Table Of ContentLECTURES.ONA.IR POLLUTION
AND
ENVIRONMENTAlIMPACT·ANALYSES
American .
Me~eotologi_cal~Ociety
LECTURES ON AIR POLLUTION AND
ENVIRONMENTAL IMPACT ANAL YSES
Sponsored by the
AMERICAN METEOROLOGICAL SOCIETY
29 September -3 October 1975
Boston, Massachusetts
DUANE A. HAUGEN
Workshop Coordinator
The tutorial lectures reproduced in this collection are unedited
manuscripts of the material presented at the AMS Workshop on
Meteorology and Environmental Assessment; their appearance here
does not constitute formal publication.
Copyright © 1982, American Meteorological Society.
ISBN 978-0-933876-42-2 ISBN 978-1-935704-23-2 (eBook)
DOI 10.1007/978-1-935704-23-2
Softcover reprint of the hardcover 1s t edition 1982
AMERICAN METEOROLOGICAL SOCIETY
45 Beacon Street, Boston, Massachusetts 02108
U.S.A.
1976
Second printing. 1982
PREFACE
In recent years, environmental impact analyses have become a highly
visible aspect of many activities in industrialized societies. Most of these
analyses deal with air pollution assessment, often in situations of complex
terrain features and limited meteorological data. There is a vast amount of
literature on the various aspects of air pollution analyses, some of which,
however, is somewhat difficult for the practitioner to obtain. These work-
shop lectures are, hopefully, a partial answer to that problem.
We have attempted to organize a systematic treatment of turbulent
diffusion as applied to the practical problems one faces in the real world.
The opening two lectures deal with the theoretical concepts on which much
of the subsequent material is based. Selected topics which follow include
the problems of plume rise, diffusion in complex terrain and along shore-
lines, urban pollution, chemical changes of the pollutant, and modern data
management concepts for obtaining the meteorological data necessary for
pollution analyses. The final lectures are intended to provide two perspec-
tives in preparing environmental impact reports, one by a frequent preparer
and the other by a frequent evaluator of such reports.
A large number of people have contributed to this workshop, not all of
whom can be properly acknowledged here, unfortunately. The reader of this
material will appreciate the outstanding effort contributed by each of the
authors. In addition, the workshop preparation and the publication of this
material was accomplished by the combined efforts of several members of
the AMS staff. It has been a distinct pleasure to have been a part of this
experience.
DUANE A. HAUGEN
Lexington, Massachusetts
September 1975
i
TABLE OF CONTENTS
Page
PREFACE i
CHAPTER 1: THE D~PERSION OF MATERIALS IN THE ATMOSPHERIC BOUNDARY 1
LAYER - THE BASIS FOR GENERALIZATION - FRANK PASQUILL
1. Introduction. . . . . • . • . . . . . . . • . . • . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2. Crosswind Spread on Statistical Theory. . . . • . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3. Vertical Spread on Gradient-Transfer Theory. • • . . . . . . . . . . . . • . . . . . . . . . . . . . . . . 10
4. Vertical Spread from A Ground Level Source on Similarity Theory. .. .. . .. ... . . 18
5. Effects of Elevation of Source on Vertical Spread Characteristics. . . . . . . .. . . . . . . 29
6. Concluding Remarks. . . . . . • . . • . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
7. Acknowledgments. . . . . • . . . . . . . • . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
List of Symbols • . . . . . . . . . • . • . . . . • . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
References ..........................•.................................... 33
CHAPTER 2: ATMOSPHERIC DISPERSION MODELS FOR ENVmONMENTAL 35
POLLUTION APPLICATIONS -- F. A. GIFFORD
1. Introduction. • • • . . . . . . . . . . . . . . . • . • . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2. Diffusion Models Applicable to Environmental Problems.. .. . • . . . . . . . . . . . . . . . . . 37
