Air pollution meteorology

and dispersion modelling

by
Gazala Habib
Air Pollution meteorology
❑Coriolis force: an effect whereby a mass moving in a rotating system
experiences a force (the Coriolis force ) acting perpendicular to the
direction of motion and to the axis of rotation. On the earth, the effect
tends to deflect moving objects to the right in the northern hemisphere
and to the left in the southern and is important in the formation of
cyclonic weather systems.
❑ Early 20th century: named after Gaspard Coriolis (1792–1843), French
engineer.
❑ The Coriolis effect is due to rotation of the earth in anti-clockwise
direction.
❑ The Coriolis effect causes the moving object to follow as curved path
❑ In northern hemisphere the curvature is towards right.
French mathematician and
❑ In southern hemisphere the curvature is towards left. physicist Gaspard-Gustave
❑ No Coriolis effect on equator and maximum Coriolis effect of poles. de Coriolis.
Coriolis effect and wind pattern

0 km/h
805 km/h

805 km/h
589 km/h
1394 km/h
273 km/h
1667 km/h
Coriolis effect and Naming of winds:
❑ Winds are named by where they come from, so N.E. trade winds are blowing towards the S.W.

Since the Earth is rotating to the East (anticlockwise), air has momentum in that direction. Coriolis effect in northern
hemisphere can be explained as below and southern hemisphere is mirror of NH:
Let's assume the earth (radius 6400 km) is 40192 km in circumference at the equator. Thus, the speed of land at the equator i s
1,667 km per hour to the east.
At 30o N it’s 33450 km around, and the speed is 1394 km/h (273 km/h less than equator).
At 60o N it’s 19312 km, and 805 km/h (589 km/h less than 30o N).
At the North Pole, it’s 0 km and 0 km/h (you'd be spinning, but not moving) (805 km/h less than 60 o N). Notice that
the change in speed increases close to the poles. This results in the Coriolis effect being strongest at the poles, and weakest at
the equator.

❑ The eastward speed of air moving towards the equator from the Subtropical High (30 N) is 1394 km/h, but as
it moves south (towards equator) the land is moving faster (1667 km/h) than that. So the land starts to slip to
the east, and the apparent motion of the wind is to the west. Thus, we have winds blowing toward the
southwest, which are then called N.E. Tradewinds.

❑ The eastward speed of air moving towards the north pole from the Subtropical High is 1394 km/h, but as it
moves north the land is moving slower (805 km/h) than that. So the apparent motion of the wind is to
the east. Thus, we have winds blowing toward the northeast. In this case they are just called the westerlies.

❑ Finally, air moving from the polar high towards the equator has no eastward speed, so the earth moving under
it starts to slip east, and the wind has an apparent west motion. Thus, they are called easterlies.

❑ Therefore, it is the inertia of the winds while the earth spins under them that generates the appearance of
winds moving east or west.
Atmosphere
• Mechanical turbulence: wind speed at ground surface is
zero and it increases with height due to pressure
gradient, this cause shearing which results in random
fluctuation of wind speed and direction to the overall
average wind velocity. The eddies form due to
mechanical turbulence. Greater the wind speed, greater
the mechanical turbulence, easier the dispersion.

