EPA-600/4-76-002
February 1976
Environmental Monitoring Series
MODELING OF THE EFFECTS OF POLLUTANTS AND
DISPERSION IN URBAN ATMOSPHERES
Environmental Sciences Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, North Carolina 27711
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into five series. These five broad
categories were established to facilitate further development and application of
environmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The five series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
This report has been assigned to the ENVIRONMENTAL MONITORING series.
This series describes research conducted to develop new or improved methods
and instrumentation for the identification and quantification of environmental
pollutants at the lowest conceivably significant concentrations. It also includes
studies to determine the ambient concentrations of pollutants in the environment
and/or the variance of pollutants as a function of time or meteorological factors.
This document is available to the public through the National Technical Informa-
tion Service. Springfield, Virginia 22161.
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EPA-600/4-76-002
February 1976
MODELING OF THE EFFECTS OF POLLUTANTS AND DISPERSION
IN URBAN ATMOSPHERES
by
R. Viskanta, R. W. Bergstrom, Jr., and R. 0. Johnson
School of Mechanical Engineering
Purdue University
West Lafayette, Indiana 47907
Grant No. R801102
Project Officer
James T. Peterson
Meteorology and Assessment Division
Environmental Sciences Research Laboratory
Research Triangle Park, North Carolina 27711
U.S. ENVIRONMENTAL PROTECTION AGENCY
OFFICE OF RESEARCH AND DEVELOPMENT
ENVIRONMENTAL SCIENCES RESEARCH LABORATORY
RESEARCH TRIANGLE PARK, NORTH CAROLINA 27711
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DISCLAIMER
This report has been reviewed by the Environmental Sciences ^search
Laboratory, U.S. Environmental Protection Agency, and approved for puo-
lication. Approval does not signify that the contents necessarily re-
flect the views and policies of the U.S. Environmental Protection Agency,
nor does mention of trade names or commercial products constitute
endorsement or recommendation for use.
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ABSTRACT
This report summarizes an effort to gain improved understanding of the
short-term effects of radiatively participating pollutants upon the thermal
structure and dispersion in an urban atmosphere. This goal was accom-
plished by constructing one- and two-dimensional numerical models of the
planetary boundary layer. In the research, special attention was focused
on the interaction of solar and thermal radiation with gaseous and particu-
late pollutants as well as natural atmospheric constituents. A number of
numerical experiments have been performed with both models, and the differ-
ences between the results for simulations with and without radiatively
participating pollutants in an urban atmosphere were examined.
The results of the numerical simulations performed with the one-dimensional
(vertical transport only) model showed that the aerosol and gaseous pollu-
tants could affect the temperature and pollutant concentration distributions.
Under the conditions investigated, the largest surface temperature reduction
due to the aerosols was 2C at noon, and the maximum rise of the atmospheric
temperature due to the additional solar heating was about 1C after a two-day
simulation period. The maximum predicted surface temperature increase at
night due to the presence of gaseous pollutants was about 3C after a two-
day simulation. Numerical experiments for different meteorological
conditions have been performed and sensitivity studies have been conducted.
The results obtained are summarized in the body of the report.
An unsteady, two-dimensional transport model which accounts for horizontal
and vertical advection as well as turbulent diffusion and radiative trans-
fer in an urban atmosphere has also been developed. As a specific example,
the city of St. Louis, Missouri was selected for the numerical simulation
of summer conditions. According to the preliminary results obtained with
the model, the urban heat island intensity was found to reach a magnitude
of about 4C before sunrise and about I.3C at noon under the particular
meteorological conditions considered. At night the radiative participation
by. the gaseous pollutants increased the surface temperature by about I.3C
above that for a simulation with nonparticipating pollutants. At noon, after
a 24-hour simulation period, the surface temperature was only about 0.3C
higher for the case with radiatively interacting pollutants. Air pollution
was shown to decrease the atmospheric stability at night. In all of the
cases considered, the pollutant concentrations in the atmosphere were always
found to be lower in the simulations with radiatively participating than with
nonparticipating pollutants.
This report was submitted in fulfillment of Grant Number R80II02 by the School
of Mechanical Engineering, Purdue University, West Lafayette, Indiana,
under the partial sponsorship of the U.S. Environmental Protection Agency.
This phase of the work was completed as of August 1975.
111
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CONTENTS
ABSTRACT i i i
LIST OF FIGURES vi
LIST OF TABLES xi
LIST OF SYMBOLS xi i i
ACKNOWLEDGMENTS xvi
SECTIONS
I SUMMARY AND CONCLUSIONS I
I I RECOMMENDATIONS 4
III INTRODUCTION 6
Background 6
Mathematical Modeling of Air Pollution 9
Objectives of the Study 10
Scope II
IV ONE-DIMENSIONAL MODELING OF THERMAL STRUCTURE AND POLLUTANT
DISPERSION IN AN URBAN ATMOSPHERE 12
Analysis 12
Physical Model 12
Basic Equations 14
Radiative Transfer Model 16
Turbulent Diffusivities 19
Method of Solution 20
Results and Discussion 21
Radiative Transfer in a Polluted Atmosphere 21
Test Simulation—O'Neill Observations 25
Urban Summer 25
Urban Summer Elevated Inversion 32
Urban Winter 34
Urban Winter Elevated Inversion 36
Effects of the Pollution Parameters 39
Summary of Surface Temperature Differences and Surface
Concentration 40
IV
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CONTENTS
V TWO-DIMENSIONAL MODELING OF THERMAL STRUCTURE AND POLLUTANT
DISPERSION IN THE URBAN ATMOSPHERE 46
Analysis 46
Physical Model 46
Governing Equations 48
Radiative Transfer Model 51
Turbulent Diffusivities 51
Method of Solution 52
Results and Discussion 53
Parameters and Initial Conditions Used in the Simulations . . -55
Some Difficulties Encountered 58
Components of the Energy Budget at the Surface 59
Surface Temperature 62
Simulations with Radiative Nonparticipating Pollutants . 62
Simulations with Radiatively Participating Pollutants . . 65
Surface Concentrations 67
Velocity Distribution 70
Temperature Distribution 73
Radiatively Nonparticipating Pollutants . 73
Radiatively Participating Pollutants 75
Concentration Distribution 85
Radiatively Nonparticipating Pollutants 85
Radiatively Participating Pollutants 8ft
Urban Heat Island 9]^
VI REFERENCES 97
APPENDIX 105
Publications 105
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FIGURES
No. Page
I Physical Model for Solar and Atmospheric Thermal Radiation
Transfer in a Polluted Urban Atmosphere 13
2 Effect of Turbidity Factor T on the Normalized Downward
Directed Scattered and Total Surface Fluxes (a) and the
Normalized Upward Directed Flux at the Atmosphere (Earth-
Atmosphere Albedo) (b) for A = 0.55 ym and p = 0.25 24
3 Temperature Profiles for the Test (The O'Neill) Simulation 26
4 Comparison of Predicted and Observed (Lettau and Davidson,
1957) Surface Temperatures for Test Simulation 26
5 Isopleths for Simulations I and 5; Top Row are Temperatures
(in C) and Bottom Row are Concentrations (in yg/m3); Column I
is Simulation I, Column 2 is Simulation 5, and Column 3 is the
Difference Between Simulations 1 and 5 29
6 Pollutant Concentration Distributions for Summer Conditions
with Radiatively Nonparticipating Pollutants (Simulation I) 31
7 Temperature Distributions for Urban Summer Inversion Condi-
tions: (a) Simulation 2 with Radiatively Nonparticipating
Pollutants, and (b) Simulation 6 with Radiatively Participating
Pollutants Consisting of 20$ by Weight Carbon Aerosol and
Ethylene as Pollutant Gas 33
8 Concentration Profiles for Summer Inversion Conditions:
(a) Simulation 2 with Radiatively Nonparticipating Pollutants,
and (b) Simulation 6 with Radiatively Participating Pollutants
Consisting of 20$ by Weight Carbon Aerosol and Ethylene as
Pollutant Gas 34
9 Isopleths for Simulations 3 and 7; Top Row are Temperatures
(in C) and Bottom Row are Concentrations (in yg/m3); Column I
is Simulation 3, Column 2 is Simulation 7, and Column 3 is
the Difference Between Simulations 3 and 7 35
10 Temperature Distributions for Urban Winter Inversion Condi-
tions: (a) Simulation 4 with Radiatively Nonparticipating
Pollutants, and (b) Simulation 8 with Radiatively Participating
Pollutants Consisting of 20$ by Weight Carbon Aerosol and
Ethylene as Pollutant Gas 38
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FIGURES
(Continued)
No.
I I
Concentration Profiles for Winter Elevated Inversion Conditions:
(a) Simulation 4 with Radiatively Nonparticipating Pollutants,
and (b) Simulation 8 with Radiatively Participating Pollutants
Consisting of 20% by Weight Carbon Aerosol and Ethylene as
Pol lutant Gas
38
12
14
Surface Temperature Difference (Simulation with Radiatively
Participating Pollutants Minus Simulation with Radiatively
Nonparticipating Pollutants) for Summer Conditions
Curve
2
3
4
5
6
7
Pol lutant
Gas
S02
Nonparticipati ng
Aerosol
Nonparticiapting
Nonabsorbing
20$ Carbon
30$ Carbon
20$ Carbon
20$ Carbon
30$ Carbon
p
(yg/m2-s)
1
1
1
1/3
1
1
41
13 Surface Pollutant Concentration Variation with Time for Summer
Conditions:
Curve
2
3
4
5
6
Pollutant
Gas
Nonparticipating
Nonparticipating
S02
m
C2H,
Aerosol
20$ Carbon
Nonparticipati ng
20% Carbon
30$ Carbon
Nonabsorbing
Nonparticipating
p
(ug/m2-s)
42
Surface Pollutant Concentration Variation with Time for Winter
Conditions:
Curve
1
2
3
4
Pollutant
Gas
Nonparticipating
Nonparticiapting
S02
m
Aerosol
Nonparticipating
20$ Carbon
20$ Carbon
30$ Carbon
Nonabsorbing
P
(yg/m-s)
I
43
vii
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FIGURES
(Conti nued)
No. Page
15 Physical Model and Coordinates 47
16 Comparison of Rectangular and Gaussian Anthropogenic Heat Source
Distributions along the City 57
17 Variation of the Surface Energy Flux Components (q^.—Turbulent,
qp — Latent, qe—Emitted, qa-j-—Absorbed Thermal, qq—Ground
Conduction, Q—Anthropogenic Heat Source) for Simulation 3 at
24:00 of the First Day 60
18 Variation of the Surface Energy Flux Components (q+—Turbulent,
q^—Latent, qe—Emitted, qa?—Absorbed Solar, qa^.—Absorbed
Thermal, qq—Ground Conduction, Q—Anthropogenic Surface Heat
Source) for Simulation 3 at 12:00 of the Second Day 60
19 Effect of Wind Speed on the Diurnal Variation of the Turbulent
Heat Flux at the Surface for Simulations I and 3 61
20 Effect of Wind Speed on the Diurnal Variation of the Latent Heat
Flux at the Surface for Simulations I and 3 61
21 Comparison of Surface Temperatures for Gaussian (Simulation 3)
and Rectangular (Simulation 7) Distributions of Anthropogenic
Heat and Pollutant Sources Along the City 62
22 Variation of Surface Temperature with Time for Simulation I;
u =12 m/s, v = 8 m/s 63
g g
23 Variation of Surface Temperature with Time for Simulation 3;
u =6 m/s, v = 4 m/s 64
g g
24 Surface Temperature Difference (Simulation 2 Minus Simulation I)
Along City; u =12 m/s, v = 8 m/s 66
il? ^3
25 Surface Temperature Difference (Simulation 5 Minus Simulation 3)
Along City; u =6 m/s, v = 4 m/s 66
y y
26 Variation of Surface Pollutant Concentration Along the City for
Simulation 3; u = 6 m/s, v = 4 m/s 67
j ^3
27 Surface Pollutant Concentration Differences (Simulation 5 Minus
Simulation 3) Along the City 69
28 Perturbation Velocities (Velocity at the Urban Center Minus
Velocity at the Upwind Rural Location) for Simulation 3 70
viii
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FIGURES
(Continued)
No.
29 Comparison of Vertical Velocity Isopleths (in cm/s) for
Simulations with Radiatively Nonparticipating (Simulation 3)
and Radiatively Participating (Simulation 5) Pollutants 72
30 Potential Temperature Isopleths (in K) for Simulation 3; Note
that the Last Digit Denoting the Temperature of the Isotherms
at 18:00, 24:00, and 06:00 Hours Has Been Truncated jU
31 Potential Temperature Distribution for Simulation 3 75
32 Potential Temperature Isopleths (in K) for Simulation 7 76
33 Comparison of Potential Temperature Isopleths (in K) Between
Simulations 3 (Part a), Simulation 4 (Part b), Simulation 5
(Part c), and Simulation 6 (Part d) at 24:00 of the First Day 77
34 Comparison of Potential Temperature Isopleths (in K) Between
Simulations 3 (Part a), Simulation 4 (Part b), Simulation 5
(Part c), and Simulation 6 (Part d) at 06:00 of the Second Day 78
35 Comparison of Potential Temperature Isopleths (in K) Between
Simulation 3 (Part a), Simulation 4 (Part b), Simulation 5
(Part c), and Simulation 6 (Part d) at 12:00 of the Second Day 79
36 Perturbation of Potential Temperature (Temperature in the
City Minus Temperature at the Upwind Rural Location) for
Simulation 3 80
37 Comparison of Surface Temperatures at the Upwind Rural Location Qk
38 Comparison of Surface Temperatures at the Center of the City 85
39 Gaseous Pollutant Concentration Isopleths for Simulation 3;
(Multiply Numbers in Parts a, c, and d by a Factor of 10 and
in Part b by a Factor of I02 to Obtain Concentrations in ug/m3) 86
40 Gaseous Pollutant Concentrations Isopleths for Simulation 7
(Multiply Numbers in the Figure by a Factor of 10 to Obtain
Concentrations in ug/m3) 87
41 Comparison of Gaseous Pollutant Concentration Isopleths for
Simulation 3 (Part a), Simulation 4 (Part b), Simulation 5
(Part c) and Simulation 6 (Part d) at 05:00 of the Second Day
(Multiply the Numbers in Parts a, b, and d by a Factor of I02
and the Numbers in Part c by 10 to Obtain Concentrations in
yg/m3) 89
ix
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FIGURES
(Conti nued)
No.
42 Comparison of Gaseous Pollutant Concentration Isopleths for
Simulation 3 (Part a), Simulation 4 (Part b), Simulation 5
(Part c), and Simulation 6 (Part d) at 06:00 of the Second Day
(Multiply the Numbers on the Figure by 10 to Obtain Concentra-
tions in yg/m3) 90
43 Comparison of Gaseous Pollutant Concentration Isopleths for
Simulation 3 (Part a), Simulation 4 (Part b), Simulation 5
(Part c), and Simulation 6 (Part d) at 12:00 of the Second Day
(Multiply the Numbers in the Figure by 10 to Obtain Concentra-
tions in yg/m3) n^
44 Comparison of Gaseous Pollutant Concentrations for Simulation 3
(Part a) and for Simulation 5 (Part b) at the Center of the City 92
45 Comparison of the Turbulent Diffusivities of Heat for Simulations
3 and 5 at z = 5 m 93
46 Comparison of the Turbulent Diffusivities of Heat for Simulations
3 and 5 at z = 200 m 93
47 Comparison of Maximum Urban Minus Upwind Rural Surface Temperature
Differences for Simulations 3, 5, and 7 9^
48 Variation of the Heating/Cooling Rates for Simulation 3 (Part a)
and for Simulation 5 (Part b) During the Diurnal Cycle 95
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TABLES
No. Page
I Eddy Diffusivity Correlation Due to Pandolfo, et al., (1971) 20
2 List of Numerical Simulations 22
3 Urban and Pollution Parameters Used in the Simulations 28
4 Comparison of the Solar and the Downward Thermal Radiant Fluxes
at the Surface for the Urban Summer Simulation I without
Radiatively Participating Pollutants and for Simulation 5 with
Radiatively Participating Pollutants 30
5 Comparison of the Solar and the Downward Thermal Radiant
Fluxes at the Surface for the Urban Winter Simulation 3 without
Radiatively Participating Pollutants and for Simulation 7 with
Radiatively Participating Pollutants 37
6 Maximum Surface Daytime (D) and Nighttime (N) Temperature and
Pollution Concentration Differences (Simulation I Minus
Simulation 5, etc.) 44
7 Effect of Time Step on Selected Meteorological Variables at
the Center of the City (z0 = I m), z = I m, and t = 13:00 hr;
Simulation Started at 12:00, Computer-CDC 6600 (Cx Denotes
the Aerosol and Ca the Pollutant Gas Concentrations) 54
8 Summary of Simulations Performed to Study the Effects of
Radiative Participation on Pollutant Dispersion and Thermal
Structure in St. Louis, Missouri, During the Summer; Computer-
CDC 7600 56
9 Variations of the Urban Surface Parameters Along the Horizontal
Direction Assumed for the Simulations 56
10 Diurnal Variation of the Absorbed Thermal Flux at the Surface
(qat in W/m2) for Simulations 3 and 5 at the Upwind Rural and
the Center of the City Locations 68
II Comparison of Aerosol Mass Loadings for Various Simulations 71
12 Surface Temperatures (in K) at the Center of the City (x =
10.5 km) for Simulations 3, 4, 5, and 6 at Selected Times :7>l
XI
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TABLES
(Continued)
No. Page
13 Comparison of Downwind Thermal Fluxes (W/m2) at the Surface
as a Function of the Horizontal Location Before Sunrise (05:00) 82
14 Ratio of the Radiative Flux Divergence (-9F/3z) to the Turbulent
Diffusion C9/9z(Ke90/9z)H in the Vertical Direction for
Simulation 3 with Radiatively Nonparticipating Pollutants (NP)
and Simulation 5 with Radiatively Participating Pollutants (P) 33
XI1
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LIST OF SYMBOLS
C Concentration of species n
n
•
C Volumetric rate of production of species n
C , Concentration of water vapor at saturated conditions
W j Sal
c Specific heat at constant pressure
D Diffusion coefficient of species n
n r
e. Emittance (emissivity) of the earth's surface in the thermal
part of the spectrum
F Net radiative flux defined by Eq. (15)
F Radiative flux in the positive z-direction
F Radiative flux in the negative z-direction
f Coriolis parameter
G Incident radiatiation defined by Eq. (14)
g Gravitational constant
I Intensity of radiation
I, Planck's function
bv
K Turbulent eddy diffusivity
k Molecular conductivity of air
L Latent heat of vaporization of water
i Mixing length, see Eq. (20)
M Ha I stead's moisture parameter, see Eq. (II)
fZ6
M Mass loading of species n in the atmosphere defined as C (z)dz
^ o
m Surface source of pollutant emissions, see Eq. (12)
P
p Pressure
p Scattering distribution function, see Eq. (16)
xiii
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Q Anthropogenic heat emission source at the surface, see Eq. (10)
*
q Volumetric rate of heat generation
r Reflectance (albedo) of the earth's surface in the solar part of
the spectrum
Ri Richardson number
T Thermodynamic temperature
T Temperature of the soil
t Time
u Horizontal north velocity component
v Horizontal west velocity component
w Vertical velocity component
x Horizontal coordinate, see Figure 15
y Horizontal coordinate
z Vertical coordinate, see Figures I and 15
z Surface roughness
a Thermal diffusivity of soil
(V- I 1 l\c
0 Potential temperature defined as 0 - T(p /p)
K Absorption coefficient or the ratio of specific heat at constant
pressure to specific heat at constant volume
X Wavelength
pi Direction cosine or dynamic viscosity
v Frequency
p Density
a Scattering coefficient or Stefan-Boltzmann constant
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p Refers to pollutants both aerosols and gases
w Refers to water vapor
A Refers to the bottom of the soil layer
6 Refers to the edge of the planetary boundary layer
v Refers to frequency or per unit frequency
1 Refers to aerosol
2 Refers to pollutant gas
00 Refers to top of the free atmosphere
Superscripts
M Refers to turbulent eddy diffusivity of momentum
9 Refers to turbulent eddy diffusivity of heat
C Refers to turbulent eddy diffusivity of mass of species n
xv
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ACKNOWLEDGMENTS
This research was supported by the Meteorology and Assessment Division,
Environmental Protection Agency, under Public Health Service Grant
No. APO 1278, and Environmental Protection Agency Grant No. R80II02.
National Science Foundation provided financial support to one of the
authors (R.W.B.) in the form of a traineeship. Computer facilities were
made available by Purdue University Computing Center and the National
Center for Atmospheric Research which is supported by the National Science
Foundation.
The authors wish to acknowledge Mr. A. Venkatram for his contributions to
this effort. They also wish to express their appreciation to
Professor Gerald M. Jurica, Department of Geosciences, Purdue University
for his valuable comments.
The support of the project by the Environmental Protection Agency and the
help provided by Drs. George W. Griffing and James T. Peterson, the Grant
Project Officer, is acknowledged with sincere thanks.
xvi
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SECTION I
SUMMARY AND CONCLUSIONS
Progress has been made toward the goal of improved understanding of the
effects of gaseous and particulate pollutants on the transport processes in
the urban atmosphere. One- and two-dimensional models have been developed
for numerically simulating the atmospheric boundary layer and sensitivity
studies have been conducted. A large number of numerical experiments have
been performed using a one-dimensional model and some preliminary numerical
simulations with the two-dimensional model have also been carried out. The
results presented in the report demonstrate that the models are currently
capable of providing results of interest to EPA.
Specifically, some interesting conclusions based on the results obtained
from the unsteady one-dimensional (vertical transport only) model are that:
I. The pollutant aerosols reduced the solar radiative flux by about
10 percent on the first day and 20 percent on the second day for
a summer simulation with relatively calm winds (ug = 3 m/s,
Vg = 2 m/s). As a result of this flux reduction, the surface
temperature was decreased by a maximum of 2C in a two-day simulation
period. However, the additional solar heating due to the aerosols
increased the atmospheric temperature during the day by a maximum
of about 1C after a two-day period.
2. Absorption and emission of thermal (long-wave) radiation increased
the downward thermal radiative flux and thus raised the nighttime
surface temperature. The maximum predicted surface temperature
increase was about 3C after a two-day simulation.
