This document provides information about air quality dispersion modeling and data interpretation. It summarizes the key steps in the modeling process including: (1) using Gaussian dispersion models to calculate pollutant concentrations from point sources based on parameters like emission rates, stack characteristics, and meteorological conditions; (2) accounting for plume rise using equations that consider factors like exit velocity and temperature; and (3) interpreting the results of a case study modeling sulfur dioxide emissions from multiple stacks at an industrial facility to evaluate model predictive capability.

1. Air Quality Dispersion Modeling and
Data Interpretation
S.K. Goya I
Scientist
Air Pollution Control Division, NEERI, Nagpur - 440 020
Preamble
Air pollution models are used for simulation of the transport and diffusion
of various pollutants (SPM, S02, NOx, CO etc.) being released into atmosphere
as a result of industrial combustion processes, domestic fuel burning during
cooking and vehicular movement. The models are extensively applied in
regulation and urban planning for impact assessment of existing or new sources,
forecasting of pollution episodes, evaluation of control strategies and design of air
quality surveillance programs.
Several mathematical models have been developed to determine ambient
air pollutant concentrations by assuming certain steady state conditions in
atmospheric boundary layer, and to account for various types of sources and
topographic conditions in the immediate vicinity of the air pollution sources.
These models vary from simple empirical relations to very complex numerical
solutions. Besides, complexity of models also varies with the scale, viz. from
micro climatic changes to air pollution forecasting or even global climatic change.
Time and space scales are used in air pollution dispersion and can be
described in terms of four geographical subdivisions: site specific (local),
regional, national and global. These form a reasonable classification scheme for
horizontal spatial and time scales of air quality models. At the lowest subdivision,
site specific or local situations involve considerations such as emissions, source
characteristics, initial plume rise, initial phase of mixing, local terrain and initial
transport. At higher spatial resolutions, the site-specific category is concerned
with interacting plumes from sources separated by 10-20 km. The regional scales
range from an urban area or large industrial complex to a region where urban
areas are represented as point sources in the air quality models.

2. The determination of time scales from the model application perspective
depends on the effects of the pollutant, the regulatory standards and the
variability of emissions and meteorology. The air quality model calculates
pollution concentrations at pre-selected times at locations called grid points,
which are referred to as receptor locations. The times and grid points are
required model inputs. The outcome of the AQM is highly dependent on the
availability of the meteorological input data.
The air pathway processes that control the fate of pollutants from sources
to receptor are transport, diffusion, transformation, and removal. Because of the
complexity of these processes, as well as the complications introduced by terrain
and the pollutants themselves, there exists a large and diverse family of air
quality models. Broadly, the air quality models can be categorized in to three
categories: empirical, semi-empirical and numerical. These posses a variety of
characteristics that can be used to further refine model classification. These
characteristics result from the ambient meteorological and topographical
conditions, the time and space scales inherent in the model application, the
mathematical procedures used to solve the system of equations, and the
pollutants and reaction mechanisms required to solve a particular air pollution
problem.
Gaussian Dispersion Models
Dispersion models are formulated from the fundamental differential
equations governing the conservation of species. Dispersion models are more
appropriate for the prediction of air quality because the models consider the
point-by-point transport, dispersion, generation and removal of pollutant species,
and provide for spatial and temporal variation of these processes, over
reasonable distances covering air sheds of size, 1-50 km.
Most of the models available use Gaussian plume equation (normal
distribution of pollutant concentration in vertical and horizontal directions within
the plume) dispersion calculations for all practical purposes from continuous point
217

3. sources. Fig. 1 depicts the dispersion in the horizontal and vertical directions
about the centerline of a plume from an elevated source.
z
Fig. 1 : Coordinate System Showing Gaussain Distribution
in the Horizontal and Vertical
For a continuous emission source with 0,0, H co-ordinates, the concentration
at a given point (x, y, z) can be calculated using Gaussian dispersion equation:
C(x,y,z,H) =
I n Uo g7
y z
exp
v v y
exp (z-H?l . _ f - ( z + H?
V 2 a
z ,
+ exp - ( 1 )
however, for determining concentration on ground (z = 0), the above equation
reduces to
C(x,y,0/H)=
71 UO..O-
exp M
-
7 + — j
2a f Iv y J l ^ z ;
-- (2)
where,
C - predicted ground level concentration at a receptor located at x meters
downwind and y meters cross wind of the source stack, pg/m3
Q - mass emission rate of pollutant, g/s

