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CLASSIFICATION OF AIR POLLUTION DISPERSION MODELS: A CRITICAL
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CLASSIFICATION OF AIR POLLUTION DISPERSION 
MODELS: A CRITICAL REVIEW 
 
Proceedings of the National Seminar on Environmental Engineering with special emphasis on Mining 
Environment, NSEEME-2004, 19-20, March 2004; Eds. Indra N. Sinha, Mrinal K. Ghose & Gurdeep Singh 
Smriti Srivastava1 and Indra N. Sinha2
Abstract:Dispersion and emission of pollutants into the air is controlled by the prevaling 
meteorological conditions like wind profile, temperature profile and stability of the atmosphere. Air 
pollution dispersion models attempt to express the interrelationships of these factors in terms of 
mathematical equations. A plethora of models exist for prediction of ground level concentration of 
air contaminants. They vary in terms of their applicability (e.g. in development facilities and other 
sources of air pollution, regulatory decision-making and environmental planning). A single model is 
seldom applicable universally. 
Air pollution models are based on the theories of atmospheric physics and thermodynamics. This 
inquest looks into the theory of air pollution modelling and critically appraises the important air 
pollution dispersion models. Major types of air pollution models are described along with their 
advantages and disadvantages. Applicability of the models and their amenability to modifications 
and revisions are particularly looked into. 
Keywords: Classification of Models, Dispersion of pollutants, 
Introduction 
Of late there has been growing realisation that, an effective environmental 
management system is one that is planned along with project inception. However, this 
involves projection of a considerable amount of ‘with project environmental scenario’. Like 
other projections in project planning, the environmental prediction involves a lot of cause-
condition effect analyses. Over the years, many models have been developed to facilitate 
environmental prediction. While models developed for water environment are often 
adaptable to other situation with minor modifications, the portability of air quality model is 
rather limited. 
To access if a region will be in compliance with the pollutant air quality standard at 
some future date it is necessary to be able to predict how the pollutant concentration for the 
region will change in response to prescribed changes in sources emissions. To predict 
changes in the pollutant concentration will change requires an air quality model, that is a 
mathematical description of atmospheric transport, diffusion and chemical reactions of 
pollutants. Air quality models sometimestermed air quality simulation models which 
operate on set of input data characterising the emissions, topography and meteorology of a 
region and produce output that describe the air quality of the region. A practical model 
consists of four functional structural levels: 
set of assumptions and approximations that reduce the actual physical problem 
to an idealised one that retain the most important features of the actual problem; 
 
1 M. Tech Student, Centre of Mining Environment, Indian School of Mines, Dhanbad, Email: smriti_sri@yahoo.co.in
2 Assistant Professor, Centre of Mining Environment, Indian School of Mines, Dhanbad, Email: indranaths@yahoo.com
1 
 
 
 
