Meteorological factors influencing the occurrence of air pollution episodes involving chimney plumes

Transcription

1 Meteorol. Appl. 9, (2002) DOI: /S Meteorological factors influencing the occurrence of air pollution episodes involving chimney plumes Bernard Fisher, Environment Agency, National Centre for Risk Assessment and Options Appraisal, Steel House, 11 Tothill Street, London SW1H 9NF, UK, and School of Earth & Environmental Sciences, University of Greenwich, Chatham Maritime, Kent ME4 4TB, UK This paper is concerned with meteorological processes that may have an influence on the occurrence of episodes of high pollution involving chimney plumes. It reviews meteorological mechanisms that could lead to or maintain high concentrations at distances beyond the range normally considered in dispersion models (distances greater than 30 km). Fundamental parameters of the atmospheric boundary layer are shown to largely determine short-range and long-range dispersion, but their values are usually not well known in specific cases. A simple estimate is provided of the magnitude of the maximum hourly average concentrations during a long-range fumigation episode from a tall stack. 1. Introduction Dispersion modelling is the technique widely used over the past 40 years to estimate the mixing and dilution of pollution in the atmosphere. It concerns itself mainly with dispersion in the atmospheric boundary layer, which is that portion of the atmosphere where the direct effect of the surface (on heat, moisture, momentum, etc.) is felt as a consequence of turbulent transfer. Dispersion modelling has been used widely to assess the acceptability of releases from industrial sources, which are generally from tall stacks. Using dispersion models (Fisher & Acres, 2000), it has been shown that pollution episodes in which UK air quality objectives are exceeded are unlikely. This does not preclude the possibility that, on occasions, ground-level concentrations may approach the limits set by a short-term air quality standard and indeed such concentrations have been observed infrequently in the UK constituting an air pollution episode. This paper addresses the question as to whether dispersion models are adequate for predicting the highest short-term concentrations arising from a source. It reviews the meteorological factors, which lead to the formation of episodes, and how well these are treated in dispersion models. For the purposes of this paper, an episode is defined as a meteorological condition with the potential for producing ground-level concentrations from a tall stack close to an air quality standard (e.g. 100 ppb for SO 2 over short periods), at any distance from the source. All dispersion models are dependent (directly or indirectly) on the vertical and horizontal spread of plumes which can be described by dispersion parameters, or in some cases by vertical or horizontal eddy diffusivities. The dispersion parameters are empirical functions of the fundamental atmospheric parameters, as are the wind, temperature and turbulence profiles. The close connection between the dispersion of material and the dispersion of heat and momentum should be recognised. It is clear that the description of dispersion is dependent on the properties of the atmospheric boundary layer. The basic properties of the boundary layer that are of importance for air pollution studies are the vertical wind profile (wind speed and direction) which determines transport, the level of turbulence which is responsible for the spread and dilution of plumes, and the height of the boundary layer. The vertical temperature profile also affects the rise of plumes and the level of turbulence. Dispersion models that make use of dispersion parameters or eddy diffusivities, which are consistent with the most appropriate description of the atmospheric boundary layer, are to be preferred. Figure 1 shows schematically the dispersion in the atmosphere of pollution released from a chimney. Most attention to modelling this behaviour centres on describing in mathematical equations the spread of airborne material as a function of downwind distance. This is shown in an idealised way in Figure 2, where the shape of the dispersing plume is assumed to have the form of a Gaussian or bell-shaped function, examples of which are drawn on the diagram. These figures illustrate that concentrations generally decrease with increasing travel distance downwind as the plume mixes or dilutes in the atmosphere. Ground-level concentrations from emissions from tall stacks tend to a maximum some distance from the stack as pollutants disperse to the ground. The distance depends upon plume height and is generally within 15 km (rather less 199

2 B Fisher in highly convective conditions) and thereafter the concentration decreases with increasing distance (Environment Agency, 1998). Most of this process occurs within the atmospheric boundary layer. The application of short-range models in flat terrain is illustrated by these figures and these models assume that the dispersion occurs within the atmospheric boundary layer. This paper is concerned with the meteorology associated with dispersion conditions leading to episodes of high concentration at short and long distances from the source. The starting point for both situations is the same, namely the description of the atmospheric boundary layer. Regional episodes associated with very persistent low wind speeds and a shallow boundary layer capped by a strong inversion will only be discussed briefly. In these episodes the very light wind speeds imply that wind direction fluctuations are very large. Puffs of pollution from all sources in a region are subject to random motion, mixing material within a confined box. It would then be appropriate to describe the situation as the build-up of pollution within a well-mixed box, covering a regional source area, capped by an elevated inversion that most material would not penetrate, apart from very buoyant plumes from tall stacks. The descriptions of symbols used in this paper are given in Table Boundary layer structure It is not possible to consider the behaviour of chimney plumes without reviewing the structure of the turbulent atmospheric boundary layer in which the plume is transported and in which it disperses. For short-range dispersion the air flow and dispersion characteristics (or turbulence levels) are generally assumed to be the same throughout the area of interest and over the duration of travel from source to receptor. Fluctuations in wind over the averaging time assumed within the model are generally treated as part of the turbulence and are included in any estimate of turbulence intensities. Generally, an averaging time of about 1 hour is adopted in dispersion models. The traditional approach, following the work of Pasquill (1961), is to classify the dispersive properties in terms of a few (normally 6 or 7) stability categories. Each stability category describes a range of atmospheric conditions, such as cloud cover, wind speed, vertical temperature profile, turbulence levels and surface radiation, but the categories differentiate broad differences in dispersion. Plume spread is modelled as depending only on downwind distance and the stability category. These stability categories form the basis for describing dispersion in many commonly used regulatory models. In recent years dispersion models have been developed using an approach which is closer to the methods commonly used for describing the flow in the atmospheric boundary layer (and indeed for describing the flow in turbulent boundary layers generally, such as in engineering flows). Such models attempt to describe the dispersion in terms of the same few fundamental parameters as are used to characterise the flow, such as wind speed u, surface heat flux H and boundary layer depth h. This approach has a number of advantages over simple classification schemes. The dispersion can be related directly back to basic physical parameters, such as wind speed, or the heating or cooling of the air at the surface. These parameters are in turn an essential part of larger- 200 Figure 1. The processes of pollutant transport.

