AN ANALYSIS
OF
COMPLEX 1 AND COMPLEX II
CANDIDATE SCREENING MODELS
by
John S. Irwin
jt
D. Bruce Turner
Meteorology and Assessment Division
Environments Sciences Reseach Laboratory
Research Triangle Park, North Carolina 27711
CNVIROivlENTAL SCIENCE'S l\£SEa!l;H L/BOr;AiW
OFFICF OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NORTH CAROLINA 27711
On assignment from National Oceanic and Atmospheric Administration,
Department of Commerce.
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DISCLAIMER
This report has been reviewed by the Environmental Sciences Research
Laboratory, U.S. Environmental Protection Agency, and approved for publication.
Mention of trade names or commercial products does not constitute endorsement
or recommendation for use.
AFFILIATION
Mr. Irwin and Mr. Turner are meteorologists in the Meteorology and Assess-
ment Division, Environmental Sciences Research Laboratory, U.S. Environmental
Protection Agency, Research Triangle Park, North Carolina. They are on
assignment from the National Oceanic and Atmospheric Administration, U.S.
Department of Commerce.
11
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FOREWORD
One area of research within the Meteorology and Assessment Division is
the mathematical modeling of air quality simulation including photochemical
and meteorological processes. The Division works to develop, evaluate,
validate and apply models which can accurately describe air quality and the
atmospheric processes that affect the transport and fate of airborne pollu-
tants, on a local as well as global scale. Within the Division, the Environ-
mental Operations Branch adapts and evaluates new and existing meteorological
dispersion and statistical technique models, tailors effective models for
recurring user application, and makes all models available through EPA's
computer network system and on magnetic tape from the National Technical
Information Service.
Complex II and Complex I are adaptations of the MPTER model and the
Valley model as proposed by a workshop panel at an EPA Regional Workshop
held in Chicago, February 25-28, 1980. The panel asked that a brief analysis
be performed to investigate whether a sequential model, capable of accepting
onsite hourly meteorological data could be recommended as a screening model
for estimating worst-case pollutant impacts in complex terrain situations.
K. L. Demerjian
Director
Meteorology and Assessment Division
Environmental Sciences Research Laboratory
Research Triangle Park, North Carolina
October 1981
111
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ABSTRACT
This study, suggested by an EPA Regional Workshop in February 1980, was
conducted as a simple analysis to investigate whether or not a sequential air
quality simulation model, capable of accepting onsite hourly meteorological
data, could be recommended as a screening model for estimating worst-case
pollutant impacts on complex terrain. The study intercompared the highest
24-h average pollutant concentration values obtained using four algorithmic
air quality simulation models: Complex I, Complex II, Valley, and Valley-BID.
Complex I and Complex II are sequential (hourly) air quality simulation models
which differ only in their characterization of lateral dispersion. Complex I
simulates lateral dispersion by assuming a uniform distribution of pollutant
spread over a 22.5° sector centered on the input hourly wind direction.
Complex II simulates lateral dispersion by assuming a Gaussian distribution as
specified by the input Pasquill stability category and the downstream distance.
Valley is the "standard EPA screening model used for estimating worst-case 24-h
concentrations. Valley-BID is the Valley model, modified to incorporate the
characterization of induced dispersion arising from buoyant plume rise into the
vertical dispersion characterization.
The models were applied and their results compared for a year's meteoro-
logial data for two different sites. Various combinations of source release
height and terrain configurations were examined.
The authors conclude that the Valley-BID (or pencil and paper calcula-
tions using the same assumptions) are most appropriate for screening analyses
for maximum 24-h concentrations resulting from plume impaction on terrain
near the height of an elevated stabilized plume.
iv
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CONTENTS
Page
Foreword , iii
Abstract iv
Figures vi
Tables. .- vii
Acknowledgment viii
1. Introduction 1
2. Conclusion and Recommendations 5
3. Analysis Procedures 11
4. Results 19
5. Special Topics 29
6. Questions for Reviewers. ..,... 41
References 43
Appendices
A. Additional figures of maximum 24-hour concentrations .... 45
B. Highest and second-highest concentrations and
concentrations for various averaging times ........ 47
C. Model estimates by hand calculations 53
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FIGURES
Number
1 Flow vector frequency, hours of stable, and hours of
calm (Knoxville 1964) 16
2 Flow vector frequency, hours of stable, and hours of
calm (St. Louis 1976) 16
3 Example runstream 18
4 Maximum 24-h concentrations resulting from Complex II
and Complex I at 1 km for the low source (Knoxville 1964) . . 21
5 Maximum 24-h concentrations resulting from Complex II
and Complex I at 5 km for the low source (Knoxville 1964) . . 21
6 Comparison of 24-h maximum concentrations as a function of
height for the low source 22
7 Comparison of 24-h maximum concentrations as a function of
height for the medium source 22
8 Comparison of 24-h maximum concentrations as a function of
height for the high source .22
9 Quadrants oriented about the direction of maximum flow 30
s
A-l Maximum 24-h concentrations resulting from Complex II and
Complex I at 1 km for the low source (St. Louis 1976) .... 46
A-2 Maximum 24-h concentrations resulting from Complex II and
Complex I at 5 km for the low source (St. Louis 1976) .... 46
A-3 Maximum 24-h concentrations resulting from Complex II at
1 km for the medium and high sources using the Knoxville
1964 data 46
B-l Second-highest concentrations as a function of
averaging time from Knoxville 1964 data 52
B-2 Five highest estimated concentrations in rank order
for 1-, 3-, 8-, and 24-h averaging times from Complex II
and Complex I using Knoxville 1964 data 52
VI
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TABLES
Name Page
1 Point Source Characteristics 13
2 Matrix of Run Numbers 17
3 Highest and Second Highest 24-h Concentrations
Resulting from Complex II and Complex I at 1 km
(Knoxville, 1964) 19
4 Highest and Second Highest 24-h Concentrations
Resulting from Complex II and Complex I at 5 km
(Knoxville, 1964) 20
5 Valley and Valley-BID Estimates of Maximum 24-h
Concentrations ( Hg/m-') 20
6 Dispersion and Wind Speed Effects Upon Model Estimates 25
7 Source Characteristics. . 0 . 36
8 Observed and Modeled S02 Concentrations 36
9 Peak to Mean Ratios During Periods of Maximum 24-h Concentrations . . 39
B-1 Highest and Second Highest 3-h and 24-h
Concentrations from Complex II (Knoxville, 1964) 48
B-2 Highest and Second Highest 3-h and 24-h
Concentrations from Complex I (Knoxville, 1964) 48
B-3 Highest and Second Highest 3-h and 24-h
Concentrations from Complex II (St. Louis, 1976) ...... 49
B-4 Highest and Second Highest 3-h and 24-h
Concentrations from Complex I (St. Louis, 1976) 49
B-5 Five Highest Model Estimates for 1, 3, 8, and 24-h
Averaging Times (Medium source; Knoxville 1964) 50
B-6 Five Highest Model Estimates for 1-, 3-, 8-, and 24-h
Averaging Times (Medium source St. Louis 1976) 51
VII
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ACKNOWLEDGMENTS
The authors are especially indebted to Tom Pierce and Alfrieda Rankins
who performed most of the computer programming and executions for this study.
The authors are also grateful for the diligent reviews and comments received.
Finally our thanks go to Joan Emory for her secretarial assistance in the
preparation of this report.
Vlll
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SECTION 1
INTRODUCTION
This report presents the results of an analysis comparing the highest
concentrations estimated for various averaging times by four air quality
simulation models: Valley, Valley with buoyancy-induced dispersion (Valley-
BID), Complex II, and Complex I. The analysis was suggested by the Complex
Terrain panel of a regional workshop sponsored by EPA and held in Chicago,
February 25-28, 1980. The panel outlined the characteristics of three of the
models mentioned (Valley-BID, Complex II, and Complex I), which will be
described later. The purpose of the sensitivity study was to see whether
or not one of the two sequential (hourly) models, Complex II or Complex I,
might provide a more detailed screening technique for use in complex terrain
situations. (Complex terrain modeling applies whenever the terrain elevation
is above the stack top of a point source.)
A more detailed screening model would allow a three-phase approach to
the modeling of air quality in complex terrain. Phase 1 would be a simple
screening procedure (most likely using Valley-BID) to determine whether or
not the source clearly poses an air quality problem or if the potential for
an air quality problem exists at all. If the simplified screening results
indicate a potential threat to air quality, further analysis (Phase 2) would
be warranted, using a detailed screening procedure. If these screening
results in turn indicate that a yet more refined analysis is necessary, a
refined model for complex terrain would be used as agreed upon with
the Regional Office on a case-by-case basis (Phase 3).
1
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Although no accepted model was available then for a more detailed
screening analysis, the panel wanted to make specific recommendations.
thus, they proposed that two sequential models (Complex II and Complex I)
be assembled and a sensitivity analysis be accomplished in order to
examine these models' usefulness for Phase 3 screening. Whether or not
either of the proposed candidate models would be ultimately selected as the
refined screening model was impossible to predetermine. Nor was it possible
to predetermine if the proposed sensitivity analysis would provide a
sufficient basis for making general recommendations regarding the use or
non-use of the proposed models in regulatory decision-making. However, the
working panel thought that the more specific the recommendations, the more
likely the recommended model assembly and sensitivity analysis would be
performed.
After discussion during the Complex Terrain session, the panel concluded
first that a data base was needed before a refined model could be developed.
The Office of Research and Development within EPA is currently collecting a
data base for use in developing this model. Secondly, the panel suggested
that the Phase 2 analysis should consist of calculations made using one of
the sequential models to estimate actual measured pollutant concentrations.
The standard VALLEY model currently characterizes the lateral bounds
of dispersion using a 22 1/2° sector; it characterizes vertical dispersion
using the Pasquill-Gifford dispersion curves. No changes were recommended
with regard to lateral dispersion. However, the panel did recommend that
the total vertical dispersion , oz, be modified such that:
2 2
az r az + (Ah/3.5)2 (Eq.1)
P-G
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where az = the total vertical dispersion arid is a function of
downstream distance,, stability category, and plume rise
azp r - the Pasquill-Gifford vertical dispersion due to
ambient turbulence which is a function of downstream
distance and stability category
Ah = the plume rise which varies as a function of downstream
distance until final rise is attained
The resulting model is the VALLEY-BID.
The sequential model Complex I uses meteorological input as currently
available for CRSTER. The model determines vertical dispersion as described
for the Valley model. Lateral dispersion dimensions in this model are bound
by a 22 1/2° sector. Plume rise is estimated using subroutine BEH072 or
equivalent. For stable conditions, the plume remains at a constant level
above mean sea level (as presently employed in CRSTER). During neutral and
unstable conditions (i.e., Pasquill categories A, B, C, arid D), the plume
follows one-half of the terrain height variation. The plume is not allowed
to approach any closer than 10 m to the ground.
Complex II is identical to Complex I except that the lateral dimensions
are given by:
°2 = + (Ah/3'5)2 (Eci- 2)
where av - the total lateral dispersion and is a function of stability,
downstream distance, and plume rise
aXP-G = the lateral dispersion due to ambient turbulence and is a
function of Pasquill stability category and downstream
distance
In this second model, avp p and 0zp_r are specified using the same Pasquill
\
stability categories. In other words, "split sigmas" are not recommended.
