EPA-600/4-76-030b
June 1976
ATMOSPHERIC DISPERSION PARAMETERS IN GAUSSIAN PLUME MODELING
Part II. Possible Requirements for Change in the Turner Workbook Values
F. Pasquill, D. Sc.
Visiting Scientist
Meteorology and Assessment Division
Environmental Sciences Research Laboratory
Research Triangle Park, North Carolina 27711
U.S. ENVIRONMENTAL PROTECTION AGENCY
OFFICE OF RESEARCH AND DEVELOPMENT
ENVIRONMENTAL SCIENCES RESEARCH LABORATORY
RESEARCH TRIANGLE PARK, NORTH CAROLINA 27711
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DISCLAIMER
This report has been reviewed by the Environmental Sciences Research
Laboratoryj U.S. Environmental Protection Agency, and approved for
publication. Mention of trade names or commerical products does not
constitute endorsement or recommendation for use.
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PREFACE
The increasing concern of the last decade in environmental issues, and
the fuller appreciation that air quality simulation modeling may provide a
unique basis for the objective management of air quality, has generated an
unprecedented interest in the development of techniques for relating air
quality and pollutant emissions through appropriate modeling of the
atmospheric transport and dispersion processes that are involved. A
multitude of recent publications in the U.S.A. and elsewhere points to the
wide interest at many different levels of local, state, regional and
national planning, and testifies to the widespread acceptance of
meteorological-type air quality modeling as an important rational basis
for air quality management. This point of view is now internationally
recognized in most industrial countries.
Earlier attitudes towards the quantitative estimation of atmospheric
dispersion of windborne material from industrial and other sources were
strongly influenced by a system introduced in 1958, and published in 1961,
by Dr. F. Pasquill of the Meteorological Office, United Kingdom. This
was followed in 1962 by the publication of his definitive textbook on
"Atmospheric Diffusion," which includes detailed consideration of the
well-known simple "Gaussian-plume" model for the average concentration
distribution in space from an elevated continuous point-source under
steady conditions. The unique feature, however, of the Pasquill system
is the method by which the critical parameters expressing the downwind
m
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spread of the plume might be estimated in terms of the ambient meteorol-
ogical conditions. These estimates were later expressed in slightly
more convenient, although exactly equivalent form, by Dr. F. Gifford,
and this so-called Pasquill-Gifford system for dispersion estimates has
been widely used ever since. It was early given some general endorsement
as a valuable practical scheme by the Public Health Service of the U.S.
Department of Health, Education, and Welfare, by the publication in 1967
of the "Workbook of Atmospheric Dispersion Estimates" (Public Health
Service Publication No. 999-AP-26) by D. B. Turner, that exclusively
utilized this system of Gaussian-plume dispersion parameters.
In spite of the gradual appearance in recent years of air quality
models based on more sophisticated formulations of the atmospheric processes,
e.g., through fluid-dynamical equations assumed to govern the physical
processes of transport and turbulent diffusion, great use continues to
be made of the simpler Gaussian-plume models. However, a direct consequence
of the unprecedented interest in the subject has been the publication of
many attempts to confirm or improve the realism of the dispersion estimates.
These and other matters relating to the substantial progress made in
recent years in understanding atmospheric dispersion, are discussed in a
much revised 2nd Edition of the Pasquill book, that was published late in
1974. Under these circumstances it seemed desirable to examine critically
the possible requirements for change in the Turner Workbook values for
dispersion, that have been so widely used since 1967. The present two-part
IV
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report was prepared to meet this need.
It was extremely fortunate that Dr. Pasquill was available for detailed
discussions during its preparation (1975-76), both while he was a Visiting
Professor at the North Carolina State University and also the Pennsylvania
State University (under research grant support of the EPA), and also as a
Visiting Scientist to the Meteorology and Assessment Division of the E.P.A.,
Research Triangle Park, N.C. Even more fortunate has been Dr. Pasquill's
willingness to assume responsibility for preparation of the second part of
the report, which critically examines the possible requirements for change
of the Turner Workbook values. The first part was prepared by Dr. Allen
Weber of the Department of Geosciences at North Carolina State University,
in consultation with Dr. Pasquill and the undersigned. It provides a
reasonably comprehensive review of current systems and possible future
developments, and is a necessary input for the critical examination of the
second part. It is perhaps unnecessary to emphasize that there are still many
problems of dispersion that are unlikely to be resolved satisfactorily in
terms of simple Gaussian-plume models. However, it is hoped that the present
publication will provide a more up-to-date basis for continuing the
successful treatment of the many important practical problems that can be
analyzed by this simple approach.
Research Triangle Park, Kenneth L. Calder
North Carolina Chief Scientist
March 1976 Meteorology and Assessment Division
Environmental Sciences Research Lab.
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ABSTRACT
The basis of the original Pasquill-Gifford curves used in the Turner
Workbook is restated and consideration given to those features of the
curves which are now regarded as specially questionable.
Data on crosswind spread from various field tests are reviewed to
emphasize the useful working relation which holds between Oy and the stan-
dard deviation of the wind direction fluctuation. Some new trial
calculations of vertical spread are carried out in the light of recent
work using the gradient-transfer approach, recent similarity analyses,
new observational data on the structure of turbulence in the convective
boundary layer, and Deardorff's modeling of the mixed layer.
Recommendations are made concerning the use of wind direction
fluctuation data for estimating Oy, for various adjustments and constraints
to be applied as an interim measure to the existing o^ curves, and for
continuing work required in the progress toward a final revision of the
Workbook.
