i

Modelling the Mass Transfer Removal Rates of Atmospheric

Pollutants: Application to a Lignite based Thermal Power

Plant

A thesis submitted in partial fulfillment of the requirements for the award

of

Bachelor of Technology in Chemical Engineering

By

JASON RYAN PICARDO (07BCH008)

CHEMICAL ENGINEERING DIVISION

SCHOOL OF MECHANICAL AND BUILDING SCIENCES

APRIL 2011

ii

School Of Mechanical and Building Sciences

Chemical Engineering Division

BONAFIDE CERTIFICATE

This is to certify that the thesis entitled “Modelling the Mass Transfer Removal Rates

of Atmospheric Pollutants: Application to a Lignite based Thermal Power Plant”

being submitted by Mr. Jason Ryan Picardo, in partial fulfillment of the requirements for

the award of a Bachelor of Technology in Chemical Engineering, to the School of

Mechanical and Building Sciences, VIT University is a record of bonafide work done

under my guidance. The contents of this project work, in full or in part, have neither been

taken from any other source nor have been submitted to any other institute or university

for the award of a degree or diploma and the same is certified.

Dr. S. Ghosh Dr. Anand Gurumoorthy

Sr. Prof SMBS Asso. Prof. SMBS

Project Guide Internal Guide

Dr. L. N. Muruganandam

Division Leader Chemical Engineering

School Seal

Internal Examiner External Examiner

iii

DEDICATED TO

Norma and Francisco Picardo

My parents, who lead me to the Lord

and taught me to Strive for Excellence

iv

ACKNOWLEDGEMENTS

Firstly, I would like to thank our honorable Chancellor Dr. G. Viswanathan and the

administration of VIT University for providing excellent academic facilities and for the

opportunity to carry out this work at VIT University.

I extend my deep gratitude to Neyveli Lignite Corporation for funding this work and

providing me with the opportunity to work on this project.

I owe not only the success of this project work but also a great deal of personal

advancement, academic and otherwise, to my project guide Dr. S Ghosh, Senior

Professor, SMBS. This work rode on his vision. His mentorship enriched and refined my

work. Scientific rigor is united with aesthetic beauty in his work and life. Knowing him

will remain a lifelong joy and privilege.

Dr. Anand Gurumoorthy, my internal department guide was supportive and encouraging.

The many discussions we had during the course of the semester have broadened my

vision with respect to research in general and complex nonlinear systems research in

particular.

I thank the Director of the School of Mechanical and Building Sciences, Sr. Prof., Dr. A.

Senthil Kumar for his constant support and encouragement throughout the duration of

this work. Studying and carrying out this work in the School of Mechanical and Building

Sciences was an enriching and enjoyable experience.

I thank the Division Leader of the Chemical Engineering Division, Dr. Muruganandam

for his enthusiastic support during the course of this work.

I am extremely grateful to Dr. Jayasankar Variyar, Prof. VIT University-Chennai who

ensured that I would be able to work on this interdisciplinary project with Prof. Ghosh.

His mentorship and friendship remain invaluable to me.

During the course of this work a large number of research papers were referenced.

Access to these papers was kindly provided by the Library. In particular I thank Dr.

Adhinarayanan, Deputy Librarian, for his efforts in this regard.

Ultimately I extend a prayer of thanksgiving to my Heavenly Father and Jesus Christ for

blessing me with this project and wonderful professors and for essentially every element

of my life.

v

ABSTRACT

This work quantifies the mass transfer removal rate of SO2, a major gaseous atmospheric

pollutant, whilst accounting for the meteorology and vegetation unique to tropical Asia.

The Neyveli Lignite Corporation (NLC) located in Tamil Nadu, India, is a large lignite

based thermal power plant which continuously emits SO2, among other pollutants. The

founding fathers of NLC took a visionary step by initiating a massive afforestation

program which has resulted in 17 million evergreen tropical trees. In this first study, the

dry deposition process of SO2 onto these trees is modelled via the well established

deposition velocity parameterization. The deposition velocity of SO2 is calculated for a

period from Nov 2008 to Oct 2009 using meteorological data provided by NLC.

Aerodynamic and quasi laminar resistances are accounted for in detail using well

established methods. The surface resistance is accounted for using a state of the art

method of Zhang et al. (2003b) as well as a simpler method of Wesely (1989). These

results are compared and it is found that Wesely (1989) is suitable for approximate

calculations. However, it cannot describe seasonal changes in the dry deposition process.

The Zhang et al. (2003b) method uses satellite derived leaf area index (LAI) data to

describe the seasonal changes in foliage. The LAI is an important parameter in the

parameterization and enables a region specific study of dry deposition and the temporal

variation in deposition velocity.

The results obtained from the method of Zhang et al. (2003b) are used to develop a

regression formula for deposition velocity. This is a non trivial non linear regression

model which accounts for the discontinuous enhancement of deposition when wet

surfaces are present. This regression formula gives a good fit for the numerical results

generated using the Zhang et al. (2003b) deposition parameterization. It can be used to

calculate the deposition velocity for the NLC region and may prove useful in other

tropical Asian countries as well. It will be a boon to environmental impact assessment

analysts who are not specialists in the area of dry deposition.

The results of deposition velocity are coupled with modelled concentration of SO2 to

establish the scavenging efficacy of the evergreen trees. A tailor made gaussian

dispersion model is used which was developed as part of a consultancy with NLC. It is

found that a considerable amount of pollution is deposited on the trees. The canopy was

found to play an active role is reducing residual SO2 levels. This is especially significant

to the township of NLC which is home to 128,133 people.

The quantification of removal mechanisms has a dual significance with respect to

environmental studies. It is essential for calculating the atmospheric budget of trace gases

as well as assessing the impact of emissions on local vegetation and structures due to acid

deposition. This first study provides a basis for region specific environmental

assessments. It will also serve as a roadmap for future studies in other Asian regions

which have hitherto largely resorted to borrowing results from the mid-latitudes.

vi

CONTENTS

Page No.

ACKNOWLEDGEMENTS iv

ABSTRACT v

NOMENCLATURE viii

LIST OF TABLES x

LIST OF FIGURES xi

Chapter 1 INTRODUCTION 1

Chapter 2 LITERATURE REVIEW 4

Chapter 3 THEORY OF DEPOSITION VELOCITY 6

3.1 Parameterization of Dry Deposition to vegetation 6

3.2 Deposition velocity- Theory of resistances 6

3.3 Aerodynamic Resistance 7

3.4 Quasi Laminar Resistance 10

3.5 Surface Resistance 11

3.5.1 Method of Wesely (1989) 11

3.5.2 Method of Zhang et al. (2003b) 12

Chapter 4 METEOROLOGICAL DATA PROVIDED BY

NEYVEL LIGNITE CORPORATION

14

Chapter 5 DEPOSITION VELOCITY BY THE METHOD

OF WESELY (1989)

16

5.1 Deposition Velocity of SO2 at NLC for three

seasons

16

5.2 Variation of Vd with meteorological factors 17

5.3 Seasonal variation in Vd 18

vii

5.4 Comparison with results from other Asia based

studies

19

Chapter 6 DEPOSITION VELOCITY BY THE METHOD

OF ZHANG et al. (2003b)

20

6.1 Leaf Area Index for NLC 20

6.2 Deposition velocity of SO2 at NLC 21

6.3 Comparison of the results obtained using Wesely

(1989) and Zhang et al. (2003b)