 
mailto:smriti_sri@yahoo.co.in
mailto:indranaths@yahoo.com
 
Indian School of Mines, Dhanbad – 826 004 
the basic mathematical relations and auxiliary conditions that describe the 
idealised physical system; 
the computational schemes are used to solve the basic equations; and 
the computer program or code that actually perform the calculations. 
Air dispersion models are used to estimate the downwind concentration of pollutants 
emitted by various pollution sources such as industrial facilities and regional public traffic. 
Dispersion models play an important role in the industrial and regulatory communities. 
To conduct a dispersion modelling analysis, a user enters data in the following four 
major categories- 
Meteorological conditions, such as wind speed, wind direction, stability class, 
temperature and mixing height. 
Emissions parameters, such as source location, source height, stack diameter, 
gas exit velocity, gas exit temperature and emission rate 
Terrain elevation 
Building parameters, such as location, height and width. 
Classification of Air Pollution Models 
Air pollution models can be categorised into 3 generic classes: deterministic 
approach, statistical models and physical models. Deterministic models basically deals with 
different types of numerical approximations (for example finite difference and finite 
techniques) in the solution of the partial equations representing the relevant physical process 
of atmospheric dispersion. For this process an emission inventory has to be available and 
other independent, mostly meteorological variables have to be known. The deterministic 
model is most suitable for long-term planning decisions. 
In contrast to the deterministic model, the statistical one calculates ambient air 
concentrations using an empirical established statistical relationship between meteorological 
and other parameters on the other hand. Only semi quantitative conclusions can be drawn on 
some particular air quality issues. The statistical model is very useful for short-term forecast 
of concentrations. The advantage of such models is their small computational efforts that 
simulate measured concentration at one point or concentration field. No emission inventory 
is needed. The disadvantages besides that concentration measurement are needed. They can 
also be used to take into account background concentration in a deterministic model. 
In physical models, a real process is simulated on a smaller scale in the laboratory by 
a physical experiment, which models the important features of the original process being 
studied. In the case of complex air pollution situation, when detailed deterministic models 
and/or experimental field measurements become very costly, laboratory simulation using 
scaled-down models in wind tunnels or water channels is often the best approach. The most 
important advantage of physical models is that the scale-model geometry, as well as flow 
speed and other essential variables can be easily changed and controlled. In general, 
physical modelling should be used as a research tool to study specific atmospheric 
processes. As the scale of the prototype atmospheric situation decreases, the accuracy of 
physical model simulation increases. 
 
 
 
 
 
 
2
 
Institute of Public Health Engineers, India 
Deterministic Model: 
Most of the deterministic model use or are equivalent to using solutions of the 
diffusion equation. The diffusion equation is based on the principle of conservation of mass. 
The turbulent fluxes of material are expressed by the gradient relationship, i.e. it is assumed 
that the turbulent flux is proportional to the gradient of concentration and the proportionality 
‘constant’ is called the diffusion coefficient. The diffusion equation reads as follows: 
+⎟
⎠
⎞
⎜
⎝
⎛
∂
∂
∂
∂
+⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
∂
∂
∂
∂
+⎟
⎠
⎞
⎜
⎝
⎛
∂
∂
∂
∂
=
∂
∂
+
∂
∂
+
∂
∂
+
∂
∂
t
ck
ty
ck
yx
ck
xt
cw
y
cv
x
cu
t
c
zyx Source terms + 
transformation term --------------------(1) 
The symbols have following measuring: 
c = the time – averaged concentration 
x, y, z = the Cartesian coordinates 
u, v, w = the components of the time-averaged wind vector 
Kx, Ky, Kz = the diffusion coefficient in the corresponding direction 
The boundary condition at the earth’s surface has to be stated and it is often assumed 
that the diffusing material (gases) is not absorbed by the ground, i.e. the material is 
‘reflected’ into the atmosphere. The other extreme case that all material reaching the surface 
is absorbed, is not appropriate, at least not for gases. Partial reflection of the material at the 
ground is the most realistic case, but it involves the statement of another parameter, which is 
usually called the deposited velocity. 
Often a boundary condition for the upper boundary of the diffusion volume is stated, 
especially in case of an inversion. In that case, too, the total reflection assumption at the 
upper boundary is used. 
The models calculate the concentration at one receptor point from one source. If more 
than one source is present then the contributions from each source at the receptor point are 
summed. 
Steady State Models 
The steady state condition implies that all variables and parameters are constant in 
time. This includes the concentration, i.e. δc/δt =0. However, steady state solutions are often 
obtained with the time-dependent equation (δc/δt ≠0), but with all meteorological and other 
parameters kept constant. One then calculates forward in time until the steady state is 
reached for the concentration. Steady state model by the nature of the inherent assumption 
of the time constancy of the parameters can be applied only for shorter distances (order of 
10 km) and for shorter travel time (order of 2 hr) therefore the models mentioned below can 
also be used for steady state modelling. 
The Gaussian Model 
The Gaussian dispersion equation for an elevated point source is obtained by 
assuming that the pollutant concentration profiles at any down wind position, x, has the 
form of a bivariate normal distribution. 
 
