MIXING HEIGHTS, WIND SPEEDS, AND POTENTIAL
FOR URBAN AIR POLLUTION THROUGHOUT
THE CONTIGUOUS UNITED STATES
U. S. ENVIRONMENTAL PROTECTION AGENCY
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MIXING HEIGHTS, WIND SPEEDS, AND POTENTIAL
FOR URBAN AIR POLLUTION THROUGHOUT
THE CONTIGUOUS UNITED STATES
REQON VI LIBRARY
U. S. ENVIRONMENTAL PROTECTION
AGENCY .
1445 ROSS AVENUE f
DALLAS, TEXAS 75202
George C. Holzworth
Division of Meteorology
ENVIRONMENTAL PROTECTION AGENCY
Office of Air Programs
Research Triangle Park, North Carolina
January 1972
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The author is a meteorologist on assignment to the Environmental Protection Agency from the National Oceanic
and Atmospheric Administration, U. S. Department of Commerce.
The AP series of reports is issued by the Office of Air Programs, Environmental Protection Agency, to report the
results of scientific and engineering studies, and information of general interest in the field of air pollution.
Information reported in this series includes coverage of Air Program intramural activities and of cooperative
studies conducted in conjunction with state and local agencies, research institutes, and industrial organizations.
Copies of AP reports are available free of charge—as supplies permit—from the Office of Technical Information
and Publications'?\Qfficg Itjf.^r. Programs, Environmental Protection Agency, Research Triangle Park, North
* '
Office of Air Programs Publication No. AP-101
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f- <,
X
-\
ACKNOWLEDGMENTS
Many staff members of the Division of Meteorology, which is under the direction of Robert A. McCormick,
have contributed substantially to this study. In particular, the perceptive suggestions of Francis Pooler, Jr., and
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CONTENTS
Page
LIST OF FIGURES v
LIST OF TABLES x
ABSTRACT xi
KEYWORDS xi
INTRODUCTION 1
BASIC PARAMETERS: MIXING HEIGHT AND WIND SPEED 3
Concepts and Computation Methods 3
Tabulations and Availability 4
Mean Mixing Height and Wind Speeds 4
URBAN DISPERSION MODEL 9
POTENTIAL FOR URBAN AIR POLLUTION 13
Fifty-Percentile Concentrations 13
Twenty-Five-Percentile Concentrations 15
Ten-Percentile Concentrations 16
EPISODE-DAYS OF HIGH METEOROLOGICAL POTENTIAL 19
Episodes Lasting 2 Days or Longer 20
Episodes Lasting 5 Days or Longer 22
Forecast Episodes 22
SUMMARY AND CONCLUSIONS 23
APPENDIX A. NCC TABULATIONS OF MIXING HEIGHT AND WIND SPEED 97
. APPENDIX B. ALLOWANCE FOR P-, C-, AND M-TYPE MIXING HEIGHTS AND WIND SPEEDS 107
APPENDIX C. DERIVATION OF URBAN DISPERSION MODEL ! .... 113
REFERENCES 117
IV
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LIST OF FIGURES
Figure Page
1 Isopleths (m x 102) of mean annual morning mixing heights (see Table B-l for data) 26
2 Isopleths (m x 102) of mean winter morning mixing heights (see Table B-l for data) 27
3 Isopleths (mx 102) of mean spring morning mixing heights (see Table B-l for data) 28
4 Isopleths (mx 102) of mean summer morning mixing heights (see Table B-l for data) 29
5 Isopleths (mx 102) of mean autumn morning mixing heights (see Table B-l for data) 30
6 Isopleths (m x 102) of mean annual afternoon mixing heights (see Table B-l for data) 31
7 Isopleths (m x 102) of mean winter afternoon mixing heights (see Table B-l for data) 32
8 Isopleths (m x 102) of mean spring afternoon mixing heights (see Table B-l for data) 33
9 Isopleths (m x 102) of mean summer afternoon mixing heights (see Table B-l for data) 34
10 Isopleths (m x 102) of mean autumn afternoon mixing heights (see Table B-l for data) 35
11 Isopleths (m sec"1) of mean annual wind speed averaged through the morning mixing layer (Figure 1) • 36
12 Isopleths (m sec"!) of mean winter wind speed averaged through the morning mixing layer (Figure 2) • 37
13 Isopleths (m sec" *) of mean spring wind speed averaged through the morning mixing layer (Figure 3) - 38
14 Isopleths (m sec"1) of mean summer wind speed averaged through the morning mixing layer
(Figure 4) 39
15 Isopleths (m sec"1) of mean autumn wind speed averaged through the morning mixing layer
(Figure 5) 40
16 Isopleths (m sec ) of mean annual wind speed averaged through the afternoon mixing layer
(Figure 6) 41
17 Isopleths (m sec"1) of mean winter wind speed averaged through the afternoon mixing layer
(Figure 7) 42
18 Isopleths (m sec"1) of mean spring wind speed averaged through the afternoon mixing layer
(FigureS) 43
19 Isopleths (m sec"1) of mean summer wind speed averaged through the afternoon mixing layer
(Figure 9) 44
20 Isopleths (m sec" *) of mean autumn wind speed averaged through the afternoon mixing layer
(Figure 10) _. _. 45
21 Data and isopleths (sec m"1) of median annual morning X/Q values (see text) for 10- (upper
numerals and dashed isopleths) and 100-km (lower numerals and solid isopleths) city sizes 45
22 Data and isopleths (sec m"1) of median winter morning X/Q values (see text) for 10- (upper
numerals and dashed isopleths and 100-km (lower numerals and solid isopleths) city sizes 47
23 Data and isopleths (sec m"1) of median spring morning X/Q values (see text) for 10- (upper
numerals and dashed isopleths) and 100-km (lower numerals and solid isopleths) city sizes 48
24 Data and isopleths (sec m"1) of median summer morning X/Q values (see text) for 10- (upper
numerals and dashed Isopleths) and 100-km (lower numerals and solid isopleths) city sizes 49
25 Data and isopleths (sec m" *) of median autumn morning X/Q values (see text) for 10- (upper
numerals and dashed isopleths) and 100-km (lower numerals and solid isopleths) city sizes 50
26 Data and isopleths (sec m" *) of median annual afternoon X/Q values (see text) for 10- (upper
numerals) and 100-km (lower numerals and solid isopleths) city sizes 51
27 Data and isopleths (sec m"1)of median winter afternoon X/Q values (see text) for 10- (upper
numerals) and 100-km (lower numerals and solid isopleths) city sizes 52
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28 Data and isopleths (sec m~') of median spring afternoon X/Q values (see text) for 10- (upper
numerals) and 100-km (lower numerals and solid isopleths) city_sizes 53
29 Data and isopleths (sec m~') of median summer afternoon X/Q values (see text) for 10- (upper
numerals) and 100-km (lower numerals and solid isopleths) city sizes 54
30 Data and isopleths (sec m )of median autumn afternoon X/Q values (see text) for 10- (upper
numerals) and 100-km (lower numerals and solid isopleths) city sizes 55
31 Data and isopleths (sec im1) of upper quartile annual morning X/Q values (see text) for 10-
(upper numerals and dashed isopleths) and 100-km (lower numerals and solid isopleths) city
sizes 56
32 Data and isopleths (sec m^1) of upper quartile winter morning X/Q values (see text) for 10-
(upper numerals and dashed isopleths) and 100-km (lower numerals and solid isopleths) city
sizes 57
33 Data and isopleths (sec nT *) of upper quartile spring morning X/Q values (see text) for 10-
(upper numerals and dashed isopleths) and 100-km (lower numerals and solid isopleths) city
sizes 58
34 Data and isopleths (sec m~1) of upper quartile summer morning X/Q values (see text) for 10-
(upper numerals and dashed isopleths) and 100-km (lower numerals and solid isopleths) city
sizes 59
35 Data and isopleths (sec m~ 1) of upper quartile autumn morning X/Q values (see text) for 10-
(uppcr numerals and dashed isopleths) and 100-km (lower numerals and solid isopleths) city
sizes 60
36 Data and isopleths (sec m~ *) of upper quartile annual afternoon X/Q values (see text) for 1 fl-
ipper numerals) and 100-km (lower numerals and solid isopleths) city sizes 61
37 Data and isopleths (sec m~ J) of upper quartile winter afternoon X/Q values (see text) for 10-
(upper numerals and dashed isopleths) and 100-km (lower numerals and solid isopleths) city
sizes 62
38 Data and isopleths (sec m^1) of upper quartile spring afternoon X/Q values (see text) for 1 fl-
ipper numerals) and 100-km (lower numerals and solid isopleths) city sizes 63
39 Data and isopleths (sec m~ *) of upper quartile summer afternoon X/Q values (see text) for 10-
(upper numerals) and 100-km (lower numerals and solid isopleths) city sizes 64
40 Data and isopleths (sec m~ *) of upper quartile autumn afternoon X/Q values (see text) for 10-
(uppcr numerals) and 100-km (lower numerals and solid isopleths) city sizes 65
41 Data and isopleths (sec m"1) of upper decile annual morning X/Q values (see text) for 10-
(upper numerals and dashed isopleths) and 100-km (lower numerals and solid isopleths) city
sizes 66
42 Data and isopleths (sec im1) of upper decile winter morning X/Q values (see text) for 10-
(upper numerals and dashed isopleths) and 100-km (lower numerals and solid isopleths) city
sizes 67
43 Data and isopleths (sec m^1) of upper decile spring morning X/Q values (see text) for 10-
(upper numerals" and dashed isopleths) and 100-km (lower numerals and solid isopleths) city
sizes __. 68
44 Data and isopleths (sec m"1) of upper decile summer morning X/Q values (see text) for 10-
(upper numerals and dashed isopleths) and 100-km (lower numerals and solid isopleths) city
sizes 69
45 Data and isopleths (sec m"1) of upper decile autumn morning X/Q values (see text) for 10-
(upper numerals and dashed isopleths) and 100-km (lower numerals and solid isopleths) city
sizes .__._ 70
46 Data and isopleths (sec m"1) of upper decile annual afternoon X/Q (see text) for 10- (upper
numerals and dashed isopleths) and 100-km (lower numerals and solid isopleths) city sizes 71
47 Data and isopleths (sec m"1) of upper decile winter afternoon X/Q values (see text) for 10-
(upper numerals and dashed isopleths) and 100-km (lower numerals and solid isopleths) city
sizes 72
vi
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48 Data and isopleths (sec m J) of upper decile spring afternoon X/Q values (see text) for 10-
(upper numerals) and 100-km (lower numerals and solid isopleths) city sizes 73
49 Data and isopleths (sec m~ 1) of upper decile summer afternoon X/Q values (see text) for 10-
(upper numerals and 100-km (lower numerals and solid isopleths) city sizes 74
50 Data and isopleths (sec m-1) of upper decile autumn afternoon X/Q values (see text) for 10-
(upper numerals and dashed isopleths) and 100-km (lower numerals and solid isopleths) city
sizes 75
51 Isopleths of total number of episode-days in 5 years with mixing heights <500 m, wind speeds
< 2.0 m sec~1, and no significant precipitation (see text) - for episodes lasting at least 2 days.
Numerals on left and right give total number of episodes and episode-days, respectively. Season
with greatest number of episode-days indicated as W (winter), SP (spring), SU (summer), or A
(autumn) 76
52 Isopleths of total number of episode-days in 5 years with mixing heights < 500 m, wind speeds
< 4.0 m sec~ l, and no significant precipitation (see text) — for episodes lasting at least 2 days.
Numerals on left and right give total number of episodes and episode-days, respectively. Season
with greatest number of episode-days indicated as W (winter), SP (spring), SU (summer), or A
(autumn) 77
53 Isopleths of total number of episode-days in 5 years with mixing heights <500 m, wind speeds
< 6.0 m sec~ !, and no significant precipitation (see text) — for episodes lasting at least 2 days.
Numerals on left and right give total number of episodes and episode-days, respectively. Season
with greatest number of episode-days indicated as W (winter), SP (spring), SU (summer), or A
(autumn) 78
54 Isopleths of total number of episode-days in 5 years with mixing heights < 7000 m, wind
speeds < 2.0 m sec~ !, and no significant precipitation (see text) — for episodes lasting at least
2 days. Numerals on left and right give total number of episodes and episode-days, respectively.
Season with greatest number of episode-days indicated as W (winter), SP (spring), SU (summer),
or A (autumn) 79
55 Isopleths of total number of episode-days in 5 years with mixing heights < 7000 m, wind
speeds < 4.0 m sec~ !, and no significant precipitation (see text) — for episodes lasting at least
2 days. Numerals on left and right give total number of episodes and episode-days, respectively.
Season with greatest number of episode-days indicated as W (winter), SP (spring), SU (summer),
or A (autumn) 80
56 Isopleths of total number of episode-days in 5 years with mixing heights < 7000 m, wind
speeds < 6.0 m sec~ ', and no significant precipitation (see text) — for episodes lasting at least
2 days. Numerals on left and right give total number of episodes and episode-days, respectively.
Season with greatest number of episode-days indicated as W (winter), SP (spring), SU (summer),
or A (autumn) 81
57 Isopleths of total number of episode-days in 5 years with mixing heights < 7500 m, wind
speeds < 2.0 m sec~ ', and no significant precipitation (see text) — for episodes lasting at least
2 days. Numerals on left and right give total number of episodes and episode-days, respectively.