22

6.4 Effect of wet surfaces due to rain 23

Chapter 7 DEVELOPMENT OF A REGRESSION

FORMULA TO CALCULATE DEPOSITION

VELOCITY

24

7.1 Requirement of a simple regression formula 24

7.2 Formulation of suitable non linear regression model 24

7.3 Analysis of the regression parameters and the

regression fit

26

Chapter 8 SCAVENGING EFFICACY OF THE MAN-

MADE CANOPY

28

8.1 Dispersion Model for predicting SO2 concentration 28

8.2 Deposition from a plume 29

8.3 Removal of residual pollution and improvement of

air quality

30

Chapter 9 CONCLUSION AND FUTURE WORK 33

PUBLICATIONS/PRESENTATIONS 35

REFERENCES 36

viii

NOMENCLATURE

F − Dry deposition flux of gas through the surface layer µg m-2

s-1

Vd − Deposition velocity m s-1

C − Concentration of the gaseous species (SO2) µg m-3

Ra − Aerodynamic resistance s m-1

Rb − Quasi laminar resistance s m-1

Rc − Surface resistance s m-1

C − Quantity diffusing through surface layer of atmosphere -

ζ − Dimensionless height scale dimensionless

L − Monin-Obhukov length m

K − Eddy Diffusivity m2 s

-1

z − Vertical coordinate from the earth‟s surface upwards m

ϕT(ζ) − Empirical dimensionless temperature profile function -

ϕM(ζ) − Empirical dimensionless momentum profile function -

k − Von Karman Constant (Value is 0.4) dimensionless

*u − Friction Velocity m s-1

z0 − Roughness length m

zr − Reference height m

η0,ηr − Expression in the calculation of aerodynamic resistance dimensionless

u, U − Unidirectional wind velocity or wind speed m s-1

d − Displacement length m

B − dimensionless transfer coefficient dimensionless

Sc − Schmidt number dimensionless

ri − i component of resistance in the surface resistance

network m s

-1

G − Solar radiation W m-2

T − Temperature ºC

Wst − Stomatal blockage factor due to surface water film dimensionless

LAI − Leaf area index m2 m

-2

ix

RH − Relative humidity %

R − Binary wet surface input (0,1) dimensionless

Q,a-e,p − Parameters of the non linear regression model for Vd dimensionless

Vd,dry − Dry surface deposition velocity m s-1

Vd,wet − Wet surface deposition velocity m s-1

q − Stack source strength of species g s-1

σy − Gaussian dispersion parameter in horizontal direction m

σz − Gaussian dispersion parameter in vertical direction m

h − Effective stack height including physical height and

plume rise m

Hmix − Height of the mixed layer of the atmosphere m

C0 − Initial residual pollutant concentration µg m-3

t − Time s

x

LIST OF TABLES

Table No. Caption Page No.

Table 1.1 Details of stacks emitting SO2 at NLC

2

Table 4.1 Meteorological data provided by NLC

14

Table 5.1 Deposition Velocity for various seasons at NLC

16

Table 6.1 Comparison of results obtained using the methods of Wesely

(1989) and Zhang et al. (2003b)

22

Table 7.1 Parameter values of the regression model of Eq. (7.2-7.3)

with the 95% confidence intervals

26

xi

LIST OF FIGURES

Fig. No. Caption Page No.

Fig. 1.1 Google Map showing the location of Neyveli Lignite

Corporation (red A marker) in Tamil Nadu, India

1

Fig. 1.2 Map of NLC and aerial view from Google Earth®

of TPS1 and

TPS2 and the Township (demarcated by a rectangle)

2

Fig. 5.1 Resistances and deposition velocity calculated for December

2008 at 14:30 IST

16

Fig. 5.2 Diurnal variation in deposition velocity for December 2008

17

Fig. 5.3 Variation of aerodynamic resistance with wind speed (Dec

2008, 14:30 IST)

17

Fig. 5.3 Variation of canopy resistance with solar insolation (Dec 2008)

18

Fig. 5.5 Variation of deposition velocity with wind speed and solar

insolation (Dec 2008)

18

Fig. 6.1 LAI over the subcontinent for 10th Dec‟08, 17

th May‟09 and

16th October‟09 respectively (MODIS MCD15A2)

20

Fig. 6.2 LAI for all months from Nov ‟08 to Oct ‟09. The markers

represent data obtained from MODIS while the red line is a

cubic spline interpolation used to obtain intermediate values of

LAI for calculation

21

Fig. 6.3 Monthly average deposition velocity (Vd)

21

Fig. 6.4 Variation of canopy resistance with solar insolation (Dec 2008

14:30 IST)

22

Fig. 6.5 Variation of deposition velocity with wind speed and solar

insolation (Dec 2008 14:30 IST)

23

Fig. 7.1 The relationship between wet surface and dry surface

deposition velocity

25

xii

Fig. No. Caption Page No.

Fig. 7.2 Plot of deposition velocities obtained from the regression model

against the original data calculated using Zhang et al. (2003b)

26

Fig. 7.3 Residual plot of the regression model

27

Fig. 8.1 The modelled ground level concentration over the township on

21st May 2009, 14:30 IST (µg m

-3)

29

Fig. 8.2 Mass of SO2 deposited per unit area per unit time on 21st May

2009, 14:30 IST (µg m-2

hr-1

)

30

Fig. 8.3 Depletion of residual SO2 concentration over the township on

21st May 2009.

32

Fig. 8.4 Depletion of residual SO2 concentration over the township

considering the higher deposition velocity of October

32

1

CHAPTER 1: INTRODUCTION

Nature‟s astonishing biological resilience is closely linked to its self cleansing mechanisms. In a

hugely populated developing world, economic growth comes with a heavy price. A multitude of

industrial and transportation processes produce noxious gases which are released into the

atmosphere. Fortunately many of these developing countries, like India, are blessed with a highly

convective tropical boundary layer which dilutes pollution. Another common feature of these

Asian nations is that their vegetative cover is dominated by evergreen plants, in contrast to many

mid-latitude nations in the developed world where the number of evergreens are far limited.

However, it is ironical that despite these natural propensities air pollution levels over Asian cities

are much higher than their mid latitude counter parts. The purpose of this work is to describe,

formulate and quantify the removal pathways of SO2, a major air pollutant, through dry

deposition whilst accounting for the endowments of nature enjoyed by tropical Asia. The

quantification of removal mechanisms has a dual significance with respect to environmental

studies. It is essential for calculating the atmospheric budget of trace gases as well as assessing

the impact of emissions on local vegetation and structures due to acid deposition. This is done

via a detailed study on Asia‟s Largest Lignite based Power Plant- Neyveli Lignite Corporation

(NLC) located in the Cuddalore district of Tamil Nadu in South India (Fig. 1.1).

Fig.1.1. Google Map showing the location of Neyveli Lignite Corporation (red A marker) in

Tamil Nadu, India

Neyveli Lignite Corporation (NLC) is a company promoted by the government of India under

the Ministry of Coals. Neyveli Thermal Power Stations are South Asia's first and only lignite

fired Thermal Power Stations and also the first pit-head power stations in India. NLC covers an

area of about fifty-four square km, which includes the Neyveli Township, home to 128,133

people. It mines twenty-four million metric tonnes per annum (MTPA) of lignite, and produces

2,490 megawatts per annum (MW/year) of electricity from three open cast mines. SO2 is

2

produced during the generation of power from lignite coal and released from elevated stacks

(Please see Table 1.1).

Stack Height

(m)

SO2 source

strength

(g s-1

) Thermal Power station-I

1 60 227.82

2 60 271.35

3 60 153.23

4 120 305.99

Thermal Power station-I

Expansion 1 220 305.07

2 220 305.07

Thermal Power station-II

1 170 359.38

2 170 359.38

3 170 359.38

4 220 317.45

5 220 317.45

6 220 317.45

7 220 317.45

Table 1.1: Details of stacks emitting SO2 at NLC

The founding fathers of NLC began a massive afforestation program which has resulted in the

presence of 17 million tropical trees. The role of these trees in mitigating air pollution seems

intuitive and a detailed quantitative investigation requires the application of dry deposition

modelling techniques. Fig. 1.2 shows a map of NLC and an aerial view from Google Earth®. The

region demarcated by a rectangle is the township of NLC which is home to 128,133 employees.

Its proximity to the Thermal Power Station One (TPS1) makes it a particularly sensitive area

which is likely to receive emissions from the stacks. Fortunately there is a considerable green

cover over the township (Fig. 1.2) which promotes the deposition of pollutants and results in a

cleaner atmosphere. The extent of this cleansing depends on the level of pollutant concentration

and the environmental factors which modulate dry deposition. The quantification of the rate of

dry deposition assumes greater significance in context of the health of the township‟s residents.

Firstly, an in depth modelling analysis of the SO2 emissions is presented. It addresses the

dispersion of SO2 in a tropical boundary layer using an atmospheric dispersion model developed

as part of a consultancy with NLC and VIT University. The dry deposition of the spatially

distributed pollutant is then analyzed via suitable well established parameterizations. While these

have seen extensive application in North America and Europe, studies in developing Asia and

particularly India are few and far apart. Regional climatology including year round high solar

3

radiation and mild, almost non-existent, winters (temperature around 25 0C) make this a unique

study. It is further set apart from investigations conducted in the mid-latitudes by the tropical

vegetation. All these factors are accounted for in the modelling analysis which is to follow,

providing a basis for region specific environmental assessments. It will also serve as a roadmap

for future studies in other Asian regions which have hitherto largely resorted to borrowing results

from the mid-latitudes.

Fig.1.2 Map of NLC and aerial view from Google Earth

® of TPS1 and TPS2 and the Township

(demarcated by a rectangle)

4

CHAPTER 2: LITERATURE REVIEW

Dry deposition is of considerable importance in calculating the overall budget of a species in the

atmosphere. Furthermore, the substance which gets deposited can affect the deposition surface in

many ways, often adversely. Hence the quantification of dry deposition is important from a dual

perspective and much work has been done on the subject. For a good review of the state of the

science the reader may refer to the references [1-3].

