Air Quality Models
Introduction
Governing Equation and Components
Types of Air Quality Models
US EPA Models
Introduction
Air quality models use mathematical and numerical techniques to simulate the
physical and chemical processes that affect air pollutants as they disperse and react in
the atmosphere. Based on inputs of meteorological data and source information like
emission rates and stack height, these models are designed to characterize primary
pollutants that are emitted directly into the atmosphere and, in some cases, secondary
pollutants that are formed as a result of complex chemical reactions within the
atmosphere. These models are important to our air quality management system
because they are widely used by agencies tasked with controlling air pollution to both
identify source contributions to air quality problems and assist in the design of
effective strategies to reduce harmful air pollutants. For example, air quality models
can be used during the permitting process to verify that a new source will not exceed
ambient air quality standards or, if necessary, determine appropriate additional control
requirements. In addition, air quality models can also be used to predict future
pollutant concentrations from multiple sources after the implementation of a new
regulatory program, in order to estimate the effectiveness of the program in reducing
harmful exposures to humans and the environment.
There are many different types of atmospheric dispersion models - all sorts of simple
models as well as complex models. In a given situation it may be justified to use a
simple model - it all depends on the conditions. A model should be fit for the purpose
for which it is applied. There are numerous ways to classify models (e.g., they can be
classified according to the policy issue they address). Examples: industrial pollution,
urban air quality, nuclear emergencies, chemical emergencies, climate change, etc.
Another option is to classify models according to model concept. Examples: Gaussian
models, Eulerian models, Lagrangian models, receptor models, etc. The most
commonly used air quality models include the followings:
Dispersion Model: Dispersion modeling uses mathematical formulations to
characterize the atmospheric processes that disperse a pollutant emitted by a source.
Based on emissions and meteorological inputs, a dispersion model can be used to
predict concentrations at selected downwind receptor locations. These air quality
models are used to determine compliance with National Ambient Air Quality
Standards (NAAQS), and other regulatory requirements such as New Source Review
(NSR) and Prevention of Significant Deterioration (PSD) regulations.
Photochemical Model: Photochemical air quality models have become widely
recognized and routinely utilized tools for regulatory analysis and attainment
demonstrations by assessing the effectiveness of control strategies. These
photochemical models are large-scale air quality models that simulate the changes of
pollutant concentrations in the atmosphere using a set of mathematical equations
characterizing the chemical and physical processes in the atmosphere. These models
are applied at multiple spatial scales from local, regional, national, and global.
There are two types of photochemical air quality models commonly used in air quality
assessments: the Lagrangian trajectory model that employs a moving frame of
reference, and the Eulerian grid model that uses a fixed coordinate system with
respect to the ground. Earlier generation modeling efforts often adopted the
Lagrangian approach to simulate the pollutants formation because of its
computational simplicity. The disadvantage of Lagrangian approach, however, is that
the physical processes it can describe are somewhat incomplete. Most of the current
operational photochemical air quality models have adopted the three-dimensional
Eulerian grid modeling mainly because of its ability to better and more fully
characterize physical processes in the atmosphere and predict the species
concentrations throughout the entire model domain.
Receptor Model: These models are observational techniques which use the chemical
and physical characteristics of gases and particles measured at source and receptor to
both identify the presence of and to quantify source contributions to receptor
concentrations. Unlike photochemical and dispersion air quality models, receptor
models do not use pollutant emissions, meteorological data and chemical
transformation mechanisms to estimate the contribution of sources to receptor
concentrations. Instead, receptor models use the chemical and physical characteristics
of gases and particles measured at source and receptor to both identify the presence of
and to quantify source contributions to receptor concentrations. These models are
therefore a natural complement to other air quality models and are used as part of
State Implementation Plans (SIPs) for identifying sources contributing to air quality
problems. The US EPA has developed the Chemical Mass Balance (CMB) and
UNMIX models as well as the Positive Matrix Factorization (PMF) method for use in
air quality management. CMB fully apportions receptor concentrations to chemically
distinct source-types depending upon the source profile database, while UNMIX and
PMF internally generate source profiles from the ambient data.
Puff Model: Quasi-instantaneous and short-term releases are frequently viewed as
"puff" releases. A puff release scenario assumes that the release time and sampling
times are very short compared to the travel time from the source to the receptor. Due
to the limited data available to estimate the diffusion coefficients for puff diffusion, a
number of models use the Pasquill-Gifford values. Since these coefficients were
developed specifically for plumes, their use in puff models is questionable. In addition,
most puff models assume a normal or Gaussian concentration distribution within the
plume. This assumption overlooks the in-puff fluctuations.
Plume Model: Continuous releases are generally modeled as a plume. The
assumption here is that the release time is much greater that the time of travel from
the source to the receptor. There are a number of approaches to modeling plumes,
each with its own focus, assumptions, and limitations. These approaches can be
categorized as:
Gaussian plume models
Meandering plume models
Probability distribution function models
K-thoery models
Statistical models
Similarity Models
Second order closure and eddy simulation models
Within these categories are a number of different models. Not all models using these
approaches are at a developmental stage where they can be practicably applied,
however. Some, like the statistical and second-order closure approaches, are too
computer-intensive for routine use. Many of the other model types have little in the
way of the field validation needed for application to real-world situations with
confidence. Of the list, the most frequently used model types for odor modeling are
the Gaussian model and the fluctuating plume-puff model.
The Gaussian model of diffusion is the most widely used model for plume dispersion.
Its most attractive feature is that it fits what we see and experience in the real world
for a range of conditions. In addition, the mathematics of the model is fairly
straightforward. On the other hand, Gaussian models need significant empirical input
to be used for practicable dispersion estimates, making the model results highly
dependent on the conditions of the sampling used to derive the empirical values. The
basic assumptions of the Gaussian model are:
Conservation of mass
Continuous emissions
Steady-state conditions
Lateral and vertical concentration profiles are normal distributions
Governing Equation
The ambient air pollutant concentrations are determined by four factors: sources,
transformation processes, transport processes, and removal mechanisms. The inputs
to air quality models can be classified into two categories: meteorological data and
source emissions. Note that topography (terrain and surface land use) is generally
specified included within the meteorological data.
Governing equation for pollution concentration:
Ci
C
C
C
 2Ci
 2Ci
U i V i W i   y