Season with greatest number of episode-days indicated as W (winter), SP (spring), SU (summer),
or A (autumn) 82
58 Isopleths of total number of episode-days in 5 years with mixing heights < 7500 m, wind
speeds < 4.0 m sec~ ', and no significant precipitation (see text) - for episodes lasting at least 2
days. Numerals on left and right give total number of episodes and episode-days, respectively.
Season with greatest number of episode-days indicated as W (winter), SP (spring), SU (summer),
or A (autumn) 83
59 Isopleths of total number of episode-days in 5 years with mixing heights < 7500 m, wind
speeds < 6.0 m sec~ l, and no significant precipitation (see text) — for episodes lasting at least
2 days. Numerals on left and right give total number of episodes and episode-days, respectively.
Season with greatest number of episode-days indicated as W (winter), SP (spring), SU (summer),
or A (autumn) 84
vii
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60 Isopleths of total number of episode-days in 5 years with mixing heights < 2000 m, wind
speeds < 2.0 m sec' ', and no significant precipitation (see text) — for episodes lasting at least
2 days. Numerals on left and right give total number of episodes and episode-days, respectively.
Season with greatest number of episode-days indicated as W (winter), SP (spring), SU (summer),
or A (autumn) 85
61 Isopleths of total number of episode-days in 5 years with mixing heights < 2000 m, wind
speeds < 4.0 m sec' !, and no significant precipitation (see text) — for episodes lasting at least
2 days. Numerals on left and right give total number of episodes and episode-days, respectively.
Season with greatest number of episode-days indicated as W (winter), SP (spring), SU (summer),
or A (autumn) 86
62 Isopleths of total number of episode-days in 5 years with mixing heights < 2000 m, wind
speeds < 6.0 m sec' !, and no significant precipitation (see text) - for episodes lasting at least
2 days. Numerals on left and right give total number of episodes and episode-days, respectively.
Season with greatest number of episode-days indicated as W (winter), SP (spring), SU (summer),
or A (autumn) 87
63 Isopleths of total number of episode-days in 5 years with mixing heights < 500 m, wind speeds
< 4.0 m sec'!, and no significant precipitation (see text) - for episodes lasting at least 5 days.
Numerals on left and right give total number of episodes and episode-days, respectively. Season
with greatest number of episode-days indicated as W (winter), SP (spring), SU (summer), or A
(autumn) 88
64 Isopleths of total number of episode-days in 5 years with mixing heights < 500 m, wind speeds
< 6.0 m sec~l, and no significant precipitation (see text) — for episodes lasting at least 5 days.
Numerals on left and right give total number of episodes and episode-days, respectively. Season
with greatest number of episode-days indicated as W (winter), SP (spring), SU (summer), or A
(autumn) 89
65 Isopleths of total number of episode-days in 5 years with mixing heights < 7000 m, wind
speeds < 4.0 m sec"}, and no significant precipitation (see text) — for episodes lasting at least
5 days. Numerals on left and right give total number of episodes and episode-days, respectively.
Season with greatest number of episode-days indicated as W (winter), SP (spring), SU (summer),
or A (autumn) 90
66 Isopleths of total number of episode-days in 5 years with mixing heights < 7000 m, wind
speeds < 6.0 m sec~ ! , and no significant precipitation (see text) - for episodes lasting at least
5 days. Numerals on left and right give total number of episodes and episode-days, respectively.
Season with greatest number of episode-days indicated as W (winter), SP (spring), SU (summer),
or A (autumn) 91
67 Isopleths of total number of episode-days in 5 years with mixing heights < 7500 m, wind
speeds < 4.0 m sec'!, and no significant precipitation (see text) — for episodes lasting at least
5 days. Numerals on left and right give total number of episodes and episode-days, respectively.
Season with greatest number of episode-days indicated as W (winter), SP (spring), SU (summer),
or A (autumn) 92
68 Isopleths of total number of episode-days in 5 years with mixing heights < 7500 m, wind
speeds < 6.0 m sec' J , and no significant precipitation (see text) — for episodes lasting at least
5 days. Numerals on left and right give total number of episodes and episode-days, respectively.
Season with greatest number of episode-days indicated as W (winter), SP (spring), SU (summer),
or A (autumn) 93
69 Isopleths of total number of episode-days in 5 years with mixing heights ^ 2000 m, wind
speeds < 4.0 m sec'', and no significant precipitation (see text) - for episodes lasting at least
5 days. Numerals on left and right give total number of episodes and episode-days, respectively.
Season with greatest number of episode-days indicated as W (winter), SP (spring), SU (summer),
or A (autumn) °4
via
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70 Isopleths of total number of episode-days in 5 years with mixing heights < 2000 m, wind
speeds < 6.0 m sec~], and no significant precipitation (see text) — for episodes lasting at least
5 days. Numerals on left and right give total number of episodes and episode-days, respectively.
Season with greatest number of episode-days indicated as W (winter), SP (spring), SU (summer),
or A (autumn) 95
71 Isopleths of total number of forecast-days of high meteorological potential for air pollution in a
5-year period. Data are based on forecasts issued since the program began, 1 August 1960 and 1
October 1963 for eastern and western parts of the United States, respectively, through 3 April
1970 •••_•_• 96
C-l Variations of X/Q (see text) with city size (S) for various combinations of mixing height (H)
and wind speed (U) 116
IX
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LIST OF TABLES
Table Page
1 Average Normalized Concentration, X/Q (sec m~~') 10
2 Episodes Lasting 5 or More Days with Wind Speed < 2 m sec~ ' 19
3 Rank of Reciprocals of H x U 20
A-l Mixing Height and Wind Speed Tabulations Prepared by the National Climatic Center 99
A-2 Example of National Climatic Center Tabulation III, Daily X/Q Values 102
A-3 Example of National Climatic Center Tabulation III, Seasonal Mean Values 103
A-4 Example of National Climatic Center Tabulation II, Episodes 104
A-5 Example of National Climatic Center Tabulation I, Mixing Heights by Wind Speeds 105
B-l Mean Seasonal and Annual Morning and Afternoon Mixing Heights (H) and Wind Speeds (U)
for NOP and All Cases 108
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ABSTRACT
The mixing-layer height and the average wind speed within the mixing layer were calculated twice for each
day of a 5-year record of upper air observations at 62 National Weather Service stations in the contiguous United
States. The times of day of these calculations are morning and mid-afternoon. A rough allowance was made for
effects of the urban "heat island" on the morning mixing heights. The morning and afternoon times coincide
approximately with those of maximum and secondary minimum concentrations of slow-reacting pollutants in
cities. These calculations illustrate the typical large diurnal variation in atmospheric dispersion. Twenty charts
present seasonal and annual, and morning and afternoon mean mixing heights and wind speeds.
A model of some general dispersion features over urban areas is described in which the normalized pollutant
concentration averaged over a city is a function of mixing height, wind speed, and city size (distance the wind
travels across the city). Frequency values of mixing height by wind speed are used with the model to calculate
average normalized concentration frequencies for each weather station. Thirty charts present isopleth analyses of
seasonal and annual, and morning and afternoon normalized pollutant concentrations that were exceeded 10, 25,
and 50 percent of the time for specified city sizes.
The occurrence of episodes during which upper limits on mixing height and wind speed were not exceeded
were determined from the daily morning and afternoon values of these parameters. Isopleths of the total number
of episode-days for episodes lasting at least 2 days and at least 5 days with various limiting mixing-height and
wind-speed values are presented in 20 charts.
KEY WORDS: Meteorology, air pollution forecasting, mathematical modeling, urban areas, mixing height, wind
speed
XI
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MIXING HEIGHTS, WIND SPEEDS, AND POTENTIAL
FOR URBAN AIR POLLUTANT THROUGHOUT
THE CONTIGUOUS UNITED STATES
INTRODUCTION
Recognition that community air pollution in the United States is a growing national problem has generated
interest in pertinent climatological information and an overall appraisal thereof in terms of quantitative pollution
potential. As used here, the potential for urban air pollution refers to certain meteorological factors that generally
are important in the transport and diffusion of pollutants emitted by myriad but non-trivial sources in urban
complexes. While a comprehensive and uniform climatology of air pollution potential for all major urban centers
would be invaluable, its preparation is precluded mainly by a lack of adequate detailed meteorological data.
The present study is based primarily upon regular measurements of temperature and winds aloft at 62
National Weather Service (NWS) stations throughout the 48 contiguous states. The spacing of these stations,
which is roughly 400 kilometers (km), establishes the overall resolution of spatial analyses. Since these upper-air
data provide only very general indications of real diffusion and transport patterns in the urban boundary layer,
which in fact are often highly complex, the results of this study should be recognized as only a general or
large-scale appraisal of community air pollution potential. It is hoped that more detailed local investigations will
follow.
Although prior investigations have made noteworthy contributions to the climatology of air pollution
potential, they have usually dealt only with certain aspects of the subject, often in a qualitative manner, and/or
have been limited to a particular location or section of the country. For example, Korshover's (1967) study of
stagnating anticyclones was categorical and was restricted to the area east of the Rockies; Hosier's (1961)
low-level inversion and wind-speed frequencies and Holzworth's (1964b) maximum mixing depths each dealt
mainly with the indicated parameters. Hosier (1964) presented available data according to geographic areas of the
United States, but made no attempt to evaluate the combined effects of the various dispersion parameters. Such
an evaluation was attempted by Holzworth (1964a), but it was based on an arbitrary classification system and
only considered data for two regions. More recently a quantitative appraisal of air pollution potential has been
presented (Holzworth, 1967) for a few selected locations. The same general approach will be followed in this
study but will be applied to the contiguous United States. Mixing-height and wind-speed data will be presented and
discussed, A simple mathematical model of urban diffusion that yields normalized pollutant concentrations
averaged over a city as a function of mixing height, wind speed, and city size will be described, and frequency
tables of mixing height by wind speed will be used in the model to generate frequencies of normalized pollutant
concentrations for different city sizes. A brief summary of this study was presented recently by Holzworth
(1970).
Figures discussed in the main body of this study are grouped together after the Summary and Conclusions;
tables and figures for each appendix are grouped at the end of the respective appendices to facilitate reference
to them.
1
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BASIC PARAMETERS: MIXING HEIGHT AND WIND SPEED
CONCEPTS AND COMPUTATION METHODS
The mixing height (or depth) is defined as the height above the surface through which relatively vigorous
vertical mixing occurs. The concept of a mixing layer in which the lapse rate is roughly dry adiabatic (unsaturated
conditions) is well founded on general theoretical principles and on practical grounds through operational use
over several years in the National Air Pollution Potential Forecasting Program (Stackpole, 1967; Gross, 1970).
Commonly, mixing heights go through a large diurnal variation. Although not measured directly, they can be
calculated approximately from routine meteorological measurements. This study centers on two times of the day,
morning and afternoon. The morning mixing height is calculated as the height above ground at which the dry
adiabatic extension of the morning minimum surface temperature plus 5°C intersected the vertical temperature
profile observed at 1200 Greenwich Median Time (GMT). The minimum temperature is determined from the
regular hourly airways reports from 0200 through 0600 Local Standard Time (LST). The "plus 5°C" is intended
to allow roughly for the usual effects of the nocturnal and early morning urban heat island since NWS upper
-air-measuring stations are located in rural or suburban surroundings. Thus, more properly, the urban morning
mixing height was calculated. The general notion of an urban nocturnal and morning mixing layer, which in
reality is often highly complex, is now fairly well established by the investigations of Duckworth and Sandberg
(1954), DeMarrais (1961), Summers (1967), and Clark (1969). The value of 5°C was determined arbitrarily after
inspection of urban-rural differences in minimum temperature for many locations. The individual differences
varied over a large range and undoubtedly depended upon a number of factors. For general application, however,
5°C is considered a slight over-estimate of an overall average minimum temperature difference — even for existing
large cities. For purposes of this report the plus 5°C is interpreted to include the effects of some surface heating
shortly after sunrise. Thus, the time of the urban morning mixing height coincides approximately with that of the
typical diurnal maximum concentration of slow-reacting pollutants in many cities, occurring around the morning
commuter rush hours. This treatment of the urban morning mixing height undoubtedly is a gross simplification of
the real situation, but it is considered reasonable for the climatological purposes of this study.
The afternoon mixing height is less complicated than the morning, but was calculated in the same way,
except that instead of the minimum temperature plus 5°C, the maximum surface temperature observed from
1200 through 1600 LST was used. Urban-rural differences of maximum surface temperature were assumed
negligible. The typical time of the afternoon mixing height may be considered to coincide approximately with the
usual mid-afternoon minimum concentration of slow-reacting urban pollutants.
The method described for determining the height of the afternoon mixing (or boundary) layer has been
compared with other methods by Hanna (1969), who found it to be the more practical. In addition, mixing
heights based on accelerometer and temperature measurements made with a light aircraft during daytime have
been found by McCaldin and Sholtes (1970) to be in good agreement with heights calculated as indicated herein
(except that McCaldin and Sholtes' calculated heights also made allowance for temperature advection aloft).
Wind speeds for both morning and afternoon were computed as arithmetic averages of speeds observed at
the surface and aloft within the mixing layer. Speeds aloft were available for 150 and 300 meters (m) above
station elevation and for 500, 1000, 1500, 2000, 2500, 3000, 4000 m. etc., above sea level. To prevent wind
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speeds near the same level from being used twice (e.g., as for a station at 190 m above sea level) only winds
separated by at least 150 m were used. Morning wind-speed calculations were based on speeds observed aloft at
1200 GMT and an average of the surface speeds observed (regular hourly airways) from 0200 through 0600 LST.
Afternoon average speeds were based on the speeds observed aloft at 0000 GMT and the average surface speed
from 1200 through 1600 LST. In this report the vertically averaged wind speeds are referred to simply as wind
speeds when there is no ambiguity.