• Thermal turbulence: This is caused by heating of the

ground surface.
Atmospheric structure

• https://www.youtube.com
/watch?v=bqiu4x-syDA

https://www.youtube.com/watch?v=ObnWb7yspxA
 Atmospheric structure
❖ Troposphere: The lowest layer of the atmosphere, extending from the Earth's surface up to the tropopause, which is at
10-15 km altitude depending on latitude and time of year; characterized by decreasing temperature with height; rapid
vertical mixing. Over the equator the average height of the tropopause is about 18 km; over the poles, about 8 km.
Contains almost all the atmospheric water vapour. Accounts for small fraction of atmosphere’s total height but it contains
80% of its total mass. The reason for decline in temperature is the increasing distance from the sun-warmed earth
(Seinfeld and Pandis, 2016).
❖ Stratosphere: Extends from the tropopause to the stratopause (From ~ 45 to 55 km altitude); The isothermal zone
extend from 11-20 km and the the increase in temperature is due to absorption of UV by O 3, which leads to slow vertical
mixing.
❖ Mesosphere: Extends from the stratopause to the mesopause (From ~ 80 to 90 km altitude); Due to presence of very
low amount of gas the solar energy absorption is low resulting in decrease in temperature with height and rapid vertical
mixing. Mesopause is the coldest point in the atmosphere.
❖ Thermosphere: Extends from 90-500 or 1000 km. The region above the mesopause; characterized by high temperatures
as a result of absorption of short-wavelength radiation by N2 and O2; rapid vertical mixing. The thermosphere is ~200 C
hotter during daytime compared to night and ~500 C hotter when Sun is very active than other time. The space begins at
100 Km and space shuttles orbit in thermosphere. Ultraviolet and X-ray photons energy from the Sun also dissociate the
gas molecules in the thermosphere. The temperature in the upper later of thermosphere may range from 500 C to 2000
C. In the upper thermosphere, atomic oxygen (O), atomic nitrogen (N), and helium (He) are the main components of air.
With absorption of high amount of UV and X-ray energy thermosphere expands and may extend up to 1000 Km the
change in air density causes the drag force on space shuttles, this force should be taken in account while designing the
space shuttle.
❖ Ionosphere: Extends 150-200 km. Ionosphere is a region of the upper mesosphere and lower thermosphere where ions
are produced by photoionization.
❖ Exosphere. The outermost region of the atmosphere (>500 km altitude) where gas molecules with sufficient energy can
escape from the Earth's gravitational attraction.
Planetary Boundary Layer (PBL)
• The troposphere can be divided into 2 parts based on turbulence
or friction. The Friction is generated by the earth's surface, but
that aloft friction is negligible in comparison. At some point in
the atmosphere, there is a zone where friction goes from
significant to insignificant. The lower layer of air which is
subjected to frictional processes is known as the planetary
boundary layer (PBL). The remaining air in the troposphere is
known as the free atmosphere (because it is free of frictional
influences.
Mixed layer
• During the daytime, surface heating leads to convective motion in the PBL. Heat
transfer from the surface forms rising warm air. Radiative cooling from clouds forms
sinking cooler air. Convective motion also leads to significant turbulence which mixes
the air within this layer. Because of the convective motion and significant mixing of air,
this sub-layer is called the convective layer or mixed layer.

• Above the mixed layer is a stable layer which prevents the continued upward motion of
thermals. This stable layer also restricts turbulence, preventing frictional influences
from reaching above the PBL.

• This stable layer is called the entrainment zone, because it is here where air from
above the PBL entrains into the mixed layer.

• During the day, the mixed layer reaches heights over one km and makes up the entire
layer of the PBL above the surface layer.

• However, the mixed layer vanishes with the sun as the thermally driven convection
ceases.
Mixed layer height and temperature
• Given an early morning sounding with surface temperature of 5 degC and a
lapse rate of 3 K/km, find the mixed layer potential temperature and depth at
10 am, when the cumulative heating is 500 K-m (0.5 K-km).

𝑄𝑑 𝜃𝑀𝐿 = 𝜃𝑠𝑢𝑟𝑓 + 𝑧𝑖 × (∆𝜃Τ∆𝑧)

