oEPA
United States Environmental Sciences Research
Environmental Protection Laboratory
Agency Research Triangle Park NC 27711
EPA-600/3-84-103
November 1984
Research and Development
Scientific Assessment
Document on Status of
Complex Terrain
Dispersion Models for
EPA Regulatory
Applications
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EPA-600/3-84-103
November 1984
SCIENTIFIC ASSESSMENT DOCUMENT ON STATUS OF COMPLEX
TERRAIN DISPERSION MODELS FOR EPA REGULATORY APPLICATIONS
by
Francis A. Schiermeier
Meteorology and Assessment Division
Environmental Sciences Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, North Carolina 27711
ENVIRONMENTAL SCIENCES RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NORTH CAROLINA 27711
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DISCLAIMER
This document has been reviewed in accordance with U.S. Environmental
Protection Agency policy and approved for publication. Mention of trade
names or commercial products does not constitute endoresement or recom-
mendation for use.
The author, Francis A. Schiermeier, is on assignment to the Environmental
Sciences Research Laboratory, U.S. Environmental Protection Agency, from the
National Oceanic and Atmospheric Administration, U.S. Department of Commerce.
n
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ABSTRACT
The U.S. Environmental Protection Agency is sponsoring the Complex
Terrain Model Development program, a multi-year integrated effort to develop,
evaluate, and refine practical plume dispersion models for calculating
ground-level air pollutant concentrations that result from large emission
sources located in mountainous terrain. The first objective of the complex
terrain program is to develop models with known accuracy and limitations for
simulating 1-hour average concentrations resulting from plume impingement on
elevated terrain obstacles during stable atmospheric conditions.
The completion date for this initial model development effort is October
1986, at which time a validated model accompanied by documentation and user's
guide is to be made available. At the present time, slightly more than
halfway through the effort, a scientific assessment document on the status of
complex terrain dispersion models for regulatory applications has been
prepared to inform potential users of the current availability of complex
terrain dispersion models, and to describe the future products of the Complex
Terrain Model Development program.
This assessment document summarizes the meteorological phenomena of
importance to complex terrain modeling and describes currently available
modeling techniques. Results from selected model evaluation studies and from
related fluid modeling simulations are also presented. Based on this current
state of model development, suggestions are'presented for model improvements
and for current and future research needs. The assessment document concludes
with a summary of major findings and associated conclusions pertinent to the
topic of complex terrain dispersion modeling.
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CONTENTS
Abstract i i i
Figures vi
Tab! es vi i i
Acknowledgements ix
1. Introduction 1
2. Meteorological Phenomena of Importance 6
Plume Interaction with Windward-Facing Terrain Features 6
Plume Interaction with Lee Sides of Terrain Features 15
Dispersion of Plumes in Valley Situations 17
Convective Circulations in Complex Terrain 20
Related Field Study Observations 20
3. Available Complex Terrain Modeling Techniques 28
Val1ey Model 29
COMPLEX I, COMPLEX II, and COMPLEX/PFM Models 30
Rough Terrain Diffusion Model 32
PLUMES Model 32
4141 Model 33
SHORTZ Model 34
Integrated Model for Plumes and Atmospherics in Complex Terrain .. 35
Complex Terrain Dispersion Model 35
VALMET and MELSAR Models 49
4. Results of Model Evaluation Studies 51
TRC Evaluation of Complex Terrain Dispersion Models 51
ERT Evaluation of Complex Terrain Dispersion Models 58
5. Fluid Modeling Studies of Complex Terrain Dispersion 72
Introduction 72
Stable Flow Simulations 73
Neutral Flow Simulations 88
Implications for Model Development 93
6. Model Improvement and Research Needs 94
Use of On-Site Meteorological Measurements 94
Improved Parameterizations of Stably Stratified Flow Trajectories . 97
Improved Parameterizations of Nonstable Flow Trajectories 99
Modeling Needs for Lee-Side Flow Trajectories 100
Flow Field Modeling Needs 101
Valley Ventilation Modeling 102
7. Summary and Conclusions 103
Phenomena of Importance 103
Validation of Available Modeling Techniques 105
Fluid Modeling Simulations 108
Model ing Improvement and Research Needs 110
EPA Regulatory Applications 112
References 114
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FIGURES
Number Page
1 Maximum hourly observed concentrations normalized by emission
rate versus 1-H /H for 153 hours of Cinder Cone Butte
tracer data ......: 12
2 Maximum hourly observed concentrations normalized by emission
rate versus 1-H /H for 34 hours of Hogback Ridge tracer data 12
L o
3 Idealized stratified flow about hills indicating domains of
individual CTDM component algorithms 38
4 Plan view of plume in two-dimensional flow around a hill 44
5 Performance statistics based on residuals of peak observed and
peak modeled concentrations for five models as applied to 153
hours of Cinder Cone Butte tracer data 60
6 Scatter plots of observed and modeled peak concentrations
normalized by emission rates for five models as applied to
153 hours of Cinder Cone Butte tracer data 61
7 Scatter plots of observed/modeled concentration ratios versus
wind speed for four models as applied to 153 hours of Cinder
Cone Butte tracer data 63
8 Scatter plots of observed/modeled concentration ratios versus
ratio of wind speed/Brunt-Vaisal a frequency for four models as
applied to 153 hours of Cinder Cone Butte tracer data 65
9 Scatter plots of observed/modeled concentration ratios versus
1-H /H for four models as applied to 153 hours of Cinder Cone
Butte tracer data 66
10 Scatter plots of observed/modeled concentration ratios versus
product of turbulence intensities for two models as applied to
153 hours of Cinder Cone Butte tracer data 67
11 Schematic diagram of plume behavior in stable flow around a
terrai n obstacle 75
12 Composite estimates of plume paths based on towing tank
simulations of Cinder Cone Butte model 77
13 Predictions (open symbols) and observations (closed symbols)
of dividing-streamline heights as functions of towing speed of
Ci nder Cone Butte model 79
VI
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FIGURES (Continued)
Number Page
14 Dividing-streamline height/hill height ratio from triangular
ridge study expressed as function of Froude number 80
15 Concentration distributions measured on surface for fully-
submerged hill (top) and half-submerged hill (bottom) 85
16 Comparison of surface concentrations for half-submerged versus
fully-submerged hill 87
17 Concentration isopleths (dashed lines) as functions of
dividing-streamline height/hill height ratio and of Froude
number 89
18 Wind rose from Westvaco Luke Mill meteorological tower for
two-year period as compared to Pittsburgh airport wind
directions (solid line) 95
19 Comparison of plume vertical standard deviations estimated
from Equation 34 with those derived from lidar observations
at Cinder Cone Butte for ranges of hourly scan frequencies 96
VII
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TABLES
Number Page
1 Model Performance for Westvaco Data Base 54
2 Model Performance for Cinder Cone Butte Data Base 55
3 Model Rankings Based on TRC Evaluation 56
4 Summary of Residual Statistics for Model Comparison 58
5 CTDM(03184) Modeling Results for Neutral Hours of
Ci nder Cone Butte Data Base 69
6 Terrain Amplification Factors for Two-Dimensional Hills 91
7 Summary of Terrain Amplification Factors for Neutral Flow 92
vm
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ACKNOWLEDGEMENTS
The author gratefully acknowledges the special contributions of the
following individuals to the preparation of this scientific assessment
document.
George C. Holzworth, of the EPA Meteorology and Assessment Division at
Research Triangle Park, was responsible for initiating the EPA Complex Terrain
Model Development program in 1979. Mr. Holzworth provided valuable expertise
and background in the review of this document.
William H. Snyder, also of the EPA Meteorology and Assessment Division,
has been instrumental over the past few years in promoting the role of fluid
modeling in the EPA Complex Terrain Model Development program. During the
preparation of this document, Dr. Snyder furnished an abundance of results
from related experiments performed in the EPA Fluid Modeling Facility.
Bruce A. Egan, of Environmental Research and Technology, Inc. , served as
Chairman of the Workshop on Dispersion in Complex Terrain conducted by the
American Meteological Society in 1983. In this capacity, Dr. Egan provided a
significant amount of material for this document from the Workshop draft
report.
In addition, as the ERT Project Director for the EPA Complex Terrain
Model Development contract, Dr. Egan and his staff contributed much of the
model description and performance evaluation statistics for the newly
developed EPA Complex Terrain Dispersion Model.
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SECTION 1
INTRODUCTION
This assessment document discusses the state-of-science of atmospheric
dispersion modeling for "regulatory use" in regions of mountainous or complex
terrain. For any type of terrain, regulatory applications of air quality
models, as required by the Clean Air Act Amendments of 1977 and by EPA
regulatory processes, place several requirements on the use and application of
dispersion models. First of all, the regulations require that specific
ambient air quality concentrations be maintained at the ground surface which
includes mountain sides and crests. Secondly, the National Ambient Air
Quality Standards (NAAQS) and Prevention of Significant Deterioration (PSD)
increments are specified for various averaging times. For example, sulfur
dioxide (S02) has ambient standards and increments for 3-hour, daily, and
annual averaging periods. Furthermore, the 3-hour and daily ambient standards
or increments for S02 must not be exceeded more than once per year at any
location (these are commonly called the highest, second-highest values).
These attributes of the ambient standards require that dispersion
modeling be applied to meet these needs. In practice, this has generally been
accomplished by requiring that one or more years of appropriate meteorological
data be input to a model and that output files be created to display the air
quality concentration values needed for regulatory decisions. The need to
utilize large quantities of meteorological input data, and the requirement to
compute concentrations for each hour of a year or more, results in substantial
computer costs for codes of significant complexity. Thus, there is
considerable interest in the development of relatively simple and
computationally-efficient algorithms to simulate transport and dispersion
processes.
One of the most difficult regulatory applications for atmospheric
dispersion models is the prediction of ambient air pollutant concentrations
resulting from source releases in regions of complex or mountainous terrain.
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The difficulties arise from the complexity of the source-receptor
configurations and the wide range of unique effects that topography has on
meteorological flows. The problem is important because, for reasons to be
described, the presence of elevated topography often imposes more stringent
limitations on emissions than for a similar source located in flat terrain.
Furthermore, it has been common practice to locate pollutant sources at the
bottoms of river valleys or adjacent to transitions from flat to mountainous
terrain. Of special significance is the fact that a common setting for much
of the energy development activities in the western United States is a source
surrounded by mountainous terrain or at least having sufficiently high terrain
features within distances subject to regulatory applications.
For releases from an elevated source located near terrain that may rise
to elevations greater than the expected plume height, generally the most
critical question is to quantify the magnitude of the plume concentrations
expected on the face of the nearby terrain feature. The notion that the
expected surface concentrations would be much larger than those that would be
anticipated in flat terrain, and could be as large or larger than what would
be expected along the elevated plume centerline, led early modelers (e.g., Van
der Hoven et al., 1972) to develop simple, "direct-impact" models for
computing concentrations on mountainsides. In the absence of more relevant
data, flat terrain dispersion rate information was used. This type of
computation would suggest that under very stable atmospheric conditions,
ground-level concentrations for elevated releases near complex terrain might
be one to two orders of magnitude larger than would be expected in the absence
of the high terrain.
The magnitude of this difference inspired many scientists to examine the
modeling issue more thoroughly. Indeed, over the past decade, a number of
efforts have been undertaken to develop reliable methods for predicting
concentrations in mountainous terrain (Egan, 1984a). In addition, as will be
described in this document, findings that help quantify the differences to be
expected between air quality concentrations in flat versus mountainous terrain
have been identified. These findings include methods for more realistically
estimating dispersion rates as might be modified by the presence of terrain as
well as methods for estimating plume trajectories as affected by terrain
objects.
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In addition to the "plume impact" problem identified above, the presence
of terrain affects air quality concentrations in a number of other ways. For
example, flow separation and ensuing turbulence on the lee sides of mountains
or hills affect the dispersion of releases from sources located downwind of
these terrain features. Snyder (1983) suggested this effect may cause
significant concentrations on the lee side of a hill under neutral stability.
"Channeling" along the axes of river valleys affects the persistence of wind
directions along such valleys. On the other hand, the "sheltering" effects of
terrain features on the air flow within deep valleys often gives rise to
prolonged stagnation episodes in such regions. Thus the complexities
introduced by the presence of significant terrain features are large and the
effects they have on an individual source depend very much on the specific
location of the source, its proximity to terrain, and the specific nature of
the terrain features. Important differences can be expected, for example, for
flow toward isolated features versus flow toward mountain ridges and as a
function of the height of the terrain features relative to expected plume
elevations. The need to have a better technical understanding of the
implications of these effects has been matched by significant attention frorc
the scientific and regulatory communities. In this context, it is relevant to
review briefly three technical workshops that have taken place within the last
several years on these topics.
In 1976, the U.S. Energy Research and Development Administration
sponsored a workshop on "Research Needs for Atmospheric Transport and
Diffusion in Complex Terrain" (Barr et al., 1977). The workshop report
recommended that a multi-year program be initiated to address the air quality
assessment aspects of oil shale development in the western United States and
other energy conversion developments in regions of complex terrain. The
workshop recommendations form the basis for the ongoing Atmospheric Studies in
Complex Terrain (ASCOT) program (Dickerson and Gudiksen, 1980) sponsored by
the U.S. Department of Energy (DOE). This program has focused on the
dispersion of near-surface releases in regions of complex terrain and how such
releases would be affected by mountain-valley circulations and drainage winds.
Field experiments have been performed in the geysers geothermal area of
northern California and in other locations in Washington, Colorado, and New
Mexico. The research efforts will result in a series of descriptions and
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mathematical models for use in assessing the effects of local flows in
dispersing low-level releases in valley situations.
To address the issues of most concern to power plants and other
facilities with significantly elevated releases, the U.S. Environmental
Protection Agency (EPA) sponsored a "Workshop on Atmospheric Dispersion Models
in Complex Terrain" in 1979 (Hovind et al., 1979). Contributions to this
workshop provided the technological basis for a series of field measurements,
fluid modeling experiments, and mathematical model development efforts needed
to develop reliable dispersion modeling techniques for complex terrain
(Holzworth, 1980; Schiermeier et al., 1983b). An outgrowth of the workshop
recommendations is the ongoing EPA-funded Complex Terrain Model Development
program which has as its first objective the development of models with known
accuracy and reliability for simulating 1-hour average concentrations
resulting from plume impingement on elevated terrain obstacles during stable
atmospheric conditions. This topic was chosen in order to focus on a major
regulatory problem upon which available resources could demonstrate
significant progress. Future objectives of the program may include extension
of the complex terrain model development effort to increased topographical
complexity, to neutral and unstable atmospheric stabilities, and to longer
averaging periods.
In 1983 under EPA sponsorship, the American Meteorological Society (AMS)
conducted a "Workshop on Dispersion in Complex Terrain" (Egan, 1984b) for
purposes of evaluating information gained from field measurements, fluid
modeling simulations, and model development efforts undertaken during the past
few years. This particular workshop also provided the opportunity to draw on
the expertise of scientists doing related work but not directly participating
in any major ongoing field experiments.
The Electric Power Research Institute (EPRI) has undertaken a
comprehensive Plume Model Validation and Development (PMV&D) effort (Bowne et
al., 1983) based on extensive field measurements. EPRI has completed
experiments at power plants located in flat terrain and in moderately complex
terrain, and plans to perform an experiment in a full complex terrain setting
where the stack height would be less than the height of nearby terrain.
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The interest and activity in complex terrain modeling is manifested by
the fact that about one-sixth of the papers at recent AMS conferences on
turbulence and diffusion and on air pollution meteorology have related to
complex terrain studies. These papers are about equally divided between
theoretical development and application-oriented topics. Because of the
site-specific nature of much of the work performed to date, a challenge for
researchers in this field is to systematically separate general conclusions
from those findings that are more likely to be very much site specific. This
document will attempt to identify some of the most significant general
advances in our understanding of this topic.
The remainder of this report will describe the status of complex terrain
modeling, with attention paid to aspects of the problem pertinent to EPA's
regulatory applications of dispersion models. The document will identify and
describe the meteorological dispersion phenomena of most importance in complex
terrain, drawing heavily from the findings of the 1983 AMS workshop on this
topic. Available modeling techniques applicable to regulatory needs will be
summarized, and evaluation studies performed to date on applicable models will
be described. The application of fluid modeling techniques will be discussed,
focusing on the contributions that these studies have made to the
understanding of flow dynamics as affected by terrain features. Directions
for model improvements and future research needs will be identified.
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SECTION 2
METEOROLOGICAL PHENOMENA OF IMPORTANCE
In this section, meteorological phenomena that are of special importance
(if not unique) to the problem of estimating air quality impacts of sources
located in or near complex terrain are described. Because the descriptions
often suggest or reflect mathematical algorithms, these are presented here as
appropriate. In the remainder of this document, the term "hill" is used
generically, with two- and three-dimensional ridges considered as specific
types of hills.
PLUME INTERACTION WITH WINDWARD-FACING TERRAIN FEATURES
Flow Parameters Affecting Plume Trajectories
If a stack is located near a hill that is taller than the stack, the
possibility exists that the highest concentrations to be expected in the area
will occur on the hillside when the airflow is from the stack toward the hill.
These high concentrations would be expected either by direct plume impaction
during certain stable conditions, or by near misses as the streamlines pass
close to the hill during other stable, neutral, or unstable conditions.
The presence of mountainous terrain has several effects on the flow
upwind of and above the obstacles. Terrain acts to distort the flow field
causing deflections, accelerations/decelerations, and associated contractions/
expansions of "stream tubes" of air. It also acts to alter the structure of
turbulence within the region of flow near the surface. The dynamics of the
flow field upstream of a hill depends critically on the ambient density (or
temperature) stratification. In stable conditions, vertical motions of air
parcels are opposed by restoring buoyancy forces. The stratification effect
can be characterized by a Froude number, Fr, given by
Fr = U/Nh (1)
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where U is a characteristic wind speed for the upstream flow; N is the
Brunt- Vai sal a frequency given by
N = [-(g/p)Op/az)]S (2)
g is the gravitational acceleration; p is the air density; and h is the hill
height. The Froude number squared can be interpreted as a ratio of inertial
to buoyancy forces in a fluid. Moderate to neutral stability (dominated by
inertial effects) includes the range 1 < Fr < », whereas strongly stable
conditions (dominated by buoyancy effects) encompass the range 0 < Fr < 1.
One of the outstanding features of strongly stable flow about
three-dimensional hills is the passage of fluid around the hill in essentially
horizontal planes below some height H , which depends on the stratification.
Above this height, fluid passes both over and around the hill. The height H
\f
is commonly called the "critical height" or "dividing-streamline height". The
idea of a region of horizontally layered flow was first described
theoretically by Drazin (1961) for axi symmetric hills and was later confirmed
in laboratory experiments for similar geometries by Riley et al. (1976),
Brighton (1978), and perhaps most convincingly by Hunt et al. (1978). The
last authors showed experimentally that for a uniform upstream velocity
profile and a constant density gradient, H is given by
Hc = h(l-Fr). (3)
This formula is consistent with a simple energy balance argument for an
air parcel as first put forth by Sheppard (1956). Sheppard postulated that
for a given environmental lapse rate, one could calculate the value of
horizontal velocity far upwind that would enable air to just surmount a hill
by equating the kinetic energy of a fluid parcel upwind to the potential
energy change associated with lifting the parcel to the hillcrest. Snyder et
al. (1982) have extended this argument to arbitrary velocity and density
profiles with the result
|pU2(Hc) = g J (h-z) (-ff)dz
He
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where H must in general be determined iteratively.
L.
For ideal two-dimensional ridges or very long finite ridges, the fluid
can be blocked (i.e., effectively become stagnant) ahead of the obstacle. For
these geometries, a well-accepted formula for the dividing-streamline height
does not yet exist. In addition, there is ambiguity about the upstream extent
of this blocked region and its variation in depth with upstream distance.
The simple energy argument of Sheppard (1956) assumes that an air parcel
has a zero horizontal velocity at hilltop. However, this assumption is
inconsistent with observed flow fields which show that fluid flow accelerates
at the top of the hill. A more complete model is required to explain
adequately this speedup phenomenon and to ensure reliable extension of the H
concept to geometries more complex than simple hill shapes. For example, if
the stratification continues to the mountaintop (h), the hydrostatic solution
of Smith (1980) is probably more applicable than potential flow solutions.
The main difference is an earlier lifting of the flow (perhaps decreasing the
windward-side concentrations).
At elevations below H , the straight-line flow will be deflected by the
terrain feature. The plume will tend to go to one side or the other and may
oscillate back and forth, being very sensitive to upstream flow direction.
Large ground-level concentrations are expected near this level as well as
large apparent lateral diffusivity.
