STOCHASTIC MODELLING STUDY OF AMBIENT AIR QUALITY OF DELHI CITY
By
PRAGATI SHARMA Centre for Energy Studies
Submitted
in fulfilment of the requirements of the degree of
Doctor of Philosophy
to the
Indian Institute of Technology, Delhi
February, 2008
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The manifestation of the mode of goodness
can be experienced when all the gates of the body are illuminated by knowledge.
- Geeta (14/11)
CERTIFICATE
The entitled thesis "Stochastic Modelling Study of Ambient Air Quality of Delhi City"
being submitted by Ms. Pragati Sharma to the Indian Institute Technology, Delhi for the award of the degree of Doctor of Philosophy, is record of original bonafide research carried out by her.
She has worked under our guidance and supervision and has fulfilled the requirements for the submission of this thesis, which has attained the standard required for a Ph. D. degree of this Institute. This work, or any part thereof, has not been submitted elsewhere for the award of any degree or diploma.
A -
Prof. Kaushik Prof Avinash Chandra
Centre for Energy Studies Centre for Energy Studies
Indian Institute of Technology, Delhi Indian Institute of Technology, Delhi
New Delhi — 110016. New Delhi - 110016
ACKNOWLEDGEMENTS
The Thesis has been accomplished under the guidance and supervision of Prof. S.C.
Kaushik and Prof. Avinash Chandra, Centre for Energy Studies, Indian Institute of Technology, Delhi. I am thankful to Prof S.C. Kaushik for giving me an opportunity to work on this topic. I am grateful to Prof Avinash Chandra for hearing and understanding the problems that I faced during the course of my research work. I take this opportunity to express my sense of gratitude and indebtedness to my supervisors for their valuable guidance and suggestions on the subject of study.
Many times while studying in a purely academic domain, one often neglects the practical aspect of a particular problem. Fortunately, regular discussion on the subject with Dr. Prateek Sharma, Associate Dean, Faculty of Applied Sciences, TERI University, Delhi has brought in practicality in my perspective to approach the problem. He has always been an inspirational support and has given ample hearing to my problems, despite his busy schedule, throughout the study period. Frequent meeting and discussions arranged by him for my benefit with other technical and field personnel in the air pollution division of CPCB and CRRI have immensely helped me in understanding the practical features of the study and has been a major factor in giving a pragmatic tilt to my research work.
There are many from behind the scene who have encouraged and supported my work and I thank them. The list is endless. I thank Prof Mukesh Khare, Department of Civil Engineering, Indian Institute of Technology, Delhi for his advice and suggestions that helped me in organising the order of my work.
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The period of research work was full of learning experiences. The circumstances were adverse against my moving ahead with work. During this, I interacted with the worst phase of my life, but all along, a strength "a Guru of my I ife and work" supported, guided and showed the light to reach the ultimate objective by putting in me the real courage to face the adversaries and work on with focussed mind.
I would also like to thank all the research scholars and staff members working at the Centre for Energy Studies, Indian Institute of Technology for their cooperation. I wish to thank to all those who directly or indirectly have been instrumental in successful completion of this endeavour.
There are few names which are very close to my heart and their right place is there, straight in a special corner of my heart, so it is better they should remain there! Who they are, the discerning one will definitely make out.
February 2008 Pragati Sharma
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ABSTRACT
The present study was undertaken to carry out a comprehensive analysis, assessment and prediction of overall ambient air quality in the capital city of Delhi. All criteria pollutants viz.
SO2, NO2, SPM, PK() and CO monitored at the six national ambient air quality monitoring (NAAQM) and ITO station were modelled using stochastic modelling tools.
The study included identification and estimation of probability density function (pdf) models of all pollutants for different averaging times. The Rollback model, which depends on the pdf, was also used to estimate the percentage source emission reduction required to meet the national ambient air quality standards (NAAQS). The models were used to evaluate the compliance with NAAQS and predict exceedance of standards at different locations in the control region for various pollutants. The air quality criterion was found to be non-compliant for SPM and PK° at all the stations.
The extreme value theory was applied for modelling extreme air pollution events and violation of standards. The developed model can be used as a predictive tool that can provide the air quality decision makers/managers with an effective means to manage the future air pollution problem.
Univariate linear stochastic time—series models were developed for different pollutants at the six NAAQM and the ITO station. The study reveals that though the univariate time-series models follow a "black-box" approach, the system characteristics are intrinsically represented by the data and fairly satisfactory forecasts can be obtained.
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Finally, principal component analysis was used to study the underlying relationships among the data. More specifically, the analysis resulted in identification of components that could be attributed to particulate sources, gasoline and coal combustion.
CONTENTS
Page No.
