xe/EPA
United States
Environmental Protection
Agency
Environmental Sciences Researc
Laboratory
Research Triangle Park NC 277
Research and Development
EPA-600/S4-81-068 Oct. 1981
Project Summary
Impact of Topographic
Circulations on the
Transport and Dispersion of
Air Pollutants
Richard T. McNider and Roger A. Pielke
A numerical mesoscale model was
used to examine slope flows and
classic mountain-plain air circulation
for idealized topography. Special
emphasis was given to turbulent
parameterization in the stable bound-
ary layer and to the unique character-
istics of turbulent mixing in the slope
flows. The numerical simulations for
idealized valley-plain configurations
produced results consistent with
previously described observations,
such as shallow sidewall flows, the
pooling of cool air in the valley, and a
deep mountain flow out of the valley.
A Lagrangian particle model, operated
in the terrain-following coordinate
system of the mesocale model, was
developed to examine pollutant trans-
port in the modeled circulations, while
a Markov statistical process was used
to evaluate turbulent dispersion.
Higher order turbulence parameters
needed for the statistical model were
directly computed from the numerical
model. Results of dispersion tests in
the modeled slope flows showed
enhanced vertical dispersion in the
slope flows compared to flow over a
flat boundary and, importantly, that
normal surface scaling parameters for
pollutant dispersion, such as friction
velocity, were inappropriate for the
slope flows.
This research was supported by U.S.
Environmenta.1 Protection Agency
Grant No. R806207010. Computer
support was provided by the National
Center for Atmospheric Research,
funded by the National Sciences
Foundation.
This Project Summary was devel-
oped by EPA's Environmental Sci-
ences Research Laboratory, Research
Triangle 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
The overall objective of this research
was to use a mesoscale, primitive
equation model [The University of
Virginia Mesoscale Model (UVMM)] to
produce dynamically consistent flow
and turbulence fields in complex
terrain. Model-predicted fields were
then to be used to examine the transport
and dispersion of pollutants. To accom-
plish the overall objective, some im-
provements to the mesoscale model
were required to properly simulate
drainage flows in complex terrain, and
special techniques were developed to
fully utilize the model flow and turbu-
lence fields to examine point and area
sources of pollution.
Modeling the Nocturnal
Boundary Layer
In the past, use of the UVMM and
most other mesoscale models has been
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primarily directed towards examining
the convective boundary layer of classic
mountain-plain air circulation with an
emphasis on sea breeze flows or heated
up-slope flows. For polluted air, the
stable boundary layer and drainage
flows are generally the most restrictive
to pollutant dispersal. Also, since
drainage flows are themselves highly
dependent upon vertical mixing processes,
a good deal of effort was expended to
incorporate an accurate nocturnal
boundary layer formulation into the
model. The formation chosen was a
local exchange coefficient scheme
proposed by Blackadar (1979). With
some modification, this scheme has
been included in the model.
This technique, in conjunction with a
surface energy budget and a long-wave
radiation parameterization, appeared to
do as well in simulating the nocturnal
boundary layer as the more complex
numerical second-order closure schemes.
A complete description of the local
exchange coefficient model is given in
McNider and Pielke (1981). McNider
and Pielke also examine boundary-layer
development over sloping terrain and
show the importance of the terrain-
induced pressure gradient and mixing
processes to the generation of strong
nocturnal jets.
The local mixing formulation allowed
a dynamically consistent surface
boundary layer and turbulent field to be
generated over a terrain obstacle. The
use of local conditions (based on local
gradient Richardson number) was
especially important to slope flow
simulation, since the shear zones above
the surface produce the mixing and
entrainment into the drainage flow.
Slope Flows
In complex terrain, under synoptic
conditions associated with large scale
air stagnation, local mesoscale circula-
tions provide the primary dilution and
transport mechanisms for pollutants. To
assess transport and dispersion of
pollutants in complex terrain, the first
step is to understand and model the
mountain-valley wind systems. Defant
(1951) provides an excellent summary
of observations and descriptive models,
including the characteristics of slope
flows and the importance of these slope
flows in producing an along-the-valley
axis component (the true mountain
wind).