3
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For the analysis, the panel recommended that both sequential models be
executed along with the modified Valley screening model (Valley-BID) in two
terrain situations, a broad valley and a narrow valley. All three models
should be executed for three stack heights in the two terrains using two
yearly periods of meteorology, one with a relatively uniform directional
distribution, and one with a skewed directional distribution.
The following section containing conclusions and recommendations, also
summarizes the major comments and recommendations made by reviewers regarding
the use or nonuse of the proposed models. Section 3 outlines the analysis
used to generate the results presented in Section 4. Section 5 contains
short discussions on technical issues that are important in assessing the
reasons for the differences in the modeled concentrations. And Section 6
lists the major questions posed to the reviewers.
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SECTION 2
CONCLUSIONS AND RECOMMENDATIONS
The original reason for examining concentrations from Complex I and
Complex II and comparing with Valley and Valley-BID was to choose one of the
two sequential models as a second level (Phase 2) screening technique.
The algorithm used in Complex I resulted in concentrations less than
those given by the algorithm used in Complex II. This result was expected
because of the uniform horizontal spreading in Complex I and the narrrower
more peaked Gaussian distribution for horizontal spreading in Complex II.
A second result of the study was that the values resulting from
Complex I were approximately the same as those obtained from Valley-BID.
The computational aspects of this study were completed, a draft report
written and circulated among the members of the previously mentioned workshop
panel. Although the conclusions reached by the authors and panelists are
not unanimous this section attempts to present opinions of both the authors
and other panel members.
It is the opinion of the authors that sequential models are useful
when the meteorological data entered to the model can be considered represen-
tative of the flow for the particular situation being simulated.
The sequential models currently available, such as RAM, MPTER and
CRSTER, employ one wind-direction to describe the flow for each hour. It is
assumed in modeling the transport that conditions are horizontally homogeneous
and stationary during each hour. These assumptions are rarely met. It is
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quite likely that the flow field is rarely horizontally homogeneous. Vio-
lations of the assumption of horizontal homogenety cause the model to improper-
ly locate the plume relative to the underlying surface. If the surface is
relatively flat, one can usually assume that the dispersion, relative to the
plume centerline, is independent of the horizontal location of the plume center-
line. In such circumstances, the modeled concentration values can still be
accepted, recognizing that the modeled locations of the maximum .impacts are
likely in error. When the dispersion relative to the plume centerline is
dependent upon the underlying terrain and when the dependency is a function
of the stability stratification (which is quite likely in complex terrain
situations), it is necessary to properly locate the plume each hour relative
to the underlying surface in order to have confidence in the modeled concen-
tration values.
For a terrain situation where there are gradual rises in elevation to
heights in excess of the elevation of the stack top but do not extend to
the general plume heights, a single wind system may give a fairly good
indication of the flow.
However, for a situation of a deep valley with sides extending to
elevations beyond the usual plume heights, the wind direction from a single
wind system may give reasonable indications of the flow for upvalley and
downvalley conditions but the occurrence of indicated wind direction across
valley may poorly represent the flow.
There, of course, exist many topographic situations between these ex-
tremes where it may be desirable to apply a screening model and the repre-
sentativeness of the meteorological data is very difficult to determine.
For situations where the representativeness of the single set of
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meteorological conditions is in doubt, the authors recommend the use of
Valley-BID for screening analysis for the 24-hour averaging time. The
version of the model using 2.6 as the stable plume rise constant should be
used for consistency with other modeling approaches. Table 8 shows that at
the distances from sources where Valley has been shown to give reasonable
estimates of concentration, Valley-BID gives nearly the same concentrations.
The inclusion of buoyancy-induced dispersion for large buoyant sources has
long been recognized as desirable. In most cases of modeling over flat
terrain, the inclusion of buoyancy-induced dispersion makes little difference
in the estimated maximum concentration. However, for nearby receptors in
complex terrain the difference can be considerable. Primarily because it is
good modeling practice (rather than existence of field data for the near
field), the use of buoyancy-induced dispersion is justified.
The screening calculations may be made with the Valley model using
the buoyancy-induced dispersion option or closely approximated by pencil and
paper calculations where terrain at plume height is being simulated.
Two of the five reviewers essentially agreed with the authors.
Although two of the five reviewers agree that measurements at one
point in a valley configuration are not necessarily representative of trajec-
tories of air motion in the vicinity, they recommended the use of a sequential
model such as Complex I (discounting calms, see later in this section) as a
more justifiable approach than decision-making with Valley-BID alone, because
Complex I considers onsite meteorological data. They reasoned that the manner
in which the model performs impact (within 10 m) whenever receptor elevations
are above plume height, and the tendency for a wind system to sense some cross-
valley flow could cause the model to overestimate concentrations sufficiently
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that it could be used as a screening tool in spite of its modeling
deficiencies. Additional conveniences seen for using one of the models for
screening are that concentrations could be calculated for elevations of
"middle terrain", i.e., above stack top but below plume level, and calcula-
tions can be made for 3-h periods as well as for 24-h periods.
One reviewer, although leaning toward the position stated in the
above paragraph, felt the issue of calms possibly obscures the screening
analysis sufficiently that it is impossible to decide defensibly on the use
of one of these models as a screening tool.
SPECIAL ISSUES HIGHLIGHTED BY REVIEW
Most modelers are aware that the meteorological conditions used for
calculation in Valley-BID are not to be taken literally, but are simply a
numerical mechanism for obtaining a value representative of the second-highest
24-h maximum concentration. The analytical routine for the Valley model "was
not proposed as a rigorous mathematical description of the physical circum-
stances which pertain to flow about a terrain feature" (Burt and Slater, 1977).
To disprove the Valley model characterization of the plume geometry
does not eliminate the possible occurrence of plume impingement. Likewise,
the meteorological scenario employed by the Valley model for screening
analyses is not meant to represent the conditions that must occur in order
for pl'jme impingement to occur. To disprove this particular meteorological
scenario does not eliminate the possible occurrence of plume impingement
resulting in concentrations as high as those generated by the Valley screening
analysis.
Physical characterization of atmospheric flow over complex terrain is
not easily achieved because the measurements needed to describe the flow
8
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adequately are extremely difficult to obtain. For instance, great difficulty
is encountered in estimating trajectories of air flow from single point
measurements a definite obstacle for the use of simple models having
straight line flow with sequential meteorological input. In addition, the
modeler must also determine whether or not impingement will occur. This
might be accomplished by considering the height of the streamline separating
flow over an obstacle from flow around the obstacle.
Calculations from models such as Complex I and Complex II may vary
greatly depending on how atmospheric calms are treated. For this study,
calms were treated consistent with other modeling practice, i.e., the meteoro-
logical preprocessor output was used directly as input to the models. Thus
calms were assigned a wind speed of 1 m/s and assigned a direction sector the
same as the previous hour and then randomized to a direction to the nearest
degree within that 10° sector. Thus a sequential series of calms will all
be assigned the same 10° sector. Since Complex II is more sensitive to
directional persistence than Complex I, results of comparisons between these
two models might be quite disparate if calms were treated in a different
manner.
One possible solution suggested by one of the reviewers to this sensi-
tivity problem would be to eliminate calculation for hours of calm, and
instead to estimate 24-h concentrations as the arithmetic average of the
concentrations resulting for the non-calm hours. If less than 18 h resulted,
no 24-h concentration would be reported. Note that following the above
suggestion (deleting data for some hours) adds significant bookkeeping
problems to initially rather simple models.
In response to the suggestion that calms be eliminated and parts of the
analyses then repeated, no plans have been made to accomplish such a reanalysis.
9
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Although modeling for flat terrain is much less sensitive to the treat-
ment of calms than complex terrain modeling is, sensitivity to calms
was raised as an issue for flat terrain modeling in the public meetings
on modeling in October 1980 and was also discussed in the proposed modeling
guidelines in October 1980 (U.S. Environmental Protection Agency, 1980).
Several reviewers questioned the manner in which the receptor networks
were set up (in all directions at the same distance). This set up was
possibly so unrealistic as to invalidate the sensitivity analysis since
receptors injrthe direction of the wind rose maxima were not situated
further away. An attempt was made to examine this factor in the analysis
under Special Topics. The effect was to reduce the concentrations no lower
than 0.7 of estimated maxima.
10
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SECTION 3
ANALYSIS PROCEDURES
MODEL FABRICATION
Complex II and Complex I are identical except for the way in which
they model lateral dispersion. Many of their features, such as buoyancy-
induced dispersion and the ability to change plume height as a function of
terrain elevation and stability, were adapted from the well-documented
MPTER model (Pierce and Turner, 1980); the MPTER source code was used as
the foundation for the Complex II and Complex I models. In August 1980,
executable versions of Complex II and I were made available on the EPA
UNIVAC computer system. The Regional Offices were notified of the models'
availability and were requested to test them. In November 1980, the
Regional Offices observed that the models did not handle receptor locations
above the mean sea level of the final effective plume height in the same
manner as the EPA Valley model. The Valley model decreases linearly the
concentrations estimated with increasing receptor elevation height (above
the plume level) to zero at and over 400 m above the undisturbed plume center-
line. Thus, in December 1980 Complex II and Complex I were reprogrammed
with regard to the treatment of the plume centerline and the resulting
surface concentrations due to the terrain interaction with the plume.
The Valley model was modified to allow certain options, including the
use of buoyancy-induced dispersion in the vertical dispersion parameter,
and the use of the constant of proportionality, 2.4 or 2.6, for estimating
11
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the final plume rise during stable conditions. The latter value of 2.6
reflects suggestions made by Briggs (1975). (Thus the Valley model available
in UNAMAP, Version 4, is capable of simulating the models referred to in this
document as Valley and Valley-BID.) A working copy of this modified version of
Valley was further adjusted for the sensitivity study to allow the receptor
locations to be input to the model in the same manner as the receptor locations
!
are input to the Complex II and Complex I models. This made it easier to achieve
congruency of receptors among the various models used in the sensitivity analysis.
In the following discussion, when reference is made to results generated
using the Valley model, note that a constant of 2.6 was used for estimating
final plume rise during stable conditions and no induced dispersion due to
buoyant plume rise was included. Furthermore, the model was run as recom-
mended to estimate worst case 24-h concentrations, i.e., Pasquill stability
category F; 6 h of occurrence; and wind speed equal to 2.5 m/s.
When reference is made to Valley-BID, notice that the constant used in
the stable plume rise is 2.6, the same meteorological conditions as with
Valley are used and induced dispersion due to buoyancy is included in the
vertical dispersion.
SOURCES
The workshop panel had suggested that the stack heights of the point
sources used in the sensitivity analysis be 1/4 of the final effective p*me
height. Based on sources examined by Mills (1979), the researchers decided
that the suggestion by the panel regarding the relationship between stack
height and plume rise would not have been typical of most power and industrial
plants. Using Mills (1979) the low, medium, and tall source characteristics
were selected for the present evaluation and are presented in Table 1.
