AICE SURVEY OF USSR AIR POLLUTION LITERATURE.
VOLUME V. EFFECTS OF METEOROLOGICAL CONDI-
TIONS AND RELIEF ON AIR POLLUTION; AIR CONTAMI
NANTS - THEIR CONCENTRATION, TRANSPORT, AND
DISPERSAL
M. Y. Nuttonson
American Institute of Crop Ecology
Silver Spring, Maryland
June 1970
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BIBLIOGRAPHIC DATA
SHUT
t. Report No.
APTD-0639
3. Recipient's Accession No.
4. Title and Subtitle
AICE Survey of USSR Air Pollution Literature
Volume V - Effects of Meteorological Conditions and Relief on
Air Pollution; Air Contaminants - Their Concentration, Trans-
and T
5' Report Date
January 1970
6.
7. Author(s)
M. Y. Nuttonson
8. Performing Organization Kept.
No.
9. Performing Organization Name and Address
American Institute of Crop Ecology
809 Dale Drive
Silver Spring, Maryland 20910
10. Project/Task/Worlt Unit No.
1 'J. Contract/Grant No.
AP00786-01
IX Sponsoring Organization Name and Address
EPA, Air Pollution Control Office
Technical Center
Research Triangle Park, N. C. 27709
13. Type of Report & Period
Covered
14.
15. Supplementary Notes
A* collection of studies of atmospheric diffusion and air pollution. Most of the re-
ports of investigation brought together in this volume deal with meteorological
conditions and relief as factors in propagation and dispersal of air pollutants in a
number of areas in the Soviet Union. Attention is also given to; the emission of
noxious pollutants to the atmosphere and their subsequent exposure to atmospheric
movements; also the intensity and structure of air turbulence in relation to
temperature and wind; and with direction frequencies and intensities of wind.
17. Key Words and Document Analysis. 17a. Descriptors
Air pollution
Diffusion
Atmospheric circulation
Toxicology
Wind (meteorology)
ITb. Identifiers/Open-Ended Terms
Dispersion
17e. COSATI Fie Id/Group
18. Availability Statement
Unlimited
19.. Security Class (This
Report)
UNCLASSIFIED
20. Security Class (This
Page
UNCLASSIFIED
21. No. of Pages
115
22. Price
FORM NTIS-3B ClO-70)
-------
This report was furnished to the
Air Pollution ControluO.ffi.ee by
the American Institute of Crop
Ecology in fulfillment of Contract
-------
AICE* SURVEY OF USSR AIR POLLUTION LITERATURE
Volume V
EFFECTS OF METEOROLOGICAL CONDITIONS AND RELIEF ON AIR POLLUTION;
AIR CONTAMINANTS - THEIR CONCENTRATION, TRANSPORT, AND DISPERSAL
Edited By
M. Y. Nuttonson
The material presented here is part of a survey of
USSR literature on air pollution
conducted by the Air Pollution Section
AMERICAN INSTITUTE OF CROP ECOLOGY
This survey is being conducted under GRANT 1 R01 AP00786 - APC
THE NATIONAL AIR POLLUTION CONTROL ADMINISTRATION
'AMERICAN INSTITUTE OF CROP ECOLOGY
809 DALE DRIVE
SILVER SPRING, MARYLAND 20910
-------
TABLE OF 'CONTENTS"
Page
PREFACE v
ORIENTATION MAP OF THE USSR viii
MAP OF CLIMATIC ZONES AND REGIONS OF THE USSR ix
MAP OF THE MAJOR INDUSTRIAL CENTERS OF THE USSR x
MAP OF THE MAIN MINING CENTERS OF THE USSR xi
/. STUDY OF POLLUTION OF CITY AIR BY INDUSTRIAL DISCHARGES .
"I N. S. Burenin and B. B. Goroshko •„ 1
D CHARACTERISTICS OF THE THERMAL REGIME OF CITIES,
G. P. Rastorguyeva 10
C- ANALYSIS OF METEOROLOGICAL CONDITIONS OF DANGEROUS AIR
POLLUTION IN CITIES,
L. R. Son'kin 18
D INFLUENCE OF THE RELIEF ON THE PROPAGATION OF IMPURITIES
FROM SOURCES \ '
M. Ye. Berlyand, Ye. G. Genikhovich, and 0. I. Kurenbin. 28
ABSORPTION OF GASEOUS IMPURITIES BY FOG DROPLETS
V. V. Klingo and R. I. Onikul / 47
€ RECORDING OF DUST CONCENTRATIONS IN THE ATMOSPHERE ,
' S. A. Kon'kov 53
COEFFICIENT OF TURBULENT EXCHANGE IN THE GROUND LAYER IN THE
DAYTIME DURING THE SUMMER IN VARIOUS GEOGRAPHICAL REGIONS
OF THE USSR
V. P. Gracheva 61
-------
Page
PHYSICAL PRINCIPLES OF CALCULATION OF DISPERSAL OF INDUSTRIAL
DISCHARGES IN THE ATMOSPHERE,
M. Ye. Berlyand and R. I. Onikul ...................... 71 //
STUDY OF THE STRUCTURE OF A SMOKE JET AND DETERMINATION OF THE
COEFFICIENT OF TURBULENT MIXING FROM THE VERTICAL
DISTRIBUTION OF CONCENTRATIONS „ >- •
V. S. Yeliseyev ................ ....................... 99
S
-------
PREFACE
Much of the background material presented in the prefaces to the
preceding volumes of this series is repeated here in view of its rele-
vance to the present volume.
Contamination of the natural environment constitutes a major problem
in all industrial regions of the Union of Soviet Socialist Republics
(USSR). The country's industry and transport are continually bringing
about massive qualitative changes in the habitat of man and vegetation
through an ever increasing pollution of air, soil, and streams. In recent
years there has been a greater awareness of the immense problems of air
and water pollution on the part of the urban and rural administrative
agencies as well as on the part of various research institutes of the USSR.
There is a mounting demand there to maintain a high quality physical
environment. Protective measures against the pollution threat are grad-
ually taking shape. Much relevant air pollution research data are being
developed and are apparently put to good use in some parts of this vast
and diverse country.
The behavior of atmospheric contaminants, notably gases and fine par-
ticles discharged into the air, is similar to that of the air masses near
the surface .of the earth — the distribution of the contaminants being
influenced by atmospheric stability, wind, precipitation, and topographic
features of a given area or region. The most outstanding and dominant
characteristic of the atmosphere is its unceasing change, a change result-
ing from variations of temperature, wind, and precipitation. These meteor-
ological conditions vary widely as a function of latitude, season, and
topography. Seasonal as well as diurnal temperature gradients, horizontal
and vertical, affect the speed of the wind flow. Generally, the greater
the wind velocity the more rapid is the dispersion of pollutants in the
atmosphere. In continental areas the temperature gradients and the conse-
quent wind flow increase during the winter season and during the daytime
periods, the latter being usually subject to more turbulent winds of
higher velocity than those that prevail during night hours that are typically
characterized by low-level stability with a minimum dispersal and dilution
of the pollutants.
Studies of atmospheric diffusion and air pollution constitute a rapidly
developing area of meteorological sciences in the USSR. Determination and
analysis of the complex set of meteorological factors causing the processes
of atmospheric diffusion are being extensively developed there in conjunction
with theoretical and experimental studies of the pattern of propagation of
contaminants in the atmosphere.
Most of the reports of investigations brought together in this volume
deal with meteorological conditions and relief as factors in propagation
-------
A_ considerable number of these investigations have been conducted in
various industrial regions of the USSR, regions that are geographically
far apart from each other and subject to distinctly different natural
and man-made environmental conditions.
Some of the material presented here deals with various noxious
pollutants emitted to the atmosphere in high concentration at or near
ground level and with the exposure of these pollutants to the continuous
mixing, diffusion, stirring, and dilution that takes place between regions
of the atmosphere as a result of air turbulence. A number of papers deal
with the intensity and structure of air turbulence in relation to temper-
ature and wind, which form the background of atmospheric diffusion and
stirring. Other papers deal with the direction frequencies and intensi-
ties of wind, which differ markedly for stable and unstable conditions of
atmosphere; with the extremely slow diffusion through an inversion; and
with the general climatology of atmospheric turbulence, diffusion, and
the dispersions of air pollutants in different parts of the country and
during different seasons of the year.
It must be borne in mind that the data presented in this volume
relate to many diverse environments in a vast land area; that the USSR
'extends for about 7,000 miles from west to east and 3,000 miles from
north to south; and that the country covers a wide range of climatic and
relief conditions throughout much of its north-south and west-east extent.
In this connection, a brief outline of the very general natural features
of the USSR may be desirable. Lowlands and plains dominate the landscape
of the major portion of the country. Its landscape can be roughly de-
scribed as one consisting of broad latitudinal climatic belts of the
lowlands and plains and of narrow, vertical climate zones of the high-
lands and mountains. Each of the broad latitudinal belts is distinct from
the other in the major features of its climate, vegetation, and soils,
though within each latitudinal belt there is a decrease in the annual pre-
cipitation as one proceeds from west to east. The latitudinal belts Include
the nearly barren and treeless tundra in the extreme north, where the winters
are severe, the summers, short and cool, and where precipitation is very
limited. There follow the belts of the taiga or coniferous forests, mixed
forests, woodlands, forest prairie or forest steppe, the steppe, and the
semi-desert. Finally in the extreme south, east of the Caspian Sea, there
are the dry deserts, hot in summer and cold in winter, and, along the
southern reaches of the Black Sea in Transcaucasia, there is a relatively
limited area, humid and more or less subtropical, which is subject to mild
winters, hot summers, and heavy precipitation.
It is hoped that the papers selected for presentation in this volume
will permit an assessment of some of the USSR studies of the meteorological
-------
and topographic aspects of air pollution. As the editor of this
volume I wish to thank my co-workers in the Air Pollution Section of
the Institute for their valuable assistance.
M. Y. Nuttonson
Silver Spring, Maryland
November 1970
-------
Middle^ Asia
-------
CLIMATIC ZONES AND REGIONS* OF THE USSR
TV vC^afvyTtiv-; =-:/^-/?!S^iiHrr«^^v'>$^
OKHOTSK
Zones: I-arctlc, Il-subarctic, Ill-temperate, IV-subtropical
Regions: 1-polar, 2-Atlantic, 3-East Siberian, 4-Pacific, 5-Atlantic,
6-Siberian, 7-Pacific, 8-Atlantic-arctic, 9-Atlantic-continental forests,
10-continental forests West Siberian, 11-continental forests East Siberian,
12-monsoon forests, 13-Pacific forests, 14-Atlantic-continental steppe,
15-continental steppe West Siberian, 16-mountainous Altay and Sayan,
17-mountainous Northern Caucasus, 18-continental desert Central Asian,
19-mountalnous Tyan-Shan, 20-western Transcaucasian, 21-eastern Trans Cau-
casian, 22-mountainous Transcaucasian highlands, 23-desert south-Turanian,
24-raountainous Pamir-Alay
* After B. P. Alisov
-------
THE MAJOR INDUSTRIAL CENTERS OF THE USSR
O C«n
-------
THE MAIN MINING CENTERS OF THE USSR
I Anthracite
• Lignite
~ Shale,
-------
STUDY OF POLLUTION OF CITY AIR BY INDUSTRIAL DISCHARGES
N. S. Burenin and B. B. Goroshko
From Trudy, Glavnaya Geofiz. Observat. im. A. I. Voeykova, No. 238,
p. 136-144, (1969)
Considerable attention is being given today to problems of study of atmo-
spheric pollution by industrial discharges, i. e., this makes it possible to
take specific steps toward improving the air reservoirs of cities. Particular
importance is assumed by data on the chemical composition of air in cities,
obtained from long-term collection and analysis of samples over a wide net-
work of points located in different parts of a city. Such data permit the
evaluation of pollution, account being taken of the dynamics of change as a
function of the meteorological conditions determining the dispersal of
impurities in the atmosphere. In addition, of considerable importance are
single short-term surveys (lasting 1-1.5 months) with the organization of a
large network of points for the collection and analysis of samples. They
permit the establishment of the spatial distribution of noxious substances in
the city air, the identification of areas of maximum and minimum pollution, etc.
A single survey of one of the major industrial and administrative centers
of the Soviet Union was carried out in August-September 1968. The city ex-
tends over 25-30 km from north to south and about 20 km from west to east. It
is situated in a hilly area where the elevations rise 50-70 m above the low
points, and this under certain meteorological conditions may substantially
affect the pollution of some of its sections. The air reservoir of the city
is heavily polluted with a number of ingredients as a result of discharges of
noxious substances from plants of the metallurgical, chemical, and machine-
building industries located over the entire territory of the city. A major
contribution to the pollution is made by automobile and especially by freight
traffic. Based on incomplete data, 355 tons of dust, 274 tons of sulfur
dioxide, and 470 tons of carbon monoxide are discharged daily into the air
by the major sources.
According to the proposed standardization of cities [3] based on the
principle of distribution of industrial enterprises, the city being surveyed
may be classified as belonging to the second type, since the industrial enter-
prises that are the sources of pollution are scattered over its entire terri-
tory. For this reason, the adopted basis of the survey was the organization
of a network of points where samples are collected two to three times a day.
In all, 29 points were set up, each of which covered an average of 20 km^.
A number of factors (distribution of sources of discharge, local topography,
etc.) were considered in the distribution of the collection points, particu-
lar attention being given to heavily polluted districts. For this reason,
the density of the points in these parts of the city was higher and amounted
to one point for 5-10 km^, and on the outskirts of the city, it was corre-
spondingly 3 to 4 times lower. The program of sample collection specified
-------
that data be obtained during the course of the entire daylight period (from
6 AM to 11 PM) in order to obtain the change of the concentration field, de-
tertninable by the meteorological conditions and by the variation of the volume
of discharge. To supplement the sampling, the concentrations of noxious sub-
stances were determined at stationary points under the plume of the main
source of discharge - a metallurgical complex - at distances of 0.5, 1, 2, 3,
5, 8, and 10 km from the center of the discharge. This made it possible to
identify the zone of influence of noxious discharges from the complex, and
the field of their possible maximum concentrations.
Considering the specific character of discharges from the industrial
enterprises into the city's atmosphere, the collection and analysis of
samples for the following ingredients were organized: dust, sulfur dioxide,
nitrogen dioxide, carbon monoxide, phenol, sulfuric acid aerosol, chromium,
manganese, and lead.
The meteorological observations were conducted at all points at a height
of 1.5 m above ground. They included measurements of temperature and air
humidity, wind velocity and direction, and the recording of particular
weather phenomena. In addition, at the meteorological station located on
the southwestern outskirts of the city, hourly gradient observations were
made, during the period of sampling to determine the air temperature and
humidity and the wind velocity at levels of 0.5 and 2 m above ground, and
the turbulence factor was calculated.
In order to characterize the pollution of the city's air basin from the
data obtained, the main characteristics of air pollution were calculated
according to districts and for the city as a whole: qav - average concen-
tration during the observation period, mg/rn^, g - frequency of concentra-
tions above MFC, %, g^ - the frequency of concentrations above 5 MFC, %;
q max - the maximum concentration, mg/m^, all listed in Table 1. The latter
also gives the maximum concentrations encountered during the period of the
survey.
It follows from Table 1 that the city's air is most heavily polluted
with carbon monoxide, phenol, dust, and lead. Thus, the frequency of phenol
and carbon monoxide concentrations above 5 MFC amounts to 43 and 26% respect-
ively, and in some of its districts reaches 59 and 32%. In terms of excess
of MFC for the city as a whole,g amounts to 86% for phenol and 83% for
carbon monoxide, and in some districts this value is much higher. The
maximum values also exceed many times the maximum permissible norms. The
air reservoir of the city is polluted less with nitrogen dioxide and sulfur
dioxide, but their maximum concentrations exceed MFC, and the frequency
above MFC amounts to 45% for nitrogen dioxide and 4% for sulfur dioxide.
Comparison of the degree of pollution of the atmosphere of individual city
districts shows that the northern district is most heavily polluted with
dust, nitrogen dioxide, carbon monoxide and lead, the central district with
sulfur dioxide, carbon monoxide, sulfuric acid aerosol and phenol, and the
southeastern district with dust, phenol, lead and carbon monoxide.
-------
The presence of a large number of collection points made it possible to
obtain not only a general pattern of the city's air pollution, but also a de-
tailed spatial distribution of the concentrations of the noxious ingredients
studied during the period of observations. Fig. 1 shows the concentration
f'felds for dust, carbon monoxide, nitrogen dioxide, and sulfur dioxide. The
schematic maps show isolines of equal concentrations. Analysis of the fields
of concentrations on the territory of the city permits the identification of
zones with high air pollution values. For example, it is evident (Fig. 1 a)
that the isoline of the average dust concentration of 0.5 ir-g/m^ surrounds
almost all of the territory of the city, this being equal to the single maxi-
mum permissible norm, and over 3 times 'the mean daily maximum permissible
norm. At the same time, in the northern and southeastern districts are seen
areas with the most dangerous air pollution, where the concentrations con-
siderably exceed even the single maximum permissible norms. These zones of
maximum pollution are in accord with the location of the main dust-producing
sources.
Table 1
Main Characteristics of Pollution of Air Reservoir with Industrial Discharges.
City District
Southwestern
Southeastern
Central
Northern
Cjty^as a
Charac-
jeristic
ftp
;
81
'28
12
36
88
30
12
01
77
32
11
Cl
83
26
Sul-
furic
Acid
0,10
0,46
8
0
0,12
0.40
11
0
0,17
0,57
29
0
0,08
0,46
G
0
0,11
0,57
11
0
Pheno
0,046
0,398
84 ,
25
0,068
0,199
94
59
0,057
0,353
02
39
0,048
0,222
83
37
0,051
0,398
86
43
Mang-
anese
0,00065
0.00135
—
0,00130
0,00260
—
...
0,00052
0,00190
—
—
0,00199
0,00227
*—
—
0,00110
0,00260
—
—
Lead
0,0021
0,0035
91
0
0,0020
0,0050
40
2
0,0012
0,0030
13
0
0,0015
0,0070
68
5
0,0017
0,0036
55
2
Chromium
0,0001
0,0003
—
0,0001
0.0006
—
—
0,0001
0.0003
—
—
0,0001
0,0004 .
—
—
0.0001
0,0006
—
—
-------
The distribution of average carbon monoxide and nitrogen dioxide concen-
trations (Fig. 1 b and c) shows that the air reservoir is heavily polluted
with these Ingredients over the entire territory of the city. It must be
noted that both in the first and in the second case, a large number of high
concentration zones there are observed which are determined not only by the
location of the major sources of atmospheric discharges, but also by the
influence of discharges from motor transport. It was noted that the samples
taken at points located near highways with heavy automobile traffic contained
carbon monoxide and nitrogen dioxide in greater amounts than in other areas.
During the period of the studies, the air currents were directed pre-
dominantly from the site of the major sources of discharge of noxious sub-
stances toward the residential areas, where the major part of the sampling
was carried out. For this reason, if special periods are excluded, the
concentration values obtained in the city may be regarded as the maximum
values.
a) "
b)
d)
Fig. 1. Isolines of average concentrations of dust (a), carbon
monoxide (b), nitrogen dioxide (o), and sulfur dioxide (d).
1 - points of measurement, 2 - city limit
-------
It is of interest to consider the change of the concentration in a daily
variation during the daytime. Two characteristic points were chosen for this
purpose where repeated samplings of sulfur dioxide and nitrogen dioxide were
carried out. The location of the collection points in relation to the indus-
trial site of the major metallurgical complex varied. The first point (Fig. 2,
curves 1, 2) was located at a distance of 150 m from the site, the second (Fig.
2, curves 3, 4) at a distance of 3.5 km. Curves 1, 3 correspond to the varia-
tion of average concentrations of sulfur dioxide, and curves 2, 4 -- to nitro-
gen dioxide. It is evident that the change of the concentrations is slight,
but the curves have the opposite course. At the point located near the indus-
trial site, maximum concentrations were observed in the mornings during a
period of slight turbulent exchange. These concentrations are due to low and
unorganized discharges.
q,
Fig. 2. Daily variation of con-
centrations of sulfur
dioxide Cit. J) pod ni-
trogen dioxide C2, V)
for two.observation
points in the city.
Hours
At the second point, located at a distance of 3.5 km, an increase in
concentration Is observed under daytime conditions. This indicates that the
influence of primarily high discharges is manifested in this case. As tur-
bulent exchange develops, mixing is intensified, and plumes from high sources,
located at a height of 100-200 m, undergo a more vigorous dispersal. As a
result, the concentrations near the ground increase [1, 2, 4, 7].
Samplings under the plume of the metallurgical complex at various dis-
tances show that the atmosphere in the range of influence of the plume is
markedly polluted with different ingredients (Fig. 3). At the same time, two
distinct maxima are observed for carbon monoxide, nitrogen dioxide and sulfur
dioxide. The first is due mainly to unorganized discharges, and the second,
at a distance of 3 km, to the discharge of noxious substances from high stacks,
The performed meteorological observations of the temperature and wind
velocity and direction at the points of sampling made it possible to obtain a
series of interesting data on the microclimatic characteristics of the terri-
tory of the city. It is known that the climate of a city differs substan-
tially from that of the surrounding region. According to studies made by
several authors [5, 6, 8, 9], this affects primarily the temperature regime
and the distribution of the wind velocity and direction.
-------
- I
The temperature regime of a city is determined by the density of its
construction, height of the buildings, distance between them, width of the
streets and plazas, their arrangement with respect to the points of the com-
pass, the vegetative cover, etc. A particularly strong temperature contrast
with different parts of the city and the region surrounding it is provided by
industrial sites, on the territory of which the air temperature is usually
higher.
The formation on the territory of a city of areas with a higher air temp-
erature, the so-called "heat islands," leads to the appearance of ascending
currents of the type of stationary breezes over the city. This explains the
formation of a cap of dense aerosol visible in clear weather above the city
from afar [5]. On the other hand, the character of the wind in the city is
affected by the fact that the buildings constitute a substantial obstacle to
the air current. As a result, the movement of air before the city and within
its confines slows down, so that an air cushion in the city is formed, which
serves to lift the masses of air. Thus, the city increases the gustiness of
the wind, decreases Its velocity near the ground and increases it at higher
leveIs.
8 KM
Pig. 3. Distribution of maximum concentrations
in the area of the metallurgical compl
rgical complex.
1 - dust, 2-- C02, 3 - N02, 4 - SOg
,A11 these aspects of the distribution of microclimatic characteristics in
a city are very important when analyzing the change of the degree of air pol-
lution as a function of the meteorological conditions and in the subsequent
forecasting of the occurrence of dangerous meteorological conditions (i. e.,
conditions under which the highest concentrations of noxious impurities in
-------
air are observed). Given below are some results of treatment of observational
data on the wind direction for the northern area and the temperature and wind
velocity for the entire territory of the city.
,•
According to observational data on the wind direction at the surface of
the ground during the course of the expedition, at 6 points of the northern
area, a number of cases of wind direction were selected for 8 rhumbs for each
point separately. Simultaneously, a selection of the wind directions based
on data of the meteorological station was made for the same period of obser-
vations. On the basis of the data obtained, the frequency of directions for
the eight rhumbs was calculated for the region as a whole, and is shown in
Table 2. It follows from the table that the transformation of the air cur-
rent under the urban conditions of the northern area has the following
characteristics:
a) There is a sharp increase in the frequency of calm situations in the
city due to the damping down of the wind velocities of all directions. For
the area as a whole, the frequency of calms amounts to 17%, whereas according
to the data of the meteorological station, it is equal to 2%. The greatest
frequency of calms is observed at points located in the central part of the
city.
b) The frequency of the wind direction for a number of rhumbs (northern,
northeastern), based on the data of the meteorological station, decreases
sharply as compared with the data obtained in the city. In the city, the
frequency of the wind direction of eastern and western rhumbs increases.
Table 2
Frequency (%) of the Wind Direction Based on Data of Observations at the Meteorological
Station and in the City
Based on data of
meteorological station
Based on data at
points of sampling
Calm
2
17
NE
2k
0
£
9
17
SE
It
0
S
1
1
sw
5
2
W
9
27
NW
21
22
N
25
14
The conclusions reached are of major importance for calculating the
atmospheric pollution of a city. The increase In the frequency of calm con-
ditions in the city indicates that stagnation periods are more frequently ob-
served here than can be determined from data of the weather station. The
change of the wind direction under urban conditions also affects the pollut-
ion of certain areas. This becomes clear from an analysis of the factual
material on atmospheric pollution. Data are frequently found which charac-
terize a heavy pollution when the observation point during the sampling was
not located under the plume of a large-capacity source, but at a distance
of 0.5-2 km from the plume axis. A detailed examination reveals that al-
though the plume is passing on the side, noxious substances which have
reached the lower layer are transported along the streets in the direction
-------
of the air stream, which does not coincide with the main direction of the wind
and can frequently be oriented at right angles to the main undisturbed stream.
This causes pollution of territories that are not in the sphere of influence
of the plume.
Thus, in comparing forecast warnings of meteorological conditions pro-
moting the heaviest pollution of the northern area by discharges from the
Industrial enterprise located on the eastern border of the area, It Is nec-
essary also to consider the wind of the northeastern rhumb in addition to the
wind of eastern direction.
According to data of meteorological measurements of the air temperature
and wind velocity at 29 points of the city, such characteristics as the devia-
tion of temperature at the point of sampling fror.i the temperature at the
weather station (AT) and the ratio of the wind velocity at the point of
sampling to the wind velocity at the weather station (r.) were calculated.
From these characteristics, the fields of distribution of AT and rv over the
territory of the city were plotted (Fig. 4).