The modeled valley has the classic
mountain-plain configuration described
by Defant, and was purposefully accen-
tuated to have a high height-to-width
ratio (19 km wide, 2 km deep) with a
sidewall slope of .25 (14°) (see Figure 1).
Shallow drainage flows developed
quickly over both sidewalls in response
to surface cooling produced by a surface
energy budget. The depth of the slope
flow and height of the downslope
velocity maximum (Figure 2) appeared
to agree well with generic observations
for similar slopes. However, the mag-
nitude of the modeled velocity generally
appeared larger than most observed
maximums. In the model, an upslope
return flow was also noted above the
shallow downslope flow.
As mentioned, the slope flows devel-
oped rapidly, reaching their maximum
within the first hour. These slope flows
gradually produced a pooling of cool air
in the valley. Later, downslope velocities
decreased throughout the night in
response to increased temperature
stratification in the valley.
The turbulent exchange processes
were directly linked to the developing
flow fields. Downward moving air
tended to deform the potential tempera-
ture field, producing a less stable profile
aloft. The return upslope flow accentu- I
ated this deformation, actually producing
an unstable layer. Because the local
turbulent exchange coefficients in the
current model were dependent upon the
local gradient Richardson number, this
unstable layer, in conjunction with the
wind shear near the top of the drainage
flow, produced a highly turbulent zone
aloft. Figure 3 shows the exchange
coefficient profile and Richardson
number over the slope.
Mountain Flows
According to Defant (1951), the
mountain wind is driven by the slope
flows, filling the valley with cooled air
from the slopes. The pool of cool air
creates a hydrostatic pressure gradient
between the interior of the valley and
plains outside the valley, causing a deep
flow out of the valley. Because the slope
flows are generally much shallower
than the deep mountain wind, their
importance to pollutant transport is
probably secondary to the mountain
wind that develops within a valley.
In the model (after starting with an
adiabatic atmosphere) definite pooling
Figure 1. Three-dimensional perspectives of the topographic configuration used
in Case A. Ridge height is 2 km; valley width is 19 km. (Note that the
vertical scale is exaggerated.)
4
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273
300
Downs/ope Component
Potential Temperature
200 -
I
100 -
Figure 2. Downs/ope component and potential temperature profiles over the
western sidewall of the two-dimensional valley at 0230 LST.
of the cooled air occurred, as illustrated
in Figure 4a by the vertical gradient of
potential temperature. The cooling in
the valley was unusual because it did
not appear to originate at the surface.
Rather, cooling occurred at all heights
within the valley, with the greatest
.cooling occurring near the surface. This
appears to be consistent with the
cooling pattern observed in deep valleys
in Colorado (C. D. Whiteman, 1980). The
pooling of cool air in the valley,
consistent with Defant's descriptive
model, produced a deep flow out of the
valley. Figure 4b shows this deep
mountain flow which extends to near
ridge height.
Pollutant Transport
Most mesoscale flows, such as sea
breeze and mountain-valley flows, are
characterized by strong vertical shear
(in both direction and speed) and
horizontal variability. In order to examine
pollutant transport in the mean meso-
scale model wind field, a Lagrangian
particle model was developed. The
Lagrangian particle model used a
volume-weighting scheme (Tuescher
and Mauser, 1974) to interpolate model
velocities in the variably spaced model
grid to the particle position. Initial
particle positions were transformed into
the terrain-following coordinate system,
and then advected in that system. For
display purposes, particles were back-
transformed into a normal z system. The
particle model could then produce
streak! ines as well as trajectories from
various positions in the model flow.
Figure 5 shows examples of streaklines
produced by the particle model in a
modeled sea breeze flow. A more
complete description of the particle
model and related experiments is given
in McNider and Pielke (1979).
Grid Cell Pollutant Transport
and Dispersion
Pollutant plumes with scales larger
than both the model grid size and the
dominant turbulent scales can be
transported and diffused satisfactorily
by using the advection equation and
gradient transfer theory as follows:
3C _ -uj 3C + 3
3t 3X| 3Xj
0)
\n the UVMM, a highly accurate
advection scheme employing an up-
stream spline interpolation technique
(Mahrer and Pielke, 1978) was used
together with a forward time-weighted
diffusion scheme (Paegle, et al., 1976)
to solve Equation 1. Mean velocities and
diffusion coefficients taken at meso-
scale model grid points were used to
transport and diffuse a passive pollutant.