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TABLE 1. POINT SOURCE CHARACTERISTICS
Source
type
Low
Medium
Tall
Stack
height
(m)
75
165
335
Stack
diameter
(m)
3
4
13
Exit
velocity
(m/s)
16
38
16
Exit
temperature
(K)
455
425
425
Emission
rate
(g/s)
700
2,750
10,000
Stable
plume rise*
(m)
91
141
231
"Assumed wind speed of 2.5 m/s, vertical temperature gradient of 0.035 K/m,
ambient temperature of 293 K.
The light wind stable plume rise estimates presented in Table 1 were made
using the Briggs (1976) plume rise equations as used in Valley, Complex II,
and Complex I. These plume rise estimates suggest that the ratio of stack
height to final effective plume height during very stable conditions ranges
from 0.45 to about 0.60.
VALLEY WALL PLACEMENT
Two valley configurations were used in the sensitivity analysis, a
narrow valley and a broad valley. The narrow valley measured approximately
2 km in total width and the broad valley measured approximately 15 km. The
intent was to investigate worst-case 24-hr concentration estimates at two
downstream points. The narrow valley was used to study the effect on concen-
tration estimates when buoyancy-induced dispersion was of primary concern.
Two kilometers was chosen as the width of the narrow valley because the distance
to final rise was generally just less than 1 km (assuming the source was in the
center of the valley). The broad valley was used to study the effect on concen-
tration estimates where buoyancy-induced dispersion was less important.
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For the actual analysis, two concentric cylindrical networks of receptors
were placed around each pollutant source. The radii of the cylinders were 1 km
and 5 km to simulate a narrow and a broad "valley". By using these receptor
networks five different terrain configurations could be simulated in each run:
flat terrain plus rising terrain at four different heights. (These networks
were not to simulate a vertical canyon wall.)
A numerical processor was written that generated receptor locations for
use as input to Complex II and Complex I. Initially, 180 receptors were gener
ated at 10° intervals and at 5 heights to form one of the cylinder walls.
The heights were selected subjectively based on the stable plume rise for the
source type. The maximum 24-h concentrations at each of the receptor locations
were plotted as depicted in Figures 5 and 6, (presented later in Section 4).
An objective analysis was not performed to determine the proximity of receptor
spacing necessary to estimate the maximum 24-h average concentration to within
some known percentage error at the given downwind distance. However, a sub-
jective analysis was performed which consisted of searching for the maximum
possible 24-h average concentration with receptors in 1° intervals and 25 m
vertical separation between receptors at the 1 km downwind distance.
The results for the low source suggest that the 24-h maximum concentration
determined using the original receptor grid (10° intervals with 25 m vertical
spacing) was within 20/°o of the highest value determined during the analysis
with -1° receptor spacing. This result most likely represents-an upper bound
on the uncertainty of locating the maximum 24-h concentration since the low
source had very strong gradients in the pattern of maximum 24-h concentrations.
In any event, the 20?o error was deemed tolerable for the purpose of judging
variations in maximum concentrations between the models used in this study.
14
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METEOROLOGICAL DATA
In seeking meteorological data for the sensitivity study, the intent
was to see if skewness in the wind direction frequency caused by terrain
channeling of the wind would affect the model results. Since the 1964
Knoxville, Tennessee, hourly surface meteorological data were readily
available they were selected for use as the site having a skewed, bimodal
wind rose, typical of sites in narrow valleys. The 1976 St. Louis surface
meteorological data were selected as representative of a more circular wind
rose site.
Figure 1 depicts the flow vector frequency relative to a completely
circular wind frequency for the 1964 Knoxville data. If wind from every
10° interval (from 10° to 360°) were as equally likely to occur, then
8784/36 = 244 hours would occur for each direction (note that 1964 and 1976
were both leap years). Therefore the flow vector frequency relative to a
frequency equal from all directions was determined by dividing the number of
hours of occurrence of each flow vector direction by 244. The hours of stable
conditions and the hours of calm assigned by the preprocessor to each flow
vector direction are also given in Figure 1. The hours of stable conditions
follow fairly well the overall frequency distribution. Figure 2 depicts the
same flow vector frequency for the 1976 St. Louis data.
A processor was constructed to convert the meteorological data into a
format compatible for input to Complex II and Complex I. The processor set
the mixing height to 5000 m; using a mixing height of 5000 m removes the
mixing height as a variable affecting the concentration results due to re-
flection effects.
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I I I I I I I I 1-1 I I I I I I I I 1 1 I
0 20 40 60 80 IDO 120 140 160 ISO 200 220 240 260 280 300 320 340 360
AZIMUTH (FLOW VECTOR SECTOR). d*grm
Figure 1. Flow vector frequency, hours of stable, and hours of calm, Knoxville. TN, 1964.
| I | | | | | | I I IJ I | I I I I I I I I I I 1 I M I I I I I I I
20 40 60 80 100 120 140 160 160 200 220
AZIMUTH (FLOW VECTOR SECTOHI. digrn
Figure 2. Flow vector frequency, hours of stable, and hours of calm. St. Louis, MO, 1976.
16
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MODEL COMPUTATIONS ACCOMPLISHED
Twenty-four basic runs were made as part of the sensitivity study.
The matrix showing the run numbers is shown in Table 2. Each of these
runs was for a single pollutant source for 180 receptors, simulating a 1-yr
period with output consisting of the high-five table. Nearly all runs were
executed in a deferred batch mode of computer operation. This rendered
costs to be 15% of those that would have been incurred under normal batch
processing. Processing was generally done overnight. As many as 4 runs
were executed per night so availability of computer facilities and turnaround
were quite adequate for the study.
Execution of the runs required 56K of core or less. Each execution of
COMPLEX II costs between $40 and $46. Each execution of COMPLEX I costs
between $29 and $34. Each execution of Valley costs about $0.25.
TABLE 2. MATRIX OF RUN NUMBERS
KNOXVILLE MET DATA
Complex II Complex I
ST. LOUIS MET DATA
Complex II Complex I
OUUJ. UB
Low
Medium
High
1 km
1
3
5
5 km
2
4
6
1 km
7
9
11
5 km
8
10
12
1 km
13
15
17
5 km
14
16
18
1 km
19
21
23
5 km
20
22
24
17
-------
Each run accessed 3 disk files and two-disk file elements. Figure 3
is an example runstream. Since many of the runstreams were similar, the
runstream itself was stored in a disk file element. This example was
stored in WRKSHP.RUN6/XQT. The compiled and'.mapped model absolute for this
run is in the element UNAMAP.COMPLEXIIABS. .-liThe hourly meteorological data
for this example is in file FORKNOX64. The'of.eceptor list is in file GRHIGH1
For each run the output was placed into a print file, in this case PFRUN6.,
so that it could be edited if further computer processing of output became
necessary.
@RUN, D/R 12ADR/70, ACCTNO., EOB. 23.50 -"'."
<§> . RUNSTREAM WRKSHP, RUN6/XQT HP
@SETC,O
@ASG, A UNAMAP.
@ASG, AGPHIGH1.
<°>ASG. A FORKNOX64.
@ASG. A PFRUNG.
@BRKPT PRINTS/PFRUNG
@XQT UNAMAP . COMPLEXIIABS
RUNS HIGH 1964 KNX/BNA 5 KM
IOPT(25)=1, BID, FINAL RISE. ZMIN=10, 1 DISTANCE. 5 HEIGHTS
INPUT BY A. RANKINS (ENVIRONMENTAL OPERATIONS BRANCH), 2/21/81
64. 1, 1,366.24,3, 1,0, 1., 1..0.
1. 1. 1, 1. 1.0, 0,0, 0, 1, 1. 1, 1. 1, 1, 1, 1. 1,0.0,0.0,0, 0, 1
10.. .07. .07. .1, .15, .35, .55. .5, .5, .5. .5. .0. .0, 10.5
HIGH STACK 0. 0. 10000. 0. 335. -425. 13. 16.
ENDP
@ADDGRHIGH1.
ENDREO
@ADD FORKNOX64.
@8RKPT PRINTS
@FR£E PFRUN6
@SYM, U PFRUN6... FD04PR
@FIN
Figure3. Example runstream.
18
-------
SECTION 4
RESULTS .
Plots were made initially to depict the variation of the maximum 24-h
concentration at each downwind distance as a function of receptor elevation
height and bearing from the source. Figures 4 and 5 are examples of such
plots and are typical of the results in general. Several other examples of
such plots are given in Appendix A. The maxima in these plots are quite
localized, spanning 10 to 15° in horizontal azimuth and 100 m in the
vertical. Tables 3 and 4 summarize the maximum 24-hour concentrations
estimated using the Knoxville meteorological data. Figures 6, 7, and 8
depict these results with the Valley and Valley-BID estimates, for comparison.
Table 5 lists the Valley and Valley-BID estimates.
TABLE 3. HIGHEST AND SECOND-HIGHEST 24-H
SULTING FROM COMPLEX II AND COMPLEX I AT 1
1964).
Source
type
Low
Medium
High
Receptor
height
(m)
200
175
150
125
450
350
275
200
550
525
500
475
Highest 24-hour
concentration, £ig/m3
Complex II
11602.1
12157.6
11744.3
8935.4
14708.9
20895.2
23066.8
2018.6
34997.4
36132.2
36929.2
32371.1
Complex 1
5145.4
5394.9
5251.0
2695.9
6882.3
9761.8
10816.7
1083.5
18534.2
19084.6
19460.2
17194.0
CONCENTRATIONS RE-
KM (KNOXVILLE, TN,
Second highest 24-hour
concentration, pg/m3
Complex II
7019.9
9018.3
8825.8
8252.0
10440.8
14997.5
18174.3
1741.3
26518.9
28410.6
30077.9
26868.7
Complex 1
3759.6
3932.3
3920.4
2253.5
5154.4
7331.7
8201.7
938.3
13983.1
14212.4
14999.4
13537.3
19
-------
TABLE 4. HIGHEST AND SECOND-HIGHEST 24-H CONCENTRATIONS RE-
SULTING FROM COMPLEX II AND COMPLEX I AT 5 KMIKNOXVILLE, TN,
1964).
Source
type
Low
Medium
High
Receptor
height
(m)
200
, 175
150
125
450
350
275
200
550
525
500
475
Highest 24-hour
concentration, jjg/m-3
Complex II Complex I
1876.7
1977.8
1978.0
1454.8
2845.0
4019.0
4505.4
1180.9
8468.5
8710.6
8852.1
8005.2
652.9
744.8
750.6
557.3
1068.5
1388.9
1 7 1 1 .9
474.1
3202.4
3321.6
3406.6
3113.9
Second highest 24-hour
concentration, ^g/m3
Complex II Complex 1
1270.0
1358.2
1400.0
1037.9
1860.4
2671.1
3234.7
877.2
5786.6
6198.8
6561.0
6052.9
508.3
537.2
555.8
418.8
773.3
1099.7
1237.4
389.7
2369.4
2434.9
2516.1
2359.3
TABLE 5. VALLEY AND VALLEY-BID ESTIMATES OF MAXIMUM 24-H CON-
CENTRATIONS (jug/m3).
Valley
Valley-BIO
Source
1 km
5km
1 km
5km
Low
Medium
Tall
7,805
31,304
112,170
743
2,982
10.685
4,426
12,5??
