United States
Environmental Protection
Agency
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Atmospheric Sciences Research _**•; s ;
Laboratory -x ^ A >
Research Triangle Park NC 27711 '/1 \
Research and Development
EPA/600/S3-85/072 Dec. 1985
Project Summary
Research on Diffusion in
Atmospheric Boundary Layers:
A Position Paper on Status and
Needs
Gary A. Briggs and Francis S. Binkowski
The introduction of a new under-
standing of atmospheric boundary lay-
ers (ABLs) has caused a major change in
the view of the diffusion of pollutants.
The turbulence parameters now stand-
ard in ABL work, have provided a
method for systematically organizing
diffusion parameters. Concurrently
with these advances, alternatives to the
operational models have emerged, but
existing experimental data sets are
inadequate for model comparisons and
evaluations. The most important know-
ledge gap is the lack of an adequate
specification of the relevant meteor-
ology both at the point of release and
downwind. A second major inadequacy
is experimental measurements of plume
characteristics up to 10O km from the
release point. There is also a great need
for formulating new operational models
based upon this newly acquired exper-
imental data and the new alternative
approaches. Finally, it is recognized that
a modest but steady effort is necessary.
This Project Summary was developed
by EPA's Atmospheric Sciences Re-
search Laboratory, Research Triangle
Park, NC, to announce key findings of
the research project that is fully docu-
mented in a separate report of the same
title (see Project Report ordering in-
formation at back).
Introduction
The purpose of this study is to review
the current state of science concerning
diffusion within the atmospheric bound-
ary layer (ABL) and to identify major
issues and research needs. The study is
limited to considering only the diffusion
of non-buoyant, conservative substances
over homogeneous and level or moder-
ately hilly terrain. Thus, chemical trans-
formation, wet and dry deposition, buoy-
ancy effects, and diffusion in complex
terrain are all topics which are excluded.
Certainly these are very important topics
both from the point of view of the research
scientist and from that of a regulator;
however, each of these topics deserve a
review study of the same scope as
attempted here. The topics that will be
included here are: a review of diffusJon
experiments and models, and a discus-
sion of research needs. We begin, how-
ever, with a highly simplified description
of the major meteorological factors af-
fecting diffusion. The main report con-
tains the necessary details and refer-
ences.
Meteorological Factors
Controlling Diffusion
Material released from the ground or
from a stack is mixed and transported by
air motion. This process dilutes the
material and carries it horizontally away
from the source. This mixing process is
called turbulent diffusion, or simply dif-
fusion. The turbulence responsible for
this mixing may result from the wind
blowing over the ground, generating
turbulent eddies, or it may result from
heated parcels of air or thermals that are
generated in air heated by contact with
ground which has been warmed by the
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sun. Thus, we distinguish between "mech-
anical" and "convective" turbulence, be-
cause in addition to having different
generative mechanisms, they have con-
siderably different diffusive properties.
The current view of the ABL divides it
into three conceptual states, the neutral
boundary layer (NBL), the convective
boundary layer (CBL), and the stable
boundary layer (SBL). The NBL occurs
when there is a negligible transfer of heat
from the ground surface to the air. This
occurs with strong winds and usually
when most of the sky is covered with
clouds. Only mechanical turbulence is
generated in the NBL which extends up to
or even into the cloud bases. The SBL
occurs when the ground is substantially
cooler than the air above it causing a
stable profile to develop. This means that
an upward moving parcel of air, for
exa mple, experiences a downward restor-
ing force because it is colder, therefore
denser, than its surroundings. Mechan-
ical turbulence is generated as the wind
blows over the ground, but vertical mo-
tions are very much restricted by the
stability. Vertical diffusion, consequently,
is restricted and plumes of effluent dilute
slowly during transport downwind. The
depth of turbulent mixing is also very
restricted in the SBL, being of the order of
100 m or less It is under these conditions
that some of the most serious air pollution
episodes can occur. The CBL occurs in the
daytime, with low to moderate wind
speeds and clear to partly cloudy condi-
tions. Then the ground is warmed and
thermals rise from the surface to gener-
ate convective turbulence. The diffusion
process is dominated by the vertical
transfer of material in the thermals and
downdrafts. The height to which these
thermals rise is called the mixing depth.