Experimental measurements of dry deposition fluxes via techniques such as eddy correlation and

accumulation, the gradient method as well as analysis of the depositing surface-natural or

surrogate, have been carried out in different parts of the world. These studies, apart from giving

local information, form a basis for the development of modelling techniques to predict the dry

deposition flux when measurements cannot be made or are inconvenient. For more information

on experimental techniques the interested reader may refer [1]. Some experimental results of

deposition velocities measured in different parts of the world are given in [4-9]

In this study we make use of deposition velocity parameterizations. The parameterization of

Wesely (1989) was the first widely adopted parameterization and is still in considerable use

today [10]. It is relatively simple and gives reasonable results. Some corrections to this model

and certain cautions regarding its application are given in [11]. Gao and Wesely (1995) identified

the problems associated with discrete seasonal categories and introduced the use of satellite

derived LAI to account for foliage characteristics and their seasonal variation [12]. The stomatal

resistance model has undergone many revisions since the work of Wesely (1989). The

parameterization of non stomatal resistance has also been improved. All these advancements are

embodied in the parameterization of Zhang et al. (2003b) [13]. Some preceding work by Zhang

and coworkers laid the foundation for this parameterization and should be read for a clear

understanding of their work [14-15].

Work has also been done to verify the various models available and generally it is found that one

or the other is better depending on the conditions (wet or dry) and climate (mid-latitude or

tropical) [7-9]. Tsai et al. (2010) and Matsuda et al. (2006) highlight the validity of Zhang et al.

(2003b), especially its treatment of the effect of wet surfaces on deposition velocity [8-9].

Feliciano et al. (2001) find that the parameterization of Wesely (1989) is suitable for dry

conditions in Portugal [7].

Dry deposition studies are far fewer in India. Xu and Carmichael (1998) and Kumar et al. (2008)

report values of SO2 deposition velocity for the Indian region [16-17]. Deposition velocities have

been calculated using the method of Wesely (1989) for the NLC region by Patra and Ghosh,

2010 and Seth et al., 2010 respectively [18-19]. However, they do not account for the effect of

wet surfaces. Further, they do not calculate the aerodynamic resistance using the detailed flux

gradient relationships employed in this work. There are no reports of calculations for the entire

year. Most importantly, the LAI based methods have never been applied to this region. This is

5

significant since the local vegetative characteristics are so far removed from those studied by

Wesely (1989). Finally, there are no simple regression formulas for deposition velocity reported

for any region. This is understandable since the regional validity of these formulas would be

restricted to the region of study. Nevertheless, they would be a boon to non experts in the area

who require values of deposition velocities for environmental assessment calculations or for use

in larger atmospheric dispersion models. This work is a first attempt in this regard.

6

CHAPTER 3: THEORY OF DEPOSITION VELOCITY

3.1 Parameterization of Dry Deposition to vegetation

The vegetative canopy is considered to be an irreversible sink for SO2 and the flux of gas (F) to

the ground is represented by a first order relationship. This flux is assumed to be uniform within

the surface layer of the atmosphere (10-100 m) [1].

CVF d (3.1)

F has units of µg m-2

s-1

. C is the concentration of the gaseous species measured at a reference

height within the surface layer (µg m-3

). Vd is a parameter called the deposition velocity and it

has the units of m s-1

(hence the term velocity). Thus the problem of determining the flux of a

species is transformed into the determination of its deposition velocity. The downward flux of

the species is negative by convention and hence the deposition velocity is positive. Its value will

depend on the reference height chosen and the assumption of uniform flux dictates that the

concentration would also vary with height so as to keep the flux constant. The reference height

in this study is taken to be 10 meters which is close to the vegetative surfaces (ensuring better

agreement with the constant flux assumption) and is the height at which instrumentation is

installed by NLC for meteorological and concentration measurements.

3.2 Deposition velocity- Theory of resistances

The process of dry deposition is usually divided into three stages:

1. Transportation from the free atmosphere to the receptor surface (turbulent layer transport)

2. Transport through the quasi-laminar, stagnant air layer near the receptor surface

(diffusive molecular transport)

3. Capture or absorption by the surface (in this case transport into the leaf stomata or cuticle

or deposition onto the ground).

According to the universally adopted inferential resistance modelling approach, the dry

deposition process is treated analogously to the flow of electrical current through a network of

resistances in series. In this analogy, the aerodynamic resistance (Ra), the quasi-laminar

resistance (Rb) and the surface resistance (Rc) refer to the aforementioned three stages of dry

deposition respectively (all have units of s m-1

). The inverse of the total resistance is the dry

deposition velocity (Vd).

1 cbad RRRV (3.2)

7

An advantage of the resistance analogy is that processes are separated and related to

„measurable‟ quantities. They allow the lumping of complex micro-physical processes into a

single parameter. The disadvantage of this simplicity is that Vd is difficult to specify and may

lead to significant deviation from measured values especially under conditions which are not

accounted for in the model. This could occur if that particular condition was a rare occurrence at

the location where the model was developed and hence it was not given much attention. For

example, the parameterization of Wesely (1989) shows errors of 60% under wet conditions

[9-10]. In the next sections we will describe the methods of calculating the resistances for gases.

Methods for calculation of resistances for particles can be found in [1].

The final step in the dry deposition process is actual uptake of the vapor molecules or

particles by the surface. Gaseous species may absorb irreversibly into the surface; particles

simply adhere. The amount of moisture on the surface and its stickiness are important

factors at this step. For moderately soluble gases, such as SO2 and O3, the presence of

surface moisture can have a marked effect on whether or not the molecule is actually

removed. For highly soluble and chemically reactive gases, such as HNO3, deposition is

rapid and irreversible on almost any surface. Solid particles may bounce off a smooth

surface; liquid particles are more likely to adhere upon contact.

3.3 Aerodynamic Resistance

Turbulent transport is the mechanism that brings material from the bulk atmosphere down

to the surface and therefore determines the aerodynamic resistance. The turbulence intensity

is principally dependent on the lower atmospheric stability and the surface roughness and

can be determined from micrometeorological measurements and surface characteristics such

as wind speed, temperature, and radiation and the surface roughness length. During daytime

conditions, the turbulence intensity is typically large over a reasonably thick layer (i.e., the well-

mixed layer), thus exposing a correspondingly ample reservoir of material to potential surface

deposition. During the night, stable stratification of the atmosphere near the surface often

reduces the intensity and vertical extent of the turbulence, effectively diminishing the

overall dry deposition flux. The aerodynamic resistance is independent of species or

whether a gas or particle is involved except that gravitational settling must be taken into

account for large particles.

The aerodynamic component of the overall dry deposition resistance is typically based on

gradient-transport theory and mass-transfer/momentum-transfer similarity (or mass-

transfer/heat-transfer similarity) [1]. It is presumed that turbulent transport of species

through the surface layer (i.e., constant-flux layer) is expressible in terms of an eddy

diffusivity multiplied by a concentration gradient, that turbulent transport of material occurs

by mechanisms that are similar to those for turbulent heat and/or momentum transport,

that measurements obtained for one of these entities thus can be applied, using scaling

parameters, to calculate the corresponding behavior of another. Expressions for the

8

aerodynamic resistance are most easily obtained by integrating the micrometeorological

flux-gradient relationships. Applications of similarity theory to turbulent transfer through

the surface layer suggest that the eddy diffusivity should be proportional to the friction

velocity and the height above the ground. Under diabatic conditions the eddy diffusivity

is modified from its neutral form by a function dependent on the dimensionless height

scale, ζ=z/L, where L is the Monin-Obukhov length.

The vertical turbulent flux of a species of concentration, C, through the (constant-flux) surface

layer is expressed as

z

CKFa

(3.3)

where K is the appropriate eddy diffusivity and Fa is, by definition, constant across the

layer. From dimensional analysis and micrometeorological measurements, the eddy

momentum (KM ) and heat diffusivity (KT) can be expressed by

M

M

zkuK (3.4)

T

T

zkuK (3.5)

where k is the von Karman constant, *u is the friction velocity, and ϕT and ϕM are

empirically determined dimensionless momentum and temperature profile functions

respectively.