Figure 6 shows particle concentrations
(emitted from an urban strip and area
sources over the land) diffused and
transported within a sea breeze flow
using this scheme.
Point Source Transport and
Diffusion
As previously mentioned, area sources
can generally be included by using the
conservation equation employing gra-
dient transfer theory. However, point
sources cannot be directly used in a
coarse grid numerical model using
Equation 1. This is due to numerical
damping and the fact that plumes (small
when compared to the turbulent scale)
either do not diffuse in a gradient
fashion, or require the effective ex-
change coefficient (K) to be a function of
travel distance.
Due to the highly sheared environ-
ment and unsteady character of the
local circulations, the subgrid scale
plume dispersion could not be easily
parameterized using analytical methods.
An alternative used in the present
investigation consisted of a conditioned
particle dispersion scheme that Hanna
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Turbulent Exchange
Coefficient
Local Gradient
Richardson Number
10
100
150
200
) x 10*
Figure 3.
Turbulent exchange coefficient over the western valley wall showing
pronounced maximum near the top of the slope flow and local gradient
Richardson number showing the unstable layer aloft created by the
deformation of the temperature field.
(1979) based upon Taylor's 1921
theorem for particle dispersion, in
which the particle velocity (using the u-
component as an example) is expressed
by:
an estimate of au and R consistent with
the model boundary layer. This was
accomplished for the vertical compo-
nent of the convective boundary layer
using;
Up = U + U'
(2)
ixm —
(4)
where u =the mesoscale wind, and
u' = a turbulent component given
by:
where
u'(t + r) = u'(t)
(3)
The variable u" is a random compo-
nent dependent upon the turbulent
energy,
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released from a height of 8 m above the
western sidewall. Figure 9 gives the
root-mean-square vertical spread in the
three experiments. Results indicated
that dispersion rates were dramatically
accelerated in the slope flows. The
failure of the dispersion curves to
coincide, which is to say dispersion is
not a function of the friction velocity
alone, points out that surface stress was
not a good indication of turbulent
energy in the slope flows.
Conclusions
The major result in this study was the
success of a numerical model to
reproduce the essential features of the
classic mountain-plain circulation,
including the deep mountain flow out of
the valley. The success of the numerical
experiment was readily expected since,
unlike direct sea breeze circulations or
slope flows, the mountain flow is a
secondary circulation and a true three-
dimensional feature. Part of the success
in the simulations must be attributed to
the turbulent parameterization scheme
incorporated into the model, which
avoided physically and numerically
troublesome superadiabatic layers aloft
as the cool air pools in the valley.
The second major result of this study
was the finding that Lagrangian particle
methods, coupled with the numerical
mesoscale model could directly examine
pollutant transport in the complex flow
field, and could provide a robust method
for explicitly incorporating parameters
characterizing the turbulent dispersion.
Techniques described in this investi-
gation allowed these turbulence pa-
rameters to be computed directly from
the mesoscale model so they were
consistent with the dynamic solution.
The models and methodologies de-
veloped in this research should be
useful for guiding the design or inter-
pretation of dispersion experiments in
complex terrain. Also, the models could
be used to shorten or extend the
parametric range of limited observations
in complex terrain.
References
Blackadar, A.K., 1979. High Resolution
Models of the Planetary Boundary
Layer. In: Advances in Environmental
and Scientific Engineering, Vol. 1,
Gordon and Breach, pp. 50-81.
Deardorff, J., 1974. Three-Dimensional
Numerical Study of the Height and
Mean Structure of the Planetary
13. 15. 17. 19. 21. 23. 25. 27. 29. 31.
Figure 4a. Contours of potential temperature at 2330 LST (y = 23). Contour
interval is 1 K.
Boundary Layer. Bound.-Layer Meteor.,
15, 1241-1251.
Defant, F., 1951. Local Winds. In:
Compendium of Meteorology. Amer.
Meteor. Soc., Boston, Mass. pp. 655-
675.
Hanna, S.R., 1979. Some Statistics of
Lagrangian and Eulerian Wind Fluctu-
ations. J. Appl. Meteor., 18. pp. 518-
531.