3. Plume Modeling Applications to Various Space and Time Scales. .. . . . . . . . . . . . . . 39
4. Buoyancy Effects ....•..•..•.•....•.••.•..•.•..............................
5. Modification of Plume Models to Adapt them to Various Environmental Problems
and Exceptional Atmospheric Flows.......... . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
6. Modeling Removal, Transformation and Resuspension. . . . . . . . . . . . . . . . . . . . . . . . . 52
7. Some Comments on the Possibilities of Future Research ...................... 54
Acknowledgment •..•..•.•....•....•..•.......•....•....................... 54
References .......••.•.....•.•.••.•.......•.............................. 54
CHAPTER 3: PLUME RISE PREDICTIONS - GARY A. BRIGGS 59
1. Introduction. . . . . . . • . • . . • • . • . • . . • . . • . . . . • . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2. The Physics of Plume Rise. • • . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3. Rise Near the Source . . . • . • . . • . . . . • . . • . • . • . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4. Rise Limited by Stable Stratification. •.. . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . • . . . . 80
5. Rise Limited by Mechanical Turbulence. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6. Rise Limited by Convective Turbulence ......•.•........................... 92
7. Summary. . • . . . . . . . . . . . . . . . . . . . . . • . • . . . . • . . • . . • . . . . . . . . . . . . . . . . . . . . . . . . . 96
Acknowledgment • . . . • . • . . • . • • . . . . • . • . . . . • . . • . . . . . . • . • . . . . . . . . . . . . . . . . . . . . 97
References ...•.•.....•............•.................................... 97
Appendix A - Symbols. • . • . • . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Appendix B - Cooling Tower Calculations .................................. 105
CHAPTER 4: TURBULENT DIFFUSION IN COMPLEX TERRAIN - BRUCE A. EGAN 112
1. Introduction. • . • . . • . . • . • . . . . . . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
2. Meteorological Aspects of Pollutant Dispersion in Complex Terrain. •.. , . . ....• 113
3. Mathematical Modeling of Air Flow and Pollutant DisperSion in Complex Terrain. 117
4. Diffusion Experiments in Complex Terrain. . . . . • . . . . . . . • . . . . . . . . . . . . . . . . . . . . 124
5. Physical Modeling of Flow Over Complex Terrain. •.... . . . . . . . . . . . . . . . . . . . . . . 129
6. Conclusions and Recommendations. . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
Acknowledgments. • . • . . . • . • . . • . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
References •..•..•.•..•..•.•..•..•...........•...............•........... 133
ii
Page
CHAPTER 5: TURBULENT DIFFUSION AND POLLUTANT TRANSPORT IN 136
SHORELINE ENVIRONMENTS - WALTER A. LYONS
1. Introduction. . • . • . . . . • . . • . . • . . . . . . • . . • . . . . • . • • . . • . • . . . . . . . . . . . . . . . . . . . . • . . 136
2. Diffusion Over Water . • . . . . . • • • . . . . • . . • . . . . . . • . . • . . . . . . . . . . . . . . . . . . . . . . . . • 139
3. Diffusion During Gradient Onshore Flows. . •• . • . . . . . . . . . . • . • . . . . . . . • . . . . • . . . 150
4. Transport in Lake/Sea Breezes. . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • 182
5. Long Range Over-Water Transport. • . . . . . . • • . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . 194
6. Transport of Photochemical Pollutants. • . . . . • . . . . • . . . . . . . . . • . . . • . . . . . . . . . . . 196
7. Summary, Conclusions, Recommendations ..•.•.........................•.• 198
8. Acknowledgments. . • . . • . . • . • . . . . . • . • . • . . • . • . . • . . • . . . . • . . • . • . • . . • . • . . • . . . . . 202
9. References. . . • . . . . • . • • . • • . . . . • . • . . . . . . . • . . • . • . . . . . . . . . . . . . . . . . . . . • . . . . . 202
CHAPTER 6: URBAN DIFFUSION PROBLEMS - STEVEN R. HANNA 209
1. Introduction. • • • • . • • . • . . . . . • . • . • • • • . . • . • • . • . • • . • . . • . . . . • . . . . • . . . . . . . • . . . . . 209
2. Input Problems.. • . • • • . • • • . • . • • . • • . • . • . • . . • . . • • . • . . . . • . . . . . . . . . • . . . . . . • • . . 209