Analysis of the temperature field shows that almost over the entire
territory of the city the air temperature was higher than outside the city.
The average increase of the air temperature in the city during the period of
observation is 0.4°. The main "heat island" is located in the southwestern
area with a 1.2° drop of mean temperatures. This zone of high air tempera-
ture coincides with the industrial residential district having a railroad
Junction. In the central district one can also distinguish a high air
temperature area that is adjacent along its northern boundary to the major
industrial site. Furthermore, three zones can be distinguished where the
air temperature is lower than outside the city: these are zones located in
the river valley.
Fig. 4. Isolines of the distribution of AT (a) and r,. (b) on the
territory of the oity, ' v
1 - points of measurement| 2 - oity limit
-------
As is evident from Fig. 4 b, the distribution of wind velocities in the
city has its specific features. At almost all the observation points it was
noted that the wind velocity in the city was 1.5-3.5 times less than outside
it (at the weather station). The wind velocity decreases from the edge of
the city towards the center. The zones of greatest air stagnation are ob-
served in the central and northern areas. The,maximum value of rv is 3.5.
The zones of greatest decrease of the wind velocity coincide with densely
populated and built-up residential districts. As follows from the performed
analysis of the degree of pollution of the air reservoir of the city, these
are the two districts (central and northern) which are the most polluted.
LITERATURE CITED
1. BepJiniiA M. E. [H Ap.]. Hiic/ienuoe peuiemie ypaonemin TypfiyjieHTuofi Aiiy-
p. ITO,
3HH H pacsei sarpjuiiemiH atMoccpepu riJinan npOMbiuuiemiux npeflnptmTHfl. Tp.
Bun. 138. 1963.
2. B epflflHAM, E., remixoBHi E. Jl., 0 H H K y n P. H. 0 pacneie aarpnaueHiin
8TMOC(pepbl BblfipOCaMH M3 AUMODblX Tpyfi SMKIpOCTaHUHft. Tp. ITO, Bbin. Io8, 1964.
3. B y p e H H H H. C., F o p o ui K o o. B., n b n H u e o B. H. 3KcneaHUHonuoe wayie-
HIIO aarpnsiiemin aoaAyuixoro flaccefiaa npowuiujieHHUx ropOAOB. Tp. TFO, sun. 234, 1968.
4. P o p o m x o B. B. HexoTopue ocaCemiocTu pacnpocipaHeHiin opcAxux npiiMeccii
OT DblCOKIIX IICTOMHIIKOD B 38DHCHMOCTII OT ClIHOriTliKO-MCTeOpOAOmweCKHX (taKTODOB. Tp.
rrO, nun. 207. 1968.
5. K p a T u e p IX A, K-niiMai ropo.ua. HJ1, M., 1958.
6. KfliiMar Oo^biuoro ropoAa. OOA peA. npocp. A. A, RM »rp HC BB. USA. MTV, lUfio.
, 7. VKasaHiifl no pacqeiy paccenoaHiin u aTMOcipepe opCAiibix uemecro (IIU.IH M ccp-
i iiiicToro rasa), coAepwauixxcn a uufipocax npoMbiiujieHHUx npeanpHHTHft. CH-369— 67.
' r'OCCTDOft CCCP. rHApOMOTeOH3A8T, Jl., 1967.
8. Garnet t A., Bach W. An Investigation of Urban Temperature Variations
By Traverses in Sheffield (1962—1963). Biomctcorology. vol. 2. part 2.
9. Lowry W. P. The Climate of Cities. Sclent. Amcr., 1967, 21. No. 2.
-------
CHARACTERISTICS OF THE THERMAL REGIME OF CITIES
G. P. Rastorguyeva
From Trudy, Glavnaya Geofiz. Observat. ira. A. I. Voeykova, No. 238
p. 145-152, (1969)
In studying urban air pollution, it is highly important to know the
characteristics of the urban meteorological regime. It is well known that
the climate of a large city and that of its surroundings differ to some ex-
tent. These differences have been noted by many investigators on the basis
of a comparison of data collected by weather stations located inside and
outside the city limits. Such studies were made on the temperature and
humidity of the air, velocity and direction of the wind, amount and nature
of the precipitation, duration of fogs, solar radiance, etc. A fairly
complete survey of completed studies, particularly those of German,
British and French authors, is given in the book of P. A. Kratzer [6].
This can be supplemented with later studies of Soviet and foreign authors
[2, 3, 5, 10, 21, 39 etc.]. These studies indicate that the mean annual
air temperature in a city is 0.5-1.5°C higher than in its environs. The
mean annual wind velocity in the city is 20-35% lower, the relative
humidity of air is 5-10% lower, the frequency of fogs at the center of the
city is higher, and the number of days with solar radiance is reduced [36].
In the city, a lag of the air temperature extremes and a decrease in the
daily amplitude of the air temperature are observed.
A certain heating of urban air is attributed by the Investigators to a
change in the thermal balance resulting from the fact that the active
surface in the city consists of materials of high heat capacity and ther-
mal conduction [4, 33, 36, 40]. The pollution of atmospheric air, the
heating of dwellings and the decrease ofthe wind velocity promote the re-
tention of heat in the city, despite a decrease of solar radiation as com-
pared to the surrounding area.
The Insufficiency of weather stations makes impossible to obtain a
complete picture of the temperature field of air In the city. Yet the
knowledge of the horizontal and vertical distribution of urban temperatures
is necessary for the solution of various problems. In particular, it is
necessary for the study of the diffusion of impurities in the atmosphere.
It follows from qualitative considerations that in certain types of
weather, overheating of the city generates circulation in which the lines
of flow are directed toward the center of maximum overheating [10, 40].
As a result, an industrial haze with very high concentrations of noxious
impurities is formed over the city. However, these problems practically
have not been studied from a quantitative standpoint.
Of late, the problems of temperature distribution in the ground layer
of air in cities are being studied both abroad and in the USSR. A widely
adopted method involves itinerary cruises around the city and its environs
-------
with more frequent temperature measurements at a height of 1.0-2.0 m above
the active surface. It was found that isotherms superimposed on the plan
of the city schematically duplicate the outline of the latter, with the
overheating maximum coinciding with the most heavily built-up part of the
city. In the literature, the phenomenon of overheating of city air has
been termed "heat islands." In the last 15-20 years, similar investiga-
tions of a number of cities in Europe, the USA, Canada, and Japan have
been carried out. In most of the published works, the conclusions are
based on observations of an episodic character made in the course of
several days at different times of the day and year, etc. Nevertheless,
they have permitted the establishment of certain relationships in the
distribution of urban air temperature, fhe most detailed investigations
were made on the Swedish city of Uppsala [52], London [21], and some
Japanese cities [33, 48, 50]. Since 1958, a special network of 58 meteoro-
logical points and 17 network stations have been set up in London [18].
Measurements of urban air temperatures have shown that heat islands are
characteristic of almost all industrial cities, and that the temperature
differences between the city and its environs vary from 1 to 10°C. The
influence of a city on the air temperature depends on the weather conditions
and some other factors. It increases in radiation-type weather (gentle
wind and clear sky) and decreases with increasing wind and cloudiness. The
diurnal variation of the difference in radiation-type weather has a maximum
in the afternoon and particularly evening hours, since the city cools more
slowly than its environs. For Japanese towns located on level ground, this
difference does not exceed 3.0-3.5°C [48, 49, 50]. In London, with its
typical urban layout, it reaches up to 4.5°C. For cities with a marked
topography and a substantial air pollution, it Increases to 7-10°C [28, 29,
47]. In the morning hours, for 1-2 hours after sunrise, the urban-rural
temperature difference is minimum and may even take negative values, since
the rural area heats up faster[39]. In advectlve type weather, the
diurnal variation of the difference is manifested slightly, and the
difference itself ranges from 1 to 2°C. For Tokyo, at a wind velocity of
6-8 m/sec, the difference is close to zero [23]. For cities located in the
zone where two opposed wind directions predominate, the temperature differ-
ence depends substantially on the wind direction. Thus, In Baku [5] it
may range from 5 to -2°C.
In the studies of Sundborg [52] and Kawamura [34], the least-squares
method was used to derive formulas relating the nocturnal and diurnal
change of the urban-rural temperature difference D™ to the cloudiness N,
wind velocity u, temperature of the environs T and amount of water vapor e.
For nighttime hours, the Sundborg formula is
Dg • 2.8-0.10 N-0.38 u-0.02 T + 0.03 e.
It is interesting to note that the numerical coefficients for the
Japanese cities and the Swedish city are approximately the same.
-------
Analysis of the annual variation of the urban-rural air temperature
difference shows that it is positive in practically all seasons of the year.
The majority of the authors note that for European cities, the maximum
values of the difference pertain to the summer period (Berlin [26], Prague
t47], Krakow [51], etc.). In London [21] they may be observed in other
seasons as well, in spring or autumn. In Saratov [2] this difference is
smallest in summer because of the aridity of the surroundings as compared
with a city with greenery. In Japanese cities, the maximum of the differ-
ence coincides with winter or spring. All the maximum seasonal values of
the difference occur in the evening hours.
The effect of highest occurrence in the city during late evening hours
was used by a number of authors for studying the heat islands of small
cities [22, 30]. It was found that small cities whose population is 1/25
that of large cities have, under similar weather conditions and with an
identical construction density, the same maximum urban-rural temperature
difference as a large city. On this basis, Chandler [22] came to the
conclusion that the intensity of a heat island is independent of the size
of the city and hence independent of the size of the population. The
opposite result was obtained by Mitchell [39]. He showed that during the
preceding 60 years (1895-1954) the intensity of the heat island increased
with the population in American cities. Fuqui [27] conducted similar
investigations in 14 Japanese cities during the period from 1900 to 1940.
The results obtained confirmed Mitchell's conclusion in reference only to
cities with an Initial population of over 200,000 people.
It is evident that the presence of a heat island in a city also gener-
ates a particular vertical distribution of temperature above the city.
Microclima tic observations made in different cities (Volgograd, Moscow,
Goteborg, and Salzburg) showed some similar characteristics of the values of
the temperature difference in the 0.5-1.5 m layer. They consist in the
fact that over asphalt, which is the predominant cover in a city, the
vertical temperature differences in the ground layer of 0.5-1.5 m have
positive values in both summer [16] and winter [54] and vary from 0.1 to
1.0°C. In the diurnal variation in summer there is a maximum in the
afternoon hours, when the difference ranges from 0.5 to 1.0°C. Early in
the morning and in the evening, it decreases from 0.1 to 0.2°C. According
to the observations in Gbteborg, the maximum temperature difference above
asphalt in the lower layer from 0.5 to 1.5 m fluctuates around 1°C in all
months of the year.
Measurement of the air temperature above the city is a difficult
problem, and such measurements have been few. In comparing the vertical
temperature distribution in the city and its environs, Japanese Investi-
gators [34] carried out special measurements by means of resistance therm-
ometers suspended from balloons up to heights of 30 m. In addition, they
used the data from a 130-meter television tower in Tokyo. Data from tele-
vision towers located in the city at the center of the heat island and also
outside the city's zone of influence were studied for Canadian t41 ] and
-------
American cities [19, 24]. One of the latest studies [19] reported for a
vertical sounding of the atmosphere over New York and its environs by means
of a helicopter.
Observations have shown that during the day, the temperature distri-
bution over the city differs little from that over a village. Both in and
around the city, superadiabatic lapse rates are observed. At night, the
influence of the city is enhanced, and the heat island can be detected at
heights 3 to 5 times greater than the height of the building [34], During
the cold period of the year, at night, the influence of the city is enhanc-
ed, and reduced during the warm period of the year. The height of the in-
fluence of warm urban air depends on its size. The larger the city, the
greater the height to which urban air spreads. As was shown by the studies
of DeMarrais [38], near-adiabatic lapse rates or moderate inversions pre-
dominate during the course of one year over the city at night. Super-
adiabatic gradients and large scale inversions are seldom observed.
A comparative analysis of inversions in nighttime was made in ref. [19].
It was shown that in most cases the ground inversions of the environs were
associated with smaller urban inversions. Several elevated inversion
layers were sometimes observed over the city. The average height of an
elevated inversion was 300 m. The intensity of the heat island was maximum
near the surface and decreased to zero at the height of 300 m. The maximum
height of the "heat cap" in the city was 500 m. The "cross-over effect",
in which the temperature under the heat island fell to values below the air
temperature of the environs at the same level, was also observed in these
studies.
Because of the rapid growth of cities, an increase in the volume of in-
dustrial production and the development of transportation, the problem of
study of the influence of the city on the climate requires additional ex-
tensive investigations.
In connection with the study of the state of atmospheric pollution in
July 1968, measurements were made on some meteorological characteristics of
Donetsk, one of the major industrial cities of the Ukraine. The peculiar-
ity of the area of observation lies in the fact that it is located on a
dissected terrain where the heights are exceeded to a maximum of 100 m. The
central, most densely built-up part of the city, coincides with high
observation points. The combined influence of the natural and urban land-
scapes on the meteorological regime of the city has been studied insuffici-
ently thus far and is of major interest.
To carry out the meteorological observations, 20 observation points
were selected on the main territory of the city, taking into account the
natural and urban features of the region studied, as much as possible in
open spaces (squares, street intersections, banks of streams). The under-
lying surface of the urban points was predominantly asphalt, and that of the
city's outskirts, soil or grass cover. The reference point selected was a
weather station located on the outskirts of this city. Twelve urban obser-
vation points were referred to four elements of the city: low and high
-------
squares with a maximum height difference up to 80 m, the river embankment
(lowest part of the city) and the streets. Seven suburban observation
points were correspondingly referred to open squares, the highway and the
river embankment.
At four points, Including the weather station, the observations were
stationary, and the remaining points were'serviced by four automobiles with
four observers. Each of the automobiles was assigned to a certain district
of the city in such a way that the transit from one point to another, the
setting up and unloading of the instruments, and the observations would last
30 minutes. At stationary points, the observations were made in the course
of a 10 minute period every 30 minutes. At the same time, observations were
made at four itinerary points. The points were toured according to a
shuttle system. The measurements included the following elements. Suction
psychroraeters were used for observations of air temperature and humidity at
heights of 0.5 and 1.5 m above the surface; the instruments were mounted on
tripods in a horizontal position. Manual anemometers measured the wind
velocity at heights of 0.5 and 2.0 m. A periodic mercury thermometer meas-
ured the surface temperature. The wind direction was recorded by means of
a light pendant and a compass. At the weather station, the form and
amount of cloudiness and at the remaining points, the condition of the sky
(clear, variable, overcast) were determined. In addition, the state of
humidity of the active surface was recorded.
From 19 to 22 June, two diurnal series (10 AM-2 PM), one morning
series (6-9:30 AM) and one nocturnal series (11 PM-3 AM) were carried out.
During this period, a typical anticyclonic weather prevailed. The wind
velocity ranged mainly from 1.5 to 2.5 m/sec with a brief intensification
during the day to 4-5 m/sec. The prevailing wind direction was southeastern.
Table 1
Values of Meteorological Parameters in the City and Suburbs
(p) compared with the Reference Station (w) at Different Times
of Day (DO - morning series, d - day, n - night).
Elements of City
and Suburb
Weather Station
High Open
Spaces
Low Open Spaces
City
Enbankments
City Streets
Suburban
Streets
Suburban
Highway
Suburban
Fnbankoents
Vup
mo
1,0
1.7
3.4
16.7
2,0
1.5
1,8
1,8
d
1.0
1,5
1.7
0.5
1,5
1,3
1,3
0,7
AT«TW-TP °c
n
-2,0
-1.8
0,2
-1,2
0.1
-2,1
3,7
mo
2.2
1,6
2.3
0,3
1.0
1.1
2.7
d
1.0
0,9
0.3
0.1
0,1
—
0.5
At0,5-2,0 "C
n
-0,6
-0.6
0.0
—
0.0
-0,3
—
-0,2
mo
0,1
0,3
0,0
—
0,1
0,0
0,0
0,0
d
0.5
0,7
0,6
0,4
0,5
0,8
0,5
0,5
r#
n
51
43
48
52
50
54
47
56
mo
40
42
52
52
41
46
46
56
d
34
32
36
35"
31
34
—
37
Ae-ew-ep «*
n
0,7
-0,1
-1,7
-0.7
-0.7
0,9
-2,1
mo
•
0,2
-1,5
1.8
0,7
1,0
—
2.9
d
0,9
0.2]
0,4
0,6
0.2
—
0,5
-------
The cloudiness varied from 0 points at night and in the mornings to 5-6
points Cu during the day. In the early morning, a light haze of industrial
origin formed over the city. The results of the observations are found in
Table 1 and Fig. 1. The table lists some meteorological parameters averag-
ed for the period of the night (11 PM-3 AM) morning (6 AM-9:30 AM) and day
(10 AM-2 PM) series. The number of cases of averaging is not uniform,
depends on the duration of the series and the number of observation points,
and varies from 4 to 19. The total number of readings for each element is
230. The table includes the following parameters: ratio of the wind velo-
city values at the weather station (uy) to the wind velocity at the observ-
ation point (up) for a height of 2 m, air temperature difference A T°C.
at a height of 1.5 m between the weather station and the observation points,
lapse rate AT8C. calculated for the standard layer of 0.5-2.0 m, relative
humidity r%, and difference in water vapor pressure Ae mb between the
weather station and the observation points. Let us examine each parameter
individually.
The wind velocity at the weather station changed only slightly in the
course of a day, but it changed differently in the city during the same
time. At night, with a general slackening of turbulent exchange, the wind
velocity in the city and at its outskirts was considerably lower than in
the open area, and amounted to about 1 in/sec at most points, and sometimes
less. This made it impossible to calculate the ratio Uy/u for the night-
time. At sunrise, the wind velocity in the city began to increase, the
ratio of velocities from morning to daytime decreased, and even fell below
unity near the water reservoirs (Table 1).
In the analysis of the temperature of the underlying surface, three
differences were examined: weather station (grass) - city (asphalt),
weather station - suburb (grass) and weather station - suburb (bare soil).
As is evident from Fig. 1, the fluctuations of the temperature differences
between the surface of the soil at the weather station and the surface of
the soil or grass at the suburban points are fairly large, particularly
during the day, and are random in character. At the same time, the temper-
ature difference between the soil surface of the weather station and the
asphalt surface changes from positive values at night to negative values
during the day. There Is a change of sign two hours after sunrise. During
the day, the asphalt surface constantly remains cooler than the soil sur-
face. The extreme values of the difference are 1° and 8°C at night and
-1° and -13°C during the day.
The air temperature difference AT at a height of 1.5 m between the
weather station (Tw) and the observation points (Tp) does not remain con-
stant during the day (Table 1). In the morning hours, because of the pres-
ence of a mist over the city, the air temperature of the latter is lower
than at the weather station, and the average temperature difference is 1.5°C.
During the day, this difference decreases to almost zero, In the evening
hours it changes sign, and at night it becomes negative. The warmest are
the central, highest parts of the city. For the 0 hr 30 min period, the
maximum temperature difference between the center of the city and suburbs Is
7.38C if the topography Is taken into account, and 3.0°C if it Is not. The
-------
12 13 14 {|0ur8
emperature Difference Between the
tatipn and The City, the weather :
uBurbs.
Bureau
1 - for asphalt, 2 - for soil, 3 - for grass
relatively high air temperature of the suburban highway is explained by the
influence of two factors: the high location of the observation point and
the presence of the asphalt strip. It is essential to note that the city
embankment at night is warmer than the suburban embankments, whereas in the
morning and during the day the differences between them are almost non-
existent.
The daily variation of the lapse rate At in the 0.5-2.0 m layer in the
city is similar to that of the gradient at the weather station. Differences
pertain only to the absolute values of At: during the day in the city and
suburb, the lapse rate in the ground layer of air is slightly increased as
compared with the lapse rate at the weather station (Table 1). In addition,
attention is drawn to the lack of inversions at urban points in lower parts
of the city.
v
The air humidity measured at a height of 1.5 m differs little in the
city from the humidity at the weather station (Table 1). One can only note
a certain decrease in air humidity over high open spaces and on city streets.
A considerable amount of greenery in the city is a consequence of the slight
humidity difference in the city and its environs.
The investigation has shown that in the city under study, a heat island
is formed in the afternoon hours, and, as in other cities, manifests itself
-------
best during the hours of the night in the summertime. Thus, we should note
an increased influence of the city on the thermal regime as a result of the
action of two factors promoting an increase in the air temperature in the
city during nighttime hours: an enhanced heat transfer in the central part
of the city and a relative increase in the air temperature of this part of
the city, as the one which is the most elevated.
LITERATURE CITED
I. A 11,1 p n .1 >i OB M. C. MiiKpooiiMaTii'iecKite ocoCeimocTK r. Jlbao&a. y«j. san.
.'li.noiii'Kfiro roc. yii-ra, Mi 1, 1951. .
2. P. 1.1 a MII ii B. H., HuiepcKan E. B., eTitcoBa JI. M. TeMnepaiypa BOS-
;tv.v.'i H ropo-ic Cnp.iTone. CO. «reorpaKHM Ha reppHTOpiiH BaKy. C6.
.llavuMi'iMiiifH 110 MiiKpoKJiMMary*, Mi 3. ToccTpoflHaflaT. M., 1965.
(i. Kp.-rriicp n. A. K^tiiMar ropoaa. M/I, M., 1958.
7. .'I ii n u u B. H. K xapaKrepucTUKe MUKpoK^HMnra reppiiTopHii r. MHMKeHTa. Tp.
l<;ii;ixfKiiro <|i;i.ni;ifla AC n ACCP, 4 (6), Awia-Ata, 1962.
M. .'I y M in c u A. A. Hcc^e^onniimi oiiMara ropoAoo o npaKTHiecKHx UCARX. C<5.
• CoiK'ri'K.-iii rdirp.Kpini 11 ncpiiofl CTpoiiTe/ibcrna KOMMynii3Ma». Peorpaijirio, 1963.
!). Mc.ib Al. H. IleKOTOpbie Meprw MiiKpoKJiHMara loro-aanaAHoft TeppHTOpHH r. Mo-
TKIIIJ. AU'rcopo.ioniti n rimpo^ornn, Mb 9, 1936.
10. Mo. 'imp aye B. B. O MHKpoK^itMare napKon n ruiomaAeft Co^biuoro ropoaa.
Uoi-iii. AirV, ccp. reorp.. Mb 2, 1966. •
II. Ccpi-Aiiiia 13. B. K nonpocy o K^iiMarc KypcKa n ero SKOHOMHKO-reorpaipHHe-
I'Kdfl DitoiiKC, y yc.iooiiii n rocTau^Hioiiuie aiieiuiiero Ten^oMaccooCMSna seMHoA nosepXHOCTH
i' ;irMi>i-(|ii-pou, Tp. Ceil. OTA. ini-Ta ociiouaHiifl H noaseMHbix coopyweHHft, Dbin. 3, 1967.
U. [Hop 6 a lib M. H. OciioBHdie npoO^eMbi iiayieHiiH MectHoro K/IHUOTB Kpynnux
inpo.ion VKpauiiiii. Co. «ripiipoAiibie n TpyAoswe pecypcw 7IeBo6epe>Kba • VKpaHHu n HX iic-
iiii.ii,:toii;iiniL'», T. 7. H.rii. cHeApa», 1966. . . .
I."). IHc po a n i> M. I. MiiKpOKJiiMaTHiiHi ocoO^iiBOCii KHiBa... 36ipiiHK reorpaipN-
iii>io i|>:iKy:ibrcTy, ,V» 5. B-BO KHiBCbKoro yHiaepcHTeTy, 1958.
1C. a T K ii n K. M. HeKoropwe cpasHHTe^bHue AaHHue na6JiK>WHHtt .>^enenTOB
siacciiBOB n OTKPUTUX npocTpaxcTB r. Bo^rorpaaa, C6. «Bonpocu
ropo;u>H». Do^rorpafl, 1967.
.. .
17. Her K II. Niichtliche Temperaturanstieg am Rarule einer Grosstadt. -Wetter
isiiii Ul»«n. 11)59, 11,. Nr I. • ' * ' . '.. •" '.' ' ;
-------
ANALYSIS OF METEOROLOGICAL CONDITIONS OF
DANGEROUS AIR POLLUTION IN CITIES
L. R. Son'kin
From Trudy, Glavnaya Geofiz. Observat. im. A. I. Voeykova, No. 234,
p. 60-68, (1968).
At the present time, in both theoretical and experimental studies
[1-4 etc.], major attention is given to the investigation of the dispersal
of noxious discharges from various industrial enterprises. It is obvious
that a natural condition for the formation of high Impurity concentrations
in air is in this case the direction of the wind from the sources of dis-
charges to the observation point. In the presence of this direction of the
wind, the concentrations of noxious pollutants in the ground layer of air
are determined by the wind velocity and the degree of turbulent exchange.
In an extensive turbulent exchange, high impurity concentrations are created
as a result of discharges from high smokestacks. Particularly unsafe con-
ditions arise when a raised inversion takes place above the source of dis-
charges [1, 2, 7].
In a city, because of the marked roughness of the underlying surface,
an intensive turbulent exchange develops in the bottom layer of air, which
may be reinforced as a result of the creation of the so-called "heat island"
and breakdown of the lower part of the ground inversion [17, 22, 24, 25 etc.].
Other things being equal, the indicated effects obviously cause a substan-
tial pollution of air by discharges from heavy Industrial enterprises in the
city as compared with the surrounding areas.
In principle, dangerous pollution of the atmosphere arising from the
transport of discharges from the direction of the sources can be predicted.