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CONTENTS
Preface iii
Abstract vi
Acknowledgements viii
1. Introduction 1
2. Restatement of the Basis and Scope of the Original 'Pasquill-
Gifford' Curves 3
3. Consideration of Some Specially Questionable Features of the
PG Estimates: 7
Crosswind spread 7
The effect of surface roughness on vertical spread .... 12
Vertical-spread behaviour in unstable conditions 14
Other aspects 19
4. Suggestions for Interim Changes in the Workbook Parameters
and Procedure 22
5. Requirements for Progress Toward a Final Revision of the
Workbook Parameters and Procedure 25
References 28
Appendices
A. Crosswind spread in relation to wind direction fluctuation. . . 30
B. Some calculations of vertical spread in unstable conditions . . 34
VII
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ACKNOWLEDGEMENTS
The writer wishes to thank Dr. G. A. Briggs, Mr. K. L. Calder, Mr.
D. B. Turner and Dr. A. H. Weber for helpful discussions during the
preparation of the review, and Drs. J. C. Kaimal and J. S. Caughey
for access to draft data summaries from the Minnesota 1973 atmospheric
boundary layer study.
vm
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SECTION 1
INTRODUCTION
As pointed out in the preface to this two-part report the dispersion
1 *
parameters or and cr adopted in the Workbook are known widely as
'Pasquill-Gifford' curves. In essence, they are estimates originally offered
tentatively by the writer, in unpublished form in the Meteorological Office
2
in 1958 and in published form in 1961.
The purpose of this second part of the report is to provide an appraisal,
against the background of subsequent dispersion research and of the review in
Part I, of the requirements for change in the Workbook curves (Figs. 3.2
and 3.3 in that publication). It was thought appropriate to begin the
appraisal with a brief restatement of the basis and scope of the original
estimates, emphasizing certain points which may sometimes be overlooked and
also certain points which in restrospect, need clarification. Consideration
of the various aspects in which the estimates are unacceptable or question-
able then follows in Section 3. It is to be noted at the outset that
completion of the appraisal to the point of a definitive full revision of
the Workbook values is not immediately possible.
There are specific points, including the consolidation of the
relation between v and wind direction fluctuation and the explicit repre-
J
sentation of the effect of surface roughness on dispersion, in respect
of which immediate recommendations for change appear fully justified.
*To facilitate frequent reference to certain publications the numeral
system or referencing has been adopted.
1
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These are presented in Section 4. There are, however, features in respect
of which further time must be allowed for a duly considered incorporation
of currently emerging material. This appears to be particularly the case
for vertical spread in very unstable conditions, which, in view of the
current state of development, is one of the topics given most attention in
Section 3 and Appendix B. Finally, and not surprisingly, there still remain
features which await theoretical clarification, and observational confirmation.
The developments which accordingly appear to be essential for progress to a
more complete revision of the 'PG' curves are briefly noted in Section 5.
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SECTION 2
RESTATEMENT OF THE BASIS AND SCOPE OF THE ORIGINAL 'PASQUILL-GIFFORD' CURVES
The formulation of the PG curves was stimulated by increasing demands
for methods of estimating dispersion which were both simple to apply in
terms of the idealized 'Gaussian plume1 description of the spread of a
continuous point source plume, and which could be applied in terms of
routinely available meteorological data. Even so, the view was adopted that
the best prospect for generality and reliability in the estimates lay with
a maximum use of the theoretical principles of turbulent diffusion and a
minimum dependence on uncritical analyses of pollution surveys.
In the latter respect it is perhaps appropriate to emphasize that the
estimates were not just a compilation of observational experience on
dispersion per se. They did embody some a priori quality in two notable
respects. First, the attempted generalization about cr was considered
as far as possible in terms of a simple adaptation of the Taylor
statistical theory. Indeed a preference was clearly stated for a direct
use of wind direction fluctuation data in estimating a~ , and the cr
J J
estimates contained in the PG curves were provided for use in the absence
of such data. Inevitably, these estimates are of limited value, derived
as they were from preliminary statistics of wind direction fluctuation and
applicable to a particular (3 min) sampling time. A second a priori
element, embodied in the o^ curves, is the gradient transfer theory result
for short distance of travel and neutral conditions of flow. Demonstration
of the correctness of this result, in terms of data on the wind profile
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over a natural rough surface, had been provided by Calder.
For extension of the estimates beyond the two fundamental 'reference
points' of the preceding paragraph it was, of course, necessary to appeal
to a subjective interpretation of the limited experience then available
on rates of dispersion in the atmosphere. Note that the o^ estimates
referred strictly to a surface release of material (i.e. H = 0 or in more
general terms effectively when H _cr) was encouraged.
Although the relevance of sampling time was made specifically clear for
cr properties, there was an implication which was not made clear originally
concerning o^. For a release which is effectively at the surface
(i.e. H < cr) it is logically necessary to expect the crz property to
become independent of sampling time T for T > tm- This limiting sampling
time T is that which is required for the vertical distribution to respond
m
to the whole spectrum of the vertical component of turbulence. Experience
on the latter property suggests that rm will at first increase near-
linearly with H and then more slowly. As a rough guide it is suggested
that the estimates of cr should be taken to apply for i > T with T = 10 min
Z lil III
for H >_ 100m, and rm = H/10 min for H (in metres) < 100. (note that the
relation between cr and sampling time is also fundamently tied to the
spectrumof the v-component in this casebut here the existence of a
clear-cut short limit to T, beyond which o~ no longer increases, is
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generally precluded by the highly variable low-frequency content of the
v-spectrum). Again, referring to o', for sampling times less than Tm
one cannot however expect a systematic increase of a* with T to be
reflected in the ground-level concentration from an effectively elevated
source, i.e., for cr" _ rm.