• 𝑧𝑖 =
0.5 ∆𝜃Τ∆𝑧
• Where
• 𝑧𝑖 = 𝑚𝑖𝑥𝑒𝑑 𝑙𝑎𝑦𝑒𝑟 ℎ𝑒𝑖𝑔ℎ𝑡
• 𝑄𝑑 = 𝐶𝑢𝑚𝑢𝑙𝑎𝑡𝑖𝑣𝑒 𝑑𝑎𝑦 𝑡𝑖𝑚𝑒 ℎ𝑒𝑎𝑡𝑖𝑛𝑔 (𝐾 − 𝑚 𝑜𝑟 𝐶 − 𝑚)
• ∆𝜃 Τ∆𝑧 = 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑙𝑎𝑝𝑠𝑒 𝑟𝑎𝑡𝑒 (𝐾/𝑚)
• 𝜃𝑀𝐿 = 𝑚𝑖𝑥𝑒𝑑 𝑙𝑎𝑦𝑒𝑟 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝐾
• 𝜃𝑠𝑢𝑟𝑓 = 𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 (𝐾)
Air parcel movement in the atmosphere
Air parcel rise and cloud formation
 Atmospheric stability
• Stability: The tendency of the atmosphere to resist or enhance vertical motion is termed stability. It is
related to both wind speed and change of air temperature with height (lapse rate).
• Neutral
• Stable
• Unstable

❑ Neutral atmosphere: when thermal structure of the atmosphere neither resists nor enhances the
mechanical turbulence.

❑ The rate of temperature decrease with altitude is called as dry adiabatic lapse rate if heat
absorption/release by moisture is involved then it is called wet adiabatic lapse rate.

❑ Dry adiabatic lapse rate is 9.8 C/km

❑ Wet adiabatic lapse rate is ~6.5 C/km

❑ When the environmental lapse rate at particular place is equal to dry adiabatic lapse rate or wet adiabatic
lapse rate then the atmosphere is called neutral.
Atmospheric stability
ELR= Environmental lapse rate; MALR=moist Adiabatic lapse rate
DALR=Dry adiabatic lapse rate

ELR<MALR<DALR ELR>DALR>MALR

https://www.youtube.com/watch?v=ObnWb7yspxA
https://www.youtube.com/watch?v=KDP_cLB8TCg
Conditional instability

MALR<ELR<DALR
Inversion
Problem
• Given the following temperature and elevation data, determine the
stability of the atmosphere.

Elevation (m) Temperature (°C)

2 14.35
324 11.13

∆𝑇 𝑇2 − 𝑇1
=
∆𝑍 𝑍2 − 𝑍1
Atmospheric dispersion

❑ Factor affecting the dispersion of pollutants

❑ Source characteristics: Buoyancy (mass or
❑ Industrial plume discharge vertical through a duct or stack density<surrounding)
Vertical velocity
❑ After leaving the stack the plume tends to expand and mix with ambient air

❑ Horizontal air will tend to bend the plume downward. While the plume is rising,
bending and moving in horizontal direction the pollutants are being diluted by
ambient air surrounding the plume.
𝐻𝑒
❑ The plume rise is affected by both upward inertia of discharge gas stream and by
its buoyancy.

❑ Vertical inertia is related to exit gas velocity and mass.

❑ The plume’s buoyancy is related to the exit gas mass relative to the surrounding
gas mass.
Atmospheric dispersion
❑Increasing the exit gas velocity or the exit gas temperature will increase the plume rise.

❑The plume rise together with physical stack height is called the effective stack height.

❑The plume rise above the discharge point affects the downwind concentration at ground.

❑Higher the plume rise, the greater distance is for diluting the contaminated gases as they
expand and mix downward.
Atmospheric dispersion
• Downwind distance: The greater the distance between the point of discharge and a
ground level receptor downwind, the greater will be the volume of air available for
diluting the contaminants discharge before it reaches the receptor.

• Wind speed and direction: Wind direction determines the direction in which the
contaminated gas stream move across local terrain. The wind speed affects the plume
rise, rate of mixing and ground level concentration.
• An increase in wind speed will decrease the plume rise by bending the plume over more rapidly.
• An increase in wind speed will also increase the rate of dilution of effluent tending to lower the
downwind concentrations
• The decrease in plume rise tend to increase the ground level concentration.
• These effect, govern the distance downwind of source at which the ground level concentration
would be maximum.

