EPA-450/3-75-059
June 1975
F SELECTED AIR POLLUTION
APPLICABLE TO COMPLEX
EVALUATION
ISPERSION MODELS
TERRAIN
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Air and Waste Management
~
Office of Air Quality Planning and Standards
^f ^™"*' ^
Research Triangle Park, North Carolina 27711
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EPA-450/3-75-059
EVALUATION
OF SELECTED AIR POLLUTION
DISPERSION MODELS
APPLICABLE TO COMPLEX
TERRAIN
by
INTERCOMP Resources Development and Engineering, Inc.
2000 West Loop South, Suite 2200
Houston, Texas 77027
Contract No. 68-02-1085
Program Element No. 2 AC 129
EPA Project Officer: Edwin L. Meyer, Jr.
Prepared for
ENVIRONMENTAL PROTECTION AGENCY
Office of Air and Waste Management
Office of Air Quality Planning and Standards
Research Triangle Park, North Carolina 27711
June 1975
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11
This report is issued by the Environmental Protection Agency to report
technical data of interest to a limited number of readers. Copies are
available free of charge to Federal employees, current contractors and
grantees, and nonprofit organizations - as supplies permit - from the
Air Pollution Technical Information Center, Environmental Protection
Agency, Research Triangle Park, North Carolina 27711; or, for a
fee, from the National Technical Information Service, 5285 Port Royal
Road, Springfield, Virginia 22161.
This report was furnished to the Environmental Protection Agency by
INTERCOM? Resources Development and Engineering, Inc., Houston,
Texas 77027, in fulfillment of Contract No. 68-02-1085. The contents
of this report are reproduced herein as received from INTERCOM?
Resources Development and Engineering, Inc. The opinions, findings,
and conclusions expressed are those of the author and not necessarily
those of the Environmental Protection Agency. .Mention of company
or product names is not to be considered as an endorsement by the
Environmental Protection Agency.
Publication No. EPA-450/3-75-059
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Ill
PREFACE
It is regretted that the Environmental Protection Agency (EPA)
and INTERCOM? Resource Development and Engineering, Inc. could not
mutually agree as to the conclusions of this study. Consequently,
as sponsor, EPA is obligated to caution against the uncritical
acceptance of the summary statements in the report.
The EPA in 1970 and 1972 evaluated the impact of several non-
ferrous smelters on air quality in mountainous regions. Similarly,
in 1971 the National Oceanic and Atmospheric Administration eval-
uated the impact of a number of power plants located in mountainous
areas. The techniques used to estimate the effects of complex
terrain on the distribution of the effluents from the sources had
not been used prior to these studies. The air quality estimates
were much greater for nearly all facilities than would result from
the use of the flat-plane formula. INTERCOMP was one of the consul-
tants retained by industry to review EPA's analyses. Results of
their model simulations were presented at formal hearings to
counter the governmental estimates.
Although generalities of the INTERCOMP model were available
in the literature and hearing records, the computer program (and
thus the technical details) were and remain proprietary. To
obtain details of the technical content of the INTERCOMP model,
EPA negotiated a contract with INTERCOMP. The contract called
for INTERCOMP to provide the computer program to EPA; to instruct
EPA personnel in the use of the computer program; and to provide
applications of the INTERCOMP and Gaussian models for comparison
with observed peak short-term concentrations in complex terrain.
The contract states that "...peak short-term concentrations shall
be the primary consideration in the evaluation...(of the models)."
This report discusses the effort of INTERCOMP to satisfy this
contract.
In bringing the contractual effort to a conclusion, it became
apparent that INTERCOMP and EPA project officers had some funda-
mental differences of a technical nature as to portions of the
report. Aside from differing interpretations of the validity of
various simplifying assumptions in each model, the basic differences
revolve around the validity of the El Paso data used for model
evaluation and around the definition of a reliable model estimate.
More specifically, EPA takes exception to statements made
in the Summary and on pp. 3-28 and 3-29, and pp. 3-40 and 3-41
in the report. EPA agrees that the El Paso data are useful to
demonstrate the degree of flexibility of models; that is, through
successive adjustments of emission rates, etc., to obtain agreement
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IV
between the modeling results and the air quality observations.
However, EPA does not agree that the El Paso emission data were
sufficiently reliable to warrant judgments on the "accuracy" of
models.
Also, EPA does not completely agree with INTERCOM?'s inter-
pretation of the NOAA's Huntington Canyon study. A case may be
made that the results of the study indicate that the basic Gaussian
model provides more reliable estimates of the peak 1-hour concen-
trations in this instance than either the EPA terrain or the
INTERCOM? models.
Further, current short-term air quality standards (24-hour
period or less) are not to be exceeded more than once per year.
Hence, if modeling results are to be used directly in source-control
decisions, a reliable model estimate must represent the near-upper
envelope of observable concentrations. However, INTERCOM? interprets
a reliable estimate as one which best fits an average of observed
data. This interpretation may lead to estimates of concentrations
that are incompatible with the definition of short-term standards.
Thus, a degree of control based on INTERCOM?'s interpretation
of a reliable model estimate may not adequately protect the quality
of the air.
INTERCOM? and EPA agree that both have worked in good faith
to resolve these differences. They agree that further expendi-
tures of effort and funds are unlikely to produce results that
are completely acceptable to either party. Hence, the report
is released with this Preface as an integral part, so that the
results of the study may be available, but with the reader
cautioned against the uncritical acceptance of the conclusions.
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V
EVALUATION OF SELECTED AIR POLLUTION DISPERSION
MODELS APPLICABLE TO COMPLEX TERRAIN
TABLE OF CONTENTS
SUMMARY ix
1.0 INTRODUCTION 1-1
1.1 General Needs and Objective 1-1
1.2 Description of Models Tested 1-2
1.3 Approach Used in Model Comparison 1-3
2.0 AIR QUALITY MODELS TESTED 2-1
2.1 The Gaussian Model 2-1
2.2 The EPA Model (C4M3D) 2-2
2.3 The INTERCOMP Model 2-3
2.4 Calculation of 3 and 24 Hour Averages
from Model Predictions 2-5
3.0 VALIDATION AND COMPARISON OF AIR QUALITY MODELS 3-1
3.1 General Comparisons 3-1
3.2 Comparison of Solution Techniques 3-3
3.3 Comparison for Huntington Canyon Tracer Data 3-10
3.3.1 Data Collected 3-10
3.3.2 Geographical Setting 3-10
3.3.3 Comparisons for a Stable
Down-Valley Flow 3-14
3.3.4 Comparison for a Neutral
Up-Valley Flow 3-19
3.3.5 Other Test Comparisons 3-25
3.3.6 Summary 3-28
3.4 Model Comparisons at El Paso 3-29
3.4.1 General Site and Data Description 3-29
3.4.2 Flow to the Northwest 3-32
3.4.3 Stable Flow 3-36
3.4.4 Summary 3-40
3.5 Validation of the INTERCOMP Flow Model 3-41
3.5.1 General 3-41
3.5.2 Navier-Stokes Flow Model 3-42
3.5.2-1 Mathematical Development 3-42
3.5.2-2 Comparison with Results
for Laminar Flow 3-43
3.5.2-3 Eddy Viscosity Model for
Turbulent Flow 3-44
3.5.3 Comparison with Modified Potential Model 3-50
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VI
TABLE OF CONTENTS (Continued)
3.5.3-1 Influence of Wake Regions on
Flow Field Around an Obstacle 3-50
3.5.3-2 Comparison for Two-Dimensional
Flow 3-50
3.5.3-3 Comparison for Three-Dimensional
Flow 3-54
3.5.4 Summary of Comparisons and Conclusions 3-61
3.5.4-1 Range of Adequacy for Modified
Potential Flow Model 3-61
3.5.4-2 Limitations 3-63
3.5.4-3 Accuracy and Expected Errors 3-63
4.0 REFERENCES
APPENDIX A - Navier-Stokes Flow Model
APPENDIX B - Comparison of Measured and Calculated Results
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Vll
ILLUSTRATIONS
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Figure 15
Figure 16
Figure 17
Figure 18
Figure 19
Figure 20
Figure 21
Page
Comparison Numerical Model with Gaussian
Plume Models 3-2
Comparison of Analytical Stack Height Concen-
trations to Model Calculations 3-5
Comparison of Analytical Groundlevel Concen-
trations to Model Calculations 3-6
Comparison Pasquill-Stability Class E to
INTERCOM? Match of that Category 3-8
Comparison Crosswind Values Class F with
INTERCOM? Match of Pasquill Class F 3-9
Huntington Canyon Terrain, Up-Canyon Orientation 3-11
Huntington Canyon Terrain, Down-Canyon
Orientation 3-13
Down-Canyon Test No. 10 3-17
Up-Canyon Test No. 5, 150° Wind 3-21
Up-Canyon Test No. 5, 135° Wind 3-23
Comparison of Measurements with Calculations
Tests 5 and 10 3-24
Comparison of Measurements with Calculations
Tests 1 and 7 3-26
Map of Sampling Grid and Terrain - El Paso 3-31
Model Match - El Paso Inversion Aloft 3-33
Model Match - El Paso Cross-Section 3-35
Terrain Vertical Cross-Section Stable
Case - El Paso 3-37
Model Match - El Paso Stable Case 3- 39
Comparison of Calculated Laminar Entrance Flow 3-45
Vertical Variation of Eddy Viscosity 3-46
Comparison of Calculated Turbulent Velocity
Profile with Power Law 3-48
Comparison-Calculated Wind Profiles and Tunnel
Experiments 3-49
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Vlll
Figure 22
Figure 23
Figure 24
Figure 25
Figure 26
Figure 27
Figure 28
Figure 29
Figure 30
Figure 31
Page
Flow Field Around Finite Length Obstacle 3-51
Flow Field Around Infinite Length Obstacle 3-52
Comparison of Navier-Stokes Solutions with •
Different Obstacles Velocity Cross-Sections 3-53
Neutral Atmosphere - Comparison of Navier-
Stokes and Potential Velocity Solutions 3-55
Differential Velocities for Stable to
Neutral Atmosphere 3-56
Stable Atmosphere - Comparison of Navier-
Stokes and Potential Velocity Solutions 3-57
Three-Dimensional Test Problem 3-58
Comparison of Navier-Stokes and Potential
Solution in Front of Obstacle - Neutral 3—59
Comparison of Navier-Stokes and Potential
Solution at Face of Obstacle - Neutral 3-60
Differential Velocities for Stable to Neutral
Atmosphere Comparison in 3-D 3-62
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IX
SUMMARY
Short-term (1 hr., 3 hr., and 24 hr.) air quality criteria
generally have a higher potential for being exceeded in the vicinity
of large point sources than do longer term standards. In cases where
terrain is unimportant, the air quality can be evaluated using the
familiar Gaussian plume models. Frequently, such evaluations must
involve geographical areas with important terrain relief. In such
cases, regulatory and policy-making agencies have made assumptions
about how the plume centerline behaves and continued to use the
Gaussian models. Recently models have become available which com-
bine wind flow calculations along with the plume dispersion assessment.
Such a model has the potential to provide more accurate air quality
predictions where terrain is important. As a consequence, the objec-
tive of this contract was to use air quality data collected in rough
terrain to test the accuracy of several models to predict short-term
concentrations.
The models tested were (1) the Gaussian calculation known as
the NOAA model, (2) the EPA Gaussian model, and (3) the INTERCOM?
combined wind flow and plume dispersion model. Two sets of data
were used in the comparison. These data were (1) the SF tracer
data collected by NOAA in Huntington Canyon, Utah, and (2) S02
ambient data in El Paso, Texas.
The model calculations represent predictions based upon the
measured or observed meteorology. That is, the calculations repre-
sent generally how the models would have been used to predict air
quality around a single source. It should be noted that the compari-
sons included in the report were for 1 hour average concentrations,
rather than the 3 or 24 hour air quality standard criteria.
The results for Huntington Canyon show the INTERCOM? combined
wind flow and dispersion model predicted groundlevel concentrations
with an accuracy comparable to that normally obtained with Gaussian
predictions in flat terrain situations. The INTERCOM? model gave
calculated results within a factor of two and one-half for all
stable tests. For stable down-canyon flows, however, Gaussian
predictions from a NOAA type model averaged a factor of fifteen fold
higher than the measured results.
The El Paso data, though limited by emission definition data,
provided comparisons over flat terrain and near, but not in, mountains.
In the flat terrain cases, results with the Gaussian (NOAA) model and
the INTERCOM? model were in close agreement. The EPA model gave lower
predicted concentrations. In the elevated terrain cases, the INTERCOM?
model predicted lower concentrations than the Gaussian type models by
factors of ten to twenty.
Comparison of the various models with observations show that the
addition of a wind flow calculation can improve air quality predic-
tions. Presently available wind flow calculations are of necessity
a simplification of the atmospheric flow processes. However, there
are a broad range of air quality evaluations in which the accuracy
of the end result can be improved by the combined approach.
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1-1
1.0 INTRODUCTION
1.1 General Needs and Objective
More and more emphasis is being placed on the need to
satisfy short-term (1 hr., 3 hr., and 24 hr.) air quality cri-
teria. These needs have generally been delineated to avoid
adverse effects on human health or plant and animal growth
processes. Certainly no group of experts agree precisely on
what concentration is sufficient to provide protection against
adverse effects, but it is clear that protection is needed.
The shorter term ambient air quality standards generally
are more likely to be exceeded in the vicinity of large isolated
point sources than are the longer term annual standards. As a
result, it is essential for regulatory and policy-making agencies
to have available to them the best technology for evaluating
ambient air quality concentrations which result from these
point source emissions.
In cases where terrain is unimportant, the state-of-the-
art method is to evaluate the short-term air quality using three-
dimensional Gaussian plume models. Present Environmental Pro-
tection Agency, EPA, practice is to use such a model to provide
assessments r>f ambient air quality and thus provide a comparison
to ambient air quality standards.
Frequently such evaluations must be for geographical areas
which do involve important terrain relief. Many of the coal
fired power plants and non-ferrous smelters are located in areas
where terrain plays an important role in the meteorology control-
ling plume dispersion. In such cases, EPA has made assumptions
about how the plume centerline behaves in the immediate vicinity
of the terrain and continued to use the cross-wind and vertical
diffusivities characteristic of the Gaussian models. Basically,
the modification of the wind flow by the terrain is being assumed
rather than any quantitative attempt made to calculate this
modification.
Within the last few years, several techniques have been
described which combine a wind flow calculational model along
with a plume dispersion calculational techniquel > 2'3'". Such
a model has the potential to provide more accurate plume disper-
sion assessments where terrain is important. As a consequence,
the objectives of this contract were to:
(1) compare one of the combined flow and dispersion
models, the INTERCOMP model, with the presently
available EPA models, and
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1-2
(2) use data from rough terrain areas to test the
relative abilities of the models in predicting
short-term air quality.
1.2 Description o_f the Models Tested
Three models have been compared with data as a result of
this contract. Two of these models are Gaussian models and
have been used by regulatory agencies to make air quality analyses
in rough terrain areas. The third model1* was developed by
INTERCOM? and includes a wind flow calculation as well as the
assessment of plume dispersion. The model is more completely
described in an associated volume which documents the equations
and methods of solution, but for which the distribution is
restricted to EPA personnel.
Of the two Gaussian models, one has become known as the
NOAA model. This nomenclature undoubtedly resulted from the
use of this model by NOAA in preparing the diffusion model
calculations presented in the Southwest Energy Study5.
The second Gaussian model is that presently employed by
EPA for making ambient air quality evaluations for rough terrain
areas. This model (the version tested was known as C4M3D) is
a modification of the plume centerline flow concept used in the
NOAA model and in addition retains angular segment averaging
for even short-term concentrations.