28.772
607
2,011
5,187
20
-------
COMPLEX II
1OOO 1OOO
200 560 668 285 584 656 448 451 538 491 502 372 346 322 658 181 384 894 642 453 795 461 499 844 879/1035\ 512 598/I)601 370 454 510 596 543 600 787 533
175599 703 297 617 698 478 483 564 525 537 398 370 338 703 194 410 955 687 484 829 492 533 899 924 1086 540 632 1216 395 486 54S 621 581 641 842 570
ISO 616 698 294 603 702 483 499 553 551 553 414 383 346 726 207 407 988 708 507 786 517 S56 927 902M048J 552 625m74J 404 506 559 619 605 662 861 5BS
125 297 392 259 351 372 280 299 276 387 303 241 187 183 380 137 221 484 379 316 427 346 353 50) 476 521 305 345 5B6 224 299 233 353 375 332 417 303
O
CO
COMPLEX I
2 200 278 406 251 357 444 434 284 313 216 177 185 271 284 276 185 236 320 346 364 384 359 265 292 473 402 402 473 /515J 356 347 406 314 284 283 330 295
5 175 297 425 259 376 472 461 289 320 230 179 188 284 302 295 197 252 342 370 380 4Q] 374 282 308 494 420 420 495 5391 380 372 434 337 304 302 353 315
< 150307 410 238 367 475 462 291 299 240 178 168 288 310 304 198 261 354 383 391 383 354 290 313 477 400 400 478 \SZSJ 388 383 447 350 310 295 359 324
*f, 125 177 204 134 203 241 243 191 173 156 127 124 152 160 155 108 127 177 212 205 219 192 178 202 269 230 200 238 270 198 213 243 212 172 140 207 156
I I I I I I I I I I I I I I I I
20
40
60
80
too
200 220 240
AZIMUTH-FLOW VECTOR SECTOR (degrees)
260
280
300
320
340
Figure 4. Maximum 24-h concentrations resulting from Complex II and Complex I at 1 km for the low source
(Knoxville, TN. 1964). (Concentrations are pg/m3 divided by 10).
COMPLEX II
HI 200 94 98 4b 84 68 64
C/l
< 175 101 104 48 88 73 68
CO
^ 150104 107 49 88 74 70
U 125 75 84 38 7t 66 58
<
t-
00
52 100 28 60 174 98 78 128
55 64 69 46 44 40 79
120
78 84 100 95 110 129 101
81 87 99 99 114 133 104
C2 64 74 76 83 96 77
u
CD
Z
g
^
UJ
_J
UJ
zoo
175
37
39
41
I
3GC
56
59
59
44
34
36
35
1
20
54
57
57
57 56
61 60
1
40
39 43
40 45
1
60
29 25 27
31 26 28
1 1
80 100
39 39
41 42
1
120
38 26
41 28
31 21
I
140
33 45
35 48
26 36
I
160
47 51
51 53
1
180
52 48
54 51
42 38
1
2'JO
38 «2
40 45
1
220
65 55
69 58
1
140
55 65
58 69
1
2GO
70
/71\ 49
I 74 \ 52
^ '
1
280
COMPLEX 1
48 56
51 60
1
300
43 38
46 41
1
3ro
39 45
42 48
1
340
AZIMUTH-FLOW VECTOR SECTOR (degrees)
Figure 5. Maximum 24-h concentrations resulting from Complex II and Complex I at 5 km for the low source
(Knoxville, TN, 1964). (Concentrations are ^g/m3 divided by 10).
21
-------
250
225
[.200
1
:
! 175
ISO
12S
too
11
\l\ 1 \
\- \
\ \
i
i '
i'
- ; D
1
i
i "
i
1
/" ° ;
// /
? X
^» o^X.
..-''/'
,':>' , ,
2 ,03
1 \ 1 1
I
\
\
\
\
\
\
1 0
1
I
1
I km
* / ° OCOMPLE 1 ~~
/ 9COMPLE
/ VALIE BtO
' O VAIL -
Skm
OCOMPLE i
O BCOMPLE -
VAll BID
1 1 1
ID4 10
Figure 6. Comparison of 24-hr maximum concentrations ai a (unction of height for the low source.
100
ISO
1 km
O COMPLEX II
COMPLEX!
VALLEY 8ID
VALLEY
Shm
O COMPLEX II
COMPLEX!
VALLCY BID
VALLEY
I
I
102 ID3 10* 10s
24htMAXIMUM CONCENTRATION. u|/m3
Figure 7. Comparison of 24-hr maximum concentrations as a function of height for the medium source.
600
<2Sl
103
I
I
1 km
CCGM?LEX!I
COMPLEX I
VALIEY BIO
VAILEV
Slim
D COMPLEX II
COMPLEX)
VALLEVSID
VALLEY
1
I04 10s
24-hrMAXIMUM CONCENTRATION. ;jg/m3
Figure 8. Comparison of 24-hr maximum concentrations as a function of height for the high source.
22
-------
How calm conditions were modeled was the determining factor in the
results just presented. The meteorological-input data used for Complex II
and Complex I were generated by a meteorological preprocessor. The processor
performs the following functions: (1) calculates Pasquill stability class
from cloud cover, ceiling height, wind speed, time of day, and time of year;
(2) converts reported wind direction (in 10° increments) to a flow vector
(wind direction ± 180°); (3) converts wind speed to m/s and converts air
temperature to Kelvin; (4) generates a randomized flow vector from the above
flow vector by using random digits to add from -4 to +5 to the flow vector to
create random flow vectors to -1° within the same 10° sector; and 5) inter-
polates twice daily mixing heights to result in hourly estimates of mixing
height. (Note that mixing height was effectively eliminated as a variable in
this sensitivity study.) Note also that the treatment of winds reported as
calm on the input is as follows: the speed is assigned 1 m/s, and the flow
vector remains the same as for the previous hour. Thus, if a sequence of
hours is reported as calm in the input data to the processor, although the
randomized flow vector is varied over 10°, the winds for this period are
all at 1 m/s and are blowing toward only one 10° sector. The developers
of the preprocessor thought this procedure was the most reasonable one to
handle calms since any topographic relief at a site might cause drainage
flows with little direction change at nighttime when calms are most pre-
valent.
For the Complex II model, day 299 of the Knoxville data and days 238 and
320 of the St. Louis data caused the highest estimates of 24-h concentra-
tion. For the Complex I model, Julian day 299 of the Knoxville data and
Julian day 320 of the St. Louis data caused the highest estimates of 24-h.
23
-------
concentration for all three sources at both distances. Day 299 had 7 h
of stable, calm conditions in which the wind directions were assigned by
the preprocessor within the same 10° sector. Of these 7 h, 6 h were
stability F or G and 1 h was stability E. Day 320 had 7 h of stable, calm
conditions in which the assigned wind directions were within the same 10°
sector. Of these 7 h, 6 h were stability F or G and 1 h was stability E.
Day 238 had 6 h of stable, calm conditions, of which 5 h were F or G and
1 h was E. The wind speed at 10 m during these stable, calm conditions was
assigned 1.0 m/s, since the meteorological preprocessor sets the wind speed
to 1 m/s whenever a calm is reported. Complex II and Complex I extrapolate
the 10 m wind speed to stack top height for use in the plume rise estimates
and for use in the dispersion calculations. Differences between these extrapo-
lated wind speeds and the 2.5 m/s speed assumed by Valley and Valley-BID
^
account for most of the differences in maximum 24-h concentrations by Complex II
and Complex I as compared with those generated using Valley and Valley-BID.
Table 6 attempts to summarize the variation in maximum concentrations
one would anticipate given the four models used in this analysis. Column
(6) of Table 6 lists the wind speeds at stack top that would be employed by
Complex II and Complex I for calm, stability category F conditions. The
differences in plume rise estimates (comparing the Valley and Valley-BID
values to the Complex II and Complex I values), reflect the effects of
differences in wind speed. Note, an ambient air temperature of 293 K was
used for the plume rise estimates. Inspection of column (4) of Table 6
reveals that by using a higher wind speed in Complex II and Complex I, the
vertical dispersion actually becomes less than that used in Valley-BID,
because the buoyancy induced dispersion is proportional to the plume rise.
24
-------
TABLE 6. DISPERSION AND WIND SPEED EFFECTS UPON MODEL ESTIMATES.
(1)
Model
type
Valley
Valley-BID
Complex 1
Complex II
(2)
Source
type
Low
Medium
Tall
Low
Medium
Tall
Low
Medium
Tall
Low
Medium
Tall
(3)
X
(km)
1
5
1
5
1
5
1
5
1
5
1
5
1
5
1
5
1
5
1
5
1
5
1
5
(4)
Vertical
dispersion
(m)
.
13.38
35.71
13.38
35.71
13.38
35.71
29.24
44.17
42.45
53.84
67.34
75.04
28.26
42.12
35.43
47.23
48.89
58.01
28.26
42.12
35.43
47.23
48.89
58.01
(5)
Lateral
dispersion
(m)
t
156.66
783.32
156.66
. 783.32
156.66
783.32
156.66
783.32
156.66
783.32
156.66
783.32
156.66
783.32
156.66
783.32
156.66
783.32
41 36
147.73
47.00
149.27
57.83
153.02
(6)
Stack top
wind
speed
(m/sl
2.5
2.5
2.5
2.5
2.5
2.5
2.5
2.5
2.5
2.5
2.5
2.5
3.0
3.0
4.7
4.7
6.9
6.9
3.0
3.0
4.7
4.7
6.9
6.9
(71
Stable-F
plume
rise
(m)
91
91
141
141
231
231
91
91
141
141
231
231
86
86
114
114
164
164
86
86
114
114
164
164
18)
Xmax (Expected)
Xmax (Valley-BID)
t
1.76
1.22
2.46
1.47
3.85
2.04
1.00
1.00
1.00
1.00
1.00
1.00
.86
.87
.63
.60
.50
.47
3.22
4.62
2.09
3.17
1.34
2.38
(9 1
X max (Calc.)
Xmax (Valley-BID)
1.76
1.22
2.49
1.48
3.90
2.06
1.00
1.00
1.00
1.00
1.00
1.00
1.22
1.24
.86
.85
.68
.66
2.75
3.26
1.83
2.24
1.28
1.71
Vatley and Valley-BID compute O2 dif-
ferently than Complex I and Complex II
because different algorithms are used to
approximate the Pasquill dispersion
curves. At 1 and 5 km the algorithms
estimate the vertical dispersion para-
meter as:
Valley Complex I
X(km) Valley-BID Complex M
1 13.38 13.95
5 35.71 33.88
1 The lateral dispersion given is the effec-
tive Oy for a sector model, computed as
( /3Wl6) X, which was found by equat-
ing Eq. 5.13 and Eq. 3.3 of WADE
(Turner, 1970) and solving for Oy.
List the ratio of the expected maximum
24-hour concentration to the Valley-BID
estimate, for the given source type. As-
sumes a 4 to 1 relationship between the
peak 1 -hour and average 4-hour concen-
trations. Ratio is computed as:
Xmax (Expected) = 1/(0z0vu) exp{-0.5(10 m/02)2)
max (Vatley-BIO) l/IOj Oy'uj exp(-0.5(lO m/0^ t2)
where primed quantities are values ap-
propriate for Valley-BID calculations.
