ENCYCLOPEDIA OF ENVIRONMENTAL SCIENCE AND ENGINEERING - URBAN AIR POLLUTION MODELING pptx

INTRODUCTION Urban air pollution models permit the quantitative estimation of air pollutant concentrations by relating changes in the rate of emission of pollutants from different sourc

INTRODUCTION

Urban air pollution models permit the quantitative estimation

of air pollutant concentrations by relating changes in the rate

of emission of pollutants from different sources and

meteo-rological conditions to observed concentrations of these

pol-lutants Many models are used to evaluate the attainment and

maintenance of air quality standards, urban planning, impact

analysis of existing or new sources, and forecasting of air

pollution episodes in urban areas

A mathematical air pollution model may serve to gain

insight into the relation between meteorological elements and

air pollution It may be likened to a transfer function where

the input consists of both the combination of weather

condi-tions and the total emission from sources of pollution, and

the output is the level of pollutant concentration observed in

time and space The mathematical model takes into

consid-eration not only the nature of the source (whether distributed

or point sources) and concentrations at the receptors, but also

the atmospheric processes that take place in transforming the

concentrations at the source of emission into those observed

at the receptor or monitoring station Among such processes

are: photochemical action, adsorption both on aerosols and

ground objects, and of course, eddy diffusion

There are a number of areas in which a valid and

practi-cal model may be of considerable value For example, the

operators of an industrial plant that will emit sulfur

diox-ide want to locate it in a particular community Knowing the

emission rate as a function of time; the distribution of wind

speeds, wind direction, and atmospheric stability; the

loca-tion of SO 2 -sensitive industrial plants; and the spatial

dis-tribution of residential areas, it is possible to calculate the

effect the new plant will have on the community

In large cities, such as Chicago, Los Angeles, or New York,

during strong anticyclonic conditions with light winds and

low dispersion rates, pollution levels may rise to a point

where health becomes affected; hospital admissions for

respiratory ailments increase, and in some cases even deaths

occur To minimize the effects of air pollution episodes,

advisories or warnings are issued by government officials

Tools for determining, even only a few hours in advance, that unusually severe air pollution conditions will arise are invaluable The availability of a workable urban air pollution model plus a forecast of the wind and stability conditions could provide the necessary information

In long-range planning for an expanding community it may be desirable to zone some areas for industrial activity and others for residential use in order to minimize the effects

of air pollution Not only the average-sized community, but also the larger megalopolis could profitably utilize the abil-ity to compute concentrations resulting from given emis-sions using a model and suitable weather data In addition, the establishment of an air pollution climatology for a city or state, which can be used in the application of a model, would represent a step forward in assuring clean air

For all these reasons, a number of groups have been devoting their attention to the development of mathematical models for determining how the atmosphere disperses mate-rials This chapter focuses on the efforts made, the necessary tools and parameters, and the models used to improve living conditions in urban areas

COMPONENTS OF AN URBAN AIR POLLUTION MODEL

A mathematical urban air pollution model comprises four essential components The first is the source inventory One must know the materials, their quantities, and from what location and at what rate they are being injected into the atmosphere, as well as the amounts being brought into a community across the boundaries The second involves the measurement of contaminant concentration at representative parts of the city, sampled properly in time as well as space

The third is the meteorological network, and the fourth is the meteorological algorithm or mathematical formula that describes how the source input is transformed into observed values of concentration at the receptors (see Figure 1) The difference between what is actually happening in the atmo-sphere and what we think happens, based on our measured

sources and imperfect mathematical formulations as well as

our imperfect sampling of air pollution levels, causes

dis-crepancies between the observed and calculated values This

makes the verification procedure a very important step in the

development of an urban air pollution model The

remain-der of this chapter is devoted to these four components, the

verification procedures, and recent research in urban air

pol-lution modeling

Accounts may be found in the literature of a number of

investigations that do not have the four components of the

mathematical urban air pollution model mentioned above,

namely the source inventory, the mathematical algorithm,

the meteorological network, and the monitoring network

Some of these have one or more of the components

miss-ing An example of this kind is the theoretical investigation,

such as that of Lucas (1958), who developed a mathematical

technique for determining the pollution levels of sulfur

diox-ide produced by the thousands of domestic fires in a large

city No measurements are presented to support this study

Another is that of Slade (1967), which discusses a

megalop-olis model Smith (1961) also presented a theoretical model,

which is essentially an urban box model Another is that of

Bouman and Schmidt (1961) on the growth of pollutant

con-centrations in the cities during stable conditions Three case

studies, each based on data from a different city, are

pre-sented to support these theoretical results Studies relevant

to the urban air pollution problem are the pollution surveys

such as the London survey (Commins and Waller, 1967), the

Japanese survey (Canno et al., 1959), and that of the capital

region in Connecticut (Yocum et al., 1967) In these studies,

analyses are made of pollution measurements, and in some cases meteorological as well as source inventory informa-tion are available, but in most cases, the mathematical algo-rithm for predicting pollution is absent Another study of this type is one on suspended particulate and iron concentrations

in Windsor, Canada, by Munn et al (1969) Early work on forecasting urban pollution is described in two papers: one

by Scott (1954) for Cleveland, Ohio, and the other by Kauper

et al (1961) for Los Angeles, California A comparison of urban models has been made by Wanta (1967) in his refresh-ing article that discusses the relation between meteorology and air pollution