The INTERCOM? model is quite a different concept from the
Gaussian models. As opposed to assuming normal concentration
distributions in the cross-wind and vertical directions, the
model arises from approximating turbulent fluctuations by a
Fickian-type eddy diffusivity. These eddy properties are height
dependent as is the windspeed. This is quite different from the
average over height wind and dispersion coefficients used in a
Gaussian model or even those used in a constant diffusivity
model.
Even so, over flat terrain there is good agreement between
the numerical model and the Gaussian results. The particular
height dependence of diffusivity and wind speed which provide
this agreement are discussed in a later section. Only in cases
where terrain modifies the air flow do the INTERCOM? model
results differ substantially from either the NOAA or EPA models.
As mentioned previously, the purpose of the contract was to
compare the models over rough terrain and show whether or not
the increased flexibility of the INTERCOM? model actually re-
sulted in more accurate concentration predictions.
The purpose of the contract was to compare the several
models tested for their predictive ability to calculate short-term
concentrations. Short-term federal air quality standards can be
exceeded on a once per year basis. Ideally, the models should
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1-3
define the next-highest 3 and 24 hour average concentration.
However, because of the diffusion parameters used, model pre-
dictions generally represent less than 1 hour averages. The
calculated 3 and 24 hour averages for comparison with standards
must then be developed from these model predictions.
1.3 Approach Used in Model Comparison
Two sets of data were used in comparing the various models.
These data were (1) the SFg tracer data collected by NOAA in
Huntington Canyon, Utah6 and (2) S02 ambient air qualjty data
around the ASARCO smelter in El Paso, Texas.
Insofar as possible, the models have been compared to the
data and with the other models on a point-by-point basis. That
is, simultaneous comparison of predictions and measurements at
all points in space where observations of significance existed.
However, because the EPA model averages concentrations over an
angular segment, only centerline concentrations could be compared
with the data and the other models.
The meteorological input to each model in terms of atmos-
pheric stability and wind conditions was kept as consistent as
possible. Flov7 and diffusion coefficients over a complete range
of atmosphexi • stability have been determined for the INTERCOMP
numerical model. Use of these particular diffusivities gives
good agreement with the Gaussian models for flat terrain cases.
These were the coefficients used for the same atmospheric
stability class as was input to the Gaussian models.
As a consequence, all model calculations actually represent
predictions based upon measured or observed meteorology. That
is, the best-fit set of coefficients has not been determined
for use. The validation of the models in this way actually
represents how they might be used in conjunction with the local
climatology at a particular site to predict concentrations for
applications such as:
(1) plant siting studies
(2) evaluation of design changes
(3) compliance with ambient air quality standards.
In this last category, there may be quite remote areas around
a particular plant in which it is impractical to place continuous
monitors. For such areas and for interpolation between monitors,
diffusion model predictions can be extremely valuable.
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2-1
2.0 AIR QUALITY MODELS TESTED
The following sections describe the models tested in somewhat
more detail. These sections will provide the basic assumptions
used in each model to cover the possibility that the above nomen-
clature for the models will not be totally descriptive to all
readers.
2.1 The Gaussian Model
The Gaussian calculational technique utilizes the various
Pasquill atmospheric stability classes. In flat terrain situa-
tions, the model is used in the classical way described in
Turners' workbook7. Where terrain is important, however, NOAA
has developed additional assumptions. For completeness, we
have summarized all the important assumptions made about this
model.
The assumptions can be listed as:
(1) A mean wind is used to represent the entire air layer
important in atmospheric diffusion.
(2) A single mean wind direction specifies the x-axis.
(3) The \>lume concentrations are assumed normally distri-
buted (Gaussian) in the cross-wind and vertical
directions.
(4) The standard deviations, ov and o™, are representative
of averaging times in the range or 10 minutes to one
hour.
(5) The source emission rate as well as wind and atmos-
pheric conditions must be constant over times signi-
ficantly greater than the travel time to a downwind
position of interest.
The above assumptions describe those necessary in the flat
terrain case. For rough, mountainous terrain additional restric-
tions were imposed by NOAA:
(6) Under neutral or unstable atmospheric conditions,
the plume centerline is assumed to flow parallel to
terrain.
(7) Under stable conditions, the plume centerline flows
horizontally until it encounters terrain at the plume
elevation.
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2-2
Some discussion of these last two points may be in order.
under neutral conditions, there is little density effect inhi-
biting vertical flow. Thus, an obstacle in the flow path will
cause substantial modification of the flow field both horizontally
and vertically. The fact that the atmosphere is of neutral
stability simply specifies that, if there is vertical flow and
it is rapid enough that little or no heat transfer takes place
to a volume of air being moved, then the density of that air
volume is the same at its new elevation as other air at that
level. That is, the adiabatic temperature change undergone
has just compensated in its effect on density for the static
pressure change.
For stable conditions, the density decreases drastically
with height. In this case as air encounters an obstacle, there
is more of a tendency to flow horizontally around the obstacle
than up and over it.
The concept expressed by assumption (7) above is that
under stable conditions vertical flow is inhibited. Carrying
this to its limit, the assumption is made that the plume must
flow horizontally on a straight line until it encounters the terrain.
The concept in item (6) is that for neutral and unstable flows there
is no retarding influence to vertical flow.
The assumption contained in item (7) cannot satisfy basic
fluid flow concepts on other than an instantaneous basis and
thus should be conservative in terms of overestimating ground-
level concentrations. Whereas item (6) could result in lower
groundlevel concentrations than actual.
2.2 The EPA Model (C4M3D)
The EPA model is a modified version of the NOAA concepts
in how it calculates terrain effects. Basically, there are two
modifications which are listed below as a continuation of the
set of Gaussian assumptions.
(8) The plume centerline does not intersect the terrain,
but after approaching within 10 m vertical distance
it remains that distance above the terrain ground
surface.
(9) Angular segment averaging of the plume concentrations
is done for short-term averages as well as for annual
averages.
As discussed previously, a stable atmosphere restricts
vertical flow. The concept of allowing the plume to remain
10 m above the terrain removes at least a portion of the con-
servatism contained in a centerline intersection assumption.
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2-3
In item (9) the averaging is performed over a 22.5 degree
angular segment. This results in concentrations which are re-
duced over the customary Gaussian model. This reduction depends
upon downwind distance and upon atmospheric stability. The
reduction in centerline concentrations is simply ay/0.157x
where ay is the cross-wind standard deviation and x is the down-
wind distance from the source. For F stability, the reduction
varies between 4 and 8 over the distance range of 100 m and
100 km. For C stability, the reduction varies between 1.25 and
2.6 over the same distance range.
The concept behind this angular segment averaging is that
for a given wind direction, the wind direction is actually dis-
tributed uniformly throughout the entire 22.5° angular segment
over a period of time of interest. For longer term averages,
annual, seasonal, or monthly, the assumption is probably valid.
The segment averaging concept VJT.S originally intended for annual
average predictions. However, because of the need to calculate
shorter term averages, the EPA model has frequently been used
for these cases as well. Certainly for shorter term averages
than 24 hour, the segment averaging is more questionable.
2.3 The INTERCOM? Model
This model is a numerical solution of the three-dimensional
material balances for the entire air stream and the pollutant
flowing with ^ lat air stream. The pollutant material balance
results from the turbulent diffusion equations which approximate
turbulent fluctuations by a Fickian-type eddy diffusion model.
The eddy diffusivity used in the model is height dependent con-
sistent both with turbulent fluctuation measurements and theory.
The wind flow over uneven topography is calculated by
numerically solving a modified form of the three-dimensional
potential flow equations. The modification allows (1) inviscid
potential flow at high elevations and (2) height-dependent
coefficients which account for surface friction (viscous effects)
in the lower boundary layer. The empirical modification causes
calculated windspeed to vary with height. This modification
over flat terrain results in velocities which vary as either
of two familiar forms, logarithmic or power law.
The numerical finite difference approach divides the region
around the plant into a number of three-dimensional cells which
can vary in size as terrain or meteorological characteristics
require. The grid cell directly above a stack and at the effec-
tive stack height is used as a volume source for pollutant. The
source volume can be set to represent the dilution occurring
during plume rise. For a true point source, the source grid
cell must be small to avoid errors due to an initial dilution
effect. The numerical procedures used in the solution of both
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2-4
the wind flow and pollutant flow are efficient requiring minimal
computer time. The steady-state solution which is a good approxi-
mation to many practical problems can be generated in a single
time step or the entire progression to steady-state can be
calculated in a series of time steps.
The modified potential flow model for wind flow calculations
represents a significant simplification of the combined momentum
and energy equations describing air flow. However, it retains
most of the important factors so necessary to a sound meteorolo-
gical and engineering analysis of pollutant dispersion in rough
terrain.
Of significance is the fact that over flat terrain the
INTERCOM? numerical model can provide good agreement with the
Gaussian models. This is true even though in the numerical
model the diffusivities (and velocities) vary only with height
unlike the Gaussian models where the standard deviations vary
with distance downwind from the source. For constant diffusion
and windspeed, the Fickian or turbulent diffusion approach gives
standard deviations which vary as
c = >/2EX/u
where a = the standard deviation
E = the eddy diffusivity
x = downwind distance
u = windspeed.
The Gaussian models indicate a varies in almost direct propor-
tion to downwind distance, x. The fact that the turbulent
diffusion model with height dependent diffusivities and velo-
cities gives the same result as the Gaussian models implies
that the additional downwind dependence of a could be due to
the assumption of uniform winds and diffusion over the thickness
of the boundary layer.
The simplification of the momentum and energy equations
used in the INTERCOM? model cause some limitations in its use.
These can be enumerated as
(1) the modified potential flow model prevents the
formation of recirculating flow in the lee of an
obstacle,
(2) the elimination of the energy balance prevents cal-
culating the driving force for natural convective
flows. However, this type of flow could be imposed
by the definition of boundary conditions.
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Illustrations are presented in this study which show that
the modified potential flow concept calculates a good approxi-
mation to the velocity fields on the upwind side of obstacles.
If the problem of interest is the recirculating flow, a more
complete solution of the Navier-Stokes momentum equations is
required. Such a model is described in a later section.
Natural convective flows of interest include land-sea
breeze and stable valley drainage flows. Situations of this
type can be studied with the model, but the flow patterns would
have to be created by source-sink combinations in the wind flow
grid instead of the natural density driving forces. The present
model does not contain this capability although air flow source-
sink can be included in a straightforward manner.
2. 4 Calculation of 3^ and 24_ H£ur_ Averages from Model Predictions
Each of the air quality models discussed above predict short-
term concentrations generally accepted as representing 1/4 to
1 hour time averages. Values of 3 and 24 hour average concentra-
tions must be developed for comparison with standards.
If the model prediction is accepted as a 1 hour average,
longer term averages might be calculated in the following way:
(1) use rueasured meteorology for each hour of an entire
year to calculate dispersion parameters;
(2) calculate the 1 hour average from a dispersion model;
and
(3) select the second highest successive 24 hour period
calculation as the predicted 24 hour average.
Recognizing that the model prediction contains uncertainty, the
predicted 1 hour average should be the probable value as opposed
to an extreme value. The three hour average could be developed
similarly.
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3-1
3.0 VALIDATION AND COMPARISON OF AIR QUALITY MODELS
3.1 General Comparisons
Extensive comparisons of the INTERCOM? model with Gaussian
models have been made. As mentioned previously, it is essential
that the numerical model be in rough agreement with the Gaussian
models for flat terrain. Particularly important is the need to
have calculated concentrations decrease roughly as the square of
downwind distance. Such a decrease with distance is in marked
contrast to what a Fickian-type turbulent diffusion model with
constant wind velocity and eddy diffusivity would give. In
the latter case, concentrations decrease in almost direct pro-
portion to the downwind distance. Thus, we were extremely in-
terested to see what height-dependent wind velocity and eddy
diffusivities would do to calcunated concentrations.
Using well-accepted power law forms for this variation of
velocity and diffusivity with height gave good agreement between
the Fickian-type turbulent diffusion results and the various
Gaussian model results. This is illustrated in Figure 1. Note
that the power law variation of velocity and diffusivity has
indeed caused a much more rapid drop-off in calculated concen-
trations than would constant value parameters. In fact, by
varying these power law forms slightly, the entire range of
atmospheric stability classes can be simulated in terms of
their effect on downwind concentration falloff.
The results obtained above are somewhat surprising when
one considers that in the turbulent diffusion model the diffu-
sivities are not functions of downwind distance at all as they
are in the Gaussian model. As mentioned in a previous section,
the deviation of the calculated concentrations for a constant
diffusivity turbulent model are still dependent upon downwind
distance, but upon the square root power as opposed to the more
direct proportion as in the Gaussian model. The above results
imply that the use of downwind distance dependence of diffusiv-
ities in the Gaussian models may indeed be compensating for the
fact that these diffusivities as well as windspeed should be
varying with height in the boundary layer.
Velocity and diffusivity height dependent forms have been
determined with the INTERCOM? numerical model which give good
agreement with the Pasquill-Gifford stability classifications
used in a Gaussian model. These values are as shown in Table I.
-------
3-2
FIGURE 1
COMPARISON NUMERICAL MODEL
WITH GAUSSIAN PLUME MODELS
1.01
NUMERICAL SOLUTIONS
E-Z6/7 •
E~Z' A
E ~ Z8" 0
I M TTT
CONSTANT VELOCITY
- AND EDDY
DIFFUSION
/
0.10
0.01
0.001
PASQUILL-G1FFORO
STABILITY
CLASS C •
CLASS D •
1 --- rr
SUTTON
; n = 0.2
,n = O.S
\
1.0
J « 5 • 7 • )OOJ)
OIMENSIONLESS DOWNWIND DISTANCE,
-------
3-3
TABLE I - POWER LAW FORMS WHICH
APPROXIMATE PASQUILL-GIFFORD STABILITY CLASSES
A B C D E
Velocity Power 0.14 0.14 0.14 0.2 0.3 0.4
Diffusivity Power 1.76 1.38 1.14 1.0 1.0 0.67
Ere£/ ft2/s 2740 1140 550 440 360 310
Ez/Ey 10 2 0.7 0.2 0.05 0.008
The value listed as Eref is for the horizontal cross-wind diffu-
sivity at a reference elevation of 30 feet. As can be noted
from Table I, there is roughly a factor of ten difference in
the horizontal diffusivity ovei the range of atmospheric stabil-
ities. Also apparent is the range in the ratio of vertical to
horizontal diffusivities, Ez/Ey, necessary for the various
stability classes. The ratio of Ez/Ey should approximate the
square of the ratio of az/0y and for a downwind distance of
10 km or so this appears to be the case. In addition, for the
analogy to be complete, the diffusivity values should be a func-
tion of the mean windspeed. The values listed above for E f
are for a windspeed of 1 MPH and should be increased or decreased
in direct pi o;cortion to the mean windspeed at the reference
height.
3.2 Comparison of Solution Techniques
Two solution techniques have been generally used for solving
the turbulent diffusion equations. Basically, these techniques
have evolved as a result of the primary interest being in two
different classes of problems. In one class, advection or
windspeed is the controlling influence. In such cases, the
partial differential equations describing turbulent diffusion
become controlled by first order space derivatives and are
fundamentally hyperbolic in nature. For such applications,
techniques involving (1) point tracking, (2) particle-in-a-
cell, or (3) method of characteristics are advantageous. The
model developed by Sklarew8 is one of this type.
In the second class of problems, turbulent diffusion is
of comparable importance to advection in spreading a trace
quantity within the air flow. In such cases, the equations
are parabolic in form and finite difference solution techniques
are more advantageous. The INTERCOM? model1* is of the latter
type.