In the mixing-height calculations, especially for afternoons, it was assumed implicitly that between the time
of a temperature-aloft measurement and a computation time significant changes in vertical temperature structure
arose only from heat input at the surface. Certainly, this is not generally true on a day-to-day basis. It is
reasonable to assume that over a period of years other influences average out (e.g., that cold air advection is
balanced by warm advection). The matter of marked cold air advection, however, did present a problem. For
example, when the maximum surface temperature between 1200 and 1600 LST was colder than the surface
temperature of the 1200 GMT sounding, the mixing height could not be calculated in the prescribed manner.
Such cases were designated type C.
The occurrence of precipitation also demanded special treatment since in such situations the assumption of
a dry adiabatic lapse rate in the mixing layer is questionable. Mixing heights (and wind speeds) during significant
precipitation were classified as type P. Significant precipitation was defined as at least two occurrences of light or
one of moderate or heavy in the regular hourly airway reports from 1000 through 2100 LST for afternoons and
from 2200 through 0900 LST for mornings. In the current study, P, C, and M (missing) mixing heights and wind
speeds have not been used, but allowance has been made for them (see Appendix B).
TABULATIONS AND AVAILABILITY
Morning and afternoon mixing heights and wind speeds for 62 stations were calculated and tabulated by the
National Climatic Center (NCC), Environmental Data Service (EDS), of the National Oceanic and Atmospheric
Administration (NOAA). The 62 stations are located by the dots of Figures 21 through 70 and are identified in
Table A-l. High-speed automatic computers were used to process meteorological observations on punched cards.
Most surface and upper-air observations were made from the same location and most calculations were for the 5
years, 1960 through 1964. The calculations were restricted to 5 years for economy and to pre-1965 because the
required hourly surface observations were on punched cards only through 1964. For most stations all hourly
surface observations through 1964 are readily available in published form (U.S. Department of Commerce) which
may be useful in further and/or more detailed studies involving the tabulations. All of the tabulations, which are
in three parts for each station, are too lengthy to publish here, but copies may be obtained at the cost of
reproduction from the Director, NCC, EDS, NOAA, Asheville, North Carolina 28801. The NCC (formerly
NWRC) tabulations are illustrated and described in detail in Appendix A.
MEAN MIXING HEIGHTS AND WIND SPEEDS
The NCC tabulations of mean non-P mixing height and wind speed were arbitrarily adjusted to allow for P,
C, and M cases at each station. The adjustment was based on the assumption that mixing-height and wind-speed
values for P and C cases generally would be greater than for non-P cases; M cases were rare. The manner in which
the allowance was made is described in Appendix B. The effect of the allowance on the mean values depended
upon thf frequency of cases other than non-P, as may be seen for each station in Table B-l.
MIXING HEIGHTS, WIND SPEEDS, AND URBAN AIR POLLUTION POTENTIAL
-------
Figures 1 through 20 present isopleths of "adjusted" seasonal and annual mean mixing height and wind
speed for morning and afternoon (see Table B-l for data). The data for all isopleth analyses in this report have
been included, not to emphasize precision but rather to permit those who might disagree with the analyses to
prepare their own. The analyses are based on data points spaced at about 400-km intervals. We have attempted to
incorporate only major topographical influences into the analyses. Thus, the large-scale nature of the analyses is
in concert with the rather gross distribution, at least in terms of urban air pollution potential, of the parameters
being considered. In regard to topographical influences, in mountainous regions most of the data points are
located at cities in the valleys and, therefore, the analyses are most appropriate to valley locations.
Urban Morning Mixing Heights
Patterns of mean annual, winter, spring, summer, and autumn morning mixing heights are shown in Figures
1 through 5, respectively. Annually (Figure 1), the morning heights range from under 300 m to over 900 m with
comparatively high values generally along the coasts and over the Great Lakes. This phenomenon is due
essentially to high relative humidities and/or low cloudiness, which inhibit formation of intense radiation
inversions. It is more pronounced along the Gulf and Atlantic Coasts than the Pacific because Gulf and Atlantic
coastal waters are warmer and provide a more copious supply of moisture to the atmosphere than those of the
Pacific. Another interesting feature of Figure 1 is the ridge of higher heights extending north-northwestward from
central New Mexico through western Montana with comparatively low heights on either side.
The pattern of annual morning heights is very similar to those of the individual seasons, and seasonal
variations generally are not large. However, a noticeable exception occurs along the central Gulf Coast where the
highest value on any of the morning charts, 1300 m, occurs at Burwood, Louisiana, in summer (Figure 4). Winter
and spring values are about half of those of summer and autumn due to the very warm and moist air there in
summer and autumn.
The summer season has the lowest and most widespread low mixing heights, with a large area over the
western high plateau having heights less than 200 m. The lowest seasonal mean height of 109 m occurs at Ely,
Nevada. Such low morning mixing heights are caused by intense radiation inversions whose formation is enhanced
by dry, thin (low-density) air. In both summer and autumn, a very large portion of the contiguous 48 states is
covered by morning mixing heights under 400 m. The smallest area covered by mixing heights under 400 m
occurs in spring.
Afternoon Mixing Heights
Patterns of mean annual, winter, spring, summer, and autumn afternoon mixing heights are displayed in
Figures 6 through 10, respectively. The general pattern of afternoon heights, as shown by the annual chart
(Figure 6), is opposite to that for mornings (Figure 1); i.e., afternoon heights are relatively low along the Pacific,
Gulf, and Atlantic Coast lines, and in the vicinity of the Great Lakes. This pattern is due primarily to the
ameliorating effect of large water bodies on maximum surface temperatures. Consequently, diurnal variations
along coast lines tend to be considerably less than over inland areas. Annually, the extreme diurnal variation
occurs over the southern Rockies where morning heights of a few hundred meters are replaced in the afternoon
by heights well above 2 km.
While the pattern of annual afternoon heights may be seen clearly in each of the seasonal patterns, the
seasonal variation of the values is much greater for afternoons than for mornings. However, because of the
Basic Parameters: Mixing Height and Wind Speed 5
-------
steadying influence of the oceans, most of this variation occurs at inland locations. Afternoon mean heights along
coast lines are remarkably steady throughout the seasons. As may be expected, lower afternoon heights occur in
winter (Figure 7) when they range from less than 600 in at northerly latitudes to over 1400 m over the southern
Rockies. Highest afternoon heights occur in summer (Figure 9) when they reach 4 km over the central Rockies.
In contrast, summer values along the California Coast are slightly less than in winter, resulting in extreme height
gradients over California. Similarly in the East, summer heights over the Appalachians are greater than in winter
but vavy little along the coast, resulting in large afternoon height gradients across the Atlantic seaboard in
summer. Actually, these gradients are likely to be greater than indicated by the analyses of available data. The
patterns and values of mean afternoon heights in spring and autumn (Figures 8 and 10), the transition months,
closely resemble those of the annual mean.
The mean afternoon mixing heights presented here correspond to the estimates of mean maximum mixing
depths presented previously by Holzworth (1964b). In comparing the two sets of data, it will be noticed that,
while the isopleth patterns are similar, the values in the current study are for the most part considerably higher
than in the earlier study. This is believed to be the result of two main factors. The earlier study used mean
temperatures based on soundings taken at 0300 GMT (i.e., for time zones in the United States varying between
1900 and 2200 LST). At these early evening hours temperatures at levels near the upper part of the afternoon
mixing layer are practically unchanged from afternoon (neglecting advection, etc., in the mean) since radiational
cooling aloft has only been under way for a short time. Thus, the dry adiabatic extrapolation of the surface
maximum temperature first intersects the evening temperature profile at a lower height than it would for a
temperature sounding taken near sunrise (e.g., 1200 GMT). This is significant although the diurnal temperature
variation near the top of the afternoon mixing layer may be only 1 or 2°C. Secondly, the earlier study used
previously prepared monthly mean temperature profiles and maximum surface temperatures that included
precipitation cases. In such cases vertical temperature profiles tend to be more stable (neglecting condensation)
and maximum surface temperatures colder, resulting in lower afternoon mixing heights than in non-precipitation
cases.
Morning Wind Speeds
Isopleths of mean annual, winter, spring, summer, and autumn morning wind speeds are depicted in Figures
11 through 15, respectively. It should be understood that, in this report, "mean wind speeds" refer to annual and
seasonal means of arithmetic averages of observed speeds within each mixing layer. The general pattern and values
of mean annual speeds (Figure 1 1) are much like those of the individual seasons. Annually, faster speeds occur
over the southern portion of the middle tier of states, over Montana, and along the Gulf and Atlantic coastlines;
slower speeds are located over the central and southern Rockies, in and near major valleys of Pacific Coast states,
and in a broad area extending southwestward from the central Appalachians. The fastest mean annual speeds
reach almost 8 m sec~ , whereas the slowest are around 2 m sec~ .
Although the annual pattern of morning speeds is similar to that for the seasons, there are certain seasonal
features worthy of mention. In the western half of the 48 states the largest area of slow speeds (e.g., less than 4.0
m sec ) exists in winter (Figure 12), whereas in the East it exists in summer (Figure 14). At most locations the
fastest speeds occur in spring (Figure 13). But noteworthy exceptions are found over Montana, along the north
Atlantic seaboard, and in the vicinity of the eastern Great Lakes where the fastest speeds occur in winter. The
area of fast winds along the Atlantic Coast and the finger of fast speeds reaching westward over the Great Lakes
in winter appear to be associated with high morning mixing heights (Figure 2), which in turn are enhanced by
cloudiness associated with cold air outbreaks over the lakes and with storms along the Atlantic Coast.
MIXING HEIGHTS, WIND SPEEDS, AND URBAN AIR POLLUTION POTENTIAL
-------
Afternoon Wind Speeds
Isopleths of mean annual, winter, spring, summer, and autumn afternoon speeds are shown in Figures 16
through 20, respectively. In general these patterns are similar to those for mornings, except the afternoon speeds
are about 1 to 2 m sec"1 faster.
Basic Parameters: Mixing Height and Wind Speed
-------
-------
URBAN DISPERSION MODEL
While the mixing-height and wind-speed data provide an opportunity for qualitative appraisal of the
large-scale features of meteorological potential for community air pollution, the value of any interpretation of the
data will be enhanced considerably if it is in quantitative terms. A quantitative interpretation can be achieved by
use of a mathematical model of dispersion over urban areas.
The model to be used here gives the average normalized concentration (X/Q)(i.e., the concentration (X)
averaged over a city and normalized for uniform average area emission rate (Q), as a function of mixing height
(H), wind speed (U), and along-wind distance (S) across the city). All units are in meters, seconds, and grams
except where indicated otherwise . The main assumptions are :
1. Steady -state conditions prevail.
2. Emissions occur at ground level and are uniform over the city.
3. Pollutants are nonreactive.
4. Lateral diffusion can be neglected.
5. Vertical diffusion from each elemental source conforms to unstable conditions and concentrations
follow a Gaussian distribution out to a defined travel time that is a function of H. Thereafter, a
uniform vertical distribution of pollutant occurs as a result of further dispersion within the mixing
layer.
The model treats the city source as a continuous series of infinitely long cross-wind line sources, much as
Lucas (1958) did, with pollutants confined within the mixing layer. As indicated in assumption 5, the model
requires two equations according to whether none or some of the pollutants emitted at ground level achieve a
uniform vertical distribution within the mixing layer before being transported beyond the downwind edge of the
city. These equations are developed in Appendix C as equations 6 and 9, respectively, and may be written as
= 3.994(S/U)°'115 (6a)
for (S/U) < 0.47 1H (i.e., when no pollutants achieve a uniform vertical distribution), and
6° (9a)
for (S/U) > 0.471H (i.e., when some pollutants achieve a uniform vertical distribution). For most cases the
term with coefficient 0.088 is very small and can be neglected.
Table 1 presents the values of X/Q as a function of H, U, and S. As pointed out in Appendix C, the variation
of X/Q with S is practically linear for cities larger than 10 km. Therefore, the data in Table 1 are given for only
two city sizes, 10 and 100 km (i.e., distance the wind travels across the city).
-------
In Table 1 the dashed line separates X/Q values to the lower right for which H has absolutely no effect for a
10-km city (i.e., all pollutants emitted over a 10-km city are transported beyond the downwind edge of the city
before any uniform vertical distribution is achieved within the mixing layer;equation 6a is used). Actually for a
given wind speed X/Q is practically constant (whole number accuracy) for mixing heights somewhat lower than
those for which there is absolutely no effect. This happens because only a small portion of all emissions (i.e.,
those from near the upwind edge of the city) are affected by the mixing layer before passing beyond the city. In
Table 1 this effect can also be seen for a 100-km city, even though equation 6a is not applicable for a 100-km
city for the largest mixing height and wind speed values considered.