3. In the simulations the net influence of particulates was to
decrease the temperature of the atmosphere-earth system, whereas
the influence of absorption and emission of thermal radiation by
gases was to increase the system temperature. The gaseous and
particulate pollutants thus had opposite and partially compensating
effects.
4. The warmer surface temperature during the night decreased the
stability of the atmosphere causing lower ground level maximum
pollutant concentrations from ground level sources. This decrease
was quite significant. In some summer simulations, for example,
the surface concentration for a simulation with radiatively
participating pollutants decreased to about 1.6 ppm (volume) from
a value of about 3.2 with radiatively nonparticipating pollutants
at 06:00 in the morning.
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5. During the day the aerosols affected the pollutant concentration
in the urban planetary boundary layer only slightly by reducing
the instability of the atmosphere. This hindered the breakup of
an elevated stable layer and in this instance increased the
pollutant concentrations.
6. The infrared cooling due to gaseous pollutants moved an elevated
stable layer upward. As a result of this modification, the
pollutant concentration in the boundary layer was significantly
decreased. For example, during the winter simulations with an
elevated inversion, the stable layer was moved from 600 m to
1000 m, and the ground level pollutant concentration decreased
from about 2.8 ppm (volume) for the simulation with radiatively
nonparticipating pollutants to about 2 ppm for the radiatively
participating one at 12:00 noon. Since advection and a removal
mechanism were not considered in the model the ground level pollu-
tant concentrations built up to high values (^ 30 ppm at 06:00 i ri
the morning) for a summer simulation with an elevated inversion.
Also, use of ethylene as a representative gaseous pollutant was
considered to be a "worst possible case."
A few specific conclusions based on a limited number of preliminary simula-
tions performed with the unsteady two-dimensional transport model for the
city of St. Louis, Missouri under the selected meteorological conditions
are that:
I. The urban heat island developed and reached a magnitude of
about 4C near sunrise and about I .3C at noon. The urban heat
island intensity is quite sensitive to wind speed and to the value
of Ha I stead's moisture parameter (latent energy transport).
2. For the meteorological conditions considered (Ug = 6 m/s, Vg =
4 m/s), the radiatively participating air pollutants increased the
surface temperature at the urban center by about I.3C just before
sunrise and about 0.3C at noon after a one-day simulation. However,
under more restrictive dispersion conditions which may arise
during stagnating air masses such as lower wind speeds, stable
upper layer temperatures, and higher pollutant concentrations, air
pollutants have the potential to more significantly modify the
surface temperature of the city.
3. The largest effect of radiatively participating air pollutants was
to decrease the stability of the atmosphere at night and hence to
increase turbulent diffusion near the surface. This was particu-
larly noticeable at heights below 500 m.
4. The feedback mechanism between pollutants, thermal structure,
stability, and dispersion has the potential of being important in
modifying pollutant concentrations under more stable atmospheric
conditions and higher pollutant loadings. However, the magnitudes
of the concentration differences predicted for simulations with
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radiatively participating and nonparticipating pollutants are
dependent on a coupling between the radiative properties of air
pollution and buoyancy enhanced turbulence, neither of which is
very well known. Thus, the magnitude of the temperature and
pollutant concentration differences between simulations with
radiatively interacting and noninteracting pollutants is uncertain.
5. The unsteady two-dimensional model is capable of simulating the
thermal structure and pollutant dispersion in the urban atmosphere.
There are, however, a very large number of parameters which affect
the temperature and pollutant concentrations in the urban planetary
boundary layer and need to be examined. Only a few numerical
simulations for unstable meteorological conditions during the day
and relatively high wind speeds have been performed. Before more
extensive simulations under more stable meteorological conditions
and other urban parameters are undertaken, improved methods of
modeling turbulence, latent energy transport, and the diurnal and
longitudinal (along the city) variation of surface pollutant and
urban heat sources must be found.
6. The research is continuing under a new EPA Grant No. R8035I4. The
major thrust of the research program will be to perform numerical
simulations for different atmospheric conditions, pollutants, and
surface parameters, and to examine the differences between the
results obtained for simulations with and without radiatively
participating pollutants. Sensitivity studies will be continued
and special consideration in the numerical experiments will be
given to simulating radiative effects of pollutant layers above
the city.
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SECTION I I
RECOMMENDATIONS
From the results of this project, there are two types of recommendations
which can be made. The first are general problems areas which need atten-
tion for improved modeling of the urban area, while the second are more
specific topics which should be investigated with the model.
Some of the problem areas which remain and require further work are the
followi ng:
I. An improved turbulent transport model is needed. The sensitivity
of the empirical eddy diffusivity correlations to the local tem-
perature and velocity gradients give rise to physically unrealistic
"jagged" diffusivity profiles. This is particularly true when the
atmosphere is composed of regions of widely differing stabilities.
An example of such a situation is the common one of an unstable
mixed layer capped by a stable layer. An improved procedure for
incorporating the change in the roughness along the urban area
into the turbulence model is also required.
2. Improved procedures for modeling the spatial and temporal variation
of air pollution and heat and water vapor source emissions in the
city must be developed. For example, how can the variation of the
anthropogenic sources along the urban area and with the time of
the day as welI as season be best approximated?
3. A more physically realistic procedure must be found for modeling
evapotranspiration at the air-soil interface and transport of water
in the soil since latent transport (evaporation or condensation)
is often a significant fraction of the net energy transport at the
earth's surface.
4. Radiative transfer in the polluted urban atmosphere is at least
two-dimensional and very complicated. Some simple approximate
(i.e., semiempirical) yet mathematically and numerically tractable
analyses must be developed to account for two-dimensional effects.
5. More efficient and computationally less time consuming numerical
procedures for solving a system of coupled conservation equations
need to be developed. There is also a great incentive to stream-
line the computer output because of the large amount of data to
be analyzed.
While these problem areas remain, the model developed predicts the time-
dependent temperature, velocity, and pollution^concentration distributions
over an urban area. The model can be used to investigate the various
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feedback mechanisms which could amplify the influence of variation in factors
such as atmospehric stability, surface temperature, planetary albedo, and
dynamics of the inversion layer which are important for understanding local
weather modification and pollutant dispersion. The conditions which are of
particular interest are periods of stagnating high pressure centers with
light winds since air pollution episodes often occur during these types of
meteorological conditions. Specifically, it is recommended that the follow-
ing topics be investigated by the model:
I. The effects of urban and pollution parameters under different
meteorological and seasonal conditions should be simulated.
Using the unsteady two-dimensional model, sensitivity studies should
be conducted to determine which of the parameters are significant
in altering temperature and concentration profiles in a polluted
urban atmosphere. For example, under what meteorological conditions
is radiative transfer important to compete with turbulent transport
and what would the pollutant concentration have to be in order to
significantly affect the thermal structure and pollutant dispersion?
Understanding the effects of pollutants is needed for developing
predictive models for the management of air resources in urban areas.
2. The thermal structure and pollutant dispersion under meteorological
conditions of interest should be simulated. The effect of the
radiatively participating pollutants on the height of the mixing
layer during the day, on the formation of a surface inversion at
night and on the dynamics (formation and breakup) of an elevated
inversion should be studied using the two-dimensional model.
3. The numerical model should be verified by comparing the predictions
of the model with available experimental data for the purpose of
confirming and improving the model. The rural and urban data on
solar (short-wave) and atmospheric (long-wave) radiative fluxes,
temperature, humidity, wind speed, etc. that will become available
from the RAPS program for the St. Louis, Missouri metropolitan
area wiI I be used for comparison with the predictions.
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SECTION I I I
INTRODUCTION
BACKGROUND
This report describes the research which was initiated under a Public
Health Service Grant No. APO 1278 and was continued under the U.S.
Environmental Protection Agency Grant No. R80II02. The work
was undertaken in June 1971 under a three-year grant which terminated in
January 1975. The primary objectives of the overall research program were
the following:
(I) Construct a physically realistic model for predicting radiative
transfer in a polluted urban atmosphere by accounting for the
radiative participation by both gaseous and particulate
pollutants and perform sensitivity studies.
(2) Develop a one-dimensional transport model for simulating the
thermal structure and dispersion in an urban atmosphere and per-
form numerical experiments and sensitivity studies under different
meteorological conditions.
(3) Develop an unsteady two-dimensional transport model in a polluted
urban atmosphere for simulating the radiative effects of air
pollutants on the thermal structure and dispersion.
The first two objectives have been completed and the results are described
in the papers and a thesis which are listed in the APPENDIX. Objective 3
has been completed; the model has been developed and checked by comparing
its predictions for limiting situations with the results of other investi-
gators and is discussed fully in this report. Improvements in the two-
dimensional transport model and numerical simulations will be performed under
a new U.S. Environmental Protection Agency Grant No. R8035I4.
The modification of the environment as a result of industrialization
and urbanization has been increasing at an accelerating rate. This modifi-
cation together with the injection of air pollutants into the atmosphere
has many observable adverse effects on a I I aspects of human, animal, and
plant life (Stern, et a I., 1973). In addition to being a health hazard
air pollution affects the environment and the quality of life. Many
atmospheric scientists consider air pollution together with modification
Of tne environment to be a potential cause of irreversible changes in the
local and global climate-
-------
The effects of air pollutants have been discussed recently by study
groups (U.S. Council on Environmental Quality, 1970; SCEP, 1970; SMIC,
1971; Broderick, 1972) which have assessed the problem of air pollution on
a global scale. Answers to questions concerning the accumulation, disper-
sion, and fate of air pollutants as well as their effects on the global
heat balance and on the global weather were sought. The effects of high
flying aircraft, the relationships between sources, routes and reservoirs,
and the role of air chemistry were also considered. The main conclusion
of these studies was that no definitive answer can be given since the
phenomena are too complicated and too little is known about the complex
interaction between the man-made and naturally produced air pollution in
the atmosphere.
The way in which the gaseous and particulate pollutants can alter the
temperature of the earth and the atmosphere is quite simple. The climate
is controlled by the balance of radiant energy (Kondratyev, 1969). The
earth's surface maintains its thermal energy balance by absorbing short-
wave solar radiant energy and by re-radiating energy back to space at longer
wavelengths. Air pollution can affect the spectral absorption and scatter-
ing characteristics of the atmosphere. Solar radiation is absorbed by
gaseous pollutants and absorbed and scattered by particulate pollutants.
This can tend to raise the temperature of the atmosphere and cool the sur-
face. However, the increased absorption and emission of thermal radiation
by pollutant gases increases the surface tempeature. Thus, the pollutants
on one hand have the effect of decreasing the earth's temperature by allow-
ing less of the solar energy to reach the earth while on the other hand,
they lead to an increase in the earth's temperature by increasing the down-
ward longwave radiation. Some studies (Atwater, 1970; Mitchell, 1971) have
shown that aerosols can produce warming or cooling of the entire earth-
atmosphere system depending on the ratio of absorption to scattering.
Estimates of the relative magnitudes of the opposing effects have been made
in terms of a globally averaged radiative energy budget (SCEP, 1970; SMIC,
1971; Mitchell, 1971; Rasool and Schneider, 1971; Ensor, et a I., 1971;
Yamamoto and Tanaka, 1972; Braslau and Dave, 1973; Reck, 1974; Wang and
Domoto, 1974).
On the local scale it has been conclusively established that the_climate
over cities differs from that found in the surrounding rural environs.
Increasing research efforts devoted to comparative studies of rural and
urban regions are well documented and reviews are available (Peterson, 1969;
Landsberg, 1970, 1972; Frisken, 1972; TenJung, 1973; Oke, I973a). One of
the better known features of an urban environment is the existence of warmer
temperatures in the urban area than in the surrounding rural regions. This
phenomenon is known as an urban heat island. The generally accepted primary
reasons for the formation of an urban heat island are (Peterson, 1969):
(I) seasonal effects such as solar radiation, anthropogenic (man-made) heat
sources; (2) the layer of gaseous and particulate pollutants over a city;
and (3) the differences in the thermal properties, moisture, surface
albedo, and surface roughness characteristics existing between urban and
rural sites.
-------
The effects of pollutants in the urban atmosphere have been receiving
increased attention (Atwater, 1970, 1971, I972a, I972b, 1974; Bergstrom and
Viskanta, I973a, I973b; Pandoifo, et a I., 1971; Zdunkowski and McQuage,
1972) and two American Meteorological Symposia (Philadelphia, 1972 and
Santa Barbara, 1974) were devoted to their discussion. As the recent survey
by Oke (I973a) indicates the main attention has been focused on the modifi-
cation by pollutants of solar and thermal fluxes reaching the earth's surface
rather than effects of pollutants on the thermal structure and pollutant
dispersion as well as the other meteorological variables in the atmosphere.
Results obtained from the modeling efforts cannot yet be considered conclusive.
Recent experimental investigations (Robinson, 1970; Kondratyev, 1972, 1973)
conclude that the solid fraction of aerosols plays a very important role
in the radiative transfer in the atmosphere, particularly in the absorption
of short-wave radiation. The net effect of air pollutants on the radiative
energy balance and the thermal structure in the atmosphere then depends on
both the concentration and distribution of gaseous and particulate pollutants
as well as concentration, size, distribution, and altitude range of the
aerosols. Thus, it is clear that considerably more work on the complex
problem of understanding the atmosphere and on the radiative transfer by
gaseous and particulate pollutants is needed before short and long-term
effects of man-made pollution can be predicted.
On a local scale, a small change in the radiative properties of the
atmosphere due to the presence of air pollutants may alter the vertical
distribution of temperature. In turn, this change in temperature near the
surface can modify significantly the atmospheric stability (Smith, 1968).
Obviously, any significant change in the vertical motion then alters the
dispersion of the pollutants themselves. So in effect, the pollutant concen-
tration distributions may well be a factor in affecting the processes that
determine their own dispersion. This interaction (the interaction between
radiation, the thermal structure, the flow field, and the pollutants) must
be accounted for when modeling transport processes in the lower atmosphere
(troposphere) over a polluted urban area (Kondratyev, 1973).
Pollutant dispersal requires the knowledge of wind speed, wind direction,
turbulent intensity, and the thickness of the boundary layer. Urban areas
are characterized by high levels of turbulence which cause what is commonly
referred to as the "mixed" layer. The dynamics of this "mixed" layer are
largely controlled by thermal effects. In fact, it is the efficacy of the
thermally enhanced turbulence that is responsible for the near uniformity
of potential temperature, wind speed, and pollutant distributions within the
"mixed" layer. The primary variables in air pollution dispersal over an
urban area are the wind speed vector and the height of the mixed layer.
Major research efforts are currently underway to predict the height of the
mixed layer and its variation from hour to hour, from day to day, and from
season to season (Carson and Smith, 1974). However, relatively few studies
have been made on the role of pollutants in modifying the growth of the
mixed layer.
Attempts have been made to use the equations to simulate the structure
of the urban planetary boundary layer and the various models which have
been developed are reviewed by Oke (I973a) and need not be repeated here.
-------
The most complete models consist of a soil layer, an analytical constant
flux layer, and a numerical transition layer which is assumed to extend to
the top of the planetary boundary layer. In constructing the models it is
generally assumed that the fluid in the upper layer is in hydrostatic
equilibrium, the flow is incompressible, and horizontal diffusion is negli-
gible in comparison to horizontal advection. Eddy diffusion coefficients
are typically specified from semi-empiricaI correlations, and many models
utilize a surface energy balance to predict the surface temperature. Most
of the analyses are for steady state. Few models have been developed for
flow over an urban area (for example, Yamada, 1972; McElroy, 1972; Wagner
and Yu, 1972; Bernstein, 1972; Yu, 1973) and most have neglected the
radiative effects of water vapor, carbon dioxide and, of course, the
pollutants (Wagner and Yu, 1972; Yu, 1973; Bornstein, 1974). Only Atwater
(1970, 1971, I972a, I972b, 1974), Bergstrom and Viskanta (I973a, I973b),
and Pandolfo, et a I . (1971) have accounted for radiative participation of
both gaseous and particulate pollutants.
An improved understanding of the transport processes (including radiative
transfer) in the urban atmosphere would be beneficial. This knowledge would
be valuable in constructing urban air quality simulation models (AQSM). In
turn, such models may be used for real-time air quality management, urban
and regional air quality planning, and perhaps most importantly in designing
and testing control strategies for meeting air quality standards.
MATHEMATICAL MODELING OF AIR POLLUTION
So far, it has not been shown with any assurance that climate is actually
subject to man's influence and. the debate continues due to the lack of
observational data as well as physical understanding of the phenomena.
The observations which are necessary to resolve the issue are exceedingly
difficult due to the magnitude of the problem. It is also clear from the
above discussion that no definitive answers can be given because too little
is known about the complex interaction between man-made and naturally
produced air pollution with the normal atmosphere. One means of studying
the effects of air pollution on the transport processes in the atmosphere
is to model the phenomena mathematically and to perform extensive measurements
over a long period of time to obtain the needed data. Such extensive
measurements have been initiated and are being carried out by the U.S.
Environmental Protection Agency over St. Louis, Missouri under the RAPS
program.
Mathematical modeling of complex phenomena has been well established
in science and technology. In a mathematical and numerical model, effects
can be isolated and studied as to their short, intermediate, and long term
influences. The model can also be used to test, for example, the impact of
new industrial development. Use of mathematical models (U.S. Presidential
Council on Environmental Quality, 1970; SCEP, 1970; SMIC, 1971; Broderick,
1972; Boughner, 1972) and of intensification of measurement programs (United
Nations Conference on the Human Environment, 1972) have been recommended
for gaining the much needed understanding of transport processes in the
polluted urban atmosphere.
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While conceptually straightforward, modeling of the influence of air
pollution on the thermal structure and pollutant dispersion in an urban
environment is a very complex problem. No model is better than the needed
input data, and the data on air pollution and urban parameters are either
unavailable or not very reliable. In addition, even with the use of the
most advanced high speed digital computers, simplifying assumptions are
necessary in order to make the problem numerically tractable.
OBJECTIVES OF THE STUDY
The primary objective of this research program was to enhance under-
standing of the effects of pollutants on the urban environment. The research
program aimed to determine the role of pollutants in modifying the thermal
structure in the atmosphere which, in turn, affects the pollutant dispersal.
The net effect of the most important pollutants on radiative flux and its
divergence, temperature, and flow fields would be predicted. Irrespective
of the precise details by which gaseous pollutants and particulate matter
might influence the energy balance in the polluted atmosphere, one important
aspect in understanding local weather modification and pollutant dispersion
involves feedback mechanisms which could amplify or dampen the influence
of factors such as atmospheric stability, lapse rate, surface temperature,
planetary albedo, dynamics of the inversion layers, and others.
To this end, the specific aims of the total project were:
I. To construct an unsteady, one-dimensional transport model applicable
to the urban atmosphere in which both gaseous and particulate pollutants
are included; to simulate the interaction of natural atmospheric
constituents and air pollutants with solar and thermal radiation in an
urban planetary boundary layer; to simulate the thermal structure and
pollutant dispersion in the boundary layer for a period of up to a few
days; and to conduct sensitivity analyses to determine which parameters
are significant in altering temperature and concentration profiles in
polluted urban atmospheres.
2. To develop an unsteady, two-dimensional transport model in which the
processes of advection, turbulent diffusion, and radiative transfer in
the polluted urban atmosphere are accounted for and to simulate the wind,
temperature, and concentration profiles in the urban planetary boundary
layer for a period of up to a few days under different meteorological
conditions to determine, for example, if radiative transfer is important
enough to compete with turbulent transport and under what conditions.
The role of pollutants in modifying the thermal structure, i.e.,
stability, surface and elevated inversions, altered turbulence, and mixing
height is of concern because the vertical temperature distribution affects,
for example: (I) forecasting of pollution episodes, (2) calculation of
pollutant dispersion, (3) micrometeorologicaI weather prediction in urban
areas, (4) prediction of visibility, and (5) identification of pollutants
by remote sensing (optical, absorption, and inversion) methods. If it is
determined that the radiative interaction of gaseous and particulate pollu-
tants with the solar and atmospheric radiation is important, this may require
10
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inclusion of radiative transfer in the air quality simulation models (AQSM)
intended for the control and management of urban air resources.
The pollutants affect the radiative transfer and through it the total
thermal energy budget of the urban atmosphere. Since under certain atmos-
pheric conditions, radiative transfer may comprise a major fraction of the
total energy budget in an urban planetary boundary layer, studies should
be conducted to identify the conditions under which the effects of pollutant
gases and aerosols contribute significantly to the energy budget in the
urban atmosphere. It was also desirable to establish any feedback mechanisms
between the pollutant concentrations and their own dispersion in the atmos-
phere. The relative role of the existing feedback mechanisms at present is
by no means clear.
SCOPE
This report is divided into two parts. The first part of the report
is concerned with the unsteady one-dimensional model and its development
as well as the discussion of the numerical simulations. The details of the
model and the numerous simulations which have been carried out are given
by Bergstrom (I972b) as wel I as in some open literature publications and will
not be repeated here. Only some of the more interesting results will be
summarized and their salient features discussed. The second part of the
report will be concerned with the construction of an unsteady two-dimensional
transport model in the polluted urban atmosphere. The numerical method of
solution of the governing equations will be discussed and some preliminary
results which have been obtained will be presented. The shortcomings of
the model, problems encountered, and suggestions for overcoming the inade-
quacies and problems are presented.
11
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SECTION IV
ONE-DIMENSIONAL MODELING OF THERMAL STRUCTURE AND
POLLUTANT DISPERSION IN AN URBAN ATMOSPHERE
The specific purpose of this section is to summarize recent work on the
effects of gaseous and particulate pollutants on the thermal structure and
the pollutant dispersion in an urban atmosphere. The short-term effects
of air pollution upon the temperature distribution and pollutant dispersion
in an urban atmosphere are predicted. This is accomplished by constructing
an unsteady, one-dimensional transport model and then solving numerically
the resultant equations. Radiative transfer is modeled by accounting for
the absorption and scattering process of solar (short-wave) radiation as
well as emission and absorption of thermal (long-wave) radiation. Results
for a few typical simulations of temperature and concentration distributions
in the urban boundary layer are presented for a period of up to two days. A
more realistic two-dimensional model for simulating the effects of air
pollution on the thermal structure and dispersion in the urban atmosphere
is presented in Section V. A detailed treatment of the present topic is
extremely difficult not only because of the lack of necessary data but also
because a two-day simulation may be beyond the capability of most available
computers in this country.