THE SOURCE INVENTORY

In the development of an urban air pollution model two types of sources are considered: (1) individual point sources, and (2) distributed sources The individual point sources are often large power-generating station stacks or the stacks of large buildings Any chimney stack may serve as a point source, but some investigators have placed lower limits on the emission rate of a stack to be considered a point source

in the model Fortak (1966), for example, considers a source

an individual point source if it emits 1 kg of SO 2 per hour, while Koogler et al (1967) use a 10-kg-per-hour criterion

In addition, when ground concentrations are calculated from the emission of an elevated point source, the effective stack height must be determined, i.e., the actual stack height plus the additional height due to plume rise

Level of uncertainty

3

2

1

Evaluation of model quality

Approximation to urban boundary layer Representation of flow in urban canopy Parameterization of roadside building geometry

representative?

Air quality monitoring data

Meteorological monitoring data

Modelled past air quality Past situation

Traffic flow data

precise?

accurate?

Atmospheric Dispersion Model

Emissions per vehicle

Measured past air quality

Future prediction

Modelled future air quality to inform AQMA declaration

Will climate change?

Will atmospheric oxidation capacity change?

How will traffic flow change?

How fast will new technology be adopted?

Emissions data

of uncertainty that can be introduced (From Colvile et al., 2002, with permission from Elsevier)

Information concerning emission rates, emission

sched-ules, or pollutant concentrations is customarily obtained by

means of a source-inventory questionnaire A municipality

with licensing power, however, has the advantage of being

able to force disclosure of information provided by a

source-inventory questionnaire, since the license may be withheld

until the desired information is furnished Merely the

aware-ness of this capability is sufficient to result in gratifying

cooperation The city of Chicago has received a very high

percentage of returns from those to whom a source-inventory

questionnaire was submitted

Information on distributed sources may be obtained in

part from questionnaires and in part from an estimate of the

population density Population-density data may be derived

from census figures or from an area survey employing aerial

photography

In addition to knowing where the sources are, one must

have information on the rate of emission as a function of

time Information on the emission for each hour would be

ideal, but nearly always one must settle for much cruder

data Usually one has available for use in the calculations

only annual or monthly emission rates Corrections for

diur-nal patterns may be applied—i.e., more fuel is burned in

the morning when people arise than during the latter part

of the evening when most retire Roberts et al (1970) have

referred to the relationship describing fuel consumption (for

domestic or commercial heating) as a function of time—e.g.,

the hourly variation of coal use—as the “janitor function.”

Consideration of changes in hourly emission patterns with

season is, of course, also essential

In addition to the classification involving point sources

and distributed sources, the source-inventory information

is often stratified according to broad general categories

to serve as a basis for estimating source strengths The

nature of the pollutants—e.g., whether sulfur dioxide or

lead—influences the grouping Frenkiel (1956) described

his sources as those due to: (1) automobiles, (2) oil and gas

heating, (3) incinerators, and (4) industry; Turner (1964)

used these categories: (1) residential, (2) commercial, and

(3) industrial; the Connecticut model (Hilst et al., 1967)

considers these classes: (1) automobiles, (2) home

heat-ing, (3) public services, (4) industrial, and (5) electric

power generally (Actually, the Connecticut model had a

number of subgroups within these categories.) In general,

each investigator used a classification tailored to his needs

and one that facilitated estimating the magnitude of the

distributed sources Although source-inventory

informa-tion could be difficult to acquire to the necessary level of

accuracy, it forms an important component of the urban air

pollution model

MATHEMATICAL EQUATIONS

The mathematical equations of urban air pollution models

describe the processes by which pollutants released to the

atmosphere are dispersed The mathematical algorithm, the

backbone of any air pollution model, can be conveniently

divided into three major components: (1) the source-emissions subroutine, (2) the chemical-kinetics subroutine, and (3) the diffusion subroutine, which includes meteorological param-eters or models Although each of these components may

be treated as an independent entity for the analysis of an existing model, their inferred relations must be considered when the model is constructed For example, an exceed-ingly rich and complex chemical-kinetic subroutine when combined with a similarly complex diffusion program may lead to a system of nonlinear differential equations so large

as to preclude a numerical solution on even the largest of computer systems Consequently, in the development of the model, one must “size” the various components and general subroutines of compatible complexity and precision

In the most general case, the system to be solved con-sists of equations of continuity and a mass balance for each specific chemical species to be considered in the model For

a concise description of such a system and a cogent devel-opment of the general solution, see Lamb and Neiburger (1971)

The mathematical formulation used to describe the atmospheric diffusion process that enjoys the widest use is a form of the Gaussian equation, also referred to as the modi-fied Sutton equation In its simplest form for a continuous ground-level point source, it may be expressed as

x

2

2 2

2

⎛

⎝

⎠

⎟ (1)

where

χ : concentration (g/m 3 )

Q: source strength (g/sec) u: wind speed at the emission point (m/sec)

σ y : perpendicular distance in meters from the

center-line of the plume in the horizontal direction to the point where the concentration falls to 0.61 times the centerline value