If Eq. (3.3) is integrated across the depth of the constant-flux (i.e., surface ) layer from z3

down to z2, the flux Fa may be written as

1

23

3

2

z

z

a dzzku

CCF

(3.6)

where, as above, C3 and C2 refer to concentrations at the top and bottom of the constant-

flux layer and ϕ(ζ) denotes either ϕT(ζ) or ϕM(ζ) whichever is deemed analogous to the

species profile function. The aerodynamic resistance is thus given by

3

2

z

z

a dzzku

R

(3.7)

The integral in Eq.(3.6) is evaluated from the bottom of the constant-flux layer (at z0, the

roughness length) to the top ( zr, the reference height implicit in the definition of Vd). If

9

suitable empirical forms of the stability dependent temperature profile are assumed then the

above equation (3.6) can be integrated to yield explicit expressions for Ra. These expressions can

be found in [1] and are given below:

)__(01_

)_____(0_

)___(10_

151

1

7.41

)(

41 unstablefor

neutralfor

stablefor

T

(3.8)

)(

)(

)(

tantan211

11lnln

1

ln1

7.4ln1

0

11

22

2

0

2

0

0

unstable

neutral

stable

z

z

u

z

z

u

z

z

u

R

r

rro

o

o

a

(3.9)

Where 0 = 41

0151 and r = Lzr 00

41,151

The theory is applicable only in the surface layer where the flux in non divergent and can be

assumed constant, that is the Richardson No. should be between -3 and 2. An approximate

maximum extent is 100m. In order to use the above equations it is necessary to determine the

friction velocity and the Monin-Obhukov length. The friction velocity can be calculated by [16]

0

*ln

)(

zdz

zkuu

(3.10)

The Monin-Obhukov length (L), by definition, is the height at which turbulence produced by

mechanical and buoyancy forces match. It characterizes atmospheric stability in the surface layer

and is positive for a stable atmosphere and negative for an unstable atmosphere. It is determined

from the Pasquill Stability classes by the method of Golder (1972) as detailed in [1]. The

roughness length (z0) is taken as 1 m as recommended for urban locations by Voldner et al.

(1985) and reproduced in [1]. The displacement length (d) is 70 – 80% of the height of the large

roughness elements [16]. The reference height (z) is taken as 10 m and the Von Karman constant

(κ) as 0.4.

10

3.4 Quasi Laminar Resistance

The resistance model for dry deposition postulates that adjacent to the surface exists a

quasi-laminar layer, across which the resistance to transfer depends on molecular properties

of the substance and surface characteristics. This layer does not usually correspond to a

laminar boundary layer in the classical sense; rather it is the consequence of many

viscous layers adjacent to the obstacles comprising the overall, effective surface seen by

the atmosphere. The depth of this layer constantly changes in response to turbulent shear

stresses adjacent to the surface or surface elements. In fact, the layer may only exist

intermittently on such surfaces as plant leaves, which are often in continuous motion.

Whether a quasi-laminar layer actually exists, physically depends on the smoothness and

the shape of the surface elements, and to some extent, the variability of the near-surface

turbulence, but, in terms of the theory, it is considered to exist.

A viscous boundary layer adjacent to the surface of some obstacle on which deposition

is occurring is an impediment to all depositing species, regardless of the orientation of

the target surface. Molecular and Brownian diffusion occur independently of direction;

molecular diffusion can occur to the underside of a leaf just as easily as it can to the

top surface. The flux across the quasi-laminar sublayer adjacent to the surface is

expressed in terms of a dimensionless transfer coefficient, B, multiplying the concentration

difference across the layer, C2-C1. Since, under steady-state conditions, this flux is equal to

that across the surface layer, we write

12 CCBuFa (3.11)

Where C1 is the concentration at the surface, and, by convention, the transfer coefficient is

dimensionalized by u . The quasi-laminar layer resistance is then given by

*

1

BuRb (3.12)

The quasi-laminar resistance Rb depends on the molecular (for gases) or Brownian (for

particles) diffusivity of the material being considered. This dependence can be accounted for

through the dimensionless Schmidt number, Sc = v/D, where v is the kinematic viscosity of

air and D is the molecular diffusivity of the species. Measurements over canopies have

shown Rb to be relatively insensitive to the canopy roughness length z0. A useful expression for

Rb for gases in terms of the Schmidt number is [1]

*

325

u

ScRb (3.13)

11

3.5 Surface Resistance

The surface or canopy resistance is the most difficult to parameterize due to the complex nature

of the processes involved in the absorption and retention of gases by vegetative surfaces. At the

same time it is often the dominating resistance especially in the tropics where the atmosphere is

highly convective. In recent studies conducted for this region, the parameterization of Wesely

(1989) [10] was used to calculate the surface resistance [18-19]. It has been used in other studies

for Asia as well [16-17]. However, the several advancements made in the science of dry

deposition and in the understanding of the dependence of surface resistance on environmental

factors have rendered the parameterization of Wesely (1989) somewhat outdated. Many of these

advancements are embodied in the work of Zhang et al. (2003b) [13]. Among these is the

inclusion of satellite derived Leaf Area Index (LAI) which allows an accurate representation of

foliage characteristics and its temporal variation. This has a marked effect on Rc and Vd.

Nevertheless, the method of Wesely (1989) remains the simplest method of calculating

deposition velocity with reasonable accuracy and therefore is still widely employed. In this work

both methods are used. While the parameterization of Wesely (1989) provides an estimate of the

magnitude of Vd and the intensity of dry deposition, the method of Zhang et al. (2003b) is used to

carry out an in depth analysis of the process and its region specific dependence on environmental

factors and meteorology.

3.5.1 Method of Wesely (1989)

The parameterization of Wesely (1989) calculates the canopy resistances by accounting for

several sub-resistances in series and parallel. This method is also detailed in Sienfeld and Pandis

(2006) [1].

1

1111

gsaccldclumst

crrrrrrr

R

(3.14)

The first term includes the leaf stomatal (rst) and mesophyll (rm) resistances, the second term

is outer surface resistance in the upper canopy (rlu), which includes the leaf cuticular resistance

in healthy vegetation and the other outer surface resistances; the third term is the resistance in the

lower canopy, which includes the resistance to transfer by buoyant convection (rdc) and the

resistance to uptake by leaves, twigs, and other exposed surfaces (rcl) and the fourth term is

resistance at the ground, which includes a transfer resistance (rac) for processes that depend only

on canopy height and a resistance for uptake by the soil, leaf litter, and so on at the ground

surface (rgs).

Of these the stomatal ( rst ) resistance is of particular interest since it accounts for the effects of

solar radiation and temperature on the opening of the stomata. This has a major effect on the

overall resistance and is responsible for day to day variations in the value of the canopy

12

resistance. The bulk canopy stomatal resistance is calculated from tabulated values of rj (where rj

is the minimum bulk canopy stomatal resistance for water vapor) , the solar radiation (G in

W m-2

), and surface air temperature ( T in °C between 0 and 40

°C ) using

TTGrr jst

40

400

1.0

2001

2

(3.15)

In a similar manner, base resistance values are provided for different land use categories (LUC)

and seasonal categories. These are then modified to account for changes in specific

environmental factors via empirical formulations. In this study, the seasonal category was kept

fixed as mid-summer for all computations due to the evergreen nature of the canopy at NLC. The

winter season represents subzero temperatures and snow covered surfaces. Clearly, these

seasonal categories were developed by Wesely (1989) for regions quite unlike Neyveli. This is

one of the reasons for adopting LAI as a direct measure of seasonal changes in foliage which

affect Rc. During rains the leaf surfaces become wet, enhancing deposition of SO2 due to

dissolution into the aqueous phase. This effect is incorporated into the model by a suitable

reduction in the outer surface resistance in the upper canopy ( rlu ). For the complete formula the

reader is referred to the original paper of Wesely (1989) [10] or the comprehensive book by

Seinfeld and Pandis (2006) [1].

3.5.2 Method of Zhang et al. (2003b)

As mentioned above, many of the latest advancements in dry deposition theory are embodied in

the work of Zhang et al. (2003b). These include a sunlit/shaded big leaf model for the calculation

of the bulk canopy stomatal resistance from the individual leaf resistance via LAI. LAI is the

ratio of leaf surface to ground surface and is around 1 for urban canopies and close to 6 for

forests. Sunlit and shaded leaves are treated differently in this canopy -stomatal -resistance

model. In Wesely‟s parameterization (1989), a base bulk stomatal resistance is provided and then

modulated with radiation and temperature. This base bulk stomatal resistance value was

specified for discrete seasonal categories and over various land types. The problem with this

approach is that the seasonal categories considered by Wesely and the corresponding change in

the canopy structure do not match the climate and vegetation characteristics in tropical Asia.

