This document discusses a one-dimensional point source air pollution steady state model, focusing specifically on the Gaussian plume model (GPM) for air quality modeling. It outlines key assumptions, model principles, advantages and disadvantages, and presents a case study analyzing pollutant concentration from a factory affecting nearby residential areas. The study involves detailed modeling steps to estimate pollutant dispersion based on various meteorological and emission parameters.

1. One dimensional point source air
pollution steady state model
Elias Barsenga
School of Chemical Engineering and Bio Engineering
Addis Ababa Institute of Technology
March, 2022
Modelling in Environmental Engineering (ChE8301)
Instructor: Prof. Zebene Kiflie

2. Outline
• Introduction
• Types of AQM
• Gaussian Plume Model (GPM)
• Assumptions
• Principles and formula
• Advantage and Disadvantages of the model
• Case study- Example
August 11, 2023 2

3. Introduction
• Air Quality Modelling (AQM) is a
mathematical representation of the
relationship between emission and air
quality considering transport, dispersion
and transformation of compound emitted
in to the air.
• it helps:
• to estimate the pollutant concentration at
various locations around pollution source
• to predict future concentrations under
specific scenarios
• to design effective control strategy to reduce
emission of the pollutant
• to identify source contribution to air quality
problems
August 11, 2023 3
Emission
Mathematical
Model
Air Quality
Model Input
Parameters
Meteorological
Data

4. Classification of AQM
• Based on time period
• Short-term vs Long-term models
• Based on pollutant type
• Non-reactive model vs reactive model
• Based on coordinate system used
• Grid based vs trajectory
• Based on level of sophistication
• Screening vs refined
• Based on pollutant source
• Point Source vs Line Source vs Area Source vs Volume source
August 11, 2023 4

5. Types of air quality models
August 11, 2023 5
Air Quality Models
Physical Wind tunnel
Statistical
Regression
Empirical
Deterministic
Dynamic
Box
Grid
Spectral
Gaussian Puff
Steady State
Gaussian Plume
model

6. Gaussian Plume Model (GPM)
• Is used to model air pollution transport
downwind direction from as stationary
(point source)
• Is the most widely used type of AQM
• It is developed based on the assumptions
• Emission is constant (steady state)
• Stability of the atmosphere can be
adequately represented by meteorological
data
• Cross wind is minimal or negligible
• Terrain is flat near the source
• The plume is reflected back into the air
when it reaches the ground (no sorption)
• Plumes of different sources do not interact
August 11, 2023 6

7. Assumptions of GPM
• Emission is constant (steady state)
• Stability of the atmosphere can be adequately represented by
meteorological data
• Cross wind is minimal or negligible
• Terrain is flat near the source
• The plume is reflected back into the air when it reaches the ground (no
sorption)
• Plumes of different sources do not interact
August 11, 2023 7

8. Principle of GPM & Formula
• As a plume travels downwind, it disperses horizontally and vertically
• The model estimate the concertation of pollutant downwind as function of:
• Effective stack height:
• The plume rises together with the physical stack height
• Increase as the exit velocity and exit temperature increase
• Mass rate of emission of the pollution
• Wind speed and direction
• Increased wind speed decrease plume rise but increases dilution
• Atmospheric stability
• The more unstable the atmosphere, the greater diluting factor
• Inversions about the stack height restrict vertical dilution
August 11, 2023 8

9. Principle of GPM & Formula
𝐶 𝑥, 𝑦, 𝑧 =
𝑄
2𝜋𝜎𝑦𝜎𝑧
exp −
𝑦2
2𝜎𝑦
2 exp −
𝑧 − 𝐻 2
2𝜎𝑧
2
+ exp −
𝑧 + 𝐻 2
2𝜎𝑧
2
• Where:
• Q = Emission rate (μg/s)
• σy = Horizontal dispersion of emission (m)
• σz = Vertical Dispersion of emission (m)
• U = average wind speed at stack height (m/s)
• H = Effective Stack Height (m)
• H = ℎ ∗ +∆𝐻
∆𝐻 =
𝑣𝑠
𝑢
∗ 𝑑 ∗ 1.5 + 0.00268 ∗ 𝑃
𝑇𝑠 − 𝑇𝑎
𝑇𝑠
∗ 𝑑
• Where:
• Vs = Gas existing velocity (m/s)
• d = stack diameter (m)
• P = Pressure (kPa)
• Ts = Temperature of gas exiting the stack (K)
• Ta = Ambient air Temperature (K)
August 11, 2023 9

