Air Pollution Modeling and Its Application III

Lagrangian models are models in which parcels of air are followed as they blow with the wind. The models keep track of the pollutant content of the parcels. This is in contrast to Eulerian models, where the integration of the mass-balance equation is performed in a geographically fixed grid. Lagrangian models are popular, because their basic principle is easy to grasp also for nonprofessionals. In addition some numerical problems associated with the advection terms in the Eulerian mass-balance equation are avoided by Lagrangian models.

Various theories are now available to describe the dispersion of passive material released from a source into the atmosphere. These theories include the eddy-diffusivity equation of diffusion, statistical theory, similarity theory, higher-order closure solutions of the basic equation of motion and continuity, and rondom walk modelling. All these methods explicitly or implicitly require some knowledge of the Lagrangian character of the turbulence field. Some methods only apply to rather idealised states of flow (e.g. statistical theory only applies to uniform flow with homogeneous turbulence) whereas others are much more versatile — (e.g. random walk modelling). Some are simple in concept and application, others are much more complex. In recent years the virtues of random walk modelling have been recognized and the technique widely exploited.

The transport of airborne sulfur and nitrogen compounds and their deposition on the earth’s surface by dry and wet processes have been simulated using Lagrangian numerical models developed at SRI over the past several years. The EURMAP model (Johnson et al., 1978; Bhumralkar et al., 1981, 1982) developed under sponsorship of Umweltbundesamt of the Federal Republic of Germany, applies to Europe; and the ENAMAP model (Bhumralkar et al., 1980; Mayerhofer et al., 1981; Endlich et al., 1982), developed under sponsorship of EPA, applies to eastern North America. Emissions data are obtained for the areas of interest and are represented on a grid mesh with spacing of 50 km for Europe and 70 km for North America. The computations are based on grid-point analyses of winds, stability, and precipitation made from standard meteorological reports, and thereby incorporate the effects of changing weather patterns. The most recent versions of the models use three layers in the vertical and correct the winds for the influences of smoothed terrain (Bhumralkar et al., 1982; Endlich et al., 1982).

In this paper results obtained with a more complex Lagrangian model, MESOS, developed to study long-range effects of atmospheric releases of radioactivity from nuclear installations, will be compared with results from simpler models based on extrapolating Gaussian plume models out to longer distances using only meteorological conditions at the source.

Personal computers are now capable of solving complex problems related to the transport and diffusion of materials released into the atmosphere. Making such calculations rapidly and “on the spot” would be of great use in planning evacuations and cleanup activities when toxic materials are spilled as the result of some accident. It would be desirable if such calculations were not limited to the simple, steady-state assumptions usually required for such applications. A more realistic simulation, accounting for wind fields which change in space and time and variations in the meteorological conditions would be better. As personal micro-computers become ever more readily available, it is no longer unreasonable to believe that these capabilities could be supplied relatively cheaply. Mass- produced personal computers are already relatively inexpensive. In fact, their cost is, on an equivalent basis, less than that of the mechanical desk calculator of 20 years ago. Personal computers are becoming more powerful every year. However, they have limitations in the amount of core storage that is available and in their speed, so their use requires careful programming and some simplifications of the theory.

By assuming that the dispersion time scale in the convective boundary layer is “infinite,” we have derived a simple relationship between the ground-level concentration and the probability density function of vertical velocities at source height. This formulation yields results that compare favorably with the water-tank experiments of Willis and Deardorff (1978).

Simulation modeling is a problem of numerical discretization of a physical system. Such discretization, performed through computer experiments, is particularly important in those cases where physical theories need to be investigated or verified but laboratory experiments are unable to reproduce the complexities of the real world (e.g. stellar evolution).

One has often opposed Eulerian and Lagrangian numerical modellings as more or less irreconciliable technics to treat atmospheric pollution problems. In fact, the use and improvement of both methods by specific scientific teams are strongly connected to objective factors such as : computing ressources, available routine data (concerning pollution and meteorology) scientific skills.

