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Air Quality Modelling
Lecture-1
What does model means?
• Models reflects a mathematical description of
hypothesis conveying the behavior of some
physical process or other.
•
Not exact replica but contain some of nature’s
essential elements.
What is mathematical modelling?
When the process of problem reduction or solution involves
transforming some idealized form of the real world situation into
mathematical terms, it goes under generic name of
mathematical modelling.
“Mathematical modelling is an activity which requires rather more
than the ability just to solve complex sets of equations difficult
through this may be”.
Mathematical modelling utilizes ANALOGY to help understand the
behavior of complex system.
What is physical modelling?
• In physical modelling nature is simulated on a
smaller scale in the laboratory by a physical
experiment.
• When detailed mathematical models and/ or
experimental field measurements become very
costly, laboratory simulation using scaled down
models in wind tunnels or water channels is
often the best approach.
Concept of mathematical modelling
applied to air pollution
Mathematical
Modelling
Source
Transport
Receptor
Source: Point, Line, Area.
Receptors: Humans.
Transport :Decides fate of air pollution
Re-entertainment: Re suspension of air pollutants.
Air Quality Models
Analogy - helps in explaining / understanding unfamiliar situations.
Ex: Children playing father/ mother game
Expectant mothers: practice nappy changing on dolls.
• Models:
– Not exact replica but contain some of nature’s essential elements.
– Ex: When expectant mother practice nappy changing to dolls, dolls are
laying still while in reality, babies do not lie still!.
– Hence, models reflects a mathematical description of hypothesis
conveying the behavior of some physical process or other.
What is air quality model
A mathematical relationship between emissions and air quality that incorporates
the transport, dispersion and transformation of compounds emitted into the air.
System approach to air quality model
Model objective
– Models are not a unique representation as they never completely
replicate a system.
– But models are useful tool in the design of new, large or otherwise
modified existing processes or systems.
– Conventional method of designing physical models replicating a
process or system is time consuming and cumbersome process.
– Physical models sometime can not replicate a system which is
having complicated heat and mass transfer processes.
– Mathematical models therefore is able to cope reasonably well with
such processes or systems provided each is built into the set of
mathematical equations.
Model categories
Broad Categories
Steady state
models
Dynamic
models
Continuous
system
Discreet
system
modelling
modelling
Empirical
model
Suggested readings:
M. Crossal A.O. Moscardini, “Learning art of mathematical modelling”,
Ellis Harmood Publication
Air Quality Models
STATISTICAL
DETERMINISTIC
REGRESSION
STEADY STATE
PHYSICAL
EMPIRICAL
WINDTUNNEL
SIMULATION
TIME DEPENDENT
GAUSSIAN PLUME
BOX
GRID
SPECTRAL
EULERIAN
PUFF
TRAJECTORY
LAGRANGIAN
Suggested readings:
Weber, E., “Air pollution assessment modelling methodology”,
NATO, challenges of modern society, vol.2, Plenum press, 1982
What is deterministic approach?
The 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 modelling is the traditional approach for the
prediction of air pollutant concentrations in urban areas.
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
  2C 

 C 

   (u or C)t  K i  2 
x
 t 
 t 
Basic mathematical equation
C
  UC  Ft  Q  R
t
where

Ft  u'C', v 'C' , w 'C'

C = pollutant concentration; t = time; U = wind vector; Q = source term; R = removal term ;
F = turbulent flux of pollutants
t
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.
 C
C
C
C  
C 
C 
C
   u
v
w
  K H
 KH
 Kz
 Q  R.
t

x

y

z

x

x

y

y

z

z


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’
Reference:
Cheremisinoff, P.N.,1989. Encyclopedia of environmental control technology:
air pollution control. Volume 2, Gulf Publishing Company, Houston.
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 x-axis 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
C( x, y, z ) 
Q
e
u y  z 2


 2

y





2
2 

y




 z H 2

  zr He 2 

 r e
 


2
2

2 
2   



z
z
e
e




Where
C : concentration of emission (gm/m3) at any receptor location at x (downwind distance from source),
y (crosswind), and z (vertical)
Q : source emission rate (gm/sec)
u : horizontal wind velocity
He : plume centre line height above ground
z : vertical standard deviation of emission distribution
y : horizontal standard deviation of emission distribution
Application: Gaussian Based Vehicular Pollutant
Dispersion Model
The basic approach for development of deterministic vehicular pollution (line source)
model is the coordinate transformation between wind coordinate system (X1, Y1, Z1) and
line source coordinate system (X, Y, Z).
A hypothetical line source is assumed to exist along Y1 that makes the wind direction
perpendicular to it (Figure 1). The concentration at receptor is given by Csanady (1972):
2
2  L
2