4. u - wind velocity at the plume center line height or at effective stack height,
m/s
H - plume center-line height or effective stack height
y - crosswind distance from the plume center line to the receptor, m
ay and az - Pasquill crosswind and vertical dispersion coefficients
The C, u, ay and oz refer to the same average period of meteorological
conditions. Based on empirical data, the dispersion coefficients (ay and az) are a
function of the atmospheric stability class (Table 1).
Table 1: Stability Categories for Dispersion Coefficients
Surface
Wind speed
at a height of
10 m (m/s)
Day Incoming Solar Radiation
(Insolation)
NightSurface
Wind speed
at a height of
10 m (m/s)
Strong Moderate Slight
>1/2 Cloud
Cover
Thinly overcast or
< 1/2 Cloud Cover
< 2 A A-B B — —
2-3 A-B B C E F
3-5 B B-C c D E
5-6 C C-D D D D
>6 C D D D D
Sky Cover
Solar Elevation Angle (degree)
Sky Cover
> 60 < 60 but > 35 < 35 but > 15
4/8 or less or any amount
of high thin clouds
Strong Moderate Slight
5/8 to 7/8 middle clouds
(7000-16000 foot base)
Moderate Slight Slight
5/8 to 7/8 low clouds
(less than 7000 foot base)
Slight Slight Slight
Insolation categories are determined using sky cover and solar elevation information.
The neutral class (D) should be assumed for all overcast conditions during day or night.
Coefficients; ay and crz can be calculated according to stability class from
the Figs. 2 & 3 respectively, as a function of downwind distance (x).
219

5. 10000
1000
100
100 1000 10000
Distance Downwind, meters
100000
Fig. 2 : Pasquill-Gifford Horizontal Dispersion Parameter, (sigma y)
as Functions of Pasquill Stability Class & Downwind Distance
10000
1000
100
100 1000 10000
Distance Downwind, meters
100000
Fig. 3 : Pasquill-Gifford Vertical Dispersion Parameter, (sigma z) as Functions of
Pasquill Stability Class and Downwind Distance

6. Plume Rise
Plume rise is calculated during the estimation of GLCs of emitted
pollutants, which are emitted from the stacks with significant gas velocities and
elevated temperatures. The resulting vertical momentum and thermal buoyancy
are modeled in the plume rise. The maximum GLC is related to the inverse of the
square of the final plume height.
Using the Briggs method for calculating the plume rise above the stack
height as a function of the downwind distance (X) from the stack, the critical
downwind distance (X*) is defined by;
X* = 14 Fb5/8
for Fb < 55m
X* = 34 Fb
2/5
for Fb > 55m
Where, Fb is the empirical buoyancy flux parameter determined by using
an empirical equation as:
Fb = g vs rs
2
(Ts-Ta)/Ts
Where, Fb is in meters and
g = acceleration of gravity, 9.8 m/s2
Vs = stack gas exit velocity, m/s
r 2
's = stack exit radius (or equivalent radius), m
Ts = gas exit temperature, °K
Ta = ambient temperature at stack exit, °K
The plume rise for unstable or neutral atmospheric conditions behaves
according to a "2/3 law", when h is the stack height (m) and H is the plume height
(m). With u as the average wind speed (m/s) at h, for x > 3.5x*, the final plume
rise (m) is empirically determined by;
H = 1.6 Fb
1/3
u"1
(3.5 x*)2/3
For x* < 3.5x*, the atmospheric turbulence comes into play and the
formula becomes;
H = 1.6 Fb
1/3
u"1
x2/3
These equations can be used for buoyant plumes (Ts >Ta) as well as for
jets - that is non-buoyant plumes with Ts s Ta. However, these semi empirical
formulas have a high degree of uncertainty.
001