25
-------
Decreasing the vertical dispersion tends to increase the maximum concentra-
tions estimated to occur during plume impaction, while a higher wind speed
tends to further dilute the pollutant and thereby lower the estimates.
Column (8) of Table 6 lists the expected maximum 24-h concentrations (as
compared to the corresponding results from Valley-BID for the given source
type) as a function of pollutant source type and dispersion model. The
assumption made in computing these ratios was that the peak 1-h concentration
is four times the maximum 24-h concentration. In other words, the worst-case
condition occurs for 6 out of 24 h. This assumption is the same one used in
the short-term options of Valley and Valley-BID for estimating the maximum
24-h concentration. Column (9) of Table 6 lists the actual results (simula-
ting 1 yr with the models) corresponding to those listed in column (8).
The differences in the results listed in columns (8) and (9) for the
Valley model reveal that the actual maxima were not sampled by the vertical
array of receptors used in the model runs. However, the differences suggest
that the Valley and Valley-BID results are within 2% of the actual maximum
values possible if one would happen to place a receptor directly on the
maximum. The results listed for Complex I are a bit higher than would be
anticipated. The primary cause for the differences is that the worst-case
condition occurred for more than 6 h (usually 7 to 8 h with the inclusion
of the hours with calms) during the 24-h period, and the 24-h concentration
was thus slightly greater. Differences in plume rise caused by using air
temperatures other than 293 K account for most of the other variations from
the expected results. Since Complex II has a narrower lateral plume than
that employed in Complex I, it is difficult to achieve the expected result
that during 6 out of the 24 h the pollutant should reach the receptor.
26
-------
This usually only occurs to within 1° of the receptor for the 3 to 4 h, but
never for 6 h. Reducing the frequency of the worst-case condition from 6 to
4 h accounts for most of the variation from the expected results listed for
Complex II.
Appendix B lists the highest and second-highest concentrations estimated
by Complex II and Complex I for the 3-h and 24-h averaging times. Also,
tables are given for the medium source for the 5 highest ranked concentrations
for various averaging times.
These results are in accord with the results discussed here in that
the differences in handling the wind speed and the differences in character-
izing the vertical and lateral dispersion describe the results. Besides the
variation caused by these differences, the persistence of the worst-case
condition during the averaging time of interest is all that is needed to
summarize the variations seen between the results by the four models.
27
-------
28
-------
SECTION 5
SPECIAL TOPICS
In formulating a position regarding the proposed screening techniques,
limitations must be recognized both in the model physics and in the present
understanding of the processes. Plume impingement on elevated terrain during
stable conditions is a complex process. The process can be summarized as a
set of questions:
o Will the plume's trajectory reach the terrain?
o What are the minimum dimensions of the plume when it
reaches and impinges on the terrain?
o What is the distribution of mass within the plume during
impingement, relative to the surface of the terrain?
o If the concentration resulting during stable plume
impingement were to result in worst-case (highest)
3-h and 24-h concentrations, what are reasonable
values for the ratios of the worst-case 3-h and 24-h
concentrations to the worst-case 1-h impingement con-
centrations?
29
-------
ALONG VERSUS CROSS VALLEY CONCENTRATION ESTIMATES
Since the sensitivity calculations were made as if terrain features
existed at all possible azimuths from the source, it was desirable to
examine what the effect would be upon the maximum concentrations if terrain
features existed in only two of the possible four quadrants of 90° azimuth
each.
The azimuth of highest flow vector frequency determined an axis referred
to as "along" (see Figure 9). This is 60° for the 1964 Knoxville data and
120° for the 1976 St. Louis data. An axis at 90° to the along axis was
referred to as "across." Quadrants were defined centered on these axes
resulting in two along quadrants (A and B in Figure 9), and two across
quadrants (C and D in Figure 9).
285'
KNOXVILLE, TN,
FLOW VECTOR
60° FREQUENCY
MAXIMUM
105°
195'
Figure 9. Quadrants oriented about the direction cf maximum flow vector frequency.
A tabulation was then made of model estimates of 24-hour concentrations
for the 24 computer runs by listing the maximum concentration in each of the
four quadrants defined above.
30
-------
The "along" quadrants were found to contain the highest 24-h concentra-
tions for both the Knoxville and St. Louis data. However, these maxima were
in quadrant B, which is opposite the quadrant of high flow vector frequency.
(For the Knoxville data the direction of maximum flow yector frequency was 60°;
the direction of the 24-h maximum concentration was 270°. For the St. Louis
data the direction of maximum flow vector frequency was 120°; the direction
of the 24-h maximum concentration was 310°.)
To assess the magnitude of the concentration on the valley sides compared
to maxima in all directions, for valley situations having the two selected wind
distributions, the ratio of the across quadrant maximum to the overall maximum
was determined corresponding to all 24 runs made with the models. Consider
first the results from the model Complex II. For the Knoxville data, the
three source sizes had concentration ratios at 1 km ranging from 0.76 to 0.82
and at 5 km from 0.90 to 0.91. For the St. Louis data, the three source sizes
had concentration ratios at 1 km ranging from 0.80 to 0.83 and at 5 km from 0.84
to 0.86. Osing Complex I, for the Knoxville data, the three source sizes had
concentration ratios at 1 km ranging from 0.82 to 0.86 and at 5 km from 0.82 to
0.83. For the St. Louis data, the three source sizes had concentration ratios
at 1 km ranging from 0.71 to 0.72 and at 5 km from 0.71 to 0.72.
Thus, if locations with these wind distributions had terrain in two
directions instead of all four, and one assumes that straight line flow
could occur as indicated by the wind vane (see caveats on this point else-
where in this document), then estimated concentrations would be between
0.7 and 0.9 of those estimated by runs with terrain in all directions
depending on distance and model used.
31
-------
A "spin off" of the above analysis is the consideration of lowest
maximum 24-h concentration among the 36 azimuths. The ratio of this
lowest 24-h maximum concentration (once a year) to the highest 24-h
maximum concentration varied from 0.15 to 0.22 for Complex II and from
f
0.27 to 0.36 for Complex I. Thus, for these wind distributions, the
azimuth with the lowest 24-h maximum had a concentration more than 1/7
that of the extreme maximum.
MODELING OF PLUME TRAJECTORIES
The sequential models still contain the inherent weakness of modeling
dispersion downstream as straight paths along the input wind direction for
the hour. In complex terrain this assumption is questionable. Hence,
whether plume impaction as modeled actually occurs is not known. Nor is it
known whether or not if the impact were to occur, it would occur as simulated.
One could argue that the characterization of the lateral dimensions as a
pie-shaped 22 1/2° sector is obviously wrong and could not be verified by
actual plume observations. But then one could also argue that it is
questionable whether a plume can maintain a Gaussian cross-section both
vertically and laterally while interacting with a sheer cliff or a steep
bluff.
Because of these arguments, and similar ones not presented, caution
must be exercised in formulating a recommendation for the use or nonuse
of the proposed models. These models were not proposed because they were
considered technically defensible; they were proposed because it was hypothe-
sized that they would yield conservative estimates of the worst-case impacts
in complex terrain.
32
-------
The question which now must be addressed is whether or not models
employing straight line-of-sight transport can successfully indicate the
duration of and the nonoccurrence or the occurrence of plume impaction.
Note that even a better representation of the plume's path in the vertical
does not resolve the issue. The algorithms employed to'estimate actual
concentrations merely attempt to estimate the size of the plume and the
distribution of the mass in relation to the receptor. The real issue is
whether or not a model capable of only straight path transport can estimate
the frequency (and the duration when it occurs) of material reaching each
modeled receptor location?
This issue will not be solved any time soon. But it is important to
realize that improper characterization of plume transport in the vicinity
of major terrain features may lead to underestimates of maximum concentra-
tions as well as overestimates. Consider the problem of an isolated point
source in a narrow valley. The air flow within the valley is primarily
constrained to be along the valley, but transport will also reflect the
cross valley component of the flow. Hence the plume might "lay-up" along
one valley wall and remain there persistently despite the fact that a single
point measure of wind direction at the stack might indicate considerable
wind direction variation.
Hewson and Gill (1944) discussed the meteorological processes affecting
SQ.2 transport within a portion of the Columbia River Valley near Trail,
B.C. Here are some of their conclusions.
(Pg. 23)
The effect of this irregular topography is to produce both
large and small eddies. When the wind velocity is high, these
eddies can be studied and largely accounted for. However, when
the winds are very light, it is almost impossible to explain
33
-------
the variations in wind directions. Frequently, during periods
of light winds, the smoke leaving each of the several stacks at
the smelter can be observed going in a direction different from
that taken by the smoke leaving the others. For instance the
smoke leaving the Dwight-Lloyd stack may be moving up river and
that from the zinc-plant stack going down river, while the
smoke from the blast-furnace stack may be moving across the
valley.
(pg. 24,25)
There are two general types of fumigations, diurnal and
nondiurnal. The diurnal fumigations occur chiefly during the
growing season. They are found at two periods of the day -
from 08 to 10 hr. and from 18 to 20 hr. The nondiurnal fumiga-
tions show few clearly defined characteristics. Usually their
strength is approximately inversely proportional to the distance
from the smelter Fumigations of this type may last several
hours, or under stagnant winter conditions they may persist con-
tinuously for several days.
(in discussing the diurnal fumigation pg 116)
ff;.. The concentration of sulfur dioxide on the west side
"'>of the valley at about 100 dkm is the interesting feature
"of this diagram. This location agrees very well with that
anticipated from study of the east-west wind components at
05 hr., shown in figure 48. From this curve it can be seen
that the sulfur dioxide will be kept on the west side of the
valley by the strong components of wind from the east in the
gas-carrying layer.
Hewson and Gill were summarizing an extensive field program complete with
pibal wind observation, temperature soundings using kites and balloons,
aircraft sampling, and surface monitors (most of which were on the Valley
floor). Considerable effort was involved, largely due to the complex
and often confusing transport that can result in the vicinity of major
terrain features. .A single wind instrument coupled with a simple line-
of-sight transport model would not have explained or predicted the observed
transport during the worst-case calm conditions.
Each complex terrain situation is most likely unique when viewed in
detail. Broadly speaking, similarities may be found with other terrain
34
-------
situations, however, it is impossible to quantitatively estimate the
importance the details of the situation have on influencing the actual
transport. What can be said is that simple models such as Valley, Valley-BID,
Complex II, and Complex I, can characterize the size the plume might have if
it were, by some process, to have reached each modeled receptor location.
Considering the crude approach used to model the transport, it is impossible
to determine whether or not a plume will affect a particular piece of real
estate. In other words, models such as Valley, Valley-BID, Complex II, and
Complex I may be able to tell something about the worst-case impacts one
might expect at any given downwind distance, but, since these models can not
model changes in transport due to complex terrain, they can not address
whether or not the impact will occur.
EVALUATION OF VALLEY (1977)
The Valley model's performance was originally reported by Burt and
Slater (1977). Their analysis consisted of a comparison of the Valley
model estimates of second-highest 24-h concentrations with actual monitoring
data. These monitoring data were the only such data available from sites
on elevated terrain near "singular" polluting facilities. Burt and Slater's
initial hypothesis (1970-1972) was that plume impingement during stable
conditions, as simulated in the Valley Model, might well approximate the
potential second-highest 24-h concentration annually; only later did field
data become available.
