United States
Environmental Protection
Agency
Atmospheric Sciences
Research Laboratory
Research Triangle Park NC 27711
Research and Development
EPA/600/S3-87/026 Dec. 1987
SERft Project Summary
Contributions of the Fluid
Modeling Facility to EPA's
Complex Terrain Model
Development Program
William H. Snyder
The contributions of the EPA Fluid
Modeling Facility (FMF) to the Complex
Terrain Model Development Program
(CTMDP) are described. These contri-
butions included a wide range of
laboratory studies and a limited amount
of numerical modeling of flow and
diffusion in neutral and stably stratified
conditions in complex terrain. The goal
of the CTMDP is the developmem of
a dispersion model valid in complex
terrain, with emphasis on plume impac-
tion on nearby hills during nighttime
stable conditions. Work at the FMF
prior to the inception of the program
divided the basic framework for the
model—the dividing-streamline con-
cept—and the focal point around which
the field program was designed.
Throughout the course of the CTMDP,
the FMF interacted vigorously with the
model developers by providing support
in various ways. Early work provided
direct support as an aid to planning the
details and strategies of the field
experiments and testing the limits of
applicability of the dividing-streamline
concept. Later work included exercises
of ' 'filling in the gaps" in the field data,
furthering the understanding of the
physical mechanisms important to
plume impaction in complex terrain and
in stably stratified flows in general,
testing various modeling assumptions,
providing data for ' 'calibration" of
various modeling parameters, and
testing the ability of the laboratory
models to simulate full-scale condi-
tions. Simultaneously, the FMF
responded to the needs of the regula-
tory arm of EPA. the Office of Air
Quality Planning and Standards
(OAQPS), by providing guidance con-
cerning expected terrain effects and by
conducting demonstration studies.
Finally, several supplemental studies
were conducted, broadening and
expanding upon the specific requests
of the model developers and the
OAQPS.
This Project Summary was devel-
oped by EPA's Atmospheric Sciences
Research Laboratory, Research Trian-
gle Park. NC. to announce key findings
of the research project that is fully
documented in a separate report of the
same title (see Project Report ordering
information at back).
Introduction
In the late 1970's the Office of Air
Quality Planning and Standards (OAQPS)
of the Environmental Protection Agency
(EPA) identified a crucial need to develop
an improved mathematical model that
dealt with plume impaction from large
sources located in mountainous terrain
under stable flow conditions. A workshop
was convened in 1979 to focus on
complex terrain modeling problems and
to develop recommendations to EPA with
respect to the design of a program of
experiments and model development
efforts. Subsequently, the EPA outlined
a plan to achieve the objective through
an integrated program of model devel-
opment, fluid modeling experiments and
field studies of plume-terrain interac-
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tions on hills of progressively increasing
size and complexity. This multi-year,
multi-faceted program is known as the
Complex Terrain Model Development
Program (CTMDP).
The Fluid Modeling Facility (FMF)
interacted vigorously with various groups
participating in the CTMDP, and provided
direct support and guidance in many
different ways. The FMF research pro-
gram has ranged from the development
of broad guidelines and physical con-
cepts to specific site studies and regu-
latory applications. The FMF has provided
laboratory data to "fill in the gaps" in
the field data and tested the validity of
convenient modeling assumptions.
The complete report summarizes the
contributions, both direct and indirect, of
the FMF to the CTMDP. The discussion
provides a historical perspective and a
comprehensive list of FMF's accomplish-
ments with respect to furthering the
physical understanding of flow and
diffusion in complex terrain. Over 65
publications have been generated from
work conducted within the FMF on
complex-terrain research. Only a few of
the most important publications are
highlighted herein.
Background
The major facilities of the FMF consist
of a meteorological wind tunnel and a
stratified water channel/towing tank.
The wind tunnel has a test section 3.7m
wide, 2.1m high, and 18.3m long, and
a speed range of 0.5 to 10m/s. The
towing tank is 2.4m wide, 1.2m deep,
and 25m long. It is density-stratified
using layered mixtures of salt water.
Research work conducted at the FMF
prior to the inception of the CTMDP had
a strong influence on the directions to
be taken in the field work and on the
type of model (i.e., physical concepts) to
be developed. The stratified towing tank
was commissioned in 1976 and rather
fundamental studies were begun imme-
diately on the structure of stably stratified
flow over idealized three-dimensional
hills and on diffusion from a point source
within a stably stratified field of
turbulence.