In the United Kingdom the Meteorological Office is collaborating with the Central Electricity Research Laboratories (CERL) in a study of the long-range transport of pollutants over the North Sea. For these experiments the plume from Eggborough power station in South Yorkshire is “labelled” with sulphur hexafluoride so that it can be uniquely identified. The movement of the plume is predicted by a numerical trajectory model, and the Hercules aircraft of the Meteorological Research Flight, Farnborough is used to intercept and sample the gases at selected distances downwind. The usual meteorological, turbulence and cloud physics instrumentation on the aircraft (Nicholls, 1978) has been augmented by chemical sampling equipment (Crabtree and Marsh, 1981) in order to measure, on a time-scale short enough to reveal the detailed structure of the plume, the concentrations of the tracer gas, sulphur and nitrogen compounds, and ozone. Several flights have been carried out so far, including one experiment in which the same portion of the plume was sampled on two successive days. Plumes have been detected at distances up to more than 600 kilometres from the source.

Formulating and solving the diffusion-deposition-resuspension problem of particulate released in the planetary boundary layer is of primary importance in assessing their environmental impact. Solid particles are originated, as it is well-known, both by industrial processes (releases from industrial stacks) and by natural processes (e.g. formation of aerosols droplets by chemical reactions in the atmosphere). The physical mechanisms governing the evolution of particles in the atmosphere have been largely investigated in recent years both in laboratory studies and on the field. For instance, as far as the mechanism of dry deposition is concerned, a detailed review of available results has been compiled by Sehmel (Sehmel G.A., 1980). Modelling of dispersion of solid particles has been generally achieved by suitable modifications of the models available to treat dispersion of gaseous pollutants. Most of these models are therefore based on the Gaussian formulation and are the most used in real world applications. More complex modelling based on the eddy-diffusivity approximation has been recently developed to study the evolution of particles in the plumes of coal-fired power plants (see e.g. Hobbs et al., 1979). This complex model includes, besides the usual mechanisms of advection and diffusion, significant phenomena as particle coagulation, and gas-to-particle conversion both in homogeneous and in heterogeneous phase.

Most trajectory models developed for simulating long-range transport of e.g. sulfur components are based on the assumption that a vertical air column is advected horizontally without being distorted by horizontal or vertical wind shears.

This paper reports on preliminary numerical and analytical results obtained as a part of a study underway for the development of a Lagrangian point source model. The analysis, for the sake of simplicity and computer time saving has been so far restricted to the two-dimensional case of dispersion from an infinite crosswind line source between two solid boundaries (ground and inversion layer) as illustrated in Fig. 1.

For many problems with turbulent dispersion the Lagrangian approach as introduced by Taylor (1921) is the most appropriate. Extension of this theory to atmospheric dispersion problems is, however, complicated by the inhomogeneity and instationarity of atmospheric turbulence. Here we first describe a method based on the Preferred Path Integration (PPI) theory relating the probability distribution of particle displacement to the probability for a particle to move along the most probable or preferred path. The theory is based on the assumption that the particle velocity fluctuations are governed by a first order autoregressive process equivalent to the Langevin model of dispersion (Lin and Ried (1962), Novikov (1963), Smith (1968), Hanna (1978) and Gifford (1982)). The PPI-model yields conditional probability distributions in the case of stationary conditions. The Langevin model has been proposed also for instationary conditions in Monte-Carlo simulations of particle dispersion (Durbin (1980), Wilson et al. (1981)), and here are presented some analytical results based on this type of model for the case of dispersion in decaying turbulence.

The derivation of one-dimensional conservation equations for a buoyant wet plume in the atmosphere is reviewed, and a small correction to the conservation of energy statement is suggested. Subsequently, an analytical solution for plume trajectory and radius is obtained under the Boussinesq, bent-over plume, and constant windspeed, lapse rate, and humidity gradient restrictions. Unlike previously published solutions, however, latent heat effects are explicitly retained in this solution for all lapse conditions, and the significance of these effects on plume predictions can be examined quantitatively. Consideration is also given to the formulation of source conditions consistent with the approximations introduced into the governing equations. It is shown that a consistent formulation of source fluxes leads to a significant change in plume outline predictions. In particular, when the analytical model presented in this paper is applied to cooling tower data from Paradise steam plant, the predicted visible plume length is increased by up to a factor of three, and brought into reasonable agreement with measurements.