ANALYSIS
Physical Model
The physical model of the atmosphere is depicted in Figure I. As shown,
the atmosphere-earth system is assumed to be composed of four layers:
(I) the "natural" atmosphere where the atmospheric variables are considered
to be time independent; (2) the "polluted" atmosphere (the planetary boundary
layer) where the atmospheric variables of horizontal, lateral and vertical
velocity, temperature, and the water vapor and pollutant species concentra-
tions are functions of height and time; (3) the soil layer where the tempera-
ture is a function of depth and time; and (4) the lithosphere where the
temperature is assumed to be constant during a few-days simulation period.
The forcing function of the model is the time dependent solar irradiation
(insolation). During the day the solar radiant energy passing through
natural and polluted atmospheric layers is depleted by absorption and
scattering while at the surface this radiation is reflected and absorbed.
This absorbed energy is partially transferred to the atmosphere by turbulent
convection (including evaporation or condensation) and to the soil by
conduction. The earth's surface emits energy in the form of long-wave
(thermal) radiation. The atmosphere also absorbs, emits, and scatters
thermal radiation. At night the emission of thermal radiation cools the
atmosphere as well as the surface while energy is transferred from the
atmosphere to the surface. The physical model of the atmosphere is thus one
where the atmosphere and the surface warm up during the day due to the
12
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Incident \ g0
Solar V-1
Rodiction \
Leaving Scattered
Solar Radiation
fiX
Leaving Thermal
Radiation
Nature)
Atmosphere
Scattering and Absorption
by Natural Gases and
Emission and
Absorption by
Natural Gases
. Scattering and
\ . Absorption by
\f^ Gases and
/)£* Aerosols, Natural
Polluted ond Polluted
Atmosphere
incident Transmitted
2 Scattered \
\ Ns""\ Reflected \ Reflected
xxy /<^ &&
Emission,
©Absorption and
Scattering by
Gases and
Aerosols, Natural
and Polluted
Incident
Emission Reflection
/
*
zs
2.
Absorption '
7
Absorption
• =~— • ~^ - . .
/ /A/ / /
Absorption
Figure I. Physical Model for Solar and Atmospheric Thermal Radiation
Transfer in a Polluted Urban Atmosphere
absorption of solar radiation while at night it cools due to the emission
of thermal radiation. The distribution of thermal energy in the atmosphere
depends upon the interaction between the turbulent vertical diffusion and
the loss or gain of energy due to the radiative processes. Air pollution
affects the energy balance by increasing both the scattering and absorption
of solar radiation and the absorption and emission of infrared thermal
radiation.
In the following analysis atmosphere is assumed to be in hydrostatic
equilibrium. Furthermore, the atmosphere is considered to be horizontally
homogeneous in such a way that both horizontal advection and diffusion can
be neglected. This is probably valid for a region with a flat uniform
terrain but, in general, would not be true for a heterogeneous urban area.
The assumption neglects the change in the temperature structure of rural
air as it is advected over a city. While this assumption can be criticized
as unrealistic, it can be argued as somewhat representative of the worst
possible case. Pollution episodes often occur in periods of stagnating
high pressure centers with light winds. Thus, as far as the large scale
processes are concerned, the neglect of horizontal advection is somewhat
reasonable. On a smaller scale, however, this assumption does not account
for the local horizontal pollutant transport. This is probably justified
for large area sources of pollution but certainly not for large point
sources such as industrial smoke stacks. The main justification of the
horizontal homogeneity assumption is that it permits the development of a
somewhat realistic yet relatively straightforward numerical model.
With this assumption it is possible to incorporate a fairly detailed descrip-
tion of radiative energy transfer without involving excessive computer time.
13
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The one-dimensional model of energy transfer should therefore be considered
as a first approximation (or a somewhat unrealistic worst case), while for
more realistic modeling of an urban area a two- or a three-dimensional model
is necessary. Even in a three-dimensional model the radiative transfer
would probably have to be considered one-dimensional because of the excessive
computer time requirements.
The horizontal homogeneity assumption implies that the mean vertical velocity
component vanishes everywhere. This is equivalent to neglecting any upward
flow generated by growth of the urban boundary layer (a result of the fully
developed or horizontal homogeneity requirement) and to neglecting any free
convection effects (vertical motion and/or cell development under lapse-
free conditions) caused by the city other than turbulent enhancement.
Basic Equations
The governing equations for the model state mathematically the conservation
principles of momentum, energy, and species and are the same set as those
used by previous investigators (Estoque, 1963; Sasamori, 1970; Zdunkowski
and McQuage, 1972). These equations for the one-dimensional, unsteady model
are as follows:
z = z
oo
Natural Atmosphere
u, v, 0, C , C = constant
w p
Polluted Atmosphere
Momentum (x-d irection);
z = Z6
- • '«' - v + P
Momentum (y-d irection) :
p l^'<« - v + £ [(" + '<]£]
Momentum (z-d irection) :
0 = ||-+pg (3)
Energy:
(1M""
-------
Species:
Surface
C
(5)
z = 0
Energy:
3T
9 T
3t as
SoiI Layer
(6)
T = constant
o
z = -z.
The conservation of energy equation in the atmosphere has been written in
terms of the potential temperature 0. In order to completely formulate the
problem it is necessary to specify the initial and boundary conditions, to
predict the divergence of the radiative flux, and to relate the turbulent
diffusivities to the other atmospheric variables.
At the edge of the outer flow the variables are solved subject to the
boundary conditions
X(z,t) = constant at z = z.
(7)
Where x represents the horizontal north velocity u, the horizontal west
velocity v, the potential temperature 0 and the concentration Cn of species n.
This boundary condition is consistent with the notion that the large scale
weather system is slowly moving. At the bottom of the soil layer the
temperature is also taken as constant, i.e.,
T (x,t) = constant
at z = -z.
(8)
At the earth's surface the two velocity components are considered to vanish,
i .e.,
u(z,t) = v(z,t) =0 at z = 0
(9)
The surface temperature is predicted by assuming that the earth's surface
cannot store energy and that it is opaque to radiation. Hence, the sum of
the radiative, convective, latent, and conductive fluxes must vanish, i.e.,
(l-rs)Fs(0,t)
efFt(0,t) -
k+pcpK
,0
pL|Dw+K
9T
- k
Q = 0 atz = 0
(10)
15
-------
where F (0,t) and F_|_(0,t) represent the downward directed solar and thermal
fluxes, respectively. Thus, the first and second terms represent the
absorption of solar and thermal (long-wave) radiation by the surface,
respectively. The third term accounts for the emission of thermal radiation
by the surface and the fourth and fifth terms represent the turbulent thermal
energy flux and the latent energy flux leaving the surface. The fifth
term is the conductive energy flux to or from the soil, and the last term
represents the anthropogenic (man-made) urban heat source.
The surface water vapor concentration is prescribed by Halstead's moisture
parameters (Pandolfo, et al., 1971) in an approximate manner by the expression
C (0,t) = MC ,(0,t) + (I-M)C (zi,t) at z = 0 (II)
w sat w
where zi is the first grid point above the surface and Csa-j- is the water
vapor concentration at saturated conditions. The values of the parameter M
range from I for water CCw(0,t) = Csa-j-)H to 0 for dry soil CCw(zi,t) -
Cw(0,t) = 03. The fraction of area which is saturated with water, the
moisture parameter M, depends on the soil type, root distribution, water
table depth, and other variables (Halstead, et al., 1957). In addition, the
soil in urban areas is partly covered by buildings, pavement, etc., and
this fraction covered cannot be readily estimated. It is therefore
recognized that Eq. (II) may not model evaporation from the soil surface
accurately enough. More detailed models for predicting the temperature
distribution in the soil and the evaporation from the earth's surface are
available, i.e., Sasamori (1970). Unfortunately, hydraulic and thermal
properties of porous soil such as moisture potential, effective permeability
(hydraulic conductivity), and moisture content as well as the thermal
diffusivities are not well known for the soil types and textures encountered
in urban areas (Eagelson, 1970).
The surface boundary condition for the pollution concentration when a surface
source is present is given by specifying the "surface" pollutant mass flux,
m , that is
P I P
m_ = -|D_ + K P
at z - 0 (12)
0
It should be emphasized that the surface is not the location where the
pollutants are introduced into the atmosphere, and this formulation then has
certain physical limitations. Again, as with the moisture parameter M,
there is little quantitative data on sources of individual pollutants at the
surface.
Radiative Transfer Model
The urban atmosphere is again considered to be cloudless, plane-parallel,
and to consist of two layers: (I) the urban (surface, planetary) boundary
layer where most pollutants are concentrated, and (2) the free atmosphere.
The idealized model was illustrated in Figure I. The top of the free
16
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atmosphere is transparent to both solar and thermal radiation. From below
the boundary layer is bounded by an opaque earth's surface which not only
emits but also reflects radiation. The emission characteristics and the
albedo of the earth's surface in the model are arbitrary but prescribed
functions of wavelength. The radiative transfer between the free atmosphere
and the planetary boundary layer is coupled. The gaseous and particulate
atmospheric constituents are considered to absorb, emit, and scatter radia-
tion. No consideration, however, is given to individual point sources of
pollutants. The following physical processes are considered in predicting
radiative transfer in the atmosphere: (I) attenuation of solar radiation
by gaseous absorbers such as ozone, water vapor, carbon dioxide,
and other gases in the natural atmosphere; (2) Rayleigh scattering by
molecules and Mie scattering by a natural aerosol in the natural atmosphere;
(3) absorption of solar radiation by natural and pollutant gases, Rayleigh
scattering by molecules and Mie scattering by both natural and pollutant
aerosols in the polluted planetary boundary layer, and finally, (4) emission
of thermal radiation by both natural and pollutant gases and aerosols in the
free and polluted atmospheres are accounted for. The radiative transfer
model is considered one-dimensional; therefore, the local radiative flux
divergence at a given horizontal position is determined from the vertical
temperature, water vapor, pollutant and aerosol concentration distributions.
A more detailed two-dimensional radiative transfer model is considered to
be impractical and too time-consuming for numerical simulations. It must
be recognized that multidimensional radiative transfer is exceedingly complex
and inclusion of it would overshadow many of the more important problem
areas of this research. In the two-dimensional transport model described
in Section V radiative transfer is considered to be quasi-two-dimensionaI.
The radiant energy flux divergence, 3F/9z, which appears in the energy
equation physically represents the net loss (or gain) of radiant energy
per unit of volume. The conservation of radiant energy equation can be
written as
|f. = f K [4*1. (z) - 6 (z)ldv (13)
3z I v bv v I
J o "-
where the spectral incident radiant energy is defined as
f2TT f+l ,..,
Gv(z) = Iv(z,u,4>)dud4> (14)
' o -i
and the radiative flux as
f2TT f+l /ic-.
F (z) = lv(z,u,4>)udyd
-------
The first term on the right-hand side of Eq. (13) represents emission and
the second term accounts for absorption of radiant energy. The spectral
intensity, lv, defining the radiation field is predicted from the equation
of transfer in the direction, y, <{> as (Chandrasekhar, I960)
31 (z,y,4>)
-,
VZ)J
f4>f=2Trfy'=i
V=o V=-i
+Kv(z)1bv(z)
p
4ir I . >V
y'=c
(16)
In writing this equation it is assumed that the atmosphere is in local
thermodynamic equilibrium, the index of refraction is equal to unity and the
radiative transfer is quasi-steady, i.e., (l/c)3/3t « y(3/3z).
The boundary conditions necessary to solve the equation of transfer (16) are
the specification of the intensity at the top of the atmosphere and at the
earth's surface. At the top of the atmosphere it is assumed that the sun
is the only source of radiation present and at the surface of the earth it
is assumed that the reflection and emission are diffuse and the radiation
characteristics of the earth's surface are known. This can be written as
- yQ)6( - cj>o), y < 0 (17)
and
l(0,v,<|>) = (rv/ir)F~(0) + evlbv(0), y > 0 (18)
where 6 is the Dirac delta function and yo,o is the direction of the inci-
dence of the solar flux. The solution of the radiative transfer equation
was accomplished (Bergstrom, I972b; Bergstrom and Viskanta, I973c) by
dividing the entire electromagnetic spectrum into a solar part (0.3y <^ A < 4y)
and a thermal part (4y <_ A. <_ 100 ym). In the solar part the i ntegrodi fferenti.
equation of radiative transfer was solved analytically using the spherical
harmonics approximation. The solutions based on the Pa-approximation of
the spherical harmonics method were found to be in good agreement with the
results of other more detailed methods. These results are discussed in
detail by Bergstrom and Viskanta (I973c, 1974).
The total radiative flux and flux divergence in the thermal spectrum were
predicted by using the total emissivity data for water vapor (Kuhn, 1963)
and carbon dioxide CShekhter (Atwater, 1970)] and neglecting multiple
scattering. The data of Kuhn was used because the overlap of the carbon
dioxide and water vapor bands had been accounted for in these data. It was
assumed that the influence of gaseous pollutants is confined to the 8-12 ym
spectral region due to the relative opacity of the water vapor and carbon
dioxide bands.
18
-------
The spectral absorption and scattering characteristics of the aerosol in a
polluted atmosphere must be specified. A truly accurate treatment is
extremely complex and not practical because of lack of data and averaging
difficulties. The absorption and scattering coefficients and the scatter-
ing distribution function were predicted using Mie electromagnetic theory
by specifying the size distribution (Deirmendjian's Haze L distribution;
Deirmendjian, 1969) and by assuming that the aerosol was composed of
absorbing (carbon-like) and nonabsorbing (quartz-like) particles. While
the latter assumption can be criticized as arbitrary, the resulting absorption
and extinction coefficients do correspond to the measured mean indices of
refraction measured by Fisher and Ha'nel (Ha'nel, 1972) for a dry aerosol over
an industrialized area. The details of the model have been given elsewhere
(Bergstrom, I972a; Bergstrom, 1973).
Turbulent Diffusivities
The governing equations also require the specification of the turbulent
diffusivities. The diffusivity for an arbitrary quantity £ in the j-direction
is defined as
(19)
where the primes (') represent instantaneous values and the bars (—) denote
time averaged quantities and v: and x; are the velocity and unit direction
vectors in the j-th direction. It is recognized that specification of the
eddy diffusivities (K's) is perhaps one of the most difficult problems
associated with the modeling of the planetary boundary layer. The modeling
of turbulence in the atmosphere has been a subject of a recent symposium
(Frankiel and Munn, 1974) and a review of the eddy exchange coefficients
is available (Oke, I973a). In view of the excessive computer time require-
ments to model turbulence using higher order models (Donaldson, 1973;
Mel lor, 1973; Wyngard, Cote and Kao, 1974), it was considered impractical
to incorporate higher-order turbulence models in the type of study being
attempted in this program. Therefore, the semiempirical expressions for the
eddy diffusivities developed by Pandolfo, et a I. (1971) were used. In this
connection it should be mentioned that other investigators (Sasamori, 1970;
Estoque, 1973) have obtained realistic results using eddy diffusivity formu-
lations which are dependent on the "constant flux" layer correlations.
Also, the accuracy of the various models has not been determined. Compari-
son with observations has shown limitations in the assumptions of the
numerical models and has given little or no indications of the level of
accuracy of the turbulent models. Therefore, while the empirical expressions
of Pandolfo, et al. and others are "crude" approximations to actual turbulent
motions, no other method has demonstrated conclusively thatjt is "better"
for simulations of atmospheric motion under diabatic conditions.
The eddy diffusivity relations employed in the calculations are presented
in Table I. The diffusivities were assumed to be valid in the entire
planetary boundary layer. The decay of turbulence in the upper part of the
19
-------
TABLE I. EDDY DIFFUSIVITY CORRELATION DUE TO PANDOLFO, ET AL., (1971)
P
0 < Ri < Ric: KM = K9 = K W = (k£)2 d + <»Ri)2
Rif < Ri < 0: KM = (k£)2 | |^- | (I - aRP'2
K0 = K°W = KM/(I - Ri)2
Ri
-------
The calculation of the divergence of the radiative flux in the solar part
of the spectrum was the most time consuming part of the model and was
evaluated at longer time steps than the other variables. The values of
3F/9y were then extrapolated between computations. Each two-day simulation
required approximately 5 minutes of CDC 6600 computer time.
RESULTS AND DISCUSSION
The effects of air pollution on the thermal structure and dispersion were
predicted by numerically simulating the temperature, velocity, water vapor,
and aerosol as well as typical gaseous pollutant concentrations in an
urban area for a period of up to two days. Since there were a great many
independent parameters the number of possible situations that could be
simulated was very large. Therefore, only several selected conditions
were considered and only some of those are discussed here. The pollutant
conditions studied were those for an urban summer and winter both with and
without an elevated inversion present. The pollutant parameters vari.ed
were the amount of aerosol, the fraction of absorbing aerosol, the amount
of pollutant gas, and the choice of pollutant gas. In total 32 numerical
experiments were performed and are summarized in Table 2. The details
are given elsewhere (Bergstrom, I972b). Before discussing the results it
is desirable to compare the predictions of the radiative and total energy
transfer models against other analyses and against measured data in order
to establish some degree of their reliability and to increase the confidence
level of the predicted results.
Radiative Transfer in a Polluted Atmosphere
Since the concentration, composition, and size distribution of the aerosol
are not very well known and vary considerably, it usually is very difficult
to compare the predicted solar flux and its divergence to experimental data.
Therefore, the results predicted by various methods were compared against
each other for typical conditions of interest in order to determine their
relative agreement. The techniques chosen were the PI- and P3-approximations
of the spherical harmonics method, the 20th order of the discrete ordinates
method (Chandrasekhar, I960; Mudgett and Richards, 1971), and an iterative
method (Herman and Browning, 1965).
Radiative fluxes and flux divergences were predicted for a homogeneous
atmosphere containing only an air pollution aerosol at a typical concentra-
tion. The radiative properties of the aerosol were evaluated according to
the model of Bergstrom (1972a). The agreement between the radiative fluxes
for different solar zenith angles predicted by the different methods was
found to be surprisingly good while the discrepancy was slightly greater
for the predicted flux divergences (Bergstrom, I972b; Bergstrom and Viskanta,
I973c). The computational time requirements for the different solution^
schemes showed much more drastic results. The computation time for a given
wavelength ranged from I to 2 seconds on a CDC 6400 computer for PI- and
Pg-approximations of the spherical harmonics method, 20 seconds for the 20th
order Gaussian quadrature of the discrete ordinates method, and 200 seconds
for the iterative procedure. While it was difficult to assess the absolute
accuracy of each method, the small relative difference (a maximum difference
21
-------
TABLE 2. LIST OF NUMERICAL SIMULATIONS
Situations: A.
Urban Summer
Urban Summer
Simu lation
Number
1
2
3
4
5
6
7
8
9
10
1 1
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
Situation
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
C. Urban Winter
D. Urban Winter
Aerosol
Pol lutants
Nonpartici pati ng
it
it
"
20$ Carbon
"
11
»
20% Carbon
"
"
ti
None
11
ii
it
20$ Carbon
it
it
"
ti
tt
11
ti
Nonabsorbi ng
11
»
11
30$ Carbon
11
it
11
Elevated Inversion
Elevated Inversion
Gaseous
Pollutants
Nonparticipati ng
Ethylene
it
11
ti
None
it
n
Ethylene
ti
SuIfur Dioxide
it
Ethylene
ti
11
n
n
it
tt
it
ti
Source*
Strength
yg/m -s
3
it
it
tt
it
11
11
tt
ii
it
ti
it
ti
11
11
tt
11
tt
it
it
I
11
it
it
3
it
ii
it
ti
it
tt
ti
*Aerosol source strength is given.
so that an aerosol concentration of
tration of I ppm (volume).
The gaseous source strength was adjusted
100 ug/m3 corresponded to a gas concen-
22
-------
of about 2 percent for the flux and about 10 percent for the flux divergence)
gave some degree of confidence in the reliability of the techniques.
Therefore, in the subsequent computations the Pa-approximation is used
throughout. The order of the approximation could be readily increased if
this was warranted in future studies. Unfortunately, the computation time
would be increased significantly.
As a specific example, the results for the spectral solar flux and flux
divergence predicted by the Pa-approximation were compared against those
obtained by Eschelbach (1972). The method employed by Eschelbach is similar
to that used by Herman and Browning (1965) and the error is claimed to be
less than I percent. The atmospheric aerosols were assumed to have a power
law distribution and indices of refraction of 1.5-0.02 i. The vertical
concentration distribution for both Rayleigh scatterers (QR) and atmospheric
aerosols (£H> where $ = a + K) was assumed to be exponential as (Eschelbach,
1972)
°R=0R n
2=0
and
exp(-z/HR) (21)
3H ~
z=0
exp(-z/Hu) (22)
n
with HR = 8 km and H|_j = 1.25 km. The single scattering albedo, to, and
percentage of Rayleigh scattering for a wavelength of 0.55 ym used in the
computations are given elsewhere (Bergstrom and Viskanta, 1974).
The normalized downward directed surface fluxes and upward directed fluxes
at the top of the atmosphere are illustrated in Figure 2. The fluxes are
shown as a function of the cosine of the solar zenith angle for three
different turbidity factors,
T = (T + T )/T (23)
1 ^TRco + THoo;/TRco
Since TRoo is constant, increasing T increases the aerosol optical thickness
THoo. The normalized total (scattered plus transmitted) flux is shown in
Figure 2a. The ratio Fx4'(0)/y0F0x represents the total transmittance of
the atmosphere to the incoming solar radiation flux (yo^oA5 at the top of
the atmosphere. The values predicted by Eschelbach (1972) are denoted by
pluses (+). As illustrated, the points for which data are available are^
in very good agreement. This is quite surprising due to the simplification
made in the P3-approximation. The normalized upward directed fluxes at the
top of the atmosphere illustrated in Figure 2b represent the total reflec-
tance or "albedo" of the earth-atmosphere system. The results are also in
very good agreement with the predictions of Eschelbach (I972)._ Equally
valid results have been obtained for the flux divergence. Additional
comparisons are given by Bergstrom and Viskanta (1974).