3. Modeling ........................ ". .............. "" " " " " " " " " " " " " " " "" " " " " " " " 212
4. Numerical Urban Diffusion Models. • • • • • • . • • • • • • • . . . . • . • . • • . • . . • . . . . . . . • • • . . 216
5. Output and Observations. ••• . • . . . . • • . . • . • . . • . • . . • . • • . • . . . . . . . . . . . . . . . . . . . . • 220
6. References. • • . • . . • . • • . • • . • • • . . • . . • . . . • • . . • . . . • . • . • . . . . . . • . . • . . . . . . . . . . . . . 224
CHAPTER 7: ATMOSPHERIC TRANSFORMATIONS OF POLLUTANTS -J. M. HALES 228
1. Introduction. • . . . . • . . • • . • . . . . • . . . . . . . • • . . . . • • . . • . • . . . • . . . . . . . . . . . . . . . . • . . . 228
2. Chemical Transformations. . • . . • . . . . • . . . . • . . • . . . . • . . . . . . . • . • . . • . . . . . 2. 2. 9. . . •
3. Physical Transformations. • . • • . . • . • . . • . • . . • . . • . . . • • . . . . • . • . . . . • . . . . . . . • . . . 234
4. Precipitation Scavenging. . • • . . . . • . • • . • . . . . . • . • . . . . • . . . . . . . . . . . . . . . . . . . . . . . 235
5. Dry Deposition. • • . • . • . . . . . . . • • . • . . • . • . . . . • • . . . . • . . . . • . . . . . . . . . . • . • . . • . • • . 237
6. Utilization of Microscopic Rate Processes to Calculate Macroscopic
Atmospheric Phenomena. . • • • . . • . . • • • • . . . • • • • . • • . • . . . . . • . • . . . . • . . • . . . . . . • . . 239
References. . . . . • . . • . . • . • . • . • • . • . . . • . • . . . . • . . . . • . • . . • . . . . • . . . . . . • . . . . . . . . . 241
CHAPTER 8: OBSERVATIONAL SYSTEMS AND TECHNIQUES IN AIR POLLUTION
METEOROLOGY - WARREN B. JOHNSON & RONALD E. RUFF 243
1. Introduction. . • • . . . . • . . • . • . . . . • . . . . . . . . . . • . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
2. The Role of Meteorological Data in Air Pollution Studies. . . . . . . . . . . . . . . . . . • . . . 243
3. Design Considerations for Field Studies. . . . • . . . . . . . . . . . . . . . . . • . . . . . . . • . . • . . . 245
4. Instrumentation Considerations. • . . • . . . . . . . . . . . . . . . •• . . . . . • . . . . . . . . • . . . . . . . • 251
5. Meteorological Tracer Techniques. . • . . • . . . . • . . • . • . . . . • . . . . . • . . . . • . • . . . . . • • • 261
6. Observational Networks and Systems. • . . . . . . . . . • . • • . • . . . . . . • • . . . . • . • • • • . • • • . 263
7. Data Management and Analysis. • . . . . • . . . . . . . . . . . . • . . . . . . . . . • . . • . . . . . . . . . . . . 268
Acknowledgments. • . . • • • . . • . . • . . . . . • . • . . . • . . . • . • . . • . . • . • . . . . . • . • . . . . . . . . . . 273
References. • . • . . . . • . . • . • . • . . • . . . . • • . • . . • . • . . • . . • . . . . . . . • . • . . . . . . . . . . . . . . . 273
CHAPTER 9: METEOROLOGICAL CONTENT OF ENVIRONMENTAL IMPACT
ASSESSMENTS - JAMES R. MAHONEY & JOHN D. SPENGLER 275
1. Introduction. "" " " " " " " " " " " " " " . "" " " "" " "" " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " 275
2. Candidates for Assessment. • • . . . . • . • • . • . • • • • . . • . • • . • . • • . • • . • . • • • • • • . •2 •7 .6 . • •
3. Choice of An Assessment Program: General Principles. • • • . . . . . . . . . . . . • . . . . • 281
4. Air Q.Iality Assessments. • . • . . • . . • • • . • . . • . . . . . • . • . . . . • . . • . . . . • . . . . . . . . . . • . 281
5. A Checklist for Planning Meteorological Assessments of Environmental Impact.. 289
References. "" " " " "" " " " " " " " "" " " " " " "" " " " "" " "" " " " " " " " " " " " " " " " " " "" " " " . "" "" " " " " 291
CHAPTER 10: FEDERAL GOVERNMENT REQUIREMENTS FOR ENVIRONMENTAL
IMPACT ASSESSMENT - ISAAC VAN DER HOVEN 293
1. Introduction. "" " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " 293
2. Federal Environmental Laws. . . . . . .• . . . . . . . • . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
3. Federal Air QIality Standards .•. . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
4. Federal Guidelines for Preparation of Environmental Impact Statements. .. .. . .. 294
References. • • • . • . . • . . . . • . . • . . . . • . . . . • . . . . . • . • . . . . • . . . . . • . . . . . . . . . . . . . . . . . 295