In conclusion of this section, and for future convenient reference,
the essential points of the background to the PG curves are summarized
in Table 1.
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SECTION 3
CONSIDERATION OF SOME SPECIALLY QUESTIONABLE FEATURES OF THE PG ESTIMATES
CROSSWIND SPREAD
Several recent discussions of the application of the Taylor statistical
theory to practical relations between crosswind spread and wind direction
fluctuation are available (Ref. 6, p 185 et seq., and Ref. 7 and 8). By
way of further demonstration of the usefulness of the approach, some of the
existing test data on v are presented in rearranged form in Appendix A.
Taken together with the previously published discussions, the following
conclusions may be drawn:
(i) Irrespective of sampling time (within the practical range of
a few minutes to about 1 hour), and irrespective of surface
roughness and stability, there is a rough conformity to a 'universal1
relation between cr/cr and distance x, when the standard deviation cr
y o o
of the wind direction is evaluated over the sampling time, for
distances of travel up to about 10 km.
(ii) At the shortest distances of interest (<0.1 km), the limiting
form cr = cr x is a reasonably good approximation on average
(or. in radians)
o
(iii) In general, we may write cr = f(x) o^ x on average, with
f(x) taking the values listed in Appendix A.
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(iv) For individual samples the departures from the foregoing
average relations are mostly within a factor of about 1.5 at
short range and about 2.0 at long range.
(In all the foregoing relations note that for generality,
irrespective of the magnitude of cr^, the quantity
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point source will have fewer very small concentrations (i.e., receptor
outside the plume) and fewer very large concentrations (which arise
partly from very narrow plumes) for a long sampling time than for a
short sampling time. This may well partly explain the difference
in calculated and observed frequency distributions reported by
Klug (Ref. 16), where the observations were for 1-hr samples, if,
as appears to be the case, the calculations were based on the PG
D"1 curves as they stand.
Further demonstration of the direct importance of the actual
wind direction variation is contained in the Idaho A.R.L. study
(Ref. 13) already referred to in Appendix 1. Here, the observed
arc distribution of concentration from a continuous point source
(at radii up to 400 m) was compared with calculated distributions.
Closest agreement was achieved by subdividing the total sampling
duration (1 hr) into 3-min sections, for each of which the plume
spread was taken in accordance with the PG curves, and then super-
imposing the 3-min distributions on the arc at positions in accordance
with the 3-min average wind directions.
The incorporation in the Workbook procedure of estimates of
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to height. In a well-mixed layer the experience is that cr per se
does not change markedly with height, though in stably stratified
flow a decrease with height is to be expected, especially in the
relatively high-frequency part of the spectrum. Noting that
o~ = cr/u, and taking into account the usual increase of wind
with height, it follows that cr per se must be expected to decrease
with height at a rate depending on the stability. In practice,
therefore, it would seem to be necessary to consider specification
of cr at a reference height which should be increased in accordance
D
with the progressive vertical spread of the plume.
Regarding the need argued above for an effective value (cT)
9 e
at some appropriate reference height, which might most logically be
set equal to o~, there is, however, an interesting simplification
which might be argued as follows. The value ultimately adopted for
cr is to be used in the expression for time-mean concentration C(x),
and it will be recalled that in the denominator of that expression
we have the product u cr, in which the mean wind speed u also
should be an effective value in relation to the vertical spread of
the plume, i.e., we should use u (T. If there is no variation of a"
with height, then to an approximation (with T the average time of travel of
of 'particles' to distance x)
ue ฐy * ue ^v T " ue ^ x/ue * ฐ^ x
10
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i.e., the need for a specific reference height is cancelled out as far
as the variation of H with height is concerned, though, of course, it
remains insofar as cr changes with height.
Provision of appropriate data for ojj requires either real-time
measurements or a climatology of the form utilized in the construction
of the PG o~ curves at short range, but now necessarily generalized in
terms of sampling duration. In principle, such a climatology is
derivable from the accumulated knowledge of the v-spectrum, though
there are considerable uncertainties arising from the poorly-defined
low-frequency form of that spectrum (e.g., see Ref 7). An interim
approach which is worth considering in the present context is to
2
consider the total cr in two parts (additive in terms of cr) representing
0
high-frequency and low-frequency contributions separately. The
relatively-high-frequency part may be represented by a a* for a
sampling duration of 3 min, say, for which we could continue to use
the 'preliminary1 climatology incorporated in the PG curves, until a
better climatology is constructed. The low-frequency part (to be
2
added in terms of cr) would require an estimate of cTfor an averaging
(smoothing) time of 3 min and for the total sampling duration of
interest (usually 1 hr). An obvious convenience is that the latter type
of statistic does not require rapid response records of wind direction
and is derivable from routine slow-response records.
11
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In terms of
-------
of eddy velocity. The r.m.s. value of the latter (or) again appears
in similarity considerations (see Appendix 2) and in the K-formulation
(see Ref. 6, p 105) used by F. B. Smith in deriving numerical solutions
of the two-dimensional equation of diffusion.