23
-------
1.0
ft 0.8
U.D
o
i
^^ * "
O
~ 0.4
0.2
0
-SCATTERED
i I i I i I
! I I . I I I ! I
1.0
0.8
0.6
0.4
0.2
0
0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 1.0
P'O
Figure 2. Effect of Turbidity Factor T on the Normalized Downward Directed
Scattered and Total Surface Fluxes (a) and the Normalized Upward
Directed Flux at the Atmosphere (Earth-Atmosphere Albedo) (b) for
A = 0.55 ym and pd = 0.25
The results obtained (Bergstrom, I972b; Bergstrom and Viskanta, 1974) show
that the lower orders of the spherical harmonics approximation to the
equation of radiative transfer predict solar fluxes and flux divergences
which are in good agreement with more detailed methods of solution for both
homogeneous and nonhomogeneous atmospheres. The approximations result in
a considerable saving of computational effort (from one to two orders of
magnitude) over other more detailed methods. This saving is of great
important in applications to time dependent problems and where integration
over wavelength by necessity must be made for the flux and the radiative
fIux divergence.
Solar heating and infrared cooling rates due to different individual pollu-
tant gases for both uniform and nonuniform pollutant concentration distribu-
tions have been computed and sensitivity studies conducted (Bergstrom, 1972b;
Bergstrom and Viskanta, 1973c). Infrared cooling rates for a mixture of
water vapor, carbon dioxide, and possible pollutant gases have been obtained.
The results, for example, show that cooling rates for a mixture of H20, COa,
and CaHU (ethylene) as a pollutant gas can be smaller than those for the
mixture of water vapor, and carbon dioxide alone. The downward directed
thermal radiative flux, however, is increased. The results also show that
large cooling rates may occur for nonuniform pollutant concentration
distributions just above the point of maximum concentration. There are,
however, numerical problems in predicting accurately the radiative flux
divergence in the regions where the pollutant concentration changes sharply.
This is analogous to large cooling rates which occur at cloud tops
-------
(Korb and Zdunkowski, 1970) and is due to the large change in the net
radiative flux above the point of maximum concentration.
Test Simulation—O'Neill Observations
The Great Plains Turbulence Study (the O'Neill Study; Lettau and Davidson,
1957) was held in 1954 and until recently was the most complete set of
measurements of the temperature, velocities, humidity, and radiation fluxes
reported. The results of the study have been analyzed in numerous publica-
tions and both Estoque (1963) and Sasamori (1970) have simulated the
conditions for the fifth observational period. Since no comparable set of
data existed for an urban area this situation was chosen to test the
numerical model. The input data and values for the physical constants were
taken from observed or published sources.
The simulation was started at 12:30 on August 24, 1954 (which was the
beginning of the data). The temperature profiles at 12:30, 18:30, 24:30,
06:30, and 08:30 are illustrated in Figure 3. These distributions show
the cooling of the surface, development of the nighttime inversion, breakup
of the inversion, and development of the super adiabatic profiles. Compari-
son of the predicted temperature profiles with those determined by Sasamori
(1970) and those observed show good agreement (Bergstrom, I972b; Figure 6.2).
Both analytical models predict a surface inversion (as did Estoque, 1963)
which was not observed. However, Deardorff (1967) has suggested that the
advection of cold air during the night may have counteracted any surface
heating effects which were present at the O'Neill site.
The predicted and observed surface temperatures as a function of time are
shown in Figure 4. As illustrated the predicted maximum surface temperatures
are somewhat high; however, the general trend is well described. A
comparison between predicted surface fluxes and those inferred by Suomi
(Lettau and Davidson, 1957) showed fairly good agreement (Bergstrom, I972b;
Bergstrom and Viskanta, I973a). Particularly encouraging is the finding
that the radiative fluxes are within 10-20 percent of the observed. The
natural aerosol conditions were not measured and were assumed to correspond
to that of high visibility (Elterman, 1970). Both the solar and thermal
radiant fluxes are underestimated. Sasamori (1970) also underpredicted
the solar flux due to the uncertainties of the atmospheric conditions.
For the purposes of this study the analysis has shown to compare reasonably
well with other one-dimensional studies as well as observed data and there-
fore establishes a high degree of confidence in the present analysis. The
advantages of the model are that a constant flux layer i_s not assumed and
the solar radiative flux does not have to be known a. ptiio>iL at the surface
but is computed.
Urban Summer
The purpose of this experiment was to simulate the summer conditions of
an urban area. The same initial variables as the O'Neill study with urban
values of the parameters zo, M, Q (anthropogenic heat source parameter),
-------
293
308
Figure 3. Temperature Profiles for the Test (The O'Neill) Simulation
36
32
o 28
•
I-
24
20
12=00 16=00 20=00 24=00 04=00 08=00 12=00 16=00 20'00
t.hr
Figure 4. Comparison of Predicted and Observed (Lettau and Davidson, 1957)
Surface Temperatures for Test Simulation
26
-------
in Table 3. The general influences of these quantities on the urban surface
temperature have been well documented, for example, Pandolfo, et al. (1971
p. 46, Figure 3.4-1) and Atwater (I972a, Figures I to 3), and they need not
be repeated here.
The pollution parameters employed in the simulations are also shown in
Table 3. The pollution source was taken to be that of an industrialized
area in the Hartford, Connecticut study (Pandoifo, et al., 1971) and was
found to give reasonable pollutant concentrations. A surface source was
used since this was shown by Uthe (1971) to be approximately valid for the
study of St. Louis, Missouri. As mentioned, pollution aerosol composition
of quartz and carbon was selected from the aerosol model of Bergstrom
(I972a). Ethylene was at first selected to simulate gaseous pollutants
since Ludwig, et a I., (1969) considered it to be representative of a
typical hydrocarbon and because it was shown to have strong absorption
characteristics in the 8 ym to 12 ym range. Obviously, other individual
gases such as ammonia or gas mixtures could have been used to simulate the
actual polluted conditions; however, in this initial study a more detailed
description of gaseous pollutants was considered to be unwarranted. Also,
ethylene was felt to be a "worst" case selection.
The results for the temperature and pollutant concentrations distributions
as a function of both height and time are shown in Figures 5a and 5b,
respectively, for the simulation with nonparticipating pollutants
(Simulation I). The temperatures are warmer at night than for the corre-
sponding O'Neill study due to the change from a rural to an urban area.
There is essentially no inversion and the warming trend during the computa-
tional period is enhanced. Temperature and pollutant concentration profiles
for a simulation with radiatively participating pollutants (Simulation 5)
are illustrated in Figures 5c and 5d, respectively. Note that the general
trends are the same as the first simulation but the magnitude of the
temperatures is different. The differences in the temperatures and pollu-
tant concentrations are illustrated in Figures 5e and 5f, respectively. The
difference is defined as the quantity in the simulation with nonparticipat-
ing pollutants minus the quantity in simulation with the radiatively partici-
pating pollutants. As shown, the temperatures are warmer at night by a
maximum of 2.2C and cooler during the day by a maximum of 0.4C. Thus, the
net effect is a reduction in diurnal temperature variation of 2.6C from a
total of about 8 to IOC.
The surface solar and thermal radiant energy fluxes for the two experiments
are presented in Table 4. It is clear from the table that the pollutants
reduce the solar flux and increase the thermal flux. This indicates the
reason why the surface temperature is cooler during the day and warmer
during the night in the simulation with participating pollutants. The
solar flux is reduced by about 10 percent on the first day and 20 percent_
on the second day (see Table 5 for results of winter simulations). This is
well within the range of observed reduction of solar fluxes in an urban
area (Peterson, 1969). The downward thermal radiation flux is increased
by about 10 percent. However, the flux is also a function of the temperature
profile, and the temperatures are somewhat warmer at night and cooler during
the day in Figure 5c. This increase agrees well with the observations of
27
-------
TABLE 3. URBAN AND POLLUTION PARAMETERS
o
M
a
(a) Urban Parameters
100 cm
0
9.09X10" erg/cm2-s
2.2x|0-2 cm2/s
4.6x|05 erg/cm-s-C
O.I
Pandolfo, et a I., 1971
Pandolfo, et al., 1971
McElroy, 1971, and
Pandolfo, et al., 1971
Pandolfo, et a I., 197!
Pandolfo, et a I., 1971
Ludwig, et al., 1969
m w
P
AerosoI
Gas
(b) Pollution Parameters
3 iagm/m2-s
20% by weight carbon
Ethylene
Pandolfo, et a I., 1971
Bergstrom, I972a
Ludwig, et a I., 1969
*The aerosol source strength was used as listed in the table. The gaseous
pollutant source strength was adjusted so that an aerosol concentration
of 100 yg/m3 equaled a gaseous pollutant concentration of 1.0 ppm at the
surface.
28
-------
ro
MD
12:30 00:30 12=30 00:30 12:30 00=30 12=30 00=30 12=30 00=30 12=30 00=30
t, hr t, hr t, hr
Figure 5. Isopleths for Simulations I and 5; Top Row are Temperatures (in C) and Bottom Row
are Concentrations (inUg/m3); Column I is Simulation I, Column 2 is Simulation 5, and
Column 3 is the difference Between Simulations I and 5
-------
TABLE 4. COMPARISON OF THE SOLAR AND THE DOWNWARD THERMAL RADIANT FLUXES
AT THE SURFACE FOR THE URBAN SUMMER SIMULATION I WITHOUT
RADIATIVELY PARTICIPATING POLLUTANTS AND FOR SIMULATION 5 WITH
RADIATIVELY PARTICIPATING POLLUTANTS
Time
Solar, F(0), erg/cm2-s Thermal, F~(0), erg/cm2-s
15 15
12:30
14:30
16:30
18:30
20:30
22:30
24:30
02:30
04:30
06:30
08:30
10:30
12:30
14:30
16:30
18:30
20:30
22:30
24:30
02:30
04:30
06:30
08:30
10:30
12:30
8.22x| 0s
7.07x|05
3.87XI05
5.37x10"
5.37x10"
3.87x|05
7.07x|05
8.28XI05
7.07x|05
3.87XI05
5.37x10"
5.37x10"
3.87x|0s
7.07x|05
8.28XI05
8.22x|05
7.00X1 0s
3.72XI05
4.91x10"
4. 21x10"
3. I4x|05
6.09x|05
7.20x|05
5.9lx|Q5
2.87x|05
3.65x10"
3.22x10"
2.44x|05
5.07x|05
6. I3x|05
3.95XI05
4.02
4.02
3.95
3.89
3.85
3.83
3.81
3.78
3.76
3.85
3.96
4.05
4.10
4.09
4.02
3-95
3.92
3.88
3.85
3.83
3.80
3.83
4.00
4.09
3.95XI05
4.33
4.38
4.34
4.31
4.30
4.29
4.28
4.27
4.25
4.32
4.43
4.53
4.62
4.61
4.51
4.50
4.47
4.45
4.43
4.41
4.39
4.32
4.54
4.66
30
-------
1200
1000
800
e. 600
N
400
200
0 40 60 120 160 200 240 280 320
CP. ^gm/m'or ppm «I08
Figure 6. Pollutant Concentration Distributions for Summer Conditions with
Radiatively Nonparticipating Pollutants (Simulation I)
Oke and Fluggle (1972) who measured an increase of about 10 percent in the
downward thermal flux in Montreal, Canada as compared to the surrounding
countryside. Thus, the alterations in the radiant flux appear to be quite
realistic and agree with available experimental evidence. However, it must
be noted that Oke and Fluggle suggested that the increase in thermal flux
could be due to the warmer temperatures and not necessarily to the presence
of pol lutants.
The effect of the radiation characteristics of the pollutants on the
pollution concentrations is larger. The maximum surface concentration at
night is reduced by 125 yg/m3 while there is little difference during the
day between the concentrations with (Simulation 5) and without (Simulation I)
radiatively participating pollutants as shown in Figures 5b and 5d, ™fPeJ-
tively. The difference (simulation with minus simulation without "d.at^ely
participating pollutants) between the values in Figures 5b and 5d is shown
in Figure 5fT This change is about 40 percent and represents a significant
difference? The resultsof Figure 6 show more clearly that the pollutant
concentrations increase at night due to the lower level of turbulence and
reach a maximum in the early morning. This max, mum ,s ^ced by the good
mixing of the next afternoon caused by the strong instab, hty
atmosphere. Since there is no allowance made in the mode for hon zonta
haze layers is often observed (Uthe, 1971).
31
-------
The reduction in the pollutant concentration is due to the fact that the
surface temperatures are warmer at night and the atmosphere is less stable.
The diffusion of pollutants is therefore enhanced and the night buildup is
thus reduced. The presence of pollutants affects the atmospheric radiation
and alters the thermal structure. This influence changes the stability and
enhances the ability of pollutants to disperse vertically.
Urban Summer Elevated Inversion
Since pollution episodes usually occur when an elevated inversion is
present, the urban summer situation was investigated with a layer of stable
air above 750 m. Because the vertical velocity was assumed to be zero, it was
not possible to include a subsidence production-term to maintain the inver-
sion. Thus, this situation physically represents an elevated inversion
which has been produced and the production process ceased. Experiments (not
presented here) using the same starting time and velocities as the urban
summer simulation (Simulation I) showed that the stable region was destroyed
by the strong afternoon mixing within one hour. Therefore, in order to
investigate the effect of pollutants under inversion conditions, the simula-
tions were started in the evening (17:00) and the velocities reduced to %
the values of the O'Neill data. The temperatures* at 6-hour invervals for
Simulation 2 are shown in Figure 7. As shown, a radiative inversion
develops at night due to the reduction in wind speed and corresponding lower
diffusivities. During the next day the mixing destroys the stable layer
while the elevated stable region inhibits the upward convective energy
transport causing the surface temperature to be greater than in the simula-
tion without the inversion (Simulation I). The reduction in wind speed
also tends to increase the surface temperature (see Figure 3). The results
of the numerical experiment are very similar to those of the O'Neill simula-
tion in that a radiative inversion develops, deepens, and is finally
destroyed. The destruction of the surface stable region has occurred by
12:00 and the elevated stable region has been moved upward to a height of
900 m.
The corresponding temperature distributions for Simulation 6 with radiatively
participating pollutants are shown in Figure 7b. Comparison of Figures 7a
and 7b reveals that the radiative properties of the 20 percent carbon aerosol
and ethylene pollutant gas have a pronounced effect on the temperature
distribution. The surface inversion does not develop since the increase in
thermal radiation increases the surface temperature about 2C. There is
cooling at two different levels: (I) at the base of the nighttime stable
layer at 100 m, and (2) at 650 m at the height of the elevated inversion.
Both of these colder regions result from the thermal radiation cooling by
the pollutants which are trapped beneath the stable regions. The temperature
profiles show that a weaker elevated inversion forms at about 100 m instead
of the radiative surface inversion. This weak elevated inversion has also
been predicted by Atwater (1970) and Pandolfo, et a I. (1971). This
^Temperature and concentration isopleths similar to those shown in Figure 5
are given by Bergstrom (I972b), but they are somewhat more difficult to
interpret and are therefore not presented here.
32
-------
1000 -
600
E 600
400
200
(o)
296 300 304 308
296
T.K
300 304 308
312
Figure 7. Temperature Distributions for Urban Summer Inversion Conditions:
(a) Simulation 2 with Radiatively Nonparticipating Pollutants and
(b) Simulation 6 with Radiatively Participating Pollutants
Consisting of 20% by Weight Carbon Aerosol and Ethylene as
Pollutant Gas
inversion then moves upward and weakens further during the early morning
hours. The base of the stable region at 750 m also cools and is moved
upward during the night.
The changes in the surface radiative flux for these two situations are
similar to simulations previously discussed and are therefore not presented.
The downward thermal radiative fluxes were larger while the solar radiative
flux were 10 to 20 percent smaller in the simulation in which the radiative
effects of pollution were considered.
The corresponding concentration profiles at six hour intervals are given
in Figures 8a and 8b for the simulation without (Simulation 2) and with
(Simulation 6) radiatively participating pollutants, respectively. As shown
(Figure 8a) the pollutants build up near the surface owing to the presence
of the surface stable layer. The elevated stable region forms a sharp
boundary at 750 m. During the next day the pollution concentration near
the surface is decreased as the destruction of the stable layer permits
vertical mixing. At the same time the boundary due to the stable region
is moved upward to above 800 m. Figure 8b indicates that there are two
distinct concentration layers during the night. The first layer is from
the surface to an altitude of about 100 m while the second is from 100 m to
the base of the elevated inversion. These layers cause the radiative cooling
which modifies the stable regions and changes the concentration profiles. _
At night the lower stable region is lifted from below 100 m to about 140 m in
Figure 8b. The upper level stable layer is moved from 740 m to 820 m and
by noon of the following day the stable region has moved upwards to a neight
of 1000 m in Figure 8a as compared to 820 m in Figure 8b. This clearly
shows the significance of the radiative properties of air_pollutants in
modifying elevated inversions and changing the concentration levels.
33
-------
10'
4 6 I02 2 4 6 I03 2 4 6 10*
/m5 or ppm x 10
Figure 8. Concentration Profiles for Summer Inversion Conditions:
(a) Simulation 2 with Radiatively Nonparticipating Pollutants,
and (b) Simulation 6 with Radiatively Participating Pollutants
Consisting of 20$ by Weight Carbon Aerosol and Ethylene as
Pollutant Gas
Urban Winter
In order to evaluate the influence of the change of season on the influence
of air pollution on the thermal structure and pollutant dispersion an urban
winter condition was simulated. The initial and free atmosphere conditions
are given by Bergstrom (I972b). The only major changes are in the solar
declination, initial temperature and humidity, and starting time. The
solar declination is that of Nebraska in January. The initial temperature
profile is presumed adiabatic at 17:00 with a surface temperature of about
I5C. The free atmosphere conditions were taken from Atwater (1970) and the
urban and pollution parameters were the same as before. The temperature
isopleths for Simulation J> without radiatively participating pollutants,
for Simulation 7 with radiatively participating pollutants, and the differ-
ence between Simulations 7 and 3 are shown in Figures 9a, 9c, and 9e,
respectively. The corresponding concentration isopleths are presented in
Figures 9b, 9d, and 9f, respectively.
The difference between day and night temperatures without radiatively
participating pollutants (Figure 9a) is only 4C which is less than that
during the summer. This is in agreement with other investigators
-------
uo
VJI
18=00
Figure 9.
06=00 18=00 O&OO 18=00 06=00 18=00 06=00
t, hr t, hr
18=00 06=00 18=00 O&OO
t, hr
Isopleths for Simulations 3 and 7; Top Row are Temperatures in C (Celsius) and Bottom
Row are Concentrations (jnyg/m3); Column I is Simulation 3, Column 2 is Simulation 7,
and Column 3 is the Difference Between Simulations 3 and 7
-------
(Pandolfo, et al., 1971). During the first night and next day the tempera-
ture differences in Figure 9c are warmer than in Figure 9a near the surface,
the maximum being -I.6C and the difference decreasing during the day to
-O.IC. The cycle is repeated during the second day as the temperatures are
0.2C smaller during the second day in Figure 9c. At 20:00 and at an altitude
of about 600 m the temperatures in Figure 9c are lower than in Figure 9a
due to the infrared cooling by pollutants.
The surface fluxes for the solar radiation and the downward thermal radiation
are shown in Table 5. The thermal radiation flux for the simulation with
radiatively participating pollutants increases quite rapidly and is 8 percent
higher within 2 hours. The average increase of thermal radiation flux is
about 20 percent while the solar radiation is reduced by about 10 to 30
percent. This decrease in the solar flux is larger than the summer simula-
tions (see Table 4) and is due to the fact that the average solar elevation
angle is lower in the winter. The larger increase in the thermal radiation
flux is apparently due to the lower specific humidities in the winter
situation. The rate of increase of the thermal radiation flux slows down
as the spectral region becomes relatively opaque.
The concentration differences are also similar to the urban summer simulation.
The maximum concentration is reduced at night whereas the differences in
concentration (Figure 9f) are very slight during the day. At an altitude
of about 600 m during the first night the concentrations are higher when
radiative participation of pollutants is accounted for. This results from
the upward movement of the stable region due to the radiative cooling.
Urban Winter Elevated Inversion
In these simulations the conditions are identical to the experiments
described in the previous subsection except that the temperatures are
isothermal above 600 m. This situation roughly corresponds to conditions
observed by Reagan and Herman (1971). Temperature and concentration isopleths
are not presented here because their interpretation is more difficult, but
they can be found elsewhere (Bergstrom, I972b). The temperature and
pollutant concentration profiles at six hour intervals are given in
Figures 10 and II. Comparison of Figures lOa and lOb reveals that the
surface temperatures are warmer for Simulation 8 with radiatively participat-
ing pollutants than for Simulation 4 with nonparticipating ones.
In the experiment without radiatively participating pollutants the stable
layer remains at about 600 m during the night, is moved up to about I km
during the next day and remains there during the next night and is destroyed
in the final day. The surface temperatures in the experiment with the
radiativeiy participating pollutants are warmer than in the corresponding
experiment (Simulation 3) without the inversion since stable layer prevented
any turbulent energy transport from the planetary boundary layer to the
free atmosphere. The maximum surface temperature during the second day
is I5C as compared to I9C with and without radiatively participating pollu-
tants, respectively.