Dispersion in Strongly Stratified Flow
Strongly stratified flow below H has insufficient kinetic energy to pass
over a hillcrest and, neglecting wind shear effects, such flows can be
considered essentially horizontal as they pass around a hill. When a plume is
directly along the stagnation streamline, the plume will "impinge" on the hill
resulting in concentrations as large as those in the elevated plume's center.
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Along the stagnation streamline, flow diverges as it approaches the hill.
Hunt et al. (1979) show that the large increase in the crosswind dispersion
coefficient, a , caused by diverging streamlines, is almost compensated by the
decrease in wind speed, U, as the stagnation point is approached, and that at
the stagnation point, a U is approximately the same as it would have been in
the absence of the hill. These arguments suggest that the concentration at
the stagnation point is approximately equal to that which would occur in the
plume without the hill. However, effects of plume meander due to larger-scale
eddies in the flow upwind of the hill need to be considered explicitly as
described below.
Surface concentrations at an assumed point of impingement or stagnation
can be estimated during plume meandering conditions by integration over the
changes in wind direction. During any single quasi-steady period, denoted by
the subscript i, the concentration at the stagnation point due to a plume with
horizontal angular spread of a . will be nonzero only if the mean wind
direction during the period lies within a ./2 of the stagnation streamline (6.
51 I
= 0 ± a ./2). If this concentration is denoted by C.(8,6 ), then the average
9 O I IS
hourly concentration C at the stagnation point is given by
c = Jci(e,es)p(e)de (5)
e
where P(6) is the hourly probability density function of wind directions. If
the wind speed, vertical plume spread, and horizontal plume spread angle are
nearly constant among quasi-steady periods during the hour, then the only
nonzero contributions to the integral in Equation 5 arise for wind directions
within ±a/2 of the stagnation wind direction. Furthermore, if the
concentration distribution within the plume during each quasi-steady period is
assumed to be uniform, and if the spread due to plume meander during the hour
is much greater than a , so that P(6) is nearly constant within the interval
a , then
6.+a/2
- f
C = C. I P(6)d6 = C.P(8d)as (6)
J6d-as/2
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where C. = QA/27t o~2
U, a and a represent averages for the relevant hour; and x is the distance
from the release to the stagnation point. Note that if P(0) is Gaussian, then
C = y exp
(7)
where aQ is the standard deviation of the wind direction about the mean
D
direction 6 . In practice, P(6) is specified by the histogram of observed
distribution of winds during each hour.
Experimental Evidence
Snyder et al. (1982) have demonstrated the validity of the integral
formula (Equation 4) using laboratory simulations under stably stratified
conditions. These tests were made at the EPA Fluid Modeling Facility at
Research Triangle Park, North Carolina and in the stratified wind tunnel at
the Japan Environment Agency. The concept of H was examined for bell-shaped
hills, a cone and hemisphere, triangular ridges, vertical fences, and for a
scale model of Cinder Cone Butte. Snyder and his co-workers have concluded
that the integral equation for estimating H accurately predicted the
separation of the flow regimes.
The EPA-sponsored Small Hill Impaction Studies, conducted at Cinder Cone
Butte near Boise, Idaho and at Hogback Ridge near Farmington, New Mexico
(Lavery et al., 1983a), have also shown that the integral formula for HC
discriminates between the flow regimes for both an isolated axisymmetric hill
(Cinder Cone Butte) and a two-dimensional ridge (Hogback Ridge). Photographs
of oil-fog plumes along with SF6 (sulfur hexafluoride) and CF3Br
(trifluoromonobromomethane) ground-level concentration patterns clearly
distinguished between the horizontal flow and the flow that goes over the
hills. The H concept and its ability to predict whether plumes impinge upon
a hill and pass around it, or travel up and over a hill, were also found by
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Ryan et al. (1984) to be valid at Steptoe Butte, a large isolated hill in
eastern Washington; by Rowe et al. (1982) at Copithorne Ridge, a 6-km long
ridge in Alberta; and by Wooldridge and Furman (1984) at San Antonio Mountain
in New Mexico.
An analysis of the observed tracer gas concentrations and the
meteorological data obtained at Cinder Cone Butte showed that the highest C /Q
(concentration/emission) occurred when the release height, H , was near or
slightly higher than H . During this situation, the plume was transported
directly toward the hill and produced high ground-level concentrations. Lower
elevation releases tended to be transported around the hill sides and releases
well above H were transported up and over the hi 11 crest. Figure 1 shows the
t»
CQ/Q values versus 1-H /H for each hour of Cinder Cone Butte tracer data.
The highest normalized concentration occurred when H ~ H .
o *•*
The Hogback Ridge experiment also showed that H discriminates between
the flow regimes, although the nature of the flow below H is still under
I*
investigation. A preliminary analysis of 34 tracer-hour concentrations showed
that the highest observed C /Q occurred when H < H as shown in Figure 2.
Since Hogback Ridge is basically two-dimensional, the higher values could be
explained by the highly variable and generally stagnant flow below H and, if
L*
the average wind were directed toward the ridge, the tracer gas would be
transported directly to a sampler near the release elevation.
Thus, there appears to be consistent agreement between field and
laboratory observations on the flow structure upwind of a three-dimensional
hill, in particular the horizontal nature of the flow below H and the
dependence of H on stratification. This is true for axisymmetric hills and
for hills with small aspect ratios where width/height ~ 10 (Snyder et al.,
1982). Field experiment verification is still needed to confirm the validity
and applicability of the dividing-streamline concept for terrain features
greater than a few hundred meters in height.
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160.0-
140.0
120.0
100.0
\ 80.0-1
o
O
60.0
40.0
20.0
.0
-2.00
-1.50
-1.00
-.50
1-HC/HS
.00
CFoBr
V
.50
1.00
Figure 1. Maximum hourly observed concentrations normalized by emission rate
versus 1-H /H for 153 hours of Cinder Cone Butte tracer data.
400.0
350.0-
300.0
(A
3.
O
250.0
X0 200.0 -
O
150.0
100.0
50.0
.0
-3.0
-2.0
-1.0
.0
CFBr
•*» *
• * • - * *«
* * « - *
1 0
Fiqure 2. Maximum hourly observed concentrations normalized by emission rate
versus 1-H /H for 34 hours of Hoqback Ridge tracer data.
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Flow Over Terrain During Neutral Conditions
It is generally accepted that the first-order effects of terrain on
altering the flow on the windward face during neutral conditions can be
estimated using modifications to potential flow theory (Hunt and Mulhearn,
1973; Hunt et al., 1979). For regulatory applications, a practical approach
involves the superpositioning of Gaussian plume spread onto trajectories
determined by potential flow approximations (Isaacs et al., 1979; Hunt et al.,
1979). Egan (1975) demonstrated that the "half-height" terrain correction
factor followed from considerations of potential flow over a sphere, but a
"terrain-following" plume assumption provided first-order estimates for
neutral flow over a two-dimensional (ridge-like) shape. Neutral conditions
often are associated with high wind speeds and synoptically persistent
meteorological conditions. Thus, neutral conditions can be of importance to
the maintenance of 24-hour average ambient air quality standards or Prevention
of Significant Deterioration (PSD) increments, especially where channeling
effects of terrain features are important.
Dispersion During Unstable Conditions
For most regulatory applications, "worst case" conditions for sources
close to high terrain are expected to occur during stable or neutral
conditions. For this reason, phenomena during unstable conditions have not
been studied in depth. Because of the differential heating of mountain slopes
during daylight hours, convection effects result in sustained and significant
updrafts and downdrafts. Also "fumigation" of pollutant material onto
hilltops in mid to late mornings has been observed to result in short
durations of high concentrations. For unstable conditions, currently
available models generally use the flow trajectories derived for neutral
dispersion.
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Turbulence Levels in Regions of Complex Terrain
In general, turbulence levels are expected to be higher over complex
terrain than over level terrain for a given atmospheric stability class,
itself sometimes difficult to estimate reliably over the depth of flow. These
enhanced turbulence levels are most likely a result of three factors:
(a) Nocturnal, radiational cooling that produces surface inversions is often
coupled with very low wind speeds in level terrain and is likely to
result in the generation of gravity-driven drainage flows in complex
terrain. These flows result in the mechanical production of turbulence
and time-dependent, nonstationary secondary motions which periodically
sweep the terrain. It is likely that peak concentrations result from
these time-dependent movements rather than from the near-stationary
drainage flows.
(b) Topographic alteration of flow direction and speed will result in the
production of shear in all directions, which not only contributes to the
production of turbulence but results in large flow meandering.
(c) In complex terrain the presence of flow stratification is a key element
in the production of rapid flow accelerations and decelerations, lee
waves, and rotors, which tend to produce shearing motions and regions of
flow reversal. During neutral and unstable atmospheric conditions, the
effects of terrain on altering turbulence levels appear to be smaller
than during stable conditions (Start et al., 1974).
Lateral turbulence levels in complex terrain are generally enhanced to a
greater extent than vertical turbulence. Observations of smoke plume
meandering and uplifting are reasons cited to justify an increase in
horizontal dispersion rates. When the atmosphere is stably stratified,
generalizations are more difficult. Air parcels downwind of a ridge may be
rapidly dispersed upward (or even upwind) by rotor zones or other eddy motions
associated with lee-side phenomena (Van Valin et al., 1982). Under stable
conditions, ridge-shaped terrain features can contribute to large-scale
stagnation of the air flow in lower upwind regions, resulting in very low
winds with little net transport of pollutant material into or out of the
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region. This topic will be discussed further in the context of phenomena
within valleys.
PLUME INTERACTION WITH LEE SIDES OF TERRAIN FEATURES
Previous discussion has focused on the phenomena of importance in
determining ambient air quality concentrations on upwind-facing slopes. Fluid
modeling shows that high concentrations can also be expected for certain
meteorological conditions on back-facing or leeward slopes of terrain features
downwind of a source. Field measurements are uncommon for these situations
because regulatory requirements have generally focused on gaining information
on the upwind-facing slopes nearest to a pollution source. This section
provides a brief overview of the current understanding of flow in the lee of
hills.
Lee-Side Flow During Neutral Conditions
Simple flow models, e.g., potential flow coupled with rapid distortion
theory, work reasonably well for predicting surface concentrations on the
upwind faces of hills, both two-dimensional and three-dimensional. However,
these simple models are inadequate for predicting wake effects, even for hills
of moderate slope (i.e., 15° for two-dimensional and 25° for three-dimensional
hills), let alone for steep hills with separated wakes. Flows on the lee
sides of hills are among phenomena expected to cause high ground-level
concentrations in the vicinity of terrain and for which no routine model
simulation techniques are available.
Snyder (1983) summarized a variety of idealized neutral-flow wind tunnel
studies in which plumes from stacks located both upwind and downwind of
various terrain shapes produced ground-level concentrations on or downwind of
the obstacle many times higher than would be expected if the terrain were not
present. When expressed in a ratio, this increased concentration over the
no-obstacle concentration is termed the "terrain amplification factor",
specifically defined as the ratio of the maximum concentration occurring in
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the presence of the hill to the maximum concentration that would occur from
the same (elevated) source if it were located in flat terrain.
Fluid modeling experiments in simulated neutral atmospheric boundary
layers showed that plumes released downwind of variously shaped
two-dimensional hills resulted in amplification factors as large as 10 to 15,
whereas plumes released upwind of the hills produced factors of 2 to 3 (see
Section 5). Two lee-side phenomena were observed to produce high factors.
One was downwind of a relatively steep hill (26°) where the flow separated
steadily near the top of the lee side and reattached on the surface downwind
of the base. In this case, pollutants from sources located on the
separation/reattachment streamline were advected directly to the ground,
producing very large terrain amplification factors.
The other case was downwind of a hill of moderate slope (16°). Here, the
flow separated intermittently but not in the mean. Pollutants downwind of
this hill were thus subjected to very small mean transport speeds and very
large turbulence intensities. This resulted in rapid diffusion directly to
the surface and consequently to large amplification factors. High
amplification factors were also observed on the lee sides of three-dimensional
objects, especially when plumes were released near the separation-reattachment
streamlines. In the three-dimensional cases, higher across-wind aspect ratios
generally produced higher terrain amplification factors.
Fluid modeling results indicate that typical downwind lengths of reversed
flow regions are 10 hill heights for two-dimensional hills and 2 to 10 hill
heights for three-dimensional hills. In addition, strong trailing vortices
downwind of three-dimensional hills have been observed in laboratory studies.
The strong downwash caused by these vortices has also resulted in large
surface concentrations.
Stratified Flow in Lee of Hills
Under strongly stratified flows, effluents released below the dividing-
streamline height on the lee sides of hills have been observed to be
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recirculated to the hill surface and to cover a narrow vertical band spread
over a nearly 180° sector of the hill surface. Whereas instantaneous
concentrations from downwind sources are observed to be considerably lower
than impingement concentrations from upwind sources, long-term average
concentrations from these downwind sources may be larger than impingement
concentrations because the wind meander will significantly reduce
time-averaged impingement concentrations, but not the lee-side concentrations.
Even simple models for predicting lee-surface concentrations from downwind
sources are not readily available.
DISPERSION OF PLUMES IN VALLEY SITUATIONS
Many air pollution sources such as cities, roads, industrial operations,
and energy production facilities are located in mountain valleys. It has been
recognized for at least 40 years (Hewson and Gill, 1944) that air pollution
problems can arise from these sources as a result of the special meteor-
ological processes that occur in valleys.
The AMS workshop attendees separated the discussion of the dynamics of
individual plumes interacting with high terrain from discussions of these
latter special flow conditions associated with valley settings (Egan, 1984b).
The processes identified as important to valley situations include nocturnal
drainage flows, fumigation, flow channeling by valley sidewalls, and
persistent low wind speed, stable flows. For purposes of discussion, it is
convenient to distinguish between relatively shallow valleys, deep draining
valleys, and closed valleys.
Shallow Valleys
Shallow valleys are defined by comparison with the effective height of a
plume from a source affecting air quality in the valley. A valley is shallow
if the plume is significantly higher than the terrain features. Under these
conditions, the plume is cut off from the valley boundary layer during stable
conditions and reacts in a manner analogous to a plume over flat terrain.
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Although the trajectory of the plume may be steered somewhat by the valley
orientation, the centerline of the plume is higher than the valley sides or
ridges forming the valley.
Preliminary results from the EPRI PMV&D project tracer studies at the
Bull Run Generating Station in Tennessee indicated that terrain influences on
lifting of plume paths were not observed because the plumes from the facility
usually followed trajectories that were parallel to the valley axes. The
PMV&D measurements were made when the plume centerline was significantly
higher than the terrain features (Reynolds et al. , 1984).
Deep, Draining Valleys
Scientific investigations have thus far focused primarily on improving
our understanding of the physics of valley meteorology, although a few
important research studies have focused directly on air pollution
investigations (e.g., Hewson and Gill, 1944; Start et al., 1975). An improved
understanding of valley nocturnal drainage flows is now becoming available
from the DOE ASCOT program (Dickerson and Gudiksen, 1983; Gudiksen and
Dickerson, 1983). Other work has focused on the breakup of nocturnal valley
temperature inversions in deep valleys (Whiteman, 1980). This work has led to
a thermodynamic model of temperature inversion breakup (Whiteman and McKee,
1982) and more recently, to an initial model of air pollution concentrations
produced on the valley floor and sidewalls due to post-sunrise fumigations of
elevated nocturnal plumes (Whiteman and Allwine, 1983). In these studies, the
effects of convective boundary layers that grow over heated valley surfaces
after sunrise, the effects of upslope flows produced over the sidewalls, and
the effects of compensating subsiding motions over the valley floor have been
simulated but need more field evaluations.
In actual valleys, topographic complications can be expected to greatly
influence the development of local circulations and the dispersion of
pollutants emitted within the valley. The diversity of valley shapes,
orientations, and the presence of tributary valleys and terrain constrictions
along the valley axes can be expected to influence the development of the
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along-valley circulations, turbulence levels, and other important aspects of
valley meteorology.
Closed Valleys
Certain valleys with weak or obstructed outflow have been characterized
as trapping valleys, in contrast with draining valleys with vigorous outflow.
The accumulation of cool air draining from the sides of the trapping valleys
will build up a deep stable layer during nighttime hours that is capped by a
stronger inversion at the interface with the above-valley air near the top of
the cold pool. Pollution plumes emitted into this domain are likely to be
confined within this temperature structure and the valley sidewalls.
In addition to diurnal trapping regimes, certain synoptic conditions
produce stagnation episodes. High pressure systems characterized by low wind
speeds, clear or foggy skies, subsidence inversions, and nocturnally-produced
ground-level inversions, may exist for 4- to 5-day periods. During these
episodes, additional emissions are not compensated by flushing so that air
quality continually degrades. The pollution conditions are not stationary as
is evidenced by sloshing of pollution centers around the valley. The DOE
ASCOT program characterized diurnal pooling and stagnation within one
California valley in 1979 and 1980 (Gudiksen and Dickerson, 1983).
The shape of a closed valley creates unique flow regimes. Limited field
data show that nighttime radiational cooling of the surrounding mountain
slopes can create a downslope drainage flow that appears to reach maximum
strength just prior to local sunrise. The drainage flow tends to move toward
the lowest point in the valley. Available data are inadequate to determine if
a gyre usually develops over the valley low point prior to sunrise. Other
observations indicate that material released at ground level within a closed
valley at night can be transported out of the valley, a phenomenon that is
difficult to explain physically. More information is needed to permit a
quantitative description of the behavior of effluents released into thermally
stratified closed valleys.
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CONVECTIVE CIRCULATIONS IN COMPLEX TERRAIN
In flat terrain, convective flows frequently lead to the fumigation of
pollutants trapped aloft or the early downwash of a looping plume, resulting
in high ground-level concentrations. Convective flows developing over hills,
ridges, or more complicated terrain may significantly alter streamline
patterns, separation and stagnation locations, and hill wake turbulence. It
is possible that nonhomogeneous radiative heating caused by slope orientation
could result in different convective scales than commonly associated with
horizontal terrain. These perturbed spatial and temporal scales could result
in worst-case ground-level concentrations from lee impingement, sudden
subsidence, or downdrafts.
RELATED FIELD STUDY OBSERVATIONS
Most of the complex terrain meteorological phenomena described in this
section have been observed in various field studies conducted during the past
couple of decades. The more recent studies have been designed specifically to
advance the science of complex terrain modeling, while some of the earlier
studies were performed primarily to determine the efficacy of tall stacks in
reducing nearby ground-level pollutant concentrations. In the remainder of
this section, a few of these field studies are described to illustrate actual
observations of the meteorological phenomena important to complex terrain
plume dispersion.
Large Power Plant Effluent Study
The EPA conducted a comprehensive field study in western Pennsylvania
between 1967 and 1972 to determine the extent and effects of power plant
emissions from tall stacks at the Keystone, Homer City, and Conemaugh
Generating Stations (Schiermeier, 1972a, 1972b). The meteorological portion
of the Large Power Plant Effluent Study (LAPPES) was conducted along three
interrelated lines of investigation: (1) determination of plume rise under a
variety of atmospheric conditions; (2) determination of plume dispersion,
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both vertical and horizontal, as a function of downwind distance and
atmospheric conditions; and (3) determination of the magnitude, area! extent,
and occurrence frequency of S02 concentrations at ground level.
A distinct advantage of this location for the study was that air quality
measurements progressed as each stack of each generating station became
operational. The 1967 and 1968 LAPPES field studies were conducted in an area
surrounding the Keystone Station. Beginning in 1969, the project area was
expanded to encircle the Homer City Station as it became operational, with
similar expansion effected in 1970 to include the Conemaugh Station.
The generating stations are located in the Chestnut Ridge sector of the
Allegheny Mountains. Typical of this area of Pennsylvania are numerous creeks
and rivers, and rolling hills rising 100 to 200 m above the valley floors.
This land, much of which is tree covered, slopes generally upward to the east
to form the foothills of the Allegheny Mountains. Prominent features include
the Chestnut Ridge, oriented northeast-southwest and situated between the
Homer City and Conemaugh Stations, and the considerably higher Laurel Ridge
immediately southeast of the Conemaugh Station.
The Conemaugh Station was most susceptible to topographic influences.
Separating this plant from Johnstown is the Laurel Ridge with some peaks
within 6 km ranging up to 200 m above the two 305-m tall stacks. During the
October 1970 measurement series, and to a lesser extent during the October
1971 series, helicopter and ground-based measurements confirmed the unique
dispersion characteristics in the area. With moderate to strong flow from the
southeast quadrant, the plume was brought to the surface within a few hundred
meters of the stacks. The S02 concentrations at the surface rapidly
diminished with distance to the northwest but increased slightly on the lee
side of Chestnut Ridge, about 12 to 14 km from the Conemaugh Station. In
addition to ground-level SQ2 measurements, this downwash on the lee side of
Laurel Ridge was confirmed by actual subsidence of pilot balloons in the
vicinity of the Conemaugh stacks.