3 Meteorological factors influencing pollution episodes Figure 2. The Gaussian plume concept. scale numerical weather prediction models. The approach also allows the meteorology of dispersion to be described in similar terms for cases involving differing spatial scales, such as emissions from tall stacks, emissions from short stacks, dispersion over short distances and over longer distances. The properties of turbulence cannot be explicitly determined from first principles since the basic nature of turbulence involves a coupled range of scales of motion, making solution by even the most powerful computers an impossible task. The problem is particularly difficult in the case of the atmospheric boundary layer, which is subject to continual variation in time and space. In the context of regulations dealing with the planning, control and management of atmospheric pollution, there is a need to have available suitable, practical regulatory models, which can be readily applied following documented procedures (Hall et al., 2000). These regulatory models will not necessarily describe unusual events. 3. Neutral (or mechanical) atmospheric boundary layer The properties of the atmospheric boundary layer are primarily derived from experimental data, analysed within a theoretical framework in which the vertical profiles of wind, temperature and turbulence are scaled by a non-dimensional combination of height and other fundamental parameters. The shape of the profiles is determined empirically (Nieustadt & van Dop, 1982). The levels of turbulence in an atmospheric boundary layer with zero heat flux at the surface in uniform, homogeneous, steady conditions are determined by the following fundamental parameters: (a) wind speed at the top of the boundary layer (or the geostrophic wind speed G), (b) Coriolis parameter f arising from the Earth s rotation, and (c) roughness of the surface described by the roughness length z 0, a measure of the height of typical surface irregularities. Near the surface, turbulence levels are related to the friction velocity u *, describing the transfer of horizontal momentum to the surface. It is more useful near the surface to scale the wind profile and turbulent velocities with respect to u *, which is proportional to G. In practice the assumption of steadiness is not satisfied. The depth of the atmospheric boundary layer or mixing height is commonly taken to be the depth to which pollution will disperse within a time scale of about an hour (Seibert et al., 2000). Hence the boundary layer depth h is not completely fixed by the geostrophic wind speed G, Coriolis parameter f and z 0, and h can be regarded as an extra parameter needed to describe the boundary layer. 4. Non-neutral (convective and stable) atmospheric boundary layer When the surface heating is non-zero, the surface sensible heat flux H is the other driving force setting up the 201

4 B Fisher Table 1. Description of symbols used in the paper. Symbol Description C max Maximum ground-level concentration (µg m 3 ) f Coriolis parameter(s 1 ) G Geostrophic wind speed (m s 1 ), wind speed at the top of the atmospheric boundary layer h Depth of atmospheric boundary layer (m) h s Stack height (m) h p Plume rise (m) H Surface sensible heat flux (W m 2 ) K y Horizontal eddy diffusivity (m 2 s 1 ) L Monin-Obukhov length (m), equal to ρc p u 3 * /k β H, where ρ is the density of air (kg m 3 ), c p is the specific heat of air (J kg 1 C 1 ), k = 0.4 is von Karman s constant and β is the buoyancy parameter equal to the acceleration of gravity divided by absolute temperature. L is proportional to u 3 * /H with a constant of proportionality equal to about l Horizontal length scale (m) Q Pollutant emission rate (kg s 1 ) Q H Heat flux out of the stack in MW S Gradient in the geostrophic wind speed G (s 1 ) t Travel time (s) u Wind speed (m s 1 ) at plume height, or speed (m s 1 ) associated with the air mass trajectory u * Friction velocity (m s 1 ) w * Convective velocity scale (m s 1 ), equal to (βhh/ρc p ) 1/3, proportional to (hh) 1/3 with a constant of proportionality equal to about w Upward velocity at top of boundary layer (w -γh) (m s 1 ) x Travel distance (m) z 0 Roughness length (m) γ Horizontal divergence of the wind field in the lower troposphere (s 1 ) ε Error in trajectory end points (m) σ y Standard deviation of the crosswind concentration profile (m) σ u Standard deviation of fluctuations in horizontal wind speed at plume height due to wind shear and turbulence (m s 1 ) structure of the boundary layer. During the day, when the flux of heat carried from the surface into the atmosphere by convection is usually positive, the heat flux acts as an extra source of turbulence over and above that caused by the wind. At night the heat flux is usually negative and this tends to drain energy down from the wind-induced turbulence, leading to much reduced turbulence levels for a given wind speed. Since the interests of boundary layer meteorology and dispersion modelling are in the main velocity and length scales, it is usual to introduce a length scale L into the equations, known as the Monin-Obukhov length, equal to u 3 * / H multiplied by a constant of proportionality. In convective boundary layers it is usual to introduce the convective velocity scale w * which is proportional to (h H) 1 3. For ideal conditions, boundary layer turbulence is determined by the values of the fundamental parameters, namely the geostrophic wind speed G or the friction velocity u *, the Coriolis parameter f, the roughness length z 0, the surface heat flux H, and the boundary layer depth h, or convenient combinations of some of these parameters (such as L and w * ). For the depth of the stable boundary layer, including the neutral case, numerous formulae have been proposed based on various combinations of u * (or G) and f and z 0 in the neutral case and u * (or G) f, z 0 and L in the stable case. 202 These have been listed by Seibert et al. (1998, 2000). The formulae assume that the atmospheric boundary layer has had time to reach equilibrium. The same authors list a number of formulae describing the evolution of the convective boundary layer. Heating at the surface produces changes in depth, which occur rapidly relative to the duration of daylight hours. The layer of air in the troposphere above the atmospheric boundary layer is known as the free atmosphere and is generally associated with stable conditions and lower turbulence than the atmospheric boundary layer. The thermal stratification of the atmospheric layer above the mixing layer is described by the Brunt- Väisälä frequency, defined as the square root of the product of the buoyancy parameter (g/t) and the vertical potential temperature gradient. 