The work reported here was initiated in 1977 both by the Electricité de France and the Observatoire du Puy de Dôme in order to provide a better theoretical understanding of waste heat effects in the atmosphere such as those caused by dry cooling towers.

SMOKA, an entrainment model for moist heat sources, contains a set of seven differential equations: horizontal and vertical motion, enthalpy, vapour, cloud water, rain water, any admixture. It respects buoyancy, conversion of sensible and latent heat, mixing of plume air and environmental air as well as mutual mixing of up to ten separate sources. The entrainment rate depends on wind shearing and RICHARDSON number and is based on modern boundary layer theories. The model is calibrated by cooling tower plume observations. The results of the verification are shown.The dependence on the marginal conditions (waste heat, wind speed, atmospheric stability, temperature, humidity) is demonstrated.The model is applied to radiosonde data of five stations (about 3650 data sets of each one). This large number allows statistical declarations on cooling tower plumes respecting regional and seasonal particularities.SMOKA can also be used for other heat sources. Calculations for the purpose of calibrating and testing the model applied to hot smoke are in preparation.

In most cases modern thermal power plants are equipped with cooling towers for heat removal. With distances of several 100 m between the cooling tower and the stack, interactions may occur between the plumes of both sources.

In order to calibrate numerical models of cooling tower plumes, EDF has developed a wide range experiment near the BUGEY nuclear power plant, including aircraft and remote sensing measurements in the plumes over short periods as well as routine measurements over long periods (photographs of the plumes, micro- meteorological networks).With all the data collected, two types of models have been validated : 1/The first type of model, used to build statistics of visible plume characteristics (length, reduction of insulation and solar radiation), was compared to routine measurements and show a fairly good agreement with observations.2/The second type (a 3D model and a spectral model of microphysics) designed for studying with more details the dynamical and microphysical processes in the plume was used to simulate particular meteorological conditions observed during the campaigns.

The motivation for the modeling of heavy gas dispersion lies in the need to estimate the impacts on the surroundings in the event of a leak of heavy gas during normal operations or a much larger release in the event of a major accident. In this presentation, we will consider the phenomenology and/or the evolution of a heavy gas spill from the early times of release to when it is diluted below a prescribed level of toxicity or lower flamability limit (LFL). To the extent the processes contributing to this phenomenology are known, they are described. From this discussion, salient processes emerge whose quantification leads to the structuring of models for heavy gas dispersion. There have been numerous efforts to model the dispersion of such heavy gases, in one to three space dimensions [Van Ulden (1974), Kaiser and Walker (1978), Zeman (1980), Colebrander (1980), Eidsvik (1980), Blackmore et al. (1982), Havens (1982), Taft et al. (1982), Hertel and Teuscher (1982), Ermak et al. (1981), and Chan et al (1982)]. We will describe some typical or representative models in each dimensionality and for various modes of solution (e.g. finite difference and finite element methods).

The Lawrence Livermore National Laboratory (LLNL), under the sponsorship of the U.S. Department of Energy, is conducting safety research related to the possible consequences of liquefied natural gas (LNG) spills. Under this program, LLNL and the Naval Weapons Center (NWC) jointly conducted the Burro and Coyote series of LNG spill experiments at China Lake, California during 1980 and 1981 respectively (Koopman et al., 1982; Koopman, 1982). LLNL is concurrently developing models for use in predicting the vapor dispersion from LNG spills (Ermak et al., 1982).

During the past few years there has been a growing interest in utilizing heavy gases as energy sources. These gases are usually found in remote areas. In order to bring the gases to market, they are liquified (e.g. liquified natural gas LNG and liquified petroleum gas LPG), transported and stored in refrigerated pressurized tanks. Because this type of fuel is both flammable and toxic, an accidental release has serious consequences.

After termination of the slumping phase of a heavy gas cloud, the height slowly starts to grow again. In Jensen (1981) it was shown that this cannot be the result of entrainment through the side wall but must be due to entrainment through the cloud top. Further, conservation equations for the density excess, Δρ, of the cloud relative to ambient air as well as for temperature difference, ΔT, between cloud and surface were given. For a cold cloud, qualitative arguments were derived to the effect that the density-jump Ri-number, controlling entrainment, would vanish faster than the temperaturejump Ri-number, controlling the general level of incloud turbulence, thus predicting that vertical growth should be an accelerating function of time in this case.