-------
3-4
One of the difficulties in using finite difference approaches
on advective controlled problems is that truncation error can
result in an artificial diffusion term9. Higher order differ-
ence techniques can be used to reduce this effect, but at the
expense of computing time and often stability of the difference
technique10. There is a question, then, of when the standard
finite difference techniques are adequate.
The aspect which allows the finite difference equations
to be accurate for a broad range of turbulent diffusion to
advection ratios is the lack of importance of the diffusivity
in the primary wind direction. In Gaussian models, for example,
diffusion in the downwind direction is normally neglected
(unless it is an instantaneous release) because calculated
answers are insensitive to the value of the downwind diffusi-
vity. This fact leads one to suspect that a finite difference
formulation would also be accurate. The effect of truncation
error will be in the primary wind flow direction, but in that
direction the value of total diffusivity is unimportant. Instead,
it is the cross-wind and vertical diffusivities which are impor-
tant in calculation of the concentration distribution. The
proof of this contention is developed in the following paragraphs.
As a verification that the numerical model is not substan-
tially influenced by truncation error, the model results for
a constant diffusivity and velocity have been compared to the
analytical solution for this case. This analytical solution
solves the equation of one-dimensional forced convection (ad-
vection) and two-dimensional diffusion (cross-wind and vertical).
This analytical solution is well-known. The effective stack
height was taken as 1000 feet. The cross-wind diffusivity was
2000 ft2/sec.; the vertical diffusivity was 500 ft2/sec. The
windspeed was 4 ft/sec. Block sizes in the downwind direction
varied from 200 feet near the source to 6400 feet at the downwind
extent of the grid. The results for concentrations along the
plume centerline are shown in Figure 2. Two numerical model
results are shown in Figure 2. The finite difference model is
the one which represents the standard INTERCOM? air quality
model. The results labeled point movement method are from a
model similar to Sklarew's8 which solves turbulent diffusion
by a technique well suited to a high advection windspeed. As
Figure 2 indicates, the point movement results are in slightly
better agreement with the analytical solution plume centerline
concentrations. The calculated results are not sufficiently
different to warrant the increased computing costs, however.
Figure 3 is a similar plot of the groundlevel concentra-
tions. The effect of space truncation error in the finite
difference approach can be seen. However, the maximum concen-
tration has been decreased only about 5% by numerical diffusion.
In contrast, the point movement method was actually affected
more than the finite difference method. This is probably
-------
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3-7
because the two ordinary differential equations solved by the point
movement approach (advection then diffusion) are uncoupled. That
is, the material is first advected then diffused. A part of the
difference in Figure 3 is also due to the numerical calculation
using a finite volume source as opposed to the analytical solu-
tion point source. It is apparent in Figure 3 that the finite
difference solution can be of acceptable accuracy for air quality
analyses.
It was mentioned earlier that power law variations of
windspeed and diffusivity result in agreement of the turbulent
diffusion approach with the Gaussian models. This is true
with one important exception. On the upwind side of -'.he maxi-
mum groundlevel concentration, the turbulent diffusion approach
does give different results from the Gaussian models This is
illustrated in Figure 4. Note that on the upstream side of
the maximum, the groundlevel coi centrations are significantly
higher with the INTERCOM? model than they are vlth the Gaussian.
To a large extent, this difference is due to the power law wind
profile which gives lower windspeeds near the ground surface.
The calculated concentrations in this region upwind from the
maximum should better approximate the effect of surface roughness.
The differences in Figure 4 are greatly exaggerated since it
is plotted on log-log paper. If plotted on linear paper, the
differences are not so apparent.
The resultant cross-wind concentration distributions are
also different as a result of the volume source in the y-direction.
Farther from the source, these differences become negligible as
shown in Figure 5. The maximum deviation is for the one shown—
namely the narrowest plume of class F stability.
There is strong evidence to indicate that measured results
near the source are higher than Gaussian point source predictions.
Plume rise or any surface roughness near the source result in
much more rapid dilution than predicted by a stable Pasquill
stability class. A recent summary by Bowne11 illustrates
modifications in the general shape of the dispersion coefficients
to account for such effects. Such modifications are generally
made to affect groundlevel concentrations for distances up to
one kilometer. Such a modification which increased concentra-
tions upwind of the one kilometer point would be in rough
agreement with the results of Figure 4.
-------
3-8
10
-7
10
-8
FIGURE 4
COMPARISON OF PASQUILL
STABILITY CATEGORY E TO
INTERCOM? MATCH OF THAT
CATEGORY
1
\
.2
III III
.5 1 2 5 10 20
1
50
1
100
DOWNWIND DISTANCE, km
PASQUILL E
INTERCOM? MATCH
-------
3-9
FIGURE 5
COMPARISON OF CROSSWIND
VALUES IN INTERCOM? MATCH
OF PASQUILL CLASS F
60Km DOWNWIND
32.5 Km DOWNWIND
14.5 Km DOWNWIND
MAXIMUM GLC
PASQUILL-F
INTERCOMP
I 2
DISTANCE CROSSWIND KILOMETERS
-------
3-10
3.3 Comparison for Huntington Canyon Tracer Data
3.3.1 Data Collected
The data collected in Huntington Canyon by the
Air Resources Laboratory (ARL) of the National Oceanic
and Atmospheric Administration (NOAA) were intended to
provide measurements of plume dispersion in rough, canyon
type terrain for comparison with flat terrain results6.
The survey was particularly oriented toward evaluating
the plume centerline intersection assumption used by ARL
in the meteorological report to the Department of Interior
which was a part of the Southwest Energy Study5. A second
objective was an evaluation of the dilution characteristics
within a canyon.
The basic approach was to release SFg tracer and
use mobile (helicopter) sampling for centerline dilution
concentrations and fixed (canyon wall and floor) sampling
for the impaction validation. No attempt was made to
gather extensive meteorological data in the canyon. Wind
and temperature data sufficient to describe diffusion
stability classes were the meteorological data collected.
The tracer releases were made at two points. Elevated
releases during lapse to neutral stability conditions were
made from the top of the stack. Wind flows during such
conditions were generally up-canyon. The second point of
tracer release was from the canyon floor and wall at a
distance of about 10 km up the canyon from the power plant
stack. These releases were during strong temperature
inversions and were always down-canyon flows.
The approximate tracer plume position was tracked
by a cloud of white smoke emitted from a smoke generator.
This enabled photographic coverage of the plume as well
as plume centerline positioning for the helicopter sampling.
The helicopter samples were one-minute samples
collected by an air pump which drew samples through a hose
hanging 28 m below the aircraft. The ground samples were
cumulative over the duration of each test run and were
processed to approximate a one-hour average concentration.
3.3.2 Geographical Setting
Figure 6 is an illustration of the terrain in
Huntington Canyon looking north up-canyon from behind the
power plant. The various side canyons are shown and
indicated by names including on the west side, Maple Gulch,
Deer Creek, Meetinghouse, North Fork, Rilda, Mill Fork,
and Little Bear. On the east side of Huntington Canyon,
the main side canyons are Fish- Creek, Bear Creek, and
-------
3-11
W
K
D
CD
H
DC
O
O
CD
O
OL.
-------
3-12
Trail. Wild Horse Ridge is also a prominent topographical
feature.
The terrain illustrated in Figure 6 was prepared
as a Calcomp plot from the digitized terrain file. This
file can be used as input to the INTERCOM? air quality
model and a plot of the type shown is normally made to
verify that the digitized terrain is an adequate repre-
sentation of the actual topography. There is a 2:1 ver-
tical to horizontal exaggeration of the distance scales
in Figure 6.
Also shown by solid circles in Figure 6 are the
monitor locations for measuring SFg concentrations during
the stack top releases. Moving up-canyon, the first set
of four monitors just east of the plant is called Fish
Ridge. Continuing up the east side of the canyon, the
next set of three were known as White Ridge. The next
two monitors indicated by open circles are actually in
the draw behind White Ridge and were called the Wild Horse
Draw monitors. The four monitors located on the south
side of Bear Creek were called Wild Horse. The four on
the north side were known as Bear Creek.
On the west side of Huntington Canyon, the monitor
located near the flat part of the canyon was called the
Meetinghouse - Dear Creek Station. The two monitors located
higher up on the ridge between Meetinghouse and Deer Creek
Canyons were known as the Blizzard stations. Further
up the canyon between the North Fork and Rilda canyons,
two monitor lines were located. On the vertical east
face two monitors were located and called Red Face. The
four located down the northerly slope were called Wet Man.
Figure 7 is a similar plot, but looking in a southerly
direction down Huntington Canyon. Again the side canyons
and ridges are shown. Two release points were used in the
down-canyon orientation. These release points are indicated
by the solid triangles — one on the canyon floor and the
other about 160 meters up the canyon wall. Two monitor
locations were on the canyon floor downwind from the re-
lease point. These monitors were called 0.4 and 0.8
(apparently because they were about 0.4 and 0.8 miles
downwind from the source). On the west side of the canyon
along a rather vertical wall, four monitors termed the
Trail station were located. On the opposite side along
the north rim of Mill Fork Canyon there were three monitors
called Mill Fork. Two sets of monitor stations farther
down the canyon were used. These were the Wet Man and
the Bear Creek stations described earlier.
-------
3-13
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-------
3-14
Both the up-canyon and down-canyon orientations
emphasize the roughness of the terrain. Though the monitor
coverage in both the vertical and crosswind directions
are by no means complete, they do represent excellent data
to test the centerline impaction concept. The plume dis-
persion in terrain such as Huntington Canyon presented a
severe test of the calculational models.
3.3.3 Comparisons for a_ Stable Down-Valley Flow
Five down-valley tests were performed. Four were
canyon floor releases and the other was an elevated canyon
wall release. The various tests were classified as to
stability by NOAA personnel. Surface windspeed were avail-
able at several points as well as the apparent oil fog
velocities during the tracer releases. Measured tempera-
ture gradients and cloud cover were also available.
A summary of the tracer release rates, the effective
windspeeds (from oil fog measurements), and the NOAA stability
classifications are given in Table II. The first six tests
were up~valley flows from stack top releases. The seventh
test was a down-valley flow from a canyon wall release. The
next four tests were down-valley flows from canyon floor
releases. Also listed in Table II are the wind directions
representative of each test. In general the wind direction
included in Table II is a composite of the several measuring
pcdnts with most weight given to the stack top anemometer.
Before showing comparisons between calculated and measured
values, a few comments are in order.
TABLE II - SUMMARY OF TEST CONDITIONS
SF5
1
2
3
4
c
6
7
8
9
10
11
5.99
5.19
5.78
3.54
5.19
6.60
7.48
6.92
7.48
4.65
6.35
HUNTINGTON CANYON
Release
Time
Min.
52
44
49
90
44
56
45
48
60
33
35
gm/sec
1.92
1.97
1.97
0.65
1.97
1.97
2.77
2.40
2.08
2.35
3.02
Effective
Wind
u,m/sec Direction
4.3
4.5
2.3
10
5.3
3.8
2.9
1.8
7.9
3.2
3.0
140°
120°
130°
140°
150°
110°
350°
240°
340°
300°
310°
Stability
Class
B
D
D
D
D
D
F
F
F
F
F*
*NOAA personnel considered much, if not all, of the stable flows to be
more stable than F.
-------
3-15
Specific wind directions at the release point in
the canyon were not included in the NOAA report. Anemometer
data at the plant site indicated winds were from the NNW
quadrant during the down-valley flow tests. For INTERCOM?
model runs, there was little sensitivity to input wind
direction. The calculated winds were for all practical
purposes forced by the terrain to follow the canyon
orientation.
In the case of the Gaussian (NOAA) model, wind
direction is extremely important. Several assumptions
could be made regarding the location of the plur.te center-
line. Some of them can be summarized as follovs:
(1) The plume could be assumed to flow horizontally
at the release elevation and down the centerline
of the canyon.
(2) The plume centerline could be assumed to flow
along the canyon floor and down the centerline
of the canyon for the canyon bottom releases.
(3) The plume could be assumed to flow horizontally
and vertically without deviating until it
encounters the canyon walls.
The first and last assumptions listed above probably repre-
sent how the Gaussian model would have been used if this
were totally a prediction without the benefit of experimental
observations. These results would not even be close to the
measured concentrations. From inspection of the tracer
results, assumption (2) appears to be most representative
and this is the one we have used. One additional restric-
tion was used in connection with the Gaussian models. No
accounting was made for canyon sidewall reflection. This
would cause calculated concentrations to be lower than they
should be. As the results will indicate, however, the
Gaussian model calculations were generally high and thus
an unfavorable bias was not introduced.
The measured and calculated results for down-canyon
flow Test 10 are shown in Table III. The results shown in
Table III are all ground surface values. NOAA also attempted
to make plume centerline measurements with a helicopter;
however, for the canyon floor releases (such as Test 10)
the aerial samples gave lower readings than the measured
groundlevel results. As a consequence, these values are
not summarized in Table III.
-------
3-16
TABLE III - COMPARISON MEASURED AND CALCULATED GROUNDLEVEL VALUES
TEST NO. 10 - DOWN-CANYON - F STABILITY
Location
0.6 km
1.2 km
Trail(1)
(2)
(3)
(4)
Mill Fork(l)
(2)
(3)
Rilda(l)
(2)
(3)
(4)
Bear Creek(1)
(2)
(3)
(4)
Wet Man(l)
(2)
(3)
(4)
Elevation
Ft.
7170
7120
7120
7250
7870
8200
7010
7250
7700
6940
7240
7550
7950
6790
6910
7090
7170
7170
7330
7400
7650
Measured
yg/m
25
35
9.5
19.0
3.7
3.4
6.1
2.1
3.4
2.8
Calculated/ yg/m'
INTERCOM? EPA GAUSSIAN
186
80
15
14
0.5
0.0
5.0
2.5
0.0
5.5
2.0
0.2
0.0
3.5
2.5
1.5
0.2
1.5
0.5
0.0
0.0
210
65
25.4
13.6
8.5
6.2
6.2
40
(1200)
( 370)
140)
0
50
0( 80)
0
50
0
0
30
9(
0.3
30
3
0
0
50)
30)
( 30)
In Table III, only centerline concentrations have been
tabulated for the EPA model. The corresponding NOAA centerline
values are shown in parenthesis under the label Gaussian. There
is no reason to evaluate crosswind values for the EPA model
since the 22.5° angular segment averaging essentially fills the
canyon to the 8000 ft. elevation point. As a consequence, the
EPA model would predict uniform concentrations throughout the
canyon width comparable to the calculated values listed.
The INTERCOM? model since it is a finite difference type
calculation has predicted concentrations in each grid block
and thus can be compared more easily on a point-by-point basis .
wind flow model has predicted correctly that peak concentration
levels do follow the canyon floor (an assumption that was used
in the Gaussian models). The values corresponding to individual
measured points are tabulated in Table III and a contour plot
is shown in Figure 8. The tabulations in Table III are actually
read from the contour plot of Figure 8, with the exception of
those values greater than 10 yg/m .