The first published reports on this work
described the flow structure observed
over a bell-shaped hill under neutral and
stably stratified conditions. Earlier theo-
retical work, model experiments, and
observations all indicated that, when the
stratification is strong enough, the air
flows in approximately horizontal planes
around the topography. Up to that time.
however, there had been little firm
laboratory or field data as to how strong
the stratification must be for any given
streamline starting below the hill top to
pass round the side rather than over the
top of the hill.
Hunt and Snyder (1980) showed evi-
dence for a dividing streamline of height
HB such that streamlines below H, would
impinge on the hill surface and follow
the surface around the sides, whereas
streamlines above H, would go over the
top. They suggested the simple forumula
as the criterion to determine whether a
plume embedded in the flow approaching
the hill would impact on the surface or
surmount the top, for 0
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parcel at some height upstream possess
sufficient kinetic energy to overcome the
potential energy required to lift itself
through the density gradient from its
upstream elevation to the hill top?" The
left-hand side may be interpreted as the
kinetic energy of the parcel far upstream
at elevation Hs, and the right-hand side
as the potential energy gained by the
parcel in being lifted from the dividing-
streamline height Ha to the hill top h
through the density gradient dp/dz. This
integral formula was persumably appli-
cable to a fluid with any shape of stable
density profile and, presumably, with any
shape of approach-flow velocity profile.
In practice, it must be solved iteratively,
because the unknown Ha is the lower
limit of integration; the formula can
easily be reduced to the simpler formulae
(1) and (2) by using the boundary con-
ditions applicable to those special cases.
The third study thus attempted to verify
this integral formula under density
profiles similar to those expected at CCB.
A typical nighttime temperature profile
in the Snake River Basin (site of CCB)
was found to consist of a strong, surface-
based inversion of depth 50 to 100m and
a weaker inversion above extending to
several hill heights. Hence, the stratified
towing tank was filled with a strong
density gradient near the surface and a
weaker gradient above. A vertical rake
of 3 tubes was positioned well upwind
of the hill (a model of CCB), and neutrally
buoyant dye was emitted from each tube.
For each tow, a particular stack height
(center tube) was chosen and the general
formula was integrated numerically
using the measured density profile to
predict the towing speed required such
that the center streamer would rise to
the elevation of the saddle point of CCB,
i.e., the minimum height of the draw
between the two peaks. If the formula
were correct, then, the lower streamer
should go around the side of the hill, the
upper streamer should go over the top,
and the center one should split. The
height of the break-point between the
two gradients was then reduced and the
process repeated. In all, 12 tows were
made, varying the height of the break-
point or the dividing-streamline height
(release height) each time.
Figure 1 shows a side view of the
impinging streamers during a typical tow,
i.e., the upper streamer going through
the draw, the lower streamer going round
the side, and the middle one splitting.
The density profiles were integrated in
accordance with Equation (3) to find the
Figure 1. Oblique view of impinging streamers on CCB. Middle dye streamer is released
on the dividing-streamline height; others at ±1 cm (±6 m full scale).
dividing-streamline heights as functions
of the towing speed. The agreement
between the predictions and observa-
tions was excellent. The results of this
set of experiments provided confidence
in the validity of the general integral
formula for predicting the height of the
dividing streamline for a wide range of
shapes of stable density profiles.
Subsequent to the field study, one
particular hour of the field data at CCB
was selected for simulation in the towing
tank. That hour was 0500 to 0600, 24
October 1980 (Case 206), which may be
characterized as very stable, i.e., light
winds and strong stable temperature
gradients. Measurements made during
the towing-tank experiments included
ground-level concentrations under var-
ious stabilities and wind directions,
vertical distributions of concentration at
selected points, plume distributions in
the absence of the hill, and visual
observations of plume characteristics
and trajectories.
This series of tows showed that the
surf ace-concentration distributions were
extremely sensitive to changes in wind
direction. For example, Figure 2 shows
that the distribution shifted from the
north side of the hill to the south side
with a shift of only 5° in wind direction.
Comparisons of individual distributions
with field results showed much larger
maximum surface concentrations and
much narrower distributions in the
model results. To account for the large
variability in the winds measured during
the hour, a matrix of 18 tows (three wind
directions x six wind speeds) was con-
ducted, and the concentration patterns
were superimposed. The resultant super-
imposed model concentrations compared
very favorably with field measurements.