2












QL
Y
'

Y
1
Z

H
1
Z

H
1




1
1
exp  
   exp  
  x  exp  
 dY1 '
C

2 ' Y  ' Z u   2   ' Z  
2   ' Z    L
 2   ' Y  


 2

 
Reference:
Csanday, G.T., 1972. Crosswind shear effects on atmospheric diffusion.
Atmospheric Environment, 6,221-232.
Numerical approach
Numerical models also comes under deterministic modelling technique which are based
on numerical approximation of partial differential equations representing atmospheric
dispersion phenomena.
Basic mathematical equation
C
  UC  Ft  Q  R
t
The term Ft in the above equation is unknown and diffused equation is not in close
form.
Reference:
Juda, K., 1986. Modelling of the air pollution in the Cracow area.
Atmospheric Environment, 20 (12), 2449-2458.
Basis for numerical approach
First order closure models, also called K- models, have their common roots in the atmospheric
diffusion equation derived by using a K-theory approximation for the closure of the turbulent
diffusion equation. The first order closure models are time dependent.
Numerical based AQM
Eulerian grid model (Danard, M.B., 1972)
Lagrangian trajectory model (Johnson, 1981)
Hybrid of eulerian-lagrangian model (Particle-in-cell) (Sklarew et al., 1972)
Random walk (Monte-Carlo) trajectory particle model (Joynt and Blackman, 1976)
Mostly used numerical based AQM
Gaussian puff model (Hanna et al., 1982)
Reference:
Danard, M.B., 1972. Numerical modelling of carbon monoxide concentration near a Highway. Journal of
Applied Meteorology, 11, 947-957.
Johnson, W.B., 1981. Interregional exchanges of air pollution: model types and application. In Air pollution
modelling and its application-I, Edited by Wispelaere, C. De., Plenum Press, New York.
Sklarew, R.C., Fabrick, A.J. and Prager, J.E., 1972. Mathematical modelling of photochemical smog the
using PIC method. Journal of Air Pollution Control Association, 22, 865-.
Joynt, R.C. and Blackman, D.R., 1976. A numerical model of pollutant transport. Atmospheric Environment,
10, 433-.
Hanna, S.R., Brigs, G.A. and Hosker, Jr. R.P., 1982. Handbook on atmospheric diffusion. National Technical
Information Centre, U.S. Department of Energy, Virginia.
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 (Comrie, 1997)
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.
Reference:
Comrie, A. C., 1997. Comparing neural networks and regression model for ozone
forecasting. Journal of Air and Waste Management Association, 47, 653-663
Box, G.E.P. and Jenkins, G.M., 1976. Time series analysis forecasting and control.
2nd Edition, Holdenday, San Francisco.
Basic mathematical equation
The Box –Jenkins (B-J) models are empirical models created from the historical data.
Statistical graphs of the autocorrelation function (ACF) and partial autocorrelation
function (PACF) to identify an appropriate time series model.
The general class of univariate B-J seasonal models, denoted by ARIMA (p, d, q)(P,
D, Q)s can be expressed as:
p B P Bs  Ds dz t  q B Q Bs at  c
Where  and  = regular and seasonal autoregressive parameters, B = backward shift operators,
 =difference operators, d and D = order of regular and seasonal differencing, s= period/span, zt =
observed data series,  and Θ = regular and seasonal moving average parameters, at = random noise,
p, P, q and Q represent the order of the model and c = constant.
Mostly used stochastic based AQM
Time series model
Univariate model
Bivariate model
Multivariate model
- 24 h avg.. CO model
with wind speed as input
- 24 h avg.. CO model
- 24 h avg.. CO model with
24
h
avg..
CO
model
- Max. daily 1-h avg..
temperature and wind
with temperature as input
CO model
speed as inputs
Max.
daily
1-h
avg..
CO
model
- Max. daily working hours
- Max. daily 1-h avg.. CO
with wind speed as input
(8 AM - 8PM) 1-hour CO
model with wind speed and
Max.
daily
1-h
avg..
CO
model
model
temperature as inputs
with
temperature
as
input
- Hourly average CO model
- Max. daily working hours
- Max. daily working hours
1-hour avg.. CO model
1-hour avg.. CO model with
with wind speed and
wind speed as input
Reference:
temperature as inputs
- Max. daily working hours
avg.. CO model with
Khare, M. and Sharma, 1-hour
P., 2002.
Modelling urban vehicle emissions. WIT press,