The
-------
Figurt b -
DOWN-CANYON TEST NO. 10
LEGEND
HI Individual Tracer Monitors
35 Measured Tracer Concentrations, /ig/m3
A Ground and Elevated Release Points
-------
3-18
The INTERCOM? model results were calculated using
the parameters of Table I for Pasquill F stability. The
calculated average windspeed in the grid block nearest the
canyon floor was matched to the observed effective smoke
cloud speed. The relative magnitude block sizes used in
both the downwind and cross-wind directions can be seen from
Figure 8. The asterisks surrounding the plot correspond to
the position of the grid block centers. As is evident, the
grid definition of the canyon floor was much finer in detail
than that describing the higher elevations. The plotted con-
centration contours have been normalized by dividing by
10 yg/m3. Thus, the band of 1's represent concentrations
between 0.05 and 0.1 of the 10 yg/m3 or 0.5 to 1.0 yg/m3,
the 2's band are 1.5 to 2.0 yg/m3 and proceeding up to the
9's band which represents any concentration greater than
8.5 yg/m3. The blank contours separating the number contours
represent the intermediate concentration levels. For example,
the blanks between the 1's and 2's represent concentrations
of 1.0 to 1.5 yg/m3.
The position of the tracer monitors have been located
as nearly as possible to their actual position and vertical
height. The plotted concentrations are calculated ground-
level concentrations regardless of the particular grid block
in which groundlevel was located. That is, a search of the
complete three-dimensional grid block concentrations has
been made to determine the concentration in those grid
blocks which correspond to the ground surface—these are
the values contoured in Figure 8.
As evident from Figure 8, the tracer plume follows
the canyon alternatingly expanding and shrinking in width
as it is effected by the side canyons. In Table III,
measured concentrations have been tabulated only for those
monitors which were listed. Monitors for which no measure-
ment was listed were either below some minimum threshold
for accurate analysis or were not analyzed. These monitor
points are denoted by a dash in Table III. The calcula-
tions do agree reasonably with the concept that concentra-
tion levels at these unlisted monitor points were low. As
examples, measurements at the entire Wet Man sampling network
were not listed. The calculations tend to support this
although concentrations on the order of 0.5 to 1.5 yg/m3
appear at the lower two elevation monitors. Similarly,
the calculation indicates a concentration slightly less
than 0.5 yg/m3 at the highest Bear station which also was
unlisted. Similar results were obtained at other stations
with the highest elevation monitors being located above any
significant calculated concentration levels.
As a summary, we consider the comparison between
INTERCOM? calculated concentrations and the measurements
of Test No. 10 to be quite good. Not all of the other
-------
3-19
comparisons were that good as will be noted later.
Gaussian type models, both EPA and NOAA, gave calculated
concentrations significantly higher than observed for Test
10. Also the vertical and horizontal distribution in cal-
culated concentrations from the INTERCOM? model is much
better than that predicted by the Gaussian (NOAA) model.
3.3.4 Comparison for a. Neutral Up-Valley Flow
Similar calculations have been made for the neutral
up-valley stack release tests. Test 5 was selected for a
detailed comparison since we had the actual tabulated data
for this test. The average wind direction at stack top dur-
ing this test was 150° with a measured speed of 6.3 m/sec,
The observed effective smoke cloud windspeed from Table II
was 5.3 m/sec. and the measured wind at about 10 m was 2.6
m/sec. The calculated windspeed in the INTERCOM? model was
about 2.6 m/sec. at the 10 m elevation, but with D stability
conditions, the calculated windspeed at stack top was slightly
less than 5 m/sec.
The INTERCOM? calculated concentration contours are
shown in Figure 9. The wind direction used in the calcula-
tion was 150° (true). Again the grid block centers are
shown by the asterisks. Note the drastic effect of terrain
on the concentration contours. The predominent flow
calculated is directly up the main part of Huntington
Canyon with apparently lesser flows moving up the Meetinghouse
and Bear Creek canyons. Calculated concentrations are in
quite good agreement with the measured values. The calcula-
tions indicate the plume is interacting (but not centerline
intersection) substantially at the ridge on which the White
Ridge monitors are located. As will be seen later, however,
the calculated concentrations on the ridge are about one-
half the centerline values at this downwind distance.
Tabulated comparisons between the models are illustra-
ted in Table IV. The EPA and Gaussian results are calculated
groundlevel concentrations for a plume which remains 183 m
(600 ft.) above the ground surface (consistent with the NOAA
model assumption for neutral stability). The Gaussian
results have been calculated as this model would have been
used in a predictive mode. That is, the measured stack
top wind direction of 150° and the effective windspeed of
5.3 m/sec. were used. Reemphasizing the point made earlier,
the plume was assumed to remain 183 m (the release height)
above any receptor. That is, there is no reduction in cal-
culated concentrations for the relative vertical positions
of the monitors only a cross-wind reduction. Also shown in
Table IV for the Gaussian model are the groundlevel center-
line values in parentheses. The centerline values for the
Gaussian model were included to provide an indication of
the maximum calculated concentration levels for comparison
with the measurements.
-------
!~20
Other wind flow assumptions could have been used
for the Gaussian model. The similar assumption as that
used in the down-valley stable cases (horizontal flow
along the minimum elevation canyon centerline) gives
somewhat better agreement with the measurements. However,
as the centerline values of Table IV show, the peak pre-
dicted concentrations of the Gaussian models are located
too far .from the stack.
The INTERCOM? model, on the other hand, predicts
a maximum at about 2 km downwind consistent with the
observations. The reason the INTERCOM? calculated maximum
is closer to the source occurs because of the terrain rise
in the downwind direction.
No attempt has been made to calculate the cross-
wind decrease in concentrations for a point-by-point compari-
son of the EPA model with the measurements. This model
because of the angular sector averaging still gives relatively
uniform predictions throughout the width of the canyon.
TABLE IV - COMPARISON MEASURED AND CALCULATED GROUNDLEVEL VALUES
Location
Deer Cr-Mtnghouse
White Ridged)
(2)
(3)
Wild Draw(l)
(2)
Wild Horsed)
(2)
(3)
(4)
Bear Creek(1)
(2)
(3)
(4)
Red Faced)
(2)
Wet Man(l)
(2)
(3)
(4)
TEST NO. 5 - UP-CANYON
Elevation
Ft.
6650
6740
6870
7080
6750
6960
6650
6740
6900
7360
6790
6910
7090
7170
6950
7380
7170
7330
7400
7650
Measured
yg/m3
0.2
1.2
1.0
1.6
0.8
1.0
1.3
1.2
1.0
0.6
0.7
0.6
0.4
0,
0
0,
0
3
4
1
,1
Calculated, yg/m'
INTERCOM? EPA GAUSSIAN
0.5
1.0
1.0
0.5
1.2
1.5
1.0
1.2
1.2
0
0
0
0
0
1,
1.
1.
1,
1,
0,
0,
0.2
0.7
0.6
0.5
0.1
0.01
0.03
0.07
0.08
0.17
0.17
0.18
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
.0(0.
.01
.03
.04
.09
.11
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
(0
(0
(0
(0
(0
(0
02)
.04)
.11)
.15)
.33)
.33)
.37)
-------
3-21
FIGURE 9
UP-CANYON TEST NO. 5
150° S. WIND
LEGEND
• Stack Release
•D Individual Tracer Monitors
1.2 Measured Tracer Concentrations,
-------
3-22
TABLE V - COMPARISON MEASURED AND CALCULATED CENTERLINE VALUES
TEST NO. 5_ - UP-CAN YON
Measured Calculated, yg/m
Location yg/m3 INTERCOMP EPA GAUSSIAN
H-l (0.8 km) 32 10 38
H-2 (1.7 km) 5.7 2.5 13
H-3 (3.9 km) 1.4 1.0 4
H-5 (1.3 km) 3.2 3.7 15
H-6 (1.8 km) 7.6 2.4 12
H-7 (2.8 km) 1.1 1.3 6
A comparison of helicopter measurements and cal-
culated centerline concentrations for Test 5 is presented
in Table V. For the range of distances included in
Table V, the concentrations for Gaussian centerline values are
for all practical purposes one-half those for a ground
release. Beyond 10 km, ground reflection begins to affect
the centerline values and the reduction over that of a
ground release is less than one-half.
Figure 10 presents the sensitivity of the INTERCOMP
results to input wind direction. In this calculation, the
specified wind direction was 135P which is more in line
with the canyon axis. For this case the calculated plume
is more narrow and results in slightly lower concentrations
at the monitors. Calculated plume centerline values were,
however, higher. A wind direction of 135° does not give
as good a match as the results of Figure 9 for a 150° wind
direction.
A summary plot in the usual Gaussian form of xu/Q
is shown in Figure 11 for both Tests 5 and 10. In Test 5,
Gaussian results are shown for the groundlevel centerline
concentrations. The upper dashed curve for Test 5 are the
Gaussian results for a ground release. As mentioned pre-
viously, a reduction by a factor of two in this curve at
a downwind distance of 10 km or less would approximate
the plume centerline predictions. Note that this represents
a conservative upper envelope for the aerial samples. The
INTERCOMP plume centerline predictions are shown as the
solid curve extending diagonally toward the upper left-hand
corner. These results appear to represent more of an
average value of the helicopter results. This is undoubtedly
a reflection of the extremely short-term (one minute) samples
whereas the diffusivities used in the INTERCOMP model more
nearly represent 15-minute to one-hour time averages.
-------
3-23
FIGURE 10
UP-CANYONTESTN0.5
135° S. WIND
lI.UU*Uii»H<.«l
niuunu u Ji
iinunnnni
m
it
LEGEND
• Stack Release
HI Individual Tracer Monitors
1.2 Measured Tracer Concentrations,
-------
3-24
FIGURE 11
COMPARISON OF MEASUREMENTS WITH
CALCULATIONS
10
-4
10
V)
a:
LU
I-
UJ
-5
Kr6
10
-7
TEST NO. 5
CLASS D STACK RELEASE
\
\
\
\
0 \
TEST NO. 10
CLASS F CANYON FLOOR RELEASE
\
\
\
10
-4
\
\
CO
OL
10
-5
/x :
x
'•'
I03 I04
DISTANCE.METERS
10
-6
I03 I04
DISTANCE.METERS
LEGEND
O AERIAL SAMPLES
X GROUND SAMPLES
GAUSSIAN MODEL
EPA MODEL
INTERCOM? MODEL
-------
3-25
The Test 10 Gaussian results represent the plume
centerline for a ground release. The INTERCOM? model
results plotted are the peak concentration predicted at
any of the monitoring sites downwind. The break in the
curve occurs primarily because the plume is narrow at the
Mill Fork monitor site and does not affect significantly
the monitor positions. The plume has widened out by the
time it reaches the Rilda site and now envelops the lower
elevation monitor points.
3.3.5 Other Test Comparisons
Figure 12 illustrates a plot of xu/Q valaes for
Tests 1 and 7. Test 1 v/as the only up-valley '..low, stack
top release which had other than neutral class D stability.
Test 7 was the only down-valley flow which was an elevated
release along the canyon wall instead of from the canyon
floor. During Test 7, the plume moved upward along the
shaded wall due to natural convection. Thus, none of
the models performed well in simulating this behavior.
We have chosen to show the Gaussian curves which
were presented in the NOAA Huntington Canyon report.
In addition, since both Test 1 and Test 7 were elevated
releases, we have added the calculated Gaussian curves
for an elevated release. Calculations for both the EPA
and NOAA models have been included on an elevated release
for Test 1. Note that for Test 1 with class B stability,
there is only a small difference between the EPA and
NOAA models.
The comparison between each of the models for Test 1
is reasonably close. Again the INTERCOM? calculations
have a maximum nearer the stack than the Gaussian models
and then it decreases more abruptly with downwind distance.
This is undoubtedly the effect of rising terrain in that
directions.
Calculated ground concentrations for Test 7 are
interesting from the standpoint that the Gaussian models
predict no increase of groundlevel values with distance
over the range in which the monitors were located. This
is because the release was at a 163 m height. The INTERCOMP
model, however, does predict significant concentrations at
ground surface. The tendency is to predict too low concen-
trations near the source and too high concentrations farther
from the source. The INTERCOMP model also underestimated
centerline concentrations near the release. This was pro-
bably due to the finite volume source represented by a grid
block instead of the more nearly point release of the tracer.
The high predictions farther from the release were undoubtedly
due to the model neglecting the natural convective flow along
the shaded wall.
-------
3-26
FIGURE 12
COMPARISON OF MEASUREMENTS
WITH CALCULATIONS
TEST NO. 1
CLASS B STACK RELEASE
10'
10
,-5
'en
CL
UJ
UJ
10
-6
10
I03 I04
DISTANCE, METERS
10
UJ
,-5
10
,-6
I \ . IO'7
LEGEND
TEST NO. 7
WA
s
\
|Q.4 CLASS F CANYON WALL RELEASE
\
\
\
X X /
X /
I03 I04
DISTANCE, METERS
o AERIAL SAMPLES
x GROUND SAMPLES
GAUSSIAN MODEL
EPA MODEL
INTERCOM? MODEL
-------
3-27
Tabulated values of the point-by-point INTERCOM?
calculations as well as the centerline Gaussian and EPA
model results are compared with the measurements for the
remaining tests in Appendix B. These calculations utilized
the tabulated stability class windspeed, and wind direction
of Table II, with the exception that the down-canyon flows
always used a wind oriented along the canyon (approximately
320°). In the down-valley comparisons, wind direction was
not important. For the up-valley flows, wind direction has
a significant effect on calculated concentrations. Two
of the up-valley flow tests have not been included in
Appendix B. These tests are 2 and 6. The wind direction
for these two cases was 120° or even more easterly and
measured groundlevel concentrations were quite sparse.
Test 2, for example, contained only two groundlevel mea-
surements. As a consequence, we have not made calculations
for these two tests with the easterly wind direction.
Statistical comparisons of the measured and calculated
results have been made. Of the many statistical compari-
sons which could have been used, we have chosen a statistic
representing the ratio of calculated to observed concentra-
tions. Such a statistic has also been used in the Huntington
Canyon report6 where Table IV summarizes a comparison of the
Gaussian results with centerline measured concentrations.
The ratio statistic for the INTERCOM? model compari-
son with data was computed as follows:
(1) the ratio of calculated to observed concen-
trations for each individual monitor point
and each test was computed;
(2) the logarithmic mean value (the arithmetic
mean of the logarithm of the above ratio) was
calculated; and
(3) the antilogarithm of the logarithmic mean value
became the mean value ratio statistic.
This ratio statistic can be compared directly to the
Table IV values from the Huntington report. The above
procedure produces an almost identical result with their
procedure which was to plot the best logarithmic mean
line of the data which had the same slope with downwind
distance as did the Gaussian calculation. The comparisons
in the Huntington report were of helicopter (centerline)
samples with calculated ground release centerline values.
Our ratio statistic was somewhat more meaningful because
all ground concentration points were included. Table VI
illustrates the ratio comparison along with a simple arith-
metic mean value comparison between calculated and measured
xralues.
-------
3-28
TABLE VI - STATISTICAL COMPARISONS
Mean Values/
Test No.
1
3
4
5
7
8
9
10
11
MEASURED CALCULATED
0.74
2.12
0.21
0.71
0.45
9.8
9.2
10.2
84.6
0.64
2.00
0.16
0.91
0.73
42.7
15.2
28.9
37.4
Mean Value, CALC/OBS
INTERCOMP GAUSSIAN
0.43
1.10
0.59
1,
2,
1,
62
30
83
0.42
1.27
0.41
1.4
3.7
5.6
14.7
14.8
18.9
11.8
The last column labeled Gaussian of Table VI comes from
the Huntington report6. The value listed for Test 7 has
been modified from that contained in the report. Their
tabulated value was 29.3. Their value was divided by two
since the elevated centerline predictions should have been
decreased by a factor of two to account for the lack of
ground reflection. In the report they had compared center-
line ground release concentrations with the helicopter
measurements, but out to distances of nearly 10 km the
ground reflection is not important.
The results of Table VI clearly show the improvement
of the INTERCOMP predictions over those of the Gaussian
(NOAA) model. The mean value, calculated to observed,
ratio from the INTERCOMP model makes results for terrain
as rough for flat terrain—roughly within a factor of two.