Table 1. AVERAGE NORMALIZED CONCENTRATION, X/Q (sec rrT1)
City size.
km
10
100
10
100
10
100
10
100
10
100
10
100
10
100
10
100
10
100
10
100
10
100
Mixing
height.
m
125
125
375
375
625
625
875
875
1250
1250
1750
1750
2250
2250
2750
2750
3250
3250
3750
3750
4500
4500
0.75
60
540
26
186
19
115
16
85
14
62
13
48
13
39
12
34
12
31
12
28
12
26
1.5
33
273
17
97
14
62
12
47
12
36
11
29
11
25
11
22
11
21
11
19
11
18
2.5
23
167
13
61
11
40
11
32
11
25
10
21
10
19
10
17
10
16
10
16
10
15
Wind speed, m sec
3.5
18
121
12
46
11
31
10
25
10
21
10
18
10
16
10
15
10
15
10
14
10
14
4.5
16
96
11
37
10
26
10
21
10
18
10
16
10
15
10
14
10
14
10
13
10
13
5.5
14
79
10
32
10
23
10
19
9
16
9
15
9
14
9
13
9
13
9
13
9
13
7.0
12
64
10
27
9
20
9
17
9
15
9
14
9
13
9
13
9
12
9
12
9
12
^.0
11
51
9
23
9
17
9
15
9
14
9
13
9
12
9
12
9
12
9
12
9
12
11.0
10
43
9
20
9
16
9
14
9
13
9
12
9
12
9
12
9
11
9
11
9
11
13.0
10
38
9
18
9
14
9
13
9
12
9
12
9
11
9
11
9
11
9
11
9
11
Dashed line separates values to lower right for which the mixing height has absolutely no effect on X/Q for a 10-km city.
10
MIXING HEIGHTS, WIND SPEEDS, AND URBAN AIR POLLUTION POTENTIAL
-------
An interesting feature of the model is that the larger the city size, the larger the effect an incremental
change in U or H has on X/Q (see Table 1). This effect is especially large at comparatively small values of U and H,
and clearly illustrates the importance of representative data in describing the meteorological potential for air
pollution during critical situations. It also indica'es that for daily forecasting purposes the input data must be
very precise if forecasts are to be reasonably accurate.
Another noteworthy characteristic of the model is that the smaller the values of H and U, and the larger the
value of S, the smaller the relative difference between X/Q values for this model and those for a "box" model
where (X/Q)BOx_=_l/2 (S/HU). Thus, for H = 125 m, U = 0.75 m sec~ l and S = 100 km; X/Q = 540 sec rrTJ
(Table 1) and (X/Q)Box = 533 sec rn~ '. This correspondence does not hold, however, for more common values
ofH, U.andS.
Although the model presented here is rather simple in comparison to the great complexities of atmospheric
dispersion and pollutant emissions in urban areas, it is in concert with the general nature of the independent
parameters and the spacing of the locations for which mixing height and wind speed are available. As such, it
provides a means of quantitatively appraising the general meteorological potential for community air pollution.
Obviously, the results of this study will be enhanced by more detailed studies of each local situation.
This model is essentially the same as that for which Miller and Holzworth (1967) obtained good
correspondence between calculated and observed average concentrations for each of several cities. The model is
derived in Appendix C.
Urban Dispersion Model 11
-------
-------
POTENTIAL FOR URBAN AIR POLLUTION
Using the frequency tabulations of mixing height by wind speed (Appendix A) as adjusted for the
occurrence of precipitation (Appendix B) and the dispersion model, cumulative frequencies of average normalized
concentration (X/Q) for various city sizes were generated for each of the 62 upper air stations. From these data
the X/Q value that was exceeded 10, 25, and 50 percent of the time was found for various city sizes for each
station. In cases where the largest X/Q value (for the smallest values of H and U) occurred more frequently than
the percentile value being considered, the desired values were obtained by extrapolation of the cumulative
frequency curve of X/Q. As shown in Appendix C, for a given mixing height and wind speed the variation of X/Q
with city size is practically linear for cities larger than 10 km. Thus, the isoplethed-maps of X/Q values that are
exceeded a specified percentage of time (Figures 21 through 50) consider only two city sizes, 10 and 100 km.
Where data are sparse, especially over water, the isopleth analyses have been extended reluctantly and should be
considered speculative.
In the interpretation of X/Q it will be recalled that this quantity is the city-wide average concentration (X)
normalized for uniform average area emission rate (Q). The units of X/Q are sec m~ , so that if Q is in
micrograms m see" *, X is in micrograms m . For example, if X/Q = 50 sec m~ and Q = 2 micrograms m
sec~ l, X (i.e., (X/Q) x Q) = 100 micrograms m"3.
Since X/Q is the average concentration normalized for emission rate, it represents the meteorological
potential for urban air pollution (i.e., non-meteorological variables for the most part are not considered).
Although city size is one of the independent variables, it determines the effectiveness of the meteorological
variables. Thus, the meteorological potential is dependent on city size. This dependency on city size may also
enter in another way. For example, the heat generated by very large cities may cause morning mixing heights to
be higher than for smaller cities. Such an effect would be most noticeable for the rarer extremes of very low
mixing heights. Because of uncertainties about these effects and because of the approximate manner in which
mixing heights are estimated, especially for mornings, these effects have not been included in this study. They
should be considered, however, in more detailed studies.
The X/Q data presented here may be applied most readily by comparing values for different parts of the
country and by projecting current measured pollutant concentrations in proportion to increases in X/Q values
with city size.
FIFTY-PERCENTILE CONCENTRATIONS
Morning
Figures 21 through 25 show data and isopleths of theoretical X/Q for 10- and 100-km cities that are
exceeded on 50 percent of all mornings annually, and in winter, spring, summer, and autumn, respectively.
Morning refe,s to the few hours centered near the morning commuter rush hours, which roughly coincide with
the diurnal maximum concentration of slow-reacting pollutants in many urban areas.
13
-------
Annually (Figure 21), the highest 50-percentile morning concentrations (i.e., X/Q) occur over southwestern
Oregon where for 10-km cities a value of almost 40 sec m is indicated. When such small cities grow to 100 km,
the concentration is expected to exceed 300 sec m" ', an increase by a factor of about eight. Concentrations of
roughly half those in southwestern Oregon are centered over Arizona and Wyoming. These areas of high
concentrations are due not only to the occurrence of slow winds (Figure 11) but also to low mixing heights
(Figure I), as indicated in Table 1. Such comparisons should be made cautiously, however, since mixing height
and wind speed frequency distributions at many stations are often anything but normal. East of the Rockies, the
annual median concentrations for 10-km cities vary between only 9 and 13secm ;for 100-km cities the values
are generally three to five times greater, except along much of the Atlantic and Gulf Coasts where the factor is
two to three. Assuming the current size of New York City is 50 km, the interpolated median morning X/Q value is
13 sec m~ ; when that city grows to 100 km the median value will increase to only 19 sec m . If New York
City were located a few hundred miles to the southwest, the annual median concentration for a 100-km city
would be around 50 sec m . Along the southern California Coast, the annual median value for a 60-km city
(approximate size of Los Angeles) is 41 sec m"" ', which increases to 63 sec in" ' for a 100-km city. In terms of
annual median morning X/Q values for 100-km cities, the meteorological potential along the southern California
Coast is about three times that along the mid-Atlantic Coast.
The seasonal patterns of median concentration for mornings are much like the annual pattern. In general
the smallest X/Q values occur in winter (Figure 22) over the eastern half of the United States and in spring (Figure
23) over the western half of the country. For most locations, the largest values occur in summer and/or autumn
(Figures 24 and 25), the area of greatest values in the East being further south and having slightly larger values in
autumn than in summer.
Afternoon
Figures 26 through 30 show theoretical X/Q values that are exceeded on 50 percent of all afternoons
annually, and in winter, spring, summer, and autumn, respectively. Afternoon refers to the several hours centered
around the usual time of daily maximum surface temperature, which in many cities roughly coincides with a
typical afternoon minimum concentration of slow-reacting pollutants.
Annually (Figure 26), the median afternoon X/Q values for a 10-km city are for the most part not much
smaller than the values for morning and they are practically uniform, being either 9 or 10 sec m~ . As indicated
in the discussion of the model, this happens mainly because the median afternoon mixing heights are so high.
Even for 100-km cities there is little variation in X/Q, with most values being near 15 sec m ; greatest values
occur near the California Coast where they are around 25 sec m'1. In terms of current large cities (around 50 km
in size), median afternoon X/Q values over most of the contiguous United States are 11 to 13 sec m" and attain
a maximum along the southern California Coast of only 17 sec irT'. In these terms there is little variation in the
meteorological potential for community air pollution.
The only seasonal pattern of afternoon median X/Q values that is appreciably different from the annual
pattern is for winter (Figure 27), and these differences are restricted to very large cities in the West. Thus, when
cities in central Wyoming reach 100 km, the winter X/Q values will exceed 55 sec m"' on half the afternoons;
similarly 35 sec m' will be exceeded over much of Washington, Oregon, and California. By comparison X/Q
along the southern California Coast will be around only 25 sec rrf l.
For the same city size, median theoretical concentrations are never greater and are usually less for
afternoons than for mornings, with the differences varying from slight to large depending upon location and city
size. Since the variation of X/Q values with city size is much more rapid for mornings than afternoons, the growth
14 MIXING HEIGHTS, WIND SPEEDS, AND URBAN AIR POLLUTION POTENTIAL
-------
of cities will affect the meteorological potential most profoundly for mornings. The general implications for
control and abatement purposes are obvious.
25-PERCENTILE CONCENTRATIONS
Morning
Figures 31 through 35 show data and isopleths of theoretical X/Q that are exceeded on 25 percent of all
mornings annually, and in winter, spring, summer, and autumn, respectively. These patterns are similar to those
for corresponding median X/Q charts (Figures 21 through 25), except that the upper quartile values arejarger in
the former, especially for 100-km cities. This happens because, as stated earlier, the rate of increase of X/Q with
decreasing wind speed and mixing height is greater for large cities than for small ones. Also, because of the
climatological variation of mixing height and wind speed, the range of X/Q values for both small and large cities is
greater for upper quartile than for median charts. For example, annually (Figure 31), the upper quartile X/Q
values for 10-km cities vary between 11 and 71 sec nT1 and for 100-km cities, between 29 and 649 sec m~ .
Thus, the patterns for quartile charts are more intense than for median charts. This is evident in Figures 31
through 35, where the isopleth patterns over the eastern United States are particularly clear when contrasted with
the flat patterns of Figures 21 through 25.
Annually (Figure 31), the centers of highest upper quartile morning concentrations in the West are almost
double the corresponding median values. In the East the increase for 100-km cities is by a factor of more than six
at several locations, and there is a large area oriented along the Appalachian Mountains where the X/Q values for a
100-km city exceed 200 sec m~ .
Seasonally, there are some rather large variations in the upper quartile values of X/Q. In general, the values
in the eastern half of the United States are equally small in winter and spring (Figures 32 and 33); they are
greatest in autumn (Figure 35) by a factor of roughly three to four over winter and spring. Over the Rockies, the
values are smallest in spring and summer, and greatest in autumn and winter by a factor of about two. In the far
West, the values are smallest in spring, except for the southern California Coast where they are smallest in
summer. Values are greatest over the northern section of the West in summer and over the southern section in
autumn and winter. Some fairly large values also occur over the upper Plains during summer. It is interesting that
at the upper quartile level, seasonal peak X/Q values in the East and West are each about 90 and 825 sec m~ for
10- and 100-km cities, although they occur in different seasons, autumn and summer.
Afternoon
Figures 36 through 40 show theoretical X/Q values that are exceeded on 25 percent of all afternoons
annually, and in winter, spring, summer, and autumn, respectively. Annually, the upper quartile concentrations
for 10-km cities are practically constant, varying only between 9 and 11 sec m~ . These values are almost the
same as for the median concentrations. Even for 100-km cities, the upper quartile afternoon concentration at
most locations is only a fraction larger than the median concentration. Annually, the largest upper quartile
afternoon concentrations for 100-km cities occur over southern California with values of only 35 to 40 sec m~'.
Upper quartile values of afternoon X/Q over the eastern United States vary slightly seasonally and spatially.
In the western United States in winter, however, the concentrations for 100-km cities exceed 75 sec irT1 over
large areas, attaining a value of 204 sec m^ over central Wyoming and 116 sec m~1 over southwestern Oregon.
While the winter patterns for 10- and 100-km cities are similar, they are much less intense for smaller cities.
Potential for Urban Air Pollution 15
-------
Notice that in Figure 37 the isopleths over Wyoming are left incomplete not only for ease of reading but also
because the extreme values may be representative of a small area.
Upper quartile charts for the other seasons are generally much like those for the annual data, except that, for
100-km cities, the X/Q values are around 45 sec irT ' over southern California in summer and autumn (as well as
in winter). The X/Q values are around 45 sec rrT ' just off the coast of Massachusetts in summer also.
TEN-PERCENTILE CONCENTRATIONS
Morning
Figures 41 through 45 show that data and isopleths of theoretical X/Q are exceeded on 10 percent of all
mornings annually, and in winter, spring, summer, and autumn, respectively. These patterns are similar to those
for corresponding upper quartile X/Q charts (Figures 31 through 35), except that upper decile values are larger
and the patterns are more intense. The increases over upper quartile and median values are generally larger in the
East than in the West. For example, annually (Figure 41) at the upper decile level the higher values in the East are
about equal to those in the far West, whereas at the median level (Figure 21) there is little pattern in the East but
a clear maximum in the far West. Annually, the largest upper decile morning X/Q values exceed 80 and 800 sec
m for 10- and 100-km cities, and there are large sections of the country where 60 and 600 sec m~ are
exceeded. These are indeed large values (e.g., in comparison to corresponding median values). It is fortuitous that
most of our very large cities are not located in areas of such high meteorological potential for community air
pollution.