A synoptic forecast of the wind direction presents no difficulties. The pos-
sibility of forecasting the temperature profiles of the boundary layer on the
basis of their relationship to synoptic situations has been demonstrated in
earlier studies [8, 9, 12].
The characteristics of formation of high impurity concentrations in
the city in the presence of stagnant air have been inadequately studied.
Their analysis poses a whole series of questions, some of which are dis-
cussed In the present paper.
In order to predict a dangerous pollution of air, it is necessary to
know the synoptic situations corresponding to the given phenomenon. There
are indications that a marked air pollution is connected with anticyclones
[10, 15, 16, 18, 20]. On the whole this is correct, but a more detailed
analysis has shown that what is dangerous is not the anticyclonic circula-
tion itself, but the gradientless pressure field frequently associated with
it. From this standpoint, areas of pressure col and diffuse cyclonic fields
-------
are also In an unfavorable position. At the same time, a heavy air pol-
lution does not have to arise at the periphery of the anticyclone.
In order to evaluace the influence of synoptic conditions and air pol-
lution in a city, the following types of synoptic situations have been dif-
ferentiated:
Type A. Gradientless pressure field. Such situations take place
primarily in anticyclonic formations in the central portions of anticyclones,
in extensions and ridges of high pressure, in .nuclei, on the axes of crests,
and also in pressure cols and in diffuse cyclonic fields. This type is
characterized by calm or by a very weak wind. In the absence of substan-
tial solar heat, it is associated with a stable stratification of the atmos-
phere, and usually ground inversions.
Type I. Intermediate field. This is observed in the presence of a
directed pressure gradient. It is characterized by the location of the area
studied between a cyclonic and an anticyclonic pressure formation or at the
periphery of one of these formations. A stable preservation of wind of a
certain direction Is observed in this situation.
Type C. Cyclone. Characterized by cloudy weather, a reinforcement of
wind, and precipitation. In a more detailed analysis, it is necessary to
consider separately the front part of the cyclone, the warm sector, the rear
and the cold northern part. Such details are not discussed In the present
paper.
Considered below are synoptic situations in which a heavy and a rela-
tively light air pollution are observed. The analysis makes use of data on
several cities in which information on air pollution is relatively complete.
In particular, the frequency of these types of synoptic situations is dis-
cussed for cases of heavy and light air pollution at three stationary points
in the city of Magnitogorsk. In the calculations, use was made of selec-
tions based on data for daily concentrations of dust and sulfur dioxide in
air for 1961-1964 given in [11]. Cases of simultaneous presence of several
observations of high impurity concentrations (in no fewer than 4 samples
out of 6, their values were higher than the MFC) and low concentrations at
all points of the city were selected. The use of the above classification
of synoptic situations for the analysis makes It possible to bring out the
role of meteorological conditions in the creation of heavy air pollution
(Table 1) much more distinctly than in past studies [10, 11]. In Table 1,
In,e is the intermediate field with transport of air from the north and
east, and Ig from the west and south. Such a subdivision of type I is re-
lated to the'location of the main industrial enterprises in the northern,
northeastern and western parts of the city; in the case of In , the impuri-
ties are carried to the residential sections of the city, where stationary
observation points are located.
It is evident from Table 1 that the most characteristic situation pro-
moting a heavy general air pollution over the city is the type A situation,
i.e., a gradientless pressure field. This situation is observed in the great
majority of days with a general air pollution. Its frequency in these cases
-------
is almost 5 times aa high as on days with pure air. A second characteris-
tic situation in which a heavy air pollution is observed is In e, which is
quite evident when its frequency in both groups of days is compared. This
is determined by the characteristics of the transport of noxious impurities
from the main industrial enterprises of the city. The steady wind of the
western and southern quarters (situation type Ifl w) leads to the purifica-
tion of air. The same result is produced by the'passage of a cyclone.
Obviously, from the standpoint of air pollution, situation A is dangerous
because of the stagnation of air, and situation In e, because of the trans-
port of impurities from the sources of discharges £o the residential areas
of the city.
Table 1
Frequency ($) of Synoptic Situations on Days with Polluted
and Relatively Pure Air in Magnitogorsk
Half-year
Cold
Warm
Days
With polluted air
With olesn air
With polluted air
With olaan air
Synoptio Situations .
A
.66
13
(A
14
In,e
23
J
27
3
's,.
9
69
7
58
C
2
15
2
26
Since a sufficient quantity of observations was available in Magnito-
gorsk, it was possible to set more rigid standards for the selection of
cases of general air pollution over the city. It was possible to select
days when out of 6 observations (3 tests for dust and 3 for sulfur dioxide)
impurity concentrations above MFC were observed in no fewer than 5; at the
same time, a fog was usually observed at the municipal weather station, a
further indication of a heavy air pollution covering a considerable part of
the city. Forty-two such days were selected. Of these, a gradientless pres-
sure field was observed in 32 cases (76%). Thus, the danger of the type A
situation was revealed even more definitely.
As an example, we shall consider one of the periods of heaviest general
air pollution over Magnitogorsk, observed on 3-7 February 19,63.
Fig. 1 gives a composite kinematic map for 3-7 February 1963, and Figs. 2
and 3, a ground level map and an ATyOQ map for 5 February 1963. It is evi-
dent from the figures that this period is characterized by the presence of a
stationary anticyclone above the area considered. The pressure gradient was
absent not only near the ground, but also at the HyQQ level (about 3 km). Con-
sequently, a fairly thick layer with very weak winds should be observed. No
wind was recorded on the surface on 3-7 February 1963. The air temperature
ranged from -15 to -25°C., and a temperature rise took place only at the end
of the period. Low temperatures combined with calm Indicate the presence of
-------
a thick ground inversion [9, 12].
Fig. 1 Composite kinematic map tor the period
5-7 February 1965.
All of the above characterizes the role of gradientless pressure fields
in the creation of high impurity concentrations in cases of general air pol-
lution in a city. It is obvious that if one considers the concentrations of
impurities at individual points of the city, the frequency of the synoptic
situations discussed earlier should be less, since in these cases one can
observe local increases of concentrations that are not connected with the
general air pollution in the city.
Fig. 2. Surface waath«?r map for Fig. 3.
3 A.M., February 5, 19&3.
Map of absolute topography of
700 rab surface for 3 A.M..
February 5, 1963.
Synoptic analysis of cases of increased and decreased air pollution at
various points of the city was based on data of 3 stationary points in
Magnitogorsk (for dust and sulfur dioxide) and 5 stationary points in Rostov-
on-Don. On the basis of data of each calendar month (1961-1964), 25% of the
highest and 25% of the lowest values of the concentrations were selected.
Synoptic situations corresponding to a high and low air pollution at various
points of the city were considered for the cold (October-March) and warm
(April-September) halves of the year. Table 2 shows the frequency of synop-
tic situations of types A and 1.
-------
As is evident from the table, during the cold half of the year, an in-
creased air pollution in gradientless pressure fields is observed at each of
the eight points considered in the two cities. The frequency of the type A
situation ranges from 33 to 55%. However, 11 sets of observations (Table 2)
definitely point to one regular pattern: the type A situation during the
cold half of the year repeats itself 2 to 3 times more often at high impurity
concentrations than at low ones. An increased air pollution in gradientless
Table 2
Frequency (%) of Gradientless Pressure Fields (Type A) and Cyclones (Type C) for Heavy (l)
and Light (2) Air Pollution at Various Points of Magnitogorsk and Rostov-on-Don
City
Magnitogorsk
Roifc OT^*on™D oft
. Impurity
Dust
Sulpbur
DioOe
*
Duct
Point
1
•)
3
For all
Points
1
•)
3
For all
Points
1 •
•2 '
3
4
5
For all
Points
Cold Season
A
/
4,')
55
47
48
•10
40
35
38
44
51
3.J
3ft
41
42
2
13
14
15
14
12
IS
12
14
24
22 '
•>•)
21
-'4
23
C
/
5
5
4
4
6
7
8
7
4
0
0
0
0
1
2
13
11
12
12
1C
14
11'
14
7
7
5
•>
24
7
Warm Season
A
/
57
53
56
56
53
47
50
52
60
42
51
52
64
53
•j
42
34
35
37
38
4K
45
43
47
(55
48
40
57
51'
C
/
6
2
3
4
5
6
2
4
0
0
0
0
5
1
1
2
12
10
14
12
9
9
9
9
0
0
0
0
0
0
fields is not random, as can be readily demonstrated statistically, even if
one does not consider the extent to which the frequencies of type A situa-
tions differ for cases of high and low impurity concentrations, and con-
siders only the fact of high frequency, which took place in the type A situ-
ation in the presence of a high air pollution. It is obvious that if the
Indicated pattern did not exist, the theoretical probability F of an in-
crease in the frequency of gradientless fields at high concentrations as
compared to low ones would be %. It is known that the probability p of
random occurrence n of the events considered can be found from the formula
p - Pn.
In the case under consideration, for n - 11 and P » %, ps* 0.057..
Thus, the probability that the fact of Increased air pollution in
gradientless fields is not random in this analysis is 99.95%. During the
warm half of the year, the heavier air pollution in gradientless fields
shows up less distinctly. It is also apparent from Table 2 that mature
cyclones promote the purification of urban air by removing the impurities.
-------
The type C situation in the cities considered, particularly in Rostov-on-Don,
occurs relatively seldom, but its frequency is invariably higher in the pres-
ence of light pollution than heavy pollution.
As follows from the above, the role of gradientless pressure fields in
the creation of high impurity concentrations increases substantially when one
considers cases cf heavy air pollution at several points of the city simul-
taneously. This is evident from the above data and is illustrated by a com-
parison of Tables 1 and 2. This fact can be viewed in a new light by analyz-
ing cases of high impurity concentrations on the basis of data from various
stationary points of Magnitogorsk and Rostov-on-Don (Table 3).
Tablo 3
Frequency (%) of Gradientless Pressure Fields (Type A) in th« Presence of Heavy Air Pollution
Impurity
High impurity concentrations dur-
ing cold half of year no less
than
it . one
Point
At. two
Points
At. three
Points
High impurity concentrations dur-
ing warm half of year no leas
than
At . one
Point
At. two
Points
At. three
Points
Dust
Sulfur dioxide
Dust
46
36
42
56
41
44
76
56
Magnitogorsk
I 56
52
53
54
Rostov-on-Don
52 I 53
I » I
75
50
39
If one considers the heavier air pollution at various points without
taking the values of impurity concentrations at other points of the city into
account, the frequency of type A synoptic situations during the cold half of
the year for Magnitogorsk is 48% for dust and 387. for sulfur dioxide, and for
Rostov-on-Don, 42% for dust. These values are relatively high, particularly
since, as is evident from Table 2, they are 2 to 3 times higher than the
corresponding frequency for cases of light air pollution.
If cases of increased air pollution are considered at two points simul-
taneously (Table 3), the type A frequency increases by 3-8% based on three
series of observations. In substantial simultaneous air pollution at all
three points in the city, the frequency of the type A situation increases
more substantially, by another 8-20% and reaches 52-76%. This pattern is
observed by analyzing three independent series of observations.
During the warm half of the year, this pattern practically is not mani-
fested, and the type A situation is not always characteristic of heavy air
pollution.
Thus, gradientless fields are not associated with a local, but with a
general increase of air pollution on the territory of the city.
-------
It is characteristic that an increase in the concentration of impurities
in stagnant air is observed in a number of cities of various countries [6, 15,
16, 17, 23, etc.]. This leads to the conclusion that the accumulation of
noxious impurities in the city in this case takes place under different pol-
lution conditions.
The possibility of creating a heavy air pollution under stagnant condi-
tions as a result of high overheated discharges results from theoretical
studies of M. Ye. Berlyand [4]. The surface concentrations of impurities
from a source of fixed height are inversely proportional to the wind velocity.
However, as the wind velocity decreases, the effective stack height H in-
creases indefinitely, and the impurity concentrations decrease.
However, as was shown by M. Ye. Berlyand, under inversion conditions, for
a rising stream, a celling of height zn is created in the atmosphere, and the
effective stack height H cannot increase Indefinitely in the absence of wind.
In this case, very high Impurity concentrations may arise in the area of
influence of discharges from heavy industrial enterprises. Particularly un-
safe conditions are possible in the area of chemical-industrial enterprises
with cold discharges.
The lack of high impurity concentrations in gradientless fields during
the warm part of the year is owing to the fact that in summer no thick in-
version layers are formed in the areas under consideration and, therefore,
H may take very high values.
The very fact of increased pollution of city air under stagnant condi-
tions, primarily in stationary anticyclones, when the given conditions per-
sist for several days, may be considered established. A further step in the
study of this problem is to determine the extent of danger of the stagnant
situation in different seasons of the year, in different cities differing in
the characteristics of discharges of noxious impurities into the air, the
average level of air pollution, the relief, etc., and also in different
parts of the same city. The first details of this problem are given below.
The magnitude of air pollution with dust and sulfur dioxide under conditions
of stationary anticyclones in Moscow, Leningrad and Magnitogorsk during the
cold and warm halves of the year was compared with its average values. The
frequency of impurity concentrations above the MFC was taken as the charac-
teristic of air pollution. The results are given in Table 4.
It is apparent from Table 4 that the effect of increased pollution of
city air in stationary anticyclones manifests itself in winter much more
than in summer, and more for dust than for sulfur dioxide. Analysis of the
data also shows that the higher the average level of air pollution (express-
ed quantitatively by the average frequency 9% of impurity concentrations
above MFC), the greater the amount Ag by which this level is exceeded in
stationary anticyclones. Thus, in Magnitogorsk, where the average level of
air pollution during the period considered was high, A8 for dust reaches 34%.
At the same time in Moscow, where the air Is comparatively clean, Ag for
-------
Table 4
Frequency ($) of Impurity Concentrations above MFC as an Average (g). During Periods
of Stationary Anticyclones (g') and Difference Between these Values &g • g'-g)
Impurity
Dust
Sulfur dioxide
Part of Year
Cold
Warm
Cold
Warm
Moscow
g
10
7
4
9
g,1
17
8
22
7
ig
7
1
18
-2
Leningrad
g
21
19
tf
!«;•
g'
33
32
32
18
AB
12
13
13
-1
Magnitogorsk
g
39
57
25
29
g1
73
78
44
33
As
34*
21
19
4
dust amounts to 7% in winter and only 1% in summer. The correlation between
g and Ag is fairly close, even if one considers the observational data for
the cold and warm part of the year in combination (Fig. 4).
Thus, the stagnant conditions are more unsafe for a city with a high
level of air pollution. If the air in the city is relatively clean on the
average, stagnant conditions do not represent any particular danger.
30
20p
tot *°
0
o
O i i i i i 1
A'' :'2 JO 40 SO S0ff%
Fig. 4. Relationship between average value of
frequency of dust concentration above
UPC (g) and deviation from average under
conditions' of stationary anticyclones 05g).
In order to adopt specific measures for decreasing air pollution when a
stagnant situation occurs, it is necessary to know the extent of participa-
tion of various discharges in the creation of high impurity concentrations
and certain other factors comprising the physical mechanism of the phenome-
non studied. A solution of this problem requires special theoretical studies,
but the analysis of the experimental material, whose results are shown in the
present paper and in references [11, 12, 14, 15], permits a qualitative eval-
uation of some aspects of the problem.
-------
High impurity concentrations are simultaneously observed at different
points of the city. Thus, a heavy air pollution occurs over a consider-
able area. This indicates the relationship of the given process not only
to discharges of specific sources but also to the general meteorological
situation.
In the presence of a heavy air pollution over a considerable area of
the city, in addition to the absence of wind near the ground, the winds
are weak in a layer of the order of at least 1 km (there are indications
that this layer amounts to 3-5 km [14, 16, 19]). It is obvious that in
this case, the discharge of impurities from the upper part of the polluted
layer of air over the city has been attenuated. At the same time, a cer-
tain reinforcement of turbulent exchange in a limited volume over the city
as a result of the formation of a heat Island, breakdown of the lower part
of the surface inversion, and appearance of local air circulation [17, 22,
24, 25] causes the arrival of high discharges into the lower layer of air.
Impurities are washed out of city air with precipitation [11, etc.].
During a certain period of time after precipitation, the air is cleaner
than before it. This indicates the presence of an impurity concentration
outside the direct action of discharges, i.e., the creation of a background
concentration in the city.
An increase in air pollution during stagnation is manifested primarily
in the area where the pollution sources are located, and as the distance
from them increases, the impurity concentrations decrease sharply.
The enumerated effects, established on the basis of an analysis of
extensive experimental material, can be used for the physical solution of
problems of propagation of impurities in city air under stagnant conditions.
In addition, the results obtained are even now useful for the practical
achievement of pure air in cities; in particular, they are and will be used
for evaluating the state of air pollution on the territory of the Soviet
Union.
-------
LITERATURE CITED
I. D cp n 11 ii A' M. E. n Ap. 0 aarpiiJiieiimi aTMoa|)epu npOMUuijiciuiuMH uuCpocaMH.
McTcopoJiorun u ni,ipojioriin, Ais 8, 1963.
2. Bop-iuinA M. Ii. n ;ip. Hnoieuiioe HCCjicAouamie aTiwoapemioii AiuptpysHH npii nop-
n aiioMajibiibix yc-noBiinx. Tpy.ibi ITO, uu;i. 158, 1964.
3. EepJiHHA M. E. n AD. HcKoiopuc aKTyaflbiiue uonpocu ar.MoccpepHort
Tpy:iu ITO, uun. 172, 1965.
4. B c p :i :i u A M. I:. 06 onacnuix yc.ioBiitix aarpiuiteuHn aTMoapcpu
ubi6pocaMii. TpyAU ITO, nun. 185, 1966.
5. Biicp B. Toxmi'iecKan MeTeopoJiormi. Pn.'ipo/iicTeoiisAaT, J\., 1966.
6. 3arp)ijiiriino aTMoc<|>epuoro iin:i;iyxa. 803, .D.uopeu, uamift, >Kcneaa, 1962.
7. McTeopcMoriiH H aioMiiaw iiieprnn. HOA pcA.: ahaA. H. K. ^CAOpoaa. H/I, M., 1959.
8. CoiiitKiiii Jl. P. Ciinomii'itcKne yc^oann (popMiiposaHHti iiHaepcxft a niOKueM 500-
MeipouoM cJioe. TpyAU ITO, uun. 172, 1965.
9. Co lib K u n Jl. P. roAOuoii X.OA » ciiHonTHiccKBH oOycflouflCHiiocTb TCMnepatypHbix
npoipiuci) B HIIM e r a e B a E. A., T e p e x o B a K. M. K sonpocy o Meteopo-
•nonmecKofi oOycJioBJieiiiiocTH 3arpH3iieHiui Bu3Ayxa HBA ropoAanui. TpyAU TiO,
Bbin. 185, 1906.
11. Co H b KM n Jl. P. HoKOTOpMc pcsyjibTaibi CHiioiiTiiKO-KflMMaTOflorHyecKoro aiia^uaa
3arp>i3iieiniH Bo:i.iyxa a ropo/iax. TpyAU fFO, uun. 207, 1968.
12. CoMbKiiii Jl. P., Marueeua T. M. HeKuropue ocoGemiocTH (pppMHpoaaiiHfl IBM-
iicparypiibix npo(|)iiJieH B iiM/KHeM 500-MeTpOBOM woe HaA EnponeiicKofl reppHTOpHefl
CCCP. TpyAW Pro, Bbin. 207, 1968.
13. C o M b K u M Jl. P., ll a j\ n K o B A. B. 06 ofipaOoiKe n anu^iDe iiaGjiiOAeHHH aa 3a-
rpiunoiiiieM BOJAyxa u ropo:ia.\. TpyAU TTO, nun. 207, 1908.
14. LUeii'iyK H. A. AspocimoriTimecKHe yc^oaim ycTaiiOBjieiiiiii A/iiiTe^biibix ncpHOAOB
MaKCiiMa^i.iioru aarpiuiii'iniH Bo:i;iy.xa B r. KeMepouo. TpyAU HHMAK (HoBOCH6Hp-
CKiiii i|)iuii
-------
INFLUENCE OF THE RELIEF ON THE PROPAGATION OF IMPURITIES FROM SOURCES
M. Ye.Berlyand, Ye. G. Genikhovich, and 0. I. Kurenbin
From Trudy, Glavnaya Geoflz.
p. 28-44, (1968)
Observat. im. A. I. Voeykova, No. 234,
1. Studies of atmospheric diffusion of impurities pertain mostly to con-
ditions of a comparatively level and horizontally homogeneous underlying sur-
face. For these conditions, the basic regularities have been studied, working
formulas have been derived, and practical recommendations have been made. The
problem of the influence of the relief on the propagation of impurities has
been studied to a considerably lesser extent. Moreover, under actual condit-
ions, residential districts and industrial facilities discharging noxious
substances are frequently laid out on rugged terrain. The roughness of the
underlying surface causes a distortion of the structure of the airstream and
hence may cause changes in the distribution of the concentration of impurities
released by the sources.
A detailed analysis of these changes is very difficult at the present
time, since it involves the solution of a problem that is complex in mathe-
matical as well as physical terms. However, for the sake of a simplified
study of the influence of the relief on the propagation of impurities, a
series of simplifications may be introduced by using methods of solution of
corresponding problems in the hydrodynamics and physics of the ground layer
of air.
.4
One of the first attempts to consider the influence of topographical
irregularities in the calculation of the field of impurity concentrations was
made in [1]. The present paper constitutes a development of this work. Like
[1], the present study is based on a numerical solution of the equation of
turbulent diffusion in an area with a curvilinear boundary. Considering that
air currents in such a case are characterized by an inhomogeneous field of
both the horizontal and vertical components of the wind velocity, u and w,
this equation is written in the form
(1)
Here q is the impurity concentration, and kz and k are the vertical and
horizontal components of the exchange coefficient. The x axis is oriented
along the average wind, the y axis is perpendicular to it, and the z axis is
oriented vertically upward. The boundary conditions used are: the absence of
impurity flow on the underlying surface homogeneous in the direction of the y
axis; a surface that, in the general case, is described by the function
z-h(x); the presence of a source at height z=H; and a decrease of the impur-
ity concentration to zero at an infinite distance from the source.
-------
According to [2], we can set k» k0 u and switch from a point source to
a linear source, as is done for the conditions of a level area. Then
?~2^?-=e~^ . (2)
where q1 satisfies the equation
and satisfies boundary conditions similar to the conditions for q
z' — z-A(je); x' = xt (4)
whereupon (3) changes into
where u, w and kz are functions of the new variables x1 and z'. The form of
the boundary conditions remains unchanged.
To solve the formulated problem, one must know the distribution of dis-
placement velocities and exchange coefficient for dissected topography con-
ditions. However, the nature of the air currents under such conditions has
been little studied, both in theory and in practice. It is, therefore, ex-
pedient to consider some simple models for the variation of u and kz (w is
determined from u from the continuity equation) for the purpose of an approxi-
mate study of the effect caused by the irregularities of the underlying sur-
face. The form of equation (5) and of the boundary conditions after trans-
formation (4) is the same as for the given problem in an area with a level
ground surface. In a numerical solution of the problem with a computer, this
makes it possible to utilize the program employed in [1, 4] for studying atmos-
pheric diffusion above a horizontally homogeneous area.
In the case of a gently sloping relief, when the slope angles are small,
the streamlines of the air currents are virtually parallel to the underlying
surface. In this case, one can speak of a complete flow past the topographic
irregularities. At the same time, the wind velocity and exchange coefficient
are functions only of the height above the underlying surface: u » u[z-h(x)],
k » k[z-h(x)]. On the basis of the continuity equation
du , dw A (6)
k -t- — r - = U
ox ' du
we obtain
-------
„-.,£.
Equation (5) is now reduced to an ordinary diffusion equation for a level
area in the absence of vertical displacement velocities. This means that in
the case under consideration, the relief has no substantial effect on the
propagation of the impurity. Hence it may also be concluded that a change of
the concentration field under the influence of the relief is possible if u and
kz are functions not only of z' but also of x1. In this connection, the
following relations were used in [1]:
A,—*, (*)£(*-*(•*)!•
where u}(x) and k^(x) are functions whose values are based on data of micro-
climatic observations.
However, on the basis of general considerations, such a model cannot be
rigorous, since there must exist a boundary layer above which the influence
of the relief on the wind velocity field is slight. This approach is suitable
mainly for low sources, since model (8) leads to a distortion of the wind
field at large heights. In the present study, an attempt is made to overcome
these difficulties by two means. The first consists in replacing model (8) by
another model"that is physically more rigorous. The second means consists in
analyzing the. propagation of the impurity above an uneven underlying surface
in a potential flow. As we know, a potential flow differs appreciably from a
real flow, mainly near the underlying surface. It may be assumed, therefore,
that it will be useful in analyzing the propagation of an impurity from high
sources. The, concluding part of the article points out a further development
of the approaches discussed, which permits one to take into account both the
influence of the ground layer of air and the characteristics of the attenua-
tion of the influence of the relief at large heights.
2. In an approximate study of the velocity field of an air flow, use may
be made of the fact that on the basis of experimental data, under conditions
of gently sloping topographical features, the distribution of the wind veloc-
ity over the height in the ground layer of air is nearly logarithmic.
As an example, reference may be made to the results obtained in expedi-
tionary studies of atmospheric pollution in the area of the Shchekino State
Regional Electric Power Plant. These studies were made over the course of
several years/ in different seasons of the year, over rugged terrain with a
height drop up to 50 m at a distance of 1 km. The gradient observations were
made on a meteorological platform located on an elevation. Analysis of the
measurements indicates, as was noted In [12], that the logarithmic law of
change of the wind velocity and temperature with the height operates in this
case. Microclimatic observations made at two points simultaneously, i. e.,
at the top of the hill and at its base, also showed that at both points the
wind velocity profile was close to logarithmic.