 
 
 
 
 
3
5 
 
 
 
 
 
 
Air Quality Models 
 
 
Deterministic Models Statistical Models Physical Models 
 
 
 Steady State Models 
 
Time Dependent Models Regression Models Empirical Orthogonal 
Models 
 
 
 
Gaussian Model Other Models Simple 
Models 
 
 
 
 Box Model Grid Model Spectral Models 
Lagrangian and 
Random Walk 
Models 
 Trajectory Models
Fig.1: Classification of Air quality Models (Modified from Weber, 1982) 
 
Considering plume for a single stack the following assumptions are made: (a) concentration 
profiles in plume are Gaussian in both the y and z directions, (b) constant mean wind speed, 
u, and direction; continuous steady pollutant emission rate Q (c) dispersion in the x direction 
is negligible compared with bulk transport by the mean wind, (d) the pollutant is stable gas 
or aerosol which does not react chemically or settle out, (e) steady state and homogeneous 
transport condition, and (f) topography is not complex. We then obtain: 
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
⎟⎟
⎠⎞
⎜⎜
⎝
⎛ −
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
= −−
2
5.0
2
5.0
2
),,(
zyzy
Hzeye
u
QzyxC
σσσσπ
-----------(2) 
where σy and σz are the dispersion coefficients in the y and z direction respectively and h is 
the pollutant release height. This expression is valid from the stack to he down wind 
distance at which the plume intersects the ground. Considering perfect reflection the ground, 
equation 2 becomes: 
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ +
−+
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ −
−
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−=
222
2
1exp
2
1exp
2
1exp
2
),,(
zzyzy
HzHzy
u
QzyxC
σσσσσπ
----(3) 
Other Models 
All the time-dependent models can be used as steady state models. 
Simple Models 
One extremely simple model for the calculation of concentrations from area sources 
(‘ATDL-Model’) has been given, where the concentration is proportional to the source 
strength and inversely proportionality constant depends on stability, mixing height and city 
size. But even with an average proportionality constant empirically obtained the model 
gives satisfactory results. 
Time-Dependent Models – 
In a time dependent model all variables can be functions of time and the 
concentration is calculated depending on time. With a relatively few exceptions all time-
dependent models go back in principle to a solution of the diffusion equation, but 
formulations and solution methods differ. The box models and the grid models are the 
methods most widely used. 
Box model 
In a box model the atmosphere is divided into a number of boxes of given length, 
width and height. In each of the boxes the concentration is assumed to be constant. For 
each box, a budget equation is solved for each time step, taking into account the fluxes of 
material across the boundaries of each box (advective and turbulent), sources, sinks, 
sedimentation, deposition, transformation etc. such a box model is graphic, easy to 
formulate and relatively to handle. 
6 
 
 
 
 
 
Institute of Public Health Engineers, India 
Grid Model – 
The grid model solves the diffusion equation after it has been transformed into a finite 
difference equation in Eulerian space. The concentration values are obtained at the grid 
points and are averages in time and space according to the chosen time step and grid size. 
The large number of existing grid models differ with respect to- 
Resolution in time and space 
Formulation of the finite differences 
Treatment of sources and sinks 
Treatment of and assumptions relating to meteorological parameters. 
Division into horizontal and vertical diffusion 
Methods to avoid numerical diffusion 
Inclusion of chemical reactions and transformations 
Grid models and also box models are mostly used for the simulation of episodes, 
because the computational effort connected with their application is large. In fact it is so 
large that the computation of, say, hourly values for an extensive time period like a year or 
more is very time consuming. Usually simulation times greater than a few days cannot be 
afforded. A combination of grid or box models on the one had and statistical models on the 
other seems a promising way of studying emission and meteorological effects separately or 
for long term planning, if a measuring network exists 
Spectral Model – 
The spectral models differ from grid models in that the diffusion equation is 
transformed into Fourier space and then solved. The advantage here is that one avoids 
numerical truncation errors. There does not seem to be an advantage in computational 
efforts. 
Lagrangian and Random Walk Models – 
Numerical diffusion is avoided, but disadvantage is that very large computer storage 
and time is needed. The same is true for random-walk models, where particles performed a 
random walk in grid space with prescribe transition probabilities. Because of the computer 
economics involved both models don’t seem to be applicable when frequency statistics of 
concentration are needed. 
Trajectory Models - 
In the trajectory model is a special type of Lagrangian model where the trajectory of 
the center of gravity of a diffusing cloud is computed first and the diffusion with respect to 
this center of gravity this taken into the account. Again large computational effort is 
required for a multiple source model. It seems to be however applicable for short forecast in 
connection with dangerous, unintentional releases of the material, example in the case of an 
accident. 
 