As a result of this efficient type of mixing,
the CBL often has a "well mixed" condi-
tion in which the vertical profile of a
pollutant becomes constant from a few
meters above the surface to the mixing
depth.
On a day without many clouds, and
with neither fronts nor shorelines nearby,
the diurnal course of the ABL is as follows:
starting about an hour before sunrise, the
ground has cooled to its minimum tem-
perature. The temperature profile is stable
but there is some vertically restricted
mechanical turbulence from the surface
to the top of the SBL. Any plumes within
this SBL are very well defined. Any
plumes above the SBL have virtually no
vertical dilution but may be spread hori-
zontally by meanders caused by large
scale horizontal eddies. As the sun comes
up, thermals begin to rise from the ground
but must work against the stable temper-
ature profile until all the air in the
developing CBL is warmed and mixed.
The CBL, thus formed, grows until the
diminished surface heating in the late
afternoon can no longer overturn stable
air above the CBL. Typically, the maxi-
mum mixing depth is of the order of a
kilometer. Any plumes beneath this
height released into the previously stable
air are mixed downward to the ground, a
process referred to as fumigation. Late in
the afternoon, the strength of the ther-
mals diminishes. Soon a new stable layer
is established at the surface and a new
SBL forms. The transitional times around
sunrise and sunset are as yet poorly
understood. Little is known about the
structure of the ABL and even less about
diffusion during these periods.
In a typical diurnal cycle, the large
changes in stability correspond to large
changes in diffusion rates. Some method
of indicating the ambient stability is
necessary and there are several indices
of stability currently used. The index most
indicative of the physical processes at the
surface is the Obukhov length, L. By
convention L is defined to be negative
with an upward flux of heat at the surf ace
(unstable conditions). In principle, this
length is defined such that at height z.= L
above the ground, the buoyant production
(or destruction) and the mechanical pro-
duction of turbulent kinetic energy are
comparable. Hence, above z = L, the
turbulent state of the ABL is dominated by
buoyancy effects and below z = L, the
turbulent state of the ABL is dominated by
the mechanical overturning caused by
the wind blowing over the surface. Pro-
files of mean wind speed and other
meteorological quantities are functions
of z/L near the surface.
Besides the Obukhov length, other
quantities of importance in describing the
turbulence in the ABL are the surface
heat flux, the surface friction velocity
scale u*, and the mixing depth. A velocity
scale analogous to u* has been developed
for the CBL. Called the convective velocity
scale, w*, it is essentially defined by the
surface heat (or buoyancy) flux the depth
of the CBL; w* has proven to characterize
the turbulent velocities within the CBL
very well. The depth of the CBL divided by
L serves as a useful indicator of the
relative importance of the thermals as a
major transfer mechanism; the larger this
ratio is, the more important thermals are
to the description of diffusion. As funda-
mental as these variables are to our
understanding of ABL processes, u* and
the surface heat flux are not easily '
measured; both are needed to determine
L using its definition. An alternative index
related to L, called the Richardson num-
ber, Ri, uses a temperature difference
and velocity differences between two
heights: in another form known as the
bulk Richardson number, only one wind
measurement is used. There are simple
methods to convert from Ri to Obukhov
length. An estimate of the site roughness
length, z0, is necessary with the bulk Ri
approach, while the velocity differences
approach strongly demands wind sensors
that are properly calibrated. With the
temperature differences, and at least one
wind velocity, the same methods that
yield the Obukhov length can be used to
obtain u* and the heat flux. The only other
essential measurement needed for char-
acterizing ABL turbulence and diffusion
is the mixing depth. This can be obtained
from good profiles of temperature and
humidity. In the case of the SBL, a profile
of wind speed is also required. In recent
years it has become possible to estimate
this depth by using remote sensors such
as lidars and acoustic sounders. Lateral
diffusion at large distances is enhanced
by wind direction changes with height,
which are best determined from wind
velocity soundings. i
Experimental and Theoretical
Bases for Our Understanding of
Diffusion
The current understanding of diffusion
processes is based upon results from field
experiments, laboratory experiments, and
theoretical models. Field experiments
may be conveniently grouped into two
classes, those in which the tracer material
is released from very near the surface and
those in which the release is elevated.