The largest model concentrations were
within a factor of two of the highest field
values, and 70% of the model concen-
trations were within a factor of two of
the observed field values.
Numerous other studies were con-
ducted to test the validity and limits of
applicability of the dividing-streamline
concept for example, examining the
effects of shear in the approach-flow
velocity profile, of the crosswind aspect
ratio of the hill, of the hill slope, and the
effect of the wind angle on a long ridge.
These results were published separately
as parts of papers on studies done for
a variety of different purposes, but the
specific aspects dealing with the validity
and applicability of the dividing-
streamline concept were extracted and
published collectively by Snyder et al
(1985).
In response to a request from the
model developers, a series of measure-
ments was made of plume characteris-
tics in flat terrain and over a three-
dimensional hill immersed in the simu-
lated neutral atmosphere boundary layer
of the meteorological wind tunnel.
Effluent was released at a number of
elevations, upwind distances, and posi-
tions laterally offset from the centerplane
determined by the wind direction and the
center of the hill. Sufficient concentra-
tion measurements were made to enable
the construction of plume cross sections
at the downwind position of the hill
center and, in a few cases, at the upwind
base of the hill. These data were analyzed
to provide the desired information on
horizontal and vertical plume deflections
and deformations effected by the hill.
One of the more dramatic examples is
shown in Figure 3. In this case, the
source was on the centerplane at ground
level, 6 hill heights upwind of the hill
center (the skirt of the hill extended to
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600 M
600 M
Scale
Source
Figure 2.
200 M
Concentration distributions measured during individual tows of CCB with
h = 0.31 andH0/h = 0.38; wind direction: 117°. 122°.
N
2 i-
7 -
05
Figure 3. Plume cross sections measured in presence ( ) and in absence ( ) of
axisymmetric CCB model at x = 0 (hill center). H,/h = 0, xs/h = -6. y,/h = 0.
5h). Plume cross sections measured at
the position of the center of the hill, both
in the presence and in the absence of
the hill are shown. The hill effected a
91% increase in the lateral plume width.
In this case, the maximum surface
concentration (at the same downwind
distance) was decreased by a factor of
2 but, of course, the area of coverage
by large concentrations was greatly
increased. Detailed data reports were
provided to the model developers imme-
diately, and the results were published
by Snyder and Lawson (1986).
As a result of these and similar
measurements, refinements were made
to CTDM. Specifically, the calculation
procedures were modified to utilize the
strain inferred or measured over the
crests of two- and three-dimensional
hills in the wind tunnel, i.e., theT-factors
in the model were adjusted in accordance
with wind-tunnel data. Substantial
improvements in the CTDM predictions
of terrain amplification factors were
obtained, as described by Strimaitis and
Snyder (1986).
One of the important overall goals in
this effort was to ascertain what circum-
stances lead to the largest ground-level
concentrations(glc's), i.e., are larger glc's
expected when the plume from an
upwind source impinges on the hill or
when the source is downwind of that hill
such that the plume is caught in a
recirculation region and downwashed to
the surface? Which are likely to lead to
larger glc's, two-dimensional or three-
dimensional hills? Stable conditions or
neutral conditions? In each of these
circumstances, what orders of magni-
tude of surface concentrations may be
expected?
A simple method used to intercompare
effects of terrain on the maximum glc
and to determine worst-case conditions
is through the the terrain amplification
factor, A, which is defined as the ratio
of the maximum ground-level concentra-
tion occurring in the presence of the
terrain feature, Xm«, to the maximum that
would occur from the same source
located in flat terrain, x™, i.e., X*=Xmx/
X™. This definition is useful only for
elevated sources, of course, because for
ground-level sources, the maximum
surface concentration occurs at the
source itself.
A wide range of neutral-flow wind-
tunnel studies was conducted at the FMF
on diffusion from sources located in the
vicinities of two- and three-dimensional
hills. Table 1 lists approximate values of
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Table 1. Summary of Terrain Amplification Factors for Sources in the Vicinity of Hills in
Neutral Flow
Source
Location
Hill Type
Downwind
Downwind
Upwind
Upwind
Top
Two -Dimensional
Three-Dimensional
Three-Dimensional
Two-Dimensional
Two-Dimensional
10-15
5-6
2-4
1-3
0.5-1
maximum terrain amplification factors
that were found in the various situations.