 
 
 
 
7
 
Indian School of Mines, Dhanbad – 826 004 
Conclusion 
So, far as regulatory applications are concerned, Gaussian approach seems to be the 
best. Gifford (1975), a leading authority in the field of atmospheric dispersion has noted: the 
Gaussian formula, properly used, is peerless as a practical diffusion-modelling tool. It is 
mathematically simple and flexible and moreover it is accord with much through not all-
working theory. 
Deriving the Gaussian dispersion equation requires the assumption of constant 
conditions for the entire plume travel distance from the emission source point to the 
downwind ground-level receptor. Yet we cannot say with any reasonable certainty that the 
wind-speed at the plume centreline height and the atmospheric stability class are known 
exactly or that they are constant for the entire plume travel distance. Whether such 
homogeneity actually occurs is a matter of pure chance, particularly for large distances. 
Also, determining the exact wind-speed and atmospheric stability class at the plume 
centreline height requires (a) the prediction of the exact plume rise and (b) the exact relation 
between wind-speed and altitude ... neither of which are achievable. 
In short, the Gaussian models assume an ideal steady-state of constant meteorological 
conditions over long distances, idealised plume geometry, uniform flat terrain, complete 
conservation of mass, and exact Gaussian distribution. Such ideal conditions rarely occur. 
References 
Cheremisinoff, P. A. (ed.) (1989). Encyclopaedia of Environmental Control Technology, Vol. 2 (Air 
Pollution Control). Gulf Publishing Company, Mousten.1066p 
Gifford, F. A. (1961). Uses of Routine Meteorological Observations for Estimating Atmospheric 
Dispersion. Nuclear Safety. pp. 47 – 62. 
Gifford, F. A.(1975) Atmospheric Dispersion Models on Air Pollution Applications. In Lectures on 
Air Pollution and Environmental Impact Analysis. Ed D. A Haugen. American Meteorological 
Society. pp 35-58 
Johnson, W.B., Sklarew, R. C and Turner, D. B. (1976). Urban Air Quality Simulation Modeling. In 
Air Pollution, Third Edition, Vol. 1 (Air Pollutants, Their Transformation and Transport) 
edited by Arthur C. Stern. Academic Press, I Florida. pp 503-562. 
Juda-Rezler, K. (1989).Air Pollution Modeling. In Encyclopedia of Environmental Control 
technology, Vol. 2 (Air Pollution Control) edited by Cheremisinoff Paul N. pp. 83 – 134. 
Pasquill, F. (1961). The Estimation of the Dispersion of Windborne Material. Meteorol. Mag. pp. 33 
– 45. 
Sarkar Ujjaini and Sarkar Priyabrata (1993). Atmospheric Dispersion Models-A Review. Indian 
Journal of Environmental Protection, Vol. 13 (4), Apr. pp 248-255. 
Seinfeld John H., (1986). Atmospheric Chemistry and Physics of Air Pollution. John Wiley & Sons, 
New York.738 p. 
Seinfeld John H., (1988). Ozone Air Quality Models A Critical Review. Journal of Air Pollution 
Control Association Vol. 38(5) May. pp 616-645 
Stern, A. C.(ed), (1976). Air Pollution, Vol. 1 (Air Pollutants, Their Transformation and Transport), 
Third Edition. Academic Press, Florida.715p 
Stern, A. C.(ed) (1977). Air Pollution, Vol. 5 (Air Quality Management), Third Edition. Academic 
Press, Florida. 700p 
Weber, E. (1982). Air Pollution: Assessment Meteorology and Modelling. Plenum Press. 329 p 
Zannetti, P., (1986). A New Mixed Segment – Puff Approach for Dispersion Modeling. Atmospheric 
Environment, Vol.20 (6). pp1121-1130.8
 