Certificate
Acknowledgements ii
Abstract iv
List of figures
List of tables xxvii
List of abbreviations xxxiii
Chapter 1 Introduction 1
1.1 General 1
1.2 Relevance and justification of study 4
1.3 Problem definition 10
1.4 Scope and objectives 10
1.4.1 Scope 10
1.4.2 Objectives 10
1.5 Organisation of thesis 12
Chapter 2 Review of relevant literature 14
2.1 Introduction 14
2.2 Deterministic modelling 17
2.3 Statistical modelling 21
2.4 Air pollution modelling — Indian perspective 38
Chapter 3 Air quality management and modeling 40
3.1 General 40
3.2 Real-time prediction 44
3.3 Air quality modelling 47
3.3.1 General 47
3.3.2 Air quality models — classification 48 3.3.2.1 Deterministic mathematical models 50
3.3.2.2 Statistical models 53
3.3.2.3 Physical models 56
Chapter 4 Site and data description 58
4.1 The study region — Delhi 58
4.1.1 General 58
4.1.2 Air quality 59
4.1.3 Site description 61
4.2 Data description 63
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Chapter 5 Research methodology and development of models 66 5.1 Statistical characteristics of ambient air quality data 66 5.2 Modelling statistical distribution of air pollution concentration 67 5.2.1 Parametric probability distribution models 67 5.2.2 Modelling the parent frequency distribution models of pollutants 67 5.2.2.1 Model identification 68 5.2.2.2 Estimation of model parameters 69 5.3 Evaluation of compliance of NAAQS and prediction of exceedances 70
5.3.1 Theory 70
5.3.1.1 Terminology 72
5.3.1.2 Assumptions 72
5.3.1.3 Prediction of number of exceedances of NAAQS and
return period 72
5.3.1.3.1 Distribution of exceedances 73 5.3.1.3.2 Expected return period 73 5.3.2 Probability of exceedances of NAAQS 75
5.4 The rollback model 75
5.5 The extreme value model 78
5.5.1 Problem definition 78
5.5.2 Theory 78
5.5.3 The Type I asymptotic distribution 79
5.5.3.1 Useable expressions 81
5.5.3.1.1 Cumulative probability estimate 81 5.5.3.1.2 Reduced random variate estimate 81 5.5.3.1.3 Return period 82 5.5.3.1.4 Relation between Gumbel variate and
return period 83
5.5.3.1.5 Probability plot 83 5.5.3.2 Parameter estimation 83 5.5.3.3 Confidence in the prediction estimate 85 5.5.3.3.1 Probability of exceedance 85 5.5.3.3.2 Confidence limits 85
5.5.4 Data description 86
5.6 The time series models 87
5.6.1 Fundamental concept and notation 87 5.6.2 Stepwise model building process 88 5.6.2.1 Models for the NAAQM stations 91 5.6.2.2 Models for the ITO station 95 5.7 The principal component analysis model 96
5.7.1 Theory 96
5.7.2 Useful results for interpreting the principal components 97 5.7.2.1 The coefficient of determination 97 5.7.2.2 Scaling of eigen vectors 97 5.7.2.3 Truncation of the principal components 98
5.7.2.4 Percentage variance 98
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5.7.2.5 Scree plot 99 5.7.2.6 Last retained eigen value 99
5.7.3 The data for PCA 100
Chapter 6 Results and discussions 101 6.1 Identification of statistical distribution models 101 6.2 Evaluation of compliance and prediction of exceedance of NAAQS 105
6.3 The rollback model 107
6.4 The order statistics (extreme value model) 108 6.4.1 Local air quality management 110
6.5 The time series models 111
6.6 Principal component analysis 113
Chapter 7 Conclusions and Contributions 115
7.1 General 115
7.2 Identification of Statistical distribution models 116 7.3 Evaluation of compliance and prediction of exceedance of NAAQS 117
7.4 The rollback model 118
7.5 The extreme value model 118
7.6 The time series models 119
7.7 The principal component analysis 120
7.8 Final remarks 121
References 123
Annexure to chapter 5 156
Annexure to chapter 6 321
Appendix I The national ambient air quality standards 388 Appendix II Description of sites and instrumentation 390
11.1 The study region- Delhi 390
II.1.1 Physiographic features 390
11.1.2 Demography 391
11.1.3 Climate 392
11.2 The ambient air quality monitoring stations 394 11.2.1 NAAQM Station I Ashok Vihar 394 11.2.2 NAAQM Station II Janak Puri 394 11.2.3 NAAQM Station III Nizamuddin 394 11.2.4 NAAQM Station IV Shahadra 395 11.2.5 NAAQM Station V Shahazada Bagh 396 11.2.6 NAAQM Station VI Sirifort 396
11.2.7 The ITO Station 397
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11.3 Instrumentation and analytical methods 397
11.3.1 Sulphur dioxide 397
11.3.2 Nitrogen dioxide 398
11.3.3 Suspended particulate matter 399 11.3.4 Respirable particulate matter 399
11.3.5 Carbon Monoxide 400
Appendix III Summary statistics 403
III.1 Measures of location(central tendency) 403
1II.1.1 Mean 403
111.1.2 Median 404
111.1.3 Mode 404
111.2 Measures of spread (variability) 404
111.2.1 Range 405
111.2.2 Interquartile range 405
111.2.3 Variance 405
111.2.4 Standard deviation 406
111.2.5 Coefficient of variation 406 111.3 Measure of skewness (coefficient of skewness) 406
111.4 Box and Wisker plot 408
Appendix IV Probability distribution models 409
IV.1 General 409
IV.2 Modelling statistical distribution of air pollution concentration 412
IV.2.1 General 412
IV.3 Characteristics of probability distribution models 415 IV.4 Characteristics of parametric probability distribution models 417
Appendix V Goodness-of-fit tests 421
V.1 Goodness-of-fit tests 422
V.1.1 Chi-square test 422
V.1.2 Kolmogorov-Smirnov test 423
V.1.3 Anderson-Darling test 423
V.2 Selecting a distribution 424
Appendix VI Estimation of distribution parameters 426 V1.1 Methods for estimating distribution parameters 426
V1.1.1 Methods of moment 427
V1.1.2 Method of maximum likelihood 427
Bio-Data 429
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