Air Pollution Meteorology
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Atmospheric thermodynamics
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Atmospheric stability
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Boundary layer development
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Effect of meteorology on plume dispersion
Atmosphere
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
Pollution cloud is interpreted by the chemical composition and physical
characteristics of the atmosphere
Concentration of gases in the atmosphere varies from trace levels to
very high levels
Four major layers of earth’s atmosphere are:

Troposphere

Stratosphere

Mesosphere

Thermosphere
Atmospheric Thermodynamics
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
A parcel of air is defined using the state variables
Three important state variables are density, pressure and temperature
The units and dimensions for the state variables are
Density
(mass/volume)
gm/cm3
ML-3
Pressure (Force/Area)
N/m2 ( Pa )
ML-1T-2
Temperature

o F, o R, o C, o K
T
Humidity is the fourth important variable that gives the amount of
water vapor present in a sample of moist air
Equation of State





Relationship between the three state variables may be written as:
f ( P, ρ ,T) = 0
For a perfect gas:
P = ρ .R .T
R is Specific gas constant
R for dry air = 0.287 Joules / gm /oK
R for water vapor = 0.461 Joules / gm /oK
R for wet air is not constant and depend on mixing ratio
Laws of Thermodynamics
First Law of Thermodynamics:

This law is based on law of conservation of total energy.

Heat added per unit mass = (Change in internal energy per unit mass)
+ (Work done by a unit mass)
Second Law of Thermodynamics:

This law can be stated as "no cyclic process exists having the
transference of heat from a colder to hotter body as its sole effect"
Specific Heat


Defined as the amount of heat needed to change the temperature of
unit mass by 1oK.
Specific heat at constant volume
Cv = lim
δQ
δT 0 δT

Specific heat at constant pressure
Cp = lim
δQ
δT 0 δT

α = const
p = const
Relationship between Cv and Cp is given by Carnot’s law:

For perfect gas, Cp – Cv = R

For dry air Cp = (7/2). R
Cv = (5/2). R

Ratio of Cp and Cv for dry air is 1.4
Processes in the Atmosphere
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An air parcel follows several different paths when it moves from one
point to another point in the atmosphere. These are:
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Isobaric change
Isosteric change
Isothermal change
Isentropic change
Adiabatic Process
–
–
–
–
–
constant pressure
constant volume
constant temperature
constant entropy (E)
δQ = 0 (no heat is added or removed )
The adiabatic law is P. αγ = constant

E=

Q
T
Statics of the Atmosphere

Vertical variation of the parameters = ?
Hydrostatic Equation:

Pressure variation in a "motionless" atmosphere
p
.g
z

or

1 p
g
 z
Pressure variation in an atmosphere:
1 p d 2 z

 2
 z dt

Relationship between pressure and elevation using gas law:

1 p  g

 z Rd T
Statics of the Atmosphere

Integration of the above equation gives
 p
  g z 1 
ln   exp 
 T . dz 
 po 
 Rd 0


Using the initial condition Z=0, P = P0


The above equation indicates that the variation of pressure depends on
vertical profile of temperature.
For iso-thermal atmosphere
  g 1 
p
 exp 
To . z 
po
 Rd




Therefore pressure decreases exponentially with height.
12.24 mb per 100m.
Lapse Rate:

Lapse rate is the rate of change of temperature with height

Lapse rate is defined as Γ = -δT
δz

Value of Γ varies throughout the atmosphere
Potential Temperature:


Concept of potential temperature is useful in comparing two air parcels
at same temperatures and different pressures
θ = To = T 1000
P
R/C
p
Atmospheric Stability
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

The ability of the atmosphere to enhance or to resist atmospheric
motions
The stability depends on the ratio of suppression to generation of
turbulence
The stability at any given time will depend upon static stability ( related
to change in temperature with height ), thermal turbulence ( caused by
solar heating ), and mechanical turbulence (a function of wind speed
and surface roughness).
Atmospheric Stability

Atmospheric stability can be determined using adiabatic lapse rate.


Γ > Γd
Unstable
Γ = Γd
Neutral
Γ < Γd
Stable
Γ is environmental lapse rate
Γd is adiabatic lapse rate (10c/100m) and dT/dZ = -10c /100 m
Atmospheric Stability Classification
Schemes to define the atmospheric stability are:

P- G Method
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P-G / NWS Method
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The STAR Method
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BNL Scheme
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Sigma Phi Method
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Sigma Omega Method
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Modified Sigma Theta Method
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NRC Temperature Difference Method
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Wind Speed ratio (UR) Method
Turbulence
Fluctuations in wind flow which have a frequency of more than
2 cycles/ hr
Types of Turbulence
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Mechanical Turbulence
Convective Turbulence
Boundary Layer Development
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

Thermal boundary Layer (TBL) development depends on two factors:

Convectively produced turbulence

Mechanically produced turbulence
Development of TBL can be predicted by two distinct approaches:

Theoretical approach

Experimental studies
Theoretical approach may be classified into three groups:

Empirical formulae
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Analytical solutions
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Numerical models
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One layer models
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Higher order closure models
Effects of Meteorology on Plume Dispersion
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Dispersion of emission into atmosphere depends on various
meteorological factors.
Height of thermal boundary layer is one of the important factors
responsible for high ground level concentrations
At 9 AM pollutants are pulled to the ground by convective eddies
Spread of plume is restricted in vertical due to thermal boundary
height at this time
Wind Velocity

A power law profile is used to describe the variation of wind speed
with height in the surface boundary layer
U = U1 (Z/Z1)p
Where U1 is the velocity at Z1 (usually 10 m)

U is the velocity at height Z.

The values of p are given in the following table.
Stability Class
Rural p
Urban p
Very Unstable
0.07
0.15
Neutral
0.15
0.25
Very Stable
0.55
0.30
Beaufort Scale
This scale is helpful in getting an idea on the magnitude of wind
speed from real life observations
Atmospheric
Wind speed
Comments
condition

Calm
< 1mph
Smoke rises vertically
Light breeze
5 mph
Wind felt on face
Gentle breeze
10 mph
Leaves in constant motion
Strong
25 mph
Large branches in motion
Violent storm
60 mph
Wide spread damage
Wind Rose Diagram (WRD)

WRD provides the graphical summary of the frequency distribution
of wind direction and wind speed over a period of time

Steps to develop a wind rose diagram from hourly observations are:

Analysis for wind direction
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Determination of frequency of wind in a given wind direction
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Analysis for mean wind speed
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Preparation of polar diagram
Determination of Maximum Mixing Height
Steps to determine the maximum mixing height for a day are:
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Plot the temperature profile, if needed
Plot the maximum surface temperature for the day on the graph for
morning temperature profile
Draw dry adiabatic line from a point of maximum surface
temperature to a point where it intersects the morning temperature
profile
Read the corresponding height above ground at the point of
intersection obtained. This is the maximum mixing height for the day