 Si
z
t
x
y
z
y 2
z 2
where Ci is the mass concentration of pollution, U, V, and W are the mean velocity
components in the x-, y-, and z-direction, respectively;  y and  z are the
dispersion coefficients for the lateral and vertical directions, and Si is the generation
rate for pollutant.
Therefore, the second to fourth terms are for transport processes, the first and second
terms on the right hand side are for the dispersion due to turbulence and the last term
is for source and transformation processes. Note that Si includes both sources and
transformation processes; however, the removal mechanisms may be shown in the
governing equation or the boundary conditions.
For inert species at steady state, the governing equation can be simplified as
U
Ci
C
C
 2Ci
 2Ci
V i W i   y


z
x
y
z
y 2
z 2
For flat terrain at stationary state, the equation is U
because V W  0 and U is constant and  
x
.
U
Ci Ci
 2Ci
 2Ci

 y


z
x

y 2
z 2
Therefore, the solution for this
 y2
Q
z2 
exp  

equation is Ci 
 . This is the Gaussian plume
 2 2 2 2 
2 U  y z
y
z 

dispersion from a continuous and steady stack emission into a uniform and stationary
domain.
Methods to solve the partial differential equation can be found in Crank (1976) “The
Mathematics of Diffusion.” Thus, the concentrations in the lateral and vertical
directions are both normal distributions. For unsteady state and reactive species,
numerical methods are used to solve the system of simultaneous partial differential
equations.
The method for chemical transformation processes for each pollutant can be divided
into two different types: explicit chemical mechanism and lumped chemical
mechanism. The chemical transformation processes for inorganic speices, like
S-containing and N-containing species are generally computed using explicit
mechanisms. However, lumped chemical mechanism is used for VOCs in the
current reactive air quality models. For example, there are 51 species and 156
chemical reactions in CB05 mechanism.
Types of Air Quality Models
 y
10 R
1   2 y 2
A. Gaussian plume models:  X  
e
V 2 y z 