Accompanying this downwash phenomenon was a persistent cloud cover over
the Conemaugh Station, caused by upslope action over Laurel Ridge. Observed
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cloud bases varied between 450 and 650 m above stack base elevation with
coverage ranging from scattered to overcast, although usually broken. This
cloud deck frequently extended as far northwest as Chestnut Ridge, with clear
skies beyond. The lee downwash appeared to be associated with neutral flow
because on days when the cloud cover dispersed sufficiently to allow surface
heating, the downwash ceased and the plume rose in a normal manner.
With winds from the opposite direction, i.e., the northwest quadrant, the
plume rose over Laurel Ridge and apparently mixed through a deep layer in the
lee of the ridge; relatively low concentrations were measured from ground
level to the upper limit of sampling imposed by cloud bases. If a lee-wave
phenomenon existed with northwest winds, it was not detected by the prevailing
sampling methods.
During the April 1971 series, the Conemaugh plume was discovered to be
intercepting ridges at considerable distances from the plant (11 to 20 km) and
flowing smoothly down the lee side for about 1 or 2 km before rising again.
That this phenomena was not confined to a particular wind direction was
evidenced by the various azimuths of occurrence, i.e., 275, 327, 353, and 060
degrees Two meteorological characteristics common to all four occurrences
were the presence of strong surface inversions near the Conemaugh Station
shortly after sunrise and the sudden disappearance of the high ground-level
S02 concentrations in the lee of the ridges as surface heating commenced.
Widows Creek Power Plant Study
The Tennessee Valley Authority (TVA) increased the stack heights at their
existing power plants during the 1970's in an effort to mitigate the problems
of plume impingement on surrounding high terrain. However, the presence of
the underlying complex terrain still affects general wind-flow patterns and
turbulence levels at plume height. Data from TVA's Widows Creek Power Plant
in Alabama were studied to determine these effects (Hanna, 1980). This plant
is in a river valley with ridges rising 300 m above the valley floor at
distances of 3 km from the plant. Stack heights are 152 m and 305 m.
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The most obvious effect of the terrain was a strong channeling of the air
flow in the valley, with cross-valley winds occurring only a small percentage
of the time. In contrast, at plume elevation (ridge-top and above) the
observed wind rose showed nearly uniform frequencies for all directions. If
the wind-direction data from the valley meteorological tower were used to
model environmental effects, they would obviously give a distorted picture of
the true impact of the plume.
The second important effect of the terrain was an enhancement of
turbulence (as measured by afi) for cross-valley wind directions. By plotting
observed aQ as a function of wind direction for neutral conditions, it was
determined that cross-valley afl observations were about 60% larger than
along-valley aQ observations. This increase was probably due to the presence
of persistent low-frequency eddies set up by the hills. The use of observed
QQ values in Pasquill's formula, a = aQ x f(x), results in good agreement
with or determined from S02 concentration observations at monitors located on
the nearby ridge.
Steptoe Butte Field Study
, An EPA-sponsored study of wind flow and diffusion around an isolated
335-m hill (Steptoe Butte, Washington) was conducted in 1981 by scientists at
Washington State University. The aims and experimental methods of this
project were similar to those of the EPA Cinder Cone Butte experiment. The
main differences between the two experiments were that there were limited
meteorological profiles at Steptoe Butte, but a wider range of atmospheric
stabilities was considered. Also, there were no measurements of the plume
aloft at Steptoe Butte. Twenty-one tracer tests were conducted, with release
heights ranging from the surface to about 190 m. A description of the
experiments with results of preliminary analysis of the data is given by Ryan
et al. (1984) and an analysis of the dividing streamline is discussed by Ryan
and Lamb (1984). Testing of diffusion models with the data is not yet
complete.
A qualitative analysis of the maximum plume impact showed that more than
half of the concentration maxima occurred on the leeward half of the hill,
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although highest concentrations occurred on the upwind half. The position of
the maxima rapidly shifted to the side of the hill as the horizontal
displacement of the source from the flow centerline increased. The magnitude
of these concentrations agrees fairly well with the predictions of potential
flow models for flow around a cylinder or a hemisphere.
Ryan and Lamb (1984) pointed out that the vertical temperature structure
at Steptoe Butte was more complex than at Cinder Cone Butte and attributed
this difference to the greater hill height (335 m versus 100 m). This
complexity influenced the calculation of the dividing-streamline height, which
is a function of the Froude number. Several approaches were tried, including
the use of a single hill Froude number (calculated over the full hill height),
a local Froude number (calculated using local temperature gradients), and
iterative solutions of the energy equation. The last method was found to be
more appropriate for stable conditions with complex vertical temperature
structures.
Tracy Power Plant Preliminary Study
The Tracy Power Plant near Reno, Nevada has been selected as the site for
the 1984 Full Scale Plume Study, the third field experiment in the EPA Complex
Terrain Model Development program. The Tracy plant is operated by Sierra
Pacific Power Company. It has three units capable of generating 53, 80, and
120 megawatts (MW). . The 120-MW unit is serviced by a 90-m stack which was
used to release oil-fog and SF6 during a preliminary experiment in 1983.
The plant is located about 40 km east of the Reno-Sparks metropolitan
area in the Truckee River Valley of the Sierra Nevada Mountains. Peaks rise
to elevations of 900 m above the stack base elevation within 6 km of the
plant. The Truckee River enters the valley through a narrow opening, flows
eastward just north of the plant, and then takes an abrupt turn to the north
about 4 km east of the plant. The river flows between two mountains at its
northward bend. The two mountains were the primary target areas for the
dispersion experiments.
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The preliminary flow visualization and tracer study that was conducted
during November 1983 was co-sponsored by the EPA and EPRI. The experimental
methods were similar to those used and tested at Cinder Cone Butte and Hogback
Ridge and at the two previous EPRI field sites. Ten experiments were
conducted for 73 hours during the preliminary study.
An analysis of the data base suggested the occurrence of stable plume
impingement. SF6 concentrations were observed during stable conditions on the
target mountains east of the plant as well as on the hills to the west. The
highest SF6 concentrations were observed on the southwest corner of one target
mountain. The elevations of the samplers that captured plume material were a
few meters below the calculated hourly values of H . During other hours of
stable plume impingement conditions, plume material was observed to stay below
H . In short, it appears that the concept of a dividing-streamline height
will be useful to distinguish flow regimes and to help simulate observed
tracer gas concentration patterns in the Tracy area.
Drainage winds and katabatic effects were seen to produce ground-level
concentrations on the valley floor in the gorge where the Truckee River bends
to the north. Visual observations, photographs, and acoustic sounder records
all suggested the turbulent transport of "old" plume material from aloft to
the valley floor. The fumigation of oil-fog by drainage winds was also
observed on the south side of one target mountain. These katabatic effects
were not observed at Cinder Cone Butte or Hogback Ridge and must be accounted
for in modeling this full-scale site.
The meteorological measurements depicted very complicated wind flows
during the November experiments. Horizontal and vertical wind shears were
common. These were probably caused by the combined effects of the complex
terrain and migratory anticyclones and cyclones moving over the area in
November. Persistent, windy neutral conditions produced ground-level
concentrations in the area south of the target mountains. These conditions
are similar to those in flat terrain, high-wind cases. The elevated terrain
often channeled plume material between peaks and through low-lying draws, as
verified by observations and photographs.
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In summary, the Tracy preliminary study captured a variety of
meteorological events and dispersion conditions. Stable flows, which can be
described by the dividing-streamline concept observed at Cinder Cone Butte and
Hogback Ridge, were also observed at the Tracy site. Other events, e.g.,
drainage winds and terrain channeling, more common to "full-scale" sites were
also observed. For these reasons, the Tracy data base is expected to be
useful in testing new dispersion concepts and in extending the modeling to
conditions typical of a full-scale site (Strimaitis et al., 1984).
Brush Creek 1982 Field Tracer Study
A set of atmospheric tracer experiments was conducted during the summer
of 1982 as part of the EPA Green River Ambient Model Assessment program.
These experiments were performed in the Brush Creek Valley of Colorado in
conjunction with the DOE ASCOT research program. The EPA portion of the field
study was designed to provide an evaluation of the initial version of the
VALMET model being developed by Pacific Northwest Laboratory.
The Brush Creek Valley is a narrow 650-m deep, near-linear valley having
no major tributaries. The valley, which drains the Roan Plateau, is a main
tributary to Roan Creek and is located approximately 50-60 km northeast of
Grand Junction, Colorado. In the Brush Creek experiments, elevated continuous
releases of SF6 were made from a dual tethered balloon release system above
the valley floor center, approximately 10 km up-valley from its confluence
with Roan Creek. Releases were effected on three clear or partly cloudy
mornings beginning at 0400-0500 local time from heights near 105 m. The
releases were continued for 3 to 6 hours to determine how concentrations on
the valley floor and sidewalls would change following sunrise during the
temperature inversion breakup period.
SF6 concentrations were detected down-valley from the release point using
an array of radio-controlled bag samplers, a balloon-borne vertical SF6
profiling system, and two portable gas chromatographs operated on one sidewall
of the valley. One continuous real-time SF6 monitor was operated on the
valley floor and another onboard a research aircraft. The initial analyses
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of the experiments can be summarized as follows:
(a) The early morning plume was carried down Brush Creek by the nocturnal
down-valley wind system. The plume was contained almost entirely in the
lowest 250 m of the valley where the temperature inversion was strongest.
The elevated plume roughly paralleled the valley floor, although it rose
somewhat relative to the floor.
(b) Diffusion of the nocturnal plume during its down-valley travel was
particularly marked in the vertical direction. This was probably caused
by the strong vertical shear that developed in the shallow but strong
down-valley flows within Brush Creek.
(c) The plume centerline was not carried down the center of the valley during
its nocturnal travel, but was displaced towards the east sidewall of the
northwest-southeast-oriented valley. This produced relatively high
nocturnal concentrations on the east sidewall at elevations of 50-150 m.
(d) The plume centerline shifted across the valley to the west sidewall after
sunrise, producing highest concentrations on the sunlit west sidewall at
elevations of 50-150 m. The cross-valley shift of the plume centerline
was caused by the strong differential heating of the two sidewalls.
(e) Decreases in SF6 concentrations in the lower part of the valley occurred
as SF6 was advected up the west sidewall in upslope flows that developed
within the growing convective boundary layer over the slope.
Concentrations increased in the higher levels of the valley as the
temperature inversion broke up and as upslope flows developed.
Further discussion of the meteorological interpretation of the tracer
experiment data summarizing the physical processes responsible for the
observed plume transport and diffusion will be presented at an AMS conference
by Whiteman et al. (1984).
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SECTION 3
AVAILABLE COMPLEX TERRAIN MODELING TECHNIQUES
In this section are briefly described the modeling techniques and
algorithms that are currently available for regulatory use or which, as part
of EPA efforts, are being currently evaluated for potential regulatory use.
As a means of identifying candidate models, it seems logical to list those
complex terrain dispersion models the EPA now uses, and those that were
submitted for evaluation in response to the March 1980 Federal Register "Call
for Models" notice. These models have also been statistically evaluated on
common data bases as will be described in the next section. In addition,
descriptions are included of the techniques being evaluated in the ongoing EPA
Complex Terrain Model Development program and of the VALMET and MELSAR models
also being developed for the EPA.
It is recognized that this list of models is not exhaustive since other
complex terrain dispersion models are in various stages of development and
availability. These range in complexity from relatively simple and
computationally-efficient algorithms to comprehensive three-dimensional
numerical grid models. However, since the theme of this assessment document
was directed to EPA regulatory applications, the above guidelines were
followed to provide an objective selection of candidate models for performance
evaluation.
A refined guideline model has not been established by the EPA for complex
terrain settings. Models presently used by the EPA as conservative screening
techniques in complex terrain settings for conditions when plume heights can
be expected to be below the maximum height of nearby terrain are Valley,
COMPLEX I, and COMPLEX II. The EPA has also developed the model COMPLEX/PFM,
which is still undergoing evaluation. The following complex terrain models
were submitted from the modeling community for evaluation by the EPA in
response to the Federal Register notice: RTDM, PLUME5, 4141, SHORTZ, and
IMPACT.
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All but one (IMPACT) of the above models are of the Gaussian plume type;
that is, ground-level concentrations are calculated on the basis of distance
from the plume center!ine to ground surface according to Gaussian plume spread
dispersion statistics. These models differ, however, in parameterization of
dispersion, the way wind speeds are used, the assumptions about plume
trajectories, and in other parameterizations. A summary description of the
COMPLEX I, COMPLEX II, and COMPLEX/PFM is given in this section followed by a
brief discussion of how the other models differ from these.
In all cases, the reader is referred to the appropriate documentation for
more complete information on each of these models. Since the Complex Terrain
Dispersion Model, now undergoing development for the EPA, is significantly
more complex than the other Gaussian type models, a detailed description is
provided to allow a more complete understanding of the algorithms involved.
VALLEY MODEL
The Valley Model (Burt, 1977) is recommended by the EPA as the initial
screen in a two-tiered screening approach for complex terrain analyses in
support of regulatory decisions. Valley is designed to provide an estimate of
the maximum 24-hour pollutant concentration expected to occur on elevated
terrain near a point source of air pollution in any 1-year period. This
concentration is computed with a steady-state, univariate Gaussian plume
dispersion equation, modified to provide a uniform crosswind distribution over
a 22.5° sector and using assumed worst-case meteorological conditions.
The model assumes that the plume travels toward nearby terrain with no
vertical deflection until the center!ine of the plume comes to within 10 m of
the local terrain surface. Thereafter, the center!ine is deflected to
maintain a stand-off distance of 10 m from the terrain surface. The plume is
considered to impinge upon the terrain at points where terrain height equals
the plume height, and the impingement point used in the calculation of maximum
plume impact is the nearest such topographic point as viewed from the source.
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Worst-case meteorological conditions are defined by that combination of
wind speed and Pasquill-Gifford dispersion stability class that produces the
highest possible concentration at the impingement point. For large sources of
air pollution, a stack-top wind speed of 2.5 m/s and Pasquill-Gifford
stability class F are recommended as those conditions that will produce the
highest concentrations during stable conditions when plume impingement is most
likely. The model estimate is implied to be a 1-hour average concentration.
The 24-hour average concentration is estimated by dividing this 1-hour average
concentration by four, on the premise that the impinging plume may affect a
specific point for no more than 6 hours in any 24-hour period.
COMPLEX I, COMPLEX II, AND COMPLEX/PFM MODELS
The COMPLEX I (EPA, 1981a) and COMPLEX II (EPA, 1981b) models are
multiple point source sequential terrain models formulated by the Complex
Terrain Team at the EPA Workshop on Air Quality Models held in Chicago in
February 1980. COMPLEX I is a univariate Gaussian horizontal sector-averaging
model (sector width = 22.5°), while COMPLEX II computes off-plume-centerline
concentrations according to a bivariate Gaussian distribution function. Both
models are very closely related to the MPTER model in both structure and
operation. Anyone who is not familiar with either COMPLEX or MPTER should
consult the MPTER user's manual (Pierce and Turner, 1980) and the analysis
report on COMPLEX I and COMPLEX II (Irwin and Turner, 1983).
Terrain treatment in the COMPLEX models varies with stability class.
Neutral and unstable classes use a 0.5 terrain adjustment, while stable
classes use no terrain adjustment when the recommended options are selected.
With 22.5° sector averaging, COMPLEX I, when used in the regulatory mode,
performs sequential Valley plume impingement calculations for stable cases.
COMPLEX II plume impingement calculations are similar, with the exception that
sector averaging is not used.
The COMPLEX/PFM model (Strimaitis et al. , 1983) is a modified version of
COMPLEX I and II that contains a Potential Flow Module (PFM). COMPLEX/PFM has
the ability to utilize potential flow theory calculations for neutral to
-30-
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moderately stable flows. The PFM option invokes either COMPLEX I, COMPLEX II,
or PFM computations depending upon the stability class and the Froude number.
Unlike previous versions, however, all sources must be located at the same
point.
The PFM option enhances the ability of COMPLEX to perform complex terrain
Gaussian plume dispersion computations in two important areas. First, it
incorporates plume deflections and distortions through streamline computations
derived from potential flow theory. This enhancement approximates at least
first-order terrain effects on plume geometry. And, because the streamline
computations vary with obstacle shape, plume height, and Froude number, plume
distortions are coupled directly to meteorological variations and the
approximate terrain geometry in a way that no single terrain adjustment could
be. Second, the use of the PFM option requires vertical temperature and wind
velocity information to characterize the Froude number, the dividing-
streamline height, and stable plume rise. Availability of the Froude number
and the dividing-streamline height removes the assumption of coupling between
the surface dispersion stability class and the dynamics of the flow aloft at
plume elevation under stable conditions. It is not necessary to identify
plume impingement with class E or F dispersion conditions.
COMPLEX II is invoked by COMPLEX/PFM whenever the stability class is
either 1, 2, or 3 (A, B, or C), regardless of the Froude number. In these
cases plume growth is rapid and the details of terrain adjustment are not so
important. PFM is always invoked for stability class 4(D), and is invoked for
stability classes 5(E) and 6(F) whenever the flow along the plume streamline
has enough kinetic energy to rise against the stable density gradient and
surmount the highest terrain elevation along the wind direction. Such a plume
is considered to be above the dividing streamline of the flow.
COMPLEX I is invoked by COMPLEX/PFM whenever the plume is found to be
beneath the dividing streamline of the flow (classes 5 and 6). Plumes beneath
the dividing streamline no longer pass over the terrain peak and therefore may
impinge on the face of the hill. Thus, when used in the regulatory mode, the
PFM option defaults to Valley-like computations for impingement cases.
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ROUGH TERRAIN DIFFUSION MODEL
The Rough Terrain Diffusion Model (RTDM) is a sequential Gaussian plume
model designed to estimate ground-level concentrations in rough (or flat)
terrain in the vicinity of one or more co-located point sources (ERT, 1982).
Off-plume-centerline concentrations are computed according to a bivariate
Gaussian distribution function. Only buoyancy-dominated sources should be
modeled with RTDM because momentum effects on the plume are ignored.
Rather than assuming full reflection (Valley-like computations) for cases
of plume impingement, RTDM uses a partial plume reflection algorithm that
takes into account the second law of thermodynamics and estimates a maximum
effect of reflection (which is less than full reflection) for a plume
approaching a terrain slope.
In stable conditions, the dividing-streamline height (H ) is
computed from the wind speed, the terrain height, and the strength of the
inversion. Plumes below this height are allowed to impinge on the
terrain. During neutral and unstable conditions or above H in stable
conditions, a "half-height" correction simulates the effect of terrain-induced
plume modifications on ground-level concentrations.
Rather than using Pasquill-Gifford stability classes, RTDM uses on-site
turbulence intensity data (i , i ) to estimate horizontal and vertical ambient
J
dispersion. Horizontal wind shear data can be used to make refined estimates
of the horizontal extent of the plume.
PLUMES MODEL
PLUMES is a multiple source, steady-state Gaussian plume dispersion model
designed for point source applications (Hsiung and Case, 1981). This model is
closely related to the CRSTER model in both structure and operation.
Off-plume centerline concentrations are computed according to a bivariate
Gaussian distribution function. The treatment of terrain by PLUMES uses
Briggs final plume rise algorithm with the determination of stable layer
-32-
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penetration dependent on plume height:
(a) When the final plume height is above the stable layer, concentration
estimates are calculated only for those receptors at or above the stable
layer top.
(b) When the plume height lies within the stable layer, concentration
estimates are calculated only for those receptors located within the
stable layer.
(c) When the plume height (H) falls below the stable layer and the receptor
lies above the stable layer base, then the concentration is set to zero.
If the receptor height (Z) is below the stable layer base, the receptor
height is redefined as follows:
If Z < H/2, then the terrain height is not modified.
If Z > H/2, then a conservative modification to the one-half plume
height correction is used.
PLUMES performs Valley-like calculations for stable cases with plume
impaction.
PLUMES uses stability categories as determined from on-site horizontal
turbulence intensity data (cO, on-site vertical temperature gradients, or
Pasquill's stability classification scheme. Pasquill-Gifford-Turner
dispersion coefficients are used for each stability category. Stability
classes A-F are utilized with stability class G assigned to class F. An
option is available to treat stability class A as class B. Enhanced
horizontal dispersion due to vertical wind directional shear may be employed.
