EPA-600/3-75-003-3
ADAPTATION
OF GAUSSIAN PLUME MODEL
TO INCORPORATE
MULTIPLE STATION
DATA INPUT
VOLUME I
by
Harvey S. Rosenblum, Bruce A. Egan,
Claire S. Ingersoll, and Michael J. Keefe
Environmental Research and Technology, Inc.
696 Virginia Road
Concord, Massachusetts 01742
Contract No. 68-02-1753
ROAP No. 21ADO-36
Program Element No. 1AA009
EPA Project Officer: D. Bruce Turner
Chemistry and Physics Laboratory
Office of Research and Development
Research Triangle Park, N. C. 27711
Prepared for
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Research and Development
Washington, D. C. 20460
June 1975
-------
EPA REVIEW NOTICE
This report has been reviewed by the National Finvironmental Research
Center - Research Triangle Park, Office of Research and Development,
EPA, and approved for publication. Approval does not ignify that the
contents necessarily reflect the views and policies of the Environmental
Protection Agency, nor does mention of trade names or commercial
products constitute endorsement or recommendation for use.
RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U b Environ-
mental Protection Agency, have been grouped into series. These broad
categories were established to facilitate further development and applica-
tion of environmental technology. Elimination of traditional grouping was
consciously planned to foster technology transfer and maximum interface
in related fields. These series are:
1. ENVIRONMENTAL HEALTH EFFECTS RESEARCH
2 . ENVIRONMENTAL PROTECTION TECHNOLOGY
3. ECOLOGICAL RESEARCH
4. ENVIRONMENTAL MONITORING
5. SOCIOECONOMIC ENVIRONMENTAL STUDIES
6. SCIENTIFIC AND TECHNICAL ASSESSMENT REPORTS
9. MISCELLANEOUS
This report has been assigned to the ECOLOGICAL RESEARCH series.
This series describes research on the effects of pollution on humans,
plant and animal species, and materials. Problems are assessed for
their long- and short-term influences. Investigations include formation ,
transport, and pathway studies to determine the fate of pollutants and
their effects. This work provides the technical basis for setting standards
to minimize undesirable changes in living organisms in the aquatic,
terrestrial, and atmospheric environments.
This document is available to the public for sale through the National
Technical Information Service, Springfield, Virginia 22161.
Publication No. EPA-600/3-75-003-a
11
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TABLE OF CONTENTS
Page
INTRODUCTION 1-1
1.1 Overview 1-1
1.2 Summary of Work Completed 1-1
MODEL MODIFICATIONS 2-1
2.1 RAM 2-1
2.1.1 Description of Model 2-1
2.1.2 Modifications to RAM 2-4
2.1.2.1 Input/Output 2-5
2.1.2.2 Selection of Significant Receptors 2-5
2.1.2.3 Plume Rise 2-8
2.1.2.4 Ventilation Wind 2-8
2.1.2.5 Plume Configuration for Point
Sources 2-8
2.1.2.6 Plume Configuration for Area Sources 2-9
2.1.2.7 Travel Time 2-11
2.1.3 Programming Accuracy 2-13
2.1.4 Illustrative Case Study Using RAM
Modifications 2-13
2.2 SCIM 2-22
2.2.1 Brief Description 2-22
2.2.2 Modifications to SCIM 2-25
2.2.2.1 Plume Rise 2-25
2.2.2.2 Ventilation Wind 2-25
2.2.2.3 Plume Configuration for
Point Sources 2-25
2.2.2.4 Plume Configuration for Area
Sources 2-26
2.2.2.5 Pollutant Decay 2-28
2.2.3 Model Case Study 2-28
2.3 COM 2-36
2.3.1 Brief Description 2-36
2.3.2 Modifications to COM 2-38
2.3.3 Example of COM Run Utilizing Model
Modifications 2-38
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TABLE OF CONTENTS (Continued)
Page
3. TECHNIQUES FOR GENERATING WIND FIELDS 3-1
3.1 Description of Methods 3-3
3.1.1 IDPL: Inverse Distance Power Law 3-3
3.1.2 SA: The Selective Angle Method 3-3
3.1.3 SR: The Selective Radius Method 3-3
3.1.4 WFM: The Weighting Factor Matrix 3-5
3.2 Analysis of Methods 3-7
3.2.1 Methodology 3-7
3.2.2 Results 3-10
3.3 Other Considerations and Guidelines for Use 3-15
4. CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK 4-1
5. REFERENCES 5-1
APPENDIX A USER'S GUIDE TO RAM MODIFICATIONS
A.I Description of Input to RAM
A.2 Fortran IV Program Listing
A.3 Test Case
APPENDIX B USER'S GUIDE TO SCIM MODIFICATIONS
B.I Description of Input to SCIM
B.2 Fortran IV Program Listing
B.3 Test Case
APPENDIX C USER'S GUIDE TO COM MODIFICATIONS
C.I Description of Input to COM
C.2 Fortran IV Program Listing
C.3 Test Case
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LIST OF ILLUSTRATIONS
Number Page
2-1 Method of Determining Significant Receptors in RAM 2-7
2-2 Method of Estimating Cross-Wind Distance in RAM 2-10
2-3 Method of Determining Plume Path in RAM for
Area Source Emissions 2-12
2-4a Monitoring Station Locations Used in RAM Case Study 2-15
2-4b Emissions Inventory Used for RAM Case Study 2-16
2-5 Pollutant Concentration Using Uniform Wind
Field in RAM 2-17
2-6 Pollutant Concentration Using Unmodified RAM 2-18
2-7 Pollutant Concentration Using Wind Fields Shown
in Figure 2-8 in Modified RAM 2-19
2-8 ' Wind Fields Used in RAM Case Study 2-21
2-9 Plume Path for Area Sources in SCIM 2-27
2-10 Emissions Inventory Used in SCIM Case Study 2-29
2-11 Emissions Inventory; Meteorological Station and
Receptor Locations Used in COM Case Study 2-40
3-1 Selective Angle Method 3-4
3-2 Selective Radius Method 3-6
3-3 Observation Point and Calculation Point
Configurations 3-8
3-4 Uniform Gradient Analytical Wind Fields 3-9
3-5 Potential Flow Field 3-14
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1. INTRODUCTION
This report describes the results of a program conducted by Environ-
mental Research £ Technology, Inc. (ERT), under contract to the United
States Environmental Protection Agency (EPA) (Contract No. 68-02-1753)
entitled Adaptation of Gaussian Plume Model to Incorporate Multiple
Station Data Input.
1.1 Overview
The most commonly used procedure for the evaluation of air pollu-
tion control strategies is based on mathematical modeling of the atmos-
pheric dispersion of pollutants through air quality simulation models.
The meteorological data input most frequently used for multiple-source
urban air pollution models is oversimplistic in that the dispersion
processes over an entire urban area are assumed to be adequately des-
cribed by meteorological observations at one point such as a neighboring
airport or National Weather Service Forecast Office. At the present
time air quality sampling networks are being established where wind
observations are available at many locations in the same urban area such
as the St. Louis Regional Air Pollution Study (RAPS) network. Also, the
prediction of detailed wind patterns is the objective of numerical
mesoscale models presently under development. Numerical dispersion
models, which are well-suited for incorporating the output of these
models or other spatially and time varying data into calculations of
pollutant concentration, may be too demanding in terms of computer time
and input data requirements to be practical for many studies or routine
use. It is, therefore, desirable to extend the usefulness of Gaussian-
plume models by adapting them for multi-station input data. Because of
this consideration and the need to improve the accuracy of air quality
simulation models, a contract for the incorporation of several modifica-
tions and potential improvements into standard Gaussian-plume urban
dispersion models was awarded.
1.2 Summary of Work Completed
Urban dispersion models provided by EPA were modified to consider
multiple station information on wind speed and direction. Three models
1-1
-------
were modified: the Real-Time Air-Quality-Simulation Model (RAM) and the
Sampled-Chronological Input Model (SCIM), both short-term models, and
the Climatological Dispersion Model (COM) a long-term model. Relatively
straightforward modifications were studied, ones which are useful,
practical approximations rather than formulations that are absolutely
consistent in a mathematical sense. The modifications had two basic
objectives: the first, to develop techniques for describing wind con-
ditions at any point within a region in which arbitrarily-located
observing stations exist; and second, to identify critical points in the
dispersion algorithms at which the additional multiple-station wind data
could be incorporated and to modify these computation routines accord-
ingly. The modifications were compared among themselves on the basis of
accuracy, computational efficiency and ease of use. Although no obser-
vational data was available to verify the various approaches, the results
of applications to hypothetical meteorological situations indicate that
more realistic results can be obtained by the incorporation of multiple-
station data.
The following sections describe the work performed including model
modifications and analysis methods. Section 2 describes the modifica-
tions made in the EPA models and examples of case studies which illus-
trate the changes. The techniques developed for generating wind fields
from arbitrarily-located observation points are detailed in Section 3.
An analysis of the accuracy and computational efficiency of each method
is given. In addition, guidelines are presented so that the most appli-
cable methods can be selected for a specific situation.
1-2
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2. MODEL MODIFICATIONS
The following sections describe the modifications made to the EPA
models. Since they involve the effect of horizontal wind variability on
plume dispersion, techniques were developed that develop wind fields
from observations at arbitrarily spaced locations. The nature of the
wind generator techniques is critically important because they affect
the model results equally as much as the dispersion algorithm changes
themselves. In this section it is assumed that wind information on
speed and direction is readily available whenever needed; the following
section describes the manner in which this information is produced.