Specifically, during the winter season at NLC, the temperature is around 25 ºC and the

vegetation is healthy. In contrast the winter seasonal category in Wesely (1989) describes

conditions of subzero temperatures and snow covered ground! Moreover, the same land use type

(e.g. agricultural) can also have widely different vegetative characteristics depending on the

geographical location. These short comings were realized by Gao and Wesely (1995) who

introduced LAI into the stomatal resistance model of Wesely (1989) [12]. In Zhang et al. (2003b)

all the resistances which are dependent on the canopy structure are related to LAI. This allows an

accurate representation of the local vegetative characteristics and the seasonal dependence of

green cover. The other improvements in Zhang et al. (2003b) include revised methods of

13

accounting for wet surfaces and their effect on stomatal and non-stomatal resistances and a new

parameterization of non-stomatal resistance which considers the effect of meteorological

variations [15].

For the above mentioned reasons, it was deemed necessary to adopt the parameterization of

Zhang et al (2003b) for an accurate and region specific study of dry deposition. The surface

resistance is represented as a combination of stomatal and non-stomatal resistances in parallel

since stomatal uptake as well as cuticular absorption and deposition onto twigs and the ground

occur simultaneously.

nsmst

st

c rrr

W

R

111

(3.16)

rst is the canopy stomatal resistance. Stomatal uptake of gaseous species is controlled by the

degree of stomatal opening. The major environmental factors which modulate stomatal opening

are solar radiation, ambient air temperature and water vapor pressure deficit and leaf water stress.

These are accounted for in the canopy resistance model. rm is the mesophyll resistance which is

treated as gas species dependent and specified as 0 for SO2 since it is highly soluble in water

[14]. Together they signify the total resistance to stomatal uptake. Wst accounts for the blocking

of stomata during rains by the film of water which develops on the leaves. However, the net

result of rain is a decrease in overall surface resistance since it greatly reduces the non-stomatal

resistance (rns) of the surface in the case of a soluble gas like SO2. The non-stomatal resistance is

a combination of the in-canopy aerodynamic resistance (rac) and resistance to deposition to the

ground (rg), in series, along with canopy cuticular resistance in parallel (rcut).

cutgacns rrrr

111

(3.17)

The presence of wet surfaces due to rain or dew considerably decreases the cuticular and ground

resistances. The friction velocity is included in the parameterization of in-canopy aerodynamic

resistance, which is one of the advancements of this method. Apart from the canopy stomatal

resistance, the LAI also has an effect on the in-canopy aerodynamic resistance and the canopy

cuticular resistance. Hence, the LAI is quite an important parameter. The formulae for each of

these terms and the parameters based on land use category are given in [13-14]. A large number

of land use types are considered and the effect of environmental factors on stomatal conductance

is accounted for via formulations which vary with the type of vegetation. Thus it is possible to

include region specific information in the model and generate results which are far more

compatible to the study area using the method of Zhang et al (2003b). In the present study, NLC

is represented by an urban canopy land use type with tropical broadleaf vegetation.

14

CHAPTER 4: METEOROLOGICAL DATA PROVIDED BY NEYVEL

LIGNITE CORPORATION

NLC provided all the necessary meteorological data for the period from November 2008 to

October 2009. This year long data set was used both in dispersion modelling as well as

calculating the dry deposition velocity. Data reading were taken three times a day at 02:30, 08:30

and 14:30. We used the data at 02:30 and 14:30 to calculate deposition velocities during the

night and day respectively. Table 4.1 gives the monthly statistical mean and standard deviations

of the important meteorological quantities namely wind speed, solar radiation and relative

humidity as well as the number of rainy days.

Month Wind (m s-1

) Solar radiation

(W m-2

)

Temperature

(ºC )

Relative

humidity (%)

Rainy

Days

MEAN STD MEAN STD MEAN STD MEAN STD

Nov'08 Day 1.18 0.24 385.22 131.34 29.57 1.71 64.17 1.24 11

Night 0.30 0.21 NA NA 22.73 1.65 59.28 0.30

Dec'08 Day 1.37 0.46 346.12 146.41 28.00 2.00 63.16 2.57 4

Night 0.55 0.39 NA NA 22.00 0.96 58.77 2.26

Jan'09 Day 1.37 0.25 400.65 110.95 29.06 1.40 64.39 0.77 1

Night 0.39 0.22 NA NA 21.71 1.25 59.45 0.21

Feb'09 Day 1.71 0.46 457.14 141.62 30.34 1.03 64.15 0.86 0

Night 0.11 0.16 NA NA 23.28 1.70 59.35 0.31

Mar'09 Day 1.60 0.69 424.84 157.93 30.52 2.22 63.59 1.17 2

Night 0.13 0.16 NA NA 24.16 1.80 59.39 0.34

Apr'09 Day 1.52 0.47 456.33 137.25 34.44 1.80 63.83 0.48 2

Night 0.29 0.39 NA NA 26.29 1.00 59.10 0.34

May'09 Day 1.84 1.81 475.45 92.38 36.65 2.36 55.57 5.43 0

Night 1.19 0.65 NA NA 27.79 1.62 52.91 4.95

Jun'09 Day 2.20 0.43 508.00 89.53 35.51 0.88 51.66 0.25 3

Night 1.07 0.51 NA NA 27.43 1.01 48.93 0.30

Jul'09 Day 2.24 0.64 422.38 138.29 34.02 1.86 51.04 2.49 4

Night 0.96 0.56 NA NA 26.63 0.98 48.43 4.76

Aug'09 Day 1.75 1.53 477.31 103.46 32.90 2.21 52.16 0.59 6

Night 0.74 0.62 NA NA 25.79 1.29 49.61 0.40

Sep'09 Day 1.82 0.84 399.29 112.63 33.65 2.04 52.11 0.66 4

Night 0.68 0.48 NA NA 25.76 1.10 50.92 2.09

Oct'09 Day 1.64 0.88 416.00 111.69 32.93 1.92 52.57 0.95 13

Night 0.51 0.70 NA NA 25.20 1.05 50.88 0.35

Table 4.1: Meteorological data provided by NLC

15

It is observed that the temperatures are generally above 25 ºC even during December and that

NLC receives considerable solar radiation throughout the year, including the month of October

which experiences the maximum rainfall. The wind speeds are lower than 2 m s-1 except for

June and July. The wind speed is grater during the day. The diurnal variation in relative humidity

is not much and is contained within 5 %. Importantly, the NE Monsoon season from October to

November is reflected in the number of rainy days which is much higher during these months.

16

CHAPTER 5: DEPOSITION VELOCITY BY THE METHOD OF WESELY

(1989)

5.1 Deposition Velocity of SO2 at NLC for three seasons

Fortran codes were written for calculating the deposition velocity. The average deposition

velocity of SO2 is computed for the months of December, May and October which represent the

three seasons experienced at NLC- mild winter, hot dry summer and wet North East Monsoon

respectively (see Table 5.1). Recent work by Seth et al. (2010) and Patra and Ghosh (2010)

present computations of deposition velocities for the NLC region [18-19]. However these studies

do not calculate the aerodynamic resistance via the detailed flux gradient relationships employed

in this study nor do they account for the effect of wet leaf surfaces.

Season Vd (cm s-1

)

Day Night

DEC 08- Mild winter 0.487 0.131

MAY 09- Hot Summer 0.443 0.122

OCT 09- NE Monsoon 0.507 0.115

Table 5.1 Deposition Velocity for various seasons at NLC

Fig. 5.1 Resistances and deposition velocity calculated for December 2008 at 14:30 IST

17

5.2 Variation of Vd with meteorological factors

It is beneficial to understand the factors which influence the deposition velocity by taking a close

look at the calculations for the month of December 2008 at 14:30 IST (daytime). The values of

the resistances and Vd computed for each day is shown in Fig. 5.1. The canopy resistance (Rc)

proves to be the controlling resistance in the dry deposition process, accounting for 80% of the

total resistance. Hence one would expect the factors which modulate Rc (solar insolation and

temperature) to have a marked affect on Vd as well. This is indeed the case. In fact the values of

Vd are substantially lower at night since there is no solar radiation and the stomata are practically

closed (see Table 5.1 and Fig. 5.2).

Fig. 5.2. Diurnal variation in deposition velocity for December 2008

Fig. 5.3. Variation of aerodynamic resistance with wind speed (Dec 2008, 14:30 IST)

In order to observe the effect of solar radiation and wind speed on the dry deposition process, the

normalized values of Ra and Rc are plotted with the normalized values of wind speed and solar

18

radiation respectively (Fig. 5.3 and Fig. 5.4). The clear anti correlation between these factors and

the resistances is observable. The variation of Rb with wind speed is much the same as Ra.

Fig. 5.6 shows the variation of Vd with both environmental factors. A close look at day 13 in

Fig. 5.6 makes it clear that the solar radiation has a stronger role to play than the wind speed.

This is because the surface resistance accounts for a major portion of the total resistance. Further,

the wind speed has no effect on surface resistance according to the parameterization of Wesely

(1989).