-------
On the basis of these assumptions, let us consider a hill of height h«
(Fig. 1). In this case, the form of the underlying surface was described by
the following relationship:
*(*)'
A0for
0 for 4, < x
The selection of formula (9) for h(x) insures the continuity of the deri-
vative dh/dx at all points of the relief under study.
In accordance with the above-indicated considerations we shall assume
that the wind velocity in the incoming flow is
(10)
where u^ is the value of u at height z,» and z is the roughness of the under-
lying surface, which is assumed to be the same°at all points of the relief.
It is assumed that expression (10) also gives the wind velocity above the hill
at z>61(x) (Fig. 1).
Fig. 1
On the windward slope C for z<&i(x) and on the leeward slope for
(Fig. 1), the change of the wind velocity is given by the following formula:
108
-------
where u^(x) is the value of u at height Zj.
On the leeward slope D for 62(#)<3<61(a:)•, the wind velocity coincides with
the velocity of the flow coming from the elevated part of the hill, i. e., I
,-X-*(*)
log
where vt^Cx) can be determined from data on the damping of a disturbance in the
air flow, assuming that the spread of the upper plateau is sufficiently great
(in practice ^(x^u^l ^^) . The equations for the determination of 6^(x) and
62(00 are found from the condition of continuity of the wind velocity u at
these levels:
z0>
— „
= u,
Hence, <$i and 62 are expressed via the ratio of the function u^(x) to its
value in the incoming flow. Usually, on the basis of tnicroclimatic studies,
the values of this ratio are determined for a height of 1 m at certain char-
acteristic points of the relief [6]. Thus it is known that the wind velocity
at the top of the hill is approximately 20-30% higher than on the level area.
In the case under consideration, one can set uj_(x) - u.(l + Yl)for Y » 0.2-0.3.
At the foot of the leeward slope, the wind velocity is attenuated: u|(x) "
U!(1-Y2) for Y2 " 0.2-0.5. The values of u (x) at other points of the relief
are then described by an interpolation relation. To this end, it is conven-
lent to use a third-degree polynomial, which provides for an adequate smooth-
ness of the functions studied.
Recently, in order to obtain more complete characteristics of the wind
velocities in a hilly area, studies involving simulation of air currents were
performed in a wind tunnel [8].
With regard to the exchange coefficient in the incoming flow we shall
assume that
k r = v~{-k.z for
' lo (14)
=.-v /5/t for
where Vis the molecular viscosity of the air, h is the height of the ground
layer of air, ki0 being approximately proportional to u^ . As the wind
velocity under hilly relief conditions changes, so does K . It may be
approximately assumed that kz under these conditions also increases in pro-
portion to the height above the underlying surface and in proportion to the
wind velocity, i. e.,
-------
(15)
Here a- klo/ul » since the exchange coefficient ah a sufficient height
should be independent of the relief, we shall assume that (15) is fulfilled
for heights z at which kz
-------
5 XKM
Fig. 2
-------
5
600
600
ZOO
Fig. 3
such an influence of the source height may serve as a confirmation of the cal-
culation scheme considered. The higher the location of the source on the
windward slope, the lower the maximum concentrations. Conversely, the maxi-
mum concentrations increase more rapidly the closer the location of the
source on the hill to the leeward slope and the lower its position on the
leeward slope. The asymmetry of the influence of the leeward and windward
slopes is manifested here. It is due to the fact that the wind is reinforced
on the windward slope, and ascending currents arise which promote the upward
transport of the impurity; whereas on the leeward side the wind becomes atten-
uated, and descending currents appear, which transport the impurity from the
source downward.
When the source is located on the leeward slope, the concentration maxi-
mum is greater than on the level area, by approximately 30% for a stack height
of H •> 50 m and 20% for H = 200 m. Since the direction of the wind is variable
and the windward slope may become leeward and vice versa, it must be concluded
that the possible concentration maxima from a source of fixed height in a hilly
area are usually higher than on level land.
The above examples pertained to a relatively rugged area with a height
drop of only 50 m. As this drop and the steepness of the slopes increase, the
influence of the relief is naturally enhanced.
As another characteristic example of an irregular topography, a scarp was
considered. In this case, one can speak only of a single leeward (windward)
slope. At a distance of 1.5-2 km from the windward slope, its influence is
-------
•light, and, therefore, the given case may be considered special as compared to
the preceding case, assuming, for example, that the length of the elevated part
in Fig. 1 is sufficiently large. Fig. 3 shows results of the calculation of
the concentration when the source is located in front of the scarp in the pres-
ence of a wind toward the scarp (1), on an elevation in the presence of an
opposite direction of the wind (2) and for a level area (3). It should be
noted that the change in the concentration of the impurity from industrial
sources located in a hilly area may also be caused by the influence of a change
in the wind velocity and the initial ascent of the impurity above the stacks.
Thus, on the leeward slope, where the wind velocity in the lower layer is
attenuated, the relative increase of the wind velocity from the level of the
wind vane to the level of relatively high stacks is greater than in the plain.
Therefore, for the same wind velocity on the wind vane level, the initial
ascent for stacks located on the leeward slope will be less, and hence the
maximum of the ground concentration increases. According to the above results
for a hilly area as well as for the conditions of a plain [3, 5], one can de-
termine the value of the unsafe wind velocity at which the ground concentration
reaches its highest values.
3. We shall now consider potential flows over the irregularities of the
area. We shall use a known postulate of fluid mechanics, according to which
the influence of the viscosity on the flow of a fluid is chiefly manifested
in the boundary layer, which consists of a narrow region near the boundary of
the underlying surface. In the remaining portion of space, the flow of the
viscous fluid is close to inviscid, 1. e., potential, flow. Moreover, it is
noteworthy that in calculating the propagation of an impurity from a source,
it is most important to assign correctly the coefficients in the equations of
turbulent diffusion (1), (3) only in the region where the concentrations are
hi|jh. Indeed, when potential flows are used in the problem under considera-
tion, neglecting the influence of the boundary layer may affect its solution
only in the region of relatively high ground concentrations. However, the
condition of absence of impurity flow is assumed at the lower boundary, and
hence for sufficiently high sources, the concentration gradients in this
region are low. It may therefore be assumed that the errors in the assign-
ment of coefficients in the region where the ground concentrations are close
to maximum will have only a slight influence on the magnitude of this maxi-
mum. In addition,one should bear in mind that the definition of potential
flow in a region with a curvilinear boundary amounts to finding a conformal
map, which converts this region into a half-plane. The apparatus of the
theory of functions of a complex variable used for this purpose is much
simpler than that which is required even for an approximate solution of the
problem of the flow of a viscous liquid. .
An attempt to use the potential flow for solving problems of atmospheric
diffusion was made recently by Stumke [16, 17]. The latter discussed equa-
tions of turbulent diffusion with constant values of the coefficients for the
region with a piecewise linear boundary (of "searp" type), whose mapping on a
half-plane is affected by a Christoffel-Schwarz integral. These interesting
studies contain a number of useful results. However, the use of the
-------
Christoffel-Schwarz formula, 1. e., conformal mapping with a discontinuous
boundary value of the derivative, has led the author to some physically un-
substantiated conclusionu (for example, the appearance of infinitely high
concentrations, etc.). The approach to the solution of the problem under con-
sideration developed in the present paper permits the elimination of these
drawbacks. It consists in the study of the equation of atmospheric diffusion
with variable coefficients. Here the conformal mapping is effected by using
functions that do not result in discontinuities of the flow velocities, etc.
To this end, the analytical function
i (/) = being the velocity potent-
ial and its imaginary part ^ being the stream function.
As we know (see for example [9] et al.), the horizontal and vertical
components of the velocity of the potential flow in the region considered are
then expressed by the formulas
—-£—8-: 07)
d<»
a> = -,i- =
dz
The curves iKx, z) = const represent streamlines of the flow studied. In
particular, the line iKx, z) = 0 is the boundary of the region.
Equally complete information on the potential flow is contained by the re-
verse function
* 00 = •*(?, *) + «(?. *).
which effects the conformal mapping of the half-plane onto the physical re-
gion of flow.
If the components of the velocity field (17) are substituted into the
equations of turbulent diffusion and, in addition, a definite model is taken
for the exchange coefficient (for example, it is related to the wind velocity),
the problems of interest to us can, generally speaking, be solved only numeri-
cally. However, a number of conclusions may be obtained analytically. To this
end, in the diffusion equation it is necessary to switch from the variables
(x, z) to the "flow" coordinates and ip. If, in the equation obtained, the
terms describing the diffusion transfer along the flow are neglected, as com-
pared with the convective terms, and if one sets 1^= kz, the turbulent diffu-
sion equation (3) will take the form:
-------
•*•*•-¥-• (18)
The initial and boundary conditions can then be written in the form:
-t/i) for ?=*H, i. e.,
a model which is a natural generalization of those usually employed for k2,
the solution of the problem (18)-(19) may be written in the form
As in the case of a horizontally inhomogeneous underlying surface
(cf. [15]), the point $m, where the maximum of the ground concentration is
reached, is determined from the condition 3qf «Q for tym Q . It is evident
from (20) that the following relations should hold:
(21)
g , . ,
Substituting it into (20) we find that the maxiumum ground concentration
q'm depends solely on
-------
is the value of function ^ on a streamline that, at an infinite distance from
the curvilinear portions of the boundary, is located at distance HQ from the
underlying surface.
At the same time, at finite distances, the necessary geometrical source
height H is the distance from the streamline ^ « ^H to the underlying surface
' (23)
This expression may be rewritten in the form
tf = //0r(#0, ?//)• (24)
where r (H0, 4> ) is a correction factor dependent on the position of the source
relative to the relief and to the source height H..
The form of the function r(H , H) is completely defined by the geometry
of the flow in the region considered. After some slight changes, the above re-
sults may also be obtained for the model
Let us now consider the conformal mapping of the half plane onto a region
with a boundary close to the one shown in Fig. 1. To do so we shall make use
of the fact that the Zhukovskiy function . 1 / , Q2\ effects the mapping
t-T\s + Ti
onto the half-pjane of a region whose boundary is made up of a real axis and
of a semicircle of radius a with its center at the origin of coordinates.
The semiellipap whose minor semiaxis coincides with the (-a, a) segment of
the real axis is then converted on the plane into a curve having a zero angle
of entry into the real axis. Combining Zhukovskiy 's map with the map
s = a + m"|/ a2 — a2, , which converts the half-plane into the region bounded by
the real axis and the semiellipse with semiaxes a and ma, we find the desired
map in the form
-1-
here
where hQ is the height of the hill and a is its half-width. The branch of the
root is fixed by the condition imyV-^>Ofor Ima>0.
Using (25), one can construct the potential flow whose complex potential
is given by the relation.
^A"' (26)
-------
constant A being determined from the requirement that at an infinite distance
from the obstacle (i. e., in the incoming flow), the velocity of the potential
flow be equal to v. Hence
Separating the real part from the imaginary part in (25) and setting
= 0, we obtain a parametric equation of the boundary of the region for which
the potential flow was constructed:
(28)
z = 0.
It can be readily seen that the function z = h(x) de terminable from (28)
has a continuous first derivative, so that the region of flow is sufficiently
smooth. The velocity components obtained from (17) undergo no discontinuity
anywhere.
2.M
-------
The geometry of the constructed potential flow is illustrated in Fig. 4,
which shows the results of a calculation of the streamlines, performed on a
UraX-4( computer. Pig. 4 a pertains to the case hQ • 50 m, a • 500 m; and
Pig. 4'b, to the case hQ - 100 m, a - 500 m.
In addition, for several points of the relief, Fig. 4 shows vertical pro-
files of the horizontal component and the flow velocity u referred to the vel-
ocity of the incoming flow v (dashed curves). As should have been expected,
the calculations show that near the top of the hill, the flow velocity in-
creases (the streamlines are condensed), whereas at the foot of the hill the
flow velocity decreases (the streamlines are spaced out).
0,8
Pig. 5
a —A0-50m, tf —/to-100 m,e — /!„—100m, (Depression)
1 — Ht-fQ m, ?—tfo-100 m, 4 —Wc-200 m,
-------
After the calculation of the streamlines, it is not difficult to determine
the correction factor r entering into (24) and to apply it to the necessary
source height. The corresponding results are shown (Fig. 5 a, b, and c) for
sources located at various points of the leeward slope of the hill shown in
Fig. 4 a, one curve pertaining to the source with height HQ • 50 m and the
other to HQ - 100 m. It is evident that when the source is located at the top
of the hill, where the streamlines are condensed, rl. If one considers that the maximum ground concen-
tration is inversely proportional to the square of the source height, one
finds that the largest variations of the maximum ground concentration may
reach 25-50% for HQ = 50 m and respectively 20-40% for HQ = 100 m.
Comparison of Figs. 5 a and 5 b shows that as the height of the hill hQ
or the steepness of the slopes hn/ a increases, the correction for the relief
increases. For example, for HQ = 50 m, the maximum correction factor r is 1.16
at hQ - 100 m and 1.1 at hQ •» 50 m.
The results are close to those obtained in the preceding section by an-
other method.
A considerable disadvantage of the potential flow scheme discussed, par-
ticularly as compared to the scheme of the preceding section, is the symmetry
2M
1SO
100
SO
0
-50
-too
Fig. 6
of flow on the windward and leeward slopes. However, if one considers that as
the wind direction changes there is also a change in the relative position of
the slopes, the results obtained may be used for an overall evaluation of the
influence of the relief without separating the windward or leeward sides.
The conformal map (25) after substitution of -hQ for hQ may be used to
construct a potential flow above a depression whose half-width is equal to a,
and whose depth is h.Q. The streamlines of this potential flow for the case
-------
hQ * 100 m and a " 500 m are shown in Fig. 6, and the correction factor r in
Fig. 5 c, in which one curve pertains to HQ « 50 m and the other to HQ • 100 m.
As is evident from these figures, in the case of a depression the maximum
value of r for HQ • 50 m is 1.32, which corresponds to a 70% increase in the
maximum concentrations of the impurity, whereas for a hill of the same height
and width, the maximum value of r is 1.18.
The results obtained may be extended to regions with boundaries of more
complex form. A relatively broad category of maps is obtained, for example,
by means of Cauchy integrals [9]
1 "i / (s) ds
— J -hh-' (29)
The form of the function £(s) is determined by the equation of the bound-
ary of the physical region of flow, but it is simpler to take some function
£(a), and to obtain the equation of the boundary from (29). In particular,
one can thus obtain art expression for the potential flow in the vicinity of
two or more hills lined up in a row.
4. In conclusion, we shall consider the possibility of development of
these approaches with the aim of providing them with a more rigorous basis and
of broadening the scope of their application.
A natural extension of work on the consideration of the influence of tur-
bulent viscosity in the vicinity of the underlying surface is the derivation
of a solution of the boundary layer equation. Above a curvilinear surface,
such an equation may be obtained from a system of equations of motion if flow
coordinates ($,$) are used and small terms are discarded, as was done, for
example, in [13]. For a sufficiently smooth topography, the boundary layer
equations thus obtained are of the form
-If- *---: <30>
where u and w are the velocity components of the flow along the directions 4>
and \|i, the boundary conditions for which are given by the relations
for»B~u: «-«-u;.
for
(31)
is the Lame coefficient of flow mapping; the velocity on the external boundary
of the boundary layer is
-------
(32)
The formulated problem may be solved numerically by using the method
described, for example, in [1], However, an additional preliminary simpli-
fication of this method is possible if a substitution of variables analogous
to the Dorodnitsyn transformation flO] is carried out in (30). We set
flfc; (33)
From the continuity equation there follows the existence of a function
G such that
If the function v is defined by the equality
dG . dO
Switching to the variables of (33) in equation (30) and considering that
the Bernoulli equation is satisfied in the external flow, we finally obtain:
du . du d . H du , ,, dV . (35)
*-3r+*-sr=-Kk--- ^ ;
du , Ov _ n
-ar+^c — °-
The boundary conditions for this equation are
forC — 0: « = -y =
For a sufficiently gentle topography, the ratio H/H/j depends relatively
little on £ and may be assumed equal to unity. The problem of flow past a
curvilinear shape is now reduced to the problem of the boundary layer on a
plane wall with a given pressure gradient, which has been studied in some
special cases. Thus, for example, for a constant k and an exponential de-
-------
where
HJ = (
1 dV
(37)
Tables of the function *' (n;B) are given, for example, in [10]. For
m » 0, a solution of the Blasius problem of flow around a flat plate is ob-
tained from (28); the case m>0 corresponds to different parts of the wind-
ward slope, and the case -l0.0904 in the given class of flows, there can be no separation at any values
of m, and at lower values of n the solution is applicable only up to the sep-
aration point.
As an example, Fig. 7 shows graphs, calculated by means of (37), of the
dependence u/V on the dimansionless argument for the values 3 • 1» 0, -0.14,
and -0.2 (respectively, n « 1, 0, -0.065, and -0.0904). The same figure gives
the experimental points obtained by S. M. Gorlin and I. M. Zrazhevskiy [7] by
subjecting a model of the hill shown in Fig. 1 to a test in a wind tunnel of
MOSCOW State University.
The most interesting conclusion may probably be reached by combining
both of the approaches presented in this paper, i. e., by splicing together
the solution of the boundary layer equations with the potential flow velocities.
-------
In so doing, to a first approximation, the reverse influence of the boundary
layer on the external flow may be considered by shifting the streamlines of
potential flow to a distance of the order of the displacement thickness.
Since on the windward slope the potential flow velocity decreases with in-
creasing height, while the wind velocity in the boundary layer increases with
the height, it becomes understandable that the longitudinal component of the
wind velocity should reach its maximum value at some distance from the under-
lying surface. This is supported by experimental data both for solid walls
[8] and for a disturbed surface [15]. At the present time, quantitative
estimates of this effect are being made.
Having thus obtained the field of the horizontal and vertical velocity of
the flow, one can obtain a numerical solution of equation (3) in accordance
with the scheme presented above.
LITERATURE CITED
1. B e p n n n A M. E., F e n it x o u M q E. Jl., fle M b si n o B H y3iin. Tpyww ITO, oun. 172, 1065.
2. Be p^ mi A M. E. K reopim TypGy;ieiiTnoM AM(|><|>y3Hit. TpyA" ITO, BMII. 136, 1963.
3. B e p n « n A M. E., F e ii H x o u im E. J1., 0 u n K y n P. H. 0 pac'ieie aarpjniienusi
aiMocipepbi BbiOpocaMH us ALIMOUUX rpyC sjieKXpocraiiuHH. TpyAw ITO, aun. 158,
1964.
4. B e p a a H A M. E., r c H it x o H n >i II. /I., »TI o >K KH n a B. n., 0 H u K y n P. H. HHC-
HKHiioe iicc/iOAOBaiiiic aTMocijiepiiofi ;;m|)(|>yymi npu nopMajibHbix n aiiOMaJibiiux
ycjiOBiiflx cTpaTiii|>iiKauiin. TpVAbi ITO, uun. 158, 1064.
5. B e p a n H A M. E., O H H K y n P. H. n:ui'iccii; c ii c K ii ii H. M. Mo;ieJiiipoBaiuic Boanyuuibix TeMenurt nu;i
pt:^be(j)OM. CM. iiacr. cO.
8. 3 p a >K c B c K H A M. M., K o p o in c n K o B. H., M e n H K H. P. HccjieAOBamie B-nnx-
IIMH pas.iH'iiitJx ijjopM peju/eijia na xapaKiepHCTiiKH BoaAyunioro noTOxa u aspoAHiia-
MiiiecKofl tpyCe. TpyAw FfO, BUU. 207, 1968.
9. JlaupeiiTbea M. M., Ill a 6 a T B. B. MeTc;iu reopnii (pyiiKiuiil KovinjieKciioro nepe-
MeiiHoro. Ou3MaTni.i, Al. 1963.
10. Jl o ii u H ii c K H ii .1. F. JlaMMiinjuibiii iiorpaiiii'iiiufl cjioii. 4>u:iMaTrH3, M., 1962.
II. FlacKoiiOB B. M. CTan.napnian nporpaMMa ;i;')i peuieuitn ypaBiicHiifi norpamimioro
c^o«. CO. «llHCACinibie MCTO;IW B ranoaoii ;inn«MiiKe», Bun. II. H:JA. MTV, M., 1963.
12. PacTopryeaa T. 11. XapaKTepwcTHKH MereopoflorHMecKoro pe>KiiMa u TypCyjieiiT-
noro oGMena u npxaeMHOM cnoc no jiaHiibiw rpa.'uieiiTHbix Ha6;iio;ieHHH. TpyAU
fro, Bbin. 172, 1965.
13. C AC 3 K n ii H. A. 0 npucTeiio'iiioM norpaimmioM cJioe B6^H3H n^acTHHKH, oOreKaeMOti
noiOKOM co CPHBOM ctpyfl. BccTiinK MTV, cep. I, .No 5, 1964.
14. Co no M a T H n a M. M. O B.'mniiiiu pejn>ca na MeTeopo^orHNccKiie xapaKTcpucriiKii
B npn3CMiio.M c/ioc i)O3;i,yxa. TpyAu TPO, BUR. 172, 1965.
15. Fra nsis J. R. D. Windstiess over water surface. Quart. J. Royal Met. Soc., v. 80,
Ni 345, 1954.
16. Stum ku II. Ucriicksiclitiiif;un|r vorcinfaclitcr Gcliindctypcn bolder Berccliiiunfj dcr
turbulvntcn Ausbreitwif,' von Scliornstcingasen. Staub. Bd. 24 (1964), S. 175/182.
17. Stumke H. Untcrsuchun^cn zur turbulunten Ausbrcitung von Schornsleingasen
uber niciit ebcncm Gelande. Staub. Bd. 26 (1966), S. 97—104.
-------
ABSORPTION OF GASEOUS IMPURITIES BY FOG DROPLETS
V. V. Klingo and R. I. Onikul
From Trudy, Glavnaya Geofiz, Observat. im. A. I. Voeykova, No. 23.4,
p. 80-84, (1968)
It has been observed that fogs are frequently associated, in the ground
layer of air, with the highest content of noxious substances discharged by in-
dustrial enterprises, automobile transportation, and other sources. In London,
Los Angeles, New York, and some other cities, under certain meteorological con-
ditions, fogs change into smogs, which have an extremely adverse influence on
the health of the population.
The various aspects of the influence of fogs on the diffusion of atmos-
pheric impurities have been treated theoretically in a number of studies [1,
2, etc.].
The turbulent diffusion of a gaseous impurity from a point source in the
presence of fogs is approximately described by the equation,
,i~ A Aft A firt
~ *1- (1)
Here u is the wind velocity along the x axis, kz and k.. are respectively
the vertical and horizontal components of the turbulent diffusion coefficient,
the x axis is parallel to the main direction of the wind, the y axis is per-
pendicular to it in the horizontal plane, the z axis is vertical upward, and
q is the impurity concentration at points not directly located in the zone
where the impurity is washed out by separate drops. Calculations quoted in
the literature [2] show that equation (1) is valid for characteristic values
of the number and dimensions of the fog droplets.
The characteristics of the structure of the atmospheric boundary layer
are taken into account by the variation of u and kz> and the use of numerical
methods makes it possible to carry out the investigation for arbitrary approxi-
mations of these functions.
The term aq in equation (1) takes into account the absorption of the im-
purity by the fog, caused by the presence of a polydisperse system of water
droplets in the air, and may be expressed as follows:
-------
N/r\ Is the distribution function of the fog droplets in size (radii) r.
To date the A. Kh. Khrgian - I. P. Mazin distribution function [7] has found
extensive applications.
P(r) is the total amount of impurity absorbed per unit time by a fog
droplet of radius r. The determination of this quantity is a complex problem,
since the fog droplets are in constant motion. However, even for the stable
stratification characteristic of fogs, the microscale of the atmospheric
turbulence substantially exceeds the size of the largest droplets. As a re-
sult, the displacement of the droplets together with the air stream does not
affect the quantity P(r), which is determined only by the molecular diffusion
of the impurity toward the droplet. For this reason, the magnitude of P(r)
depends only on the flow around the fog droplet because of its settling by
gravity. Neglecting the effect of flow around the droplet
Here D is the coefficient of molecular diffusion of the impurity in air.
In deriving this formula, the boundary condition used is the hypothesis of
complete absorption of the impurity on the surface of the droplet, which is
usually fulfilled. V. 6. Levich [5] points out that for gases highly soluble
in water, the rate of their absorption on the surface of the droplet is de-
termined only by the rate of diffusive supply, i. e., the processes considered
follow diffusion kinetics. Formula (3) has been known for a long time and
widely applied in various investigations: [1, 2, 5, 6, etc.].
In [l] and [2], a formula is given for calculating the coefficient a,
based on the function proposed by Khrgian-Mazin for N(r) and formula (3) for
P(r). Its use has made it possible to solve the problem of influence of
fogs on the diffusion of impurities to a first approximation. The object of
the present paper is to find a correction to the quantity P(r), caused by
the flow of an airstream around a droplet during its settling, from the so-
lution of the equation of molecular diffusion for a moving medium:
Ac = PeV grade. (4)
Here c is a dimensionless concentration of the impurity near the droplet,
normalized to the quantity q; the quantity c is a function of the dimensionless
radius vector of point r, normalized to the droplet radius RQ; the velocity
vector of the motion of the droplet relative to the medium V is normalized to
the settling rate of the droplet UQ^ The Peclet number Pe is the determining
parameter for the process studied.
