Grantee Research Project Results
Final Report: Lagrangian Modeling of Pollutant Dispersal in the Atmospheric Boundary Layer
EPA Grant Number: R823419Title: Lagrangian Modeling of Pollutant Dispersal in the Atmospheric Boundary Layer
Investigators: Weil, Jeffrey C.
Institution: University of Colorado at Boulder
EPA Project Officer: Hahn, Intaek
Project Period: October 1, 1995 through September 30, 1997 (Extended to September 30, 1998)
Project Amount: $164,473
RFA: Exploratory Research - Chemistry and Physics of Air (1995) RFA Text | Recipients Lists
Research Category: Air , Safer Chemicals
Objective:
The overall aim of this research program was to improve our understanding and predictive capability of buoyant plume dispersion due to elevated sources in the convective boundary layer (CBL). The focus was on the prediction of the mean and root-mean-square (rms) fluctuating concentrations due to such plumes. There were two key objectives. The first was to further develop a hybrid Lagrangian dispersion model to address highly buoyant plumes that "loft" or temporarily remain near the top of the CBL and disperse downwards slowly. The hybrid model is a statistical approach based on the meandering of a small plume by the large eddies in the CBL. The second was to modify an analytical probability density function (PDF) model to account for highly buoyant plume dispersion. The key advantage of this model is its capture of the essential physics of dispersion while remaining relatively simple; the simplicity makes the model useful in air quality applications.Summary/Accomplishments (Outputs/Outcomes):
The model developments, results, and their significance are presented below for each of the two approaches. The degree of plume buoyancy is characterized by the dimensionless buoyancy fluxIn the hybrid Lagrangian model, the mean
and rms
concentration
fields
are found by averaging an assumed Gaussian plume concentration field
over
the PDF of the randomly-varying plume centroid. The two main features are:
(1) a Lagrangian particle model to represent the plume centroid meander due
to the large CBL eddies, and (2) an entrainment model to describe the rise and
growth of a buoyant plume relative to those eddies. The centroid is assumed
to behave as a wandering "fluid particle" with random vertical and
lateral velocities obtained from a stochastic model. The model equations
require
an assumed form for the velocity PDFs and the CBL velocity statistics,
which
are obtained from parameterizations of turbulence measurements.
For buoyant releases, the plume rise velocity is superposed initially on the
local random velocity in the environment. Plume material that rises into the
elevated inversion can later reenter the CBL due to entrainment by the large
CBL eddies. In modeling this behavior, we superpose the incremental velocity
changes due to the ambient turbulence and plume buoyancy. The buoyancy
increment
is proportional to the mean potential temperature difference, between
the plume
and the environment. The
is
determined by the source buoyancy and entrainment, and
it decreases with travel
time or distance.
For low-to-moderate fluxes
,
the
is
found from a standard entrainment
model for a round bent-over plume as used
in an earlier formulation. However,
for high buoyancy
the
plume growth and
are
obtained from a new model that accounts for the reduced mixing imposed by the
highly stable plume-ambient interface. The entrainment velocity is proportional
to
and inversely proportional to a Richardson number based on
and
,
i.e.
, the interfacial stability is incorporated through the Richardson number.
The
model is consistent with the enhanced lateral spread of lofting plumes as
found by Briggs (1985).
The model was evaluated by comparing predicted
plume quantities with laboratory
convection tank data obtained under another
research program; the data covered
the range .
The main features of the predicted spatial
statistics-the mean plume height
and the lateral
and vertical
dispersion
parameters-were in reasonable agreement with the data. The
mean height and
displayed a monotonic increase with distance and plume
buoyancy
in both the model and experiment, whereas the
decreased
with
near
the source. The latter was attributed to: (1) the greater plume rise with
increasing
,
which led to a reduced vertical meander, and (2) the "
squashing" of
the vertical depth as the rapidly-rising plume was
abruptly halted by the elevated
inversion.
For the concentration fields,
the results showed that the ground-level concentration
(GLC) along the plume
centerline varied systematically with distance and ,
and was in general
agreement with the experiments (Weil, 1998). An increase
in buoyancy led to
a significant reduction in the concentrations near the source
by comparison
to the nonbuoyant case,
.
In addition, the surface values of
the concentration fluctuation intensity,
increase,
but the
trend was not followed for
,
possibly due to
reduced plume meandering.
The hybrid Lagrangian model is an initial effort
to predict buoyant plume dispersion
and the associated and
over
a wide
range of source buoyancy
.
. In addition to the results discussed here, it also was found that
the modeled
values together with a gamma cumulative distribution function
could be used
to estimate the peak concentration values, e.g., the 99th
percentile values.
The study also showed that some improvements can and
should be made to the model
to correct two deficiencies: (1) the modeled
concentration contours were nearly
normal to the CBL top whereas the data
showed that the contours were nearly
horizontal there, and (2) laboratory
measurements showed that the lofting plume
was entrained incrementally into
the CBL instead of the plume continuing to
grow by entrainment. These
deficiencies can be addressed by modeling the plume
as a collection of
buoyant particles rather than as a meandering plume, and
by including
removal or "extrainment" of material from the lofting
plume. These
aspects are currently being addressed under another research program.
