Urban Air Pollution Modelling

It was certainly not my intention in writing this book to produce a treatise on urbanism. Nevertheless, it will be necessary to look somewhat closer into the genesis and the structure of urban areas. Some reading about urbanism would be extremely useful (for a few titles, see Pelican Books (1967) and Hall (1968)), although a few general ideas will be discussed here. This is motivated by the fact that towns are very complex organisations; to explain the methods for calculating air pollution concentrations (or by the same argument public transport economics, for example) without mentioning the basic phenomena (the town and the urban area to which it applies) would indeed be contrary to reason and difficult to understand. It would be like explaining the interpretation of an electrocardiogram without previous knowledge of human anatomy in general or that of the heart in particular.

It is necessary first of all to define the words ‘model’ and ‘modelling’ clearly and definitively, as the colloquial use of technical jargon frequently causes the meanings of words to deviate from their original sense.

In this chapter we shall discuss in general the current methods which, under the rather vague heading gaussian plume concept, are used for the computation of concentration fields resulting from large numbers of distributed urban and industrial sources.

Chapter 3 contains a selection of the most typical short-time plume and sector models. Many papers could be cited which mainly describe the local implementation of one of these models without basically changing the inferences to be drawn from chapter 3. A fairly representative but by no means exhaustive list of papers with the application, and in some cases with the validation, of these models is as follows: Milford et al. (1971 a, b), Moriguchi (1971), Ping (1972), Yoshida et al. (1972), Legrand (1973), Matsuzaki et al. (1973), Mills and Reeves (1973), Murase et al. (1973), Nakano et al. (1973), Sadelski (1973), Shiozawa et al. (1973), Shoda et al. (1973), Kawashima et al. (1976), Gibson and Peters (1977).

Modern methods of atmospheric research, including air pollution calculations, are based on well-known physical laws related to what is usually called a ‘volume element’, ‘parcel’ or ‘box’ of air. Such an element is a volume of identifiable air that maintains some sort of integrity as it moves around from point to point.

The boundary between the numerical advection—diffusion methods of volume elements and the multi-box models tends to be blurred. In the latter, the region to be studied is divided into cells not necessarily identical in area and height. No diffusion between the boxes is assumed; the concentration in each cell or box is considered uniform. This is perhaps the most important difference from previously outlined models where a (variable) diffusion constant had to be used. As Scriven and Fisher (1975) pointed out, in the ideal box model infinite diffusivity inside the individual box is assumed. The mass-conservation equation is solved for each of the boxes. The uniform concentration within a particular box at any time is a function of the box volume, of the rate at which material is being imported, of the emission rate, of the concentration within the box in the preceding time increment and of the residual fractions of these three terms in describing the amount of material remaining in the box. For box n, the functional relationship is, as expressed by Reiquam (1969, 1970, 1971), where x_n,t is the concentration, V_n.t the volume, q_n.t the rate at which pollutants are advected into box n, Q _n.t the emission rate within box n, r_n.t the residual of x _n,t-1 remaining, r_n.t the residual of Q_n.t remaining, p _n.t the residual of remaining, all at the end of time increment, and x _n.t-1 the concentration in box n at time t −1. The residual fractions are simple geometrical relationships between the resultant wind vector and the box dimensions.

The assumption of proportionality between emissions and air quality (ambient concentration) leads directly to the long-term simple box model, which is source oriented. The independent variable (input) for the box model is the source strength, and its output is the concentration value. However, if we use a past or present measured concentration as input and investigate the changes in source strength in order to find some other concentration (the desired air quality), we arrive at the receptor-oriented symmetrical counterpart of the box model which is called the rollback model or proportional scaling model. where R is the percentage reduction required, x_a the measured concentration, x_b the background concentration and x_c the desired air quality.

Input parameters such as diffusion constants and inversion heights are the permanent basic problems of atmospheric modelling. Quite often they are inserted into the computational formulae based on the results of previous experiences made in more or less similar conditions. The next step, that of computing diffusion parameters from real-time monitoring network observations and of using them as input values, was performed by Shieh et al. (1970, 1972). They expressed the diffusion parameters as with i = x, y, z and where a _i (x) is the diffusion parameter at a distance x, u is the wind velocity, t is the diffusion time and α, p are constants.