5. Determination of fundamental parameters The atmospheric boundary layer can rarely be described exactly even when remote sensing equipment is available or detailed numerical weather prediction models have been applied. If the fundamental parameters are to be useful for describing turbulent dispersion in a practical way, they must be available at any site. This is a necessary preliminary before using these para-

5 Meteorological factors influencing pollution episodes meters to describe the dispersion of a passive nonreacting chemical in the atmosphere. The Coriolis parameter f is fixed by the latitude of the site, and the roughness length z 0 is fixed by the nature of the surface at the site of interest. The geostrophic wind speed G is determined by synoptic meteorology on a regular basis at any location from numerical forecast models or surface pressure charts. Estimates of the friction velocity u * can also be made routinely from the wind and temperature measurements near the ground at a nearby site, provided a representative value of z 0 is known. The direct measurement of the surface sensible heat flux H requires sophisticated instrumentation and therefore H cannot normally be directly obtained from synoptic stations. Processing of routinely measured data is required. A number of different methods have been proposed and used to determine the surface heat flux on a routine basis. In other words H is derived from other more readily derived parameters, such as time of day, time of year and cloud cover using formulae and models. Similarly, at most locations, measurements of the mixing layer depth h are not available, except when sophisticated equipment is available, and even then interpretation may be difficult. Instead, a large number of diverse formulae and methods have been proposed for determining h, based on theoretical arguments and empirical measurements. Surface heat flux and mixing depth are the two fundamental parameters for which the literature contains the widest diversity of formulae. Measurements of wind, temperature and turbulence are normally measured at a standard height of 10 m above ground on a routine basis. Hence the description of turbulence throughout the boundary layer relies on formulae which include the height dependence of these quantities up to the mixing height. A number of formulae for the profiles of wind, temperature and turbulence have been proposed in the literature. These formulae consist of empirically determined relationships between the required quantities and the fundamental parameters, and are normally expressed in non-dimensional form. 6. Specific studies of boundary layer structure Because more recent methods of calculating dispersion emphasise the way in which dispersion varies with height in the boundary layer, the height dependence of the wind, temperature and turbulence is of high priority. A wide variety of remote sensing measurement techniques, such as sodar, and in-situ measurement techniques, such as radiosondes, are available, leading to atmospheric profiles from which the mixing height can be estimated, but these measurement techniques are not generally routinely available. Instead, a number of operational methods have been developed. In situations determined by mechanical turbulence these usually rely on formulae to describe the height of mixing. The height is an evolving quantity in situations driven by convective turbulence, and the methods depend on solving equations describing the evolution of the boundary layer as heat is fed into it. Although in-situ measurements are to be preferred when estimating mixing layer depth, for practical use methods based on simple computer models are generally applied. Seibert et al. (1998, 2000) have tried five methods for calculating the mixing height. The methods are based on similar principles with variations in the choice of those parameters which are not measured or cannot be measured routinely. They have used three datasets to test the mixing height routines. The datasets come from fairly uniform terrain in the Netherlands, Switzerland and Germany and consist of a mixture of tower, remote sensing (sodar and electromagnetic profiler) and radiosonde data, together with measurements of turbulent fluxes at the surface. The intercomparison is further complicated because the measurement methods themselves give different results and need to be interpreted using models. The data consisted of a number of days on which the hourly evolution of the mixing height could be estimated from measurements. Seibert et al. (1998) recommend ways of estimating mixing height when profile data are available. When computer codes in meteorological pre-processors are used to calculate the mixing height from routine data, these should be designed so as to allow for the substitution of measured or estimated values when appropriate. As these methods are by no means perfect, it is suggested that these methods need further attention. Estimates of dispersion are frequently required at sites for which no routine meteorological dataset exists from which turbulence can be estimated. In lowland areas, with broadly flat, homogenous terrain, it is normally possible to use a nearby site or interpolate between sites at which a long series of observations have been made. In regions of complex terrain this is no longer possible and formidable problems exist. Simple theories of the boundary layer, based on a few fundamental parameters, no longer apply. In such terrain, the wind flow may no longer be interpolated directly from the available observational network or from the synoptic wind field. Dispersion in complex terrain is most sensitive to the wind flow because the wind field determines where the pollution cloud will travel. The fundamental parameters that determine the structure of the atmospheric boundary layer can be clearly identified but there remain the difficulties of obtaining reliable values for application to dispersion models. Normally, data from a nearby site representative of the location are used, but the inaccuracies involved have not been quantified. Estimating the extent to which point measurements are representative is very difficult. 203