4141 MODEL
Model 4141 (ENVIROPLAN, 1981) is a modified version of the bivariate
Gaussian distribution CRSTER model. The modifications include the location of
the plume centerline above ground level in complex terrain, stability
classification, dispersion-rate calculations as a function of the stability
class, and the minimum approach of the plume centerline to the ground.
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The 4141 model uses Turner stability categories with class G treated as
class F, and Pasquill-Gifford dispersion rates including buoyancy-induced
dispersion. The horizontal dispersion rates are 1.82 times the original
Pasquill-Gifford dispersion rates, which accounts for differences in sampling
times.
The effective stack height is reduced by half of the increase in ground
elevation above stack base for unstable and neutral conditions (half-height)
and by 0.75 of the increase in ground elevations above stack base for stable
conditions (quarter-height). The CRSTER-like minimum terrain approach of plume
center!ine is eliminated although, through the use of the quarter-height
correction, there are no pure cases of impingement. Valley-like calculations
in effect occur whenever the plume is close to impinging on the terrain
feature.
SHORTZ MODEL
SHORTZ is a bivariate Gaussian dispersion model designed to calculate
average ground-level concentrations produced by emissions from multiple stack,
building, and area sources (Bjorklund and Bowers, 1979). The steady-state
Gaussian plume equation for a continuous source is used to calculate
ground-level concentrations.
Rather than using Pasquill-Gifford-Turner a's, vertical and lateral plume
dimensions are calculated by using on-site turbulent intensities (i , i ) in
simple power law expressions that include the effects of the initial source
dimension. Techniques for enhancing horizontal dispersion due to vertical
wind direction shear and for including buoyancy-induced dispersion are used.
When SHORTZ is applied in complex terrain, the plume axis is assumed to
remain at the plume stabilization height and the plume is allowed to mix to
the ground as long as the stabilization height is within the surface mixing
layer. An effective mixing height is defined to be terrain-following in order
to prevent a physically unrealistic compression of plumes as they pass over
elevated terrain. SHORTZ performs Valley-like calculations for impingement
cases.
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INTEGRATED MODEL FOR PLUMES AND ATMOSPHERICS IN COMPLEX TERRAIN
The Integrated Model for Plumes and Atmospherics in Complex Terrain
(IMPACT) is a three-dimensional grid model used to calculate the impact of
either inert or reactive pollutants, in simple or complex terrain, emitted
from either point or area sources (Tran et al., 1979). Unlike Gaussian-type
models, IMPACT determines concentrations as a function of advection,
diffusion, source, and chemistry. This formulation allows for the treatment
of single, multiple point or area sources, the effects of arbitrary vertical
temperature stratifications, shear flows caused by atmospheric boundary layers
or by terrain effects, terrain channeling, and chemical transformations.
The method of calculating diffusivities from the DEPICT model using
empirical formulations is used. The vertical diffusivity,
Dv = .45 ua££, (8)
is a function of the windspeed (u), the standard deviation of the wind vane
fluctuation (a ), and the turbulence length scale (£). o is empirically
o £
related to stability and £ is empirically related to height and stability.
The horizontal diffusivity is then calculated using the following formulation,
DH = aDv, (9)
where a is empirically related to stability.
Wind fields are objectively-determined, non-divergent flow fields based
on local data. The plume rise and terrain impaction are controlled by the
wind and diffusivity fields. The Briggs layered plume rise algorithm
including the penetration of stable layers is used.
COMPLEX TERRAIN DISPERSION MODEL
As part of the EPA Complex Terrain Model Development program,
Environmental Research and Technology, Inc. (ERT) has produced the Complex
-35-
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Terrain Dispersion Model (CTDM). In its current stage of ongoing development,
the CTDM is a point source plume model that incorporates several concepts
about stratified flow and dispersion over an isolated hill. A central feature
of CTDM is its use of the dividing-streamline height (H ) to separate the flow
into two discrete layers. This basic concept was suggested by theoretical
arguments of Drazin (1961) and Sheppard (1956), and was demonstrated through
laboratory experiments by Riley et al. (1976), Brighton (1978), Hunt and
Snyder (1980), Snyder et al. (1980), and Snyder and Hunt (1984). The flow
below H is constrained to move in horizontal planes, allowing no motion in
the vertical. Consequently, plume material below H travels along and around
the terrain, rather than up and over the terrain. The flow above H is
allowed to rise up and over the terrain. Two separate components of CTDM
compute ground-level concentrations resulting from material in each of these
flow regimes. LIFT simulates the flow above H and WRAP handles the flow
\f
below H .
The LIFT Component
The flow above H is considered to be weakly stratified. That is, the
stratification is strong enough to influence the flow pattern (e.g., lee
waves) and the diffusion, but not strong enough to inhibit significant
vertical motions. To simplify the modeling task, H is assumed to be a level
surface, and the flow above H "sees" only that portion of the hill that lies
above H .
A fluid modeling study was performed by Snyder and Lawson (1983) at the
EPA Fluid Modeling Facility to assess the utility of this approximation. The
results of this study confirmed that this approximation is reasonable with
regard to estimating the locations and values of maximum ground-level
concentrations and areas of coverage on the windward side of the hill. Poorer
correspondence was found in the lee of the hill for plumes released well above
H , and this is apparently due to lee-wave effects.
The plume is allowed to develop as if the terrain were perfectly flat
until it reaches the point where the H surface intersects the hill (at x =
-36-
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s , see Figure 3). If H is zero, then this zone extends from the source to
U I*
the base of the hill, although it could conceptually extend to any point where
the hill is thought to exert a significant influence on the flow. Beyond SQ)
the plume material below H is disregarded by the LIFT component, and the
evolution of the remaining material is modeled as if the terrain were flat and
the lower boundary were H (with full reflection). However, the wind speed,
plume height above H , plume spread, and lateral position of the plume
centerline relative to the receptor are all modified to reflect the net
alteration of these properties between s and s (the distance to the receptor)
induced by the presence of the hill. The simplicity of the Gaussian plume
solution is retained in this way, while the full dilution of the plume from
the source to the hill (s ) as well as the effects of the hill on both flow
and dispersion beyond s are explicitly incorporated.
Aside from the obvious distinction of incorporating the primary influence
of H on the plume-terrain interaction, this approach differs notably from the
current regulatory modeling approach (at least as embodied in COMPLEX I and
II) in that the terrain influence only affects the plume once it is over the
terrain. The "partial height" modeling approach of COMPLEX and similar models
actually "lowers" the plume at the source. If this technique were engineered
to produce the "correct" hill-influenced ground-level concentrations, the
partial height factor would need to be a function of downwind distance,
terrain shape, and distance between source and terrain. As employed in
regulatory modeling, however, the partial height factor depends only on the
stability class and the heights of the source and receptor, so that its use
has led to problems of interpreting "surface reflection" from sloping terrain,
as well as to problems in justifying values chosen for the partial height
factor.
Terrain-induced modifications to the plume arise from the distortion of
the flow over the hill. A streamline of the flow will be deflected to the
side (unless it lies in a plane of symmetry) and will pass closer to the hill
surface. Adjacent streamlines are deflected in much the same way, but are
generally displaced by differing amounts, which in turn changes the spacing
between streamlines and hence causes changes in the local speed of the flow.
As a result, the plume trajectory is curved, the time of travel does not vary
linearly with distance, the plume distorts so that it is thinner in the
-37-
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I
LI/FT
WRAP
WRAP
H,
'Flat-Terrain'
Domain
LIFT Component
WRAP Component
Figure 3. Idealized stratified flow about hills indicatinq domains of indi-
vidual CTDM component algorithms. The s dimension is the distance
from the source to the intersection of H with the hill surface for
the LIFT domain, and from the source to the terrain contour equal
in height to the receptor elevation for the WRAP domain.
-38-
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vertical direction and wider in the lateral direction, and the turbulence
statistics vary. In addition, as shown by Hunt and Mulhearn (1973), turbulent
diffusion across streamlines is enhanced by the contraction of the distance
between streamlines in the vertical direction, and is retarded by the
expansion of the distance between streamlines in the lateral direction.
Hunt and Mulhearn explicitly track these changes through the use of line
integrals along the streamline that coincides with the plume centerline. The
LIFT component has been designed to take average values of the changes in flow
properties over the interval between s and s. These average values then
guide the distortion applied to the concentration distribution at s and the
flow speed used in the ensuing calculation. In essence, LIFT distorts the
plume at s by an amount representative of the actual distortion in the flow
between s and s, and then a flat terrain computation is used to estimate the
effect of these distortions on the diffusion of material to the surface over
the interval s-s . Hence, a continuous process is represented by a two-step
process in which the distortion of the flow and the diffusion of the plume in
the distorted flow are treated successively. This approach, while not as
rigorous as the Hunt and Mulhearn approach, allows development of a modeling
framework in which the terrain effects appear as simple factors within the
flat terrain solution.
Quantities in the distorted flow are related to quantities of the
undistorted flow by means of terrain factors. These factors are local in the
sense that they depend on the position of the receptor on the terrain, even
though they represent the average terrain effect on the flow from s to s. T,
and Tp are factors that specify the amount of streamline distortion in the
vertical and lateral directions; T specifies the resultant change in the flow
speed; and T and T specify changes in the diffusivity in the vertical and
lateral directions.
The factor T, accounts for the effective contraction of the distance
between streamlines in the vertical. A simple model for the change in
streamline spacing applies a constant depression factor to all streamlines
over a particular location on the terrain. But note that the perturbation
caused by a hill should decrease with height, so that this simple model must
-39-
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be viewed as an approximation to be applied at plume centerline height.
Similarly, T. is evaluated for a particular plume path.
The speed factor, TU, is obtained by conserving mass. The condition
Tu^hT£ = * must be maintained at every point in the flow. The factor T
(denoting either T or T ) should account for the effective diffusivity
between s and s . In the present form of CTDM, the magnitudes of these
terrain effect factors are scaled from potential flow calculations.
The concentration on the hill surface at the point (s,£) is then given by
Qe
C(s,£) =
a,
ye
27tayeazeu
-0.5 ns nc
a
ze
1-erf
°V\
ze aze
ze
ze ze
(10)
where T = T./T , T = T./T , and the source is located at (0, L, Hg).
The terrain-induced modifications are easier to observe if H is set to zero:
Qe
a,
C(s,£) =
*§_' e"°-5
7tCTveCTzeu
The effective plume size (subscripted by e) is given by
(11)
aze2 = az*(s0) + af /T
(12)
(13)
where
a*2 = a2(s) - a2(sj.
(14)
-40-
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If T and T are not equal to unity, the effective size of the plume
differs from the unmodified plume and the effective lateral distance from the
plume center! ine to the receptor is altered. For illustration, let L = 0.
Then if T, > I, which is generally the case because the streamlines are
deflected to the side to some degree, the apparent receptor location (£/!„)
lies nearer the plume centerline. Aside from this lateral shift in the impact
region on the terrain, the influence of the terrain is exhibited only through
changes in the rate of effective plume growth. When T is less than unity
(again, this is generally the case), cr exceeds a at s and so more plume
material may lie "nearer" the surface. Furthermore, because T is generally
i/
greater than unity, a is less than o at s, so the plume is not fully
diluted by the increase in a . As a consequence, Equation 10 may estimate
ground-level concentrations in excess of flat terrain estimates even when H
is zero.
If HC is nonzero, but less than HS, Equation 10 will estimate even
greater ground-level concentrations because the flow over the depth H beneath
the plume is "removed," allowing the less dilute portion of the plume to
approach nearer the surface. In particular, if H = H , then Equation 10
places the centerline concentration at ground level, producing a centerline
"impingement" result.
In the use of Equation 10, the terrain factors should be regarded as
local terrain effects factors for a particular receptor. The degree of flow
deformation depends on whether the flow must go directly over the crest, or
pass to one side in approaching the receptor. Once the local factors are
obtained, they are applied to the entire plume.
If there should be a good deal of meander over the averaging period for
the model computation, it is not apparent that Equation 10 is appropriate.
Therefore, consider Equation 10 appropriate for a "filament" plume. The
"filament" plume is defined to be a plume described by the flow field
statistics obtained for a sampling period commensurate with the time of travel
from the source to the hill. The mean concentration at a receptor for an
averaging period greater than the time of travel is a weighted average of many
"filament" plumes:
-41-
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cm = J C(s,£|e.) p(e.) de..
(15)
P(0) is the probability that the wind is from the 6 direction during the
averaging period, and C (s,£|6) is the concentration resulting from a
"filament" plume from direction 6. For a distribution of wind directions that
has a single dominant mode at 6 , P(6) may be approximated by a Gaussian
distribution:
P(fl) =
aym/s
(16)
Using a similar arc-length notation for lateral distance, C (s,£ ! 0) may be
written as
C(s,6 I 6) =
F,(8) _
-^ - e
ye
ye
(17)
where F (6) denotes the vertical distribution portion of Equation 10, and 6
is the direction from the apparent or effective receptor location to the
source.
By assuming that the "filament" plume is narrow, set F (6) to F (6 ), and
evaluate a for a plume from 6 . This makes explicit the use of the terrain
factors that are local to the receptor. The solution of the integral gives
m a.
-0.5
-------
Because a is viewed as the statistic for just the meander component of the
wind fluctuations over the averaging period, and a is viewed as the measure
(including the terrain modification) of the mean "filament" plume spread,
a y = a in the absence of meander, and Equation 10 is obtained once again.
The WRAP Component
The flow below H is considered to be completely two-dimensional,
allowing no motion in the vertical. Consequently, the flow must pass to one
side or the other of the hill, and the one streamline that actually touches
and passes round both sides of the hill, separates the two flows and is termed
the stagnation streamline (Figure 4). The flow en either side of the
stagnation streamline undergoes distortion such that a streamline in the flow
is deflected to the side, but passes closer to the hill surface than its
initial distance from the stagnation streamline. Adjacent streamlines are
displaced by differing amounts, which in turn changes the horizontal spacing
between streamlines, and hence causes changes in the local speed of the flow.
The effect of these distortions on ground-level concentrations is not unlike
those formulated in LIFT for flow over a two-dimensional hill, wherein T£ = 0.
The primary difference between the WRAP and LIFT formulations arises from
the location of solid boundaries and the relationship between the position of
these boundaries and the wind direction fluctuations. The terrain effect is
modeled in WRAP by re-initializing the flow at s . Note that receptors below
H experience an s different from that for receptors above H (Figure 3).
Below H , s is the distance along the stagnation streamline to the terrain
contour equal in height to the receptor elevation. The concentration at a
receptor downwind of s is composed of concentrations from that part of the
concentration distribution at s that lies below H , and that also lies on the
same side of the stagnation streamline as the receptor. Reflection of plume
material is allowed from the plane z = 0 over the entire distance s, and
reflection is also allowed from the "stagnation streamline" beyond s . Note
that the stagnation streamline forms the boundary of the hill surface in
horizontal cross section.
-43-
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ro
-o
c
O
3
o
O
I/)
E
O)
T3
I
O
O)
E
3
a
M-
O
CD
>
C
OJ
S-
-44-
-------
The terrain influences are incorporated by deforming the source
distribution at s , and by altering the flow in which the source elements
diffuse. For a receptor located on the hillside at a distance s and a height
H , the concentration due to a source located at (0, L, H ) contains contri-
butions from those elements below H , and on the same side of the stagnation
streamline as L.
Noting that T, = 1 for this two-dimensional flow, the concentration is given
by
C(SfO.Hr) = _ e -- 2 , + sign(
V e
-0
Ble -o + B26
Most of the notation here has already been encountered in the description of
the LIFT component. The factor sign(y ) denotes the sign of the receptor
position in the coordinate system with x-axis aligned with the flow, and it
results from the choice of integrating over the "positive" or "negative"
portion of the flow. The factors B-. and B,, are given by
B -_
bo bo
(21)
where
).,-b9+b,\ /b-,+b9-b, \
BO = erf( L * 6 + erf 1 ^ 6 (22)
\ ' ^ bo ;
bO = V2 ^2e ^2o °*2
(23)
b2 = h CTzo2/Taz
-45-
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The concentration estimate from Equation 20 is quite sensitive to the
wind direction. The wind direction determines the stagnation streamline, and
this in turn prescribes the relative position of both the source and the
receptor in the undistorted flow through the quantities s, s , and L (Figure
4). Because the terrain effects are characterized through factors that are
local in the context discussed previously, they also depend on s, s , and L.
Therefore, the notion of a "filament" plume is implicit in the foregoing
development, as it was in the development of the LIFT component.
If the distribution of wind directions over the averaging time is highly
non-Gaussian, then the mean concentration is probably best estimated by
simulating a sequence of "filament" plumes. However, for distributions closer
in shape to the Gaussian distribution, an expression in the form of Equation
15 may be used with the Gaussian distribution specified in Equation 16.
Integrating Equation 20 within Equation 15 to obtain the mean
concentration C is simplified if we expect the "filament" plume to be narrow
so that concentrations for wind directions much different from the stagnation
streamline orientation 6 through the source (and therefore 6 as well) are
insignificant. In that case, s and s may be treated as constants, and L can
be represented by the small-angle approximation so that
F7(e )s r** _n c/(6-e )s\2 _n
L b e I——-—— 1 e
CTym
0
, (e-ejr
-------
= awt ; t « TL (25)
0.5
az = (2Kzt) ; t » TL. (26)
In Equations 25 and 26, a is the standard deviation of vertical velocity
w
fluctuations, t is the travel time from the source, T. is the dispersion time
scale, and K is the eddy diffusivity defined by
K = oJL , where £ = a T, . (27)
t- W W L
In a stably stratified flow, a fluid element must overcome a stable
potential temperature gradient in order to be displaced vertically. Simple
energy arguments suggest that this gradient imposes a length scale of the
order of a /N on vertical motion, where N is the Brunt- Vai sal a frequency.
Consequently, the mixing length S, is proportional to this length scale so
that
£s = y2 aw/N (28)
where y is an undetermined constant.
Surface-layer relationships (Businger, 1973) in the limit of z-less
stratification are employed to estimate y.
Assuming that KH = K , we find that
2 -]
(29)
With p = 4.7 and a = 1.3, y equals 0.52. Note that when N is small, Ag can
become very large, and it becomes necessary to consider the effect of the
ground on limiting the length scale. In the absence of stratification, one
expects the mixing length to scale with height, so
£n = aHs (30)
-47-
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where the subscript n is used to distinguish the neutral length scale £ from
the stable scale £ .
o
Surf ace- layer relationships indicate that
a = k/a*H(0). (31)
If the values of k = 0.35 and *H(0) = 0.74 (Businger, 1973) are used, a equals
0.36.
Interpolation between 8. and 8, is accomplished with the following
formulation for £
1/8. = l/£s + l/2n. (32)
Equation 32 has been used by other investigators (see Hunt et al., 1983 for
example). Then the dispersion time scale is given by
TL = A/ow. (33)
The a formulation, which interpolates between the linear and square-root
growth rates, is one used by other authors (Deardorff and Willis, 1975):
o- =ot/(l + t/2T.)V (34)
/. W U
Formulation of o
Past versions of CTDM have estimated a by assuming that the transverse
spread of the plume grows linearly with time. This implies that the
Lagrangian time scale for the transverse spectrum is long compared to the time
of travel to the hill. While this may be the case for many of the Cinder Cone
Butte experiments, there are some experiment hours in which the linear growth
law appears to overestimate the dilution of the plume. This was deduced from
comparisons of observed ground-level SF6 concentrations with estimates of the
plume "centerline" concentrations.
-48-
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The Lagrangian time scale can be incorporated into the expression for a
by means of the interpolation contained in the a formulation:
"y = V 1 * ' (35)
The Lagrangian time scale for the transverse spectrum T,-,- cannot be estimated
from the flow properties, but it may be estimated from the turbulence
measurements. Pasquill and Smith (1983) point out that if the turbulence is
assumed to be isotropic, and if the longitudinal correlogram is modeled by an
exponential with an Eulerian time scale of Tr, then
. 1 - I (1 - e-
-------
Northwest Laboratory to be used for these respective problems. Neither of
these models has been fully evaluated with field data, although an evaluation
of VALMET is underway. A review of the overall program is given by
Schiermeier et al. (1983a) and descriptions of VALMET and MELSAR are given by
Whiteman and Allwine (1983) and Allwine and Whiteman (1984), respectively.
The VALMET (Valley Meteorology) model is intended for use primarily for
the morning fumigation period in deep valleys, where upslope flows generated
by solar heating cause polluted air at mid-valley to descend to the ground.