σ z : perpendicular distance in meters from the

center-line of the plume in the vertical direction to the point where the concentration falls to 0.61 times the center-line value

x, y, z: spatial coordinates downwind, cross-origin at

the point source

Any consistent system of units may be used

From an examination of the variables it is readily seen that several kinds of meteorological measurements are

nec-essary The wind speed, u, appears explicitly in the equation;

the wind direction is necessary for determining the direction

of pollutant transport from source to receptor

Further, the values of σ y and σ z depend upon

atmo-spheric stability, which in turn depends upon the varia-tion of temperature with height, another meteorological parameter At the present time, data on atmospheric stabil-ity over large urban areas are uncommon Several authors have proposed diagrams or equations to determine these values

The temperature variation with height may be obtained

by means of thermal elements mounted on radio or

tele-vision towers Tethered or free balloons carrying suitable

sensors may also be used Helicopter soundings of

temper-ature have been used for this purpose in New York City;

Cincinnati, Ohio; and elsewhere There is little doubt that

as additional effort is devoted to the development of urban

air pollution models, adequate stability measurements will

become available In a complete study, measurements of

precipitation, solar radiation, and net radiation flux may

be used to advantage Another meteorological variable of

importance is the hourly temperature for hour-to-hour

pre-dictions, or the average daily temperature for 24-hour

cal-culations The source strength, Q, when applied to an area

source consisting of residential units burning coal for space

heating, is a direct function of the number of degree-hours

or degree-days The number of degree-days is defined as

the difference between the average temperature for the

day and 65 If the average temperature exceeds 65, the

degree-day value is considered zero An analogous

defi-nition applies for the degree-hour Turner (1968) points

out that in St Louis the degree-day or degree-hour values

explain nearly all the variance of the output of gas as well

as of steam produced by public utilities

THE USE OF GRIDS

In the development of a mathematical urban air pollution

model, two different grids may be used: one based on

exist-ing pollution sources and the other on the location of the

instruments that form the monitoring network

The Pollution-Source Grid

In the United States, grid squares 1 mile on a side are frequently

used, such as was done by Davidson, Koogler, and Turner

Fortak, of West Germany, used a square 100  100 m The

Connecticut model is based on a 5000-ft grid, and Clarke’s

Cincinnati model on sectors of a circle Sources of pollution

may be either point sources, such as the stacks of a public

utility, or distributed sources, such as the sources

represent-ing the emission of many small homes in a residential area

The Monitoring Grid

In testing the model, one resorts to measurements obtained

by instruments at monitoring stations Such monitoring

sta-tions may also be located on a grid Furthermore, this grid

may be used in the computation of concentrations by means

of the mathematical equation—e.g., concentrations are

cal-culated for the midpoints of the grid squares The emission

grid and monitoring grid may be identical or they may be

different For example, Turner used a source grid of 17 

16 miles, but a measurement grid of 9  11 miles In the

Connecticut model, the source grid covers the entire state,

and calculations based on the model also cover the entire

state Fortak used 480  800-m rectangles

TYPES OF URBAN AIR POLLUTION MODELS

Source-Oriented Models

In applying the mathematical algorithm, one may proceed

by determining the source strength for a given point source and then calculating the isopleths of concentration down-wind arising from this source The calculation is repeated for each area source and point source Contributions made

by each of the sources at a selected point downwind are then summed to determine the calculated value of the concentra-tion Isopleths of concentration may then be drawn to pro-vide a computed distribution of the pollutants

In the source-oriented model, detailed information is needed both on the strength and on the time variations of the source emissions The Turner model (1964) is a good example of a source-oriented model

It must be emphasized that each urban area must be

“calibrated” to account for the peculiar characteristics of the terrain, buildings, forestation, and the like Further, local phenomena such as lake or sea breezes and mountain-valley effects may markedly influence the resulting concentrations;

for example, Knipping and Abdub (2003) included sea-salt aerosol in their model to predict urban ozone formation

Specifically, one would have to determine such relations as the variations of σ y and σ z with distance or the magnitude of the effective stack heights A network of pollution-monitoring stations is necessary for this purpose The use of an algorithm without such a calibration is likely to lead to disappointing results

Receptor-Oriented Models

Several types of receptor-oriented models have been devel-oped Among these are: the Clarke model, the regression model, the Argonne tabulation prediction scheme, and the Martin model

The Clarke Model

In the Clarke model (Clarke, 1964), one of the most well known, the receptor or monitoring station is located at the center of concentric circles having radii of 1, 4, 10, and 20 km respectively These circles are divided into 16 equal sec-tors of 22 1/2 A source inventory is obtained for each of the 64 (16  4) annular sectors Also, for the 1-km-radius circle and for each of the annular rings, a chart is prepared

relating x/Q (the concentration per unit source strength)

and wind speed for various stability classes and for vari-ous mixing heights In refining his model, Clarke (1967) considers separately the contributions to the concentration levels made by transportation, industry and commerce, space heating, and strong-point sources such as utility stacks The following equations are then used to calculate the pollutant concentration

i

Ti

Q

Q

( )

∑

1 4

i

Ii

Q Q

( )

∑

1 4

i

Si

Q Q

( )