• Stability: More unstable the atmosphere, the greater the diluting power.
Dispersion modelling
• A dispersion model is a mathematical description of the
meteorological transport and dispersion process that is quantified in
terms of source and meteorological parameters during a particular
time.
• The meteorological parameters required as input include wind
direction, wind speed and atmospheric stability.
• In some models vertical mixing and lapse rate can also be included.
• Stack physical height, diameter of stack at discharge point, the exit
gas temperature and velocity, and mass rate of emission of pollutants.
 Gausian Dispersion model
• Assumptions
1. Atmospheric stability: Atmospheric stability is uniform through out the layer in which the contaminated
gas stream is discharged.

2. Turbulent diffusion: Turbulent diffusion is a random activity and hence the dilution of the contaminated
gas stream in both the horizontal and vertical direction can be described by the normal or Gaussian
equation.

3. Effective height: The contaminated gas stream is released into the atmosphere at a distance above ground
level that is equal to the physical stack height plus the plume rise.

4. Diffusion: No diffusion in x direction.

5. No reaction no deposition: The pollutant material that reaches ground level is totally reflected back into
the atmosphere that means no reaction no deposition at ground.
1. The ground reflection is accounted for by assuming a virtual source located at a distance of –H with
respect to ground level, and emitting an imaginary plume with the same source strength as the real
source being modelled.
2. The same general idea can be used to establish other boundary layer conditions for the equations, such
as limiting horizontal or vertical mixing.
Gaussian dispersion model
 Gausian dispersion model
• 𝜒 𝑥, 𝑦, 𝑧, 𝐻 =

• 𝜒 𝑥, 𝑦, 𝑧, 𝐻 = 𝐷𝑜𝑤𝑛𝑤𝑖𝑛𝑑 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛, 𝑔/𝑚3

𝑔
• 𝐸 = 𝑒𝑚𝑖𝑠𝑠𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑝𝑜𝑙𝑙𝑢𝑡𝑎𝑛𝑡,
𝑠
• 𝑠𝑦 , 𝑠𝑧 = 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑝𝑙𝑢𝑚𝑒 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛, 𝑚
• 𝑢 = 𝑤𝑖𝑛𝑑 𝑠𝑝𝑒𝑒𝑑, 𝑚/𝑠
• 𝑥, 𝑦, 𝑧 𝑎𝑛𝑑 𝐻 = 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑠, 𝑚

Gausian distribution curve

 Gausian dispersion model

• When concentration at ground level z=0

2 2
𝐸 1 𝑦 1 −𝐻
𝜒 𝑥, 𝑦, 0, 𝐻 = 𝑒𝑥𝑝 − 𝑒𝑥𝑝 −
𝜋𝑠𝑦 𝑠𝑧 𝑢 2 𝑠𝑦 2 𝑠𝑧

• Ground level concentration at the centre of the plume (z=0, y=0)

•
Plume rise

• 𝐻 = ℎ + Δ𝐻
• Oak ridge formula (US Weather Bureau,1953)
𝑣𝑠 𝑑 𝑇𝑠 −𝑇𝑎
Plume rise Δ𝐻 = 𝑢
1.5 + 2.68 × 10−2 𝑃 𝑇𝑠
𝑑

• 𝑣𝑠 = 𝑠𝑡𝑎𝑐𝑘 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦, 𝑚/𝑠

• 𝑑 = 𝑠𝑡𝑎𝑐𝑘 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟, 𝑚
• 𝑢 = 𝑤𝑖𝑛𝑑 𝑠𝑝𝑒𝑒𝑑, 𝑚/𝑠
• 𝑃 = 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 (𝑘𝑃𝑎)
• 𝑇𝑠 = 𝑆𝑡𝑎𝑐𝑘 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒, 𝐾
• 𝑇𝑎 = 𝐴𝑖𝑟 𝑇𝑒𝑚𝑝𝑟𝑎𝑡𝑢𝑟𝑒, 𝐾
 Pasquill Stability classes