2
6
B. Puff model
( z  H )2 
   ( z  H2)2

2

 e z  e 2 z 2 




C. Box models
EKMA approach
D. Lagrangian models (Forward- or Backward-trajectory analysis)
2580.00
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2560.00
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45
11
730
741
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6
48
53
54 49
55
56
57
2500.00
59
8
50
74458
13
51
60
7
52
2480.00
2460.00
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120.00
140.00
160.00
180.00
200.00
220.00
240.00
E. Three-dimensional Grid models
The horizontal scale of three-dimensional grid models can be up to several hundreds or even thousands kilometers and the vertical scale may be
up to several tens kilometers. Therefore, both the horizontal and vertical coordinates are computed in various ways and their definitions are
shown in the followings:
Horizontal coordinates:
Coordinate
Map Parameters
Map Scale (m)
Lat.-long
N/A
N/A
M=1
Lambert
P  1  P  2 two lat. determine the
projection cone.
P  0 , central meridian
P  0 , P  0 : lat. & long. of coordinate
Mercator
origin with in the tangent circle.
Pr :angle between cylinder axis and the North
m
Note
1
sin( / 2  1 )  tan( / 4   / 2) 


sin( / 2   )  tan( / 4  1 / 2) 
 sin( / 2  2 )   tan( / 4  2 / 2) 
n  ln 


 sin( / 2  1 )   tan( / 4  1 / 2) 
2
( x , x )  (long, lat) are in degrees
1
( x cent , x
cent
)  (0 , 0 ) for the center of
1
1
2
coordinate system. ( x , x ) are in meters.
1
cos 0
m
cos 
2
( x cent , x
2
cent
)  (0 , 0 ) for the center of
1
2
coordinate system. ( x , x ) are in meters.
polar axis.
P  0 , P  0 : lat. & long. of the point of
Stereo-graphic
tangency.
2
Pr :angle from true north to x -axis
1
1  sin 0
m
1  sin 
( x cent , x
P is the UTM zone P , P not used
m=1
cent
)  (0 , 0 ) for the center of
1
2
coordinate system. ( x , x ) are in meters.
1
UTM
2
( x cent , x
2
cent
) are offset from the UTM
1
2
coordinate origin. ( x , x ) are in meters.
Vertical coordinates:
1. Height coordinate: suitable for representing surface and PBL parameterizations
and time independent and intuitive
2. Pressure coordinate: suitable for describing weather; often used for hydrostatic
atmosphere; and time dependant
3. Time independent terrain-influenced coordinate: Accounts for topography and
time independent
Terrain-influenced height coordinate -  z 
z  zsfc
H  zsfc
Often used for non-hydrostatic atmosphere
Terrain-influenced reference Pressure -  po 
P  Ptop
Psfc  Ptop
Sigma-z with logarithmic transformation
4. Time-dependent terrain-influenced coordinates
Hydrostatic pressure (normalized) -  p 
5. Step-mountain Eta coordinate
P  Ptop
P sfc  Ptop
 P  Ptop   Po ( zsfc )  Ptop 
 

 P sfc  Ptop   Po ( zsfc )  Ptop 
   p sfc  

Comparison of different vertical coordinates
Comparison of scales for different types of air quality models
E. Receptor Model
The total concentration at a receptor site is the sum of the contributions from all
sources.
For example, Fetotal = Fesoil + Feauto + Fecoal +….
In general, the concentration of element i at the receptor site can be expressed as:
m
Ci   f ij aij s j
i  1,2,.....
j 1
where Ci is the concentration of elemenet i,
aij is the fraction of element i from source j,
fij is the fraction representing any modification to the source composition aij
due to atmospheric processes that occur between sources and receptor,
and
sj is the contribution from sources j at the receptor.
Thus, the fijaij is the fraction of species i in any particular concentration from source j
at the receptor. Generally, the value of fij is assumed to be one, that is, the source
signature aij is not modified by atmospheric processes occurring between sources and
receptors. Therefore,
m
Ci   aij s j
j 1
i  1,2,....., n
US EPA Models
The US EPA models are grouped below into four categories.
Preferred and recommended models