The EPA model because of the angular segment averag-
ing in general gave improved results over the NOAA model
for the down-canyon flows. However, the Gaussian model
was a better approximation for the neutral to unstable
up-valley tests. Both of the Gaussian type models are
difficult to use in terrain as complex as Huntington
Canyon if the multiple reflections from canyon walls are
included. The INTERCOMP model automatically accounts
for these factors.
3.3.6 Summary
The results from the Huntington tests clearly show
the INTERCOMP model gave better predicted results than the
Gaussian models in terms of comparison with averages of
point-by-point observed data. The data corresponded to
time averages ranging from one-half to 1 hour.
-------
3-29
Our comparisons of the models have been aimed,
in general, at calculations as the models would have been
used in a predictive study. That is, no attempt was made
to adjust diffusion coefficients to give a best match
and for the Gaussian models no attempt was made to move
the plume centerline location so that it best matches
the measured concentrations. As pointed out previously,
the INTERCOM? predictive results for Huntington Canyon
provide accuracy comparable to Gaussian model results
for flat terrain. That is, the addition of a simplified
flow model to a calculation based upon Pasquill stability
classes has given results for Huntington Canyon comparable
to the Gaussian model accuracy with flat terrain. Whereas
the Gaussian model accuracy was significantly decreased
by the presence of elevated terrain.
The INTERCOMP model with the simplified flow model
did provide adequate predictions at a number of different
space points. That is, the comparison of calculated and
observed results was simultaneously good at many space
points both in the cross-wind, downwind, and vertical
directions instead of simply good for an isolated space
point.
3.4 Model Comparisons at El Paso
3.4.1 General Site and Data Description
El Paso/ Texas, is the site of a large smelting
complex for American Smelting and Refining Company (ASARCO).
The plant area emits significant quantities of sulfur oxides
from two tall stacks, one for the copper process and one
for the lead. The present stack heights are 252 meters
(826 feet) for the copper stack and 186 meters (610 feet)
for the lead stack. Even these heights are not sufficient
to prevent significant groundlevel concentrations and an
intermittent process curtailment system has been in operation
for the last few years. A large system of as many as
twenty-two sulfur dioxide monitoring sites was established
in the vicinity of the smelter and a feedback system of
control has been utilized.
The data available to EPA for analysis at El Paso
was the monitored sulfur dioxide concentrations for the
period July, 1970, through December, 1971. Although less
complete, the meteorological data for periods from February
through December, 1971, was also included. The meteorologi-
cal data sheets also provided volumetric flow rates and
percent sulfur dioxide from both tall stacks. These were
converted to source emission rates by the EPA suggested
method. There is some question about the accuracy of
the S02 stack measurements; however, the reported percent-
ages were taken at face value. Also included in the data
-------
3-30
were temperature measurements at four levels up to 800
feet, as well as the rawinsonde and hourly surface obser-
vations at the El Paso International Airport.
Figure 13 provides an overall view of the topography
and monitor site locations around the ASARCO plant. The
plant site (lower center of the figure) lies in the Rio
Grande Valley on the Texas side of the southward flowing
river. The most prominent topographic feature is the
relatively long ridgeline of the Franklin Mountains.
These mountains are northeast of the plant and extend
from a position due east of the plant to 15 miles or more
northward. The city of El Paso lies mostly off the figure
to the southeast. The Missouri monitor site is located
in the downtown area. Residential areas extend east of
downtown along the Rio Grande Valley and northward along
both sides of the Franklin Mountains. A fairly evenly
spaced line of monitors runs due north-south through the
residential area on the west side of the mountain ridge.
These monitors were expected to include concentrations
for stable plumes directed at a mountain line-ridge.
Other monitors were placed on the Texas side of the Rio
Grande some four miles west of the plant. These instru-
ments should monitor fumigation or unstable maximum
groundlevel concentrations.
The meteorological measurements at the plant site
reflect for the most part local terrain effects. The
measured wind directions tend to be mostly parallel to
the river valley. This is not too surprising consider-
ing that even the ZINC station, 165 feet above ground,
is below the 4000 foot contour which defines a one-mile
wide valley. The stack emissions generally respond because
of their greater height to much less localized meteorology.
The Franklin Mountains are offset on the Mexican side of
the river as the equally high Sierra Muleros. These
mountains start about 10 miles south of the plant site.
The two mountain chains channel the flow from the stacks
in a northwest or southeast direction. Inversions, both
radiative and synoptic occur with relatively high frequency
and intensity. In general, stable flows tend to take the
plume northwest or southeast of the plant site. In this
case, the plume is not interacting with the mountain ridge.
On some occasions, however, the synoptic flow will be from
the southwest directing the plume at the Franklin Mountains
even during nocturnal inversions. During the day when
local effects predominate and winds are flowing along
the valley, the plume can be trapped below synoptic sub-
sidence inversions or the breakup of nocturnal inversions
can lead to fumigation.
-------
3-31
o
rH
W
H
En
-------
3-32
The available groundlevel sulfur dioxide concentra-
tions showed 62 half-hour readings exceeding one part per
million. These were associated with 39 different "events"
of one or more sites above 1 ppm. A review of these
"events" resulted in a list of five occasions which in
terms of data availability were suitable to test against
model calculations. One case for each of the two types
of flow was selected for model comparison.
3.4.2 Flow to the Northwest
The case selected from among the available data
at the cluster of monitors to the northwest of the plant
was for October 21, 1971. The actual concentrations at
the five monitor stations are shown in the boxes in
Figure 14. It can be readily seen that the plume center-
line appears to lie somewhere among the monitor stations.
The time period for which the concentrations are shown
is the half-hour ending at 10:30 a.m. Temperature measure-
ments over the 800 feet on the copper stack indicated a
+6°F temperature difference at 6:00 a.m. which was altered
to isothermal by 9:00 a.m. and at 10:00 a.m. reached the
dry adiabatic lapse rate. This strongly indicates that
inversion breakup was occurring and probably passed through
plume height between 10:00 and 10:30 fumigating the plume
to the ground.
The early morning rawinsonde at the airport indi-
cated that the surface based inversion extended beyond
600 meters. The inversion is, therefore, deep enough
to include the entire plume.
The maximum groundlevel concentrations would result
with an inversion base slightly above the plume height
that was present while the plume was in the stable inver-
sion layer. The model calculations were, therefore, per-
formed for such a situation with an inversion base of
500 m above the plant elevation.
In the INTERCOM? model the diffusion coefficients
in the inversion layer were set to approximate Pasquill
F stability and those below the inversion base were set
to approximate Pasquill C. In the EPA model (C4M3D) and
Gaussian calculations, Pasquill C stability and a mixing
depth of 500 meters were utilized. That constitutes a
perfectly reflecting surface at the 500 m height.
The windspeed of 10 miles per hour as recorded at
the plant site was utilized in the models and a wind
-------
3-33
D
O
H
-------
3-34
direction of 125° true was used to line up the copper
stack and the two central monitor stations. The plant
site anemometer was actually recording a direction 20°
more southerly. The INTERCOM? model wind flow calculation
simulated a more southerly direction near groundlevel
because of the influence of the Sierra Del Christo Key.
This effect can be seen in the groundlevel concentration
isopleths of Figure 2 close to the plant site.
The model calculations for each monitor station
are presented in Figure 14. All values are in SC>2 con-
centrations in ppm (1 ppm is equivalent to 2270 yg/m^).
The INTERCOM? model calculations are shown by isopleths.
Turner's workbook Gaussian plume model calculations (the
multiple reflection equation) with a 500 m mixing depth
provide the calculations labeled Gaussian. Both the
INTERCOMP and Gaussian results are in good agreement with
the measured concentration levels at the five stations.
The width of the plume is reasonably approximated by
either of the two models. The INTERCOMP model did predict
peak concentrations closer to the stack than did the
Gaussian model. The cross-section of Figure 15 illustrates
the topography which leads to downward flow and causes this
effect. The EPA model because of 22.5° sector averaging
predicted concentrations of roughly one-half the peak
values of the other two models.
A vertical cross-section along the plume centerline
from the INTERCOMP model calculations is presented in
Figure 15. Added to the plumes from the two tall stacks
is a fugitive emission equal to 3% of the total sulfur
dioxides from the two stacks. The reason for inclusion
of these values is described more fully in the next section.
As evident from Figure 15, the INTERCOMP model allows
pollutant to diffuse into the inversion layer because
there is only a change of coefficient and not a totally
reflecting surface. Partial reflection does occur at
that boundary and the isopleths of concentration approach
uniformity in the vertical at a distance beyond 3-4 miles
to some extent confirming the uniform vertical mixing
assumption often utilized with the Gaussian model.
In this fumigation case there is comparatively
flat terrain. The results, however, indicate that the
EPA model gave values about one-half those of the INTERCOMP
centerline calculations. The Gaussian calculations were
in the same range as the INTERCOMP calculations. The
INTERCOMP model gives reasonable values at all monitors
while accounting for the terrain effects which are present.
-------
3-35
O
H
dsw
-------
3-36
3.4.3 Stable Flow
In general, stable flows are directed along the
river valley and the plume moves southeast or northwest
of the plant. On occasion stable plumes are directed at
the Franklin Mountains because of the influence of synoptic
wind patterns. Several cases of high groundlevel concen-
trations of sulfur dioxide at the monitor sites east of
the plant were found under these conditions. The data
from December 8, 1971, were chosen as representative.
Winds recorded at the plant site on this day were directed
at the monitor receiving the highest concentration.
The initial attempts to simulate this case were
completely unsuccessful because essentially no concentra-
tion reached groundlevel at the monitor sites. The
vertical cross-section provided in Figure 16 is for the
centerline of the December 8 stable plume. It graphically
shows the reason for the model's inability to simulate
measured stable ground concentrations. The emissions
from the copper and lead stacks are so high above the
monitor sites that no material diffuses down to them
with the restriction to vertical diffusion imposed by a
stable atmosphere. During the half-hour ending at 1:30 a.m.
on December 8, there was a temperature differential of
+13°F over the 800 feet of the copper stack. This cer-
tainly indicates a stable atmosphere with little vertical
transfer.
It is possible, however, to explain high ground-
level concentrations at the monitor sites in terms of
drainage. Several cases in the data appear to exhibit
this drainage effect. The Rim monitor (see Figure 13)
on several occasions responded to high sulfur dioxide
concentrations during stable conditions and then in the
following half-hour McKelligon, Robinson and Zork, all
at lower elevations, would have peak values. This indi-
cates that pollutant was draining down along the terrain
to produce relatively high concentrations at lower ele-
vations. Diffusion does occur during this drainage
process so that the monitored values would not reflect
maximum groundlevel concentrations. Another mechanism
exists for getting groundlevel concentrations at the
Park Hill site (most northerly of the line of monitors).
When the stable plume travels due north from the plant
site and the wind direction then shifts to the north,
the stable plume is swept back along the mountainside
draining as it returns and effecting the low level monitor
sites. In both mechanisms, however, significant dilution
will occur and concentrations in the 1-2 ppm range are
not probable. No attempt was made to model this type of
situation.
-------
3-37
Sg
W
OJ
H
UU_J
»-
-------
3-38
The monitor alLtto uo not have individual anemo-
meters so that in the case of December 8 it is difficult
to tell whether drainage is an important influence. The
temperature measurements up the stacks show that the
temperature profile was isothermal above 500 feet and
that the total +13°F differential was in the lowest 500
feet. This creates a situation where the steepest slopes
on the Franklin Mountains may well be isothermal and
drainage flows would then not be as important. This
factor along with the wind direction at the plant being
toward the monitors virtually necessitated stable winds
directed at the terrain. To get significant measured
concentration levels, we required a source of sulfur
dioxide lower than 500 feet above ground. There is a
350 foot zinc process stack which could be the source,
but no measurements of sulfur dioxide emission were
available. Fugitive emissions from the plant process
buildings are another potential source of sulfur dioxide.
The major monitor of interest (Park Hill) is situated
almost 300 feet above the plant site. A few runs with
the INTERCOM? model showed relatively little difference
in predicted concentrations for a range of plume heights
between 100 and 300 feet. A source emission strength
of 3% of the combined emissions for the two stacks gave
best agreement with the concentrations found at the
monitors. The results for 3% fugitive emissions with
a 200 foot plume height are shown in Figure 17. The
fugitive emissions were considered to be emitted between
the two stacks as an approximation. As in earlier figures,
the INTERCOMP model values are shown in isopleth form.
The INTERCOMP model prediction at the Park Hill monitor
was 1.51 ppm. The maximum value of 2.14 ppm was located
a little north of the monitor. The Park Hill monitor is
actually located on a small plateau not evident in Figure
17 which drops off in elevation both to the south and
north. As a consequence, changes in the wind direction
result in highest ground concentrations on either side
of the monitor rather than at the measurement site.
Other wind directions and source strengths also do not
agree as well with the values at the other three monitors.
In the cases of the EPA and Gaussian calculations,
the height of the source emission has more effect on the
results. The values shown in Figure 17 are for a 200 foot
effective fugitive emission height. These calculations
indicate much higher values at the Park Hill monitor.
In the case of the EPA model, a value more than twice
the measured value at the monitor and a maximum of 4.76
ppm downhill from the monitor were calculated. This is
similar in location to the INTERCOMP model simulation.
The Gaussian calculations, without benefit of sector
averaging and the EPA model restriction for the centerline
-------
3-39
r-
H
O
%
(O
\
V
.
MATCH
1
_J
UJ
Q
O
2
UJ
CO
<
O
UJ
_l
m
-------
3-40
remaining 10 m above groundlevel, yield values an order
of magnitude higher than the EPA model. This calculation
assumes plume centerline values are along the ground from
the point of intersection of the terrain on up the side
of side of the mountain. The position of the maximum is
the same. If the source height were increased to 300
feet, the predicted maximums for the EPA model and the
Gaussian would be to shift the monitor location and are
about the same magnitude as those predicted for the lower
source height.
Smelting personnel generally agree that a fugitive
emission level of 3% is not out of line with normal opera-
tions and, in fact, may be low. To obtain a best fit of
the monitored data, fugitive emissions of less than 1.5%
would be required for the EPA model and less than 0.3%
for the Gaussian calculations.
Almost certainly the plumes from the two tall
stacks interacted with the Franklin Mountains at eleva-
tions above the monitor sites. The initial runs with
the INTERCOM? model indicated maximum concentrations
on the order of 10 ppm. Gaussian intersecting calcula-
tions show values of 400 ppm. Both of these calculations
are for F stability. Neither set of calculations can be
compared to monitored data.
The stable case plume simulation shows the flexi-
bility of the INTERCOMP model as an evaluation tool for
determining what unknown source rates might be. Simulating
the results at a series of monitors gives some confidence
in the approximate 3% level for fugitive emissions. The
comparison between the models is not extremely definitive
since the source rate and its resultant plume height are
not known.
3.4.4 Summary
In summary, the ASARCO smelter data provide data
useful in comparing the three models. Two types of atmos-
pheric conditions were examined. In the limited mixing
cases, the same mixing depth and atmospheric stability
were used in the mixing layer for each model. Results
indicated good agreement between the INTERCOMP model and
the Gaussian (NOAA) model. Both models were in good
agreement with measured data for such an atmospheric
condition. The EPA model, because of the angular sector
averaging even for short-term peak concentrations, was
lower by a factor of roughly two.