• The values of 𝑠𝑦 , 𝑠𝑧 vary with

• Turbulent structure of the atmosphere
• Height above the surface
• Surface roughness
• Sampling time over which the concentration
is to be estimated
• Wind speed and distance from the source
A=Very unstable atmospheric condition
B=unstable atmospheric condition
C=slightly unstable atmosphere to neutral
D=stable conditions
E= Stable atmospheric condition
F=Very stable atmospheric condition
Horizontal dispersion
coefficient

𝑠𝑦 = 𝑎𝑥 0.894
𝑠𝑧 = 𝑐𝑥 𝑑 + 𝑓
Vertical dispersion
coefficient
 Problem

• It has been estimated that the emission of SO2 from a coal fired power
plant is 1656.2 g/s. A 3 km downwind on an overcast afternoon, what is
the centreline concentration of SO2 if the wind speed is 4.5 m/s.
• Stack parameters:
• Height=120 m
• Dimeter=1.2 m
• Exit velocity=10 m/s
• Temperature= 315 °C
• Atmospheric conditions:
• Pressure=95.0 kPa
• Temperature=25 °C
• Steps
𝑣𝑠 𝑑 −2 𝑇𝑠 −𝑇𝑎
• Δ𝐻 = 1.5 + 2.68 × 10 𝑃 𝑑
𝑢 𝑇𝑠
• Stability
• Overcast, wind velocity 4.5 m/s
• Stability class from Table 3.1 is D
• Determine the 𝑠𝑦 and 𝑠𝑧 using figure
• 𝑠𝑦 = 190 𝑚
• 𝑠𝑧 = 65 𝑚
 𝐸 1 −𝐻 2
𝜒 𝑥, 0,0, 𝐻 = 𝑒𝑥𝑝 −
𝜋𝑠𝑦 𝑠𝑧 𝑢 2 𝑠𝑧

1656.2 1 128 2
𝜒 𝑥, 0,0, 𝐻 = 𝜋190∗65∗4.5
𝑒𝑥𝑝 − 2 65

10 −3 𝑔
𝜒 𝑥, 0,0, 𝐻 = 1.36 × 𝑚3 𝑜𝑓 𝑆𝑂2
Problems
• A dumpsite fire emits 3 g/s of Nox. Determine the Nox concentration at 2 km
downwind if the wind speed is 5 m/s and the stability class is D. what is the
maximum concentration at ground level and also at 50 m above ground.
[Ans: 25.5 mg/m3; 15.5 mg/m3].
• A 915 MW power plant with a load factor of 72.5% and efficiency of 40% uses
coal as a fuel source. The coal has a 1% sulphur content and a calorific value
of 30 MJ/kg. The stack tip is 200 m high with a diameter of 7 m. If neutral
conditions prevail, determine the maximum ground level concentration of
SO2 at 1, 10, and 100 km from the plant. u=6.5 m/s; Ts=150 C, Ta=20 C, Vs=15
m/s P=95 KPa. [Ans: 1X10-20 mgm-3; 4.8X10-2 mgm-3; 2.2X10-2 mgm-3]
𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑙𝑜𝑎𝑑
[Hint: 𝑙𝑜𝑎𝑑 𝑓𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 𝑝𝑜𝑤𝑒𝑟 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑢𝑛𝑖𝑡 = 𝑝𝑒𝑎𝑘 𝑙𝑜𝑎𝑑
; peak load is the maximum design load=915 MW; 32 g sulfur produce 64
g SO2]
 Problems
• Determine the stack height for an industry source emitting 150 kg/d of 1,2
dichloromethane (C4H4Cl2) if the residential complex is sited 1.5 km
downwind and the ambient limit should not exceed 700 mgm-3. The neutral
condition (D) occur 85% of the time and this is to be the design atmospheric
condition. The characteristics are:
Gas exit velocity = 15m/s
Gas exit temperature = 150 C
Stack tip diameter= 3 m
Ambient temperature= 20 C
Horizontal wind velocity at stack top= 6 m/s
Emission rate 150 kg/d
 Inversion aloft