Although the theoretical dependence of
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VERTICAL SPREAD BEHAVIOUR IN UNSTABLE CONDITIONS
The PG curve for stability category A contains a pronounced mono-
tonic increase of do-'/dx with x. This shape was based on the experience
n
provided by the 'Prairie Grass1 dispersion study. It should be
recalled, however, that the study provided direct measurements of crz
(i.e. values derived from an observed vertical distribution) only
for a distance of travel of 100 m, and indirect estimates (i.e., from
the reduction of ground-level concentration with distance) only
up to 800 m downwind. For greater distances the PG curve is essentially
a subjective extrapolation. The further evidence and argument which
may now be brought to bear on the acceptability of this curve (and to
a lesser degree on that of the B and C curves) is summarized below.
(i) The new and essentially theoretical derivations ' of cr
from numerical solutions of the two-dimensional diffusion equation
using plausible profiles of K based on early-stage data on turbulence
over the whole depth of the boundary layer (and not on dispersion
data), yield a or ,x curve in unstable conditions which does show the
property of dol/dx increasing with x, but only transiently. This
increase does not continue beyond a
-------
convenient similarity representation of the foregoing numerical
7 R
solutions , using new data on the w-spectrum in the
atmospheric mixing layer, obtained in a joint U.S.A.F.C.R.L.
g
and U.K. Meteorological Office boundary layer study. It is
to be emphasized that these new estimates of o^ do not explicitly
contain any contribution from mechanisms other than that of gradient-
transfer.
(iii) Early results of the 2nd-order closure modelling developed
by ARAP (Fig. 16 of Ref. 10) also show a section with do^/dx
increasing with x. This curve is for a condition equated with
Category C and was evaluated for a specified depth of mixing.
(iv) The existence of a regime with increasing doi/dx is
predictable on similarity grounds for the special case of effectively-
windless convection. In such conditions, postulating reasonably
that the 'velocity' of vertical spread (dcr/dt) must, in the
region sufficiently below any upper limiting boundary, be
determined completely by two parameters, namely, a buoyancy
parameter determined by the surface heat flux H , and the height z
as the only relevant length scale, it follows on dimensional
grounds that
1/3
dcr/dt ซ (gHoz/pcpT) / (1)
On integrating
o~z(t) - (gH0/PcpT)1/2t3/2 (2)
15
-------
3/2 -M
This prediction of ol growing as t ' has been ascribed to Yaglom
and has been found by Deardorff and Willis (Fig. 3 of Ref. 11)
to be substantially confirmed by laboratory-convection-tank data
over the range 0.15 < o"I/z. < 0.4, z. being the total depth of
the mixed layer. It is noteworthy that in Deardorff's considera-
tions this relation emerges as a special regime in an overall
'mixed-layer1 relation between o"7z. and the dimensionless time t*
1/3
formed by w*t/z., with w* = (9H0zi/PcD"0
The simple relation
-------
does not emerge strongly until z/z^ is nearly 0.5. (In the
later stages of this review, however, it has been learned that
a more recent presentation and discussion of laboratory data is
in course of publication by Deardorff, and it has yet to be
clearly settled how far the new results confirm or modify the
foregoing statements.)
v
(v) In regard to the relation between d1 /w* and z/z., which on
W 1
Deardorff's hypothesis is expected to be a universal function,
it is noteworthy that the form demonstrated by Deardorff's
laboratory data is not completely confirmed by the atmospheric
data recently acquired in Minnesota and referred to in (ii)
above. There is agreement up to z/z. =0.5 (and up to 0.1 both
support d proportional to z ' and independent of z.), but for
W \
larger z/z. the two sets of data diverge (see Fig. 1 of Ref. 11
and Fig. 14 of Ref. 9), the laboratory data showing a distinct
fall in ^w/w* as the top of the layer is approached whereas
the atmospheric data show, if anything, a very slight increase.
Details of new estimates of & for unstable conditions, using
both the gradient-transfer approach, and the free-convection law in
Eq. 3, are set out in Appendix B. Three cases have been considered,
the first referring to relatively smooth open country (to which the
PG curves apply), and the second and third to an urban area, for
which estimates are available from the St. Louis tracer study.
17
-------
Specific conclusions which emerge from these results are set out at
the end of the appendix. It is clear that a closer approach to the
extrapolated (long-range) section of the PG 'A' curve and to the
St. Louis 'B' and 'C' curves has been achieved in terras of the 'free-
convection' law and, implicitly, in terms of the Deardorff 'mixed-
layer1 law. Up to a point this is not surprising and it is clear that
final revision of the PG curves must take into account the new insight
into the effects of convective motion. However, because of the
discrepancies and conflicts which have been noted in (iv) and (v) above
and which have not been resolvable in the present review, and because
the latest report on the Deardorff modelling has not been available
to us in time for full consideration, it would certainly not be
appropriate to attempt a final revision immediately.
Aside from the magnitude of
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OTHER ASPECTS
There are several features which have not been given extensive
consideration during the preparation of this review, and these are
noted below with brief comment and reference.
(i) Vertical Spread in Stable Flow
From the resume1 given in Part I it is evident that estimates
of cr in stable conditions vary over a wide range. In view of the
expected (though not yet well-documented) decrease of cr with
w
height a dependence on height of release H is also to be expected
over the distance of travel for which cr < H. The BNL curves may
be thought to contain some evidence of this dependence, as the
'stable1 curve falls distinctly below the PG 'F1 curve, despite the
fact that it refers to a much rougher surface. However, the evidence
is somewhat ambiguous, since the precise equivalence of the stability
classifications in the two cases is in some doubt. This particular
point, as well as the more general question of the dispersive
character of stable flow, is in need of further critical examination.
One obvious and preeminent requirement is continued progress in the
description of the characteristic profiles of the intensity and scale
of turbulence, in the distinction between turbulence and wave-motion,
and in the ongoing work to which our attention has been drawn in the
course of the present review (G. A. Briggs - private communcation).