36
-------
TABLE 5. COMPARISON OF THE SOLAR AND THE DOWNWARD THERMAL RADIANT FLUXES
AT THE SURFACE FOR THE URBAN WINTER SIMULATION 3 WITHOUT
RADIATIVELY PARTICIPATING POLLUTANTS AND FOR SIMULATION 7 WITH
RADIATIVELY PARTICIPATING POLLUTANTS
Time
Solar, F(0), erg/cm2-s
3 7
Thermal, F,(0), erg/cm2-s
17:00
19:00
21:00
23:00
01:00
03:00
05:00
07:00
09:00
1 1:00
13:00
15:00
17:00
19:00
21:00
23:00
01 :00
03:00
05:00
07:00
09:00
1 1 :00
13:00
15:00
17:00
4.869x10*
4.879x10*
2.738X105
3.838x|05
2.738XI05
4.879x10*
4.879x10*
2.738XI05
3.837XI05
2.738x|05
4.879x10*
4.87x|0*
3.92x|0*
2.I8XI05
3.08x|05
2.07x|05
3.56x|0*
2.99x|0*
1 .64x| 0s
2.37x|05
1 .57x|05
2.75x|0s
2.76XI05
2.74
2.72
2.70
2.69
2.68
2.67
2.67
2.66
2.71
2.75
2.77
2.74
2.71
2.70
2.69
2.68
2.67
2.66
2.65
2.65
2.69
2.72
2.73
2.71
2.76x|05
3.13
3.19
3.22
3.24
3.24
3.25
3.25
3.25
3.29
3.38
3.35
3.34
3.33
3.32
3.32
3.31
3.31
3.30
3.30
3.30
3.33
3.36
3.38
3.37
37
-------
1000 -
eoo
600
400
zoo
(a)
276 280 284 288 276 280 284 288 292
Figure 10. Temperature Distributions for Urban Winter Inversion Conditions:
(a) Simulation 4 with Radiatively Nonparticipating Pollutants and
(b) Simulation 8 with Radiatively Participating Pollutants
Consisting of 20$ by Weight Carbon Aerosol and Ethylene as
Pollutant Gas
4 6 K?
or pprp n!0
Figure II. Concentration Profiles for Winter Elevated Inversion Conditions:
(a) Simulation 4 with Radiatively Nonparticipating Pollutants, and
(b) Simulation 8 with Radiatively Participating Pollutants
Consisting of 20% by Weight Carbon Aerosol and Ethylene as
Pollutant Gas
38
-------
As in the summer simulation the radiative properties of air pollution
(specifically the strong radiative cooling which occurs at the base of a
sharp concentration gradient) cause the elevated stable region to move
upward. Figure lOb shows that during the night the stable region is moved
upward to about I km. The temperature and concentration differences
illustrate this motion (Bergstrom, I972b) since the temperatures are lower
and concentrations are higher in the experiment with radiatively participat-
ing pollutants at about 500 m during the first night (from about midnight
to about 08:00 in the morning). Consequently, this lifting of the stable
layer results in a much lower surface pollutant concentration (450 yg/m3
for the aerosol and 4.5 ppm for the gas versus 750 yg/m3 for the aerosol
and 7.5 ppm for the aerosol with and without radiatively participating
pollutants, respectively, at 06:00 in the morning). Again, the results
clearly show the significance of the radiatively participating air pollutants
in modifying elevated inversions and changing the concentration levels.
Effects of Other Pollution Parameters
In the previous subsection the various pollution parameters such as the
radiative characteristics of the pollutant aerosol or gas were kept constant.
The effects of pollutant aerosol alone, the effects of the gaseous pollu-
tant alone, the choice of the gaseous pollutant, the source strength, and
increased as well as decreased aerosol absorption on the thermal structure
and pollution dispersion for the summer elevated inversion conditions have
also been studied (Bergstrom, I972b). This situation (urban summer elevated
inversion) was selected for the simulations because the most serious pollu-
tion episodes occur under these condtiions. Here, only the effects of the
choice of gaseous pollutant and decreasing aerosol absorption are summarized
while the isopleths and a more detailed discussion of the results are
given by Bergstrom (I972b).
As explained before, ethylene was chosen since it can be considered to be
a representative hydrocarbon and is a strong absorber in the 8 to 12 jam
region. This choice, however, may be criticized as an oversimplification
of an urban atmosphere. Therefore, to investigate the sensitivity of the
predicted effects to the choice of gaseous pollutant, sulfur dioxide was
considered. The emittance of sulfur dioxide (S02) as published by Chan and
Tien (1971) was used. Comparison of results (Bergstrom, I972b; Figures 6.4
and 6.11) show that when S02 is chosen as the pollutant gas, the influences
due to the gaseous pollutant on the thermal structure are smaller than when
C2hU is considered as a gaseous pollutant. This is due to the fact that
sulfur dioxide is a weaker absorber than ethylene. The surface temperatures
are 0.75C warmer during the second night than for Simulation 2 with
radiatively nonparticipating gaseous pollutant and the stable layer is moved
slightly upward. However, the infrared cooling is not large enough to form
a noticeable elevated inversion at 100 m. Thus, sulfur dioxide has the
same qualitative effects as ethylene and only a magnitude of the results is
altered. This finding is quite significant since a high concentration of
sulfur dioxide beneath stable regions is often observed (Hoffert, 1972).
However, it should be mentioned that while the concentrations of the gaseous
pollutant are reasonable for hydrocarbons (Bergstrom, I972b) they are some
what too high for sulfur dioxide.
39
-------
Since the radiative properties of aerosols are not well known, the amount
of absorption by the aerosol was varied to determine their relative
influence on the results. In this simulation it was assumed that the
aerosol was nonabsorbing (i.e., only scattering). The effects due to aerosol
absorption were clearly shown (Figures 6.4 and 6.15 of Bergstrom, I972b).
The temperatures during the day in Experiment 26 for a nonabsorbing aerosol
are lower than those for Experiment 6 with an absorbing aerosol at
altitudes higher than 10 m. This is due to the solar heating of the
aerosols and is as large as 0.9C. The surface temperatures during the day
are somewhat higher for the simulation with the nonabsorbing aerosol
(Simulation 26) since then a larger fraction of the incident solar radiation
reaches the surface.
Summary of Surface Temperature Differences and Surface Concentration
The differences in the surface temperatures for the urban summer simulations
in the absence of an elevated stable layer are shown in Figure 12. For the
conditions with ethylene alone the temperature is I.5C warmer during the
first night, reduces to 0.8C warmer during the day, and rises to 2.3C
warmer during the next night. The simulation with only an aerosol present
is essentially the same as the one with nonparticipating pollutants during
the first night (1C cooler during the day, slightly cooler during the next
night, and 2C cooler during the last day). This shows quite clearly the
warming tendency of the gas (infrared properties) and the cooling tendency
of the aerosol (solar properties). At night the presence of gaseous pollu-
tants in the atmosphere increases the downward thermal radiative flux at
the surface (see Table 4) and consequently raises the temperature while
during the day the flux reaching the surface is reduced as a result of the
attenuation of the incoming solar radiation, and the surface temperature
is decreased.
The other temperature differences (Figure 12) lie between these two extremes.
For the simulation with both ethylene and aerosol it is almost as warm
during the night as with ethylene alone, but the surface is cooler during
the day. The reduction of the source strength by one-third shows that
temperature differences are decreased but not proportionately. In the
simulation with sulfur dioxide the surface is cooler than in the simula-
tions with ethylene due to the reduction in absorptance, but the influence
of sulfur dioxide is still apparent. The effect of increased absorption
by the aerosol increases the cooling of the surface; compare curves 3 and 4.
Thus, in these simulations the aerosol and the gas had somewhat compen-
sating effects. However, whether the effects cancel or one dominates over
the other is clearly a function of the radiative properties of the gaseous
and particulate pollutant and the atmospheric conditions. It should be
mentioned that considerations by other investigators of the influence of
aerosols on the temperature of the atmosphere have indicated that for most
combinations of aerosol properties and surface reflectance the effect of
increasing aerosol concentrations is one of cooling the earth-atmosphere
system. However, there are combinations of aerosol absorption and surface
reflection characteristics for which the effect of the aerosol is that of
warming the earth-atmosphere system (Yamamoto and Tanaka, 1972) and since
-------
o
12 16 20 24 4 6 12 16 20 24 4 8 12
Figure 12. Surface Temperature Difference (Simulation with Radiatively
Participating Pollutants Minus Simulation with Radiatively
Nonparticipating Pollutants) for Summer Conditions:
Curve
2
3
4
5
6
7
Pol lutant
Gas
S02
Nonparticipating
Aerosol
Nonparticipating
Nonabsorbi ng
20% Carbon
30% Carbon
20% Carbon
20>? Carbon
30% Carbon
mp
(ug/m2-s)
/3
the absorption properties of the aerosols
stiI I in doubt.
are not well known, this issue is
The surface pollutant concentrations as a funct.on of time are shown .n
Figure 13 for the summer simulation without an elevated stable region. In
all the simulations the concentration builds up to a peak during the night
and is reduced during the morning and then increases again, bince ™^&^
pollutant can escape from the planetary boundary layer» the a g .
tration increases during the two days. The h.ghest pol '^^ ^^j °^
are found in the simulations in which only the aerosoI radiafive propert.es
are accounted for (Curve I). These are only si'Sjtly higher than the
values with radiatively nonparticipating pollutants (Curve 2). Ihe
concentrations for the simulation with sulfur dioxide show that rne
results are decreased due to the slightly warmer surface temperatures
-------
12
12
Figure 13. Surface Pollutant Concentration Variation with Time for Summer
Conditions:
Curve
2
3
4
5
6
Pol lutant
Gas
Nonparticipati ng
Nonpartici pati ng
S02
Aerosol
Carbon
Nonpartici pati ng
20$ Carbon
30$ Carbon
Nonabsorbi ng
Nonparticipati ng
m
(Ug/m2-s)
I
There is a large reduction in pollutant concentrations in the simulations
with ethylene as the pollutant gas owing to the decreased stability at
night. The presence of the aerosols leads to a slight increase in the
concentration.
The surface pollutant concentrations are shown in Figure 14 for the winter
simulation without an elevated stable region. The general trend is the same
as for the summer except in this case there is no perceptible difference
between the results of the simulations without radiatively participating
pollutants and that with 20 percent by weight carbon aerosol only. The
reduction in concentration due to ethylene during the first night is some-
what larger than in the summer case (the surface temperature difference
was also larger). Again, the variation in the aerosol absorption properties
only had a slight effect during the day. In both Figures 13 and 14 the
surface concentrations during the day were only slightly different for the
-------
400
350
„ 300
N0
K
| 250
a.
fc.
^ 200
A
*
*
o
ISO
100
50
I
Figure 14.
12 18 24 6 12 18 24 6 12 \S
t.hr
Surface Pollutant Concentration Variation with Time for Winter
Conditions:
Curve
Pollutant
Gas
Aerosol
nip
(yg/m2-s)
I Nonparticipating Nonparticipating
I Nonparticipating 20% Carbon
2 S02 20$ Carbon
3 c2Hit 33% Carbon
4 C2H<, Nonabsorbing
various simulations. However, the concentrations at night were substantially
different showing the influence of the infrared radiative properties of air
pollutants.
The maximum daytime and nighttime differences from the radiativeIy non-
participating Simulations I to 4 (see Table 2) are presented in Table 6.
The results are similar to those already discussed and are only briefly
commented upon. The temperature difference is negative at night in every
instance when gaseous pollutants are considered to be radiatively Part|c>-
pating and is due to warmer surface temperatures. The differences increase
(become less negative) during the day and sometimes become ?°s^[V.e ,f*r^
result of the cooling effect of the aerosols. The concentration differences
are always positive at night (the dispersion of pollutants is_enhanced) and
is negative only in five instances during the day (four of which are
simulations where the pollutant gases are considered transparent), mis
-------
TABLE 6. MAXIMUM SURFACE DAYTIME (D) AND NIGHTTIME (N) TEMPERATURE AND
POLLUTION CONCENTRATION DIFFERENCES (SIMULATION I-SIMULATION 5, ETC.)
c
o
_l_
ro
ZJ
E=
c
O
-I-
(D
ZJ
-f-
AT, C
A
CO CO
yg/ma
D N D N D
5
6
7
8
9
10
1 1
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
-1 .5
-2.1
-1.6
-1.6
0
0
0
0
-1 .5
-2.0
-1 .5
-1.5
-0.25
-0.25
-0.25
-0.25
-1.25
-1.5
-1.25
-1.0
-1.5
-2.0
-1.5
-1.5
-1.5
-2.0
-1.5
-1 .5
O.I
0.5
-O.I
-O.I
1.0
1.75
0.5
0.5
-0.75
0
-0.75
-0.75
0-75
0.5
0.5
0.5
0
0
-0.25
-0.25
0
0.5
-0.25
0
0
0.5
0
-0.25
-2.2
-2.8
-1.5
-3.0
0
0.5
0
0
-2.25
-3.0
-1 .5
-3.25
-0.50
-0.75
-0.25
-0.5
-1.75
-2.5
-1.0
-2.5
-1 .75
-2.75
-1.25
-2.75
-2.25
-2.75
-1 .5
-3.25
0.4
0.9
O.I
-1 .1
1 .75
2.0
1 .25
1 .25
-1.5
-1.0
-1 .25
-2.25
1.50
1.25
1.00
1.00
-0.5
0
-0.5
-1.25
0
0.5
0
-1.0
0.5
1 .0
0.25
-1 .5
125
>IOOO
200
150
0
0
0
0
100
>IOOO
200
150
0
750
0
0
~__
100
>IOOO
200
150
100
>IOOO
200
150
0
0
0
50
0
-200
0
0
0
0
0
50
0
0
0
50
«.._
0
50
0
50
0
50
0
50
125
>IOOO
75
225
0
- 200
0
0
150
>IOOO
50
250
0
900
0
0
..__
150
>IOOO
50
200
100
>IOOO
50
200
0
0
0
150
- 50
-300
0
-100
0
0
0
150
0
- 50
0
50
___
0
0
0
150
0
50
0
150
-------
illustrates the importance of the gaseous pollutants in influencing the
pollutant dispersion. The table also clearly shows that the magnitude of
the effect of air pollution on the temperature and pollutant concentrations
is dependent upon the meteorological conditions, specific types of pollu-
tants present, and their concentration distributions.
-------
SECTION V
TWO-DIMENSIONAL MODELING OF THERMAL STRUCTURE AND POLLUTANT
DISPERSION IN THE URBAN ATMOSPHERE
The results of simulations previously discussed have shown that a one-
dimensional (vertical transport only) model is not adequate to describe the
transport phenomena in the planetary urban boundary layer due to the neglect
of advection. Therefore, work was initiated to develop a more realistic
(two-dimensional) model for the thermal structure and pollutant dispersion.
A two-dimensional transport model has been constructed for the prediction
of the time dependent velocity, temperature, humidity, and pollutant concen-
tration profiles. It should be emphasized that the flow field in the urban
area is three-dimensional and would require a very fine grid for accurate
simulation over the city. The increased computational time would be too
expensive for numerical simulations on most present day computers. Since
the primary objective of this research was to simulate the thermal struc-
ture, and two-dimensional model should provide a more realistic description
than the one-dimensional one even though some details of the complicated
urban flow field have been ignored. The temperature distribution should
not be extremely sensitive to the wind profile. Advection, turbulent
diffusion, and radiative transfer as well as radiative participation of
pollutants are all included. Surface and elevated pollutant sources are
considered, but chemical reactions and particle deposition have been
neglected. In addition, pollutant removal processes have been neglected
including washout by precipitation. The physical model and the numerical
method of solution are described and some preliminary numerical results are
presented in this section.
ANALYSIS
Physical Model
As in the case of the one-dimensional model, the earth-atmosphere system
is assumed to be composed of four layers: (I) the "free" ("natural")
atmosphere where the meteorological variables are considered to be time
independent; (2) the "polluted" atmosphere (the planetary boundary layer)
where the meteorological variables such as horizontal, vertical, and lateral
wind velocities, temperature, water vapor and pollutant concentrations are
functions of height, distance along the urban area, and time; (3) the soil
layer where the temperature is assumed to be a function of depth and time
only, and where the physical properties of the soil such as thermal
conductivity and diffusivity, surface albedo, and thermal emittance vary
with the distance along the horizontal axis; and (4) the lithosphere where
the earth's temperature is assumed to be constant during a few day simula-
tion period. The atmosphere is assumed to be cloud-free. The variation
in topography of the urban area is not accounted for, i.e., the terrain
-------
z=za
FREE
ATMOSPHERE
ATMOSPHERE
U, V, 0, p, Cw, C,, C2 SPECIFIED
PLANETARY
BOUNDARY
LAYER ,z
Z=0f
SOIL LAY!K
2=-Z
EARTH - . /
(LITHOSPHERE) CONSVANV.
TEMPERATURE
REGION //
\A
%^-*|%^DOWNWINb VRURAL
V>\\\\^»>>.V s ^-^>>S.\v^.vs
Figure 15. Physical Model and Coordinates
is assumed uniform even though the region modeled starts in a rural
includes the city, and ends again in a rural area, see Figure 15.
area,
In the free atmosphere the meteorological variables, including the
geostrophic winds, are assumed to be constant. The primary forcing function
for the model is the time-dependent solar irradiation.
In the polluted planetary boundary layer the transport of momentum, energy,
and species is assumed to take place by vertical and horizontal advection
as well as vertical and horizontal turbulent diffusion. In addition,
energy is also transport by solar (short-wave) and thermal (long-wave)
radiation. The interaction of both gaseous and particulate pollutants as
well as natural atmospheric constituents with solar and thermal radiation
is accounted for; however, the radiative energy transport in both the solar
and thermal parts of the spectrum is assumed to be quasi-one-dimensional and
will be described in greater detail in another subsection.
The coupling between the planetary boundary and soil layers is affected by
energy and species balances at the atmosphere-soil interface. The horizontal
variation of the urban parameters such as man-made heat and pollutant sources,
surface solar albedo (reflectance) and thermal emittance, surface roughness,
thermal diffusivity and conductivity of the soil and moisture parameter
are prescribed but arbitrary functions of position along the urban area.
The variation of these parameters with the time of day (i.e., solar angle
for reflectance and emittance) is neglected. It is well recognized that
the anthropogenic pollutant and heat emissions, for example, vary during
the diurnal cycle. A more realistic modeling of the sources during the day
-------
must await observational data. The surface temperature and pollutant
concentrations are determined from energy (including heat conduction in
the soil) and mass balances at the interface.
In the soil layer heat conduction is considered to be one-dimensional and
only the variation of the physical properties of the soil with the distance
along the urban area is accounted for. The water content in the soil is
assumed to be constant. Data on the hydraulic properties of soil such as
moisture potential, effective permeability, thermal liquid diffusivity,
liquid and vapor diffusivities as well as the fraction of the area covered
by concrete and buildings are not available (Eagelson, 1970) to warrant
more detailed modeling of the moisture migration phenomena in the soil
characterizing the urban area.
Governing Equations
The conservation equations of mass, momentum, energy, and species for a
planetary boundary layer are well known (Haltiner and Martin, 1957; Plate,
1971). Turbulent eddy diffusivities (K-theory) are used to close the problem.
The detailed discussion of the conservation equations appropriate for an
unsteady two-dimensional planetary boundary layer is given by Johnson (1975).
The final equations of the model are:
7. - Z
oo
Natural Atmosphere
z = Z6
U, v, 9, C , C = constant
Polluted Atmosphere
Mass:
9x ' 9z ~ (24)
Momentum (x-direction):
f9u ,811.81/1 ,. . , 9
P hvT + U -^— + V •*— = pf (V - V ) + -r—
K(3t 8x 8zJ K g 8x
Momentum (y-direction):
/ 8v 9v
P 34- U 1~ W •}-, ~
1 * / ^ . 3 f f j. JM } 9v 1
- = -pf (u - u ) + -7T- y + pK I-?—
} H 9 9x LI y,xj9xj
-------
Momentum (z-direction):
(26)
Energy:
30. + u 30 + 39] = _9_ F f. 0]
,9t 3x V 3zj 3x [_ [ pCpKxJ
(27)
Species:
3C
3t
+ u
3C
n
3x
+ w
Surface
Energy:
3T
9 T
3t
= a
"* "^ i
3C
n
3t
3
3x
"fo ,
I n
c 1
h K n
x J
3C
n
3x
3z
D + K
n z
C i3C
n| n
3z
SoiI Layer
T = constant
s
'3F
~W
(K-
(28)
+ c
(29)
2 = 0
(30)
at
z = -z.
The upstream is taken in a rural area upwind of the city under consideration.
At this location (x = 0) it is assumed that only background pollution is
present and that the flow is fully developed, parallel and possessing no
vertical velocity component. The meteorological variables at this point are
predicted from the one-dimensional model given in Section IV.
At the edge of the outer flow, the meteorological variables are specified
and held constant during the simulation; that is,
X(t,x,z) = constant
at z = z.
(31)
-------
where x represents the horizontal east velocity u, the horizontal north
velocity v, the potential temperature 0, and the species concentration Cn.
Implicit in those assumptions is the idea that the planetary boundary layer
thickness remains essentially constant. At the bottom of the soil layer
the temperature remains constant,
T (t,x,z) = constant
at z = -z.
(32)
At the earth's surface the velocities vanish,
u(t,z,x) = v(t,x,z) = w(t,z,x) =0 at z = 0
(33)
Along the earth's surface (any x) the surface temperature at any instant
of time t is predicted from an energy balance:
- rs(x)]F~(x,0)
ef(x)F~(x,0) - ef(x)aTf (x,0)
K0 m
p zJ8z
D + KWU^
w z 3z
- k
z=0
8T
z=0
+ Q(x) = 0
at z - 0
(34)
This boundary condition is identical to that for the one-dimensional model
[Eq. (IO)H except the physical characteristics of the soil, and the urban
parameters are functions of position. In the above equation the first two
terms account for absorption of the solar and thermal radiation; the third
term represents thermal emission; the fourth and fifth terms account for
sensible and latent heat transfer by molecular and turbulent diffusion,
respectively; the sixth term represents soil heat conduction; and the final
term represents the anthropogenic heat sources.
The water vapor concentration Cw at the surface at any instant of time
is prescribed by Ha I stead's moisture parameter M (Pandolfo, et a I., 1971),
see Eq. (II). In writing this equation the anthropogenic water vapor sources
have been neglected (Bornstein and Tarn, 1975).
The boundary condition for the pollutant concentration CD, p = I, 2, ..., N,
when a surface source is present is written by specifying the surface
pollutant mass flux, m , i.e.,
P'
= - D
at z = 0
(35)
Downwind of the city (i.e., in the rural area) it is assumed that all of
the meteorological and air pollution variables change very slowly, or
50
-------
= 0 at x - L (36)
This condition physically implies that the downstream rural area is far
away from the city center and that nearly fully developed conditions have
been reached.
Radiative Transfer Model
The radiative transfer model used is identical to that described in Section IV.
However, since the water vapor content as well as the radiation character-
istics of the earth surface vary along the horizontal direction, and since
both the gaseous as well as the particulate pollutants are being advected
downwind, it is obvious that the radiative transfer is not one-dimensional.
Certainly, the radiation field in the urban atmosphere is three-dimensional.
Because the analysis of multidimensional radiative transfer is very complex,
it does not appear to be warranted at the present time. Hence, it is
assumed that the radiative transfer can be approximated by a quasi-two-
dimensional field based on the vertical temperature, water vapor, and pollu-
tant distributions at several predetermined horizontal positions. The
radiative fluxes were then evaluated at a few prescribed horizontal locations
while interpolation was used to determine the radiative fluxes between the
locations.