In 1980, a series of spills of up to 20 m3 of LNG and refrigerated liquid propane onto the sea was performed by Shell Research Ltd. at Maplin Sands in the south of England. Both instantaneous and continuous releases of liquid were made, and some were ignited. Gas concentration and temperature were monitored from an extensive array of floating pontoons up to 650 m downwind, and meteorological profiles were obtained at two locations.Results from the continuous spills are presented; these were performed at liquid flow rates of up to 5.8 m3/min, and in wind speeds from about 2 to 10 m/s. A comparison is made of the measurements with predictions from the dense gas dispersion model HEGADAS II. The propane measurements provide data on dense gas dispersion without the effects of large temperature difference and low molecular weight, which are present for LNG. In general, the model agrees well with the propane data, but is found to be conservative for LNG dispersion.

In the discussion on the merits of complex versus simple air pollution models, generally two criteria are considered: the physical credibility of the model, andthe accuracy of model results in a comparison with measurements.

The use of acoustics to study atmospheric properties is well-established. A review of atmospheric effects on acoustic signals can be found in Thomson (1975) and the history of acoustic sounder development is given by Gaynor (1982). However, the use of Doppler acoustic sounders in air pollution applications, as pointed out by Gaynor (1982), has gained acceptance only very recently. Doppler acoustic sounders with proven reliability have become commercially available only in the past decade and, even now, only a limited number of units are routinely being used to collect wind data.

To compare the results of modeling with full scale situations in air pollution problems, it is necessary to measure accurately the successive states of the local atmosphere; from this point of view remote sensing techniques are useful so far as they are able to probe great atmospheric volumes with the necessary spatial and temporal continuity.

Observations of the penetration of elevated inversions by a plume from a tar sands plant in northern Alberta, Canada are compared with the predictions of a numerical plume rise model. Timemean plume behaviour was recorded simultaneously by ground-based photography and aircraft monitoring of sulphur dioxide concentration. Supporting data on source conditions as well as atmospheric temperature and wind profiles were also obtained concurrently with the plume measurements.The results of the comparison indicate that reasonable predictions of the position and the relative penetration of the buoyant plume into the inversion are possible with a simple one-dimensional plume model, given the measured atmospheric wind and temperature profiles.

The SODAR technique is very interesting for EDF because it is now the only one able to determine, on a routine basis, the vertical distribution of wind velocity and direction and to give information on the vertical thermal structure and the turbulence in the first five hundred meters of the atmosphere.

The evaluation of the air pollution impact on a large urban area from industries partially or totally surrounding it, is a cause for concern in many European cities. The problem is particularly important in Milan, a city with about 2 million inhabitants and an area of about 190 km2, located at the centre of the Po Valley in an industrial region. The continental climate characterized by frequent and prolonged temperature inversions, much fog during the winter and winds scarcely exceeding 2 m. s-1, leads to pollution build-up.

Increasing attention is being paid to the meso-scale transport and dispersion of airborne pollutants. The reasons are the growing emission of pollutants, and their impact to the oecosystem over hundreds of kilometers.

Over the past 15 years we have witnessed the development of atmospheric dispersion models which include increasingly complex approximations of photochemistry. Unlike existing Gaussian or analytic schemes, the models simulate atmospheric chemical reactions, some of which act at very rapid rates, and therefore involve time steps much shorter than are generally regarded as necessary for transport and dispersion of inert species. The computational demands rise rapidly with the number of chemical species considered, and it is not unusual to see present-day models for urban and regional scales having computer simulation speeds comparable to the real-world events. Computer restrictions have tended to engender decisions to diminish the spatial resolution of the models in order to increase the number of species and reactions treated.

A photochemical dispersion model has been used to calculate concentrationlevels for an area covering the Netherlands and its surroundings during a given episode. The agreement between measured and calculated concentrations of O₃, and to a somewhat less extent of NO₂, showed to be remarkably good. With this model the influence of traffic emissions, the emissions from industry and the inflow of emissions from outside the area during the episode considered on the existing concentration levels of O₃, NO₂ and NO has been determined. The emissions from outside the area showed to have a large influence on the O₃-concentrations. The influence of industry on O₃- and NO₂-levels is larger than that of traffic.The model has proven to be a valuable tool in determining the influence of different source categories and control regulations on the concentration levels.