6 B Fisher It should be recognised that the methods used to determine surface heat flux, mixing height and turbulent profiles from readily measured parameters are themselves based on models. These are often analogous to dispersion models but involve the dispersion of momentum, heat or water vapour rather than pollution. 7. Accuracy of description of the boundary layer One of the recurring themes of boundary layer meteorology is the use of empirical data, using scaled quantities involving non-dimensional combinations of parameters, and applying conservation laws to describe the structure of atmospheric turbulence. It is therefore not surprising that a choice of formulae for some quantities is available with no clear preferred formula. In the real world the atmospheric boundary layer is never really steady; it is always subject to time variations caused by disturbances such as cumulonimbus clouds, rain and weather systems, etc. In addition, there are always variations in space from changes at the surface in roughness, topography or large-scale air motions. Despite these difficulties, attempts to summarise the turbulent properties of the boundary layer in terms of a few non-dimensional combinations of the fundamental parameters have been reasonably successful, leading to descriptions of boundary layer profiles in terms of simple scaling laws, which provide a framework for describing different kinds of turbulent boundary layers, and through these to better ways of describing dispersion. The usefulness of these scaling parameters decreases as the complexity of the flow increases, e.g. due to complex terrain, coastal effects, the rural-urban interface or baroclinicity (when the vertical component of flow becomes important). In such situations it can become impossible to represent the flow in terms of a few fundamental parameters, and in cases of very extreme terrain it is not clear that even the concept of the atmospheric boundary layer remains useful. Situations involving dispersion over longer distances usually start to involve effects caused by changes in terrain. Therefore longer-range transport shifts the emphasis to changes in atmospheric flow. Before discussing episodes of high pollution occurring at long distances from a source it is appropriate to discuss short-range episodes. 8. Variability in short-range dispersion In regulatory models of dispersion up to 30 km or so from a source, the traditional and boundary-layer scaling approaches do not differ fundamentally in the 204 way short-range episodes are described. The maximum ground-level concentration around tall stacks is typically highest in high wind speed conditions, when plume rise is not as great as normal, or in highly convective conditions with light winds when thermals and down draughts promote rapid vertical mixing. For given meteorological conditions, the highest maximum ground-level concentrations occur when the top of the boundary layer is just above the effective height of the plume. Scriven (1969) has shown that a stable layer close to the source height (h effective plume height) can increase the maximum ground-level concentration by up to a factor of two, relative to the maximum ground-level concentration when a stable elevated layer is not present (h >> effective plume height). For regulatory purposes dispersion models are applied in broadly two principal ways. Sequential, usually hourly, meteorological data are entered into the model and a time-series of hourly average predicted concentrations is obtained. These may be used to obtain peak concentrations over a range of meteorological conditions or some statistical average, such as the mean or a percentile, by processing the model s results. Alternatively, a climatology is used as input data to the model. This contains a limited number of categories of meteorological conditions and the frequency with which they occur. By running the model over these categories and taking a weighted average according to the relative frequency with which each occurs, the mean concentration may be obtained in a way that is computationally efficient. The same quantity can be estimated by running sequential data of a year or more. This will avoid the error introduced by the discrete categories, but the calculation is more laborious. Episodes correspond to the least frequently occurring conditions. The enormous increases in computing power have made the use of sequential data easier. Also, the increased complexity of models and the range of problems tackled make statistical data less convenient. (If the meteorological input is characterised by a large number of parameters e.g. humidity for condensing plumes, lapse rate above the boundary layer for plumes which penetrate the inversion, precipitation for washout, as well as the basic parameters of wind speed and direction, surface heat flux and boundary layer depth then one needs a large number of categories to represent the climatology accurately; as the number of parameters increases, the number of categories required rapidly multiplies, so that eventually a sequential approach may be preferred.) The spatial variability of meteorology and the temporal variability can be important in many cases, even over relatively short ranges if the terrain is complex, and such effects cannot be included in a statistical approach. However, it is still not always practical to routinely run the most complex dispersion models for, say, 10 years of hourly data.