10. August 11, 2023 10

11. Atmospheric Stability vs Plume behavior
• Unstable atmosphere:
• Rapid mixing occurs due to the high turbulence
in the atmosphere and this produces a looping
plume.
• This may create higher concentration close to the
stack if the plume touches the ground.
• Stable atmosphere:
• vertical dispersion is suppressed by the stability
of the atmosphere and produces a fanning plume.
• the pollution doesn’t spread towards the ground,
resulting in very low pollution concertation at
the ground level.
• Neutral Atmosphere:
• Since the atmospheric stability doesn’t encourage
or suppress the dispersion, the plume tend to
spread equally in vertical and horizontal direction
forming a coning plume
August 11, 2023 11

12. Advantage and disadvantage of GPM
Advantage
• Produce results that match closely
with experimental data
• Simple in their mathematics
• Quicker than numerical models
• Do not require super computers
Disadvantage
• Not suitable if the pollutant is
reactive in nature
• Unable to predict concentrations
beyond radius of approximately 20
Km
• For greater distances, wind
variations, mixing depths and
temporal variations become
predominant
August 11, 2023 12

13. Steps of GPM Modelling
August 11, 2023 13
•Step 1:
•Determine
the atmospheric
stability class
•Step 2:
•Calculate wind
speed at
the stack height
•Step 3:
•Calculate effec
tive stack height
•Step 4:
•Determine disp
ersion
parameters
σy and σz
•Step 5:
•Calculate
downwind
pollutant
•concentration

14. Maximum ground level pollutant
concentration estimation with gaussian
plume model- A Case Study
August 11, 2023 14

15. residential houses that reside bordering the
factory were valued less significantly than their
equivalents built away from the factory.
በተለይም በንፋስ ስልክ ላፍቶ ክፍለከተማ በሚገኘው
የጀሞ የጋራ መኖሪያ ቤቶች አከባቢ ንዋሪዎች
ከመስታወት ፋብሪካው በሚወጣው ጭስ ከፍተኛ የሆነ
የጤና ችግር እየዳረጋቸው መሆኑን በማስሳት ዘለቄታዊ
መፍትሄ እንዲሰጣቸው ጠይቀዋል ፡፡
August 11, 2023 15

16. About the factory
• Ethiopia Hansom International Glass
was established in 2007, the only
manufacturer of glass in East Africa at
the time.
• It produces clear sheet glass products
to meet domestic demand, but also
exports glass to other neighbouring
countries.
• The enterprise’s annual production
capacity is 42,000 tonnes,
• The main raw materials are silicon
sand, soda ash limestone, feldspar and
dolomite.
August 11, 2023 16
Source: https://www.cccme.cn/products/detail-8084770.aspx

17. Objective:
• to estimate the maximum ground level pollutant that concentration that reaches
condominium housing sites near the factory
• to investigate the effect of different parameters on the concentration of
pollutant reaching the sites
August 11, 2023 17

18. Assumptions
• In addition to the general assumption of the GPM, the following
assumptions are taken for the modelling in this case study
• The factory is assumed to work for 300 days a year and average stack height
of 51m with average emission rate of PM10 =1.6 g/s
• The emission released from the factory are assumed to be non-reactive
• The emissions reaches the study location with out blockage
• The three site are assumed to lie in the same line downwind direction
• Only dispersion of PM is considered for this modelling neglecting other
pollutants
August 11, 2023 18