Turbulent Di ff usi vities
Specification of eddy di ff usi vities associated with the numerical modeling
of the planetary boundary layer is a very difficult problem and has been a
subject of a recent review (Oke, I973a). In the numerical calculations,
it was assumed that the semiempi rical equations for the eddy dif f usivi ties
in the vertical (z) direction as given in Section IV were valid for the
entire boundary layer. Implicit in those correlations are the definitions:
KM = KM = KM, K6E K0and K°n = K°n.
x,z y,z z z
Following the procedures adopted by other investigators (Olfe and Lee, 1971;
McPherson, 1968) the eddy di ff usi vities in the horizontal direction are taken
as constant, i.e.,
x,x y,x xxx
Even though Kx was small, inclusion of this horizontal turbulent diffusion
improved the stability of the numerical method particularly under very
stable meteorological conditions which occurred late at night and early
in the morning.
It is recognized that the semiempi rical eddy diffusivity equations which
are used are based on similarity theories for equilibrium surface layers
51
-------
and may not be applicable for nonequiIibrium boundary layers. For example,
when air flows over an inhomogeneous terrain the flow field changes and it
takes time for the turbulence to "adjust." Available predictions (Shir,
1972) show that the adjusting process is rather slow, and the transition
region, i.e., the region where the air is adjusting to the new surface
condition, is a significant portion of the boundary layer above the new
surface layer. In this region the eddy diffusivity is not only a function
of height, but also a function of downwind distance from the change in condi-
tions as well as parameters representing the different surface conditions.
Method of Solution
The finite-difference scheme used to obtain the numerical solution of the
model equations was the alternating direction implicit (A.D.I.) method
(Ames, 1969). The method has recently been applied (Roache, 1972) to many
fluid flow problems.
The unsteady, two-dimensional conservation equations of momentum, energy,
and species can be written in the following general form:
3<) . 3 , 3<|> 8 L 3) . „ 82 . Q ,,,.
•5T- + u TT- + w -tr- = -*- K -^-H + K TT-TT + 3 (37)
3t 3x 8z 3z [ z 3zJ x 3x2
In this equation, may represent the horizontal velocity u(x,z,t), the
lateral velocity v(x,z,t), the potential temperature 0(x,z,t), or the nth
species concentration Cn(x,z,t). The turbulent eddy diffusivities (K's)
and the source term 3, i.e., the Coriolis force term in the momentum equa-
tions or the divergence of the radiative flux in the energy equation, are
known functions over the entire two-dimensional field.
The alternating direction implicit (A.D.I.) algorithm is a two-step method
which employs two finite-difference equations which are used at successive
time steps of increment At/2. The first equation is written explicitly in
the x-direction while the second is written explicitly in the z-direction
so that the results of the first time step are utilized in the second time
step. The finite difference approximations for the spatial derivatives and
the numerical algorithm are discussed in detail by Johnson (1975) and only
the selection of a suitable grid and time steps is summarized here.
The grid spacing should be so selected as to optimize computer storage
requirements with respect to the accuracy of the results. Taylor and
Delage (1971) have shown that the accuracy of the solution depends on the
type of vertical grid spacing. The spacing should be finer near the surface
and courser aloft. Therefore, to improve the resolution near the surface,
a logarithmic-uniform grid spacing was chosen in the vertical (z-direction).
The logarithmic spacing extended from the earth surface to about 1 km and
from there to the top of the boundary layer (^ 2 km) the spacing was uniform.
This was accomplished by using the transformation: £ = A£nT_(z+B)/BU, where
A and B were arbitrary constants. Equidistant spacing was chosen for the
horizontal (x) direction.
52
-------
The number of grid points and their spacing in the vertical (z) and the
horizontal (x) directions can be varied. The only limitation is the
computer core storage and computational time requirements. The results
reported here have been obtained using 22 nodes in the vertical direction
and 17 in the horizontal. With the many dependent variables (and numerous
auxiliary functions) that need to be evaluated and stored at different times,
the storage requirements exceed 128,000 bytes (octal) on the NCAR's CDC 760o'
digital computer [maximum high speed core storage is 150,000 bytes (octal)].
A much finer grid spacing would necessitate using the slower disk storage
(large core memory) and thereby increase the computer time requirements.
Three distinct time steps (one for the two-dimensional momentum equations,
one for the other two-dimensional transport equations, and one for the one-
dimensional transport equations) must be selected and a balance must be made
between computational time and the actual time steps employed. Table 7 shows
the values of some of the variables computed for different values of the
time steps used to solve the respective finite difference equation. In this
table, ^Transport 's "^ne "t"'me step used to solve all unsteady two-dimensional
conservation equations except the x- and y-momentum equations while ^t|V|omenfum
is the time step used for solution of the unsteady two-dimensional x- and
y-momentum equations. Likewise, AtQ_N.|. is the time step used to solve all
unsteady, one-dimensional transport equations by the Crank-Nicholson scheme
at the upwind boundary. As can be seen in Table 7, the solutions to the
partial differential equations appear to approach a limiting value as the
time steps approach zero, thus implying convergence.
In order to obtain some appreciation for the sensitivity of the model
numerical experiments were performed using different horizontal grid spacing
and different vertical coordinate distributions. The details of these
studies are given by Johnson (1975). It was found that the results were
considerably more sensitive to the vertical spacing than to either the time
step or the horizontal spacing particularly at the surface. This should
be expected since the gradients near the surface are quite large and hence
sensitive to the vertical grid size. Two numerical experiments were also
performed to check the model for downwind error propagation. This was
accomplished by positioning a small city at different horizontal locations
(Johnson, 1975). If the numerical scheme was behaving correctly, then the
upwind and downwind results would be independent of the horizontal location
of the center of the city. The results showed that the meteorological^
variables downwind of the city are independent of the horizontal position
of the city and yield identical results regardless of the location of the
urban center.
RESULTS AND DISCUSSION
The unsteady two-dimensional transport model developed has been tested and
some numerical experiments have been performed. Some of these preliminary
results are presented and discussed in this section of the report. Short-
comings of the model are indicated and improvements are suggested.
53
-------
TABLE 7. EFFECT OF TIME STEP ON SELECTED METEOROLOGICAL VARIABLES AT THE
CENTER OF THE CITY (zo = I m), z = I m, and t = I hr; SIMULATION
STARTED AT 12:00, COMPUTER-CDC 6600 (Ci DENOTES THE AEROSOL AND
C2 THE POLLUTANT GAS CONCENTRATIONS)
MeteorologicaI
Variable
0
u
V
w
Cw
Ci
C2
Computationa 1
AtT
Transport
At,. ,
Momentum
AtC.N.I.
(K)
(m/s)
(m/s)
(cm/s)
(kg/m3)
(yg/m3)
(ug/m3)
(s)
45.0 s
22.5 s
1 1.25 s
305.256
1 .0009
1 .0067
4.6918
0.02068
546.80
546.80
182.4
Time Steps
20.0 s
15.0 s
7.5 s
306.315
0.9415
0.9417
4.3644
0.01994
544.15
544.15
215.8
15.0 s
7.5 s
3.75 s
306.318
0.9414
0.9419
4.3606
0.01994
544.30
544.30
316.2
Time
-------
Prior to modeling the unsteady thermal structure and pollutant dispersion
in the urban atmosphere the model was used to simulate some of the experi-
mental observations of the Great Plains Turbulence Study (Lettau and
Davidson, 1957). Since the test simulations using the one-dimensional
model have already been discussed in Section IV, the details are omitted
here but they are given elsewhere (Johnson, 1975). The results obtained
were very similar to those already discussed. It was found that perturba-
tion of the surface roughness parameter z0 from 0.01 to 0.05 cm caused a
slight change in the peak surface temperature. On the other hand, changing
Halstead's moisture parameter from M = 0.01 to M = O.I significantly increased
the evaporation and resulted in a much cooler (about 7C) surface temperature
during the day.
Parameters and Initial Conditions Used in the Simulations
In the preliminary numerical experiments the city of St. Louis, Missouri was
modeled and the simulations were performed for typical summer conditions.
The simulations discussed in the report are summarized in Table 8. The
effects of wind speed, choice of gaseous pollutant, pollutant source flux,
and the type of pollutant source flux and urban heat flux distributions
along the urban area were studied. The horizontal grid spacing Ax was
selected to be I .5 km. With 17 nodal points, the total horizontal extent
of the area modeled was only 24 km, somewhat smaller than the size of the
St. Louis Metropolitan area. Since for most of the simulations, the
geostrophic wind speeds were relatively low, the vertical grid spacing with
the first point located at 5 m above the ground was used.
The urban surface parameters and their assumed variation along the area are
presented in Table 9. The horizontal distribution was established by
selecting the values of the parameters at the rural and urban center loca-
tions and, for the lack of any other data or information, a Gaussian distri-
bution curve was fitted between the rural and urban positions. In the table,
the values of kg and ag were obtained by computing the urban-rural values
of thermal admittance from a recent study carried out over St. Louis by
Dabberdt and Davis (1974) with the soil heat capacity data of Pandolfo, et a I .
(1971). The thermal emittance, et, were obtained from Wolfe (1964) and these
values were representative of folIiage, concrete, asphalt, and bricks. The
solar reflectance of the surface, rs, were obtained from albedo measurements
obtained by Dabberdt and Davis (1974) over St. Louis. The surface roughness
parameter of I m at the urban center was taken from Pandolfo, et a I.^(1971).
This same value was also used in the simulations with the one-dimensional
model. The rural value of 20 cm was selected because it was considered to
be a more realistic value of the undulating countryside surrounding the
St. Louis metropolitan area. Finally the moisture parameter M was estimated
for the model using the results of Johnson (1975) as a basis.
Figure 16 illustrates the assumed Gaussian and rectangular distributions for
the anthropogenic heat source Q along the urban area. The polIutant source
fluxes had similar type of distributions. To compare the results, the areas
under the two curves had to be equal. This was accomplished by first _ _
evaluating the area under the rectangular distribution and then determining
the Gaussian distribution by adjusting the value of the standard deviation.
55
-------
TABLE 8. SUMMARY OF SIMULATIONS PERFORMED TO STUDY THE EFFECTS OF RADIATIVE PARTICIPATION ON POLLUTANT
DISPERSION AND THERMAL STRUCTURE IN ST. LOUIS, MISSOURI, DURING THE SUMMER, COMPUTER-CDC 7600
Simulation
Number
1
2
3
4
5
6
7
8
Distribution
Q, mi, rri2
Gaussian
Gaussian
Gaussian
Gaussian
Gaussian
Gaussian
Rectangular
Rectangular
u (m/s)
9
12
12
6
6
6
6
6
6
v (m/s)
9
8
8
4
4
4
4
4
4
Pol lutant
Gas
C2Hi,
C2Hi,
CjfU
S02
C2H,,
C2H^
C2Hi»
C2Hi,
Mean Pollutant Source
Flux (ug/m2-s)
2.5
2.5
2.5
2.5
2.5
5.0
2.5
2.5
Radiative
Interaction
Nonparticipating
Participating
NonpartIc i pat i ng
Participating
Participating
Participating
Nonparticipating
Participating
TABLE 9, VARIATIONS OF THE URBAN SURFACE PARAMETERS ALONG THE HORIZONTAL DIRECTION ASSUMED FOR THE
SIMULATIONS
CT\
Node Horizontal
No. Location, x(km)
I 0
2 1.5
3 3.0
4 4.5
5 6.0
6 7.5
7 9.0
8 10.5
9 12.0
10 13.5
It 15.0
12 16.5
13 18.0
14 19.5
15 21.0
16 22.5
17 24.0
r
0.180
0.166
0.153
0.142
0.132
0.126
0.121
0.120
0.121
0.126
0.132
0.142
0.153
0.166
0.180
0.180
0.180
et
0.900
0.913
0.924
0.933
0.941
0.946
0.949
0.950
0.949
0.946
0.941
0.933
0.924
0.913
0.900
0.900
0.900
k
g
(W/m-K)
0.100
0.153
0.200
0.296
0.372
0.438
0.483
0.500
0.483
0.438
0.372
0.296
0.200
0.153
0.100
0.100
0.100
a
s
(m2/s)x|07
25.00
20.11
15.24
10.67
6.70
3.62
1.67
1.00
1.67
3.62
6.70
10.67
15.24
20.11
25.00
25.00
25.00
M
0.1000
0.0886
0.0780
0.0687
0.0608
0.0549
0.0512
0.0500
0.0512
0.0549
0.0608
0.0686
0.0780
0,0886
0.1000
0.1000
0.1000
ZQ
(m)
0.200
0.307
0.440
0.591
0.744
0.877
0.968
1.000
0.968
0.877
0.744
0.591
0.440
0.307
0.200
0.200
0.200
-------
32
24
0
(W/m2)
16
GAUSSIAN
12
16
20
24
x (km)
Figure 16. Comparison of Rectangular and Gaussian Anthropogenic Heat Source
Distributions Along the City
The pollutant source flux was modified to yield typical concentrations
observed in the urban atmosphere (Stern, et a I., 1972). The mean man-made
urban heat source parameters (based on the rectangular distribution) of
20 W/m2 was characteristic of Columbus, Ohio (McElroy, 1972) while the rural
value of 2 W/m2 was obtained for the whole of West Germany (Oke, I973a).
The simulations were started at noon (12:00) solar time and continued for a
24-hour period. The initial conditions used in Simulations I and 2 were
identical to those employed for the one-dimensional model and were imposed
over the entire model (no x-variation). The data were taken from Lettau
and Davidson (1957) for August 24, 1954. For the remaining simulations
(3 through 8), the initial horizontal and lateral velocity fields were
simply divided by two while the other variables remained the same. The
pollutant concentration profiles were initialized to a constant background
value of 50 ppm. In the experiments, the large-scale synoptic gradients
were zero thus allowing the use of time-independent boundary condition at the
top of the planetary boundary layer for temperature, pressure, water vapor,
and pollutant concentrations. The lower soil boundary beneath the surface
(z = -ZA = -50 cm) was held constant at a temperature of 295.5 K (Pandolfo,
et al., 1971), and the soil layer grid spacing was 5 cm. The time step for
the momentum equations was 22.5 s while the upwind boundary condition time
step was 11.25 s. Both time steps were held constant. The time step for
the transport equations was equal to 45 s during the day (05:00 to 20:00)
and during the night (20:00 to 05:00) the value was raised to 90 s. The
computational time per 24-hour simulation on the NCAR CDC 7600 computer
took about 8 minutes.
57
-------
Some Difficulties Encountered
Many problems were encountered when the entire model was assembled and
simulations were attempted. Only a few of the more important ones will be
mentioned here. A more detailed discussion is given by Johnson (1975).
Late in the afternoon when the atmosphere changed from free convection
conditions to forced convection conditions (the turbulent diffusivity
equations changed from the free convection to the forced convection correla-
tions), a difficulty arose in that the diffusivities were not continuous
(see Table I). As the Richardson number approached Ri-j- from the left
(negative side) the diffusivities predicted for free convection conditions
were smaller than those predicted when Ri-j- was approached from the right
under forced convection conditions. This caused a pollutant buildup at
the surface near sundown that was physically unrealistic. As yet, this
problem has not been corrected, and all that can really be said is that an
improved turbulence model is required.
Late at night it was found that the atmosphere became quite stable especially
in the simulations with the lower geostrophic winds (ug - 2.4 m/s, Vg - 1.6
m/s) and a very deep surface inversion resulted. The Richardson numbers
computed for these cases were found to exceed Ric which caused the diffusi-
vities predicted from the Pandolfo, et al. (1971) eddy diffusivity-Richardson
number correlations to be meaningless. In order to overcome this difficulty,
the cubic polynomial developed by O'Brien (1970) and used by Bornstein (1973)
was employed for diffusivity prediction in the transition layer. This
polynomial can be written as (Bornstein, 1973; p. 45)
r H*)2r p r r i
K(z) = K(H*) + nrV I K - K +
-------
time the velocity was quite small U I m/s) at the first grid point near the
surface and small oscillations with a magnitude of about ±5% were observed
which always disappeared soon after sunrise. It should also be mentioned
that these oscillations did not show up in the v or w velocity components
unless they had already become very large in u. It was felt that these
oscillations were related to discretization errors which become quite
prevalent when attempting to predict small numbers with high accuracy. Other
investigators have noted the presence of similar oscillations and some
attribute them to the finite-difference approximations (Yu, 1973; p. 27).
Yu (1973) has employed a three-point horizontal filter to suppress the high
frequency components of these oscillations which are thought to be the
principal cause of these horizontal instabilities.
Components of the Energy Budget at the Surface
The surface temperature is a very important parameter as far as the "forcing"
of the model is concerned. For this reason, the surface energy budget,
Eq. (34), and the budget components are considered first. Figures 17 and 18
illustrate the variation along the urban area of the energy budget components
at the surface for Simulation 3 at midnight (24:00) and noon (12:00) of
the next day, respectively. Inspection of Figure 17 shows that the emitted
(qe) and the absorbed thermal (qat^ fluxes are the dominant components.
The turbulent (qf), the latent (q&), the ground conduction (qg), and the
anthropogenic heat (Q) fluxes are significantly smaller. The results indicate
that for the meteorological conditions of Simulation 3 thermal radiation
dominates in establishing the surface temperature at midnight and in the
early morning of the next day. The variations of the various energy budget
components along the urban area are found to be relatively small.
At noon (Figure 18) the absorbed solar flux (qas) is the largest term in
the energy balance and the anthropogenic heat source (Q) is the smallest.
At the urban center (x = 10.5 km) the heat conduction term into the soil
(qg) amounts to about 10 percent of the absorbed solar flux. All of the
components of the energy budget that were computed are important, and they
must be included in the surface energy budget in order to correctly predict
the surface temperature.
The only two components of the energy budget which depend to any great degree
on the wind speed are the turbulent (qf) and the latent (qA) fluxes. Their
diurnal variation is illustrated in Figures 19 and 20. The results show
that, as expected, these two fluxes are quite sensitive to the wind speed.
The turbulent flux is higher at the urban center than at the upwind rural
location because of increased turbulent mixing over the city. Johnson
(1975) has found that the latent flux is quite sensitive to the Ha I stead s
moisture parameter. Since the parameter is larger at the upwind rural
location than at the urban center (see Table 9) the latent heat f I ux i s
also larger there. The results also show that for the conditions of Simula-
tion 3 condensation occurs at the surface late at night.
The energy budget components at the surface for simulations with radiatively
participating pollutants and the differences between the radiatively non-
interacting and interacting pollutants are discussed in a later section.
59
-------
400
200
q
(W/m2)
-200
-400
qgxio
12
x (km)
16
20
24
Figure 17. Variation of the Surface Energy Flux Components (qt—Turbulent,
qA—Latent, qe~Emitted, qat—Absorbed Thermal, q —Ground
Conduction, Q—Anthropogenic Heat Source) for Simulation 3 at
24:00 of the First day
600 r
400
200
q
(W/m2)
0
-200
-400
12
x (km)
16
20
24
Figure 18. Variation of the Surface Energy Flux Components (q-j-—Turbulent,
q,, — Latent, qe—Emitted, qas—Absorbed Solar, qa-j-—Absorbed
Thermal, qq—Ground Conduction, Q—Anthropogenic Surface Heat
Source) for Simulation 3 at 12:00 of the Second Day
60
-------
600
400
(W/m2)200
•Ug=12m/s, Vg=8m/s
Ug» 6 m/s, v_= 4 m/s
-200
12=00 16=00 20:00 24:00 04=00 08=00 12=00
TIME
Figure 19. Effect of Wind Speed on the Diurnal Variation of the Turbulent
Heat Flux at the Surface for Simulations I and 3
600
Uga12m/s, Vg=8m/s
Ug= 6 m/s, Vg= 4 m/s
(W/m2)
12=00 16-00 20=00 24:00 04=00 08=00 12=00
TIME
Figure 20. Effect of Wind Speed on the Diurnal Variation of the Latent
Heat Flux at the Surface for Simulations I and 3
61
-------
T
(C)
36
32
28
20
16
RECTANGULAR
GAUSSIAN
18=
12
X (km)
16
20
24
Figure 21 .
Comparison of Surface Temperatures for Gaussian (Simulation 3)
and Rectangular (Simulation 7) Distributions of Anthropogenic
Heat and Pollutant Sources Along the City
Surface Temperature
Simulations with Radiatively Nonparticipating Pollutants
A comparison of the surface temperatures for the Gaussian (Simulation 3)
and the rectangular (Simulation 7) distributions of anthropogenic heat
sources is illustrated in Figure 21. The figure shows that the difference
between the two results is only about 1C and the maximum difference occurs
late at night (05:00) when the anthropogenic heat source is a significant
component of the energy budget. At noon (12:00) the surface temperatures
in the city differ by only about O.IC. The surface temperatures predicted
along the urban area are consistent with the urban heat source distribution,
see Figure 16.
The diurnal variation of the surface temperature for Simulations I and 3
is illustrated in Figures 22 and 23, respectively. Temperatures at four
positions along the urban area—"upwind rural" (node I, x = 0 km), "upwind
residential" (node 4, x = 4.5 km), "urban center" (node 8, x = 10.5 km),
and "downwind residential" (node 12, x = 16.5 km)—are shown in the figures.
Inspection of the figures reveals that the amplitudes of the diurnal surface
temperature variations are smaller for the higher wind speeds (Simulation I).
62
-------
ON
U>
292
12:00
12:00
Figure 22. Variation of Surface Temperature with Time for Simulation I;
u =12 m/s, v = 8 m/s
-------
310
292
12:00
Ifc'OO
Figure 23. Variation of Surface Temperature with Time for Simulation 3;
u = 6 m/s, v =4 m/s
ip J
6k
-------
This is due to the fact that the turbulent and latent energy fluxes are
larger and dominate surface energy balance, see Figures 19 and 20. The
minimum temperature occurs just before sunrise (between 05:00 and'o6:00).
The surface temperature drops sharply during the late afternoon and rises
rapidly after sunrise. During the first few hours of the simulation an
initial transient is noted in the surface temperatures presented in Figures 22
and 23. This is due to the fact that the assumed initial velocity, tempera-
ture, and water vapor concentration profiles were too "far" away from the
quasi-steady solution induced by the diurnal cycle, and it took about 2 to
3 hours for the system to adjust. The temperatures after a 24-hour simula-
tion period are about 2C cooler in Simulation I (Figure 22) and about 1C
warmer in Simulation 3 (Figure 23) than the assumed initial surface tempera-
tures. The surface temperatures at the downwind residential location are
slightly warmer than at the upwind residential location. This is attributed
to the heating of air as it flows over the warm city. For higher wind
speeds (Simulation I, Figure 22) the maximum surface temperature difference
(about I.4C) between the urban center and upwind rural locations occurs in
the evening at 19:00 and remains almost constant throughout the night. On
the other hand, for the lower wind speeds (Simulation 3, Figure 23) the
maximum difference occurs just before the sunrise, and the difference is
considerably higher.