The fundamental physical mechanism is discussed by Whiteman and McKee (1977,
1982), who conducted numerous meteorological studies of the structure of winds
and temperatures in Colorado mountain valleys. They observed that the
mid-valley inversion descended in the early morning as mass lost in upslope
flows was replaced by air above the valley floor. They developed an Eulerian
grid model to simulate the observed phenomena, and included the differential
solar heating of the valley walls. In their later work for the EPA, they
added an air pollution concentration field to the model, beginning with a
stable Gaussian plume oriented along the valley axis before sunrise. The
Eulerian grid model then accounted for fumigation after sunrise.
Two field experiments have been conducted in the Green River oil shale
region in 1980 and 1982, including meteorological observations and SF6 tracer
data. Analysis of these data and evaluation of VALMET are currently underway
(Whiteman et al. , 1984).
The MELSAR (Mesoscale Location-Specific Air Resources) model is a
puff-trajectory model suitable for calculating transport and dispersion over a
500-km by 500-km region, including the effects of underlying complex terrain.
The flow module is a three-dimensional, mass-consistent flow model using a
terrain-following coordinate system (Drake et al., 1981). Pollutant
concentrations are described in a Gaussian fashion about a puff center of
mass, where continuous sources are approximated by puff release rates of one
per hour. The model has not yet been tested with observations.
-50-
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SECTION 4
RESULTS OF MODEL EVALUATION STUDIES
A number of model evaluation studies performed over the past few years
have focused on the application of dispersion models to complex terrain
settings. The discussion here attempts to draw out some of the more important
findings and suggestions for appropriate modeling techniques that have emerged
from two of these efforts.
TRC EVALUATION OF COMPLEX TERRAIN DISPERSION MODELS
This study (Wackter and Londergan, 1984) was sponsored by the EPA Office
of Air Quality Planning and Standards, and was performed by TRC Environmental
Consultants, Inc., using statistical measures recommended by the American
Meteorological Society (Fox, 1981). Two field measurement data bases were
used for testing: the Cinder Cone Butte (CCB) tracer data base resulting from
the first field experiment of the EPA Complex Terrain Model Development
program and the Westvaco Luke Mill S02 data base. Both data bases have
representative and detailed meteorological data. The CCB data base provides a
fine spatial resolution having some 94 tracer samplers; the TRC evaluation
used 104 study hours. The Westvaco data base included a full year of hourly
S02 data at 11 continuous-monitoring stations.
The eight complex terrain models evaluated on these data bases were
described in Section 3, including COMPLEX I, COMPLEX II, COMPLEX/PFM, RTDM,
PLUME5, 4141, SHORTZ, and IMPACT. The reader is referred to the TRC study
report for an examination of the evaluation tests and the complete statistical
results. The TRC report does not conclude which model performed best. It
leaves the interpretation of the statistics largely to the readers.
As a separate activity within the EPA Meteorology and Assessment
Division, a scientific review of the models tested is currently being
performed. This separate, independent review will be based on an
-51-
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interpretation of the TRC statistical evaluation and also on a review of the
theoretical bases of the model algorithms. Unfortunately, this separate
review is not scheduled to be completed in time for input to this assessment
document. The findings from the TRC evaluation that follow are therefore
stated in relatively general terms and can be expected to be qualified or
altered after the separate review is completed.
The TRC report presents eleven different statistical performance measures
for each of the eight models tested. No recommendations are made regarding
the relative importance of each of the performance measures. Both the
Westvaco and CCB data bases are sorted into sets of the 25 highest values
unpaired in time and space, the highest values for each event (paired in
time), and all events paired in time and location. Statistics for 1-hour
averaging times are presented for the CCB data base. Statistics for I-, 3-
and 24-hour averages are presented for the Westvaco data set. In addition,
for the Westvaco data base, statistics for the highest and second-highest
values are presented for each station. For both data bases, some breakdown of
performance measures by meteorological condition and source receptor geometry
is presented.
None of the models score "best" for all statistical measures and for all
subsets of the data. Therefore the specific ranking of models based on the
statistics depends upon one's weighting of the relative importance of the
various measures. Nevertheless, some of the statistical measures are, in
practice, somewhat redundant (such as differences of averages versus median
difference; average absolute residual versus root-mean-square (r.m.s.) error;
and the Pearson versus Spearman correlation coefficients). For overview
purposes, it is possible to focus attention on a few of the performance
measures.
Bias is an important measure because it characterizes a model's tendency
to over- or underpredict. While minimum bias is statistically ideal, for EPA
regulatory purposes overprediction is preferred to underprediction. The
r.m.s. error is another important performance measure because it characterizes
the variability of the observed versus predicted differences. The r.m.s.
error squared can be shown to be approximately equal to the sum of the bias
squared plus the standard deviation of the observed minus predicted residuals
-52-
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squared and as such, it includes consideration of the "noise" component of the
residuals. Thus it would appear that, for EPA regulatory applications, the
better models would show a minimum absolute value of bias, preferably where
the bias is not significantly positive (tendency to under-predict), and
minimum r.m.s. errors.
Tables 1 and 2 identify the models that showed superior performance by
data subsets for the measures of minimum absolute value of bias, minimum
r.m.s. error, minimum absolute value of bias if bias is less than or equal to
zero, and minimum r.m.s. error if bias is less than or equal to zero. Table I
addresses the Westvaco data set. For computational economy, the total 1-year
data set was run for all models except IMPACT. A smaller subset of about 460
hours was used to test IMPACT with the other models. Table 2 presents the
results for the CCB analyses in which all eight models were included in the
comparisons.
Table 3 displays the relative rankings for the measures of minimum value
of bias and minimum r.m.s. error. Considering first the total data set from
Westvaco, the models that achieved the minimum absolute value of bias criteria
for any of the given subsets were RTDM, 4141, and PLUME5. The model that had
the lowest r.m.s. error for all categories was RTDM. The four models that did
not show either lowest bias or lowest r.m.s. errors for any of the categories
were COMPLEX I, COMPLEX II, COMPLEX/PFM, and SHORTZ. In the IMPACT case hours
subset of the Westvaco data set, IMPACT also did not show either minimum bias
or minimum r.m.s. errors. However, it did demonstrate minimum r.m.s. errrr
for the CCB data base.
It is appropriate to try to identify some of the reasons for the
differences in performance of the various models. First of all, for nearly
all of the Westvaco data subsets, a comparison of the performance of COMPLEX
I, COMPLEX II, and COMPLEX/PFM shows that COMPLEX/PFM outperformed the other
two. COMPLEX II showed the greatest biases and r.m.s. errors. This suggests
that the algorithms that are different in COMPLEX/PFM result in improvements.
The primary differences are in the use of potential flow theory to develop
plume trajectories when a nonzero H is calculated and the use of H in
c t*
distinguishing the trajectories and the plume dispersion rates during stable
conditions.
-53-
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TABLE 2. MODEL PERFORMANCE FOR CINDER CONE BUTTE DATA BASE
Total Data Set
No. of Lowest Lowest
data Lowest Lowest I bias I for r.m.s. for
pairs I bias I r.m.s. bias<0 bias<0
Data subset
Highest 25 values
unpaired in time,
space
25
RTDM NA*
RTDM
NA
Highest values paired
by event
104
RTDM IMPACT RTDM
RTDM
All values paired by
time and space
3836
RTDM IMPACT RTDM
RTDM
*NA - Not applicable
-55-
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TABLE 3. MODEL RANKINGS BASED ON TRC EVALUATION
Data subset
CXI
*Bias
rms
CXII
Bias rms
CX/PFM
RTDM
4141
Bias rms Bias rms Bias
Westvaco
Highest 25
values unpaired
in time, space
1 hour
3 hour
24 hour
Highest values
paired by
station
1 hour
3 hour
24 hour
Second highest
values paired
by station
1 hour
3 hour
24 hour
Highest values
paired by event
1 hour
3 hour
24 hour
All values
paired by time
and space
1 hour
3 hour
24 hour
Highest 25
values unpaired
in time, space
Highest values
paired by
event
All values
paired by time
and space
6
6
6
5
6
6
5
6
6
6
6
6
6
6
6
3
3
6
4
6
5
6
6
6
6
6
6
6
6
6
3
3
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
8
8
j.
6
7
7
7
7
7
7
7
7
7
7
7
7
8
8
5
4
4
6
4
4
6
5
4
3
3
2
2
2
2
Cinder
5
5
5
6
4
4
5
5
4
5
4
3
5
5
3
Cone
4
5
rms
PLUME5
Bias
SHORTZ
rms Bias
rms
IMPACT**
Bias
rms
Data Base
1
1
1
1
1
1
1
1
1
2
2
3
4
4
4
Butte
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Data
2
2
2
2
2
2
2
2
2
2
2
1
1
1
3
3
3
2
2
2
2
2
2
2
2
2
2
2
2
4
5
5
4
5
5
4
4
5
4
4
4
1
1
1
5
5
6
4
4
5
4
5
5
3
4
5
3
3
3
3
3
3
3
3
3
5
5
5
5
5
5
3
3
3
3
3
3
3
3
4
4
3
4
7
N>
8
8
8
8
8
8
7
7
8
8
8
8
i
8
8
8
8
8
8
8
8
8
8
8
8
Base
7
7
8
5
7
6
6
4
4.
6
6
4
4
2
6
4
2
2
3
1
1
*Minimum absolute value of bias. NA - Not applicable. Identical rankings.
**IMPACT ranking for Westvaco calculated on IMPACT case hours data subset.
-56-
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Along the same lines, the features of COMPLEX I, COMPLEX II, and
COMPLEX/PFM that probably account for the major differences in their bias
versus the bias of other models are the level plume/10-m minimum approach
algorithm in combination with the dispersion coefficients for strongly stable
conditions. These features apparently cause these models to overpredict.
Model 4141, which uses the same diffusion coefficients, utilizes a 0.25
terrain correction factor under the same conditions and has less bias and
smaller variances. The SHORTZ model uses similar trajectory assumptions as
COMPLEX I and II for stable conditions if the plume lies within the mixed
layer, but uses on-site turbulence data for the computation of dispersion
coefficients. The fact that SHORTZ performs better than COMPLEX I and II
suggests that the dispersion rates are better parameterized in this model.
RTDM also uses on-site turbulence statistics and assumes either a 0.5 terrain
correction factor for the plume height relative to H if the plume is above H
or direct impact if the plume is below H . RTDM appears to perform better
than SHORTZ in predicting the highest values, reinforcing the notion that the
trajectory assumptions in COMPLEX I and II need improvement. The ranking of
performance of the other models did not change appreciably with changes in
averaging time.
For the CCB data set, the RTDM, SHORTZ, COMPLEX II, and COMPLEX/PFM
models showed performance consistent with that achieved with the full Westvaco
data set. IMPACT, which ranked relatively poorly for the Westvaco tests,
ranked highly at CCB. COMPLEX I also showed improved performance at CCB where
the average of the highest 25 predicted values was within a factor of 2 of the
observed. Model 4141, on the other hand, showed considerably poorer
performance at CCB. One difference in the two complex terrain settings is the
roughness of the upwind fetches. Relatively flat terrain surrounds CCB,
whereas Luke, Maryland is surrounded by mountainous terrain. The fact that
the RTDM and SHORTZ models use on-site turbulence data may be one reason that
their performance is consistent at the two sites.
It should be noted that differences in the model rankings in Table 3 were
occasionally minimal or even nonexistent as in two of the CCB data subsets.
Consideration of additional statistics in the TRC report is suggested to
present a complete record of model performance.
-57-
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ERT EVALUATION OF COMPLEX TERRAIN DISPERSION MODELS
The most recent complete evaluation of the Complex Terrain Dispersion
Model (CTDM) using Cinder Cone Butte (CCB) data is reported in the Third
Milestone Report (Lavery et al., 1983b). This evaluation intercompares
Valley, COMPLEX I, COMPLEX II, and CTDM version 11083. Note, however, that
the CTDM version described in Section 3 is a more recent upgrade that has not
been fully evaluated at this time, although the terrain-enhanced a form
(11083-E) is similar in many respects. Model comparisons are based on the
results from 153 tracer hours of data from the CCB experiments.
Overall residual statistics developed by comparing model calculations
with tracer gas concentrations sampled at CCB are given in Table 4. The
columns labeled "Peak concentrations" in Table 4 summarize the error in
estimating 1-hour maximum concentrations, regardless of location, over the 153
tracer hours. The columns titled "All concentrations" summarize the mean
errors in estimating concentrations observed at all sampling points (paired in
space and time).
TABLE 4. SUMMARY* OF RESIDUAL STATISTICS FOR MODEL COMPARISON
Model
Peak
ma
concentrations
a
ra
(unpai
mg
red in
sg
space)
rg
Al
m
1
a
concentrations
sa
ra
CTDM(11083-E) 3.3 27.4 0.90 1.37 3.2 0.99 0.50 12.7 1.13
(1.23) (3.3)
CTDM(11083) 2.8 33.7 0.88 2.08 6.9 1.18 -0.51 15.4 1.01
(1.70) (5.2)
Valley -41.0 25.5 1.63 0.24 3.0 5.52
COMPLEX I -15.0 37.9 0.93 0.65 3.8 1.29 -6.04 21.9 0.99
(0.53) (3.2)
COMPLEX II -60.1 99.7 0.94 0.38 5,0 1.09 -5.61 36.9 0.99
(0.32) (4.6)
Note: ( ) values of m , s are calculated directly from the CQ/C ratios, with
the C = 0 values removed.
*Based on the 153 tracer hours from the Cinder Cone Butte data base. Arithmetic
_r Q o
m and s statistics carry units of 10 s/m or ps/m .
a a
-58-
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The residual statistics suggest that CTDM(11083-E) has the best overall
performance. The CTDM(11083-E) log-normal statistics for bias (m ) and noise
(s ) are close to the desired value of 1.0, and the corresponding arithmetic
statistics (m and s ) of the set of paired concentrations are the lowest of
a a
all the models. CTDM(11083-E) and CTDM(11083) underestimate peak concentra-
tions while COMPLEX I overestimates them.
COMPLEX II and Valley simulate the observations much more poorly than do
the other models. Both models substantially overestimate the peak concentra-
tions, and COMPLEX II does a poor job in reproducing the distribution of the
tracer gas concentrations observed on CCB. The measure of model resolution
(r) identifies Valley as less responsive to changes in meteorology for
predicting peak concentrations than the other models, but the resolution
statistics of the other four models are not significantly different. Figure 5
shows plots corresponding to Table 4 of the log-normal and arithmetic
performance statistics based on residuals of the peak observed and peak
modeled concentrations for the five models.
Scatter plots of peak observed concentrations scaled by the emission rate
(C /Q) versus peak modeled concentrations scaled by the emission rate (C /Q)
show that three of the models exhibit qualitatively similar patterns, while
two show patterns that are distinctly different from the rest (Figure 6).
The Valley model is not designed to use on-site meteorological
measurements, but uses "worst-case" meteorology instead. Therefore, model
estimates of C /Q depend only on the distance from the source of the nearest
terrain feature at the elevation of the release. At CCB, this leads to a
relatively narrow band of C /Q values that is unlike the pattern of the other
models evaluated. Valley overestimates most C /Q values, but it
underestimates the seven largest C /Q values. This indicates that the
standard "worst-case" meteorological conditions contained in Valley for
screening large power plant plumes are probably not appropriate on the scale
of the CCB tracer plumes.
-59-
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C0/Q 1000
COMPLEX I
2000
C0/Q flOOO
.00 500 100.0 1500 2000
Cp/Q
COMPLEX II
200.0
180.0
160.0
140.0
1200
C0/Q 100.0
80.0
600
400
200
0
00 500 1000 15002000 25003000 35O 0 40004500 500.O
CTDM (11083)
20001
1800
1600
140 0
1200
CQ/Q !000
CTDM (11083-E)
20001
1800
1600
1400
1200
C0/Qiooo
80 0
60 0
400
200
0
•. '•/
00 500 100015002000 2500
OO 500 1000 1500 2000 2500
Cp/Q
Figure 6. Scatter plots of observed and modeled peak concentrations normalized
by emission rates for five models as applied to 153 hours of Cinder
Cone Butte tracer data.
-61-
-------
COMPLEX II is the other model with a distinctly different scatter plot
pattern. This pattern is nearly the opposite of the Valley pattern. Valley
concentration estimates cover a range much narrower than the range of
observations, while COMPLEX II estimates cover a range much greater than the
observations. In both cases, model estimates appear to be poorly correlated
with the observations.
COMPLEX I, CTDM(11083), and CTDM(11083-E) display similar patterns of
scatter in that the range of estimated and observed peak hourly concentrations
are nearly the same, and the visual correlation between observations and
estimates is much better than that indicated by the Valley and COMPLEX II
patterns. Among these three models, COMPLEX I is biased toward
overestimation; CTDM(11083) and CTDM(11083-E) are somewhat biased toward
underestimation of C /Q values of less than 100.
To help understand the noise in the model calculations, the residuals
based on the peak concentrations have been plotted against several
meteorological parameters. These plots show where a model might be doing
comparatively better or worse, thereby indicating areas for improvement.
Scatter plots of C /C (between 0 and 10) vs. wind speed are given in
Figure 7 for CTDM(11083), CTDM(11083-E), COMPLEX I, and COMPLEX II. There is
considerable scatter in all of the plots, but some trend can be seen in the
patterns. CTDM(11083) exhibits a distinct bias toward underestimating
observed peak concentrations for wind speeds in excess of about 5 m/s.
Because H is probably small (or zero) compared to the source heights when
source-height wind speeds are as great as 5 m/s, this tendency suggests that
the LIFT component of CTDM(11083) is underestimating the amount of plume
material on the surface under the more nearly "neutral" flow conditions. When
a is enhanced as in CTDM(11083-E), the figure shows that much of this bias at
larger wind speeds is reduced, although it is not eliminated.
COMPLEX I exhibits a bias towards overestimating peak observed
concentrations at the lower wind speeds. COMPLEX II appears to exhibit the
same behavior, except that a few large underestimates also occur at light wind
speeds. The overestimates for light winds may be the result of using
-62-
-------
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-63-
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Pasqui11-Gifford-Turner a values in COMPLEX II and 22.5° sector-averaging in
COMPLEX I. At very low wind speeds, the wind direction often underwent large
variations at CCB. The 22.5° sector within COMPLEX I may underestimate the
plume meander in these conditions, and thereby consistently overestimate
concentrations on the hill. COMPLEX II would also certainly underestimate the
meander, but its narrow Gaussian plume might also nearly miss the hill at
times, thereby producing both the underestimates and the overestimates
indicated in Figure 7.
Scatter plots of CQ/C against other modeling parameters also reflect the
patterns just described. For example, parameter u/N (Figure 8), the ratio of
the mean wind speed to the Brunt-Vaisal a frequency, distinguishes between the
"stable" (e.g., u/N relatively small) and the more "neutral" hours. The
patterns of model performance are similar to those discussed above for the
plots against wind speed. Parameter 1-H /H (Figure 9), where H is the plume
Co S
release height, orders model performance in the near-neutral limit when
I-HC/HS is greater than approximately 0.5, and in the very stable limit when
l-Hc/Hs is less than zero. Figure 9 indicates that CTDM(11083) and
CTDM(11083=E) are most prone to overestimate peak concentrations when H
I*
exceeds 0.5 H , but is less than 1.5 H and CTDM(11083) generally produces
o S
underestimates for H less than 0.5 H . The bias toward overestimating peak
concentrations with COMPLEX I increases as H increases.
Figure 10 contains a plot of C /C vs. the product of the crosswind
vertical and horizontal turbulence intensities for CTDM(11083) and
CTDM(11083-E). (The other models in the ERT evaluation do not use these
turbulence data.) Large turbulence intensity products imply a relatively
large dilution of plume material. The figure indicates that modeled and
observed peak concentrations most nearly agree when the plume is well diluted.
When the dilution is much weaker, the plume is more compact, exhibiting
considerably less meander. Under these conditions, the peak modeled
concentration is very sensitive to plume path assumptions, wind direction, and
postulated flow distortion/plume dispersion effects. This sensitivity is
illustrated in the figure by the large scatter for low values of iyiz- The
figure also shows that the bulk of the CCB data falls into this category.
-64-
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-66-
-------
10.0"
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CTDM(11083)
.00
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.10
.15
.20
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2.0-
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.00
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.15
.20
Figure 10. Scatter plots of observed/modeled concentration ratios versus product
of turbulence intensities for two models as applied to 153 hours of
Cinder Cone Butte tracer data.
-67-
-------
A recent version of CTDM(03184) has been tested on the, "neutral" hours
from the CCB SF6 data base. The results are listed in Table 5. The measure
of how well the higher concentrations are simulated is C /C , where the
op
geometric mean of the three highest observed and modeled concentrations form
the ratio. The measure of how well the overall patterns match is r2, the
correlation coefficient for observed and modeled concentrations paired in
space and time. The relative magnitude of the observed "impact" is measured
by C U/Q. In Table 5, this scaled concentration has been divided by 100 for
convenience. Note that the units are ppT-m/lOOg.