iii
CHAPTER 1
THE DISPERSION OF MATERIAL IN THE ATMOSPHERIC BOUNDARY LAYER -
THE BASIS FOR GENERALIZATION
F. Pas quill
37 Arbor Lane
Winnersh, Wokingham
Berks. RGII 5JE
ENGLAND
1. INTRODUCTION quasi-stationary mixing depth characteristic of
the middle part of the day, and the heights given
The purpose of these first two lectures is in the diagram are typical of this condition.
to summarize the basis on which it is possible to The whole flow is characterized firstly by the
prescribe general laws for the action of the atmos wind speed immediately above the mixing layer
pheric boundary layer in dispersing and diluting (the geostrophic wind) and then by the various
pollutants. It is, of course, implicit in this parameters (listed in Fig. 2) representing the
statement that there is some extent of order in effects of surface heating and friction.
the essentially turbulent structure of the layer
and in the processes of transfer which the turbu Within the mixing layer are generated
ence brings about. To that extent we can think in characteristic profiles of temperature, wind speed,
terms of a quasi-ideal flow, governed by simplified wind direction, shearing stress, heat flux, r.m.s.
equations of motion and thermodynamics, and char turbulent velocity, scale of turbulence. A general
acterised by a limited number of prescribable schematic outline is given in Fig. 3. Progress in
physical parameters. On the other hand there are formulating and establishing profile laws is rea
important aspects of airflow (e.g. that over sonably complete for the surface-stress layer and
irregular terrain) which are not describable in the effort is now being concentrated on the rela
such simple terms and which must be given special tively unexplored outer layer. Also, in general
consideration as in subsequent lectures in this the detail is more complete for the mean fields of
series. temperature and wind than for the properties of
vertical flux and turbulence. The profiles of
The structure and transfer properties in intensity and scale of turbulence are of pre
the quasi-ideal form of boundary layer were the eminent significance to dispersion of pollution,
subject of a previous workshop and the detailed so it is appropriate to recall the approximate
papers on which the lectures were then based are magnitudes currently ascribed to these properties,
now available in published form (Haugen, 1973). and these are summarized in Table 1. It is also
In this lecture we first recall briefly certain particularly appropriate to note at this point that
outstanding features which are essential to the improvement in this aspect of description of the
subsequent cohsiderations of dispersion. turbulence of the mixing layer is a continuing and
important need.
(a) The diffusive structure of the flow
(b) Current working theories of dispersion
In the well-mixed state typical of daytime
conditions the boundary layer has a more-or-less The current working theories of dispersion
well-defined upper boundary - i.e. an interface are constructed from gradient-transfer (K) theory,
with the essentially non-turbulent flow above. or G.I. Taylor's statistical theory, or similarity
The interface is most clearly defined when convec theory (dimensional analysis). Full discussion of
tive motions generated by surface heating reach or the background and current state of these theories
penetrate into a layer with stable density strati can be found elsewhere (e.g. by the present writer,
fication. This stable stratification is a quasi 1974), and important specific applications are con
permanent feature of the atmosphere clear of the sidered in subsequent sections. In this introduc
ground, above a height which is usually in the tory section it is useful to note certain general
range 1/2 - 2 km in middle latitudes. It also features.
exists at or close to the ground as a result of
nocturnal cooling. The usual overall effect is a At the outset it is essential to recall the
diurnal cycle of the depth (h') over which mixing fundamental difference in the character of the two
is effective - ranging from a quite shallow layer distinct 'features of dispersion;
during the night to a maximum in the afternoon.