(i i) The Effect of Elevation of Release and Plume Rise on Dispersion
The possibly special importance of elevation of release in stable
19
-------
conditions has already been mentioned, but as noted in Part I there
is a more general problem arising from the inapplicability of either
the simple statistical or gradient-transfer treatment in the crucial
stage of dispersion at which cr is similar to H (see Ref. 8). This
is one of the problems for which the Znd-order closure modelling
seems to be specially necessary.
For strongly buoyant plumes there is also the contribution to
spread (both vertical and horizontal) associated with the entrainment
induced by relative vertical motion of plume and surrounding air.
As previously discussed (Ref. 6, p 271), the addition to the 'passive1
dispersion represented in the PG curves may be especially important
for cr in stable conditions. It is to be noted, however, that for
maximum ground-level concentration per se the resultant effect may
not often be important, since the major part of the dispersion to
ground level may often depend predominantly on the 'passive' part
of the process. The condition for maximum ground-level is roughly
1/2
represented by cr = (H + AH)/2 ' , where H is the stack height and
AH the height of rise. The data on rising plumes suggest that the
induced cr is roughly AH/3.5 which obviously cannot be the major
contribution to the required cr even when AH is very large compared
with H .
(iii) Vertical Spread in an Evolving Mixed Layer
Allowance for the more or less abrupt termination of the upward
vertical dispersion by an overhead stable layer is included in the
20
-------
Workbook (see pp 7 and 36 thereof). This procedure needs to be
generalized in terms of the typical evolution of the depth of the
mixed layer in the surface heating cycle following nocturnal
stabilization of the boundary layer, as discussed in Ref. 6, p 379.
If the mixed layer is of depth h'(t) at time t, it is clear that the
o*(x) appropriate to a source at distance x upwind is in accordance
with unbounded o~,x curves only up to a certain limit depending on
h1. One simple rule may be stated immediately on the basis of the
conventional 'image source1 principle, for the case of the ground-
level crosswind-integrated concentration (CWIC) from a ground-level
source, with constant h1. The curve of CWIC against x is found to
be adjusted quite sharply (for practical purposes effectively
suddenly at the distance defined by o~ = 0.8h') from the vertically-
unbounded form
CWIC = 21/2Q/TT1/2"ucr, 0 0.8h', (5)
For source-heights and receptor-heights other than zero, the curve
is, of course, more complex, but nevertheless derivable on the
same principle.
21
-------
Section 4
SUGGESTIONS FOR INTERIM CHANGES IN THE WORKBOOK PARAMETERS AND PROCEDURE
Suggestions for the more satisfactory estimation of crosswind spread
have already been considered at some length (see p. 7). For vertical spread
(see p. 14), there are significant current developments which should be
incorporated as soon as an adequate clarification and consolidation of the
results have been achieved. In the meantime, it would be reasonable to
retain the present Workbook values of a* with adjustments for roughness (in
accordance with the discussion on p. 12), for induced spread of buoyant
plumes (see p. 19), and for the effects of urban-heating on lines which are
briefly considered below.
Ideally, the or curves for urban flow should be related to surface
roughness and surface heat flux, with the latter representing the total
effect of natural and man-made contributions, as was attempted in Appendix B
for the unstable conditions. Until this can be satisfactorily accomplished,
a reasonable simple procedure would be to adjust the PG curves for roughness
as already discussed and then apply an additional correction for 'urban-
heating' in accordance with the practical experience of the St. Louis study.
This latter correction could be applied conveniently in the form of an
'adjusted (urban) stability category,' appropriately more unstable than the
estimated 'open country1 category. The experience suggests that this
adjustment should be roughly 'half a stability category.1
The foregoing suggestions are collected in summary form in Table 2.
22
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Notes on Table 2
* This formula is strictly true only for small values (i.e., when
tan e = e). For larger values (i.e., with wide and usually slow
variation of wind direction) an appropriate procedure is to use the
formula in a formula for concentration in which the y-distribution
of concentration is replaced by an arc distribution at a radius r.
f For correct evaluation this tfi should be for an effectively infinitesi-
u
mal averaging time (i.e., no loss of variance by 'smoothing' of the
complete wind fluctuation). As an alternative one could continue to use
the PG or" values, which refer to a sampling time of 3 min, and add to
this value squared the square of the value obtained from the above
formula with a oC obtained from 3-min averages over the sampling time
H
of interest.
24
-------
SECTION 5
REQUIREMENTS FOR PROGRESS TOWARD A FINAL REVISION
OF THE WORKBOOK PARAMETERS AND PROCEDURE
In view of the conflicts of evidence and gaps in knowledge which so
obviously exist at presents by far the most important issue is the identi-
fication of the points at which new measurements and further critical
analyses are most required. A short list of those which seem to the writer
to be the most urgent is given below.
VERTICAL DISPERSION IN THE CONVECTIVELY MIXED LAYER
The present review has been a vivid reminder, if such were needed,
of the very inadequate background of high-quality test data on the
crucial features of vertical dispersion beyond the first kilometre of
travel from a source. Improvement in this respect is vital, not only
for resolution of the difliculties encountered here, but also as an ultimate
essential test of the emerging 2nd-order closure treatments of dispersion,
which treatments are seen by some as the main future hope of improved
dispersion estimates. The necessity for this advanced type of treatment,
especially in respect of convective transfer, has recently beem emphasized
by Lumley.