A brief review of the highlights and main features of each model is
given. For a more complete description, the reader is referred to the
original user's manuals in these programs.
2.1 RAM
2.111 Description of Model
RAM is a version of the Gaussian plume model that estimates pollu-
tant concentrations from both area and point sources for periods of
several hours to one day. It provides model values of one-hour concen-
trations at receptors. A series of consecutive hourly observations of
wind direction, wind speed, atmospheric stability, mixing depth and
temperature is used for input. The calculation of hourly concentrations
assumes steady-state conditions for each hour that are independent of
previous or future conditions. The average pollutant concentration for
the period is then calculated by averaging the modeled hourly concentra-
tions. The principal limitation of the model is the restriction of its
use to inert pollutants in regions of relatively smooth terrain. The
former limitation to conditions, where the designation of a single wind
vector is accurate, is eliminated by modifications described later in
this report.
Pollutant concentrations due to emissions from large stationary or
"point" sources is given by standard Gaussian plume equations:
2-1
-------
For stable conditions or unlimited mixing,
Q
2uua a ~^F
y z
i/M2
i 2W j
{exp
+ exp
1
2
1
" 2
z-H2l
a
z
2 '
^1_\
L O /
\ Z /
For unstable or neutral conditions and a > 1.6 L,
exp
p 2ira Lu
y
For other conditions:
xp ~ 2uua a exp I "2 I a
p y z V y
2 a
{
exp
2 a
z-H
exp - y
}
N=J
+ 2
N=l
i
rl , z-H -2NL.2
- y ( — )
exp
, 1 fz-H +2NL.2 ,
+ exp - y (— ) I + exp
I rz+H -2NL.2
l J
j_ rz+H_+2NL 2
2 l a J
z
-3
P
Q =
u =
(2-1)
(2-2)
(2-3)
y =
z =
IT _
L =
concentration due to point sources, g m
emission rate, g sec
wind speed, m sec
horizontal standard deviation of plume width; function of
travel time, stability, m
vertical standard deviation of plume depth; function of
travel time, stability, m
receptor crosswind distance from plume centerline, m
receptor height, m
effective plume height, m
mixing depth, m
2-2
-------
The summation is terminated when successive terms contribute a specified
small amount to the total. Area source contributions are determined
from
*a = Qa
idt
(2-4)
X0 = concentration due to area sources, g m
3.
-2 -1
Q = area source strength, g m sec
-3
line source strength for line source of infinite crosswind
., -1 -1
strength, g m sec
travel time between source-receptor pair, sec
The integrand is determined from the following equations:
For stable or unlimited mixing conditions;
m i / iM2 iM2l
n = — \ exP ~T I + exP ~T I ~T~ 1
Qo fc— 1 2 I a r2la f
XJI /2TT a I I z I z I
z ^ L J L J /
If a > 1.6 L; and
z
l_
L
For all other conditions;
exp <-T
z-H
exp -T
z+H
N=J
2
N=l
exP
1 /z-H-2NL\2
' — -
exp ( -y
z-H+2NL
1 /z+H+2NL\2
"2V CTz /
(2-5)
(2-6)
(2-7)
2-3
-------
The term z is the receptor height. The value of J in Equation 2-7 is
determined as in Equation 2-3.
The integration of Equation 2-4 is complicated in the multiple
station case by the variation of wind speed, u, with location. As a
result, the travel time, T = x/u, where x is distance, varies with down-
wind distance. The modification developed to account for this is des-
cribed later.
The narrow plume hypothesis (Calder, 1971) is utilized to select
those area sources that affect pollutant concentrations at the receptor
for which calculations are being made. The integration of Equations 2-
5, 2-6 and 2-7 in RAM is accomplished at the outset of the program. The
results are stored for fixed values of the travel time T. Pollutant
concentrations for values of T are determined by interpolation between
the stored values.
The dispersion parameters a and a are functions of downwind
travel time of the form AT where A, and B are empirical constants
dependent upon travel time and atmospheric stability.
Many of the computational schemes were designed by Turner and
Hrenko (1974) so that RAM could be used on a real-time basis in an
inexpensive manner. For this reason computational efficiency and model
input simplicity were highly desirable. The method described above for
integrating Equation 2-4 for fixed travel times and interpolating
between them and a scheme for establishing significant receptors at the
locations of expected maximum concentrations that uses the resultant
wind as guidance are directed to this objective. The model includes the
use of Brigg's (1971) plume rise, a power law to express the vertical
variation of wind speed, identification of the most significant point
and area source contributions, flexible input and output, and card
punching for contour mapping.
2.1.2 Modifications to RAM
The following areas were modified in RAM:
• Input/Output
• Selection of Significant Receptors
2-4
-------
• Plume Rise
• Ventilation Wind
• Plume Configuration for Point Sources
• Plume Configuration for Area Sources
• Travel Time
2.1.2.1 Input/Output
The format of RAM's input data was altered to incorporate the extra
data required in the multi-station model. The details of the changes
such as data type, column numbers and sequence are described in Appendix
A. It is sufficient to mention here that wind data from the monitoring
locations and the height of each instrument are required for model input
and are listed in the output. One value per hour of mixing depth,
atmospheric stability class and temperature is assumed to be represen-
tative of the entire region.
The tabulation of model results remains the same except that a
summary of the hourly inputs from the several station locations is
listed for each hour. In addition, the resultant wind at each obser-
vation point is given where appropriate.
2.1.2.2 Selection of Significant Receptors
RAM selects two additional receptor locations for each significant
point source (the point sources whose emissions exceed a pre-specified
level) and one location for each significant area source where maximum
concentrations are expected to occur as a result of each source's pol-
lutant emission during the period. The source-receptor geometry is
determined by the resultant wind for the period. The receptor is placed
at distance x downwind where
max
x = uT (2-8)
max max
2-5
-------
where
x = downwind distance at which maximum concentration is
max
expected to occur
T = travel time to x
max max
u = wind speed
T is calculated from
max
T = aHb (2-9)
max *• J
where
H = effective height of source, assuming u = 3 m sec"
a,b = empirical constants which are functions of the type of
source (point or area), H, and the modal stability class
for the period.
For a point source the significant receptors are located at travel times
of T and 2T from the source location. For area sources the signifi-
max max
cant receptor is placed downwind of the area source center as determined
by the travel time T from the intersection of the resultant wind
max
azimuth with the source boundary.
In the multiple station case both the distance downwind of the
source as well as the azimuth of the resultant wind are changed because
the resultant wind is a function of location. The selection of signi-
ficant receptors must take this into account in order for this part of
the program to retain its original purpose of identifying locations of
expected maximum concentration. The approach developed to handle this
situation is shown in Figure 2-1 in which significant receptors R, and
R- are selected downwind from point source P. This is done by first
using the wind at P to determine point A at distance
x = T lu I (2-10)
max max ' p1
The resultant wind at point B, the midpoint of line segment PA, is then
used as the approximate average wind along the path trajectory starting
2-6
-------
m
ft
m
•H 4->
5 C
G 0)
S S
O U)
Q CD
(NO
OS C
•H
T3 rH
O
r-(
c£ to
4->
» c
l/> -H
H O
O PH
4-> 13
Pn'H
8 e
c -
nJ Q
o
•H
C
CM
OS
CO
rt
•H h I-
C O oi
•H +J
6 o o>
H c w
S -H 3
I
fsl
(U
f-l
a
•H
2-7
-------
at P. Point R.. is thus defined as the receptor location at distance
|u |T downwind from P in the direction of UD. Since RAM selects a
p max D
second significant receptor for each point source at distance x = 2x ,
IT13.X
the process is repeated starting at point R , to determine the location
of R in the multi-station case. The resultant wind u at point D, the
midpoint of line segment R..C, is used to determine R?. The procedure
for selecting the appropriate significant receptor downwind of an area
source case is similar with point P denoting the area source center.
Only one receptor is selected at distance x for area sources.
max
2.1.2.3 Plume Rise
Brigg's plume rise is modified so that the wind speed at the source
is used when wind speed is involved in the calculation. The speed at
the source is determined by field generator techniques for each point
source considered and hence varies from source to source.
2.1.2.4 Ventilation Wind
The wind speed term in the denominator of Eqs. 2-1, 2-2 and 2-3 is
sometimes referred to as the ventilation wind speed. This term is
the same quantity that is used to calculate plume rise. Emissions
emanating from a source will be diluted by the mixing of ambient air
with the effluent gases. The rate at which this occurs will be dif-
ferent for each source in the multiple-station case because the wind
speed varies from location to location. The change implemented in RAM
to account for this is the replacement of the ventilating wind speed by
a horizontally varying value which is evaluated at each source separately.
2.1.2.5 Plume Configuration for Point Sources
The trajectory of a plume emitted in an atmosphere of varying winds
will be curved. Plume configuration can be approximated by a series of
straight lines joined end to end. The accuracy of this type of plume
path is a function of the length of each line segment and the curvature
of the wind field; an exact replication of the plume path can be obtained
if infinitesimally small line segments are used. However, the calcula-
tion of crosswind and downwind distance, necessary for Gaussian-plume
models, becomes very complicated and computationally expensive for large
2-8
-------
emissions inventories. Therefore, the approximate scheme (shown in
Figure 2-2) was developed which would be valid for the majority of cases
encountered on the urban area scale. This scheme is most applicable to
situations where the wind field varies uniformly between the source-
receptor pair so that the wind conditions at the mid-point of a line join-
ing the two is an approximation of the wind conditions between the two
locations.