(See Fig. 1). (i) the time-dependent spread of a par
ticular volume of polluted air - i.e. the
It is customary to think of the mixing instantaneous source, puff or cluster
layer as having the several layers indicated in
Fig. 2. The divisions are most familiar for the
1
DEPTH (h I)
......
or
HEAT
FLUX (H)
-
hI
TIME
SUNRISE SUNSET
Fig. 1. Diurnal evolution or mixing layer.
Stable atmosphere (v )
g
-
___ interface with
stable flow (ca 1 km)
buoyancy
Outer layer dominated (H,h I)
buoyancy
affected (u*,H)
Surface-stress
layer (0 - 30m) virtually
neutral ( u* )
___ Earth I s surface &
roughness elements (wakes)
Fig. 2. Structure of atmospheric boundary layer.
2
F. Pas'iu1ll
I
,
--I - h' )
/
/ \ J
/
\ I
\
\
"
\
/
/
/
TEMPERATURE (T) STRESS (,) TURBULENCE (0 )
WIND SPEED ( u) HEAT FLUX (H) SPECTRUM SCALE (~)
WIND VEER ( C()
Fig. 3. Schematic form of boundary layer profiles
in daytime mixing regime.
Table 1. Simplified summary of rough magnitudes of
turbulence in the boundary layer
r.m.s. eddy velocity spectrum scale
(J Am
Vertical component w
Neutral 1.3 u* in s.s.l. 3 z in s.s.l., thereafter
flow i.e. 0.1 u(lOm), there increasing less rapidly
after decreasing slowly with z and tending to a
with z constant
Light wind Increased x4 at 10m, 5 z over most of m.l
convective increasing slowly with z
over about first half of
m.l., then decreasing
Light wind Reduced x2 at 10m, 0.5 z at low level, but
stable decreasing rapidly with maximum reached at about
=
z and increasing z 100m
stability
Crosswind component v
uho)
Neutral 0.2 % 300m, independent of height
flow
Light wind 0.6 :;i"(10) several-fold increase over
convective neutral value
Light wind 0.3 m/sec at 10m, behaviour very uncertain, may
stable relatively insensitive even be increased
to both wind speed and
stability
Abbreviations: s.s.l surface-stress layer
m.l. mixing layer
3
(ii) the time-mean distribution in a (c) New advances and future trends
vertical plane a given distance downwind of a
continuous release of pollution - i.e. the ~ There are several areas of crucial interest
tinuous point source, which may be of interest in which stUdies and analyses are in progress, and
either in isolation or as an elementary component from which improvements in the whole scientific
of ~ or ~ releases. basis of estimating dispersion may be expected
progressively to emerge. These are enumerated
Practical concern is mostly with (ii), below and discussion of them is continued in sub
though there may also be concern with (i) in that sequent sections.
a continuous plume from a stack release is just a
continuous series of puffs. Accordingly the (i) The form of the Lagrangian autocorre
instantaneous concentration experienced downwind lation. Earlier considerations of conceivable
of a continuous point source is determined by the functional forms of the Lagrangian autocorrelation
instantaneous distribution in the vertical plane coefficient suggested that the precise form is
and by the ever-varying position of the affected unlikely to be of great significance. This meant
zone relative to the receptor. The time-mean that the essential flow parameters were reduced to
concentration is the integral with respect to time two, i.e. the intensity and scale of turbulence.
of this instantaneous concentration (or, in an Reappraisal of field data on dispersion, in terms
alternative simplified way, for a uniform instan of the Taylor statistical theory, is now pointing
taneous concentration across the plume section, it to the possibility that the form of the correlation
is the instantaneous concentration multiplied by function may in fact be signficantly different. from
the fraction of time over which the plume cross those originally admitted (Section 2(b)).
section includes the receptor).