AERMOD - An atmospheric dispersion model based on atmospheric boundary
layer turbulence structure and scaling concepts, including treatment of
multiple ground-level and elevated point, area, and volume sources. It handles
flat or complex, rural or urban terrain and includes algorithms for building
effects and plume penetration of inversions aloft. It uses Gaussian dispersion
for stable atmospheric conditions (i.e., low turbulence) and non-Gaussian
dispersion for unstable conditions (high turbulence). Algorithms for plume
depletion by wet and dry deposition are also included in the model. This
model was in development for approximately 14 years before being officially
accepted by the U.S. EPA.

CALPUFF - A non-steady-state puff dispersion model that simulates the
effects of time- and space-varying meteorological conditions on pollution
transport, transformation, and removal. CALPUFF can be applied for
long-range transport and for complex terrain.

BLP - A Gaussian plume dispersion model designed to handle unique
modelling problems associated with industrial sources where plume rise and
downwash effects from stationary line sources are important.

CALINE3 - A steady-state Gaussian dispersion model designed to determine
pollution concentrations at receptor locations downwind of highways located
in relatively uncomplicated terrain.

CAL3QHC and CAL3QHCR - CAL3QHC is a CALINE3 based model with
queuing calculations and a traffic model to calculate delays and queues that
occur at signalized intersections. CAL3QHCR is a more refined version based
on CAL3QHC that requires local meteorological data.

CTDMPLUS - A Complex Terrain Dispersion Model (CTDM) plus algorithms
for unstable situations (i.e., highly turbulent atmospheric conditions). It is a
refined point source Gaussian air quality model for use in all stability
conditions (i.e., all conditions of atmospheric turbulence) for complex terrain.

OCD - Offshore and Coastal Dispersion Model (OCD) is a Gaussian model
developed to determine the impact of offshore emissions from point, area or
line sources on the air quality of coastal regions. It incorporates overwater
plume transport and dispersion as well as changes that occur as the plume
crosses the shoreline.
Alternative models

ADAM - Air Force Dispersion Assessment Model (ADAM) is a modified box
and Gaussian dispersion model which incorporates thermodynamics,
chemistry, heat transfer, aerosol loading, and dense gas effects.

ADMS-3 - Atmospheric Dispersion Modelling System (ADMS-3) is an
advanced dispersion model developed in the United Kingdom for calculating
concentrations of pollutants emitted both continuously from point, line,
volume and area sources, or discretely from point sources.

AFTOX - A Gaussian dispersion model that handles continuous or puff, liquid
or gas, elevated or surface releases from point or area sources.

SLAB - A model for denser-than-air gaseous plume releases that utilizes the
one-dimensional equations of momentum, conservation of mass and energy,
and the equation of state. SLAB handles point source ground-level releases,
elevated jet releases, releases from volume sources and releases from the
evaporation of volatile liquid spill pools.

DEGADIS - Dense Gas Dispersion (DEGADIS) is a model that simulates the
dispersion at ground level of area source clouds of denser-than-air gases or
aerosols released with zero momentum into the atmosphere over flat, level
terrain.

HGSYSTEM - A collection of computer programs developed by Shell
Research Ltd. and designed to predict the source-term and subsequent
dispersion of accidental chemical releases with an emphasis on dense gas
behavior.

HOTMAC and RAPTAD - HOTMAC is a model for weather forecasting used
in conjunction with RAPTAD which is a puff model for pollutant transport and
dispersion. These models are used for complex terrain, coastal regions, urban
areas, and around buildings where other models fail.

HYROAD - The Hybrid Roadway Model integrates three individual modules
simulating the pollutant emissions from vehicular traffic and the dispersion of
those emissions. The dispersion module is a puff model that determines
concentrations of carbon monoxide (CO) or other gaseous pollutants and
particulate matter (PM) from vehicle emissions at receptors within 500 meters
of the roadway intersections.