In Figure 2-2 the wind direction at the midpoint of a line segment
joining the point source-receptor pair of interest is used to determine
point C, the distance of closest approach of the plume to R. From C the
cross-wind distance y_ is determined. Note that the dotted segment PC
K
is not the expected plume centerline but a reasonably close approxima-
tion of the actual plume path in Figure 2-2. It appears that this kind
of approximation is reasonably accurate in wind fields that vary uni-
formly over the distance between the source and the receptor and is
expecially appropriate for receptor locations relatively close to the
actual trajectory centerline (where the contribution from an upwind
source is most significant).
2.1.2.6 Plume Configuration for Area Sources
The method of successive approximation is also used to determine
the contribution from area sources. In the single-station version of
RAM only those area sources lying directly upwind of a particular
receptor are considered in the calculation of pollutant concentration.
This feature remains in the multi-station case, except that the upwind
direction is a curved path and varies from place to place. Because of
the neglect of crosswind dispersion in the area source calculations, it
is feasible to describe the upwind direction as a multi-segmented path
and avoid the mathematical complexity that would be involved in the
point-source calculations. The bends in the path are made at the
intersections with area source boundaries because it is at these points
that the integral in Eq. 2-4 is evaluated. By utilizing the average
wind speed and direction between the receptor and the successive bound-
aries of area sources, the location of each intersection and the travel
time from the intersection to the receptor can be calculated.
2-9
-------
O
c
•H
+->
C
0)
>
PL,
!-i O
DO
bo p:
c -H
• H 4->
4-> rt
TO ^
•H 'MI
T3 rH
O Cu
CM
I
CM
0)
•H
P-
2-10
-------
In Figure 2-3, the wind directions at the receptors, Rp and R., in
the diagram, are used to determine the first guess upwind intersection
point with the area source boundaries, B and H in the diagram. The wind
conditions at the midpoint of these segments, A and G respectively, are
used to determine new intersection points, C and H, and the travel times
along the segments. The process is repeated from intersection point to
intersection point and traces a multi-jointed plume path. From the
information on travel time, it is possible to determine area source
contributions as before from the tabulation of integral values from Eq.
2-4 stored internally. For instance, the contribution C from area
source III to pollutant concentration at point RF, is given by
LJ
C = 0 f / X_ \ rn _ / X_ \ rj,
L ^iii o_ !F q, l1'
where
QTTT = area source III strength
Tp = travel time from point F to RF
•T C
T = travel time from point C to Rp
LJ C
The values of the ratio ^ are stored internally for specified values of
T. The evaluation of ^- at other points is done by linear interpolation
on the stored values.
2.1.2.7 Travel Time
Since RAM uses plume travel time to determine the diffusion para-
meters, a and a , it is necessary to estimate the average wind speed
over the plume path. In the multi-station case, where the wind speed
can be expected to vary from place to place, an exact determination of
travel time would require a sophisticated iterative algorithm. Since
such a scheme would be used repeatedly during the course of a diffusion
calculation, a fair amount of computer time would be involved. With
such factors in mind, an approximation similar to that described in the
two previous sub-sections was adopted. The wind speed at the midpoint
2-11
-------
tt.
2-12
-------
of the source-receptor pair is used as the average wind speed over the
path taken by the plume centerline, segment PC in Figure 2-2 and R^C,
CF, R,H, etc., in Figure 2-3. Thus travel time T in Figure 2-2 is
T - PC
- |UA| (2-11)
The wind speed |U.| is modified by a power-law relationship to give wind
speed at stack level if stack height exceeds 10 m.
2.1.3 Programming Accuracy
In order to check programming accuracy, a comparison of unmodified
and modified RAM runs was made using the identical meteorological and
emissions data input. In the unmodified version the meteorological
input took the form of a single wind direction and wind speed; in the
modified version the comparable input consisted of 25 observing points
being assigned the same wind parameters. The accuracy check was ex-
tended to include multiple station input utilizing each of the four
objective analysis techniques for generating wind fields discussed in
Section 3. In all cases the final version of the modified RAM produced
modeled pollutant concentrations identical to those produced by the
original, unmodified program.
2.1.4 Illustrative Case Study Using RAM Modifications
The modified RAM was applied to meteorological conditions simulat-
ing a sea breeze phenomenon to illustrate the more realistic results
produced by the multiple-station model. The selective angle method was
used with a selection angle of 45 degrees (see Section 3.1.2). The
meteorological input consisted of wind speed and direction from 25
stations over a 21-hour period. For comparison RAM was run for the same
period using wind data from only one of the 25 stations. The results
clearly show the advantage of diffusion calculations which incorporate
multi-station data when the wind varies significantly over an area.
2-13
-------
The locations for the 25 monitoring stations were assigned by
superimposing the configuration of the St. Louis RAPS network on a
square grid 30 kilometers on a side (Figure 2-4a). The coordinates of
the stations are given in Table 2-1. For the single-station case, only
wind data from station 16 near the center of the grid was used. The
emissions inventory used is shown in Figure 2-4b.
Figure 2-5 shows SO- concentrations resulting during hour one. The
wind field is uniform across the region with a 10 meter per second wind
at 315 degrees. This pattern represents both the single and multiple
station cases.
In subsequent hours the wind direction turns until at most stations
it is in the range 180 to 220 degrees immediately prior to the onset of
the sea breeze. A comparison of multi-station and single-station model
runs for hour 18, shown in Figures 2-6a and 2-7a respectively, reveals a
close similarity between the two since the wind directions at most
stations are within 60 degrees of each other (the wind field is shown in
Figure 2-8). The multiple-station case shows a narrower band of concen-
trations since Station 23, the most eastern station, has a wind direc-
tion of 90°, indicating the edge of flow reversal.
During hour 19 the sea breeze front has penetrated to Station 16
(Figure 2-8), and the wind has shifted to an easterly direction there.
The single station case produces isopleths of SCL shown in Figure 2-5.
All pollutant material is transported to the west, and a pattern of
pollutant concentration markedly different from that of the previous
hour results. Because the meteorological conditions for hours 20 and 21
are unchanged at Station 16, the concentration patterns for hours 20 and
21 for the single-station case are almost identical to that shown for
hour 19 and are not shown again. For the multiple-station case, the
concentration patterns for hours 18, 19, 20 and 21 show the effect of
the sea breeze's progress across the grid (Figure 2-7). The transition
from hour to hour is uniform and smooth. A band of high concentrations
is found in the vicinity of the sea breeze front, where the northeast-
ward movement of emitted material is prevented by the easterly flow in
the eastern part of the grid.
2-14
-------
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fO
8
• • \ 5
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O
CVJ
t/i
C
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c
o
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4-»
cd
•P
00 LD f-H
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f-l
O
4->
•H
I
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CM
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D O
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ii i i i I
S
•
ro ^j- \o .._
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i i5 i i i i <
o o
o
ro
O
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| 1
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to
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Hour 18
Hour 19
Hour 21
•0
m
J5
Distance (km)
Figure 2-8 Wind Fields Used in RAM Case Study - Numbers indicate
wind speed (m/s); arrows indicate wind direction at
observing stations (•). Configuration of stations
simulates RAPS network.
2-21
-------
A comparison of multiple- and single-station model runs reveals
that the locations of areas of maximum concentration are different. The
results of the multi-station cases show that the location of maximum
concentration occurs in the vicinity of the sea breeze front, in the
area where onshore and offshore flow patterns converge. The movement of
the front inland causes the zone of maximum concentration to move
roughly in concert with the front because the pollutant material which
is emitted completely in the southwest corner of the grid is no longer
transported to the northeast unimpeded. Observations during lake breeze
cases along Lake Michigan confirm the existence of a concentration
maximum at the sea breeze front (Lyons, 1972). It should be noted,
however, that this is due to the fumigation of elevated plumes as well
as surface confluence in the wind field. In the single station case,
the meteorological conditions for the whole region are given by the
observations at a single point. This being the case, the pattern of
model calculated concentrations undergoes a dramatic change within one
hour in response to the 180° shift in wind direction with the passage of
the sea breeze at one point. When multiple-station data are included,
the shift in pollutant pattern is more smooth and gradual. In the
absence of suitable field data, no definitive assessment of the accuracy
of these modifications can be made. However, the use of multi-station
data produces results which are in reasonable agreement with expected
values.
2.2 SCIM
2.2.1 Description of Model
The purpose of SCIM is to provide a method of estimating the air
quality characteristics of a particular pollutant over a specified area
from randomly sampled hourly concentration values in order to estimate
the frequency of short-term concentrations and the mean long-term con-
centration. Conventional emission inventory data in the form of the
Implementation Planning Program (IPP) data and standard weather data in
the form of punched cards or magnetic tape from the National Weather
Service (NWS) are used as input data. The historical sequence of hourly
or 3-hourly surface observations and twice daily upper air meteorologi-
2-22
-------
cal data is sampled at pre-specified time intervals to provide the mete-
orological setting for the conventional Gaussian plume calculations to
follow. Concentrations due to point and area source emissions are de-
termined at preselected receptor points. Thus, a sample of hourly
concentrations is obtained for the period of meteorological record.