Pe = -<>. = Re Pr; Re^-fL; Pr==JL. (5)
Here v is the molecular viscosity of air, and Re and Pr are the Reynolds
and Prandtl numbers. The quantities v and D for air are close to one another,
i. e., PrasL, Pe*&e [5, 6]. For droplet radii RQ characteristic of a fog and
settling rates UQ determined by them, the values of Pe and Re are substanti-
ally less than unity and reach 0.2-0.3 for only the largest droplets. Under
-------
such conditions, approximate formulas of Stokes and Oseen are known for V [4].
The Stokes formula was obtained by neglecting the inertia terms in the equation
of motion for a viscous liquid and applies only to very small distances from
the droplet surface. The Stokes velocity distribution was used in the study of
many problems [6], [8l, [9], similar in mathematical formulation to the problem
of interest to us (evaporation of droplets, heat emission from spherical bodies
exposed to blowing, etc.)* As indicated in [4], Oseen's solution for low given
Re values yields better results at a considerable distance from the droplet than
does the Stokes solution.
We shall utilize the smallness of the parameter Pe and seek the solution of
equation (4) in the form of a series in powers of the small parameter e«Pe
i + ••• (6)
Substituting (6) into (4) and equating terms in £ of the same order of
smallness, for the zero approximation to the desired solution we obtain the
Laplace equation
for the first approximation, the Poisson equation
AC[ = V grad c0-~l. (9)
The solution of (7) for a spherically symmetrical region is of the form
For boundary conditions (9) for P(r), formula (3) results from (10), i. e.,
as should have been expected, the zero approximation describes the absorption
of an impurity that is stationary relative to the medium of droplets.
For C£ at i>l, homogeneous boundary conditions are assumed.
On the basis of the first approximation, we shall evaluate the correction
to the absorption of an impurity by a droplet caused by settling of the latter.
The solution of equation (S) is written in general form via the Green
function [3]
-------
Here Q is the radius vector of a point with variable coordinates located
inside the area of solution and do is the volume element
(12)
GI and GO are respectively the singular and nonslngular parts of the Green
function.
The singular part of the Green function has the following form:
where
... CO . ...
Tr^TT-S^^ PWCOS°): (14)
Pwx) are Legendre polynomials, 6 is the angle between vectors r and Q, and r
ana p are the moduli of these vectors.
where H(x) is the Heaviside unit function,
Of°r X<0~>
for
In order for the nonsingular part of the Green function GQ to satisfy the
boundary conditions, it must be chosen in the following form:
fp . (16)
From (10) it follows that
(17)
We shall subsequently use a spherical coordinate system whose origin is
at the center of the droplet, and the polar axis is directed vertically down-
ward.
Equation (14) will then be rewritten as
co r
TF=TT-2o*('>. P)[^ (cos »,)/>, (cos &,) + (18)
» ~1
+ 2 2 [* + "!! cos (
-------
In deriving (19) It was considered that
f, 2 COS/l(^-?,)^ (C08dr
and • .
The formula for the radial component of the dimensionless relative wind
velocity V according to Oseen is
<20>
— .
When this formula is used, better results should be expected than when
the Stokes formula is employed, since c^ is expressed in terms of the velocity
field over the entire space, and not only in the area adjacent to the droplet.
In order to solve the problem of absorption of an impurity by a droplet,
it is necessary to define the total flow of impurity PI
(21)
It is much simpler to find P^ than to determine the solution for ci.
Indeed, if one considers that because of the orthogonality of the Legendre
polynomials the contribution to PI is made only by the term of the series
entering into (19) corresponding to k- 0, then
(22)
After some simple but cumbersome transformations we find that
/>ira_^.p0PeRe^-4.p0Re», (23)
where PQ is the flow of impurity onto the droplet in the zero approximation.
Finally,
/>«P0 + PlSsip0(l-i-RePe).
From the solution obtained it follows the motion of fog droplets slightly
decreases the absorption of the impurity from air, but this correction does
not exceed a few per cent. This permits the use of formula (3) in studying
the characteristics of diffusion of gaseous impurities in fogs.
The results obtained in the present paper may be applied to the evaluation
of the trapping of an impurity by cloud droplets, to the study of evaporation
-------
of fine droplets, etc. In particular, from the solution obtained it follows
that at low Re numbers and assuming an Oseen-type flow, the evaporation of a
falling droplet is somewhat less than the evaporation of a stationary droplet,
As in the case of the problem considered above, this is also because of the
fact that the first-approximation correction has a sign opposite to the sign
of the flow in the zero approximation.
LITERATURE CITED
1. B e p n si H A M. E., 0 >i H K y n P. H., P H 6 o a a F. B. K reopnH atMOC(j)epHofl
B yc-noBHHx TVMaxa. TpyAU ITO, sun. 207, 1968.
2. 3 H M H H A. T. BbiMHBaHHe paAHoaKTHBiiux aspoapjieft 113 aTMoc(pepw ocaAKaiini. C6.
«Bonpocw HAepHOft Meieopo^orHH*. AroMHaAar, M., 1962.
3. HaaHeHKo R. H., COKOJIOB A. A. K^accHiecKan Teopiis no-ns. TocTexHaAaT,
M.-^.. 1951.
4. KOM H H H. E., KiiCe^b H. A., Pose H. B. TeopeTUMecxan niApOMexauHKa. HacTbll.
H3MaTrH3, M., 1963.
5. JleBHI B. F. H3HKO-XIIMHieCK4H THApOAHHaMliKa. ll3MaTrH3, M., 1959.
6. 4>yKc H. A. HcnapeHHe H pocr xane^b B raaootipaaxoft cpeae. Hsa. AH CCCP, At.,
1958.
7. X p r H a H A. X., M a 3 n H H. FI. O pacnpeAeJiemiH Kane^b ryMaua no pasMepaM a 06-
. TpyAU UAO, sun. 7. 1962.
H. L,
8. F r i s c h H. L, Steady-state diffusion into a streaming sphere at low Reyholds num-
ber. J. Chem. Phys. 22, 123, 1954.
9. K r o n I g R., B r u i j s t e n J. On the theory of the heat and mass transfer from
a sphere in a flowing medium at low values of Reyholds' number. App. Sc. Res.
vol. A. 2, N 5-6, 439. 1951.
-------
RECORDING OF DUST CONCENTRATIONS IN THE ATMOSPHERE
S. A. Kon'kov
From Trudy, Glavnaya Geoflz. Observat. im. A. I. Voeykova, No. 234,
p. 181-187, (1968).
In organizing a system for control of the degree of atmospheric pollution
with industrial discharges, it is very important to develop methods for re-
cording the concentration of noxious substances in the ground layer of air.
At the present time, determinations of dusrt and ash concentrations in the
atmosphere are made by means of the suction method [1], which yields discrete
values of the weight concentration averaged over 20 minutes.
The accuracy of the method is low, and large random errors are possible.
An increase in the accuracy and decrease in the interval of sampling are
associated with considerable technical difficulties.
The use of instruments and techniques providing for automatic recording
and processing of data makes it possible to obtain time and space character-
istics of concentration fields with a great accuracy and reliability.
Among the methods for studying aerosols that offer the possibility of a
simple conversion of the measured quantities into an electric signal and
hence its automatic recording (ionization, radiometric, electric quantities,
etc.), the optical methods, which are relative, have become comparatively
popular. They permit the determination of the concentration without precipi-
tation of the solid phase of the aerosol, and quick response measurements in
an undistorted flow.
Methods which involve the use of precipitation of the solid phase on a
filter make it possible to increase the sensitivity and also to perform a
further analysis of the aerosol studied (chemical, gravimetric, dispersion
analysis).
A convenient method is the determination of the concentration from the
optical density of the solid phase of the aerosol deposited on a filter, since
by obtaining the relative value of the concentration, one can switch to a con-
stant calibration of the instrument and to the determination of the concentra-
tion by weight. The humidity content of air has no appreciable influence on
the optical density of the filter, but depends on the physical properties and
the particle size composition of the aerosol studied.
A filtration method using an automatic collection of samples from the
atmosphere and a photometric determination of the aerosol concentration are
-------
used in many countries. In Czechoslovakia, an instrument has been constructed
for automatic sampling and measurement of aerosol samples, i. e., an automatic
recording aerosol concentrometer [3]. It operates on the principle of ultra-
filtration by means of a tape membrane filter 15 mm wide which during the
sampling moves continuously at rates from 6 cm/hr to 18 cm/hr. Simultaneously
with the sampling, photometric readings are taken on the tape (the absorption
of light by the aerosol track on the tape filter is measured) in order to ob-
tain the variation of the aerosol concentration with time. Each value is
averaged over 2 or 6 min. Thus, the instrument records the variation of the
concentration of aerosols in the course of 8-24 hr, and the sample on the
filter is kept for further processing, mainly microscopic. In determining
the weight concentration for each type of aerosol, it is necessary to carry
out a multiple calibration of the instrument.
The weight of the sample of solid-phase aerosol on the filter is deter-
mined by measuring the change of the optical density of the filter. The light
flux Io, which has passed through the filter alone, and the light flux I, which
has passed through the same filter with the collected solid-phase aerosol I,
are related by the Lambert-Beer law as follows:
/- = /„,-*', (1)
where k is the light absorption coefficient and I is the path length in the
given medium.
Known instruments of this type [3] can record only relative values of the
aerosol concentration. However, according to. the existing experimental data,
the values of coefficient k are constant for 24 hours at the same location
with a sufficient degree of accuracy. Their change with time can be related
to the daily variation of meteorological elements and to the change of the
conditions of discharge from the sources of particles. On this basis, a
method for recording dust: concentration that provides a constant calibration
of the instrument by the gravimetric method (during a certain period of time)
with continuous recording of the optical density of the dust sample on the
filter is proposed in the present paper.
The optical density of the filter with the collected sample is given by
the relations
D--=\s-f- it-ill 0 = s/, (2)
where e=0.4343fc.
The weight of the sample of solid-phase aerosol on the filter may be
expressed as
where P0 is the weight of the filter alone, P is the weight of the same
filter with the sample, which occupies an area S, and y is the specific
gravity of the sample on the filter. It then follows from (2) that
-------
i-A
For the weight concentration 1s=~y~~ we obtain from (3)
,
£) = 8_. „„,,, tf-
where 70 is the volume of air pumped through the filter and reduced to
standard conditions.
It is apparent from (4) that the weight concentration of the aerosol
q may be determined via the optical density of the filter, knowing the
coefficient kt which is a quantity characteristic of each aerosol and de-
pends on its physical properties and dispersity.
The method essentially consists in the following. The tape filter is
weighed before and after the sampling, processed in a photometric instru-
ment to determine the decrease of the light flux in relative units, then
A "
the calibration coefficient A/= -> where ^.V, — is the total
change of the light flux, is determined. The calculation of the concentra-
tion at any instant of time is defined as Q - MN^ , where N. is the change
of the light flux on the given portion of filter.
To record the dust concentration over a longer period of time, use is
made of an intake tube permitting collection of the sample on the filter,
suction of air through the filter, and rewinding of the tape filter. Sub-
sequent gravimetric and photometric analyses are carried out in the labor-
atory, thus simplifying the processing of the tapes. If necessary, the
sampler may be combined with the photometric instrument. In this case,
the density of the sample is measured and recorded during the sampling.
The sampler includes an aspirator with an air flowmeter and a cart-
ridge with a tape transport system. The tape filter is wound Inside the
cartridge from the feeding reel to the take-up reel by means of a synch rous
motor via a reducer. The tape passes in front of a slit with a nozzle,
from which the air, after passing through the filter, is sucked into an
air tube connected to the flowmeter and aspirator.
To test the method, samples were taken during an 8-hour interval on
a fine-fibered LFS-250 tape filter. The transport rate of the filter was
6 cm/hr, the slit size was 10 x 30 mm, and the exposure of each portion
of the filter, 10 min. The aspirator provides for an air flow of 50 Z/min
and is designed for operation on 220 V alternating current.
The system for photometric processing of the filter tape (Fig. 1)
consists of the tape transport mechanism of a recording photometer using
the simplest differential circuit. The sensing elements used were FSK-2
photoresistors, and the illuminator was an 8W incandescent bulb.
-------
The unbalanced signal is fed into an EPP-09 recorder.
This method differs from similar ones developed in other countries in
the fact that the sampling is made on NEL-4 tape filter, which has better
filtering properties. The photometric instrument uses a simple measuring
circuit including FSK-type sensing elements.
Tests of the combined sampler and photometric instrument were also per-
formed. The use of round AFA-30 filters of FPP fabric is possible for taking
samples during a 20-minute period. In this case, there is no need for a tape
transport system, the photometric analysis is performed simultaneously with
the sampling, but the recording is made in the form of traces of integrated
values of attenuation of the light flux as the solid phase deposits on the
filter. The circuit of the photometer is identical to the one described above.
A drawback of this instrument lies in the limitation of the time of sampling
on one filter and in the difficulty of eliminating the influence of sunlight
on the measuring circuit of the photometer.
In the development of the instrument, considerable attention was concen-
trated on the selection of the filtering material, since its characteristics
determine the accuracy of the method. The applicability of filters to the
mechod is determined by their mechanical, filtering and optical properties.
Tests were made on filters of cellulose filter paper, membrane filters,
and filters from fine-fiber polymer materials FPP-15, NEL and LFS developed
at the L. Ya. Karpov NIFKhl. The cellulose-paper filters have a number of
serious disadvantages in both filtering and optical properties, and in gravi-
metric analysis. Membrane filters are characterized by a high filtering
efficiency and an adequate mechanical strength, which makes it possible to
increase the accuracy of the measurements considerably as compared with the
cellulose-paper filters. However, their hydraulic resistance is very high,
and coarse particles deposited on the filter may fall away. Filters made of
fine-fibered filtering materials are characterized by a high filtering
efficiency at high linear suction velocities and by a moderate hydraulic
resistance.
i
Disadvantages of the FPP-15 fabric are its low optical homogeneity, low
mechanical strength, and the possibility of separation of the fibers during
the suction of air. These disadvantages have been eliminated in NEL and LFS
filters, which surpass the membrane filters in optical homogeneity.
The general accuracy of determination of the weight concentration is not
a constant quantity in the absence of a rigid calibration of the instrument.
The accuracy category of the recording system is 0.5, and the stability of
the photometric circuit, 95%. The reproducibility of; successive processing
steps of the same tape lies within a single division. The overall sensitiv-
ity based on the weight concentration, obtained by processing ten filters,
amounts to an average of 0.013 mg m3/div. Without preliminary photometric
analysis of the filter alone (before sampling), the magnitude of the optical
inhomogeneity of the filter alone is within the total error of determination
-------
i
T--P--TT--
. -!''.» .1
Fig. 1. Photometric instrument for processing filter tape.
of the concentration. Fig. 2 shows graphs of the change in the optical
density of tape filters made of different filtering materials. The observa-
tional material is insufficient for a definitive evaluation of the filters,
but one can reach the preliminary conclusion that the KEL and LFS type
filters surpass the others in optical homogeneity. The technical character-
istics of these filters, based on the data of [2], are given in the table.
As a result of the tests, NEL filters 50 mm wide were taken for subsequent
work.
Measurements made with different light filters by absorption (Fig. 3 a)
and by a reflectometric method (Fig. 3 b) repeat the measurements of absorp-
tion of incident light flux without a light filter with sufficient accuracy,
indicating the homogeneity of the optical properties of the particles collec-
ted on the filter.
The results obtained permit the assumption that by perfecting the
measurement circuit one can increase the accuracy of the recording of the
dust concentration in the atmosphere.
The models of instruments described require certain structural improve-
ments, but on the whole they meet the requirements of the method. These in-
struments were used in Leningrad in the autumn of 1967 to carry out measure-
ments of dust concentration, an analysis of which is given below.
-------
The Intake tube was located at a height of 2 m above the surface of
the ground In an open area. There were no heavy sources of industrial
atmospheric pollution within a radius of 2-3 km. The samples were taken
in September-November in the daytime (9 A.M.-5 PiM.) with the exception
of days with precipitation (20 series in all).
div
£ =,__,__
rTV>-T-/rT"r--r?-r-r--fn
10 20 30 W SO SO 70 80
cm
Pig. 2. Change of.the optical density cf tape filters from
various filtering materials.
a - NEL filter; b - cellulose-paper filter;
o - LFS filtur; d - membrane filter.
Table
Parameter
Resistance. at air flow rate of
0.06Z /mm cm2, mm HoO
Breakthrough coefficient, %
Tape weight, ng/crf-
Fiber diameter, y
Working temperature range, dog.
NEL
1,6-30
10
6
1,5
50
LFS
1,6-W
5
0,3tO,l
0,5^0,1
50
The data obtained from the recording of dust concentration in the
atmosphere in the course of the day were compared with the meteorological
conditions. The highest values of the concentrations, 0.4-0.9 mg/m^, were
usually observed in the morning hours. In the second half of the day, the
magnitude of the dust concentration decreased. Of the total number of
observations, it is possible to isolate cases where the average concentra-
tion was 0.1-0.2 mg/m3 and underwent little change during the entire day.
At the same time, the meteorological conditions were characterized by a
relatively stable west-east transport at a wind velocity of 4-15 in/sec
in the lower 500-meter layer.
-------
01
IO
n, div.
100r-
30 -
80 -
70
60
SO
30
20
10
J I L
J L
to
20
30
_L L
SO
J L
n, div.
/OO r-
30 -
80 -
60
30
20
10
V
I I I I I I
60
70
20
30
A I I I I I L_J
SO
GO
70
Fig. 3a. Measurements of change in the optical density of tape filter performed with different light filters, based
on the absorption of light flux:
1 - with red light filter; 2 - without light filter? 3 - with green light filter; 4 - with blue light filter.
Fig. 3b. Measurement of change ir, the optical density of tape filter performed without light filters based on
-------
As an example, Fig. A gives the results of processing of the recorder
tapes (the sampling was made on November 20, 21, and 22 1967).
The method of measurements described above enables one to obtain the
values of the weight concentration of dust with the necessary accuracy and
to record the cycle of concentration change simultaneously with the sampling
and afterwards.
20 ' 21 22 NOV. I, cm
Pig. 4. Dust concentrations in atmospheric air
recorded November 20, 21, and 22 1967
in Leningrad.
LITERATURE CITED
1. HiiCTpyKTiiiiiio-MCTOjui'itiCKiii- yK(i:i:iiiiia no opraiiiciaimn iicc.ne.rtouajiiiH aTMOc<|)epnoro
uo3;iy.\a. Akvinn, M., i'JUl
2. C n y p a w ii K. u ;i|>. Aspoaojni. Aro\;mnut, IOG7.
3. Polydorova M. Autoniulifchu Kt-ffisirifrffcrSt zur Mcssung der Konzcnlralionen
von Acrosolt'ii. Iiitcnialionales symposium Libico, oklobcr, 1965.
-------
COEFFICIENT OF TURBULENT EXCHANGE IN THE GROUND LAYER IN THE DAYTIME
DURING THE SUMMER IN VARIOUS GEOGRAPHICAL REGIONS OF THE USSR
V. P. Gracheva
From Trudy, Glavnaya Geofiz. Observat. im. A. I. Voeykova, No. 234,
p. 152-161, (1968)
In the study of the diffusion of impurities in the atmosphere and in the
solution of a great many other problems it is important to know the character-
istics of distribution of the vertical component of the turbulence coefficient
in the ground layer of air under various climatic conditions.
It is known from theoretical studies [1, 2] and studies involving analysis
of experimental material [3] that, for example, in the presence of discharges
of noxious substances into the air from high smokestacks, the impurity concen-
tration at some distance from the source increases with an intensification of
turbulent exchange. A heavier air pollution at high values of the turbulence
coefficient is also observed in cities, where sources of discharges of differ-
ent heights are present [4]. For this reason, the study of the maximum inten-
sity of turbulent exchange in different geographical regions is of substantial
interest. According to the available literature data, the maximum turbulent
exchange is usually observed in the superadiabatlc state of the atmosphere,
which usually occurs in summer at noontime.
Some patterns of distribution of one of the characteristics of turbulence
in the ground layer were studied in [5] over the territory of the USSR under
these conditions. The object of the present paper was to make an additional
study of the characteristics of this distribution by using data on the verti-
cal component of the turbulence coefficient, a component calculated by the
heat balance method. This method is characterized by a certain degree of
objectivity, and is independent of many hypotheses underlying other methods
of calculation of the turbulence coefficient. By analyzing a large volume of
experimental material [6, 7, etc. ] it has now been established that in the
lowest layer, which is of the order of several meters, the change of air
temperature and humidity with the height is adequately described by a loga-
rithmic law.
Representing the variations of air temperature and humidity with the
height in accordance with the logarithmic law and assuming the turbulence
coefficients for heat and moisture in the ground layer to be approximately
equal in magnitude, we write the following formula for the vertical component
of the turbulent exchange coefficient at a height of 1 m:
*»-«(/?-(>).
Here R is the radiation balance at the level of the underlying surface in
-------
rt
cal/cm min; Q is the heat flow between the underlying surface and the sub-
jacent layers of the soil in cal/cm^ min; ot= 0.74 . where At0 and At" mb
At +1.56Ae
are the differences of temperatures and absolute humidity of air between the
heights of 0.5 and 2.0 m. The numerical factors 0.74 and 1.56 were obtained
by substituting the values L»600 cal/g, p=1.293 x 10~3 g/cm3, cp=0.24 cal/g
deg and p»1000 mb.
To calculate the turbulence coefficient from formula (1), as in [5], use
was made of observational material of heat balance stations for the 1 P.M.
period in July during the period of operation of the stations from 1955 to
1967. Up to 1961-1962, the tables of gradient observations contained all the
necessary initial data for the calculation of kj for each day: the measured
values of R, At and Ae, calculated from the measured temperature and humidity
of air at two levels, and Q, determined from the temperature and humidity of
the soil according to the method presented in [8]. The calculation of the
values of the turbulence coefficient for each day is therefore relatively easy,
particularly since the value of a in (1) has been tabulated. From the values
of ki calculated for each day, one can readily compute the mean monthly values
of the turbulence coefficient for individual years and then the average for a
number of years.
From 1962 on, the calculation of daily values of the heat flow in the
soil was not made at the stations; its calculation for each day at a large
number of stations in the course of several years is very laborious. It is
of interest, therefore, to examine the possibility of using mean monthly
values of the initial data for calculating the turbulence coefficient. On the
basis of observational material of 30 stations (pflOO cases) located in differ-
ent geographical regions, the turbulence coefficient was calculated for a
number of years for 1 P.M. in July from both the mean monthly values of the
initial data in individual years k'i (R, Q, At, Se) and daily values k"i(R, Q,
At, Ae). Before 1962, the mean monthly values of the meteorological para-
meters on the network of heat balance stations were not computed. They were
calculated by first using the mean monthly values available from a number of
stations, calculated under the direction of T. A. Ogneva and kindly supplied
to the author. From 1962 on, the heat flow between the underlying surface and
the subjacent layers was calculated daily at all of the above-indicated stat-
ions. Results of the comparison of mean monthly values of ki for the indi-
vidual years are shown in the form of points in Fig. 1. Mean monthly values
of k] calculated by the heat balance method from initial data averaged over a
month are laid off along the x axis, and values of ki calculated from daily
data and then averaged over the month are laid off along the y axis. Of the
100 cases considered, in only 10 was the relative averaging error
T.ffi 'Q,M, &)-*,(/?. Q, A/, V)
£,
-------
It is evident from Fig. 1 that deviations from the bisector are observed
on both of its sides, with a certain exaggeration of the £' yalues calculated
from initial data averaged over the month.
0,2
0,1
0.1
Fig. 1.
The calculation of the turbulence coefficient by the heat balance method
from both daily and mean monthly initial data may in some cases involve con-
siderable errors, for example, at low values of the difference between the
radiation balance and the heat flow into the soil or at low values of the dif-
ferences in air temperatures and humidity at the two levels. Allowing for
the accuracy of the measurement of meteorological parameters with network in-
struments (0.01 cal/cm2 min. for R and Q and 0.2° C. and 0.2 mb for At and
Ae), possible relative errors in the calculation of the turbulence coeffic-
ient from formula (1) were determined for different values of the initial
data (Fig. 2).
In determining the turbulence coefficient from formula (1), only cases
assumed to contain a relative error of no more than 40% were considered.
In addition, the computation of mean monthly values of ki from the calculated
daily values was made only when the number of k-, values computed with a rela-
tive error of 40% or less was greater than or equal to 10 per month. In
addition to the above-mentioned 30 stations, the data of heat balance obser-
vations of 39 stations (total of 69 stations) were also considered for the
same period. The calculation of the turbulence coefficient based on data
of these stations was made only on the basis of mean monthly initial data.
-------
The great majority of the stations are located on the European territory
of the USSR, with the exception of its northeastern part, and also in Kazakhstan
and Central Asia, while approximately one-third of all the stations are located
on the territory of Siberia and the Far East. The series of kj_ values calcu-
lated for the individual years during the above indicated observation period
from 1955 to 1967 at the different stations were found to be different as a
result of both the limitations adopted in the treatment ( A/SI ^40%), and an un-
' ki ^
coordinated opening of the heat balance stations, some of which were opened in
the last 2-3 years.
R-O cal/m2 min.
Fig. 2. Possible relative
errors (%) of the calcula-
tion of the turbulence
coefficient (k) by the heat
balance method.
0,2-
The present paper uses only the data of the existing stations, which are
considered more or less representative of the heat balance observations. At
37 stations, the kj values calculated for the individual years were averaged
over 3 years or more; at 28 stations, over 1 to 2 years, and at 4 stations,
because of the above-indicated limitations of treatment, the turbulence co-
efficient could not be determined.