We must distinguish quite clearly between forecast and calculation. The latter term is used to denote the operation of taking some formula (for example, plume, statistical time series, etc.) and then of substituting into this formula some assumed (for example, for the next winter season, etc.) or meteorologically forcasted parameters. The forecast, on the other hand, is a process which uses knowledge that is available a specific day (for example, past statistical record, that day’s pollution concentration, that day’s meteorological forecast, etc.) to predict (a) a time (for example, the next day, or even a given hour, etc.) and (b) a pollutant concentration for that time. The upper limit of the time span is that for which a forecasting skill can be demonstrated and might be for a few hours or a few days in advance. We exclude from forecasting the climatological estimate of long-term averages, although it is implied that they are often taken into account by the forecaster. In order to be termed a pollution forecast, the pollution concentration estimate must refer to a specific day or hour and not to a probability of occurrence within a given time span.

If a number of air quality observations have been made at a given place, the information is usually concentrated in tables or graphs. Often, a further step towards concentration is undertaken by condensing groups of figures into averages coupled with their standard deviations: these are called descriptive statistical parameters, and the tabulation, averaging, etc., process is called descriptive statistics. However, we are interested not only in the adequate representation of observed or observable data but also in the relationships that permit conclusions to be drawn from these observations (that is, samples) for other as yet unobserved samples or even for the whole population of observable samples. Thus even the most complex statistical model is based on a group of observations, and statistical models are essentially empirical. This basic simple statement encompasses all the limitations of these models from the most simple to the mathematically most complex.

In the introduction to section 3.3 it was stressed that, because there are an extremely large number of combinations of plume rise equations, wind direction and speed class, vertical wind profile laws, number and specification of stability classes, choice of dispersion parameters and mixing heights, etc., each air pollution specialist could have his own particular gaussian plume model. A list of the gaussian long-term models, as complete as possible up to the beginning of 1977, was provided by Jost and Gutsche (1977) in the form of a table, and most of the variants listed either are basically identical with one of the main prototypes discussed below or represent experimental programmes only which have not yet attained widespread use.

It was pointed out by Gifford and Hanna (1973, where further references may be found) and Hanna (1971) that, if equation 6.1 is applied to yearly, seasonal, etc., averages that is, to long-term averages, the estimates for the pollutant concentrations compare favourably with those obtained from other models. Writing equation 6.1 as where Q_tot is the total yearly, seasonal, etc., pollutant emission of the source, A is the area within which the pollutant is being emitted and ū is the yearly, seasonal, etc., average wind velocity and using published average urban pollutant concentrations, Gifford and Hanna obtained table 12.1.

The basic box model given in equation 6.2 requires proportionality between pollutant concentration and the source strength per area unit. If the wind speed is averaged over a whole year or over an even longer period, this mean value is subject to only relatively slight changes. Hence equation 6.2 may be written where Q_A is the source strength per area unit and ū is a long-term average of the wind speed.

It is evident that pollutant concentration distributions are only an indication of the wind field. At the same time, it has been observed that the log-normal function is a convenient empirical representation of the wind velocity distribution (Benarie, 1969). The fact that we are concerned at this point with a rough approximation appropriate to the argument that follows below (without pretending to describe general physical properties of the wind) was stressed and in a subsequent discussion by Benarie (1972, appendix); Benkala and Seinfeld (1976) also discussed this.

The terms validation, assessment, evaluation, cross-evaluation and other similar expressions are employed rather loosely in air pollution modelling. For example, all authors do not use the word validation in the same sense, and it is all too infrequently defined. The meaning has to be guessed from the context and sometimes is fundamentally different from the meaning attributed to the same term by another author. For this reason we shall start this chapter with a few definitions. Some of them may seem arbitrary to some readers, whereas other readers may have already accepted our definitions. Their use will at least be consistent within this text.

It should be noted that the contents of this chapter have not been indexed because a further time delay would have resulted.