∑

1 4

i p

1

4

∑

where

: concentration (g/m 3 )

Q: source strength (g/sec) T: subscript to denote transportation sources I: subscript to denote industrial and commercial

sources

S: subscript to denote space-heating sources p: subscript to denote point sources

i: refers to the annular sectors

The above equations with some modification are taken

from Clarke’s report (1967) Values of the constants a, b, and

c can be determined from information concerning the

diur-nal variation of transportation, industrial and commercial,

and space-heating sources The coefficient k i represents a

calibration factor applied to the point sources

The Linear Regression-Type Model

A second example of the receptor-oriented model is one

developed by Roberts and Croke (Roberts et al., 1970) using

regression techniques Here,

i

n

1

∑

In applying this equation, it is necessary first to stratify

the data by wind direction, wind speed, and time of day

C 0 represents the background level of the pollutant; Q 1

represents one type of source, such as commercial and

industrial emissions; and Q 2 may represent contributions

due to large individual point sources It is assumed that

there are n point sources The coefficients C 1 and C 2 and k i

represent the 1/ s y s z term as well as the contribution of the

exponential factor of the Gaussian-type diffusion equation

(see Equation 1)

Multiple discriminant analysis techniques for

indi-vidual monitoring stations may be used to determine

the probability that pollutant concentrations fall within

a given range or that they exceed a given critical value

Meteorological variables, such as temperature, wind

speed, and stability, are used as the independent variable

in the discriminant function

The Martin Model

A diffusion model specifically suited to the estimation

of long-term average values of air quality was developed

by Martin (1971) The basic equation of the model is the Gaussian diffusion equation for a continuous point source It

is modified to allow for a multiplicity of point sources and a variety of meteorological conditions

The model is receptor-oriented The equations for the ground-level concentration within a given 22 1/2 sector

at the receptor for a given set of meteorological conditions (i.e., wind speed and atmospheric stability) and a specified source are listed in his work The assumption is made that all wind directions within a 22 1/2 sector corresponding to

a 16-point compass occur with equal probability

In order to estimate long-term air quality, the single-point-source equations cited above are evaluated to deter-mine the contribution from a given source at the receptor for each possible combination of wind speed and atmospheric stability Then, using Martin’s notation, the long-term aver-age is given by

S L N

( , , ) ( ,x r , )

∑

∑

∑

where D n indicates the wind-direction sector in which transport from a particular source ( n ) to the receptor occurs; r n is the

distance from a particular source to the receptor; F ( D n , L, S )

denotes the relative frequency of winds blowing into the given

wind-direction sector ( D n ) for a given wind-speed class ( S ) and atmospheric stability class ( L ); and N is the total number of sources The joint frequency distribution F ( D n , L, S ) is

deter-mined by the use of hourly meteorological data

A system of modified average mixing heights based on tabulated climatological values is developed for the model

In addition, adjustments are made in the values of some mixing heights to take into account the urban influence

Martin has also incorporated the exponential time decay of pollutant concentrations, since he compared his calculations with measured sulfur-dioxide concentrations for St Louis, Missouri

The Tabulation Prediction Scheme

This method, developed at the Argonne National Laboratory, consists of developing an ordered set of combinations of rel-evant meteorological variables and presenting the percentile distribution of SO 2 concentrations for each element in the set In this table, the independent variables are wind direc-tion, hour of day, wind speed, temperature, and stability The

10, 50, 75, 90, 98, and 99 percentile values are presented

as well as the minimum and the maximum values Also presented are the interquartile range and the 75 to 95 per-centile ranges to provide measures of dispersion and skew-ness, respectively Since the meteorological variables are ordered, it is possible to look up any combination of meteo-rological variables just as one would look up a name in a telephone book or a word in a dictionary This method, of