Fig. 5.4. Variation of canopy resistance with solar insolation (Dec 2008)

Fig. 5.5. Variation of deposition velocity with wind speed and solar insolation (Dec 2008)

5.3 Seasonal variation in Vd

It must be remembered that seasonal variation in foliage characteristics is ignored in these results

since the seasonal category was kept constant. This was done since the difference between

19

seasons represented in Wesely (1989) was too great for them to be used in our study for tropical

Neyveli. Hence the seasonal variation in Vd is solely attributable to meteorological variations.

While high solar radiation stimulates stomatal opening and increases dry deposition, high

temperatures (close to 40°C) cause the stomata to close. Thus in the month of May, although

strong solar radiation is incident, high temperatures above 35°C reduce the value of deposition

velocity. During the month of December, the temperature is around 20°C and solar radiation is

sufficient for the deposition velocity to be higher than it is in peak summer (May). In October,

although the onset of the North East Monsoon would lead to reduced solar insolation, the

presence of moisture on the leaf surfaces increases dry deposition due to dissolution of SO2. We

obtain the highest values for Vd during the North East (NE) Monsoon season.

5.4 Comparison with results from other Asia based studies

It is interesting to compare our results of deposition velocity with those obtained by other

modelling and experimental studies. Xu and Carmichael (1998) have employed the methods

described in this paper to calculate deposition velocities of SO2 for the entire Asia region,

including South India [16]. However, the spatial resolution of these results is limited. Moreover

our calculations consider the meteorological and climatic conditions unique to NLC as well as

the effect of wet leaf surfaces. Nevertheless some results are comparable. Their values of Vd

(daytime) for May and August are 0.3 and 0.45 respectively. Their value for December is much

lower at 0.2 as compared to our result of 0.487. This is due to the mild winter experienced at

NLC with optimum temperatures of around 20°C for stomatal opening.

Matsuda et al. (2006) performed field experiments to determine the dry deposition velocity of

SO2 over a tropical forest in Northern Thailand [9]. They report values of deposition velocity up

to 0.31 cm s-1

(daytime) and 0.11 cm s-1

(nighttime) for the dry season. The night time value is

nearly the same as our results. Generally the values of Vd (daytime) at NLC predicted by Wesely

(1989) are higher, possibly due to year round higher solar insolation and the fixed seasonal

category.

20

CHAPTER 6: DEPOSITION VELOCITY BY THE METHOD OF ZHANG

et al. (2003b)

6.1 Leaf Area Index for NLC

As described in section 3.5.2, LAI is a key parameter which captures the local vegetative

characteristics and its seasonal dependence. In this work, the LAI over NLC was obtained from

MODIS satellite data (product MCD15A2) [20]. The data is available in 1 km resolution and is

free to download. From the LAI data, which agrees with personal sampling of the vegetation, it

was observed that the trees are at their lush best during October, the month of the onset of the NE

monsoon and are at their leanest in May which is the peak of the dry summer season. Images

provided by the MODIS product (MCD15A2) of LAI over the peninsular part of the Indian

subcontinent are displayed below (Fig. 6.1).

Fig. 6.1 LAI over the subcontinent for 10

th Dec‟08, 17

th May‟09 and 16

th October‟09

respectively (MODIS MCD15A2)

Although there is a seasonal variation, there are no bare periods without any green cover-this is

in sharp contrast to trees in the mid-latitudes. Moreover, it is comforting to note that the month

of the least vegetative cover (i.e. May) is the hottest month when the boundary layer is at its most

convective, leading to dilution of pollutants. Values of LAI are available with a spacing of 8

days. The data obtained for the period from November „08 to October‟09 are presented in Fig

6.2. Cubic spline interpolation was used to obtain intermediate values of LAI for deposition

velocity calculation.

21

Fig 6.2 LAI for all months from Nov ‟08 to Oct ‟09. The markers represent data obtained from

MODIS while the red line is a cubic spline interpolation used to obtain intermediate values of

LAI for calculation

6.2 Deposition velocity of SO2 at NLC

The deposition velocity was calculated for each day from Nov‟ 08 to Oct ‟09 using the method

of Zhang et al. (2003b) as detailed in section 3.5.2. The monthly average value of Vd is displayed

in Fig 6.3.

Fig 6.3 Monthly average deposition velocity (Vd)

The average daytime value for the entire period is around 3.5 cm s-1

. The night time value is

lower due to the closed stomata in the absence of solar radiation. A comparison of Fir 6.3 with

Fig 6.2 shows that LAI has an effect on Vd. There is a decrease in daytime Vd from Nov‟ 08 to

May‟ 09 which corresponds to the decrease with LAI during this period. However, the variation

22

in Vd is not very large which justifies the use of the simpler method of Wesely (1989) for

approximate calculations.

6.3 Comparison of the results obtained using Wesely (1989) and Zhang et al. (2003b)

Table 6.1 shows a comparison of the Vd values computed using the methods of Wesely (1989)

and Zhang et al. (2003b).

Season LAI

Zhang et al.

(2003b) Wesely (1989)

Vd (cm s-1

) Vd (cm s-1

)

Day Night Day Night

DEC 08- Mild winter 0.91 0.334 0.105 0.487 0.131

MAY 09- Hot

Summer 0.54 0.215 0.145 0.443 0.122

OCT 09- NE

Monsoon 1.06 0.478 0.214 0.507 0.115

Table 6.1 Comparison of results obtained using the methods of Wesely (1989) and Zhang et al.

(2003b)

The Vd values obtained using the method of Wesely (1989) are generally higher than that of

Zhang et al. (2003b). This is to be expected since the Wesely (1989) method treats the region as

a forest while the LAI used in Zhang et al. (2003b) more accurately represents the urban canopy.

the LAI of a forest is around 6 while that of NLC is about 1 (typical of urban canopies). Apart

from this the general variation seems similar since the effect of LAI is not large in terms of the

magnitude of change in Vd. The variation with meteorology remains similar especially since the

computation of Ra and Rb for both cases is the same.

Fig. 6.4. Variation of canopy resistance with solar insolation (Dec 2008 14:30 IST)

23

However, one important difference is that Zhang et al. (2003b) considers the affect of wind

speed in the non stomatal resistance calculation. This increases the overall effect of wind speed

on the dry deposition process. Fig 6.4 demonstrates this fact as Rc is no longer solely controlled

by solar radiation as was the case for Wesely (1989) (please see Fig 5.4). Fig 5.5 showed that Rc

was the dominating factor on days 10 to 15 of Dec 08. But in this case wind speed plays the

major role (Fig 6.5).

Fig. 6.5 Variation of deposition velocity with wind speed and solar insolation (Dec 2008 14:30

IST)

6.4 Effect of wet surfaces due to rain

Another important factor is the effect of wet surfaces. The large peaks present in Fig 6.5 are due

to the presence of wet surfaces on those days when it rained. These wet surfaces are accounted

for to different extents in both methods which is why these peaks are not present in Fig 5.5. The

method of Zhang et al. (2003b) receives support from the work of Matsuda et al. (2006) who

performed field experiments to determine the dry deposition velocity of SO2 over a tropical

forest in Northern Thailand [9]. Although they studied a full fledged forest as opposed to an

urban canopy, the vegetative characteristics of the region are similar to our study area. They

observed much higher values of SO2 deposition velocity during the rainy season as compared to

the dry season with maximum values of 1.39 cm s-1 and 0.31 cm s-1 in the wet season and dry

season respectively (daytime). They emphasize the importance of accounting for the effect of

wet surfaces on non-stomatal resistance in order to accurately model the higher observed values

of Vd during the rains. Moreover, they found that the value of deposition velocity predicted for

tropical broadleaf trees by Zhang et al., (2003b) during the wet season was consistent with their

experimental observations. This effect will be considered in greater detail in Chapter 7.

24

CHAPTER 7: DEVELOPMENT OF A REGRESSION FORMULA TO

CALCULATE DEPOSITION VELOCITY

7.1 Requirement of a simple regression formula

There are no simple regression formulae for deposition velocity reported for any region. This is

understandable since the spatial validity of these formulas would be restricted to the region of

study. It would be applicable to regions with similar foliage characteristics and temporal

variation in foliage structure. This is reflected by the LAI and its variation through the year.

Moreover, the climatology would have to be similar to the original study region and the values of

the meteorological variables should fall in the same ranges. Nevertheless, a simple formula

would be a boon to workers who are not familiar with the science of dry deposition. It will

provide easy calculation of deposition velocity for application in environmental assessment

calculations or for use in atmospheric dispersion models.

In this work the deposition velocity has been calculated for a period which spans an entire year

(Nov „08 to Oct „09). Thus all possible variation in deposition velocity should be included in

these results. The method of Zhang et al. (2003b) is quite complex. In addition, one is required to

compute friction velocity and Monin-Obhukov length in order to determine the aerodynamic

resistance. Hence a computer code would be required even for a few computations of deposition

velocity. Thus a simple formula would be valuable to the environmental department at NLC and

possibly to workers in other parts of tropical Asia.