7 Meteorological factors influencing pollution episodes Some work on climatologies for dispersion applications for a site in flat terrain in the UK has been reported by Davies & Thomson (1997) who considered the issues of the number of years of data required, the differences between using sequential data and statistical categories, the differences between different choices of statistical categories, and the differences caused by using meteorological data from meteorological sites at various distances from the location of interest. They found that using only three years data gave acceptable predictions but that one year was not long enough. The differences arising from the use of sequential and statistical data were small. Perhaps the most interesting result was that predictions for a large power station type source were more sensitive to how the data were treated than predictions for a smaller factory source. This implies that the type of source needs to be considered in any future consideration of these issues. The traditional approach to dispersion based on stability categories does not provide a means for treating the variation of turbulence and dispersion with height, and is most applicable to near ground-level sources over short distances. Over longer travel distances the variation of meteorological conditions in space and time becomes increasingly important to the description of dispersion. A framework based on fundamental boundary layer parameters also applies to longer-range transport, albeit that the fundamental parameters are varying in space and time, and the atmospheric boundary layer may be transformed between different states (different fundamental parameters G, h, H and z 0 ). It is possible in principle to relate specific meteorological conditions to a traditional stability category. However, the same dispersion category may arise for different combinations of surface heat flux and geostrophic wind (Clarke, 1979). It is often the relative importance of wind speed and heat flux in producing turbulence that is important, rather than the absolute size of each. This is because if the wind speed is increased and the heat flux is also increased in magnitude, then the turbulent velocities can remain proportional to the wind speed. As a result, although the plume spreads faster in time, it also travels downwind faster and can have a similar width at a given downwind distance. This relative importance can be characterised quantitatively via the Monin-Obukhov length, L, or by the Richardson number. These effects are not quantitatively represented in the use of the stability category, although they may reflect this qualitatively. Although some traditional dispersion models make allowance for surface roughness, and most treat the mixing height as a limit to vertical dispersion, they do not generally allow for the full effect of changing roughness length, mixing height and source height. Models which rely on describing plume spread in terms of the fundamental parameters should, in principle, encompass a fuller description of the dependence of plume spread on atmospheric conditions. They should be preferable when considering episodes related to infrequently occurring atmospheric conditions. Under these conditions it is better to use an approach in which underlying relationships are described, rather than extrapolating from empirical data into situations for which few measurements are available. 9. Longer-range transport In designing regulatory models of dispersion over distances greater than 30 km from a source, the usual approach adopted is to assume almost uniform mixing within the atmospheric boundary layer and to characterise the height of the atmospheric boundary layer in simple terms. The models also require information about the wind flow. Depending on its sophistication, the model will require greater or lesser information about turbulence levels. The movement of air parcels over longer distances is described by trajectories in which the synoptic structure of the atmosphere is considered. So-called geostrophic trajectories can be drawn based on the surface pressure field, or wind speeds at various heights available from numerical weather forecasting models can be applied. Such trajectories are very uncertain in two types of atmospheric conditions: high pressure systems leading to episodes of high ozone in the summer, and high particle and NO 2 concentrations in winter. In this case, winds are light and it is not possible to define accurately where an air parcel is coming from or going to. The second condition is one of high wet deposition associated with precipitation. In this case the air mass trajectory is involved in three-dimensional movement in very disturbed conditions so that accurate assessment of air movement is not possible. Neither stationary high pressure systems nor conditions of persistent precipitation are associated with the kind of longer-range episode which has been attributed to plumes from point sources with tall stacks. Episodes involving point sources may involve persistent, moderate to high winds, for which the tracking of trajectories is more accurate. However, errors associated with any attempt to plot trajectories increases with distance from the source. The European Tracer Experiments (ETEX), summarised by Van Dop et al. (1998), showed that models are not able to predict accurately the concentration field from a 12 h release of tracer travelling up to 72 h downwind in simple meteorological conditions. The best models achieved correlation coefficients between measured and calculated logarithmic concentrations of greater than 0.6 (Ryall & Maryon, 1998), with more than 50% of predictions within a factor of 5 of observations, and the overlap between the predicted and measured clouds being over 70%. 205