course, can be applied only as long as the source

distribu-tion and terrain have not changed appreciably For

contin-ued use of this method, one must be cognizant of changes

in the sources as well as changes in the terrain due to new

construction

In preparing the tabulation, the data are first stratified

by season and also by the presence or absence of

precipita-tion Further, appropriate group intervals must be selected

for the meteorological variables to assure that within each

grouping the pollution values are not sensitive to changes

in that variable For example, of the spatial distribution of

the sources, one finds that the pollution concentration at a

station varies markedly with changes in wind direction If

one plots percentile isopleths for concentration versus wind

direction, one may choose sectors in which the SO 2

concen-trations are relatively insensitive to direction change With

the exception of wind direction and hour of day, the

meteo-rological variables of the table vary monotonically with SO 2

concentration The tabulation prediction method has

advan-tages over other receptor-oriented technique in that (1) it is

easier to use, (2) it provides predictions of pollution

con-centrations more rapidly, (3) it provides the entire percentile

distribution of pollutant concentration to allow a forecaster

to fine-tune his prediction based on synoptic conditions, and

(4) it takes into account nonlinearities in the relationships

of the meteorological variables and SO 2 concentrations In

a sense, one may consider the tabulation as representing a

nonlinear regression hypersurface passing through the data

that represents points plotted in n -dimensional space The

analytic form of the hypersurface need not be determined in

the use of this method

The disadvantages of this method are that (1) at least

2 years of meteorological data are necessary, (2) changes in

the emission sources degrade the method, and (3) the model

could not predict the effect of adding, removing, or

modify-ing important pollution sources; however, it can be designed

to do so

Where a network of stations is available such as exists in

New York City, Los Angeles, or Chicago, then the

receptor-oriented technique may be applied to each of the stations

to obtain isopleths or concentration similar to that obtained

in the source-oriented model It would be ideal to have a

source-oriented model that could be applied to any city,

given the source inventory Unfortunately, the nature of the

terrain, general inaccuracies in source-strength information,

and the influence of factors such as synoptic effect or the

peculiar geometries of the buildings produce substantial

errors Similarly, a receptor-oriented model, such as the

Clarke model or one based on regression techniques, must

be tailored to the location Every urban area must therefore

be calibrated, whether one desires to apply a source-oriented

model or a tabulation prediction scheme The tabulation

pre-diction scheme, however, does not require detailed

informa-tion on the distribuinforma-tion and strength of emission sources

Perhaps the optimum system would be one that would

make use of the advantages of both the source-oriented

model, with its prediction capability concerning the effects

of changes in the sources, and the tabulation prediction

scheme, which could provide the probability distributions

of pollutant concentrations It appears possible to develop

a hybrid system by developing means for appropriately modifying the percentile entries when sources are modified, added, or removed The techniques for constructing such a system would, of course, have general applicability

The Fixed-Volume Trajectory Model

In the trajectory model, the path of a parcel of air is predicted

as it is acted upon by the wind The parcel is usually con-sidered as a fixed-volume chemical reactor with pollutant inputs only from sources along its path; in addition, various mathematical constraints placed on mass transport into and out of the cell make the problem tractable Examples of this technique are discussed by Worley (1971) In this model, derived pollution concentrations are known only along the path of the parcel considered Consequently, its use is limited

to the “strategy planning” problem Also, initial concentra-tions at the origin of the trajectory and meteorological vari-ables along it must be well known, since input errors along the path are not averageable but, in fact, are propagated

The Basic Approach

Attempts have been made to solve the entire system of three-dimensional time-dependent continuity equations The ever-increasing capability of computer systems to handle such complex problems easily has generally renewed interest in this approach One very ambitious treatment is that of Lamb and Neiburger (1971), who have applied their model to carbon-monoxide concentrations in the Los Angeles basin However, chemical reactions, although allowed for in their general for-mulation, are not considered because of the relative inertness

of CO Nevertheless, the validity of the diffusion and emission subroutines is still tested by this procedure

The model of Friedlander and Seinfeld (1969) also considers the general equation of diffusion and chemical reaction These authors extend the Lagrangian similarity hypothesis to reacting species and develop, as a result, a set of ordinary differential equations describing a variable-volume chemical reactor By limiting their chemical system

to a single irreversible bimolecular reaction of the form

A  B  C, they obtain analytical solutions for the

ground-level concentration of the product as a function of the mean position of the pollution cloud above ground level These solutions are also functions of the appropriate meteorologi-cal variables, namely solar radiation, temperature, wind con-ditions, and atmospheric stability

ADAPTATION OF THE BASIC EQUATION TO URBAN AIR POLLUTION MODELS

The basic equation, (1), is the continuous point-source equa-tion with the source located at the ground It is obvious that the sources of an urban complex are for the most part located above the ground The basic equation must, therefore, be modified

to represent the actual conditions Various authors have

proposed mathematical algorithms that include appropriate

modifications of Equation (1) In addition, a source-oriented

model developed by Roberts et al (1970) to allow for

time-varying sources of emission is discussed below; see the section

“Time-Dependent Emissions (the Roberts Model).”

Chemical Kinetics: Removal or Transformation

of Pollutants

In the chemical-kinetics portion of the model, many

differ-ent approaches, ranging in order from the extremely simple

to the very complex, have been tried Obviously the simplest

approach is to assume no chemical reactions are occurring at

all Although this assumption may seem contradictory to our

intent and an oversimplification, it applies to any pollutant

that has a long residence time in the atmosphere For

exam-ple, the reaction of carbon monoxide with other constituents

of the urban atmosphere is so small that it can be considered

inert over the time scale of the dispersion process, for which

the model is valid (at most a few hours)