Model performance in estimating peak concentration is generally worse
when the scaled observed "peak" concentration is relatively large or small.
The two greatest values (360 and 379) are associated with C /C values of 8.76
and 4.90, respectively. The lowest value (73) is associated with the C(/C
value ot 0.37. The remaining experiment hours have scaled observed "peak"
concentrations ranging from 104 to 303. The "peak" impact estimated from CTDM
is presented as the scaled "peak" modeled concentration in the table for
comparison. Results for the two experiment 202 hours stand out from the rest
in that the scaled peak observed values are considerably greater than the rest
of the hours in the table, while the scaled peak modeled values are
considerably smaller. A direct impingement of the plume on the windward face
would be needed to even approach the size of the observed peak concentrations
in each case. Because these two hours appear to be outliers and are so unlike
the others, they have been set aside during performance of the following
statistical analyses.
Model performance in estimating the distribution of plume material over
the hill is characterized by the r2 statistic. Relative to the performance in
most hours, experiments 201(18), 202(19), 214(10), 218(3), and 218(6) are
subpar. Of these, 202(19) and 214(10) are clearly the worst. The
concentration distribution for 202(19) shows a region of higher concentrations
below the plume release height on the north side of the hill. The model is
incapable of bringing plume material to the surface in this area. In 214(10),
it appears as though the plume experienced a more northerly component than
indicated by the data archive (the release was northwest of the hill).
Nonetheless, the magnitudes of the concentration estimates are similar to the
magnitudes of the observations for this hour.
-68-
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TABLE 5. CTDM(03184) MODELING RESULTS FOR NEUTRAL HOURS
OF CINDER CONE BUTTE DATA BASE
Experiment
(hour)
201(18)
202(18)
202(19)
214(10)
217(9)
217(10)
218(3)
218(4)
218(5)
218(6)
218(7)
218(8)
218(9)
218(10)
Hs
30
50
50
24
40
40
30
30
30
30
30
30
15
15
U(HS)
6.8
10.3
9.9
2.4
6.7
5.8
5.5
6.7
8.7
8.1
7.2
7.9
6.9
8.5
*
H;
27.2
48.1
48.1
19.3
37.1
35.8
26.3
26.8
27.1
27.0
27.3
27.4
12.0
12.3
<
401
206
298
834
330
360
174
561
439
185
315
411
404
345
-------
The overall model performance for the 12 hours remaining after removing
experiments 202(18) and 202(19) can be characterized by the r.m.s. error and
bias of the observed and modeled concentrations. For all concentrations
paired in space and time, r.m.s. error = 1459 ppT-s/g and bias = 37 ppT-s/g,
where the mean value of the observations is 782 ppT-s/g. For the highest and
second highest observed and predicted concentrations paired by event, the
r.m.s. error and bias equal 5233 and -1180 ppT-s/g, respectively, for the
highest, and equal 1941 and -230 ppT-s/g for the second highest. The mean
observed concentrations are 3231 and 2971 ppT-s/g, respectively. If the
r.m.s. error is squared and scaled by C 2 to characterize the performance for
these 12 hours, we obtain the r.m.s./C 2 value of 3.48 for all concentrations
paired by event, and values of 2.62 and 0.43 for the highest and second
highest concentrations paired by events.
The pattern of observed and modeled concentrations in 214(10) prompted
two modifications. The first was to re-evaluate the winds used to drive the
model, and the second was to try modeling each 5-min period individually when
the meteorology appeared to vary significantly during the hour. Wind
directions for 214(10) were estimated to be consistent with the impact zones
resolved by the 10-min samplers; 10-m wind directions measured by the
cup-and-vane sets were substituted for 218(3) and photo estimates of wind
direction were substituted for 201(18). Furthermore, the 5-min simulation was
selected for 201(18), 214(10), 218(4), 218(5), 218(6), 218(7), and 218(10).
Hours 217(9), 217(10), and 218(9) were judged to be insensitive to alternate
wind direction estimates and the 5-min simulation technique.
These model runs are generally more successful than the previous runs.
Experiment 214(10) in particular shows a dramatic improvement. This im-
provement is, no doubt, due in part to "fixing" the modeling wind directions
to conform with the tracer results, but an equally important element is the
use of the sequence of 5-min meteorology. As a morning transition hour, the
temperature structure and the turbulence changed significantly during the
hour. An explicit modeling of such changes appears necessary to providing
good modeling results.
-70-
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Overall statistics for the second modeling runs can be formed by
including the results for those hours not remodeled, and excluding 202(18) and
202(19). The r.m.s. error and bias for all concentration residuals equal 917
and 0.5 ppT-s/g, respectively, with a mean observed concentration equal to 782
ppT-s/g. These values represent a substantial improvement. For the highest
and second highest observed and predicted concentrations paired by event, the
r.m.s. error and bias equal 1562 and 114 ppT-s/g for the highest, and 1204 and
68 ppT-s/g for the second highest.
Again, these statistics indicate a substantial improvement in model
performance. The r.m.s. error for the three sets of data pairs drops by
approximately 40% or more, and the bias values lie much closer to zero. In
terms of the performance measure, r.m.s./C 2, these data produce 1.38 for all
concentrations paired by event, and 0.23 and 0.16 for the highest and second
highest concentrations paired by event.
These results show that the newer version of CTDM does very well in
estimating the peak observed concentrations for the neutral hours (H = 0) in
the CCB data base, especially when the "unexplainable" hours are removed. The
tendency toward underestimating the peak concentrations seen in CTDM(11083) is
virtually absent. Because H is zero in these experiment hours, the success
of CTDM(03184) is attributed to its a and a formulations (with detailed
on-site turbulence measurements), and its method for incorporating terrain
effects in the limit of weak stratification.
-71-
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SECTION 5
FLUID MODELING STUDIES OF COMPLEX TERRAIN DISPERSION
INTRODUCTION
Wind tunnel studies of the dispersion of pollutants from industrial
plants located in or near mountainous terrain have been conducted over the
last four decades. These studies were generally performed to answer specific
engineering questions such as good-engineering-practice stack heights or
locations to avoid aerodynamic downwash. The results have not been generally
transferable to other sites. More recently, studies have attempted to
simulate the atmospheric boundary layer including stratification, and to
investigate the effects of wind shear and turbulence intensity. These generic
studies have utilized idealized terrain features to understand the basic
physical processes of complex terrain transport and diffusion.
Laboratory experiments are probably most useful as a complement to other
forms of complex terrain research -- theoretical modeling and field
observations -- but in some circumstances they may provide the only practical
and economically viable means of studying a problem. A main advantage of
laboratory experiments is the opportunity to isolate a particular
meteorological phenomenon from the complexity of others occurring
simultaneously and then to study that phenomenon over a range of controlled
conditions.
The general requirements for attaining similarity between laboratory and
full-scale flows are addressed in several articles (e.g., Cermak et al., 1966;
Snyder, 1972; Cermak, 1976; Snyder, 1981) and are generally agreed upon.
Besides matching the boundary conditions, strict similarity requires the
equality of four dimensionless parameters in model and prototype: the Rossby
number, the Reynolds (Re) number, the Froude (Fr) or bulk Richardson (Rifa)
number, and the Peclet (Pe) number. For the typical (although not exclusive)
problem in which Coriolis effects are not simulated, the Rossby number is not
-72-
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matched. In addition, the Reynolds and Peclet numbers need not be matched,
provided that Re exceeds some critical value, i.e., large scale turbulence is
independent of Re. The single most important parameter that must be simulated
is Fr, which measures the ratio of inertial to buoyancy forces in the flow.
The importance of simulating buoyancy forces cannot be overemphasized for
atmospheric problems. This buoyancy simulation is basically what sets
laboratory simulation of atmospheric flows apart from that of neutrally
stratified shear flows which are more typical in mechanical and aerospace
engineering applications.
The Rossby number represents the ratio of advective or local
accelerations to Coriolis accelerations. Snyder (1981) concluded from a
review of the literature that the Rossby number needs to be considered when
modeling prototype flows with length scales greater than about 5 km under
neutral or stable conditions in relatively flat terrain. In modeling flows in
complex terrain, we may expect local accelerations to be much more significant
than in flat terrain; therefore, prototypes with length scales significantly
larger than 5 km may be modeled ignoring the Rossby number. Despite this
apparent relaxation of Rossby number similarity in complex terrain, very few
fluid modeling studies have considered length scales larger than a few km.
This section attempts to summarize the results of recent stratified
towing-tank and wind tunnel studies designed to obtain basic understanding of
flow and diffusion in complex terrain. The summary follows the recent reviews
by Snyder (1984a, 1984b) and highlights the work at the EPA Fluid Modeling
Facility at Research Triangle Park, North Carolina.
STABLE FLOW SIMULATIONS
Although the complete physics of dispersion around obstacles in stably
stratified flows is complicated and only partially understood, for an ideal
flow with a constant velocity U and Brunt-Vaisala frequency N approaching a
hill of height h, the essential flow properties are described by the hill
Froude number, Fr
Fr = UQ/Nh. (39)
-73-
-------
The hill Froude number is the square root of the ratio of the kinetic energy
of the approaching fluid to the potential energy it acquires in surmounting
the hill.
Experiments and theory (Sheppard, 1956; Drazin, 1961; Hunt and Snyder,
1980; Snyder et al. , 1980; Rowe et al. , 1982) indicate that the Froude number
divides the atmosphere (or fluid) into two distinct regimes of flow about the
hill (Figure 11). In region 1, which extends from the base of the hill to a
height h(l - Fr), the flow does not have enough kinetic energy to go over the
hill and remains roughly horizontal as it goes around the hill. (On the
downwind side, this flow separates into a horizontally recirculating wake.)
In region 2, which lies above the dividing streamline that separates the two
regions, the flow has enough energy to pass up and over the hill. The concept
of the dividing-streamline height H = h(l - Fr) is related to the notion that
a fluid parcel can rise only through a height U /N.
If the wind speed and stratification are functions of height (as is
generally the case), H is defined as follows
12 fh 2
4 IT(H)= \ r(z)(h - z)dz (40)
2 c J^
where U is the wind speed at z -- H and N(z) is the local Brunt-Vaisala
frequency defined by
N(z) = [g/0(z) (86/3Z)]15 (41)
where g is the acceleration due to gravity and 0 is the potential temperature
(°K). The left-hand side of Equation 40 is the kinetic energy of the fluid at
z = H , and the right-hand side is the potential energy gained by the fluid in
rising through the height h - H .
Note that H , as defined, depends only on the height of the hill; it does
not account for the shape of the hill as "seen" by the flow. We do not expect
a sharp boundary between regions 1 and 2; nevertheless, the concept of a
well-defined H is useful in studying stable flows over hills.
-74-
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01
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-75-
-------
Verification of the Dividing-Streamline Concept
Several towing tank experiments were run at the EPA Fluid Modeling
Facility to test the applicability of the integral formula (Equation 40) for
the dividing-streamline height in strongly stable flows over hills.
Additional tests were conducted in the stratified wind tunnel of the National
Institute for Environmental Studies of the Japan Environment Agency (Ogawa et
al., 1981). Simulations were performed for several hill shapes and aspect
ratios, e.g. ,
bell-shaped hills (Hunt and Snyder, 1980),
cone and hemisphere (Snyder et al., 1980),
truncated, steep-sided ridges of various crosswind aspect ratios
(Castro et al., 1983),
vertical fences (Snyder et al., 1982),
"infinite" triangular ridge and a long sinusoidal ridge, and
a model of Cinder Cone Butte.
The concept of H was found to be valid when interpreted as a necessary but
not sufficient condition for wide ranges of hill shapes, density profile
shapes and wind angles, and in strong shear flows as well. For example,
Figure 12 illustrates the composite estimates of the plume paths and
dispersion for a towing tank simulation of Cinder Cone Butte. Dye streamers
were released at 0.125, 0.25, 0.375, 0.5, 0.75, and 1.25 of the hill height.
The qualitative results corroborate the suggestions of Hunt and Snyder (1980)
that plumes released below H tend to impinge upon and pass around the sides
of the target hill and that plumes released above H tend to pass over the
nilIcrest.
Twelve tows of the Cinder Cone Butte model were performed in the Fluid
Modeling Facility towing tank to examine the validity of the integral formula
(Equation 40) for the dividing-steam!ine height with non-uniform density
gradients. For each tow, a particular source height was chosen and Equation
40 was integrated numerically using the measured density profile to predict
the towing speed required such that the center tracer streamer (of three)
would rise just to the elevation of the saddle point, i.e., the minimum height
of the draw between the two peaks of Cinder Cone Butte. If the formula were
-76-
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270
.5, 0.75, 1.25
180
Figure 12. Composite estimates of plume oaths based on towing tank simulations
of Cinder Cone Butte model.
-77-
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correct, the lower streamer would be observed to go around the sides of the
hill, the upper streamer over the top, and the center one, because of its
finite thickness, would split with the upper portions going over and the lower
portions around the sides.
Figure 13 shows the results of the integrations of Equation 40 for each
density profile as well as the experimentally observed results of the twelve
tows. The agreement between the predictions and observations is regarded as
excellent. The error bars indicate the best judgment of variability during
the observations. For example, tow number 0 showed little or no deviation of
the splitting of the center streamer, so that the error was judged as zero.
Tow number 3, on the other hand, showed occasional wisps of the lower streamer
rising over the top and of the upper streamer going around the hill.
From previous work as well as current studies with the Cinder Cone Butte
model, it is concluded that the integral formula of Sheppard (1956) is valid
for predicting the height of the dividing streamline for a wide range of
shapes of stable density profiles and a wide range of roughly axisymmetric
hill shapes.
Another series of 12 tows was made with steep-sided triangular ridges of
various crosswind aspect ratios to ascertain effects on the
dividing-streamline height as a three-dimensional hill is elongated into a
two-dimensional ridge. For example, Figure 14 shows the observations made
during the tows of triangular ridges with aspect ratios of 1 (L = h) and 8 (L
= 8 h). It is apparent that the dividing-streamline height followed the
"1-Fr" rule for Fr < 0.25, and deviated strongly for Fr > 0.25, but there were
no observable differences due to variations in aspect ratio. The deviation
from the "1-Fr" rule is due to the formation of an upwind vortex that produces
a downward flow on the front face of the ridge. It is apparently due to the
combination of the steep upwind slope of the ridge and the shear in the
approach flow.
Notice that the data in Figure 14 are on the opposite side of the "1-Fr"
line from the "l-2Fr" line suggested by Baines (1979), even for the ridge with
aspect ratio 8. From the studies with the truncated triangular and sinusoidal
-78-
-------
o
X
12 eta i I i i I i i I I I I i I i
Figure 13. Predictions (open symbols) and observations (closed symbols) of
dividinq-streamline heights as functions of towing speed of Cinder
Cone Butte model.
-79-
-------
u
X
0 + t '< i I i ' i i i ' i i i i i i i i I i .' i
I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' '
0 .1 .2 ,3 .11 .5 .6 .7 .8 .9 1
Fr
Figure 14. Dividinq-streamline heiqht/hill heiqht ratio from triangular ridqe
study expressed as function of Froude number.
-80-
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ridges perpendicular to the wind, it was concluded that the aspect ratio, per
se, does not have a significant influence on the dividing-streamline height
H . Deviations from the H /h = 1-Fr rule are attributed to the combination of
shear in the approach flow and the steep slope of the triangular ridges, which
resulted in the formation of an upwind vortex with downward flow on the front
face of the ridges. The "1-Fr" rule was validated for the sinusoidal ridge
with a length-to-height ratio greater than 16:1; in this case, the shear in
the approach flow was much less pronounced and the upwind slope was
substantially smaller. Note that the above deviations from the "1-Fr" rule do
not invalidate Sheppard's concept. The rule should be interpreted as a
necessary but not sufficient condition, i.e., a fluid parcel may possess
sufficient kinetic energy to surmount a hill, but it does not necessarily do
so.
In the Japanese stratified wind tunnel studies (Snyder et al., 1982), a
range of operating modes was found that yielded reasonably strong shear layers
with depths more than twice the hill heights in conjunction with strong stable
temperature gradients. These provided dividing-streamline heights as large as
0.75 h. In the vertical fence (solid wall) studies with a stratified approach
flow, the shear was found to have an overwhelming influence. Conclusions are:
(1) as in the triangular ridge studies, the crosswind aspect ratio was
relatively unimportant, the basic flow structure was independent of aspect
ratio; (2) the shear (in conjunction with the steep slope) created an upwind
vortex such that plumes were downwashed on the front faces; and (3) under
strong enough stratification, there was a limit to the downward penetration of
elevated streamlines on the upwind side of the fence; the extent of this
penetration was apparently predictable as a balance between kinetic and
potential energies. With these same shear flows approaching the much lower
sloped Cinder Cone Butte model, however, there was no evidence of upwind
vortex formation. Limited concentration measurements on the Butte model
suggested that Sheppard's integral formula correctly predicted the height of
the dividing streamline.
From the sinusoidal ridge studies with wind angles at other than 90°, it
was concluded that the effects of deviations in wind direction (from 90°) are
relatively insignificant until the wind direction is something like 45° to the
-81-
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ridge axis. At 30°, significant departures from the H /h = 1 - Fr rule were
observed. The fluid had sufficient kinetic energy to surmount the ridge but,
presumably, found a path requiring less potential energy round the end of the
ridge. When the plume streamers were moved closer to the upstream stagnation
streamlines (upwind of the upwind edge of the ridge), they behaved according
to the Hc/h = 1 - Fr rule.
These experiments suggest that the lateral offset of the source from the
(probably contorted) plane of stagnation streamlines is an important parameter
to consider in determining the location and value of surface concentrations,
especially when the wind is at a small angle to the ridge axis (say, <45°).
The two-dimensional triangular ridge studies showed that steady-state
conditions are not established in strongly stratified flows (say, Fr < 1). A
squashing phenomenon and upstream columnar disturbances continuously changed
the shapes of the "approach flow" velocity and density profiles. Thus, these
experiments have no analog in the real atmosphere. Further, since long ridges
cut by periodic small gaps require very long tow distances in order for steady
state to be established, it is concluded that previous laboratory studies may
not be representative; specifically the H /h = 1 - 2Fr formula proposed for
flow about ridges with small gaps is not expected to be valid in the real
atmosphere. Finally, a suggestion is made that the gap ratio (the fraction of
area removed from a model that spans the width of the towing tank) must exceed
25% in order for steady-state conditions to be established in the usual size
and shape of a towing tank. More work is required to establish firmly the
relationships between model size and shape, stability, and tank size and shape
in order to determine limits of applicability of fluid modeling and ranges of
transferability to the atmosphere.
Flows and Diffusion in the Lower Layer
The main characteristic of plumes emitted upwind of a hill but below HC
is that they impinge on the hill surface, split, and travel round the sides of
the hill (Figure 12). Upwind, the plumes are largely constrained to move in
horizontal planes and vertical diffusion is severely limited. They are
-82-
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frequently rolled up within an upwind vortex as they impinge on the hill
surface. The plumes can lose significant elevation in traveling round the
sides of the hill (Hunt and Snyder, 1980). Plumes that hug the hill surface
leave it at the point where the flow separates (generally 100° to 110° from
the upstream stagnation point, much as a streamline separates from the surface
of a two-dimensional cylinder). Plumes emitted close enough to the stagnation
line tend to be entrained into the wake region and rather rapidly regain their
upstream elevation while mixing through the depth of the hydraulic jump.
Beyond that point, these entrained plumes tend to be vigorously mixed
horizontally across the wake, leading to small wake concentrations. Whether
or not they are entrained, plumes are generally affected by vortex shedding or
low frequency oscillations of the wake. These wake oscillations appear to
induce oscillations in the plume upwind of the hill, causing it to waft from
one side of the hill to the other.
Snyder and Hunt (1984) showed that under these conditions (H < H ), the
maximum surface concentration was essentially equal to the concentration
measured at the plume center!ine in the absence of the hill (at the same
downstream distance). The location of the maximum concentration was on the
upstream face. A small lateral displacement of the source from the stagnation
streamline did not appreciably change the magnitude of the maximum
concentration, but moved its location to the side of the hill. Consequently,
small oscillations in wind direction may be expected to result in a covering
of the hill with the maximum concentration for short periods, but to
significantly reduce the average concentration. Finally, a slightly larger
displacement of the source (i.e., a distance comparable to the plume width in
the absence of the hill) caused the plume to miss the hill entirely,
indicating a very strong sensitivity of surface concentration to wind
direction.