The data from previous experiments has
been very useful in formulating our
current understanding of the diffusion
process but there are major inadequacies.
First, the tracers used in most early field
studies were not conservative. This
means that as a cloud or plume of tracer
was transported downwind, the material
stuck to the ground or deposited, thus
reduci ng the concentration further down-
wind by an uncertain amount. The theo-
retical view of diffusion prevalent at the
time of the earlier experiments was that
the vertical profile of concentration was
Gaussian. If this were true and the tracer
were conservative, the standard deviation
of the concentration, Sigma-z, is easily
obtained from ground samples alone.
When deposition occurs, however, the
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Sigma-z estimate is biased by an un-
known amount to be an overestimate. A
second difficulty with these data is that
with one notable exception, the Prairie
Grass experiment done in 1956, the
experiments did not take sufficient mete-
orological data for either interpretation
using contemporary concept or for val-
idation of current diffusion models. Two
recent experiments, one in Copenhagen,
Denmark and one under EPA sponsorship
in Boulder, CO, had extensive meteor-
ological data. The Danish experiment
used a conservative tracer, while the
EPA-sponsored experiment used remote
sensing to get concentration profiles at
several locations downwind of the source.
This experiment, named Convective Dif-
fusion Observed with Remote Sensors
(CONDORS), was designed to verify some
new insights into CBL diffusion that were
gained from numerical experiments and
laboratory studies.
Laboratory studies of ABL diffusion are
gaining wider acceptance as the scien-
tific community has learned how to
simulate ABL processes more faithfully.
The major problem faced in a laboratory
simulation is to maintain the proper
balance of forces and yet attain the
required reduction in scale. In strictly
neutral conditions, this is not too difficult.
One problem is that if the scale reduction
factor is very large, viscous effects smooth
out turbulent eddies in the laboratory
which would not be smoothed in the
atmosphere. This is usually overcome by
making the bottom of the wind tunnel
have a rougher texture than strict scaling
would predict. A major difficulty is proper-
ly simulating buoyancy effects. Since
gravity cannot be easily scaled down on
the earth's surface, density differences
must be exaggerated. This distorts other
aspects of the simulation so that tech-
nical trade-offs are necessary. The most
effective use of laboratory work then is to
examine a particular, but important as-
pect of the diffusion problem. One such
application which illustrates this point is
the work done at the EPA Fluid Modeling
Facility that showed that a tall slender
building required a shorter stack for good
plume dilution than would have been
predicted by using building height alone.
Experimental work alone is insufficient
for an understanding of diffusion. A
proper conceptual framework is also
necessary. Most current applications of
diffusion models are based upon the
Gaussian distribution in both vertical and
horizontal directions in order to character-
ize the diffusion. The Gaussian distribu-
tions are based upon empirical data
collected primarily during near surface
releases over relatively flat terrain. Un-
fortunately, most of the model applica-
tions are for situations that were not
considered in the experimental situations
which provided the empirical data for the
formulation of these models. Finally, for
diffusion of non-buoyant releases within
a CBL, the Gaussian assumption for the
vertical distribution of material was re-
cently shown to be incorrect. Current
practice has adjusted the necessary pa-
rameters so that surface concentrations
are nearly correct for the CBL case even
though the vertical profile is not. There
are, however, several modeling methods
that have been demonstrated to be super-
ior for particular applications. In the
interest of brevity, only three examples
will be mentioned. The first is the statis-
tical method which relates the standard
deviations of the concentration distribu-
tion directly to the observed turbulent
intensities of the wind field. Since the
statistics of the wind field tend to be fairly
uniform in the horizontal direction, this
method has the greatest success in
characterizing the horizontal concentra-
tion distribution for transport over an area
of homogeneous land use. A second
approach is to simulate the diffusion as a
random walk or "Monte Carlo" process.