The relationships between SO_x and NO_x emissions and the distribution of these compounds are complex and not fully understood. It is known that these trace species may be transported long distances (thousands of kilometers) from source areas, and result in high ambient levels over broad regions. In addition, NO_x and SO_x have been related to a number of environmental problems including acid rain, tropospheric haze and resulting reduced visibility, and have been correlated with a variety of adverse health indicators.

Photochemical air pollution has long been recognized as one of the major causes of such adverse environmental impacts as: visibility degradation, plant deterioration, eye irritation and lung function impairment. In addition, oxidation of both nitrogenous and sulfurous emissions can lead to acidic deposition products, notably nitric acid (HNO₃) and sulfuric acid (H₂SO₄), that can have major long term impacts on ecosystems. Indeed, the consequences of acid deposition from photochemical reactions may be felt for extended periods after the removal of the source and, in some cases, may be irreversible. This situation, coupled with the need for a methodology for relating changes in precursor emissions to ambient air quality, was one of the major motivations for the research reported in this paper.

An advanced Eulerian photochemical dispersion model is applied to the Rhine-Ruhr area in the FRG. One of the main features of this area are the complicated wind conditions induced by the complexity of the terrain. Therefore, special emphasis is given in the preparation of the three dimensional wind field as input for the dispersion model. Two methods of wind field generation are discussed, one based on interpolation of surface winds, the other on a prognostic mesoscale model. The calculated concentrations of ozone, NO and NO₂, utilizing both of the wind fields, are compared with measurements. Preliminary results are presented.

In Grenland, Norway, a combination of industrial emissions and urban areas may cause high oxidant episodes. To clarify the local oxidant formation potential within the area, a model describing both photochemical and dispersion effects was developed. This paper describes the results of a cooperation between Institute of Geophysics, University of Oslo, and Norwegian Institute for Air Research (NILU) (1).

To promote better practices in air pollution modeling, the American Meteorological Society sponsored a workshop on stability classification schemes and sigma curves (Hanna et al., 1977). The participants at this workshop reviewed the bases and limitations of the popular dispersion parameter schemes and suggested that the standard deviation of the crosswind concentration distribution, σ_y, might be viewed as (1)$${\sigma _y} = {\sigma _v}\;\;t\;{f_y},$$, where σ_y is the standard deviation of the horizontal crosswind component of the wind, t is the downstream travel time and f_y is a nondimensional function. The standard deviation of the vertical concentration distribution, σ_z, was viewed as (2)$${\sigma _z} = {\sigma _w}\,\,t\;\;{f_z},$$, whereσ_w is the standard deviation of the vertical component of the wind, and f_z is a nondimensional function. Small-angle approximations, such as σ_v t = σ_a X and σ_w t = σ_e X (where σ_a is the standard deviation of the horizontal wind angle, σ_e is the standard deviation of the vertical wind angle, and X = u t), allow restatement of (1) and (2) in various forms.

This paper deals with estimates of vertical diffusion from sources near the ground in strongly unstable, or convective conditions. We will compare the ground level concentrations predicted by three diffusion models. For the comparison the observations of the Prairie grass experiment are used (Barad, 1958). The models describe the dispersion of a passive contaminant released from a continuous crosswind line source.

When the construction of the new 600 MWe fossil fuel power plant of Langerlo, in the northern part of Belgium, started, the electric power company initiated a SO₂ monitoring programme in order to determine the already existing SO₂-pollution in the vicinity of the planned power plant. Daily measurements in eight monitoring stations (Fig. 1) were started in 1973 by the N.V. Vinçotte. These measurements continued once the plant became operational. The statistical interpretation of the data collected during several successive years, respectively without and with the power plant emitting sulphur dioxide, made it possible to define the measured impact of the new source as a function of time and space.