The relatively high X/Q values over the upper Plains (Figure 41) were unexpected, perhaps because most
cities in the area are not large and have not often experienced pollutant concentrations that generated widespread
interest. However, without effective abatement efforts, this situation is bound to become worse as cities grow.
Other regions that face a similar prospect show up clearly in the isopleth analyses.
The pattern of annual upper decile morning concentrations (Figure 41) is generally similar to that of each
of the seasons, but with differences in magnitude. In the eastern United States the area of high X/Q values along
the Appalachian Mountains is clearly highest in autumn (Figure 45) when, for some locations, they exceed 100
and 1000 sec m~ for 10- and 100-km cities, and are almost double the values in winter (Figure 42). In the upper
Plains the highest values occur in summer and the lowest in winter. Along the south Atlantic Coast, over Florida,
and along the Gulf Coast the concentrations are relatively low throughout the year, but they are lowest in
summer. The two regions of moderately high concentrations over the Rockies are highest in winter and autumn,
lowest in spring and summer. Highest X/Q values over western Oregon are around 100 and 1000 sec m~ l for 10- and
100-km cities, and occur in summer, but values are almost as high in autumn when they extend southward
through interior California. Over southern California the highest concentrations are comparatively moderate and
are attained in autumn and winter.
Afternoon
Figures 46 through 50 show the theoretical X/Q values that are expected to be exceeded on 10 percent of
all afternoons annually, and in winter, spring, summer, and autumn, respectively. Annually (Figure 46), even at
the upper decile level, there is little variation in afternoon X/Q values east of the Rockies for 10- or 100-km cities,
and the values are only slightly larger than at the upper quartile level. In the western United States, however,
16 MIXING HEIGHTS, WIND SPEEDS, AND URBAN AIR POLLUTION POTENTIAL
-------
there are two areas where the upper decile X/Q values for 100-km cities exceed 50 sec m 1; over Wyoming and
Oregon peak values are near 150 and 100 sec m~ , respectively. For more realistic city sizes, however, the values
are much smaller.
Seasonally, most of the higher upper decile X/Q values shown annually are accounted for in winter (Figure
47); for 10- and 100-km cities, values of 70 and 650 sec m~1, respectively, are reached over Wyoming and values
of a little less than half are reached over Oregon. Notice that in these two regions the isopleths are left incomplete
for clarity and because the extreme values may not be generally respresentative. Nevertheless, X/Q values of over
100 sec m~ for 50-km cities are indicated for the two western regions. East of the Rockies, in winter, there is no
significant variation in X/Q for 10-km cities, and for 100-km cities the variation is not large. The X/Q values for
autumn afternoons (Figure 50) are very similar to those shown annually (Figure 46). In spring and summer
(Figures 48 and 49), there is practically no variation in X/Q for 10-km cities, and even for 100-km cities the
variation for the most part is rather small.
Potential for Urban Air Pollution 17
-------
-------
EPISODE-DAYS OF HIGH METEOROLOGICAL POTENTIAL
The classic study of the occurrence of episodes with restricted dispersion is the contribution of Korshover
(1967) who based his determinations largely upon the magnitude of sea-level pressure gradients. However, his
study was confined to the United States east of the Rocky Mountains because of problems inherent in the
reduction of pressure to sea level for stations located in high and irregular terrain. The current study does not
suffer from this limitation. Tabulations were made of episodes during which specified meteorological conditions
were satisfied at each of the 62 upper air stations. This report is concerned with episodes lasting at least 2 days
and episodes lasting at least 5 days with no precipitation cases and upper limits on mixing height and wind speed
determined by the following matrix:
Wind speed,
m sec"1
Mixing height, m
500 1000 1500 2000
2
4
6
The phrase, "episodes lasting at least 2 or 5 days," means that the conditions were satisfied in at least five or
eleven consecutive computation times, respectively (e.g., morning of day 1, to afternoon of day 1, to morning of
day 2, etc.). A defined precipitation event terminated an episode and was not counted as part of the episode. For
the seven stations for which full 5-year tabulations were not available (Table A-l), the episode data were
extrapolated to 5 years.
Figures 51 through 70 include the data for episodes lasting at least 2 and 5 days for mixing height-wind
speed limits in the foregoing matrix, with four exceptions. Figures are omitted for episodes of 5 days or longer
characterized by wind speeds 2.0 m sec~ or less and any of the four specified mixing heights since these
conditions only occurred as listed in Table 2.
Table 2. EPISODES LASTING 5 OR MORE DAYS WITH
WIND SPEED< 2.0 msec"1
Location
Medford, Ore.
Lander, Wyo.
Winnemucca, Nev.
Mixing Heights, m
500
4 (24)a
2(15)
0(0)
1000
9(59)
2(19)
0(0)
1500
10 (69)
2 (19)
1 (7)
2000
10(69)
2(19)
1 (7)
The first figure is the number of episodes; the number of episode-days is
given in parentheses.
19
-------
These episodes all occurred in winter. Each of the six most severe episodes (i.e., at Medford and Lander) was
clearly associated with a quasi-stationary anticyclone.
Before discussing the episode maps, it is of interest to consider the relative severity of the various mixing
height (H) and wind speed (U) limits (e.g., is an episode with H < 1000 m and U < 4.0 m sec"1 more severe than
one of equal duration with H < 1500 m and U < 2.0 m sec"1?). This can be done conveniently and roughly by
ranking the reciprocal of H x U as in Table 3.
Table 3. RANK OF RECIPROCALS OF H x U
Wind speed.
m sec"1
2
4
6
Episodes at Mixing Height, m
500
1
2
3
1000
2
4
5
1500
3
5
7
2000
4
6
8
This is practically the same ranking that is obtained using X/Q values for a city size of about 40 km or larger. The
total number of episodes and episode-days for a given duration and severity ranking may be approximated by
summing the occurrences for appropriate limiting conditions. For example, for episodes of 2 days or longer with
a severity ranking of 2 (H < 500 m, U < 4.0 m sec" l; and H < 1000 m, U < 2.0 m sec' ') at Lander, Wyoming,
the total number of episode-days is the sum of 154 (Figure 52, for H < 500 m, U < 4.0 m sec" 1) plus 94 (Figure
54, for H < 1000 m, U < 2.0 m sec"1) minus 71 (Figure 51, for H < 500 m, U < 2.0 in sec"'), which totals
177. This total is an underestimate, however, since episodes were determined separately for each set of
mixing-height and wind-speed conditions; episodes were not determined for multiple sets of conditions that may
be rated of approximately equal severity. Limiting mixing-height and wind-speed conditions of like severity have
not been combined in order to show the contributions of individual component conditions and since other
definitions of severity may be employed. The severity of various limiting meteorological conditions, together with
various episode durations, could be ranked in terms of Duration/(H x U), but this seems to be a gross over-
simplification, and is not considered further in the present study.
As mentioned, in mountainous regions most of the NWS observation data used in this study were obtained
in valleys and, therefore, are most appropriate to valley locations, although such details may not be shown by the
isopleth analyses.
EPISODES LASTING 2 DAYS OR LONGER
Figure 51 shows that episodes of 2 days or longer with extreme limiting conditions of H < 500 m and U <
2.0 m sec" 1 occur at only 11 of the 62 locations, mostly in the West. It is perhaps surprising that the total
number of such episode-days in 5 years is as high as 71 at Lander, Wyoming, and 52 at Medford, Oregon.
Increasing the wind-speed limit to 4.0 m sec" with H < 500 m (Figure 52) results in some occurrences at almost
two-thirds of the stations, although the total episode-days at many stations is small. At Lander the episode-days
totaled 154, an increase of 83 over Figure 51, whereas at Medford the increase is only 3 episode-days. This
happens because at Medford, with H < 500 m, episodes with 2.0 <\J < 4.0 m sec" l occur rarely. In Figure 52,
also notice the effect of relatively slow winds over California and fast winds over the middle tier of states. Figure
53 for H < 500 m and U < 6.0 m sec" shows increases over Figure 52 much as expected from the previous
20
MIXING HEIGHTS, WIND SPEEDS, AND URBAN AIR POLLUTION POTENTIAL
-------
discussion. The comparatively very large frequency of episode-days over southern California is due to the
occurrence of persistent low mixing heights and fairly slow winds with sparse precipitation.
Considering episodes with H < 1000 m, Figure 54 shows that with U < 2.0 m sec" the pattern of
episode-days is much like that of Figure 51 (H < 500 m, U < 2.0 sec"1). In both figures, the very limiting
conditions occur at only two stations in the East and in the West are greatest by far at Medford and Lander.
Increasing the wind speed limit to 4.0 m sec~ 1 with H < 1000 m (Figure 55) results in some episode-days at all
except 6 of the 62 stations. Most of these zero and other low occurrences are at stations in relatively windy
regions. In Figure 55 the greatest number of episode-days in the East barely exceeds 20, whereas m the West 100
is exceeded at many locations. The greatest number of episode-days in Figure 55 is 471 at San Diego, California
(isopleths incomplete in this area), and it is surprising that the values are more than twice those at nearby Santa
Monica (Los Angeles). This happens because the episode criterion most often not satisfied at both locations is
afternoon U < 4.0 m sec"1, and, while afternoon wind speeds at both locations are typically near the critical
value, they are usually around 1 m sec" faster at Santa Monica than at San Diego. This difference between San
Diego and Santa Monica occurs on most charts where the limiting wind speed is 4.0 m sec" . The comparatively
small frequency of episodes at Ely, Nevada, is also interesting. Over the central and southern Rockies the
afternoon mixing heights in spring, summer, and autumn are usually so high as to largely eliminate the occurrence
of low mixing-height episodes from all seasons except winter, but then the morning wind speeds (Figure 12) at
Ely are considerably faster than at nearby stations. Relatively low frequencies occur at Ely on most of the
episode figures. For H < 1000 m and U < 6.0 m sec" Figure 56 shows that these conditions occur at all
stations. In the West, 100 episode-days is exceeded at most stations and 600 episode-days is exceeded over much
of California, whereas in the East the greatest number of corresponding episode-days is 87 at Burwood. Louisiana
(near New Orleans).
Figure 57 shows that for H < 1500 m and U < 2.0 m sec"1 the episode frequencies are very similar to
those for H < 1000 m and U < 2.0 m sec" (Figure 54). Apparently for these conditions the mixing heights are
less effective than wind speeds in limiting the occurrence of episodes. Figure 58 is particularly important because
the limiting conditions of H < 1500 m and U < 4.0 m sec"l have been used, in one form or another, as criteria in
the National Air Pollution Potential Forecasting Program (Stackpole, 1967; Gross, 1970). Clearly, the
meteorological potential for episodes is much greater in the West than in the East, with barely 100 episode-days
at one eastern station and over 100 days at most western stations. Several western stations have more than 200
episode-days. Figure 59 shows that with H < 1500 m and U < 6.0 m sec" 1, episodes are quite frequent at most
stations. However, the severity of such potential episodes is markedly reduced by wind speeds at 6.0 m sec" ,
except perhaps for very large cities.
For the greatest mixing heights considered, H < 2000 m and U < 2.0 m sec"1, Figure 60 shows that in the
West episode data are practically unchanged from the conditions of Figure 57 (H < 1500 m and U < 2.0 m
sec" ), but that in the East the number of stations meeting the criteria almost doubles. Figure 61 illustrates that
episodes with H < 2000 m and U < 4.0 m sec" occur at all stations and such episode-days have a frequency
greater than 100 over most of the West and over much the East. For the least limiting conditions, H < 2000 m
and U < 6.0 m sec" , Figure 62 shows that the total episode-days in 5 years is less than 100 at only 12 stations
and is more than 200 (i.e., 1 day in about 9) at well over half the stations.
For H < 500 and < 1000 m (Figures 51 through 56) the season with the greatest number of episode-days
is winter for most stations. For H < 1500 and 2000 m (Figures 57 through 62) the predominant season with the
greatest number of episode-days continues to be winter in the West but shifts to autumn in the East. This is
probably due in part to the more frequent occurrence of winter cyclonic storms in the East than in the West. This
general effect of storminess may also be seen in the Pacific Northwest Region of Figures 58 through 62 where
autumn or summer is the season with the greatest number of episode-days at several stations. As a general rule for
the same limiting conditions, the average duration of episodes in the West tends to be greater than in the East.
Episode-Days of High Meteorological Potential 21
-------
EPISODES LASTING 5 DAYS OR LONGER
For 5-day episodes the frequencies and isoline patterns of Figures 63 through 70 are much like those with
corresponding limits on H and U for 2-day episodes (Figures 51 through 62), except that 5-day episodes generally
occur much less frequently. As indicated, 5-day episodes with U < 2.0 m sec"1 only occur at three stations.
Five-day episodes with the least limiting conditions, H < 2000 m and U < 6.0 m sec"! (Figure 70), did not occur
once in the 7 years considered at seven stations. For the important condition of H < 1500 m and U < 4.0 m
sec"1, 5-day episodes (Figure 67) occur at only 24 stations, whereas 3-day episodes (Figure 58) occur at 60
stations. This difference occurs mainly in the East. In general, the discussion regarding 2-day episodes is
applicable to 5-day episodes.