The main conclusion of these results is that the model predicts an urban
heat island for Simulation 3 having a magnitude of about 4C just before
sunrise and about I .4C at noon. For a simulation with lower wind speeds
(ug = 3 m/s and Vg = 2 m/s) which are not reported here, the maximum urban
heat island reached an intensity of about 8C. The simulated results compare
well with nighttime and daytime observed temperature excesses between the
urban and rural locations (Peterson, 1969; Oke, I973b; DeMarrais, 1975).
Simulations with Radiatively Participating Pollutants
The local surface temperature differences along the city between Simulations
2 and I (see Table 8 for parameters) and between Simulations 5 and 3 are
presented in Figures 24 and 25, respectively. The difference is defined
as the local surface temperature for a simulation with radiatively partici-
pating pollutants minus the surface temperature for a simulation without
radiatively participating pollutants. The temperature differences are a
result of the complex interactions of the flow of air over a rough Durban
area, the anthropogenic heat and pollutant sources, and the radiative
participation of the aerosol and gaseous pollutants. Individual influences
cannot be readily attributed. As expected, the results show that the
differences between the simulations with radiatively participating and
nonparticipating pollutants are considerably smaller for higher wind^speeds
(uq = 12 m/s, vq = 8 m/s; Figure 24) than for lower wind speeds (ug - 6 m/s,
vg = 4 m/s; Figure 25). The surface temperature difference is largest during
the night, reaches a maximum before the sunrise (05:00), and is smallest at
noon.
Comparison of the local surface temperatures along the city for a simulation
with radiatively participating pollutants having a surface source f|ux ot
2.5 ug/m2s (Simulation 5) and one having a surface flux of 5.0 ug/m s
65
-------
0.6
0.5
AT
(K)
02
OSOO
06--00
8
12 16
x (km)
20 24
Figure 24. Surface Temperature Difference (Simulation 2 minus Simulation I)
Along City; u =12 m/s, v = 8 m/s
s3 O
2.0
AT
(K)
1.5
1.0
0.5
12:00
12 16
x (km)
20 24
Figure 25. Surface Temperature Difference (Simulation 5 minus Simulation 3)
Along City; u =6 m/s, v =4 m/s
66
-------
400
300
Ca
^
200
100
24=00
12
x (km)
16
20
24
Figure 26. Variation of Surface Pollutant Concentration Along the City
for Simulation 3; u =6 m/s, v ~ 4 m/s
y y
(Simulation 6) showed that there is little difference between the surface
temperatures for the two simulations. The differences were greatest down-
wind of the city center just before sunrise and were less than 0.3C higher
for Simulation 6 than for Simulation 5. The reason for this small difference
(see Table 10) is that the thermal absorbed flux (qaf) which enters the
energy budget at the surface is not altered significantly by the radiatively
participating pollutants. The reason for this is that even though the
pollutant source flux at the surface for Simulation 6 is twice that for
Simulation 5, the total mass loading of aerosol and pollutant gas in the
atmosphere is only about 12 percent larger for Simulation 6. This finding
will be discussed later.
Surface Concentrations
The variation of the surface pollutant gas concentrations along the urban
area for Simulation 3 is shown in Figure 26. The pollutants build up during
the night and reach a maximum surface concentration just before sunrise.
After sunrise the atmosphere becomes unstable and by noon the surface
concentrations are significantly reduced. At the center of the city
(x = 10.5 km), for example, the gaseous pollutant concentration at the
surface increases to 404 ug/m3 before sunrise (05:00) and by noon (12:00)
is reduced to 175 yg/m3. Because of the effective vertical dispersion
during the day, the maximum concentration occurs in the immediate vicinity
of the peak pollutant surface source flux (x = 1-0.5 km), while at night and
early in the morning the maximum concentration occurs downwind of the urban
center because of the horizontal advection. The downwind residential and
rural pollutant concentrations predicted appear to be too high. This may be
due to the fact that a zero gradient pollutant concentration condition
67
-------
TABLE 10. DIURNAL VARIATION OF THE ABSORBED THERMAL FLUX AT THE SURFACE
(qat in W/m2) FOR SIMULATIONS 3, 5, AND 6 AT THE UPWIND RURAL AND
THE CENTER OF THE CITY LOCATIONS
Simulation 3
Simulation 5
Simulation 6
Tl fY1£*
1 1 1 1C?
12:00
14:00
16:00
18:00
20:00
22:00
24:00
02:00
04:00
06:00
08:00
10:00
12:00
Upwi nd
Rural
363.4
370.1
370.6
360.1
343.9
338.4
333.9
329.1
324.2
328.4
345.6
362.3
374.9
Urban
Center
383.6
396.3
395.6
383.5
368.7
362.3
357.6
353.6
349.7
351.2
367.5
386.3
400.8
Upwi nd
Rural
381.5
387.7
388.8
377.7
362.8
356.8
352.8
348.7
344.8
348.0
363.8
380.1
392.2
Urban
Center
402.7
417.3
416.2
403.6
389.2
382.0
377.3
373.7
370.5
372.1
388.0
406.7
420.9
Upwi nd
Rural
381.5
387.7
388.8
377.6
362.7
356.7
352.4
348.6
344.8
348.0
363.7
380.1
392.1
Urban
Center
402.7
418.5
417.5
404.7
390.3
382.7
377.9
374.3
371 .7
372.9
388.9
407.8
422.1
68
-------
AC
-40 —
-50 -
-60
24
Figure 27. Surface Pollutant Concentration
Simulation 3) Along the City
Differences (Simulation 5 minus
was imposed at the downwind rural position (x = 24 km) or maybe
because no sinks were considered. The surface pollutant concentrations
predicted also appear high. The modeling of pollutant sources is considered
to be the most important reason for this result. Modeling of the spatial
and diurnal variation of the pollutant sources produced by human activity
is very difficult because of the lack of data. Use of a constant (time
independent) pollutant source is, of course, unrealistic. It is well known
that each of the different pollutants have their own diurnal variation
(Peterson, 1970, 1972; Turner, 1968). For example, the production of carbon
monoxide can be related to the daijy automobile traffic count (Lin and
Goodin, 1975). Furthermore, location of the source at the surface ignores
the fact that pollutants are injected directly into the atmosphere at some
height and not at the surface. Pollutants must diffuse from the vicinity of
the surface before1 they can be dispersed throughout the atmosphere. Since
the turbulent diffusivities are generally small near the surface, high
pollutant concentrations naturally result.
The difference between the surface pollutant concentrations for Simulation 5
with radiatively participating pollutants and Simulation 3 with radiatively
nonparticipating ones are illustrated in Figure 27. The results show that
69
-------
1200
1000 -
800 -
z
(m)
600 -
400 -
200 -
-60 -40 -20 0
Au' (cm/s)
-60
-40 -20 0
Av' (cm/s)
20
Figure 28. Perturbation Velocities (Velocity at the Urban Center minus
Velocity at the Upwind Rural Location) for Simulation 3
However,
is relatively
of results
13, it is
the radiative participation of pollutants in the atmosphere enhances their
own dispersion and reduces the pollutant surface concentrations. The
reduction is greatest at night and amounts to about 10 percent.
the pollutant mass loading for these simulations, see Table II,
small compared to that used by Bergstrom (I972b). On the basis
obtained with'the one-dimensional model and presented in Figure
expected that the reduction would be larger for greater mass loadings and
more restrictive dispersion conditions such as would arise, for example,
under lower wind speeds and stable upper layer temperatures.
Velocity Distribution
Results of simulations show that prevailing flow decelerates on encountering
the roughness elements of the city and accelerates on leaving the urban area.
This is indicated in Figure 28 where the perturbation velocities (velocity
at the urban center minus the velocity at the upwind rural location) are
presented at two different times during the course of Simulation 3. The
differences are greatest at night and the maximum is seen to occur at or
below 50 meters. The trends found at consistent with those found by other
investigators modeling flow over rough strips (Estoque and Bhumralkar, 1970)
or over an urban area (Bornstein, 1972; Wagner and Yu, 1972).
70
-------
TABLE II. COMPARISON OF AEROSOL MASS LOADINGS (Mi) FOR VARIOUS SIMULATIONS
Sou rce
Simulation 3
Simulation 4
Simulation 5
Simulation 6
Bergstrom (I972b)
Simulation 3
Simu 1 at ion 4
Simulation 5
Simulation 6
Bergstrom (I972b)
Time
(hr)
05:00
05:00
05:00
05:00
05:00
12:00
12:00
12:00
12:00
12:00
Ug
(m/s)
6
6
6
6
12
6
6
6
6
12
V
g
(m/s)
4
4
4
4
8
4
4
4
4
8
Mi
(Ug-km/m3)
119.9
1 19.9
1 19.8
132.0
161 .0
122.0
122.0
121.5
136.2
211. 1
TABLE 12. SURFACE TEMPERATURES (IN K) AT THE CENTER OF THE CITY (x = 10.5 km)
FOR SIMULATIONS 3, 4, 5, AND 6 AT SELECTED TIMES
Simulation Number
Time
(hr) 345
18:00
24:00
05:00
06:00
09:00
12:00
304.01
297.50
295.58
297.48
306.67
310.58
304.05
297.62
295.77
297.65
305.73
310.61
304.39
298.28
296.72
298.49
306.24
310.98
304.39
298.30
296.74
298.51
306.25
310.98
71
-------
12
x(km)
18
24
Ca) Nonparticipating Simulation (b) Participating Simulation 5;
3; t = 24:00 hr t = 24:00 hr
I03
12
x(km)
(c) Nonparticipating Simulation (d) Participating Simulation 5;
3; t = 12:00 hr t = 12:00 hr
Figure 29. Comparison of Vertical Velocity Isopleths (in cm/s) for
Simulations with Radiatively Nonparticipating (Simulation 3)
and Radiatively Participating (Simulation 5) Pollutants
72
-------
As a consequence of the decrease in horizontal wind speed the continuity
of mass requires upward vertical motion ahead of the urban center and down-
ward motion downwind of the urban area, Figure 29. The magnitude of the
vertical velocity is, however, small and is generally confined to the upper
regions of the boundary layer. The net effect of the radiatively participat-
ing pollutants is a relatively minor factor in establishing the flow over
the urban area.
Temperature Distribution
Radiatively Nonparticipating Pollutants
Figure 30 illustrates the isopleths of the two-dimensional potential tempera-
ture fields at six hour intervals for Simulation 3. At 18:00 the boundary
layer is nearly adiabatic, especially in the upwind rural area, with a ther-
mal plume having a temperature of about 305K forming at a height of about
100 m downwind of the city center (x = 10.5 km). This plume is not felt
downwind, and the upwind and downwind rural temperatures near the surface
are virtually identical. A surface temperature inversion develops at night
over the urban area. The inversion is seen to be deeper over the rural area
than over the city. This is indicative of the nocturnal urban heat island
which decreases the stability of the atmosphere. The magnitude of this
island is larger at night than during the day. This type of behavior is well
documented (Peterson, 1969; Oke, I973a). For Simulation I with higher wind
speeds (ug = 12 m/s and Vg = 8 m/s) the surface inversion was found to be
less deep, and the magnitude of the nocturnal heat island was smaller.
The variation of temperature in the atmosphere during the diurnal cycle is
more clearly illustrated in Figure 31 in which a comparison of the upwind
rural and urban center potential temperature profiles are presented for
Simulation 3. During the night a surface inversion develops and is seen to
be larger in the upwind rural location than at the urban center. The inver-
sion reaches a maximum before sunrise (05:00) and by 06:00 the breakup of
the stable surface layer is noted. The surface inversion erodes rapidly
after sunrise due to heating by absorption of solar radiation and by 09:00
all traces of the inversion have then disappeared. The low-level nocturnal
temperature structure over the center of the city differs significantly from
that in upwind rural location. The profiles also indicate distinct regions
of stability particularly at night, and this is in agreement with observa-
tions of Clarke and McElroy (1974) over the city of St. Louis, Missouri. _
Of course, pollutants injected into the layers having different stabilities
are dispersed at different rates.
The potential temperature isopleths over the urban area for Simulation 7
having a rectangular distribution of anthropogenic heat sources are presented
in Figure 32. A comparison of Figures 30 and 32 reveals that the difference
between the two simulations is quite small. The maximum difference occurs
just before sunrise when the contribution of urban heat source Q to the
surface energy balance is the largest. Due to the assumed shape of Q (see
Figure 16), the temperature profiles for Simulation 7 define the urban area
more sharply.
73
-------
z(m)
(a) t = 18:00 hr
6 12 18
x (km)
(b) t = 24:00 hr
z(m)
d t = 2:00 hr
0 6 12
x (km)
(c) t = 06:00 hr
Figure 30. Potential Temperature Isopleths (in K) for Simulation 3; Note
that the Last Digit Denoting the Temperature of the Isotherms
at 18:00, 24:00, and 06:00 Hours has been Truncated
-------
1200
a) UPWIND
10001- RURAL
800
600
400
200
Figure 31. Potential Temperature Distribution for Simulation 3
Radiatively Participating Pollutants
A comparison of potential temperature isopleths for the four simulations
(3 through 6) having a Gaussian distribution of anthropogenic heat and
pollutant sources at times 24:00, 06:00, and 12:00 are given in Figures 33,
34, and 35, respectively. A summary of the surface temperatures at the urban
center for several different times during the diurnal cycle is given in
Table 12. The results show that the maximum surface temperature difference
between Simulation 3 with radiatively nonparticipating pollutants and
Simulations 4, 5, and 6 with radiatively participating pollutants occurs
late at night before sunrise (05:00) and reaches 1.16 K. Note also that
there is surprisingly little difference between temperatures for Simulations
5 and 6 which have surface pollutant sources of 2.5 and 5.0 ug/m2s, respec-
tively. This indicates that at night for Simulation 5 the gaseous pollutant
concentration distribution and the total mass in the atmosphere are such
that a "saturation" condition may have been reached, and an additional
increase in pollutant concentration (Simulation 6) does not affect the net
thermal (long-wave) radiative transfer in the atmosphere. This may also be
due to the fact that the total mass of the representative pollutant gas
(ethylene, CzhM present in the atmosphere was only about 12 percent greater
than for Simulation 5 (see Table II). During the day the aerosols and
gaseous pollutants appear to have compensating effect on the surface energy
balance and therefore on the surface temperature. The aerosols decrease
the solar flux while the gaseous pollutants increase the thermal flux inci-
dent on the surface. Careful comparison of the potential temperature iso-
pleths presented in Figures 33, 34, and 35 reveals that the maximum
temperature difference between the simulations with radiatively interacting
75
-------
z(m)
6 12
x(km)
(a) t = 18:00 hr
18
6 12
x(km)
(b) t = 24:00 hr
18
10
10
z(m)
6 12
x(km)
(c) t = 06:00 hr
18
6 12
x(km)
(d) t = 12:00 hr
18
Figure 32. Potential Temperature Isopleths (in K) for Simulation 7
76
-------
) 6 12
x(km)
(a) Nonparticipating Simula-
tion 3; m = 2.5 yg/m2s
24
(b) Participating Simulation 4;
S02, m = 2.5 ug/m2s
I03 F
1 1 i 11 ill i i i
(c) Participating Simulation 5;
, m = 2.5 ug/m2s
(d) Participating Simulation 6;
, mp = 5.0 yg/m s
Figure 33. Comparison of Potential Temperature Isopleths (in K) between
Simulations 3 (Part a), Simulation 4 (Part b), Simulation 5
(Part c), and Simulation 6 (Part d) at 24:00 of the First Day
77
-------
IOZ
z(m)
IOJ
10°
10
-1
_22i
"W
) 6 12 18
x(km)
(a) Nonparticipating Simula-
tion 3; m = 2.5 yg/m2s
TIT
-w
-9W
-»r
5D1
TIT
-55T
12
x(km)
-2W-
»T
18
24
(b) Participating Simulation 4;
S02, m =2.5 yg/m2s
10
3 -
10
z(m)
0 6 12
x(km)
(c) Participating Simulation 5;
CzHif, m =2.5 ug/m2s
Figure 34. Comparison of Potential Temperature Isopleths (in K) between
Simulations 3 (Part a), Simulation 4 (Part b), Simulation 5
(Part c), and Simulation 6 (Part d) at 12:00 of the Second Day
(d) Participating Simulation 6;
, m =5.0 ug/m2s
78
-------
) 6 12 18
x(km)
(a) Nonparticipating Simula-
tion 3; m = 2.5 yg/m2s
(b) Participating Simulation 4;
S02, m =2.5 ng/m2s
10
c? and slation 6 (Part d) at 12=00 of the Second Day
79
-------
600 r
500 -
400 -
300 -
(b)
200 -
100 -'
Figure 36. Perturbation of Potential Temperature (Temperature in the City
Minus Temperature at the Upwind Rural Location) for Simulation "5
and noninteracting pollutants occurs at the surface. The results also show
that the presence of radiativeiy participating pollutants in the urban
atmosphere reduces the amplitude of the diurnal temperature variations.
For example, in Simulation 3 the amplitude (maximum surface temperature
minus minimum surface temperature) at the urban center is ISC while for
Simultion 5 it is I4.2C.
The net effect of the city and the human activity on the temperature
distribution can be examined by comparing the potential temperature perturba-
tions at the urban center presented in Figures 36a and 36b for Simulations 3
and 5, respectively. The perturbation is defined as the temperature at the
urban center minus the temperature at the upwind rural location. The pertur-
bations are seen to be largest at the surface and are confined to about the
lowest 600 meters of the planetary boundary layer. The maximum surface
temperature perturbation (urban heat island intensity) for Simulation 3 with
radiativeiy nonparticipating pollutants is 4.07C while for Simulation 5 with
radiativeiy participating onesis3.42C and occurs in the morning (05:00).
The primary reason for the smaller urban center-rural temperature difference
is the change in the upwind rural conditions between Simulations 3 and 5.
For Simulation 5 the presence of background pollutants increased the downward
thermal flux incident on the surface, and as a result, the rural temperature
was somewhat higher than for Simulation 3.
80
-------
When the pollutant gas is assumed to have the radiative properties sulfur
dioxide (Simulation 4), the temperature distributions predicted are
practically identical to those for the radiatively nonparticipating pollu-
tant gas (Simulation 3). The reader should compare parts a and b of
Figures 33, 34, and 35. This is due to the fact that S02 is a weakly
absorbing gas. The result are consistent with those obtained using the one-
dimensional model, Table 6.
When ethylene is considered to be the representative pollutant gas,
considerably larger temperature differences are noted (see Table 12) between
the simulations with radiatively interacting (parts c and d) and the simula-
tions with radiative noninteracting (part a) pollutant gas. The difference
increases throughout the night, reaches a maximum of about I.2C before
sunrise and becomes only about 0.4C at noon. The reason the temperatures
for Simulations 5 and 6 are higher than those for Simulation 3 is because
ethylene is a much stronger absorber than sulfur dioxide. The temperatures
downwind of the urban center are higher than those upwind due to the urban
heat sources and other modifications of the environment. In Table 13 are
listed the downward thermal fluxes at the surface as a function of the
position along the city just before sunrise (05:00). It is interesting to
note that the fluxes for the participating simulations show a pronounced
increase in these surface values thus indicating that the presence of
radiatively participating pollutant gases definitely modify the surface
energy budget and contribute to the formation of thermal structure in
the urban planetary boundary layer late at night and early in the morning
up to sunrise. If the maximum values of the thermal fluxes for the simula-
tions with radiatively participating pollutants are compared against the
fluxes for the upwind rural nonparticipating Simulation 3, maximum increases
in the downward thermal fluxes over the urban area of 2.3, 8.6, and 8.8
percent are noted for Simulations 4, 5, and 6, respectively. These computa-
tions agree well with the experimental observations made by Oke and Fuggle
(1972) who measured an increase in the downward thermal flux of approximately
10 percent in Montreal, Canada.
In Table 14 are presented the ratios of the radiative flux divergence
(-3Fz/9z) to the net transport by turbulent diffusion C3/9z(K°8G/3z)3 in
the vertical direction for Simulation 3 with radiatively nonparticipating
pollutants and for Simulation 5 with radiatively participating ones at
several locations along the city. Inspection of the table indicates that
the transport of energy by thermal radiation may be important in determining
the thermal structure during the night. In the table, there is a large
variation in the ratio of the divergence of the radiative flux to the
divergence of sensible turbulent flux in the vertical direction with respect
to both space and time. While the accuracy in determing this ratio from
finite-difference approximations may not be satisfactory, the trends
(and the table is intended only as an order of magnitude estimate) clearly
show that thermal radiative transfer contributes significantJy to the energy
transport during the night. Likewise, turbulent diffusion dominates energy
transport in the PBL during the day.
81
-------
TABLE 13. COMPARISON OF DOWNWIND THERMAL FLUXES (IN W/m2) AT THE SURFACE AS
A FUNCTION OF THE HORIZONTAL LOCATION BEFORE SUNRISE (05:00)
Node
Number
1
2
3
4
5
6
7
8
9
10
1 1
12
13
14
15
16
17
Hori zonta 1
Location
(km)
0
1 .5
3.0
4.5
6.0
7.5
9.0
10.5
12.0
13.5
15.0
16.5
18.0
19.5
21.0
22.5
24.0
3
358.0
358.8
359.6
361 .2
362.8
364.2
365.5
366.3
366.6
366. 1
364.6
362.4
359.6
358.5
358.6
360.0
360.0
Simu
4
361 .9
362.7
363.6
365. 1
366.7
368. 1
369.3
370.2
370.5
370.1
368.8
365.9
365.3
364.1
362.5
362.5
362.5
lation
5
380.7
381 .5
382.6
383.8
385. 1
386.3
387.5
388.3
388.7
388.6
387.9
386.4
384.2
383.2
382.3
382.4
382.4
6
380.7
381 .6
382.7
383.9
385.3
386.8
388.1
389-1
389.6
389.5
388.9
387.5
385.2
384.2
383.2
383.3
383.3
The simulated effects of pollutants on the temperature structure (temperature
difference with and without radiatively participating pollutants) was always
about I .2C higher (Simulation 6 minus Simulation 3) at the surface, see
Figures 34d and 34a, respectively. This difference is, however, smaller than
the 4.2C change induced by urbanization before sunrise (05:00) for Simulation
3 with radiatively nonparticipating pollutants, see Figure 31. The results
are consistent in trends with the simulations of Atwater (I972b, 1974)
but are different in order of magnitude. The simulations show a thermal
plume downwind of the urban center, but no elevated inversions were induced
by the radiatively interacting pollutants possibly indicating limitations
of the turbulence model.