19. Modelling Parameters
August 11, 2023 19
Monthly average meteorological data for Addis Ababa
Months
Parameters
Surface Wind Speed Solar Radiation Cloud Cover Overcast Ambient Temperature (Ta)
m/s W/m2 % K
January 3.35 670.00 48 283.15
February 3.44 700.00 51 284.26
March 3.44 710.00 57 285.37
April 3.17 660.00 65 285.93
May 3.08 670.00 61 285.93
June 2.28 580.00 65 285.37
July 2.10 480.00 74 285.37
August 2.01 520.00 66 285.37
September 2.32 610.00 49 284.82
October 3.40 690.00 40 283.71
November 3.44 690.00 39 282.59
December 3.35 660.00 43 282.04
Average 2.95 636.67 55 284.49
Source: https://weatherspark.com/y/100668/Average-Weather-in-Addis-Ababa-Ethiopia-Year-Round

20. Modelling Parameters
August 11, 2023 20
Emission related data
Parameter Unit Quantity Source of Data
Exit velocity of stack gas m/s 10.63 Reznik, R. B. (1976)
Stack height M 51 Reznik, R. B. (1976)
Stack gas temperature K 710 Reznik, R. B. (1976)
Stack diameter M 2.42 Reznik, R. B. (1976)
Production rate ton//year 42000
UNIDO 2022 Report on Chemical
industries Ethiopia
Emission Rate (Emission factor 1.35 g/kg) g/s 1.6 Reznik, R. B. (1976)

21. Selected receptor locations
August 11, 2023 21
Parameter Unit Quantity Source of Data
Condominium Site 1 m 400
Google Map
Condominium Site 2 m 700
Condominium Site 3 m 2000

22. Step 1- Determination of Stability Class
• Was determined by using the wind speed, incoming solar radiation and the cloud
coverage
• Based on the result found:
• The atmospheric stability of the city in the day time is slightly unstable or class “C”.
• On the other hand, during the night time the atmospheric condition becomes more stable
August 11, 2023 22
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Avg
Day Time C B B C C C C C C B B C C
p value 0.2 0.15 0.15 0.2 0.2 0.2 0.2 0.2 0.2 0.15 0.15 0.2 0.2
Night Time D E E E E F F F E D D D F
p value 0.25 0.4 0.4 0.4 0.4 0.6 0.6 0.6 0.4 0.25 0.25 0.25 0.6

23. Step 2 – Determination of wind speed at the stack height
• First determine the wind speed (𝑢) at the height of the stack (51m)
𝑢
𝑢𝑜
=
𝑧
𝑧𝑜
𝑝
• Where:
• 𝑢 𝑎𝑛𝑑 𝑢0 are wind speed at height 𝑧 𝑎𝑛𝑑 𝑧𝑜respectively
• 𝑝 is a function of atmospheric stability class
• Therefore: wind speed at the height of the stack :
𝑢 = 𝑢𝑜 ∗
𝑧
𝑧𝑜
𝑝
= 4 ∗
51
10
0.2
= 5.54
𝑚
𝑠
August 11, 2023 23
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Avg.
Wind speed @ 10m above surface (m) 3.35 3.44 3.44 3.17 3.08 2.28 2.10 2.01 2.32 3.40 3.44 3.35 2.95
Day Time wind speed @ stack height (m) 4.64 4.40 4.40 4.40 4.27 3.16 2.91 2.79 3.22 4.34 4.40 4.64 4.09
Night Time wind speed @ stack height (m) 5.04 6.60 6.60 6.09 5.92 6.06 5.58 5.35 3.49 5.11 5.17 5.04 7.84