Flows and Diffusion in the Upper Layer
In the upper layer (Figure 11), buoyancy and inertia! forces control the
flow as it passes over the hill. Rowe et al. (1982), Bass et al. (1981), and
Weil et al. (1981), have suggested that this upper layer flow is approximately
-83-
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potential flow. However, the stratification above may have important effects
on the vertical convergence and horizontal divergence of the streamlines (as
well as on the diffusion). A different approximation is to treat plumes in
the upper layer as if a ground plane were inserted at the dividing-streamline
height. By definition, the dividing-streamline height of the upper layer flow
is zero. Therefore, the Froude number of the upper layer flow is unity and
the flow must be treated as if F = 1.
To test this approximation, Snyder and Lawson (1983) conducted a series
of tows in a stably stratified salt-water towing tank wherein the density
gradient was linear and the dividing-streamline height was half the hill
height. Effluent was released at three elevations above the
dividing-streamline height. Pairs of tows were made such that, in one tow,
the hill (upside-down) was fully immersed in the water and the towing speed
was adjusted to provide a "natural" dividing-streamline surface. In the
second tow of the pair, the hill was raised out of the water to the point
where only the top half of the hill was immersed, thus forcing a flat
dividing-streamline surface, while all other conditions were maintained
identical. Concentration distributions were measured on the hill surface for
each pair of tows and these were compared to ascertain effects of an assumed
flat dividing-streamline surface as is used in the CTDM model. The first run
simulated an emission at 0.6 h, where h is the hill height. The physical
model was a fourth-order polynomial (bell-shaped) hill. Concentrations were
measured at 100 points on the hill surface.
Figure 15 shows the concentration distributions measured in both the
fully-immersed and half-immersed cases for Fr = 0.5 and H /h = 0.6. The most
j
obvious difference between the two cases is the absence of lee-side
concentrations below half the hill height in the half-immersed case. Of
course, in the half-immersed case, concentrations at positions below half the
hill height were zero because that portion of the hill was outside the water.
In the fully-immersed case, the plume diffused to some extent below half the
hill height around the upwind side, but also this plume "hugged" the hill
surface as it was swept down the lee side to a much lower elevation than the
release height.
-84-
-------
Fiqure 15. Concentration distributions measured on surface for fully-submerged
hill (top) and half-submerged hill (bottom). Arrows indicate flow
direction.
-85-
-------
Figure 16 presents a scatter diagram comparing, on a point-to-point
basis, the surface concentrations measured in the half- and fully-immersed
cases. Measurements at points below half the hill height are not included
here because, in the half-immersion case, these ports were out of the water.
Within the region of large concentrations, the two cases compare quite
favorably, the half-immersed case yielding concentrations approximately 10 to
20% larger than the fully-immersed case. In the region of low concentrations,
quite large differences occurred (worst case, a factor of 10). However, a
close examination showed that in all cases where concentrations differed by
more than a factor of 2, the port locations were very close to half the hill
height, i.e., either at 0.505 h or 0.59 h.
These results and the results of simulations for releases at 0.7 h and
0.8 h suggested that the assumption of a flat dividing-streamline surface is a
reasonable approximation to make, at least with regard to predicting the
locations and values of maximum concentrations and areas of coverage on the
windward side of the hill. When the stack heights are relatively close to the
dividing-streamline height, the lee-side concentrations are also predicted
reasonably well. The apparent cause of the relatively poor agreement between
lee-side concentration patterns in the higher stack cases is the presence of a
hydraulic jump at the downwind base of the hill in the full-immersion case
that was absent in the half-immersion case.
Hill Concentrations During Stable Conditions
Again, plumes emitted above H are transported over the hilltop; however,
if the release height is close to the dividing-streamline height, they spread
broadly but thinly to cover the entire hill surface above H . Unlike plumes
L*
released at or below H , plume material reaches the hill surface only by
diffusion perpendicular to the plume centerline. Plume meander as observed at
or below H is absent. As H is increased relative to H , the point of first
c s c
contact of the plume with the hill surface moves toward the hilltop. Further
increases in H move the contact point to the lee side of the hill. These
features, in combination with the steadiness in the flow and thus the plume
direction, have resulted in some of the largest surface concentrations
-86-
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100
10
LU
CD
on
CO
«/>
>-
_J
_l
U.
X
1.0
0.1
I i t i i t
0.1
1.0
10
1 I J
100
X (HALF SUBMERGED)
Fiqure 16. Comparison of surface concentrations for half-submerged versus
fully-submerged hill.
-87-
-------
observed under any conditions. With still further increases in H , the plume
moves off the hill surface and surface concentrations diminish rapidly.
Figure 17 presents an overview of the maximum surface concentrations
measured in Hc/h x Fr space for the bell-shaped hill of Snyder and Hunt
(1984). Overlaid on this graph are the dividing-streamline height (H /h =
1 - Fr), the boundary layer, and somewhat speculative concentration isopleths.
The graph suggests that the largest concentrations occur when the source
release is near the dividing-streamline (the solid line in the graph) and that
they decrease rapidly with distance to the right of this line (larger stack
heights or Froude numbers). This rapid decrease is due to the fact that as
the stack height or Froude number is increased, the contact point moves upward
over the hill crest and then down the lee side. Further increases in H - H
o \f
much above the thickness of the plume in the absence of the hill result in the
plume lifting off the surface with no contact at all. Note that if H - H
J \f
approximates the plume thickness, a significant surface concentration can
arise because of the downward deflection of the streamlines onto the hill.
If the source height is less than the dividing-streamline height (left of the
line), the measurements suggest that the maximum surface concentrations are
roughly uniform in this region.
NEUTRAL FLOW SIMULATIONS
The effects of terrain on the flow can be demonstrated through the
deflection of streamlines over and around ridges and hills. For example, the
displacement of the mean streamlines determines how near to the surface the
centerline of the plume will reach, which in turn determines the ground-level
concentrations. The convergence and divergence of the streamlines in the
directions normal to and, in the case of three-dimensional flows, parallel to
the surface affect the plume width (Hunt et al. , 1979). If flow separation
occurs, the size and shape of the recirculating cavity that ensues and the
position of the source with respect to this cavity can be very important in
determining subsequent plume behavior.
-88-
-------
01
Figure 17. Concentration isopleths (dashed lines) as functions of dividing-
streamline height/hill heiqht ratio and of Froude number. Numbers
represent concentrations measured at those points. Stippled area
depicts surface boundary layer. Striped area represents roughly
uniform concentrations. Vertical arrows indicate depth of plume
at the location of the hill.
-89-
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A simple way to evaluate the effects of terrain on ground-level
concentrations is to calculate a terrain amplification factor A, which is
defined as the ratio of the maximum surface concentration occurring in the
presence of the terrain to the maximum that would occur from a source of the
same height in flat terrain.
Two-Dimensional Hills
Numerous studies have been conducted on two-dimensional terrain features.
Perhaps the most illustrative is a series of smooth-shaped ridges by
Khurshudyan et al. (1981). Three hill shapes were generated from a set of
parametric equations. The aspect ratios (streamwise half-length/height) of
the hills were 3, 5, and 8; maximum slopes were 26°, 16°, and 10°,
respectively. These hills are referred to by their aspect ratios, e.g., hill
5. Ground-level concentrations were measured downwind of sources of various
heights located at the upwind bases, the tops, and the downwind bases of the
hills.
Table 6 summarizes the observed terrain amplification factors for the
stacks at the three locations. The maximum A of 15 occurred with a stack of
height one-fourth the hill height and located at the downwind base of hill 5.
This was due to the very small mean transport but very large turbulent
dispersion at that location. Amplification factors nearly as large occurred
when the source was located near the separation-reattachment streamline
downwind of hill 3, because in this case the plume was advected directly
toward the surface (reattachment point). Upwind sources resulted in terrain
amplification factors in the range of 1.1 to 3, with the larger values being
observed for the steeper hills. Finally, the hilltop source location
resulted in amplification factors less than unity, with smaller values being
observed for steeper hills.
Three-Dimensional Hills
Two studies have been conducted to determine the effects of the crosswind
aspect ratio of a hill (truncated ridge) on dispersion from nearby sources.
-90-
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TABLE 6. TERRAIN AMPLIFICATION FACTORS FOR TWO-DIMENSIONAL HILLS
Source location
Hill Hg/h
8 1/4
1/2
1
1-1/2
5 1/4
1/2
1
1-1/2
3 1/4
1/2
1
1-1/2
Upwi nd
1.5
1.1
1.5
1.2
2.0
2.0
1.7
1.2
2.8
2.5
1.8
1.9
Top
0.9
0.6
0.8
0.8
0.5
0.6
0.9
1.0
0.3
0.7
0.9
0.9
Downwi nd
3.4
3.0
2.4
1.7
15.0
8.0
5.6
2.9
7.5
6.4
10.8
7.8
Triangular ridges of different crosswind lengths were constructed by cutting a
cone in half and inserting straight triangular sections between the two
halves. Snyder and Britter (1984) investigated surface concentrations on the
ridges resulting from upwind sources. Ground-level concentrations were
measured downwind of stacks of height 0, 0.5, and 1.0 h, with stacks located
3.7 h upwind of the hill centers.
For the ground-level source, downwind concentrations were reduced by the
presence of the hills due to the excess turbulence and divergence of the flow
around the hills. For the elevated sources, the maximum ground-level
concentrations occurred at the crest or on the lee sides of the hills. The
maximum values for the cone were 2 to 3 times those for the two-dimensional
ridge and 2 to 4 times those in flat terrain. Castro and Snyder (1982)
extended this study by locating sources at various downwind positions. Flow
separation was observed on the lee sides of these hills because of the steep
lee slopes and the salient edges at the crests.
-91-
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The cases discussed above are summarized in Table 7 by listing them in
order of decreasing A. From the standpoint of a fixed stack height, it
appears that the worst location for a source is just downwind of a
two-dimensional ridge and the best is on top of a ridge.
TABLE 7. SUMMARY OF TERRAIN AMPLIFICATION FACTORS FOR NEUTRAL FLOW
Source
location
Downwi nd
Downwind
Upwi nd
Upwi nd
Top
Hill
type
Two-dimensional
Three-dimensional
Three-dimensional
Two-dimensional
Two-dimensional
Amp! ification
factor
10-15
5-6
2-4
1-3
0.5-1
Sources downwind of terrain obstacles generally result in larger surface
concentrations because of the excess turbulence generated by the hills and
because the effluent is generally emitted into streamlines that are descending
toward the surface. Maximum terrain amplification factors are considerably
larger downwind of two-dimensional hills than those downwind of
three-dimensional hills. A probable cause of this effect is that, in
three-dimensional flows, lateral and vertical turbulence intensities are
enhanced by roughly equal factors, whereas in two-dimensional flows, the
lateral turbulence intensities are not enhanced as much as are the vertical
turbulence intensities (because of the two-dimensionality). Since the maximum
surface concentration depends upon the ratio a /a (Pasquill, 1974), we may
expect the A's downwind of two-dimensional hills to be larger than those
downwind of three-dimensional hills. Also, the sizes of the recirculating
cavity regions of three-dimensional hills are generally much smaller than
those of two-dimensional ridges.
With regard to upwind sources, terrain amplification factors are larger
for three-dimensional hills because, in such flows, streamlines can impinge on
the surface and/or approach the surface more closely than in two-dimensional
flows (see Hunt and Snyder, 1980; Hunt et al., 1979; Egan, 1975).
-92-
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IMPLICATIONS FOR MODEL DEVELOPMENT
Wind tunnel and towing tank modeling have proved useful in performing
generic studies to understand the basic physics of flow and diffusion in
complex terrain. The fluid modeling studies have demonstrated the
applicability of the dividing-streamline concept to a wide variety of hill
shapes, slopes, and aspect ratios. H forms the boundary between a lower
\*
layer of horizontal flow and an upper layer that passes over the hilltop.
Plumes released in the lower layer impact on the hill surface; the
resulting surface concentrations essentially equal those observed at the
center of the plume in the absence of the hill. For practical purposes, a
plume released in the upper layer can be treated as a release from a shorter
stack upwind of a shorter hill, i.e., as if a ground plane were inserted at
the dividing-streamline height.
These results are being used directly in the complex terrain modeling
approaches and have proved to be quite useful to the modelers. Strongly
stratified towing-tank experiments on flows over two-dimensional ridges were
found to have no analog in the real atmosphere because of the unsteadiness
created by the finite length of the tank. Another limitation of fluid
modeling studies is that they cannot simulate the variability of the real
atmospheric boundary layer. Reasonable attempts have been made to account for
wind direction and speed variability by changing the tow speed and hill
orientation. But real atmospheric turbulence, especially low-frequenc"
meandering common in stable conditions, must be kept in mind in transferring
the fluid modeling results to the real world.
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SECTION 6
MODEL IMPROVEMENT AND RESEARCH NEEDS
Previous sections have described the present state of understanding and
of disperson model development for flow phenomena in complex terrain. This
section provides some suggestions, based on the information available, of how
the performance of air quality models to be applied to complex terrain
settings can be (and are being) improved. Identification of research needs to
reach closure on outstanding complex terrain issues is also provided.
USE OF ON-SITE METEOROLOGICAL MEASUREMENTS
A model cannot perform better than allowed by the quality and
representativeness of the input information. Experience with the Complex
Terrain Model Development field experiments, fluid modeling experiments, and
subsequent data analyses shows that to obtain an understanding of plume
behavior, one needs to have reliable information about flow conditions. For
complex terrain settings especially, one cannot expect that meteorological
data obtained for model input from an off-site location is necessarily
representative of the local conditions of interest.
Figure 18 compares a wind rose from an on-site meteorological tower at
the Westvaco Luke Mill site to the Pittsburgh, Pennsylvania airport rose,
which was the nearest National Weather Service observation station. The
on-site measurements clearly show the effects of flow channeling in altering
the frequency of occurrence of winds by direction. Great uncertainty would
need to be associated with model predictions using the off-site Pittsburgh
data, about 150 km distant.
Figure 19 from Venkatram et al. (1983) shows the ability to estimate
vertical plume spread during stable conditions. This was achieved using
on-site a data at Cinder Cone Butte, with the predicted values compared to az
derived from various ranges of lidar scan sampling frequencies (scans/hour).
-94-
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LEGEND
Over 18.5 MPH
15.5+to18.5 MPH
11.5+to15.5 MPH
7.5+toll.5 MPH
3.5+to 7.5 MPH
1.5+to 3.5 MPH
T
Figure 18. Wind rose from Westvaco Luke Mill meteorological tower for two-year
period as compared to Pittsburgh airport wind directions (solid line)
-95-
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60.0-
N 10.0.
3 5.0
.1
2-3 Scans
.1 .5 1.0 5.0 10.0
Observed Sigma-Z
60.0
60.0
10.0
5.0
1.0
.5
.1
(-6 Scans
.5 1.0 5.0 10.0 60.0
Observed Sigma-Z
60.0
.1
.5 1.0 5.0 10.0
Observed Sigma-Z
60.0
60.0-
|io.o
u
w 5.0
T3
01
U
Q
•H
3
O
3 i.o
.5
.1
10-12 Scans
.5 1.0 5.0 10.0 60.0
Observed Sigma-Z
Fiqure 19. Comparison of plume vertical standard deviations estimated from
Equation 34 with those derived from lidar observations at Cinder
Cone Butte for ranges of hourly scan frequencies.
-96-
-------
The comparison is generally good, especially in the highest sampling rate
category of 10-12 scans/hour. During such stable conditions, when the flow
aloft is largely uncoupled from the surface, it is especially important to
obtain meteorological information (particularly turbulence data) that are
representative of conditions at expected plume height.
Hanna (1980, 1983) and Dittenhoefer (1983) have demonstrated that
improvements to understanding dispersion rates are possible using on-site
turbulence data. Lavery et al. (1983a) have stressed the advantage of using
on-site wind direction data to determine probability density functions for
direct input to replace the use of a 's in modeling applications.
IMPROVED PARAMETERIZATION OF STABLY STRATIFIED FLOW TRAJECTORIES
The Complex Terrain Model Development program is yielding considerable
information on the behavior of plumes in stable flows. Although further
verification work is required, especially for full-scale conditions, it is
possible to draw some strongly supported conclusions at this time.
The use of Froude number to characterize the relative importance of
inertia! versus buoyancy forces on the flow is well established for
laboratory- scale experiments and carries over to the scales of the Cinder Cone
Butte and Hogback Ridge experiments. The related parameter of critical or
dividing-streamline height, H , is important in relating the implications rf
large or small Fr to the expected behavior of an elevated plume. There are
alternative forms of defining Fr and H , the choice of which depends largely
upon the detail of the meteorological data available. The simplified form is
Hc = h(l-Fr) (42)
where h is a characteristic hill height and Fr = U/Nh, and where N is the
Brunt-Vaisala frequency given by
N = [(g/6(z) oe/az)] (43)
-97-
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where 0 is potential temperature (°K) and U is the characteristic wind speed.
This is appropriate for conditions of relatively constant values of wind speed
and potential temperature gradient as a function of height.
For more general conditions Snyder et al. (1982) have demonstrated the
applicability of solving
dZ
Hc " 3Z
where H must be determined iteratively. This is the form of the equation for
obtaining HC that is currently being used in the Complex Terrain Model
Development program. Ryan and Lamb (1984) confirmed the superiority of this
equation to Equation 42 for arbitrary wind and temperature profiles in the
case of the 335-m tall Steptoe Butte.
Recommendations for Flow above H
The Cinder Cone Butte and Hogback Ridge field data and fluid modeling
results, as well as other model validation evidence, suggest that some
modification of flow trajectories to allow lifting of the plume over a terrain
object be incorporated into models for plumes in stable flow above H . The
approach being pursued in the CTDM model is described by the LIFT algorithms
in Section 3. Simpler algorithms will also be pursued to ascertain how much
parameterization is necessary to provide model improvement. The fluid
modeling tests of Snyder and Lawson (1983), demonstrating the limits of
applicability of replacing the dividing-streamline height with a flat surface,
can be used as guidance in structuring the algorithms for plume heights at
varying elevations relative to H . The progress achieved in parameterizing
the flow above H during stably stratified conditions will also be relevant to
neutral (and perhaps unstable) flow parameter!'zations.
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Recommendations for Flow below H
Field and physical modeling experiments support the contention that
plumes transported in a stable flow below H can impinge on a terrain feature
or can flow around the sides. If impingement occurs, the maximum surface
concentrations can be as large as the elevated plume center!ine
concentrations. The COMPLEX I, COMPLEX II, and SHORTZ models assume a full
doubling of the elevated plume centerline concentrations during impaction
because full reflection at the surface is assumed. This factor probably
contributes to the tendency for these models to overpredict during stable
conditions. COMPLEX I and II allow a minimum 10-m standoff distance in the
Gaussian exponential term, but this does not affect concentrations very much
for most full-scale situations. (This 10-m standoff distance is important for
many of the Cinder Cone Butte simulation runs, however.) The RTDM model uses
a partial reflection coefficient that depends upon plume growth rate and
terrain slope rather than full doubling. The CTDM model uses a spatial
integration upwind of the point of plume centerline impingement to calculate
the effect of surface reflection on the concentration at the point of
interest. An adjustment recognizing the limited effects of reflection is
recommended for use in refined models.
The parameterization of the vertical and horizontal dispersion for flow
below H should account for increased meandering on horizontal dispersion as
well as the possibility of increased effective vertical dispersion due to wind
shear effects. None of the currently available models formally parameterize
these expected changes in a or a due to upwind effects. Models that use
on-site turbulence data representative of these conditions should show
improved performance, however, because such effects would be reflected
directly in the measured values.
IMPROVED PARAMETERIZATION OF NONSTABLE FLOW TRAJECTORIES
The COMPLEX I and II models, as well as a number of other models,
simulate the effects of deformation of flow passing up and over terrain with
"half-height" plume path coefficients. The COMPLEX/PFM model, for certain
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sets of conditions, uses a potential flow theory to develop more site-specific
trajectories and combined deformation effects. It appears to show improvement
over COMPLEX I and II. Theory suggests that a plume passing over a
two-dimensional ridge would be better described using a terrain-following
algorithm versus a half-height correction. However, vertical dispersion rates
will be increased due to changes in the boundary layer flow. This will tend
to increase the ground-level concentrations upwind over those to be expected
in the absence of the hill. More analysis of field and physical experimental
data is needed regarding this issue before a specific change to the current
EPA models is recommended. Observations during nonstable conditions at the
Cinder Cone Butte and Hogback Ridge field experiments are currently available
for such analyses.