Moreover, due to the complex nature of the empirical formulae used in the surface resistance

parameterization of Zhang et al. (2003b) or Wesely (1989) for that matter, it is difficult to

identify the impact of an individual input on the deposition velocity. For example, wind speed

affects Vd through the aerodynamic resistance as well as the non stomatal resistance. A

regression formula with explicit dependencies on each input will help in identifying the

individual effects of each input on Vd and their relative magnitudes. A sensitivity study will be

much easier to implement. One will then be able to identify the most significant inputs. These

would have to be carefully measured to reduce error in Vd. On the other hand it may be possible

to neglect an input without greatly reducing accuracy. With the above considerations in mind, a

regression formula for deposition velocity of SO2 over NLC will be developed in this section.

7.2 Formulation of suitable non linear regression model

The important meteorological inputs are wind speed (U, m s-1

), LAI (m2 m

-2), solar radiation

(G, W m-2

), temperature (T, C) and relative humidity (RH, %). An obvious regression model

would be of the following form:

edcba

d RHTGLAIUQV (7.1)

25

However, this form would be valid for dry surfaces only. The presence of wet surfaces during a

rainy day greatly increases the deposition velocity (see section 6.3). This presence of wet

surfaces can be indicated by a binary variable R. R is 0 for dry surfaces and 1 for wet surfaces.

When R=1 there will be a discontinuous increase in deposition velocity. R acts as an on-off

switch in the Zhang et al. (2003b) parameterization. In order to capture this effect in a regression

formulae one must suitably modify Eq (7.1). Any such modification would depend on the degree

of enhancement of dry deposition due to wet surfaces. Specifically, the dependence of this

increase on the absolute magnitude of dry surface Vd is important. To identify this dependence,

the deposition velocity calculations were repeated for the entire period from Nov ‟08 to Oct ‟09

considering only dry surfaces and only wet surfaces. The resultant deposition velocities can be

termed as the dry surface deposition velocity Vd,dry and the wet surface deposition velocity Vd,wet.

The results are depicted in Fig. 7.1.

Fig. 7.1 The relationship between wet surface and dry surface deposition velocity

The exponential relationship between Vd,wet and Vd,dry is clear. Based on these results the

following non linear regression model is proposed.

edcba

dryd RHTGLAIUCV , (7.2)

RVRpVQV dryddrydd 1exp ,, (7.3)

Where R=0 for dry surfaces and R=1 for wet surfaces

Eq. (7.2) is adequate for the dry surface deposition velocity. Eq. (7.3) accounts for the effect of

wet surfaces as well. When the surface is wet R has a value of one and the deposition velocity is

given a value which is exponentially related to the magnitude of the dry surface deposition

velocity. If the surface is indeed dry, then the expression reduces to Eq. (7.1).

26

7.3 Analysis of the regression parameters and the regression fit

The above regression model was adopted and the results obtained using the Zhang et al. (2003b)

method were fitted to the same. A nonlinear least squares regression function, available in

Matlab, called „nlinfit‟ was used [21]. The parameter values and the 95% confidence intervals

are presented in Table 7.1.

Parameter Value

95%

confidence

interval

C 0.3285 0.2065

a 0.5508 0.0286

b 0.0765 0.0220

c 0.0336 0.0256

d -0.3537 0.1227

e 0.1379 0.0835

Q 0.1204 0.0144

p 6.6270 0.4293

Table 7.1 Parameter values of the regression model of Eq. (7.2-7.3) with the 95% confidence

intervals

The fit of the regression model is depicted in Fig 7.2 and Fig. 7.3. The small magnitude of the

residuals and their random nature indicate that the model describes the data well. Since all the

confidence intervals (Table 7.1) are smaller in magnitude than their respective parameter values,

all the inputs considered are significant. In other words none of the parameter values can be zero

which would indicate that Vd is independent of that particular input variable. This is not

unexpected since the data used for the regression was obtained from a model which used exactly

these inputs. In order to comment on the relative importance of the inputs it is necessary to

compute the normalized sensitivity of Vd to each of the inputs. This study will be taken up in the

near future as many useful conclusions can be drawn from it.

Only the exponent of temperature is negative in the regression model. This indicates an inverse

relationship between temperature and deposition velocity. The stomata of a plant close at

extremes of temperature (0 ºC and 40 ºC) with optimum temperatures around 25 ºC. Since

temperatures at NLC are above 25 ºC throughout the year, any increase in temperature would

result in closure of the stomata. This in turn increases the surface resistance which results in a

decrease in deposition velocity. All the other inputs have a positive effect on deposition velocity.

Any further comment regarding the relationship between inputs and deposition velocity would

have to await a further sensitivity analysis.

27

Fig. 7.2 Plot of deposition velocities obtained from the regression model against the original data

calculated using Zhang et al. (2003b)

Fig 7.3 Residual plot of the regression model

The regression formula developed here can be applied to NLC to calculate deposition velocity of

SO2 for NLC. The extensive calculations are simplified and only a hand calculator is required to

implement the formula. However, the above formula must be verified with new data from NLC

to establish its validity. This will be done shortly as soon as data is made available. In addition

the possibility of applying this formula to other tropical regions in Asia must be investigated.

Data from regions like Thailand can be used to calculate deposition velocity using the

Zhang et al. (2003) surface parameterization and compared with the results of the regression

model. If they prove to be satisfactory then this would be a significant result. It would encourage

the development of similar regression models for various regions which would greatly simplify

all calculations involving dry deposition.

28

CHAPTER 8: SCAVENGING EFFICACY OF THE MAN-MADE CANOPY

In this chapter we investigate the role of the urban canopy in improving air quality, especially in

the township. The flux of SO2 to the ground at any location in NLC can be computed from Eq.

(3.1) using the calculated deposition velocity (section 6.2) if the concentration at the reference

height is known. In the absence of concentration measurements, modelled values can be used to

study the removal of SO2 by the canopy. On the 21st of May 2009, a southwest wind transported

pollution directly over the township. The wind speed was 2.3 m s-1

and the solar radiation was

359 W m-2

.This situation provides an ideal setting for our study. However, before analyzing the

deposition of SO2, it is necessary to predict the concentration of SO2 over the township.

8.1 Dispersion Model for predicting SO2 concentration

In this study, a tailor made steady state atmospheric gaussian-dispersion model is used which

was developed as part of a consultancy with NLC [22]. This model is based on the gaussian

plume formula which is applicable to the steady state emission of a gas from an elevated stack

with a totally reflecting ground. Although this model does not account for deposition, the error in

predicted SO2 concentrations is relatively small especially since the township is close to the

stacks and the source strengths are high. The accuracy is sufficient for the purposes of this study.

The gaussian plume equation which predicts the concentration (µg m-3

) at any point around the

stack is given by:

2

2

2

2

2

26

2exp

2exp

2exp

2

10),,(

zzyzy

hzhzy

u

qzyxC

(8.1)

The stack is taken to be at the origin with the x axis along the centerline of the plume which is in

the mean direction of the wind. The y axis is along the horizontal and the z axis along the

vertical. According to this model, as the plume travels with a mean speed u m s-1

along the wind

direction, it disperses horizontally and vertically so that the average steady state concentration at

any cross section of the plume follows the normal Gaussian probability distribution. σy and σz (in

meters) are the standard deviations of the concentration in the y and z directions. q is the source

strength (g s-1

) and h is the effective stack height (the vertical rise of the plume, before it bends

over, added to the physical stack height- m). The dispersion parameters (σy and σz) depend on

atmospheric stability and distance from the stack and are computed using the formulae

recommended by Briggs (1973) based on the Pasquill atmospheric stability classes (Turner,

1969) as detailed in Seinfeld and Pandis (2006). A detailed exposition of gaussian plume

dispersion models can be found in [1,23].

29

8.2 Deposition from a plume

The ground level concentration computed from the dispersion model is shown in Fig. 8.1. The

township is demarcated by a rectangle and the white markers represent the two power stations

(TPS1 and TPS2) with TPS1 on the edge of the township. The text markers indicate the locations

of air quality monitoring stations. From Fig. 8.1 it is clear that much of the township experiences

concentrations above 10 μg m-3

. Areas closer to TPS1 receive higher amounts of the polluting

gas and the concentration in the narrow region surrounding the plume centerline exceeds

100 μg m-3

.