FORECAST EPISODES
For the most part there is fair qualitative agreement between the patterns of objectively derived
episode-days with limiting conditions like those used as forecast criteria (Figure 58) and actual forecast-days of
high air pollution potential (Figure 71). Notable exceptions occur, however, in the vicinity of Ely, Nevada, where
the condition seems to have been relatively over-forecast and in the vicinity of Lander, Wyoming, where it seems
to have been relatively under-forecast. Notice that in Figure 71 the actual forecast-days have been adjusted to a
5-year base for comparison with Figure 58. The number of derived episode-days in 5 years tends to be somewhat
greater than forecast, especially in the West. This is due, at least in part, to the conservative nature of the
forecasts and to the forecast requirement that meteorological conditions be met over a large area (minimum size
about 75,000 square miles). In regard to the latter requirement, inspection of derived episodes indicates that they
often occurred simultaneously at several adjacent stations in association with slow-moving anticyclones.
Especially along the California Coast, however, episodes of limited dispersion are often confined to rather small
areas.
22 MIXING HEIGHTS, WIND SPEEDS, AND URBAN AIR POLLUTION POTENTIAL
-------
SUMMARY AND CONCLUSIONS
This study is based upon regular surface observations and upper air measurements of temperature and wind
during 5 years at 62 NWS stations in the contiguous United States. These observations have been used to derive
climatological statistics on morning (after sunrise) and afternoon mixing heights over cities and vertically averaged
wind speeds through the corresponding heights. The method of deriving these data is given in some detail along
with sources for obtaining copies of the data in the hope that they will be used in other applications, particularly
more detailed and specific studies of air pollution meteorology.
Annual and seasonal isoplethed maps of mean morning and afternoon mixing heights and wind speeds are
presented. Morning mixing heights over most of the United States usually range in any season from around 300 to
800 m, with the higher values commonly found adjacent to large bodies of water. Afternoon mixing heights
display a large seasonal variation. Winter values range from 600 m over northern central and northwestern states
to 1400 m over the southern Rockies. In summer, the range is from 600 m along the California Coast to 4 km
over the southern Rockies with relatively low heights along all coasts. Maps of mean morning wind speed generally
display isopleth patterns that are similar from season to season although irregular variations occur in some areas
(e.g., over the northern Rockies and from the Great Lakes eastward to the Atlantic Coast). Fastest average speeds
reach 9 m see" in spring over Oklahoma and in winter over the northern Rockies and along the middle Atlantic
Coast. Slowest speeds are 2 m sec"1 and only occur in the far West, but morning winds of 3 m see" or less
occur in all seasons over much of California and Oregon; in summer, autumn, and winter over parts of the
Rockies; and in summer over the middle Appalachians and part of Mississippi. Seasonal patterns of afternoon
speeds are much like those for mornings except most afternoon speeds are around 1 to 2 m see" * faster.
A simple model of dispersion over urban areas is developed in which the theoretical city-wide average
pollutant concentration (x), normalized for uniform average area emission rate (Q), is a function of mixing
height, wind speed, and city size (i.e., along-wind distance across the city). For city sizes greater than 10 km,
the variation of X/Q with city size is practically linear. Frequency tabulations of mixing height by wind speed are
used in the model to generate cumulative frequencies of X/Q for each of the 62 observation locations. Isopleth
maps of annual and seasonal X/Q values for 10- and 100-km cities that were exceeded on 10, 25, and 50 percent
of mornings^ and afternoons are presented in 30 figures. This information may be utilized most readily by
comparing X/Q values (for a given city size) for different areas, and for different city sizes in accordance with
anticipated changes in city size and emission rates. In such evaluations, the assumptions in the model should not
be overlooked and care should be exercised in interpreting between data locations.
The isoplethed X/Q charts show that over the United States both large and small variations in these
theoretical values may occur spatially, diurnally, and seasonally as well as with city size and for different
percentile values of the cumulative frequencies. Thus, in terms of the concepts used in this study, the
meteorological potential is anything but simple and is summarized only briefly. Annually, the median X/Q values
for mornings (Figure 21) vary from 9 to 39 Sec m"1 for 10-km cities and from 17 to 329 sec m"1 for 100-km
cities with comparatively low values and flat isopleth patterns east of the Rockies and clearly defined patterns in
the West. At the upper quartile level the isopleths of morning annual X/Q values (Figure 31) show an additional
area of high values along the axis of the Appalachians, butjhe highest values remain in the far West centered over
Oregon. In the upper decile chart of morning annual X/Q values (Figure 41), the isopleth patterns are quite
intense with a range of values from 16 to 95 sec m"1 for 10-km cities and from 96 to 890 sec m~ for
23
-------
100-km cities. Highest concentrations are centered over Oregon with values almost as high over Mississippi and
extending northeastward along the Appalachians. A new area of relatively high values is located over the upper
Plains and secondary high centers over Wyoming and Arizona persist from the median chart. In general,
comparatively high morning concentrations occur over much of the West at the median, upper quartile, and upper
decile levels; along the Appalachians extending into Mississippi at the upper quartile and decile levels; and over
the upper Plains at the upper decile level. As a rule, the highest morning X/Q values occur in autumn and/or
summer.
For afternoons the annual chart of median X/Q values (Figure 26) indicates that 10-km cities have a value
of 9 or 10 sec m and 100-km cities have a range only from 13 to 26 sec m . This results in practically no
isopleth pattern for 10-km cities and a very flat pattern for 100-km cities. At the upper quartile level, the
afternoon annual values of X/Q (Figure 36) are not much greater than the median values, even for 100-km cities.
At the upper decile level the afternoon annual X/Q values (Figure 46) for 10-km cities range only from 10 to 22
sec m"1 and for 100-km cities from 20 to 150 sec m^1. While there are some clear-cut isopleth patterns for
upper decile annual afternoon concentrations, these are confined mostly to the West. However, even for 100-km
cities the afternoon isopleth patterns are rather flat compared with those on the corresponding morning chart.
This lack of spatial variation in the afternoon concentratkms_occurs largely because the afternoon mixing heights
are generally so high as to have little or no effect on the X/Q values even for 100-km cities. In view of the large
seasonal variation of afternoon mixing heights, it is not surprising to find that at most places the highest
afternoon X/Q values occur in winter and are considerably larger than corresponding annual values.
Morning and afternoon X/Q charts indicate that in some areas the diurnal variations are exceptionally large,
particuarly at the upper decile and quartile frequencies for large cities (e.g., along the Appalachians some upper
decile diurnal variations for 100-km cities exceed a factor of 25). This could happen because the more extreme
morning mixing heights for large cities are underestimated. Practical allowance for such effects (for city sizes of
up to 100 km) have reduced the morning X/Q values but the values are still considerably greater than afternoon
values, and they still increase with city size. Consideration of emission control strategies for preventing and
alleviating the widespread occurrence of undesirable pollutant concentrations over cities should recgonize that
large diurnal variations in X/Q occur in many regions and also that the magnitude of this variation increases with
city size. Added effects of morning X/Q values should also be carefully considered in those places where
recirculation of contaiminated air occurs, since such effects are not included in the dispersion model. Episodes of
at least a day during which high X/Q values may be expected are especially indicated for those areas where both
the morning and afternoon values are relatively large. The more outstanding areas of such coincidence are
centered in Wyoming and Oregon; they occur mainly in winter and autumn at upper decile and quartile
frequencies. As cities in these areas grow, they could experience very serious air pollution problems. Other
applications of the data presented in Figures 21 through 50 are readily apparent (e.g., for specific locations, and
for variations of city size and emission rate). However, because of the gross nature of the urban dispersion model
and the input parameters, the derived X/Q values should be recognized as only generally representative of real
situations.
Finally, this study has objectively determined the episodic occurrence of several limited dispersion
conditions during 5 years at each of the 62 upper air stations. Two episode durations are included, at least 2 days
and at least 5 days. The most limited dispersion conditions considered—mixing heights 500 m or less and wind
speeds 2.0 m sec or less with no significant precipitation during episodes lasting at least 5 days—occurred at
only two stations (a total of six episodes and 39 episode-days). The least-limited dispersion conditions
considered-mixing heights 2000 m or less and wind speeds 6.0 m sec" * or less with no significant precipitation
during episodes lasting at least 2 days (Figure 62)-occurred at all stations, and at San Diego and Santa Monica,
California, such episode-days were more common than not. Intermediate limiting conditions of mixing
heights—1500 m or less and wind speeds 4.0 m see" or less with no significant precipitation during episodes
lasting at least 2 days (Figure 58)—are of interest because such criteria have been used in the National Air
Pollution Potential Forecasting Program. Figure 58 shows that total episode-days with these conditions are at a
24 MIXING HEIGHTS, WIND SPEEDS, AND URBAN AIR POLLUTION POTENTIAL
-------
minimum through the middle tier of states with no days in 5 years at two stations. In the East, the total number
of these episode-days barely exceeds 100 at one station, but in the West 100 days is exceeded at most stations
and 200 days is not uncommon. Episodes with these same limiting conditions, but lasting at least 5 days (Figure
67), are extremely rare in all but the western states where 100 days in 5 years is exceeded at several stations.
Summary and Conclusions 25
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MIXING HEIGHTS, WIND SPEEDS, AND URBAN AIR POLLUTION POTENTIAL
-------
APPENDIX A. NCC TABULATIONS
OF MIXING HEIGHT AND WIND SPEED
This appendix provides a detailed description of the subject tabulations for the benefit of those interested
in obtaining copies. The 62 NWS upper-air (combined radiosonde and rawinsonde) stations for which tabulations
of mixing height and vertically averaged wind speed were prepared are listed in Table A-l along with pertinent
information. Station locations may be seen in Figures 21 through 70. All tabulations were accomplished by the
National Climatic Center (NCC) (formerly the National Weather Records Center) under Job Order 6234, except
those for Washington, D.C., which were under Job Order 7717. With few exceptions, each upper-air and
corresponding surface (airways) observing station was at the same location (e.g., airport). For each station, there
are three tabulations. The cover page of each tabulation includes the tabulation number (I, II, or III), upper-air
station name and WBAN number, and period of record. Each tabulation is prefaced by an explanation page. (For
clarity the tabulations are described in reverse numerical order, i.e., Ill, II, and I.)
TABULATION III
Table A-2 is an example of NCC Tabulation III. The station is Peoria, Illinois (WBAN number 14842), the
year is 1960 (60), the month is April (04), and the data for mornings are indicated on the left and for afternoons
on the right.
Column T gives the classification of a mixing-height calculation. If the regular hourly airways observations
from 2200 through 0900 LST included at least two occurrences of light precipitation or one of moderate or
heavy, the morning calculation is classified as P. A similar classification is employed for afternoons considering
hourly observations from 1000 through 2100 LST. P cases are of interest because the assumption of a dry
adiabatic lapse rate in the mixing layer may not be valid. If the surface temperature that is to be extended dry
adiabatically (the morning minimum plus 5°C or the afternoon maximum) is less than the surface temperature of
the 1200 GMT vertical temperature profile observation, no mixing height can be calculated. This condition is
indicated by a letter C. Such cases occurred especially in the afternoon with strong cold air advection after the
1200 GMT upper air observation but before noon LST. For C cases the speeds are averaged through 4000 m
above the station. "M" indicated missing. A blank in the T-column indicates that none of the foregoing types
occurred (i.e., the conditions of greatest interest in this study).
Column 1 gives the mixing height in meters (m); column 2, the vertically averaged wind speed through the
mixing layer in m sec~ , based on surface winds and on winds aloft observed at 1200 GMT for morning and 0000
GMT for afternoons; column 3, the average surface wind speed (used in the vertically averaged speed) in m see" ,
based on the five regular hourly airways reports from 0200 through 0600 LST for mornings, and from 1200
through 1600 LST for afternoons; column 4 gives the number of wind levels used to calculate the vertically
averaged speed of column 2. Column 4 is not included for some stations.
As illustrated in Table A-3 for the seasons, Tabulation III also gives the monthly and seasonal mean mixing
heights (column 1), means of vertically averaged speeds (column 2), mean surface speeds (column 3), and total
number of occurrences (column N), all by classification of the mixing-height calculation (column T). A blank in
the T-column designates the non-P and non-C cases.
97
-------
Five years of records are processed for most stations. Tabulation III consists of 63 pages; one page of
explanations, one page for each month of each year, one page for all monthly means, and one page for all
seasonal means.
TABULATION II
NCC Tabulation II is a temporal analysis of the daily morning and afternoon mixing heights and wind
speeds of Tabulation III (columns 1 and 2 therein). By month and season, it gives the frequencies of episodes of
specified duration or longer during which consecutive calculations of non-P mixing height and wind speed did not
exceed specified values. Table A-4 is an example of NCC Tabulation II. The letters A, B, C, D, E, F, G specify the
upper limits of the mixing height as 250, 500, 750, 1000, 1500, 2000, 3000 m, and in the next column the
numbers 2, 4, 6, 8 for each mixing height specify the upper limits of the vertically averaged wind speed as 2.0,
4.0, 6.0, 8.0 m see"'. The column headings 2, 3, 4, ... . , 121 are the prescribed minimum number of
consecutive calculations (e.g., morning to afternoon of day 1 to morning to afternoon of day 2, etc.) during
which the meteorological criteria were satisfied. Thus, if the criteria were met in eight consecutive computations,
that episode contributes a frequency count of one to each of the appropriate cells for 8, 7, 6, 5, 4, 3 and 2 or
more consecutive computations. However, it does not contribute a frequency count of two to a duration of four
or more consecutive calculations or a frequency count of four to a duration of two or more consecutive
calculations. Table A-4 is for all Januarys (01) of the years considered; for mixing heights not greater than 500 m
(B) and wind speeds not greater than 4.0 m sec~' (4), there were seven separate episodes that lasted through at
least two consecutive computations, three that lasted through at least three, one through at least four, and one
that lasted through at least five consecutive computations. On the other hand, for these same conditions one
episode persisted through exactly five consecutive computations, none through exactly four consecutive
computations, two through exactly three consecutive computations, and four through exactly two consecutive
computations. In Table A-4 the column at the far right gives the total number of occurrences of specified
conditions without regard to consecutiveness. For example, in Table A-4 there were 62 occurrences (morning and
afternoon) of a mixing height 500 m or less (B) with a wind speed of 4.0 m sec or less (4); P cases are not
included. It was assumed that the mixing height and wind speed computations were separated by 12-hour
intervals and that the duration of an episode lasting through exactly two consecutive computations was 12 hours;
the duration of an episode lasting through exactly three consecutive computations was 24 hours; etc.