Institute of Public Health Engineers, India 
 
AEROPOL Developed at Tartu observatory and most extensively used by 
Hendrikson and Co Environmental consultants. The model relies on 
stationary Gaussian dispersion and enables to use point, are and line 
sources and calculate also dry and wet deposition. AEROPOL is 
described by Kassik (1997, 2000) and validated in internationally 
accepted way. 
AirViro Developed by indie AB (Sweden) and used by Tallinn City 
Government for urban air pollution calculations (Gaussian and 
numerical dispersion schemes) 
ALOHA ALOHA (Areal Locations of Hazardous Atmospheres) is a program for 
the evaluation of gas transport and dispersion in atmosphere in 
emergency conditions. It takes into account both the toxicological and 
physical properties of the pollutant and the characteristics of the site 
under study, such as the atmospheric conditions and the release 
conditions. 
APRAC-3 Computes hourly averages of carbon monoxide for urban locations. 
*BLP Buoyant line plume model is a Gaussian plume dispersion model for 
aluminum reduction plants and graphite electrode plants. 
*CALINE-3 Calculates carbon monoxide concentrations near highways and arterial 
streets. 
CALINE 4 An improved version of CALINE 3 that includes emissions from 
highways, intersections and parking lots. 
CALMPRO A processor for output of short-term models that calculates 
concentration for non-calm hours based on recommendations in EPA’s 
modelling guideline 
CAP88-PC Developed by USEPA and OAK Ridge National laboratory, used by the 
Institute of Physics (Tartu) for studies of dispersion and further 
migration of radio-nuclei from industrial emissions 
*CDM-2 This climatological dispersion model determines long-term quasi-stable 
pollutant concentrations. 
CHAVG A somewhat slower post-processor than RUNAVG that determines the 
second-highest non-overlapping running average. 
COMPLEX 1 A multiple point source code with terrain adjustment using sequential 
meteorological date to calculate concentration using the VALLEY 
algorithm 
COMPLEX II A multiple point source code with terrain adjustment that use a 
Pasquill-Gifford sigma y. 
CCOMPLEX/PFM A modified version of complex I and II, which contains an option for 
potential flow computations. 
DEGADIS A U.S. Coast Guard model that analyses the effects of dense gas 
releases and calculates the shape of the area in which concentrations 
will exceed a user-selected values. 
DIMULA DIMULA (Multiple Source Dispersion Models) is an air pollution 
simulation model based on the gaussian plume approximation, with a 
special correction to deal with calm conditions (where the classical 
analytical formula is not applicable). It works on short ranges and both 
 
 
 
 
 
9
 
Indian School of Mines, Dhanbad – 826 004 
short and long term time horizons, non reactive primary pollutant, 
point, areal, or line sources, and flat terrains. DIMULA has a user 
interface to allow easy data input and display of output conccentrations. 
HIWAY 2 COMPUTES THE hourly concentrations of non-reactive pollutants 
downwind of roadways 
INPUFF An integrated puff model for analysing non-continuous accident 
releases of substances over a period of minutes to several hours 
*ISCLT Industrial source complex long-term is a steady state Gaussian plume 
model, which can be used to calculate long-term pollutant 
concentrations from an industrial source complex. 
*ISCST Industrial source complex short-term is a steady state Gaussian plume 
model, which can be used to calculate short-term pollutant 
concentrations from an industrial source complex. 
KAPPA-G The model (A Non Gaussian Plume Dispersion Model) simulates air 
pollution from a point source using a Gaussian approximation for the 
horizontal diffusion, but a Demuth solution of the vertical diffusion. It 
may thus use information about the vertical wind profile or try to 
eveluate it through the Similarity Theory. The program may take into 
account multiple point sources and many time intervals, each 
characterized by different meteorological conditions. 
LONGZ Designed to calculate the long-term pollutant concentration produced at 
a large number of receptors by emissions from multiple stack, building 
and area sources in urban areas. 
MESOPLUME A mesoscale plume segment (or ‘bent plume’) model designed to 
calculate concentrations of SO2 and SO4 over large distance. 
MESOPAC and MESOFILE are ancillary processors. 
MESOPUFF-2 A variable-trajectory regional-scale Gaussian puff model especially 
designed to simulate the air quality of multiple point sources at long 
distances. 
MPDA-1.1 A processor of meteorological data for use with TUPOS-2. 
MPTDS A modification of MPTER to explicitly account for gravitational 
setting and/or deposition loss of a pollutant. 
*MPTER A multiple point source Gaussian model with optional terrain 
adjustments. 
MPTER (NYC 
VERSION) 
A version of MPTER modified by the New York City Department of 
Environment Protection, 
OCD Offshore and coastal dispersion model employs direct measurement of 
atmospheric turbulence to calculate onshore concentrations from 
offshore emissions. 
PAL-2 (Point, area and line source algorithm) – this short-term Gaussian 
steady-state algorithm estimates concentrations of stable pollutants 
from point, area and line sources. 
PALDS A modification of PAL and has the capability to explicitly treat the 
gravitational settling and/or deposition loss of pollutant on calculated 
concentrations. 
PBM A simple stationary single cell numerical model that calculates hourly 
averages of ozone and other photochemical pollutants. 
 