8 B Fisher It may be readily shown (Sykes & Hatton, 1976) that errors in trajectory end points are large when wind speed and direction fluctuations are large, or when the gradient in the mean wind speed is high (corresponding to the centres of high and low pressure systems). A formula for the ratio of trajectory end points to the length of the trajectory is: where ε is the error in trajectory end points, t is the travel time, u is the speed associated with the air mass trajectory (u may taken to be proportional to the geostrophic wind speed G), S is the gradient of u (S is a measure of the vorticity and is high in the region of depressions) and δu is the error in the estimate of the trajectory speed. It can be seen that errors will build up rapidly when δu/u is large, which occurs in high pressure areas with slack pressure gradients, or when S is large in the regions of depressions when S is comparable with f (=10 4 s 1 in moderate latitudes), when it is not possible to track trajectories for more than, say, six hours before errors swamp the analysis. 10. Empirical measurements of plumes at medium distances Aircraft measurements have been undertaken (Fisher & Callander, 1984) to look at dispersion over distances of 100 km or more. Although limited to six flights studying transport from the UK, it was possible to describe the crosswind spread (σ y ) with distance (x) using a horizontal eddy diffusivity (K y ) equal to m 2 s 1 (K y = σ y 2 /(2x/u) where u is the wind speed G). This value of K y was thought to be low compared with other estimates and is associated with travel over the North Sea under conditions of low lateral dispersion. It was suggested that over land higher horizontal turbulence generated by topographic features causes greater lateral dispersion and the reason for the low value of K y measured is the generally lower rate of lateral spread over the sea (Crabtree, 1984). In an extreme case of poor lateral dispersion, distinct plumes were still distinguishable on the far side of the North Sea from power station sources 150 km apart (Cocks et al., 1983). Low rates of lateral spread will tend to cause longer-range episodes of high concentration. The ratio of the fluxes of SO 2 to NOx on these flights were consistent with source inventories. Typically some 60 to 70% of the NOx and SO 2 remained airborne as the pollution crossed the coast suggesting that over travel distances of about 100 km, or travel times of a few hours, deposition is not an efficient loss mechanism over short distances. The extreme event was an example of an episode associated with poor lateral mixing in which widths of plumes were very narrow. 206 St ε δu ( e 1) = ut u St (1) Oxidation of NO to NO 2 by ozone is potentially very rapid but is limited by the amount of ozone present in the boundary layer. Horizontal mixing of ozone into power station plumes provides a source of ozone, but the presence of narrow plumes implies slow lateral mixing and a rate of oxidation which is dispersion limited. Ozone concentrations were low within major plumes (ozone concentrations equalled 3 to 5 ppb), but between plumes where NOx was low, the ozone concentration remained equal to background levels of 20 to 30 ppb. Freiberg (1977) showed that the oxidation of pollutants within plumes tends towards limits after long times, which are dependent on the reaction rate and the rate of dispersion. Peak instantaneous SO 2 concentrations after some 100 km of travel have been found to be of the order of 100 ppb from the combined emissions from groups of major power stations, reaching 200 ppb in one case (Fisher & Callander, 1984) when the plumes from nearby power stations overlapped. These flights illustrate the potential for medium-range episodes of high ground-level SO 2 over the Midlands. On one occasion higher rates of removal were found over part of the plume travel path and never satisfactorily explained. Without evidence to corroborate measurements (no duplicate observations), such events are hard to explain and the behaviour seen on the majority of other occasions is more likely to be typical. On these other occasions multiple traverses through the plume were made. Other examples of plumes detected at medium-range distances of about 100 km are illustrated by a number of flights conducted by the Meteorological Office in 1971 and 1973 in steady south-westerly winds. It was estimated that about 60% of the total SO 2 emitted from central England was still airborne over the coast. The fraction of SO 2 emitted from tall stacks was above 70% (Fisher & Maul, 1976). Occasions when aircraft measurements were made to intercept power station plumes suggested that peak short-term depth-averaged concentrations within the Eggborough and Ferrybridge plumes at distances 50 to 100 km downwind in June 1975 under conditions of deep mixing (h equal to about 1250 m and 1680 m) were about 100 ppb (Fisher et al., 1977). The effective plume height at Eggborough was thought to be about 500 m. Instantaneous concentrations a factor of two or more higher are to be expected within plumes from power stations on full load, with lighter winds and shallower atmospheric boundary layers. Some long-range transport models may require more complex parameter values than those routinely available. For example, Lagrangian particle flow models require profiles of the Lagrangian time scale. Estimates of the Lagrangian time scale amount in effect to making estimates of the size of turbulent eddies (Ryall &

9 Meteorological factors influencing pollution episodes Maryon, 1998; Malcolm et al., 1999). Similarly Eulerian grid models generally require eddy diffusivities which depend on turbulence levels and eddy size. Potentially, such models may lead to better predictions but are limited by the lack of routinely available data. 11. Conditions leading to longer-range pollution episodes There are two situations leading to longer-range episodes associated with elevated point sources: plume fumigation episodes and regional pollution episodes. In plume fumigation episodes an elevated plume from a high stack escapes from the boundary layer (of height h) near the point of emission and travels with limited dispersion without coming to the ground near the point of emission (within 30 km) (see Figure 3). Changes in meteorology, such as the development of a convective boundary layer due to surface heating (an increase in h), may lead to changed conditions and the plume becomes absorbed into a deeper boundary layer and disperses to the ground. Although turbulence mixing may be lower