For each station Tabulation II consists of 17 pages, which comprise one page of explanations, one page for
each month of all years, and one page for each season of all years.
TABULATION I
An example of NCC Tabulation I is shown as Table A-5. It gives frequency counts of mixing heights by
vertically averaged wind speeds, both in class intervals. There are separate tables for mornings and for afternoons
of each month and season for all years. The major portion of each table is for both non-P and non-C cases (both
indicated as "NOP"). However, there are column and row totals of P cases, column totals of C cases, the number
of missing cases, and column and row totals of all cases. Thus, in Table A-5, autumn (04) afternoons (02), there
were ten occurrences of non-P mixing heights 751 to 1000 m with a wind speed of 4.1 to 5.0 m sec~ (5); there
were 61 occurrences of non-P and 7 of P mixing heights 751 to 1000 m for all wind speeds. The total of all
mixing heights 751 to 1000 m is 68. For all speeds the total non-P cases are 381, total P cases are 53, total C cases
are 18, and 3 are missing for an accumulated total of 455 calculations for 5 years of autumns.
For each station, Tabulation I consists of 33 pages, which comprise one page of explanations and one page
for each time (morning or afternoon) of each month and season for all years.
98 MIXING HEIGHTS, WIND SPEEDS, AND URBAN AIR POLLUTION POTENTIAL
-------
Table A-1. MIXING HEIGHT AND WIND SPEED TABULATIONS
PREPARED BY THE NATIONAL CLIMATIC CENTER
Upper-air observing station
Location
Albany, New York
Albuquerque, New Mexico
Amarillo, Texas
Athens, Georgia
Bismarck, North Dakota
Boise, Idaho
Brownsville, Texas
Buffalo, New York
Burwood, Louisiana
Cape Hatteras, North Carolina
Caribou, Maine
Charleston, South Carolina
Columbia, Missouri
Dayton, Ohio
Denver, Colorado
Dodge City, Kansas
El Paso, Texas
Ely, Nevada
Flint, Michigan
Glasgow, Montana
Grand Junction, Colorado
Great Falls, Montana
Green Bay, Wisconsin
Greensboro, North Carolina
Huntington, West Virginia
International Falls, Minnesota
Jackson, Mississippi
Jacksonville, Florida
Lake Charles, Louisiana
Lander, Wyoming
Las Vegas, Nevada
Little Rock, Arkansas
Medford, Oregon
Miami, Florida
Midland, Texas
Montgomery, Alabama
Nantucket, Massachusetts
Nashville, Tennessee
New York, New York
North Platte, Nebraska
Oakland, California
Oklahoma City, Oklahoma
Peoria, Illinois
NWS
Abbr.
ALB
ABO
AMA
ANN
BIS
BOI
BRO
BUF
BRJ
HAT
CAR
CHS
CBI
DAY
DEN
DDC
ELP
ELY
FNT
GGW
GJT
GTF
GRB
GSO
HTS
INL
JAN
JAX
LCH
LND
LAS
LIT
MFR
MIA
MAF
MGM
ACK
BNA
JFK
LBF
OAK
OKC
PIA
WBAN no.
14735
23050
23047
13873
24011
24131
12919
14733
12863
93729
14607
13880
13983
93815
23062
13985
23044
23154
14826
94008
23066
24143
14898
13723
03860
14918
13956
13889
03937
24021
23169
13963
24225
12839
23023
13895
14756
13897
94789
24023
23230
13976
14842
Date
tabulations
completed
5/13/68
6/12/68
7/1/68
7/1/68
5/13/68
6/12/68
6/26/68
7/1/68
7/1/68
7/1/68
7/1/68
12/8/67
9/12/66
5/1 7/66
12/8/67
6/26/68
7/1/68
7/1/68
10/27/67
6/12/68
6/12/68
7/1/68
7/1/68
5/13/68
10/19/67
7/1/68
7/1/68
7/1/68
12/8/67
7/1/68
7/1/68
5/13/68
6/12/68
6/26/68
6/12/68
12/8/67
7/23/68
9/12/66
5/17/66
6/12/68
12/8/67
5/13/68
6/12/68
Years of
tabulations
(inclusive)
1960-1964
. 1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1961-1964
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1962-1964
1960-1964
1959-1962
1960-1964
1962-1964
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
Remarks
a
b
c
d
'Letters under remarks indicate footnotes given in text at end of table.
Appendix A. NCC Tabulations of Mixing Height and Wind Speed
99
-------
Table A-1 (continued)
Upper-air observing station
Location
Pittsburgh, Pennsylvania
Portland, Maine
Rapid City, South Dakota
St. Cloud, Minnesota
Salem, Oregon
Salt Lake City, Utah
San Antonio, Texas
San Diego, California
Santa Monica, California
Sault Ste. Marie, Michigan
Seattle, Washington
Shreveport, Louisiana
Spokane, Washington
Tampa, Florida
Topeka, Kansas
Tucson, Arizona
Washington, D.C.
Winnemucca, Nevada
Winslow, Arizona
NWS
Abbr.
PIT
PWM
RAP
STC
SLE
SLC
SAT
SAN
SMO
SSM
SEA
SHV
GEG
TPA
TOP
TUS
DIA
WMC
INW
WBAN no.
94823
14764
24090
14926
24232
24127
12921
03131
93197
14847
24233
13957
24157
12842
13996
23160
93734
24128
23194
Date
tabulations
completed
9/12/66
7/23/68
7/1/68
12/8/67
6/26/68
9/12/66
12/8/67
7/1/68
5/17/66
7/1/68
12/8/67
6/26/68
5/13/68
5/13/68
7/1/68
12/8/67
3/22/67
6/12/68
7/1/68
Years of
tabulations
(inclusive)
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1959-1961
1960-1964
1960-1964
1960-1964
1960-1964
1960-1964
1961-1964
1960-1964
1962-1964
Remarks*
f
g
h
i
Footnotes for Table A-1:
a. At Caribou from 1 August 1963 through 31 December 1964, the hourly airways observations from 0000
through 0400 EST were not taken. Thus, the afternoon computations were not affected in any way. The 0500
and 0600 EST reports were deemed adequate for determining the morning minimum temperature and the average
surface wind speed. The only problem arose in the determination of morning P cases, but this was solved by
appraisal of hourly precipitation amounts (from automatic precipitation gage records) for the missing hourly
reports. This appraisal was only necessary for those mornings when P cases were not determined in the usual
manner from the available hourly reports. In order to compare the results, Tabulations I, H, and III were prepared
separately for 1960 through 1962 and 1963 through 1964, as well as the complete period 1960 through 1964.
None of the differences in the tabulations could be ascribed to the alternate method of determining P cases.
b. The Dayton upper-air soundings were made from Sulphur Grove (979-ft elevation), about 6 miles
east-southeast of Cox-Dayton Airport (1002-ft elevation) where the hourly airways observations were made.
c. At Huntington, some of the wind reports for levels aloft within a mixing layer were occasionally missing,
necessitating computation of a vertically averaged speed based on incomplete data. Investigation showed,
however, that this rarely happened more than a few times a month.
d. At Lander from 1 January 1960 through 31 March 1962, many of the hourly surface observations from
1900 through 0600 MST were not taken (about eight missing per day). All observations for 1200 through 1600
MST were available, however, so that the afternoon maximum temperature and surface wind speed were
determined as usual. The 0200 and 0500 MST observations were always taken and were deemed adequate for
100 MIXING HEIGHTS, WIND SPEEDS, AND URBAN AIR POLLUTION POTENTIAL
-------
determining morning minimum temperatures and average surface wind speeds. The main problem that arose in
determining P cases was solved by evaluation of hourly precipitation amounts (from automatic precipitation gage
records) for the missing hourly reports. To check these results, Tabulations I, II, and III were prepared separately
for 1960 through 1961 and 1962 through 1964, in addition to the entire period of 1960 through 1964. The
differences in the tabulations between periods could not be ascribed to the methods of determining P cases.
e. The New York surface and upper-air observations were made at J. F. Kennedy (formerly Idlewild)
International Airport.
f. The initial set of tabulations for Portland produced a surprising number of C cases for morning mixing
height in the warmer months. This was found to be due to a comparatively late release of the scheduled 1200
GMT radiosonde and an early sunrise (0358 EST on June 15), which together frequently resulted in the surface
temperature of the 1200 GMT sounding being greater than the minimum surface temperature plus 5°C. To
overcome this problem in computing the urban morning mixing height, the hourly temperature at 0600 EST plus
5°C was used instead of the minimum hourly temperature from 0200 to 0600 EST plus 5°C. It should be noted
that upper-air soundings are permitted to begin up to an hour ahead of schedule. Most stations begin a sounding
from 45 to 60 minutes prior to schedule, but at Portland the 1200 GMT sounding was seldom begun before 1130
GMT (0630 EST).
g. The San Diego upper-air soundings were made at Montgomery Field (elevation 407 ft) and were used
with hourly surface reports for Lindbergh Field (elevation 19 ft). Lindbergh Field is on the shore of San Diego
Bay and Montgomery Field is on the coastal plain about 7 miles to the north-northeast.
h. Hourly surface weather observations at Los Angeles International Airport (elevation 97 ft) were used
with upper-air soundings at Santa Monica Municipal Airport, Clover Field (elevation 125 ft), about 7 miles to the
north-northwest. Both locations are about 2 miles from the coast and in similar suburban or residential
surroundings.
i. Upper-air soundings at Dulles International Airport (elevation 279 ft),located in rural surroundings about
23 miles west-northwest of the Capitol, were available for 1961 through 1964, but hourly surface observations
there were only available for 1963 through 1964. However, hourly surface observations at Washington National
Airport (elevation 14 ft), located in suburban surroundings on the shore of the Potomac River about 4 miles
south of the Capitol, were available for 1961 through 1963. Investigation showed that minimum temperatures at
National Airport averaged 4.4°F warmer than at Dulles Airport, undoubtedly due to the proximity of National
Airport to the built-up area and possibly due to the proximity of the water. Therefore, all calculations of the
urban morning mixing height that used hourly observations at National Airport were obtained by adding 2.5°C
instead of 5.0°C to the minimum hourly temperature observed from 0200 through 0600 EST. For comparative
purposes six sets of tabulations were obtained for various periods of record involving the two-surface observation
stations. Comparison of the 1963 mixing heights and wind speeds based on hourly observations at Dulles Airport
did not show complete agreement, but it was deemed adequate for climatological purposes. Thus, in keeping with
a policy of using surface and upper-air data for the same location whenever possible, the tabulations were based
on hourly observations at National Airport for 1961 through 1962, hourly observations at Dulles Airport for
1963 through 1964, and upper-air soundings at Dulles Airport for 1961 through 1964. The user who is only inter-
ested in the 4 years of data used in this report should specifically request only the Fj, F2, and F3 special tabula-
tions of regular Tabulations I, II, and III, respectively. These mixing-depth and wind-speed tabulations were pre-
pared by the NCC under Job Number 7717.
Appendix A. NCC Tabulations of Mixing Height and Wind Speed 101
-------
Table A-2. EXAMPLE OF NATIONAL CLIMATIC CENTER
TABULATION III, DAILYX/Q VALUES
Station
14842
Yr
60
Mo
04
Day
01
02
03
04
05
06
07
08.