Statistical techniques due to Larsen (1972) are implemented to determine
the frequency distribution of pollutant concentrations as well as the
long-term mean concentration.
Concentrations due to point source emissions, X-* are determined
from the standard Gaussian plume equation with a chemical decay term:
^p 2im oy(x) CTZ ,
(1 / y \2 kx
-1(5^1) --
C2-12)
where
X = pollutant concentration due to point source
emissions, g m
Q = pollutant emission rate at source, g sec"
u = wind speed, m sec~
a (x) = horizontal diffusion parameter, m
a (x) = vertical diffusion parameter, m
&t
H = effective height of the source, m
y = crosswind distance between source and receptor, m
x = downwind distance from source to receptor, m
z = height of receptor above ground or reference level, m
k = chemical decay constant, sec"
Whereas in RAM the horizontal and vertical standard deviations of
the plume a and a are given as functions of travel time, in SCIM these
2-23
-------
quantities are specified as the more conventional functions of downwind
distance. The relationships used in SCIM are those given by McElroy
(1969) for urban areas and those given by Turner (1970) for rural areas.
Calder's (1971) narrow plume hypothesis is invoked for the process
of identifying those area sources contributing to pollutant concentra-
tions. The concentration, XA> at a single receptor from all area
sources is
1 TXd ~r , v \ ( i ru l 2^
XA = I qM e kX, I 1 [H-Z 1 I
A r?- I ~ • J, . exp (- —) exp < -•=- —r^r i
fa J0 uaz(x) u [ \ 2 KM] /
(2-13)
I k ^ J I I
where
-2 1
q = pollutant emission rate from area sources, g m sec
x, = distance from receptor to upwind edge of the source
area, m
Only area sources whose boundaries intersect the upwind azimuth of a
receptor are considered.
The Briggs (1969) formulation of plume rise is used to determine
effective plume height.
The vertical wind speed variation is given by a. power law whose
exponent is a function of Turner-Pasqui11 atmospheric stability class.
A unique feature of SCIM is that time varying patterns of emissions are
linked to the chronology of weather observations, so that variations in
emission rates and in dispersive processes are accounted for. In the
emission algorithm, the emission rates are related to ambient air temp-
erature and time of day, a feature which is especially applicable where
emissions are related to space-heating requirements.
The need for the incorporation of multi-station data input exists
when continuous meteorological observations are available from several
sites within the same region.
2-24
-------
The modifications to SCIM were developed on the assumption that the
complete input requirements of the present single-station version of
SCIM are met at one station and that observations only of wind direction
and speed exist at the other stations. The specific algorithm modifica-
tions consist of changes in the calculation of Briggs' plume rise and
point- and area-source pollutant contributions. Since plume growth is a
function of downwind distance, many of the modifications are simpler and
more straightforward than the parallel changes required for RAM.
2.2.2 Modifications to SCIM
In order to incorporate multi-station data input, changes were made
to SCIM in the following model areas:
• Plume Rise
• Ventilation Wind
• Plume Configuration For Point Sources
• Plume Configuration For Area Sources
• Pollutant Decay
2.2.2.1 Plume Rise
As in RAM, the modification to the calculation of plume rise in
SCIM is to use the wind speed at the source as determined by one of the
techniques discussed in Section 3.
2.2.2.2 Ventilation Wind
Similarly, the wind speed at the source is used for u in the
denominator of Equation 2-12. Thus, u can vary from location to loca-
tion in the multiple station case.
2.2.2.3 Plume Configuration for Point Sources
The plume centerline azimuth is defined as the wind direction
calculated at the midpoint of the line joining the source-receptor pair,
and thus varies from pair to pair. The calculation proceeds as in the
unmodified version with the determination of downwind and crosswind
distance.
2-25
-------
2.2.2.4 Plume Configuration for Area Sources
Equation 2-13, which expresses pollutant concentrations due to area
source emissions, is an integral of the product of two exponentials and
a factor that is inversely related to wind speed along a prescribed
path. Also, the integration includes the effect of the vertical dis-
persion parameter, a , which is a function of downwind distance and
Li
stability.
The integration is accomplished in piecewise fashion; the integral
is evaluated numerically by the trapezoidal rule on-line intervals in
the upwind direction. The length of each integrating interval increases
with increasing distance from the receptor in a manner determined in-
ternally.
The modifications to SCIM were made in the evaluation of the inte-
gral in Equation 2-13: first, the upwind direction is taken to be the
average wind direction over the plume path interval, and second, the
wind speed u is taken to be the average wind speed over that path.
Since wind direction and speed may vary over the path of the plume in
the multi-station case, the integration is accomplished on a series of
connected line segments that approximates a curved path. The value of
wind speed used varies from interval to interval in response to changing
wind conditions.
This modification to SCIM is shown schematically in Figure 2-9.
The integration begins at the receptor location R. The location B
upwind of R is determined by using the wind direction at R as the azi-
muth and the internally prescribed integration interval for distance. A
new location B1 is then determined by using the wind direction at A, the
midpoint of the segment RB, as the azimuth for the upwind direction.
The selection of wind conditions at A as the average wind conditions
affecting plume travel in the first upwind interval yields a reasonable
first-order approximation to the actual plume conditions. The wind
speed at A is used for u in the denominator of the integrand in Equation
2-13. In the next upwind integration interval, points C and C1, cor-
responding to the first and second guesses of upwind direction, are
virtually coincident because the wind field varies little over that
2-26
-------
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2-27
-------
interval. It may be expected in the general case that the wind field
will vary little over some integration intervals. The process is re-
peated until the desired upwind integration distance has been achieved.
2.2.2.5 Pollutant Decay
SCIM incorporates the effect of chemical decay of the pollutant and
physical transformation from one species to another. The half-life of
pollutant decay rate, k (Equation 2-13), is input externally, and the
amount of chemical decay is determined by the travel time experienced by
the plume. Since travel time t is given by the ratio of downwind dis-
tance to wind speed,
t = - (2-14)
u v '
it is necessary to determine the appropriate wind speed in the multiple
station case.
For point sources, the term x in Equation 2-14 in the multi-station
version is the downwind distance determined for the particular source-
receptor pair by the method described in Section 2.2.2.3. The wind
speed at the mid-point of the line segment joining the source-receptor
pair is used for u.
2.2.3 Model Case Study
Three runs were made with SCIM for the purpose of illustrating the
changes. The emissions inventory and the locations of receptors and
observation stations that were used for all of these runs are shown in
Figure 2-10. The emissions inventory was designed so that the model
results could be readily interpreted. Four area sources of varying
strengths are located symmetrically on the grid. In addition there are
five point sources, one of which is located at the center of the modeled
area. The point sources were assumed to have low stacks so that non-
zero pollutant concentrations could be assured at the four receptor
locations, each at the center of an area source. The dimensions of the
square grid were set at 10 km on a side.
For the single station SCIM calculations, a series of 3-hourly
surface National Weather Service observations from El Paso, Texas for
2-28
-------
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2-29
-------
the period 0200 on 1 March through 1100 on 4 March 1971 were used.
Since suitable upper air data were not available in time for this cal-
culation, it was assumed that the morning mixing depth was 500 m and the
afternoon depth 1500 m on all days. The wind observations at El Paso
for the period are shown as Station #1 in Table 2-2 and at location SI
in Figure 2-10.
The hypothetical wind data for the multi-station case was developed
for Stations S2 and S3 in Figure 2-10 for the hours modeled. It was
assumed that wind conditions at S2 and S3 were similar to those observed
at SI except that topographical barriers, indicated by dashed lines in
Figure 2-10, caused channeling and/or blockage of the wind, depending on
the orientation of the SI wind with respect to the barriers. This would
result in an increase or decrease in the wind speed depending on the
wind direction and orientation of nearby barriers. An appropriate
change in wind direction was also made based on the same considerations.
The results of this are shown in Table 2-2.
A test of programming accuracy was performed on a multiple station
case by assigning Station 1 data to all three stations. This run dupli-
cated the results of the single-station case.
A comparison of the multiple station case with all 3 stations used
for meteorological input and a single station case with only Station 1
is made in Table 2-3. The multi-station case was run using a selective
angle of 45° (see Section 3.1.2). The results at receptor 1 are very
similar for both cases due to the close proximity of this receptor to
Station 1. The effect of the multiple-station data can be seen most
readily at the other three receptors. For instance, during the hour
ending at 1700 on 1 March, the wind speed and direction at Station 3 are
markedly different than the wind conditions at Station 1 because of the
topographic barrier just to the west of the station, which blocks the
wind from that direction. As a result, the wind speed at sources P4 and
P2 are lower in the multi-station case and yields higher pollutant
concentration at receptors R2 and R4 than in the single-station case.