The source data for that study are given in Table 7, and the model
estimates and monitoring results are given in Table 8.
-------
TABLE 7. SOURCE CHARACTERISTICS.
Site
name
Crusher
Source
name
Garfield
Stack
height
(m)
124
124
29
32
15
Plume "
rise
(m)
160
140
49
64
15
Emission
rate
(g/sl
3324
2072
202
134
2222
Distance
to receptor
(km)
6.4
6.7
7.0
7.0
7.0
Plume height '
above receptor
(m);
+71
+20
196
178
244
(T/PI(P0/T0) +
1.1145
Lower- Garfield
Lake Point
124
124
29
32
15
160
140
49
64
15
3324
2072
202
134
2222
4.5
4.5
4.5
4.5
4.5
+74
+23
-193
-175
-241
1.1550
#106
#107
Phelps
Mine
Jones
Ranch
Navajo
Gen. Stn.,
Arizona
Navajo
Gen. Stn..
Arizona
Morenci
Smelter,
Arizona
Miami
Smelter,
Arizona
236
236
183
183
84
61
205
203
111
121
96
83
523
465
5522
8060
815
3105
22.8
23.2
4.7
4.7
2.9
2.9
97
169
41
-31
+43
+7
1.1550
1.2220
1.1282
1.1086
* For stability F; with 2.5 m/s wind speed at stack top; 2.4 constant used in plume rise formula.
+ Negative indicates undisturbed stable plume final effective height is estimated to be below receptor
elevation height.
t T is station temperature (K) and P is station pressure (mb). To and Po are standard temperature and
pressure, 298 K and 1013.2 mb respectively. Used to convert model estimates to STP or ppm.
TABLE 8. OBSERVED AND MODELED S02 CONCENTRATIONS.
Site
name
Crusher
Lower-*
Lake Point
#106
#107
Phelps
Mine
Jones
Ranch
Valley*
(2.4)
24801
US
36
25
15490
8610
Valley
(2.6)
2014
0.94
38
27
15902
7820
Valley-
BID
2199
1.08
27
19
11006
6357
Complex 1 Complex II
3527 10966
1.88 5. 57
22 77
15 52
8556 25438
8601 23998
Observed maximum 24-h
Highest Second highest Period
2564
6130
2.66
221
32
30
2547
2042
2642
2473
3130
L20
2J4
19
15
2416
1760
1548
4/73' 1/74
2/74- 1/75
3/75'12/75
V76- V7e
10/74- 2/75
10/74- 2/75
1975
1974
1975
Underscore indicates concentrations are reported in ppm, otherwise concentrations are reported in £/g/m3
reduced to STP.
Valley (2.4) refers to the constant of 2.4 used to estimate the final plume rise during stable conditions. Like-
wise (2.6) refers to a constant of 2.6 being used in the stable plume rise estimates. Note, Valley-BID,
Complex I, and Complex II use the 2.6 factor.
As was done by Burt and Slater (1977), a 3 hour half life was assumed in all model estimates, and for re-
ceptors above the undisturbed plume centerline all the models reduced the concentration estimates by
(401-Za)/400 where Za is the height (m) of the receptor above the centerline.
36
-------
The results listed for Complex II and Complex I are actually
results generated using the approximation formula outlined in Appendix C.
The intent was to estimate the magnitude of plume impingement concentrations,
not to estimate whether or not plume impingement would occur. This latter
task was beyond the capabilities of any of the models employed in this
analysis.
In looking at the differences in model estimates and observed concentra-
tions, note that the emissions data are rough engineering estimates for
all but the Navajo Generating Station.
It would seem all the models had difficulty for the Phelps Mine and
Jones Ranch facilities. Perhaps plume impingement at the monitor sites
never occurred or perhaps the emission rates were poorly characterized.
The results indicate that Valley and Valley-BID performed better than
Complex II and Complex I. As an aside, the Complex II results appear much
better if all the estimates are divided by 2.0. This suggests that the
overall dimensions of the plume may be well characterized by Complex II,
but that the mass distribution is not quite appropriate. Complex II might
provide useful results if reflection from 10 m below the centerline in the
concentration algorithm were ignored.
WITHIN PLUME MASS DISTRIBUTION
Indoubtedly, the most controversial feature of the. Valley model is the
characterization of the mass distribution employed when plume impingement
occurs. For receptor locations on terrain that extends above the modeled
stable plume rise, the Valley model assumed that dispersion of material down-
ward from the final effective plume height is inhibited. This assumption seems
reasonable. However, controversy arises because impingement concentrations
37
-------
are modeled by Valley as if the plume were restricted from dispersing any
more than 10 m downward from the final effective plume height over the
entire downstream transport. This effectively reduces the dispersion in
the vertical to a rate 1/2 of that it would have if the plume were allowed
to freely disperse downward (as it is allowed to disperse upward) during
downstream transport. This causes concentrations to be two times higher
than they otherwise would be.
It is important to realize that "effective" lateral dispersion, ex-
pressed as the ratio of centerline concentration of the sector-averaged
Valley Model plume to that of the Gaussian plume (see Appendix C) ranges
from just over 4.0 to almost 8.0 during F stability. Hence, the Valley
model's maximum concentration estimates for receptors at plume elevation
are from two to four times lower than would be estimated using no re-
striction to vertical dispersion and using the Pasquill F curve for the
lateral dispersion.
EXTRAPOLATING TO LONGER AVERAGING TIMES
The extrapolation of short-term peak concentrations to the longer
averaging times is at best a difficult process. The basic assumption in
Valley is that in 6 h the entire plume has "swung across" a receptor; no
assumption is made about the horizontal distribution of pollutant, except
for mathematical convenience. Table 9 lists the peak to mean 502 concen-
tration ratios observed during 1975 and 1976 at several monitoring networks
operated by American Electric Power (AEP): Clifty Creek, Tanner Creek,
Muskingum, and Gavin-Kyger-Sporn (Mills et al., 1980). These data would
suggest that the 1:4 ratio is perhaps on the low side but within the ob-
served range.
38
-------
Table 9. PEAK TO MEAN RATIOS DURING PERIODS OF MAXIMUM 24-H CONCENTRATIONS
Receptor
network
Clifty
Creek
Tanners
Creek
Muskingum
Gavin-
Kyger-Sporn
Year
1975
1976
1975
1976
1975
1976
1975
1976
Peak 1-h/24-h Concentration
during
Highest 24-h Second-highest
concentration 24-h concentration
5.73
2.78
1.69
2.39
. 2.28
5.58
3.25
2.10
2.44
3.76
1.62
3.70
5.09
3.67
3.86
2.05
39
-------
SECTION 6
QUESTIONS FOR REVIEWERS
The following questions were asked of the reviewers (Team B of the
Chicago Workshop) of the first draft. Their replies to these questions
are discussed in Section 2. Conclusions and Recommendations.
1. Based upon the summary information given in Figures 7 through 9, do you
see any use for Complex II or Complex I as screening techniques?
2. Does the point that none of these models can be used for estimating
concentrations and frequency of occurrence at a specific point come
across clearly?
3. Do you agree or disagree with our recommendation on the labeling of the
Valley-BID results as a screening model estimate valid if plume impinge-
ment occurs? NOTE: this implies that Valley-BID is not sensitive enough
to judge whether or not impingement will occur, only that if impingement
occurs then, thus and so may occur.
4. Does the analysis discussed in this draft include all the computations
that you wanted in the sensitivity analysis?
5. Are there questions about sensitivity that you believe can be answered
by the computations made that are either not stated here or that
insufficient information from the computations are presented so that
the reader can infer the appropriate answer?
6. Please give particular attention to review of the recommendations made in
Section 2. On which point or points do you disagree? Are there additional
points that should be included here?
41
-------
REFERENCES
Briggs, G. A. 1975: Chapter 3Plume rise predictions. In: Lectures on
Air Pollution and Environmental Impact Analysis, Duane A. Haugen, ed.
Amer. Meteorol. Soc. Boston, MA. 296 pp.
Burt, E. W. 1977: Valley Model User's Guide. EPA-450/2-77-018, U. S.
Environmental Protection Agency. Research Triangle Park, NC. 112 p.
Burt, E. W., and H. H. Slater. 1977: Evaluation of the Valley Model.
Preprints, Joint AMS/APCA Conference on Applications of Air Pollution
Meteorology. Amer. Meteorol. Soc. Boston, MA.
Hewson, E. W., and G. C. Gill. 1944: Meteorological Investigations in the
Columbia River Valley, near Trail, B.C. Part III of Report Submitted
to the Trial Smelter Arbitral Tribunal (by R.S. Dean and R. E.
Swain).U.S. Bureau of Mines, Bulletin 453.
Mills, M. T. 1979: Data Base for the Evaluation of Short-Range Dispersion
Models. R-001-EPA-79. Teknekron Research, Inc. Waltham, MA.
Mills, M.T., R. Caiazza, D. D. Hergert, and D.A, Lynn. 1980: Evaluation of
Point Source Dispersion Models. Volume II, Appendices (DRAFT REPORT)
R-030-EPA-79. Teknekron Research, Inc. Waltham, MA. 808 pp.
Pierce, T. E., and D. B. Turner. 1980: User's Guide for MPTER.
EPA-600/8-80-016. U.S. Environmental Protection Agency. Research
Triangle Park, NC 247 pp.
Turner, D. B. 1970: Workbook of Atmospheric Dispersion Estimates,
Office of Air Programs Publication No. AP-26. U.S. Environmental
Protection Agency. Research Triangle Park, NC. 84 pp.
U. S. Environmental Protection Agency, 1980a: Regional Workshop on Air
Quality Modeling: A Summary Report. Office of Air Quality Planning
and Standards USEPA. March 1980 draft. Research Triangle Park, NC.
U. S. Environmental Protection Agency, 1980b: Guideline on Air Quality Models.
Office of Air Quality Planning and Standards, USEPA. OAQPS Guideline
Series. October 1980 Proposed Revisions. Research Triangle Park, NC.
43
-------
APPENDIX A
ADDITIONAL FIGURES OF MAXIMUM 24-H CONCENTRATIONS
Figures A-1 and A-2 are similar to Figures 5 and 6 but are the result
of using the St. Louis meteorological data.
Figures A-3 gives maximum 24-h concentrations resulting from Complex II
at 1 km for the medium and high sources using the Knoxville data.
45
-------
E COMPLEX It
1000
UJ 700 483 494 739 336 254 667 381 479 554 747 807 727 996 69S 67B 990 156 403 245 244 379 646 573 404 586 B50 569 164 305 581 765(1083) 493 496 487 795
C/l fv . I
< 175 517 578 781 360 770 696 40? S07 581 799 863 7SOjl046| 740 7171035 150 431 257 762 398 690 553 «M 621 908 608 816 372 615 81111341525 531 512 313
^ 150 545 537 779 367 281 658 399 512 578 813 875 658\1016/ 758 687 983 154 423 26? 273 398 714 573 447 604 933 616 834 331 675 B30J1094/ 542 555 579 375
CO
O
COMPLEX I
200 323 299 374 309 225 392 275 393 426 334 491 371 388 381 362 479 303 165 215 2M 2BO 768 777 358 288 355 334 333 736 393/521 545J 327 771 271 771
175346 318 390 372 241 410 285 411 447 357 p?A 382 405 405 377 (SoT) 315 168 223 220 294 284 237 375 304 379 357 3S5 752 4081543 4731340 790 781 281
150 363 324 373 304 246 390 264 400 435 3651525/344 388 406 355 482 29? 160 776 224 794 745 238 368 297 391 364 361 758 J93\S33 5S4J341 30? 76? 76?