From the standpoint of a fixed stack
height, the worst location for a source
appears to be just downwind of a two-
dimensional ridge. Downwind sources
generally result in larger glc's because
of the excess turbulence generated by
the hills and because the effluent is
generally emitted into a low speed region
where the streamlines are descending
toward the surface. Maximum A's are
considerably larger than those down-
wind of three-dimensional hills. Also, the
sizes of the recirculating cavity regions
downwind of three-dimensional hills are
generally much smaller than those
downwind 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.
The maximum terrain amplification
factors as listed in Table 1 are useful only
for scoping a particular problem or for
finding the worst possible situation. They
do not provide practical estimates for use
by, say, an air pollution meteorologist in
determining the maximum glc resulting
from a particular power plant or for
determining the best location for that
plant. For that purpose, the concept of
a "window" of excess concentrations is
more useful. For any given plant location
(say, upwind of a hill), there is a limited
range of stack heights A/s for which a
significant amplification of the glc will
occur. (For sake of argument, we will
here define significant as a factor of 2.)
This amplification can occur only if the
position of the maximum glc lies on or
near the hill surface. For small H,, Xmx
will occur upwind of the hill and thus
be little influenced by the hill, so that
A (=x™/Xm*) will approach unity. If Ha
is too large (for example, H£>h, the hill
height), Xm* will lie well beyond the hill
and A will again approach unity. In either
case, there is little amplification. A
"window" of intermediate stack heights
and locations exists, however, where A's
will significantly exceed unity. These
"windows" of critical Ha values have
been measured by Lawson and Snyder
(1985) for two typical hill shapes that
might be found in the real world, one
axisymmetric, the other two-
dimensional. The results are shown in
Figure 4. The 1.4-window, for example,
extends to about 14/7 upstream, 10/7
downstream, and as high as 1.8/7 in the
vertical for the axisymmetric hill. For the
two-dimensional hill, this 1.4-window
extends about 8/7 upstream, 15/7 down-
stream, and as high as 2.2/7 in the
vertical.
Such contour maps as provided in
Figure 4 can be very useful for the
practioner. Once an acceptable terrain
amplification factor (or "excess concen-
tration") is decided upon, it is a simple
matter to trace the window on the
contour map to determine the area (plant
location and/or stack height) to be
avoided. Conversely, from such maps,
the likely maximum glc for a potential
site and stack height can be estimated.
The use of terrain amplification factors
simplifies the application of these data
to full-scale situations. The expected
maximum glc in flat terrain is calculated
(from mathematical models or standard
curves), then the concentration in the
presence of the hill is simply the product
of this quantity and the TAF.
Summary
The EPA Fluid Modeling Facility has
conducted a wide range of laboratory
studies and a limited amount of numer-
ical modeling of flow and diffusion in
association with the CTMDP The goal
of the CTMDP is the development of a
dispersion model valid in complex ter-
rain, with emphasis on plume impaction
on nearby hills during nighttime stable
conditions. Work at the FMF prior to the
inception of the program provided the
basic framework for the model—the
dividing-streamline concept—and the
focal point around which to design the
field program.
•c;..
-15
-15
Figure 4.
-10
Contours of constant terrain amplification factors over (a) axisymmetric hill and
(b) two-dimensional ridge. Note that vertical scale is exaggerated by a factor of 3.
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Throughout the course of the CTMDP,
the FMF interacted vigorously with the
model developers by providing support in
various ways. Early work provided direct
support in planning the details and
strategies of the field experiments and
solidifying and testing the limits of
applicability of the dividing-streamline
concept. Later work included excerises
of "filling in the gaps" in the field data,
furthering the understanding of the
typical mechanisms important to plume
impaction in complex terrain and in
stably stratified flows in general, and
testing the ability of the laboratory
models to simulate full-scale field con-
ditions. And, as the needs arose, the FMF
tested various modeling assumptions,
concepts, and hypotheses and provided
data for "calibration" of various param-
eters within the CTDM model.
Simultaneously, the FMF responded to
the needs of the regulatory arm of EPA,
OAQPS, by providing guidance concern-
ing expected terrain effects and by
providing a demonstration study—an
example for industries to follow in
conducting good-engineering-practice
stack height determinations in complex
terrain. Also, a broad range of supple-
mental studies was conducted, expand-
ing and enlarging upon the specific
requests of the OAQPS and the CTDM
model developers to provide information
of general use to the scientific and air
pollution modeling communities. Many
of the data sets generated in the course
of this program have been provided to
and used by various groups (nationally
and internationally) in the development,
testing and evaluation of complex terrain
dispersion models.