Fig.8.1 The modelled ground level concentration over the township on 21

st May 2009, 14:30 IST

(µg m-3

)

Due to the presence of the evergreen canopy, there is a continuous deposition of material from

the plume onto the trees. This flux is greater in regions of higher concentration and can be

evaluated using Eq. (3.1). Material will be deposited as long as the plume remains aloft over the

canopy and the wind direction does not change. Considerable amount of pollution is deposited

and contours of the mass flux are shown in Fig. 8.2. Approximately 1.91 kg of SO2 is deposited

onto the canopy within the township, in an hour. However, this amount is insignificant when

compared to the source strength of the emissions from the stacks which continuously pump

pollution into the atmosphere (see Table 1.1). Since the township is very close to TPS 1 there is

no perceivable change in the ambient air concentration while the plume remains aloft. However,

areas surrounding NLC would benefit as the plume would have travelled a greater distance and

much more SO2 would have been deposited over the canopy which extends beyond the township.

30

This study can be generalized for a wind driven plume, over any part of NLC with a canopy

cover.

Fig.8.2. Mass of SO2 deposited per unit area per unit time on 21

st May 2009, 14:30 IST (µg m

-2

hr-1

)

8.3 Removal of residual pollution and improvement of air quality

In the previous section the deposition of SO2 from a plume was analyzed. However, at any time

only a small region of NLC can be directly affected by the plume. The other regions will

experience residual pollution, left over from a previous visit of the plume or transported from

other affected parts of NLC. The trees can reduce the residual SO2 levels in these regions which

do not receive a constant supply of SO2 for a considerable period of time. These conditions are

analogous to those prevalent in cities at night. There is a buildup of pollutants during the day

when sources of gaseous pollutants are numerous. At night the emissions subside due to low

levels of traffic and urban activity. Since there is no replenishment of pollution, dry deposition

onto urban trees can result in improved air quality by the morning. In NLC, this situation is

realized when a change in wind direction causes the plume to move away from the township or if

a period of calm follows the plume‟s visit over the township. In either case, SO2 will be left over

the township and diluted by the convective motion of the atmosphere. The mixed layer of the

atmosphere, within which this dilution is restricted, is the well mixed region of the atmosphere

adjacent to the earth‟s surface. The height of the mixed layer varies with the time of day, the

location of the site (latitude) and the atmospheric stability. The residual SO2 confined within the

mixed layer over the township will be gradually depleted due to dry deposition onto the trees. A

first order removal of species from the bottom of a closed stirred tank is a simple way to model

this process. A mass balance on SO2 for a mixed layer of height Hmix yields:

31

mix

d

H

CV

dt

dC

(8.2)

This equation when integrated yields the following expression for the time dependent

concentration in the mixed layer of the atmosphere, where C0 is the initial residual concentration.

mix

d

H

tVCtC exp0

(8.3)

The initial residual pollutant concentration (C0) can be obtained by first estimating the total

amount of pollution left over a given area and then distributing it uniformly throughout the

mixed layer. This is done by integrating the plume concentration predicted by the dispersion

model throughout the atmosphere for all points within a designated zone (in this case, the

township) up to the mixing height and then dividing by the total volume of the region of

integration. The present calculation requires an estimation of the height of the mixed layer. This

height varies in the summer from 500 m in the morning up to 2-3 km in the late afternoon with

an average of 1000 m [1]. At night the inversion layer is much lower, sometimes only 100 m

which can result in high pollution levels. At NLC, this is not much of a concern since the stacks

are elevated and most of the pollution is transported above this height. A detailed method for

estimating the mixed layer height and its day time variation is given by [24]. For the purpose of

this work, representative values of 1000 m and 500 m are used. The cleansing of the atmosphere

over the township due to the removal of SO2 by the canopy is depicted in Fig. 8.3. At lower

mixing heights, the concentration is much higher, but so is the intensity of the cleansing action.

The deposition velocity is low in May and so is the removal of SO2. However, it is nature‟s boon

that the lowest values of deposition velocity coincide with the hottest month (May) when the day

time mixing height is high and pollution episodes are unlikely. This is in contrast to mid-latitudes

where the lowest deposition velocity values occur during winter when the mixing height is low.

The above calculation is repeated using the deposition velocity of October (Table 3) and the

results are depicted in Fig 8.4. A comparison with Fig. 8.4 clearly demonstrates the accelerated

pace of atmospheric cleansing due to the higher deposition velocity of October.

As mentioned previously, the height of the mixed layer can be very low at night. This can be a

problem in polluted cities of developing countries where the majority of emissions have ground

sources such as moving vehicles and burning garbage. In such cases the pollutants can become

highly concentrated and have a harmful impact on the health of the local population. The

presence of pollutant tolerant vegetation can be a mitigating factor as the removal by deposition

increases with increase in concentration of the deposition species.

32

Fig.8.3. Depletion of residual SO2 concentration over the township on 21

st May 2009.

Fig.8.4. Depletion of residual SO2 concentration over the township considering the higher

deposition velocity of October

33

CHAPTER 9: CONCLUSION AND FUTURE WORK

At the end of the first decade of the twenty first century, the developing nations of the world are

in a quandary. Constant industrialization and rising per capita energy consumption implies

increasing fossil fuel derived energy usage. In most countries, renewable energy sources alone

will not be able to meet the exorbitant energy demands in the foreseeable future. At the same

time, the pollution caused by toxic emissions from thermal power plants and industries can no

longer be ignored. Sustainable development implies the maintenance of a delicate balance

between human progress and conservation/promotion of Nature. Environmental impact

assessment studies of new and existing projects form an important component of the roadmap to

sustainability. Such studies often turn to mathematical modelling methods for analyzing the

impacts of polluting releases, especially gaseous emissions in the context of thermal power

plants. Thus far, most studies in Asia have resorted to borrowing results from mid latitude

analyses or adopting hasty adaptations of models which were developed for regions quite unlike

their own. The widely different climatology, ecology and general environment of the Asian

region demands region specific studies and analyses.

In this work a detailed modelling study of the removal mechanisms of gaseous pollutants is

presented for the Neyveli Lignite Corporation (NLC), located in Tamil Nadu, India. Removal of

SO2 via dry deposition is addressed with a particular emphasis on using local meteorological data

and determining region specific model parameters. The deposition velocity is computed for each

day of a year long period from Nov „08 to Oct ‟09. Using this data it was possible to develop a

regression formula for calculating the deposition velocity at NLC at any time of the year. This

greatly reduces computation and will be especially useful to non technical workers. However,

this formula is valid only for NLC. Although it is possible that it may represent other tropical

Asian regions, this remains to be verified. The sensitivity of deposition velocity to each of the

inputs must also be studied. Thus one can determine the input variables which must be most

carefully measured and if any of them can be left out without greatly compromising accuracy.

The visionary founders of NLC started an afforestation program several decades ago and now the

thriving township is receiving the full benefits of this action. The presence of the green canopy

provides a round-the-year removal mechanism for pollutants and thus contributes to better living

conditions in terms of real air quality improvement apart from aesthetic benefits. However, the

ability of the vegetation to survive under daily pollutant stress is a matter which begs further

investigation, especially in context of the continued urbanization in India and other developing

countries of Asia. The response of the vegetation may be quite different from that of European

and North American plants and calls for another region specific study. The trees at NLC have

been able to survive the continuous exposure to the emissions of the power plants but this is, in

part, due to the convective atmosphere and the elevated emission sources.

34

At various points in the analysis, it was observed that nature has provided the region with several

advantages as far as mitigation of pollution was concerned. These include the fact that the leanest

state of the vegetative canopy coincides with the hot summer when the convective boundary

layer will ensure dilution of polluting emissions. This study is an example of the important

inferences that can result from region specific studies that may be missed if unsuitably adapted,

borrowed models are used. Most importantly, it is hoped that more such studies are carried out in

developing countries where sustainable development is as yet only an ideal and Nature‟s

resilience is constantly put to the test.

35

PUBLICATIONS/PRESENTATIONS

1. Picardo, J. R. and Ghosh, S. Establishing the Efficacy of the Cleansing Action of

Tropical Evergreens: A Modeling Analysis of Asia‟s Largest Lignite based Power Plant.

Proc. 1st EnvironmentAsia International Conference, Bangkok, Thailand, 2011

2. Picardo, J. R. and Ghosh, S. Establishing the Efficacy of the Cleansing Action of

Tropical Evergreens: A Modeling Analysis of Asia‟s Largest Lignite based Power Plant.

EnvironmentAsia. Accepted

3. Picardo, J. R. and Ghosh, S. Removal Mechanisms in a Tropical Boundary Layer:

Quantification of Air Pollutant Removal Rates around a Heavily Afforested Power Plant.

Air Pollution/ Book 4, Moldoveanu, A. (Ed.), ISBN 978-953-307-527-3, Intech. Accepted

36

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