in the free atmosphere than in the boundary layer, the plume is affected by the vertical and horizontal shear in wind speed and direction leading to dilution of the timeaveraged plume. The maximum ground-level concentration will occur after re-entrainment into the boundary layer. This has been described by models of plume fumigation. Venkatram (1988) has described the theory in the simple case in which the plume is assumed to mix rapidly to the ground. (See example in Appendix.) Because the plume from other sources may not necessarily be absorbed in the boundary layer at the same time, this type of episode provides a more distinct signature from the individual source, consisting of a short-duration pulse of pollutant concentrations with ratios of individual pollutants that match the source characteristics. Although rare this mechanism has been suggested to explain occasional elevated sulphur dioxide concentrations in areas remote from power stations. Close inspection of such episodes is necessary in order to check whether other local sources of sulphur dioxide (e.g. cement kilns, domestic coal burning) could also have had an air quality impact in the area. These fumigation episodes occur infrequently, perhaps once every few years at a specified location (Bray et al., 2000). The other type of pollution episode, the regional pollution episode, occurs during very persistent low wind speeds (G low) in combination with a shallow boundary layer (h low) capped by a strong inversion. Under these conditions, emissions from all sources including those from tall stacks can be trapped in the boundary layer. Mixing in the boundary layer is slow due to the low wind speeds, so exceptionally high concentrations can build up. The episode ends if the wind speed G increases (due to synoptic changes) and greater mixing occurs. In this kind of regional episode a relatively large area is affected. All sources in the region whose plumes are trapped in the boundary layer will contribute to the episode. So in this kind of episode the atmospheric composition is characteristic of the mixture of sources within the region, not of any one individual source. Figure 3. Schematic representation of a plume fumigation episode. 207

10 B Fisher 12. Modelling of fumigation episodes Broadly speaking the fumigation part of episodes can be described by the dispersion incorporated in shortrange models. Traditional Gaussian models, as well as more recently developed dispersion models based on boundary layer scaling, such as ADMS (Carruthers et al., 1995), are able to simulate the fumigation process. Traditionally such events have been studied in association with convective boundary layers associated with shoreline fumigation (reviewed by Venkatram, 1988). Complex modelling is unnecessary as illustrated by the example in the Appendix. However, dispersion models do not generally carry over concentrations from hour to hour. Instead the model starts afresh for each hour with a new set of meteorological conditions and a new release. Consequently the effect of changing conditions on a release after the first hour is not described. Modelling of long-range episodes therefore requires the facility to model the evolving trajectory of the plume, hour to hour. The Meteorological Office model NAME (Ryall & Maryon, 1996; Ryall & Maryon, 1998) is one example of a model which is able to model episodes in this way. The model uses a numerical weather forecasting model to describe the air mass trajectories. It addresses the problem of boundary layer depth and parameterisation, but inevitably suffers from being unable to resolve features which occur on a fine scale, such as plume structure near or above the top of the boundary layer (Malcolm et al., 1999). Sulphur dioxide is generally the pollutant of concern from major stationary point sources during such episodes. However, distant episodes are rare because the necessary combination of stack height, plume buoyancy, boundary layer depth and strong elevated inversion occur infrequently. For example, monitoring data suggest that distant fumigation episodes occur at most about 4 to 5 times per year across central England (Bray et al., 2000) and last for a few hours. The impact of fumigation episodes is felt in different locations, so that at any given location in central England fumigation events would be expected to occur less than once per year on average. The plume from a point source can be considered as a series of puffs or clouds each of which delineates a trajectory in the atmosphere as the puff travels downwind. The crosswind spread of the plume is determined by the spread between adjacent trajectories (Sykes & Hatton, 1976). The time-averaged spread can be considered analogous to the error between the end points of trajectories given by equation (1), where ε is now the crosswind spread, δu is replaced by σ u, the standard deviation of fluctuations in the horizontal wind speed caused by turbulence and vertical wind shear, and S is the horizontal wind shear. ε will be high in the conditions similar to those when the errors in trajectory end 208 points are large (i.e. when wind speed and direction fluctuations are large) or when the gradient in the mean wind speed is high (corresponding to the centres of high and low pressure systems). The mechanisms of wind shear, turbulence and the change in wind flow with time, all lead to a spreading of the puffs constituting a plume. There are therefore always mechanisms present in the atmosphere which promote mixing and dilution. 