24. Step 3: Determination of the effective stack height
∆ℎ =
𝑣𝑠
𝑢
∗ 𝑑 ∗ 1.5 + 0.00268 ∗ 𝑃
𝑇𝑠 − 𝑇𝑎
𝑇𝑠
∗ 𝑑
• The effective stack heigh (H):
𝐻 = ∆ℎ + ℎ
August 11, 2023 24
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
18.00
20.00
Day Time Night Time
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Avg.
Plume raising height (m) 10.47 11.06 11.05 11.05 11.37 15.38 16.69 17.43 15.09 11.21 11.07 10.48 11.89
Effective stack height (m) 61.47 62.06 62.05 62.05 62.37 66.38 67.69 68.43 66.09 62.21 62.07 61.48 62.89
Plume raising height (m) 9.66 7.36 7.36 7.98 8.21 8.02 8.70 9.09 13.92 9.53 9.41 9.66 6.20
Effective stack height (m) 60.66 58.36 58.36 58.98 59.21 59.02 59.70 60.09 64.92 60.53 60.41 60.66 57.20

25. Step 4: Calculating dispersion parameters
To determine 𝜎𝑦 and 𝜎𝑧: 𝜎𝑦 = 𝑎𝑥0.894
& 𝜎𝑧 = 𝑐𝑥𝑑
+ 𝑓
August 11, 2023 25
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Avg.
Site 1
(x = 400m)
a 104 156 156 104 104 104 104 104 104 156 156 104 104
c 61 106.6 106.6 61 61 61 61 61 61 106.6 106.6 61 61
d 0.911 1.149 1.149 0.911 0.911 0.911 0.911 0.911 0.911 1.149 1.149 0.911 0.911
F 0.911 1.149 1.149 0.911 0.911 0.911 0.911 0.911 0.911 1.149 1.149 0.911 0.911
Sy 45.84 68.76 68.76 45.84 45.84 45.84 45.84 45.84 45.84 68.76 68.76 45.84 45.84
Sz 26.47 40.50 40.50 26.47 26.47 26.47 26.47 26.47 26.47 40.50 40.50 26.47 26.47
Site 2
(x = 700m)
a 104 156 156 104 104 104 104 104 104 156 156 104 104
c 61 106.6 106.6 61 61 61 61 61 61 106.6 106.6 61 61
d 0.911 1.149 1.149 0.911 0.911 0.911 0.911 0.911 0.911 1.149 1.149 0.911 0.911
f 0 3.3 3.3 0 0 0 0 0 0 3.3 3.3 0 0
Sy 75.61 113.41 113.41 75.61 75.61 75.61 75.61 75.61 75.61 113.41 113.41 75.61 75.61
Sz 44.08 74.06 74.06 44.08 44.08 44.08 44.08 44.08 44.08 74.06 74.06 44.08 44.08
Site 3
(x 2000 m)
a 104 156 156 104 104 104 104 104 104 156 156 104 104
c 61 108.2 108.2 61 61 61 61 61 61 108.2 108.2 61 61
d 0.911 1.098 1.098 0.911 0.911 0.911 0.911 0.911 0.911 1.098 1.098 0.911 0.911
f 0 2 2 0 0 0 0 0 0 2 2 0 0
Sy 193.27 289.90 289.90 193.27 193.27 193.27 193.27 193.27 193.27 289.90 289.90 193.27 193.27
Sz 114.70 233.61 233.61 114.70 114.70 114.70 114.70 114.70 114.70 233.61 233.61 114.70 114.70

26. Step 5: Ground level concentration calculation
• The maximum concentration at distance “x” occurs at the centre of the plume or C (x,0,0)
𝐶 𝑥, 0,0 =
𝑄
𝜋𝑢𝜎𝑦𝜎𝑧
𝑒𝑥𝑝
−
𝐻2
2𝜎𝑧
2
August 11, 2023 26
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Avg.
Day Time
Site 1 6.10 12.87 12.87 6.13 6.13 5.73 5.49 5.33 5.78 12.96 12.86 6.10 6.11
Site 2 12.45 9.72 9.72 12.91 13.15 15.58 16.16 16.44 15.43 9.83 9.72 12.45 13.52
Site 3 4.29 1.65 1.65 4.52 4.64 6.16 6.64 6.90 6.05 1.67 1.65 4.29 4.84
Night Time
Site 1 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.0
Site 2 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.0
Site 3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