The convective case is of specific practical importance in the familiar
'looping' and 'fumigation1 aspects of power-plant plumes, and is of
general importance as the condition for the 'upper bound1 to a family
of curves such as those of the PG system. Despite the various
25
-------
attempts in the past to obtain definitive data on vertical spread there
still remains a particular need for good measurements, say, by aircraft
sampling of the plume from a surface release of passive tracer, of the
progress to the stage of near-uniform distribution with height. This
should be considered in the first instance over an ideal (Kansas- or
Minnesota-type) site, with supporting data on the surface heat flux,
the mixing depth, and the wind profile. The experience of the Minnesota
boundary layer study (Ref. 9) confirms that a useful study of the role
of convective transfer is feasible even in moderate winds, although the
preference should be for winds ?s light as possible consistent with
predictability of the plume trajectory. The tracer sampling (crosswind
traverses at several levels in the mixed layer) should be at intervals
of downwind distance of, say, one mixing depth up to at least 5 mixing
depths.
VERTICAL DISPERSION IN STABLE FLOW
The very stable condition represents the 'lower bound' to the family
of cr curves and is, of course, the most serious condition for pollution
from low-level sources. From the discussions which have been held during
the present review there are signs that a concentration of effort might
now be timely, especially in the respect of marshalling newly available
turbulence data (or acquiring such data) and appraising the significance
thereof in terms of effective eddy diffusivity. Whether an adequate
background of dispersion data already exists in a form appropriate for
testing of new ideas has yet to be seen, but should a need become
-------
apparent for new data in this context, the observational requirement will
be less of a problem than for the convective case, for the obvious
reason that crucial data will be obtainable from sampling on masts or
towers.
CRITICAL STUDY AND ANALYSIS OF 2ND-ORDER CLOSURE CALCULATIONS OF
VERTICAL DISPERSION
The potential importance of the 2nd-order closure approach has
already been noted in respect of convective mixing. Another important
feature for which it could be the most profitable means of improved
understanding is the case of the elevated source for the range over
which cr
-------
REFERENCES
1. Turner, D. B. (1970 revised). Workbook of Atmospheric Dispersion
Estimates, U.S.D.H.E.W., Environmental Health Service.
2. Pasquill, F. (1961). The Estimation of the Dispersion of Windborne
Material, Met. Mag., 90, 33.
3. Calder, K. L. (1949). Eddy Diffusion and Evaporation in Flow over
Aerodynamically Smooth and Rough Surfaces, Quart. J. Mech. & Appl.
Math., II, p 153.
4. Haugen, D. A. (Ed) (1959). Project Prairie Grass, A Field Program
in Diffusion, Geophysical Research Papers No 59, Geophysics Research
Directorate, AFCRC, Bedford, Mass.
5. Smith, F. B. (1972). A Scheme for Estimating the Vertical Dispersion
of a Plume from a Source near Ground Level, Proceedings of the Third
Meeting of the Expert Panel on Air Pollution Modeling, NATO/CCMS.
6. Pasquill, F. (1974). Atmospheric Diffusion, 2nd Ed., John Wiley &
Sons, New York.
7. Pasquill, F. (1975). Some Topics Relating to the Modeling of Dispersion
in the Boundary Layer, EPA-650/4-75-015.
8. Pasquill, F. (1975). The Dispersion of Materials in the Atmospheric
Boundary Layer - the Basis for Generalization; Lectures on Air
Pollution and Environmental Impact Analyses, Ameriran Meteorological Soc.
9. Kaimal, J. C., J. S. Caughey, et al (1976). Turbulence Structure in
the Convective Boundary Layer, Unpublished Draft.
10. Lewellen, W. S. and L. Teske (1975). Turbulence Modeling and its
Application to Atmospheric Diffusion, Part 1, EP/>-6QO/4-75-016a.
Deardorff, J. W. and G. E. Willis (1974). Computer and Laboratory
Modeling of the Vertical Diffusion of Non-Buoyant Particles in the Mixed
Layer, Turbulent Diffusion in Environmental Pollution; Advances in
Geophysics, 18B, pp 187-200, Academic Press.
12. McElroy, J. L. and F. Pooler (1968). St. Louis Dispersion Study, Vol II-
Analysis, U.S.D.H.E.W.
13. Slade, D. H., (Ed) (1968). Meteorology and Atomic Energy, U.S. Atomic
Energy Commission, Div. Tech. Inf.
14. Sagendorf, J. F. and C. R. Dickson (1974). Diffusion under Low Windspeed
Inversion Conditions, NOAA Technical Memorandum ERL, ARL-52.
28
-------
15. Pasquill, F (1970). Prediction of Diffusion over an Urban Area-Current
Practice and Future Prospects; Proceedings of Symposium on Multiple
Source Urban Diffusion Models, U.S. Environmental Protection Agency.
16. Klug, W. (1975). Dispersion from Tall Stacks, EPA-600/4-75-006.
17. Lumley, J. L. (1976) Turbulent Transport in Urban Air Pollution Modeling,
Draft.
18. Draxler, R. R. (1976). Determination of Atmospheric Diffusion Parameters,
Atmos. Environ., 10, pp 99-105.
29
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APPENDIX A. CROSSWIND SPREAD IN RELATION TO WIND DIRECTION FLUCTUATION
The relation between crosswind spread from a continuous point source
and the crosswind component of turbulence, cr, has been developed on useful
lines in terms of the G. I. Taylor statistical theory (Ref 6, p 185).