175233 20? 181 145 146 195 135 233 734 197 267 166 ?7B 269 735 776 136 1?? 138 137 IM 270 158 704 168 708 181
I I I I I I I I I I I I I I
360 70 40 60 80 100 120 140 160 180 700 770 240 760
AZIMUTH-FLOW VECTOR SECTOR (degrees)
176
171 731 319 302 236 187 152 138
I t I I
?BO 300 320 340
Figure A-1. Maximum 24-h concentrations resulting from Complex II and Complex I at 1 km for the low source
(St. Louis, MO, 1976). (Concentrations are pg/m3 divided by 10).
?
tO
<
m
^
o
<
i-
V)
LU
>
o
m
<
z
o
K
<
>
UJ
_j
UJ
200
175
150
ISO
60
64
68
1
360
ISO
104 110 147 24 60 30
108 tit 145 22 61 31
©54 55 SS 52 70 43 22 31
54 55 55 52 70 43 22 3!
T 35 i i i i i i i i
20 40 60 80 100 120 140 160 180
COMPLEX
ISO
36 61 94 91 61 86 126 86 1 10 41 88 126 M54 1 71
38 53 101 96 64 91 135 92 116 43 93 134 1 162 76
40 54 105 100 67 91 140 94 122 44 95 138 U63/ >B
COMPI
0~~
1 1 1 1 1 1 1
700 220 240 260 280 300 320
s*
58
no
50
LEX
35
38
40
II
65
70
72
59
|
38
38
38
i
47
SO
5t
39
8
38
38
28
340
AZIMUTH-FLOW VECTOR SECTOR (degrees)
Figure A-2. Maximum 24-h concentrations resulting from Complex
(St. Louis, MO, 1976). (Concentrations are pg/m3 divided by 10).
and Complex I at 5 km for the low source
MEDIUM SOURCE
Ut 4SO 675 897 388 761 935 598 568 717 621 604 502 442 455 830 253 499 1080 822 567 1032 697 642 1004 1137 1304 669 746 1471 479 596 6S3 787 662 723 994 631
tO /~N / -i
< 3SO 9691270 56510901329 856 8221010 907 870 70S 63S 6361195 352 712n552.11SS 8161468 837 931 1446/1621 1852) 954 1067 2090 690 858 9351108 96310401475 909
m , . / 1500 / 1500 --*
^ 27511761377 6M 1253(1561} 998 1002 1125 1116 10W 825 772 7331453 412 8291887/1442 9991577 968 1137M761 1824 20«)l068 1196 2307 837 1042 1129 1239 1179 l2tWl714)ll«
Ti ^^ >' V- -^ M500
H 200 104 144 133 143 159 114 135 112 170 119 102 90 93 137 53 95 167 152 134 161 145 161 184 176 176 129 133 202 102 116 1?7 133 146 118 147 10?
2
4501091 1509 1100 1507 1659 1038 1178 1179 1621 1064 986 806 884 1548 579 1040 1808 1652 1205 1669 1278 1476 1831 1880 1890 1262 1425 2206 1036 1297 1142 1348 1423 1262 1652 1106
j I I I I I I I I I I I I I I I I | I
Uj 360 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340
AZIMUTH-FLOW VECTOR SECTOR (degrees)
Figure A-3. Maximum 24-h concentrations resulting from Complex 11 at 1 km for the meduim and high sources
using the Knoxville, TN, 1964 data. (Concentrations are pg/m3 divided by 10).
46
-------
APPENDIX B
HIGHEST AND SECOND HIGHEST CONCENTRATIONS
AND
CONCENTRATIONS FOR VARIOUS AVERAGING TIMES
Tables B-1 through B-4 give the highest and second highest concentra-
tions estimated from the two models Complex II and Complex I for two aver-
aging times, 24-h and 3-h. The azimuth of the receptor relative to the
source,the elevation above the source stack base, the Julian day of the
estimate,and the hour ending the period, if appropriate, are listed with
each estimated concentration. Tables B-1 and B-2 are for Knoxville data;
Figures B-3 and B-4 are St. Louis data. Tables B-1 and B-3 are for Complex II;
Tables B-2 and B-4 are. for Complex I.
Tables B-5 and B-6 give the five highest model estimates for four
different averaging times. Tables B-5 is for Knoxville data; Table B-6
is for St. Louis data.
Using data from Table B-5 (Knoxville), the second highest from both
models for each distance as a function of averaging time was graphed.
This is displayed in Figure B-1.
The five highest concentrations using the Knoxville data (again
from Table B-5) are displayed in Figure B-2 in rank order for the four
averaging times for the two models, Complex II and Complex I.
47
-------
TABLE B-1. HIGHEST AND SECOND-HIGHEST 3-H AND 24-H CONCENTRATIONS FROM
COMPLEX II (KNOXVILLE, TN, 1964).
Source
Low
24-hour
High
Second high
3-hour
High
Second high
Medium
24-hour
High
Second high
3-hour
High
Second high
High
24-hour
High
Second high
3-hour
High
Second high
Cone.
12157
9018
51053
45054
23067
18174
96704
86935
36929
30078
147174
132200
Azi.
270°
270°
330°
270°
270°
270°
_
330°
270°
270"
270°
330°
270°
1 km
Elev.
175m.
150m.
150m.
150m.
275m.
275m.
275m.
275m.
500m.
500m.
Day Hour
299
22
249 3
299 6
299
22
249 3
299 6
299
22
500m. 249 3
500m.
TABLE B-2. HIGHEST AND SECOND-
22 3
Cone.
1978
1400
8950
7758
4505
3235
20306
17633
8852
6561
40702
34907
HIGHEST 3-H AND 24-H
COMPLEX I (KNOXVILLE,
Source
Low
24-hour
High
Second high
3-hour
High
Second high
Medium
24-hour
High
Second high
3-hour
High
Second high
High
24-hour
High
Second high
3-hour
High
Second high
Cone.
5394
3932
15637
15563
10817
8202
32444
32341
19460
14999
58758
58613
Azi.
270°
250°
120°
320°
270°
270°
120°
320°
270°
270"
120°
320°
1 km
Elev.
175m
175m
150m
150m
275m
275m
275m
275m
500m
500m
500m
500m
Dav Hour
. 299
309
. 207 3
245 3
. 299
22
207 3
245 3
299
22
. 207 3
. 245 3
Azi.
270°
270°
330°
270°
270°
270°
330°
270°
270°
270°
330°
270°
5 km
Elev.
150m.
150m.
150m.
150m.
275m.
275m.
275m.
275m.
500m.
500m.
500m.
500m.
Dav
299
22
249
299
299
22
249
299
299
22
249
299
CONCENTRATIONS
Hour
3
6
3
6
3
6
FROM
TN, 1964).
Cone.
751
556
2170
2165
1712
1237
4953
4943
3406
2516
9972
9958
Azi.
270°
240°
110°
320°
270°
250°
110°
320°
270°
270°
110°
320°
5km
Elev.
150m.
150m.
150m.
150m.
275m.
275,n.
275m.
275m.
500m.
500m.
500m.
500m.
Day
299
350
207
245
299
309
207
245
299
22
207
245
Hour
3
3
3
3
3
3
48
-------
TABLE B-3. HIGHEST AND SECOND-HIGHEST 3-H AND 24-H CONCENTRATIONS FROM
COMPLEX II (ST. LOUIS, MO, 1976).
Source
Low
24-hour
High
Second high
3-hour
High
Second high
Medium
24-hour
High
Second high
3-hour
High
Second high
High
24-hour
High
Second high
3-hour
High
Second high
Cone.
11343
11163
51218
43741
22476
22138
96691
83855
37693
36559
145823
128851
Azi.
310°
310°
150°
100°
310°
310°
150°
100°
310°
310°
270°
100°
1 km
Elev.
175m.
175m.
150m.
150m.
275m.
275m.
275m.
275m.
500m.
500m.
500m.
500m.
Day Hour
238
320
305 24
302 3
320
238
305 24
302 3
320
238
262 3
302 3
TABLE 3-4. HIGHEST AND SECOND-HIGHEST 3-H
COMPLEX
Source
Low
24-hour
High
Second high
3-hour
High
Second high
Medium
24-hour
High
Second high
3-hour
High
Second high
High
24-hour
High
Second high
3-hour
High
Second high
Cone.
5726
5560
15665
15612
11689
11438
32482
32410
21242
20672
58799
58712
Azi.
310°
310°
360°
360°
310°
310°
360°
360°
310°
310°
360°
360°
1 km
Elev.
175m.
175m.
150m.
150m.
27Sm.
275m.
275m.
275m.
500m.
500m.
500m.
500m.
I (ST. LOUIS,
Day Hour
320
232
235 24
236 3
320
232
235 24
236 3
320
232
235 24
236 3
Cone.
1627
1541
9452
7295
3772
3549
21442
16563
7587
7161
42224
32910
AND 24-H
MO, 1976)
Cone.
801
775
2172
2168
1831
1775
4955
4949
3637
3536
9975
9967
Azi.
310°
310°
150°
100°
310°
310°
150°
100°
310°
310°
150°
100°
5km
Elev.
150m.
150m.
150m.
150m.
275m.
275m.
275m.
275m.
500m.
500m.
500m.
500m.
Day
238
320
305
302
238
320
305
302
238
320
305
302
CONCENTRATIONS
Azi.
310°
310°
360"
360°
310°
310°
360°
360°
310°
310°
360°
360°
5 km
Elev.
150m.
150m.
150m.
150m.
275m.
275m.
275m.
275m.
500m.
500m.
500m.
500m.
Day
320
232
235
236
320
232
235
236
320
232
235
236
Hour
24
3
24
3
24
3
FROM
Hour
24
3
24
3
24
3
-------
TABLE B-5. FIVE HIGHEST MODEL ESTIMATES FOR 1-, 3-, 8-,
AND 24-H AVERAGING TIMES (MEDIUM SOURCE;
KNOXVILLE, TN, 1964).
Averaging
time
(H)
1-H
Highest
Highest 2"d high
Highest 3rd high
Highest 4th high
Highest 5th high
3-H
8-H
24-H
/(b)
(c>/jb)
Complex II
1-km
109044.8
(a) 108163.8
107647.3
107647.3
106309.6
96704.0
86935.4
76877.1
69812.1
58769.4
69133.3
49693.0
39627.6
34317.6
31050.5
(c) 23066.8
(b) 18174.3
14005.0
12486.0
11439.2
5.95
1.27
Complex I
1-km
37717.7
37638.0
37563.3
37560.2
37549.3
32444.2
32341.0
32120.9
32016.4
31677.9
29447.4
22761.4
22279.2
20061.8
17997.1
10816.7
8201.7
8157.8
7656.7
6979.2
4.59
1.32
Complex II
5-km
26072.8
25990.9
25938.4
25938.4
25808.8
20305.9
17633.2
14281.1
12807.7
12236.4
13419.4
8920.0
6186.6
6175.1
6007.6
4505.4
3234.7
2308.2
2259.0
2007.1
8.04
1.39
Complex I
5-km
5406.9
5406.6
5406.2
5405.7
5405.3
4952.6
4943.4
4923.6
4915.1
4884.3
4614.8
3483.1
3386.6
3077.7
2666.2
1711.9
1237.4
1231.5
1176.1
1093.8
4.37
1.38
(a) Second highest 1-H
(b) Second highest 24-H
(c) Highest 24-H
50
-------
TABLE B-6. FIVE HIGHEST MODEL ESTIMATES FOR 1-, 3-, 8-,
AND 24-H AVERAGING TIMES (MEDIUM SOURCE;
ST. LOUIS, MO, 1976).