Mahrer, Y. and R.A. Pielke, 1978. Test of
an Upstream Spline Interpolation Tech-
nique for the Advective Terms in a
Numerical Mesoscale Model. Mon.
Wea. Rev., 106. pp. 818-830.
McNider, R.T. and R.A. Pielke, 1979.
Application of the University of Virginia
Mesoscale Model to Pollutant Transport.
Proceedings of Fourth Symposium on
Turbulence, Diffusion and Air Pollution.
Amer. Meteor. Soc., Reno, Nev.
McNider, R.T., S.R. Hanna, and R.A.
Pielke, 1980. Subgrid Scale Plume
Dispersion in Coarse Grid Mesoscale
Models. Second Conference on Appli-
cations of Air Pollution Meteorology.
New Orleans, La.
McNider, R.T., and R.A. Pielke, 1981.
Diurnal Boundary Layer Development
Over Sloping Terrain. Submitted to J.
Atmos. Sciences.
Paegle, J., W.G. Zdunkowski, and R.M.
Welch, 1976. Implicit Differencing of
Predictive Equations for the Boundary
Layer. Mon. Wea. Rev., 104. pp. 1321-
1324.
Smith, F.B., 1980. Personal Communi-
cation on June 15, 1980.
Tuescher, LH. and L.E. Hauser, 1974.
Development of Modeling Techniques
for Photochemical Air Pollution. EPA-
650/4-74-003. pp. 91.
Whitenidn, C.D., 1980. Personal Com-
munication to University of Virginia.
Nov. 19, 1980.
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5. 7.
11. 13. 15. 17. 19. 21. 23. 25. 27. 29. 31.
Figure 4b. Contours of the mountain wind (v-component) for the same time and
location as 4a. Contour interval is 1 m/s.
-------
I 1 I I I I I I I I 1 I I I 1 I I I I I I I I 1 I 1 I
3. 5. 7. 9. 11. 13. 15. 17. 19. 21. 23. 25. 27. 29. 31.
X
(A) Plan view showing x-y distributions of particles.
Figure 5a. Particle streaklines at 19OO EST from 50-m release heights.
3. 5. 7. 9. 11. 13. 15. 17. 19. 21.23. 25. 27. 29. 31.
i
N
0.
(B)
r
(Bj Vertical view, looking northward, showing x-y distributions of particles. Particles
were released at 10-min intervals, beginning at sunrise.
Figure 5b. Particle streaklines at 19OO EST from 50-m release heights.
-------
I
N
3 -
2 -
N
2 -
Sea
Figure 6b.
Figure 6. Contours of panicle concentrations in a two-dimensional version of the
mesoscale model. Synoptic flow is from the east (R). Particles are emitted
over land areas and the urban strip. Figure 6a shows particles well-
mixed within the convective boundary layer, while Figure 6b shows
capture of particles within the nocturnal boundary layer carried out to
sea in a shallow land breeze.
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70"
N
Irwin (1979)
X X X X Deardorff (1974)
• • • • Model - Wangara 33
1400 LST
I I I I I I
.5
1.0
o-w/W*
Figure 7.
Plot of model-extracted, scaled
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28.
26.
24.
22.
20.
18.
16.
^-
14.
12.
10.
8.
6.
4.
2.
Figure 8.
0.17
0.15
2. 4. 6. 8. 10. 12. 14. 16. 18. 20. 22. 24. 26. 28. 30. 32. 34. 36.
X
Trajectories of particles released an hour apart from a height of 2 m.
Final heights (in km) are given on the side of the end of each trajectory.
.1
o Flat boundary, no wind
• Slope case, no wind
X Slope case with wind
10
U*f/H
100
Figure 9. Vertical dispersion of the three cases described. Root-mean-square
spread is scaled by the boundary layer height.
10
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Richard T. McNider and Roger A. Pielke are with the Department of Environ-
mental Sciences. University of Virginia, Charlottesville, VA 22903.
George C. Holzworth is the EPA Project Officer (see below).
The complete report, entitled "Impact of Topographic Circulations on the Trans-
port and Dispersion of Air Pollutants," (Order No. PB 82-102 435; Cost:
$17.00, 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 Project Officer can be contacted at:
Environmental Sciences Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
11
U.S. GOVERNMENT PRINTING OFFICE: 1981 --559-092/3352
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