Neglecting the variation with height of the r.m.s. and scale of the
v-component, the result for travel time T or distance downwind x may be
put in the forms:
Qy = o; T f^T/^) *
-------
where f(x) approximates to the required limit when x < 0.1 km, and is a
slowly decreasing function at longer range. The upper and lower bounds
only of these cr data are reproduced in Fig. 1.
It has also been noted (Ref 6, p 295) that measurements of cr and cTQ
in two large towns in England are also related in conformity with the
bounds of the U.S.A. tests. Data obtained in the St. Louis urban dispersion
12
study , for a sampling time of 1 hr, have now been analyzed on the same
basis and the individual hourly values are plotted on Fig. 1, with
discrimination according to day or night. The property cr was actually
D
observed at two levels on a television tower, and in the present analysis
choice was made of the upper level (459 ft) as the more appropriate to the
average magnitude of vertical spread cr also deduced in these tests.
These data too are strikingly consistent with the bounds of the open-site
data. Finally, the overall range of some data pertaining to very light
winds and stable conditions, with very large values of cr, obtained in
a
field tests in Idaho, are shown.
The overall impression from these data and other data which have been
reviewed previously (Ref 6, p 185) is that the crosswind spread may be
usefully represented on average by the simple equation (3), with f(x) as
now determined by eye from Fig. 1 taking approximate values as follows:
x (km) 0.1 0.2 C.4 1 24 10 >10 ,
f(x) 0.8 0.7 0.65 0.6 0.5 0.4 0.33 0.33(10/x)1
31
-------
the value for x > 10 km being set on the reasonable assumption that the
'large x1 limit, corresponding to the 'large T1 limit referred to earlier,
is effectively operative for such distances, at any rate in respect of
the direct effect of the crosswind component of turbulence (see Ref. 6, p 362
for earlier discussions of this aspect).
Departures from the simple average relation are presumably a consequence
partly of variations of
-------
DAY
EVENING X
ST,LOUIS DATA (REF.12)
_._^_ IDAHO A.R.L DATA (REF.13)
VARIOUS l),S, TESTS (REF.W) JH
DISTANCE (KM)
1
10
Fig. A-l. Various Data on Crosswind Spread Normalized in Accordance
with the Standard Deviation of Wind Direction Fluctuation
33
-------
APPENDIX B. SOME CALCULATIONS OF VERTICAL SPREAD IN UNSTABLE CONDITIONS
Vertical spreads derived by F. B. Smith from numerical solutions of
o
the two-dimensional equation of diffusion have been shown to approximate
to certain simple similarity relations. With I the mean vertical
displacement of passive particles at distance x downwind of a continuous
release at the surface, one relation is
d I/dx = 0.75 (K/uz)? (1)
the subscript outside the parentheses denoting the height to which all
quantities inside refer. Substituting the basic form of eddy diffusivity K
adopted in Smith's solutions, i.e., 0.1 cr", X - where \ is the equivalent
W nT Ml
wavelength ( = U/n ) for maximum value of the product of frequency (n)
and spectral density S(n) of the vertical component,
dZ/dx = 0.075 ((TXm/uz} ,0\
w m z (ฃ.)
This relation may be used to obtain new Z/x or o^/x curves from new a^
and x data in convective conditions, recently made available from the
'Minnesota' boundary layer experiment (Ref 9).
For convenience we may integrate (2) in separate sections of the 2
range, for which simple mathematical forms may be prescribed as approximations
to the observed profiles of cr and X contained in Figs. 5 and 14 of Ref 9:
Section A
-3L
-------
where L is the Monin-Obukhov length, and h' the mixing depth
Section B
O.lh1 < z
-------
Section A (Eq. (3) and (4) applicable)
x(Z) - x(-3L) = [_2.79uch'u^u/w* | Z1""* - (-31)""" J (9)
Section B (Eq. (5) and (6) applicable)
r If 1
x(Z) - x(O.lh') = 8.9uc/w^h'ฐ'6 Jjl1-6 - (O.lh1)1*6] (10)
Note that if, as usual, wind speed is specified at a given low reference
level (say, 10m), then for such a given wind speed u is proportional
to h1 ' (in accordance with Eq. (8), and remembering that w* is
1/3
proportional to h1 ' it follows that, as required by definition, the
relation between Z and x in Eq. (9) is independent of h1. Note also
that if the variation of wind with height is disregarded in Section A
Eq. (9) reduces to
x(Z) - x(-3L) =J2.61 uh|1/3/w* ]\f/3 - (-3L)2/3J (11)
which for large values of-Z/3L is of the same form as Eq. 3 in the
main text.
In the trial calculations carried out here, Eq. (9) and (10) have
been used in the slightly rearranged forms
x(Z) - x(-3L) = fA [(Z/-3L)0'74 - l] (12)
with fA= 2.79uch'ฐ-26(-3L)ฐ-74/w*
x(Z) - x(O.lh') = fB [(Z/O.lh1)1-6 - l] (13)
with fB = 8.9uch' (0.1)1-6/w*
36
-------
The Z,x data calculated from these equations were ultimately converted
to cr,x data by assuming
-------
It seems unlikely, however, that any plausible deviations from these
choices would basically change the implications listed below.
Note in particular that the largest magnitudes of &ฃ are essentially
1/2
set by H ' , so a substantial latitude in the value adopted for HQ
would have a minor effect.
The conclusions may now be summarized as follows:
1. For a smooth surface, gradient-transfer calculations using
the latest data available on the intensity and scale of the
w-component in convective conditions give
-------
and Willis'(Ref. 11) tank data) the calculations approach closer
to the PG curve, but are still on the low side of the curve.