temperature as input
Southampton, UK. - Hourly average CO model with
wind speed as input
Sharma, P. and Khare,- M.,
2001.
Short-time,
real
– time prediction of extreme
Hourly
average
CO model
with
temperature
as inputdue to vehicular exhaust emissions using
ambient carbon monoxide
concentrations
transfer function noise models. Transportation Research D6, 141-146.
Physical modelling approach – Wind Tunnel
•
Double walled panel with thermocole
26 m long, suction
type, low wind
speed, 16 m test
section, 8 panels, 2
m each
Toughned glass panel
2.0m
Ø1.8m
•
•
EWT consists of
entrance section,
honeycomb
section, wire mesh
screen filters, test
section,
exit
contraction section,
transition
and
diffuser section
2.0m
Diffuser
Air in
Power section
Transition section
Contraction cone
Test section
3.0m 0.6m
0.6m2.5m
0.8m
Speed control unit
4
5
6
7
8
8 panels of 2m each = 16m
Heating arrangement
Turntable
5.0m
Plenum chamber
for prevention of
surge and other
disturbances, 6 m
x 5 m wall
3
3.0m
Turntable of 1.8 m
diameter
1
•
Cross section of the panel of test
section
Turntable in panel no. 2 at test section floor
3.5m
Door with handle
Layout of environmental wind tunnel
ENVIRONMENTAL WIND TUNNEL- IIT DELHI
Basis for physical approach
•
The physical simulation studies using wind tunnels have shown high potential to
understand complex urban dispersion phenomenon.
•
The pollutant concentrations measured within the physical model can be converted to
equivalent atmospheric concentrations through the use of appropriate scaling
relationship.
•
In the physical simulation studies of exhaust dispersion, the model vehicle movement
system (MVMS) plays a vital role. The vehicle-induced turbulence can be understood
accurately by using MVMS.
Design consideration for MVMS*
• maintenance of ‘‘no slip’’ boundary condition in atmospheric boundary layer (ABL)
flow,
• variations in traffic volume and traffic speed for two-way traffic,
• operation of MVMS for various street configurations,
• variation in approaching wind directions and wind speed,
• operation of vehicles in different lanes.
Reference:
*Ahmad, K., Khare, M. and Chaudhry, K.K. 2005. Wind tunnel simulation studies on
dispersion at urban street canyons and intersections- a review. Journal of Wind Engineering
and Industrial Aerodynamics, 93, 697-71
Eskridge, R.E. and Hunt, J.C.R., 1979. Highway modelling-I: prediction of velocity and
turbulence fields in the wake of vehicles. Journal of Applied Meteorology, 18 (4), 387- 400.
Plan of MVMS for urban street
DESIGNED IN ENVIRONMENTAL WIND TUNNEL- IIT DELHI
PLAN OF MVMS FOR URBAN INTERSECTION
DESIGNED IN ENVIRONMENTAL WIND TUNNEL- IIT DELHI
Wind tunnel based AQM
•
Development, testing and validation of atmospheric dispersion models through EWT
generated database in a variety of atmospheric conditions.
•
Systematic understanding of the pollutants dispersion characteristics for line source
(automobile exhaust emissions), point source (stack emissions) and area source (low
level areal emissions) in plain and complex terrains, such as, hills and valleys.
•
Understanding of the dispersive behavior of toxic gases from accidental releases.
•
Studies on the effects of pollutants on plants and buildings under dynamic
environmental conditions for various geographical conditions.
•
Simulation of ‘heat islands’ and its effect on pollutant dispersion.
•
Location of ‘hot spots’ at the urban intersections.
Reference:
Eskridge, P.E. and Thompson, R.S., 1982. Experimental and theoretical study of the wake of a blockshaped vehicle in a shear-free boundary flow. Atmospheric Environment, 16 (12), 2821-2836.
Snyder, W.H., 1972. Fluid models for the study of air pollution meteorology: similarity facilities, review
of literature and recommendations, U.S. Environmental Protection Agency, Washington.
LIMITATIONS OF MODELS
Deterministic models:
•
Inadequate dispersion parameters
•
Inadequate treatment of dispersion upwind of the road
•
Requires a cumbersome numerical integration especially when the wind forms a
small angle with the roadways.
•
Gaussian based plume models perform poorly when wind speeds are less than 1m/s.
•
Numerical models have common limitations arising from employing the K-theory for