-------
3-41
In the stable flows with winds directed at high
terrain, our study showed little effect of the stack emis-
sions on concentrations measured at the monitors. Instead
a fugitive emission was hypothesized to be responsible for
these measured concentration levels. At a fugitive level
of 3% of the combined stack emissions, good agreement was
obtained between calculated concentrations with the INTERCOMP
model and the measured values. Both the EPA model and the
Gaussian (NOAA) model calculated concentration levels much
higher than measured values for the 3% emission levels.
Of course, a reduction in emission level could have been
used; however, this caused the Gaussian type models to
give poor agreement with measured values in terms of
crosswind spread.
The finding that stack emissions are, in all pro-
bability, not affecting monitored concentration levels
is interesting from the standpoint of intermittent process
curtailment effectiveness. It would appear that the fugi-
tive emissions would have to be quantified to provide
realistic control. It is probable that plant curtailment
affects fugitive levels in exactly the same way as it
affects the stack emissions although this point would
need investigation.
3.5 Validation of the INTERCOMP Flow Model
3.5.1 General
Every mathematical model of physical phenomena
is subject to the assumptions used in its formulation.
Therefore, most mathematical models are restricted to
a certain class of problems. Such a model is considered
to be valid, if it simulates correctly the physical
phenomena that were intended to be included in its
formulation. Specifically, the INTERCOMP flow model
is designed to simulate air flow over terrain on a
large scale necessary for ambient air quality studies.
Because this model is based on a "modified potential"
flow concept12, there is certainly a question of the
adequacy of such a model for a complete range of pro-
blems which are of interest. Ultimately, this can best
be answered by extensive comparison to field data.
However, it is possible to obtain a reliable answer
also by comparison of the model with more sophisticated
calculation techniques—in this case with a model based
solving Navier-Stokes equations for viscous, slightly
compressible flow. Although at the present time, the use
of a Navier-Stokes formulation for large-scale air quality
models appears to be impractical because of cost (see
reference 13, 14, 15, and 16), such models can serve as
a standard for comparison of simpler models. Two such
-------
3-42
models have been reported for solving air quality pro-
blems2'3. In making comparisons between the "modified
potential" model results and the Navier-Stokes model
results, one has to bear in mind that the potential
formulation cannot simulate phenomena that are unique
to viscous flow, i.e. wakes and vortices. However, in
many cases wakes will not form due to atmospheric stability
or will only exist on a small scale below the resolution
limit of simulation (e.g. for flow over gently sloped
terrain), Even in the case when a wake develops on the
downstream side of an obstacle, the simplified solution
may be adequate for cases where it can be shown that the
presence of the wake does not affect the flow in the
regions of real interest—e.g. on the upwind side or
above the obstacle. Thus, the Navier-Stokes model can
also serve to determine a range of adequacy for the
"modified potential" flow model.
In the comparisons included in this report no
attempt has been made to verify the modified potential
model for all flow conditions. Rather two basic condi-
tions of neutral and stable conditions were investigated.
3.5.2 Navier-Stokes Flow Model
3.5.2-1 Mathematical Development
The numerical model is based on the "primitive
variable" formulation used by the Los Alamos
group17'18'19 as well as the Colorado group20
and others21'22. This formulation has been
chosen in preference to the vector potential
formulation2 3, because it can be easily extended
to turbulent flow and variable density. For a
current survey of computational approaches to the
Navier-Stokes equations, see reference 24 and 20.
The details and equations used in our calculational
model are developed in Appendix A.
The particular form of the momentum and con-
tinuity equations used are subject to the following
assumptions:
(1) Pressure changes do not affect density.
(2) Density changes have a negligible effect on
viscous terms. This assumption is quite
justified in view of the uncertainties asso-
ciated with turbulent viscosities.
-------
3-43
(3) Turbulent effects are included as Reynolds
stresses expressed through a turbulent eddy
viscosity (this will be discussed in more
detail later) .
(4) Density can be described as a function of
position. Although the model includes the
capability for solving simultaneously an
energy equation, buoyancy effects were simu-
lated by a stable temperature field. This
would be the case at steady-state which was
of primary interest and it greatly simplifies
the calculations.
The numerical solution method disc:,:etizes the
momentum and continuity equations. The finite
difference discretization of the momentum equations
also satisfies the discretized continuity equation
(see Appendix A) .
The momentum equations use a forward difference
for the time derivatives. The procedure consists
of implicitly solving for the pressure field with
the righthand side evaluated at the old time level,
then an explicit updating of the velocity field
using the new pressures. Central time differencing,
preferred by some authors16'25'26, gives smaller
time truncation errors, but introduces weak instabi-
lity and increases core requirements.
The program has the capability of solving both
two-dimensional and three-dimensional problems.
The solution method for the pressure equation is
LSOR, with direct elimination as an option for
two-dimensional problems. Handling of boundary
conditions permits arbitrary specification of
terrain as in the standard INTERCOM? air quality
simulator. The program has a restart capability
and an automatic time step control, based on the
convective stability condition.
3.5.2-2 Comparison with Results for Laminar Flow
_^«^_^_ — "• ' .. . - - _ -
The problem chosen for testing of the laminar
flow model is the flow in an entrance region of
a straight channel. Steady-state solutions of
incompressible Navier-Stokes equations for this
problem are given by Morihara and Cheng27, who
also compare many of the earlier results reported
in boundary layer literature. Because the INTERCOM?
Navier-Stokes model does not have the capability to
solve directly for the steady-state velocities,
•jriP teady solutions were computed until reasonably
close to steady-state. Comparison of results of
-------
3-44
Re = 200 are shown in Figure 18 where the contin-
uous lines show literature results27 and the
circles result from the INTERCOM? model. The
agreement with literature values27 is satisfactory.
The main difference is that our solution has almost
no bulges in the velocity profile (although they
have been observed in runs other than those shown).
The reason for this difference is the relatively
course grid used and the fact that the referenced
work27 used higher order approximations for con-
vective terms. The differences closer to the inlet
are due to the fact that our solution is not quite
at steady-state.
Similar results were obtained from other
Reynolds numbers.
3.5.2-3 Eddy Viscosity Model for Turbulent Flow
Presently, the most practical way of treating
turbulent flow is via the eddy viscosity concept '
29'30. The turbulent (eddy) viscosity is a complex
tensor function of the flow field. Many turbulent
models have been proposed for calculation of eddy
viscosity coefficients, some of them very complex
(see reference 20 and especially 31). While it
is necessary to construct complex turbulence models
as tools for better understanding of the turbulence
phenomenon, their present accuracy does not justify
their use for practical calculations. Our aim has
been to use the simplest approach that would be
adequate for the class of problems of interest.
In air pollution applications, there is generally
one direction of the prevailing wind. Over flat
terrain, the velocity distribution often follows
an approximate power law dependence on height.
Our turbulent viscosity model then is based
on the assumption that over a flat surface, the
velocity variation in the vertical will approxi-
mately follow a power law dependence. If the
thickness of the boundary layer, ZOT, is sufficient
so that turbulence essentially disappears at z^
(see e.g., Sutton29, Chapter 7), then the viscosity
at the top of the boundary layer, y , can be taken
as the molecular viscosity. Molecular viscosity
is generally negligible compared to the maximum
turbulent viscosity, y^. An example of the varia-
tion of this viscosity model and the resultant
velocity versus height are shown in Figure 19 for
a power law exponent of a = 1/7. As shown in
Appendi:: A, the above development of turbulent
viscosity can be interpreted in terms of Prandtl's
mixing length hypothesis and agrees well with
experimental results for one-dimensional flow.
-------
3-45
Q
UJ
CO
fe
o ui
CO
2
if
o 7i
°
3 i *
0*0
(0 (O _1
i.i w ^
LU \s
us
OQ
<
O:
s
<
UJ
2
o: o
o o
-------
J-46
FIGURE 19
VERTICAL VARIATION OF
EDDY VISCOSITY
u =u/ u.
N
>x
N
II
IN
0.5-
0
-------
3-47
The above procedure defines only one component
(namely yxz) of the viscosity tensor. The remaining
components are obtained by scaling of yxz using ratios
of turbulent fluctuations (dependent upon stability)
and derivatives of velocities based on the "order of
magnitude" argument common in boundary layer theory.
Our experience has shown that a change of some compo-
nents of viscosity by an order of magnitude did not
have a noticeable effect on the results; therefore,
this approximation seems justifiable. However, the
simulator is not restricted to the above described
treatment of turbulence, and could use a more elabo-
rate model of turbulence if desired.
To test if this turbulence model g ,.ves numeri-
cal solutions that approximate a power law, the
"entrance region" was solved again in turbulent
flow. Because of the symmetry condition at z^,
the result also represents a solution of turbulent
flow over flat terrain, with uniform inlet velocity.
Figure 20 shows an example of the velocity profile
at a large distance from the entrance, where the
velocities are fully developed. In this case, the
Reynolds number, corresponding to the maximum eddy
viscosity is 10^ (Re was calculated from a molecular
viscosity of about 10^).
This can be compared with a one-dimensional
exact solution for the same eddy viscosity model
which results in a power law velocity profile. As
evident in the log-log plot, the numerical solution
follows a power law variation near the ground, but
deviates at the top of the boundary layer. This is
due to_ the fact that the boundary condition at the
top (z = 1) is 9u/9z = 0, which is not satisfied by
a power law velocity profile. Thus, the numerical
model gives a more realistic approximation than the
exact power law profile for atmospheric flow which
should approach a condition of nearly zero vertical
gradient at the top of the turbulent boundary layer.
An additional test of the numerical model was
performed in three-dimensional flow by numerical
simulation of wind tunnel measurements obtained
by Halitsky32. Figure 21 shows the caluclated and
measured u-velocities at a distance 12 m behind the
building (the wind tunnel results were scaled to
the original size). Although this comparison is
only qualitatively significant, because of diffi-
culties in scaling and generating the turbulence
in wind tunnel tests, the agreement confirms the
validity of the numerical results.
-------
3-48
UJ
CO
2/2 = Z
I-OC
in
6
s
s?
cc ^
ui y
5 ^
80;
Z5
z/z = z
-------
3-49
W
UJ
UJ
<
_J
CL
M
UJ
-------
3-50
3.5.3 Comparison with the Modified Potential Model
3.5.3-1 Influence of Wake Regions on Flow Field
Around an Obstacle
As mentioned before, the modified-potential
model cannot simulate wake regions behind build-
ings or other obstacles. It is, therefore, important
to establish the effect of such a wake on the flow
field upstream and above the obstacle.
This question was investigated by solving
flow fields around obstacles of the same height,
but of different lengths in the direction of
flow. The flow fields at a time close to steady-
state were then compared. Figures 22 and 23
show the two respective flow fields in the two-
dimensional case, first for a short obstacle,
and second for an obstacle of "infinite" length.
Recirculation develops in the first case in the
wake region behind the obstacle. In both cases
it was assumed that a fully developed flat terrain
velocity profile exists at the entrance to the
simulated region, i.e., the entrance velocity
satisfies a power law profile. The comparison
of the horizontal velocities, u, are shown in
Figure 24. It is evident that the presence of
a wake on the downstream side does not affect
the velocity profile in front of the obstacle
and only slightly affects it above the wake (in
cross-section B-B). Similar results were ob-
tained in the three-dimensional cases. It may,
therefore, be concluded that the simulation of
a wake is not important for the flow field except
directly behind the obstacle. Consequently, the
comparisons with the modified potential model
were carried out for obstacles extending to
infinity, for which recirculation regions are
not present.
3.5.3-2 Comparison for Two-Dimensional Flow
All two-dimensional runs were made with a
16x7 grid. Irregular grid spacing was used in order
to obtain adequate definition around the upstream
side of the obstacle. The influx velocity was
assumed to satisfy a power law profile according
to a prescribed exponent a. The first series of
runs were made without the effect of density,
-------
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CM
w
OS
D
O
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1§
UJU
CM
W
«
D
O
-------
CO
CO
CO UJ
E^F
* P O
es«
" °v>
ing
||5
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fes§
^ E uj
CO
i
CD
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^ H-
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UJ
CO
CD
o
u <
e 2
o
LJ
-------
3-54
and a = 1/7 which corresponds to a neutral atmos-
phere. It was found that the modified potential
solution gives good agreement with the Navier-
Stokes solution (presented in Figure 23) when
K /K =1 for the flow coefficients in the poten-
tial model. Figure 25 shows the comparison
of these two results at four vertical cross-
sections. The agreement is good except on the
top of the obstacle, where the potential solution
does not reflect the amount of viscous friction
that it should.
A second series of runs simulated stable
atmospheric conditions. For the Navier-Stokes
solution it was assumed that the ground is an
isothermal surface and a constant density gradient
of -0.001g/cni3/m was assumed. The effect of
density variations is best seen by plotting the
velocity difference between the stable and neutral
cases as shown on Figure 26. In stable flow
velocities at the ground decrease and at the top
of the boundary layer increase causing the circu-
lation pattern of Figure 26. In the modified
potential model, a best match was obtained for
this case with KZ/KX = 0.7. Comparison of these
two results is in Figure 27 and has the same
character as the results of Figure 25.
3.5.3-3 Comparison for Three-Dimensional Flow
The example for three-dimensional testing
has the same grid in the x-z plane as the two-
dimensional problem. The dimension of the obstacle
in the y direction is 10 m. Because x-z is a
symmetry plane, only one-half of the problem
need be solved as shown in Figure 28. Illus-
tration of the three-dimensional results is more
complicated, mainly because it is difficult to
display the data in three dimensions19'2.
In the neutral case, the velocity field in
the symmetry plane (x-z) is very similar to the
field obtained in the two-dimensional case, and
y-velocities are small except around the upstream
side of the obstacle. The modified potential
model gave good results when KZ/KX = 1. Figures
29 and 30 show a comparison of u-velocities in
the two planes perpendicular to the x-axis.
Figure 29 gives a two-dimensional velocity profile
-------
3-55
in
3
H
-------
ra
K
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O
H
I t
H L>
oo
CO O
£-*
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EH EH
2
W W
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W OQ
fe <
EM EH
H CO
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K
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/ /
/ /
-------
8§
"i 3,
y 5
UJ CC >-
X UJ t
o z
UJ Z <
_i o p
00 to z
-------
3-58
W
oc
CN
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EM
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3-59
8
CTN
CNJ
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3-60
tn
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UJ CO
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-------
3-61
in the plane A (Figure 28) in front of the obstacle
and Figure 30 in plane B through the face of the
obstacle. The agreement is generally good with
the exception of velocities close to surface,
especially on the side of the obstacle. Good
agreement was also found in the z and y components
of the velocity field.
In the stable case, the imposed density gradient
causes superimposed circulation at the front side
of the obstacle similar to Figure 26. Also, the
density gradient in the y direction (:>n the side
of the obstacle) has an effect of superimposing
transversal circulation patterns. Tne three-
dimensional equivalent of Figure 26 showing
the difference between stable and neutral velocity
fields is schematically shown ir Figure 31. In
this case, u-velocities on tor of the obstacle
are decreased and v-velocities, which were small
in the neutral case, increase in the downstream
direction. A true circulation pattern is formed
on the side of the obstacle if it is long enough.
Comparison runs with the modified potential model
showed that it is possible to obtain a good match
of velocities on the upstream side of the upstream
side of the obstacle by reducing KZ/KX.
3.5.4 Summary of Comparisons and Conclusions
3.5.4-1 Range of Adequacy for the Modified Potential
Flow Model
Numerical comparisons described in the pre-
ceeding paragraphs show convincingly that the modi-
fied potential model will be adequate for many
situations typical in air pollution modeling,
particularly:
(a) for flow over terrain where no wakes and
recirculation regions are expected to develop
because of stability, and
(b) for flow around buildings or over rough
terrain, if the areas directly behind ob-
stacles are not of primary interest.