Receptor 3 shows increased impact from source P2 because of wind shifts
to the northwest and a decrease in wind speed at Station 3. During hour
0500 on 3 March, however, the concentrations are decreased at all recep-
tors in the multi-station case because of increased wind speed away from
2-30
-------
TABLE 2-2
MULTIPLE STATION WIND INPUT FOR SCIM
WD = Wind Direction, Tens of Degrees
WS = Wind Speed, Knots
Month, Day,
Hour
30102
30105
30108
30111
30114
30117
30120
30123
30202
30205
30208
30211
30214
30217
30220
30223
30302
30305
30308
30311
30314
30317
30320
30323
30403
30405
30408
30411
Station 1
(El Paso Data)
WD
35
15
36
16
24
27
33
31
30
30
29
34
03
02
02
12
12
12
00
18
00
24
24
04
00
08
01
17
WS
05
06
05
10
15
28
13
14
22
15
17
10
11
09
06
07
03
03
00
03
00
08
06
04
00
03
03
03
Station 2
WD
33
15
02
16
24
26
31
30
29
29
28
01
03
02
02
12
12
12
18
18
18
24
24
04
08
08
03
18
WS
04
07
04
12
17
23
08
07
16
10
14
05
10
08
07
09
05
05
01
05
02
10
08
04
02
06
03
06
Station 3
WD
35
14
36
15
30
31
33
31
31
31
30
34
03
02
02
12
12
12
00
18
18
20
20
04
07
08
02
17
WS
07
07
06
10
05
06
14
13
15
10
10
10
12
10
08
10
08
08
00
03
03
04
03
05
05
06
06
08
2-31
-------
TABLE 2-3
MULTIPLE AND SINGLE STATION SCIM CONCENTRATIONS, yg m
-3
Month , Day , Hour
30102
30105
30108
30111
30114
30117
30120
30123
30202
30205
30208
30211
30214
30217
Single Station Run
Receptor
Rl
54.0
78.3
56.6
16.5
7.8
4.7
22.8
R2
42.9
206.1
59.0
25.2
10.8
6.8
23.5
13.9 18.1
R3
170.1
250.6
210.8
63.6
33.2
17.4
78.3
49.3
7.1 9.5 26.2
\
| 16.0 21.8 ) 61.1
| 21.0
19.0
29.4
19.9
23.3 19.2
61.4 39.2
30220 JJ160.7 87.0
30223
30302
30305
30308 Calm*
30311
30314 Calm*
30317
30320
30323
30402 Calm*
30405
30408
30411
117.1
= 226.8
J400.5
26.7
20.0
38.4
196.6
494.7
109.3
24.7
167.7
325.2
574.3
36.0
27.9
53.2
111.7
371.8
108.3
31.8
80.9
64.4
56.9
135.2
R4
111.1
259.3
157.2
60.5
26.3
15.2
56.3
39.1
21.7
50.5
69.1
50.1
42.5
89.1
323.4 198.2
169.8
329.2
581.3
160.2
87.6
171.2
276.3
533.2
364.5
121.2
125.0
242.3
427.8
137.0
69.2
138.8
209.5
367.8
271.2
103.4
Multiple Station Run
Receptor
Rl
45.8
78.0
55.1
16.4
8.2
5.1
23.1
14.7
7.5
17.1
22.3
19.7
23.5
60.6
137.3
110.0
192.1
339.1
26.4
20.7
39.7
190.9
330.6
100.8
24.0
R2
31.3
202.7
50.4
26.1
31.4
27.0
22.0
19.5
14.5
34.3
48.4
20.2
18.0
36.0
66.9
132.0
189.1
333.9
33.5
41.2
79.5
94.2
196.0
61.5
18.4
R3
180.7
228.1
262.1
58.2
33.7
19.6
90.8
63.5
31.1
75.1
91.3
118.4
61.0
148.4
279.0
140.6
211.9
374.1
123.6
86.2
165.6
273.9
301.3
347.8
75.1
R4
113.6
224.1
182.8
51.6
28.4
33.7
73.7
58.4
29.3
72.4
93.8
87.4
45.3
95.8
168.4
97.2
143.6
253.4
88.0
64.7
126.9
202.2
185.6
243.4
54.3
* Cases of calm winds are not considered by SCIM and are deleted from
the sample.
2-32
-------
Station 1. This kind of analytic reasoning can be extended for every
hour of the modeling period to account for differences between single-
station and multi-station calculations.
For typical applications of SCIM it would be desirable to select a
sampling interval not divisible into 24 rather than the three-hour
interval chosen here so that all hours of the day would be sampled.
However, in order to obtain a sample large enough to allow the appli-
cation of Larsen's statistical techniques from a limited historical
record, a short sampling interval was used. The results of the sta-
tistical techniques in the form of frequency distributions are shown in
Tables 2-4 and 2-5. Comparable geometric means of pollutant concentra-
tion are obtained for both cases with significantly higher arithmetic
means and standard deviations for the single-station case. This indi-
cates a wider range of concentrations in the single-station case with a
few hours of much higher and lower values. An inspection of the results
in Table 2-3 bears this out. These results are purely a function of the
specific inputs provided and are not expected to be generally true.
2-33
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2-35
in in in in
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tr ^
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u
lu
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-------
N
n=l
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6 6 <
£=1 m=l
16
1 % (f
k=l K
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6
3) Z
i=l
£, m)
6
£
m=l
QnS
n
(k,S
(Pn, z; UA, Pm)
-,m) Sfp, z; U., P
x m
2.3 COM
2.3.1 Brief Description
The purpose of COM is to calculate long-term pollutant concentra-
tions for time periods of several months and longer from emissions
inventory data and the joint frequency distribution of observed wind
direction, wind speed and atmospheric stability classes. The usual
application is in urban areas for non-reactive pollutants.
For point sources, the average concentration, x and x.» due to
p A
point sources and area sources respectively, is
xp
11—i x/—J. m—j. 11
1A f<*> 16 66
dp (2-16)
" *" '0 k=l * 1=1 m=l * "'
where
N = number of point sources
k = wind sector appropriate to the nth point source
k = index identifying wind direction sector
0 = emission rate of the nth point source
p = distance from the receptor to an infinitesimal area source
q (p) = QA(P> 9) d6 for the k sector where Q,(P, 9) is emission
rate of the area source at distance p per unit area and unit
time
p = distance from the receptor to the nth point source
= joint frequency function
m = index identifying the Pasquill stability class
H = index specifying wind speed
S(p,z; U0, P ) = dispersion function defined below
Jo m
2-36
-------
z = height of receptor above ground level
U = representative wind speed
JC
P = Pasquill stability category
If the receptor is presumed to be at ground level (z=0), the functional
form of S(p , 0; U , P ) is
Tl Xr In
r i f
S(p, 0; U , P ) = - exp - \ (^-.} 2\ exp I"0-692 p I (2-17)
/27u£oz(p) I VVV J I U£T1/2J
if a (p) <_ 0.8L; or
Z
S(p, 0;U£f Pm) - i-L exp F-0.692X1 (2-18)
if a (p) > 0.8L
Z
with
a (p) = vertical dispersion function
H = effective stack height of source distribution
L = afternoon mixing height
T , = assumed half-life of pollutant, hours
Removal by physical and chemical processes is incorporated by the expres-
sion exp 1"' T—— . The total concentration for the averaging
I U£ 4/2 J
period is the sum of concentrations due to the point and area source emis-
sions for the period.
The vertical dispersion parameter, a (x), is given by a power-law
expression ax +c, where a, b and c are empirical constants that are
functions of stability and downwind distance. The use of Pasquill-
Turner stability classes has been modified to account for urban heat
island effects, which are particularly important during the nighttime
hours. Plume rise is given by Briggs (1971). The calculation of area-
source contributions is made by selecting only those sources lying
directly upwind of a given receptor.
2-37
-------
The modifications implemented in the COM to incorporate multiple-
station data input were addressed to situations in which joint fre-
quency distributions of wind direction, wind speed, and atmospheric
stability class (wind roses) are available at several locations within a
region. This often occurs in metropolitan areas serviced by several
airports at which NWS meteorological stations exist, such as New York
City or Chicago. The same situation also exists at the site of compre-
hensive urban field experiments such as the St. Louis RAPS, where in-
strumented towers are continuously recording meteorological variables.
The description of the modifications to COM to accept this type of data
input follows.
2.3.2 Modifications to COM
The modification to CDM involved the derivation of a new joint
frequency distribution of weather classes on the basis of inverse dis-
tance power law weighting of the individual weather class frequencies
from the wind roses included. Thus, the frequency of occurrence of a
given weather class f. is
1 N
A.g. .
(2-19)
f.
E
_ J=l
N
E
j=l
A.g. .
3 1J
A.
D
where
N = the number of stations for which wind roses are included
A. = weighting factor
g.. = frequency of occurrence of weather class i at station j
The same options are available in this method as exist for RAM and SCIM
in the selection of weighting factors, A., in the wind field generator
technique. In addition, the exponent of the power law desired in the inverse
distance weighting can be varied as described in Section 3.
The calculation of long-term pollutant concentration is unaffected;
the Gaussian-plume calculation proceeds with the same parameters for
each weather class considered as in the unaltered model. The modifica-
tion occurs when the frequency of occurrence of the class is used to
2-38
-------
weight the calculated pollutant concentration in order to obtain the
long-term means. The frequency of occurrence of an individual class
will vary from place to place in response to the proximity to observa-
tion locations.
2.3.3 Example of COM Run Utilizing Model Modifications
Several test runs were made using the modified version for COM.
The unmodified model was run with the input shown in Appendix C for 3
simulated day-night STAR wind roses for Newark, New Jersey (EWR), John
F. Kennedy (JFK) and LaGuardia Airports (LGA) in New York City. This
case was chosen as representative of the type for which the COM modif-
ications would be most applicable, e.g., an urban area in which climat-
ological wind roses are available at several locations.