The most significant contributions
included (1) the conceptual framework
for the mathematical model (i.e., the
division of the flow-field into two
regimes, a lower layer below the
dividing-streamline height which flows
in essentially horizontal planes around
the hill, and an upper layer above the
dividing-streamline height which is
treated as modified potential flow over
a cut-off hill) and the detailed experimen-
tal validation and establishment of limits
of applicability of these concepts, (2)
verification of the integral formula for the
height of the dividing-streamline—this
allowed computations of the dividing-
streamline height under arbitrary
approach-flow conditions, including
shear in the approaching wind-speed
profile and nonlinear temperature gra-
dients, (3) demonstration of the extreme
sensitivity of surface concentration
patterns to wind direction under strongly
stratified conditions, (4) measurements
of plume deflections and deformations
over hills in neutral flow—these permit-
ted adjustment of the T-factors in CTDM
and resulted in substantial improve-
ments in the CTDM predictions, and (5)
the introduction of the concept of "win-
dows of excess concentration" and
measurements of terrain amplification
factors—these provided simple and
practical methods for estimation and
intercomparison of effects of terrain and
source locations on maximum ground-
level concentrations that may result from
sources placed in the vicinities of hills.
Only the highlights of the FMF con-
tributions to the CTMDP are contained
in the present summary. The complete
report provides much more detail and a
comprehensive list of over 65 publica-
tions generated from the work conducted
at the FMF on complex-terrain research.
References
Hunt, J. C. Ft., Puttock, J. S., and Snyder,
W. H. 1979. Turbulent Diffusion from
a Point Source in Stratified and Neutral
Flows Around a Three-Dimensional
Hill: Part I. Diffusion Equation Analysis.
Atmos. Envir., 13:1227-1239.
Hunt, J. C. R. and Snyder, W. H. 1980.
Experiments on Stably and Neutrally
Stratifed Flow Over a Model Three-
Dimensional Hill. J. Fluid Mech.,
96:671-704.
Lawson, R. E., Jr., and Snyder, W. H.
1985. Stack Heights and Locations in
Complex Terrain. Preprints Vol: 7th
Symp. Turb. Diff, Nov. 12-15, Boulder,
CO, 223-226. Amer. Meteorol. Soc.,
Boston, MA.
Snyder, W. H., Britter, R. E., and Hunt,
J. C. R. 1980. A Fluid Modeling Study
of the Flow Structure and Plume
Impingement on a Three-Dimensional
Hill in Stably Stratified Flow. Proc. Fifth
Int. Conf. on Wind Engr. (J. E. Cermak,
ed.), 1:319-329. Pergamon Press, NY,
NY.
Snyder, W. H. and Lawson, R. E., Jr.
1986. Laboratory Observations of
Plume Deformations in Neutral Flow
Over a Three-Dimensional Hill. Pre-
print Vol: AMS 5th Jt. Conf. Appl. Air
Poll. Meteorol. with APCA, Nov.,
Chapel Hill, NC. Amer. Meteorol. Soc.,
Boston, MA.
Snyder, W. H., Thompson, R. S., Eskridge,
R. E., Lawson, R. E., Jr., Castro, I. P.,
Lee, J. T., Hunt, J. C. R., and Ogawa,
Y. 1985. The Structure of Strongly
Stratified Flow Over Hills: Dividing-
Streamline Concept. J. Fluid Mech.,
152:249-288.
Strimaitis, D. G. and Snyder, W. H. 1986.
An Evaluation of the Complex Terrain
Dispersion Model Against Laboratory
Observations: Neutral Flow Over 2-D
and 3-D Hills. Preprint Vol: AMS 5th
Jt. Conf. Appl. Air Poll. Meteorol. with
APCA, Nov., Chapel Hill, NC, Amer.
Meteorol. Soc., Boston, MA.
The EPA author William H. Snyder (also the EPA Project Officer, see below)
is with the Atmospheric Sciences Research Laboratory, Research Triangle
Park, NC 27711.
The complete report, entitled "Contributions of the Fluid Modeling Facility to
EPA's Complex Terrain Model Development Program," (Order No. PB 87-
227 682/AS; Cost: $13.95, subject to change) will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 703-487-4650
The EPA Officer can be contacted at:
Atmospheric Sciences Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
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