-------
J-62
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K
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-------
3-63
3.5.4-2 Limitations
The basic limitation of the modified potential
model is given by the fact that it cannot simulate
properly viscous effects. Therefore, the model
will not be adequate, for example, for investiga-
tion of downwash of pollutants in a wake behind
a building, for investigation of pollutant sources
located in building cavities, and other similar
applications. These cases represent mostly simu-
lations on a much smaller scale than is usual in
typical air quality studies. Similar limitations
are found when temperature effects ere considered.
The model will be adequate if thermal effects are
relatively uniform and are mainly reflected in a
change in the stability of the atmosphere.
3.5.4-3 Accuracy and Expected Errors
The results of this study show that the
INTERCOMP modified potential model is generally
an adequate flow model for environmental engineer-
ing studies. A different simplified model was
also proposed by Hino30. Such simplifications
of the problem at present, still seem to be the
only way for solving practical size problems
efficiently.
The problem is the large computer require-
ments for numerical integration of the full Navier-
Stokes equations. For the examples given here,
computer time for the Navier-Stokes solutions was
10-100 times more than for the modified potential
model. For a large three-dimensional problem
this ratio would probably be closer to the
upper end of this range.
It is important, for this reason, to continue
development and improvement of simplified flow
models. Navier-Stokes models can then be used
for validation of these models and in situations
where the simple models are known not to be
adequate.
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4-1
4.0 REFERENCES
1. Hino, M., Computer Experiment on Smoke Diffusion Over Compli-
cated Topography, Atmos. Env. 2_, 1968.
2. Hotchkiss, R. S., Numerical Calculation of Three-Dimensional
Flows of Air and Particulates About Structures, Proceedings
Air Pollution, Turbulence, and Diffusion Symposium, Dec.,
1971.
3. Djuric, D. and Thomas, V., A Numerical Study of Convective
Transport of a Gaseous Air Pollutant in the Vicinity of
Tall Buildings, Proceedings Air Pollution, Tur1 ulence, and
Diffusion Symposium, Dec., 1971.
4. Lantz, R. B., Coats, K. H. and Kloepfer, C. V., A Three-
Dimensional Numerical Model for Calculating the Spread and
Dilution of Air Pollutants, Proceedings Air Pollution,
Turbulence, and Diffusion Symposium, Dec., 1971.
5. Van der Hoven, I., et. al., Report of Meteorology Work
Group, Southwest Energy Study, Appendix E, 1972.
6. Start, G. E., Dickson, G. R., and Wendell L. L., Diffusion
in a Canyon within Rough Mountainous Terrain, NOAA Tech.
Memo ERL, ARL-38, August, 1973.
7. Turner, D. B., Workbook of Atmospheric Dispersion Estimates,
US DHEN 999-AP-26, 1969.
8. Sklarew, R. C., Fabrick, A. J. and Prager, J. E., Mathematical
Modeling of Photochemical Smog Using the PICK Method, APCA
Journal, 22, 1972.
9. Lantz, R. B., Quantitative Evaluation of Numerical Diffusion
(Truncation Error), SPE Journal, 1971.
10. Price, H. S., Varga, R. S. and Warren, V. E., Application of
Oscillation Matrices to Diffusion-Convection Equations,
Journal Math, and Physics, 45, 1966.
11. Bowne, N. E., Diffusion Rates, Presented at 66th Annual
Meeting of APCA, Chicago, Illinois, Time, 1973.
12. Lantz, R. B., McCulloch, R. C., and Agrawal, R. K., The
Use of Three-Dimensional Numerical Air Pollution Models
in Planning Plant Location, Design and Operation, J. Canada
Pet. Tech., July-Sept., 1972.
13. Hirt, C. W., Heuristic Stability Theory for Finite-Difference
Equations, J. of Comput. Physics, 2, 1968.
-------
4-2
14. Deardorff, J. W., A Numerical Study of Three-Dimensional
Turbulent Flow at Large Reynolds Numbers, J. Fluid Mech.,
1970, Vol. 41 (2).
15. Deardorff, J. W., Numerical Study of that Transport by
Internal Gravity Waves Above a Growing Unstable Layer,
Phys. of Fluids Supplement II, 1969.
16. Fox, D. G., Numerical Simulation of Three-Dimensional Shape -
Preserving Convective Elements, J. of Atm. Sci., Vol. 29,
March, 1972.
17. Welch, J. E., Marlow, F. H., Shannon, J. P., and Daly, B. J.f
The MAC Method, Report LA-3425, Los Alamos Scientific Labora-
tory of the University of California, 1965.
18. Harlow, F. H. and Welch, J. E., Numerical Calculation of
Time-Dependent Viscous Incompressible Flow of Fluid with
a Free Surface, Phys. Fluids, 8^ 1965.
19. Hirt, C. W. and Cook, J. L., Calculating Three-Dimensional
Flows Around Structures and Over Rough Terrain, J. Comp.
Physics, 10, 1972.
20. Fox, D. G. and Deardorff, J. W., Computer Methods for Simu-
lation of Multidimensional, Nonlinear, Subsonic, Incompressi-
ble Flow, J. Heat Transfer, Trans. ASME, Nov., 1972.
21. Williams, G. P., Numerical Integration of the Three-Dimensional
Navier-Stokes Equations for Incompressible Flow, J. Fluid
Mech., 1969, Vol. 37, Part 4.
22. Lilly, D. K., Numerical Solutions for the Shape-Preserving
Two-Dimensional Thermal Convection Element, J. Atm. Sci.,
21, 1964.
23. Aziz, K. and Heliums, J. D., Numerical Solution of the Three-
Dimensional Equations of Motion for Laminar Natural Convection,
Phys. Fluids, 10, 1967.
24. Ames, W. F., Some Computation in Fluid Mechanics, SIAM
Review, 15_ (2) , 1973.
25. Deardorff, J. W., Numerical Study of Heat Transport by
Internal Gravity Waves Above a Growing Unstable Layer,
Phys. of Fluids, Supplement II, 1969.
26. Deardorff, J. W., A Three-Dimensional Numerical Investiga-
tion of the Idealized Planetary Boundary Layer, Geoph. Fluid
Dynamics, Vol. 1, 1970.
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4-3
27. Morihara, H. and Cheng, R. Ta-Shun, Numerical Solution of
the Viscous Flow in the Entrance Region of Parallel Plates,
J. Comput. Physics, 11, 1973.
28. Hinze, J. 0., Turbulence, McGraw-Hill, New York, 1959.
29. Button, 0. G., Micrometeorology, McGraw-Hill, Hew York, 1953
30. Schlichtling, H., Boundary-Layer Theory, 6th Edition,
McGraw-Hill, 1968.
31. Launder, B. E. and Spalding, D. B., Mathematical Models of
Turbulence, Academic Press, London and New York, 1972.
32. Halitsky, J., Validation of Scaling Procedures for Wind
Tunnel Model Testing of Diffusion Near Buildings, Report
No. TR-69-8, Geophysical Sci. Laboratory, N3W York Univ.,
1969.
-------
A-l
APPENDIX A
NAVIER-STOKES FLOW MODEL
Mathematical Development
The numerical model is based on the "primitive variable"
formulation used by the Los Alamos group17'18'19 as well as the
Colorado group20 and others21'22. This formulation has been chosen
ir. preference to the vector-potential formulation2 3 because it
can be easily extended to turbulent flow and variable density.
For current survey of computational approaches to Navier-Stokes
equations, see reference 24 and 20.
The equations solved are
Du
Dt
nDV -
PDt '
VyVu
VyVv
Dt
= 7r£- + VyVw - pg
0 2
(A-l)
whPr-P n^H - iPJi + 3PU + 9PUV + 9PUW
where pDt ~ 3t + at + 3y + gz
and
3p 3pu
3t 8x
3pv 5pw
3y 3z
= 0
(A-2)
p = f (x,y,z)
(A-3)
These equations can be derived from the full Navier-Stokes equation
if it is assumed that:
(1) Pressure changes do not affect density.
(2) Density changes have a negligible effect on viscous terms.
This assumption is quite justified in view of the uncer-
tainties associated with turbulent viscosities.
Turbulent effects are included as Reynolds stresses ex-
pressed through a turbulent eddy viscosity (this will
be discussed in more detail later).
-------
A-2
(4) Density can be prescribed as a function of position.
Thus, although the model does not solve simultaneously
the energy equation, it can approximate the buoyancy
effects in cases when the temperature field is relatively
stable. Such cases are often of practical interest.
This model is more comprehensive than the incompressible,
laminar viscosity model, used e.g. in reference 19.
The pressure equation can be obtained from (A-l) by differen-
tiating each equation with respect to its direction coordinate
and summing
- [ VyVu + VyVv + VyVw] =
or V2p = -RI - RV (A-4)
Therefore, both inertia terras, RI, and viscous terras/ RV, act as
'sourcefe in the 'pressure equation. It is worth noting that the
right-hand side of (A-4) is much more complicated than for the
case of laminar incompressible flow, where it can be shown that
RV = 0 by continuity and
.
\. — • - ••'••--JT'1--- Vy
3x2 3y2 3z2
In the original MAC method and its later applications, the entire
right-hand side was also carried in the computation in order to
help the approximate solution satisfy continuity when iterative
methods were used. In the present turbulent model, the viscous
terms must be retained because they do not cancel out in (A-4) ,
regardless of the solution method used.
The numerical solution method employs equations (A-l) and
(A-4), discretized by finite differences. With suitable discre-
tization, the finite-difference equations will also satisfy the
discretized continuity equation (A-2).
The momentum equations (A-l) use a forward difference for
the time derivative. The procedure consists of implicitly solving
for the pressure field with the right-hand side evaluated at the
old time level, then an explicit updating of the velocity field
using the new pressures. Central time differencing, preferred by
some authors16'75'26, gives smaller time truncation errors, but
introduces weak instability and increases core requirements.
-------
A-3
Boundary Conditions
The region in which the equations are solved is rectangular
in the x and y direction as shown on Figure A-l. In the z direction,
ILLUSTRATION OF
ATI!
it is bounded by ground surface of variable elevation and by a
constant elevation z^, which is assumed to be the top of the
turbulent boundary layer. It is assumed that the wind at x = 0
is in the direction of the x-axis and the velocity profile is
known, i.e.,
u = U(y,z), v=w=0atx=0
(A-5)
The y boundaries and the boundary at z^ are assumed to be no-
friction surfaces without flow across the boundary.
=< v = 0 at y = 0, L
(A-6)
H = = o, w = 0 at z = z
(A-7)
At the groundlevel, friction is important. Therefore, the boundary
conditions are:
-------
A-4
u = v = w = Oat the ground (A-8)
Finally, at the outflow face, we specify a vertical pressure gra-
dient that corresponds to one-dimensional flow over flat terrain
(uniform pressure if gravity is neglected). Since the flow is
incompressible with respect to pressure, pressure level is not
important. Therefore, we can arbitrarily choose pressure at say
zm to obtain:
p = p(z), p(zj = P, g| = -pg at x = LX (A-9)
Model of Turbulence
Consider one-dimensional flow over a flat plate at steady-
state, for fully developed (w = 0), incompressible flow, equations
(A-4) reduce to
9£ - pi _ 3_ 1"
3x 8"z (yxz 3z
Define shear stress, T, by
Since at steady-state P1 = const, we can integrate the equation
to obtain
T(Z) = P'z + C± (A-12)
which shows that shear stress varies linearly with height. Let
us now assume that the velocity over the flat surface is given by
u = UOT (^)a (A-13)
CO
Differentiating and substitution into (A-ll) and (A-12) gives
zm 1-a
(—) (P'z + C,) (A-14)
i — r: v 1 \f ^ ' <— n
xz U a z 1
00 CO
-------
A-5
The constant C, cannot be determined from the value of y at x = 0,
since ;, (0) = 0, but from the value y^ = y (ZOT) . Since 3u/9z(zoo) =
Uf a/z , we have
^xz = STS (f-> ^'(z - zj + Tj (A-15)
OO OO
In order to obtain the pressure gradient, we must relate it to the
magnitude of the eddy viscosity. It is convenient to choose the
maximum viscosity, y , which is equal to
ZT — ru T
/ T \ J- Ud «. T
oo f I — ry I oo l—ry
\J-VA/ /T X-*-*-*/ i-il \ t -* ~\ f* \
— -
U ,. ,2-a P'z
oo (2-a) o
at the height
ZM =
If the height of the boundary layer z^ is chosen such that turbu-
lence essentially disappears at z^, the viscosity y will
essentially be the molecular viscosity, vu, the shear stress,
T^, can be neglected in comparison to the maximum turbulent shear
stress at the ground, thus T = P'z^. The expressions (A-16) and
(A-17) then simplify to
z ,, ,1-a z /n vl-a
„ - - °° d-a) P. - __ !1_ (1-a) T ra-is^
yM " iTa ,0 .2-a P ~ U a ,, .2-a To (A lb}
00 (2-a) °° (2-a)
and
ZM =
Therefore, equation (A-18) allows us to calculate y from the
measured values of T . The final expression for y is then
o L xz
, 2-a
(l-a)
-------
A-6
It is easy to see that the derivation of equation (A-19) can be
interpreted as a derivation of the mixing length £(z) in Prandtl ' s
model of turbulence in order to satisfy the power law velocity
profile. By Prandtl 's hypothesis
06— 1
Since 8u/9z = (U^a/z^) (z/z^) , we obtain by comparison with
(A- 20) for y = 0.
The equation (A-22) agrees very well with the measured mixing
length in pipes, reported in reference 30, except for the region
close to the centerline, which is to be expected. However, it is
more important that the eddy viscosity itself agree with measurement
rather than the mixing length, since £ is itself derived from
observed values of v.
Comparison of y by formula (A-20) with measurements by
Nikuradse30, ChapterxzXX is in Figure A-2. The agreement is
excellent up to z/z^ = 1/2 and acceptable for larger z. It is
clear that a function derived from a power law velocity profile
cannot fit exactly experimental data in a tube or channel at the
centerline because the boundary conditions are different at z^.
However, the model can be used with the boundary conditions
3u/3z = 0 at z = zm and will produce a solution that deviates
from the power law as z •> zro (Figure 20) in agreement with
experimental results30,
The one-dimensional analysis presented thus far established
only one component of the viscosity tensor. The other components
can be obtained from the definitions of the turbulent stresses:
-------
A-7
XX
xy
xz
yx
yy
yz
zx
zy
zz
3u
i r: —
XX dX
= y
xy 3y
=y ^
XZ dZ
yyx 8x
= y
zx
yyz 9z
3w
3y
8w
yzz 9z
= -p u'
= -p u v
= -p u w
= -p v
= -p v'w'
•5— = -P W'U1
7J- = -P W'V'
= -p w1
(A-23)
The task of generating all nine stress components as functions of
position and the current flow field is, in general, the subject
of theoretical models of turbulence. Our approach is based on
the model for y which gives correct results in one-dimensional
shear flow. The work2 6 concluded that in the planetary boundary
layer this is indeed the most important component and, therefore,
we can expect that the relations for other components may be consider-
ably simplified without significant loss of accuracy.
The starting point is provided by experimental evidence, that
22 22
the ratios of turbulent fluctuations w1 /u1 , v1 /u1 ,
etc. remain approximately constant29'30
u'w'/xi'2,
These ratios perhaps
should be a function of atmospheric stability as the mass diffusi-
vities are. Furthermore, we can make a simplification that the
burbulence is approximately homogeneous in the x-y (horizontal)
2
1
• 2
plane, v1 ^u' , v'w1 ^u'w1. Then the structure of turbulence
is determined by y , a fluctuation ratio
-------
A-8
1
CN
I
H
'2/2
-------
A-9
r =
and two correlation coefficients
(A-24)
xz
u'w1
/~72
.yw
(A-25)
xy
u'V
u'v'
u^2"
(A-26)
Using equations (A-24) through (A-26), we can express all viscosity
components as a function of yvry and the three constants. We can
write this in matrix form as
xz
y = y
xz
rif;
xz
3
~E$
xz
3w
in
3x
15.
iy.