A comparison was made using model runs of each wind rose separately
as a single-station case and together as a multiple-station case. The
selective angle method with 9 equal to 45 degrees was used. The rela-
tive poisition of the airports was estimated and superimposed on a 900
square kilometer grid (Figure 2-11). The wind roses are given in
Appendix C-3.
The model results are shown in Table 2-6. The mean concentrations
at receptors 10, 18 and 7 are the same as the corresponding single-
station calculation using the observation point closest to that loca-
tion, JFK, LGA and EWR respectively. For the remaining sector points,
the mean concentrations reflect proximity to each of the three stations.
Although the wind roses are similar, differences of more than 25 percent
occur between the results of the single-station and multi-station runs.
2-39
-------
1 I 1 1 1 1 1 I 1 1 1 1 1 1
X X X ^. X X
Q:
^«
^
^
•
x x x x x
™"
C\l
<£
x • x
-
r^
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to
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ro
— '
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5
X • X
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rr\
x x x ^ x x
X
I , , <
5
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1 1 1 1 1 1
X
CVJ
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8
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2-40
-------
TABLE 2-6
COMPARISON OF COM RESULTS
Receptor #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Receptor Coordinates, Km
X
3
9
15
21
27
3
9
15
21
27
y
3
3
3
3
3
9
9
9
9
9
i
3 j 15
9
15
21
15
15
15
27 i 15
3
9
15
21
27
3
9
15
21
27
21
21
21
21
21
27
27
27
27
27
Receptor Cencentrations, yg m
Wind Rose Used
JFK
13
9
8
8
9
8
12
19
14
8
7
14
136
18
9
6
8
21
14
9
12
7
12
8
12
LGA
15
12
9
9
9
10
15
19
15
11
7
14
136
18
9
7
8
16
13
8
11
6
7
6
8
EWR
14
11
7
9
7
8
15
15
15
9
5
14
157
21
9
7
9
16
22
10
11
8
4
7
7
Multi-station
Case
14
11
8
8
9
8
15
16
14
8
5
14
149
18
9
7
8
16
13
8
11
7
7
7
9
Station:
JFK
LGA
EWR
Locations:
x y
26.75 10.00
22.50 17.25
10.00 12.75
2-41
-------
3. TECHNIQUES FOR GENERATING WIND FIELDS
The preceding chapter describes the steps in the diffusion calcu-
lations at which changes were made in order to accommodate multiple
station wind data input. Implicit in the discussion of these changes is
the ability to generate the required wind information from the available
meteorological observations. The means by which this information is
approximated has a critically important effect on the model results.
For instance, if the wind conditions at the closest observation point
are selected as representative of conditions at a given location, serious
errors and discontinuities may develop in the model output if the nearest
station is not as representative of the conditions as, for example, a
weighted average of several closest stations and that the estimates
differ greatly. The meteorological analyst would know how to "draw the
contours" in this situation on the basis of his experience with the
observed data. In data-sparse areas for example, the analyst will space
the isopleths based on his experience and intuition of actual conditions.
Any method which is developed to simulate the analyst's product must
have the flexibility and capability of accepting new information and
experience as it is gained in order to produce a more accurate result.
Several techniques are described for estimating wind speed and
direction at any point in a region in which arbitrarily spaced wind
observations exist. These methods determine wind direction and speed by
interpolating the horizontal orthogonal (u, v) wind components from
available data on the basis of inverse-distance power-law weighting.
More sophisticated analysis methods that develop analytic expressions
for the wind field by minimizing the error in estimating the field while
satisfying dynamic relationships between meteorological variables
such as wind, temperature, pressure and humidity (e.g. Panofsky, 1949)
were considered impractical for the purpose of this study. The primary
objection to their use is that they would require generally unfeasible
costs for site studies and computer time in order to simulate the complex
variations of surface roughness and thermal characteristics, and their
effects on the wind flow. This degree of complexity is beyond the scope
of EPA's stated goal of "relatively straight-forward modifications" in
the basic multiple-source Gaussian plume algorithms.
3-1
-------
Four different schemes were developed: the basic inverse distance
power-law weighting (IDPL), selective angle (SA), selective radius (SR)
and weighting factor matrix (WFM) approach. All are described by the
following equation:
Z U.F. /r? (3-1)
. i ip' ip v }
U =
P E F. /rn
i IP IP
where
U = parameter value at point p
U. = parameter value at observation point i
F. = weighting factor
r. = distance between p and i
ip F
n = exponent of inverse distance power law (n = 1,2,3....)
The difference in methods arises from the specification of i's, the ob-
servation points considered in the summation of Equation 3-1, and the
values of F. used.
Since no real data of the type suitable for verification was avail-
able, several sets of hypothetical observations were generated for this
purpose. Analytically determined scalar fields were superimposed on a
grid in which a randomly spaced array of observation points were situated.
The field was then sampled throughout the grid utilizing the techniques
for generating wind fields. A comparison was made between the estimated
values and those calculated from the analytic flow. Two different kinds
of analytical fields were used: a constant-gradient, linearly varying
field and a physical analogue, potential field of flow around an obstacle.
The results were evaluated on the basis of accuracy, computational
efficiency and ease of use. A sensitivity analysis was performed to
determine the response to the variation of critical parameters. In the
potential flow case the effect of observational error is also investigated.
Guidelines for the proper usage of each of the methods are included at
the conclusion of this section.
3-2
-------
3.1 Description of Methods
3.1.1 IDPL: Inverse Distance Power Law
This method is the most basic and straightforward of the four; all
observation points are considered in the summation and F. = 1 for all i
ip
and p in Equation 3-1.
3.1.2 SA: The Selective Angle Method
Elimination of redundant or superfluous data is the goal of the
selective angle method. The assumption is made that accuracy as well as
computation time can be optimized for certain situations by eliminating
data determined to contribute little useful information to the calculation
of wind conditions at the point in question. In this method, observation
stations are selected as inputs to a wind field calculation only if they
are the closest stations to the receptor within a specified angular
sector. This scheme eliminates the distant stations and leaves a ring of
close-by stations around the calculation point.
The first step locates the observation point nearest the calculation
point. A pre-selected angle 6 bisected by the line connecting the
observation station and receptor is constructed (as in Figure 3-1). All
points in this sector are eliminated from the summation in Equation 3-1.
In Figure 3-1, Stations 2, 3, and 4 are eliminated because they are in
the angular sector bisected by Station 1. The process is continued with
the closest non-rejected station until all possible sectors have been
scanned. The ring of remaining stations then provides the values input
to Equation 3-1. The choice of 9 determines the maximum number of
stations to be included. For instance, if 9 = 45°, no more than 8
stations will be considered in Equation 3-1; if 9 = 360°, only the
closest station will be used.
3.1.3 SR: The Selective Radius Method
The selective radius method, like the SA method, assumes an improve-
ment can be made in accuracy and computational efficiency by eliminating
redundant stations. The scheme utilizes the inverse-distance power-law
3-3
-------
Figure 3-1 Selective Angle Method - R is calculation point; 0 is
selective angle. 1 and 5 are included stations; stations
surrounded by dashed circles are excluded from calculation.
Procedure is repeated for closest station not within angular
sectors until all stations have been either included or excluded,
3-4
-------
weighting of Equation 3-1. An attempt is made to reduce the degree of
redundancy when groups of stations are located close together. These
stations may provide a large amount of data while representing only a
small portion of the entire wind field. The selective radius method is
designed to select one station from each grouping. It also decreases
computation time by dealing with a smaller number of stations.
This method is accomplished by first selecting the station closest
to the calculation point of interest, location 1 in the example given in
Figure 3-2. All stations within a specified radius, r, of that first
station (stations 2, 3, 4) are eliminated as inputs. The process is
then repeated for the next closest station (station 5, in Figure 3-2)
and so on. When all possible eliminations have been made, the remaining
stations are included in Equation 3-1 for the calculation of parameter
values.
3.1.4 WFM: The Weighting Factor Matrix
This' method involves the specification of the array F. in Equation
3-1. Although the effect of distance is taken into account in the
inverse-distance weighting scheme, it may be desirable under certain
situations to assign a higher relative weight to one observation point
than another, even though both are at comparable distances from the
calculation point. This would be the case when a greater amount of
confidence is expressed in the quality of a particular set of observations
relative to others in the same region. Also, this would occur when
topographic or man-made barriers exist within a region, effectively
blocking the exchange of air between two adjacent areas and decoupling
the atmospheric flow at one location from the other. Even though two
locations may be close in terms of separation on a horizontal plane, the
wind flow at one place may bear no resemblance to that occurring at the
other. In the interpolation scheme, it is necessary to account for this
effect when calculating wind conditions in either of these two areas.
The method is implemented by directly inputing the matrix F. .
The p index is given by a grid which divides the modeled region into a
maximum of 100 (10 x 10) squares. Thus, in the calculation at the point
in grid square p, the weighting associated with observation point i is
3-5
-------
Figure 3-2 Selective Radius Method - R is calculation point; r is
selective radius. 1 and 5 are included station points;
stations surrounded by dashed circles are excluded from
calculation. Procedure is repeated for next closest
station not within radii until all stations have been
either included or excluded.
o
m
3-6
-------
F. . If a weighting factor F. is set to zero for a particular station-
grid square pair, the data from station i is completely eliminated for
all calculation points in the p grid square.