The manner in which the mean value of the turbulence coefficient devi-
ates from the period of averaging can be determined by using, according to
[9], a successive averaging over all the longer periods beginning with the
last year of observations. To this end, data on the turbulence coefficient
were selected at several stations with longer series of observations. Aver-
age values for 1, 2, 3, etc. years were calculated starting in 1967. Re-
sults of the calculation are shown in Table 1. Average values of ki from
the longest observation period at our disposal (they were different at differ-
ent stations) were arbitrarily taken as the norm. Deviations (%) of the mean
values for 1, 2, 3, etc. years from the norm (part II of the table) were then
calculated.
-------
It is obvious from the table that for a relatively short averaging period
(1-2 years), the deviation from the norm does not exceed 20% at most stations,
and that deviations in excess of 30% are observed at only 2 stations.
Table 2 gives mean values of the turbulence coefficient for increasing
periods of averaging and deviation from the norm (according to the data of
[5]). Analysis of this table shows that at the majority of the stations con-
sidered, deviations of the norm for averaging periods of 1 to 3 years also do
not exceed 20%, and at only three stations out of 26 are the deviations less
than 30%. It should be noted that the averages for short periods (1-3 years)
frequently differ from averages for longer periods by no more than 10%. Hence,
short series of observations can be used without a large error, especially
when the aim is to determine the basic patterns of distribution of some element.
Values of k^ computed for several years or even for 1 to 2 years give some
idea of the distribution of the turbulence coefficient in the ground layer over
the territory of the USSR.
The average July values of the turbulence coefficient for 1 P.M. and
values of kj/ui, where u-|_ is the wind velocity at a height of 1 m, are shown in
Table 3. Values of k"i were calculated from mean monthly initial data for indi-
vidual years and then averaged over the indicated period. The k^ values were
calculated from daily initial data, then averaged over the month and over the
entire period.
It is apparent from the table that the highest values of the turbulence
coefficient in the ground layer (0.20-0.25 m2/sec.) in July at noon are observed,
as in [5], in the desert of Central Asia, Kazakhstan, regions of the lower Volga,
and in the south of the Ukraine. In the central regions of the European terri-
tory and also in the foothills of the Southern Ural, Pamir, Tyan'-Shan', Altay,
and Sayan, the values of the turbulence coefficient obtained by the heat balance
method were somewhat higher (0.15-0.20 m2/sec.) as compared to ki (0.12-0.15 m2/
sec.) for the same regions in [5]. As far as Transbaykal'ye, northern Siberia,
and the northeast of the European territory are concerned, the ki values here
were approximately the same in magnitude as in [5] and equal to 0.12-0.18 m2/sec.
The highest values of the turbulence coefficient are found in the regions where
the highest wind velocities are observed in July, whereas on the contrary, the
values of the ratio kj/uj in these regions are minimum, of the order of 0.05-
0.06. The maximum kj/u^ values (0.10 and slightly higher) are observed in the
foothills, and are of the order of 0.06-0.08 on the remaining territory. The
ki/uj values in different regions of the USSR together with other parameters
are necessary for refining the coefficient characterizing the influence of
meteorological conditions on the dispersal of noxious impurities in the atmos-
phere fioL
-------
Table 1
Bean Value of the Turbulence Coefficient (k-|) for Various Averaging Periods.
Year
1967
1966
-1965
196-1
1963
1962
1961
1960
1959
1958
1957
1956
1955
«
o'
•g
>
ft
•3
.«
•H
Z
0.113
0,122
0,131
0,128
0,139
0,138
0,130
0,140
d)
J3
c
(0
1
o
0.164
0.160
0.179
0,175
0,174
0,172
0,167
0,167
^
1
0
0.251
0,262
0,237
0,234
0,217
0,207
0,203
>
£
{/]
0,210
0,232
0,226
0.236
0,230
0,224
0.235
in
"8
i
o
h
«
a.
0.234
0,164
0,154
0.166
0,155
0,166
§
O
I*
g
»
'0.164
0,177
0,150
0,151
0.157
0.158
'>
A
01
H
0.210
0.191
0,205
0.197
0.191
0,197
•g
c
• H
«H
O
3Z
0.185
0,209
0,205
0,216
0,208
0,203
t
eO
1
0.130
0.148
0,161
0,161
0,172
0.180
•g
«
. -a
>H
0,162
0.160
0.175
0.164
0.158
,
0.166
Si
en
0.175
0,157
0,165
0,182
0.169
1
• H
O.
0,241
0,201
0,216
0.202
0.235
1
t£
0>
t,
0>
CD
0.276
0,235
0,227
0,242
0,229
?
O
g.
•H
C
0
•g
•<
0.161
0.180
0,205
0,226
0,230
0
EH
O.VJ-16
0.207
0,235
0,207
0,209
^
1
K
0.23-5
0.200
0,199
0,201
0.213
°
1
£
0.115
0.136
0.166
0,188
0.189
o .
c
• H
•8
1
o
ft
0.165
0,182
0,178
0,184
0.172
Deviation (#) of the mean value of the turbulence coefficient from the norm
Averaging
Period
1
2
3
4
5
6
7
8
—19.3
—12.8
-6.4
—8.6
—0,7
—1.4
-7.2
0.0
-1.8
-4.2
7.2
4.8
4,2
3.0
0.0
0.0
23,6
29.1
16.8
15,2
6.9
2.0
0.0
—10.6
1.3
—3.8
0.4
-2,1
—4.7
0,0
41.0
—1.2
—7.2
0.0
-6.6
0.0
5.1
12.0
-5.1
—4,4
—0,6
0.0
6.6
-3.0
4.1
0.0
-3.0
o.o
—8.9
3,0
1.0
6.4
2.5
0,0
—27,8
—17,8
-10.6
—8.9
-4.4
0.0
•
-2,4
-3.6
5.4
-1.2
—4,8
o.o
3.6
-7)1
—2,4
7.7
0.0
2,6
—14,5
-8.1
-14.0
0,0
20,6
2.6
-0.9
5.7
0.0
—30.0
— 2i,8
—10,9
-1.7
0.0
17,7
—1,0
12,4
-1.0
o.o
10.3
—6.1
—6.6
—5,6
o.o
-39,2
-28.0
-12.2
-0.5
0,0
-4,1
5.8
3.5
7.0
0.0
-------
Table 2
Mean Value of the Turbulence Coefficient (k1) for Various Averaging Periods.
Year
1966
1965
1964
1963
1962
1961
1960
1959
1958
1957
1950
1955
1951
Sobakino
0,145
0,159
0,159
0,156
0,143
0.13S
0.132
0,131
0,130
0,130
0,130
0,130
Riga
0,143
0,132
0,126
0,127
0,126
0,123
0,124
0,124
0,128
0,128
0,132
0,135
Nikolayev-
skoye
0,166
0,184
0,186
0,180
0,171
0,173
0,173
0,168
0,165
0,164
0,162
Torzhok
0,136
0,158
0,152
0,143
0,148
0,148
0,151
0,148
0.14S
0,147
0,148
Pavelets
0,138
0,160
0,158
0,161
0,160
0,157
0,156
, 0,151
0,150
. 0,150
0,154
Smolensk ;
0,160
0,170
0,157
0,159
0,161
0,154
0,119
0,149
0.1 -'.7
0,146
Askaniva-
Nova
0,170
0,175
0,174
0,173
0,172
0,171
0,179
0,181
0.1S7
0,190
Kuybjfc.
shev
0,149
0,156
0,156
0,146
0,144
0,146
0,146
0,140
0,146
0,150
Artem
Island
0,196
0,190
0,205
0,197
0,194
0,199
0,207
0,207
0,206
0,205
Solyanka
0,165
0,163
0,151
0,166
0,160
0,157
0,157
0,158
0,165
0,164
Tiyri-
koyya
0,142
0,151
0,139
0,134
0,130
0,130
0,130
0,134
0,139
Kostroma
0,108
0,128
0,133
0,136
0,127
0,121
0.12S
0,193
0,134
Gi«ant
0,140
0,146
0,146
0,14!
0.154
0.15"
0.15S
0,145
0.142
—I
I
deviation
of the mean value of the turbulence coefficient from the
Averaging
Period
1
2
3
4
5
6
7
8
9
10
11
12
11,5
22,3
22,3
20,0
10,0
6.2
1.5
0.8
0.0
0,0
0.0
0,0
5,9
—2,2
-6,7
—5,9
—6.7
—8,9
—8,2
—8,2
—5,2
—5,2
-2,2
0,0
2,5
13,6
14,8
11,1
5,6
6,8
6.8
3,7
1,8
1.2
0,0
—8,1
6,8
2,7
—3,4
0,0
0,0
2,0
0,0
0,0
0.7
0,0
—10,4
3,9
2.6
4.6
3.9
2,0
. 1,3
—2,0
—2.6
—2,6
0,0
9,6
16,4
7,5
8,9
10,3
5,5
2,1
2,1
0,7
0,0
—10,5
—7,9
-8,4
—9,0
—9,5
—10,0
—5,8
-4,7
—1.6
0,0
—0,7
' 4,0
4,0
—2,7
—4,0
—2,7
—2,7
—2,7
—2.7
0,0
—4,4
—7,3
0,0
—3,9
-5.4
—0,5
1,0
1,0
0,5
o.o
0.6
—0,6
—7,9
1,2
—2,4
—4.3
—4,3
—3,7
0,6
0,0
2,2
8,6
0,0
—3,6
-6,5
—6,5
—6,5
—3,6
0,0
—19,4
—4,5
—0.7
1,5
—5,2
—9,7
—4,5
—3,0
0.0
—1.4
2.8
2,8
1.4
8,4
11.2
11,2
4.2
0,0
-------
Table 2 (Coot'd)
Year
1966
1965
1964
1963
1962
1961
1960
1959
1958
1957
1956
1955
1954
Beki-
Bent
0,198
0,185
0,167
0,167
0,172
0,171
0,1 S4
0,187
0,190
Tandy
0,221
0,216
0,202
0,222
0,222
0,220
0,229
0,2.36
0,242
Borispol'
0,180
0,182
0,166
0,163
0,165
0,171
0,171
0,168
Poltava
0,162
0,187
0,175
0,167
0,169
0,164
0,166
0,167
Kanennaya
Step'
0,134
0,131
0.128
0,130
0,142
O',147
0.14S
0,162
Beregovo
0,147
0.116
0,129
0,131
0.133
0.132
0,129
0.129
Nolinsk
0,169
0,150
0.150
0.147
0,141
0,138
0,148
0.149
Dushanbe
0,128
0,136
0,129
0.127
0,124
0,126
0,127
0,125
Frunze
0,146
0,163
0,154
0,154
0,154
0,156
0,157
0,157
Yakutsk
0,139
0,157
0.155
0,152
0,153
0,150
0,148
0.148
Fort
Shevch-
enko
0,167
0.16S
0.165
0.178
0.174
0.179
0,177
Vys.
Dubrova
0,136
0,116
0.118
0,115
0,113
0,112
0,107
Kaloykovo
0.195
O.I9S
0,203
0.204
0.202
0,201
0,201
oo
I
deviation (#) of mean value of turbulence coefficient from the norm
Averaging
Period
1
2
3
4
5
6
7
8
9
10
11
12
4.2
-2.6
—12,1
—12,1
—9,5
—10,0
-3.2
-lie
0,0
—8,7
—10.8
—16,5
—8,3
-8,3
—9,1
—5,4
—2,5
0.0
7.1
8,3
—1,2
—3,0
—1,8
1,8
1,8
o.o
-3,0
12,0
4,8
o.o
1.2
—1,8
0.6
0,0
-17,3
—17.3
—21,0
—19,8
—12.3
-9,2
—8,6
o.o
14,0
—10,1
0.0
1,6
3,1
2,3
0,0
0,0
13,4
0.7
0,7
—1,3
-5,4
—7.4
-0,7
o.o
2,4
8,8
3.2
1,6
-0,8
0.8
1,6
o.o
-7,0
3.8
-1.9
-1,9
—1,9
—0.6
0,0
0,0
-6.1
6.1
4,7
2.7
3,4
1,4
0.0
0.0
«
—5,6
—5,1
-6,8
0,6
-1,7
1,1
0,0
27.1
8.4
10.3
7.5
5.6
4.7
0,0
—3,0
-1,5
1.0
1,5
0,5
0,0
0,0
-------
Table 3
Mean Values of the Turbulence Coefficient (k^) at a Height of 1 m Calculated by
the Heat Balance Method and kj,/ui Values for \ P.M. in July.
Station
Khibiny
Petrozavodsk
Arkhangelsk
Kargopol1
Ust'Vym'
Voyeykovo
Nikola yevskoye
Tiyrikoyya
Riga
Pinsk
Smolensk
Toropets
Torzhok
Kostroma
Nolinsk
Cheben'ki
Sovetsk
S. I. Nebo]'sin
station
Pavelets
Kamennaya Step1
Borispol1
Poltava
Beregovo
Askaniya-Novh
Nikitskiy sad
G igant
Astrakhan'
Kalmykovo
Ural'sk
Yershov
Kuybyshev
Kushnarenkovo
Rudnyy
TseVinograd
Ogurtsovo
Karasust
Balkhash
Aydarly
Churuk
Fort Shevchenko
Tandy
Beki-Bent
Ak-Molla
Chardzhou
Terraez
Fergana
Dushanbe
Frunze
Telavi
Nakhichevan'
Artem Island
Solyanka
Khakasskaya
Kyzyl
Khomutovo
Chita
Mangut
Skovorodino
ToJstovka
Primorskaya
Yakutsk
Turukhansk
Tura
Oymyakon
Verkhoyansk
*l
M2/seo.
O.M6
0.166
0,196
0,140
0,161
0,210
0,140
0,187
0,169
0,235
0,212
0,180
0,186
0,158
0,203
0,160
0,200
0,180
0,200
0,149
0,194
0,208
0,229
0,230
0.305
0,203
0,224
0,223
0,200
0,200
0,235
0,242
0,213
0,199
0, 162
0.249
0,274
0,216
0,180
0,241
0,209
0,190
0,241
0,201 .
0,211
0,231
0,167
0,196
0,194
0.23K
0,205
0,1«0
0,178
0,1 N8
0,1*9
0,178
0,152
0,172
0,177
0,246
0,166
0,122
0,095
0,135
0,115
*i
«2/sec.
0,149
0,151
0,196
0,158
0,148
0,187
0,192
0,227
0,196
0,168
0,193
0,204
0,239
0,212
0,210
,
0,203
0,214
0,220
0,197
0,158
0,172
0,186
0,206
0,200
0,198
0,180
0,174
0,198
0,153
0,115
*!/«,
M2/sec.
0,002
0,065
0,094
0,070
0,074
0,072
0,056
0,074
0.074
0,103
0,082
0,072
0,071
0.074
0,083
0,050
0,058
0,078
0,080
0,035
0,000
0,075
0,111
0,080
0,179
0,088
0.101
0,004
0,001
0,060
0,108
0,104
0,004
0,054
0,057
0,068
0,005
0,076
'0,055
0,049
0,058'
0,070
0,070
0,087
0,087
0, 196
0,142
0,125
0,104
0,099
0,053
0,079
0,109
0,109
0,096
0,083
0,071
0,090
0,071
0,086
0,080
0,068
0,048
0.079
0,053
Averaging Period
1963, 1966—1967
19G2— 1967
1964, 1960
1904
1906—1967
1967
1900— 1907
1960—1907
1956, 1959. 1901, 1907
1903—1967
1965-1967
1961, 1965-1967
1958, 1905—1967
1956, 1958, 1960—1901,
1963, 1905
1957. 1959, 1961—1962.
1965, 1967
1967
1965-1967
1966-1967
1963, 1905—1967
1957
1958, 1965-1966
1958, 1904, 1900—1967
1959, 1901 — 1964
1956, 1959, 1964, 1966—1967
1960—1907
1 958, 1 960— 1 963, 1 905— 1 967
1958, 1903-1964, 1967
1962—1963, 1966
1967
1900—1907
1955, 1960—1961, 1964—1967
1960-1907
1962—1963, 1965—1967
1905-1966'
1905, 1966.
1966—1967
1905—1907
1904, 1907
1905—1967
1966
1959, 1903, 1965—1967
1966—1907
1965—1966
I960
1966—1907
1904—1967
1959, 1961 — 1967
1904—1967 . •
1902—1906
1906
1907
1960, 1963—1967
1965-1967
1905—1967
1903—1967
1904—1967
1966—1967
* 1962—1965, 1967
1967
1965—1967
1957, 1900, 1902, 1964—1965,
1907
1907
1965 "
1967
1904—1900
-------
Literature Cited
I. B c p ji >i ii A M. E., T c n ii x o 11 n M K. Jl., O ii it K y n V. M. O pac'ieic .•larpn.iiiciiiiti at-
Moc(|icpu ubiOpocaiMii ID MMMOUMX rpyC) j^cKipocTamuiii. Tpynu I'l'O, nun. 158,
106-1.
2. OepJMiiiA M. Fi. n ;ip. Miicncpuoii ;ui<|>(pyjiiH npu iiop-
Majii.iiux n anoMa.nbiiux ytvioniuix CTpaTiKJuiKamiK. TpyAU FFO, uhin. 158, 1064.
3. fopoiiiKo 15. I). llcKUTUpuc ncoCciinocTii paciipocTpanoi.'iin iipeAnux npiiMeceii OT
HIilCOKIIX IICTOMIIIIKOII U n.lllllCIIMOCTII OT CIIIIOIITIIKO-ML'TC'OpOAOril'ICCKIIX (j)aKTOpOU.
Tpy;iu n'O, i,un. L>07, IOCS.
'I. Cnni. KIIII Jl. P., M 11 ji ii K o n /t B. Od (io|).if)OTKc n an;i.iu:ic> ii;i0^io;iennii aa :ia-
rpii.'iiicuiu'M iioi/iyxa n roponax. Tpy;iu M'O, nun. 207, 1!)(>8.
5. Fpa'ioiia B. FI. rcoi'pai|)ii>iccKoe paciipcACJiciini; KOi(|)(|)iiunt;iiTa TypfiyjicimiocTii B npu-
ru-MiiOM c;ioc aT.vioci|)cpi>i ^C-TOM H /uieiiiidc upoMii. Tpy;iui fl'O, uun. 207, 1008.
6. FopoiiiKO b. 15. ii jip. Mcicopoflorii'iccKHp iiafijnoAemui npw HccJiCAOuaiiini npoMuuj-
;ic'iini4x :iarp>i iiii'iiuii npu ic.Miiuro CJIKH uo:i ii;i6jiio,npiniiiM n oiipeACJiciuiio coc'raujiiiiouaix TLMIAO-
uoro Oa.'ianca. rn.li|)OMrTi>oii.i;iaT, Jl., liMM.
0. ApojAou O. A.,-0 p ji o n a B. U., Ill u e p U,. A. K uoiipocy 06 niiTiiMajn,iioii HJM-
TeJii.uocTii in-pi OAU ocpcAiieniiii npn KJiiiMaTujioni'iccKiix iiccJieAOuainiHx. TpyAU
Pro. uun. 181, 1068.
10. VKanaiuoi no p«c
-------
PHYSICAL PRINCIPLES OF CALCULATION OF DISPERSAL OF
INDUSTRIAL DISCHARGES IN THE ATMOSPHERE
M. Ye. Berlyand and R. I. Onikul
From Trudy, Glavnaya Geofiz. Observat. im. A. I. Voeykova, No. 234,
p. 3-27, (1968).
1. Introduction
One of the chief applications of studies of atmospheric diffusion is
the calculation of dispersal of industrial discharges in the atmosphere.
Studies along these lines have laid the basis for the consideration of
meteorological conditions in the design and operation of enterprises dis-
charging noxious substances into the atmosphere, and for determining the
permissible discharge and the height of smokestacks at which the required
air purity is ensured in the surrounding area.
To date, many studies have been published dealing with atmospheric
diffusion and related investigations of turbulent exchange. In the
Soviet Union, the most extensive studies have been conducted at the
A. I. Voeykov Main Geophysical Observatory (GGO), the Atmospheric Physics
Institute, the Applied Geophysics Institute, the Leningrad Hydrometeorolog-
ical Institute, and others. Numerous studies have been made in England,
the U.S.A., Japan, and other countries. A number of books and special
papers [5, 6, 34, 51 etc.] have been devoted to a review of the results
ob tained.
The results of the completed studies have found practical applica-
tions comparatively recently. The first attempts to adjust the discharges
Into the atmosphere to certain meteorological characteristics were under-
taken 20-30 years ago. In 1936, Bosanquet and Pearson [46] and in 1947
Sutton [52], who used his 1932 studies, proposed working formulas for de-
termining the surface concentration of an impurity from high sources. As
a result of the rapid development of industry and the associated increase
in air pollution, the results of these calculations, particularly Button's
formulas, were rapidly adopted in many countries. Interest In them grew
with the start of construction of atomic reactors and the consequent need
to evaluate possible air pollution by radioactive substances. From then
on, studies dealing with the experimental verification of the working
formulas and their further theoretical generalization expanded considerably.
In the Soviet Union, among the first studies dealing with the calcula-
tion of dispersal of industrial discharges were those carried out by G. V.
Sheleykhovskiy [44], N. V. Dergachev [27] and P. I. Andreyev [1], who used
Button's formula or similar relations.
The experimental studies performed showed that the indicated working
formulas reflect, mainly in a qualitative manner, some characteristics of
-------
the propagation of impurities in the atmosphere. However, in a quantita-
tive sense, there are considerable discrepancies between the observed and
the calculated data. This has led to the introduction of correction coef-
ficients into the working formulas and to the development of other empir-
ical and theoretical relations. The studies of Pasquill [51], Mead [49],
Hawkins and Nonhebel [50], Wipperman [53], Cramer [48], etc. have received
considerable attention. They are essentially based on relations of the
type of Button or Bosanquet-Pearson formulas. Part of these studies give
a more detailed representation of the dependence of the parameters con-
tained in the formulas on the meteorological conditions. In the practical
calculation of impurity concentrations from industrial sources, it becomes
necessary to consider the initial ascent as well. A considerable number
of methods also have been proposed for calculating this ascent.
As a result, a large number of highly diversified working formulas
are now available. However, very few methods of calculation are known
which have been sufficiently approved and recommended for broad applica-
tions as standard documents in various countries. Among such documents
can be included the Handbook of the German Engineering Society, Mead's
method recommended to the World Meteorological Organization for calculating
the dispersal of discharges from atomic reactors, etc. In the USSR, the
first standard document of this kind was the work [19], officially ratified
in 1963 and now generally used in the design of electric power plants. A
distinctive feature of this method is its theoretical soundness and extens-
ive experimental validation. To date, considerable experience has been accum-
ulated on the application of the method in the USSR; it has attracted the
attention of experts and found acceptance in countries of S.E.V. Council of
Economic Mutual Assistance, Yugoslovia, France, Japan and elsewhere.
The problem has naturally arisen of generalizing the given method and
extending it to a broader category of industrial enterprises. Heat and
power stations are in the category of large sources characterized by heavy
discharges of sulfur dioxide and ash, and also by a substantial overheating
of the stack gases relative to the surroundings. The discharges are ejected
from relatively high stacks located close to each other, and, in practice,
an electric power plant may be treated as a single source. To generalize
the method, it was necessary to study the conditions of dispersal of impuri-
ties in the atmosphere over a wider range of variation of stack heights and
volumes and temperatures of discharges, in the presence of differences in
the parameters of the individual sources, their scatter, etc.
Given below are some results of studies along these lines, forming the
basis of the "Recommendations on the Calculation of the Dispersal in the
Atmosphere of Noxious Substances (Dust and Sulfur Dioxide) Contained in
Discharges of Industrial Enterprises" [43], ratified in 1967 by the USSR
Office of State Construction, section of construction standards and regula-
tions (SN 369-67).
2. Initial Assumptions
In the last few years, the Main Geophysical Observatory has carried
out an extensive group of theoretical studies on the atmospheric diffusion
-------
of impurities from industrial sources [9, 12, etc.]- The characteristics
of the propagation of an impurity were studied on the basis of the solution
of the turbulent diffusion equation •
/
da , dq d ,
-
Axis x is parallel to the wind, axis y is perpendicular to it in the hori-
zontal plane, axis z is oriented along the vertical, q is the impurity con-
centration, u is the wind velocity, w is the velocity of ordered displace-
ment of the impurity along the vertical , and kz and ky are the vertical and
horizontal components of the exchange coefficient.
The initial condition (for x = 0) taken was the presence of a point
source of impurity at height z = H, and the boundary conditions taken were
the absence of turbulent flow of the impurity on the underlying surface
(or the complete absorption of the impurity in the case of a water surface)
and a decrease of the concentration to zero at a sufficiently large distance
from the source. The thickness of the air layer in which the dispersal of
the impurity from major industrial enterprises takes place is very large.
In such a layer, the variation of the wind velocity and components of the
exchange coefficient with the height is frequently complex in character.
For this reason, a sufficiently general solution of equation (1) with the
indicated boundary conditions may be obtained only by numerical methods.
In addition, it is first necessary to carry out the possible simplifica-
tions of the problem, primarily, in accord with the available data and con-
cepts of the parameters and physical mechanisms of the processes studied.
In this connection, it is essential to use the results of [2], accord-
ing to which the horizontal component of the exchange coefficient ky changes
with the height in proportion to the wind velocity, i.e., ky • kgu. In this
case ^
q(x, yt z) = yL&Le-u* .
The quantity q' (x,z) satisfies the equation
and the initial condition of the presence of a linear source at height
z • H. In addition, the same boundary conditions are preserved for q1 as
for q.