3x
xy
xz
xz
3u
3zT
3w
37
i£ i
9y
3u 3u
iz. i3z_
37 Jz
3u
r 3z
ijj 3w
Tz
= y A (A-2
xz y
Matrix A depends on the current velocity field and will be, therefore
different for each grid point and time step. The uncertainty in
the data often justifies further simplification of the model (A-27),
similar to the "order of magnitude" argument, common in boundary
layer theory. The simplification consists of replacing the local
values of derivatives by "mean value" estimates as follows:
-------
A-10
3x
3u °
' 3z z
3v
max
3v
max
r-
3v max
' 8z z
w
3w ^ max
x
3w
W
max
W
3w n max
—
If we now define ratios as
V W
max _ 0 max _
U y ' ~U s
co •* oo
(A-28)
we obtain a constant "average" matrix A:
Ay=
Tp
r
xy
1)
xz
Jx
x
x_
z R
z R
oo 2
z R R
oo y y
Z R if) R
00 z xz z
(A-29)
The use of (A-29) is considerably simpler than the corresponding
(A-27).
Computing Details
The program has the capability of solving both 2-D and 3-D
problems. The solution method for the pressure equation is LSOR,
with direct elimination as an option for 2-D problems. Handling
of boundary conditions permits arbitrary specification of terrain
as in the standard INTERCOM? air quality simulator. The program
has a restart capability and an automatic time step control, based
on the convective stability condition:
At <
mm
Ay Az,
w
(A-30)
-------
A-ll
The condition (III-5) alone is not sufficient for stability in
all cases, but it is always necessary.
The optional modes in which the program can run include the
laminar viscosity case, a constant density case, and different
input velocity profiles.
-------
B-l
APPENDIX B
•V
* COMPARISON OF MEASURED AND CALCULATED RESULTS
Results for Test 1 through 11 are summarized in the follow-
ing tables. Tests 2 and 6 have been omitted because they were
for easterly winds and contained only a few data points at the
monitors north of the release point. Test 2, for example, con-
tained only two groundlevel measured points.
A few comments concerning each test result are included in
the appendix.
* j
,1
-------
B-2
COMPARISON MEASURED AND CALCULATED VALUES
TEST NO. 1 - UP-CANYON
Location
Deer Cr-Mtnghouse
White Ridge(1)
(2)
(3)
(4)
Wild Draw(l)
(2)
Wild Horsed)
(2)
(3)
(4)
Bear Creek(1)
(2)
(3)
(4)
Red Face(l)
(2)
Wet Man(l)
(2)
(3)
(4)
Measured
yg/m3
0.5
0.3
0.1
0.6
1.6
1.3
0.8
Calculated, yg/m'
INTERCOMP EPA GAUSSIAN
1.6
2.0
1.3
1.0
0.7
0.3
0.7
0.5
0.5
0.2
0.1
1.2
0.9
0.9
0.6
0.6
0.5
1.8
1.3
1.0
1.0
0.7
0.7
0.6
Comments
*
Test No. 1 was a stack top release under Pasquill B stability.
Each of the models gave calculated results which peaked closer to
the stack than the measured results would indicate. As a conse- *
quence, the calculated results are decreasing while measured values
are still increasing. This resulted in a negative correlation
coefficient, R = -0.56. *
Comparison of the calculated and measured results indicate
the calculations would be in better agreement if the stability
were more nearly class C.
-------
B-3
COMPARISON MEASURED AND CALCULATED GROUNDLEVEL VALUES
TEST NO. 3 - UP-CANYON
Location
Deer Cr-Mtnghouse
White Ridged)
(2)
(3)
Wild Draw(l)
(2)
Wild Horsed)
(2)
(3)
(4)
Bear Creek(1)
(2)
(3)
(4)
Red Faced)
(2)
Wet Man(l)
(2)
(3)
Measured
yg/m3
1.7
0.4
3.4
0.3
4.3
2.4
2.2
2.6
1.8
Calculated, yg/m"
INTERCOM?
1.2
0.7
0.7
0.7
1.8
1.4
3.0
2.8
2.5
1.7
2.5
2.6
2.7
2.3
1.6
1.1
1.1
0.2
0.0
EPA GAUSSIAN
0.02
0.06
0.15
0.17
0.34
0.34
0.43
0.04
0.09
0.26
0.34
0.77
0.77
0.86
Comments
Test 3 calculations from the INTERCOM? model are in fair
agreement with the measured results. A more northerly wind
direction than the 135° would have improved the calculated
result. Gaussian results have not reached the peak concentra-
tion within the monitored area. The correlation coefficient
between INTERCOM?'s calculation and the measurements was
0.67.
-------
B-4
COMPARISON MEASURED AND CALCULATED GROUNDLEVEL VALUES
TEST NO. 4 - UP-CANYON
Measured
Location
Deer Cr-Mtnghouse
White Ridged)
(2)
Wild Draw(l)
(2)
Wild Horsed)
(2)
(3)
(4)
Bear Creek(1)
(2)
(3)
(4)
Red Faced)
(2)
Wet Man(l)
(2)
(3)
Calculated, pg/m'
0.2
0.2
0.2
0.2
0.2
0.1
0.4
INTERCOMP
0.1
0.0
0.0
0.1
o.i.
0.2
0.2
0.2
0.1
0.2
0.2
0.2
0.2
0.1
0.1
0.1
0.0
0.0
EPA
0.0
0.0
0.01
0.03
0.03
0.03
0.03
GAUSSIAN
0.0
0.01
0.02
0.03
0.06
0.06
0.06
Comments
Test 4 calculated results from the INTERCOMP model were
generally at the correct magnitude. There were few measured
points available for comparison. This is a high wind neutral
stability case, 10 m/sec. Because the measured concentrations
are so uniform, the linear correlation coefficient came out
negative, R = -0.54, even though the results appear reasonably
good.
-------
B-5
COMPARISON MEASURED AND CALCULATED GROUNDLEVEL VALUES
Location
Deer Cr-Mtnghouse
White Ridge (1)
(2)
(3)
Wild Draw(l)
(2)
Wild Horsed)
(2)
(3)
(4)
Bear Creek (1)
(2)
(3)
(4)
Red Faced)
(2)
Wet Man(l)
(2)
(3)
(4)
TEST NO. 5 -
Measured
yg/m3
0.2
1.2
1.0
1.6
0.8
1.0
1.3
1.2
1.0
0.6
0.7
0.6
0.4
0.3
0.4
0.1
0.1
0.2
UP-CANYON
Calculated, y
INTERCOMP EPA
0.5 0.01
1.0
1.0 0.03
0.5
}'l 0.07
j, • D
1.0
IJ °-°8
1.0
1.0
!• 0 017
1.0 U'i/
1.0
°'5 0 17
0.5 °'1/
0.7
0.6 0 lfi
0.5 °'18
0.1
g/m3
GAUSSIAN
0.02
0.04
0.11
0.15
0.33
0.33
0.37
Comments
Test 5 has been discussed in some detail in the text.
The results are generally good as evidenced by the 0.76 cor-
relation coefficient.
-------
B-6
COMPARISON MEASURED AND CALCULATED GROUNDLEVEL VALUES
TEST NO. 7 - DOWN-CANYON
Measured
Location
0.6 km
1.2 km
Trail(1)
(2)
(3)
(4)
Mill Fork(l)
(2)
(3)
Rilda(l)
(2)
(3)
(4)
Bear Creek(1)
(2)
(3)
(4)
Wet Man(l)
(2)
(3)
(4)
Calculated, yg/m"
INTERCOM? EPA GAUSSIAN
1.0
0.9
1.1
0.3
1.6
0.2
0.2
0.0
0.
0,
0.
0,
0.1
0.0
0.0
0.2
0.3
0.5
1.0
1.5
1.5
0.5
0.8
0.6
0.2
0.1
0.7
0.8
1.0
1.1
0.6
0.5
0.5
0.5
135
43
17
10
770
240
86
58
34
24
24
Comments
Test 7 was the stable down-canyon release, but unlike
the remaining stable cases was an elevated wall release.
The measured results as the photographic evidence indicated
in the Huntington report were considerably influenced by
the flow up the shaded canyon wall. The correlation coeffi-
cient for this test was extremely low, only 0.06.
-------
B-7
COMPARISON MEASURED AND CALCULATED GROUNDLEVEL VALUES
TEST NO. 8 - DOWN-CANYON
Location
0.6 km
1.3 km
Trail(1)
(2)
(3)
(4)
Mill Fork(l)
(2)
(3)
Rilda(l)
(2)
(3)
(4)
Bear Creek(1)
(2)
(3)
(4)
Wet Man(l)
(2)
(3)
(4)
Measured
ug/m3
30
25
27
4
Calculated, yg/m"
5
3
2
1.3
0.8
0.5
INTERCOM?
280
120
23
20
0.5
0.0
5
3
0.5
8
3
0.7
0.0
5
3
2
0.2
1.5
0.3
0.0
0.0
EPA
185
60
25
12
GAUSSIAN
1070
325
120
80
46
33
33
Comments
Test 8 results were in good agreement with the measure-
ments. The linear correlation coefficient for this test was
0.77. Most of the disagreement between calculated and measured
results occurred at the closest two monitor points to the
release point. The peak concentrations in the release must
have flowed around these monitor stations because higher con-
centrations were often recorded downstream. The flow solution
in the INTERCOMP model did not reflect this result.
-------
B-8
COMPARISON MEASURED AND CALCULATED GROUNDLEVEL VALUES
TEST NO. 9 - DOWN-CANYON
Location
0.6 km
1.3 km
Trail(1)
(2)
(3)
(4)
Mill Fork(l)
(2)
(3)
Hilda(1)
(2)
(3)
(4)
Bear Creek(1)
(2)
(3)
(4)
Wet Man(l)
(2)
(3)
(4)
Measured
yg/m3
6
12
24
16
8
7
6
2
12
6
2
Calculated, yg/m"
INTERCOM? EPA GAUSSIAN
90
50
16
2
0.0
0.0
3
0.5
0.0
2
1
0.0
0.0
1.5
1
0.3
0.0
0.5
0.0
0.0
0.0
37
12
210
48
16
11
Comments
Test No. 9 calculations did not agree well with the
measured results. This was one of the tests mentioned as
being more stable than class F. INTERCOM? calculations as
well as the Gaussian results would have been in better agree-
ment if the more stable atmospheric condition has been used.
The correlation coefficient was equal to 0.05.
-------
B-9
COMPARISON MEASURED AND CALCULATED GROUNDLEVEL VALUES
Location
0.6 km
1.2 km
Trail (1)
(2)
(3)
(4)
Mill Fork(l)
(2)
(3)
Rilda(l)
(2)
(3)
(4)
Bear Creek (1)
(2)
(3)
(4)
Wet Man(l)
(2)
(3)
(4)
TEST
Elevation
Ft.
7170
7120
7120
7250
7870
8200
7010
7250
7700
6940
7240
7550
7950
6790
6910
7090
7170
7170
7330
7400
7650
NO. 10 -
Measured
yg/m3
25
35
9.5
19.0
3.7
3.4
6.1
2.1
3.4
2.8
2.0
-
DOWN-CANYON
Calculated,
INTERCOM? EPA
186 105
80 32
15
14 13
0.5 1J
0.0
5.0
2.5 7
0.0
5.5
2.50 4
0.2 *
0.0
3.5
2.5
1.5 J
0.2
1.5
0.5
0.0 J
0.0
3
yg/m
GAUSSIAN
590
180
60
40
25
15
15
Comments
Test No. 10 results were in good agreement with the
measurements. This test is discussed in detail in the text.
The correlation coefficient was 0.74.
-------
B-10
COMPARISON MEASURED AND CALCULATED GROUNDLEVEL VALUES
Location
0.6 km
1.3 km
Trail (1)
(2)
(3)
(4)
Mill Fork(l)
(2)
(3)
Rilda(l)
(2)
(3)
(4)
Bear Creek (1)
(2)
(3)
(4)
Wet Man(l)
(2)
(3)
(4)
TEST NO. 11
Measured
pg/m3
210
210
200
60
130
80
32
2.6
3.0
2.0
0.6
-
- DOWN-CANYON
Calculated ,
INTERCOM? EPA
240 140
103 45
19
18 18
0.5 18
0.0
6.4
5.2 10
0.2
7.1
3.2 fi
0.3 6
0.0
4.5
3.2
1.9 b
0.3
2.0
0.5 ,-
0.0 D
0.0
yg/m
GAUSSIAN
800
250
90
60
35
25
25
Comments
This test was again one of those mentioned as being
more stable than class F. The INTERCOM? calculation again
appears low and would have been in better agreement if a
more stable class could have been used. The correlation
coefficient was 0.68.
-------
B-l I
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1 REPORT NO. 2.
EPA-450/3-75-059
4. TITLE A\D SUBTITLE
Evaluation of Selected Air Pollution Dispersion
Models Applicable to Complex Terrain
7 AUTHOR(S)
Ronald B. Lantz, Antonin Settari, and
Gale F. Hoffnagle
9. PERFORMING ORGANIZATION NAME AND ADDRESS
INTERCOM? Resource Development & Engineering, Inc.
2000 West Loop South, Suite 2200
Houston, Texas 77027
12. SPONSORING AGENCY NAME AND ADDRESS
Office of Air Quality Planning and Standards
Environmental Protection Agency
Research Triangle Park, N.C. 27711
3. RECIPIENT'S ACCESSION-NO.
5. REPORT DATE
Prepared September 18, 197^
6. PERFORMING ORGANIZATION CODE
8. PERFORMING ORGANIZATION REPORT
NO.
10. PROGRAM ELEMENT NO.
2AC 1 29
11. CONTRACT/GRANT NO.
68-02-1085
13. TYPE OF REPORT AND PERIOD COVERED
FINAL July 19,1973-Sept. , 197
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
16. ABSTRACT
A comparison has been made of three models which attempt to predict the
dispersion of pollutants frr situations with complex terrain. The three models
are 1) a Gaussian calculation with terrain assumptions known as the NOAA model,
2) an EPA model, C4M3D also known as the "valley" model, which substitutes dif-
ferent terrain assumptions in the Gaussian calculations, and 3) the INTERCOM?
combined wind flow and plume dispersion model which uses a numerical calcula-
tional method. Predictions made by each of these models are compared to
measurements of ambient concentration data taken in Huntington Canyon, Utah
and at El Paso, Texas. The results indicate that the INTERCOM? model has a
predictive accuracy for terrain situations comparable to that normally expected for
Gaussian predictions in flat terrain, i.e. a factor of two to three. For
stable atmospheres, however, the Gaussian predictions of the NOAA model averaged
a factor of fifteen higher than the measured results.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS C. COSATI Field/Group
Air Pol Iution
Atmospheric Diffusion
Mathematical Models
Terrain Models
Complex terrain
Rough terrain
Model comparison
NOAA model
C^M3D valley model
INTERCOM? air quality
model
13/B
k
1 DISTRIBUTION STATEMENT
Release unlimited
19. SECURITY CLASS (ThisReport)
Unclassi fied
21. NO. OF PAGES
103
20 SECURITY CLASS (Thispage)
Unclassi fied
22 PRICE
EPA Form 2220-1 (9-73)
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