Considerable simplification of the general problem can

be effected if chemical reactions are not included and all

vari-ables and parameters are assumed to be time-independent

(steady-state solution) In this instance, a solution is obtained

that forms the basis for most diffusion models: the use of the

normal bivariate or Gaussian distribution for the downwind

diffusion of effluents from a continuous point source Its use

allows steady-state concentrations to be calculated both at

the ground and at any altitude Many modifications to the

basic equation to account for plume rise, elevated sources,

area sources, inversion layers, and variations in chimney

heights have been proposed and used Further discussion of

these topics is deferred to the following four sections

The second level of pseudo-kinetic complexity assumes

first-order or pseudo-first-order reactions are responsible for

the removal of a particular pollutant; as a result, its

concentra-tion decays exponentially with time In this case, a

characteris-tic residence time or half-life describes the temporal behavior

of the pollutant Often, the removal of pollutants by chemical

reaction is included in the Gaussian diffusion model by simply

multiplying the appropriate diffusion equation by an

exponen-tial term of the form exp(− t / T ), where T represents the half-life

of the pollutant under consideration Equations employing this

procedure are developed below The interaction of sulfur

diox-ide with other atmospheric constituents has been treated in this

way by many investigators; for examples, see Roberts et al

(1970) and Martin (1971) Chemical reactions are not the only

removal mechanism for pollutant Some other processes

con-tributing to their disappearance may be absorption by plants,

soil-bacteria action, impact or adsorption on surfaces, and

washout (for example, see Figure 2 ) To the extent that these

processes are simulated by or can be fitted to an exponential

decay, the above approximation proves useful and valid

These three reactions appear in almost every

chemical-kinetic model On the other hand, many different sets of

equa-tions describing the subsequent reacequa-tions have been proposed

For example, Hecht and Seinfeld (1972) recently studied the

propylene-NO-air system and list some 81 reactions that can occur Any attempt to find an analytical solution for a model utilizing all these reactions and even a simple diffusion sub-model will almost certainly fail Consequently, the number of equations in the chemical-kinetic subroutine is often reduced

by resorting to a “lumped parameter” stratagem Here, three general types of chemical processes are identified: (1) a chain-initiating process involving the inorganic reactions shown above as well as subsequent interactions of product oxidants with source and product hydrocarbons, to yield (2) chain-propagating reactions in which free radicals are produced;

these free radicals in turn react with the hydrocarbon mix to produce other free radicals and organic compounds to oxide

NO to NO 2 , and to participate in (3) chain-terminating reac-tions; here, nonreactive end products (for example, peroxy-acetylnitrate) and aerosol production serve to terminate the chain In the lumped-parameter representation, reaction-rate equations typical of these three categories (and usually selected from the rate-determining reactions of each category) are employed, with adjusted rate constants determined from appropriate smog-chamber data An attempt is usually made

to minimize the number of equations needed to fit well a large sample of smog-chamber data See, for examples, the studies

of Friedlander and Seinfeld (1969) and Hecht and Seinfeld (1972) Lumped parameter subroutines are primarily designed

to simulate atmospheric conditions with a simplified chemical-kinetic scheme in order to reduce computing time when used with an atmospheric diffusion model

Elevated Sources and Plume Rise

When hot gases leave a stack, the plume rises to a certain height dependent upon its exit velocity, temperature, wind speed at the stack height, and atmospheric stability There are several equations used to determine the total or virtual height at which the model considers the pollutants to be emitted The most commonly used is Holland’s equation:

a

1 5  2 68 10−2( )⎛ 

⎝⎜

⎞

⎠⎟

⎛

⎝⎜

⎞

⎠⎟

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

where

∆ H: plume rise

v s : stack velocity (m/sec) d: stack diameter (m) u: wind speed (m/sec)

P: pressure (kPa)

T s : gas exit temperature (K)

T a : air temperature (K)

The virtual or effective stack height is

H
h  ∆ H

where

H: effective stack height h: physical stack height

With the origin of the coordinate system at the ground, but

the source at a height H, Equation (2) becomes



T

0 693 2

2

2

2

⎝

⎠

⎟ ⎛⎝⎜ ⎞⎠⎟

1/2

(3)

Mixing of Pollutants under an Inversion Lid

When the lapse rate in the lowermost layer, i.e., from the

ground to about 200 m, is near adiabatic, but a pronounced

inversion exists above this layer, the inversion is believed to

act as a lid preventing the upward diffusion of pollutants The

pollutants below the lid are assumed to be uniformly mixed

By integrating Equation (3) with respect to z and distributing

the pollutants uniformly over a height H, one obtains



T

2

0 693 2

2

⎝

⎜ ⎞⎠⎟ ⎛⎝⎜ ⎞⎠⎟

1/2

Those few measurements of concentration with height that

do exist do not support the assumption that the

concentra-tion is uniform in the lowermost layer One is tempted to

say that the mixing-layer thickness, H, may be determined

by the height of the inversion; however, during transitional

conditions, i.e., at dawn and dusk, the thickness of the layer

containing high concentrations of pollutants may differ from

that of the layer from the ground to the inversion base

The thermal structure of the lower layer as well as

pollut-ant concentration as a function of height may be determined

by helicopter or balloon soundings

The Area Source

When pollution arises from many small point sources such

as small dwellings, one may consider the region as an area

source Preliminary work on the Chicago model indicates

that contribution to observed SO 2 levels in the lowest tens of

feet is substantially from dwellings and exceeds that

emanat-ing from tall stacks, such as power-generatemanat-ing stacks For

a rigorous treatment, one should consider the emission Q

as the emission in units per unit area per second, and then

integrate Q along x and along y for the length of the square

Downwind, beyond the area-source square, the plume may

be treated as originating from a point source This point

source is considered to be at a virtual origin upwind of the

area-source square As pointed out by Turner, the

approxi-mate equation for an area source can be calculated as



Q

y

T



2

2 0 2

2

2

0 693

⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟

)