MODELING NEEDS FOR LEE-SIDE FLOW TRAJECTORIES
Theory and experiments suggest that under different combinations of
atmospheric stability, hill size and shape, and location of releases relative
to terrain features, the maximum surface concentrations occur on the lee side
of the hill (Snyder, 1983). This can occur under stable conditions with the
source above the dividing-streamline and upwind of the hill, or under
nonstable conditions with the source in the wake cavity region downwind of the
hill and below the region of flow separation (Huber et al., 1976). The
existence of separation depends upon the slope and shape of the hill, the
crosswind aspect ratio, surface roughness, and the degree of air flow
stratification. Under neutral conditions, terrain amplification factors as
large as 15 have been observed.
As described in Section 5, wind tunnel and towing tank experiments can
provide information on the systematic variation of these effects with
atmospheric stability and terrain geometry. Field data from the Cinder Cone
Butte and Hogback Ridge experiments also contain considerable information on
concentrations observed on the lee side for conditions of the source upwind of
terrain features. For strongly stable flows (Fr < 1) with sources in the lee
of terrain, the horizontal flow below the dividing streamline is observed to
separate in traveling round the sides of hills, forming horizontally
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recirculating cavity regions. Effluents from a source placed within such a
cavity region will be transported "upwind" toward the hill surface and cover a
narrow vertical band spread over a wide sector of the hill surface. Whereas
short-term concentrations are likely to be considerably smaller than those
from upwind sources (impingement), longer-term concentrations may be larger
because, whereas the wind meander will significantly reduce impingement
concentrations, such meander will not significantly reduce the concentrations
from lee sources. The stratified towing tank provides an ideal setting to
examine the potential for large concentrations and to provide physical
descriptions and measurements upon which mathematical modelers may construct
and/or improve complex terrain dispersion models.
There are two issues that need to be addressed: (1) provide guidance
regarding when the maximum concentrations would be expected to occur on the
windward side of terrain versus the leeward side for purposes of deciding
which aspect should be emphasized in modeling, and (2) develop and validate
reliable mathematical algorithms for conditions when the lee-side
concentrations are of concern.
FLOW FIELD MODELING NEEDS
To date, the EPA Complex Terrain Model Development study has focused on
the dynamics of plume interactions with elevated terrain features under
conditions of stable flow toward the terrain. There are many topographical
and meteorological settings where stable flows toward the crests of high
terrain may occur very infrequently or not at all. Site-specific
meteorological data can shed light on this issue for some locations, but a
reliable fluid dynamical modeling approach would be a much less expensive
alternative means of determining whether or not such flows occur. The ASCOT
program (Dickerson and Gudiksen, 1983) has developed models that can be
applied to flows within mountain valleys. Wooldridge and Furman (1984) have
studied the wind fields around a more isolated terrain feature. A number of
wind flow models have been proposed for general use, but comprehensive
validation efforts are needed before they could be deemed reliable.
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VALLEY VENTILATION MODELING
This review document has emphasized the modeling needs for compliance
with the ambient air quality standards. The meteorological conditions that
tend to be constraining are those which, for a single source, result in the
maximum impact on high terrain. Another air quality issue is the buildup of
emissions from multiple sources in a confined valley during conditions of
general atmospheric stagnation.
The ASCOT program is developing models for predicting the effects, of
slope flows and valley drainage winds on dispersion in valleys. However,
dispersion models are needed that will couple the effects of synoptic-scale
conditions to the overall ventilation rate of valleys having differing
topographic features. The EPA Green River Ambient Model Assessment program is
one current effort to meet this need, but more field verification of the
component models is needed. Similarly, the effort to couple the valley
component (VALMET) with the mesoscale component (MELSAR) during conditions of
valley out-venting has not yet been completed.
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SECTION 7
SUMMARY AND CONCLUSIONS
The purpose of this document was to assess the current understanding of
dispersion processes in complex terrain and to assess the ability of currently
available or currently-being-developed disperson models to meet EPA regulatory
needs. The major findings are summarized below together with associated
conclusions.
PHENOMENA OF IMPORTANCE
The primary meteorological conditions of concern for sources located in
mountainous terrain settings are those in which plumes are embedded in stable
flow that is advecting toward terrain features at or above plume elevation.
For some settings, multi-hour persistence of plumes embedded in neutrally
stable air flows may also be of paramount concern. Fumigation associated with
temperature inversion breakup can be important to still other settings.
Multi-source regions need to be concerned about the buildup of pollution in
stagnant valleys.
Our knowledge of flow behavior during stable conditions has improved
considerably over the past several years, largely as a result of research
efforts undertaken including theoretical work, fluid modeling efforts, and
field measurement programs. It is now widely acknowledged that stably
stratified flow behaves differently depending upon details of the temperature
gradients, velocity profiles, and terrain geometry. The effects of
stability-related and inertial forces can be parameterized by the Froude
number, Fr. The implications on flow behavior at any elevation relative to
the terrain depends upon the related parameter H , the critical or
\*
dividing-streamline height, and the ratios of the hill height to hill length
and width. The fluid modeling experiments and field studies show that H in
L*
particular can be interpreted as a height that separates a lower flow that
tends to pass around the side of an obstacle from an upper flow that can
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flow up and over the top of an obstacle. With these two parameters, it is
possible to differentiate the conditions that give rise to direct impingement
on windward slopes, passage of a plume up and over a feature, or the drawing
down of a plume surmounting the obstacle to pass closely along the leeward
slope.
An equally important aspect of modeling the concentrations expected on
high terrain is the estimation of atmospheric turbulence levels in both the
vertical and horizontal directions. The presence of terrain features upwind
of a source is known to disturb the flow by vortex shedding, formation of
regions of separation, and the general creation of shear in the flow. The
principal effect of upwind terrain is to increase the horizontal dispersion
rates over those that would be expected over flat terrain, especially during
stable atmospheric conditions. The effect obviously depends upon the nature
of the terrain upwind of the region of interest and cannot readily be
generalized. A way of incorporating these phenomena into models is by
measuring directly the wind direction variations with time and using this
information to construct estimates of the crosswind spread or probability
density functions for the concentration distributions. Similarly, vertical
dispersion rates in complex terrain can differ from those expected over flat
terrain due to the creation of shear caused by flow accelerations,
decelerations, and distortions in general. Again, direct measurements of
vertical wind velocity variations are desirable for purposes of estimating the
vertical dispersion rates.
Other phenomena of concern are the effects of flow separation in the lee
of terrain features in drawing emissions from sources downwind back to the
leeward surface. Observations near existing sources have identified that such
recirculation occurs. Fluid modeling efforts have indicated that the
magnitude of the concentrations on the leeward faces can be quite large.
The buildup of pollution in deep, contained valleys during conditions of
synoptic-scale stagnation is a problem associated with the presence of
multiple sources in such settings. Whereas impingement phenomena associated
with a single source emitting into stable flows or persistent neutral flows
result in peak concentrations over 1-, 3- and 24-hour averaging times, stag-
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nation within valleys can result in the buildup of high concentrations over
multi-day periods. A better understanding of the meteorological conditions
which are associated with stagnation and with the eventual purging of such
regions is needed.
VALIDATION OF AVAILABLE MODELING TECHNIQUES
Although there are a large number of models and model variations in the
dispersion modeling community, this review considered only those complex
terrain models that are presently being used by EPA in regulatory practice,
models presently being developed by EPA, and models submitted to EPA in
response to a formal "Call for Models" published in the March 1980
Federal Register. The models received were to undergo model evaluation tests
and scientific peer review. Available dispersion models for complex terrain
applications are largely adaptations or outgrowths of the Gaussian plume
equation approach, although they possess considerably differing levels of
sophistication. This is due, in part, to the need to examine extensive time
series of meteorological data to estimate the peak 3- and 24-hour and annual
averages. Another reason is that very complicated numerical models have not
consistently performed better than models of the Gaussian type. Only one
non-Gaussian type model was submitted to the EPA in response to the
Federal Register "Call for Models." The EPA screening models, COMPLEX I and
COMPLEX II, are presently applied by the EPA and sometimes used as reference
models in model comparison studies. Current guidance allows the use of
alternative models in regulatory applications if such an alternative model is
shown to be superior in source-specific model validation programs.
TRC Model Evaluation Efforts
Under contract to the EPA Office of Air Quality Planning and Standards,
TRC Environmental Services, Inc., performed a statistical evaluation of the
currently available EPA complex terrain dispersion models and the models
submitted in response to the Federal Register notice, A preliminary review of
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the statistical results suggests the following observations based upon a
review of the bias and total r.m.s. errors tabulated for each model.
(a) The COMPLEX II model overpredicted the observed highest concentrations
for both the Westvaco and the Cinder Cone Butte data sets. It generally
rated the most poorly among the Gaussian plume type models.
(b) The COMPLEX I model showed improvement over COMPLEX II, but it over-
predicted the largest concentrations at Westvaco by a significant factor.
The improvement over COMPLEX II is probably associated with the use of
sector averaging in parameterizing the crosswind spread of the plume.
(c) The EPA model, COMPLEX/PFM, performed somewhat better than COMPLEX I and
II, which have the same algorithms for many of the meteorological
conditions. The differences in the algorithms, which should be
associated with the improvements, are in the use of the dividing-
streamline height H in defining flow regimes for certain meteorological
\f
conditions and in the associated use of potential flow theory to estimate
plume trajectories and dispersion adjustments for flows above H .
(d) The SHORTZ model contains a direct-impaction assumption for both stable
and nonstable conditions. It uses on-site turbulence measurements
directly to predict dispersion rates rather than identifying stability
classifications for these purposes. This model tended to overpredict for
both the Westvaco and Cinder Cone Butte data sets but to a lesser degree
than COMPLEX II and to a lesser degree for Westvaco than COMPLEX I. The
use of turbulence measurements may account for its improved performance
over COMPLEX I and II.
(e) The RTDM and 4141 models performed generally better than the other models
for the Westvaco data set. The RTDM model contains consideration of
Froude number and dividing-streamline heights. It also allows the use of
on-site turbulence data directly to estimate dispersion rates. RTDM
performed well also at Cinder Cone Butte.
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The 4141 model uses the Pasquill-Gifford dispersion coefficients with a
0.25 plume path coefficient for stable flow. The combination of
parameters worked reasonably well at Westvaco but did not result in
superior performance when applied to the Cinder Cone Butte data.
(f) The PLUMES model generally showed the most consistent, average-level
performance for the Westvaco data set except for achieving minimum bias
for the category of all values paired by time and space. PLUMES
performed less well when applied to the Cinder Cone Butte data.
(g) The IMPACT model, a "K-theory" numerical model, was tested for
computational economy on only one-fifteenth of the entire Westvaco data
set. The other seven models were also run on this reduced data set.
(All eight models, including IMPACT, were run on the entire Cinder Cone
Butte data set.) In comparison to the other models, IMPACT performed
less well on the Westvaco data subset. On the other hand, it performed
better than RTDM for some statistical performance measures on the Cinder
Cone Butte data set. The reasons for the difference in performance for
the two data sets has not yet been determined.
The tentative interpretations of this model evaluation study support the
concepts of the use of the dividing-streamline height and the parameterization
of plume trajectories on the basis of H during stable conditions. Other
things being equal, the use of on-site turbulence data appears to improve
model performance. This latter factor is also associated with the models
(RTDM and SHORTZ) that showed the most consistent, better-than-average
performance both at Westvaco and at Cinder Cone Butte.
ERT Model Evaluation Efforts
Model evaluation work performed on the Cinder Cone Butte base and in
association with the EPA Complex Terrain Model Development program shows that
the inclusion of H in the structure of the model to differentiate between two
distinct flow regimes, and the explicit use of on-site meteorological data
improved model performance.
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The CTDM(11083-E) model generally performed better than Valley, COMPLEX
I, and COMPLEX II, especially for the more stable hours. However, CTDM
(11083-E) tended toward underestimation during the less stable hours. The
latest version of CTDM, incorporating a better formulation of terrain effects
and revised formulations of a and a , no longer exhibits such a strong
tendency toward underestimating the less stable hours.
Both COMPLEX models tend toward overestimation. COMPLEX II is decidedly
worse, especially at low wind speeds (very stable). This is apparently the
result of the COMPLEX impingement algorithm in combination with
Pasquill-Gifford a and a coefficients for stable conditions. COMPLEX I
fares better due to its 22.5° sector averaging in the crosswind direction.
Even so, COMPLEX I tends to overestimate by greater margins as H increases.
FLUID MODELING SIMULATIONS
The use of fluid modeling techniques in wind tunnels and towing tanks
provides powerful tools to test theoretical development work and to
investigate systematically the effects of changes in flow conditions, terrain
geometry, and the addition or subtraction of complicating factors in flows.
While field experiments provide the ultimate test, the impossibility of
controlling the meteorological conditions that occur limits systematic
investigations of the effects of different conditions to only those captured
in a given experiment. Field verification studies are necessary, however, to
assure that the results of laboratory experiments apply to full-scale
phenomena.
In the EPA Complex Terrain Model Development program, integral use of
fluid modeling has been accomplished via experiments performed at the EPA
Fluid Modeling Facility. Experiments have been performed to test the
applicability of results in several research areas:
(a) Applicability of Dividing-Streamline Concept. Tests have been performed
to test the applicability of the dividing-streamline concept HC for
several hill slopes and aspect ratios ranging from ridges to hemispheres
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and including a scaled model of Cinder Cone Butte. The concept of HC was
found to be valid when interpreted as a necessary but not sufficient
condition for a wide range of geometries and flow profiles.
(b) Flow Behavior Above and Below H . The behavior of the flow above and
below H as described in the discussion of phenomena was investigated
systematically with towing tank experiments.
(c) Hi 11-Surface Concentrations. Towing tank and wind tunnel experiments
have been used to show that when a plume is embedded below H and the
stable flow impinges upon a hill surface, the maximum ground-level
concentration to be expected is about equal to the centerline
concentration expected in the absence of the hill. Full doubling due to
"reflection" effects does not occur under these circumstances.
(d) Flat Dividing-Streamline Surface. Experimental results with a fully- and
half-submerged model of a bell-shaped hill support the notion that the
dividing streamline acts somewhat as a solid (or flat) surface for
purposes of simulating the effect on flow trajectories above H and not
far into the wake of the object. This concept can greatly simplify the
mathematical algorithms needed to parameterize the effects of H in
dispersion models.
(e) Lee-Side Effects. Quantification of the terrain amplification factors
associated with the placement of sources in the lee of terrain features
having separated flow regimes was performed in the wind tunnel. The
tunnel allows a systematic investigation of these effects to be performed
as a function of hill shape, relative stack height, etc.
(f) Limitations to the Use of Fluid Models. Strongly stratified towing tank
experiments on flows over two-dimensional ridges were found to have no
analog in the real atmosphere because of the unsteadiness created by the
finite length of the tank. Another limitation of fluid modeling studies
is that they cannot simulate the total variability of the real
atmospheric boundary layer. Reasonable attempts have been made to
account for wind direction and speed variability by changing the tow
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speed and hill orientation. But real atmospheric turbulence, especially
low-frequency meandering common in stable conditions, must be kept in
mind and accounted for separately in transferring the fluid modeling
results to full-scale flows.
MODELING IMPROVEMENT AND RESEARCH NEEDS
The first recommendation is to encourage the continuation of the current
close coordination of research efforts involving mathematical modeling,
laboratory experiments, and field studies. Integrated programs that recognize
the attributes and limitations of each of these tools have a high probability
of success.
In addition to the above, some other specific recommendations are made.
(a) Stable Plume Impingement. The dividing-streamline concept has been
reasonably well established through laboratory studies and supported
through field studies. Full incorporation of the concept into
mathematical models is currently proceeding. Fluid modeling research in
this area should be closely coordinated with mathematical modeling to
provide very specific guidancs and data for validation of modeling
concepts and techniques, both for sources below the dividing-streamline
height, where the plume will impinge on the windward face of the hill,
and for sources somewhat above the dividing-streamline height, where the
maximum concentration may occur on the lee side of the hill.
Verification at a full-scale site is underway and will be necessary to
assure users of the relevance to situations where the ratio of
dividing-streamline height to lower boundary-layer height is larger.
(b) Use of On-site Meteorological Measurements. In complex terrain settings,
the spatial and temporal variability of flow conditions is very different
from conditions over level terrain. Therefore, the use of on-site
meteorological data, especially turbulence information, is highly
recommended as the basic input information for complex terrain dispersion
models. Models that use these data appear to perform better and more
consistently that those that do not.
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(c) Modeling Needs for Predictions During Neutral and Transitional Conditions.
The primary focus for the EPA Complex Terrain Model Development program
has been the phenomena associated with stable atmospheric conditions.
The bulk of the experiments were performed during nighttime hours. Some
data are also available for analysis of the flow phenomena during the
morning transitional hours and other hours of steady neutral flow. For
topographic settings where persistent neutral conditions or transitional
fumigation are important, model algorithms developed on the basis of
these data would be appropriate. For moderately stratified flows (Fr >
1), plume path coefficients need to be determined as functions of the
approach flow stratification and the hill shape (slope and crosswind
aspect ratio) so that refined parameter!zations may be included in
mathematical models. Currently available models typically include only a
half-height plume correction for neutral or unstable conditions and for
stable conditions when the plume height is above the dividing-streamline
height. Fluid modeling research could provide data for a much improved
parameterization of the effects of stratification (from neutral through
strongly stable) and hill shape on plume trajectories (streamline
displacements) and plume deformations (streamline deformations).
(d) Modeling Needs for Predictions of Lee-side Phenomena. The presence or
absence of separation on the lee side of a hill will have dramatic
consequences on plume behavior from both upwind and downwind sources.
The existence of separation, however, is dependent upon the slope of the
hill, the crosswind aspect ratio, the stratification of the approach
flow, and the surface roughness of the hill, and may be conditional upon
the existence of a salient edge from which the flow may separate. The
stratification may either enhance or inhibit separation. The stratified
towing tank provides an ideal setting wherein each parameter may be
controlled and varied independently so that the parameter space in which
separation occurs can be determined. Under neutral conditions, recent
fluid modeling studies have shown that very significant terrain effects
are observed when sources are placed downwind of hills where the flow
separates steadily or intermittently. Terrain amplification factors as
large as 15 have been observed. Fluid modeling research should be
continued to map the fields of terrain amplification factors as functions
of hill shape and slope.
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(e) Modeling Needs for Predictions During Stagnation Conditions in Deep
Valleys. The DOE ASCOT program is addressing the dynamics of local flows
and drainage winds in valley settings primarily associated with western
energy development activities. When this work nears completion, efforts
will be needed to transfer the results to more general valley settings.
Fluid modeling research can provide useful input on the phenomena
associated with coupling/decoupling between free-air cross-valley winds
and valley drainage flow regimes, including the case of a stagnant air
mass trapped within a valley.
EPA REGULATORY APPLICATIONS
As mentioned in Section 4, a separate scientific review is being
performed by personnel in the EPA Meteorology and Assessment Division of the
complex terrain dispersion models submitted for testing in response to the
March 1980 Federal Register "Call for Models" notice. This separate,
independent review will be based on an interpretation of the TRC statistical
evaluations and on a review of the theoretical bases on the model algorithms.
The findings from both the TRC and ERT evaluations that are contained in this
assessment document are stated in relatively general terms and can be expected
to be qualified or altered after the more comprehensive review is completed.
Identification of existing dispersion model(s) with the best overall
statistical performance is expected to arise from a consideration of the
results presented in this assessment document combined with the conclusions
formulated by the EPA inhouse review of the TRC model evaluations. The
various statistical performance measures of the superior model(s) must then be
ranked based on their relative importance to statutory requirements in order
to select the "best" complex terrain dispersion model to meet EPA regulatory
applications.
In addition to this current evaluation process, the EPA Office of
Research and Development is actively pursuing improvements to existing
dispersion modeling capabilities through the Complex Terrain Model Development
program. The goal of this program by 1986 is the development of models with
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known accuracy and defined reliability for simulating 1-hour average
concentrations resulting from plume impingement on elevated terrain obstacles
during stable atmospheric conditions. Future objectives of this program may
include extension of the complex terrain model development effort to increased
topographical complexity (e.g., lee side impingement), to neutral and unstable
atmospheric stabilities, and to longer averaging periods.
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Egan, B. A., 1984b: Report of AMS Workshop on Dispersion in Complex
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Hsiung, J. and H. Case, 1981: User's Manual for Pacific Gas and Electric
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Lavery, T. F., B. R. Greene, B. A., Egan, and F. A. Schiermeier, 1983a: The
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Ryan, W., B. Lamb, and E. Robinson, 1984: An Atmospheric Tracer Investigation
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Opatija, Yugoslavia, 5
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