(ii) The effective eddy diffusivity. The
In the foregoing view of the continuous most effective and reliable approach requires ap
point source the continuous wandering of the plume propriate specification of the K-profile in accord
cross-section in a vertical plane is a manifestation ance with the known physical properties of the flow.
of dispersive motions on scales larger than the Use of momentum-transfer laws, together with a
plume section itself. By definition this part of Reynolds analogy, is particularly effective for
the dispersive action cannot be regarded as a short-range vertical dispersion (Section 3(b)).
gradient-transfer process and must be considered However, extension to longer range necessarily
on a more appropriate basis. Such a basis is involves the wind profile over the whole depth of
found in the Taylor statistical theory, and this the planetary boundary layer and, as it appears at
has provided a useful approach especially for present, the upper part of the K-profile is not
crosswind spread. This inapplicability of the thereby sensitively prescribed. An alternative
gradient-transfer approach is of course equally which avoids this difficulty is the use of actual
relevant to vertical spread from an elevated data on the turbulence (the intensity and scale)
source, in that vertical dispersive motions of and of a suggested formulation of K which has basis
larger scale than the plume cross-section itself in the simple statistical theory (Sections 3(a) and
are likely to be operative, at least in the early 3(b)) •
stages of dispersion.
(iii) Extension of Lagrangian similarity
On the other hand, for vertical dispersion theory. Important limitations in the original
from a ground-level source there appears to be a form of the theory arise firstly from the difficulty
convenient simplification arising from the scaling of making satisfactory allowance for thermal strati
of the vertical component with respect to height fication, and secondly from the inherent restriction
above ground. Provided the plume is dynamically to quite small vertical spread (i.e. within the
passive (and thus remains in contact with the depth of the surface-stress layer). An alternative
ground) it is at no stage acted on by motions of formulation is under consideration, in which the
larger.(vertical) scale than itself, and the original determining parameters, ~ and H, which
vertical redistribution within the plume must refer to the surface (z=O) , are replaced by proper
always be under the action of motions smaller ties of turbulence (intensity and scale) which are
than itself. Thus the vertical spread process functions of height and which automatically in
may be expected to have in some degree the char corporate the effects of thermal stratification.
acter of a gradient-transfer action, and there is Full examination of the potential of the alterna
good observational evidence (Calder 1949) that tive method is hampered by the lack of critical
this is effectively so for short-range dispersion observational data, but first impressions based on
in a neutral atmospheric boundary layer. A con comparisons with vertical spread derived from the
sequence of this particular feature is that the gradient-transfer method are encouraging. (See
vertical spread from a ground-level source does Section 4(b)).
not exhibit the dependence on sampling time that
is so markedly evident in the crosswind spread. (iv) Scaling of rate of vertical spread
in relation to mixing depth. The need to incorpo
The overall position regarding the areas rate a limited depth of mixing above which the
of application and limitations of the various determining parameters (intensity of turbulence or
approaches, the essential assumptions and the K) go to zero has long been accepted. However, a
physical parameters which need to be specified, further development which has been pursued by
is now summarized in Table 2. Further details, Deardorff recognizes that the depth of mixing also
including relevant formulae and certain comparison~ determines the structure and profile of vertical
with data, are given in the subsequent sections of IlUXJ.ng. From this idea and dimensional analysis
the paper. there follow certain simple relations for vertical
dispersion (Section 4(c)), which are supported by
4
F. Pasquill
Table 2. Current working theories of dispersion
Nature of Statistical Gradient- transfer Similarity
theory
Basic Rms eddy velocity Eddy diffusivity K Friction velocity
quantities and Lagrangian Heat flux
auto-correlation
R(~)
Limitations Homogeneity Small-scale Surface-stress
action layer
Data Spectrum of Profile of Profile of wind
required turbulence u & K and temperature
Dispersion o ,0 (elevated o (ground o (ground source
y z
property source) Z source) Z at short range)
o (ground
y
source)
5
