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

1163 U URBAN AIR POLLUTION MODELING 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 C021_001_r03.indd 1163C021_001_r03.indd 1163 11/18/2005 1:31:34 PM11/18/2005 1:31:34 PM © 2006 by Taylor & Francis Group, LLC 1164 URBAN AIR POLLUTION MODELING 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 Predicting the future Modelling the science Describe case using available data 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 FIGURE 1 Schematic diagram showing flow of data into and out of the atmospheric dispersion model, and three categories of uncertainty that can be introduced (From Colvile et al., 2002, with permission from Elsevier). C021_001_r03.indd 1164C021_001_r03.indd 1164 11/18/2005 1:31:34 PM11/18/2005 1:31:34 PM © 2006 by Taylor & Francis Group, LLC URBAN AIR POLLUTION MODELING 1165 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 ss ss Qu yz yz yz ϭϪϪ 1 22 2 2 2 2 ␲ exp ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ (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. C021_001_r03.indd 1165C021_001_r03.indd 1165 11/18/2005 1:31:35 PM11/18/2005 1:31:35 PM © 2006 by Taylor & Francis Group, LLC 1166 URBAN AIR POLLUTION MODELING 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 65Њ. If the average temperature exceeds 65Њ, 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 ϫ 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 ϫ 16 miles, but a measurement grid of 9 ϫ 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 ϫ 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 1/2Њ. A source inventory is obtained for each of the 64 (16 ϫ 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. ␹␹ T Ti i Ti Qϭ ϭ Q ( ) ∑ 1 4 C021_001_r03.indd 1166C021_001_r03.indd 1166 11/18/2005 1:31:35 PM11/18/2005 1:31:35 PM © 2006 by Taylor & Francis Group, LLC URBAN AIR POLLUTION MODELING 1167 ␹␹ I Ii i Ii QQϭ ϭ ( ) ∑ 1 4 ␹␹ S Si i Si QQϭ ϭ ( ) ∑ 1 4 ␹␹␹␹ ␹ Total ϭϩϩϩ ϭ abc k TIS i 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, ␹ϭ ϩ ϩ ϩ ϭ CCQCQ kQ ii i n 01122 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 1/2Њ 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 1/2Њ 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 ␹ϭ FD LS LS nn SLN (, ,,)(,)xr ∑∑∑ 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 C021_001_r03.indd 1167C021_001_r03.indd 1167 11/18/2005 1:31:35 PM11/18/2005 1:31:35 PM © 2006 by Taylor & Francis Group, LLC 1168 URBAN AIR POLLUTION MODELING 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 distribution 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 ϩ B ϩ 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 C021_001_r03.indd 1168C021_001_r03.indd 1168 11/18/2005 1:31:35 PM11/18/2005 1:31:35 PM © 2006 by Taylor & Francis Group, LLC URBAN AIR POLLUTION MODELING 1169 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 reactions 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: ⌬H v u P TT T d ssa a ϭϩϫ Ϫ 15 268 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 ϭ h ϩ ∆ H where H: effective stack height h: physical stack height C021_001_r03.indd 1169C021_001_r03.indd 1169 11/18/2005 1:31:35 PM11/18/2005 1:31:35 PM © 2006 by Taylor & Francis Group, LLC 1170 URBAN AIR POLLUTION MODELING With the origin of the coordinate system at the ground, but the source at a height H, Equation (2) becomes ␹ Qu yzH t T yz yz ϭϪϪ Ϫ Ϫ 1 22 0 693 2 2 2 2 pss ss exp () exp . ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 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 ␹ QuH yt T y y ϭϪϪ 1 2 0 693 2 2 ps s exp exp . ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 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-generating 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 xx zh t T yy z ϭ Ϫ ϩ Ϫ Ϫ Ϫexp ( exp . 2 2 0 2 2 2 2 2 0 693 s s () ⎡ ⎣ ⎤ ⎦ ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ) 1/2 ⎛⎛ ⎝ ⎜ ⎞ ⎠ ⎟ () ⎡ ⎣ ⎤ ⎦ ps s uxx yy z0 ϩ where σ y ( x y 0 ϩ x ) represents the standard deviation of the horizontal crosswind concentration as a function of the dis- tance x y 0 ϩ 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 ) ϭ 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 ) ϭ 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 xx zh xx yy zz ϭ Ϫ ϩ Ϫ Ϫ ϩ Ϫexp exp 2 0 2 2 0 2 2 2 s s () ⎡ ⎣ ⎤ ⎦ ( ) () ⎡ ⎣ ⎤ ⎦ ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ 00 693 0 . t T uxx xx yy zz 1/2 0 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ () ⎡ ⎣ ⎤ ⎦ () ⎡ ⎣ ⎤ ⎦ ps sϩϩ where σ z ( x z 0 ϩ x ) represents the standard deviation of the vertical crosswind concentration as a function of the dis- tance x z 0 ϩ 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 ϩ x ) and σ z ( x z 0 ϩ 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 C021_001_r03.indd 1170C021_001_r03.indd 1170 11/18/2005 1:31:35 PM11/18/2005 1:31:35 PM © 2006 by Taylor & Francis Group, LLC URBAN AIR POLLUTION MODELING 1171 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 ϩ x ) and σ z ( x z 0 ϩ 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 180Њ 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 ϭ 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 C021_001_r03.indd 1171C021_001_r03.indd 1171 11/18/2005 1:31:36 PM11/18/2005 1:31:36 PM © 2006 by Taylor & Francis Group, LLC 1172 URBAN AIR POLLUTION MODELING mean square of the deviations abou t the Y obs ϭ 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 Ͻ Y obs and similarly for Y calc Ͼ Y obs . The square of the linear correlation coefficient between calculated and observed values or the square of the correla- tion ratio for nonlinear relationships 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, R SS y y yy y 2 2 2 2 11ϭϪϭϪϭ Ϫ s s s unexplained variance total variance 2 22 explained variance total variance ϭ 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 Ϫ Ϫ ϪϩϪ () [| | | |] CC CC CC po po oo R R CCCC oopp op ϭ ϪϪ()() ss ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ The bias Biasϭ ϪCC C po o The fractional bias FBϭ Ϫ ϩ CC CC po po 05.( ) The normalized mean of the square of the error NMSE ϭ Ϫ()CC CC po po 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 reduction at the source. A lot of attention 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 C021_001_r03.indd 1172C021_001_r03.indd 1172 11/18/2005 1:31:36 PM11/18/2005 1:31:36 PM © 2006 by Taylor & Francis Group, LLC [...]... 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