For certain models of the variation of u and k with height, equations
(1) and (3) were solved analytically [2, 20, 30, 33, etc.]. In [7, 10, 11,
12, etc.], a numerical solution of this problem was obtained. The terms of
equation (3) were approximated by finite differences, and the equation thus
transformed was solved by means of the difference factorization method,
using computers.
-------
In assigning the meteorological parameters u and kz contained in
(1), one must differentiate between normal weather conditions, observed
relatively frequently, and abnormal conditions, encountered less frequent-
ly but of substantial Interest, particularly in cases where they may lead
to heavy atmospheric pollution.
Under normal conditions above a relatively flat area, the wind velocity
u changes with the height in an approximately logarithmic manner, and the
exchange coefficient k increases linearly with the height in the ground
layer of air and remains approximately constant in the superjacent layer.
(4)
. , // ^ ,
v -f- K\ — npH 2 > h.
Here u^ and k, are values of u and k for z • Zi (usually z-j «• 1m), ZQ is
the roughness of the underlying surface, v is the coefficient of molecular
diffusion for air, and h is the height of the ground layer. As was shown
in [10], the consideration of small deviations of u and kz from (4) is non-
essential. In the case of considerable deviations which may take place
under abnormal conditions, the solution of the problems by numerical methods
proves to be particularly effective.
Usually, the diffusion of a light impurity (w*0) and that of a heavy
Impurity having a definite settling rate are studied separately.
Let us examine the general methods of calculating the parameters of the
problem. For a given type of dependence of u and kz on z, the calculations
may be carried out for definite values of u^ and ki, and the change to other
values of these quantities can be achieved on the basis of similarity con-
siderations. Indeed, if ZQ and h are fixed and one considers that substan-
tial changes in v have little effect on the results [10], the following
relation is valid for the concentration of a light'impurity:
where M is the capacity of the source.
Thus, it is sufficient to determine the "standard" function $n in numer-
ical calculations of Increased accuracy for only one pair of values ui and ki
for different H values. Further calculations of the concentration are made
on the basis of (5), as is done in the presence of an analytical solution of
the problem.
To evaluate the pollution of the ground layer of air, the surface con-
centration (-z - 0) is usually employed. Of special practical importance is
the determination of qm, the maximum surface concentration, reached at some
distance xm when y = 0. The structure of formula (5) indicates that the max-
imum on the function q for y = z • 0 depends only on H. Thus,
(6)
-------
and
Calculations performed in [9] and recently indicate that the functions
and i(H) are adequately approximated by a power function, i.e.,
and
where C^, 8^ (i " 1» 2) are constants that, as was shown by the calculations,
depend relatively little on h and ZQ. For h » 100 m and ZQ « 0.01 m,
, 82*0.2.
In the case of a heavy impurity for constant values of w, from an
analysis of equation (1) and the initial condition at x » 0, similarly to
(5) and (6) , we obtain
a «JL1/JEI «]>,(.*>£. JL // -4-fc (10)
•»• •«, K .*o«i -I "i ' *i ' '
and for the maximum surface concentration
If as was done in [11], the factor l/H^l is separated in ij^, as in (8),
formula (11) may be transformed to the form
where q is defined by formula (6), and xm is some function that is found
from the results of the calculation.
Similarly we can write that
/71t£f li T2 I * h I \ J- ••*/
or
7,, w \
*««—^(tf.-jj-J, $14)
where
-------
According to (11), in the range of w values from 0 to 0.25 in/sec and
H values from 100 to 250 m, xm changes from 1 to 2-2.5 and depends on h.
Recently, additional calculations were made for a wider range of variation
of the initial parameters. It turns .out that as w increases, Xm. increases
approximately in proportion to w, and the proportionality coefficient is a
complex function of H. In analyzing the relationships obtained, it is use-
ful to make use of simpler cases admitting an analytical solution of the
problem. Thus, N. Ye. Berlyand's results [2] for a light impurity may be
compared with those of L. S. Gandin and R. E. Soloveychik [20] for a heavy
impurity. In these results, consideration is given to the case where the
exchange coefficient increases indefinitely with the height according to
the linear law (k - k-^z) for u - u^zn. In this case it turns out that
Xp, * Xm (TT-) » i«e., xm *8 independent of H. When the components of the ex-
change coefficient ky, kz and the wind velocity u take constant values, the
surface concentration of the heavy impurity on axis x from the source at
height H (with the condition for z - 0: k dq *, o) is given by the formula
dz
2/M
(15)
where
r (a) = e"' eric (o); o
4kzx wf-f
°1 ,,W2 ' °2 ZIT"
According to (15), the concentration maximum q,
ally. Fig. 1 shows the dependence x
m
on
is determined numeric-
is evident from this
wH
figure, Xm. increases in approximately linear fashion with ^2 = over a
4&j
wide range of variation of the parameters.
%-m
S
*
3
2
1
0
3af
Fig. 1.
When a model for kz with a "break" is used, according to which kz = k,h
for z>h, the analog of (Jo is the parameter wH^ Data of calculations for
relatively small H values at which the "break" of kz does not play a substan-
tial part, confirm that Xm depends little on H, and for greater heights xm
increases with H. At sufficiently large H (400-500 m) and w (0.2-0.3 m/sec),
X™ reaches 4-5.
-------
The concentration q of both the light and heavy impurity obtained by
solving equation (1), which pertains to a steady state, is formally inde-
pendent of time. However, q is indirectly a function of time, since the
coefficients contained in (1) are time-dependent. As was shown in [12],
the values of the components of the exchange coefficient kz and k are de-
termined by the action of turbulent eddies of comparatively small size with
a characteristic time T usually of the order of 2-3 min. If the time T to
which the concentrations studied are referred is much greater than T, one
should take into consideration the action of larger eddies, which cause
fluctuations of the wind direction averaged over the interval T. Within
the framework of the above scheme, ky and k being kept constant in time,
this effect may be taken into account by determining the average concentra-
tion q for the time period T.
On the basis of the above dependence of q on y (5) according to [9 and
12 ]
(y coa f — A" sin V)'J
Here U)() is the probability of deviation of the wind direction by
angle 4>, and in accordance with the observational data
Vt_
'
where 4>g is the dispersion of the wind direction averaged over time T, in
the course of time T.
For sufficiently large x values it was found in [9] that
le~W (17)
Taking (5) into account, we find that
*f-,", *)• <18>
It should be noted that q in the case of large x values is independent
of kg, and the effect of horizontal dispersal shows up in (18) only via the
dispersion of the wind direction g.
For other x values, a more accurate expression for q is given in [9 and
12].
The formulas obtained permit one to evaluate the dependence of the im-
purity concentration on the sample intake time t in cases involving an ex-
perimental determination of the concentration. To this end, the time t
should be included in the indicated averaging period T, and one should also
-------
allow for the duration of the transport of the impurity from the sources
to the point of observation at a distance x« One can approximately set
x _
7=3/_j-__) where u is the average transport velocity.
u
The time interval T and hence the time of sample Intake t determine
first of all the dispersion of the_ wind direction $()• As T increases,
(|>Q rises, and the concentration q decreases. At small T values these
changes show up more clearly, and at large T values they slow down. The
dependence of <(>Q on T and on the interior average interval T and also on
the meteorological conditions is described in [21].
In accordance with (18) and with the use of power approximations simi-
lar to those contained in formulas (8) and (9) , the maximum concentration
qm and distance x^ at which it is reached are given by the formulas
Mk\ 1
"
o \
"'
"1
The quantity 33 amounts to about 2.3-2.5, and 34 is approximately
equal to 32 •
In determining q|y.g for x^=xm it is expedient to make use of the
fact that according to the calculations, q is approximately dependent on
-4- only [10]. 7m
If long periods of time T*, including periods of many years, are
studied, the probability of the wind direction fl(a) at angle a (measured
clockwise from the north-south direction) is determined by large-scale^
eddies and usually characterized by the wind rose. The concentration q
average for the period T* at a stationary observation point is then defined
by the relation ' «
Here q is the concentration q calculated according to (17) and averaged
for different wind directions over the values of the wind velocity u, and
exchange coefficient k,.
It follows from (17) that q is different from zero in a comparatively
small angular sector within which one can assume that fi(a) - J2a - const.
Then
-------
By <)>Q is meant the average value of this parameter for the given wind
direction.
Comparison of (22) and (18) shows that the average concentration is
independent of the parameters of horizontal diffusion <)>Q and kg.
If P is the frequency of the winds in the direction of a given rhumb
(in fractions of unity), or a total number of rhumbs n, and PQ = _ is the
frequency of winds of one rhumb for a circular wind rose, then n
P
o
_P__
PU
(23)
The stack and flue gases coining from the chimneys have a definite exit
velocity. In addition, they frequently possess buoyancy, since their initial
temperature is higher than that of the surrounding air. Thus, in the vicin-
ity of the discharge source there is created a field of vertical velocities
that occasionally extends over large distances, these velocities decreasing
with the distance from the source, which promotes the ascent of the impurity.
The problem therefore arises of finding the field of displacement velocities
of air near the source in order to allow for it in solving equation (1).
Because of the complexity of this problem, due to. the nonlinearity of the
equations describing the propagation of the overheated jet in the driving
stream, it is usually solved with considerable simplifying assumptions. The
initial ascent of the impurity is considered for the most part in the absence
of the horizontal wind velocity and with some other assumptions. It is
assumed that at a certain height above the stack the vertical velocities are
low, and as was mentioned above, the concept of an effective ascent of the
smoke jet AH above the mouths of the stacks is introduced.
The paper [12] points to the drawbacks of such an approach and formu-
lates a more general statement of the problem for an overheated jet in a
driving turbulent flow. Here the propagation of the impurity along axis y
is approximately described by a relation of type (2), and the determination
of the horizontal and vertical velocity components u and w is done by solv-
ing the following system of equations:
equation of motion
equation of heat influx
fix ~"~ dz dz * dz ' •
equation of continuity
du . i)"jy r\ f 2 4 ^
dx Oz
for suitable boundary conditions. Here i) is the difference between the
-------
temperature of the jet and that of the surrounding air, T is the temperature
of the surrounding air (°K), and g is the acceleration due to gravity.
The solution of system (24) together with diffusion equation (1) is
carried out numerically according to the scheme given in [12].
The paper [9] gives a formula for calculating AH, approximately ob-
tained from theoretical considerations
A//-1,5 ^(2,5+ 3,3^), (25)
where u is the wind velocity at the height of the vane, WQ is the initial
exit velocity of the gases, and AT is the difference between the temperature
of the exiting gases and that of the atmosphere at the level of the stack
orifice.
The quantity q-m substantially depends on the meteorological conditions,
according to the parameters contained in (19) and (25). Of particular impor-
tance is the dependence of T on the wind velocity u. On the one hand, at
a fixed height of the source, qm increases with decreasing wind velocity at
height Zi" 1 m (the transition from ui to u at the vane height zv is achieved
in accordance with (4)). On the other hand, as the wind velocity u decreases
at sufficiently small values of u, the effective source height He » H + AH
increases rapidly by virtue of (25). Therefore, each case has some "unsafe"
wind velocity UM at which the highest concentration ~qm. is reached. The value
of Ujj is determined from the condition
d(/m A oe.\
—i^i-= U. \*o/
In the general case, when analyzing the influence of the wind velocity
u on qm it is also necessary to consider the dependence on u of the coeffic-
ients contained in (19), in particular, the quantity ^i . It is known ([15]
etc.) that_.i_ depends on the number B =—j-, where 6T is the temperature
Ui ' Ui
difference at two levels in the ground layer of air (usually 0.5 and 2 m).
The quantity $Q also depends on B [21]. In the case of unstable stratifi-
cation (6T>0), _fet_ and 6Q increase with B; in a stable stratification (6T<0),
«i
decreases with Increasing absolute value of B, while 4>0 has a tendency
to increase. The values of Q reach a certain minimum under close to equi-
librium conditions. Thus, the ratio ^ decreases with a reinforcement of
stability in the presence of a stable inversion stratification and, in gen-
eral, is less than in an unstable state of the atmosphere. Consequently,
other things being equal, the impurity concentration (by virtue of its pro-
portionality to _&i \rLn a superadiabatic temperature gradient is greater
'
-------
than in an inversion gradient.
In an unstable stratification, excluding the case of slight winds
(up to 1-2 m/sec) , the quantity __*'... depends relatively little on the wind
velocity u and increases slightly with increasing B. It may be approxi-
mately assumeri that _.^i_ is independent of u, . Taking this assumption into
account and assuming that B^ • 2.3 and 6 A " 0.2, we can obtain the follow-
ing equation for UM from (19), (25) and (26) :
(27)
where for convenience of presentation, the following notation has been in-
troduced: .
#2 AT"
Here D =» 2Rrt is the diameter of the stack orifice and Vi =
.. 0 4
volume of the gases exiting from the stack.
From the solution of equation (27) it follows that
(28)
is the
then
A',,
where
0,65 IK-
0,
M
(29)
(30)
(31)
0,30
0,170?
(32)
For thie case in which the wind velocity u ^ u , for the highest con-
centration q and distance xmu at which it is reached, the following form
^mu
ulas can be written down on the basis of (19), (25) and (29):
?,««. =
-------
The use of numerical methods of solution of the problem made it possi-
ble to study the above- indicated anomalous conditions and also the problem
of propagation of the impurity over a dissected topography. These results
have been presented in sufficient detail in [10, 12, 13, and 14], and we
shall consider below only some conclusions of practical importance.
3. Practical Recommendations
In designing industrial enterprises it is important to determine the
highest possible impurity concentration, since, in order to meet the sani-
tary requirements, it must not exceed the permissible value. In order to
find this value (excluding anomalous conditions, which will be discussed
later), in (30) it is necessary to take &i for unfavorable meteorological
conditions, in particular, for an unsafe wind velocity and stratification
for which ~ i will reach the highest value q«.
">l «
M
The working formula for determining the highest concentration q^ can
be given in the following form:
AMmF
where
The coefficient m is determined from the graph of Fig. 2; it is normal-
ized so that for f • fg » 0.42 m/sec2 deg, m = 1. The adopted value of fg
corresponds to the frequently occurring discharge parameters H, Wg, D and
AT for major industrial and power facilities (for example, H - 120 m, D • 6 m,
wg - 10 m/sec, AT « 100°).
The coefficient F determines the influence of the settling rate of a
heavy impurity and is found via the function xm» allowing for the density and
the characteristic particle size distribution. The distributions of the dis-
persity of the dust and ash may be quite different. They depend on the
efficiency and type of the dust and ash catchers. The estimates performed
showed that for practical calculations one can approximately assume F = 2 if
the efficiency of the purification is above 90%, and F » 2.5 for a lower de-
gree of purification. These values pertain to cases where wH does not exceed
100 nr/sec, i.e., for average settling rates of the particles they apply to
stacks whose height does not exceed 250-300 m. At higher settling rates of
the particles, this condition may fail to be fulfilled for lower stacks as
well. The quantity w increases with the size and density of the dust parti-
cles. It should be kept in mind that as a rule, the density of the dust is
below the density of the substance of which it is constituted, since the
structure of dust particles frequently consists of loose conglomerates. Their
density is usually close to 1 g/cm3, but in some cases reaches 3-4 g/cm3 and
more.
-------
The coefficient A is taken for unfavorable meteorological conditions
usually observed in the daytime in summer in the presence of a highly de-
veloped turbulent exchange.
The value of the parameter a entering into the coefficient A depends
to some extent on the roughness of the underlying surface ZQ and on the
height of the ground layer h; the latter is taken such that qM reaches its
highest values [9]. For a medium roughness for the conditions of a flat
area, a is approximately equal to 0.3.
o,Q-
Sf m/seo deg
Fig. 2.
According to the observations in the area of the Shchekino State
Regional Electric Power Plant (SREPP) , on the average, A = 120 if it is
assumed in (34) that q is expressed in mg/m^, M in g/sec, N in m, v in
m^/sec, and AT in °C. This value of A may be assigned to areas with a
flat or moderately dissected topography in the central part of the European
territory of the USSR and in other regions with similar climatic conditions.
As was noted in [9], it may be postulated that in the southern regions of the
USSR and in forested regions characterized by a marked vertical turbulent
exchange in the atmosphere, A amounts to approximately 200.
In regions where the conditions of turbulent exchange are intermediate
in character, A is taken equal to 160. Expeditionary studies carried out in
the vicinity of the Suvorovo and Moldavian SREPP in Leningrad, Cherkassy,
Krasnoyarsk, Balakovo, and other regions confirmed the validity of these re-
sults. In determining the coefficients A, data on the distribution of the
rate of turbulent exchange over the territory in the daytime in summer were
used [26]. It was assumed that in regions with high average values of &i
(which correspond to large average B) , the average concentrations of noxious
substances would increase in accordance with formulas (18) and (23). The
values of the coefficients A for different regions of the USSR are given in
[43].
According to (29) , the unsafe velocity UM is found approximately from
the formula
(36)
-------
The distance x» at which the maximum concentration qM is attained is
determined in accordance with formula (31) by selecting tne parameters it
contains for unfavorable conditions. The calculations show that, basically,
Xvj - (20-25) H. In addition, the ratio_*M_depends to some extent on H, it
//
is smaller for low stacks and greater for high ones.
The ratio _fiLalso de-
H
pends to some extent on the quantity —L, determined at the unsafe wind
Ml
velocity
creases,
and for conditions of highly developed turbulence. As UM de-
usual ly increases, and therefore -fiLwill be somewhat less, but
for practical purposes a detailed calculation of x^ is not necessary and it
is sufficient to confine oneself to the approximate relation
xu»2Qtf. (37)
It should be kept in mind that concentrations of noxious substances
differing from the maximum concentration q^ by no more than 30% are ob-
served at distances of (10-40) H.
From formulas (33), allowing for (36) and the above-mentioned depend-
ence of the meteorological parameters on the wind velocity under unsafe
conditions, we shall obtain formulas for the highest concentration q^u with
u unequal to UM and for the distance xjju at which this concentration is
reached,
-a r- jf ~jc n (38)
The quantities r and p depend chiefly on u t which permits the plot-
ting of convenient working graphs (Fig. 3). The graph for r shows that the
dependence of the concentration maximum q« on the wind velocity u is asym-
metrical in character. For uUM» tne decrease of q^ is slower. Analysis of the variation of the coef-
ficient p shows that, at wind velocities u substantially lower than UM, the
maximum concentrations qjju are observed at distances several times greater
than x^ = 20 H. At wind velocities u much greater than ujj, the quantities
-------
Calculations performed in [10] showed that for the usual effective
source heights (excepting the cases of slight winds) one can approximately
assume ^ to be a function of _£__, and <1 to be a function of __£_ . It
-------
chambers where the concentrations are determined at which, independently
of the time spent by animals in the chamber, the investigated impurities
have no appreciable effect on them.
The above formulas (with the indicated values of coefficient A) are
used to determine the single concentrations that should be compared with
MPC8 and with the single concentrations obtained from observations. When
it is necessary to calculate single concentrations for shorter time inter
vals, the above-mentioned methods [9, 12] can be used.
To use MPCj, two alternatives are possible. In the first, the calcu-
lation is made only for cases of wind directions that are very stable in
the course of 24 hours or longer. In so doing, it is necessary to antici-
pate a set of measures such that the calculated concentrations do not ex-
ceed MPCj. In this case, the average daily concentrations will be closest
to the single concentrations, but such conditions are observed very seldom
and their discussion is of no practical significance.
It is more logical to relate the concept of mean daily MFC to a
regime established in the course of a period of many years. In this case,
the name "mean daily MFC" has an arbitrary meaning. Accordingly, the cal-
culated concentration should be determined for points that are fixed in
the area, allowing for the climatological data on the atmospheric diffusion
parameters - the wind velocity and direction and the coefficient of verti-
cal turbulent exchange. It will be shown that at the present time such an
approach involves a definite contradiction between the recommended values
of single and average daily MFC's. Indeed, we s_hall use the relation (23)
obtained above between the single concentration q_and average concentration
q. For the evaluations we shall assume that q « q and that the wind rose
is circular, i.e. . P - 1. Then " _ _jPo 7 For <£n = 0.1, we have ~ ,
"•"— — ij — — i^"n~ */ • *J cj i
/>«, V2;i "^~o7
q 25
If we consider that the unsafe wind velocities and the intense turbulent
exchange are not observed during the entire period, the averaging should
be carried out over the possible values of the wind velocity and exchange
coefficient, i.e., it should be assumed that q is always less than "q ^ and "°q
Q
is less than — . According to the experimental data of Chamberlain [47] and
some other authors, -^. » Therefore, in order to obtain consistent re-
q 40
suits in determining the permissible discharge, the necessary stack height,
etc. when calculated data are used, the ratio MP^s should also be no less
MPCd
than 1 - -i. In the tables for MFC [36], the ratio Mpcs ranges mainly from
25 40 5^
-i to 1. For this reason, the requirement q^ < MPC8 turns out to be a con-
siderably stricter condition than the requirement that the average concen-
tration for many years be less than MFC,.
-------
Taking the planning experience into account, one must admit that the
use of single concentrations in the calculations permits the achievement
of the necessary atmospheric purity in more real terms. Therefore, it
appears necessary at the present time to use single concentrations as the
base. Thus, in designing and operating industrial enterprises the follow
ing condition should be fulfilled
' <7«< MPC_ (41)
O
It then follows from formula (34) that the minimum stack height of a
single source is given by
Since m depends on f and f on H, calculations using formula (42) should be
carried out by successive approximations, setting first m ° 1. Two to
three approximations are usually sufficient.
Let us now consider the case of a group of sources, when the calcula-
tion is made on the basis of a superposition of concentration fields from
individual sources. Analysis of the above formulas indicates that if the
distance between the stacks does not exceed their average height by a fac-
tor of more than 3-4, the sources may be treated as being located at a
single point. If at the same time the discharge is distributed uniformly
among N stacks of identical height and diameter, the total concentration will
be given by the formula
AMmF -,Y~N~
1u — fji y y w • (43)
where M is the total discharge from all the stacks and V = --- - — is the
4
total volume of stack gases.
Accordingly, it follows from (36) that
(44)
For sources with different unsafe wind velocities, the calculations are
simplified if one introduces into the discussion the weighted-mean unsafe
wind velocity
(45)
tul
l-l
where v^. and qMi are the values of the unsafe velocity and highest concen-
tration for the i-th source, and N is the total number of sources.
The calculations performed showed that in this case it is practically
sufficient at first to determine for each source the highest concentration
^Mu an<^ distance xMu at which this concentration is reached at a wind velocity
-------
u » uj^. Then, if the sources are located close to each other or are
grouped along a certain line, the distribution of concentration from the
sum of the sources is found by graphical summation. The highest concen-
tration value taken is q^, and the distance from some arbitrary origin of
coordinates is taken as XM.
In the general case, when the sources cannot be reduced to a point
or a straight line, one has to sum up the fields of the concentration from
individual sources by considering its distribution both along the wind and
in the direction at right angles to the wind. Obviously, the different
wind directions must be considered, since the relative position of the
sources changes as a function of these directions, and the concentrations
produced by the latter add up in different ways. It is understandable that
such calculations become very cumbersome even for a relatively small number
of sources. They can be simplified because the concentrations perpendicu-
lar to the wind direction decrease much faster than those in the direction
parallel to the wind. Experience with the calculations showed that in order
to determine the highest total concentration it is sufficient to consider
only those directions that .pass through pairs of main sources. At the same
time, in each direction it is first necessary to carry out the calculations
at points corresponding to the maxima of concentrations from the largest
sources. A program for the "Ural-4" computer was written for a large num-
ber of sources in accordance with the scheme presented above. According to
the program, the print-out consists of the maximum total concentration with
the characteristics of the conditions under which it is observed, and also
the contribution of individual sources to this maximum. The availability of
such a program considerably simplifies the selection of the most effective
variants of arrangement of the sources and their parameters in planning
major facilities, permits plotting of the total fields of concentrations
for all of the sources in a city, etc.
In planning new enterprises discharging noxious impurities in areas
where the air is already polluted by the same substances from other indus-
trial enterprises, and also in expanding the operating enterprises, in addi-
tion to the increase of discharges into the atmosphere, the initial or back-
ground concentration q^ should be taken into consideration. In this case,
the sum q^ + q^ should not exceed the MFC. The background concentration q^
can be determined by means of the above methods of calculation for a group
of sources.
An important problem in the practical application of the results pre-
sented above is the determination of the boundaries of the sanitary protec-
tive zone (SPZ), i.e., the allowed difference between enterprises discharg-
ing noxious substances into the atmosphere and residential areas. Thus far,
the problem of the SPZ has essentially been solved empirically. On the
basis of the experience of sanitation surveys, a model classification of
Industrial facilities has been established for the size and the required gap
between the enterprises and residential districts [37]. The data on which
this classification is based mostly fail to reflect the modern tendency to
discharge the bulk of noxious substances through high smokestacks and air
-------
ducts. Analysis shows that this classification considers chiefly the
pollution of areas close to the enterprises, which is caused by random
discharges (i.e., outside stacks). Therefore, the width 1Q of a sanitary
protective zone (SPZ) which has now been established is useful when, accord-
ing to the calculations, the concentration q^ from orderly discharges is
less than the MFC, since the method discussed above does not allow for ran-
dom discharges. However, the width of the SPZ for different classes of
enterprises was established primarily for conditions when there is no marked
prevalence of winds of definite directions. Under conditions where the mean
annual wind rose differs substantially from circular, namely, for a frequency
P of winds of certain directions which is greater than the mean value PQ, the
width of the SPZ should be corrected by taking into account the characteris-
tics of the wind regime of the area under consideration. For these wind
directions, taking into account the above dependence of the average concen-
tration on the frequency of the wind direction P [23], the width of the gap 1
from the enterprises to the outer limits of the SPZ is given by the formula
/ _/ p
l~—l°~f^' (46)
and in the directions for which the wind frequency P^Q, 1 = IQ should be
taken.