1/2

⎛⎛

⎝⎜

⎞

⎠⎟

p u s y x y0x s z

where σ y ( x y 0  x ) represents the standard deviation of the

horizontal crosswind concentration as a function of the

dis-tance x y 0  x from the virtual origin Since the plume is

con-sidered to extend to the point where the concentration falls

to 0.1 that of the centerline concentration, σ y ( x y 0 )
S /403 where σ y ( x y 0 ) is the standard deviation of the concentration

at the downwind side of the square of side length S The distance x y 0 from the virtual origin to the downwind side of the grid square may be determined, and is that distance for

which σ y ( x y 0 )
S /403 The distance x is measured from the

downwind side of the grid square Other symbols have been previously defined

Correction for Variation in Chimney Heights for Area Sources

In any given area, chimneys are likely to vary in height above ground, and the plume rises vary as well The variation of effective stack height may be taken into account in a manner similar to the handling of the area source To illustrate, visu-alize the points representing the effective stack height pro-jected onto a plane perpendicular to the ground and parallel both to two opposite sides of the given grid square and to the horizontal component of the wind vector The distribution

of the points on this projection plane would be similar to the distribution of the sources on a horizontal plane

Based on Turner’s discussion (1967), the equation for an area source and for a source having a Gaussian distribution

of effective chimney heights may be written as



Q

y

x x

z h

x x





2

0 2

2

0

2

2⎡⎣s ( )⎤⎦ 2 s

( )

⎡⎣ ⎤⎦

⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟

00 693

0

T

u y x y x z x z x

1/2

0

⎛

⎝⎜

⎞

⎠⎟

⎡⎣ ⎤⎦⎡⎣ ( )⎤⎦

where σ z ( x z 0  x ) represents the standard deviation of the

vertical crosswind concentration as a function of the

dis-tance x z 0  x from the virtual origin The value of σ z ( x z 0 ) is arbitrarily chosen after examining the distribution of

effec-tive chimney heights, and the distance x z 0 represents the dis-tance from the virtual origin to the downwind side of the grid

square The value x z 0 may be determined and represents the

distance corresponding to the value for σ z ( x z 0 ) The value of x y 0 usually differs from that of x z 0 The other symbols retain their previous definition

In determining the values of σ y ( x y 0  x ) and σ z ( x z 0  x ), one

must know the distance from the source to the point in question

or the receptor If the wind direction changes within the aver-aging interval, or if there is a change of wind direction due to local terrain effects, the trajectories are curved There are sev-eral ways of handling curved trajectories In the Connecticut model, for example, analytic forms for the trajectories were developed The selection of appropriate trajectory or stream-line equations (steady state was assumed) was based on the

wind and stability conditions In the St Louis model, Turner

developed a computer program using the available winds to

provide pollutant trajectories Distances obtained from the

tra-jectories are then used in the Pasquill diagrams or equations to

determine the values of σ y ( x y 0  x ) and σ z ( x z 0  x )

Time-Dependent Emissions (The Roberts Model)

The integrated puff transport algorithm of Roberts et al

(1970), a source-oriented model, uses a three-dimensional

Gaussian puff kernel as a basis It is designed to simulate the

time-dependent or transient emissions from a single source

Concentrations are calculated by assuming that dispersion

occurs from Gaussian diffusion of a puff whose centroid

moves with the mean wind Time-varying source emissions

as well as variable wind speeds and directions are

approxi-mated by a time series of piecewise continuous emission and

meteorological parameters In addition, chemical reactions

are modeled by the inclusion of a removal process described

by an exponential decay with time

The usual approximation for inversion lids of constant

height, namely uniform mixing arising from the

superpo-sition of an infinite number of multiple source reflections,

is made Additionally, treatments for lids that are steadily

rising or steadily falling and the fumigation phenomenon are

incorporated

The output consists of calculated concentrations for a

given source for each hour of a 24-hour period The

concen-trations can be obtained for a given receptor or for a uniform

horizontal or vertical grid up to 1000 points

The preceding model also forms the basis for two other

models, one whose specific aim is the design of optimal

control strategies, and a second that repetitively applies the

single-source algorithm to each point and area source in the

model region

METEOROLOGICAL MEASUREMENTS

Wind speed and direction data measured by weather bureaus are

used by most investigators, even though some have a number

of stations and towers of their own Pollutants are measured

for periods of 1 hour, 2 hours, 12 hours, or 24 hours 12- and

24-hour samples of pollutants such as SO 2 leave much to be

desired, since many features of their variations with time are

obscured Furthermore, one often has difficulty in determining

a representative wind direction or even a representative wind

speed for such a long period

The total amount of data available varies considerably in

the reviewed studies Frenkiel’s study (1956) was based on

data for 1 month only A comparatively large amount of data

was gathered by Davidson (1967), but even these in truth

represent a small sample One of the most extensive studies

is the one carried out by the Argonne National Laboratory

and the city of Chicago in which 15-minute readings of SO 2

for 8 stations and wind speed and direction for at least 13

stations are available for a 3-year period

In the application of the mathematical equations, one is required to make numerous arbitrary decisions: for example, one must choose the way to handle the vertical variation of wind with height when a high stack, about 500 ft, is used as

a point source; or how to test changes in wind direction or stability when a change occurs halfway through the 1-hour

or 2-hour measuring period In the case of an elevated point source, Turner in his St Louis model treated the plume as one originating from the point source up to the time of a change in wind direction and as a combination of an instantaneous line puff and a continuous point source thereafter The occurrence

of precipitation presents serious problems, since adequate diffusion measurements under these conditions are lacking