27. Results
August 11, 2023 27

28. Average maximum ground level pollutant concentration at the 3 sites
• The average pollutant concentration in the day time at site 2 (x=700m) is than both sites (x=400m & x=2000m).
• The concentration of pollutant at all the three locations in much higher in the day time than in the night time.
• Both situation are a result of the stability of the atmosphere,
August 11, 2023 28
6.11
13.52
4.84
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
400m 700m 2000m
Concentration
(μg/m
3
)
Receptor location
(a) (b)
Maximum ground level concentration at the three sites
0.00E+00
2.00E-13
4.00E-13
6.00E-13
8.00E-13
1.00E-12
1.20E-12
400m 700m 2000m
Concentration
(μg/m
3
)
Receptor location

29. August 11, 2023 29
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
18.00
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Concentration
(μg/m
3
)
Month
400m 700m 2000m 2 per. Mov. Avg. (400m) 2 per. Mov. Avg. (700m) 2 per. Mov. Avg. (2000m)
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
C B B C C C C C C B B C

30. August 11, 2023 30
0.0
0.0
0.0
0.0
0.1
0.1
0.1
0.1
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Concentration
(μg/m
3
)
Months
C(400) C(700) C(2000) 2 per. Mov. Avg. (C(400)) 2 per. Mov. Avg. (C(700)) 2 per. Mov. Avg. (C(2000))
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Avg
D E E E E F F F E D D D F

31. August 11, 2023 31
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
Concentration
(μg/m3)
Distance (m)
Class C (Day Time) Class F (Night Time)
Effect of distance from source location on maximum ground level concentration

32. August 11, 2023 32
Effect of stack height on maximum ground level concentration during (a) day time and (b) night time
0.00
20.00
40.00
60.00
80.00
100.00
120.00
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100105110115120
Concentration
(μg/m
3
)
Stack Height (m)
(b)
Site 1 Site 2 Site 3
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100105110115120
Concentration
(μg/m
3
)
Stack Height (m)
(a)
Site 1 Site 2 Site 3

33. Conclusion
• Due to the difference in atmospheric stability, the amount of pollution
reaching the site in the day time is significantly higher than the amount
reaching at the night time
• The site which is located is the most affected by pollution both in the
day and night time compared to the other two sites
• The stack height and distance from source location have significant
effect on the amount pollutant reaching a location
August 11, 2023 33

34. Recommendation
• Even if most of the outcomes of this model are inline with estimations
found in literature, it is necessary to make real time measurements on
the ground considering most of the data are literature approximations.
• Other contaminants should have to be included in the modelling to
make a concrete conclusion on the effect of the pollutants on health
August 11, 2023 34

35. References
1. Reznik, R. B. (1976). Source assessment: Flat glass manufacturing plants. Final Report.
2. Bayou, T., & Assefa, A. (1989). Solar radiation maps fot Ethiopia. Zede Journal, 8, 7-15.
3. Elperin, T., Fominykh, A., & Krasovitov, B. (2016). Effect of raindrop size distribution on scavenging of aerosol particles from
Gaussian air pollution plumes and puffs in turbulent atmosphere. Process Safety and Environmental Protection, 102, 303-315.
4. Coulter, C. T. (1994). An evaluation of a solar radiation/delta-T method for estimating Pasquill-Gifford (PG) stability
categories (No. CONF-940115-). American Meteorological Society, Boston, MA (United States).
5. Supporting the improvement of the development strategy and policy for ETHIOPIA’S TECHNOLOGY-BASED CHEMICAL
INDUSTRY. (n.d.). Retrieved March 16, 2022, from https://open.unido.org/api/documents/14100685/download/UNIDO-
Publication-2019-14100685
6. Otaru, A. J., Odigure, J. O., Okafor, J. O., & Abdulkareem, A. S. (2013). Model prediction of particulate dispersion from a
cement mill stack: case study of a cement plant in Nigeria. IOSR Journal Of Environmental Science, Toxicology And Food
Technology, 3(2), 97-110.
August 11, 2023 35

36. August 11, 2023 36
Thank You !!!