7. Air Pollution Modeling and Input Data Requirement
Number of air pollution models suggested/recommended by international
agencies like USEPA are available for predicting ground level concentration of
pollutants from a single source or multiple sources at desired receptor locations.
Simple screening models, i.e. PTMAX (Point Maximum) require only point
source characteristics (like pollutant emission rate, stack height, stack tip
diameter, flue gas exit temperature and velocity). The model computes short-term
(1 hr average) maximum ground level concentrations (GLCs) and the distance of
maximum GLC occurrence from a single source, as a function of wind speed and
stability class. The model does not require meteorological data input.
Another screening model, PTDIS (Point Distance) also computes short
term (1 hr average) maximum GLCs and the distance of maximum GLC
occurrence from a single source for a given set of meteorological conditions like
wind speed, temperature, mixing height and stability class for that hour.
Many advanced models like MPTER (Multiple Point Sources with Terrain
Adjustment) and Industrial Source Complex - Short Term (ISCST) model, in
addition to source characteristics need hourly meteorological data. These models
can take up more than 100 point sources and GLCs at several hundred receptor
locations for different averaging periods up to 24 hours. These models are also
based on gaussian dispersion and are widely used for the prediction of GLCs in
EIA and regional air pollution modeling. The details of these models are well
documented and also available on the internet. Further, more sophisticated
models are developed for specific applications, e.g. coastal region, valley
situation etc.
Data input requirements for one of the widely used model, ISCST are
discussed here briefly. The following data pertaining to source characteristics,
meteorological parameters and receptor network are required as input to the
model:

8. 1. Source data
• Emission rate, (g/s)
• Stack height, (m)
• Stack top inner diameter, (m)
• Stack gas exit velocity, (m/s)
• Stack gas exit temperature, (°K)
2. Hourly meteorological data for the simulation period
• Wind speed, (m/s)
• Wind direction (degree)
• Pasquill-Giffford stability class (1 to 6)
• Mixing height, (m)
• Ambient temperature, (°K)
3. Receptor data
• Scaled receptor coordinates (x, y), (m)
• Gridded receptor coordinates generated by the model, (m)
• Height of receptor, (m)
During computations, the model considers the following options
1. Gradual Plume Rise
2. Stack-tip down wash
3. Buoyancy-induced dispersion
4. Calm processing routine
5. Missing data processing routine
6. Default wind profile exponents
7. Default vertical potential temperature gradients
8. Uniform terrain
9. No wet / dry depletion / deposition
223

9. 10. Use upper bound concentration estimates for sources influenced by
building down wash from super-squat buildings
Data Interpretation - A Case Study
Most of the air pollution models being used by USEPA and other
regulatory agencies are based on gaussian dispersion, which involves number of
assumptions and uncertainties leading to the belief that the gaussian models
normally over / under predict the ground level concentration of pollutants than the
actual concentration levels7
. The order of difference between predicted and
actual concentrations may even extend up to 80 times or even higher in some
extreme cases; however, 4-6 times variation is quite common. In order to
minimize such variations, various parameters, which have a significant bearing
on the model output results, are discussed here. A careful evaluation of these
parameters shall certainly help in understanding the predictive capability of the air
quality model and the results obtained.
Model Input Data
Source Characteristics
A total S02 emission rate of 800 kg/hr from seven major stacks in a typical
refinery is considered. Details of the individual stacks with respect to physical
height, top inside diameter, exit gas temperature and velocity along with S02
emission rate is given in Table 2. All the stack characteristics differ in one or the
other parameters.