Recent work in this area has allowed for
vertical and horizontal inhomogeneities
in the flow field. A disadvantage to this
approach is that it generates individual
material trajectories and then constructs
the distributions directly. For realistic
cases, a very large number of trajectories
must be calculated. Finally, a third
method is numerical simulation of the
diffusion process by solution of the rele-
vant governing partial differential equa-
tions in an Eulerian framework. There
has been great progress made in formu-
lating these models which require a
number of simplifying assumptions. For
example the laboratory work on surface
releases in the CBL inspired a set of
numerical simulations that in turn in-
cluded a prediction about unexpected
behavior of an elevated release. The
numerical work predicted that the plume
centerline for a non-buoyant release
would descent to the surface, then rise
again. This prediction inspired further
laboratory work that verified the finding.
The CONDORS experiment was conduc-
ted specifically to confirm the numerical
and laboratory findings for diffusion in
the CBL. Here is an example of how the
various methods for studying diffusion
interact in the discovery and confirmation
of major new findings in diffusion theory.
All of the work mentioned in this example
was supported by EPA.
Needs for Future Work
Before listing the future needs it is
imperative to state at the outset that the
human and fiscal resources for these
endeavors are not trivial. A modest steady
commitment of personnel and funds for
an extended period is necessary, as the
work described requires a sustained
scientific effort.
The first major need is for field data for
selected meteorological scenarios for the
development, testing, and evaluation of
diffusion meteorology models. The char-
acterization of'those meteorological var-
iables important to the diffusion process
is a major impediment to the implementa-
tion of new and emerging approaches to
diffusion characterization. To meet these
needs requires detailed profiles of the
relevant variables within the first kilo-
meter or so of the atmosphere. In addition,
sufficient measurements are needed to
characterize the surface energy balance,
the forcing of the wi nd fields by the large-
scale migratory pressure systems, the
horizontal temperature field and the cloud
conditions. These studies should be con-
ducted over a variety of terrain types
using a minimum of preparation and
personnel. This would allow the study of
the meteorological events of interest at
the locations of interest. A portable
instrumented tower, a tethersonde (a
tethered balloon carrying an instrument
package), and an acoustic sounder would
be the basic tools for such studies. The
development of such meteorological field
studies would greatly facilitate the trans-
fer of theoretical results into practical
operational models useful for decision
making.
A second major need is for the compar-
ison, evaluation, and construction of new
operational models. An interdisciplinary
team with skills in meteorology, chem-
istry, numerical modeling, and statistics
is required to meet this need. Such a team
would evaluate the models not only with
respect to experimental data, but also
with respect to the expected uncertainty
in the model inputs. These type of com-
parisons are necessary to make improve-
ments in the operational models.
A third major need is for diffusion
experiments, both in the field and in
laboratory settings. The laboratory studies
are needed to test theoretical results in
specific simplified situations that are free
of confounding influences. The field data
are needed because there is a wide
disparity between the flat homogeneous
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land where the best of the previous field
studies have been conducted and the
complex woodlands and urban-suburban
developments typical of the American
landscape. One example of important
information to be gained from such field
studies is the characterization of the
concentration field at 100 km downwind
from the source. Current models extra-
polate to this distance based upon
measurements to only 3 km. Vertical and
lateral profiles of concentration even at
widely spaced plume transects would
improve the current situation consider-
ably. Other examples include the char-
acterization of releases made during the
hours of transition, that is near sunrise
and sunset, as the behavior of the atmos-
phere during these periods is very poorly
understood. For any of these examples, a
good diffusion experiment is of necessity
a good meteorological experiment, since
a full complement of meteorological
measurements is essential to the success
of the experiment and to the continued
usefulness of the data set.
The EPA authors, Gary A. Briggs (also the EPA Project Officer, see below) and
Francis S. Binkowski are with Atmospheric Sciences Research Laboratory.
Research Triangle Park. NC 27711.
The complete report, entitled "Research on Diffusion in Atmospheric Boundary
Layers: A Position Paper on Status and Needs, "(Order No. PB 86-122 587'/AS;
Cost: $22.95, 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 Project Officer can be contacted at:
Atmospheric Sciences Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
United States
Environmental Protection
Agency
Center for Environmental Research
Information
Cincinnati OH 45268
Official Business
Penalty for Private Use S300
EPA/600/S3-85/072
0000329 PS
U S ENVIR PROTECTION AGENCY
REGION 5 LIBRARY
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