the closure of diffusion equation. The K-theory diffusion equation is valid only if the
size of the ‘plume’ or ‘puff’ of pollutants is greater than the size of the dominant
turbulent eddies.
•
The Gaussian puff model relative diffusion parameters are derived from very few
field experiments, which limits its applicability.
•
The other limitations of numerical models are large computational costs in terms of
time and storage of data. It also requires large amounts of input data.
LIMITATIONS OF MODELS
Statistical models:
•
Require long historical data sets and lack of physical interpretation.
•
Regression modelling often underperforms when used to model non-linear systems.
•
Time series modelling requires considerable knowledge in time series statistics i.e.
autocorrelation function (ACF) and partial auto correlation function (PACF) to
identify an appropriate air quality model.
•
Statistical models are site specific.
•
Hybrid model prediction accuracy depends on the selection of suitable deterministic
model and identification of appropriate statistical distribution parameter.
•
Application of hybrid approach to strongly auto correlated and/or non-stationary
data requires specific treatment for auto correlation /non stationary to increase
prediction accuracy.
LIMITATIONS OF MODELS
•
In ANN based vehicular pollution model, the main problem facing when training
neural network model, is deciding upon the network architecture (i.e., number of
hidden layers, number of nodes in hidden layers and their interconnection).
•
At present, no procedures has been established for selecting proper network
architecture, rather than training several network architecture and choose the best out
of them.
•
Multilayer neural network performs well when used for interpolation, but poorly, if
used for extrapolation.
•
No thumb rules exist in selection of data set for training, testing and validation of
neural network based model.
LIMITATIONS OF MODELS*
Physical models: wind tunnel
•
The major limitations of wind tunnel studies are construction and operational cost.
•
Simulation of real time air pollution dispersion is expensive.
•
Real time forecast is not possible.
*Reference:
Juda, K., 1989. Air pollution modelling. In: Cheremisinoff, P.N. (Eds.), Encyclopedia of Environmental Control
Technology, Vol. 2: Air Pollution Control, Gulf Publishing Company, Houston, Texas, USA, pp.83-134.
Nagendra, S.M.S. and Khare, M., 2002. Line source emission modelling- review. Atmospheric Environment, 36
(13), 2083-2098.
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
C = x qa / (Lu)
where C = steady state concentration
x = distance over which the emission takes place
qa = Area emission rate
L = mixing height
u = mean wind speed through vertical extent box
Box model
u
C = uniform
L
qa
x
Suggested reading:
Lyons, T.J. and Scott, W.D. “Principles of air pollution
meteorology”, Behavan press, 1990
Line source model
– Application
• motor vehicle travelling along a straight section of highway
OR
agricultural burning along the edge of a field
OR
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
- Model:
C (x) = (2q)/(2 z u)
u
Line source
q = emission per unit of distance along
the line (gm/m-sec)
q (gm/sec)
x
Receptor
CONCLUSIONS
•
Air pollution in cities is a serious public health problem. Therefore, there is need for
reliable air quality management system for abatement of urban air pollution
problem.
•
Several air quality models have been developed using deterministic, statistical and
physical approaches for urban air quality management.
•
These three modelling approaches have been used in the development and validation
of vehicular pollution dispersion models pertaining to urban context in Delhi.
•
Limitations of deterministic modelling approach is
describing vehicular pollution dispersion phenomena.
•
Limitations of statistical modelling approach is selection of modelling parameters
representing the appropriate statistical distribution of air quality data.
•
Limitations of physical modelling approach is high cost involvement in simulating
real time vehicular pollution dispersion in laboratory.
assumptions considered in