Air quality model
Model categories
Deterministic approach
Deterministic mathematical models calculate
the pollutant concentrations from emission
inventory and meteorological variables
according to the solution of various equations
that represent the relevant physical processes.
Deterministic approach: Basics
• What is Transport ?
– It is also termed as advection
– Most obvious effect of atmosphere on emission
– Advection: implies transport of pollutant downwind of
source
•
• What is Dilution?
– It is also termed as “mixing”.
– It is accomplished through “turbulence”
– Mainly atmospheric turbulence is active
What is Dispersion?
Dispersion = Advection (Transport) + Dilution
= Advection +Diffusion
Basic Mathematical Equation
Deterministic based AQM
The deterministic based air quality model
is developed by relating the rate of change
of pollutant concentration in terms of
average wind and turbulent diffusion
which, in turn, is derived from the mass
conservation principle.
where C = pollutant concentration; t = time; x, y, z = position of the receptor relative to the source;
u, v, w =wind speed coordinate in x, y and z direction;
Kx, Ky, Kz = coefficients of turbulent diffusion in x, y and z direction;
Q = source strength;
R = sink (changes caused by chemical reaction).
• The above diffusion equation is derived in
several ways under different set of
assumptions for development of air quality
models
• Gaussian model is one of the mostly used air
quality model based on ‘deterministic
principle’
Gaussian plume Dispersion model:
Assumptions
• Steady-state conditions, which imply that the
rate of emission from the point source is
constant.
• Homogeneous flow, which implies that the
wind speed is constant both in time and with
height (wind direction shear is not
considered).
• Pollutant is conservative and no gravity
fallout.
• Perfect reflection of the plume at the
underlying surface, i.e. no ground absorption.
• The turbulent diffusion in the x-direction is
neglected relative to advection in the
transport direction , which implies that the
model should be applied for average wind
speeds of more than 1 m/s (> 1 m/s).
• The coordinate system is directed with its xaxis into the direction of the flow, and the v
(lateral) and w (vertical) components of the
time averaged wind vector are set to zero.
• The terrain underlying the plume is flat
• All variables are ensemble averaged, which
implies long-term averaging with stationary
conditions.
Gaussian Plume Dispersion Model
Statistical Approach
• Statistical models calculate pollutant
concentrations by statistical methods from
meteorological and emission parameters after
an appropriate statistical relationship has
been obtained empirically from measured
concentration
Basis for statistical approach
Regression and multiple regression models
• Regression models describes the relationship between
predictors (meteorological and emission parameters)
and predictant (pollutant concentrations)
Time series models (Box and Jenkins, 1976)
• Time series analysis is purely based on statistical
method applicable to non repeatable experiments.
• Box-Jenkins approach extracts all the trends and serial
correlations among the air quality data until only a
sequence of white noise (shock) remains.
• The extraction is accomplished via the difference,
autoregressive and moving average operators.
Box Model
• Application : Area source
• Principle :
(i) It assumes uniform mixing throughout the
volume of a three dimensional box.
(ii) Steady state emission and atmospheric
conditions.
(iii) No upwind background concentration.
Model description
Line source model
Application
• motor vehicle travelling along a straight section of highway
• agricultural burning along the edge of a field
• line of industrial sources on the bank of a river
Assumption
• Infinite length source continuously emitting the pollution
• Ground level source
• Wind blowing perpendicular to the line source
Surface Wind Speed
Insolation
Cloud
cover
<2
2 to 3
3 to 5
5 to 6
>6
A
A-B
B
C
C
A-B
B
B-C
C-D
D
B
C
C
D
D
D
D
D
D
D
≥ 0.5 cloud
cover
E
D
D
D
≤ 0.4 cloud
cover
F
E
D
D
Strong sun
Day
Mod. Sun
Slight sun
Day or
Overcast
Night
Night
A 200-MW power plant has a 100-m stack with radius 2.5 m, flue
gas exit velocity 13.5 m/s, and gas exit temperature 145 degrees
Celsius. Ambient temperature is 15 degrees Celsius, wind speed
at the stack is 5 m/s, and the atmosphere is stable, Class E, with a
lapse rate of 5 C/km. if it emits 300 g/s of SO2, estimate the
concentration at a ground level at a distance of 10 km directly
downwind.
Sig y =
Sig z =
C=
= g/m3
[K] = [°C] + 273.15
EFFECTIVE STACK HEIGHT
• A power plant burns 104 kg hr-1 of coal that
contains 2.5% sulfur. The stack is 50 m high, and
the plume typically rises 30 m.
a) Calculate the ground-level concentration of
sulfur dioxide (SO2) (in micrograms m-3) 800 m
downwind from the source directly under the
plume under the following conditions: Wind
speed = 4 m s-1, moderately sunny day
(moderately unstable conditions).
b) Repeat the above calculation for a stack height
of 75 m and a wind speed of 6 m s-1.