13. Convergence and divergence The influence of large-scale convergence and divergence on concentrations within the atmospheric boundary layer can be assessed in terms of the concentration within a regional box with sides of length l, of area l 2 and of depth equal to the boundary layer height. If the horizontal divergence in the lower troposphere equals γ (positive in areas of high pressure) then the area of the box increases to l 2 e γt after a time t, and the concentration decreases as e γt as a result of dilution. The upward velocity at the top of the boundary layer equals γh, and typically has a value of about 0.01 m s 1 (Brunt, 1934). Since this is of the same order of magnitude as the deposition velocity of reactive gases such as SO 2, the reduction in concentration from additional horizontal dispersion is comparable to the reduction caused by dry deposition. Both processes are slow relative to the duration of regional episodes and only reduce concentrations slowly. However, the small downward velocity in high pressure systems encourages the formation of elevated inversions at the top of the boundary layer and increases the strength of the inversion. When γ is negative (convergence) there is an overall upward velocity in the lower troposphere and removal of material from the boundary layer into the free atmosphere (Pedgley, 1962). This represents a removal process from the boundary layer with a time constant of order w/h. This rate is comparable with the removal of airborne material from the atmosphere by wet removal processes and is not associated with episodes of high concentration. 14. Conclusions Formulae for the fundamental parameters and profiles of turbulence in the atmospheric boundary layer have been widely and successfully exploited to reduce data to manageable proportions. However, the comparisons between the formulae and observations considered by Seibert et al. (1998) have not been able to produce consistently good agreement for a number of reasons. Accepting the need for better empirical data for use in testing current methods, it is reasonable to conclude that all current methods, regardless of further testing, are likely to be associated with errors in certain non-

11 Meteorological factors influencing pollution episodes ideal situations. Further improvements may come from the widespread introduction of remote sensing. The other line of approach is to exploit the use of improved numerical weather prediction models and high speed computing. At the present time in practical applications of air quality dispersion models, the limitations on the accuracy of predictions arising from limitations in the description of meteorological data should be recognised when interpreting episodes. Models based on the use of fundamental parameters of the atmospheric boundary layer do have a useful degree of skill and are to be recommended. Interpretation of individual episodes will always be incomplete and will probably suffer from a limited description of the atmospheric boundary layer. However, the interpretation should include an estimate of the fundamental boundary layer parameters ( e.g. h and G) which have been associated with the episode. Without this the classification of episode occurrences is not possible in a systematic way. It is always preferable to be able to study a number of similar episodes in order to increase confidence in the interpretation and to reduce uncertainties. Typical concentrations at long distances can be estimated given broad estimates of the boundary layer parameters. This should be attempted in order to associate measured concentrations quantitatively with suspected emissions. Acknowledgements Research for this paper was carried out under a contract with TXU Europe Power while the author was at the University of Greenwich. The author thanks Mr D Acres and Mr P Simmons of TXU for useful scientific discussions. Appendix. Simple estimates of the ground-level concentration from power stations during longrange fumigation episodes As an example of the application of simple ideas on fumigation one may consider the highest ground-level concentration of the grounded plume at distance x, from a coal-fired power station, after rapid mixing through the boundary layer (see Figure 3) after the start of fumigation: C max = Q 2πuσy ( hp + hs) (A1) where Q is the emission rate, and typically u G is the wind speed (in m s 1 ), σ y (=0.08x 7/u), x is the distance downwind, h s is the stack height and h p is the plume rise (= αq H 1/4 /u, α is a constant = 500 when Q H is the heat flux out of the stack in MW). The formula is consistent with dispersion in the near field in the ALMANAC model (Bennett, 1989). Thus: C (A2) If one considers the highest ground-level concentration for various wind speeds, this arises when h s = h p. For a typical 2,000 MW power station, h s = 200 m, Q H = 2000/7, so that h s = h p when u = 10 m s 1. Then: (A3) Since Q = 10 kg s 1 SO 2, for a major coal-fired power station burning coal without flue gas desulphurisation, u = 10 m s 1, h s = 200 m, at a distance of 50 km from the stack one expects a worst case, one-hour average ground-level concentration of about 300 µgm ppb. At longer distances the maximum concentration is expected to be smaller. Peak concentrations may occur at longer distances, but will be of smaller magnitude than the peak concentrations that arise following fumigation closer to the point of emission. References max C = max Q 14 / Q 2 u0. 08 u 7 H π x hs + α u Q 3Q = 2 2 hu0. 067x uhs x π s Bennett, M. (1989). The ALMANAC plume dispersion model. CEGB Report RD/L/3491/R89. Bray, S. Arbuthnott, A. Hewitt, C. N. Fisher, B. Baldwin, D. & Shears, P. (2000). The Role of Power Stations in Air Pollution Episodes. TXU Report, Ipswich. Brunt, D. (1934). Physical and Dynamical Meteorology. Cambridge University Press, London. 411 pp. Carruthers, D. J., Edmunds, H. A., Ellis, K. L., McHugh, C. A., Davies, B. M. & Thomson, D. J. (1995). Atmospheric Dispersion Modelling System (ADMS): comparison with data from the Kincaid experiment. Int. J. Environ. Pollut., 5: Clarke, R. H. (1979). A model for short and medium range dispersion of radionuclides released to the atmosphere. NRPB Report R91, Harwell. Cocks, A. T., Kallend, A. S. & Marsh, A. R. W. (1983). Dispersion limitations of oxidation in power plant plumes during long-range transport. Nature, 305: Cosemans, G., Erbrink, J., Fisher, B. E. A., Kretzschmar, J. G. & Thomson, D. J. (1997). Meteorological data for dispersion modelling: a brief report on the COST 710 programme on pre-processing and harmonization. Int. J. Environ. Pollut., 8: Crabtree, J. (1984) Studies of plume transport and dispersion over distances of travel up to several hundred kilometres. In C. De Wispelaere (ed.), Air Pollution Modeling and its Application III. Plenum Press, New York and London. pp