Furthermore, the chemical and physical effects of precipita-tion on pollutants are only poorly understood In carrying forward a pollutant from a source, one must decide on how long to apply the calculations For example, if a 2-mph wind is present over the measuring grid and a source is 10 miles away, one must take account of the transport for a total of 5 hours

Determining a representative wind speed and wind direc-tion over an urban complex with its variety of buildings and other obstructions to the flow is frequently difficult, since the horizontal wind field is quite heterogeneous This is so for light winds, especially during daytime when convective processes are taking place With light-wind conditions, the wind direction may differ by 180 within a distance of 1 mile

Numerous land stations are necessary to depict the true wind field With high winds, those on the order of 20 mph, the wind direction is quite uniform over a large area, so that fewer stations are necessary.

METHODS FOR EVALUATING URBAN AIR POLLUTION MODELS

To determine the effectiveness of a mathematical model, validation tests must be applied These usually include a comparison of observed and calculated values Validation tests are necessary not only for updating the model because

of changes in the source configuration or modification in terrain characteristics due to new construction, but also for comparing the effectiveness of the model with any other that may be suggested Of course, the primary objective is to see how good the model really is, both for incident control as well as for long-range planning

Scatter Plots and Correlation Measures

Of the validation techniques appearing in the literature, the most common involves the preparation of a scatter diagram

relating observed and calculated values ( Y obs vs Y calc ). The

degree of scatter about the Y obs
Y calc line provides a mea-sure of the effectiveness of the model At times, one finds that a majority of the points lies either above the line or below the line, indicating systematic errors

It is useful to determine whether the model is equally effective at all concentration levels To test this, the calcu-lated scale may be divided into uniform bandwidths and the

mean square of the deviations abou t the Y obs
Y calc line

cal-culated for each bandwidth Another test for systematic error

as a function of bandwidth consists of an examination of the

mean of the difference between calculated and observed

values for Y calc Y obs and similarly for Y calc obs

The square of the linear correlation coefficient between

calculated and observed values or the square of the

correla-tion ratio for nonlinear relacorrela-tionships represent measures of

the effectiveness of the mathematical equation For a linear

relationship between the dependent variable, e.g., pollutant

concentration, and the independent variables,

y

y

2 2

2

2

s

s s

unexplained variance total variance

2

2

explained variance total variance

where

R 2 : square of the correlation coefficient between observed and calculated values

S y 2 : average of the square of the deviations about the regression line, plane, or hyperplane

σ y 2 : variance of the observed values

Statistical Analysis

Several statistical parameters can be calculated to evaluate

the performance of a model Among those commonly used

for air pollution models are Kukkonen, Partanen, Karppinen,

Walden, et al (2003); Lanzani and Tamponi (1995):

The index of agreement

IA = 1

2

2

[| | | |]

R

R C o C o C p C p

s s

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

The bias

Bias
C C

C

o

The fractional bias



0 5 ( )

The normalized mean of the square of the error

NMSE
(C C )

C C

2

where

C p : predicted concentrations

C o : predicted observed concentrations

σ o : standard deviation of the observations

σ p : standard deviation of the predictions

The overbar concentrations refer to the average overall values

The parameters IA and R 2 are measures of the correla-tion of two time series of values, the bias is a measurement of the overall tendency of the model, the FB is a measure of the agreement of the mean values, and the NMSE is a normalized estimation of the deviation in absolute value

The IA varies from 0.0 to 1.0 (perfect agreement between the observed and predicted values) A value of 0 for the bias, FB, or NMSE indicates perfect agreement between the model and the data

Thus there are a number of ways of presenting the results

of a comparison between observed and calculated values and

of calculating measures of merit In the last analysis the effec-tiveness of the model must be judged by how well it works to provide the needed information, whether it will be used for day-to-day control, incident alerts, or long-range planning

RECENT RESEARCH IN URBAN AIR POLLUTION MODELING

With advances in computer technology and the advent of new mathematical tools for system modeling, the field of urban air pollution modeling is undergoing an ever-increasing level of complexity and accuracy The main focus of recent research is on particles, ozone, hydrocarbons, and other substances rather than the classic sulfur and nitrogen com-pounds This is due to the advances in technology for pollu-tion reducpollu-tion at the source A lot of attenpollu-tion is being devoted

to air pollution models for the purpose of urban planning and regulatory- standards implementation Simply, a model can tell if a certain highway should be constructed without increasing pollution levels beyond the regulatory maxima or

if a new regulatory value can be feasibly obtained in the time frame allowed Figure 2 shows an example of the distribution

of particulate matter (PM 10 ) in a city As can be inferred, the presence of particulate matter of this size is obviously a traffic-related pollutant

Also, some modern air pollution models include meteo-rological forecasting to overcome one of the main obstacles that simpler models have: the assumption of average wind speeds, direction, and temperatures

At street level, the main characteristic of the flow is the creation of a vortex that increases concentration of pollut-ants on the canyon side opposite to the wind direction, as