ISC3 - A Gaussian model used to assess pollutant concentrations from a wide
variety of sources associated with an industrial complex. This model accounts
for: settling and dry deposition of particles; downwash; point, area, line, and
volume sources; plume rise as a function of downwind distance; separation of
point sources; and limited terrain adjustment. ISC3 operates in both long-term
and short-term modes.

OBODM - A model for evaluating the air quality impacts of the open burning
and detonation (OB/OD) of obsolete munitions and solid propellants. It uses
dispersion and deposition algorithms taken from existing models for
instantaneous and quasi-continuous sources to predict the transport and
dispersion of pollutants released by the open burning and detonation
operations.

PLUVUEII - A model that estimates atmospheric visibility degradation and
atmospheric discoloration caused by plumes resulting from the emissions of
particles, nitrogen oxides, and sulfur oxides. The model predicts the transport,
dispersion, chemical reactions, optical effects and surface deposition of such
emissions from a single point or area source.

SCIPUFF - A puff dispersion model that uses a collection of Gaussian puffs to
predict three-dimensional, time-dependent pollutant concentrations. In
addition to the average concentration value, SCIPUFF predicts the statistical
variance in the concentrations resulting from the random fluctuations of the
wind.

SDM - Shoreline Dispersion Model (SDM) is a Gaussian dispersion model
used to determine ground-level concentrations from tall stationary point
source emissions near a shoreline.
Screening models
These are models that are often used before applying a refined air quality model to
determine if refined modelling is needed.

AERSCREEN - The screening version of AERMOD. It produces estimates of
concentrations, without the need for meteorological data, that are equal to or
greater than the estimates produced by AERMOD with a full set of
meteorological data. AERSCREEN is still under development and is not
currently available to the public.

CTSCREEN - The screening version of CTDMPLUS.

SCREEN3 - The screening version of ISC3.

TSCREEN - Toxics Screening Model (TSCREEN) is a Gaussian model for
screening toxic air pollutant emissions and their subsequent dispersion from
possible releases at superfund sites. It contains 3 modules: SCREEN3, PUFF,
and RVD (Relief Valve Discharge).

VALLEY - A screening, complex terrain, Gaussian dispersion model for
estimating 24-hour or annual concentrations resulting from up to 50 point and
area emission sources.

COMPLEX1 - A multiple point source screening model with terrain
adjustment that uses the plume impaction algorithm of the VALLEY model.

RTDM3.2 - Rough Terrain Diffusion Model (RTDM3.2) is a Gaussian model
for estimating ground-level concentrations of one or more co-located point
sources in rough (or flat) terrain.

VISCREEN - A model that calculates the impact of specified emissions for
specific transport and dispersion conditions.
Photochemical models
Photochemical air quality models have become widely utilized tools for assessing the
effectiveness of control strategies adopted by regulatory agencies. These models are
large-scale air quality models that simulate the changes of pollutant concentrations in
the atmosphere by characterizing the chemical and physical processes in the
atmosphere. These models are applied at multiple geographical scales ranging from
local and regional to national and global.

Models-3/CMAQ - The latest version of the Community Multi-scale Air
Quality (CMAQ) model has state-of-the-science capabilities for conducting
urban to regional scale simulations of multiple air quality issues, including
tropospheric ozone, fine particles, toxics, acid deposition, and visibility
degradation.

CAMx - The Comprehensive Air quality Model with extensions (CAMx)
simulates air quality over many geographic scales. It handles a variety of inert
and chemically active pollutants, including ozone, particulate matter, inorganic
and organic PM2.5/PM10, and mercury and other toxics.

REMSAD - The Regional Modeling System for Aerosols and Deposition
(REMSAD) calculates the concentrations of both inert and chemically reactive
pollutants by simulating the atmospheric processes that affect pollutant
concentrations over regional scales. It includes processes relevant to regional
haze, particulate matter and other airborne pollutants, including soluble acidic
components and mercury.
References:
US EPA website: www.epa.gov/ttn/scram
Tonnesen G., J. Olaguer, M. Bergin, T. Russell, A. Hanna, P. Makar, D. Derwent, and
Z. Wang (1999) Air Quality Models,