10. Table 2 : Stack Details and SO2 Emission Rate
Stack
No.
Stack
Coordinates
(m)
Stack
Height
(m)
Stack
Diameter
(m)
Stack
Tempe-
rature
(°K)
Exit
Gas
Velocity
(m/s)
so2
Emission
Rate (g/s)
Stack
No.
X Y
Stack
Height
(m)
Stack
Diameter
(m)
Stack
Tempe-
rature
(°K)
Exit
Gas
Velocity
(m/s)
so2
Emission
Rate (g/s)
1 0 0 70 1.9 573 13.0 70.0
2 -600 -600 100 2.4 673 8.0 12.0
3 -200 -900 100 2.1 483 7.0 55.0
4 + 1230 -560 60 1.0 573 2.0 27.0
5 -600 -200 70 3.1 463 10.0 15.0
6 -250 -600 100 5.0 483 2.0 18.0
7 -240 -800 70 3.5 463 10.0 25.0
Out of 7 stacks, 3 are of 100 m, 3 of 70 m and one is of 60 m height. Stack
diameter varies from 1.9 to 5.0 m and exit gas velocity ranges between 2 & 13
m/s. The spatial distribution of the stacks is shown in Fig. 4.
-10 -8 -6 -4 -2 0 2 4 6 8 10
10
8
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1 1
J
1 / l
' ' • 1 •
A
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i.
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r
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• -8
• -10
10 -8 -6 -4 -2 0 2 4 6 8 10
Distance along X-axis in Km
Figure^. : Stack Locations and Study Area

11. Meteorological Data
Hourly surface (wind speed, wind direction & temperature) and upper air
(mixing height & stability class) meteorological data is either generated for the
specific study region or is collected from the nearby meteorological station.
Minimum data required is for one day, to calculate 24 hourly pollutant
concentrations. In this study, one month met data is averaged for the winter
season.
Receptor Data
Ground level concentrations of pollutant can be predicted within the
defined study/impact zone (e.g. 10 km X 10 km) of the emission sources. The
study area can be divided into any suitable square grid size (e.g. 400 mX400 m).
Prediction of Air Quality
The S02 concentration levels in ambient air are then predicted for the
given emission sources under the given meteorological scenario using ISCST
(Version 3) model. The model predicts pollutant concentration at the center of the
each grid. However, first few highest GLCs can be tabulated separately, as given
in Table 3.
Table 3 : Predicted First Five Highest GLCs of S02
Rank
Concentration
(l^g/m3
)
Direction
(Degree)
Distance
(Km)
1 32 124° 1.4
2 31 117° 1.8
3 31 98° 2.8
4 31 99° 2.4
5 30 97° 3.2
Direction and distance are with respect to major source
Maximum GLC of 32 [jg/m3
is predicted occurring at a distance of 1.4 km
from the major emission source in south-east direction, which is much lower that
the CPCB Standards of 80 pg/m3
for mixed use area category.
Depending upon the user's requirement, the pollutant concentrations can
be computed for different averaging periods ranging from 1 hour to 24 hours, and
for the whole simulation period. In the present case study, diurnal variation in the
predicted 8 hourly concentration at selected receptors is presented in Table 4,
which indicates occurrence of maximum GLC during 8-16 hrs at a distance of
about 1.4 km from the major source in SE direction. No concentration is predicted
in the W direction, as the wind was from N-W sector.
99R

13. Table 4 : Diurnal Variation in S02 Cone, at Selected Receptors
Period
(hrs)
S02 Concentration at Receptors
Period
(hrs)
0.4,-0.8
(Km)
1.2,-0.8
(Km)
- 1.6, 0.0
(Km)
-0.4,-1.2
(Km)
0 - 8 0.032 0.85 0.00 0.027
8 - 1 6 41.28 91.78 0.00 28.38
1 6 - 2 4 0.11 1.97 0.00 39.38
0 - 2 4 13.81 31.53 0.00 22.59
Further, S02 concentration isopleths can be drawn (using a graphical
package, SURFER) to show the spatial coverage of pollutant conc. depending
upon the prevalence of wind direction in the study region, as shown in Fig. 5.
X-axis : Distance in East Direction (Km);
Y-axis : Distance in North Direction (Km);
Z-axis : S02 Concentration (pg/m3
)
Fig. 5 : Predicted Iso-Concentration Zones of S 0 2
227