A complex winter storm occurred in eastern United States on 14–15 January 1980. During its passage, five sequential samples of precipitation were collected at State College, Pennsylvania as part of an intensive study of the storm by the Dept. of Meteorology at the Penn State University. Twenty four-hour back trajectories from State College were calculated for each precipitation sample, using the horizontal and vertical winds predicted by a 3D numerical primitive equation model. The source regions of the precipitating atmosphere were then compared with some chemical properties of the rainfall. The rainfall samples were analyzed for the following ions: hydronium (H₃O+), sulfate (SO₄=), nitrate (NO₃−), chloride (Cl−) and sodium (Na+) among others. Some of the concentrations changed significantly during the period of the precipitation event. Of perhaps greatest interest is the ratio of Cl− to Na+ (Cl−/Na+) which decreased from values of 0.9 and 1.15 near the beginning of the event to less than 0.6 during the sampling period of about 12 h. Because the Cl−/Na+ ratio in the sea water is 1.18, the data suggest a source region which changes from maritime to continental during the observation period. The transport model results support this hypothesis.

In long range transport problems the source receptor relationships are conveniently studied by the use of a transfer matrix when the model uses linear chemistry and scavenging phenomena. The size of the transfer matrix depends on the number of sources and receptors chosen. It is expected that each element of the transfer matrix will have a degree of uncertainty associated with it, which is attributed to the modelling errors and the variability of the atmospheric variables. The latter source of uncertainty is best understood if one considers the fact that models are designed to give ensemble average values which are difficult to obtain in the atmosphere because of the large number of scales which govern atmospheric flows.

A K-model describing the dispersion of a passive substance was formulated in terms of Monin-Obukhov similarity theory, and then solved numerically for the case of the release of a passive substance from a point-source at ground-level. An extensive analysis was undertaken to evaluate this numerical model. To do this, we applied the widely used set of dispersion data for ground-level sources that was obtained during the Prairie Grass experiments. We simulated these dispersion experiments. Since SO₂, which was used as tracer, is known to deposit on the ground, also the effect of deposition of the tracer was investigated. The simulations showed that the vertical concentration profile is greatly affected by deposition. At a height of 1.5 m, where the measurements were made, the effect is still weak 50 m from the source, but 800 m downwind the deposition causes a decrease in the concentration by about a factor of 2. When consideration is given to the effect of deposition, the numerical solution of the diffusion equation yields excellent agreement with the measurements of the crosswind-integrated ground-level concentrations for both the 200 m and 800 m distance. Indeed, at 800 m the predictions are consistent with measurements even into the convective regime, where the use of K-models becomes dubious.

Atmospheric diffusion models are used in a rapidly increasing number of studies for controlling and/or managing air quality. In general these studies try to find the least-cost control strategy by solving the following mathematical program: (1)$${\text{select}}\;x$$(2)$${\rm{thatminimizes}}\,\gamma \left( x \right)$$(3)$${\text{subject}}\;\;{\text{to C}}\left( {x,q} \right) < {c^x}$$

The mathematical description of plume rise is well established and has been reviewed by Briggs1. As the ground level concentration of pollutants is a strong function of the effective rise of the plume above the chimney, Δh, it is important that this quantity can be calculated over a wide range of meteorological conditions. However, as noted by Briggs1 various formulae give a range of values of Δh that differ by more than an order of magnitude. In order to clarify the situation equations have been used that are closely based upon the physics of plume rise. Schatzmann2, 3, 4 has presented a description of plume rise based upon the equations of conservation of mass, momentum, concentration and thermal energy. To close the system of equations an entrainment function is used and this paper discusses the application of this model to a variety of situations.

Tracer experiments were carried out to quantify the diffuse leakages of hydrocarbons at two petrochemical complexes in Norway. Single tracer (SF₆) and dual tracer (SF₆/CBrF₃) experiments were performed for different test designs and different meteorological conditions.A simple proportionality model was applied to estimate leakage rates of ethylene, propylene, ethane, propane and isobutane from different parts of the plants. A discussion of uncertainties in the release rate estimates is also included.Dispersion models were applied to verify concentration profiles and to identify leakage areas. A model using K_z for estimating vertical spread and σ_Θ for estimating horizontal spread, including building size parameters as initial dilution factors, was best correlated to measured tracer concentrations.