Figures 37 and 38 illustrate the diurnal variation of the surface temperature
for the first five simulations listed in Table 8 at the upstream rural
location and the urban center, respectively. From the figures it is
evident that the decrease in geostrophic wind speed causes an increase in
the amplitude of the .diurnal surface temperature variation while radiative
participation by pollutants decreases it. During the day, the influence of
radiatively participating pollutants is quite small (O.I8C difference between
Simulations 5 and 3 at 12:00) while at night it is considerably larger
(I.I2C difference between Simulations 5 and 3 at 05:00). For higher geostro-
phic wind speeds, the effect of radiatively participating pollutants on the
surface temperature and the vertical thermal structure is even smaller.
82
-------
TABLE 14. RATIO OF THE RADIATIVE FLUX DIVERGENCE (-3F/3z) TO THE TURBULENT
DIFFUSION [3/3z(KP3e/3z)I] IN THE VERTICAL DIRECTION BETWEEN
SIMULATION 3 WITH RADIATIVELY NONPARTICI APT ING POLLUTANTS (NP)
AND SIMULATION 5 WITH RADIATIVELY PARTICI PAT ING-POLLUTANTS (P)
Upwind Rural
z(m) NP P_
50 -0.597 -0.426
250 -1.025 -0.842
1000 -1.909 -1.76
50
250
1000
50
250
1000
50
250
1000
-60.9
-0.583
-2.02
31 .2
-1.16
-3.02
0.0974
-0.368
-1 .08
25.87
0.531
7. 16
-9.67
-1 .28
-2.80
0.148
-0.439
-1 .23
50 -0.0470 -0.0708
250 -0.0302 -0.0367
1000 -0.313 -0.0921
50 -0-165 -0.258
250 -0.0436 -0.0748
1000 -0.128 -0.102
Upwind
Residential
NP
-0.517
-0.928
-1 .92
P
t = 18
-0.493
-0.793
-1 .62
Urban Center
NP
:00
-0.388
-1 .52
-1.90
P
-0.410
-1.29
-1 .60
Downwi nd
Residential
NP
-0.434
-1.31
-1.90
P
-0.423
-1.15
-1 .58
t = 24:00
-0.502
-0.460
-1 .94
-1 .203
-0.868
-1.76
0.0395
-0.303
-1 .06
-0.0662
-0.0273
-0.138
-0. 162
-0.0291
-O.I 01
-0.519
-0.428
3.04
t = 05
174
-0.868
-2.55
t = 06
0.0622
-0.368
-1.18
t = 09
-0.0776
-0.0292
-0.103
t = 12
-0.200
-0.0442
-0.0916
0.405
-0.388
-1 .83
:00
0.188
-0.485
-1 .22
:00
0.0253
-0.336
-0.965
:00
-0.0782
-0.0221
-0.168
:00
-0.224
-0.0275
-0.0821
0.513
-0.377
7.78
0.291
-0.531
-2.32
0.0530
-0.625
-1 .091
-0.0824
-0.0194
-0.165
-0.263
-0.0471
-0.0715
0.51 1
-0.792
-1 .88
0.972
-2.38
-2.90
0.0115
-0.177
-1.01
-0.0812
-0.0232
-O.I 17
=0.325
-0.0371
-0.056
3.34
-0.994
23.4
0.528
-2.28
-2.20
0.0173
-0.477
-1.13
-0.0869
-0.0191
-0.120
-0.463
-0.0486
-0.0710
83
-------
Ug-6m/», Vg*4m/t
PARTICIPATING, C2H4
Ug«6m/», Vg>4m/t
PARTICIPATING, SOZ
Ug*6m/s, Vg'4m/s
PARTICIPATING. C2H4
Ug • 12 m/«, Vg « Om/»
NON-PARTICIPATING
Ug-6m/>, vg«4m/t
NON-PARTICIPATING
2B4
IZ:00
12:00
Figure 37. Comparison of Surface Temperatures at the Upwind Rural Location
-------
(Jj
DC
314
312
310
308
306
304
1
-------
z(m)
24
(a) t = 24:00 hr
(b) t = 05:00 hr
z(m)
6 12
x(km)
(c) t = 06:00 hr
(d) t - 12:00 hr
Figure 39.
Gaseous Pollutant Concentration Isopleths for Simulation 3;
(Multiply Numbers in Parts a, c, and d by a Factor of 10 and
in Part b by a Factor of I02 to Obtain Concentrations in yg/m3)
86
-------
I03 L
io2 t
z(m)
10
10
(a) t = 18:00 hr
(b) t = 24:00 hr
24
IO3 t
z(m)
(c) t = 06:00 hr
(d) t = 12:00 hr
Figure 40.
Gaseous Pollutant Concentration Isopleths for Simulation 7
(Multiply Numbers in the Figure by a Factor of 10 to Obtain
Concentrations in yg/m3)
24
87
-------
present the maximum pollutant concentrations which typically occurred just
before sunrise (05:00). The total pollutant mass injected into the atmos-
phere is identical for both simulations, and since the aerosol emission flux
at the surface was assumed to be identical to that of the pollutant gas, the
aerosol concentrations are identical to those of the pollutant gas. The
results show the buildup of pollutant concentration during the night. After
sunrise, the atmosphere becomes unstable and the pollutant is dispersed
rather effectively by vertical diffusion and horizontal advection. All of
the isopleths show the formation of a pollutant plume downwind of the urban
center. As expected from the pollutant surface emission distribution (see
Figure 16), the pollutant concentrations over the urban center (x = 10.5 km)
are higher for the Gaussian than for the rectangular distribution. For
example, the surface emission at the center of the city for Simulation 3
is 4.344 yg/m2s and for Simulation 7, it is 2.5 yg/m2s while the correspond-
ing ground pollutant concentrations are 404.4 yg/m3 and 336.4 yg/m3. The
reason the surface concentrations have not changed proportionately with the
emissions is because the temperatures are not the same. Since differences
in stability between the two simulations change the turbulent diffusivities,
the ground pollutant concentrations are also different.
Results presented in Figure 39b at 05:00 show unreasonably high pollutant
concentrations downwind of the urban center (x = 16.5, 18, and 19.5 km)
in the vicinity of the surface. The surface concentration at x = 18 km
exceeds MOO yg/m3 which is unreasonably high. A careful examination of
the figure reveals that most of the unreaIisticaIly high concentrations
are confined to depths less than 10 meters. As already discussed, modeling
of all pollutant emission as surface sources is not realistic. The surface
concentrations are very sensitive to the turbulent diffusivities at the
first few grid points above the ground. The diurnal trends in the surface
pollutant concentrations can be explained on the basis of the diurnal varia-
tion of the turbulent diffusivity at the first vertical grid point. This is
discussed in the next subsection.
Radiatively Participating Pollutants
The pollutant gas concentration isopleths (in yg/m3) just before sunrise
(05:00) for Simulations 3, 4, 5, and 6 are presented in Parts a, b, c, and d
of Figure 41, respectively. At 05:00 the surface concentration builds up
to a high value of about MOO yg/m3 in Simulation 3 (Figure 4la) while the
radiatively participating Simulation 5 illustrated in Figure 4lc, the
surface concentration increases to only 560 yg/m3. It is interesting to
note that for Simulation 6 (Figure 4ld), which is identical to Simulation 5
(Figure 4lc) except that the pollutant emission flux has been doubled,
predicts a buildup of 1200 yg/m3. This is almost the same for Simulation 3
(Figure 4la). The influence of thermal radiation transfer* by pollutants is
certainly evident in the peak concentrations that occur just before sunrise.
After sunrise (06:00), the breakup of the stable layer near the surface is
noted as shown in Figure 42. In a period of one hour (from 05:00 to 06:00)
the ground pollutant concentrations at the urban center for Simulations 3, 4,
5, and 6 have decreased by 25, 26, 30, and 32 percent, respectively. The
pollutants disperse most rapidly for Simulations 5 and 6 with the radiatively
88
-------
z(m)
24
(a) Nonparticipating Simula-
tion 3; m = 2.5 yg/m2s
(b) Participating Simulation 4;
S02, mp = 2.5 yg/m2s
z(m)
12
x(km)
(c) Participating Simulation 5; (d) Participating Simulation 6;
C2l-k, m = 2.5 ug/m2s m = 5.0 yg/m2s
Figure 41. Comparison of Gaseous Pollutant Concentration Isopleths for
Simulation 3 (Part a), Simulation 4 (Part b), Simulation 5
(Part c), and Simulation 6 (Part d) at 05:00 of the Second Day
(Multiply the Numbers in Parts a, b, and d on the Figure by
I02 and the Numbers in Part c by 10 to Obtain Concentrations
in ug/m3)
89
-------
z(m)
I I I I I I I I 1
0
24
(a) Nonparticipating Simulation (b) Participating Simulation 4;
3; m = 2.5 yg/m2s SO , m = 2.5 yg/m2s
z(m)
(c) Participating Simulation 5;
C2Hn,m = 2.5 yg/m2s
(d) Participating Simulation 6;
, m = 5.0 ug/m2s
Figure 42. Comparison of Gaseous Pollutant Concentration Isopleths for
Simulation 3 (Part a), Simulation 4 (Part b), Simulation 5
(Part c), and Simulation 6 (Part d) at 06:00 of the Second Day
(Multiply the Numbers on the Figure by 10 to Obtain Concentra-
tions in iag/m3)
90
-------
z(m)
12 18 24
x(km)
(a) Nonparticipating Simulation (b) Participating Simulation 4;
3; m = 2.5 ug/m2s
m =2.5 yg/m2s
10
3 .
10
2 ,
z(m)
10
iou :
12
x(km)
(c) Participating Simulation 5; (d) Participating Simulation 6;
m = 5.0 ug/m2s
, m = 2.5 yg/ms
Figure 43. Comparison of Gaseous Pollutant Concentration Isopleths for
Simulation 3 (Part a), Simulation 4 (Part b), Simulation 5
(Part c), and Simulation 6 (Part d) at 12:00 of the Second Day
(Multiply the Numbers in the Figure by 10 to Obtain Concentra-
tions in u.g/m3)
91
-------
500r
400 -
b) PARTICIPATING
(SIMULATION 5)
300 -
z
(m)
200 -
100 -
a) NONPARTICIPATING
(SIMULATION 3)
100 200
C2 (/xg/m3)
400
Figure 44. Comparison of Gaseous Pollutant Concentrations for Simulation 3
(Part a) and for Simulation 5 (Part b) at the Center of the City
participating pollutant gas having properties of ethylene. By noon (Figure 43)
turbulent diffusion and advection dominate the transport, and the isopleths
of pollutant gas concentrations are almost identical for all four simulations
(3 through 6).
The gaseous pollutant concentration buildup at the urban center for Simula-
tion 3 with radiatively noninteracting pollutants and for Simulation 5 with
radiatively interacting pollutants are illustrated in Figure 44. Because the
pollutant source is located at the surface, the increase in the concentra-
tions is largest at that point. The pollutant dispersion and their concen-
trations near the ground (say, up to 10 m from the surface) are very sensitive
to the turbulent diffusivities and their variation with time of the day during
the diurnal cycle. In turn, the turbulent diffusivities are strongly
influenced by the temperature and stability of the atmosphere. The diffusivi-
ties in the vicinity of the surface are relatively low (see Figure 45)
particularly at night. As a result of the low diffusivities sharp concentra-
tion gradients are evident near the surface in Figure 44. Above 200 m the
vertical dispersion is quite effective because of much higher diffusivities
(Figure 46), and the concentration gradients are quite small. The
pollutant concentrations above 500 m exceed only slightly the initial
background value of 50 ppm.
Figures 45 and 46 show large variations of the diffusivities during the
diurnal cycle and, what has already been indicated before, that the
diffusivities are higher in the city than in the rural area because of
increased roughness and higher temperatures. This difference in diffusivi-
ties between urban and rural locations is much larger near the surface
(Figure 45) than at the height of, say, 200 m (Figure 46). At noon the
92
-------
RADIATIVELY NONPARTICIPATIN6
RADIATIVELY PARTICIPATING
Figure 45.
12=00 16=00 20=00 24=00 04:00 08:00 !2=00
TIME
Comparison of the Turbulent Diffusivities of Heat for
Simulations 3 and 5 at z = 200 m
24
20
(m2/s)
12
0
RADIATIVELY NONPARTICIPATING /t
RADIATIVELY PARTICIPATING
UPWIND RURAL
i I L
J L.
Figure 46.
12=00 l&OO 20=00 24:00 04=00 03:00 12:00
TIME
Comparison of the Turbulent Diffusivities of Heat for
Simulations 3 and 5 at z = 200 m
93
-------
u-r, max
K) 2
"NONPARTICIPATING
• PARTICIPATING
GAUSSIAN
I I t
Figure 47.
12:00 16:00 20:00 24:00 04:CO O&OO 12:00
TIME
Comparison of Maximum Urban Minus Upwind Rural Surface Tempera-
ture Differences for Simulations 3, 5, and 7
diffusivities in the city are about 40% higher than in the rural area while
before sunrise they are higher by about a factor of 2. The results also show
that the diffusivities are larger for Simulation 5 with radiatively partici-
pating pollutants than for Simulation 3. This is due to decreased atmospheric
stability for the simulation with interacting pollutants as a result of
warmer nighttime temperatures. The radiatively participating pollutants are
seen to affect the diffusivities much less than the urbanization (urban-rural
parameter differences). This then explains why the difference between the
pollutant concentration profiles presented in Figures 44a and 44b for the
two simulations are relatively small.
The results presented show that the radiative participation by pollutants
may have the potential of affecting their own dispersion, especially the
peak concentrations before and after sunrise. The meteorological conditions
considered in the numerical simulations were not critical for pollutant
dispersion. Under more adverse dispersion conditions such as may arise for
lower wind speeds and/or stable elevated layers, the coupling between the
radiatively participating pollutants and their dispersion is expected to
be stronger. Comparison of results presented in Figure 8 with those given
in Figure 44 clearly show that an urban area cannot be realistically
simulated using a one-dimensional model that neglects horizontal and verti-
cal advection.
Urban Heat Island
The urban heat island is a well known and accepted physical phenomenon
(Peterson, 1969; Oke, I973b). In order to partially verify the predictions
of the two-dimensional transport model, the urban heat island intensity
-------
6r-
(K/hr)
AT/At
(K/hr)
o) NCNPARTICIPATING
(SIMULATION 3)
UPWIND RURAL
URBAN CENTER
b) PARTICIPATING
(SIMULATION 5)
12:00 l&OO 20:00 24:00 04OO 0800 12OO
TIME
Figure 48. Variation of the Heating/Cooling Rates for Simulation 3 (Part a)
and for Simulation 5 (Part b) during the Diurnal Cycle
(difference between upwind and rural
ATU_
r.max
) was determined. The resu
and highest urban temperatures,
ts for Simulations 5 and 5 without and
with radiatively participating pollutants, respectively, having Gaussian
distributions of anthropogenic heat and pollutant sources and for Simulation 7
without radiatively participating pollutants having a rectangular distri-
bution of sources are shown in Figure 47. For the Gaussian distribution
of urban heat sources, the maximum temperature during the night occurred
at the urban center whereas for the rectangular distribution during the
night it occurred from I .5 to 6 km downwind of the center. The results
presented in Figure 47 show that there is a double peak in ATu_r max. The
first smaller peak is noted in the evening at about 20:00. It arises due
to the more rapid cooling at the upwind rural area than in the city. The
second peak occurs before sunrise and increases to a value of about 4K for
Simulation 3. The second peak is primarily due to the differences in the
urban/rural parameters. This can be more readily seen by comparing Figures
38 and 39. For Simulations I and 2 with higher wind speeds (ug = 12 m/s
m/s) it was found that the maximum urban heat island intensity
before
and VQ = 8
in
occurred
sunrise.
the evening at 19:00 and there was not second peak
95
-------
The results of Figure 47 show that the maximum urban-rural surface tempera-
ture difference for the rectangular distribution of urban heat sources is
approximately 0.6K lower than the corresponding results for the Gaussian
distribution. This is indicative of the lower heat emissions employed a
small distance downwind of the urban center (see Figure 16). For the
population of the city and wind speeds considered in the simulations, the
urban heat island intensity is in good agreement with the observations and
empirical correlation of Oke (I973b). Urban-rural temperature differences
of about 3K have been observed by Clarke and McElroy (1974) for the city of
St. Louis, Missouri near sunrise on August 7, 12, 13, 21, and 22, 1973.
The heating/cooling rates (AT/At) evaluated from the surface temperature
versus time plots (see Figures 37 and 38) have been determined for
Simulations 3 and 5 and are presented in Figure 48. The results are not
given for the first few hours of the simulation because of the transient
introduced by the choice of the assumed initial profiles. The slopes were
evaluated graphically and are therefore subject to considerable inaccuracies;
however, the trends indicated seem reasonable. The rural cooling/heating
rates are expected to show larger changes because of the lower heat capaci-
tance and considerably lower conductivity of the soil. The cooling rates of
about 0.5K/hr predicted at night are in reasonably good agreement with the
results reported by Oke and Maxwell (1975) for Montreal and Vancouver. The
variations at sunset and sunrise are more extreme. The maximum cooling
rate measured by Oke and Maxwell was about 3K/hr while the predicted values
are about 4K/hr. The agreement is reasonable in view of the fact that the
meteorological conditions in the simulations were different from those under
which the field data were obtained ("summer nights with calm and clear
conditions"). In addition, urban cooling rates depend on the man-made
structures, shading, etc. which are not modeled in the numerical experiments.
96
-------
SECTION VI
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10U
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APPEND IX
PUBLICATIONS
PAPERS
R. W. Bergstrom, Jr., "Predictions of the Spectral Absorption and Extinc-
tion Coefficients of an Urban Aerosol Model," Atmospheric Environment,
6, 247-258, 1972.
R. W. Bergstrom, Jr., and R. Viskanta, "Prediction of the Solar Radiant
Flux and Heating Rates in a Polluted Atmosphere," Tellus, XXV, 486-
498, 1973.
R. W. Bergstrom, Jr., and R. Viskanta, "Modeling of the Effects of Gaseous
and Particulate Pollutants in the Urban Atmosphere. Part I: Thermal
Structure," J. Appl. Meteor., j_2, 901-912, 1973.
R. W. Bergstrom, Jr., and R. Viskanta, "Modeling of the Effects of Gaseous
and Particulate Pollutants in the Urban Atmosphere. Part II: Pollutant
Dispersion," J. Appl. Meteor., 12, 913-918.
R. W. Bergstrom, Jr., and R. Viskanta, "Spherical Harmonics Approximation
for Radiative Transfer in Polluted Atmospheres," A1AA 8th Thermophysics
Conference, Palm Springs, California, July 16-18, 1973, AIAA Paper
No. 73-749.
R. W. Bergstrom, Jr., and R. Viskanta, "Modeling of Thermal Structure and
Dispersion in Polluted Urban Atmospheres," AlChE-ASME 14th National
Heat Transfer Conference, Atlanta, Georgia, August 5-8, 1973, ASME
Paper No. 73-HT-8.
R. W. Bergstrom, Jr., and R. Viskanta, "Spherical Harmonics Approximation
for Radiative Transfer in Polluted Atmospheres," in Progress in
Astronautics and Aeronautics, Volume 35, MIT Press, Cambridge, Mass.,
pp. 23-40.
R. Viskanta, R. 0. Johnson, and R. W. Bergstrom, Jr., "Effect of Urbaniza-
tion on the Thermal Structure in the Atmosphere," Conference on
Metropolitan Physical Environment, Syracuse, New York, August 25-29,
1975 (to be published in Proceedings of the Conference).
105
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THESES
R. W. Bergstrom, Jr., "Theoretical Study of the Thermal Structure and
Dispersion in Polluted Urban Atmospheres," Ph.D. Thesis, Purdue
University, August 1972.
R. 0. Johnson, "The Development of Two-dimensional Transport Model in a
Polluted Urban Atmospheres," M.S. Thesis, Purdue University, August 1975.
106
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
REPORT NO.
EPA-600/4-76-OQ2
3. RECIPIENT'S ACCESSIOf*NO.
ITLE AND SUBTITLE
MODELING OF THE EFFECTS OF POLLUTANTS AND DISPERSION
IN URBAN ATMOSPHERES
5. REPORT DATE
February 1976 (Issuing Date)
6. PERFORMING ORGANIZATION CODE
AUTHOR(S)
R. Viskanta, R. W. Bergstrom, Jr., and R. 0. Johnson
8. PERFORMING ORGANIZATION REPORT NO.
. PERFORMING ORGANIZATION NAME AND ADDRESS
Purdue Research Foundation
West Lafayette, IN 47907
10. PROGRAM ELEMENT NO.
P.E. 1AA009 (ROAP 26AAS)
11.X30XOOWSX/GRANT NO.
R801102
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Sciences Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
Final 6/1/71 - 1/31/75
14. SPONSORING AGENCY CODE
EPA-ORD
15. SUPPLEMENTARY NOTES
16. ABSTRACT
The short-term effects of radiatively participating pollutants upon the thermal
structure and dispersion in an urban atmosphere were studied by constructing one-
and two-dimensional transport models for the planetary boundary layer. Special
attention was focused on the interaction of solar and thermal radiation with
gaseous and particulate pollutants as well as natural atmospheric constituents.
17.
KEY WORDS AND DOCUMENT ANALYSIS
a.
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
cos AT i Field/Group
Meteorology
*Air pollution
*Atmospheric diffusion
Mathematical models
Boundary layer
*Solar radiation
*Thermal radiation
04B
13B
12A
20D
03B
20M
8. DISTRIBUTION STATEMENT
SECURITY CLASS (ThisRejort)
RELEASE TO PUBLIC
20. SECURITY CLASS (This page)
UNCLASSIFIED
107
^U.S.fiOYERNMENm.NT.NGOFF.CE: 1976-657-695/538o Region No. 5-,,
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