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Daily mixing depths and average wind speeds
Morning
T
P
P
P
P
P
P
P
P
P
1
498
1237
1084
784
424
151
300
461
1825
123
582
86
151
608
413
234
562
153
254
213
238
180
189
103
130
484
59
278
830
1145
2
9.7
11.8
6.5
3.0
8.0
7.5
9.0
9.0
9.2
2.2
13.7
1.5
7.0
8.3
6.3
8.5
7.0
3.5
6.5
10.0
4.5
6.5
6.5
5.1
3.0
12.7
1.5
4.5
14.8
15.3
3
5.9
5.7
3.8
2.3
5.5
4.7
5.4
4.7
6.5
2.2
9.0
1.5
4.5
4.2
3.5
6.5
4.3
2.7
5.3
8.3
4.0
5.1
4.6
5.1
3.0
7.4
1.5
3.7
7.3
6.9
4
3
4
4
3
3
2
3
3
6
1
3
1
2
3
3
2
3
2
2
2
2
2
2
1
1
3
1
2
4
4
Afternoon
T
P
P
P
P
P
C
P
C
1
811
304
1038
1116
1644
1200
1545
342
1867
1728
909
1715
1518
469
1799
165
—
1671
1762
1034
1628
335
1394
1982
1188
1021
1374
1406
778
-
2
17.8
13.7
8.8
9.8
11.4
15.0
13.4
12.7
6.8
9.2
13.8
10.0
12.4
2.0
7.0
8.5
19.6
2.6
12.8
14.0
8.0
13.3
11.6
11.7
8.5
8.0
5.2
8.4
5.0
15.8
3
10.3
11.0
6.7
4.9
10.1
11.3
10.5
11.5
6.4
6.2
10.3
6.7
8.5
2.9
5.1
7.4
12.7
4.0
9.5
9.7
5.8
9.8
8.4
7.5
5.1
7.7
4.7
5.3
5.7
10.0
4
4
3
4
4
5
4
5
3
6
5
4
5
5
3
5
2
9
5
5
4
5
3
5
6
4
4
5
5
3
9
102
MIXING HEIGHTS, WIND SPEEDS, AND URBAN AIR POLLUTION POTENTIAL
-------
Table A-3. EXAMPLE OF NATIONAL CLIMATIC CENTER
TABULATION III, SEASONAL MEAN VALUES
Station
14842
14842
14842
14842
Season
01
02
03
04
Seasonal means of
daily mixing depths and average wind speed
Morning
T
P
C
P
C
P
C
P
C
1
327
675
361
695
272
548
273
690
2
5.2
7.9
14.5
5.7
8.1
3.8
5.9
4.4
8.1
3
3.8
5.4
4.4
3.9
5.4
2.6
4.0
3.1
5.0
N
313
128
2
327
129
383
70
374
78
Afternoon
T
P
C
P
C
P
C
P
C
1
533
388
1353
718
1498
1034
1068
608
2
6.8
6.6
13.3
8.2
8.3
12.6
5.8
5.8
5.6
6.7
7.8
12.6
3
5.4
5.4
7.3
6.2
6.1
8.1
4.7
4.4
5.1
5.1
5.8
6.6
N
290
110
43
332
105
19
391
61
1
381
53
18
Appendix A. NCC Tabulations of Mixing Height and Wind Speed
103
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Appendix A. NCC Tabulations of Mixing Height and Wind Speed
105
-------
-------
APPENDIX B. ALLOWANCE FOR P-, C-, AND M-TYPE
MIXING HEIGHTS AND WIND SPEEDS
NCC tabulations of mean mixing heights and wind speeds are given separately for precipitation (P) and
non-precipitation (non-P) cases. These tabulations show a distinct tendency for P mixing heights to be higher in
the morning and lower in the afternoon than non-P heights. In the calculations, this happens because of the
effects of dense cloudiness. Actually, morning and afternoon mixing heights with precipitation may be expected
to be higher than without because in the mixing layer above the condensation level the (slower) pseudoadiabatic
lapse rate would be more appropriate than the dry adiabatic lapse rate. However, the effectiveness of this
consideration is highly dependent on such assumptions as the water vapor content of the initially lifted parcel,
the amount of entrainment as the parcel rises, etc. In view of such complexities and the intended climatological
use of the derived data, it was decided to allow for all mixing-height and wind-speed cases other than non-P in an
arbitrary manner. C cases (Appendix A, Tabulation III) were treated as P cases since marked cold air advection
was assumed to be generally indicative of a comparatively deep mixing layer. Wind speeds for P and C cases were
assumed faster than otherwise. The number of missing (M) cases was insignificant.
In allowing for P, C, and M cases, it was assumed that the morning and afternoon mixing heights and wind
speeds generally were greater than for non-P cases. The allowance was made through use of NCC Tabulation I (see
Table A-5), frequencies of mixing-height classes by wind speed classes. One-half of the total P, C, and M
frequencies were proportionately redistributed among the non-P frequencies for mixing-height classes above the
mean height (for all speed classes). The remaining one-half of P, C, and M frequencies were redistributed among
the non-P frequencies for wind speed classes above the mean speed (for all mixing height classes). Thus, the non-P
part of each table of mixing-height class by wind-speed class (see Table A-5) was divided into four sections
according to the mean height and mean speed. Approximately one-fourth of the P, C, and M frequencies was
redistributed in the upper-right section of the frequency table (i.e. in the non-P section with speeds above the
mean and heights below the mean); one-fourth was redistributed in the lower left section (i.e., non-P heights
above the mean and speeds below); and one-half was redistributed in the lower-right section (i.e., non-P heights
and speeds both above the mean). In the redistributions each individual (cell) frequency of non-P mixing height
by wind speed was increased in proportion of its frequency to the total non-P frequency of all cells being
considered. The total frequencies of all non-P cells above the mean mixing height and above the mean wind speed
each was considered separately. Cells with zero non-P frequencies were unaffected by redistributions as were cells
below both the mean mixing height and mean wind speed. Due allowance was made for mean heights and wind
speeds that fell within a class interval.
Mean mixing heights and wind speeds given in NCC Tabulation III (see Table A-3) are based on averages of
the actual values. The means finally arrived at after the redistributions are the NCC Tabulation III means plus the
increase in mean value between the mean based on frequency counts by class intervals before (non-P cases only)
and after (all cases) the redistributions. Table B-l gives mean seasonal and annual values of mixing height and
wind speed for both before and after allowance for P, C, and M cases. Percentage frequencies of non-P cases are
given also.
107
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Appendix B. Allowance for P-, C-, and M-Type Mixing Heights and Wind Speeds
109
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111
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APPENDIX C. DERIVATION OF URBAN DISPERSION MODEL
Following the discussion in the main body of this report, consider a city with along-wind length S (meters
m) and cross-wind width 2B located in a rectangular coordinate system with the wind along the x-axis and the
origin at ground-level of the midpoint along the upwind side of the city:
-2
Assume a uniform average area emission rate Q (g m sec ) at ground-level over the city, perfect reflection
from the ground, and no restriction on vertical mixing. The ground-level concentration X(g m ) within the city
(i.e., o < x < S) along the center-line wind through the city and at distance x from the origin may be written
X(x,o,o) =
2Q
o-B
2nayaz\J
exp
dy0 dx0
(1)
where x0,y0 = downwind and lateral distances (m) of infinitesimal area source dx0dy0 from origin.
Oy,az = lateral and vertical diffusion functions - lateral and vertical standard deviations (m) of Gaussian
concentration distributions at downwind distance x—xn from source.
-li
U = average wind speed (m sec ) through the mixing layer.
For situations where x and thus ay is not large compared to 2B, the error in concentration at (x,o,o) will not be
large if in equation (1) — B and B are replaced by —°° and °°, yielding
X(x,o,o) =
20
(2)
In addition to he foregoing assumption, the general nature of the model being developed here suggests that it is
more appropriate for large than small cities, say larger than about 10 km.
In this model, it is desirable to consider travel time t instead of travel distance x from the upwind
edge of the city. The effect of this consideration is that the faster the winds, the less steep the profile of the
upper edge of the pollutant plume. In terms of the travel time from the source to the place where the
concentration is desired (i.e., in terms of t—10 = T) equation (2) becomes
X(t,o,o)
f'
J
dr
(3)
113
-------
with oz now a function of r. To integrate equation (3) a mathematical expression is needed for OZ(T). Smith and
Singer (1966) have given expressions for 0z(x) for classes of atmospheric stability. Using the wind speeds of
Singer and Smith (1966) that correspond to their stability classes, their expressions for az(x) may be converted to
tH
equation (3) is modified to
tH
tH is the travel time where, assuming a Gaussian vertical distribution, the ground-level concentration from a
source equals the concentration resulting from a uniform vertical distribution within the mixing layer. This is
given by 20/\/2?r oz = Q/H, or, using equation (4) with T - tH ,
tH =0.471 H1'130 (8)
114 MIXING HEIGHTS, WIND SPEEDS, AND URBAN AIR POLLUTION POTENTIAL
-------
To obtain the normalized concentration averaged over the city, X/Q (sec m ), for T > tH equation (7) is
appropriately integrated again, yielding
X/Q= 1/T 3.9994tHU15 + 4.453 tHal 15 (T-tH)
(9)
Equations (6) and (9) for T < tH and T > tH, respectively, were used to generate values of X/Q as a
function of H, U, and S. For S greater than about 10 km, the variation of X/Q against S is practically linear, as
shown in Figure C-l, and permits simple interpolation according to S. Table 1, which is discussed in the main
body of this report, gives values of X/Q for S-values of 10 and 100 km as a function of various combinations of H
and U. The values of H and U that were used are the mid-points of the class intervals in NCC Tabulation I (see
Appendix A) with three exceptions. For the upper unbounded class intervals of H greater than 4000 m and U
greater than 12.0 m sec" , values of 4500 m and 13.0 m sec were assumed; for the U-interval of calm—1.0 m
sec^ , a value of 0.75 m sec" was assumed.
Although the model has been presented only in terms of a uniform average area emission rate, it can be
, shown that the resulting average concentrations are the same as those for which the emission rate varies linearly
along the wind through the city (no lateral variation) from zero at the upwind edge of the city, to a value of 2Q at
the center of the city (i.e., at x = S/2), to zero at the downwind edge of the city. In the case of the variable emis-
sion rate, the highest concentration does not necessarily occur at the downwind edge of the city, but usually near
the middle of the city. Nevertheless, it view of the assumptions in the model, the average concentration over the
city is considered most appropriate for applications in this study.
Appendix C. Derivation of Urban Dispersion Model 115
-------
500
300
o
. 0)
i
IX
200
100
10 20
H = 125 m, U = 0.75 m sec'1
40
60 80
s, km
H : 125, U : 1 .5
H -- 375, U - 0.75
H : 125, U : 2.5
H : 625, U : 0.75
H -- 125, U : 4.5
H = 125, U -" 7.0
H - 125, U - 11.0
H =375, U = 5.5
H - 1250, U = 3.5
H : 4500, U = 13.0
100
120
140
Figure C-1. Variation of X/Q (see text) with city size (S) for vari-
ous combinations of mixing height (H) and wind speed (U).
116
MIXING HEIGHTS, WIND SPEEDS, AND URBAN AIR POLLUTION POTENTIAL
-------
REFERENCES
Clark, J.F., 1969: Nocturnal urban boundary layer over Cincinnati, Ohio. Mon. Weather Rev. 97: 582-589.
DeMarrais, G.A., 1961: Vertical temperature differences observed over an urban area. Bull. Amer. Meteor. Soc.
42: 548-554.
Duckworth, F.S., and J.S. Sandberg, 1954: The effect of cities upon horizontal and vertical temperature
gradients. Bull. Amer. Meteor. Soc. 35: 198-207.
Gross, E., 1970: The national air pollution potential forecast program. ESSA Tech. Memo, WBTM NMC 47,
National Meteorological Center, Suitland, Maryland. 28 pp.
Hanna, S.R., 1969: The thickness of the planetary boundary layer. Atmos. Env. 3: 519-536.
Holzworth, G.C., 1964a: Some meteorological aspects of community air pollution. Air Eng. 6: 26-28 and 33-37.
Holzworth, G.C., 1964b: Estimates of mean maximum mixing depths in the contiguous United States. Mon.
Weather Rev. 92: 235-242.
Holzworth, G.C., 1967: Mixing depths, wind speeds, and air pollution potential for selected locations in the
United States./. Appl. Meteor. 6: 1039-1044.
Holzworth, G.C., 1970: Meteorological potential for urban air pollution in the contiguous United States. Paper
No. ME-20C. Presented at the Second International Clean Air Congress, Washington, D.C., December 6-11,
1970. 22 p.
Hosier, C.R., 1961: Low-level inversion frequency in the contiguous United States. Mon. Weather Rev. 89:
319-339.
Hosier, C.R., 1964: Climatological estimates of diffusion conditions in the United States. Nuclear Safety 5:
184-192.
Korshover, J., 1967: Climatology of stagnating anticyclones east of the Rocky Mountains, 1936-1965. Public
Health Service Publication No. 999-AP-34, Cincinnati, Ohio, 15 p.
Lucas, D.H., 1958: The atmospheric pollution of cities. Int. J. Air Poll. 1: 71-86.
McCaldin, R.O., and R.F. Sholtes, 1970: Mixing height determinations by means of an instrumented aircraft.
Paper No. ME-39G. Presented at the Second International Clean Air Congress, Washington, D.C., December
6-11,1970. 23 p.
Miller, M.E., and G.C. Holzworth, 1967: An Atmospheric diffusion model for metropolitan areas. J. Air Poll.
Control Assoc. 17: 46-50.
117
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Singer, I.A., and M. E. Smith, 1966: Atmospheric dispersion at Brookhaven National Lab oratory. Int. J. Air and
Water Poll. 10: 125-135.
Smith, M.E., and I.A. Singer, 1966: An improved method of estimating concentrations and related phenomena
from a point source emission./ Appl. Meteor. 5: 631-639.
Stackpole, J.D., 1967: The air pollution potential forecast program. Weather Bureau Tech. Memo., WBTM-NMC
43, National Meteorological Center, Suitland, Maryland. 8 p.
Summers, P.W., 1967: An urban heat island model; its role in air pollution problems with application to
Montreal. Proc. First Canadian Conf. on Micrometeorology, Toronto, Ontario, Canada. April 12-14, 1965.
Dept. of Transport, Canada.
U.S. Dept. Commerce, Weather Bureau. Local climatological data (supplement). Published monthly through 1964
for selected stations.
*U.S GOVERNMENT PRINTING OFFICE. 1972-184-482 45 1-3
118 MIXING HEIGHTS, WIND SPEEDS, AND URBAN AIR POLLUTION POTENTIAL
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