used to
provide the air pollution distribution.
17. " KEY WORDS AND DOCUMENT ANALYSIS
a. ' DESCRIPTORS
Meteorology
Air pollution
IB. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
b.lDENTIFIERS/OPEN ENDED TERMS
Objective Variational
Analysis
St.' Louis, MO.
Model algorithms
19. SECURITY CLASS (This Report)
UNCLASSIFIED
20. SECURITY CLASS (This page)
UNCLASSIFIED
c. COSATI Field/Croup
55C
68A
21. NO. OF PAGES
22. PRICE
EPA Form 2220-1 (Rev. t— 77) PREVIOUS EDITION is OBSOLETE
-------
U.S. ENVIRONMENTAL PROTECTION AGENCY
OFFICE OF RESEARCH AND DEVELOPMENT .
ENVIRONMENTAL MONITORING SYSTEMS LABORATORY-LAS VEGAS
P.O. BOX 15027. LAS VEGAS. NEVADA 89114 • 702/798-2100 (FTS 595-2100)
Date: NOV. j Q 1099
Reply to
Attn of: AMD
Subject: Report: Meteorological and Air Pollution Network Selection
To: Glenn E. Schweitzer
Director
The enclosed report is forwarded for your approval. It's the third
in a series on developing optimum sampling networks for ambient air
quality in urban areas. The report describes experience with the
Objective Variational Analysis Model specifically, using CO as the study
pollutant.
The model generally predicted air quality trends well, but failed to
accurately preoict . nsolute rssgni tudes of CO concentrations. Model
errors and model vs. reality differences are cited as sources of such
discrepancies.
Although need for some model improvement is cited, the test results
show it contains the essential ingredient for developing optimum
sampling networks. The authors conclude the greatest utilization
jf this technique may be in improving an existing network in an urban area.
iavid N. McNelis
Director
Advanced Monitoring Systems Division
Enclosure
cc:
—•>> G. S. Douglas, ODC-I
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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
Research Triangle Institute
P.O. Box 12194
Research Triangle Park
North Carolina 27707
Contract No. 68-03-2187
Project Officer
James L. McElroy
Advanced Monitoring Systems Division
Environmental Monitoring System Laboratory
Las Vegas, Nevada 89114
ENVIRONMENTAL MONITORING SYSTEMS LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
LAS VEGAS, NEVADA 89114
-------
PROJECT SUMMARY I
i
!
OPTIMUM METEOROLOGICAL AND AIR POLLUTION SAMPLING NETWORK SELECTION IN CITIES j
Volume III: Objective Variational Analysis Model
i
by - j
Walter D. Bach, Jr. and Fred M. Vukovich ''
Research Triangle Institute
P.O. Box 12194 >
Research Triangle Park, NC 27709 j
Contract No. 68-03-2187 j
Project Officer
James L. McElroy :
Advanced Monitoring Systems Division
Environmental Monitoring Systems Laboratory
Las Vegas, Nevada 89114
. ABSTRACT
This report is the third in a series of reports on the development"and
application of a procedure to establish an optimum sampling network 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 available data were described in the second report
(EPA-600/4-79-069). This report discusses the development and application to
St. Louis of the Objective Variational Analysis Model which is used to provide
the air pollution distribution.
-------
CttOlARY
^otectlon Agency (EPA)x-to -develop and-'
optimum sampling network (OSN) for ambient
'—a-iT-quairty" in ari""ur ban "area
^Conventional networks are often designed to monitor specific sources or
concentration characteristics of a subsection 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
requirements change. As stations are moved, valuable time histories of
pollutants are lost.
*
ItTI hat. L alien
knowledge of the wind distribution about the urban area should give a
principal guidance for design of a network for air quality monitors.
T
Distribution 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
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source and should remain relative;!" unaffected by source changes. Thus, by
having a sampling netvork that will accurately depict the distribution of --
winds about the urban area, the distribution of pollutants should follow from
a knowledge of the source distribution.
approach involves six steps. Though, in the initial case, the
technique 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 (backward elimination) was developed,
and an optimum set of sites for monitoring winds was selected using
the methodology and the statistical model.
lAt. ?
(A) An DSNJaas developed for St. Louis, and wind and air quality
monitoring stations were established at the indicated sites.
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(5) i.'ind 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 distribution for an area by combining the
emissions inventory, the observed pollutant concentrations, and the
estimated wind fields.
With minor modifications resul
constraints, the first four steps
and economic
leted for the St. Louis
area as described in the first report (Vol. I). Results of the comparison of
fcjfe
the wind field obtained from the OSN aria that
were described in the second reporf-(Vol. II).
development and application of the Objective Variational Analysis Model (OVAM)
to,.St. Louis for the pollutant carbon monoxide (CO).
available data
™-vuume>-discusses the
. The OVAM obtains an analysis of air quality in an area by solving an
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 n'rofl|ir'lTLinfliDqa1i_"'f variability than is possible
using the observations
Hi
to
Adapted for field data and applied
"obtained from the OSN for St. Louis for selected days
in the August 1975 and February 1976 periods of intensive study by the
the
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Regional Air Pollution Study (RAPS) program. Measurements of CO concentra-
tions and winds at the 19-station OSN and the 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-ststion.OSN and an objective analysis model (the Barnes method). The OVAM,
essentially, adjusted the initial field to conform simultaneously with the
observations, the transport associated with the wind distribution, and the
emissions inventory.
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 ate
•described below. -.
) The principal parameters in the OVAM were the weights which placed
emphasis on an obserrvation (if the grid point was near an observation point)
or the continuity equation (if the grid point was not near an observation
y*~
'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 sensitive to the ratio of the
-------
•.:c-ights for the observations and the continuity equation, but v.-es 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
ves half the resolvable spatial scale in the model. Kovever, other RAPS
studies have shown observed 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 therefore 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 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 distribution of sources and winds. Upwind of the stronger
area sources, the concentrations tended to decrease; downwind, they increased.
Large percentage changes between the initial CO distribution 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 that
varied little from the initial distributions. 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 observations 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 decreased by 20 to 30 percent of its initial
value regardless of the number of stations deleted. However, large percent
changes of concentration occurred, depending upon the location of"the-deleted
data. In most daytime cases, the largest changes occurred when observations
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. Concentration changes were primarily controlled by changes
5
in the initial distribution that resulted from the deleted observations.
When stations were deleted in regions 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 observations, suggesting that if initial conditions 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 -Baiter the winds. However, further investigation is required
on the initialization'-iaethodology 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 discrepancies 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
observations not necessarily representative of an area, and
(2) The OVAM values used for comparisons were at grid points up to 0.7
km from an observation, and plumes downwind of principal sources
developed with strong gradients which may be 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
objective analysis procedure to determine the initial concentration field.
The initialization 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 concentration, the plume extended
8
-------
over alinost 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 nore .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 that station was completely
dependent on the initialization technique.
Except for some improvements needed for the OVAM, the essential
ingredients for the OSN technique have been developed 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 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 sampling network and would not want to
undertake the economic 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
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existing network). The algorithm would then establish the nininura 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 inventory, then the air pollution distribution can be determined
using the OVAM.
10
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