The weighting factor method is the most general of all four methods
because it incorporates the largest amount of flexibility. The user can
tailor the matrix for the specific case and has a great deal of freedom
in doing so. In addition, the weighting factor method can be used in
conjunction with any of the other methods. The principal drawback of
this method is that the user must be careful in his selection of matrix
values and perform a fair amount of preliminary work before implementing
this method successfully.
3.2 Analysis of Methods
3.2.1 Methodology
Analytical wind fields were selected so that each of the techniques
for generating wind-fields could be evaluated and compared. It is
sufficient for this purpose to consider only scalar fields because the
wind field vector may be resolved into components that are scalars.
First, a network of observing stations was randomly located on the
field. The field was then uniformly sampled at 25 locations, designated
as calculation locations, by means of each of the wind-field generator
techniques. The weighting factor matrix method was not used because it
was assumed that all of the observations were equally representative,
i.e., F. = 1 in Equation 3-1 for all i and p. Five, 10 and 20 station
networks were used, shown in Figure 3-3 with the calculation locations.
Five sets of analytical wind fields were used. Figure 3-4 shows the
fields characterized by uniform gradients of parameter values. They are
the east-west (EW), north-south CNS), diagonal CD) and circular (C)
gradient fields. These patterns were chosen in order that the results
of the analysis reflect properties of the schemes themselves and not
peculiarities of the wind fields. The linear variations test both
orthogonal and transverse directional gradients so that the variation in
accuracy of the different methods to gradients in all directions can be
determined. The circular case was chosen in order to evaluate the
properties of each method in a case where the wind field gradient undergoes
a sign reversal.
3-7
-------
1.0
1.0
0.5
0.5
0
0
0.5
1.0
0
0
0.5
1.0
5 Station Case
10 Station Case
I.VJ
0.5 ,
0
i *
•
"
* . "
•
,«
• i
I.U
0.5
0
i
X X X X X
X X X X X
- X X X X , X -
X X X X X
X X X X X
1
0
0.5
1.0
0
0.5
1.0
20 Station Case
Calculation Locations
N
JO
in
Figure 3-3 Observation Point (•) and Calculation Point (x)
Configurations used in comparison of Techniques for
Generating Wind Fields
3-8
-------
1.0
1.0
-15
0.5
0.5
// 13 15
7
0
0
0.5
1.0
0
0.5
1.0
Linear East-West Variation (E-W) Linear North-South Variation (N-S)
1.0
Linear Diagonal Variation (D)
Linear Circular Variation (C)
m
m
Figure 3-4 Uniform Gradient, Analytical Wind Fields used in
Comparison of Techniques for Generating Wind Fields
3-9
-------
The calculated values obtained using the techniques for generating
wind fields were compared with the values derived from the analytical
expressions describing the wind fields. The root-mean square (RMS)
error for all stations was then calculated from:
RMS =/Z A. - C. (3-2)
V i — —
* N
where
A. = analytically determined value at calculation location i
C. = calculated parameter value at i
N = 25, the number of calculation points.
An RMS value of zero would indicate perfect replication of the wind
field at all points.
3.2. -2 Results
A summary of the results of the RMS error analysis is given in
Tables 3-1 and 3-2.
Overall, the selective angle method produced the lowest RMS values
in both uniform gradient and potential flow cases. In most of the cases
this method was successful in minimizing the error regardless of the
density of the observation network by eliminating from the calculations
the stations which would contribute unnecessary additional information.
A ring of stations more or less uniformly distributed about the calculation
point remained after the elimination. Generally, the larger the number
of observation points, the more complete the areal coverage which should
produce more accurate results. This effect, however, was not uniform
for all cases studied. In fact, due to the uneven north-south distribution
of observation points in the 10 station case, all of the methods exhibited
a decrease in accuracy (an increase in the RMS error) in the north-south
and diagonal fields in going from 5 to 10 stations. This effect is
minimized in the selective angle method. The east-west field shows
increases in accuracy with increasing station numbers in all cases. In
the 20 station case a further gain in accuracy is achieved by the selective
angle technique relative to the other methods.
3-10
-------
TABLE 3-1
RESULTS OF R.M.S. ERROR ANALYSIS OF WIND FIELD GENERATOR TECHNIQUES,
UNIFORM GRADIENT FIELDS
N is power law exponent,
Selective Angle is 45°,
Selective radius is 1/10 of the grid length
Wind Field
East-West
North -South
Diagonal
Circular
Method
Selective Angle, N=2
Selective Radius, N=2
Inverse Distance, N=2
Inverse Distance, N=l
Inverse Distance, N=3
Selective Angle, N=2
Selective Radius, N=2
Inverse Distance, N=2
Inverse Distance, N=l
Inverse Distance, N=3
1
Selective Angle, N=2
Selective Radius, N=2
Inverse Distance, N=2
Inverse Distance, N=l
Inverse Distance, N=3
Selective Angle, N=2
Selective Radius, N=2
Inverse Distance, N=2
Inverse Distance, N=l
Inverse Distance, N=3
No. of Observation Points
5
1.879
1.966
1.966
2.445
1/742
1.719
2.167
2.168
2.450
2.062
0.689
0.953
0.953
1.330
0.823
1.858
1.740
1.740
1.735
1.861
10
0.948
1.364
1.334
1.880 .
1.137
1.799
2.354
2.484
2.864
2.291
1.107
1.372
1.476
1.779
1.347
1.844
1.756
1.735
1.775
1.830
20
•0.448
0.906
0.979
1.712
0.795
0.775
1.383
1.450
1.931
1.294
0.730
0.863
1.016
1.401
0.924
0.921
1.323
1.295
1.591
1.285
3-11
-------
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3-12
-------
The selective radius method performed with approximately the same
accuracy as the non-selective IDPL. Apparently, this method achieved
small gains in eliminating from consideration observation points which
are very close together. With uneven groupings, the radius length would
be suitable for some regions of the study area while being inadequate in
others. Stations at relatively large distances would be included while
the ring of stations nearest the calculation location would be elimin-
ated. No radius tested produced results as accurate as those produced
by the search angle method with a 45° search angle.
In the uniform gradient cases, the effect of varying the power law
in the inverse distance weighting was investigated. For the fields
used, values of N = 2 and N = 3 produced the, best results, with N = 3
holding a slight edge. This can be attributed to the ability of each
method to assign a small weight to distant observation points. A 1/r
2
weighting is more effective in doing this than the 1/r , which in turn
is more effective than 1/r. In the circular case, however, where a
reversal in field gradients tends to minimize the penalty in weighting
far-away and unnecessary information, the differences in accuracy are
smaller.
A second flow field was used to compare the wind field techniques
in order to provide an analogue to physically realistic flow situations.
Surface flow fields can be very complex, however, they can be approximated
to first-order by a non-divergent, irrotational flow which is determined
by boundary conditions. A simple case is found in Figure 3-5 where a
uniform flow field of 10 m sec is perturbed by an obstacle indicated
by the stippled area. The striped section of the flow field was chosen
as the field for the techniques comparison because the flow varied
significantly from one side of the square to the other and would provide
for useful, non-trivial results.
The flow field is given by
MX
u +
(x-x)Q2 + (y-yo)2 (3-3)
3-13
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vfx y) =
*• >yj 9 2 f^-dl
(x-xor + (y-yor l J
where
M = obstacle parameter which determines the shape and size of the
42 -1
obstacle = 3 x 10 m sec in this case
x,y = cartesian space coordinates
x , y = coordinates of "origin" of obstacle, shown in Figure 3-5
for this case
U = velocity of unperturbed flow = 10 m sec" in this case.
In the potential flow field case the selective angle method generates
the most accurate values (Table 3-2). A second potential flow case was
studied in order to determine the effect of error in observations on the
accuracy of the wind field generating methods. At each of the observation
points the true wind condition is known from the analytic expression
which describes the field Equations 3-3 and 3-4. A random error is
introduced to the true wind condition varying to a maximum of 20% of the
actual value. This new value is then used for the station observation.
The effect of this error on the performance of the wind generator
schemes is not immediately evident from the results in Table 3-2. One
would expect that the non-selective IDPL weighting would gain in accu-
racy relative to the selective angle because the effect of large error
at any one location is minimized by including all stations. It is
possible for the selective angle method to lose in accuracy by providing
values which are biased by the error at any one of the included stations.
The gain in accuracy by the non-selective scheme is shown to a small
degree in Table 3-2, in which the selective angle method is shown to
have a 73% advantage in RMS error in predicting the flow speed r in the
no-error case but only a 43% advantage in the 20% error case.
3.3 Other Considerations and Guidelines for Use
Several different methods have been presented, and it is important
that the user select the one that is most suitable for his particular
3-15
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case. Each method is used in conjunction with the model modifications
described in Section 2 involving the diffusion calculations. The main
considerations are accuracy, computational efficiency and ease of use.
The results of the analytical wind fields analysis indicate that
the search angle technique is the most accurate given a relatively dense
network of observation stations and reasonably accurate observations.
An inverse-square distance power-law which is the most frequently used
for applications of this sort should be adequate for most purposes but
it may be desirable to use a higher power law where gradients are large.
If accuracy of the observations is low and the density of stations is
moderate, it may be preferable to use a non-selective power law weighting
utilizing an N = 3 power law in order to average the error effect and
still assign small weights to far away stations. The selective radius
technique is most accurate in cases where a cluster of stations surrounds
a calculation point and only the parameter value at the closest station
is desired to represent conditions at the calculation point. Thus,
situations where the density of monitoring stations is uneven would be
candidates for the use of this method.