Averaging
time
(H)
1-H
Highest
Highest 2nd high
Highest 3rd high
Highest 4th high
Highest 5th high
3-H
8-H
24-H
(a)/(b.
/(b)
Complex II
1-km
109189.6
(a) 107851.2
107145.6
106852.9
100405.2
96690.5
83855.0
77653.3
66292.6
65192.6
61749.3
60951.1
43777.2
43707.9
41404.2
(c) 22475.9
(b> 22137.5
16052.3
15519.6
14592.4
4.87
1.02
Complex 1
1-km
37852.9
37661.3
37606.6
37597.1
37565.4
32482.3
32409.6
32308.3
32259.7
31760.0
30459.5
26259.1
24060.8
20882.4
20713.6
11688.7
11437.8
10637.4
8112.0
7987.3
3.29
1.02
Complex II
5-km
26084.9
25958.0
25890.0
25861.6
21845.0
21442.4
16563.0
13485.0
11617.2
10889.8
11103.0
9750.1
6845.9
5860.9
5042.4
3771.7
3549.3
2525.6
2275.9
1778.8
7.31
1.06
Complex I
5-km
5406.1
5405.5
5404.5
5404.2
5404.2
4955.5
4949.0
4940.1
4935.7
4935.2
4795.3
3969.6
3733.9
3173.0
3085.6
1831.3
1774.6
1645.8
1254.3
1205.1
3.05
1.03
(a) Second highest 1-H
(b) Second highest 24-H
(c) Highest 24-H
51
-------
10'
HIGHEST SECOND HIGH. MEDIUM SO
Ol km, COMPLEX II
I km,COMPLEX I
D S km. COMPLEX II
5 km, COMPLEX I
I
AVERAGING TIME, hi
Figure B-1. Highest second-high concentrations as a function of averaging time from Knoxville.
TN, 1964 data.
ID*
5,10*
Sxl O3
MEDIUM SOURCE. 1 km
COMPLEX II COMPLEX!
u. O t-hf 1-hr
I 3 h- 3 hr
, Bht A Bhf
> 24-hr 24-hr
Figure B-2. Five highest estimated conceniraiions in rank order for 1 , 3-, 8-. and 24-hr averaging
times from Complex II and Complex I using Knoxville, TN, 1964 data.
52
-------
TABLE B-6. FIVE HIGHEST MODEL ESTIMATES FOR 1-, 3-, 8-,
AND 24-H AVERAGING TIMES (MEDIUM SOURCE;
ST. LOUIS, MO, 1976).
Averaging
time
(H)
1-H
Highest
Highest 2nd high
Highest 3rd high
Highest 4th high
Highest 5th high
3-H
8-H
24-H
/(b)
Complex II
1-km
109189.6
(a) 107851.2
107145.6
106852.9
100405.2
96690.5
83855.0
77658.3
66292.6
65192.6
61749.3
60951.1
43777.2
43707.9
41404.2
(c) 22475.9
22137.5
16052.3
15519.6
14592.4
4.87
1.02
Complex I
1-km
37852.9
37661.3
37606.6
37597.1
37565.4
32482.3
32409.6
32308.3
32259.7
31760.0
30459.5
26259.1
24060.8
20882.4
20713.6
11688.7
11437.8
10637.4
8112.0
7987.3
3.29
1.02
Complex II
5-km
26084.9
25958.0
25890.0
25861.6
21845.0
21442.4
16563.0
13485.0
11617.2
10889.8
11103.0
9750.1
6845.9
5860.9
5042.4
3771.7
3549.3
2525.6
2275.9
1778.8
7.31
1.06
Complex I
5-km
5406.1
5405.5
5404.5
5404.2
5404.2
4955.5
4949.0
4940.1
4935.7
4935.2
4795.3
3969.6
3733.9
3173.0
3085.6
1831.3
1774.6
1645.8
1254.3
1205.1
3.05
1.03
Second highest 1-H
(b) Second highest 24-H
Highest 24-H
51
-------
HIGHEST SECOND-HIGH. MEDIUM SOURCE
Ol'in. COMPLEX II
1 km.COMPLEX I
O S km. COMPLEX II
Sim.COMPLEX I
I I
AVERAGINGTIME.br
Figure B-l. Highest second-high concentrations as a function of averaging time from KnoxvilEe,
TN. 1964 data.
to*
in*
s.u'
MEDIUM SOURCE. 1 km
COMPLEX II COMPLEX I
. O 1-hr 1-hr
D 3-hr 1-lir
A Ik' A I-hr
Figure B-2, Five highest estimated concentrations in rank order for 1-. 3-, 8-, and 24-hr averaging
times from Complex II and Complex I using Knoxville, TIN, 1964 data.
52
-------
APPENDIX C
MODEL ESTIMATES BY HAND CALCULATIONS
The results from the Valley and Valley-BID models, when executed in
their screening mode, for estimating worst-case 24-h concentrations can be
duplicated rather simply using a calculator. The procedure for duplicating
the Valley and Valley-BID results can also be made to approximate the
results from Complex II and Complex I, generated in this sensitivity
analysis. The computations of plume rise, vertical dispersion, and
lateral dispersion need be computed only once per downwind distance. Then
equation (C-1) can be used to approximate the various models. Equation
(C-1) will tend to overestimate the maximum concentrations for 3-, 8-, and
24-h averaging times from Complex II and Complex I as downwind distance
increases beyond 5 km. However, it would not be that difficult to further
investigate the variation of R as a function of downwind distance and
thereby develop a simple tool for screening analyses in complex terrain
situations.
The following discussion outlines the four-step procedure. The first
step is to determine the wind speed which is a constant for Valley and
Valley-BID and is a function of stack height for C^-n^lex II and Complex I.
The second step is to compute the stable plume rise. The third step is to
compute the vertical and lateral dispersion for the downwind distance of
interest, and the fourth step is to substitute the results into equation
(C-1). The procedures lend themselves to programmable pocket calculators.
53
-------
The factor R has been chosen to slightly overestimate the sequential
model results for the 1- to 5-km downwind distance range. Generally, the
results of Equation (C-1) are within 15% of actual modeled results for
Complex II and Complex I. There is no error as far as Valley and Valley-BID
is concerned, except for those minor differences introduced by the characteriza-
tion used for the vertical dispersion during Pasquill F stability category.
This particular characterization of °z is from Vogtx^ ( /?"77/ t
If the receptor elevation is above the undisturbed height of the plume,
the concentration resulting from equation (C-1) should be multiplied by
(401-ZR)/400, where ZR is the height in meters of the receptor elevation above
the undisturbed plume. For instance, say we had a stack height of 100 m, a
plume rise of 150 m, and a receptor elevation above stack base of 275 m. In
such a case, the receptor would be 25 m above the undisturbed final plume height
and ZR would equal 25 m and H in equation (C-1) would equal 10 m.
1. Compute wind speed at stack top during 1-h period of assumed
worst-case stable conditions.
A. Valley or Valley-BID
u = 2.5 m/s
B. Complex II or Complex I
u = (hs/10)°-55
where hs = stack height (m)
2. Compute stable plume rise
Vsd2T 1/3
5.007 S y (Tg - T)
U Ig
Ah = -^ or
54
-------
Vs = stack gas exit velocity (m/s)
d = stack exit diameter (m)
T = ambient air temperature, ~293 K
Ts = stack gas exit temperature (K)
u = assumed wind speed at stack top (m/s)
Vf = stack gas volume flow (m-Vs), equal to
U/4))Vsd2
3. Compute vertical arid lateral dispersion
A. Valley
°z0 = OoVc) exP (~3-8 + 1'419 lnX-0.055 In2 X)
L. I ,?
<>y0 = (/27/16)X
X = downwind distance (m)
B. Valley-BID or Complex I
°z = [°ZQ2 + (Ah/3.5)2 ]1/2
where az is as given for Valley
°y0 = as given for Valley
Ah = stable plume rise (m)
C. Complex II
az = as given for Valley-BID
°y = [ay02 + ^h/3.
a = (-0.0029 In! 0.054)X
55
-------
4. Compute concentration estimate
Y _ R Q 1D6 '
\ _ -
X r maximum concentration for averaging time (
H = minimum separation between plume centerline and receptor,
no less than 10 m.
Q = emission rate (g/s)
R = ratio of maximum concentration for averaging time of
interest to 1-h peak.
Averaging Time (h)
Valley or
Valley-BID
Complex II
Iopt(25)=1
Complex I
Iopt(25)=1
3
Not
applicable
0.90
, 0.95 :
8
Not
applicable
0.60
0.85
24
0.25
0.20
0.35
REFERENCES APPENDIX C
Vogt, Kurt-Jurgen, 1977: Empirical investigations of the diffusion of waste
air plumes in the atmosphere, Nuclear Technology 34, 43-57.
56
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
2.
3. RECIPIENT'S ACCESSION-NO.
4. TITLE AND SUBTITLE
AN ANALYSIS OF COMPLEX I AND COMPLEX II
CANDIDATE SCREENING MODELS
5. REPORT DATE
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
John S. Irwin and D. Bruce Turner
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
10. PROGRAM ELEMENT NO.
CDTA1D/04-1315 (FY-82)
(Same as Block 12)
11. CONTRACT/GRANT NO.
12. SPONSORING AGENCY NAME AND ADDRESS
13. TYPE OF REPORT AND PERIOD COVERED
Environmental Sciences Research Laboratory RTP, NC
Office of Research and Development
U.S. Environmental Protection Agency
Rpsearrh Triangle Park. MH 27711
14. SPONSORING AGENCY CODE
EPA/600/09
15. SUPPLEMENTARY NOTES
16. ABSTRACT
This study, suggested by an EPA Regional Workshop in February 1980, was
conducted as a simple analysis to investigate whether or not a sequential air
quality simulation model, capable of accepting onsite hourly meteorological
data, could be recommended as a screening model for estimating worst-case . .
pollutant impacts on complex terrain. The study intercompared the highest
24-h average pollutant concentration values obtained using "our algorithmic
air quality simulation models: Complex I, Complex II, Valley, and Valley-BID.
The models were applied and their results compared for a year's meteorological
data for two different sites. Various combinations of source release height.and.
terrain configurations were examined. .. . '
The authors conclude that the Valley-BID (or pencil and paper calculations'using
the same assumptions) are most appropriate for screening analyses for maximum 24-h
concentrations resulting from plume impaction on terrain near the height of an
elevated stabilised plume.
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