 
 
 
 
 
10
 
Institute of Public Health Engineers, India 
 
PEM-2 An EPA developed modification of the TEM8B model for use in urban 
area. 
PRISE The model PRISE (Plume Rise and Dispersion Model) calculates all of 
the phases (rising, bending over the (quasi-) equilibrium dispersion) of 
the behaviour of the plume emitted by a stack in atmosphere or by a 
pipe in deep water, in one continuous formulation, taking fully into 
account the ambient meteorological (hydraulic) conditions. 
PTPLU-2 A point source dispersion Gaussian screening model for estimating 
maximum surface concentrations for one-hour concentrations. 
PTDIS Estimated short-term concentrations directly downwind of a point 
source at distance specified by the user. 
PTMAX Performs an analysis of the maximum short-term concentrations from a 
single point source as a function of stability and wind speed. 
PTMTP Estimates the concentrations from a number of point sources at a 
number of arbitrarily located receptor points at or above ground level. 
PULVUE-2 A visibility model designed to predict the transport, atmospheric 
diffusion, chemical conversion, optical effects and surface deposition of 
point-source emissions. 
ROADWAY-2 A finite difference model which predicts pollutant concentration near a 
roadway 
RUNAVG A post-processor for determining the second-highest non-overlapping 
running average. 
SHORTZ Designed to calculate the short-term pollutant concentrations produced 
at a large number of receptors by emissions from multiple stack, 
building and area sources in urban areas. 
SPILLS A model available from NTIS especially useful foe calculating the 
evaporation rate of substances from a liquid pool and their dispersion in 
the atmosphere. 
TCM2B Texas climatological model is a climatological Gaussian plume model 
for determining long-term average pollutant concentrations of non-
reactive pollutants. 
TEM8AB Taxes episodic model is a sequential, steady state Gaussian plume 
model for determining short-term concentrations of non-reactive 
pollutants. 
TRPUF A Trinity Consultants, Inc. model employed to study the dispersion of 
individual puff releases. 
TUPOS-P The post-processor for TUPOS 2 
TUPOS-2 An improved version of MPTER that estimates dispersion directly from 
fluctuation statistics at plume level 
VALLEYA steady state, univariant Gaussian plume dispersion model useful for 
calculating concentrations on any type of terrain. 
 
 
 
 
 
 
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https://www.researchgate.net/publication/228712544
	CLASSIFICATION OF AIR POLLUTION DISPERSION MODELS: A CRITICA
	Introduction
	Classification of Air Pollution Models
	Deterministic Model:
	Steady State Models
	The Gaussian Model
	Other Models
	Simple Models
	Time-Dependent Models –
	Box model
	Grid Model –
	Spectral Model –
	Lagrangian and Random Walk Models –
	Trajectory Models -
	Conclusion
	References