In cases where, on the basis of calculations in accordance with the
above scheme, q>MPC up to a distance LQ exceeding IQ, the distance 1 from
the pollution source to the outer limits of the SPZ should be greater than
IQ. To calculate the distance 1 it is necessary to consider the character-
istics of the distribution of average concentrations in accordance with formu-
la (23). In addition, it is necessary to take into account the study of the
nature of the decrease of single concentrations with the distance x for
x>xjij (cf . , for example, Fig. 4). It follows from Fig. 4 that at these dis-
tances, as x increases, the concentration q decreases in approximately in-
verse proportion to x. Including in the sanitary protective zone a terri-
tory with approximately the same average concentrations, one can roughly
assume that
t^Lo-fr- nP» P>f>o (47)
in the directions for which P
-------
discharges because of the limitation of their initial ascent [4]. Under
these conditions, the effective ascent AH cannot exceed a definite limit
independently of the decrease of the wind velocity u, the values of the
unsafe velocity decrease, and the surface concentrations rise sharply.
Despite a marked influence of elevated inversions on the distribution of
the impurity concentrations, it should be kept in mind that in many geo-
graphical areas they are observed for a comparatively short period of
time. For this reason, it was proposed above that the stack height and
other discharge parameters be determined from relatively frequent unsafe
weather conditions. During periods of elevated inversions, however, par-
ticularly when a thick inversion of several hundred meters with average
temperature gradients of approximately 3-4° per 100 m is located above
the stacks, and the wind is directed from the sources of pollution toward
residential areas, a relatively short term decrease of the output of the
enterprises should be recommended in order to reduce the discharges into
the atmosphere. This is economically more expedient than a sharp increase
of the stack height during construction. In some cases it is also neces-
sary to consider possible deviations in the vertical profile of the wind
from the logarithmic distribution. Calculations made in [12] have shown
that the presence of still layers around the underlying surface, provided
there is a well developed turbulence (convection), may also lead to a con-
siderable increase (double or more) of the surface concentrations, this
increase being greater the thicker these layers are.
The propagation of the concentration from the source in the presence
of a fog changes substantially. The important effect of the increase of
the surface concentrations in this case was pointed out in [13]. It turns
out that in addition to a redistribution of the impurities because of
their absorption from the air by droplets, in the fog layer the concen-
trations Increase because of an additional transport of the impurities
from layers of air located above the fog. As sulfur dioxide and some other
ingredients dissolve in the fog, their toxicity increases. It should also
be noted that fogs are frequently associated with inversion and still
conditions that may cause a mutual reinforcement of dangerous effects.
Under dissected topography conditions, air movements arise that result
in substantial concentration changes. According to theoretical studies
[12, 14], it turns out that under such conditions, the concentration maxi-
mum is higher than on a flat topography. For a height of irregularities
of 50-100 m with a slope angle of about 5-6°, the difference in the concen-
tration maxima, depending on the location of the source in different forms
of the relief, amounts to 50% or more. An increase o,f the concentration
is sometimes observed even when the stacks are located in high areas, in
the vicinity of leeward slopes, since here the wind velocities decrease and
descending currents arise. On the other hand, in the case of gentle slopes
of the relief (the slope angles for the most part do not exceed a few
degrees), the air flow around them is practically complete and the increase
of the concentration is slight. The influence of a hilly relief on the dis-
tribution of concentration manifests itself in areas where the wind velocity
changes appreciably at a fixed height. In this connection, a major impor-
tance is assumed by a microclimatic study of the area, analogous to the one
-------
discussed in [31, 39]. Considerable possibilities are offered by experi-
mental work involving wind tunnel simulation of air streams in complex
forms of the relief, under urban conditions, etc. [23, 29].
4. Experimental Verification
The above conclusions from theoretical investigations have been con-
firmed with extensive experimental material.
One of the first most complete sets of experimental studies of
atmospheric pollution by industrial discharges was completed in the region
of the Shchekino SREPP. The work was done in 1962-1965 during periods in
different seasons of the year and covering a broad range of variations in
meteorological conditions. Results of a comparison of the calculated and
experimental data obtained were given in [9; 25, 35]. They were shown to
agree within 20-30% in terms of the concentrations q^ and character of the
dependence of the highest concentrations q on the distances to the source x
and on the wind velocities u. The observations confirmed the calculated
values of the unsafe wind velocity, which amounts to about 5 m/sec, the
general character of the dependence of pollution on the stability of the
ground layers of the atmosphere, and also the validity of formula (25) for
the magnitude of the initial ascent of the smoke plume.
Similar expeditionary studies by the Main Geophysical Observatory in
cooperation with the Moscow Scientific Research Institute of Hygiene and
other organizations were carried out during the summer-autumn season in
the area of the Cherepet1 (1964) and Moldavian SREPP (1965) and also in
the region of the Nevskiy chemical plant. In these expeditions, the con-
centrations of noxious substances were measured at several points located
at various distances, including considerable distances, from the source,
and the discharge of noxious substances, volume, velocity and temperature
of the escaping gases were simultaneously determined. The meteorological
observations included gradient measurements of the temperature and velocity
of the wind, and aerological measurements of the distribution of these ele-
ments and characteristics necessary for calculating the turbulent exchange
coefficient in the boundary layer of the atmosphere were also carried out.
Photographs of the smoke plume were taken and its parameters were deter-
mined visually both from the ground and from observations in an airplane
and helicopter.
For the Cherepet' SREPP, whose main discharge takes place from three
stacks 140 m high, the calculated concentration maxima q^ were 4.2 mg/m^
for ash and 1.4 mg/m^ for sulfur dioxide, and the corresponding experimental
qM values were 3.7 mg/rn^ and 1.8 mg/m^. The calculated and experimental
data on the unsafe wind velocity differed by no more than 1 m/sec.
A characteristic feature of the Moldavian SREPP was the discharge of
the impurity through a single stack of 180 m (one of the highest in the
USSR at that time) under conditions of a highly developed convection
characteristic of the south of the European territory of the USSR. Since
-------
wet ash purification was used, the overheating of the stack gases was
approximately 40°C, which was substantially below that of the Shchekino
and Cherepet' SREPP, where it reached 100-150°C. According to the results
given in [22], the calculated values of q« for sulfur dioxide were 0.26
^, and the unsafe velocity u^ « 2.5 m/sec; from experimental data,
0.3 mg/m^ and ity - 2-3 m/sec. A satisfactory agreement was also noted
in the distribution of the concentration q with the distance x. The zone
of highest concentrations was observed at a distance of 3-4 km from the
stacks, which corresponds to the results of the calculations.
In order to study the distribution of impurities pouring into the
atmosphere at relatively low temperatures, observations were made in the
region of the Nevskiy Chemical Plant. From plant stacks 100 m high, nitrogen
oxides were discharged with a temperature contrast of only 15-20°C relative
to the ambient air. According to experimental data [24], q^ « 0.17 mg/m->,
and according to calculations, q^ = 0.20 mg/rn^, and the unsafe velocities
in these cases decrease compared to those cited above and amount to 1-2 m/sec
according to calculations as well as observations.
On the basis of observational data on the smoke- plume from the Nevskiy
plant and from the stacks of the Cherepet1 and Moldavian SREPP, a satisfactory
agreement was noted between the calculated and observed initial ascents of
the smoke plume.
A series of theoretical conclusions have been confirmed by experimental
studies of the discharge of aerosols from specially constructed high sources.
They include experiments on the dumping of heavy fluorescent particles from
a 300-meter meteorological mast in the city of Obninsk [17]. Analysis of
these experiments showed a good agreement between the calculations and experi-
ments on settling of the impurity on the underlying surface. It was found
from both theoretical and experimental data that under convective conditions,
the propagation of the impurity depends relatively slightly on the settling
rates of the particles, and that the role of gravity settling Increases sub-
stantially in a stable stratification. Experiments on spraying of a liquid
aerosol from heights of 100 to 400 m were analyzed in [28]. In the majority
of experiments, confirmation of the theory by experimental data was obtained
with respect both to the values of the maximum precipitation of the liquid
and to the distances where they were observed. In the great majority of
cases, the differences did not exceed 30% of the calculated values. The
data given in [17 and 28] on the determination of the turbulent characteris-
tics k^ and <{>Q as the result of solution of the reverse diffusion problem
are in accord with the results of gradient and fluctuation observations.
In order to confirm the theoretical conclusions, in addition to the
indicated data of observations in the area of the Shchekino SREPP, use was
also made in [35] of data obtained from a survey of seven heat and power
plants with stack heights of 40 to 150 m, made by the Moscow Scientific
Research Institute of Hygiene from 1953 to 1958. This confirmed both the
calculated values of the concentration maximum and their dependence on the
stack height.
-------
In 1963-1965, a number of public health organizations carried out a
comprehensive cycle of surveys of atmospheric pollution around heat and
power plants located in various climatic zones of the USSR. This material
was presented to the Main Geophysical Observatory for analysis by the
Sanitary Epidemiological Administration of the Ministry of Public Health
of the USSR. Some results of its treatment and comparisons with the pre-
ceding formulas will be cited.
The concentrations of sulfur dioxide and ash around the Pridneprovskaya
SREPP with stack heights of 100-120 tn were determined by the Ukrainian
Institute of Communal Hygiene in 1963. Fig. 6 shows the distribution of
highest concentrations obtained versus the distance based on experimental
and calculated data.
q mg/m
Fig. 6.
Highest concentrations of sulfur
dioxide and dust at various dis-
tances from the Pridneprovskaya SREPP.
1 - measured dust concentrations,
2 - calculated ash concentrations,
3 - measured sulfur dioxide concentra-
tions, 4 - calculated sulfur dioxide
concentrations.
According to the results of the survey of the Serov SREPP with stacks
120 m high, carried out in 1963 by the Sverdlovsk Institute of Labor
Hygiene and Professional Diseases, it was found that qM for sulfur dioxide
amounts to 0.26 mg/m^, and for ash 4.5 mg/m^; according to calculations,
these values are 0.25 and 4.4 mg/m-*, respectively.
-------
The Novosibirsk Scientific Research Sanitation Institute carried out
a survey of the Kemerovo SREPP; for sulfur dioxide it was found that q^ -
3.2 mg/nr, and according to calculations, qM • 3.0 mg/rn^.
Data of surveys of a number of other SREPP and heat and power plants
(HPP) were used to compile Table 1, which lists experimental and calculated
values of qM for sulfur dioxide. It should be noted that these experimental
data are not complete; in particular, the number of samples taken was small,
but a definite agreement between them and the calculated values can be seen.
In many cases, agreement also exists for the dust concentrations. How-
ever, these data are not cited here, since the available information on the
efficiency of the ash catchers was not always reliable and was chiefly based
on specifications rather than factual data.
According to Tamson's data [42] pertaining to a Baltic SREPP with a
height of 150 m, the highest measured concentration of sulfur dioxide
q^j » 0.4 mg/m3, and the concentration calculated by means of the above
formula q^ = 0.6 mg/m3.
Table 1
Name
Minsk HPP
Tallinn HPP
Bobruysk HPP
Alma At a SREPP
Karaganda SREPP
Daugavpils HPP
Stack
height,
m
100
104
65
60
70-100
-
qM mg/m3
Experimental
0.22
less than MPC
Traces
Traces
0.6
Traces
Calculated
0.29
0.16
0.1
0.27
1.0
0.8
On the basis of the indicated data for heat and power plants, a graph
of
-------
by the State Institute for the Design and Planning of Metallurgical Plants.
The calculated data turned out to be slightly higher than the experimental
ones. This may apparently be explained by the fact that the limited amount
of observations did not permit the establishment of possible values of the
highest concentrations.
10*
10 r
M
1,0
0,1
o /
o 2
• §
so
100 150 180
50
100 150 //m
Fig. 7.
Graph of maximum concentrations of sulfur
dioxide (a) and dust (b) normalized to the
quantity of noxious substances discharged,
versus stack height H.
1 - experimental data, 2 - calculated data
In 1962-1963 a substantial modernization of the Chimkent lead plant
was carried out in order to purify the air reservoir in the adjacent areas;
in particular, the discharge of sulfur dioxide into the atmosphere was con-
siderably reduced, the height of stacks of the sintering section was raised
from 70 to 120 m, etc. According to data of the State Institute for the
Design and Planning of Nonferrous Metals Industry Establishments, the State
Institute of Nonferrous Metals and the State Institute for the Design and
Planning of Metallurgical Plants, the maximum concentration of sulfur dioxide
q^ before the modernization of the plant was 10 mg/m^, and after some
modernization, it dropped to approximately 2 mg/m^. Our calculations gave
for qM values, respectively, equal to 8.5 mg/m^ and 2.5 mg/m^.
Finally, we shall refer to the results of a survey of one of the major
metallurgical plants in the south of the Ukraine, made in the summer of 1967.
The distribution of dust up to a distance of 18 km from the plant is given
in [16], based on observational data.
On the basis of observational data, the maximum dust concentration was
4 rag/m^, and according to calculated data, 3 mg/m^.
-------
On the whole, it may be concluded that there is a satisfactory agree-
ment between the calculated and experimental data, particularly if it is
considered that only approximate values for the discharge parameters were
known.
Some theoretical conclusions used in developing a method for calculat-
ing the dispersal of discharges from high stacks, in particular, conclusions
of the theory of summer convective conditions, have been definitely confirmed
by analyzing data of regular observations of pollution of city air reservoirs
[All.
m
2
10
i. 5
i.O
0.5
0
/m^
-1
2
i
7XKN
Fig. 8.
Highest sulfur dioxide concentrations
at various distances from the Chelyabinsk
Metallurgical Plant.
1 - calculated, 2 - experimental.
In summing up the discussion of the experimental verification of the
method of calculation, let us note that the theoretical considerations of
the patterns of dispersal of noxious discharges from various industrial
enterprises in the atmosphere have been substantially confirmed for differ-
ent meteorological conditions and climatic zones. The experimental data
pertained to the most common ingredients of industrial discharges - sulfur
dioxide and dust (ash); a complex characteristic of the discharge parameters
is the quantity f introduced above (28); the experiments covered enterprises
for which f reached 5-6, and sometimes even higher values. All of this
forms a basis for the use of the method described for a broad class of
operating and planned facilities, primarily for enterprises of the metal-
lurgical, petroleum refining, chemical, and a number of other branches of
industry.
-------
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-------
LITERATURE (Cont'd)
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or xiiMii'iecKoro J.'IUOAH. Tpy/iu I'l'O, 111.11:. liSij, l!)(i(j.
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cToro ra.ia), co;iep>Kamii.\csi u uwCpocax iipoMuiii^cinibix npeAnpiinTiiA. (CH 369-67).
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STUDY OF THE STRUCTURE OF A SMOKE JET AND DETERMINATION OF
THE COEFFICIENT OF TURBULENT MIXING FROM
THE VERTICAL DISTRIBUTION OF CONCENTRATIONS
V. S. Yeliseyev
From Trudy, Glavnaya Geoflz. Observat. im. A. I. Voeykova, No. 234,
p. 95-99, (1968).
In the study of the diffusion of gases from plant stacks in the ground
layer of the atmosphere, the usual methods of air sample collection may
prove to be very difficult. Indeed, if the investigations are conducted in
an urban residential district, it is extremely difficult and sometimes im-
possible to carry out the sampling above a smoke jet, which changes direction
with variations in the wind direction. The difficulties increase if the
sampling is performed above an invisible smoke plume such as is observed,
for example, in the case of industrial plants producing synthetic fiber.
At the same time, in order to solve a number of technical problems
connected with the installation of air pipes supplying clean air into the
shop of industrial enterprises and in connection with some meteorological
problems, it is of major interest to study the vertical concentration pro-
file. The literature contains a relatively small amount of data on the
study of the structure of smoke jets.
In the U.S.A. in 1943, Hewson and Gill [6] measured the concentration
of sulfur dioxide in the Columbia River valley, using light monoplanes and
captive balloons 1200 ft 3 in volume. In 1958, Stewart et al. [7] studied
the vertical profile of concentrations in a radioactive plume using mobile
balloons. However, all these studies were made relatively close to the
source.
To overcome the above-mentioned obstacles, we attempted to develop the
technique of sampling by using a helicopter. The great maneuverability of
the helicopter in air, the possibility of measuring the concentrations in
the smoke jet itself and the small investment of time on collecting the air
samples at different points permit the use of the helicopter for the study of
atmospheric pollution. The main elements of the planning and execution of
observations from a helicopter consist in the following:
Selection of the type of helicopter as a function of its flight
characteristics.
Study of the effect of the air currents created by the helicopter pro-
peller on the sampling process, and study of the principle of arrangement
of the instrumentation inside the helicopter.
Determination of the type of instruments used for sampling gaseous
ingredients.
-------
Study of the flight technique of the helicopter and collection of air
samples.
Chemical analysis of the air samples.
Reduction of the data obtained to a form suitable for comparison with
calculated values .
Correlation of the concentrations of gaseous ingredients with meteorolog-
ical parameters.
In March 1967 in the city of Krasnoyarsk, an MI-1 helicopter was used
for the study of the structure of a smoke jet. The study of the character-
istics of the air currents generated by the helicopter propeller and their
influence on the process of sample collection, as well as the arrangement of
the Instruments, were described in [4]. During the collection of representa-
tive samples from the helicopter, the suction apparatus for taking the samples
was mounted in the nose of the helicopter and was moved slightly in front of
the Pitot tube.
The air samples were collected for analysis for hydrogen sulfide
and carbon disulfide (CS2> , discharged by the stacks of a synthetic fiber
plant. The chemical analysis was performed in the water chemistry laboratory
after the flights.
The smoke plume from the stacks of the synthetic fiber plant included a
small visible portion ("100-200 m from the source) , which aided in the deter-
mination of the direction of the smoke Jet. At a given height and velocity
of the flight (60-70 km/hr) , the measurements were made at distances of 0.5,
1.5 and 3 km from the source and along the vertical at three heights depend-
ing on the ascent of the smoke jet; on the whole, for all the days of flight,
the samples were taken at heights of 50, 100, 150, 200, 250 and 300 m above
the earth's surface. The helicopter flew through the smoke jet in a perpen-
dicular direction without going beyond it.
However, since at these distances the smoke jet was invisible, its
width was calculated during the flight. Data on the initial visible portion
of the jet were used for this purpose, and the coefficient of horizontal mix-
ing was calculated in accordance with [5], and the width of the smoke plume
was then calculated at different distances. The time of sample collection
was 20 min. In five days, 196 samples for hydrogen sulfide and carbon disul-
fide were taken. At the same time, automobiles with mounted equipment were
used to measure the concentrations of the same gases near the earth's surface.
Since on the earth's surface the concentration was measured on the jet axis,
in plotting the vertical profile of the impurity distribution it was necessary
to switch from the integrated average value to the axial concentration.
In order to obtain this relationship, use may be made of calculations of
the transverse distribution of the concentration in the jet as a function of
the dispersion of horizontal fluctuations of the wind direction Q, in accord-
ance with [2]. If the effective width of the smoke jet is denoted by R, and
the concentration on the jet axis qlysQ^qoCx, z) , then
-------
whence
y
I7 ^
(1)
As an example, Fig. la shows the vertical profile of the axial concen-
tration of hydrogen sulfide (to the left of zero) and carbon disulfide (to
the right of zero), which occurred in the smoke jet of 21 March 1967 at 10-
11 hr and 15-16 hr at a distance of 500 m from the source. Fig. Ib shows
the vertical profile of the temperature (1) and wind (2) for the same
period of time.
Analysis of the graph (Fig. 1) shows that the concentration of carbon
disulfide at a distance of 500 m from the source at 10-11 hr on the plume
axis is almost 20 times the value at the earth's surface and approximately
50 times the MFC. The hydrogen sulfide concentration at the same distance
from the source and at the same height is almost 30 times the MFC and 110
times the concentration at the earth's surface.
At the same time, analysis of the graph (Fig. 1) shows that the layer
in which the smoke jet spreads is highly stratified, an inversion begins at
the earth's surface, and its upper boundary is located at a height of 475 m.
7 ^ 3 4- 5 6 7 3 3 1G 11 L'm/seo
t 2 3 4 5 S 7 8 9 1C ?Z
-------
It will be shown below that the coefficient of turbulent mixing in the
layer of propagation of the smoke jet was 0.2-0.A m^/sec at that time. Be-
cause of such slight vertical mixing, the profile of the vertical concentra-
tion distribution is characterized by a large maximum on the axis of the
smoke jet. By 15-16 hrs, a rearrangement of the temperature field took
place. The layer of the atmosphere had now begun to be characterized by a
stable state and a higher degree of turbulence (k=8 m2/sec). In addition
to the rearrangement of the temperature field and turbulent mixing, a change
occurred in the distribution of the gaseous ingredients in height.
At 15-16 hrs, the concentration began to be more evenly distributed in
the vertical direction and the dispersal of the impurity occurred much faster.
Thus, the maximum carbon disulflde concentration on the axis of the smoke
jet was only 20 times the MFC, and the hydrogen sulfide concentration,
13 times the MFC.
On the basis of the data obtained, an attempt was made to calculate the
vertical coefficient of turbulent mixing from the distribution of the con-
centration in the smoke jet.
The equation of turbulent diffusion [1] for a linear source can be used
for this purpose. When the impurity source is located at a sufficient
height, where the exchange coefficient undergoes little change with height,
for the calculation one can take the solution of the diffusion equation with
constant coefficients
C\ _. — ——" .—L- I /o\
7,tv ~\^ ~:^ L '"•••<•<" J-/, 4KX''U (2)
where Q is the capacity of the source; u is the average wind velocity; x is
the distance from the source; k is the coefficient of turbulent mixing; H is
the effective source height; z is the vertical distance from the earth's sur-
face.
From the ratio of the integrated concentrations at three neighboring
levels one can obtain a system of two equations:
(x, *!
(3)
The quantity S was determined from equation (4), which was solved
numerically with a computer
-------
Thus, the coefficient of vertical turbulent mixing in the smoke jet
may be determined from the formula
*/)"
(zj~x,)S-\-\i\
I-!
~-lt.S
(5)
where i and j are consecutive numbers of the height levels at which the
concentration is being determined.
The calculated values of the coefficient of turbulent mixing k are
given in Table 1. For comparison, the same table lists values of the
coefficient of turbulent mixing calculated from the formula k=k^h, where h
is the height of the ground layer of the atmosphere.
The coefficients of turbulent mixing at a height of 1 m were calculated
by using data of meteorological observations for the same period according
to M. I. Budyko's formula [3]. It is assumed that the coefficient of turbu-
lent mixing increases linearly up to the height of the ground sublayer, and
above this height the quantity h is assumed to be constant. For our calcu-
lations, h was taken as 100 m. Analysis of the data obtained shows a satis-
factory agreement of the coefficients of turbulent mixing calculated from
the distribution of concentrations in the plume and from the corresponding
formula. The difference in the exchange coefficients of 21 March at 10 A.M.
is obviously due to the fact that the layer in which the smoke jet was
spreading was at that time subjected to the influence of the inversion state
of the atmosphere, whereas the calculation of k-^ can be carried out only for
an equilibrium state of the atmosphere.
Table 1
Date
17 111 1967
20
•'>i
. i
22
23
Time, hr.
11
12
11
13
10
15
Distance
From
Source , m
50;>
1,500
50!)
30U)
r,oo
f)(!l>
i;> r,oo
14
1°
13
1500
2000
-1000
k ra^/sec from the
distribution of
Hydrogen
Sulfide
4
_
20
24
0,2
8
—
•1
.'»
• "
Carbon
Disulfide
4 •'
Si 5
16
—
0,4
a
14
IK
4
1,3
O /
k=k^h nr/sec.
5
1 O
iy
i •*
I**
11
.>
The good agreement of the data obtained also indicates a representative
character of the concentrations measured in the smoke jet.
-------
LITERATURE CITED
1. B c p Ji n ii A M. 1:., I'o 11 H x u 11 M'i I7,. .'I., ,/i o >K K n M a Li. 11, O n u K y .1 P. II. Hue-
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cijicpu iifi.'iiutii ii|)o.\ii.iiii.'U'iini.ix iipc,uipii>iTiiii. T|i. 1TO, HIJII. I3t>, 1%3.
2. 1> L> p ;i n n ;i M. II, I'f n n x o » n >i I:. ./I., }[ c M i. >i n o » n M B. Iv. IK'Xoiopi.ie aKrya.ii>-
IIMC iioiipocu iiccJK'.aoii.'-niii aTMOa]>i'piH)i't ^iiii|)i|)y:iiin. Tp. 1TO, nun. 172, I!)ii5.
3. liy.'iUKo M. H. TypCiy.: ..ibiii oljMcii 11 iniwinix c.ionx aT.\ioc(|iepu. McTeopo.'ioriin 11
rn:i|>o.normi, jNV '2, l!)-iu.
4. F o p o in K o 13. ii., I: n u c o e u B. C., 11 a :i a p e n K o U. c/\. K TCxmiKe liafi.iioacmiM
aiMOapcpiioro :mrp>i:iiic'ini>i c IIOMOIUI.IO iii-pTuJic'ra. Tp. ITO, BUII. 207, 19G7.
5. Efliiceea B. C. K iionpocy o rop:i:>uirr:i;ii5.
G. Hews on \V. E., and Gill G. C. Mcleoroloiyical Invcstii,'ation in Columbia l
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