• When an inversion is present, plume cannot

disperse vertically once it reaches the inversion
layer.
• The plume will begin to mix downward when it
reaches the base of the inversion layer.
• The downward mixing will begin at a distance
𝑋𝐿 from the stack.
• 𝑋𝐿 distance is a function of the stability in the
• When the plume reaches twice the initial contact with the layer below the inversion.
inversion base, the plume is said to be completely mixed • Empirically
throughout the layer below the inversion.
• Beyond the distance 2𝑋𝐿 the concentration of pollutants • 𝑠𝑧 = 0.47 𝐿 − 𝐻
may be estimated by using the following equation. • L= height to bottom of inversion layer, m
• H= effective stack height, m
𝐸 1 𝑦2
𝜒= 1 𝑒𝑥𝑝 −
2 𝑠𝑦
2𝜋 2 𝑠𝑦 (𝑢)(𝐿)
 Problems

• Determine the distance downwind from the stack at which we must

switch to the inversion form of the dispersion model given the
following meteorological situation:
• Effective stack height=50 m
• Inversion base=350 m
• Wind speed= 7.3 m/s
• Cloud cover= none
• Time= 11:30 h
• Season= summer
• 𝑠𝑧 = 0.47 𝐿 − 𝐻
• 𝑠𝑧 = 0.47 350 − 50 = 141
• Stability class for wind speed >6
m/s On clear day

141 = 61𝑥 0.911 + 0

𝑥 = 2.4 𝑚
Plume behaviour
 Plume behaviour

• Looping plume
• Wavy plume occurs in super adiabatic environment (ELR>DALR) that means the
atmosphere is highly unstable.

• Unstable atmosphere rapid air movement takes place both in upward and
downward direction and plume becomes looping plume.
• The pollutant dispersion is better and the concentration does not build up near
ground.
 Plume behaviour
• Conning Plume
• Under sub-adiabatic conditions (ELR<DALR) the vertical mixing is low and atmosphere
is slightly stable, the plume attains conning like structure.

• Also when horizontal wind velocity is greater than 32 km/h and the cloud blocking
solar radiation at day time and terrestrial radiation night time, neutral plume tends to
form cone like structure, called conning plume.
Plume behaviour
• Fanning
• Fanning occurs in stable conditions.
• The inversion lapse rate discourages vertical motion without
prohibiting horizontal motion, and the plume may extend
downwind from the source for a long distance.
• Fanning plumes often occur in the early morning during a
radiation inversion.
 Plume behaviour

• Lofting
• When conditions are unstable above an inversion below, the release
of a plume above the inversion results in effective dispersion without
noticeable effects on ground level concentrations around the source.
Plume behaviour

• Fumigation
• If the plume is released just under an inversion layer, a serious air pollution
situation could develop. As the ground warms in the morning, air below an
inversion layer becomes unstable. When the instability reaches the level of the
plume that is still trapped below the inversion layer, the pollutants can be
rapidly transported down toward the ground. This is known as fumigation.
Ground-level pollutant concentrations can be very high when fumigation
occurs. Sufficiently tall stacks can prevent fumigation in most cases.
Some basic problems

• What is the density of oxygen at a temperature 273 K and pressure

98KPa?
• Show that one mole of any ideal gas will occupy 22.414 L at standard
temperature and pressure (STP: 273.16K and 101.325 kPa).
• A sample of air contains 8.583 moles/m3 of oxygen and 15.93
moles/m3 of nitrogen at STP. Determine the partial pressure of O2
and N2 in 1 m3 of the air.