S-EPA
United States
Environmental Protection
Agency
Environmental Sciences Research
Laboratory
Research Triangle Park NC 27711
Research and Development
EPA-600/S3-82-079 Nov. 1982
Project Summary
Analytical Solutions of a
Gradient-Transfer Model for
Plume Deposition and
Sedimentation
K. Shankar Rao
The air pollution literature was
reviewed for methods to incorporate
dry deposition in a Gaussian plume
model. A gradient-transfer or K-
theory model for the atmospheric
transport and ground deposition of
gaseous and particulate pollutants
emitted from an elevated continuous
point source is outlined. This
analytical plume model treats gravi-
tational settling and dry deposition in a
physically realistic and more straight-
forward manner than other
approaches. For practical application
of the model, the eddy diffusivity
coefficients in the analytical solutions
are expressed in terms of the widely
used Gaussian plume dispersion
parameters.
This Project Summary was developed
by EPA's Environmental Sciences
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
Pollutant gases and suspended part-
icles released into the atmosphere are
transported by the wind, diffused and
diluted by turbulence, and removed by
several natural processes. An important
removal mechanism is dry deposition on
the earth's surface by gravitational
settling, eddy impaction, chemical
absorption, and other processes. Dry
deposition of airborne pollutants affects
their concentrations and residence
times. Moreover, dry deposition of
acidic and toxic pollutants may
adver&ely impact the local ecology,
human health, organisms, structures,
and ancient monuments. It is important
therefore, to obtain reliable estimates of
dry deposition and its effects.
In this study, the air pollution
literature was reviewed for methods to
incorporate dry deposition in a
Gaussian plume model. A gradient-
transfer or K-theory model for diffusion
and dry deposition of gaseous and
particulate pollutants from an elevated
continuous point source was
formulated. The model was applied to
study two deposition case types. The
ground-level concentrations predicted
by the model were compared with
corresponding results from a source
depletion model. A field study to
measure one or more of the model
parameters was proposed.
Conclusions
An atmospheric transport and
deposition model for gaseous or
suspended particulate pollutants
emitted from an elevated point source
was formulated. This analytical model,
based on gradient-transfer or K-theory,
treats gravitational settling and dry
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deposition in a more physically realistic
and straightforward manner than the
usual tilted-pfume source depletion
approach. Essentially the method
consists of solving the atmospheric
advection-diffusion equation subject to
a radiation boundary condition that
equates the sum of the turbulent flux
and the gravitational settling flux to the
pollution deposition flux at the surface.
Though several analytical solutions of
this problem are available in the air
pollution literature of the past two
decades, the approach has not been
widely used. This may be attributed to
the complexity of the available
solutions, and the usual difficulty in
specifying the eddy diffusivity (K) coeff-
icients under different atmospheric
stability conditions. In the model
developed in this study, the K
coefficients in the analytical solutions
are expressed in terms of the widely
used Gaussian plume dispersion
parameters, which are functions of
downwind distance and stability class.
This allows one to utilize the vast
amount of empirical data on these
parameters, for a variety of diffusion
conditions, within the framework of the
standard turbulence-typing schemes.
In order to facilitate comparison of
results from different models, the new
diffusion-deposition algorithms for
stability and mixing conditions are
presented as analytical extensions of
the well-known Gaussian plume
diffusion algorithms presently used in
EPA models. In the limit when settling
and deposition velocities are zero, the
new algorithms reduce to the current
Gaussian plume equations. Thus the
atmospheric transport and deposition
model outlined here retains the ease of
application, and is subject to the basic
assumptions and limitations,
associated with Gaussian plume type
models.
The parameterized deposition model
was applied to study two important
deposition cases: (1) pollutant particles
having an appreciable settling velocity
that is equal to the dry deposition
velocity, and (2) gases or fine suspended
particles that deposit on the ground
without significant settling. The
variations with downwind distance of
ground-level concentrations, vertical
concentration profiles, surface
deposition fluxes, and net deposition
and suspension ratios were obtained.
Deposition velocity and atmospheric
stability had significant effects on these
results.
Four types of Gaussian diffusion-
deposition models were briefly
reviewed, and the ground-level concen-
trations predicted by the present
analytical gradient-transfer model have
been compared with corresponding
results from the source depletion
model. A systematic comparison of the
performance of the various models has
not been done and none of them has
been satisf actori ly tested aga i nst obser-
vations. General statements on the
relative merits and deficiencies of these
models are, at present, somewhat
subjective, and largely rely on the key
physical assumptions used in the model
formulations and on the complexity of
the methods.
A field study is proposed to measure
one or more of the model parameters,
and to obtain a good data set for model
validation over a distance of at least 10
km from the source. The proposed
study, based on a modified Bowen ratio-
turbulent variance approach that avoids
the difficulties associated with the well-
known vertical gradient and eddy-
correlation methods, will provide
needed data on mean concentrations,
ground deposition flux, and deposition
velocity.
K. Shankar Rao is with the National Oceanic and Atmospheric Administration,
Oak Ridge. TN 37830.
Jack H. Shreffler is the EPA Project Officer (see below).
The complete report, entitled "Analytical Solutions of a Gradient- Transfer Model
for Plume Deposition and Sedimentation," {Order No. PB 82-215 153; Cost:
$11.50, subject to change) will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, V'A 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Environmental Sciences Research Laboratory
U.S. Environmental Protect/on Agency
Research Triangle Park, NC 27711
•k U S. GOVERNMENT PRINTING OFFICE: 1982 659-O17/O866
United States
Environmental Protection
Agency
Center for Environmental Research
Information
Cincinnati OH 45268
Postage and
Fees Paid
Environmental
Protection
Agency
EPA 335
Official Business
Penalty for Private Use $300
0000329
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