3. Over a rough (urban) surface, when even with large heat flux
the magnitude of -L is relatively large and accordingly when the
gradient-transfer assumption should be more realistic over a
greater height range, the gradient-transfer calculations still fall
below those inferred from ground-level concentrations of tracer in
the St. Louis study. The 'free-convection' law, which by the same
argument about -L should be less valid (compared with a smooth
surface and small -L) does give a closer approach to the St. Louis
data, though with a more rapid variation of o^ with x than was
inferred from the concentration data.
4. The implications regarding Deardorff's laboratory law for
the 'mixed layer' are at present ambiguous. Over the bottom
half of this layer the laboratory data on cr^ are consistent
with the 'free-convection' law, which on first principles might
be expected to fail above z/h' =0.1, and which in respect of ff*
w
apparently does fail in both laboratory and atmospheric data.
It is understood, however, that a more recent statement of the
laboratory data on ffi is in course of publication, and it is
clearly desirable that this should be fully considered in the
present context before drawing final conclusions.
39
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TABLE B-l. DATA USED IN SPECIMEN CALCULATIONS OF EQ. (12), (13) and (14)
Case
ZQ cm
2
H mw/cm
IT (10m) m/sec
approx -3L nr1'
assumed h' knr '
u (from Eq. 8) m/sec
w* m/sec
fft in Eq. 12 m
fg in Eq. 13 m
Stability Category^111'
'Workbook1 Stability
Category^1 v)
1
3
26
2
10
3
2.58
2.75
115
630
A
2
100
40
4
250
5
5.36
3.80
2140
1575
A
B
3
100
30
5
600
3
6.45
2.90
--
1490
B
C
Notes: (i) Estimated from the nomogram on p 338 of Ref. 6
(ii) In cases 2 and 3 these values of h1 have been
adoped as necessarily larger than the derived
rfz values in the St. Louis urban study.
(iii) In accordance with F. B. Smith's nomogram, p 374
of Ref. 6 and the magnitudes of H and Tf(lOm)
P
(iv) Obtained as in (iii) but for (H - 15) mw/cm on
2
the supposition that 15 mw/cm is the typical
man-made contribution to H in a modern city. The
'Workbook1 stability category is then the category
which would be assessed in the normal way in the
Workbook.
40
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B-l. Vertical Spread cr from a Continuous Source H
at Ground Level as a Function of Distance Downwind.
Flow Conditions as in Case 1 of Table 1.
Curve Identification:
Pasquill-Gifford curve with letter referring
to stability category
From F. B. Smith nomograms for the same
conditions
Calculations from Eq. (12) and (13), the
broken lines being an extension of Eq. (12)
(steeper slope) and the large (Z/O.lh1)
limit of Eq. (13)
FP
0,1
1
10
100
DISTANCE DOWNWIND KM
41
-------
Fig, B-2. As for Fig. 1, with Flow Conditions as in Case 2
of Table 1, and with 'St. Louis B1 from Fig. 10 of
Ref. 12
0,1
1
10
DISTANCE DOWNWIND KM
42
-------
Fig. B-3. As for Fig. 1, with Flow Conditions as in
Case 3 of Table 1, and with 'St. Louis C' from
Fig. 10 of Ref. 12
1
10
100
DISTANCE DOWNWIND KM
43
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TECHNICAL REPORT DATA
(Please read Instruction* on the reverse before completing)
2.
1. REPORT NO.
EPA-6QO/4-76-03Qb i
4. TITLE AND SUBTITLE ATMOSPHERIC DISPERSION PARAMETERS
GAUSSIAN PLUME MODELING. Part II. Possible
Requirements for Change in the Turner Workbook Values
3. RECIPIENT'S ACCESSION-NO.
IN
6. PERFORMING ORGANIZATION CODE
7 AUTHOR(S)
8. PERFORMING ORGANIZATION REPORT NO.
F. Pasquill
REPORT DATE
June 1976
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Meteorology and Assessment Division
Environmental Sciences Research Laboratory
Research Triangle Park, North Carolina 27711
10. PROGRAM ELEMENT NO.
1AA009
11. CONTRACT/GRANT NO.
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Sciences Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, North Carolina 27711
13. TYPE OF REPORT AND PERIOD COVERED
In-house <3an - Mar 1976
14. SPONSORING AGENCY CODE
EPA-ORD
IB. SUPPLEMENTARY NOTES
16. ABSTRACT
The basis of the original Pasquill-Gifford curves used in the Turner Workbook
is restated and consideration given to those features of the curves which are now
regarded as specially questionable.
Data on crosswind spread from various field tests are reviewed to emphasize
the useful working relation which holds between Oy and the standard deviation of
the wind direction fluctuation. Some new trial calculations of vertical spread
are carried out in the light of recent work using the gradient-transfer approach,
recent similarity analyses, new observational data on the structure of turbulence
in the convective boundary layer, and Deardorff's modeling of the mixed layer.
Recommendations are made concerning the use of wind direction fluctuation
data for estimating Oy, for various adjustments and constraints to be applied as
an interim measure to the existing 0$ curves, and for continuing work required
in the progress toward a final revision of the Workbook.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
Air pollution
*Atmospheric diffusion
*Wind (meteorology)
*P1umes
*Mathematical models
b.IDENTIFIERS/OPEN ENDED TERMS
Gaussian plume
COSATl Field/Group
13B
04A
04B
21B
12A
13. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19 SECURITY CLASS (This Report)
UNCLASSIFIED
21 NO. OF PAGES
53
20. SECURITY CLASS (This page)
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (9-73)
44
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