In the
PDF approach, one assumes that plume sections are emitted into a traveling
train of convective elements-updrafts and downdrafts-that move with the mean
wind speed in the CBL. The vertical and lateral velocities in each element are
assumed to be random variables and characterized by their PDFs. The mean
concentration
is found from the PDF of tracer particle position, which in
turn is derived
from the vertical velocity
PDF.
In the CBL, the
is
positively skewed and results in a non-Gaussian vertical concentration
distribution.
For buoyant plumes, the model was extended earlier by
superposing the displacements
due to plume rise and the random to obtain the
concentration field (Weil et
al., 1986). This approach worked well for weak-
to-moderate buoyancy
,
but for high
,
a separate treatment was required to account
for the lofting behavior. However,
the above separation did not maintain
continuity of the predicted concentration
field with
Under this program,
we introduced a new and simplified treatment of plume interaction
with the
elevated inversion. This included an "indirect" source to
address
the lofting behavior and the dispersion of "nonpenetrating"
plumes
and a "penetrated" source to account for plume material that
initially penetrated the elevated inversion but subsequently fumigated into
the CBL. The treatment resulted in a continuous variation of with
,
thus
overcoming a limitation of the earlier PDF models. A novel treatment of
plume rise for the indirect source was found using an energy argument governing
the descent of buoyant plume elements from the CBL top. In addition, we
included
the effects of surface shear as well as convection in
parameterizing the
PDF
so that the model is applicable in the limit
of a neutral boundary layer. The
new model is described in detail in Weil et
al. (1997).
The crosswind-integrated concentration (CWIC) distribution
was
found from the PDF of the particle height, and the concentration was obtained
assuming a Gaussian crosswind distribution.
Comparisons between the modeled
crosswind-integrated concentration fields and
convection tank data showed
fair-to-good agreement in the lower half of the
CBL. Near the source, the
predicted
contours
exhibited an upward tilt due to the plume rise. However,
the predicted contour
behavior near the CBL top differed from the
measurements due to the assumed
quasi-reflection there. Overall, the
predicted
profiles at the surface were in agreement with the data over a
wide range of
the buoyancy flux and showed a progressive reduction in the
with increasing
The model also was evaluated with GLCs measured near several
Maryland power
plants and the Kincaid (Illinois) power plant. Correlation
plots for each data
set exhibited considerable scatter, but the correlation
coefficient between
the predicted and observed logarithm of the concentration
was
for both sets, thus demonstrating an overall consistency
of model performance.
In addition, the statistics of the predicted-to-
observed GLC
,were good with a geometric mean near 1
and a geometric standard deviation of
~ 2. These results were similar to
those obtained earlier by Weil et al. (1986).
Thus, in addition to
maintaining a continuous variation of
with
,
,were good with a geometric
mean near 1 and a geometric standard deviation of
~ 2. These results were
similar to those obtained earlier by Weil et al. (1986).
Thus, in addition
to maintaining a continuous variation of
In addition to the high modification,
we extended the PDF model to estimate the
field using the meandering plume concept of a small plume driven about by the
large CBL eddies. The small plume grows through relative dispersion from both
buoyancy-induced and ambient turbulence. Initial results showed that the
surface
variation with downstream distance was qualitatively similar
to that obtained
in convection tank experiments for low-to-moderate buoyancy.
However, further
model development and testing of the approach is required
to address highly
buoyant plumes; this is being carried out partially under
another program.
Journal Articles on this Report : 1 Displayed | Download in RIS Format
Other project views: | All 3 publications | 1 publications in selected types | All 1 journal articles |
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Type | Citation | ||
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|
Weil JC, Corio LA, Brower RP. A PDF dispersion model for buoyant plumes in the convective boundary layer. Journal of Applied Meteorology 1997;36(8):982-1003. |
R823419 (Final) |
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Supplemental Keywords:
air, ambient air, atmosphere, atmospheric dispersion, buoyant plumes, chemicals, engineering, exposure, Lagrangian stochastic modeling, mean and fluctuating concentrations, modeling, physics, risk assessment, toxics., RFA, Scientific Discipline, Air, Geographic Area, particulate matter, air toxics, Environmental Chemistry, State, tropospheric ozone, Atmospheric Sciences, Engineering, Chemistry, & Physics, EPA Region, ambient air quality, Lagrangian approach, ambient aerosol, particulates, air pollutants, stratospheric ozone, atmospheric particles, air quality models, power plants, modeling, ambient emissions, Langraian modeling, buoyant plume dispersal, entrainment model, air pollution models, atmospheric aerosols, Region 8, convective boundry layers, pollution dispersion modelsProgress and Final Reports:
Original AbstractThe perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Conclusions drawn by the principal investigators have not been reviewed by the Agency.