All of the above considerations can be accounted for in the weight-
ing factor matrix (WFM) method. Variability in the reliability and
accuracy of the observation field can be included in the assignment of
relative matrix weights. All stations are first considered as if they
were at comparable distances. Then each would be compared on the basis
of its areal representativeness and observational reliability. Finally,
the weights are assigned on the basis of the user's judgment of the
relative weight of these factors. It may be useful to establish a
matrix and then inspect the model results obtained to see if changes
could be made to increase the accuracy of the method. One way to
establish the matrix values is to establish regression relationships
between observations at a point and the network of stations surrounding
that point. A large amount of historical data and a relatively large
network would be required. The explained variance at a location due to
each of the other stations could then be used as a guide in assigning
weights to the stations.
The WFM method has the capability for incorporating the effect of
natural and/or man-made obstructions to airflow. For example, a zero
weight would be assigned to an observation station if a location on the
3-16
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opposite side of a topographic barrier were being considered. The
effect of tall buildings and urban heat island could likewise be included.
The WFM method is the most difficult to use because of the large
amount of preparatory work required. A poorly selected matrix would be
reflected in the model results. On the other hand, non-selective
methods that do not discriminate between possible included stations are
easily implemented and can be used in a straightforward manner. After
some consideration of the nature of the available data network, it
should be possible to obtain more accurate results from either of the
two selective schemes.
The use of any of these methods carries with it a penalty in com-
puter time. At any point in the program at which data from the inter-
polation schemes is required, a subroutine is called to produce the
desired value. In the non-selective IDPL method all stations are
included in the calculation. A reduction in calculation time is achieved
by selecting a smaller number of stations, but a compensating effect
results from the logic used to achieve the elimination. The amount of
computer time required for a particular run will thus depend on the
number of stations input, because of the number of calculations and
eliminations to be achieved, and on the size of the emissions inventory,
because that determines the number of times wind generator schemes are
used.
The actual amount of computer time varies with the system effici-
ency. However, an example of the amount of computer time used in a RAM
application on an IBM 360/75 system is illustrative. When the model was
run for a small emissions inventory (Figure 2-4b) for the single station
cases, 2 minutes of execution time was required to run for 24 hours, or
5 seconds per hour. Using the search angle method in a multi-station
case with 25 stations and 9 equal to 45° required 30 seconds of time for
an hour; with 8 = 360° (selecting only the closest station), 20 seconds
was used. This time was increased dramatically to 120 seconds for one
hour's calculation using the non-selective IDPL weighting.
3-17
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4. CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK
Modifications that allow the utilization of multiple-station wind
data input were implemented in three standard Gaussian-plume models.
The short-term models., RAM and SCIM, were modified so that a series of
concurrent wind observations at several locations can be input. The
model results in the multi-station cases show the effect of horizontal
variability in the wind fields. Modifications of the long-term model,
COM, involved the use of joint frequency distributions of weather
classes, or wind roses obtained at several locations to determine an
interpolated wind rose for the desired location intermediate or adjacent
to the observation points. The modifications involved essentially two
parts of the programs; the determination of the proper parametric value
from discrete observation points using a wind field generator and the
alteration of dispersion calculations (only in SCIM and RAM) to incor-
porate the effects of a varying wind field. In cases where a continuous
wind field is available from an external source, such as a numerical
flow model, the results can be used directly in the dispersion models.
Since all of the modifications are relatively straightforward, the
simplifications limit their application to situations where the varia-
tions in the wind field are approximately of the same horizontal length
as the average source-receptor distance. Where the source-receptor
separation is large, this may not be valid. However, in these cases
pollutant concentrations will often be low because of large distance
separation. More sophisticated mathematical treatments not practical in
the present study would be required to handle highly perturbed fields
accurately.
The results of case studies utilizing generated model input indi-
cate that the model predictions in the multiple-station case were more
reasonable than those obtained using the unmodified single-station
version. In RAM, the series of hourly concentration values showed a
uniform transition from one pattern to another as a sea breeze front
moved across the region. The corresponding single-station calculation
showed an abrupt change in concentration patterns with the passage of
the front. It was clear that in this case a single wind vector was a
poor representation of the total flow field. The SCIM case study des-
cribed a situation where consistent deviations in wind conditions due to
4-1
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topographic effects resulted in changes of model estimates of frequency
distributions of pollutant concentration in the direction that would be
expected. Wind roses compiled from wind observations at locations
within the same region were used to illustrate the changes implemented
in COM. Model predictions in the multi-station case differed somewhat
from the single-station cases, in which each of the three wind roses was
used separately. Since the wind roses were fairly similar these differ-
ences were not large; however, they showed the advantage of using multi-
station wind rose input over the selection of a single wind rose to
represent conditions over a whole region.
No verification was done during this program because suitable input
data was not available. It is anticipated that with the establishment
of the St. Louis RAPS a large amount of multi-station wind data suitable
for verification of all the models will become available. It can then be
determined which of the implemented changes best describes urban area '
diffusion and how these changes are to be used on a continuing basis.
Also, as experience is gained with the collection and analysis of St.
Louis data it should become apparent which of the various parameters,
particularly the establishment of the weighting factor matrix, should
be selected to yield the most accurate results.
Another item which requires further investigation is the develop-
ment of plume trajectories in curved wind fields. One approach is to
define the wind field explicitly by relatively simple balanced equations.
These methods fit analytic expressions, usually in the form of a power
series, to observed data so that the difference between calculated and
observed values is minimized. It should be possible to develop simple
mathematical treatments which are sufficiently accurate for the flows
encountered in the St. Louis RAPS once enough data has been collected.
More exact plume trajectories could then be constructed than are pre-
sently practical by means of interpolation techniques.
4-2
-------
5. REFERENCES
Briggs, G. A., 1969: Plume Rise, U.S. Atomic Energy Comm., Div. of
Tech. Info., NTIS Pub. No. TID-25075.
, 1971: Some Recent Analyses of Plume Rise Observation, pp.
1029-1032, in Proc. Sec. Intl. Clean Air Congress, ed. H.M. Englund
and W.T. Berry, Academic Press, New York.
Calder, R. L., 1971: A Climatological Model for Multiple Source Urban
Air Pollution, 33 pp. in Proc. 2nd Meeting of the Expert Panel on
Air Pollution Modeling, NATO Committee on the Challenges of Modern
Society, Paris, France, July 1971.
Larsen, R. I., 1971: A Mathematical Model for Relating Air Quality
Measurements to Air Quality Standards, Environmental Protection
Agency, Office of Air Programs, Research Triangle Park, N.C. 1971.
McElroy, J. L., 1969: A Comparative Study of Urban and Rural Dispersion,
J. App. Meteorology, 8, 19-31.
Panofsky, H., 1949: Objective Weather Map Analysis, J. Meteorology,
6, 386-392.
Turner, D. B., 1970: Workbook of Atmospheric Dispersion Estimates,
U.S. Dept. of Health, Education, and Welfare, National Air Pollution
Control Administration, Cincinnati, Ohio.
Turner, D. B. and J. Hrenko, 1974: RAM: Real-Time Air-Quality-Simulation
Model, U.S. Environmental Protection Agency, Research Triangle Park,
N.C., 170pp. (unpublished).
5-1
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1 REPORT NO.
21ADO-36
3. RECIPIENT'S ACCESSION-NO.
4. TITLE AND SUBTITLE
Adaptation of Gaussian Plume Model to Incorporate
Multiple Station Data Input, Volume 1
5. REPORT DATE
June 1975
6. PERFORMING ORGANIZATION CODE
7 AUTHOR(S)
Harvey S. Rosenblum, Bruce A. Egan, Michael J. Keefe,
Claire S. Ingersoll
8. PERFORMING ORGANIZATION REPORT NO.
ERT P-1121
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Environmental Research § Technology, Inc.
696 Virginia Road
Concord, Massachusetts 01742
10. PROGRAM ELEMENT NO.
1AA009
11. CONTRACT/GRANT NO.
EPA-68-02-1753
12. SPONSORING AGENCY NAME AND ADDRESS
United States Environmental Protection Agency
Office of Research § Development
Washington, D. C. 20460
13. TYPE OF REPORT AND PERIOD COVERED
Final Report
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
16. ABSTRACT
EPA urban dispersion models were modified to consider multiple
station information on wind speed and direction. Three models were modified:
the Real-Time Air-Quality-Simulation Model (RAM) and the Sampled-Chronological
Input Model (SCIM), both short-term averaging models, and the Climatological
Dispersion Model (COM), a long term averaging model. Relatively straight
forward modifications, which are useful and practical approximations have
been made. The modifications had two basic objectives: the first, to
develop techniques for describing wind conditions at any point within a
region in which arbitrarily-located observing points exist; and second, to
identify critical points in the dispersion algorithms at which the additional
multiple-station wind data could be incorporated and to modify these computation
routines accordingly. The modifications were compared among themselves on the
basis of accuracy, computational efficiency and ease of use. Although no
observational data was available to verify the various approaches, the results
of applications to hypothetical meteorological situations indicate that more
realistic results can be obtained by the incorporation of multiple-station
data.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Group
13. DISTRIBUTION STATEMENT
19. SECURITY CLASS (ThisReport)
21. NO. OF PAGES
20. SECURITY CLASS (Thispage)
22. PRICE
EPA Form 2220-1 (9-73)
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